LMFDB - Embedded newform 177.10.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,10,Mod(1,177)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$91.1613430010$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q-36.1747 q^{2} -81.0000 q^{3} +796.607 q^{4} +898.892 q^{5} +2930.15 q^{6} -4674.69 q^{7} -10295.5 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-36.1747 q^{2} -81.0000 q^{3} +796.607 q^{4} +898.892 q^{5} +2930.15 q^{6} -4674.69 q^{7} -10295.5 q^{8} +6561.00 q^{9} -32517.1 q^{10} -58345.2 q^{11} -64525.1 q^{12} +57332.9 q^{13} +169105. q^{14} -72810.3 q^{15} -35424.5 q^{16} -510308. q^{17} -237342. q^{18} -168147. q^{19} +716063. q^{20} +378650. q^{21} +2.11062e6 q^{22} +2.17501e6 q^{23} +833939. q^{24} -1.14512e6 q^{25} -2.07400e6 q^{26} -531441. q^{27} -3.72389e6 q^{28} +244852. q^{29} +2.63389e6 q^{30} +6.46606e6 q^{31} +6.55279e6 q^{32} +4.72596e6 q^{33} +1.84602e7 q^{34} -4.20204e6 q^{35} +5.22654e6 q^{36} -4.04614e6 q^{37} +6.08266e6 q^{38} -4.64396e6 q^{39} -9.25459e6 q^{40} -8.50617e6 q^{41} -1.36975e7 q^{42} -1.02337e7 q^{43} -4.64781e7 q^{44} +5.89763e6 q^{45} -7.86802e7 q^{46} -3.48588e7 q^{47} +2.86939e6 q^{48} -1.85009e7 q^{49} +4.14243e7 q^{50} +4.13350e7 q^{51} +4.56718e7 q^{52} -5.20000e7 q^{53} +1.92247e7 q^{54} -5.24460e7 q^{55} +4.81285e7 q^{56} +1.36199e7 q^{57} -8.85743e6 q^{58} +1.21174e7 q^{59} -5.80011e7 q^{60} +2.99414e7 q^{61} -2.33907e8 q^{62} -3.06706e7 q^{63} -2.18908e8 q^{64} +5.15361e7 q^{65} -1.70960e8 q^{66} -2.13498e8 q^{67} -4.06515e8 q^{68} -1.76176e8 q^{69} +1.52007e8 q^{70} -1.52154e8 q^{71} -6.75491e7 q^{72} +1.83932e8 q^{73} +1.46368e8 q^{74} +9.27546e7 q^{75} -1.33947e8 q^{76} +2.72745e8 q^{77} +1.67994e8 q^{78} +7.72399e7 q^{79} -3.18428e7 q^{80} +4.30467e7 q^{81} +3.07708e8 q^{82} -1.73619e8 q^{83} +3.01635e8 q^{84} -4.58712e8 q^{85} +3.70202e8 q^{86} -1.98330e7 q^{87} +6.00695e8 q^{88} -6.72303e8 q^{89} -2.13345e8 q^{90} -2.68013e8 q^{91} +1.73263e9 q^{92} -5.23751e8 q^{93} +1.26100e9 q^{94} -1.51146e8 q^{95} -5.30776e8 q^{96} +1.37731e9 q^{97} +6.69264e8 q^{98} -3.82803e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9}+O(q^{10}) $ 22 * q + 36 * q^2 - 1782 * q^3 + 5718 * q^4 + 808 * q^5 - 2916 * q^6 + 21249 * q^7 + 9435 * q^8 + 144342 * q^9	\( 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9} + 68441 q^{10} - 68033 q^{11} - 463158 q^{12} + 283817 q^{13} + 80285 q^{14} - 65448 q^{15} + 1067674 q^{16} + 436893 q^{17} + 236196 q^{18} + 1207580 q^{19} + 4209677 q^{20} - 1721169 q^{21} + 5460442 q^{22} + 2421966 q^{23} - 764235 q^{24} + 7441842 q^{25} - 2736526 q^{26} - 11691702 q^{27} + 4095246 q^{28} - 2320594 q^{29} - 5543721 q^{30} - 3178024 q^{31} - 20786874 q^{32} + 5510673 q^{33} - 13809336 q^{34} - 2630800 q^{35} + 37515798 q^{36} + 3981807 q^{37} - 24156377 q^{38} - 22989177 q^{39} - 29544450 q^{40} - 885225 q^{41} - 6503085 q^{42} + 12360835 q^{43} - 117711882 q^{44} + 5301288 q^{45} + 161066949 q^{46} + 75901252 q^{47} - 86481594 q^{48} + 170907951 q^{49} - 61318927 q^{50} - 35388333 q^{51} - 100762 q^{52} - 34790192 q^{53} - 19131876 q^{54} + 151773316 q^{55} - 417630344 q^{56} - 97813980 q^{57} - 432929294 q^{58} + 266581942 q^{59} - 340983837 q^{60} - 290555332 q^{61} + 158267098 q^{62} + 139414689 q^{63} - 131794443 q^{64} - 650690086 q^{65} - 442295802 q^{66} + 86645184 q^{67} + 62738541 q^{68} - 196179246 q^{69} + 429714610 q^{70} - 36567631 q^{71} + 61903035 q^{72} + 907807228 q^{73} - 171827242 q^{74} - 602789202 q^{75} + 1744504396 q^{76} - 310688725 q^{77} + 221658606 q^{78} + 2508604687 q^{79} + 3509441927 q^{80} + 947027862 q^{81} + 1759214793 q^{82} + 2185672083 q^{83} - 331714926 q^{84} + 2868860198 q^{85} + 2397001564 q^{86} + 187968114 q^{87} + 7683735877 q^{88} + 1320145942 q^{89} + 449041401 q^{90} + 3894639897 q^{91} + 3505964640 q^{92} + 257419944 q^{93} + 5406355552 q^{94} + 3093659122 q^{95} + 1683736794 q^{96} + 3904552980 q^{97} + 6137683116 q^{98} - 446364513 q^{99}+O(q^{100}) \) 22 * q + 36 * q^2 - 1782 * q^3 + 5718 * q^4 + 808 * q^5 - 2916 * q^6 + 21249 * q^7 + 9435 * q^8 + 144342 * q^9 + 68441 * q^10 - 68033 * q^11 - 463158 * q^12 + 283817 * q^13 + 80285 * q^14 - 65448 * q^15 + 1067674 * q^16 + 436893 * q^17 + 236196 * q^18 + 1207580 * q^19 + 4209677 * q^20 - 1721169 * q^21 + 5460442 * q^22 + 2421966 * q^23 - 764235 * q^24 + 7441842 * q^25 - 2736526 * q^26 - 11691702 * q^27 + 4095246 * q^28 - 2320594 * q^29 - 5543721 * q^30 - 3178024 * q^31 - 20786874 * q^32 + 5510673 * q^33 - 13809336 * q^34 - 2630800 * q^35 + 37515798 * q^36 + 3981807 * q^37 - 24156377 * q^38 - 22989177 * q^39 - 29544450 * q^40 - 885225 * q^41 - 6503085 * q^42 + 12360835 * q^43 - 117711882 * q^44 + 5301288 * q^45 + 161066949 * q^46 + 75901252 * q^47 - 86481594 * q^48 + 170907951 * q^49 - 61318927 * q^50 - 35388333 * q^51 - 100762 * q^52 - 34790192 * q^53 - 19131876 * q^54 + 151773316 * q^55 - 417630344 * q^56 - 97813980 * q^57 - 432929294 * q^58 + 266581942 * q^59 - 340983837 * q^60 - 290555332 * q^61 + 158267098 * q^62 + 139414689 * q^63 - 131794443 * q^64 - 650690086 * q^65 - 442295802 * q^66 + 86645184 * q^67 + 62738541 * q^68 - 196179246 * q^69 + 429714610 * q^70 - 36567631 * q^71 + 61903035 * q^72 + 907807228 * q^73 - 171827242 * q^74 - 602789202 * q^75 + 1744504396 * q^76 - 310688725 * q^77 + 221658606 * q^78 + 2508604687 * q^79 + 3509441927 * q^80 + 947027862 * q^81 + 1759214793 * q^82 + 2185672083 * q^83 - 331714926 * q^84 + 2868860198 * q^85 + 2397001564 * q^86 + 187968114 * q^87 + 7683735877 * q^88 + 1320145942 * q^89 + 449041401 * q^90 + 3894639897 * q^91 + 3505964640 * q^92 + 257419944 * q^93 + 5406355552 * q^94 + 3093659122 * q^95 + 1683736794 * q^96 + 3904552980 * q^97 + 6137683116 * q^98 - 446364513 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−36.1747	−1.59871	−0.799355	−	0.600859i	$-0.794825\pi$
$2$	−36.1747	−1.59871	−0.799355	+	0.600859i	$0.794825\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	796.607	1.55587
$5$	898.892	0.643195	0.321597	−	0.946876i	$-0.395780\pi$
$5$	898.892	0.643195	0.321597	+	0.946876i	$0.395780\pi$
$6$	2930.15	0.923015
$7$	−4674.69	−0.735888	−0.367944	−	0.929848i	$-0.619938\pi$
$7$	−4674.69	−0.735888	−0.367944	+	0.929848i	$0.619938\pi$
$8$	−10295.5	−0.888678
$9$	6561.00	0.333333
$10$	−32517.1	−1.02828
$11$	−58345.2	−1.20154	−0.600769	−	0.799422i	$-0.705139\pi$
$11$	−58345.2	−1.20154	−0.600769	+	0.799422i	$0.705139\pi$
$12$	−64525.1	−0.898283
$13$	57332.9	0.556748	0.278374	−	0.960473i	$-0.410204\pi$
$13$	57332.9	0.556748	0.278374	+	0.960473i	$0.410204\pi$
$14$	169105.	1.17647
$15$	−72810.3	−0.371349
$16$	−35424.5	−0.135134
$17$	−510308.	−1.48188	−0.740939	−	0.671573i	$-0.765619\pi$
$17$	−510308.	−1.48188	−0.740939	+	0.671573i	$0.765619\pi$
$18$	−237342.	−0.532903
$19$	−168147.	−0.296004	−0.148002	−	0.988987i	$-0.547284\pi$
