LMFDB - Embedded newform 471.8.a.c.1.19

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			1.19
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)

$f(q)$	$=$	$q-6.65005 q^{2} -27.0000 q^{3} -83.7769 q^{4} +355.102 q^{5} +179.551 q^{6} -1545.65 q^{7} +1408.33 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-6.65005 q^{2} -27.0000 q^{3} -83.7769 q^{4} +355.102 q^{5} +179.551 q^{6} -1545.65 q^{7} +1408.33 q^{8} +729.000 q^{9} -2361.45 q^{10} +7280.99 q^{11} +2261.98 q^{12} +7540.71 q^{13} +10278.7 q^{14} -9587.76 q^{15} +1358.00 q^{16} +29394.2 q^{17} -4847.89 q^{18} -5070.15 q^{19} -29749.4 q^{20} +41732.7 q^{21} -48418.9 q^{22} +65010.1 q^{23} -38024.8 q^{24} +47972.7 q^{25} -50146.1 q^{26} -19683.0 q^{27} +129490. q^{28} +208053. q^{29} +63759.1 q^{30} +204074. q^{31} -189297. q^{32} -196587. q^{33} -195473. q^{34} -548866. q^{35} -61073.3 q^{36} +387148. q^{37} +33716.8 q^{38} -203599. q^{39} +500100. q^{40} +144627. q^{41} -277524. q^{42} -527028. q^{43} -609978. q^{44} +258870. q^{45} -432320. q^{46} -1.09822e6 q^{47} -36666.0 q^{48} +1.56551e6 q^{49} -319020. q^{50} -793644. q^{51} -631737. q^{52} +414869. q^{53} +130893. q^{54} +2.58550e6 q^{55} -2.17679e6 q^{56} +136894. q^{57} -1.38356e6 q^{58} +1.10444e6 q^{59} +803233. q^{60} +3.33712e6 q^{61} -1.35710e6 q^{62} -1.12678e6 q^{63} +1.08501e6 q^{64} +2.67772e6 q^{65} +1.30731e6 q^{66} -2.93739e6 q^{67} -2.46256e6 q^{68} -1.75527e6 q^{69} +3.64998e6 q^{70} +4.78031e6 q^{71} +1.02667e6 q^{72} -195954. q^{73} -2.57455e6 q^{74} -1.29526e6 q^{75} +424762. q^{76} -1.12539e7 q^{77} +1.35394e6 q^{78} -2.43478e6 q^{79} +482229. q^{80} +531441. q^{81} -961777. q^{82} -6.93517e6 q^{83} -3.49623e6 q^{84} +1.04380e7 q^{85} +3.50476e6 q^{86} -5.61743e6 q^{87} +1.02540e7 q^{88} -1.76645e6 q^{89} -1.72150e6 q^{90} -1.16553e7 q^{91} -5.44634e6 q^{92} -5.50999e6 q^{93} +7.30323e6 q^{94} -1.80042e6 q^{95} +5.11101e6 q^{96} -1.19072e6 q^{97} -1.04107e7 q^{98} +5.30784e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−6.65005	−0.587787	−0.293893	−	0.955838i	$-0.594951\pi$
$2$	−6.65005	−0.587787	−0.293893	+	0.955838i	$0.594951\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	−83.7769	−0.654507
$5$	355.102	1.27045	0.635226	−	0.772326i	$-0.280907\pi$
$5$	355.102	1.27045	0.635226	+	0.772326i	$0.280907\pi$
$6$	179.551	0.339359
$7$	−1545.65	−1.70321	−0.851607	−	0.524180i	$-0.824372\pi$
$7$	−1545.65	−1.70321	−0.851607	+	0.524180i	$0.824372\pi$
$8$	1408.33	0.972497
$9$	729.000	0.333333
$10$	−2361.45	−0.746755
$11$	7280.99	1.64936	0.824681	−	0.565598i	$-0.191355\pi$
$11$	7280.99	1.64936	0.824681	+	0.565598i	$0.191355\pi$
$12$	2261.98	0.377880
$13$	7540.71	0.951942	0.475971	−	0.879461i	$-0.342097\pi$
$13$	7540.71	0.951942	0.475971	+	0.879461i	$0.342097\pi$
$14$	10278.7	1.00113
$15$	−9587.76	−0.733496
$16$	1358.00	0.0828858
$17$	29394.2	1.45108	0.725539	−	0.688181i	$-0.241590\pi$
$17$	29394.2	1.45108	0.725539	+	0.688181i	$0.241590\pi$
$18$	−4847.89	−0.195929
$19$	−5070.15	−0.169583	−0.0847917	−	0.996399i	$-0.527022\pi$
$19$	−5070.15	−0.169583	−0.0847917	+	0.996399i	$0.527022\pi$
$20$	−29749.4	−0.831520
$21$	41732.7	0.983351
$22$	−48418.9	−0.969473
$23$	65010.1	1.11412	0.557062	−	0.830471i	$-0.311929\pi$
$23$	65010.1	1.11412	0.557062	+	0.830471i	$0.311929\pi$
$24$	−38024.8	−0.561471
$25$	47972.7	0.614050
$26$	−50146.1	−0.559539
$27$	−19683.0	−0.192450
$28$	129490.	1.11477
$29$	208053.	1.58410	0.792048	−	0.610459i	$-0.209015\pi$
$29$	208053.	1.58410	0.792048	+	0.610459i	$0.209015\pi$
$30$	63759.1	0.431139
$31$	204074.	1.23033	0.615164	−	0.788399i	$-0.289090\pi$
$31$	204074.	1.23033	0.615164	+	0.788399i	$0.289090\pi$
$32$	−189297.	−1.02122
$33$	−196587.	−0.952259
$34$	−195473.	−0.852925
$35$	−548866.	−2.16385
$36$	−61073.3	−0.218169
$37$	387148.	1.25652	0.628262	−	0.778002i	$-0.283767\pi$
$37$	387148.	1.25652	0.628262	+	0.778002i	$0.283767\pi$
$38$	33716.8	0.0996789
$39$	−203599.	−0.549604
$40$	500100.	1.23551
$41$	144627.	0.327722	0.163861	−	0.986483i	$-0.447605\pi$
$41$	144627.	0.327722	0.163861	+	0.986483i	$0.447605\pi$
$42$	−277524.	−0.578001
$43$	−527028.	−1.01087	−0.505433	−	0.862866i	$-0.668667\pi$
$43$	−527028.	−1.01087	−0.505433	+	0.862866i	$0.668667\pi$
$44$	−609978.	−1.07952
$45$	258870.	0.423484
$46$	−432320.	−0.654867
$47$	−1.09822e6	−1.54294	−0.771468	−	0.636268i	$-0.780477\pi$
$47$	−1.09822e6	−1.54294	−0.771468	+	0.636268i	$0.780477\pi$
$48$	−36666.0	−0.0478541
$49$	1.56551e6	1.90094
$50$	−319020.	−0.360930
$51$	−793644.	−0.837780
$52$	−631737.	−0.623053
$53$	414869.	0.382777	0.191389	−	0.981514i	$-0.438701\pi$
$53$	414869.	0.382777	0.191389	+	0.981514i	$0.438701\pi$
$54$	130893.	0.113120
$55$	2.58550e6	2.09544
$56$	−2.17679e6	−1.65637
$57$	136894.	0.0979091
$58$	−1.38356e6	−0.931110
$59$	1.10444e6	0.700101	0.350051	−	0.936731i	$-0.386164\pi$
$59$	1.10444e6	0.700101	0.350051	+	0.936731i	$0.386164\pi$
$60$	803233.	0.480078
$61$	3.33712e6	1.88243	0.941213	−	0.337815i	$-0.109688\pi$
$61$	3.33712e6	1.88243	0.941213	+	0.337815i	$0.109688\pi$
$62$	−1.35710e6	−0.723170
$63$	−1.12678e6	−0.567738
$64$	1.08501e6	0.517372
$65$	2.67772e6	1.20940
$66$	1.30731e6	0.559725
$67$	−2.93739e6	−1.19316	−0.596582	−	0.802552i	$-0.703475\pi$
$67$	−2.93739e6	−1.19316	−0.596582	+	0.802552i	$0.703475\pi$
$68$	−2.46256e6	−0.949740
$69$	−1.75527e6	−0.643240
$70$	3.64998e6	1.27188
$71$	4.78031e6	1.58508	0.792541	−	0.609819i	$-0.208758\pi$
$71$	4.78031e6	1.58508	0.792541	+	0.609819i	$0.208758\pi$
$72$	1.02667e6	0.324166
$73$	−195954.	−0.0589553	−0.0294777	−	0.999565i	$-0.509384\pi$
$73$	−195954.	−0.0589553	−0.0294777	+	0.999565i	$0.509384\pi$
$74$	−2.57455e6	−0.738568
$75$	−1.29526e6	−0.354522
$76$	424762.	0.110994
$77$	−1.12539e7	−2.80922
$78$	1.35394e6	0.323050
$79$	−2.43478e6	−0.555605	−0.277802	−	0.960638i	$-0.589606\pi$
