LMFDB - Embedded newform 177.12.a.d.1.27

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:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.27
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)

$f(q)$	$=$	$q+84.6034 q^{2} +243.000 q^{3} +5109.73 q^{4} +8362.85 q^{5} +20558.6 q^{6} -41724.2 q^{7} +259033. q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+84.6034 q^{2} +243.000 q^{3} +5109.73 q^{4} +8362.85 q^{5} +20558.6 q^{6} -41724.2 q^{7} +259033. q^{8} +59049.0 q^{9} +707526. q^{10} +833970. q^{11} +1.24167e6 q^{12} +2.33929e6 q^{13} -3.53001e6 q^{14} +2.03217e6 q^{15} +1.14503e7 q^{16} -3.86460e6 q^{17} +4.99575e6 q^{18} +1.20325e6 q^{19} +4.27319e7 q^{20} -1.01390e7 q^{21} +7.05567e7 q^{22} -4.06402e7 q^{23} +6.29450e7 q^{24} +2.11092e7 q^{25} +1.97912e8 q^{26} +1.43489e7 q^{27} -2.13200e8 q^{28} -4.76409e7 q^{29} +1.71929e8 q^{30} -1.88831e8 q^{31} +4.38237e8 q^{32} +2.02655e8 q^{33} -3.26958e8 q^{34} -3.48934e8 q^{35} +3.01725e8 q^{36} -3.93536e8 q^{37} +1.01799e8 q^{38} +5.68448e8 q^{39} +2.16625e9 q^{40} +2.32464e8 q^{41} -8.57793e8 q^{42} -1.33808e9 q^{43} +4.26137e9 q^{44} +4.93818e8 q^{45} -3.43830e9 q^{46} +2.07896e9 q^{47} +2.78243e9 q^{48} -2.36415e8 q^{49} +1.78591e9 q^{50} -9.39098e8 q^{51} +1.19532e10 q^{52} +3.09305e9 q^{53} +1.21397e9 q^{54} +6.97437e9 q^{55} -1.08080e10 q^{56} +2.92391e8 q^{57} -4.03058e9 q^{58} +7.14924e8 q^{59} +1.03839e10 q^{60} +8.26252e9 q^{61} -1.59757e10 q^{62} -2.46377e9 q^{63} +1.36261e10 q^{64} +1.95632e10 q^{65} +1.71453e10 q^{66} +1.60347e10 q^{67} -1.97471e10 q^{68} -9.87556e9 q^{69} -2.95210e10 q^{70} -1.52068e9 q^{71} +1.52956e10 q^{72} -3.03821e10 q^{73} -3.32945e10 q^{74} +5.12953e9 q^{75} +6.14831e9 q^{76} -3.47968e10 q^{77} +4.80926e10 q^{78} +4.55729e10 q^{79} +9.57574e10 q^{80} +3.48678e9 q^{81} +1.96672e10 q^{82} -2.27476e9 q^{83} -5.18075e10 q^{84} -3.23191e10 q^{85} -1.13206e11 q^{86} -1.15767e10 q^{87} +2.16026e11 q^{88} +2.81381e10 q^{89} +4.17787e10 q^{90} -9.76052e10 q^{91} -2.07660e11 q^{92} -4.58859e10 q^{93} +1.75887e11 q^{94} +1.00626e10 q^{95} +1.06492e11 q^{96} -1.58701e10 q^{97} -2.00015e10 q^{98} +4.92451e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9}+O(q^{10}) $ 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9} + 616281 q^{10} + 1082362 q^{11} + 7099002 q^{12} + 503712 q^{13} + 1321669 q^{14} + 6454566 q^{15} + 34870338 q^{16} + 13513579 q^{17} + 5668704 q^{18} + 35971687 q^{19} + 96105997 q^{20} + 34586919 q^{21} - 47598882 q^{22} + 61380539 q^{23} + 80756433 q^{24} + 294744746 q^{25} + 62820734 q^{26} + 401769396 q^{27} + 148068294 q^{28} + 322339307 q^{29} + 149756283 q^{30} + 151247077 q^{31} + 466383494 q^{32} + 263013966 q^{33} + 684479860 q^{34} + 960297361 q^{35} + 1725057486 q^{36} + 863508437 q^{37} + 992640509 q^{38} + 122402016 q^{39} + 3067680252 q^{40} + 3081170377 q^{41} + 321165567 q^{42} + 2554238300 q^{43} + 4350123570 q^{44} + 1568459538 q^{45} - 1987059155 q^{46} + 6203398333 q^{47} + 8473492134 q^{48} + 10327857997 q^{49} + 17577682253 q^{50} + 3283799697 q^{51} + 32137181618 q^{52} + 14571770754 q^{53} + 1377495072 q^{54} + 18251419334 q^{55} + 33498842836 q^{56} + 8741119941 q^{57} + 11860778276 q^{58} + 20017880372 q^{59} + 23353757271 q^{60} + 2761613771 q^{61} + 13785829526 q^{62} + 8404621317 q^{63} + 86547545293 q^{64} + 32034985256 q^{65} - 11566528326 q^{66} + 39381333296 q^{67} + 38995496621 q^{68} + 14915470977 q^{69} + 8551800364 q^{70} + 26130020296 q^{71} + 19623813219 q^{72} + 41382402799 q^{73} + 23815315058 q^{74} + 71622973278 q^{75} + 10611720128 q^{76} - 8426124313 q^{77} + 15265438362 q^{78} + 59825111206 q^{79} + 4009687655 q^{80} + 97629963228 q^{81} - 39592715115 q^{82} + 35433122727 q^{83} + 35980595442 q^{84} - 8950496085 q^{85} - 182032360688 q^{86} + 78328451601 q^{87} - 220003602335 q^{88} + 102303043039 q^{89} + 36390776769 q^{90} - 111146323655 q^{91} - 163000203526 q^{92} + 36753039711 q^{93} - 81314346008 q^{94} + 208102168887 q^{95} + 113331189042 q^{96} - 171891031490 q^{97} + 72304707792 q^{98} + 63912393738 q^{99}+O(q^{100}) \) 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9 + 616281 * q^10 + 1082362 * q^11 + 7099002 * q^12 + 503712 * q^13 + 1321669 * q^14 + 6454566 * q^15 + 34870338 * q^16 + 13513579 * q^17 + 5668704 * q^18 + 35971687 * q^19 + 96105997 * q^20 + 34586919 * q^21 - 47598882 * q^22 + 61380539 * q^23 + 80756433 * q^24 + 294744746 * q^25 + 62820734 * q^26 + 401769396 * q^27 + 148068294 * q^28 + 322339307 * q^29 + 149756283 * q^30 + 151247077 * q^31 + 466383494 * q^32 + 263013966 * q^33 + 684479860 * q^34 + 960297361 * q^35 + 1725057486 * q^36 + 863508437 * q^37 + 992640509 * q^38 + 122402016 * q^39 + 3067680252 * q^40 + 3081170377 * q^41 + 321165567 * q^42 + 2554238300 * q^43 + 4350123570 * q^44 + 1568459538 * q^45 - 1987059155 * q^46 + 6203398333 * q^47 + 8473492134 * q^48 + 10327857997 * q^49 + 17577682253 * q^50 + 3283799697 * q^51 + 32137181618 * q^52 + 14571770754 * q^53 + 1377495072 * q^54 + 18251419334 * q^55 + 33498842836 * q^56 + 8741119941 * q^57 + 11860778276 * q^58 + 20017880372 * q^59 + 23353757271 * q^60 + 2761613771 * q^61 + 13785829526 * q^62 + 8404621317 * q^63 + 86547545293 * q^64 + 32034985256 * q^65 - 11566528326 * q^66 + 39381333296 * q^67 + 38995496621 * q^68 + 14915470977 * q^69 + 8551800364 * q^70 + 26130020296 * q^71 + 19623813219 * q^72 + 41382402799 * q^73 + 23815315058 * q^74 + 71622973278 * q^75 + 10611720128 * q^76 - 8426124313 * q^77 + 15265438362 * q^78 + 59825111206 * q^79 + 4009687655 * q^80 + 97629963228 * q^81 - 39592715115 * q^82 + 35433122727 * q^83 + 35980595442 * q^84 - 8950496085 * q^85 - 182032360688 * q^86 + 78328451601 * q^87 - 220003602335 * q^88 + 102303043039 * q^89 + 36390776769 * q^90 - 111146323655 * q^91 - 163000203526 * q^92 + 36753039711 * q^93 - 81314346008 * q^94 + 208102168887 * q^95 + 113331189042 * q^96 - 171891031490 * q^97 + 72304707792 * q^98 + 63912393738 * 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 $

$2$	84.6034	1.86949	0.934744	−	0.355321i	$-0.115629\pi$
$2$	84.6034	1.86949	0.934744	+	0.355321i	$0.115629\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	5109.73	2.49499
$5$	8362.85	1.19679	0.598397	−	0.801200i	$-0.295805\pi$
$5$	8362.85	1.19679	0.598397	+	0.801200i	$0.295805\pi$
$6$	20558.6	1.07935
$7$	−41724.2	−0.938316	−0.469158	−	0.883114i	$-0.655443\pi$
$7$	−41724.2	−0.938316	−0.469158	+	0.883114i	$0.655443\pi$
$8$	259033.	2.79486
$9$	59049.0	0.333333
$10$	707526.	2.23739
$11$	833970.	1.56132	0.780658	−	0.624958i	$-0.214884\pi$
$11$	833970.	1.56132	0.780658	+	0.624958i	$0.214884\pi$
$12$	1.24167e6	1.44048
$13$	2.33929e6	1.74741	0.873707	−	0.486452i	$-0.161709\pi$
$13$	2.33929e6	1.74741	0.873707	+	0.486452i	$0.161709\pi$
$14$	−3.53001e6	−1.75417
$15$	2.03217e6	0.690969
$16$	1.14503e7	2.72997
$17$	−3.86460e6	−0.660139	−0.330070	−	0.943957i	$-0.607072\pi$
