LMFDB - Embedded newform 177.10.a.a.1.9

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			1.9
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)

$f(q)$	$=$	$q-16.6893 q^{2} +81.0000 q^{3} -233.469 q^{4} -1238.34 q^{5} -1351.83 q^{6} +5162.18 q^{7} +12441.3 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-16.6893 q^{2} +81.0000 q^{3} -233.469 q^{4} -1238.34 q^{5} -1351.83 q^{6} +5162.18 q^{7} +12441.3 q^{8} +6561.00 q^{9} +20667.0 q^{10} +35034.8 q^{11} -18911.0 q^{12} -150094. q^{13} -86152.9 q^{14} -100306. q^{15} -88100.2 q^{16} -77825.8 q^{17} -109498. q^{18} -975192. q^{19} +289114. q^{20} +418136. q^{21} -584704. q^{22} +1.25531e6 q^{23} +1.00775e6 q^{24} -419640. q^{25} +2.50496e6 q^{26} +531441. q^{27} -1.20521e6 q^{28} +4.34772e6 q^{29} +1.67402e6 q^{30} +8.89787e6 q^{31} -4.89963e6 q^{32} +2.83782e6 q^{33} +1.29885e6 q^{34} -6.39253e6 q^{35} -1.53179e6 q^{36} +1.60624e7 q^{37} +1.62752e7 q^{38} -1.21576e7 q^{39} -1.54066e7 q^{40} +4.19074e6 q^{41} -6.97838e6 q^{42} +1.36518e7 q^{43} -8.17953e6 q^{44} -8.12475e6 q^{45} -2.09502e7 q^{46} -4.18175e7 q^{47} -7.13611e6 q^{48} -1.37055e7 q^{49} +7.00347e6 q^{50} -6.30389e6 q^{51} +3.50424e7 q^{52} +1.42148e7 q^{53} -8.86935e6 q^{54} -4.33849e7 q^{55} +6.42243e7 q^{56} -7.89906e7 q^{57} -7.25601e7 q^{58} +1.21174e7 q^{59} +2.34182e7 q^{60} +1.20881e7 q^{61} -1.48499e8 q^{62} +3.38690e7 q^{63} +1.26878e8 q^{64} +1.85868e8 q^{65} -4.73610e7 q^{66} +1.80246e8 q^{67} +1.81699e7 q^{68} +1.01680e8 q^{69} +1.06687e8 q^{70} -4.01126e8 q^{71} +8.16275e7 q^{72} -3.63565e8 q^{73} -2.68070e8 q^{74} -3.39908e7 q^{75} +2.27677e8 q^{76} +1.80856e8 q^{77} +2.02902e8 q^{78} +3.93427e8 q^{79} +1.09098e8 q^{80} +4.30467e7 q^{81} -6.99402e7 q^{82} -3.21042e8 q^{83} -9.76218e7 q^{84} +9.63748e7 q^{85} -2.27838e8 q^{86} +3.52165e8 q^{87} +4.35879e8 q^{88} +9.37868e8 q^{89} +1.35596e8 q^{90} -7.74813e8 q^{91} -2.93077e8 q^{92} +7.20727e8 q^{93} +6.97903e8 q^{94} +1.20762e9 q^{95} -3.96870e8 q^{96} -1.46116e9 q^{97} +2.28735e8 q^{98} +2.29863e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−16.6893	−0.737568	−0.368784	−	0.929515i	$-0.620226\pi$
$2$	−16.6893	−0.737568	−0.368784	+	0.929515i	$0.620226\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	−233.469	−0.455994
$5$	−1238.34	−0.886084	−0.443042	−	0.896501i	$-0.646101\pi$
$5$	−1238.34	−0.886084	−0.443042	+	0.896501i	$0.646101\pi$
$6$	−1351.83	−0.425835
$7$	5162.18	0.812628	0.406314	−	0.913734i	$-0.366814\pi$
$7$	5162.18	0.812628	0.406314	+	0.913734i	$0.366814\pi$
$8$	12441.3	1.07389
$9$	6561.00	0.333333
$10$	20667.0	0.653547
$11$	35034.8	0.721493	0.360747	−	0.932664i	$-0.382522\pi$
$11$	35034.8	0.721493	0.360747	+	0.932664i	$0.382522\pi$
$12$	−18911.0	−0.263268
$13$	−150094.	−1.45754	−0.728768	−	0.684761i	$-0.759907\pi$
$13$	−150094.	−1.45754	−0.728768	+	0.684761i	$0.759907\pi$
$14$	−86152.9	−0.599368
$15$	−100306.	−0.511581
$16$	−88100.2	−0.336075
$17$	−77825.8	−0.225997	−0.112999	−	0.993595i	$-0.536046\pi$
$17$	−77825.8	−0.225997	−0.112999	+	0.993595i	$0.536046\pi$
$18$	−109498.	−0.245856
$19$	−975192.	−1.71672	−0.858359	−	0.513050i	$-0.828516\pi$
$19$	−975192.	−1.71672	−0.858359	+	0.513050i	$0.828516\pi$
$20$	289114.	0.404049
$21$	418136.	0.469171
$22$	−584704.	−0.532150
$23$	1.25531e6	0.935356	0.467678	−	0.883899i	$-0.345091\pi$
$23$	1.25531e6	0.935356	0.467678	+	0.883899i	$0.345091\pi$
$24$	1.00775e6	0.620013
$25$	−419640.	−0.214856
$26$	2.50496e6	1.07503
$27$	531441.	0.192450
$28$	−1.20521e6	−0.370553
$29$	4.34772e6	1.14149	0.570743	−	0.821129i	$-0.306655\pi$
$29$	4.34772e6	1.14149	0.570743	+	0.821129i	$0.306655\pi$
$30$	1.67402e6	0.377325
$31$	8.89787e6	1.73045	0.865223	−	0.501387i	$-0.167177\pi$
$31$	8.89787e6	1.73045	0.865223	+	0.501387i	$0.167177\pi$
$32$	−4.89963e6	−0.826016
$33$	2.83782e6	0.416554
$34$	1.29885e6	0.166688
$35$	−6.39253e6	−0.720056
$36$	−1.53179e6	−0.151998
$37$	1.60624e7	1.40898	0.704488	−	0.709716i	$-0.251177\pi$
$37$	1.60624e7	1.40898	0.704488	+	0.709716i	$0.251177\pi$
$38$	1.62752e7	1.26620
$39$	−1.21576e7	−0.841508
$40$	−1.54066e7	−0.951560
$41$	4.19074e6	0.231613	0.115807	−	0.993272i	$-0.463055\pi$
$41$	4.19074e6	0.231613	0.115807	+	0.993272i	$0.463055\pi$
$42$	−6.97838e6	−0.346045
$43$	1.36518e7	0.608951	0.304475	−	0.952520i	$-0.401519\pi$
$43$	1.36518e7	0.608951	0.304475	+	0.952520i	$0.401519\pi$
$44$	−8.17953e6	−0.328997
$45$	−8.12475e6	−0.295361
$46$	−2.09502e7	−0.689888
$47$	−4.18175e7	−1.25002	−0.625011	−	0.780616i	$-0.714906\pi$
$47$	−4.18175e7	−1.25002	−0.625011	+	0.780616i	$0.714906\pi$
$48$	−7.13611e6	−0.194033
$49$	−1.37055e7	−0.339636
$50$	7.00347e6	0.158471
$51$	−6.30389e6	−0.130480
$52$	3.50424e7	0.664627
$53$	1.42148e7	0.247457	0.123728	−	0.992316i	$-0.460515\pi$
$53$	1.42148e7	0.247457	0.123728	+	0.992316i	$0.460515\pi$
$54$	−8.86935e6	−0.141945
$55$	−4.33849e7	−0.639303
$56$	6.42243e7	0.872676
$57$	−7.89906e7	−0.991148
$58$	−7.25601e7	−0.841923
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	2.34182e7	0.233278
$61$	1.20881e7	0.111783	0.0558914	−	0.998437i	$-0.482200\pi$
$61$	1.20881e7	0.111783	0.0558914	+	0.998437i	$0.482200\pi$
$62$	−1.48499e8	−1.27632
$63$	3.38690e7	0.270876
$64$	1.26878e8	0.945318
$65$	1.85868e8	1.29150
$66$	−4.73610e7	−0.307237
$67$	1.80246e8	1.09277	0.546385	−	0.837534i	$-0.316004\pi$
$67$	1.80246e8	1.09277	0.546385	+	0.837534i	$0.316004\pi$
$68$	1.81699e7	0.103053
$69$	1.01680e8	0.540028
$70$	1.06687e8	0.531090
$71$	−4.01126e8	−1.87335	−0.936674	−	0.350201i	$-0.886113\pi$
$71$	−4.01126e8	−1.87335	−0.936674	+	0.350201i	$0.886113\pi$
$72$	8.16275e7	0.357965
$73$	−3.63565e8	−1.49840	−0.749202	−	0.662341i	$-0.769563\pi$
$73$	−3.63565e8	−1.49840	−0.749202	+	0.662341i	$0.769563\pi$
$74$	−2.68070e8	−1.03922
$75$	−3.39908e7	−0.124047
$76$	2.27677e8	0.782813
$77$	1.80856e8	0.586305
$78$	2.02902e8	0.620669
$79$	3.93427e8	1.13643	0.568214	−	0.822881i	$-0.307635\pi$
$79$	3.93427e8	1.13643	0.568214	+	0.822881i	$0.307635\pi$
