LMFDB - Embedded newform 471.8.a.c.1.14

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			1.14
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)

$f(q)$	$=$	$q-10.6994 q^{2} -27.0000 q^{3} -13.5238 q^{4} -456.397 q^{5} +288.883 q^{6} -1238.76 q^{7} +1514.21 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-10.6994 q^{2} -27.0000 q^{3} -13.5238 q^{4} -456.397 q^{5} +288.883 q^{6} -1238.76 q^{7} +1514.21 q^{8} +729.000 q^{9} +4883.15 q^{10} +2315.63 q^{11} +365.143 q^{12} +9271.23 q^{13} +13253.9 q^{14} +12322.7 q^{15} -14470.1 q^{16} +20999.3 q^{17} -7799.83 q^{18} +50017.2 q^{19} +6172.23 q^{20} +33446.5 q^{21} -24775.8 q^{22} +55891.3 q^{23} -40883.8 q^{24} +130173. q^{25} -99196.2 q^{26} -19683.0 q^{27} +16752.8 q^{28} -177085. q^{29} -131845. q^{30} -129977. q^{31} -38999.0 q^{32} -62522.1 q^{33} -224678. q^{34} +565366. q^{35} -9858.86 q^{36} +434137. q^{37} -535151. q^{38} -250323. q^{39} -691082. q^{40} +423404. q^{41} -357856. q^{42} -506046. q^{43} -31316.2 q^{44} -332713. q^{45} -598001. q^{46} +999769. q^{47} +390692. q^{48} +710984. q^{49} -1.39277e6 q^{50} -566980. q^{51} -125382. q^{52} -1.91594e6 q^{53} +210595. q^{54} -1.05685e6 q^{55} -1.87575e6 q^{56} -1.35046e6 q^{57} +1.89470e6 q^{58} -1.18880e6 q^{59} -166650. q^{60} -860432. q^{61} +1.39067e6 q^{62} -903056. q^{63} +2.26943e6 q^{64} -4.23136e6 q^{65} +668946. q^{66} +2.77572e6 q^{67} -283990. q^{68} -1.50907e6 q^{69} -6.04905e6 q^{70} +5.48905e6 q^{71} +1.10386e6 q^{72} +5.60947e6 q^{73} -4.64499e6 q^{74} -3.51467e6 q^{75} -676423. q^{76} -2.86852e6 q^{77} +2.67830e6 q^{78} +4.79921e6 q^{79} +6.60409e6 q^{80} +531441. q^{81} -4.53015e6 q^{82} +4.77996e6 q^{83} -452325. q^{84} -9.58399e6 q^{85} +5.41437e6 q^{86} +4.78129e6 q^{87} +3.50637e6 q^{88} +9.15557e6 q^{89} +3.55982e6 q^{90} -1.14848e7 q^{91} -755864. q^{92} +3.50939e6 q^{93} -1.06969e7 q^{94} -2.28277e7 q^{95} +1.05297e6 q^{96} +2.80682e6 q^{97} -7.60707e6 q^{98} +1.68810e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−10.6994	−0.945698	−0.472849	−	0.881143i	$-0.656774\pi$
$2$	−10.6994	−0.945698	−0.472849	+	0.881143i	$0.656774\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	−13.5238	−0.105655
$5$	−456.397	−1.63285	−0.816427	−	0.577448i	$-0.804049\pi$
$5$	−456.397	−1.63285	−0.816427	+	0.577448i	$0.804049\pi$
$6$	288.883	0.545999
$7$	−1238.76	−1.36504	−0.682518	−	0.730869i	$-0.739115\pi$
$7$	−1238.76	−1.36504	−0.682518	+	0.730869i	$0.739115\pi$
$8$	1514.21	1.04562
$9$	729.000	0.333333
$10$	4883.15	1.54419
$11$	2315.63	0.524561	0.262280	−	0.964992i	$-0.415526\pi$
$11$	2315.63	0.524561	0.262280	+	0.964992i	$0.415526\pi$
$12$	365.143	0.0609998
$13$	9271.23	1.17040	0.585202	−	0.810887i	$-0.301015\pi$
$13$	9271.23	1.17040	0.585202	+	0.810887i	$0.301015\pi$
$14$	13253.9	1.29091
$15$	12322.7	0.942729
$16$	−14470.1	−0.883182
$17$	20999.3	1.03665	0.518326	−	0.855183i	$-0.326556\pi$
$17$	20999.3	1.03665	0.518326	+	0.855183i	$0.326556\pi$
$18$	−7799.83	−0.315233
$19$	50017.2	1.67294	0.836472	−	0.548010i	$-0.184614\pi$
$19$	50017.2	1.67294	0.836472	+	0.548010i	$0.184614\pi$
$20$	6172.23	0.172519
$21$	33446.5	0.788104
$22$	−24775.8	−0.496076
$23$	55891.3	0.957849	0.478924	−	0.877856i	$-0.341027\pi$
$23$	55891.3	0.957849	0.478924	+	0.877856i	$0.341027\pi$
$24$	−40883.8	−0.603687
$25$	130173.	1.66622
$26$	−99196.2	−1.10685
$27$	−19683.0	−0.192450
$28$	16752.8	0.144223
$29$	−177085.	−1.34831	−0.674153	−	0.738591i	$-0.735491\pi$
$29$	−177085.	−1.34831	−0.674153	+	0.738591i	$0.735491\pi$
$30$	−131845.	−0.891537
$31$	−129977.	−0.783612	−0.391806	−	0.920048i	$-0.628150\pi$
$31$	−129977.	−0.783612	−0.391806	+	0.920048i	$0.628150\pi$
$32$	−38999.0	−0.210392
$33$	−62522.1	−0.302855
$34$	−224678.	−0.980359
$35$	565366.	2.22891
$36$	−9858.86	−0.0352183
$37$	434137.	1.40903	0.704516	−	0.709688i	$-0.251164\pi$
$37$	434137.	1.40903	0.704516	+	0.709688i	$0.251164\pi$
$38$	−535151.	−1.58210
$39$	−250323.	−0.675733
$40$	−691082.	−1.70734
$41$	423404.	0.959426	0.479713	−	0.877426i	$-0.340741\pi$
$41$	423404.	0.959426	0.479713	+	0.877426i	$0.340741\pi$
$42$	−357856.	−0.745309
$43$	−506046.	−0.970623	−0.485311	−	0.874341i	$-0.661294\pi$
$43$	−506046.	−0.970623	−0.485311	+	0.874341i	$0.661294\pi$
$44$	−31316.2	−0.0554223
$45$	−332713.	−0.544285
$46$	−598001.	−0.905836
$47$	999769.	1.40461	0.702307	−	0.711874i	$-0.252153\pi$
$47$	999769.	1.40461	0.702307	+	0.711874i	$0.252153\pi$
$48$	390692.	0.509906
$49$	710984.	0.863324
$50$	−1.39277e6	−1.57574
$51$	−566980.	−0.598511
$52$	−125382.	−0.123659
$53$	−1.91594e6	−1.76773	−0.883865	−	0.467742i	$-0.845068\pi$
$53$	−1.91594e6	−1.76773	−0.883865	+	0.467742i	$0.845068\pi$
$54$	210595.	0.182000
$55$	−1.05685e6	−0.856531
$56$	−1.87575e6	−1.42730
$57$	−1.35046e6	−0.965875
$58$	1.89470e6	1.27509
$59$	−1.18880e6	−0.753577	−0.376788	−	0.926299i	$-0.622972\pi$
$59$	−1.18880e6	−0.753577	−0.376788	+	0.926299i	$0.622972\pi$
$60$	−166650.	−0.0996039
$61$	−860432.	−0.485358	−0.242679	−	0.970107i	$-0.578026\pi$
$61$	−860432.	−0.485358	−0.242679	+	0.970107i	$0.578026\pi$
$62$	1.39067e6	0.741061
$63$	−903056.	−0.455012
$64$	2.26943e6	1.08215
$65$	−4.23136e6	−1.91110
$66$	668946.	0.286410
$67$	2.77572e6	1.12749	0.563746	−	0.825948i	$-0.309360\pi$
$67$	2.77572e6	1.12749	0.563746	+	0.825948i	$0.309360\pi$
$68$	−283990.	−0.109527
$69$	−1.50907e6	−0.553014
$70$	−6.04905e6	−2.10787
$71$	5.48905e6	1.82009	0.910046	−	0.414507i	$-0.136046\pi$
$71$	5.48905e6	1.82009	0.910046	+	0.414507i	$0.136046\pi$
$72$	1.10386e6	0.348539
$73$	5.60947e6	1.68769	0.843843	−	0.536590i	$-0.180288\pi$
$73$	5.60947e6	1.68769	0.843843	+	0.536590i	$0.180288\pi$
$74$	−4.64499e6	−1.33252
$75$	−3.51467e6	−0.961990
$76$	−676423.	−0.176755
$77$	−2.86852e6	−0.716044
$78$	2.67830e6	0.639040
$79$	4.79921e6	1.09515	0.547577	−	0.836755i	$-0.315550\pi$
