LMFDB - Embedded newform 177.10.a.c.1.20

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:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
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)

$f(q)$	$=$	$q+38.7622 q^{2} -81.0000 q^{3} +990.507 q^{4} -782.368 q^{5} -3139.74 q^{6} +8972.92 q^{7} +18548.0 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+38.7622 q^{2} -81.0000 q^{3} +990.507 q^{4} -782.368 q^{5} -3139.74 q^{6} +8972.92 q^{7} +18548.0 q^{8} +6561.00 q^{9} -30326.3 q^{10} +23175.9 q^{11} -80231.1 q^{12} +55195.9 q^{13} +347810. q^{14} +63371.8 q^{15} +211820. q^{16} -644241. q^{17} +254319. q^{18} +772218. q^{19} -774941. q^{20} -726807. q^{21} +898347. q^{22} +1.30489e6 q^{23} -1.50239e6 q^{24} -1.34103e6 q^{25} +2.13951e6 q^{26} -531441. q^{27} +8.88774e6 q^{28} +2.54967e6 q^{29} +2.45643e6 q^{30} +3.89754e6 q^{31} -1.28594e6 q^{32} -1.87725e6 q^{33} -2.49722e7 q^{34} -7.02013e6 q^{35} +6.49872e6 q^{36} -1.24288e7 q^{37} +2.99328e7 q^{38} -4.47087e6 q^{39} -1.45113e7 q^{40} +3.06543e7 q^{41} -2.81726e7 q^{42} +2.82292e7 q^{43} +2.29559e7 q^{44} -5.13312e6 q^{45} +5.05805e7 q^{46} -2.18793e7 q^{47} -1.71574e7 q^{48} +4.01597e7 q^{49} -5.19811e7 q^{50} +5.21835e7 q^{51} +5.46719e7 q^{52} +1.06767e8 q^{53} -2.05998e7 q^{54} -1.81321e7 q^{55} +1.66430e8 q^{56} -6.25496e7 q^{57} +9.88309e7 q^{58} +1.21174e7 q^{59} +6.27702e7 q^{60} +1.31642e8 q^{61} +1.51077e8 q^{62} +5.88714e7 q^{63} -1.58298e8 q^{64} -4.31835e7 q^{65} -7.27661e7 q^{66} +2.37913e8 q^{67} -6.38125e8 q^{68} -1.05696e8 q^{69} -2.72115e8 q^{70} -3.67874e8 q^{71} +1.21693e8 q^{72} +1.69715e8 q^{73} -4.81766e8 q^{74} +1.08623e8 q^{75} +7.64887e8 q^{76} +2.07955e8 q^{77} -1.73301e8 q^{78} -3.64180e7 q^{79} -1.65721e8 q^{80} +4.30467e7 q^{81} +1.18823e9 q^{82} -4.16778e8 q^{83} -7.19907e8 q^{84} +5.04033e8 q^{85} +1.09423e9 q^{86} -2.06524e8 q^{87} +4.29865e8 q^{88} +1.10229e9 q^{89} -1.98971e8 q^{90} +4.95269e8 q^{91} +1.29250e9 q^{92} -3.15701e8 q^{93} -8.48090e8 q^{94} -6.04158e8 q^{95} +1.04161e8 q^{96} +7.85297e8 q^{97} +1.55668e9 q^{98} +1.52057e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9}+O(q^{10}) $ 22 * q + 36 * q^2 - 1782 * q^3 + 5718 * q^4 + 808 * q^5 - 2916 * q^6 + 21249 * q^7 + 9435 * q^8 + 144342 * q^9	\( 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9} + 68441 q^{10} - 68033 q^{11} - 463158 q^{12} + 283817 q^{13} + 80285 q^{14} - 65448 q^{15} + 1067674 q^{16} + 436893 q^{17} + 236196 q^{18} + 1207580 q^{19} + 4209677 q^{20} - 1721169 q^{21} + 5460442 q^{22} + 2421966 q^{23} - 764235 q^{24} + 7441842 q^{25} - 2736526 q^{26} - 11691702 q^{27} + 4095246 q^{28} - 2320594 q^{29} - 5543721 q^{30} - 3178024 q^{31} - 20786874 q^{32} + 5510673 q^{33} - 13809336 q^{34} - 2630800 q^{35} + 37515798 q^{36} + 3981807 q^{37} - 24156377 q^{38} - 22989177 q^{39} - 29544450 q^{40} - 885225 q^{41} - 6503085 q^{42} + 12360835 q^{43} - 117711882 q^{44} + 5301288 q^{45} + 161066949 q^{46} + 75901252 q^{47} - 86481594 q^{48} + 170907951 q^{49} - 61318927 q^{50} - 35388333 q^{51} - 100762 q^{52} - 34790192 q^{53} - 19131876 q^{54} + 151773316 q^{55} - 417630344 q^{56} - 97813980 q^{57} - 432929294 q^{58} + 266581942 q^{59} - 340983837 q^{60} - 290555332 q^{61} + 158267098 q^{62} + 139414689 q^{63} - 131794443 q^{64} - 650690086 q^{65} - 442295802 q^{66} + 86645184 q^{67} + 62738541 q^{68} - 196179246 q^{69} + 429714610 q^{70} - 36567631 q^{71} + 61903035 q^{72} + 907807228 q^{73} - 171827242 q^{74} - 602789202 q^{75} + 1744504396 q^{76} - 310688725 q^{77} + 221658606 q^{78} + 2508604687 q^{79} + 3509441927 q^{80} + 947027862 q^{81} + 1759214793 q^{82} + 2185672083 q^{83} - 331714926 q^{84} + 2868860198 q^{85} + 2397001564 q^{86} + 187968114 q^{87} + 7683735877 q^{88} + 1320145942 q^{89} + 449041401 q^{90} + 3894639897 q^{91} + 3505964640 q^{92} + 257419944 q^{93} + 5406355552 q^{94} + 3093659122 q^{95} + 1683736794 q^{96} + 3904552980 q^{97} + 6137683116 q^{98} - 446364513 q^{99}+O(q^{100}) \) 22 * q + 36 * q^2 - 1782 * q^3 + 5718 * q^4 + 808 * q^5 - 2916 * q^6 + 21249 * q^7 + 9435 * q^8 + 144342 * q^9 + 68441 * q^10 - 68033 * q^11 - 463158 * q^12 + 283817 * q^13 + 80285 * q^14 - 65448 * q^15 + 1067674 * q^16 + 436893 * q^17 + 236196 * q^18 + 1207580 * q^19 + 4209677 * q^20 - 1721169 * q^21 + 5460442 * q^22 + 2421966 * q^23 - 764235 * q^24 + 7441842 * q^25 - 2736526 * q^26 - 11691702 * q^27 + 4095246 * q^28 - 2320594 * q^29 - 5543721 * q^30 - 3178024 * q^31 - 20786874 * q^32 + 5510673 * q^33 - 13809336 * q^34 - 2630800 * q^35 + 37515798 * q^36 + 3981807 * q^37 - 24156377 * q^38 - 22989177 * q^39 - 29544450 * q^40 - 885225 * q^41 - 6503085 * q^42 + 12360835 * q^43 - 117711882 * q^44 + 5301288 * q^45 + 161066949 * q^46 + 75901252 * q^47 - 86481594 * q^48 + 170907951 * q^49 - 61318927 * q^50 - 35388333 * q^51 - 100762 * q^52 - 34790192 * q^53 - 19131876 * q^54 + 151773316 * q^55 - 417630344 * q^56 - 97813980 * q^57 - 432929294 * q^58 + 266581942 * q^59 - 340983837 * q^60 - 290555332 * q^61 + 158267098 * q^62 + 139414689 * q^63 - 131794443 * q^64 - 650690086 * q^65 - 442295802 * q^66 + 86645184 * q^67 + 62738541 * q^68 - 196179246 * q^69 + 429714610 * q^70 - 36567631 * q^71 + 61903035 * q^72 + 907807228 * q^73 - 171827242 * q^74 - 602789202 * q^75 + 1744504396 * q^76 - 310688725 * q^77 + 221658606 * q^78 + 2508604687 * q^79 + 3509441927 * q^80 + 947027862 * q^81 + 1759214793 * q^82 + 2185672083 * q^83 - 331714926 * q^84 + 2868860198 * q^85 + 2397001564 * q^86 + 187968114 * q^87 + 7683735877 * q^88 + 1320145942 * q^89 + 449041401 * q^90 + 3894639897 * q^91 + 3505964640 * q^92 + 257419944 * q^93 + 5406355552 * q^94 + 3093659122 * q^95 + 1683736794 * q^96 + 3904552980 * q^97 + 6137683116 * q^98 - 446364513 * 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 $

$2$	38.7622	1.71306	0.856531	−	0.516095i	$-0.172615\pi$
$2$	38.7622	1.71306	0.856531	+	0.516095i	$0.172615\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	990.507	1.93458
$5$	−782.368	−0.559817	−0.279908	−	0.960027i	$-0.590304\pi$
$5$	−782.368	−0.559817	−0.279908	+	0.960027i	$0.590304\pi$
$6$	−3139.74	−0.989037
$7$	8972.92	1.41251	0.706257	−	0.707956i	$-0.250382\pi$
$7$	8972.92	1.41251	0.706257	+	0.707956i	$0.250382\pi$
$8$	18548.0	1.60100
$9$	6561.00	0.333333
$10$	−30326.3	−0.959001
$11$	23175.9	0.477275	0.238638	−	0.971109i	$-0.423299\pi$
$11$	23175.9	0.477275	0.238638	+	0.971109i	$0.423299\pi$
$12$	−80231.1	−1.11693
$13$	55195.9	0.535996	0.267998	−	0.963419i	$-0.413638\pi$
$13$	55195.9	0.535996	0.267998	+	0.963419i	$0.413638\pi$
$14$	347810.	2.41973
$15$	63371.8	0.323210
$16$	211820.	0.808030
$17$	−644241.	−1.87080	−0.935401	−	0.353588i	$-0.884961\pi$
$17$	−644241.	−1.87080	−0.935401	+	0.353588i	$0.884961\pi$
$18$	254319.	0.571021
$19$	772218.	1.35940	0.679702	−	0.733489i	$-0.262109\pi$
