LMFDB - Embedded newform 177.10.a.c.1.6

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			1.6
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)

$f(q)$	$=$	$q-20.5236 q^{2} -81.0000 q^{3} -90.7810 q^{4} -622.721 q^{5} +1662.41 q^{6} +1394.83 q^{7} +12371.2 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-20.5236 q^{2} -81.0000 q^{3} -90.7810 q^{4} -622.721 q^{5} +1662.41 q^{6} +1394.83 q^{7} +12371.2 q^{8} +6561.00 q^{9} +12780.5 q^{10} +81914.7 q^{11} +7353.26 q^{12} +22151.8 q^{13} -28627.0 q^{14} +50440.4 q^{15} -207423. q^{16} +512258. q^{17} -134655. q^{18} +850265. q^{19} +56531.3 q^{20} -112982. q^{21} -1.68119e6 q^{22} +1.92743e6 q^{23} -1.00207e6 q^{24} -1.56534e6 q^{25} -454634. q^{26} -531441. q^{27} -126624. q^{28} -601830. q^{29} -1.03522e6 q^{30} -843126. q^{31} -2.07701e6 q^{32} -6.63509e6 q^{33} -1.05134e7 q^{34} -868593. q^{35} -595614. q^{36} +1.61227e7 q^{37} -1.74505e7 q^{38} -1.79429e6 q^{39} -7.70384e6 q^{40} +2.86947e7 q^{41} +2.31879e6 q^{42} +1.17712e7 q^{43} -7.43630e6 q^{44} -4.08567e6 q^{45} -3.95579e7 q^{46} +759231. q^{47} +1.68013e7 q^{48} -3.84080e7 q^{49} +3.21265e7 q^{50} -4.14929e7 q^{51} -2.01096e6 q^{52} -6.97578e7 q^{53} +1.09071e7 q^{54} -5.10101e7 q^{55} +1.72558e7 q^{56} -6.88715e7 q^{57} +1.23517e7 q^{58} +1.21174e7 q^{59} -4.57903e6 q^{60} +7.60079e7 q^{61} +1.73040e7 q^{62} +9.15151e6 q^{63} +1.48828e8 q^{64} -1.37944e7 q^{65} +1.36176e8 q^{66} -2.31398e8 q^{67} -4.65033e7 q^{68} -1.56122e8 q^{69} +1.78267e7 q^{70} -2.17666e7 q^{71} +8.11678e7 q^{72} +3.17363e8 q^{73} -3.30896e8 q^{74} +1.26793e8 q^{75} -7.71879e7 q^{76} +1.14257e8 q^{77} +3.68254e7 q^{78} +5.20051e7 q^{79} +1.29167e8 q^{80} +4.30467e7 q^{81} -5.88920e8 q^{82} -4.88211e8 q^{83} +1.02566e7 q^{84} -3.18994e8 q^{85} -2.41588e8 q^{86} +4.87482e7 q^{87} +1.01339e9 q^{88} +3.00615e8 q^{89} +8.38528e7 q^{90} +3.08980e7 q^{91} -1.74974e8 q^{92} +6.82932e7 q^{93} -1.55822e7 q^{94} -5.29478e8 q^{95} +1.68238e8 q^{96} +6.18576e7 q^{97} +7.88272e8 q^{98} +5.37443e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−20.5236	−0.907024	−0.453512	−	0.891250i	$-0.649829\pi$
$2$	−20.5236	−0.907024	−0.453512	+	0.891250i	$0.649829\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	−90.7810	−0.177307
$5$	−622.721	−0.445583	−0.222792	−	0.974866i	$-0.571517\pi$
$5$	−622.721	−0.445583	−0.222792	+	0.974866i	$0.571517\pi$
$6$	1662.41	0.523671
$7$	1394.83	0.219574	0.109787	−	0.993955i	$-0.464983\pi$
$7$	1394.83	0.219574	0.109787	+	0.993955i	$0.464983\pi$
$8$	12371.2	1.06785
$9$	6561.00	0.333333
$10$	12780.5	0.404155
$11$	81914.7	1.68692	0.843461	−	0.537190i	$-0.180514\pi$
$11$	81914.7	1.68692	0.843461	+	0.537190i	$0.180514\pi$
$12$	7353.26	0.102368
$13$	22151.8	0.215111	0.107556	−	0.994199i	$-0.465698\pi$
$13$	22151.8	0.215111	0.107556	+	0.994199i	$0.465698\pi$
$14$	−28627.0	−0.199159
$15$	50440.4	0.257258
$16$	−207423.	−0.791256
$17$	512258.	1.48754	0.743769	−	0.668436i	$-0.233036\pi$
$17$	512258.	1.48754	0.743769	+	0.668436i	$0.233036\pi$
$18$	−134655.	−0.302341
$19$	850265.	1.49680	0.748399	−	0.663249i	$-0.230823\pi$
$19$	850265.	1.49680	0.748399	+	0.663249i	$0.230823\pi$
$20$	56531.3	0.0790049
$21$	−112982.	−0.126771
$22$	−1.68119e6	−1.53008
$23$	1.92743e6	1.43616	0.718081	−	0.695959i	$-0.245021\pi$
$23$	1.92743e6	1.43616	0.718081	+	0.695959i	$0.245021\pi$
$24$	−1.00207e6	−0.616521
$25$	−1.56534e6	−0.801456
$26$	−454634.	−0.195111
$27$	−531441.	−0.192450
$28$	−126624.	−0.0389320
$29$	−601830.	−0.158009	−0.0790047	−	0.996874i	$-0.525174\pi$
$29$	−601830.	−0.158009	−0.0790047	+	0.996874i	$0.525174\pi$
$30$	−1.03522e6	−0.233339
$31$	−843126.	−0.163970	−0.0819851	−	0.996634i	$-0.526126\pi$
$31$	−843126.	−0.163970	−0.0819851	+	0.996634i	$0.526126\pi$
$32$	−2.07701e6	−0.350158
$33$	−6.63509e6	−0.973945
$34$	−1.05134e7	−1.34923
$35$	−868593.	−0.0978386
$36$	−595614.	−0.0591022
$37$	1.61227e7	1.41426	0.707130	−	0.707083i	$-0.249989\pi$
$37$	1.61227e7	1.41426	0.707130	+	0.707083i	$0.249989\pi$
$38$	−1.74505e7	−1.35763
$39$	−1.79429e6	−0.124195
$40$	−7.70384e6	−0.475814
$41$	2.86947e7	1.58590	0.792948	−	0.609289i	$-0.208545\pi$
$41$	2.86947e7	1.58590	0.792948	+	0.609289i	$0.208545\pi$
$42$	2.31879e6	0.114985
$43$	1.17712e7	0.525066	0.262533	−	0.964923i	$-0.415442\pi$
$43$	1.17712e7	0.525066	0.262533	+	0.964923i	$0.415442\pi$
$44$	−7.43630e6	−0.299103
$45$	−4.08567e6	−0.148528
$46$	−3.95579e7	−1.30263
$47$	759231.	0.0226952	0.0113476	−	0.999936i	$-0.496388\pi$
$47$	759231.	0.0226952	0.0113476	+	0.999936i	$0.496388\pi$
$48$	1.68013e7	0.456832
$49$	−3.84080e7	−0.951787
$50$	3.21265e7	0.726940
$51$	−4.14929e7	−0.858831
$52$	−2.01096e6	−0.0381407
$53$	−6.97578e7	−1.21437	−0.607186	−	0.794560i	$-0.707702\pi$
$53$	−6.97578e7	−1.21437	−0.607186	+	0.794560i	$0.707702\pi$
$54$	1.09071e7	0.174557
$55$	−5.10101e7	−0.751664
$56$	1.72558e7	0.234471
$57$	−6.88715e7	−0.864176
$58$	1.23517e7	0.143318
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	−4.57903e6	−0.0456135
$61$	7.60079e7	0.702869	0.351435	−	0.936212i	$-0.385694\pi$
$61$	7.60079e7	0.702869	0.351435	+	0.936212i	$0.385694\pi$
$62$	1.73040e7	0.148725
$63$	9.15151e6	0.0731914
$64$	1.48828e8	1.10886
$65$	−1.37944e7	−0.0958499
$66$	1.36176e8	0.883392
$67$	−2.31398e8	−1.40289	−0.701444	−	0.712724i	$-0.747461\pi$
$67$	−2.31398e8	−1.40289	−0.701444	+	0.712724i	$0.747461\pi$
$68$	−4.65033e7	−0.263751
$69$	−1.56122e8	−0.829169
$70$	1.78267e7	0.0887420
$71$	−2.17666e7	−0.101655	−0.0508274	−	0.998707i	$-0.516186\pi$
$71$	−2.17666e7	−0.101655	−0.0508274	+	0.998707i	$0.516186\pi$
$72$	8.11678e7	0.355949
$73$	3.17363e8	1.30799	0.653993	−	0.756500i	$-0.273092\pi$
$73$	3.17363e8	1.30799	0.653993	+	0.756500i	$0.273092\pi$
$74$	−3.30896e8	−1.28277
$75$	1.26793e8	0.462721
$76$	−7.71879e7	−0.265392
$77$	1.14257e8	0.370405
$78$	3.68254e7	0.112647
$79$	5.20051e7	0.150219	0.0751093	−	0.997175i	$-0.476069\pi$
$79$	5.20051e7	0.150219	0.0751093	+	0.997175i	$0.476069\pi$
