LMFDB - Embedded newform 177.10.a.b.1.13

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:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
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)

$f(q)$	$=$	$q+11.8993 q^{2} -81.0000 q^{3} -370.407 q^{4} -236.774 q^{5} -963.842 q^{6} +4185.56 q^{7} -10500.0 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+11.8993 q^{2} -81.0000 q^{3} -370.407 q^{4} -236.774 q^{5} -963.842 q^{6} +4185.56 q^{7} -10500.0 q^{8} +6561.00 q^{9} -2817.44 q^{10} -25832.4 q^{11} +30003.0 q^{12} +10977.2 q^{13} +49805.2 q^{14} +19178.7 q^{15} +64705.7 q^{16} -74869.7 q^{17} +78071.2 q^{18} +575877. q^{19} +87702.6 q^{20} -339030. q^{21} -307387. q^{22} +1.18652e6 q^{23} +850501. q^{24} -1.89706e6 q^{25} +130621. q^{26} -531441. q^{27} -1.55036e6 q^{28} +971729. q^{29} +228213. q^{30} +7.66093e6 q^{31} +6.14596e6 q^{32} +2.09243e6 q^{33} -890896. q^{34} -991030. q^{35} -2.43024e6 q^{36} -1.34632e7 q^{37} +6.85252e6 q^{38} -889153. q^{39} +2.48613e6 q^{40} +3.71716e6 q^{41} -4.03422e6 q^{42} +1.42413e7 q^{43} +9.56851e6 q^{44} -1.55347e6 q^{45} +1.41188e7 q^{46} +5.03480e7 q^{47} -5.24116e6 q^{48} -2.28347e7 q^{49} -2.25737e7 q^{50} +6.06445e6 q^{51} -4.06603e6 q^{52} -4.53012e7 q^{53} -6.32377e6 q^{54} +6.11644e6 q^{55} -4.39484e7 q^{56} -4.66460e7 q^{57} +1.15629e7 q^{58} -1.21174e7 q^{59} -7.10391e6 q^{60} -1.39439e8 q^{61} +9.11596e7 q^{62} +2.74614e7 q^{63} +4.00032e7 q^{64} -2.59911e6 q^{65} +2.48984e7 q^{66} -1.76510e8 q^{67} +2.77323e7 q^{68} -9.61083e7 q^{69} -1.17926e7 q^{70} -4.76874e7 q^{71} -6.88906e7 q^{72} -1.70848e8 q^{73} -1.60202e8 q^{74} +1.53662e8 q^{75} -2.13309e8 q^{76} -1.08123e8 q^{77} -1.05803e7 q^{78} -7.11694e7 q^{79} -1.53206e7 q^{80} +4.30467e7 q^{81} +4.42315e7 q^{82} -3.04121e8 q^{83} +1.25579e8 q^{84} +1.77272e7 q^{85} +1.69462e8 q^{86} -7.87100e7 q^{87} +2.71241e8 q^{88} -6.08801e8 q^{89} -1.84852e7 q^{90} +4.59457e7 q^{91} -4.39496e8 q^{92} -6.20535e8 q^{93} +5.99106e8 q^{94} -1.36353e8 q^{95} -4.97823e8 q^{96} -5.99259e8 q^{97} -2.71717e8 q^{98} -1.69487e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9}+O(q^{10}) $ 21 * q + 20 * q^2 - 1701 * q^3 + 4950 * q^4 + 2058 * q^5 - 1620 * q^6 - 17167 * q^7 - 2853 * q^8 + 137781 * q^9	\( 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9} - 31559 q^{10} - 38751 q^{11} - 400950 q^{12} - 58915 q^{13} + 3453 q^{14} - 166698 q^{15} + 1655714 q^{16} - 64233 q^{17} + 131220 q^{18} - 1937236 q^{19} - 1065507 q^{20} + 1390527 q^{21} - 5386882 q^{22} - 1838574 q^{23} + 231093 q^{24} + 4565755 q^{25} - 839702 q^{26} - 11160261 q^{27} - 4471034 q^{28} + 15658544 q^{29} + 2556279 q^{30} - 14282802 q^{31} - 2205286 q^{32} + 3138831 q^{33} + 19005532 q^{34} - 8633300 q^{35} + 32476950 q^{36} + 7531195 q^{37} + 26649773 q^{38} + 4772115 q^{39} + 17775672 q^{40} + 18338245 q^{41} - 279693 q^{42} - 22480305 q^{43} - 80230922 q^{44} + 13502538 q^{45} - 83894107 q^{46} - 110397260 q^{47} - 134112834 q^{48} + 130653638 q^{49} + 65575693 q^{50} + 5202873 q^{51} + 177908014 q^{52} + 145498338 q^{53} - 10628820 q^{54} + 86448944 q^{55} + 354387888 q^{56} + 156916116 q^{57} + 115508368 q^{58} - 254464581 q^{59} + 86306067 q^{60} + 287595506 q^{61} + 819899030 q^{62} - 112632687 q^{63} + 822446413 q^{64} + 77238206 q^{65} + 436337442 q^{66} - 392860610 q^{67} + 167325073 q^{68} + 148924494 q^{69} - 424902116 q^{70} - 248960491 q^{71} - 18718533 q^{72} - 758406074 q^{73} - 923266846 q^{74} - 369826155 q^{75} - 2312747568 q^{76} - 878126795 q^{77} + 68015862 q^{78} - 1925801029 q^{79} - 1898919861 q^{80} + 903981141 q^{81} - 3249102191 q^{82} - 1650336307 q^{83} + 362153754 q^{84} - 2342480762 q^{85} - 3609864952 q^{86} - 1268342064 q^{87} - 5987792887 q^{88} - 574997526 q^{89} - 207058599 q^{90} - 4481387117 q^{91} - 5317166770 q^{92} + 1156906962 q^{93} - 5360726568 q^{94} - 2789231462 q^{95} + 178628166 q^{96} - 4651540898 q^{97} - 5566652976 q^{98} - 254245311 q^{99}+O(q^{100}) \) 21 * q + 20 * q^2 - 1701 * q^3 + 4950 * q^4 + 2058 * q^5 - 1620 * q^6 - 17167 * q^7 - 2853 * q^8 + 137781 * q^9 - 31559 * q^10 - 38751 * q^11 - 400950 * q^12 - 58915 * q^13 + 3453 * q^14 - 166698 * q^15 + 1655714 * q^16 - 64233 * q^17 + 131220 * q^18 - 1937236 * q^19 - 1065507 * q^20 + 1390527 * q^21 - 5386882 * q^22 - 1838574 * q^23 + 231093 * q^24 + 4565755 * q^25 - 839702 * q^26 - 11160261 * q^27 - 4471034 * q^28 + 15658544 * q^29 + 2556279 * q^30 - 14282802 * q^31 - 2205286 * q^32 + 3138831 * q^33 + 19005532 * q^34 - 8633300 * q^35 + 32476950 * q^36 + 7531195 * q^37 + 26649773 * q^38 + 4772115 * q^39 + 17775672 * q^40 + 18338245 * q^41 - 279693 * q^42 - 22480305 * q^43 - 80230922 * q^44 + 13502538 * q^45 - 83894107 * q^46 - 110397260 * q^47 - 134112834 * q^48 + 130653638 * q^49 + 65575693 * q^50 + 5202873 * q^51 + 177908014 * q^52 + 145498338 * q^53 - 10628820 * q^54 + 86448944 * q^55 + 354387888 * q^56 + 156916116 * q^57 + 115508368 * q^58 - 254464581 * q^59 + 86306067 * q^60 + 287595506 * q^61 + 819899030 * q^62 - 112632687 * q^63 + 822446413 * q^64 + 77238206 * q^65 + 436337442 * q^66 - 392860610 * q^67 + 167325073 * q^68 + 148924494 * q^69 - 424902116 * q^70 - 248960491 * q^71 - 18718533 * q^72 - 758406074 * q^73 - 923266846 * q^74 - 369826155 * q^75 - 2312747568 * q^76 - 878126795 * q^77 + 68015862 * q^78 - 1925801029 * q^79 - 1898919861 * q^80 + 903981141 * q^81 - 3249102191 * q^82 - 1650336307 * q^83 + 362153754 * q^84 - 2342480762 * q^85 - 3609864952 * q^86 - 1268342064 * q^87 - 5987792887 * q^88 - 574997526 * q^89 - 207058599 * q^90 - 4481387117 * q^91 - 5317166770 * q^92 + 1156906962 * q^93 - 5360726568 * q^94 - 2789231462 * q^95 + 178628166 * q^96 - 4651540898 * q^97 - 5566652976 * q^98 - 254245311 * 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 $

$2$	11.8993	0.525879	0.262940	−	0.964812i	$-0.415308\pi$
$2$	11.8993	0.525879	0.262940	+	0.964812i	$0.415308\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	−370.407	−0.723451
$5$	−236.774	−0.169422	−0.0847108	−	0.996406i	$-0.526997\pi$
$5$	−236.774	−0.169422	−0.0847108	+	0.996406i	$0.526997\pi$
$6$	−963.842	−0.303617
$7$	4185.56	0.658889	0.329444	−	0.944175i	$-0.393139\pi$
$7$	4185.56	0.658889	0.329444	+	0.944175i	$0.393139\pi$
$8$	−10500.0	−0.906327
$9$	6561.00	0.333333
$10$	−2817.44	−0.0890952
$11$	−25832.4	−0.531983	−0.265992	−	0.963975i	$-0.585699\pi$
$11$	−25832.4	−0.531983	−0.265992	+	0.963975i	$0.585699\pi$
$12$	30003.0	0.417685
$13$	10977.2	0.106597	0.0532987	−	0.998579i	$-0.483026\pi$
$13$	10977.2	0.106597	0.0532987	+	0.998579i	$0.483026\pi$
$14$	49805.2	0.346496
$15$	19178.7	0.0978156
$16$	64705.7	0.246832
$17$	−74869.7	−0.217413	−0.108707	−	0.994074i	$-0.534671\pi$
$17$	−74869.7	−0.217413	−0.108707	+	0.994074i	$0.534671\pi$
$18$	78071.2	0.175293
$19$	575877.	1.01377	0.506884	−	0.862014i	$-0.330797\pi$
$19$	575877.	1.01377	0.506884	+	0.862014i	$0.330797\pi$
