LMFDB - Embedded newform 177.10.a.a.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)

$f(q)$	$=$	$q+2.31191 q^{2} +81.0000 q^{3} -506.655 q^{4} -66.4563 q^{5} +187.265 q^{6} -1904.69 q^{7} -2355.04 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+2.31191 q^{2} +81.0000 q^{3} -506.655 q^{4} -66.4563 q^{5} +187.265 q^{6} -1904.69 q^{7} -2355.04 q^{8} +6561.00 q^{9} -153.641 q^{10} -51285.5 q^{11} -41039.1 q^{12} +118285. q^{13} -4403.48 q^{14} -5382.96 q^{15} +253963. q^{16} +412063. q^{17} +15168.4 q^{18} +216219. q^{19} +33670.4 q^{20} -154280. q^{21} -118567. q^{22} -730788. q^{23} -190758. q^{24} -1.94871e6 q^{25} +273464. q^{26} +531441. q^{27} +965023. q^{28} -2.16650e6 q^{29} -12444.9 q^{30} +7.53898e6 q^{31} +1.79292e6 q^{32} -4.15413e6 q^{33} +952652. q^{34} +126579. q^{35} -3.32416e6 q^{36} +2.06192e7 q^{37} +499880. q^{38} +9.58108e6 q^{39} +156507. q^{40} -3.10914e7 q^{41} -356682. q^{42} -1.98819e7 q^{43} +2.59841e7 q^{44} -436020. q^{45} -1.68951e6 q^{46} -2.28396e7 q^{47} +2.05710e7 q^{48} -3.67257e7 q^{49} -4.50524e6 q^{50} +3.33771e7 q^{51} -5.99297e7 q^{52} -3.27629e7 q^{53} +1.22864e6 q^{54} +3.40825e6 q^{55} +4.48562e6 q^{56} +1.75138e7 q^{57} -5.00874e6 q^{58} +1.21174e7 q^{59} +2.72731e6 q^{60} -8.93784e7 q^{61} +1.74294e7 q^{62} -1.24967e7 q^{63} -1.25884e8 q^{64} -7.86078e6 q^{65} -9.60396e6 q^{66} +7.39877e7 q^{67} -2.08774e8 q^{68} -5.91938e7 q^{69} +292639. q^{70} +3.75295e8 q^{71} -1.54514e7 q^{72} -3.48461e7 q^{73} +4.76697e7 q^{74} -1.57845e8 q^{75} -1.09549e8 q^{76} +9.76832e7 q^{77} +2.21506e7 q^{78} -4.51823e8 q^{79} -1.68774e7 q^{80} +4.30467e7 q^{81} -7.18804e7 q^{82} -4.70214e8 q^{83} +7.81668e7 q^{84} -2.73842e7 q^{85} -4.59651e7 q^{86} -1.75486e8 q^{87} +1.20779e8 q^{88} +2.05108e8 q^{89} -1.00804e6 q^{90} -2.25297e8 q^{91} +3.70257e8 q^{92} +6.10657e8 q^{93} -5.28032e7 q^{94} -1.43692e7 q^{95} +1.45226e8 q^{96} -9.28232e8 q^{97} -8.49066e7 q^{98} -3.36484e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9}+O(q^{10}) $ 21 * q - 66 * q^2 + 1701 * q^3 + 5206 * q^4 - 2964 * q^5 - 5346 * q^6 - 30775 * q^7 - 24621 * q^8 + 137781 * q^9	\( 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9} - 54663 q^{10} - 151769 q^{11} + 421686 q^{12} - 153611 q^{13} - 286771 q^{14} - 240084 q^{15} + 805530 q^{16} - 723621 q^{17} - 433026 q^{18} - 549388 q^{19} - 527311 q^{20} - 2492775 q^{21} + 2973158 q^{22} + 169962 q^{23} - 1994301 q^{24} + 8035779 q^{25} - 2337392 q^{26} + 11160261 q^{27} - 22659054 q^{28} - 16845442 q^{29} - 4427703 q^{30} - 19307976 q^{31} - 44923568 q^{32} - 12293289 q^{33} - 35547496 q^{34} - 34882596 q^{35} + 34156566 q^{36} - 41561129 q^{37} - 52335371 q^{38} - 12442491 q^{39} - 125735038 q^{40} - 68169291 q^{41} - 23228451 q^{42} - 25719587 q^{43} - 126277032 q^{44} - 19446804 q^{45} - 292814271 q^{46} - 174095332 q^{47} + 65247930 q^{48} + 7479350 q^{49} - 227877439 q^{50} - 58613301 q^{51} - 232397708 q^{52} - 228390500 q^{53} - 35075106 q^{54} - 29426208 q^{55} + 326778474 q^{56} - 44500428 q^{57} + 480343762 q^{58} + 254464581 q^{59} - 42712191 q^{60} - 183928964 q^{61} - 21753862 q^{62} - 201914775 q^{63} + 310571245 q^{64} + 5308466 q^{65} + 240825798 q^{66} - 82724114 q^{67} - 138336205 q^{68} + 13766922 q^{69} + 1030274876 q^{70} - 404721965 q^{71} - 161538381 q^{72} + 154162574 q^{73} + 36352054 q^{74} + 650898099 q^{75} + 1068940636 q^{76} - 448535481 q^{77} - 189328752 q^{78} + 272529635 q^{79} - 345587859 q^{80} + 903981141 q^{81} - 38412637 q^{82} + 432518643 q^{83} - 1835383374 q^{84} - 126211490 q^{85} - 3699273072 q^{86} - 1364480802 q^{87} + 170111045 q^{88} - 1255621070 q^{89} - 358643943 q^{90} + 1448885849 q^{91} + 1568933320 q^{92} - 1563946056 q^{93} - 1908445164 q^{94} - 2896546490 q^{95} - 3638809008 q^{96} + 1007235486 q^{97} - 9506868248 q^{98} - 995756409 q^{99}+O(q^{100}) \) 21 * q - 66 * q^2 + 1701 * q^3 + 5206 * q^4 - 2964 * q^5 - 5346 * q^6 - 30775 * q^7 - 24621 * q^8 + 137781 * q^9 - 54663 * q^10 - 151769 * q^11 + 421686 * q^12 - 153611 * q^13 - 286771 * q^14 - 240084 * q^15 + 805530 * q^16 - 723621 * q^17 - 433026 * q^18 - 549388 * q^19 - 527311 * q^20 - 2492775 * q^21 + 2973158 * q^22 + 169962 * q^23 - 1994301 * q^24 + 8035779 * q^25 - 2337392 * q^26 + 11160261 * q^27 - 22659054 * q^28 - 16845442 * q^29 - 4427703 * q^30 - 19307976 * q^31 - 44923568 * q^32 - 12293289 * q^33 - 35547496 * q^34 - 34882596 * q^35 + 34156566 * q^36 - 41561129 * q^37 - 52335371 * q^38 - 12442491 * q^39 - 125735038 * q^40 - 68169291 * q^41 - 23228451 * q^42 - 25719587 * q^43 - 126277032 * q^44 - 19446804 * q^45 - 292814271 * q^46 - 174095332 * q^47 + 65247930 * q^48 + 7479350 * q^49 - 227877439 * q^50 - 58613301 * q^51 - 232397708 * q^52 - 228390500 * q^53 - 35075106 * q^54 - 29426208 * q^55 + 326778474 * q^56 - 44500428 * q^57 + 480343762 * q^58 + 254464581 * q^59 - 42712191 * q^60 - 183928964 * q^61 - 21753862 * q^62 - 201914775 * q^63 + 310571245 * q^64 + 5308466 * q^65 + 240825798 * q^66 - 82724114 * q^67 - 138336205 * q^68 + 13766922 * q^69 + 1030274876 * q^70 - 404721965 * q^71 - 161538381 * q^72 + 154162574 * q^73 + 36352054 * q^74 + 650898099 * q^75 + 1068940636 * q^76 - 448535481 * q^77 - 189328752 * q^78 + 272529635 * q^79 - 345587859 * q^80 + 903981141 * q^81 - 38412637 * q^82 + 432518643 * q^83 - 1835383374 * q^84 - 126211490 * q^85 - 3699273072 * q^86 - 1364480802 * q^87 + 170111045 * q^88 - 1255621070 * q^89 - 358643943 * q^90 + 1448885849 * q^91 + 1568933320 * q^92 - 1563946056 * q^93 - 1908445164 * q^94 - 2896546490 * q^95 - 3638809008 * q^96 + 1007235486 * q^97 - 9506868248 * q^98 - 995756409 * 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 $

$2$	2.31191	0.102173	0.0510864	−	0.998694i	$-0.483732\pi$
$2$	2.31191	0.102173	0.0510864	+	0.998694i	$0.483732\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	−506.655	−0.989561
$5$	−66.4563	−0.0475523	−0.0237761	−	0.999717i	$-0.507569\pi$
$5$	−66.4563	−0.0475523	−0.0237761	+	0.999717i	$0.507569\pi$
$6$	187.265	0.0589895
$7$	−1904.69	−0.299836	−0.149918	−	0.988698i	$-0.547901\pi$
$7$	−1904.69	−0.299836	−0.149918	+	0.988698i	$0.547901\pi$
$8$	−2355.04	−0.203279
$9$	6561.00	0.333333
$10$	−153.641	−0.00485855
$11$	−51285.5	−1.05615	−0.528077	−	0.849196i	$-0.677087\pi$
$11$	−51285.5	−1.05615	−0.528077	+	0.849196i	$0.677087\pi$
$12$	−41039.1	−0.571323
$13$	118285.	1.14864	0.574320	−	0.818631i	$-0.305266\pi$
$13$	118285.	1.14864	0.574320	+	0.818631i	$0.305266\pi$
$14$	−4403.48	−0.0306351
$15$	−5382.96	−0.0274543
$16$	253963.	0.968791
$17$	412063.	1.19658	0.598292	−	0.801278i	$-0.295846\pi$
$17$	412063.	1.19658	0.598292	+	0.801278i	$0.295846\pi$
$18$	15168.4	0.0340576
$19$	216219.	0.380631	0.190315	−	0.981723i	$-0.439049\pi$
$19$	216219.	0.380631	0.190315	+	0.981723i	$0.439049\pi$
$20$	33670.4	0.0470559
$21$	−154280.	−0.173110
$22$	−118567.	−0.107910