$17$	−3.86460e6	−0.660139	−0.330070	+	0.943957i	$0.607072\pi$
$18$	4.99575e6	0.623163
$19$	1.20325e6	0.111484	0.0557420	−	0.998445i	$-0.482248\pi$
$19$	1.20325e6	0.111484	0.0557420	+	0.998445i	$0.482248\pi$
$20$	4.27319e7	2.98599
$21$	−1.01390e7	−0.541737
$22$	7.05567e7	2.91886
$23$	−4.06402e7	−1.31660	−0.658298	−	0.752758i	$-0.728723\pi$
$23$	−4.06402e7	−1.31660	−0.658298	+	0.752758i	$0.728723\pi$
$24$	6.29450e7	1.61361
$25$	2.11092e7	0.432316
$26$	1.97912e8	3.26677
$27$	1.43489e7	0.192450
$28$	−2.13200e8	−2.34109
$29$	−4.76409e7	−0.431312	−0.215656	−	0.976469i	$-0.569189\pi$
$29$	−4.76409e7	−0.431312	−0.215656	+	0.976469i	$0.569189\pi$
$30$	1.71929e8	1.29176
$31$	−1.88831e8	−1.18463	−0.592316	−	0.805706i	$-0.701786\pi$
$31$	−1.88831e8	−1.18463	−0.592316	+	0.805706i	$0.701786\pi$
$32$	4.38237e8	2.30879
$33$	2.02655e8	0.901426
$34$	−3.26958e8	−1.23412
$35$	−3.48934e8	−1.12297
$36$	3.01725e8	0.831662
$37$	−3.93536e8	−0.932986	−0.466493	−	0.884525i	$-0.654483\pi$
$37$	−3.93536e8	−0.932986	−0.466493	+	0.884525i	$0.654483\pi$
$38$	1.01799e8	0.208418
$39$	5.68448e8	1.00887
$40$	2.16625e9	3.34487
$41$	2.32464e8	0.313360	0.156680	−	0.987649i	$-0.449921\pi$
$41$	2.32464e8	0.313360	0.156680	+	0.987649i	$0.449921\pi$
$42$	−8.57793e8	−1.01277
$43$	−1.33808e9	−1.38806	−0.694028	−	0.719948i	$-0.744165\pi$
$43$	−1.33808e9	−1.38806	−0.694028	+	0.719948i	$0.744165\pi$
$44$	4.26137e9	3.89546
$45$	4.93818e8	0.398931
$46$	−3.43830e9	−2.46136
$47$	2.07896e9	1.32224	0.661118	−	0.750282i	$-0.270082\pi$
$47$	2.07896e9	1.32224	0.661118	+	0.750282i	$0.270082\pi$
$48$	2.78243e9	1.57615
$49$	−2.36415e8	−0.119563
$50$	1.78591e9	0.808210
$51$	−9.39098e8	−0.381132
$52$	1.19532e10	4.35978
$53$	3.09305e9	1.01594	0.507972	−	0.861374i	$-0.330395\pi$
$53$	3.09305e9	1.01594	0.507972	+	0.861374i	$0.330395\pi$
$54$	1.21397e9	0.359783
$55$	6.97437e9	1.86857
$56$	−1.08080e10	−2.62246
$57$	2.92391e8	0.0643653
$58$	−4.03058e9	−0.806332
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	1.03839e10	1.72396
$61$	8.26252e9	1.25256	0.626280	−	0.779598i	$-0.284577\pi$
$61$	8.26252e9	1.25256	0.626280	+	0.779598i	$0.284577\pi$
$62$	−1.59757e10	−2.21466
$63$	−2.46377e9	−0.312772
$64$	1.36261e10	1.58628
$65$	1.95632e10	2.09130
$66$	1.71453e10	1.68521
$67$	1.60347e10	1.45094	0.725471	−	0.688253i	$-0.241622\pi$
$67$	1.60347e10	1.45094	0.725471	+	0.688253i	$0.241622\pi$
$68$	−1.97471e10	−1.64704
$69$	−9.87556e9	−0.760137
$70$	−2.95210e10	−2.09938
$71$	−1.52068e9	−0.100027	−0.0500134	−	0.998749i	$-0.515926\pi$
$71$	−1.52068e9	−0.100027	−0.0500134	+	0.998749i	$0.515926\pi$
$72$	1.52956e10	0.931620
$73$	−3.03821e10	−1.71531	−0.857654	−	0.514228i	$-0.828079\pi$
$73$	−3.03821e10	−1.71531	−0.857654	+	0.514228i	$0.828079\pi$
$74$	−3.32945e10	−1.74421
$75$	5.12953e9	0.249598
$76$	6.14831e9	0.278151
$77$	−3.47968e10	−1.46501
$78$	4.80926e10	1.88607
$79$	4.55729e10	1.66632	0.833158	−	0.553034i	$-0.186530\pi$
$79$	4.55729e10	1.66632	0.833158	+	0.553034i	$0.186530\pi$
$80$	9.57574e10	3.26721
$81$	3.48678e9	0.111111
$82$	1.96672e10	0.585824
$83$	−2.27476e9	−0.0633880	−0.0316940	−	0.999498i	$-0.510090\pi$
$83$	−2.27476e9	−0.0633880	−0.0316940	+	0.999498i	$0.510090\pi$
$84$	−5.18075e10	−1.35163
$85$	−3.23191e10	−0.790051
$86$	−1.13206e11	−2.59495
$87$	−1.15767e10	−0.249018
$88$	2.16026e11	4.36366
$89$	2.81381e10	0.534133	0.267067	−	0.963678i	$-0.413946\pi$
$89$	2.81381e10	0.534133	0.267067	+	0.963678i	$0.413946\pi$
$90$	4.17787e10	0.745798
$91$	−9.76052e10	−1.63963
$92$	−2.07660e11	−3.28489
$93$	−4.58859e10	−0.683948
$94$	1.75887e11	2.47190
$95$	1.00626e10	0.133423
$96$	1.06492e11	1.33298
$97$	−1.58701e10	−0.187644	−0.0938219	−	0.995589i	$-0.529908\pi$
$97$	−1.58701e10	−0.187644	−0.0938219	+	0.995589i	$0.529908\pi$
$98$	−2.00015e10	−0.223521
$99$	4.92451e10	0.520439
$100$	1.07862e11	1.07862
$101$	−1.87250e11	−1.77277	−0.886387	−	0.462945i	$-0.846793\pi$
$101$	−1.87250e11	−1.77277	−0.886387	+	0.462945i	$0.846793\pi$
$102$	−7.94509e10	−0.712521
$103$	−1.75027e11	−1.48765	−0.743824	−	0.668375i	$-0.766990\pi$
$103$	−1.75027e11	−1.48765	−0.743824	+	0.668375i	$0.766990\pi$
$104$	6.05954e11	4.88378
$105$	−8.47909e10	−0.648348
$106$	2.61683e11	1.89930
$107$	7.01252e9	0.0483352	0.0241676	−	0.999708i	$-0.492306\pi$
$107$	7.01252e9	0.0483352	0.0241676	+	0.999708i	$0.492306\pi$
$108$	7.33191e10	0.480160
$109$	−3.07918e10	−0.191686	−0.0958428	−	0.995396i	$-0.530555\pi$
$109$	−3.07918e10	−0.191686	−0.0958428	+	0.995396i	$0.530555\pi$
$110$	5.90055e11	3.49328
$111$	−9.56293e10	−0.538660
$112$	−4.77756e11	−2.56158
$113$	2.69177e11	1.37438	0.687190	−	0.726477i	$-0.258844\pi$
$113$	2.69177e11	1.37438	0.687190	+	0.726477i	$0.258844\pi$
$114$	2.47373e10	0.120330
$115$	−3.39868e11	−1.57569
$116$	−2.43432e11	−1.07612
$117$	1.38133e11	0.582472
$118$	6.04850e10	0.243387
$119$	1.61247e11	0.619419
$120$	5.26400e11	1.93116
$121$	4.10195e11	1.43771
$122$	6.99037e11	2.34165
$123$	5.64887e10	0.180919
$124$	−9.64875e11	−2.95564
$125$	−2.31809e11	−0.679401
$126$	−2.08444e11	−0.584724
$127$	6.68074e11	1.79434	0.897168	−	0.441689i	$-0.145621\pi$
$127$	6.68074e11	1.79434	0.897168	+	0.441689i	$0.145621\pi$
$128$	2.55302e11	0.656750
$129$	−3.25154e11	−0.801394
$130$	1.65511e12	3.90965
$131$	4.75138e10	0.107604	0.0538019	−	0.998552i	$-0.482866\pi$
$131$	4.75138e10	0.107604	0.0538019	+	0.998552i	$0.482866\pi$
$132$	1.03551e12	2.24905
$133$	−5.02049e10	−0.104607
$134$	1.35659e12	2.71252
$135$	1.19998e11	0.230323
$136$	−1.00106e12	−1.84500
$137$	−7.27161e11	−1.28726	−0.643632	−	0.765335i	$-0.722573\pi$
$137$	−7.27161e11	−1.28726	−0.643632	+	0.765335i	$0.722573\pi$
$138$	−8.35506e11	−1.42107
$139$	1.00611e11	0.164462	0.0822310	−	0.996613i	$-0.473795\pi$
$139$	1.00611e11	0.164462	0.0822310	+	0.996613i	$0.473795\pi$
$140$	−1.78296e12	−2.80180
$141$	5.05188e11	0.763393
$142$	−1.28655e11	−0.186999
$143$	1.95090e12	2.72827
$144$	6.76131e11	0.909991
$145$	−3.98414e11	−0.516191
$146$	−2.57043e12	−3.20675
$147$	−5.74487e10	−0.0690296
$148$	−2.01087e12	−2.32779
$149$	−6.61117e11	−0.737486	−0.368743	−	0.929531i	$-0.620212\pi$
$149$	−6.61117e11	−0.737486	−0.368743	+	0.929531i	$0.620212\pi$
$150$	4.33976e11	0.466620
$151$	−1.55267e12	−1.60956	−0.804779	−	0.593574i	$-0.797716\pi$
$151$	−1.55267e12	−1.60956	−0.804779	+	0.593574i	$0.797716\pi$
$152$	3.11683e11	0.311582
$153$	−2.28201e11	−0.220046
$154$	−2.94393e12	−2.73882
$155$	−1.57916e12	−1.41776
$156$	2.90462e12	2.51712
$157$	3.02419e11	0.253023	0.126512	−	0.991965i	$-0.459622\pi$
$157$	3.02419e11	0.253023	0.126512	+	0.991965i	$0.459622\pi$
$158$	3.85562e12	3.11516
$159$	7.51611e11	0.586556
$160$	3.66491e12	2.76315
$161$	1.69568e12	1.23538
$162$	2.94994e11	0.207721
$163$	9.80622e11	0.667529	0.333764	−	0.942657i	$-0.391681\pi$
$163$	9.80622e11	0.667529	0.333764	+	0.942657i	$0.391681\pi$
$164$	1.18783e12	0.781830
$165$	1.69477e12	1.07882
