LMFDB - Embedded newform 177.12.a.a.1.3

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:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
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)

$f(q)$	$=$	$q-70.0902 q^{2} -243.000 q^{3} +2864.64 q^{4} +3425.74 q^{5} +17031.9 q^{6} -19416.7 q^{7} -57238.6 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-70.0902 q^{2} -243.000 q^{3} +2864.64 q^{4} +3425.74 q^{5} +17031.9 q^{6} -19416.7 q^{7} -57238.6 q^{8} +59049.0 q^{9} -240111. q^{10} -662510. q^{11} -696108. q^{12} +1.45490e6 q^{13} +1.36092e6 q^{14} -832455. q^{15} -1.85492e6 q^{16} +1.01042e7 q^{17} -4.13876e6 q^{18} +4.12705e6 q^{19} +9.81352e6 q^{20} +4.71827e6 q^{21} +4.64355e7 q^{22} -8.18826e6 q^{23} +1.39090e7 q^{24} -3.70924e7 q^{25} -1.01974e8 q^{26} -1.43489e7 q^{27} -5.56220e7 q^{28} -1.12718e8 q^{29} +5.83470e7 q^{30} -6.52662e7 q^{31} +2.47236e8 q^{32} +1.60990e8 q^{33} -7.08205e8 q^{34} -6.65167e7 q^{35} +1.69154e8 q^{36} -6.08937e6 q^{37} -2.89266e8 q^{38} -3.53541e8 q^{39} -1.96085e8 q^{40} -6.32776e8 q^{41} -3.30704e8 q^{42} +9.00775e8 q^{43} -1.89786e9 q^{44} +2.02287e8 q^{45} +5.73917e8 q^{46} -1.96782e9 q^{47} +4.50745e8 q^{48} -1.60032e9 q^{49} +2.59982e9 q^{50} -2.45532e9 q^{51} +4.16777e9 q^{52} +5.33676e9 q^{53} +1.00572e9 q^{54} -2.26959e9 q^{55} +1.11139e9 q^{56} -1.00287e9 q^{57} +7.90045e9 q^{58} +7.14924e8 q^{59} -2.38469e9 q^{60} -6.94170e9 q^{61} +4.57452e9 q^{62} -1.14654e9 q^{63} -1.35300e10 q^{64} +4.98411e9 q^{65} -1.12838e10 q^{66} -4.15991e9 q^{67} +2.89449e10 q^{68} +1.98975e9 q^{69} +4.66217e9 q^{70} +1.26410e10 q^{71} -3.37988e9 q^{72} +1.33068e10 q^{73} +4.26805e8 q^{74} +9.01346e9 q^{75} +1.18225e10 q^{76} +1.28638e10 q^{77} +2.47798e10 q^{78} +3.13876e10 q^{79} -6.35447e9 q^{80} +3.48678e9 q^{81} +4.43514e10 q^{82} +3.96569e9 q^{83} +1.35161e10 q^{84} +3.46144e10 q^{85} -6.31356e10 q^{86} +2.73905e10 q^{87} +3.79212e10 q^{88} +3.45441e10 q^{89} -1.41783e10 q^{90} -2.82494e10 q^{91} -2.34564e10 q^{92} +1.58597e10 q^{93} +1.37925e11 q^{94} +1.41382e10 q^{95} -6.00784e10 q^{96} +2.67913e10 q^{97} +1.12167e11 q^{98} -3.91206e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9}+O(q^{10}) $ 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9} - 859751 q^{10} + 579094 q^{11} - 5606010 q^{12} - 2018538 q^{13} + 4157413 q^{14} - 925344 q^{15} + 20190274 q^{16} - 13084493 q^{17} - 4605822 q^{18} + 9917231 q^{19} + 10165633 q^{20} + 24013017 q^{21} - 89820518 q^{22} - 63513223 q^{23} + 28587735 q^{24} + 218986852 q^{25} - 77999532 q^{26} - 373071582 q^{27} - 444601862 q^{28} + 81530981 q^{29} + 208919493 q^{30} - 408861231 q^{31} - 26253128 q^{32} - 140719842 q^{33} - 508910076 q^{34} - 75731421 q^{35} + 1362260430 q^{36} - 802381301 q^{37} + 732704675 q^{38} + 490504734 q^{39} - 646130800 q^{40} - 1354472849 q^{41} - 1010251359 q^{42} + 282952194 q^{43} + 1846047996 q^{44} + 224858592 q^{45} + 9629305849 q^{46} - 1196794197 q^{47} - 4906236582 q^{48} + 10889725683 q^{49} - 6236232091 q^{50} + 3179531799 q^{51} - 1968200812 q^{52} - 8276044236 q^{53} + 1119214746 q^{54} - 6672895076 q^{55} + 2579741342 q^{56} - 2409887133 q^{57} - 9401656060 q^{58} + 18588031774 q^{59} - 2470248819 q^{60} - 21181559029 q^{61} - 6117706514 q^{62} - 5835163131 q^{63} + 42975855037 q^{64} + 25680681860 q^{65} + 21826385874 q^{66} + 26234163394 q^{67} + 19707344091 q^{68} + 15433713189 q^{69} + 129203099090 q^{70} + 52088830406 q^{71} - 6946819605 q^{72} + 20943384867 q^{73} + 41969200146 q^{74} - 53213805036 q^{75} + 223987219368 q^{76} + 94604773153 q^{77} + 18953886276 q^{78} + 68965662774 q^{79} + 218947784293 q^{80} + 90656394426 q^{81} + 11938614923 q^{82} + 17947446393 q^{83} + 108038252466 q^{84} - 52849386709 q^{85} + 384986147852 q^{86} - 19812028383 q^{87} - 49061112607 q^{88} + 38570593981 q^{89} - 50767436799 q^{90} - 226268806999 q^{91} - 79559686310 q^{92} + 99353279133 q^{93} - 16709400108 q^{94} - 252795831501 q^{95} + 6379510104 q^{96} - 186894587836 q^{97} - 252443311612 q^{98} + 34194921606 q^{99}+O(q^{100}) \) 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9 - 859751 * q^10 + 579094 * q^11 - 5606010 * q^12 - 2018538 * q^13 + 4157413 * q^14 - 925344 * q^15 + 20190274 * q^16 - 13084493 * q^17 - 4605822 * q^18 + 9917231 * q^19 + 10165633 * q^20 + 24013017 * q^21 - 89820518 * q^22 - 63513223 * q^23 + 28587735 * q^24 + 218986852 * q^25 - 77999532 * q^26 - 373071582 * q^27 - 444601862 * q^28 + 81530981 * q^29 + 208919493 * q^30 - 408861231 * q^31 - 26253128 * q^32 - 140719842 * q^33 - 508910076 * q^34 - 75731421 * q^35 + 1362260430 * q^36 - 802381301 * q^37 + 732704675 * q^38 + 490504734 * q^39 - 646130800 * q^40 - 1354472849 * q^41 - 1010251359 * q^42 + 282952194 * q^43 + 1846047996 * q^44 + 224858592 * q^45 + 9629305849 * q^46 - 1196794197 * q^47 - 4906236582 * q^48 + 10889725683 * q^49 - 6236232091 * q^50 + 3179531799 * q^51 - 1968200812 * q^52 - 8276044236 * q^53 + 1119214746 * q^54 - 6672895076 * q^55 + 2579741342 * q^56 - 2409887133 * q^57 - 9401656060 * q^58 + 18588031774 * q^59 - 2470248819 * q^60 - 21181559029 * q^61 - 6117706514 * q^62 - 5835163131 * q^63 + 42975855037 * q^64 + 25680681860 * q^65 + 21826385874 * q^66 + 26234163394 * q^67 + 19707344091 * q^68 + 15433713189 * q^69 + 129203099090 * q^70 + 52088830406 * q^71 - 6946819605 * q^72 + 20943384867 * q^73 + 41969200146 * q^74 - 53213805036 * q^75 + 223987219368 * q^76 + 94604773153 * q^77 + 18953886276 * q^78 + 68965662774 * q^79 + 218947784293 * q^80 + 90656394426 * q^81 + 11938614923 * q^82 + 17947446393 * q^83 + 108038252466 * q^84 - 52849386709 * q^85 + 384986147852 * q^86 - 19812028383 * q^87 - 49061112607 * q^88 + 38570593981 * q^89 - 50767436799 * q^90 - 226268806999 * q^91 - 79559686310 * q^92 + 99353279133 * q^93 - 16709400108 * q^94 - 252795831501 * q^95 + 6379510104 * q^96 - 186894587836 * q^97 - 252443311612 * q^98 + 34194921606 * 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 $

$2$	−70.0902	−1.54879	−0.774395	−	0.632702i	$-0.781946\pi$
$2$	−70.0902	−1.54879	−0.774395	+	0.632702i	$0.781946\pi$
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	2864.64	1.39875
$5$	3425.74	0.490252	0.245126	−	0.969491i	$-0.421171\pi$
$5$	3425.74	0.490252	0.245126	+	0.969491i	$0.421171\pi$
$6$	17031.9	0.894194
$7$	−19416.7	−0.436654	−0.218327	−	0.975876i	$-0.570060\pi$
$7$	−19416.7	−0.436654	−0.218327	+	0.975876i	$0.570060\pi$
$8$	−57238.6	−0.617582
$9$	59049.0	0.333333
$10$	−240111.	−0.759298
$11$	−662510.	−1.24032	−0.620159	−	0.784476i	$-0.712932\pi$
$11$	−662510.	−1.24032	−0.620159	+	0.784476i	$0.712932\pi$
$12$	−696108.	−0.807569
$13$	1.45490e6	1.08679	0.543394	−	0.839478i	$-0.317139\pi$
$13$	1.45490e6	1.08679	0.543394	+	0.839478i	$0.317139\pi$
$14$	1.36092e6	0.676285
$15$	−832455.	−0.283047
$16$	−1.85492e6	−0.442247
$17$	1.01042e7	1.72597	0.862984	−	0.505232i	$-0.168593\pi$
$17$	1.01042e7	1.72597	0.862984	+	0.505232i	$0.168593\pi$
