LMFDB - Embedded newform 177.14.a.b.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,14,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, 14, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 14 $
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:	$189.798744245$
Analytic rank:	$1$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
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)

$f(q)$	$=$	$q+52.9360 q^{2} -729.000 q^{3} -5389.78 q^{4} -33150.0 q^{5} -38590.4 q^{6} -413060. q^{7} -718965. q^{8} +531441. q^{9} +O(q^{10})$	\(q+52.9360 q^{2} -729.000 q^{3} -5389.78 q^{4} -33150.0 q^{5} -38590.4 q^{6} -413060. q^{7} -718965. q^{8} +531441. q^{9} -1.75483e6 q^{10} +2.37030e6 q^{11} +3.92915e6 q^{12} -1.44816e7 q^{13} -2.18658e7 q^{14} +2.41664e7 q^{15} +6.09389e6 q^{16} -9.80573e7 q^{17} +2.81324e7 q^{18} +2.31816e8 q^{19} +1.78671e8 q^{20} +3.01121e8 q^{21} +1.25474e8 q^{22} +7.61140e8 q^{23} +5.24126e8 q^{24} -1.21779e8 q^{25} -7.66597e8 q^{26} -3.87420e8 q^{27} +2.22630e9 q^{28} -2.21082e9 q^{29} +1.27927e9 q^{30} +6.65917e8 q^{31} +6.21235e9 q^{32} -1.72795e9 q^{33} -5.19076e9 q^{34} +1.36930e10 q^{35} -2.86435e9 q^{36} +3.56511e9 q^{37} +1.22714e10 q^{38} +1.05571e10 q^{39} +2.38337e10 q^{40} +5.94111e10 q^{41} +1.59401e10 q^{42} +3.00720e9 q^{43} -1.27754e10 q^{44} -1.76173e10 q^{45} +4.02917e10 q^{46} +7.04075e10 q^{47} -4.44245e9 q^{48} +7.37295e10 q^{49} -6.44648e9 q^{50} +7.14837e10 q^{51} +7.80524e10 q^{52} -2.38186e11 q^{53} -2.05085e10 q^{54} -7.85755e10 q^{55} +2.96976e11 q^{56} -1.68994e11 q^{57} -1.17032e11 q^{58} -4.21805e10 q^{59} -1.30251e11 q^{60} +4.48921e11 q^{61} +3.52510e10 q^{62} -2.19517e11 q^{63} +2.78936e11 q^{64} +4.80064e11 q^{65} -9.14708e10 q^{66} -1.96931e11 q^{67} +5.28507e11 q^{68} -5.54871e11 q^{69} +7.24850e11 q^{70} -4.00518e11 q^{71} -3.82088e11 q^{72} -2.04862e11 q^{73} +1.88723e11 q^{74} +8.87767e10 q^{75} -1.24943e12 q^{76} -9.79076e11 q^{77} +5.58849e11 q^{78} +1.96050e12 q^{79} -2.02013e11 q^{80} +2.82430e11 q^{81} +3.14499e12 q^{82} +4.20575e11 q^{83} -1.62297e12 q^{84} +3.25060e12 q^{85} +1.59189e11 q^{86} +1.61169e12 q^{87} -1.70416e12 q^{88} +4.35059e11 q^{89} -9.32589e11 q^{90} +5.98176e12 q^{91} -4.10237e12 q^{92} -4.85453e11 q^{93} +3.72709e12 q^{94} -7.68469e12 q^{95} -4.52880e12 q^{96} -6.74801e12 q^{97} +3.90295e12 q^{98} +1.25968e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q - 52 q^{2} - 22599 q^{3} + 126886 q^{4} + 33486 q^{5} + 37908 q^{6} - 1135539 q^{7} - 1519749 q^{8} + 16474671 q^{9}+O(q^{10}) $ 31 * q - 52 * q^2 - 22599 * q^3 + 126886 * q^4 + 33486 * q^5 + 37908 * q^6 - 1135539 * q^7 - 1519749 * q^8 + 16474671 * q^9	\( 31 q - 52 q^{2} - 22599 q^{3} + 126886 q^{4} + 33486 q^{5} + 37908 q^{6} - 1135539 q^{7} - 1519749 q^{8} + 16474671 q^{9} - 3854663 q^{10} + 3943968 q^{11} - 92499894 q^{12} - 48510022 q^{13} - 51427459 q^{14} - 24411294 q^{15} + 370110498 q^{16} + 83288419 q^{17} - 27634932 q^{18} - 180425297 q^{19} + 753620445 q^{20} + 827807931 q^{21} + 2300196142 q^{22} - 1305810279 q^{23} + 1107897021 q^{24} + 8070954867 q^{25} + 464550322 q^{26} - 12010035159 q^{27} - 9887169562 q^{28} + 6248352277 q^{29} + 2810049327 q^{30} - 