$19$	−168147.	−0.296004	−0.148002	+	0.988987i	$0.547284\pi$
$20$	716063.	1.00073
$21$	378650.	0.424865
$22$	2.11062e6	1.92091
$23$	2.17501e6	1.62064	0.810318	−	0.585990i	$-0.199294\pi$
$23$	2.17501e6	1.62064	0.810318	+	0.585990i	$0.199294\pi$
$24$	833939.	0.513079
$25$	−1.14512e6	−0.586300
$26$	−2.07400e6	−0.890079
$27$	−531441.	−0.192450
$28$	−3.72389e6	−1.14495
$29$	244852.	0.0642853	0.0321427	−	0.999483i	$-0.489767\pi$
$29$	244852.	0.0642853	0.0321427	+	0.999483i	$0.489767\pi$
$30$	2.63389e6	0.593679
$31$	6.46606e6	1.25751	0.628756	−	0.777603i	$-0.283565\pi$
$31$	6.46606e6	1.25751	0.628756	+	0.777603i	$0.283565\pi$
$32$	6.55279e6	1.10472
$33$	4.72596e6	0.693709
$34$	1.84602e7	2.36909
$35$	−4.20204e6	−0.473319
$36$	5.22654e6	0.518624
$37$	−4.04614e6	−0.354922	−0.177461	−	0.984128i	$-0.556788\pi$
$37$	−4.04614e6	−0.354922	−0.177461	+	0.984128i	$0.556788\pi$
$38$	6.08266e6	0.473224
$39$	−4.64396e6	−0.321439
$40$	−9.25459e6	−0.571593
$41$	−8.50617e6	−0.470118	−0.235059	−	0.971981i	$-0.575528\pi$
$41$	−8.50617e6	−0.470118	−0.235059	+	0.971981i	$0.575528\pi$
$42$	−1.36975e7	−0.679236
$43$	−1.02337e7	−0.456485	−0.228242	−	0.973604i	$-0.573298\pi$
$43$	−1.02337e7	−0.456485	−0.228242	+	0.973604i	$0.573298\pi$
$44$	−4.64781e7	−1.86944
$45$	5.89763e6	0.214398
$46$	−7.86802e7	−2.59093
$47$	−3.48588e7	−1.04201	−0.521005	−	0.853554i	$-0.674443\pi$
$47$	−3.48588e7	−1.04201	−0.521005	+	0.853554i	$0.674443\pi$
$48$	2.86939e6	0.0780195
$49$	−1.85009e7	−0.458470
$50$	4.14243e7	0.937324
$51$	4.13350e7	0.855562
$52$	4.56718e7	0.866229
$53$	−5.20000e7	−0.905237	−0.452618	−	0.891704i	$-0.649510\pi$
$53$	−5.20000e7	−0.905237	−0.452618	+	0.891704i	$0.649510\pi$
$54$	1.92247e7	0.307672
$55$	−5.24460e7	−0.772823
$56$	4.81285e7	0.653967
$57$	1.36199e7	0.170898
$58$	−8.85743e6	−0.102774
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	−5.80011e7	−0.577771
$61$	2.99414e7	0.276878	0.138439	−	0.990371i	$-0.455792\pi$
$61$	2.99414e7	0.276878	0.138439	+	0.990371i	$0.455792\pi$
$62$	−2.33907e8	−2.01040
$63$	−3.06706e7	−0.245296
$64$	−2.18908e8	−1.63099
$65$	5.15361e7	0.358098
$66$	−1.70960e8	−1.10904
$67$	−2.13498e8	−1.29437	−0.647183	−	0.762335i	$-0.724053\pi$
$67$	−2.13498e8	−1.29437	−0.647183	+	0.762335i	$0.724053\pi$
$68$	−4.06515e8	−2.30561
$69$	−1.76176e8	−0.935675
$70$	1.52007e8	0.756700
$71$	−1.52154e8	−0.710592	−0.355296	−	0.934754i	$-0.615620\pi$
$71$	−1.52154e8	−0.710592	−0.355296	+	0.934754i	$0.615620\pi$
$72$	−6.75491e7	−0.296226
$73$	1.83932e8	0.758063	0.379032	−	0.925384i	$-0.376257\pi$
$73$	1.83932e8	0.758063	0.379032	+	0.925384i	$0.376257\pi$
$74$	1.46368e8	0.567417
$75$	9.27546e7	0.338501
$76$	−1.33947e8	−0.460544
$77$	2.72745e8	0.884197
$78$	1.67994e8	0.513887
$79$	7.72399e7	0.223110	0.111555	−	0.993758i	$-0.464417\pi$
$79$	7.72399e7	0.223110	0.111555	+	0.993758i	$0.464417\pi$
$80$	−3.18428e7	−0.0869174
$81$	4.30467e7	0.111111
$82$	3.07708e8	0.751582
$83$	−1.73619e8	−0.401555	−0.200778	−	0.979637i	$-0.564347\pi$
$83$	−1.73619e8	−0.401555	−0.200778	+	0.979637i	$0.564347\pi$
$84$	3.01635e8	0.661035
$85$	−4.58712e8	−0.953136
$86$	3.70202e8	0.729787
$87$	−1.98330e7	−0.0371152
$88$	6.00695e8	1.06778
$89$	−6.72303e8	−1.13582	−0.567911	−	0.823090i	$-0.692248\pi$
$89$	−6.72303e8	−1.13582	−0.567911	+	0.823090i	$0.692248\pi$
$90$	−2.13345e8	−0.342761
$91$	−2.68013e8	−0.409704
$92$	1.73263e9	2.52150
$93$	−5.23751e8	−0.726024
$94$	1.26100e9	1.66587
$95$	−1.51146e8	−0.190388
$96$	−5.30776e8	−0.637809
$97$	1.37731e9	1.57964	0.789820	−	0.613338i	$-0.210174\pi$
$97$	1.37731e9	1.57964	0.789820	+	0.613338i	$0.210174\pi$
$98$	6.69264e8	0.732960
$99$	−3.82803e8	−0.400513
$100$	−9.12209e8	−0.912209
$101$	−7.06551e7	−0.0675612	−0.0337806	−	0.999429i	$-0.510755\pi$
$101$	−7.06551e7	−0.0675612	−0.0337806	+	0.999429i	$0.510755\pi$
$102$	−1.49528e9	−1.36780
$103$	3.47159e8	0.303921	0.151961	−	0.988387i	$-0.451441\pi$
$103$	3.47159e8	0.303921	0.151961	+	0.988387i	$0.451441\pi$
$104$	−5.90274e8	−0.494770
$105$	3.40365e8	0.273271
$106$	1.88108e9	1.44721
$107$	−2.17084e9	−1.60103	−0.800516	−	0.599311i	$-0.795441\pi$
$107$	−2.17084e9	−1.60103	−0.800516	+	0.599311i	$0.795441\pi$
$108$	−4.23349e8	−0.299428
$109$	1.68021e9	1.14010	0.570051	−	0.821609i	$-0.306923\pi$
$109$	1.68021e9	1.14010	0.570051	+	0.821609i	$0.306923\pi$
$110$	1.89722e9	1.23552
$111$	3.27737e8	0.204914
$112$	1.65599e8	0.0994433
$113$	−3.34940e8	−0.193248	−0.0966239	−	0.995321i	$-0.530804\pi$
$113$	−3.34940e8	−0.193248	−0.0966239	+	0.995321i	$0.530804\pi$
$114$	−4.92695e8	−0.273216
$115$	1.95510e9	1.04238
$116$	1.95050e8	0.100020
$117$	3.76161e8	0.185583
$118$	−4.38342e8	−0.208134
$119$	2.38553e9	1.09050
$120$	7.49622e8	0.330010
$121$	1.04621e9	0.443695
$122$	−1.08312e9	−0.442647
$123$	6.89000e8	0.271423
$124$	5.15090e9	1.95653
$125$	−2.78499e9	−1.02030
$126$	1.10950e9	0.392157
$127$	4.31503e9	1.47186	0.735931	−	0.677056i	$-0.236745\pi$
$127$	4.31503e9	1.47186	0.735931	+	0.677056i	$0.236745\pi$
$128$	4.56388e9	1.50276
$129$	8.28933e8	0.263552
$130$	−1.86430e9	−0.572494
$131$	−4.44468e9	−1.31862	−0.659310	−	0.751871i	$-0.729152\pi$
$131$	−4.44468e9	−1.31862	−0.659310	+	0.751871i	$0.729152\pi$
$132$	3.76473e9	1.07932
$133$	7.86034e8	0.217826
$134$	7.72322e9	2.06932
$135$	−4.77708e8	−0.123783
$136$	5.25390e9	1.31691
$137$	−2.71704e9	−0.658951	−0.329476	−	0.944164i	$-0.606872\pi$
$137$	−2.71704e9	−0.658951	−0.329476	+	0.944164i	$0.606872\pi$
$138$	6.37310e9	1.49587
$139$	−1.44384e9	−0.328060	−0.164030	−	0.986455i	$-0.552449\pi$
$139$	−1.44384e9	−0.328060	−0.164030	+	0.986455i	$0.552449\pi$
$140$	−3.34737e9	−0.736424
$141$	2.82356e9	0.601605
$142$	5.50411e9	1.13603
$143$	−3.34510e9	−0.668954
$144$	−2.32420e8	−0.0450446
$145$	2.20095e8	0.0413480
$146$	−6.65369e9	−1.21192
$147$	1.49857e9	0.264698
$148$	−3.22318e9	−0.552213
$149$	2.95833e9	0.491709	0.245855	−	0.969307i	$-0.420931\pi$
$149$	2.95833e9	0.491709	0.245855	+	0.969307i	$0.420931\pi$
$150$	−3.35537e9	−0.541164
$151$	4.00966e9	0.627640	0.313820	−	0.949482i	$-0.398391\pi$
$151$	4.00966e9	0.627640	0.313820	+	0.949482i	$0.398391\pi$
$152$	1.73116e9	0.263052
$153$	−3.34813e9	−0.493959
$154$	−9.86647e9	−1.41357
$155$	5.81229e9	0.808825
$156$	−3.69941e9	−0.500118
$157$	1.25451e10	1.64788	0.823940	−	0.566678i	$-0.191771\pi$
$157$	1.25451e10	1.64788	0.823940	+	0.566678i	$0.191771\pi$
$158$	−2.79413e9	−0.356689
$159$	4.21200e9	0.522639
$160$	5.89025e9	0.710549
$161$	−1.01675e10	−1.19261
$162$	−1.55720e9	−0.177634
$163$	1.20770e10	1.34003	0.670013	−	0.742349i	$-0.266288\pi$
$163$	1.20770e10	1.34003	0.670013	+	0.742349i	$0.266288\pi$
$164$	−6.77607e9	−0.731443
$165$	4.24813e9	0.446190
$166$	6.28060e9	0.641970
$167$	−8.77986e9	−0.873501	−0.436750	−	0.899583i	$-0.643871\pi$
$167$	−8.77986e9	−0.873501	−0.436750	+	0.899583i	$0.643871\pi$
$168$	−3.89841e9	−0.377568
$169$	−7.31744e9	−0.690031