$23$	−730788.	−0.544523	−0.272261	−	0.962223i	$-0.587772\pi$
$23$	−730788.	−0.544523	−0.272261	+	0.962223i	$0.587772\pi$
$24$	−190758.	−0.117363
$25$	−1.94871e6	−0.997739
$26$	273464.	0.117360
$27$	531441.	0.192450
$28$	965023.	0.296706
$29$	−2.16650e6	−0.568810	−0.284405	−	0.958704i	$-0.591796\pi$
$29$	−2.16650e6	−0.568810	−0.284405	+	0.958704i	$0.591796\pi$
$30$	−12444.9	−0.00280509
$31$	7.53898e6	1.46617	0.733086	−	0.680136i	$-0.238079\pi$
$31$	7.53898e6	1.46617	0.733086	+	0.680136i	$0.238079\pi$
$32$	1.79292e6	0.302263
$33$	−4.15413e6	−0.609771
$34$	952652.	0.122258
$35$	126579.	0.0142579
$36$	−3.32416e6	−0.329854
$37$	2.06192e7	1.80869	0.904345	−	0.426802i	$-0.140360\pi$
$37$	2.06192e7	1.80869	0.904345	+	0.426802i	$0.140360\pi$
$38$	499880.	0.0388901
$39$	9.58108e6	0.663168
$40$	156507.	0.00966639
$41$	−3.10914e7	−1.71835	−0.859177	−	0.511678i	$-0.829024\pi$
$41$	−3.10914e7	−1.71835	−0.859177	+	0.511678i	$0.829024\pi$
$42$	−356682.	−0.0176872
$43$	−1.98819e7	−0.886848	−0.443424	−	0.896312i	$-0.646236\pi$
$43$	−1.98819e7	−0.886848	−0.443424	+	0.896312i	$0.646236\pi$
$44$	2.59841e7	1.04513
$45$	−436020.	−0.0158508
$46$	−1.68951e6	−0.0556354
$47$	−2.28396e7	−0.682730	−0.341365	−	0.939931i	$-0.610889\pi$
$47$	−2.28396e7	−0.682730	−0.341365	+	0.939931i	$0.610889\pi$
$48$	2.05710e7	0.559332
$49$	−3.67257e7	−0.910098
$50$	−4.50524e6	−0.101942
$51$	3.33771e7	0.690849
$52$	−5.99297e7	−1.13665
$53$	−3.27629e7	−0.570350	−0.285175	−	0.958475i	$-0.592052\pi$
$53$	−3.27629e7	−0.570350	−0.285175	+	0.958475i	$0.592052\pi$
$54$	1.22864e6	0.0196632
$55$	3.40825e6	0.0502226
$56$	4.48562e6	0.0609504
$57$	1.75138e7	0.219757
$58$	−5.00874e6	−0.0581169
$59$	1.21174e7	0.130189
$59$	1.21174e7	0.130189
$60$	2.72731e6	0.0271677
$61$	−8.93784e7	−0.826510	−0.413255	−	0.910615i	$-0.635608\pi$
$61$	−8.93784e7	−0.826510	−0.413255	+	0.910615i	$0.635608\pi$
$62$	1.74294e7	0.149803
$63$	−1.24967e7	−0.0999454
$64$	−1.25884e8	−0.937908
$65$	−7.86078e6	−0.0546205
$66$	−9.60396e6	−0.0623021
$67$	7.39877e7	0.448563	0.224281	−	0.974524i	$-0.427997\pi$
$67$	7.39877e7	0.448563	0.224281	+	0.974524i	$0.427997\pi$
$68$	−2.08774e8	−1.18409
$69$	−5.91938e7	−0.314380
$70$	292639.	0.00145677
$71$	3.75295e8	1.75271	0.876355	−	0.481665i	$-0.159968\pi$
$71$	3.75295e8	1.75271	0.876355	+	0.481665i	$0.159968\pi$
$72$	−1.54514e7	−0.0677597
$73$	−3.48461e7	−0.143616	−0.0718078	−	0.997418i	$-0.522877\pi$
$73$	−3.48461e7	−0.143616	−0.0718078	+	0.997418i	$0.522877\pi$
$74$	4.76697e7	0.184799
$75$	−1.57845e8	−0.576045
$76$	−1.09549e8	−0.376657
$77$	9.76832e7	0.316673
$78$	2.21506e7	0.0677578
$79$	−4.51823e8	−1.30511	−0.652554	−	0.757742i	$-0.726303\pi$
$79$	−4.51823e8	−1.30511	−0.652554	+	0.757742i	$0.726303\pi$
$80$	−1.68774e7	−0.0460682
$81$	4.30467e7	0.111111
$82$	−7.18804e7	−0.175569
$83$	−4.70214e8	−1.08754	−0.543768	−	0.839235i	$-0.683003\pi$
$83$	−4.70214e8	−1.08754	−0.543768	+	0.839235i	$0.683003\pi$
$84$	7.81668e7	0.171303
$85$	−2.73842e7	−0.0569003
$86$	−4.59651e7	−0.0906118
$87$	−1.75486e8	−0.328402
$88$	1.20779e8	0.214694
$89$	2.05108e8	0.346519	0.173259	−	0.984876i	$-0.444570\pi$
$89$	2.05108e8	0.346519	0.173259	+	0.984876i	$0.444570\pi$
$90$	−1.00804e6	−0.00161952
$91$	−2.25297e8	−0.344404
$92$	3.70257e8	0.538838
$93$	6.10657e8	0.846495
$94$	−5.28032e7	−0.0697565
$95$	−1.43692e7	−0.0180998
$96$	1.45226e8	0.174512
$97$	−9.28232e8	−1.06459	−0.532297	−	0.846558i	$-0.678671\pi$
$97$	−9.28232e8	−1.06459	−0.532297	+	0.846558i	$0.678671\pi$
$98$	−8.49066e7	−0.0929874
$99$	−3.36484e8	−0.352052
$100$	9.87323e8	0.987323
$101$	−1.09966e9	−1.05150	−0.525752	−	0.850638i	$-0.676216\pi$
$101$	−1.09966e9	−1.05150	−0.525752	+	0.850638i	$0.676216\pi$
$102$	7.71648e7	0.0705860
$103$	1.31181e8	0.114843	0.0574215	−	0.998350i	$-0.481712\pi$
$103$	1.31181e8	0.114843	0.0574215	+	0.998350i	$0.481712\pi$
$104$	−2.78565e8	−0.233495
$105$	1.02529e7	0.00823180
$106$	−7.57449e7	−0.0582743
$107$	1.41720e9	1.04521	0.522607	−	0.852574i	$-0.324960\pi$
$107$	1.41720e9	1.04521	0.522607	+	0.852574i	$0.324960\pi$
$108$	−2.69257e8	−0.190441
$109$	2.15601e8	0.146296	0.0731478	−	0.997321i	$-0.476696\pi$
$109$	2.15601e8	0.146296	0.0731478	+	0.997321i	$0.476696\pi$
$110$	7.87955e6	0.00513138
$111$	1.67016e9	1.04425
$112$	−4.83721e8	−0.290479
$113$	−9.24420e8	−0.533355	−0.266678	−	0.963786i	$-0.585926\pi$
$113$	−9.24420e8	−0.533355	−0.266678	+	0.963786i	$0.585926\pi$
$114$	4.04902e7	0.0224532
$115$	4.85655e7	0.0258933
$116$	1.09767e9	0.562872
$117$	7.76067e8	0.382880
$118$	2.80142e7	0.0133018
$119$	−7.84854e8	−0.358779
$120$	1.26771e7	0.00558089
$121$	2.72256e8	0.115463
$122$	−2.06635e8	−0.0844469
$123$	−2.51840e9	−0.992092
$124$	−3.81966e9	−1.45087
$125$	2.59302e8	0.0949970
$126$	−2.88912e7	−0.0102117
$127$	−3.33077e9	−1.13613	−0.568065	−	0.822984i	$-0.692308\pi$
$127$	−3.33077e9	−1.13613	−0.568065	+	0.822984i	$0.692308\pi$
$128$	−1.20901e9	−0.398092
$129$	−1.61043e9	−0.512022
$130$	−1.81734e7	−0.00558073
$131$	−5.99263e9	−1.77786	−0.888929	−	0.458046i	$-0.848550\pi$
$131$	−5.99263e9	−1.77786	−0.888929	+	0.458046i	$0.848550\pi$
$132$	2.10471e9	0.603406
$133$	−4.11832e8	−0.114127
$134$	1.71053e8	0.0458309
$135$	−3.53176e7	−0.00915144
$136$	−9.70424e8	−0.243241
$137$	−9.77396e8	−0.237044	−0.118522	−	0.992951i	$-0.537816\pi$
$137$	−9.77396e8	−0.237044	−0.118522	+	0.992951i	$0.537816\pi$
$138$	−1.36851e8	−0.0321211
$139$	−6.15322e9	−1.39809	−0.699046	−	0.715077i	$-0.746392\pi$
$139$	−6.15322e9	−1.39809	−0.699046	+	0.715077i	$0.746392\pi$
$140$	−6.41319e7	−0.0141090
$141$	−1.85001e9	−0.394174
$142$	8.67647e8	0.179079
$143$	−6.06630e9	−1.21314
$144$	1.66625e9	0.322930
$145$	1.43977e8	0.0270482
$146$	−8.05611e7	−0.0146736
$147$	−2.97479e9	−0.525445
$148$	−1.04468e10	−1.78981
$149$	6.61664e9	1.09976	0.549882	−	0.835242i	$-0.314673\pi$
$149$	6.61664e9	1.09976	0.549882	+	0.835242i	$0.314673\pi$
$150$	−3.64924e8	−0.0588561
$151$	−9.46985e9	−1.48234	−0.741169	−	0.671319i	$-0.765728\pi$
$151$	−9.46985e9	−1.48234	−0.741169	+	0.671319i	$0.765728\pi$
$152$	−5.09205e8	−0.0773742
$153$	2.70355e9	0.398862
$154$	2.25835e8	0.0323554
$155$	−5.01013e8	−0.0697198
$156$	−4.85430e9	−0.656245
$157$	1.10136e10	1.44671	0.723355	−	0.690477i	$-0.242599\pi$
$157$	1.10136e10	1.44671	0.723355	+	0.690477i	$0.242599\pi$
$158$	−1.04457e9	−0.133347
$159$	−2.65380e9	−0.329292
$160$	−1.19151e8	−0.0143733
$161$	1.39193e9	0.163268
$162$	9.95201e7	0.0113525
$163$	3.97578e9	0.441142	0.220571	−	0.975371i	$-0.429208\pi$
$163$	3.97578e9	0.441142	0.220571	+	0.975371i	$0.429208\pi$
$164$	1.57526e10	1.70042
$165$	2.76068e8	0.0289960
$166$	−1.08709e9	−0.111117
$167$	−1.18492e10	−1.17887	−0.589434	−	0.807817i	$-0.700649\pi$
$167$	−1.18492e10	−1.17887	−0.589434	+	0.807817i	$0.700649\pi$
$168$	3.63336e8	0.0351897
$169$	3.38682e9	0.319376
$170$	−6.33097e7	−0.00581367
$171$	1.41862e9	0.126877
$172$	1.00732e10	0.877590