$79$	−2.43478e6	−0.555605	−0.277802	+	0.960638i	$0.589606\pi$
$80$	482229.	0.105302
$81$	531441.	0.111111
$82$	−961777.	−0.192631
$83$	−6.93517e6	−1.33132	−0.665662	−	0.746253i	$-0.731851\pi$
$83$	−6.93517e6	−1.33132	−0.665662	+	0.746253i	$0.731851\pi$
$84$	−3.49623e6	−0.643610
$85$	1.04380e7	1.84353
$86$	3.50476e6	0.594174
$87$	−5.61743e6	−0.914578
$88$	1.02540e7	1.60400
$89$	−1.76645e6	−0.265605	−0.132803	−	0.991142i	$-0.542398\pi$
$89$	−1.76645e6	−0.265605	−0.132803	+	0.991142i	$0.542398\pi$
$90$	−1.72150e6	−0.248918
$91$	−1.16553e7	−1.62136
$92$	−5.44634e6	−0.729201
$93$	−5.50999e6	−0.710330
$94$	7.30323e6	0.906917
$95$	−1.80042e6	−0.215448
$96$	5.11101e6	0.589600
$97$	−1.19072e6	−0.132467	−0.0662336	−	0.997804i	$-0.521098\pi$
$97$	−1.19072e6	−0.132467	−0.0662336	+	0.997804i	$0.521098\pi$
$98$	−1.04107e7	−1.11735
$99$	5.30784e6	0.549787
$100$	−4.01900e6	−0.401900
$101$	9.55359e6	0.922661	0.461330	−	0.887228i	$-0.347372\pi$
$101$	9.55359e6	0.922661	0.461330	+	0.887228i	$0.347372\pi$
$102$	5.27777e6	0.492436
$103$	−1.60100e7	−1.44365	−0.721825	−	0.692076i	$-0.756696\pi$
$103$	−1.60100e7	−1.44365	−0.721825	+	0.692076i	$0.756696\pi$
$104$	1.06198e7	0.925761
$105$	1.48194e7	1.24930
$106$	−2.75890e6	−0.224991
$107$	−1.37591e7	−1.08579	−0.542897	−	0.839799i	$-0.682673\pi$
$107$	−1.37591e7	−1.08579	−0.542897	+	0.839799i	$0.682673\pi$
$108$	1.64898e6	0.125960
$109$	8.54273e6	0.631835	0.315918	−	0.948787i	$-0.397688\pi$
$109$	8.54273e6	0.631835	0.315918	+	0.948787i	$0.397688\pi$
$110$	−1.71937e7	−1.23167
$111$	−1.04530e7	−0.725454
$112$	−2.09900e6	−0.141172
$113$	−2.59793e7	−1.69376	−0.846881	−	0.531783i	$-0.821522\pi$
$113$	−2.59793e7	−1.69376	−0.846881	+	0.531783i	$0.821522\pi$
$114$	−910353.	−0.0575497
$115$	2.30852e7	1.41544
$116$	−1.74300e7	−1.03680
$117$	5.49718e6	0.317314
$118$	−7.34459e6	−0.411510
$119$	−4.54333e7	−2.47150
$120$	−1.35027e7	−0.713323
$121$	3.35256e7	1.72039
$122$	−2.21920e7	−1.10646
$123$	−3.90493e6	−0.189211
$124$	−1.70966e7	−0.805258
$125$	−1.07072e7	−0.490331
$126$	7.49316e6	0.333709
$127$	1.81492e7	0.786222	0.393111	−	0.919491i	$-0.371399\pi$
$127$	1.81492e7	0.786222	0.393111	+	0.919491i	$0.371399\pi$
$128$	1.70146e7	0.717112
$129$	1.42297e7	0.583624
$130$	−1.78070e7	−0.710868
$131$	−1.26526e7	−0.491735	−0.245867	−	0.969303i	$-0.579073\pi$
$131$	−1.26526e7	−0.491735	−0.245867	+	0.969303i	$0.579073\pi$
$132$	1.64694e7	0.623260
$133$	7.83671e6	0.288837
$134$	1.95338e7	0.701326
$135$	−6.98948e6	−0.244499
$136$	4.13967e7	1.41117
$137$	4.13836e7	1.37501	0.687505	−	0.726180i	$-0.258706\pi$
$137$	4.13836e7	1.37501	0.687505	+	0.726180i	$0.258706\pi$
$138$	1.16726e7	0.378088
$139$	−2.81837e7	−0.890114	−0.445057	−	0.895502i	$-0.646817\pi$
$139$	−2.81837e7	−0.890114	−0.445057	+	0.895502i	$0.646817\pi$
$140$	4.59822e7	1.41626
$141$	2.96520e7	0.890814
$142$	−3.17893e7	−0.931690
$143$	5.49038e7	1.57010
$144$	989982.	0.0276286
$145$	7.38801e7	2.01252
$146$	1.30310e6	0.0346532
$147$	−4.22686e7	−1.09751
$148$	−3.24340e7	−0.822403
$149$	−7.01094e7	−1.73630	−0.868149	−	0.496304i	$-0.834690\pi$
$149$	−7.01094e7	−1.73630	−0.868149	+	0.496304i	$0.834690\pi$
$150$	8.61355e6	0.208383
$151$	−3.62595e7	−0.857043	−0.428521	−	0.903532i	$-0.640965\pi$
$151$	−3.62595e7	−0.857043	−0.428521	+	0.903532i	$0.640965\pi$
$152$	−7.14043e6	−0.164919
$153$	2.14284e7	0.483693
$154$	7.48389e7	1.65122
$155$	7.24670e7	1.56307
$156$	1.70569e7	0.359720
$157$	−3.86989e6	−0.0798087
$157$	−3.86989e6	−0.0798087
$158$	1.61914e7	0.326577
$159$	−1.12015e7	−0.220996
$160$	−6.72196e7	−1.29741
$161$	−1.00483e8	−1.89759
$162$	−3.53411e6	−0.0653096
$163$	8.88997e7	1.60784	0.803922	−	0.594735i	$-0.202743\pi$
$163$	8.88997e7	1.60784	0.803922	+	0.594735i	$0.202743\pi$
$164$	−1.21164e7	−0.214497
$165$	−6.98084e7	−1.20980
$166$	4.61192e7	0.782535
$167$	8.33846e7	1.38541	0.692705	−	0.721221i	$-0.256419\pi$
$167$	8.33846e7	1.38541	0.692705	+	0.721221i	$0.256419\pi$
$168$	5.87732e7	0.956306
$169$	−5.88620e6	−0.0938062
$170$	−6.94129e7	−1.08360
$171$	−3.69614e6	−0.0565278
$172$	4.41527e7	0.661619
$173$	5.68224e7	0.834369	0.417184	−	0.908822i	$-0.363017\pi$
$173$	5.68224e7	0.834369	0.417184	+	0.908822i	$0.363017\pi$
$174$	3.73562e7	0.537577
$175$	−7.41492e7	−1.04586
$176$	9.88759e6	0.136709
$177$	−2.98199e7	−0.404204
$178$	1.17470e7	0.156119
$179$	−7.00437e6	−0.0912816	−0.0456408	−	0.998958i	$-0.514533\pi$
$179$	−7.00437e6	−0.0912816	−0.0456408	+	0.998958i	$0.514533\pi$
$180$	−2.16873e7	−0.277173
$181$	2.17840e7	0.273063	0.136531	−	0.990636i	$-0.456405\pi$
$181$	2.17840e7	0.273063	0.136531	+	0.990636i	$0.456405\pi$
$182$	7.75085e7	0.953015
$183$	−9.01023e7	−1.08682
$184$	9.15554e7	1.08348
$185$	1.37477e8	1.59635
$186$	3.66417e7	0.417523
$187$	2.14019e8	2.39335
$188$	9.20056e7	1.00986
$189$	3.04231e7	0.327784
$190$	1.19729e7	0.126637
$191$	1.83475e8	1.90529	0.952644	−	0.304088i	$-0.0983516\pi$
$191$	1.83475e8	1.90529	0.952644	+	0.304088i	$0.0983516\pi$
$192$	−2.92952e7	−0.298705
$193$	4.22666e7	0.423201	0.211600	−	0.977356i	$-0.432132\pi$
$193$	4.22666e7	0.423201	0.211600	+	0.977356i	$0.432132\pi$
$194$	7.91834e6	0.0778624
$195$	−7.22985e7	−0.698246
$196$	−1.31153e8	−1.24418
$197$	1.75540e7	0.163585	0.0817926	−	0.996649i	$-0.473935\pi$
$197$	1.75540e7	0.163585	0.0817926	+	0.996649i	$0.473935\pi$
$198$	−3.52974e7	−0.323158
$199$	1.28491e8	1.15581	0.577906	−	0.816103i	$-0.303870\pi$
$199$	1.28491e8	1.15581	0.577906	+	0.816103i	$0.303870\pi$
$200$	6.75612e7	0.597162
$201$	7.93096e7	0.688874
$202$	−6.35319e7	−0.542328
$203$	−3.21578e8	−2.69805
$204$	6.64890e7	0.548333
$205$	5.13574e7	0.416356
$206$	1.06467e8	0.848558
$207$	4.73924e7	0.371375
$208$	1.02403e7	0.0789025
$209$	−3.69157e7	−0.279704
$210$	−9.85495e7	−0.734323
$211$	−1.57388e8	−1.15341	−0.576704	−	0.816953i	$-0.695661\pi$
$211$	−1.57388e8	−1.15341	−0.576704	+	0.816953i	$0.695661\pi$