$20$	87702.6	0.122568
$21$	−339030.	−0.380410
$22$	−307387.	−0.279759
$23$	1.18652e6	0.884098	0.442049	−	0.896991i	$-0.354252\pi$
$23$	1.18652e6	0.884098	0.442049	+	0.896991i	$0.354252\pi$
$24$	850501.	0.523268
$25$	−1.89706e6	−0.971296
$26$	130621.	0.0560573
$27$	−531441.	−0.192450
$28$	−1.55036e6	−0.476674
$29$	971729.	0.255126	0.127563	−	0.991830i	$-0.459285\pi$
$29$	971729.	0.255126	0.127563	+	0.991830i	$0.459285\pi$
$30$	228213.	0.0514392
$31$	7.66093e6	1.48989	0.744944	−	0.667127i	$-0.232476\pi$
$31$	7.66093e6	1.48989	0.744944	+	0.667127i	$0.232476\pi$
$32$	6.14596e6	1.03613
$33$	2.09243e6	0.307141
$34$	−890896.	−0.114333
$35$	−991030.	−0.111630
$36$	−2.43024e6	−0.241150
$37$	−1.34632e7	−1.18097	−0.590487	−	0.807047i	$-0.701064\pi$
$37$	−1.34632e7	−1.18097	−0.590487	+	0.807047i	$0.701064\pi$
$38$	6.85252e6	0.533119
$39$	−889153.	−0.0615440
$40$	2.48613e6	0.153551
$41$	3.71716e6	0.205439	0.102720	−	0.994710i	$-0.467246\pi$
$41$	3.71716e6	0.205439	0.102720	+	0.994710i	$0.467246\pi$
$42$	−4.03422e6	−0.200050
$43$	1.42413e7	0.635248	0.317624	−	0.948217i	$-0.397115\pi$
$43$	1.42413e7	0.635248	0.317624	+	0.948217i	$0.397115\pi$
$44$	9.56851e6	0.384864
$45$	−1.55347e6	−0.0564738
$46$	1.41188e7	0.464929
$47$	5.03480e7	1.50502	0.752510	−	0.658581i	$-0.228843\pi$
$47$	5.03480e7	1.50502	0.752510	+	0.658581i	$0.228843\pi$
$48$	−5.24116e6	−0.142509
$49$	−2.28347e7	−0.565866
$50$	−2.25737e7	−0.510785
$51$	6.06445e6	0.125524
$52$	−4.06603e6	−0.0771180
$53$	−4.53012e7	−0.788622	−0.394311	−	0.918977i	$-0.629017\pi$
$53$	−4.53012e7	−0.788622	−0.394311	+	0.918977i	$0.629017\pi$
$54$	−6.32377e6	−0.101206
$55$	6.11644e6	0.0901294
$56$	−4.39484e7	−0.597169
$57$	−4.66460e7	−0.585299
$58$	1.15629e7	0.134165
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	−7.10391e6	−0.0707648
$61$	−1.39439e8	−1.28944	−0.644718	−	0.764421i	$-0.723025\pi$
$61$	−1.39439e8	−1.28944	−0.644718	+	0.764421i	$0.723025\pi$
$62$	9.11596e7	0.783501
$63$	2.74614e7	0.219630
$64$	4.00032e7	0.298047
$65$	−2.59911e6	−0.0180599
$66$	2.48984e7	0.161519
$67$	−1.76510e8	−1.07012	−0.535060	−	0.844814i	$-0.679711\pi$
$67$	−1.76510e8	−1.07012	−0.535060	+	0.844814i	$0.679711\pi$
$68$	2.77323e7	0.157288
$69$	−9.61083e7	−0.510434
$70$	−1.17926e7	−0.0587039
$71$	−4.76874e7	−0.222711	−0.111355	−	0.993781i	$-0.535519\pi$
$71$	−4.76874e7	−0.222711	−0.111355	+	0.993781i	$0.535519\pi$
$72$	−6.88906e7	−0.302109
$73$	−1.70848e8	−0.704136	−0.352068	−	0.935974i	$-0.614521\pi$
$73$	−1.70848e8	−0.704136	−0.352068	+	0.935974i	$0.614521\pi$
$74$	−1.60202e8	−0.621049
$75$	1.53662e8	0.560778
$76$	−2.13309e8	−0.733411
$77$	−1.08123e8	−0.350518
$78$	−1.05803e7	−0.0323647
$79$	−7.11694e7	−0.205576	−0.102788	−	0.994703i	$-0.532776\pi$
$79$	−7.11694e7	−0.205576	−0.102788	+	0.994703i	$0.532776\pi$
$80$	−1.53206e7	−0.0418187
$81$	4.30467e7	0.111111
$82$	4.42315e7	0.108036
$83$	−3.04121e8	−0.703388	−0.351694	−	0.936115i	$-0.614394\pi$
$83$	−3.04121e8	−0.703388	−0.351694	+	0.936115i	$0.614394\pi$
$84$	1.25579e8	0.275208
$85$	1.77272e7	0.0368345
$86$	1.69462e8	0.334064
$87$	−7.87100e7	−0.147297
$88$	2.71241e8	0.482151
$89$	−6.08801e8	−1.02854	−0.514269	−	0.857629i	$-0.671937\pi$
$89$	−6.08801e8	−1.02854	−0.514269	+	0.857629i	$0.671937\pi$
$90$	−1.84852e7	−0.0296984
$91$	4.59457e7	0.0702358
$92$	−4.39496e8	−0.639602
$93$	−6.20535e8	−0.860187
$94$	5.99106e8	0.791459
$95$	−1.36353e8	−0.171754
$96$	−4.97823e8	−0.598211
$97$	−5.99259e8	−0.687293	−0.343646	−	0.939099i	$-0.611662\pi$
$97$	−5.99259e8	−0.687293	−0.343646	+	0.939099i	$0.611662\pi$
$98$	−2.71717e8	−0.297577
$99$	−1.69487e8	−0.177328
$100$	7.02685e8	0.702685
$101$	−1.03425e9	−0.988965	−0.494483	−	0.869188i	$-0.664642\pi$
$101$	−1.03425e9	−0.988965	−0.494483	+	0.869188i	$0.664642\pi$
$102$	7.21626e7	0.0660102
$103$	1.11407e8	0.0975318	0.0487659	−	0.998810i	$-0.484471\pi$
$103$	1.11407e8	0.0975318	0.0487659	+	0.998810i	$0.484471\pi$
$104$	−1.15261e8	−0.0966121
$105$	8.02734e7	0.0644496
$106$	−5.39053e8	−0.414720
$107$	−4.84503e8	−0.357330	−0.178665	−	0.983910i	$-0.557178\pi$
$107$	−4.84503e8	−0.357330	−0.178665	+	0.983910i	$0.557178\pi$
$108$	1.96849e8	0.139228
$109$	1.80758e9	1.22653	0.613264	−	0.789878i	$-0.289856\pi$
$109$	1.80758e9	1.22653	0.613264	+	0.789878i	$0.289856\pi$
$110$	7.27813e7	0.0473972
$111$	1.09052e9	0.681835
$112$	2.70829e8	0.162635
$113$	−5.89242e8	−0.339970	−0.169985	−	0.985447i	$-0.554372\pi$
$113$	−5.89242e8	−0.339970	−0.169985	+	0.985447i	$0.554372\pi$
$114$	−5.55054e8	−0.307797
$115$	−2.80937e8	−0.149785
$116$	−3.59935e8	−0.184571
$117$	7.20214e7	0.0355324
$118$	−1.44188e8	−0.0684636
$119$	−3.13371e8	−0.143251
$120$	−2.01376e8	−0.0886529
$121$	−1.69063e9	−0.716994
$122$	−1.65922e9	−0.678087
$123$	−3.01090e8	−0.118610
$124$	−2.83766e9	−1.07786
$125$	9.11624e8	0.333980
$126$	3.26772e8	0.115499
$127$	−2.92506e9	−0.997743	−0.498871	−	0.866676i	$-0.666252\pi$
$127$	−2.92506e9	−0.997743	−0.498871	+	0.866676i	$0.666252\pi$
$128$	−2.67072e9	−0.879394
$129$	−1.15355e9	−0.366760
$130$	−3.09276e7	−0.00949732
$131$	6.59454e9	1.95643	0.978214	−	0.207599i	$-0.0665650\pi$
$131$	6.59454e9	1.95643	0.978214	+	0.207599i	$0.0665650\pi$
$132$	−7.75049e8	−0.222201
$133$	2.41037e9	0.667960
$134$	−2.10034e9	−0.562754
$135$	1.25831e8	0.0326052
$136$	7.86133e8	0.197047
$137$	−3.35904e9	−0.814652	−0.407326	−	0.913283i	$-0.633539\pi$
$137$	−3.35904e9	−0.814652	−0.407326	+	0.913283i	$0.633539\pi$
$138$	−1.14362e9	−0.268427
$139$	6.25873e9	1.42207	0.711033	−	0.703159i	$-0.248228\pi$
$139$	6.25873e9	1.42207	0.711033	+	0.703159i	$0.248228\pi$
$140$	3.67084e8	0.0807588
$141$	−4.07819e9	−0.868924
$142$	−5.67447e8	−0.117119
$143$	−2.83568e8	−0.0567080
$144$	4.24534e8	0.0822775
$145$	−2.30080e8	−0.0432238
$146$	−2.03297e9	−0.370290
$147$	1.84961e9	0.326703
$148$	4.98686e9	0.854376
$149$	−1.91528e8	−0.0318341	−0.0159171	−	0.999873i	$-0.505067\pi$
$149$	−1.91528e8	−0.0318341	−0.0159171	+	0.999873i	$0.505067\pi$
$150$	1.82847e9	0.294902
$151$	−5.18282e9	−0.811279	−0.405639	−	0.914033i	$-0.632951\pi$
$151$	−5.18282e9	−0.811279	−0.405639	+	0.914033i	$0.632951\pi$
$152$	−6.04672e9	−0.918805
$153$	−4.91220e8	−0.0724711
$154$	−1.28659e9	−0.184330
$155$	−1.81391e9	−0.252419
$156$	3.29348e8	0.0445241
$157$	6.75931e9	0.887879	0.443940	−	0.896057i	$-0.353580\pi$
$157$	6.75931e9	0.887879	0.443940	+	0.896057i	$0.353580\pi$
$158$	−8.46865e8	−0.108108
$159$	3.66940e9	0.455311
$160$	−1.45520e9	−0.175543
$161$	4.96626e9	0.582522
$162$	5.12225e8	0.0584310
$163$	−1.32321e10	−1.46819	−0.734097	−	0.679045i	$-0.762394\pi$
$163$	−1.32321e10	−1.46819	−0.734097	+	0.679045i	$0.762394\pi$
$164$	−1.37686e9	−0.148625
$165$	−4.95432e8	−0.0520362
$166$	−3.61882e9	−0.369897
$167$	−1.29087e10	−1.28427	−0.642137	−	0.766590i	$-0.721952\pi$
$167$	−1.29087e10	−1.28427	−0.642137	+	0.766590i	$0.721952\pi$
$168$	3.55982e9	0.344776
$169$	−1.04840e10	−0.988637
