LMFDB - Embedded newform 177.12.a.b.1.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,12,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, 12, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 12 $
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:	$135.996742959$
Analytic rank:	$1$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.22
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)

$f(q)$	$=$	$q+57.7377 q^{2} +243.000 q^{3} +1285.65 q^{4} +767.893 q^{5} +14030.3 q^{6} -31308.7 q^{7} -44016.6 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+57.7377 q^{2} +243.000 q^{3} +1285.65 q^{4} +767.893 q^{5} +14030.3 q^{6} -31308.7 q^{7} -44016.6 q^{8} +59049.0 q^{9} +44336.4 q^{10} +611667. q^{11} +312412. q^{12} -176895. q^{13} -1.80769e6 q^{14} +186598. q^{15} -5.17442e6 q^{16} -451731. q^{17} +3.40936e6 q^{18} +5.30807e6 q^{19} +987239. q^{20} -7.60801e6 q^{21} +3.53163e7 q^{22} -4.82528e7 q^{23} -1.06960e7 q^{24} -4.82385e7 q^{25} -1.02135e7 q^{26} +1.43489e7 q^{27} -4.02519e7 q^{28} +6.91351e7 q^{29} +1.07737e7 q^{30} +1.50685e8 q^{31} -2.08613e8 q^{32} +1.48635e8 q^{33} -2.60819e7 q^{34} -2.40417e7 q^{35} +7.59161e7 q^{36} -1.05510e8 q^{37} +3.06476e8 q^{38} -4.29855e7 q^{39} -3.38000e7 q^{40} +2.19294e8 q^{41} -4.39269e8 q^{42} -1.08755e9 q^{43} +7.86387e8 q^{44} +4.53433e7 q^{45} -2.78601e9 q^{46} -2.42981e9 q^{47} -1.25738e9 q^{48} -9.97092e8 q^{49} -2.78518e9 q^{50} -1.09771e8 q^{51} -2.27425e8 q^{52} -1.46158e9 q^{53} +8.28473e8 q^{54} +4.69695e8 q^{55} +1.37810e9 q^{56} +1.28986e9 q^{57} +3.99171e9 q^{58} -7.14924e8 q^{59} +2.39899e8 q^{60} -1.10059e10 q^{61} +8.70020e9 q^{62} -1.84875e9 q^{63} -1.44765e9 q^{64} -1.35837e8 q^{65} +8.58185e9 q^{66} -4.40368e9 q^{67} -5.80766e8 q^{68} -1.17254e10 q^{69} -1.38811e9 q^{70} -5.15856e9 q^{71} -2.59913e9 q^{72} +1.29872e10 q^{73} -6.09192e9 q^{74} -1.17219e10 q^{75} +6.82430e9 q^{76} -1.91505e10 q^{77} -2.48189e9 q^{78} -1.77050e10 q^{79} -3.97340e9 q^{80} +3.48678e9 q^{81} +1.26615e10 q^{82} -3.33159e10 q^{83} -9.78121e9 q^{84} -3.46881e8 q^{85} -6.27929e10 q^{86} +1.67998e10 q^{87} -2.69235e10 q^{88} +4.53170e10 q^{89} +2.61802e9 q^{90} +5.53836e9 q^{91} -6.20360e10 q^{92} +3.66164e10 q^{93} -1.40292e11 q^{94} +4.07603e9 q^{95} -5.06931e10 q^{96} -8.62927e10 q^{97} -5.75699e10 q^{98} +3.61183e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9}+O(q^{10}) $ 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9} - 383719 q^{10} - 1816556 q^{11} + 6352506 q^{12} - 3951804 q^{13} - 6207867 q^{14} - 4176684 q^{15} + 28295194 q^{16} - 17723275 q^{17} - 7558272 q^{18} - 19573013 q^{19} - 48468099 q^{20} - 30758697 q^{21} - 1729910 q^{22} - 88593797 q^{23} - 86458671 q^{24} + 345714963 q^{25} - 6676346 q^{26} + 387420489 q^{27} + 126954286 q^{28} - 276632427 q^{29} - 93243717 q^{30} - 357680917 q^{31} - 859842334 q^{32} - 441423108 q^{33} + 232730000 q^{34} - 510315139 q^{35} + 1543658958 q^{36} - 660238257 q^{37} - 2067286961 q^{38} - 960288372 q^{39} - 3388951110 q^{40} - 1671147569 q^{41} - 1508511681 q^{42} - 1883107790 q^{43} - 3895687630 q^{44} - 1014934212 q^{45} - 1720344243 q^{46} - 5818572501 q^{47} + 6875732142 q^{48} - 18858180 q^{49} - 21474519647 q^{50} - 4306755825 q^{51} - 42214560062 q^{52} - 11444513368 q^{53} - 1836660096 q^{54} - 24401486484 q^{55} - 50583585764 q^{56} - 4756242159 q^{57} - 45017395090 q^{58} - 19302956073 q^{59} - 11777748057 q^{60} + 408637955 q^{61} - 28543084070 q^{62} - 7474363371 q^{63} + 33067284293 q^{64} - 21656714730 q^{65} - 420368130 q^{66} - 49803132690 q^{67} - 16500749319 q^{68} - 21528292671 q^{69} - 45808890782 q^{70} - 34127492216 q^{71} - 21009457053 q^{72} - 55734362153 q^{73} - 40367816298 q^{74} + 84008736009 q^{75} - 14840406404 q^{76} - 99723443615 q^{77} - 1622352078 q^{78} - 76484916442 q^{79} + 93882788915 q^{80} + 94143178827 q^{81} + 52951239205 q^{82} - 140433865655 q^{83} + 30849891498 q^{84} + 34329063335 q^{85} + 175223869508 q^{86} - 67221679761 q^{87} + 268823645069 q^{88} - 1191878597 q^{89} - 22658223231 q^{90} + 201632581559 q^{91} - 206501888812 q^{92} - 86916462831 q^{93} + 319770144384 q^{94} - 81387074885 q^{95} - 208941687162 q^{96} - 144896178730 q^{97} + 135739195260 q^{98} - 107265815244 q^{99}+O(q^{100}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9 - 383719 * q^10 - 1816556 * q^11 + 6352506 * q^12 - 3951804 * q^13 - 6207867 * q^14 - 4176684 * q^15 + 28295194 * q^16 - 17723275 * q^17 - 7558272 * q^18 - 19573013 * q^19 - 48468099 * q^20 - 30758697 * q^21 - 1729910 * q^22 - 88593797 * q^23 - 86458671 * q^24 + 345714963 * q^25 - 6676346 * q^26 + 387420489 * q^27 + 126954286 * q^28 - 276632427 * q^29 - 93243717 * q^30 - 357680917 * q^31 - 859842334 * q^32 - 441423108 * q^33 + 232730000 * q^34 - 510315139 * q^35 + 1543658958 * q^36 - 660238257 * q^37 - 2067286961 * q^38 - 960288372 * q^39 - 3388951110 * q^40 - 1671147569 * q^41 - 1508511681 * q^42 - 1883107790 * q^43 - 3895687630 * q^44 - 1014934212 * q^45 - 1720344243 * q^46 - 5818572501 * q^47 + 6875732142 * q^48 - 18858180 * q^49 - 21474519647 * q^50 - 4306755825 * q^51 - 42214560062 * q^52 - 11444513368 * q^53 - 1836660096 * q^54 - 24401486484 * q^55 - 50583585764 * q^56 - 4756242159 * q^57 - 45017395090 * q^58 - 19302956073 * q^59 - 11777748057 * q^60 + 408637955 * q^61 - 28543084070 * q^62 - 7474363371 * q^63 + 33067284293 * q^64 - 21656714730 * q^65 - 420368130 * q^66 - 49803132690 * q^67 - 16500749319 * q^68 - 21528292671 * q^69 - 45808890782 * q^70 - 34127492216 * q^71 - 21009457053 * q^72 - 55734362153 * q^73 - 40367816298 * q^74 + 84008736009 * q^75 - 14840406404 * q^76 - 99723443615 * q^77 - 1622352078 * q^78 - 76484916442 * q^79 + 93882788915 * q^80 + 94143178827 * q^81 + 52951239205 * q^82 - 140433865655 * q^83 + 30849891498 * q^84 + 34329063335 * q^85 + 175223869508 * q^86 - 67221679761 * q^87 + 268823645069 * q^88 - 1191878597 * q^89 - 22658223231 * q^90 + 201632581559 * q^91 - 206501888812 * q^92 - 86916462831 * q^93 + 319770144384 * q^94 - 81387074885 * q^95 - 208941687162 * q^96 - 144896178730 * q^97 + 135739195260 * q^98 - 107265815244 * 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 $

$2$	57.7377	1.27584	0.637918	−	0.770104i	$-0.279796\pi$
$2$	57.7377	1.27584	0.637918	+	0.770104i	$0.279796\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	1285.65	0.627757
$5$	767.893	0.109892	0.0549459	−	0.998489i	$-0.482501\pi$
$5$	767.893	0.109892	0.0549459	+	0.998489i	$0.482501\pi$
$6$	14030.3	0.736604
$7$	−31308.7	−0.704086	−0.352043	−	0.935984i	$-0.614513\pi$
$7$	−31308.7	−0.704086	−0.352043	+	0.935984i	$0.614513\pi$
$8$	−44016.6	−0.474921
$9$	59049.0	0.333333
$10$	44336.4	0.140204
$11$	611667.	1.14513	0.572565	−	0.819859i	$-0.305948\pi$
$11$	611667.	1.14513	0.572565	+	0.819859i	$0.305948\pi$
$12$	312412.	0.362436
$13$	−176895.	−0.132138	−0.0660690	−	0.997815i	$-0.521046\pi$
$13$	−176895.	−0.132138	−0.0660690	+	0.997815i	$0.521046\pi$
$14$	−1.80769e6	−0.898298
$15$	186598.	0.0634461
$16$	−5.17442e6	−1.23368