$79$	4.79921e6	1.09515	0.547577	+	0.836755i	$0.315550\pi$
$80$	6.60409e6	1.44211
$81$	531441.	0.111111
$82$	−4.53015e6	−0.907327
$83$	4.77996e6	0.917594	0.458797	−	0.888541i	$-0.348281\pi$
$83$	4.77996e6	0.917594	0.458797	+	0.888541i	$0.348281\pi$
$84$	−452325.	−0.0832670
$85$	−9.58399e6	−1.69270
$86$	5.41437e6	0.917916
$87$	4.78129e6	0.778445
$88$	3.50637e6	0.548489
$89$	9.15557e6	1.37664	0.688320	−	0.725407i	$-0.258348\pi$
$89$	9.15557e6	1.37664	0.688320	+	0.725407i	$0.258348\pi$
$90$	3.55982e6	0.514729
$91$	−1.14848e7	−1.59764
$92$	−755864.	−0.101201
$93$	3.50939e6	0.452419
$94$	−1.06969e7	−1.32834
$95$	−2.28277e7	−2.73167
$96$	1.05297e6	0.121470
$97$	2.80682e6	0.312258	0.156129	−	0.987737i	$-0.450098\pi$
$97$	2.80682e6	0.312258	0.156129	+	0.987737i	$0.450098\pi$
$98$	−7.60707e6	−0.816444
$99$	1.68810e6	0.174854
$100$	−1.76044e6	−0.176044
$101$	−1.24478e7	−1.20218	−0.601089	−	0.799182i	$-0.705266\pi$
$101$	−1.24478e7	−1.20218	−0.601089	+	0.799182i	$0.705266\pi$
$102$	6.06632e6	0.566011
$103$	−1.04687e7	−0.943978	−0.471989	−	0.881604i	$-0.656464\pi$
$103$	−1.04687e7	−0.943978	−0.471989	+	0.881604i	$0.656464\pi$
$104$	1.40386e7	1.22379
$105$	−1.52649e7	−1.28686
$106$	2.04993e7	1.67174
$107$	1.28365e7	1.01299	0.506493	−	0.862244i	$-0.330942\pi$
$107$	1.28365e7	1.01299	0.506493	+	0.862244i	$0.330942\pi$
$108$	266189.	0.0203333
$109$	−1.18842e6	−0.0878973	−0.0439487	−	0.999034i	$-0.513994\pi$
$109$	−1.18842e6	−0.0878973	−0.0439487	+	0.999034i	$0.513994\pi$
$110$	1.13076e7	0.810020
$111$	−1.17217e7	−0.813505
$112$	1.79249e7	1.20558
$113$	1.55073e7	1.01102	0.505511	−	0.862820i	$-0.331304\pi$
$113$	1.55073e7	1.01102	0.505511	+	0.862820i	$0.331304\pi$
$114$	1.44491e7	0.913426
$115$	−2.55086e7	−1.56403
$116$	2.39486e6	0.142455
$117$	6.75873e6	0.390135
$118$	1.27194e7	0.712656
$119$	−2.60130e7	−1.41507
$120$	1.86592e7	0.985733
$121$	−1.41250e7	−0.724836
$122$	9.20607e6	0.459002
$123$	−1.14319e7	−0.553925
$124$	1.75779e6	0.0827924
$125$	−2.37546e7	−1.08783
$126$	9.66212e6	0.430304
$127$	−7.34987e6	−0.318395	−0.159198	−	0.987247i	$-0.550891\pi$
$127$	−7.34987e6	−0.318395	−0.159198	+	0.987247i	$0.550891\pi$
$128$	−1.92896e7	−0.812995
$129$	1.36632e7	0.560389
$130$	4.52728e7	1.80732
$131$	−8.31196e6	−0.323038	−0.161519	−	0.986870i	$-0.551639\pi$
$131$	−8.31196e6	−0.323038	−0.161519	+	0.986870i	$0.551639\pi$
$132$	845538.	0.0319981
$133$	−6.19593e7	−2.28363
$134$	−2.96984e7	−1.06627
$135$	8.98326e6	0.314243
$136$	3.17974e7	1.08394
$137$	−1.87095e7	−0.621641	−0.310821	−	0.950469i	$-0.600604\pi$
$137$	−1.87095e7	−0.621641	−0.310821	+	0.950469i	$0.600604\pi$
$138$	1.61460e7	0.522985
$139$	−5.47977e7	−1.73066	−0.865328	−	0.501206i	$-0.832890\pi$
$139$	−5.47977e7	−1.73066	−0.865328	+	0.501206i	$0.832890\pi$
$140$	−7.64591e6	−0.235495
$141$	−2.69937e7	−0.810954
$142$	−5.87293e7	−1.72126
$143$	2.14688e7	0.613948
$144$	−1.05487e7	−0.294394
$145$	8.08210e7	2.20159
$146$	−6.00177e7	−1.59604
$147$	−1.91966e7	−0.498440
$148$	−5.87119e6	−0.148871
$149$	3.94749e7	0.977618	0.488809	−	0.872391i	$-0.337431\pi$
$149$	3.94749e7	0.977618	0.488809	+	0.872391i	$0.337431\pi$
$150$	3.76047e7	0.909752
$151$	2.93611e7	0.693989	0.346994	−	0.937867i	$-0.387202\pi$
$151$	2.93611e7	0.693989	0.346994	+	0.937867i	$0.387202\pi$
$152$	7.57366e7	1.74926
$153$	1.53085e7	0.345550
$154$	3.06913e7	0.677162
$155$	5.93212e7	1.27953
$156$	3.38533e6	0.0713944
$157$	−3.86989e6	−0.0798087
$157$	−3.86989e6	−0.0798087
$158$	−5.13485e7	−1.03568
$159$	5.17303e7	1.02060
$160$	1.77990e7	0.343539
$161$	−6.92360e7	−1.30750
$162$	−5.68608e6	−0.105078
$163$	−6.95690e7	−1.25823	−0.629114	−	0.777313i	$-0.716582\pi$
$163$	−6.95690e7	−1.25823	−0.629114	+	0.777313i	$0.716582\pi$
$164$	−5.72603e6	−0.101368
$165$	2.85349e7	0.494519
$166$	−5.11424e7	−0.867767
$167$	−8.18963e7	−1.36068	−0.680341	−	0.732895i	$-0.738168\pi$
$167$	−8.18963e7	−1.36068	−0.680341	+	0.732895i	$0.738168\pi$
$168$	5.06452e7	0.824054
$169$	2.32073e7	0.369846
$170$	1.02543e8	1.60078
$171$	3.64625e7	0.557648
$172$	6.84367e6	0.102551
$173$	7.99469e7	1.17393	0.586963	−	0.809614i	$-0.300324\pi$
$173$	7.99469e7	1.17393	0.586963	+	0.809614i	$0.300324\pi$
$174$	−5.11568e7	−0.736174
$175$	−1.61253e8	−2.27444
$176$	−3.35074e7	−0.463283
$177$	3.20977e7	0.435078
$178$	−9.79587e7	−1.30189
$179$	7.82776e7	1.02012	0.510061	−	0.860138i	$-0.329623\pi$
$179$	7.82776e7	1.02012	0.510061	+	0.860138i	$0.329623\pi$
$180$	4.49955e6	0.0575063
$181$	−1.26654e8	−1.58761	−0.793805	−	0.608173i	$-0.791903\pi$
$181$	−1.26654e8	−1.58761	−0.793805	+	0.608173i	$0.791903\pi$
$182$	1.22880e8	1.51089
$183$	2.32317e7	0.280222
$184$	8.46314e7	1.00154
$185$	−1.98139e8	−2.30075
$186$	−3.75482e7	−0.427852
$187$	4.86266e7	0.543786
$188$	−1.35207e7	−0.148404
$189$	2.43825e7	0.262701
$190$	2.44241e8	2.58334
$191$	8.45824e7	0.878341	0.439171	−	0.898404i	$-0.355272\pi$
$191$	8.45824e7	0.878341	0.439171	+	0.898404i	$0.355272\pi$
$192$	−6.12747e7	−0.624779
$193$	1.63906e8	1.64113	0.820567	−	0.571550i	$-0.193658\pi$
$193$	1.63906e8	1.64113	0.820567	+	0.571550i	$0.193658\pi$
$194$	−3.00312e7	−0.295302
$195$	1.14247e8	1.10337
$196$	−9.61522e6	−0.0912143
$197$	−6.63789e7	−0.618583	−0.309292	−	0.950967i	$-0.600092\pi$
$197$	−6.63789e7	−0.618583	−0.309292	+	0.950967i	$0.600092\pi$
$198$	−1.80616e7	−0.165359
$199$	1.48097e7	0.133218	0.0666088	−	0.997779i	$-0.478782\pi$
$199$	1.48097e7	0.133218	0.0666088	+	0.997779i	$0.478782\pi$
$200$	1.97110e8	1.74222
$201$	−7.49444e7	−0.650958
$202$	1.33184e8	1.13690
$203$	2.19366e8	1.84049
$204$	7.66773e6	0.0632355
$205$	−1.93240e8	−1.56660
$206$	1.12008e8	0.892719
$207$	4.07448e7	0.319283
$208$	−1.34155e8	−1.03368
$209$	1.15821e8	0.877560
$210$	1.63324e8	1.21698
$211$	−1.21576e8	−0.890962	−0.445481	−	0.895291i	$-0.646967\pi$
$211$	−1.21576e8	−0.890962	−0.445481	+	0.895291i	$0.646967\pi$
