LMFDB - Embedded newform 471.8.a.c.1.10

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			1.10
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)

$f(q)$	$=$	$q-15.7094 q^{2} -27.0000 q^{3} +118.786 q^{4} +126.488 q^{5} +424.154 q^{6} +1592.00 q^{7} +144.749 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-15.7094 q^{2} -27.0000 q^{3} +118.786 q^{4} +126.488 q^{5} +424.154 q^{6} +1592.00 q^{7} +144.749 q^{8} +729.000 q^{9} -1987.05 q^{10} -3507.15 q^{11} -3207.22 q^{12} -4943.43 q^{13} -25009.4 q^{14} -3415.17 q^{15} -17478.5 q^{16} -32311.7 q^{17} -11452.2 q^{18} -24983.0 q^{19} +15024.9 q^{20} -42984.1 q^{21} +55095.3 q^{22} +17811.0 q^{23} -3908.23 q^{24} -62125.9 q^{25} +77658.4 q^{26} -19683.0 q^{27} +189107. q^{28} +200405. q^{29} +53650.3 q^{30} +157971. q^{31} +256049. q^{32} +94693.0 q^{33} +507599. q^{34} +201369. q^{35} +86594.9 q^{36} -402051. q^{37} +392468. q^{38} +133473. q^{39} +18309.0 q^{40} -539993. q^{41} +675255. q^{42} -705540. q^{43} -416600. q^{44} +92209.5 q^{45} -279801. q^{46} +389819. q^{47} +471920. q^{48} +1.71093e6 q^{49} +975961. q^{50} +872417. q^{51} -587209. q^{52} -223413. q^{53} +309208. q^{54} -443611. q^{55} +230441. q^{56} +674541. q^{57} -3.14824e6 q^{58} +1.93272e6 q^{59} -405674. q^{60} -2.51657e6 q^{61} -2.48163e6 q^{62} +1.16057e6 q^{63} -1.78514e6 q^{64} -625283. q^{65} -1.48757e6 q^{66} +3.14472e6 q^{67} -3.83818e6 q^{68} -480897. q^{69} -3.16339e6 q^{70} -1.20326e6 q^{71} +105522. q^{72} -4.71395e6 q^{73} +6.31599e6 q^{74} +1.67740e6 q^{75} -2.96762e6 q^{76} -5.58339e6 q^{77} -2.09678e6 q^{78} +2.31658e6 q^{79} -2.21082e6 q^{80} +531441. q^{81} +8.48297e6 q^{82} +7.20406e6 q^{83} -5.10590e6 q^{84} -4.08704e6 q^{85} +1.10836e7 q^{86} -5.41092e6 q^{87} -507657. q^{88} -5.45832e6 q^{89} -1.44856e6 q^{90} -7.86996e6 q^{91} +2.11570e6 q^{92} -4.26522e6 q^{93} -6.12383e6 q^{94} -3.16004e6 q^{95} -6.91333e6 q^{96} +1.72226e7 q^{97} -2.68777e7 q^{98} -2.55671e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−15.7094	−1.38853	−0.694265	−	0.719720i	$-0.744270\pi$
$2$	−15.7094	−1.38853	−0.694265	+	0.719720i	$0.744270\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	118.786	0.928014
$5$	126.488	0.452536	0.226268	−	0.974065i	$-0.427347\pi$
$5$	126.488	0.452536	0.226268	+	0.974065i	$0.427347\pi$
$6$	424.154	0.801668
$7$	1592.00	1.75429	0.877144	−	0.480227i	$-0.159446\pi$
$7$	1592.00	1.75429	0.877144	+	0.480227i	$0.159446\pi$
$8$	144.749	0.0999542
$9$	729.000	0.333333
$10$	−1987.05	−0.628360
$11$	−3507.15	−0.794474	−0.397237	−	0.917716i	$-0.630031\pi$
$11$	−3507.15	−0.794474	−0.397237	+	0.917716i	$0.630031\pi$
$12$	−3207.22	−0.535789
$13$	−4943.43	−0.624060	−0.312030	−	0.950072i	$-0.601009\pi$
$13$	−4943.43	−0.624060	−0.312030	+	0.950072i	$0.601009\pi$
$14$	−25009.4	−2.43588
$15$	−3415.17	−0.261272
$16$	−17478.5	−1.06680
$17$	−32311.7	−1.59510	−0.797552	−	0.603250i	$-0.793872\pi$
$17$	−32311.7	−1.59510	−0.797552	+	0.603250i	$0.793872\pi$
$18$	−11452.2	−0.462843
$19$	−24983.0	−0.835616	−0.417808	−	0.908535i	$-0.637202\pi$
$19$	−24983.0	−0.835616	−0.417808	+	0.908535i	$0.637202\pi$
$20$	15024.9	0.419960
$21$	−42984.1	−1.01284
$22$	55095.3	1.10315
$23$	17811.0	0.305240	0.152620	−	0.988285i	$-0.451229\pi$
$23$	17811.0	0.305240	0.152620	+	0.988285i	$0.451229\pi$
$24$	−3908.23	−0.0577086
$25$	−62125.9	−0.795211
$26$	77658.4	0.866526
$27$	−19683.0	−0.192450
$28$	189107.	1.62800
$29$	200405.	1.52586	0.762930	−	0.646481i	$-0.223760\pi$
$29$	200405.	1.52586	0.762930	+	0.646481i	$0.223760\pi$
$30$	53650.3	0.362784
$31$	157971.	0.952383	0.476192	−	0.879342i	$-0.342017\pi$
$31$	157971.	0.952383	0.476192	+	0.879342i	$0.342017\pi$
$32$	256049.	1.38133
$33$	94693.0	0.458690
$34$	507599.	2.21485
$35$	201369.	0.793879
$36$	86594.9	0.309338
$37$	−402051.	−1.30489	−0.652447	−	0.757835i	$-0.726257\pi$
$37$	−402051.	−1.30489	−0.652447	+	0.757835i	$0.726257\pi$
$38$	392468.	1.16028
$39$	133473.	0.360301
$40$	18309.0	0.0452329
$41$	−539993.	−1.22361	−0.611807	−	0.791007i	$-0.709557\pi$
$41$	−539993.	−1.22361	−0.611807	+	0.791007i	$0.709557\pi$
$42$	675255.	1.40636
$43$	−705540.	−1.35326	−0.676631	−	0.736322i	$-0.736561\pi$
$43$	−705540.	−1.35326	−0.676631	+	0.736322i	$0.736561\pi$
$44$	−416600.	−0.737284
$45$	92209.5	0.150845
$46$	−279801.	−0.423834
$47$	389819.	0.547672	0.273836	−	0.961776i	$-0.411707\pi$
$47$	389819.	0.547672	0.273836	+	0.961776i	$0.411707\pi$
$48$	471920.	0.615919
$49$	1.71093e6	2.07753
$50$	975961.	1.10417
$51$	872417.	0.920934
$52$	−587209.	−0.579137
$53$	−223413.	−0.206131	−0.103065	−	0.994675i	$-0.532865\pi$
$53$	−223413.	−0.206131	−0.103065	+	0.994675i	$0.532865\pi$
$54$	309208.	0.267223
$55$	−443611.	−0.359528
$56$	230441.	0.175348
$57$	674541.	0.482443
$58$	−3.14824e6	−2.11870
$59$	1.93272e6	1.22514	0.612570	−	0.790416i	$-0.290136\pi$
$59$	1.93272e6	1.22514	0.612570	+	0.790416i	$0.290136\pi$
$60$	−405674.	−0.242464
$61$	−2.51657e6	−1.41956	−0.709782	−	0.704421i	$-0.751207\pi$
$61$	−2.51657e6	−1.41956	−0.709782	+	0.704421i	$0.751207\pi$
$62$	−2.48163e6	−1.32241
$63$	1.16057e6	0.584763
$64$	−1.78514e6	−0.851220
$65$	−625283.	−0.282410
$66$	−1.48757e6	−0.636905
$67$	3.14472e6	1.27738	0.638690	−	0.769464i	$-0.279477\pi$
$67$	3.14472e6	1.27738	0.638690	+	0.769464i	$0.279477\pi$
$68$	−3.83818e6	−1.48028
$69$	−480897.	−0.176230
$70$	−3.16339e6	−1.10232
$71$	−1.20326e6	−0.398984	−0.199492	−	0.979899i	$-0.563929\pi$
$71$	−1.20326e6	−0.398984	−0.199492	+	0.979899i	$0.563929\pi$
$72$	105522.	0.0333181
$73$	−4.71395e6	−1.41826	−0.709129	−	0.705079i	$-0.750912\pi$
$73$	−4.71395e6	−1.41826	−0.709129	+	0.705079i	$0.750912\pi$
$74$	6.31599e6	1.81188
$75$	1.67740e6	0.459115
$76$	−2.96762e6	−0.775464
$77$	−5.58339e6	−1.39374
$78$	−2.09678e6	−0.500289
$79$	2.31658e6	0.528631	0.264316	−	0.964436i	$-0.414854\pi$