$17$	−451731.	−0.0771633	−0.0385816	−	0.999255i	$-0.512284\pi$
$17$	−451731.	−0.0771633	−0.0385816	+	0.999255i	$0.512284\pi$
$18$	3.40936e6	0.425279
$19$	5.30807e6	0.491804	0.245902	−	0.969295i	$-0.420916\pi$
$19$	5.30807e6	0.491804	0.245902	+	0.969295i	$0.420916\pi$
$20$	987239.	0.0689854
$21$	−7.60801e6	−0.406504
$22$	3.53163e7	1.46100
$23$	−4.82528e7	−1.56322	−0.781608	−	0.623770i	$-0.785600\pi$
$23$	−4.82528e7	−1.56322	−0.781608	+	0.623770i	$0.785600\pi$
$24$	−1.06960e7	−0.274196
$25$	−4.82385e7	−0.987924
$26$	−1.02135e7	−0.168586
$27$	1.43489e7	0.192450
$28$	−4.02519e7	−0.441995
$29$	6.91351e7	0.625907	0.312953	−	0.949768i	$-0.398682\pi$
$29$	6.91351e7	0.625907	0.312953	+	0.949768i	$0.398682\pi$
$30$	1.07737e7	0.0809468
$31$	1.50685e8	0.945323	0.472662	−	0.881244i	$-0.343293\pi$
$31$	1.50685e8	0.945323	0.472662	+	0.881244i	$0.343293\pi$
$32$	−2.08613e8	−1.09905
$33$	1.48635e8	0.661142
$34$	−2.60819e7	−0.0984477
$35$	−2.40417e7	−0.0773733
$36$	7.59161e7	0.209252
$37$	−1.05510e8	−0.250141	−0.125071	−	0.992148i	$-0.539916\pi$
$37$	−1.05510e8	−0.250141	−0.125071	+	0.992148i	$0.539916\pi$
$38$	3.06476e8	0.627461
$39$	−4.29855e7	−0.0762899
$40$	−3.38000e7	−0.0521899
$41$	2.19294e8	0.295607	0.147803	−	0.989017i	$-0.452780\pi$
$41$	2.19294e8	0.295607	0.147803	+	0.989017i	$0.452780\pi$
$42$	−4.39269e8	−0.518633
$43$	−1.08755e9	−1.12817	−0.564085	−	0.825717i	$-0.690771\pi$
$43$	−1.08755e9	−1.12817	−0.564085	+	0.825717i	$0.690771\pi$
$44$	7.86387e8	0.718864
$45$	4.53433e7	0.0366306
$46$	−2.78601e9	−1.99441
$47$	−2.42981e9	−1.54537	−0.772687	−	0.634787i	$-0.781088\pi$
$47$	−2.42981e9	−1.54537	−0.772687	+	0.634787i	$0.781088\pi$
$48$	−1.25738e9	−0.712264
$49$	−9.97092e8	−0.504263
$50$	−2.78518e9	−1.26043
$51$	−1.09771e8	−0.0445502
$52$	−2.27425e8	−0.0829505
$53$	−1.46158e9	−0.480072	−0.240036	−	0.970764i	$-0.577159\pi$
$53$	−1.46158e9	−0.480072	−0.240036	+	0.970764i	$0.577159\pi$
$54$	8.28473e8	0.245535
$55$	4.69695e8	0.125841
$56$	1.37810e9	0.334385
$57$	1.28986e9	0.283943
$58$	3.99171e9	0.798554
$59$	−7.14924e8	−0.130189
$59$	−7.14924e8	−0.130189
$60$	2.39899e8	0.0398287
$61$	−1.10059e10	−1.66844	−0.834221	−	0.551431i	$-0.814082\pi$
$61$	−1.10059e10	−1.66844	−0.834221	+	0.551431i	$0.814082\pi$
$62$	8.70020e9	1.20608
$63$	−1.84875e9	−0.234695
$64$	−1.44765e9	−0.168529
$65$	−1.35837e8	−0.0145209
$66$	8.58185e9	0.843508
$67$	−4.40368e9	−0.398478	−0.199239	−	0.979951i	$-0.563847\pi$
$67$	−4.40368e9	−0.398478	−0.199239	+	0.979951i	$0.563847\pi$
$68$	−5.80766e8	−0.0484398
$69$	−1.17254e10	−0.902523
$70$	−1.38811e9	−0.0987157
$71$	−5.15856e9	−0.339318	−0.169659	−	0.985503i	$-0.554267\pi$
$71$	−5.15856e9	−0.339318	−0.169659	+	0.985503i	$0.554267\pi$
$72$	−2.59913e9	−0.158307
$73$	1.29872e10	0.733230	0.366615	−	0.930373i	$-0.380517\pi$
$73$	1.29872e10	0.733230	0.366615	+	0.930373i	$0.380517\pi$
$74$	−6.09192e9	−0.319139
$75$	−1.17219e10	−0.570378
$76$	6.82430e9	0.308733
$77$	−1.91505e10	−0.806271
$78$	−2.48189e9	−0.0973334
$79$	−1.77050e10	−0.647361	−0.323680	−	0.946167i	$-0.604920\pi$
$79$	−1.77050e10	−0.647361	−0.323680	+	0.946167i	$0.604920\pi$
$80$	−3.97340e9	−0.135571
$81$	3.48678e9	0.111111
$82$	1.26615e10	0.377146
$83$	−3.33159e10	−0.928372	−0.464186	−	0.885738i	$-0.653653\pi$
$83$	−3.33159e10	−0.928372	−0.464186	+	0.885738i	$0.653653\pi$
$84$	−9.78121e9	−0.255186
$85$	−3.46881e8	−0.00847962
$86$	−6.27929e10	−1.43936
$87$	1.67998e10	0.361368
$88$	−2.69235e10	−0.543847
$89$	4.53170e10	0.860233	0.430116	−	0.902773i	$-0.358473\pi$
$89$	4.53170e10	0.860233	0.430116	+	0.902773i	$0.358473\pi$
$90$	2.61802e9	0.0467347
$91$	5.53836e9	0.0930365
$92$	−6.20360e10	−0.981320
$93$	3.66164e10	0.545783
$94$	−1.40292e11	−1.97164
$95$	4.07603e9	0.0540453
$96$	−5.06931e10	−0.634537
$97$	−8.62927e10	−1.02030	−0.510152	−	0.860084i	$-0.670411\pi$
$97$	−8.62927e10	−1.02030	−0.510152	+	0.860084i	$0.670411\pi$
$98$	−5.75699e10	−0.643357
$99$	3.61183e10	0.381710
$100$	−6.20176e10	−0.620176
$101$	2.05179e11	1.94252	0.971259	−	0.238024i	$-0.0764998\pi$
$101$	2.05179e11	1.94252	0.971259	+	0.238024i	$0.0764998\pi$
$102$	−6.33791e9	−0.0568388
$103$	5.31584e10	0.451821	0.225911	−	0.974148i	$-0.427464\pi$
$103$	5.31584e10	0.451821	0.225911	+	0.974148i	$0.427464\pi$
$104$	7.78632e9	0.0627551
$105$	−5.84214e9	−0.0446715
$106$	−8.43885e10	−0.612493
$107$	−1.56956e11	−1.08185	−0.540924	−	0.841071i	$-0.681925\pi$
$107$	−1.56956e11	−1.08185	−0.540924	+	0.841071i	$0.681925\pi$
$108$	1.84476e10	0.120812
$109$	−1.01690e11	−0.633044	−0.316522	−	0.948585i	$-0.602515\pi$
$109$	−1.01690e11	−0.633044	−0.316522	+	0.948585i	$0.602515\pi$
$110$	2.71191e10	0.160552
$111$	−2.56390e10	−0.144419
$112$	1.62004e11	0.868616
$113$	−2.78402e11	−1.42148	−0.710741	−	0.703454i	$-0.751640\pi$
$113$	−2.78402e11	−1.42148	−0.710741	+	0.703454i	$0.751640\pi$
$114$	7.44737e10	0.362265
$115$	−3.70530e10	−0.171785
$116$	8.88833e10	0.392917
$117$	−1.04455e10	−0.0440460
$118$	−4.12781e10	−0.166100
$119$	1.41431e10	0.0543296
$120$	−8.21340e9	−0.0301319
$121$	8.88246e10	0.311325
$122$	−6.35455e11	−2.12866
$123$	5.32883e10	0.170669
$124$	1.93727e11	0.593433
$125$	−7.45367e10	−0.218457
$126$	−1.06742e11	−0.299433
$127$	−5.49853e10	−0.147682	−0.0738408	−	0.997270i	$-0.523526\pi$
$127$	−5.49853e10	−0.147682	−0.0738408	+	0.997270i	$0.523526\pi$
$128$	3.43656e11	0.884034
$129$	−2.64276e11	−0.651349
$130$	−7.84289e9	−0.0185263
$131$	2.07559e11	0.470055	0.235028	−	0.971989i	$-0.424482\pi$
$131$	2.07559e11	0.470055	0.235028	+	0.971989i	$0.424482\pi$
$132$	1.91092e11	0.415036
$133$	−1.66189e11	−0.346272
$134$	−2.54259e11	−0.508393
$135$	1.10184e10	0.0211487
$136$	1.98836e10	0.0366465
$137$	−2.81121e11	−0.497656	−0.248828	−	0.968548i	$-0.580045\pi$
$137$	−2.81121e11	−0.497656	−0.248828	+	0.968548i	$0.580045\pi$
$138$	−6.76999e11	−1.15147
$139$	9.52056e11	1.55626	0.778128	−	0.628106i	$-0.216169\pi$
$139$	9.52056e11	1.55626	0.778128	+	0.628106i	$0.216169\pi$
$140$	−3.09092e10	−0.0485717
$141$	−5.90443e11	−0.892222
$142$	−2.97843e11	−0.432914
$143$	−1.08201e11	−0.151315
$144$	−3.05544e11	−0.411226
$145$	5.30884e10	0.0687821
$146$	7.49852e11	0.935481
$147$	−2.42293e11	−0.291136
$148$	−1.35649e11	−0.157028
$149$	5.16185e11	0.575812	0.287906	−	0.957659i	$-0.407041\pi$
$149$	5.16185e11	0.575812	0.287906	+	0.957659i	$0.407041\pi$
$150$	−6.76799e11	−0.727709
$151$	−4.34940e11	−0.450875	−0.225437	−	0.974258i	$-0.572381\pi$
$151$	−4.34940e11	−0.450875	−0.225437	+	0.974258i	$0.572381\pi$
$152$	−2.33643e11	−0.233568
$153$	−2.66743e10	−0.0257211
$154$	−1.10571e12	−1.02867
$155$	1.15710e11	0.103883
$156$	−5.52642e10	−0.0478915
$157$	3.95592e11	0.330978	0.165489	−	0.986212i	$-0.447080\pi$
$157$	3.95592e11	0.330978	0.165489	+	0.986212i	$0.447080\pi$
$158$	−1.02225e12	−0.825926
$159$	−3.55165e11	−0.277170
$160$	−1.60193e11	−0.120777
$161$	1.51073e12	1.10064
$162$	2.01319e11	0.141760
$163$	3.86564e11	0.263141	0.131571	−	0.991307i	$-0.457998\pi$
$163$	3.86564e11	0.263141	0.131571	+	0.991307i	$0.457998\pi$
$164$	2.81934e11	0.185569