$212$	2.59108e7	0.186769
$213$	−1.48204e8	−1.05083
$214$	−1.37342e8	−0.957979
$215$	2.30958e8	1.58489
$216$	−2.98043e7	−0.201229
$217$	1.61011e8	1.06966
$218$	1.27153e7	0.0831244
$219$	−1.51456e8	−0.974386
$220$	1.42926e7	0.0904966
$221$	1.94689e8	1.21330
$222$	1.25415e8	0.769331
$223$	−4.12995e7	−0.249389	−0.124695	−	0.992195i	$-0.539795\pi$
$223$	−4.12995e7	−0.249389	−0.124695	+	0.992195i	$0.539795\pi$
$224$	4.83105e7	0.287193
$225$	9.48962e7	0.555405
$226$	−1.65918e8	−0.956122
$227$	3.08012e7	0.174774	0.0873872	−	0.996174i	$-0.472148\pi$
$227$	3.08012e7	0.174774	0.0873872	+	0.996174i	$0.472148\pi$
$228$	1.82634e7	0.102049
$229$	−3.98835e6	−0.0219467	−0.0109733	−	0.999940i	$-0.503493\pi$
$229$	−3.98835e6	−0.0219467	−0.0109733	+	0.999940i	$0.503493\pi$
$230$	2.72926e8	1.47910
$231$	7.74499e7	0.413408
$232$	−2.68144e8	−1.40981
$233$	−7.60510e7	−0.393876	−0.196938	−	0.980416i	$-0.563100\pi$
$233$	−7.60510e7	−0.393876	−0.196938	+	0.980416i	$0.563100\pi$
$234$	−7.23141e7	−0.368950
$235$	−4.56291e8	−2.29353
$236$	1.60771e7	0.0796190
$237$	−1.29579e8	−0.632287
$238$	2.78323e8	1.33823
$239$	−5.93279e7	−0.281103	−0.140552	−	0.990073i	$-0.544888\pi$
$239$	−5.93279e7	−0.281103	−0.140552	+	0.990073i	$0.544888\pi$
$240$	−1.78310e8	−0.832602
$241$	3.58610e8	1.65030	0.825149	−	0.564915i	$-0.191091\pi$
$241$	3.58610e8	1.65030	0.825149	+	0.564915i	$0.191091\pi$
$242$	1.51128e8	0.685476
$243$	−1.43489e7	−0.0641500
$244$	1.16363e7	0.0512804
$245$	−3.24491e8	−1.40968
$246$	1.22314e8	0.523846
$247$	4.63721e8	1.95802
$248$	−1.96813e8	−0.819358
$249$	−1.29059e8	−0.529773
$250$	2.54159e8	1.02876
$251$	3.05364e8	1.21888	0.609439	−	0.792833i	$-0.291395\pi$
$251$	3.05364e8	1.21888	0.609439	+	0.792833i	$0.291395\pi$
$252$	1.22128e7	0.0480742
$253$	1.29424e8	0.502450
$254$	7.86389e7	0.301106
$255$	2.58768e8	0.977281
$256$	−8.41012e7	−0.313301
$257$	−1.85226e8	−0.680668	−0.340334	−	0.940305i	$-0.610540\pi$
$257$	−1.85226e8	−0.680668	−0.340334	+	0.940305i	$0.610540\pi$
$258$	−1.46188e8	−0.529959
$259$	−5.37792e8	−1.92338
$260$	5.72242e7	0.201917
$261$	−1.29095e8	−0.449436
$262$	8.89326e7	0.305497
$263$	3.86636e8	1.31056	0.655280	−	0.755386i	$-0.272551\pi$
$263$	3.86636e8	1.31056	0.655280	+	0.755386i	$0.272551\pi$
$264$	−9.46719e7	−0.316670
$265$	8.74428e8	2.88645
$266$	6.62924e8	2.15962
$267$	−2.47201e8	−0.794804
$268$	−3.75383e7	−0.119125
$269$	2.12523e7	0.0665693	0.0332846	−	0.999446i	$-0.489403\pi$
$269$	2.12523e7	0.0665693	0.0332846	+	0.999446i	$0.489403\pi$
$270$	−9.61151e7	−0.297179
$271$	−5.59122e8	−1.70653	−0.853265	−	0.521477i	$-0.825381\pi$
$271$	−5.59122e8	−1.70653	−0.853265	+	0.521477i	$0.825381\pi$
$272$	−3.03860e8	−0.915552
$273$	3.10091e8	0.922400
$274$	2.00179e8	0.587885
$275$	3.01433e8	0.874031
$276$	2.04083e7	0.0584286
$277$	−9.37618e7	−0.265062	−0.132531	−	0.991179i	$-0.542310\pi$
$277$	−9.37618e7	−0.265062	−0.132531	+	0.991179i	$0.542310\pi$
$278$	5.86300e8	1.63668
$279$	−9.47534e7	−0.261204
$280$	8.56085e8	2.33058
$281$	6.30252e8	1.69450	0.847251	−	0.531193i	$-0.178256\pi$
$281$	6.30252e8	1.69450	0.847251	+	0.531193i	$0.178256\pi$
$282$	2.88816e8	0.766918
$283$	1.23335e7	0.0323469	0.0161734	−	0.999869i	$-0.494852\pi$
$283$	1.23335e7	0.0323469	0.0161734	+	0.999869i	$0.494852\pi$
$284$	−7.42329e7	−0.192301
$285$	6.16347e8	1.57713
$286$	−2.29702e8	−0.580609
$287$	−5.24496e8	−1.30965
$288$	−2.84303e7	−0.0701306
$289$	3.06301e7	0.0746459
$290$	−8.64733e8	−2.08204
$291$	−7.57842e7	−0.180282
$292$	−7.58614e7	−0.178312
$293$	4.08591e8	0.948970	0.474485	−	0.880263i	$-0.342634\pi$
$293$	4.08591e8	0.948970	0.474485	+	0.880263i	$0.342634\pi$
$294$	2.05391e8	0.471374
$295$	5.42566e8	1.23048
$296$	6.57377e8	1.47331
$297$	−4.55786e7	−0.100952
$298$	−4.22356e8	−0.924532
$299$	5.18182e8	1.12107
$300$	4.75318e7	0.101639
$301$	6.26870e8	1.32494
$302$	−3.14145e8	−0.656304
$303$	3.36092e8	0.694078
$304$	−7.23751e8	−1.47751
$305$	3.92699e8	0.792519
$306$	−1.63791e8	−0.326786
$307$	7.98024e8	1.57410	0.787049	−	0.616890i	$-0.211608\pi$
$307$	7.98024e8	1.57410	0.787049	+	0.616890i	$0.211608\pi$
$308$	3.87933e7	0.0756535
$309$	2.82655e8	0.545006
$310$	−6.34698e8	−1.21005
$311$	−1.07149e8	−0.201988	−0.100994	−	0.994887i	$-0.532202\pi$
$311$	−1.07149e8	−0.201988	−0.100994	+	0.994887i	$0.532202\pi$
$312$	−3.79043e8	−0.706557
$313$	−9.73176e8	−1.79385	−0.896925	−	0.442183i	$-0.854204\pi$
$313$	−9.73176e8	−1.79385	−0.896925	+	0.442183i	$0.854204\pi$
$314$	4.14054e7	0.0754749
$315$	4.12152e8	0.742969
$316$	−6.49036e7	−0.115708
$317$	−2.82812e8	−0.498644	−0.249322	−	0.968421i	$-0.580208\pi$
$317$	−2.82812e8	−0.498644	−0.249322	+	0.968421i	$0.580208\pi$
$318$	−5.53481e8	−0.965179
$319$	−4.10064e8	−0.707269
$320$	−1.03576e9	−1.76699
$321$	−3.46586e8	−0.584848
$322$	7.40780e8	1.23650
$323$	1.05032e9	1.73426
$324$	−7.18711e6	−0.0117394
$325$	1.20687e9	1.95015
$326$	7.44344e8	1.18990
$327$	3.20872e7	0.0507476
$328$	6.41124e8	1.00319
$329$	−1.23847e9	−1.91735
$330$	−3.05305e8	−0.467665
$331$	−7.10387e7	−0.107671	−0.0538353	−	0.998550i	$-0.517145\pi$
$331$	−7.10387e7	−0.107671	−0.0538353	+	0.998550i	$0.517145\pi$
$332$	−6.46432e7	−0.0969482
$333$	3.16486e8	0.469678
$334$	8.76238e8	1.28680
$335$	−1.26683e9	−1.84103
$336$	−4.83973e8	−0.696040
$337$	1.79225e8	0.255090	0.127545	−	0.991833i	$-0.459290\pi$
$337$	1.79225e8	0.255090	0.127545	+	0.991833i	$0.459290\pi$
$338$	−2.48303e8	−0.349763
$339$	−4.18696e8	−0.583714
$340$	1.29612e8	0.178842
$341$	−3.00980e8	−0.411052
$342$	−3.90125e8	−0.527367
$343$	1.39433e8	0.186568
$344$	−7.66262e8	−1.01490
$345$	6.88733e8	0.902992
$346$	−8.55381e8	−1.11018
$347$	2.13541e8	0.274365	0.137182	−	0.990546i	$-0.456195\pi$
$347$	2.13541e8	0.274365	0.137182	+	0.990546i	$0.456195\pi$
$348$	−6.46613e7	−0.0822465
$349$	−2.77955e8	−0.350014	−0.175007	−	0.984567i	$-0.555995\pi$