$79$	2.31658e6	0.528631	0.264316	+	0.964436i	$0.414854\pi$
$80$	−2.21082e6	−0.482767
$81$	531441.	0.111111
$82$	8.48297e6	1.69902
$83$	7.20406e6	1.38294	0.691471	−	0.722404i	$-0.256963\pi$
$83$	7.20406e6	1.38294	0.691471	+	0.722404i	$0.256963\pi$
$84$	−5.10590e6	−0.939929
$85$	−4.08704e6	−0.721843
$86$	1.10836e7	1.87904
$87$	−5.41092e6	−0.880955
$88$	−507657.	−0.0794110
$89$	−5.45832e6	−0.820718	−0.410359	−	0.911924i	$-0.634597\pi$
$89$	−5.45832e6	−0.820718	−0.410359	+	0.911924i	$0.634597\pi$
$90$	−1.44856e6	−0.209453
$91$	−7.86996e6	−1.09478
$92$	2.11570e6	0.283267
$93$	−4.26522e6	−0.549859
$94$	−6.12383e6	−0.760459
$95$	−3.16004e6	−0.378146
$96$	−6.91333e6	−0.797514
$97$	1.72226e7	1.91601	0.958004	−	0.286756i	$-0.0925768\pi$
$97$	1.72226e7	1.91601	0.958004	+	0.286756i	$0.0925768\pi$
$98$	−2.68777e7	−2.88471
$99$	−2.55671e6	−0.264825
$100$	−7.37967e6	−0.737967
$101$	6.09927e6	0.589052	0.294526	−	0.955644i	$-0.404838\pi$
$101$	6.09927e6	0.589052	0.294526	+	0.955644i	$0.404838\pi$
$102$	−1.37052e7	−1.27874
$103$	−6.41226e6	−0.578204	−0.289102	−	0.957298i	$-0.593357\pi$
$103$	−6.41226e6	−0.578204	−0.289102	+	0.957298i	$0.593357\pi$
$104$	−715557.	−0.0623775
$105$	−5.43696e6	−0.458346
$106$	3.50969e6	0.286219
$107$	1.07939e7	0.851795	0.425898	−	0.904771i	$-0.359958\pi$
$107$	1.07939e7	0.851795	0.425898	+	0.904771i	$0.359958\pi$
$108$	−2.33806e6	−0.178596
$109$	2.18461e7	1.61578	0.807890	−	0.589334i	$-0.200610\pi$
$109$	2.18461e7	1.61578	0.807890	+	0.589334i	$0.200610\pi$
$110$	6.96887e6	0.499216
$111$	1.08554e7	0.753381
$112$	−2.78259e7	−1.87148
$113$	1.41915e7	0.925237	0.462619	−	0.886557i	$-0.346910\pi$
$113$	1.41915e7	0.925237	0.462619	+	0.886557i	$0.346910\pi$
$114$	−1.05966e7	−0.669886
$115$	2.25287e6	0.138132
$116$	2.38052e7	1.41602
$117$	−3.60376e6	−0.208020
$118$	−3.03618e7	−1.70114
$119$	−5.14404e7	−2.79827
$120$	−494343.	−0.0261152
$121$	−7.18708e6	−0.368811
$122$	3.95339e7	1.97111
$123$	1.45798e7	0.706454
$124$	1.87647e7	0.883825
$125$	−1.77400e7	−0.812398
$126$	−1.82319e7	−0.811960
$127$	1.23858e7	0.536550	0.268275	−	0.963342i	$-0.413546\pi$
$127$	1.23858e7	0.536550	0.268275	+	0.963342i	$0.413546\pi$
$128$	−4.73085e6	−0.199390
$129$	1.90496e7	0.781306
$130$	9.82283e6	0.392134
$131$	1.07258e7	0.416851	0.208426	−	0.978038i	$-0.433166\pi$
$131$	1.07258e7	0.416851	0.208426	+	0.978038i	$0.433166\pi$
$132$	1.12482e7	0.425671
$133$	−3.97730e7	−1.46591
$134$	−4.94017e7	−1.77368
$135$	−2.48966e6	−0.0870906
$136$	−4.67710e6	−0.159437
$137$	1.32939e7	0.441704	0.220852	−	0.975307i	$-0.429116\pi$
$137$	1.32939e7	0.441704	0.220852	+	0.975307i	$0.429116\pi$
$138$	7.55462e6	0.244701
$139$	2.18112e7	0.688856	0.344428	−	0.938813i	$-0.388073\pi$
$139$	2.18112e7	0.688856	0.344428	+	0.938813i	$0.388073\pi$
$140$	2.39198e7	0.736731
$141$	−1.05251e7	−0.316199
$142$	1.89025e7	0.554001
$143$	1.73373e7	0.495800
$144$	−1.27418e7	−0.355601
$145$	2.53487e7	0.690507
$146$	7.40534e7	1.96929
$147$	−4.61952e7	−1.19946
$148$	−4.77580e7	−1.21096
$149$	−4.43097e7	−1.09736	−0.548678	−	0.836034i	$-0.684869\pi$
$149$	−4.43097e7	−1.09736	−0.548678	+	0.836034i	$0.684869\pi$
$150$	−2.63510e7	−0.637495
$151$	−3.97616e7	−0.939820	−0.469910	−	0.882714i	$-0.655714\pi$
$151$	−3.97616e7	−0.939820	−0.469910	+	0.882714i	$0.655714\pi$
$152$	−3.61627e6	−0.0835233
$153$	−2.35553e7	−0.531702
$154$	8.77119e7	1.93524
$155$	1.99814e7	0.430988
$156$	1.58547e7	0.334365
$157$	−3.86989e6	−0.0798087
$157$	−3.86989e6	−0.0798087
$158$	−3.63922e7	−0.734020
$159$	6.03215e6	0.119010
$160$	3.23871e7	0.625104
$161$	2.83552e7	0.535478
$162$	−8.34863e6	−0.154281
$163$	−4.09993e7	−0.741514	−0.370757	−	0.928730i	$-0.620902\pi$
$163$	−4.09993e7	−0.741514	−0.370757	+	0.928730i	$0.620902\pi$
$164$	−6.41435e7	−1.13553
$165$	1.19775e7	0.207574
$166$	−1.13172e8	−1.92026
$167$	7.85651e7	1.30533	0.652667	−	0.757645i	$-0.273650\pi$
$167$	7.85651e7	1.30533	0.652667	+	0.757645i	$0.273650\pi$
$168$	−6.22191e6	−0.101237
$169$	−3.83110e7	−0.610549
$170$	6.42050e7	1.00230
$171$	−1.82126e7	−0.278539
$172$	−8.38081e7	−1.25585
$173$	4.03418e7	0.592371	0.296185	−	0.955130i	$-0.404285\pi$
$173$	4.03418e7	0.592371	0.296185	+	0.955130i	$0.404285\pi$
$174$	8.50025e7	1.22323
$175$	−9.89046e7	−1.39503
$176$	6.12997e7	0.847548
$177$	−5.21833e7	−0.707335
$178$	8.57470e7	1.13959
$179$	5.01871e7	0.654043	0.327022	−	0.945017i	$-0.393955\pi$
$179$	5.01871e7	0.654043	0.327022	+	0.945017i	$0.393955\pi$
$180$	1.09532e7	0.139987
$181$	−7.41843e7	−0.929902	−0.464951	−	0.885336i	$-0.653928\pi$
$181$	−7.41843e7	−0.929902	−0.464951	+	0.885336i	$0.653928\pi$
$182$	1.23632e8	1.52014
$183$	6.79474e7	0.819586
$184$	2.57813e6	0.0305100
$185$	−5.08545e7	−0.590511
$186$	6.70041e7	0.763495
$187$	1.13322e8	1.26727
$188$	4.63050e7	0.508248
$189$	−3.13354e7	−0.337613
$190$	4.96424e7	0.525067
$191$	1.51425e7	0.157246	0.0786232	−	0.996904i	$-0.474948\pi$
$191$	1.51425e7	0.157246	0.0786232	+	0.996904i	$0.474948\pi$
$192$	4.81987e7	0.491452
$193$	2.63700e7	0.264034	0.132017	−	0.991247i	$-0.457855\pi$
$193$	2.63700e7	0.264034	0.132017	+	0.991247i	$0.457855\pi$
$194$	−2.70557e8	−2.66043
$195$	1.68826e7	0.163049
$196$	2.03235e8	1.92797
$197$	−1.34290e8	−1.25144	−0.625722	−	0.780046i	$-0.715196\pi$
$197$	−1.34290e8	−1.25144	−0.625722	+	0.780046i	$0.715196\pi$
$198$	4.01645e7	0.367717
$199$	1.82123e7	0.163825	0.0819124	−	0.996640i	$-0.473897\pi$
$199$	1.82123e7	0.163825	0.0819124	+	0.996640i	$0.473897\pi$
$200$	−8.99267e6	−0.0794847
$201$	−8.49074e7	−0.737495
$202$	−9.58161e7	−0.817916
$203$	3.19045e8	2.67680
$204$	1.03631e8	0.854640
$205$	−6.83025e7	−0.553730
$206$	1.00733e8	0.802853
$207$	1.29842e7	0.101747
$208$	8.64038e7	0.665750
$209$	8.76190e7	0.663875
$210$	8.54115e7	0.636427
$211$	6.96815e7	0.510657	0.255328	−	0.966854i	$-0.417816\pi$
$211$	6.96815e7	0.510657	0.255328	+	0.966854i	$0.417816\pi$