$80$	1.29167e8	0.352570
$81$	4.30467e7	0.111111
$82$	−5.88920e8	−1.43845
$83$	−4.88211e8	−1.12916	−0.564581	−	0.825378i	$-0.690962\pi$
$83$	−4.88211e8	−1.12916	−0.564581	+	0.825378i	$0.690962\pi$
$84$	1.02566e7	0.0224774
$85$	−3.18994e8	−0.662822
$86$	−2.41588e8	−0.476247
$87$	4.87482e7	0.0912268
$88$	1.01339e9	1.80137
$89$	3.00615e8	0.507874	0.253937	−	0.967221i	$-0.418274\pi$
$89$	3.00615e8	0.507874	0.253937	+	0.967221i	$0.418274\pi$
$90$	8.38528e7	0.134718
$91$	3.08980e7	0.0472329
$92$	−1.74974e8	−0.254641
$93$	6.82932e7	0.0946682
$94$	−1.55822e7	−0.0205851
$95$	−5.29478e8	−0.666948
$96$	1.68238e8	0.202164
$97$	6.18576e7	0.0709448	0.0354724	−	0.999371i	$-0.488706\pi$
$97$	6.18576e7	0.0709448	0.0354724	+	0.999371i	$0.488706\pi$
$98$	7.88272e8	0.863294
$99$	5.37443e8	0.562307
$100$	1.42103e8	0.142103
$101$	−6.13240e7	−0.0586387	−0.0293193	−	0.999570i	$-0.509334\pi$
$101$	−6.13240e7	−0.0586387	−0.0293193	+	0.999570i	$0.509334\pi$
$102$	8.51584e8	0.778981
$103$	−3.77156e8	−0.330182	−0.165091	−	0.986278i	$-0.552792\pi$
$103$	−3.77156e8	−0.330182	−0.165091	+	0.986278i	$0.552792\pi$
$104$	2.74045e8	0.229706
$105$	7.03560e7	0.0564871
$106$	1.43168e9	1.10146
$107$	−7.46450e7	−0.0550521	−0.0275260	−	0.999621i	$-0.508763\pi$
$107$	−7.46450e7	−0.0550521	−0.0275260	+	0.999621i	$0.508763\pi$
$108$	4.82448e7	0.0341227
$109$	1.11834e9	0.758849	0.379425	−	0.925223i	$-0.376122\pi$
$109$	1.11834e9	0.758849	0.379425	+	0.925223i	$0.376122\pi$
$110$	1.04691e9	0.681778
$111$	−1.30594e9	−0.816524
$112$	−2.89321e8	−0.173739
$113$	1.15233e9	0.664847	0.332424	−	0.943130i	$-0.392134\pi$
$113$	1.15233e9	0.664847	0.332424	+	0.943130i	$0.392134\pi$
$114$	1.41349e9	0.783829
$115$	−1.20025e9	−0.639930
$116$	5.46348e7	0.0280161
$117$	1.45338e8	0.0717037
$118$	−2.48692e8	−0.118085
$119$	7.14514e8	0.326625
$120$	6.24011e8	0.274711
$121$	4.35208e9	1.84571
$122$	−1.55996e9	−0.637520
$123$	−2.32427e9	−0.915618
$124$	7.65398e7	0.0290730
$125$	2.19103e9	0.802698
$126$	−1.87822e8	−0.0663864
$127$	4.74924e9	1.61997	0.809986	−	0.586450i	$-0.199475\pi$
$127$	4.74924e9	1.61997	0.809986	+	0.586450i	$0.199475\pi$
$128$	−1.99107e9	−0.655603
$129$	−9.53469e8	−0.303147
$130$	2.83110e8	0.0869382
$131$	2.49512e9	0.740235	0.370118	−	0.928985i	$-0.379317\pi$
$131$	2.49512e9	0.740235	0.370118	+	0.928985i	$0.379317\pi$
$132$	6.02341e8	0.172687
$133$	1.18598e9	0.328658
$134$	4.74913e9	1.27245
$135$	3.30940e8	0.0857525
$136$	6.33727e9	1.58846
$137$	−2.63323e9	−0.638625	−0.319312	−	0.947650i	$-0.603452\pi$
$137$	−2.63323e9	−0.638625	−0.319312	+	0.947650i	$0.603452\pi$
$138$	3.20419e9	0.752077
$139$	−7.10811e9	−1.61506	−0.807528	−	0.589829i	$-0.799195\pi$
$139$	−7.10811e9	−1.61506	−0.807528	+	0.589829i	$0.799195\pi$
$140$	7.88518e7	0.0173474
$141$	−6.14977e7	−0.0131031
$142$	4.46729e8	0.0922033
$143$	1.81456e9	0.362876
$144$	−1.36090e9	−0.263752
$145$	3.74773e8	0.0704063
$146$	−6.51344e9	−1.18638
$147$	3.11105e9	0.549515
$148$	−1.46363e9	−0.250758
$149$	7.33933e9	1.21988	0.609942	−	0.792446i	$-0.291193\pi$
$149$	7.33933e9	1.21988	0.609942	+	0.792446i	$0.291193\pi$
$150$	−2.60225e9	−0.419699
$151$	−1.29484e9	−0.202683	−0.101342	−	0.994852i	$-0.532314\pi$
$151$	−1.29484e9	−0.202683	−0.101342	+	0.994852i	$0.532314\pi$
$152$	1.05188e10	1.59835
$153$	3.36092e9	0.495846
$154$	−2.34498e9	−0.335966
$155$	5.25033e8	0.0730624
$156$	1.62888e8	0.0220205
$157$	6.63139e9	0.871077	0.435538	−	0.900170i	$-0.356558\pi$
$157$	6.63139e9	0.871077	0.435538	+	0.900170i	$0.356558\pi$
$158$	−1.06733e9	−0.136252
$159$	5.65038e9	0.701118
$160$	1.29340e9	0.156024
$161$	2.68845e9	0.315344
$162$	−8.83475e8	−0.100780
$163$	9.25376e9	1.02677	0.513386	−	0.858158i	$-0.328391\pi$
$163$	9.25376e9	1.02677	0.513386	+	0.858158i	$0.328391\pi$
$164$	−2.60494e9	−0.281190
$165$	4.13182e9	0.433973
$166$	1.00199e10	1.02418
$167$	6.95721e9	0.692167	0.346083	−	0.938204i	$-0.387511\pi$
$167$	6.95721e9	0.692167	0.346083	+	0.938204i	$0.387511\pi$
$168$	−1.39772e9	−0.135372
$169$	−1.01138e10	−0.953727
$170$	6.54691e9	0.601196
$171$	5.57859e9	0.498932
$172$	−1.06860e9	−0.0930977
$173$	−1.69325e10	−1.43718	−0.718592	−	0.695431i	$-0.755213\pi$
$173$	−1.69325e10	−1.43718	−0.718592	+	0.695431i	$0.755213\pi$
$174$	−1.00049e9	−0.0827449
$175$	−2.18339e9	−0.175979
$176$	−1.69910e10	−1.33479
$177$	−9.81506e8	−0.0751646
$178$	−6.16972e9	−0.460654
$179$	2.79100e9	0.203199	0.101599	−	0.994825i	$-0.467604\pi$
$179$	2.79100e9	0.203199	0.101599	+	0.994825i	$0.467604\pi$
$180$	3.70902e8	0.0263350
$181$	−7.62877e9	−0.528325	−0.264162	−	0.964478i	$-0.585095\pi$
$181$	−7.62877e9	−0.528325	−0.264162	+	0.964478i	$0.585095\pi$
$182$	−6.34139e8	−0.0428414
$183$	−6.15664e9	−0.405802
$184$	2.38447e10	1.53360
$185$	−1.00399e10	−0.630171
$186$	−1.40162e9	−0.0858664
$187$	4.19615e10	2.50936
$188$	−6.89238e7	−0.00402401
$189$	−7.41272e8	−0.0422571
$190$	1.08668e10	0.604938
$191$	−2.67707e10	−1.45549	−0.727746	−	0.685847i	$-0.759432\pi$
$191$	−2.67707e10	−1.45549	−0.727746	+	0.685847i	$0.759432\pi$
$192$	−1.20551e10	−0.640199
$193$	1.34722e10	0.698923	0.349461	−	0.936951i	$-0.386365\pi$
$193$	1.34722e10	0.698923	0.349461	+	0.936951i	$0.386365\pi$
$194$	−1.26954e9	−0.0643486
$195$	1.11734e9	0.0553390
$196$	3.48672e9	0.168758
$197$	−1.23673e10	−0.585030	−0.292515	−	0.956261i	$-0.594492\pi$
$197$	−1.23673e10	−0.585030	−0.292515	+	0.956261i	$0.594492\pi$
$198$	−1.10303e10	−0.510026
$199$	−1.39648e10	−0.631241	−0.315620	−	0.948886i	$-0.602213\pi$
$199$	−1.39648e10	−0.631241	−0.315620	+	0.948886i	$0.602213\pi$
$200$	−1.93652e10	−0.855831
$201$	1.87432e10	0.809958
$202$	1.25859e9	0.0531867
$203$	−8.39453e8	−0.0346948
$204$	3.76677e9	0.152276
$205$	−1.78688e10	−0.706649
$206$	7.74061e9	0.299483
$207$	1.26459e10	0.478721
$208$	−4.59478e9	−0.170208
$209$	6.96492e10	2.52498
$210$	−1.44396e9	−0.0512352
$211$	7.16560e9	0.248875	0.124438	−	0.992227i	$-0.460287\pi$
$211$	7.16560e9	0.248875	0.124438	+	0.992227i	$0.460287\pi$
$212$	6.33269e9	0.215316
