LMFDB - Embedded newform 177.12.a.d.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,12,Mod(1,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$135.996742959$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q-47.6933 q^{2} +243.000 q^{3} +226.652 q^{4} +10067.2 q^{5} -11589.5 q^{6} +19897.8 q^{7} +86866.1 q^{8} +59049.0 q^{9} +O(q^{10})$	\(q-47.6933 q^{2} +243.000 q^{3} +226.652 q^{4} +10067.2 q^{5} -11589.5 q^{6} +19897.8 q^{7} +86866.1 q^{8} +59049.0 q^{9} -480139. q^{10} -256850. q^{11} +55076.4 q^{12} +1.87281e6 q^{13} -948992. q^{14} +2.44633e6 q^{15} -4.60712e6 q^{16} +3.91960e6 q^{17} -2.81624e6 q^{18} -1.36502e7 q^{19} +2.28175e6 q^{20} +4.83516e6 q^{21} +1.22500e7 q^{22} +4.09884e7 q^{23} +2.11085e7 q^{24} +5.25208e7 q^{25} -8.93203e7 q^{26} +1.43489e7 q^{27} +4.50987e6 q^{28} -2.21762e7 q^{29} -1.16674e8 q^{30} +2.03908e8 q^{31} +4.18268e7 q^{32} -6.24144e7 q^{33} -1.86939e8 q^{34} +2.00315e8 q^{35} +1.33836e7 q^{36} +7.60284e8 q^{37} +6.51025e8 q^{38} +4.55092e8 q^{39} +8.74500e8 q^{40} -1.05040e9 q^{41} -2.30605e8 q^{42} +6.64995e8 q^{43} -5.82155e7 q^{44} +5.94459e8 q^{45} -1.95487e9 q^{46} +1.48540e9 q^{47} -1.11953e9 q^{48} -1.58140e9 q^{49} -2.50489e9 q^{50} +9.52463e8 q^{51} +4.24475e8 q^{52} +9.91182e8 q^{53} -6.84347e8 q^{54} -2.58576e9 q^{55} +1.72844e9 q^{56} -3.31701e9 q^{57} +1.05765e9 q^{58} +7.14924e8 q^{59} +5.54466e8 q^{60} +8.36215e9 q^{61} -9.72503e9 q^{62} +1.17494e9 q^{63} +7.44051e9 q^{64} +1.88539e10 q^{65} +2.97675e9 q^{66} -1.21766e10 q^{67} +8.88385e8 q^{68} +9.96019e9 q^{69} -9.55371e9 q^{70} +4.45588e9 q^{71} +5.12936e9 q^{72} +6.92941e9 q^{73} -3.62604e10 q^{74} +1.27626e10 q^{75} -3.09385e9 q^{76} -5.11074e9 q^{77} -2.17048e10 q^{78} -1.11775e9 q^{79} -4.63809e10 q^{80} +3.48678e9 q^{81} +5.00969e10 q^{82} -6.93121e10 q^{83} +1.09590e9 q^{84} +3.94595e10 q^{85} -3.17158e10 q^{86} -5.38881e9 q^{87} -2.23115e10 q^{88} -4.21667e10 q^{89} -2.83517e10 q^{90} +3.72647e10 q^{91} +9.29011e9 q^{92} +4.95495e10 q^{93} -7.08437e10 q^{94} -1.37420e11 q^{95} +1.01639e10 q^{96} -7.55087e10 q^{97} +7.54224e10 q^{98} -1.51667e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9}+O(q^{10}) $ 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9} + 616281 q^{10} + 1082362 q^{11} + 7099002 q^{12} + 503712 q^{13} + 1321669 q^{14} + 6454566 q^{15} + 34870338 q^{16} + 13513579 q^{17} + 5668704 q^{18} + 35971687 q^{19} + 96105997 q^{20} + 34586919 q^{21} - 47598882 q^{22} + 61380539 q^{23} + 80756433 q^{24} + 294744746 q^{25} + 62820734 q^{26} + 401769396 q^{27} + 148068294 q^{28} + 322339307 q^{29} + 149756283 q^{30} + 151247077 q^{31} + 466383494 q^{32} + 263013966 q^{33} + 684479860 q^{34} + 960297361 q^{35} + 1725057486 q^{36} + 863508437 q^{37} + 992640509 q^{38} + 122402016 q^{39} + 3067680252 q^{40} + 3081170377 q^{41} + 321165567 q^{42} + 2554238300 q^{43} + 4350123570 q^{44} + 1568459538 q^{45} - 1987059155 q^{46} + 6203398333 q^{47} + 8473492134 q^{48} + 10327857997 q^{49} + 17577682253 q^{50} + 3283799697 q^{51} + 32137181618 q^{52} + 14571770754 q^{53} + 1377495072 q^{54} + 18251419334 q^{55} + 33498842836 q^{56} + 8741119941 q^{57} + 11860778276 q^{58} + 20017880372 q^{59} + 23353757271 q^{60} + 2761613771 q^{61} + 13785829526 q^{62} + 8404621317 q^{63} + 86547545293 q^{64} + 32034985256 q^{65} - 11566528326 q^{66} + 39381333296 q^{67} + 38995496621 q^{68} + 14915470977 q^{69} + 8551800364 q^{70} + 26130020296 q^{71} + 19623813219 q^{72} + 41382402799 q^{73} + 23815315058 q^{74} + 71622973278 q^{75} + 10611720128 q^{76} - 8426124313 q^{77} + 15265438362 q^{78} + 59825111206 q^{79} + 4009687655 q^{80} + 97629963228 q^{81} - 39592715115 q^{82} + 35433122727 q^{83} + 35980595442 q^{84} - 8950496085 q^{85} - 182032360688 q^{86} + 78328451601 q^{87} - 220003602335 q^{88} + 102303043039 q^{89} + 36390776769 q^{90} - 111146323655 q^{91} - 163000203526 q^{92} + 36753039711 q^{93} - 81314346008 q^{94} + 208102168887 q^{95} + 113331189042 q^{96} - 171891031490 q^{97} + 72304707792 q^{98} + 63912393738 q^{99}+O(q^{100}) \) 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9 + 616281 * q^10 + 1082362 * q^11 + 7099002 * q^12 + 503712 * q^13 + 1321669 * q^14 + 6454566 * q^15 + 34870338 * q^16 + 13513579 * q^17 + 5668704 * q^18 + 35971687 * q^19 + 96105997 * q^20 + 34586919 * q^21 - 47598882 * q^22 + 61380539 * q^23 + 80756433 * q^24 + 294744746 * q^25 + 62820734 * q^26 + 401769396 * q^27 + 148068294 * q^28 + 322339307 * q^29 + 149756283 * q^30 + 151247077 * q^31 + 466383494 * q^32 + 263013966 * q^33 + 684479860 * q^34 + 960297361 * q^35 + 1725057486 * q^36 + 863508437 * q^37 + 992640509 * q^38 + 122402016 * q^39 + 3067680252 * q^40 + 3081170377 * q^41 + 321165567 * q^42 + 2554238300 * q^43 + 4350123570 * q^44 + 1568459538 * q^45 - 1987059155 * q^46 + 6203398333 * q^47 + 8473492134 * q^48 + 10327857997 * q^49 + 17577682253 * q^50 + 3283799697 * q^51 + 32137181618 * q^52 + 14571770754 * q^53 + 1377495072 * q^54 + 18251419334 * q^55 + 33498842836 * q^56 + 8741119941 * q^57 + 11860778276 * q^58 + 20017880372 * q^59 + 23353757271 * q^60 + 2761613771 * q^61 + 13785829526 * q^62 + 8404621317 * q^63 + 86547545293 * q^64 + 32034985256 * q^65 - 11566528326 * q^66 + 39381333296 * q^67 + 38995496621 * q^68 + 14915470977 * q^69 + 8551800364 * q^70 + 26130020296 * q^71 + 19623813219 * q^72 + 41382402799 * q^73 + 23815315058 * q^74 + 71622973278 * q^75 + 10611720128 * q^76 - 8426124313 * q^77 + 15265438362 * q^78 + 59825111206 * q^79 + 4009687655 * q^80 + 97629963228 * q^81 - 39592715115 * q^82 + 35433122727 * q^83 + 35980595442 * q^84 - 8950496085 * q^85 - 182032360688 * q^86 + 78328451601 * q^87 - 220003602335 * q^88 + 102303043039 * q^89 + 36390776769 * q^90 - 111146323655 * q^91 - 163000203526 * q^92 + 36753039711 * q^93 - 81314346008 * q^94 + 208102168887 * q^95 + 113331189042 * q^96 - 171891031490 * q^97 + 72304707792 * q^98 + 63912393738 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−47.6933	−1.05388	−0.526942	−	0.849901i	$-0.676661\pi$
$2$	−47.6933	−1.05388	−0.526942	+	0.849901i	$0.676661\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	226.652	0.110670
$5$	10067.2	1.44070	0.720352	−	0.693609i	$-0.243980\pi$
$5$	10067.2	1.44070	0.720352	+	0.693609i	$0.243980\pi$
$6$	−11589.5	−0.608460
$7$	19897.8	0.447472	0.223736	−	0.974650i	$-0.428175\pi$
$7$	19897.8	0.447472	0.223736	+	0.974650i	$0.428175\pi$
$8$	86866.1	0.937250
$9$	59049.0	0.333333
$10$	−480139.	−1.51833
$11$	−256850.	−0.480860	−0.240430	−	0.970666i	$-0.577289\pi$
$11$	−256850.	−0.480860	−0.240430	+	0.970666i	$0.577289\pi$
$12$	55076.4	0.0638953
$13$	1.87281e6	1.39896	0.699478	−	0.714654i	$-0.253416\pi$
$13$	1.87281e6	1.39896	0.699478	+	0.714654i	$0.253416\pi$
$14$	−948992.	−0.471583
$15$	2.44633e6	0.831790
$16$	−4.60712e6	−1.09842
$17$	3.91960e6	0.669534	0.334767	−	0.942301i	$-0.391342\pi$
$17$	3.91960e6	0.669534	0.334767	+	0.942301i	$0.391342\pi$