$166$	−1.92453e11	−0.118503
$167$	2.07278e11	0.123484	0.0617422	−	0.998092i	$-0.480334\pi$
$167$	2.07278e11	0.123484	0.0617422	+	0.998092i	$0.480334\pi$
$168$	−2.62633e12	−1.51408
$169$	3.68013e12	2.05346
$170$	−2.73430e12	−1.47699
$171$	7.10510e10	0.0371613
$172$	−6.83725e12	−3.46318
$173$	−1.44980e12	−0.711304	−0.355652	−	0.934618i	$-0.615741\pi$
$173$	−1.44980e12	−0.711304	−0.355652	+	0.934618i	$0.615741\pi$
$174$	−9.79431e11	−0.465536
$175$	−8.80764e11	−0.405649
$176$	9.54924e12	4.26235
$177$	1.73727e11	0.0751646
$178$	2.38058e12	0.998556
$179$	−3.45738e12	−1.40623	−0.703114	−	0.711077i	$-0.748208\pi$
$179$	−3.45738e12	−1.40623	−0.703114	+	0.711077i	$0.748208\pi$
$180$	2.52328e12	0.995328
$181$	1.09603e12	0.419365	0.209682	−	0.977770i	$-0.432757\pi$
$181$	1.09603e12	0.419365	0.209682	+	0.977770i	$0.432757\pi$
$182$	−8.25773e12	−3.06526
$183$	2.00779e12	0.723166
$184$	−1.05271e13	−3.67970
$185$	−3.29109e12	−1.11659
$186$	−3.88210e12	−1.27863
$187$	−3.22296e12	−1.03069
$188$	1.06230e13	3.29896
$189$	−5.98697e11	−0.180579
$190$	8.51333e11	0.249434
$191$	−1.70993e12	−0.486737	−0.243369	−	0.969934i	$-0.578252\pi$
$191$	−1.70993e12	−0.486737	−0.243369	+	0.969934i	$0.578252\pi$
$192$	3.31114e12	0.915842
$193$	−2.98457e12	−0.802263	−0.401131	−	0.916021i	$-0.631383\pi$
$193$	−2.98457e12	−0.802263	−0.401131	+	0.916021i	$0.631383\pi$
$194$	−1.34266e12	−0.350798
$195$	4.75385e12	1.20741
$196$	−1.20802e12	−0.298307
$197$	−1.82010e12	−0.437049	−0.218525	−	0.975831i	$-0.570124\pi$
$197$	−1.82010e12	−0.437049	−0.218525	+	0.975831i	$0.570124\pi$
$198$	4.16630e12	0.972954
$199$	−5.04285e12	−1.14547	−0.572736	−	0.819740i	$-0.694118\pi$
$199$	−5.04285e12	−1.14547	−0.572736	+	0.819740i	$0.694118\pi$
$200$	5.46797e12	1.20826
$201$	3.89644e12	0.837702
$202$	−1.58419e13	−3.31418
$203$	1.98778e12	0.404707
$204$	−4.79854e12	−0.950918
$205$	1.94406e12	0.375028
$206$	−1.48079e13	−2.78114
$207$	−2.39976e12	−0.438865
$208$	2.67857e13	4.77039
$209$	1.00348e12	0.174062
$210$	−7.17360e12	−1.21208
$211$	5.27572e12	0.868416	0.434208	−	0.900813i	$-0.357028\pi$
$211$	5.27572e12	0.868416	0.434208	+	0.900813i	$0.357028\pi$
$212$	1.58047e13	2.53477
$213$	−3.69525e11	−0.0577505
$214$	5.93283e11	0.0903621
$215$	−1.11902e13	−1.66122
$216$	3.71684e12	0.537871
$217$	7.87882e12	1.11156
$218$	−2.60509e12	−0.358354
$219$	−7.38285e12	−0.990333
$220$	3.56372e13	4.66207
$221$	−9.04043e12	−1.15354
$222$	−8.09056e12	−1.00702
$223$	1.32774e13	1.61226	0.806132	−	0.591736i	$-0.201557\pi$
$223$	1.32774e13	1.61226	0.806132	+	0.591736i	$0.201557\pi$
$224$	−1.82851e13	−2.16637
$225$	1.24648e12	0.144105
$226$	2.27733e13	2.56939
$227$	−1.35694e13	−1.49424	−0.747119	−	0.664691i	$-0.768563\pi$
$227$	−1.35694e13	−1.49424	−0.747119	+	0.664691i	$0.768563\pi$
$228$	1.49404e12	0.160591
$229$	−1.01069e13	−1.06052	−0.530262	−	0.847834i	$-0.677907\pi$
$229$	−1.01069e13	−1.06052	−0.530262	+	0.847834i	$0.677907\pi$
$230$	−2.87540e13	−2.94574
$231$	−8.45562e12	−0.845823
$232$	−1.23406e13	−1.20546
$233$	1.42233e13	1.35688	0.678441	−	0.734655i	$-0.262656\pi$
$233$	1.42233e13	1.35688	0.678441	+	0.734655i	$0.262656\pi$
$234$	1.16865e13	1.08892
$235$	1.73861e13	1.58244
$236$	3.65307e12	0.324820
$237$	1.10742e13	0.962048
$238$	1.36421e13	1.15800
$239$	1.46054e13	1.21151	0.605753	−	0.795653i	$-0.292872\pi$
$239$	1.46054e13	1.21151	0.605753	+	0.795653i	$0.292872\pi$
$240$	2.32691e13	1.88633
$241$	2.03371e12	0.161137	0.0805685	−	0.996749i	$-0.474326\pi$
$241$	2.03371e12	0.161137	0.0805685	+	0.996749i	$0.474326\pi$
$242$	3.47039e13	2.68778
$243$	8.47289e11	0.0641500
$244$	4.22193e13	3.12512
$245$	−1.97710e12	−0.143092
$246$	4.77914e12	0.338225
$247$	2.81476e12	0.194809
$248$	−4.89134e13	−3.31088
$249$	−5.52768e11	−0.0365971
$250$	−1.96119e13	−1.27013
$251$	3.57265e12	0.226353	0.113176	−	0.993575i	$-0.463898\pi$
$251$	3.57265e12	0.226353	0.113176	+	0.993575i	$0.463898\pi$
$252$	−1.25892e13	−0.780362
$253$	−3.38927e13	−2.05562
$254$	5.65213e13	3.35449
$255$	−7.85354e12	−0.456136
$256$	−6.30676e12	−0.358498
$257$	5.96097e11	0.0331654	0.0165827	−	0.999862i	$-0.494721\pi$
$257$	5.96097e11	0.0331654	0.0165827	+	0.999862i	$0.494721\pi$
$258$	−2.75092e13	−1.49820
$259$	1.64200e13	0.875436
$260$	9.99625e13	5.21775
$261$	−2.81315e12	−0.143771
$262$	4.01983e12	0.201164
$263$	−1.30936e13	−0.641654	−0.320827	−	0.947138i	$-0.603961\pi$
$263$	−1.30936e13	−0.641654	−0.320827	+	0.947138i	$0.603961\pi$
$264$	5.24943e13	2.51936
$265$	2.58667e13	1.21588
$266$	−4.24750e12	−0.195562
$267$	6.83756e12	0.308382
$268$	8.19331e13	3.62008
$269$	−3.49476e13	−1.51279	−0.756397	−	0.654113i	$-0.773042\pi$
$269$	−3.49476e13	−1.51279	−0.756397	+	0.654113i	$0.773042\pi$
$270$	1.01522e13	0.430586
$271$	3.90867e13	1.62442	0.812209	−	0.583366i	$-0.198265\pi$
$271$	3.90867e13	1.62442	0.812209	+	0.583366i	$0.198265\pi$
$272$	−4.42509e13	−1.80216
$273$	−2.37181e13	−0.946639
$274$	−6.15203e13	−2.40653
$275$	1.76044e13	0.674982
$276$	−5.04615e13	−1.89653
$277$	1.20697e13	0.444689	0.222345	−	0.974968i	$-0.428629\pi$
$277$	1.20697e13	0.444689	0.222345	+	0.974968i	$0.428629\pi$
$278$	8.51206e12	0.307460
$279$	−1.11503e13	−0.394877
$280$	−9.03853e13	−3.13855
$281$	2.53214e12	0.0862189	0.0431095	−	0.999070i	$-0.486274\pi$
$281$	2.53214e12	0.0862189	0.0431095	+	0.999070i	$0.486274\pi$
$282$	4.27407e13	1.42715
$283$	−2.23091e13	−0.730561	−0.365280	−	0.930898i	$-0.619027\pi$
$283$	−2.23091e13	−0.730561	−0.365280	+	0.930898i	$0.619027\pi$
$284$	−7.77026e12	−0.249566
$285$	2.44522e12	0.0770321
$286$	1.65053e14	5.10046
$287$	−9.69938e12	−0.294031
$288$	2.58775e13	0.769597
$289$	−1.93368e13	−0.564216
$290$	−3.37072e13	−0.965013
$291$	−3.85643e12	−0.108336
$292$	−1.55244e14	−4.27967
$293$	−2.21776e13	−0.599989	−0.299994	−	0.953941i	$-0.596985\pi$
$293$	−2.21776e13	−0.599989	−0.299994	+	0.953941i	$0.596985\pi$
$294$	−4.86036e12	−0.129050
$295$	5.97881e12	0.155809
$296$	−1.01939e14	−2.60757
$297$	1.19666e13	0.300475
$298$	−5.59327e13	−1.37872
$299$	−9.50692e13	−2.30064
$300$	2.62105e13	0.622743
$301$	5.58305e13	1.30243
$302$	−1.31361e14	−3.00905
$303$	−4.55017e13	−1.02351
$304$	1.37777e13	0.304348
$305$	6.90982e13	1.49906
$306$	−1.93066e13	−0.411374
$307$	7.62507e13	1.59582	0.797908	−	0.602779i	$-0.205940\pi$
$307$	7.62507e13	1.59582	0.797908	+	0.602779i	$0.205940\pi$
$308$	−1.77802e14	−3.65518
$309$	−4.25316e13	−0.858895
$310$	−1.33603e14	−2.65049
$311$	−4.11400e12	−0.0801829	−0.0400915	−	0.999196i	$-0.512765\pi$
$311$	−4.11400e12	−0.0801829	−0.0400915	+	0.999196i	$0.512765\pi$
$312$	1.47247e14	2.81965
$313$	−1.75400e13	−0.330017	−0.165008	−	0.986292i	$-0.552765\pi$
$313$	−1.75400e13	−0.330017	−0.165008	+	0.986292i	$0.552765\pi$
$314$	2.55857e13	0.473024
$315$	−2.06042e13	−0.374324
$316$	2.32865e14	4.15744
$317$	−4.87458e13	−0.855286	−0.427643	−	0.903948i	$-0.640656\pi$
$317$	−4.87458e13	−0.855286	−0.427643	+	0.903948i	$0.640656\pi$
$318$	6.35889e13	1.09656