$213$	1.76309e9	0.0586904
$214$	1.53198e9	0.0499336
$215$	−7.33019e9	−0.233960
$216$	−6.57459e9	−0.205507
$217$	−1.17602e9	−0.0360036
$218$	−2.29524e10	−0.688295
$219$	−2.57064e10	−0.755167
$220$	4.63075e9	0.133275
$221$	1.13474e10	0.319986
$222$	2.68026e10	0.740607
$223$	−1.21184e10	−0.328151	−0.164075	−	0.986448i	$-0.552464\pi$
$223$	−1.21184e10	−0.328151	−0.164075	+	0.986448i	$0.552464\pi$
$224$	−2.89708e9	−0.0768856
$225$	−1.02702e10	−0.267152
$226$	−2.36499e10	−0.603033
$227$	−5.58818e10	−1.39686	−0.698431	−	0.715677i	$-0.746118\pi$
$227$	−5.58818e10	−1.39686	−0.698431	+	0.715677i	$0.746118\pi$
$228$	6.25222e9	0.153224
$229$	−1.38507e9	−0.0332823	−0.0166412	−	0.999862i	$-0.505297\pi$
$229$	−1.38507e9	−0.0332823	−0.0166412	+	0.999862i	$0.505297\pi$
$230$	2.46335e10	0.580432
$231$	−9.25486e9	−0.213853
$232$	−7.44539e9	−0.168730
$233$	−6.40947e10	−1.42469	−0.712345	−	0.701830i	$-0.752367\pi$
$233$	−6.40947e10	−1.42469	−0.712345	+	0.701830i	$0.752367\pi$
$234$	−2.98286e9	−0.0650370
$235$	−4.72789e8	−0.0101126
$236$	−1.10003e9	−0.0230834
$237$	−4.21241e9	−0.0867288
$238$	−1.46644e10	−0.296257
$239$	−3.09544e10	−0.613666	−0.306833	−	0.951763i	$-0.599269\pi$
$239$	−3.09544e10	−0.613666	−0.306833	+	0.951763i	$0.599269\pi$
$240$	−1.04625e10	−0.203556
$241$	−4.40383e10	−0.840919	−0.420459	−	0.907311i	$-0.638131\pi$
$241$	−4.40383e10	−0.840919	−0.420459	+	0.907311i	$0.638131\pi$
$242$	−8.93204e10	−1.67410
$243$	−3.48678e9	−0.0641500
$244$	−6.90008e9	−0.124623
$245$	2.39175e10	0.424100
$246$	4.77025e10	0.830487
$247$	1.88349e10	0.321978
$248$	−1.04305e10	−0.175095
$249$	3.95451e10	0.651921
$250$	−4.49678e10	−0.728067
$251$	−4.30727e10	−0.684968	−0.342484	−	0.939524i	$-0.611268\pi$
$251$	−4.30727e10	−0.684968	−0.342484	+	0.939524i	$0.611268\pi$
$252$	−8.30783e8	−0.0129773
$253$	1.57885e11	2.42269
$254$	−9.74716e10	−1.46935
$255$	2.58385e10	0.382681
$256$	−3.53362e10	−0.514209
$257$	−1.25399e11	−1.79306	−0.896530	−	0.442983i	$-0.853920\pi$
$257$	−1.25399e11	−1.79306	−0.896530	+	0.442983i	$0.853920\pi$
$258$	1.95686e10	0.274962
$259$	2.24885e10	0.310535
$260$	1.25227e9	0.0169948
$261$	−3.94861e9	−0.0526698
$262$	−5.12088e10	−0.671411
$263$	−7.79571e10	−1.00474	−0.502372	−	0.864652i	$-0.667539\pi$
$263$	−7.79571e10	−1.00474	−0.502372	+	0.864652i	$0.667539\pi$
$264$	−8.20844e10	−1.04002
$265$	4.34397e10	0.541103
$266$	−2.43406e10	−0.298101
$267$	−2.43498e10	−0.293221
$268$	2.10066e10	0.248742
$269$	−4.10376e10	−0.477856	−0.238928	−	0.971037i	$-0.576796\pi$
$269$	−4.10376e10	−0.477856	−0.238928	+	0.971037i	$0.576796\pi$
$270$	−6.79208e9	−0.0777796
$271$	−2.74189e9	−0.0308807	−0.0154404	−	0.999881i	$-0.504915\pi$
$271$	−2.74189e9	−0.0308807	−0.0154404	+	0.999881i	$0.504915\pi$
$272$	−1.06254e11	−1.17702
$273$	−2.50274e9	−0.0272699
$274$	5.40433e10	0.579248
$275$	−1.28225e11	−1.35199
$276$	1.41729e10	0.147017
$277$	9.28261e10	0.947351	0.473676	−	0.880699i	$-0.342927\pi$
$277$	9.28261e10	0.947351	0.473676	+	0.880699i	$0.342927\pi$
$278$	1.45884e11	1.46490
$279$	−5.53175e9	−0.0546567
$280$	−1.07456e10	−0.104477
$281$	1.26706e11	1.21232	0.606161	−	0.795342i	$-0.292709\pi$
$281$	1.26706e11	1.21232	0.606161	+	0.795342i	$0.292709\pi$
$282$	1.26216e9	0.0118848
$283$	1.54310e11	1.43007	0.715033	−	0.699090i	$-0.246412\pi$
$283$	1.54310e11	1.43007	0.715033	+	0.699090i	$0.246412\pi$
$284$	1.97599e9	0.0180241
$285$	4.28877e10	0.385062
$286$	−3.72412e10	−0.329137
$287$	4.00244e10	0.348222
$288$	−1.36273e10	−0.116719
$289$	1.43820e11	1.21277
$290$	−7.69169e9	−0.0638603
$291$	−5.01047e9	−0.0409600
$292$	−2.88105e10	−0.231915
$293$	8.19074e10	0.649260	0.324630	−	0.945841i	$-0.394760\pi$
$293$	8.19074e10	0.649260	0.324630	+	0.945841i	$0.394760\pi$
$294$	−6.38500e10	−0.498423
$295$	−7.54574e9	−0.0580100
$296$	1.99458e11	1.51021
$297$	−4.35329e10	−0.324648
$298$	−1.50630e11	−1.10646
$299$	4.26960e10	0.308935
$300$	−1.15104e10	−0.0820435
$301$	1.64189e10	0.115291
$302$	2.65747e10	0.183839
$303$	4.96724e9	0.0338551
$304$	−1.76364e11	−1.18435
$305$	−4.73318e10	−0.313187
$306$	−6.89783e10	−0.449745
$307$	5.97432e10	0.383854	0.191927	−	0.981409i	$-0.438526\pi$
$307$	5.97432e10	0.383854	0.191927	+	0.981409i	$0.438526\pi$
$308$	−1.03724e10	−0.0656752
$309$	3.05496e10	0.190631
$310$	−1.07756e10	−0.0662693
$311$	3.43145e10	0.207996	0.103998	−	0.994577i	$-0.466836\pi$
$311$	3.43145e10	0.207996	0.103998	+	0.994577i	$0.466836\pi$
$312$	−2.21976e10	−0.132621
$313$	−7.38980e10	−0.435194	−0.217597	−	0.976039i	$-0.569822\pi$
$313$	−7.38980e10	−0.435194	−0.217597	+	0.976039i	$0.569822\pi$
$314$	−1.36100e11	−0.790088
$315$	−5.69884e9	−0.0326129
$316$	−4.72107e9	−0.0266348
$317$	−1.09134e11	−0.607004	−0.303502	−	0.952831i	$-0.598156\pi$
$317$	−1.09134e11	−0.607004	−0.303502	+	0.952831i	$0.598156\pi$
$318$	−1.15966e11	−0.635931
$319$	−4.92988e10	−0.266550
$320$	−9.26786e10	−0.494088
$321$	6.04624e9	0.0317843
$322$	−5.51767e10	−0.286025
$323$	4.35555e11	2.22654
$324$	−3.90783e9	−0.0197007
$325$	−3.46751e10	−0.172402
$326$	−1.89921e11	−0.931307
$327$	−9.05857e10	−0.438122
$328$	3.54990e11	1.69349
$329$	1.05900e9	0.00498327
$330$	−8.47998e10	−0.393624
$331$	−8.21888e10	−0.376346	−0.188173	−	0.982136i	$-0.560257\pi$
$331$	−8.21888e10	−0.376346	−0.188173	+	0.982136i	$0.560257\pi$
$332$	4.43203e10	0.200208
$333$	1.05781e11	0.471420
$334$	−1.42787e11	−0.627812
$335$	1.44097e11	0.625104
$336$	2.34350e10	0.100308
$337$	1.40309e11	0.592586	0.296293	−	0.955097i	$-0.404249\pi$
$337$	1.40309e11	0.592586	0.296293	+	0.955097i	$0.404249\pi$
$338$	2.07572e11	0.865054
$339$	−9.33383e10	−0.383850
$340$	2.89586e10	0.117523
$341$	−6.90645e10	−0.276605
$342$	−1.14493e11	−0.452544
$343$	−1.09859e11	−0.428562
$344$	1.45625e11	0.560689
$345$	9.72205e10	0.369464
$346$	3.47515e11	1.30356
$347$	6.18546e10	0.229029	0.114514	−	0.993422i	$-0.463469\pi$
$347$	6.18546e10	0.229029	0.114514	+	0.993422i	$0.463469\pi$
$348$	−4.42542e9	−0.0161751
