LMFDB - Embedded newform 471.8.a.c.1.17

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			1.17
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)

$f(q)$	$=$	$q-8.95758 q^{2} -27.0000 q^{3} -47.7618 q^{4} +476.788 q^{5} +241.855 q^{6} +984.094 q^{7} +1574.40 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-8.95758 q^{2} -27.0000 q^{3} -47.7618 q^{4} +476.788 q^{5} +241.855 q^{6} +984.094 q^{7} +1574.40 q^{8} +729.000 q^{9} -4270.87 q^{10} -2919.95 q^{11} +1289.57 q^{12} -1431.95 q^{13} -8815.10 q^{14} -12873.3 q^{15} -7989.31 q^{16} +20172.9 q^{17} -6530.08 q^{18} +18680.6 q^{19} -22772.2 q^{20} -26570.5 q^{21} +26155.7 q^{22} +3261.92 q^{23} -42508.8 q^{24} +149202. q^{25} +12826.8 q^{26} -19683.0 q^{27} -47002.0 q^{28} +242826. q^{29} +115313. q^{30} -162855. q^{31} -129958. q^{32} +78838.5 q^{33} -180701. q^{34} +469204. q^{35} -34818.3 q^{36} +517481. q^{37} -167333. q^{38} +38662.8 q^{39} +750655. q^{40} +460743. q^{41} +238008. q^{42} +369436. q^{43} +139462. q^{44} +347579. q^{45} -29218.9 q^{46} +313005. q^{47} +215711. q^{48} +144898. q^{49} -1.33649e6 q^{50} -544670. q^{51} +68392.6 q^{52} -481761. q^{53} +176312. q^{54} -1.39220e6 q^{55} +1.54936e6 q^{56} -504375. q^{57} -2.17513e6 q^{58} -319815. q^{59} +614851. q^{60} +453891. q^{61} +1.45879e6 q^{62} +717404. q^{63} +2.18674e6 q^{64} -682739. q^{65} -706203. q^{66} +2.72796e6 q^{67} -963495. q^{68} -88071.8 q^{69} -4.20294e6 q^{70} -4.69550e6 q^{71} +1.14774e6 q^{72} -2.66237e6 q^{73} -4.63538e6 q^{74} -4.02845e6 q^{75} -892217. q^{76} -2.87350e6 q^{77} -346325. q^{78} +4.39210e6 q^{79} -3.80921e6 q^{80} +531441. q^{81} -4.12714e6 q^{82} -8.73826e6 q^{83} +1.26906e6 q^{84} +9.61822e6 q^{85} -3.30925e6 q^{86} -6.55629e6 q^{87} -4.59716e6 q^{88} -3.36582e6 q^{89} -3.11346e6 q^{90} -1.40918e6 q^{91} -155795. q^{92} +4.39708e6 q^{93} -2.80377e6 q^{94} +8.90668e6 q^{95} +3.50887e6 q^{96} +1.69061e7 q^{97} -1.29793e6 q^{98} -2.12864e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−8.95758	−0.791746	−0.395873	−	0.918305i	$-0.629558\pi$
$2$	−8.95758	−0.791746	−0.395873	+	0.918305i	$0.629558\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	−47.7618	−0.373139
$5$	476.788	1.70581	0.852905	−	0.522067i	$-0.174839\pi$
$5$	476.788	1.70581	0.852905	+	0.522067i	$0.174839\pi$
$6$	241.855	0.457115
$7$	984.094	1.08441	0.542205	−	0.840246i	$-0.317590\pi$
$7$	984.094	1.08441	0.542205	+	0.840246i	$0.317590\pi$
$8$	1574.40	1.08718
$9$	729.000	0.333333
$10$	−4270.87	−1.35057
$11$	−2919.95	−0.661455	−0.330728	−	0.943726i	$-0.607294\pi$
$11$	−2919.95	−0.661455	−0.330728	+	0.943726i	$0.607294\pi$
$12$	1289.57	0.215432
$13$	−1431.95	−0.180770	−0.0903852	−	0.995907i	$-0.528810\pi$
$13$	−1431.95	−0.180770	−0.0903852	+	0.995907i	$0.528810\pi$
$14$	−8815.10	−0.858577
$15$	−12873.3	−0.984850
$16$	−7989.31	−0.487629
$17$	20172.9	0.995860	0.497930	−	0.867217i	$-0.334094\pi$
$17$	20172.9	0.995860	0.497930	+	0.867217i	$0.334094\pi$
$18$	−6530.08	−0.263915
$19$	18680.6	0.624817	0.312408	−	0.949948i	$-0.398864\pi$
$19$	18680.6	0.624817	0.312408	+	0.949948i	$0.398864\pi$
$20$	−22772.2	−0.636503
$21$	−26570.5	−0.626084
$22$	26155.7	0.523704
$23$	3261.92	0.0559018	0.0279509	−	0.999609i	$-0.491102\pi$
$23$	3261.92	0.0559018	0.0279509	+	0.999609i	$0.491102\pi$
$24$	−42508.8	−0.627682
$25$	149202.	1.90979
$26$	12826.8	0.143124
$27$	−19683.0	−0.192450
$28$	−47002.0	−0.404635
$29$	242826.	1.84885	0.924424	−	0.381366i	$-0.124546\pi$
$29$	242826.	1.84885	0.924424	+	0.381366i	$0.124546\pi$
$30$	115313.	0.779750
$31$	−162855.	−0.981827	−0.490914	−	0.871208i	$-0.663337\pi$
$31$	−162855.	−0.981827	−0.490914	+	0.871208i	$0.663337\pi$
$32$	−129958.	−0.701099
$33$	78838.5	0.381891
$34$	−180701.	−0.788468
$35$	469204.	1.84980
$36$	−34818.3	−0.124380
$37$	517481.	1.67953	0.839766	−	0.542948i	$-0.182692\pi$
$37$	517481.	1.67953	0.839766	+	0.542948i	$0.182692\pi$
$38$	−167333.	−0.494696
$39$	38662.8	0.104368
$40$	750655.	1.85452
$41$	460743.	1.04403	0.522017	−	0.852935i	$-0.325180\pi$
$41$	460743.	1.04403	0.522017	+	0.852935i	$0.325180\pi$
$42$	238008.	0.495699
$43$	369436.	0.708597	0.354298	−	0.935132i	$-0.384720\pi$
$43$	369436.	0.708597	0.354298	+	0.935132i	$0.384720\pi$
$44$	139462.	0.246814
$45$	347579.	0.568603
$46$	−29218.9	−0.0442600
$47$	313005.	0.439753	0.219876	−	0.975528i	$-0.429435\pi$
$47$	313005.	0.439753	0.219876	+	0.975528i	$0.429435\pi$
$48$	215711.	0.281533
$49$	144898.	0.175944
$50$	−1.33649e6	−1.51206
$51$	−544670.	−0.574960
$52$	68392.6	0.0674524
$53$	−481761.	−0.444494	−0.222247	−	0.974990i	$-0.571339\pi$
$53$	−481761.	−0.444494	−0.222247	+	0.974990i	$0.571339\pi$
$54$	176312.	0.152372
$55$	−1.39220e6	−1.12832
$56$	1.54936e6	1.17894
$57$	−504375.	−0.360738
$58$	−2.17513e6	−1.46382
$59$	−319815.	−0.202730	−0.101365	−	0.994849i	$-0.532321\pi$
$59$	−319815.	−0.202730	−0.101365	+	0.994849i	$0.532321\pi$
$60$	614851.	0.367485
$61$	453891.	0.256033	0.128017	−	0.991772i	$-0.459139\pi$
$61$	453891.	0.256033	0.128017	+	0.991772i	$0.459139\pi$
$62$	1.45879e6	0.777358
$63$	717404.	0.361470
$64$	2.18674e6	1.04272
$65$	−682739.	−0.308360
$66$	−706203.	−0.302361
$67$	2.72796e6	1.10809	0.554046	−	0.832486i	$-0.313083\pi$
$67$	2.72796e6	1.10809	0.554046	+	0.832486i	$0.313083\pi$
$68$	−963495.	−0.371594
$69$	−88071.8	−0.0322749
$70$	−4.20294e6	−1.46457
$71$	−4.69550e6	−1.55696	−0.778481	−	0.627668i	$-0.784009\pi$
$71$	−4.69550e6	−1.55696	−0.778481	+	0.627668i	$0.784009\pi$
$72$	1.14774e6	0.362392
$73$	−2.66237e6	−0.801010	−0.400505	−	0.916295i	$-0.631165\pi$
$73$	−2.66237e6	−0.801010	−0.400505	+	0.916295i	$0.631165\pi$
$74$	−4.63538e6	−1.32976
$75$	−4.02845e6	−1.10262
$76$	−892217.	−0.233143
$77$	−2.87350e6	−0.717288
$78$	−346325.	−0.0826328
$79$	4.39210e6	1.00225	0.501126	−	0.865374i	$-0.332919\pi$
$79$	4.39210e6	1.00225	0.501126	+	0.865374i	$0.332919\pi$