$212$	−2.65383e7	−0.191292
$213$	3.24880e7	0.230353
$214$	−1.69566e8	−1.18274
$215$	−8.92421e7	−0.612400
$216$	−2.84910e6	−0.0192362
$217$	2.51491e8	1.67075
$218$	−3.43190e8	−2.24356
$219$	1.27277e8	0.818831
$220$	−5.26947e7	−0.333647
$221$	1.59731e8	0.995442
$222$	−1.70532e8	−1.04609
$223$	−3.64026e7	−0.219819	−0.109910	−	0.993942i	$-0.535056\pi$
$223$	−3.64026e7	−0.219819	−0.109910	+	0.993942i	$0.535056\pi$
$224$	4.07632e8	2.42326
$225$	−4.52898e7	−0.265070
$226$	−2.22940e8	−1.28472
$227$	1.22406e8	0.694565	0.347283	−	0.937761i	$-0.387104\pi$
$227$	1.22406e8	0.694565	0.347283	+	0.937761i	$0.387104\pi$
$228$	8.01259e7	0.447714
$229$	1.18292e8	0.650926	0.325463	−	0.945555i	$-0.394480\pi$
$229$	1.18292e8	0.650926	0.325463	+	0.945555i	$0.394480\pi$
$230$	−3.53913e7	−0.191800
$231$	1.50752e8	0.804674
$232$	2.90084e7	0.152516
$233$	3.94632e7	0.204384	0.102192	−	0.994765i	$-0.467414\pi$
$233$	3.94632e7	0.204384	0.102192	+	0.994765i	$0.467414\pi$
$234$	5.66130e7	0.288842
$235$	4.93073e7	0.247841
$236$	2.29579e8	1.13695
$237$	−6.25477e7	−0.305205
$238$	8.08099e8	3.88549
$239$	1.65520e8	0.784255	0.392127	−	0.919911i	$-0.371739\pi$
$239$	1.65520e8	0.784255	0.392127	+	0.919911i	$0.371739\pi$
$240$	5.96921e7	0.278726
$241$	1.50143e8	0.690947	0.345473	−	0.938429i	$-0.387718\pi$
$241$	1.50143e8	0.690947	0.345473	+	0.938429i	$0.387718\pi$
$242$	1.12905e8	0.512104
$243$	−1.43489e7	−0.0641500
$244$	−2.98933e8	−1.31738
$245$	2.16412e8	0.940156
$246$	−2.29040e8	−0.980932
$247$	1.23502e8	0.521475
$248$	2.28662e7	0.0951947
$249$	−1.94510e8	−0.798442
$250$	2.78685e8	1.12804
$251$	−3.18929e8	−1.27302	−0.636510	−	0.771268i	$-0.719623\pi$
$251$	−3.18929e8	−1.27302	−0.636510	+	0.771268i	$0.719623\pi$
$252$	1.37859e8	0.542668
$253$	−6.24659e7	−0.242505
$254$	−1.94573e8	−0.745015
$255$	1.10350e8	0.416756
$256$	3.02816e8	1.12808
$257$	3.64246e8	1.33853	0.669266	−	0.743023i	$-0.266609\pi$
$257$	3.64246e8	1.33853	0.669266	+	0.743023i	$0.266609\pi$
$258$	−2.99258e8	−1.08487
$259$	−6.40067e8	−2.28916
$260$	−7.42748e7	−0.262080
$261$	1.46095e8	0.508620
$262$	−1.68496e8	−0.578810
$263$	2.54984e8	0.864307	0.432154	−	0.901800i	$-0.357754\pi$
$263$	2.54984e8	0.864307	0.432154	+	0.901800i	$0.357754\pi$
$264$	1.37067e7	0.0458480
$265$	−2.82590e7	−0.0932817
$266$	6.24811e8	2.03546
$267$	1.47375e8	0.473842
$268$	3.73548e8	1.18543
$269$	1.51467e8	0.474444	0.237222	−	0.971456i	$-0.423763\pi$
$269$	1.51467e8	0.474444	0.237222	+	0.971456i	$0.423763\pi$
$270$	3.91111e7	0.120928
$271$	−2.74933e8	−0.839140	−0.419570	−	0.907723i	$-0.637819\pi$
$271$	−2.74933e8	−0.839140	−0.419570	+	0.907723i	$0.637819\pi$
$272$	5.64761e8	1.70166
$273$	2.12489e8	0.632072
$274$	−2.08840e8	−0.613319
$275$	2.17885e8	0.631775
$276$	−5.71238e7	−0.163544
$277$	1.57883e8	0.446331	0.223165	−	0.974781i	$-0.428361\pi$
$277$	1.57883e8	0.446331	0.223165	+	0.974781i	$0.428361\pi$
$278$	−3.42642e8	−0.956497
$279$	1.15161e8	0.317461
$280$	2.91480e7	0.0793515
$281$	−1.57252e8	−0.422791	−0.211395	−	0.977401i	$-0.567801\pi$
$281$	−1.57252e8	−0.422791	−0.211395	+	0.977401i	$0.567801\pi$
$282$	1.65343e8	0.439051
$283$	9.53656e7	0.250115	0.125057	−	0.992150i	$-0.460089\pi$
$283$	9.53656e7	0.250115	0.125057	+	0.992150i	$0.460089\pi$
$284$	−1.42930e8	−0.370263
$285$	8.53211e7	0.218323
$286$	−2.72360e8	−0.688433
$287$	−8.59671e8	−2.14657
$288$	1.86660e8	0.460445
$289$	6.33710e8	1.54436
$290$	−3.98214e8	−0.958789
$291$	−4.65010e8	−1.10621
$292$	−5.59951e8	−1.31616
$293$	1.23355e8	0.286498	0.143249	−	0.989687i	$-0.454245\pi$
$293$	1.23355e8	0.286498	0.143249	+	0.989687i	$0.454245\pi$
$294$	7.25699e8	1.66549
$295$	2.44465e8	0.554420
$296$	−5.81965e7	−0.130430
$297$	6.90312e7	0.152897
$298$	6.96080e8	1.52371
$299$	−8.80475e7	−0.190488
$300$	1.99251e8	0.426066
$301$	−1.12322e9	−2.37401
$302$	6.24632e8	1.30497
$303$	−1.64680e8	−0.340089
$304$	4.36665e8	0.891438
$305$	−3.18315e8	−0.642404
$306$	3.70040e8	0.738283
$307$	−2.02593e8	−0.399614	−0.199807	−	0.979835i	$-0.564032\pi$
$307$	−2.02593e8	−0.399614	−0.199807	+	0.979835i	$0.564032\pi$
$308$	−6.63228e8	−1.29341
$309$	1.73131e8	0.333826
$310$	−3.13896e8	−0.598439
$311$	4.73860e8	0.893283	0.446641	−	0.894713i	$-0.352620\pi$
$311$	4.73860e8	0.893283	0.446641	+	0.894713i	$0.352620\pi$
$312$	1.93200e7	0.0360136
$313$	−9.63311e8	−1.77567	−0.887833	−	0.460166i	$-0.847790\pi$
$313$	−9.63311e8	−1.77567	−0.887833	+	0.460166i	$0.847790\pi$
$314$	6.07938e7	0.110817
$315$	1.46798e8	0.264626
$316$	2.75177e8	0.490577
$317$	−1.92076e8	−0.338661	−0.169331	−	0.985559i	$-0.554161\pi$
$317$	−1.92076e8	−0.338661	−0.169331	+	0.985559i	$0.554161\pi$
$318$	−9.47616e7	−0.165249
$319$	−7.02849e8	−1.21226
$320$	−2.25798e8	−0.385208
$321$	−2.91435e8	−0.491784
$322$	−4.45443e8	−0.743528
$323$	8.07244e8	1.33289
$324$	6.31277e7	0.103113
$325$	3.07115e8	0.496260
$326$	6.44075e8	1.02961
$327$	−5.89846e8	−0.932871
$328$	−7.81635e7	−0.122305
$329$	6.20594e8	0.960775
$330$	−1.88160e8	−0.288222
$331$	1.23161e9	1.86670	0.933352	−	0.358964i	$-0.116870\pi$
$331$	1.23161e9	1.86670	0.933352	+	0.358964i	$0.116870\pi$
$332$	8.55741e8	1.28339
$333$	−2.93095e8	−0.434965
$334$	−1.23421e9	−1.81250
$335$	3.97768e8	0.578060
$336$	7.51298e8	1.08050
$337$	4.46629e8	0.635685	0.317843	−	0.948143i	$-0.397042\pi$
$337$	4.46629e8	0.635685	0.317843	+	0.948143i	$0.397042\pi$
$338$	6.01844e8	0.847765
$339$	−3.83170e8	−0.534186
$340$	−4.85482e8	−0.669880
$341$	−5.54028e8	−0.756644
$342$	2.86109e8	0.386759
$343$	1.41273e9	1.89029
$344$	−1.02126e8	−0.135264
$345$	−6.08276e7	−0.0797505
$346$	−6.33746e8	−0.822525
$347$	1.68632e8	0.216664	0.108332	−	0.994115i	$-0.465449\pi$
$347$	1.68632e8	0.216664	0.108332	+	0.994115i	$0.465449\pi$
$348$	−6.42741e8	−0.817539
$349$	−1.05136e9	−1.32392	−0.661961	−	0.749538i	$-0.730276\pi$