$18$	−2.81624e6	−0.351294
$19$	−1.36502e7	−1.26472	−0.632361	−	0.774674i	$-0.717914\pi$
$19$	−1.36502e7	−1.26472	−0.632361	+	0.774674i	$0.717914\pi$
$20$	2.28175e6	0.159442
$21$	4.83516e6	0.258348
$22$	1.22500e7	0.506771
$23$	4.09884e7	1.32788	0.663939	−	0.747786i	$-0.268883\pi$
$23$	4.09884e7	1.32788	0.663939	+	0.747786i	$0.268883\pi$
$24$	2.11085e7	0.541122
$25$	5.25208e7	1.07563
$26$	−8.93203e7	−1.47434
$27$	1.43489e7	0.192450
$28$	4.50987e6	0.0495217
$29$	−2.21762e7	−0.200769	−0.100385	−	0.994949i	$-0.532007\pi$
$29$	−2.21762e7	−0.200769	−0.100385	+	0.994949i	$0.532007\pi$
$30$	−1.16674e8	−0.876610
$31$	2.03908e8	1.27922	0.639608	−	0.768701i	$-0.279097\pi$
$31$	2.03908e8	1.27922	0.639608	+	0.768701i	$0.279097\pi$
$32$	4.18268e7	0.220359
$33$	−6.24144e7	−0.277625
$34$	−1.86939e8	−0.705611
$35$	2.00315e8	0.644674
$36$	1.33836e7	0.0368900
$37$	7.60284e8	1.80246	0.901231	−	0.433339i	$-0.142665\pi$
$37$	7.60284e8	1.80246	0.901231	+	0.433339i	$0.142665\pi$
$38$	6.51025e8	1.33287
$39$	4.55092e8	0.807688
$40$	8.74500e8	1.35030
$41$	−1.05040e9	−1.41593	−0.707966	−	0.706246i	$-0.750387\pi$
$41$	−1.05040e9	−1.41593	−0.707966	+	0.706246i	$0.750387\pi$
$42$	−2.30605e8	−0.272269
$43$	6.64995e8	0.689830	0.344915	−	0.938634i	$-0.387908\pi$
$43$	6.64995e8	0.689830	0.344915	+	0.938634i	$0.387908\pi$
$44$	−5.82155e7	−0.0532168
$45$	5.94459e8	0.480234
$46$	−1.95487e9	−1.39943
$47$	1.48540e9	0.944725	0.472363	−	0.881404i	$-0.343401\pi$
$47$	1.48540e9	0.944725	0.472363	+	0.881404i	$0.343401\pi$
$48$	−1.11953e9	−0.634174
$49$	−1.58140e9	−0.799769
$50$	−2.50489e9	−1.13358
$51$	9.52463e8	0.386556
$52$	4.24475e8	0.154822
$53$	9.91182e8	0.325564	0.162782	−	0.986662i	$-0.447953\pi$
$53$	9.91182e8	0.325564	0.162782	+	0.986662i	$0.447953\pi$
$54$	−6.84347e8	−0.202820
$55$	−2.58576e9	−0.692777
$56$	1.72844e9	0.419393
$57$	−3.31701e9	−0.730188
$58$	1.05765e9	0.211587
$59$	7.14924e8	0.130189
$59$	7.14924e8	0.130189
$60$	5.54466e8	0.0920542
$61$	8.36215e9	1.26766	0.633832	−	0.773471i	$-0.281481\pi$
$61$	8.36215e9	1.26766	0.633832	+	0.773471i	$0.281481\pi$
$62$	−9.72503e9	−1.34814
$63$	1.17494e9	0.149157
$64$	7.44051e9	0.866190
$65$	1.88539e10	2.01548
$66$	2.97675e9	0.292584
$67$	−1.21766e10	−1.10183	−0.550913	−	0.834563i	$-0.685720\pi$
$67$	−1.21766e10	−1.10183	−0.550913	+	0.834563i	$0.685720\pi$
$68$	8.88385e8	0.0740973
$69$	9.96019e9	0.766651
$70$	−9.55371e9	−0.679411
$71$	4.45588e9	0.293098	0.146549	−	0.989203i	$-0.453183\pi$
$71$	4.45588e9	0.293098	0.146549	+	0.989203i	$0.453183\pi$
$72$	5.12936e9	0.312417
$73$	6.92941e9	0.391219	0.195610	−	0.980682i	$-0.437331\pi$
$73$	6.92941e9	0.391219	0.195610	+	0.980682i	$0.437331\pi$
$74$	−3.62604e10	−1.89958
$75$	1.27626e10	0.621013
$76$	−3.09385e9	−0.139967
$77$	−5.11074e9	−0.215172
$78$	−2.17048e10	−0.851209
$79$	−1.11775e9	−0.0408693	−0.0204346	−	0.999791i	$-0.506505\pi$
$79$	−1.11775e9	−0.0408693	−0.0204346	+	0.999791i	$0.506505\pi$
$80$	−4.63809e10	−1.58250
$81$	3.48678e9	0.111111
$82$	5.00969e10	1.49223
$83$	−6.93121e10	−1.93143	−0.965716	−	0.259600i	$-0.916409\pi$
$83$	−6.93121e10	−1.93143	−0.965716	+	0.259600i	$0.916409\pi$
$84$	1.09590e9	0.0285913
$85$	3.94595e10	0.964600
$86$	−3.17158e10	−0.727000
$87$	−5.38881e9	−0.115914
$88$	−2.23115e10	−0.450687
$89$	−4.21667e10	−0.800432	−0.400216	−	0.916421i	$-0.631065\pi$
$89$	−4.21667e10	−0.800432	−0.400216	+	0.916421i	$0.631065\pi$
$90$	−2.83517e10	−0.506111
$91$	3.72647e10	0.625994
$92$	9.29011e9	0.146956
$93$	4.95495e10	0.738556
$94$	−7.08437e10	−0.995630
$95$	−1.37420e11	−1.82209
$96$	1.01639e10	0.127224
$97$	−7.55087e10	−0.892796	−0.446398	−	0.894835i	$-0.647293\pi$
$97$	−7.55087e10	−0.892796	−0.446398	+	0.894835i	$0.647293\pi$
$98$	7.54224e10	0.842863
$99$	−1.51667e10	−0.160287
$100$	1.19039e10	0.119039
$101$	−1.30355e11	−1.23413	−0.617065	−	0.786912i	$-0.711679\pi$
$101$	−1.30355e11	−1.23413	−0.617065	+	0.786912i	$0.711679\pi$
$102$	−4.54261e10	−0.407385
$103$	−1.76189e11	−1.49752	−0.748762	−	0.662839i	$-0.769351\pi$
$103$	−1.76189e11	−1.49752	−0.748762	+	0.662839i	$0.769351\pi$
$104$	1.62683e11	1.31117
$105$	4.86767e10	0.372203
$106$	−4.72728e10	−0.343106
$107$	1.22677e11	0.845573	0.422787	−	0.906229i	$-0.361052\pi$
$107$	1.22677e11	0.845573	0.422787	+	0.906229i	$0.361052\pi$
$108$	3.25221e9	0.0212984
$109$	6.96262e10	0.433438	0.216719	−	0.976234i	$-0.430464\pi$
$109$	6.96262e10	0.433438	0.216719	+	0.976234i	$0.430464\pi$
$110$	1.23324e11	0.730106
$111$	1.84749e11	1.04065
$112$	−9.16715e10	−0.491513
$113$	8.22738e10	0.420078	0.210039	−	0.977693i	$-0.432641\pi$
$113$	8.22738e10	0.420078	0.210039	+	0.977693i	$0.432641\pi$
$114$	1.58199e11	0.769533
$115$	4.12640e11	1.91308
$116$	−5.02627e9	−0.0222191
$117$	1.10587e11	0.466319
$118$	−3.40971e10	−0.137204
$119$	7.79914e10	0.299598
$120$	2.12504e11	0.779596
$121$	−2.19340e11	−0.768773
$122$	−3.98819e11	−1.33597
$123$	−2.55247e11	−0.817489
$124$	4.62161e10	0.141571
$125$	3.71749e10	0.108954
$126$	−5.60370e10	−0.157194
$127$	3.47214e10	0.0932560	0.0466280	−	0.998912i	$-0.485152\pi$
$127$	3.47214e10	0.0932560	0.0466280	+	0.998912i	$0.485152\pi$
$128$	−4.40524e11	−1.13322
$129$	1.61594e11	0.398273
$130$	−8.99207e11	−2.12408
$131$	3.74267e11	0.847598	0.423799	−	0.905756i	$-0.360696\pi$
$131$	3.74267e11	0.847598	0.423799	+	0.905756i	$0.360696\pi$
$132$	−1.41464e10	−0.0307247
$133$	−2.71609e11	−0.565928
$134$	5.80740e11	1.16120
$135$	1.44454e11	0.277263
$136$	3.40481e11	0.627521
$137$	−8.59009e11	−1.52067	−0.760334	−	0.649532i	$-0.774965\pi$
$137$	−8.59009e11	−1.52067	−0.760334	+	0.649532i	$0.774965\pi$
$138$	−4.75035e11	−0.807961
$139$	6.85989e11	1.12134	0.560668	−	0.828040i	$-0.310544\pi$
$139$	6.85989e11	1.12134	0.560668	+	0.828040i	$0.310544\pi$
$140$	4.54019e10	0.0713460
$141$	3.60952e11	0.545437
$142$	−2.12516e11	−0.308891
$143$	−4.81029e11	−0.672703
$144$	−2.72046e11	−0.366141
$145$	−2.23252e11	−0.289249
$146$	−3.30486e11	−0.412300
$147$	−3.84281e11	−0.461747
$148$	1.72320e11	0.199478
$149$	1.04015e12	1.16030	0.580152	−	0.814508i	$-0.302993\pi$
$149$	1.04015e12	1.16030	0.580152	+	0.814508i	$0.302993\pi$
$150$	−6.08688e11	−0.654475
$151$	5.73329e11	0.594335	0.297167	−	0.954825i	$-0.403958\pi$
$151$	5.73329e11	0.594335	0.297167	+	0.954825i	$0.403958\pi$
$152$	−1.18574e12	−1.18536
$153$	2.31449e11	0.223178
$154$	2.43748e11	0.226766
$155$	2.05278e12	1.84297
$156$	1.03147e11	0.0893867
$157$	−1.08917e10	−0.00911269	−0.00455635	−	0.999990i	$-0.501450\pi$
$157$	−1.08917e10	−0.00911269	−0.00455635	+	0.999990i	$0.501450\pi$
$158$	5.33094e10	0.0430714
$159$	2.40857e11	0.187964
$160$	4.21080e11	0.317471
$161$	8.15580e11	0.594188
$162$	−1.66296e11	−0.117098
$163$	2.44839e12	1.66667	0.833335	−	0.552769i	$-0.186429\pi$
$163$	2.44839e12	1.66667	0.833335	+	0.552769i	$0.186429\pi$
$164$	−2.38075e11	−0.156701
$165$	−6.28340e11	−0.399975
$166$	3.30572e12	2.03550
$167$	2.37729e12	1.41625	0.708127	−	0.706085i	$-0.249540\pi$
$167$	2.37729e12	1.41625	0.708127	+	0.706085i	$0.249540\pi$