$19$	772218.	1.35940	0.679702	+	0.733489i	$0.262109\pi$
$20$	−774941.	−1.08301
$21$	−726807.	−0.815515
$22$	898347.	0.817602
$23$	1.30489e6	0.972298	0.486149	−	0.873876i	$-0.338401\pi$
$23$	1.30489e6	0.972298	0.486149	+	0.873876i	$0.338401\pi$
$24$	−1.50239e6	−0.924338
$25$	−1.34103e6	−0.686605
$26$	2.13951e6	0.918195
$27$	−531441.	−0.192450
$28$	8.88774e6	2.73263
$29$	2.54967e6	0.669412	0.334706	−	0.942323i	$-0.391363\pi$
$29$	2.54967e6	0.669412	0.334706	+	0.942323i	$0.391363\pi$
$30$	2.45643e6	0.553680
$31$	3.89754e6	0.757989	0.378994	−	0.925399i	$-0.376270\pi$
$31$	3.89754e6	0.757989	0.378994	+	0.925399i	$0.376270\pi$
$32$	−1.28594e6	−0.216794
$33$	−1.87725e6	−0.275555
$34$	−2.49722e7	−3.20480
$35$	−7.02013e6	−0.790749
$36$	6.49872e6	0.644861
$37$	−1.24288e7	−1.09024	−0.545118	−	0.838360i	$-0.683515\pi$
$37$	−1.24288e7	−1.09024	−0.545118	+	0.838360i	$0.683515\pi$
$38$	2.99328e7	2.32874
$39$	−4.47087e6	−0.309458
$40$	−1.45113e7	−0.896267
$41$	3.06543e7	1.69420	0.847100	−	0.531433i	$-0.178346\pi$
$41$	3.06543e7	1.69420	0.847100	+	0.531433i	$0.178346\pi$
$42$	−2.81726e7	−1.39703
$43$	2.82292e7	1.25919	0.629595	−	0.776924i	$-0.283221\pi$
$43$	2.82292e7	1.25919	0.629595	+	0.776924i	$0.283221\pi$
$44$	2.29559e7	0.923329
$45$	−5.13312e6	−0.186606
$46$	5.05805e7	1.66561
$47$	−2.18793e7	−0.654023	−0.327012	−	0.945020i	$-0.606042\pi$
$47$	−2.18793e7	−0.654023	−0.327012	+	0.945020i	$0.606042\pi$
$48$	−1.71574e7	−0.466517
$49$	4.01597e7	0.995196
$50$	−5.19811e7	−1.17620
$51$	5.21835e7	1.08011
$52$	5.46719e7	1.03693
$53$	1.06767e8	1.85864	0.929320	−	0.369275i	$-0.120394\pi$
$53$	1.06767e8	1.85864	0.929320	+	0.369275i	$0.120394\pi$
$54$	−2.05998e7	−0.329679
$55$	−1.81321e7	−0.267187
$56$	1.66430e8	2.26144
$57$	−6.25496e7	−0.784852
$58$	9.88309e7	1.14675
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	6.27702e7	0.625278
$61$	1.31642e8	1.21734	0.608669	−	0.793424i	$-0.291704\pi$
$61$	1.31642e8	1.21734	0.608669	+	0.793424i	$0.291704\pi$
$62$	1.51077e8	1.29848
$63$	5.88714e7	0.470838
$64$	−1.58298e8	−1.17941
$65$	−4.31835e7	−0.300060
$66$	−7.27661e7	−0.472043
$67$	2.37913e8	1.44238	0.721192	−	0.692735i	$-0.243594\pi$
$67$	2.37913e8	1.44238	0.721192	+	0.692735i	$0.243594\pi$
$68$	−6.38125e8	−3.61922
$69$	−1.05696e8	−0.561356
$70$	−2.72115e8	−1.35460
$71$	−3.67874e8	−1.71805	−0.859027	−	0.511930i	$-0.828931\pi$
$71$	−3.67874e8	−1.71805	−0.859027	+	0.511930i	$0.828931\pi$
$72$	1.21693e8	0.533667
$73$	1.69715e8	0.699469	0.349735	−	0.936849i	$-0.386272\pi$
$73$	1.69715e8	0.699469	0.349735	+	0.936849i	$0.386272\pi$
$74$	−4.81766e8	−1.86764
$75$	1.08623e8	0.396412
$76$	7.64887e8	2.62988
$77$	2.07955e8	0.674158
$78$	−1.73301e8	−0.530120
$79$	−3.64180e7	−0.105195	−0.0525974	−	0.998616i	$-0.516750\pi$
$79$	−3.64180e7	−0.105195	−0.0525974	+	0.998616i	$0.516750\pi$
$80$	−1.65721e8	−0.452349
$81$	4.30467e7	0.111111
$82$	1.18823e9	2.90227
$83$	−4.16778e8	−0.963948	−0.481974	−	0.876186i	$-0.660080\pi$
$83$	−4.16778e8	−0.963948	−0.481974	+	0.876186i	$0.660080\pi$
$84$	−7.19907e8	−1.57768
$85$	5.04033e8	1.04731
$86$	1.09423e9	2.15707
$87$	−2.06524e8	−0.386485
$88$	4.29865e8	0.764118
$89$	1.10229e9	1.86227	0.931134	−	0.364677i	$-0.118821\pi$
$89$	1.10229e9	1.86227	0.931134	+	0.364677i	$0.118821\pi$
$90$	−1.98971e8	−0.319667
$91$	4.95269e8	0.757102
$92$	1.29250e9	1.88099
$93$	−3.15701e8	−0.437625
$94$	−8.48090e8	−1.12038
$95$	−6.04158e8	−0.761017
$96$	1.04161e8	0.125166
$97$	7.85297e8	0.900661	0.450330	−	0.892862i	$-0.351306\pi$
$97$	7.85297e8	0.900661	0.450330	+	0.892862i	$0.351306\pi$
$98$	1.55668e9	1.70483
$99$	1.52057e8	0.159092
$100$	−1.32830e9	−1.32830
$101$	1.47978e9	1.41498	0.707491	−	0.706722i	$-0.249827\pi$
$101$	1.47978e9	1.41498	0.707491	+	0.706722i	$0.249827\pi$
$102$	2.02275e9	1.85029
$103$	1.56660e8	0.137148	0.0685741	−	0.997646i	$-0.478155\pi$
$103$	1.56660e8	0.137148	0.0685741	+	0.997646i	$0.478155\pi$
$104$	1.02377e9	0.858130
$105$	5.68630e8	0.456539
$106$	4.13852e9	3.18397
$107$	−2.04239e9	−1.50630	−0.753149	−	0.657850i	$-0.771466\pi$
$107$	−2.04239e9	−1.50630	−0.753149	+	0.657850i	$0.771466\pi$
$108$	−5.26396e8	−0.372311
$109$	6.43154e8	0.436411	0.218205	−	0.975903i	$-0.429980\pi$
$109$	6.43154e8	0.436411	0.218205	+	0.975903i	$0.429980\pi$
$110$	−7.02838e8	−0.457708
$111$	1.00673e9	0.629448
$112$	1.90065e9	1.14135
$113$	−2.17696e9	−1.25602	−0.628012	−	0.778204i	$-0.716131\pi$
$113$	−2.17696e9	−1.25602	−0.628012	+	0.778204i	$0.716131\pi$
$114$	−2.42456e9	−1.34450
$115$	−1.02091e9	−0.544309
$116$	2.52547e9	1.29503
$117$	3.62140e8	0.178665
$118$	4.69695e8	0.223022
$119$	−5.78072e9	−2.64253
$120$	1.17542e9	0.517460
$121$	−1.82083e9	−0.772208
$122$	5.10274e9	2.08538
$123$	−2.48300e9	−0.978147
$124$	3.86054e9	1.46639
$125$	2.57724e9	0.944190
$126$	2.28198e9	0.806575
$127$	5.22667e8	0.178282	0.0891412	−	0.996019i	$-0.471588\pi$
$127$	5.22667e8	0.178282	0.0891412	+	0.996019i	$0.471588\pi$
$128$	−5.47757e9	−1.80361
$129$	−2.28657e9	−0.726994
$130$	−1.67389e9	−0.514021
$131$	−5.05312e9	−1.49913	−0.749563	−	0.661932i	$-0.769737\pi$
$131$	−5.05312e9	−1.49913	−0.749563	+	0.661932i	$0.769737\pi$
$132$	−1.85942e9	−0.533084
$133$	6.92905e9	1.92018
$134$	9.22202e9	2.47090
$135$	4.15782e8	0.107737
$136$	−1.19494e10	−2.99516
$137$	−6.98295e9	−1.69354	−0.846771	−	0.531957i	$-0.821457\pi$
$137$	−6.98295e9	−1.69354	−0.846771	+	0.531957i	$0.821457\pi$
$138$	−4.09702e9	−0.961639
$139$	−1.15010e9	−0.261317	−0.130658	−	0.991427i	$-0.541709\pi$
$139$	−1.15010e9	−0.261317	−0.130658	+	0.991427i	$0.541709\pi$
$140$	−6.95348e9	−1.52977
$141$	1.77222e9	0.377601
$142$	−1.42596e10	−2.94314
$143$	1.27921e9	0.255818
$144$	1.38975e9	0.269343
$145$	−1.99478e9	−0.374748
$146$	6.57854e9	1.19823
$147$	−3.25294e9	−0.574577
$148$	−1.23108e10	−2.10915
$149$	−4.91077e9	−0.816228	−0.408114	−	0.912931i	$-0.633813\pi$
$149$	−4.91077e9	−0.816228	−0.408114	+	0.912931i	$0.633813\pi$
$150$	4.21047e9	0.679078
$151$	4.74005e9	0.741970	0.370985	−	0.928639i	$-0.379020\pi$
$151$	4.74005e9	0.741970	0.370985	+	0.928639i	$0.379020\pi$
$152$	1.43231e10	2.17641
$153$	−4.22686e9	−0.623601
$154$	8.06080e9	1.15487
$155$	−3.04931e9	−0.424335
$156$	−4.42843e9	−0.598672
$157$	−2.35916e9	−0.309891	−0.154946	−	0.987923i	$-0.549520\pi$
$157$	−2.35916e9	−0.309891	−0.154946	+	0.987923i	$0.549520\pi$
$158$	−1.41164e9	−0.180205
$159$	−8.64812e9	−1.07309
$160$	1.00608e9	0.121365
$161$	1.17087e10	1.37338
$162$	1.66858e9	0.190340
$163$	9.30511e9	1.03247	0.516235	−	0.856447i	$-0.327333\pi$
$163$	9.30511e9	1.03247	0.516235	+	0.856447i	$0.327333\pi$
$164$	3.03633e10	3.27757
$165$	1.46870e9	0.154260
$166$	−1.61552e10	−1.65130
$167$	3.05481e9	0.303920	0.151960	−	0.988387i	$-0.451441\pi$
$167$	3.05481e9	0.303920	0.151960	+	0.988387i	$0.451441\pi$
$168$	−1.34808e10	−1.30564
$169$	−7.55791e9	−0.712708
$170$	1.95374e10	1.79410