$319$	−3.97311e13	−0.673414
$320$	1.13953e14	1.89846
$321$	1.70404e12	0.0279063
$322$	1.43460e14	2.30953
$323$	−4.65010e12	−0.0735950
$324$	1.78165e13	0.277221
$325$	4.93805e13	0.755435
$326$	8.29639e13	1.24794
$327$	−7.48241e12	−0.110670
$328$	6.02158e13	0.875799
$329$	−8.67432e13	−1.24068
$330$	1.43383e14	2.01684
$331$	−9.07401e13	−1.25529	−0.627647	−	0.778498i	$-0.715982\pi$
$331$	−9.07401e13	−1.25529	−0.627647	+	0.778498i	$0.715982\pi$
$332$	−1.16234e13	−0.158152
$333$	−2.32379e13	−0.310995
$334$	1.75364e13	0.230853
$335$	1.34096e14	1.73648
$336$	−1.16095e14	−1.47893
$337$	3.04335e13	0.381405	0.190703	−	0.981648i	$-0.438923\pi$
$337$	3.04335e13	0.381405	0.190703	+	0.981648i	$0.438923\pi$
$338$	3.11351e14	3.83891
$339$	6.54101e13	0.793499
$340$	−1.65142e14	−1.97117
$341$	−1.57479e14	−1.84959
$342$	6.01115e12	0.0694727
$343$	9.23667e13	1.05050
$344$	−3.46608e14	−3.87942
$345$	−8.25879e13	−0.909727
$346$	−1.22658e14	−1.32977
$347$	−1.29876e14	−1.38586	−0.692928	−	0.721007i	$-0.743680\pi$
$347$	−1.29876e14	−1.38586	−0.692928	+	0.721007i	$0.743680\pi$
$348$	−5.91541e13	−0.621296
$349$	−3.61280e13	−0.373511	−0.186756	−	0.982406i	$-0.559797\pi$
$349$	−3.61280e13	−0.373511	−0.186756	+	0.982406i	$0.559797\pi$
$350$	−7.45157e13	−0.758356
$351$	3.35663e13	0.336290
$352$	3.65477e14	3.60475
$353$	2.38748e13	0.231835	0.115917	−	0.993259i	$-0.463019\pi$
$353$	2.38748e13	0.231835	0.115917	+	0.993259i	$0.463019\pi$
$354$	1.46979e13	0.140519
$355$	−1.27172e13	−0.119712
$356$	1.43778e14	1.33266
$357$	3.91831e13	0.357622
$358$	−2.92506e14	−2.62893
$359$	−6.93415e13	−0.613725	−0.306863	−	0.951754i	$-0.599279\pi$
$359$	−6.93415e13	−0.613725	−0.306863	+	0.951754i	$0.599279\pi$
$360$	1.27915e14	1.11496
$361$	−1.15042e14	−0.987571
$362$	9.27282e13	0.783998
$363$	9.96774e13	0.830061
$364$	−4.98736e14	−4.09085
$365$	−2.54081e14	−2.05287
$366$	1.69866e14	1.35195
$367$	8.80717e13	0.690515	0.345257	−	0.938508i	$-0.387792\pi$
$367$	8.80717e13	0.690515	0.345257	+	0.938508i	$0.387792\pi$
$368$	−4.65343e14	−3.59427
$369$	1.37268e13	0.104453
$370$	−2.78437e14	−2.08746
$371$	−1.29055e14	−0.953277
$372$	−2.34465e14	−1.70644
$373$	−1.81012e14	−1.29810	−0.649051	−	0.760745i	$-0.724834\pi$
$373$	−1.81012e14	−1.29810	−0.649051	+	0.760745i	$0.724834\pi$
$374$	−2.72674e14	−1.92686
$375$	−5.63297e13	−0.392252
$376$	5.38520e14	3.69546
$377$	−1.11446e14	−0.753680
$378$	−5.06518e13	−0.337590
$379$	−1.16547e14	−0.765570	−0.382785	−	0.923837i	$-0.625035\pi$
$379$	−1.16547e14	−0.765570	−0.382785	+	0.923837i	$0.625035\pi$
$380$	5.14174e13	0.332890
$381$	1.62342e14	1.03596
$382$	−1.44666e14	−0.909950
$383$	1.92120e14	1.19119	0.595593	−	0.803287i	$-0.296917\pi$
$383$	1.92120e14	1.19119	0.595593	+	0.803287i	$0.296917\pi$
$384$	6.20385e13	0.379175
$385$	−2.91000e14	−1.75331
$386$	−2.52505e14	−1.49982
$387$	−7.90125e13	−0.462685
$388$	−8.10918e13	−0.468169
$389$	5.69375e13	0.324098	0.162049	−	0.986783i	$-0.448190\pi$
$389$	5.69375e13	0.324098	0.162049	+	0.986783i	$0.448190\pi$
$390$	4.02191e14	2.25724
$391$	1.57058e14	0.869136
$392$	−6.12392e13	−0.334161
$393$	1.15459e13	0.0621251
$394$	−1.53986e14	−0.817058
$395$	3.81119e14	1.99424
$396$	2.51629e14	1.29849
$397$	−4.41681e13	−0.224782	−0.112391	−	0.993664i	$-0.535851\pi$
$397$	−4.41681e13	−0.224782	−0.112391	+	0.993664i	$0.535851\pi$
$398$	−4.26643e14	−2.14145
$399$	−1.21998e13	−0.0603950
$400$	2.41707e14	1.18021
$401$	2.52610e14	1.21663	0.608313	−	0.793697i	$-0.291846\pi$
$401$	2.52610e14	1.21663	0.608313	+	0.793697i	$0.291846\pi$
$402$	3.29652e14	1.56607
$403$	−4.41730e14	−2.07004
$404$	−9.56795e14	−4.42305
$405$	2.91595e13	0.132977
$406$	1.68173e14	0.756594
$407$	−3.28198e14	−1.45669
$408$	−2.43257e14	−1.06521
$409$	3.55254e14	1.53483	0.767416	−	0.641150i	$-0.221542\pi$
$409$	3.55254e14	1.53483	0.767416	+	0.641150i	$0.221542\pi$
$410$	1.64474e14	0.701110
$411$	−1.76700e14	−0.743202
$412$	−8.94341e14	−3.71166
$413$	−2.98297e13	−0.122158
$414$	−2.03028e14	−0.820453
$415$	−1.90235e13	−0.0758623
$416$	1.02516e15	4.03441
$417$	2.44486e13	0.0949522
$418$	8.48977e13	0.325407
$419$	9.22171e13	0.348846	0.174423	−	0.984671i	$-0.444194\pi$
$419$	9.22171e13	0.348846	0.174423	+	0.984671i	$0.444194\pi$
$420$	−4.33259e14	−1.61762
$421$	1.86118e14	0.685862	0.342931	−	0.939361i	$-0.388580\pi$
$421$	1.86118e14	0.685862	0.342931	+	0.939361i	$0.388580\pi$
$422$	4.46343e14	1.62349
$423$	1.22761e14	0.440745
$424$	8.01202e14	2.83942
$425$	−8.15785e13	−0.285389
$426$	−3.12631e13	−0.107964
$427$	−3.44747e14	−1.17530
$428$	3.58321e13	0.120596
$429$	4.74069e14	1.57517
$430$	−9.46728e14	−3.10562
$431$	3.23754e14	1.04855	0.524276	−	0.851548i	$-0.324336\pi$
$431$	3.23754e14	1.04855	0.524276	+	0.851548i	$0.324336\pi$
$432$	1.64300e14	0.525383
$433$	−2.99481e14	−0.945554	−0.472777	−	0.881182i	$-0.656748\pi$
$433$	−2.99481e14	−0.945554	−0.472777	+	0.881182i	$0.656748\pi$
$434$	6.66575e14	2.07805
$435$	−9.68146e13	−0.298023
$436$	−1.57338e14	−0.478253
$437$	−4.89005e13	−0.146779
$438$	−6.24614e14	−1.85142
$439$	3.70047e14	1.08318	0.541592	−	0.840642i	$-0.317822\pi$
$439$	3.70047e14	1.08318	0.541592	+	0.840642i	$0.317822\pi$
$440$	1.80659e15	5.22240
$441$	−1.39600e13	−0.0398542
$442$	−7.64851e14	−2.15652
$443$	6.09130e14	1.69625	0.848124	−	0.529798i	$-0.177732\pi$
$443$	6.09130e14	1.69625	0.848124	+	0.529798i	$0.177732\pi$
$444$	−4.88640e14	−1.34395
$445$	2.35315e14	0.639247
$446$	1.12331e15	3.01411
$447$	−1.60651e14	−0.425788
$448$	−5.68538e14	−1.48844
$449$	5.33593e14	1.37992	0.689962	−	0.723846i	$-0.257627\pi$
$449$	5.33593e14	1.37992	0.689962	+	0.723846i	$0.257627\pi$
$450$	1.05456e14	0.269403
$451$	1.93868e14	0.489255
$452$	1.37542e15	3.42906
$453$	−3.77300e14	−0.929279
$454$	−1.14802e15	−2.79346
$455$	−8.16258e14	−1.96230
$456$	7.57389e13	0.179892
$457$	−6.70685e14	−1.57391	−0.786955	−	0.617011i	$-0.788343\pi$
$457$	−6.70685e14	−1.57391	−0.786955	+	0.617011i	$0.788343\pi$
$458$	−8.55074e14	−1.98264
$459$	−5.54528e13	−0.127044
$460$	−1.73663e15	−3.93133
$461$	5.51775e14	1.23426	0.617131	−	0.786861i	$-0.288295\pi$
$461$	5.51775e14	1.23426	0.617131	+	0.786861i	$0.288295\pi$
$462$	−7.15374e14	−1.58126
$463$	4.84132e14	1.05747	0.528735	−	0.848787i	$-0.322666\pi$
$463$	4.84132e14	1.05747	0.528735	+	0.848787i	$0.322666\pi$
$464$	−5.45504e14	−1.17747
$465$	−3.83737e14	−0.818545
$466$	1.20334e15	2.53668
$467$	2.12854e14	0.443443	0.221722	−	0.975110i	$-0.428832\pi$
$467$	2.12854e14	0.443443	0.221722	+	0.975110i	$0.428832\pi$
$468$	7.05822e14	1.45326
$469$	−6.69036e14	−1.36144
$470$	1.47092e15	2.95836
$471$	7.34878e13	0.146083
$472$	1.85189e14	0.363860
$473$	−1.11592e15	−2.16719
$474$	9.36916e14	1.79854
$475$	2.53997e13	0.0481963
$476$	8.23932e14	1.54544
$477$	1.82642e14	0.338648
$478$	1.23567e15	2.26490
$479$	2.43424e13	0.0441081	0.0220540	−	0.999757i	$-0.492979\pi$
$479$	2.43424e13	0.0441081	0.0220540	+	0.999757i	$0.492979\pi$