$165$	1.14136e11	0.0726541
$166$	−1.92358e12	−1.18445
$167$	5.98599e11	0.356612	0.178306	−	0.983975i	$-0.442938\pi$
$167$	5.98599e11	0.356612	0.178306	+	0.983975i	$0.442938\pi$
$168$	3.34879e11	0.193057
$169$	−1.76087e12	−0.982540
$170$	−2.00281e10	−0.0108186
$171$	3.13436e11	0.163935
$172$	−1.39821e12	−0.708216
$173$	−1.33216e12	−0.653585	−0.326793	−	0.945096i	$-0.605968\pi$
$173$	−1.33216e12	−0.653585	−0.326793	+	0.945096i	$0.605968\pi$
$174$	9.69984e11	0.461046
$175$	1.51028e12	0.695583
$176$	−3.16502e12	−1.41272
$177$	−1.73727e11	−0.0751646
$178$	2.61650e12	1.09752
$179$	2.08528e12	0.848151	0.424075	−	0.905627i	$-0.360599\pi$
$179$	2.08528e12	0.848151	0.424075	+	0.905627i	$0.360599\pi$
$180$	5.82955e10	0.0229951
$181$	1.41045e12	0.539666	0.269833	−	0.962907i	$-0.413032\pi$
$181$	1.41045e12	0.539666	0.269833	+	0.962907i	$0.413032\pi$
$182$	3.19772e11	0.118699
$183$	−2.67443e12	−0.963275
$184$	2.12392e12	0.742404
$185$	−8.10206e10	−0.0274885
$186$	2.11415e12	0.696329
$187$	−2.76309e11	−0.0883621
$188$	−3.12387e12	−0.970120
$189$	−4.49246e11	−0.135501
$190$	2.35341e11	0.0689529
$191$	−1.45386e12	−0.413845	−0.206923	−	0.978357i	$-0.566345\pi$
$191$	−1.45386e12	−0.413845	−0.206923	+	0.978357i	$0.566345\pi$
$192$	−3.51780e11	−0.0973003
$193$	−3.75147e11	−0.100841	−0.0504204	−	0.998728i	$-0.516056\pi$
$193$	−3.75147e11	−0.100841	−0.0504204	+	0.998728i	$0.516056\pi$
$194$	−4.98234e12	−1.30174
$195$	−3.30083e10	−0.00838364
$196$	−1.28191e12	−0.316555
$197$	4.20784e12	1.01040	0.505202	−	0.863001i	$-0.331418\pi$
$197$	4.20784e12	1.01040	0.505202	+	0.863001i	$0.331418\pi$
$198$	2.08539e12	0.487000
$199$	−3.91360e12	−0.888966	−0.444483	−	0.895787i	$-0.646613\pi$
$199$	−3.91360e12	−0.888966	−0.444483	+	0.895787i	$0.646613\pi$
$200$	2.12329e12	0.469186
$201$	−1.07010e12	−0.230062
$202$	1.18466e13	2.47833
$203$	−2.16453e12	−0.440692
$204$	−1.41126e11	−0.0279667
$205$	1.68394e11	0.0324848
$206$	3.06924e12	0.576450
$207$	−2.84928e12	−0.521072
$208$	9.15330e11	0.163016
$209$	3.24677e12	0.563180
$210$	−3.37312e11	−0.0569935
$211$	2.79478e12	0.460038	0.230019	−	0.973186i	$-0.426121\pi$
$211$	2.79478e12	0.460038	0.230019	+	0.973186i	$0.426121\pi$
$212$	−1.87908e12	−0.301368
$213$	−1.25353e12	−0.195906
$214$	−9.06227e12	−1.38026
$215$	−8.35125e11	−0.123977
$216$	−6.31590e11	−0.0913986
$217$	−4.71775e12	−0.665589
$218$	−5.87137e12	−0.807660
$219$	3.15589e12	0.423330
$220$	6.03861e11	0.0789973
$221$	7.99090e10	0.0101962
$222$	−1.48034e12	−0.184255
$223$	−4.52337e12	−0.549269	−0.274634	−	0.961549i	$-0.588557\pi$
$223$	−4.52337e12	−0.549269	−0.274634	+	0.961549i	$0.588557\pi$
$224$	6.53141e12	0.773826
$225$	−2.84843e12	−0.329308
$226$	−1.60743e13	−1.81358
$227$	8.80338e12	0.969410	0.484705	−	0.874678i	$-0.338927\pi$
$227$	8.80338e12	0.969410	0.484705	+	0.874678i	$0.338927\pi$
$228$	1.65831e12	0.178247
$229$	−1.80722e13	−1.89633	−0.948167	−	0.317773i	$-0.897065\pi$
$229$	−1.80722e13	−1.89633	−0.948167	+	0.317773i	$0.897065\pi$
$230$	−2.13935e12	−0.219169
$231$	−4.65357e12	−0.465501
$232$	−3.04309e12	−0.297256
$233$	−1.92283e11	−0.0183435	−0.00917176	−	0.999958i	$-0.502920\pi$
$233$	−1.92283e11	−0.0183435	−0.00917176	+	0.999958i	$0.502920\pi$
$234$	−6.03099e11	−0.0561954
$235$	−1.86583e12	−0.169824
$236$	−9.19140e11	−0.0817270
$237$	−4.30231e12	−0.373754
$238$	8.16591e11	0.0693156
$239$	−1.75634e13	−1.45686	−0.728432	−	0.685118i	$-0.759751\pi$
$239$	−1.75634e13	−1.45686	−0.728432	+	0.685118i	$0.759751\pi$
$240$	−9.65536e11	−0.0782721
$241$	−1.04779e13	−0.830195	−0.415098	−	0.909777i	$-0.636253\pi$
$241$	−1.04779e13	−0.830195	−0.415098	+	0.909777i	$0.636253\pi$
$242$	5.12853e12	0.397199
$243$	8.47289e11	0.0641500
$244$	−1.41497e13	−1.04738
$245$	−7.65660e11	−0.0554144
$246$	3.07675e12	0.217745
$247$	−9.38972e11	−0.0649860
$248$	−6.63263e12	−0.448954
$249$	−8.09576e12	−0.535996
$250$	−4.30358e12	−0.278715
$251$	2.43473e13	1.54257	0.771286	−	0.636489i	$-0.219614\pi$
$251$	2.43473e13	1.54257	0.771286	+	0.636489i	$0.219614\pi$
$252$	−2.37684e12	−0.147332
$253$	−2.95146e13	−1.79009
$254$	−3.17473e12	−0.188418
$255$	−8.42921e10	−0.00489571
$256$	2.28067e13	1.29641
$257$	2.40790e13	1.33969	0.669847	−	0.742499i	$-0.266360\pi$
$257$	2.40790e13	1.33969	0.669847	+	0.742499i	$0.266360\pi$
$258$	−1.52587e13	−0.831014
$259$	3.30339e12	0.176121
$260$	−1.74638e11	−0.00911559
$261$	4.08236e12	0.208636
$262$	1.19840e13	0.599713
$263$	9.76345e12	0.478461	0.239231	−	0.970963i	$-0.423105\pi$
$263$	9.76345e12	0.478461	0.239231	+	0.970963i	$0.423105\pi$
$264$	−6.54240e12	−0.313990
$265$	−1.12234e12	−0.0527560
$266$	−9.59537e12	−0.441787
$267$	1.10120e13	0.496656
$268$	−5.66158e12	−0.250148
$269$	−1.82600e12	−0.0790429	−0.0395214	−	0.999219i	$-0.512583\pi$
$269$	−1.82600e12	−0.0790429	−0.0395214	+	0.999219i	$0.512583\pi$
$270$	6.36179e11	0.0269823
$271$	1.28811e13	0.535330	0.267665	−	0.963512i	$-0.413748\pi$
$271$	1.28811e13	0.535330	0.267665	+	0.963512i	$0.413748\pi$
$272$	2.33745e12	0.0951947
$273$	1.34582e12	0.0537146
$274$	−1.62313e13	−0.634928
$275$	−2.95059e13	−1.13130
$276$	−1.50747e13	−0.566565
$277$	−2.52373e13	−0.929830	−0.464915	−	0.885355i	$-0.653915\pi$
$277$	−2.52373e13	−0.929830	−0.464915	+	0.885355i	$0.653915\pi$
$278$	5.49696e13	1.98553
$279$	8.89779e12	0.315108
$280$	1.05823e12	0.0367462
$281$	2.28432e13	0.777809	0.388904	−	0.921278i	$-0.372854\pi$
$281$	2.28432e13	0.777809	0.388904	+	0.921278i	$0.372854\pi$
$282$	−3.40909e13	−1.13833
$283$	−4.62625e13	−1.51497	−0.757485	−	0.652852i	$-0.773572\pi$
$283$	−4.62625e13	−1.51497	−0.757485	+	0.652852i	$0.773572\pi$
$284$	−6.63208e12	−0.213009
$285$	9.90476e11	0.0312030
$286$	−6.24728e12	−0.193053
$287$	−6.86579e12	−0.208133
$288$	−1.23184e13	−0.366350
$289$	−3.40678e13	−0.994046
$290$	3.06520e12	0.0877547
$291$	−2.09691e13	−0.589073
$292$	1.66970e13	0.460290
$293$	6.20018e13	1.67738	0.838692	−	0.544605i	$-0.183321\pi$
$293$	6.20018e13	1.67738	0.838692	+	0.544605i	$0.183321\pi$
$294$	−1.39895e13	−0.371442
$295$	−5.48985e11	−0.0143067
$296$	4.64420e12	0.118797
$297$	8.77675e12	0.220381
$298$	2.98033e13	0.734642
$299$	8.53568e12	0.206560
$300$	−1.50703e13	−0.358059
$301$	3.40499e13	0.794328
$302$	−2.51124e13	−0.575242
$303$	4.98585e13	1.12151
$304$	−2.74662e13	−0.606728
$305$	−8.45134e12	−0.183348
$306$	−1.54011e12	−0.0328159
$307$	6.67094e13	1.39613	0.698065	−	0.716034i	$-0.254045\pi$
$307$	6.67094e13	1.39613	0.698065	+	0.716034i	$0.254045\pi$
$308$	−2.46208e13	−0.506142
$309$	1.29175e13	0.260859
$310$	6.68082e12	0.132538
$311$	3.21602e13	0.626811	0.313406	−	0.949619i	$-0.398530\pi$
$311$	3.21602e13	0.626811	0.313406	+	0.949619i	$0.398530\pi$
$312$	1.89208e12	0.0362317
$313$	−3.95632e13	−0.744384	−0.372192	−	0.928156i	$-0.621394\pi$
$313$	−3.95632e13	−0.744384	−0.372192	+	0.928156i	$0.621394\pi$
$314$	2.28406e13	0.422274
$315$	−1.41964e12	−0.0257911
$316$	−2.27623e13	−0.406385
$317$	−5.69351e13	−0.998973	−0.499487	−	0.866322i	$-0.666478\pi$
$317$	−5.69351e13	−0.998973	−0.499487	+	0.866322i	$0.666478\pi$