$349$	−4.01370e11	−1.44821	−0.724103	−	0.689692i	$-0.757746\pi$
$349$	−4.01370e11	−1.44821	−0.724103	+	0.689692i	$0.757746\pi$
$350$	4.48111e10	0.159617
$351$	−1.17724e10	−0.0413982
$352$	−1.70138e11	−0.590689
$353$	−1.75083e11	−0.600148	−0.300074	−	0.953916i	$-0.597011\pi$
$353$	−1.75083e11	−0.600148	−0.300074	+	0.953916i	$0.597011\pi$
$354$	2.01441e10	0.0681761
$355$	1.35545e10	0.0452956
$356$	−2.72902e10	−0.0900495
$357$	−5.78757e10	−0.188577
$358$	−5.72814e10	−0.184306
$359$	−1.97901e11	−0.628815	−0.314407	−	0.949288i	$-0.601806\pi$
$359$	−1.97901e11	−0.628815	−0.314407	+	0.949288i	$0.601806\pi$
$360$	−5.05449e10	−0.158605
$361$	4.00263e11	1.24040
$362$	1.56570e11	0.479204
$363$	−3.52518e11	−1.06562
$364$	−2.80495e9	−0.00837471
$365$	−1.97629e11	−0.582817
$366$	1.26357e11	0.368072
$367$	6.04032e11	1.73805	0.869025	−	0.494768i	$-0.164747\pi$
$367$	6.04032e11	1.73805	0.869025	+	0.494768i	$0.164747\pi$
$368$	−3.99793e11	−1.13637
$369$	1.88266e11	0.528632
$370$	2.06056e11	0.571580
$371$	−9.73006e10	−0.266645
$372$	−6.19973e9	−0.0167853
$373$	4.45130e11	1.19069	0.595343	−	0.803472i	$-0.297016\pi$
$373$	4.45130e11	1.19069	0.595343	+	0.803472i	$0.297016\pi$
$374$	−8.61201e11	−2.27605
$375$	−1.77473e11	−0.463438
$376$	9.39263e9	0.0242349
$377$	−1.33316e10	−0.0339896
$378$	1.52136e10	0.0383282
$379$	9.08604e10	0.226203	0.113101	−	0.993583i	$-0.463922\pi$
$379$	9.08604e10	0.226203	0.113101	+	0.993583i	$0.463922\pi$
$380$	4.80666e10	0.118254
$381$	−3.84688e11	−0.935291
$382$	5.49432e11	1.32017
$383$	−4.85742e11	−1.15348	−0.576741	−	0.816927i	$-0.695676\pi$
$383$	−4.85742e11	−1.15348	−0.576741	+	0.816927i	$0.695676\pi$
$384$	1.61276e11	0.378513
$385$	−7.11506e10	−0.165046
$386$	−2.76497e11	−0.633940
$387$	7.72310e10	0.175022
$388$	−5.61550e9	−0.0125790
$389$	7.75466e11	1.71708	0.858538	−	0.512751i	$-0.171373\pi$
$389$	7.75466e11	1.71708	0.858538	+	0.512751i	$0.171373\pi$
$390$	−2.29319e10	−0.0501938
$391$	9.87342e11	2.13635
$392$	−4.75155e11	−1.01636
$393$	−2.02104e11	−0.427375
$394$	2.53823e11	0.530637
$395$	−3.23847e10	−0.0669349
$396$	−4.87896e10	−0.0997008
$397$	−9.45110e11	−1.90952	−0.954762	−	0.297372i	$-0.903890\pi$
$397$	−9.45110e11	−1.90952	−0.954762	+	0.297372i	$0.903890\pi$
$398$	2.86608e11	0.572551
$399$	−9.60642e10	−0.189751
$400$	3.24688e11	0.634156
$401$	8.14221e11	1.57251	0.786254	−	0.617903i	$-0.212018\pi$
$401$	8.14221e11	1.57251	0.786254	+	0.617903i	$0.212018\pi$
$402$	−3.84679e11	−0.734652
$403$	−1.86767e10	−0.0352718
$404$	5.56706e9	0.0103970
$405$	−2.68061e10	−0.0495092
$406$	1.72286e10	0.0314690
$407$	1.32069e12	2.38575
$408$	−5.13319e11	−0.917099
$409$	−1.23209e11	−0.217714	−0.108857	−	0.994057i	$-0.534719\pi$
$409$	−1.23209e11	−0.217714	−0.108857	+	0.994057i	$0.534719\pi$
$410$	3.66733e11	0.640947
$411$	2.13291e11	0.368710
$412$	3.42386e10	0.0585435
$413$	1.69017e10	0.0285861
$414$	−2.59539e11	−0.434212
$415$	3.04019e11	0.503135
$416$	−4.60094e10	−0.0753229
$417$	5.75757e11	0.932454
$418$	−1.42945e12	−2.29022
$419$	−1.88285e11	−0.298436	−0.149218	−	0.988804i	$-0.547676\pi$
$419$	−1.88285e11	−0.298436	−0.149218	+	0.988804i	$0.547676\pi$
$420$	−6.38699e9	−0.0100155
$421$	6.21132e11	0.963639	0.481819	−	0.876271i	$-0.339976\pi$
$421$	6.21132e11	0.963639	0.481819	+	0.876271i	$0.339976\pi$
$422$	−1.47064e11	−0.225736
$423$	4.98131e9	0.00756506
$424$	−8.62992e11	−1.29676
$425$	−8.01859e11	−1.19220
$426$	−3.61850e10	−0.0532336
$427$	1.06018e11	0.154332
$428$	6.77635e9	0.00976110
$429$	−1.46979e11	−0.209506
$430$	1.50442e11	0.212208
$431$	5.05784e11	0.706021	0.353010	−	0.935619i	$-0.385158\pi$
$431$	5.05784e11	0.706021	0.353010	+	0.935619i	$0.385158\pi$
$432$	1.10233e11	0.152277
$433$	−7.19626e11	−0.983810	−0.491905	−	0.870649i	$-0.663699\pi$
$433$	−7.19626e11	−0.983810	−0.491905	+	0.870649i	$0.663699\pi$
$434$	2.41362e10	0.0326562
$435$	−3.03566e10	−0.0406491
$436$	−1.01524e11	−0.134549
$437$	1.63883e12	2.14964
$438$	5.27588e11	0.684955
$439$	1.85748e11	0.238690	0.119345	−	0.992853i	$-0.461921\pi$
$439$	1.85748e11	0.238690	0.119345	+	0.992853i	$0.461921\pi$
$440$	−6.31058e11	−0.802661
$441$	−2.51995e11	−0.317262
$442$	−2.32890e11	−0.290235
$443$	4.70420e11	0.580321	0.290161	−	0.956978i	$-0.406291\pi$
$443$	4.70420e11	0.580321	0.290161	+	0.956978i	$0.406291\pi$
$444$	1.18554e11	0.144775
$445$	−1.87200e11	−0.226300
$446$	2.48714e11	0.297641
$447$	−5.94486e11	−0.704300
$448$	2.07591e11	0.243476
$449$	−1.22800e12	−1.42590	−0.712951	−	0.701214i	$-0.752642\pi$
$449$	−1.22800e12	−1.42590	−0.712951	+	0.701214i	$0.752642\pi$
$450$	2.10782e11	0.242313
$451$	2.35052e12	2.67528
$452$	−1.04609e11	−0.117882
$453$	1.04882e11	0.117019
$454$	1.14690e12	1.26699
$455$	−1.92409e10	−0.0210462
$456$	−8.52026e11	−0.922807
$457$	1.09592e12	1.17532	0.587659	−	0.809108i	$-0.300049\pi$
$457$	1.09592e12	1.17532	0.587659	+	0.809108i	$0.300049\pi$
$458$	2.84267e10	0.0301879
$459$	−2.72235e11	−0.286277
$460$	1.08960e11	0.113464
$461$	3.49508e11	0.360415	0.180208	−	0.983629i	$-0.442323\pi$
$461$	3.49508e11	0.360415	0.180208	+	0.983629i	$0.442323\pi$
$462$	1.89943e11	0.193970
$463$	2.77251e11	0.280387	0.140194	−	0.990124i	$-0.455227\pi$
$463$	2.77251e11	0.280387	0.140194	+	0.990124i	$0.455227\pi$
$464$	1.24833e11	0.125026
$465$	−4.25276e10	−0.0421826
$466$	1.31545e12	1.29223
$467$	5.83135e11	0.567340	0.283670	−	0.958922i	$-0.408448\pi$
$467$	5.83135e11	0.567340	0.283670	+	0.958922i	$0.408448\pi$
$468$	−1.31939e10	−0.0127136
$469$	−3.22762e11	−0.308038
$470$	9.70335e9	0.00917236
$471$	−5.37143e11	−0.502916
$472$	1.49907e11	0.139022
$473$	9.64237e11	0.885745
$474$	8.64539e10	0.0786651
$475$	−1.33096e12	−1.19962
$476$	−6.48644e10	−0.0579128
$477$	−4.57681e11	−0.404791
$478$	6.35296e11	0.556610
$479$	−2.16228e12	−1.87673	−0.938367	−	0.345642i	$-0.887661\pi$
$479$	−2.16228e12	−1.87673	−0.938367	+	0.345642i	$0.887661\pi$
$480$	−1.04765e11	−0.0900807
$481$	3.57146e11	0.304223
$482$	9.03826e11	0.762734
$483$	−2.17764e11	−0.182064