$480$	8.90574e14	1.59530
$481$	−9.20596e14	−1.63031
$482$	1.72059e14	0.301244
$483$	4.12050e14	0.713249
$484$	2.09599e15	3.58706
$485$	−1.32719e14	−0.224571
$486$	7.16835e13	0.119928
$487$	3.19615e14	0.528711	0.264355	−	0.964425i	$-0.414841\pi$
$487$	3.19615e14	0.528711	0.264355	+	0.964425i	$0.414841\pi$
$488$	2.14026e15	3.50073
$489$	2.38291e14	0.385398
$490$	−1.67269e14	−0.267509
$491$	−8.96191e14	−1.41727	−0.708635	−	0.705576i	$-0.750689\pi$
$491$	−8.96191e14	−1.41727	−0.708635	+	0.705576i	$0.750689\pi$
$492$	2.88642e14	0.451390
$493$	1.84113e14	0.284726
$494$	2.38139e14	0.364193
$495$	4.11830e14	0.622858
$496$	−2.16218e15	−3.23401
$497$	6.34492e13	0.0938568
$498$	−4.67660e13	−0.0684178
$499$	4.57995e14	0.662686	0.331343	−	0.943510i	$-0.392498\pi$
$499$	4.57995e14	0.662686	0.331343	+	0.943510i	$0.392498\pi$
$500$	−1.18448e15	−1.69510
$501$	5.03685e13	0.0712937
$502$	3.02259e14	0.423163
$503$	4.97125e13	0.0688401	0.0344201	−	0.999407i	$-0.489042\pi$
$503$	4.97125e13	0.0688401	0.0344201	+	0.999407i	$0.489042\pi$
$504$	−6.38199e14	−0.874154
$505$	−1.56594e15	−2.12165
$506$	−2.86744e15	−3.84296
$507$	8.94270e14	1.18556
$508$	3.41368e15	4.47684
$509$	−5.88078e14	−0.762934	−0.381467	−	0.924382i	$-0.624581\pi$
$509$	−5.88078e14	−0.762934	−0.381467	+	0.924382i	$0.624581\pi$
$510$	−6.64436e14	−0.852741
$511$	1.26767e15	1.60950
$512$	−1.05643e15	−1.32696
$513$	1.72654e13	0.0214551
$514$	5.04318e13	0.0620023
$515$	−1.46373e15	−1.78041
$516$	−1.66145e15	−1.99947
$517$	1.73380e15	2.06443
$518$	1.38919e15	1.63662
$519$	−3.52302e14	−0.410672
$520$	5.06750e15	5.84488
$521$	7.20684e14	0.822503	0.411251	−	0.911522i	$-0.365092\pi$
$521$	7.20684e14	0.822503	0.411251	+	0.911522i	$0.365092\pi$
$522$	−2.38002e14	−0.268777
$523$	−2.88311e14	−0.322182	−0.161091	−	0.986940i	$-0.551501\pi$
$523$	−2.88311e14	−0.322182	−0.161091	+	0.986940i	$0.551501\pi$
$524$	2.42783e14	0.268470
$525$	−2.14026e14	−0.234202
$526$	−1.10776e15	−1.19957
$527$	7.29756e14	0.782022
$528$	2.32046e15	2.46087
$529$	6.98813e14	0.733424
$530$	2.18841e15	2.27307
$531$	4.22156e13	0.0433963
$532$	−2.56534e14	−0.260994
$533$	5.43801e14	0.547571
$534$	5.78480e14	0.576516
$535$	5.86447e13	0.0578473
$536$	4.15352e15	4.05518
$537$	−8.40144e14	−0.811886
$538$	−2.95668e15	−2.82815
$539$	−1.97163e14	−0.186675
$540$	6.13157e14	0.574653
$541$	1.26624e15	1.17471	0.587354	−	0.809330i	$-0.300170\pi$
$541$	1.26624e15	1.17471	0.587354	+	0.809330i	$0.300170\pi$
$542$	3.30687e15	3.03683
$543$	2.66336e14	0.242120
$544$	−1.69361e15	−1.52412
$545$	−2.57507e14	−0.229408
$546$	−2.00663e15	−1.76973
$547$	1.71013e15	1.49313	0.746567	−	0.665310i	$-0.231701\pi$
$547$	1.71013e15	1.49313	0.746567	+	0.665310i	$0.231701\pi$
$548$	−3.71560e15	−3.21171
$549$	4.87893e14	0.417520
$550$	1.48939e15	1.26187
$551$	−5.73241e13	−0.0480844
$552$	−2.55810e15	−2.12448
$553$	−1.90149e15	−1.56353
$554$	1.02114e15	0.831342
$555$	−7.99734e14	−0.644665
$556$	5.14097e14	0.410331
$557$	−1.96611e15	−1.55383	−0.776915	−	0.629606i	$-0.783217\pi$
$557$	−1.96611e15	−1.55383	−0.776915	+	0.629606i	$0.783217\pi$
$558$	−9.43351e14	−0.738219
$559$	−3.13017e15	−2.42551
$560$	−3.99541e15	−3.06568
$561$	−7.83180e14	−0.595067
$562$	2.14227e14	0.161185
$563$	−5.69053e14	−0.423991	−0.211995	−	0.977271i	$-0.567996\pi$
$563$	−5.69053e14	−0.423991	−0.211995	+	0.977271i	$0.567996\pi$
$564$	2.58138e15	1.90466
$565$	2.25109e15	1.64485
$566$	−1.88742e15	−1.36578
$567$	−1.45483e14	−0.104257
$568$	−3.93906e14	−0.279561
$569$	−1.72352e15	−1.21143	−0.605714	−	0.795682i	$-0.707113\pi$
$569$	−1.72352e15	−1.21143	−0.605714	+	0.795682i	$0.707113\pi$
$570$	2.06874e14	0.144011
$571$	−9.17717e14	−0.632718	−0.316359	−	0.948640i	$-0.602460\pi$
$571$	−9.17717e14	−0.632718	−0.316359	+	0.948640i	$0.602460\pi$
$572$	9.96858e15	6.80699
$573$	−4.15513e14	−0.281018
$574$	−8.20600e14	−0.549688
$575$	−8.57881e14	−0.569185
$576$	8.04606e14	0.528761
$577$	−1.49567e15	−0.973571	−0.486785	−	0.873522i	$-0.661831\pi$
$577$	−1.49567e15	−0.973571	−0.486785	+	0.873522i	$0.661831\pi$
$578$	−1.63596e15	−1.05480
$579$	−7.25251e14	−0.463187
$580$	−2.03579e15	−1.28789
$581$	9.49128e13	0.0594779
$582$	−3.26267e14	−0.202533
$583$	2.57951e15	1.58621
$584$	−7.86996e15	−4.79404
$585$	1.15518e15	0.697098
$586$	−1.87630e15	−1.12167
$587$	−1.79820e15	−1.06495	−0.532474	−	0.846447i	$-0.678737\pi$
$587$	−1.79820e15	−1.06495	−0.532474	+	0.846447i	$0.678737\pi$
$588$	−2.93548e14	−0.172228
$589$	−2.27212e14	−0.132068
$590$	5.05827e14	0.291284
$591$	−4.42283e14	−0.252330
$592$	−4.50612e15	−2.54703
$593$	−2.03936e15	−1.14207	−0.571035	−	0.820926i	$-0.693458\pi$
$593$	−2.03936e15	−1.14207	−0.571035	+	0.820926i	$0.693458\pi$
$594$	1.01241e15	0.561735
$595$	1.34849e15	0.741317
$596$	−3.37813e15	−1.84002
$597$	−1.22541e15	−0.661339
$598$	−8.04318e15	−4.30102
$599$	−1.56407e15	−0.828723	−0.414362	−	0.910112i	$-0.635995\pi$
$599$	−1.56407e15	−0.828723	−0.414362	+	0.910112i	$0.635995\pi$
$600$	1.32872e15	0.697591
$601$	−2.69354e15	−1.40124	−0.700622	−	0.713533i	$-0.747094\pi$
$601$	−2.69354e15	−1.40124	−0.700622	+	0.713533i	$0.747094\pi$
$602$	4.72345e15	2.43489
$603$	9.46834e14	0.483647
$604$	−7.93374e15	−4.01583
$605$	3.43040e15	1.72064
$606$	−3.84959e15	−1.91344
$607$	2.20891e15	1.08803	0.544013	−	0.839077i	$-0.316904\pi$
$607$	2.20891e15	1.08803	0.544013	+	0.839077i	$0.316904\pi$
$608$	5.27311e14	0.257393
$609$	4.83031e14	0.233657
$610$	5.84594e15	2.80247
$611$	4.86331e15	2.31049
$612$	−1.16604e15	−0.549013
$613$	−8.80658e14	−0.410936	−0.205468	−	0.978664i	$-0.565872\pi$
$613$	−8.80658e14	−0.410936	−0.205468	+	0.978664i	$0.565872\pi$
$614$	6.45107e15	2.98336
$615$	4.72407e14	0.216522
$616$	−9.01351e15	−4.09449
$617$	2.63733e15	1.18740	0.593699	−	0.804687i	$-0.297667\pi$
$617$	2.63733e15	1.18740	0.593699	+	0.804687i	$0.297667\pi$
$618$	−3.59832e15	−1.60569
$619$	2.06251e15	0.912214	0.456107	−	0.889925i	$-0.349243\pi$
$619$	2.06251e15	0.912214	0.456107	+	0.889925i	$0.349243\pi$
$620$	−8.06911e15	−3.53729
$621$	−5.83142e14	−0.253379
$622$	−3.48058e14	−0.149901
$623$	−1.17404e15	−0.501186
$624$	6.50892e15	2.75419
$625$	−2.96931e15	−1.24542
$626$	−1.48395e15	−0.616963
$627$	2.43845e14	0.100495
$628$	1.54528e15	0.631290
$629$	1.52086e15	0.615901
$630$	−1.74318e15	−0.699794
$631$	−1.59131e15	−0.633277	−0.316639	−	0.948546i	$-0.602554\pi$
$631$	−1.59131e15	−0.633277	−0.316639	+	0.948546i	$0.602554\pi$
$632$	1.18049e16	4.65712
$633$	1.28200e15	0.501380
$634$	−4.12406e15	−1.59895
$635$	5.58700e15	2.14745
$636$	3.84053e15	1.46345
$637$	−5.53043e14	−0.208926
$638$	−3.36139e15	−1.25894
$639$	−8.97946e13	−0.0333423
$640$	2.13506e15	0.785994
$641$	6.17294e14	0.225306	0.112653	−	0.993634i	$-0.464065\pi$
$641$	6.17294e14	0.225306	0.112653	+	0.993634i	$0.464065\pi$
$642$	1.44168e14	0.0521706
$643$	3.78440e15	1.35780	0.678902	−	0.734229i	$-0.262456\pi$
$643$	3.78440e15	1.35780	0.678902	+	0.734229i	$0.262456\pi$
