LMFDB - Embedded newform 177.10.a.b.1.19

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			1.19
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)

$f(q)$	$=$	$q+34.8201 q^{2} -81.0000 q^{3} +700.437 q^{4} -913.273 q^{5} -2820.43 q^{6} -1305.26 q^{7} +6561.40 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+34.8201 q^{2} -81.0000 q^{3} +700.437 q^{4} -913.273 q^{5} -2820.43 q^{6} -1305.26 q^{7} +6561.40 q^{8} +6561.00 q^{9} -31800.2 q^{10} +67784.1 q^{11} -56735.4 q^{12} +35597.5 q^{13} -45449.3 q^{14} +73975.1 q^{15} -130155. q^{16} +122703. q^{17} +228454. q^{18} -426361. q^{19} -639690. q^{20} +105726. q^{21} +2.36025e6 q^{22} +62806.5 q^{23} -531474. q^{24} -1.11906e6 q^{25} +1.23951e6 q^{26} -531441. q^{27} -914253. q^{28} -602445. q^{29} +2.57582e6 q^{30} +5.48687e6 q^{31} -7.89146e6 q^{32} -5.49051e6 q^{33} +4.27254e6 q^{34} +1.19206e6 q^{35} +4.59557e6 q^{36} -6.71960e6 q^{37} -1.48459e7 q^{38} -2.88339e6 q^{39} -5.99235e6 q^{40} -3.26258e7 q^{41} +3.68139e6 q^{42} -520430. q^{43} +4.74785e7 q^{44} -5.99198e6 q^{45} +2.18693e6 q^{46} -4.65341e7 q^{47} +1.05426e7 q^{48} -3.86499e7 q^{49} -3.89657e7 q^{50} -9.93898e6 q^{51} +2.49338e7 q^{52} -9.11193e7 q^{53} -1.85048e7 q^{54} -6.19054e7 q^{55} -8.56434e6 q^{56} +3.45353e7 q^{57} -2.09772e7 q^{58} -1.21174e7 q^{59} +5.18149e7 q^{60} +6.62621e7 q^{61} +1.91053e8 q^{62} -8.56381e6 q^{63} -2.08142e8 q^{64} -3.25102e7 q^{65} -1.91180e8 q^{66} -1.85333e7 q^{67} +8.59461e7 q^{68} -5.08733e6 q^{69} +4.15076e7 q^{70} +3.02257e8 q^{71} +4.30494e7 q^{72} -2.05549e8 q^{73} -2.33977e8 q^{74} +9.06437e7 q^{75} -2.98639e8 q^{76} -8.84759e7 q^{77} -1.00400e8 q^{78} +4.56363e8 q^{79} +1.18867e8 q^{80} +4.30467e7 q^{81} -1.13603e9 q^{82} -3.38841e8 q^{83} +7.40545e7 q^{84} -1.12062e8 q^{85} -1.81214e7 q^{86} +4.87981e7 q^{87} +4.44759e8 q^{88} -3.61357e8 q^{89} -2.08641e8 q^{90} -4.64640e7 q^{91} +4.39920e7 q^{92} -4.44436e8 q^{93} -1.62032e9 q^{94} +3.89384e8 q^{95} +6.39208e8 q^{96} -5.78879e8 q^{97} -1.34579e9 q^{98} +4.44732e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	34.8201	1.53884	0.769422	−	0.638741i	$-0.220544\pi$
$2$	34.8201	1.53884	0.769422	+	0.638741i	$0.220544\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	700.437	1.36804
$5$	−913.273	−0.653485	−0.326742	−	0.945113i	$-0.605951\pi$
$5$	−913.273	−0.653485	−0.326742	+	0.945113i	$0.605951\pi$
$6$	−2820.43	−0.888452
$7$	−1305.26	−0.205474	−0.102737	−	0.994709i	$-0.532760\pi$
$7$	−1305.26	−0.205474	−0.102737	+	0.994709i	$0.532760\pi$
$8$	6561.40	0.566359
$9$	6561.00	0.333333
$10$	−31800.2	−1.00561
$11$	67784.1	1.39592	0.697961	−	0.716136i	$-0.254091\pi$
$11$	67784.1	1.39592	0.697961	+	0.716136i	$0.254091\pi$
$12$	−56735.4	−0.789839
$13$	35597.5	0.345680	0.172840	−	0.984950i	$-0.444706\pi$
$13$	35597.5	0.345680	0.172840	+	0.984950i	$0.444706\pi$
$14$	−45449.3	−0.316192
$15$	73975.1	0.377290
$16$	−130155.	−0.496503
$17$	122703.	0.356317	0.178159	−	0.984002i	$-0.442986\pi$
$17$	122703.	0.356317	0.178159	+	0.984002i	$0.442986\pi$
$18$	228454.	0.512948
$19$	−426361.	−0.750562	−0.375281	−	0.926911i	$-0.622454\pi$
$19$	−426361.	−0.750562	−0.375281	+	0.926911i	$0.622454\pi$
$20$	−639690.	−0.893994
$21$	105726.	0.118630
$22$	2.36025e6	2.14811
$23$	62806.5	0.0467982	0.0233991	−	0.999726i	$-0.492551\pi$
$23$	62806.5	0.0467982	0.0233991	+	0.999726i	$0.492551\pi$
$24$	−531474.	−0.326988
$25$	−1.11906e6	−0.572958
$26$	1.23951e6	0.531947
$27$	−531441.	−0.192450
$28$	−914253.	−0.281096
$29$	−602445.	−0.158171	−0.0790855	−	0.996868i	$-0.525200\pi$
$29$	−602445.	−0.158171	−0.0790855	+	0.996868i	$0.525200\pi$
$30$	2.57582e6	0.580590
$31$	5.48687e6	1.06708	0.533540	−	0.845775i	$-0.320861\pi$
$31$	5.48687e6	1.06708	0.533540	+	0.845775i	$0.320861\pi$
$32$	−7.89146e6	−1.33040
$33$	−5.49051e6	−0.805936
$34$	4.27254e6	0.548316
$35$	1.19206e6	0.134274
$36$	4.59557e6	0.456014
$37$	−6.71960e6	−0.589434	−0.294717	−	0.955585i	$-0.595225\pi$
$37$	−6.71960e6	−0.589434	−0.294717	+	0.955585i	$0.595225\pi$
$38$	−1.48459e7	−1.15500
$39$	−2.88339e6	−0.199578
$40$	−5.99235e6	−0.370107
$41$	−3.26258e7	−1.80316	−0.901579	−	0.432614i	$-0.857591\pi$
$41$	−3.26258e7	−1.80316	−0.901579	+	0.432614i	$0.857591\pi$
$42$	3.68139e6	0.182553
$43$	−520430.	−0.0232142	−0.0116071	−	0.999933i	$-0.503695\pi$
$43$	−520430.	−0.0232142	−0.0116071	+	0.999933i	$0.503695\pi$
$44$	4.74785e7	1.90968
$45$	−5.99198e6	−0.217828
$46$	2.18693e6	0.0720152
$47$	−4.65341e7	−1.39101	−0.695506	−	0.718520i	$-0.744820\pi$
$47$	−4.65341e7	−1.39101	−0.695506	+	0.718520i	$0.744820\pi$
$48$	1.05426e7	0.286656
$49$	−3.86499e7	−0.957781
$50$	−3.89657e7	−0.881693
$51$	−9.93898e6	−0.205720
$52$	2.49338e7	0.472904
$53$	−9.11193e7	−1.58624	−0.793120	−	0.609066i	$-0.791545\pi$
$53$	−9.11193e7	−1.58624	−0.793120	+	0.609066i	$0.791545\pi$
$54$	−1.85048e7	−0.296151
$55$	−6.19054e7	−0.912213
$56$	−8.56434e6	−0.116372
$57$	3.45353e7	0.433337
$58$	−2.09772e7	−0.243400
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	5.18149e7	0.516148
$61$	6.62621e7	0.612746	0.306373	−	0.951911i	$-0.400884\pi$
$61$	6.62621e7	0.612746	0.306373	+	0.951911i	$0.400884\pi$
$62$	1.91053e8	1.64207
$63$	−8.56381e6	−0.0684912
$64$	−2.08142e8	−1.55078
$65$	−3.25102e7	−0.225896
$66$	−1.91180e8	−1.24021
$67$	−1.85333e7	−0.112361	−0.0561807	−	0.998421i	$-0.517892\pi$
$67$	−1.85333e7	−0.112361	−0.0561807	+	0.998421i	$0.517892\pi$
$68$	8.59461e7	0.487457
$69$	−5.08733e6	−0.0270190
$70$	4.15076e7	0.206627
$71$	3.02257e8	1.41160	0.705802	−	0.708409i	$-0.250587\pi$
$71$	3.02257e8	1.41160	0.705802	+	0.708409i	$0.250587\pi$
$72$	4.30494e7	0.188786
$73$	−2.05549e8	−0.847154	−0.423577	−	0.905860i	$-0.639226\pi$
$73$	−2.05549e8	−0.847154	−0.423577	+	0.905860i	$0.639226\pi$
$74$	−2.33977e8	−0.907048
$75$	9.06437e7	0.330797
$76$	−2.98639e8	−1.02680
$77$	−8.84759e7	−0.286825
$78$	−1.00400e8	−0.307120
$79$	4.56363e8	1.31822	0.659111	−	0.752046i	$-0.270933\pi$
