LMFDB - Embedded newform 471.8.a.c.1.20

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			1.20
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)

$f(q)$	$=$	$q-3.69501 q^{2} -27.0000 q^{3} -114.347 q^{4} -349.671 q^{5} +99.7651 q^{6} +479.777 q^{7} +895.473 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-3.69501 q^{2} -27.0000 q^{3} -114.347 q^{4} -349.671 q^{5} +99.7651 q^{6} +479.777 q^{7} +895.473 q^{8} +729.000 q^{9} +1292.04 q^{10} +1140.73 q^{11} +3087.37 q^{12} +569.886 q^{13} -1772.78 q^{14} +9441.11 q^{15} +11327.6 q^{16} -13343.4 q^{17} -2693.66 q^{18} +17744.5 q^{19} +39983.8 q^{20} -12954.0 q^{21} -4215.02 q^{22} +4194.61 q^{23} -24177.8 q^{24} +44144.6 q^{25} -2105.73 q^{26} -19683.0 q^{27} -54861.0 q^{28} +199056. q^{29} -34885.0 q^{30} -20406.5 q^{31} -156476. q^{32} -30799.8 q^{33} +49303.9 q^{34} -167764. q^{35} -83358.9 q^{36} +198598. q^{37} -65565.9 q^{38} -15386.9 q^{39} -313121. q^{40} +582171. q^{41} +47865.0 q^{42} -722361. q^{43} -130440. q^{44} -254910. q^{45} -15499.1 q^{46} -354654. q^{47} -305846. q^{48} -593357. q^{49} -163115. q^{50} +360271. q^{51} -65164.7 q^{52} -946771. q^{53} +72728.8 q^{54} -398882. q^{55} +429627. q^{56} -479101. q^{57} -735514. q^{58} -2.22359e6 q^{59} -1.07956e6 q^{60} -699785. q^{61} +75402.1 q^{62} +349757. q^{63} -871756. q^{64} -199273. q^{65} +113806. q^{66} -1.66324e6 q^{67} +1.52577e6 q^{68} -113254. q^{69} +619889. q^{70} -1.16770e6 q^{71} +652800. q^{72} -5.54631e6 q^{73} -733821. q^{74} -1.19191e6 q^{75} -2.02903e6 q^{76} +547298. q^{77} +56854.8 q^{78} +5.25358e6 q^{79} -3.96094e6 q^{80} +531441. q^{81} -2.15112e6 q^{82} -4.69403e6 q^{83} +1.48125e6 q^{84} +4.66579e6 q^{85} +2.66913e6 q^{86} -5.37452e6 q^{87} +1.02150e6 q^{88} +6.61276e6 q^{89} +941894. q^{90} +273418. q^{91} -479641. q^{92} +550976. q^{93} +1.31045e6 q^{94} -6.20472e6 q^{95} +4.22486e6 q^{96} -1.57749e7 q^{97} +2.19246e6 q^{98} +831596. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.69501	−0.326595	−0.163298	−	0.986577i	$-0.552213\pi$
$2$	−3.69501	−0.326595	−0.163298	+	0.986577i	$0.552213\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	−114.347	−0.893335
$5$	−349.671	−1.25102	−0.625510	−	0.780216i	$-0.715109\pi$
$5$	−349.671	−1.25102	−0.625510	+	0.780216i	$0.715109\pi$
$6$	99.7651	0.188560
$7$	479.777	0.528684	0.264342	−	0.964429i	$-0.414845\pi$
$7$	479.777	0.528684	0.264342	+	0.964429i	$0.414845\pi$
$8$	895.473	0.618355
$9$	729.000	0.333333
$10$	1292.04	0.408577
$11$	1140.73	0.258411	0.129205	−	0.991618i	$-0.458757\pi$
$11$	1140.73	0.258411	0.129205	+	0.991618i	$0.458757\pi$
$12$	3087.37	0.515767
$13$	569.886	0.0719426	0.0359713	−	0.999353i	$-0.488548\pi$
$13$	569.886	0.0719426	0.0359713	+	0.999353i	$0.488548\pi$
$14$	−1772.78	−0.172666
$15$	9441.11	0.722277
$16$	11327.6	0.691384
$17$	−13343.4	−0.658711	−0.329355	−	0.944206i	$-0.606831\pi$
$17$	−13343.4	−0.658711	−0.329355	+	0.944206i	$0.606831\pi$
$18$	−2693.66	−0.108865
$19$	17744.5	0.593506	0.296753	−	0.954954i	$-0.404096\pi$
$19$	17744.5	0.593506	0.296753	+	0.954954i	$0.404096\pi$
$20$	39983.8	1.11758
$21$	−12954.0	−0.305236
$22$	−4215.02	−0.0843957
$23$	4194.61	0.0718859	0.0359430	−	0.999354i	$-0.488557\pi$
$23$	4194.61	0.0718859	0.0359430	+	0.999354i	$0.488557\pi$
$24$	−24177.8	−0.357007
$25$	44144.6	0.565051
$26$	−2105.73	−0.0234961
$27$	−19683.0	−0.192450
$28$	−54861.0	−0.472292
$29$	199056.	1.51559	0.757797	−	0.652490i	$-0.226276\pi$
$29$	199056.	1.51559	0.757797	+	0.652490i	$0.226276\pi$
$30$	−34885.0	−0.235892
$31$	−20406.5	−0.123028	−0.0615138	−	0.998106i	$-0.519593\pi$
$31$	−20406.5	−0.123028	−0.0615138	+	0.998106i	$0.519593\pi$
$32$	−156476.	−0.844157
$33$	−30799.8	−0.149193
$34$	49303.9	0.215132
$35$	−167764.	−0.661394
$36$	−83358.9	−0.297778
$37$	198598.	0.644569	0.322284	−	0.946643i	$-0.395549\pi$
$37$	198598.	0.644569	0.322284	+	0.946643i	$0.395549\pi$
$38$	−65565.9	−0.193836
$39$	−15386.9	−0.0415361
$40$	−313121.	−0.773574
$41$	582171.	1.31919	0.659594	−	0.751622i	$-0.270728\pi$
$41$	582171.	1.31919	0.659594	+	0.751622i	$0.270728\pi$
$42$	47865.0	0.0996886
$43$	−722361.	−1.38553	−0.692763	−	0.721165i	$-0.743607\pi$
$43$	−722361.	−1.38553	−0.692763	+	0.721165i	$0.743607\pi$
$44$	−130440.	−0.230847
$45$	−254910.	−0.417007
$46$	−15499.1	−0.0234776
$47$	−354654.	−0.498268	−0.249134	−	0.968469i	$-0.580146\pi$
$47$	−354654.	−0.498268	−0.249134	+	0.968469i	$0.580146\pi$
$48$	−305846.	−0.399171
$49$	−593357.	−0.720493
$50$	−163115.	−0.184543
$51$	360271.	0.380307
$52$	−65164.7	−0.0642689
$53$	−946771.	−0.873533	−0.436766	−	0.899575i	$-0.643876\pi$
$53$	−946771.	−0.873533	−0.436766	+	0.899575i	$0.643876\pi$
$54$	72728.8	0.0628533
$55$	−398882.	−0.323277
$56$	429627.	0.326914
$57$	−479101.	−0.342661
$58$	−735514.	−0.494986
$59$	−2.22359e6	−1.40952	−0.704762	−	0.709443i	$-0.748946\pi$
$59$	−2.22359e6	−1.40952	−0.704762	+	0.709443i	$0.748946\pi$
$60$	−1.07956e6	−0.645235
$61$	−699785.	−0.394739	−0.197370	−	0.980329i	$-0.563240\pi$
$61$	−699785.	−0.394739	−0.197370	+	0.980329i	$0.563240\pi$
$62$	75402.1	0.0401803
$63$	349757.	0.176228
$64$	−871756.	−0.415686
$65$	−199273.	−0.0900017
$66$	113806.	0.0487259
$67$	−1.66324e6	−0.675605	−0.337803	−	0.941217i	$-0.609684\pi$
$67$	−1.66324e6	−0.675605	−0.337803	+	0.941217i	$0.609684\pi$
$68$	1.52577e6	0.588449
$69$	−113254.	−0.0415034
$70$	619889.	0.216008
$71$	−1.16770e6	−0.387192	−0.193596	−	0.981081i	$-0.562015\pi$
$71$	−1.16770e6	−0.387192	−0.193596	+	0.981081i	$0.562015\pi$
$72$	652800.	0.206118
$73$	−5.54631e6	−1.66868	−0.834342	−	0.551247i	$-0.814152\pi$
$73$	−5.54631e6	−1.66868	−0.834342	+	0.551247i	$0.814152\pi$
$74$	−733821.	−0.210513
$75$	−1.19191e6	−0.326233
$76$	−2.02903e6	−0.530200
$77$	547298.	0.136618
$78$	56854.8	0.0135655
$79$	5.25358e6	1.19884	0.599419	−	0.800436i	$-0.295399\pi$