$644$	8.66447e15	3.08226
$645$	−2.71922e15	−0.959104
$646$	−3.93414e14	−0.137585
$647$	1.55551e14	0.0539385	0.0269693	−	0.999636i	$-0.491414\pi$
$647$	1.55551e14	0.0539385	0.0269693	+	0.999636i	$0.491414\pi$
$648$	9.03192e14	0.310540
$649$	5.96226e14	0.203266
$650$	4.17776e15	1.41228
$651$	1.91455e15	0.641759
$652$	5.01072e15	1.66547
$653$	3.34271e15	1.10173	0.550867	−	0.834593i	$-0.314297\pi$
$653$	3.34271e15	1.10173	0.550867	+	0.834593i	$0.314297\pi$
$654$	−6.33037e14	−0.206896
$655$	3.97351e14	0.128780
$656$	2.66179e15	0.855465
$657$	−1.79403e15	−0.571769
$658$	−7.33877e15	−2.31943
$659$	−3.60961e15	−1.13133	−0.565666	−	0.824634i	$-0.691381\pi$
$659$	−3.60961e15	−1.13133	−0.565666	+	0.824634i	$0.691381\pi$
$660$	8.65983e15	2.69165
$661$	−1.38581e15	−0.427164	−0.213582	−	0.976925i	$-0.568513\pi$
$661$	−1.38581e15	−0.427164	−0.213582	+	0.976925i	$0.568513\pi$
$662$	−7.67692e15	−2.34676
$663$	−2.19682e15	−0.665995
$664$	−5.89239e14	−0.177160
$665$	−4.19856e14	−0.125193
$666$	−1.96601e15	−0.581402
$667$	1.93613e15	0.567863
$668$	1.05913e15	0.308092
$669$	3.22641e15	0.930841
$670$	1.13450e16	3.24633
$671$	6.89070e15	1.95564
$672$	−4.44328e15	−1.25076
$673$	4.91580e15	1.37250	0.686248	−	0.727368i	$-0.259256\pi$
$673$	4.91580e15	1.37250	0.686248	+	0.727368i	$0.259256\pi$
$674$	2.57477e15	0.713033
$675$	3.02894e14	0.0831993
$676$	1.88045e16	5.12335
$677$	−5.64277e15	−1.52495	−0.762474	−	0.647019i	$-0.776015\pi$
$677$	−5.64277e15	−1.52495	−0.762474	+	0.647019i	$0.776015\pi$
$678$	5.53392e15	1.48344
$679$	6.62167e14	0.176069
$680$	−8.37171e15	−2.20808
$681$	−3.29737e15	−0.862698
$682$	−1.33233e16	−3.45778
$683$	2.35724e15	0.606863	0.303431	−	0.952853i	$-0.401868\pi$
$683$	2.35724e15	0.606863	0.303431	+	0.952853i	$0.401868\pi$
$684$	3.63051e14	0.0927171
$685$	−6.08114e15	−1.54059
$686$	7.81453e15	1.96390
$687$	−2.45596e15	−0.612294
$688$	−1.53215e16	−3.78935
$689$	7.23555e15	1.77528
$690$	−6.98721e15	−1.70072
$691$	5.04014e15	1.21706	0.608532	−	0.793529i	$-0.291759\pi$
$691$	5.04014e15	1.21706	0.608532	+	0.793529i	$0.291759\pi$
$692$	−7.40810e15	−1.77469
$693$	−2.05472e15	−0.488336
$694$	−1.09880e16	−2.59084
$695$	8.41398e14	0.196827
$696$	−2.99876e15	−0.695970
$697$	−8.98380e14	−0.206861
$698$	−3.05655e15	−0.698275
$699$	3.45626e15	0.783396
$700$	−4.50047e15	−1.01209
$701$	4.87111e15	1.08687	0.543437	−	0.839450i	$-0.317123\pi$
$701$	4.87111e15	1.08687	0.543437	+	0.839450i	$0.317123\pi$
$702$	2.83982e15	0.628690
$703$	−4.73524e14	−0.104013
$704$	1.13637e16	2.47669
$705$	4.22482e15	0.913625
$706$	2.01989e15	0.433412
$707$	7.81285e15	1.66342
$708$	8.87696e14	0.187535
$709$	3.22633e15	0.676323	0.338162	−	0.941088i	$-0.390195\pi$
$709$	3.22633e15	0.676323	0.338162	+	0.941088i	$0.390195\pi$
$710$	−1.07592e15	−0.223799
$711$	2.69103e15	0.555439
$712$	7.28869e15	1.49283
$713$	7.67412e15	1.55968
$714$	3.31503e15	0.668570
$715$	1.63151e16	3.26517
$716$	−1.76663e16	−3.50852
$717$	3.54912e15	0.699463
$718$	−5.86653e15	−1.14735
$719$	−4.59517e15	−0.891851	−0.445926	−	0.895070i	$-0.647125\pi$
$719$	−4.59517e15	−0.891851	−0.445926	+	0.895070i	$0.647125\pi$
$720$	5.65438e15	1.08907
$721$	7.30287e15	1.39589
$722$	−9.73298e15	−1.84625
$723$	4.94192e14	0.0930325
$724$	5.60044e15	1.04631
$725$	−1.00566e15	−0.186463
$726$	8.43305e15	1.55179
$727$	3.10063e15	0.566253	0.283127	−	0.959083i	$-0.408628\pi$
$727$	3.10063e15	0.566253	0.283127	+	0.959083i	$0.408628\pi$
$728$	−2.52830e16	−4.58253
$729$	2.05891e14	0.0370370
$730$	−2.14961e16	−3.83782
$731$	5.17116e15	0.916310
$732$	1.02593e16	1.80429
$733$	9.75564e14	0.170288	0.0851440	−	0.996369i	$-0.472865\pi$
$733$	9.75564e14	0.170288	0.0851440	+	0.996369i	$0.472865\pi$
$734$	7.45116e15	1.29091
$735$	−4.80435e14	−0.0826142
$736$	−1.78100e16	−3.03974
$737$	1.33725e16	2.26538
$738$	1.16133e15	0.195275
$739$	−4.50555e15	−0.751976	−0.375988	−	0.926625i	$-0.622697\pi$
$739$	−4.50555e15	−0.751976	−0.375988	+	0.926625i	$0.622697\pi$
$740$	−1.68166e16	−2.78588
$741$	6.83988e14	0.112473
$742$	−1.09185e16	−1.78214
$743$	8.84938e15	1.43375	0.716877	−	0.697200i	$-0.245571\pi$
$743$	8.84938e15	1.43375	0.716877	+	0.697200i	$0.245571\pi$
$744$	−1.18860e16	−1.91154
$745$	−5.52882e15	−0.882619
$746$	−1.53142e16	−2.42679
$747$	−1.34323e14	−0.0211293
$748$	−1.64685e16	−2.57155
$749$	−2.92592e14	−0.0453537
$750$	−4.76568e15	−0.733311
$751$	1.14600e16	1.75051	0.875257	−	0.483658i	$-0.160692\pi$
$751$	1.14600e16	1.75051	0.875257	+	0.483658i	$0.160692\pi$
$752$	2.38048e16	3.60967
$753$	8.68155e14	0.130685
$754$	−9.42871e15	−1.40900
$755$	−1.29848e16	−1.92631
$756$	−3.05918e15	−0.450542
$757$	−8.50505e15	−1.24351	−0.621755	−	0.783211i	$-0.713580\pi$
$757$	−8.50505e15	−1.24351	−0.621755	+	0.783211i	$0.713580\pi$
$758$	−9.86026e15	−1.43122
$759$	−8.23593e15	−1.18681
$760$	2.60656e15	0.372900
$761$	−8.64759e15	−1.22823	−0.614115	−	0.789217i	$-0.710487\pi$
$761$	−8.64759e15	−1.22823	−0.614115	+	0.789217i	$0.710487\pi$
$762$	1.37347e16	1.93672
$763$	1.28476e15	0.179862
$764$	−8.73728e15	−1.21440
$765$	−1.90841e15	−0.263350
$766$	1.62540e16	2.22691
$767$	1.67242e15	0.227494
$768$	−1.53254e15	−0.206979
$769$	1.13675e16	1.52430	0.762148	−	0.647403i	$-0.224145\pi$
$769$	1.13675e16	1.52430	0.762148	+	0.647403i	$0.224145\pi$
$770$	−2.46196e16	−3.27780
$771$	1.44852e14	0.0191480
$772$	−1.52504e16	−2.00164
$773$	3.63774e15	0.474072	0.237036	−	0.971501i	$-0.423824\pi$
$773$	3.63774e15	0.474072	0.237036	+	0.971501i	$0.423824\pi$
$774$	−6.68472e15	−0.864984
$775$	−3.98606e15	−0.512135
$776$	−4.11087e15	−0.524438
$777$	3.99006e15	0.505433
$778$	4.81711e15	0.605897
$779$	2.79713e14	0.0349347
$780$	2.42909e16	3.01247
$781$	−1.26820e15	−0.156174
$782$	1.32876e16	1.62484
$783$	−6.83595e14	−0.0830059
$784$	−2.70703e15	−0.326403
$785$	2.52908e15	0.302817
$786$	9.76818e14	0.116142
$787$	−3.07958e15	−0.363605	−0.181803	−	0.983335i	$-0.558193\pi$
$787$	−3.07958e15	−0.363605	−0.181803	+	0.983335i	$0.558193\pi$
$788$	−9.30021e15	−1.09043
$789$	−3.18173e15	−0.370459
$790$	3.22440e16	3.72820
$791$	−1.12312e16	−1.28960
$792$	1.27561e16	1.45455
$793$	1.93284e16	2.18874
$794$	−3.73677e15	−0.420227
$795$	6.28561e15	0.701986
$796$	−2.57676e16	−2.85794
$797$	6.95265e15	0.765825	0.382913	−	0.923785i	$-0.374921\pi$
$797$	6.95265e15	0.765825	0.382913	+	0.923785i	$0.374921\pi$
$798$	−1.03214e15	−0.112908
$799$	−8.03437e15	−0.872860
$800$	9.25083e15	0.998127
$801$	1.66153e15	0.178044
$802$	2.13717e16	2.27447
$803$	−2.53378e16	−2.67814
$804$	1.99098e16	2.09005
$805$	1.41807e16	1.47850
$806$	−3.73719e16	−3.86992
$807$	−8.49226e15	−0.873412
$808$	−4.85038e16	−4.95465
$809$	−3.82506e15	−0.388080	−0.194040	−	0.980994i	$-0.562159\pi$
$809$	−3.82506e15	−0.388080	−0.194040	+	0.980994i	$0.562159\pi$
$810$	2.46699e15	0.248599
$811$	2.36486e15	0.236695	0.118348	−	0.992972i	$-0.462240\pi$
$811$	2.36486e15	0.236695	0.118348	+	0.992972i	$0.462240\pi$