$171$	5.06652e9	0.453135
$172$	2.79613e10	2.43601
$173$	1.61535e10	1.37107	0.685534	−	0.728041i	$-0.259569\pi$
$173$	1.61535e10	1.37107	0.685534	+	0.728041i	$0.259569\pi$
$174$	−8.00530e9	−0.662074
$175$	−1.20329e10	−0.969839
$176$	4.90912e9	0.385653
$177$	−9.81506e8	−0.0751646
$178$	4.27273e10	3.19018
$179$	−1.09942e10	−0.800436	−0.400218	−	0.916420i	$-0.631066\pi$
$179$	−1.09942e10	−0.800436	−0.400218	+	0.916420i	$0.631066\pi$
$180$	−5.08439e9	−0.361004
$181$	−1.47891e10	−1.02421	−0.512104	−	0.858924i	$-0.671134\pi$
$181$	−1.47891e10	−1.02421	−0.512104	+	0.858924i	$0.671134\pi$
$182$	1.91977e10	1.29696
$183$	−1.06630e10	−0.702830
$184$	2.42031e10	1.55665
$185$	9.72387e9	0.610332
$186$	−1.22372e10	−0.749679
$187$	−1.49308e10	−0.892887
$188$	−2.16716e10	−1.26526
$189$	−4.76858e9	−0.271838
$190$	−2.34185e10	−1.30367
$191$	−7.33579e9	−0.398838	−0.199419	−	0.979914i	$-0.563906\pi$
$191$	−7.33579e9	−0.398838	−0.199419	+	0.979914i	$0.563906\pi$
$192$	1.28221e10	0.680934
$193$	−2.32650e10	−1.20697	−0.603484	−	0.797375i	$-0.706221\pi$
$193$	−2.32650e10	−1.20697	−0.603484	+	0.797375i	$0.706221\pi$
$194$	3.04398e10	1.54289
$195$	3.49786e9	0.173240
$196$	3.97785e10	1.92529
$197$	1.54023e10	0.728598	0.364299	−	0.931282i	$-0.381309\pi$
$197$	1.54023e10	0.728598	0.364299	+	0.931282i	$0.381309\pi$
$198$	5.89406e9	0.272534
$199$	−3.60701e9	−0.163045	−0.0815227	−	0.996671i	$-0.525978\pi$
$199$	−3.60701e9	−0.163045	−0.0815227	+	0.996671i	$0.525978\pi$
$200$	−2.48733e10	−1.09926
$201$	−1.92709e10	−0.832761
$202$	5.73595e10	2.42395
$203$	2.28780e10	0.945554
$204$	5.16881e10	2.08956
$205$	−2.39830e10	−0.948442
$206$	6.07247e9	0.234943
$207$	8.56140e9	0.324099
$208$	1.16916e10	0.433101
$209$	1.78968e10	0.648810
$210$	2.20414e10	0.782080
$211$	1.86756e10	0.648639	0.324320	−	0.945948i	$-0.394865\pi$
$211$	1.86756e10	0.648639	0.324320	+	0.945948i	$0.394865\pi$
$212$	1.05753e11	3.59570
$213$	2.97978e10	0.991919
$214$	−7.91674e10	−2.58038
$215$	−2.20857e10	−0.704916
$216$	−9.85715e9	−0.308113
$217$	3.49723e10	1.07067
$218$	2.49300e10	0.747599
$219$	−1.37470e10	−0.403839
$220$	−1.79599e10	−0.516895
$221$	−3.55594e10	−1.00274
$222$	3.90231e10	1.07828
$223$	4.34537e10	1.17667	0.588335	−	0.808617i	$-0.299784\pi$
$223$	4.34537e10	1.17667	0.588335	+	0.808617i	$0.299784\pi$
$224$	−1.15387e10	−0.306224
$225$	−8.79847e9	−0.228868
$226$	−8.43838e10	−2.15165
$227$	5.10212e10	1.27536	0.637682	−	0.770300i	$-0.279893\pi$
$227$	5.10212e10	1.27536	0.637682	+	0.770300i	$0.279893\pi$
$228$	−6.19558e10	−1.51836
$229$	−7.68627e10	−1.84695	−0.923476	−	0.383655i	$-0.874665\pi$
$229$	−7.68627e10	−1.84695	−0.923476	+	0.383655i	$0.874665\pi$
$230$	−3.95725e10	−0.932435
$231$	−1.68444e10	−0.389225
$232$	4.72913e10	1.07173
$233$	8.12834e9	0.180676	0.0903380	−	0.995911i	$-0.471205\pi$
$233$	8.12834e9	0.180676	0.0903380	+	0.995911i	$0.471205\pi$
$234$	1.40373e10	0.306065
$235$	1.71177e10	0.366133
$236$	1.20023e10	0.251861
$237$	2.94986e9	0.0607343
$238$	−2.24073e11	−4.52683
$239$	3.68954e8	0.00731445	0.00365722	−	0.999993i	$-0.498836\pi$
$239$	3.68954e8	0.00731445	0.00365722	+	0.999993i	$0.498836\pi$
$240$	1.34234e10	0.261164
$241$	−5.72365e10	−1.09294	−0.546470	−	0.837479i	$-0.684029\pi$
$241$	−5.72365e10	−1.09294	−0.546470	+	0.837479i	$0.684029\pi$
$242$	−7.05792e10	−1.32284
$243$	−3.48678e9	−0.0641500
$244$	1.30393e11	2.35504
$245$	−3.14197e10	−0.557127
$246$	−9.62466e10	−1.67563
$247$	4.26232e10	0.728635
$248$	7.22914e10	1.21354
$249$	3.37590e10	0.556535
$250$	9.98993e10	1.61746
$251$	−5.86523e10	−0.932725	−0.466362	−	0.884594i	$-0.654436\pi$
$251$	−5.86523e10	−0.932725	−0.466362	+	0.884594i	$0.654436\pi$
$252$	5.83125e10	0.910876
$253$	3.02420e10	0.464054
$254$	2.02597e10	0.305409
$255$	−4.08267e10	−0.604663
$256$	−1.31274e11	−1.91029
$257$	−2.92462e10	−0.418186	−0.209093	−	0.977896i	$-0.567051\pi$
$257$	−2.92462e10	−0.418186	−0.209093	+	0.977896i	$0.567051\pi$
$258$	−8.86324e10	−1.24539
$259$	−1.11522e11	−1.53997
$260$	−4.27735e10	−0.580491
$261$	1.67284e10	0.223137
$262$	−1.95870e11	−2.56810
$263$	−3.94332e9	−0.0508232	−0.0254116	−	0.999677i	$-0.508090\pi$
$263$	−3.94332e9	−0.0508232	−0.0254116	+	0.999677i	$0.508090\pi$
$264$	−3.48191e10	−0.441164
$265$	−8.35310e10	−1.04050
$266$	2.68585e11	3.28938
$267$	−8.92858e10	−1.07518
$268$	2.35654e11	2.79041
$269$	−3.59825e10	−0.418992	−0.209496	−	0.977809i	$-0.567182\pi$
$269$	−3.59825e10	−0.418992	−0.209496	+	0.977809i	$0.567182\pi$
$270$	1.61166e10	0.184560
$271$	−2.98145e10	−0.335789	−0.167894	−	0.985805i	$-0.553697\pi$
$271$	−2.98145e10	−0.335789	−0.167894	+	0.985805i	$0.553697\pi$
$272$	−1.36463e11	−1.51167
$273$	−4.01168e10	−0.437113
$274$	−2.70674e11	−2.90114
$275$	−3.10794e10	−0.327700
$276$	−1.04693e11	−1.08599
$277$	7.15684e9	0.0730403	0.0365201	−	0.999333i	$-0.488373\pi$
$277$	7.15684e9	0.0730403	0.0365201	+	0.999333i	$0.488373\pi$
$278$	−4.45802e10	−0.447652
$279$	2.55717e10	0.252663
$280$	−1.30209e11	−1.26599
$281$	1.01358e11	0.969795	0.484898	−	0.874571i	$-0.338857\pi$
$281$	1.01358e11	0.969795	0.484898	+	0.874571i	$0.338857\pi$
$282$	6.86953e10	0.646854
$283$	6.48347e10	0.600853	0.300427	−	0.953805i	$-0.402871\pi$
$283$	6.48347e10	0.600853	0.300427	+	0.953805i	$0.402871\pi$
$284$	−3.64382e11	−3.32372
$285$	4.89368e10	0.439373
$286$	4.95851e10	0.438232
$287$	2.75059e11	2.39308
$288$	−8.43707e9	−0.0722646
$289$	2.96458e11	2.49990
$290$	−7.73221e10	−0.641967
$291$	−6.36091e10	−0.519997
$292$	1.68104e11	1.35318
$293$	−1.83636e11	−1.45564	−0.727819	−	0.685769i	$-0.759466\pi$
$293$	−1.83636e11	−1.45564	−0.727819	+	0.685769i	$0.759466\pi$
$294$	−1.26091e11	−0.984286
$295$	−9.48023e9	−0.0728819
$296$	−2.30528e11	−1.74547
$297$	−1.23166e10	−0.0918517
$298$	−1.90352e11	−1.39825
$299$	7.20247e10	0.521148
$300$	1.07592e11	0.766891
$301$	2.53299e11	1.77862
$302$	1.83735e11	1.27104
$303$	−1.19862e11	−0.816941
$304$	1.63571e11	1.09844
$305$	−1.02993e11	−0.681486
$306$	−1.63842e11	−1.06827
$307$	−3.31583e10	−0.213044	−0.106522	−	0.994310i	$-0.533971\pi$
$307$	−3.31583e10	−0.213044	−0.106522	+	0.994310i	$0.533971\pi$
$308$	2.05981e11	1.30421
$309$	−1.26894e10	−0.0791825
$310$	−1.18198e11	−0.726912
$311$	−2.91372e11	−1.76614	−0.883071	−	0.469239i	$-0.844528\pi$
$311$	−2.91372e11	−1.76614	−0.883071	+	0.469239i	$0.844528\pi$
$312$	−8.29255e10	−0.495442
$313$	1.72605e11	1.01649	0.508245	−	0.861212i	$-0.330294\pi$
$313$	1.72605e11	1.01649	0.508245	+	0.861212i	$0.330294\pi$
$314$	−9.14463e10	−0.530863
$315$	−4.60591e10	−0.263583
$316$	−3.60723e10	−0.203508
$317$	−1.11801e11	−0.621843	−0.310922	−	0.950436i	$-0.600638\pi$
$317$	−1.11801e11	−0.621843	−0.310922	+	0.950436i	$0.600638\pi$
$318$	−3.35220e11	−1.83826
$319$	5.90909e10	0.319494
$320$	1.23847e11	0.660255
$321$	1.65433e11	0.869662
$322$	4.53855e11	2.35269
$323$	−4.97494e11	−2.54318