$349$	−1.05136e9	−1.32392	−0.661961	+	0.749538i	$0.730276\pi$
$350$	1.55373e9	1.93704
$351$	9.73015e7	0.120100
$352$	−8.98003e8	−1.09743
$353$	8.41730e8	1.01850	0.509250	−	0.860619i	$-0.329923\pi$
$353$	8.41730e8	1.01850	0.509250	+	0.860619i	$0.329923\pi$
$354$	8.19770e8	0.982156
$355$	−1.52198e8	−0.180555
$356$	−6.48371e8	−0.761638
$357$	1.38889e9	1.61558
$358$	−7.88410e8	−0.908159
$359$	1.12031e9	1.27793	0.638964	−	0.769237i	$-0.279363\pi$
$359$	1.12031e9	1.27793	0.638964	+	0.769237i	$0.279363\pi$
$360$	1.33473e7	0.0150776
$361$	−2.69722e8	−0.301746
$362$	1.16539e9	1.29120
$363$	1.94051e8	0.212933
$364$	−9.34839e8	−1.01597
$365$	−5.96257e8	−0.641813
$366$	−1.06741e9	−1.13802
$367$	−9.52566e8	−1.00592	−0.502960	−	0.864309i	$-0.667756\pi$
$367$	−9.52566e8	−1.00592	−0.502960	+	0.864309i	$0.667756\pi$
$368$	−3.11310e8	−0.325631
$369$	−3.93655e8	−0.407871
$370$	7.98895e8	0.819943
$371$	−3.55675e8	−0.361613
$372$	−5.06648e8	−0.510277
$373$	−1.00657e9	−1.00430	−0.502149	−	0.864781i	$-0.667457\pi$
$373$	−1.00657e9	−1.00430	−0.502149	+	0.864781i	$0.667457\pi$
$374$	−1.78022e9	−1.75964
$375$	4.78980e8	0.469038
$376$	5.64260e7	0.0547421
$377$	−9.90686e8	−0.952229
$378$	4.92261e8	0.468785
$379$	−8.88333e8	−0.838182	−0.419091	−	0.907944i	$-0.637651\pi$
$379$	−8.88333e8	−0.838182	−0.419091	+	0.907944i	$0.637651\pi$
$380$	−3.75368e8	−0.350925
$381$	−3.34416e8	−0.309777
$382$	−2.37880e8	−0.218341
$383$	6.98814e8	0.635573	0.317787	−	0.948162i	$-0.397060\pi$
$383$	6.98814e8	0.635573	0.317787	+	0.948162i	$0.397060\pi$
$384$	1.27733e8	0.115118
$385$	−7.06231e8	−0.630716
$386$	−4.14257e8	−0.366619
$387$	−5.14338e8	−0.451087
$388$	2.04580e9	1.77808
$389$	7.09331e8	0.610978	0.305489	−	0.952196i	$-0.401180\pi$
$389$	7.09331e8	0.610978	0.305489	+	0.952196i	$0.401180\pi$
$390$	−2.65216e8	−0.226399
$391$	−5.75505e8	−0.486889
$392$	2.47656e8	0.207657
$393$	−2.89597e8	−0.240669
$394$	2.10962e9	1.73767
$395$	2.93019e8	0.239225
$396$	−3.03701e8	−0.245761
$397$	−1.37751e8	−0.110491	−0.0552456	−	0.998473i	$-0.517594\pi$
$397$	−1.37751e8	−0.110491	−0.0552456	+	0.998473i	$0.517594\pi$
$398$	−2.86105e8	−0.227476
$399$	1.07387e9	0.846344
$400$	1.08587e9	0.848334
$401$	1.01559e9	0.786530	0.393265	−	0.919425i	$-0.371346\pi$
$401$	1.01559e9	0.786530	0.393265	+	0.919425i	$0.371346\pi$
$402$	1.33385e9	1.02403
$403$	−7.80919e8	−0.594345
$404$	7.24507e8	0.546648
$405$	6.72207e7	0.0502818
$406$	−5.01201e9	−3.71681
$407$	1.41005e9	1.03670
$408$	1.26282e8	0.0920512
$409$	2.43650e9	1.76090	0.880452	−	0.474136i	$-0.157240\pi$
$409$	2.43650e9	1.76090	0.880452	+	0.474136i	$0.157240\pi$
$410$	1.07299e9	0.768870
$411$	−3.58936e8	−0.255018
$412$	−7.61686e8	−0.536582
$413$	3.07689e9	2.14925
$414$	−2.03975e8	−0.141278
$415$	9.11225e8	0.625832
$416$	−1.26576e9	−0.862036
$417$	−5.88903e8	−0.397711
$418$	−1.37644e9	−0.921810
$419$	−9.12772e8	−0.606196	−0.303098	−	0.952959i	$-0.598021\pi$
$419$	−9.12772e8	−0.606196	−0.303098	+	0.952959i	$0.598021\pi$
$420$	−6.45834e8	−0.425352
$421$	−4.99528e8	−0.326267	−0.163133	−	0.986604i	$-0.552160\pi$
$421$	−4.99528e8	−0.326267	−0.163133	+	0.986604i	$0.552160\pi$
$422$	−1.09466e9	−0.709062
$423$	2.84178e8	0.182557
$424$	−3.23389e7	−0.0206037
$425$	2.00740e9	1.26844
$426$	−5.10368e8	−0.319853
$427$	−4.00639e9	−2.49032
$428$	1.28216e9	0.790478
$429$	−4.68108e8	−0.286250
$430$	1.40194e9	0.850335
$431$	8.48938e8	0.510747	0.255373	−	0.966843i	$-0.417802\pi$
$431$	8.48938e8	0.510747	0.255373	+	0.966843i	$0.417802\pi$
$432$	3.44030e8	0.205306
$433$	−2.67299e9	−1.58230	−0.791151	−	0.611621i	$-0.790518\pi$
$433$	−2.67299e9	−1.58230	−0.791151	+	0.611621i	$0.790518\pi$
$434$	−3.95077e9	−2.31989
$435$	−6.84415e8	−0.398664
$436$	2.59501e9	1.49947
$437$	−4.44972e8	−0.255063
$438$	−1.99944e9	−1.13697
$439$	2.14708e9	1.21122	0.605610	−	0.795762i	$-0.292929\pi$
$439$	2.14708e9	1.21122	0.605610	+	0.795762i	$0.292929\pi$
$440$	−6.42123e7	−0.0359364
$441$	1.24727e9	0.692509
$442$	−2.50928e9	−1.38220
$443$	−1.88553e8	−0.103044	−0.0515219	−	0.998672i	$-0.516407\pi$
$443$	−1.88553e8	−0.103044	−0.0515219	+	0.998672i	$0.516407\pi$
$444$	1.28946e9	0.699148
$445$	−6.90410e8	−0.371404
$446$	5.71864e8	0.305226
$447$	1.19636e9	0.633558
$448$	−2.84194e9	−1.49328
$449$	−3.45743e9	−1.80257	−0.901284	−	0.433228i	$-0.857374\pi$
$449$	−3.45743e9	−1.80257	−0.901284	+	0.433228i	$0.857374\pi$
$450$	7.11476e8	0.368058
$451$	1.89384e9	0.972130
$452$	1.68575e9	0.858633
$453$	1.07356e9	0.542605
$454$	−1.92293e9	−0.964424
$455$	−9.95453e8	−0.495428
$456$	9.76392e7	0.0482222
$457$	2.18337e9	1.07009	0.535046	−	0.844823i	$-0.320294\pi$
$457$	2.18337e9	1.07009	0.535046	+	0.844823i	$0.320294\pi$
$458$	−1.85830e9	−0.903830
$459$	6.35992e8	0.306978
$460$	2.67609e8	0.128188
$461$	−7.44789e8	−0.354062	−0.177031	−	0.984205i	$-0.556649\pi$
$461$	−7.44789e8	−0.354062	−0.177031	+	0.984205i	$0.556649\pi$
$462$	−2.36822e9	−1.11731
$463$	−4.97962e8	−0.233164	−0.116582	−	0.993181i	$-0.537194\pi$
$463$	−4.97962e8	−0.233164	−0.116582	+	0.993181i	$0.537194\pi$
$464$	−3.50277e9	−1.62779
$465$	−5.39498e8	−0.248831
$466$	−6.19944e8	−0.283793
$467$	3.37590e9	1.53384	0.766921	−	0.641742i	$-0.221788\pi$
$467$	3.37590e9	1.53384	0.766921	+	0.641742i	$0.221788\pi$
$468$	−4.28076e8	−0.193046
$469$	5.00640e9	2.24089
$470$	−7.74590e8	−0.344135
$471$	1.04487e8	0.0460776
$472$	2.79759e8	0.122458
$473$	2.47443e9	1.07513
$474$	9.82588e8	0.423787
$475$	1.55209e9	0.664491
$476$	−6.11039e9	−2.59684
$477$	−1.62868e8	−0.0687103
$478$	−2.60022e9	−1.08896
$479$	−1.70550e9	−0.709050	−0.354525	−	0.935047i	$-0.615357\pi$
$479$	−1.70550e9	−0.709050	−0.354525	+	0.935047i	$0.615357\pi$
$480$	−8.74452e8	−0.360904
$481$	1.98751e9	0.814332
$482$	−2.35865e9	−0.959400
$483$	−7.65590e8	−0.309159
$484$	−8.53723e8	−0.342262
$485$	2.17844e9	0.867063
$486$	2.25413e8	0.0890742