$812$	1.01570e16	1.00974
$813$	9.49807e15	0.937858
$814$	−2.77666e16	−2.72326
$815$	8.20080e15	0.798894
$816$	−1.07530e16	−1.04048
$817$	−1.61006e15	−0.154746
$818$	3.00557e16	2.86935
$819$	−5.76349e15	−0.546542
$820$	9.93363e15	0.935690
$821$	9.06895e15	0.848535	0.424268	−	0.905537i	$-0.360532\pi$
$821$	9.06895e15	0.848535	0.424268	+	0.905537i	$0.360532\pi$
$822$	−1.49494e16	−1.38941
$823$	−3.29647e15	−0.304334	−0.152167	−	0.988355i	$-0.548625\pi$
$823$	−3.29647e15	−0.304334	−0.152167	+	0.988355i	$0.548625\pi$
$824$	−4.53378e16	−4.15777
$825$	4.27788e15	0.389701
$826$	−2.52369e15	−0.228374
$827$	6.81130e15	0.612280	0.306140	−	0.951987i	$-0.400962\pi$
$827$	6.81130e15	0.612280	0.306140	+	0.951987i	$0.400962\pi$
$828$	−1.22621e16	−1.09496
$829$	−1.68410e16	−1.49389	−0.746943	−	0.664888i	$-0.768479\pi$
$829$	−1.68410e16	−1.49389	−0.746943	+	0.664888i	$0.768479\pi$
$830$	−1.60945e15	−0.141824
$831$	2.93293e15	0.256742
$832$	3.18754e16	2.77190
$833$	9.13648e14	0.0789280
$834$	2.06843e15	0.177512
$835$	1.73343e15	0.147785
$836$	5.12751e15	0.434282
$837$	−2.70952e15	−0.227983
$838$	7.80188e15	0.652164
$839$	−1.98817e16	−1.65106	−0.825528	−	0.564362i	$-0.809122\pi$
$839$	−1.98817e16	−1.65106	−0.825528	+	0.564362i	$0.809122\pi$
$840$	−2.19636e16	−1.81204
$841$	−9.93085e15	−0.813970
$842$	1.57462e16	1.28221
$843$	6.15310e14	0.0497785
$844$	2.69575e16	2.16669
$845$	3.07763e16	2.45757
$846$	1.03860e16	0.823968
$847$	−1.71151e16	−1.34903
$848$	3.54165e16	2.77350
$849$	−5.42111e15	−0.421790
$850$	−6.90182e15	−0.533531
$851$	1.59934e16	1.22837
$852$	−1.88817e15	−0.144087
$853$	8.99393e15	0.681914	0.340957	−	0.940079i	$-0.389249\pi$
$853$	8.99393e15	0.681914	0.340957	+	0.940079i	$0.389249\pi$
$854$	−2.91668e16	−2.19720
$855$	5.94189e14	0.0444745
$856$	1.81647e15	0.135090
$857$	8.47743e15	0.626426	0.313213	−	0.949683i	$-0.398595\pi$
$857$	8.47743e15	0.626426	0.313213	+	0.949683i	$0.398595\pi$
$858$	4.01078e16	2.94475
$859$	−5.01820e15	−0.366088	−0.183044	−	0.983105i	$-0.558595\pi$
$859$	−5.01820e15	−0.366088	−0.183044	+	0.983105i	$0.558595\pi$
$860$	−5.71789e16	−4.14471
$861$	−2.35695e15	−0.169759
$862$	2.73907e16	1.96026
$863$	4.83064e15	0.343515	0.171757	−	0.985139i	$-0.445056\pi$
$863$	4.83064e15	0.343515	0.171757	+	0.985139i	$0.445056\pi$
$864$	6.28823e15	0.444327
$865$	−1.21245e16	−0.851285
$866$	−2.53371e16	−1.76770
$867$	−4.69883e15	−0.325750
$868$	4.02587e16	2.77333
$869$	3.80064e16	2.60165
$870$	−8.19084e15	−0.557151
$871$	3.75099e16	2.53540
$872$	−7.97609e15	−0.535734
$873$	−9.37112e14	−0.0625480
$874$	−4.13714e15	−0.274402
$875$	9.67207e15	0.637493
$876$	−3.77244e16	−2.47087
$877$	1.89494e16	1.23338	0.616692	−	0.787204i	$-0.288472\pi$
$877$	1.89494e16	1.23338	0.616692	+	0.787204i	$0.288472\pi$
$878$	3.13072e16	2.02500
$879$	−5.38916e15	−0.346404
$880$	7.98589e16	5.10115
$881$	1.46720e16	0.931366	0.465683	−	0.884952i	$-0.345809\pi$
$881$	1.46720e16	0.931366	0.465683	+	0.884952i	$0.345809\pi$
$882$	−1.18107e15	−0.0745071
$883$	2.25724e15	0.141512	0.0707562	−	0.997494i	$-0.477459\pi$
$883$	2.25724e15	0.141512	0.0707562	+	0.997494i	$0.477459\pi$
$884$	−4.61942e16	−2.87806
$885$	1.45285e15	0.0899565
$886$	5.15344e16	3.17112
$887$	−1.67295e16	−1.02307	−0.511533	−	0.859264i	$-0.670922\pi$
$887$	−1.67295e16	−1.02307	−0.511533	+	0.859264i	$0.670922\pi$
$888$	−2.47711e16	−1.50548
$889$	−2.78749e16	−1.68365
$890$	1.99084e16	1.19507
$891$	2.90788e15	0.173480
$892$	6.78439e16	4.02258
$893$	2.50152e15	0.147408
$894$	−1.35917e16	−0.796005
$895$	−2.89136e16	−1.68297
$896$	−1.06523e16	−0.616239
$897$	−2.31018e16	−1.32827
$898$	4.51438e16	2.57975
$899$	8.99607e15	0.510946
$900$	6.36916e15	0.359541
$901$	−1.19534e16	−0.670664
$902$	1.64019e16	0.914656
$903$	1.35668e16	0.751961
$904$	6.97258e16	3.84120
$905$	9.16597e15	0.501893
$906$	−3.19208e16	−1.73728
$907$	−1.99339e16	−1.07833	−0.539165	−	0.842200i	$-0.681260\pi$
$907$	−1.99339e16	−1.07833	−0.539165	+	0.842200i	$0.681260\pi$
$908$	−6.93362e16	−3.72810
$909$	−1.10569e16	−0.590925
$910$	−6.90582e16	−3.66849
$911$	−2.99803e16	−1.58301	−0.791506	−	0.611161i	$-0.790703\pi$
$911$	−2.99803e16	−1.58301	−0.791506	+	0.611161i	$0.790703\pi$
$912$	3.34797e15	0.175716
$913$	−1.89709e15	−0.0989687
$914$	−5.67422e16	−2.94241
$915$	1.67909e16	0.865480
$916$	−5.16433e16	−2.64599
$917$	−1.98248e15	−0.100966
$918$	−4.69149e15	−0.237507
$919$	−9.47937e15	−0.477028	−0.238514	−	0.971139i	$-0.576660\pi$
$919$	−9.47937e15	−0.477028	−0.238514	+	0.971139i	$0.576660\pi$
$920$	−8.80369e16	−4.40384
$921$	1.85289e16	0.921345
$922$	4.66821e16	2.30744
$923$	−3.55731e15	−0.174788
$924$	−4.32059e16	−2.11032
$925$	−8.30723e15	−0.403345
$926$	4.09592e16	1.97693
$927$	−1.03352e16	−0.495883
$928$	−2.08780e16	−0.995808
$929$	3.92007e16	1.85869	0.929346	−	0.369209i	$-0.120371\pi$
$929$	3.92007e16	1.85869	0.929346	+	0.369209i	$0.120371\pi$
$930$	−3.24654e16	−1.53026
$931$	−2.84467e14	−0.0133293
$932$	7.26772e16	3.38540
$933$	−9.99702e14	−0.0462936
$934$	1.80081e16	0.829012
$935$	−2.69532e16	−1.23352
$936$	3.57810e16	1.62793
$937$	−9.36599e15	−0.423629	−0.211815	−	0.977310i	$-0.567937\pi$
$937$	−9.36599e15	−0.423629	−0.211815	+	0.977310i	$0.567937\pi$
$938$	−5.66028e16	−2.54520
$939$	−4.26223e15	−0.190535
$940$	8.88382e16	3.94818
$941$	1.34341e16	0.593563	0.296781	−	0.954945i	$-0.404087\pi$
$941$	1.34341e16	0.593563	0.296781	+	0.954945i	$0.404087\pi$
$942$	6.21731e15	0.273101
$943$	−9.44737e15	−0.412569
$944$	8.18612e15	0.355412
$945$	−5.00682e15	−0.216116
$946$	−9.44108e16	−4.05154
$947$	−5.73643e15	−0.244746	−0.122373	−	0.992484i	$-0.539050\pi$
$947$	−5.73643e15	−0.244746	−0.122373	+	0.992484i	$0.539050\pi$
$948$	5.65863e16	2.40030
$949$	−7.10726e16	−2.99735
$950$	2.14890e15	0.0901025
$951$	−1.18452e16	−0.493800
$952$	4.17684e16	1.73119
$953$	3.82327e16	1.57552	0.787759	−	0.615983i	$-0.211241\pi$
$953$	3.82327e16	1.57552	0.787759	+	0.615983i	$0.211241\pi$
$954$	1.54521e16	0.633098
$955$	−1.42999e16	−0.582524
$956$	7.46298e16	3.02269
$957$	−9.65466e15	−0.388796
$958$	2.05945e15	0.0824595
$959$	3.03403e16	1.20786
$960$	2.76906e16	1.09607
$961$	1.02486e16	0.403354
$962$	−7.78856e16	−3.04785
$963$	4.14082e14	0.0161117
$964$	1.03917e16	0.402035
$965$	−2.49595e16	−0.960143
$966$	3.48608e16	1.33341
$967$	1.62733e16	0.618915	0.309458	−	0.950913i	$-0.399852\pi$
$967$	1.62733e16	0.618915	0.309458	+	0.950913i	$0.399852\pi$
$968$	1.06254e17	4.01819
$969$	−1.12997e15	−0.0424901
$970$	−1.12285e16	−0.419833
$971$	2.16123e16	0.803518	0.401759	−	0.915745i	$-0.368399\pi$
$971$	2.16123e16	0.803518	0.401759	+	0.915745i	$0.368399\pi$
$972$	4.32942e15	0.160053
$973$	−4.19793e15	−0.154317
$974$	2.70405e16	0.988419
$975$	1.19995e16	0.436151
$976$	9.46086e16	3.41945
$977$	−4.14225e16	−1.48873	−0.744366	−	0.667772i	$-0.767248\pi$
$977$	−4.14225e16	−1.48873	−0.744366	+	0.667772i	$0.767248\pi$
$978$	2.01602e16	0.720497