$170$	2.10941e8	0.0193705
$171$	3.77833e9	0.337923
$172$	−5.27509e9	−0.459571
$173$	1.16986e10	0.992948	0.496474	−	0.868051i	$-0.334628\pi$
$173$	1.16986e10	0.992948	0.496474	+	0.868051i	$0.334628\pi$
$174$	−9.36593e8	−0.0774603
$175$	−7.94027e9	−0.639976
$176$	−1.67150e9	−0.131311
$177$	9.81506e8	0.0751646
$178$	−7.24430e9	−0.540887
$179$	−1.47861e10	−1.07650	−0.538252	−	0.842784i	$-0.680915\pi$
$179$	−1.47861e10	−1.07650	−0.538252	+	0.842784i	$0.680915\pi$
$180$	5.75417e8	0.0408561
$181$	1.06044e10	0.734398	0.367199	−	0.930142i	$-0.380317\pi$
$181$	1.06044e10	0.734398	0.367199	+	0.930142i	$0.380317\pi$
$182$	5.46721e8	0.0369355
$183$	1.12945e10	0.744456
$184$	−1.24585e10	−0.801282
$185$	3.18773e9	0.200082
$186$	−7.38393e9	−0.452355
$187$	1.93407e9	0.115660
$188$	−1.86493e10	−1.08881
$189$	−2.22438e9	−0.126803
$190$	−1.62250e9	−0.0903219
$191$	1.74635e10	0.949471	0.474735	−	0.880129i	$-0.342544\pi$
$191$	1.74635e10	0.949471	0.474735	+	0.880129i	$0.342544\pi$
$192$	−3.24026e9	−0.172078
$193$	3.68522e9	0.191186	0.0955929	−	0.995421i	$-0.469525\pi$
$193$	3.68522e9	0.191186	0.0955929	+	0.995421i	$0.469525\pi$
$194$	−7.13075e9	−0.361433
$195$	2.10528e8	0.0104269
$196$	8.45814e9	0.409376
$197$	−2.92499e10	−1.38365	−0.691826	−	0.722064i	$-0.743194\pi$
$197$	−2.92499e10	−1.38365	−0.691826	+	0.722064i	$0.743194\pi$
$198$	−2.01677e9	−0.0932530
$199$	−3.10443e10	−1.40328	−0.701639	−	0.712533i	$-0.747548\pi$
$199$	−3.10443e10	−1.40328	−0.701639	+	0.712533i	$0.747548\pi$
$200$	1.99192e10	0.880312
$201$	1.42973e10	0.617834
$202$	−1.23069e10	−0.520076
$203$	4.06723e9	0.168099
$204$	−2.24631e9	−0.0908102
$205$	−8.80125e8	−0.0348058
$206$	1.32567e9	0.0512900
$207$	7.78477e9	0.294699
$208$	7.10287e8	0.0263117
$209$	−1.48763e10	−0.539308
$210$	9.55197e8	0.0338927
$211$	−7.45417e9	−0.258898	−0.129449	−	0.991586i	$-0.541321\pi$
$211$	−7.45417e9	−0.258898	−0.129449	+	0.991586i	$0.541321\pi$
$212$	1.67799e10	0.570529
$213$	3.86268e9	0.128582
$214$	−5.76524e9	−0.187912
$215$	−3.37198e9	−0.107625
$216$	5.58014e9	0.174423
$217$	3.20652e10	0.981671
$218$	2.15089e10	0.645005
$219$	1.38387e10	0.406533
$220$	−2.26557e9	−0.0652042
$221$	−8.21859e8	−0.0231757
$222$	1.29764e10	0.358563
$223$	−1.40269e10	−0.379831	−0.189915	−	0.981800i	$-0.560821\pi$
$223$	−1.40269e10	−0.379831	−0.189915	+	0.981800i	$0.560821\pi$
$224$	2.57243e10	0.682695
$225$	−1.24466e10	−0.323765
$226$	−7.01156e9	−0.178783
$227$	−2.64313e9	−0.0660696	−0.0330348	−	0.999454i	$-0.510517\pi$
$227$	−2.64313e9	−0.0660696	−0.0330348	+	0.999454i	$0.510517\pi$
$228$	1.72780e10	0.423435
$229$	7.05707e10	1.69576	0.847881	−	0.530187i	$-0.177878\pi$
$229$	7.05707e10	1.69576	0.847881	+	0.530187i	$0.177878\pi$
$230$	−3.34295e9	−0.0787690
$231$	8.75797e9	0.202372
$232$	−1.02032e10	−0.231227
$233$	−4.79787e9	−0.106647	−0.0533233	−	0.998577i	$-0.516981\pi$
$233$	−4.79787e9	−0.106647	−0.0533233	+	0.998577i	$0.516981\pi$
$234$	8.57003e8	0.0186858
$235$	−1.19211e10	−0.254983
$236$	4.48835e9	0.0941853
$237$	5.76472e9	0.118689
$238$	−3.72890e9	−0.0753328
$239$	−6.36448e10	−1.26175	−0.630874	−	0.775885i	$-0.717303\pi$
$239$	−6.36448e10	−1.26175	−0.630874	+	0.775885i	$0.717303\pi$
$240$	1.24097e9	0.0241441
$241$	−3.20440e10	−0.611885	−0.305942	−	0.952050i	$-0.598971\pi$
$241$	−3.20440e10	−0.611885	−0.305942	+	0.952050i	$0.598971\pi$
$242$	−2.01173e10	−0.377052
$243$	−3.48678e9	−0.0641500
$244$	5.16491e10	0.932843
$245$	5.40666e9	0.0958698
$246$	−3.58275e9	−0.0623748
$247$	6.32151e9	0.108065
$248$	−8.04398e10	−1.35033
$249$	2.46338e10	0.406101
$250$	1.08477e10	0.175633
$251$	6.51872e10	1.03665	0.518323	−	0.855185i	$-0.326557\pi$
$251$	6.51872e10	1.03665	0.518323	+	0.855185i	$0.326557\pi$
$252$	−1.01719e10	−0.158891
$253$	−3.06507e10	−0.470326
$254$	−3.48062e10	−0.524692
$255$	−1.43590e9	−0.0212664
$256$	−5.22613e10	−0.760503
$257$	−4.28183e10	−0.612252	−0.306126	−	0.951991i	$-0.599033\pi$
$257$	−4.28183e10	−0.612252	−0.306126	+	0.951991i	$0.599033\pi$
$258$	−1.37264e10	−0.192872
$259$	−5.63509e10	−0.778130
$260$	9.62729e8	0.0130654
$261$	6.37551e9	0.0850419
$262$	7.84704e10	1.02884
$263$	1.34491e11	1.73338	0.866689	−	0.498849i	$-0.166244\pi$
$263$	1.34491e11	1.73338	0.866689	+	0.498849i	$0.166244\pi$
$264$	−2.19705e10	−0.278370
$265$	1.07261e10	0.133609
$266$	2.86816e10	0.351266
$267$	4.93129e10	0.593827
$268$	6.53805e10	0.774179
$269$	1.08095e11	1.25869	0.629346	−	0.777126i	$-0.283323\pi$
$269$	1.08095e11	1.25869	0.629346	+	0.777126i	$0.283323\pi$
$270$	1.49730e9	0.0171464
$271$	4.11140e10	0.463050	0.231525	−	0.972829i	$-0.425628\pi$
$271$	4.11140e10	0.463050	0.231525	+	0.972829i	$0.425628\pi$
$272$	−4.84449e9	−0.0536646
$273$	−3.72160e9	−0.0405507
$274$	−3.99701e10	−0.428408
$275$	4.90057e10	0.516714
$276$	3.55992e10	0.369274
$277$	1.37905e11	1.40741	0.703703	−	0.710494i	$-0.251528\pi$
$277$	1.37905e11	1.40741	0.703703	+	0.710494i	$0.251528\pi$
$278$	7.44745e10	0.747835
$279$	5.02633e10	0.496629
$280$	1.04058e10	0.101173
$281$	3.43222e10	0.328395	0.164197	−	0.986427i	$-0.447497\pi$
$281$	3.43222e10	0.328395	0.164197	+	0.986427i	$0.447497\pi$
$282$	−4.85276e10	−0.456949
$283$	2.76964e10	0.256675	0.128338	−	0.991731i	$-0.459036\pi$
$283$	2.76964e10	0.256675	0.128338	+	0.991731i	$0.459036\pi$
$284$	1.76638e10	0.161120
$285$	1.10446e10	0.0991622
$286$	−3.37425e9	−0.0298216
$287$	1.55584e10	0.135362
$288$	4.03236e10	0.345377
$289$	−1.12982e11	−0.952731
$290$	−2.73779e9	−0.0227305
$291$	4.85400e10	0.396809
$292$	6.32832e10	0.509408
$293$	4.86080e10	0.385304	0.192652	−	0.981267i	$-0.438291\pi$
$293$	4.86080e10	0.385304	0.192652	+	0.981267i	$0.438291\pi$
$294$	2.20091e10	0.171806
$295$	2.86907e9	0.0220568
$296$	1.41364e11	1.07035
$297$	1.37284e10	0.102380
$298$	−2.27904e9	−0.0167409
$299$	1.30247e10	0.0942425
$300$	−5.69175e10	−0.405696
$301$	5.96080e10	0.418558
$302$	−6.16719e10	−0.426635
$303$	8.37746e10	0.570979
$304$	3.72625e10	0.250231
$305$	3.30155e10	0.218458
$306$	−5.84517e9	−0.0381110
$307$	7.92006e10	0.508869	0.254434	−	0.967090i	$-0.418111\pi$
$307$	7.92006e10	0.508869	0.254434	+	0.967090i	$0.418111\pi$
$308$	4.00495e10	0.253583
$309$	−9.02399e9	−0.0563100
$310$	−2.15842e10	−0.132742
$311$	1.37118e11	0.831140	0.415570	−	0.909561i	$-0.363582\pi$
$311$	1.37118e11	0.831140	0.415570	+	0.909561i	$0.363582\pi$
$312$	9.33612e9	0.0557790
$313$	−1.44336e11	−0.850010	−0.425005	−	0.905191i	$-0.639728\pi$
$313$	−1.44336e11	−0.850010	−0.425005	+	0.905191i	$0.639728\pi$
$314$	8.04310e10	0.466917
$315$	−6.50215e9	−0.0372100
$316$	2.63616e10	0.148724
$317$	6.54419e9	0.0363990	0.0181995	−	0.999834i	$-0.494207\pi$
$317$	6.54419e9	0.0363990	0.0181995	+	0.999834i	$0.494207\pi$
$318$	4.36633e10	0.239439
$319$	−2.51021e10	−0.135723
$320$	−9.47172e9	−0.0504956
$321$	3.92447e10	0.206305
$322$	5.90949e10	0.306336
$323$	−4.31157e10	−0.220406
$324$	−1.59448e10	−0.0803835
$325$	−2.08244e10	−0.103538