$168$	4.20012e11	0.242137
$169$	1.71524e12	0.957080
$170$	−1.88195e12	−1.01658
$171$	−8.06032e11	−0.421574
$172$	1.50722e11	0.0763434
$173$	7.48267e11	0.367116	0.183558	−	0.983009i	$-0.441239\pi$
$173$	7.48267e11	0.367116	0.183558	+	0.983009i	$0.441239\pi$
$174$	2.57010e11	0.122160
$175$	1.04505e12	0.481312
$176$	1.18334e12	0.528188
$177$	1.73727e11	0.0751646
$178$	2.01107e12	0.843562
$179$	−1.89651e11	−0.0771372	−0.0385686	−	0.999256i	$-0.512280\pi$
$179$	−1.89651e11	−0.0771372	−0.0385686	+	0.999256i	$0.512280\pi$
$180$	1.34735e11	0.0531475
$181$	−1.13759e12	−0.435266	−0.217633	−	0.976031i	$-0.569834\pi$
$181$	−1.13759e12	−0.435266	−0.217633	+	0.976031i	$0.569834\pi$
$182$	−1.77728e12	−0.659724
$183$	2.03200e12	0.731886
$184$	3.56051e12	1.24455
$185$	7.65394e12	2.59681
$186$	−2.36318e12	−0.778352
$187$	−1.00675e12	−0.321953
$188$	3.36669e11	0.104553
$189$	2.85512e11	0.0861160
$190$	6.55401e12	1.92027
$191$	2.41641e12	0.687839	0.343920	−	0.938999i	$-0.388245\pi$
$191$	2.41641e12	0.687839	0.343920	+	0.938999i	$0.388245\pi$
$192$	1.80805e12	0.500095
$193$	−1.61769e12	−0.434841	−0.217421	−	0.976078i	$-0.569764\pi$
$193$	−1.61769e12	−0.434841	−0.217421	+	0.976078i	$0.569764\pi$
$194$	3.60126e12	0.940903
$195$	4.58151e12	1.16364
$196$	−3.58428e11	−0.0885103
$197$	3.30183e12	0.792850	0.396425	−	0.918067i	$-0.370251\pi$
$197$	3.30183e12	0.792850	0.396425	+	0.918067i	$0.370251\pi$
$198$	7.23351e11	0.168924
$199$	−6.57007e12	−1.49238	−0.746188	−	0.665736i	$-0.768118\pi$
$199$	−6.57007e12	−1.49238	−0.746188	+	0.665736i	$0.768118\pi$
$200$	4.56228e12	1.00813
$201$	−2.95890e12	−0.636139
$202$	6.21707e12	1.30063
$203$	−4.41257e11	−0.0898386
$204$	2.15878e11	0.0427801
$205$	−1.05746e13	−2.03994
$206$	8.40303e12	1.57822
$207$	2.42033e12	0.442626
$208$	−8.62823e12	−1.53664
$209$	3.50606e12	0.608155
$210$	−2.32155e12	−0.392258
$211$	9.22870e12	1.51910	0.759551	−	0.650447i	$-0.225419\pi$
$211$	9.22870e12	1.51910	0.759551	+	0.650447i	$0.225419\pi$
$212$	2.24653e11	0.0360301
$213$	1.08278e12	0.169220
$214$	−5.85086e12	−0.891136
$215$	6.69465e12	0.993840
$216$	1.24643e12	0.180374
$217$	4.05731e12	0.572413
$218$	−3.32070e12	−0.456793
$219$	1.68385e12	0.225871
$220$	−5.86068e11	−0.0766696
$221$	7.34065e12	0.936649
$222$	−8.81129e12	−1.09673
$223$	−4.71766e12	−0.572862	−0.286431	−	0.958101i	$-0.592469\pi$
$223$	−4.71766e12	−0.572862	−0.286431	+	0.958101i	$0.592469\pi$
$224$	8.32261e11	0.0986042
$225$	3.10130e12	0.358542
$226$	−3.92391e12	−0.442713
$227$	1.08803e13	1.19812	0.599059	−	0.800705i	$-0.295542\pi$
$227$	1.08803e13	1.19812	0.599059	+	0.800705i	$0.295542\pi$
$228$	−7.51806e11	−0.0808098
$229$	−6.39892e12	−0.671446	−0.335723	−	0.941961i	$-0.608981\pi$
$229$	−6.39892e12	−0.671446	−0.335723	+	0.941961i	$0.608981\pi$
$230$	−1.96802e13	−2.01616
$231$	−1.24191e12	−0.124229
$232$	−1.92636e12	−0.188171
$233$	6.18274e12	0.589826	0.294913	−	0.955524i	$-0.404709\pi$
$233$	6.18274e12	0.589826	0.294913	+	0.955524i	$0.404709\pi$
$234$	−5.27427e12	−0.491446
$235$	1.49539e13	1.36107
$236$	1.62039e11	0.0144080
$237$	−2.71614e11	−0.0235959
$238$	−3.71967e12	−0.315741
$239$	7.82182e12	0.648813	0.324406	−	0.945918i	$-0.394835\pi$
$239$	7.82182e12	0.648813	0.324406	+	0.945918i	$0.394835\pi$
$240$	−1.12705e13	−0.913657
$241$	−2.29486e13	−1.81829	−0.909145	−	0.416480i	$-0.863264\pi$
$241$	−2.29486e13	−1.81829	−0.909145	+	0.416480i	$0.863264\pi$
$242$	1.04610e13	0.810197
$243$	8.47289e11	0.0641500
$244$	1.89530e12	0.140292
$245$	−1.59203e13	−1.15223
$246$	1.21736e13	0.861538
$247$	−2.55642e13	−1.76929
$248$	1.77127e13	1.19895
$249$	−1.68428e13	−1.11511
$250$	−1.77299e12	−0.114825
$251$	1.14535e13	0.725660	0.362830	−	0.931855i	$-0.381810\pi$
$251$	1.14535e13	0.725660	0.362830	+	0.931855i	$0.381810\pi$
$252$	2.66304e11	0.0165072
$253$	−1.05279e13	−0.638524
$254$	−1.65598e12	−0.0982810
$255$	9.58866e12	0.556912
$256$	5.77188e12	0.328093
$257$	1.26561e13	0.704155	0.352077	−	0.935971i	$-0.385475\pi$
$257$	1.26561e13	0.704155	0.352077	+	0.935971i	$0.385475\pi$
$258$	−7.70694e12	−0.419734
$259$	1.51280e13	0.806551
$260$	4.27328e12	0.223053
$261$	−1.30948e12	−0.0669231
$262$	−1.78501e13	−0.893269
$263$	−3.37616e13	−1.65450	−0.827248	−	0.561837i	$-0.810095\pi$
$263$	−3.37616e13	−1.65450	−0.827248	+	0.561837i	$0.810095\pi$
$264$	−5.42170e12	−0.260204
$265$	9.97845e12	0.469041
$266$	1.29540e13	0.596422
$267$	−1.02465e13	−0.462130
$268$	−2.75984e12	−0.121939
$269$	2.88764e13	1.24999	0.624993	−	0.780630i	$-0.285102\pi$
$269$	2.88764e13	1.24999	0.624993	+	0.780630i	$0.285102\pi$
$270$	−6.88947e12	−0.292203
$271$	6.85896e12	0.285054	0.142527	−	0.989791i	$-0.454477\pi$
$271$	6.85896e12	0.285054	0.142527	+	0.989791i	$0.454477\pi$
$272$	−1.80581e13	−0.735431
$273$	9.05532e12	0.361418
$274$	4.09690e13	1.60261
$275$	−1.34899e13	−0.517226
$276$	2.25750e12	0.0848452
$277$	−8.47203e11	−0.0312139	−0.0156070	−	0.999878i	$-0.504968\pi$
$277$	−8.47203e11	−0.0312139	−0.0156070	+	0.999878i	$0.504968\pi$
$278$	−3.27171e13	−1.18176
$279$	1.20405e13	0.426406
$280$	1.74006e13	0.604221
$281$	−3.05709e13	−1.04093	−0.520467	−	0.853882i	$-0.674242\pi$
$281$	−3.05709e13	−1.04093	−0.520467	+	0.853882i	$0.674242\pi$
$282$	−1.72150e13	−0.574827
$283$	7.56230e12	0.247644	0.123822	−	0.992304i	$-0.460485\pi$
$283$	7.56230e12	0.247644	0.123822	+	0.992304i	$0.460485\pi$
$284$	1.00993e12	0.0324371
$285$	−3.33930e13	−1.05198
$286$	2.29419e13	0.708950
$287$	−2.09006e13	−0.633590
$288$	2.46983e12	0.0734528
$289$	−1.89086e13	−0.551724
$290$	1.06476e13	0.304835
$291$	−1.83486e13	−0.515456
$292$	1.57056e12	0.0432962
$293$	6.01099e13	1.62620	0.813101	−	0.582123i	$-0.197778\pi$
$293$	6.01099e13	1.62620	0.813101	+	0.582123i	$0.197778\pi$
$294$	1.83276e13	0.486627
$295$	7.19730e12	0.187564
$296$	6.60429e13	1.68936
$297$	−3.68551e12	−0.0925416
$298$	−4.96082e13	−1.22283
$299$	7.67634e13	1.85764
$300$	2.89266e12	0.0687274
$301$	1.32319e13	0.308679
$302$	−2.73440e13	−0.626359
$303$	−3.16763e13	−0.712526
$304$	6.28882e13	1.38920
$305$	8.41836e13	1.82633
$306$	−1.10385e13	−0.235204
$307$	−4.07056e13	−0.851910	−0.425955	−	0.904744i	$-0.640062\pi$
$307$	−4.07056e13	−0.851910	−0.425955	+	0.904744i	$0.640062\pi$
$308$	−1.15836e12	−0.0238130
$309$	−4.28139e13	−0.864596
$310$	−9.79040e13	−1.94228
$311$	−1.69524e13	−0.330408	−0.165204	−	0.986259i	$-0.552828\pi$
$311$	−1.69524e13	−0.330408	−0.165204	+	0.986259i	$0.552828\pi$
$312$	3.95321e13	0.757006
$313$	−4.57468e13	−0.860730	−0.430365	−	0.902655i	$-0.641615\pi$
$313$	−4.57468e13	−0.860730	−0.430365	+	0.902655i	$0.641615\pi$
$314$	5.19460e11	0.00960372
$315$	1.18284e13	0.214891
$316$	−2.53341e11	−0.00452300
$317$	−9.76435e13	−1.71324	−0.856619	−	0.515950i	$-0.827439\pi$
$317$	−9.76435e13	−1.71324	−0.856619	+	0.515950i	$0.827439\pi$
$318$	−1.14873e13	−0.198093
$319$	5.69594e12	0.0965420
$320$	7.49053e13	1.24792
$321$	2.98104e13	0.488192
$322$	−3.88977e13	−0.626205
$323$	−5.35035e13	−0.846775