$80$	1.09098e8	0.297791
$81$	4.30467e7	0.111111
$82$	−6.99402e7	−0.170830
$83$	−3.21042e8	−0.742523	−0.371261	−	0.928528i	$-0.621075\pi$
$83$	−3.21042e8	−0.742523	−0.371261	+	0.928528i	$0.621075\pi$
$84$	−9.76218e7	−0.213939
$85$	9.63748e7	0.200253
$86$	−2.27838e8	−0.449142
$87$	3.52165e8	0.659037
$88$	4.35879e8	0.774807
$89$	9.37868e8	1.58448	0.792240	−	0.610210i	$-0.208915\pi$
$89$	9.37868e8	1.58448	0.792240	+	0.610210i	$0.208915\pi$
$90$	1.35596e8	0.217849
$91$	−7.74813e8	−1.18443
$92$	−2.93077e8	−0.426517
$93$	7.20727e8	0.999074
$94$	6.97903e8	0.921976
$95$	1.20762e9	1.52116
$96$	−3.96870e8	−0.476900
$97$	−1.46116e9	−1.67581	−0.837903	−	0.545820i	$-0.816218\pi$
$97$	−1.46116e9	−1.67581	−0.837903	+	0.545820i	$0.816218\pi$
$98$	2.28735e8	0.250505
$99$	2.29863e8	0.240498
$100$	9.79729e7	0.0979729
$101$	−1.32906e9	−1.27086	−0.635430	−	0.772159i	$-0.719177\pi$
$101$	−1.32906e9	−1.27086	−0.635430	+	0.772159i	$0.719177\pi$
$102$	1.05207e8	0.0962376
$103$	−2.90148e8	−0.254011	−0.127005	−	0.991902i	$-0.540537\pi$
$103$	−2.90148e8	−0.254011	−0.127005	+	0.991902i	$0.540537\pi$
$104$	−1.86737e9	−1.56524
$105$	−5.17795e8	−0.415725
$106$	−2.37234e8	−0.182516
$107$	−2.13497e9	−1.57458	−0.787288	−	0.616585i	$-0.788516\pi$
$107$	−2.13497e9	−1.57458	−0.787288	+	0.616585i	$0.788516\pi$
$108$	−1.24075e8	−0.0877561
$109$	−1.57453e8	−0.106839	−0.0534196	−	0.998572i	$-0.517012\pi$
$109$	−1.57453e8	−0.106839	−0.0534196	+	0.998572i	$0.517012\pi$
$110$	7.24062e8	0.471529
$111$	1.30106e9	0.813473
$112$	−4.54789e8	−0.273104
$113$	−2.00171e9	−1.15491	−0.577455	−	0.816422i	$-0.695954\pi$
$113$	−2.00171e9	−1.15491	−0.577455	+	0.816422i	$0.695954\pi$
$114$	1.31829e9	0.731038
$115$	−1.55450e9	−0.828804
$116$	−1.01506e9	−0.520510
$117$	−9.84769e8	−0.485845
$118$	−2.02230e8	−0.0960231
$119$	−4.01751e8	−0.183652
$120$	−1.24793e9	−0.549383
$121$	−1.13051e9	−0.479448
$122$	−2.01742e8	−0.0824474
$123$	3.39450e8	0.133722
$124$	−2.07738e9	−0.789073
$125$	2.93829e9	1.07646
$126$	−5.65249e8	−0.199789
$127$	6.34005e8	0.216260	0.108130	−	0.994137i	$-0.465514\pi$
$127$	6.34005e8	0.216260	0.108130	+	0.994137i	$0.465514\pi$
$128$	3.91104e8	0.128780
$129$	1.10580e9	0.351578
$130$	−3.10199e9	−0.952567
$131$	−2.57578e9	−0.764167	−0.382083	−	0.924128i	$-0.624793\pi$
$131$	−2.57578e9	−0.764167	−0.382083	+	0.924128i	$0.624793\pi$
$132$	−6.62542e8	−0.189946
$133$	−5.03411e9	−1.39505
$134$	−3.00817e9	−0.805991
$135$	−6.58104e8	−0.170527
$136$	−9.68256e8	−0.242697
$137$	2.21465e9	0.537110	0.268555	−	0.963264i	$-0.413454\pi$
$137$	2.21465e9	0.537110	0.268555	+	0.963264i	$0.413454\pi$
$138$	−1.69697e9	−0.398307
$139$	6.77480e9	1.53932	0.769662	−	0.638451i	$-0.220425\pi$
$139$	6.77480e9	1.53932	0.769662	+	0.638451i	$0.220425\pi$
$140$	1.49246e9	0.328341
$141$	−3.38722e9	−0.721701
$142$	6.69450e9	1.38172
$143$	−5.25852e9	−1.05160
$144$	−5.78025e8	−0.112025
$145$	−5.38395e9	−1.01145
$146$	6.06763e9	1.10517
$147$	−1.11015e9	−0.196089
$148$	−3.75008e9	−0.642485
$149$	−6.74700e9	−1.12143	−0.560716	−	0.828008i	$-0.689474\pi$
$149$	−6.74700e9	−1.12143	−0.560716	+	0.828008i	$0.689474\pi$
$150$	5.67281e8	0.0914930
$151$	−6.62600e9	−1.03718	−0.518591	−	0.855022i	$-0.673543\pi$
$151$	−6.62600e9	−1.03718	−0.518591	+	0.855022i	$0.673543\pi$
$152$	−1.21327e10	−1.84357
$153$	−5.10615e8	−0.0753325
$154$	−3.01835e9	−0.432440
$155$	−1.10186e10	−1.53332
$156$	2.83843e9	0.383723
$157$	−5.54638e9	−0.728553	−0.364277	−	0.931291i	$-0.618684\pi$
$157$	−5.54638e9	−0.728553	−0.364277	+	0.931291i	$0.618684\pi$
$158$	−6.56600e9	−0.838192
$159$	1.15140e9	0.142869
$160$	6.06740e9	0.731919
$161$	6.48015e9	0.760097
$162$	−7.18417e8	−0.0819520
$163$	−5.30888e9	−0.589059	−0.294530	−	0.955642i	$-0.595163\pi$
$163$	−5.30888e9	−0.589059	−0.294530	+	0.955642i	$0.595163\pi$
$164$	−9.78407e8	−0.105614
$165$	−3.51418e9	−0.369102
$166$	5.35794e9	0.547661
$167$	3.80378e9	0.378435	0.189217	−	0.981935i	$-0.439405\pi$
$167$	3.80378e9	0.378435	0.189217	+	0.981935i	$0.439405\pi$
$168$	5.20217e9	0.503840
$169$	1.19238e10	1.12441
$170$	−1.60842e9	−0.147700
$171$	−6.39824e9	−0.572239
$172$	−3.18727e9	−0.277678
$173$	−8.19884e8	−0.0695897	−0.0347949	−	0.999394i	$-0.511078\pi$
$173$	−8.19884e8	−0.0695897	−0.0347949	+	0.999394i	$0.511078\pi$
$174$	−5.87737e9	−0.486084
$175$	−2.16625e9	−0.174598
$176$	−3.08657e9	−0.242476
$177$	9.81506e8	0.0751646
$178$	−1.56523e10	−1.16866
$179$	1.23784e10	0.901209	0.450604	−	0.892724i	$-0.351209\pi$
$179$	1.23784e10	0.901209	0.450604	+	0.892724i	$0.351209\pi$
$180$	1.89688e9	0.134683
$181$	−5.53512e9	−0.383331	−0.191665	−	0.981460i	$-0.561389\pi$
$181$	−5.53512e9	−0.383331	−0.191665	+	0.981460i	$0.561389\pi$
$182$	1.29311e10	0.873600
$183$	9.79139e8	0.0645378
$184$	1.56178e10	1.00447
$185$	−1.98908e10	−1.24847
$186$	−1.20284e10	−0.736885
$187$	−2.72661e9	−0.163056
$188$	9.76309e9	0.570003
$189$	2.74339e9	0.156390
$190$	−2.01543e10	−1.12196
$191$	5.39092e9	0.293098	0.146549	−	0.989203i	$-0.453183\pi$
$191$	5.39092e9	0.293098	0.146549	+	0.989203i	$0.453183\pi$
$192$	1.02772e10	0.545780
$193$	1.87568e10	0.973086	0.486543	−	0.873657i	$-0.338258\pi$
$193$	1.87568e10	0.973086	0.486543	+	0.873657i	$0.338258\pi$
$194$	2.43856e10	1.23602
$195$	1.50553e10	0.745647
$196$	3.19982e9	0.154872
$197$	−4.09941e10	−1.93920	−0.969601	−	0.244693i	$-0.921313\pi$
$197$	−4.09941e10	−1.93920	−0.969601	+	0.244693i	$0.921313\pi$
$198$	−3.83624e9	−0.177383
$199$	3.27876e10	1.48208	0.741039	−	0.671462i	$-0.234333\pi$
$199$	3.27876e10	1.48208	0.741039	+	0.671462i	$0.234333\pi$
$200$	−5.22087e9	−0.230732
$201$	1.45999e10	0.630911
$202$	2.21810e10	0.937344
$203$	2.24437e10	0.927603
$204$	1.47176e9	0.0594979
$205$	−5.18955e9	−0.205229
$206$	4.84235e9	0.187350
$207$	8.23611e9	0.311785
$208$	1.32233e10	0.489842
$209$	−3.41656e10	−1.23860
$210$	8.64161e9	0.306625
$211$	−3.75829e10	−1.30533	−0.652664	−	0.757647i	$-0.726349\pi$
$211$	−3.75829e10	−1.30533	−0.652664	+	0.757647i	$0.726349\pi$