$79$	5.25358e6	1.19884	0.599419	+	0.800436i	$0.295399\pi$
$80$	−3.96094e6	−0.864935
$81$	531441.	0.111111
$82$	−2.15112e6	−0.430841
$83$	−4.69403e6	−0.901100	−0.450550	−	0.892751i	$-0.648772\pi$
$83$	−4.69403e6	−0.901100	−0.450550	+	0.892751i	$0.648772\pi$
$84$	1.48125e6	0.272678
$85$	4.66579e6	0.824060
$86$	2.66913e6	0.452506
$87$	−5.37452e6	−0.875029
$88$	1.02150e6	0.159789
$89$	6.61276e6	0.994301	0.497150	−	0.867664i	$-0.334380\pi$
$89$	6.61276e6	0.994301	0.497150	+	0.867664i	$0.334380\pi$
$90$	941894.	0.136192
$91$	273418.	0.0380349
$92$	−479641.	−0.0642183
$93$	550976.	0.0710300
$94$	1.31045e6	0.162732
$95$	−6.20472e6	−0.742488
$96$	4.22486e6	0.487374
$97$	−1.57749e7	−1.75495	−0.877475	−	0.479622i	$-0.840774\pi$
$97$	−1.57749e7	−1.75495	−0.877475	+	0.479622i	$0.840774\pi$
$98$	2.19246e6	0.235310
$99$	831596.	0.0861369
$100$	−5.04780e6	−0.504780
$101$	1.82538e7	1.76290	0.881452	−	0.472274i	$-0.156567\pi$
$101$	1.82538e7	1.76290	0.881452	+	0.472274i	$0.156567\pi$
$102$	−1.33120e6	−0.124206
$103$	1.43144e7	1.29075	0.645376	−	0.763865i	$-0.276701\pi$
$103$	1.43144e7	1.29075	0.645376	+	0.763865i	$0.276701\pi$
$104$	510318.	0.0444861
$105$	4.52963e6	0.381856
$106$	3.49832e6	0.285292
$107$	−3.27766e6	−0.258655	−0.129328	−	0.991602i	$-0.541282\pi$
$107$	−3.27766e6	−0.258655	−0.129328	+	0.991602i	$0.541282\pi$
$108$	2.25069e6	0.171922
$109$	2.31316e7	1.71085	0.855427	−	0.517923i	$-0.173295\pi$
$109$	2.31316e7	1.71085	0.855427	+	0.517923i	$0.173295\pi$
$110$	1.47387e6	0.105581
$111$	−5.36215e6	−0.372142
$112$	5.43474e6	0.365524
$113$	−1.45872e6	−0.0951034	−0.0475517	−	0.998869i	$-0.515142\pi$
$113$	−1.45872e6	−0.0951034	−0.0475517	+	0.998869i	$0.515142\pi$
$114$	1.77028e6	0.111912
$115$	−1.46673e6	−0.0899307
$116$	−2.27615e7	−1.35393
$117$	415447.	0.0239809
$118$	8.21618e6	0.460344
$119$	−6.40185e6	−0.348250
$120$	8.45426e6	0.446623
$121$	−1.81859e7	−0.933224
$122$	2.58571e6	0.128920
$123$	−1.57186e7	−0.761634
$124$	2.33342e6	0.109905
$125$	1.18819e7	0.544130
$126$	−1.29236e6	−0.0575553
$127$	6.94753e6	0.300966	0.150483	−	0.988613i	$-0.451917\pi$
$127$	6.94753e6	0.300966	0.150483	+	0.988613i	$0.451917\pi$
$128$	2.32501e7	0.979918
$129$	1.95037e7	0.799934
$130$	736313.	0.0293941
$131$	254867.	0.00990523	0.00495262	−	0.999988i	$-0.498424\pi$
$131$	254867.	0.00990523	0.00495262	+	0.999988i	$0.498424\pi$
$132$	3.52187e6	0.133280
$133$	8.51339e6	0.313777
$134$	6.14568e6	0.220650
$135$	6.88257e6	0.240759
$136$	−1.19486e7	−0.407317
$137$	8.81652e6	0.292938	0.146469	−	0.989215i	$-0.453209\pi$
$137$	8.81652e6	0.292938	0.146469	+	0.989215i	$0.453209\pi$
$138$	418476.	0.0135548
$139$	4.63121e7	1.46266	0.731329	−	0.682025i	$-0.238900\pi$
$139$	4.63121e7	1.46266	0.731329	+	0.682025i	$0.238900\pi$
$140$	1.91833e7	0.590847
$141$	9.57567e6	0.287675
$142$	4.31465e6	0.126455
$143$	650089.	0.0185907
$144$	8.25784e6	0.230461
$145$	−6.96042e7	−1.89604
$146$	2.04936e7	0.544984
$147$	1.60206e7	0.415977
$148$	−2.27091e7	−0.575816
$149$	5.98553e7	1.48235	0.741175	−	0.671312i	$-0.234269\pi$
$149$	5.98553e7	1.48235	0.741175	+	0.671312i	$0.234269\pi$
$150$	4.40410e6	0.106546
$151$	−7.66359e7	−1.81139	−0.905697	−	0.423926i	$-0.860652\pi$
$151$	−7.66359e7	−1.81139	−0.905697	+	0.423926i	$0.860652\pi$
$152$	1.58897e7	0.366997
$153$	−9.72732e6	−0.219570
$154$	−2.02227e6	−0.0446187
$155$	7.13556e6	0.153910
$156$	1.75945e6	0.0371057
$157$	−3.86989e6	−0.0798087
$157$	−3.86989e6	−0.0798087
$158$	−1.94120e7	−0.391535
$159$	2.55628e7	0.504334
$160$	5.47152e7	1.05606
$161$	2.01248e6	0.0380049
$162$	−1.96368e6	−0.0362884
$163$	−7.02004e7	−1.26965	−0.634823	−	0.772657i	$-0.718927\pi$
$163$	−7.02004e7	−1.26965	−0.634823	+	0.772657i	$0.718927\pi$
$164$	−6.65695e7	−1.17848
$165$	1.07698e7	0.186644
$166$	1.73445e7	0.294295
$167$	−2.76654e7	−0.459653	−0.229826	−	0.973232i	$-0.573816\pi$
$167$	−2.76654e7	−0.459653	−0.229826	+	0.973232i	$0.573816\pi$
$168$	−1.15999e7	−0.188744
$169$	−6.24237e7	−0.994824
$170$	−1.72401e7	−0.269134
$171$	1.29357e7	0.197835
$172$	8.25998e7	1.23774
$173$	4.34872e7	0.638558	0.319279	−	0.947661i	$-0.396559\pi$
$173$	4.34872e7	0.638558	0.319279	+	0.947661i	$0.396559\pi$
$174$	1.98589e7	0.285780
$175$	2.11796e7	0.298734
$176$	1.29218e7	0.178661
$177$	6.00369e7	0.813790
$178$	−2.44342e7	−0.324734
$179$	−1.18400e8	−1.54300	−0.771501	−	0.636228i	$-0.780494\pi$
$179$	−1.18400e8	−1.54300	−0.771501	+	0.636228i	$0.780494\pi$
$180$	2.91482e7	0.372527
$181$	8.01161e7	1.00426	0.502128	−	0.864793i	$-0.332551\pi$
$181$	8.01161e7	1.00426	0.502128	+	0.864793i	$0.332551\pi$
$182$	−1.01028e6	−0.0124220
$183$	1.88942e7	0.227903
$184$	3.75616e6	0.0444510
$185$	−6.94440e7	−0.806369
$186$	−2.03586e6	−0.0231981
$187$	−1.52213e7	−0.170218
$188$	4.05536e7	0.445120
$189$	−9.44345e6	−0.101745
$190$	2.29265e7	0.242493
$191$	1.57802e8	1.63868	0.819341	−	0.573306i	$-0.194339\pi$
$191$	1.57802e8	1.63868	0.819341	+	0.573306i	$0.194339\pi$
$192$	2.35374e7	0.239996
$193$	−7.93173e7	−0.794177	−0.397089	−	0.917780i	$-0.629979\pi$
$193$	−7.93173e7	−0.794177	−0.397089	+	0.917780i	$0.629979\pi$
$194$	5.82882e7	0.573159
$195$	5.38036e6	0.0519625
$196$	6.78486e7	0.643642
$197$	−2.02670e8	−1.88867	−0.944337	−	0.328980i	$-0.893295\pi$
$197$	−2.02670e8	−1.88867	−0.944337	+	0.328980i	$0.893295\pi$
$198$	−3.07275e6	−0.0281319
$199$	1.41815e8	1.27566	0.637832	−	0.770176i	$-0.279831\pi$
$199$	1.41815e8	1.27566	0.637832	+	0.770176i	$0.279831\pi$
$200$	3.95303e7	0.349402
$201$	4.49075e7	0.390061
$202$	−6.74479e7	−0.575756
$203$	9.55026e7	0.801270
$204$	−4.11959e7	−0.339741
$205$	−2.03568e8	−1.65033
$206$	−5.28917e7	−0.421553
$207$	3.05787e6	0.0239620
$208$	6.45546e6	0.0497400
$209$	2.02417e7	0.153368
$210$	−1.67370e7	−0.124712
$211$	2.04267e8	1.49696	0.748479	−	0.663158i	$-0.230784\pi$
$211$	2.04267e8	1.49696	0.748479	+	0.663158i	$0.230784\pi$
$212$	1.08260e8	0.780358
$213$	3.15278e7	0.223545