$79$	4.56363e8	1.31822	0.659111	+	0.752046i	$0.270933\pi$
$80$	1.18867e8	0.324457
$81$	4.30467e7	0.111111
$82$	−1.13603e9	−2.77478
$83$	−3.38841e8	−0.783691	−0.391846	−	0.920031i	$-0.628163\pi$
$83$	−3.38841e8	−0.783691	−0.391846	+	0.920031i	$0.628163\pi$
$84$	7.40545e7	0.162291
$85$	−1.12062e8	−0.232848
$86$	−1.81214e7	−0.0357231
$87$	4.87981e7	0.0913200
$88$	4.44759e8	0.790593
$89$	−3.61357e8	−0.610495	−0.305247	−	0.952273i	$-0.598739\pi$
$89$	−3.61357e8	−0.610495	−0.305247	+	0.952273i	$0.598739\pi$
$90$	−2.08641e8	−0.335204
$91$	−4.64640e7	−0.0710281
$92$	4.39920e7	0.0640219
$93$	−4.44436e8	−0.616079
$94$	−1.62032e9	−2.14055
$95$	3.89384e8	0.490481
$96$	6.39208e8	0.768107
$97$	−5.78879e8	−0.663918	−0.331959	−	0.943294i	$-0.607710\pi$
$97$	−5.78879e8	−0.663918	−0.331959	+	0.943294i	$0.607710\pi$
$98$	−1.34579e9	−1.47388
$99$	4.44732e8	0.465307
$100$	−7.83830e8	−0.783830
$101$	1.11912e9	1.07012	0.535058	−	0.844815i	$-0.320290\pi$
$101$	1.11912e9	1.07012	0.535058	+	0.844815i	$0.320290\pi$
$102$	−3.46076e8	−0.316571
$103$	−2.19095e9	−1.91807	−0.959037	−	0.283282i	$-0.908577\pi$
$103$	−2.19095e9	−1.91807	−0.959037	+	0.283282i	$0.908577\pi$
$104$	2.33569e8	0.195779
$105$	−9.65568e7	−0.0775230
$106$	−3.17278e9	−2.44098
$107$	−1.99859e9	−1.47399	−0.736997	−	0.675895i	$-0.763757\pi$
$107$	−1.99859e9	−1.47399	−0.736997	+	0.675895i	$0.763757\pi$
$108$	−3.72241e8	−0.263280
$109$	1.72291e8	0.116908	0.0584539	−	0.998290i	$-0.481383\pi$
$109$	1.72291e8	0.116908	0.0584539	+	0.998290i	$0.481383\pi$
$110$	−2.15555e9	−1.40375
$111$	5.44287e8	0.340310
$112$	1.69887e8	0.102018
$113$	1.65253e9	0.953445	0.476723	−	0.879054i	$-0.341825\pi$
$113$	1.65253e9	0.953445	0.476723	+	0.879054i	$0.341825\pi$
$114$	1.20252e9	0.666839
$115$	−5.73595e7	−0.0305819
$116$	−4.21975e8	−0.216384
$117$	2.33555e8	0.115227
$118$	−4.21927e8	−0.200340
$119$	−1.60160e8	−0.0732137
$120$	4.85380e8	0.213681
$121$	2.23674e9	0.948596
$122$	2.30725e9	0.942921
$123$	2.64269e9	1.04105
$124$	3.84321e9	1.45981
$125$	2.80574e9	1.02790
$126$	−2.98193e8	−0.105397
$127$	−1.14606e8	−0.0390921	−0.0195460	−	0.999809i	$-0.506222\pi$
$127$	−1.14606e8	−0.0390921	−0.0195460	+	0.999809i	$0.506222\pi$
$128$	−3.20708e9	−1.05600
$129$	4.21548e7	0.0134027
$130$	−1.13201e9	−0.347619
$131$	−3.87344e9	−1.14915	−0.574574	−	0.818453i	$-0.694832\pi$
$131$	−3.87344e9	−1.14915	−0.574574	+	0.818453i	$0.694832\pi$
$132$	−3.84576e9	−1.10255
$133$	5.56513e8	0.154221
$134$	−6.45332e8	−0.172907
$135$	4.85351e8	0.125763
$136$	8.05107e8	0.201803
$137$	−2.67007e8	−0.0647561	−0.0323780	−	0.999476i	$-0.510308\pi$
$137$	−2.67007e8	−0.0647561	−0.0323780	+	0.999476i	$0.510308\pi$
$138$	−1.77141e8	−0.0415780
$139$	7.18570e9	1.63269	0.816343	−	0.577568i	$-0.195998\pi$
$139$	7.18570e9	1.63269	0.816343	+	0.577568i	$0.195998\pi$
$140$	8.34963e8	0.183692
$141$	3.76926e9	0.803102
$142$	1.05246e10	2.17224
$143$	2.41294e9	0.482542
$144$	−8.53949e8	−0.165501
$145$	5.50197e8	0.103362
$146$	−7.15723e9	−1.30364
$147$	3.13064e9	0.552975
$148$	−4.70666e9	−0.806371
$149$	−2.77970e9	−0.462020	−0.231010	−	0.972951i	$-0.574203\pi$
$149$	−2.77970e9	−0.462020	−0.231010	+	0.972951i	$0.574203\pi$
$150$	3.15622e9	0.509046
$151$	−1.97660e9	−0.309402	−0.154701	−	0.987961i	$-0.549441\pi$
$151$	−1.97660e9	−0.309402	−0.154701	+	0.987961i	$0.549441\pi$
$152$	−2.79753e9	−0.425088
$153$	8.05057e8	0.118772
$154$	−3.08074e9	−0.441379
$155$	−5.01101e9	−0.697320
$156$	−2.01964e9	−0.273032
$157$	1.85219e9	0.243297	0.121649	−	0.992573i	$-0.461182\pi$
$157$	1.85219e9	0.243297	0.121649	+	0.992573i	$0.461182\pi$
$158$	1.58906e10	2.02854
$159$	7.38066e9	0.915816
$160$	7.20705e9	0.869396
$161$	−8.19789e7	−0.00961580
$162$	1.49889e9	0.170983
$163$	−7.67652e9	−0.851766	−0.425883	−	0.904778i	$-0.640036\pi$
$163$	−7.67652e9	−0.851766	−0.425883	+	0.904778i	$0.640036\pi$
$164$	−2.28523e10	−2.46680
$165$	5.01434e9	0.526667
$166$	−1.17985e10	−1.20598
$167$	1.72701e10	1.71819	0.859093	−	0.511819i	$-0.171028\pi$
$167$	1.72701e10	1.71819	0.859093	+	0.511819i	$0.171028\pi$
$168$	6.93712e8	0.0671873
$169$	−9.33732e9	−0.880505
$170$	−3.90200e9	−0.358316
$171$	−2.79736e9	−0.250187
$172$	−3.64528e8	−0.0317580
$173$	−1.40653e10	−1.19383	−0.596914	−	0.802305i	$-0.703607\pi$
$173$	−1.40653e10	−1.19383	−0.596914	+	0.802305i	$0.703607\pi$
$174$	1.69915e9	0.140527
$175$	1.46066e9	0.117728
$176$	−8.82247e9	−0.693080
$177$	9.81506e8	0.0751646
$178$	−1.25825e10	−0.939456
$179$	3.57355e9	0.260173	0.130086	−	0.991503i	$-0.458475\pi$
$179$	3.57355e9	0.260173	0.130086	+	0.991503i	$0.458475\pi$
$180$	−4.19701e9	−0.297998
$181$	−1.99450e9	−0.138128	−0.0690638	−	0.997612i	$-0.522001\pi$
$181$	−1.99450e9	−0.138128	−0.0690638	+	0.997612i	$0.522001\pi$
$182$	−1.61788e9	−0.109301
$183$	−5.36723e9	−0.353769
$184$	4.12099e8	0.0265046
$185$	6.13683e9	0.385186
$186$	−1.54753e10	−0.948050
$187$	8.31735e9	0.497391
$188$	−3.25942e10	−1.90296
$189$	6.93669e8	0.0395434
$190$	1.35584e10	0.754774
$191$	−1.81344e10	−0.985947	−0.492973	−	0.870044i	$-0.664090\pi$
$191$	−1.81344e10	−0.985947	−0.492973	+	0.870044i	$0.664090\pi$
$192$	1.68595e10	0.895341
$193$	1.18946e10	0.617080	0.308540	−	0.951211i	$-0.400160\pi$
$193$	1.18946e10	0.617080	0.308540	+	0.951211i	$0.400160\pi$
$194$	−2.01566e10	−1.02167
$195$	2.63333e9	0.130421
$196$	−2.70718e10	−1.31028
$197$	−2.80544e10	−1.32710	−0.663550	−	0.748132i	$-0.730951\pi$
$197$	−2.80544e10	−1.32710	−0.663550	+	0.748132i	$0.730951\pi$
$198$	1.54856e10	0.716035
$199$	9.08899e9	0.410844	0.205422	−	0.978674i	$-0.434143\pi$
$199$	9.08899e9	0.410844	0.205422	+	0.978674i	$0.434143\pi$
$200$	−7.34259e9	−0.324500
$201$	1.50120e9	0.0648719
$202$	3.89679e10	1.64674
$203$	7.86348e8	0.0324999
$204$	−6.96163e9	−0.281433
$205$	2.97963e10	1.17834
$206$	−7.62891e10	−2.95162
$207$	4.12074e8	0.0155994
$208$	−4.63320e9	−0.171631
$209$	−2.89005e10	−1.04773
$210$	−3.36211e9	−0.119296
$211$	1.39839e10	0.485689	0.242844	−	0.970065i	$-0.421920\pi$
$211$	1.39839e10	0.485689	0.242844	+	0.970065i	$0.421920\pi$
