LMFDB - Embedded newform 177.10.a.a.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,10,Mod(1,177)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	177.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:	$91.1613430010$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.56630 q^{2} +81.0000 q^{3} -509.547 q^{4} -1262.61 q^{5} +126.871 q^{6} -7655.10 q^{7} -1600.05 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+1.56630 q^{2} +81.0000 q^{3} -509.547 q^{4} -1262.61 q^{5} +126.871 q^{6} -7655.10 q^{7} -1600.05 q^{8} +6561.00 q^{9} -1977.63 q^{10} +70322.7 q^{11} -41273.3 q^{12} -47687.6 q^{13} -11990.2 q^{14} -102272. q^{15} +258382. q^{16} +389608. q^{17} +10276.5 q^{18} +511521. q^{19} +643360. q^{20} -620063. q^{21} +110147. q^{22} +172172. q^{23} -129604. q^{24} -358937. q^{25} -74693.2 q^{26} +531441. q^{27} +3.90063e6 q^{28} +4.84225e6 q^{29} -160188. q^{30} -187258. q^{31} +1.22393e6 q^{32} +5.69613e6 q^{33} +610244. q^{34} +9.66542e6 q^{35} -3.34314e6 q^{36} -2.06095e7 q^{37} +801196. q^{38} -3.86269e6 q^{39} +2.02024e6 q^{40} +1.23789e7 q^{41} -971207. q^{42} -3.93068e7 q^{43} -3.58327e7 q^{44} -8.28400e6 q^{45} +269673. q^{46} -3.33132e7 q^{47} +2.09289e7 q^{48} +1.82470e7 q^{49} -562203. q^{50} +3.15582e7 q^{51} +2.42990e7 q^{52} +1.91650e7 q^{53} +832398. q^{54} -8.87902e7 q^{55} +1.22486e7 q^{56} +4.14332e7 q^{57} +7.58443e6 q^{58} +1.21174e7 q^{59} +5.21121e7 q^{60} -1.21058e8 q^{61} -293303. q^{62} -5.02251e7 q^{63} -1.30374e8 q^{64} +6.02109e7 q^{65} +8.92187e6 q^{66} +2.99688e6 q^{67} -1.98523e8 q^{68} +1.39459e7 q^{69} +1.51390e7 q^{70} -1.08294e8 q^{71} -1.04979e7 q^{72} +7.68824e7 q^{73} -3.22808e7 q^{74} -2.90739e7 q^{75} -2.60644e8 q^{76} -5.38327e8 q^{77} -6.05015e6 q^{78} +3.66431e8 q^{79} -3.26236e8 q^{80} +4.30467e7 q^{81} +1.93891e7 q^{82} +4.97567e8 q^{83} +3.15951e8 q^{84} -4.91924e8 q^{85} -6.15664e7 q^{86} +3.92222e8 q^{87} -1.12520e8 q^{88} +4.74027e8 q^{89} -1.29752e7 q^{90} +3.65053e8 q^{91} -8.77296e7 q^{92} -1.51679e7 q^{93} -5.21785e7 q^{94} -6.45852e8 q^{95} +9.91384e7 q^{96} -3.38070e8 q^{97} +2.85803e7 q^{98} +4.61387e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9}+O(q^{10}) $ 21 * q - 66 * q^2 + 1701 * q^3 + 5206 * q^4 - 2964 * q^5 - 5346 * q^6 - 30775 * q^7 - 24621 * q^8 + 137781 * q^9	\( 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9} - 54663 q^{10} - 151769 q^{11} + 421686 q^{12} - 153611 q^{13} - 286771 q^{14} - 240084 q^{15} + 805530 q^{16} - 723621 q^{17} - 433026 q^{18} - 549388 q^{19} - 527311 q^{20} - 2492775 q^{21} + 2973158 q^{22} + 169962 q^{23} - 1994301 q^{24} + 8035779 q^{25} - 2337392 q^{26} + 11160261 q^{27} - 22659054 q^{28} - 16845442 q^{29} - 4427703 q^{30} - 19307976 q^{31} - 44923568 q^{32} - 12293289 q^{33} - 35547496 q^{34} - 34882596 q^{35} + 34156566 q^{36} - 41561129 q^{37} - 52335371 q^{38} - 12442491 q^{39} - 125735038 q^{40} - 68169291 q^{41} - 23228451 q^{42} - 25719587 q^{43} - 126277032 q^{44} - 19446804 q^{45} - 292814271 q^{46} - 174095332 q^{47} + 65247930 q^{48} + 7479350 q^{49} - 227877439 q^{50} - 58613301 q^{51} - 232397708 q^{52} - 228390500 q^{53} - 35075106 q^{54} - 29426208 q^{55} + 326778474 q^{56} - 44500428 q^{57} + 480343762 q^{58} + 254464581 q^{59} - 42712191 q^{60} - 183928964 q^{61} - 21753862 q^{62} - 201914775 q^{63} + 310571245 q^{64} + 5308466 q^{65} + 240825798 q^{66} - 82724114 q^{67} - 138336205 q^{68} + 13766922 q^{69} + 1030274876 q^{70} - 404721965 q^{71} - 161538381 q^{72} + 154162574 q^{73} + 36352054 q^{74} + 650898099 q^{75} + 1068940636 q^{76} - 448535481 q^{77} - 189328752 q^{78} + 272529635 q^{79} - 345587859 q^{80} + 903981141 q^{81} - 38412637 q^{82} + 432518643 q^{83} - 1835383374 q^{84} - 126211490 q^{85} - 3699273072 q^{86} - 1364480802 q^{87} + 170111045 q^{88} - 1255621070 q^{89} - 358643943 q^{90} + 1448885849 q^{91} + 1568933320 q^{92} - 1563946056 q^{93} - 1908445164 q^{94} - 2896546490 q^{95} - 3638809008 q^{96} + 1007235486 q^{97} - 9506868248 q^{98} - 995756409 q^{99}+O(q^{100}) \) 21 * q - 66 * q^2 + 1701 * q^3 + 5206 * q^4 - 2964 * q^5 - 5346 * q^6 - 30775 * q^7 - 24621 * q^8 + 137781 * q^9 - 54663 * q^10 - 151769 * q^11 + 421686 * q^12 - 153611 * q^13 - 286771 * q^14 - 240084 * q^15 + 805530 * q^16 - 723621 * q^17 - 433026 * q^18 - 549388 * q^19 - 527311 * q^20 - 2492775 * q^21 + 2973158 * q^22 + 169962 * q^23 - 1994301 * q^24 + 8035779 * q^25 - 2337392 * q^26 + 11160261 * q^27 - 22659054 * q^28 - 16845442 * q^29 - 4427703 * q^30 - 19307976 * q^31 - 44923568 * q^32 - 12293289 * q^33 - 35547496 * q^34 - 34882596 * q^35 + 34156566 * q^36 - 41561129 * q^37 - 52335371 * q^38 - 12442491 * q^39 - 125735038 * q^40 - 68169291 * q^41 - 23228451 * q^42 - 25719587 * q^43 - 126277032 * q^44 - 19446804 * q^45 - 292814271 * q^46 - 174095332 * q^47 + 65247930 * q^48 + 7479350 * q^49 - 227877439 * q^50 - 58613301 * q^51 - 232397708 * q^52 - 228390500 * q^53 - 35075106 * q^54 - 29426208 * q^55 + 326778474 * q^56 - 44500428 * q^57 + 480343762 * q^58 + 254464581 * q^59 - 42712191 * q^60 - 183928964 * q^61 - 21753862 * q^62 - 201914775 * q^63 + 310571245 * q^64 + 5308466 * q^65 + 240825798 * q^66 - 82724114 * q^67 - 138336205 * q^68 + 13766922 * q^69 + 1030274876 * q^70 - 404721965 * q^71 - 161538381 * q^72 + 154162574 * q^73 + 36352054 * q^74 + 650898099 * q^75 + 1068940636 * q^76 - 448535481 * q^77 - 189328752 * q^78 + 272529635 * q^79 - 345587859 * q^80 + 903981141 * q^81 - 38412637 * q^82 + 432518643 * q^83 - 1835383374 * q^84 - 126211490 * q^85 - 3699273072 * q^86 - 1364480802 * q^87 + 170111045 * q^88 - 1255621070 * q^89 - 358643943 * q^90 + 1448885849 * q^91 + 1568933320 * q^92 - 1563946056 * q^93 - 1908445164 * q^94 - 2896546490 * q^95 - 3638809008 * q^96 + 1007235486 * q^97 - 9506868248 * q^98 - 995756409 * 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 $

$2$	1.56630	0.0692215	0.0346107	−	0.999401i	$-0.488981\pi$
$2$	1.56630	0.0692215	0.0346107	+	0.999401i	$0.488981\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	−509.547	−0.995208
$5$	−1262.61	−0.903451	−0.451726	−	0.892157i	$-0.649191\pi$
$5$	−1262.61	−0.903451	−0.451726	+	0.892157i	$0.649191\pi$
$6$	126.871	0.0399650
$7$	−7655.10	−1.20506	−0.602531	−	0.798095i	$-0.705841\pi$
$7$	−7655.10	−1.20506	−0.602531	+	0.798095i	$0.705841\pi$
$8$	−1600.05	−0.138111
$9$	6561.00	0.333333
$10$	−1977.63	−0.0625382
$11$	70322.7	1.44820	0.724099	−	0.689696i	$-0.242256\pi$
$11$	70322.7	1.44820	0.724099	+	0.689696i	$0.242256\pi$
$12$	−41273.3	−0.574584
$13$	−47687.6	−0.463084	−0.231542	−	0.972825i	$-0.574377\pi$
$13$	−47687.6	−0.463084	−0.231542	+	0.972825i	$0.574377\pi$
$14$	−11990.2	−0.0834162
$15$	−102272.	−0.521608
$16$	258382.	0.985648
$17$	389608.	1.13138	0.565689	−	0.824619i	$-0.308610\pi$
$17$	389608.	1.13138	0.565689	+	0.824619i	$0.308610\pi$
$18$	10276.5	0.0230738
$19$	511521.	0.900476	0.450238	−	0.892909i	$-0.351339\pi$