$212$	−3.47565e7	−0.250530
$213$	−1.29068e8	−0.915147
$214$	9.14989e7	0.638216
$215$	−1.87149e8	−1.28426
$216$	−2.77201e7	−0.187157
$217$	−3.15427e8	−2.09551
$218$	−5.68096e7	−0.371384
$219$	5.29075e6	0.0340379
$220$	−2.16605e8	−1.37148
$221$	2.21653e8	1.38134
$222$	6.95128e7	0.426412
$223$	2.94928e8	1.78094	0.890468	−	0.455045i	$-0.150377\pi$
$223$	2.94928e8	1.78094	0.890468	+	0.455045i	$0.150377\pi$
$224$	2.92587e8	1.73935
$225$	3.49721e7	0.204683
$226$	1.72763e8	0.995570
$227$	1.30847e8	0.742461	0.371230	−	0.928541i	$-0.378936\pi$
$227$	1.30847e8	0.742461	0.371230	+	0.928541i	$0.378936\pi$
$228$	−1.14686e7	−0.0640821
$229$	−1.07364e8	−0.590790	−0.295395	−	0.955375i	$-0.595451\pi$
$229$	−1.07364e8	−0.590790	−0.295395	+	0.955375i	$0.595451\pi$
$230$	−1.53518e8	−0.831978
$231$	3.03855e8	1.62190
$232$	2.93007e8	1.54053
$233$	3.56184e7	0.184471	0.0922355	−	0.995737i	$-0.470599\pi$
$233$	3.56184e7	0.184471	0.0922355	+	0.995737i	$0.470599\pi$
$234$	−3.65565e7	−0.186513
$235$	−3.89981e8	−1.96023
$236$	−9.25267e7	−0.458221
$237$	6.57392e7	0.320778
$238$	3.02134e8	1.45271
$239$	2.85889e8	1.35458	0.677289	−	0.735717i	$-0.263154\pi$
$239$	2.85889e8	1.35458	0.677289	+	0.735717i	$0.263154\pi$
$240$	−1.30202e7	−0.0607964
$241$	−1.82750e8	−0.841004	−0.420502	−	0.907292i	$-0.638146\pi$
$241$	−1.82750e8	−0.841004	−0.420502	+	0.907292i	$0.638146\pi$
$242$	−2.22947e8	−1.01122
$243$	−1.43489e7	−0.0641500
$244$	−2.79574e8	−1.23206
$245$	5.55915e8	2.41505
$246$	2.59680e7	0.111216
$247$	−3.82326e7	−0.161434
$248$	2.87402e8	1.19649
$249$	1.87250e8	0.768640
$250$	7.12032e7	0.288210
$251$	−2.62167e8	−1.04645	−0.523226	−	0.852194i	$-0.675272\pi$
$251$	−2.62167e8	−1.04645	−0.523226	+	0.852194i	$0.675272\pi$
$252$	9.43983e7	0.371588
$253$	4.73338e8	1.83759
$254$	−1.20693e8	−0.462131
$255$	−2.81825e8	−1.06436
$256$	−2.52029e8	−0.938881
$257$	−3.88270e8	−1.42681	−0.713407	−	0.700749i	$-0.752849\pi$
$257$	−3.88270e8	−1.42681	−0.713407	+	0.700749i	$0.752849\pi$
$258$	−9.46285e7	−0.343047
$259$	−5.98396e8	−2.14013
$260$	−2.24331e8	−0.791559
$261$	1.51671e8	0.528032
$262$	8.41405e7	0.289035
$263$	1.56299e8	0.529799	0.264899	−	0.964276i	$-0.414661\pi$
$263$	1.56299e8	0.529799	0.264899	+	0.964276i	$0.414661\pi$
$264$	−2.76858e8	−0.926070
$265$	1.47321e8	0.486300
$266$	−5.21145e7	−0.169775
$267$	4.76942e7	0.153347
$268$	2.46086e8	0.780934
$269$	−4.50029e8	−1.40964	−0.704819	−	0.709387i	$-0.748972\pi$
$269$	−4.50029e8	−1.40964	−0.704819	+	0.709387i	$0.748972\pi$
$270$	4.64804e7	0.143713
$271$	2.93830e8	0.896815	0.448408	−	0.893829i	$-0.351991\pi$
$271$	2.93830e8	0.896815	0.448408	+	0.893829i	$0.351991\pi$
$272$	3.99174e7	0.120274
$273$	3.14694e8	0.936094
$274$	−2.75203e8	−0.808213
$275$	3.49288e8	1.01279
$276$	1.47051e8	0.421005
$277$	−1.13650e8	−0.321285	−0.160643	−	0.987013i	$-0.551357\pi$
$277$	−1.13650e8	−0.321285	−0.160643	+	0.987013i	$0.551357\pi$
$278$	1.87423e8	0.523197
$279$	1.48770e8	0.410109
$280$	−7.72982e8	−2.10434
$281$	1.69126e8	0.454714	0.227357	−	0.973812i	$-0.426992\pi$
$281$	1.69126e8	0.454714	0.227357	+	0.973812i	$0.426992\pi$
$282$	−1.97187e8	−0.523609
$283$	−1.43588e8	−0.376588	−0.188294	−	0.982113i	$-0.560296\pi$
$283$	−1.43588e8	−0.376588	−0.188294	+	0.982113i	$0.560296\pi$
$284$	−4.00479e8	−1.03745
$285$	4.86114e7	0.124389
$286$	−3.65113e8	−0.922882
$287$	−2.23544e8	−0.558182
$288$	−1.37997e8	−0.340405
$289$	4.53682e8	1.10563
$290$	−4.91307e8	−1.18293
$291$	3.21494e7	0.0764800
$292$	1.64164e7	0.0385867
$293$	3.21093e8	0.745752	0.372876	−	0.927881i	$-0.378372\pi$
$293$	3.21093e8	0.745752	0.372876	+	0.927881i	$0.378372\pi$
$294$	2.81089e8	0.645101
$295$	3.92190e8	0.889445
$296$	5.45230e8	1.22197
$297$	−1.43312e8	−0.317420
$298$	4.66231e8	1.02057
$299$	4.90222e8	1.06058
$300$	1.08513e8	0.232037
$301$	8.14603e8	1.72172
$302$	2.41127e8	0.503758
$303$	−2.57947e8	−0.532698
$304$	−6.88527e6	−0.0140561
$305$	1.18502e9	2.39153
$306$	−1.42500e8	−0.284308
$307$	−1.88935e8	−0.372674	−0.186337	−	0.982486i	$-0.559662\pi$
$307$	−1.88935e8	−0.372674	−0.186337	+	0.982486i	$0.559662\pi$
$308$	9.42816e8	1.83865
$309$	4.32271e8	0.833491
$310$	−4.81909e8	−0.918754
$311$	7.91500e8	1.49207	0.746036	−	0.665906i	$-0.231955\pi$
$311$	7.91500e8	1.49207	0.746036	+	0.665906i	$0.231955\pi$
$312$	−2.86734e8	−0.534488
$313$	1.75065e8	0.322697	0.161348	−	0.986898i	$-0.448416\pi$
$313$	1.75065e8	0.322697	0.161348	+	0.986898i	$0.448416\pi$
$314$	2.57350e7	0.0469105
$315$	−4.00123e8	−0.721284
$316$	2.03979e8	0.363647
$317$	−7.35626e8	−1.29703	−0.648515	−	0.761202i	$-0.724610\pi$
$317$	−7.35626e8	−1.29703	−0.648515	+	0.761202i	$0.724610\pi$
$318$	7.44903e7	0.129899
$319$	1.51483e9	2.61275
$320$	3.85288e8	0.657296
$321$	3.71497e8	0.626884
$322$	6.68218e8	1.11538
$323$	−1.49033e8	−0.246079
$324$	−4.45225e7	−0.0727230
$325$	3.61748e8	0.584540
$326$	−5.91187e8	−0.945069
$327$	−2.30654e8	−0.364790
$328$	2.03682e8	0.318709
$329$	1.69747e9	2.62795
$330$	4.64229e8	0.711105
$331$	−1.91413e8	−0.290118	−0.145059	−	0.989423i	$-0.546337\pi$
$331$	−1.91413e8	−0.290118	−0.145059	+	0.989423i	$0.546337\pi$
$332$	5.81007e8	0.871360
$333$	2.82231e8	0.418841
$334$	−5.54512e8	−0.814326
$335$	−1.04308e9	−1.51586
$336$	5.66730e7	0.0815058
$337$	3.30060e8	0.469773	0.234886	−	0.972023i	$-0.424528\pi$
$337$	3.30060e8	0.469773	0.234886	+	0.972023i	$0.424528\pi$
$338$	3.91435e7	0.0551380
$339$	7.01440e8	0.977893
$340$	−8.74459e8	−1.20660
$341$	1.48586e9	2.02925
$342$	2.45795e7	0.0332263
$343$	−1.14682e9	−1.53449
$344$	−7.42227e8	−0.983065
$345$	−6.23301e8	−0.817205
$346$	−3.77872e8	−0.490431
$347$	−7.15557e8	−0.919372	−0.459686	−	0.888082i	$-0.652038\pi$
$347$	−7.15557e8	−0.919372	−0.459686	+	0.888082i	$0.652038\pi$
$348$	4.70611e8	0.598597
$349$	−8.31091e8	−1.04655	−0.523275	−	0.852164i	$-0.675290\pi$