$212$	−3.31872e9	−0.112839
$213$	−3.24912e10	−1.08158
$214$	3.56310e10	1.16136
$215$	−1.69056e10	−0.539581
$216$	6.61183e9	0.206671
$217$	4.59324e10	1.40621
$218$	2.62776e9	0.0788011
$219$	−2.94488e10	−0.865104
$220$	1.01290e10	0.291518
$221$	1.16812e10	0.329399
$222$	−2.17137e10	−0.599991
$223$	4.06649e10	1.10115	0.550577	−	0.834784i	$-0.314408\pi$
$223$	4.06649e10	1.10115	0.550577	+	0.834784i	$0.314408\pi$
$224$	−2.52928e10	−0.671243
$225$	−2.75326e9	−0.0716185
$226$	3.34070e10	0.851824
$227$	−2.68733e10	−0.671746	−0.335873	−	0.941907i	$-0.609031\pi$
$227$	−2.68733e10	−0.671746	−0.335873	+	0.941907i	$0.609031\pi$
$228$	1.84418e10	0.451957
$229$	−1.51366e10	−0.363720	−0.181860	−	0.983324i	$-0.558212\pi$
$229$	−1.51366e10	−0.363720	−0.181860	+	0.983324i	$0.558212\pi$
$230$	2.59435e10	0.611299
$231$	1.46493e10	0.338504
$232$	5.40913e10	1.22583
$233$	−7.80036e10	−1.73386	−0.866928	−	0.498433i	$-0.833909\pi$
$233$	−7.80036e10	−1.73386	−0.866928	+	0.498433i	$0.833909\pi$
$234$	1.64350e10	0.358344
$235$	5.17843e10	1.10762
$236$	−2.82903e9	−0.0593654
$237$	3.18676e10	0.656117
$238$	6.70492e9	0.135456
$239$	−7.06123e10	−1.39988	−0.699938	−	0.714203i	$-0.746789\pi$
$239$	−7.06123e10	−1.39988	−0.699938	+	0.714203i	$0.746789\pi$
$240$	8.83693e9	0.171930
$241$	−1.02931e11	−1.96548	−0.982742	−	0.184981i	$-0.940778\pi$
$241$	−1.02931e11	−1.96548	−0.982742	+	0.184981i	$0.940778\pi$
$242$	1.88674e10	0.353625
$243$	3.48678e9	0.0641500
$244$	−2.82220e9	−0.0509723
$245$	1.69721e10	0.300946
$246$	−5.66516e9	−0.0986289
$247$	1.46371e11	2.50218
$248$	1.10701e11	1.85832
$249$	−2.60044e10	−0.428696
$250$	−4.90378e10	−0.793965
$251$	6.64645e9	0.105696	0.0528479	−	0.998603i	$-0.483170\pi$
$251$	6.64645e9	0.105696	0.0528479	+	0.998603i	$0.483170\pi$
$252$	−7.90737e9	−0.123518
$253$	4.39796e10	0.674853
$254$	−1.05811e10	−0.159506
$255$	7.80636e9	0.115616
$256$	−7.14890e10	−1.04030
$257$	−5.93058e10	−0.848005	−0.424002	−	0.905661i	$-0.639375\pi$
$257$	−5.93058e10	−0.848005	−0.424002	+	0.905661i	$0.639375\pi$
$258$	−1.84549e10	−0.259312
$259$	8.29172e10	1.14497
$260$	−4.33943e10	−0.588915
$261$	2.85254e10	0.380495
$262$	4.29879e10	0.563625
$263$	−5.21758e10	−0.672462	−0.336231	−	0.941779i	$-0.609152\pi$
$263$	−5.21758e10	−0.672462	−0.336231	+	0.941779i	$0.609152\pi$
$264$	3.53062e10	0.447335
$265$	−1.76028e10	−0.219268
$266$	8.40156e10	1.02895
$267$	7.59673e10	0.914799
$268$	−4.20818e10	−0.498296
$269$	7.23099e9	0.0842000	0.0421000	−	0.999113i	$-0.486595\pi$
$269$	7.23099e9	0.0842000	0.0421000	+	0.999113i	$0.486595\pi$
$270$	1.09833e10	0.125775
$271$	3.44520e8	0.00388018	0.00194009	−	0.999998i	$-0.499382\pi$
$271$	3.44520e8	0.00388018	0.00194009	+	0.999998i	$0.499382\pi$
$272$	6.85647e9	0.0759522
$273$	−6.27599e10	−0.683833
$274$	−3.69609e10	−0.396155
$275$	−1.47020e10	−0.155017
$276$	−2.37392e10	−0.246250
$277$	−5.13370e10	−0.523928	−0.261964	−	0.965078i	$-0.584370\pi$
$277$	−5.13370e10	−0.523928	−0.261964	+	0.965078i	$0.584370\pi$
$278$	−1.13066e11	−1.13536
$279$	5.83789e10	0.576816
$280$	−7.95315e10	−0.773264
$281$	−1.88645e11	−1.80496	−0.902479	−	0.430735i	$-0.858254\pi$
$281$	−1.88645e11	−1.80496	−0.902479	+	0.430735i	$0.858254\pi$
$282$	5.65301e10	0.532303
$283$	3.40056e10	0.315145	0.157573	−	0.987507i	$-0.449633\pi$
$283$	3.40056e10	0.315145	0.157573	+	0.987507i	$0.449633\pi$
$284$	9.36505e10	0.854236
$285$	9.78171e10	0.878240
$286$	8.77607e10	0.775627
$287$	2.16333e10	0.188215
$288$	−3.21465e10	−0.275339
$289$	−1.12531e11	−0.948925
$290$	8.98541e10	0.746014
$291$	−1.18354e11	−0.967527
$292$	8.48811e10	0.683264
$293$	1.12493e11	0.891704	0.445852	−	0.895107i	$-0.352901\pi$
$293$	1.12493e11	0.891704	0.445852	+	0.895107i	$0.352901\pi$
$294$	1.85275e10	0.144629
$295$	−1.50054e10	−0.115358
$296$	1.99838e11	1.51309
$297$	1.86189e10	0.138851
$298$	1.12602e11	0.827132
$299$	−1.88415e11	−1.36331
$300$	7.93580e9	0.0565647
$301$	7.04731e10	0.494850
$302$	1.10583e11	0.764992
$303$	−1.07654e11	−0.733731
$304$	8.59146e10	0.576947
$305$	−1.49692e10	−0.0990489
$306$	8.52178e9	0.0555628
$307$	−2.81159e11	−1.80646	−0.903231	−	0.429154i	$-0.858812\pi$
$307$	−2.81159e11	−1.80646	−0.903231	+	0.429154i	$0.858812\pi$
$308$	−4.22242e10	−0.267352
$309$	−2.35020e10	−0.146653
$310$	1.83892e11	1.13093
$311$	2.44428e11	1.48159	0.740796	−	0.671730i	$-0.234449\pi$
$311$	2.44428e11	1.48159	0.740796	+	0.671730i	$0.234449\pi$
$312$	−1.51257e11	−0.903691
$313$	2.00787e11	1.18246	0.591230	−	0.806503i	$-0.298643\pi$
$313$	2.00787e11	1.18246	0.591230	+	0.806503i	$0.298643\pi$
$314$	9.25650e10	0.537357
$315$	−4.19414e10	−0.240019
$316$	−9.18529e10	−0.518204
$317$	−3.84791e10	−0.214022	−0.107011	−	0.994258i	$-0.534128\pi$
$317$	−3.84791e10	−0.214022	−0.107011	+	0.994258i	$0.534128\pi$
$318$	−1.92160e10	−0.105376
$319$	1.52321e11	0.823574
$320$	−1.57119e11	−0.837631
$321$	−1.72932e11	−0.909082
$322$	−1.08149e11	−0.560623
$323$	7.58951e10	0.387974
$324$	−1.00501e10	−0.0506660
$325$	6.29855e10	0.313160
$326$	8.86013e10	0.434471
$327$	−1.27537e10	−0.0616836
$328$	5.21383e10	0.248728
$329$	−2.15869e11	−1.01580
$330$	5.86490e10	0.272238
$331$	2.96271e11	1.35663	0.678317	−	0.734769i	$-0.262710\pi$
$331$	2.96271e11	1.35663	0.678317	+	0.734769i	$0.262710\pi$
$332$	7.49532e10	0.338586
$333$	1.05386e11	0.469659
$334$	−6.34822e10	−0.279121
$335$	−2.23206e11	−0.968285
$336$	−3.68379e10	−0.157677
$337$	3.27569e11	1.38347	0.691733	−	0.722153i	$-0.256847\pi$
$337$	3.27569e11	1.38347	0.691733	+	0.722153i	$0.256847\pi$
$338$	−1.98999e11	−0.829328
$339$	−1.62139e11	−0.666788
$340$	−2.25005e10	−0.0913140
$341$	3.11735e11	1.24851
$342$	1.06782e11	0.422065
$343$	−2.79063e11	−1.08863
$344$	1.69847e11	0.653949
$345$	−1.25915e11	−0.478510
$346$	1.36833e10	0.0513271
$347$	2.08345e9	0.00771438	0.00385719	−	0.999993i	$-0.498772\pi$
$347$	2.08345e9	0.00771438	0.00385719	+	0.999993i	$0.498772\pi$
$348$	−8.22196e10	−0.300517
$349$	1.21788e10	0.0439432	0.0219716	−	0.999759i	$-0.493006\pi$
