LMFDB - Embedded newform 471.8.a.c.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,8,Mod(1,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("471.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	471.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:	$147.133347003$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	471.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-16.8482 q^{2} -27.0000 q^{3} +155.860 q^{4} +189.080 q^{5} +454.900 q^{6} +904.411 q^{7} -469.396 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-16.8482 q^{2} -27.0000 q^{3} +155.860 q^{4} +189.080 q^{5} +454.900 q^{6} +904.411 q^{7} -469.396 q^{8} +729.000 q^{9} -3185.64 q^{10} -4295.36 q^{11} -4208.23 q^{12} +1028.88 q^{13} -15237.7 q^{14} -5105.15 q^{15} -12041.7 q^{16} +18116.3 q^{17} -12282.3 q^{18} -23622.5 q^{19} +29470.0 q^{20} -24419.1 q^{21} +72368.8 q^{22} -75914.6 q^{23} +12673.7 q^{24} -42373.9 q^{25} -17334.8 q^{26} -19683.0 q^{27} +140962. q^{28} -88522.6 q^{29} +86012.4 q^{30} +44356.9 q^{31} +262963. q^{32} +115975. q^{33} -305226. q^{34} +171006. q^{35} +113622. q^{36} +212638. q^{37} +397996. q^{38} -27779.9 q^{39} -88753.2 q^{40} +595868. q^{41} +411417. q^{42} -319430. q^{43} -669476. q^{44} +137839. q^{45} +1.27902e6 q^{46} +994129. q^{47} +325125. q^{48} -5584.23 q^{49} +713921. q^{50} -489140. q^{51} +160362. q^{52} +315708. q^{53} +331622. q^{54} -812165. q^{55} -424527. q^{56} +637809. q^{57} +1.49144e6 q^{58} -1.74504e6 q^{59} -795691. q^{60} +2.17760e6 q^{61} -747332. q^{62} +659315. q^{63} -2.88910e6 q^{64} +194541. q^{65} -1.95396e6 q^{66} -2.98324e6 q^{67} +2.82361e6 q^{68} +2.04969e6 q^{69} -2.88113e6 q^{70} -4.54654e6 q^{71} -342190. q^{72} +5.25536e6 q^{73} -3.58255e6 q^{74} +1.14409e6 q^{75} -3.68182e6 q^{76} -3.88477e6 q^{77} +468040. q^{78} -2.03441e6 q^{79} -2.27684e6 q^{80} +531441. q^{81} -1.00393e7 q^{82} +6.94337e6 q^{83} -3.80597e6 q^{84} +3.42543e6 q^{85} +5.38181e6 q^{86} +2.39011e6 q^{87} +2.01622e6 q^{88} +7.77346e6 q^{89} -2.32234e6 q^{90} +930534. q^{91} -1.18321e7 q^{92} -1.19764e6 q^{93} -1.67492e7 q^{94} -4.46654e6 q^{95} -7.09999e6 q^{96} -1.30158e7 q^{97} +94084.0 q^{98} -3.13131e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{2} - 1296 q^{3} + 3214 q^{4} + 428 q^{5} - 54 q^{6} - 680 q^{7} + 2355 q^{8} + 34992 q^{9}+O(q^{10}) $ 48 * q + 2 * q^2 - 1296 * q^3 + 3214 * q^4 + 428 * q^5 - 54 * q^6 - 680 * q^7 + 2355 * q^8 + 34992 * q^9	\( 48 q + 2 q^{2} - 1296 q^{3} + 3214 q^{4} + 428 q^{5} - 54 q^{6} - 680 q^{7} + 2355 q^{8} + 34992 q^{9} + 6185 q^{10} + 11989 q^{11} - 86778 q^{12} - 2393 q^{13} + 18201 q^{14} - 11556 q^{15} + 208150 q^{16} + 62538 q^{17} + 1458 q^{18} - 39882 q^{19} + 113423 q^{20} + 18360 q^{21} - 93716 q^{22} + 195618 q^{23} - 63585 q^{24} + 886490 q^{25} + 294399 q^{26} - 944784 q^{27} - 60819 q^{28} + 421501 q^{29} - 166995 q^{30} + 392689 q^{31} - 341578 q^{32} - 323703 q^{33} + 50837 q^{34} + 697874 q^{35} + 2343006 q^{36} - 410396 q^{37} + 677216 q^{38} + 64611 q^{39} + 3232376 q^{40} + 3832958 q^{41} - 491427 q^{42} - 1751932 q^{43} + 4888297 q^{44} + 312012 q^{45} + 1163150 q^{46} + 106461 q^{47} - 5620050 q^{48} + 8202048 q^{49} - 2159111 q^{50} - 1688526 q^{51} - 3605030 q^{52} + 1755534 q^{53} - 39366 q^{54} - 1220729 q^{55} - 4430622 q^{56} + 1076814 q^{57} - 10000202 q^{58} - 2037752 q^{59} - 3062421 q^{60} + 1274098 q^{61} + 97748 q^{62} - 495720 q^{63} + 15135201 q^{64} + 6139645 q^{65} + 2530332 q^{66} - 7751257 q^{67} + 1700631 q^{68} - 5281686 q^{69} - 20935703 q^{70} - 12592217 q^{71} + 1716795 q^{72} + 12508355 q^{73} - 14999956 q^{74} - 23935230 q^{75} - 23946874 q^{76} + 1874177 q^{77} - 7948773 q^{78} - 5103480 q^{79} + 3128449 q^{80} + 25509168 q^{81} + 11622426 q^{82} + 3040643 q^{83} + 1642113 q^{84} - 13756076 q^{85} + 964635 q^{86} - 11380527 q^{87} - 29653500 q^{88} + 28462995 q^{89} + 4508865 q^{90} + 3016621 q^{91} + 22938254 q^{92} - 10602603 q^{93} - 10070348 q^{94} - 2579984 q^{95} + 9222606 q^{96} + 16208760 q^{97} + 6323227 q^{98} + 8739981 q^{99}+O(q^{100}) \) 48 * q + 2 * q^2 - 1296 * q^3 + 3214 * q^4 + 428 * q^5 - 54 * q^6 - 680 * q^7 + 2355 * q^8 + 34992 * q^9 + 6185 * q^10 + 11989 * q^11 - 86778 * q^12 - 2393 * q^13 + 18201 * q^14 - 11556 * q^15 + 208150 * q^16 + 62538 * q^17 + 1458 * q^18 - 39882 * q^19 + 113423 * q^20 + 18360 * q^21 - 93716 * q^22 + 195618 * q^23 - 63585 * q^24 + 886490 * q^25 + 294399 * q^26 - 944784 * q^27 - 60819 * q^28 + 421501 * q^29 - 166995 * q^30 + 392689 * q^31 - 341578 * q^32 - 323703 * q^33 + 50837 * q^34 + 697874 * q^35 + 2343006 * q^36 - 410396 * q^37 + 677216 * q^38 + 64611 * q^39 + 3232376 * q^40 + 3832958 * q^41 - 491427 * q^42 - 1751932 * q^43 + 4888297 * q^44 + 312012 * q^45 + 1163150 * q^46 + 106461 * q^47 - 5620050 * q^48 + 8202048 * q^49 - 2159111 * q^50 - 1688526 * q^51 - 3605030 * q^52 + 1755534 * q^53 - 39366 * q^54 - 1220729 * q^55 - 4430622 * q^56 + 1076814 * q^57 - 10000202 * q^58 - 2037752 * q^59 - 3062421 * q^60 + 1274098 * q^61 + 97748 * q^62 - 495720 * q^63 + 15135201 * q^64 + 6139645 * q^65 + 2530332 * q^66 - 7751257 * q^67 + 1700631 * q^68 - 5281686 * q^69 - 20935703 * q^70 - 12592217 * q^71 + 1716795 * q^72 + 12508355 * q^73 - 14999956 * q^74 - 23935230 * q^75 - 23946874 * q^76 + 1874177 * q^77 - 7948773 * q^78 - 5103480 * q^79 + 3128449 * q^80 + 25509168 * q^81 + 11622426 * q^82 + 3040643 * q^83 + 1642113 * q^84 - 13756076 * q^85 + 964635 * q^86 - 11380527 * q^87 - 29653500 * q^88 + 28462995 * q^89 + 4508865 * q^90 + 3016621 * q^91 + 22938254 * q^92 - 10602603 * q^93 - 10070348 * q^94 - 2579984 * q^95 + 9222606 * q^96 + 16208760 * q^97 + 6323227 * q^98 + 8739981 * 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 $

$2$	−16.8482	−1.48918	−0.744590	−	0.667522i	$-0.767355\pi$
$2$	−16.8482	−1.48918	−0.744590	+	0.667522i	$0.767355\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	155.860	1.21766
$5$	189.080	0.676472	0.338236	−	0.941061i	$-0.390170\pi$
$5$	189.080	0.676472	0.338236	+	0.941061i	$0.390170\pi$
$6$	454.900	0.859779
$7$	904.411	0.996604	0.498302	−	0.867004i	$-0.333957\pi$
$7$	904.411	0.996604	0.498302	+	0.867004i	$0.333957\pi$
$8$	−469.396	−0.324134
$9$	729.000	0.333333
$10$	−3185.64	−1.00739
$11$	−4295.36	−0.973027	−0.486513	−	0.873673i	$-0.661731\pi$
$11$	−4295.36	−0.973027	−0.486513	+	0.873673i	$0.661731\pi$
$12$	−4208.23	−0.703016
$13$	1028.88	0.129887	0.0649434	−	0.997889i	$-0.479313\pi$
$13$	1028.88	0.129887	0.0649434	+	0.997889i	$0.479313\pi$
$14$	−15237.7	−1.48412
$15$	−5105.15	−0.390561
$16$	−12041.7	−0.734965
$17$	18116.3	0.894331	0.447165	−	0.894451i	$-0.352434\pi$
$17$	18116.3	0.894331	0.447165	+	0.894451i	$0.352434\pi$
$18$	−12282.3	−0.496394