$80$	−3.80921e6	−0.831802
$81$	531441.	0.111111
$82$	−4.12714e6	−0.826610
$83$	−8.73826e6	−1.67746	−0.838729	−	0.544549i	$-0.816701\pi$
$83$	−8.73826e6	−1.67746	−0.838729	+	0.544549i	$0.816701\pi$
$84$	1.26906e6	0.233616
$85$	9.61822e6	1.69875
$86$	−3.30925e6	−0.561028
$87$	−6.55629e6	−1.06743
$88$	−4.59716e6	−0.719119
$89$	−3.36582e6	−0.506088	−0.253044	−	0.967455i	$-0.581432\pi$
$89$	−3.36582e6	−0.506088	−0.253044	+	0.967455i	$0.581432\pi$
$90$	−3.11346e6	−0.450189
$91$	−1.40918e6	−0.196029
$92$	−155795.	−0.0208591
$93$	4.39708e6	0.566858
$94$	−2.80377e6	−0.348173
$95$	8.90668e6	1.06582
$96$	3.50887e6	0.404779
$97$	1.69061e7	1.88080	0.940402	−	0.340065i	$-0.110449\pi$
$97$	1.69061e7	1.88080	0.940402	+	0.340065i	$0.110449\pi$
$98$	−1.29793e6	−0.139303
$99$	−2.12864e6	−0.220485
$100$	−7.12615e6	−0.712615
$101$	−1.64385e7	−1.58759	−0.793793	−	0.608188i	$-0.791897\pi$
$101$	−1.64385e7	−1.58759	−0.793793	+	0.608188i	$0.791897\pi$
$102$	4.87892e6	0.455222
$103$	−1.11353e7	−1.00409	−0.502045	−	0.864841i	$-0.667419\pi$
$103$	−1.11353e7	−1.00409	−0.502045	+	0.864841i	$0.667419\pi$
$104$	−2.25447e6	−0.196529
$105$	−1.26685e7	−1.06798
$106$	4.31541e6	0.351926
$107$	6.31526e6	0.498365	0.249183	−	0.968457i	$-0.419838\pi$
$107$	6.31526e6	0.498365	0.249183	+	0.968457i	$0.419838\pi$
$108$	940095.	0.0718106
$109$	8.96809e6	0.663296	0.331648	−	0.943403i	$-0.392395\pi$
$109$	8.96809e6	0.663296	0.331648	+	0.943403i	$0.392395\pi$
$110$	1.24707e7	0.893340
$111$	−1.39720e7	−0.969679
$112$	−7.86223e6	−0.528789
$113$	1.92882e7	1.25753	0.628765	−	0.777596i	$-0.283561\pi$
$113$	1.92882e7	1.25753	0.628765	+	0.777596i	$0.283561\pi$
$114$	4.51798e6	0.285613
$115$	1.55524e6	0.0953578
$116$	−1.15978e7	−0.689877
$117$	−1.04389e6	−0.0602568
$118$	2.86477e6	0.160510
$119$	1.98521e7	1.07992
$120$	−2.02677e7	−1.07071
$121$	−1.09611e7	−0.562477
$122$	−4.06576e6	−0.202713
$123$	−1.24401e7	−0.602774
$124$	7.77824e6	0.366358
$125$	3.38887e7	1.55192
$126$	−6.42621e6	−0.286192
$127$	−2.39920e7	−1.03933	−0.519665	−	0.854370i	$-0.673943\pi$
$127$	−2.39920e7	−1.03933	−0.519665	+	0.854370i	$0.673943\pi$
$128$	−2.95327e6	−0.124471
$129$	−9.97476e6	−0.409108
$130$	6.11569e6	0.244143
$131$	3.18371e6	0.123733	0.0618663	−	0.998084i	$-0.480295\pi$
$131$	3.18371e6	0.123733	0.0618663	+	0.998084i	$0.480295\pi$
$132$	−3.76547e6	−0.142498
$133$	1.83834e7	0.677557
$134$	−2.44359e7	−0.877327
$135$	−9.38462e6	−0.328283
$136$	3.17603e7	1.08268
$137$	−1.79272e7	−0.595650	−0.297825	−	0.954620i	$-0.596261\pi$
$137$	−1.79272e7	−0.595650	−0.297825	+	0.954620i	$0.596261\pi$
$138$	788910.	0.0255535
$139$	1.37118e7	0.433055	0.216527	−	0.976277i	$-0.430527\pi$
$139$	1.37118e7	0.433055	0.216527	+	0.976277i	$0.430527\pi$
$140$	−2.24100e7	−0.690231
$141$	−8.45113e6	−0.253891
$142$	4.20604e7	1.23272
$143$	4.18123e6	0.119571
$144$	−5.82421e6	−0.162543
$145$	1.15776e8	3.15378
$146$	2.38484e7	0.634196
$147$	−3.91224e6	−0.101581
$148$	−2.47158e7	−0.626699
$149$	4.64979e7	1.15155	0.575774	−	0.817609i	$-0.304701\pi$
$149$	4.64979e7	1.15155	0.575774	+	0.817609i	$0.304701\pi$
$150$	3.60852e7	0.872991
$151$	−4.02167e7	−0.950578	−0.475289	−	0.879830i	$-0.657656\pi$
$151$	−4.02167e7	−0.950578	−0.475289	+	0.879830i	$0.657656\pi$
$152$	2.94107e7	0.679286
$153$	1.47061e7	0.331953
$154$	2.57396e7	0.567910
$155$	−7.76473e7	−1.67481
$156$	−1.84660e6	−0.0389437
$157$	−3.86989e6	−0.0798087
$157$	−3.86989e6	−0.0798087
$158$	−3.93426e7	−0.793529
$159$	1.30075e7	0.256629
$160$	−6.19626e7	−1.19594
$161$	3.21003e6	0.0606204
$162$	−4.76043e6	−0.0879717
$163$	2.78627e7	0.503925	0.251963	−	0.967737i	$-0.418924\pi$
$163$	2.78627e7	0.503925	0.251963	+	0.967737i	$0.418924\pi$
$164$	−2.20059e7	−0.389570
$165$	3.75893e7	0.651434
$166$	7.82737e7	1.32812
$167$	8.31141e7	1.38092	0.690458	−	0.723373i	$-0.257409\pi$
$167$	8.31141e7	1.38092	0.690458	+	0.723373i	$0.257409\pi$
$168$	−4.18326e7	−0.680664
$169$	−6.06980e7	−0.967322
$170$	−8.61560e7	−1.34498
$171$	1.36181e7	0.208272
$172$	−1.76449e7	−0.264405
$173$	−7.64914e7	−1.12318	−0.561592	−	0.827414i	$-0.689811\pi$
$173$	−7.64914e7	−1.12318	−0.561592	+	0.827414i	$0.689811\pi$
$174$	5.87285e7	0.845136
$175$	1.46829e8	2.07099
$176$	2.33284e7	0.322545
$177$	8.63501e6	0.117046
$178$	3.01496e7	0.400693
$179$	−3.98731e7	−0.519631	−0.259815	−	0.965658i	$-0.583662\pi$
$179$	−3.98731e7	−0.519631	−0.259815	+	0.965658i	$0.583662\pi$
$180$	−1.66010e7	−0.212168
$181$	4.08588e7	0.512166	0.256083	−	0.966655i	$-0.417568\pi$
$181$	4.08588e7	0.512166	0.256083	+	0.966655i	$0.417568\pi$
$182$	1.26228e7	0.155205
$183$	−1.22550e7	−0.147821
$184$	5.13556e6	0.0607751
$185$	2.46729e8	2.86496
$186$	−3.93872e7	−0.448808
$187$	−5.89039e7	−0.658716
$188$	−1.49497e7	−0.164089
$189$	−1.93699e7	−0.208695
$190$	−7.97823e7	−0.843857
$191$	−1.49431e8	−1.55176	−0.775880	−	0.630881i	$-0.782694\pi$
$191$	−1.49431e8	−1.55176	−0.775880	+	0.630881i	$0.782694\pi$
$192$	−5.90421e7	−0.602015
$193$	645913.	0.00646731	0.00323365	−	0.999995i	$-0.498971\pi$
$193$	645913.	0.00646731	0.00323365	+	0.999995i	$0.498971\pi$
$194$	−1.51438e8	−1.48912
$195$	1.84339e7	0.178032
$196$	−6.92056e6	−0.0656516
$197$	1.47466e8	1.37423	0.687115	−	0.726549i	$-0.258877\pi$
$197$	1.47466e8	1.37423	0.687115	+	0.726549i	$0.258877\pi$
$198$	1.90675e7	0.174568
$199$	−1.21758e8	−1.09525	−0.547624	−	0.836724i	$-0.684468\pi$
$199$	−1.21758e8	−1.09525	−0.547624	+	0.836724i	$0.684468\pi$
$200$	2.34904e8	2.07627
$201$	−7.36548e7	−0.639757
$202$	1.47249e8	1.25697
$203$	2.38963e8	2.00491
$204$	2.60144e7	0.214540
$205$	2.19677e8	1.78092
$206$	9.97456e7	0.794984
$207$	2.37794e6	0.0186339
$208$	1.14403e7	0.0881489
$209$	−5.45463e7	−0.413288
$210$	1.13479e8	0.845569
$211$	−1.55030e7	−0.113613	−0.0568065	−	0.998385i	$-0.518092\pi$
$211$	−1.55030e7	−0.113613	−0.0568065	+	0.998385i	$0.518092\pi$