$349$	1.21788e10	0.0439432	0.0219716	+	0.999759i	$0.493006\pi$
$350$	3.61532e10	0.128778
$351$	−7.97663e10	−0.280503
$352$	−1.71657e11	−0.595965
$353$	−3.66036e11	−1.25469	−0.627346	−	0.778741i	$-0.715859\pi$
$353$	−3.66036e11	−1.25469	−0.627346	+	0.778741i	$0.715859\pi$
$354$	−1.63806e10	−0.0554390
$355$	4.96731e11	1.65994
$356$	−2.18963e11	−0.722513
$357$	−3.25418e10	−0.106031
$358$	−2.06586e11	−0.664702
$359$	4.38842e11	1.39439	0.697193	−	0.716883i	$-0.254432\pi$
$359$	4.38842e11	1.39439	0.697193	+	0.716883i	$0.254432\pi$
$360$	−1.01083e11	−0.317187
$361$	6.28312e11	1.94712
$362$	9.23771e10	0.282732
$363$	−9.15715e10	−0.276809
$364$	1.80895e11	0.540095
$365$	4.50217e11	1.32771
$366$	−1.63411e10	−0.0476010
$367$	−5.63859e11	−1.62246	−0.811229	−	0.584729i	$-0.801201\pi$
$367$	−5.63859e11	−1.62246	−0.811229	+	0.584729i	$0.801201\pi$
$368$	−1.10593e11	−0.314350
$369$	2.74954e10	0.0772043
$370$	3.31962e11	0.920832
$371$	7.33793e10	0.201090
$372$	−1.68267e11	−0.455572
$373$	3.13939e11	0.839760	0.419880	−	0.907580i	$-0.362072\pi$
$373$	3.13939e11	0.839760	0.419880	+	0.907580i	$0.362072\pi$
$374$	4.55051e10	0.120265
$375$	2.38001e11	0.621497
$376$	−5.20265e11	−1.34239
$377$	−6.52567e11	−1.66375
$378$	−4.57852e10	−0.115348
$379$	2.46108e11	0.612701	0.306351	−	0.951919i	$-0.400892\pi$
$379$	2.46108e11	0.612701	0.306351	+	0.951919i	$0.400892\pi$
$380$	−2.81942e11	−0.693638
$381$	5.13544e10	0.124858
$382$	−8.99704e10	−0.216179
$383$	4.38027e11	1.04017	0.520087	−	0.854113i	$-0.325899\pi$
$383$	4.38027e11	1.04017	0.520087	+	0.854113i	$0.325899\pi$
$384$	3.16795e10	0.0743511
$385$	−2.23961e11	−0.519516
$386$	−3.13037e11	−0.717716
$387$	8.95695e10	0.202984
$388$	3.41134e11	0.764157
$389$	−6.89652e11	−1.52706	−0.763531	−	0.645771i	$-0.776536\pi$
$389$	−6.89652e11	−1.52706	−0.763531	+	0.645771i	$0.776536\pi$
$390$	−2.51261e11	−0.549965
$391$	−9.76958e10	−0.211388
$392$	−1.70515e11	−0.364733
$393$	−2.08638e11	−0.441192
$394$	6.84160e11	1.43029
$395$	−4.87196e11	−1.00697
$396$	−5.36659e10	−0.109666
$397$	1.59295e11	0.321844	0.160922	−	0.986967i	$-0.448553\pi$
$397$	1.59295e11	0.321844	0.160922	+	0.986967i	$0.448553\pi$
$398$	−5.47201e11	−1.09313
$399$	−4.07763e11	−0.805434
$400$	3.69703e10	0.0722077
$401$	1.49763e11	0.289238	0.144619	−	0.989487i	$-0.453804\pi$
$401$	1.49763e11	0.289238	0.144619	+	0.989487i	$0.453804\pi$
$402$	−2.43662e11	−0.465339
$403$	−1.33552e12	−2.52219
$404$	3.10293e11	0.579504
$405$	−5.33065e10	−0.0984538
$406$	−3.74568e11	−0.684170
$407$	5.62744e11	1.01657
$408$	−7.84287e10	−0.140121
$409$	−7.42138e11	−1.31138	−0.655692	−	0.755029i	$-0.727623\pi$
$409$	−7.42138e11	−1.31138	−0.655692	+	0.755029i	$0.727623\pi$
$410$	8.66098e10	0.151370
$411$	1.79387e11	0.310100
$412$	6.77406e10	0.115827
$413$	6.25520e10	0.105795
$414$	−1.37455e11	−0.229963
$415$	3.97559e11	0.657937
$416$	7.35406e11	1.20395
$417$	5.48759e11	0.888729
$418$	5.70199e11	0.913551
$419$	−2.21707e11	−0.351411	−0.175706	−	0.984443i	$-0.556221\pi$
$419$	−2.21707e11	−0.351411	−0.175706	+	0.984443i	$0.556221\pi$
$420$	1.20889e11	0.189568
$421$	−2.98540e11	−0.463163	−0.231581	−	0.972816i	$-0.574390\pi$
$421$	−2.98540e11	−0.463163	−0.231581	+	0.972816i	$0.574390\pi$
$422$	6.27231e11	0.962768
$423$	−2.74365e11	−0.416674
$424$	1.76851e11	0.265742
$425$	3.26588e10	0.0485568
$426$	5.42254e11	0.797737
$427$	6.24011e10	0.0908378
$428$	4.98448e11	0.717998
$429$	−4.25940e11	−0.607142
$430$	2.82141e11	0.397978
$431$	−9.42123e11	−1.31510	−0.657552	−	0.753409i	$-0.728408\pi$
$431$	−9.42123e11	−1.31510	−0.657552	+	0.753409i	$0.728408\pi$
$432$	−4.68200e10	−0.0646778
$433$	9.76275e10	0.133468	0.0667339	−	0.997771i	$-0.478742\pi$
$433$	9.76275e10	0.133468	0.0667339	+	0.997771i	$0.478742\pi$
$434$	−7.66577e11	−1.03717
$435$	−4.36100e11	−0.583962
$436$	3.67603e10	0.0487180
$437$	−1.22417e12	−1.60574
$438$	4.91478e11	0.638073
$439$	−5.14664e11	−0.661353	−0.330677	−	0.943744i	$-0.607277\pi$
$439$	−5.14664e11	−0.661353	−0.330677	+	0.943744i	$0.607277\pi$
$440$	−5.39766e11	−0.686544
$441$	−8.99220e10	−0.113212
$442$	−1.94951e11	−0.242954
$443$	9.70725e11	1.19751	0.598756	−	0.800932i	$-0.295662\pi$
$443$	9.70725e11	1.19751	0.598756	+	0.800932i	$0.295662\pi$
$444$	−3.03757e11	−0.370939
$445$	−1.16140e12	−1.40398
$446$	−6.78667e11	−0.812175
$447$	−5.46507e11	−0.647459
$448$	6.54969e11	0.768192
$449$	−9.41306e11	−1.09301	−0.546503	−	0.837457i	$-0.684041\pi$
$449$	−9.41306e11	−1.09301	−0.546503	+	0.837457i	$0.684041\pi$
$450$	4.59498e10	0.0528235
$451$	1.46821e11	0.167107
$452$	4.67337e11	0.526632
$453$	−5.36706e11	−0.598818
$454$	4.48496e11	0.495458
$455$	9.59482e11	1.04951
$456$	−9.82747e11	−1.06439
$457$	−9.91302e11	−1.06312	−0.531561	−	0.847020i	$-0.678394\pi$
$457$	−9.91302e11	−1.06312	−0.531561	+	0.847020i	$0.678394\pi$
$458$	2.52618e11	0.268268
$459$	−4.13598e10	−0.0434932
$460$	3.62929e11	0.377930
$461$	−8.44394e10	−0.0870745	−0.0435372	−	0.999052i	$-0.513863\pi$
$461$	−8.44394e10	−0.0870745	−0.0435372	+	0.999052i	$0.513863\pi$
$462$	−2.44486e11	−0.249669
$463$	1.87338e12	1.89457	0.947285	−	0.320391i	$-0.103814\pi$
$463$	1.87338e12	1.89457	0.947285	+	0.320391i	$0.103814\pi$
$464$	−3.83035e11	−0.383625
$465$	−8.92505e11	−0.885263
$466$	1.30182e12	1.27884
$467$	−4.33922e11	−0.422169	−0.211084	−	0.977468i	$-0.567699\pi$
$467$	−4.33922e11	−0.422169	−0.211084	+	0.977468i	$0.567699\pi$
$468$	2.29913e11	0.221542
$469$	9.30461e11	0.888015
$470$	−8.64241e11	−0.816948
$471$	−4.49257e11	−0.420630
$472$	1.50756e11	0.139809
$473$	4.78288e11	0.439354
$474$	−5.31846e11	−0.483931
$475$	4.09229e11	0.368846
$476$	9.37963e10	0.0837441
$477$	9.32633e10	0.0824856
$478$	1.17847e12	1.03250
$479$	−5.72342e11	−0.496759	−0.248380	−	0.968663i	$-0.579898\pi$
$479$	−5.72342e11	−0.496759	−0.248380	+	0.968663i	$0.579898\pi$
$480$	4.91460e11	0.422574
$481$	−2.41088e12	−2.05363
$482$	1.71784e12	1.44968
$483$	5.24892e11	0.438842
$484$	2.63940e11	0.218625
$485$	1.80941e12	1.48490
$486$	−5.81918e10	−0.0473150