$324$	4.26381e10	0.214954
$325$	−7.40191e10	−0.368018
$326$	3.60686e11	1.76869
$327$	−5.20954e10	−0.251962
$328$	5.68576e11	2.71242
$329$	−1.96321e11	−0.923817
$330$	5.69299e10	0.264258
$331$	−3.47020e11	−1.58902	−0.794509	−	0.607253i	$-0.792271\pi$
$331$	−3.47020e11	−1.58902	−0.794509	+	0.607253i	$0.792271\pi$
$332$	−4.12822e11	−1.86484
$333$	−8.15451e10	−0.363412
$334$	1.18411e11	0.520635
$335$	−1.86135e11	−0.807471
$336$	−1.53952e11	−0.658961
$337$	−4.91604e10	−0.207625	−0.103813	−	0.994597i	$-0.533104\pi$
$337$	−4.91604e10	−0.207625	−0.103813	+	0.994597i	$0.533104\pi$
$338$	−2.92961e11	−1.22091
$339$	1.76334e11	0.725166
$340$	4.99248e11	2.02610
$341$	9.03288e10	0.361769
$342$	1.96389e11	0.776248
$343$	−1.73949e9	−0.00678574
$344$	5.23595e11	2.01596
$345$	8.26933e10	0.314257
$346$	6.26144e11	2.34872
$347$	−3.01656e11	−1.11694	−0.558469	−	0.829526i	$-0.688611\pi$
$347$	−3.01656e11	−1.11694	−0.558469	+	0.829526i	$0.688611\pi$
$348$	−2.04563e11	−0.747688
$349$	−2.94274e11	−1.06179	−0.530894	−	0.847438i	$-0.678144\pi$
$349$	−2.94274e11	−1.06179	−0.530894	+	0.847438i	$0.678144\pi$
$350$	−4.66422e11	−1.66140
$351$	−2.93334e10	−0.103153
$352$	−2.98028e10	−0.103470
$353$	8.08325e10	0.277077	0.138538	−	0.990357i	$-0.455760\pi$
$353$	8.08325e10	0.277077	0.138538	+	0.990357i	$0.455760\pi$
$354$	−3.80453e10	−0.128762
$355$	2.87813e11	0.961796
$356$	1.09183e12	3.60271
$357$	4.68238e11	1.52567
$358$	−4.26161e11	−1.37120
$359$	2.24898e11	0.714596	0.357298	−	0.933990i	$-0.383698\pi$
$359$	2.24898e11	0.714596	0.357298	+	0.933990i	$0.383698\pi$
$360$	−9.52089e10	−0.298756
$361$	2.73632e11	0.847978
$362$	−5.73257e11	−1.75453
$363$	1.47487e11	0.445835
$364$	4.90567e11	1.46468
$365$	−1.32780e11	−0.391575
$366$	−4.13322e11	−1.20399
$367$	−3.79754e11	−1.09271	−0.546355	−	0.837554i	$-0.683985\pi$
$367$	−3.79754e11	−1.09271	−0.546355	+	0.837554i	$0.683985\pi$
$368$	2.76403e11	0.785646
$369$	2.01123e11	0.564733
$370$	3.76918e11	1.04554
$371$	9.58012e11	2.62536
$372$	−3.12704e11	−0.846622
$373$	4.33543e11	1.15969	0.579845	−	0.814726i	$-0.303113\pi$
$373$	4.33543e11	1.15969	0.579845	+	0.814726i	$0.303113\pi$
$374$	−5.78752e11	−1.52957
$375$	−2.08756e11	−0.545128
$376$	−4.05817e11	−1.04709
$377$	1.40732e11	0.358802
$378$	−1.84841e11	−0.465676
$379$	−6.05335e11	−1.50702	−0.753510	−	0.657436i	$-0.771641\pi$
$379$	−6.05335e11	−1.50702	−0.753510	+	0.657436i	$0.771641\pi$
$380$	−5.98423e11	−1.47225
$381$	−4.23360e10	−0.102931
$382$	−2.84351e11	−0.683235
$383$	−2.57434e11	−0.611324	−0.305662	−	0.952140i	$-0.598878\pi$
$383$	−2.57434e11	−0.611324	−0.305662	+	0.952140i	$0.598878\pi$
$384$	4.43683e11	1.04132
$385$	−1.62698e11	−0.377405
$386$	−9.01804e11	−2.06761
$387$	1.85212e11	0.419730
$388$	7.77842e11	1.74240
$389$	−8.88676e11	−1.96775	−0.983875	−	0.178856i	$-0.942760\pi$
$389$	−8.88676e11	−1.96775	−0.983875	+	0.178856i	$0.942760\pi$
$390$	1.35585e11	0.296770
$391$	−8.40664e11	−1.81898
$392$	7.44882e11	1.59331
$393$	4.09302e11	0.865521
$394$	5.97027e11	1.24813
$395$	2.84923e10	0.0588899
$396$	1.50613e11	0.307776
$397$	7.40056e11	1.49523	0.747614	−	0.664133i	$-0.231199\pi$
$397$	7.40056e11	1.49523	0.747614	+	0.664133i	$0.231199\pi$
$398$	−1.39816e11	−0.279307
$399$	−5.61253e11	−1.10861
$400$	−2.84056e11	−0.554798
$401$	−5.52820e11	−1.06766	−0.533831	−	0.845591i	$-0.679248\pi$
$401$	−5.52820e11	−1.06766	−0.533831	+	0.845591i	$0.679248\pi$
$402$	−7.46984e11	−1.42657
$403$	2.15128e11	0.406279
$404$	1.46573e12	2.73740
$405$	−3.36784e10	−0.0622019
$406$	8.86802e11	1.61979
$407$	−2.88047e11	−0.520342
$408$	9.67898e11	1.72925
$409$	1.05922e11	0.187168	0.0935842	−	0.995611i	$-0.470168\pi$
$409$	1.05922e11	0.187168	0.0935842	+	0.995611i	$0.470168\pi$
$410$	−9.29633e11	−1.62474
$411$	5.65619e11	0.977767
$412$	1.55173e11	0.265325
$413$	1.08728e11	0.183894
$414$	3.31858e11	0.555202
$415$	3.26074e11	0.539634
$416$	−7.09788e10	−0.116201
$417$	9.31578e10	0.150871
$418$	6.93719e11	1.11145
$419$	5.41868e11	0.858876	0.429438	−	0.903096i	$-0.358712\pi$
$419$	5.41868e11	0.858876	0.429438	+	0.903096i	$0.358712\pi$
$420$	5.63232e11	0.883213
$421$	5.16303e11	0.801005	0.400502	−	0.916296i	$-0.368836\pi$
$421$	5.16303e11	0.801005	0.400502	+	0.916296i	$0.368836\pi$
$422$	7.23907e11	1.11116
$423$	−1.43550e11	−0.218008
$424$	1.98031e12	2.97568
$425$	8.63943e11	1.28450
$426$	1.15503e12	1.69922
$427$	1.18122e12	1.71951
$428$	−2.02300e12	−2.91406
$429$	−1.03616e11	−0.147696
$430$	−8.56088e11	−1.20756
$431$	−5.12189e11	−0.714962	−0.357481	−	0.933920i	$-0.616364\pi$
$431$	−5.12189e11	−0.714962	−0.357481	+	0.933920i	$0.616364\pi$
$432$	−1.12570e11	−0.155506
$433$	4.81703e11	0.658543	0.329272	−	0.944235i	$-0.393197\pi$
$433$	4.81703e11	0.658543	0.329272	+	0.944235i	$0.393197\pi$
$434$	1.35560e12	1.83412
$435$	1.61577e11	0.216361
$436$	6.37048e11	0.844273
$437$	1.00766e12	1.32175
$438$	−5.32862e11	−0.691801
$439$	−1.13484e12	−1.45830	−0.729148	−	0.684356i	$-0.760084\pi$
$439$	−1.13484e12	−1.45830	−0.729148	+	0.684356i	$0.760084\pi$
$440$	−3.36313e11	−0.427766
$441$	2.63488e11	0.331732
$442$	−1.37836e12	−1.71776
$443$	2.63450e11	0.324999	0.162499	−	0.986709i	$-0.448044\pi$
$443$	2.63450e11	0.324999	0.162499	+	0.986709i	$0.448044\pi$
$444$	9.97173e11	1.21772
$445$	−8.62399e11	−1.04253
$446$	1.68436e12	2.01571
$447$	3.97772e11	0.471249
$448$	−1.42040e12	−1.66594
$449$	3.92678e11	0.455961	0.227981	−	0.973666i	$-0.426788\pi$
$449$	3.92678e11	0.455961	0.227981	+	0.973666i	$0.426788\pi$
$450$	−3.41048e11	−0.392066
$451$	7.10441e11	0.808600
$452$	−2.15630e12	−2.42988
$453$	−3.83944e11	−0.428377
$454$	1.97769e12	2.18478
$455$	−3.87482e11	−0.423839
$456$	−1.16017e12	−1.25655
$457$	−2.03984e11	−0.218763	−0.109382	−	0.994000i	$-0.534887\pi$
$457$	−2.03984e11	−0.218763	−0.109382	+	0.994000i	$0.534887\pi$
$458$	−2.97937e12	−3.16395
$459$	3.42376e11	0.360036
$460$	−1.01121e12	−1.05301
$461$	4.72398e11	0.487140	0.243570	−	0.969883i	$-0.421681\pi$
$461$	4.72398e11	0.487140	0.243570	+	0.969883i	$0.421681\pi$
$462$	−6.52925e11	−0.666767
$463$	1.40807e12	1.42399	0.711997	−	0.702182i	$-0.247791\pi$
$463$	1.40807e12	1.42399	0.711997	+	0.702182i	$0.247791\pi$
$464$	5.40073e11	0.540905
$465$	2.46994e11	0.244990
$466$	3.15072e11	0.309509
$467$	1.98958e12	1.93569	0.967845	−	0.251549i	$-0.0809398\pi$
$467$	1.98958e12	1.93569	0.967845	+	0.251549i	$0.0809398\pi$
$468$	3.58702e11	0.345643
$469$	2.13477e12	2.03739
$470$	6.63518e11	0.627209
$471$	1.91092e11	0.178916
$472$	2.24752e11	0.208433
$473$	6.54237e11	0.600980
$474$	1.14343e11	0.104042
$475$	−1.03556e12	−0.933373
$476$	−5.72584e12	−5.11220
$477$	7.00498e11	0.619547
$478$	1.43015e10	0.0125301
$479$	9.67025e11	0.839320	0.419660	−	0.907681i	$-0.362149\pi$
$479$	9.67025e11	0.839320	0.419660	+	0.907681i	$0.362149\pi$
$480$	−8.14925e10	−0.0700700
$481$	−6.86017e11	−0.584362
$482$	−2.21861e12	−1.87228