$487$	1.42238e9	0.558038	0.279019	−	0.960286i	$-0.409991\pi$
$487$	1.42238e9	0.558038	0.279019	+	0.960286i	$0.409991\pi$
$488$	−3.64272e8	−0.141891
$489$	1.10698e9	0.428113
$490$	−3.39970e9	−1.30543
$491$	−2.47906e9	−0.945152	−0.472576	−	0.881290i	$-0.656676\pi$
$491$	−2.47906e9	−0.945152	−0.472576	+	0.881290i	$0.656676\pi$
$492$	1.73187e9	0.655599
$493$	−6.47542e9	−2.43391
$494$	−1.94014e9	−0.724083
$495$	−3.23393e8	−0.119843
$496$	−2.76110e9	−1.01601
$497$	−1.91559e9	−0.699933
$498$	3.05563e9	1.10866
$499$	1.34890e9	0.485990	0.242995	−	0.970028i	$-0.421870\pi$
$499$	1.34890e9	0.485990	0.242995	+	0.970028i	$0.421870\pi$
$500$	−2.10726e9	−0.753917
$501$	−2.12126e9	−0.753635
$502$	5.01018e9	1.76763
$503$	5.33822e9	1.87029	0.935144	−	0.354268i	$-0.115270\pi$
$503$	5.33822e9	1.87029	0.935144	+	0.354268i	$0.115270\pi$
$504$	1.67992e8	0.0584495
$505$	7.71483e8	0.266567
$506$	9.81302e8	0.336725
$507$	1.03440e9	0.352500
$508$	1.47125e9	0.497926
$509$	5.38274e9	1.80922	0.904610	−	0.426241i	$-0.140163\pi$
$509$	5.38274e9	1.80922	0.904610	+	0.426241i	$0.140163\pi$
$510$	−1.73354e9	−0.578678
$511$	−7.50463e9	−2.48803
$512$	−4.15152e9	−1.36698
$513$	4.91740e8	0.160814
$514$	−5.72209e9	−1.85859
$515$	−8.11073e8	−0.261658
$516$	2.26282e9	0.725063
$517$	−1.36715e9	−0.435112
$518$	1.00551e10	3.17856
$519$	−1.08923e9	−0.342006
$520$	−9.05092e7	−0.0282281
$521$	−6.20687e9	−1.92283	−0.961415	−	0.275103i	$-0.911288\pi$
$521$	−6.20687e9	−1.92283	−0.961415	+	0.275103i	$0.911288\pi$
$522$	−2.29507e9	−0.706234
$523$	−1.08406e9	−0.331358	−0.165679	−	0.986180i	$-0.552982\pi$
$523$	−1.08406e9	−0.331358	−0.165679	+	0.986180i	$0.552982\pi$
$524$	1.27408e9	0.386844
$525$	2.67042e9	0.805420
$526$	−4.00565e9	−1.20012
$527$	−5.10432e9	−1.51915
$528$	−1.65509e9	−0.489332
$529$	−3.08759e9	−0.906829
$530$	4.43933e8	0.129524
$531$	1.40895e9	0.408380
$532$	−4.72447e9	−1.36039
$533$	2.66942e9	0.763609
$534$	−2.31517e9	−0.657943
$535$	1.36530e9	0.385468
$536$	4.55195e8	0.127679
$537$	−1.35505e9	−0.377612
$538$	−2.37946e9	−0.658779
$539$	−6.00049e9	−1.65054
$540$	−2.95736e8	−0.0808213
$541$	5.59109e9	1.51812	0.759060	−	0.651020i	$-0.225659\pi$
$541$	5.59109e9	1.51812	0.759060	+	0.651020i	$0.225659\pi$
$542$	4.31904e9	1.16517
$543$	2.00298e9	0.536879
$544$	−8.27340e9	−2.20337
$545$	2.76327e9	0.731198
$546$	−3.33808e9	−0.877651
$547$	−2.36959e9	−0.619038	−0.309519	−	0.950893i	$-0.600168\pi$
$547$	−2.36959e9	−0.619038	−0.309519	+	0.950893i	$0.600168\pi$
$548$	1.57913e9	0.409908
$549$	−1.83458e9	−0.473188
$550$	−3.42284e9	−0.877238
$551$	−5.00670e9	−1.27503
$552$	−6.96095e7	−0.0176150
$553$	3.68801e9	0.927372
$554$	−2.48025e9	−0.619743
$555$	1.37307e9	0.340932
$556$	2.59087e9	0.639268
$557$	−9.74295e8	−0.238890	−0.119445	−	0.992841i	$-0.538111\pi$
$557$	−9.74295e8	−0.238890	−0.119445	+	0.992841i	$0.538111\pi$
$558$	−1.80911e9	−0.440804
$559$	3.48778e9	0.844517
$560$	−3.51963e9	−0.846913
$561$	−3.05970e9	−0.731659
$562$	2.47034e9	0.587057
$563$	4.04615e8	0.0955571	0.0477785	−	0.998858i	$-0.484786\pi$
$563$	4.04615e8	0.0955571	0.0477785	+	0.998858i	$0.484786\pi$
$564$	−1.25024e9	−0.293437
$565$	1.79505e9	0.418703
$566$	−1.49814e9	−0.347292
$567$	8.46056e8	0.194921
$568$	−1.74171e8	−0.0398801
$569$	5.78294e9	1.31600	0.658000	−	0.753018i	$-0.271403\pi$
$569$	5.78294e9	1.31600	0.658000	+	0.753018i	$0.271403\pi$
$570$	−1.34034e9	−0.303148
$571$	4.38897e9	0.986589	0.493295	−	0.869862i	$-0.335792\pi$
$571$	4.38897e9	0.986589	0.493295	+	0.869862i	$0.335792\pi$
$572$	2.05943e9	0.460109
$573$	−4.08848e8	−0.0907863
$574$	1.35049e10	2.98058
$575$	−1.10652e9	−0.242730
$576$	−1.30137e9	−0.283740
$577$	−7.75970e9	−1.68163	−0.840813	−	0.541325i	$-0.817923\pi$
$577$	−7.75970e9	−1.68163	−0.840813	+	0.541325i	$0.817923\pi$
$578$	−9.95522e9	−2.14439
$579$	−7.11990e8	−0.152440
$580$	3.01107e9	0.640800
$581$	1.14689e10	2.42608
$582$	7.30503e9	1.53600
$583$	7.83543e8	0.163766
$584$	−6.82340e8	−0.141761
$585$	−4.55831e8	−0.0941366
$586$	−1.93784e9	−0.397811
$587$	8.23688e9	1.68085	0.840426	−	0.541927i	$-0.182305\pi$
$587$	8.23688e9	1.68085	0.840426	+	0.541927i	$0.182305\pi$
$588$	−5.48733e9	−1.11312
$589$	−3.94659e9	−0.795826
$590$	−3.84040e9	−0.769829
$591$	3.62583e9	0.722521
$592$	7.02725e9	1.39207
$593$	1.37339e9	0.270460	0.135230	−	0.990814i	$-0.456823\pi$
$593$	1.37339e9	0.270460	0.135230	+	0.990814i	$0.456823\pi$
$594$	−1.08444e9	−0.212302
$595$	−6.50658e9	−1.26632
$596$	−5.26337e9	−1.01836
$597$	−4.91733e8	−0.0945843
$598$	1.38317e9	0.264498
$599$	7.80568e9	1.48394	0.741970	−	0.670433i	$-0.233891\pi$
$599$	7.80568e9	1.48394	0.741970	+	0.670433i	$0.233891\pi$
$600$	2.42802e8	0.0458905
$601$	7.14220e9	1.34206	0.671029	−	0.741431i	$-0.265852\pi$
$601$	7.14220e9	1.34206	0.671029	+	0.741431i	$0.265852\pi$
$602$	1.76452e10	3.29638
$603$	2.29250e9	0.425793
$604$	−4.72312e9	−0.872167
$605$	−9.09077e8	−0.166900
$606$	2.58703e9	0.472224
$607$	9.20012e9	1.66968	0.834840	−	0.550492i	$-0.185560\pi$
$607$	9.20012e9	1.66968	0.834840	+	0.550492i	$0.185560\pi$
$608$	−6.39688e9	−1.15426
$609$	−8.61421e9	−1.54545
$610$	5.00055e9	0.891997
$611$	−1.92704e9	−0.341781
$612$	−2.79803e9	−0.493427
$613$	−6.08690e9	−1.06730	−0.533648	−	0.845707i	$-0.679179\pi$
$613$	−6.08690e9	−1.06730	−0.533648	+	0.845707i	$0.679179\pi$
$614$	3.18262e9	0.554876
$615$	1.84417e9	0.319696
$616$	−8.08191e8	−0.139310
$617$	−3.87218e9	−0.663678	−0.331839	−	0.943336i	$-0.607669\pi$
$617$	−3.87218e9	−0.663678	−0.331839	+	0.943336i	$0.607669\pi$
$618$	−2.71979e9	−0.463528
$619$	5.15676e9	0.873896	0.436948	−	0.899487i	$-0.356059\pi$
$619$	5.15676e9	0.873896	0.436948	+	0.899487i	$0.356059\pi$
$620$	2.37351e9	0.399963
$621$	−3.50574e8	−0.0587434
$622$	−7.44407e9	−1.24035
$623$	−8.68966e9	−1.43978
$624$	−2.33290e9	−0.384371
$625$	2.60969e9	0.427572
$626$	1.51331e10	2.46556
$627$	−2.36571e9	−0.383289