$487$	−2.71725e8	−0.000218902 0	−0.000109451	−	1.00000i	$-0.500035\pi$
$487$	−2.71725e8	−0.000218902 0	−0.000109451		1.00000i	$0.500035\pi$
$488$	1.50392e11	0.120043
$489$	−4.30020e11	−0.340094
$490$	−2.83252e11	−0.221968
$491$	−1.17741e10	−0.00914240	−0.00457120	−	0.999990i	$-0.501455\pi$
$491$	−1.17741e10	−0.00914240	−0.00457120	+	0.999990i	$0.501455\pi$
$492$	−7.92509e10	−0.0609764
$493$	−3.38365e11	−0.257973
$494$	−2.44282e12	−1.84552
$495$	−2.84649e11	−0.213101
$496$	−7.83903e11	−0.581561
$497$	−2.07069e12	−1.52234
$498$	4.33993e11	0.316192
$499$	6.69043e11	0.483060	0.241530	−	0.970393i	$-0.422351\pi$
$499$	6.69043e11	0.483060	0.241530	+	0.970393i	$0.422351\pi$
$500$	−6.85999e11	−0.490861
$501$	3.08106e11	0.218489
$502$	−1.10924e11	−0.0779578
$503$	1.37546e12	0.958058	0.479029	−	0.877799i	$-0.340989\pi$
$503$	1.37546e12	0.958058	0.479029	+	0.877799i	$0.340989\pi$
$504$	4.21376e11	0.290892
$505$	1.64582e12	1.12609
$506$	−7.33987e11	−0.497750
$507$	9.65827e11	0.649178
$508$	−1.48020e11	−0.0986131
$509$	−1.63049e11	−0.107668	−0.0538341	−	0.998550i	$-0.517144\pi$
$509$	−1.63049e11	−0.107668	−0.0538341	+	0.998550i	$0.517144\pi$
$510$	−1.30282e11	−0.0852746
$511$	−1.87679e12	−1.21765
$512$	9.92852e11	0.638513
$513$	−5.18257e11	−0.330383
$514$	9.89770e11	0.625461
$515$	3.59302e11	0.225075
$516$	−2.58169e11	−0.160317
$517$	−1.46507e12	−0.901883
$518$	−1.38383e12	−0.844496
$519$	−6.64106e10	−0.0401777
$520$	2.31244e12	1.38693
$521$	−2.29938e12	−1.36723	−0.683614	−	0.729843i	$-0.739593\pi$
$521$	−2.29938e12	−1.36723	−0.683614	+	0.729843i	$0.739593\pi$
$522$	−4.76067e11	−0.280641
$523$	1.95322e12	1.14155	0.570773	−	0.821108i	$-0.306644\pi$
$523$	1.95322e12	1.14155	0.570773	+	0.821108i	$0.306644\pi$
$524$	6.01365e11	0.348455
$525$	−1.75467e11	−0.100804
$526$	8.70775e11	0.495987
$527$	−6.92484e11	−0.391076
$528$	−2.50012e11	−0.139994
$529$	−2.25340e11	−0.125109
$530$	2.93777e11	0.161725
$531$	7.95020e10	0.0433963
$532$	1.17531e12	0.636136
$533$	−6.29006e11	−0.337584
$534$	−1.26784e12	−0.674726
$535$	2.64381e12	1.39521
$536$	2.24250e12	1.17352
$537$	1.00265e12	0.520313
$538$	−1.20680e11	−0.0621032
$539$	−4.80170e11	−0.245045
$540$	1.53647e11	0.0777592
$541$	−1.65773e12	−0.832005	−0.416002	−	0.909363i	$-0.636569\pi$
$541$	−1.65773e12	−0.832005	−0.416002	+	0.909363i	$0.636569\pi$
$542$	−5.74977e9	−0.00286190
$543$	−4.48345e11	−0.221316
$544$	3.81318e11	0.186677
$545$	1.94980e11	0.0946684
$546$	1.04742e12	0.504373
$547$	1.49021e12	0.711711	0.355856	−	0.934541i	$-0.384189\pi$
$547$	1.49021e12	0.711711	0.355856	+	0.934541i	$0.384189\pi$
$548$	−5.17053e11	−0.244919
$549$	7.93102e10	0.0372609
$550$	2.45365e11	0.114335
$551$	−4.23986e12	−1.95961
$552$	1.26504e12	0.579933
$553$	2.03094e12	0.923493
$554$	8.56777e11	0.386433
$555$	−1.61115e12	−0.720805
$556$	−1.58171e12	−0.701923
$557$	−1.32765e12	−0.584433	−0.292216	−	0.956352i	$-0.594393\pi$
$557$	−1.32765e12	−0.584433	−0.292216	+	0.956352i	$0.594393\pi$
$558$	−9.74300e11	−0.425440
$559$	−2.04906e12	−0.887567
$560$	5.63183e11	0.241993
$561$	−2.20855e11	−0.0941402
$562$	3.14834e12	1.33128
$563$	1.28033e12	0.537072	0.268536	−	0.963270i	$-0.413460\pi$
$563$	1.28033e12	0.537072	0.268536	+	0.963270i	$0.413460\pi$
$564$	7.90810e11	0.329091
$565$	2.47880e12	1.02335
$566$	−5.67527e11	−0.232441
$567$	2.22215e11	0.0902920
$568$	−4.99054e12	−2.01178
$569$	2.33110e12	0.932302	0.466151	−	0.884705i	$-0.345640\pi$
$569$	2.33110e12	0.932302	0.466151	+	0.884705i	$0.345640\pi$
$570$	−1.63249e12	−0.647761
$571$	2.22629e12	0.876433	0.438217	−	0.898869i	$-0.355610\pi$
$571$	2.22629e12	0.876433	0.438217	+	0.898869i	$0.355610\pi$
$572$	1.22770e12	0.479524
$573$	4.36664e11	0.169220
$574$	−3.61044e11	−0.138821
$575$	−5.26780e11	−0.200966
$576$	8.32449e11	0.315106
$577$	3.83505e12	1.44039	0.720194	−	0.693772i	$-0.244053\pi$
$577$	3.83505e12	1.44039	0.720194	+	0.693772i	$0.244053\pi$
$578$	1.87806e12	0.699896
$579$	1.51930e12	0.561811
$580$	1.25699e12	0.461216
$581$	−1.65727e12	−0.603395
$582$	1.97523e12	0.713616
$583$	4.98012e11	0.178538
$584$	−4.52323e12	−1.60913
$585$	1.21948e12	0.430499
$586$	−1.87742e12	−0.657692
$587$	−3.47195e11	−0.120699	−0.0603493	−	0.998177i	$-0.519221\pi$
$587$	−3.47195e11	−0.120699	−0.0603493	+	0.998177i	$0.519221\pi$
$588$	2.59185e11	0.0894154
$589$	−8.67713e12	−2.97069
$590$	2.50429e11	0.0850845
$591$	−3.32052e12	−1.11960
$592$	−1.41510e12	−0.473522
$593$	2.82977e12	0.939733	0.469867	−	0.882737i	$-0.344302\pi$
$593$	2.82977e12	0.939733	0.469867	+	0.882737i	$0.344302\pi$
$594$	−3.10736e11	−0.102412
$595$	4.97504e11	0.162731
$596$	1.57522e12	0.511366
$597$	2.65580e12	0.855678
$598$	3.14451e12	1.00554
$599$	3.70847e12	1.17699	0.588497	−	0.808499i	$-0.299720\pi$
$599$	3.70847e12	1.17699	0.588497	+	0.808499i	$0.299720\pi$
$600$	−4.22891e11	−0.133213
$601$	−4.83713e12	−1.51235	−0.756175	−	0.654370i	$-0.772934\pi$
$601$	−4.83713e12	−1.51235	−0.756175	+	0.654370i	$0.772934\pi$
$602$	−1.17614e12	−0.364986
$603$	1.18259e12	0.364256
$604$	1.54696e12	0.472949
$605$	1.39996e12	0.424831
$606$	1.79666e12	0.541176
$607$	3.15555e12	0.943466	0.471733	−	0.881741i	$-0.343629\pi$
$607$	3.15555e12	0.943466	0.471733	+	0.881741i	$0.343629\pi$
$608$	4.77808e12	1.41804
$609$	1.81794e12	0.535552
$610$	2.49825e11	0.0730553
$611$	6.27657e12	1.82195
$612$	1.19213e11	0.0343512
$613$	3.36352e12	0.962104	0.481052	−	0.876692i	$-0.340255\pi$
$613$	3.36352e12	0.962104	0.481052	+	0.876692i	$0.340255\pi$
$614$	4.69233e12	1.33239
$615$	−4.20354e11	−0.118489
$616$	2.25008e12	0.629630
$617$	−3.33692e11	−0.0926964	−0.0463482	−	0.998925i	$-0.514758\pi$
$617$	−3.33692e11	−0.0926964	−0.0463482	+	0.998925i	$0.514758\pi$
$618$	3.92231e11	0.108167
$619$	1.06153e12	0.290619	0.145310	−	0.989386i	$-0.453582\pi$
$619$	1.06153e12	0.290619	0.145310	+	0.989386i	$0.453582\pi$
$620$	2.57250e12	0.699185
$621$	6.67125e11	0.180009
$622$	−4.07931e12	−1.09277
$623$	4.84144e12	1.28759
$624$	1.07109e12	0.282810