$214$	1.21110e7	0.0844756
$215$	2.52589e8	1.73332
$216$	−1.76256e7	−0.119002
$217$	−9.79057e6	−0.0650428
$218$	−8.54714e7	−0.558757
$219$	1.49750e8	0.963415
$220$	4.56109e7	0.288795
$221$	−7.60421e6	−0.0473894
$222$	1.98132e7	0.121540
$223$	−3.74569e7	−0.226185	−0.113093	−	0.993584i	$-0.536076\pi$
$223$	−3.74569e7	−0.226185	−0.113093	+	0.993584i	$0.536076\pi$
$224$	−7.50737e7	−0.446293
$225$	3.21814e7	0.188350
$226$	5.38996e6	0.0310603
$227$	−3.05553e8	−1.73379	−0.866895	−	0.498490i	$-0.833888\pi$
$227$	−3.05553e8	−1.73379	−0.866895	+	0.498490i	$0.833888\pi$
$228$	5.47837e7	0.306111
$229$	−2.29199e7	−0.126121	−0.0630607	−	0.998010i	$-0.520086\pi$
$229$	−2.29199e7	−0.126121	−0.0630607	+	0.998010i	$0.520086\pi$
$230$	5.41958e6	0.0293710
$231$	−1.47771e7	−0.0788762
$232$	1.78250e8	0.937175
$233$	−2.20997e8	−1.14457	−0.572283	−	0.820056i	$-0.693942\pi$
$233$	−2.20997e8	−1.14457	−0.572283	+	0.820056i	$0.693942\pi$
$234$	−1.53508e6	−0.00783204
$235$	1.24012e8	0.623343
$236$	2.54261e8	1.25918
$237$	−1.41847e8	−0.692149
$238$	2.36549e7	0.113737
$239$	2.05456e8	0.973476	0.486738	−	0.873548i	$-0.338187\pi$
$239$	2.05456e8	0.973476	0.486738	+	0.873548i	$0.338187\pi$
$240$	1.06945e8	0.499370
$241$	−3.87118e7	−0.178149	−0.0890746	−	0.996025i	$-0.528391\pi$
$241$	−3.87118e7	−0.178149	−0.0890746	+	0.996025i	$0.528391\pi$
$242$	6.71970e7	0.304787
$243$	−1.43489e7	−0.0641500
$244$	8.00183e7	0.352635
$245$	2.07480e8	0.901351
$246$	5.80804e7	0.248746
$247$	1.01123e7	0.0426984
$248$	−1.82735e7	−0.0760747
$249$	1.26739e8	0.520250
$250$	−4.39038e7	−0.177710
$251$	4.42462e7	0.176611	0.0883056	−	0.996093i	$-0.471855\pi$
$251$	4.42462e7	0.176611	0.0883056	+	0.996093i	$0.471855\pi$
$252$	−3.99937e7	−0.157431
$253$	4.78494e6	0.0185761
$254$	−2.56711e7	−0.0982940
$255$	−1.25976e8	−0.475771
$256$	2.56756e7	0.0956489
$257$	5.11447e8	1.87947	0.939734	−	0.341906i	$-0.111073\pi$
$257$	5.11447e8	1.87947	0.939734	+	0.341906i	$0.111073\pi$
$258$	−7.20664e7	−0.261255
$259$	9.52828e7	0.340773
$260$	2.27862e7	0.0804017
$261$	1.45112e8	0.505198
$262$	−941736.	−0.00323500
$263$	4.18935e8	1.42004	0.710021	−	0.704180i	$-0.248685\pi$
$263$	4.18935e8	1.42004	0.710021	+	0.704180i	$0.248685\pi$
$264$	−2.75804e7	−0.0922544
$265$	3.31058e8	1.09281
$266$	−3.14570e7	−0.102478
$267$	−1.78544e8	−0.574060
$268$	1.90186e8	0.603542
$269$	−4.23823e8	−1.32755	−0.663776	−	0.747931i	$-0.731047\pi$
$269$	−4.23823e8	−1.32755	−0.663776	+	0.747931i	$0.731047\pi$
$270$	−2.54311e7	−0.0786308
$271$	2.96355e8	0.904523	0.452262	−	0.891885i	$-0.350617\pi$
$271$	2.96355e8	0.904523	0.452262	+	0.891885i	$0.350617\pi$
$272$	−1.51149e8	−0.455422
$273$	−7.38229e6	−0.0219595
$274$	−3.25771e7	−0.0956721
$275$	5.03573e7	0.146015
$276$	1.29503e7	0.0370764
$277$	5.02407e8	1.42029	0.710144	−	0.704056i	$-0.248630\pi$
$277$	5.02407e8	1.42029	0.710144	+	0.704056i	$0.248630\pi$
$278$	−1.71123e8	−0.477697
$279$	−1.48763e7	−0.0410092
$280$	−1.50228e8	−0.408976
$281$	−3.69454e8	−0.993317	−0.496659	−	0.867946i	$-0.665440\pi$
$281$	−3.69454e8	−0.993317	−0.496659	+	0.867946i	$0.665440\pi$
$282$	−3.53821e7	−0.0939533
$283$	7.39944e7	0.194065	0.0970324	−	0.995281i	$-0.469065\pi$
$283$	7.39944e7	0.194065	0.0970324	+	0.995281i	$0.469065\pi$
$284$	1.33523e8	0.345892
$285$	1.67527e8	0.428676
$286$	−2.40208e6	−0.00607165
$287$	2.79312e8	0.697434
$288$	−1.14071e8	−0.281386
$289$	−2.32293e8	−0.566100
$290$	2.57188e8	0.619237
$291$	4.25921e8	1.01322
$292$	6.34203e8	1.49069
$293$	−7.04108e8	−1.63532	−0.817660	−	0.575701i	$-0.804729\pi$
$293$	−7.04108e8	−1.63532	−0.817660	+	0.575701i	$0.804729\pi$
$294$	−5.91963e7	−0.135856
$295$	7.77525e8	1.76334
$296$	1.77839e8	0.398572
$297$	−2.24531e7	−0.0497311
$298$	−2.21166e8	−0.484128
$299$	2.39045e6	0.00517166
$300$	1.36291e8	0.291435
$301$	−3.46572e8	−0.732506
$302$	2.83170e8	0.591593
$303$	−4.92853e8	−1.01781
$304$	2.01003e8	0.410341
$305$	2.44694e8	0.493827
$306$	3.59425e7	0.0717106
$307$	−7.42272e8	−1.46413	−0.732063	−	0.681237i	$-0.761442\pi$
$307$	−7.42272e8	−1.46413	−0.732063	+	0.681237i	$0.761442\pi$
$308$	−6.25819e7	−0.122045
$309$	−3.86488e8	−0.745215
$310$	−2.63659e7	−0.0502663
$311$	3.73436e8	0.703972	0.351986	−	0.936005i	$-0.385507\pi$
$311$	3.73436e8	0.703972	0.351986	+	0.936005i	$0.385507\pi$
$312$	−1.37786e7	−0.0256840
$313$	−1.73849e8	−0.320455	−0.160227	−	0.987080i	$-0.551223\pi$
$313$	−1.73849e8	−0.320455	−0.160227	+	0.987080i	$0.551223\pi$
$314$	1.42993e7	0.0260651
$315$	−1.22300e8	−0.220465
$316$	−6.00730e8	−1.07096
$317$	2.10612e7	0.0371344	0.0185672	−	0.999828i	$-0.494090\pi$
$317$	2.10612e7	0.0371344	0.0185672	+	0.999828i	$0.494090\pi$
$318$	−9.44547e7	−0.164713
$319$	2.27070e8	0.391646
$320$	3.04828e8	0.520031
$321$	8.84969e7	0.149335
$322$	−7.43611e6	−0.0124122
$323$	−2.36771e8	−0.390949
$324$	−6.07687e7	−0.0992595
$325$	2.51574e7	0.0406513
$326$	2.59391e8	0.414661
$327$	−6.24553e8	−0.987762
$328$	5.21318e8	0.815727
$329$	−1.70155e8	−0.263426
$330$	−3.97945e7	−0.0609571
$331$	3.54502e8	0.537304	0.268652	−	0.963237i	$-0.413422\pi$
$331$	3.54502e8	0.537304	0.268652	+	0.963237i	$0.413422\pi$
$332$	5.36748e8	0.804984
$333$	1.44778e8	0.214856
$334$	1.02224e8	0.150120
$335$	5.81586e8	0.845196
$336$	−1.46738e8	−0.211035
$337$	−4.09526e8	−0.582878	−0.291439	−	0.956589i	$-0.594134\pi$
$337$	−4.09526e8	−0.582878	−0.291439	+	0.956589i	$0.594134\pi$
$338$	2.30656e8	0.324905
$339$	3.93853e7	0.0549080
$340$	−5.33519e8	−0.736162
$341$	−2.32784e7	−0.0317916
$342$	−4.77975e7	−0.0646122
$343$	−6.79796e8	−0.909597
$344$	−6.46855e8	−0.856747
$345$	3.96018e7	0.0519215
$346$	−1.60685e8	−0.208550
$347$	9.74433e8	1.25198	0.625992	−	0.779829i	$-0.284694\pi$
$347$	9.74433e8	1.25198	0.625992	+	0.779829i	$0.284694\pi$
$348$	6.14560e8	0.781694
$349$	−7.24145e8	−0.911877	−0.455939	−	0.890011i	$-0.650696\pi$
$349$	−7.24145e8	−0.911877	−0.455939	+	0.890011i	$0.650696\pi$