$483$	−9.48404e11	−0.792924
$484$	−1.80354e12	−1.49390
$485$	−6.14391e11	−0.504205
$486$	−1.35155e11	−0.109893
$487$	1.03101e11	0.0830585	0.0415292	−	0.999137i	$-0.486777\pi$
$487$	1.03101e11	0.0830585	0.0415292	+	0.999137i	$0.486777\pi$
$488$	2.44170e12	1.94896
$489$	−7.53714e11	−0.596097
$490$	−1.21790e12	−0.954394
$491$	9.83800e11	0.763906	0.381953	−	0.924182i	$-0.375252\pi$
$491$	9.83800e11	0.763906	0.381953	+	0.924182i	$0.375252\pi$
$492$	−2.45943e12	−1.89231
$493$	−1.64260e12	−1.25234
$494$	1.65217e12	1.24820
$495$	−1.18964e11	−0.0890622
$496$	8.25578e11	0.612478
$497$	−3.30091e12	−2.42678
$498$	1.30857e12	0.953380
$499$	3.95589e11	0.285622	0.142811	−	0.989750i	$-0.454386\pi$
$499$	3.95589e11	0.285622	0.142811	+	0.989750i	$0.454386\pi$
$500$	2.55277e12	1.82661
$501$	−2.47440e11	−0.175469
$502$	−2.27349e12	−1.59782
$503$	6.12598e9	0.00426697	0.00213348	−	0.999998i	$-0.499321\pi$
$503$	6.12598e9	0.00426697	0.00213348	+	0.999998i	$0.499321\pi$
$504$	1.09194e12	0.753812
$505$	−1.15773e12	−0.792131
$506$	1.17225e12	0.794953
$507$	6.12191e11	0.411482
$508$	5.17705e11	0.344902
$509$	6.88882e11	0.454899	0.227449	−	0.973790i	$-0.426961\pi$
$509$	6.88882e11	0.454899	0.227449	+	0.973790i	$0.426961\pi$
$510$	−1.58253e12	−1.03583
$511$	1.52284e12	0.988010
$512$	−2.28395e12	−1.46883
$513$	−4.10388e11	−0.261617
$514$	−1.13365e12	−0.716379
$515$	−1.22566e11	−0.0767778
$516$	−2.26486e12	−1.40643
$517$	−5.07072e11	−0.312149
$518$	−4.32285e12	−2.63807
$519$	−1.30843e12	−0.791586
$520$	−8.00966e11	−0.480396
$521$	2.58272e12	1.53570	0.767852	−	0.640627i	$-0.221325\pi$
$521$	2.58272e12	1.53570	0.767852	+	0.640627i	$0.221325\pi$
$522$	6.48430e11	0.382248
$523$	1.15585e12	0.675531	0.337765	−	0.941230i	$-0.390329\pi$
$523$	1.15585e12	0.675531	0.337765	+	0.941230i	$0.390329\pi$
$524$	−5.00515e12	−2.90019
$525$	9.74667e11	0.559937
$526$	−1.52852e11	−0.0870633
$527$	−2.51095e12	−1.41805
$528$	−3.97639e11	−0.222657
$529$	−9.84099e10	−0.0546372
$530$	−3.23785e12	−1.78244
$531$	7.95020e10	0.0433963
$532$	6.86327e12	3.71474
$533$	1.69199e12	0.908085
$534$	−3.46091e12	−1.84185
$535$	1.59790e12	0.843251
$536$	4.41280e12	2.30926
$537$	8.90534e11	0.462132
$538$	−1.39476e12	−0.717760
$539$	9.30737e11	0.474982
$540$	4.11835e11	0.208426
$541$	6.25431e11	0.313900	0.156950	−	0.987607i	$-0.449834\pi$
$541$	6.25431e11	0.313900	0.156950	+	0.987607i	$0.449834\pi$
$542$	−1.15568e12	−0.575227
$543$	1.19792e12	0.591326
$544$	8.28456e11	0.405578
$545$	−5.03183e11	−0.244310
$546$	−1.55501e12	−0.748802
$547$	−1.04302e12	−0.498139	−0.249069	−	0.968486i	$-0.580125\pi$
$547$	−1.04302e12	−0.498139	−0.249069	+	0.968486i	$0.580125\pi$
$548$	−6.91666e12	−3.27630
$549$	8.63705e11	0.405779
$550$	−1.20471e12	−0.561370
$551$	1.96890e12	0.910001
$552$	−1.96045e12	−0.898732
$553$	−3.26776e11	−0.148589
$554$	2.77415e11	0.125123
$555$	−7.87633e11	−0.352375
$556$	−1.13918e12	−0.505539
$557$	−2.65888e12	−1.17044	−0.585221	−	0.810874i	$-0.698992\pi$
$557$	−2.65888e12	−1.17044	−0.585221	+	0.810874i	$0.698992\pi$
$558$	9.91217e11	0.432827
$559$	1.55814e12	0.674921
$560$	−1.48701e12	−0.638949
$561$	1.20940e12	0.515509
$562$	3.92886e12	1.66132
$563$	−3.94005e11	−0.165277	−0.0826387	−	0.996580i	$-0.526335\pi$
$563$	−3.94005e11	−0.165277	−0.0826387	+	0.996580i	$0.526335\pi$
$564$	1.75540e12	0.730500
$565$	1.70319e12	0.703143
$566$	2.51313e12	1.02930
$567$	3.86255e11	0.156946
$568$	−6.82332e12	−2.75061
$569$	−8.48239e11	−0.339245	−0.169622	−	0.985509i	$-0.554255\pi$
$569$	−8.48239e11	−0.339245	−0.169622	+	0.985509i	$0.554255\pi$
$570$	1.89690e12	0.752674
$571$	9.38062e11	0.369291	0.184646	−	0.982805i	$-0.440886\pi$
$571$	9.38062e11	0.369291	0.184646	+	0.982805i	$0.440886\pi$
$572$	1.26707e12	0.494901
$573$	5.94199e11	0.230269
$574$	1.06619e13	4.09950
$575$	−1.74989e12	−0.667585
$576$	−1.03859e12	−0.393137
$577$	2.77817e12	1.04344	0.521721	−	0.853116i	$-0.325290\pi$
$577$	2.77817e12	1.04344	0.521721	+	0.853116i	$0.325290\pi$
$578$	1.14914e13	4.28249
$579$	1.88447e12	0.696843
$580$	−1.97585e12	−0.724982
$581$	−3.73972e12	−1.36159
$582$	−2.46563e12	−0.890787
$583$	2.47442e12	0.887083
$584$	3.14788e12	1.11985
$585$	−2.83327e11	−0.100020
$586$	−7.11813e12	−2.49360
$587$	3.10109e12	1.07806	0.539030	−	0.842286i	$-0.318791\pi$
$587$	3.10109e12	1.07806	0.539030	+	0.842286i	$0.318791\pi$
$588$	−3.22206e12	−1.11157
$589$	3.00975e12	1.03041
$590$	−3.67475e11	−0.124851
$591$	−1.24759e12	−0.420656
$592$	−2.63266e12	−0.880943
$593$	−2.44676e12	−0.812540	−0.406270	−	0.913753i	$-0.633171\pi$
$593$	−2.44676e12	−0.812540	−0.406270	+	0.913753i	$0.633171\pi$
$594$	−4.77418e11	−0.157348
$595$	4.52265e12	1.47934
$596$	−4.86415e12	−1.57906
$597$	2.92168e11	0.0941343
$598$	2.79183e12	0.892759
$599$	−3.55102e12	−1.12702	−0.563511	−	0.826108i	$-0.690550\pi$
$599$	−3.55102e12	−1.12702	−0.563511	+	0.826108i	$0.690550\pi$
$600$	2.01474e12	0.634655
$601$	4.12990e11	0.129123	0.0645616	−	0.997914i	$-0.479435\pi$
$601$	4.12990e11	0.129123	0.0645616	+	0.997914i	$0.479435\pi$
$602$	9.81842e12	3.04689
$603$	1.56095e12	0.480795
$604$	4.69505e12	1.43540
$605$	1.42456e12	0.432295
$606$	−4.64612e12	−1.39947
$607$	−3.64443e12	−1.08963	−0.544817	−	0.838555i	$-0.683401\pi$
$607$	−3.64443e12	−1.08963	−0.544817	+	0.838555i	$0.683401\pi$
$608$	−9.93027e11	−0.294710
$609$	−1.85312e12	−0.545916
$610$	−3.99222e12	−1.16743
$611$	−1.20765e12	−0.350554
$612$	−4.18674e12	−1.20641
$613$	−3.75688e11	−0.107462	−0.0537310	−	0.998555i	$-0.517111\pi$
$613$	−3.75688e11	−0.107462	−0.0537310	+	0.998555i	$0.517111\pi$
$614$	−1.28529e12	−0.364958
$615$	1.94262e12	0.547583
$616$	3.85715e12	1.07933
$617$	−3.87030e12	−1.07513	−0.537565	−	0.843222i	$-0.680656\pi$
$617$	−3.87030e12	−1.07513	−0.537565	+	0.843222i	$0.680656\pi$
$618$	−4.91870e11	−0.135645
$619$	1.65184e12	0.452231	0.226116	−	0.974100i	$-0.427397\pi$
$619$	1.65184e12	0.452231	0.226116	+	0.974100i	$0.427397\pi$
$620$	−3.02036e12	−0.820911
$621$	−6.93473e11	−0.187119
$622$	−1.12942e13	−3.02551
$623$	9.89079e12	2.63048
$624$	−9.47021e11	−0.250051
$625$	6.02843e11	0.158032
$626$	6.69054e12	1.74131
$627$	−1.44964e12	−0.374590
$628$	−2.33677e12	−0.599511
$629$	8.00711e12	2.03961
$630$	−1.78535e12	−0.451534
$631$	−1.53939e12	−0.386560	−0.193280	−	0.981144i	$-0.561913\pi$
$631$	−1.53939e12	−0.386560	−0.193280	+	0.981144i	$0.561913\pi$
$632$	−6.75481e11	−0.168417
$633$	−1.51272e12	−0.374492
$634$	−4.33367e12	−1.06526
$635$	−4.08918e11	−0.0998055
$636$	−8.56603e12	−2.07598
$637$	2.21665e12	0.533421
$638$	2.29049e12	0.547313
$639$	−2.41362e12	−0.572685
$640$	4.28548e12	1.00969
$641$	5.68465e12	1.32997	0.664986	−	0.746856i	$-0.268438\pi$
$641$	5.68465e12	1.32997	0.664986	+	0.746856i	$0.268438\pi$
$642$	6.41256e12	1.48979
$643$	−2.55828e12	−0.590198	−0.295099	−	0.955467i	$-0.595353\pi$
