LMFDB - Embedded newform 177.12.a.d.1.28

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			1.28
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)

$f(q)$	$=$	$q+90.0154 q^{2} +243.000 q^{3} +6054.78 q^{4} -4744.07 q^{5} +21873.7 q^{6} +21263.4 q^{7} +360672. q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+90.0154 q^{2} +243.000 q^{3} +6054.78 q^{4} -4744.07 q^{5} +21873.7 q^{6} +21263.4 q^{7} +360672. q^{8} +59049.0 q^{9} -427039. q^{10} -588604. q^{11} +1.47131e6 q^{12} +621501. q^{13} +1.91403e6 q^{14} -1.15281e6 q^{15} +2.00658e7 q^{16} +3.27910e6 q^{17} +5.31532e6 q^{18} +1.04620e7 q^{19} -2.87243e7 q^{20} +5.16699e6 q^{21} -5.29834e7 q^{22} -1.01386e7 q^{23} +8.76432e7 q^{24} -2.63220e7 q^{25} +5.59447e7 q^{26} +1.43489e7 q^{27} +1.28745e8 q^{28} +1.61672e8 q^{29} -1.03771e8 q^{30} -2.14992e7 q^{31} +1.06758e9 q^{32} -1.43031e8 q^{33} +2.95170e8 q^{34} -1.00875e8 q^{35} +3.57528e8 q^{36} +5.53711e8 q^{37} +9.41740e8 q^{38} +1.51025e8 q^{39} -1.71105e9 q^{40} +8.75163e8 q^{41} +4.65109e8 q^{42} +1.09912e8 q^{43} -3.56386e9 q^{44} -2.80132e8 q^{45} -9.12630e8 q^{46} -1.69519e9 q^{47} +4.87600e9 q^{48} -1.52520e9 q^{49} -2.36938e9 q^{50} +7.96822e8 q^{51} +3.76305e9 q^{52} -6.43282e8 q^{53} +1.29162e9 q^{54} +2.79237e9 q^{55} +7.66909e9 q^{56} +2.54226e9 q^{57} +1.45529e10 q^{58} +7.14924e8 q^{59} -6.97999e9 q^{60} -4.14865e9 q^{61} -1.93526e9 q^{62} +1.25558e9 q^{63} +5.50037e10 q^{64} -2.94844e9 q^{65} -1.28750e10 q^{66} +5.36946e9 q^{67} +1.98542e10 q^{68} -2.46368e9 q^{69} -9.08028e9 q^{70} -1.79208e10 q^{71} +2.12973e10 q^{72} -9.32422e9 q^{73} +4.98425e10 q^{74} -6.39624e9 q^{75} +6.33450e10 q^{76} -1.25157e10 q^{77} +1.35946e10 q^{78} +2.29404e9 q^{79} -9.51936e10 q^{80} +3.48678e9 q^{81} +7.87781e10 q^{82} +4.59676e10 q^{83} +3.12850e10 q^{84} -1.55563e10 q^{85} +9.89381e9 q^{86} +3.92862e10 q^{87} -2.12293e11 q^{88} +3.18049e10 q^{89} -2.52162e10 q^{90} +1.32152e10 q^{91} -6.13869e10 q^{92} -5.22431e9 q^{93} -1.52593e11 q^{94} -4.96323e10 q^{95} +2.59422e11 q^{96} -9.75679e10 q^{97} -1.37291e11 q^{98} -3.47565e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	90.0154	1.98908	0.994539	−	0.104363i	$-0.0332804\pi$
$2$	90.0154	1.98908	0.994539	+	0.104363i	$0.0332804\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	6054.78	2.95643
$5$	−4744.07	−0.678915	−0.339458	−	0.940621i	$-0.610244\pi$
$5$	−4744.07	−0.678915	−0.339458	+	0.940621i	$0.610244\pi$
$6$	21873.7	1.14840
$7$	21263.4	0.478181	0.239091	−	0.970997i	$-0.423151\pi$
$7$	21263.4	0.478181	0.239091	+	0.970997i	$0.423151\pi$
$8$	360672.	3.89150
$9$	59049.0	0.333333
$10$	−427039.	−1.35042
$11$	−588604.	−1.10195	−0.550977	−	0.834521i	$-0.685745\pi$
$11$	−588604.	−1.10195	−0.550977	+	0.834521i	$0.685745\pi$
$12$	1.47131e6	1.70690
$13$	621501.	0.464252	0.232126	−	0.972686i	$-0.425432\pi$
$13$	621501.	0.464252	0.232126	+	0.972686i	$0.425432\pi$
$14$	1.91403e6	0.951140
$15$	−1.15281e6	−0.391972
$16$	2.00658e7	4.78407
$17$	3.27910e6	0.560126	0.280063	−	0.959982i	$-0.409645\pi$
$17$	3.27910e6	0.560126	0.280063	+	0.959982i	$0.409645\pi$
$18$	5.31532e6	0.663026
$19$	1.04620e7	0.969324	0.484662	−	0.874701i	$-0.338943\pi$
$19$	1.04620e7	0.969324	0.484662	+	0.874701i	$0.338943\pi$
$20$	−2.87243e7	−2.00717
$21$	5.16699e6	0.276078
$22$	−5.29834e7	−2.19187
$23$	−1.01386e7	−0.328454	−0.164227	−	0.986423i	$-0.552513\pi$
$23$	−1.01386e7	−0.328454	−0.164227	+	0.986423i	$0.552513\pi$
$24$	8.76432e7	2.24676
$25$	−2.63220e7	−0.539074
$26$	5.59447e7	0.923433
$27$	1.43489e7	0.192450
$28$	1.28745e8	1.41371
$29$	1.61672e8	1.46368	0.731838	−	0.681479i	$-0.238663\pi$
$29$	1.61672e8	1.46368	0.731838	+	0.681479i	$0.238663\pi$
$30$	−1.03771e8	−0.779663
$31$	−2.14992e7	−0.134876	−0.0674378	−	0.997723i	$-0.521482\pi$
$31$	−2.14992e7	−0.134876	−0.0674378	+	0.997723i	$0.521482\pi$
$32$	1.06758e9	5.62438
$33$	−1.43031e8	−0.636213
$34$	2.95170e8	1.11414
$35$	−1.00875e8	−0.324645
$36$	3.57528e8	0.985478
$37$	5.53711e8	1.31272	0.656362	−	0.754446i	$-0.272094\pi$
$37$	5.53711e8	1.31272	0.656362	+	0.754446i	$0.272094\pi$
$38$	9.41740e8	1.92806
$39$	1.51025e8	0.268036
$40$	−1.71105e9	−2.64200
$41$	8.75163e8	1.17972	0.589858	−	0.807507i	$-0.299184\pi$
$41$	8.75163e8	1.17972	0.589858	+	0.807507i	$0.299184\pi$
$42$	4.65109e8	0.549141
$43$	1.09912e8	0.114017	0.0570086	−	0.998374i	$-0.481844\pi$
$43$	1.09912e8	0.114017	0.0570086	+	0.998374i	$0.481844\pi$
$44$	−3.56386e9	−3.25785
$45$	−2.80132e8	−0.226305
$46$	−9.12630e8	−0.653321
$47$	−1.69519e9	−1.07815	−0.539075	−	0.842258i	$-0.681226\pi$
$47$	−1.69519e9	−1.07815	−0.539075	+	0.842258i	$0.681226\pi$
$48$	4.87600e9	2.76208
$49$	−1.52520e9	−0.771343
$50$	−2.36938e9	−1.07226
$51$	7.96822e8	0.323389
$52$	3.76305e9	1.37253
$53$	−6.43282e8	−0.211293	−0.105646	−	0.994404i	$-0.533691\pi$
$53$	−6.43282e8	−0.211293	−0.105646	+	0.994404i	$0.533691\pi$
$54$	1.29162e9	0.382798
$55$	2.79237e9	0.748133
$56$	7.66909e9	1.86084
$57$	2.54226e9	0.559640
$58$	1.45529e10	2.91137
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	−6.97999e9	−1.15884
$61$	−4.14865e9	−0.628916	−0.314458	−	0.949271i	$-0.601823\pi$
$61$	−4.14865e9	−0.628916	−0.314458	+	0.949271i	$0.601823\pi$
$62$	−1.93526e9	−0.268278
$63$	1.25558e9	0.159394
$64$	5.50037e10	6.40327
$65$	−2.94844e9	−0.315188
$66$	−1.28750e10	−1.26548
$67$	5.36946e9	0.485869	0.242934	−	0.970043i	$-0.421890\pi$
$67$	5.36946e9	0.485869	0.242934	+	0.970043i	$0.421890\pi$
$68$	1.98542e10	1.65598
$69$	−2.46368e9	−0.189633
$70$	−9.08028e9	−0.645744
$71$	−1.79208e10	−1.17879	−0.589396	−	0.807844i	$-0.700634\pi$
$71$	−1.79208e10	−1.17879	−0.589396	+	0.807844i	$0.700634\pi$
$72$	2.12973e10	1.29717
$73$	−9.32422e9	−0.526425	−0.263213	−	0.964738i	$-0.584782\pi$
$73$	−9.32422e9	−0.526425	−0.263213	+	0.964738i	$0.584782\pi$
$74$	4.98425e10	2.61111
$75$	−6.39624e9	−0.311234
$76$	6.33450e10	2.86574
$77$	−1.25157e10	−0.526933
$78$	1.35946e10	0.533145
$79$	2.29404e9	0.0838787	0.0419394	−	0.999120i	$-0.486646\pi$