$625$	−2.81899e12	−0.738982
$626$	−3.35098e12	−0.872144
$627$	−2.76742e12	−0.715106
$628$	1.29491e12	0.332216
$629$	−1.25007e12	−0.318425
$630$	6.99970e11	0.177030
$631$	6.83930e12	1.71743	0.858716	−	0.512451i	$-0.171262\pi$
$631$	6.83930e12	1.71743	0.858716	+	0.512451i	$0.171262\pi$
$632$	4.89475e12	1.22040
$633$	−3.04422e12	−0.753632
$634$	6.42187e11	0.157855
$635$	−7.85113e11	−0.191624
$636$	−2.68816e11	−0.0651475
$637$	2.05712e12	0.495031
$638$	−2.54213e12	−0.607441
$639$	−2.63179e12	−0.624450
$640$	−4.84320e11	−0.114110
$641$	4.26714e12	0.998335	0.499167	−	0.866506i	$-0.333639\pi$
$641$	4.26714e12	0.998335	0.499167	+	0.866506i	$0.333639\pi$
$642$	2.88611e12	0.670510
$643$	−2.12525e12	−0.490299	−0.245149	−	0.969485i	$-0.578837\pi$
$643$	−2.12525e12	−0.490299	−0.245149	+	0.969485i	$0.578837\pi$
$644$	−1.51291e12	−0.346599
$645$	−1.36935e12	−0.311527
$646$	−1.26663e12	−0.286157
$647$	−6.71843e12	−1.50729	−0.753647	−	0.657279i	$-0.771707\pi$
$647$	−6.71843e12	−1.50729	−0.753647	+	0.657279i	$0.771707\pi$
$648$	5.35558e11	0.119322
$649$	4.24529e11	0.0939304
$650$	−1.05118e12	−0.230976
$651$	3.72052e12	0.811875
$652$	1.23946e12	0.268608
$653$	−7.51268e12	−1.61691	−0.808454	−	0.588559i	$-0.799695\pi$
$653$	−7.51268e12	−1.61691	−0.808454	+	0.588559i	$0.799695\pi$
$654$	2.12849e11	0.0454958
$655$	3.18969e12	0.677116
$656$	−3.69205e11	−0.0778394
$657$	−2.38535e12	−0.499468
$658$	3.60270e12	0.749224
$659$	−2.68952e12	−0.555507	−0.277754	−	0.960652i	$-0.589590\pi$
$659$	−2.68952e12	−0.555507	−0.277754	+	0.960652i	$0.589590\pi$
$660$	8.20452e11	0.168308
$661$	3.74262e11	0.0762552	0.0381276	−	0.999273i	$-0.487861\pi$
$661$	3.74262e11	0.0762552	0.0381276	+	0.999273i	$0.487861\pi$
$662$	−4.94454e12	−1.00061
$663$	9.46178e11	0.190179
$664$	−3.99418e12	−0.797391
$665$	6.23394e12	1.23613
$666$	−1.75881e12	−0.346405
$667$	5.45775e12	1.06770
$668$	−8.88064e11	−0.172564
$669$	3.29386e12	0.635751
$670$	3.72513e12	0.714176
$671$	4.23505e11	0.0806505
$672$	−2.04871e12	−0.387543
$673$	−9.54535e10	−0.0179359	−0.00896797	−	0.999960i	$-0.502855\pi$
$673$	−9.54535e10	−0.0179359	−0.00896797	+	0.999960i	$0.502855\pi$
$674$	−5.46689e12	−1.02040
$675$	−2.23014e11	−0.0413490
$676$	−2.78384e12	−0.512724
$677$	7.02943e12	1.28609	0.643044	−	0.765829i	$-0.277671\pi$
$677$	7.02943e12	1.28609	0.643044	+	0.765829i	$0.277671\pi$
$678$	2.70597e12	0.491801
$679$	−7.54274e12	−1.36181
$680$	1.19903e12	0.215050
$681$	−2.17674e12	−0.387833
$682$	−5.20262e12	−0.920857
$683$	1.65634e12	0.291243	0.145622	−	0.989340i	$-0.453482\pi$
$683$	1.65634e12	0.291243	0.145622	+	0.989340i	$0.453482\pi$
$684$	1.49379e12	0.260938
$685$	−2.74249e12	−0.475924
$686$	4.65735e12	0.802935
$687$	−1.22606e12	−0.209994
$688$	−1.20273e12	−0.204653
$689$	−2.13356e12	−0.360677
$690$	2.10143e12	0.352934
$691$	−6.66811e12	−1.11263	−0.556316	−	0.830971i	$-0.687786\pi$
$691$	−6.66811e12	−1.11263	−0.556316	+	0.830971i	$0.687786\pi$
$692$	1.91418e11	0.0317325
$693$	1.18659e12	0.195435
$694$	−3.47713e10	−0.00568988
$695$	−8.38951e12	−1.36397
$696$	4.38140e12	0.707736
$697$	−3.26147e11	−0.0523439
$698$	−2.03256e11	−0.0324111
$699$	−6.31829e12	−1.00104
$700$	5.05753e11	0.0796155
$701$	−6.53867e12	−1.02272	−0.511362	−	0.859366i	$-0.670859\pi$
$701$	−6.53867e12	−1.02272	−0.511362	+	0.859366i	$0.670859\pi$
$702$	1.33124e12	0.206890
$703$	−1.56640e13	−2.41882
$704$	4.44516e12	0.682040
$705$	4.19453e12	0.639488
$706$	6.10886e12	0.925420
$707$	−6.86083e12	−1.03274
$708$	−2.29151e11	−0.0342746
$709$	−2.15440e10	−0.00320198	−0.00160099	−	0.999999i	$-0.500510\pi$
$709$	−2.15440e10	−0.00320198	−0.00160099	+	0.999999i	$0.500510\pi$
$710$	−8.29006e12	−1.22432
$711$	2.58127e12	0.378809
$712$	1.16683e13	1.70156
$713$	1.11696e13	1.61858
$714$	5.43098e11	0.0782053
$715$	6.51183e12	0.931807
$716$	−2.88997e12	−0.410946
$717$	−5.71960e12	−0.808219
$718$	−7.32395e12	−1.02845
$719$	−2.79294e12	−0.389746	−0.194873	−	0.980828i	$-0.562429\pi$
$719$	−2.79294e12	−0.389746	−0.194873	+	0.980828i	$0.562429\pi$
$720$	7.15792e11	0.0992637
$721$	−1.49780e12	−0.206416
$722$	−1.04861e13	−1.43613
$723$	−8.33741e12	−1.13477
$724$	1.29228e12	0.174797
$725$	−1.82448e12	−0.245254
$726$	1.52826e12	0.204166
$727$	−1.32795e13	−1.76310	−0.881548	−	0.472094i	$-0.843498\pi$
$727$	−1.32795e13	−1.76310	−0.881548	+	0.472094i	$0.843498\pi$
$728$	−9.63970e12	−1.27196
$729$	2.82430e11	0.0370370
$730$	−7.51378e12	−0.979277
$731$	−1.06246e12	−0.137621
$732$	−2.28599e11	−0.0294289
$733$	−5.45238e12	−0.697619	−0.348809	−	0.937194i	$-0.613414\pi$
$733$	−5.45238e12	−0.697619	−0.348809	+	0.937194i	$0.613414\pi$
$734$	9.41038e12	1.19667
$735$	1.37474e12	0.173751
$736$	−6.15057e12	−0.772619
$737$	6.31487e12	0.788426
$738$	−4.58878e11	−0.0569434
$739$	6.21424e12	0.766457	0.383229	−	0.923653i	$-0.374812\pi$
$739$	6.21424e12	0.766457	0.383229	+	0.923653i	$0.374812\pi$
$740$	4.64387e12	0.569295
$741$	1.18560e13	1.44463
$742$	−1.22465e12	−0.148318
$743$	−7.16003e12	−0.861917	−0.430958	−	0.902372i	$-0.641824\pi$
$743$	−7.16003e12	−0.861917	−0.430958	+	0.902372i	$0.641824\pi$
$744$	8.96679e12	1.07290
$745$	8.35508e12	0.993682
$746$	−5.23940e12	−0.619379
$747$	−2.10635e12	−0.247508
$748$	6.36579e11	0.0743524
$749$	−1.10211e13	−1.27955
$750$	−3.97206e12	−0.458396
$751$	6.95263e11	0.0797571	0.0398786	−	0.999205i	$-0.487303\pi$
$751$	6.95263e11	0.0797571	0.0398786	+	0.999205i	$0.487303\pi$
$752$	3.68413e12	0.420102
$753$	5.38362e11	0.0610235
$754$	1.08909e13	1.22713
$755$	8.20524e12	0.919030
$756$	−6.40497e11	−0.0713130
$757$	−5.88840e12	−0.651727	−0.325864	−	0.945417i	$-0.605655\pi$
$757$	−5.88840e12	−0.651727	−0.325864	+	0.945417i	$0.605655\pi$
$758$	−4.10735e12	−0.451909
$759$	3.56235e12	0.389627
$760$	1.50244e13	1.63356
$761$	−6.31218e12	−0.682257	−0.341129	−	0.940017i	$-0.610809\pi$
$761$	−6.31218e12	−0.682257	−0.341129	+	0.940017i	$0.610809\pi$
$762$	−8.57066e11	−0.0920909
$763$	−8.12798e11	−0.0868205
$764$	−1.25861e12	−0.133651