$19$	−23622.5	−0.790113	−0.395056	−	0.918657i	$-0.629275\pi$
$19$	−23622.5	−0.790113	−0.395056	+	0.918657i	$0.629275\pi$
$20$	29470.0	0.823713
$21$	−24419.1	−0.575390
$22$	72368.8	1.44901
$23$	−75914.6	−1.30100	−0.650501	−	0.759506i	$-0.725441\pi$
$23$	−75914.6	−1.30100	−0.650501	+	0.759506i	$0.725441\pi$
$24$	12673.7	0.187139
$25$	−42373.9	−0.542385
$26$	−17334.8	−0.193425
$27$	−19683.0	−0.192450
$28$	140962.	1.21352
$29$	−88522.6	−0.674002	−0.337001	−	0.941504i	$-0.609413\pi$
$29$	−88522.6	−0.674002	−0.337001	+	0.941504i	$0.609413\pi$
$30$	86012.4	0.581617
$31$	44356.9	0.267421	0.133711	−	0.991020i	$-0.457311\pi$
$31$	44356.9	0.267421	0.133711	+	0.991020i	$0.457311\pi$
$32$	262963.	1.41863
$33$	115975.	0.561777
$34$	−305226.	−1.33182
$35$	171006.	0.674175
$36$	113622.	0.405886
$37$	212638.	0.690135	0.345067	−	0.938578i	$-0.387856\pi$
$37$	212638.	0.690135	0.345067	+	0.938578i	$0.387856\pi$
$38$	397996.	1.17662
$39$	−27779.9	−0.0749902
$40$	−88753.2	−0.219267
$41$	595868.	1.35023	0.675113	−	0.737714i	$-0.264095\pi$
$41$	595868.	1.35023	0.675113	+	0.737714i	$0.264095\pi$
$42$	411417.	0.856859
$43$	−319430.	−0.612683	−0.306342	−	0.951922i	$-0.599105\pi$
$43$	−319430.	−0.612683	−0.306342	+	0.951922i	$0.599105\pi$
$44$	−669476.	−1.18481
$45$	137839.	0.225491
$46$	1.27902e6	1.93743
$47$	994129.	1.39669	0.698345	−	0.715761i	$-0.253920\pi$
$47$	994129.	1.39669	0.698345	+	0.715761i	$0.253920\pi$
$48$	325125.	0.424332
$49$	−5584.23	−0.00678074
$50$	713921.	0.807710
$51$	−489140.	−0.516342
$52$	160362.	0.158158
$53$	315708.	0.291286	0.145643	−	0.989337i	$-0.453475\pi$
$53$	315708.	0.291286	0.145643	+	0.989337i	$0.453475\pi$
$54$	331622.	0.286593
$55$	−812165.	−0.658225
$56$	−424527.	−0.323033
$57$	637809.	0.456172
$58$	1.49144e6	1.00371
$59$	−1.74504e6	−1.10617	−0.553086	−	0.833124i	$-0.686550\pi$
$59$	−1.74504e6	−1.10617	−0.553086	+	0.833124i	$0.686550\pi$
$60$	−795691.	−0.475571
$61$	2.17760e6	1.22835	0.614177	−	0.789168i	$-0.289488\pi$
$61$	2.17760e6	1.22835	0.614177	+	0.789168i	$0.289488\pi$
$62$	−747332.	−0.398238
$63$	659315.	0.332201
$64$	−2.88910e6	−1.37763
$65$	194541.	0.0878648
$66$	−1.95396e6	−0.836588
$67$	−2.98324e6	−1.21179	−0.605893	−	0.795546i	$-0.707184\pi$
$67$	−2.98324e6	−1.21179	−0.605893	+	0.795546i	$0.707184\pi$
$68$	2.82361e6	1.08899
$69$	2.04969e6	0.751133
$70$	−2.88113e6	−1.00397
$71$	−4.54654e6	−1.50757	−0.753783	−	0.657123i	$-0.771773\pi$
$71$	−4.54654e6	−1.50757	−0.753783	+	0.657123i	$0.771773\pi$
$72$	−342190.	−0.108045
$73$	5.25536e6	1.58115	0.790575	−	0.612366i	$-0.209782\pi$
$73$	5.25536e6	1.58115	0.790575	+	0.612366i	$0.209782\pi$
$74$	−3.58255e6	−1.02774
$75$	1.14409e6	0.313146
$76$	−3.68182e6	−0.962088
$77$	−3.88477e6	−0.969722
$78$	468040.	0.111674
$79$	−2.03441e6	−0.464242	−0.232121	−	0.972687i	$-0.574567\pi$
$79$	−2.03441e6	−0.464242	−0.232121	+	0.972687i	$0.574567\pi$
$80$	−2.27684e6	−0.497184
$81$	531441.	0.111111
$82$	−1.00393e7	−2.01073
$83$	6.94337e6	1.33290	0.666449	−	0.745551i	$-0.267813\pi$
$83$	6.94337e6	1.33290	0.666449	+	0.745551i	$0.267813\pi$
$84$	−3.80597e6	−0.700628
$85$	3.42543e6	0.604990
$86$	5.38181e6	0.912396
$87$	2.39011e6	0.389135
$88$	2.01622e6	0.315391
$89$	7.77346e6	1.16882	0.584412	−	0.811457i	$-0.301325\pi$
$89$	7.77346e6	1.16882	0.584412	+	0.811457i	$0.301325\pi$
$90$	−2.32234e6	−0.335796
$91$	930534.	0.129446
$92$	−1.18321e7	−1.58418
$93$	−1.19764e6	−0.154396
$94$	−1.67492e7	−2.07992
$95$	−4.46654e6	−0.534489
$96$	−7.09999e6	−0.819046
$97$	−1.30158e7	−1.44800	−0.724000	−	0.689800i	$-0.757698\pi$
$97$	−1.30158e7	−1.44800	−0.724000	+	0.689800i	$0.757698\pi$
$98$	94084.0	0.0100978
$99$	−3.13131e6	−0.324342
$100$	−6.60440e6	−0.660440
$101$	1.27359e7	1.23000	0.615000	−	0.788527i	$-0.289156\pi$
$101$	1.27359e7	1.23000	0.615000	+	0.788527i	$0.289156\pi$
$102$	8.24111e6	0.768927
$103$	1.14681e7	1.03410	0.517049	−	0.855956i	$-0.327030\pi$
$103$	1.14681e7	1.03410	0.517049	+	0.855956i	$0.327030\pi$
$104$	−482954.	−0.0421007
$105$	−4.61715e6	−0.389235
$106$	−5.31909e6	−0.433777
$107$	−5.11026e6	−0.403274	−0.201637	−	0.979460i	$-0.564626\pi$
$107$	−5.11026e6	−0.403274	−0.201637	+	0.979460i	$0.564626\pi$
$108$	−3.06780e6	−0.234339
$109$	−2.09959e7	−1.55289	−0.776447	−	0.630183i	$-0.782980\pi$
$109$	−2.09959e7	−1.55289	−0.776447	+	0.630183i	$0.782980\pi$
$110$	1.36835e7	0.980217
$111$	−5.74121e6	−0.398449
$112$	−1.08906e7	−0.732469
$113$	7.61856e6	0.496705	0.248352	−	0.968670i	$-0.420111\pi$
$113$	7.61856e6	0.496705	0.248352	+	0.968670i	$0.420111\pi$
$114$	−1.07459e7	−0.679322
$115$	−1.43539e7	−0.880091
$116$	−1.37972e7	−0.820704
$117$	750057.	0.0432956
$118$	2.94007e7	1.64729
$119$	1.63846e7	0.891294
$120$	2.39634e6	0.126594
$121$	−1.03709e6	−0.0532192
$122$	−3.66886e7	−1.82924
$123$	−1.60884e7	−0.779553
$124$	6.91349e6	0.325628
$125$	−2.27839e7	−1.04338
$126$	−1.11082e7	−0.494708
$127$	2.78781e7	1.20767	0.603837	−	0.797108i	$-0.293638\pi$
$127$	2.78781e7	1.20767	0.603837	+	0.797108i	$0.293638\pi$
$128$	1.50168e7	0.632912
$129$	8.62461e6	0.353733
$130$	−3.27766e6	−0.130847
$131$	−4.67355e7	−1.81634	−0.908170	−	0.418602i	$-0.862520\pi$
$131$	−4.67355e7	−1.81634	−0.908170	+	0.418602i	$0.862520\pi$
$132$	1.80758e7	0.684053
$133$	−2.13645e7	−0.787429
$134$	5.02621e7	1.80457
$135$	−3.72166e6	−0.130187
$136$	−8.50372e6	−0.289883
$137$	4.44968e7	1.47845	0.739225	−	0.673459i	$-0.235192\pi$
$137$	4.44968e7	1.47845	0.739225	+	0.673459i	$0.235192\pi$
$138$	−3.45335e7	−1.11857
$139$	−1.28273e7	−0.405119	−0.202560	−	0.979270i	$-0.564926\pi$
$139$	−1.28273e7	−0.405119	−0.202560	+	0.979270i	$0.564926\pi$
$140$	2.66530e7	0.820915
$141$	−2.68415e7	−0.806379
$142$	7.66008e7	2.24504
$143$	−4.41943e6	−0.126383
$144$	−8.77838e6	−0.244988
$145$	−1.67378e7	−0.455943
$146$	−8.85432e7	−2.35462
$147$	150774.	0.00391486
$148$	3.31418e7	0.840349
$149$	−2.45358e7	−0.607642	−0.303821	−	0.952729i	$-0.598262\pi$
$149$	−2.45358e7	−0.607642	−0.303821	+	0.952729i	$0.598262\pi$
$150$	−1.92759e7	−0.466331
$151$	−7.07256e7	−1.67170	−0.835848	−	0.548961i	$-0.815024\pi$
$151$	−7.07256e7	−1.67170	−0.835848	+	0.548961i	$0.815024\pi$
$152$	1.10883e7	0.256102
$153$	1.32068e7	0.298110
$154$	6.54511e7	1.44409
$155$	8.38700e6	0.180903
$156$	−4.32978e6	−0.0913125
$157$	−3.86989e6	−0.0798087
$157$	−3.86989e6	−0.0798087
$158$	3.42761e7	0.691340
$159$	−8.52411e6	−0.168174
$160$	4.97209e7	0.959664
$161$	−6.86579e7	−1.29658
$162$	−8.95380e6	−0.165465
$163$	9.48095e7	1.71473	0.857364	−	0.514710i	$-0.172100\pi$
$163$	9.48095e7	1.71473	0.857364	+	0.514710i	$0.172100\pi$
$164$	9.28722e7	1.64412
$165$	2.19284e7	0.380027
$166$	−1.16983e8	−1.98493
$167$	8.84108e7	1.46892	0.734459	−	0.678653i	$-0.237436\pi$