$212$	2.30097e7	0.165858
$213$	1.26779e8	0.898912
$214$	−5.65694e7	−0.394579
$215$	1.76143e8	1.20873
$216$	−3.09889e7	−0.209227
$217$	−1.60265e8	−1.06470
$218$	−8.03324e7	−0.525162
$219$	7.18839e7	0.462463
$220$	6.64937e7	0.421019
$221$	−2.88867e7	−0.180022
$222$	1.25155e8	0.767739
$223$	−1.08112e7	−0.0652842	−0.0326421	−	0.999467i	$-0.510392\pi$
$223$	−1.08112e7	−0.0652842	−0.0326421	+	0.999467i	$0.510392\pi$
$224$	−1.27891e8	−0.760278
$225$	1.08768e8	0.636595
$226$	−1.72776e8	−0.995644
$227$	1.12408e8	0.637835	0.318917	−	0.947783i	$-0.396681\pi$
$227$	1.12408e8	0.637835	0.318917	+	0.947783i	$0.396681\pi$
$228$	2.40899e7	0.134605
$229$	8.64796e7	0.475871	0.237936	−	0.971281i	$-0.423529\pi$
$229$	8.64796e7	0.475871	0.237936	+	0.971281i	$0.423529\pi$
$230$	−1.39312e7	−0.0754991
$231$	7.75845e7	0.414127
$232$	3.82305e8	2.01003
$233$	7.68503e7	0.398015	0.199008	−	0.979998i	$-0.436228\pi$
$233$	7.68503e7	0.398015	0.199008	+	0.979998i	$0.436228\pi$
$234$	9.35077e6	0.0477081
$235$	1.49237e8	0.750135
$236$	1.52749e7	0.0756462
$237$	−1.18587e8	−0.578651
$238$	−1.77827e8	−0.855022
$239$	−5.48807e7	−0.260032	−0.130016	−	0.991512i	$-0.541503\pi$
$239$	−5.48807e7	−0.260032	−0.130016	+	0.991512i	$0.541503\pi$
$240$	1.02849e8	0.480241
$241$	−1.42771e8	−0.657021	−0.328511	−	0.944500i	$-0.606547\pi$
$241$	−1.42771e8	−0.657021	−0.328511	+	0.944500i	$0.606547\pi$
$242$	9.81848e7	0.445339
$243$	−1.43489e7	−0.0641500
$244$	−2.16786e7	−0.0955360
$245$	6.90855e7	0.300127
$246$	1.11433e8	0.477244
$247$	−2.67497e7	−0.112948
$248$	−2.56399e8	−1.06742
$249$	2.35933e8	0.968481
$250$	−3.03561e8	−1.22873
$251$	2.83174e8	1.13030	0.565152	−	0.824987i	$-0.308818\pi$
$251$	2.83174e8	1.13030	0.565152	+	0.824987i	$0.308818\pi$
$252$	−3.42645e7	−0.134878
$253$	−9.52462e6	−0.0369765
$254$	2.14910e8	0.822885
$255$	−2.59692e8	−0.980772
$256$	−2.53449e8	−0.944171
$257$	−1.73041e8	−0.635890	−0.317945	−	0.948109i	$-0.602993\pi$
$257$	−1.73041e8	−0.635890	−0.317945	+	0.948109i	$0.602993\pi$
$258$	8.93497e7	0.323910
$259$	5.09250e8	1.82130
$260$	3.26088e7	0.115061
$261$	1.77020e8	0.616283
$262$	−2.85184e7	−0.0979648
$263$	−2.71853e8	−0.921486	−0.460743	−	0.887533i	$-0.652417\pi$
$263$	−2.71853e8	−0.921486	−0.460743	+	0.887533i	$0.652417\pi$
$264$	1.24123e8	0.415183
$265$	−2.29698e8	−0.758222
$266$	−1.64671e8	−0.536453
$267$	9.08772e7	0.292190
$268$	−1.30292e8	−0.413472
$269$	−4.17753e8	−1.30854	−0.654270	−	0.756261i	$-0.727024\pi$
$269$	−4.17753e8	−1.30854	−0.654270	+	0.756261i	$0.727024\pi$
$270$	8.40635e7	0.259917
$271$	−1.61285e7	−0.0492267	−0.0246133	−	0.999697i	$-0.507835\pi$
$271$	−1.61285e7	−0.0492267	−0.0246133	+	0.999697i	$0.507835\pi$
$272$	−1.61168e8	−0.485610
$273$	3.80478e7	0.113177
$274$	1.60585e8	0.471603
$275$	−4.35662e8	−1.26324
$276$	4.20646e6	0.0120430
$277$	−1.76102e8	−0.497834	−0.248917	−	0.968525i	$-0.580075\pi$
$277$	−1.76102e8	−0.497834	−0.248917	+	0.968525i	$0.580075\pi$
$278$	−1.22825e8	−0.342869
$279$	−1.18721e8	−0.327276
$280$	7.38715e8	2.01106
$281$	2.45220e8	0.659301	0.329650	−	0.944103i	$-0.393069\pi$
$281$	2.45220e8	0.659301	0.329650	+	0.944103i	$0.393069\pi$
$282$	7.57017e7	0.201018
$283$	−1.99243e8	−0.522554	−0.261277	−	0.965264i	$-0.584144\pi$
$283$	−1.99243e8	−0.522554	−0.261277	+	0.965264i	$0.584144\pi$
$284$	2.24265e8	0.580963
$285$	−2.40480e8	−0.615350
$286$	−3.74537e7	−0.0946702
$287$	4.53414e8	1.13216
$288$	−9.47396e7	−0.233700
$289$	−3.39086e6	−0.00826357
$290$	−1.03708e9	−2.49699
$291$	−4.56466e8	−1.08588
$292$	1.27159e8	0.298888
$293$	2.45041e8	0.569118	0.284559	−	0.958658i	$-0.408153\pi$
$293$	2.45041e8	0.569118	0.284559	+	0.958658i	$0.408153\pi$
$294$	3.50442e7	0.0804267
$295$	−1.52484e8	−0.345818
$296$	8.14722e8	1.82595
$297$	5.74733e7	0.127297
$298$	−4.16509e8	−0.911733
$299$	−4.67092e6	−0.0101054
$300$	1.92406e8	0.411428
$301$	3.63559e8	0.768409
$302$	3.60245e8	0.752616
$303$	4.43840e8	0.916594
$304$	−1.49245e8	−0.304679
$305$	2.16410e8	0.436744
$306$	−1.31731e8	−0.262823
$307$	6.16309e8	1.21567	0.607833	−	0.794065i	$-0.292039\pi$
$307$	6.16309e8	1.21567	0.607833	+	0.794065i	$0.292039\pi$
$308$	1.37243e8	0.267648
$309$	3.00654e8	0.579712
$310$	6.95532e8	1.32602
$311$	4.11327e8	0.775400	0.387700	−	0.921786i	$-0.373270\pi$
$311$	4.11327e8	0.775400	0.387700	+	0.921786i	$0.373270\pi$
$312$	6.08706e7	0.113466
$313$	6.60114e8	1.21679	0.608393	−	0.793636i	$-0.291815\pi$
$313$	6.60114e8	1.21679	0.608393	+	0.793636i	$0.291815\pi$
$314$	3.46649e7	0.0631882
$315$	3.42050e8	0.616599
$316$	−2.09774e8	−0.373979
$317$	1.03547e9	1.82571	0.912854	−	0.408287i	$-0.133874\pi$
$317$	1.03547e9	1.82571	0.912854	+	0.408287i	$0.133874\pi$
$318$	−1.16516e8	−0.203185
$319$	−7.09037e8	−1.22293
$320$	1.04261e9	1.77868
$321$	−1.70512e8	−0.287731
$322$	−2.87541e7	−0.0479960
$323$	3.76842e8	0.622230
$324$	−2.53826e7	−0.0414599
$325$	−2.13650e8	−0.345233
$326$	−2.49582e8	−0.398981
$327$	−2.42138e8	−0.382954
$328$	7.25393e8	1.13505
$329$	3.08026e8	0.476872
$330$	−3.36709e8	−0.515770
$331$	−7.07979e8	−1.07306	−0.536528	−	0.843883i	$-0.680264\pi$
$331$	−7.07979e8	−1.07306	−0.536528	+	0.843883i	$0.680264\pi$
$332$	4.17355e8	0.625924
$333$	3.77244e8	0.559844
$334$	−7.44501e8	−1.09333
$335$	1.30066e9	1.89019
$336$	2.12280e8	0.305297
$337$	−1.42519e7	−0.0202847	−0.0101423	−	0.999949i	$-0.503228\pi$
$337$	−1.42519e7	−0.0202847	−0.0101423	+	0.999949i	$0.503228\pi$
$338$	5.43707e8	0.765873
$339$	−5.20783e8	−0.726035
$340$	−4.59383e8	−0.633868
$341$	4.75528e8	0.649435
$342$	−1.21986e8	−0.164899
$343$	−6.67851e8	−0.893614
$344$	5.81639e8	0.770370
$345$	−4.19916e7	−0.0550548
$346$	6.85178e8	0.889276
$347$	1.39180e9	1.78823	0.894116	−	0.447836i	$-0.147805\pi$
$347$	1.39180e9	1.78823	0.894116	+	0.447836i	$0.147805\pi$
$348$	3.13140e8	0.398301
$349$	6.70732e8	0.844617	0.422308	−	0.906452i	$-0.361220\pi$