26730150789 q^{31} - 24001343230 q^{32} - 2875152672 q^{33} - 36571033348 q^{34} + 10255900979 q^{35} + 67432422726 q^{36} - 43284776933 q^{37} - 36293696947 q^{38} + 35363806038 q^{39} - 105980683856 q^{40} - 9961079285 q^{41} + 37490617611 q^{42} - 51755851288 q^{43} - 59623729442 q^{44} + 17795833326 q^{45} - 202287132683 q^{46} - 82747063727 q^{47} - 269810553042 q^{48} + 535277836542 q^{49} + 526974390461 q^{50} - 60717257451 q^{51} + 544982341446 q^{52} + 561701818494 q^{53} + 20145865428 q^{54} - 521861534450 q^{55} - 228056576664 q^{56} + 131530041513 q^{57} + 10555409160 q^{58} - 1307596542871 q^{59} - 549389304405 q^{60} + 618193248201 q^{61} - 1486611437386 q^{62} - 603471981699 q^{63} + 679062548045 q^{64} - 1130583307122 q^{65} - 1676842987518 q^{66} - 4137387490592 q^{67} - 3901389300295 q^{68} + 951935693391 q^{69} - 819291947844 q^{70} - 3766439869810 q^{71} - 807656928309 q^{72} - 2386775553523 q^{73} + 3060770694642 q^{74} - 5883726098043 q^{75} - 847741068784 q^{76} + 1650423006137 q^{77} - 338657184738 q^{78} + 787155757766 q^{79} + 13999832121779 q^{80} + 8755315630911 q^{81} + 10083281915577 q^{82} + 8743877051639 q^{83} + 7207746610698 q^{84} + 15373177520565 q^{85} + 18939443838984 q^{86} - 4555048809933 q^{87} + 39713314506713 q^{88} + 11026795445259 q^{89} - 2048525959383 q^{90} + 23285721962531 q^{91} + 40411079823254 q^{92} + 19486279925181 q^{93} + 35237377585624 q^{94} + 13730236994039 q^{95} + 17496979214670 q^{96} + 10134565481560 q^{97} + 70916776240976 q^{98} + 2095986297888 q^{99}+O(q^{100}) \) 31 * q - 52 * q^2 - 22599 * q^3 + 126886 * q^4 + 33486 * q^5 + 37908 * q^6 - 1135539 * q^7 - 1519749 * q^8 + 16474671 * q^9 - 3854663 * q^10 + 3943968 * q^11 - 92499894 * q^12 - 48510022 * q^13 - 51427459 * q^14 - 24411294 * q^15 + 370110498 * q^16 + 83288419 * q^17 - 27634932 * q^18 - 180425297 * q^19 + 753620445 * q^20 + 827807931 * q^21 + 2300196142 * q^22 - 1305810279 * q^23 + 1107897021 * q^24 + 8070954867 * q^25 + 464550322 * q^26 - 12010035159 * q^27 - 9887169562 * q^28 + 6248352277 * q^29 + 2810049327 * q^30 - 26730150789 * q^31 - 24001343230 * q^32 - 2875152672 * q^33 - 36571033348 * q^34 + 10255900979 * q^35 + 67432422726 * q^36 - 43284776933 * q^37 - 36293696947 * q^38 + 35363806038 * q^39 - 105980683856 * q^40 - 9961079285 * q^41 + 37490617611 * q^42 - 51755851288 * q^43 - 59623729442 * q^44 + 17795833326 * q^45 - 202287132683 * q^46 - 82747063727 * q^47 - 269810553042 * q^48 + 535277836542 * q^49 + 526974390461 * q^50 - 60717257451 * q^51 + 544982341446 * q^52 + 561701818494 * q^53 + 20145865428 * q^54 - 521861534450 * q^55 - 228056576664 * q^56 + 131530041513 * q^57 + 10555409160 * q^58 - 1307596542871 * q^59 - 549389304405 * q^60 + 618193248201 * q^61 - 1486611437386 * q^62 - 603471981699 * q^63 + 679062548045 * q^64 - 1130583307122 * q^65 - 1676842987518 * q^66 - 4137387490592 * q^67 - 3901389300295 * q^68 + 951935693391 * q^69 - 819291947844 * q^70 - 3766439869810 * q^71 - 807656928309 * q^72 - 2386775553523 * q^73 + 3060770694642 * q^74 - 5883726098043 * q^75 - 847741068784 * q^76 + 1650423006137 * q^77 - 338657184738 * q^78 + 787155757766 * q^79 + 13999832121779 * q^80 + 8755315630911 * q^81 + 10083281915577 * q^82 + 8743877051639 * q^83 + 7207746610698 * q^84 + 15373177520565 * q^85 + 18939443838984 * q^86 - 4555048809933 * q^87 + 39713314506713 * q^88 + 11026795445259 * q^89 - 2048525959383 * q^90 + 23285721962531 * q^91 + 40411079823254 * q^92 + 19486279925181 * q^93 + 35237377585624 * q^94 + 13730236994039 * q^95 + 17496979214670 * q^96 + 10134565481560 * q^97 + 70916776240976 * q^98 + 2095986297888 * 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 $

$2$	52.9360	0.584866	0.292433	−	0.956286i	$-0.405535\pi$
$2$	52.9360	0.584866	0.292433	+	0.956286i	$0.405535\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	−5389.78	−0.657932
$5$	−33150.0	−0.948809	−0.474405	−	0.880307i	$-0.657337\pi$
$5$	−33150.0	−0.948809	−0.474405	+	0.880307i	$0.657337\pi$
$6$	−38590.4	−0.337673
$7$	−413060.	−1.32702	−0.663508	−	0.748170i	$-0.730933\pi$
$7$	−413060.	−1.32702	−0.663508	+	0.748170i	$0.730933\pi$
$8$	−718965.	−0.969668
$9$	531441.	0.333333
$10$	−1.75483e6	−0.554926
$11$	2.37030e6	0.403414	0.201707	−	0.979446i	$-0.435351\pi$
$11$	2.37030e6	0.403414	0.201707	+	0.979446i	$0.435351\pi$
$12$	3.92915e6	0.379857
$13$	−1.44816e7	−0.832116	−0.416058	−	0.909338i	$-0.636589\pi$
$13$	−1.44816e7	−0.832116	−0.416058	+	0.909338i	$0.636589\pi$
$14$	−2.18658e7	−0.776126
$15$	2.41664e7	0.547795
$16$	6.09389e6	0.0908060
$17$	−9.80573e7	−0.985285	−0.492642	−	0.870232i	$-0.663969\pi$
$17$	−9.80573e7	−0.985285	−0.492642	+	0.870232i	$0.663969\pi$
$18$	2.81324e7	0.194955
$19$	2.31816e8	1.13043	0.565216	−	0.824943i	$-0.308793\pi$
$19$	2.31816e8	1.13043	0.565216	+	0.824943i	$0.308793\pi$
$20$	1.78671e8	0.624252
$21$	3.01121e8	0.766153
$22$	1.25474e8	0.235943
$23$	7.61140e8	1.07210	0.536048	−	0.844188i	$-0.319917\pi$
$23$	7.61140e8	1.07210	0.536048	+	0.844188i	$0.319917\pi$
$24$	5.24126e8	0.559838
$25$	−1.21779e8	−0.0997611
$26$	−7.66597e8	−0.486676
$27$	−3.87420e8	−0.192450
$28$	2.22630e9	0.873085
$29$	−2.21082e9	−0.690187	−0.345093	−	0.938568i	$-0.612153\pi$
$29$	−2.21082e9	−0.690187	−0.345093	+	0.938568i	$0.612153\pi$
$30$	1.27927e9	0.320387
$31$	6.65917e8	0.134763	0.0673813	−	0.997727i	$-0.478536\pi$
$31$	6.65917e8	0.134763	0.0673813	+	0.997727i	$0.478536\pi$
$32$	6.21235e9	1.02278
$33$	−1.72795e9	−0.232911
$34$	−5.19076e9	−0.576259
$35$	1.36930e10	1.25908
$36$	−2.86435e9	−0.219311
$37$	3.56511e9	0.228435	0.114217	−	0.993456i	$-0.463564\pi$
$37$	3.56511e9	0.228435	0.114217	+	0.993456i	$0.463564\pi$
$38$	1.22714e10	0.661151
$39$	1.05571e10	0.480422
$40$	2.38337e10	0.920030
$41$	5.94111e10	1.95332	0.976658	−	0.214801i	$-0.0689101\pi$
$41$	5.94111e10	1.95332	0.976658	+	0.214801i	$0.0689101\pi$
$42$	1.59401e10	0.448097
$43$	3.00720e9	0.0725467	0.0362734	−	0.999342i	$-0.488451\pi$
$43$	3.00720e9	0.0725467	0.0362734	+	0.999342i	$0.488451\pi$
$44$	−1.27754e10	−0.265419
$45$	−1.76173e10	−0.316270
$46$	4.02917e10	0.627032
$47$	7.04075e10	0.952759	0.476379	−	0.879240i	$-0.341949\pi$
$47$	7.04075e10	0.952759	0.476379	+	0.879240i	$0.341949\pi$
$48$	−4.44245e9	−0.0524269
$49$	7.37295e10	0.760969
$50$	−6.44648e9	−0.0583469
$51$	7.14837e10	0.568854
$52$	7.80524e10	0.547475
$53$	−2.38186e11	−1.47612	−0.738061	−	0.674734i	$-0.764258\pi$