$484$	−3.95086e11	−0.327256
$485$	−3.85201e10	−0.0316118
$486$	7.15614e10	0.0581856
$487$	1.78439e12	1.43750	0.718752	−	0.695266i	$-0.244714\pi$
$487$	1.78439e12	1.43750	0.718752	+	0.695266i	$0.244714\pi$
$488$	9.40313e11	0.750556
$489$	−7.49554e11	−0.592807
$490$	−4.90874e11	−0.384669
$491$	6.26155e11	0.486200	0.243100	−	0.970001i	$-0.421836\pi$
$491$	6.26155e11	0.486200	0.243100	+	0.970001i	$0.421836\pi$
$492$	2.11000e11	0.162345
$493$	−3.08292e11	−0.235045
$494$	−3.86560e11	−0.292042
$495$	−3.34677e11	−0.250555
$496$	1.74884e11	0.129742
$497$	−3.03608e10	−0.0223208
$498$	−8.11608e11	−0.591309
$499$	6.26144e11	0.452087	0.226043	−	0.974117i	$-0.427421\pi$
$499$	6.26144e11	0.452087	0.226043	+	0.974117i	$0.427421\pi$
$500$	−1.98904e11	−0.142324
$501$	−5.63534e11	−0.399623
$502$	8.84008e11	0.621283
$503$	2.68291e12	1.86875	0.934373	−	0.356295i	$-0.115960\pi$
$503$	2.68291e12	1.86875	0.934373	+	0.356295i	$0.115960\pi$
$504$	1.13216e11	0.0781571
$505$	3.81878e10	0.0261284
$506$	−3.24037e12	−2.19744
$507$	8.19218e11	0.550635
$508$	−4.31141e11	−0.287232
$509$	2.90119e12	1.91578	0.957891	−	0.287133i	$-0.0927022\pi$
$509$	2.90119e12	1.91578	0.957891	+	0.287133i	$0.0927022\pi$
$510$	−5.30300e11	−0.347101
$511$	4.42669e11	0.287200
$512$	1.74465e12	1.12200
$513$	−4.51866e11	−0.288059
$514$	2.57364e12	1.62635
$515$	2.34863e11	0.147124
$516$	8.65569e10	0.0537500
$517$	6.21922e10	0.0382850
$518$	−4.61545e11	−0.281663
$519$	1.37153e12	0.829759
$520$	−1.70654e11	−0.102353
$521$	−1.86142e12	−1.10682	−0.553408	−	0.832910i	$-0.686673\pi$
$521$	−1.86142e12	−1.10682	−0.553408	+	0.832910i	$0.686673\pi$
$522$	8.10397e10	0.0477728
$523$	−3.02664e12	−1.76890	−0.884451	−	0.466634i	$-0.845467\pi$
$523$	−3.02664e12	−1.76890	−0.884451	+	0.466634i	$0.845467\pi$
$524$	−2.26509e11	−0.131249
$525$	1.76855e11	0.101602
$526$	1.59996e12	0.911326
$527$	−4.31898e11	−0.243912
$528$	1.37627e12	0.770639
$529$	1.91384e12	1.06256
$530$	−8.91540e11	−0.490794
$531$	7.95020e10	0.0433963
$532$	−1.07664e11	−0.0582733
$533$	6.35639e11	0.341144
$534$	4.99747e11	0.265959
$535$	4.64830e10	0.0245303
$536$	−2.86268e12	−1.49807
$537$	−2.26071e11	−0.117317
$538$	8.42241e11	0.433427
$539$	−3.14619e12	−1.60559
$540$	−3.00430e10	−0.0152045
$541$	1.90660e12	0.956913	0.478457	−	0.878111i	$-0.341196\pi$
$541$	1.90660e12	0.956913	0.478457	+	0.878111i	$0.341196\pi$
$542$	5.62734e10	0.0280096
$543$	6.17931e11	0.305028
$544$	−1.06396e12	−0.520873
$545$	−6.96416e11	−0.338130
$546$	5.13653e10	0.0247345
$547$	−3.53996e12	−1.69066	−0.845328	−	0.534248i	$-0.820595\pi$
$547$	−3.53996e12	−1.69066	−0.845328	+	0.534248i	$0.820595\pi$
$548$	2.39047e11	0.113232
$549$	4.98688e11	0.234290
$550$	2.63163e12	1.22629
$551$	−5.11715e11	−0.236508
$552$	−1.93142e12	−0.885425
$553$	7.25384e10	0.0329841
$554$	−1.90513e12	−0.859271
$555$	8.13235e11	0.363829
$556$	6.45282e11	0.286360
$557$	−1.31009e12	−0.576704	−0.288352	−	0.957524i	$-0.593107\pi$
$557$	−1.31009e12	−0.576704	−0.288352	+	0.957524i	$0.593107\pi$
$558$	1.13532e11	0.0495750
$559$	2.60753e11	0.112948
$560$	1.80166e11	0.0774153
$561$	−3.39888e12	−1.44878
$562$	−2.60046e12	−1.09961
$563$	1.94733e12	0.816866	0.408433	−	0.912788i	$-0.366075\pi$
$563$	1.94733e12	0.816866	0.408433	+	0.912788i	$0.366075\pi$
$564$	5.58282e9	0.00232326
$565$	−7.17577e11	−0.296245
$566$	−3.16701e12	−1.29711
$567$	6.00430e10	0.0243971
$568$	−2.69280e11	−0.108552
$569$	−2.69619e12	−1.07831	−0.539156	−	0.842206i	$-0.681257\pi$
$569$	−2.69619e12	−1.07831	−0.539156	+	0.842206i	$0.681257\pi$
$570$	−8.80211e11	−0.349261
$571$	−2.34419e12	−0.922848	−0.461424	−	0.887180i	$-0.652661\pi$
$571$	−2.34419e12	−0.922848	−0.461424	+	0.887180i	$0.652661\pi$
$572$	−1.64727e11	−0.0643403
$573$	2.16843e12	0.840329
$574$	−8.21445e11	−0.315846
$575$	−3.01709e12	−1.15102
$576$	9.76462e11	0.369619
$577$	2.78968e12	1.04776	0.523882	−	0.851791i	$-0.324483\pi$
$577$	2.78968e12	1.04776	0.523882	+	0.851791i	$0.324483\pi$
$578$	−2.95171e12	−1.10001
$579$	−1.09124e12	−0.403523
$580$	−3.40222e10	−0.0124835
$581$	−6.80973e11	−0.247935
$582$	1.02833e11	0.0371517
$583$	−5.71420e12	−2.04855
$584$	3.92618e12	1.39673
$585$	−9.05049e10	−0.0319500
$586$	−1.68104e12	−0.588895
$587$	−4.68401e12	−1.62834	−0.814172	−	0.580624i	$-0.802809\pi$
$587$	−4.68401e12	−1.62834	−0.814172	+	0.580624i	$0.802809\pi$
$588$	−2.82424e11	−0.0974326
$589$	−7.16880e11	−0.245430
$590$	1.54866e11	0.0526165
$591$	1.00175e12	0.337767
$592$	−3.34421e12	−1.11904
$593$	1.28628e12	0.427159	0.213579	−	0.976926i	$-0.431488\pi$
$593$	1.28628e12	0.427159	0.213579	+	0.976926i	$0.431488\pi$
$594$	8.93452e11	0.294464
$595$	−4.44943e11	−0.145539
$596$	−6.66272e11	−0.216294
$597$	1.13115e12	0.364447
$598$	−8.76276e11	−0.280211
$599$	3.76469e12	1.19484	0.597419	−	0.801929i	$-0.296193\pi$
$599$	3.76469e12	1.19484	0.597419	+	0.801929i	$0.296193\pi$
$600$	1.56859e12	0.494114
$601$	2.63327e12	0.823303	0.411652	−	0.911341i	$-0.364952\pi$
$601$	2.63327e12	0.823303	0.411652	+	0.911341i	$0.364952\pi$
$602$	−3.36975e11	−0.104572
$603$	−1.51820e12	−0.467630
$604$	1.17546e11	0.0359371
$605$	−2.71013e12	−0.822415
$606$	−1.01946e11	−0.0307074
$607$	−1.72983e12	−0.517194	−0.258597	−	0.965985i	$-0.583260\pi$
$607$	−1.72983e12	−0.517194	−0.258597	+	0.965985i	$0.583260\pi$
$608$	−1.76601e12	−0.524115
$609$	6.79957e10	0.0200311
$610$	9.71419e11	0.284068
$611$	1.68183e10	0.00488199
$612$	−3.05108e11	−0.0879169
$613$	1.40396e12	0.401590	0.200795	−	0.979633i	$-0.435648\pi$
$613$	1.40396e12	0.401590	0.200795	+	0.979633i	$0.435648\pi$
$614$	−1.22615e12	−0.348165
$615$	1.44737e12	0.407984
$616$	1.41351e12	0.395535
$617$	−7.15165e12	−1.98666	−0.993329	−	0.115313i	$-0.963213\pi$
$617$	−7.15165e12	−1.98666	−0.993329	+	0.115313i	$0.963213\pi$
$618$	−6.26989e11	−0.172907
$619$	−2.44272e11	−0.0668754	−0.0334377	−	0.999441i	$-0.510646\pi$
$619$	−2.44272e11	−0.0668754	−0.0334377	+	0.999441i	$0.510646\pi$
$620$	−4.76630e10	−0.0129544
$621$	−1.02432e12	−0.276390