$79$	2.29404e9	0.0838787	0.0419394	+	0.999120i	$0.486646\pi$
$80$	−9.51936e10	−3.24798
$81$	3.48678e9	0.111111
$82$	7.87781e10	2.34655
$83$	4.59676e10	1.28092	0.640460	−	0.767992i	$-0.278744\pi$
$83$	4.59676e10	1.28092	0.640460	+	0.767992i	$0.278744\pi$
$84$	3.12850e10	0.816206
$85$	−1.55563e10	−0.380278
$86$	9.89381e9	0.226789
$87$	3.92862e10	0.845053
$88$	−2.12293e11	−4.28825
$89$	3.18049e10	0.603739	0.301869	−	0.953349i	$-0.402389\pi$
$89$	3.18049e10	0.603739	0.301869	+	0.953349i	$0.402389\pi$
$90$	−2.52162e10	−0.450139
$91$	1.32152e10	0.221997
$92$	−6.13869e10	−0.971052
$93$	−5.22431e9	−0.0778705
$94$	−1.52593e11	−2.14452
$95$	−4.96323e10	−0.658089
$96$	2.59422e11	3.24724
$97$	−9.75679e10	−1.15362	−0.576809	−	0.816879i	$-0.695702\pi$
$97$	−9.75679e10	−1.15362	−0.576809	+	0.816879i	$0.695702\pi$
$98$	−1.37291e11	−1.53426
$99$	−3.47565e10	−0.367318
$100$	−1.59374e11	−1.59374
$101$	9.80401e9	0.0928188	0.0464094	−	0.998923i	$-0.485222\pi$
$101$	9.80401e9	0.0928188	0.0464094	+	0.998923i	$0.485222\pi$
$102$	7.17263e10	0.643246
$103$	−9.59142e10	−0.815226	−0.407613	−	0.913155i	$-0.633639\pi$
$103$	−9.59142e10	−0.815226	−0.407613	+	0.913155i	$0.633639\pi$
$104$	2.24158e11	1.80664
$105$	−2.45126e10	−0.187434
$106$	−5.79053e10	−0.420277
$107$	2.37078e11	1.63411	0.817054	−	0.576561i	$-0.195606\pi$
$107$	2.37078e11	1.63411	0.817054	+	0.576561i	$0.195606\pi$
$108$	8.68794e10	0.568966
$109$	1.03474e11	0.644149	0.322075	−	0.946714i	$-0.395620\pi$
$109$	1.03474e11	0.644149	0.322075	+	0.946714i	$0.395620\pi$
$110$	2.51357e11	1.48810
$111$	1.34552e11	0.757901
$112$	4.26667e11	2.28765
$113$	−3.08231e11	−1.57379	−0.786893	−	0.617090i	$-0.788312\pi$
$113$	−3.08231e11	−1.57379	−0.786893	+	0.617090i	$0.788312\pi$
$114$	2.28843e11	1.11317
$115$	4.80982e10	0.222993
$116$	9.78885e11	4.32726
$117$	3.66990e10	0.154751
$118$	6.43542e10	0.258956
$119$	6.97247e10	0.267842
$120$	−4.15785e11	−1.52536
$121$	6.11425e10	0.214301
$122$	−3.73442e11	−1.25096
$123$	2.12664e11	0.681109
$124$	−1.30173e11	−0.398751
$125$	3.56517e11	1.04490
$126$	1.13022e11	0.317047
$127$	−5.23118e11	−1.40501	−0.702505	−	0.711679i	$-0.747935\pi$
$127$	−5.23118e11	−1.40501	−0.702505	+	0.711679i	$0.747935\pi$
$128$	2.76478e12	7.11223
$129$	2.67087e10	0.0658278
$130$	−2.65405e11	−0.626933
$131$	8.46273e10	0.191654	0.0958271	−	0.995398i	$-0.469450\pi$
$131$	8.46273e10	0.191654	0.0958271	+	0.995398i	$0.469450\pi$
$132$	−8.66019e11	−1.88092
$133$	2.22457e11	0.463513
$134$	4.83334e11	0.966432
$135$	−6.80722e10	−0.130657
$136$	1.18268e12	2.17973
$137$	−7.39998e11	−1.30999	−0.654994	−	0.755634i	$-0.727329\pi$
$137$	−7.39998e11	−1.30999	−0.654994	+	0.755634i	$0.727329\pi$
$138$	−2.21769e11	−0.377195
$139$	−8.02588e11	−1.31193	−0.655966	−	0.754790i	$-0.727739\pi$
$139$	−8.02588e11	−1.31193	−0.655966	+	0.754790i	$0.727739\pi$
$140$	−6.10774e11	−0.959790
$141$	−4.11930e11	−0.622470
$142$	−1.61315e12	−2.34471
$143$	−3.65818e11	−0.511584
$144$	1.18487e12	1.59469
$145$	−7.66981e11	−0.993712
$146$	−8.39323e11	−1.04710
$147$	−3.70623e11	−0.445335
$148$	3.35259e12	3.88098
$149$	7.05576e11	0.787081	0.393541	−	0.919307i	$-0.371250\pi$
$149$	7.05576e11	0.787081	0.393541	+	0.919307i	$0.371250\pi$
$150$	−5.75760e11	−0.619070
$151$	−8.65293e11	−0.896994	−0.448497	−	0.893784i	$-0.648041\pi$
$151$	−8.65293e11	−0.896994	−0.448497	+	0.893784i	$0.648041\pi$
$152$	3.77334e12	3.77213
$153$	1.93628e11	0.186709
$154$	−1.12660e12	−1.04811
$155$	1.01994e11	0.0915691
$156$	9.14422e11	0.792430
$157$	−1.27602e12	−1.06760	−0.533802	−	0.845610i	$-0.679237\pi$
$157$	−1.27602e12	−1.06760	−0.533802	+	0.845610i	$0.679237\pi$
$158$	2.06499e11	0.166841
$159$	−1.56318e11	−0.121990
$160$	−5.06466e12	−3.81848
$161$	−2.15580e11	−0.157061
$162$	3.13864e11	0.221009
$163$	−2.20168e12	−1.49873	−0.749364	−	0.662158i	$-0.769641\pi$
$163$	−2.20168e12	−1.49873	−0.749364	+	0.662158i	$0.769641\pi$
$164$	5.29891e12	3.48775
$165$	6.78547e11	0.431935
$166$	4.13779e12	2.54785
$167$	3.30928e12	1.97148	0.985741	−	0.168272i	$-0.0538186\pi$
$167$	3.30928e12	1.97148	0.985741	+	0.168272i	$0.0538186\pi$
$168$	1.86359e12	1.07436
$169$	−1.40590e12	−0.784470
$170$	−1.40031e12	−0.756404
$171$	6.17770e11	0.323108
$172$	6.65495e11	0.337084
$173$	−9.65749e11	−0.473817	−0.236909	−	0.971532i	$-0.576134\pi$
$173$	−9.65749e11	−0.473817	−0.236909	+	0.971532i	$0.576134\pi$
$174$	3.53636e12	1.68088
$175$	−5.59693e11	−0.257775
$176$	−1.18108e13	−5.27182
$177$	1.73727e11	0.0751646
$178$	2.86293e12	1.20088
$179$	−1.63846e12	−0.666416	−0.333208	−	0.942853i	$-0.608131\pi$
$179$	−1.63846e12	−0.666416	−0.333208	+	0.942853i	$0.608131\pi$
$180$	−1.69614e12	−0.669056
$181$	−3.00300e10	−0.0114901	−0.00574505	−	0.999983i	$-0.501829\pi$
$181$	−3.00300e10	−0.0114901	−0.00574505	+	0.999983i	$0.501829\pi$
$182$	1.18957e12	0.441568
$183$	−1.00812e12	−0.363105
$184$	−3.65670e12	−1.27818
$185$	−2.62684e12	−0.891228
$186$	−4.70268e11	−0.154890
$187$	−1.93009e12	−0.617233
$188$	−1.02640e13	−3.18748
$189$	3.05106e11	0.0920260
$190$	−4.46768e12	−1.30899
$191$	1.05648e12	0.300731	0.150365	−	0.988630i	$-0.451955\pi$
$191$	1.05648e12	0.300731	0.150365	+	0.988630i	$0.451955\pi$
$192$	1.33659e13	3.69693
$193$	6.63183e12	1.78266	0.891329	−	0.453357i	$-0.149774\pi$
$193$	6.63183e12	1.78266	0.891329	+	0.453357i	$0.149774\pi$
$194$	−8.78261e12	−2.29464
$195$	−7.16472e11	−0.181974
$196$	−9.23472e12	−2.28042
$197$	−1.88834e12	−0.453435	−0.226718	−	0.973961i	$-0.572799\pi$
$197$	−1.88834e12	−0.453435	−0.226718	+	0.973961i	$0.572799\pi$
$198$	−3.12862e12	−0.730624
$199$	6.18965e12	1.40596	0.702982	−	0.711207i	$-0.251851\pi$
$199$	6.18965e12	1.40596	0.702982	+	0.711207i	$0.251851\pi$
$200$	−9.49358e12	−2.09781
$201$	1.30478e12	0.280517
$202$	8.82512e11	0.184624
$203$	3.43768e12	0.699902
$204$	4.82458e12	0.956078
$205$	−4.15183e12	−0.800928
$206$	−8.63376e12	−1.62155
$207$	−5.98674e11	−0.109485
$208$	1.24709e13	2.22101
$209$	−6.15796e12	−1.06815