$349$	−8.31091e8	−1.04655	−0.523275	+	0.852164i	$0.675290\pi$
$350$	4.93095e8	0.614742
$351$	−1.48424e8	−0.183201
$352$	−1.37827e9	−1.68435
$353$	4.65460e8	0.563211	0.281605	−	0.959530i	$-0.409133\pi$
$353$	4.65460e8	0.563211	0.281605	+	0.959530i	$0.409133\pi$
$354$	1.98304e8	0.237586
$355$	1.69750e9	2.01377
$356$	1.47988e8	0.173840
$357$	1.22670e9	1.42692
$358$	4.65794e7	0.0536541
$359$	1.26942e8	0.144802	0.0724008	−	0.997376i	$-0.476934\pi$
$359$	1.26942e8	0.144802	0.0724008	+	0.997376i	$0.476934\pi$
$360$	3.64573e8	0.411837
$361$	−8.68165e8	−0.971241
$362$	−1.44865e8	−0.160503
$363$	−9.05191e8	−0.993270
$364$	9.76447e8	1.06119
$365$	−6.95836e7	−0.0749000
$366$	5.99185e8	0.638818
$367$	4.52608e8	0.477960	0.238980	−	0.971025i	$-0.423187\pi$
$367$	4.52608e8	0.477960	0.238980	+	0.971025i	$0.423187\pi$
$368$	8.82837e7	0.0923450
$369$	1.05433e8	0.109241
$370$	−9.14229e8	−0.938315
$371$	−6.41245e8	−0.651951
$372$	4.61609e8	0.464916
$373$	−7.99783e8	−0.797979	−0.398989	−	0.916956i	$-0.630639\pi$
$373$	−7.99783e8	−0.797979	−0.398989	+	0.916956i	$0.630639\pi$
$374$	−1.42324e9	−1.40678
$375$	2.89094e8	0.283093
$376$	−1.54666e9	−1.50050
$377$	1.56887e9	1.50797
$378$	−2.02315e8	−0.192667
$379$	1.14184e9	1.07738	0.538689	−	0.842505i	$-0.318920\pi$
$379$	1.14184e9	1.07738	0.538689	+	0.842505i	$0.318920\pi$
$380$	1.50834e8	0.141012
$381$	−4.90029e8	−0.453925
$382$	−1.22012e9	−1.11990
$383$	−1.04863e9	−0.953733	−0.476866	−	0.878976i	$-0.658227\pi$
$383$	−1.04863e9	−0.953733	−0.476866	+	0.878976i	$0.658227\pi$
$384$	−4.59394e8	−0.414025
$385$	−3.99628e9	−3.56898
$386$	−2.81075e8	−0.248752
$387$	−3.84203e8	−0.336956
$388$	9.97547e7	0.0867007
$389$	−6.83302e8	−0.588558	−0.294279	−	0.955720i	$-0.595079\pi$
$389$	−6.83302e8	−0.588558	−0.294279	+	0.955720i	$0.595079\pi$
$390$	4.80789e8	0.410420
$391$	1.91092e9	1.61668
$392$	2.20474e9	1.84866
$393$	3.41621e8	0.283903
$394$	−1.16735e8	−0.0961532
$395$	−8.64598e8	−0.705869
$396$	−4.44674e8	−0.359839
$397$	−1.56898e9	−1.25849	−0.629247	−	0.777206i	$-0.716636\pi$
$397$	−1.56898e9	−1.25849	−0.629247	+	0.777206i	$0.716636\pi$
$398$	−8.54472e8	−0.679371
$399$	−2.11591e8	−0.166760
$400$	6.51469e7	0.0508960
$401$	−1.66039e9	−1.28589	−0.642945	−	0.765912i	$-0.722288\pi$
$401$	−1.66039e9	−1.28589	−0.642945	+	0.765912i	$0.722288\pi$
$402$	−5.27413e8	−0.404911
$403$	1.53886e9	1.17120
$404$	−8.00370e8	−0.603888
$405$	1.88716e8	0.141161
$406$	2.13851e9	1.58588
$407$	2.81882e9	2.07246
$408$	−1.11771e9	−0.814739
$409$	−1.71423e9	−1.23890	−0.619451	−	0.785035i	$-0.712645\pi$
$409$	−1.71423e9	−1.23890	−0.619451	+	0.785035i	$0.712645\pi$
$410$	−3.41529e8	−0.244728
$411$	−1.11736e9	−0.793862
$412$	1.34127e9	0.944878
$413$	−1.70709e9	−1.19242
$414$	−3.15161e8	−0.218289
$415$	−2.46269e9	−1.69138
$416$	−1.42743e9	−0.972139
$417$	7.60959e8	0.513907
$418$	2.45491e8	0.164407
$419$	−1.63122e9	−1.08334	−0.541669	−	0.840592i	$-0.682207\pi$
$419$	−1.63122e9	−1.08334	−0.541669	+	0.840592i	$0.682207\pi$
$420$	−1.24152e9	−0.817676
$421$	2.02984e9	1.32579	0.662896	−	0.748712i	$-0.269327\pi$
$421$	2.02984e9	1.32579	0.662896	+	0.748712i	$0.269327\pi$
$422$	1.04664e9	0.677958
$423$	−8.00604e8	−0.514312
$424$	5.84272e8	0.372250
$425$	1.41012e9	0.891035
$426$	8.58311e8	0.537912
$427$	−5.15804e9	−3.20617
$428$	1.15270e9	0.710660
$429$	−1.48240e9	−0.906496
$430$	1.24455e9	0.754870
$431$	1.56009e9	0.938595	0.469297	−	0.883040i	$-0.344507\pi$
$431$	1.56009e9	0.938595	0.469297	+	0.883040i	$0.344507\pi$
$432$	−2.67295e7	−0.0159514
$433$	−1.82796e9	−1.08208	−0.541040	−	0.840997i	$-0.681969\pi$
$433$	−1.82796e9	−1.08208	−0.541040	+	0.840997i	$0.681969\pi$
$434$	2.09761e9	1.23171
$435$	−1.99476e9	−1.16193
$436$	−7.15683e8	−0.413540
$437$	−3.29611e8	−0.188937
$438$	−3.51837e7	−0.0200070
$439$	−1.45027e9	−0.818130	−0.409065	−	0.912505i	$-0.634145\pi$
$439$	−1.45027e9	−0.818130	−0.409065	+	0.912505i	$0.634145\pi$
$440$	3.64122e9	2.03781
$441$	1.14125e9	0.633646
$442$	−1.47401e9	−0.811935
$443$	−1.97372e9	−1.07863	−0.539316	−	0.842104i	$-0.681317\pi$
$443$	−1.97372e9	−1.07863	−0.539316	+	0.842104i	$0.681317\pi$
$444$	8.75718e8	0.474814
$445$	−6.27271e8	−0.337439
$446$	−1.96128e9	−1.04681
$447$	1.89295e9	1.00245
$448$	−1.67705e9	−0.881195
$449$	−2.34760e9	−1.22395	−0.611973	−	0.790879i	$-0.709624\pi$
$449$	−2.34760e9	−1.22395	−0.611973	+	0.790879i	$0.709624\pi$
$450$	−2.32566e8	−0.120310
$451$	1.05303e9	0.540533
$452$	2.17646e9	1.10858
$453$	9.79006e8	0.494814
$454$	−8.70139e8	−0.436409
$455$	−4.13884e9	−2.05986
$456$	1.92792e8	0.0952163
$457$	6.12644e8	0.300263	0.150131	−	0.988666i	$-0.452030\pi$
$457$	6.12644e8	0.300263	0.150131	+	0.988666i	$0.452030\pi$
$458$	7.13974e8	0.347259
$459$	−5.78567e8	−0.279260
$460$	−1.93401e9	−0.926416
$461$	1.60836e9	0.764591	0.382295	−	0.924040i	$-0.375134\pi$
$461$	1.60836e9	0.764591	0.382295	+	0.924040i	$0.375134\pi$
$462$	−2.02065e9	−0.953332
$463$	−2.96337e8	−0.138756	−0.0693782	−	0.997590i	$-0.522102\pi$
$463$	−2.96337e8	−0.138756	−0.0693782	+	0.997590i	$0.522102\pi$
$464$	2.82536e8	0.131299
$465$	−1.95661e9	−0.902441
$466$	−2.36864e8	−0.108430
$467$	1.97046e9	0.895277	0.447639	−	0.894215i	$-0.352265\pi$
$467$	1.97046e9	0.895277	0.447639	+	0.894215i	$0.352265\pi$
$468$	−4.60536e8	−0.207684
$469$	4.54020e9	2.03222
$470$	2.59339e9	1.15220
$471$	1.04487e8	0.0460776
$472$	1.55541e9	0.680846
$473$	−3.83728e9	−1.66728
$474$	−4.37169e8	−0.188549
$475$	−2.43229e8	−0.104133
$476$	3.80626e9	1.61761
$477$	3.02440e8	0.127592
$478$	−1.90117e9	−0.796204
$479$	9.74126e8	0.404987	0.202493	−	0.979284i	$-0.435096\pi$
$479$	9.74126e8	0.404987	0.202493	+	0.979284i	$0.435096\pi$
$480$	1.81493e9	0.749058
$481$	2.91937e9	1.19614
$482$	1.21530e9	0.494331
$483$	2.71304e9	1.09557
$484$	−2.80867e9	−1.12601
$485$	−4.22827e8	−0.168293
$486$	9.54209e7	0.0377065
$487$	−3.65086e9	−1.43233	−0.716165	−	0.697931i	$-0.754104\pi$