$349$	6.70732e8	0.844617	0.422308	+	0.906452i	$0.361220\pi$
$350$	−1.31523e9	−1.63970
$351$	2.81851e7	0.0347893
$352$	3.79471e8	0.463745
$353$	3.66391e7	0.0443337	0.0221668	−	0.999754i	$-0.492943\pi$
$353$	3.66391e7	0.0443337	0.0221668	+	0.999754i	$0.492943\pi$
$354$	−7.73488e7	−0.0926706
$355$	−2.23876e9	−2.65588
$356$	1.60758e8	0.188841
$357$	−5.36006e8	−0.623492
$358$	3.57167e8	0.411415
$359$	1.49839e9	1.70921	0.854604	−	0.519280i	$-0.173800\pi$
$359$	1.49839e9	1.70921	0.854604	+	0.519280i	$0.173800\pi$
$360$	5.47228e8	0.618172
$361$	−5.44908e8	−0.609604
$362$	−3.65996e8	−0.405505
$363$	2.95949e8	0.324746
$364$	6.73048e7	0.0731461
$365$	−1.26939e9	−1.36637
$366$	1.09776e8	0.117037
$367$	−7.23485e6	−0.00764009	−0.00382004	−	0.999993i	$-0.501216\pi$
$367$	−7.23485e6	−0.00764009	−0.00382004	+	0.999993i	$0.501216\pi$
$368$	−2.60605e7	−0.0272593
$369$	3.35881e8	0.348012
$370$	−2.21009e9	−2.26832
$371$	−4.74098e8	−0.482014
$372$	−2.10012e8	−0.211517
$373$	−8.75454e8	−0.873479	−0.436740	−	0.899588i	$-0.643867\pi$
$373$	−8.75454e8	−0.873479	−0.436740	+	0.899588i	$0.643867\pi$
$374$	5.27637e8	0.521536
$375$	−9.14995e8	−0.896002
$376$	4.92795e8	0.478089
$377$	−3.47715e8	−0.334217
$378$	1.73508e8	0.165233
$379$	1.16874e9	1.10276	0.551380	−	0.834254i	$-0.314102\pi$
$379$	1.16874e9	1.10276	0.551380	+	0.834254i	$0.314102\pi$
$380$	−4.25398e8	−0.397698
$381$	6.47784e8	0.600057
$382$	1.33854e9	1.22860
$383$	−4.27464e8	−0.388780	−0.194390	−	0.980924i	$-0.562273\pi$
$383$	−4.27464e8	−0.388780	−0.194390	+	0.980924i	$0.562273\pi$
$384$	7.97383e7	0.0718634
$385$	−1.37005e9	−1.22356
$386$	−5.78582e6	−0.00512046
$387$	2.69318e8	0.236199
$388$	−8.07467e8	−0.701801
$389$	−2.01058e9	−1.73180	−0.865900	−	0.500217i	$-0.833254\pi$
$389$	−2.01058e9	−1.73180	−0.865900	+	0.500217i	$0.833254\pi$
$390$	−1.65124e8	−0.140956
$391$	6.58025e7	0.0556703
$392$	2.28127e8	0.191282
$393$	−8.59603e7	−0.0714371
$394$	−1.32094e9	−1.08804
$395$	2.09410e9	1.70965
$396$	1.01668e8	0.0822715
$397$	1.63040e9	1.30776	0.653879	−	0.756599i	$-0.273141\pi$
$397$	1.63040e9	1.30776	0.653879	+	0.756599i	$0.273141\pi$
$398$	1.09066e9	0.867159
$399$	−4.96353e8	−0.391188
$400$	−1.19202e9	−0.931267
$401$	9.01827e8	0.698422	0.349211	−	0.937044i	$-0.386450\pi$
$401$	9.01827e8	0.698422	0.349211	+	0.937044i	$0.386450\pi$
$402$	6.59769e8	0.506525
$403$	2.33201e8	0.177485
$404$	7.85132e8	0.592390
$405$	2.53385e8	0.189534
$406$	−2.14053e9	−1.58738
$407$	−1.51102e9	−1.11094
$408$	−8.57528e8	−0.625083
$409$	−1.91377e8	−0.138311	−0.0691557	−	0.997606i	$-0.522031\pi$
$409$	−1.91377e8	−0.138311	−0.0691557	+	0.997606i	$0.522031\pi$
$410$	−1.96777e9	−1.41004
$411$	4.84035e8	0.343899
$412$	5.31843e8	0.374665
$413$	−3.14728e8	−0.219842
$414$	−2.13006e7	−0.0147533
$415$	−4.16630e9	−2.86142
$416$	1.86094e8	0.126738
$417$	−3.70219e8	−0.250024
$418$	4.88602e8	0.327219
$419$	2.86940e9	1.90565	0.952823	−	0.303527i	$-0.0981641\pi$
$419$	2.86940e9	1.90565	0.952823	+	0.303527i	$0.0981641\pi$
$420$	6.05071e8	0.398505
$421$	−2.90289e9	−1.89602	−0.948010	−	0.318241i	$-0.896908\pi$
$421$	−2.90289e9	−1.89602	−0.948010	+	0.318241i	$0.896908\pi$
$422$	1.38870e8	0.0899526
$423$	2.28181e8	0.146584
$424$	−7.58484e8	−0.483243
$425$	3.00984e9	1.90188
$426$	−1.13563e9	−0.711710
$427$	4.46671e8	0.277645
$428$	−3.01628e8	−0.185959
$429$	−1.12893e8	−0.0690346
$430$	−1.57781e9	−0.957007
$431$	−1.14980e9	−0.691754	−0.345877	−	0.938280i	$-0.612419\pi$
$431$	−1.14980e9	−0.691754	−0.345877	+	0.938280i	$0.612419\pi$
$432$	1.57254e8	0.0938442
$433$	6.52474e7	0.0386238	0.0193119	−	0.999814i	$-0.493852\pi$
$433$	6.52474e7	0.0386238	0.0193119	+	0.999814i	$0.493852\pi$
$434$	1.43558e9	0.842974
$435$	−3.12596e9	−1.82084
$436$	−4.28332e8	−0.247501
$437$	6.09345e7	0.0349284
$438$	−6.43906e8	−0.366153
$439$	−1.50475e9	−0.848863	−0.424431	−	0.905460i	$-0.639526\pi$
$439$	−1.50475e9	−0.848863	−0.424431	+	0.905460i	$0.639526\pi$
$440$	−2.19187e9	−1.22668
$441$	1.05630e8	0.0586481
$442$	2.58755e8	0.142532
$443$	1.37942e9	0.753845	0.376923	−	0.926245i	$-0.376982\pi$
$443$	1.37942e9	0.753845	0.376923	+	0.926245i	$0.376982\pi$
$444$	6.67327e8	0.361825
$445$	−1.60479e9	−0.863290
$446$	9.68424e7	0.0516885
$447$	−1.25544e9	−0.664846
$448$	2.15196e9	1.13074
$449$	8.26055e8	0.430672	0.215336	−	0.976540i	$-0.430915\pi$
$449$	8.26055e8	0.430672	0.215336	+	0.976540i	$0.430915\pi$
$450$	−9.74301e8	−0.504022
$451$	−1.34534e9	−0.690582
$452$	−9.21240e8	−0.469233
$453$	1.08585e9	0.548816
$454$	−1.00691e9	−0.505003
$455$	−6.71879e8	−0.334388
$456$	−7.94089e8	−0.392186
$457$	1.55693e9	0.763064	0.381532	−	0.924356i	$-0.375397\pi$
$457$	1.55693e9	0.763064	0.381532	+	0.924356i	$0.375397\pi$
$458$	−7.74648e8	−0.376769
$459$	−3.97064e8	−0.191653
$460$	−7.42812e7	−0.0355817
$461$	−8.75277e8	−0.416095	−0.208047	−	0.978119i	$-0.566711\pi$
$461$	−8.75277e8	−0.416095	−0.208047	+	0.978119i	$0.566711\pi$
$462$	−6.94970e8	−0.327883
$463$	1.06705e9	0.499633	0.249816	−	0.968293i	$-0.419630\pi$
$463$	1.06705e9	0.499633	0.249816	+	0.968293i	$0.419630\pi$
$464$	−1.94001e9	−0.901552
$465$	2.09648e9	0.966952
$466$	−6.88393e8	−0.315127
$467$	−2.95956e8	−0.134468	−0.0672338	−	0.997737i	$-0.521417\pi$
$467$	−2.95956e8	−0.134468	−0.0672338	+	0.997737i	$0.521417\pi$
$468$	4.98582e7	0.0224841
$469$	2.68456e9	1.20162
$470$	−1.33680e9	−0.593916
$471$	1.04487e8	0.0460776
$472$	−5.03517e8	−0.220403
$473$	−1.07873e9	−0.468705
$474$	1.06225e9	0.458144
$475$	2.78718e9	1.19327
$476$	−9.48170e8	−0.402960
$477$	−3.51204e8	−0.148165
$478$	4.91598e8	0.205879
$479$	−4.27246e9	−1.77625	−0.888125	−	0.459601i	$-0.847992\pi$
$479$	−4.27246e9	−1.77625	−0.888125	+	0.459601i	$0.847992\pi$
$480$	1.67299e9	0.690477
$481$	−7.41009e8	−0.303610
$482$	1.27888e9	0.520194
$483$	−8.66709e7	−0.0349992
$484$	5.23521e8	0.209882
$485$	8.06065e9	3.20829
$486$	1.28531e8	0.0507905