$173$	−1.55109e10	−1.31653	−0.658264	−	0.752787i	$-0.728709\pi$
$173$	−1.55109e10	−1.31653	−0.658264	+	0.752787i	$0.728709\pi$
$174$	−4.05708e8	−0.0335538
$175$	3.71169e9	0.299158
$176$	−1.30246e10	−1.02319
$177$	9.81506e8	0.0751646
$178$	4.74190e8	0.0354048
$179$	−2.04589e10	−1.48951	−0.744755	−	0.667338i	$-0.767434\pi$
$179$	−2.04589e10	−1.48951	−0.744755	+	0.667338i	$0.767434\pi$
$180$	2.20912e8	0.0156853
$181$	−1.25668e10	−0.870305	−0.435152	−	0.900357i	$-0.643306\pi$
$181$	−1.25668e10	−0.870305	−0.435152	+	0.900357i	$0.643306\pi$
$182$	−5.20865e8	−0.0351888
$183$	−7.23965e9	−0.477186
$184$	1.72103e9	0.110690
$185$	−1.37028e9	−0.0860073
$186$	1.41178e9	0.0864888
$187$	−2.11329e10	−1.26378
$188$	1.15718e10	0.675603
$189$	−1.01223e9	−0.0577035
$190$	−3.32202e7	−0.00184931
$191$	2.61909e10	1.42397	0.711985	−	0.702195i	$-0.247796\pi$
$191$	2.61909e10	1.42397	0.711985	+	0.702195i	$0.247796\pi$
$192$	−1.01966e10	−0.541501
$193$	2.59647e10	1.34702	0.673512	−	0.739177i	$-0.264785\pi$
$193$	2.59647e10	1.34702	0.673512	+	0.739177i	$0.264785\pi$
$194$	−2.14599e9	−0.108773
$195$	−6.36723e8	−0.0315352
$196$	1.86073e10	0.900598
$197$	−1.11591e9	−0.0527877	−0.0263938	−	0.999652i	$-0.508402\pi$
$197$	−1.11591e9	−0.0527877	−0.0263938	+	0.999652i	$0.508402\pi$
$198$	−7.77921e8	−0.0359701
$199$	2.98397e10	1.34882	0.674412	−	0.738356i	$-0.264397\pi$
$199$	2.98397e10	1.34882	0.674412	+	0.738356i	$0.264397\pi$
$200$	4.58928e9	0.202819
$201$	5.99301e9	0.258978
$202$	−2.54231e9	−0.107435
$203$	4.12651e9	0.170550
$204$	−1.69107e10	−0.683637
$205$	2.06622e9	0.0817117
$206$	3.03279e8	0.0117338
$207$	−4.79470e9	−0.181508
$208$	3.00400e10	1.11279
$209$	−1.10889e10	−0.402005
$210$	2.37038e7	0.000841066 0
$211$	−4.53349e10	−1.57457	−0.787284	−	0.616590i	$-0.788514\pi$
$211$	−4.53349e10	−1.57457	−0.787284	+	0.616590i	$0.788514\pi$
$212$	1.65995e10	0.564396
$213$	3.03989e10	1.01193
$214$	3.27644e9	0.106792
$215$	1.32128e9	0.0421716
$216$	−1.25156e9	−0.0391211
$217$	−1.43594e10	−0.439611
$218$	4.98449e8	0.0149474
$219$	−2.82254e9	−0.0829165
$220$	−1.72681e9	−0.0496983
$221$	4.87408e10	1.37445
$222$	3.86125e9	0.106694
$223$	4.29880e10	1.16406	0.582030	−	0.813167i	$-0.302258\pi$
$223$	4.29880e10	1.16406	0.582030	+	0.813167i	$0.302258\pi$
$224$	−3.41496e9	−0.0906295
$225$	−1.27855e10	−0.332580
$226$	−2.13717e9	−0.0544944
$227$	−4.70552e10	−1.17623	−0.588113	−	0.808779i	$-0.700129\pi$
$227$	−4.70552e10	−1.17623	−0.588113	+	0.808779i	$0.700129\pi$
$228$	−8.87345e9	−0.217463
$229$	2.65931e10	0.639012	0.319506	−	0.947584i	$-0.396483\pi$
$229$	2.65931e10	0.639012	0.319506	+	0.947584i	$0.396483\pi$
$230$	1.12279e8	0.00264559
$231$	7.91234e9	0.182831
$232$	5.10218e9	0.115627
$233$	−2.79305e10	−0.620837	−0.310418	−	0.950600i	$-0.600469\pi$
$233$	−2.79305e10	−0.620837	−0.310418	+	0.950600i	$0.600469\pi$
$234$	1.79420e9	0.0391200
$235$	1.51784e9	0.0324654
$236$	−6.13932e9	−0.128830
$237$	−3.65977e10	−0.753505
$238$	−1.81451e9	−0.0366575
$239$	−6.43052e10	−1.27484	−0.637420	−	0.770516i	$-0.719998\pi$
$239$	−6.43052e10	−1.27484	−0.637420	+	0.770516i	$0.719998\pi$
$240$	−1.36707e9	−0.0265975
$241$	−2.46077e10	−0.469889	−0.234944	−	0.972009i	$-0.575491\pi$
$241$	−2.46077e10	−0.469889	−0.234944	+	0.972009i	$0.575491\pi$
$242$	6.29430e8	0.0117972
$243$	3.48678e9	0.0641500
$244$	4.52840e10	0.817882
$245$	2.44066e9	0.0432772
$246$	−5.82232e9	−0.101365
$247$	2.55755e10	0.437208
$248$	−1.77546e10	−0.298042
$249$	−3.80873e10	−0.627890
$250$	5.99481e8	0.00970612
$251$	−2.02230e10	−0.321599	−0.160799	−	0.986987i	$-0.551407\pi$
$251$	−2.02230e10	−0.321599	−0.160799	+	0.986987i	$0.551407\pi$
$252$	6.33151e9	0.0989020
$253$	3.74788e10	0.575100
$254$	−7.70043e9	−0.116082
$255$	−2.21812e9	−0.0328514
$256$	6.16574e10	0.897234
$257$	6.69980e10	0.957995	0.478997	−	0.877816i	$-0.341000\pi$
$257$	6.69980e10	0.957995	0.478997	+	0.877816i	$0.341000\pi$
$258$	−3.72317e9	−0.0523147
$259$	−3.92733e10	−0.542311
$260$	3.98270e9	0.0540503
$261$	−1.42144e10	−0.189603
$262$	−1.38544e10	−0.181649
$263$	5.85641e10	0.754798	0.377399	−	0.926051i	$-0.376819\pi$
$263$	5.85641e10	0.754798	0.377399	+	0.926051i	$0.376819\pi$
$264$	9.78312e9	0.123954
$265$	2.17730e9	0.0271214
$266$	−9.52118e8	−0.0116607
$267$	1.66137e10	0.200063
$268$	−3.74863e10	−0.443880
$269$	4.85172e9	0.0564951	0.0282476	−	0.999601i	$-0.491007\pi$
$269$	4.85172e9	0.0564951	0.0282476	+	0.999601i	$0.491007\pi$
$270$	−8.16511e7	−0.000935029 0
$271$	1.61545e11	1.81942	0.909708	−	0.415248i	$-0.136305\pi$
$271$	1.61545e11	1.81942	0.909708	+	0.415248i	$0.136305\pi$
$272$	1.04649e11	1.15924
$273$	−1.82490e10	−0.198842
$274$	−2.25965e9	−0.0242194
$275$	9.99405e10	1.05377
$276$	2.99908e10	0.311098
$277$	−9.49694e10	−0.969225	−0.484613	−	0.874729i	$-0.661039\pi$
$277$	−9.49694e10	−0.969225	−0.484613	+	0.874729i	$0.661039\pi$
$278$	−1.42257e10	−0.142847
$279$	4.94632e10	0.488724
$280$	−2.98098e8	−0.00289833
$281$	1.41795e10	0.135670	0.0678349	−	0.997697i	$-0.478391\pi$
$281$	1.41795e10	0.135670	0.0678349	+	0.997697i	$0.478391\pi$
$282$	−4.27706e9	−0.0402739
$283$	5.25711e10	0.487201	0.243601	−	0.969876i	$-0.421671\pi$
$283$	5.25711e10	0.487201	0.243601	+	0.969876i	$0.421671\pi$
$284$	−1.90145e11	−1.73441
$285$	−1.16390e9	−0.0104500
$286$	−1.40247e10	−0.123950
$287$	5.92196e10	0.515225
$288$	1.17633e10	0.100754
$289$	5.12080e10	0.431815
$290$	3.32862e8	0.00276359
$291$	−7.51868e10	−0.614643
$292$	1.76550e10	0.142116
$293$	2.09217e11	1.65841	0.829207	−	0.558941i	$-0.188792\pi$
$293$	2.09217e11	1.65841	0.829207	+	0.558941i	$0.188792\pi$
$294$	−6.87743e9	−0.0536863
$295$	−8.05275e8	−0.00619078
$296$	−4.85590e10	−0.367669
$297$	−2.72552e10	−0.203257
$298$	1.52971e10	0.112366
$299$	−8.64412e10	−0.625461
$300$	7.99732e10	0.570031
$301$	3.78689e10	0.265909
$302$	−2.18934e10	−0.151455
$303$	−8.90722e10	−0.607086
$304$	5.49117e10	0.368751
$305$	5.93976e9	0.0393024
$306$	6.25035e9	0.0407528
$307$	1.53968e11	0.989251	0.494626	−	0.869106i	$-0.335305\pi$
$307$	1.53968e11	0.989251	0.494626	+	0.869106i	$0.335305\pi$
$308$	−4.94917e10	−0.313368
$309$	1.06257e10	0.0663046
$310$	−1.15830e9	−0.00712347
$311$	−2.79730e10	−0.169558	−0.0847789	−	0.996400i	$-0.527018\pi$
$311$	−2.79730e10	−0.169558	−0.0847789	+	0.996400i	$0.527018\pi$
$312$	−2.25638e10	−0.134808
$313$	2.14977e11	1.26603	0.633014	−	0.774141i	$-0.281818\pi$
$313$	2.14977e11	1.26603	0.633014	+	0.774141i	$0.281818\pi$
$314$	2.54625e10	0.147814
$315$	8.30484e8	0.00475263
$316$	2.28918e11	1.29148
$317$	2.33306e11	1.29766	0.648828	−	0.760935i	$-0.275259\pi$
$317$	2.33306e11	1.29766	0.648828	+	0.760935i	$0.275259\pi$
$318$	−6.13534e9	−0.0336447
$319$	1.11110e11	0.600751
$320$	8.36578e9	0.0445997
$321$	1.14793e11	0.603454
$322$	3.21801e9	0.0166815
$323$	8.90961e10	0.455457
$324$	−2.18098e10	−0.109951
$325$	−2.30503e11	−1.14604
$326$	9.19164e9	0.0450727
$327$	1.74637e10	0.0844638
$328$	7.32214e10	0.349306