$765$	6.32315e11	0.0667509
$766$	−7.31034e12	−0.767199
$767$	−1.81875e12	−0.189755
$768$	−5.79061e12	−0.600618
$769$	−1.64038e13	−1.69151	−0.845757	−	0.533569i	$-0.820851\pi$
$769$	−1.64038e13	−1.69151	−0.845757	+	0.533569i	$0.820851\pi$
$770$	3.73774e12	0.383178
$771$	−4.80377e12	−0.489596
$772$	−4.37913e12	−0.443721
$773$	6.75582e12	0.680566	0.340283	−	0.940323i	$-0.389477\pi$
$773$	6.75582e12	0.680566	0.340283	+	0.940323i	$0.389477\pi$
$774$	−1.49485e12	−0.149714
$775$	−3.73390e12	−0.371796
$776$	−1.81787e13	−1.79964
$777$	6.71629e12	0.661051
$778$	1.15098e13	1.12631
$779$	−4.08677e12	−0.397614
$780$	−3.51494e12	−0.340011
$781$	−1.40534e13	−1.35161
$782$	1.63047e12	0.155913
$783$	2.31056e12	0.219679
$784$	1.20746e12	0.114143
$785$	6.86830e12	0.645559
$786$	3.48202e12	0.325409
$787$	1.56632e13	1.45544	0.727719	−	0.685875i	$-0.240580\pi$
$787$	1.56632e13	1.45544	0.727719	+	0.685875i	$0.240580\pi$
$788$	9.57084e12	0.884264
$789$	−4.22624e12	−0.388246
$790$	8.13093e12	0.742709
$791$	−1.03332e13	−0.938512
$792$	2.85980e12	0.258269
$793$	−1.81436e12	−0.162927
$794$	−2.65852e12	−0.237382
$795$	−1.42582e12	−0.126594
$796$	−7.65489e12	−0.675819
$797$	1.43951e13	1.26372	0.631860	−	0.775083i	$-0.282292\pi$
$797$	1.43951e13	1.26372	0.631860	+	0.775083i	$0.282292\pi$
$798$	6.80526e12	0.594062
$799$	3.25448e12	0.282502
$800$	2.05608e12	0.177474
$801$	6.15335e12	0.528160
$802$	−2.49943e12	−0.213333
$803$	−1.27374e13	−1.08109
$804$	−3.40863e12	−0.287692
$805$	−8.02463e12	−0.673509
$806$	2.22888e13	1.86028
$807$	5.85710e11	0.0486129
$808$	−1.65352e13	−1.36477
$809$	−1.15711e13	−0.949742	−0.474871	−	0.880055i	$-0.657505\pi$
$809$	−1.15711e13	−0.949742	−0.474871	+	0.880055i	$0.657505\pi$
$810$	8.89645e11	0.0726163
$811$	7.84788e12	0.637028	0.318514	−	0.947918i	$-0.396816\pi$
$811$	7.84788e12	0.637028	0.318514	+	0.947918i	$0.396816\pi$
$812$	−5.23990e12	−0.422981
$813$	2.79061e10	0.00224022
$814$	−9.39177e12	−0.749787
$815$	6.57420e12	0.521956
$816$	5.55374e11	0.0438510
$817$	−1.33131e13	−1.04540
$818$	1.23857e13	0.967234
$819$	−5.08355e12	−0.394811
$820$	1.21160e12	0.0935830
$821$	−2.29251e12	−0.176103	−0.0880515	−	0.996116i	$-0.528064\pi$
$821$	−2.29251e12	−0.176103	−0.0880515	+	0.996116i	$0.528064\pi$
$822$	−2.99383e12	−0.228720
$823$	−8.03820e12	−0.610745	−0.305372	−	0.952233i	$-0.598781\pi$
$823$	−8.03820e12	−0.610745	−0.305372	+	0.952233i	$0.598781\pi$
$824$	−3.60982e12	−0.272781
$825$	−1.19086e12	−0.0894990
$826$	−1.04395e12	−0.0780311
$827$	1.50364e13	1.11782	0.558908	−	0.829230i	$-0.311221\pi$
$827$	1.50364e13	1.11782	0.558908	+	0.829230i	$0.311221\pi$
$828$	−1.92288e12	−0.142172
$829$	−5.18678e12	−0.381419	−0.190710	−	0.981647i	$-0.561079\pi$
$829$	−5.18678e12	−0.381419	−0.190710	+	0.981647i	$0.561079\pi$
$830$	−6.63495e12	−0.485273
$831$	−4.15830e12	−0.302490
$832$	−1.90437e13	−1.37783
$833$	1.06664e12	0.0767569
$834$	−9.15838e12	−0.655498
$835$	−4.71037e12	−0.335325
$836$	7.97661e12	0.564794
$837$	4.72869e12	0.333025
$838$	3.70012e12	0.259189
$839$	−1.41530e13	−0.986099	−0.493050	−	0.870001i	$-0.664118\pi$
$839$	−1.41530e13	−0.986099	−0.493050	+	0.870001i	$0.664118\pi$
$840$	−6.44205e12	−0.446444
$841$	4.39550e12	0.302989
$842$	4.98242e12	0.341614
$843$	−1.52802e13	−1.04209
$844$	8.77445e12	0.595222
$845$	−1.47657e13	−0.996320
$846$	4.57894e12	0.307325
$847$	−5.83591e12	−0.389613
$848$	−1.25233e12	−0.0831642
$849$	2.75445e12	0.181949
$850$	−5.45051e11	−0.0358139
$851$	2.01634e13	1.31790
$852$	7.58569e12	0.493193
$853$	−2.92961e13	−1.89469	−0.947346	−	0.320210i	$-0.896246\pi$
$853$	−2.92961e13	−1.89469	−0.947346	+	0.320210i	$0.896246\pi$
$854$	−1.04143e12	−0.0669990
$855$	7.92319e12	0.507052
$856$	−2.65618e13	−1.69093
$857$	−1.94036e13	−1.22877	−0.614384	−	0.789007i	$-0.710595\pi$
$857$	−1.94036e13	−1.22877	−0.614384	+	0.789007i	$0.710595\pi$
$858$	7.10862e12	0.447809
$859$	2.45006e12	0.153535	0.0767676	−	0.997049i	$-0.475540\pi$
$859$	2.45006e12	0.153535	0.0767676	+	0.997049i	$0.475540\pi$
$860$	3.94693e12	0.246046
$861$	1.75230e12	0.108666
$862$	1.57233e13	0.969978
$863$	2.43811e13	1.49625	0.748127	−	0.663556i	$-0.230953\pi$
$863$	2.43811e13	1.49625	0.748127	+	0.663556i	$0.230953\pi$
$864$	−2.60386e12	−0.158967
$865$	1.01530e12	0.0616623
$866$	−1.62933e12	−0.0984415
$867$	−9.11501e12	−0.547862
$868$	−1.07238e13	−0.641223
$869$	1.37836e13	0.819925
$870$	7.27818e12	0.430711
$871$	−2.70539e13	−1.59275
$872$	−1.95892e12	−0.114734
$873$	−9.58664e12	−0.558602
$874$	2.04305e13	1.18434
$875$	1.51680e13	0.874764
$876$	6.87537e12	0.394482
$877$	2.54386e13	1.45209	0.726046	−	0.687646i	$-0.241356\pi$
$877$	2.54386e13	1.45209	0.726046	+	0.687646i	$0.241356\pi$
$878$	8.58936e12	0.487793
$879$	9.11192e12	0.514826
$880$	3.82222e12	0.214854
$881$	2.62242e13	1.46660	0.733299	−	0.679906i	$-0.237979\pi$
$881$	2.62242e13	1.46660	0.733299	+	0.679906i	$0.237979\pi$
$882$	1.50073e12	0.0835015
$883$	−3.51862e13	−1.94782	−0.973910	−	0.226933i	$-0.927130\pi$
$883$	−3.51862e13	−1.94782	−0.973910	+	0.226933i	$0.927130\pi$
$884$	−2.72720e12	−0.150204
$885$	−1.21544e12	−0.0666021
$886$	−1.62007e13	−0.883245
$887$	−7.20872e12	−0.391023	−0.195511	−	0.980701i	$-0.562637\pi$
$887$	−7.20872e12	−0.391023	−0.195511	+	0.980701i	$0.562637\pi$
$888$	1.61869e13	0.873584
$889$	3.27284e12	0.175739
$890$	1.93829e13	1.03553
$891$	1.50813e12	0.0801659
$892$	−9.49399e12	−0.502120
$893$	4.07801e13	2.14594
$894$	9.12080e12	0.477545
$895$	−1.53286e13	−0.798547
$896$	2.01895e12	0.104650
$897$	−1.52616e13	−0.787110
$898$	1.57097e13	0.806165
$899$	3.86854e13	1.97528
$900$	6.42800e11	0.0326576
$901$	−1.10628e12	−0.0559246
$902$	−2.45034e12	−0.123253
$903$	5.70832e12	0.285702
$904$	−2.49039e13	−1.24025
$905$	6.85436e12	0.339663
$906$	8.95722e12	0.441668
$907$	1.82394e13	0.894905	0.447453	−	0.894308i	$-0.352331\pi$
$907$	1.82394e13	0.894905	0.447453	+	0.894308i	$0.352331\pi$
$908$	6.27409e12	0.306312
$909$	−8.71994e12	−0.423620
$910$	−1.60130e13	−0.774083