$326$	−1.57452e11	−0.772092
$327$	−1.46414e11	−0.708136
$328$	−3.90302e10	−0.186195
$329$	2.10735e11	0.991641
$330$	−5.89528e9	−0.0273648
$331$	−2.27735e11	−1.04281	−0.521403	−	0.853310i	$-0.674591\pi$
$331$	−2.27735e11	−1.04281	−0.521403	+	0.853310i	$0.674591\pi$
$332$	1.12648e11	0.508866
$333$	−8.83320e10	−0.393658
$334$	−1.53604e11	−0.675373
$335$	4.17929e10	0.181301
$336$	−2.19372e10	−0.0938974
$337$	4.60566e10	0.194517	0.0972585	−	0.995259i	$-0.468993\pi$
$337$	4.60566e10	0.194517	0.0972585	+	0.995259i	$0.468993\pi$
$338$	−1.24752e11	−0.519904
$339$	4.77286e10	0.196282
$340$	−6.56627e9	−0.0266479
$341$	−1.97900e11	−0.792596
$342$	4.49594e10	0.177706
$343$	−2.64478e11	−1.03173
$344$	−1.49534e11	−0.575742
$345$	2.27559e10	0.0864786
$346$	1.39205e11	0.522171
$347$	1.44580e11	0.535335	0.267668	−	0.963511i	$-0.413747\pi$
$347$	1.44580e11	0.535335	0.267668	+	0.963511i	$0.413747\pi$
$348$	2.91547e10	0.106562
$349$	−4.92873e11	−1.77836	−0.889182	−	0.457553i	$-0.848726\pi$
$349$	−4.92873e11	−1.77836	−0.889182	+	0.457553i	$0.848726\pi$
$350$	−9.44835e10	−0.336550
$351$	−5.83373e9	−0.0205147
$352$	−1.58765e11	−0.551205
$353$	−5.00845e11	−1.71679	−0.858395	−	0.512989i	$-0.828538\pi$
$353$	−5.00845e11	−1.71679	−0.858395	+	0.512989i	$0.828538\pi$
$354$	1.16792e10	0.0395275
$355$	1.12911e10	0.0377320
$356$	2.25504e11	0.744097
$357$	2.53831e10	0.0827061
$358$	−1.75944e11	−0.566111
$359$	1.96532e11	0.624466	0.312233	−	0.950006i	$-0.398923\pi$
$359$	1.96532e11	0.624466	0.312233	+	0.950006i	$0.398923\pi$
$360$	1.63115e10	0.0511838
$361$	8.94644e9	0.0277247
$362$	1.26185e11	0.386205
$363$	1.36941e11	0.413956
$364$	−1.70186e10	−0.0508122
$365$	4.04523e10	0.119296
$366$	1.34397e11	0.391494
$367$	4.01737e11	1.15596	0.577982	−	0.816050i	$-0.303840\pi$
$367$	4.01737e11	1.15596	0.577982	+	0.816050i	$0.303840\pi$
$368$	7.67747e10	0.218224
$369$	2.43883e10	0.0684798
$370$	3.79317e10	0.105219
$371$	−1.89611e11	−0.519614
$372$	2.29851e11	0.622303
$373$	−2.55522e11	−0.683500	−0.341750	−	0.939791i	$-0.611020\pi$
$373$	−2.55522e11	−0.683500	−0.341750	+	0.939791i	$0.611020\pi$
$374$	2.30140e10	0.0608233
$375$	−7.38415e10	−0.192823
$376$	−5.28655e11	−1.36404
$377$	1.06669e10	0.0271957
$378$	−2.64685e10	−0.0666832
$379$	−4.55440e11	−1.13385	−0.566924	−	0.823770i	$-0.691867\pi$
$379$	−4.55440e11	−1.13385	−0.566924	+	0.823770i	$0.691867\pi$
$380$	5.05059e10	0.124256
$381$	2.36930e11	0.576047
$382$	2.07803e11	0.499307
$383$	−4.42583e11	−1.05099	−0.525497	−	0.850795i	$-0.676121\pi$
$383$	−4.42583e11	−1.05099	−0.525497	+	0.850795i	$0.676121\pi$
$384$	2.16328e11	0.507719
$385$	2.56007e10	0.0593853
$386$	4.38515e10	0.100541
$387$	9.34375e10	0.211749
$388$	2.21970e11	0.497223
$389$	−1.20591e11	−0.267018	−0.133509	−	0.991048i	$-0.542625\pi$
$389$	−1.20591e11	−0.267018	−0.133509	+	0.991048i	$0.542625\pi$
$390$	2.50513e9	0.00548328
$391$	−8.88346e10	−0.192215
$392$	2.39765e11	0.512859
$393$	−5.34158e11	−1.12954
$394$	−3.48053e11	−0.727634
$395$	1.68510e10	0.0348289
$396$	6.27790e10	0.128288
$397$	−4.20019e11	−0.848617	−0.424308	−	0.905518i	$-0.639483\pi$
$397$	−4.20019e11	−0.848617	−0.424308	+	0.905518i	$0.639483\pi$
$398$	−3.69406e11	−0.737954
$399$	−1.95240e11	−0.385647
$400$	−1.22751e11	−0.239747
$401$	4.58107e11	0.884743	0.442372	−	0.896832i	$-0.354137\pi$
$401$	4.58107e11	0.884743	0.442372	+	0.896832i	$0.354137\pi$
$402$	1.70128e11	0.324906
$403$	8.40955e10	0.158818
$404$	3.83095e11	0.715468
$405$	−1.01923e10	−0.0188246
$406$	4.83971e10	0.0884000
$407$	3.47787e11	0.628258
$408$	−6.36768e10	−0.113765
$409$	−6.42534e11	−1.13538	−0.567690	−	0.823243i	$-0.692163\pi$
$409$	−6.42534e11	−1.13538	−0.567690	+	0.823243i	$0.692163\pi$
$410$	−1.04729e10	−0.0183037
$411$	2.72082e11	0.470339
$412$	−4.12661e10	−0.0705595
$413$	−5.07179e10	−0.0857800
$414$	9.26332e10	0.154976
$415$	7.20078e10	0.119169
$416$	6.74654e10	0.110449
$417$	−5.06957e11	−0.821030
$418$	−1.77017e11	−0.283611
$419$	−1.02142e12	−1.61898	−0.809488	−	0.587136i	$-0.800255\pi$
$419$	−1.02142e12	−1.61898	−0.809488	+	0.587136i	$0.800255\pi$
$420$	−2.97338e10	−0.0466261
$421$	−4.44401e11	−0.689454	−0.344727	−	0.938703i	$-0.612028\pi$
$421$	−4.44401e11	−0.689454	−0.344727	+	0.938703i	$0.612028\pi$
$422$	−8.86993e10	−0.136149
$423$	3.30334e11	0.501673
$424$	4.75664e11	0.714749
$425$	1.42033e11	0.211173
$426$	4.59632e10	0.0676187
$427$	−5.83629e11	−0.849594
$428$	1.79463e11	0.258511
$429$	2.29690e10	0.0327404
$430$	−4.01241e10	−0.0565976
$431$	1.51261e11	0.211144	0.105572	−	0.994412i	$-0.466333\pi$
$431$	1.51261e11	0.211144	0.105572	+	0.994412i	$0.466333\pi$
$432$	−3.43872e10	−0.0475029
$433$	−5.86010e11	−0.801142	−0.400571	−	0.916266i	$-0.631188\pi$
$433$	−5.86010e11	−0.801142	−0.400571	+	0.916266i	$0.631188\pi$
$434$	3.81554e11	0.516240
$435$	1.86365e10	0.0249552
$436$	−6.69539e11	−0.887332
$437$	6.83291e11	0.896270
$438$	1.64670e11	0.213787
$439$	−1.29798e12	−1.66793	−0.833963	−	0.551820i	$-0.813933\pi$
$439$	−1.29798e12	−1.66793	−0.833963	+	0.551820i	$0.813933\pi$
$440$	−6.42227e10	−0.0816867
$441$	−1.49819e11	−0.188622
$442$	−9.77954e9	−0.0121876
$443$	−4.17677e10	−0.0515257	−0.0257628	−	0.999668i	$-0.508201\pi$
$443$	−4.17677e10	−0.0515257	−0.0257628	+	0.999668i	$0.508201\pi$
$444$	−4.03935e11	−0.493274
$445$	1.44148e11	0.174257
$446$	−1.66910e11	−0.199745
$447$	1.55137e10	0.0183795
$448$	1.67436e11	0.196380
$449$	2.60197e11	0.302130	0.151065	−	0.988524i	$-0.451730\pi$
$449$	2.60197e11	0.302130	0.151065	+	0.988524i	$0.451730\pi$
$450$	−1.48106e11	−0.170262
$451$	−9.60232e10	−0.109290
$452$	2.18259e11	0.245952
$453$	4.19809e11	0.468392
$454$	−3.14513e10	−0.0347446
$455$	−1.08787e10	−0.0118995
$456$	4.89784e11	0.530472
$457$	−9.53046e11	−1.02209	−0.511047	−	0.859553i	$-0.670742\pi$
$457$	−9.53046e11	−1.02209	−0.511047	+	0.859553i	$0.670742\pi$
$458$	8.39741e11	0.891766
$459$	3.97888e10	0.0418412
$460$	1.04061e11	0.108362
$461$	4.57852e11	0.472140	0.236070	−	0.971736i	$-0.424141\pi$
$461$	4.57852e11	0.472140	0.236070	+	0.971736i	$0.424141\pi$
$462$	1.04214e11	0.106423
$463$	−3.51961e11	−0.355943	−0.177971	−	0.984036i	$-0.556953\pi$
$463$	−3.51961e11	−0.355943	−0.177971	+	0.984036i	$0.556953\pi$
$464$	6.28763e10	0.0629733
$465$	1.46926e11	0.145734
$466$	−5.70912e10	−0.0560832
$467$	1.19947e11	0.116698	0.0583492	−	0.998296i	$-0.481416\pi$
$467$	1.19947e11	0.116698	0.0583492	+	0.998296i	$0.481416\pi$
$468$	−2.66772e10	−0.0257060
$469$	−7.38792e11	−0.705090
$470$	−1.41853e11	−0.134090
$471$	−5.47504e11	−0.512617
$472$	1.27232e11	0.117994
$473$	−3.67889e11	−0.337941
$474$	6.85961e10	0.0624161
$475$	−1.09247e12	−0.984669
$476$	1.16075e11	0.103635
$477$	−2.97221e11	−0.262874
$478$	−7.57328e11	−0.663527
$479$	1.99573e12	1.73218	0.866088	−	0.499892i	$-0.166627\pi$
$479$	1.99573e12	1.73218	0.866088	+	0.499892i	$0.166627\pi$
$480$	1.17871e11	0.101350
$481$	−1.47788e11	−0.125889
$482$	−3.81300e11	−0.321777
