LMFDB - Embedded newform 546.8.a.r.1.1

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			1.1
Root			$390.179$ 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)

$f(q)$	$=$	$q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -356.179 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -356.179 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} -2849.43 q^{10} -7505.72 q^{11} -1728.00 q^{12} +2197.00 q^{13} -2744.00 q^{14} +9616.83 q^{15} +4096.00 q^{16} -16070.3 q^{17} +5832.00 q^{18} +2775.91 q^{19} -22795.4 q^{20} +9261.00 q^{21} -60045.7 q^{22} -32534.4 q^{23} -13824.0 q^{24} +48738.4 q^{25} +17576.0 q^{26} -19683.0 q^{27} -21952.0 q^{28} -168180. q^{29} +76934.6 q^{30} -220119. q^{31} +32768.0 q^{32} +202654. q^{33} -128562. q^{34} +122169. q^{35} +46656.0 q^{36} -211079. q^{37} +22207.3 q^{38} -59319.0 q^{39} -182364. q^{40} -824216. q^{41} +74088.0 q^{42} +640034. q^{43} -480366. q^{44} -259654. q^{45} -260275. q^{46} -85878.7 q^{47} -110592. q^{48} +117649. q^{49} +389907. q^{50} +433898. q^{51} +140608. q^{52} -1.72649e6 q^{53} -157464. q^{54} +2.67338e6 q^{55} -175616. q^{56} -74949.7 q^{57} -1.34544e6 q^{58} +2.81760e6 q^{59} +615477. q^{60} -1.08363e6 q^{61} -1.76095e6 q^{62} -250047. q^{63} +262144. q^{64} -782525. q^{65} +1.62123e6 q^{66} +1.27353e6 q^{67} -1.02850e6 q^{68} +878428. q^{69} +977355. q^{70} -2.65081e6 q^{71} +373248. q^{72} +4.18663e6 q^{73} -1.68864e6 q^{74} -1.31594e6 q^{75} +177658. q^{76} +2.57446e6 q^{77} -474552. q^{78} -7.94649e6 q^{79} -1.45891e6 q^{80} +531441. q^{81} -6.59373e6 q^{82} -5.50842e6 q^{83} +592704. q^{84} +5.72390e6 q^{85} +5.12028e6 q^{86} +4.54085e6 q^{87} -3.84293e6 q^{88} +4.44064e6 q^{89} -2.07723e6 q^{90} -753571. q^{91} -2.08220e6 q^{92} +5.94321e6 q^{93} -687030. q^{94} -988722. q^{95} -884736. q^{96} +5.97700e6 q^{97} +941192. q^{98} -5.47167e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−356.179	−1.27430	−0.637152	−	0.770738i	$-0.719888\pi$
$5$	−356.179	−1.27430	−0.637152	+	0.770738i	$0.719888\pi$
$6$	−216.000	−0.408248
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	−2849.43	−0.901069
$11$	−7505.72	−1.70027	−0.850135	−	0.526565i	$-0.823480\pi$
$11$	−7505.72	−1.70027	−0.850135	+	0.526565i	$0.823480\pi$
$12$	−1728.00	−0.288675
$13$	2197.00	0.277350
$13$	2197.00	0.277350
$14$	−2744.00	−0.267261
$15$	9616.83	0.735720
$16$	4096.00	0.250000
$17$	−16070.3	−0.793328	−0.396664	−	0.917964i	$-0.629832\pi$
$17$	−16070.3	−0.793328	−0.396664	+	0.917964i	$0.629832\pi$
$18$	5832.00	0.235702
$19$	2775.91	0.0928471	0.0464236	−	0.998922i	$-0.485218\pi$
$19$	2775.91	0.0928471	0.0464236	+	0.998922i	$0.485218\pi$
$20$	−22795.4	−0.637152
$21$	9261.00	0.218218
$22$	−60045.7	−1.20227
$23$	−32534.4	−0.557564	−0.278782	−	0.960354i	$-0.589931\pi$
$23$	−32534.4	−0.557564	−0.278782	+	0.960354i	$0.589931\pi$
$24$	−13824.0	−0.204124
$25$	48738.4	0.623851
$26$	17576.0	0.196116
$27$	−19683.0	−0.192450
$28$	−21952.0	−0.188982
$29$	−168180.	−1.28050	−0.640252	−	0.768165i	$-0.721170\pi$
$29$	−168180.	−1.28050	−0.640252	+	0.768165i	$0.721170\pi$
$30$	76934.6	0.520232
$31$	−220119.	−1.32706	−0.663531	−	0.748148i	$-0.730943\pi$
$31$	−220119.	−1.32706	−0.663531	+	0.748148i	$0.730943\pi$
$32$	32768.0	0.176777
$33$	202654.	0.981651
$34$	−128562.	−0.560968
$35$	122169.	0.481642
$36$	46656.0	0.166667
$37$	−211079.	−0.685078	−0.342539	−	0.939504i	$-0.611287\pi$
$37$	−211079.	−0.685078	−0.342539	+	0.939504i	$0.611287\pi$
$38$	22207.3	0.0656528
$39$	−59319.0	−0.160128
$40$	−182364.	−0.450535
$41$	−824216.	−1.86766	−0.933830	−	0.357718i	$-0.883555\pi$
$41$	−824216.	−1.86766	−0.933830	+	0.357718i	$0.883555\pi$
$42$	74088.0	0.154303
$43$	640034.	1.22762	0.613810	−	0.789454i	$-0.289636\pi$
$43$	640034.	1.22762	0.613810	+	0.789454i	$0.289636\pi$
$44$	−480366.	−0.850135
$45$	−259654.	−0.424768
$46$	−260275.	−0.394257
$47$	−85878.7	−0.120654	−0.0603272	−	0.998179i	$-0.519214\pi$
$47$	−85878.7	−0.120654	−0.0603272	+	0.998179i	$0.519214\pi$
$48$	−110592.	−0.144338
$49$	117649.	0.142857
$50$	389907.	0.441129
$51$	433898.	0.458028
$52$	140608.	0.138675
$53$	−1.72649e6	−1.59293	−0.796466	−	0.604683i	$-0.793300\pi$
$53$	−1.72649e6	−1.59293	−0.796466	+	0.604683i	$0.793300\pi$
$54$	−157464.	−0.136083
$55$	2.67338e6	2.16666
$56$	−175616.	−0.133631
$57$	−74949.7	−0.0536053
$58$	−1.34544e6	−0.905452
$59$	2.81760e6	1.78606	0.893032	−	0.449994i	$-0.148574\pi$
$59$	2.81760e6	1.78606	0.893032	+	0.449994i	$0.148574\pi$
$60$	615477.	0.367860
$61$	−1.08363e6	−0.611261	−0.305630	−	0.952150i	$-0.598867\pi$
$61$	−1.08363e6	−0.611261	−0.305630	+	0.952150i	$0.598867\pi$
$62$	−1.76095e6	−0.938375
$63$	−250047.	−0.125988
$64$	262144.	0.125000
$65$	−782525.	−0.353428
$66$	1.62123e6	0.694132
$67$	1.27353e6	0.517305	0.258653	−	0.965970i	$-0.416721\pi$
$67$	1.27353e6	0.517305	0.258653	+	0.965970i	$0.416721\pi$
$68$	−1.02850e6	−0.396664
$69$	878428.	0.321910
$70$	977355.	0.340572
$71$	−2.65081e6	−0.878970	−0.439485	−	0.898250i	$-0.644839\pi$
$71$	−2.65081e6	−0.878970	−0.439485	+	0.898250i	$0.644839\pi$
$72$	373248.	0.117851
$73$	4.18663e6	1.25961	0.629803	−	0.776755i	$-0.283136\pi$
$73$	4.18663e6	1.25961	0.629803	+	0.776755i	$0.283136\pi$
$74$	−1.68864e6	−0.484423
$75$	−1.31594e6	−0.360181
$76$	177658.	0.0464236
$77$	2.57446e6	0.642641
$78$	−474552.	−0.113228
$79$	−7.94649e6	−1.81335	−0.906673	−	0.421835i	$-0.861386\pi$
$79$	−7.94649e6	−1.81335	−0.906673	+	0.421835i	$0.861386\pi$
$80$	−1.45891e6	−0.318576
$81$	531441.	0.111111
$82$	−6.59373e6	−1.32063
$83$	−5.50842e6	−1.05744	−0.528718	−	0.848798i	$-0.677327\pi$
$83$	−5.50842e6	−1.05744	−0.528718	+	0.848798i	$0.677327\pi$
$84$	592704.	0.109109
$85$	5.72390e6	1.01094
$86$	5.12028e6	0.868058
$87$	4.54085e6	0.739299
$88$	−3.84293e6	−0.601136