$324$	7.90286e11	0.0122967
$325$	9.83612e13	1.50475
$326$	−1.16772e14	−1.75648
$327$	1.69192e13	0.250246
$328$	−9.12440e13	−1.32708
$329$	2.95562e13	0.422738
$330$	2.99676e13	0.421527
$331$	7.91062e13	1.09435	0.547176	−	0.837018i	$-0.315703\pi$
$331$	7.91062e13	1.09435	0.547176	+	0.837018i	$0.315703\pi$
$332$	−1.57097e13	−0.213751
$333$	4.48940e13	0.600821
$334$	−1.13381e14	−1.49257
$335$	−1.22584e14	−1.58740
$336$	−2.22762e13	−0.283775
$337$	−6.52137e13	−0.817287	−0.408643	−	0.912694i	$-0.633998\pi$
$337$	−6.52137e13	−0.817287	−0.408643	+	0.912694i	$0.633998\pi$
$338$	−8.18055e13	−1.00865
$339$	1.99925e13	0.242532
$340$	8.94357e12	0.106752
$341$	−5.23736e13	−0.615125
$342$	3.84424e13	0.444290
$343$	−7.08109e13	−0.805346
$344$	5.77655e13	0.646543
$345$	1.00271e14	1.10452
$346$	−3.56873e13	−0.386897
$347$	1.40426e14	1.49843	0.749215	−	0.662327i	$-0.230431\pi$
$347$	1.40426e14	1.49843	0.749215	+	0.662327i	$0.230431\pi$
$348$	−1.22138e12	−0.0128282
$349$	−9.96355e13	−1.03009	−0.515044	−	0.857164i	$-0.672224\pi$
$349$	−9.96355e13	−1.03009	−0.515044	+	0.857164i	$0.672224\pi$
$350$	−4.98418e13	−0.507247
$351$	2.68727e13	0.269229
$352$	−1.07432e13	−0.105962
$353$	−1.16903e13	−0.113518	−0.0567591	−	0.998388i	$-0.518077\pi$
$353$	−1.16903e13	−0.113518	−0.0567591	+	0.998388i	$0.518077\pi$
$354$	−8.28560e12	−0.0792147
$355$	4.48583e13	0.422267
$356$	−9.55716e12	−0.0885837
$357$	1.89519e13	0.172973
$358$	9.04509e12	0.0812936
$359$	1.09916e14	0.972840	0.486420	−	0.873725i	$-0.338302\pi$
$359$	1.09916e14	0.972840	0.486420	+	0.873725i	$0.338302\pi$
$360$	5.16384e13	0.450100
$361$	6.98385e13	0.599522
$362$	5.42555e13	0.458719
$363$	−5.32996e13	−0.443851
$364$	8.44612e12	0.0692787
$365$	6.97599e13	0.563631
$366$	−9.69129e13	−0.771322
$367$	1.86818e14	1.46472	0.732361	−	0.680917i	$-0.238418\pi$
$367$	1.86818e14	1.46472	0.732361	+	0.680917i	$0.238418\pi$
$368$	−1.88839e14	−1.45857
$369$	−6.20249e13	−0.471978
$370$	−3.65042e14	−2.73674
$371$	1.97223e13	0.145681
$372$	1.12305e13	0.0817359
$373$	−1.50943e14	−1.08247	−0.541233	−	0.840873i	$-0.682042\pi$
$373$	−1.50943e14	−1.08247	−0.541233	+	0.840873i	$0.682042\pi$
$374$	4.80151e13	0.339300
$375$	9.03350e12	0.0629048
$376$	1.29031e14	0.885444
$377$	−4.15316e13	−0.280868
$378$	−1.36170e13	−0.0907562
$379$	6.75399e13	0.443654	0.221827	−	0.975086i	$-0.428798\pi$
$379$	6.75399e13	0.443654	0.221827	+	0.975086i	$0.428798\pi$
$380$	−3.11465e13	−0.201650
$381$	8.43730e12	0.0538414
$382$	−1.15247e14	−0.724902
$383$	1.30035e14	0.806245	0.403123	−	0.915146i	$-0.367925\pi$
$383$	1.30035e14	0.806245	0.403123	+	0.915146i	$0.367925\pi$
$384$	−1.07047e14	−0.654266
$385$	−5.14509e13	−0.309998
$386$	7.71531e13	0.458272
$387$	3.92673e13	0.229943
$388$	−1.71142e13	−0.0988056
$389$	2.60472e13	0.148265	0.0741325	−	0.997248i	$-0.476381\pi$
$389$	2.60472e13	0.148265	0.0741325	+	0.997248i	$0.476381\pi$
$390$	−2.18507e14	−1.22634
$391$	1.60658e14	0.889060
$392$	−1.37370e14	−0.749583
$393$	9.09470e13	0.489361
$394$	−1.57475e14	−0.835571
$395$	−1.12527e13	−0.0588805
$396$	−3.43756e12	−0.0177389
$397$	3.22209e14	1.63980	0.819899	−	0.572508i	$-0.194029\pi$
$397$	3.22209e14	1.63980	0.819899	+	0.572508i	$0.194029\pi$
$398$	3.13348e14	1.57279
$399$	−6.60011e13	−0.326738
$400$	−2.41969e14	−1.18149
$401$	3.46864e14	1.67057	0.835286	−	0.549815i	$-0.185302\pi$
$401$	3.46864e14	1.67057	0.835286	+	0.549815i	$0.185302\pi$
$402$	1.41120e14	0.670417
$403$	3.81879e14	1.78957
$404$	−2.95453e13	−0.136581
$405$	3.51022e13	0.160078
$406$	2.10450e13	0.0946794
$407$	−1.95278e14	−0.866733
$408$	8.27368e13	0.362299
$409$	−1.91290e14	−0.826447	−0.413224	−	0.910630i	$-0.635597\pi$
$409$	−1.91290e14	−0.826447	−0.413224	+	0.910630i	$0.635597\pi$
$410$	5.04337e14	2.14986
$411$	−2.08739e14	−0.877959
$412$	−3.99336e13	−0.165731
$413$	1.42254e13	0.0582559
$414$	−1.15433e14	−0.466476
$415$	−6.97780e14	−2.78262
$416$	7.83335e13	0.308272
$417$	1.66695e14	0.647404
$418$	−1.67215e14	−0.640924
$419$	2.19873e14	0.831755	0.415877	−	0.909421i	$-0.363475\pi$
$419$	2.19873e14	0.831755	0.415877	+	0.909421i	$0.363475\pi$
$420$	1.10327e13	0.0411916
$421$	−1.43384e14	−0.528384	−0.264192	−	0.964470i	$-0.585105\pi$
$421$	−1.43384e14	−0.528384	−0.264192	+	0.964470i	$0.585105\pi$
$422$	−4.40147e14	−1.60096
$423$	8.77115e13	0.314908
$424$	8.61002e13	0.305135
$425$	2.05861e14	0.720168
$426$	−5.16413e13	−0.178338
$427$	1.66388e14	0.567244
$428$	2.78049e13	0.0935795
$429$	−1.16890e14	−0.388385
$430$	−3.19290e14	−1.04739
$431$	5.57672e13	0.180615	0.0903076	−	0.995914i	$-0.471215\pi$
$431$	5.57672e13	0.180615	0.0903076	+	0.995914i	$0.471215\pi$
$432$	−6.61071e13	−0.211391
$433$	−3.40207e14	−1.07414	−0.537069	−	0.843538i	$-0.680468\pi$
$433$	−3.40207e14	−1.07414	−0.537069	+	0.843538i	$0.680468\pi$
$434$	−1.93507e14	−0.603257
$435$	−5.42503e13	−0.166998
$436$	1.57809e13	0.0479685
$437$	−5.59502e14	−1.67940
$438$	−8.03082e13	−0.238041
$439$	3.95069e14	1.15643	0.578213	−	0.815886i	$-0.303750\pi$
$439$	3.95069e14	1.15643	0.578213	+	0.815886i	$0.303750\pi$
$440$	−2.24615e14	−0.649306
$441$	−9.33804e13	−0.266590
$442$	−3.50100e14	−0.987119
$443$	−6.07338e14	−1.69126	−0.845629	−	0.533771i	$-0.820774\pi$
$443$	−6.07338e14	−1.69126	−0.845629	+	0.533771i	$0.820774\pi$
$444$	4.18737e13	0.115169
$445$	−4.24501e14	−1.15318
$446$	2.25001e14	0.603730
$447$	2.52757e14	0.669902
$448$	1.48050e14	0.387596
$449$	6.28780e14	1.62609	0.813043	−	0.582203i	$-0.197809\pi$
$449$	6.28780e14	1.62609	0.813043	+	0.582203i	$0.197809\pi$
$450$	−1.47911e14	−0.377861
$451$	2.69794e14	0.680866
$452$	1.86475e13	0.0464900
$453$	1.39319e14	0.343139
$454$	−5.18918e14	−1.26268
$455$	3.75152e14	0.901871
$456$	−2.88135e14	−0.684368
$457$	8.41019e13	0.197363	0.0986817	−	0.995119i	$-0.468537\pi$
$457$	8.41019e13	0.197363	0.0986817	+	0.995119i	$0.468537\pi$
$458$	3.05185e14	0.707626
$459$	5.62420e13	0.128852
$460$	9.35256e13	0.211720
$461$	−5.29887e14	−1.18530	−0.592650	−	0.805460i	$-0.701918\pi$
$461$	−5.29887e14	−1.18530	−0.592650	+	0.805460i	$0.701918\pi$
$462$	5.92308e13	0.130923
$463$	−5.25570e14	−1.14798	−0.573991	−	0.818862i	$-0.694606\pi$
$463$	−5.25570e14	−1.14798	−0.573991	+	0.818862i	$0.694606\pi$
$464$	1.02168e14	0.220529
$465$	4.98826e14	1.06404
$466$	−2.94876e14	−0.621607
$467$	−7.96126e13	−0.165859	−0.0829295	−	0.996555i	$-0.526428\pi$
$467$	−7.96126e13	−0.165859	−0.0829295	+	0.996555i	$0.526428\pi$
$468$	2.50648e13	0.0516075
$469$	−2.42287e14	−0.493036
$470$	−7.13199e14	−1.43441
$471$	−2.64668e12	−0.00526122
$472$	6.21027e13	0.122020
$473$	−1.70804e14	−0.331712
$474$	1.29542e13	0.0248673
$475$	−7.16921e14	−1.36037
$476$	1.76769e13	0.0331565
$477$	5.85283e13	0.108521
$478$	−3.73048e14	−0.683773
$479$	3.82897e14	0.693803	0.346902	−	0.937902i	$-0.387234\pi$
$479$	3.82897e14	0.693803	0.346902	+	0.937902i	$0.387234\pi$
$480$	1.02322e14	0.183292
$481$	1.42386e15	2.52157
$482$	1.09450e15	1.91627
$483$	1.98186e14	0.343055