$212$	−6.38233e10	−2.17004
$213$	−2.44828e10	−0.814990
$214$	−6.95909e10	−2.26825
$215$	4.75294e8	0.0151701
$216$	−3.48700e9	−0.108996
$217$	−7.16179e9	−0.219257
$218$	5.99919e9	0.179903
$219$	1.66495e10	0.489105
$220$	−4.33609e10	−1.24795
$221$	4.36793e9	0.123172
$222$	1.89521e10	0.523684
$223$	2.21746e10	0.600459	0.300230	−	0.953867i	$-0.402937\pi$
$223$	2.21746e10	0.600459	0.300230	+	0.953867i	$0.402937\pi$
$224$	1.03004e10	0.273362
$225$	−7.34214e9	−0.190986
$226$	5.75411e10	1.46720
$227$	−3.93832e10	−0.984453	−0.492226	−	0.870467i	$-0.663817\pi$
$227$	−3.93832e10	−0.984453	−0.492226	+	0.870467i	$0.663817\pi$
$228$	2.41898e10	0.592824
$229$	−2.26140e10	−0.543398	−0.271699	−	0.962382i	$-0.587586\pi$
$229$	−2.26140e10	−0.543398	−0.271699	+	0.962382i	$0.587586\pi$
$230$	−1.99726e9	−0.0470608
$231$	7.16655e9	0.165598
$232$	−3.95289e9	−0.0895815
$233$	6.74922e10	1.50021	0.750105	−	0.661319i	$-0.230003\pi$
$233$	6.74922e10	1.50021	0.750105	+	0.661319i	$0.230003\pi$
$234$	8.13240e9	0.177316
$235$	4.24983e10	0.909006
$236$	−8.48745e9	−0.178104
$237$	−3.69654e10	−0.761076
$238$	−5.57678e9	−0.112665
$239$	9.04335e10	1.79283	0.896414	−	0.443217i	$-0.146163\pi$
$239$	9.04335e10	1.79283	0.896414	+	0.443217i	$0.146163\pi$
$240$	−9.62825e9	−0.187326
$241$	7.42878e10	1.41854	0.709269	−	0.704938i	$-0.249025\pi$
$241$	7.42878e10	1.41854	0.709269	+	0.704938i	$0.249025\pi$
$242$	7.78835e10	1.45974
$243$	−3.48678e9	−0.0641500
$244$	4.64124e10	0.838263
$245$	3.52979e10	0.625895
$246$	9.20187e10	1.60202
$247$	−1.51774e10	−0.259454
$248$	3.60016e10	0.604350
$249$	2.74462e10	0.452464
$250$	9.76961e10	1.58178
$251$	−1.00228e10	−0.159388	−0.0796939	−	0.996819i	$-0.525394\pi$
$251$	−1.00228e10	−0.159388	−0.0796939	+	0.996819i	$0.525394\pi$
$252$	−5.99842e9	−0.0936988
$253$	4.25729e9	0.0653266
$254$	−3.99057e9	−0.0601566
$255$	9.07700e9	0.134435
$256$	−5.10222e9	−0.0742471
$257$	−8.19063e10	−1.17117	−0.585583	−	0.810613i	$-0.699134\pi$
$257$	−8.19063e10	−1.17117	−0.585583	+	0.810613i	$0.699134\pi$
$258$	1.46783e9	0.0206247
$259$	8.77083e9	0.121113
$260$	−2.27714e10	−0.309036
$261$	−3.95264e9	−0.0527236
$262$	−1.34873e11	−1.76836
$263$	1.14867e11	1.48045	0.740225	−	0.672359i	$-0.234719\pi$
$263$	1.14867e11	1.48045	0.740225	+	0.672359i	$0.234719\pi$
$264$	−3.60255e10	−0.456449
$265$	8.32167e10	1.03658
$266$	1.93778e10	0.237322
$267$	2.92700e10	0.352469
$268$	−1.29814e10	−0.153715
$269$	−2.34014e10	−0.272494	−0.136247	−	0.990675i	$-0.543504\pi$
$269$	−2.34014e10	−0.272494	−0.136247	+	0.990675i	$0.543504\pi$
$270$	1.68999e10	0.193530
$271$	−3.31269e10	−0.373095	−0.186547	−	0.982446i	$-0.559730\pi$
$271$	−3.31269e10	−0.373095	−0.186547	+	0.982446i	$0.559730\pi$
$272$	−1.59705e10	−0.176913
$273$	3.76358e9	0.0410081
$274$	−9.29721e9	−0.0996495
$275$	−7.58544e10	−0.799804
$276$	−3.56335e9	−0.0369631
$277$	8.16288e10	0.833076	0.416538	−	0.909118i	$-0.363243\pi$
$277$	8.16288e10	0.833076	0.416538	+	0.909118i	$0.363243\pi$
$278$	2.50207e11	2.51245
$279$	3.59993e10	0.355693
$280$	7.82158e9	0.0760472
$281$	−2.57241e10	−0.246129	−0.123064	−	0.992399i	$-0.539272\pi$
$281$	−2.57241e10	−0.246129	−0.123064	+	0.992399i	$0.539272\pi$
$282$	1.31246e11	1.23585
$283$	2.86834e10	0.265822	0.132911	−	0.991128i	$-0.457568\pi$
$283$	2.86834e10	0.265822	0.132911	+	0.991128i	$0.457568\pi$
$284$	2.11712e11	1.93113
$285$	−3.15401e10	−0.283179
$286$	8.40189e10	0.742557
$287$	4.25852e10	0.370502
$288$	−5.17759e10	−0.443467
$289$	−1.03532e11	−0.873038
$290$	1.91579e10	0.159058
$291$	4.68892e10	0.383313
$292$	−1.43974e11	−1.15894
$293$	8.31371e10	0.659008	0.329504	−	0.944154i	$-0.393119\pi$
$293$	8.31371e10	0.659008	0.329504	+	0.944154i	$0.393119\pi$
$294$	1.09009e11	0.850942
$295$	1.10665e10	0.0850765
$296$	−4.40900e10	−0.333832
$297$	−3.60233e10	−0.268645
$298$	−9.67895e10	−0.710976
$299$	2.23575e9	0.0161772
$300$	6.34902e10	0.452545
$301$	6.79296e8	0.00476991
$302$	−6.88253e10	−0.476121
$303$	−9.06488e10	−0.617831
$304$	5.54932e10	0.372657
$305$	−6.05153e10	−0.400420
$306$	2.80321e10	0.182772
$307$	−3.09958e10	−0.199150	−0.0995751	−	0.995030i	$-0.531748\pi$
$307$	−3.09958e10	−0.199150	−0.0995751	+	0.995030i	$0.531748\pi$
$308$	−6.19719e10	−0.392389
$309$	1.77467e11	1.10740
$310$	−1.74484e11	−1.07307
$311$	−3.74590e10	−0.227057	−0.113528	−	0.993535i	$-0.536215\pi$
$311$	−3.74590e10	−0.227057	−0.113528	+	0.993535i	$0.536215\pi$
$312$	−1.89191e10	−0.113033
$313$	−2.70736e11	−1.59440	−0.797199	−	0.603717i	$-0.793686\pi$
$313$	−2.70736e11	−1.59440	−0.797199	+	0.603717i	$0.793686\pi$
$314$	6.44933e10	0.374396
$315$	7.82110e9	0.0447580
$316$	3.19654e11	1.80338
$317$	3.47299e11	1.93169	0.965843	−	0.259127i	$-0.0834349\pi$
$317$	3.47299e11	1.93169	0.965843	+	0.259127i	$0.0834349\pi$
$318$	2.56995e11	1.40930
$319$	−4.08362e10	−0.220794
$320$	1.90090e11	1.01341
$321$	1.61886e11	0.851011
$322$	−2.85451e9	−0.0147972
$323$	−5.23160e10	−0.267438
$324$	3.01515e10	0.152005
$325$	−3.98356e10	−0.198060
$326$	−2.67297e11	−1.31073
$327$	−1.39556e10	−0.0674967
$328$	−2.14071e11	−1.02124
$329$	6.07391e10	0.285816
$330$	1.74600e11	0.810458
$331$	−1.37406e11	−0.629185	−0.314593	−	0.949227i	$-0.601868\pi$
$331$	−1.37406e11	−0.629185	−0.314593	+	0.949227i	$0.601868\pi$
$332$	−2.37337e11	−1.07212
$333$	−4.40873e10	−0.196478
$334$	6.01346e11	2.64402
$335$	1.69260e10	0.0734265
$336$	−1.37608e10	−0.0589003
$337$	−2.32579e11	−0.982282	−0.491141	−	0.871080i	$-0.663420\pi$
$337$	−2.32579e11	−0.982282	−0.491141	+	0.871080i	$0.663420\pi$
$338$	−3.25126e11	−1.35496
$339$	−1.33855e11	−0.550472
$340$	−7.84922e10	−0.318545
$341$	3.71923e11	1.48956
$342$	−9.74042e10	−0.384999
$343$	1.03120e11	0.402272
$344$	−3.41475e9	−0.0131476
$345$	4.64612e9	0.0176565
$346$	−4.89755e11	−1.83711
$347$	1.41713e11	0.524719	0.262360	−	0.964970i	$-0.415499\pi$
$347$	1.41713e11	0.524719	0.262360	+	0.964970i	$0.415499\pi$
$348$	3.41800e10	0.124930