$170$	1.65937e10	1.52379
$171$	−1.10321e9	−0.0986680
$172$	−8.15226e9	−0.710232
$173$	−3.23450e9	−0.274536	−0.137268	−	0.990534i	$-0.543832\pi$
$173$	−3.23450e9	−0.274536	−0.137268	+	0.990534i	$0.543832\pi$
$174$	7.17451e8	0.0593364
$175$	5.35307e9	0.431451
$176$	2.06685e9	0.162368
$177$	−9.81506e8	−0.0751646
$178$	2.43204e10	1.81585
$179$	2.22715e10	1.62147	0.810737	−	0.585411i	$-0.199067\pi$
$179$	2.22715e10	1.62147	0.810737	+	0.585411i	$0.199067\pi$
$180$	4.69809e9	0.333576
$181$	−2.16773e10	−1.50125	−0.750623	−	0.660731i	$-0.770247\pi$
$181$	−2.16773e10	−1.50125	−0.750623	+	0.660731i	$0.770247\pi$
$182$	9.69530e9	0.654998
$183$	−2.42526e9	−0.159856
$184$	−2.23929e10	−1.44022
$185$	−3.63704e9	−0.228284
$186$	1.89465e10	1.16070
$187$	2.97740e10	1.78053
$188$	−2.77687e10	−1.62123
$189$	2.48432e9	0.141622
$190$	5.46765e9	0.304375
$191$	2.81443e10	1.53017	0.765086	−	0.643928i	$-0.222696\pi$
$191$	2.81443e10	1.53017	0.765086	+	0.643928i	$0.222696\pi$
$192$	1.77315e10	0.941652
$193$	−4.41397e9	−0.228992	−0.114496	−	0.993424i	$-0.536525\pi$
$193$	−4.41397e9	−0.228992	−0.114496	+	0.993424i	$0.536525\pi$
$194$	−4.98237e10	−2.52539
$195$	−4.17442e9	−0.206748
$196$	−1.47379e10	−0.713320
$197$	−2.04044e10	−0.965219	−0.482609	−	0.875836i	$-0.660311\pi$
$197$	−2.04044e10	−0.965219	−0.482609	+	0.875836i	$0.660311\pi$
$198$	1.38478e10	0.640304
$199$	1.01977e10	0.460962	0.230481	−	0.973077i	$-0.425970\pi$
$199$	1.01977e10	0.460962	0.230481	+	0.973077i	$0.425970\pi$
$200$	1.17896e10	0.521032
$201$	1.72933e10	0.747303
$202$	2.55592e9	0.108011
$203$	−1.14460e9	−0.0473068
$204$	3.29277e10	1.33115
$205$	−7.64613e9	−0.302377
$206$	−1.25584e10	−0.485882
$207$	1.42702e10	0.540212
$208$	−2.03099e9	−0.0752355
$209$	9.81055e9	0.355660
$210$	−1.23126e10	−0.436881
$211$	−1.33425e10	−0.463410	−0.231705	−	0.972786i	$-0.574430\pi$
$211$	−1.33425e10	−0.463410	−0.231705	+	0.972786i	$0.574430\pi$
$212$	−4.14236e10	−1.40843
$213$	1.23245e10	0.410260
$214$	7.85293e10	2.55959
$215$	−9.19903e9	−0.293609
$216$	5.47148e9	0.171026
$217$	−3.02268e10	−0.925387
$218$	−6.07810e10	−1.82269
$219$	−1.48985e10	−0.437668
$220$	−4.17788e10	−1.20241
$221$	−2.92574e10	−0.825033
$222$	−1.18558e10	−0.327598
$223$	−2.17210e10	−0.588178	−0.294089	−	0.955778i	$-0.595016\pi$
$223$	−2.17210e10	−0.588178	−0.294089	+	0.955778i	$0.595016\pi$
$224$	−3.06323e10	−0.812948
$225$	−7.51312e9	−0.195433
$226$	1.21164e10	0.308947
$227$	3.32500e10	0.831141	0.415571	−	0.909561i	$-0.363582\pi$
$227$	3.32500e10	0.831141	0.415571	+	0.909561i	$0.363582\pi$
$228$	1.08497e10	0.265895
$229$	−9.20653e9	−0.221226	−0.110613	−	0.993864i	$-0.535281\pi$
$229$	−9.20653e9	−0.221226	−0.110613	+	0.993864i	$0.535281\pi$
$230$	−7.07250e10	−1.66647
$231$	−2.20924e10	−0.510492
$232$	−2.52088e9	−0.0571290
$233$	5.05237e10	1.12303	0.561517	−	0.827465i	$-0.310218\pi$
$233$	5.05237e10	1.12303	0.561517	+	0.827465i	$0.310218\pi$
$234$	−1.36075e10	−0.296693
$235$	−3.13343e10	−0.670215
$236$	9.65277e9	0.202557
$237$	−6.25643e9	−0.128813
$238$	−8.62958e10	−1.74338
$239$	1.89053e10	0.374794	0.187397	−	0.982284i	$-0.439995\pi$
$239$	1.89053e10	0.374794	0.187397	+	0.982284i	$0.439995\pi$
$240$	2.57927e9	0.0501818
$241$	−3.30262e10	−0.630640	−0.315320	−	0.948985i	$-0.602112\pi$
$241$	−3.30262e10	−0.630640	−0.315320	+	0.948985i	$0.602112\pi$
$242$	−3.78463e10	−0.709340
$243$	−3.48678e9	−0.0641500
$244$	2.38515e10	0.430787
$245$	−1.66303e10	−0.294885
$246$	−2.49243e10	−0.433926
$247$	−9.64035e9	−0.164800
$248$	−6.65716e10	−1.11752
$249$	1.40631e10	0.231838
$250$	1.00746e11	1.63116
$251$	−8.61853e8	−0.0137057	−0.00685285	−	0.999977i	$-0.502181\pi$
$251$	−8.61853e8	−0.0137057	−0.00685285	+	0.999977i	$0.502181\pi$
$252$	−2.44324e10	−0.381649
$253$	−1.26901e11	−1.94726
$254$	−1.56095e11	−2.35308
$255$	3.71557e10	0.550293
$256$	−5.30162e10	−0.771488
$257$	1.23018e11	1.75902	0.879510	−	0.475881i	$-0.157871\pi$
$257$	1.23018e11	1.75902	0.879510	+	0.475881i	$0.157871\pi$
$258$	−2.99864e10	−0.421342
$259$	1.89144e10	0.261183
$260$	4.10540e10	0.557154
$261$	1.60647e9	0.0214284
$262$	1.60785e11	2.10809
$263$	2.48000e10	0.319632	0.159816	−	0.987147i	$-0.448910\pi$
$263$	2.48000e10	0.319632	0.159816	+	0.987147i	$0.448910\pi$
$264$	−4.86563e10	−0.616484
$265$	−4.67424e10	−0.582244
$266$	−2.84345e10	−0.348240
$267$	5.44566e10	0.655767
$268$	−1.70074e11	−2.01387
$269$	−1.65665e11	−1.92906	−0.964528	−	0.263979i	$-0.914965\pi$
$269$	−1.65665e11	−1.92906	−0.964528	+	0.263979i	$0.914965\pi$
$270$	1.72809e10	0.197893
$271$	3.14041e10	0.353691	0.176846	−	0.984239i	$-0.443411\pi$
$271$	3.14041e10	0.353691	0.176846	+	0.984239i	$0.443411\pi$
$272$	1.80774e10	0.200252
$273$	2.17091e10	0.236543
$274$	9.82880e10	1.05347
$275$	6.68121e10	0.704463
$276$	−1.40343e11	−1.45579
$277$	1.64597e11	1.67982	0.839911	−	0.542725i	$-0.182607\pi$
$277$	1.64597e11	1.67982	0.839911	+	0.542725i	$0.182607\pi$
$278$	5.22306e10	0.524473
$279$	4.24238e10	0.419170
$280$	4.32623e10	0.420628
$281$	−1.74325e11	−1.66794	−0.833971	−	0.551808i	$-0.813938\pi$
$281$	−1.74325e11	−1.66794	−0.833971	+	0.551808i	$0.813938\pi$
$282$	−1.02141e11	−0.961791
$283$	1.53298e11	1.42069	0.710344	−	0.703855i	$-0.248540\pi$
$283$	1.53298e11	1.42069	0.710344	+	0.703855i	$0.248540\pi$
$284$	−1.21207e11	−1.10559
$285$	1.22428e10	0.109921
$286$	1.21008e11	1.06946
$287$	3.97637e10	0.345954
$288$	4.29929e10	0.368239
$289$	1.41826e11	1.19596
$290$	−7.96187e9	−0.0661034
$291$	−1.11562e11	−0.912006
$292$	1.46522e11	1.17945
$293$	5.26361e10	0.417233	0.208617	−	0.977997i	$-0.433104\pi$
$293$	5.26361e10	0.417233	0.208617	+	0.977997i	$0.433104\pi$
$294$	−5.42104e10	−0.423174
$295$	1.08922e10	0.0837368
$296$	4.16572e10	0.315411
$297$	3.10070e10	0.231236
$298$	−1.07017e11	−0.786100
$299$	1.24700e11	0.902286
$300$	7.38889e10	0.526664
$301$	4.78395e10	0.335921
$302$	−1.45048e11	−1.00341
$303$	5.72306e9	0.0390064
$304$	5.95652e9	0.0400001
$305$	2.69141e10	0.178086
$306$	1.21118e11	0.789697
$307$	2.34703e11	1.50798	0.753991	−	0.656885i	$-0.228126\pi$
$307$	2.34703e11	1.50798	0.753991	+	0.656885i	$0.228126\pi$
$308$	2.17271e11	1.37570
$309$	−2.81199e10	−0.175469
$310$	−2.10258e11	−1.29308
$311$	3.48562e10	0.211280	0.105640	−	0.994404i	$-0.466311\pi$
$311$	3.48562e10	0.211280	0.105640	+	0.994404i	$0.466311\pi$
$312$	4.78122e10	0.285656
$313$	1.77039e11	1.04260	0.521301	−	0.853373i	$-0.325447\pi$
$313$	1.77039e11	1.04260	0.521301	+	0.853373i	$0.325447\pi$
$314$	−4.53814e11	−2.63448
$315$	−2.75696e10	−0.157773
$316$	6.15298e10	0.347131
$317$	2.30912e8	0.00128434	0.000642169	−	1.00000i	$-0.499796\pi$
$317$	2.30912e8	0.00128434	0.000642169		1.00000i	$0.499796\pi$
$318$	−1.52368e11	−0.835547
$319$	−1.42859e10	−0.0772413
$320$	−1.96774e11	−1.04904
$321$	1.75838e11	0.924357
$322$	3.67805e11	1.90663
$323$	8.58067e10	0.438642
$324$	3.42913e10	0.172875
$325$	−6.56529e10	−0.326422