$487$	−3.65086e9	−1.43233	−0.716165	+	0.697931i	$0.754104\pi$
$488$	4.69976e9	1.83065
$489$	−2.40029e9	−0.928289
$490$	−3.69686e9	−1.41954
$491$	−4.60410e9	−1.75533	−0.877667	−	0.479270i	$-0.840901\pi$
$491$	−4.60410e9	−1.75533	−0.877667	+	0.479270i	$0.840901\pi$
$492$	3.27143e8	0.123840
$493$	6.11556e9	2.29865
$494$	2.54248e8	0.0948886
$495$	1.88483e9	0.698479
$496$	2.77132e8	0.101977
$497$	−7.38871e9	−2.69973
$498$	−1.24522e9	−0.451797
$499$	5.80100e8	0.209002	0.104501	−	0.994525i	$-0.466675\pi$
$499$	5.80100e8	0.209002	0.104501	+	0.994525i	$0.466675\pi$
$500$	8.97013e8	0.320925
$501$	−2.25138e9	−0.799867
$502$	1.74342e9	0.615091
$503$	5.95430e8	0.208614	0.104307	−	0.994545i	$-0.466738\pi$
$503$	5.95430e8	0.208614	0.104307	+	0.994545i	$0.466738\pi$
$504$	−1.58688e9	−0.552124
$505$	3.39250e9	1.17220
$506$	−3.14772e9	−1.08011
$507$	1.58927e8	0.0541590
$508$	−1.52049e9	−0.514588
$509$	3.79191e9	1.27452	0.637258	−	0.770650i	$-0.280069\pi$
$509$	3.79191e9	1.27452	0.637258	+	0.770650i	$0.280069\pi$
$510$	1.87415e9	0.625617
$511$	3.02876e8	0.100414
$512$	−5.01866e8	−0.165250
$513$	9.97958e7	0.0326364
$514$	2.58201e9	0.838663
$515$	−5.68520e9	−1.83409
$516$	−1.19212e9	−0.381986
$517$	−7.99614e9	−2.54486
$518$	3.97936e9	1.25794
$519$	−1.53420e9	−0.481723
$520$	3.77111e9	1.17614
$521$	−3.49724e9	−1.08341	−0.541706	−	0.840568i	$-0.682221\pi$
$521$	−3.49724e9	−1.08341	−0.541706	+	0.840568i	$0.682221\pi$
$522$	−1.00862e9	−0.310370
$523$	3.72318e9	1.13804	0.569020	−	0.822323i	$-0.307323\pi$
$523$	3.72318e9	1.13804	0.569020	+	0.822323i	$0.307323\pi$
$524$	1.06000e9	0.321844
$525$	2.00203e9	0.603827
$526$	−1.03940e9	−0.311409
$527$	5.99858e9	1.78530
$528$	−2.66965e8	−0.0789288
$529$	8.21486e8	0.241271
$530$	−9.79692e8	−0.285841
$531$	8.05138e8	0.233367
$532$	−6.56535e8	−0.189046
$533$	1.09059e9	0.311973
$534$	−3.17169e8	−0.0901355
$535$	−4.88590e9	−1.37945
$536$	−4.13681e9	−1.16035
$537$	1.89118e8	0.0527015
$538$	2.99272e9	0.828567
$539$	1.13984e10	3.13534
$540$	5.85557e8	0.160026
$541$	6.71557e9	1.82344	0.911722	−	0.410807i	$-0.134753\pi$
$541$	6.71557e9	1.82344	0.911722	+	0.410807i	$0.134753\pi$
$542$	−1.95398e9	−0.527136
$543$	−5.88168e8	−0.157653
$544$	−5.56423e9	−1.48186
$545$	3.03354e9	0.802717
$546$	−2.09273e9	−0.550223
$547$	4.61579e9	1.20584	0.602921	−	0.797801i	$-0.294003\pi$
$547$	4.61579e9	1.20584	0.602921	+	0.797801i	$0.294003\pi$
$548$	−3.46699e9	−0.899953
$549$	2.43276e9	0.627475
$550$	−2.32278e9	−0.595305
$551$	−1.05486e9	−0.268636
$552$	−2.47200e9	−0.625549
$553$	3.76334e9	0.946314
$554$	7.55779e8	0.188847
$555$	−3.71188e9	−0.921655
$556$	2.36114e9	0.582585
$557$	−1.88934e9	−0.463251	−0.231626	−	0.972805i	$-0.574404\pi$
$557$	−1.88934e9	−0.463251	−0.231626	+	0.972805i	$0.574404\pi$
$558$	−9.89325e8	−0.241057
$559$	−3.97416e9	−0.962286
$560$	−7.45360e8	−0.179353
$561$	−5.77851e9	−1.38180
$562$	−1.12470e9	−0.267275
$563$	3.31714e9	0.783402	0.391701	−	0.920093i	$-0.371887\pi$
$563$	3.31714e9	0.783402	0.391701	+	0.920093i	$0.371887\pi$
$564$	−2.48415e9	−0.583044
$565$	−9.22529e9	−2.15184
$566$	9.54869e8	0.221353
$567$	−8.21424e8	−0.189246
$568$	6.73223e9	1.54149
$569$	−7.13245e9	−1.62310	−0.811550	−	0.584282i	$-0.801376\pi$
$569$	−7.13245e9	−1.62310	−0.811550	+	0.584282i	$0.801376\pi$
$570$	−3.23268e8	−0.0731141
$571$	−6.26084e9	−1.40736	−0.703682	−	0.710516i	$-0.748462\pi$
$571$	−6.26084e9	−1.40736	−0.703682	+	0.710516i	$0.748462\pi$
$572$	−4.59967e9	−1.02764
$573$	−4.95383e9	−1.10002
$574$	1.48658e9	0.328092
$575$	3.11871e9	0.684128
$576$	7.90970e8	0.172457
$577$	7.43914e7	0.0161216	0.00806078	−	0.999968i	$-0.497434\pi$
$577$	7.43914e7	0.0161216	0.00806078	+	0.999968i	$0.497434\pi$
$578$	−3.01701e9	−0.649873
$579$	−1.14120e9	−0.244335
$580$	−6.18945e9	−1.31721
$581$	1.07194e10	2.26753
$582$	−2.13795e8	−0.0449539
$583$	3.02066e9	0.631338
$584$	−2.75967e8	−0.0573339
$585$	1.95206e9	0.403132
$586$	−2.13528e9	−0.438343
$587$	−1.89803e8	−0.0387320	−0.0193660	−	0.999812i	$-0.506165\pi$
$587$	−1.89803e8	−0.0387320	−0.0193660	+	0.999812i	$0.506165\pi$
$588$	3.54113e9	0.718326
$589$	−1.03468e9	−0.208643
$590$	−2.60808e9	−0.522804
$591$	−4.73958e8	−0.0944460
$592$	5.25747e8	0.104148
$593$	1.06867e9	0.210452	0.105226	−	0.994448i	$-0.466443\pi$
$593$	1.06867e9	0.210452	0.105226	+	0.994448i	$0.466443\pi$
$594$	9.53030e8	0.186575
$595$	−1.61335e10	−3.13992
$596$	5.87355e9	1.13642
$597$	−3.46926e9	−0.667308
$598$	−3.26000e9	−0.623396
$599$	−1.67749e9	−0.318908	−0.159454	−	0.987205i	$-0.550973\pi$
$599$	−1.67749e9	−0.318908	−0.159454	+	0.987205i	$0.550973\pi$
$600$	−1.82415e9	−0.344772
$601$	4.96615e9	0.933167	0.466584	−	0.884477i	$-0.345485\pi$
$601$	4.96615e9	0.933167	0.466584	+	0.884477i	$0.345485\pi$
$602$	−5.41715e9	−1.01201
$603$	−2.14136e9	−0.397722
$604$	3.03771e9	0.560940
$605$	1.19050e10	2.18568
$606$	1.71536e9	0.313113
$607$	1.50031e9	0.272282	0.136141	−	0.990689i	$-0.456530\pi$
$607$	1.50031e9	0.272282	0.136141	+	0.990689i	$0.456530\pi$
$608$	9.59763e8	0.173181
$609$	8.68261e9	1.55772
$610$	−7.88044e9	−1.40571
$611$	−8.28138e9	−1.46879
$612$	−1.79520e9	−0.316580
$613$	−4.29156e8	−0.0752495	−0.0376248	−	0.999292i	$-0.511979\pi$
$613$	−4.29156e8	−0.0752495	−0.0376248	+	0.999292i	$0.511979\pi$
$614$	1.25643e9	0.219053
$615$	−1.38665e9	−0.240383
$616$	−1.58492e10	−2.73196
$617$	−4.97360e9	−0.852458	−0.426229	−	0.904615i	$-0.640158\pi$
$617$	−4.97360e9	−0.852458	−0.426229	+	0.904615i	$0.640158\pi$
$618$	−2.87462e9	−0.489915
$619$	−9.80561e8	−0.166172	−0.0830859	−	0.996542i	$-0.526478\pi$
$619$	−9.80561e8	−0.166172	−0.0830859	+	0.996542i	$0.526478\pi$
$620$	−6.07106e9	−1.02304
$621$	−1.27959e9	−0.214413
$622$	−5.26352e9	−0.877020
$623$	2.73032e9	0.452383
$624$	−2.76488e8	−0.0455544
$625$	−7.55000e9	−1.23699
$626$	−1.16419e9	−0.189677
$627$	9.96725e8	0.161487