$89$	4.44064e6	0.667698	0.333849	−	0.942626i	$-0.391652\pi$
$89$	4.44064e6	0.667698	0.333849	+	0.942626i	$0.391652\pi$
$90$	−2.07723e6	−0.300356
$91$	−753571.	−0.104828
$92$	−2.08220e6	−0.278782
$93$	5.94321e6	0.766180
$94$	−687030.	−0.0853155
$95$	−988722.	−0.118315
$96$	−884736.	−0.102062
$97$	5.97700e6	0.664940	0.332470	−	0.943114i	$-0.392118\pi$
$97$	5.97700e6	0.664940	0.332470	+	0.943114i	$0.392118\pi$
$98$	941192.	0.101015
$99$	−5.47167e6	−0.566756
$100$	3.11926e6	0.311926
$101$	−2.84477e6	−0.274740	−0.137370	−	0.990520i	$-0.543865\pi$
$101$	−2.84477e6	−0.274740	−0.137370	+	0.990520i	$0.543865\pi$
$102$	3.47119e6	0.323875
$103$	−1.45832e7	−1.31499	−0.657494	−	0.753460i	$-0.728384\pi$
$103$	−1.45832e7	−1.31499	−0.657494	+	0.753460i	$0.728384\pi$
$104$	1.12486e6	0.0980581
$105$	−3.29857e6	−0.278076
$106$	−1.38119e7	−1.12637
$107$	−1.89107e6	−0.149233	−0.0746163	−	0.997212i	$-0.523773\pi$
$107$	−1.89107e6	−0.149233	−0.0746163	+	0.997212i	$0.523773\pi$
$108$	−1.25971e6	−0.0962250
$109$	9.23714e6	0.683195	0.341598	−	0.939846i	$-0.389032\pi$
$109$	9.23714e6	0.683195	0.341598	+	0.939846i	$0.389032\pi$
$110$	2.13870e7	1.53206
$111$	5.69915e6	0.395530
$112$	−1.40493e6	−0.0944911
$113$	1.36594e7	0.890547	0.445273	−	0.895395i	$-0.353107\pi$
$113$	1.36594e7	0.890547	0.445273	+	0.895395i	$0.353107\pi$
$114$	−599597.	−0.0379047
$115$	1.15880e7	0.710506
$116$	−1.07635e7	−0.640252
$117$	1.60161e6	0.0924500
$118$	2.25408e7	1.26294
$119$	5.51211e6	0.299850
$120$	4.92382e6	0.260116
$121$	3.68486e7	1.89092
$122$	−8.66904e6	−0.432227
$123$	2.22538e7	1.07829
$124$	−1.40876e7	−0.663531
$125$	1.04669e7	0.479328
$126$	−2.00038e6	−0.0890871
$127$	3.41065e7	1.47749	0.738743	−	0.673987i	$-0.235420\pi$
$127$	3.41065e7	1.47749	0.738743	+	0.673987i	$0.235420\pi$
$128$	2.09715e6	0.0883883
$129$	−1.72809e7	−0.708766
$130$	−6.26020e6	−0.249912
$131$	7.43598e6	0.288994	0.144497	−	0.989505i	$-0.453844\pi$
$131$	7.43598e6	0.288994	0.144497	+	0.989505i	$0.453844\pi$
$132$	1.29699e7	0.490825
$133$	−952138.	−0.0350929
$134$	1.01882e7	0.365790
$135$	7.01067e6	0.245240
$136$	−8.22799e6	−0.280484
$137$	1.36234e7	0.452652	0.226326	−	0.974052i	$-0.427328\pi$
$137$	1.36234e7	0.452652	0.226326	+	0.974052i	$0.427328\pi$
$138$	7.02742e6	0.227625
$139$	4.13662e7	1.30645	0.653227	−	0.757162i	$-0.273415\pi$
$139$	4.13662e7	1.30645	0.653227	+	0.757162i	$0.273415\pi$
$140$	7.81884e6	0.240821
$141$	2.31872e6	0.0696598
$142$	−2.12065e7	−0.621526
$143$	−1.64901e7	−0.471570
$144$	2.98598e6	0.0833333
$145$	5.99021e7	1.63175
$146$	3.34930e7	0.890676
$147$	−3.17652e6	−0.0824786
$148$	−1.35091e7	−0.342539
$149$	−7.21056e7	−1.78574	−0.892868	−	0.450318i	$-0.851311\pi$
$149$	−7.21056e7	−1.78574	−0.892868	+	0.450318i	$0.851311\pi$
$150$	−1.05275e7	−0.254686
$151$	1.68206e6	0.0397577	0.0198788	−	0.999802i	$-0.493672\pi$
$151$	1.68206e6	0.0397577	0.0198788	+	0.999802i	$0.493672\pi$
$152$	1.42127e6	0.0328264
$153$	−1.17153e7	−0.264443
$154$	2.05957e7	0.454416
$155$	7.84017e7	1.69108
$156$	−3.79642e6	−0.0800641
$157$	−3.18358e7	−0.656548	−0.328274	−	0.944583i	$-0.606467\pi$
$157$	−3.18358e7	−0.656548	−0.328274	+	0.944583i	$0.606467\pi$
$158$	−6.35719e7	−1.28223
$159$	4.66151e7	0.919680
$160$	−1.16713e7	−0.225267
$161$	1.11593e7	0.210739
$162$	4.25153e6	0.0785674
$163$	−9.32110e7	−1.68582	−0.842909	−	0.538057i	$-0.819159\pi$
$163$	−9.32110e7	−1.68582	−0.842909	+	0.538057i	$0.819159\pi$
$164$	−5.27498e7	−0.933830
$165$	−7.21812e7	−1.25092
$166$	−4.40674e7	−0.747720
$167$	4.68184e7	0.777873	0.388937	−	0.921265i	$-0.372843\pi$
$167$	4.68184e7	0.777873	0.388937	+	0.921265i	$0.372843\pi$
$168$	4.74163e6	0.0771517
$169$	4.82681e6	0.0769231
$170$	4.57912e7	0.714843
$171$	2.02364e6	0.0309490
$172$	4.09622e7	0.613810
$173$	5.84637e7	0.858469	0.429235	−	0.903193i	$-0.358783\pi$
$173$	5.84637e7	0.858469	0.429235	+	0.903193i	$0.358783\pi$
$174$	3.63268e7	0.522763
$175$	−1.67173e7	−0.235794
$176$	−3.07434e7	−0.425067
$177$	−7.60751e7	−1.03118
$178$	3.55251e7	0.472134
$179$	−1.04704e8	−1.36451	−0.682255	−	0.731114i	$-0.739001\pi$
$179$	−1.04704e8	−1.36451	−0.682255	+	0.731114i	$0.739001\pi$
$180$	−1.66179e7	−0.212384
$181$	5.59187e7	0.700942	0.350471	−	0.936574i	$-0.386022\pi$
$181$	5.59187e7	0.700942	0.350471	+	0.936574i	$0.386022\pi$
$182$	−6.02857e6	−0.0741249
$183$	2.92580e7	0.352912
$184$	−1.66576e7	−0.197129
$185$	7.51820e7	0.872998
$186$	4.75457e7	0.541771
$187$	1.20619e8	1.34887
$188$	−5.49624e6	−0.0603272
$189$	6.75127e6	0.0727393
$190$	−7.90977e6	−0.0836617
$191$	−5.29705e7	−0.550069	−0.275034	−	0.961434i	$-0.588689\pi$
$191$	−5.29705e7	−0.550069	−0.275034	+	0.961434i	$0.588689\pi$
$192$	−7.07789e6	−0.0721688
$193$	1.46969e8	1.47155	0.735774	−	0.677227i	$-0.236818\pi$
$193$	1.46969e8	1.47155	0.735774	+	0.677227i	$0.236818\pi$
$194$	4.78160e7	0.470183
$195$	2.11282e7	0.204052
$196$	7.52954e6	0.0714286
$197$	−8.47740e7	−0.790007	−0.395003	−	0.918680i	$-0.629257\pi$
$197$	−8.47740e7	−0.790007	−0.395003	+	0.918680i	$0.629257\pi$
$198$	−4.37733e7	−0.400757
$199$	−1.83215e8	−1.64807	−0.824033	−	0.566541i	$-0.808281\pi$
$199$	−1.83215e8	−1.64807	−0.824033	+	0.566541i	$0.808281\pi$
$200$	2.49540e7	0.220565
$201$	−3.43853e7	−0.298666
$202$	−2.27581e7	−0.194271
$203$	5.76856e7	0.483985
$204$	2.77695e7	0.229014
$205$	2.93568e8	2.37997
$206$	−1.16665e8	−0.929837
$207$	−2.37175e7	−0.185855
$208$	8.99891e6	0.0693375
$209$	−2.08352e7	−0.157865
$210$	−2.63886e7	−0.196629
$211$	1.65562e8	1.21331	0.606655	−	0.794966i	$-0.292511\pi$
$211$	1.65562e8	1.21331	0.606655	+	0.794966i	$0.292511\pi$
$212$	−1.10495e8	−0.796466
$213$	7.15718e7	0.507474
$214$	−1.51285e7	−0.105523
$215$	−2.27967e8	−1.56436
$216$	−1.00777e7	−0.0680414
$217$	7.55008e7	0.501583
$218$	7.38971e7	0.483092
$219$	−1.13039e8	−0.727234
$220$	1.71096e8	1.08333