$18$	−4.13876e6	−0.516263
$19$	4.12705e6	0.382380	0.191190	−	0.981553i	$-0.438765\pi$
$19$	4.12705e6	0.382380	0.191190	+	0.981553i	$0.438765\pi$
$20$	9.81352e6	0.685741
$21$	4.71827e6	0.252102
$22$	4.64355e7	1.92099
$23$	−8.18826e6	−0.265270	−0.132635	−	0.991165i	$-0.542344\pi$
$23$	−8.18826e6	−0.265270	−0.132635	+	0.991165i	$0.542344\pi$
$24$	1.39090e7	0.356561
$25$	−3.70924e7	−0.759653
$26$	−1.01974e8	−1.68321
$27$	−1.43489e7	−0.192450
$28$	−5.56220e7	−0.610770
$29$	−1.12718e8	−1.02048	−0.510241	−	0.860032i	$-0.670444\pi$
$29$	−1.12718e8	−1.02048	−0.510241	+	0.860032i	$0.670444\pi$
$30$	5.83470e7	0.438381
$31$	−6.52662e7	−0.409448	−0.204724	−	0.978820i	$-0.565630\pi$
$31$	−6.52662e7	−0.409448	−0.204724	+	0.978820i	$0.565630\pi$
$32$	2.47236e8	1.30253
$33$	1.60990e8	0.716098
$34$	−7.08205e8	−2.67316
$35$	−6.65167e7	−0.214070
$36$	1.69154e8	0.466250
$37$	−6.08937e6	−0.0144365	−0.00721826	−	0.999974i	$-0.502298\pi$
$37$	−6.08937e6	−0.0144365	−0.00721826	+	0.999974i	$0.502298\pi$
$38$	−2.89266e8	−0.592226
$39$	−3.53541e8	−0.627457
$40$	−1.96085e8	−0.302771
$41$	−6.32776e8	−0.852980	−0.426490	−	0.904492i	$-0.640250\pi$
$41$	−6.32776e8	−0.852980	−0.426490	+	0.904492i	$0.640250\pi$
$42$	−3.30704e8	−0.390453
$43$	9.00775e8	0.934415	0.467208	−	0.884148i	$-0.345260\pi$
$43$	9.00775e8	0.934415	0.467208	+	0.884148i	$0.345260\pi$
$44$	−1.89786e9	−1.73490
$45$	2.02287e8	0.163417
$46$	5.73917e8	0.410848
$47$	−1.96782e9	−1.25154	−0.625772	−	0.780006i	$-0.715216\pi$
$47$	−1.96782e9	−1.25154	−0.625772	+	0.780006i	$0.715216\pi$
$48$	4.50745e8	0.255331
$49$	−1.60032e9	−0.809334
$50$	2.59982e9	1.17654
$51$	−2.45532e9	−0.996488
$52$	4.16777e9	1.52015
$53$	5.33676e9	1.75291	0.876456	−	0.481482i	$-0.159901\pi$
$53$	5.33676e9	1.75291	0.876456	+	0.481482i	$0.159901\pi$
$54$	1.00572e9	0.298065
$55$	−2.26959e9	−0.608069
$56$	1.11139e9	0.269669
$57$	−1.00287e9	−0.220767
$58$	7.90045e9	1.58051
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	−2.38469e9	−0.395913
$61$	−6.94170e9	−1.05233	−0.526164	−	0.850383i	$-0.676370\pi$
$61$	−6.94170e9	−1.05233	−0.526164	+	0.850383i	$0.676370\pi$
$62$	4.57452e9	0.634149
$63$	−1.14654e9	−0.145551
$64$	−1.35300e10	−1.57510
$65$	4.98411e9	0.532800
$66$	−1.12838e10	−1.10909
$67$	−4.15991e9	−0.376420	−0.188210	−	0.982129i	$-0.560268\pi$
$67$	−4.15991e9	−0.376420	−0.188210	+	0.982129i	$0.560268\pi$
$68$	2.89449e10	2.41420
$69$	1.98975e9	0.153154
$70$	4.66217e9	0.331550
$71$	1.26410e10	0.831498	0.415749	−	0.909479i	$-0.363519\pi$
$71$	1.26410e10	0.831498	0.415749	+	0.909479i	$0.363519\pi$
$72$	−3.37988e9	−0.205861
$73$	1.33068e10	0.751274	0.375637	−	0.926767i	$-0.377424\pi$
$73$	1.33068e10	0.751274	0.375637	+	0.926767i	$0.377424\pi$
$74$	4.26805e8	0.0223592
$75$	9.01346e9	0.438586
$76$	1.18225e10	0.534854
$77$	1.28638e10	0.541589
$78$	2.47798e10	0.971800
$79$	3.13876e10	1.14765	0.573824	−	0.818979i	$-0.305459\pi$
$79$	3.13876e10	1.14765	0.573824	+	0.818979i	$0.305459\pi$
$80$	−6.35447e9	−0.216812
$81$	3.48678e9	0.111111
$82$	4.43514e10	1.32109
$83$	3.96569e9	0.110507	0.0552535	−	0.998472i	$-0.482403\pi$
$83$	3.96569e9	0.110507	0.0552535	+	0.998472i	$0.482403\pi$
$84$	1.35161e10	0.352628
$85$	3.46144e10	0.846160
$86$	−6.31356e10	−1.44721
$87$	2.73905e10	0.589175
$88$	3.79212e10	0.765997
$89$	3.45441e10	0.655736	0.327868	−	0.944724i	$-0.393670\pi$
$89$	3.45441e10	0.655736	0.327868	+	0.944724i	$0.393670\pi$
$90$	−1.41783e10	−0.253099
$91$	−2.82494e10	−0.474550
$92$	−2.34564e10	−0.371047
$93$	1.58597e10	0.236395
$94$	1.37925e11	1.93838
$95$	1.41382e10	0.187462
$96$	−6.00784e10	−0.752015
$97$	2.67913e10	0.316774	0.158387	−	0.987377i	$-0.449371\pi$
$97$	2.67913e10	0.316774	0.158387	+	0.987377i	$0.449371\pi$
$98$	1.12167e11	1.25349
$99$	−3.91206e10	−0.413439
$100$	−1.06256e11	−1.06256
$101$	4.49865e9	0.0425907	0.0212954	−	0.999773i	$-0.493221\pi$
$101$	4.49865e9	0.0425907	0.0212954	+	0.999773i	$0.493221\pi$
$102$	1.72094e11	1.54335
$103$	9.34612e10	0.794377	0.397188	−	0.917737i	$-0.369986\pi$
$103$	9.34612e10	0.794377	0.397188	+	0.917737i	$0.369986\pi$
$104$	−8.32765e10	−0.671180
$105$	1.61636e10	0.123594
$106$	−3.74055e11	−2.71489
$107$	9.02495e10	0.622063	0.311031	−	0.950400i	$-0.399326\pi$
$107$	9.02495e10	0.622063	0.311031	+	0.950400i	$0.399326\pi$
$108$	−4.11045e10	−0.269190
$109$	3.59947e10	0.224074	0.112037	−	0.993704i	$-0.464262\pi$
$109$	3.59947e10	0.224074	0.112037	+	0.993704i	$0.464262\pi$
$110$	1.59076e11	0.941771
$111$	1.47972e9	0.00833493
$112$	3.60164e10	0.193109
$113$	−1.23124e11	−0.628653	−0.314326	−	0.949315i	$-0.601779\pi$
$113$	−1.23124e11	−0.628653	−0.314326	+	0.949315i	$0.601779\pi$
$114$	7.02916e10	0.341922
$115$	−2.80509e10	−0.130049
$116$	−3.22897e11	−1.42740
$117$	8.59104e10	0.362263
$118$	−5.01092e10	−0.201635
$119$	−1.96191e11	−0.753650
$120$	4.76486e10	0.174805
$121$	1.53608e11	0.538388
$122$	4.86545e11	1.62984
$123$	1.53765e11	0.492468
$124$	−1.86964e11	−0.572716
$125$	−2.94342e11	−0.862674
$126$	8.03612e10	0.225428
$127$	1.28688e11	0.345636	0.172818	−	0.984954i	$-0.444713\pi$
$127$	1.28688e11	0.345636	0.172818	+	0.984954i	$0.444713\pi$
$128$	4.41980e11	1.13697
$129$	−2.18888e11	−0.539485
$130$	−3.49338e11	−0.825196
$131$	6.02975e11	1.36555	0.682774	−	0.730630i	$-0.260773\pi$
$131$	6.02975e11	1.36555	0.682774	+	0.730630i	$0.260773\pi$
$132$	4.61179e11	1.00164
$133$	−8.01338e10	−0.166967
$134$	2.91569e11	0.582995
$135$	−4.91557e10	−0.0943491
$136$	−5.78350e11	−1.06593
$137$	9.53644e10	0.168820	0.0844099	−	0.996431i	$-0.473099\pi$
$137$	9.53644e10	0.168820	0.0844099	+	0.996431i	$0.473099\pi$
$138$	−1.39462e11	−0.237203
$139$	−1.03821e12	−1.69709	−0.848543	−	0.529127i	$-0.822519\pi$
$139$	−1.03821e12	−1.69709	−0.848543	+	0.529127i	$0.822519\pi$
$140$	−1.90547e11	−0.299431
$141$	4.78179e11	0.722580
$142$	−8.86012e11	−1.28782
$143$	−9.63887e11	−1.34796
$144$	−1.09531e11	−0.147416
$145$	−3.86144e11	−0.500293
$146$	−9.32678e11	−1.16357
$147$	3.88877e11	0.467269
$148$	−1.74439e10	−0.0201931
$149$	8.53346e11	0.951920	0.475960	−	0.879467i	$-0.342101\pi$
$149$	8.53346e11	0.951920	0.475960	+	0.879467i	$0.342101\pi$
$150$	−6.31755e11	−0.679277
$151$	−7.65158e11	−0.793191	−0.396595	−	0.917994i	$-0.629808\pi$
$151$	−7.65158e11	−0.793191	−0.396595	+	0.917994i	$0.629808\pi$
$152$	−2.36227e11	−0.236151
$153$	5.96643e11	0.575323
$154$	−9.01626e11	−0.838808
$155$	−2.23585e11	−0.200733
$156$	−1.01277e12	−0.877657
$157$	−4.07737e11	−0.341139	−0.170570	−	0.985346i	$-0.554561\pi$
$157$	−4.07737e11	−0.341139	−0.170570	+	0.985346i	$0.554561\pi$
$158$	−2.19996e12	−1.77747
$159$	−1.29683e12	−1.01204
$160$	8.46968e11	0.638568
$161$	1.58989e11	0.115831
$162$	−2.44390e11	−0.172088
$163$	−2.63213e12	−1.79174	−0.895871	−	0.444314i	$-0.853448\pi$
$163$	−2.63213e12	−1.79174	−0.895871	+	0.444314i	$0.853448\pi$
$164$	−1.81268e12	−1.19311
$165$	5.51510e11	0.351069
$166$	−2.77956e11	−0.171152
$167$	2.43531e12	1.45082	0.725411	−	0.688316i	$-0.241650\pi$