$318$	−2.05064e13	−0.353623
$319$	4.22877e13	0.716745
$320$	−1.11164e12	−0.0185200
$321$	−3.81403e13	−0.624606
$322$	8.72262e13	1.40423
$323$	−2.39782e12	−0.0379492
$324$	4.48277e12	0.0697508
$325$	8.53315e12	0.130542
$326$	2.23193e13	0.335725
$327$	−2.47108e13	−0.365488
$328$	−9.65255e12	−0.140390
$329$	7.60741e13	1.08808
$330$	6.58994e12	0.0926947
$331$	−1.03518e14	−1.43206	−0.716032	−	0.698068i	$-0.754043\pi$
$331$	−1.03518e14	−1.43206	−0.716032	+	0.698068i	$0.754043\pi$
$332$	−4.28325e13	−0.582792
$333$	−6.23028e12	−0.0833804
$334$	3.45618e13	0.454978
$335$	−3.38156e12	−0.0437895
$336$	3.93671e13	0.501495
$337$	1.36947e14	1.71628	0.858140	−	0.513416i	$-0.171620\pi$
$337$	1.36947e14	1.71628	0.858140	+	0.513416i	$0.171620\pi$
$338$	−1.01669e14	−1.25356
$339$	−6.76518e13	−0.820693
$340$	−4.45966e11	−0.00532314
$341$	9.21689e13	1.08252
$342$	1.80971e13	0.209154
$343$	9.31252e13	1.05913
$344$	4.78704e13	0.535791
$345$	−9.00387e12	−0.0991800
$346$	−7.69158e13	−0.833867
$347$	6.86009e12	0.0732011	0.0366005	−	0.999330i	$-0.488347\pi$
$347$	6.86009e12	0.0732011	0.0366005	+	0.999330i	$0.488347\pi$
$348$	2.15986e13	0.226851
$349$	1.30525e14	1.34944	0.674720	−	0.738074i	$-0.264264\pi$
$349$	1.30525e14	1.34944	0.674720	+	0.738074i	$0.264264\pi$
$350$	8.72003e13	0.887450
$351$	−2.53825e12	−0.0254300
$352$	−1.27602e14	−1.25856
$353$	9.94528e13	0.965731	0.482865	−	0.875695i	$-0.339596\pi$
$353$	9.94528e13	0.965731	0.482865	+	0.875695i	$0.339596\pi$
$354$	−1.00306e13	−0.0958977
$355$	−3.96122e12	−0.0372883
$356$	5.82616e13	0.540017
$357$	3.43677e12	0.0313672
$358$	1.20399e14	1.08210
$359$	3.87309e13	0.342798	0.171399	−	0.985202i	$-0.445171\pi$
$359$	3.87309e13	0.342798	0.171399	+	0.985202i	$0.445171\pi$
$360$	−1.99586e12	−0.0173966
$361$	−8.83146e13	−0.758129
$362$	8.14360e13	0.688525
$363$	2.15844e13	0.179743
$364$	7.12037e12	0.0584043
$365$	9.97278e12	0.0805760
$366$	−1.54416e14	−1.22898
$367$	8.39212e13	0.657974	0.328987	−	0.944335i	$-0.393293\pi$
$367$	8.39212e13	0.657974	0.328987	+	0.944335i	$0.393293\pi$
$368$	2.49680e14	1.92851
$369$	1.29491e13	0.0985356
$370$	−4.67795e12	−0.0350708
$371$	4.57602e13	0.338012
$372$	4.70758e13	0.342619
$373$	1.53158e14	1.09835	0.549175	−	0.835708i	$-0.314942\pi$
$373$	1.53158e14	1.09835	0.549175	+	0.835708i	$0.314942\pi$
$374$	−1.59534e13	−0.112735
$375$	−1.81124e13	−0.126126
$376$	1.06952e14	0.733931
$377$	−1.22297e13	−0.0827061
$378$	−2.59384e13	−0.172878
$379$	2.08444e14	1.36922	0.684609	−	0.728910i	$-0.259973\pi$
$379$	2.08444e14	1.36922	0.684609	+	0.728910i	$0.259973\pi$
$380$	5.24033e12	0.0339273
$381$	−1.33614e13	−0.0852640
$382$	−8.39424e13	−0.527999
$383$	1.76796e14	1.09617	0.548087	−	0.836421i	$-0.315356\pi$
$383$	1.76796e14	1.09617	0.548087	+	0.836421i	$0.315356\pi$
$384$	8.35084e13	0.510398
$385$	−1.47055e13	−0.0886026
$386$	−2.16601e13	−0.128656
$387$	−6.42190e13	−0.376056
$388$	−1.10942e14	−0.640503
$389$	−6.21201e12	−0.0353598	−0.0176799	−	0.999844i	$-0.505628\pi$
$389$	−6.21201e12	−0.0353598	−0.0176799	+	0.999844i	$0.505628\pi$
$390$	−1.90582e12	−0.0106961
$391$	2.17973e13	0.120623
$392$	4.38886e13	0.239485
$393$	5.04368e13	0.271386
$394$	2.42951e14	1.28911
$395$	−1.35955e13	−0.0711397
$396$	4.64354e13	0.239621
$397$	−5.02332e13	−0.255648	−0.127824	−	0.991797i	$-0.540799\pi$
$397$	−5.02332e13	−0.255648	−0.127824	+	0.991797i	$0.540799\pi$
$398$	−2.25963e14	−1.13417
$399$	−4.03839e13	−0.199920
$400$	2.49606e14	1.21878
$401$	2.74376e14	1.32145	0.660727	−	0.750626i	$-0.270248\pi$
$401$	2.74376e14	1.32145	0.660727	+	0.750626i	$0.270248\pi$
$402$	−6.17849e13	−0.293521
$403$	−2.66554e13	−0.124913
$404$	2.63788e14	1.21943
$405$	2.67748e12	0.0122102
$406$	−1.24975e14	−0.562251
$407$	−6.45371e13	−0.286444
$408$	4.83173e12	0.0211578
$409$	−6.90128e13	−0.298161	−0.149081	−	0.988825i	$-0.547631\pi$
$409$	−6.90128e13	−0.298161	−0.149081	+	0.988825i	$0.547631\pi$
$410$	9.72269e12	0.0414453
$411$	−6.83123e13	−0.287322
$412$	6.83429e13	0.283634
$413$	2.23833e13	0.0916642
$414$	−1.64511e14	−0.664803
$415$	−2.55830e13	−0.102021
$416$	3.69027e13	0.145226
$417$	2.31350e14	0.898505
$418$	1.87461e14	0.718525
$419$	1.10162e14	0.416728	0.208364	−	0.978051i	$-0.433186\pi$
$419$	1.10162e14	0.416728	0.208364	+	0.978051i	$0.433186\pi$
$420$	−7.51093e12	−0.0280429
$421$	−1.03181e14	−0.380232	−0.190116	−	0.981762i	$-0.560886\pi$
$421$	−1.03181e14	−0.380232	−0.190116	+	0.981762i	$0.560886\pi$
$422$	1.61364e14	0.586933
$423$	−1.43478e14	−0.515125
$424$	6.43339e13	0.227996
$425$	2.17908e13	0.0762314
$426$	−7.23759e13	−0.249943
$427$	3.44580e14	1.17473
$428$	−2.01790e14	−0.679138
$429$	−2.62928e13	−0.0873619
$430$	−4.82182e13	−0.158174
$431$	−4.66155e14	−1.50975	−0.754876	−	0.655867i	$-0.772303\pi$
$431$	−4.66155e14	−1.50975	−0.754876	+	0.655867i	$0.772303\pi$
$432$	−7.42473e13	−0.237421
$433$	1.42455e14	0.449775	0.224887	−	0.974385i	$-0.427799\pi$
$433$	1.42455e14	0.449775	0.224887	+	0.974385i	$0.427799\pi$
$434$	−2.72392e14	−0.849182
$435$	1.29005e13	0.0397114
$436$	−1.30738e14	−0.397398
$437$	−2.56129e14	−0.768796
$438$	1.82214e14	0.540100
$439$	2.26682e14	0.663531	0.331766	−	0.943362i	$-0.392356\pi$
$439$	2.26682e14	0.663531	0.331766	+	0.943362i	$0.392356\pi$
$440$	−2.06743e13	−0.0597643
$441$	−5.88773e13	−0.168088
$442$	4.61377e12	0.0130087
$443$	−6.57349e14	−1.83052	−0.915262	−	0.402858i	$-0.868017\pi$
$443$	−6.57349e14	−1.83052	−0.915262	+	0.402858i	$0.868017\pi$
$444$	−3.29627e13	−0.0906601
$445$	3.47986e13	0.0945326
$446$	−2.61169e14	−0.700777
$447$	1.25433e14	0.332445
$448$	4.53242e13	0.118659
$449$	5.33560e14	1.37984	0.689919	−	0.723887i	$-0.257646\pi$
$449$	5.33560e14	1.37984	0.689919	+	0.723887i	$0.257646\pi$
$450$	−1.64462e14	−0.420143
$451$	1.34135e14	0.338509
$452$	−3.57927e14	−0.892345
$453$	−1.05690e14	−0.260313
$454$	5.08287e14	1.23681
$455$	4.25286e12	0.0102240
$456$	−5.67753e13	−0.134851
$457$	−5.08957e14	−1.19438	−0.597189	−	0.802100i	$-0.703716\pi$
$457$	−5.08957e14	−1.19438	−0.597189	+	0.802100i	$0.703716\pi$
$458$	−1.04345e15	−2.41941
$459$	−6.48184e12	−0.0148501
$460$	−4.76370e13	−0.107839
$461$	5.82777e14	1.30361	0.651804	−	0.758387i	$-0.274012\pi$
$461$	5.82777e14	1.30361	0.651804	+	0.758387i	$0.274012\pi$
$462$	−2.68687e14	−0.593902
$463$	4.23300e14	0.924598	0.462299	−	0.886724i	$-0.347025\pi$
$463$	4.23300e14	0.924598	0.462299	+	0.886724i	$0.347025\pi$
$464$	−3.57734e14	−0.772168
$465$	2.81175e13	0.0599771
$466$	−1.11020e13	−0.0234033
$467$	−7.50974e14	−1.56452	−0.782262	−	0.622950i	$-0.785934\pi$
$467$	−7.50974e14	−1.56452	−0.782262	+	0.622950i	$0.785934\pi$
$468$	−1.34292e13	−0.0276502
$469$	1.37874e14	0.280563
$470$	−1.07729e14	−0.216668
$471$	9.61288e13	0.191090
$472$	3.14685e13	0.0618294
$473$	−6.65221e14	−1.29190
$474$	−2.48406e14	−0.476849
$475$	−2.56053e14	−0.485865
$476$	1.81830e13	0.0341058
$477$	−8.63050e13	−0.160024
$478$	−1.01407e15	−1.85872
$479$	−4.43724e14	−0.804021	−0.402011	−	0.915635i	$-0.631688\pi$
$479$	−4.43724e14	−0.804021	−0.402011	+	0.915635i	$0.631688\pi$
$480$	−3.89268e13	−0.0697304