$487$	5.01035e8	0.196570	0.0982848	−	0.995158i	$-0.468664\pi$
$487$	5.01035e8	0.196570	0.0982848	+	0.995158i	$0.468664\pi$
$488$	7.14605e8	0.278354
$489$	−7.52292e8	−0.290941
$490$	−6.18839e8	−0.237625
$491$	−6.80943e8	−0.259613	−0.129806	−	0.991539i	$-0.541436\pi$
$491$	−6.80943e8	−0.259613	−0.129806	+	0.991539i	$0.541436\pi$
$492$	5.94159e8	0.224918
$493$	4.89851e9	1.84119
$494$	2.39613e8	0.0894264
$495$	−1.01491e9	−0.376105
$496$	1.30110e9	0.478767
$497$	−4.62082e9	−1.68838
$498$	−2.11339e9	−0.766790
$499$	−2.59463e9	−0.934812	−0.467406	−	0.884043i	$-0.654811\pi$
$499$	−2.59463e9	−0.934812	−0.467406	+	0.884043i	$0.654811\pi$
$500$	−1.61858e9	−0.579082
$501$	−2.24408e9	−0.797272
$502$	−2.53655e9	−0.894913
$503$	−2.04515e9	−0.716533	−0.358267	−	0.933619i	$-0.616632\pi$
$503$	−2.04515e9	−0.716533	−0.358267	+	0.933619i	$0.616632\pi$
$504$	1.12948e9	0.392982
$505$	−7.83769e9	−2.70812
$506$	8.53176e7	0.0292760
$507$	1.63885e9	0.558484
$508$	1.14590e9	0.387814
$509$	−4.03413e9	−1.35593	−0.677966	−	0.735093i	$-0.737138\pi$
$509$	−4.03413e9	−1.35593	−0.677966	+	0.735093i	$0.737138\pi$
$510$	2.32621e9	0.776522
$511$	−2.62002e9	−0.868623
$512$	2.64831e9	0.872015
$513$	−3.67690e8	−0.120246
$514$	1.55003e9	0.503463
$515$	−5.30919e9	−1.71279
$516$	4.76412e8	0.152654
$517$	−9.13958e8	−0.290877
$518$	−4.56165e9	−1.44201
$519$	2.06527e9	0.648471
$520$	−1.07490e9	−0.335242
$521$	3.36983e9	1.04394	0.521970	−	0.852964i	$-0.325197\pi$
$521$	3.36983e9	1.04394	0.521970	+	0.852964i	$0.325197\pi$
$522$	−1.58567e9	−0.487939
$523$	3.59445e9	1.09869	0.549346	−	0.835595i	$-0.314877\pi$
$523$	3.59445e9	1.09869	0.549346	+	0.835595i	$0.314877\pi$
$524$	−1.52060e8	−0.0461694
$525$	−3.96438e9	−1.19569
$526$	2.43514e9	0.729583
$527$	−3.28527e9	−0.977762
$528$	−6.29866e8	−0.186221
$529$	−3.39419e9	−0.996875
$530$	2.05754e9	0.600319
$531$	−2.33145e8	−0.0675765
$532$	−8.78025e8	−0.252823
$533$	−6.59762e8	−0.188731
$534$	−8.14040e8	−0.231340
$535$	3.01104e9	0.850116
$536$	4.29489e9	1.20469
$537$	1.07657e9	0.300009
$538$	3.74206e9	1.03603
$539$	−4.23093e8	−0.116379
$540$	4.48226e8	0.122495
$541$	−2.28712e9	−0.621009	−0.310504	−	0.950572i	$-0.600498\pi$
$541$	−2.28712e9	−0.621009	−0.310504	+	0.950572i	$0.600498\pi$
$542$	1.44472e8	0.0389750
$543$	−1.10319e9	−0.295699
$544$	−2.62164e9	−0.698196
$545$	4.27588e9	1.13146
$546$	−3.40816e8	−0.0896078
$547$	6.65338e9	1.73815	0.869074	−	0.494682i	$-0.164716\pi$
$547$	6.65338e9	1.73815	0.869074	+	0.494682i	$0.164716\pi$
$548$	8.56236e8	0.222260
$549$	3.30886e8	0.0853445
$550$	3.90248e9	1.00016
$551$	4.53612e9	1.15519
$552$	−1.38660e8	−0.0350885
$553$	4.32224e9	1.08685
$554$	1.57745e9	0.394158
$555$	−6.66168e9	−1.65409
$556$	−6.54900e8	−0.161589
$557$	−2.78053e8	−0.0681764	−0.0340882	−	0.999419i	$-0.510853\pi$
$557$	−2.78053e8	−0.0681764	−0.0340882	+	0.999419i	$0.510853\pi$
$558$	1.06346e9	0.259119
$559$	−5.29015e8	−0.128093
$560$	−3.74862e9	−0.902014
$561$	1.59041e9	0.380310
$562$	−2.19658e9	−0.521998
$563$	−1.61355e9	−0.381068	−0.190534	−	0.981681i	$-0.561022\pi$
$563$	−1.61355e9	−0.381068	−0.190534	+	0.981681i	$0.561022\pi$
$564$	4.03641e8	0.0947367
$565$	9.19641e9	2.14511
$566$	1.78474e9	0.413730
$567$	5.22988e8	0.120490
$568$	−7.39260e9	−1.69269
$569$	5.15066e9	1.17212	0.586058	−	0.810269i	$-0.300679\pi$
$569$	5.15066e9	1.17212	0.586058	+	0.810269i	$0.300679\pi$
$570$	2.15412e9	0.487201
$571$	−6.06315e9	−1.36293	−0.681463	−	0.731853i	$-0.738656\pi$
$571$	−6.06315e9	−1.36293	−0.681463	+	0.731853i	$0.738656\pi$
$572$	−1.99703e8	−0.0446168
$573$	4.03464e9	0.895909
$574$	−4.06149e9	−0.896384
$575$	4.86685e8	0.106760
$576$	1.59414e9	0.347574
$577$	2.49972e9	0.541721	0.270860	−	0.962619i	$-0.412692\pi$
$577$	2.49972e9	0.541721	0.270860	+	0.962619i	$0.412692\pi$
$578$	3.03739e7	0.00654265
$579$	−1.74396e7	−0.00373390
$580$	−5.52968e9	−1.17680
$581$	−8.59927e9	−1.81905
$582$	4.08883e9	0.859743
$583$	1.40672e9	0.294013
$584$	−4.19163e9	−0.870840
$585$	−4.97717e8	−0.102787
$586$	−2.19498e9	−0.450597
$587$	3.91673e9	0.799265	0.399633	−	0.916675i	$-0.369138\pi$
$587$	3.91673e9	0.799265	0.399633	+	0.916675i	$0.369138\pi$
$588$	1.86855e8	0.0379040
$589$	−3.04222e9	−0.613462
$590$	1.36589e9	0.273800
$591$	−3.98157e9	−0.793412
$592$	−4.13432e9	−0.818989
$593$	1.36180e9	0.268177	0.134088	−	0.990969i	$-0.457189\pi$
$593$	1.36180e9	0.268177	0.134088	+	0.990969i	$0.457189\pi$
$594$	−5.14822e8	−0.100787
$595$	9.46523e9	1.84214
$596$	−2.22082e9	−0.429687
$597$	3.28747e9	0.632342
$598$	4.18401e7	0.00800090
$599$	7.52895e9	1.43133	0.715666	−	0.698442i	$-0.246123\pi$
$599$	7.52895e9	1.43133	0.715666	+	0.698442i	$0.246123\pi$
$600$	−6.34240e9	−1.19874
$601$	5.51990e9	1.03722	0.518609	−	0.855011i	$-0.326450\pi$
$601$	5.51990e9	1.03722	0.518609	+	0.855011i	$0.326450\pi$
$602$	−3.25661e9	−0.608385
$603$	1.98868e9	0.369364
$604$	1.92082e9	0.354697
$605$	−5.22612e9	−0.959479
$606$	−3.97573e9	−0.725709
$607$	7.58621e8	0.137678	0.0688389	−	0.997628i	$-0.478071\pi$
$607$	7.58621e8	0.137678	0.0688389	+	0.997628i	$0.478071\pi$
$608$	−2.42770e9	−0.438058
$609$	−6.45200e9	−1.15753
$610$	−1.93851e9	−0.345790
$611$	−4.48209e8	−0.0794943
$612$	−7.02388e8	−0.123865
$613$	−2.66430e9	−0.467167	−0.233583	−	0.972337i	$-0.575045\pi$
$613$	−2.66430e9	−0.467167	−0.233583	+	0.972337i	$0.575045\pi$
$614$	−5.52064e9	−0.962498
$615$	−5.93127e9	−1.02822
$616$	−4.52404e9	−0.779819
$617$	5.21718e9	0.894206	0.447103	−	0.894483i	$-0.352456\pi$
$617$	5.21718e9	0.894206	0.447103	+	0.894483i	$0.352456\pi$
$618$	−2.69313e9	−0.458984
$619$	8.33335e9	1.41222	0.706110	−	0.708102i	$-0.250448\pi$
$619$	8.33335e9	1.41222	0.706110	+	0.708102i	$0.250448\pi$
$620$	3.70857e9	0.624937
$621$	−6.42043e7	−0.0107583
$622$	−3.68449e9	−0.613919
$623$	−3.31229e9	−0.548807
$624$	−3.08889e8	−0.0508928
$625$	4.50132e9	0.737497
$626$	−5.91303e9	−0.963384