$329$	4.35025e10	0.204707
$330$	6.38244e8	0.00296261
$331$	−1.32503e11	−0.606738	−0.303369	−	0.952873i	$-0.598111\pi$
$331$	−1.32503e11	−0.606738	−0.303369	+	0.952873i	$0.598111\pi$
$332$	2.38236e11	1.07618
$333$	1.35283e11	0.602897
$334$	−2.73943e10	−0.120448
$335$	−4.91695e9	−0.0213302
$336$	−3.91814e10	−0.167708
$337$	−3.77882e11	−1.59596	−0.797979	−	0.602685i	$-0.794097\pi$
$337$	−3.77882e11	−1.59596	−0.797979	+	0.602685i	$0.794097\pi$
$338$	7.83002e9	0.0326316
$339$	−7.48780e10	−0.307933
$340$	1.38743e10	0.0563063
$341$	−3.86640e11	−1.54850
$342$	3.27971e9	0.0129634
$343$	1.46813e11	0.572717
$344$	4.68225e10	0.180278
$345$	3.93380e9	0.0149495
$346$	−3.58598e10	−0.134513
$347$	−5.13729e11	−1.90218	−0.951090	−	0.308914i	$-0.900034\pi$
$347$	−5.13729e11	−1.90218	−0.951090	+	0.308914i	$0.900034\pi$
$348$	8.89110e10	0.324974
$349$	4.77122e11	1.72153	0.860765	−	0.509002i	$-0.169985\pi$
$349$	4.77122e11	1.72153	0.860765	+	0.509002i	$0.169985\pi$
$350$	8.58109e9	0.0305658
$351$	6.28615e10	0.221056
$352$	−9.19507e10	−0.319237
$353$	1.57630e11	0.540323	0.270162	−	0.962815i	$-0.412923\pi$
$353$	1.57630e11	0.540323	0.270162	+	0.962815i	$0.412923\pi$
$354$	2.26915e9	0.00767978
$355$	−2.49407e10	−0.0833454
$356$	−1.03919e11	−0.342902
$357$	−6.35732e10	−0.207141
$358$	−4.72991e10	−0.152187
$359$	−1.17398e11	−0.373022	−0.186511	−	0.982453i	$-0.559718\pi$
$359$	−1.17398e11	−0.373022	−0.186511	+	0.982453i	$0.559718\pi$
$360$	1.02684e9	0.00322213
$361$	−2.75937e11	−0.855120
$362$	−2.90533e10	−0.0889215
$363$	2.20527e10	0.0666626
$364$	1.14148e11	0.340809
$365$	2.31575e9	0.00682925
$366$	−1.67374e10	−0.0487555
$367$	3.08329e11	0.887192	0.443596	−	0.896227i	$-0.353703\pi$
$367$	3.08329e11	0.887192	0.443596	+	0.896227i	$0.353703\pi$
$368$	−1.85593e11	−0.527529
$369$	−2.03991e11	−0.572785
$370$	−3.16795e9	−0.00878762
$371$	6.24034e10	0.171012
$372$	−3.09393e11	−0.837658
$373$	−5.75361e11	−1.53904	−0.769522	−	0.638620i	$-0.779505\pi$
$373$	−5.75361e11	−1.53904	−0.769522	+	0.638620i	$0.779505\pi$
$374$	−4.88572e10	−0.129124
$375$	2.10034e10	0.0548466
$376$	5.37882e10	0.138785
$377$	−2.56264e11	−0.653358
$378$	−2.34019e9	−0.00589573
$379$	2.91299e11	0.725207	0.362604	−	0.931943i	$-0.381888\pi$
$379$	2.91299e11	0.725207	0.362604	+	0.931943i	$0.381888\pi$
$380$	7.28020e9	0.0179109
$381$	−2.69792e11	−0.655945
$382$	6.05510e10	0.145491
$383$	−6.52162e11	−1.54868	−0.774338	−	0.632772i	$-0.781917\pi$
$383$	−6.52162e11	−1.54868	−0.774338	+	0.632772i	$0.781917\pi$
$384$	−9.79295e10	−0.229839
$385$	−6.49167e9	−0.0150585
$386$	6.00280e10	0.137629
$387$	−1.30445e11	−0.295616
$388$	4.70293e11	1.05348
$389$	2.32127e10	0.0513987	0.0256993	−	0.999670i	$-0.491819\pi$
$389$	2.32127e10	0.0513987	0.0256993	+	0.999670i	$0.491819\pi$
$390$	−1.47205e9	−0.00322204
$391$	−3.01131e11	−0.651568
$392$	8.64905e10	0.185004
$393$	−4.85403e11	−1.02645
$394$	−2.57989e9	−0.00539347
$395$	3.00265e10	0.0620609
$396$	1.70481e11	0.348376
$397$	−2.94489e11	−0.594993	−0.297496	−	0.954723i	$-0.596152\pi$
$397$	−2.94489e11	−0.594993	−0.297496	+	0.954723i	$0.596152\pi$
$398$	6.89865e10	0.137813
$399$	−3.33584e10	−0.0658911
$400$	−4.94899e11	−0.966600
$401$	−6.28022e11	−1.21290	−0.606451	−	0.795121i	$-0.707407\pi$
$401$	−6.28022e11	−1.21290	−0.606451	+	0.795121i	$0.707407\pi$
$402$	1.38553e10	0.0264605
$403$	8.91748e11	1.68411
$404$	5.57147e11	1.04053
$405$	−2.86073e9	−0.00528359
$406$	9.54012e9	0.0174256
$407$	−1.05747e12	−1.91026
$408$	−7.86043e10	−0.140435
$409$	3.47418e11	0.613900	0.306950	−	0.951726i	$-0.400692\pi$
$409$	3.47418e11	0.613900	0.306950	+	0.951726i	$0.400692\pi$
$410$	4.77691e9	0.00834872
$411$	−7.91691e10	−0.136857
$412$	−6.64637e10	−0.113644
$413$	−2.30799e10	−0.0390353
$414$	−1.10849e10	−0.0185451
$415$	3.12487e10	0.0517148
$416$	2.12075e11	0.347192
$417$	−4.98411e11	−0.807189
$418$	−2.56366e10	−0.0410740
$419$	1.58933e11	0.251913	0.125956	−	0.992036i	$-0.459800\pi$
$419$	1.58933e11	0.251913	0.125956	+	0.992036i	$0.459800\pi$
$420$	−5.19468e9	−0.00814586
$421$	9.69796e11	1.50456	0.752282	−	0.658841i	$-0.228953\pi$
$421$	9.69796e11	1.50456	0.752282	+	0.658841i	$0.228953\pi$
$422$	−1.04810e11	−0.160878
$423$	−1.49851e11	−0.227577
$424$	7.71579e10	0.115940
$425$	−8.02991e11	−1.19388
$426$	7.02794e10	0.103392
$427$	1.70238e11	0.247818
$428$	−7.18033e11	−1.03430
$429$	−4.91370e11	−0.700408
$430$	3.05467e9	0.00430880
$431$	−5.04058e11	−0.703611	−0.351805	−	0.936073i	$-0.614432\pi$
$431$	−5.04058e11	−0.703611	−0.351805	+	0.936073i	$0.614432\pi$
$432$	1.34966e11	0.186444
$433$	5.44129e11	0.743886	0.371943	−	0.928256i	$-0.378692\pi$
$433$	5.44129e11	0.743886	0.371943	+	0.928256i	$0.378692\pi$
$434$	−3.31977e10	−0.0449164
$435$	1.16622e10	0.0156163
$436$	−1.09235e11	−0.144768
$437$	−1.58011e11	−0.207262
$438$	−6.52545e9	−0.00847182
$439$	−1.07969e12	−1.38743	−0.693713	−	0.720252i	$-0.744026\pi$
$439$	−1.07969e12	−1.38743	−0.693713	+	0.720252i	$0.744026\pi$
$440$	−8.02655e9	−0.0102092
$441$	−2.40958e11	−0.303366
$442$	1.12684e11	0.140431
$443$	7.29394e11	0.899798	0.449899	−	0.893079i	$-0.351460\pi$
$443$	7.29394e11	0.899798	0.449899	+	0.893079i	$0.351460\pi$
$444$	−8.46193e11	−1.03335
$445$	−1.36307e10	−0.0164778
$446$	9.93844e10	0.118935
$447$	5.35948e11	0.634949
$448$	2.39770e11	0.281219
$449$	4.06817e11	0.472379	0.236190	−	0.971707i	$-0.424101\pi$
$449$	4.06817e11	0.472379	0.236190	+	0.971707i	$0.424101\pi$
$450$	−2.95588e10	−0.0339806
$451$	1.59454e12	1.81485
$452$	4.68362e11	0.527787
$453$	−7.67058e11	−0.855828
$454$	−1.08787e11	−0.120178
$455$	1.49724e10	0.0163772
$456$	−4.12456e10	−0.0446720
$457$	8.28426e11	0.888445	0.444223	−	0.895916i	$-0.353480\pi$
$457$	8.28426e11	0.888445	0.444223	+	0.895916i	$0.353480\pi$
$458$	6.14808e10	0.0652897
$459$	2.18987e11	0.230283
$460$	−2.46059e10	−0.0256230
$461$	−1.71341e12	−1.76688	−0.883442	−	0.468540i	$-0.844780\pi$
$461$	−1.71341e12	−1.76688	−0.883442	+	0.468540i	$0.844780\pi$
$462$	1.82926e10	0.0186804
$463$	1.18389e12	1.19728	0.598641	−	0.801017i	$-0.295708\pi$
$463$	1.18389e12	1.19728	0.598641	+	0.801017i	$0.295708\pi$
$464$	−5.50209e11	−0.551058
$465$	−4.05820e10	−0.0402528
$466$	−6.45728e10	−0.0634327
$467$	−1.00024e12	−0.973143	−0.486571	−	0.873641i	$-0.661753\pi$
$467$	−1.00024e12	−0.973143	−0.486571	+	0.873641i	$0.661753\pi$
$468$	−3.93198e11	−0.378883
$469$	−1.40924e11	−0.134495
$470$	3.50910e9	0.00331708
$471$	8.92102e11	0.835258
$472$	−2.85368e10	−0.0264647
$473$	1.01965e12	0.936649
$474$	−8.46105e10	−0.0769877
$475$	−4.21349e11	−0.379770
$476$	3.97650e11	0.355034
$477$	−2.14958e11	−0.190117
$478$	−1.48668e11	−0.130254
$479$	−1.87270e12	−1.62540	−0.812698	−	0.582685i	$-0.802002\pi$
$479$	−1.87270e12	−1.62540	−0.812698	+	0.582685i	$0.802002\pi$
$480$	−9.65121e9	−0.00829843
$481$	2.43894e12	2.07754
$482$	−5.68908e10	−0.0480099
$483$	1.12746e11	0.0942626
$484$	−1.37940e11	−0.114258
$485$	6.16869e10	0.0506238