$210$	−2.20651e12	−0.372820
$211$	−4.68349e12	−0.770931	−0.385466	−	0.922722i	$-0.625959\pi$
$211$	−4.68349e12	−0.770931	−0.385466	+	0.922722i	$0.625959\pi$
$212$	−3.89493e12	−0.624672
$213$	−4.35476e12	−0.680576
$214$	2.13407e13	3.25037
$215$	−5.21432e11	−0.0774080
$216$	5.17524e12	0.748920
$217$	−4.57145e11	−0.0644950
$218$	9.31428e12	1.28126
$219$	−2.26578e12	−0.303932
$220$	1.69072e13	2.21181
$221$	2.03797e12	0.260040
$222$	1.21117e13	1.50753
$223$	4.76732e12	0.578892	0.289446	−	0.957194i	$-0.406529\pi$
$223$	4.76732e12	0.578892	0.289446	+	0.957194i	$0.406529\pi$
$224$	2.27003e13	2.68947
$225$	−1.55429e12	−0.179691
$226$	−2.77456e13	−3.13038
$227$	1.17328e13	1.29199	0.645995	−	0.763342i	$-0.276443\pi$
$227$	1.17328e13	1.29199	0.645995	+	0.763342i	$0.276443\pi$
$228$	1.53928e13	1.65454
$229$	−1.16508e13	−1.22253	−0.611267	−	0.791425i	$-0.709340\pi$
$229$	−1.16508e13	−1.22253	−0.611267	+	0.791425i	$0.709340\pi$
$230$	4.32958e12	0.443550
$231$	−3.04131e12	−0.304225
$232$	5.83104e13	5.69589
$233$	−2.40369e12	−0.229309	−0.114654	−	0.993405i	$-0.536576\pi$
$233$	−2.40369e12	−0.229309	−0.114654	+	0.993405i	$0.536576\pi$
$234$	3.30348e12	0.307811
$235$	8.04207e12	0.731972
$236$	4.32871e12	0.384895
$237$	5.57451e11	0.0484274
$238$	6.27630e12	0.532759
$239$	−1.15411e13	−0.957321	−0.478661	−	0.878000i	$-0.658878\pi$
$239$	−1.15411e13	−0.957321	−0.478661	+	0.878000i	$0.658878\pi$
$240$	−2.31320e13	−1.87522
$241$	−1.59399e13	−1.26297	−0.631484	−	0.775389i	$-0.717554\pi$
$241$	−1.59399e13	−1.26297	−0.631484	+	0.775389i	$0.717554\pi$
$242$	5.50377e12	0.426261
$243$	8.47289e11	0.0641500
$244$	−2.51191e13	−1.85935
$245$	7.23563e12	0.523677
$246$	1.91431e13	1.35478
$247$	6.50214e12	0.450011
$248$	−7.75416e12	−0.524868
$249$	1.11701e13	0.739539
$250$	3.20920e13	2.07839
$251$	1.99313e13	1.26279	0.631394	−	0.775462i	$-0.282483\pi$
$251$	1.99313e13	1.26279	0.631394	+	0.775462i	$0.282483\pi$
$252$	7.60225e12	0.471237
$253$	5.96761e12	0.361941
$254$	−4.70887e13	−2.79467
$255$	−3.78018e12	−0.219554
$256$	1.36225e14	7.74351
$257$	−1.15688e13	−0.643657	−0.321829	−	0.946798i	$-0.604298\pi$
$257$	−1.15688e13	−0.643657	−0.321829	+	0.946798i	$0.604298\pi$
$258$	2.40420e12	0.130937
$259$	1.17737e13	0.627720
$260$	−1.78522e13	−0.931832
$261$	9.54655e12	0.487892
$262$	7.61776e12	0.381215
$263$	2.50884e13	1.22947	0.614733	−	0.788735i	$-0.289264\pi$
$263$	2.50884e13	1.22947	0.614733	+	0.788735i	$0.289264\pi$
$264$	−5.15871e13	−2.47582
$265$	3.05177e12	0.143450
$266$	2.00245e13	0.921963
$267$	7.72859e12	0.348569
$268$	3.25109e13	1.43644
$269$	2.63018e13	1.13854	0.569270	−	0.822151i	$-0.307226\pi$
$269$	2.63018e13	1.13854	0.569270	+	0.822151i	$0.307226\pi$
$270$	−6.12754e12	−0.259888
$271$	−3.39473e13	−1.41083	−0.705414	−	0.708796i	$-0.749239\pi$
$271$	−3.39473e13	−1.41083	−0.705414	+	0.708796i	$0.749239\pi$
$272$	6.57979e13	2.67968
$273$	3.21129e12	0.128170
$274$	−6.66113e13	−2.60567
$275$	1.54932e13	0.594034
$276$	−1.49170e13	−0.560637
$277$	1.29011e13	0.475323	0.237662	−	0.971348i	$-0.423619\pi$
$277$	1.29011e13	0.475323	0.237662	+	0.971348i	$0.423619\pi$
$278$	−7.22453e13	−2.60954
$279$	−1.26951e12	−0.0449585
$280$	−3.63827e13	−1.26335
$281$	−2.41900e13	−0.823667	−0.411833	−	0.911259i	$-0.635111\pi$
$281$	−2.41900e13	−0.823667	−0.411833	+	0.911259i	$0.635111\pi$
$282$	−3.70801e13	−1.23814
$283$	−4.58976e13	−1.50302	−0.751509	−	0.659723i	$-0.770674\pi$
$283$	−4.58976e13	−1.50302	−0.751509	+	0.659723i	$0.770674\pi$
$284$	−1.08507e14	−3.48502
$285$	−1.20607e13	−0.379948
$286$	−3.29293e13	−1.01758
$287$	1.86089e13	0.564118
$288$	6.30394e13	1.87479
$289$	−2.35194e13	−0.686258
$290$	−6.90401e13	−1.97657
$291$	−2.37090e13	−0.666042
$292$	−5.64560e13	−1.55634
$293$	−4.78140e13	−1.29355	−0.646775	−	0.762681i	$-0.723883\pi$
$293$	−4.78140e13	−1.29355	−0.646775	+	0.762681i	$0.723883\pi$
$294$	−3.33618e13	−0.885806
$295$	−3.39165e12	−0.0883873
$296$	1.99708e14	5.10846
$297$	−8.44582e12	−0.212071
$298$	6.35128e13	1.56557
$299$	−6.30115e12	−0.152485
$300$	−3.87278e13	−0.920144
$301$	2.33711e12	0.0545208
$302$	−7.78897e13	−1.78419
$303$	2.38237e12	0.0535890
$304$	2.09928e14	4.63731
$305$	1.96815e13	0.426981
$306$	1.74295e13	0.371378
$307$	5.44154e13	1.13883	0.569417	−	0.822049i	$-0.307169\pi$
$307$	5.44154e13	1.13883	0.569417	+	0.822049i	$0.307169\pi$
$308$	−7.57797e13	−1.55784
$309$	−2.33072e13	−0.470671
$310$	9.18101e12	0.182138
$311$	−8.40639e12	−0.163843	−0.0819214	−	0.996639i	$-0.526106\pi$
$311$	−8.40639e12	−0.163843	−0.0819214	+	0.996639i	$0.526106\pi$
$312$	5.44704e13	1.04306
$313$	3.17403e12	0.0597196	0.0298598	−	0.999554i	$-0.490494\pi$
$313$	3.17403e12	0.0597196	0.0298598	+	0.999554i	$0.490494\pi$
$314$	−1.14862e14	−2.12355
$315$	−5.95655e12	−0.108215
$316$	1.38899e13	0.247982
$317$	−7.69862e13	−1.35079	−0.675394	−	0.737457i	$-0.736026\pi$
$317$	−7.69862e13	−1.35079	−0.675394	+	0.737457i	$0.736026\pi$
$318$	−1.40710e13	−0.242647
$319$	−9.51605e13	−1.61290
$320$	−2.60941e14	−4.34728
$321$	5.76100e13	0.943453
$322$	−1.94056e13	−0.312406
$323$	3.43059e13	0.542944
$324$	2.11117e13	0.328493
$325$	−1.63591e13	−0.250266
$326$	−1.98185e14	−2.98109
$327$	2.51442e13	0.371900
$328$	3.15646e14	4.59087
$329$	−3.60453e13	−0.515551
$330$	6.10797e13	0.859152
$331$	1.08163e14	1.49632	0.748158	−	0.663521i	$-0.230939\pi$
$331$	1.08163e14	1.49632	0.748158	+	0.663521i	$0.230939\pi$
$332$	2.78323e14	3.78695
$333$	3.26961e13	0.437575
$334$	2.97886e14	3.92143
$335$	−2.54731e13	−0.329864
$336$	1.03680e14	1.32078
$337$	−9.40925e13	−1.17921	−0.589604	−	0.807692i	$-0.700716\pi$
$337$	−9.40925e13	−1.17921	−0.589604	+	0.807692i	$0.700716\pi$
$338$	−1.26552e14	−1.56037
$339$	−7.49003e13	−0.908626
$340$	−9.41898e13	−1.12427
$341$	1.26545e13	0.148627
$342$	5.56088e13	0.642687
$343$	−7.44754e13	−0.847023
$344$	3.96423e13	0.443698
$345$	1.16879e13	0.128745
$346$	−8.69323e13	−0.942460
$347$	6.85093e13	0.731034	0.365517	−	0.930805i	$-0.380892\pi$