$643$	−2.55828e12	−0.590198	−0.295099	+	0.955467i	$0.595353\pi$
$644$	1.15975e13	2.65693
$645$	1.78894e12	0.406983
$646$	−1.92839e13	−4.35662
$647$	2.20782e12	0.495331	0.247665	−	0.968846i	$-0.420337\pi$
$647$	2.20782e12	0.495331	0.247665	+	0.968846i	$0.420337\pi$
$648$	7.98429e11	0.177889
$649$	2.80830e11	0.0621359
$650$	−2.86914e12	−0.630437
$651$	−2.83276e12	−0.618151
$652$	9.21678e12	1.99740
$653$	3.11675e12	0.670800	0.335400	−	0.942076i	$-0.391129\pi$
$653$	3.11675e12	0.670800	0.335400	+	0.942076i	$0.391129\pi$
$654$	−2.01933e12	−0.431626
$655$	3.95340e12	0.839237
$656$	6.49321e12	1.36897
$657$	1.11350e12	0.233156
$658$	−7.60985e12	−1.58256
$659$	−1.69500e12	−0.350095	−0.175047	−	0.984560i	$-0.556008\pi$
$659$	−1.69500e12	−0.350095	−0.175047	+	0.984560i	$0.556008\pi$
$660$	1.45475e12	0.298429
$661$	−3.82564e12	−0.779468	−0.389734	−	0.920928i	$-0.627433\pi$
$661$	−3.82564e12	−0.779468	−0.389734	+	0.920928i	$0.627433\pi$
$662$	−1.34513e13	−2.72209
$663$	2.88031e12	0.578934
$664$	−7.73039e12	−1.54328
$665$	−5.42106e12	−1.07495
$666$	−3.16087e12	−0.622547
$667$	3.32705e12	0.650868
$668$	3.02581e12	0.587960
$669$	−3.51975e12	−0.679351
$670$	−7.21501e12	−1.38325
$671$	3.05092e12	0.581005
$672$	9.34632e11	0.176799
$673$	−3.10596e12	−0.583618	−0.291809	−	0.956477i	$-0.594257\pi$
$673$	−3.10596e12	−0.583618	−0.291809	+	0.956477i	$0.594257\pi$
$674$	−1.90556e12	−0.355675
$675$	7.12676e11	0.132137
$676$	−7.48616e12	−1.37879
$677$	−5.54110e12	−1.01379	−0.506893	−	0.862009i	$-0.669206\pi$
$677$	−5.54110e12	−1.01379	−0.506893	+	0.862009i	$0.669206\pi$
$678$	6.83509e12	1.24225
$679$	7.04641e12	1.27220
$680$	9.34879e12	1.67674
$681$	−4.13272e12	−0.736332
$682$	3.50134e12	0.619733
$683$	−8.19430e12	−1.44085	−0.720425	−	0.693533i	$-0.756053\pi$
$683$	−8.19430e12	−1.44085	−0.720425	+	0.693533i	$0.756053\pi$
$684$	5.01842e12	0.876627
$685$	5.46323e12	0.948074
$686$	−6.74262e10	−0.0116244
$687$	6.22588e12	1.06634
$688$	5.97953e12	1.01746
$689$	5.89310e12	0.996224
$690$	3.20537e12	0.538341
$691$	−7.97079e12	−1.32999	−0.664997	−	0.746846i	$-0.731567\pi$
$691$	−7.97079e12	−1.32999	−0.664997	+	0.746846i	$0.731567\pi$
$692$	1.60001e13	2.65244
$693$	1.36439e12	0.224719
$694$	−1.16928e13	−1.91338
$695$	8.99798e11	0.146290
$696$	−3.83059e12	−0.618763
$697$	−1.97488e13	−3.16951
$698$	−1.14067e13	−1.81891
$699$	−6.58396e11	−0.104313
$700$	−1.19187e13	−1.87624
$701$	−6.03771e12	−0.944368	−0.472184	−	0.881500i	$-0.656534\pi$
$701$	−6.03771e12	−0.944368	−0.472184	+	0.881500i	$0.656534\pi$
$702$	−1.13703e12	−0.176707
$703$	−9.59771e12	−1.48207
$704$	−3.66869e12	−0.562904
$705$	−1.38653e12	−0.211387
$706$	3.13324e12	0.474650
$707$	1.32780e13	1.99868
$708$	−9.72189e11	−0.145412
$709$	7.31879e12	1.08775	0.543877	−	0.839165i	$-0.316956\pi$
$709$	7.31879e12	1.08775	0.543877	+	0.839165i	$0.316956\pi$
$710$	1.11563e13	1.64762
$711$	−2.38939e11	−0.0350650
$712$	2.04453e13	2.98149
$713$	5.08586e12	0.736991
$714$	1.81499e13	2.61356
$715$	−1.00081e12	−0.143211
$716$	−1.08899e13	−1.54851
$717$	−2.98853e10	−0.00422300
$718$	8.71754e12	1.22415
$719$	−8.32682e12	−1.16198	−0.580991	−	0.813910i	$-0.697335\pi$
$719$	−8.32682e12	−1.16198	−0.580991	+	0.813910i	$0.697335\pi$
$720$	−1.08730e12	−0.150783
$721$	1.40570e12	0.193724
$722$	1.06066e13	1.45264
$723$	4.63616e12	0.631009
$724$	−1.46487e13	−1.98141
$725$	−3.41918e12	−0.459622
$726$	5.71692e12	0.763743
$727$	1.05665e13	1.40290	0.701450	−	0.712719i	$-0.252537\pi$
$727$	1.05665e13	1.40290	0.701450	+	0.712719i	$0.252537\pi$
$728$	9.18623e12	1.21212
$729$	2.82430e11	0.0370370
$730$	−5.14684e12	−0.670792
$731$	−1.81864e13	−2.35569
$732$	−1.05618e13	−1.35968
$733$	8.59093e11	0.109919	0.0549595	−	0.998489i	$-0.482497\pi$
$733$	8.59093e11	0.109919	0.0549595	+	0.998489i	$0.482497\pi$
$734$	−1.47201e13	−1.87188
$735$	2.54500e12	0.321658
$736$	−1.67802e12	−0.210788
$737$	5.51383e12	0.688415
$738$	7.79597e12	0.967424
$739$	1.46767e13	1.81021	0.905105	−	0.425189i	$-0.139792\pi$
$739$	1.46767e13	1.81021	0.905105	+	0.425189i	$0.139792\pi$
$740$	9.63156e12	1.18074
$741$	−3.45248e12	−0.420678
$742$	3.71346e13	4.49740
$743$	7.23429e12	0.870856	0.435428	−	0.900224i	$-0.356597\pi$
$743$	7.23429e12	0.870856	0.435428	+	0.900224i	$0.356597\pi$
$744$	−5.85560e12	−0.700638
$745$	3.84203e12	0.456938
$746$	1.68051e13	1.98662
$747$	−2.73448e12	−0.321316
$748$	−1.47891e13	−1.72737
$749$	−1.83262e13	−2.12767
$750$	−8.09185e12	−0.933839
$751$	2.69122e12	0.308723	0.154361	−	0.988014i	$-0.450668\pi$
$751$	2.69122e12	0.308723	0.154361	+	0.988014i	$0.450668\pi$
$752$	−4.63448e12	−0.528471
$753$	4.75084e12	0.538509
$754$	5.45506e12	0.614651
$755$	−3.70846e12	−0.415367
$756$	−4.72331e12	−0.525894
$757$	1.82924e12	0.202460	0.101230	−	0.994863i	$-0.467722\pi$
$757$	1.82924e12	0.202460	0.101230	+	0.994863i	$0.467722\pi$
$758$	−2.34641e13	−2.58162
$759$	−2.44960e12	−0.267921
$760$	−1.12059e13	−1.21839
$761$	−1.71665e12	−0.185545	−0.0927727	−	0.995687i	$-0.529573\pi$
$761$	−1.71665e12	−0.185545	−0.0927727	+	0.995687i	$0.529573\pi$
$762$	−1.64104e12	−0.176328
$763$	5.77097e12	0.616436
$764$	−7.26615e12	−0.771586
$765$	3.30696e12	0.349102
$766$	−9.97870e12	−1.04724
$767$	6.68829e11	0.0697808
$768$	1.06332e13	1.10291
$769$	3.03361e12	0.312817	0.156409	−	0.987692i	$-0.450008\pi$
$769$	3.03361e12	0.312817	0.156409	+	0.987692i	$0.450008\pi$
$770$	−6.30651e12	−0.646518
$771$	2.36894e12	0.241440
$772$	−2.30442e13	−2.33498
$773$	−4.55357e12	−0.458717	−0.229358	−	0.973342i	$-0.573663\pi$
$773$	−4.55357e12	−0.458717	−0.229358	+	0.973342i	$0.573663\pi$
$774$	7.17922e12	0.719024
$775$	−5.22670e12	−0.520439
$776$	1.45657e13	1.44196
$777$	9.03331e12	0.889104
$778$	−3.44470e13	−3.37088
$779$	2.36718e13	2.30310
$780$	3.46466e12	0.335146
$781$	−8.52581e12	−0.819985
$782$	−3.25860e13	−3.11602
$783$	−1.35500e12	−0.128828
$784$	8.50665e12	0.804149
$785$	1.84573e12	0.173482
$786$	1.58655e13	1.48269
$787$	−1.85363e13	−1.72241	−0.861205	−	0.508258i	$-0.830289\pi$
$787$	−1.85363e13	−1.72241	−0.861205	+	0.508258i	$0.830289\pi$
$788$	1.52561e13	1.40953
$789$	3.19409e11	0.0293428
$790$	1.10442e12	0.100882
$791$	−1.95337e13	−1.77415
$792$	2.82035e12	0.254706
$793$	7.26611e12	0.652488
$794$	2.86862e13	2.56142
$795$	6.76601e12	0.600732
$796$	−3.57277e12	−0.315425
$797$	4.37734e12	0.384280	0.192140	−	0.981368i	$-0.438457\pi$
$797$	4.37734e12	0.384280	0.192140	+	0.981368i	$0.438457\pi$
$798$	−2.17554e13	−1.89913
$799$	1.40955e13	1.22355
$800$	1.72448e12	0.148852
$801$	7.23215e12	0.620756
$802$	−2.14285e13	−1.82897
$803$	3.93330e12	0.333839
$804$	−1.90880e13	−1.61105
$805$	−9.16051e12	−0.768844
$806$	8.33883e12	0.695981
$807$	2.91458e12	0.241905
$808$	2.74469e13	2.26539
$809$	−9.22845e12	−0.757461	−0.378730	−	0.925507i	$-0.623639\pi$
$809$	−9.22845e12	−0.757461	−0.378730	+	0.925507i	$0.623639\pi$
$810$	−1.30545e12	−0.106556