$326$	−4.36880e11	−2.14231
$327$	−1.36097e11	−0.658238
$328$	8.75757e10	0.417783
$329$	1.62954e11	0.766802
$330$	−1.53675e11	−0.713328
$331$	7.38318e9	0.0338078	0.0169039	−	0.999857i	$-0.494619\pi$
$331$	7.38318e9	0.0338078	0.0169039	+	0.999857i	$0.494619\pi$
$332$	−1.38306e11	−0.624769
$333$	−2.65467e10	−0.118307
$334$	3.17608e11	1.39647
$335$	−1.91912e11	−0.832530
$336$	−1.34135e10	−0.0574136
$337$	4.06055e11	1.71495	0.857473	−	0.514530i	$-0.172033\pi$
$337$	4.06055e11	1.71495	0.857473	+	0.514530i	$0.172033\pi$
$338$	2.64706e11	1.10316
$339$	2.71302e10	0.111572
$340$	−3.65413e11	−1.48296
$341$	−3.77263e11	−1.51095
$342$	3.99083e10	0.157741
$343$	2.75126e11	1.07327
$344$	1.05362e11	0.405668
$345$	−1.58363e11	−0.601821
$346$	1.17007e11	0.438904
$347$	5.29349e11	1.96002	0.980008	−	0.198957i	$-0.0637555\pi$
$347$	5.29349e11	1.96002	0.980008	+	0.198957i	$0.0637555\pi$
$348$	−1.57991e10	−0.0577464
$349$	3.08680e11	1.11377	0.556884	−	0.830591i	$-0.311997\pi$
$349$	3.08680e11	1.11377	0.556884	+	0.830591i	$0.311997\pi$
$350$	−1.93646e11	−0.689765
$351$	−3.04691e10	−0.107146
$352$	−3.82324e11	−1.32736
$353$	3.72155e11	1.27567	0.637833	−	0.770175i	$-0.279831\pi$
$353$	3.72155e11	1.27567	0.637833	+	0.770175i	$0.279831\pi$
$354$	3.55057e10	0.120166
$355$	−1.36770e11	−0.457049
$356$	−5.35561e11	−1.76719
$357$	−1.93228e11	−0.629598
$358$	−8.05663e11	−2.59227
$359$	5.49485e11	1.74595	0.872973	−	0.487769i	$-0.162189\pi$
$359$	5.49485e11	1.74595	0.872973	+	0.487769i	$0.162189\pi$
$360$	−6.07193e10	−0.190531
$361$	−2.94414e11	−0.912382
$362$	7.84170e11	2.40006
$363$	−8.47430e10	−0.256167
$364$	−2.13501e11	−0.637447
$365$	1.65335e11	0.487582
$366$	8.77328e10	0.255563
$367$	−3.94449e11	−1.13499	−0.567497	−	0.823376i	$-0.692088\pi$
$367$	−3.94449e11	−1.13499	−0.567497	+	0.823376i	$0.692088\pi$
$368$	−7.70486e10	−0.219003
$369$	−5.58090e10	−0.156706
$370$	1.31569e11	0.364960
$371$	2.43084e11	0.666152
$372$	−4.17223e11	−1.12960
$373$	−3.12062e11	−0.834739	−0.417369	−	0.908737i	$-0.637048\pi$
$373$	−3.12062e11	−0.834739	−0.417369	+	0.908737i	$0.637048\pi$
$374$	−1.07706e12	−2.84656
$375$	2.25584e11	0.589071
$376$	3.58890e11	0.926011
$377$	1.40381e10	0.0357908
$378$	−8.98695e10	−0.226412
$379$	−1.54226e11	−0.383955	−0.191977	−	0.981399i	$-0.561490\pi$
$379$	−1.54226e11	−0.383955	−0.191977	+	0.981399i	$0.561490\pi$
$380$	−1.20404e11	−0.296220
$381$	−3.49518e11	−0.849780
$382$	−1.01811e12	−2.44630
$383$	4.33365e11	1.02911	0.514553	−	0.857459i	$-0.327958\pi$
$383$	4.33365e11	1.02911	0.514553	+	0.857459i	$0.327958\pi$
$384$	−3.69675e11	−0.867619
$385$	2.45169e11	0.568711
$386$	1.59674e11	0.366092
$387$	−6.71436e10	−0.152162
$388$	1.09717e12	2.45772
$389$	−2.14366e11	−0.474660	−0.237330	−	0.971429i	$-0.576272\pi$
$389$	−2.14366e11	−0.474660	−0.237330	+	0.971429i	$0.576272\pi$
$390$	1.51008e11	0.330530
$391$	−1.10992e12	−2.40158
$392$	1.90477e11	0.407432
$393$	3.60019e11	0.761306
$394$	7.38122e11	1.54310
$395$	6.94303e10	0.143503
$396$	−3.04943e11	−0.623147
$397$	3.59774e10	0.0726895	0.0363448	−	0.999339i	$-0.488429\pi$
$397$	3.59774e10	0.0726895	0.0363448	+	0.999339i	$0.488429\pi$
$398$	−3.68900e11	−0.736944
$399$	−6.36688e10	−0.125762
$400$	4.05652e10	0.0792290
$401$	2.39655e11	0.462846	0.231423	−	0.972853i	$-0.425662\pi$
$401$	2.39655e11	0.462846	0.231423	+	0.972853i	$0.425662\pi$
$402$	−6.25581e11	−1.19472
$403$	3.70718e11	0.700117
$404$	−5.62843e10	−0.105117
$405$	3.86944e10	0.0714661
$406$	4.14057e10	0.0756298
$407$	2.36073e11	0.426452
$408$	−4.25566e11	−0.760320
$409$	8.16510e11	1.44280	0.721401	−	0.692518i	$-0.243499\pi$
$409$	8.16510e11	1.44280	0.721401	+	0.692518i	$0.243499\pi$
$410$	2.76596e11	0.483414
$411$	2.20080e11	0.380446
$412$	2.76549e11	0.472862
$413$	−5.66449e10	−0.0958044
$414$	−5.16221e11	−0.863642
$415$	−1.56065e11	−0.258278
$416$	3.75691e11	0.615050
$417$	1.16951e11	0.189406
$418$	−3.54894e11	−0.568597
$419$	1.35929e10	0.0215452	0.0107726	−	0.999942i	$-0.496571\pi$
$419$	1.35929e10	0.0215452	0.0107726	+	0.999942i	$0.496571\pi$
$420$	2.71137e11	0.425175
$421$	−1.99138e11	−0.308948	−0.154474	−	0.987997i	$-0.549368\pi$
$421$	−1.99138e11	−0.308948	−0.154474	+	0.987997i	$0.549368\pi$
$422$	4.82660e11	0.740858
$423$	−2.28708e11	−0.347337
$424$	5.35369e11	0.804464
$425$	5.84363e11	0.868825
$426$	−4.45833e11	−0.655887
$427$	−1.39967e11	−0.203751
$428$	−1.72930e12	−2.49100
$429$	2.70953e11	0.386221
$430$	3.32772e11	0.469395
$431$	7.02282e11	0.980310	0.490155	−	0.871635i	$-0.336940\pi$
$431$	7.02282e11	0.980310	0.490155	+	0.871635i	$0.336940\pi$
$432$	1.88260e10	0.0260065
$433$	−2.80736e11	−0.383798	−0.191899	−	0.981415i	$-0.561465\pi$
$433$	−2.80736e11	−0.383798	−0.191899	+	0.981415i	$0.561465\pi$
$434$	1.09344e12	1.47942
$435$	−1.78277e10	−0.0238723
$436$	1.33846e12	1.77385
$437$	−3.65721e11	−0.479715
$438$	5.38949e11	0.699704
$439$	5.49999e11	0.706760	0.353380	−	0.935480i	$-0.385032\pi$
$439$	5.49999e11	0.706760	0.353380	+	0.935480i	$0.385032\pi$
$440$	5.39960e11	0.686791
$441$	−1.21384e11	−0.152823
$442$	1.05838e12	1.31899
$443$	−1.23621e11	−0.152501	−0.0762507	−	0.997089i	$-0.524295\pi$
$443$	−1.23621e11	−0.152501	−0.0762507	+	0.997089i	$0.524295\pi$
$444$	2.61078e11	0.318820
$445$	−6.04328e11	−0.730555
$446$	7.85751e11	0.940325
$447$	−2.39625e11	−0.283888
$448$	1.02333e12	1.20022
$449$	−8.83485e11	−1.02587	−0.512933	−	0.858429i	$-0.671441\pi$
$449$	−8.83485e11	−1.02587	−0.512933	+	0.858429i	$0.671441\pi$
$450$	2.71785e11	0.312441
$451$	4.96294e11	0.564865
$452$	−2.66816e11	−0.300669
$453$	−3.24782e11	−0.362368
$454$	−1.20281e12	−1.32875
$455$	−2.40915e11	−0.263520
$456$	−1.40224e11	−0.151873
$457$	−9.77143e11	−1.04794	−0.523969	−	0.851738i	$-0.675549\pi$
$457$	−9.77143e11	−1.04794	−0.523969	+	0.851738i	$0.675549\pi$
$458$	3.33043e11	0.353676
$459$	2.71199e11	0.285187
$460$	1.55744e12	1.62182
$461$	2.51148e11	0.258986	0.129493	−	0.991580i	$-0.458665\pi$
$461$	2.51148e11	0.258986	0.129493	+	0.991580i	$0.458665\pi$
$462$	7.99184e11	0.816128
$463$	4.80930e11	0.486371	0.243185	−	0.969980i	$-0.421808\pi$
$463$	4.80930e11	0.486371	0.243185	+	0.969980i	$0.421808\pi$
$464$	−8.67375e9	−0.00868712
$465$	−4.70795e11	−0.466975
$466$	−1.82768e12	−1.79541
$467$	−5.63309e10	−0.0548051	−0.0274026	−	0.999624i	$-0.508724\pi$
$467$	−5.63309e10	−0.0548051	−0.0274026	+	0.999624i	$0.508724\pi$
$468$	2.99652e11	0.288743
$469$	9.98036e11	0.952508
$470$	1.13351e12	1.07148
$471$	−1.01615e12	−0.951404
$472$	−1.24755e11	−0.115696
$473$	5.97089e11	0.548484
$474$	2.26324e11	0.205934
$475$	1.92548e11	0.173547
$476$	1.90033e12	1.69667
$477$	−3.41172e11	−0.301746
$478$	−6.83892e11	−0.599186
$479$	2.33976e11	0.203078	0.101539	−	0.994832i	$-0.467623\pi$
$479$	2.33976e11	0.203078	0.101539	+	0.994832i	$0.467623\pi$
$480$	−4.77110e11	−0.410236
$481$	−2.31977e11	−0.197602
$482$	1.19471e12	1.00821
$483$	8.23566e11	0.688552