$628$	−4.59688e8	−0.0740636
$629$	1.29910e10	2.08144
$630$	−2.30611e9	−0.367441
$631$	1.00101e10	1.58611	0.793057	−	0.609148i	$-0.208488\pi$
$631$	1.00101e10	1.58611	0.793057	+	0.609148i	$0.208488\pi$
$632$	3.35323e8	0.0528389
$633$	−1.88140e9	−0.294828
$634$	3.01740e9	0.470241
$635$	1.56665e9	0.242808
$636$	7.16535e8	0.110443
$637$	−8.45787e9	−1.29650
$638$	1.10413e10	1.68325
$639$	−8.77177e8	−0.132995
$640$	−5.98394e8	−0.0902314
$641$	2.29784e8	0.0344601	0.0172300	−	0.999852i	$-0.494515\pi$
$641$	2.29784e8	0.0344601	0.0172300	+	0.999852i	$0.494515\pi$
$642$	4.57828e9	0.682857
$643$	−1.04623e10	−1.55198	−0.775992	−	0.630743i	$-0.782750\pi$
$643$	−1.04623e10	−1.55198	−0.775992	+	0.630743i	$0.782750\pi$
$644$	3.36819e9	0.496932
$645$	2.40954e9	0.353569
$646$	−1.26813e10	−1.85076
$647$	3.02552e9	0.439172	0.219586	−	0.975593i	$-0.429529\pi$
$647$	3.02552e9	0.439172	0.219586	+	0.975593i	$0.429529\pi$
$648$	7.69256e7	0.0111060
$649$	−6.77832e9	−0.973343
$650$	−4.82460e9	−0.689071
$651$	−6.79024e9	−0.964610
$652$	−4.87013e9	−0.688136
$653$	2.89905e9	0.407436	0.203718	−	0.979030i	$-0.434697\pi$
$653$	2.89905e9	0.407436	0.203718	+	0.979030i	$0.434697\pi$
$654$	9.26614e9	1.29532
$655$	1.35668e9	0.188640
$656$	9.43827e9	1.30536
$657$	−3.43647e9	−0.472752
$658$	−9.74916e9	−1.33406
$659$	−5.85022e9	−0.796294	−0.398147	−	0.917322i	$-0.630347\pi$
$659$	−5.85022e9	−0.796294	−0.398147	+	0.917322i	$0.630347\pi$
$660$	1.42276e9	0.192631
$661$	1.34380e10	1.80979	0.904896	−	0.425632i	$-0.139948\pi$
$661$	1.34380e10	1.80979	0.904896	+	0.425632i	$0.139948\pi$
$662$	−1.93479e10	−2.59197
$663$	−4.31273e9	−0.574719
$664$	1.04278e9	0.138231
$665$	−5.03079e9	−0.663378
$666$	4.60435e9	0.603961
$667$	3.56941e9	0.465753
$668$	9.33242e9	1.21137
$669$	9.82871e8	0.126913
$670$	−6.24871e9	−0.802654
$671$	8.82599e9	1.12781
$672$	−1.10061e10	−1.39907
$673$	−7.73408e9	−0.978039	−0.489019	−	0.872273i	$-0.662645\pi$
$673$	−7.73408e9	−0.978039	−0.489019	+	0.872273i	$0.662645\pi$
$674$	−7.01628e9	−0.882668
$675$	1.22282e9	0.153038
$676$	−4.55081e9	−0.566598
$677$	1.23704e9	0.153223	0.0766116	−	0.997061i	$-0.475590\pi$
$677$	1.23704e9	0.153223	0.0766116	+	0.997061i	$0.475590\pi$
$678$	6.01938e9	0.741733
$679$	2.74184e10	3.36123
$680$	−5.91595e8	−0.0721512
$681$	−3.30497e9	−0.401007
$682$	8.70346e9	1.05062
$683$	2.25723e9	0.271084	0.135542	−	0.990772i	$-0.456722\pi$
$683$	2.25723e9	0.271084	0.135542	+	0.990772i	$0.456722\pi$
$684$	−2.16340e9	−0.258488
$685$	1.68152e9	0.199887
$686$	−2.21931e10	−2.62473
$687$	−3.19389e9	−0.375812
$688$	1.23318e10	1.44366
$689$	1.10443e9	0.128638
$690$	9.55566e8	0.110736
$691$	−9.37548e9	−1.08099	−0.540493	−	0.841348i	$-0.681762\pi$
$691$	−9.37548e9	−1.08099	−0.540493	+	0.841348i	$0.681762\pi$
$692$	4.79203e9	0.549729
$693$	−4.07029e9	−0.464579
$694$	−2.64911e9	−0.300844
$695$	2.75885e9	0.311732
$696$	−7.83226e8	−0.0880552
$697$	1.74481e10	1.95179
$698$	1.65163e10	1.83831
$699$	−1.06551e9	−0.118001
$700$	−1.17485e10	−1.29461
$701$	2.88790e9	0.316642	0.158321	−	0.987388i	$-0.449392\pi$
$701$	2.88790e9	0.316642	0.158321	+	0.987388i	$0.449392\pi$
$702$	−1.52855e9	−0.166763
$703$	1.00444e10	1.09039
$704$	6.26074e9	0.676272
$705$	−1.33130e9	−0.143091
$706$	−1.32231e10	−1.41422
$707$	9.71007e9	1.03337
$708$	−6.19864e9	−0.656417
$709$	6.86967e9	0.723892	0.361946	−	0.932199i	$-0.382112\pi$
$709$	6.86967e9	0.723892	0.361946	+	0.932199i	$0.382112\pi$
$710$	2.39094e9	0.250705
$711$	1.68879e9	0.176210
$712$	−7.90087e8	−0.0820342
$713$	2.81362e9	0.290705
$714$	−2.18187e10	−2.24329
$715$	2.19296e9	0.224367
$716$	5.96152e9	0.606962
$717$	−4.46903e9	−0.452790
$718$	−1.75994e10	−1.77444
$719$	1.98924e10	1.99589	0.997945	−	0.0640712i	$-0.0204085\pi$
$719$	1.98924e10	1.99589	0.997945	+	0.0640712i	$0.0204085\pi$
$720$	−1.61169e9	−0.160922
$721$	−1.02083e10	−1.01434
$722$	4.23718e9	0.418983
$723$	−4.05385e9	−0.398918
$724$	−8.81205e9	−0.862963
$725$	−1.24503e10	−1.21338
$726$	−3.04843e9	−0.295664
$727$	1.43772e9	0.138772	0.0693862	−	0.997590i	$-0.477896\pi$
$727$	1.43772e9	0.138772	0.0693862	+	0.997590i	$0.477896\pi$
$728$	−1.13917e9	−0.109428
$729$	3.87420e8	0.0370370
$730$	9.36685e9	0.891176
$731$	2.27972e10	2.15859
$732$	8.07119e9	0.760587
$733$	6.09213e8	0.0571354	0.0285677	−	0.999592i	$-0.490905\pi$
$733$	6.09213e8	0.0571354	0.0285677	+	0.999592i	$0.490905\pi$
$734$	1.49643e10	1.39675
$735$	−5.84312e9	−0.542799
$736$	4.56050e9	0.421638
$737$	−1.10290e10	−1.01485
$738$	6.18409e9	0.566342
$739$	−1.38883e10	−1.26588	−0.632940	−	0.774201i	$-0.718152\pi$
$739$	−1.38883e10	−1.26588	−0.632940	+	0.774201i	$0.718152\pi$
$740$	−6.04079e9	−0.548003
$741$	−3.33454e9	−0.301074
$742$	5.58744e9	0.502110
$743$	−1.01220e10	−0.905324	−0.452662	−	0.891682i	$-0.649526\pi$
$743$	−1.01220e10	−0.905324	−0.452662	+	0.891682i	$0.649526\pi$
$744$	−6.17387e8	−0.0549607
$745$	−5.60464e9	−0.496593
$746$	1.58126e10	1.39450
$747$	5.25176e9	0.460981
$748$	1.34611e10	1.17604
$749$	1.71839e10	1.49429
$750$	−7.52450e9	−0.651273
$751$	8.36078e9	0.720290	0.360145	−	0.932896i	$-0.382727\pi$
$751$	8.36078e9	0.720290	0.360145	+	0.932896i	$0.382727\pi$
$752$	−6.81346e9	−0.584259
$753$	8.61107e9	0.734979
$754$	1.55631e10	1.32220
$755$	−5.02936e9	−0.425303
$756$	−3.72220e9	−0.313310
$757$	−1.71508e9	−0.143697	−0.0718487	−	0.997416i	$-0.522890\pi$
$757$	−1.71508e9	−0.143697	−0.0718487	+	0.997416i	$0.522890\pi$
$758$	1.39552e10	1.16384
$759$	1.68658e9	0.140010
$760$	−4.57413e8	−0.0377973
$761$	−4.65775e9	−0.383115	−0.191558	−	0.981481i	$-0.561354\pi$
$761$	−4.65775e9	−0.383115	−0.191558	+	0.981481i	$0.561354\pi$
$762$	5.25348e9	0.430135
$763$	3.47791e10	2.83454
$764$	1.79872e9	0.145927
$765$	−2.97945e9	−0.240614
$766$	−1.09780e10	−0.882512
$767$	−9.55424e9	−0.764562
$768$	−8.17605e9	−0.651297
$769$	1.93924e10	1.53776	0.768881	−	0.639391i	$-0.220814\pi$