$167$	8.84108e7	1.46892	0.734459	+	0.678653i	$0.237436\pi$
$168$	1.14622e7	0.186503
$169$	−6.16899e7	−0.983129
$170$	−5.77121e7	−0.900940
$171$	−1.72208e7	−0.263371
$172$	−4.97865e7	−0.746040
$173$	−6.52551e7	−0.958193	−0.479096	−	0.877762i	$-0.659036\pi$
$173$	−6.52551e7	−0.958193	−0.479096	+	0.877762i	$0.659036\pi$
$174$	−4.02689e7	−0.579492
$175$	−3.83234e7	−0.540543
$176$	5.17233e7	0.715141
$177$	4.71160e7	0.638649
$178$	−1.30968e8	−1.74059
$179$	9.00373e7	1.17337	0.586687	−	0.809814i	$-0.300432\pi$
$179$	9.00373e7	1.17337	0.586687	+	0.809814i	$0.300432\pi$
$180$	2.14837e7	0.274571
$181$	1.23418e8	1.54704	0.773521	−	0.633771i	$-0.218494\pi$
$181$	1.23418e8	1.54704	0.773521	+	0.633771i	$0.218494\pi$
$182$	−1.56778e7	−0.192768
$183$	−5.87952e7	−0.709191
$184$	3.56340e7	0.421698
$185$	4.02054e7	0.466857
$186$	2.01780e7	0.229923
$187$	−7.78159e7	−0.870208
$188$	1.54945e8	1.70069
$189$	−1.78015e7	−0.191797
$190$	7.52530e7	0.795951
$191$	1.17905e8	1.22437	0.612187	−	0.790713i	$-0.290290\pi$
$191$	1.17905e8	1.22437	0.612187	+	0.790713i	$0.290290\pi$
$192$	7.80057e7	0.795376
$193$	1.87152e8	1.87389	0.936943	−	0.349483i	$-0.113643\pi$
$193$	1.87152e8	1.87389	0.936943	+	0.349483i	$0.113643\pi$
$194$	2.19292e8	2.15633
$195$	−5.25261e6	−0.0507288
$196$	−870361.	−0.00825663
$197$	7.59353e7	0.707639	0.353819	−	0.935314i	$-0.384883\pi$
$197$	7.59353e7	0.707639	0.353819	+	0.935314i	$0.384883\pi$
$198$	5.27569e7	0.483004
$199$	−8.99373e7	−0.809010	−0.404505	−	0.914536i	$-0.632556\pi$
$199$	−8.99373e7	−0.809010	−0.404505	+	0.914536i	$0.632556\pi$
$200$	1.98901e7	0.175805
$201$	8.05474e7	0.699625
$202$	−2.14577e8	−1.83169
$203$	−8.00608e7	−0.671713
$204$	−7.62376e7	−0.628729
$205$	1.12667e8	0.913390
$206$	−1.93217e8	−1.53996
$207$	−5.53417e7	−0.433667
$208$	−1.23895e7	−0.0954623
$209$	1.01467e8	0.768801
$210$	7.77905e7	0.579641
$211$	−1.61354e8	−1.18247	−0.591237	−	0.806498i	$-0.701360\pi$
$211$	−1.61354e8	−1.18247	−0.591237	+	0.806498i	$0.701360\pi$
$212$	4.92063e7	0.354687
$213$	1.22756e8	0.870394
$214$	8.60985e7	0.600547
$215$	−6.03977e7	−0.414463
$216$	9.23912e6	0.0623796
$217$	4.01169e7	0.266513
$218$	3.53742e8	2.31254
$219$	−1.41895e8	−0.912877
$220$	−1.26584e8	−0.801494
$221$	1.86396e7	0.116162
$222$	9.67289e7	0.593363
$223$	9.83911e7	0.594140	0.297070	−	0.954856i	$-0.403991\pi$
$223$	9.83911e7	0.594140	0.297070	+	0.954856i	$0.403991\pi$
$224$	2.37826e8	1.41381
$225$	−3.08905e7	−0.180795
$226$	−1.28359e8	−0.739683
$227$	1.67435e7	0.0950068	0.0475034	−	0.998871i	$-0.484874\pi$
$227$	1.67435e7	0.0950068	0.0475034	+	0.998871i	$0.484874\pi$
$228$	9.94091e7	0.555462
$229$	1.87041e8	1.02923	0.514615	−	0.857422i	$-0.327935\pi$
$229$	1.87041e8	1.02923	0.514615	+	0.857422i	$0.327935\pi$
$230$	2.41837e8	1.31061
$231$	1.04889e8	0.559869
$232$	4.15521e7	0.218467
$233$	1.61499e8	0.836419	0.418209	−	0.908351i	$-0.362658\pi$
$233$	1.61499e8	0.836419	0.418209	+	0.908351i	$0.362658\pi$
$234$	−1.26371e7	−0.0644750
$235$	1.87970e8	0.944822
$236$	−2.71982e8	−1.34694
$237$	5.49292e7	0.268030
$238$	−2.76050e8	−1.32730
$239$	2.01777e8	0.956048	0.478024	−	0.878347i	$-0.341353\pi$
$239$	2.01777e8	0.956048	0.478024	+	0.878347i	$0.341353\pi$
$240$	6.14746e7	0.287049
$241$	−4.76737e6	−0.0219391	−0.0109696	−	0.999940i	$-0.503492\pi$
$241$	−4.76737e6	−0.0219391	−0.0109696	+	0.999940i	$0.503492\pi$
$242$	1.74731e7	0.0792530
$243$	−1.43489e7	−0.0641500
$244$	3.39402e8	1.49572
$245$	−1.05587e6	−0.00458698
$246$	2.71060e8	1.16090
$247$	−2.43049e7	−0.102625
$248$	−2.08210e7	−0.0866802
$249$	−1.87471e8	−0.769549
$250$	3.83867e8	1.55378
$251$	1.11476e8	0.444961	0.222481	−	0.974937i	$-0.428585\pi$
$251$	1.11476e8	0.444961	0.222481	+	0.974937i	$0.428585\pi$
$252$	1.02761e8	0.404508
$253$	3.26080e8	1.26591
$254$	−4.69694e8	−1.79844
$255$	−9.24865e7	−0.349291
$256$	1.16799e8	0.435111
$257$	−2.33996e8	−0.859889	−0.429945	−	0.902855i	$-0.641467\pi$
$257$	−2.33996e8	−0.859889	−0.429945	+	0.902855i	$0.641467\pi$
$258$	−1.45309e8	−0.526772
$259$	1.92312e8	0.687791
$260$	3.03213e7	0.106989
$261$	−6.45329e7	−0.224667
$262$	7.87407e8	2.70486
$263$	3.32723e8	1.12782	0.563908	−	0.825838i	$-0.309297\pi$
$263$	3.32723e8	1.12782	0.563908	+	0.825838i	$0.309297\pi$
$264$	−5.44380e7	−0.182091
$265$	5.96939e7	0.197047
$266$	3.59952e8	1.17262
$267$	−2.09883e8	−0.674821
$268$	−4.64969e8	−1.47554
$269$	2.45094e8	0.767714	0.383857	−	0.923392i	$-0.374595\pi$
$269$	2.45094e8	0.767714	0.383857	+	0.923392i	$0.374595\pi$
$270$	6.27030e7	0.193872
$271$	−5.91003e8	−1.80384	−0.901919	−	0.431906i	$-0.857841\pi$
$271$	−5.91003e8	−1.80384	−0.901919	+	0.431906i	$0.857841\pi$
$272$	−2.18151e8	−0.657302
$273$	−2.51244e7	−0.0747355
$274$	−7.49688e8	−2.20168
$275$	1.82011e8	0.527755
$276$	3.19466e8	0.914624
$277$	−4.01115e8	−1.13394	−0.566970	−	0.823739i	$-0.691884\pi$
$277$	−4.01115e8	−1.13394	−0.566970	+	0.823739i	$0.691884\pi$
$278$	2.16116e8	0.603296
$279$	3.23362e7	0.0891403
$280$	−8.02694e7	−0.218523
$281$	2.45456e8	0.659936	0.329968	−	0.943992i	$-0.392962\pi$
$281$	2.45456e8	0.659936	0.329968	+	0.943992i	$0.392962\pi$
$282$	4.52229e8	1.20084
$283$	−2.36353e8	−0.619881	−0.309940	−	0.950756i	$-0.600309\pi$
$283$	−2.36353e8	−0.619881	−0.309940	+	0.950756i	$0.600309\pi$
$284$	−7.08625e8	−1.83570
$285$	1.20597e8	0.308587
$286$	7.44592e7	0.188208
$287$	5.38909e8	1.34564
$288$	1.91700e8	0.472877
$289$	−8.21384e7	−0.200172
$290$	2.82001e8	0.678982
$291$	3.51426e8	0.836003
$292$	8.19103e8	1.92530
$293$	−2.51771e8	−0.584749	−0.292375	−	0.956304i	$-0.594445\pi$
$293$	−2.51771e8	−0.584749	−0.292375	+	0.956304i	$0.594445\pi$
$294$	−2.54027e6	−0.00582994
$295$	−3.29951e8	−0.748295
$296$	−9.98112e7	−0.223696
$297$	8.45455e7	0.187259
$298$	4.13382e8	0.904889
$299$	−7.81073e7	−0.168983
$300$	1.78319e8	0.381305
$301$	−2.88896e8	−0.610603
$302$	1.19160e9	2.48946
$303$	−3.43870e8	−0.710141
$304$	2.84455e8	0.580705
$305$	4.11740e8	0.830948
$306$	−2.22510e8	−0.443940
$307$	−6.00508e8	−1.18450	−0.592249	−	0.805755i	$-0.701760\pi$
$307$	−6.00508e8	−1.18450	−0.592249	+	0.805755i	$0.701760\pi$
$308$	−6.05481e8	−1.18079
$309$	−3.09639e8	−0.597037
$310$	−1.41305e8	−0.269397
$311$	−6.31357e8	−1.19018	−0.595092	−	0.803658i	$-0.702884\pi$
$311$	−6.31357e8	−1.19018	−0.595092	+	0.803658i	$0.702884\pi$
$312$	1.30398e7	0.0243068
$313$	1.36902e7	0.0252351	0.0126175	−	0.999920i	$-0.495984\pi$
$313$	1.36902e7	0.0252351	0.0126175	+	0.999920i	$0.495984\pi$
$314$	6.52006e7	0.118850
$315$	1.24663e8	0.224725
$316$	−3.17085e8	−0.565289
$317$	1.06734e9	1.88190	0.940950	−	0.338545i	$-0.109935\pi$
$317$	1.06734e9	1.88190	0.940950	+	0.338545i	$0.109935\pi$
$318$	1.43615e8	0.250441
$319$	3.80236e8	0.655822
$320$	−5.46271e8	−0.931929
$321$	1.37977e8	0.232830
$322$	1.15676e9	1.93085