$484$	8.33418e11	0.690333
$485$	1.23805e12	1.01602
$486$	1.26133e11	0.102557
$487$	−1.54104e12	−1.24147	−0.620733	−	0.784022i	$-0.713165\pi$
$487$	−1.54104e12	−1.24147	−0.620733	+	0.784022i	$0.713165\pi$
$488$	−3.08264e11	−0.246055
$489$	−9.78234e11	−0.773665
$490$	6.01596e11	0.471436
$491$	−4.63630e11	−0.360002	−0.180001	−	0.983666i	$-0.557610\pi$
$491$	−4.63630e11	−0.360002	−0.180001	+	0.983666i	$0.557610\pi$
$492$	5.48862e11	0.422299
$493$	−1.24950e11	−0.0952630
$494$	3.48736e11	0.263467
$495$	−3.44098e11	−0.257608
$496$	−2.29057e11	−0.169932
$497$	7.11272e11	0.522916
$498$	−5.08729e11	−0.370642
$499$	2.14250e12	1.54692	0.773462	−	0.633843i	$-0.218523\pi$
$499$	2.14250e12	1.54692	0.773462	+	0.633843i	$0.218523\pi$
$500$	−2.21854e12	−1.58746
$501$	7.11168e11	0.504316
$502$	3.11772e10	0.0219114
$503$	8.16297e11	0.568581	0.284291	−	0.958738i	$-0.408242\pi$
$503$	8.16297e11	0.568581	0.284291	+	0.958738i	$0.408242\pi$
$504$	3.15771e11	0.217989
$505$	−6.35113e10	−0.0434550
$506$	4.59061e12	3.11310
$507$	5.92712e11	0.398390
$508$	3.43738e12	2.29003
$509$	−1.36465e12	−0.901136	−0.450568	−	0.892742i	$-0.648779\pi$
$509$	−1.36465e12	−0.901136	−0.450568	+	0.892742i	$0.648779\pi$
$510$	−1.34409e12	−0.879759
$511$	−8.59827e11	−0.557849
$512$	−4.18863e11	−0.269375
$513$	8.93601e10	0.0569660
$514$	−4.45015e12	−2.81216
$515$	3.12058e11	0.195480
$516$	6.60333e11	0.410053
$517$	2.03384e12	1.25202
$518$	−6.84223e11	−0.417555
$519$	2.61995e11	0.158504
$520$	−5.30592e11	−0.318234
$521$	−1.64297e12	−0.976920	−0.488460	−	0.872586i	$-0.662441\pi$
$521$	−1.64297e12	−0.976920	−0.488460	+	0.872586i	$0.662441\pi$
$522$	−5.81136e10	−0.0342579
$523$	2.27813e12	1.33144	0.665719	−	0.746203i	$-0.268125\pi$
$523$	2.27813e12	1.33144	0.665719	+	0.746203i	$0.268125\pi$
$524$	−3.54066e12	−2.05160
$525$	−4.33599e11	−0.249098
$526$	−8.97132e11	−0.511000
$527$	−3.29968e12	−1.86348
$528$	−1.67415e11	−0.0937435
$529$	2.92951e12	1.62646
$530$	1.69089e12	0.930838
$531$	7.95020e10	0.0433963
$532$	6.26160e11	0.338909
$533$	−4.87683e11	−0.261737
$534$	−1.96995e12	−1.04838
$535$	−1.95135e12	−1.02978
$536$	2.19808e12	1.15028
$537$	−1.80399e12	−0.936158
$538$	5.99287e12	3.08400
$539$	1.07944e12	0.550869
$540$	−3.80545e11	−0.192590
$541$	−3.39774e12	−1.70530	−0.852652	−	0.522479i	$-0.825007\pi$
$541$	−3.39774e12	−1.70530	−0.852652	+	0.522479i	$0.825007\pi$
$542$	−1.13603e12	−0.565450
$543$	1.75586e12	0.866745
$544$	−3.34394e12	−1.63706
$545$	1.51033e12	0.733308
$546$	−7.85319e11	−0.378163
$547$	−2.14411e11	−0.102401	−0.0512005	−	0.998688i	$-0.516305\pi$
$547$	−2.14411e11	−0.102401	−0.0512005	+	0.998688i	$0.516305\pi$
$548$	−2.16441e12	−1.02524
$549$	1.96446e11	0.0922927
$550$	−2.41691e12	−1.12623
$551$	−4.11710e10	−0.0190287
$552$	1.81383e12	0.831514
$553$	−3.61072e11	−0.164184
$554$	−5.95424e12	−2.68555
$555$	2.94600e11	0.131800
$556$	−1.15018e12	−0.510420
$557$	2.17048e12	0.955450	0.477725	−	0.878510i	$-0.341462\pi$
$557$	2.17048e12	0.955450	0.477725	+	0.878510i	$0.341462\pi$
$558$	−1.53467e12	−0.670132
$559$	−5.86730e11	−0.254147
$560$	1.48855e11	0.0639614
$561$	−2.41169e12	−1.02799
$562$	6.30615e12	2.66656
$563$	9.89772e11	0.415191	0.207595	−	0.978215i	$-0.433436\pi$
$563$	9.89772e11	0.415191	0.207595	+	0.978215i	$0.433436\pi$
$564$	2.24927e12	0.936020
$565$	−3.01075e11	−0.124296
$566$	−5.54552e12	−2.27127
$567$	−2.01230e11	−0.0817653
$568$	1.56651e12	0.631488
$569$	−3.94076e12	−1.57607	−0.788033	−	0.615632i	$-0.788901\pi$
$569$	−3.94076e12	−1.57607	−0.788033	+	0.615632i	$0.788901\pi$
$570$	−4.42880e11	−0.175731
$571$	−8.16947e11	−0.321611	−0.160806	−	0.986986i	$-0.551409\pi$
$571$	−8.16947e11	−0.321611	−0.160806	+	0.986986i	$0.551409\pi$
$572$	−2.66473e12	−1.04081
$573$	−2.27969e12	−0.883446
$574$	−1.43844e12	−0.553080
$575$	−2.49064e12	−0.950180
$576$	−1.43625e12	−0.543663
$577$	7.47676e11	0.280816	0.140408	−	0.990094i	$-0.455159\pi$
$577$	7.47676e11	0.280816	0.140408	+	0.990094i	$0.455159\pi$
$578$	−5.13052e12	−1.91199
$579$	3.57531e11	0.132209
$580$	1.75329e11	0.0643322
$581$	8.11614e11	0.295499
$582$	4.03572e12	1.45803
$583$	3.03395e12	1.08768
$584$	−1.89369e12	−0.673674
$585$	3.38128e11	0.119366
$586$	−1.90409e12	−0.667035
$587$	−2.57396e12	−0.894808	−0.447404	−	0.894332i	$-0.647651\pi$
$587$	−2.57396e12	−0.894808	−0.447404	+	0.894332i	$0.647651\pi$
$588$	1.19377e12	0.411836
$589$	−1.08725e12	−0.372228
$590$	−3.94022e11	−0.133871
$591$	1.65276e12	0.557269
$592$	1.43332e11	0.0479619
$593$	2.53540e12	0.841979	0.420989	−	0.907066i	$-0.361683\pi$
$593$	2.53540e12	0.841979	0.420989	+	0.907066i	$0.361683\pi$
$594$	−1.12167e12	−0.369680
$595$	2.14433e12	0.701401
$596$	2.35662e12	0.765037
$597$	−8.26017e11	−0.266136
$598$	−4.51096e12	−1.44249
$599$	3.20638e12	1.01764	0.508820	−	0.860873i	$-0.330082\pi$
$599$	3.20638e12	1.01764	0.508820	+	0.860873i	$0.330082\pi$
$600$	−9.54959e11	−0.300818
$601$	−2.22462e12	−0.695537	−0.347769	−	0.937580i	$-0.613061\pi$
$601$	−2.22462e12	−0.695537	−0.347769	+	0.937580i	$0.613061\pi$
$602$	−1.73058e12	−0.537041
$603$	−1.40076e12	−0.431455
$604$	3.19412e12	0.976528
$605$	9.40430e11	0.285382
$606$	−2.07030e11	−0.0623600
$607$	1.85983e12	0.556062	0.278031	−	0.960572i	$-0.410318\pi$
$607$	1.85983e12	0.556062	0.278031	+	0.960572i	$0.410318\pi$
$608$	−1.10183e12	−0.327001
$609$	9.27130e10	0.0273126
$610$	−9.73609e11	−0.284709
$611$	−1.99855e12	−0.580137
$612$	−2.66714e12	−0.768537
$613$	4.96907e11	0.142136	0.0710679	−	0.997471i	$-0.477359\pi$
$613$	4.96907e11	0.142136	0.0710679	+	0.997471i	$0.477359\pi$
$614$	−8.49031e12	−2.41083
$615$	6.19336e11	0.174578
$616$	−2.80806e12	−0.785767
$617$	−4.67093e12	−1.29754	−0.648769	−	0.760985i	$-0.724716\pi$
$617$	−4.67093e12	−1.29754	−0.648769	+	0.760985i	$0.724716\pi$
$618$	1.01723e12	0.280524
$619$	−3.58040e11	−0.0980220	−0.0490110	−	0.998798i	$-0.515607\pi$
$619$	−3.58040e11	−0.0980220	−0.0490110	+	0.998798i	$0.515607\pi$
$620$	4.63011e12	1.25843
$621$	−1.15589e12	−0.311892
$622$	−1.26091e12	−0.337776
$623$	3.14281e12	0.835837
$624$	1.64510e11	0.0434372
$625$	−2.66843e11	−0.0699514
$626$	−6.40432e12	−1.66682
$627$	−7.94655e11	−0.205341
$628$	9.99350e12	2.56389
$629$	2.06478e12	0.525951
$630$	9.97321e11	0.252233
$631$	9.90994e11	0.248851	0.124425	−	0.992229i	$-0.460291\pi$
$631$	9.90994e11	0.248851	0.124425	+	0.992229i	$0.460291\pi$
$632$	−7.95227e11	−0.198273
$633$	1.08074e12	0.267550
$634$	−8.35315e9	−0.00205328
$635$	3.87875e12	0.946694
$636$	3.35531e12	0.813159
$637$	−1.06071e12	−0.255252
$638$	5.16788e11	0.123486
$639$	−9.98281e11	−0.236864
$640$	4.10244e12	0.966568
$641$	−3.94375e12	−0.922675	−0.461337	−	0.887225i	$-0.652630\pi$
$641$	−3.94375e12	−0.922675	−0.461337	+	0.887225i	$0.652630\pi$
$642$	−6.36087e12	−1.47778
$643$	6.09002e12	1.40498	0.702489	−	0.711695i	$-0.252072\pi$
$643$	6.09002e12	1.40498	0.702489	+	0.711695i	$0.252072\pi$