$349$	−9.57812e10	−0.345594	−0.172797	−	0.984957i	$-0.555280\pi$
$349$	−9.57812e10	−0.345594	−0.172797	+	0.984957i	$0.555280\pi$
$350$	5.08604e10	0.181165
$351$	−1.89180e10	−0.0665261
$352$	−5.34916e11	−1.85713
$353$	9.36174e10	0.320901	0.160450	−	0.987044i	$-0.448705\pi$
$353$	9.36174e10	0.320901	0.160450	+	0.987044i	$0.448705\pi$
$354$	3.41761e10	0.115667
$355$	−2.76043e11	−0.922462
$356$	−2.53108e11	−0.835182
$357$	1.29730e10	0.0422700
$358$	1.24431e11	0.400365
$359$	5.09847e11	1.62000	0.809999	−	0.586431i	$-0.199467\pi$
$359$	5.09847e11	1.62000	0.809999	+	0.586431i	$0.199467\pi$
$360$	−3.93158e10	−0.123369
$361$	−1.40904e11	−0.436656
$362$	−6.94486e10	−0.212557
$363$	−1.81176e11	−0.547672
$364$	−3.25451e10	−0.0971694
$365$	1.87722e11	0.553602
$366$	−1.86887e11	−0.544396
$367$	4.06963e10	0.117100	0.0585501	−	0.998284i	$-0.481352\pi$
$367$	4.06963e10	0.117100	0.0585501	+	0.998284i	$0.481352\pi$
$368$	−8.17461e9	−0.0232355
$369$	−2.14058e11	−0.601053
$370$	2.13685e11	0.592742
$371$	1.18934e11	0.325930
$372$	−3.11300e11	−0.842822
$373$	3.23363e11	0.864969	0.432484	−	0.901641i	$-0.357637\pi$
$373$	3.23363e11	0.864969	0.432484	+	0.901641i	$0.357637\pi$
$374$	2.89611e11	0.765407
$375$	−2.27265e11	−0.593461
$376$	−3.05329e11	−0.787813
$377$	−2.14455e10	−0.0546765
$378$	2.41536e10	0.0608512
$379$	4.33723e11	1.07978	0.539891	−	0.841735i	$-0.318466\pi$
$379$	4.33723e11	1.07978	0.539891	+	0.841735i	$0.318466\pi$
$380$	2.72739e11	0.670998
$381$	9.28305e9	0.0225698
$382$	−6.31442e11	−1.51722
$383$	−3.26234e11	−0.774702	−0.387351	−	0.921932i	$-0.626610\pi$
$383$	−3.26234e11	−0.774702	−0.387351	+	0.921932i	$0.626610\pi$
$384$	2.59773e11	0.609683
$385$	8.08027e10	0.187436
$386$	4.14170e11	0.949590
$387$	−3.41454e9	−0.00773807
$388$	−4.05468e11	−0.908268
$389$	−7.50132e11	−1.66098	−0.830490	−	0.557033i	$-0.811940\pi$
$389$	−7.50132e11	−1.66098	−0.830490	+	0.557033i	$0.811940\pi$
$390$	9.16926e10	0.200698
$391$	7.70657e9	0.0166750
$392$	−2.53598e11	−0.542448
$393$	3.13749e11	0.663461
$394$	−9.76857e11	−2.04220
$395$	−4.16784e11	−0.861438
$396$	3.11507e11	0.636560
$397$	−5.03118e10	−0.101651	−0.0508256	−	0.998708i	$-0.516185\pi$
$397$	−5.03118e10	−0.101651	−0.0508256	+	0.998708i	$0.516185\pi$
$398$	3.16479e11	0.632225
$399$	−4.50775e10	−0.0890394
$400$	1.45651e11	0.284475
$401$	8.16322e11	1.57656	0.788282	−	0.615314i	$-0.210971\pi$
$401$	8.16322e11	1.57656	0.788282	+	0.615314i	$0.210971\pi$
$402$	5.22719e10	0.0998277
$403$	1.95319e11	0.368868
$404$	7.83874e11	1.46396
$405$	−3.93134e10	−0.0726094
$406$	2.73807e10	0.0500124
$407$	−4.55482e11	−0.822804
$408$	−6.52137e10	−0.116511
$409$	−9.72499e11	−1.71844	−0.859220	−	0.511607i	$-0.829050\pi$
$409$	−9.72499e11	−1.71844	−0.859220	+	0.511607i	$0.829050\pi$
$410$	1.03751e12	1.81328
$411$	2.16276e10	0.0373869
$412$	−1.53462e12	−2.62400
$413$	1.58163e10	0.0267504
$414$	1.43484e10	0.0240051
$415$	3.09455e11	0.512130
$416$	−2.80916e11	−0.459893
$417$	−5.82042e11	−0.942631
$418$	−1.00632e12	−1.61229
$419$	1.26868e11	0.201090	0.100545	−	0.994933i	$-0.467941\pi$
$419$	1.26868e11	0.201090	0.100545	+	0.994933i	$0.467941\pi$
$420$	−6.76320e10	−0.106055
$421$	2.96147e10	0.0459450	0.0229725	−	0.999736i	$-0.492687\pi$
$421$	2.96147e10	0.0459450	0.0229725	+	0.999736i	$0.492687\pi$
$422$	4.86921e11	0.747399
$423$	−3.05310e11	−0.463671
$424$	−5.97870e11	−0.898381
$425$	−1.37312e11	−0.204155
$426$	−8.52492e11	−1.25414
$427$	−8.64893e10	−0.125903
$428$	−1.39988e12	−2.01649
$429$	−1.95448e11	−0.278596
$430$	1.65498e10	0.0233445
$431$	−8.45775e11	−1.18061	−0.590306	−	0.807180i	$-0.700993\pi$
$431$	−8.45775e11	−1.18061	−0.590306	+	0.807180i	$0.700993\pi$
$432$	6.91699e10	0.0955521
$433$	−7.36248e11	−1.00653	−0.503267	−	0.864131i	$-0.667869\pi$
$433$	−7.36248e11	−1.00653	−0.503267	+	0.864131i	$0.667869\pi$
$434$	−2.49374e11	−0.337402
$435$	−4.45659e10	−0.0596762
$436$	1.20679e11	0.159935
$437$	−2.67783e10	−0.0351250
$438$	5.79735e11	0.752656
$439$	−6.89894e11	−0.886528	−0.443264	−	0.896391i	$-0.646180\pi$
$439$	−6.89894e11	−0.886528	−0.443264	+	0.896391i	$0.646180\pi$
$440$	−4.06186e11	−0.516640
$441$	−2.53582e11	−0.319260
$442$	1.52092e11	0.189542
$443$	7.68420e11	0.947942	0.473971	−	0.880540i	$-0.342820\pi$
$443$	7.68420e11	0.947942	0.473971	+	0.880540i	$0.342820\pi$
$444$	3.81239e11	0.465559
$445$	3.30018e11	0.398949
$446$	7.72120e11	0.924013
$447$	2.25156e11	0.266747
$448$	2.71679e11	0.318643
$449$	−1.22056e11	−0.141726	−0.0708629	−	0.997486i	$-0.522575\pi$
$449$	−1.22056e11	−0.141726	−0.0708629	+	0.997486i	$0.522575\pi$
$450$	−2.55654e11	−0.293898
$451$	−2.21151e12	−2.51707
$452$	1.15749e12	1.30435
$453$	1.60105e11	0.178633
$454$	−1.37133e12	−1.51492
$455$	4.24343e10	0.0464158
$456$	2.26600e11	0.245425
$457$	1.71755e11	0.184198	0.0920992	−	0.995750i	$-0.470642\pi$
$457$	1.71755e11	0.184198	0.0920992	+	0.995750i	$0.470642\pi$
$458$	−7.87422e11	−0.836205
$459$	−6.52096e10	−0.0685732
$460$	−4.01767e10	−0.0418374
$461$	−2.81481e10	−0.0290265	−0.0145132	−	0.999895i	$-0.504620\pi$
$461$	−2.81481e10	−0.0290265	−0.0145132	+	0.999895i	$0.504620\pi$
$462$	2.49540e11	0.254830
$463$	3.34262e10	0.0338043	0.0169022	−	0.999857i	$-0.494620\pi$
$463$	3.34262e10	0.0338043	0.0169022	+	0.999857i	$0.494620\pi$
$464$	7.84115e10	0.0785324
$465$	4.05892e11	0.402598
$466$	2.35008e12	2.30859
$467$	2.55215e10	0.0248302	0.0124151	−	0.999923i	$-0.496048\pi$
$467$	2.55215e10	0.0248302	0.0124151	+	0.999923i	$0.496048\pi$
$468$	1.63591e11	0.157635
$469$	2.41908e10	0.0230873
$470$	1.47980e12	1.39882
$471$	−1.50027e11	−0.140468
$472$	−7.95069e10	−0.0737337
$473$	−3.52769e10	−0.0324052
$474$	−1.28714e12	−1.17118
$475$	4.77123e11	0.430040
$476$	−1.12182e11	−0.100159
$477$	−5.97834e11	−0.528747
$478$	3.14890e12	2.75888
$479$	−1.97153e12	−1.71117	−0.855586	−	0.517661i	$-0.826803\pi$
$479$	−1.97153e12	−1.71117	−0.855586	+	0.517661i	$0.826803\pi$
$480$	−5.83771e11	−0.501946
$481$	−2.39201e11	−0.203756
$482$	2.58671e12	2.18291