$350$	−7.82586e7	−0.0975650
$351$	−1.12171e7	−0.0138454
$352$	−1.78498e8	−0.218139
$353$	9.75133e8	1.17992	0.589960	−	0.807433i	$-0.299144\pi$
$353$	9.75133e8	1.17992	0.589960	+	0.807433i	$0.299144\pi$
$354$	−2.21837e8	−0.265780
$355$	4.08310e8	0.484385
$356$	−7.56149e8	−0.888244
$357$	1.72850e8	0.201062
$358$	4.37489e8	0.503938
$359$	−4.12986e8	−0.471090	−0.235545	−	0.971863i	$-0.575688\pi$
$359$	−4.12986e8	−0.471090	−0.235545	+	0.971863i	$0.575688\pi$
$360$	−2.28265e8	−0.257858
$361$	−5.79006e8	−0.647750
$362$	−2.96029e8	−0.327986
$363$	4.91019e8	0.538797
$364$	−3.12645e7	−0.0339780
$365$	1.93938e9	2.08756
$366$	−6.98142e7	−0.0744320
$367$	−2.62023e8	−0.276699	−0.138350	−	0.990383i	$-0.544180\pi$
$367$	−2.62023e8	−0.276699	−0.138350	+	0.990383i	$0.544180\pi$
$368$	4.75150e7	0.0497008
$369$	4.24403e8	0.439730
$370$	2.56596e8	0.263356
$371$	−4.54239e8	−0.461823
$372$	−6.30024e7	−0.0634536
$373$	1.16942e9	1.16678	0.583390	−	0.812192i	$-0.301726\pi$
$373$	1.16942e9	1.16678	0.583390	+	0.812192i	$0.301726\pi$
$374$	5.62426e7	0.0555923
$375$	−3.20812e8	−0.314153
$376$	−3.17583e8	−0.308106
$377$	1.13439e8	0.109036
$378$	3.48936e7	0.0332295
$379$	−4.01956e8	−0.379263	−0.189632	−	0.981855i	$-0.560729\pi$
$379$	−4.01956e8	−0.379263	−0.189632	+	0.981855i	$0.560729\pi$
$380$	7.09491e8	0.663291
$381$	−1.87583e8	−0.173763
$382$	−5.83078e8	−0.535186
$383$	2.70174e8	0.245724	0.122862	−	0.992424i	$-0.460793\pi$
$383$	2.70174e8	0.245724	0.122862	+	0.992424i	$0.460793\pi$
$384$	−6.27753e8	−0.565756
$385$	−1.91374e8	−0.170911
$386$	2.93078e8	0.259375
$387$	−5.26601e8	−0.461842
$388$	1.80381e9	1.56776
$389$	6.87286e8	0.591989	0.295995	−	0.955190i	$-0.404349\pi$
$389$	6.87286e8	0.591989	0.295995	+	0.955190i	$0.404349\pi$
$390$	−1.98804e7	−0.0169707
$391$	−5.59702e7	−0.0473520
$392$	−5.31335e8	−0.445520
$393$	−6.88142e6	−0.00571879
$394$	7.48865e8	0.616832
$395$	−1.83702e9	−1.49977
$396$	−9.50904e7	−0.0769491
$397$	−4.89156e8	−0.392357	−0.196178	−	0.980568i	$-0.562853\pi$
$397$	−4.89156e8	−0.392357	−0.196178	+	0.980568i	$0.562853\pi$
$398$	−5.24007e8	−0.416626
$399$	−2.29861e8	−0.181159
$400$	5.00054e8	0.390667
$401$	4.83436e7	0.0374398	0.0187199	−	0.999825i	$-0.494041\pi$
$401$	4.83436e7	0.0374398	0.0187199	+	0.999825i	$0.494041\pi$
$402$	−1.65933e8	−0.127392
$403$	−1.16294e7	−0.00885093
$404$	−2.08727e9	−1.57486
$405$	−1.85829e8	−0.139002
$406$	−3.52883e8	−0.261691
$407$	2.26548e8	0.166563
$408$	3.22613e8	0.235164
$409$	2.02031e9	1.46011	0.730057	−	0.683386i	$-0.239493\pi$
$409$	2.02031e9	1.46011	0.730057	+	0.683386i	$0.239493\pi$
$410$	7.52185e8	0.538991
$411$	−2.38046e8	−0.169128
$412$	−1.63681e9	−1.15307
$413$	−1.06683e9	−0.745193
$414$	−1.12988e7	−0.00782587
$415$	1.64137e9	1.12729
$416$	−8.91736e7	−0.0607309
$417$	−1.25043e9	−0.844466
$418$	−7.47933e7	−0.0500894
$419$	1.75332e9	1.16442	0.582212	−	0.813037i	$-0.302187\pi$
$419$	1.75332e9	1.16442	0.582212	+	0.813037i	$0.302187\pi$
$420$	−5.17949e8	−0.341126
$421$	−1.98800e9	−1.29846	−0.649229	−	0.760593i	$-0.724908\pi$
$421$	−1.98800e9	−1.29846	−0.649229	+	0.760593i	$0.724908\pi$
$422$	−7.54768e8	−0.488900
$423$	−2.58543e8	−0.166089
$424$	−8.47808e8	−0.540153
$425$	−5.89039e8	−0.372205
$426$	−1.16495e8	−0.0730088
$427$	−3.35741e8	−0.208692
$428$	3.74791e8	0.231066
$429$	−1.75524e7	−0.0107334
$430$	−9.33316e8	−0.566095
$431$	3.08901e9	1.85844	0.929221	−	0.369524i	$-0.120479\pi$
$431$	3.08901e9	1.85844	0.929221	+	0.369524i	$0.120479\pi$
$432$	−2.22962e8	−0.133057
$433$	1.09527e9	0.648355	0.324178	−	0.945996i	$-0.394912\pi$
$433$	1.09527e9	0.648355	0.324178	+	0.945996i	$0.394912\pi$
$434$	3.61762e7	0.0212427
$435$	1.87931e9	1.09468
$436$	−2.64503e9	−1.52837
$437$	7.44311e7	0.0426648
$438$	−5.53328e8	−0.314647
$439$	−2.43549e9	−1.37392	−0.686958	−	0.726697i	$-0.741054\pi$
$439$	−2.43549e9	−1.37392	−0.686958	+	0.726697i	$0.741054\pi$
$440$	−3.57188e8	−0.199900
$441$	−4.32557e8	−0.240164
$442$	2.80976e7	0.0154772
$443$	−1.13653e9	−0.621109	−0.310555	−	0.950556i	$-0.600515\pi$
$443$	−1.13653e9	−0.621109	−0.310555	+	0.950556i	$0.600515\pi$
$444$	6.13146e8	0.332448
$445$	−2.31229e9	−1.24389
$446$	1.38403e8	0.0738711
$447$	−1.61609e9	−0.855835
$448$	−4.18249e8	−0.219766
$449$	1.26607e9	0.660079	0.330039	−	0.943967i	$-0.392938\pi$
$449$	1.26607e9	0.660079	0.330039	+	0.943967i	$0.392938\pi$
$450$	−1.18911e8	−0.0615144
$451$	6.64103e8	0.340892
$452$	1.66800e8	0.0849593
$453$	2.06917e9	1.04581
$454$	1.12902e9	0.566248
$455$	−9.56064e7	−0.0475825
$456$	−4.29022e8	−0.211886
$457$	−1.95144e7	−0.00956418	−0.00478209	−	0.999989i	$-0.501522\pi$
$457$	−1.95144e7	−0.00956418	−0.00478209	+	0.999989i	$0.501522\pi$
$458$	8.46892e7	0.0411907
$459$	2.62638e8	0.126769
$460$	1.67716e8	0.0803383
$461$	2.44677e9	1.16316	0.581580	−	0.813489i	$-0.302435\pi$
$461$	2.44677e9	1.16316	0.581580	+	0.813489i	$0.302435\pi$
$462$	5.46013e7	0.0257606
$463$	−2.74617e9	−1.28586	−0.642931	−	0.765924i	$-0.722282\pi$
$463$	−2.74617e9	−1.28586	−0.642931	+	0.765924i	$0.722282\pi$
$464$	2.25484e9	1.04786
$465$	−1.92660e8	−0.0888600
$466$	8.16585e8	0.373810
$467$	2.14258e9	0.973482	0.486741	−	0.873546i	$-0.338186\pi$
$467$	2.14258e9	0.973482	0.486741	+	0.873546i	$0.338186\pi$
$468$	−4.75051e7	−0.0214230
$469$	−7.97984e8	−0.357182
$470$	−4.58226e8	−0.203581
$471$	1.04487e8	0.0460776
$472$	−1.99117e9	−0.871586
$473$	−8.24022e8	−0.358035
$474$	5.24124e8	0.226053
$475$	7.83323e8	0.335362
$476$	7.32031e8	0.311104
$477$	−6.90196e8	−0.291178
$478$	−7.59160e8	−0.317933
$479$	2.82467e9	1.17434	0.587169	−	0.809464i	$-0.300242\pi$
$479$	2.82467e9	1.17434	0.587169	+	0.809464i	$0.300242\pi$
$480$	−1.47731e9	−0.609715
$481$	1.13178e8	0.0463720
$482$	1.43040e8	0.0581827
$483$	−5.43369e7	−0.0219422
$484$	2.07950e9	0.833682
$485$	5.51601e9	2.19548
$486$	5.30193e7	0.0209511