$483$	−4.02267e11	−0.336319
$484$	6.26222e11	0.518710
$485$	1.41889e11	0.116442
$486$	−4.14903e10	−0.0337352
$487$	−6.44151e11	−0.518929	−0.259464	−	0.965753i	$-0.583546\pi$
$487$	−6.44151e11	−0.518929	−0.259464	+	0.965753i	$0.583546\pi$
$488$	1.46411e12	1.16865
$489$	1.07180e12	0.847662
$490$	6.43354e10	0.0504159
$491$	1.01386e11	0.0787244	0.0393622	−	0.999225i	$-0.487467\pi$
$491$	1.01386e11	0.0787244	0.0393622	+	0.999225i	$0.487467\pi$
$492$	1.11526e11	0.0858088
$493$	−7.27530e10	−0.0554677
$494$	7.52215e10	0.0568291
$495$	4.01300e10	0.0300431
$496$	4.95705e11	0.367753
$497$	−1.99599e11	−0.146742
$498$	2.93124e11	0.213560
$499$	−1.90534e12	−1.37569	−0.687845	−	0.725857i	$-0.741443\pi$
$499$	−1.90534e12	−1.37569	−0.687845	+	0.725857i	$0.741443\pi$
$500$	−3.37672e11	−0.241618
$501$	1.04560e12	0.741476
$502$	7.75681e11	0.545150
$503$	4.69546e11	0.327056	0.163528	−	0.986539i	$-0.447713\pi$
$503$	4.69546e11	0.327056	0.163528	+	0.986539i	$0.447713\pi$
$504$	−2.88346e11	−0.199056
$505$	2.44884e11	0.167552
$506$	−3.64722e11	−0.247334
$507$	8.49204e11	0.570790
$508$	1.08346e12	0.721818
$509$	−9.05674e11	−0.598056	−0.299028	−	0.954244i	$-0.596662\pi$
$509$	−9.05674e11	−0.598056	−0.299028	+	0.954244i	$0.596662\pi$
$510$	−1.70862e10	−0.0111836
$511$	−7.15093e11	−0.463947
$512$	7.45536e11	0.479462
$513$	−3.06045e11	−0.195100
$514$	−5.09507e11	−0.321971
$515$	−2.63783e10	−0.0165240
$516$	4.27283e11	0.265333
$517$	−1.30061e12	−0.800646
$518$	−6.70536e11	−0.409202
$519$	−9.47587e11	−0.573279
$520$	2.72907e10	0.0163682
$521$	−4.04998e11	−0.240815	−0.120407	−	0.992725i	$-0.538420\pi$
$521$	−4.04998e11	−0.240815	−0.120407	+	0.992725i	$0.538420\pi$
$522$	7.58640e10	0.0447217
$523$	1.73293e12	1.01280	0.506399	−	0.862299i	$-0.330976\pi$
$523$	1.73293e12	1.01280	0.506399	+	0.862299i	$0.330976\pi$
$524$	−2.44266e12	−1.41538
$525$	6.43162e11	0.369490
$526$	1.60035e12	0.911547
$527$	−5.73571e11	−0.323921
$528$	1.35392e11	0.0758123
$529$	−3.93318e11	−0.218370
$530$	1.27634e11	0.0702624
$531$	−7.95020e10	−0.0433963
$532$	−8.92816e11	−0.483236
$533$	4.08040e10	0.0218993
$534$	5.86789e11	0.312281
$535$	1.14718e11	0.0605394
$536$	1.85336e12	0.969879
$537$	1.19767e12	0.621519
$538$	1.28625e12	0.661920
$539$	5.89876e11	0.301031
$540$	−4.66088e10	−0.0235883
$541$	2.03592e11	0.102182	0.0510909	−	0.998694i	$-0.483730\pi$
$541$	2.03592e11	0.102182	0.0510909	+	0.998694i	$0.483730\pi$
$542$	4.89227e11	0.243508
$543$	−8.58955e11	−0.424005
$544$	−4.60146e11	−0.225269
$545$	−4.27986e11	−0.207800
$546$	−4.42844e10	−0.0213247
$547$	−1.51327e11	−0.0722727	−0.0361363	−	0.999347i	$-0.511505\pi$
$547$	−1.51327e11	−0.0722727	−0.0361363	+	0.999347i	$0.511505\pi$
$548$	1.24421e12	0.589361
$549$	−9.14858e11	−0.429812
$550$	5.83133e11	0.271729
$551$	5.59596e11	0.258638
$552$	1.00914e12	0.462621
$553$	−2.97884e11	−0.135451
$554$	1.64097e12	0.740126
$555$	−2.58206e11	−0.115518
$556$	−2.31828e12	−1.02880
$557$	−2.02940e12	−0.893344	−0.446672	−	0.894698i	$-0.647391\pi$
$557$	−2.02940e12	−0.893344	−0.446672	+	0.894698i	$0.647391\pi$
$558$	5.98098e11	0.261167
$559$	1.56330e11	0.0677157
$560$	−6.41252e10	−0.0275539
$561$	−1.56659e11	−0.0667765
$562$	4.08409e11	0.172696
$563$	−3.83974e12	−1.61070	−0.805348	−	0.592802i	$-0.798022\pi$
$563$	−3.83974e12	−1.61070	−0.805348	+	0.592802i	$0.798022\pi$
$564$	1.51059e12	0.628624
$565$	1.39517e11	0.0575982
$566$	3.29567e11	0.134980
$567$	1.80175e11	0.0732099
$568$	5.00719e11	0.201849
$569$	2.59199e12	1.03664	0.518319	−	0.855187i	$-0.326558\pi$
$569$	2.59199e12	1.03664	0.518319	+	0.855187i	$0.326558\pi$
$570$	1.31422e11	0.0521474
$571$	2.26611e11	0.0892110	0.0446055	−	0.999005i	$-0.485797\pi$
$571$	2.26611e11	0.0892110	0.0446055	+	0.999005i	$0.485797\pi$
$572$	1.05035e11	0.0410255
$573$	−1.41455e12	−0.548177
$574$	1.85134e11	0.0711839
$575$	−2.25091e12	−0.858722
$576$	2.62461e11	0.0993491
$577$	4.33956e12	1.62988	0.814938	−	0.579548i	$-0.196771\pi$
$577$	4.33956e12	1.62988	0.814938	+	0.579548i	$0.196771\pi$
$578$	−1.34441e12	−0.501022
$579$	−2.98503e11	−0.110381
$580$	8.52232e10	0.0312703
$581$	−1.27291e12	−0.463454
$582$	5.77591e11	0.208673
$583$	1.17024e12	0.419534
$584$	1.79390e12	0.638177
$585$	−1.70528e10	−0.00601996
$586$	5.78401e11	0.202624
$587$	5.17738e12	1.79986	0.899931	−	0.436033i	$-0.143617\pi$
$587$	5.17738e12	1.79986	0.899931	+	0.436033i	$0.143617\pi$
$588$	−6.85109e11	−0.236353
$589$	4.41175e12	1.51040
$590$	3.41399e10	0.0115992
$591$	2.36924e12	0.798852
$592$	−8.71144e11	−0.291503
$593$	7.39550e11	0.245596	0.122798	−	0.992432i	$-0.460813\pi$
$593$	7.39550e11	0.245596	0.122798	+	0.992432i	$0.460813\pi$
$594$	1.63358e11	0.0538396
$595$	7.41981e10	0.0242698
$596$	7.09432e10	0.0230304
$597$	2.51459e12	0.810183
$598$	1.54985e11	0.0495602
$599$	−8.86839e11	−0.281465	−0.140732	−	0.990048i	$-0.544946\pi$
$599$	−8.86839e11	−0.281465	−0.140732	+	0.990048i	$0.544946\pi$
$600$	−1.61345e12	−0.508248
$601$	3.84620e12	1.20253	0.601266	−	0.799049i	$-0.294663\pi$
$601$	3.84620e12	1.20253	0.601266	+	0.799049i	$0.294663\pi$
$602$	7.09293e11	0.220111
$603$	−1.15808e12	−0.356707
$604$	1.91975e12	0.586921
$605$	4.00298e11	0.121474
$606$	9.96858e11	0.300266
$607$	−6.84903e11	−0.204776	−0.102388	−	0.994745i	$-0.532648\pi$
$607$	−6.84903e11	−0.204776	−0.102388	+	0.994745i	$0.532648\pi$
$608$	3.53932e12	1.05040
$609$	−3.29445e11	−0.0970522
$610$	3.92860e11	0.114883
$611$	5.52680e11	0.160431
$612$	1.81951e11	0.0524293
$613$	−1.76600e12	−0.505149	−0.252574	−	0.967578i	$-0.581277\pi$
$613$	−1.76600e12	−0.505149	−0.252574	+	0.967578i	$0.581277\pi$
$614$	9.42431e11	0.267604
$615$	7.12901e10	0.0200952
$616$	1.13529e12	0.317684
$617$	−1.34640e12	−0.374018	−0.187009	−	0.982358i	$-0.559879\pi$
$617$	−1.34640e12	−0.374018	−0.187009	+	0.982358i	$0.559879\pi$
$618$	−1.07379e11	−0.0296123
$619$	9.78641e11	0.267926	0.133963	−	0.990986i	$-0.457230\pi$
$619$	9.78641e11	0.267926	0.133963	+	0.990986i	$0.457230\pi$
$620$	6.71884e11	0.182613
$621$	−6.30567e11	−0.170145
$622$	1.63161e12	0.437079
$623$	−2.54817e12	−0.677693
$624$	−5.75332e10	−0.0151911
$625$	3.48935e12	0.914713
$626$	−1.71749e12	−0.447003
$627$	1.20498e12	0.311369
$628$	−2.50370e12	−0.642337
$629$	1.00798e12	0.256759
$630$	−7.73709e10	−0.0195680
$631$	1.69265e11	0.0425046	0.0212523	−	0.999774i	$-0.493235\pi$
$631$	1.69265e11	0.0425046	0.0212523	+	0.999774i	$0.493235\pi$
$632$	7.47280e11	0.186319
$633$	6.03788e11	0.149475
$634$	7.78713e10	0.0191415
$635$	6.92578e11	0.169039
$636$	−1.35917e12	−0.329395
$637$	−2.50661e11	−0.0603198
$638$	−2.98697e11	−0.0713737
$639$	−3.12877e11	−0.0742370
$640$	6.32357e11	0.148988
$641$	−5.73879e12	−1.34264	−0.671319	−	0.741169i	$-0.734272\pi$
$641$	−5.73879e12	−1.34264	−0.671319	+	0.741169i	$0.734272\pi$
$642$	4.66984e11	0.108491
$643$	−7.62978e12	−1.76020	−0.880101	−	0.474787i	$-0.842525\pi$
$643$	−7.62978e12	−1.76020	−0.880101	+	0.474787i	$0.842525\pi$