$483$	6.64029e9	0.00555169
$484$	1.56670e12	1.29772
$485$	5.28674e11	0.433860
$486$	−1.21410e11	−0.0987169
$487$	2.05628e11	0.165654	0.0828269	−	0.996564i	$-0.473605\pi$
$487$	2.05628e11	0.165654	0.0828269	+	0.996564i	$0.473605\pi$
$488$	4.34772e11	0.347035
$489$	6.21798e11	0.491767
$490$	1.22908e12	0.963155
$491$	2.82095e11	0.219042	0.109521	−	0.993984i	$-0.465068\pi$
$491$	2.82095e11	0.219042	0.109521	+	0.993984i	$0.465068\pi$
$492$	1.85104e12	1.42421
$493$	−7.39221e10	−0.0563590
$494$	−5.28478e11	−0.399260
$495$	−4.06161e11	−0.304071
$496$	−7.14145e11	−0.529809
$497$	−3.94524e11	−0.290048
$498$	9.55677e11	0.696272
$499$	1.70553e11	0.123142	0.0615709	−	0.998103i	$-0.480389\pi$
$499$	1.70553e11	0.123142	0.0615709	+	0.998103i	$0.480389\pi$
$500$	1.96525e12	1.40622
$501$	−1.39888e12	−0.991995
$502$	−3.48993e11	−0.245273
$503$	3.31028e11	0.230573	0.115286	−	0.993332i	$-0.463221\pi$
$503$	3.31028e11	0.230573	0.115286	+	0.993332i	$0.463221\pi$
$504$	−5.61907e10	−0.0387906
$505$	−1.02206e12	−0.699304
$506$	1.48239e11	0.100528
$507$	7.56323e11	0.508360
$508$	−8.02740e10	−0.0534796
$509$	−1.19140e12	−0.786732	−0.393366	−	0.919382i	$-0.628689\pi$
$509$	−1.19140e12	−0.786732	−0.393366	+	0.919382i	$0.628689\pi$
$510$	3.16062e11	0.206874
$511$	2.68295e11	0.174068
$512$	1.46436e12	0.941747
$513$	2.26586e11	0.144446
$514$	−2.85198e12	−1.80224
$515$	2.00094e12	1.25343
$516$	2.95268e10	0.0183355
$517$	−3.15427e12	−1.94174
$518$	3.05401e11	0.186374
$519$	1.13929e12	0.689257
$520$	−2.13313e11	−0.127939
$521$	2.38998e12	1.42110	0.710550	−	0.703647i	$-0.248446\pi$
$521$	2.38998e12	1.42110	0.710550	+	0.703647i	$0.248446\pi$
$522$	−1.37631e11	−0.0811335
$523$	−8.44568e11	−0.493602	−0.246801	−	0.969066i	$-0.579379\pi$
$523$	−8.44568e11	−0.493602	−0.246801	+	0.969066i	$0.579379\pi$
$524$	−2.71310e12	−1.57208
$525$	−1.18314e11	−0.0679701
$526$	3.99967e12	2.27818
$527$	6.73258e11	0.380219
$528$	7.14620e11	0.400150
$529$	−1.79721e12	−0.997810
$530$	2.89761e12	1.59514
$531$	−7.95020e10	−0.0433963
$532$	3.89802e11	0.210980
$533$	−1.16140e12	−0.623316
$534$	1.01918e12	0.542395
$535$	1.82525e12	0.963233
$536$	−1.21605e11	−0.0636369
$537$	−2.89458e11	−0.150211
$538$	−8.14840e11	−0.419326
$539$	−2.61985e12	−1.33699
$540$	3.39958e11	0.172049
$541$	−7.01041e11	−0.351849	−0.175924	−	0.984404i	$-0.556291\pi$
$541$	−7.01041e11	−0.351849	−0.175924	+	0.984404i	$0.556291\pi$
$542$	−1.15348e12	−0.574135
$543$	1.61554e11	0.0797480
$544$	−9.68309e11	−0.474044
$545$	−1.57349e11	−0.0763974
$546$	1.31048e11	0.0631050
$547$	9.24049e11	0.441318	0.220659	−	0.975351i	$-0.429179\pi$
$547$	9.24049e11	0.441318	0.220659	+	0.975351i	$0.429179\pi$
$548$	−1.87022e11	−0.0885890
$549$	4.34746e11	0.204249
$550$	−2.64125e12	−1.23077
$551$	2.56859e11	0.118717
$552$	−3.33800e10	−0.0153024
$553$	−5.95673e11	−0.270860
$554$	2.84232e12	1.28197
$555$	−4.97083e11	−0.222387
$556$	5.03313e12	2.23358
$557$	2.45138e11	0.107910	0.0539551	−	0.998543i	$-0.482817\pi$
$557$	2.45138e11	0.107910	0.0539551	+	0.998543i	$0.482817\pi$
$558$	1.25350e12	0.547357
$559$	−1.85260e10	−0.00802468
$560$	−1.55153e11	−0.0666674
$561$	−6.73705e11	−0.287169
$562$	−8.95717e11	−0.378754
$563$	9.57177e11	0.401518	0.200759	−	0.979641i	$-0.435659\pi$
$563$	9.57177e11	0.401518	0.200759	+	0.979641i	$0.435659\pi$
$564$	2.64013e12	1.09868
$565$	−1.50921e12	−0.623062
$566$	9.98758e11	0.409059
$567$	−5.61872e10	−0.0228304
$568$	1.98323e12	0.799475
$569$	2.78904e12	1.11545	0.557724	−	0.830027i	$-0.311675\pi$
$569$	2.78904e12	1.11545	0.557724	+	0.830027i	$0.311675\pi$
$570$	−1.09823e12	−0.435769
$571$	1.09475e12	0.430977	0.215489	−	0.976506i	$-0.430866\pi$
$571$	1.09475e12	0.430977	0.215489	+	0.976506i	$0.430866\pi$
$572$	1.69012e12	0.660137
$573$	1.46889e12	0.569237
$574$	1.48282e12	0.570144
$575$	−7.02841e10	−0.0268134
$576$	−1.36562e12	−0.516925
$577$	−2.45219e11	−0.0921008	−0.0460504	−	0.998939i	$-0.514663\pi$
$577$	−2.45219e11	−0.0921008	−0.0460504	+	0.998939i	$0.514663\pi$
$578$	−3.60498e12	−1.34347
$579$	−9.63462e11	−0.356271
$580$	3.85378e11	0.141404
$581$	4.42276e11	0.161028
$582$	1.63268e12	0.589860
$583$	−6.17644e12	−2.21427
$584$	−1.34869e12	−0.479793
$585$	−2.13299e11	−0.0752988
$586$	2.89484e12	1.01411
$587$	−4.06626e12	−1.41359	−0.706796	−	0.707417i	$-0.749860\pi$
$587$	−4.06626e12	−1.41359	−0.706796	+	0.707417i	$0.749860\pi$
$588$	2.19282e12	0.756493
$589$	−2.33939e12	−0.800910
$590$	3.85335e11	0.130919
$591$	2.27241e12	0.766201
$592$	8.74592e11	0.292656
$593$	3.27334e11	0.108704	0.0543519	−	0.998522i	$-0.482691\pi$
$593$	3.27334e11	0.108704	0.0543519	+	0.998522i	$0.482691\pi$
$594$	−1.25433e12	−0.413403
$595$	1.46270e11	0.0478441
$596$	−1.94701e12	−0.632062
$597$	−7.36208e11	−0.237201
$598$	7.78491e10	0.0248942
$599$	−5.51362e12	−1.74991	−0.874956	−	0.484202i	$-0.839110\pi$
$599$	−5.51362e12	−1.74991	−0.874956	+	0.484202i	$0.839110\pi$
$600$	5.94750e11	0.187350
$601$	1.67559e12	0.523881	0.261941	−	0.965084i	$-0.415638\pi$
$601$	1.67559e12	0.523881	0.261941	+	0.965084i	$0.415638\pi$
$602$	2.36531e10	0.00734014
$603$	−1.21597e11	−0.0374538
$604$	−1.38448e12	−0.423274
$605$	−2.04275e12	−0.619893
$606$	−3.15640e12	−0.950746
$607$	−4.84043e12	−1.44722	−0.723611	−	0.690208i	$-0.757519\pi$
$607$	−4.84043e12	−1.44722	−0.723611	+	0.690208i	$0.757519\pi$
$608$	3.36461e12	0.998548
$609$	−6.36942e10	−0.0187639
$610$	−2.10715e12	−0.616185
$611$	−1.65650e12	−0.480845
$612$	5.63892e11	0.162486
$613$	−3.98712e12	−1.14048	−0.570240	−	0.821478i	$-0.693150\pi$
$613$	−3.98712e12	−1.14048	−0.570240	+	0.821478i	$0.693150\pi$
$614$	−1.07928e12	−0.306461
$615$	−2.41350e12	−0.680313
$616$	−5.80527e11	−0.162446
$617$	1.01386e12	0.281641	0.140820	−	0.990035i	$-0.455026\pi$
$617$	1.01386e12	0.281641	0.140820	+	0.990035i	$0.455026\pi$
$618$	6.17942e12	1.70412
$619$	−1.11173e12	−0.304361	−0.152181	−	0.988353i	$-0.548630\pi$
$619$	−1.11173e12	−0.304361	−0.152181	+	0.988353i	$0.548630\pi$
$620$	−3.50990e12	−0.953964