$167$	2.43531e12	1.45082	0.725411	+	0.688316i	$0.241650\pi$
$168$	−2.70067e11	−0.155694
$169$	3.24575e11	0.181108
$170$	−2.42613e12	−1.31052
$171$	2.43698e11	0.127460
$172$	2.58040e12	1.30701
$173$	2.68448e12	1.31706	0.658531	−	0.752554i	$-0.271178\pi$
$173$	2.68448e12	1.31706	0.658531	+	0.752554i	$0.271178\pi$
$174$	−1.91981e12	−0.912509
$175$	7.20214e11	0.331705
$176$	1.22890e12	0.548526
$177$	−1.73727e11	−0.0751646
$178$	−2.42120e12	−1.01560
$179$	2.10047e12	0.854330	0.427165	−	0.904174i	$-0.359512\pi$
$179$	2.10047e12	0.854330	0.427165	+	0.904174i	$0.359512\pi$
$180$	5.79479e11	0.228580
$181$	1.55084e12	0.593383	0.296691	−	0.954973i	$-0.404117\pi$
$181$	1.55084e12	0.593383	0.296691	+	0.954973i	$0.404117\pi$
$182$	1.98001e12	0.734978
$183$	1.68683e12	0.607562
$184$	4.68685e11	0.163826
$185$	−2.08606e10	−0.00707754
$186$	−1.11161e12	−0.366126
$187$	−6.69413e12	−2.14075
$188$	−5.63709e12	−1.75060
$189$	2.78609e11	0.0840340
$190$	−9.90950e11	−0.290340
$191$	−1.58977e12	−0.452532	−0.226266	−	0.974065i	$-0.572652\pi$
$191$	−1.58977e12	−0.452532	−0.226266	+	0.974065i	$0.572652\pi$
$192$	3.28779e12	0.909383
$193$	6.85823e10	0.0184351	0.00921757	−	0.999958i	$-0.497066\pi$
$193$	6.85823e10	0.0184351	0.00921757	+	0.999958i	$0.497066\pi$
$194$	−1.87781e12	−0.490616
$195$	−1.21114e12	−0.307612
$196$	−4.58434e12	−1.13206
$197$	−8.56601e11	−0.205691	−0.102845	−	0.994697i	$-0.532795\pi$
$197$	−8.56601e11	−0.205691	−0.102845	+	0.994697i	$0.532795\pi$
$198$	2.74197e12	0.640331
$199$	−7.42003e12	−1.68544	−0.842721	−	0.538350i	$-0.819048\pi$
$199$	−7.42003e12	−1.68544	−0.842721	+	0.538350i	$0.819048\pi$
$200$	2.12312e12	0.469148
$201$	1.01086e12	0.217326
$202$	−3.15312e11	−0.0659641
$203$	2.18862e12	0.445597
$204$	−7.03361e12	−1.39384
$205$	−2.16773e12	−0.418175
$206$	−6.55072e12	−1.23032
$207$	−4.83509e11	−0.0884235
$208$	−2.69872e12	−0.480628
$209$	−2.73421e12	−0.474272
$210$	−1.13291e12	−0.191421
$211$	−3.72312e12	−0.612850	−0.306425	−	0.951895i	$-0.599133\pi$
$211$	−3.72312e12	−0.612850	−0.306425	+	0.951895i	$0.599133\pi$
$212$	1.52879e13	2.45189
$213$	−3.07177e12	−0.480066
$214$	−6.32561e12	−0.963445
$215$	3.08582e12	0.458099
$216$	8.21312e11	0.118854
$217$	1.26726e12	0.178787
$218$	−2.52287e12	−0.347044
$219$	−3.23356e12	−0.433748
$220$	−6.50156e12	−0.850537
$221$	1.47006e13	1.87576
$222$	−1.03714e11	−0.0129091
$223$	−1.17804e13	−1.43049	−0.715243	−	0.698875i	$-0.753684\pi$
$223$	−1.17804e13	−1.43049	−0.715243	+	0.698875i	$0.753684\pi$
$224$	−4.80052e12	−0.568754
$225$	−2.19027e12	−0.253218
$226$	8.62978e12	0.973651
$227$	−1.59234e13	−1.75345	−0.876724	−	0.480994i	$-0.840276\pi$
$227$	−1.59234e13	−1.75345	−0.876724	+	0.480994i	$0.840276\pi$
$228$	−2.87287e12	−0.308798
$229$	−1.55582e13	−1.63254	−0.816272	−	0.577668i	$-0.803963\pi$
$229$	−1.55582e13	−1.63254	−0.816272	+	0.577668i	$0.803963\pi$
$230$	1.96609e12	0.201419
$231$	−3.12590e12	−0.312687
$232$	6.45184e12	0.630231
$233$	3.92685e12	0.374616	0.187308	−	0.982301i	$-0.440024\pi$
$233$	3.92685e12	0.374616	0.187308	+	0.982301i	$0.440024\pi$
$234$	−6.02148e12	−0.561069
$235$	−6.74123e12	−0.613573
$236$	2.04800e12	0.182102
$237$	−7.62718e12	−0.662595
$238$	1.37510e13	1.16725
$239$	−2.94919e12	−0.244632	−0.122316	−	0.992491i	$-0.539032\pi$
$239$	−2.94919e12	−0.244632	−0.122316	+	0.992491i	$0.539032\pi$
$240$	1.54414e12	0.125177
$241$	1.62453e13	1.28716	0.643580	−	0.765378i	$-0.277448\pi$
$241$	1.62453e13	1.28716	0.643580	+	0.765378i	$0.277448\pi$
$242$	−1.07664e13	−0.833850
$243$	−8.47289e11	−0.0641500
$244$	−1.98855e13	−1.47195
$245$	−5.48227e12	−0.396778
$246$	−1.07774e13	−0.762730
$247$	6.00444e12	0.415565
$248$	3.73575e12	0.252868
$249$	−9.63664e11	−0.0638012
$250$	2.06305e13	1.33610
$251$	4.69952e12	0.297747	0.148874	−	0.988856i	$-0.452435\pi$
$251$	4.69952e12	0.297747	0.148874	+	0.988856i	$0.452435\pi$
$252$	−3.28442e12	−0.203590
$253$	5.42481e12	0.329020
$254$	−9.01980e12	−0.535318
$255$	−8.41129e12	−0.488530
$256$	−3.26907e12	−0.185825
$257$	3.31576e13	1.84480	0.922402	−	0.386231i	$-0.126223\pi$
$257$	3.31576e13	1.84480	0.922402	+	0.386231i	$0.126223\pi$
$258$	1.53419e13	0.835549
$259$	1.18236e11	0.00630376
$260$	1.42777e13	0.745255
$261$	−6.65590e12	−0.340160
$262$	−4.22626e13	−2.11495
$263$	−1.73861e13	−0.852012	−0.426006	−	0.904720i	$-0.640080\pi$
$263$	−1.73861e13	−0.852012	−0.426006	+	0.904720i	$0.640080\pi$
$264$	−9.21485e12	−0.442249
$265$	1.82824e13	0.859369
$266$	5.61660e12	0.258597
$267$	−8.39422e12	−0.378589
$268$	−1.19166e13	−0.526517
$269$	4.37856e12	0.189537	0.0947684	−	0.995499i	$-0.469789\pi$
$269$	4.37856e12	0.189537	0.0947684	+	0.995499i	$0.469789\pi$
$270$	3.44533e12	0.146127
$271$	3.90100e13	1.62123	0.810615	−	0.585579i	$-0.199133\pi$
$271$	3.90100e13	1.62123	0.810615	+	0.585579i	$0.199133\pi$
$272$	−1.87424e13	−0.763303
$273$	6.86461e12	0.273981
$274$	−6.68412e12	−0.261466
$275$	2.45741e13	0.942211
$276$	5.69992e12	0.214224
$277$	4.37063e13	1.61030	0.805148	−	0.593074i	$-0.202086\pi$
$277$	4.37063e13	1.61030	0.805148	+	0.593074i	$0.202086\pi$
$278$	7.27684e13	2.62843
$279$	−3.85390e12	−0.136483
$280$	3.80733e12	0.132206
$281$	3.37117e13	1.14788	0.573940	−	0.818898i	$-0.305414\pi$
$281$	3.37117e13	1.14788	0.573940	+	0.818898i	$0.305414\pi$
$282$	−3.35157e13	−1.11912
$283$	−5.53312e13	−1.81194	−0.905972	−	0.423338i	$-0.860858\pi$
$283$	−5.53312e13	−1.81194	−0.905972	+	0.423338i	$0.860858\pi$
$284$	3.62120e13	1.16306
$285$	−3.43558e12	−0.108231
$286$	6.75591e13	2.08771
$287$	1.22864e13	0.372457
$288$	1.45991e13	0.434176
$289$	6.78229e13	1.97896
$290$	2.70649e13	0.774849
$291$	−6.51029e12	−0.182889
$292$	3.81193e13	1.05085
$293$	−3.18979e13	−0.862959	−0.431479	−	0.902123i	$-0.642008\pi$
$293$	−3.18979e13	−0.862959	−0.431479	+	0.902123i	$0.642008\pi$
$294$	−2.72565e13	−0.723702
$295$	2.44915e12	0.0638254
$296$	3.48547e11	0.00891573
$297$	9.50630e12	0.238699
$298$	−5.98112e13	−1.47432
$299$	−1.19131e13	−0.288293
$300$	2.58203e13	0.613472
$301$	−1.74901e13	−0.408016
$302$	5.36301e13	1.22849
$303$	−1.09317e12	−0.0245898
$304$	−7.65533e12	−0.169106
$305$	−2.37805e13	−0.515907
$306$	−4.18188e13	−0.891054
$307$	−2.27684e13	−0.476509	−0.238255	−	0.971203i	$-0.576575\pi$
$307$	−2.27684e13	−0.476509	−0.238255	+	0.971203i	$0.576575\pi$
$308$	3.68502e13	0.757548
$309$	−2.27111e13	−0.458634
$310$	1.56711e13	0.310893
$311$	−9.71409e13	−1.89330	−0.946651	−	0.322261i	$-0.895557\pi$
$311$	−9.71409e13	−1.89330	−0.946651	+	0.322261i	$0.895557\pi$
$312$	2.02362e13	0.387506
$313$	−5.13532e13	−0.966214	−0.483107	−	0.875561i	$-0.660492\pi$
$313$	−5.13532e13	−0.966214	−0.483107	+	0.875561i	$0.660492\pi$
$314$	2.85784e13	0.528353
$315$	−3.92775e12	−0.0713568
$316$	8.99141e13	1.60527
$317$	−1.29652e13	−0.227486	−0.113743	−	0.993510i	$-0.536284\pi$
$317$	−1.29652e13	−0.227486	−0.113743	+	0.993510i	$0.536284\pi$
$318$	9.08953e13	1.56744
$319$	7.46770e13	1.26572
$320$	−4.63502e13	−0.772195
$321$	−2.19306e13	−0.359148
$322$	−1.11436e13	−0.179398