$644$	−1.83954e12	−0.421426
$645$	2.73130e11	0.0621371
$646$	−5.13046e11	−0.115907
$647$	3.78174e12	0.848442	0.424221	−	0.905559i	$-0.360548\pi$
$647$	3.78174e12	0.848442	0.424221	+	0.905559i	$0.360548\pi$
$648$	−4.51991e11	−0.100703
$649$	3.13021e11	0.0692583
$650$	−2.47796e11	−0.0544483
$651$	−2.59729e12	−0.566768
$652$	4.90125e12	1.06217
$653$	−6.52719e12	−1.40481	−0.702404	−	0.711779i	$-0.747890\pi$
$653$	−6.52719e12	−1.40481	−0.702404	+	0.711779i	$0.747890\pi$
$654$	−1.74222e12	−0.372394
$655$	−1.56141e12	−0.331461
$656$	2.40521e11	0.0507091
$657$	−1.12093e12	−0.234712
$658$	2.50759e12	0.521483
$659$	−8.14077e12	−1.68144	−0.840719	−	0.541471i	$-0.817868\pi$
$659$	−8.14077e12	−1.68144	−0.840719	+	0.541471i	$0.817868\pi$
$660$	1.83511e11	0.0376457
$661$	−6.28394e12	−1.28034	−0.640170	−	0.768233i	$-0.721136\pi$
$661$	−6.28394e12	−1.28034	−0.640170	+	0.768233i	$0.721136\pi$
$662$	−2.70988e12	−0.548390
$663$	6.65706e10	0.0133805
$664$	3.19327e12	0.637499
$665$	−5.70711e11	−0.113167
$666$	−1.05109e12	−0.207016
$667$	1.15298e12	0.225556
$668$	4.78147e12	0.929110
$669$	1.13618e12	0.219295
$670$	4.97306e11	0.0953426
$671$	3.60204e12	0.685958
$672$	−2.08367e12	−0.394154
$673$	−4.54764e12	−0.854512	−0.427256	−	0.904131i	$-0.640520\pi$
$673$	−4.54764e12	−0.854512	−0.427256	+	0.904131i	$0.640520\pi$
$674$	5.48041e11	0.102292
$675$	1.00818e12	0.186926
$676$	3.88335e12	0.715230
$677$	9.68222e12	1.77144	0.885719	−	0.464221i	$-0.153666\pi$
$677$	9.68222e12	1.77144	0.885719	+	0.464221i	$0.153666\pi$
$678$	5.67936e11	0.103220
$679$	−2.50823e12	−0.452849
$680$	−1.86136e11	−0.0333841
$681$	2.14093e11	0.0381453
$682$	−2.35487e12	−0.416810
$683$	1.20065e12	0.211117	0.105559	−	0.994413i	$-0.466337\pi$
$683$	1.20065e12	0.211117	0.105559	+	0.994413i	$0.466337\pi$
$684$	−1.39952e12	−0.244470
$685$	7.95331e11	0.138020
$686$	−3.14710e12	−0.542566
$687$	−5.71623e12	−0.979049
$688$	9.21496e11	0.156800
$689$	−4.97281e11	−0.0840650
$690$	2.70779e11	0.0454773
$691$	−2.62792e12	−0.438491	−0.219245	−	0.975670i	$-0.570360\pi$
$691$	−2.62792e12	−0.438491	−0.219245	+	0.975670i	$0.570360\pi$
$692$	−4.33325e12	−0.718350
$693$	−7.09396e11	−0.116839
$694$	1.72040e12	0.281522
$695$	−1.48190e12	−0.240929
$696$	8.26456e11	0.133499
$697$	−2.78302e11	−0.0446652
$698$	−5.86484e12	−0.935205
$699$	3.88628e11	0.0615724
$700$	2.94113e12	0.462991
$701$	−2.63768e12	−0.412563	−0.206282	−	0.978493i	$-0.566136\pi$
$701$	−2.63768e12	−0.412563	−0.206282	+	0.978493i	$0.566136\pi$
$702$	−6.94173e10	−0.0107882
$703$	−7.75314e12	−1.19723
$704$	−1.03338e12	−0.158556
$705$	9.65609e11	0.147214
$706$	−5.95970e12	−0.902824
$707$	−4.32893e12	−0.651618
$708$	−3.63557e11	−0.0543779
$709$	6.76875e12	1.00601	0.503003	−	0.864285i	$-0.332229\pi$
$709$	6.76875e12	1.00601	0.503003	+	0.864285i	$0.332229\pi$
$710$	1.34356e11	0.0198425
$711$	−4.66942e11	−0.0685252
$712$	6.39242e12	0.932193
$713$	9.08986e12	1.31721
$714$	3.02041e11	0.0434934
$715$	6.71414e10	0.00960756
$716$	5.47688e12	0.778797
$717$	5.15523e12	0.728470
$718$	2.33859e12	0.328394
$719$	−5.03693e12	−0.702887	−0.351444	−	0.936209i	$-0.614309\pi$
$719$	−5.03693e12	−0.702887	−0.351444	+	0.936209i	$0.614309\pi$
$720$	−1.00518e11	−0.0139396
$721$	4.66302e11	0.0642626
$722$	1.06456e11	0.0145799
$723$	2.59556e12	0.353272
$724$	−3.92794e12	−0.531301
$725$	−1.84343e12	−0.247803
$726$	1.62950e12	0.217691
$727$	−7.13148e12	−0.946836	−0.473418	−	0.880838i	$-0.656980\pi$
$727$	−7.13148e12	−0.946836	−0.473418	+	0.880838i	$0.656980\pi$
$728$	−4.82430e11	−0.0636566
$729$	2.82430e11	0.0370370
$730$	4.81353e11	0.0627352
$731$	−1.06625e12	−0.138111
$732$	−4.18358e12	−0.538577
$733$	6.89412e12	0.882086	0.441043	−	0.897486i	$-0.354609\pi$
$733$	6.89412e12	0.882086	0.441043	+	0.897486i	$0.354609\pi$
$734$	4.78038e12	0.607897
$735$	−4.37940e11	−0.0553505
$736$	7.29232e12	0.916042
$737$	4.55968e12	0.569286
$738$	2.90203e11	0.0360121
$739$	9.41890e12	1.16172	0.580858	−	0.814005i	$-0.302717\pi$
$739$	9.41890e12	1.16172	0.580858	+	0.814005i	$0.302717\pi$
$740$	−1.18076e12	−0.144750
$741$	−5.12043e11	−0.0623913
$742$	−2.25624e12	−0.273254
$743$	−9.53131e12	−1.14737	−0.573684	−	0.819076i	$-0.694486\pi$
$743$	−9.53131e12	−1.14737	−0.573684	+	0.819076i	$0.694486\pi$
$744$	6.51563e12	0.779611
$745$	4.53487e10	0.00539339
$746$	−3.04053e12	−0.359439
$747$	−1.99534e12	−0.234463
$748$	−7.16391e11	−0.0836745
$749$	−2.02791e12	−0.235441
$750$	−8.78661e11	−0.101402
$751$	−2.76101e12	−0.316729	−0.158364	−	0.987381i	$-0.550622\pi$
$751$	−2.76101e12	−0.316729	−0.158364	+	0.987381i	$0.550622\pi$
$752$	3.25780e12	0.371488
$753$	−5.28016e12	−0.598508
$754$	1.26928e11	0.0143017
$755$	1.22716e12	0.137448
$756$	8.23925e11	0.0917359
$757$	−1.15173e12	−0.127473	−0.0637366	−	0.997967i	$-0.520302\pi$
$757$	−1.15173e12	−0.127473	−0.0637366	+	0.997967i	$0.520302\pi$
$758$	−5.41941e12	−0.596267
$759$	2.48271e12	0.271543
$760$	1.43170e12	0.155665
$761$	−1.51598e13	−1.63856	−0.819278	−	0.573396i	$-0.805626\pi$
$761$	−1.51598e13	−1.63856	−0.819278	+	0.573396i	$0.805626\pi$
$762$	2.81930e12	0.302931
$763$	7.56571e12	0.808145
$764$	−6.46861e12	−0.686896
$765$	1.16308e11	0.0122782
$766$	−5.26643e12	−0.552696
$767$	−1.33015e11	−0.0138778
$768$	4.23317e12	0.439076
$769$	−1.24406e13	−1.28284	−0.641419	−	0.767191i	$-0.721654\pi$
$769$	−1.24406e13	−1.28284	−0.641419	+	0.767191i	$0.721654\pi$
$770$	3.04630e11	0.0312295
$771$	3.46828e12	0.353484
$772$	−1.36503e12	−0.138314
$773$	1.80557e13	1.81890	0.909448	−	0.415818i	$-0.136505\pi$
$773$	1.80557e13	1.81890	0.909448	+	0.415818i	$0.136505\pi$
$774$	1.11184e12	0.111355
$775$	−1.45333e13	−1.44712
$776$	6.29223e12	0.622912
$777$	4.56443e12	0.449254
$778$	−1.43494e12	−0.140419
$779$	2.14062e12	0.208268
$780$	−7.79811e10	−0.00754334
$781$	1.23188e12	0.118479
$782$	−1.05707e12	−0.101082
$783$	−5.16416e11	−0.0490989
$784$	−1.47754e12	−0.139674
$785$	−1.60043e12	−0.150426
$786$	−6.35610e12	−0.594004
$787$	4.66959e12	0.433903	0.216951	−	0.976182i	$-0.430389\pi$
$787$	4.66959e12	0.433903	0.216951	+	0.976182i	$0.430389\pi$
$788$	1.08344e13	1.00100
$789$	−1.08938e13	−1.00077
$790$	2.00515e11	0.0183158
$791$	−2.46630e12	−0.224002
$792$	1.77961e12	0.160717
$793$	−1.53065e12	−0.137450
$794$	−4.99793e12	−0.446270
$795$	−8.68818e11	−0.0771395
$796$	1.14990e13	1.01520
$797$	−6.81590e12	−0.598358	−0.299179	−	0.954197i	$-0.596713\pi$
$797$	−6.81590e12	−0.598358	−0.299179	+	0.954197i	$0.596713\pi$
$798$	−2.32321e12	−0.202804
$799$	−3.76954e12	−0.327211
$800$	−1.16593e13	−1.00639
$801$	−3.99435e12	−0.342846
$802$	5.45115e12	0.465268
$803$	4.41341e12	0.374589
$804$	−5.29582e12	−0.446973
$805$	−1.17588e12	−0.0986918
$806$	1.00068e12	0.0835192
$807$	−8.75567e12	−0.726706
$808$	1.08597e13	0.896326
$809$	1.08706e13	0.892244	0.446122	−	0.894972i	$-0.352805\pi$
$809$	1.08706e13	0.892244	0.446122	+	0.894972i	$0.352805\pi$
$810$	−1.21282e11	−0.00989947