$481$	1.86643e13	0.0330531
$482$	−6.04970e14	−1.05919
$483$	3.67108e14	0.635454
$484$	1.14197e14	0.195436
$485$	−6.62635e13	−0.112123
$486$	4.89205e13	0.0818449
$487$	−7.27988e14	−1.20425	−0.602123	−	0.798403i	$-0.705678\pi$
$487$	−7.27988e14	−1.20425	−0.602123	+	0.798403i	$0.705678\pi$
$488$	4.84441e14	0.792378
$489$	9.39350e13	0.151925
$490$	−4.42075e13	−0.0706997
$491$	8.60184e14	1.36033	0.680163	−	0.733061i	$-0.261909\pi$
$491$	8.60184e14	1.36033	0.680163	+	0.733061i	$0.261909\pi$
$492$	6.85100e13	0.107139
$493$	−3.12305e13	−0.0482970
$494$	−5.42141e13	−0.0829114
$495$	2.77350e13	0.0419469
$496$	−7.79707e14	−1.16622
$497$	1.61508e14	0.238909
$498$	−4.67431e14	−0.683842
$499$	8.30567e14	1.20177	0.600885	−	0.799335i	$-0.294815\pi$
$499$	8.30567e14	1.20177	0.600885	+	0.799335i	$0.294815\pi$
$500$	−9.58279e13	−0.137138
$501$	1.45460e14	0.205890
$502$	1.40576e15	1.96807
$503$	−9.93211e14	−1.37536	−0.687682	−	0.726012i	$-0.741372\pi$
$503$	−9.93211e14	−1.37536	−0.687682	+	0.726012i	$0.741372\pi$
$504$	8.13755e13	0.111462
$505$	1.57555e14	0.213467
$506$	−1.70411e15	−2.28386
$507$	−4.27891e14	−0.567269
$508$	−7.06917e13	−0.0927082
$509$	−7.02188e14	−0.910973	−0.455486	−	0.890243i	$-0.650535\pi$
$509$	−7.02188e14	−0.910973	−0.455486	+	0.890243i	$0.650535\pi$
$510$	−4.86683e12	−0.00624612
$511$	−4.06612e14	−0.516257
$512$	6.13001e14	0.769974
$513$	7.61650e13	0.0946477
$514$	1.39026e15	1.70923
$515$	4.08199e13	0.0496515
$516$	−3.39765e14	−0.408889
$517$	−1.48623e15	−1.76966
$518$	1.90730e14	0.224701
$519$	−3.23714e14	−0.377347
$520$	5.97906e12	0.00689627
$521$	5.24597e13	0.0598713	0.0299356	−	0.999552i	$-0.490470\pi$
$521$	5.24597e13	0.0598713	0.0299356	+	0.999552i	$0.490470\pi$
$522$	2.35706e14	0.266185
$523$	−1.30605e15	−1.45949	−0.729744	−	0.683721i	$-0.760361\pi$
$523$	−1.30605e15	−1.45949	−0.729744	+	0.683721i	$0.760361\pi$
$524$	2.66847e14	0.295080
$525$	3.66999e14	0.401595
$526$	5.63719e14	0.610438
$527$	−6.80690e13	−0.0729442
$528$	−7.69100e14	−0.815636
$529$	1.37552e15	1.44365
$530$	−6.48013e13	−0.0673080
$531$	−4.22156e13	−0.0433963
$532$	−2.13660e14	−0.217375
$533$	−3.87920e13	−0.0390609
$534$	6.35810e14	0.633651
$535$	−1.20525e14	−0.118886
$536$	1.93835e14	0.189246
$537$	5.06723e14	0.489680
$538$	−1.05429e14	−0.100846
$539$	−6.09888e14	−0.577447
$540$	1.41658e13	0.0132762
$541$	1.79348e15	1.66384	0.831919	−	0.554896i	$-0.187242\pi$
$541$	1.79348e15	1.66384	0.831919	+	0.554896i	$0.187242\pi$
$542$	7.43725e14	0.682993
$543$	3.42739e14	0.311576
$544$	9.42371e13	0.0848063
$545$	−7.80873e13	−0.0695664
$546$	7.77046e13	0.0685311
$547$	5.56315e14	0.485725	0.242863	−	0.970061i	$-0.421914\pi$
$547$	5.56315e14	0.485725	0.242863	+	0.970061i	$0.421914\pi$
$548$	−3.61422e14	−0.312407
$549$	−6.49887e14	−0.556147
$550$	−1.70360e15	−1.44336
$551$	3.66974e14	0.307824
$552$	5.16113e14	0.428627
$553$	5.54320e14	0.455798
$554$	−1.45714e15	−1.18631
$555$	−1.96880e13	−0.0158705
$556$	1.22401e15	0.976951
$557$	−1.38496e15	−1.09454	−0.547272	−	0.836955i	$-0.684334\pi$
$557$	−1.38496e15	−1.09454	−0.547272	+	0.836955i	$0.684334\pi$
$558$	5.13738e14	0.402026
$559$	1.92383e14	0.149074
$560$	1.24402e14	0.0954538
$561$	−6.71430e13	−0.0510159
$562$	1.31892e15	0.992356
$563$	−1.56070e15	−1.16285	−0.581424	−	0.813601i	$-0.697504\pi$
$563$	−1.56070e15	−1.16285	−0.581424	+	0.813601i	$0.697504\pi$
$564$	−7.59101e14	−0.560099
$565$	−2.13783e14	−0.156209
$566$	−2.67109e15	−1.93285
$567$	−1.09167e14	−0.0782318
$568$	2.27062e14	0.161149
$569$	−1.84518e15	−1.29695	−0.648474	−	0.761237i	$-0.724592\pi$
$569$	−1.84518e15	−1.29695	−0.648474	+	0.761237i	$0.724592\pi$
$570$	5.71878e13	0.0398100
$571$	4.13817e14	0.285305	0.142653	−	0.989773i	$-0.454437\pi$
$571$	4.13817e14	0.285305	0.142653	+	0.989773i	$0.454437\pi$
$572$	−1.39108e14	−0.0949892
$573$	−3.53287e14	−0.238934
$574$	−3.96415e14	−0.265543
$575$	2.32764e15	1.54434
$576$	−8.54825e13	−0.0561764
$577$	1.66743e15	1.08537	0.542687	−	0.839935i	$-0.317407\pi$
$577$	1.66743e15	1.08537	0.542687	+	0.839935i	$0.317407\pi$
$578$	−1.96700e15	−1.26824
$579$	−9.11608e13	−0.0582205
$580$	6.82529e13	0.0431784
$581$	1.04308e15	0.653654
$582$	−1.21071e15	−0.751560
$583$	−8.94002e14	−0.549745
$584$	−5.71652e14	−0.348226
$585$	−8.02101e12	−0.00484030
$586$	3.57985e15	2.14007
$587$	−7.03963e14	−0.416908	−0.208454	−	0.978032i	$-0.566843\pi$
$587$	−7.03963e14	−0.416908	−0.208454	+	0.978032i	$0.566843\pi$
$588$	−3.11504e14	−0.182763
$589$	7.99846e14	0.464914
$590$	−3.16972e13	−0.0182530
$591$	1.02251e15	0.583357
$592$	5.45955e14	0.308594
$593$	−7.55214e13	−0.0422930	−0.0211465	−	0.999776i	$-0.506732\pi$
$593$	−7.55214e13	−0.0422930	−0.0211465	+	0.999776i	$0.506732\pi$
$594$	5.06750e14	0.281169
$595$	1.08604e13	0.00597038
$596$	6.63631e14	0.361470
$597$	−9.51006e14	−0.513245
$598$	4.92831e14	0.263537
$599$	2.71915e15	1.44074	0.720370	−	0.693590i	$-0.243972\pi$
$599$	2.71915e15	1.44074	0.720370	+	0.693590i	$0.243972\pi$
$600$	5.15960e14	0.270884
$601$	1.61250e15	0.838862	0.419431	−	0.907787i	$-0.362230\pi$
$601$	1.61250e15	0.838862	0.419431	+	0.907787i	$0.362230\pi$
$602$	1.96596e15	1.01343
$603$	−2.60033e14	−0.132826
$604$	−5.59179e14	−0.283040
$605$	6.82078e13	0.0342121
$606$	2.87872e15	1.43087
$607$	1.64305e15	0.809306	0.404653	−	0.914470i	$-0.367392\pi$
$607$	1.64305e15	0.809306	0.404653	+	0.914470i	$0.367392\pi$
$608$	−1.10734e15	−0.540517
$609$	−5.25981e14	−0.254434
$610$	−4.87961e14	−0.233922
$611$	4.29821e14	0.204203
$612$	−3.42937e13	−0.0161466
$613$	−3.09734e14	−0.144529	−0.0722647	−	0.997385i	$-0.523023\pi$
$613$	−3.09734e14	−0.144529	−0.0722647	+	0.997385i	$0.523023\pi$
$614$	3.85165e15	1.78123
$615$	4.09197e13	0.0187551
$616$	8.42939e14	0.382915
$617$	−9.03783e14	−0.406908	−0.203454	−	0.979085i	$-0.565217\pi$
$617$	−9.03783e14	−0.406908	−0.203454	+	0.979085i	$0.565217\pi$
$618$	7.45826e14	0.332814
$619$	−1.48358e14	−0.0656164	−0.0328082	−	0.999462i	$-0.510445\pi$
$619$	−1.48358e14	−0.0656164	−0.0328082	+	0.999462i	$0.510445\pi$
$620$	1.48762e14	0.0652135
$621$	−6.92374e14	−0.300841
$622$	1.85686e15	0.799708
$623$	−1.41882e15	−0.605678
$624$	2.22425e14	0.0941172
$625$	2.29816e15	0.963917
$626$	−2.28429e15	−0.949712
$627$	7.88966e14	0.325152
$628$	5.08591e14	0.207774
$629$	4.76622e13	0.0193017
$630$	−8.19668e13	−0.0329052
$631$	−3.20112e15	−1.27392	−0.636958	−	0.770898i	$-0.719808\pi$
$631$	−3.20112e15	−1.27392	−0.636958	+	0.770898i	$0.719808\pi$
$632$	7.79312e14	0.307445
$633$	6.79131e14	0.265603
$634$	−3.28730e15	−1.27453
$635$	−4.22229e13	−0.0162290
$636$	−4.56616e14	−0.173995
$637$	1.76381e14	0.0666323
$638$	2.44159e15	0.914449
$639$	−3.04608e14	−0.113106
$640$	2.63891e14	0.0971482
$641$	−5.27613e14	−0.192573	−0.0962866	−	0.995354i	$-0.530697\pi$
$641$	−5.27613e14	−0.192573	−0.0962866	+	0.995354i	$0.530697\pi$
$642$	−2.20213e15	−0.796894
$643$	−1.27373e15	−0.457001	−0.228501	−	0.973544i	$-0.573382\pi$
$643$	−1.27373e15	−0.457001	−0.228501	+	0.973544i	$0.573382\pi$
$644$	1.94227e15	0.690934
$645$	−2.02935e14	−0.0715780