$323$	4.17005e13	0.659975
$324$	9.98839e12	0.155417
$325$	−5.39658e13	−0.825581
$326$	1.84487e14	2.77503
$327$	−8.74670e12	−0.129369
$328$	3.62192e13	0.526785
$329$	3.82086e13	0.546491
$330$	−3.86555e13	−0.543732
$331$	−6.87540e13	−0.951140	−0.475570	−	0.879678i	$-0.657758\pi$
$331$	−6.87540e13	−0.951140	−0.475570	+	0.879678i	$0.657758\pi$
$332$	1.13603e13	0.154572
$333$	−3.59571e11	−0.00481218
$334$	−1.70692e14	−2.24702
$335$	−1.42508e13	−0.184541
$336$	−8.75199e12	−0.111491
$337$	−8.03327e13	−1.00676	−0.503382	−	0.864064i	$-0.667911\pi$
$337$	−8.03327e13	−1.00676	−0.503382	+	0.864064i	$0.667911\pi$
$338$	−2.27495e13	−0.280498
$339$	2.99191e13	0.362953
$340$	9.91578e13	1.18357
$341$	4.32395e13	0.507846
$342$	−1.70809e13	−0.197409
$343$	6.94662e13	0.790052
$344$	−5.15592e13	−0.577078
$345$	6.81636e12	0.0750841
$346$	−1.88156e14	−2.03985
$347$	6.13215e13	0.654336	0.327168	−	0.944966i	$-0.393906\pi$
$347$	6.13215e13	0.654336	0.327168	+	0.944966i	$0.393906\pi$
$348$	7.84641e13	0.824109
$349$	−2.53450e12	−0.0262031	−0.0131015	−	0.999914i	$-0.504170\pi$
$349$	−2.53450e12	−0.0262031	−0.0131015	+	0.999914i	$0.504170\pi$
$350$	−5.04800e13	−0.513742
$351$	−2.08762e13	−0.209152
$352$	−1.63797e14	−1.61555
$353$	1.10956e14	1.07743	0.538714	−	0.842489i	$-0.318910\pi$
$353$	1.10956e14	1.07743	0.538714	+	0.842489i	$0.318910\pi$
$354$	1.21765e13	0.116414
$355$	4.33049e13	0.407644
$356$	9.89565e13	0.917211
$357$	4.76743e13	0.435120
$358$	−1.47223e14	−1.32318
$359$	3.70842e13	0.328223	0.164112	−	0.986442i	$-0.447524\pi$
$359$	3.70842e13	0.328223	0.164112	+	0.986442i	$0.447524\pi$
$360$	−1.15786e13	−0.100924
$361$	−9.94577e13	−0.853786
$362$	−1.08699e14	−0.919026
$363$	−3.73268e13	−0.310838
$364$	−8.09245e13	−0.663777
$365$	4.55857e13	0.368314
$366$	−1.18230e14	−0.940987
$367$	−9.94812e13	−0.779970	−0.389985	−	0.920821i	$-0.627520\pi$
$367$	−9.94812e13	−0.779970	−0.389985	+	0.920821i	$0.627520\pi$
$368$	1.51886e13	0.117315
$369$	−3.73648e13	−0.284327
$370$	1.46212e12	0.0109616
$371$	−1.03622e14	−0.765415
$372$	4.54323e13	0.330658
$373$	−3.99225e13	−0.286299	−0.143149	−	0.989701i	$-0.545723\pi$
$373$	−3.99225e13	−0.286299	−0.143149	+	0.989701i	$0.545723\pi$
$374$	4.69194e14	3.31557
$375$	7.15250e13	0.498065
$376$	1.12635e14	0.772931
$377$	−1.63994e14	−1.10905
$378$	−1.95278e13	−0.130151
$379$	−1.52327e14	−1.00060	−0.500299	−	0.865853i	$-0.666777\pi$
$379$	−1.52327e14	−1.00060	−0.500299	+	0.865853i	$0.666777\pi$
$380$	4.05009e13	0.262213
$381$	−3.12713e13	−0.199553
$382$	1.11427e14	0.700878
$383$	−1.88218e14	−1.16699	−0.583496	−	0.812116i	$-0.698316\pi$
$383$	−1.88218e14	−1.16699	−0.583496	+	0.812116i	$0.698316\pi$
$384$	−1.07401e14	−0.656428
$385$	4.40680e13	0.265515
$386$	−4.80695e12	−0.0285522
$387$	5.31899e13	0.311472
$388$	7.67475e13	0.443088
$389$	−2.80258e14	−1.59527	−0.797636	−	0.603139i	$-0.793916\pi$
$389$	−2.80258e14	−1.59527	−0.797636	+	0.603139i	$0.793916\pi$
$390$	8.48891e13	0.476427
$391$	−8.27358e13	−0.457848
$392$	9.16000e13	0.499830
$393$	−1.46523e14	−0.788399
$394$	6.00394e13	0.318571
$395$	1.07526e14	0.562637
$396$	−1.12066e14	−0.578299
$397$	−2.00577e14	−1.02078	−0.510392	−	0.859942i	$-0.670500\pi$
$397$	−2.00577e14	−1.02078	−0.510392	+	0.859942i	$0.670500\pi$
$398$	5.20072e14	2.61040
$399$	1.94725e13	0.0963987
$400$	6.88034e13	0.335954
$401$	8.95389e13	0.431239	0.215619	−	0.976477i	$-0.430823\pi$
$401$	8.95389e13	0.431239	0.215619	+	0.976477i	$0.430823\pi$
$402$	−7.08512e13	−0.336592
$403$	−9.49557e13	−0.444983
$404$	1.28870e13	0.0595738
$405$	1.19448e13	0.0544725
$406$	−1.53401e14	−0.690136
$407$	4.03427e12	0.0179059
$408$	1.40539e14	0.615413
$409$	−5.10887e12	−0.0220723	−0.0110361	−	0.999939i	$-0.503513\pi$
$409$	−5.10887e12	−0.0220723	−0.0110361	+	0.999939i	$0.503513\pi$
$410$	1.51936e14	0.647666
$411$	−2.31736e13	−0.0974681
$412$	2.67733e14	1.11114
$413$	−1.38815e13	−0.0568475
$414$	3.38893e13	0.136949
$415$	1.35854e13	0.0541763
$416$	3.59704e14	1.41557
$417$	2.52285e14	0.979813
$418$	1.91642e14	0.734548
$419$	−2.25293e13	−0.0852257	−0.0426129	−	0.999092i	$-0.513568\pi$
$419$	−2.25293e13	−0.0852257	−0.0426129	+	0.999092i	$0.513568\pi$
$420$	4.63028e13	0.172877
$421$	1.05584e14	0.389087	0.194544	−	0.980894i	$-0.437677\pi$
$421$	1.05584e14	0.389087	0.194544	+	0.980894i	$0.437677\pi$
$422$	2.60955e14	0.949176
$423$	−1.16198e14	−0.417181
$424$	−3.05469e14	−1.08257
$425$	−3.74789e14	−1.31114
$426$	2.15301e14	0.743521
$427$	1.34785e14	0.459503
$428$	2.58533e14	0.870111
$429$	2.34224e14	0.778246
$430$	−2.16286e14	−0.709500
$431$	−2.21242e14	−0.716544	−0.358272	−	0.933617i	$-0.616634\pi$
$431$	−2.21242e14	−0.716544	−0.358272	+	0.933617i	$0.616634\pi$
$432$	2.66160e13	0.0851104
$433$	2.77234e14	0.875311	0.437656	−	0.899143i	$-0.355809\pi$
$433$	2.77234e14	0.875311	0.437656	+	0.899143i	$0.355809\pi$
$434$	−8.88223e13	−0.276903
$435$	9.38329e13	0.288844
$436$	1.03112e14	0.313424
$437$	−3.37934e13	−0.101434
$438$	2.26641e14	0.671785
$439$	−5.73176e14	−1.67777	−0.838887	−	0.544306i	$-0.816793\pi$
$439$	−5.73176e14	−1.67777	−0.838887	+	0.544306i	$0.816793\pi$
$440$	1.29908e14	0.375532
$441$	−9.44971e13	−0.269778
$442$	−1.03037e15	−2.90516
$443$	−3.67632e14	−1.02375	−0.511874	−	0.859061i	$-0.671049\pi$
$443$	−3.67632e14	−1.02375	−0.511874	+	0.859061i	$0.671049\pi$
$444$	4.23886e12	0.0116585
$445$	1.18339e14	0.321476
$446$	8.25692e14	2.21552
$447$	−2.07363e14	−0.549591
$448$	2.62708e14	0.687772
$449$	−1.71819e14	−0.444341	−0.222171	−	0.975008i	$-0.571314\pi$
$449$	−1.71819e14	−0.444341	−0.222171	+	0.975008i	$0.571314\pi$
$450$	1.53517e14	0.392181
$451$	4.19221e14	1.05797
$452$	−3.52706e14	−0.879328
$453$	1.85933e14	0.457949
$454$	1.11607e15	2.71572
$455$	−9.67752e13	−0.232649
$456$	5.74031e13	0.136342
$457$	4.34071e14	1.01864	0.509322	−	0.860576i	$-0.329896\pi$
$457$	4.34071e14	1.01864	0.509322	+	0.860576i	$0.329896\pi$
$458$	1.09048e15	2.52847
$459$	−1.44984e14	−0.332163
$460$	−8.03557e13	−0.181907
$461$	−3.43568e14	−0.768524	−0.384262	−	0.923224i	$-0.625544\pi$
$461$	−3.43568e14	−0.768524	−0.384262	+	0.923224i	$0.625544\pi$
$462$	2.19095e14	0.484286
$463$	−6.49507e14	−1.41869	−0.709347	−	0.704860i	$-0.751010\pi$
$463$	−6.49507e14	−1.41869	−0.709347	+	0.704860i	$0.751010\pi$
$464$	2.09083e14	0.451305
$465$	5.43312e13	0.115893
$466$	−2.75234e14	−0.580202
$467$	−4.46394e14	−0.929983	−0.464992	−	0.885315i	$-0.653943\pi$
$467$	−4.46394e14	−0.929983	−0.464992	+	0.885315i	$0.653943\pi$
$468$	2.46103e14	0.506715
$469$	8.07718e13	0.164365
$470$	4.72494e14	0.950295
$471$	9.90800e13	0.196957
$472$	−4.09213e13	−0.0804023
$473$	−5.96773e14	−1.15897
$474$	5.34591e14	1.02622
$475$	−1.53082e14	−0.290476
$476$	−5.62016e14	−1.05417
$477$	3.15130e14	0.584304
$478$	2.06709e14	0.378884
$479$	1.92556e13	0.0348910	0.0174455	−	0.999848i	$-0.494447\pi$
$479$	1.92556e13	0.0348910	0.0174455	+	0.999848i	$0.494447\pi$
$480$	−2.05813e14	−0.368677
$481$	−8.85942e12	−0.0156894
$482$	−1.13863e15	−1.99354