$811$	−2.22237e12	−0.180395	−0.0901973	−	0.995924i	$-0.528750\pi$
$811$	−2.22237e12	−0.180395	−0.0901973	+	0.995924i	$0.528750\pi$
$812$	−1.50653e12	−0.121612
$813$	−3.33023e12	−0.267342
$814$	4.13841e12	0.330388
$815$	3.13300e12	0.248743
$816$	3.92404e11	0.0309833
$817$	8.20126e12	0.643994
$818$	−7.64569e12	−0.597072
$819$	3.01450e11	0.0234119
$820$	3.26004e11	0.0251803
$821$	−1.89934e13	−1.45901	−0.729505	−	0.683975i	$-0.760250\pi$
$821$	−1.89934e13	−1.45901	−0.729505	+	0.683975i	$0.760250\pi$
$822$	3.23758e12	0.247342
$823$	2.41144e13	1.83222	0.916111	−	0.400925i	$-0.131311\pi$
$823$	2.41144e13	1.83222	0.916111	+	0.400925i	$0.131311\pi$
$824$	−1.16978e12	−0.0883957
$825$	−3.96946e12	−0.298325
$826$	−6.03507e11	−0.0451099
$827$	−1.28933e13	−0.958497	−0.479249	−	0.877679i	$-0.659091\pi$
$827$	−1.28933e13	−0.958497	−0.479249	+	0.877679i	$0.659091\pi$
$828$	−2.88353e12	−0.213201
$829$	1.20665e13	0.887334	0.443667	−	0.896192i	$-0.353677\pi$
$829$	1.20665e13	0.887334	0.443667	+	0.896192i	$0.353677\pi$
$830$	8.56842e11	0.0626685
$831$	−1.11703e13	−0.812567
$832$	4.39123e11	0.0317711
$833$	1.70963e12	0.123027
$834$	−6.03243e12	−0.431763
$835$	3.05644e12	0.217584
$836$	5.51028e12	0.390163
$837$	−4.07133e12	−0.286729
$838$	−1.21541e13	−0.851386
$839$	1.09334e13	0.761771	0.380886	−	0.924622i	$-0.375619\pi$
$839$	1.09334e13	0.761771	0.380886	+	0.924622i	$0.375619\pi$
$840$	−8.42872e11	−0.0584124
$841$	−1.35629e13	−0.934911
$842$	−5.28805e12	−0.362569
$843$	−2.78010e12	−0.189599
$844$	2.76108e12	0.187300
$845$	2.48234e12	0.167496
$846$	3.93073e12	0.263820
$847$	−7.07624e12	−0.472419
$848$	−2.93125e12	−0.194657
$849$	−2.24341e12	−0.148191
$850$	1.69009e12	0.111051
$851$	−1.59744e13	−1.04410
$852$	−1.43076e12	−0.0930229
$853$	6.39450e12	0.413557	0.206779	−	0.978388i	$-0.433702\pi$
$853$	6.39450e12	0.413557	0.206779	+	0.978388i	$0.433702\pi$
$854$	−6.94477e12	−0.446784
$855$	−8.94609e11	−0.0572513
$856$	5.08729e12	0.323858
$857$	−4.53813e12	−0.287384	−0.143692	−	0.989622i	$-0.545898\pi$
$857$	−4.53813e12	−0.287384	−0.143692	+	0.989622i	$0.545898\pi$
$858$	2.73314e11	0.0172175
$859$	−4.99842e12	−0.313230	−0.156615	−	0.987660i	$-0.550058\pi$
$859$	−4.99842e12	−0.313230	−0.156615	+	0.987660i	$0.550058\pi$
$860$	1.24900e12	0.0778611
$861$	−1.26023e12	−0.0781511
$862$	1.79990e12	0.111036
$863$	4.53292e12	0.278182	0.139091	−	0.990280i	$-0.455582\pi$
$863$	4.53292e12	0.278182	0.139091	+	0.990280i	$0.455582\pi$
$864$	−3.26621e12	−0.199404
$865$	−2.76992e12	−0.168227
$866$	−6.97310e12	−0.421304
$867$	9.15157e12	0.550060
$868$	−1.18772e13	−0.710191
$869$	1.83848e12	0.109363
$870$	2.21761e11	0.0131234
$871$	−1.93758e12	−0.114072
$872$	−1.89796e13	−1.11163
$873$	−3.93174e12	−0.229098
$874$	8.13067e12	0.471330
$875$	3.81565e12	0.220056
$876$	−5.12594e12	−0.294107
$877$	4.25995e12	0.243168	0.121584	−	0.992581i	$-0.461203\pi$
$877$	4.25995e12	0.243168	0.121584	+	0.992581i	$0.461203\pi$
$878$	−1.54450e13	−0.877128
$879$	−3.93725e12	−0.222456
$880$	3.95768e11	0.0222469
$881$	1.07615e13	0.601841	0.300920	−	0.953649i	$-0.402706\pi$
$881$	1.07615e13	0.601841	0.300920	+	0.953649i	$0.402706\pi$
$882$	−1.78273e12	−0.0991923
$883$	−2.51265e13	−1.39094	−0.695471	−	0.718554i	$-0.744804\pi$
$883$	−2.51265e13	−1.39094	−0.695471	+	0.718554i	$0.744804\pi$
$884$	3.04422e11	0.0167665
$885$	−2.32395e11	−0.0127345
$886$	−4.97006e11	−0.0270963
$887$	1.29291e13	0.701311	0.350655	−	0.936505i	$-0.385959\pi$
$887$	1.29291e13	0.701311	0.350655	+	0.936505i	$0.385959\pi$
$888$	−1.14505e13	−0.617966
$889$	−1.22430e13	−0.657401
$890$	1.71526e12	0.0916379
$891$	−1.11200e12	−0.0591093
$892$	5.19567e12	0.274789
$893$	2.89943e13	1.52574
$894$	1.84602e11	0.00966537
$895$	3.50096e12	0.182383
$896$	−1.11785e13	−0.579423
$897$	−1.05500e12	−0.0544110
$898$	3.09616e12	0.158884
$899$	7.44434e12	0.380109
$900$	4.61032e12	0.234228
$901$	3.39169e12	0.171457
$902$	−1.14261e12	−0.0574735
$903$	−4.82825e12	−0.241654
$904$	6.18704e12	0.308124
$905$	−2.51084e12	−0.124423
$906$	4.99542e12	0.246318
$907$	1.13077e13	0.554806	0.277403	−	0.960754i	$-0.410526\pi$
$907$	1.13077e13	0.554806	0.277403	+	0.960754i	$0.410526\pi$
$908$	9.79033e11	0.0477981
$909$	−6.78574e12	−0.329655
$910$	−1.29449e11	−0.00625768
$911$	−8.95975e12	−0.430986	−0.215493	−	0.976505i	$-0.569136\pi$
$911$	−8.95975e12	−0.430986	−0.215493	+	0.976505i	$0.569136\pi$
$912$	−3.01826e12	−0.144471
$913$	7.85618e12	0.374191
$914$	−1.13406e13	−0.537498
$915$	−2.67425e12	−0.126127
$916$	−2.61399e13	−1.22680
$917$	2.76018e13	1.28907
$918$	4.73459e11	0.0220034
$919$	1.85630e13	0.858477	0.429239	−	0.903191i	$-0.358782\pi$
$919$	1.85630e13	0.858477	0.429239	+	0.903191i	$0.358782\pi$
$920$	2.94985e12	0.135754
$921$	−6.41525e12	−0.293796
$922$	5.44811e12	0.248289
$923$	−5.23475e11	−0.0237404
$924$	−3.24401e12	−0.146406
$925$	2.55405e13	1.14708
$926$	−4.18808e12	−0.187183
$927$	7.30944e11	0.0325106
$928$	5.97220e12	0.264344
$929$	−3.05904e13	−1.34746	−0.673728	−	0.738980i	$-0.735308\pi$
$929$	−3.05904e13	−1.34746	−0.673728	+	0.738980i	$0.735308\pi$
$930$	1.74832e12	0.0766386
$931$	−1.31500e13	−0.573656
$932$	1.77716e12	0.0771536
$933$	−1.11066e13	−0.479859
$934$	1.42729e12	0.0613693
$935$	−4.57936e11	−0.0195953
$936$	−7.56226e11	−0.0322040
$937$	3.38827e13	1.43599	0.717993	−	0.696050i	$-0.245061\pi$
$937$	3.38827e13	1.43599	0.717993	+	0.696050i	$0.245061\pi$
$938$	−8.79110e12	−0.370792
$939$	1.16912e13	0.490754
$940$	4.41566e12	0.184468
$941$	3.41437e13	1.41957	0.709785	−	0.704418i	$-0.248792\pi$
$941$	3.41437e13	1.41957	0.709785	+	0.704418i	$0.248792\pi$
$942$	−6.51491e12	−0.269575
$943$	4.41049e12	0.181629
$944$	−7.84062e11	−0.0321349
$945$	5.26674e11	0.0214832
$946$	−4.37761e12	−0.177716
$947$	3.30474e13	1.33525	0.667624	−	0.744499i	$-0.267311\pi$
$947$	3.30474e13	1.33525	0.667624	+	0.744499i	$0.267311\pi$
$948$	−2.13529e12	−0.0858657
$949$	−1.87543e12	−0.0750590
$950$	−1.29997e13	−0.517817
$951$	−5.30080e11	−0.0210150
$952$	3.29040e12	0.129832
$953$	−3.77689e12	−0.148326	−0.0741628	−	0.997246i	$-0.523628\pi$
$953$	−3.77689e12	−0.148326	−0.0741628	+	0.997246i	$0.523628\pi$
$954$	−3.53672e12	−0.138240
$955$	−4.13490e12	−0.160861
$956$	2.35745e13	0.912813
$957$	2.03327e12	0.0783595
$958$	2.37478e13	0.910915
$959$	−1.40594e13	−0.536765
$960$	7.67209e11	0.0291537
$961$	3.22502e13	1.21977
$962$	−1.75857e12	−0.0662022
$963$	−3.17882e12	−0.119110
$964$	1.18693e13	0.442669
$965$	−8.72563e11	−0.0323910
$966$	−4.78669e12	−0.176863
$967$	4.64428e13	1.70804	0.854022	−	0.520237i	$-0.174156\pi$
$967$	4.64428e13	1.70804	0.854022	+	0.520237i	$0.174156\pi$
$968$	1.77517e13	0.649831
$969$	3.49237e12	0.127252
$970$	1.68838e12	0.0612345
$971$	−9.18432e12	−0.331559	−0.165779	−	0.986163i	$-0.553014\pi$
$971$	−9.18432e12	−0.331559	−0.165779	+	0.986163i	$0.553014\pi$
$972$	1.29153e12	0.0464094
$973$	2.61963e13	0.936983
$974$	−7.66494e12	−0.272894