$221$	−3.53065e7	−0.220030
$222$	4.55932e7	0.279682
$223$	2.92424e8	1.76582	0.882909	−	0.469543i	$-0.155581\pi$
$223$	2.92424e8	1.76582	0.882909	+	0.469543i	$0.155581\pi$
$224$	−1.12394e7	−0.0668153
$225$	3.55303e7	0.207950
$226$	1.09275e8	0.629712
$227$	2.88122e8	1.63488	0.817441	−	0.576012i	$-0.195392\pi$
$227$	2.88122e8	1.63488	0.817441	+	0.576012i	$0.195392\pi$
$228$	−4.79678e6	−0.0268027
$229$	−7.75197e7	−0.426568	−0.213284	−	0.976990i	$-0.568416\pi$
$229$	−7.75197e7	−0.426568	−0.213284	+	0.976990i	$0.568416\pi$
$230$	9.27044e7	0.502404
$231$	−6.95104e7	−0.371029
$232$	−8.61080e7	−0.452726
$233$	2.75907e8	1.42895	0.714475	−	0.699661i	$-0.246666\pi$
$233$	2.75907e8	1.42895	0.714475	+	0.699661i	$0.246666\pi$
$234$	1.28129e7	0.0653720
$235$	3.05882e7	0.153750
$236$	1.80326e8	0.893032
$237$	2.14555e8	1.04694
$238$	4.40969e7	0.212026
$239$	−2.14321e8	−1.01548	−0.507740	−	0.861510i	$-0.669519\pi$
$239$	−2.14321e8	−1.01548	−0.507740	+	0.861510i	$0.669519\pi$
$240$	3.93905e7	0.183930
$241$	6.61344e7	0.304346	0.152173	−	0.988354i	$-0.451373\pi$
$241$	6.61344e7	0.304346	0.152173	+	0.988354i	$0.451373\pi$
$242$	2.94789e8	1.33708
$243$	−1.43489e7	−0.0641500
$244$	−6.93523e7	−0.305630
$245$	−4.19041e7	−0.182043
$246$	1.78031e8	0.762469
$247$	6.09868e6	0.0257512
$248$	−1.12701e8	−0.469188
$249$	1.48727e8	0.610511
$250$	8.37352e7	0.338936
$251$	3.68420e8	1.47057	0.735285	−	0.677758i	$-0.237048\pi$
$251$	3.68420e8	1.47057	0.735285	+	0.677758i	$0.237048\pi$
$252$	−1.60030e7	−0.0629941
$253$	2.44194e8	0.948009
$254$	2.72852e8	1.04474
$255$	−1.54545e8	−0.583667
$256$	1.67772e7	0.0625000
$257$	−2.60448e8	−0.957097	−0.478548	−	0.878061i	$-0.658837\pi$
$257$	−2.60448e8	−0.957097	−0.478548	+	0.878061i	$0.658837\pi$
$258$	−1.38247e8	−0.501173
$259$	7.24003e7	0.258935
$260$	−5.00816e7	−0.176714
$261$	−1.22603e8	−0.426834
$262$	5.94879e7	0.204350
$263$	1.81155e8	0.614052	0.307026	−	0.951701i	$-0.400666\pi$
$263$	1.81155e8	0.614052	0.307026	+	0.951701i	$0.400666\pi$
$264$	1.03759e8	0.347066
$265$	6.14938e8	2.02988
$266$	−7.61711e6	−0.0248144
$267$	−1.19897e8	−0.385496
$268$	8.15058e7	0.258653
$269$	−5.00047e8	−1.56631	−0.783155	−	0.621827i	$-0.786391\pi$
$269$	−5.00047e8	−1.56631	−0.783155	+	0.621827i	$0.786391\pi$
$270$	5.60853e7	0.173411
$271$	−8.44196e7	−0.257662	−0.128831	−	0.991667i	$-0.541123\pi$
$271$	−8.44196e7	−0.257662	−0.128831	+	0.991667i	$0.541123\pi$
$272$	−6.58240e7	−0.198332
$273$	2.03464e7	0.0605228
$274$	1.08988e8	0.320074
$275$	−3.65816e8	−1.06071
$276$	5.62194e7	0.160955
$277$	−5.05664e8	−1.42950	−0.714748	−	0.699382i	$-0.753459\pi$
$277$	−5.05664e8	−1.42950	−0.714748	+	0.699382i	$0.753459\pi$
$278$	3.30930e8	0.923802
$279$	−1.60467e8	−0.442354
$280$	6.25507e7	0.170286
$281$	−1.25449e8	−0.337283	−0.168641	−	0.985677i	$-0.553938\pi$
$281$	−1.25449e8	−0.337283	−0.168641	+	0.985677i	$0.553938\pi$
$282$	1.85498e7	0.0492569
$283$	−1.51960e8	−0.398544	−0.199272	−	0.979944i	$-0.563858\pi$
$283$	−1.51960e8	−0.398544	−0.199272	+	0.979944i	$0.563858\pi$
$284$	−1.69652e8	−0.439485
$285$	2.66955e7	0.0683095
$286$	−1.31920e8	−0.333450
$287$	2.82706e8	0.705909
$288$	2.38879e7	0.0589256
$289$	−1.52084e8	−0.370631
$290$	4.79216e8	1.15382
$291$	−1.61379e8	−0.383903
$292$	2.67944e8	0.629803
$293$	4.33667e7	0.100721	0.0503604	−	0.998731i	$-0.483963\pi$
$293$	4.33667e7	0.100721	0.0503604	+	0.998731i	$0.483963\pi$
$294$	−2.54122e7	−0.0583212
$295$	−1.00357e9	−2.27599
$296$	−1.08073e8	−0.242212
$297$	1.47735e8	0.327217
$298$	−5.76845e8	−1.26271
$299$	−7.14780e7	−0.154640
$300$	−8.42199e7	−0.180090
$301$	−2.19532e8	−0.463996
$302$	1.34564e7	0.0281129
$303$	7.68087e7	0.158621
$304$	1.13701e7	0.0232118
$305$	3.85966e8	0.778932
$306$	−9.37220e7	−0.186989
$307$	−8.17920e8	−1.61334	−0.806671	−	0.591001i	$-0.798733\pi$
$307$	−8.17920e8	−1.61334	−0.806671	+	0.591001i	$0.798733\pi$
$308$	1.64765e8	0.321321
$309$	3.93746e8	0.759209
$310$	6.27214e8	1.19578
$311$	8.61446e8	1.62393	0.811964	−	0.583708i	$-0.198399\pi$
$311$	8.61446e8	1.62393	0.811964	+	0.583708i	$0.198399\pi$
$312$	−3.03713e7	−0.0566139
$313$	2.15722e8	0.397640	0.198820	−	0.980036i	$-0.436289\pi$
$313$	2.15722e8	0.397640	0.198820	+	0.980036i	$0.436289\pi$
$314$	−2.54686e8	−0.464250
$315$	8.90614e7	0.160547
$316$	−5.08575e8	−0.906673
$317$	1.12172e8	0.197778	0.0988890	−	0.995098i	$-0.468471\pi$
$317$	1.12172e8	0.197778	0.0988890	+	0.995098i	$0.468471\pi$
$318$	3.72921e8	0.650312
$319$	1.26231e9	2.17720
$320$	−9.33701e7	−0.159288
$321$	5.10588e7	0.0861595
$322$	8.92743e7	0.149015
$323$	−4.46098e7	−0.0736582
$324$	3.40122e7	0.0555556
$325$	1.07078e8	0.173025
$326$	−7.45688e8	−1.19205
$327$	−2.49403e8	−0.394443
$328$	−4.21999e8	−0.660317
$329$	2.94564e7	0.0456031
$330$	−5.77449e8	−0.884535
$331$	5.07956e8	0.769889	0.384945	−	0.922940i	$-0.374221\pi$
$331$	5.07956e8	0.769889	0.384945	+	0.922940i	$0.374221\pi$
$332$	−3.52539e8	−0.528718
$333$	−1.53877e8	−0.228359
$334$	3.74547e8	0.550039
$335$	−4.53604e8	−0.659204
$336$	3.79331e7	0.0545545
$337$	−8.81685e8	−1.25490	−0.627450	−	0.778657i	$-0.715901\pi$
$337$	−8.81685e8	−1.25490	−0.627450	+	0.778657i	$0.715901\pi$
$338$	3.86145e7	0.0543928
$339$	−3.68803e8	−0.514157
$340$	3.66330e8	0.505471
$341$	1.65215e9	2.25636
$342$	1.61891e7	0.0218843
$343$	−4.03536e7	−0.0539949
$344$	3.27698e8	0.434029
$345$	−3.12877e8	−0.410211
$346$	4.67709e8	0.607029
$347$	3.23488e8	0.415629	0.207814	−	0.978168i	$-0.433365\pi$
$347$	3.23488e8	0.415629	0.207814	+	0.978168i	$0.433365\pi$
$348$	2.90615e8	0.369649
$349$	1.46992e9	1.85100	0.925499	−	0.378750i	$-0.123646\pi$
$349$	1.46992e9	1.85100	0.925499	+	0.378750i	$0.123646\pi$
$350$	−1.33738e8	−0.166731
$351$	−4.32436e7	−0.0533761
$352$	−2.45947e8	−0.300568
$353$	1.28684e9	1.55709	0.778543	−	0.627591i	$-0.215959\pi$