$646$	−1.38445e14	−0.0484170
$647$	−2.40342e14	−0.0833404	−0.0416702	−	0.999131i	$-0.513268\pi$
$647$	−2.40342e14	−0.0833404	−0.0416702	+	0.999131i	$0.513268\pi$
$648$	−1.53476e14	−0.0527690
$649$	−4.37295e14	−0.149083
$650$	4.92685e14	0.166550
$651$	−1.14641e15	−0.384278
$652$	4.96984e14	0.165189
$653$	−4.23654e15	−1.39633	−0.698166	−	0.715935i	$-0.746000\pi$
$653$	−4.23654e15	−1.39633	−0.698166	+	0.715935i	$0.746000\pi$
$654$	−1.42674e15	−0.466303
$655$	1.59383e14	0.0516552
$656$	−1.13472e15	−0.364684
$657$	7.66881e14	0.244410
$658$	4.39235e15	1.38821
$659$	−1.68977e14	−0.0529613	−0.0264806	−	0.999649i	$-0.508430\pi$
$659$	−1.68977e14	−0.0529613	−0.0264806	+	0.999649i	$0.508430\pi$
$660$	1.46738e14	0.0456091
$661$	−4.17874e15	−1.28806	−0.644032	−	0.764999i	$-0.722739\pi$
$661$	−4.17874e15	−1.28806	−0.644032	+	0.764999i	$0.722739\pi$
$662$	−5.97690e15	−1.82708
$663$	1.94179e13	0.00588678
$664$	1.46645e15	0.440903
$665$	−1.27615e14	−0.0380525
$666$	−3.59722e14	−0.106380
$667$	−3.33596e15	−0.978428
$668$	7.69587e14	0.223866
$669$	−1.09918e15	−0.317120
$670$	−1.95244e14	−0.0558683
$671$	−6.73194e15	−1.91058
$672$	1.58713e15	0.446768
$673$	1.61754e15	0.451619	0.225809	−	0.974172i	$-0.427497\pi$
$673$	1.61754e15	0.451619	0.225809	+	0.974172i	$0.427497\pi$
$674$	7.90701e15	2.18969
$675$	−6.92169e14	−0.190126
$676$	−2.26385e15	−0.616796
$677$	−6.13926e15	−1.65912	−0.829562	−	0.558415i	$-0.811410\pi$
$677$	−6.13926e15	−1.65912	−0.829562	+	0.558415i	$0.811410\pi$
$678$	−3.90606e15	−1.04707
$679$	2.70171e15	0.718381
$680$	1.52685e13	0.00402715
$681$	2.13922e15	0.559689
$682$	5.32163e15	1.38112
$683$	−3.50206e15	−0.901592	−0.450796	−	0.892627i	$-0.648860\pi$
$683$	−3.50206e15	−0.901592	−0.450796	+	0.892627i	$0.648860\pi$
$684$	4.02968e14	0.102911
$685$	−2.15870e14	−0.0546884
$686$	5.37684e15	1.35128
$687$	−4.39153e15	−1.09485
$688$	5.62746e15	1.39180
$689$	2.58547e14	0.0634357
$690$	−5.19863e14	−0.126537
$691$	4.80077e15	1.15926	0.579631	−	0.814879i	$-0.303197\pi$
$691$	4.80077e15	1.15926	0.579631	+	0.814879i	$0.303197\pi$
$692$	−1.71268e15	−0.410293
$693$	−1.13082e15	−0.268757
$694$	3.96086e14	0.0933925
$695$	7.31077e14	0.171020
$696$	−7.39471e14	−0.171621
$697$	−9.90617e13	−0.0228100
$698$	7.53621e15	1.72166
$699$	−4.67247e13	−0.0105906
$700$	1.94169e15	0.436657
$701$	−6.26270e15	−1.39737	−0.698687	−	0.715427i	$-0.746232\pi$
$701$	−6.26270e15	−1.39737	−0.698687	+	0.715427i	$0.746232\pi$
$702$	−1.46553e14	−0.0324445
$703$	−5.60056e14	−0.123020
$704$	−8.85482e14	−0.192988
$705$	−4.53397e14	−0.0980480
$706$	5.74218e15	1.23211
$707$	−6.42388e15	−1.36770
$708$	−2.23351e14	−0.0471851
$709$	−1.05603e15	−0.221371	−0.110686	−	0.993855i	$-0.535305\pi$
$709$	−1.05603e15	−0.221371	−0.110686	+	0.993855i	$0.535305\pi$
$710$	−2.28712e14	−0.0475738
$711$	−1.04546e15	−0.215787
$712$	−1.99470e15	−0.408542
$713$	−7.27096e15	−1.47774
$714$	1.98432e14	0.0400194
$715$	−8.30867e13	−0.0166283
$716$	2.68093e15	0.532433
$717$	−4.26789e15	−0.841121
$718$	2.23624e15	0.437354
$719$	6.77471e15	1.31487	0.657433	−	0.753513i	$-0.271642\pi$
$719$	6.77471e15	1.31487	0.657433	+	0.753513i	$0.271642\pi$
$720$	−2.34625e14	−0.0451904
$721$	−1.66432e15	−0.318121
$722$	−5.09909e15	−0.967248
$723$	−2.54613e15	−0.479313
$724$	1.81334e15	0.338779
$725$	−3.33497e15	−0.618348
$726$	1.24623e15	0.229323
$727$	−1.58102e15	−0.288734	−0.144367	−	0.989524i	$-0.546115\pi$
$727$	−1.58102e15	−0.288734	−0.144367	+	0.989524i	$0.546115\pi$
$728$	−2.43779e14	−0.0441850
$729$	2.05891e14	0.0370370
$730$	5.75806e14	0.102802
$731$	4.91282e14	0.0870533
$732$	−3.43837e15	−0.604703
$733$	−1.09216e15	−0.190641	−0.0953203	−	0.995447i	$-0.530388\pi$
$733$	−1.09216e15	−0.190641	−0.0953203	+	0.995447i	$0.530388\pi$
$734$	4.84542e15	0.839466
$735$	−1.86055e14	−0.0319935
$736$	1.00662e16	1.71805
$737$	−2.69359e15	−0.456310
$738$	7.47650e14	0.125715
$739$	9.43152e14	0.157412	0.0787059	−	0.996898i	$-0.474921\pi$
$739$	9.43152e14	0.157412	0.0787059	+	0.996898i	$0.474921\pi$
$740$	−1.04164e14	−0.0172561
$741$	−2.28170e14	−0.0375197
$742$	2.64209e15	0.431248
$743$	8.73746e15	1.41562	0.707810	−	0.706403i	$-0.249683\pi$
$743$	8.73746e15	1.41562	0.707810	+	0.706403i	$0.249683\pi$
$744$	−1.61173e15	−0.259204
$745$	3.96375e14	0.0632771
$746$	8.84298e15	1.40131
$747$	−1.96727e15	−0.309457
$748$	−3.55235e14	−0.0554699
$749$	4.91408e15	0.761715
$750$	−1.04577e15	−0.160916
$751$	−6.60026e15	−1.00819	−0.504094	−	0.863649i	$-0.668173\pi$
$751$	−6.60026e15	−1.00819	−0.504094	+	0.863649i	$0.668173\pi$
$752$	1.25728e16	1.90649
$753$	5.91639e15	0.890604
$754$	−7.06113e14	−0.105519
$755$	−3.33987e14	−0.0495475
$756$	−5.77571e14	−0.0850620
$757$	4.74650e14	0.0693978	0.0346989	−	0.999398i	$-0.488953\pi$
$757$	4.74650e14	0.0693978	0.0346989	+	0.999398i	$0.488953\pi$
$758$	1.20351e16	1.74690
$759$	−7.17205e15	−1.03351
$760$	−1.79413e14	−0.0256672
$761$	2.30042e15	0.326733	0.163366	−	0.986565i	$-0.447765\pi$
$761$	2.30042e15	0.326733	0.163366	+	0.986565i	$0.447765\pi$
$762$	−7.71459e14	−0.108783
$763$	3.18379e15	0.445717
$764$	−1.86915e15	−0.259794
$765$	−2.04830e13	−0.00282654
$766$	1.02078e16	1.39854
$767$	1.26467e14	0.0172029
$768$	5.54203e15	0.748484
$769$	−9.46185e15	−1.26877	−0.634383	−	0.773019i	$-0.718746\pi$
$769$	−9.46185e15	−1.26877	−0.634383	+	0.773019i	$0.718746\pi$
$770$	−8.49064e14	−0.113042
$771$	5.85119e15	0.773473
$772$	−4.82307e14	−0.0633035
$773$	−2.44917e15	−0.319177	−0.159589	−	0.987184i	$-0.551017\pi$
$773$	−2.44917e15	−0.319177	−0.159589	+	0.987184i	$0.551017\pi$
$774$	−3.70786e15	−0.479786
$775$	−7.26881e15	−0.933907
$776$	3.79831e15	0.484563
$777$	8.02723e14	0.101683
$778$	−3.58667e14	−0.0451132
$779$	1.16403e15	0.145381
$780$	−4.24370e13	−0.00526289
$781$	−3.15532e15	−0.388564
$782$	1.25852e15	0.153895
$783$	9.92013e14	0.120456
$784$	5.15938e15	0.622098
$785$	3.03772e14	0.0363718
$786$	2.91210e15	0.346245
$787$	9.69972e15	1.14524	0.572622	−	0.819819i	$-0.305926\pi$
$787$	9.69972e15	1.14524	0.572622	+	0.819819i	$0.305926\pi$
$788$	5.40980e15	0.634288
$789$	2.37252e15	0.276240
$790$	−7.84975e14	−0.0907625
$791$	8.71641e15	1.00085
$792$	−1.58980e15	−0.181282
$793$	1.94689e15	0.220464
$794$	−2.90035e15	−0.326165
$795$	−2.72728e14	−0.0304587
$796$	−5.03151e15	−0.558054
$797$	−1.59788e16	−1.76005	−0.880024	−	0.474930i	$-0.842473\pi$
$797$	−1.59788e16	−1.76005	−0.880024	+	0.474930i	$0.842473\pi$
$798$	−2.33167e15	−0.255066
$799$	1.09762e15	0.119246
$800$	1.00632e16	1.08578
$801$	2.67592e15	0.286744
$802$	1.58419e16	1.68596
$803$	7.94384e15	0.839644
$804$	−1.37576e15	−0.144423
$805$	1.16008e15	0.120951
$806$	−1.53902e15	−0.159369
$807$	−4.43717e14	−0.0456354
$808$	−9.03127e15	−0.922543
$809$	−6.91165e15	−0.701237	−0.350618	−	0.936518i	$-0.614029\pi$
$809$	−6.91165e15	−0.701237	−0.350618	+	0.936518i	$0.614029\pi$
$810$	1.54591e14	0.0155782
$811$	6.24820e15	0.625374	0.312687	−	0.949856i	$-0.398771\pi$
$811$	6.24820e15	0.625374	0.312687	+	0.949856i	$0.398771\pi$
$812$	−2.78282e15	−0.276648
$813$	3.13010e15	0.309073