$347$	6.85093e13	0.731034	0.365517	+	0.930805i	$0.380892\pi$
$348$	2.37869e14	2.49834
$349$	−2.38246e13	−0.246312	−0.123156	−	0.992387i	$-0.539302\pi$
$349$	−2.38246e13	−0.246312	−0.123156	+	0.992387i	$0.539302\pi$
$350$	−5.03810e13	−0.512735
$351$	8.91787e12	0.0893453
$352$	−6.28380e14	−6.19781
$353$	−7.75626e13	−0.753167	−0.376584	−	0.926383i	$-0.622901\pi$
$353$	−7.75626e13	−0.753167	−0.376584	+	0.926383i	$0.622901\pi$
$354$	1.56381e13	0.149508
$355$	8.50176e13	0.800300
$356$	1.92572e14	1.78491
$357$	1.69431e13	0.154639
$358$	−1.47487e14	−1.32555
$359$	−8.23546e13	−0.728901	−0.364450	−	0.931223i	$-0.618743\pi$
$359$	−8.23546e13	−0.728901	−0.364450	+	0.931223i	$0.618743\pi$
$360$	−1.01036e14	−0.880667
$361$	−7.03719e12	−0.0604101
$362$	−2.70317e12	−0.0228547
$363$	1.48576e13	0.123727
$364$	8.00151e13	0.656318
$365$	4.42347e13	0.357398
$366$	−9.07465e13	−0.722244
$367$	5.25620e13	0.412106	0.206053	−	0.978541i	$-0.433938\pi$
$367$	5.25620e13	0.412106	0.206053	+	0.978541i	$0.433938\pi$
$368$	−2.03439e14	−1.57135
$369$	5.16775e13	0.393239
$370$	−2.36456e14	−1.77272
$371$	−1.36783e13	−0.101036
$372$	−3.16320e13	−0.230219
$373$	1.05859e14	0.759156	0.379578	−	0.925160i	$-0.376069\pi$
$373$	1.05859e14	0.759156	0.379578	+	0.925160i	$0.376069\pi$
$374$	−1.73738e14	−1.22772
$375$	8.66336e13	0.603274
$376$	−6.11405e14	−4.19562
$377$	1.00479e14	0.679514
$378$	2.74642e13	0.183047
$379$	−1.98561e14	−1.30430	−0.652151	−	0.758090i	$-0.726133\pi$
$379$	−1.98561e14	−1.30430	−0.652151	+	0.758090i	$0.726133\pi$
$380$	−3.00513e14	−1.94560
$381$	−1.27118e14	−0.811183
$382$	9.50996e13	0.598177
$383$	−3.16269e14	−1.96094	−0.980468	−	0.196677i	$-0.936985\pi$
$383$	−3.16269e14	−1.96094	−0.980468	+	0.196677i	$0.936985\pi$
$384$	6.71842e14	4.10625
$385$	5.93752e13	0.357743
$386$	5.96967e14	3.54585
$387$	6.49022e12	0.0380057
$388$	−5.90752e14	−3.41060
$389$	−1.20875e14	−0.688043	−0.344021	−	0.938962i	$-0.611789\pi$
$389$	−1.20875e14	−0.688043	−0.344021	+	0.938962i	$0.611789\pi$
$390$	−6.44935e13	−0.361960
$391$	−3.32455e13	−0.183976
$392$	−5.50095e14	−3.00168
$393$	2.05644e13	0.110652
$394$	−1.69979e14	−0.901918
$395$	−1.08831e13	−0.0569466
$396$	−2.10443e14	−1.08595
$397$	2.87851e14	1.46494	0.732470	−	0.680799i	$-0.238367\pi$
$397$	2.87851e14	1.46494	0.732470	+	0.680799i	$0.238367\pi$
$398$	5.57164e14	2.79657
$399$	5.40570e13	0.267609
$400$	−5.28172e14	−2.57896
$401$	−2.75577e14	−1.32724	−0.663620	−	0.748070i	$-0.730981\pi$
$401$	−2.75577e14	−1.32724	−0.663620	+	0.748070i	$0.730981\pi$
$402$	1.17450e14	0.557970
$403$	−1.33618e13	−0.0626162
$404$	5.93611e13	0.274413
$405$	−1.65415e13	−0.0754351
$406$	3.09444e14	1.39216
$407$	−3.25916e14	−1.44656
$408$	2.87391e14	1.25847
$409$	1.68315e14	0.727185	0.363592	−	0.931558i	$-0.381550\pi$
$409$	1.68315e14	0.727185	0.363592	+	0.931558i	$0.381550\pi$
$410$	−3.73729e14	−1.59311
$411$	−1.79820e14	−0.756322
$412$	−5.80739e14	−2.41016
$413$	1.52017e13	0.0622539
$414$	−5.38899e13	−0.217774
$415$	−2.18073e14	−0.869636
$416$	6.63501e14	2.61113
$417$	−1.95029e14	−0.757444
$418$	−5.54311e14	−2.12463
$419$	1.78714e14	0.676053	0.338026	−	0.941137i	$-0.390241\pi$
$419$	1.78714e14	0.676053	0.338026	+	0.941137i	$0.390241\pi$
$420$	−1.48418e14	−0.554135
$421$	3.52030e13	0.129726	0.0648632	−	0.997894i	$-0.479339\pi$
$421$	3.52030e13	0.129726	0.0648632	+	0.997894i	$0.479339\pi$
$422$	−4.21586e14	−1.53344
$423$	−1.00099e14	−0.359383
$424$	−2.32014e14	−0.822245
$425$	−8.63124e13	−0.301949
$426$	−3.91996e14	−1.35372
$427$	−8.82142e13	−0.300736
$428$	1.43546e15	4.83113
$429$	−8.88938e13	−0.295363
$430$	−4.69369e13	−0.153971
$431$	1.56002e14	0.505248	0.252624	−	0.967565i	$-0.418706\pi$
$431$	1.56002e14	0.505248	0.252624	+	0.967565i	$0.418706\pi$
$432$	2.87923e14	0.920694
$433$	−4.45742e14	−1.40734	−0.703672	−	0.710525i	$-0.748458\pi$
$433$	−4.45742e14	−1.40734	−0.703672	+	0.710525i	$0.748458\pi$
$434$	−4.11501e13	−0.128286
$435$	−1.86376e14	−0.573720
$436$	6.26514e14	1.90439
$437$	−1.06070e14	−0.318379
$438$	−2.03956e14	−0.604544
$439$	3.42891e13	0.100369	0.0501846	−	0.998740i	$-0.484019\pi$
$439$	3.42891e13	0.100369	0.0501846	+	0.998740i	$0.484019\pi$
$440$	1.00713e15	2.91136
$441$	−9.00613e13	−0.257114
$442$	1.83448e14	0.517239
$443$	3.69424e14	1.02874	0.514369	−	0.857569i	$-0.328026\pi$
$443$	3.69424e14	1.02874	0.514369	+	0.857569i	$0.328026\pi$
$444$	8.14680e14	2.24068
$445$	−1.50885e14	−0.409888
$446$	4.29132e14	1.15146
$447$	1.71455e14	0.454422
$448$	1.16956e15	3.06192
$449$	5.78238e14	1.49538	0.747691	−	0.664047i	$-0.231163\pi$
$449$	5.78238e14	1.49538	0.747691	+	0.664047i	$0.231163\pi$
$450$	−1.39910e14	−0.357420
$451$	−5.15124e14	−1.29999
$452$	−1.86627e15	−4.65279
$453$	−2.10266e14	−0.517880
$454$	1.05613e15	2.56987
$455$	−6.26938e13	−0.150717
$456$	9.16922e14	2.17784
$457$	5.45503e14	1.28014	0.640071	−	0.768316i	$-0.278905\pi$
$457$	5.45503e14	1.28014	0.640071	+	0.768316i	$0.278905\pi$
$458$	−1.04875e15	−2.43172
$459$	4.70515e13	0.107796
$460$	2.91224e14	0.659263
$461$	1.67172e14	0.373947	0.186973	−	0.982365i	$-0.440132\pi$
$461$	1.67172e14	0.373947	0.186973	+	0.982365i	$0.440132\pi$
$462$	−2.73765e14	−0.605128
$463$	−6.81858e14	−1.48935	−0.744677	−	0.667425i	$-0.767397\pi$
$463$	−6.81858e14	−1.48935	−0.744677	+	0.667425i	$0.767397\pi$
$464$	3.24407e15	7.00232
$465$	2.47845e13	0.0528675
$466$	−2.16369e14	−0.456114
$467$	4.20182e14	0.875377	0.437688	−	0.899127i	$-0.355797\pi$
$467$	4.20182e14	0.875377	0.437688	+	0.899127i	$0.355797\pi$
$468$	2.22204e14	0.457510
$469$	1.14173e14	0.232333
$470$	7.23910e14	1.45595
$471$	−3.10073e14	−0.616381
$472$	2.57853e14	0.506630
$473$	−6.46948e13	−0.125642
$474$	5.01792e13	0.0963259
$475$	−2.75380e14	−0.522537
$476$	4.22168e14	0.791857
$477$	−3.79852e13	−0.0704308
$478$	−1.03887e15	−1.90419
$479$	−8.59317e14	−1.55707	−0.778535	−	0.627601i	$-0.784037\pi$
$479$	−8.59317e14	−1.55707	−0.778535	+	0.627601i	$0.784037\pi$
$480$	−1.23071e15	−2.20460
$481$	3.44132e14	0.609434