$975$	1.68678e12	0.0597775
$976$	−9.02248e12	−0.318274
$977$	−3.16019e13	−1.10965	−0.554826	−	0.831966i	$-0.687215\pi$
$977$	−3.16019e13	−1.10965	−0.554826	+	0.831966i	$0.687215\pi$
$978$	1.27536e13	0.445768
$979$	1.57268e13	0.547166
$980$	−2.00267e12	−0.0693571
$981$	1.18595e13	0.408842
$982$	1.20642e12	0.0413995
$983$	3.93532e13	1.34428	0.672139	−	0.740425i	$-0.265376\pi$
$983$	3.93532e13	1.34428	0.672139	+	0.740425i	$0.265376\pi$
$984$	3.16145e12	0.107500
$985$	6.92562e12	0.234420
$986$	−8.65709e11	−0.0291693
$987$	−1.70695e13	−0.572524
$988$	−2.34153e12	−0.0781797
$989$	1.68977e13	0.561621
$990$	4.77518e11	0.0157991
$991$	−3.64226e12	−0.119961	−0.0599805	−	0.998200i	$-0.519104\pi$
$991$	−3.64226e12	−0.119961	−0.0599805	+	0.998200i	$0.519104\pi$
$992$	4.70837e13	1.54372
$993$	1.84465e13	0.602065
$994$	−2.37508e12	−0.0771684
$995$	7.35048e12	0.237745
$996$	−9.12452e12	−0.293794
$997$	−4.88557e11	−0.0156598	−0.00782991	−	0.999969i	$-0.502492\pi$
$997$	−4.88557e11	−0.0156598	−0.00782991	+	0.999969i	$0.502492\pi$
$998$	−2.26722e13	−0.723447
$999$	7.15489e12	0.227278

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.b.1.13	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.b.1.13	✓	21	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)

\(f(q)\)	\(=\)	\(q+11.8993 q^{2} -81.0000 q^{3} -370.407 q^{4} -236.774 q^{5} -963.842 q^{6} +4185.56 q^{7} -10500.0 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+11.8993 q^{2} -81.0000 q^{3} -370.407 q^{4} -236.774 q^{5} -963.842 q^{6} +4185.56 q^{7} -10500.0 q^{8} +6561.00 q^{9} -2817.44 q^{10} -25832.4 q^{11} +30003.0 q^{12} +10977.2 q^{13} +49805.2 q^{14} +19178.7 q^{15} +64705.7 q^{16} -74869.7 q^{17} +78071.2 q^{18} +575877. q^{19} +87702.6 q^{20} -339030. q^{21} -307387. q^{22} +1.18652e6 q^{23} +850501. q^{24} -1.89706e6 q^{25} +130621. q^{26} -531441. q^{27} -1.55036e6 q^{28} +971729. q^{29} +228213. q^{30} +7.66093e6 q^{31} +6.14596e6 q^{32} +2.09243e6 q^{33} -890896. q^{34} -991030. q^{35} -2.43024e6 q^{36} -1.34632e7 q^{37} +6.85252e6 q^{38} -889153. q^{39} +2.48613e6 q^{40} +3.71716e6 q^{41} -4.03422e6 q^{42} +1.42413e7 q^{43} +9.56851e6 q^{44} -1.55347e6 q^{45} +1.41188e7 q^{46} +5.03480e7 q^{47} -5.24116e6 q^{48} -2.28347e7 q^{49} -2.25737e7 q^{50} +6.06445e6 q^{51} -4.06603e6 q^{52} -4.53012e7 q^{53} -6.32377e6 q^{54} +6.11644e6 q^{55} -4.39484e7 q^{56} -4.66460e7 q^{57} +1.15629e7 q^{58} -1.21174e7 q^{59} -7.10391e6 q^{60} -1.39439e8 q^{61} +9.11596e7 q^{62} +2.74614e7 q^{63} +4.00032e7 q^{64} -2.59911e6 q^{65} +2.48984e7 q^{66} -1.76510e8 q^{67} +2.77323e7 q^{68} -9.61083e7 q^{69} -1.17926e7 q^{70} -4.76874e7 q^{71} -6.88906e7 q^{72} -1.70848e8 q^{73} -1.60202e8 q^{74} +1.53662e8 q^{75} -2.13309e8 q^{76} -1.08123e8 q^{77} -1.05803e7 q^{78} -7.11694e7 q^{79} -1.53206e7 q^{80} +4.30467e7 q^{81} +4.42315e7 q^{82} -3.04121e8 q^{83} +1.25579e8 q^{84} +1.77272e7 q^{85} +1.69462e8 q^{86} -7.87100e7 q^{87} +2.71241e8 q^{88} -6.08801e8 q^{89} -1.84852e7 q^{90} +4.59457e7 q^{91} -4.39496e8 q^{92} -6.20535e8 q^{93} +5.99106e8 q^{94} -1.36353e8 q^{95} -4.97823e8 q^{96} -5.99259e8 q^{97} -2.71717e8 q^{98} -1.69487e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9}+O(q^{10}) \) 21 * q + 20 * q^2 - 1701 * q^3 + 4950 * q^4 + 2058 * q^5 - 1620 * q^6 - 17167 * q^7 - 2853 * q^8 + 137781 * q^9	\( 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9} - 31559 q^{10} - 38751 q^{11} - 400950 q^{12} - 58915 q^{13} + 3453 q^{14} - 166698 q^{15} + 1655714 q^{16} - 64233 q^{17} + 131220 q^{18} - 1937236 q^{19} - 1065507 q^{20} + 1390527 q^{21} - 5386882 q^{22} - 1838574 q^{23} + 231093 q^{24} + 4565755 q^{25} - 839702 q^{26} - 11160261 q^{27} - 4471034 q^{28} + 15658544 q^{29} + 2556279 q^{30} - 14282802 q^{31} - 2205286 q^{32} + 3138831 q^{33} + 19005532 q^{34} - 8633300 q^{35} + 32476950 q^{36} + 7531195 q^{37} + 26649773 q^{38} + 4772115 q^{39} + 17775672 q^{40} + 18338245 q^{41} - 279693 q^{42} - 22480305 q^{43} - 80230922 q^{44} + 13502538 q^{45} - 83894107 q^{46} - 110397260 q^{47} - 134112834 q^{48} + 130653638 q^{49} + 65575693 q^{50} + 5202873 q^{51} + 177908014 q^{52} + 145498338 q^{53} - 10628820 q^{54} + 86448944 q^{55} + 354387888 q^{56} + 156916116 q^{57} + 115508368 q^{58} - 254464581 q^{59} + 86306067 q^{60} + 287595506 q^{61} + 819899030 q^{62} - 112632687 q^{63} + 822446413 q^{64} + 77238206 q^{65} + 436337442 q^{66} - 392860610 q^{67} + 167325073 q^{68} + 148924494 q^{69} - 424902116 q^{70} - 248960491 q^{71} - 18718533 q^{72} - 758406074 q^{73} - 923266846 q^{74} - 369826155 q^{75} - 2312747568 q^{76} - 878126795 q^{77} + 68015862 q^{78} - 1925801029 q^{79} - 1898919861 q^{80} + 903981141 q^{81} - 3249102191 q^{82} - 1650336307 q^{83} + 362153754 q^{84} - 2342480762 q^{85} - 3609864952 q^{86} - 1268342064 q^{87} - 5987792887 q^{88} - 574997526 q^{89} - 207058599 q^{90} - 4481387117 q^{91} - 5317166770 q^{92} + 1156906962 q^{93} - 5360726568 q^{94} - 2789231462 q^{95} + 178628166 q^{96} - 4651540898 q^{97} - 5566652976 q^{98} - 254245311 q^{99}+O(q^{100}) \) 21 * q + 20 * q^2 - 1701 * q^3 + 4950 * q^4 + 2058 * q^5 - 1620 * q^6 - 17167 * q^7 - 2853 * q^8 + 137781 * q^9 - 31559 * q^10 - 38751 * q^11 - 400950 * q^12 - 58915 * q^13 + 3453 * q^14 - 166698 * q^15 + 1655714 * q^16 - 64233 * q^17 + 131220 * q^18 - 1937236 * q^19 - 1065507 * q^20 + 1390527 * q^21 - 5386882 * q^22 - 1838574 * q^23 + 231093 * q^24 + 4565755 * q^25 - 839702 * q^26 - 11160261 * q^27 - 4471034 * q^28 + 15658544 * q^29 + 2556279 * q^30 - 14282802 * q^31 - 2205286 * q^32 + 3138831 * q^33 + 19005532 * q^34 - 8633300 * q^35 + 32476950 * q^36 + 7531195 * q^37 + 26649773 * q^38 + 4772115 * q^39 + 17775672 * q^40 + 18338245 * q^41 - 279693 * q^42 - 22480305 * q^43 - 80230922 * q^44 + 13502538 * q^45 - 83894107 * q^46 - 110397260 * q^47 - 134112834 * q^48 + 130653638 * q^49 + 65575693 * q^50 + 5202873 * q^51 + 177908014 * q^52 + 145498338 * q^53 - 10628820 * q^54 + 86448944 * q^55 + 354387888 * q^56 + 156916116 * q^57 + 115508368 * q^58 - 254464581 * q^59 + 86306067 * q^60 + 287595506 * q^61 + 819899030 * q^62 - 112632687 * q^63 + 822446413 * q^64 + 77238206 * q^65 + 436337442 * q^66 - 392860610 * q^67 + 167325073 * q^68 + 148924494 * q^69 - 424902116 * q^70 - 248960491 * q^71 - 18718533 * q^72 - 758406074 * q^73 - 923266846 * q^74 - 369826155 * q^75 - 2312747568 * q^76 - 878126795 * q^77 + 68015862 * q^78 - 1925801029 * q^79 - 1898919861 * q^80 + 903981141 * q^81 - 3249102191 * q^82 - 1650336307 * q^83 + 362153754 * q^84 - 2342480762 * q^85 - 3609864952 * q^86 - 1268342064 * q^87 - 5987792887 * q^88 - 574997526 * q^89 - 207058599 * q^90 - 4481387117 * q^91 - 5317166770 * q^92 + 1156906962 * q^93 - 5360726568 * q^94 - 2789231462 * q^95 + 178628166 * q^96 - 4651540898 * q^97 - 5566652976 * q^98 - 254245311 * q^99

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