$621$	−3.33780e10	−0.00900632
$622$	−1.30432e12	−0.349405
$623$	4.71666e11	0.125441
$624$	3.75289e11	0.0990913
$625$	−3.76746e11	−0.0987617
$626$	−9.42705e12	−2.45353
$627$	2.34094e12	0.604905
$628$	1.29734e12	0.332841
$629$	−8.24518e11	−0.210026
$630$	2.72331e11	0.0688755
$631$	5.31416e12	1.33445	0.667225	−	0.744856i	$-0.267482\pi$
$631$	5.31416e12	1.33445	0.667225	+	0.744856i	$0.267482\pi$
$632$	2.99438e12	0.746587
$633$	−1.13270e12	−0.280413
$634$	1.20930e13	2.97256
$635$	1.04666e11	0.0255461
$636$	5.16969e12	1.25287
$637$	−1.37584e12	−0.331085
$638$	−1.42192e12	−0.339768
$639$	1.98311e12	0.470535
$640$	2.92894e12	0.690081
$641$	−5.10915e12	−1.19533	−0.597664	−	0.801747i	$-0.703904\pi$
$641$	−5.10915e12	−1.19533	−0.597664	+	0.801747i	$0.703904\pi$
$642$	5.63687e12	1.30957
$643$	9.16548e11	0.211449	0.105725	−	0.994395i	$-0.466284\pi$
$643$	9.16548e11	0.211449	0.105725	+	0.994395i	$0.466284\pi$
$644$	−5.74211e10	−0.0131548
$645$	−3.84988e10	−0.00875848
$646$	−1.82165e12	−0.411546
$647$	−1.56251e12	−0.350554	−0.175277	−	0.984519i	$-0.556082\pi$
$647$	−1.56251e12	−0.350554	−0.175277	+	0.984519i	$0.556082\pi$
$648$	2.82447e11	0.0629288
$649$	−8.21365e11	−0.181733
$650$	−1.38708e12	−0.304783
$651$	5.80105e11	0.126588
$652$	−5.37692e12	−1.16525
$653$	4.18928e12	0.901634	0.450817	−	0.892616i	$-0.351133\pi$
$653$	4.18928e12	0.901634	0.450817	+	0.892616i	$0.351133\pi$
$654$	−4.85934e11	−0.103867
$655$	3.53751e12	0.750951
$656$	4.24643e12	0.895274
$657$	−1.34861e12	−0.282385
$658$	2.11494e12	0.439827
$659$	2.80694e12	0.579761	0.289880	−	0.957063i	$-0.406384\pi$
$659$	2.80694e12	0.579761	0.289880	+	0.957063i	$0.406384\pi$
$660$	3.51223e12	0.720502
$661$	6.73837e12	1.37293	0.686465	−	0.727163i	$-0.259162\pi$
$661$	6.73837e12	1.37293	0.686465	+	0.727163i	$0.259162\pi$
$662$	−4.78448e12	−0.968218
$663$	−3.53802e11	−0.0711131
$664$	−2.22328e12	−0.443851
$665$	−5.08248e11	−0.100781
$666$	−1.53512e12	−0.302349
$667$	−3.78375e10	−0.00740212
$668$	1.20966e13	2.35055
$669$	−1.79614e12	−0.346675
$670$	5.89364e11	0.112992
$671$	4.49152e12	0.855346
$672$	−8.34333e11	−0.157826
$673$	6.34420e12	1.19209	0.596045	−	0.802951i	$-0.296738\pi$
$673$	6.34420e12	1.19209	0.596045	+	0.802951i	$0.296738\pi$
$674$	−8.09843e12	−1.51158
$675$	5.94713e11	0.110266
$676$	−6.54021e12	−1.20457
$677$	1.72678e12	0.315928	0.157964	−	0.987445i	$-0.449507\pi$
$677$	1.72678e12	0.315928	0.157964	+	0.987445i	$0.449507\pi$
$678$	−4.66083e12	−0.847090
$679$	7.55587e11	0.136418
$680$	−7.35282e11	−0.131875
$681$	3.19004e12	0.568374
$682$	1.29504e13	2.29220
$683$	1.07112e12	0.188342	0.0941708	−	0.995556i	$-0.469980\pi$
$683$	1.07112e12	0.188342	0.0941708	+	0.995556i	$0.469980\pi$
$684$	−1.95937e12	−0.342267
$685$	2.43850e11	0.0423171
$686$	3.59065e12	0.619034
$687$	1.83174e12	0.313731
$688$	6.77367e10	0.0115259
$689$	−3.24362e12	−0.548331
$690$	1.61778e11	0.0271706
$691$	−2.31254e12	−0.385868	−0.192934	−	0.981212i	$-0.561800\pi$
$691$	−2.31254e12	−0.385868	−0.192934	+	0.981212i	$0.561800\pi$
$692$	−9.85186e12	−1.63321
$693$	−5.80491e11	−0.0956083
$694$	4.93446e12	0.807461
$695$	−6.56250e12	−1.06694
$696$	3.20184e11	0.0517199
$697$	−4.00330e12	−0.642496
$698$	−3.33511e12	−0.531815
$699$	−5.46687e12	−0.866146
$700$	1.02310e12	0.161056
$701$	1.00626e13	1.57390	0.786950	−	0.617017i	$-0.211659\pi$
$701$	1.00626e13	1.57390	0.786950	+	0.617017i	$0.211659\pi$
$702$	−6.58724e11	−0.102373
$703$	2.86498e12	0.442407
$704$	−1.41087e13	−2.16476
$705$	−3.44237e12	−0.524815
$706$	3.25977e12	0.493816
$707$	−1.46074e12	−0.219880
$708$	6.87484e11	0.102828
$709$	1.11083e12	0.165098	0.0825488	−	0.996587i	$-0.473694\pi$
$709$	1.11083e12	0.165098	0.0825488	+	0.996587i	$0.473694\pi$
$710$	−9.61182e12	−1.41953
$711$	2.99420e12	0.439407
$712$	−2.37101e12	−0.345759
$713$	3.44611e11	0.0499375
$714$	4.51719e11	0.0650469
$715$	−2.20368e12	−0.315334
$716$	2.50305e12	0.355927
$717$	−7.32511e12	−1.03509
$718$	1.77529e13	2.49293
$719$	−8.25712e12	−1.15225	−0.576127	−	0.817360i	$-0.695437\pi$
$719$	−8.25712e12	−1.15225	−0.576127	+	0.817360i	$0.695437\pi$
$720$	7.79889e11	0.108152
$721$	2.85976e12	0.394113
$722$	−4.90628e12	−0.671946
$723$	−6.01731e12	−0.818993
$724$	−1.39702e12	−0.188964
$725$	6.74171e11	0.0906252
$726$	−6.30856e12	−0.842783
$727$	2.11241e12	0.280462	0.140231	−	0.990119i	$-0.455216\pi$
$727$	2.11241e12	0.280462	0.140231	+	0.990119i	$0.455216\pi$
$728$	−3.04869e11	−0.0402274
$729$	2.82430e11	0.0370370
$730$	6.53650e12	0.851907
$731$	−6.38585e10	−0.00827162
$732$	−3.75941e12	−0.483971
$733$	−6.44023e12	−0.824012	−0.412006	−	0.911181i	$-0.635172\pi$
$733$	−6.44023e12	−0.824012	−0.412006	+	0.911181i	$0.635172\pi$
$734$	1.41705e12	0.180199
$735$	−2.85913e12	−0.361361
$736$	−4.95635e11	−0.0622604
$737$	−1.25627e12	−0.156848
$738$	−7.45351e12	−0.924927
$739$	−9.42197e12	−1.16210	−0.581048	−	0.813869i	$-0.697357\pi$
$739$	−9.42197e12	−1.16210	−0.581048	+	0.813869i	$0.697357\pi$
$740$	4.29846e12	0.526951
$741$	1.22937e12	0.149796
$742$	4.14130e12	0.501556
$743$	−1.14547e12	−0.137890	−0.0689449	−	0.997620i	$-0.521963\pi$
$743$	−1.14547e12	−0.137890	−0.0689449	+	0.997620i	$0.521963\pi$
$744$	−2.91613e12	−0.348922
$745$	2.53863e12	0.301923
$746$	1.12595e13	1.33105
$747$	−2.22314e12	−0.261230
$748$	5.82578e12	0.680451
$749$	2.60868e12	0.302867
$750$	−7.91338e12	−0.913243
$751$	4.56219e12	0.523352	0.261676	−	0.965156i	$-0.415725\pi$
$751$	4.56219e12	0.523352	0.261676	+	0.965156i	$0.415725\pi$
$752$	6.05667e12	0.690642
$753$	8.11843e11	0.0920226
$754$	−7.46735e11	−0.0841386
$755$	1.80517e12	0.202189
$756$	4.85872e11	0.0540970
$757$	−9.37649e12	−1.03779	−0.518894	−	0.854839i	$-0.673656\pi$
$757$	−9.37649e12	−1.03779	−0.518894	+	0.854839i	$0.673656\pi$
$758$	1.51023e13	1.66162
$759$	−3.44840e11	−0.0377164
$760$	2.55491e12	0.277788
$761$	1.75158e13	1.89321	0.946605	−	0.322394i	$-0.104488\pi$
$761$	1.75158e13	1.89321	0.946605	+	0.322394i	$0.104488\pi$
$762$	3.23236e11	0.0347314