$19$	511521.	0.900476	0.450238	+	0.892909i	$0.351339\pi$
$20$	643360.	0.899122
$21$	−620063.	−0.695743
$22$	110147.	0.100246
$23$	172172.	0.128288	0.0641442	−	0.997941i	$-0.479568\pi$
$23$	172172.	0.128288	0.0641442	+	0.997941i	$0.479568\pi$
$24$	−129604.	−0.0797386
$25$	−358937.	−0.183776
$26$	−74693.2	−0.0320554
$27$	531441.	0.192450
$28$	3.90063e6	1.19929
$29$	4.84225e6	1.27132	0.635662	−	0.771968i	$-0.280727\pi$
$29$	4.84225e6	1.27132	0.635662	+	0.771968i	$0.280727\pi$
$30$	−160188.	−0.0361065
$31$	−187258.	−0.0364178	−0.0182089	−	0.999834i	$-0.505796\pi$
$31$	−187258.	−0.0364178	−0.0182089	+	0.999834i	$0.505796\pi$
$32$	1.22393e6	0.206339
$33$	5.69613e6	0.836118
$34$	610244.	0.0783156
$35$	9.66542e6	1.08872
$36$	−3.34314e6	−0.331736
$37$	−2.06095e7	−1.80784	−0.903921	−	0.427700i	$-0.859324\pi$
$37$	−2.06095e7	−1.80784	−0.903921	+	0.427700i	$0.859324\pi$
$38$	801196.	0.0623322
$39$	−3.86269e6	−0.267362
$40$	2.02024e6	0.124777
$41$	1.23789e7	0.684154	0.342077	−	0.939672i	$-0.388870\pi$
$41$	1.23789e7	0.684154	0.342077	+	0.939672i	$0.388870\pi$
$42$	−971207.	−0.0481604
$43$	−3.93068e7	−1.75331	−0.876657	−	0.481116i	$-0.840232\pi$
$43$	−3.93068e7	−1.75331	−0.876657	+	0.481116i	$0.840232\pi$
$44$	−3.58327e7	−1.44126
$45$	−8.28400e6	−0.301150
$46$	269673.	0.00888030
$47$	−3.33132e7	−0.995808	−0.497904	−	0.867232i	$-0.665897\pi$
$47$	−3.33132e7	−0.995808	−0.497904	+	0.867232i	$0.665897\pi$
$48$	2.09289e7	0.569064
$49$	1.82470e7	0.452177
$50$	−562203.	−0.0127212
$51$	3.15582e7	0.653201
$52$	2.42990e7	0.460865
$53$	1.91650e7	0.333632	0.166816	−	0.985988i	$-0.446651\pi$
$53$	1.91650e7	0.333632	0.166816	+	0.985988i	$0.446651\pi$
$54$	832398.	0.0133217
$55$	−8.87902e7	−1.30838
$56$	1.22486e7	0.166433
$57$	4.14332e7	0.519890
$58$	7.58443e6	0.0880029
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	5.21121e7	0.519109
$61$	−1.21058e8	−1.11946	−0.559730	−	0.828675i	$-0.689095\pi$
$61$	−1.21058e8	−1.11946	−0.559730	+	0.828675i	$0.689095\pi$
$62$	−293303.	−0.00252089
$63$	−5.02251e7	−0.401688
$64$	−1.30374e8	−0.971365
$65$	6.02109e7	0.418374
$66$	8.92187e6	0.0578773
$67$	2.99688e6	0.0181691	0.00908455	−	0.999959i	$-0.497108\pi$
$67$	2.99688e6	0.0181691	0.00908455	+	0.999959i	$0.497108\pi$
$68$	−1.98523e8	−1.12596
$69$	1.39459e7	0.0740673
$70$	1.51390e7	0.0753625
$71$	−1.08294e8	−0.505755	−0.252878	−	0.967498i	$-0.581377\pi$
$71$	−1.08294e8	−0.505755	−0.252878	+	0.967498i	$0.581377\pi$
$72$	−1.04979e7	−0.0460371
$73$	7.68824e7	0.316865	0.158433	−	0.987370i	$-0.449356\pi$
$73$	7.68824e7	0.316865	0.158433	+	0.987370i	$0.449356\pi$
$74$	−3.22808e7	−0.125141
$75$	−2.90739e7	−0.106103
$76$	−2.60644e8	−0.896161
$77$	−5.38327e8	−1.74517
$78$	−6.05015e6	−0.0185072
$79$	3.66431e8	1.05845	0.529225	−	0.848482i	$-0.322483\pi$
$79$	3.66431e8	1.05845	0.529225	+	0.848482i	$0.322483\pi$
$80$	−3.26236e8	−0.890485
$81$	4.30467e7	0.111111
$82$	1.93891e7	0.0473581
$83$	4.97567e8	1.15080	0.575401	−	0.817872i	$-0.304846\pi$
$83$	4.97567e8	1.15080	0.575401	+	0.817872i	$0.304846\pi$
$84$	3.15951e8	0.692410
$85$	−4.91924e8	−1.02214
$86$	−6.15664e7	−0.121367
$87$	3.92222e8	0.733999
$88$	−1.12520e8	−0.200013
$89$	4.74027e8	0.800844	0.400422	−	0.916331i	$-0.368864\pi$
$89$	4.74027e8	0.800844	0.400422	+	0.916331i	$0.368864\pi$
$90$	−1.29752e7	−0.0208461
$91$	3.65053e8	0.558046
$92$	−8.77296e7	−0.127674
$93$	−1.51679e7	−0.0210258
$94$	−5.21785e7	−0.0689313
$95$	−6.45852e8	−0.813536
$96$	9.91384e7	0.119130
$97$	−3.38070e8	−0.387734	−0.193867	−	0.981028i	$-0.562103\pi$
$97$	−3.38070e8	−0.387734	−0.193867	+	0.981028i	$0.562103\pi$
$98$	2.85803e7	0.0313003
$99$	4.61387e8	0.482733
$100$	1.82895e8	0.182895
$101$	3.15186e8	0.301384	0.150692	−	0.988581i	$-0.451850\pi$
$101$	3.15186e8	0.301384	0.150692	+	0.988581i	$0.451850\pi$
$102$	4.94298e7	0.0452155
$103$	−2.29811e7	−0.0201188	−0.0100594	−	0.999949i	$-0.503202\pi$
$103$	−2.29811e7	−0.0201188	−0.0100594	+	0.999949i	$0.503202\pi$
$104$	7.63025e7	0.0639571
$105$	7.82899e8	0.628570
$106$	3.00183e7	0.0230945
$107$	9.85007e8	0.726461	0.363230	−	0.931699i	$-0.381674\pi$
$107$	9.85007e8	0.726461	0.363230	+	0.931699i	$0.381674\pi$
$108$	−2.70794e8	−0.191528
$109$	−1.24273e9	−0.843253	−0.421626	−	0.906770i	$-0.638541\pi$
$109$	−1.24273e9	−0.843253	−0.421626	+	0.906770i	$0.638541\pi$
$110$	−1.39072e8	−0.0905678
$111$	−1.66937e9	−1.04376
$112$	−1.97794e9	−1.18777
$113$	8.64168e8	0.498592	0.249296	−	0.968427i	$-0.419801\pi$
$113$	8.64168e8	0.498592	0.249296	+	0.968427i	$0.419801\pi$
$114$	6.48969e7	0.0359875
$115$	−2.17386e8	−0.115902
$116$	−2.46735e9	−1.26523
$117$	−3.12878e8	−0.154361
$118$	1.89795e7	0.00901187
$119$	−2.98249e9	−1.36338
$120$	1.63640e8	0.0720399
$121$	2.58733e9	1.09728
$122$	−1.89613e8	−0.0774906
$123$	1.00269e9	0.394996
$124$	9.54168e7	0.0362433
$125$	2.91924e9	1.06948
$126$	−7.86677e7	−0.0278054
$127$	−4.00552e9	−1.36629	−0.683145	−	0.730283i	$-0.739388\pi$
$127$	−4.00552e9	−1.36629	−0.683145	+	0.730283i	$0.739388\pi$
$128$	−8.30858e8	−0.273579
$129$	−3.18385e9	−1.01228
$130$	9.43085e7	0.0289605
$131$	4.81457e9	1.42836	0.714178	−	0.699964i	$-0.246801\pi$
$131$	4.81457e9	1.42836	0.714178	+	0.699964i	$0.246801\pi$
$132$	−2.90245e9	−0.832112
$133$	−3.91574e9	−1.08513
$134$	4.69403e6	0.00125769
$135$	−6.71004e8	−0.173869
$136$	−6.23393e8	−0.156256
$137$	−7.36777e9	−1.78687	−0.893436	−	0.449190i	$-0.851712\pi$
$137$	−7.36777e9	−1.78687	−0.893436	+	0.449190i	$0.851712\pi$
$138$	2.18435e7	0.00512705
$139$	−2.19930e9	−0.499709	−0.249855	−	0.968283i	$-0.580383\pi$
$139$	−2.19930e9	−0.499709	−0.249855	+	0.968283i	$0.580383\pi$
$140$	−4.92498e9	−1.08350
$141$	−2.69837e9	−0.574930
$142$	−1.69621e8	−0.0350091
$143$	−3.35352e9	−0.670638
$144$	1.69524e9	0.328549
$145$	−6.11388e9	−1.14858
$146$	1.20421e8	0.0219339
$147$	1.47800e9	0.261064
$148$	1.05015e10	1.79918
$149$	−3.43090e9	−0.570255	−0.285128	−	0.958490i	$-0.592036\pi$
$149$	−3.43090e9	−0.570255	−0.285128	+	0.958490i	$0.592036\pi$
$150$	−4.55385e7	−0.00734459
$151$	−8.57766e9	−1.34268	−0.671340	−	0.741149i	$-0.734281\pi$
$151$	−8.57766e9	−1.34268	−0.671340	+	0.741149i	$0.734281\pi$
$152$	−8.18459e8	−0.124366
$153$	2.55622e9	0.377126
$154$	−8.43183e8	−0.120803
$155$	2.36434e8	0.0329017
$156$	1.96822e9	0.266081
$157$	2.32463e9	0.305356	0.152678	−	0.988276i	$-0.451210\pi$
$157$	2.32463e9	0.305356	0.152678	+	0.988276i	$0.451210\pi$
$158$	5.73942e8	0.0732674
$159$	1.55237e9	0.192623
$160$	−1.54535e9	−0.186417
$161$	−1.31799e9	−0.154596
$162$	6.74242e7	0.00769127
$163$	−1.53845e10	−1.70702	−0.853510	−	0.521076i	$-0.825531\pi$
$163$	−1.53845e10	−1.70702	−0.853510	+	0.521076i	$0.825531\pi$
$164$	−6.30761e9	−0.680876
$165$	−7.19201e9	−0.755392
$166$	7.79341e8	0.0796602
$167$	−3.00233e8	−0.0298699	−0.0149350	−	0.999888i	$-0.504754\pi$
$167$	−3.00233e8	−0.0298699	−0.0149350	+	0.999888i	$0.504754\pi$
$168$	9.92133e8	0.0960900
$169$	−8.33040e9	−0.785553