$53$	−2.38186e11	−1.47612	−0.738061	+	0.674734i	$0.764258\pi$
$54$	−2.05085e10	−0.112558
$55$	−7.85755e10	−0.382763
$56$	2.96976e11	1.28676
$57$	−1.68994e11	−0.652655
$58$	−1.17032e11	−0.403667
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	−1.30251e11	−0.360412
$61$	4.48921e11	1.11564	0.557822	−	0.829961i	$-0.311637\pi$
$61$	4.48921e11	1.11564	0.557822	+	0.829961i	$0.311637\pi$
$62$	3.52510e10	0.0788180
$63$	−2.19517e11	−0.442338
$64$	2.78936e11	0.507382
$65$	4.80064e11	0.789519
$66$	−9.14708e10	−0.136222
$67$	−1.96931e11	−0.265967	−0.132984	−	0.991118i	$-0.542456\pi$
$67$	−1.96931e11	−0.265967	−0.132984	+	0.991118i	$0.542456\pi$
$68$	5.28507e11	0.648250
$69$	−5.54871e11	−0.618975
$70$	7.24850e11	0.736395
$71$	−4.00518e11	−0.371059	−0.185529	−	0.982639i	$-0.559400\pi$
$71$	−4.00518e11	−0.371059	−0.185529	+	0.982639i	$0.559400\pi$
$72$	−3.82088e11	−0.323223
$73$	−2.04862e11	−0.158440	−0.0792198	−	0.996857i	$-0.525243\pi$
$73$	−2.04862e11	−0.158440	−0.0792198	+	0.996857i	$0.525243\pi$
$74$	1.88723e11	0.133604
$75$	8.87767e10	0.0575971
$76$	−1.24943e12	−0.743747
$77$	−9.79076e11	−0.535337
$78$	5.58849e11	0.280983
$79$	1.96050e12	0.907384	0.453692	−	0.891159i	$-0.350107\pi$
$79$	1.96050e12	0.907384	0.453692	+	0.891159i	$0.350107\pi$
$80$	−2.02013e11	−0.0861576
$81$	2.82430e11	0.111111
$82$	3.14499e12	1.14243
$83$	4.20575e11	0.141200	0.0706002	−	0.997505i	$-0.477509\pi$
$83$	4.20575e11	0.141200	0.0706002	+	0.997505i	$0.477509\pi$
$84$	−1.62297e12	−0.504076
$85$	3.25060e12	0.934847
$86$	1.59189e11	0.0424301
$87$	1.61169e12	0.398479
$88$	−1.70416e12	−0.391178
$89$	4.35059e11	0.0927925	0.0463962	−	0.998923i	$-0.485226\pi$
$89$	4.35059e11	0.0927925	0.0463962	+	0.998923i	$0.485226\pi$
$90$	−9.32589e11	−0.184975
$91$	5.98176e12	1.10423
$92$	−4.10237e12	−0.705366
$93$	−4.85453e11	−0.0778052
$94$	3.72709e12	0.557236
$95$	−7.68469e12	−1.07256
$96$	−4.52880e12	−0.590501
$97$	−6.74801e12	−0.822545	−0.411272	−	0.911513i	$-0.634915\pi$
$97$	−6.74801e12	−0.822545	−0.411272	+	0.911513i	$0.634915\pi$
$98$	3.90295e12	0.445065
$99$	1.25968e12	0.134471
$100$	6.56360e11	0.0656360
$101$	−8.27950e10	−0.00776095	−0.00388048	−	0.999992i	$-0.501235\pi$
$101$	−8.27950e10	−0.00776095	−0.00388048	+	0.999992i	$0.501235\pi$
$102$	3.78406e12	0.332704
$103$	−4.93712e12	−0.407410	−0.203705	−	0.979032i	$-0.565298\pi$
$103$	−4.93712e12	−0.407410	−0.203705	+	0.979032i	$0.565298\pi$
$104$	1.04117e13	0.806876
$105$	−9.98216e12	−0.726933
$106$	−1.26086e13	−0.863334
$107$	7.69066e12	0.495415	0.247708	−	0.968835i	$-0.420323\pi$
$107$	7.69066e12	0.495415	0.247708	+	0.968835i	$0.420323\pi$
$108$	2.08811e12	0.126619
$109$	3.61733e12	0.206593	0.103296	−	0.994651i	$-0.467061\pi$
$109$	3.61733e12	0.206593	0.103296	+	0.994651i	$0.467061\pi$
$110$	−4.15948e12	−0.223865
$111$	−2.59897e12	−0.131887
$112$	−2.51714e12	−0.120501
$113$	−3.57321e13	−1.61454	−0.807269	−	0.590184i	$-0.799055\pi$
$113$	−3.57321e13	−1.61454	−0.807269	+	0.590184i	$0.799055\pi$
$114$	−8.94585e12	−0.381716
$115$	−2.52318e13	−1.01721
$116$	1.19158e13	0.454096
$117$	−7.69610e12	−0.277372
$118$	−2.23287e12	−0.0761431
$119$	4.05035e13	1.30749
$120$	−1.73748e13	−0.531179
$121$	−2.89044e13	−0.837257
$122$	2.37641e13	0.652502