$763$	−2.24885e11	−0.0240215
$764$	−1.27020e13	−1.34882
$765$	−7.35237e11	−0.0776159
$766$	−1.13595e13	−1.19215
$767$	−4.31347e11	−0.0450037
$768$	4.13280e11	0.0428666
$769$	1.85532e13	1.91316	0.956580	−	0.291470i	$-0.0941442\pi$
$769$	1.85532e13	1.91316	0.956580	+	0.291470i	$0.0941442\pi$
$770$	2.81355e12	0.288434
$771$	6.63441e12	0.676172
$772$	8.33141e12	0.844191
$773$	−9.95968e12	−1.00332	−0.501658	−	0.865066i	$-0.667276\pi$
$773$	−9.95968e12	−1.00332	−0.501658	+	0.865066i	$0.667276\pi$
$774$	−1.18894e11	−0.0119077
$775$	−6.14012e12	−0.611392
$776$	−3.79826e12	−0.376016
$777$	−7.10437e11	−0.0699247
$778$	−2.61197e13	−2.55599
$779$	1.39104e13	1.35338
$780$	1.84448e12	0.178422
$781$	2.04882e13	1.97049
$782$	2.68343e11	0.0256602
$783$	3.20164e11	0.0304400
$784$	5.03049e12	0.475541
$785$	−1.69155e12	−0.158991
$786$	1.09248e13	1.02096
$787$	−2.93761e12	−0.272965	−0.136483	−	0.990642i	$-0.543580\pi$
$787$	−2.93761e12	−0.272965	−0.136483	+	0.990642i	$0.543580\pi$
$788$	−1.96504e13	−1.81553
$789$	−9.30422e12	−0.854739
$790$	−1.45124e13	−1.32562
$791$	−2.15698e12	−0.195908
$792$	2.91806e12	0.263531
$793$	2.35876e12	0.211814
$794$	−1.75186e12	−0.156425
$795$	−6.74056e12	−0.598472
$796$	6.36627e12	0.562051
$797$	−6.03187e11	−0.0529529	−0.0264764	−	0.999649i	$-0.508429\pi$
$797$	−6.03187e11	−0.0529529	−0.0264764	+	0.999649i	$0.508429\pi$
$798$	−1.56960e12	−0.137018
$799$	−5.70990e12	−0.495641
$800$	8.83100e12	0.762263
$801$	−2.37087e12	−0.203498
$802$	2.84244e13	2.42609
$803$	−1.39330e13	−1.18256
$804$	1.05150e12	0.0887475
$805$	7.48691e10	0.00628378
$806$	6.80101e12	0.567630
$807$	1.89552e12	0.157325
$808$	7.34300e12	0.606070
$809$	1.12693e13	0.924975	0.462488	−	0.886626i	$-0.346957\pi$
$809$	1.12693e13	0.924975	0.462488	+	0.886626i	$0.346957\pi$
$810$	−1.36890e12	−0.111735
$811$	−6.55655e12	−0.532208	−0.266104	−	0.963944i	$-0.585736\pi$
$811$	−6.55655e12	−0.532208	−0.266104	+	0.963944i	$0.585736\pi$
$812$	5.50788e11	0.0444613
$813$	2.68328e12	0.215406
$814$	−1.58599e13	−1.26617
$815$	7.01075e12	0.556616
$816$	1.29361e12	0.102141
$817$	2.21891e11	0.0174237
$818$	−3.38625e13	−2.64441
$819$	−3.04850e11	−0.0236760
$820$	2.08704e13	1.61201
$821$	−9.21418e12	−0.707803	−0.353902	−	0.935283i	$-0.615145\pi$
$821$	−9.21418e12	−0.707803	−0.353902	+	0.935283i	$0.615145\pi$
$822$	7.53074e11	0.0575327
$823$	−4.75017e12	−0.360919	−0.180460	−	0.983582i	$-0.557759\pi$
$823$	−4.75017e12	−0.360919	−0.180460	+	0.983582i	$0.557759\pi$
$824$	−1.43757e13	−1.08632
$825$	6.14420e12	0.461767
$826$	5.50725e11	0.0411647
$827$	1.61227e13	1.19857	0.599285	−	0.800536i	$-0.295452\pi$
$827$	1.61227e13	1.19857	0.599285	+	0.800536i	$0.295452\pi$
$828$	2.88632e11	0.0213406
$829$	−6.58919e12	−0.484548	−0.242274	−	0.970208i	$-0.577893\pi$
$829$	−6.58919e12	−0.484548	−0.242274	+	0.970208i	$0.577893\pi$
$830$	1.07752e13	0.788089
$831$	−6.61194e12	−0.480977
$832$	−7.40931e12	−0.536072
$833$	−4.74248e12	−0.341274
$834$	−2.02667e13	−1.45056
$835$	−1.57723e13	−1.12281
$836$	−2.02430e13	−1.43333
$837$	−2.91595e12	−0.205360
$838$	4.41756e12	0.309446
$839$	−1.34080e13	−0.934189	−0.467095	−	0.884207i	$-0.654699\pi$
$839$	−1.34080e13	−0.934189	−0.467095	+	0.884207i	$0.654699\pi$
$840$	−6.33548e11	−0.0439059
$841$	−1.41442e13	−0.974982
$842$	1.03119e12	0.0707021
$843$	2.08366e12	0.142103
$844$	9.79486e12	0.664442
$845$	8.52752e12	0.575397
$846$	−1.06309e13	−0.713517
$847$	−2.91953e12	−0.194912
$848$	1.18597e13	0.787573
$849$	−2.32335e12	−0.153473
$850$	−4.78122e12	−0.314162
$851$	−4.22035e11	−0.0275845
$852$	−1.71487e13	−1.11494
$853$	−1.09860e13	−0.710508	−0.355254	−	0.934770i	$-0.615606\pi$
$853$	−1.09860e13	−0.710508	−0.355254	+	0.934770i	$0.615606\pi$
$854$	−3.01156e12	−0.193745
$855$	2.55475e12	0.163494
$856$	−1.31135e13	−0.834810
$857$	2.81411e13	1.78208	0.891042	−	0.453922i	$-0.149975\pi$
$857$	2.81411e13	1.78208	0.891042	+	0.453922i	$0.149975\pi$
$858$	−6.80553e12	−0.428715
$859$	−2.38495e12	−0.149455	−0.0747274	−	0.997204i	$-0.523809\pi$
$859$	−2.38495e12	−0.149455	−0.0747274	+	0.997204i	$0.523809\pi$
$860$	3.32914e11	0.0207534
$861$	−3.44940e12	−0.213909
$862$	−2.94500e13	−1.81678
$863$	−1.95313e13	−1.19862	−0.599310	−	0.800517i	$-0.704558\pi$
$863$	−1.95313e13	−1.19862	−0.599310	+	0.800517i	$0.704558\pi$
$864$	4.19384e12	0.256036
$865$	1.28455e13	0.780148
$866$	−2.56362e13	−1.54890
$867$	8.38607e12	0.504049
$868$	−5.01639e12	−0.299952
$869$	3.09342e13	1.84013
$870$	−1.55179e12	−0.0918324
$871$	−6.59740e11	−0.0388411
$872$	1.13047e12	0.0662118
$873$	−3.79802e12	−0.221306
$874$	−9.32421e11	−0.0540519
$875$	−3.66222e12	−0.211207
$876$	1.16619e13	0.669115
$877$	−1.20441e13	−0.687507	−0.343753	−	0.939060i	$-0.611698\pi$
$877$	−1.20441e13	−0.687507	−0.343753	+	0.939060i	$0.611698\pi$
$878$	−2.40222e13	−1.36423
$879$	−6.73410e12	−0.380478
$880$	8.05732e12	0.452917
$881$	1.89332e13	1.05884	0.529422	−	0.848359i	$-0.322409\pi$
$881$	1.89332e13	1.05884	0.529422	+	0.848359i	$0.322409\pi$
$882$	−8.82974e12	−0.491292
$883$	3.36047e13	1.86027	0.930136	−	0.367214i	$-0.119688\pi$
$883$	3.36047e13	1.86027	0.930136	+	0.367214i	$0.119688\pi$
$884$	3.05946e12	0.168504
$885$	−8.96383e11	−0.0491189
$886$	2.67564e13	1.45874
$887$	1.38919e13	0.753540	0.376770	−	0.926307i	$-0.377035\pi$
$887$	1.38919e13	0.753540	0.376770	+	0.926307i	$0.377035\pi$
$888$	3.57129e12	0.192738
$889$	1.49590e11	0.00803239
$890$	1.14912e13	0.613920
$891$	2.91788e12	0.155102
$892$	1.55319e13	0.821453
$893$	1.98404e13	1.04404
$894$	7.83995e12	0.410482
$895$	−3.26363e12	−0.170019
$896$	4.18607e12	0.216981
$897$	−1.81096e11	−0.00933991
$898$	−4.24998e12	−0.218094
$899$	−3.30554e12	−0.168781
$900$	−5.14271e12	−0.261277
$901$	−1.11806e13	−0.565204
$902$	−7.70050e13	−3.87338
$903$	−5.50230e10	−0.00275391
$904$	1.08429e13	0.539992
$905$	1.82152e12	0.0902642
$906$	5.57485e12	0.274888
$907$	−3.69220e13	−1.81156	−0.905781	−	0.423747i	$-0.860715\pi$
$907$	−3.69220e13	−1.81156	−0.905781	+	0.423747i	$0.860715\pi$