$170$	−7.70501e8	−0.0707544
$171$	3.35609e9	0.300159
$172$	2.00287e10	1.74491
$173$	−1.67251e9	−0.141959	−0.0709794	−	0.997478i	$-0.522612\pi$
$173$	−1.67251e9	−0.141959	−0.0709794	+	0.997478i	$0.522612\pi$
$174$	6.14339e8	0.0508085
$175$	2.74770e9	0.221461
$176$	1.81701e10	1.42741
$177$	9.81506e8	0.0751646
$178$	7.42469e8	0.0554356
$179$	−6.15034e9	−0.447776	−0.223888	−	0.974615i	$-0.571875\pi$
$179$	−6.15034e9	−0.447776	−0.223888	+	0.974615i	$0.571875\pi$
$180$	4.22108e9	0.299707
$181$	−8.76056e9	−0.606706	−0.303353	−	0.952878i	$-0.598106\pi$
$181$	−8.76056e9	−0.606706	−0.303353	+	0.952878i	$0.598106\pi$
$182$	5.71784e8	0.0386287
$183$	−9.80568e9	−0.646320
$184$	−2.75484e8	−0.0177181
$185$	2.60218e10	1.63330
$186$	−2.37575e7	−0.00145544
$187$	2.73983e10	1.63846
$188$	1.69746e10	0.991036
$189$	−4.06823e9	−0.231914
$190$	−1.01160e9	−0.0563141
$191$	−1.67491e10	−0.910631	−0.455315	−	0.890330i	$-0.650473\pi$
$191$	−1.67491e10	−0.910631	−0.455315	+	0.890330i	$0.650473\pi$
$192$	−1.05603e10	−0.560818
$193$	−1.80329e10	−0.935532	−0.467766	−	0.883852i	$-0.654941\pi$
$193$	−1.80329e10	−0.935532	−0.467766	+	0.883852i	$0.654941\pi$
$194$	−5.29520e8	−0.0268395
$195$	4.87708e9	0.241548
$196$	−9.29768e9	−0.450010
$197$	−1.37553e10	−0.650686	−0.325343	−	0.945596i	$-0.605480\pi$
$197$	−1.37553e10	−0.650686	−0.325343	+	0.945596i	$0.605480\pi$
$198$	7.22672e8	0.0334155
$199$	4.32422e9	0.195465	0.0977325	−	0.995213i	$-0.468841\pi$
$199$	4.32422e9	0.195465	0.0977325	+	0.995213i	$0.468841\pi$
$200$	5.74317e8	0.0253815
$201$	2.42748e8	0.0104899
$202$	4.93676e8	0.0208622
$203$	−3.70679e10	−1.53203
$204$	−1.60804e10	−0.650071
$205$	−1.56297e10	−0.618100
$206$	−3.59953e7	−0.00139265
$207$	1.12962e9	0.0427628
$208$	−1.23216e10	−0.456438
$209$	3.59715e10	1.30407
$210$	1.22626e9	0.0435106
$211$	4.13380e10	1.43575	0.717874	−	0.696173i	$-0.245115\pi$
$211$	4.13380e10	1.43575	0.717874	+	0.696173i	$0.245115\pi$
$212$	−9.76548e9	−0.332034
$213$	−8.77179e9	−0.291998
$214$	1.54282e9	0.0502867
$215$	4.96292e10	1.58403
$216$	−8.50333e8	−0.0265795
$217$	1.43348e9	0.0438857
$218$	−1.94649e9	−0.0583712
$219$	6.22748e9	0.182942
$220$	4.52428e10	1.30211
$221$	−1.85795e10	−0.523923
$222$	−2.61474e9	−0.0722504
$223$	−2.32540e10	−0.629688	−0.314844	−	0.949143i	$-0.601952\pi$
$223$	−2.32540e10	−0.629688	−0.314844	+	0.949143i	$0.601952\pi$
$224$	−9.36931e9	−0.248652
$225$	−2.35498e9	−0.0612585
$226$	1.35355e9	0.0345132
$227$	−4.52075e10	−1.13004	−0.565021	−	0.825077i	$-0.691132\pi$
$227$	−4.52075e10	−1.13004	−0.565021	+	0.825077i	$0.691132\pi$
$228$	−2.11121e10	−0.517399
$229$	2.87089e10	0.689853	0.344927	−	0.938630i	$-0.387904\pi$
$229$	2.87089e10	0.689853	0.344927	+	0.938630i	$0.387904\pi$
$230$	−3.40493e8	−0.00802292
$231$	−4.36045e10	−1.00757
$232$	−7.74785e9	−0.175584
$233$	−3.08637e10	−0.686034	−0.343017	−	0.939329i	$-0.611449\pi$
$233$	−3.08637e10	−0.686034	−0.343017	+	0.939329i	$0.611449\pi$
$234$	−4.90062e8	−0.0106851
$235$	4.20616e10	0.899664
$236$	−6.17436e9	−0.129565
$237$	2.96809e10	0.611096
$238$	−4.67148e9	−0.0943753
$239$	8.32138e10	1.64970	0.824849	−	0.565352i	$-0.191260\pi$
$239$	8.32138e10	1.64970	0.824849	+	0.565352i	$0.191260\pi$
$240$	−2.64251e10	−0.514122
$241$	8.23801e10	1.57306	0.786531	−	0.617551i	$-0.211875\pi$
$241$	8.23801e10	1.57306	0.786531	+	0.617551i	$0.211875\pi$
$242$	4.05254e9	0.0759553
$243$	3.48678e9	0.0641500
$244$	6.16846e10	1.11410
$245$	−2.30388e10	−0.408520
$246$	1.57051e9	0.0273422
$247$	−2.43932e10	−0.416996
$248$	2.99623e8	0.00502970
$249$	4.03029e10	0.664415
$250$	4.57241e9	0.0740312
$251$	−5.57439e10	−0.886474	−0.443237	−	0.896404i	$-0.646170\pi$
$251$	−5.57439e10	−0.886474	−0.443237	+	0.896404i	$0.646170\pi$
$252$	2.55920e10	0.399763
$253$	1.21076e10	0.185787
$254$	−6.27386e9	−0.0945765
$255$	−3.98458e10	−0.590136
$256$	6.54503e10	0.952428
$257$	1.16114e10	0.166030	0.0830150	−	0.996548i	$-0.473545\pi$
$257$	1.16114e10	0.166030	0.0830150	+	0.996548i	$0.473545\pi$
$258$	−4.98688e9	−0.0700713
$259$	1.57768e11	2.17856
$260$	−3.06803e10	−0.416369
$261$	3.17700e10	0.423775
$262$	7.54107e9	0.0988729
$263$	−7.57102e10	−0.975784	−0.487892	−	0.872904i	$-0.662234\pi$
$263$	−7.57102e10	−0.975784	−0.487892	+	0.872904i	$0.662234\pi$
$264$	−9.11411e9	−0.115477
$265$	−2.41980e10	−0.301421
$266$	−6.13324e9	−0.0751143
$267$	3.83962e10	0.462367
$268$	−1.52705e9	−0.0180820
$269$	−4.47812e9	−0.0521448	−0.0260724	−	0.999660i	$-0.508300\pi$
$269$	−4.47812e9	−0.0521448	−0.0260724	+	0.999660i	$0.508300\pi$
$270$	−1.05099e9	−0.0120355
$271$	−1.93242e10	−0.217640	−0.108820	−	0.994061i	$-0.534707\pi$
$271$	−1.93242e10	−0.217640	−0.108820	+	0.994061i	$0.534707\pi$
$272$	1.00668e11	1.11514
$273$	2.95693e10	0.322188
$274$	−1.15402e10	−0.123690
$275$	−2.52414e10	−0.266143
$276$	−7.10610e9	−0.0737124
$277$	−8.11879e10	−0.828576	−0.414288	−	0.910146i	$-0.635969\pi$
$277$	−8.11879e10	−0.828576	−0.414288	+	0.910146i	$0.635969\pi$
$278$	−3.44476e9	−0.0345906
$279$	−1.22860e9	−0.0121393
$280$	−1.54652e10	−0.150364
$281$	−8.77671e10	−0.839757	−0.419878	−	0.907580i	$-0.637927\pi$
$281$	−8.77671e10	−0.839757	−0.419878	+	0.907580i	$0.637927\pi$
$282$	−4.22646e9	−0.0397975
$283$	3.52404e10	0.326589	0.163295	−	0.986577i	$-0.447788\pi$
$283$	3.52404e10	0.326589	0.163295	+	0.986577i	$0.447788\pi$
$284$	5.51807e10	0.503332
$285$	−5.23140e10	−0.469695
$286$	−5.25262e9	−0.0464225
$287$	−9.47615e10	−0.824448
$288$	8.03021e9	0.0687797
$289$	3.32065e10	0.280016
$290$	−9.57619e9	−0.0795063
$291$	−2.73837e10	−0.223858
$292$	−3.91752e10	−0.315347
$293$	−1.31525e11	−1.04257	−0.521283	−	0.853384i	$-0.674547\pi$
$293$	−1.31525e11	−1.04257	−0.521283	+	0.853384i	$0.674547\pi$
$294$	2.31500e9	0.0180713
$295$	−1.52995e10	−0.117619
$296$	3.29763e10	0.249683
$297$	3.73723e10	0.278706
$298$	−5.37382e9	−0.0394739
$299$	−8.21046e9	−0.0594083
$300$	1.48145e10	0.105594
$301$	3.00898e11	2.11285
$302$	−1.34352e10	−0.0929423
$303$	2.55300e10	0.174004
$304$	1.32168e11	0.887552
$305$	1.52849e11	1.01138
$306$	4.00381e9	0.0261052
$307$	−2.24505e10	−0.144246	−0.0721230	−	0.997396i	$-0.522977\pi$
$307$	−2.24505e10	−0.144246	−0.0721230	+	0.997396i	$0.522977\pi$
$308$	2.74303e11	1.73681
$309$	−1.86147e9	−0.0116156
$310$	3.70328e8	0.00227750
$311$	7.33514e10	0.444618	0.222309	−	0.974976i	$-0.428641\pi$
$311$	7.33514e10	0.444618	0.222309	+	0.974976i	$0.428641\pi$
$312$	6.18051e9	0.0369257
$313$	−2.62675e11	−1.54693	−0.773463	−	0.633842i	$-0.781477\pi$
$313$	−2.62675e11	−1.54693	−0.773463	+	0.633842i	$0.781477\pi$
$314$	3.64108e9	0.0211372
$315$	6.34148e10	0.362905
$316$	−1.86714e11	−1.05338
$317$	3.34297e11	1.85937	0.929685	−	0.368354i	$-0.120079\pi$
$317$	3.34297e11	1.85937	0.929685	+	0.368354i	$0.120079\pi$
$318$	2.43148e9	0.0133336
$319$	3.40520e11	1.84113
$320$	1.64612e11	0.877581
$321$	7.97855e10	0.419422
$322$	−2.06438e9	−0.0107013
$323$	1.99292e11	1.01878
$324$	−2.19343e10	−0.110579