$627$	1.47275e9	0.238612
$628$	1.84833e8	0.0297797
$629$	1.04391e10	1.67258
$630$	−3.06394e9	−0.488189
$631$	9.75022e9	1.54494	0.772470	−	0.635051i	$-0.219021\pi$
$631$	9.75022e9	1.54494	0.772470	+	0.635051i	$0.219021\pi$
$632$	6.91492e9	1.08963
$633$	4.18582e8	0.0655945
$634$	−9.27533e9	−1.44550
$635$	−1.14391e10	−1.77290
$636$	−6.21263e8	−0.0957581
$637$	−2.07487e8	−0.0318055
$638$	6.35126e9	0.968250
$639$	−3.42302e9	−0.518987
$640$	−1.40808e9	−0.212324
$641$	9.48093e9	1.42183	0.710915	−	0.703278i	$-0.248281\pi$
$641$	9.48093e9	1.42183	0.710915	+	0.703278i	$0.248281\pi$
$642$	1.52737e9	0.227810
$643$	3.94925e9	0.585836	0.292918	−	0.956138i	$-0.405374\pi$
$643$	3.94925e9	0.585836	0.292918	+	0.956138i	$0.405374\pi$
$644$	−1.53317e8	−0.0226198
$645$	−4.75585e9	−0.697861
$646$	−3.37559e9	−0.492648
$647$	1.04723e10	1.52011	0.760056	−	0.649858i	$-0.225171\pi$
$647$	1.04723e10	1.52011	0.760056	+	0.649858i	$0.225171\pi$
$648$	8.36701e8	0.120797
$649$	9.33843e8	0.134096
$650$	1.91379e9	0.273337
$651$	4.32714e9	0.614707
$652$	−1.33077e9	−0.188034
$653$	1.24354e9	0.174768	0.0873842	−	0.996175i	$-0.472149\pi$
$653$	1.24354e9	0.174768	0.0873842	+	0.996175i	$0.472149\pi$
$654$	2.16897e9	0.303202
$655$	1.51796e9	0.211064
$656$	−3.68102e9	−0.509102
$657$	−1.94087e9	−0.267003
$658$	−2.75917e9	−0.377562
$659$	3.05625e9	0.415996	0.207998	−	0.978129i	$-0.433305\pi$
$659$	3.05625e9	0.415996	0.207998	+	0.978129i	$0.433305\pi$
$660$	−1.79533e9	−0.243075
$661$	−4.27553e9	−0.575818	−0.287909	−	0.957658i	$-0.592960\pi$
$661$	−4.27553e9	−0.575818	−0.287909	+	0.957658i	$0.592960\pi$
$662$	6.34178e9	0.849587
$663$	7.79942e8	0.103936
$664$	−1.37575e10	−1.82369
$665$	8.76501e9	1.15578
$666$	−3.37919e9	−0.443254
$667$	7.92077e8	0.103354
$668$	−3.96967e9	−0.515273
$669$	2.91903e8	0.0376918
$670$	−1.16507e10	−1.49655
$671$	−1.32534e9	−0.169355
$672$	3.45306e9	0.438947
$673$	−5.90964e9	−0.747323	−0.373661	−	0.927565i	$-0.621898\pi$
$673$	−5.90964e9	−0.747323	−0.373661	+	0.927565i	$0.621898\pi$
$674$	1.27663e8	0.0160603
$675$	−2.93674e9	−0.367538
$676$	2.89904e9	0.360945
$677$	−9.53064e9	−1.18049	−0.590244	−	0.807225i	$-0.700969\pi$
$677$	−9.53064e9	−1.18049	−0.590244	+	0.807225i	$0.700969\pi$
$678$	4.66495e9	0.574835
$679$	1.66372e10	2.03956
$680$	1.51429e10	1.84684
$681$	−3.03503e9	−0.368254
$682$	−4.25958e9	−0.514187
$683$	7.88767e9	0.947275	0.473638	−	0.880720i	$-0.342941\pi$
$683$	7.88767e9	0.947275	0.473638	+	0.880720i	$0.342941\pi$
$684$	−6.50426e8	−0.0777144
$685$	−8.54749e9	−1.01607
$686$	5.98233e9	0.707515
$687$	−2.33495e9	−0.274744
$688$	−2.95154e9	−0.345532
$689$	6.89859e8	0.0803513
$690$	3.76143e8	0.0435894
$691$	1.10956e10	1.27932	0.639658	−	0.768660i	$-0.279076\pi$
$691$	1.10956e10	1.27932	0.639658	+	0.768660i	$0.279076\pi$
$692$	3.65336e9	0.419104
$693$	−2.09478e9	−0.239096
$694$	−1.24672e10	−1.41582
$695$	6.53762e9	0.738709
$696$	−1.03222e10	−1.16049
$697$	9.29454e9	1.03971
$698$	−6.00813e9	−0.668722
$699$	−2.07496e9	−0.229794
$700$	−7.01280e9	−0.772767
$701$	−1.62792e10	−1.78492	−0.892462	−	0.451122i	$-0.851024\pi$
$701$	−1.62792e10	−1.78492	−0.892462	+	0.451122i	$0.851024\pi$
$702$	−2.52471e8	−0.0275443
$703$	9.66684e9	1.04940
$704$	−6.38517e9	−0.689713
$705$	−4.02940e9	−0.433090
$706$	−3.28198e8	−0.0351010
$707$	−1.61770e10	−1.72159
$708$	−4.12423e8	−0.0436744
$709$	−1.58876e10	−1.67416	−0.837080	−	0.547080i	$-0.815739\pi$
$709$	−1.58876e10	−1.67416	−0.837080	+	0.547080i	$0.815739\pi$
$710$	2.00539e10	2.10278
$711$	3.20184e9	0.334084
$712$	−5.29915e9	−0.550207
$713$	−5.31220e8	−0.0548859
$714$	4.80132e9	0.493647
$715$	1.99356e9	0.203966
$716$	1.90441e9	0.193894
$717$	1.48178e9	0.150130
$718$	−1.34220e10	−1.35326
$719$	−4.51892e9	−0.453402	−0.226701	−	0.973964i	$-0.572794\pi$
$719$	−4.51892e9	−0.453402	−0.226701	+	0.973964i	$0.572794\pi$
$720$	−2.77691e9	−0.277267
$721$	−1.09582e10	−1.08884
$722$	4.88106e9	0.482652
$723$	3.85481e9	0.379331
$724$	−1.95149e9	−0.191109
$725$	3.62301e10	3.53091
$726$	−2.65099e9	−0.257116
$727$	−1.78425e9	−0.172221	−0.0861105	−	0.996286i	$-0.527444\pi$
$727$	−1.78425e9	−0.172221	−0.0861105	+	0.996286i	$0.527444\pi$
$728$	−2.21861e9	−0.213118
$729$	3.87420e8	0.0370370
$730$	1.13706e10	1.08182
$731$	7.45260e9	0.705663
$732$	5.85322e8	0.0551577
$733$	1.50703e10	1.41337	0.706687	−	0.707527i	$-0.250189\pi$
$733$	1.50703e10	1.41337	0.706687	+	0.707527i	$0.250189\pi$
$734$	6.48068e7	0.00604901
$735$	−1.86531e9	−0.173279
$736$	−4.23913e8	−0.0391927
$737$	−7.96548e9	−0.732953
$738$	−3.00869e9	−0.275537
$739$	−5.69703e9	−0.519270	−0.259635	−	0.965707i	$-0.583602\pi$
$739$	−5.69703e9	−0.519270	−0.259635	+	0.965707i	$0.583602\pi$
$740$	−1.17842e10	−1.06903
$741$	7.22242e8	0.0652108
$742$	4.24677e9	0.381632
$743$	−8.70397e9	−0.778496	−0.389248	−	0.921133i	$-0.627265\pi$
$743$	−8.70397e9	−0.778496	−0.389248	+	0.921133i	$0.627265\pi$
$744$	6.92277e9	0.616275
$745$	2.21697e10	1.96432
$746$	7.84195e9	0.691573
$747$	−6.37019e9	−0.559153
$748$	2.81335e9	0.245793
$749$	6.21481e9	0.540432
$750$	8.19614e9	0.709406
$751$	−1.16505e10	−1.00371	−0.501853	−	0.864953i	$-0.667348\pi$
$751$	−1.16505e10	−1.00371	−0.501853	+	0.864953i	$0.667348\pi$
$752$	−2.50069e9	−0.214436
$753$	−7.64569e9	−0.652581
$754$	3.11468e9	0.264615
$755$	−1.91749e10	−1.62150
$756$	9.25141e8	0.0778721
$757$	−9.90689e9	−0.830045	−0.415023	−	0.909811i	$-0.636226\pi$
$757$	−9.90689e9	−0.830045	−0.415023	+	0.909811i	$0.636226\pi$
$758$	−1.04691e10	−0.873105
$759$	2.57165e8	0.0213484
$760$	1.40227e10	1.15873
$761$	3.86410e9	0.317835	0.158918	−	0.987292i	$-0.449200\pi$
$761$	3.86410e9	0.317835	0.158918	+	0.987292i	$0.449200\pi$
$762$	−5.80257e9	−0.475093
$763$	8.82544e9	0.719284
$764$	7.13709e9	0.579021
$765$	7.01169e9	0.566249
$766$	3.82904e9	0.307815
$767$	4.57961e8	0.0366475
$768$	6.84312e9	0.545118