$814$	−3.72623e15	−0.365456
$815$	2.96840e14	0.0289171
$816$	5.67999e14	0.0549607
$817$	−5.77282e15	−0.554838
$818$	−3.98464e15	−0.380405
$819$	3.27034e14	0.0310122
$820$	2.16495e14	0.0203926
$821$	−4.24084e15	−0.396793	−0.198397	−	0.980122i	$-0.563573\pi$
$821$	−4.24084e15	−0.396793	−0.198397	+	0.980122i	$0.563573\pi$
$822$	−3.94420e15	−0.366576
$823$	−8.63566e15	−0.797253	−0.398627	−	0.917113i	$-0.630513\pi$
$823$	−8.63566e15	−0.797253	−0.398627	+	0.917113i	$0.630513\pi$
$824$	−2.33985e15	−0.214579
$825$	−7.16993e15	−0.653158
$826$	1.29236e15	0.116948
$827$	1.31604e15	0.118301	0.0591506	−	0.998249i	$-0.481161\pi$
$827$	1.31604e15	0.118301	0.0591506	+	0.998249i	$0.481161\pi$
$828$	−3.66316e15	−0.327107
$829$	2.97790e15	0.264156	0.132078	−	0.991239i	$-0.457835\pi$
$829$	2.97790e15	0.264156	0.132078	+	0.991239i	$0.457835\pi$
$830$	−1.47711e15	−0.130161
$831$	−6.13265e15	−0.536837
$832$	2.56083e14	0.0222691
$833$	4.50417e14	0.0389106
$834$	1.33576e16	1.14634
$835$	4.59660e14	0.0391887
$836$	4.17420e15	0.353540
$837$	2.16216e15	0.181928
$838$	6.36048e15	0.531677
$839$	1.13670e16	0.943963	0.471982	−	0.881608i	$-0.343539\pi$
$839$	1.13670e16	0.943963	0.471982	+	0.881608i	$0.343539\pi$
$840$	2.57151e14	0.0212154
$841$	−7.42084e15	−0.608241
$842$	−5.95744e15	−0.485114
$843$	5.55091e15	0.449068
$844$	3.59310e15	0.288792
$845$	−1.35216e15	−0.107973
$846$	−8.28408e15	−0.657215
$847$	−2.78098e15	−0.219199
$848$	7.56284e15	0.592254
$849$	−1.12418e16	−0.874669
$850$	1.25815e15	0.0972588
$851$	5.09116e15	0.391025
$852$	−1.61160e15	−0.122981
$853$	−7.56111e14	−0.0573279	−0.0286640	−	0.999589i	$-0.509125\pi$
$853$	−7.56111e14	−0.0573279	−0.0286640	+	0.999589i	$0.509125\pi$
$854$	1.98953e16	1.49876
$855$	2.40686e14	0.0180151
$856$	6.90866e15	0.513793
$857$	4.30205e15	0.317893	0.158946	−	0.987287i	$-0.449190\pi$
$857$	4.30205e15	0.317893	0.158946	+	0.987287i	$0.449190\pi$
$858$	−1.51809e15	−0.111459
$859$	−7.93376e15	−0.578784	−0.289392	−	0.957211i	$-0.593453\pi$
$859$	−7.93376e15	−0.578784	−0.289392	+	0.957211i	$0.593453\pi$
$860$	−1.07368e15	−0.0778272
$861$	−1.66839e15	−0.120165
$862$	−2.69148e16	−1.92620
$863$	8.00449e15	0.569212	0.284606	−	0.958645i	$-0.408137\pi$
$863$	8.00449e15	0.569212	0.284606	+	0.958645i	$0.408137\pi$
$864$	−2.99337e15	−0.211512
$865$	−1.02295e15	−0.0718237
$866$	8.22504e15	0.573839
$867$	−8.27848e15	−0.573913
$868$	−6.06535e15	−0.417828
$869$	−1.08295e16	−0.741313
$870$	7.44844e14	0.0506652
$871$	7.78991e14	0.0526541
$872$	4.47606e15	0.300646
$873$	−5.09550e15	−0.340101
$874$	−1.47883e16	−0.980858
$875$	2.33365e15	0.153812
$876$	4.05736e15	0.265749
$877$	−1.79798e16	−1.17027	−0.585136	−	0.810936i	$-0.698959\pi$
$877$	−1.79798e16	−1.17027	−0.585136	+	0.810936i	$0.698959\pi$
$878$	1.30881e16	0.846557
$879$	1.50664e16	0.968439
$880$	−2.43040e15	−0.155247
$881$	1.88670e14	0.0119766	0.00598832	−	0.999982i	$-0.498094\pi$
$881$	1.88670e14	0.0119766	0.00598832	+	0.999982i	$0.498094\pi$
$882$	−3.39944e15	−0.214452
$883$	−1.68989e16	−1.05944	−0.529719	−	0.848173i	$-0.677703\pi$
$883$	−1.68989e16	−1.05944	−0.529719	+	0.848173i	$0.677703\pi$
$884$	1.02735e14	0.00640074
$885$	−1.33403e14	−0.00825998
$886$	−3.79539e16	−2.33545
$887$	−1.37705e16	−0.842110	−0.421055	−	0.907035i	$-0.638340\pi$
$887$	−1.37705e16	−0.842110	−0.421055	+	0.907035i	$0.638340\pi$
$888$	1.12854e15	0.0685876
$889$	1.72152e15	0.103981
$890$	2.00919e15	0.120608
$891$	2.13275e15	0.127237
$892$	−5.81545e15	−0.344807
$893$	−1.28976e16	−0.760021
$894$	7.24221e15	0.424145
$895$	1.60127e15	0.0932049
$896$	−1.07594e16	−0.622436
$897$	2.07417e15	0.119258
$898$	3.08065e16	1.76045
$899$	1.04176e16	0.591684
$900$	−3.66208e15	−0.206725
$901$	6.60242e14	0.0370439
$902$	7.74463e15	0.431881
$903$	8.27413e15	0.458606
$904$	1.22543e16	0.675091
$905$	1.08307e15	0.0593049
$906$	−6.10232e15	−0.332116
$907$	3.12244e16	1.68910	0.844549	−	0.535479i	$-0.179869\pi$
$907$	3.12244e16	1.68910	0.844549	+	0.535479i	$0.179869\pi$
$908$	1.13180e16	0.608554
$909$	1.21156e16	0.647506
$910$	2.45551e14	0.0130441
$911$	−5.20052e15	−0.274597	−0.137298	−	0.990530i	$-0.543842\pi$
$911$	−5.20052e15	−0.274597	−0.137298	+	0.990530i	$0.543842\pi$
$912$	−6.67429e15	−0.350294
$913$	−2.03782e16	−1.06311
$914$	−2.93860e16	−1.52383
$915$	−2.05368e15	−0.105856
$916$	−2.32344e16	−1.19044
$917$	−6.49839e15	−0.330959
$918$	−3.74247e14	−0.0189463
$919$	−1.74241e16	−0.876831	−0.438416	−	0.898772i	$-0.644460\pi$
$919$	−1.74241e16	−0.876831	−0.438416	+	0.898772i	$0.644460\pi$
$920$	1.63094e15	0.0815842
$921$	1.62104e16	0.806056
$922$	3.36482e16	1.66319
$923$	9.12524e14	0.0448368
$924$	−5.98284e15	−0.292221
$925$	5.08965e15	0.247120
$926$	2.44404e16	1.17964
$927$	3.13895e15	0.150607
$928$	−1.44225e16	−0.687903
$929$	2.23911e16	1.06167	0.530834	−	0.847476i	$-0.321879\pi$
$929$	2.23911e16	1.06167	0.530834	+	0.847476i	$0.321879\pi$
$930$	1.62344e15	0.0765209
$931$	−5.29264e15	−0.247998
$932$	−2.47208e14	−0.0115153
$933$	7.81493e15	0.361890
$934$	−4.33595e16	−1.99607
$935$	−2.12176e14	−0.00971027
$936$	4.59774e14	0.0209184
$937$	4.29067e16	1.94069	0.970347	−	0.241716i	$-0.0777104\pi$
$937$	4.29067e16	1.94069	0.970347	+	0.241716i	$0.0777104\pi$
$938$	7.96051e15	0.357952
$939$	−9.61385e15	−0.429771
$940$	−2.39880e15	−0.106608
$941$	−1.15004e15	−0.0508125	−0.0254063	−	0.999677i	$-0.508088\pi$
$941$	−1.15004e15	−0.0508125	−0.0254063	+	0.999677i	$0.508088\pi$
$942$	5.55026e15	0.243800
$943$	−1.05815e16	−0.462098
$944$	3.69932e15	0.160611
$945$	−3.44972e14	−0.0148905
$946$	−3.84083e16	−1.64825
$947$	−2.07712e16	−0.886211	−0.443105	−	0.896469i	$-0.646123\pi$
$947$	−2.07712e16	−0.886211	−0.443105	+	0.896469i	$0.646123\pi$
$948$	−5.53125e15	−0.234627
$949$	−2.29737e15	−0.0968874
$950$	−1.47839e16	−0.619884
$951$	−1.38352e16	−0.576757
$952$	−6.22531e14	−0.0258023
$953$	−3.15594e16	−1.30052	−0.650262	−	0.759710i	$-0.725341\pi$
$953$	−3.15594e16	−1.30052	−0.650262	+	0.759710i	$0.725341\pi$
$954$	−4.98306e15	−0.204164
$955$	−1.11641e15	−0.0454783
$956$	−2.25803e16	−0.914557
$957$	1.02759e16	0.413813
$958$	−2.56196e16	−1.02580
$959$	8.80152e15	0.350393
$960$	−2.70129e14	−0.0106925
$961$	−2.70254e15	−0.106364
$962$	1.07763e15	0.0421704
$963$	−9.26808e15	−0.360616
$964$	−1.34709e16	−0.521161
$965$	−2.88073e14	−0.0110816
$966$	2.11960e16	0.810735
$967$	−3.56924e16	−1.35747	−0.678735	−	0.734383i	$-0.737471\pi$
$967$	−3.56924e16	−1.35747	−0.678735	+	0.734383i	$0.737471\pi$
$968$	−3.90975e15	−0.147855
$969$	−5.82670e14	−0.0219100
$970$	−3.82591e15	−0.143051
$971$	−3.46074e16	−1.28666	−0.643328	−	0.765590i	$-0.722447\pi$
$971$	−3.46074e16	−1.28666	−0.643328	+	0.765590i	$0.722447\pi$
$972$	1.08931e15	0.0402706
$973$	−2.98076e16	−1.09574
$974$	−4.20324e16	−1.53642
$975$	2.07356e15	0.0753686
$976$	5.69491e16	2.05832
$977$	−1.47083e16	−0.528618	−0.264309	−	0.964438i	$-0.585144\pi$
$977$	−1.47083e16	−0.528618	−0.264309	+	0.964438i	$0.585144\pi$
$978$	5.42359e15	0.193831
$979$	2.77189e16	0.985079
$980$	−9.84368e14	−0.0347868
$981$	−6.00471e15	−0.211015