$486$	8.06113e9	0.00655439
$487$	−1.59310e12	−1.28340	−0.641701	−	0.766955i	$-0.721771\pi$
$487$	−1.59310e12	−1.28340	−0.641701	+	0.766955i	$0.721771\pi$
$488$	2.10489e11	0.168012
$489$	3.22038e11	0.254693
$490$	5.64258e9	0.00442176
$491$	−7.08110e11	−0.549837	−0.274919	−	0.961468i	$-0.588651\pi$
$491$	−7.08110e11	−0.549837	−0.274919	+	0.961468i	$0.588651\pi$
$492$	1.27596e12	0.981736
$493$	−8.92733e11	−0.680629
$494$	5.91282e10	0.0446708
$495$	2.23615e10	0.0167409
$496$	1.91462e12	1.42041
$497$	−7.14822e11	−0.525526
$498$	−8.80544e10	−0.0641533
$499$	−9.15454e11	−0.660974	−0.330487	−	0.943811i	$-0.607213\pi$
$499$	−9.15454e11	−0.660974	−0.330487	+	0.943811i	$0.607213\pi$
$500$	−1.31376e11	−0.0940053
$501$	−9.59786e11	−0.680620
$502$	−4.67538e10	−0.0328587
$503$	−5.42714e11	−0.378021	−0.189010	−	0.981975i	$-0.560528\pi$
$503$	−5.42714e11	−0.378021	−0.189010	+	0.981975i	$0.560528\pi$
$504$	2.94302e10	0.0203168
$505$	7.30792e10	0.0500014
$506$	8.66476e10	0.0587596
$507$	2.74333e11	0.184392
$508$	1.68755e12	1.12427
$509$	−1.26506e12	−0.835376	−0.417688	−	0.908591i	$-0.637159\pi$
$509$	−1.26506e12	−0.835376	−0.417688	+	0.908591i	$0.637159\pi$
$510$	−5.12809e9	−0.00335652
$511$	6.63712e10	0.0430612
$512$	7.61557e11	0.489765
$513$	1.14908e11	0.0732524
$514$	1.54893e11	0.0978811
$515$	−8.71783e9	−0.00546105
$516$	8.15933e11	0.506677
$517$	1.17134e12	0.721069
$518$	−9.07962e10	−0.0554094
$519$	−1.25638e12	−0.760098
$520$	1.85124e10	0.0111032
$521$	7.82364e10	0.0465199	0.0232600	−	0.999729i	$-0.492595\pi$
$521$	7.82364e10	0.0465199	0.0232600	+	0.999729i	$0.492595\pi$
$522$	−3.28623e10	−0.0193723
$523$	−2.77023e12	−1.61904	−0.809521	−	0.587092i	$-0.800273\pi$
$523$	−2.77023e12	−1.61904	−0.809521	+	0.587092i	$0.800273\pi$
$524$	3.03620e12	1.75930
$525$	3.00647e11	0.172719
$526$	1.35395e11	0.0771198
$527$	3.10653e12	1.75440
$528$	−1.05499e12	−0.590741
$529$	−1.26710e12	−0.703495
$530$	5.03373e9	0.00277108
$531$	7.95020e10	0.0433963
$532$	2.08657e11	0.112935
$533$	−3.67764e12	−1.97377
$534$	3.84094e10	0.0204410
$535$	−9.41821e10	−0.0497023
$536$	−1.74244e11	−0.0911834
$537$	−1.65717e12	−0.859969
$538$	1.12167e10	0.00577227
$539$	1.88350e12	0.961205
$540$	1.78938e10	0.00905590
$541$	4.11901e11	0.206731	0.103366	−	0.994643i	$-0.467039\pi$
$541$	4.11901e11	0.206731	0.103366	+	0.994643i	$0.467039\pi$
$542$	3.73478e11	0.185895
$543$	−1.01791e12	−0.502471
$544$	7.38795e11	0.361684
$545$	−1.43280e10	−0.00695668
$546$	−4.21901e10	−0.0203162
$547$	1.13699e12	0.543019	0.271509	−	0.962436i	$-0.412477\pi$
$547$	1.13699e12	0.543019	0.271509	+	0.962436i	$0.412477\pi$
$548$	4.95203e11	0.234569
$549$	−5.86412e11	−0.275503
$550$	2.31053e11	0.107666
$551$	−4.68439e11	−0.216506
$552$	1.39404e11	0.0639070
$553$	8.60585e11	0.391319
$554$	−2.19561e11	−0.0990285
$555$	−1.10992e11	−0.0496564
$556$	3.11756e12	1.38350
$557$	1.99820e12	0.879612	0.439806	−	0.898093i	$-0.355047\pi$
$557$	1.99820e12	0.879612	0.439806	+	0.898093i	$0.355047\pi$
$558$	1.14354e11	0.0499343
$559$	−2.35173e12	−1.01867
$560$	3.21463e10	0.0138129
$561$	−1.71176e12	−0.729643
$562$	3.27818e10	0.0138618
$563$	2.68941e12	1.12815	0.564077	−	0.825722i	$-0.309232\pi$
$563$	2.68941e12	1.12815	0.564077	+	0.825722i	$0.309232\pi$
$564$	9.37318e11	0.390059
$565$	6.14336e10	0.0253623
$566$	1.21540e11	0.0497787
$567$	−8.19908e10	−0.0333151
$568$	−8.83833e11	−0.356289
$569$	1.26023e12	0.504017	0.252009	−	0.967725i	$-0.418909\pi$
$569$	1.26023e12	0.504017	0.252009	+	0.967725i	$0.418909\pi$
$570$	−2.69083e9	−0.00106770
$571$	−2.08633e12	−0.821336	−0.410668	−	0.911785i	$-0.634704\pi$
$571$	−2.08633e12	−0.821336	−0.410668	+	0.911785i	$0.634704\pi$
$572$	3.07352e12	1.20048
$573$	2.12147e12	0.822130
$574$	1.36910e11	0.0526420
$575$	1.42409e12	0.543291
$576$	−8.25924e11	−0.312636
$577$	9.10416e11	0.341939	0.170970	−	0.985276i	$-0.445310\pi$
$577$	9.10416e11	0.341939	0.170970	+	0.985276i	$0.445310\pi$
$578$	1.18388e11	0.0441198
$579$	2.10314e12	0.777704
$580$	−7.29469e10	−0.0267658
$581$	8.95613e11	0.326083
$582$	−1.73825e11	−0.0627999
$583$	1.68026e12	0.602378
$584$	8.20639e10	0.0291941
$585$	−5.15746e10	−0.0182068
$586$	4.83691e11	0.169445
$587$	−4.36065e12	−1.51593	−0.757966	−	0.652294i	$-0.773807\pi$
$587$	−4.36065e12	−1.51593	−0.757966	+	0.652294i	$0.773807\pi$
$588$	1.50719e12	0.519960
$589$	1.63007e12	0.558070
$590$	−1.86172e9	−0.000632530 0
$591$	−9.03890e10	−0.0304770
$592$	5.23651e12	1.75224
$593$	−4.56249e12	−1.51515	−0.757575	−	0.652748i	$-0.773616\pi$
$593$	−4.56249e12	−1.51515	−0.757575	+	0.652748i	$0.773616\pi$
$594$	−6.30116e10	−0.0207674
$595$	5.21585e10	0.0170608
$596$	−3.35236e12	−1.08828
$597$	2.41701e12	0.778743
$598$	−1.99844e11	−0.0639052
$599$	4.09645e12	1.30013	0.650066	−	0.759878i	$-0.274741\pi$
$599$	4.09645e12	1.30013	0.650066	+	0.759878i	$0.274741\pi$
$600$	3.71732e11	0.117098
$601$	−2.16427e12	−0.676670	−0.338335	−	0.941026i	$-0.609864\pi$
$601$	−2.16427e12	−0.676670	−0.338335	+	0.941026i	$0.609864\pi$
$602$	8.75494e10	0.0271687
$603$	4.85434e11	0.149521
$604$	4.79795e12	1.46686
$605$	−1.80931e10	−0.00549053
$606$	−2.05927e11	−0.0620278
$607$	−5.62833e12	−1.68279	−0.841397	−	0.540418i	$-0.818266\pi$
$607$	−5.62833e12	−1.68279	−0.841397	+	0.540418i	$0.818266\pi$
$608$	3.87664e11	0.115051
$609$	3.34247e11	0.0984669
$610$	1.37322e10	0.00401564
$611$	−2.70159e12	−0.784212
$612$	−1.36976e12	−0.394698
$613$	−5.37170e12	−1.53653	−0.768263	−	0.640135i	$-0.778878\pi$
$613$	−5.37170e12	−1.53653	−0.768263	+	0.640135i	$0.778878\pi$
$614$	3.55959e11	0.101075
$615$	1.67364e11	0.0471763
$616$	−2.30048e11	−0.0643731
$617$	5.20100e12	1.44479	0.722393	−	0.691482i	$-0.243042\pi$
$617$	5.20100e12	1.44479	0.722393	+	0.691482i	$0.243042\pi$
$618$	2.45656e10	0.00677453
$619$	3.02993e12	0.829515	0.414757	−	0.909932i	$-0.363866\pi$
$619$	3.02993e12	0.829515	0.414757	+	0.909932i	$0.363866\pi$
$620$	2.53841e11	0.0689920
$621$	−3.88371e11	−0.104793
$622$	−6.46711e10	−0.0173242
$623$	−3.90667e11	−0.103899
$624$	2.43324e12	0.642471
$625$	3.78884e12	0.993221
$626$	4.97008e11	0.129354
$627$	−8.98203e11	−0.232098
$628$	−5.58010e12	−1.43161
$629$	8.49641e12	2.16425
$630$	1.92000e9	0.000485590 0
$631$	−7.43674e11	−0.186746	−0.0933728	−	0.995631i	$-0.529765\pi$
$631$	−7.43674e11	−0.186746	−0.0933728	+	0.995631i	$0.529765\pi$
$632$	1.06406e12	0.265301
$633$	−3.67213e12	−0.909077
$634$	5.39383e11	0.132585
$635$	2.21351e11	0.0540255
$636$	1.34456e12	0.325854
$637$	−4.34410e12	−1.04538
$638$	2.56876e11	0.0613805
$639$	2.46231e12	0.584237
$640$	8.03461e10	0.0189302
$641$	−2.70635e12	−0.633175	−0.316587	−	0.948563i	$-0.602537\pi$
$641$	−2.70635e12	−0.633175	−0.316587	+	0.948563i	$0.602537\pi$
$642$	2.65392e11	0.0616566
$643$	7.61624e12	1.75708	0.878540	−	0.477670i	$-0.158518\pi$
$643$	7.61624e12	1.75708	0.878540	+	0.477670i	$0.158518\pi$
$644$	−7.05227e11	−0.161563
$645$	1.07023e11	0.0243478