$123$	−4.33107e13	−1.12775
$124$	−3.58914e12	−0.0886645
$125$	4.45033e13	1.04346
$126$	−1.16204e13	−0.258709
$127$	3.87874e13	0.820288	0.410144	−	0.912021i	$-0.365478\pi$
$127$	3.87874e13	0.820288	0.410144	+	0.912021i	$0.365478\pi$
$128$	−3.61258e13	−0.726027
$129$	−2.19225e12	−0.0418849
$130$	2.54127e13	0.461763
$131$	−1.07756e13	−0.186286	−0.0931428	−	0.995653i	$-0.529691\pi$
$131$	−1.07756e13	−0.186286	−0.0931428	+	0.995653i	$0.529691\pi$
$132$	9.31326e12	0.153240
$133$	−9.57537e13	−1.50010
$134$	−1.04248e13	−0.155555
$135$	1.28430e13	0.182598
$136$	7.04998e13	0.955399
$137$	−1.24590e13	−0.160990	−0.0804952	−	0.996755i	$-0.525650\pi$
$137$	−1.24590e13	−0.160990	−0.0804952	+	0.996755i	$0.525650\pi$
$138$	−2.93727e13	−0.362017
$139$	−1.48455e13	−0.174581	−0.0872906	−	0.996183i	$-0.527821\pi$
$139$	−1.48455e13	−0.174581	−0.0872906	+	0.996183i	$0.527821\pi$
$140$	−7.38020e13	−0.828391
$141$	−5.13271e13	−0.550076
$142$	−2.12018e13	−0.217020
$143$	−3.43257e13	−0.335687
$144$	3.23854e12	0.0302687
$145$	7.32888e13	0.654855
$146$	−1.08446e13	−0.0926660
$147$	−5.37488e13	−0.439346
$148$	−1.92152e13	−0.150295
$149$	3.89395e13	0.291528	0.145764	−	0.989319i	$-0.453436\pi$
$149$	3.89395e13	0.291528	0.145764	+	0.989319i	$0.453436\pi$
$150$	4.69948e12	0.0336866
$151$	1.15177e14	0.790706	0.395353	−	0.918529i	$-0.370622\pi$
$151$	1.15177e14	0.790706	0.395353	+	0.918529i	$0.370622\pi$
$152$	−1.66667e14	−1.09614
$153$	−5.21116e13	−0.328428
$154$	−5.18284e13	−0.313100
$155$	−2.20752e13	−0.127864
$156$	−5.69002e13	−0.316085
$157$	1.43467e14	0.764550	0.382275	−	0.924049i	$-0.375141\pi$
$157$	1.43467e14	0.764550	0.382275	+	0.924049i	$0.375141\pi$
$158$	1.03781e14	0.530698
$159$	1.73637e14	0.852240
$160$	−2.05940e14	−0.970420
$161$	−3.14396e14	−1.42269
$162$	1.49507e13	0.0649851
$163$	−9.35409e11	−0.00390645	−0.00195322	−	0.999998i	$-0.500622\pi$
$163$	−9.35409e11	−0.00390645	−0.00195322	+	0.999998i	$0.500622\pi$
$164$	−3.20213e14	−1.28515
$165$	5.72816e13	0.220988
$166$	2.22636e13	0.0825833
$167$	3.04805e14	1.08734	0.543670	−	0.839299i	$-0.317034\pi$
$167$	3.04805e14	1.08734	0.543670	+	0.839299i	$0.317034\pi$
$168$	−2.16495e14	−0.742913
$169$	−9.31593e13	−0.307583
$170$	1.72074e14	0.546760
$171$	1.23196e14	0.376810
$172$	−1.62082e13	−0.0477308
$173$	2.18937e14	0.620896	0.310448	−	0.950590i	$-0.399521\pi$
$173$	2.18937e14	0.620896	0.310448	+	0.950590i	$0.399521\pi$
$174$	8.53164e13	0.233057
$175$	5.03019e13	0.132385
$176$	1.44444e13	0.0366324
$177$	3.07496e13	0.0751646
$178$	2.30303e13	0.0542712
$179$	1.26997e14	0.288569	0.144284	−	0.989536i	$-0.453912\pi$
$179$	1.26997e14	0.288569	0.144284	+	0.989536i	$0.453912\pi$
$180$	9.49532e13	0.208084
$181$	−8.92312e14	−1.88628	−0.943140	−	0.332396i	$-0.892143\pi$
$181$	−8.92312e14	−1.88628	−0.943140	+	0.332396i	$0.892143\pi$
$182$	3.16650e14	0.645827
$183$	−3.27263e14	−0.644117
$184$	−5.47233e14	−1.03958
$185$	−1.18184e14	−0.216741
$186$	−2.56980e13	−0.0455056
$187$	−2.32425e14	−0.397478
$188$	−3.79481e14	−0.626850
$189$	1.60028e14	0.255384
$190$	−4.06797e14	−0.627306
$191$	−1.04194e15	−1.55284	−0.776418	−	0.630219i	$-0.782965\pi$
$191$	−1.04194e15	−1.55284	−0.776418	+	0.630219i	$0.782965\pi$
$192$	−2.03344e14	−0.292937