$325$	1.71168e10	0.0851035
$326$	−2.40968e10	−0.118162
$327$	−1.00661e11	−0.486852
$328$	−1.98068e10	−0.0944893
$329$	2.55016e11	1.20001
$330$	−1.12649e10	−0.0522893
$331$	7.00734e10	0.320869	0.160434	−	0.987047i	$-0.448710\pi$
$331$	7.00734e10	0.320869	0.160434	+	0.987047i	$0.448710\pi$
$332$	−2.53534e11	−1.14529
$333$	−1.35219e11	−0.602614
$334$	−4.70256e8	−0.00206764
$335$	−3.78390e9	−0.0164149
$336$	−1.60213e11	−0.685758
$337$	−2.08582e11	−0.880931	−0.440466	−	0.897769i	$-0.645187\pi$
$337$	−2.08582e11	−0.880931	−0.440466	+	0.897769i	$0.645187\pi$
$338$	−1.30479e10	−0.0543771
$339$	6.99976e10	0.287862
$340$	2.50658e11	1.01725
$341$	−1.31685e10	−0.0527401
$342$	5.25665e9	0.0207774
$343$	1.69229e11	0.660161
$344$	6.28929e10	0.242152
$345$	−1.76083e10	−0.0669162
$346$	−2.61966e9	−0.00982659
$347$	−1.07644e11	−0.398574	−0.199287	−	0.979941i	$-0.563863\pi$
$347$	−1.07644e11	−0.398574	−0.199287	+	0.979941i	$0.563863\pi$
$348$	−1.99856e11	−0.730482
$349$	−1.72136e11	−0.621093	−0.310547	−	0.950558i	$-0.600512\pi$
$349$	−1.72136e11	−0.621093	−0.310547	+	0.950558i	$0.600512\pi$
$350$	4.30372e9	0.0153299
$351$	−2.53431e10	−0.0891206
$352$	8.60700e10	0.298820
$353$	−4.23810e11	−1.45273	−0.726365	−	0.687309i	$-0.758792\pi$
$353$	−4.23810e11	−1.45273	−0.726365	+	0.687309i	$0.758792\pi$
$354$	1.53734e9	0.00520300
$355$	1.36733e11	0.456925
$356$	−2.41539e11	−0.797006
$357$	−2.41582e11	−0.787149
$358$	−9.63329e9	−0.0309957
$359$	1.84294e11	0.585579	0.292790	−	0.956177i	$-0.405416\pi$
$359$	1.84294e11	0.585579	0.292790	+	0.956177i	$0.405416\pi$
$360$	1.32548e10	0.0415923
$361$	−6.10344e10	−0.189144
$362$	−1.37217e10	−0.0419971
$363$	2.09574e11	0.633515
$364$	−1.86012e11	−0.555372
$365$	−9.70727e10	−0.286272
$366$	−1.53587e10	−0.0447392
$367$	−5.29663e11	−1.52406	−0.762031	−	0.647540i	$-0.775798\pi$
$367$	−5.29663e11	−1.52406	−0.762031	+	0.647540i	$0.775798\pi$
$368$	4.44861e10	0.126447
$369$	8.12178e10	0.228051
$370$	4.07581e10	0.113059
$371$	−1.46710e11	−0.402048
$372$	7.72876e9	0.0209251
$373$	4.37611e11	1.17057	0.585286	−	0.810827i	$-0.300982\pi$
$373$	4.37611e11	1.17057	0.585286	+	0.810827i	$0.300982\pi$
$374$	4.29140e10	0.113417
$375$	2.36458e11	0.617467
$376$	5.33028e10	0.137532
$377$	−2.30915e11	−0.588730
$378$	−6.37209e9	−0.0160535
$379$	−5.01861e11	−1.24942	−0.624708	−	0.780858i	$-0.714782\pi$
$379$	−5.01861e11	−1.24942	−0.624708	+	0.780858i	$0.714782\pi$
$380$	3.29092e11	0.809638
$381$	−3.24447e11	−0.788827
$382$	−2.62342e10	−0.0630352
$383$	−4.53506e11	−1.07693	−0.538467	−	0.842647i	$-0.680996\pi$
$383$	−4.53506e11	−1.07693	−0.538467	+	0.842647i	$0.680996\pi$
$384$	−6.72995e10	−0.157951
$385$	6.79698e11	1.57668
$386$	−2.82450e10	−0.0647589
$387$	−2.57892e11	−0.584438
$388$	1.72262e11	0.385876
$389$	−2.98127e11	−0.660128	−0.330064	−	0.943958i	$-0.607070\pi$
$389$	−2.98127e11	−0.660128	−0.330064	+	0.943958i	$0.607070\pi$
$390$	7.63899e9	0.0167203
$391$	6.70796e10	0.145143
$392$	−2.91961e10	−0.0624507
$393$	3.89980e11	0.824662
$394$	−2.15450e10	−0.0450415
$395$	−4.62660e11	−0.956258
$396$	−2.35098e11	−0.480420
$397$	−4.25238e11	−0.859161	−0.429581	−	0.903029i	$-0.641339\pi$
$397$	−4.25238e11	−0.859161	−0.429581	+	0.903029i	$0.641339\pi$
$398$	6.77304e9	0.0135304
$399$	−3.17175e11	−0.626500
$400$	−9.27427e10	−0.181138
$401$	−8.08814e10	−0.156207	−0.0781033	−	0.996945i	$-0.524886\pi$
$401$	−8.08814e10	−0.156207	−0.0781033	+	0.996945i	$0.524886\pi$
$402$	3.80216e8	0.000726128 0
$403$	8.92988e9	0.0168645
$404$	−1.60602e11	−0.299940
$405$	−5.43513e10	−0.100383
$406$	−5.80596e10	−0.106049
$407$	−1.44932e12	−2.61811
$408$	−5.04948e10	−0.0902144
$409$	9.44992e11	1.66983	0.834917	−	0.550376i	$-0.185516\pi$
$409$	9.44992e11	1.66983	0.834917	+	0.550376i	$0.185516\pi$
$410$	−2.44809e10	−0.0427858
$411$	−5.96789e11	−1.03165
$412$	1.17099e10	0.0200224
$413$	−9.27596e10	−0.156886
$414$	1.76933e9	0.00296010
$415$	−6.28234e11	−1.03969
$416$	−5.83663e10	−0.0955525
$417$	−1.78143e11	−0.288507
$418$	5.63422e10	0.0902695
$419$	−5.00997e11	−0.794095	−0.397047	−	0.917798i	$-0.629965\pi$
$419$	−5.00997e11	−0.794095	−0.397047	+	0.917798i	$0.629965\pi$
$420$	−3.98924e11	−0.625559
$421$	3.45900e11	0.536637	0.268319	−	0.963330i	$-0.413532\pi$
$421$	3.45900e11	0.536637	0.268319	+	0.963330i	$0.413532\pi$
$422$	6.47478e10	0.0993846
$423$	−2.18568e11	−0.331936
$424$	−3.06650e10	−0.0460784
$425$	−1.39845e11	−0.207920
$426$	−1.37393e10	−0.0202125
$427$	9.26709e11	1.34902
$428$	−5.01907e11	−0.722980
$429$	−2.71635e11	−0.387193
$430$	7.77344e10	0.109649
$431$	−1.75665e11	−0.245210	−0.122605	−	0.992456i	$-0.539125\pi$
$431$	−1.75665e11	−0.245210	−0.122605	+	0.992456i	$0.539125\pi$
$432$	1.37315e11	0.189688
$433$	1.69288e11	0.231436	0.115718	−	0.993282i	$-0.463083\pi$
$433$	1.69288e11	0.231436	0.115718	+	0.993282i	$0.463083\pi$
$434$	2.24526e9	0.00303783
$435$	−4.95224e11	−0.663133
$436$	6.33229e11	0.839212
$437$	8.80695e10	0.115520
$438$	9.75412e9	0.0126635
$439$	1.27660e12	1.64045	0.820226	−	0.572039i	$-0.193848\pi$
$439$	1.27660e12	1.64045	0.820226	+	0.572039i	$0.193848\pi$
$440$	1.42069e11	0.180702
$441$	1.19718e11	0.150726
$442$	−2.91010e10	−0.0362667
$443$	−8.36857e11	−1.03237	−0.516184	−	0.856478i	$-0.672648\pi$
$443$	−8.36857e11	−1.03237	−0.516184	+	0.856478i	$0.672648\pi$
$444$	8.50623e11	1.03876
$445$	−5.98512e11	−0.723523
$446$	−3.64228e10	−0.0435879
$447$	−2.77903e11	−0.329237
$448$	9.98029e11	1.17056
$449$	8.15501e11	0.946926	0.473463	−	0.880814i	$-0.343004\pi$
$449$	8.15501e11	0.946926	0.473463	+	0.880814i	$0.343004\pi$
$450$	−3.68862e9	−0.00424040
$451$	8.70515e11	0.990791
$452$	−4.40334e11	−0.496203
$453$	−6.94791e11	−0.775197
$454$	−7.08086e10	−0.0782231
$455$	−4.60920e11	−0.504167
$456$	−6.62952e10	−0.0718026
$457$	1.19348e12	1.27995	0.639976	−	0.768395i	$-0.278944\pi$
$457$	1.19348e12	1.27995	0.639976	+	0.768395i	$0.278944\pi$
$458$	4.49668e10	0.0477526
$459$	2.07054e11	0.217734
$460$	1.10768e11	0.115347
$461$	−1.82587e12	−1.88285	−0.941427	−	0.337217i	$-0.890514\pi$
$461$	−1.82587e12	−1.88285	−0.941427	+	0.337217i	$0.890514\pi$
$462$	−6.82978e10	−0.0697458
$463$	−1.63020e11	−0.164864	−0.0824322	−	0.996597i	$-0.526269\pi$
$463$	−1.63020e11	−0.164864	−0.0824322	+	0.996597i	$0.526269\pi$
$464$	1.25115e12	1.25308
$465$	1.91512e10	0.0189958
$466$	−4.83419e10	−0.0474883
$467$	7.89092e11	0.767718	0.383859	−	0.923392i	$-0.374595\pi$
$467$	7.89092e11	0.767718	0.383859	+	0.923392i	$0.374595\pi$
$468$	1.59426e11	0.153622
$469$	−2.29414e10	−0.0218949
$470$	6.58812e10	0.0622761
$471$	1.88295e11	0.176297
$472$	−1.93884e10	−0.0179806
$473$	−2.76416e12	−2.53915
$474$	4.64893e10	0.0423010
$475$	−1.83603e11	−0.165485
$476$	1.51972e12	1.35685
$477$	1.25742e11	0.111211
$478$	1.30338e11	0.114195
$479$	1.31506e12	1.14140	0.570699	−	0.821159i	$-0.306672\pi$
$479$	1.31506e12	1.14140	0.570699	+	0.821159i	$0.306672\pi$
$480$	−1.25173e11	−0.107628