$811$	1.34091e13	1.08844	0.544222	−	0.838941i	$-0.316825\pi$
$811$	1.34091e13	1.08844	0.544222	+	0.838941i	$0.316825\pi$
$812$	2.26608e13	1.82925
$813$	2.41498e12	0.193868
$814$	−1.11653e13	−0.891379
$815$	−7.28002e12	−0.577994
$816$	1.10535e13	0.872760
$817$	2.17991e13	1.71175
$818$	4.10578e12	0.320631
$819$	3.24946e12	0.252367
$820$	−2.37553e13	−1.83484
$821$	−4.11930e11	−0.0316431	−0.0158216	−	0.999875i	$-0.505036\pi$
$821$	−4.11930e11	−0.0316431	−0.0158216	+	0.999875i	$0.505036\pi$
$822$	2.19246e13	1.67498
$823$	1.90727e13	1.44915	0.724573	−	0.689198i	$-0.242037\pi$
$823$	1.90727e13	1.44915	0.724573	+	0.689198i	$0.242037\pi$
$824$	2.90572e12	0.219574
$825$	2.51743e12	0.189197
$826$	4.21454e12	0.315021
$827$	−5.32819e12	−0.396100	−0.198050	−	0.980192i	$-0.563461\pi$
$827$	−5.32819e12	−0.396100	−0.198050	+	0.980192i	$0.563461\pi$
$828$	8.48012e12	0.626997
$829$	−7.10890e12	−0.522766	−0.261383	−	0.965235i	$-0.584178\pi$
$829$	−7.10890e12	−0.522766	−0.261383	+	0.965235i	$0.584178\pi$
$830$	1.26393e13	0.924427
$831$	−5.79704e11	−0.0421698
$832$	−8.73740e12	−0.632160
$833$	−2.58725e13	−1.86181
$834$	3.61100e12	0.258452
$835$	−2.38998e12	−0.170140
$836$	1.77269e13	1.25518
$837$	−2.07131e12	−0.145875
$838$	2.10040e13	1.47131
$839$	−2.40461e13	−1.67539	−0.837694	−	0.546141i	$-0.816096\pi$
$839$	−2.40461e13	−1.67539	−0.837694	+	0.546141i	$0.816096\pi$
$840$	1.05469e13	0.730920
$841$	−8.00631e12	−0.551887
$842$	2.00130e13	1.37217
$843$	−8.21001e12	−0.559912
$844$	1.84983e13	1.25485
$845$	5.91307e12	0.398986
$846$	−5.56432e12	−0.373461
$847$	−1.63381e13	−1.09076
$848$	2.26154e13	1.50184
$849$	−5.25161e12	−0.346903
$850$	3.34883e13	2.20043
$851$	−1.62182e13	−1.06003
$852$	2.95149e13	1.91895
$853$	1.82317e13	1.17911	0.589557	−	0.807727i	$-0.299302\pi$
$853$	1.82317e13	1.17911	0.589557	+	0.807727i	$0.299302\pi$
$854$	4.57865e13	2.94562
$855$	−3.96388e12	−0.253672
$856$	−3.78821e13	−2.41158
$857$	1.43832e13	0.910838	0.455419	−	0.890277i	$-0.349489\pi$
$857$	1.43832e13	0.910838	0.455419	+	0.890277i	$0.349489\pi$
$858$	−4.01639e12	−0.253013
$859$	2.27585e13	1.42618	0.713089	−	0.701074i	$-0.247296\pi$
$859$	2.27585e13	1.42618	0.713089	+	0.701074i	$0.247296\pi$
$860$	−2.18760e13	−1.36372
$861$	−2.22798e13	−1.38165
$862$	−1.98536e13	−1.22477
$863$	5.25755e12	0.322652	0.161326	−	0.986901i	$-0.448423\pi$
$863$	5.25755e12	0.322652	0.161326	+	0.986901i	$0.448423\pi$
$864$	6.83403e11	0.0417220
$865$	−1.26380e13	−0.767547
$866$	1.86719e13	1.12813
$867$	−2.40131e13	−1.44332
$868$	3.46403e13	2.07130
$869$	−8.44020e11	−0.0502069
$870$	6.26309e12	0.370640
$871$	1.31318e13	0.773113
$872$	1.19292e13	0.698694
$873$	5.15234e12	0.300220
$874$	3.90591e13	2.26423
$875$	2.31254e13	1.33368
$876$	−1.36164e13	−0.781260
$877$	−2.87054e13	−1.63857	−0.819287	−	0.573384i	$-0.805630\pi$
$877$	−2.87054e13	−1.63857	−0.819287	+	0.573384i	$0.805630\pi$
$878$	−4.39890e13	−2.49815
$879$	1.48745e13	0.840414
$880$	−3.84074e12	−0.215895
$881$	−1.61488e13	−0.903128	−0.451564	−	0.892239i	$-0.649134\pi$
$881$	−1.61488e13	−0.903128	−0.451564	+	0.892239i	$0.649134\pi$
$882$	1.02134e13	0.568278
$883$	1.27707e13	0.706957	0.353478	−	0.935443i	$-0.384999\pi$
$883$	1.27707e13	0.706957	0.353478	+	0.935443i	$0.384999\pi$
$884$	−3.52219e13	−1.93989
$885$	7.67899e11	0.0420784
$886$	1.02119e13	0.556743
$887$	−2.89772e13	−1.57181	−0.785905	−	0.618347i	$-0.787803\pi$
$887$	−2.89772e13	−1.57181	−0.785905	+	0.618347i	$0.787803\pi$
$888$	1.86728e13	1.00775
$889$	4.68985e12	0.251826
$890$	−3.34285e13	−1.78592
$891$	9.97645e11	0.0530306
$892$	4.30412e13	2.27637
$893$	−1.68956e13	−0.889082
$894$	1.54185e13	0.807280
$895$	8.60154e12	0.448098
$896$	−4.91498e13	−2.54763
$897$	−5.83400e12	−0.300885
$898$	1.52211e13	0.781090
$899$	9.93745e12	0.507407
$900$	−8.71494e12	−0.442765
$901$	−6.87836e13	−3.47715
$902$	2.75382e13	1.38518
$903$	−2.05172e13	−1.02689
$904$	−4.03782e13	−2.01090
$905$	1.15705e13	0.573368
$906$	−1.48825e13	−0.733836
$907$	−3.02300e13	−1.48322	−0.741609	−	0.670833i	$-0.765937\pi$
$907$	−3.02300e13	−1.48322	−0.741609	+	0.670833i	$0.765937\pi$
$908$	5.05369e13	2.46730
$909$	9.70884e12	0.471661
$910$	−1.50197e13	−0.726062
$911$	−1.91108e13	−0.919278	−0.459639	−	0.888106i	$-0.652021\pi$
$911$	−1.91108e13	−0.919278	−0.459639	+	0.888106i	$0.652021\pi$
$912$	−1.32493e13	−0.634184
$913$	−9.65919e12	−0.460068
$914$	−7.90688e12	−0.374755
$915$	8.34241e12	0.393456
$916$	−7.61330e13	−3.57309
$917$	−4.53412e13	−2.11754
$918$	1.32712e13	0.616764
$919$	−2.36415e13	−1.09334	−0.546670	−	0.837348i	$-0.684105\pi$
$919$	−2.36415e13	−1.09334	−0.546670	+	0.837348i	$0.684105\pi$
$920$	−1.89357e13	−0.871438
$921$	2.68582e12	0.123001
$922$	1.83112e13	0.834501
$923$	−2.03052e13	−0.920871
$924$	−1.66845e13	−0.752989
$925$	1.66673e13	0.748561
$926$	5.45797e13	2.43939
$927$	1.02784e12	0.0457160
$928$	−3.27873e12	−0.145124
$929$	2.93560e13	1.29308	0.646542	−	0.762878i	$-0.276215\pi$
$929$	2.93560e13	1.29308	0.646542	+	0.762878i	$0.276215\pi$
$930$	9.57402e12	0.419683
$931$	3.10121e13	1.35287
$932$	8.05118e12	0.349533
$933$	2.36011e13	1.01968
$934$	7.71205e13	3.31596
$935$	1.16814e13	0.499853
$936$	6.71697e12	0.286043
$937$	7.21413e12	0.305742	0.152871	−	0.988246i	$-0.451148\pi$
$937$	7.21413e12	0.305742	0.152871	+	0.988246i	$0.451148\pi$
$938$	8.27485e13	3.49017
$939$	−1.39810e13	−0.586871
$940$	1.69552e13	0.708316
$941$	−6.11502e12	−0.254240	−0.127120	−	0.991887i	$-0.540573\pi$
$941$	−6.11502e12	−0.254240	−0.127120	+	0.991887i	$0.540573\pi$
$942$	7.40715e12	0.306494
$943$	4.00006e13	1.64727
$944$	2.56670e12	0.105197
$945$	3.73078e12	0.152180
$946$	2.53597e13	1.02952
$947$	4.26509e13	1.72327	0.861635	−	0.507528i	$-0.169441\pi$
$947$	4.26509e13	1.72327	0.861635	+	0.507528i	$0.169441\pi$
$948$	2.92186e12	0.117496
$949$	9.36760e12	0.374913
$950$	−4.01407e13	−1.59893
$951$	9.05592e12	0.359021
$952$	−1.07221e14	−4.23070
$953$	−1.29373e13	−0.508071	−0.254035	−	0.967195i	$-0.581758\pi$
$953$	−1.29373e13	−0.508071	−0.254035	+	0.967195i	$0.581758\pi$
$954$	2.71528e13	1.06132
$955$	5.73929e12	0.223276
$956$	3.65451e11	0.0141504
$957$	−4.78636e12	−0.184460
$958$	3.74840e13	1.43781
$959$	−6.26574e13	−2.39215
$960$	−1.00316e13	−0.381198
$961$	−1.12488e13	−0.425453
$962$	−2.65915e13	−1.00105
$963$	−1.34001e13	−0.502099
$964$	−5.66931e13	−2.11438
$965$	1.82018e13	0.675681
$966$	−3.67622e13	−1.35833
$967$	3.65748e13	1.34513	0.672563	−	0.740040i	$-0.265193\pi$
$967$	3.65748e13	1.34513	0.672563	+	0.740040i	$0.265193\pi$
$968$	−3.37726e13	−1.23631
$969$	4.02970e13	1.46830
$970$	−2.38152e13	−0.863735
$971$	−2.65482e13	−0.958404	−0.479202	−	0.877705i	$-0.659074\pi$
$971$	−2.65482e13	−0.958404	−0.479202	+	0.877705i	$0.659074\pi$
$972$	−3.45368e12	−0.124104
$973$	−1.03197e13	−0.369114
$974$	3.99643e12	0.142284
$975$	5.99555e12	0.212475
$976$	2.78845e13	0.983646