$484$	−4.97138e13	−0.0850801
$485$	−7.60162e14	−1.28625
$486$	−4.04100e13	−0.0676066
$487$	1.08358e15	1.79246	0.896231	−	0.443587i	$-0.146294\pi$
$487$	1.08358e15	1.79246	0.896231	+	0.443587i	$0.146294\pi$
$488$	7.26388e14	1.18812
$489$	5.94960e14	0.962252
$490$	7.59294e14	1.21432
$491$	−6.31358e14	−0.998453	−0.499226	−	0.866472i	$-0.666382\pi$
$491$	−6.31358e14	−0.998453	−0.499226	+	0.866472i	$0.666382\pi$
$492$	−5.78521e13	−0.0904714
$493$	−8.69217e13	−0.134422
$494$	1.21924e15	1.86463
$495$	−1.52687e14	−0.230926
$496$	−9.39426e14	−1.40512
$497$	8.86622e13	0.131153
$498$	8.03291e14	1.17520
$499$	2.71326e14	0.392589	0.196295	−	0.980545i	$-0.437109\pi$
$499$	2.71326e14	0.392589	0.196295	+	0.980545i	$0.437109\pi$
$500$	8.42576e12	0.0120580
$501$	5.77681e14	0.817675
$502$	−5.46256e14	−0.764761
$503$	2.14150e14	0.296547	0.148274	−	0.988946i	$-0.452628\pi$
$503$	2.14150e14	0.296547	0.148274	+	0.988946i	$0.452628\pi$
$504$	1.02063e14	0.139798
$505$	−1.31232e15	−1.77802
$506$	5.02109e14	0.672930
$507$	4.16803e14	0.552570
$508$	7.86968e12	0.0103206
$509$	−7.12359e13	−0.0924168	−0.0462084	−	0.998932i	$-0.514714\pi$
$509$	−7.12359e13	−0.0924168	−0.0462084	+	0.998932i	$0.514714\pi$
$510$	−4.57315e14	−0.586920
$511$	1.37880e14	0.175060
$512$	6.26913e14	0.787450
$513$	−1.95866e14	−0.243396
$514$	−6.03612e14	−0.742097
$515$	−1.77373e15	−2.15749
$516$	3.66255e13	0.0440769
$517$	−3.81525e14	−0.454281
$518$	−7.21503e14	−0.850011
$519$	1.81829e14	0.211954
$520$	1.63777e15	1.88901
$521$	5.83431e14	0.665859	0.332929	−	0.942952i	$-0.391963\pi$
$521$	5.83431e14	0.665859	0.332929	+	0.942952i	$0.391963\pi$
$522$	6.24534e13	0.0705291
$523$	−8.94909e14	−1.00005	−0.500023	−	0.866012i	$-0.666675\pi$
$523$	−8.94909e14	−1.00005	−0.500023	+	0.866012i	$0.666675\pi$
$524$	8.48284e13	0.0938036
$525$	2.53947e14	0.277886
$526$	1.61020e15	1.74365
$527$	7.99236e14	0.856479
$528$	2.87551e14	0.304949
$529$	7.27243e14	0.763262
$530$	−4.75905e14	−0.494314
$531$	4.22156e13	0.0433963
$532$	−6.15608e13	−0.0626311
$533$	−1.96719e15	−1.98083
$534$	4.88690e14	0.487031
$535$	1.23501e15	1.21822
$536$	−1.05773e15	−1.03269
$537$	−4.60852e13	−0.0445352
$538$	−1.37721e15	−1.31734
$539$	4.06183e14	0.384577
$540$	3.27407e13	0.0306847
$541$	1.14946e15	1.06637	0.533186	−	0.845998i	$-0.320994\pi$
$541$	1.14946e15	1.06637	0.533186	+	0.845998i	$0.320994\pi$
$542$	−3.27127e14	−0.300414
$543$	−2.76435e14	−0.251301
$544$	1.63944e14	0.147538
$545$	7.00942e14	0.624456
$546$	−4.31878e14	−0.380892
$547$	1.43162e15	1.24996	0.624982	−	0.780639i	$-0.285106\pi$
$547$	1.43162e15	1.24996	0.624982	+	0.780639i	$0.285106\pi$
$548$	−1.94696e14	−0.168292
$549$	4.93777e14	0.422554
$550$	6.43380e14	0.545096
$551$	3.02710e14	0.253917
$552$	8.65203e14	0.718544
$553$	−2.22408e13	−0.0182879
$554$	4.04059e13	0.0328958
$555$	1.85991e15	1.49927
$556$	1.55481e14	0.124098
$557$	1.90773e15	1.50770	0.753848	−	0.657049i	$-0.228196\pi$
$557$	1.90773e15	1.50770	0.753848	+	0.657049i	$0.228196\pi$
$558$	−5.74253e14	−0.449382
$559$	1.24541e15	0.965042
$560$	−9.22877e14	−0.708124
$561$	−2.44640e14	−0.185879
$562$	1.45803e15	1.09702
$563$	−1.75838e15	−1.31014	−0.655070	−	0.755568i	$-0.727361\pi$
$563$	−1.75838e15	−1.31014	−0.655070	+	0.755568i	$0.727361\pi$
$564$	8.18106e13	0.0603635
$565$	8.28269e14	0.605208
$566$	−3.60671e14	−0.260988
$567$	6.93793e13	0.0497191
$568$	3.87065e14	0.274706
$569$	1.20198e15	0.844853	0.422426	−	0.906397i	$-0.361178\pi$
$569$	1.20198e15	0.844853	0.422426	+	0.906397i	$0.361178\pi$
$570$	1.59262e15	1.10867
$571$	−2.41179e15	−1.66280	−0.831402	−	0.555672i	$-0.812461\pi$
$571$	−2.41179e15	−1.66280	−0.831402	+	0.555672i	$0.812461\pi$
$572$	−1.09026e14	−0.0744480
$573$	5.87187e14	0.397124
$574$	9.96819e14	0.667730
$575$	2.15275e15	1.42830
$576$	4.39355e14	0.288730
$577$	1.37637e15	0.895915	0.447957	−	0.894055i	$-0.352152\pi$
$577$	1.37637e15	0.895915	0.447957	+	0.894055i	$0.352152\pi$
$578$	9.01815e14	0.581453
$579$	−3.93099e14	−0.251056
$580$	−5.06006e13	−0.0320112
$581$	−1.37916e15	−0.864262
$582$	8.75106e14	0.543230
$583$	−2.54585e14	−0.156551
$584$	6.01931e14	0.366671
$585$	1.11331e15	0.671827
$586$	−2.86684e15	−1.71383
$587$	−3.61030e14	−0.213813	−0.106906	−	0.994269i	$-0.534095\pi$
$587$	−3.61030e14	−0.213813	−0.106906	+	0.994269i	$0.534095\pi$
$588$	−8.70981e13	−0.0511015
$589$	−2.78339e15	−1.61785
$590$	−3.43263e14	−0.197670
$591$	8.02346e14	0.457752
$592$	−3.50271e15	−1.97986
$593$	5.56473e14	0.311633	0.155817	−	0.987786i	$-0.450199\pi$
$593$	5.56473e14	0.311633	0.155817	+	0.987786i	$0.450199\pi$
$594$	1.75774e14	0.0975281
$595$	7.85157e14	0.431631
$596$	2.35752e14	0.128411
$597$	−1.59653e15	−0.861623
$598$	−3.66110e15	−1.95774
$599$	−2.56924e15	−1.36131	−0.680656	−	0.732603i	$-0.738305\pi$
$599$	−2.56924e15	−1.36131	−0.680656	+	0.732603i	$0.738305\pi$
$600$	1.10863e15	0.582044
$601$	−2.73554e15	−1.42309	−0.711547	−	0.702638i	$-0.752005\pi$
$601$	−2.73554e15	−1.42309	−0.711547	+	0.702638i	$0.752005\pi$
$602$	−6.31075e14	−0.325312
$603$	−7.19013e14	−0.367275
$604$	1.29946e14	0.0657750
$605$	−2.20814e15	−1.10757
$606$	1.51075e15	0.750919
$607$	2.21689e15	1.09196	0.545980	−	0.837798i	$-0.316158\pi$
$607$	2.21689e15	1.09196	0.545980	+	0.837798i	$0.316158\pi$
$608$	−5.70945e14	−0.278692
$609$	−1.07225e14	−0.0518684
$610$	−4.01500e15	−1.92474
$611$	2.78187e15	1.32163
$612$	5.24583e13	0.0246991
$613$	3.99454e15	1.86395	0.931974	−	0.362524i	$-0.118085\pi$
$613$	3.99454e15	1.86395	0.931974	+	0.362524i	$0.118085\pi$
$614$	1.94139e15	0.897813
$615$	−2.56962e15	−1.17776
$616$	−4.43950e14	−0.201670
$617$	4.38705e14	0.197517	0.0987585	−	0.995111i	$-0.468513\pi$
$617$	4.38705e14	0.197517	0.0987585	+	0.995111i	$0.468513\pi$
$618$	2.04194e15	0.911183
$619$	−3.34765e14	−0.148061	−0.0740306	−	0.997256i	$-0.523586\pi$
$619$	−3.34765e14	−0.148061	−0.0740306	+	0.997256i	$0.523586\pi$
$620$	4.65267e14	0.203961
$621$	5.88139e14	0.255550
$622$	8.08518e14	0.348211
$623$	−8.39024e14	−0.358171
$624$	−2.09666e15	−0.887182
$625$	−2.19024e15	−0.918655
$626$	2.18182e15	0.907109
$627$	8.51971e14	0.351118
$628$	−2.46862e12	−0.00100850
$629$	2.98001e15	1.20681
$630$	−5.64137e14	−0.226470
$631$	1.03484e15	0.411823	0.205911	−	0.978571i	$-0.433984\pi$
$631$	1.03484e15	0.411823	0.205911	+	0.978571i	$0.433984\pi$
$632$	−9.70949e13	−0.0383047
$633$	2.24257e15	0.877054
$634$	4.65694e15	1.80555
$635$	3.49548e14	0.134354
$636$	5.45908e13	0.0208020
$637$	−2.96166e15	−1.11884
$638$	−2.71658e14	−0.101744
$639$	2.63115e14	0.0976993
$640$	−4.43485e15	−1.63264
$641$	−2.48580e15	−0.907291	−0.453646	−	0.891182i	$-0.649877\pi$
$641$	−2.48580e15	−0.907291	−0.453646	+	0.891182i	$0.649877\pi$
$642$	−1.42176e15	−0.514497
$643$	4.42130e15	1.58632	0.793158	−	0.609016i	$-0.208436\pi$
$643$	4.42130e15	1.58632	0.793158	+	0.609016i	$0.208436\pi$
$644$	1.84853e14	0.0657588
$645$	1.62680e15	0.573794
$646$	2.55176e15	0.892402
$647$	1.68139e15	0.583037	0.291518	−	0.956565i	$-0.405840\pi$