$622$	−7.04257e11	−0.188658
$623$	4.19309e11	0.111516
$624$	3.72177e11	0.0982696
$625$	1.69291e12	0.443787
$626$	1.51665e12	0.394732
$627$	−5.64159e12	−1.45780
$628$	−6.02005e11	−0.154448
$629$	8.25897e12	2.10377
$630$	1.16961e11	0.0295807
$631$	1.41979e12	0.356525	0.178263	−	0.983983i	$-0.442952\pi$
$631$	1.41979e12	0.356525	0.178263	+	0.983983i	$0.442952\pi$
$632$	6.43368e11	0.160410
$633$	−5.80414e11	−0.143688
$634$	2.23982e12	0.550568
$635$	−2.95745e12	−0.721832
$636$	−5.12948e11	−0.124313
$637$	−8.50806e11	−0.204740
$638$	1.01179e12	0.241767
$639$	−1.42810e11	−0.0338849
$640$	1.23988e12	0.292126
$641$	−4.08479e12	−0.955672	−0.477836	−	0.878449i	$-0.658579\pi$
$641$	−4.08479e12	−0.955672	−0.477836	+	0.878449i	$0.658579\pi$
$642$	−1.24091e11	−0.0288292
$643$	3.67936e10	0.00848835	0.00424418	−	0.999991i	$-0.498649\pi$
$643$	3.67936e10	0.00848835	0.00424418	+	0.999991i	$0.498649\pi$
$644$	−2.44060e11	−0.0559127
$645$	5.93746e11	0.135077
$646$	−8.93916e12	−2.01953
$647$	5.07128e12	1.13775	0.568877	−	0.822423i	$-0.307378\pi$
$647$	5.07128e12	1.13775	0.568877	+	0.822423i	$0.307378\pi$
$648$	5.32542e11	0.118650
$649$	9.92591e11	0.219619
$650$	7.11659e11	0.156373
$651$	9.52577e10	0.0207867
$652$	−8.40066e11	−0.182054
$653$	−3.13277e12	−0.674248	−0.337124	−	0.941460i	$-0.609454\pi$
$653$	−3.13277e12	−0.674248	−0.337124	+	0.941460i	$0.609454\pi$
$654$	1.85915e12	0.397387
$655$	−1.55376e12	−0.329836
$656$	−5.95194e12	−1.25485
$657$	2.08222e12	0.435996
$658$	−2.17345e10	−0.00451995
$659$	7.60700e12	1.57119	0.785595	−	0.618741i	$-0.212357\pi$
$659$	7.60700e12	1.57119	0.785595	+	0.618741i	$0.212357\pi$
$660$	−3.75090e11	−0.0769464
$661$	3.64344e11	0.0742344	0.0371172	−	0.999311i	$-0.488183\pi$
$661$	3.64344e11	0.0742344	0.0371172	+	0.999311i	$0.488183\pi$
$662$	1.68681e12	0.341355
$663$	−9.19140e11	−0.184744
$664$	−6.03978e12	−1.20577
$665$	−7.38534e11	−0.146445
$666$	−2.17101e12	−0.427590
$667$	−1.15999e12	−0.226927
$668$	−6.31582e11	−0.122726
$669$	9.81591e11	0.189458
$670$	−2.95738e12	−0.566984
$671$	6.22617e12	1.18569
$672$	2.34664e11	0.0443899
$673$	−9.76993e12	−1.83579	−0.917896	−	0.396821i	$-0.870113\pi$
$673$	−9.76993e12	−1.83579	−0.917896	+	0.396821i	$0.870113\pi$
$674$	−2.87965e12	−0.537490
$675$	8.31888e11	0.154240
$676$	9.18141e11	0.169102
$677$	8.73125e11	0.159745	0.0798725	−	0.996805i	$-0.474549\pi$
$677$	8.73125e11	0.159745	0.0798725	+	0.996805i	$0.474549\pi$
$678$	1.91564e12	0.348161
$679$	8.62811e10	0.0155776
$680$	−3.94635e12	−0.707792
$681$	4.52642e12	0.806479
$682$	1.41745e12	0.250887
$683$	4.68690e10	0.00824123	0.00412062	−	0.999992i	$-0.498688\pi$
$683$	4.68690e10	0.00824123	0.00412062	+	0.999992i	$0.498688\pi$
$684$	−5.06430e11	−0.0884641
$685$	1.63977e12	0.284560
$686$	2.25471e12	0.388716
$687$	1.12191e11	0.0192155
$688$	−2.44162e12	−0.415461
$689$	−1.54526e12	−0.261225
$690$	−1.99532e12	−0.335113
$691$	5.64962e12	0.942688	0.471344	−	0.881949i	$-0.343769\pi$
$691$	5.64962e12	0.942688	0.471344	+	0.881949i	$0.343769\pi$
$692$	1.53715e12	0.254822
$693$	7.49643e11	0.123468
$694$	−1.26948e12	−0.207735
$695$	4.42637e12	0.719642
$696$	6.03077e11	0.0974162
$697$	1.46991e13	2.35908
$698$	8.23756e12	1.31356
$699$	5.19167e12	0.822545
$700$	1.98211e11	0.0312023
$701$	1.55240e12	0.242814	0.121407	−	0.992603i	$-0.461259\pi$
$701$	1.55240e12	0.242814	0.121407	+	0.992603i	$0.461259\pi$
$702$	2.41611e11	0.0375492
$703$	1.37085e13	2.11686
$704$	1.21912e13	1.87056
$705$	3.82959e10	0.00583850
$706$	3.59334e12	0.544349
$707$	−8.55368e10	−0.0128755
$708$	8.91021e10	0.0133272
$709$	−6.23477e12	−0.926643	−0.463322	−	0.886190i	$-0.653343\pi$
$709$	−6.23477e12	−0.926643	−0.463322	+	0.886190i	$0.653343\pi$
$710$	−2.78188e11	−0.0410842
$711$	3.41205e11	0.0500729
$712$	3.71899e12	0.542331
$713$	−1.62507e12	−0.235488
$714$	1.18782e12	0.171044
$715$	−1.12996e12	−0.161691
$716$	−2.53370e11	−0.0360285
$717$	2.50731e12	0.354300
$718$	4.06164e12	0.570350
$719$	4.36189e12	0.608689	0.304344	−	0.952562i	$-0.401563\pi$
$719$	4.36189e12	0.608689	0.304344	+	0.952562i	$0.401563\pi$
$720$	8.47463e11	0.117523
$721$	−5.26070e11	−0.0724995
$722$	−8.21484e12	−1.12508
$723$	3.56710e12	0.485505
$724$	6.92548e11	0.0936755
$725$	9.42071e11	0.126638
$726$	7.23495e12	0.966542
$727$	9.05985e12	1.20286	0.601432	−	0.798924i	$-0.294597\pi$
$727$	9.05985e12	1.20286	0.601432	+	0.798924i	$0.294597\pi$
$728$	3.82247e11	0.0504374
$729$	2.82430e11	0.0370370
$730$	4.05606e12	0.528629
$731$	6.02990e12	0.781056
$732$	5.58906e11	0.0719514
$733$	1.13791e13	1.45592	0.727962	−	0.685618i	$-0.240468\pi$
$733$	1.13791e13	1.45592	0.727962	+	0.685618i	$0.240468\pi$
$734$	−1.23969e13	−1.57645
$735$	−1.93732e12	−0.244854
$736$	−4.00329e12	−0.502883
$737$	−1.89549e13	−2.36656
$738$	−3.86390e12	−0.479482
$739$	−7.99980e12	−0.986686	−0.493343	−	0.869835i	$-0.664225\pi$
$739$	−7.99980e12	−0.986686	−0.493343	+	0.869835i	$0.664225\pi$
$740$	9.11436e11	0.111733
$741$	−1.52562e12	−0.185894
$742$	1.99696e12	0.241853
$743$	6.88412e12	0.828702	0.414351	−	0.910117i	$-0.364009\pi$
$743$	6.88412e12	0.828702	0.414351	+	0.910117i	$0.364009\pi$
$744$	8.44872e11	0.101091
$745$	−4.57036e12	−0.543560
$746$	−9.13568e12	−1.07998
$747$	−3.20315e12	−0.376387
$748$	−3.80930e12	−0.444927
$749$	−1.04117e11	−0.0120880
$750$	3.64239e12	0.420350
$751$	6.54436e12	0.750736	0.375368	−	0.926876i	$-0.377516\pi$
$751$	6.54436e12	0.750736	0.375368	+	0.926876i	$0.377516\pi$
$752$	−1.57482e11	−0.0179577
$753$	3.48889e12	0.395467
$754$	2.73613e11	0.0308294
$755$	8.06321e11	0.0903123
$756$	6.72934e10	0.00749246
$757$	−1.72596e12	−0.191029	−0.0955145	−	0.995428i	$-0.530450\pi$
$757$	−1.72596e12	−0.191029	−0.0955145	+	0.995428i	$0.530450\pi$
$758$	−1.86478e12	−0.205171
$759$	−1.27887e13	−1.39874
$760$	−6.55031e12	−0.712197
$761$	−1.30920e13	−1.41506	−0.707531	−	0.706682i	$-0.750191\pi$
$761$	−1.30920e13	−1.41506	−0.707531	+	0.706682i	$0.750191\pi$
$762$	7.89520e12	0.848332
$763$	1.55990e12	0.166624