$911$	3.59657e13	1.73004	0.865020	−	0.501737i	$-0.167306\pi$
$911$	3.59657e13	1.73004	0.865020	+	0.501737i	$0.167306\pi$
$912$	6.95908e12	0.333100
$913$	−1.12476e13	−0.535725
$914$	1.65441e13	0.784125
$915$	−1.21251e12	−0.0571859
$916$	3.53392e12	0.165854
$917$	−1.32966e13	−0.620983
$918$	6.90264e11	0.0320792
$919$	3.31634e13	1.53369	0.766847	−	0.641830i	$-0.221824\pi$
$919$	3.31634e13	1.53369	0.766847	+	0.641830i	$0.221824\pi$
$920$	−1.93401e13	−0.890048
$921$	−2.27739e13	−1.04296
$922$	1.40923e12	0.0642233
$923$	6.02068e13	2.73047
$924$	−3.42016e12	−0.154356
$925$	−6.74044e12	−0.302726
$926$	−3.12653e13	−1.39737
$927$	−1.90366e12	−0.0846703
$928$	−2.13022e13	−0.942885
$929$	4.54694e11	0.0200285	0.0100142	−	0.999950i	$-0.496812\pi$
$929$	4.54694e11	0.0200285	0.0100142	+	0.999950i	$0.496812\pi$
$930$	1.48952e13	0.652941
$931$	1.33655e13	0.583059
$932$	1.82114e13	0.790628
$933$	1.97986e13	0.855398
$934$	7.24184e12	0.311378
$935$	3.37647e12	0.144481
$936$	−1.22518e13	−0.521746
$937$	−2.05486e13	−0.870871	−0.435436	−	0.900220i	$-0.643406\pi$
$937$	−2.05486e13	−0.870871	−0.435436	+	0.900220i	$0.643406\pi$
$938$	−1.55287e13	−0.654971
$939$	1.62637e13	0.682693
$940$	−1.20900e13	−0.505070
$941$	1.05780e13	0.439796	0.219898	−	0.975523i	$-0.429428\pi$
$941$	1.05780e13	0.439796	0.219898	+	0.975523i	$0.429428\pi$
$942$	7.49776e12	0.310243
$943$	5.26069e12	0.216641
$944$	−1.06754e12	−0.0437533
$945$	−3.39725e12	−0.138575
$946$	−7.98227e12	−0.324053
$947$	−5.86586e12	−0.237005	−0.118502	−	0.992954i	$-0.537809\pi$
$947$	−5.86586e12	−0.237005	−0.118502	+	0.992954i	$0.537809\pi$
$948$	−7.44009e12	−0.299185
$949$	5.45690e13	2.18398
$950$	−6.82973e12	−0.272049
$951$	−3.11680e12	−0.123565
$952$	−4.99831e12	−0.197223
$953$	−1.52754e12	−0.0599894	−0.0299947	−	0.999550i	$-0.509549\pi$
$953$	−1.52754e12	−0.0599894	−0.0299947	+	0.999550i	$0.509549\pi$
$954$	−1.55650e12	−0.0608387
$955$	−6.67579e12	−0.259709
$956$	1.64858e13	0.638335
$957$	1.23380e13	0.475491
$958$	9.55196e12	0.366393
$959$	1.14324e13	0.436470
$960$	−1.27266e13	−0.483606
$961$	5.27324e13	1.99445
$962$	4.02358e13	1.51469
$963$	−1.40075e13	−0.524859
$964$	2.40312e13	0.896249
$965$	−2.32273e13	−0.862235
$966$	−8.76006e12	−0.323676
$967$	−1.28750e13	−0.473510	−0.236755	−	0.971569i	$-0.576084\pi$
$967$	−1.28750e13	−0.473510	−0.236755	+	0.971569i	$0.576084\pi$
$968$	−1.40651e13	−0.514876
$969$	6.14750e12	0.223997
$970$	−3.01976e13	−1.09522
$971$	−1.83107e13	−0.661025	−0.330513	−	0.943802i	$-0.607222\pi$
$971$	−1.83107e13	−0.661025	−0.330513	+	0.943802i	$0.607222\pi$
$972$	−8.14056e11	−0.0292520
$973$	3.49727e13	1.25090
$974$	4.53489e9	0.000161455 0
$975$	5.10183e12	0.180803
$976$	−1.06497e12	−0.0375675
$977$	−4.64360e13	−1.63053	−0.815265	−	0.579088i	$-0.803409\pi$
$977$	−4.64360e13	−1.63053	−0.815265	+	0.579088i	$0.803409\pi$
$978$	7.17670e12	0.250842
$979$	3.28580e13	1.14319
$980$	−3.96246e12	−0.137230
$981$	−1.03305e12	−0.0356130
$982$	1.96501e11	0.00674314
$983$	−1.65522e13	−0.565413	−0.282706	−	0.959206i	$-0.591232\pi$
$983$	−1.65522e13	−0.565413	−0.282706	+	0.959206i	$0.591232\pi$
$984$	4.22320e12	0.143603
$985$	5.07646e13	1.71829
$986$	5.64705e12	0.190272
$987$	−1.74854e13	−0.586474
$988$	−3.41730e13	−1.14098
$989$	1.71373e13	0.569586
$990$	4.75057e12	0.157176
$991$	−5.38376e13	−1.77319	−0.886593	−	0.462551i	$-0.846934\pi$
$991$	−5.38376e13	−1.77319	−0.886593	+	0.462551i	$0.846934\pi$
$992$	−4.35962e13	−1.42938
$993$	2.39979e13	0.783253
$994$	3.45582e13	1.12283
$995$	−4.06022e13	−1.31325
$996$	6.07121e12	0.195483
$997$	−1.14792e11	−0.00367946	−0.00183973	−	0.999998i	$-0.500586\pi$
$997$	−1.14792e11	−0.00367946	−0.00183973	+	0.999998i	$0.500586\pi$
$998$	−1.11658e13	−0.356290
$999$	8.53624e12	0.271158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.a.1.9	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.a.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-16.6893 q^{2} +81.0000 q^{3} -233.469 q^{4} -1238.34 q^{5} -1351.83 q^{6} +5162.18 q^{7} +12441.3 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-16.6893 q^{2} +81.0000 q^{3} -233.469 q^{4} -1238.34 q^{5} -1351.83 q^{6} +5162.18 q^{7} +12441.3 q^{8} +6561.00 q^{9} +20667.0 q^{10} +35034.8 q^{11} -18911.0 q^{12} -150094. q^{13} -86152.9 q^{14} -100306. q^{15} -88100.2 q^{16} -77825.8 q^{17} -109498. q^{18} -975192. q^{19} +289114. q^{20} +418136. q^{21} -584704. q^{22} +1.25531e6 q^{23} +1.00775e6 q^{24} -419640. q^{25} +2.50496e6 q^{26} +531441. q^{27} -1.20521e6 q^{28} +4.34772e6 q^{29} +1.67402e6 q^{30} +8.89787e6 q^{31} -4.89963e6 q^{32} +2.83782e6 q^{33} +1.29885e6 q^{34} -6.39253e6 q^{35} -1.53179e6 q^{36} +1.60624e7 q^{37} +1.62752e7 q^{38} -1.21576e7 q^{39} -1.54066e7 q^{40} +4.19074e6 q^{41} -6.97838e6 q^{42} +1.36518e7 q^{43} -8.17953e6 q^{44} -8.12475e6 q^{45} -2.09502e7 q^{46} -4.18175e7 q^{47} -7.13611e6 q^{48} -1.37055e7 q^{49} +7.00347e6 q^{50} -6.30389e6 q^{51} +3.50424e7 q^{52} +1.42148e7 q^{53} -8.86935e6 q^{54} -4.33849e7 q^{55} +6.42243e7 q^{56} -7.89906e7 q^{57} -7.25601e7 q^{58} +1.21174e7 q^{59} +2.34182e7 q^{60} +1.20881e7 q^{61} -1.48499e8 q^{62} +3.38690e7 q^{63} +1.26878e8 q^{64} +1.85868e8 q^{65} -4.73610e7 q^{66} +1.80246e8 q^{67} +1.81699e7 q^{68} +1.01680e8 q^{69} +1.06687e8 q^{70} -4.01126e8 q^{71} +8.16275e7 q^{72} -3.63565e8 q^{73} -2.68070e8 q^{74} -3.39908e7 q^{75} +2.27677e8 q^{76} +1.80856e8 q^{77} +2.02902e8 q^{78} +3.93427e8 q^{79} +1.09098e8 q^{80} +4.30467e7 q^{81} -6.99402e7 q^{82} -3.21042e8 q^{83} -9.76218e7 q^{84} +9.63748e7 q^{85} -2.27838e8 q^{86} +3.52165e8 q^{87} +4.35879e8 q^{88} +9.37868e8 q^{89} +1.35596e8 q^{90} -7.74813e8 q^{91} -2.93077e8 q^{92} +7.20727e8 q^{93} +6.97903e8 q^{94} +1.20762e9 q^{95} -3.96870e8 q^{96} -1.46116e9 q^{97} +2.28735e8 q^{98} +2.29863e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9}+O(q^{10}) \) 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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