$349$	−2.77955e8	−0.350014	−0.175007	+	0.984567i	$0.555995\pi$
$350$	1.72531e9	2.15094
$351$	−1.82486e8	−0.225244
$352$	−9.03075e7	−0.110363
$353$	−1.21632e9	−1.47176	−0.735881	−	0.677111i	$-0.763232\pi$
$353$	−1.21632e9	−1.47176	−0.735881	+	0.677111i	$0.763232\pi$
$354$	−3.43424e8	−0.411452
$355$	−2.50519e9	−2.97195
$356$	−1.23818e8	−0.145449
$357$	7.02352e8	0.816989
$358$	−8.37520e8	−0.964728
$359$	−1.36721e9	−1.55957	−0.779786	−	0.626046i	$-0.784672\pi$
$359$	−1.36721e9	−1.55957	−0.779786	+	0.626046i	$0.784672\pi$
$360$	−5.03799e8	−0.569113
$361$	1.60784e9	1.79874
$362$	1.35512e9	1.50140
$363$	3.81375e8	0.418484
$364$	1.55319e8	0.168799
$365$	−2.56014e9	−2.75575
$366$	−2.48564e8	−0.265005
$367$	5.76786e7	0.0609093	0.0304547	−	0.999536i	$-0.490304\pi$
$367$	5.76786e7	0.0609093	0.0304547	+	0.999536i	$0.490304\pi$
$368$	−8.08751e8	−0.845955
$369$	3.08661e8	0.319809
$370$	2.11996e9	2.17581
$371$	2.37339e9	2.41302
$372$	−4.74603e7	−0.0478002
$373$	−1.66362e9	−1.65987	−0.829935	−	0.557860i	$-0.811623\pi$
$373$	−1.66362e9	−1.65987	−0.829935	+	0.557860i	$0.811623\pi$
$374$	−5.20273e8	−0.514258
$375$	6.41373e8	0.628061
$376$	1.51386e9	1.46869
$377$	−1.64180e9	−1.57806
$378$	−2.60877e8	−0.248436
$379$	4.59162e8	0.433240	0.216620	−	0.976256i	$-0.430497\pi$
$379$	4.59162e8	0.433240	0.216620	+	0.976256i	$0.430497\pi$
$380$	3.08717e8	0.288614
$381$	1.98446e8	0.183826
$382$	−9.04977e8	−0.830646
$383$	−1.93853e6	−0.00176310	−0.000881548	−	1.00000i	$-0.500281\pi$
$383$	−1.93853e6	−0.00176310	−0.000881548		1.00000i	$0.500281\pi$
$384$	5.20819e8	0.469383
$385$	1.30918e9	1.16920
$386$	−1.75369e9	−1.55202
$387$	−3.68908e8	−0.323541
$388$	−3.79589e7	−0.0329916
$389$	4.77990e8	0.411713	0.205857	−	0.978582i	$-0.434002\pi$
$389$	4.77990e8	0.411713	0.205857	+	0.978582i	$0.434002\pi$
$390$	−1.22237e9	−1.04346
$391$	1.17368e9	0.992955
$392$	1.07658e9	0.902705
$393$	2.24423e8	0.186506
$394$	7.10211e8	0.584993
$395$	−2.19034e9	−1.78823
$396$	−2.28295e7	−0.0184741
$397$	2.22328e9	1.78331	0.891655	−	0.452715i	$-0.149544\pi$
$397$	2.22328e9	1.78331	0.891655	+	0.452715i	$0.149544\pi$
$398$	−1.58455e8	−0.125984
$399$	1.67290e9	1.31845
$400$	−1.88361e9	−1.47157
$401$	1.43087e9	1.10814	0.554071	−	0.832470i	$-0.313074\pi$
$401$	1.43087e9	1.10814	0.554071	+	0.832470i	$0.313074\pi$
$402$	8.01857e8	0.615610
$403$	−1.20505e9	−0.917143
$404$	1.68342e8	0.127016
$405$	−2.42548e8	−0.181428
$406$	−2.34707e9	−1.74055
$407$	1.00530e9	0.739123
$408$	−8.58529e8	−0.625812
$409$	−7.41724e8	−0.536056	−0.268028	−	0.963411i	$-0.586372\pi$
$409$	−7.41724e8	−0.536056	−0.268028	+	0.963411i	$0.586372\pi$
$410$	2.06754e9	1.48153
$411$	5.05156e8	0.358905
$412$	1.41577e8	0.0997358
$413$	1.47264e9	1.02866
$414$	−4.35943e8	−0.301945
$415$	−2.18156e9	−1.49830
$416$	−3.61569e8	−0.246244
$417$	1.47954e9	0.999195
$418$	−1.23921e9	−0.829907
$419$	5.48264e7	0.0364117	0.0182058	−	0.999834i	$-0.494205\pi$
$419$	5.48264e7	0.0364117	0.0182058	+	0.999834i	$0.494205\pi$
$420$	2.06440e8	0.135963
$421$	−1.33021e9	−0.868826	−0.434413	−	0.900714i	$-0.643044\pi$
$421$	−1.33021e9	−0.868826	−0.434413	+	0.900714i	$0.643044\pi$
$422$	1.30079e9	0.842582
$423$	7.28831e8	0.468205
$424$	−2.90114e9	−1.84837
$425$	2.73354e9	1.72728
$426$	1.58569e9	0.993769
$427$	1.06587e9	0.662531
$428$	−1.73598e8	−0.107027
$429$	−5.79657e8	−0.354463
$430$	−2.47110e9	−1.49882
$431$	9.84643e8	0.592391	0.296195	−	0.955127i	$-0.404282\pi$
$431$	9.84643e8	0.592391	0.296195	+	0.955127i	$0.404282\pi$
$432$	2.84814e8	0.169969
$433$	−2.15087e9	−1.27323	−0.636614	−	0.771183i	$-0.719665\pi$
$433$	−2.15087e9	−1.27323	−0.636614	+	0.771183i	$0.719665\pi$
$434$	−1.72271e9	−1.01158
$435$	−2.18217e9	−1.27109
$436$	1.60719e7	0.00928677
$437$	2.79552e9	1.60243
$438$	1.62048e9	0.921475
$439$	1.43692e9	0.810602	0.405301	−	0.914183i	$-0.367167\pi$
$439$	1.43692e9	0.810602	0.405301	+	0.914183i	$0.367167\pi$
$440$	−1.60029e9	−0.895603
$441$	5.18308e8	0.287775
$442$	−2.08305e9	−1.14742
$443$	−2.62945e9	−1.43698	−0.718492	−	0.695536i	$-0.755167\pi$
$443$	−2.62945e9	−1.43698	−0.718492	+	0.695536i	$0.755167\pi$
$444$	1.58522e8	0.0859507
$445$	−4.17858e9	−2.24785
$446$	4.41878e8	0.235847
$447$	−1.06582e9	−0.564428
$448$	−2.81128e9	−1.47717
$449$	1.99361e9	1.03939	0.519695	−	0.854352i	$-0.326046\pi$
$449$	1.99361e9	1.03939	0.519695	+	0.854352i	$0.326046\pi$
$450$	−1.01533e9	−0.525246
$451$	9.80449e8	0.503277
$452$	−2.09717e8	−0.106819
$453$	−7.92749e8	−0.400675
$454$	−3.29553e8	−0.165284
$455$	5.24164e9	2.60872
$456$	−2.04489e9	−1.00993
$457$	3.93396e8	0.192807	0.0964037	−	0.995342i	$-0.469266\pi$
$457$	3.93396e8	0.192807	0.0964037	+	0.995342i	$0.469266\pi$
$458$	4.26728e7	0.0207549
$459$	−4.13328e8	−0.199504
$460$	3.44974e8	0.165247
$461$	2.21293e9	1.05200	0.525999	−	0.850485i	$-0.323692\pi$
$461$	2.21293e9	1.05200	0.525999	+	0.850485i	$0.323692\pi$
$462$	−8.28664e8	−0.390960
$463$	−2.66829e9	−1.24939	−0.624697	−	0.780868i	$-0.714777\pi$
$463$	−2.66829e9	−1.24939	−0.624697	+	0.780868i	$0.714777\pi$
$464$	2.56243e9	1.19080
$465$	−1.60167e9	−0.738734
$466$	8.13697e8	0.372488
$467$	2.47532e9	1.12466	0.562330	−	0.826913i	$-0.309905\pi$
$467$	2.47532e9	1.12466	0.562330	+	0.826913i	$0.309905\pi$
$468$	−9.14038e7	−0.0412196
$469$	−3.43845e9	−1.53907
$470$	4.88202e9	2.16899
$471$	1.04487e8	0.0460776
$472$	−1.80010e9	−0.787952
$473$	−1.17182e9	−0.509150
$474$	1.38641e9	0.597953
$475$	6.51089e9	2.78748
$476$	3.51796e8	0.149509
$477$	−1.39672e9	−0.589243
$478$	6.34770e8	0.265839
$479$	2.57992e9	1.07259	0.536293	−	0.844032i	$-0.319824\pi$
$479$	2.57992e9	1.07259	0.536293	+	0.844032i	$0.319824\pi$
$480$	−4.80574e8	−0.198343
$481$	4.02499e9	1.64914
$482$	−3.83689e9	−1.56068
$483$	1.86937e9	0.754884
$484$	1.91024e8	0.0765824
$485$	−1.28102e9	−0.509872
$486$	1.53524e8	0.0606666
$487$	−4.59856e9	−1.80414	−0.902071	−	0.431588i	$-0.857953\pi$