$193$	9.41290e14	1.31099	0.655497	−	0.755198i	$-0.272459\pi$
$193$	9.41290e14	1.31099	0.655497	+	0.755198i	$0.272459\pi$
$194$	−3.57213e14	−0.481078
$195$	−3.49967e14	−0.455829
$196$	−3.97386e14	−0.500666
$197$	−1.45040e15	−1.76790	−0.883950	−	0.467581i	$-0.845126\pi$
$197$	−1.45040e15	−1.76790	−0.883950	+	0.467581i	$0.845126\pi$
$198$	6.66822e13	0.0786477
$199$	9.13225e14	1.04240	0.521198	−	0.853436i	$-0.325485\pi$
$199$	9.13225e14	1.04240	0.521198	+	0.853436i	$0.325485\pi$
$200$	8.75547e13	0.0967351
$201$	1.43563e14	0.153556
$202$	−4.38284e12	−0.00453912
$203$	9.13201e14	0.915888
$204$	−3.85281e14	−0.374267
$205$	−1.96948e15	−1.85332
$206$	−2.61351e14	−0.238280
$207$	4.04501e14	0.357365
$208$	−8.82491e13	−0.0755611
$209$	5.49473e14	0.456032
$210$	−5.28416e14	−0.425158
$211$	2.36901e15	1.84812	0.924062	−	0.382242i	$-0.124848\pi$
$211$	2.36901e15	1.84812	0.924062	+	0.382242i	$0.124848\pi$
$212$	1.28377e15	0.971188
$213$	2.91978e14	0.214231
$214$	4.07113e14	0.289751
$215$	−9.96889e13	−0.0688330
$216$	2.78542e14	0.186613
$217$	−2.75064e14	−0.178832
$218$	1.91487e14	0.120829
$219$	1.49345e14	0.0914752
$220$	4.23505e14	0.251832
$221$	1.42002e15	0.819871
$222$	−1.37579e14	−0.0771361
$223$	2.40543e15	1.30982	0.654909	−	0.755707i	$-0.272707\pi$
$223$	2.40543e15	1.30982	0.654909	+	0.755707i	$0.272707\pi$
$224$	−2.56607e15	−1.35724
$225$	−6.47182e13	−0.0332537
$226$	−1.89151e15	−0.944288
$227$	3.69060e15	1.79031	0.895156	−	0.445753i	$-0.147064\pi$
$227$	3.69060e15	1.79031	0.895156	+	0.445753i	$0.147064\pi$
$228$	9.10838e14	0.429402
$229$	−2.39631e14	−0.109802	−0.0549012	−	0.998492i	$-0.517484\pi$
$229$	−2.39631e14	−0.109802	−0.0549012	+	0.998492i	$0.517484\pi$
$230$	−1.33567e15	−0.594934
$231$	7.13747e14	0.309077
$232$	1.58950e15	0.669252
$233$	1.57644e15	0.645452	0.322726	−	0.946493i	$-0.395401\pi$
$233$	1.57644e15	0.645452	0.322726	+	0.946493i	$0.395401\pi$
$234$	−4.07401e14	−0.162225
$235$	−2.33401e15	−0.903986
$236$	2.27344e14	0.0856554
$237$	−1.42920e15	−0.523878
$238$	2.14410e15	0.764705
$239$	−3.05022e15	−1.05863	−0.529315	−	0.848425i	$-0.677551\pi$
$239$	−3.05022e15	−1.05863	−0.529315	+	0.848425i	$0.677551\pi$
$240$	1.47267e14	0.0497431
$241$	−3.78943e15	−1.24584	−0.622922	−	0.782284i	$-0.714055\pi$
$241$	−3.78943e15	−1.24584	−0.622922	+	0.782284i	$0.714055\pi$
$242$	−1.53008e15	−0.489683
$243$	−2.05891e14	−0.0641500
$244$	−2.41958e15	−0.734018
$245$	−2.44414e15	−0.722014
$246$	−2.29270e15	−0.659581
$247$	−3.35705e15	−0.940650
$248$	−4.78771e14	−0.130675
$249$	−3.06599e14	−0.0815220
$250$	2.35583e15	0.610286
$251$	−1.61252e14	−0.0407030	−0.0203515	−	0.999793i	$-0.506479\pi$
$251$	−1.61252e14	−0.0407030	−0.0203515	+	0.999793i	$0.506479\pi$
$252$	1.18315e15	0.291028
$253$	1.80413e15	0.432498
$254$	2.05325e15	0.479759
$255$	−2.36969e15	−0.539734
$256$	−4.19740e15	−0.932010
$257$	−6.41643e15	−1.38908	−0.694541	−	0.719453i	$-0.744393\pi$
$257$	−6.41643e15	−1.38908	−0.694541	+	0.719453i	$0.744393\pi$
$258$	−1.16049e14	−0.0244970
$259$	−1.47261e15	−0.303136
$260$	−2.58744e15	−0.519450
$261$	−1.17492e15	−0.230062
$262$	−5.70419e14	−0.108952
$263$	−5.44228e15	−1.01407	−0.507036	−	0.861925i	$-0.669259\pi$