$644$	−8.09948e12	−1.85554
$645$	7.45121e11	0.169515
$646$	−3.10403e12	−0.701260
$647$	−8.53763e12	−1.91544	−0.957719	−	0.287704i	$-0.907108\pi$
$647$	−8.53763e12	−1.91544	−0.957719	+	0.287704i	$0.907108\pi$
$648$	−4.43190e11	−0.0987420
$649$	−7.06989e11	−0.156427
$650$	2.37497e12	0.521854
$651$	2.44837e12	0.534272
$652$	9.62059e12	2.08491
$653$	−2.31918e12	−0.499144	−0.249572	−	0.968356i	$-0.580290\pi$
$653$	−2.31918e12	−0.499144	−0.249572	+	0.968356i	$0.580290\pi$
$654$	4.92326e12	1.05233
$655$	−3.99529e12	−0.848130
$656$	3.01327e11	0.0635288
$657$	1.20678e12	0.252688
$658$	−5.89480e12	−1.22589
$659$	3.93884e12	0.813549	0.406774	−	0.913529i	$-0.366654\pi$
$659$	3.93884e12	0.813549	0.406774	+	0.913529i	$0.366654\pi$
$660$	3.38409e12	0.694214
$661$	−4.00845e12	−0.816714	−0.408357	−	0.912822i	$-0.633898\pi$
$661$	−4.00845e12	−0.816714	−0.408357	+	0.912822i	$0.633898\pi$
$662$	−2.67084e11	−0.0540489
$663$	2.36985e12	0.476333
$664$	1.78750e12	0.356853
$665$	7.06560e11	0.140104
$666$	9.60318e11	0.189139
$667$	5.32554e11	0.104183
$668$	−6.99409e12	−1.35906
$669$	1.75940e12	0.339584
$670$	6.94234e12	1.33097
$671$	−1.74694e12	−0.332680
$672$	2.48121e12	0.469356
$673$	−1.29844e12	−0.243979	−0.121990	−	0.992531i	$-0.538927\pi$
$673$	−1.29844e12	−0.243979	−0.121990	+	0.992531i	$0.538927\pi$
$674$	−1.46889e13	−2.74170
$675$	6.08563e11	0.112834
$676$	−5.82912e12	−1.07360
$677$	8.66231e12	1.58484	0.792419	−	0.609978i	$-0.208822\pi$
$677$	8.66231e12	1.58484	0.792419	+	0.609978i	$0.208822\pi$
$678$	−9.81425e11	−0.178371
$679$	−6.43849e12	−1.16244
$680$	4.72269e12	0.847031
$681$	−2.69325e12	−0.479860
$682$	1.36474e13	2.41557
$683$	3.03372e12	0.533436	0.266718	−	0.963775i	$-0.414061\pi$
$683$	3.03372e12	0.533436	0.266718	+	0.963775i	$0.414061\pi$
$684$	−8.78825e11	−0.153515
$685$	−2.44233e12	−0.423834
$686$	−9.95261e12	−1.71585
$687$	7.45729e11	0.127725
$688$	3.62525e11	0.0616865
$689$	−2.98131e12	−0.503989
$690$	5.72873e12	0.962137
$691$	7.07473e11	0.118048	0.0590240	−	0.998257i	$-0.481201\pi$
$691$	7.07473e11	0.118048	0.0590240	+	0.998257i	$0.481201\pi$
$692$	−2.57663e12	−0.427144
$693$	1.78948e12	0.294732
$694$	−1.91490e13	−3.13350
$695$	−1.29786e12	−0.211007
$696$	2.04191e11	0.0329834
$697$	4.34077e12	0.696657
$698$	−1.11664e13	−1.78059
$699$	−4.09242e12	−0.648384
$700$	4.26429e12	0.671283
$701$	5.38606e12	0.842442	0.421221	−	0.906958i	$-0.361602\pi$
$701$	5.38606e12	0.842442	0.421221	+	0.906958i	$0.361602\pi$
$702$	1.10221e12	0.171296
$703$	6.80345e11	0.105058
$704$	1.27722e13	1.95970
$705$	2.53808e12	0.386949
$706$	−1.34626e13	−2.03942
$707$	3.30290e11	0.0497174
$708$	−7.81874e11	−0.116947
$709$	−5.97478e12	−0.888002	−0.444001	−	0.896026i	$-0.646441\pi$
$709$	−5.97478e12	−0.888002	−0.444001	+	0.896026i	$0.646441\pi$
$710$	4.94760e12	0.730689
$711$	5.06771e11	0.0743701
$712$	6.92173e12	1.00938
$713$	1.40637e13	2.03797
$714$	6.98996e12	1.00654
$715$	−3.00688e12	−0.430268
$716$	1.77416e13	2.52281
$717$	−1.53133e12	−0.216387
$718$	−1.98774e13	−2.79126
$719$	−3.16517e12	−0.441689	−0.220844	−	0.975309i	$-0.570881\pi$
$719$	−3.16517e12	−0.441689	−0.220844	+	0.975309i	$0.570881\pi$
$720$	−2.08921e11	−0.0289725
$721$	−1.62286e12	−0.223652
$722$	1.06503e13	1.45863
$723$	2.67512e12	0.364100
$724$	−1.72683e13	−2.33575
$725$	−2.80384e11	−0.0376905
$726$	3.06555e12	0.409537
$727$	5.47097e12	0.726372	0.363186	−	0.931717i	$-0.381689\pi$
$727$	5.47097e12	0.726372	0.363186	+	0.931717i	$0.381689\pi$
$728$	2.75935e12	0.364095
$729$	2.82430e11	0.0370370
$730$	−5.98095e12	−0.779502
$731$	5.22236e12	0.676454
$732$	−1.93198e12	−0.248715
$733$	−2.58003e12	−0.330108	−0.165054	−	0.986285i	$-0.552780\pi$
$733$	−2.58003e12	−0.330108	−0.165054	+	0.986285i	$0.552780\pi$
$734$	1.42691e13	1.81452
$735$	1.34706e12	0.170252
$736$	1.42524e13	1.79035
$737$	1.24566e13	1.55523
$738$	2.01887e12	0.250527
$739$	7.87394e12	0.971163	0.485582	−	0.874191i	$-0.338608\pi$
$739$	7.87394e12	0.971163	0.485582	+	0.874191i	$0.338608\pi$
$740$	−2.89729e12	−0.355181
$741$	7.80868e11	0.0951471
$742$	−8.79348e12	−1.06498
$743$	1.97110e12	0.237279	0.118640	−	0.992937i	$-0.462147\pi$
$743$	1.97110e12	0.237279	0.118640	+	0.992937i	$0.462147\pi$
$744$	5.39230e12	0.645202
$745$	2.65922e12	0.316265
$746$	1.12887e13	1.33450
$747$	−1.13911e12	−0.133852
$748$	2.37182e13	2.77028
$749$	1.01480e13	1.17818
$750$	−8.16042e12	−0.941753
$751$	1.05866e13	1.21444	0.607219	−	0.794535i	$-0.292285\pi$
$751$	1.05866e13	1.21444	0.607219	+	0.794535i	$0.292285\pi$
$752$	1.23486e12	0.140811
$753$	6.98101e10	0.00791299
$754$	−5.07822e11	−0.0572190
$755$	3.60425e12	0.403695
$756$	1.97903e12	0.220345
$757$	6.82958e12	0.755897	0.377949	−	0.925827i	$-0.376630\pi$
$757$	6.82958e12	0.755897	0.377949	+	0.925827i	$0.376630\pi$
$758$	5.57906e12	0.613832
$759$	1.02790e13	1.12425
$760$	1.55613e12	0.169194
$761$	3.87107e12	0.418409	0.209204	−	0.977872i	$-0.432913\pi$
$761$	3.87107e12	0.418409	0.209204	+	0.977872i	$0.432913\pi$
$762$	1.26437e13	1.35855
$763$	−7.85445e12	−0.838987
$764$	2.24199e13	2.38075
$765$	−3.00961e12	−0.317712
$766$	−1.56769e13	−1.64524
$767$	6.94723e11	0.0724824
$768$	4.29432e12	0.445419
$769$	−3.32827e12	−0.343202	−0.171601	−	0.985167i	$-0.554894\pi$
$769$	−3.32827e12	−0.343202	−0.171601	+	0.985167i	$0.554894\pi$
$770$	−8.86890e12	−0.909204
$771$	−9.96448e12	−1.01557
$772$	−3.51619e12	−0.356283
$773$	1.09993e13	1.10805	0.554023	−	0.832502i	$-0.313092\pi$
$773$	1.09993e13	1.10805	0.554023	+	0.832502i	$0.313092\pi$
$774$	2.42890e12	0.243262
$775$	−7.40440e12	−0.737279
$776$	−1.41801e13	−1.40379
$777$	−1.53207e12	−0.150794
$778$	7.75462e12	0.758844
$779$	1.43029e12	0.139157
$780$	−3.32537e12	−0.321673
$781$	8.87744e12	0.853804
$782$	4.01511e13	3.83944
$783$	−1.30124e11	−0.0123717
$784$	6.55385e11	0.0619547
$785$	1.12767e13	1.05991
$786$	−1.30236e13	−1.21711
$787$	−4.00733e12	−0.372365	−0.186182	−	0.982515i	$-0.559612\pi$
$787$	−4.00733e12	−0.372365	−0.186182	+	0.982515i	$0.559612\pi$
$788$	−1.62543e13	−1.50176
$789$	−2.00880e12	−0.184540
$790$	−2.51162e12	−0.229420
$791$	1.56574e12	0.142209
$792$	3.94116e12	0.355927
$793$	1.71663e12	0.154151
$794$	−1.30147e12	−0.116209
$795$	3.78614e12	0.336158
$796$	8.12358e12	0.717198
$797$	−1.15951e13	−1.01792	−0.508959	−	0.860791i	$-0.669970\pi$
$797$	−1.15951e13	−1.01792	−0.508959	+	0.860791i	$0.669970\pi$
$798$	2.30320e12	0.201056
$799$	1.77887e13	1.54413
$800$	−7.50372e12	−0.647697
$801$	−4.41098e12	−0.378607
$802$	−8.66944e12	−0.739956
$803$	−1.07316e13	−0.910842
$804$	1.37760e13	1.16271
$805$	−9.13947e12	−0.767078
$806$	−1.34106e13	−1.11928
$807$	1.34188e13	1.11374
$808$	7.27433e11	0.0600401
$809$	8.25765e12	0.677779	0.338890	−	0.940826i	$-0.389949\pi$
$809$	8.25765e12	0.677779	0.338890	+	0.940826i	$0.389949\pi$
$810$	−1.39976e12	−0.114254
$811$	−8.98093e12	−0.729000	−0.364500	−	0.931203i	$-0.618760\pi$