$482$	−1.43484e15	−2.51214
$483$	−5.23861e13	−0.0906789
$484$	3.70204e14	0.633566
$485$	4.62868e14	0.783210
$486$	7.62690e13	0.127599
$487$	1.41922e14	0.234768	0.117384	−	0.993087i	$-0.462549\pi$
$487$	1.41922e14	0.234768	0.117384	+	0.993087i	$0.462549\pi$
$488$	−1.49630e15	−2.44743
$489$	−5.35009e14	−0.865291
$490$	6.51319e14	1.04163
$491$	4.48121e14	0.708675	0.354338	−	0.935118i	$-0.384706\pi$
$491$	4.48121e14	0.708675	0.354338	+	0.935118i	$0.384706\pi$
$492$	1.28764e15	2.01365
$493$	5.30138e14	0.819843
$494$	5.85293e14	0.895107
$495$	1.64887e14	0.249378
$496$	−4.31400e14	−0.645254
$497$	−3.81057e14	−0.563676
$498$	1.00548e15	1.47100
$499$	−8.99589e14	−1.30164	−0.650821	−	0.759232i	$-0.725575\pi$
$499$	−8.99589e14	−1.30164	−0.650821	+	0.759232i	$0.725575\pi$
$500$	2.15863e15	3.08918
$501$	8.04155e14	1.13824
$502$	1.79412e15	2.51178
$503$	−1.10437e15	−1.52930	−0.764649	−	0.644446i	$-0.777088\pi$
$503$	−1.10437e15	−1.52930	−0.764649	+	0.644446i	$0.777088\pi$
$504$	4.52852e14	0.620281
$505$	−4.65109e13	−0.0630161
$506$	5.37177e14	0.719929
$507$	−3.41633e14	−0.452914
$508$	−3.16736e15	−4.15382
$509$	−7.82388e14	−1.01502	−0.507510	−	0.861646i	$-0.669434\pi$
$509$	−7.82388e14	−1.01502	−0.507510	+	0.861646i	$0.669434\pi$
$510$	−3.40274e14	−0.436710
$511$	−1.98264e14	−0.251727
$512$	6.60011e15	8.29022
$513$	1.50118e14	0.186547
$514$	−1.04137e15	−1.28029
$515$	4.55023e14	0.553470
$516$	1.61715e14	0.194616
$517$	9.97792e14	1.18807
$518$	1.05982e15	1.24858
$519$	−2.34677e14	−0.273559
$520$	−1.06342e15	−1.22655
$521$	2.20872e14	0.252077	0.126039	−	0.992025i	$-0.459774\pi$
$521$	2.20872e14	0.252077	0.126039	+	0.992025i	$0.459774\pi$
$522$	8.59336e14	0.970455
$523$	6.53132e14	0.729864	0.364932	−	0.931034i	$-0.381092\pi$
$523$	6.53132e14	0.729864	0.364932	+	0.931034i	$0.381092\pi$
$524$	5.12399e14	0.566613
$525$	−1.36005e14	−0.148826
$526$	2.25834e15	2.44551
$527$	−7.04981e13	−0.0755474
$528$	−2.87003e15	−3.04368
$529$	−8.50019e14	−0.892118
$530$	2.74707e14	0.285333
$531$	4.22156e13	0.0433963
$532$	1.34693e15	1.37034
$533$	5.43915e14	0.547685
$534$	6.95692e14	0.693330
$535$	−1.12471e15	−1.10942
$536$	1.93661e15	1.89076
$537$	−3.98147e14	−0.384755
$538$	2.36757e15	2.26465
$539$	8.97736e14	0.849984
$540$	−4.12162e14	−0.386280
$541$	−1.55078e14	−0.143868	−0.0719342	−	0.997409i	$-0.522917\pi$
$541$	−1.55078e14	−0.143868	−0.0719342	+	0.997409i	$0.522917\pi$
$542$	−3.05578e15	−2.80625
$543$	−7.29730e12	−0.00663381
$544$	3.50070e15	3.15036
$545$	−4.90889e14	−0.437323
$546$	2.89066e14	0.254940
$547$	1.57164e15	1.37222	0.686108	−	0.727499i	$-0.259318\pi$
$547$	1.57164e15	1.37222	0.686108	+	0.727499i	$0.259318\pi$
$548$	−4.48052e15	−3.87289
$549$	−2.44974e14	−0.209639
$550$	1.39463e15	1.18158
$551$	1.69141e15	1.41878
$552$	−8.88579e14	−0.737957
$553$	4.87790e13	0.0401092
$554$	1.16130e15	0.945456
$555$	−6.38322e14	−0.514551
$556$	−4.85949e15	−3.87864
$557$	−1.96635e15	−1.55402	−0.777009	−	0.629489i	$-0.783264\pi$
$557$	−1.96635e15	−1.55402	−0.777009	+	0.629489i	$0.783264\pi$
$558$	−1.14275e14	−0.0894260
$559$	6.83107e13	0.0529327
$560$	−2.02413e15	−1.55312
$561$	−4.69012e14	−0.356360
$562$	−2.17748e15	−1.63834
$563$	−2.25469e15	−1.67993	−0.839963	−	0.542643i	$-0.817423\pi$
$563$	−2.25469e15	−1.67993	−0.839963	+	0.542643i	$0.817423\pi$
$564$	−2.49414e15	−1.84029
$565$	1.46227e15	1.06847
$566$	−4.13149e15	−2.98962
$567$	7.41407e13	0.0531312
$568$	−6.46354e15	−4.58727
$569$	1.96100e15	1.37835	0.689176	−	0.724594i	$-0.257973\pi$
$569$	1.96100e15	1.37835	0.689176	+	0.724594i	$0.257973\pi$
$570$	−1.08565e15	−0.755747
$571$	−1.59452e15	−1.09934	−0.549669	−	0.835382i	$-0.685246\pi$
$571$	−1.59452e15	−1.09934	−0.549669	+	0.835382i	$0.685246\pi$
$572$	−2.21495e15	−1.51246
$573$	2.56725e14	0.173627
$574$	1.67509e15	1.12208
$575$	2.66868e14	0.177061
$576$	3.24791e15	2.13442
$577$	9.92961e14	0.646346	0.323173	−	0.946340i	$-0.395250\pi$
$577$	9.92961e14	0.646346	0.323173	+	0.946340i	$0.395250\pi$
$578$	−2.11711e15	−1.36502
$579$	1.61153e15	1.02922
$580$	−4.64390e15	−2.93784
$581$	9.77424e14	0.612512
$582$	−2.13417e15	−1.32481
$583$	3.78638e14	0.232834
$584$	−3.36298e15	−2.04858
$585$	−1.74103e14	−0.105063
$586$	−4.30399e15	−2.57297
$587$	7.38416e14	0.437312	0.218656	−	0.975802i	$-0.429833\pi$
$587$	7.38416e14	0.437312	0.218656	+	0.975802i	$0.429833\pi$
$588$	−2.24404e15	−1.31660
$589$	−2.24924e14	−0.130738
$590$	−3.05301e14	−0.175809
$591$	−4.58866e14	−0.261791
$592$	1.11107e16	6.28016
$593$	−2.79759e14	−0.156669	−0.0783345	−	0.996927i	$-0.524960\pi$
$593$	−2.79759e14	−0.156669	−0.0783345	+	0.996927i	$0.524960\pi$
$594$	−7.60254e14	−0.421826
$595$	−3.30779e14	−0.181842
$596$	4.27211e15	2.32695
$597$	1.50409e15	0.811734
$598$	−5.67201e14	−0.303305
$599$	−2.24022e15	−1.18698	−0.593490	−	0.804842i	$-0.702250\pi$
$599$	−2.24022e15	−1.18698	−0.593490	+	0.804842i	$0.702250\pi$
$600$	−2.30694e15	−1.21117
$601$	9.90368e14	0.515213	0.257607	−	0.966250i	$-0.417066\pi$
$601$	9.90368e14	0.515213	0.257607	+	0.966250i	$0.417066\pi$
$602$	2.10376e14	0.108446
$603$	3.17061e14	0.161956
$604$	−5.23915e15	−2.65190
$605$	−2.90064e14	−0.145492
$606$	2.14450e14	0.106593
$607$	3.52329e15	1.73544	0.867722	−	0.497050i	$-0.165583\pi$
$607$	3.52329e15	1.73544	0.867722	+	0.497050i	$0.165583\pi$
$608$	1.11690e16	5.45185
$609$	8.35356e14	0.404089
$610$	1.77164e15	0.849298
$611$	−1.05356e15	−0.500533
$612$	1.17237e15	0.551992
$613$	6.22851e14	0.290637	0.145319	−	0.989385i	$-0.453579\pi$
$613$	6.22851e14	0.290637	0.145319	+	0.989385i	$0.453579\pi$
$614$	4.89822e15	2.26523
$615$	−1.00889e15	−0.462416
$616$	−4.51405e15	−2.05056
$617$	2.26300e15	1.01886	0.509432	−	0.860511i	$-0.329855\pi$
$617$	2.26300e15	1.01886	0.509432	+	0.860511i	$0.329855\pi$
$618$	−2.09800e15	−0.936202
$619$	7.67582e14	0.339489	0.169745	−	0.985488i	$-0.445706\pi$
$619$	7.67582e14	0.339489	0.169745	+	0.985488i	$0.445706\pi$
$620$	6.17549e14	0.270718
$621$	−1.45478e14	−0.0632110