$979$	2.34663e16	0.833951
$980$	−1.01025e16	−0.357013
$981$	−1.81823e15	−0.0638952
$982$	−7.58208e16	−2.64957
$983$	2.56592e16	0.891658	0.445829	−	0.895118i	$-0.352909\pi$
$983$	2.56592e16	0.891658	0.445829	+	0.895118i	$0.352909\pi$
$984$	1.46324e16	0.505643
$985$	−1.52212e16	−0.523058
$986$	1.55766e16	0.532291
$987$	−2.10786e16	−0.716304
$988$	1.43827e16	0.486045
$989$	5.43799e16	1.82751
$990$	3.48422e16	1.16443
$991$	−1.89946e16	−0.631284	−0.315642	−	0.948878i	$-0.602220\pi$
$991$	−1.89946e16	−0.631284	−0.315642	+	0.948878i	$0.602220\pi$
$992$	−8.27527e16	−2.73507
$993$	−2.20498e16	−0.724744
$994$	5.36801e15	0.175464
$995$	−4.21726e16	−1.37089
$996$	−2.82449e15	−0.0913092
$997$	3.58445e16	1.15239	0.576194	−	0.817313i	$-0.304537\pi$
$997$	3.58445e16	1.15239	0.576194	+	0.817313i	$0.304537\pi$
$998$	3.87479e16	1.23888
$999$	−5.64682e15	−0.179553

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.d.1.27	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.d.1.27	✓	28	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)

\(f(q)\)	\(=\)	\(q+84.6034 q^{2} +243.000 q^{3} +5109.73 q^{4} +8362.85 q^{5} +20558.6 q^{6} -41724.2 q^{7} +259033. q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+84.6034 q^{2} +243.000 q^{3} +5109.73 q^{4} +8362.85 q^{5} +20558.6 q^{6} -41724.2 q^{7} +259033. q^{8} +59049.0 q^{9} +707526. q^{10} +833970. q^{11} +1.24167e6 q^{12} +2.33929e6 q^{13} -3.53001e6 q^{14} +2.03217e6 q^{15} +1.14503e7 q^{16} -3.86460e6 q^{17} +4.99575e6 q^{18} +1.20325e6 q^{19} +4.27319e7 q^{20} -1.01390e7 q^{21} +7.05567e7 q^{22} -4.06402e7 q^{23} +6.29450e7 q^{24} +2.11092e7 q^{25} +1.97912e8 q^{26} +1.43489e7 q^{27} -2.13200e8 q^{28} -4.76409e7 q^{29} +1.71929e8 q^{30} -1.88831e8 q^{31} +4.38237e8 q^{32} +2.02655e8 q^{33} -3.26958e8 q^{34} -3.48934e8 q^{35} +3.01725e8 q^{36} -3.93536e8 q^{37} +1.01799e8 q^{38} +5.68448e8 q^{39} +2.16625e9 q^{40} +2.32464e8 q^{41} -8.57793e8 q^{42} -1.33808e9 q^{43} +4.26137e9 q^{44} +4.93818e8 q^{45} -3.43830e9 q^{46} +2.07896e9 q^{47} +2.78243e9 q^{48} -2.36415e8 q^{49} +1.78591e9 q^{50} -9.39098e8 q^{51} +1.19532e10 q^{52} +3.09305e9 q^{53} +1.21397e9 q^{54} +6.97437e9 q^{55} -1.08080e10 q^{56} +2.92391e8 q^{57} -4.03058e9 q^{58} +7.14924e8 q^{59} +1.03839e10 q^{60} +8.26252e9 q^{61} -1.59757e10 q^{62} -2.46377e9 q^{63} +1.36261e10 q^{64} +1.95632e10 q^{65} +1.71453e10 q^{66} +1.60347e10 q^{67} -1.97471e10 q^{68} -9.87556e9 q^{69} -2.95210e10 q^{70} -1.52068e9 q^{71} +1.52956e10 q^{72} -3.03821e10 q^{73} -3.32945e10 q^{74} +5.12953e9 q^{75} +6.14831e9 q^{76} -3.47968e10 q^{77} +4.80926e10 q^{78} +4.55729e10 q^{79} +9.57574e10 q^{80} +3.48678e9 q^{81} +1.96672e10 q^{82} -2.27476e9 q^{83} -5.18075e10 q^{84} -3.23191e10 q^{85} -1.13206e11 q^{86} -1.15767e10 q^{87} +2.16026e11 q^{88} +2.81381e10 q^{89} +4.17787e10 q^{90} -9.76052e10 q^{91} -2.07660e11 q^{92} -4.58859e10 q^{93} +1.75887e11 q^{94} +1.00626e10 q^{95} +1.06492e11 q^{96} -1.58701e10 q^{97} -2.00015e10 q^{98} +4.92451e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9}+O(q^{10}) \) 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9} + 616281 q^{10} + 1082362 q^{11} + 7099002 q^{12} + 503712 q^{13} + 1321669 q^{14} + 6454566 q^{15} + 34870338 q^{16} + 13513579 q^{17} + 5668704 q^{18} + 35971687 q^{19} + 96105997 q^{20} + 34586919 q^{21} - 47598882 q^{22} + 61380539 q^{23} + 80756433 q^{24} + 294744746 q^{25} + 62820734 q^{26} + 401769396 q^{27} + 148068294 q^{28} + 322339307 q^{29} + 149756283 q^{30} + 151247077 q^{31} + 466383494 q^{32} + 263013966 q^{33} + 684479860 q^{34} + 960297361 q^{35} + 1725057486 q^{36} + 863508437 q^{37} + 992640509 q^{38} + 122402016 q^{39} + 3067680252 q^{40} + 3081170377 q^{41} + 321165567 q^{42} + 2554238300 q^{43} + 4350123570 q^{44} + 1568459538 q^{45} - 1987059155 q^{46} + 6203398333 q^{47} + 8473492134 q^{48} + 10327857997 q^{49} + 17577682253 q^{50} + 3283799697 q^{51} + 32137181618 q^{52} + 14571770754 q^{53} + 1377495072 q^{54} + 18251419334 q^{55} + 33498842836 q^{56} + 8741119941 q^{57} + 11860778276 q^{58} + 20017880372 q^{59} + 23353757271 q^{60} + 2761613771 q^{61} + 13785829526 q^{62} + 8404621317 q^{63} + 86547545293 q^{64} + 32034985256 q^{65} - 11566528326 q^{66} + 39381333296 q^{67} + 38995496621 q^{68} + 14915470977 q^{69} + 8551800364 q^{70} + 26130020296 q^{71} + 19623813219 q^{72} + 41382402799 q^{73} + 23815315058 q^{74} + 71622973278 q^{75} + 10611720128 q^{76} - 8426124313 q^{77} + 15265438362 q^{78} + 59825111206 q^{79} + 4009687655 q^{80} + 97629963228 q^{81} - 39592715115 q^{82} + 35433122727 q^{83} + 35980595442 q^{84} - 8950496085 q^{85} - 182032360688 q^{86} + 78328451601 q^{87} - 220003602335 q^{88} + 102303043039 q^{89} + 36390776769 q^{90} - 111146323655 q^{91} - 163000203526 q^{92} + 36753039711 q^{93} - 81314346008 q^{94} + 208102168887 q^{95} + 113331189042 q^{96} - 171891031490 q^{97} + 72304707792 q^{98} + 63912393738 q^{99}+O(q^{100}) \) 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9 + 616281 * q^10 + 1082362 * q^11 + 7099002 * q^12 + 503712 * q^13 + 1321669 * q^14 + 6454566 * q^15 + 34870338 * q^16 + 13513579 * q^17 + 5668704 * q^18 + 35971687 * q^19 + 96105997 * q^20 + 34586919 * q^21 - 47598882 * q^22 + 61380539 * q^23 + 80756433 * q^24 + 294744746 * q^25 + 62820734 * q^26 + 401769396 * q^27 + 148068294 * q^28 + 322339307 * q^29 + 149756283 * q^30 + 151247077 * q^31 + 466383494 * q^32 + 263013966 * q^33 + 684479860 * q^34 + 960297361 * q^35 + 1725057486 * q^36 + 863508437 * q^37 + 992640509 * q^38 + 122402016 * q^39 + 3067680252 * q^40 + 3081170377 * q^41 + 321165567 * q^42 + 2554238300 * q^43 + 4350123570 * q^44 + 1568459538 * q^45 - 1987059155 * q^46 + 6203398333 * q^47 + 8473492134 * q^48 + 10327857997 * q^49 + 17577682253 * q^50 + 3283799697 * q^51 + 32137181618 * q^52 + 14571770754 * q^53 + 1377495072 * q^54 + 18251419334 * q^55 + 33498842836 * q^56 + 8741119941 * q^57 + 11860778276 * q^58 + 20017880372 * q^59 + 23353757271 * q^60 + 2761613771 * q^61 + 13785829526 * q^62 + 8404621317 * q^63 + 86547545293 * q^64 + 32034985256 * q^65 - 11566528326 * q^66 + 39381333296 * q^67 + 38995496621 * q^68 + 14915470977 * q^69 + 8551800364 * q^70 + 26130020296 * q^71 + 19623813219 * q^72 + 41382402799 * q^73 + 23815315058 * q^74 + 71622973278 * q^75 + 10611720128 * q^76 - 8426124313 * q^77 + 15265438362 * q^78 + 59825111206 * q^79 + 4009687655 * q^80 + 97629963228 * q^81 - 39592715115 * q^82 + 35433122727 * q^83 + 35980595442 * q^84 - 8950496085 * q^85 - 182032360688 * q^86 + 78328451601 * q^87 - 220003602335 * q^88 + 102303043039 * q^89 + 36390776769 * q^90 - 111146323655 * q^91 - 163000203526 * q^92 + 36753039711 * q^93 - 81314346008 * q^94 + 208102168887 * q^95 + 113331189042 * q^96 - 171891031490 * q^97 + 72304707792 * q^98 + 63912393738 * q^99

Introduction

L-functions

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