$483$	−3.86344e13	−0.0668752
$484$	4.40033e14	0.753071
$485$	9.17801e13	0.155299
$486$	5.93867e13	0.0993549
$487$	−6.15329e14	−1.01788	−0.508942	−	0.860801i	$-0.669963\pi$
$487$	−6.15329e14	−1.01788	−0.508942	+	0.860801i	$0.669963\pi$
$488$	3.97333e14	0.649899
$489$	6.39608e14	1.03446
$490$	3.84254e14	0.614525
$491$	9.75978e14	1.54345	0.771724	−	0.635958i	$-0.219395\pi$
$491$	9.75978e14	1.54345	0.771724	+	0.635958i	$0.219395\pi$
$492$	4.40480e14	0.688840
$493$	−1.13893e15	−1.76132
$494$	−4.20853e14	−0.643624
$495$	−1.34017e14	−0.202690
$496$	1.21063e14	0.181077
$497$	−2.45447e14	−0.363077
$498$	6.75434e13	0.0988147
$499$	−7.05491e14	−1.02079	−0.510397	−	0.859939i	$-0.670502\pi$
$499$	−7.05491e14	−1.02079	−0.510397	+	0.859939i	$0.670502\pi$
$500$	−8.43183e14	−1.20667
$501$	−5.91781e14	−0.837633
$502$	−3.29391e14	−0.461148
$503$	1.04627e15	1.44883	0.724417	−	0.689362i	$-0.242109\pi$
$503$	1.04627e15	1.44883	0.724417	+	0.689362i	$0.242109\pi$
$504$	6.56263e13	0.0898897
$505$	1.54112e13	0.0208802
$506$	−3.80226e14	−0.509582
$507$	−7.88717e13	−0.104563
$508$	3.68646e14	0.483459
$509$	−7.28565e13	−0.0945194	−0.0472597	−	0.998883i	$-0.515049\pi$
$509$	−7.28565e13	−0.0945194	−0.0472597	+	0.998883i	$0.515049\pi$
$510$	5.89549e14	0.756631
$511$	−2.58375e14	−0.328047
$512$	−6.76045e14	−0.849162
$513$	−5.92186e13	−0.0735890
$514$	−2.32402e15	−2.85722
$515$	3.20174e14	0.389445
$516$	−6.27037e14	−0.754605
$517$	1.30370e15	1.55231
$518$	−8.28717e12	−0.00976320
$519$	−6.52328e14	−0.760406
$520$	−2.85284e14	−0.329048
$521$	−9.60568e14	−1.09628	−0.548139	−	0.836387i	$-0.684663\pi$
$521$	−9.60568e14	−1.09628	−0.548139	+	0.836387i	$0.684663\pi$
$522$	4.66513e14	0.526837
$523$	1.46279e15	1.63465	0.817323	−	0.576180i	$-0.195457\pi$
$523$	1.46279e15	1.63465	0.817323	+	0.576180i	$0.195457\pi$
$524$	1.72731e15	1.91006
$525$	−1.75012e14	−0.191510
$526$	1.21860e15	1.31959
$527$	−6.59462e14	−0.706694
$528$	−2.98623e14	−0.316692
$529$	−8.85762e14	−0.929632
$530$	−1.28141e15	−1.33098
$531$	4.22156e13	0.0433963
$532$	−2.29555e14	−0.233546
$533$	−9.20626e14	−0.927008
$534$	5.88353e14	0.586355
$535$	3.09172e14	0.304968
$536$	2.38107e14	0.232470
$537$	−5.10415e14	−0.493248
$538$	−3.06894e14	−0.293553
$539$	1.06023e15	1.00383
$540$	−1.40813e14	−0.131971
$541$	6.17096e14	0.572490	0.286245	−	0.958157i	$-0.407593\pi$
$541$	6.17096e14	0.572490	0.286245	+	0.958157i	$0.407593\pi$
$542$	−2.73422e15	−2.51095
$543$	−3.76854e14	−0.342590
$544$	2.49812e15	2.24812
$545$	1.23308e14	0.109853
$546$	−4.81142e14	−0.424340
$547$	−6.62825e14	−0.578720	−0.289360	−	0.957220i	$-0.593443\pi$
$547$	−6.62825e14	−0.578720	−0.289360	+	0.957220i	$0.593443\pi$
$548$	2.73185e14	0.236137
$549$	−4.09900e14	−0.350776
$550$	−1.72241e15	−1.45929
$551$	−4.65193e14	−0.390211
$552$	−1.13890e14	−0.0945850
$553$	−6.09444e14	−0.501124
$554$	−3.06339e15	−2.49401
$555$	5.06913e12	0.00408622
$556$	−2.97410e15	−2.37380
$557$	2.08314e14	0.164632	0.0823161	−	0.996606i	$-0.473768\pi$
$557$	2.08314e14	0.164632	0.0823161	+	0.996606i	$0.473768\pi$
$558$	2.70121e14	0.211383
$559$	1.31054e15	1.01551
$560$	1.23383e14	0.0946719
$561$	1.62667e15	1.23596
$562$	−2.36286e15	−1.77782
$563$	1.17930e15	0.878674	0.439337	−	0.898322i	$-0.355213\pi$
$563$	1.17930e15	0.878674	0.439337	+	0.898322i	$0.355213\pi$
$564$	1.36981e15	1.01071
$565$	−4.21791e14	−0.308198
$566$	3.87818e15	2.80632
$567$	−6.77020e13	−0.0485171
$568$	−7.23555e14	−0.513518
$569$	−2.24886e15	−1.58069	−0.790343	−	0.612665i	$-0.790098\pi$
$569$	−2.24886e15	−1.58069	−0.790343	+	0.612665i	$0.790098\pi$
$570$	2.40801e14	0.167628
$571$	−4.46356e14	−0.307739	−0.153870	−	0.988091i	$-0.549174\pi$
$571$	−4.46356e14	−0.307739	−0.153870	+	0.988091i	$0.549174\pi$
$572$	−2.76119e15	−1.88546
$573$	3.86313e14	0.261270
$574$	−8.61160e14	−0.576857
$575$	3.03723e14	0.201513
$576$	−7.98932e14	−0.525032
$577$	2.81221e14	0.183055	0.0915273	−	0.995803i	$-0.470825\pi$
$577$	2.81221e14	0.183055	0.0915273	+	0.995803i	$0.470825\pi$
$578$	−4.75372e15	−3.06500
$579$	−1.66655e13	−0.0106435
$580$	−1.10616e15	−0.699786
$581$	−7.70008e13	−0.0482533
$582$	4.56308e14	0.283257
$583$	−3.53566e15	−2.17417
$584$	−7.61664e14	−0.463973
$585$	2.94307e14	0.177600
$586$	2.23573e15	1.33654
$587$	−2.71962e15	−1.61064	−0.805320	−	0.592840i	$-0.798007\pi$
$587$	−2.71962e15	−1.61064	−0.805320	+	0.592840i	$0.798007\pi$
$588$	1.11399e15	0.653593
$589$	−2.69356e14	−0.156564
$590$	−1.71661e14	−0.0988522
$591$	2.08154e14	0.118755
$592$	1.12953e13	0.00638451
$593$	−1.67708e15	−0.939187	−0.469594	−	0.882883i	$-0.655600\pi$
$593$	−1.67708e15	−0.939187	−0.469594	+	0.882883i	$0.655600\pi$
$594$	−6.66299e14	−0.369695
$595$	−6.72098e14	−0.369479
$596$	2.44453e15	1.33150
$597$	1.80307e15	0.973091
$598$	8.34993e14	0.446505
$599$	−1.44572e14	−0.0766015	−0.0383008	−	0.999266i	$-0.512194\pi$
$599$	−1.44572e14	−0.0766015	−0.0383008	+	0.999266i	$0.512194\pi$
$600$	−5.15918e14	−0.270862
$601$	2.98266e15	1.55165	0.775827	−	0.630946i	$-0.217333\pi$
$601$	2.98266e15	1.55165	0.775827	+	0.630946i	$0.217333\pi$
$602$	1.22589e15	0.631931
$603$	−2.45638e14	−0.125473
$604$	−2.19190e15	−1.10948
$605$	5.26223e14	0.263946
$606$	7.66207e13	0.0380844
$607$	−1.60781e14	−0.0791949	−0.0395974	−	0.999216i	$-0.512608\pi$
$607$	−1.60781e14	−0.0791949	−0.0395974	+	0.999216i	$0.512608\pi$
$608$	1.02036e15	0.498060
$609$	−5.31835e14	−0.257265
$610$	1.66678e15	0.799031
$611$	−2.86298e15	−1.36016
$612$	1.70917e15	0.804733
$613$	8.60595e14	0.401575	0.200787	−	0.979635i	$-0.435650\pi$
$613$	8.60595e14	0.401575	0.200787	+	0.979635i	$0.435650\pi$
$614$	1.59584e15	0.738013
$615$	5.26758e14	0.241434
$616$	−7.36306e14	−0.334476
$617$	3.61157e15	1.62603	0.813014	−	0.582244i	$-0.197825\pi$
$617$	3.61157e15	1.62603	0.813014	+	0.582244i	$0.197825\pi$
$618$	1.59182e15	0.710327
$619$	5.25634e14	0.232479	0.116240	−	0.993221i	$-0.462916\pi$
$619$	5.25634e14	0.232479	0.116240	+	0.993221i	$0.462916\pi$
$620$	−6.40491e14	−0.280775
$621$	1.17493e14	0.0510513
$622$	6.80863e15	2.93233
$623$	−6.70734e14	−0.286329
$624$	6.55789e14	0.277491
$625$	8.02815e14	0.336725
$626$	3.59936e15	1.49646
$627$	6.64413e14	0.273821
$628$	−1.16802e15	−0.477169
$629$	−6.15282e13	−0.0249170
$630$	2.75297e14	0.110517
$631$	1.03394e15	0.411465	0.205733	−	0.978608i	$-0.434042\pi$
$631$	1.03394e15	0.411465	0.205733	+	0.978608i	$0.434042\pi$
$632$	−1.79658e15	−0.708766
$633$	9.04719e14	0.353829
$634$	9.08736e14	0.352328
$635$	4.40853e14	0.169449
$636$	−3.71496e15	−1.41560
$637$	−2.32830e15	−0.879574
$638$	−5.23413e15	−1.96034
$639$	7.46440e14	0.277166
$640$	1.51411e15	0.557400
$641$	−4.90083e15	−1.78875	−0.894377	−	0.447313i	$-0.852381\pi$
$641$	−4.90083e15	−1.78875	−0.894377	+	0.447313i	$0.852381\pi$
$642$	1.53712e15	0.556245
$643$	−4.26885e15	−1.53162	−0.765810	−	0.643067i	$-0.777662\pi$
$643$	−4.26885e15	−1.53162	−0.765810	+	0.643067i	$0.777662\pi$
$644$	4.55448e14	0.162019
$645$	−7.49855e14	−0.264484
$646$	−2.92280e15	−1.02216