$481$	9.82818e11	0.837183
$482$	1.29032e11	0.108890
$483$	−1.06757e11	−0.0892558
$484$	−1.31836e12	−1.09202
$485$	4.26851e11	0.350299
$486$	5.46136e9	0.00444056
$487$	−9.35122e11	−0.753335	−0.376667	−	0.926349i	$-0.622930\pi$
$487$	−9.35122e11	−0.753335	−0.376667	+	0.926349i	$0.622930\pi$
$488$	1.93699e11	0.154610
$489$	−1.24614e12	−0.985549
$490$	−3.60858e10	−0.0282783
$491$	−1.15701e12	−0.898404	−0.449202	−	0.893430i	$-0.648292\pi$
$491$	−1.15701e12	−0.898404	−0.449202	+	0.893430i	$0.648292\pi$
$492$	−5.10917e11	−0.393104
$493$	1.88658e12	1.43835
$494$	−3.82071e10	−0.0288651
$495$	−5.82553e11	−0.436126
$496$	−4.83841e10	−0.0358951
$497$	8.28999e11	0.609467
$498$	6.31266e10	0.0459918
$499$	7.24363e11	0.523002	0.261501	−	0.965203i	$-0.415782\pi$
$499$	7.24363e11	0.523002	0.261501	+	0.965203i	$0.415782\pi$
$500$	−1.48749e12	−1.06436
$501$	−2.43189e10	−0.0172454
$502$	−8.73119e10	−0.0613630
$503$	2.19638e12	1.52986	0.764929	−	0.644115i	$-0.222774\pi$
$503$	2.19638e12	1.52986	0.764929	+	0.644115i	$0.222774\pi$
$504$	8.03628e10	0.0554776
$505$	−3.97957e11	−0.272286
$506$	1.89641e10	0.0128604
$507$	−6.74762e11	−0.453539
$508$	2.04100e12	1.35974
$509$	−2.72117e12	−1.79691	−0.898453	−	0.439070i	$-0.855308\pi$
$509$	−2.72117e12	−1.79691	−0.898453	+	0.439070i	$0.855308\pi$
$510$	−6.24106e10	−0.0408500
$511$	−5.88543e11	−0.381842
$512$	5.27914e11	0.339507
$513$	2.71843e11	0.173297
$514$	1.81870e10	0.0114928
$515$	2.90161e10	0.0181764
$516$	1.62232e12	1.00743
$517$	−2.34267e12	−1.44213
$518$	2.47113e11	0.150803
$519$	−1.35474e11	−0.0819599
$520$	−9.63405e10	−0.0577822
$521$	−2.05716e12	−1.22320	−0.611602	−	0.791166i	$-0.709475\pi$
$521$	−2.05716e12	−1.22320	−0.611602	+	0.791166i	$0.709475\pi$
$522$	4.97614e10	0.0293343
$523$	3.46063e11	0.202254	0.101127	−	0.994874i	$-0.467755\pi$
$523$	3.46063e11	0.202254	0.101127	+	0.994874i	$0.467755\pi$
$524$	−2.45325e12	−1.42151
$525$	2.22563e11	0.127861
$526$	−1.18585e11	−0.0675452
$527$	−7.29573e10	−0.0412022
$528$	1.47178e12	0.824118
$529$	−1.77151e12	−0.983542
$530$	−3.79014e10	−0.0208648
$531$	7.95020e10	0.0433963
$532$	1.99525e12	1.07993
$533$	−5.90318e11	−0.316821
$534$	6.01400e10	0.0320057
$535$	−1.24368e12	−0.656322
$536$	−4.79517e9	−0.00250936
$537$	−4.98178e11	−0.258523
$538$	−7.01410e9	−0.00360954
$539$	1.28317e12	0.654842
$540$	3.41908e11	0.173036
$541$	−2.55356e12	−1.28162	−0.640808	−	0.767701i	$-0.721401\pi$
$541$	−2.55356e12	−1.28162	−0.640808	+	0.767701i	$0.721401\pi$
$542$	−3.02675e10	−0.0150654
$543$	−7.09605e11	−0.350282
$544$	4.76853e11	0.233448
$545$	1.56909e12	0.761838
$546$	4.63145e10	0.0223023
$547$	1.49657e12	0.714752	0.357376	−	0.933961i	$-0.383672\pi$
$547$	1.49657e12	0.714752	0.357376	+	0.933961i	$0.383672\pi$
$548$	3.75422e12	1.77831
$549$	−7.94260e11	−0.373153
$550$	−3.95356e10	−0.0184228
$551$	2.47691e12	1.14480
$552$	−2.23142e10	−0.0102295
$553$	−2.80507e12	−1.27550
$554$	−1.27165e11	−0.0573553
$555$	2.10777e12	0.942984
$556$	1.12064e12	0.497315
$557$	−3.27414e12	−1.44128	−0.720641	−	0.693308i	$-0.756153\pi$
$557$	−3.27414e12	−1.44128	−0.720641	+	0.693308i	$0.756153\pi$
$558$	−1.92436e9	−0.000840297 0
$559$	1.87445e12	0.811932
$560$	2.49737e12	1.07309
$561$	2.21926e12	0.945965
$562$	−1.37470e11	−0.0581292
$563$	2.88899e12	1.21188	0.605938	−	0.795512i	$-0.292798\pi$
$563$	2.88899e12	1.21188	0.605938	+	0.795512i	$0.292798\pi$
$564$	1.37494e12	0.572175
$565$	−1.09111e12	−0.450453
$566$	5.51972e10	0.0226070
$567$	−3.29527e11	−0.133896
$568$	1.73275e11	0.0698505
$569$	2.95747e12	1.18281	0.591405	−	0.806375i	$-0.298574\pi$
$569$	2.95747e12	1.18281	0.591405	+	0.806375i	$0.298574\pi$
$570$	−8.19396e10	−0.0325130
$571$	3.90974e12	1.53917	0.769584	−	0.638546i	$-0.220464\pi$
$571$	3.90974e12	1.53917	0.769584	+	0.638546i	$0.220464\pi$
$572$	1.70877e12	0.667425
$573$	−1.35668e12	−0.525753
$574$	−1.48425e11	−0.0570695
$575$	−6.17988e10	−0.0235763
$576$	−8.55386e11	−0.323788
$577$	−2.05289e12	−0.771036	−0.385518	−	0.922700i	$-0.625977\pi$
$577$	−2.05289e12	−0.771036	−0.385518	+	0.922700i	$0.625977\pi$
$578$	5.20114e10	0.0193831
$579$	−1.46067e12	−0.540129
$580$	3.11531e12	1.14308
$581$	−3.80893e12	−1.38679
$582$	−4.28911e10	−0.0154958
$583$	1.34774e12	0.483166
$584$	−1.23016e11	−0.0437626
$585$	3.95044e11	0.139458
$586$	−2.06008e11	−0.0721680
$587$	1.06817e12	0.371336	0.185668	−	0.982612i	$-0.440555\pi$
$587$	1.06817e12	0.371336	0.185668	+	0.982612i	$0.440555\pi$
$588$	−7.53112e11	−0.259813
$589$	−9.57864e10	−0.0327933
$590$	−2.39637e10	−0.00814178
$591$	−1.11418e12	−0.375674
$592$	−5.32513e12	−1.78190
$593$	4.14756e11	0.137736	0.0688679	−	0.997626i	$-0.478061\pi$
$593$	4.14756e11	0.137736	0.0688679	+	0.997626i	$0.478061\pi$
$594$	5.85364e10	0.0192924
$595$	3.76572e12	1.23175
$596$	1.74820e12	0.567523
$597$	3.50262e11	0.112852
$598$	−1.28601e10	−0.00411233
$599$	3.83346e12	1.21666	0.608331	−	0.793683i	$-0.291839\pi$
$599$	3.83346e12	1.21666	0.608331	+	0.793683i	$0.291839\pi$
$600$	4.65197e10	0.0146540
$601$	−3.57132e11	−0.111659	−0.0558295	−	0.998440i	$-0.517780\pi$
$601$	−3.57132e11	−0.111659	−0.0558295	+	0.998440i	$0.517780\pi$
$602$	4.71297e11	0.146255
$603$	1.96626e10	0.00605636
$604$	4.37072e12	1.33625
$605$	−3.26679e12	−0.991339
$606$	3.99878e10	0.0120448
$607$	4.67518e12	1.39781	0.698906	−	0.715213i	$-0.253670\pi$
$607$	4.67518e12	1.39781	0.698906	+	0.715213i	$0.253670\pi$
$608$	6.26066e11	0.185803
$609$	−3.00250e12	−0.884515
$610$	2.39408e11	0.0700090
$611$	1.58862e12	0.461143
$612$	−1.30251e12	−0.375319
$613$	6.41882e12	1.83604	0.918022	−	0.396530i	$-0.129786\pi$
$613$	6.41882e12	1.83604	0.918022	+	0.396530i	$0.129786\pi$
$614$	−3.51643e10	−0.00998493
$615$	−1.26601e12	−0.356860
$616$	8.61351e11	0.241028
$617$	7.98940e11	0.221938	0.110969	−	0.993824i	$-0.464605\pi$
$617$	7.98940e11	0.221938	0.110969	+	0.993824i	$0.464605\pi$
$618$	−2.91562e9	−0.000804049 0
$619$	−2.64407e12	−0.723877	−0.361938	−	0.932202i	$-0.617885\pi$
$619$	−2.64407e12	−0.723877	−0.361938	+	0.932202i	$0.617885\pi$
$620$	−1.20474e11	−0.0327440
$621$	9.14992e10	0.0246891
$622$	1.14890e11	0.0307771
$623$	−3.62872e12	−0.965067
$624$	−9.98049e11	−0.263525
$625$	−2.98481e12	−0.782451
$626$	−4.11429e11	−0.107080
$627$	2.91369e12	0.752904
$628$	−1.18451e12	−0.303892
$629$	−8.02964e12	−2.04535
$630$	9.93268e10	0.0251208
$631$	−6.50229e12	−1.63281	−0.816403	−	0.577483i	$-0.804035\pi$
$631$	−6.50229e12	−1.63281	−0.816403	+	0.577483i	$0.804035\pi$
$632$	−5.86308e11	−0.146184
$633$	3.34838e12	0.828930
$634$	5.23611e11	0.128708
$635$	5.05742e12	1.23438
$636$	−7.91004e11	−0.191700
$637$	−8.70153e11	−0.209396
$638$	5.33357e11	0.127446
$639$	−7.10515e11	−0.168585
$640$	1.04905e12	0.247165
$641$	−1.12461e12	−0.263111	−0.131556	−	0.991309i	$-0.541997\pi$
$641$	−1.12461e12	−0.263111	−0.131556	+	0.991309i	$0.541997\pi$
$642$	1.24968e11	0.0290330
$643$	−3.47734e12	−0.802228	−0.401114	−	0.916028i	$-0.631377\pi$