$764$	2.43027e12	0.258069
$765$	−2.09292e12	−0.220941
$766$	9.96918e12	1.04624
$767$	2.68421e11	0.0280051
$768$	2.86223e12	0.296879
$769$	−9.00628e12	−0.928703	−0.464351	−	0.885651i	$-0.653713\pi$
$769$	−9.00628e12	−0.928703	−0.464351	+	0.885651i	$0.653713\pi$
$770$	1.46027e12	0.149701
$771$	1.01573e13	1.03522
$772$	−1.22302e12	−0.123924
$773$	1.52547e13	1.53672	0.768362	−	0.640015i	$-0.221072\pi$
$773$	1.52547e13	1.53672	0.768362	+	0.640015i	$0.221072\pi$
$774$	−1.58506e12	−0.158749
$775$	1.31978e12	0.131415
$776$	7.65256e11	0.0757581
$777$	−1.82157e12	−0.179288
$778$	−1.59154e13	−1.55743
$779$	2.43981e13	2.37377
$780$	−1.01434e11	−0.00981197
$781$	−1.78300e12	−0.171484
$782$	−2.02638e13	−1.93772
$783$	3.19837e11	0.0304089
$784$	7.96671e12	0.753107
$785$	−4.12951e12	−0.388137
$786$	4.14791e12	0.387640
$787$	−1.59730e12	−0.148422	−0.0742112	−	0.997243i	$-0.523644\pi$
$787$	−1.59730e12	−0.148422	−0.0742112	+	0.997243i	$0.523644\pi$
$788$	1.12272e12	0.103730
$789$	6.31453e12	0.580089
$790$	6.64651e11	0.0607116
$791$	1.60730e12	0.145983
$792$	6.64884e12	0.600458
$793$	1.68371e12	0.151195
$794$	1.93971e13	1.73198
$795$	−3.51862e12	−0.312406
$796$	1.26774e12	0.111923
$797$	8.04243e12	0.706033	0.353016	−	0.935617i	$-0.385156\pi$
$797$	8.04243e12	0.706033	0.353016	+	0.935617i	$0.385156\pi$
$798$	1.97159e12	0.172109
$799$	3.88922e11	0.0337600
$800$	3.25123e12	0.280636
$801$	1.97234e12	0.169291
$802$	−1.67108e13	−1.42630
$803$	2.59967e13	2.20647
$804$	−1.70153e12	−0.143611
$805$	−1.67415e12	−0.140512
$806$	3.83314e11	0.0319924
$807$	3.32405e12	0.275890
$808$	−7.58654e11	−0.0626171
$809$	3.37778e12	0.277245	0.138622	−	0.990345i	$-0.455733\pi$
$809$	3.37778e12	0.277245	0.138622	+	0.990345i	$0.455733\pi$
$810$	5.50158e11	0.0449061
$811$	1.01734e12	0.0825795	0.0412898	−	0.999147i	$-0.486853\pi$
$811$	1.01734e12	0.0825795	0.0412898	+	0.999147i	$0.486853\pi$
$812$	7.62064e10	0.00615162
$813$	2.22093e11	0.0178290
$814$	−2.71052e13	−2.16393
$815$	−5.76251e12	−0.457512
$816$	8.60657e12	0.679555
$817$	1.00087e13	0.785917
$818$	2.52869e12	0.197472
$819$	2.02722e11	0.0157443
$820$	1.62215e12	0.125294
$821$	2.01419e13	1.54724	0.773618	−	0.633653i	$-0.218445\pi$
$821$	2.01419e13	1.54724	0.773618	+	0.633653i	$0.218445\pi$
$822$	−4.37751e12	−0.334429
$823$	−9.23318e12	−0.701539	−0.350770	−	0.936462i	$-0.614080\pi$
$823$	−9.23318e12	−0.701539	−0.350770	+	0.936462i	$0.614080\pi$
$824$	−4.66589e12	−0.352584
$825$	1.03862e13	0.780574
$826$	−3.46884e11	−0.0259283
$827$	1.65328e13	1.22906	0.614528	−	0.788895i	$-0.289346\pi$
$827$	1.65328e13	1.22906	0.614528	+	0.788895i	$0.289346\pi$
$828$	−1.14801e12	−0.0848804
$829$	−1.69704e13	−1.24795	−0.623973	−	0.781446i	$-0.714483\pi$
$829$	−1.69704e13	−1.24795	−0.623973	+	0.781446i	$0.714483\pi$
$830$	−6.23958e12	−0.456356
$831$	−7.51891e12	−0.546953
$832$	3.29681e12	0.238528
$833$	−1.96748e13	−1.41582
$834$	−1.18166e13	−0.845758
$835$	−4.33240e12	−0.308418
$836$	−6.32283e12	−0.447696
$837$	4.48072e11	0.0315561
$838$	3.86428e12	0.270689
$839$	−2.03267e13	−1.41624	−0.708122	−	0.706090i	$-0.750458\pi$
$839$	−2.03267e13	−1.41624	−0.708122	+	0.706090i	$0.750458\pi$
$840$	8.70392e11	0.0603195
$841$	−1.41449e13	−0.975033
$842$	−1.27479e13	−0.874044
$843$	−1.02632e13	−0.699935
$844$	−6.50501e11	−0.0441273
$845$	6.29808e12	0.424965
$846$	−1.02235e11	−0.00686169
$847$	6.07043e12	0.405269
$848$	1.44694e13	0.960878
$849$	−1.24991e13	−0.825649
$850$	1.64571e13	1.08135
$851$	3.10754e13	2.03111
$852$	−1.60055e11	−0.0104062
$853$	−5.58034e12	−0.360903	−0.180451	−	0.983584i	$-0.557756\pi$
$853$	−5.58034e12	−0.360903	−0.180451	+	0.983584i	$0.557756\pi$
$854$	−2.17588e12	−0.139983
$855$	−3.47391e12	−0.222316
$856$	−9.23451e11	−0.0587871
$857$	1.54397e13	0.977746	0.488873	−	0.872355i	$-0.337408\pi$
$857$	1.54397e13	0.977746	0.488873	+	0.872355i	$0.337408\pi$
$858$	3.01654e12	0.190028
$859$	6.97305e10	0.00436972	0.00218486	−	0.999998i	$-0.499305\pi$
$859$	6.97305e10	0.00436972	0.00218486	+	0.999998i	$0.499305\pi$
$860$	6.65443e11	0.0414828
$861$	−3.24197e12	−0.201046
$862$	−1.03805e13	−0.640378
$863$	2.35934e13	1.44791	0.723955	−	0.689848i	$-0.242323\pi$
$863$	2.35934e13	1.44791	0.723955	+	0.689848i	$0.242323\pi$
$864$	1.10381e12	0.0673879
$865$	1.05442e13	0.640385
$866$	1.47693e13	0.892339
$867$	−1.16494e13	−0.700194
$868$	1.06760e11	0.00638368
$869$	4.25998e12	0.253407
$870$	6.23027e11	0.0368697
$871$	−5.12588e12	−0.301777
$872$	1.38353e13	0.810334
$873$	4.05848e11	0.0236483
$874$	−3.36347e13	−1.94978
$875$	3.05612e12	0.176252
$876$	2.33365e12	0.133896
$877$	−9.54680e12	−0.544954	−0.272477	−	0.962162i	$-0.587843\pi$
$877$	−9.54680e12	−0.544954	−0.272477	+	0.962162i	$0.587843\pi$
$878$	−3.81222e12	−0.216497
$879$	−6.63450e12	−0.374851
$880$	1.05807e13	0.594758
$881$	1.75702e13	0.982617	0.491308	−	0.870986i	$-0.336519\pi$
$881$	1.75702e13	0.982617	0.491308	+	0.870986i	$0.336519\pi$
$882$	5.17185e12	0.287765
$883$	−2.87218e13	−1.58997	−0.794983	−	0.606632i	$-0.792520\pi$
$883$	−2.87218e13	−1.58997	−0.794983	+	0.606632i	$0.792520\pi$
$884$	−1.03013e12	−0.0567357
$885$	6.11205e11	0.0334921
$886$	−9.65471e12	−0.526366
$887$	3.24486e13	1.76011	0.880055	−	0.474872i	$-0.157506\pi$
$887$	3.24486e13	1.76011	0.880055	+	0.474872i	$0.157506\pi$
$888$	−1.61561e13	−0.871922
$889$	6.62440e12	0.355704
$890$	3.84201e12	0.205260
$891$	3.52616e12	0.187436
$892$	1.10012e12	0.0581833
$893$	6.45547e11	0.0339701
$894$	1.22010e13	0.638818
$895$	−1.73801e12	−0.0905419
$896$	−2.77721e12	−0.143953
$897$	−3.45838e12	−0.178364
$898$	2.52030e13	1.29333
$899$	5.07419e11	0.0259088
$900$	9.32341e11	0.0473678
$901$	−3.57340e13	−1.80642
$902$	−4.82412e13	−2.42655
$903$	−1.32993e12	−0.0665632
$904$	1.42557e13	0.709955
$905$	4.75060e12	0.235413
$906$	−2.15255e12	−0.106139
$907$	1.03571e13	0.508167	0.254083	−	0.967182i	$-0.418226\pi$
$907$	1.03571e13	0.508167	0.254083	+	0.967182i	$0.418226\pi$
$908$	5.07300e12	0.247673
$909$	−4.02347e11	−0.0195462