$769$	1.93924e10	1.53776	0.768881	+	0.639391i	$0.220814\pi$
$770$	1.10945e10	0.875768
$771$	−9.83464e9	−0.772802
$772$	3.13238e9	0.245027
$773$	−9.72720e9	−0.757460	−0.378730	−	0.925507i	$-0.623639\pi$
$773$	−9.72720e9	−0.757460	−0.378730	+	0.925507i	$0.623639\pi$
$774$	8.07996e9	0.626348
$775$	−9.81409e9	−0.757346
$776$	2.49295e9	0.191513
$777$	1.72818e10	1.32165
$778$	−1.11432e10	−0.848361
$779$	1.34906e10	1.02247
$780$	2.00542e9	0.151312
$781$	4.22001e9	0.316982
$782$	9.04085e9	0.676060
$783$	−3.94456e9	−0.293652
$784$	−2.99045e10	−2.21631
$785$	−4.89494e8	−0.0361163
$786$	4.54940e9	0.334176
$787$	8.45791e9	0.618517	0.309258	−	0.950978i	$-0.399919\pi$
$787$	8.45791e9	0.618517	0.309258	+	0.950978i	$0.399919\pi$
$788$	−1.59517e10	−1.16136
$789$	−6.88457e9	−0.499008
$790$	−4.60316e9	−0.332171
$791$	2.25929e10	1.62313
$792$	−3.70082e8	−0.0264703
$793$	1.24405e10	0.885894
$794$	2.16399e9	0.153420
$795$	7.62993e8	0.0538562
$796$	2.16337e9	0.152032
$797$	−2.32431e10	−1.62626	−0.813130	−	0.582081i	$-0.802238\pi$
$797$	−2.32431e10	−1.62626	−0.813130	+	0.582081i	$0.802238\pi$
$798$	−1.68699e10	−1.17517
$799$	−1.25957e10	−0.873595
$800$	−1.59073e10	−1.09845
$801$	−3.97911e9	−0.273573
$802$	−1.59544e10	−1.09212
$803$	1.65325e10	1.12677
$804$	−1.00858e10	−0.684406
$805$	3.58658e9	0.242323
$806$	1.22678e10	0.825265
$807$	−4.08961e9	−0.273920
$808$	8.82865e8	0.0588782
$809$	−1.27103e9	−0.0843986	−0.0421993	−	0.999109i	$-0.513436\pi$
$809$	−1.27103e9	−0.0843986	−0.0421993	+	0.999109i	$0.513436\pi$
$810$	−1.05600e9	−0.0698178
$811$	−3.58758e9	−0.236172	−0.118086	−	0.993003i	$-0.537676\pi$
$811$	−3.58758e9	−0.236172	−0.118086	+	0.993003i	$0.537676\pi$
$812$	3.78980e10	2.48411
$813$	7.42319e9	0.484478
$814$	−2.21511e10	−1.43949
$815$	−5.18590e9	−0.335562
$816$	−1.52486e10	−0.982456
$817$	1.76265e10	1.13081
$818$	−3.82761e10	−2.44507
$819$	−5.73720e9	−0.364927
$820$	−8.11336e9	−0.513869
$821$	−6.17277e9	−0.389295	−0.194648	−	0.980873i	$-0.562356\pi$
$821$	−6.17277e9	−0.389295	−0.194648	+	0.980873i	$0.562356\pi$
$822$	5.63868e9	0.354100
$823$	1.87069e10	1.16977	0.584887	−	0.811115i	$-0.301139\pi$
$823$	1.87069e10	1.16977	0.584887	+	0.811115i	$0.301139\pi$
$824$	−9.28170e8	−0.0577939
$825$	−5.88289e9	−0.364755
$826$	−4.83362e10	−2.98430
$827$	1.00812e10	0.619786	0.309893	−	0.950771i	$-0.399707\pi$
$827$	1.00812e10	0.619786	0.309893	+	0.950771i	$0.399707\pi$
$828$	1.54234e9	0.0944223
$829$	2.73676e10	1.66838	0.834192	−	0.551474i	$-0.185934\pi$
$829$	2.73676e10	1.66838	0.834192	+	0.551474i	$0.185934\pi$
$830$	−1.43148e10	−0.868986
$831$	−4.26285e9	−0.257689
$832$	8.82470e9	0.531213
$833$	−5.52832e10	−3.31387
$834$	9.25133e9	0.552234
$835$	9.93751e9	0.590711
$836$	1.04079e10	0.616086
$837$	−3.10935e9	−0.183286
$838$	1.43391e10	0.841721
$839$	−2.32724e10	−1.36042	−0.680212	−	0.733015i	$-0.738112\pi$
$839$	−2.32724e10	−1.36042	−0.680212	+	0.733015i	$0.738112\pi$
$840$	−7.86995e8	−0.0458136
$841$	2.29121e10	1.32825
$842$	7.84729e9	0.453031
$843$	4.24582e9	0.244098
$844$	8.27718e9	0.473897
$845$	−4.84587e9	−0.276295
$846$	−4.46427e9	−0.253486
$847$	−1.14419e10	−0.647000
$848$	3.90493e9	0.219901
$849$	−2.57487e9	−0.144404
$850$	−3.15350e10	−1.76127
$851$	−7.16093e9	−0.398305
$852$	3.85912e9	0.213771
$853$	−1.19568e10	−0.659619	−0.329809	−	0.944048i	$-0.606984\pi$
$853$	−1.19568e10	−0.659619	−0.329809	+	0.944048i	$0.606984\pi$
$854$	6.29381e10	3.45789
$855$	−2.30367e9	−0.126049
$856$	1.56241e9	0.0851405
$857$	−1.33882e9	−0.0726592	−0.0363296	−	0.999340i	$-0.511567\pi$
$857$	−1.33882e9	−0.0726592	−0.0363296	+	0.999340i	$0.511567\pi$
$858$	7.35371e9	0.397467
$859$	−1.33653e10	−0.719455	−0.359728	−	0.933057i	$-0.617130\pi$
$859$	−1.33653e10	−0.719455	−0.359728	+	0.933057i	$0.617130\pi$
$860$	−1.06007e10	−0.568316
$861$	2.32111e10	1.23932
$862$	−1.33363e10	−0.709187
$863$	−1.16534e10	−0.617187	−0.308593	−	0.951194i	$-0.599858\pi$
$863$	−1.16534e10	−0.617187	−0.308593	+	0.951194i	$0.599858\pi$
$864$	−5.03982e9	−0.265838
$865$	5.10274e9	0.268069
$866$	4.19911e10	2.19707
$867$	−1.71102e10	−0.891636
$868$	2.98735e10	1.55048
$869$	−8.12460e9	−0.419984
$870$	1.07518e10	0.553557
$871$	−1.55457e10	−0.797162
$872$	3.16221e9	0.161504
$873$	1.25553e10	0.638669
$874$	6.99025e9	0.354163
$875$	−2.82422e10	−1.42518
$876$	1.51187e10	0.759887
$877$	1.10773e10	0.554544	0.277272	−	0.960791i	$-0.410570\pi$
$877$	1.10773e10	0.554544	0.277272	+	0.960791i	$0.410570\pi$
$878$	−3.37294e10	−1.68181
$879$	−3.33059e9	−0.165410
$880$	7.75366e9	0.383546
$881$	−2.19531e10	−1.08163	−0.540817	−	0.841140i	$-0.681885\pi$
$881$	−2.19531e10	−1.08163	−0.540817	+	0.841140i	$0.681885\pi$
$882$	−1.95939e10	−0.961569
$883$	−3.47849e10	−1.70031	−0.850155	−	0.526533i	$-0.823492\pi$
$883$	−3.47849e10	−1.70031	−0.850155	+	0.526533i	$0.823492\pi$
$884$	1.89738e10	0.923784
$885$	−6.60055e9	−0.320095
$886$	2.96207e9	0.143079
$887$	−3.28665e10	−1.58132	−0.790661	−	0.612254i	$-0.790263\pi$
$887$	−3.28665e10	−1.58132	−0.790661	+	0.612254i	$0.790263\pi$
$888$	1.57131e9	0.0753036
$889$	1.97182e10	0.941263
$890$	1.08459e10	0.515706
$891$	−1.86384e9	−0.0882749
$892$	−4.32412e9	−0.203995
$893$	−9.73885e9	−0.457644
$894$	−1.87942e10	−0.879715
$895$	6.34805e9	0.295978
$896$	−7.53153e9	−0.349788
$897$	2.37728e9	0.109978
$898$	5.43143e10	2.50292
$899$	3.16581e10	1.45320
$900$	−5.37978e9	−0.245989
$901$	7.21887e9	0.328800
$902$	−2.97511e10	−1.34983
$903$	3.03270e10	1.37064
$904$	2.05420e9	0.0924813
$905$	−9.38341e9	−0.420814
$906$	−1.68651e10	−0.753424
$907$	2.64659e9	0.117777	0.0588886	−	0.998265i	$-0.481244\pi$
$907$	2.64659e9	0.117777	0.0588886	+	0.998265i	$0.481244\pi$
$908$	1.45401e10	0.644567
$909$	4.44637e9	0.196351
$910$	1.56380e10	0.687917
$911$	−4.37502e10	−1.91719	−0.958596	−	0.284770i	$-0.908083\pi$