$353$	1.28684e9	1.55709	0.778543	+	0.627591i	$0.215959\pi$
$354$	−6.08601e8	−0.729157
$355$	9.44162e8	1.12008
$356$	2.84201e8	0.333849
$357$	−1.48827e8	−0.173118
$358$	−8.37630e8	−0.964854
$359$	−1.45809e9	−1.66323	−0.831616	−	0.555351i	$-0.812584\pi$
$359$	−1.45809e9	−1.66323	−0.831616	+	0.555351i	$0.812584\pi$
$360$	−1.32943e8	−0.150178
$361$	−8.86166e8	−0.991379
$362$	4.47350e8	0.495641
$363$	−9.94912e8	−1.09172
$364$	−4.82285e7	−0.0524142
$365$	−1.49119e9	−1.60512
$366$	2.34064e8	0.249546
$367$	−8.89101e8	−0.938901	−0.469451	−	0.882959i	$-0.655548\pi$
$367$	−8.89101e8	−0.938901	−0.469451	+	0.882959i	$0.655548\pi$
$368$	−1.33261e8	−0.139391
$369$	−6.00854e8	−0.622553
$370$	6.01456e8	0.617302
$371$	5.92184e8	0.602072
$372$	3.80365e8	0.383090
$373$	−2.98628e8	−0.297954	−0.148977	−	0.988841i	$-0.547598\pi$
$373$	−2.98628e8	−0.297954	−0.148977	+	0.988841i	$0.547598\pi$
$374$	9.64953e8	0.953796
$375$	−2.82606e8	−0.276740
$376$	−4.39699e7	−0.0426578
$377$	−3.69491e8	−0.355148
$378$	5.40102e7	0.0514344
$379$	−7.55911e8	−0.713236	−0.356618	−	0.934250i	$-0.616070\pi$
$379$	−7.55911e8	−0.713236	−0.356618	+	0.934250i	$0.616070\pi$
$380$	−6.32782e7	−0.0591577
$381$	−9.20874e8	−0.853027
$382$	−4.23764e8	−0.388957
$383$	1.16913e9	1.06333	0.531664	−	0.846955i	$-0.321567\pi$
$383$	1.16913e9	1.06333	0.531664	+	0.846955i	$0.321567\pi$
$384$	−5.66231e7	−0.0510310
$385$	−9.16968e8	−0.818921
$386$	1.17575e9	1.04054
$387$	4.66585e8	0.409206
$388$	3.82528e8	0.332470
$389$	3.70209e8	0.318878	0.159439	−	0.987208i	$-0.449032\pi$
$389$	3.70209e8	0.318878	0.159439	+	0.987208i	$0.449032\pi$
$390$	1.69025e8	0.144287
$391$	5.22837e8	0.442331
$392$	6.02363e7	0.0505076
$393$	−2.00772e8	−0.166851
$394$	−6.78192e8	−0.558619
$395$	2.83037e9	2.31075
$396$	−3.50187e8	−0.283378
$397$	−3.90037e8	−0.312852	−0.156426	−	0.987690i	$-0.549997\pi$
$397$	−3.90037e8	−0.312852	−0.156426	+	0.987690i	$0.549997\pi$
$398$	−1.46572e9	−1.16536
$399$	2.57077e7	0.0202609
$400$	1.99632e8	0.155963
$401$	9.42418e8	0.729858	0.364929	−	0.931035i	$-0.381093\pi$
$401$	9.42418e8	0.729858	0.364929	+	0.931035i	$0.381093\pi$
$402$	−2.75082e8	−0.211189
$403$	−4.83601e8	−0.368061
$404$	−1.82065e8	−0.137370
$405$	−1.89288e8	−0.141589
$406$	4.61485e8	0.342229
$407$	1.58430e9	1.16482
$408$	2.22156e8	0.161937
$409$	−1.69995e9	−1.22858	−0.614290	−	0.789080i	$-0.710557\pi$
$409$	−1.69995e9	−1.22858	−0.614290	+	0.789080i	$0.710557\pi$
$410$	2.34855e9	1.68289
$411$	−3.67833e8	−0.261339
$412$	−9.33324e8	−0.657494
$413$	−9.66436e8	−0.675068
$414$	−1.89740e8	−0.131419
$415$	1.96198e9	1.34749
$416$	7.19913e7	0.0490290
$417$	−1.11689e9	−0.754281
$418$	−1.66682e8	−0.111627
$419$	8.67590e8	0.576190	0.288095	−	0.957602i	$-0.406978\pi$
$419$	8.67590e8	0.576190	0.288095	+	0.957602i	$0.406978\pi$
$420$	−2.11109e8	−0.139038
$421$	−2.13921e9	−1.39723	−0.698614	−	0.715499i	$-0.746199\pi$
$421$	−2.13921e9	−1.39723	−0.698614	+	0.715499i	$0.746199\pi$
$422$	1.32449e9	0.857939
$423$	−6.26056e7	−0.0402181
$424$	−8.83960e8	−0.563187
$425$	−7.83240e8	−0.494919
$426$	5.72575e8	0.358838
$427$	3.71685e8	0.231035
$428$	−1.21028e8	−0.0746163
$429$	4.45232e8	0.272261
$430$	−1.82373e9	−1.10617
$431$	−1.26935e9	−0.763677	−0.381838	−	0.924229i	$-0.624709\pi$
$431$	−1.26935e9	−0.763677	−0.381838	+	0.924229i	$0.624709\pi$
$432$	−8.06216e7	−0.0481125
$433$	1.77878e9	1.05297	0.526483	−	0.850186i	$-0.323510\pi$
$433$	1.77878e9	1.05297	0.526483	+	0.850186i	$0.323510\pi$
$434$	6.04006e8	0.354672
$435$	−1.61736e9	−0.942092
$436$	5.91177e8	0.341598
$437$	−9.03126e7	−0.0517682
$438$	−9.04312e8	−0.514232
$439$	−1.14147e9	−0.643932	−0.321966	−	0.946751i	$-0.604344\pi$
$439$	−1.14147e9	−0.643932	−0.321966	+	0.946751i	$0.604344\pi$
$440$	1.36877e9	0.766030
$441$	8.57661e7	0.0476190
$442$	−2.82452e8	−0.155584
$443$	−9.84229e8	−0.537877	−0.268939	−	0.963157i	$-0.586673\pi$
$443$	−9.84229e8	−0.537877	−0.268939	+	0.963157i	$0.586673\pi$
$444$	3.64745e8	0.197765
$445$	−1.58166e9	−0.850851
$446$	2.33939e9	1.24862
$447$	1.94685e9	1.03100
$448$	−8.99154e7	−0.0472456
$449$	7.14366e8	0.372442	0.186221	−	0.982508i	$-0.440376\pi$
$449$	7.14366e8	0.372442	0.186221	+	0.982508i	$0.440376\pi$
$450$	2.84242e8	0.147043
$451$	6.18633e9	3.17552
$452$	8.74201e8	0.445273
$453$	−4.54155e7	−0.0229541
$454$	2.30498e9	1.15604
$455$	2.68406e8	0.133583
$456$	−3.83742e7	−0.0189523
$457$	−5.28807e8	−0.259173	−0.129587	−	0.991568i	$-0.541365\pi$
$457$	−5.28807e8	−0.259173	−0.129587	+	0.991568i	$0.541365\pi$
$458$	−6.20158e8	−0.301629
$459$	3.16312e8	0.152676
$460$	7.41635e8	0.355253
$461$	1.12605e9	0.535311	0.267655	−	0.963515i	$-0.413751\pi$
$461$	1.12605e9	0.535311	0.267655	+	0.963515i	$0.413751\pi$
$462$	−5.56083e8	−0.262357
$463$	−1.93722e9	−0.907078	−0.453539	−	0.891236i	$-0.649839\pi$
$463$	−1.93722e9	−0.907078	−0.453539	+	0.891236i	$0.649839\pi$
$464$	−6.88864e8	−0.320126
$465$	−2.11685e9	−0.976346
$466$	2.20726e9	1.01042
$467$	−3.55991e9	−1.61745	−0.808723	−	0.588190i	$-0.799841\pi$
$467$	−3.55991e9	−1.61745	−0.808723	+	0.588190i	$0.799841\pi$
$468$	1.02503e8	0.0462250
$469$	−4.36820e8	−0.195523
$470$	2.44705e8	0.108718
$471$	8.59566e8	0.379058
$472$	1.44261e9	0.631469
$473$	−4.80392e9	−2.08728
$474$	1.71644e9	0.740295
$475$	1.35294e8	0.0579228
$476$	3.52775e8	0.149925
$477$	−1.25861e9	−0.530977
$478$	−1.71457e9	−0.718053
$479$	8.33162e8	0.346382	0.173191	−	0.984888i	$-0.444592\pi$
$479$	8.33162e8	0.346382	0.173191	+	0.984888i	$0.444592\pi$
$480$	3.15124e8	0.130058
$481$	−4.63742e8	−0.190006
$482$	5.29075e8	0.215205
$483$	−3.01301e8	−0.121670
$484$	2.35831e9	0.945458
$485$	−2.12888e9	−0.847336
$486$	−1.14791e8	−0.0453609
$487$	8.53756e8	0.334952	0.167476	−	0.985876i	$-0.446438\pi$
$487$	8.53756e8	0.334952	0.167476	+	0.985876i	$0.446438\pi$
$488$	−5.54819e8	−0.216113