$646$	2.05982e11	0.0465353
$647$	3.39864e12	0.762492	0.381246	−	0.924474i	$-0.375495\pi$
$647$	3.39864e12	0.762492	0.381246	+	0.924474i	$0.375495\pi$
$648$	−1.01377e11	−0.0225866
$649$	−6.21445e11	−0.137500
$650$	−5.32901e11	−0.117095
$651$	−1.16312e12	−0.253810
$652$	−2.01435e12	−0.436537
$653$	−7.24539e12	−1.55938	−0.779690	−	0.626165i	$-0.784624\pi$
$653$	−7.24539e12	−1.55938	−0.779690	+	0.626165i	$0.784624\pi$
$654$	4.03744e10	0.00862990
$655$	3.98248e11	0.0845412
$656$	−7.89606e12	−1.66473
$657$	−2.28625e11	−0.0478719
$658$	1.00574e11	0.0209155
$659$	−5.42798e12	−1.12113	−0.560563	−	0.828112i	$-0.689415\pi$
$659$	−5.42798e12	−1.12113	−0.560563	+	0.828112i	$0.689415\pi$
$660$	−1.39871e11	−0.0286933
$661$	−1.19116e12	−0.242697	−0.121349	−	0.992610i	$-0.538722\pi$
$661$	−1.19116e12	−0.242697	−0.121349	+	0.992610i	$0.538722\pi$
$662$	−3.06336e11	−0.0619921
$663$	3.94801e12	0.793537
$664$	1.10737e12	0.221074
$665$	2.73688e10	0.00542699
$666$	3.12761e11	0.0615997
$667$	1.58325e12	0.309730
$668$	6.00346e12	1.16656
$669$	3.48203e12	0.672071
$670$	−1.13675e10	−0.00217937
$671$	4.58382e12	0.872923
$672$	−2.76612e11	−0.0523249
$673$	3.67244e12	0.690060	0.345030	−	0.938592i	$-0.387869\pi$
$673$	3.67244e12	0.690060	0.345030	+	0.938592i	$0.387869\pi$
$674$	−8.73628e11	−0.163064
$675$	−1.03562e12	−0.192015
$676$	−1.71595e12	−0.316042
$677$	1.04927e13	1.91972	0.959860	−	0.280479i	$-0.0904932\pi$
$677$	1.04927e13	1.91972	0.959860	+	0.280479i	$0.0904932\pi$
$678$	−1.73111e11	−0.0314624
$679$	1.76800e12	0.319203
$680$	6.44908e10	0.0115666
$681$	−3.81147e12	−0.679094
$682$	−8.93877e11	−0.158215
$683$	−8.23433e12	−1.44789	−0.723944	−	0.689858i	$-0.757673\pi$
$683$	−8.23433e12	−1.44789	−0.723944	+	0.689858i	$0.757673\pi$
$684$	−7.18749e11	−0.125552
$685$	6.49542e10	0.0112720
$686$	3.39417e11	0.0585161
$687$	2.15404e12	0.368934
$688$	−5.04925e12	−0.859170
$689$	−3.87536e12	−0.655127
$690$	9.09459e9	0.00152743
$691$	−6.64111e11	−0.110813	−0.0554063	−	0.998464i	$-0.517645\pi$
$691$	−6.64111e11	−0.110813	−0.0554063	+	0.998464i	$0.517645\pi$
$692$	7.85869e12	1.30278
$693$	6.40899e11	0.105558
$694$	−1.18769e12	−0.194351
$695$	4.08920e11	0.0664825
$696$	4.13277e11	0.0667574
$697$	−1.28116e13	−2.05616
$698$	1.10306e12	0.175894
$699$	−2.26237e12	−0.358440
$700$	−1.88055e12	−0.296035
$701$	−1.00530e13	−1.57241	−0.786205	−	0.617966i	$-0.787957\pi$
$701$	−1.00530e13	−1.57241	−0.786205	+	0.617966i	$0.787957\pi$
$702$	1.45330e11	0.0225859
$703$	4.45827e12	0.688443
$704$	6.45602e12	0.990576
$705$	1.22945e11	0.0187439
$706$	3.64427e11	0.0552064
$707$	2.09451e12	0.315279
$708$	−4.97285e11	−0.0743799
$709$	−8.17137e12	−1.21447	−0.607235	−	0.794522i	$-0.707721\pi$
$709$	−8.17137e12	−1.21447	−0.607235	+	0.794522i	$0.707721\pi$
$710$	−5.76607e10	−0.00851564
$711$	−2.96441e12	−0.435036
$712$	−4.83036e11	−0.0704401
$713$	−5.50939e12	−0.798364
$714$	−1.46975e11	−0.0211642
$715$	4.03144e11	0.0576877
$716$	1.03656e13	1.47396
$717$	−5.20872e12	−0.736029
$718$	−2.71412e11	−0.0381127
$719$	−3.94171e12	−0.550054	−0.275027	−	0.961437i	$-0.588687\pi$
$719$	−3.94171e12	−0.550054	−0.275027	+	0.961437i	$0.588687\pi$
$720$	−1.10733e11	−0.0153561
$721$	−2.49860e11	−0.0344341
$722$	−6.37941e11	−0.0873701
$723$	−1.99323e12	−0.271290
$724$	6.36704e12	0.861219
$725$	4.22187e12	0.567523
$726$	5.09838e10	0.00681111
$727$	3.78831e12	0.502968	0.251484	−	0.967861i	$-0.419081\pi$
$727$	3.78831e12	0.502968	0.251484	+	0.967861i	$0.419081\pi$
$728$	5.30582e11	0.0700102
$729$	2.82430e11	0.0370370
$730$	5.35379e9	0.000697764 0
$731$	−8.19258e12	−1.06119
$732$	3.66800e12	0.472204
$733$	1.11628e13	1.42825	0.714126	−	0.700017i	$-0.246824\pi$
$733$	1.11628e13	1.42825	0.714126	+	0.700017i	$0.246824\pi$
$734$	7.12829e11	0.0906469
$735$	1.97693e11	0.0249861
$736$	−1.31024e12	−0.164589
$737$	−3.79450e12	−0.473752
$738$	−4.71608e11	−0.0585231
$739$	−5.41764e12	−0.668205	−0.334103	−	0.942537i	$-0.608433\pi$
$739$	−5.41764e12	−0.668205	−0.334103	+	0.942537i	$0.608433\pi$
$740$	6.94258e11	0.0851095
$741$	2.07162e12	0.252422
$742$	1.44271e11	0.0174727
$743$	7.35609e12	0.885518	0.442759	−	0.896641i	$-0.354000\pi$
$743$	7.35609e12	0.885518	0.442759	+	0.896641i	$0.354000\pi$
$744$	−1.43812e12	−0.172075
$745$	−4.39718e11	−0.0522963
$746$	−1.33018e12	−0.157249
$747$	−3.08507e12	−0.362512
$748$	1.07071e13	1.25059
$749$	−2.69934e12	−0.313393
$750$	4.85580e10	0.00560383
$751$	−1.05347e13	−1.20849	−0.604245	−	0.796798i	$-0.706525\pi$
$751$	−1.05347e13	−1.20849	−0.604245	+	0.796798i	$0.706525\pi$
$752$	−5.80042e12	−0.661423
$753$	−1.63806e12	−0.185675
$754$	−5.92458e11	−0.0667555
$755$	6.29332e11	0.0704885
$756$	5.12853e11	0.0571011
$757$	9.67726e12	1.07108	0.535539	−	0.844511i	$-0.320109\pi$
$757$	9.67726e12	1.07108	0.535539	+	0.844511i	$0.320109\pi$
$758$	6.73456e11	0.0740965
$759$	3.03578e12	0.332034
$760$	3.38399e10	0.00367932
$761$	−8.20057e12	−0.886366	−0.443183	−	0.896431i	$-0.646151\pi$
$761$	−8.20057e12	−0.886366	−0.443183	+	0.896431i	$0.646151\pi$
$762$	−6.23735e11	−0.0670197
$763$	−4.10653e11	−0.0438647
$764$	−1.32698e13	−1.40910
$765$	−1.79668e11	−0.0189668
$766$	−1.50774e12	−0.158233
$767$	1.43330e12	0.149540
$768$	4.99425e12	0.518018
$769$	3.67559e12	0.379016	0.189508	−	0.981879i	$-0.439311\pi$
$769$	3.67559e12	0.379016	0.189508	+	0.981879i	$0.439311\pi$
$770$	−1.50081e10	−0.00153857
$771$	5.42684e12	0.553098
$772$	−1.31551e13	−1.33296
$773$	9.52868e12	0.959898	0.479949	−	0.877297i	$-0.340655\pi$
$773$	9.52868e12	0.959898	0.479949	+	0.877297i	$0.340655\pi$
$774$	−3.01577e11	−0.0302039
$775$	−1.46913e13	−1.46286
$776$	2.18602e12	0.216410
$777$	−3.18114e12	−0.313103
$778$	5.36656e10	0.00525155
$779$	−6.72256e12	−0.654058
$780$	3.22599e11	0.0312059
$781$	−1.92472e13	−1.85113
$782$	−6.96186e11	−0.0665725
$783$	−1.15137e12	−0.109467
$784$	−9.32697e12	−0.881695
$785$	−7.31924e11	−0.0687943
$786$	−1.12221e12	−0.104875
$787$	1.32251e13	1.22889	0.614444	−	0.788961i	$-0.289380\pi$
$787$	1.32251e13	1.22889	0.614444	+	0.788961i	$0.289380\pi$
$788$	5.65383e11	0.0522366
$789$	4.74369e12	0.435783
$790$	6.94185e10	0.00634094
$791$	1.76074e12	0.159919
$792$	7.92433e11	0.0715647
$793$	−1.05721e13	−0.949363
$794$	−6.80832e11	−0.0607921
$795$	1.76362e11	0.0156586
$796$	−1.51184e13	−1.33474
$797$	6.09773e12	0.535311	0.267655	−	0.963515i	$-0.413751\pi$
$797$	6.09773e12	0.535311	0.267655	+	0.963515i	$0.413751\pi$
$798$	−7.71215e10	−0.00673229
$799$	−9.41137e12	−0.816944
$800$	−3.49387e12	−0.301580
$801$	1.34571e12	0.115506
$802$	−1.45193e12	−0.123926
$803$	1.78710e12	0.151680
$804$	−3.03639e12	−0.256274
$805$	−9.25023e10	−0.00776375
$806$	2.06164e12	0.172070
$807$	3.92990e11	0.0326175
$808$	2.58973e12	0.213749
$809$	1.66134e13	1.36361	0.681806	−	0.731533i	$-0.261195\pi$
$809$	1.66134e13	1.36361	0.681806	+	0.731533i	$0.261195\pi$
$810$	−6.61374e9	−0.000539839 0
$811$	−9.14648e12	−0.742438	−0.371219	−	0.928545i	$-0.621060\pi$