$487$	−4.59856e9	−1.80414	−0.902071	+	0.431588i	$0.857953\pi$
$488$	−1.30288e9	−0.507498
$489$	1.87836e9	0.726438
$490$	3.47184e9	1.33313
$491$	−5.45869e8	−0.208115	−0.104057	−	0.994571i	$-0.533183\pi$
$491$	−5.45869e8	−0.208115	−0.104057	+	0.994571i	$0.533183\pi$
$492$	1.54603e8	0.0585248
$493$	−3.71865e9	−1.39772
$494$	−4.96151e9	−1.85170
$495$	−7.70442e8	−0.285510
$496$	1.88078e9	0.692073
$497$	−6.79962e9	−2.48449
$498$	1.38085e9	0.501006
$499$	−4.31543e9	−1.55479	−0.777396	−	0.629012i	$-0.783460\pi$
$499$	−4.31543e9	−1.55479	−0.777396	+	0.629012i	$0.783460\pi$
$500$	3.21252e8	0.114935
$501$	2.21120e9	0.785590
$502$	−3.26720e9	−1.15269
$503$	−3.49460e9	−1.22436	−0.612181	−	0.790717i	$-0.709708\pi$
$503$	−3.49460e9	−1.22436	−0.612181	+	0.790717i	$0.709708\pi$
$504$	−1.36742e9	−0.475768
$505$	5.68115e9	1.96298
$506$	−1.38475e9	−0.475166
$507$	−6.26597e8	−0.213531
$508$	9.93983e7	0.0336400
$509$	−1.67979e9	−0.564602	−0.282301	−	0.959326i	$-0.591098\pi$
$509$	−1.67979e9	−0.564602	−0.282301	+	0.959326i	$0.591098\pi$
$510$	−2.76865e9	−0.924213
$511$	−6.94879e9	−2.30375
$512$	3.36890e9	1.10928
$513$	−9.84488e8	−0.321958
$514$	1.98180e9	0.643707
$515$	4.77788e9	1.54138
$516$	−1.84779e8	−0.0592078
$517$	2.31510e9	0.736805
$518$	5.75403e9	1.81894
$519$	−2.15857e9	−0.677766
$520$	−6.40719e9	−1.99828
$521$	2.74132e9	0.849236	0.424618	−	0.905373i	$-0.360408\pi$
$521$	2.74132e9	0.849236	0.424618	+	0.905373i	$0.360408\pi$
$522$	1.38123e9	0.425031
$523$	3.25024e8	0.0993480	0.0496740	−	0.998765i	$-0.484182\pi$
$523$	3.25024e8	0.0993480	0.0496740	+	0.998765i	$0.484182\pi$
$524$	1.12409e8	0.0341305
$525$	4.35384e9	1.31315
$526$	−4.13675e9	−1.23939
$527$	−2.72943e9	−0.812333
$528$	9.04699e8	0.267476
$529$	−2.80986e8	−0.0825259
$530$	−9.35582e9	−2.72971
$531$	−8.66637e8	−0.251192
$532$	8.37926e8	0.241276
$533$	3.92548e9	1.12292
$534$	2.64489e9	0.751645
$535$	−5.85854e9	−1.65406
$536$	4.20303e9	1.17892
$537$	−2.11350e9	−0.588968
$538$	−2.27386e8	−0.0629545
$539$	1.64638e9	0.452866
$540$	−1.21488e8	−0.0332013
$541$	4.51399e9	1.22566	0.612831	−	0.790214i	$-0.290031\pi$
$541$	4.51399e9	1.22566	0.612831	+	0.790214i	$0.290031\pi$
$542$	5.98224e9	1.61386
$543$	3.41966e9	0.916607
$544$	−8.18951e8	−0.218103
$545$	5.42389e8	0.143524
$546$	−3.31777e9	−0.872312
$547$	−1.92793e9	−0.503658	−0.251829	−	0.967772i	$-0.581032\pi$
$547$	−1.92793e9	−0.503658	−0.251829	+	0.967772i	$0.581032\pi$
$548$	2.53024e8	0.0656794
$549$	−6.27255e8	−0.161786
$550$	−3.22514e9	−0.826569
$551$	−8.85729e9	−2.25564
$552$	−2.28505e9	−0.578240
$553$	−5.94507e9	−1.49492
$554$	1.00319e9	0.250668
$555$	5.34975e9	1.32834
$556$	7.41074e8	0.182852
$557$	1.23800e9	0.303549	0.151774	−	0.988415i	$-0.451501\pi$
$557$	1.23800e9	0.303549	0.151774	+	0.988415i	$0.451501\pi$
$558$	1.01380e9	0.247020
$559$	−4.69167e9	−1.13602
$560$	−8.18088e9	−1.96853
$561$	−1.31292e9	−0.313955
$562$	−6.74329e9	−1.60249
$563$	2.69742e9	0.637043	0.318522	−	0.947916i	$-0.396814\pi$
$563$	2.69742e9	0.637043	0.318522	+	0.947916i	$0.396814\pi$
$564$	3.65058e8	0.0856812
$565$	−7.07747e9	−1.65085
$566$	−1.31960e8	−0.0305904
$567$	−6.58328e8	−0.151671
$568$	8.31160e9	1.90312
$569$	−7.13604e7	−0.0162392	−0.00811960	−	0.999967i	$-0.502585\pi$
$569$	−7.13604e7	−0.0162392	−0.00811960	+	0.999967i	$0.502585\pi$
$570$	−6.59452e9	−1.49149
$571$	4.65162e9	1.04563	0.522815	−	0.852446i	$-0.324882\pi$
$571$	4.65162e9	1.04563	0.522815	+	0.852446i	$0.324882\pi$
$572$	−2.90340e8	−0.0648665
$573$	−2.28373e9	−0.507111
$574$	5.61177e9	1.23853
$575$	7.27554e9	1.59598
$576$	1.65442e9	0.360717
$577$	1.77006e9	0.383594	0.191797	−	0.981435i	$-0.438568\pi$
$577$	1.77006e9	0.383594	0.191797	+	0.981435i	$0.438568\pi$
$578$	−3.27722e8	−0.0705925
$579$	−4.42546e9	−0.947509
$580$	−1.09301e9	−0.232608
$581$	−5.92122e9	−1.25255
$582$	8.10842e8	0.170493
$583$	−4.43661e9	−0.927282
$584$	8.49393e9	1.76467
$585$	−3.08466e9	−0.637033
$586$	−4.37167e9	−0.897440
$587$	−5.54966e9	−1.13249	−0.566243	−	0.824238i	$-0.691604\pi$
$587$	−5.54966e9	−1.13249	−0.566243	+	0.824238i	$0.691604\pi$
$588$	2.59611e8	0.0526626
$589$	−6.50109e9	−1.31094
$590$	−5.80510e9	−1.16366
$591$	1.79223e9	0.357139
$592$	−6.28199e9	−1.24443
$593$	2.32977e9	0.458799	0.229399	−	0.973332i	$-0.426324\pi$
$593$	2.32977e9	0.458799	0.229399	+	0.973332i	$0.426324\pi$
$594$	4.87662e8	0.0954699
$595$	1.18723e10	2.31060
$596$	−5.33851e8	−0.103290
$597$	−3.99863e8	−0.0769132
$598$	−5.54421e9	−1.06019
$599$	4.44687e9	0.845396	0.422698	−	0.906271i	$-0.361083\pi$
$599$	4.44687e9	0.845396	0.422698	+	0.906271i	$0.361083\pi$
$600$	−5.32196e9	−1.00587
$601$	−3.49187e9	−0.656142	−0.328071	−	0.944653i	$-0.606398\pi$
$601$	−3.49187e9	−0.656142	−0.328071	+	0.944653i	$0.606398\pi$
$602$	−6.70710e9	−1.25299
$603$	2.02350e9	0.375831
$604$	−3.97074e8	−0.0733233
$605$	6.44661e9	1.18355
$606$	−3.59596e9	−0.656389
$607$	−5.86644e9	−1.06467	−0.532334	−	0.846534i	$-0.678685\pi$
$607$	−5.86644e9	−1.06467	−0.532334	+	0.846534i	$0.678685\pi$
$608$	−1.95062e9	−0.351974
$609$	−5.92288e9	−1.06261
$610$	−4.20162e9	−0.749484
$611$	9.26909e9	1.64397
$612$	−2.07029e8	−0.0365091
$613$	6.04198e9	1.05942	0.529709	−	0.848180i	$-0.322301\pi$
$613$	6.04198e9	1.05942	0.529709	+	0.848180i	$0.322301\pi$
$614$	−8.53834e9	−1.48862
$615$	5.21748e9	0.904478
$616$	−4.34355e9	−0.748707
$617$	3.65017e9	0.625627	0.312813	−	0.949815i	$-0.398729\pi$
$617$	3.65017e9	0.625627	0.312813	+	0.949815i	$0.398729\pi$
$618$	−3.02422e9	−0.515411
$619$	6.57436e9	1.11413	0.557065	−	0.830469i	$-0.311927\pi$
$619$	6.57436e9	1.11413	0.557065	+	0.830469i	$0.311927\pi$
$620$	−8.02249e8	−0.135188
$621$	−1.10011e9	−0.184338
$622$	1.14642e9	0.191020
$623$	−1.13416e10	−1.87916
$624$	3.62219e9	0.596796
$625$	6.71741e8	0.110058
$626$	1.04124e10	1.69644
$627$	−3.12718e9	−0.506660
$628$	5.23357e7	0.00843217