$489$	2.51670e9	0.973307
$490$	−3.35233e8	−0.128724
$491$	−4.44043e9	−1.69293	−0.846466	−	0.532443i	$-0.821274\pi$
$491$	−4.44043e9	−1.69293	−0.846466	+	0.532443i	$0.821274\pi$
$492$	1.42425e9	0.539147
$493$	2.70270e9	1.01586
$494$	4.87895e7	0.0182088
$495$	1.94889e9	0.722220
$496$	−9.01607e8	−0.331766
$497$	9.09227e8	0.332220
$498$	1.18982e9	0.431696
$499$	−1.71385e8	−0.0617476	−0.0308738	−	0.999523i	$-0.509829\pi$
$499$	−1.71385e8	−0.0617476	−0.0308738	+	0.999523i	$0.509829\pi$
$500$	6.69881e8	0.239664
$501$	−1.26410e9	−0.449105
$502$	2.94736e9	1.03985
$503$	−1.62786e9	−0.570332	−0.285166	−	0.958478i	$-0.592049\pi$
$503$	−1.62786e9	−0.570332	−0.285166	+	0.958478i	$0.592049\pi$
$504$	−1.28024e8	−0.0445435
$505$	1.01325e9	0.350102
$506$	1.95355e9	0.670344
$507$	−1.30324e8	−0.0444116
$508$	2.18281e9	0.738743
$509$	4.20928e9	1.41480	0.707401	−	0.706812i	$-0.249867\pi$
$509$	4.20928e9	1.41480	0.707401	+	0.706812i	$0.249867\pi$
$510$	−1.23636e9	−0.412715
$511$	−1.43601e9	−0.476086
$512$	1.34218e8	0.0441942
$513$	−5.46383e7	−0.0178684
$514$	−2.08359e9	−0.676769
$515$	5.19422e9	1.67570
$516$	−1.10598e9	−0.354383
$517$	6.44581e8	0.205145
$518$	5.79202e8	0.183095
$519$	−1.57852e9	−0.495637
$520$	−4.00653e8	−0.124956
$521$	−7.80158e8	−0.241685	−0.120843	−	0.992672i	$-0.538560\pi$
$521$	−7.80158e8	−0.241685	−0.120843	+	0.992672i	$0.538560\pi$
$522$	−9.80824e8	−0.301817
$523$	2.32391e9	0.710335	0.355168	−	0.934803i	$-0.384424\pi$
$523$	2.32391e9	0.710335	0.355168	+	0.934803i	$0.384424\pi$
$524$	4.75903e8	0.144497
$525$	4.51366e8	0.136135
$526$	1.44924e9	0.434200
$527$	3.53738e9	1.05280
$528$	8.30072e8	0.245413
$529$	−2.34634e9	−0.689122
$530$	4.91950e9	1.43534
$531$	2.05403e9	0.595354
$532$	−6.09369e7	−0.0175465
$533$	−1.81080e9	−0.517996
$534$	−9.59178e8	−0.272587
$535$	6.73558e8	0.190168
$536$	6.52047e8	0.182895
$537$	2.82700e9	0.787800
$538$	−4.00037e9	−1.10755
$539$	−8.83040e8	−0.242896
$540$	4.48683e8	0.122620
$541$	4.54066e9	1.23290	0.616451	−	0.787393i	$-0.288570\pi$
$541$	4.54066e9	1.23290	0.616451	+	0.787393i	$0.288570\pi$
$542$	−6.75357e8	−0.182195
$543$	−1.50980e9	−0.404689
$544$	−5.26592e8	−0.140242
$545$	−3.29007e9	−0.870598
$546$	1.62771e8	0.0427960
$547$	4.44342e9	1.16081	0.580405	−	0.814328i	$-0.302894\pi$
$547$	4.44342e9	1.16081	0.580405	+	0.814328i	$0.302894\pi$
$548$	8.71900e8	0.226326
$549$	−7.89966e8	−0.203754
$550$	−2.92653e9	−0.750039
$551$	−4.66852e8	−0.118891
$552$	4.49755e8	0.113812
$553$	2.72565e9	0.685380
$554$	−4.04531e9	−1.01081
$555$	−2.02991e9	−0.504025
$556$	2.64744e9	0.653227
$557$	6.67789e8	0.163737	0.0818684	−	0.996643i	$-0.473911\pi$
$557$	6.67789e8	0.163737	0.0818684	+	0.996643i	$0.473911\pi$
$558$	−1.28373e9	−0.312792
$559$	1.40616e9	0.340480
$560$	5.00406e8	0.120410
$561$	−3.25672e9	−0.778771
$562$	−1.00359e9	−0.238495
$563$	−4.39812e9	−1.03870	−0.519348	−	0.854563i	$-0.673825\pi$
$563$	−4.39812e9	−1.03870	−0.519348	+	0.854563i	$0.673825\pi$
$564$	1.48398e8	0.0348299
$565$	−4.86518e9	−1.13483
$566$	−1.21568e9	−0.281813
$567$	−1.82284e8	−0.0419961
$568$	−1.35721e9	−0.310763
$569$	−7.16581e9	−1.63069	−0.815347	−	0.578972i	$-0.803454\pi$
$569$	−7.16581e9	−1.63069	−0.815347	+	0.578972i	$0.803454\pi$
$570$	2.13564e8	0.0483021
$571$	−1.98106e9	−0.445319	−0.222660	−	0.974896i	$-0.571474\pi$
$571$	−1.98106e9	−0.445319	−0.222660	+	0.974896i	$0.571474\pi$
$572$	−1.05536e9	−0.235785
$573$	1.43020e9	0.317582
$574$	2.26165e9	0.499153
$575$	−1.58567e9	−0.347837
$576$	1.91103e8	0.0416667
$577$	−7.86735e9	−1.70496	−0.852478	−	0.522763i	$-0.824901\pi$
$577$	−7.86735e9	−1.70496	−0.852478	+	0.522763i	$0.824901\pi$
$578$	−1.21667e9	−0.262075
$579$	−3.96816e9	−0.849599
$580$	3.83373e9	0.815875
$581$	1.88939e9	0.399673
$582$	−1.29103e9	−0.271461
$583$	1.29585e10	2.70841
$584$	2.14355e9	0.445338
$585$	−5.70461e8	−0.117809
$586$	3.46933e8	0.0712204
$587$	−1.86121e9	−0.379806	−0.189903	−	0.981803i	$-0.560817\pi$
$587$	−1.86121e9	−0.379806	−0.189903	+	0.981803i	$0.560817\pi$
$588$	−2.03297e8	−0.0412393
$589$	−6.11031e8	−0.123214
$590$	−8.02855e9	−1.60937
$591$	2.28890e9	0.456111
$592$	−8.64581e8	−0.171269
$593$	9.71905e8	0.191396	0.0956979	−	0.995410i	$-0.469492\pi$
$593$	9.71905e8	0.191396	0.0956979	+	0.995410i	$0.469492\pi$
$594$	1.18188e9	0.231377
$595$	−1.96330e9	−0.382100
$596$	−4.61476e9	−0.892868
$597$	4.94680e9	0.951512
$598$	−5.71824e8	−0.109347
$599$	−7.80541e9	−1.48389	−0.741945	−	0.670461i	$-0.766096\pi$
$599$	−7.80541e9	−1.48389	−0.741945	+	0.670461i	$0.766096\pi$
$600$	−6.73759e8	−0.127343
$601$	−6.38951e9	−1.20062	−0.600312	−	0.799766i	$-0.704957\pi$
$601$	−6.38951e9	−1.20062	−0.600312	+	0.799766i	$0.704957\pi$
$602$	−1.75625e9	−0.328095
$603$	9.28403e8	0.172435
$604$	1.07652e8	0.0198788
$605$	−1.31247e10	−2.40960
$606$	6.14470e8	0.112162
$607$	−3.76538e9	−0.683359	−0.341680	−	0.939817i	$-0.610996\pi$
$607$	−3.76538e9	−0.683359	−0.341680	+	0.939817i	$0.610996\pi$
$608$	9.09611e7	0.0164132
$609$	−1.55751e9	−0.279429
$610$	3.08773e9	0.550788
$611$	−1.88675e8	−0.0334635
$612$	−7.49776e8	−0.132221
$613$	4.01054e9	0.703219	0.351610	−	0.936147i	$-0.385634\pi$
$613$	4.01054e9	0.703219	0.351610	+	0.936147i	$0.385634\pi$
$614$	−6.54336e9	−1.14080
$615$	−7.92635e9	−1.37407
$616$	1.31812e9	0.227208
$617$	1.41032e9	0.241724	0.120862	−	0.992669i	$-0.461434\pi$
$617$	1.41032e9	0.241724	0.120862	+	0.992669i	$0.461434\pi$
$618$	3.14997e9	0.536842
$619$	−9.58969e9	−1.62513	−0.812563	−	0.582873i	$-0.801929\pi$
$619$	−9.58969e9	−1.62513	−0.812563	+	0.582873i	$0.801929\pi$
$620$	5.01771e9	0.845541
$621$	6.40374e8	0.107303
$622$	6.89157e9	1.14829
$623$	−1.52314e9	−0.252366
$624$	−2.42971e8	−0.0400320
$625$	−7.53577e9	−1.23466
$626$	1.72578e9	0.281174
$627$	5.62551e8	0.0911435
$628$	−2.03749e9	−0.328274