$647$	1.68139e15	0.583037	0.291518	+	0.956565i	$0.405840\pi$
$648$	3.02883e14	0.104139
$649$	−1.83628e14	−0.0626027
$650$	−4.69117e15	−1.58583
$651$	9.85927e14	0.330483
$652$	5.54933e14	0.184450
$653$	2.19708e15	0.724142	0.362071	−	0.932151i	$-0.382070\pi$
$653$	2.19708e15	0.724142	0.362071	+	0.932151i	$0.382070\pi$
$654$	−8.06931e14	−0.263730
$655$	3.76783e15	1.22114
$656$	4.83930e15	1.55529
$657$	4.09175e14	0.130406
$658$	−1.40963e15	−0.445516
$659$	5.21720e15	1.63519	0.817594	−	0.575795i	$-0.195307\pi$
$659$	5.21720e15	1.63519	0.817594	+	0.575795i	$0.195307\pi$
$660$	−1.42414e14	−0.0442652
$661$	5.47364e13	0.0168721	0.00843603	−	0.999964i	$-0.497315\pi$
$661$	5.47364e13	0.0168721	0.00843603	+	0.999964i	$0.497315\pi$
$662$	−3.77284e15	−1.15332
$663$	1.78378e15	0.540775
$664$	−6.02087e15	−1.81024
$665$	−2.73435e15	−0.815334
$666$	−2.14114e15	−0.633195
$667$	−9.08966e14	−0.266597
$668$	5.38817e14	0.156737
$669$	−1.14639e15	−0.330742
$670$	5.84644e15	1.67294
$671$	−2.14782e15	−0.609569
$672$	2.02239e14	0.0569292
$673$	−7.52893e14	−0.210208	−0.105104	−	0.994461i	$-0.533518\pi$
$673$	−7.52893e14	−0.210208	−0.105104	+	0.994461i	$0.533518\pi$
$674$	3.11026e15	0.861325
$675$	7.53616e14	0.207004
$676$	3.88762e14	0.105920
$677$	−5.26803e15	−1.42368	−0.711838	−	0.702344i	$-0.752137\pi$
$677$	−5.26803e15	−1.42368	−0.711838	+	0.702344i	$0.752137\pi$
$678$	−9.53510e14	−0.255601
$679$	−1.50246e15	−0.399501
$680$	3.42769e15	0.904072
$681$	2.64392e15	0.691733
$682$	2.49787e15	0.648270
$683$	−2.69775e15	−0.694525	−0.347262	−	0.937768i	$-0.612889\pi$
$683$	−2.69775e15	−0.694525	−0.347262	+	0.937768i	$0.612889\pi$
$684$	−1.82689e14	−0.0466556
$685$	−8.64783e15	−2.19083
$686$	3.37721e15	0.848741
$687$	−1.55494e15	−0.387660
$688$	−3.06371e15	−0.757724
$689$	1.85629e15	0.455450
$690$	−4.78228e15	−1.16403
$691$	−8.85718e14	−0.213878	−0.106939	−	0.994266i	$-0.534105\pi$
$691$	−8.85718e14	−0.213878	−0.106939	+	0.994266i	$0.534105\pi$
$692$	1.69596e14	0.0406287
$693$	−3.01784e14	−0.0717238
$694$	−6.69740e15	−1.57917
$695$	6.90601e15	1.61551
$696$	−4.68105e14	−0.108641
$697$	−4.11714e15	−0.948015
$698$	4.75195e15	1.08559
$699$	1.50241e15	0.340536
$700$	2.36862e14	0.0532668
$701$	−1.95996e15	−0.437319	−0.218659	−	0.975801i	$-0.570168\pi$
$701$	−1.95996e15	−0.437319	−0.218659	+	0.975801i	$0.570168\pi$
$702$	−1.28165e15	−0.283736
$703$	−1.03780e16	−2.27961
$704$	−1.91109e15	−0.416516
$705$	3.63379e15	0.785813
$706$	5.57550e14	0.119635
$707$	−2.59378e15	−0.552239
$708$	3.93755e13	0.00831846
$709$	−5.58013e15	−1.16974	−0.584871	−	0.811126i	$-0.698855\pi$
$709$	−5.58013e15	−1.16974	−0.584871	+	0.811126i	$0.698855\pi$
$710$	−2.13944e15	−0.445020
$711$	−6.60022e13	−0.0136231
$712$	−3.66286e15	−0.750205
$713$	8.35786e15	1.69864
$714$	−9.03880e14	−0.182293
$715$	−4.84263e15	−0.969165
$716$	−4.29848e13	−0.00853676
$717$	1.90070e15	0.374592
$718$	−5.24226e15	−1.02526
$719$	−8.80656e15	−1.70922	−0.854609	−	0.519272i	$-0.826203\pi$
$719$	−8.80656e15	−1.70922	−0.854609	+	0.519272i	$0.826203\pi$
$720$	−2.73874e15	−0.527500
$721$	−3.50577e15	−0.670100
$722$	−3.33083e15	−0.631826
$723$	−5.57652e15	−1.04979
$724$	−2.57837e14	−0.0481708
$725$	−1.16471e15	−0.215953
$726$	2.54204e15	0.467768
$727$	−1.26060e15	−0.230217	−0.115109	−	0.993353i	$-0.536722\pi$
$727$	−1.26060e15	−0.230217	−0.115109	+	0.993353i	$0.536722\pi$
$728$	3.23704e15	0.586713
$729$	2.05891e14	0.0370370
$730$	−3.32708e15	−0.594001
$731$	2.60651e15	0.461865
$732$	4.60557e14	0.0809977
$733$	1.28404e15	0.224134	0.112067	−	0.993701i	$-0.464253\pi$
$733$	1.28404e15	0.224134	0.112067	+	0.993701i	$0.464253\pi$
$734$	−8.90997e15	−1.54365
$735$	−3.86864e15	−0.665240
$736$	1.71442e15	0.292609
$737$	3.12754e15	0.529824
$738$	2.95817e15	0.497409
$739$	−1.92179e15	−0.320746	−0.160373	−	0.987056i	$-0.551270\pi$
$739$	−1.92179e15	−0.320746	−0.160373	+	0.987056i	$0.551270\pi$
$740$	1.73478e15	0.287389
$741$	−6.21211e15	−1.02150
$742$	−9.40624e14	−0.153530
$743$	4.74326e15	0.768491	0.384245	−	0.923231i	$-0.374462\pi$
$743$	4.74326e15	0.768491	0.384245	+	0.923231i	$0.374462\pi$
$744$	4.30418e15	0.692212
$745$	1.04714e16	1.67165
$746$	7.19897e15	1.14079
$747$	−4.09281e15	−0.643811
$748$	−2.28181e14	−0.0356305
$749$	2.44100e15	0.378370
$750$	−4.30837e14	−0.0662943
$751$	−4.09969e15	−0.626226	−0.313113	−	0.949716i	$-0.601372\pi$
$751$	−4.09969e15	−0.626226	−0.313113	+	0.949716i	$0.601372\pi$
$752$	−6.84342e15	−1.03771
$753$	2.78321e15	0.418960
$754$	1.98078e15	0.296002
$755$	5.77183e15	0.856260
$756$	6.47118e13	0.00953045
$757$	−1.11823e16	−1.63495	−0.817476	−	0.575963i	$-0.804627\pi$
$757$	−1.11823e16	−1.63495	−0.817476	+	0.575963i	$0.804627\pi$
$758$	−3.22120e15	−0.467560
$759$	−2.55827e15	−0.368652
$760$	−1.19371e16	−1.70775
$761$	−1.23688e16	−1.75676	−0.878379	−	0.477964i	$-0.841375\pi$
$761$	−1.23688e16	−1.75676	−0.878379	+	0.477964i	$0.841375\pi$
$762$	−4.02403e14	−0.0567425
$763$	1.38541e15	0.193951
$764$	5.47684e14	0.0761231
$765$	2.33004e15	0.321533
$766$	−6.20180e15	−0.849688
$767$	1.33891e15	0.182129
$768$	1.40257e15	0.189425
$769$	−2.71460e14	−0.0364008	−0.0182004	−	0.999834i	$-0.505794\pi$
$769$	−2.71460e14	−0.0364008	−0.0182004	+	0.999834i	$0.505794\pi$
$770$	2.45387e15	0.326702
$771$	3.07543e15	0.406544
$772$	−3.66653e14	−0.0481238
$773$	−7.15121e15	−0.931949	−0.465974	−	0.884798i	$-0.654296\pi$
$773$	−7.15121e15	−0.931949	−0.465974	+	0.884798i	$0.654296\pi$
$774$	−1.87279e15	−0.242333
$775$	1.07094e16	1.37596
$776$	−6.55914e15	−0.836773
$777$	3.67610e15	0.465662
$778$	−1.24228e15	−0.156254
$779$	1.43382e16	1.79076
$780$	1.03841e15	0.128780
$781$	−1.14449e15	−0.140939
$782$	−7.66233e15	−0.936966
$783$	−3.18204e14	−0.0386381
$784$	7.28571e15	0.878484
$785$	−1.09649e14	−0.0131287
$786$	−4.33756e15	−0.515729
$787$	5.43037e15	0.641163	0.320581	−	0.947221i	$-0.396122\pi$
$787$	5.43037e15	0.641163	0.320581	+	0.947221i	$0.396122\pi$
$788$	7.48367e14	0.0877446
$789$	−8.20406e15	−0.955224
$790$	5.36677e14	0.0620532
$791$	1.63707e15	0.187973
$792$	−1.31747e15	−0.150229
$793$	1.56607e16	1.77341
$794$	−1.53672e16	−1.72816
$795$	2.42476e15	0.270801
$796$	−1.48912e15	−0.165161
$797$	2.89325e15	0.318688	0.159344	−	0.987223i	$-0.449062\pi$
$797$	2.89325e15	0.318688	0.159344	+	0.987223i	$0.449062\pi$
$798$	3.14781e15	0.344344
$799$	5.82218e15	0.632526
$800$	2.19678e15	0.237023
$801$	−2.48990e15	−0.266811
$802$	−1.65431e16	−1.76059
$803$	−1.77982e15	−0.188122
$804$	−6.70641e14	−0.0704015
$805$	8.21062e15	0.856049
$806$	−1.82131e16	−1.88600
$807$	7.01696e15	0.721680
$808$	−1.13235e16	−1.15669
$809$	7.66943e14	0.0778120	0.0389060	−	0.999243i	$-0.487613\pi$
$809$	7.66943e14	0.0778120	0.0389060	+	0.999243i	$0.487613\pi$
$810$	−1.67414e15	−0.168704
$811$	2.35899e15	0.236108	0.118054	−	0.993007i	$-0.462334\pi$
$811$	2.35899e15	0.236108	0.118054	+	0.993007i	$0.462334\pi$
$812$	−1.00012e14	−0.00994243
$813$	1.66673e15	0.164576
$814$	9.31348e15	0.913435