$323$	−4.27953e8	−0.706622
$324$	8.28306e7	0.135295
$325$	−4.35978e7	−0.0704487
$326$	−1.59737e9	−2.55354
$327$	5.66889e8	0.896564
$328$	−2.79698e8	−0.437654
$329$	8.99101e8	1.39195
$330$	−3.69454e8	−0.565928
$331$	6.36900e8	0.965324	0.482662	−	0.875807i	$-0.339670\pi$
$331$	6.36900e8	0.965324	0.482662	+	0.875807i	$0.339670\pi$
$332$	1.08220e9	1.62301
$333$	1.55013e8	0.230045
$334$	−1.48956e9	−2.18749
$335$	−5.64070e8	−0.819740
$336$	2.94047e8	0.422891
$337$	−1.14123e9	−1.62431	−0.812155	−	0.583442i	$-0.801705\pi$
$337$	−1.14123e9	−1.62431	−0.812155	+	0.583442i	$0.801705\pi$
$338$	1.03936e9	1.46406
$339$	−2.05701e8	−0.286773
$340$	5.33888e8	0.736672
$341$	−1.90529e8	−0.260208
$342$	2.90139e8	0.392207
$343$	−7.49872e8	−1.00336
$344$	1.49939e8	0.198591
$345$	3.87555e8	0.508121
$346$	1.09943e9	1.42692
$347$	7.42633e8	0.954159	0.477080	−	0.878860i	$-0.341695\pi$
$347$	7.42633e8	0.954159	0.477080	+	0.878860i	$0.341695\pi$
$348$	3.72523e8	0.473834
$349$	1.20748e8	0.152052	0.0760260	−	0.997106i	$-0.475777\pi$
$349$	1.20748e8	0.152052	0.0760260	+	0.997106i	$0.475777\pi$
$350$	6.45678e8	0.804967
$351$	−2.02515e7	−0.0249967
$352$	−1.12952e9	−1.38036
$353$	6.70359e8	0.811141	0.405570	−	0.914064i	$-0.367073\pi$
$353$	6.70359e8	0.811141	0.405570	+	0.914064i	$0.367073\pi$
$354$	−7.93818e8	−0.951064
$355$	−8.59658e8	−1.01983
$356$	1.21157e9	1.42323
$357$	−4.42384e8	−0.514589
$358$	−1.51696e9	−1.74737
$359$	−6.56150e8	−0.748466	−0.374233	−	0.927335i	$-0.622094\pi$
$359$	−6.56150e8	−0.748466	−0.374233	+	0.927335i	$0.622094\pi$
$360$	−6.47011e7	−0.0730892
$361$	−3.35847e8	−0.375722
$362$	−2.07936e9	−2.30382
$363$	2.80015e7	0.0307261
$364$	1.45033e8	0.157621
$365$	9.93683e8	1.06960
$366$	9.90591e8	1.05611
$367$	5.08217e8	0.536683	0.268341	−	0.963324i	$-0.413524\pi$
$367$	5.08217e8	0.536683	0.268341	+	0.963324i	$0.413524\pi$
$368$	9.14138e8	0.956191
$369$	4.34388e8	0.450075
$370$	−6.77388e8	−0.695234
$371$	2.85529e8	0.290297
$372$	−1.86664e8	−0.188001
$373$	−1.80635e9	−1.80228	−0.901138	−	0.433533i	$-0.857267\pi$
$373$	−1.80635e9	−1.80228	−0.901138	+	0.433533i	$0.857267\pi$
$374$	1.31106e9	1.29590
$375$	6.15165e8	0.602396
$376$	−4.66640e8	−0.452714
$377$	−9.10795e7	−0.0875439
$378$	2.99923e8	0.285620
$379$	8.94572e8	0.844069	0.422035	−	0.906580i	$-0.361316\pi$
$379$	8.94572e8	0.844069	0.422035	+	0.906580i	$0.361316\pi$
$380$	−6.96157e8	−0.650826
$381$	−7.52708e8	−0.697251
$382$	−1.98647e9	−1.82331
$383$	2.14756e9	1.95321	0.976605	−	0.215041i	$-0.0689886\pi$
$383$	2.14756e9	1.95321	0.976605	+	0.215041i	$0.0689886\pi$
$384$	−4.05454e8	−0.365412
$385$	−7.34530e8	−0.655990
$386$	−3.15316e9	−2.79055
$387$	−2.32864e8	−0.204228
$388$	−2.02864e9	−1.76317
$389$	1.28115e9	1.10351	0.551757	−	0.834005i	$-0.313958\pi$
$389$	1.28115e9	1.10351	0.551757	+	0.834005i	$0.313958\pi$
$390$	8.84969e7	0.0755443
$391$	−1.37529e9	−1.16353
$392$	2.62122e6	0.00219787
$393$	1.26186e9	1.04866
$394$	−1.27937e9	−1.05380
$395$	−3.84666e8	−0.314047
$396$	−4.88048e8	−0.394938
$397$	−9.90648e8	−0.794607	−0.397304	−	0.917687i	$-0.630054\pi$
$397$	−9.90648e8	−0.794607	−0.397304	+	0.917687i	$0.630054\pi$
$398$	1.51528e9	1.20476
$399$	5.76841e8	0.454622
$400$	5.10252e8	0.398634
$401$	1.02038e9	0.790233	0.395117	−	0.918631i	$-0.370704\pi$
$401$	1.02038e9	0.790233	0.395117	+	0.918631i	$0.370704\pi$
$402$	−1.35708e9	−1.04187
$403$	4.56382e7	0.0347345
$404$	1.98502e9	1.49772
$405$	1.00485e8	0.0751636
$406$	1.34888e9	1.00030
$407$	−9.13354e8	−0.671519
$408$	2.29600e8	0.167364
$409$	6.95390e8	0.502570	0.251285	−	0.967913i	$-0.419147\pi$
$409$	6.95390e8	0.502570	0.251285	+	0.967913i	$0.419147\pi$
$410$	−1.89822e9	−1.36020
$411$	−1.20141e9	−0.853583
$412$	1.78742e9	1.25918
$413$	−1.57823e9	−1.10242
$414$	9.32406e8	0.645809
$415$	1.31285e9	0.901668
$416$	2.70558e8	0.184261
$417$	3.46337e8	0.233896
$418$	−1.70954e9	−1.14488
$419$	−2.41088e9	−1.60113	−0.800564	−	0.599248i	$-0.795467\pi$
$419$	−2.41088e9	−1.60113	−0.800564	+	0.599248i	$0.795467\pi$
$420$	−7.19631e8	−0.473956
$421$	2.30923e9	1.50827	0.754135	−	0.656719i	$-0.228056\pi$
$421$	2.30923e9	1.50827	0.754135	+	0.656719i	$0.228056\pi$
$422$	2.71852e9	1.76092
$423$	7.24720e8	0.465563
$424$	−1.48192e8	−0.0944156
$425$	−7.67657e8	−0.485072
$426$	−2.06822e9	−1.29617
$427$	1.96945e9	1.22418
$428$	−7.96487e8	−0.491050
$429$	1.19324e8	0.0729674
$430$	1.01759e9	0.617211
$431$	2.48239e9	1.49348	0.746741	−	0.665115i	$-0.231617\pi$
$431$	2.48239e9	1.49348	0.746741	+	0.665115i	$0.231617\pi$
$432$	2.37016e8	0.141444
$433$	1.30054e9	0.769869	0.384935	−	0.922944i	$-0.374224\pi$
$433$	1.30054e9	0.769869	0.384935	+	0.922944i	$0.374224\pi$
$434$	−6.75896e8	−0.396886
$435$	4.51921e8	0.263239
$436$	−3.27243e9	−1.89090
$437$	1.79329e9	1.02794
$438$	2.39067e9	1.35944
$439$	2.21111e9	1.24734	0.623670	−	0.781688i	$-0.285641\pi$
$439$	2.21111e9	1.24734	0.623670	+	0.781688i	$0.285641\pi$
$440$	3.81227e8	0.213353
$441$	−4.07091e6	−0.00226025
$442$	−3.14043e8	−0.172986
$443$	−2.85869e9	−1.56226	−0.781132	−	0.624365i	$-0.785358\pi$
$443$	−2.85869e9	−1.56226	−0.781132	+	0.624365i	$0.785358\pi$
$444$	−8.94828e8	−0.485176
$445$	1.46980e9	0.790678
$446$	−1.65771e9	−0.884782
$447$	6.62466e8	0.350822
$448$	−2.61293e9	−1.37295
$449$	−3.07312e8	−0.160220	−0.0801101	−	0.996786i	$-0.525527\pi$
$449$	−3.07312e8	−0.160220	−0.0801101	+	0.996786i	$0.525527\pi$
$450$	5.20449e8	0.269237
$451$	−2.55946e9	−1.31381
$452$	1.18743e9	0.604817
$453$	1.90959e9	0.965154
$454$	−2.82097e8	−0.141482
$455$	1.75945e8	0.0875664
$456$	−2.99385e8	−0.147861
$457$	1.48219e9	0.726436	0.363218	−	0.931704i	$-0.381678\pi$
$457$	1.48219e9	0.726436	0.363218	+	0.931704i	$0.381678\pi$
$458$	−3.15129e9	−1.53271
$459$	−3.56583e8	−0.172114
$460$	−2.23720e9	−1.07165
$461$	−1.96730e8	−0.0935228	−0.0467614	−	0.998906i	$-0.514890\pi$
$461$	−1.96730e8	−0.0935228	−0.0467614	+	0.998906i	$0.514890\pi$
$462$	−1.76718e9	−0.833747
$463$	1.17817e9	0.551666	0.275833	−	0.961206i	$-0.411046\pi$
$463$	1.17817e9	0.551666	0.275833	+	0.961206i	$0.411046\pi$
$464$	1.06596e9	0.495368
$465$	−2.26449e8	−0.104444
$466$	−2.72096e9	−1.24558
$467$	−3.24336e8	−0.147362	−0.0736811	−	0.997282i	$-0.523475\pi$
$467$	−3.24336e8	−0.147362	−0.0736811	+	0.997282i	$0.523475\pi$
$468$	1.16904e8	0.0527193
$469$	−2.69807e9	−1.20767
$470$	−3.16694e9	−1.40701
$471$	1.04487e8	0.0460776
$472$	8.19114e8	0.358548
$473$	1.37207e9	0.596157
$474$	−9.25455e8	−0.399146
$475$	1.00098e9	0.428545
$476$	2.55371e9	1.08529
$477$	2.30151e8	0.0970953
$478$	−3.39958e9	−1.42373
$479$	3.94840e9	1.64152	0.820760	−	0.571272i	$-0.193550\pi$
$479$	3.94840e9	1.64152	0.820760	+	0.571272i	$0.193550\pi$
$480$	−1.34246e9	−0.554062
$481$	2.18780e8	0.0896394
$482$	8.03214e7	0.0326713