$628$	3.24207e8	0.0522353
$629$	1.13799e10	1.82331
$630$	2.66084e9	0.423961
$631$	−7.68296e8	−0.121738	−0.0608690	−	0.998146i	$-0.519387\pi$
$631$	−7.68296e8	−0.121738	−0.0608690	+	0.998146i	$0.519387\pi$
$632$	−3.42897e9	−0.540324
$633$	4.24948e9	0.665920
$634$	4.89195e9	0.762377
$635$	6.44483e9	0.998858
$636$	9.38424e8	0.144644
$637$	1.18050e10	1.80958
$638$	−1.00737e10	−1.53574
$639$	3.48485e9	0.528361
$640$	6.04193e9	0.911057
$641$	1.32876e10	1.99271	0.996355	−	0.0853022i	$-0.0271856\pi$
$641$	1.32876e10	1.99271	0.996355	+	0.0853022i	$0.0271856\pi$
$642$	−2.47047e9	−0.368474
$643$	5.16776e9	0.766592	0.383296	−	0.923626i	$-0.374789\pi$
$643$	5.16776e9	0.766592	0.383296	+	0.923626i	$0.374789\pi$
$644$	8.41816e9	1.24199
$645$	5.05302e9	0.741467
$646$	9.91078e8	0.144642
$647$	−9.83370e9	−1.42742	−0.713710	−	0.700441i	$-0.752987\pi$
$647$	−9.83370e9	−1.42742	−0.713710	+	0.700441i	$0.752987\pi$
$648$	7.48442e8	0.108055
$649$	8.04143e9	1.15472
$650$	−2.40564e9	−0.343585
$651$	8.51653e9	1.20984
$652$	−7.44774e9	−1.05234
$653$	−5.95618e9	−0.837090	−0.418545	−	0.908196i	$-0.637460\pi$
$653$	−5.95618e9	−0.837090	−0.418545	+	0.908196i	$0.637460\pi$
$654$	1.53386e9	0.214419
$655$	−4.49297e9	−0.624726
$656$	1.96404e8	0.0271635
$657$	−1.42850e8	−0.0196518
$658$	−1.12883e10	−1.54467
$659$	−9.38796e9	−1.27783	−0.638914	−	0.769279i	$-0.720616\pi$
$659$	−9.38796e9	−1.27783	−0.638914	+	0.769279i	$0.720616\pi$
$660$	5.84833e9	0.791823
$661$	1.01856e10	1.37177	0.685886	−	0.727709i	$-0.259415\pi$
$661$	1.01856e10	1.37177	0.685886	+	0.727709i	$0.259415\pi$
$662$	1.27291e9	0.170527
$663$	−5.98464e9	−0.797518
$664$	−9.76698e9	−1.29471
$665$	2.78283e9	0.366954
$666$	−1.87685e9	−0.246189
$667$	1.35256e10	1.76488
$668$	−6.98570e9	−0.906760
$669$	−7.96305e9	−1.02822
$670$	6.93650e9	0.891002
$671$	2.42975e10	3.10480
$672$	−7.89985e9	−1.00421
$673$	9.51493e9	1.20324	0.601621	−	0.798782i	$-0.294522\pi$
$673$	9.51493e9	1.20324	0.601621	+	0.798782i	$0.294522\pi$
$674$	−2.19491e9	−0.276126
$675$	−9.44246e8	−0.118174
$676$	4.93127e8	0.0613968
$677$	1.05360e10	1.30502	0.652508	−	0.757782i	$-0.273717\pi$
$677$	1.05360e10	1.30502	0.652508	+	0.757782i	$0.273717\pi$
$678$	−4.66461e9	−0.574793
$679$	1.84044e9	0.225620
$680$	1.47001e10	1.79282
$681$	−3.53287e9	−0.428660
$682$	−9.88102e9	−1.19277
$683$	9.84162e9	1.18194	0.590968	−	0.806695i	$-0.298746\pi$
$683$	9.84162e9	1.18194	0.590968	+	0.806695i	$0.298746\pi$
$684$	3.09651e8	0.0369978
$685$	1.46954e10	1.74689
$686$	7.62639e9	0.901955
$687$	2.89882e9	0.341093
$688$	−7.15704e8	−0.0837865
$689$	3.12841e9	0.364382
$690$	4.14498e9	0.480342
$691$	−3.23960e9	−0.373524	−0.186762	−	0.982405i	$-0.559799\pi$
$691$	−3.23960e9	−0.373524	−0.186762	+	0.982405i	$0.559799\pi$
$692$	−4.76040e9	−0.546100
$693$	−8.20409e9	−0.936405
$694$	4.75849e9	0.540395
$695$	−1.00081e10	−1.13085
$696$	−7.91118e9	−0.889424
$697$	4.25120e9	0.475551
$698$	5.52680e9	0.615148
$699$	−9.61696e8	−0.106504
$700$	6.21198e9	0.684522
$701$	2.64388e9	0.289887	0.144944	−	0.989440i	$-0.453700\pi$
$701$	2.64388e9	0.289887	0.144944	+	0.989440i	$0.453700\pi$
$702$	9.87025e8	0.107683
$703$	−1.96290e9	−0.213086
$704$	7.89992e9	0.853333
$705$	1.05295e10	1.13174
$706$	−3.09533e9	−0.331048
$707$	−1.47666e10	−1.57149
$708$	2.49822e9	0.264554
$709$	1.60484e9	0.169110	0.0845552	−	0.996419i	$-0.473053\pi$
$709$	1.60484e9	0.169110	0.0845552	+	0.996419i	$0.473053\pi$
$710$	−1.12884e10	−1.18367
$711$	−1.77496e9	−0.185202
$712$	−2.48774e9	−0.258300
$713$	1.32668e10	1.37074
$714$	−8.15761e9	−0.838724
$715$	1.94965e10	1.99473
$716$	5.86804e8	0.0597444
$717$	−7.71899e9	−0.782067
$718$	−8.44168e8	−0.0851125
$719$	−6.61705e9	−0.663916	−0.331958	−	0.943294i	$-0.607709\pi$
$719$	−6.61705e9	−0.663916	−0.331958	+	0.943294i	$0.607709\pi$
$720$	3.51545e8	0.0351008
$721$	2.47460e10	2.45884
$722$	5.77334e9	0.570883
$723$	4.93425e9	0.485554
$724$	−1.82500e9	−0.178721
$725$	9.98086e9	0.972714
$726$	6.01957e9	0.583831
$727$	5.62987e9	0.543410	0.271705	−	0.962381i	$-0.412412\pi$
$727$	5.62987e9	0.543410	0.271705	+	0.962381i	$0.412412\pi$
$728$	−1.64145e10	−1.57677
$729$	3.87420e8	0.0370370
$730$	4.62734e8	0.0440252
$731$	−1.54916e10	−1.46685
$732$	7.54849e9	0.711330
$733$	−2.75209e9	−0.258107	−0.129053	−	0.991638i	$-0.541194\pi$
$733$	−2.75209e9	−0.258107	−0.129053	+	0.991638i	$0.541194\pi$
$734$	−3.00987e9	−0.280938
$735$	−1.50097e10	−1.39433
$736$	−1.23062e10	−1.13776
$737$	−2.13871e10	−1.96796
$738$	−7.01136e8	−0.0642103
$739$	−2.01571e10	−1.83727	−0.918635	−	0.395107i	$-0.870707\pi$
$739$	−2.01571e10	−1.83727	−0.918635	+	0.395107i	$0.870707\pi$
$740$	−1.15174e10	−1.04482
$741$	1.03228e9	0.0932038
$742$	4.26431e9	0.383208
$743$	2.59777e9	0.232349	0.116174	−	0.993229i	$-0.462937\pi$
$743$	2.59777e9	0.232349	0.116174	+	0.993229i	$0.462937\pi$
$744$	−7.75986e9	−0.690794
$745$	−2.48960e10	−2.20588
$746$	5.31860e9	0.469041
$747$	−5.05574e9	−0.443775
$748$	−1.79298e10	−1.56647
$749$	2.12669e10	1.84934
$750$	−1.92249e9	−0.166398
$751$	1.68686e10	1.45325	0.726624	−	0.687036i	$-0.241088\pi$
$751$	1.68686e10	1.45325	0.726624	+	0.687036i	$0.241088\pi$
$752$	−1.49139e9	−0.127887
$753$	7.07850e9	0.604170
$754$	−1.04330e10	−0.886363
$755$	−1.28758e10	−1.08883
$756$	−2.54875e9	−0.214537
$757$	6.98227e9	0.585007	0.292504	−	0.956264i	$-0.405512\pi$
$757$	6.98227e9	0.585007	0.292504	+	0.956264i	$0.405512\pi$
$758$	−7.59329e9	−0.633269
$759$	−1.27801e10	−1.06093
$760$	−2.53558e9	−0.209522
$761$	−1.66922e10	−1.37299	−0.686494	−	0.727136i	$-0.740851\pi$
$761$	−1.66922e10	−1.37299	−0.686494	+	0.727136i	$0.740851\pi$
$762$	3.25872e9	0.266811
$763$	−1.32041e10	−1.07615
$764$	−1.53710e10	−1.24702
$765$	7.60927e9	0.614509
$766$	6.97344e9	0.560591
$767$	8.32828e9	0.666456
$768$	6.80478e9	0.542063
$769$	7.07974e9	0.561403	0.280702	−	0.959795i	$-0.409433\pi$