$911$	−4.37502e10	−1.91719	−0.958596	+	0.284770i	$0.908083\pi$
$912$	−1.17900e10	−0.514672
$913$	−2.52657e10	−1.09871
$914$	−3.42995e10	−1.48585
$915$	8.59452e9	0.370892
$916$	1.40514e10	0.604069
$917$	1.70755e10	0.731277
$918$	−9.99107e9	−0.426248
$919$	3.83837e9	0.163133	0.0815667	−	0.996668i	$-0.474008\pi$
$919$	3.83837e9	0.163133	0.0815667	+	0.996668i	$0.474008\pi$
$920$	3.26101e8	0.0138069
$921$	5.47002e9	0.230717
$922$	1.17002e10	0.491626
$923$	5.94823e9	0.248990
$924$	1.79072e10	0.746749
$925$	2.49778e10	1.03767
$926$	7.82269e9	0.323756
$927$	−4.67454e9	−0.192735
$928$	5.13135e10	2.10772
$929$	4.62524e10	1.89269	0.946345	−	0.323159i	$-0.104745\pi$
$929$	4.62524e10	1.89269	0.946345	+	0.323159i	$0.104745\pi$
$930$	8.47520e9	0.345509
$931$	−4.27442e10	−1.73601
$932$	4.68767e9	0.189671
$933$	−1.27942e10	−0.515737
$934$	−5.30334e10	−2.12978
$935$	1.43339e10	0.573485
$936$	−5.21641e8	−0.0207925
$937$	2.09810e10	0.833179	0.416589	−	0.909095i	$-0.363225\pi$
$937$	2.09810e10	0.833179	0.416589	+	0.909095i	$0.363225\pi$
$938$	−7.86477e10	−3.11154
$939$	2.60094e10	1.02518
$940$	5.85701e9	0.230000
$941$	−4.36158e10	−1.70640	−0.853198	−	0.521587i	$-0.825340\pi$
$941$	−4.36158e10	−1.70640	−0.853198	+	0.521587i	$0.825340\pi$
$942$	−1.64143e9	−0.0639801
$943$	−9.61782e9	−0.373496
$944$	−3.37810e10	−1.30698
$945$	−3.96354e9	−0.152782
$946$	−3.88719e10	−1.49285
$947$	1.93710e10	0.741186	0.370593	−	0.928795i	$-0.379154\pi$
$947$	1.93710e10	0.741186	0.370593	+	0.928795i	$0.379154\pi$
$948$	−7.42978e9	−0.283235
$949$	2.33031e10	0.885078
$950$	−2.43824e10	−0.922665
$951$	5.18605e9	0.195526
$952$	−7.44596e9	−0.279699
$953$	2.34024e10	0.875861	0.437931	−	0.899009i	$-0.355712\pi$
$953$	2.34024e10	0.875861	0.437931	+	0.899009i	$0.355712\pi$
$954$	2.55856e9	0.0954063
$955$	1.91534e9	0.0711597
$956$	1.96614e10	0.727800
$957$	1.89769e10	0.699896
$958$	2.67924e10	0.984537
$959$	2.11640e10	0.774876
$960$	6.09654e9	0.222400
$961$	−2.55775e9	−0.0929664
$962$	−3.12226e10	−1.13072
$963$	7.86875e9	0.283932
$964$	1.78348e10	0.641208
$965$	3.33548e9	0.119485
$966$	1.20270e10	0.429276
$967$	−3.37784e10	−1.20128	−0.600642	−	0.799518i	$-0.705088\pi$
$967$	−3.37784e10	−1.20128	−0.600642	+	0.799518i	$0.705088\pi$
$968$	−1.04032e9	−0.0368642
$969$	−2.17956e10	−0.769547
$970$	−3.42221e10	−1.20394
$971$	4.66004e9	0.163351	0.0816755	−	0.996659i	$-0.473973\pi$
$971$	4.66004e9	0.163351	0.0816755	+	0.996659i	$0.473973\pi$
$972$	−1.70445e9	−0.0595321
$973$	3.47236e10	1.20845
$974$	−2.23447e10	−0.774852
$975$	−8.29210e9	−0.286516
$976$	4.39859e10	1.51440
$977$	3.90269e10	1.33885	0.669426	−	0.742879i	$-0.266540\pi$
$977$	3.90269e10	1.33885	0.669426	+	0.742879i	$0.266540\pi$
$978$	−1.73900e10	−0.594448
$979$	1.91431e10	0.652039
$980$	2.57067e10	0.872478
$981$	1.59258e10	0.538593
$982$	3.89446e10	1.31237
$983$	−2.87524e10	−0.965466	−0.482733	−	0.875768i	$-0.660356\pi$
$983$	−2.87524e10	−0.965466	−0.482733	+	0.875768i	$0.660356\pi$
$984$	2.11041e9	0.0706130
$985$	−1.69860e10	−0.566324
$986$	1.01725e11	3.37955
$987$	−1.67560e10	−0.554704
$988$	1.46702e10	0.483936
$989$	−1.25664e10	−0.413069
$990$	5.08031e9	0.166405
$991$	2.07809e10	0.678277	0.339138	−	0.940737i	$-0.389865\pi$
$991$	2.07809e10	0.678277	0.339138	+	0.940737i	$0.389865\pi$
$992$	4.04484e10	1.31556
$993$	−3.32535e10	−1.07774
$994$	3.00929e10	0.971877
$995$	2.30364e9	0.0741367
$996$	−2.31050e10	−0.740966
$997$	4.44396e10	1.42016	0.710080	−	0.704121i	$-0.248659\pi$
$997$	4.44396e10	1.42016	0.710080	+	0.704121i	$0.248659\pi$
$998$	−2.11904e10	−0.674811
$999$	7.91357e9	0.251127

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.8.a.c.1.10	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.8.a.c.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-15.7094 q^{2} -27.0000 q^{3} +118.786 q^{4} +126.488 q^{5} +424.154 q^{6} +1592.00 q^{7} +144.749 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-15.7094 q^{2} -27.0000 q^{3} +118.786 q^{4} +126.488 q^{5} +424.154 q^{6} +1592.00 q^{7} +144.749 q^{8} +729.000 q^{9} -1987.05 q^{10} -3507.15 q^{11} -3207.22 q^{12} -4943.43 q^{13} -25009.4 q^{14} -3415.17 q^{15} -17478.5 q^{16} -32311.7 q^{17} -11452.2 q^{18} -24983.0 q^{19} +15024.9 q^{20} -42984.1 q^{21} +55095.3 q^{22} +17811.0 q^{23} -3908.23 q^{24} -62125.9 q^{25} +77658.4 q^{26} -19683.0 q^{27} +189107. q^{28} +200405. q^{29} +53650.3 q^{30} +157971. q^{31} +256049. q^{32} +94693.0 q^{33} +507599. q^{34} +201369. q^{35} +86594.9 q^{36} -402051. q^{37} +392468. q^{38} +133473. q^{39} +18309.0 q^{40} -539993. q^{41} +675255. q^{42} -705540. q^{43} -416600. q^{44} +92209.5 q^{45} -279801. q^{46} +389819. q^{47} +471920. q^{48} +1.71093e6 q^{49} +975961. q^{50} +872417. q^{51} -587209. q^{52} -223413. q^{53} +309208. q^{54} -443611. q^{55} +230441. q^{56} +674541. q^{57} -3.14824e6 q^{58} +1.93272e6 q^{59} -405674. q^{60} -2.51657e6 q^{61} -2.48163e6 q^{62} +1.16057e6 q^{63} -1.78514e6 q^{64} -625283. q^{65} -1.48757e6 q^{66} +3.14472e6 q^{67} -3.83818e6 q^{68} -480897. q^{69} -3.16339e6 q^{70} -1.20326e6 q^{71} +105522. q^{72} -4.71395e6 q^{73} +6.31599e6 q^{74} +1.67740e6 q^{75} -2.96762e6 q^{76} -5.58339e6 q^{77} -2.09678e6 q^{78} +2.31658e6 q^{79} -2.21082e6 q^{80} +531441. q^{81} +8.48297e6 q^{82} +7.20406e6 q^{83} -5.10590e6 q^{84} -4.08704e6 q^{85} +1.10836e7 q^{86} -5.41092e6 q^{87} -507657. q^{88} -5.45832e6 q^{89} -1.44856e6 q^{90} -7.86996e6 q^{91} +2.11570e6 q^{92} -4.26522e6 q^{93} -6.12383e6 q^{94} -3.16004e6 q^{95} -6.91333e6 q^{96} +1.72226e7 q^{97} -2.68777e7 q^{98} -2.55671e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{2} - 1296 q^{3} + 3214 q^{4} + 428 q^{5} - 54 q^{6} - 680 q^{7} + 2355 q^{8} + 34992 q^{9}+O(q^{10}) \) 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

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