$910$	3.94892e11	0.0190894
$911$	−1.32787e13	−0.638739	−0.319369	−	0.947630i	$-0.603471\pi$
$911$	−1.32787e13	−0.638739	−0.319369	+	0.947630i	$0.603471\pi$
$912$	1.42855e13	0.683784
$913$	−3.99917e13	−1.90481
$914$	−2.24922e13	−1.06604
$915$	3.83387e12	0.180818
$916$	1.25738e11	0.00590117
$917$	3.48027e12	0.162537
$918$	5.58724e12	0.259660
$919$	−4.00751e13	−1.85334	−0.926670	−	0.375877i	$-0.877342\pi$
$919$	−4.00751e13	−1.85334	−0.926670	+	0.375877i	$0.877342\pi$
$920$	−1.48486e13	−0.683347
$921$	−4.83920e12	−0.221618
$922$	−7.17317e12	−0.326905
$923$	−4.82168e11	−0.0218671
$924$	8.40165e11	0.0379176
$925$	−2.52375e13	−1.13347
$926$	−5.69019e12	−0.254318
$927$	−2.47452e12	−0.110061
$928$	1.25001e12	0.0553282
$929$	8.42283e11	0.0371012	0.0185506	−	0.999828i	$-0.494095\pi$
$929$	8.42283e11	0.0371012	0.0185506	+	0.999828i	$0.494095\pi$
$930$	8.72821e11	0.0382606
$931$	−3.26570e13	−1.42463
$932$	5.81858e12	0.252607
$933$	−2.77947e12	−0.120087
$934$	−1.19680e13	−0.514591
$935$	−2.61303e13	−1.11813
$936$	1.79801e12	0.0765686
$937$	2.55688e13	1.08363	0.541817	−	0.840497i	$-0.317737\pi$
$937$	2.55688e13	1.08363	0.541817	+	0.840497i	$0.317737\pi$
$938$	6.62424e12	0.279398
$939$	5.98574e12	0.251260
$940$	4.29203e10	0.00179303
$941$	−2.70330e13	−1.12393	−0.561967	−	0.827160i	$-0.689955\pi$
$941$	−2.70330e13	−1.12393	−0.561967	+	0.827160i	$0.689955\pi$
$942$	1.10241e13	0.456157
$943$	5.53071e13	2.27760
$944$	−2.51342e12	−0.103013
$945$	4.61606e11	0.0188290
$946$	−1.97896e13	−0.803392
$947$	−3.12375e13	−1.26212	−0.631062	−	0.775733i	$-0.717381\pi$
$947$	−3.12375e13	−1.26212	−0.631062	+	0.775733i	$0.717381\pi$
$948$	3.82407e11	0.0153776
$949$	7.03015e12	0.281363
$950$	2.73160e13	1.08808
$951$	8.83982e12	0.350454
$952$	8.83944e12	0.348785
$953$	−3.49467e13	−1.37242	−0.686211	−	0.727402i	$-0.740727\pi$
$953$	−3.49467e13	−1.37242	−0.686211	+	0.727402i	$0.740727\pi$
$954$	9.39327e12	0.367155
$955$	1.66707e13	0.648543
$956$	2.81007e12	0.108807
$957$	3.99320e12	0.153892
$958$	4.43779e13	1.70224
$959$	−3.67291e12	−0.140226
$960$	7.50696e12	0.285262
$961$	−2.57288e13	−0.973114
$962$	−7.32992e12	−0.275938
$963$	−4.89746e11	−0.0183507
$964$	3.99784e12	0.149101
$965$	−8.38940e12	−0.311428
$966$	4.46931e12	0.165137
$967$	2.47408e13	0.909903	0.454952	−	0.890516i	$-0.349657\pi$
$967$	2.47408e13	0.909903	0.454952	+	0.890516i	$0.349657\pi$
$968$	5.38406e13	1.97093
$969$	−3.52799e13	−1.28550
$970$	7.90571e11	0.0286727
$971$	2.81788e13	1.01727	0.508634	−	0.860983i	$-0.330151\pi$
$971$	2.81788e13	1.01727	0.508634	+	0.860983i	$0.330151\pi$
$972$	3.16534e11	0.0113742
$973$	−9.91464e12	−0.354625
$974$	−3.66221e13	−1.30385
$975$	2.80868e12	0.0995364
$976$	−1.57658e13	−0.556149
$977$	4.77088e13	1.67522	0.837612	−	0.546266i	$-0.183951\pi$
$977$	4.77088e13	1.67522	0.837612	+	0.546266i	$0.183951\pi$
$978$	1.53836e13	0.537690
$979$	2.46248e13	0.856744
$980$	−2.17126e12	−0.0751958
$981$	7.33744e12	0.252950
$982$	−1.28510e13	−0.440996
$983$	1.11374e13	0.380446	0.190223	−	0.981741i	$-0.439079\pi$
$983$	1.11374e13	0.380446	0.190223	+	0.981741i	$0.439079\pi$
$984$	−2.87542e13	−0.977738
$985$	7.70141e12	0.260680
$986$	6.32727e12	0.213192
$987$	−8.57791e10	−0.00287710
$988$	−1.70985e12	−0.0570888
$989$	2.26882e13	0.754080
$990$	6.86878e12	0.227259
$991$	−3.95333e13	−1.30206	−0.651031	−	0.759051i	$-0.725663\pi$
$991$	−3.95333e13	−1.30206	−0.651031	+	0.759051i	$0.725663\pi$
$992$	1.75118e12	0.0574154
$993$	6.65730e12	0.217283
$994$	6.23113e11	0.0202455
$995$	8.69616e12	0.281270
$996$	−3.58994e12	−0.115590
$997$	2.77111e12	0.0888230	0.0444115	−	0.999013i	$-0.485859\pi$
$997$	2.77111e12	0.0888230	0.0444115	+	0.999013i	$0.485859\pi$
$998$	−1.28507e13	−0.410054
$999$	−8.56825e12	−0.272175

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.c.1.6	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.c.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-20.5236 q^{2} -81.0000 q^{3} -90.7810 q^{4} -622.721 q^{5} +1662.41 q^{6} +1394.83 q^{7} +12371.2 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-20.5236 q^{2} -81.0000 q^{3} -90.7810 q^{4} -622.721 q^{5} +1662.41 q^{6} +1394.83 q^{7} +12371.2 q^{8} +6561.00 q^{9} +12780.5 q^{10} +81914.7 q^{11} +7353.26 q^{12} +22151.8 q^{13} -28627.0 q^{14} +50440.4 q^{15} -207423. q^{16} +512258. q^{17} -134655. q^{18} +850265. q^{19} +56531.3 q^{20} -112982. q^{21} -1.68119e6 q^{22} +1.92743e6 q^{23} -1.00207e6 q^{24} -1.56534e6 q^{25} -454634. q^{26} -531441. q^{27} -126624. q^{28} -601830. q^{29} -1.03522e6 q^{30} -843126. q^{31} -2.07701e6 q^{32} -6.63509e6 q^{33} -1.05134e7 q^{34} -868593. q^{35} -595614. q^{36} +1.61227e7 q^{37} -1.74505e7 q^{38} -1.79429e6 q^{39} -7.70384e6 q^{40} +2.86947e7 q^{41} +2.31879e6 q^{42} +1.17712e7 q^{43} -7.43630e6 q^{44} -4.08567e6 q^{45} -3.95579e7 q^{46} +759231. q^{47} +1.68013e7 q^{48} -3.84080e7 q^{49} +3.21265e7 q^{50} -4.14929e7 q^{51} -2.01096e6 q^{52} -6.97578e7 q^{53} +1.09071e7 q^{54} -5.10101e7 q^{55} +1.72558e7 q^{56} -6.88715e7 q^{57} +1.23517e7 q^{58} +1.21174e7 q^{59} -4.57903e6 q^{60} +7.60079e7 q^{61} +1.73040e7 q^{62} +9.15151e6 q^{63} +1.48828e8 q^{64} -1.37944e7 q^{65} +1.36176e8 q^{66} -2.31398e8 q^{67} -4.65033e7 q^{68} -1.56122e8 q^{69} +1.78267e7 q^{70} -2.17666e7 q^{71} +8.11678e7 q^{72} +3.17363e8 q^{73} -3.30896e8 q^{74} +1.26793e8 q^{75} -7.71879e7 q^{76} +1.14257e8 q^{77} +3.68254e7 q^{78} +5.20051e7 q^{79} +1.29167e8 q^{80} +4.30467e7 q^{81} -5.88920e8 q^{82} -4.88211e8 q^{83} +1.02566e7 q^{84} -3.18994e8 q^{85} -2.41588e8 q^{86} +4.87482e7 q^{87} +1.01339e9 q^{88} +3.00615e8 q^{89} +8.38528e7 q^{90} +3.08980e7 q^{91} -1.74974e8 q^{92} +6.82932e7 q^{93} -1.55822e7 q^{94} -5.29478e8 q^{95} +1.68238e8 q^{96} +6.18576e7 q^{97} +7.88272e8 q^{98} +5.37443e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9}+O(q^{10}) \) 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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