$769$	7.07974e9	0.561403	0.280702	+	0.959795i	$0.409433\pi$
$770$	2.65755e10	2.09780
$771$	1.04833e10	0.823772
$772$	−3.54096e9	−0.276988
$773$	1.10214e9	0.0858241	0.0429121	−	0.999079i	$-0.486336\pi$
$773$	1.10214e9	0.0858241	0.0429121	+	0.999079i	$0.486336\pi$
$774$	2.55497e9	0.198058
$775$	9.78995e9	0.755483
$776$	−1.67692e9	−0.128824
$777$	1.61567e10	1.23560
$778$	4.54399e9	0.345946
$779$	−7.33282e8	−0.0555763
$780$	6.05694e9	0.457007
$781$	3.48054e10	2.61437
$782$	−1.27077e10	−0.950263
$783$	−4.09511e9	−0.304859
$784$	2.12596e9	0.157561
$785$	−1.37421e9	−0.101393
$786$	−2.27179e9	−0.166874
$787$	−2.40006e10	−1.75514	−0.877568	−	0.479452i	$-0.840835\pi$
$787$	−2.40006e10	−1.75514	−0.877568	+	0.479452i	$0.840835\pi$
$788$	−1.47062e9	−0.107068
$789$	−4.22007e9	−0.305879
$790$	5.74962e9	0.414901
$791$	4.01550e10	2.88484
$792$	7.47517e9	0.534666
$793$	2.51643e10	1.79196
$794$	1.04338e10	0.739726
$795$	−3.97767e9	−0.280766
$796$	−1.07646e10	−0.756487
$797$	−1.83469e10	−1.28369	−0.641844	−	0.766835i	$-0.721830\pi$
$797$	−1.83469e10	−1.28369	−0.641844	+	0.766835i	$0.721830\pi$
$798$	1.40709e9	0.0980194
$799$	−3.22814e10	−2.23892
$800$	−9.08106e9	−0.627078
$801$	−1.28774e9	−0.0885351
$802$	1.10416e10	0.755829
$803$	−1.42674e9	−0.0972387
$804$	−6.64431e9	−0.450873
$805$	−3.56818e10	−2.41080
$806$	−1.02335e10	−0.688416
$807$	1.21508e10	0.813855
$808$	1.34546e10	0.897285
$809$	1.00505e10	0.667371	0.333685	−	0.942685i	$-0.391708\pi$
$809$	1.00505e10	0.667371	0.333685	+	0.942685i	$0.391708\pi$
$810$	−1.25497e9	−0.0829728
$811$	1.58132e10	1.04099	0.520495	−	0.853865i	$-0.325747\pi$
$811$	1.58132e10	1.04099	0.520495	+	0.853865i	$0.325747\pi$
$812$	2.69408e10	1.76589
$813$	−7.93340e9	−0.517776
$814$	−1.87453e10	−1.21817
$815$	3.15685e10	2.04269
$816$	−1.07777e9	−0.0694401
$817$	2.67211e9	0.171426
$818$	1.13997e10	0.728211
$819$	−8.49674e9	−0.540454
$820$	−4.30256e9	−0.272508
$821$	9.59661e8	0.0605225	0.0302613	−	0.999542i	$-0.490366\pi$
$821$	9.59661e8	0.0605225	0.0302613	+	0.999542i	$0.490366\pi$
$822$	7.43047e9	0.466622
$823$	−2.57357e9	−0.160930	−0.0804648	−	0.996757i	$-0.525640\pi$
$823$	−2.57357e9	−0.160930	−0.0804648	+	0.996757i	$0.525640\pi$
$824$	−2.25473e10	−1.40394
$825$	−9.43078e9	−0.584735
$826$	1.13522e10	0.700890
$827$	−1.50898e10	−0.927713	−0.463857	−	0.885910i	$-0.653535\pi$
$827$	−1.50898e10	−0.927713	−0.463857	+	0.885910i	$0.653535\pi$
$828$	−3.97038e9	−0.243067
$829$	−1.04980e10	−0.639981	−0.319990	−	0.947421i	$-0.603680\pi$
$829$	−1.04980e10	−0.639981	−0.319990	+	0.947421i	$0.603680\pi$
$830$	1.63770e10	0.994173
$831$	3.06855e9	0.185494
$832$	8.18172e9	0.492508
$833$	4.60168e10	2.75841
$834$	−5.06041e9	−0.302068
$835$	2.96101e10	1.76010
$836$	3.09268e9	0.183068
$837$	−4.01678e9	−0.236777
$838$	1.08477e10	0.636772
$839$	5.18694e9	0.303211	0.151605	−	0.988441i	$-0.451556\pi$
$839$	5.18694e9	0.303211	0.151605	+	0.988441i	$0.451556\pi$
$840$	2.08705e10	1.21494
$841$	2.60362e10	1.50936
$842$	−1.34986e10	−0.779283
$843$	−4.56640e9	−0.262529
$844$	1.31855e10	0.754913
$845$	−2.09020e9	−0.119176
$846$	5.32406e9	0.302306
$847$	−5.18190e10	−2.93020
$848$	5.63393e8	0.0317268
$849$	3.87688e9	0.217423
$850$	−9.37736e9	−0.523738
$851$	2.51685e10	1.39992
$852$	1.08129e10	0.598970
$853$	−3.11895e9	−0.172063	−0.0860313	−	0.996292i	$-0.527419\pi$
$853$	−3.11895e9	−0.172063	−0.0860313	+	0.996292i	$0.527419\pi$
$854$	3.43012e10	1.88455
$855$	−1.31251e9	−0.0718159
$856$	−1.93773e10	−1.05593
$857$	5.00295e9	0.271515	0.135757	−	0.990742i	$-0.456653\pi$
$857$	5.00295e9	0.271515	0.135757	+	0.990742i	$0.456653\pi$
$858$	9.85805e9	0.532826
$859$	−3.01761e10	−1.62438	−0.812190	−	0.583393i	$-0.801725\pi$
$859$	−3.01761e10	−1.62438	−0.812190	+	0.583393i	$0.801725\pi$
$860$	1.56787e10	0.840556
$861$	6.03568e9	0.322266
$862$	−1.03747e10	−0.551694
$863$	1.47647e10	0.781964	0.390982	−	0.920398i	$-0.372135\pi$
$863$	1.47647e10	0.781964	0.390982	+	0.920398i	$0.372135\pi$
$864$	3.72592e9	0.196533
$865$	2.01778e10	1.06003
$866$	1.21560e10	0.636032
$867$	−1.22494e10	−0.638335
$868$	2.64255e10	1.37153
$869$	−1.77276e10	−0.916393
$870$	1.32653e10	0.682966
$871$	−2.21500e10	−1.13582
$872$	1.20310e10	0.614458
$873$	−8.68034e8	−0.0441557
$874$	2.19193e9	0.111055
$875$	1.65496e10	0.835139
$876$	−4.43242e8	−0.0222780
$877$	1.23210e10	0.616806	0.308403	−	0.951256i	$-0.400205\pi$
$877$	1.23210e10	0.616806	0.308403	+	0.951256i	$0.400205\pi$
$878$	9.64435e9	0.480886
$879$	−8.66951e9	−0.430560
$880$	3.51110e9	0.173682
$881$	2.75582e10	1.35780	0.678898	−	0.734232i	$-0.262458\pi$
$881$	2.75582e10	1.35780	0.678898	+	0.734232i	$0.262458\pi$
$882$	−7.58939e9	−0.372449
$883$	−1.33853e10	−0.654284	−0.327142	−	0.944975i	$-0.606086\pi$
$883$	−1.33853e10	−0.654284	−0.327142	+	0.944975i	$0.606086\pi$
$884$	−1.85694e10	−0.904098
$885$	−1.05891e10	−0.513522
$886$	1.31253e10	0.634005
$887$	−3.54863e10	−1.70737	−0.853687	−	0.520787i	$-0.825639\pi$
$887$	−3.54863e10	−1.70737	−0.853687	+	0.520787i	$0.825639\pi$
$888$	−1.47212e10	−0.705502
$889$	−2.80524e10	−1.33910
$890$	4.17138e9	0.198342
$891$	3.86942e9	0.183262
$892$	−2.47081e10	−1.16563
$893$	5.56816e9	0.261656
$894$	−1.25882e10	−0.589228
$895$	−2.48727e9	−0.115969
$896$	−2.62987e10	−1.22140
$897$	−1.32360e10	−0.612327
$898$	1.56117e10	0.719419
$899$	4.24581e10	1.94896
$900$	−2.92985e9	−0.133967
$901$	1.21948e10	0.555439
$902$	−7.00269e9	−0.317718
$903$	−2.19943e10	−0.994037
$904$	−3.65873e10	−1.64718
$905$	7.73555e9	0.346913
$906$	−6.51044e9	−0.290845
$907$	3.45898e10	1.53930	0.769649	−	0.638467i	$-0.220431\pi$
$907$	3.45898e10	1.53930	0.769649	+	0.638467i	$0.220431\pi$
$908$	−1.09620e10	−0.485946
$909$	6.96457e9	0.307554
$910$	2.75235e10	1.21076
$911$	−2.00961e10	−0.880640	−0.440320	−	0.897841i	$-0.645135\pi$
$911$	−2.00961e10	−0.880640	−0.440320	+	0.897841i	$0.645135\pi$