$487$	−1.71459e9	−0.672681	−0.336341	−	0.941740i	$-0.609189\pi$
$487$	−1.71459e9	−0.672681	−0.336341	+	0.941740i	$0.609189\pi$
$488$	−6.26639e8	−0.244089
$489$	1.89541e9	0.733031
$490$	−7.66638e8	−0.294377
$491$	−1.24935e9	−0.476321	−0.238161	−	0.971226i	$-0.576544\pi$
$491$	−1.24935e9	−0.476321	−0.238161	+	0.971226i	$0.576544\pi$
$492$	1.79738e9	0.680395
$493$	−2.65608e9	−0.998338
$494$	−3.73651e7	−0.0139451
$495$	−2.90785e8	−0.107759
$496$	−2.31157e8	−0.0850593
$497$	−5.60234e8	−0.204702
$498$	−4.68301e8	−0.169911
$499$	−4.77137e9	−1.71906	−0.859531	−	0.511084i	$-0.829244\pi$
$499$	−4.77137e9	−1.71906	−0.859531	+	0.511084i	$0.829244\pi$
$500$	−1.35866e9	−0.486090
$501$	7.46967e8	0.265381
$502$	−1.63490e8	−0.0576804
$503$	1.87732e9	0.657736	0.328868	−	0.944376i	$-0.393333\pi$
$503$	1.87732e9	0.657736	0.328868	+	0.944376i	$0.393333\pi$
$504$	3.13198e8	0.108971
$505$	−6.38282e9	−2.20543
$506$	−1.76804e7	−0.00606686
$507$	1.68544e9	0.574362
$508$	−7.94428e8	−0.268863
$509$	1.92997e8	0.0648692	0.0324346	−	0.999474i	$-0.489674\pi$
$509$	1.92997e8	0.0648692	0.0324346	+	0.999474i	$0.489674\pi$
$510$	4.65483e8	0.155385
$511$	−2.66099e9	−0.882207
$512$	−3.07088e9	−1.01116
$513$	−3.49264e8	−0.114220
$514$	−1.88980e9	−0.613826
$515$	−5.00532e9	−1.61476
$516$	−2.23019e9	−0.714609
$517$	−4.04566e8	−0.128758
$518$	−3.52071e8	−0.111295
$519$	−1.17415e9	−0.368671
$520$	−1.78443e8	−0.0556530
$521$	1.44143e9	0.446540	0.223270	−	0.974757i	$-0.428327\pi$
$521$	1.44143e9	0.446540	0.223270	+	0.974757i	$0.428327\pi$
$522$	−5.36190e8	−0.164995
$523$	4.40628e9	1.34684	0.673420	−	0.739260i	$-0.264825\pi$
$523$	4.40628e9	1.34684	0.673420	+	0.739260i	$0.264825\pi$
$524$	−2.91433e7	−0.00884869
$525$	−5.71849e8	−0.172474
$526$	−1.54797e9	−0.463779
$527$	2.72292e8	0.0810396
$528$	−3.48889e8	−0.103150
$529$	−3.38723e9	−0.994832
$530$	−1.22326e9	−0.356906
$531$	−1.62100e9	−0.469842
$532$	−9.73480e8	−0.280308
$533$	3.31771e8	0.0949059
$534$	6.59723e8	0.187485
$535$	1.14610e9	0.323583
$536$	−1.48939e9	−0.417764
$537$	3.19680e9	0.890853
$538$	1.56603e9	0.433573
$539$	−6.76863e8	−0.186183
$540$	−7.87001e8	−0.215078
$541$	−3.06217e9	−0.831457	−0.415728	−	0.909489i	$-0.636473\pi$
$541$	−3.06217e9	−0.831457	−0.415728	+	0.909489i	$0.636473\pi$
$542$	−1.09503e9	−0.295413
$543$	−2.16313e9	−0.579808
$544$	2.08792e9	0.556055
$545$	−8.08845e9	−2.14031
$546$	2.72776e7	0.00717186
$547$	5.36423e8	0.140137	0.0700684	−	0.997542i	$-0.477678\pi$
$547$	5.36423e8	0.140137	0.0700684	+	0.997542i	$0.477678\pi$
$548$	−1.00814e9	−0.261692
$549$	−5.10144e8	−0.131580
$550$	−1.86071e8	−0.0476879
$551$	3.53215e9	0.899515
$552$	−1.01416e8	−0.0256638
$553$	2.52054e9	0.633806
$554$	−1.85640e9	−0.463860
$555$	1.87499e9	0.465557
$556$	−5.29565e9	−1.30664
$557$	4.78417e9	1.17304	0.586520	−	0.809935i	$-0.300497\pi$
$557$	4.78417e9	1.17304	0.586520	+	0.809935i	$0.300497\pi$
$558$	5.49682e7	0.0133934
$559$	−4.11664e8	−0.0996784
$560$	−1.90037e9	−0.457277
$561$	4.10974e8	0.0982753
$562$	1.36513e9	0.324413
$563$	2.27034e9	0.536180	0.268090	−	0.963394i	$-0.413608\pi$
$563$	2.27034e9	0.536180	0.268090	+	0.963394i	$0.413608\pi$
$564$	−1.09495e9	−0.256990
$565$	5.10070e8	0.118976
$566$	−2.73410e8	−0.0633806
$567$	2.54973e8	0.0587427
$568$	−1.04564e9	−0.239422
$569$	6.04986e9	1.37674	0.688371	−	0.725359i	$-0.258326\pi$
$569$	6.04986e9	1.37674	0.688371	+	0.725359i	$0.258326\pi$
$570$	−6.19015e8	−0.140004
$571$	−3.19674e9	−0.718589	−0.359294	−	0.933224i	$-0.616983\pi$
$571$	−3.19674e9	−0.718589	−0.359294	+	0.933224i	$0.616983\pi$
$572$	−7.43357e7	−0.0166078
$573$	−4.26064e9	−0.946094
$574$	−1.03206e9	−0.227779
$575$	1.85169e8	0.0406192
$576$	−6.35510e8	−0.138562
$577$	−2.12629e7	−0.00460793	−0.00230397	−	0.999997i	$-0.500733\pi$
$577$	−2.12629e7	−0.00460793	−0.00230397	+	0.999997i	$0.500733\pi$
$578$	8.58323e8	0.184886
$579$	2.14157e9	0.458518
$580$	7.95902e9	1.69380
$581$	−2.25209e9	−0.476397
$582$	−1.57378e9	−0.330913
$583$	−1.08001e9	−0.225730
$584$	−4.96657e9	−1.03184
$585$	−1.45270e8	−0.0300006
$586$	2.60168e9	0.534088
$587$	−1.64306e9	−0.335289	−0.167644	−	0.985848i	$-0.553616\pi$
$587$	−1.64306e9	−0.335289	−0.167644	+	0.985848i	$0.553616\pi$
$588$	−1.83191e9	−0.371607
$589$	−3.62103e8	−0.0730177
$590$	−2.87296e9	−0.575900
$591$	5.47208e9	1.09043
$592$	2.24965e9	0.445644
$593$	3.18381e8	0.0626982	0.0313491	−	0.999508i	$-0.490020\pi$
$593$	3.18381e8	0.0626982	0.0313491	+	0.999508i	$0.490020\pi$
$594$	8.29643e7	0.0162420
$595$	2.23854e9	0.435667
$596$	−6.84427e9	−1.32424
$597$	−3.82900e9	−0.736505
$598$	−8.83272e6	−0.00168904
$599$	3.72970e9	0.709055	0.354528	−	0.935046i	$-0.384642\pi$
$599$	3.72970e9	0.709055	0.354528	+	0.935046i	$0.384642\pi$
$600$	−1.06732e9	−0.201727
$601$	−6.68557e8	−0.125625	−0.0628127	−	0.998025i	$-0.520007\pi$
$601$	−6.68557e8	−0.125625	−0.0628127	+	0.998025i	$0.520007\pi$
$602$	1.28059e9	0.239233
$603$	−1.21250e9	−0.225202
$604$	8.76308e9	1.61818
$605$	6.35908e9	1.16748
$606$	1.82109e9	0.332413
$607$	7.46688e8	0.135512	0.0677562	−	0.997702i	$-0.478416\pi$
$607$	7.46688e8	0.135512	0.0677562	+	0.997702i	$0.478416\pi$
$608$	−2.77659e9	−0.501013
$609$	−2.57857e9	−0.462614
$610$	−9.04147e8	−0.161282
$611$	−2.02113e8	−0.0358467
$612$	1.11229e9	0.196150
$613$	3.07413e8	0.0539026	0.0269513	−	0.999637i	$-0.491420\pi$
$613$	3.07413e8	0.0539026	0.0269513	+	0.999637i	$0.491420\pi$
$614$	2.74270e9	0.478177
$615$	5.49634e9	0.952820
$616$	4.90091e8	0.0844781
$617$	4.50514e9	0.772165	0.386083	−	0.922464i	$-0.373828\pi$
$617$	4.50514e9	0.772165	0.386083	+	0.922464i	$0.373828\pi$
$618$	1.42808e9	0.243384
$619$	−9.84390e9	−1.66821	−0.834103	−	0.551608i	$-0.814014\pi$
$619$	−9.84390e9	−1.66821	−0.834103	+	0.551608i	$0.814014\pi$
$620$	−8.15929e8	−0.137493
$621$	−8.25625e7	−0.0138345
$622$	−1.37985e9	−0.229914
$623$	3.17265e9	0.525671
$624$	−1.74297e8	−0.0287174
$625$	−7.60357e9	−1.24577