$982$	4.96651e16	1.73555
$983$	−1.80346e16	−0.626703	−0.313352	−	0.949637i	$-0.601452\pi$
$983$	−1.80346e16	−0.626703	−0.313352	+	0.949637i	$0.601452\pi$
$984$	−2.34557e15	−0.0810541
$985$	3.23117e15	0.111035
$986$	−1.80318e15	−0.0616191
$987$	1.84860e16	0.628201
$988$	−1.20719e15	−0.0407954
$989$	5.24775e16	1.76357
$990$	1.60136e15	0.0535173
$991$	−1.30716e16	−0.434435	−0.217218	−	0.976123i	$-0.569698\pi$
$991$	−1.30716e16	−0.434435	−0.217218	+	0.976123i	$0.569698\pi$
$992$	−3.14349e16	−1.03896
$993$	−2.51549e16	−0.826802
$994$	9.32509e15	0.304809
$995$	−3.00523e15	−0.0976901
$996$	−1.04083e16	−0.336475
$997$	2.94100e16	0.945522	0.472761	−	0.881191i	$-0.343257\pi$
$997$	2.94100e16	0.945522	0.472761	+	0.881191i	$0.343257\pi$
$998$	4.79551e16	1.53326
$999$	−1.51396e15	−0.0481397

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.b.1.22	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.b.1.22	✓	27	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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+57.7377 q^{2} +243.000 q^{3} +1285.65 q^{4} +767.893 q^{5} +14030.3 q^{6} -31308.7 q^{7} -44016.6 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+57.7377 q^{2} +243.000 q^{3} +1285.65 q^{4} +767.893 q^{5} +14030.3 q^{6} -31308.7 q^{7} -44016.6 q^{8} +59049.0 q^{9} +44336.4 q^{10} +611667. q^{11} +312412. q^{12} -176895. q^{13} -1.80769e6 q^{14} +186598. q^{15} -5.17442e6 q^{16} -451731. q^{17} +3.40936e6 q^{18} +5.30807e6 q^{19} +987239. q^{20} -7.60801e6 q^{21} +3.53163e7 q^{22} -4.82528e7 q^{23} -1.06960e7 q^{24} -4.82385e7 q^{25} -1.02135e7 q^{26} +1.43489e7 q^{27} -4.02519e7 q^{28} +6.91351e7 q^{29} +1.07737e7 q^{30} +1.50685e8 q^{31} -2.08613e8 q^{32} +1.48635e8 q^{33} -2.60819e7 q^{34} -2.40417e7 q^{35} +7.59161e7 q^{36} -1.05510e8 q^{37} +3.06476e8 q^{38} -4.29855e7 q^{39} -3.38000e7 q^{40} +2.19294e8 q^{41} -4.39269e8 q^{42} -1.08755e9 q^{43} +7.86387e8 q^{44} +4.53433e7 q^{45} -2.78601e9 q^{46} -2.42981e9 q^{47} -1.25738e9 q^{48} -9.97092e8 q^{49} -2.78518e9 q^{50} -1.09771e8 q^{51} -2.27425e8 q^{52} -1.46158e9 q^{53} +8.28473e8 q^{54} +4.69695e8 q^{55} +1.37810e9 q^{56} +1.28986e9 q^{57} +3.99171e9 q^{58} -7.14924e8 q^{59} +2.39899e8 q^{60} -1.10059e10 q^{61} +8.70020e9 q^{62} -1.84875e9 q^{63} -1.44765e9 q^{64} -1.35837e8 q^{65} +8.58185e9 q^{66} -4.40368e9 q^{67} -5.80766e8 q^{68} -1.17254e10 q^{69} -1.38811e9 q^{70} -5.15856e9 q^{71} -2.59913e9 q^{72} +1.29872e10 q^{73} -6.09192e9 q^{74} -1.17219e10 q^{75} +6.82430e9 q^{76} -1.91505e10 q^{77} -2.48189e9 q^{78} -1.77050e10 q^{79} -3.97340e9 q^{80} +3.48678e9 q^{81} +1.26615e10 q^{82} -3.33159e10 q^{83} -9.78121e9 q^{84} -3.46881e8 q^{85} -6.27929e10 q^{86} +1.67998e10 q^{87} -2.69235e10 q^{88} +4.53170e10 q^{89} +2.61802e9 q^{90} +5.53836e9 q^{91} -6.20360e10 q^{92} +3.66164e10 q^{93} -1.40292e11 q^{94} +4.07603e9 q^{95} -5.06931e10 q^{96} -8.62927e10 q^{97} -5.75699e10 q^{98} +3.61183e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9}+O(q^{10}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9	\( 27 q - 128 q^{2} + 6561 q^{3} + 26142 q^{4} - 17188 q^{5} - 31104 q^{6} - 126579 q^{7} - 355797 q^{8} + 1594323 q^{9} - 383719 q^{10} - 1816556 q^{11} + 6352506 q^{12} - 3951804 q^{13} - 6207867 q^{14} - 4176684 q^{15} + 28295194 q^{16} - 17723275 q^{17} - 7558272 q^{18} - 19573013 q^{19} - 48468099 q^{20} - 30758697 q^{21} - 1729910 q^{22} - 88593797 q^{23} - 86458671 q^{24} + 345714963 q^{25} - 6676346 q^{26} + 387420489 q^{27} + 126954286 q^{28} - 276632427 q^{29} - 93243717 q^{30} - 357680917 q^{31} - 859842334 q^{32} - 441423108 q^{33} + 232730000 q^{34} - 510315139 q^{35} + 1543658958 q^{36} - 660238257 q^{37} - 2067286961 q^{38} - 960288372 q^{39} - 3388951110 q^{40} - 1671147569 q^{41} - 1508511681 q^{42} - 1883107790 q^{43} - 3895687630 q^{44} - 1014934212 q^{45} - 1720344243 q^{46} - 5818572501 q^{47} + 6875732142 q^{48} - 18858180 q^{49} - 21474519647 q^{50} - 4306755825 q^{51} - 42214560062 q^{52} - 11444513368 q^{53} - 1836660096 q^{54} - 24401486484 q^{55} - 50583585764 q^{56} - 4756242159 q^{57} - 45017395090 q^{58} - 19302956073 q^{59} - 11777748057 q^{60} + 408637955 q^{61} - 28543084070 q^{62} - 7474363371 q^{63} + 33067284293 q^{64} - 21656714730 q^{65} - 420368130 q^{66} - 49803132690 q^{67} - 16500749319 q^{68} - 21528292671 q^{69} - 45808890782 q^{70} - 34127492216 q^{71} - 21009457053 q^{72} - 55734362153 q^{73} - 40367816298 q^{74} + 84008736009 q^{75} - 14840406404 q^{76} - 99723443615 q^{77} - 1622352078 q^{78} - 76484916442 q^{79} + 93882788915 q^{80} + 94143178827 q^{81} + 52951239205 q^{82} - 140433865655 q^{83} + 30849891498 q^{84} + 34329063335 q^{85} + 175223869508 q^{86} - 67221679761 q^{87} + 268823645069 q^{88} - 1191878597 q^{89} - 22658223231 q^{90} + 201632581559 q^{91} - 206501888812 q^{92} - 86916462831 q^{93} + 319770144384 q^{94} - 81387074885 q^{95} - 208941687162 q^{96} - 144896178730 q^{97} + 135739195260 q^{98} - 107265815244 q^{99}+O(q^{100}) \) 27 * q - 128 * q^2 + 6561 * q^3 + 26142 * q^4 - 17188 * q^5 - 31104 * q^6 - 126579 * q^7 - 355797 * q^8 + 1594323 * q^9 - 383719 * q^10 - 1816556 * q^11 + 6352506 * q^12 - 3951804 * q^13 - 6207867 * q^14 - 4176684 * q^15 + 28295194 * q^16 - 17723275 * q^17 - 7558272 * q^18 - 19573013 * q^19 - 48468099 * q^20 - 30758697 * q^21 - 1729910 * q^22 - 88593797 * q^23 - 86458671 * q^24 + 345714963 * q^25 - 6676346 * q^26 + 387420489 * q^27 + 126954286 * q^28 - 276632427 * q^29 - 93243717 * q^30 - 357680917 * q^31 - 859842334 * q^32 - 441423108 * q^33 + 232730000 * q^34 - 510315139 * q^35 + 1543658958 * q^36 - 660238257 * q^37 - 2067286961 * q^38 - 960288372 * q^39 - 3388951110 * q^40 - 1671147569 * q^41 - 1508511681 * q^42 - 1883107790 * q^43 - 3895687630 * q^44 - 1014934212 * q^45 - 1720344243 * q^46 - 5818572501 * q^47 + 6875732142 * q^48 - 18858180 * q^49 - 21474519647 * q^50 - 4306755825 * q^51 - 42214560062 * q^52 - 11444513368 * q^53 - 1836660096 * q^54 - 24401486484 * q^55 - 50583585764 * q^56 - 4756242159 * q^57 - 45017395090 * q^58 - 19302956073 * q^59 - 11777748057 * q^60 + 408637955 * q^61 - 28543084070 * q^62 - 7474363371 * q^63 + 33067284293 * q^64 - 21656714730 * q^65 - 420368130 * q^66 - 49803132690 * q^67 - 16500749319 * q^68 - 21528292671 * q^69 - 45808890782 * q^70 - 34127492216 * q^71 - 21009457053 * q^72 - 55734362153 * q^73 - 40367816298 * q^74 + 84008736009 * q^75 - 14840406404 * q^76 - 99723443615 * q^77 - 1622352078 * q^78 - 76484916442 * q^79 + 93882788915 * q^80 + 94143178827 * q^81 + 52951239205 * q^82 - 140433865655 * q^83 + 30849891498 * q^84 + 34329063335 * q^85 + 175223869508 * q^86 - 67221679761 * q^87 + 268823645069 * q^88 - 1191878597 * q^89 - 22658223231 * q^90 + 201632581559 * q^91 - 206501888812 * q^92 - 86916462831 * q^93 + 319770144384 * q^94 - 81387074885 * q^95 - 208941687162 * q^96 - 144896178730 * q^97 + 135739195260 * q^98 - 107265815244 * q^99

Introduction

L-functions

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