$647$	−9.88713e14	−0.342844	−0.171422	−	0.985198i	$-0.554836\pi$
$647$	−9.88713e14	−0.342844	−0.171422	+	0.985198i	$0.554836\pi$
$648$	−1.99579e14	−0.0686202
$649$	−4.73645e14	−0.161476
$650$	3.78247e15	1.27865
$651$	−3.07943e14	−0.103223
$652$	−7.54011e15	−2.50620
$653$	−3.20209e15	−1.05538	−0.527692	−	0.849436i	$-0.676943\pi$
$653$	−3.20209e15	−1.05538	−0.527692	+	0.849436i	$0.676943\pi$
$654$	6.13058e14	0.200366
$655$	2.06564e15	0.669463
$656$	1.17375e15	0.377227
$657$	7.85754e14	0.250425
$658$	−2.67805e15	−0.846400
$659$	6.20183e14	0.194379	0.0971896	−	0.995266i	$-0.469015\pi$
$659$	6.20183e14	0.194379	0.0971896	+	0.995266i	$0.469015\pi$
$660$	1.57988e15	0.491058
$661$	−3.73583e14	−0.115154	−0.0575771	−	0.998341i	$-0.518337\pi$
$661$	−3.73583e14	−0.115154	−0.0575771	+	0.998341i	$0.518337\pi$
$662$	4.81899e15	1.47312
$663$	−3.57225e15	−1.08297
$664$	−2.26991e14	−0.0682471
$665$	−2.74518e14	−0.0818561
$666$	2.52024e13	0.00745305
$667$	9.22967e14	0.270704
$668$	6.97630e15	2.02934
$669$	2.86264e15	0.825892
$670$	9.98840e14	0.285815
$671$	4.59895e15	1.30522
$672$	1.16653e15	0.328370
$673$	2.48508e15	0.693837	0.346918	−	0.937895i	$-0.387228\pi$
$673$	2.48508e15	0.693837	0.346918	+	0.937895i	$0.387228\pi$
$674$	5.63054e15	1.55927
$675$	5.32236e14	0.146195
$676$	9.29790e14	0.253325
$677$	1.35648e15	0.366586	0.183293	−	0.983058i	$-0.441324\pi$
$677$	1.35648e15	0.366586	0.183293	+	0.983058i	$0.441324\pi$
$678$	−2.09704e15	−0.562138
$679$	−5.20200e14	−0.138320
$680$	−1.98128e15	−0.522573
$681$	3.86938e15	1.01235
$682$	−3.03067e15	−0.786546
$683$	−5.28071e14	−0.135950	−0.0679749	−	0.997687i	$-0.521654\pi$
$683$	−5.28071e14	−0.135950	−0.0679749	+	0.997687i	$0.521654\pi$
$684$	6.98108e14	0.178285
$685$	3.26694e14	0.0827643
$686$	−4.86890e15	−1.22362
$687$	3.78065e15	0.942549
$688$	−1.67086e15	−0.413242
$689$	7.76445e15	1.90504
$690$	−4.77761e14	−0.116289
$691$	1.72140e15	0.415674	0.207837	−	0.978163i	$-0.433358\pi$
$691$	1.72140e15	0.415674	0.207837	+	0.978163i	$0.433358\pi$
$692$	7.69007e15	1.84224
$693$	7.59594e14	0.180530
$694$	−4.29804e15	−1.01343
$695$	−3.55664e15	−0.832000
$696$	−1.56780e15	−0.363864
$697$	−6.39369e15	−1.47222
$698$	1.77643e14	0.0405830
$699$	−9.54224e14	−0.216285
$700$	2.06315e15	0.463973
$701$	5.47245e15	1.22105	0.610524	−	0.791998i	$-0.290959\pi$
$701$	5.47245e15	1.22105	0.610524	+	0.791998i	$0.290959\pi$
$702$	1.46322e15	0.323933
$703$	−2.51311e13	−0.00552023
$704$	8.96375e15	1.95362
$705$	1.63812e15	0.354246
$706$	−7.77690e15	−1.66871
$707$	−8.73492e13	−0.0185974
$708$	−4.97665e14	−0.105137
$709$	3.41159e14	0.0715158	0.0357579	−	0.999360i	$-0.488615\pi$
$709$	3.41159e14	0.0715158	0.0357579	+	0.999360i	$0.488615\pi$
$710$	−3.03525e15	−0.631355
$711$	1.85340e15	0.382549
$712$	−1.97726e15	−0.404970
$713$	5.34416e14	0.108614
$714$	−3.34150e15	−0.673910
$715$	−3.30203e15	−0.660842
$716$	6.01711e15	1.19500
$717$	7.16653e14	0.141239
$718$	−2.59924e15	−0.508349
$719$	−9.73487e14	−0.188939	−0.0944694	−	0.995528i	$-0.530115\pi$
$719$	−9.73487e14	−0.188939	−0.0944694	+	0.995528i	$0.530115\pi$
$720$	−3.75225e14	−0.0722708
$721$	−1.81471e15	−0.346868
$722$	6.97102e15	1.32234
$723$	−3.94760e15	−0.743143
$724$	4.44260e15	0.829995
$725$	4.18099e15	0.775211
$726$	2.61625e15	0.481424
$727$	−7.93057e14	−0.144832	−0.0724161	−	0.997375i	$-0.523071\pi$
$727$	−7.93057e14	−0.144832	−0.0724161	+	0.997375i	$0.523071\pi$
$728$	1.61696e15	0.293073
$729$	2.05891e14	0.0370370
$730$	−3.19511e15	−0.570441
$731$	9.10161e15	1.61277
$732$	4.83217e15	0.849828
$733$	1.18996e14	0.0207711	0.0103855	−	0.999946i	$-0.496694\pi$
$733$	1.18996e14	0.0207711	0.0103855	+	0.999946i	$0.496694\pi$
$734$	6.97266e15	1.20801
$735$	1.33219e15	0.229080
$736$	−2.02444e15	−0.345522
$737$	2.75598e15	0.466880
$738$	2.61891e15	0.440362
$739$	3.87846e15	0.647314	0.323657	−	0.946175i	$-0.395088\pi$
$739$	3.87846e15	0.647314	0.323657	+	0.946175i	$0.395088\pi$
$740$	−5.97582e13	−0.00989972
$741$	−1.45908e15	−0.239927
$742$	7.26292e15	1.18547
$743$	8.40639e15	1.36198	0.680991	−	0.732292i	$-0.261549\pi$
$743$	8.40639e15	1.36198	0.680991	+	0.732292i	$0.261549\pi$
$744$	−9.07786e14	−0.145993
$745$	2.92334e15	0.466681
$746$	2.79818e15	0.443416
$747$	2.34170e14	0.0368357
$748$	−1.91763e16	−2.99437
$749$	−1.75235e15	−0.271626
$750$	−5.01321e15	−0.771398
$751$	1.22233e16	1.86710	0.933549	−	0.358449i	$-0.116694\pi$
$751$	1.22233e16	1.86710	0.933549	+	0.358449i	$0.116694\pi$
$752$	3.65014e15	0.553491
$753$	−1.14198e15	−0.171905
$754$	1.14944e16	1.71768
$755$	−2.62123e15	−0.388864
$756$	7.98115e14	0.117543
$757$	1.63077e14	0.0238433	0.0119216	−	0.999929i	$-0.496205\pi$
$757$	1.63077e14	0.0238433	0.0119216	+	0.999929i	$0.496205\pi$
$758$	1.06766e16	1.54972
$759$	−1.31823e15	−0.189960
$760$	−8.09251e14	−0.115773
$761$	−7.28896e15	−1.03526	−0.517631	−	0.855604i	$-0.673186\pi$
$761$	−7.28896e15	−1.03526	−0.517631	+	0.855604i	$0.673186\pi$
$762$	2.19181e15	0.309066
$763$	−6.98899e14	−0.0978429
$764$	−4.55411e15	−0.632980
$765$	2.04394e15	0.282053
$766$	1.31923e16	1.80743
$767$	1.04014e15	0.141488
$768$	7.94383e14	0.107286
$769$	9.15102e15	1.22708	0.613542	−	0.789662i	$-0.289744\pi$
$769$	9.15102e15	1.22708	0.613542	+	0.789662i	$0.289744\pi$
$770$	−3.08874e15	−0.411228
$771$	−8.05729e15	−1.06510
$772$	1.96464e14	0.0257862
$773$	1.29011e15	0.168128	0.0840641	−	0.996460i	$-0.473210\pi$
$773$	1.29011e15	0.168128	0.0840641	+	0.996460i	$0.473210\pi$
$774$	−3.72809e15	−0.482404
$775$	2.42088e15	0.311038
$776$	−1.53350e15	−0.195634
$777$	−2.87313e13	−0.00363948
$778$	1.96433e16	2.47074
$779$	−2.61150e15	−0.326162
$780$	−3.46948e15	−0.430273
$781$	−8.37481e15	−1.03132
$782$	5.79897e15	0.709111
$783$	1.61738e15	0.196392
$784$	2.96846e15	0.357925
$785$	−1.39680e15	−0.167244
$786$	1.02698e16	1.22106
$787$	1.65538e15	0.195450	0.0977252	−	0.995213i	$-0.468843\pi$
$787$	1.65538e15	0.195450	0.0977252	+	0.995213i	$0.468843\pi$
$788$	−2.45385e15	−0.287710
$789$	4.22483e15	0.491910
$790$	−7.53650e15	−0.871406
$791$	2.39066e15	0.274503
$792$	2.23921e15	0.255332
$793$	−1.00995e16	−1.14366
$794$	1.40585e16	1.58098
$795$	−4.44261e15	−0.496157
$796$	−2.12557e16	−2.35751
$797$	−2.41106e13	−0.00265575	−0.00132788	−	0.999999i	$-0.500423\pi$
$797$	−2.41106e13	−0.00265575	−0.00132788	+	0.999999i	$0.500423\pi$
$798$	−1.36483e15	−0.149301
$799$	−1.98832e16	−2.16013
$800$	−9.17059e15	−0.989470
$801$	2.03979e15	0.218579
$802$	−6.27580e15	−0.667898
$803$	−8.81590e15	−0.931819
$804$	2.89574e15	0.303985
$805$	5.44657e14	0.0567865
$806$	6.65547e15	0.689185
$807$	−1.06399e15	−0.109429
$808$	−2.57497e14	−0.0263032
$809$	1.21304e16	1.23072	0.615361	−	0.788245i	$-0.289010\pi$
$809$	1.21304e16	1.23072	0.615361	+	0.788245i	$0.289010\pi$
$810$	−8.37216e14	−0.0843664
$811$	8.99516e15	0.900315	0.450157	−	0.892949i	$-0.351368\pi$
$811$	8.99516e15	0.900315	0.450157	+	0.892949i	$0.351368\pi$
$812$	6.26961e15	0.623279
$813$	−9.47943e15	−0.936018
$814$	−2.82763e14	−0.0277325