$769$	2.48643e10	1.97167	0.985833	−	0.167728i	$-0.0536430\pi$
$769$	2.48643e10	1.97167	0.985833	+	0.167728i	$0.0536430\pi$
$770$	1.22723e10	0.968746
$771$	4.67210e9	0.367131
$772$	−3.08499e7	−0.00241320
$773$	2.10836e10	1.64178	0.820891	−	0.571084i	$-0.193477\pi$
$773$	2.10836e10	1.64178	0.820891	+	0.571084i	$0.193477\pi$
$774$	−2.41244e9	−0.187009
$775$	−2.42983e10	−1.87508
$776$	2.66170e10	2.04477
$777$	−1.37497e10	−1.05153
$778$	1.80099e10	1.37115
$779$	8.60694e9	0.652330
$780$	−8.80438e8	−0.0664305
$781$	1.37106e10	1.02986
$782$	−5.89431e8	−0.0440767
$783$	−4.77953e9	−0.355811
$784$	−1.15763e9	−0.0857955
$785$	−1.84512e9	−0.136138
$786$	7.69996e8	0.0565600
$787$	1.84018e9	0.134570	0.0672851	−	0.997734i	$-0.478566\pi$
$787$	1.84018e9	0.134570	0.0672851	+	0.997734i	$0.478566\pi$
$788$	−7.04322e9	−0.512778
$789$	7.34003e9	0.532020
$790$	−1.87581e10	−1.35361
$791$	1.89814e10	1.36368
$792$	−3.35133e9	−0.239706
$793$	−6.49950e8	−0.0462833
$794$	−1.46044e10	−1.03541
$795$	6.20184e9	0.437760
$796$	5.81539e9	0.408680
$797$	1.76351e10	1.23388	0.616942	−	0.787009i	$-0.288371\pi$
$797$	1.76351e10	1.23388	0.616942	+	0.787009i	$0.288371\pi$
$798$	4.44612e9	0.309721
$799$	6.31423e9	0.437932
$800$	−1.93900e10	−1.33895
$801$	−2.45369e9	−0.168696
$802$	−8.07819e9	−0.552973
$803$	7.77397e9	0.529832
$804$	3.51788e9	0.238718
$805$	1.53051e9	0.103407
$806$	−2.08892e9	−0.140523
$807$	1.12793e10	0.755486
$808$	−2.58808e10	−1.72599
$809$	2.02986e10	1.34786	0.673932	−	0.738793i	$-0.264604\pi$
$809$	2.02986e10	1.34786	0.673932	+	0.738793i	$0.264604\pi$
$810$	−2.26971e9	−0.150063
$811$	−6.93174e9	−0.456320	−0.228160	−	0.973624i	$-0.573271\pi$
$811$	−6.93174e9	−0.456320	−0.228160	+	0.973624i	$0.573271\pi$
$812$	−1.14133e10	−0.748109
$813$	4.35469e8	0.0284210
$814$	1.35351e10	0.879579
$815$	1.32846e10	0.859601
$816$	4.35153e9	0.280367
$817$	6.90127e9	0.442743
$818$	1.71427e9	0.109507
$819$	−1.02729e9	−0.0653430
$820$	−1.04921e10	−0.664532
$821$	1.20303e10	0.758707	0.379353	−	0.925252i	$-0.376146\pi$
$821$	1.20303e10	0.758707	0.379353	+	0.925252i	$0.376146\pi$
$822$	−4.33578e9	−0.272280
$823$	−2.31718e10	−1.44898	−0.724488	−	0.689287i	$-0.757924\pi$
$823$	−2.31718e10	−1.44898	−0.724488	+	0.689287i	$0.757924\pi$
$824$	−1.75315e10	−1.09162
$825$	1.17629e10	0.729331
$826$	2.81920e9	0.174059
$827$	−1.85015e10	−1.13746	−0.568731	−	0.822523i	$-0.692566\pi$
$827$	−1.85015e10	−1.13746	−0.568731	+	0.822523i	$0.692566\pi$
$828$	−1.13574e8	−0.00695304
$829$	−3.18265e10	−1.94021	−0.970103	−	0.242694i	$-0.921969\pi$
$829$	−3.18265e10	−1.94021	−0.970103	+	0.242694i	$0.921969\pi$
$830$	3.73200e10	2.26552
$831$	4.75475e9	0.287425
$832$	−3.13132e9	−0.188493
$833$	2.92301e9	0.175216
$834$	3.31626e9	0.197956
$835$	3.96278e10	2.35558
$836$	2.60522e9	0.154214
$837$	3.20547e9	0.188953
$838$	−2.57029e10	−1.50879
$839$	−9.06375e9	−0.529835	−0.264918	−	0.964271i	$-0.585345\pi$
$839$	−9.06375e9	−0.529835	−0.264918	+	0.964271i	$0.585345\pi$
$840$	−1.99453e10	−1.16108
$841$	4.17144e10	2.41824
$842$	2.60028e10	1.50117
$843$	−6.62094e9	−0.380647
$844$	7.40452e8	0.0423934
$845$	−2.89401e10	−1.65007
$846$	−2.04395e9	−0.116058
$847$	−1.07867e10	−0.609956
$848$	3.84894e9	0.216748
$849$	5.37957e9	0.301697
$850$	−2.69609e10	−1.50580
$851$	1.68798e9	0.0938889
$852$	−6.05517e9	−0.335419
$853$	2.76848e10	1.52728	0.763642	−	0.645639i	$-0.223409\pi$
$853$	2.76848e10	1.52728	0.763642	+	0.645639i	$0.223409\pi$
$854$	−4.00109e9	−0.219824
$855$	6.49297e9	0.355273
$856$	9.94274e9	0.541811
$857$	1.78241e9	0.0967332	0.0483666	−	0.998830i	$-0.484598\pi$
$857$	1.78241e9	0.0967332	0.0483666	+	0.998830i	$0.484598\pi$
$858$	1.01125e9	0.0546579
$859$	3.34498e9	0.180060	0.0900302	−	0.995939i	$-0.471304\pi$
$859$	3.34498e9	0.180060	0.0900302	+	0.995939i	$0.471304\pi$
$860$	−8.41287e9	−0.451024
$861$	−1.22422e10	−0.653654
$862$	1.02994e10	0.547693
$863$	1.79019e10	0.948116	0.474058	−	0.880494i	$-0.342789\pi$
$863$	1.79019e10	0.948116	0.474058	+	0.880494i	$0.342789\pi$
$864$	2.55797e9	0.134926
$865$	−3.64702e10	−1.91594
$866$	−5.84459e8	−0.0305803
$867$	9.15533e7	0.00477098
$868$	7.65452e9	0.397282
$869$	−1.28247e10	−0.662945
$870$	2.80011e10	1.44164
$871$	−3.90631e9	−0.200310
$872$	1.41194e10	0.721120
$873$	1.23246e10	0.626935
$874$	−5.45826e8	−0.0276544
$875$	3.33497e10	1.68292
$876$	−3.43330e9	−0.172563
$877$	−2.81182e10	−1.40763	−0.703815	−	0.710383i	$-0.748522\pi$
$877$	−2.81182e10	−1.40763	−0.703815	+	0.710383i	$0.748522\pi$
$878$	1.34789e10	0.672084
$879$	−6.61611e9	−0.328581
$880$	1.11227e10	0.550200
$881$	6.65303e9	0.327796	0.163898	−	0.986477i	$-0.447593\pi$
$881$	6.65303e9	0.327796	0.163898	+	0.986477i	$0.447593\pi$
$882$	−9.46193e8	−0.0464344
$883$	−8.64433e9	−0.422541	−0.211271	−	0.977428i	$-0.567760\pi$
$883$	−8.64433e9	−0.422541	−0.211271	+	0.977428i	$0.567760\pi$
$884$	1.37968e9	0.0671731
$885$	4.11707e9	0.199658
$886$	−1.23562e10	−0.596854
$887$	−1.31316e10	−0.631807	−0.315904	−	0.948791i	$-0.602308\pi$
$887$	−1.31316e10	−0.631807	−0.315904	+	0.948791i	$0.602308\pi$
$888$	−2.19975e10	−1.05421
$889$	−2.36104e10	−1.12706
$890$	1.43750e10	0.683506
$891$	−1.55178e9	−0.0734950
$892$	5.16363e8	0.0243600
$893$	5.84711e9	0.274765
$894$	1.12457e10	0.526389
$895$	−1.90110e10	−0.886391
$896$	−2.90630e9	−0.134978
$897$	1.26115e8	0.00583435
$898$	−7.39945e9	−0.340983
$899$	−3.95453e10	−1.81525
$900$	−5.19496e9	−0.237538
$901$	−9.71853e9	−0.442654
$902$	1.20510e10	0.546766
$903$	−9.81610e9	−0.443641
$904$	3.03674e10	1.36716
$905$	1.94810e10	0.873658
$906$	−9.72661e9	−0.434523
$907$	3.05836e10	1.36101	0.680507	−	0.732741i	$-0.261760\pi$
$907$	3.05836e10	1.36101	0.680507	+	0.732741i	$0.261760\pi$
$908$	−5.36882e9	−0.238001
$909$	−1.19837e10	−0.529196
$910$	6.01841e9	0.264751
$911$	1.72557e10	0.756168	0.378084	−	0.925771i	$-0.376583\pi$
$911$	1.72557e10	0.756168	0.378084	+	0.925771i	$0.376583\pi$