$815$	2.46485e16	2.40118
$816$	−4.38811e15	−0.424601
$817$	−9.07733e15	−0.872443
$818$	9.12327e15	0.870979
$819$	2.20044e15	0.208665
$820$	−2.39675e15	−0.225760
$821$	−1.62872e16	−1.52391	−0.761955	−	0.647630i	$-0.775760\pi$
$821$	−1.62872e16	−1.52391	−0.761955	+	0.647630i	$0.775760\pi$
$822$	9.95546e15	0.925266
$823$	−3.12466e15	−0.288472	−0.144236	−	0.989543i	$-0.546073\pi$
$823$	−3.12466e15	−0.288472	−0.144236	+	0.989543i	$0.546073\pi$
$824$	−1.53048e16	−1.40355
$825$	−3.27806e15	−0.298621
$826$	−6.78457e14	−0.0613949
$827$	−8.65810e14	−0.0778291	−0.0389146	−	0.999243i	$-0.512390\pi$
$827$	−8.65810e14	−0.0778291	−0.0389146	+	0.999243i	$0.512390\pi$
$828$	5.48572e14	0.0489854
$829$	1.32091e16	1.17171	0.585857	−	0.810414i	$-0.300758\pi$
$829$	1.32091e16	1.17171	0.585857	+	0.810414i	$0.300758\pi$
$830$	3.32794e16	2.93256
$831$	−2.05870e14	−0.0180214
$832$	1.39346e16	1.21176
$833$	−6.19847e15	−0.535473
$834$	−7.95026e15	−0.682288
$835$	2.39327e16	2.04040
$836$	7.94654e14	0.0673044
$837$	2.92585e15	0.246185
$838$	−1.04865e16	−0.876572
$839$	1.47090e16	1.22149	0.610747	−	0.791826i	$-0.290869\pi$
$839$	1.47090e16	1.22149	0.610747	+	0.791826i	$0.290869\pi$
$840$	4.22835e15	0.348847
$841$	−1.17087e16	−0.959692
$842$	6.83846e15	0.556855
$843$	−7.42872e15	−0.600983
$844$	2.09170e15	0.168119
$845$	1.72677e16	1.37887
$846$	−4.18325e15	−0.331877
$847$	−4.36438e15	−0.344004
$848$	−4.56649e15	−0.357607
$849$	1.83764e15	0.142978
$850$	−9.81817e15	−0.758973
$851$	3.11628e16	2.39345
$852$	2.45414e14	0.0187276
$853$	9.35697e15	0.709440	0.354720	−	0.934973i	$-0.384576\pi$
$853$	9.35697e15	0.709440	0.354720	+	0.934973i	$0.384576\pi$
$854$	−7.93561e15	−0.597809
$855$	−8.11450e15	−0.607363
$856$	1.06564e16	0.792514
$857$	1.71450e16	1.26690	0.633451	−	0.773783i	$-0.281638\pi$
$857$	1.71450e16	1.26690	0.633451	+	0.773783i	$0.281638\pi$
$858$	5.57488e15	0.409313
$859$	2.02187e16	1.47499	0.737496	−	0.675351i	$-0.236008\pi$
$859$	2.02187e16	1.47499	0.737496	+	0.675351i	$0.236008\pi$
$860$	1.51736e15	0.109988
$861$	−5.07885e15	−0.365803
$862$	−2.65972e15	−0.190347
$863$	−2.31489e16	−1.64615	−0.823077	−	0.567930i	$-0.807744\pi$
$863$	−2.31489e16	−1.64615	−0.823077	+	0.567930i	$0.807744\pi$
$864$	6.00169e14	0.0424080
$865$	7.53297e15	0.528905
$866$	1.62256e16	1.13202
$867$	−4.59480e15	−0.318538
$868$	9.19598e14	0.0633489
$869$	2.87094e14	0.0196524
$870$	2.58738e15	0.175996
$871$	−2.28043e16	−1.54141
$872$	6.04816e15	0.406240
$873$	−4.45871e15	−0.297599
$874$	2.66845e16	1.76989
$875$	7.39698e14	0.0487540
$876$	3.81647e14	0.0249971
$877$	−1.34296e16	−0.874110	−0.437055	−	0.899435i	$-0.643979\pi$
$877$	−1.34296e16	−0.874110	−0.437055	+	0.899435i	$0.643979\pi$
$878$	−1.88421e16	−1.21874
$879$	1.46067e16	0.938888
$880$	1.19129e16	0.760962
$881$	1.10383e16	0.700705	0.350352	−	0.936618i	$-0.386062\pi$
$881$	1.10383e16	0.700705	0.350352	+	0.936618i	$0.386062\pi$
$882$	4.45362e15	0.280954
$883$	−2.83712e16	−1.77866	−0.889331	−	0.457264i	$-0.848830\pi$
$883$	−2.83712e16	−1.77866	−0.889331	+	0.457264i	$0.848830\pi$
$884$	1.66377e15	0.103659
$885$	1.74894e15	0.108290
$886$	2.89660e16	1.78239
$887$	6.60674e15	0.404024	0.202012	−	0.979383i	$-0.435252\pi$
$887$	6.60674e15	0.404024	0.202012	+	0.979383i	$0.435252\pi$
$888$	1.60484e16	0.975351
$889$	6.90880e14	0.0417295
$890$	2.02459e16	1.21532
$891$	−8.95579e14	−0.0534289
$892$	−1.06927e15	−0.0633986
$893$	−2.02761e16	−1.19481
$894$	−1.20548e16	−0.705999
$895$	−1.90926e15	−0.111132
$896$	−8.76546e15	−0.507085
$897$	1.86535e16	1.07251
$898$	−2.99886e16	−1.71371
$899$	−4.52189e15	−0.256827
$900$	7.02916e14	0.0396798
$901$	3.88504e15	0.217976
$902$	−1.28674e16	−0.717553
$903$	3.21536e15	0.178216
$904$	7.14681e15	0.393718
$905$	−1.14524e16	−0.627089
$906$	−6.64459e15	−0.361629
$907$	−2.35979e16	−1.27654	−0.638269	−	0.769813i	$-0.720349\pi$
$907$	−2.35979e16	−1.27654	−0.638269	+	0.769813i	$0.720349\pi$
$908$	2.46605e15	0.132596
$909$	−7.69735e15	−0.411377
$910$	−1.78922e16	−0.950467
$911$	−1.51944e15	−0.0802294	−0.0401147	−	0.999195i	$-0.512772\pi$
$911$	−1.51944e15	−0.0802294	−0.0401147	+	0.999195i	$0.512772\pi$
$912$	1.52818e16	0.802054
$913$	1.78028e16	0.928750
$914$	−4.01110e15	−0.207998
$915$	2.04566e16	1.05443
$916$	−1.45033e15	−0.0743089
$917$	7.44710e15	0.379276
$918$	−2.68237e15	−0.135795
$919$	3.25419e16	1.63760	0.818799	−	0.574080i	$-0.194640\pi$
$919$	3.25419e16	1.63760	0.818799	+	0.574080i	$0.194640\pi$
$920$	3.58444e16	1.79303
$921$	−9.89147e15	−0.491850
$922$	2.52721e16	1.24917
$923$	8.34500e15	0.410031
$924$	−2.81481e14	−0.0137484
$925$	3.99307e16	1.93877
$926$	2.50662e16	1.20984
$927$	−1.04038e16	−0.499175
$928$	−9.27558e14	−0.0442412
$929$	1.52117e16	0.721261	0.360630	−	0.932709i	$-0.382562\pi$
$929$	1.52117e16	0.721261	0.360630	+	0.932709i	$0.382562\pi$
$930$	−2.37907e16	−1.12137
$931$	2.15865e16	1.01149
$932$	1.40133e15	0.0652759
$933$	−4.11944e15	−0.190761
$934$	3.79699e15	0.174796
$935$	−1.01352e16	−0.463838
$936$	9.60629e15	0.437057
$937$	−2.78623e16	−1.26023	−0.630114	−	0.776503i	$-0.716992\pi$
$937$	−2.78623e16	−1.26023	−0.630114	+	0.776503i	$0.716992\pi$
$938$	1.15554e16	0.519602
$939$	−1.11165e16	−0.496943
$940$	3.38932e15	0.150629
$941$	3.85825e15	0.170470	0.0852349	−	0.996361i	$-0.472836\pi$
$941$	3.85825e15	0.170470	0.0852349	+	0.996361i	$0.472836\pi$
$942$	1.26229e14	0.00554471
$943$	−4.30542e16	−1.88019
$944$	−3.29374e15	−0.143002
$945$	2.87431e15	0.124068
$946$	8.14619e15	0.349585
$947$	9.91197e15	0.422897	0.211449	−	0.977389i	$-0.432182\pi$
$947$	9.91197e15	0.422897	0.211449	+	0.977389i	$0.432182\pi$
$948$	−6.15619e13	−0.00261135
$949$	1.29774e16	0.547299
$950$	3.41923e16	1.43367
$951$	−2.37274e16	−0.989138
$952$	6.77481e15	0.280798
$953$	−7.57779e15	−0.312271	−0.156135	−	0.987736i	$-0.549904\pi$
$953$	−7.57779e15	−0.312271	−0.156135	+	0.987736i	$0.549904\pi$
$954$	−2.79141e15	−0.114369
$955$	2.43265e16	0.990972
$956$	1.77283e15	0.0718040
$957$	1.38411e15	0.0557386
$958$	−1.82616e16	−0.731188
$959$	−1.70924e16	−0.680457
$960$	1.82020e16	0.720488
$961$	1.61698e16	0.636395
$962$	−6.79087e16	−2.65744
$963$	7.24394e15	0.281858
$964$	−5.20135e15	−0.201230
$965$	−1.62857e16	−0.626477
$966$	−9.45214e15	−0.361540
$967$	−3.22702e16	−1.22731	−0.613657	−	0.789573i	$-0.710302\pi$
$967$	−3.22702e16	−1.22731	−0.613657	+	0.789573i	$0.710302\pi$
$968$	−1.90532e16	−0.720533
$969$	−1.30013e16	−0.488886
$970$	3.62547e16	1.35556
$971$	−4.14383e16	−1.54062	−0.770312	−	0.637667i	$-0.779900\pi$
$971$	−4.14383e16	−1.54062	−0.770312	+	0.637667i	$0.779900\pi$
$972$	1.92040e14	0.00709948
$973$	1.36497e16	0.501767
$974$	−5.16793e16	−1.88905
$975$	2.39018e16	0.868770
$976$	−3.85254e16	−1.39243
$977$	2.39601e16	0.861128	0.430564	−	0.902560i	$-0.358315\pi$
$977$	2.39601e16	0.861128	0.430564	+	0.902560i	$0.358315\pi$
$978$	−2.83756e16	−1.01410
$979$	1.08305e16	0.384896
$980$	−3.60838e15	−0.127517
$981$	4.11136e15	0.144479
$982$	3.01116e16	1.05225