$622$	−7.56704e14	−0.325896
$623$	6.76279e14	0.288696
$624$	3.03044e15	1.28230
$625$	−4.06088e14	−0.170326
$626$	2.85711e14	0.118787
$627$	−1.49638e15	−0.616697
$628$	−7.72603e15	−3.15630
$629$	1.81567e15	0.735291
$630$	−5.36182e14	−0.215248
$631$	−6.54986e14	−0.260658	−0.130329	−	0.991471i	$-0.541603\pi$
$631$	−6.54986e14	−0.260658	−0.130329	+	0.991471i	$0.541603\pi$
$632$	8.27395e14	0.326414
$633$	−1.13809e15	−0.445097
$634$	−6.92995e15	−2.68682
$635$	2.48171e15	0.953883
$636$	−9.46468e14	−0.360655
$637$	−9.47912e14	−0.358097
$638$	−8.56591e15	−3.20819
$639$	−1.05821e15	−0.392931
$640$	−1.31163e16	−4.82860
$641$	2.56665e15	0.936800	0.468400	−	0.883517i	$-0.344831\pi$
$641$	2.56665e15	0.936800	0.468400	+	0.883517i	$0.344831\pi$
$642$	5.18579e15	1.87660
$643$	−1.92275e14	−0.0689863	−0.0344932	−	0.999405i	$-0.510982\pi$
$643$	−1.92275e14	−0.0689863	−0.0344932	+	0.999405i	$0.510982\pi$
$644$	−1.30529e15	−0.464339
$645$	−1.26708e14	−0.0446915
$646$	3.08806e15	1.07996
$647$	3.87327e15	1.34309	0.671543	−	0.740965i	$-0.265632\pi$
$647$	3.87327e15	1.34309	0.671543	+	0.740965i	$0.265632\pi$
$648$	1.25758e15	0.432389
$649$	−4.20807e14	−0.143462
$650$	−1.47257e15	−0.497799
$651$	−1.11086e14	−0.0372362
$652$	−1.33307e16	−4.43089
$653$	3.72959e15	1.22925	0.614623	−	0.788821i	$-0.289308\pi$
$653$	3.72959e15	1.22925	0.614623	+	0.788821i	$0.289308\pi$
$654$	2.26337e15	0.739738
$655$	−4.01478e14	−0.130117
$656$	1.75609e16	5.64384
$657$	−5.50586e14	−0.175475
$658$	−3.24463e15	−1.02547
$659$	3.54547e15	1.11123	0.555615	−	0.831440i	$-0.312483\pi$
$659$	3.54547e15	1.11123	0.555615	+	0.831440i	$0.312483\pi$
$660$	4.10845e15	1.27699
$661$	5.28845e15	1.63012	0.815061	−	0.579374i	$-0.196703\pi$
$661$	5.28845e15	1.63012	0.815061	+	0.579374i	$0.196703\pi$
$662$	9.73630e15	2.97629
$663$	4.95226e14	0.150134
$664$	1.65792e16	4.98470
$665$	−1.05535e15	−0.314686
$666$	2.94315e15	0.870370
$667$	−1.63912e15	−0.480750
$668$	2.00369e16	5.82855
$669$	1.15846e15	0.334223
$670$	−2.29297e15	−0.656125
$671$	2.44191e15	0.693036
$672$	5.51617e15	1.55277
$673$	−2.32076e15	−0.647959	−0.323979	−	0.946064i	$-0.605021\pi$
$673$	−2.32076e15	−0.647959	−0.323979	+	0.946064i	$0.605021\pi$
$674$	−8.46978e15	−2.34554
$675$	−3.77691e14	−0.103745
$676$	−8.51239e15	−2.31923
$677$	−3.30853e15	−0.894122	−0.447061	−	0.894503i	$-0.647529\pi$
$677$	−3.30853e15	−0.894122	−0.447061	+	0.894503i	$0.647529\pi$
$678$	−6.74218e15	−1.80733
$679$	−2.07462e15	−0.551639
$680$	−5.61071e15	−1.47985
$681$	2.85107e15	0.745930
$682$	1.13910e15	0.295630
$683$	−6.50721e15	−1.67526	−0.837628	−	0.546241i	$-0.816058\pi$
$683$	−6.50721e15	−1.67526	−0.837628	+	0.546241i	$0.816058\pi$
$684$	3.74046e15	0.955248
$685$	3.51060e15	0.889372
$686$	−6.70393e15	−1.68479
$687$	−2.83115e15	−0.705830
$688$	2.20548e15	0.545465
$689$	−3.99801e14	−0.0980929
$690$	1.05209e15	0.256084
$691$	2.39777e15	0.579000	0.289500	−	0.957178i	$-0.406511\pi$
$691$	2.39777e15	0.579000	0.289500	+	0.957178i	$0.406511\pi$
$692$	−5.84740e15	−1.40081
$693$	−7.39039e14	−0.175644
$694$	6.16689e15	1.45408
$695$	3.80753e15	0.890691
$696$	1.41694e16	3.28852
$697$	2.86975e15	0.660790
$698$	−2.14458e15	−0.489934
$699$	−5.84097e14	−0.132392
$700$	−3.38882e15	−0.762094
$701$	7.29132e15	1.62689	0.813443	−	0.581645i	$-0.197591\pi$
$701$	7.29132e15	1.62689	0.813443	+	0.581645i	$0.197591\pi$
$702$	8.02745e14	0.177715
$703$	5.79291e15	1.27246
$704$	−3.23754e16	−7.05611
$705$	1.95422e15	0.422604
$706$	−6.98183e15	−1.49811
$707$	2.08466e14	0.0443842
$708$	1.05188e15	0.222219
$709$	4.81756e15	1.00989	0.504944	−	0.863152i	$-0.331513\pi$
$709$	4.81756e15	1.00989	0.504944	+	0.863152i	$0.331513\pi$
$710$	7.65290e15	1.59186
$711$	1.35461e14	0.0279596
$712$	1.14711e16	2.34945
$713$	2.17972e14	0.0443004
$714$	1.52514e15	0.307588
$715$	1.73546e15	0.347322
$716$	−9.92053e15	−1.97021
$717$	−2.80448e15	−0.552710
$718$	−7.41319e15	−1.44984
$719$	3.86958e14	0.0751027	0.0375513	−	0.999295i	$-0.488044\pi$
$719$	3.86958e14	0.0751027	0.0375513	+	0.999295i	$0.488044\pi$
$720$	−5.62109e15	−1.08266
$721$	−2.03946e15	−0.389826
$722$	−6.33455e14	−0.120160
$723$	−3.87340e15	−0.729175
$724$	−1.81825e14	−0.0339697
$725$	−4.25551e15	−0.789029
$726$	1.33742e15	0.246102
$727$	8.85033e15	1.61629	0.808147	−	0.588981i	$-0.200471\pi$
$727$	8.85033e15	1.61629	0.808147	+	0.588981i	$0.200471\pi$
$728$	4.76635e15	0.863899
$729$	2.05891e14	0.0370370
$730$	3.98180e15	0.710893
$731$	3.60414e14	0.0638640
$732$	−6.10395e15	−1.07350
$733$	−8.82369e14	−0.154020	−0.0770102	−	0.997030i	$-0.524537\pi$
$733$	−8.82369e14	−0.154020	−0.0770102	+	0.997030i	$0.524537\pi$
$734$	4.73139e15	0.819711
$735$	1.75826e15	0.302345
$736$	−1.08237e16	−1.84735
$737$	−3.16048e15	−0.535405
$738$	4.65177e15	0.782183
$739$	−8.70042e15	−1.45210	−0.726049	−	0.687643i	$-0.758645\pi$
$739$	−8.70042e15	−1.45210	−0.726049	+	0.687643i	$0.758645\pi$
$740$	−1.59049e16	−2.63486
$741$	1.58002e15	0.259814
$742$	−1.23126e15	−0.200969
$743$	−1.20333e14	−0.0194961	−0.00974803	−	0.999952i	$-0.503103\pi$
$743$	−1.20333e14	−0.0194961	−0.00974803	+	0.999952i	$0.503103\pi$
$744$	−1.88426e15	−0.303033
$745$	−3.34730e15	−0.534362
$746$	9.52898e15	1.51002
$747$	2.71434e15	0.426973
$748$	−1.16863e16	−1.82481
$749$	5.04108e15	0.781400
$750$	7.79836e15	1.19996
$751$	5.43170e15	0.829691	0.414846	−	0.909892i	$-0.363836\pi$
$751$	5.43170e15	0.829691	0.414846	+	0.909892i	$0.363836\pi$
$752$	−3.40153e16	−5.15794
$753$	4.84331e15	0.729071
$754$	9.04467e15	1.35161
$755$	4.10501e15	0.608983
$756$	1.84735e15	0.272069
$757$	−6.39731e15	−0.935340	−0.467670	−	0.883903i	$-0.654907\pi$
$757$	−6.39731e15	−0.935340	−0.467670	+	0.883903i	$0.654907\pi$
$758$	−1.78735e16	−2.59436
$759$	1.45013e15	0.208967
$760$	−1.79010e16	−2.56095
$761$	5.88991e15	0.836552	0.418276	−	0.908320i	$-0.362634\pi$
$761$	5.88991e15	0.836552	0.418276	+	0.908320i	$0.362634\pi$
$762$	−1.14426e16	−1.61351
$763$	2.20021e15	0.308020
$764$	6.39675e15	0.889091