$629$	3.39211e9	0.543492
$630$	7.12492e8	0.113524
$631$	−7.67583e9	−1.21625	−0.608125	−	0.793842i	$-0.708078\pi$
$631$	−7.67583e9	−1.21625	−0.608125	+	0.793842i	$0.708078\pi$
$632$	−4.06860e9	−0.641114
$633$	−4.47017e9	−0.700504
$634$	8.97378e8	0.139850
$635$	−1.21480e10	−1.88277
$636$	2.98337e9	0.459840
$637$	2.58475e8	0.0396214
$638$	1.00985e10	1.53951
$639$	−1.93244e9	−0.292990
$640$	−7.46961e8	−0.112634
$641$	−6.28456e9	−0.942480	−0.471240	−	0.882005i	$-0.656193\pi$
$641$	−6.28456e9	−0.942480	−0.471240	+	0.882005i	$0.656193\pi$
$642$	4.08471e8	0.0609240
$643$	2.44480e9	0.362665	0.181333	−	0.983422i	$-0.441959\pi$
$643$	2.44480e9	0.362665	0.181333	+	0.983422i	$0.441959\pi$
$644$	7.14194e8	0.105370
$645$	6.15510e9	0.903184
$646$	−3.56878e8	−0.0520842
$647$	7.83211e7	0.0113688	0.00568439	−	0.999984i	$-0.498191\pi$
$647$	7.83211e7	0.0113688	0.00568439	+	0.999984i	$0.498191\pi$
$648$	2.72098e8	0.0392837
$649$	−2.11481e10	−3.03679
$650$	8.56625e8	0.122347
$651$	−2.03852e9	−0.289589
$652$	−5.96550e9	−0.842909
$653$	−1.02149e10	−1.43562	−0.717811	−	0.696238i	$-0.754856\pi$
$653$	−1.02149e10	−1.43562	−0.717811	+	0.696238i	$0.754856\pi$
$654$	−1.99522e9	−0.278913
$655$	−2.64854e9	−0.368266
$656$	−3.37599e9	−0.466915
$657$	3.05205e9	0.419869
$658$	2.35651e8	0.0322462
$659$	−4.57175e9	−0.622276	−0.311138	−	0.950365i	$-0.600710\pi$
$659$	−4.57175e9	−0.622276	−0.311138	+	0.950365i	$0.600710\pi$
$660$	−4.61960e9	−0.625461
$661$	1.10823e10	1.49253	0.746266	−	0.665648i	$-0.231845\pi$
$661$	1.10823e10	1.49253	0.746266	+	0.665648i	$0.231845\pi$
$662$	4.06365e9	0.544394
$663$	9.53274e8	0.127034
$664$	−2.82031e9	−0.373860
$665$	3.39132e8	0.0447190
$666$	−1.23102e9	−0.161474
$667$	5.47162e9	0.713962
$668$	2.99638e9	0.388937
$669$	−7.89545e9	−1.01950
$670$	−3.62883e9	−0.466128
$671$	8.13342e9	1.03931
$672$	3.03464e8	0.0385758
$673$	1.22126e9	0.154438	0.0772190	−	0.997014i	$-0.475396\pi$
$673$	1.22126e9	0.154438	0.0772190	+	0.997014i	$0.475396\pi$
$674$	−7.05348e9	−0.887348
$675$	−9.59317e8	−0.120060
$676$	3.08916e8	0.0384615
$677$	1.31735e9	0.163170	0.0815848	−	0.996666i	$-0.474002\pi$
$677$	1.31735e9	0.163170	0.0815848	+	0.996666i	$0.474002\pi$
$678$	−2.95043e9	−0.363564
$679$	−2.05011e9	−0.251324
$680$	2.93064e9	0.357422
$681$	−7.77930e9	−0.943899
$682$	1.32172e10	1.59549
$683$	−3.30209e9	−0.396567	−0.198284	−	0.980145i	$-0.563537\pi$
$683$	−3.30209e9	−0.396567	−0.198284	+	0.980145i	$0.563537\pi$
$684$	1.29513e8	0.0154745
$685$	−4.85238e9	−0.576817
$686$	−3.22829e8	−0.0381802
$687$	2.09303e9	0.246279
$688$	2.62158e9	0.306905
$689$	−3.79309e9	−0.441800
$690$	−2.50302e9	−0.290063
$691$	−1.58840e10	−1.83141	−0.915706	−	0.401849i	$-0.868368\pi$
$691$	−1.58840e10	−1.83141	−0.915706	+	0.401849i	$0.868368\pi$
$692$	3.74168e9	0.429235
$693$	1.87678e9	0.214214
$694$	2.58791e9	0.293894
$695$	−1.47338e10	−1.66482
$696$	2.32492e9	0.261382
$697$	1.32454e10	1.48167
$698$	1.17594e10	1.30885
$699$	−7.44949e9	−0.825005
$700$	−1.06990e9	−0.117897
$701$	1.08169e10	1.18601	0.593005	−	0.805199i	$-0.297942\pi$
$701$	1.08169e10	1.18601	0.593005	+	0.805199i	$0.297942\pi$
$702$	−3.45948e8	−0.0377426
$703$	−5.85938e8	−0.0636075
$704$	−1.96758e9	−0.212534
$705$	−8.25881e8	−0.0887678
$706$	1.02947e10	1.10103
$707$	9.75755e8	0.103842
$708$	−4.86881e9	−0.515592
$709$	1.11238e10	1.17217	0.586085	−	0.810250i	$-0.300669\pi$
$709$	1.11238e10	1.17217	0.586085	+	0.810250i	$0.300669\pi$
$710$	7.55330e9	0.792013
$711$	−5.79299e9	−0.604448
$712$	2.27361e9	0.236067
$713$	7.16143e9	0.739922
$714$	−1.19062e9	−0.122413
$715$	5.87341e9	0.600923
$716$	−6.70104e9	−0.682255
$717$	5.78666e9	0.586288
$718$	−1.16647e10	−1.17608
$719$	5.88745e9	0.590713	0.295356	−	0.955387i	$-0.404562\pi$
$719$	5.88745e9	0.590713	0.295356	+	0.955387i	$0.404562\pi$
$720$	−1.06354e9	−0.106192
$721$	5.00203e9	0.497019
$722$	−7.08933e9	−0.701011
$723$	−1.78563e9	−0.175714
$724$	3.57880e9	0.350471
$725$	−8.19680e9	−0.798843
$726$	−7.95930e9	−0.771963
$727$	3.66339e9	0.353601	0.176800	−	0.984247i	$-0.443425\pi$
$727$	3.66339e9	0.353601	0.176800	+	0.984247i	$0.443425\pi$
$728$	−3.85828e8	−0.0370625
$729$	3.87420e8	0.0370370
$730$	−1.19295e10	−1.13499
$731$	−1.02855e10	−0.973905
$732$	1.87251e9	0.176456
$733$	1.21576e10	1.14020	0.570102	−	0.821574i	$-0.306904\pi$
$733$	1.21576e10	1.14020	0.570102	+	0.821574i	$0.306904\pi$
$734$	−7.11281e9	−0.663904
$735$	1.13141e9	0.105103
$736$	−1.06609e9	−0.0985643
$737$	−9.55875e9	−0.879558
$738$	−4.80683e9	−0.440212
$739$	−1.03201e10	−0.940652	−0.470326	−	0.882493i	$-0.655864\pi$
$739$	−1.03201e10	−0.940652	−0.470326	+	0.882493i	$0.655864\pi$
$740$	4.81165e9	0.436499
$741$	−1.64664e8	−0.0148674
$742$	4.73748e9	0.425729
$743$	−9.76148e9	−0.873081	−0.436541	−	0.899685i	$-0.643796\pi$
$743$	−9.76148e9	−0.873081	−0.436541	+	0.899685i	$0.643796\pi$
$744$	3.04292e9	0.270886
$745$	2.56825e10	2.27557
$746$	−2.38902e9	−0.210685
$747$	−4.01564e9	−0.352478
$748$	7.71962e9	0.674436
$749$	6.48636e8	0.0564046
$750$	−2.26085e9	−0.195685
$751$	−3.56446e9	−0.307082	−0.153541	−	0.988142i	$-0.549068\pi$
$751$	−3.56446e9	−0.307082	−0.153541	+	0.988142i	$0.549068\pi$
$752$	−3.51759e8	−0.0301636
$753$	−9.94735e9	−0.849034
$754$	−2.95593e9	−0.251127
$755$	−5.99112e8	−0.0506634
$756$	4.32081e8	0.0363696
$757$	6.66060e9	0.558056	0.279028	−	0.960283i	$-0.409988\pi$
$757$	6.66060e9	0.558056	0.279028	+	0.960283i	$0.409988\pi$
$758$	−6.04729e9	−0.504334
$759$	−6.59323e9	−0.547333
$760$	−5.06226e8	−0.0418308
$761$	1.16411e10	0.957520	0.478760	−	0.877946i	$-0.341086\pi$
$761$	1.16411e10	0.957520	0.478760	+	0.877946i	$0.341086\pi$
$762$	−7.36699e9	−0.603181
$763$	−3.16834e9	−0.258223
$764$	−3.39011e9	−0.275034
$765$	4.17272e9	0.336980
$766$	9.35305e9	0.751887
$767$	6.19026e9	0.495365
$768$	−4.52985e8	−0.0360844