$483$	1.85376e9	0.748582
$484$	−1.61641e8	−0.0648028
$485$	−2.46102e9	−0.979532
$486$	2.41753e8	0.0955310
$487$	−4.23904e9	−1.66309	−0.831546	−	0.555455i	$-0.812544\pi$
$487$	−4.23904e9	−1.66309	−0.831546	+	0.555455i	$0.812544\pi$
$488$	−1.02216e9	−0.398151
$489$	−2.55986e9	−0.989999
$490$	1.77894e7	0.00683085
$491$	2.02435e9	0.771791	0.385896	−	0.922542i	$-0.373893\pi$
$491$	2.02435e9	0.771791	0.385896	+	0.922542i	$0.373893\pi$
$492$	−2.50755e9	−0.949230
$493$	−1.60370e9	−0.602781
$494$	4.09492e8	0.152827
$495$	−5.92068e8	−0.219408
$496$	−5.34132e8	−0.196545
$497$	−4.11194e9	−1.50245
$498$	3.15854e9	1.14600
$499$	−2.28851e9	−0.824521	−0.412261	−	0.911066i	$-0.635261\pi$
$499$	−2.28851e9	−0.824521	−0.412261	+	0.911066i	$0.635261\pi$
$500$	−3.55111e9	−1.27048
$501$	−2.38709e9	−0.848081
$502$	−1.87816e9	−0.662628
$503$	−5.19586e9	−1.82041	−0.910205	−	0.414158i	$-0.864076\pi$
$503$	−5.19586e9	−1.82041	−0.910205	+	0.414158i	$0.864076\pi$
$504$	−3.09480e8	−0.107678
$505$	2.40810e9	0.832061
$506$	−5.49385e9	−1.88517
$507$	1.66563e9	0.567610
$508$	4.34509e9	1.47054
$509$	−2.62748e9	−0.883136	−0.441568	−	0.897228i	$-0.645578\pi$
$509$	−2.62748e9	−0.883136	−0.441568	+	0.897228i	$0.645578\pi$
$510$	1.55823e9	0.520158
$511$	4.75301e9	1.57578
$512$	−3.89001e9	−1.28087
$513$	4.64962e8	0.152057
$514$	3.94240e9	1.28053
$515$	2.16839e9	0.699539
$516$	1.34424e9	0.430726
$517$	−4.27014e9	−1.35902
$518$	−3.24010e9	−1.02425
$519$	1.76189e9	0.553213
$520$	−9.13169e7	−0.0284800
$521$	−1.12239e8	−0.0347705	−0.0173852	−	0.999849i	$-0.505534\pi$
$521$	−1.12239e8	−0.0347705	−0.0173852	+	0.999849i	$0.505534\pi$
$522$	1.08726e9	0.334570
$523$	1.95206e9	0.596674	0.298337	−	0.954461i	$-0.403568\pi$
$523$	1.95206e9	0.596674	0.298337	+	0.954461i	$0.403568\pi$
$524$	−7.28421e9	−2.21168
$525$	1.03473e9	0.312083
$526$	−5.60577e9	−1.67952
$527$	8.03583e8	0.239163
$528$	−1.39653e9	−0.412887
$529$	2.35819e9	0.692604
$530$	−1.00573e9	−0.293438
$531$	−1.27213e9	−0.368724
$532$	−3.32988e9	−0.958820
$533$	6.13079e8	0.175377
$534$	3.53615e9	1.00493
$535$	−9.66247e8	−0.272803
$536$	1.40032e9	0.392781
$537$	−2.43101e9	−0.677448
$538$	−4.12938e9	−1.14327
$539$	2.39863e7	0.00659784
$540$	−5.80059e8	−0.158524
$541$	−4.94576e9	−1.34290	−0.671448	−	0.741052i	$-0.734327\pi$
$541$	−4.94576e9	−1.34290	−0.671448	+	0.741052i	$0.734327\pi$
$542$	9.95731e9	2.68624
$543$	−3.33227e9	−0.893185
$544$	4.76391e9	1.26872
$545$	−3.96990e9	−1.05049
$546$	4.23300e8	0.111295
$547$	1.66957e9	0.436162	0.218081	−	0.975931i	$-0.430020\pi$
$547$	1.66957e9	0.436162	0.218081	+	0.975931i	$0.430020\pi$
$548$	6.93528e9	1.80025
$549$	1.58747e9	0.409452
$550$	−3.06655e9	−0.785923
$551$	2.09113e9	0.532537
$552$	−9.62117e8	−0.243468
$553$	−1.83995e9	−0.462665
$554$	6.75805e9	1.68864
$555$	−1.08555e9	−0.269540
$556$	−1.99927e9	−0.493297
$557$	2.91407e9	0.714507	0.357254	−	0.934007i	$-0.383713\pi$
$557$	2.91407e9	0.714507	0.357254	+	0.934007i	$0.383713\pi$
$558$	−5.44805e8	−0.132746
$559$	−3.28657e8	−0.0795795
$560$	−2.05920e9	−0.495495
$561$	2.10103e9	0.502415
$562$	−4.13548e9	−0.982764
$563$	3.15370e9	0.744802	0.372401	−	0.928072i	$-0.378535\pi$
$563$	3.15370e9	0.744802	0.372401	+	0.928072i	$0.378535\pi$
$564$	−4.18352e9	−0.981895
$565$	1.44051e9	0.336007
$566$	3.98211e9	0.923115
$567$	4.80641e8	0.110734
$568$	2.13413e9	0.488653
$569$	3.06375e9	0.697204	0.348602	−	0.937271i	$-0.386656\pi$
$569$	3.06375e9	0.697204	0.348602	+	0.937271i	$0.386656\pi$
$570$	−2.03183e9	−0.459543
$571$	6.12224e9	1.37621	0.688104	−	0.725612i	$-0.258443\pi$
$571$	6.12224e9	1.37621	0.688104	+	0.725612i	$0.258443\pi$
$572$	−6.88813e8	−0.153892
$573$	−3.18342e9	−0.706892
$574$	−9.07963e9	−2.00390
$575$	3.21679e9	0.705644
$576$	−2.10616e9	−0.459210
$577$	−1.74564e9	−0.378302	−0.189151	−	0.981948i	$-0.560574\pi$
$577$	−1.74564e9	−0.378302	−0.189151	+	0.981948i	$0.560574\pi$
$578$	1.38388e9	0.298092
$579$	−5.05309e9	−1.08189
$580$	−2.60876e9	−0.555184
$581$	6.27966e9	1.32837
$582$	−5.92087e9	−1.24496
$583$	−1.35608e9	−0.283429
$584$	−2.46685e9	−0.512504
$585$	1.41821e8	0.0292883
$586$	4.24188e9	0.870797
$587$	−4.32030e8	−0.0881619	−0.0440809	−	0.999028i	$-0.514036\pi$
$587$	−4.32030e8	−0.0881619	−0.0440809	+	0.999028i	$0.514036\pi$
$588$	2.34997e7	0.00476697
$589$	−1.04782e9	−0.211293
$590$	5.55907e9	1.11435
$591$	−2.05025e9	−0.408555
$592$	−2.56051e9	−0.507225
$593$	4.66012e9	0.917711	0.458855	−	0.888511i	$-0.348260\pi$
$593$	4.66012e9	0.917711	0.458855	+	0.888511i	$0.348260\pi$
$594$	−1.42444e9	−0.278863
$595$	3.09799e9	0.602935
$596$	−3.82415e9	−0.739901
$597$	2.42831e9	0.467082
$598$	1.31596e9	0.251646
$599$	−4.39395e9	−0.835335	−0.417668	−	0.908600i	$-0.637152\pi$
$599$	−4.39395e9	−0.835335	−0.417668	+	0.908600i	$0.637152\pi$
$600$	−5.37033e8	−0.101501
$601$	−4.81668e8	−0.0905081	−0.0452541	−	0.998976i	$-0.514410\pi$
$601$	−4.81668e8	−0.0905081	−0.0452541	+	0.998976i	$0.514410\pi$
$602$	4.86736e9	0.909298
$603$	−2.17478e9	−0.403929
$604$	−1.10233e10	−2.03556
$605$	−1.96093e8	−0.0360013
$606$	5.79357e9	1.05753
$607$	7.52671e9	1.36598	0.682990	−	0.730427i	$-0.260679\pi$
$607$	7.52671e9	1.36598	0.682990	+	0.730427i	$0.260679\pi$
$608$	−6.21185e9	−1.12088
$609$	2.16164e9	0.387813
$610$	−6.93706e9	−1.23743
$611$	1.02284e9	0.181412
$612$	2.05841e9	0.362997
$613$	5.72607e9	1.00403	0.502013	−	0.864860i	$-0.332593\pi$
$613$	5.72607e9	1.00403	0.502013	+	0.864860i	$0.332593\pi$
$614$	1.01175e10	1.76393
$615$	−3.04200e9	−0.527346
$616$	1.82349e9	0.314320
$617$	−1.29666e9	−0.222243	−0.111121	−	0.993807i	$-0.535444\pi$
$617$	−1.29666e9	−0.222243	−0.111121	+	0.993807i	$0.535444\pi$
$618$	5.21685e9	0.889096
$619$	2.25397e9	0.381971	0.190985	−	0.981593i	$-0.438832\pi$
$619$	2.25397e9	0.381971	0.190985	+	0.981593i	$0.438832\pi$
$620$	1.30720e9	0.220278
$621$	1.49423e9	0.250378
$622$	1.06372e10	1.77240
$623$	7.03040e9	1.16486
$624$	3.34516e8	0.0551152
$625$	−9.97515e8	−0.163433
$626$	−2.30655e8	−0.0375796
$627$	−2.73961e9	−0.443867
$628$	−6.03163e8	−0.0971798
$629$	3.85221e9	0.617209
$630$	−2.10034e9	−0.334656
$631$	2.25295e9	0.356985	0.178492	−	0.983941i	$-0.442878\pi$
$631$	2.25295e9	0.356985	0.178492	+	0.983941i	$0.442878\pi$
$632$	9.54946e8	0.150477
$633$	4.35656e9	0.682701
$634$	−1.79828e10	−2.80249
$635$	5.27118e9	0.816958
$636$	−1.32857e9	−0.204779
$637$	−5.74553e6	−0.000880729 0
$638$	−6.40627e9	−0.976637
$639$	−3.31442e9	−0.502522
$640$	2.83938e9	0.428147
$641$	8.69989e9	1.30470	0.652350	−	0.757918i	$-0.273783\pi$
$641$	8.69989e9	1.30470	0.652350	+	0.757918i	$0.273783\pi$
$642$	−2.32466e9	−0.346726
$643$	1.25049e10	1.85500	0.927498	−	0.373827i	$-0.121955\pi$
$643$	1.25049e10	1.85500	0.927498	+	0.373827i	$0.121955\pi$