$643$	−3.47734e12	−0.802228	−0.401114	+	0.916028i	$0.631377\pi$
$644$	6.71579e11	0.153855
$645$	4.01997e12	0.914543
$646$	3.12152e11	0.0705213
$647$	1.55048e12	0.347855	0.173927	−	0.984758i	$-0.444354\pi$
$647$	1.55048e12	0.347855	0.173927	+	0.984758i	$0.444354\pi$
$648$	−6.88770e10	−0.0153457
$649$	8.52125e11	0.188539
$650$	2.68101e10	0.00589099
$651$	1.16112e11	0.0253374
$652$	7.83911e12	1.69884
$653$	6.59037e12	1.41840	0.709202	−	0.705005i	$-0.249055\pi$
$653$	6.59037e12	1.41840	0.709202	+	0.705005i	$0.249055\pi$
$654$	−1.57666e11	−0.0337006
$655$	−6.07893e12	−1.29045
$656$	3.19847e12	0.674335
$657$	5.04426e11	0.105622
$658$	3.99432e11	0.0830665
$659$	4.86030e12	1.00387	0.501937	−	0.864904i	$-0.332621\pi$
$659$	4.86030e12	1.00387	0.501937	+	0.864904i	$0.332621\pi$
$660$	3.66466e12	0.751772
$661$	−3.92824e12	−0.800372	−0.400186	−	0.916434i	$-0.631055\pi$
$661$	−3.92824e12	−0.800372	−0.400186	+	0.916434i	$0.631055\pi$
$662$	1.09756e11	0.0222110
$663$	−1.50494e12	−0.302487
$664$	−7.96133e11	−0.158939
$665$	4.94406e12	0.980362
$666$	−2.11794e11	−0.0417138
$667$	8.33700e11	0.163096
$668$	1.52983e11	0.0297268
$669$	−1.88357e12	−0.363551
$670$	−5.92673e9	−0.00113626
$671$	−8.51310e12	−1.62120
$672$	−7.58914e11	−0.143559
$673$	−6.51980e12	−1.22509	−0.612543	−	0.790438i	$-0.709853\pi$
$673$	−6.51980e12	−1.22509	−0.612543	+	0.790438i	$0.709853\pi$
$674$	−3.26702e11	−0.0609794
$675$	−1.90754e11	−0.0353676
$676$	4.24473e12	0.781789
$677$	−5.00751e12	−0.916163	−0.458082	−	0.888910i	$-0.651463\pi$
$677$	−5.00751e12	−0.916163	−0.458082	+	0.888910i	$0.651463\pi$
$678$	1.09637e11	0.0199262
$679$	2.58796e12	0.467244
$680$	7.87103e11	0.141170
$681$	−3.66181e12	−0.652429
$682$	−2.06258e10	−0.00365075
$683$	9.04640e12	1.59068	0.795340	−	0.606164i	$-0.207292\pi$
$683$	9.04640e12	1.59068	0.795340	+	0.606164i	$0.207292\pi$
$684$	−1.71008e12	−0.298720
$685$	9.30263e12	1.61435
$686$	2.65063e11	0.0456973
$687$	2.32542e12	0.398287
$688$	−1.01562e13	−1.72815
$689$	−9.13934e11	−0.154500
$690$	−2.75799e10	−0.00463204
$691$	−2.16278e12	−0.360879	−0.180439	−	0.983586i	$-0.557752\pi$
$691$	−2.16278e12	−0.360879	−0.180439	+	0.983586i	$0.557752\pi$
$692$	8.52224e11	0.141279
$693$	−3.53196e12	−0.581724
$694$	−1.68604e11	−0.0275898
$695$	2.77686e12	0.451463
$696$	−6.27576e11	−0.101374
$697$	4.82291e12	0.774036
$698$	−2.69617e11	−0.0429930
$699$	−2.49996e12	−0.396082
$700$	−1.40008e12	−0.220400
$701$	−5.76596e12	−0.901864	−0.450932	−	0.892558i	$-0.648908\pi$
$701$	−5.76596e12	−0.901864	−0.450932	+	0.892558i	$0.648908\pi$
$702$	−3.96950e10	−0.00616906
$703$	−1.05422e13	−1.62792
$704$	−9.16827e12	−1.40673
$705$	3.40699e12	0.519421
$706$	−6.63815e11	−0.100560
$707$	−2.41278e12	−0.363187
$708$	−5.00123e11	−0.0748044
$709$	6.21591e12	0.923839	0.461920	−	0.886922i	$-0.347161\pi$
$709$	6.21591e12	0.923839	0.461920	+	0.886922i	$0.347161\pi$
$710$	2.14165e11	0.0316290
$711$	2.40415e12	0.352817
$712$	−7.58467e11	−0.110606
$713$	−3.22406e10	−0.00467197
$714$	−3.78390e11	−0.0544876
$715$	4.23419e12	0.605889
$716$	3.13389e12	0.445630
$717$	6.74032e12	0.952454
$718$	2.88660e11	0.0405347
$719$	−4.25926e12	−0.594367	−0.297183	−	0.954820i	$-0.596047\pi$
$719$	−4.25926e12	−0.594367	−0.297183	+	0.954820i	$0.596047\pi$
$720$	−2.14043e12	−0.296828
$721$	1.75922e11	0.0242444
$722$	−9.55983e10	−0.0130928
$723$	6.67279e12	0.908207
$724$	4.46391e12	0.603799
$725$	−1.73806e12	−0.233638
$726$	3.28256e11	0.0438528
$727$	−1.28038e13	−1.69994	−0.849970	−	0.526831i	$-0.823380\pi$
$727$	−1.28038e13	−1.69994	−0.849970	+	0.526831i	$0.823380\pi$
$728$	−5.84104e11	−0.0770724
$729$	2.82430e11	0.0370370
$730$	−1.52045e11	−0.0198162
$731$	−1.53142e13	−1.98366
$732$	4.99645e12	0.643223
$733$	−1.18736e13	−1.51919	−0.759597	−	0.650394i	$-0.774604\pi$
$733$	−1.18736e13	−1.51919	−0.759597	+	0.650394i	$0.774604\pi$
$734$	−8.29613e11	−0.105498
$735$	−1.86615e12	−0.235859
$736$	2.10726e11	0.0264709
$737$	2.10749e11	0.0263125
$738$	1.27212e11	0.0157860
$739$	5.84625e11	0.0721070	0.0360535	−	0.999350i	$-0.488521\pi$
$739$	5.84625e11	0.0721070	0.0360535	+	0.999350i	$0.488521\pi$
$740$	−1.32593e13	−1.62547
$741$	−1.97585e12	−0.240753
$742$	−2.29793e11	−0.0278304
$743$	1.47498e13	1.77557	0.887784	−	0.460261i	$-0.152244\pi$
$743$	1.47498e13	1.77557	0.887784	+	0.460261i	$0.152244\pi$
$744$	2.42694e10	0.00290390
$745$	4.33189e12	0.515198
$746$	6.85431e11	0.0810287
$747$	3.26454e12	0.383600
$748$	−1.39607e13	−1.63061
$749$	−7.54032e12	−0.875431
$750$	3.70365e11	0.0427419
$751$	−6.15776e12	−0.706388	−0.353194	−	0.935550i	$-0.614904\pi$
$751$	−6.15776e12	−0.706388	−0.353194	+	0.935550i	$0.614904\pi$
$752$	−8.60751e12	−0.981516
$753$	−4.51526e12	−0.511806
$754$	−3.61683e11	−0.0407528
$755$	1.08303e13	1.21305
$756$	2.07296e12	0.230803
$757$	−2.91598e11	−0.0322740	−0.0161370	−	0.999870i	$-0.505137\pi$
$757$	−2.91598e11	−0.0322740	−0.0161370	+	0.999870i	$0.505137\pi$
$758$	−7.86067e11	−0.0864864
$759$	9.80715e11	0.107264
$760$	1.03340e12	0.112358
$761$	−1.10879e13	−1.19844	−0.599222	−	0.800583i	$-0.704523\pi$
$761$	−1.10879e13	−1.19844	−0.599222	+	0.800583i	$0.704523\pi$
$762$	−5.08183e11	−0.0546038
$763$	9.51323e12	1.01617
$764$	8.53447e12	0.906267
$765$	−3.22751e12	−0.340715
$766$	−7.10328e11	−0.0745469
$767$	−5.77847e11	−0.0602884
$768$	5.30148e12	0.549884
$769$	1.71448e13	1.76792	0.883962	−	0.467559i	$-0.154866\pi$
$769$	1.71448e13	1.76792	0.883962	+	0.467559i	$0.154866\pi$
$770$	1.06461e12	0.109140
$771$	9.40525e11	0.0958574
$772$	9.18862e12	0.931049
$773$	−8.64430e12	−0.870808	−0.435404	−	0.900235i	$-0.643394\pi$
$773$	−8.64430e12	−0.870808	−0.435404	+	0.900235i	$0.643394\pi$
$774$	−4.03937e11	−0.0404557
$775$	6.72138e10	0.00669269
$776$	5.40929e11	0.0535504
$777$	1.27792e13	1.25779
$778$	−4.66958e11	−0.0456951
$779$	6.33205e12	0.616064
$780$	−2.48510e12	−0.240391
$781$	−7.61550e12	−0.732434
$782$	1.05067e11	0.0100470
$783$	2.57337e12	0.244666
$784$	4.71468e12	0.445687
$785$	−2.93511e12	−0.275874
$786$	6.10827e11	0.0570843
$787$	−2.01047e13	−1.86815	−0.934076	−	0.357075i	$-0.883774\pi$
$787$	−2.01047e13	−1.86815	−0.934076	+	0.357075i	$0.883774\pi$
$788$	7.00896e12	0.647569
$789$	−6.13253e12	−0.563369
$790$	−7.24666e11	−0.0661936
$791$	−6.61529e12	−0.600834
$792$	−7.38243e11	−0.0666708
$793$	5.77295e12	0.518404
$794$	−6.66051e11	−0.0594724
$795$	−1.96004e12	−0.174025
$796$	−2.20339e12	−0.194528
$797$	4.09905e12	0.359850	0.179925	−	0.983680i	$-0.442415\pi$
$797$	4.09905e12	0.359850	0.179925	+	0.983680i	$0.442415\pi$
$798$	−4.96792e11	−0.0433672
$799$	−1.29791e13	−1.12663
$800$	−4.39313e11	−0.0379201
$801$	3.11009e12	0.266948
$802$	−1.26685e11	−0.0108128
$803$	5.40658e12	0.458884
$804$	−1.23691e11	−0.0104397
$805$	1.66411e12	0.139670
$806$	1.39869e10	0.00116738
$807$	−3.62728e11	−0.0301058
$808$	−5.04313e11	−0.0416245
$809$	8.96580e12	0.735903	0.367952	−	0.929845i	$-0.380059\pi$
$809$	8.96580e12	0.735903	0.367952	+	0.929845i	$0.380059\pi$