$977$	−4.69416e13	−1.64828	−0.824142	−	0.566383i	$-0.808342\pi$
$977$	−4.69416e13	−1.64828	−0.824142	+	0.566383i	$0.808342\pi$
$978$	−2.92156e13	−1.02115
$979$	2.55466e13	0.888814
$980$	−3.11214e13	−1.07781
$981$	4.21973e12	0.145470
$982$	3.81342e13	1.30862
$983$	−2.90451e13	−0.992161	−0.496081	−	0.868276i	$-0.665228\pi$
$983$	−2.90451e13	−0.992161	−0.496081	+	0.868276i	$0.665228\pi$
$984$	−4.60547e13	−1.56601
$985$	−1.20503e13	−0.407881
$986$	−6.36709e13	−2.14533
$987$	1.59020e13	0.533366
$988$	4.22186e13	1.40961
$989$	3.68361e13	1.22431
$990$	−4.61132e12	−0.152569
$991$	−1.03200e13	−0.339898	−0.169949	−	0.985453i	$-0.554360\pi$
$991$	−1.03200e13	−0.339898	−0.169949	+	0.985453i	$0.554360\pi$
$992$	−5.01201e12	−0.164327
$993$	2.81086e13	0.917419
$994$	−1.27950e14	−4.15722
$995$	2.82201e12	0.0912756
$996$	3.34385e13	1.07666
$997$	2.28352e13	0.731940	0.365970	−	0.930627i	$-0.380737\pi$
$997$	2.28352e13	0.731940	0.365970	+	0.930627i	$0.380737\pi$
$998$	1.53339e13	0.489289
$999$	6.60516e12	0.209816

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.c.1.20	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.c.1.20	✓	22	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)

\(f(q)\)	\(=\)	\(q+38.7622 q^{2} -81.0000 q^{3} +990.507 q^{4} -782.368 q^{5} -3139.74 q^{6} +8972.92 q^{7} +18548.0 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+38.7622 q^{2} -81.0000 q^{3} +990.507 q^{4} -782.368 q^{5} -3139.74 q^{6} +8972.92 q^{7} +18548.0 q^{8} +6561.00 q^{9} -30326.3 q^{10} +23175.9 q^{11} -80231.1 q^{12} +55195.9 q^{13} +347810. q^{14} +63371.8 q^{15} +211820. q^{16} -644241. q^{17} +254319. q^{18} +772218. q^{19} -774941. q^{20} -726807. q^{21} +898347. q^{22} +1.30489e6 q^{23} -1.50239e6 q^{24} -1.34103e6 q^{25} +2.13951e6 q^{26} -531441. q^{27} +8.88774e6 q^{28} +2.54967e6 q^{29} +2.45643e6 q^{30} +3.89754e6 q^{31} -1.28594e6 q^{32} -1.87725e6 q^{33} -2.49722e7 q^{34} -7.02013e6 q^{35} +6.49872e6 q^{36} -1.24288e7 q^{37} +2.99328e7 q^{38} -4.47087e6 q^{39} -1.45113e7 q^{40} +3.06543e7 q^{41} -2.81726e7 q^{42} +2.82292e7 q^{43} +2.29559e7 q^{44} -5.13312e6 q^{45} +5.05805e7 q^{46} -2.18793e7 q^{47} -1.71574e7 q^{48} +4.01597e7 q^{49} -5.19811e7 q^{50} +5.21835e7 q^{51} +5.46719e7 q^{52} +1.06767e8 q^{53} -2.05998e7 q^{54} -1.81321e7 q^{55} +1.66430e8 q^{56} -6.25496e7 q^{57} +9.88309e7 q^{58} +1.21174e7 q^{59} +6.27702e7 q^{60} +1.31642e8 q^{61} +1.51077e8 q^{62} +5.88714e7 q^{63} -1.58298e8 q^{64} -4.31835e7 q^{65} -7.27661e7 q^{66} +2.37913e8 q^{67} -6.38125e8 q^{68} -1.05696e8 q^{69} -2.72115e8 q^{70} -3.67874e8 q^{71} +1.21693e8 q^{72} +1.69715e8 q^{73} -4.81766e8 q^{74} +1.08623e8 q^{75} +7.64887e8 q^{76} +2.07955e8 q^{77} -1.73301e8 q^{78} -3.64180e7 q^{79} -1.65721e8 q^{80} +4.30467e7 q^{81} +1.18823e9 q^{82} -4.16778e8 q^{83} -7.19907e8 q^{84} +5.04033e8 q^{85} +1.09423e9 q^{86} -2.06524e8 q^{87} +4.29865e8 q^{88} +1.10229e9 q^{89} -1.98971e8 q^{90} +4.95269e8 q^{91} +1.29250e9 q^{92} -3.15701e8 q^{93} -8.48090e8 q^{94} -6.04158e8 q^{95} +1.04161e8 q^{96} +7.85297e8 q^{97} +1.55668e9 q^{98} +1.52057e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9}+O(q^{10}) \) 22 * q + 36 * q^2 - 1782 * q^3 + 5718 * q^4 + 808 * q^5 - 2916 * q^6 + 21249 * q^7 + 9435 * q^8 + 144342 * q^9	\( 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9} + 68441 q^{10} - 68033 q^{11} - 463158 q^{12} + 283817 q^{13} + 80285 q^{14} - 65448 q^{15} + 1067674 q^{16} + 436893 q^{17} + 236196 q^{18} + 1207580 q^{19} + 4209677 q^{20} - 1721169 q^{21} + 5460442 q^{22} + 2421966 q^{23} - 764235 q^{24} + 7441842 q^{25} - 2736526 q^{26} - 11691702 q^{27} + 4095246 q^{28} - 2320594 q^{29} - 5543721 q^{30} - 3178024 q^{31} - 20786874 q^{32} + 5510673 q^{33} - 13809336 q^{34} - 2630800 q^{35} + 37515798 q^{36} + 3981807 q^{37} - 24156377 q^{38} - 22989177 q^{39} - 29544450 q^{40} - 885225 q^{41} - 6503085 q^{42} + 12360835 q^{43} - 117711882 q^{44} + 5301288 q^{45} + 161066949 q^{46} + 75901252 q^{47} - 86481594 q^{48} + 170907951 q^{49} - 61318927 q^{50} - 35388333 q^{51} - 100762 q^{52} - 34790192 q^{53} - 19131876 q^{54} + 151773316 q^{55} - 417630344 q^{56} - 97813980 q^{57} - 432929294 q^{58} + 266581942 q^{59} - 340983837 q^{60} - 290555332 q^{61} + 158267098 q^{62} + 139414689 q^{63} - 131794443 q^{64} - 650690086 q^{65} - 442295802 q^{66} + 86645184 q^{67} + 62738541 q^{68} - 196179246 q^{69} + 429714610 q^{70} - 36567631 q^{71} + 61903035 q^{72} + 907807228 q^{73} - 171827242 q^{74} - 602789202 q^{75} + 1744504396 q^{76} - 310688725 q^{77} + 221658606 q^{78} + 2508604687 q^{79} + 3509441927 q^{80} + 947027862 q^{81} + 1759214793 q^{82} + 2185672083 q^{83} - 331714926 q^{84} + 2868860198 q^{85} + 2397001564 q^{86} + 187968114 q^{87} + 7683735877 q^{88} + 1320145942 q^{89} + 449041401 q^{90} + 3894639897 q^{91} + 3505964640 q^{92} + 257419944 q^{93} + 5406355552 q^{94} + 3093659122 q^{95} + 1683736794 q^{96} + 3904552980 q^{97} + 6137683116 q^{98} - 446364513 q^{99}+O(q^{100}) \) 22 * q + 36 * q^2 - 1782 * q^3 + 5718 * q^4 + 808 * q^5 - 2916 * q^6 + 21249 * q^7 + 9435 * q^8 + 144342 * q^9 + 68441 * q^10 - 68033 * q^11 - 463158 * q^12 + 283817 * q^13 + 80285 * q^14 - 65448 * q^15 + 1067674 * q^16 + 436893 * q^17 + 236196 * q^18 + 1207580 * q^19 + 4209677 * q^20 - 1721169 * q^21 + 5460442 * q^22 + 2421966 * q^23 - 764235 * q^24 + 7441842 * q^25 - 2736526 * q^26 - 11691702 * q^27 + 4095246 * q^28 - 2320594 * q^29 - 5543721 * q^30 - 3178024 * q^31 - 20786874 * q^32 + 5510673 * q^33 - 13809336 * q^34 - 2630800 * q^35 + 37515798 * q^36 + 3981807 * q^37 - 24156377 * q^38 - 22989177 * q^39 - 29544450 * q^40 - 885225 * q^41 - 6503085 * q^42 + 12360835 * q^43 - 117711882 * q^44 + 5301288 * q^45 + 161066949 * q^46 + 75901252 * q^47 - 86481594 * q^48 + 170907951 * q^49 - 61318927 * q^50 - 35388333 * q^51 - 100762 * q^52 - 34790192 * q^53 - 19131876 * q^54 + 151773316 * q^55 - 417630344 * q^56 - 97813980 * q^57 - 432929294 * q^58 + 266581942 * q^59 - 340983837 * q^60 - 290555332 * q^61 + 158267098 * q^62 + 139414689 * q^63 - 131794443 * q^64 - 650690086 * q^65 - 442295802 * q^66 + 86645184 * q^67 + 62738541 * q^68 - 196179246 * q^69 + 429714610 * q^70 - 36567631 * q^71 + 61903035 * q^72 + 907807228 * q^73 - 171827242 * q^74 - 602789202 * q^75 + 1744504396 * q^76 - 310688725 * q^77 + 221658606 * q^78 + 2508604687 * q^79 + 3509441927 * q^80 + 947027862 * q^81 + 1759214793 * q^82 + 2185672083 * q^83 - 331714926 * q^84 + 2868860198 * q^85 + 2397001564 * q^86 + 187968114 * q^87 + 7683735877 * q^88 + 1320145942 * q^89 + 449041401 * q^90 + 3894639897 * q^91 + 3505964640 * q^92 + 257419944 * q^93 + 5406355552 * q^94 + 3093659122 * q^95 + 1683736794 * q^96 + 3904552980 * q^97 + 6137683116 * q^98 - 446364513 * q^99

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