$644$	−1.07011e10	−1.57880
$645$	1.63074e9	0.239291
$646$	7.21022e9	1.05229
$647$	−5.08467e9	−0.738070	−0.369035	−	0.929415i	$-0.620312\pi$
$647$	−5.08467e9	−0.738070	−0.369035	+	0.929415i	$0.620312\pi$
$648$	−2.49456e8	−0.0360149
$649$	7.49556e9	1.07634
$650$	7.34543e8	0.104911
$651$	−1.08316e9	−0.153871
$652$	1.47770e10	2.08796
$653$	1.06646e10	1.49882	0.749408	−	0.662109i	$-0.230338\pi$
$653$	1.06646e10	1.49882	0.749408	+	0.662109i	$0.230338\pi$
$654$	−9.55104e9	−1.33515
$655$	−8.83673e9	−1.22870
$656$	−7.17525e9	−0.992369
$657$	3.83116e9	0.527050
$658$	−1.51482e10	−2.07286
$659$	1.11347e10	1.51558	0.757790	−	0.652499i	$-0.226279\pi$
$659$	1.11347e10	1.51558	0.757790	+	0.652499i	$0.226279\pi$
$660$	3.41778e9	0.462743
$661$	−7.62629e9	−1.02709	−0.513545	−	0.858063i	$-0.671668\pi$
$661$	−7.62629e9	−1.02709	−0.513545	+	0.858063i	$0.671668\pi$
$662$	−1.07306e10	−1.43754
$663$	−5.03269e8	−0.0670660
$664$	−3.25919e9	−0.432037
$665$	−4.03959e9	−0.532674
$666$	−2.61168e9	−0.342578
$667$	6.72015e9	0.876877
$668$	1.37797e10	1.78864
$669$	−2.65656e9	−0.343027
$670$	9.50354e9	1.22074
$671$	−9.35357e9	−1.19522
$672$	−6.42131e9	−0.816265
$673$	4.94512e9	0.625351	0.312676	−	0.949860i	$-0.398775\pi$
$673$	4.94512e9	0.625351	0.312676	+	0.949860i	$0.398775\pi$
$674$	1.92276e10	2.41889
$675$	8.34045e8	0.104382
$676$	−9.61501e9	−1.19712
$677$	−8.93221e9	−1.10637	−0.553183	−	0.833060i	$-0.686587\pi$
$677$	−8.93221e9	−1.10637	−0.553183	+	0.833060i	$0.686587\pi$
$678$	3.46568e9	0.427056
$679$	−1.17716e10	−1.44308
$680$	−1.60788e9	−0.196098
$681$	−4.52074e8	−0.0548522
$682$	3.21006e9	0.387496
$683$	4.00291e9	0.480732	0.240366	−	0.970682i	$-0.422733\pi$
$683$	4.00291e9	0.480732	0.240366	+	0.970682i	$0.422733\pi$
$684$	−2.68405e9	−0.320696
$685$	8.41343e9	1.00013
$686$	1.26340e10	1.49419
$687$	−5.05010e9	−0.594226
$688$	3.84647e9	0.450301
$689$	3.24827e8	0.0378342
$690$	−6.52959e9	−0.756684
$691$	1.49401e10	1.72259	0.861294	−	0.508107i	$-0.169655\pi$
$691$	1.49401e10	1.72259	0.861294	+	0.508107i	$0.169655\pi$
$692$	−1.01707e10	−1.16675
$693$	−2.83199e9	−0.323241
$694$	−1.25120e10	−1.42092
$695$	−2.42538e9	−0.274052
$696$	−1.12191e9	−0.126132
$697$	1.07949e10	1.20755
$698$	−2.03439e9	−0.226433
$699$	−4.36047e9	−0.482906
$700$	−5.97309e9	−0.658198
$701$	9.53942e9	1.04595	0.522973	−	0.852349i	$-0.324823\pi$
$701$	9.53942e9	1.04595	0.522973	+	0.852349i	$0.324823\pi$
$702$	3.41201e8	0.0372246
$703$	−5.02304e9	−0.545284
$704$	1.24097e10	1.34047
$705$	−5.07518e9	−0.545493
$706$	−1.12943e10	−1.20793
$707$	1.15185e10	1.22582
$708$	7.34352e9	0.777657
$709$	1.48288e10	1.56259	0.781296	−	0.624161i	$-0.214559\pi$
$709$	1.48288e10	1.56259	0.781296	+	0.624161i	$0.214559\pi$
$710$	1.44836e10	1.51871
$711$	−1.48309e9	−0.154747
$712$	−3.64883e9	−0.378856
$713$	−3.36734e9	−0.347915
$714$	7.45335e9	0.766316
$715$	−8.35624e8	−0.0854948
$716$	1.40332e10	1.42877
$717$	−5.44799e9	−0.551975
$718$	1.10549e10	1.11460
$719$	1.01558e9	0.101897	0.0509487	−	0.998701i	$-0.483776\pi$
$719$	1.01558e9	0.101897	0.0509487	+	0.998701i	$0.483776\pi$
$720$	−1.65981e9	−0.165728
$721$	1.03719e10	1.03059
$722$	5.65841e9	0.559518
$723$	1.28719e8	0.0126666
$724$	1.92359e10	1.88377
$725$	3.75104e9	0.365569
$726$	−4.71773e8	−0.0457567
$727$	5.60160e9	0.540681	0.270341	−	0.962765i	$-0.412864\pi$
$727$	5.60160e9	0.540681	0.270341	+	0.962765i	$0.412864\pi$
$728$	−4.36789e8	−0.0419577
$729$	3.87420e8	0.0370370
$730$	−1.67417e10	−1.59283
$731$	−5.78689e9	−0.547942
$732$	−9.16384e9	−0.863553
$733$	−1.07807e10	−1.01107	−0.505535	−	0.862806i	$-0.668705\pi$
$733$	−1.07807e10	−1.01107	−0.505535	+	0.862806i	$0.668705\pi$
$734$	−8.56252e9	−0.799218
$735$	2.85084e7	0.00264830
$736$	−1.99627e10	−1.84564
$737$	1.28141e10	1.17910
$738$	−7.31863e9	−0.670243
$739$	1.58534e10	1.44499	0.722496	−	0.691375i	$-0.242995\pi$
$739$	1.58534e10	1.44499	0.722496	+	0.691375i	$0.242995\pi$
$740$	6.26644e9	0.568473
$741$	6.56231e8	0.0592507
$742$	−4.81064e9	−0.432304
$743$	−5.69257e9	−0.509152	−0.254576	−	0.967053i	$-0.581936\pi$
$743$	−5.69257e9	−0.509152	−0.254576	+	0.967053i	$0.581936\pi$
$744$	5.62166e8	0.0500448
$745$	−4.63922e9	−0.411053
$746$	3.04337e10	2.68391
$747$	5.06171e9	0.444299
$748$	−1.21284e10	−1.05962
$749$	−4.62177e9	−0.401904
$750$	−1.03644e10	−0.897077
$751$	2.04554e10	1.76225	0.881127	−	0.472879i	$-0.156785\pi$
$751$	2.04554e10	1.76225	0.881127	+	0.472879i	$0.156785\pi$
$752$	−1.19710e10	−1.02652
$753$	−3.00984e9	−0.256899
$754$	1.53452e9	0.130369
$755$	−1.33728e10	−1.13086
$756$	−2.77455e9	−0.233543
$757$	−1.24902e10	−1.04648	−0.523242	−	0.852184i	$-0.675278\pi$
$757$	−1.24902e10	−1.04648	−0.523242	+	0.852184i	$0.675278\pi$
$758$	−1.50719e10	−1.25697
$759$	−8.80416e9	−0.730873
$760$	2.09658e9	0.173246
$761$	−5.70958e9	−0.469632	−0.234816	−	0.972040i	$-0.575449\pi$
$761$	−5.70958e9	−0.469632	−0.234816	+	0.972040i	$0.575449\pi$
$762$	1.26817e10	1.03833
$763$	−1.89889e10	−1.54762
$764$	1.83767e10	1.49087
$765$	2.49713e9	0.201663
$766$	−3.61824e10	−2.90868
$767$	−1.79544e9	−0.143677
$768$	−3.15358e9	−0.251212
$769$	5.32693e9	0.422410	0.211205	−	0.977442i	$-0.432261\pi$
$769$	5.32693e9	0.422410	0.211205	+	0.977442i	$0.432261\pi$
$770$	1.23755e10	0.976888
$771$	6.31789e9	0.496457
$772$	2.91695e10	2.28175
$773$	7.33962e9	0.571538	0.285769	−	0.958299i	$-0.407751\pi$
$773$	7.33962e9	0.571538	0.285769	+	0.958299i	$0.407751\pi$
$774$	3.92334e9	0.304132
$775$	−1.87957e9	−0.145045
$776$	6.10955e9	0.469346
$777$	−5.19242e9	−0.397096
$778$	−2.15851e10	−1.64333
$779$	−1.40759e10	−1.06683
$780$	−8.18674e8	−0.0617703
$781$	1.95290e10	1.46690
$782$	2.31711e10	1.73270
$783$	1.74239e9	0.129712
$784$	6.72435e7	0.00498361
$785$	−7.31718e8	−0.0539884
$786$	−2.12600e10	−1.56165
$787$	−2.19564e9	−0.160565	−0.0802823	−	0.996772i	$-0.525582\pi$
$787$	−2.19564e9	−0.160565	−0.0802823	+	0.996772i	$0.525582\pi$
$788$	1.18353e10	0.861663
$789$	−8.98353e9	−0.651145
$790$	6.48092e9	0.467673
$791$	6.89030e9	0.495018
$792$	1.46983e9	0.105130
$793$	2.24050e9	0.159547
$794$	1.66906e10	1.18331
$795$	−1.61174e9	−0.113765
$796$	−1.40177e10	−0.985099
$797$	−2.46698e10	−1.72608	−0.863040	−	0.505136i	$-0.831442\pi$
$797$	−2.46698e10	−1.72608	−0.863040	+	0.505136i	$0.831442\pi$
$798$	−9.71871e9	−0.677015
$799$	1.80099e10	1.24910
$800$	−1.11427e10	−0.769444
$801$	5.66685e9	0.389608
$802$	−1.71915e10	−1.17680
$803$	−2.25737e10	−1.53850
$804$	1.25542e10	0.851905
$805$	−1.29818e10	−0.877102
$806$	−7.68919e8	−0.0517259
$807$	−6.61754e9	−0.443240
$808$	−5.97819e9	−0.398685
$809$	1.82019e10	1.20864	0.604320	−	0.796742i	$-0.293445\pi$
$809$	1.82019e10	1.20864	0.604320	+	0.796742i	$0.293445\pi$
$810$	−1.69298e9	−0.111932
$811$	1.23872e10	0.815456	0.407728	−	0.913103i	$-0.366321\pi$