$765$	−9.18583e14	−0.126759
$766$	−2.84691e16	−3.90046
$767$	4.44326e14	0.0604404
$768$	3.31027e16	4.47072
$769$	6.84426e15	0.917765	0.458883	−	0.888497i	$-0.348250\pi$
$769$	6.84426e15	0.917765	0.458883	+	0.888497i	$0.348250\pi$
$770$	5.34469e15	0.711579
$771$	−2.81121e15	−0.371616
$772$	4.01542e16	5.27031
$773$	−1.31536e15	−0.171418	−0.0857092	−	0.996320i	$-0.527316\pi$
$773$	−1.31536e15	−0.171418	−0.0857092	+	0.996320i	$0.527316\pi$
$774$	5.84220e14	0.0755963
$775$	5.65902e14	0.0727079
$776$	−3.51900e16	−4.48931
$777$	2.86102e15	0.362414
$778$	−1.08807e16	−1.36857
$779$	9.15593e15	1.14353
$780$	−4.33808e15	−0.537993
$781$	1.05483e16	1.29897
$782$	−2.99261e15	−0.365942
$783$	2.31981e15	0.281684
$784$	−3.06043e16	−3.69015
$785$	6.05353e15	0.724813
$786$	1.85112e15	0.220095
$787$	1.08874e16	1.28547	0.642736	−	0.766088i	$-0.277799\pi$
$787$	1.08874e16	1.28547	0.642736	+	0.766088i	$0.277799\pi$
$788$	−1.14335e16	−1.34055
$789$	6.09649e15	0.709833
$790$	−9.79644e14	−0.113271
$791$	−6.55403e15	−0.752555
$792$	−1.25357e16	−1.42942
$793$	−2.57839e15	−0.291975
$794$	2.59110e16	2.91388
$795$	7.41581e14	0.0828208
$796$	3.74770e16	4.15664
$797$	1.09094e16	1.20166	0.600828	−	0.799378i	$-0.294838\pi$
$797$	1.09094e16	1.20166	0.600828	+	0.799378i	$0.294838\pi$
$798$	4.86596e15	0.532296
$799$	−5.55869e15	−0.603900
$800$	−2.81008e16	−3.03196
$801$	1.87805e15	0.201246
$802$	−2.48062e16	−2.63998
$803$	5.48827e15	0.580096
$804$	7.90014e15	0.829329
$805$	1.02273e15	0.106631
$806$	−1.20277e15	−0.124549
$807$	6.39134e15	0.657336
$808$	3.53603e15	0.361205
$809$	−1.02958e16	−1.04459	−0.522293	−	0.852766i	$-0.674923\pi$
$809$	−1.02958e16	−1.04459	−0.522293	+	0.852766i	$0.674923\pi$
$810$	−1.48899e15	−0.150046
$811$	1.19843e16	1.19949	0.599745	−	0.800191i	$-0.295269\pi$
$811$	1.19843e16	1.19949	0.599745	+	0.800191i	$0.295269\pi$
$812$	2.08144e16	2.06921
$813$	−8.24919e15	−0.814542
$814$	−2.93375e16	−2.87732
$815$	1.04449e16	1.01751
$816$	1.59889e16	1.54711
$817$	1.14990e15	0.110520
$818$	1.51509e16	1.44643
$819$	7.80344e14	0.0739988
$820$	−2.51384e16	−2.36789
$821$	1.15068e16	1.07663	0.538316	−	0.842743i	$-0.319061\pi$
$821$	1.15068e16	1.07663	0.538316	+	0.842743i	$0.319061\pi$
$822$	−1.61865e16	−1.50438
$823$	7.52036e15	0.694288	0.347144	−	0.937812i	$-0.387152\pi$
$823$	7.52036e15	0.694288	0.347144	+	0.937812i	$0.387152\pi$
$824$	−3.45935e16	−3.17245
$825$	3.76485e15	0.342966
$826$	1.36839e15	0.123828
$827$	−3.18421e14	−0.0286234	−0.0143117	−	0.999898i	$-0.504556\pi$
$827$	−3.18421e14	−0.0286234	−0.0143117	+	0.999898i	$0.504556\pi$
$828$	−3.62484e15	−0.323684
$829$	3.24172e15	0.287558	0.143779	−	0.989610i	$-0.454075\pi$
$829$	3.24172e15	0.287558	0.143779	+	0.989610i	$0.454075\pi$
$830$	−1.96299e16	−1.72978
$831$	3.13498e15	0.274428
$832$	3.41849e16	2.97273
$833$	−5.00128e15	−0.432049
$834$	−1.75556e16	−1.50662
$835$	−1.56994e16	−1.33847
$836$	−3.72851e16	−3.15791
$837$	−3.08490e14	−0.0259568
$838$	1.60870e16	1.34472
$839$	9.15007e15	0.759860	0.379930	−	0.925015i	$-0.375948\pi$
$839$	9.15007e15	0.759860	0.379930	+	0.925015i	$0.375948\pi$
$840$	−8.84099e15	−0.729398
$841$	1.39372e16	1.14235
$842$	3.16881e15	0.258036
$843$	−5.87818e15	−0.475544
$844$	−2.83575e16	−2.27921
$845$	6.66967e15	0.532589
$846$	−9.01045e15	−0.714841
$847$	1.30009e15	0.102475
$848$	−1.29080e16	−1.01084
$849$	−1.11531e16	−0.867768
$850$	−7.76945e15	−0.600601
$851$	−5.61385e15	−0.431169
$852$	−2.63671e16	−2.01208
$853$	−1.44974e16	−1.09918	−0.549592	−	0.835433i	$-0.685217\pi$
$853$	−1.44974e16	−1.09918	−0.549592	+	0.835433i	$0.685217\pi$
$854$	−7.94064e15	−0.598187
$855$	−2.93074e15	−0.219363
$856$	8.55074e16	6.35913
$857$	2.06155e16	1.52335	0.761674	−	0.647961i	$-0.224378\pi$
$857$	2.06155e16	1.52335	0.761674	+	0.647961i	$0.224378\pi$
$858$	−8.00181e15	−0.587500
$859$	−9.62447e15	−0.702125	−0.351063	−	0.936352i	$-0.614180\pi$
$859$	−9.62447e15	−0.702125	−0.351063	+	0.936352i	$0.614180\pi$
$860$	−3.15715e15	−0.228852
$861$	4.52196e15	0.325694
$862$	1.40426e16	1.00498
$863$	2.06923e15	0.147147	0.0735733	−	0.997290i	$-0.476560\pi$
$863$	2.06923e15	0.147147	0.0735733	+	0.997290i	$0.476560\pi$
$864$	1.53186e16	1.08241
$865$	4.58158e15	0.321682
$866$	−4.01237e16	−2.79932
$867$	−5.71521e15	−0.396212
$868$	−2.76791e15	−0.190675
$869$	−1.35028e15	−0.0924304
$870$	−1.67767e16	−1.14117
$871$	3.33713e15	0.225566
$872$	3.73202e16	2.50671
$873$	−5.76129e15	−0.384540
$874$	−9.54792e15	−0.633280
$875$	7.58075e15	0.499652
$876$	−1.37188e16	−0.898554
$877$	2.48074e16	1.61467	0.807335	−	0.590094i	$-0.200909\pi$
$877$	2.48074e16	1.61467	0.807335	+	0.590094i	$0.200909\pi$
$878$	3.08654e15	0.199642
$879$	−1.16188e16	−0.746831
$880$	5.60313e16	3.57912
$881$	1.23608e16	0.784654	0.392327	−	0.919826i	$-0.371670\pi$
$881$	1.23608e16	0.784654	0.392327	+	0.919826i	$0.371670\pi$
$882$	−8.10691e15	−0.511420
$883$	−1.28976e15	−0.0808585	−0.0404293	−	0.999182i	$-0.512873\pi$
$883$	−1.28976e15	−0.0808585	−0.0404293	+	0.999182i	$0.512873\pi$
$884$	1.23394e16	0.768790
$885$	−8.24171e14	−0.0510304
$886$	3.32538e16	2.04624
$887$	−4.40428e15	−0.269336	−0.134668	−	0.990891i	$-0.542997\pi$
$887$	−4.40428e15	−0.269336	−0.134668	+	0.990891i	$0.542997\pi$
$888$	4.85290e16	2.94937
$889$	−1.11232e16	−0.671849
$890$	−1.35819e16	−0.815298
$891$	−2.05233e15	−0.122439
$892$	2.88650e16	1.71145
$893$	−1.77350e16	−1.04508
$894$	1.54336e16	0.903880
$895$	7.77298e15	0.452440
$896$	5.87885e16	3.40093
$897$	−1.53118e15	−0.0880375
$898$	5.20504e16	2.97443
$899$	−3.47581e15	−0.197414
$900$	−9.41085e15	−0.531245
$901$	−2.10939e15	−0.118351
$902$	−4.63691e16	−2.58579
$903$	5.67917e14	0.0314776
$904$	−1.11170e17	−6.12439
$905$	1.42465e14	0.00780081
$906$	−1.89272e16	−1.03010
$907$	1.98356e16	1.07301	0.536507	−	0.843896i	$-0.319744\pi$
$907$	1.98356e16	1.07301	0.536507	+	0.843896i	$0.319744\pi$
$908$	7.10394e16	3.81968
$909$	5.78917e14	0.0309396
$910$	−5.64341e15	−0.299788
$911$	1.21906e16	0.643684	0.321842	−	0.946793i	$-0.395698\pi$