$983$	−5.49845e16	−1.91072	−0.955358	−	0.295452i	$-0.904530\pi$
$983$	−5.49845e16	−1.91072	−0.955358	+	0.295452i	$0.904530\pi$
$984$	−2.21723e16	−0.766192
$985$	3.32403e16	1.14226
$986$	4.14558e15	0.141665
$987$	7.18216e15	0.244068
$988$	−5.79418e15	−0.195807
$989$	2.72571e16	0.916010
$990$	7.28213e15	0.243369
$991$	−2.23721e16	−0.743534	−0.371767	−	0.928326i	$-0.621248\pi$
$991$	−2.23721e16	−0.743534	−0.371767	+	0.928326i	$0.621248\pi$
$992$	8.52880e15	0.281886
$993$	1.92228e16	0.631824
$994$	−4.22860e15	−0.138220
$995$	−6.61423e16	−2.15007
$996$	−3.81746e15	−0.123409
$997$	1.06303e15	0.0341760	0.0170880	−	0.999854i	$-0.494560\pi$
$997$	1.06303e15	0.0341760	0.0170880	+	0.999854i	$0.494560\pi$
$998$	−1.29404e16	−0.413743
$999$	1.09092e16	0.346884

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.12.a.d.1.6	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.12.a.d.1.6	✓	28	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-47.6933 q^{2} +243.000 q^{3} +226.652 q^{4} +10067.2 q^{5} -11589.5 q^{6} +19897.8 q^{7} +86866.1 q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q-47.6933 q^{2} +243.000 q^{3} +226.652 q^{4} +10067.2 q^{5} -11589.5 q^{6} +19897.8 q^{7} +86866.1 q^{8} +59049.0 q^{9} -480139. q^{10} -256850. q^{11} +55076.4 q^{12} +1.87281e6 q^{13} -948992. q^{14} +2.44633e6 q^{15} -4.60712e6 q^{16} +3.91960e6 q^{17} -2.81624e6 q^{18} -1.36502e7 q^{19} +2.28175e6 q^{20} +4.83516e6 q^{21} +1.22500e7 q^{22} +4.09884e7 q^{23} +2.11085e7 q^{24} +5.25208e7 q^{25} -8.93203e7 q^{26} +1.43489e7 q^{27} +4.50987e6 q^{28} -2.21762e7 q^{29} -1.16674e8 q^{30} +2.03908e8 q^{31} +4.18268e7 q^{32} -6.24144e7 q^{33} -1.86939e8 q^{34} +2.00315e8 q^{35} +1.33836e7 q^{36} +7.60284e8 q^{37} +6.51025e8 q^{38} +4.55092e8 q^{39} +8.74500e8 q^{40} -1.05040e9 q^{41} -2.30605e8 q^{42} +6.64995e8 q^{43} -5.82155e7 q^{44} +5.94459e8 q^{45} -1.95487e9 q^{46} +1.48540e9 q^{47} -1.11953e9 q^{48} -1.58140e9 q^{49} -2.50489e9 q^{50} +9.52463e8 q^{51} +4.24475e8 q^{52} +9.91182e8 q^{53} -6.84347e8 q^{54} -2.58576e9 q^{55} +1.72844e9 q^{56} -3.31701e9 q^{57} +1.05765e9 q^{58} +7.14924e8 q^{59} +5.54466e8 q^{60} +8.36215e9 q^{61} -9.72503e9 q^{62} +1.17494e9 q^{63} +7.44051e9 q^{64} +1.88539e10 q^{65} +2.97675e9 q^{66} -1.21766e10 q^{67} +8.88385e8 q^{68} +9.96019e9 q^{69} -9.55371e9 q^{70} +4.45588e9 q^{71} +5.12936e9 q^{72} +6.92941e9 q^{73} -3.62604e10 q^{74} +1.27626e10 q^{75} -3.09385e9 q^{76} -5.11074e9 q^{77} -2.17048e10 q^{78} -1.11775e9 q^{79} -4.63809e10 q^{80} +3.48678e9 q^{81} +5.00969e10 q^{82} -6.93121e10 q^{83} +1.09590e9 q^{84} +3.94595e10 q^{85} -3.17158e10 q^{86} -5.38881e9 q^{87} -2.23115e10 q^{88} -4.21667e10 q^{89} -2.83517e10 q^{90} +3.72647e10 q^{91} +9.29011e9 q^{92} +4.95495e10 q^{93} -7.08437e10 q^{94} -1.37420e11 q^{95} +1.01639e10 q^{96} -7.55087e10 q^{97} +7.54224e10 q^{98} -1.51667e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9}+O(q^{10}) \) 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9	\( 28 q + 96 q^{2} + 6804 q^{3} + 29214 q^{4} + 26562 q^{5} + 23328 q^{6} + 142333 q^{7} + 332331 q^{8} + 1653372 q^{9} + 616281 q^{10} + 1082362 q^{11} + 7099002 q^{12} + 503712 q^{13} + 1321669 q^{14} + 6454566 q^{15} + 34870338 q^{16} + 13513579 q^{17} + 5668704 q^{18} + 35971687 q^{19} + 96105997 q^{20} + 34586919 q^{21} - 47598882 q^{22} + 61380539 q^{23} + 80756433 q^{24} + 294744746 q^{25} + 62820734 q^{26} + 401769396 q^{27} + 148068294 q^{28} + 322339307 q^{29} + 149756283 q^{30} + 151247077 q^{31} + 466383494 q^{32} + 263013966 q^{33} + 684479860 q^{34} + 960297361 q^{35} + 1725057486 q^{36} + 863508437 q^{37} + 992640509 q^{38} + 122402016 q^{39} + 3067680252 q^{40} + 3081170377 q^{41} + 321165567 q^{42} + 2554238300 q^{43} + 4350123570 q^{44} + 1568459538 q^{45} - 1987059155 q^{46} + 6203398333 q^{47} + 8473492134 q^{48} + 10327857997 q^{49} + 17577682253 q^{50} + 3283799697 q^{51} + 32137181618 q^{52} + 14571770754 q^{53} + 1377495072 q^{54} + 18251419334 q^{55} + 33498842836 q^{56} + 8741119941 q^{57} + 11860778276 q^{58} + 20017880372 q^{59} + 23353757271 q^{60} + 2761613771 q^{61} + 13785829526 q^{62} + 8404621317 q^{63} + 86547545293 q^{64} + 32034985256 q^{65} - 11566528326 q^{66} + 39381333296 q^{67} + 38995496621 q^{68} + 14915470977 q^{69} + 8551800364 q^{70} + 26130020296 q^{71} + 19623813219 q^{72} + 41382402799 q^{73} + 23815315058 q^{74} + 71622973278 q^{75} + 10611720128 q^{76} - 8426124313 q^{77} + 15265438362 q^{78} + 59825111206 q^{79} + 4009687655 q^{80} + 97629963228 q^{81} - 39592715115 q^{82} + 35433122727 q^{83} + 35980595442 q^{84} - 8950496085 q^{85} - 182032360688 q^{86} + 78328451601 q^{87} - 220003602335 q^{88} + 102303043039 q^{89} + 36390776769 q^{90} - 111146323655 q^{91} - 163000203526 q^{92} + 36753039711 q^{93} - 81314346008 q^{94} + 208102168887 q^{95} + 113331189042 q^{96} - 171891031490 q^{97} + 72304707792 q^{98} + 63912393738 q^{99}+O(q^{100}) \) 28 * q + 96 * q^2 + 6804 * q^3 + 29214 * q^4 + 26562 * q^5 + 23328 * q^6 + 142333 * q^7 + 332331 * q^8 + 1653372 * q^9 + 616281 * q^10 + 1082362 * q^11 + 7099002 * q^12 + 503712 * q^13 + 1321669 * q^14 + 6454566 * q^15 + 34870338 * q^16 + 13513579 * q^17 + 5668704 * q^18 + 35971687 * q^19 + 96105997 * q^20 + 34586919 * q^21 - 47598882 * q^22 + 61380539 * q^23 + 80756433 * q^24 + 294744746 * q^25 + 62820734 * q^26 + 401769396 * q^27 + 148068294 * q^28 + 322339307 * q^29 + 149756283 * q^30 + 151247077 * q^31 + 466383494 * q^32 + 263013966 * q^33 + 684479860 * q^34 + 960297361 * q^35 + 1725057486 * q^36 + 863508437 * q^37 + 992640509 * q^38 + 122402016 * q^39 + 3067680252 * q^40 + 3081170377 * q^41 + 321165567 * q^42 + 2554238300 * q^43 + 4350123570 * q^44 + 1568459538 * q^45 - 1987059155 * q^46 + 6203398333 * q^47 + 8473492134 * q^48 + 10327857997 * q^49 + 17577682253 * q^50 + 3283799697 * q^51 + 32137181618 * q^52 + 14571770754 * q^53 + 1377495072 * q^54 + 18251419334 * q^55 + 33498842836 * q^56 + 8741119941 * q^57 + 11860778276 * q^58 + 20017880372 * q^59 + 23353757271 * q^60 + 2761613771 * q^61 + 13785829526 * q^62 + 8404621317 * q^63 + 86547545293 * q^64 + 32034985256 * q^65 - 11566528326 * q^66 + 39381333296 * q^67 + 38995496621 * q^68 + 14915470977 * q^69 + 8551800364 * q^70 + 26130020296 * q^71 + 19623813219 * q^72 + 41382402799 * q^73 + 23815315058 * q^74 + 71622973278 * q^75 + 10611720128 * q^76 - 8426124313 * q^77 + 15265438362 * q^78 + 59825111206 * q^79 + 4009687655 * q^80 + 97629963228 * q^81 - 39592715115 * q^82 + 35433122727 * q^83 + 35980595442 * q^84 - 8950496085 * q^85 - 182032360688 * q^86 + 78328451601 * q^87 - 220003602335 * q^88 + 102303043039 * q^89 + 36390776769 * q^90 - 111146323655 * q^91 - 163000203526 * q^92 + 36753039711 * q^93 - 81314346008 * q^94 + 208102168887 * q^95 + 113331189042 * q^96 - 171891031490 * q^97 + 72304707792 * q^98 + 63912393738 * q^99

Introduction

L-functions

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