$815$	−9.01700e15	−0.878406
$816$	4.55441e15	0.440693
$817$	3.71754e15	0.357301
$818$	3.58082e14	0.0341853
$819$	−1.66810e15	−0.158183
$820$	−6.20976e15	−0.584923
$821$	9.08905e15	0.850416	0.425208	−	0.905096i	$-0.360201\pi$
$821$	9.08905e15	0.850416	0.425208	+	0.905096i	$0.360201\pi$
$822$	1.62424e15	0.150958
$823$	−1.46245e16	−1.35015	−0.675077	−	0.737748i	$-0.735889\pi$
$823$	−1.46245e16	−1.35015	−0.675077	+	0.737748i	$0.735889\pi$
$824$	−5.34959e15	−0.490593
$825$	−5.97151e15	−0.543986
$826$	9.72957e14	0.0880448
$827$	−9.76403e15	−0.877705	−0.438853	−	0.898559i	$-0.644615\pi$
$827$	−9.76403e15	−0.877705	−0.438853	+	0.898559i	$0.644615\pi$
$828$	−1.38508e15	−0.123682
$829$	−6.18201e15	−0.548378	−0.274189	−	0.961676i	$-0.588409\pi$
$829$	−6.18201e15	−0.548378	−0.274189	+	0.961676i	$0.588409\pi$
$830$	−9.52207e14	−0.0839077
$831$	−1.06206e16	−0.929705
$832$	−1.96848e16	−1.71180
$833$	−1.61699e16	−1.39688
$834$	−1.76827e16	−1.51752
$835$	8.34275e15	0.711269
$836$	−7.83254e15	−0.663389
$837$	9.36498e14	0.0787983
$838$	1.57908e15	0.131997
$839$	4.06156e15	0.337289	0.168645	−	0.985677i	$-0.446061\pi$
$839$	4.06156e15	0.337289	0.168645	+	0.985677i	$0.446061\pi$
$840$	−9.25180e14	−0.0763291
$841$	5.04886e14	0.0413824
$842$	−7.40041e15	−0.602614
$843$	−8.19195e15	−0.662728
$844$	−1.06654e16	−0.857224
$845$	1.11191e15	0.0887886
$846$	8.14432e15	0.646127
$847$	−2.98257e15	−0.235089
$848$	−9.89924e15	−0.775220
$849$	1.34455e16	1.04613
$850$	2.62691e16	2.03067
$851$	4.98614e13	0.00382958
$852$	−8.79952e15	−0.671492
$853$	−7.72221e15	−0.585493	−0.292746	−	0.956190i	$-0.594569\pi$
$853$	−7.72221e15	−0.585493	−0.292746	+	0.956190i	$0.594569\pi$
$854$	−9.44712e15	−0.711674
$855$	8.34846e14	0.0624875
$856$	−5.16576e15	−0.384174
$857$	−1.63335e16	−1.20694	−0.603468	−	0.797387i	$-0.706215\pi$
$857$	−1.63335e16	−1.20694	−0.603468	+	0.797387i	$0.706215\pi$
$858$	−1.64168e16	−1.20534
$859$	−2.01926e16	−1.47310	−0.736548	−	0.676386i	$-0.763545\pi$
$859$	−2.01926e16	−1.47310	−0.736548	+	0.676386i	$0.763545\pi$
$860$	8.83978e15	0.640767
$861$	−2.98561e15	−0.215038
$862$	1.55069e16	1.10978
$863$	−1.02354e16	−0.727858	−0.363929	−	0.931427i	$-0.618565\pi$
$863$	−1.02354e16	−0.727858	−0.363929	+	0.931427i	$0.618565\pi$
$864$	−3.54757e15	−0.250672
$865$	9.19633e15	0.645693
$866$	−1.94314e16	−1.35567
$867$	−1.64810e16	−1.14256
$868$	3.63023e15	0.250078
$869$	−2.07946e16	−1.42345
$870$	−6.57677e15	−0.447360
$871$	−6.05225e15	−0.409088
$872$	−2.06029e15	−0.138384
$873$	1.58200e15	0.105591
$874$	2.36858e15	0.157100
$875$	5.71515e15	0.376690
$876$	−9.26298e15	−0.606706
$877$	−2.94855e16	−1.91916	−0.959578	−	0.281442i	$-0.909187\pi$
$877$	−2.94855e16	−1.91916	−0.959578	+	0.281442i	$0.909187\pi$
$878$	4.01741e16	2.59852
$879$	7.75119e15	0.498230
$880$	4.20990e15	0.268916
$881$	4.35657e15	0.276552	0.138276	−	0.990394i	$-0.455844\pi$
$881$	4.35657e15	0.276552	0.138276	+	0.990394i	$0.455844\pi$
$882$	6.62333e15	0.417829
$883$	1.91271e16	1.19912	0.599562	−	0.800328i	$-0.295341\pi$
$883$	1.91271e16	1.19912	0.599562	+	0.800328i	$0.295341\pi$
$884$	4.21119e16	2.62372
$885$	−5.95143e14	−0.0368496
$886$	2.57674e16	1.58557
$887$	−2.54821e16	−1.55831	−0.779157	−	0.626829i	$-0.784353\pi$
$887$	−2.54821e16	−1.55831	−0.779157	+	0.626829i	$0.784353\pi$
$888$	−8.46970e13	−0.00514750
$889$	−2.49871e15	−0.150923
$890$	−8.29442e15	−0.497899
$891$	−2.31003e15	−0.137813
$892$	−3.37467e16	−2.00089
$893$	−8.12127e15	−0.478565
$894$	1.45341e16	0.851202
$895$	7.19568e15	0.418837
$896$	−8.58181e15	−0.496460
$897$	2.89489e15	0.166446
$898$	1.20428e16	0.688191
$899$	7.35668e15	0.417834
$900$	−6.27434e15	−0.354188
$901$	5.39236e16	3.02547
$902$	−2.93833e16	−1.63857
$903$	4.25010e15	0.235568
$904$	7.04744e15	0.388244
$905$	5.31278e15	0.290907
$906$	−1.30321e16	−0.709267
$907$	1.89738e16	1.02639	0.513197	−	0.858271i	$-0.328461\pi$
$907$	1.89738e16	1.02639	0.513197	+	0.858271i	$0.328461\pi$
$908$	−4.56148e16	−2.45264
$909$	2.65641e14	0.0141969
$910$	6.78300e15	0.360325
$911$	1.73615e15	0.0916719	0.0458359	−	0.998949i	$-0.485405\pi$
$911$	1.73615e15	0.0916719	0.0458359	+	0.998949i	$0.485405\pi$
$912$	1.86025e15	0.0976334
$913$	−2.62731e15	−0.137064
$914$	−3.04242e16	−1.57766
$915$	5.77865e15	0.297859
$916$	−4.45687e16	−2.28352
$917$	−1.17078e16	−0.596271
$918$	1.01620e16	0.514450
$919$	6.66355e15	0.335328	0.167664	−	0.985844i	$-0.446378\pi$
$919$	6.66355e15	0.335328	0.167664	+	0.985844i	$0.446378\pi$
$920$	1.60559e15	0.0803161
$921$	5.53272e15	0.275113
$922$	2.40808e16	1.19028
$923$	1.83914e16	0.903662
$924$	−8.95459e15	−0.437371
$925$	2.25869e14	0.0109667
$926$	4.55241e16	2.19726
$927$	5.51879e15	0.264792
$928$	−2.78680e16	−1.32921
$929$	−3.02861e16	−1.43601	−0.718004	−	0.696039i	$-0.754944\pi$
$929$	−3.02861e16	−1.43601	−0.718004	+	0.696039i	$0.754944\pi$
$930$	−3.80808e15	−0.179494
$931$	−6.60458e15	−0.309473
$932$	1.12490e16	0.523995
$933$	2.36052e16	1.09310
$934$	3.12878e16	1.44035
$935$	−2.29324e16	−1.04951
$936$	−4.91739e15	−0.223727
$937$	−1.38014e16	−0.624247	−0.312123	−	0.950042i	$-0.601040\pi$
$937$	−1.38014e16	−0.624247	−0.312123	+	0.950042i	$0.601040\pi$
$938$	−5.66132e15	−0.254567
$939$	1.24788e16	0.557844
$940$	−1.93112e16	−0.858235
$941$	3.48870e16	1.54142	0.770709	−	0.637187i	$-0.219902\pi$
$941$	3.48870e16	1.54142	0.770709	+	0.637187i	$0.219902\pi$
$942$	−6.94454e15	−0.305045
$943$	5.18134e15	0.226270
$944$	−1.32613e15	−0.0575756
$945$	9.54442e14	0.0411979
$946$	4.18280e16	1.79500
$947$	5.17522e15	0.220802	0.110401	−	0.993887i	$-0.464786\pi$
$947$	5.17522e15	0.220802	0.110401	+	0.993887i	$0.464786\pi$
$948$	−2.18491e16	−0.926805
$949$	1.93601e16	0.816476
$950$	1.07296e16	0.449886
$951$	3.15055e15	0.131339
$952$	1.12297e16	0.465440
$953$	2.81904e16	1.16169	0.580846	−	0.814013i	$-0.302722\pi$
$953$	2.81904e16	1.16169	0.580846	+	0.814013i	$0.302722\pi$
$954$	−2.20876e16	−0.904964
$955$	−5.44613e15	−0.221855
$956$	−8.44837e15	−0.342180
$957$	−1.81465e16	−0.730764
$958$	−1.34963e15	−0.0540388
$959$	−1.85167e15	−0.0737158
$960$	1.12631e16	0.445827
$961$	−2.11488e16	−0.832352
$962$	6.20959e14	0.0242997
$963$	5.32914e15	0.207354
$964$	4.65368e16	1.80042
$965$	2.34945e14	0.00903787
$966$	2.70790e15	0.103576
$967$	−1.11969e16	−0.425844	−0.212922	−	0.977069i	$-0.568298\pi$
$967$	−1.11969e16	−0.425844	−0.212922	+	0.977069i	$0.568298\pi$
$968$	−8.79234e15	−0.332499
$969$	−1.01332e16	−0.381037
$970$	−6.43289e15	−0.240526
$971$	1.55940e16	0.579764	0.289882	−	0.957062i	$-0.406384\pi$
$971$	1.55940e16	0.579764	0.289882	+	0.957062i	$0.406384\pi$
$972$	−2.42718e15	−0.0897299
$973$	2.01586e16	0.741038
$974$	4.31286e16	1.57649
$975$	1.31137e16	0.476650
$976$	1.28763e16	0.465389
$977$	−2.06463e16	−0.742032	−0.371016	−	0.928626i	$-0.620991\pi$
$977$	−2.06463e16	−0.742032	−0.371016	+	0.928626i	$0.620991\pi$
$978$	−4.48303e16	−1.60217
$979$	−2.28858e16	−0.813321
$980$	−1.57048e16	−0.554993
$981$	2.12545e15	0.0746915