$811$	−9.14648e12	−0.742438	−0.371219	+	0.928545i	$0.621060\pi$
$812$	−2.09072e12	−0.168769
$813$	1.30852e13	1.05044
$814$	−2.44477e12	−0.195176
$815$	−2.64216e11	−0.0209773
$816$	8.47654e12	0.669288
$817$	−4.29885e12	−0.337561
$818$	8.03199e11	0.0627239
$819$	−1.47817e12	−0.114801
$820$	−1.04686e12	−0.0808587
$821$	1.42232e12	0.109258	0.0546289	−	0.998507i	$-0.482602\pi$
$821$	1.42232e12	0.109258	0.0546289	+	0.998507i	$0.482602\pi$
$822$	−1.83032e11	−0.0139831
$823$	−6.31868e12	−0.480095	−0.240048	−	0.970761i	$-0.577163\pi$
$823$	−6.31868e12	−0.480095	−0.240048	+	0.970761i	$0.577163\pi$
$824$	−3.08937e11	−0.0233452
$825$	8.09518e12	0.608392
$826$	−5.33585e10	−0.00398835
$827$	1.17040e13	0.870081	0.435040	−	0.900411i	$-0.356734\pi$
$827$	1.17040e13	0.870081	0.435040	+	0.900411i	$0.356734\pi$
$828$	2.42926e12	0.179613
$829$	−6.67758e12	−0.491048	−0.245524	−	0.969391i	$-0.578960\pi$
$829$	−6.67758e12	−0.491048	−0.245524	+	0.969391i	$0.578960\pi$
$830$	7.22441e10	0.00528385
$831$	−7.69252e12	−0.559582
$832$	−1.48902e13	−1.07732
$833$	−1.51333e13	−1.08901
$834$	−1.15228e12	−0.0824728
$835$	7.87455e11	0.0560579
$836$	5.61826e12	0.397808
$837$	4.00652e12	0.282165
$838$	3.67438e11	0.0257386
$839$	−2.68487e11	−0.0187066	−0.00935330	−	0.999956i	$-0.502977\pi$
$839$	−2.68487e11	−0.0187066	−0.00935330	+	0.999956i	$0.502977\pi$
$840$	−2.41459e10	−0.00167335
$841$	−9.81344e12	−0.676456
$842$	2.24208e12	0.153726
$843$	1.14854e12	0.0783290
$844$	2.29692e13	1.55813
$845$	−2.25076e11	−0.0151871
$846$	−3.46442e11	−0.0232522
$847$	−5.18564e11	−0.0346200
$848$	−8.32057e12	−0.552550
$849$	4.25826e12	0.281286
$850$	−1.85644e12	−0.121982
$851$	−1.50683e13	−0.984873
$852$	−1.54018e13	−1.00136
$853$	−8.26573e12	−0.534577	−0.267289	−	0.963617i	$-0.586128\pi$
$853$	−8.26573e12	−0.534577	−0.267289	+	0.963617i	$0.586128\pi$
$854$	3.93576e11	0.0253202
$855$	−9.42760e10	−0.00603328
$856$	−3.33756e12	−0.212470
$857$	−2.19334e13	−1.38897	−0.694484	−	0.719508i	$-0.744367\pi$
$857$	−2.19334e13	−1.38897	−0.694484	+	0.719508i	$0.744367\pi$
$858$	−1.13600e12	−0.0715627
$859$	3.54754e12	0.222309	0.111155	−	0.993803i	$-0.464545\pi$
$859$	3.54754e12	0.222309	0.111155	+	0.993803i	$0.464545\pi$
$860$	−6.69431e11	−0.0417314
$861$	4.79679e12	0.297465
$862$	−1.16534e12	−0.0718900
$863$	1.86855e13	1.14672	0.573359	−	0.819304i	$-0.305640\pi$
$863$	1.86855e13	1.14672	0.573359	+	0.819304i	$0.305640\pi$
$864$	9.52830e11	0.0581706
$865$	1.03080e12	0.0626039
$866$	1.25798e12	0.0760050
$867$	4.14785e12	0.249309
$868$	7.27529e12	0.435022
$869$	2.31720e13	1.37840
$870$	2.69619e10	0.00159556
$871$	8.75163e12	0.515237
$872$	−5.07748e11	−0.0297388
$873$	−6.09013e12	−0.354864
$874$	−3.65306e11	−0.0211766
$875$	−4.93890e11	−0.0284835
$876$	1.43005e12	0.0820509
$877$	7.73856e12	0.441735	0.220868	−	0.975304i	$-0.429111\pi$
$877$	7.73856e12	0.441735	0.220868	+	0.975304i	$0.429111\pi$
$878$	−2.49615e12	−0.141757
$879$	1.69466e13	0.957486
$880$	8.65568e11	0.0486552
$881$	−2.62226e13	−1.46651	−0.733254	−	0.679954i	$-0.762000\pi$
$881$	−2.62226e13	−1.46651	−0.733254	+	0.679954i	$0.762000\pi$
$882$	−5.57072e11	−0.0309958
$883$	1.14258e13	0.632503	0.316251	−	0.948675i	$-0.397576\pi$
$883$	1.14258e13	0.632503	0.316251	+	0.948675i	$0.397576\pi$
$884$	−2.46948e13	−1.36010
$885$	−6.52273e10	−0.00357425
$886$	1.68629e12	0.0919350
$887$	2.65841e13	1.44200	0.721001	−	0.692934i	$-0.243682\pi$
$887$	2.65841e13	1.44200	0.721001	+	0.692934i	$0.243682\pi$
$888$	−3.93328e12	−0.212274
$889$	6.34409e12	0.340653
$890$	−3.15129e10	−0.00168358
$891$	−2.20767e12	−0.117351
$892$	−2.17801e13	−1.15191
$893$	−4.93838e12	−0.259868
$894$	1.23906e12	0.0648746
$895$	1.35962e12	0.0708296
$896$	2.30279e12	0.119362
$897$	−7.00173e12	−0.361110
$898$	9.40524e11	0.0482643
$899$	−1.63332e13	−0.833973
$900$	6.47783e12	0.329108
$901$	−1.35004e13	−0.682472
$902$	3.68642e12	0.185428
$903$	3.06738e12	0.153523
$904$	2.17704e12	0.108420
$905$	8.35144e11	0.0413850
$906$	−1.77337e12	−0.0874424
$907$	5.90778e12	0.289862	0.144931	−	0.989442i	$-0.453704\pi$
$907$	5.90778e12	0.289862	0.144931	+	0.989442i	$0.453704\pi$
$908$	2.38407e13	1.16395
$909$	−7.21485e12	−0.350502
$910$	3.46148e10	0.00167331
$911$	−2.75232e13	−1.32393	−0.661967	−	0.749533i	$-0.730278\pi$
$911$	−2.75232e13	−1.32393	−0.661967	+	0.749533i	$0.730278\pi$
$912$	4.44785e12	0.212899
$913$	2.41152e13	1.14861
$914$	1.91524e12	0.0907750
$915$	4.81120e11	0.0226913
$916$	−1.34735e13	−0.632341
$917$	1.14141e13	0.533066
$918$	5.06278e11	0.0235287
$919$	−2.28256e13	−1.05561	−0.527804	−	0.849366i	$-0.676984\pi$
$919$	−2.28256e13	−1.05561	−0.527804	+	0.849366i	$0.676984\pi$
$920$	−1.14373e11	−0.00526357
$921$	1.24714e13	0.571144
$922$	−3.96126e12	−0.180528
$923$	4.43917e13	2.01323
$924$	−4.00883e12	−0.180923
$925$	−4.01808e13	−1.80460
$926$	2.73704e12	0.122330
$927$	8.60681e11	0.0382810
$928$	−3.88435e12	−0.171930
$929$	1.55548e13	0.685161	0.342580	−	0.939489i	$-0.388699\pi$
$929$	1.55548e13	0.685161	0.342580	+	0.939489i	$0.388699\pi$
$930$	−9.38220e10	−0.00411274
$931$	−7.94082e12	−0.346411
$932$	1.41511e13	0.614356
$933$	−2.26581e12	−0.0978942
$934$	−2.31245e12	−0.0994288
$935$	1.40441e12	0.0600956
$936$	−1.82767e12	−0.0778316
$937$	1.18680e13	0.502980	0.251490	−	0.967860i	$-0.419079\pi$
$937$	1.18680e13	0.502980	0.251490	+	0.967860i	$0.419079\pi$
$938$	−3.25803e11	−0.0137418
$939$	1.74132e13	0.730941
$940$	−7.69021e11	−0.0321264
$941$	1.60605e13	0.667736	0.333868	−	0.942620i	$-0.391646\pi$
$941$	1.60605e13	0.667736	0.333868	+	0.942620i	$0.391646\pi$
$942$	2.06246e12	0.0853407
$943$	2.27212e13	0.935683
$944$	3.07736e12	0.126126
$945$	6.72692e10	0.00274393
$946$	2.35734e12	0.0957001
$947$	4.70957e13	1.90286	0.951430	−	0.307866i	$-0.0996149\pi$
$947$	4.70957e13	1.90286	0.951430	+	0.307866i	$0.0996149\pi$
$948$	1.85424e13	0.745639
$949$	−4.12177e12	−0.164963
$950$	−9.74120e11	−0.0388022
$951$	1.88978e13	0.749202
$952$	1.84836e12	0.0729324
$953$	−8.41327e12	−0.330405	−0.165203	−	0.986260i	$-0.552828\pi$
$953$	−8.41327e12	−0.330405	−0.165203	+	0.986260i	$0.552828\pi$
$954$	−4.96962e11	−0.0194248
$955$	−1.74055e12	−0.0677130
$956$	3.25806e13	1.26153
$957$	8.99990e12	0.346844
$958$	−4.32952e12	−0.166071
$959$	1.86164e12	0.0710742
$960$	6.77628e11	0.0257496
$961$	3.03966e13	1.14966
$962$	5.63861e12	0.212268
$963$	9.29827e12	0.348404
$964$	1.24676e13	0.464983
$965$	−1.72552e12	−0.0640540
$966$	2.60659e11	0.00963108
$967$	−4.14309e12	−0.152372	−0.0761861	−	0.997094i	$-0.524274\pi$
$967$	−4.14309e12	−0.152372	−0.0761861	+	0.997094i	$0.524274\pi$
$968$	−6.41172e11	−0.0234712
$969$	7.21678e12	0.262958
$970$	1.42614e11	0.00517238
$971$	−1.40316e13	−0.506546	−0.253273	−	0.967395i	$-0.581507\pi$
$971$	−1.40316e13	−0.506546	−0.253273	+	0.967395i	$0.581507\pi$
$972$	−1.76660e12	−0.0634803
$973$	1.17200e13	0.419199
$974$	−3.68310e12	−0.131129