$263$	−5.44228e15	−1.01407	−0.507036	+	0.861925i	$0.669259\pi$
$264$	1.24234e15	0.225847
$265$	7.89586e15	1.40056
$266$	−5.06882e15	−0.877357
$267$	−3.17158e14	−0.0535738
$268$	1.06142e15	0.174988
$269$	6.88971e15	1.10869	0.554347	−	0.832286i	$-0.312968\pi$
$269$	6.88971e15	1.10869	0.554347	+	0.832286i	$0.312968\pi$
$270$	6.79857e14	0.106796
$271$	1.04055e16	1.59574	0.797868	−	0.602833i	$-0.205961\pi$
$271$	1.04055e16	1.59574	0.797868	+	0.602833i	$0.205961\pi$
$272$	−5.97550e14	−0.0894698
$273$	−4.36070e15	−0.637528
$274$	−6.59531e14	−0.0941578
$275$	−2.88652e14	−0.0402450
$276$	2.99063e15	0.407243
$277$	−1.29214e16	−1.71866	−0.859331	−	0.511420i	$-0.829120\pi$
$277$	−1.29214e16	−1.71866	−0.859331	+	0.511420i	$0.829120\pi$
$278$	−7.85860e14	−0.102107
$279$	3.53896e14	0.0449208
$280$	−9.84476e15	−1.22089
$281$	−4.81022e15	−0.582873	−0.291436	−	0.956590i	$-0.594133\pi$
$281$	−4.81022e15	−0.582873	−0.291436	+	0.956590i	$0.594133\pi$
$282$	−2.71705e15	−0.321721
$283$	4.84010e15	0.560070	0.280035	−	0.959990i	$-0.409654\pi$
$283$	4.84010e15	0.560070	0.280035	+	0.959990i	$0.409654\pi$
$284$	2.15870e15	0.244131
$285$	5.60214e15	0.619245
$286$	−1.81706e15	−0.196332
$287$	−2.45403e16	−2.59208
$288$	3.30150e15	0.340926
$289$	−2.89353e14	−0.0292141
$290$	3.87962e15	0.383003
$291$	4.91930e15	0.474896
$292$	1.10416e15	0.104242
$293$	−1.84190e16	−1.70069	−0.850346	−	0.526224i	$-0.823607\pi$
$293$	−1.84190e16	−1.70069	−0.850346	+	0.526224i	$0.823607\pi$
$294$	−2.84525e15	−0.256958
$295$	1.39829e15	0.123524
$296$	−2.56319e15	−0.221506
$297$	−9.18303e14	−0.0776371
$298$	2.06130e15	0.170505
$299$	−1.10225e16	−0.892108
$300$	−4.78486e14	−0.0378950
$301$	−1.24216e15	−0.0962706
$302$	6.09701e15	0.462457
$303$	6.03575e13	0.00448079
$304$	1.41266e15	0.102650
$305$	−1.48817e16	−1.05853
$306$	−2.75858e15	−0.192086
$307$	1.62920e16	1.11064	0.555321	−	0.831636i	$-0.312595\pi$
$307$	1.62920e16	1.11064	0.555321	+	0.831636i	$0.312595\pi$
$308$	5.27700e15	0.352215
$309$	3.59916e15	0.235218
$310$	−1.16857e15	−0.0747833
$311$	−2.56749e15	−0.160904	−0.0804519	−	0.996758i	$-0.525636\pi$
$311$	−2.56749e15	−0.160904	−0.0804519	+	0.996758i	$0.525636\pi$
$312$	−7.59016e15	−0.465850
$313$	−1.03513e16	−0.622237	−0.311119	−	0.950371i	$-0.600704\pi$
$313$	−1.03513e16	−0.622237	−0.311119	+	0.950371i	$0.600704\pi$
$314$	7.59460e15	0.447159
$315$	7.27700e15	0.419695
$316$	−1.05667e16	−0.596996
$317$	7.88032e15	0.436173	0.218086	−	0.975929i	$-0.430019\pi$
$317$	7.88032e15	0.436173	0.218086	+	0.975929i	$0.430019\pi$
$318$	9.19167e15	0.498446
$319$	−5.24031e15	−0.278431
$320$	−9.24674e15	−0.481408
$321$	−5.60649e15	−0.286028
$322$	−1.66429e16	−0.832081
$323$	−2.27312e16	−1.11380
$324$	−1.52223e15	−0.0731035
$325$	1.76355e15	0.0830128
$326$	−4.95168e13	−0.00228475
$327$	−2.63703e15	−0.119277
$328$	−4.27145e16	−1.89407
$329$	−2.90825e16	−1.26433
$330$	3.03226e15	0.129249
$331$	1.80611e16	0.754855	0.377427	−	0.926039i	$-0.376809\pi$
$331$	1.80611e16	0.754855	0.377427	+	0.926039i	$0.376809\pi$
$332$	−2.26680e15	−0.0929002
$333$	1.89465e15	0.0761449
$334$	1.61352e16	0.635949
$335$	6.52828e15	0.252352
$336$	1.83500e15	0.0695713
$337$	−1.30441e16	−0.485087	−0.242543	−	0.970141i	$-0.577982\pi$