$629$	9.11656e9	1.46068
$630$	−4.40976e9	−0.702624
$631$	6.70535e9	1.06247	0.531237	−	0.847223i	$-0.321727\pi$
$631$	6.70535e9	1.06247	0.531237	+	0.847223i	$0.321727\pi$
$632$	7.26703e9	1.14511
$633$	3.28255e9	0.514397
$634$	3.02591e9	0.471567
$635$	3.35446e9	0.519893
$636$	−6.99591e8	−0.107831
$637$	6.59170e9	1.01044
$638$	4.38742e9	0.668863
$639$	4.00152e9	0.606697
$640$	8.80370e9	1.32750
$641$	1.17608e10	1.76373	0.881865	−	0.471503i	$-0.156288\pi$
$641$	1.17608e10	1.76373	0.881865	+	0.471503i	$0.156288\pi$
$642$	3.70824e9	0.553090
$643$	5.23932e9	0.777206	0.388603	−	0.921405i	$-0.372958\pi$
$643$	5.23932e9	0.777206	0.388603	+	0.921405i	$0.372958\pi$
$644$	9.36334e8	0.138143
$645$	−6.23586e9	−0.915034
$646$	−1.12378e10	−1.64009
$647$	6.24704e8	0.0906795	0.0453397	−	0.998972i	$-0.485563\pi$
$647$	6.24704e8	0.0906795	0.0453397	+	0.998972i	$0.485563\pi$
$648$	8.04715e8	0.116180
$649$	−2.75283e9	−0.395297
$650$	−1.29127e10	−1.84425
$651$	−4.34729e9	−0.617568
$652$	9.40838e8	0.132938
$653$	6.31463e9	0.887466	0.443733	−	0.896159i	$-0.353654\pi$
$653$	6.31463e9	0.887466	0.443733	+	0.896159i	$0.353654\pi$
$654$	−3.43313e8	−0.0479919
$655$	3.79355e9	0.527475
$656$	−6.12668e9	−0.847348
$657$	4.08930e9	0.562562
$658$	1.32509e10	1.81323
$659$	−7.84070e9	−1.06722	−0.533612	−	0.845729i	$-0.679166\pi$
$659$	−7.84070e9	−1.06722	−0.533612	+	0.845729i	$0.679166\pi$
$660$	−3.85901e8	−0.0522483
$661$	6.12926e8	0.0825473	0.0412737	−	0.999148i	$-0.486858\pi$
$661$	6.12926e8	0.0825473	0.0412737	+	0.999148i	$0.486858\pi$
$662$	7.60068e8	0.101824
$663$	−5.25660e9	−0.700500
$664$	7.23787e9	0.959451
$665$	2.82780e10	3.72883
$666$	−3.38620e9	−0.444173
$667$	−9.89751e9	−1.29147
$668$	1.10755e9	0.143763
$669$	1.11509e9	0.143985
$670$	1.35543e10	1.74106
$671$	−1.99245e9	−0.254600
$672$	−1.30438e9	−0.165811
$673$	−4.65572e8	−0.0588754	−0.0294377	−	0.999567i	$-0.509372\pi$
$673$	−4.65572e8	−0.0588754	−0.0294377	+	0.999567i	$0.509372\pi$
$674$	−1.91759e9	−0.241238
$675$	−2.56220e9	−0.320663
$676$	−3.13851e8	−0.0390760
$677$	−6.35069e9	−0.786612	−0.393306	−	0.919408i	$-0.628669\pi$
$677$	−6.35069e9	−0.786612	−0.393306	+	0.919408i	$0.628669\pi$
$678$	4.47978e9	0.552017
$679$	−3.47698e9	−0.426244
$680$	−1.45122e10	−1.76992
$681$	−8.31633e8	−0.100906
$682$	3.22029e9	0.388731
$683$	4.85673e9	0.583272	0.291636	−	0.956529i	$-0.405800\pi$
$683$	4.85673e9	0.583272	0.291636	+	0.956529i	$0.405800\pi$
$684$	−4.93112e8	−0.0589182
$685$	8.53895e9	1.01505
$686$	−1.49184e9	−0.176437
$687$	1.07685e8	0.0126709
$688$	7.32251e9	0.857237
$689$	−1.77631e10	−2.06896
$690$	−7.36900e9	−0.853958
$691$	−1.24944e9	−0.144060	−0.0720300	−	0.997402i	$-0.522948\pi$
$691$	−1.24944e9	−0.144060	−0.0720300	+	0.997402i	$0.522948\pi$
$692$	−1.08119e9	−0.124031
$693$	−2.09115e9	−0.238681
$694$	−2.28475e9	−0.259466
$695$	2.50095e10	2.82591
$696$	7.23990e9	0.813955
$697$	8.89117e9	0.994590
$698$	2.97394e9	0.331008
$699$	2.05338e9	0.227404
$700$	2.18076e9	0.240306
$701$	5.45420e9	0.598023	0.299012	−	0.954249i	$-0.403343\pi$
$701$	5.45420e9	0.598023	0.299012	+	0.954249i	$0.403343\pi$
$702$	1.95248e9	0.213013
$703$	2.17143e10	2.35723
$704$	5.25518e9	0.567653
$705$	1.23199e10	1.32417
$706$	1.30139e10	1.39184
$707$	1.54199e10	1.64102
$708$	−4.34083e8	−0.0459680
$709$	−7.30504e9	−0.769770	−0.384885	−	0.922965i	$-0.625759\pi$
$709$	−7.30504e9	−0.769770	−0.384885	+	0.922965i	$0.625759\pi$
$710$	2.68039e10	2.81056
$711$	3.49862e9	0.365051
$712$	1.38635e10	1.43944
$713$	−7.26460e9	−0.750582
$714$	−7.51472e9	−0.772625
$715$	−9.79829e9	−1.00249
$716$	−1.05861e9	−0.107781
$717$	1.60185e9	0.162295
$718$	1.46283e10	1.47489
$719$	−9.04087e9	−0.907108	−0.453554	−	0.891229i	$-0.649844\pi$
$719$	−9.04087e9	−0.907108	−0.453554	+	0.891229i	$0.649844\pi$
$720$	4.81438e9	0.480703
$721$	1.29682e10	1.28856
$722$	−1.72029e10	−1.70107
$723$	−9.68246e9	−0.952800
$724$	1.71284e9	0.167739
$725$	−2.30517e10	−2.24657
$726$	−4.08047e9	−0.395760
$727$	−8.95674e9	−0.864529	−0.432264	−	0.901747i	$-0.642285\pi$
$727$	−8.95674e9	−0.864529	−0.432264	+	0.901747i	$0.642285\pi$
$728$	−1.73905e10	−1.67052
$729$	3.87420e8	0.0370370
$730$	2.73919e10	2.60610
$731$	−1.06266e10	−1.00620
$732$	−3.14181e8	−0.0296068
$733$	4.85536e9	0.455362	0.227681	−	0.973736i	$-0.426886\pi$
$733$	4.85536e9	0.455362	0.227681	+	0.973736i	$0.426886\pi$
$734$	−6.17124e8	−0.0576018
$735$	8.76126e9	0.813881
$736$	−2.17971e9	−0.201524
$737$	6.42755e9	0.591438
$738$	−3.30248e9	−0.302442
$739$	2.66176e8	0.0242613	0.0121306	−	0.999926i	$-0.496139\pi$
$739$	2.66176e8	0.0242613	0.0121306	+	0.999926i	$0.496139\pi$
$740$	2.67959e9	0.243085
$741$	−1.25205e10	−1.13046
$742$	−2.53937e10	−2.28199
$743$	1.89177e10	1.69203	0.846015	−	0.533159i	$-0.178995\pi$
$743$	1.89177e10	1.69203	0.846015	+	0.533159i	$0.178995\pi$
$744$	5.31396e9	0.473056
$745$	−1.80162e10	−1.59631
$746$	1.77997e10	1.56974
$747$	3.48459e9	0.305865
$748$	−6.57617e8	−0.0574536
$749$	−1.59014e10	−1.38276
$750$	−6.86228e9	−0.593956
$751$	1.66411e10	1.43365	0.716825	−	0.697253i	$-0.245595\pi$
$751$	1.66411e10	1.43365	0.716825	+	0.697253i	$0.245595\pi$
$752$	−1.44667e10	−1.24053
$753$	−8.24483e9	−0.703719
$754$	1.75662e10	1.49237
$755$	−1.34003e10	−1.13318
$756$	−3.29745e8	−0.0277557
$757$	−2.85616e9	−0.239302	−0.119651	−	0.992816i	$-0.538178\pi$
$757$	−2.85616e9	−0.239302	−0.119651	+	0.992816i	$0.538178\pi$
$758$	−4.91274e9	−0.409715
$759$	−3.49444e9	−0.290089
$760$	−3.45660e10	−2.85628
$761$	1.57557e10	1.29596	0.647982	−	0.761656i	$-0.275613\pi$
$761$	1.57557e10	1.29596	0.647982	+	0.761656i	$0.275613\pi$
$762$	−2.12325e9	−0.173844
$763$	1.47216e9	0.119983
$764$	−1.14388e9	−0.0928010
$765$	−6.98673e9	−0.564234
$766$	2.07410e7	0.00166736
$767$	−1.10217e10	−0.881989
$768$	2.27073e9	0.180885
$769$	−1.94993e10	−1.54624	−0.773120	−	0.634260i	$-0.781305\pi$