$975$	−1.86707e13	−0.661669
$976$	−2.26988e13	−0.800716
$977$	−1.55480e13	−0.545945	−0.272972	−	0.962022i	$-0.588007\pi$
$977$	−1.55480e13	−0.545945	−0.272972	+	0.962022i	$0.588007\pi$
$978$	7.44523e11	0.0260227
$979$	−1.05191e13	−0.365978
$980$	−1.23657e12	−0.0428255
$981$	1.41456e12	0.0487652
$982$	−1.63709e12	−0.0561784
$983$	4.09312e13	1.39818	0.699090	−	0.715033i	$-0.253589\pi$
$983$	4.09312e13	1.39818	0.699090	+	0.715033i	$0.253589\pi$
$984$	5.93093e12	0.201672
$985$	7.41595e10	0.00251017
$986$	−2.06392e12	−0.0695418
$987$	3.52370e12	0.118188
$988$	−1.29580e13	−0.432644
$989$	1.45294e13	0.482909
$990$	5.16977e10	0.00171046
$991$	3.33333e13	1.09786	0.548930	−	0.835868i	$-0.315035\pi$
$991$	3.33333e13	1.09786	0.548930	+	0.835868i	$0.315035\pi$
$992$	1.35168e13	0.443170
$993$	−1.07328e13	−0.350300
$994$	−1.65260e12	−0.0536945
$995$	−1.98303e12	−0.0641396
$996$	1.92971e13	0.621335
$997$	1.23092e13	0.394548	0.197274	−	0.980348i	$-0.436791\pi$
$997$	1.23092e13	0.394548	0.197274	+	0.980348i	$0.436791\pi$
$998$	−2.11645e12	−0.0675336
$999$	1.09579e13	0.348083

Twists

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

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

\(f(q)\)	\(=\)	\(q+2.31191 q^{2} +81.0000 q^{3} -506.655 q^{4} -66.4563 q^{5} +187.265 q^{6} -1904.69 q^{7} -2355.04 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+2.31191 q^{2} +81.0000 q^{3} -506.655 q^{4} -66.4563 q^{5} +187.265 q^{6} -1904.69 q^{7} -2355.04 q^{8} +6561.00 q^{9} -153.641 q^{10} -51285.5 q^{11} -41039.1 q^{12} +118285. q^{13} -4403.48 q^{14} -5382.96 q^{15} +253963. q^{16} +412063. q^{17} +15168.4 q^{18} +216219. q^{19} +33670.4 q^{20} -154280. q^{21} -118567. q^{22} -730788. q^{23} -190758. q^{24} -1.94871e6 q^{25} +273464. q^{26} +531441. q^{27} +965023. q^{28} -2.16650e6 q^{29} -12444.9 q^{30} +7.53898e6 q^{31} +1.79292e6 q^{32} -4.15413e6 q^{33} +952652. q^{34} +126579. q^{35} -3.32416e6 q^{36} +2.06192e7 q^{37} +499880. q^{38} +9.58108e6 q^{39} +156507. q^{40} -3.10914e7 q^{41} -356682. q^{42} -1.98819e7 q^{43} +2.59841e7 q^{44} -436020. q^{45} -1.68951e6 q^{46} -2.28396e7 q^{47} +2.05710e7 q^{48} -3.67257e7 q^{49} -4.50524e6 q^{50} +3.33771e7 q^{51} -5.99297e7 q^{52} -3.27629e7 q^{53} +1.22864e6 q^{54} +3.40825e6 q^{55} +4.48562e6 q^{56} +1.75138e7 q^{57} -5.00874e6 q^{58} +1.21174e7 q^{59} +2.72731e6 q^{60} -8.93784e7 q^{61} +1.74294e7 q^{62} -1.24967e7 q^{63} -1.25884e8 q^{64} -7.86078e6 q^{65} -9.60396e6 q^{66} +7.39877e7 q^{67} -2.08774e8 q^{68} -5.91938e7 q^{69} +292639. q^{70} +3.75295e8 q^{71} -1.54514e7 q^{72} -3.48461e7 q^{73} +4.76697e7 q^{74} -1.57845e8 q^{75} -1.09549e8 q^{76} +9.76832e7 q^{77} +2.21506e7 q^{78} -4.51823e8 q^{79} -1.68774e7 q^{80} +4.30467e7 q^{81} -7.18804e7 q^{82} -4.70214e8 q^{83} +7.81668e7 q^{84} -2.73842e7 q^{85} -4.59651e7 q^{86} -1.75486e8 q^{87} +1.20779e8 q^{88} +2.05108e8 q^{89} -1.00804e6 q^{90} -2.25297e8 q^{91} +3.70257e8 q^{92} +6.10657e8 q^{93} -5.28032e7 q^{94} -1.43692e7 q^{95} +1.45226e8 q^{96} -9.28232e8 q^{97} -8.49066e7 q^{98} -3.36484e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9}+O(q^{10}) \) 21 * q - 66 * q^2 + 1701 * q^3 + 5206 * q^4 - 2964 * q^5 - 5346 * q^6 - 30775 * q^7 - 24621 * q^8 + 137781 * q^9	\( 21 q - 66 q^{2} + 1701 q^{3} + 5206 q^{4} - 2964 q^{5} - 5346 q^{6} - 30775 q^{7} - 24621 q^{8} + 137781 q^{9} - 54663 q^{10} - 151769 q^{11} + 421686 q^{12} - 153611 q^{13} - 286771 q^{14} - 240084 q^{15} + 805530 q^{16} - 723621 q^{17} - 433026 q^{18} - 549388 q^{19} - 527311 q^{20} - 2492775 q^{21} + 2973158 q^{22} + 169962 q^{23} - 1994301 q^{24} + 8035779 q^{25} - 2337392 q^{26} + 11160261 q^{27} - 22659054 q^{28} - 16845442 q^{29} - 4427703 q^{30} - 19307976 q^{31} - 44923568 q^{32} - 12293289 q^{33} - 35547496 q^{34} - 34882596 q^{35} + 34156566 q^{36} - 41561129 q^{37} - 52335371 q^{38} - 12442491 q^{39} - 125735038 q^{40} - 68169291 q^{41} - 23228451 q^{42} - 25719587 q^{43} - 126277032 q^{44} - 19446804 q^{45} - 292814271 q^{46} - 174095332 q^{47} + 65247930 q^{48} + 7479350 q^{49} - 227877439 q^{50} - 58613301 q^{51} - 232397708 q^{52} - 228390500 q^{53} - 35075106 q^{54} - 29426208 q^{55} + 326778474 q^{56} - 44500428 q^{57} + 480343762 q^{58} + 254464581 q^{59} - 42712191 q^{60} - 183928964 q^{61} - 21753862 q^{62} - 201914775 q^{63} + 310571245 q^{64} + 5308466 q^{65} + 240825798 q^{66} - 82724114 q^{67} - 138336205 q^{68} + 13766922 q^{69} + 1030274876 q^{70} - 404721965 q^{71} - 161538381 q^{72} + 154162574 q^{73} + 36352054 q^{74} + 650898099 q^{75} + 1068940636 q^{76} - 448535481 q^{77} - 189328752 q^{78} + 272529635 q^{79} - 345587859 q^{80} + 903981141 q^{81} - 38412637 q^{82} + 432518643 q^{83} - 1835383374 q^{84} - 126211490 q^{85} - 3699273072 q^{86} - 1364480802 q^{87} + 170111045 q^{88} - 1255621070 q^{89} - 358643943 q^{90} + 1448885849 q^{91} + 1568933320 q^{92} - 1563946056 q^{93} - 1908445164 q^{94} - 2896546490 q^{95} - 3638809008 q^{96} + 1007235486 q^{97} - 9506868248 q^{98} - 995756409 q^{99}+O(q^{100}) \) 21 * q - 66 * q^2 + 1701 * q^3 + 5206 * q^4 - 2964 * q^5 - 5346 * q^6 - 30775 * q^7 - 24621 * q^8 + 137781 * q^9 - 54663 * q^10 - 151769 * q^11 + 421686 * q^12 - 153611 * q^13 - 286771 * q^14 - 240084 * q^15 + 805530 * q^16 - 723621 * q^17 - 433026 * q^18 - 549388 * q^19 - 527311 * q^20 - 2492775 * q^21 + 2973158 * q^22 + 169962 * q^23 - 1994301 * q^24 + 8035779 * q^25 - 2337392 * q^26 + 11160261 * q^27 - 22659054 * q^28 - 16845442 * q^29 - 4427703 * q^30 - 19307976 * q^31 - 44923568 * q^32 - 12293289 * q^33 - 35547496 * q^34 - 34882596 * q^35 + 34156566 * q^36 - 41561129 * q^37 - 52335371 * q^38 - 12442491 * q^39 - 125735038 * q^40 - 68169291 * q^41 - 23228451 * q^42 - 25719587 * q^43 - 126277032 * q^44 - 19446804 * q^45 - 292814271 * q^46 - 174095332 * q^47 + 65247930 * q^48 + 7479350 * q^49 - 227877439 * q^50 - 58613301 * q^51 - 232397708 * q^52 - 228390500 * q^53 - 35075106 * q^54 - 29426208 * q^55 + 326778474 * q^56 - 44500428 * q^57 + 480343762 * q^58 + 254464581 * q^59 - 42712191 * q^60 - 183928964 * q^61 - 21753862 * q^62 - 201914775 * q^63 + 310571245 * q^64 + 5308466 * q^65 + 240825798 * q^66 - 82724114 * q^67 - 138336205 * q^68 + 13766922 * q^69 + 1030274876 * q^70 - 404721965 * q^71 - 161538381 * q^72 + 154162574 * q^73 + 36352054 * q^74 + 650898099 * q^75 + 1068940636 * q^76 - 448535481 * q^77 - 189328752 * q^78 + 272529635 * q^79 - 345587859 * q^80 + 903981141 * q^81 - 38412637 * q^82 + 432518643 * q^83 - 1835383374 * q^84 - 126211490 * q^85 - 3699273072 * q^86 - 1364480802 * q^87 + 170111045 * q^88 - 1255621070 * q^89 - 358643943 * q^90 + 1448885849 * q^91 + 1568933320 * q^92 - 1563946056 * q^93 - 1908445164 * q^94 - 2896546490 * q^95 - 3638809008 * q^96 + 1007235486 * q^97 - 9506868248 * q^98 - 995756409 * q^99

Introduction

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