$626$	6.42372e8	0.104659
$627$	−5.46527e8	−0.0885473
$628$	4.42510e8	0.0712959
$629$	−2.64997e9	−0.424584
$630$	4.51899e8	0.0720028
$631$	−8.03177e9	−1.27265	−0.636324	−	0.771422i	$-0.719546\pi$
$631$	−8.03177e9	−1.27265	−0.636324	+	0.771422i	$0.719546\pi$
$632$	4.70444e9	0.741306
$633$	−5.51521e9	−0.864269
$634$	−7.78213e7	−0.0121279
$635$	−2.42935e9	−0.376514
$636$	−2.92303e9	−0.450540
$637$	−3.38146e8	−0.0518342
$638$	−8.39026e8	−0.127910
$639$	−8.51251e8	−0.129064
$640$	−8.12988e9	−1.22590
$641$	−1.27581e10	−1.91329	−0.956647	−	0.291252i	$-0.905928\pi$
$641$	−1.27581e10	−1.91329	−0.956647	+	0.291252i	$0.905928\pi$
$642$	−3.26997e8	−0.0487720
$643$	1.13786e10	1.68791	0.843955	−	0.536414i	$-0.180221\pi$
$643$	1.13786e10	1.68791	0.843955	+	0.536414i	$0.180221\pi$
$644$	−2.30120e8	−0.0339512
$645$	−6.81989e9	−1.00073
$646$	8.74871e8	0.127682
$647$	1.11682e10	1.62113	0.810565	−	0.585649i	$-0.199160\pi$
$647$	1.11682e10	1.62113	0.810565	+	0.585649i	$0.199160\pi$
$648$	4.75891e8	0.0687061
$649$	−2.53653e9	−0.364236
$650$	−9.29568e7	−0.0132765
$651$	2.64345e8	0.0375525
$652$	8.02720e9	1.13422
$653$	4.49329e9	0.631492	0.315746	−	0.948844i	$-0.397745\pi$
$653$	4.49329e9	0.631492	0.315746	+	0.948844i	$0.397745\pi$
$654$	2.30773e9	0.322599
$655$	−8.91196e7	−0.0123916
$656$	6.59462e9	0.912066
$657$	−4.04326e9	−0.556228
$658$	6.28723e8	0.0860338
$659$	−2.35497e9	−0.320543	−0.160272	−	0.987073i	$-0.551237\pi$
$659$	−2.35497e9	−0.320543	−0.160272	+	0.987073i	$0.551237\pi$
$660$	−1.23149e9	−0.166736
$661$	1.44616e10	1.94765	0.973823	−	0.227306i	$-0.0729916\pi$
$661$	1.44616e10	1.94765	0.973823	+	0.227306i	$0.0729916\pi$
$662$	−1.30989e9	−0.175481
$663$	2.05314e8	0.0273603
$664$	−4.20338e9	−0.557199
$665$	−2.97688e9	−0.392542
$666$	−5.34956e8	−0.0701711
$667$	8.34963e8	0.108950
$668$	3.16346e9	0.410624
$669$	1.01134e9	0.130588
$670$	−2.14896e9	−0.276037
$671$	−7.98270e8	−0.102005
$672$	2.02699e9	0.257667
$673$	1.55015e10	1.96030	0.980149	−	0.198264i	$-0.0635302\pi$
$673$	1.55015e10	1.96030	0.980149	+	0.198264i	$0.0635302\pi$
$674$	1.51320e9	0.190365
$675$	−8.68899e8	−0.108744
$676$	7.13796e9	0.888712
$677$	−8.82108e9	−1.09260	−0.546301	−	0.837589i	$-0.683964\pi$
$677$	−8.82108e9	−1.09260	−0.546301	+	0.837589i	$0.683964\pi$
$678$	−1.45529e8	−0.0179327
$679$	−7.56842e9	−0.927814
$680$	4.17809e9	0.509561
$681$	8.24994e9	1.00100
$682$	8.60138e7	0.0103830
$683$	−3.63039e8	−0.0435995	−0.0217997	−	0.999762i	$-0.506940\pi$
$683$	−3.63039e8	−0.0435995	−0.0217997	+	0.999762i	$0.506940\pi$
$684$	−1.47916e9	−0.176733
$685$	−3.08288e9	−0.366471
$686$	2.51185e9	0.297070
$687$	6.18837e8	0.0728162
$688$	−8.18264e9	−0.957930
$689$	−5.39552e8	−0.0628443
$690$	−1.46329e8	−0.0169573
$691$	−4.62421e9	−0.533168	−0.266584	−	0.963812i	$-0.585895\pi$
$691$	−4.62421e9	−0.533168	−0.266584	+	0.963812i	$0.585895\pi$
$692$	−4.97263e9	−0.570446
$693$	3.98980e8	0.0455392
$694$	−3.60053e9	−0.408892
$695$	−1.61940e10	−1.82981
$696$	−4.81274e9	−0.541078
$697$	−7.76813e9	−0.868964
$698$	2.67572e9	0.297815
$699$	5.96692e9	0.660815
$700$	−2.42182e9	−0.266869
$701$	1.31027e10	1.43664	0.718320	−	0.695712i	$-0.244911\pi$
$701$	1.31027e10	1.43664	0.718320	+	0.695712i	$0.244911\pi$
$702$	4.14471e7	0.00452183
$703$	3.52402e9	0.382556
$704$	−9.94443e8	−0.107418
$705$	−3.34833e9	−0.359887
$706$	−3.60312e9	−0.385356
$707$	8.75775e9	0.932019
$708$	−6.86504e9	−0.726987
$709$	1.84631e10	1.94555	0.972777	−	0.231742i	$-0.0744425\pi$
$709$	1.84631e10	1.94555	0.972777	+	0.231742i	$0.0744425\pi$
$710$	−1.50871e9	−0.158198
$711$	3.82986e9	0.399612
$712$	5.92155e9	0.614830
$713$	−8.55973e7	−0.00884396
$714$	−6.38681e8	−0.0656660
$715$	−2.27317e8	−0.0232574
$716$	1.35387e10	1.37842
$717$	−5.54730e9	−0.562037
$718$	1.52598e9	0.153856
$719$	2.85032e9	0.285985	0.142992	−	0.989724i	$-0.454328\pi$
$719$	2.85032e9	0.285985	0.142992	+	0.989724i	$0.454328\pi$
$720$	−2.88753e9	−0.288312
$721$	6.86771e9	0.682400
$722$	2.13943e9	0.211552
$723$	1.04522e9	0.102855
$724$	−9.16103e9	−0.897138
$725$	8.78727e9	0.856388
$726$	−1.81432e9	−0.175969
$727$	1.49186e9	0.143998	0.0719990	−	0.997405i	$-0.477062\pi$
$727$	1.49186e9	0.143998	0.0719990	+	0.997405i	$0.477062\pi$
$728$	2.44839e8	0.0235191
$729$	3.87420e8	0.0370370
$730$	−7.16603e9	−0.681786
$731$	9.63874e9	0.912661
$732$	−2.16049e9	−0.203594
$733$	4.97243e9	0.466342	0.233171	−	0.972436i	$-0.425090\pi$
$733$	4.97243e9	0.466342	0.233171	+	0.972436i	$0.425090\pi$
$734$	9.68176e8	0.0903687
$735$	−5.60195e9	−0.520395
$736$	−6.56356e8	−0.0606830
$737$	−1.89732e9	−0.174584
$738$	−1.56817e9	−0.143614
$739$	1.25579e10	1.14462	0.572311	−	0.820037i	$-0.306047\pi$
$739$	1.25579e10	1.14462	0.572311	+	0.820037i	$0.306047\pi$
$740$	7.94071e9	0.720358
$741$	−2.73033e8	−0.0246519
$742$	1.67841e9	0.150829
$743$	7.26456e9	0.649753	0.324877	−	0.945756i	$-0.394677\pi$
$743$	7.26456e9	0.649753	0.324877	+	0.945756i	$0.394677\pi$
$744$	4.93384e8	0.0439218
$745$	−2.09296e10	−1.85445
$746$	−4.32101e9	−0.381065
$747$	−3.42195e9	−0.300367
$748$	1.74050e9	0.152062
$749$	−1.57255e9	−0.136747
$750$	1.18540e9	0.102601
$751$	1.44218e10	1.24245	0.621227	−	0.783631i	$-0.286635\pi$
$751$	1.44218e10	1.24245	0.621227	+	0.783631i	$0.286635\pi$
$752$	−4.01739e9	−0.344494
$753$	−1.19465e9	−0.101967
$754$	−4.19159e8	−0.0356106
$755$	2.67973e10	2.26609
$756$	1.07983e9	0.0908927
$757$	1.42657e9	0.119525	0.0597624	−	0.998213i	$-0.480966\pi$
$757$	1.42657e9	0.119525	0.0597624	+	0.998213i	$0.480966\pi$
$758$	1.48523e9	0.123866
$759$	−1.29193e8	−0.0107249
$760$	−5.55616e9	−0.459121
$761$	1.87500e9	0.154225	0.0771126	−	0.997022i	$-0.475430\pi$
$761$	1.87500e9	0.154225	0.0771126	+	0.997022i	$0.475430\pi$
$762$	6.93121e8	0.0567501
$763$	1.10980e10	0.904501
$764$	−1.80441e10	−1.46389
$765$	3.40136e9	0.274687
$766$	−9.98296e8	−0.0802525
$767$	−1.26719e9	−0.101405