$811$	−8.98093e12	−0.729000	−0.364500	+	0.931203i	$0.618760\pi$
$812$	−9.11800e11	−0.0736033
$813$	−2.54373e12	−0.204204
$814$	−8.53984e12	−0.681774
$815$	1.08559e13	0.861898
$816$	−1.46427e12	−0.115615
$817$	1.72077e12	0.135121
$818$	−2.95370e13	−2.30662
$819$	−1.75844e12	−0.136568
$820$	−6.09096e12	−0.470461
$821$	−1.51505e13	−1.16381	−0.581905	−	0.813257i	$-0.697692\pi$
$821$	−1.51505e13	−1.16381	−0.581905	+	0.813257i	$0.697692\pi$
$822$	−7.96133e12	−0.608222
$823$	1.47489e12	0.112063	0.0560313	−	0.998429i	$-0.482155\pi$
$823$	1.47489e12	0.112063	0.0560313	+	0.998429i	$0.482155\pi$
$824$	−3.57419e12	−0.270088
$825$	−5.41178e12	−0.406722
$826$	2.04911e12	0.153163
$827$	1.16616e13	0.866925	0.433463	−	0.901172i	$-0.357292\pi$
$827$	1.16616e13	0.866925	0.433463	+	0.901172i	$0.357292\pi$
$828$	1.13678e13	0.840501
$829$	2.04853e13	1.50642	0.753210	−	0.657780i	$-0.228505\pi$
$829$	2.04853e13	1.50642	0.753210	+	0.657780i	$0.228505\pi$
$830$	5.64558e12	0.412912
$831$	−1.33324e13	−0.969845
$832$	−1.25506e13	−0.908050
$833$	9.44116e12	0.679396
$834$	−4.23068e12	−0.302805
$835$	−7.89214e12	−0.561831
$836$	7.81515e12	0.553362
$837$	−3.43633e12	−0.242008
$838$	−4.91720e11	−0.0344445
$839$	8.04580e12	0.560584	0.280292	−	0.959915i	$-0.409569\pi$
$839$	8.04580e12	0.560584	0.280292	+	0.959915i	$0.409569\pi$
$840$	−3.50425e12	−0.242850
$841$	−1.44472e13	−0.995867
$842$	7.20376e12	0.493918
$843$	1.41203e13	0.962987
$844$	−1.06287e13	−0.721007
$845$	−6.57759e12	−0.443825
$846$	8.27345e12	0.555290
$847$	−4.89070e12	−0.326510
$848$	1.84208e12	0.122328
$849$	−1.24172e13	−0.820234
$850$	−2.11391e13	−1.38900
$851$	−8.80038e12	−0.575199
$852$	9.81775e12	0.638313
$853$	−2.14040e13	−1.38428	−0.692140	−	0.721763i	$-0.743332\pi$
$853$	−2.14040e13	−1.38428	−0.692140	+	0.721763i	$0.743332\pi$
$854$	5.06326e12	0.325739
$855$	−9.91668e11	−0.0634627
$856$	2.23500e13	1.42280
$857$	2.80212e13	1.77449	0.887245	−	0.461299i	$-0.152617\pi$
$857$	2.80212e13	1.77449	0.887245	+	0.461299i	$0.152617\pi$
$858$	−9.80163e12	−0.617455
$859$	−1.79329e13	−1.12378	−0.561891	−	0.827211i	$-0.689926\pi$
$859$	−1.79329e13	−1.12378	−0.561891	+	0.827211i	$0.689926\pi$
$860$	−7.32801e12	−0.456818
$861$	−3.22086e12	−0.199737
$862$	−2.54048e13	−1.56723
$863$	−1.96418e13	−1.20540	−0.602701	−	0.797967i	$-0.705909\pi$
$863$	−1.96418e13	−1.20540	−0.602701	+	0.797967i	$0.705909\pi$
$864$	−3.48242e12	−0.212603
$865$	−2.90747e12	−0.176580
$866$	1.01555e13	0.613582
$867$	−1.14879e13	−0.690488
$868$	−2.40789e13	−1.43978
$869$	−4.50657e12	−0.268076
$870$	6.44911e11	0.0381648
$871$	−1.22405e13	−0.720636
$872$	−1.72987e13	−1.01318
$873$	9.03652e12	0.526547
$874$	1.32298e13	0.766925
$875$	1.30189e13	0.750826
$876$	−1.18683e13	−0.680955
$877$	2.23088e12	0.127344	0.0636718	−	0.997971i	$-0.479719\pi$
$877$	2.23088e12	0.127344	0.0636718	+	0.997971i	$0.479719\pi$
$878$	−1.98960e13	−1.12990
$879$	−4.26352e12	−0.240890
$880$	1.85787e12	0.104435
$881$	−2.49429e13	−1.39494	−0.697469	−	0.716615i	$-0.745691\pi$
$881$	−2.49429e13	−1.39494	−0.697469	+	0.716615i	$0.745691\pi$
$882$	4.39104e12	0.244320
$883$	−1.27104e13	−0.703614	−0.351807	−	0.936073i	$-0.614433\pi$
$883$	−1.27104e13	−0.703614	−0.351807	+	0.936073i	$0.614433\pi$
$884$	−2.33067e13	−1.28365
$885$	−8.82268e11	−0.0483455
$886$	4.47193e12	0.243805
$887$	−1.03838e13	−0.563251	−0.281625	−	0.959524i	$-0.590874\pi$
$887$	−1.03838e13	−0.563251	−0.281625	+	0.959524i	$0.590874\pi$
$888$	−3.37423e12	−0.182103
$889$	−2.01714e13	−1.08313
$890$	2.18614e13	1.16794
$891$	−2.51157e12	−0.133504
$892$	−1.73031e13	−0.915129
$893$	5.86139e12	0.308439
$894$	8.66834e12	0.453855
$895$	2.00196e13	1.04292
$896$	−2.13347e13	−1.10586
$897$	−1.01007e13	−0.520935
$898$	3.19598e13	1.64006
$899$	1.58322e12	0.0808395
$900$	−5.98500e12	−0.304070
$901$	2.65360e13	1.34145
$902$	−1.79533e13	−0.903055
$903$	−3.87500e12	−0.193944
$904$	3.44840e12	0.171735
$905$	−1.94856e13	−0.965594
$906$	1.17489e13	0.579322
$907$	1.26702e13	0.621659	0.310829	−	0.950466i	$-0.399393\pi$
$907$	1.26702e13	0.621659	0.310829	+	0.950466i	$0.399393\pi$
$908$	2.64871e13	1.29315
$909$	−4.63568e11	−0.0225204
$910$	8.71503e12	0.421291
$911$	2.60368e13	1.25243	0.626217	−	0.779649i	$-0.284602\pi$
$911$	2.60368e13	1.25243	0.626217	+	0.779649i	$0.284602\pi$
$912$	−4.82478e11	−0.0230941
$913$	1.01298e13	0.482484
$914$	3.53478e13	1.67535
$915$	−2.18004e12	−0.102818
$916$	−7.33398e12	−0.344199
$917$	2.07775e13	0.970356
$918$	−9.81052e12	−0.455932
$919$	1.59208e13	0.736283	0.368141	−	0.929770i	$-0.379994\pi$
$919$	1.59208e13	0.736283	0.368141	+	0.929770i	$0.379994\pi$
$920$	−2.01288e13	−0.926345
$921$	−1.90110e13	−0.870634
$922$	−9.08521e12	−0.414043
$923$	−8.72342e12	−0.395621
$924$	−1.75989e13	−0.794260
$925$	4.63330e12	0.208091
$926$	−1.73975e13	−0.777566
$927$	2.27771e12	0.101307
$928$	1.60446e12	0.0710172
$929$	1.91960e13	0.845551	0.422775	−	0.906234i	$-0.361056\pi$
$929$	1.91960e13	0.845551	0.422775	+	0.906234i	$0.361056\pi$
$930$	1.70309e13	0.746558
$931$	3.11087e12	0.135709
$932$	4.02475e13	1.74730
$933$	−2.82336e12	−0.121983
$934$	2.03775e12	0.0876175
$935$	2.67636e13	1.14523
$936$	−3.87279e12	−0.164923
$937$	4.35148e13	1.84421	0.922103	−	0.386946i	$-0.126470\pi$
$937$	4.35148e13	1.84421	0.922103	+	0.386946i	$0.126470\pi$
$938$	−3.61036e13	−1.52278
$939$	−1.43401e13	−0.601947
$940$	−2.49611e13	−1.04277
$941$	−3.71803e13	−1.54582	−0.772912	−	0.634514i	$-0.781200\pi$
$941$	−3.71803e13	−1.54582	−0.772912	+	0.634514i	$0.781200\pi$
$942$	3.67590e13	1.52102
$943$	−1.85010e13	−0.761890
$944$	−4.29252e11	−0.0175929
$945$	2.23314e12	0.0910903
$946$	−2.15995e13	−0.876867
$947$	2.06568e13	0.834620	0.417310	−	0.908764i	$-0.362973\pi$
$947$	2.06568e13	0.834620	0.417310	+	0.908764i	$0.362973\pi$
$948$	−4.98391e12	−0.200416
$949$	1.05454e13	0.422050
$950$	−6.96536e12	−0.277452
$951$	−1.87038e10	−0.000741512 0
$952$	−2.45604e13	−0.969099
$953$	−1.41965e13	−0.557525	−0.278763	−	0.960360i	$-0.589924\pi$
$953$	−1.41965e13	−0.557525	−0.278763	+	0.960360i	$0.589924\pi$
$954$	1.23418e13	0.482404
$955$	2.52987e13	0.984199
$956$	1.50601e13	0.583131
$957$	1.15716e12	0.0445953
$958$	−8.46402e12	−0.324662
$959$	1.27013e13	0.484914
$960$	1.59387e13	0.605666
$961$	1.53703e13	0.581334
$962$	8.39168e12	0.315908
$963$	−1.42429e13	−0.533678
$964$	−2.63089e13	−0.981195
$965$	−3.96768e12	−0.147287
$966$	−2.97922e13	−1.10079
$967$	−4.32059e13	−1.58900	−0.794500	−	0.607264i	$-0.792267\pi$
$967$	−4.32059e13	−1.58900	−0.794500	+	0.607264i	$0.792267\pi$
$968$	−1.07713e13	−0.394302
$969$	−6.95034e12	−0.253250
$970$	−4.47861e13	−1.62432
$971$	2.39954e13	0.866245	0.433123	−	0.901335i	$-0.357412\pi$
$971$	2.39954e13	0.866245	0.433123	+	0.901335i	$0.357412\pi$
$972$	−2.77760e12	−0.0998093
$973$	6.74952e12	0.241416
$974$	5.57468e13	1.98474
$975$	5.31789e12	0.188460
$976$	−1.06066e12	−0.0374156