$982$	−6.84066e16	−2.39048
$983$	−3.86690e16	−1.34375	−0.671875	−	0.740665i	$-0.734511\pi$
$983$	−3.86690e16	−1.34375	−0.671875	+	0.740665i	$0.734511\pi$
$984$	−8.80127e15	−0.304139
$985$	−2.93449e15	−0.100840
$986$	7.98277e16	2.72791
$987$	−9.28468e15	−0.315517
$988$	1.72006e16	0.581273
$989$	−7.37579e15	−0.247873
$990$	9.39328e15	0.313924
$991$	−4.43033e16	−1.47242	−0.736208	−	0.676755i	$-0.763386\pi$
$991$	−4.43033e16	−1.47242	−0.736208	+	0.676755i	$0.763386\pi$
$992$	−1.61362e16	−0.533318
$993$	1.67072e16	0.549141
$994$	1.72035e16	0.562330
$995$	−2.54191e16	−0.826292
$996$	−2.76055e15	−0.0892420
$997$	2.59343e16	0.833780	0.416890	−	0.908957i	$-0.363120\pi$
$997$	2.59343e16	0.833780	0.416890	+	0.908957i	$0.363120\pi$
$998$	4.94480e16	1.58100
$999$	8.73758e13	0.00277831

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.a.1.3	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.a.1.3	✓	26	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)

\(f(q)\)	\(=\)	\(q-70.0902 q^{2} -243.000 q^{3} +2864.64 q^{4} +3425.74 q^{5} +17031.9 q^{6} -19416.7 q^{7} -57238.6 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-70.0902 q^{2} -243.000 q^{3} +2864.64 q^{4} +3425.74 q^{5} +17031.9 q^{6} -19416.7 q^{7} -57238.6 q^{8} +59049.0 q^{9} -240111. q^{10} -662510. q^{11} -696108. q^{12} +1.45490e6 q^{13} +1.36092e6 q^{14} -832455. q^{15} -1.85492e6 q^{16} +1.01042e7 q^{17} -4.13876e6 q^{18} +4.12705e6 q^{19} +9.81352e6 q^{20} +4.71827e6 q^{21} +4.64355e7 q^{22} -8.18826e6 q^{23} +1.39090e7 q^{24} -3.70924e7 q^{25} -1.01974e8 q^{26} -1.43489e7 q^{27} -5.56220e7 q^{28} -1.12718e8 q^{29} +5.83470e7 q^{30} -6.52662e7 q^{31} +2.47236e8 q^{32} +1.60990e8 q^{33} -7.08205e8 q^{34} -6.65167e7 q^{35} +1.69154e8 q^{36} -6.08937e6 q^{37} -2.89266e8 q^{38} -3.53541e8 q^{39} -1.96085e8 q^{40} -6.32776e8 q^{41} -3.30704e8 q^{42} +9.00775e8 q^{43} -1.89786e9 q^{44} +2.02287e8 q^{45} +5.73917e8 q^{46} -1.96782e9 q^{47} +4.50745e8 q^{48} -1.60032e9 q^{49} +2.59982e9 q^{50} -2.45532e9 q^{51} +4.16777e9 q^{52} +5.33676e9 q^{53} +1.00572e9 q^{54} -2.26959e9 q^{55} +1.11139e9 q^{56} -1.00287e9 q^{57} +7.90045e9 q^{58} +7.14924e8 q^{59} -2.38469e9 q^{60} -6.94170e9 q^{61} +4.57452e9 q^{62} -1.14654e9 q^{63} -1.35300e10 q^{64} +4.98411e9 q^{65} -1.12838e10 q^{66} -4.15991e9 q^{67} +2.89449e10 q^{68} +1.98975e9 q^{69} +4.66217e9 q^{70} +1.26410e10 q^{71} -3.37988e9 q^{72} +1.33068e10 q^{73} +4.26805e8 q^{74} +9.01346e9 q^{75} +1.18225e10 q^{76} +1.28638e10 q^{77} +2.47798e10 q^{78} +3.13876e10 q^{79} -6.35447e9 q^{80} +3.48678e9 q^{81} +4.43514e10 q^{82} +3.96569e9 q^{83} +1.35161e10 q^{84} +3.46144e10 q^{85} -6.31356e10 q^{86} +2.73905e10 q^{87} +3.79212e10 q^{88} +3.45441e10 q^{89} -1.41783e10 q^{90} -2.82494e10 q^{91} -2.34564e10 q^{92} +1.58597e10 q^{93} +1.37925e11 q^{94} +1.41382e10 q^{95} -6.00784e10 q^{96} +2.67913e10 q^{97} +1.12167e11 q^{98} -3.91206e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9}+O(q^{10}) \) 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9	\( 26 q - 78 q^{2} - 6318 q^{3} + 23070 q^{4} + 3808 q^{5} + 18954 q^{6} - 98819 q^{7} - 117645 q^{8} + 1535274 q^{9} - 859751 q^{10} + 579094 q^{11} - 5606010 q^{12} - 2018538 q^{13} + 4157413 q^{14} - 925344 q^{15} + 20190274 q^{16} - 13084493 q^{17} - 4605822 q^{18} + 9917231 q^{19} + 10165633 q^{20} + 24013017 q^{21} - 89820518 q^{22} - 63513223 q^{23} + 28587735 q^{24} + 218986852 q^{25} - 77999532 q^{26} - 373071582 q^{27} - 444601862 q^{28} + 81530981 q^{29} + 208919493 q^{30} - 408861231 q^{31} - 26253128 q^{32} - 140719842 q^{33} - 508910076 q^{34} - 75731421 q^{35} + 1362260430 q^{36} - 802381301 q^{37} + 732704675 q^{38} + 490504734 q^{39} - 646130800 q^{40} - 1354472849 q^{41} - 1010251359 q^{42} + 282952194 q^{43} + 1846047996 q^{44} + 224858592 q^{45} + 9629305849 q^{46} - 1196794197 q^{47} - 4906236582 q^{48} + 10889725683 q^{49} - 6236232091 q^{50} + 3179531799 q^{51} - 1968200812 q^{52} - 8276044236 q^{53} + 1119214746 q^{54} - 6672895076 q^{55} + 2579741342 q^{56} - 2409887133 q^{57} - 9401656060 q^{58} + 18588031774 q^{59} - 2470248819 q^{60} - 21181559029 q^{61} - 6117706514 q^{62} - 5835163131 q^{63} + 42975855037 q^{64} + 25680681860 q^{65} + 21826385874 q^{66} + 26234163394 q^{67} + 19707344091 q^{68} + 15433713189 q^{69} + 129203099090 q^{70} + 52088830406 q^{71} - 6946819605 q^{72} + 20943384867 q^{73} + 41969200146 q^{74} - 53213805036 q^{75} + 223987219368 q^{76} + 94604773153 q^{77} + 18953886276 q^{78} + 68965662774 q^{79} + 218947784293 q^{80} + 90656394426 q^{81} + 11938614923 q^{82} + 17947446393 q^{83} + 108038252466 q^{84} - 52849386709 q^{85} + 384986147852 q^{86} - 19812028383 q^{87} - 49061112607 q^{88} + 38570593981 q^{89} - 50767436799 q^{90} - 226268806999 q^{91} - 79559686310 q^{92} + 99353279133 q^{93} - 16709400108 q^{94} - 252795831501 q^{95} + 6379510104 q^{96} - 186894587836 q^{97} - 252443311612 q^{98} + 34194921606 q^{99}+O(q^{100}) \) 26 * q - 78 * q^2 - 6318 * q^3 + 23070 * q^4 + 3808 * q^5 + 18954 * q^6 - 98819 * q^7 - 117645 * q^8 + 1535274 * q^9 - 859751 * q^10 + 579094 * q^11 - 5606010 * q^12 - 2018538 * q^13 + 4157413 * q^14 - 925344 * q^15 + 20190274 * q^16 - 13084493 * q^17 - 4605822 * q^18 + 9917231 * q^19 + 10165633 * q^20 + 24013017 * q^21 - 89820518 * q^22 - 63513223 * q^23 + 28587735 * q^24 + 218986852 * q^25 - 77999532 * q^26 - 373071582 * q^27 - 444601862 * q^28 + 81530981 * q^29 + 208919493 * q^30 - 408861231 * q^31 - 26253128 * q^32 - 140719842 * q^33 - 508910076 * q^34 - 75731421 * q^35 + 1362260430 * q^36 - 802381301 * q^37 + 732704675 * q^38 + 490504734 * q^39 - 646130800 * q^40 - 1354472849 * q^41 - 1010251359 * q^42 + 282952194 * q^43 + 1846047996 * q^44 + 224858592 * q^45 + 9629305849 * q^46 - 1196794197 * q^47 - 4906236582 * q^48 + 10889725683 * q^49 - 6236232091 * q^50 + 3179531799 * q^51 - 1968200812 * q^52 - 8276044236 * q^53 + 1119214746 * q^54 - 6672895076 * q^55 + 2579741342 * q^56 - 2409887133 * q^57 - 9401656060 * q^58 + 18588031774 * q^59 - 2470248819 * q^60 - 21181559029 * q^61 - 6117706514 * q^62 - 5835163131 * q^63 + 42975855037 * q^64 + 25680681860 * q^65 + 21826385874 * q^66 + 26234163394 * q^67 + 19707344091 * q^68 + 15433713189 * q^69 + 129203099090 * q^70 + 52088830406 * q^71 - 6946819605 * q^72 + 20943384867 * q^73 + 41969200146 * q^74 - 53213805036 * q^75 + 223987219368 * q^76 + 94604773153 * q^77 + 18953886276 * q^78 + 68965662774 * q^79 + 218947784293 * q^80 + 90656394426 * q^81 + 11938614923 * q^82 + 17947446393 * q^83 + 108038252466 * q^84 - 52849386709 * q^85 + 384986147852 * q^86 - 19812028383 * q^87 - 49061112607 * q^88 + 38570593981 * q^89 - 50767436799 * q^90 - 226268806999 * q^91 - 79559686310 * q^92 + 99353279133 * q^93 - 16709400108 * q^94 - 252795831501 * q^95 + 6379510104 * q^96 - 186894587836 * q^97 - 252443311612 * q^98 + 34194921606 * q^99

Introduction

L-functions

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