$912$	4.02961e9	0.175906
$913$	2.55152e10	1.10956
$914$	−1.39463e10	−0.604153
$915$	−5.84306e9	−0.252154
$916$	−4.13042e9	−0.177566
$917$	3.13307e9	0.134177
$918$	3.55673e9	0.151741
$919$	−3.94574e8	−0.0167696	−0.00838482	−	0.999965i	$-0.502669\pi$
$919$	−3.94574e8	−0.0167696	−0.00838482	+	0.999965i	$0.502669\pi$
$920$	2.44858e9	0.103671
$921$	−1.66403e10	−0.701865
$922$	7.84037e9	0.329441
$923$	6.72374e9	0.281453
$924$	−3.70557e9	−0.154527
$925$	7.72092e10	3.20755
$926$	−9.55818e9	−0.395582
$927$	−8.11765e9	−0.334697
$928$	−3.15572e10	−1.29623
$929$	1.65605e10	0.677672	0.338836	−	0.940845i	$-0.389967\pi$
$929$	1.65605e10	0.677672	0.338836	+	0.940845i	$0.389967\pi$
$930$	−1.87794e10	−0.765580
$931$	2.70677e9	0.109933
$932$	−3.67050e9	−0.148515
$933$	−1.11058e10	−0.447677
$934$	2.65105e9	0.106464
$935$	−2.80847e10	−1.12364
$936$	−1.64351e9	−0.0655098
$937$	−1.73896e9	−0.0690560	−0.0345280	−	0.999404i	$-0.510993\pi$
$937$	−1.73896e9	−0.0690560	−0.0345280	+	0.999404i	$0.510993\pi$
$938$	−2.40472e10	−0.951381
$939$	−1.78231e10	−0.702511
$940$	−7.12783e9	−0.279904
$941$	−2.06392e10	−0.807477	−0.403738	−	0.914874i	$-0.632289\pi$
$941$	−2.06392e10	−0.807477	−0.403738	+	0.914874i	$0.632289\pi$
$942$	−9.35952e8	−0.0364817
$943$	1.50291e9	0.0583634
$944$	2.55510e9	0.0988568
$945$	−9.23535e9	−0.355993
$946$	9.66283e9	0.371095
$947$	−2.78302e10	−1.06486	−0.532430	−	0.846474i	$-0.678721\pi$
$947$	−2.78302e10	−1.06486	−0.532430	+	0.846474i	$0.678721\pi$
$948$	5.66391e9	0.215917
$949$	3.81239e9	0.144799
$950$	−2.49664e10	−0.944763
$951$	−2.79578e10	−1.05407
$952$	3.12551e10	1.17406
$953$	6.52265e9	0.244117	0.122059	−	0.992523i	$-0.461050\pi$
$953$	6.52265e9	0.244117	0.122059	+	0.992523i	$0.461050\pi$
$954$	3.14593e9	0.117309
$955$	−7.12470e10	−2.64701
$956$	2.62120e9	0.0970280
$957$	1.91440e10	0.706059
$958$	3.82709e10	1.40634
$959$	−1.76421e10	−0.645929
$960$	−2.81506e10	−1.02692
$961$	−9.90866e8	−0.0360150
$962$	6.63765e9	0.240382
$963$	4.60382e9	0.166122
$964$	6.81898e9	0.245160
$965$	3.07964e8	0.0110320
$966$	7.76362e8	0.0277105
$967$	−1.65215e10	−0.587565	−0.293782	−	0.955872i	$-0.594914\pi$
$967$	−1.65215e10	−0.587565	−0.293782	+	0.955872i	$0.594914\pi$
$968$	−1.72571e10	−0.611512
$969$	−1.01747e10	−0.359244
$970$	−7.22039e10	−2.54015
$971$	−1.29217e10	−0.452952	−0.226476	−	0.974017i	$-0.572721\pi$
$971$	−1.29217e10	−0.452952	−0.226476	+	0.974017i	$0.572721\pi$
$972$	6.85329e8	0.0239369
$973$	1.34937e10	0.469609
$974$	−4.48806e9	−0.155633
$975$	5.76856e9	0.199320
$976$	−3.62627e9	−0.124849
$977$	3.08243e10	1.05745	0.528727	−	0.848792i	$-0.322669\pi$
$977$	3.08243e10	1.05745	0.528727	+	0.848792i	$0.322669\pi$
$978$	6.73872e9	0.230352
$979$	9.82802e9	0.334755
$980$	−3.29964e9	−0.111989
$981$	6.53774e9	0.221099
$982$	6.09960e9	0.205547
$983$	−4.16024e10	−1.39695	−0.698476	−	0.715634i	$-0.746138\pi$
$983$	−4.16024e10	−1.39695	−0.698476	+	0.715634i	$0.746138\pi$
$984$	−1.95856e10	−0.655322
$985$	7.03099e10	2.34417
$986$	−4.38788e10	−1.45776
$987$	−8.31671e9	−0.275322
$988$	1.27761e9	0.0421454
$989$	1.20507e9	0.0396118
$990$	9.09115e9	0.297780
$991$	1.94365e9	0.0634396	0.0317198	−	0.999497i	$-0.489902\pi$
$991$	1.94365e9	0.0634396	0.0317198	+	0.999497i	$0.489902\pi$
$992$	2.11644e10	0.688358
$993$	1.91154e10	0.619529
$994$	4.13913e10	1.33677
$995$	−5.80529e10	−1.86829
$996$	−1.12686e10	−0.361378
$997$	−1.22910e10	−0.392785	−0.196392	−	0.980525i	$-0.562923\pi$
$997$	−1.22910e10	−0.392785	−0.196392	+	0.980525i	$0.562923\pi$
$998$	2.32416e10	0.740133
$999$	−1.01856e10	−0.323226

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.8.a.c.1.17	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.8.a.c.1.17	✓	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)

\(f(q)\)	\(=\)	\(q-8.95758 q^{2} -27.0000 q^{3} -47.7618 q^{4} +476.788 q^{5} +241.855 q^{6} +984.094 q^{7} +1574.40 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-8.95758 q^{2} -27.0000 q^{3} -47.7618 q^{4} +476.788 q^{5} +241.855 q^{6} +984.094 q^{7} +1574.40 q^{8} +729.000 q^{9} -4270.87 q^{10} -2919.95 q^{11} +1289.57 q^{12} -1431.95 q^{13} -8815.10 q^{14} -12873.3 q^{15} -7989.31 q^{16} +20172.9 q^{17} -6530.08 q^{18} +18680.6 q^{19} -22772.2 q^{20} -26570.5 q^{21} +26155.7 q^{22} +3261.92 q^{23} -42508.8 q^{24} +149202. q^{25} +12826.8 q^{26} -19683.0 q^{27} -47002.0 q^{28} +242826. q^{29} +115313. q^{30} -162855. q^{31} -129958. q^{32} +78838.5 q^{33} -180701. q^{34} +469204. q^{35} -34818.3 q^{36} +517481. q^{37} -167333. q^{38} +38662.8 q^{39} +750655. q^{40} +460743. q^{41} +238008. q^{42} +369436. q^{43} +139462. q^{44} +347579. q^{45} -29218.9 q^{46} +313005. q^{47} +215711. q^{48} +144898. q^{49} -1.33649e6 q^{50} -544670. q^{51} +68392.6 q^{52} -481761. q^{53} +176312. q^{54} -1.39220e6 q^{55} +1.54936e6 q^{56} -504375. q^{57} -2.17513e6 q^{58} -319815. q^{59} +614851. q^{60} +453891. q^{61} +1.45879e6 q^{62} +717404. q^{63} +2.18674e6 q^{64} -682739. q^{65} -706203. q^{66} +2.72796e6 q^{67} -963495. q^{68} -88071.8 q^{69} -4.20294e6 q^{70} -4.69550e6 q^{71} +1.14774e6 q^{72} -2.66237e6 q^{73} -4.63538e6 q^{74} -4.02845e6 q^{75} -892217. q^{76} -2.87350e6 q^{77} -346325. q^{78} +4.39210e6 q^{79} -3.80921e6 q^{80} +531441. q^{81} -4.12714e6 q^{82} -8.73826e6 q^{83} +1.26906e6 q^{84} +9.61822e6 q^{85} -3.30925e6 q^{86} -6.55629e6 q^{87} -4.59716e6 q^{88} -3.36582e6 q^{89} -3.11346e6 q^{90} -1.40918e6 q^{91} -155795. q^{92} +4.39708e6 q^{93} -2.80377e6 q^{94} +8.90668e6 q^{95} +3.50887e6 q^{96} +1.69061e7 q^{97} -1.29793e6 q^{98} -2.12864e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{2} - 1296 q^{3} + 3214 q^{4} + 428 q^{5} - 54 q^{6} - 680 q^{7} + 2355 q^{8} + 34992 q^{9}+O(q^{10}) \) 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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