$811$	1.23872e10	0.815456	0.407728	+	0.913103i	$0.366321\pi$
$812$	−1.24783e10	−0.817917
$813$	1.59571e10	1.04145
$814$	1.53883e10	1.00001
$815$	1.79266e10	1.15997
$816$	5.89006e9	0.379494
$817$	7.54575e9	0.484089
$818$	−1.17160e10	−0.748418
$819$	6.78360e8	0.0431486
$820$	1.75602e10	1.11220
$821$	1.56882e10	0.989402	0.494701	−	0.869063i	$-0.335278\pi$
$821$	1.56882e10	0.989402	0.494701	+	0.869063i	$0.335278\pi$
$822$	2.02416e10	1.27114
$823$	1.92347e10	1.20278	0.601388	−	0.798957i	$-0.294614\pi$
$823$	1.92347e10	1.20278	0.601388	+	0.798957i	$0.294614\pi$
$824$	−5.38308e9	−0.335186
$825$	−4.91429e9	−0.304700
$826$	2.65903e10	1.64170
$827$	−2.79350e9	−0.171743	−0.0858714	−	0.996306i	$-0.527367\pi$
$827$	−2.79350e9	−0.171743	−0.0858714	+	0.996306i	$0.527367\pi$
$828$	−8.62558e9	−0.528059
$829$	−2.95401e9	−0.180083	−0.0900413	−	0.995938i	$-0.528700\pi$
$829$	−2.95401e9	−0.180083	−0.0900413	+	0.995938i	$0.528700\pi$
$830$	−2.21191e10	−1.34275
$831$	1.08301e10	0.654680
$832$	−2.97255e9	−0.178936
$833$	−1.01166e8	−0.00606423
$834$	−5.83513e9	−0.348313
$835$	1.67167e10	0.993683
$836$	1.58147e10	0.936137
$837$	−8.73077e8	−0.0514652
$838$	4.06188e10	2.38437
$839$	−8.14457e9	−0.476103	−0.238052	−	0.971252i	$-0.576509\pi$
$839$	−8.14457e9	−0.476103	−0.238052	+	0.971252i	$0.576509\pi$
$840$	2.16727e9	0.126164
$841$	−9.41363e9	−0.545722
$842$	−3.89062e10	−2.24609
$843$	−6.62732e9	−0.381014
$844$	−2.51487e10	−1.43985
$845$	−1.16643e10	−0.665060
$846$	−1.22102e10	−0.693308
$847$	−9.37957e8	−0.0530384
$848$	−3.80165e9	−0.214085
$849$	6.38153e9	0.357888
$850$	1.29336e10	0.722360
$851$	−1.61423e10	−0.897866
$852$	1.91329e10	1.05984
$853$	−1.31128e10	−0.723391	−0.361696	−	0.932296i	$-0.617802\pi$
$853$	−1.31128e10	−0.723391	−0.361696	+	0.932296i	$0.617802\pi$
$854$	−3.31815e10	−1.82303
$855$	−3.25611e9	−0.178163
$856$	2.39873e9	0.130715
$857$	1.19832e10	0.650341	0.325171	−	0.945655i	$-0.394578\pi$
$857$	1.19832e10	0.650341	0.325171	+	0.945655i	$0.394578\pi$
$858$	−2.01040e9	−0.108662
$859$	−6.36777e9	−0.342777	−0.171388	−	0.985204i	$-0.554825\pi$
$859$	−6.36777e9	−0.342777	−0.171388	+	0.985204i	$0.554825\pi$
$860$	−9.41361e9	−0.504675
$861$	−1.45506e10	−0.776906
$862$	−4.18237e10	−2.22407
$863$	−1.34824e10	−0.714049	−0.357024	−	0.934095i	$-0.616209\pi$
$863$	−1.34824e10	−0.714049	−0.357024	+	0.934095i	$0.616209\pi$
$864$	−5.17589e9	−0.273015
$865$	−1.23384e10	−0.648191
$866$	−2.19117e10	−1.14647
$867$	2.21774e9	0.115569
$868$	6.25263e9	0.324522
$869$	8.73853e9	0.451720
$870$	−7.61404e9	−0.392011
$871$	−3.06941e9	−0.157395
$872$	9.85539e9	0.503345
$873$	−9.48849e9	−0.482667
$874$	−3.02137e10	−1.53078
$875$	−2.06060e10	−1.03984
$876$	−2.21158e10	−1.11157
$877$	−4.06098e9	−0.203297	−0.101649	−	0.994820i	$-0.532412\pi$
$877$	−4.06098e9	−0.203297	−0.101649	+	0.994820i	$0.532412\pi$
$878$	−3.72531e10	−1.85751
$879$	6.79782e9	0.337605
$880$	9.77982e9	0.483773
$881$	1.36499e10	0.672532	0.336266	−	0.941767i	$-0.390836\pi$
$881$	1.36499e10	0.672532	0.336266	+	0.941767i	$0.390836\pi$
$882$	6.85873e7	0.00336592
$883$	−5.53470e9	−0.270540	−0.135270	−	0.990809i	$-0.543190\pi$
$883$	−5.53470e9	−0.270540	−0.135270	+	0.990809i	$0.543190\pi$
$884$	2.90517e9	0.141445
$885$	8.90868e9	0.432028
$886$	4.81637e10	2.32649
$887$	2.58475e10	1.24361	0.621807	−	0.783170i	$-0.286399\pi$
$887$	2.58475e10	1.24361	0.621807	+	0.783170i	$0.286399\pi$
$888$	2.69490e9	0.129151
$889$	2.52132e10	1.20357
$890$	−2.47635e10	−1.17746
$891$	−2.28273e9	−0.108114
$892$	1.53353e10	0.723460
$893$	−2.34838e10	−1.10354
$894$	−1.11613e10	−0.522438
$895$	1.70242e10	0.793755
$896$	1.35814e10	0.630762
$897$	2.10890e9	0.0975623
$898$	5.17764e9	0.238597
$899$	−3.92659e9	−0.180242
$900$	−4.81461e9	−0.220147
$901$	5.71945e9	0.260506
$902$	4.31223e10	1.95649
$903$	7.80019e9	0.352532
$904$	−3.57612e9	−0.160999
$905$	2.33358e10	1.04653
$906$	−3.21731e10	−1.43729
$907$	2.21143e10	0.984120	0.492060	−	0.870561i	$-0.336244\pi$
$907$	2.21143e10	0.984120	0.492060	+	0.870561i	$0.336244\pi$
$908$	2.60964e9	0.115686
$909$	9.28448e9	0.410000
$910$	−2.96435e9	−0.130402
$911$	1.11270e10	0.487601	0.243801	−	0.969825i	$-0.421606\pi$
$911$	1.11270e10	0.487601	0.243801	+	0.969825i	$0.421606\pi$
$912$	−7.68028e9	−0.335270
$913$	−2.98242e10	−1.29694
$914$	−2.49722e10	−1.08179
$915$	−1.11170e10	−0.479748
$916$	2.91523e10	1.25325
$917$	−4.22681e10	−1.81017
$918$	6.00777e9	0.256309
$919$	6.31702e9	0.268478	0.134239	−	0.990949i	$-0.457141\pi$
$919$	6.31702e9	0.268478	0.134239	+	0.990949i	$0.457141\pi$
$920$	6.73766e9	0.285267
$921$	1.62137e10	0.683871
$922$	3.31454e9	0.139272
$923$	−4.67786e9	−0.195813
$924$	1.63480e10	0.681730
$925$	−9.01027e9	−0.374319
$926$	−1.98501e10	−0.821530
$927$	8.36025e9	0.344699
$928$	−2.32781e10	−0.956159
$929$	4.37179e9	0.178897	0.0894487	−	0.995991i	$-0.471490\pi$
$929$	4.37179e9	0.178897	0.0894487	+	0.995991i	$0.471490\pi$
$930$	3.81525e9	0.155536
$931$	1.31914e8	0.00535755
$932$	2.51713e10	1.01847
$933$	1.70466e10	0.687153
$934$	5.46446e9	0.219449
$935$	−1.47134e10	−0.588671
$936$	−3.52074e8	−0.0140336
$937$	2.57183e10	1.02130	0.510650	−	0.859789i	$-0.329405\pi$
$937$	2.57183e10	1.02130	0.510650	+	0.859789i	$0.329405\pi$
$938$	4.54576e10	1.79844
$939$	−3.69636e8	−0.0145695
$940$	2.92970e10	1.15047
$941$	2.20000e9	0.0860715	0.0430357	−	0.999074i	$-0.486297\pi$
$941$	2.20000e9	0.0860715	0.0430357	+	0.999074i	$0.486297\pi$
$942$	−1.76042e9	−0.0686178
$943$	−4.52350e10	−1.75665
$944$	2.10132e10	0.812998
$945$	−3.36591e9	−0.129745
$946$	−2.31168e10	−0.887786
$947$	−1.07120e10	−0.409869	−0.204934	−	0.978776i	$-0.565698\pi$
$947$	−1.07120e10	−0.409869	−0.204934	+	0.978776i	$0.565698\pi$
$948$	8.56128e9	0.326370
$949$	5.40716e9	0.205370
$950$	−1.68646e10	−0.638182
$951$	−2.88183e10	−1.08652
$952$	−7.69085e9	−0.288898
$953$	−4.12156e10	−1.54254	−0.771270	−	0.636508i	$-0.780378\pi$
$953$	−4.12156e10	−1.54254	−0.771270	+	0.636508i	$0.780378\pi$
$954$	−3.87762e9	−0.144592
$955$	2.22934e10	0.828255
$956$	3.14491e10	1.16414
$957$	−1.02664e10	−0.378639
$958$	−6.65232e10	−2.44452
$959$	4.02433e10	1.47343
$960$	1.47493e10	0.538050
$961$	−2.55451e10	−0.928486
$962$	−3.68603e9	−0.133489
$963$	−3.72538e9	−0.134425
$964$	−7.43044e8	−0.0267144
$965$	3.53866e10	1.26763
$966$	−3.12325e10	−1.11477
$967$	1.06841e10	0.379968	0.189984	−	0.981787i	$-0.439156\pi$
$967$	1.06841e10	0.379968	0.189984	+	0.981787i	$0.439156\pi$
$968$	4.86806e8	0.0172501
$969$	1.15547e10	0.407968
$970$	4.14636e10	1.45870
$971$	−4.83468e10	−1.69473	−0.847364	−	0.531012i	$-0.821812\pi$
$971$	−4.83468e10	−1.69473	−0.847364	+	0.531012i	$0.821812\pi$
$972$	−2.23643e9	−0.0781129
$973$	−1.16011e10	−0.403743
$974$	7.14201e10	2.47665