$810$	−8.51306e10	−0.00694869
$811$	−1.92603e13	−1.56340	−0.781699	−	0.623656i	$-0.785647\pi$
$811$	−1.92603e13	−1.56340	−0.781699	+	0.623656i	$0.785647\pi$
$812$	1.88878e13	1.52468
$813$	−1.56526e12	−0.125655
$814$	−2.27007e12	−0.181230
$815$	1.94246e13	1.54221
$816$	8.15407e12	0.643827
$817$	−2.01062e13	−1.57882
$818$	1.48014e12	0.115588
$819$	2.39511e12	0.186015
$820$	7.96407e12	0.615138
$821$	−1.71082e13	−1.31419	−0.657096	−	0.753807i	$-0.728215\pi$
$821$	−1.71082e13	−1.31419	−0.657096	+	0.753807i	$0.728215\pi$
$822$	−9.34753e11	−0.0714124
$823$	−1.41958e13	−1.07860	−0.539301	−	0.842113i	$-0.681311\pi$
$823$	−1.41958e13	−1.07860	−0.539301	+	0.842113i	$0.681311\pi$
$824$	3.67709e10	0.00277863
$825$	−2.04455e12	−0.153658
$826$	−1.45290e11	−0.0108599
$827$	−2.10229e13	−1.56285	−0.781427	−	0.623997i	$-0.785508\pi$
$827$	−2.10229e13	−1.56285	−0.781427	+	0.623997i	$0.785508\pi$
$828$	−5.75594e11	−0.0425579
$829$	−1.46485e13	−1.07720	−0.538602	−	0.842560i	$-0.681047\pi$
$829$	−1.46485e13	−1.07720	−0.538602	+	0.842560i	$0.681047\pi$
$830$	−9.84005e11	−0.0719691
$831$	−6.57622e12	−0.478379
$832$	6.21724e12	0.449824
$833$	7.10916e12	0.511583
$834$	−2.79026e11	−0.0199709
$835$	3.79077e11	0.0269860
$836$	−1.83292e13	−1.29782
$837$	−9.95167e10	−0.00700860
$838$	−7.84714e11	−0.0549684
$839$	1.72197e13	1.19976	0.599882	−	0.800088i	$-0.295214\pi$
$839$	1.72197e13	1.19976	0.599882	+	0.800088i	$0.295214\pi$
$840$	−1.25268e12	−0.0868126
$841$	8.94024e12	0.616264
$842$	5.41784e11	0.0371468
$843$	−7.10914e12	−0.484834
$844$	−2.10636e13	−1.42887
$845$	1.05181e13	0.709709
$846$	−3.42343e11	−0.0229771
$847$	−1.98063e13	−1.32229
$848$	4.95190e12	0.328844
$849$	2.85447e12	0.188557
$850$	−2.19039e11	−0.0143925
$851$	−3.54838e12	−0.231925
$852$	4.46964e12	0.290599
$853$	−3.92321e12	−0.253729	−0.126865	−	0.991920i	$-0.540491\pi$
$853$	−3.92321e12	−0.253729	−0.126865	+	0.991920i	$0.540491\pi$
$854$	1.45151e12	0.0933811
$855$	−4.23743e12	−0.271179
$856$	−1.57606e12	−0.100332
$857$	2.76305e13	1.74975	0.874873	−	0.484353i	$-0.160945\pi$
$857$	2.76305e13	1.74975	0.874873	+	0.484353i	$0.160945\pi$
$858$	−4.25462e11	−0.0268021
$859$	−2.03071e13	−1.27256	−0.636281	−	0.771457i	$-0.719528\pi$
$859$	−2.03071e13	−1.27256	−0.636281	+	0.771457i	$0.719528\pi$
$860$	−2.52884e13	−1.57644
$861$	−7.67568e12	−0.475995
$862$	−2.75145e11	−0.0169738
$863$	−1.34096e13	−0.822940	−0.411470	−	0.911423i	$-0.634984\pi$
$863$	−1.34096e13	−0.822940	−0.411470	+	0.911423i	$0.634984\pi$
$864$	6.50447e11	0.0397100
$865$	2.11174e12	0.128253
$866$	2.65156e11	0.0160203
$867$	2.68972e12	0.161667
$868$	−7.30425e11	−0.0436754
$869$	2.57684e13	1.53285
$870$	−7.75671e11	−0.0459030
$871$	−1.42914e11	−0.00841382
$872$	1.98843e12	0.116463
$873$	−2.21808e12	−0.129245
$874$	1.37944e11	0.00799650
$875$	−2.23470e13	−1.28880
$876$	−3.17319e12	−0.182066
$877$	1.15867e13	0.661399	0.330699	−	0.943736i	$-0.392715\pi$
$877$	1.15867e13	0.661399	0.330699	+	0.943736i	$0.392715\pi$
$878$	1.99954e12	0.113555
$879$	−1.06535e13	−0.601926
$880$	−2.29418e13	−1.28960
$881$	1.40889e12	0.0787929	0.0393964	−	0.999224i	$-0.487456\pi$
$881$	1.40889e12	0.0787929	0.0393964	+	0.999224i	$0.487456\pi$
$882$	1.87515e11	0.0104334
$883$	4.99843e12	0.276701	0.138350	−	0.990383i	$-0.455820\pi$
$883$	4.99843e12	0.276701	0.138350	+	0.990383i	$0.455820\pi$
$884$	9.46710e12	0.521413
$885$	−1.23926e12	−0.0679076
$886$	−1.31077e12	−0.0714620
$887$	1.40515e13	0.762197	0.381099	−	0.924534i	$-0.375546\pi$
$887$	1.40515e13	0.762197	0.381099	+	0.924534i	$0.375546\pi$
$888$	2.67108e12	0.144155
$889$	3.06627e13	1.64646
$890$	−9.37450e11	−0.0500833
$891$	3.02716e12	0.160911
$892$	1.18490e13	0.626671
$893$	−1.70404e13	−0.896701
$894$	−4.35280e11	−0.0227903
$895$	7.76549e12	0.404544
$896$	6.36030e12	0.329679
$897$	−6.65047e11	−0.0342994
$898$	1.27732e12	0.0655476
$899$	−9.06751e11	−0.0462988
$900$	1.19997e12	0.0609650
$901$	7.46685e12	0.377464
$902$	1.36349e12	0.0685840
$903$	2.43727e13	1.21986
$904$	−1.38271e12	−0.0688611
$905$	1.10612e13	0.548129
$906$	−1.08825e12	−0.0536603
$907$	−2.44121e13	−1.19777	−0.598883	−	0.800837i	$-0.704389\pi$
$907$	−2.44121e13	−1.19777	−0.598883	+	0.800837i	$0.704389\pi$
$908$	2.30353e13	1.12463
$909$	2.06793e12	0.100461
$910$	−7.21941e11	−0.0348992
$911$	−6.54472e12	−0.314817	−0.157409	−	0.987534i	$-0.550314\pi$
$911$	−6.54472e12	−0.314817	−0.157409	+	0.987534i	$0.550314\pi$
$912$	1.07056e13	0.512428
$913$	3.49902e13	1.66659
$914$	1.86936e12	0.0886001
$915$	1.23808e13	0.583919
$916$	−1.46285e13	−0.686548
$917$	−3.68560e13	−1.72126
$918$	3.24309e11	0.0150718
$919$	−2.52922e13	−1.16968	−0.584841	−	0.811148i	$-0.698843\pi$
$919$	−2.52922e13	−1.16968	−0.584841	+	0.811148i	$0.698843\pi$
$920$	3.47829e11	0.0160074
$921$	−1.81849e12	−0.0832805
$922$	−2.85987e12	−0.130334
$923$	5.16426e12	0.234207
$924$	2.22185e13	1.00275
$925$	7.39751e12	0.332237
$926$	−2.55339e11	−0.0114121
$927$	−1.50779e11	−0.00670627
$928$	5.92658e12	0.262324
$929$	1.41243e13	0.622151	0.311075	−	0.950385i	$-0.399311\pi$
$929$	1.41243e13	0.622151	0.311075	+	0.950385i	$0.399311\pi$
$930$	2.99966e10	0.00131492
$931$	9.33370e12	0.407174
$932$	1.57265e13	0.682747
$933$	5.94146e12	0.256700
$934$	1.23596e12	0.0531426
$935$	−3.45934e13	−1.48027
$936$	5.00621e11	0.0213190
$937$	2.38027e13	1.00878	0.504391	−	0.863475i	$-0.331717\pi$
$937$	2.38027e13	1.00878	0.504391	+	0.863475i	$0.331717\pi$
$938$	−3.59332e10	−0.00151560
$939$	−2.12767e13	−0.893118
$940$	−2.14323e13	−0.895353
$941$	3.60757e13	1.49990	0.749949	−	0.661495i	$-0.230078\pi$
$941$	3.60757e13	1.49990	0.749949	+	0.661495i	$0.230078\pi$
$942$	2.94927e11	0.0122035
$943$	2.13129e12	0.0877689
$944$	3.13090e12	0.128320
$945$	5.13660e12	0.209523
$946$	−4.32951e12	−0.175764
$947$	3.64992e13	1.47472	0.737359	−	0.675501i	$-0.236073\pi$
$947$	3.64992e13	1.47472	0.737359	+	0.675501i	$0.236073\pi$
$948$	−1.51238e13	−0.608168
$949$	−3.66634e12	−0.146735
$950$	−2.87579e11	−0.0114551
$951$	2.70781e13	1.07351
$952$	4.77213e12	0.188298
$953$	−8.43079e12	−0.331093	−0.165547	−	0.986202i	$-0.552939\pi$
$953$	−8.43079e12	−0.331093	−0.165547	+	0.986202i	$0.552939\pi$
$954$	1.96950e11	0.00769817
$955$	2.11477e13	0.822710
$956$	−4.24013e13	−1.64179
$957$	2.75821e13	1.06298
$958$	2.05979e12	0.0790092
$959$	5.64010e13	2.15329
$960$	1.33336e13	0.506672
$961$	−2.64046e13	−0.998674
$962$	1.53939e12	0.0579510
$963$	6.46263e12	0.242154
$964$	−4.19765e13	−1.56552
$965$	2.27686e13	0.845207
$966$	−1.67215e11	−0.00617841
$967$	3.44781e13	1.26802	0.634008	−	0.773326i	$-0.281409\pi$
$967$	3.44781e13	1.26802	0.634008	+	0.773326i	$0.281409\pi$
$968$	−4.13986e12	−0.151547
$969$	1.61427e13	0.588192
$970$	6.68578e11	0.0242482
$971$	1.93005e13	0.696757	0.348378	−	0.937354i	$-0.386732\pi$
$971$	1.93005e13	0.696757	0.348378	+	0.937354i	$0.386732\pi$
$972$	−1.77668e12	−0.0638426
$973$	1.68358e13	0.602181