$908$	−2.75855e13	−1.34677
$909$	7.34255e12	0.356705
$910$	1.47756e12	0.0714266
$911$	1.87155e13	0.900260	0.450130	−	0.892963i	$-0.351378\pi$
$911$	1.87155e13	0.900260	0.450130	+	0.892963i	$0.351378\pi$
$912$	−4.49495e12	−0.215153
$913$	−2.29681e13	−1.09397
$914$	5.98052e12	0.283453
$915$	4.90174e12	0.231183
$916$	−1.58397e13	−0.743391
$917$	5.05585e12	0.236120
$918$	−2.27060e12	−0.105524
$919$	−4.00592e12	−0.185260	−0.0926301	−	0.995701i	$-0.529527\pi$
$919$	−4.00592e12	−0.185260	−0.0926301	+	0.995701i	$0.529527\pi$
$920$	−3.76359e11	−0.0173204
$921$	2.51066e12	0.114979
$922$	−9.80117e11	−0.0446672
$923$	1.07596e13	0.487963
$924$	5.01972e12	0.226546
$925$	7.51962e12	0.337721
$926$	1.16390e12	0.0520196
$927$	−1.43748e13	−0.639358
$928$	4.75417e12	0.210431
$929$	−1.03981e13	−0.458020	−0.229010	−	0.973424i	$-0.573549\pi$
$929$	−1.03981e13	−0.458020	−0.229010	+	0.973424i	$0.573549\pi$
$930$	1.41332e13	0.619536
$931$	1.64788e13	0.718874
$932$	4.72741e13	2.05235
$933$	3.03418e12	0.131091
$934$	8.88661e11	0.0382098
$935$	−7.59600e12	−0.325037
$936$	1.53245e12	0.0652596
$937$	9.12371e11	0.0386673	0.0193336	−	0.999813i	$-0.493846\pi$
$937$	9.12371e11	0.0386673	0.0193336	+	0.999813i	$0.493846\pi$
$938$	8.42327e11	0.0355278
$939$	2.19296e13	0.920526
$940$	2.97674e13	1.24356
$941$	2.95495e13	1.22856	0.614281	−	0.789088i	$-0.289446\pi$
$941$	2.95495e13	1.22856	0.614281	+	0.789088i	$0.289446\pi$
$942$	−5.22396e12	−0.216158
$943$	−2.04911e12	−0.0843846
$944$	1.57714e12	0.0646392
$945$	−6.33509e11	−0.0258410
$946$	−1.22834e12	−0.0498666
$947$	−1.67431e13	−0.676490	−0.338245	−	0.941058i	$-0.609833\pi$
$947$	−1.67431e13	−0.676490	−0.338245	+	0.941058i	$0.609833\pi$
$948$	−2.58920e13	−1.04118
$949$	−7.31702e12	−0.292844
$950$	1.66135e13	0.661765
$951$	−2.81312e13	−1.11526
$952$	−1.05087e12	−0.0414653
$953$	1.69592e13	0.666021	0.333011	−	0.942923i	$-0.391936\pi$
$953$	1.69592e13	0.666021	0.333011	+	0.942923i	$0.391936\pi$
$954$	−2.08166e13	−0.813659
$955$	1.65617e13	0.644301
$956$	6.33430e13	2.45266
$957$	3.30773e12	0.127476
$958$	−6.86488e13	−2.63323
$959$	3.48514e11	0.0133057
$960$	−1.53973e13	−0.585092
$961$	3.66611e12	0.138660
$962$	−8.32898e12	−0.313548
$963$	−1.31127e13	−0.491332
$964$	5.20339e13	1.94062
$965$	−1.08630e13	−0.403252
$966$	2.31215e11	0.00854318
$967$	3.38548e13	1.24509	0.622546	−	0.782584i	$-0.286099\pi$
$967$	3.38548e13	1.24509	0.622546	+	0.782584i	$0.286099\pi$
$968$	1.46762e13	0.537246
$969$	4.23760e12	0.154405
$970$	1.84085e13	0.667644
$971$	5.39236e13	1.94667	0.973335	−	0.229387i	$-0.0736720\pi$
$971$	5.39236e13	1.94667	0.973335	+	0.229387i	$0.0736720\pi$
$972$	−2.44227e12	−0.0877599
$973$	−9.37921e12	−0.335474
$974$	7.15998e12	0.254916
$975$	3.22669e12	0.114350
$976$	−8.62437e12	−0.304231
$977$	2.81619e13	0.988864	0.494432	−	0.869216i	$-0.335376\pi$
$977$	2.81619e13	0.988864	0.494432	+	0.869216i	$0.335376\pi$
$978$	2.16510e13	0.756753
$979$	−2.44943e13	−0.852203
$980$	2.47240e13	0.856251
$981$	1.13040e12	0.0389693
$982$	9.82255e12	0.337072
$983$	−3.04185e13	−1.03908	−0.519538	−	0.854447i	$-0.673896\pi$
$983$	−3.04185e13	−1.03908	−0.519538	+	0.854447i	$0.673896\pi$
$984$	1.73398e13	0.589611
$985$	2.56213e13	0.867239
$986$	−2.57397e12	−0.0867277
$987$	−4.91987e12	−0.165016
$988$	−1.06308e13	−0.354944
$989$	−3.26864e10	−0.00108638
$990$	−1.41426e13	−0.467918
$991$	−2.64875e12	−0.0872387	−0.0436194	−	0.999048i	$-0.513889\pi$
$991$	−2.64875e12	−0.0872387	−0.0436194	+	0.999048i	$0.513889\pi$
$992$	−4.32994e13	−1.41964
$993$	1.11299e13	0.363260
$994$	−1.37373e13	−0.446338
$995$	−8.30072e12	−0.268480
$996$	1.92243e13	0.618990
$997$	7.48989e12	0.240075	0.120038	−	0.992769i	$-0.461698\pi$
$997$	7.48989e12	0.240075	0.120038	+	0.992769i	$0.461698\pi$
$998$	5.93865e12	0.189496
$999$	3.57107e12	0.113437

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.b.1.19	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.b.1.19	✓	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)

\(f(q)\)	\(=\)	\(q+34.8201 q^{2} -81.0000 q^{3} +700.437 q^{4} -913.273 q^{5} -2820.43 q^{6} -1305.26 q^{7} +6561.40 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+34.8201 q^{2} -81.0000 q^{3} +700.437 q^{4} -913.273 q^{5} -2820.43 q^{6} -1305.26 q^{7} +6561.40 q^{8} +6561.00 q^{9} -31800.2 q^{10} +67784.1 q^{11} -56735.4 q^{12} +35597.5 q^{13} -45449.3 q^{14} +73975.1 q^{15} -130155. q^{16} +122703. q^{17} +228454. q^{18} -426361. q^{19} -639690. q^{20} +105726. q^{21} +2.36025e6 q^{22} +62806.5 q^{23} -531474. q^{24} -1.11906e6 q^{25} +1.23951e6 q^{26} -531441. q^{27} -914253. q^{28} -602445. q^{29} +2.57582e6 q^{30} +5.48687e6 q^{31} -7.89146e6 q^{32} -5.49051e6 q^{33} +4.27254e6 q^{34} +1.19206e6 q^{35} +4.59557e6 q^{36} -6.71960e6 q^{37} -1.48459e7 q^{38} -2.88339e6 q^{39} -5.99235e6 q^{40} -3.26258e7 q^{41} +3.68139e6 q^{42} -520430. q^{43} +4.74785e7 q^{44} -5.99198e6 q^{45} +2.18693e6 q^{46} -4.65341e7 q^{47} +1.05426e7 q^{48} -3.86499e7 q^{49} -3.89657e7 q^{50} -9.93898e6 q^{51} +2.49338e7 q^{52} -9.11193e7 q^{53} -1.85048e7 q^{54} -6.19054e7 q^{55} -8.56434e6 q^{56} +3.45353e7 q^{57} -2.09772e7 q^{58} -1.21174e7 q^{59} +5.18149e7 q^{60} +6.62621e7 q^{61} +1.91053e8 q^{62} -8.56381e6 q^{63} -2.08142e8 q^{64} -3.25102e7 q^{65} -1.91180e8 q^{66} -1.85333e7 q^{67} +8.59461e7 q^{68} -5.08733e6 q^{69} +4.15076e7 q^{70} +3.02257e8 q^{71} +4.30494e7 q^{72} -2.05549e8 q^{73} -2.33977e8 q^{74} +9.06437e7 q^{75} -2.98639e8 q^{76} -8.84759e7 q^{77} -1.00400e8 q^{78} +4.56363e8 q^{79} +1.18867e8 q^{80} +4.30467e7 q^{81} -1.13603e9 q^{82} -3.38841e8 q^{83} +7.40545e7 q^{84} -1.12062e8 q^{85} -1.81214e7 q^{86} +4.87981e7 q^{87} +4.44759e8 q^{88} -3.61357e8 q^{89} -2.08641e8 q^{90} -4.64640e7 q^{91} +4.39920e7 q^{92} -4.44436e8 q^{93} -1.62032e9 q^{94} +3.89384e8 q^{95} +6.39208e8 q^{96} -5.78879e8 q^{97} -1.34579e9 q^{98} +4.44732e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more