$975$	1.17714e9	0.0406736
$976$	−2.62220e10	−0.902798
$977$	−4.78833e10	−1.64268	−0.821339	−	0.570440i	$-0.806773\pi$
$977$	−4.78833e10	−1.64268	−0.821339	+	0.570440i	$0.806773\pi$
$978$	4.31289e10	1.47429
$979$	−3.33898e10	−1.13730
$980$	−1.64568e8	−0.00558538
$981$	−1.53060e10	−0.517631
$982$	−3.41065e10	−1.14934
$983$	5.33627e10	1.79185	0.895923	−	0.444210i	$-0.146515\pi$
$983$	5.33627e10	1.79185	0.895923	+	0.444210i	$0.146515\pi$
$984$	7.55184e9	0.252680
$985$	1.43578e10	0.478698
$986$	2.70194e10	0.897649
$987$	−2.42757e10	−0.803641
$988$	−3.78817e9	−0.124962
$989$	2.42494e10	0.797102
$990$	9.97525e9	0.326739
$991$	−1.35974e10	−0.443810	−0.221905	−	0.975068i	$-0.571227\pi$
$991$	−1.35974e10	−0.443810	−0.221905	+	0.975068i	$0.571227\pi$
$992$	1.16642e10	0.379371
$993$	−1.71963e10	−0.557330
$994$	6.92785e10	2.23741
$995$	−1.70053e10	−0.547273
$996$	−2.92193e10	−0.937048
$997$	−4.30098e9	−0.137447	−0.0687234	−	0.997636i	$-0.521893\pi$
$997$	−4.30098e9	−0.137447	−0.0687234	+	0.997636i	$0.521893\pi$
$998$	3.85573e10	1.22786
$999$	−4.18534e9	−0.132816

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.8.a.c.1.7	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.8.a.c.1.7	✓	48	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:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	471.a (trivial)

\(f(q)\)	\(=\)	\(q-16.8482 q^{2} -27.0000 q^{3} +155.860 q^{4} +189.080 q^{5} +454.900 q^{6} +904.411 q^{7} -469.396 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-16.8482 q^{2} -27.0000 q^{3} +155.860 q^{4} +189.080 q^{5} +454.900 q^{6} +904.411 q^{7} -469.396 q^{8} +729.000 q^{9} -3185.64 q^{10} -4295.36 q^{11} -4208.23 q^{12} +1028.88 q^{13} -15237.7 q^{14} -5105.15 q^{15} -12041.7 q^{16} +18116.3 q^{17} -12282.3 q^{18} -23622.5 q^{19} +29470.0 q^{20} -24419.1 q^{21} +72368.8 q^{22} -75914.6 q^{23} +12673.7 q^{24} -42373.9 q^{25} -17334.8 q^{26} -19683.0 q^{27} +140962. q^{28} -88522.6 q^{29} +86012.4 q^{30} +44356.9 q^{31} +262963. q^{32} +115975. q^{33} -305226. q^{34} +171006. q^{35} +113622. q^{36} +212638. q^{37} +397996. q^{38} -27779.9 q^{39} -88753.2 q^{40} +595868. q^{41} +411417. q^{42} -319430. q^{43} -669476. q^{44} +137839. q^{45} +1.27902e6 q^{46} +994129. q^{47} +325125. q^{48} -5584.23 q^{49} +713921. q^{50} -489140. q^{51} +160362. q^{52} +315708. q^{53} +331622. q^{54} -812165. q^{55} -424527. q^{56} +637809. q^{57} +1.49144e6 q^{58} -1.74504e6 q^{59} -795691. q^{60} +2.17760e6 q^{61} -747332. q^{62} +659315. q^{63} -2.88910e6 q^{64} +194541. q^{65} -1.95396e6 q^{66} -2.98324e6 q^{67} +2.82361e6 q^{68} +2.04969e6 q^{69} -2.88113e6 q^{70} -4.54654e6 q^{71} -342190. q^{72} +5.25536e6 q^{73} -3.58255e6 q^{74} +1.14409e6 q^{75} -3.68182e6 q^{76} -3.88477e6 q^{77} +468040. q^{78} -2.03441e6 q^{79} -2.27684e6 q^{80} +531441. q^{81} -1.00393e7 q^{82} +6.94337e6 q^{83} -3.80597e6 q^{84} +3.42543e6 q^{85} +5.38181e6 q^{86} +2.39011e6 q^{87} +2.01622e6 q^{88} +7.77346e6 q^{89} -2.32234e6 q^{90} +930534. q^{91} -1.18321e7 q^{92} -1.19764e6 q^{93} -1.67492e7 q^{94} -4.46654e6 q^{95} -7.09999e6 q^{96} -1.30158e7 q^{97} +94084.0 q^{98} -3.13131e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{2} - 1296 q^{3} + 3214 q^{4} + 428 q^{5} - 54 q^{6} - 680 q^{7} + 2355 q^{8} + 34992 q^{9}+O(q^{10}) \) 48 * q + 2 * q^2 - 1296 * q^3 + 3214 * q^4 + 428 * q^5 - 54 * q^6 - 680 * q^7 + 2355 * q^8 + 34992 * q^9	\( 48 q + 2 q^{2} - 1296 q^{3} + 3214 q^{4} + 428 q^{5} - 54 q^{6} - 680 q^{7} + 2355 q^{8} + 34992 q^{9} + 6185 q^{10} + 11989 q^{11} - 86778 q^{12} - 2393 q^{13} + 18201 q^{14} - 11556 q^{15} + 208150 q^{16} + 62538 q^{17} + 1458 q^{18} - 39882 q^{19} + 113423 q^{20} + 18360 q^{21} - 93716 q^{22} + 195618 q^{23} - 63585 q^{24} + 886490 q^{25} + 294399 q^{26} - 944784 q^{27} - 60819 q^{28} + 421501 q^{29} - 166995 q^{30} + 392689 q^{31} - 341578 q^{32} - 323703 q^{33} + 50837 q^{34} + 697874 q^{35} + 2343006 q^{36} - 410396 q^{37} + 677216 q^{38} + 64611 q^{39} + 3232376 q^{40} + 3832958 q^{41} - 491427 q^{42} - 1751932 q^{43} + 4888297 q^{44} + 312012 q^{45} + 1163150 q^{46} + 106461 q^{47} - 5620050 q^{48} + 8202048 q^{49} - 2159111 q^{50} - 1688526 q^{51} - 3605030 q^{52} + 1755534 q^{53} - 39366 q^{54} - 1220729 q^{55} - 4430622 q^{56} + 1076814 q^{57} - 10000202 q^{58} - 2037752 q^{59} - 3062421 q^{60} + 1274098 q^{61} + 97748 q^{62} - 495720 q^{63} + 15135201 q^{64} + 6139645 q^{65} + 2530332 q^{66} - 7751257 q^{67} + 1700631 q^{68} - 5281686 q^{69} - 20935703 q^{70} - 12592217 q^{71} + 1716795 q^{72} + 12508355 q^{73} - 14999956 q^{74} - 23935230 q^{75} - 23946874 q^{76} + 1874177 q^{77} - 7948773 q^{78} - 5103480 q^{79} + 3128449 q^{80} + 25509168 q^{81} + 11622426 q^{82} + 3040643 q^{83} + 1642113 q^{84} - 13756076 q^{85} + 964635 q^{86} - 11380527 q^{87} - 29653500 q^{88} + 28462995 q^{89} + 4508865 q^{90} + 3016621 q^{91} + 22938254 q^{92} - 10602603 q^{93} - 10070348 q^{94} - 2579984 q^{95} + 9222606 q^{96} + 16208760 q^{97} + 6323227 q^{98} + 8739981 q^{99}+O(q^{100}) \) 48 * q + 2 * q^2 - 1296 * q^3 + 3214 * q^4 + 428 * q^5 - 54 * q^6 - 680 * q^7 + 2355 * q^8 + 34992 * q^9 + 6185 * q^10 + 11989 * q^11 - 86778 * q^12 - 2393 * q^13 + 18201 * q^14 - 11556 * q^15 + 208150 * q^16 + 62538 * q^17 + 1458 * q^18 - 39882 * q^19 + 113423 * q^20 + 18360 * q^21 - 93716 * q^22 + 195618 * q^23 - 63585 * q^24 + 886490 * q^25 + 294399 * q^26 - 944784 * q^27 - 60819 * q^28 + 421501 * q^29 - 166995 * q^30 + 392689 * q^31 - 341578 * q^32 - 323703 * q^33 + 50837 * q^34 + 697874 * q^35 + 2343006 * q^36 - 410396 * q^37 + 677216 * q^38 + 64611 * q^39 + 3232376 * q^40 + 3832958 * q^41 - 491427 * q^42 - 1751932 * q^43 + 4888297 * q^44 + 312012 * q^45 + 1163150 * q^46 + 106461 * q^47 - 5620050 * q^48 + 8202048 * q^49 - 2159111 * q^50 - 1688526 * q^51 - 3605030 * q^52 + 1755534 * q^53 - 39366 * q^54 - 1220729 * q^55 - 4430622 * q^56 + 1076814 * q^57 - 10000202 * q^58 - 2037752 * q^59 - 3062421 * q^60 + 1274098 * q^61 + 97748 * q^62 - 495720 * q^63 + 15135201 * q^64 + 6139645 * q^65 + 2530332 * q^66 - 7751257 * q^67 + 1700631 * q^68 - 5281686 * q^69 - 20935703 * q^70 - 12592217 * q^71 + 1716795 * q^72 + 12508355 * q^73 - 14999956 * q^74 - 23935230 * q^75 - 23946874 * q^76 + 1874177 * q^77 - 7948773 * q^78 - 5103480 * q^79 + 3128449 * q^80 + 25509168 * q^81 + 11622426 * q^82 + 3040643 * q^83 + 1642113 * q^84 - 13756076 * q^85 + 964635 * q^86 - 11380527 * q^87 - 29653500 * q^88 + 28462995 * q^89 + 4508865 * q^90 + 3016621 * q^91 + 22938254 * q^92 - 10602603 * q^93 - 10070348 * q^94 - 2579984 * q^95 + 9222606 * q^96 + 16208760 * q^97 + 6323227 * q^98 + 8739981 * q^99

Introduction

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