$974$	−1.46468e12	−0.0521469
$975$	1.38646e12	0.0491346
$976$	−3.12791e13	−1.10339
$977$	3.95365e12	0.138827	0.0694133	−	0.997588i	$-0.477887\pi$
$977$	3.95365e12	0.138827	0.0694133	+	0.997588i	$0.477887\pi$
$978$	−1.95184e12	−0.0682211
$979$	3.33348e13	1.15978
$980$	1.17394e13	0.406562
$981$	−8.15356e12	−0.281084
$982$	−1.81223e12	−0.0621889
$983$	1.92951e13	0.659106	0.329553	−	0.944137i	$-0.393102\pi$
$983$	1.92951e13	0.659106	0.329553	+	0.944137i	$0.393102\pi$
$984$	−1.60435e12	−0.0545534
$985$	1.73676e13	0.587864
$986$	2.95495e12	0.0995645
$987$	2.06563e13	0.692827
$988$	1.24295e13	0.414998
$989$	−6.76753e12	−0.224930
$990$	−9.12454e11	−0.0301893
$991$	2.76855e13	0.911845	0.455922	−	0.890020i	$-0.349309\pi$
$991$	2.76855e13	0.911845	0.455922	+	0.890020i	$0.349309\pi$
$992$	−2.29191e11	−0.00751441
$993$	5.67595e12	0.185254
$994$	1.29846e12	0.0421882
$995$	−5.45981e12	−0.176593
$996$	−2.05362e13	−0.661232
$997$	−3.27614e13	−1.05011	−0.525054	−	0.851069i	$-0.675955\pi$
$997$	−3.27614e13	−1.05011	−0.525054	+	0.851069i	$0.675955\pi$
$998$	1.13457e12	0.0362030
$999$	−1.09527e13	−0.347919

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.a.1.12	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.a.1.12	✓	21	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+1.56630 q^{2} +81.0000 q^{3} -509.547 q^{4} -1262.61 q^{5} +126.871 q^{6} -7655.10 q^{7} -1600.05 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+1.56630 q^{2} +81.0000 q^{3} -509.547 q^{4} -1262.61 q^{5} +126.871 q^{6} -7655.10 q^{7} -1600.05 q^{8} +6561.00 q^{9} -1977.63 q^{10} +70322.7 q^{11} -41273.3 q^{12} -47687.6 q^{13} -11990.2 q^{14} -102272. q^{15} +258382. q^{16} +389608. q^{17} +10276.5 q^{18} +511521. q^{19} +643360. q^{20} -620063. q^{21} +110147. q^{22} +172172. q^{23} -129604. q^{24} -358937. q^{25} -74693.2 q^{26} +531441. q^{27} +3.90063e6 q^{28} +4.84225e6 q^{29} -160188. q^{30} -187258. q^{31} +1.22393e6 q^{32} +5.69613e6 q^{33} +610244. q^{34} +9.66542e6 q^{35} -3.34314e6 q^{36} -2.06095e7 q^{37} +801196. q^{38} -3.86269e6 q^{39} +2.02024e6 q^{40} +1.23789e7 q^{41} -971207. q^{42} -3.93068e7 q^{43} -3.58327e7 q^{44} -8.28400e6 q^{45} +269673. q^{46} -3.33132e7 q^{47} +2.09289e7 q^{48} +1.82470e7 q^{49} -562203. q^{50} +3.15582e7 q^{51} +2.42990e7 q^{52} +1.91650e7 q^{53} +832398. q^{54} -8.87902e7 q^{55} +1.22486e7 q^{56} +4.14332e7 q^{57} +7.58443e6 q^{58} +1.21174e7 q^{59} +5.21121e7 q^{60} -1.21058e8 q^{61} -293303. q^{62} -5.02251e7 q^{63} -1.30374e8 q^{64} +6.02109e7 q^{65} +8.92187e6 q^{66} +2.99688e6 q^{67} -1.98523e8 q^{68} +1.39459e7 q^{69} +1.51390e7 q^{70} -1.08294e8 q^{71} -1.04979e7 q^{72} +7.68824e7 q^{73} -3.22808e7 q^{74} -2.90739e7 q^{75} -2.60644e8 q^{76} -5.38327e8 q^{77} -6.05015e6 q^{78} +3.66431e8 q^{79} -3.26236e8 q^{80} +4.30467e7 q^{81} +1.93891e7 q^{82} +4.97567e8 q^{83} +3.15951e8 q^{84} -4.91924e8 q^{85} -6.15664e7 q^{86} +3.92222e8 q^{87} -1.12520e8 q^{88} +4.74027e8 q^{89} -1.29752e7 q^{90} +3.65053e8 q^{91} -8.77296e7 q^{92} -1.51679e7 q^{93} -5.21785e7 q^{94} -6.45852e8 q^{95} +9.91384e7 q^{96} -3.38070e8 q^{97} +2.85803e7 q^{98} +4.61387e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9}+O(q^{10}) \) 21 * q - 66 * q^2 + 1701 * q^3 + 5206 * q^4 - 2964 * q^5 - 5346 * q^6 - 30775 * q^7 - 24621 * q^8 + 137781 * q^9	\( 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9} - 54663 q^{10} - 151769 q^{11} + 421686 q^{12} - 153611 q^{13} - 286771 q^{14} - 240084 q^{15} + 805530 q^{16} - 723621 q^{17} - 433026 q^{18} - 549388 q^{19} - 527311 q^{20} - 2492775 q^{21} + 2973158 q^{22} + 169962 q^{23} - 1994301 q^{24} + 8035779 q^{25} - 2337392 q^{26} + 11160261 q^{27} - 22659054 q^{28} - 16845442 q^{29} - 4427703 q^{30} - 19307976 q^{31} - 44923568 q^{32} - 12293289 q^{33} - 35547496 q^{34} - 34882596 q^{35} + 34156566 q^{36} - 41561129 q^{37} - 52335371 q^{38} - 12442491 q^{39} - 125735038 q^{40} - 68169291 q^{41} - 23228451 q^{42} - 25719587 q^{43} - 126277032 q^{44} - 19446804 q^{45} - 292814271 q^{46} - 174095332 q^{47} + 65247930 q^{48} + 7479350 q^{49} - 227877439 q^{50} - 58613301 q^{51} - 232397708 q^{52} - 228390500 q^{53} - 35075106 q^{54} - 29426208 q^{55} + 326778474 q^{56} - 44500428 q^{57} + 480343762 q^{58} + 254464581 q^{59} - 42712191 q^{60} - 183928964 q^{61} - 21753862 q^{62} - 201914775 q^{63} + 310571245 q^{64} + 5308466 q^{65} + 240825798 q^{66} - 82724114 q^{67} - 138336205 q^{68} + 13766922 q^{69} + 1030274876 q^{70} - 404721965 q^{71} - 161538381 q^{72} + 154162574 q^{73} + 36352054 q^{74} + 650898099 q^{75} + 1068940636 q^{76} - 448535481 q^{77} - 189328752 q^{78} + 272529635 q^{79} - 345587859 q^{80} + 903981141 q^{81} - 38412637 q^{82} + 432518643 q^{83} - 1835383374 q^{84} - 126211490 q^{85} - 3699273072 q^{86} - 1364480802 q^{87} + 170111045 q^{88} - 1255621070 q^{89} - 358643943 q^{90} + 1448885849 q^{91} + 1568933320 q^{92} - 1563946056 q^{93} - 1908445164 q^{94} - 2896546490 q^{95} - 3638809008 q^{96} + 1007235486 q^{97} - 9506868248 q^{98} - 995756409 q^{99}+O(q^{100}) \) 21 * q - 66 * q^2 + 1701 * q^3 + 5206 * q^4 - 2964 * q^5 - 5346 * q^6 - 30775 * q^7 - 24621 * q^8 + 137781 * q^9 - 54663 * q^10 - 151769 * q^11 + 421686 * q^12 - 153611 * q^13 - 286771 * q^14 - 240084 * q^15 + 805530 * q^16 - 723621 * q^17 - 433026 * q^18 - 549388 * q^19 - 527311 * q^20 - 2492775 * q^21 + 2973158 * q^22 + 169962 * q^23 - 1994301 * q^24 + 8035779 * q^25 - 2337392 * q^26 + 11160261 * q^27 - 22659054 * q^28 - 16845442 * q^29 - 4427703 * q^30 - 19307976 * q^31 - 44923568 * q^32 - 12293289 * q^33 - 35547496 * q^34 - 34882596 * q^35 + 34156566 * q^36 - 41561129 * q^37 - 52335371 * q^38 - 12442491 * q^39 - 125735038 * q^40 - 68169291 * q^41 - 23228451 * q^42 - 25719587 * q^43 - 126277032 * q^44 - 19446804 * q^45 - 292814271 * q^46 - 174095332 * q^47 + 65247930 * q^48 + 7479350 * q^49 - 227877439 * q^50 - 58613301 * q^51 - 232397708 * q^52 - 228390500 * q^53 - 35075106 * q^54 - 29426208 * q^55 + 326778474 * q^56 - 44500428 * q^57 + 480343762 * q^58 + 254464581 * q^59 - 42712191 * q^60 - 183928964 * q^61 - 21753862 * q^62 - 201914775 * q^63 + 310571245 * q^64 + 5308466 * q^65 + 240825798 * q^66 - 82724114 * q^67 - 138336205 * q^68 + 13766922 * q^69 + 1030274876 * q^70 - 404721965 * q^71 - 161538381 * q^72 + 154162574 * q^73 + 36352054 * q^74 + 650898099 * q^75 + 1068940636 * q^76 - 448535481 * q^77 - 189328752 * q^78 + 272529635 * q^79 - 345587859 * q^80 + 903981141 * q^81 - 38412637 * q^82 + 432518643 * q^83 - 1835383374 * q^84 - 126211490 * q^85 - 3699273072 * q^86 - 1364480802 * q^87 + 170111045 * q^88 - 1255621070 * q^89 - 358643943 * q^90 + 1448885849 * q^91 + 1568933320 * q^92 - 1563946056 * q^93 - 1908445164 * q^94 - 2896546490 * q^95 - 3638809008 * q^96 + 1007235486 * q^97 - 9506868248 * q^98 - 995756409 * q^99

Introduction

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