$768$	−6.93240e8	−0.0552229
$769$	1.46045e10	1.15810	0.579049	−	0.815292i	$-0.303424\pi$
$769$	1.46045e10	1.15810	0.579049	+	0.815292i	$0.303424\pi$
$770$	7.07129e8	0.0558189
$771$	−1.38091e10	−1.08511
$772$	9.06969e9	0.709467
$773$	−1.87798e10	−1.46239	−0.731194	−	0.682169i	$-0.761037\pi$
$773$	−1.87798e10	−1.46239	−0.731194	+	0.682169i	$0.761037\pi$
$774$	1.94579e9	0.150835
$775$	−9.00838e8	−0.0695169
$776$	−1.41260e10	−1.08518
$777$	−2.57264e9	−0.196746
$778$	−2.53952e9	−0.193341
$779$	1.03303e10	0.782947
$780$	−6.15227e8	−0.0464199
$781$	−1.33203e9	−0.100054
$782$	2.06810e8	0.0154650
$783$	−3.91802e9	−0.291676
$784$	−6.72133e9	−0.498137
$785$	1.35319e9	0.0998423
$786$	2.54269e7	0.00186773
$787$	8.50848e9	0.622215	0.311107	−	0.950375i	$-0.399300\pi$
$787$	8.50848e9	0.622215	0.311107	+	0.950375i	$0.399300\pi$
$788$	2.31747e10	1.68722
$789$	−1.13112e10	−0.819862
$790$	6.78780e9	0.489818
$791$	−6.99858e8	−0.0502797
$792$	7.44672e8	0.0532631
$793$	−3.98798e8	−0.0283986
$794$	1.80744e9	0.128142
$795$	−8.93857e9	−0.630933
$796$	−1.62161e10	−1.13960
$797$	1.81308e10	1.26857	0.634283	−	0.773101i	$-0.281295\pi$
$797$	1.81308e10	1.26857	0.634283	+	0.773101i	$0.281295\pi$
$798$	8.49339e8	0.0591658
$799$	4.73229e9	0.328214
$800$	−6.90759e9	−0.476992
$801$	4.82070e9	0.331434
$802$	−1.78630e8	−0.0122277
$803$	−6.32687e9	−0.431206
$804$	−5.13503e9	−0.348455
$805$	−7.03704e8	−0.0475450
$806$	4.29706e7	0.00289067
$807$	1.14432e10	0.766463
$808$	1.63458e10	1.09010
$809$	6.32456e9	0.419962	0.209981	−	0.977705i	$-0.432660\pi$
$809$	6.32456e9	0.419962	0.209981	+	0.977705i	$0.432660\pi$
$810$	6.86640e8	0.0453975
$811$	−1.34866e10	−0.887832	−0.443916	−	0.896068i	$-0.646411\pi$
$811$	−1.34866e10	−0.887832	−0.443916	+	0.896068i	$0.646411\pi$
$812$	−1.09204e10	−0.715803
$813$	−8.00159e9	−0.522227
$814$	−8.37096e8	−0.0543988
$815$	2.45470e10	1.58835
$816$	4.08102e9	0.262938
$817$	−1.28179e10	−0.822319
$818$	−7.46506e9	−0.476867
$819$	1.99322e8	0.0126783
$820$	2.32774e10	1.47430
$821$	−2.89481e10	−1.82566	−0.912829	−	0.408343i	$-0.866107\pi$
$821$	−2.89481e10	−1.82566	−0.912829	+	0.408343i	$0.866107\pi$
$822$	8.79581e8	0.0552363
$823$	−9.81602e9	−0.613813	−0.306906	−	0.951740i	$-0.599294\pi$
$823$	−9.81602e9	−0.613813	−0.306906	+	0.951740i	$0.599294\pi$
$824$	1.28182e10	0.798142
$825$	−1.35965e9	−0.0843019
$826$	3.94193e9	0.243377
$827$	1.26928e10	0.780351	0.390175	−	0.920741i	$-0.372414\pi$
$827$	1.26928e10	0.780351	0.390175	+	0.920741i	$0.372414\pi$
$828$	−3.49658e8	−0.0214061
$829$	−1.79703e10	−1.09550	−0.547751	−	0.836641i	$-0.684516\pi$
$829$	−1.79703e10	−1.09550	−0.547751	+	0.836641i	$0.684516\pi$
$830$	−6.06486e9	−0.368169
$831$	−1.35650e10	−0.820004
$832$	−4.96802e8	−0.0299055
$833$	7.91739e9	0.474596
$834$	4.62033e9	0.275799
$835$	9.67379e9	0.575035
$836$	−2.31458e9	−0.137009
$837$	4.01661e8	0.0236767
$838$	−6.47851e9	−0.380296
$839$	8.25721e9	0.482688	0.241344	−	0.970440i	$-0.422412\pi$
$839$	8.25721e9	0.482688	0.241344	+	0.970440i	$0.422412\pi$
$840$	4.05616e9	0.236123
$841$	2.23735e10	1.29703
$842$	7.34565e9	0.424070
$843$	9.97525e9	0.573492
$844$	−2.33573e10	−1.33729
$845$	2.18278e10	1.24455
$846$	9.55318e8	0.0542440
$847$	−8.72517e9	−0.493381
$848$	−1.07247e10	−0.603946
$849$	−1.99785e9	−0.112043
$850$	2.17650e9	0.121561
$851$	8.33042e8	0.0463354
$852$	−3.60511e9	−0.199701
$853$	−8.33225e9	−0.459664	−0.229832	−	0.973230i	$-0.573818\pi$
$853$	−8.33225e9	−0.459664	−0.229832	+	0.973230i	$0.573818\pi$
$854$	1.24056e9	0.0681580
$855$	−4.52324e9	−0.247496
$856$	−2.93506e9	−0.159941
$857$	1.80915e10	0.981843	0.490922	−	0.871204i	$-0.336660\pi$
$857$	1.80915e10	0.981843	0.490922	+	0.871204i	$0.336660\pi$
$858$	6.48562e7	0.00350547
$859$	6.03914e9	0.325087	0.162543	−	0.986701i	$-0.448030\pi$
$859$	6.03914e9	0.325087	0.162543	+	0.986701i	$0.448030\pi$
$860$	−2.88827e10	−1.54844
$861$	−7.54143e9	−0.402664
$862$	−1.14139e10	−0.606959
$863$	1.27862e10	0.677180	0.338590	−	0.940934i	$-0.390050\pi$
$863$	1.27862e10	0.677180	0.338590	+	0.940934i	$0.390050\pi$
$864$	3.07992e9	0.162458
$865$	−1.52062e10	−0.798848
$866$	−4.04702e9	−0.211750
$867$	6.27191e9	0.326838
$868$	1.11952e9	0.0581050
$869$	5.99294e9	0.309792
$870$	−6.94407e9	−0.357517
$871$	−9.47857e8	−0.0486048
$872$	2.07137e10	1.05791
$873$	−1.14999e10	−0.584983
$874$	−2.75023e8	−0.0139341
$875$	5.70068e9	0.287673
$876$	−1.71235e10	−0.860653
$877$	1.83814e9	0.0920196	0.0460098	−	0.998941i	$-0.485349\pi$
$877$	1.83814e9	0.0920196	0.0460098	+	0.998941i	$0.485349\pi$
$878$	8.99914e9	0.448715
$879$	1.90109e10	0.944153
$880$	−4.51838e9	−0.223508
$881$	2.55384e10	1.25828	0.629141	−	0.777291i	$-0.283407\pi$
$881$	2.55384e10	1.25828	0.629141	+	0.777291i	$0.283407\pi$
$882$	1.59830e9	0.0784366
$883$	1.16987e9	0.0571842	0.0285921	−	0.999591i	$-0.490898\pi$
$883$	1.16987e9	0.0571842	0.0285921	+	0.999591i	$0.490898\pi$
$884$	8.69518e8	0.0423346
$885$	−2.09932e10	−1.01807
$886$	4.19949e9	0.202851
$887$	1.94586e10	0.936220	0.468110	−	0.883670i	$-0.344935\pi$
$887$	1.94586e10	0.936220	0.468110	+	0.883670i	$0.344935\pi$
$888$	−4.80166e9	−0.230116
$889$	3.33326e9	0.159116
$890$	8.54392e9	0.406249
$891$	6.06233e8	0.0287123
$892$	4.28308e9	0.202059
$893$	−6.29315e9	−0.295725
$894$	5.97147e9	0.279512
$895$	4.14011e10	1.93033
$896$	1.11549e10	0.518067
$897$	−6.45421e7	−0.00298586
$898$	−4.67814e9	−0.215579
$899$	−4.06204e9	−0.186460
$900$	−3.67985e9	−0.168260
$901$	1.26331e10	0.575405
$902$	−2.45386e9	−0.111334
$903$	9.35745e9	0.422912
$904$	−1.30624e9	−0.0588076
$905$	−2.80142e10	−1.25634
$906$	−7.64559e9	−0.341556
$907$	2.71882e10	1.20992	0.604958	−	0.796257i	$-0.293190\pi$
$907$	2.71882e10	1.20992	0.604958	+	0.796257i	$0.293190\pi$
$908$	3.49391e10	1.54886
$909$	1.33070e10	0.587634
$910$	3.53266e8	0.0155402
$911$	1.96616e10	0.861596	0.430798	−	0.902448i	$-0.358232\pi$