$769$	6.06456e9	0.480903	0.240451	−	0.970661i	$-0.422705\pi$
$769$	6.06456e9	0.480903	0.240451	+	0.970661i	$0.422705\pi$
$770$	−7.33575e9	−0.579064
$771$	7.03211e9	0.552580
$772$	9.40600e9	0.735774
$773$	−4.87535e9	−0.379645	−0.189822	−	0.981818i	$-0.560791\pi$
$773$	−4.87535e9	−0.379645	−0.189822	+	0.981818i	$0.560791\pi$
$774$	3.73268e9	0.289353
$775$	−1.07282e10	−0.827889
$776$	3.06023e9	0.235092
$777$	−1.95481e9	−0.149496
$778$	2.96168e9	0.225480
$779$	−2.28795e9	−0.173407
$780$	1.35220e9	0.102026
$781$	1.98962e10	1.49449
$782$	4.18270e9	0.312775
$783$	3.31028e9	0.246433
$784$	4.81890e8	0.0357143
$785$	1.13392e10	0.836642
$786$	−1.60617e9	−0.117981
$787$	1.35287e9	0.0989336	0.0494668	−	0.998776i	$-0.484248\pi$
$787$	1.35287e9	0.0989336	0.0494668	+	0.998776i	$0.484248\pi$
$788$	−5.42554e9	−0.395003
$789$	−4.89119e9	−0.354523
$790$	2.26430e10	1.63395
$791$	−4.68517e9	−0.336595
$792$	−2.80149e9	−0.200379
$793$	−2.38074e9	−0.169533
$794$	−3.12030e9	−0.221220
$795$	−1.66033e10	−1.17195
$796$	−1.17257e10	−0.824033
$797$	1.47844e10	1.03443	0.517214	−	0.855856i	$-0.326969\pi$
$797$	1.47844e10	1.03443	0.517214	+	0.855856i	$0.326969\pi$
$798$	2.05662e8	0.0143266
$799$	1.38010e9	0.0957185
$800$	1.59706e9	0.110282
$801$	3.23722e9	0.222566
$802$	7.53935e9	0.516087
$803$	−3.14237e10	−2.14167
$804$	−2.20066e9	−0.149333
$805$	−3.97470e9	−0.268546
$806$	−3.86881e9	−0.260258
$807$	1.35013e10	0.904309
$808$	−1.45652e9	−0.0971353
$809$	−2.00980e8	−0.0133455	−0.00667273	−	0.999978i	$-0.502124\pi$
$809$	−2.00980e8	−0.0133455	−0.00667273	+	0.999978i	$0.502124\pi$
$810$	−1.51430e9	−0.100119
$811$	1.02811e10	0.676809	0.338405	−	0.941001i	$-0.390113\pi$
$811$	1.02811e10	0.676809	0.338405	+	0.941001i	$0.390113\pi$
$812$	3.69188e9	0.241992
$813$	2.27933e9	0.148761
$814$	1.26744e10	0.823650
$815$	3.31998e10	2.14824
$816$	1.77725e9	0.114507
$817$	1.77668e9	0.113981
$818$	−1.35996e10	−0.868737
$819$	−5.49353e8	−0.0349428
$820$	1.87884e10	1.18998
$821$	−1.08015e9	−0.0681213	−0.0340607	−	0.999420i	$-0.510844\pi$
$821$	−1.08015e9	−0.0681213	−0.0340607	+	0.999420i	$0.510844\pi$
$822$	−2.94266e9	−0.184795
$823$	−8.00736e9	−0.500714	−0.250357	−	0.968154i	$-0.580548\pi$
$823$	−8.00736e9	−0.500714	−0.250357	+	0.968154i	$0.580548\pi$
$824$	−7.46659e9	−0.464919
$825$	9.87704e9	0.612404
$826$	−7.73149e9	−0.477345
$827$	1.60107e10	0.984330	0.492165	−	0.870502i	$-0.336206\pi$
$827$	1.60107e10	0.984330	0.492165	+	0.870502i	$0.336206\pi$
$828$	−1.51792e9	−0.0929273
$829$	−1.70468e10	−1.03920	−0.519602	−	0.854408i	$-0.673920\pi$
$829$	−1.70468e10	−1.03920	−0.519602	+	0.854408i	$0.673920\pi$
$830$	1.56959e10	0.952822
$831$	1.36529e10	0.825320
$832$	5.75930e8	0.0346688
$833$	−1.89066e9	−0.113333
$834$	−8.93510e9	−0.533357
$835$	−1.66757e10	−0.991247
$836$	−1.33345e9	−0.0789325
$837$	4.33260e9	0.255393
$838$	6.94072e9	0.407428
$839$	1.28512e10	0.751237	0.375618	−	0.926774i	$-0.377430\pi$
$839$	1.28512e10	0.751237	0.375618	+	0.926774i	$0.377430\pi$
$840$	−1.68887e9	−0.0983147
$841$	1.10345e10	0.639688
$842$	−1.71137e10	−0.987989
$843$	3.38712e9	0.194730
$844$	1.05960e10	0.606655
$845$	−1.71921e9	−0.0980234
$846$	−5.00845e8	−0.0284385
$847$	−1.26391e10	−0.714699
$848$	−7.07168e9	−0.398233
$849$	4.10292e9	0.230100
$850$	−6.26592e9	−0.349960
$851$	6.86733e9	0.381975
$852$	4.58060e9	0.253737
$853$	−4.40731e9	−0.243137	−0.121569	−	0.992583i	$-0.538792\pi$
$853$	−4.40731e9	−0.243137	−0.121569	+	0.992583i	$0.538792\pi$
$854$	2.97348e9	0.163366
$855$	−7.20778e8	−0.0394385
$856$	−9.68226e8	−0.0527617
$857$	−1.04953e10	−0.569587	−0.284794	−	0.958589i	$-0.591925\pi$
$857$	−1.04953e10	−0.569587	−0.284794	+	0.958589i	$0.591925\pi$
$858$	3.56185e9	0.192518
$859$	3.04414e10	1.63866	0.819328	−	0.573325i	$-0.194347\pi$
$859$	3.04414e10	1.63866	0.819328	+	0.573325i	$0.194347\pi$
$860$	−1.45899e10	−0.782180
$861$	−7.63307e9	−0.407557
$862$	−1.01548e10	−0.540001
$863$	−1.44946e10	−0.767659	−0.383829	−	0.923404i	$-0.625395\pi$
$863$	−1.44946e10	−0.767659	−0.383829	+	0.923404i	$0.625395\pi$
$864$	−6.44973e8	−0.0340207
$865$	−2.08235e10	−1.09395
$866$	1.42302e10	0.744559
$867$	4.10627e9	0.213984
$868$	4.83205e9	0.250791
$869$	5.96441e10	3.08318
$870$	−1.29388e10	−0.666159
$871$	2.79794e9	0.143475
$872$	4.72942e9	0.241546
$873$	4.35723e9	0.221647
$874$	−7.22501e8	−0.0366057
$875$	−3.59015e9	−0.181169
$876$	−7.23450e9	−0.363617
$877$	1.93578e10	0.969074	0.484537	−	0.874771i	$-0.338988\pi$
$877$	1.93578e10	0.969074	0.484537	+	0.874771i	$0.338988\pi$
$878$	−9.13179e9	−0.455329
$879$	−1.17090e9	−0.0581512
$880$	1.09502e10	0.541665
$881$	−7.70488e9	−0.379621	−0.189811	−	0.981821i	$-0.560787\pi$
$881$	−7.70488e9	−0.379621	−0.189811	+	0.981821i	$0.560787\pi$
$882$	6.86129e8	0.0336718
$883$	7.96120e9	0.389149	0.194574	−	0.980888i	$-0.437667\pi$
$883$	7.96120e9	0.389149	0.194574	+	0.980888i	$0.437667\pi$
$884$	−2.25961e9	−0.110015
$885$	2.70963e10	1.31404
$886$	−7.87383e9	−0.380337
$887$	−3.45970e10	−1.66459	−0.832293	−	0.554336i	$-0.812972\pi$
$887$	−3.45970e10	−1.66459	−0.832293	+	0.554336i	$0.812972\pi$
$888$	2.91796e9	0.139841
$889$	−1.16985e10	−0.558437
$890$	−1.26533e10	−0.601642
$891$	−3.98884e9	−0.188919
$892$	1.87151e10	0.882909
$893$	−2.38392e8	−0.0112024
$894$	1.55748e10	0.729024
$895$	3.72933e10	1.73880
$896$	−7.19323e8	−0.0334077
$897$	1.92991e9	0.0892817
$898$	5.71493e9	0.263356
$899$	3.70195e10	1.69931
$900$	2.27394e9	0.103975
$901$	2.77451e10	1.26372
$902$	4.94907e10	2.24543
$903$	5.92736e9	0.267888
$904$	6.99361e9	0.314856
$905$	−1.99171e10	−0.893213
$906$	−3.63324e8	−0.0162310
$907$	−1.75994e9	−0.0783197	−0.0391599	−	0.999233i	$-0.512468\pi$
$907$	−1.75994e9	−0.0783197	−0.0391599	+	0.999233i	$0.512468\pi$
$908$	1.84398e10	0.817441
$909$	−2.07384e9	−0.0915800
$910$	2.14725e9	0.0944577