$977$	1.45550e13	0.511077	0.255538	−	0.966799i	$-0.417747\pi$
$977$	1.45550e13	0.511077	0.255538	+	0.966799i	$0.417747\pi$
$978$	3.53873e13	1.23687
$979$	3.92256e13	1.36473
$980$	−1.32478e13	−0.458804
$981$	1.10238e13	0.380034
$982$	1.67717e13	0.575539
$983$	4.62268e13	1.57908	0.789538	−	0.613701i	$-0.210320\pi$
$983$	4.62268e13	1.57908	0.789538	+	0.613701i	$0.210320\pi$
$984$	−7.09363e12	−0.241207
$985$	−1.83414e13	−0.620824
$986$	4.52002e12	0.152298
$987$	−1.31993e13	−0.442713
$988$	−7.67956e12	−0.256407
$989$	−2.22585e13	−0.739796
$990$	1.24476e13	0.411840
$991$	1.20817e13	0.397922	0.198961	−	0.980007i	$-0.436243\pi$
$991$	1.20817e13	0.397922	0.198961	+	0.980007i	$0.436243\pi$
$992$	4.23707e13	1.38920
$993$	−5.98038e11	−0.0195190
$994$	−2.57300e13	−0.835991
$995$	9.16666e12	0.296488
$996$	1.12028e13	0.360710
$997$	−5.11913e13	−1.64085	−0.820423	−	0.571757i	$-0.806262\pi$
$997$	−5.11913e13	−1.64085	−0.820423	+	0.571757i	$0.806262\pi$
$998$	−7.75043e13	−2.47308
$999$	2.15028e12	0.0683048

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.c.1.4	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.c.1.4	✓	22	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-36.1747 q^{2} -81.0000 q^{3} +796.607 q^{4} +898.892 q^{5} +2930.15 q^{6} -4674.69 q^{7} -10295.5 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-36.1747 q^{2} -81.0000 q^{3} +796.607 q^{4} +898.892 q^{5} +2930.15 q^{6} -4674.69 q^{7} -10295.5 q^{8} +6561.00 q^{9} -32517.1 q^{10} -58345.2 q^{11} -64525.1 q^{12} +57332.9 q^{13} +169105. q^{14} -72810.3 q^{15} -35424.5 q^{16} -510308. q^{17} -237342. q^{18} -168147. q^{19} +716063. q^{20} +378650. q^{21} +2.11062e6 q^{22} +2.17501e6 q^{23} +833939. q^{24} -1.14512e6 q^{25} -2.07400e6 q^{26} -531441. q^{27} -3.72389e6 q^{28} +244852. q^{29} +2.63389e6 q^{30} +6.46606e6 q^{31} +6.55279e6 q^{32} +4.72596e6 q^{33} +1.84602e7 q^{34} -4.20204e6 q^{35} +5.22654e6 q^{36} -4.04614e6 q^{37} +6.08266e6 q^{38} -4.64396e6 q^{39} -9.25459e6 q^{40} -8.50617e6 q^{41} -1.36975e7 q^{42} -1.02337e7 q^{43} -4.64781e7 q^{44} +5.89763e6 q^{45} -7.86802e7 q^{46} -3.48588e7 q^{47} +2.86939e6 q^{48} -1.85009e7 q^{49} +4.14243e7 q^{50} +4.13350e7 q^{51} +4.56718e7 q^{52} -5.20000e7 q^{53} +1.92247e7 q^{54} -5.24460e7 q^{55} +4.81285e7 q^{56} +1.36199e7 q^{57} -8.85743e6 q^{58} +1.21174e7 q^{59} -5.80011e7 q^{60} +2.99414e7 q^{61} -2.33907e8 q^{62} -3.06706e7 q^{63} -2.18908e8 q^{64} +5.15361e7 q^{65} -1.70960e8 q^{66} -2.13498e8 q^{67} -4.06515e8 q^{68} -1.76176e8 q^{69} +1.52007e8 q^{70} -1.52154e8 q^{71} -6.75491e7 q^{72} +1.83932e8 q^{73} +1.46368e8 q^{74} +9.27546e7 q^{75} -1.33947e8 q^{76} +2.72745e8 q^{77} +1.67994e8 q^{78} +7.72399e7 q^{79} -3.18428e7 q^{80} +4.30467e7 q^{81} +3.07708e8 q^{82} -1.73619e8 q^{83} +3.01635e8 q^{84} -4.58712e8 q^{85} +3.70202e8 q^{86} -1.98330e7 q^{87} +6.00695e8 q^{88} -6.72303e8 q^{89} -2.13345e8 q^{90} -2.68013e8 q^{91} +1.73263e9 q^{92} -5.23751e8 q^{93} +1.26100e9 q^{94} -1.51146e8 q^{95} -5.30776e8 q^{96} +1.37731e9 q^{97} +6.69264e8 q^{98} -3.82803e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9}+O(q^{10}) \) 22 * q + 36 * q^2 - 1782 * q^3 + 5718 * q^4 + 808 * q^5 - 2916 * q^6 + 21249 * q^7 + 9435 * q^8 + 144342 * q^9	\( 22 q + 36 q^{2} - 1782 q^{3} + 5718 q^{4} + 808 q^{5} - 2916 q^{6} + 21249 q^{7} + 9435 q^{8} + 144342 q^{9} + 68441 q^{10} - 68033 q^{11} - 463158 q^{12} + 283817 q^{13} + 80285 q^{14} - 65448 q^{15} + 1067674 q^{16} + 436893 q^{17} + 236196 q^{18} + 1207580 q^{19} + 4209677 q^{20} - 1721169 q^{21} + 5460442 q^{22} + 2421966 q^{23} - 764235 q^{24} + 7441842 q^{25} - 2736526 q^{26} - 11691702 q^{27} + 4095246 q^{28} - 2320594 q^{29} - 5543721 q^{30} - 3178024 q^{31} - 20786874 q^{32} + 5510673 q^{33} - 13809336 q^{34} - 2630800 q^{35} + 37515798 q^{36} + 3981807 q^{37} - 24156377 q^{38} - 22989177 q^{39} - 29544450 q^{40} - 885225 q^{41} - 6503085 q^{42} + 12360835 q^{43} - 117711882 q^{44} + 5301288 q^{45} + 161066949 q^{46} + 75901252 q^{47} - 86481594 q^{48} + 170907951 q^{49} - 61318927 q^{50} - 35388333 q^{51} - 100762 q^{52} - 34790192 q^{53} - 19131876 q^{54} + 151773316 q^{55} - 417630344 q^{56} - 97813980 q^{57} - 432929294 q^{58} + 266581942 q^{59} - 340983837 q^{60} - 290555332 q^{61} + 158267098 q^{62} + 139414689 q^{63} - 131794443 q^{64} - 650690086 q^{65} - 442295802 q^{66} + 86645184 q^{67} + 62738541 q^{68} - 196179246 q^{69} + 429714610 q^{70} - 36567631 q^{71} + 61903035 q^{72} + 907807228 q^{73} - 171827242 q^{74} - 602789202 q^{75} + 1744504396 q^{76} - 310688725 q^{77} + 221658606 q^{78} + 2508604687 q^{79} + 3509441927 q^{80} + 947027862 q^{81} + 1759214793 q^{82} + 2185672083 q^{83} - 331714926 q^{84} + 2868860198 q^{85} + 2397001564 q^{86} + 187968114 q^{87} + 7683735877 q^{88} + 1320145942 q^{89} + 449041401 q^{90} + 3894639897 q^{91} + 3505964640 q^{92} + 257419944 q^{93} + 5406355552 q^{94} + 3093659122 q^{95} + 1683736794 q^{96} + 3904552980 q^{97} + 6137683116 q^{98} - 446364513 q^{99}+O(q^{100}) \) 22 * q + 36 * q^2 - 1782 * q^3 + 5718 * q^4 + 808 * q^5 - 2916 * q^6 + 21249 * q^7 + 9435 * q^8 + 144342 * q^9 + 68441 * q^10 - 68033 * q^11 - 463158 * q^12 + 283817 * q^13 + 80285 * q^14 - 65448 * q^15 + 1067674 * q^16 + 436893 * q^17 + 236196 * q^18 + 1207580 * q^19 + 4209677 * q^20 - 1721169 * q^21 + 5460442 * q^22 + 2421966 * q^23 - 764235 * q^24 + 7441842 * q^25 - 2736526 * q^26 - 11691702 * q^27 + 4095246 * q^28 - 2320594 * q^29 - 5543721 * q^30 - 3178024 * q^31 - 20786874 * q^32 + 5510673 * q^33 - 13809336 * q^34 - 2630800 * q^35 + 37515798 * q^36 + 3981807 * q^37 - 24156377 * q^38 - 22989177 * q^39 - 29544450 * q^40 - 885225 * q^41 - 6503085 * q^42 + 12360835 * q^43 - 117711882 * q^44 + 5301288 * q^45 + 161066949 * q^46 + 75901252 * q^47 - 86481594 * q^48 + 170907951 * q^49 - 61318927 * q^50 - 35388333 * q^51 - 100762 * q^52 - 34790192 * q^53 - 19131876 * q^54 + 151773316 * q^55 - 417630344 * q^56 - 97813980 * q^57 - 432929294 * q^58 + 266581942 * q^59 - 340983837 * q^60 - 290555332 * q^61 + 158267098 * q^62 + 139414689 * q^63 - 131794443 * q^64 - 650690086 * q^65 - 442295802 * q^66 + 86645184 * q^67 + 62738541 * q^68 - 196179246 * q^69 + 429714610 * q^70 - 36567631 * q^71 + 61903035 * q^72 + 907807228 * q^73 - 171827242 * q^74 - 602789202 * q^75 + 1744504396 * q^76 - 310688725 * q^77 + 221658606 * q^78 + 2508604687 * q^79 + 3509441927 * q^80 + 947027862 * q^81 + 1759214793 * q^82 + 2185672083 * q^83 - 331714926 * q^84 + 2868860198 * q^85 + 2397001564 * q^86 + 187968114 * q^87 + 7683735877 * q^88 + 1320145942 * q^89 + 449041401 * q^90 + 3894639897 * q^91 + 3505964640 * q^92 + 257419944 * q^93 + 5406355552 * q^94 + 3093659122 * q^95 + 1683736794 * q^96 + 3904552980 * q^97 + 6137683116 * q^98 - 446364513 * q^99

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