$911$	1.21906e16	0.643684	0.321842	+	0.946793i	$0.395698\pi$
$912$	5.10126e16	2.67735
$913$	−2.70567e16	−1.41151
$914$	4.91037e16	2.54630
$915$	4.78260e15	0.246517
$916$	−7.05430e16	−3.61434
$917$	1.79946e15	0.0916454
$918$	4.23536e15	0.214415
$919$	−1.73177e16	−0.871476	−0.435738	−	0.900074i	$-0.643513\pi$
$919$	−1.73177e16	−0.871476	−0.435738	+	0.900074i	$0.643513\pi$
$920$	1.73476e16	0.867775
$921$	1.32229e16	0.657507
$922$	1.50481e16	0.743809
$923$	−1.11378e16	−0.547257
$924$	−1.84145e16	−0.899421
$925$	−1.45747e16	−0.707655
$926$	−6.13777e16	−2.96244
$927$	−5.66364e15	−0.271742
$928$	1.72597e17	8.23227
$929$	−2.53708e16	−1.20295	−0.601476	−	0.798891i	$-0.705420\pi$
$929$	−2.53708e16	−1.20295	−0.601476	+	0.798891i	$0.705420\pi$
$930$	2.23098e15	0.105158
$931$	−1.59566e16	−0.747681
$932$	−1.45538e16	−0.677937
$933$	−2.04275e15	−0.0945947
$934$	3.78229e16	1.74119
$935$	9.15648e15	0.419049
$936$	1.32363e16	0.602212
$937$	1.80295e16	0.815484	0.407742	−	0.913097i	$-0.366316\pi$
$937$	1.80295e16	0.815484	0.407742	+	0.913097i	$0.366316\pi$
$938$	1.02773e16	0.462129
$939$	7.71289e14	0.0344791
$940$	4.86929e16	2.16403
$941$	−2.64189e16	−1.16727	−0.583636	−	0.812015i	$-0.698371\pi$
$941$	−2.64189e16	−1.16727	−0.583636	+	0.812015i	$0.698371\pi$
$942$	−2.79114e16	−1.22603
$943$	−8.87292e15	−0.387482
$944$	1.43455e16	0.622832
$945$	−1.44744e15	−0.0624779
$946$	−5.82353e15	−0.249911
$947$	−1.54160e16	−0.657728	−0.328864	−	0.944377i	$-0.606666\pi$
$947$	−1.54160e16	−0.657728	−0.328864	+	0.944377i	$0.606666\pi$
$948$	3.37524e15	0.143172
$949$	−5.79501e15	−0.244394
$950$	−2.47884e16	−1.03937
$951$	−1.87076e16	−0.779877
$952$	2.51477e16	1.04231
$953$	4.38869e16	1.80852	0.904262	−	0.426979i	$-0.140422\pi$
$953$	4.38869e16	1.80852	0.904262	+	0.426979i	$0.140422\pi$
$954$	−3.41925e15	−0.140092
$955$	−5.01201e15	−0.204171
$956$	−6.98786e16	−2.83026
$957$	−2.31240e16	−0.931209
$958$	−7.73518e16	−3.09713
$959$	−1.57348e16	−0.626412
$960$	−6.34087e16	−2.50990
$961$	−2.49463e16	−0.981809
$962$	3.09772e16	1.21221
$963$	1.39992e16	0.544703
$964$	−9.65127e16	−3.73388
$965$	−3.14618e16	−1.21027
$966$	−4.71555e15	−0.180368
$967$	−3.51677e16	−1.33751	−0.668756	−	0.743482i	$-0.733173\pi$
$967$	−3.51677e16	−1.33751	−0.668756	+	0.743482i	$0.733173\pi$
$968$	2.20524e16	0.833951
$969$	8.33634e15	0.313469
$970$	4.16653e16	1.55787
$971$	4.18939e16	1.55756	0.778780	−	0.627298i	$-0.215839\pi$
$971$	4.18939e16	1.55756	0.778780	+	0.627298i	$0.215839\pi$
$972$	5.13014e15	0.189655
$973$	−1.70657e16	−0.627341
$974$	1.27751e16	0.466972
$975$	−3.97527e15	−0.144491
$976$	−8.32461e16	−3.00877
$977$	−1.37276e16	−0.493370	−0.246685	−	0.969096i	$-0.579341\pi$
$977$	−1.37276e16	−0.493370	−0.246685	+	0.969096i	$0.579341\pi$
$978$	−4.81591e16	−1.72113
$979$	−1.87205e16	−0.665292
$980$	4.38101e16	1.54821
$981$	6.11005e15	0.214716
$982$	4.03378e16	1.40961
$983$	2.64631e16	0.919594	0.459797	−	0.888024i	$-0.347922\pi$
$983$	2.64631e16	0.919594	0.459797	+	0.888024i	$0.347922\pi$
$984$	7.67020e16	2.65054
$985$	8.95839e15	0.307844
$986$	4.77206e16	1.63073
$987$	−8.75901e15	−0.297653
$988$	3.93690e16	1.33043
$989$	−1.11436e15	−0.0374494
$990$	1.48424e16	0.496032
$991$	−4.03847e16	−1.34218	−0.671092	−	0.741374i	$-0.734174\pi$
$991$	−4.03847e16	−1.34218	−0.671092	+	0.741374i	$0.734174\pi$
$992$	−2.29521e16	−0.758592
$993$	2.62835e16	0.863898
$994$	−3.43010e16	−1.12120
$995$	−2.93641e16	−0.954531
$996$	6.76326e16	2.18640
$997$	3.76433e16	1.21022	0.605110	−	0.796142i	$-0.293129\pi$
$997$	3.76433e16	1.21022	0.605110	+	0.796142i	$0.293129\pi$
$998$	−8.09769e16	−2.58907
$999$	7.94514e15	0.252634

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.d.1.28	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.d.1.28	✓	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)

\(f(q)\)	\(=\)	\(q+90.0154 q^{2} +243.000 q^{3} +6054.78 q^{4} -4744.07 q^{5} +21873.7 q^{6} +21263.4 q^{7} +360672. q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+90.0154 q^{2} +243.000 q^{3} +6054.78 q^{4} -4744.07 q^{5} +21873.7 q^{6} +21263.4 q^{7} +360672. q^{8} +59049.0 q^{9} -427039. q^{10} -588604. q^{11} +1.47131e6 q^{12} +621501. q^{13} +1.91403e6 q^{14} -1.15281e6 q^{15} +2.00658e7 q^{16} +3.27910e6 q^{17} +5.31532e6 q^{18} +1.04620e7 q^{19} -2.87243e7 q^{20} +5.16699e6 q^{21} -5.29834e7 q^{22} -1.01386e7 q^{23} +8.76432e7 q^{24} -2.63220e7 q^{25} +5.59447e7 q^{26} +1.43489e7 q^{27} +1.28745e8 q^{28} +1.61672e8 q^{29} -1.03771e8 q^{30} -2.14992e7 q^{31} +1.06758e9 q^{32} -1.43031e8 q^{33} +2.95170e8 q^{34} -1.00875e8 q^{35} +3.57528e8 q^{36} +5.53711e8 q^{37} +9.41740e8 q^{38} +1.51025e8 q^{39} -1.71105e9 q^{40} +8.75163e8 q^{41} +4.65109e8 q^{42} +1.09912e8 q^{43} -3.56386e9 q^{44} -2.80132e8 q^{45} -9.12630e8 q^{46} -1.69519e9 q^{47} +4.87600e9 q^{48} -1.52520e9 q^{49} -2.36938e9 q^{50} +7.96822e8 q^{51} +3.76305e9 q^{52} -6.43282e8 q^{53} +1.29162e9 q^{54} +2.79237e9 q^{55} +7.66909e9 q^{56} +2.54226e9 q^{57} +1.45529e10 q^{58} +7.14924e8 q^{59} -6.97999e9 q^{60} -4.14865e9 q^{61} -1.93526e9 q^{62} +1.25558e9 q^{63} +5.50037e10 q^{64} -2.94844e9 q^{65} -1.28750e10 q^{66} +5.36946e9 q^{67} +1.98542e10 q^{68} -2.46368e9 q^{69} -9.08028e9 q^{70} -1.79208e10 q^{71} +2.12973e10 q^{72} -9.32422e9 q^{73} +4.98425e10 q^{74} -6.39624e9 q^{75} +6.33450e10 q^{76} -1.25157e10 q^{77} +1.35946e10 q^{78} +2.29404e9 q^{79} -9.51936e10 q^{80} +3.48678e9 q^{81} +7.87781e10 q^{82} +4.59676e10 q^{83} +3.12850e10 q^{84} -1.55563e10 q^{85} +9.89381e9 q^{86} +3.92862e10 q^{87} -2.12293e11 q^{88} +3.18049e10 q^{89} -2.52162e10 q^{90} +1.32152e10 q^{91} -6.13869e10 q^{92} -5.22431e9 q^{93} -1.52593e11 q^{94} -4.96323e10 q^{95} +2.59422e11 q^{96} -9.75679e10 q^{97} -1.37291e11 q^{98} -3.47565e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9}+O(q^{10}) \) 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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