$911$	−2.98095e10	−1.30629	−0.653146	−	0.757232i	$-0.726551\pi$
$911$	−2.98095e10	−1.30629	−0.653146	+	0.757232i	$0.726551\pi$
$912$	−3.06994e8	−0.0134013
$913$	4.13446e10	1.79792
$914$	−4.23045e9	−0.183263
$915$	−1.04211e10	−0.449717
$916$	−4.96126e9	−0.213284
$917$	−2.55054e9	−0.109229
$918$	2.53049e9	0.107958
$919$	3.27566e10	1.39218	0.696089	−	0.717956i	$-0.254922\pi$
$919$	3.27566e10	1.39218	0.696089	+	0.717956i	$0.254922\pi$
$920$	5.93308e9	0.251202
$921$	2.20838e10	0.931463
$922$	9.00843e9	0.378522
$923$	−5.82383e9	−0.243782
$924$	−4.44867e9	−0.185515
$925$	−1.02877e10	−0.427387
$926$	−1.54977e10	−0.641401
$927$	−1.06311e10	−0.438330
$928$	−5.51091e9	−0.226363
$929$	−4.44117e10	−1.81737	−0.908683	−	0.417486i	$-0.862911\pi$
$929$	−4.44117e10	−1.81737	−0.908683	+	0.417486i	$0.862911\pi$
$930$	−1.69348e10	−0.690381
$931$	3.26583e8	0.0132639
$932$	1.76581e10	0.714475
$933$	−2.32590e10	−0.937575
$934$	−2.84793e10	−1.14371
$935$	−4.29620e10	−1.71887
$936$	8.20026e8	0.0326860
$937$	−2.70253e10	−1.07320	−0.536602	−	0.843835i	$-0.680292\pi$
$937$	−2.70253e10	−1.07320	−0.536602	+	0.843835i	$0.680292\pi$
$938$	−3.49456e9	−0.138256
$939$	−5.82451e9	−0.229578
$940$	1.95764e9	0.0768752
$941$	−3.12862e10	−1.22402	−0.612010	−	0.790850i	$-0.709639\pi$
$941$	−3.12862e10	−1.22402	−0.612010	+	0.790850i	$0.709639\pi$
$942$	6.87653e9	0.268035
$943$	2.68153e10	1.04134
$944$	1.15409e10	0.446516
$945$	−2.40466e9	−0.0926920
$946$	−3.84313e10	−1.47593
$947$	3.80554e10	1.45610	0.728051	−	0.685523i	$-0.240426\pi$
$947$	3.80554e10	1.45610	0.728051	+	0.685523i	$0.240426\pi$
$948$	1.37315e10	0.523468
$949$	9.19803e9	0.349352
$950$	1.08235e9	0.0409576
$951$	−3.02865e9	−0.114187
$952$	2.82220e9	0.106013
$953$	1.78132e10	0.666681	0.333340	−	0.942807i	$-0.391824\pi$
$953$	1.78132e10	0.666681	0.333340	+	0.942807i	$0.391824\pi$
$954$	−1.00689e10	−0.375458
$955$	1.88670e10	0.700955
$956$	−1.37165e10	−0.507740
$957$	−3.40823e10	−1.25701
$958$	6.66530e9	0.244929
$959$	−4.67284e9	−0.171087
$960$	2.52099e9	0.0919650
$961$	2.09397e10	0.761095
$962$	−3.70993e9	−0.134355
$963$	−1.37859e9	−0.0497442
$964$	4.23260e9	0.152173
$965$	−5.23472e10	−1.87520
$966$	−2.41041e9	−0.0860340
$967$	1.49059e10	0.530109	0.265054	−	0.964233i	$-0.414610\pi$
$967$	1.49059e10	0.530109	0.265054	+	0.964233i	$0.414610\pi$
$968$	1.88665e10	0.668540
$969$	1.20446e9	0.0425266
$970$	−1.70311e10	−0.599157
$971$	2.94577e10	1.03260	0.516299	−	0.856408i	$-0.327309\pi$
$971$	2.94577e10	1.03260	0.516299	+	0.856408i	$0.327309\pi$
$972$	−9.18330e8	−0.0320750
$973$	−1.41886e10	−0.493793
$974$	6.83004e9	0.236847
$975$	−2.89111e9	−0.0998961
$976$	−4.43855e9	−0.152815
$977$	1.84802e10	0.633980	0.316990	−	0.948429i	$-0.397328\pi$
$977$	1.84802e10	0.633980	0.316990	+	0.948429i	$0.397328\pi$
$978$	2.01336e10	0.688232
$979$	−3.33302e10	−1.13527
$980$	−2.68186e9	−0.0910217
$981$	6.73387e9	0.227732
$982$	−3.55234e10	−1.19708
$983$	−4.33131e10	−1.45439	−0.727197	−	0.686429i	$-0.759177\pi$
$983$	−4.33131e10	−1.45439	−0.727197	+	0.686429i	$0.759177\pi$
$984$	1.13940e10	0.381234
$985$	3.01947e10	1.00671
$986$	2.16216e10	0.718321
$987$	−7.95323e8	−0.0263289
$988$	3.90316e8	0.0128756
$989$	−2.08231e10	−0.684476
$990$	1.55911e10	0.510687
$991$	−8.95161e9	−0.292175	−0.146088	−	0.989272i	$-0.546668\pi$
$991$	−8.95161e9	−0.292175	−0.146088	+	0.989272i	$0.546668\pi$
$992$	−7.21286e9	−0.234594
$993$	−1.37148e10	−0.444496
$994$	7.27382e9	0.234915
$995$	6.52572e10	2.10014
$996$	9.51855e9	0.305255
$997$	−4.71755e9	−0.150759	−0.0753795	−	0.997155i	$-0.524017\pi$
$997$	−4.71755e9	−0.150759	−0.0753795	+	0.997155i	$0.524017\pi$
$998$	−1.37108e9	−0.0436621
$999$	4.15468e9	0.131843

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.8.a.r.1.1	✓	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)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -356.179 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -356.179 q^{5} -216.000 q^{6} -343.000 q^{7} +512.000 q^{8} +729.000 q^{9} -2849.43 q^{10} -7505.72 q^{11} -1728.00 q^{12} +2197.00 q^{13} -2744.00 q^{14} +9616.83 q^{15} +4096.00 q^{16} -16070.3 q^{17} +5832.00 q^{18} +2775.91 q^{19} -22795.4 q^{20} +9261.00 q^{21} -60045.7 q^{22} -32534.4 q^{23} -13824.0 q^{24} +48738.4 q^{25} +17576.0 q^{26} -19683.0 q^{27} -21952.0 q^{28} -168180. q^{29} +76934.6 q^{30} -220119. q^{31} +32768.0 q^{32} +202654. q^{33} -128562. q^{34} +122169. q^{35} +46656.0 q^{36} -211079. q^{37} +22207.3 q^{38} -59319.0 q^{39} -182364. q^{40} -824216. q^{41} +74088.0 q^{42} +640034. q^{43} -480366. q^{44} -259654. q^{45} -260275. q^{46} -85878.7 q^{47} -110592. q^{48} +117649. q^{49} +389907. q^{50} +433898. q^{51} +140608. q^{52} -1.72649e6 q^{53} -157464. q^{54} +2.67338e6 q^{55} -175616. q^{56} -74949.7 q^{57} -1.34544e6 q^{58} +2.81760e6 q^{59} +615477. q^{60} -1.08363e6 q^{61} -1.76095e6 q^{62} -250047. q^{63} +262144. q^{64} -782525. q^{65} +1.62123e6 q^{66} +1.27353e6 q^{67} -1.02850e6 q^{68} +878428. q^{69} +977355. q^{70} -2.65081e6 q^{71} +373248. q^{72} +4.18663e6 q^{73} -1.68864e6 q^{74} -1.31594e6 q^{75} +177658. q^{76} +2.57446e6 q^{77} -474552. q^{78} -7.94649e6 q^{79} -1.45891e6 q^{80} +531441. q^{81} -6.59373e6 q^{82} -5.50842e6 q^{83} +592704. q^{84} +5.72390e6 q^{85} +5.12028e6 q^{86} +4.54085e6 q^{87} -3.84293e6 q^{88} +4.44064e6 q^{89} -2.07723e6 q^{90} -753571. q^{91} -2.08220e6 q^{92} +5.94321e6 q^{93} -687030. q^{94} -988722. q^{95} -884736. q^{96} +5.97700e6 q^{97} +941192. q^{98} -5.47167e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 48 q^{2} - 162 q^{3} + 384 q^{4} + 203 q^{5} - 1296 q^{6} - 2058 q^{7} + 3072 q^{8} + 4374 q^{9}+O(q^{10}) \) 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

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