$911$	1.96616e10	0.861596	0.430798	+	0.902448i	$0.358232\pi$
$912$	−5.42708e9	−0.236910
$913$	−5.35465e9	−0.232854
$914$	7.21057e7	0.00312362
$915$	−6.60675e9	−0.285111
$916$	2.62082e9	0.112669
$917$	1.22279e8	0.00523674
$918$	−9.70448e8	−0.0414021
$919$	1.74787e10	0.742856	0.371428	−	0.928462i	$-0.378868\pi$
$919$	1.74787e10	0.742856	0.371428	+	0.928462i	$0.378868\pi$
$920$	−1.31342e9	−0.0556091
$921$	2.00413e10	0.845314
$922$	−9.04083e9	−0.379883
$923$	−6.65454e8	−0.0278556
$924$	1.68971e9	0.0704629
$925$	8.76705e9	0.364214
$926$	1.01471e10	0.419957
$927$	1.04352e10	0.430250
$928$	−3.11476e10	−1.27940
$929$	1.12795e10	0.461568	0.230784	−	0.973005i	$-0.425871\pi$
$929$	1.12795e10	0.461568	0.230784	+	0.973005i	$0.425871\pi$
$930$	7.11880e8	0.0290213
$931$	−1.05288e10	−0.427617
$932$	2.52703e10	1.02248
$933$	−1.00828e10	−0.406438
$934$	−7.91684e9	−0.317935
$935$	5.32243e9	0.212946
$936$	3.72022e8	0.0148287
$937$	−1.99872e10	−0.793711	−0.396856	−	0.917881i	$-0.629899\pi$
$937$	−1.99872e10	−0.793711	−0.396856	+	0.917881i	$0.629899\pi$
$938$	2.94855e9	0.116654
$939$	4.69392e9	0.185015
$940$	−1.41804e10	−0.556854
$941$	1.09073e10	0.426732	0.213366	−	0.976972i	$-0.431557\pi$
$941$	1.09073e10	0.426732	0.213366	+	0.976972i	$0.431557\pi$
$942$	−3.86080e8	−0.0150487
$943$	2.44198e9	0.0948311
$944$	−2.51880e10	−0.974523
$945$	3.30210e9	0.127285
$946$	3.04477e9	0.116932
$947$	−6.33889e9	−0.242543	−0.121271	−	0.992619i	$-0.538697\pi$
$947$	−6.33889e9	−0.242543	−0.121271	+	0.992619i	$0.538697\pi$
$948$	1.62197e10	0.618321
$949$	−3.16076e9	−0.120050
$950$	−2.89438e9	−0.109528
$951$	−5.68653e8	−0.0214395
$952$	−5.73268e9	−0.215342
$953$	8.32766e9	0.311672	0.155836	−	0.987783i	$-0.450193\pi$
$953$	8.32766e9	0.311672	0.155836	+	0.987783i	$0.450193\pi$
$954$	2.55028e9	0.0950973
$955$	−5.51786e10	−2.05002
$956$	−2.34932e10	−0.869641
$957$	−6.13090e9	−0.226117
$958$	−1.04372e10	−0.383534
$959$	4.22996e9	0.154871
$960$	−8.23035e9	−0.300240
$961$	−2.70962e10	−0.984864
$962$	−4.18195e8	−0.0151449
$963$	−2.38942e9	−0.0862184
$964$	4.42658e9	0.159147
$965$	2.77349e10	0.993532
$966$	2.00775e8	0.00716621
$967$	−2.47481e10	−0.880136	−0.440068	−	0.897964i	$-0.645046\pi$
$967$	−2.47481e10	−0.880136	−0.440068	+	0.897964i	$0.645046\pi$
$968$	−1.62850e10	−0.577063
$969$	6.39282e9	0.225714
$970$	−2.03817e10	−0.717033
$971$	2.85423e9	0.100051	0.0500255	−	0.998748i	$-0.484070\pi$
$971$	2.85423e9	0.100051	0.0500255	+	0.998748i	$0.484070\pi$
$972$	1.64075e9	0.0573075
$973$	2.22195e10	0.773284
$974$	6.33543e9	0.219695
$975$	−6.79250e8	−0.0234700
$976$	−7.92691e9	−0.272916
$977$	−6.47902e9	−0.222269	−0.111134	−	0.993805i	$-0.535448\pi$
$977$	−6.47902e9	−0.222269	−0.111134	+	0.993805i	$0.535448\pi$
$978$	−7.00355e9	−0.239404
$979$	7.54340e9	0.256938
$980$	−2.37247e10	−0.805209
$981$	1.68629e10	0.570285
$982$	4.61636e9	0.155564
$983$	2.98554e10	1.00250	0.501252	−	0.865302i	$-0.332873\pi$
$983$	2.98554e10	1.00250	0.501252	+	0.865302i	$0.332873\pi$
$984$	−1.40756e10	−0.470960
$985$	7.08677e10	2.36277
$986$	9.81424e9	0.326053
$987$	4.59418e9	0.152089
$988$	−1.15631e9	−0.0381440
$989$	−3.03002e9	−0.0995998
$990$	1.07445e9	0.0351936
$991$	−2.26159e10	−0.738168	−0.369084	−	0.929396i	$-0.620329\pi$
$991$	−2.26159e10	−0.738168	−0.369084	+	0.929396i	$0.620329\pi$
$992$	3.19313e9	0.103855
$993$	−9.57155e9	−0.310213
$994$	2.07007e9	0.0668548
$995$	−4.95885e10	−1.59588
$996$	−1.44922e10	−0.464758
$997$	−5.13860e9	−0.164215	−0.0821074	−	0.996623i	$-0.526165\pi$
$997$	−5.13860e9	−0.164215	−0.0821074	+	0.996623i	$0.526165\pi$
$998$	1.76303e10	0.561438
$999$	−3.90901e9	−0.124047

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.8.a.c.1.20	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.8.a.c.1.20	✓	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)

\(f(q)\)	\(=\)	\(q-3.69501 q^{2} -27.0000 q^{3} -114.347 q^{4} -349.671 q^{5} +99.7651 q^{6} +479.777 q^{7} +895.473 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-3.69501 q^{2} -27.0000 q^{3} -114.347 q^{4} -349.671 q^{5} +99.7651 q^{6} +479.777 q^{7} +895.473 q^{8} +729.000 q^{9} +1292.04 q^{10} +1140.73 q^{11} +3087.37 q^{12} +569.886 q^{13} -1772.78 q^{14} +9441.11 q^{15} +11327.6 q^{16} -13343.4 q^{17} -2693.66 q^{18} +17744.5 q^{19} +39983.8 q^{20} -12954.0 q^{21} -4215.02 q^{22} +4194.61 q^{23} -24177.8 q^{24} +44144.6 q^{25} -2105.73 q^{26} -19683.0 q^{27} -54861.0 q^{28} +199056. q^{29} -34885.0 q^{30} -20406.5 q^{31} -156476. q^{32} -30799.8 q^{33} +49303.9 q^{34} -167764. q^{35} -83358.9 q^{36} +198598. q^{37} -65565.9 q^{38} -15386.9 q^{39} -313121. q^{40} +582171. q^{41} +47865.0 q^{42} -722361. q^{43} -130440. q^{44} -254910. q^{45} -15499.1 q^{46} -354654. q^{47} -305846. q^{48} -593357. q^{49} -163115. q^{50} +360271. q^{51} -65164.7 q^{52} -946771. q^{53} +72728.8 q^{54} -398882. q^{55} +429627. q^{56} -479101. q^{57} -735514. q^{58} -2.22359e6 q^{59} -1.07956e6 q^{60} -699785. q^{61} +75402.1 q^{62} +349757. q^{63} -871756. q^{64} -199273. q^{65} +113806. q^{66} -1.66324e6 q^{67} +1.52577e6 q^{68} -113254. q^{69} +619889. q^{70} -1.16770e6 q^{71} +652800. q^{72} -5.54631e6 q^{73} -733821. q^{74} -1.19191e6 q^{75} -2.02903e6 q^{76} +547298. q^{77} +56854.8 q^{78} +5.25358e6 q^{79} -3.96094e6 q^{80} +531441. q^{81} -2.15112e6 q^{82} -4.69403e6 q^{83} +1.48125e6 q^{84} +4.66579e6 q^{85} +2.66913e6 q^{86} -5.37452e6 q^{87} +1.02150e6 q^{88} +6.61276e6 q^{89} +941894. q^{90} +273418. q^{91} -479641. q^{92} +550976. q^{93} +1.31045e6 q^{94} -6.20472e6 q^{95} +4.22486e6 q^{96} -1.57749e7 q^{97} +2.19246e6 q^{98} +831596. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{2} - 1296 q^{3} + 3214 q^{4} + 428 q^{5} - 54 q^{6} - 680 q^{7} + 2355 q^{8} + 34992 q^{9}+O(q^{10}) \) 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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