$769$	−1.94993e10	−1.54624	−0.773120	+	0.634260i	$0.781305\pi$
$770$	−1.40074e10	−1.10571
$771$	5.00110e9	0.392984
$772$	−2.21663e9	−0.173394
$773$	3.38638e9	0.263698	0.131849	−	0.991270i	$-0.457909\pi$
$773$	3.38638e9	0.263698	0.131849	+	0.991270i	$0.457909\pi$
$774$	3.94707e9	0.305972
$775$	−1.69195e10	−1.30567
$776$	4.25013e9	0.326502
$777$	1.45204e10	1.11046
$778$	−5.11418e9	−0.389357
$779$	2.11775e10	1.60506
$780$	−1.54505e9	−0.116577
$781$	1.27106e10	0.954748
$782$	−1.25576e10	−0.939036
$783$	3.48556e9	0.259482
$784$	−1.02880e10	−0.762472
$785$	1.76621e9	0.130316
$786$	−2.40118e9	−0.176379
$787$	1.09007e10	0.797156	0.398578	−	0.917134i	$-0.369504\pi$
$787$	1.09007e10	0.797156	0.398578	+	0.917134i	$0.369504\pi$
$788$	8.97696e8	0.0653563
$789$	−1.04392e10	−0.756652
$790$	2.34353e10	1.69112
$791$	−1.92098e10	−1.38008
$792$	2.55614e9	0.182830
$793$	−7.97727e9	−0.568065
$794$	−2.37876e10	−1.68647
$795$	−2.36096e10	−1.66649
$796$	−2.00284e8	−0.0140751
$797$	1.92449e7	0.00134652	0.000673259	−	1.00000i	$-0.499786\pi$
$797$	1.92449e7	0.00134652	0.000673259		1.00000i	$0.499786\pi$
$798$	−1.78990e10	−1.24686
$799$	2.09944e10	1.45609
$800$	−5.07662e9	−0.350558
$801$	6.67441e9	0.458880
$802$	−1.53094e10	−1.04797
$803$	1.29895e10	0.885293
$804$	1.01353e9	0.0687768
$805$	3.15991e10	2.13495
$806$	1.28933e10	0.867341
$807$	−5.73813e8	−0.0384338
$808$	−1.88487e10	−1.25702
$809$	−1.07946e10	−0.716780	−0.358390	−	0.933572i	$-0.616674\pi$
$809$	−1.07946e10	−0.716780	−0.358390	+	0.933572i	$0.616674\pi$
$810$	2.59511e9	0.171576
$811$	−2.24387e10	−1.47715	−0.738576	−	0.674170i	$-0.764501\pi$
$811$	−2.24387e10	−1.47715	−0.738576	+	0.674170i	$0.764501\pi$
$812$	−2.96666e9	−0.194456
$813$	1.50963e10	0.985266
$814$	−1.07561e10	−0.698987
$815$	3.17511e10	2.05450
$816$	8.20423e9	0.528594
$817$	−2.53110e10	−1.62380
$818$	7.93596e9	0.506948
$819$	−8.37245e9	−0.532548
$820$	2.61334e9	0.165519
$821$	−1.32125e10	−0.833267	−0.416633	−	0.909075i	$-0.636790\pi$
$821$	−1.32125e10	−0.833267	−0.416633	+	0.909075i	$0.636790\pi$
$822$	−5.40484e9	−0.339416
$823$	1.82471e10	1.14102	0.570510	−	0.821290i	$-0.306745\pi$
$823$	1.82471e10	1.14102	0.570510	+	0.821290i	$0.306745\pi$
$824$	−1.58518e10	−0.987039
$825$	−8.13870e9	−0.504622
$826$	−1.57563e10	−0.972802
$827$	−2.87244e10	−1.76596	−0.882981	−	0.469408i	$-0.844467\pi$
$827$	−2.87244e10	−1.76596	−0.882981	+	0.469408i	$0.844467\pi$
$828$	−5.51025e8	−0.0337338
$829$	−1.46621e10	−0.893832	−0.446916	−	0.894576i	$-0.647478\pi$
$829$	−1.46621e10	−0.893832	−0.446916	+	0.894576i	$0.647478\pi$
$830$	2.33412e10	1.41694
$831$	2.53157e9	0.153033
$832$	2.10404e10	1.26655
$833$	1.49301e10	0.894966
$834$	−1.58301e10	−0.944937
$835$	3.73772e10	2.22180
$836$	−1.56635e9	−0.0927184
$837$	2.55834e9	0.150806
$838$	−5.86607e8	−0.0344345
$839$	−9.16487e9	−0.535747	−0.267873	−	0.963454i	$-0.586321\pi$
$839$	−9.16487e9	−0.535747	−0.267873	+	0.963454i	$0.586321\pi$
$840$	−2.31143e10	−1.34556
$841$	1.41092e10	0.817932
$842$	1.42324e10	0.821647
$843$	−1.70168e10	−0.978321
$844$	1.64417e9	0.0941344
$845$	−1.05917e10	−0.603905
$846$	−7.79802e9	−0.442780
$847$	1.74975e10	0.989428
$848$	2.77237e10	1.56123
$849$	−3.33003e8	−0.0186755
$850$	−2.92471e10	−1.63349
$851$	2.42645e10	1.34964
$852$	2.00429e9	0.111025
$853$	−2.57032e10	−1.41797	−0.708984	−	0.705225i	$-0.750846\pi$
$853$	−2.57032e10	−1.41797	−0.708984	+	0.705225i	$0.750846\pi$
$854$	−1.14041e10	−0.626555
$855$	−1.66414e10	−0.910558
$856$	1.94372e10	1.05919
$857$	−5.93459e9	−0.322075	−0.161038	−	0.986948i	$-0.551484\pi$
$857$	−5.93459e9	−0.322075	−0.161038	+	0.986948i	$0.551484\pi$
$858$	6.20196e9	0.335215
$859$	−8.75307e9	−0.471177	−0.235589	−	0.971853i	$-0.575702\pi$
$859$	−8.75307e9	−0.471177	−0.235589	+	0.971853i	$0.575702\pi$
$860$	−3.12343e9	−0.167451
$861$	1.41614e10	0.756127
$862$	−1.05350e10	−0.560223
$863$	2.26154e10	1.19775	0.598876	−	0.800842i	$-0.295614\pi$
$863$	2.26154e10	1.19775	0.598876	+	0.800842i	$0.295614\pi$
$864$	7.67618e8	0.0404899
$865$	−3.64875e10	−1.91685
$866$	2.30129e10	1.20409
$867$	−8.27012e8	−0.0430968
$868$	−2.17748e9	−0.113015
$869$	1.11132e10	0.574474
$870$	2.33478e10	1.20207
$871$	2.57343e10	1.31962
$872$	−1.79952e9	−0.0919068
$873$	2.04617e9	0.104086
$874$	−2.99103e10	−1.51541
$875$	2.94262e10	1.48493
$876$	2.04826e9	0.102949
$877$	−3.13064e10	−1.56724	−0.783619	−	0.621242i	$-0.786629\pi$
$877$	−3.13064e10	−1.56724	−0.783619	+	0.621242i	$0.786629\pi$
$878$	−1.53742e10	−0.766585
$879$	−1.10320e10	−0.547888
$880$	1.52927e10	0.756473
$881$	−1.89949e10	−0.935881	−0.467941	−	0.883760i	$-0.655004\pi$
$881$	−1.89949e10	−0.935881	−0.467941	+	0.883760i	$0.655004\pi$
$882$	−5.54556e9	−0.272148
$883$	4.37542e9	0.213874	0.106937	−	0.994266i	$-0.465896\pi$
$883$	4.37542e9	0.213874	0.106937	+	0.994266i	$0.465896\pi$
$884$	−2.63294e9	−0.128191
$885$	−1.46493e10	−0.710419
$886$	2.81334e10	1.35895
$887$	1.81463e10	0.873081	0.436541	−	0.899685i	$-0.356204\pi$
$887$	1.81463e10	0.873081	0.436541	+	0.899685i	$0.356204\pi$
$888$	−1.77492e10	−0.850614
$889$	9.10473e9	0.434621
$890$	4.47081e10	2.12579
$891$	1.23062e9	0.0582845
$892$	5.58526e8	0.0263491
$893$	5.00056e10	2.34984
$894$	1.14036e10	0.533779
$895$	−3.57257e10	−1.66571
$896$	2.38952e10	1.10977
$897$	−1.39909e10	−0.647250
$898$	−2.13304e10	−0.982949
$899$	2.30170e10	1.05655
$900$	−1.28336e9	−0.0586812
$901$	−4.02333e10	−1.83252
$902$	−1.04902e10	−0.475948
$903$	−1.69255e10	−0.764952
$904$	2.34813e10	1.05714
$905$	5.78044e10	2.59234
$906$	8.48190e9	0.378917
$907$	1.79770e10	0.800003	0.400001	−	0.916514i	$-0.369010\pi$
$907$	1.79770e10	0.800003	0.400001	+	0.916514i	$0.369010\pi$
$908$	−4.16550e8	−0.0184657
$909$	−9.07447e9	−0.400726
$910$	−5.60822e10	−2.46706
$911$	−9.78598e9	−0.428835	−0.214417	−	0.976742i	$-0.568785\pi$
$911$	−9.78598e9	−0.428835	−0.214417	+	0.976742i	$0.568785\pi$