$912$	1.85902e8	0.00811527
$913$	−5.04949e10	−2.19583
$914$	−4.07411e9	−0.176490
$915$	−3.19955e10	−1.38075
$916$	8.99459e9	0.386676
$917$	1.95566e10	0.837529
$918$	3.84750e9	0.164145
$919$	−1.80236e10	−0.766016	−0.383008	−	0.923745i	$-0.625112\pi$
$919$	−1.80236e10	−0.766016	−0.383008	+	0.923745i	$0.625112\pi$
$920$	3.25115e10	1.37651
$921$	5.10126e9	0.215163
$922$	−1.06956e10	−0.449416
$923$	3.60469e10	1.50891
$924$	−2.54560e10	−1.06155
$925$	1.85725e10	0.771568
$926$	1.97066e9	0.0815592
$927$	−1.16713e10	−0.481216
$928$	−3.93837e10	−1.61770
$929$	3.85122e10	1.57595	0.787977	−	0.615705i	$-0.211129\pi$
$929$	3.85122e10	1.57595	0.787977	+	0.615705i	$0.211129\pi$
$930$	1.30115e10	0.530443
$931$	−7.93735e9	−0.322368
$932$	−2.98400e9	−0.120738
$933$	−2.13705e10	−0.861448
$934$	−1.31036e10	−0.526232
$935$	7.59986e10	3.04064
$936$	7.74182e9	0.308587
$937$	3.17180e10	1.25955	0.629777	−	0.776776i	$-0.283146\pi$
$937$	3.17180e10	1.25955	0.629777	+	0.776776i	$0.283146\pi$
$938$	−3.01925e10	−1.19451
$939$	−4.72676e9	−0.186309
$940$	3.26714e10	1.28298
$941$	1.30152e10	0.509200	0.254600	−	0.967046i	$-0.418056\pi$
$941$	1.30152e10	0.509200	0.254600	+	0.967046i	$0.418056\pi$
$942$	−6.94844e8	−0.0270838
$943$	9.40222e9	0.365123
$944$	1.49983e9	0.0580284
$945$	1.08033e10	0.416434
$946$	2.55181e10	0.980008
$947$	6.88863e8	0.0263577	0.0131789	−	0.999913i	$-0.495805\pi$
$947$	6.88863e8	0.0263577	0.0131789	+	0.999913i	$0.495805\pi$
$948$	−5.50742e9	−0.209952
$949$	−1.47763e9	−0.0561221
$950$	1.61748e9	0.0612078
$951$	1.98619e10	0.748840
$952$	−6.39849e10	−2.40352
$953$	−1.41581e10	−0.529883	−0.264941	−	0.964264i	$-0.585353\pi$
$953$	−1.41581e10	−0.529883	−0.264941	+	0.964264i	$0.585353\pi$
$954$	−2.01124e9	−0.0749971
$955$	6.51525e10	2.42058
$956$	−2.39509e10	−0.886581
$957$	−4.09005e10	−1.50847
$958$	−6.47798e9	−0.238046
$959$	−6.39647e10	−2.34194
$960$	−1.04028e10	−0.379490
$961$	1.41334e10	0.513706
$962$	−1.94139e10	−0.703074
$963$	−1.00304e10	−0.361932
$964$	1.53102e10	0.550443
$965$	1.50090e10	0.537657
$966$	−1.80419e10	−0.643964
$967$	−4.25843e10	−1.51446	−0.757228	−	0.653151i	$-0.773447\pi$
$967$	−4.25843e10	−1.51446	−0.757228	+	0.653151i	$0.773447\pi$
$968$	4.72150e10	1.67308
$969$	4.02390e9	0.142074
$970$	2.81182e9	0.0989206
$971$	8.25104e9	0.289229	0.144614	−	0.989488i	$-0.453806\pi$
$971$	8.25104e9	0.289229	0.144614	+	0.989488i	$0.453806\pi$
$972$	1.20211e9	0.0419866
$973$	4.35622e10	1.51605
$974$	2.42784e10	0.841905
$975$	−9.76719e9	−0.337484
$976$	4.53181e9	0.156026
$977$	−4.06482e10	−1.39447	−0.697237	−	0.716841i	$-0.745587\pi$
$977$	−4.06482e10	−1.39447	−0.697237	+	0.716841i	$0.745587\pi$
$978$	1.59621e10	0.545636
$979$	−1.28615e10	−0.438079
$980$	−4.65728e10	−1.58067
$981$	6.22765e9	0.210612
$982$	3.06175e10	1.03176
$983$	−4.37943e10	−1.47055	−0.735276	−	0.677768i	$-0.762948\pi$
$983$	−4.37943e10	−1.47055	−0.735276	+	0.677768i	$0.762948\pi$
$984$	−5.49942e9	−0.184007
$985$	6.23346e9	0.207827
$986$	−4.06688e10	−1.35111
$987$	−4.58318e10	−1.51725
$988$	3.20300e9	0.105659
$989$	−3.42621e10	−1.12623
$990$	−1.25342e10	−0.410556
$991$	6.98186e9	0.227884	0.113942	−	0.993487i	$-0.463652\pi$
$991$	6.98186e9	0.227884	0.113942	+	0.993487i	$0.463652\pi$
$992$	−3.86304e10	−1.25643
$993$	5.16816e9	0.167499
$994$	4.91353e10	1.58687
$995$	4.56275e10	1.46840
$996$	−1.56872e10	−0.503080
$997$	−3.45419e9	−0.110386	−0.0551928	−	0.998476i	$-0.517577\pi$
$997$	−3.45419e9	−0.110386	−0.0551928	+	0.998476i	$0.517577\pi$
$998$	−3.85769e9	−0.122849
$999$	−7.62022e9	−0.241818

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.8.a.c.1.19	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.8.a.c.1.19	✓	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)

\(f(q)\)	\(=\)	\(q-6.65005 q^{2} -27.0000 q^{3} -83.7769 q^{4} +355.102 q^{5} +179.551 q^{6} -1545.65 q^{7} +1408.33 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-6.65005 q^{2} -27.0000 q^{3} -83.7769 q^{4} +355.102 q^{5} +179.551 q^{6} -1545.65 q^{7} +1408.33 q^{8} +729.000 q^{9} -2361.45 q^{10} +7280.99 q^{11} +2261.98 q^{12} +7540.71 q^{13} +10278.7 q^{14} -9587.76 q^{15} +1358.00 q^{16} +29394.2 q^{17} -4847.89 q^{18} -5070.15 q^{19} -29749.4 q^{20} +41732.7 q^{21} -48418.9 q^{22} +65010.1 q^{23} -38024.8 q^{24} +47972.7 q^{25} -50146.1 q^{26} -19683.0 q^{27} +129490. q^{28} +208053. q^{29} +63759.1 q^{30} +204074. q^{31} -189297. q^{32} -196587. q^{33} -195473. q^{34} -548866. q^{35} -61073.3 q^{36} +387148. q^{37} +33716.8 q^{38} -203599. q^{39} +500100. q^{40} +144627. q^{41} -277524. q^{42} -527028. q^{43} -609978. q^{44} +258870. q^{45} -432320. q^{46} -1.09822e6 q^{47} -36666.0 q^{48} +1.56551e6 q^{49} -319020. q^{50} -793644. q^{51} -631737. q^{52} +414869. q^{53} +130893. q^{54} +2.58550e6 q^{55} -2.17679e6 q^{56} +136894. q^{57} -1.38356e6 q^{58} +1.10444e6 q^{59} +803233. q^{60} +3.33712e6 q^{61} -1.35710e6 q^{62} -1.12678e6 q^{63} +1.08501e6 q^{64} +2.67772e6 q^{65} +1.30731e6 q^{66} -2.93739e6 q^{67} -2.46256e6 q^{68} -1.75527e6 q^{69} +3.64998e6 q^{70} +4.78031e6 q^{71} +1.02667e6 q^{72} -195954. q^{73} -2.57455e6 q^{74} -1.29526e6 q^{75} +424762. q^{76} -1.12539e7 q^{77} +1.35394e6 q^{78} -2.43478e6 q^{79} +482229. q^{80} +531441. q^{81} -961777. q^{82} -6.93517e6 q^{83} -3.49623e6 q^{84} +1.04380e7 q^{85} +3.50476e6 q^{86} -5.61743e6 q^{87} +1.02540e7 q^{88} -1.76645e6 q^{89} -1.72150e6 q^{90} -1.16553e7 q^{91} -5.44634e6 q^{92} -5.50999e6 q^{93} +7.30323e6 q^{94} -1.80042e6 q^{95} +5.11101e6 q^{96} -1.19072e6 q^{97} -1.04107e7 q^{98} +5.30784e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{2} - 1296 q^{3} + 3214 q^{4} + 428 q^{5} - 54 q^{6} - 680 q^{7} + 2355 q^{8} + 34992 q^{9}+O(q^{10}) \) 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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