$912$	1.95413e10	0.853043
$913$	1.10686e10	0.481334
$914$	−4.20909e9	−0.182338
$915$	−1.06029e10	−0.457561
$916$	5.39377e7	0.00231877
$917$	1.02965e10	0.440959
$918$	4.42235e9	0.188670
$919$	3.08706e10	1.31202	0.656011	−	0.754751i	$-0.272242\pi$
$919$	3.08706e10	1.31202	0.656011	+	0.754751i	$0.272242\pi$
$920$	−3.86255e10	−1.63537
$921$	−2.15467e10	−0.908806
$922$	−2.36770e10	−0.994873
$923$	5.08903e10	2.13024
$924$	−1.04742e9	−0.0436786
$925$	5.65130e10	2.34775
$926$	2.85490e10	1.18155
$927$	−7.63167e9	−0.314659
$928$	6.90614e9	0.283673
$929$	4.52197e10	1.85043	0.925215	−	0.379444i	$-0.123885\pi$
$929$	4.52197e10	1.85043	0.925215	+	0.379444i	$0.123885\pi$
$930$	1.71369e10	0.698620
$931$	3.55614e10	1.44429
$932$	1.02850e9	0.0416149
$933$	2.89301e9	0.116618
$934$	−2.64843e10	−1.06359
$935$	−2.21930e10	−0.887924
$936$	1.02342e10	0.407931
$937$	2.51357e10	0.998164	0.499082	−	0.866555i	$-0.333671\pi$
$937$	2.51357e10	0.998164	0.499082	+	0.866555i	$0.333671\pi$
$938$	3.67892e10	1.45549
$939$	2.62757e10	1.03568
$940$	6.17080e9	0.242322
$941$	4.23443e10	1.65665	0.828326	−	0.560246i	$-0.189293\pi$
$941$	4.23443e10	1.65665	0.828326	+	0.560246i	$0.189293\pi$
$942$	−1.11794e9	−0.0435755
$943$	2.36646e10	0.918984
$944$	1.72020e10	0.665546
$945$	−1.11281e10	−0.428953
$946$	1.25377e10	0.481503
$947$	2.06011e10	0.788252	0.394126	−	0.919056i	$-0.371047\pi$
$947$	2.06011e10	0.788252	0.394126	+	0.919056i	$0.371047\pi$
$948$	1.75240e9	0.0668042
$949$	5.20067e10	1.97527
$950$	−6.96623e10	−2.63612
$951$	7.63593e9	0.287892
$952$	−3.93893e10	−1.47962
$953$	−1.90908e10	−0.714496	−0.357248	−	0.934010i	$-0.616285\pi$
$953$	−1.90908e10	−0.714496	−0.357248	+	0.934010i	$0.616285\pi$
$954$	1.49440e10	0.557246
$955$	−3.86032e10	−1.43420
$956$	8.02339e8	0.0296999
$957$	1.10717e10	0.408342
$958$	−2.76035e10	−1.01434
$959$	2.31766e10	0.848563
$960$	2.79656e10	1.02017
$961$	−1.06185e10	−0.385951
$962$	−4.30648e10	−1.55959
$963$	9.35781e9	0.337662
$964$	−4.84977e9	−0.174362
$965$	−7.48061e10	−2.67973
$966$	−2.00011e10	−0.713893
$967$	−3.16846e10	−1.12682	−0.563411	−	0.826177i	$-0.690511\pi$
$967$	−3.16846e10	−1.12682	−0.563411	+	0.826177i	$0.690511\pi$
$968$	−2.13883e10	−0.757900
$969$	−2.83587e10	−1.00128
$970$	1.37061e10	0.482185
$971$	−2.21542e10	−0.776583	−0.388292	−	0.921537i	$-0.626935\pi$
$971$	−2.21542e10	−0.776583	−0.388292	+	0.921537i	$0.626935\pi$
$972$	1.94052e8	0.00677776
$973$	6.78813e10	2.36241
$974$	4.92016e10	1.70617
$975$	−3.25854e10	−1.12592
$976$	1.24505e10	0.428660
$977$	−1.09848e10	−0.376844	−0.188422	−	0.982088i	$-0.560337\pi$
$977$	−1.09848e10	−0.376844	−0.188422	+	0.982088i	$0.560337\pi$
$978$	−2.00973e10	−0.686991
$979$	2.12010e10	0.722131
$980$	4.38836e9	0.148940
$981$	−8.66355e8	−0.0292991
$982$	5.84044e9	0.196814
$983$	4.36794e10	1.46669	0.733347	−	0.679854i	$-0.237957\pi$
$983$	4.36794e10	1.46669	0.733347	+	0.679854i	$0.237957\pi$
$984$	−1.73103e10	−0.579192
$985$	3.02951e10	1.01006
$986$	3.97872e10	1.32183
$987$	3.34388e10	1.10698
$988$	−6.27127e9	−0.206874
$989$	−2.82836e10	−0.929710
$990$	8.24324e9	0.270007
$991$	2.27500e10	0.742545	0.371273	−	0.928524i	$-0.378922\pi$
$991$	2.27500e10	0.742545	0.371273	+	0.928524i	$0.378922\pi$
$992$	5.06899e9	0.164866
$993$	1.91804e9	0.0621636
$994$	7.27516e10	2.34958
$995$	−6.75911e9	−0.217525
$996$	1.74537e9	0.0559731
$997$	−2.02661e10	−0.647646	−0.323823	−	0.946118i	$-0.604968\pi$
$997$	−2.02661e10	−0.647646	−0.323823	+	0.946118i	$0.604968\pi$
$998$	4.61723e10	1.47036
$999$	−8.54512e9	−0.271168

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.8.a.c.1.14	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.8.a.c.1.14	✓	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)

\(f(q)\)	\(=\)	\(q-10.6994 q^{2} -27.0000 q^{3} -13.5238 q^{4} -456.397 q^{5} +288.883 q^{6} -1238.76 q^{7} +1514.21 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-10.6994 q^{2} -27.0000 q^{3} -13.5238 q^{4} -456.397 q^{5} +288.883 q^{6} -1238.76 q^{7} +1514.21 q^{8} +729.000 q^{9} +4883.15 q^{10} +2315.63 q^{11} +365.143 q^{12} +9271.23 q^{13} +13253.9 q^{14} +12322.7 q^{15} -14470.1 q^{16} +20999.3 q^{17} -7799.83 q^{18} +50017.2 q^{19} +6172.23 q^{20} +33446.5 q^{21} -24775.8 q^{22} +55891.3 q^{23} -40883.8 q^{24} +130173. q^{25} -99196.2 q^{26} -19683.0 q^{27} +16752.8 q^{28} -177085. q^{29} -131845. q^{30} -129977. q^{31} -38999.0 q^{32} -62522.1 q^{33} -224678. q^{34} +565366. q^{35} -9858.86 q^{36} +434137. q^{37} -535151. q^{38} -250323. q^{39} -691082. q^{40} +423404. q^{41} -357856. q^{42} -506046. q^{43} -31316.2 q^{44} -332713. q^{45} -598001. q^{46} +999769. q^{47} +390692. q^{48} +710984. q^{49} -1.39277e6 q^{50} -566980. q^{51} -125382. q^{52} -1.91594e6 q^{53} +210595. q^{54} -1.05685e6 q^{55} -1.87575e6 q^{56} -1.35046e6 q^{57} +1.89470e6 q^{58} -1.18880e6 q^{59} -166650. q^{60} -860432. q^{61} +1.39067e6 q^{62} -903056. q^{63} +2.26943e6 q^{64} -4.23136e6 q^{65} +668946. q^{66} +2.77572e6 q^{67} -283990. q^{68} -1.50907e6 q^{69} -6.04905e6 q^{70} +5.48905e6 q^{71} +1.10386e6 q^{72} +5.60947e6 q^{73} -4.64499e6 q^{74} -3.51467e6 q^{75} -676423. q^{76} -2.86852e6 q^{77} +2.67830e6 q^{78} +4.79921e6 q^{79} +6.60409e6 q^{80} +531441. q^{81} -4.53015e6 q^{82} +4.77996e6 q^{83} -452325. q^{84} -9.58399e6 q^{85} +5.41437e6 q^{86} +4.78129e6 q^{87} +3.50637e6 q^{88} +9.15557e6 q^{89} +3.55982e6 q^{90} -1.14848e7 q^{91} -755864. q^{92} +3.50939e6 q^{93} -1.06969e7 q^{94} -2.28277e7 q^{95} +1.05297e6 q^{96} +2.80682e6 q^{97} -7.60707e6 q^{98} +1.68810e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{2} - 1296 q^{3} + 3214 q^{4} + 428 q^{5} - 54 q^{6} - 680 q^{7} + 2355 q^{8} + 34992 q^{9}+O(q^{10}) \) 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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