$337$	−1.30441e16	−0.485087	−0.242543	+	0.970141i	$0.577982\pi$
$338$	−4.93148e15	−0.179895
$339$	2.60487e16	0.932154
$340$	−1.75200e16	−0.615066
$341$	1.57842e15	0.0543651
$342$	6.52152e15	0.220384
$343$	9.56625e15	0.317198
$344$	−2.16208e15	−0.0703463
$345$	1.83940e16	0.587289
$346$	1.15896e16	0.363141
$347$	2.45147e16	0.753851	0.376925	−	0.926244i	$-0.376981\pi$
$347$	2.45147e16	0.753851	0.376925	+	0.926244i	$0.376981\pi$
$348$	−8.68664e15	−0.262172
$349$	−1.99669e16	−0.591489	−0.295744	−	0.955267i	$-0.595568\pi$
$349$	−1.99669e16	−0.591489	−0.295744	+	0.955267i	$0.595568\pi$
$350$	2.66278e15	0.0774272
$351$	5.61046e15	0.160141
$352$	1.47251e16	0.412603
$353$	−3.57892e16	−0.984502	−0.492251	−	0.870453i	$-0.663826\pi$
$353$	−3.57892e16	−0.984502	−0.492251	+	0.870453i	$0.663826\pi$
$354$	1.62776e15	0.0439612
$355$	1.32772e16	0.352064
$356$	−2.34487e15	−0.0610511
$357$	−2.95271e16	−0.754878
$358$	6.72273e15	0.168774
$359$	−4.42811e15	−0.109170	−0.0545852	−	0.998509i	$-0.517384\pi$
$359$	−4.42811e15	−0.109170	−0.0545852	+	0.998509i	$0.517384\pi$
$360$	1.26662e16	0.306677
$361$	1.16855e16	0.277875
$362$	−4.72355e16	−1.10322
$363$	2.10713e16	0.483391
$364$	−3.22403e16	−0.726508
$365$	6.79120e15	0.150329
$366$	−1.73240e16	−0.376722
$367$	−7.27825e16	−1.55488	−0.777442	−	0.628955i	$-0.783483\pi$
$367$	−7.27825e16	−1.55488	−0.777442	+	0.628955i	$0.783483\pi$
$368$	4.63830e15	0.0973527
$369$	3.15735e16	0.651105
$370$	−6.25617e15	−0.126764
$371$	9.83849e16	1.95884
$372$	2.61649e15	0.0511905
$373$	2.72476e16	0.523868	0.261934	−	0.965086i	$-0.415640\pi$
$373$	2.72476e16	0.523868	0.261934	+	0.965086i	$0.415640\pi$
$374$	−1.23037e16	−0.232471
$375$	−3.24429e16	−0.602444
$376$	−5.06206e16	−0.923860
$377$	3.20161e16	0.574315
$378$	8.47124e15	0.149366
$379$	3.61868e14	0.00627185	0.00313592	−	0.999995i	$-0.499002\pi$
$379$	3.61868e14	0.00627185	0.00313592	+	0.999995i	$0.499002\pi$
$380$	4.14188e16	0.705674
$381$	−2.82760e16	−0.473594
$382$	−5.51561e16	−0.908200
$383$	6.39805e16	1.03575	0.517876	−	0.855456i	$-0.326723\pi$
$383$	6.39805e16	1.03575	0.517876	+	0.855456i	$0.326723\pi$
$384$	2.63357e16	0.419172
$385$	3.24564e16	0.507932
$386$	4.98281e16	0.766756
$387$	1.59815e15	0.0241822
$388$	3.63703e16	0.541178
$389$	7.05074e16	1.03172	0.515860	−	0.856673i	$-0.327472\pi$
$389$	7.05074e16	1.03172	0.515860	+	0.856673i	$0.327472\pi$
$390$	−1.85259e16	−0.266599
$391$	−7.46353e16	−1.05632
$392$	−5.30090e16	−0.737887
$393$	7.85543e15	0.107552
$394$	−7.67785e16	−1.03398
$395$	−6.49907e16	−0.860934
$396$	−6.78937e15	−0.0884730
$397$	8.31775e16	1.06627	0.533135	−	0.846030i	$-0.321014\pi$
$397$	8.31775e16	1.06627	0.533135	+	0.846030i	$0.321014\pi$
$398$	4.83425e16	0.609662
$399$	6.98045e16	0.866083
$400$	−7.42106e14	−0.00905891
$401$	1.42240e17	1.70837	0.854187	−	0.519966i	$-0.174056\pi$
$401$	1.42240e17	1.70837	0.854187	+	0.519966i	$0.174056\pi$
$402$	7.59965e15	0.0898099
$403$	−9.64352e15	−0.112138
$404$	4.46247e14	0.00510618
$405$	−9.36255e15	−0.105423
$406$	4.83413e16	0.535672
$407$	8.45039e15	0.0921538
$408$	−5.13943e16	−0.551600
$409$	1.76353e17	1.86287	0.931433	−	0.363912i	$-0.118559\pi$
$409$	1.76353e17	1.86287	0.931433	+	0.363912i	$0.118559\pi$
$410$	−1.04256e17	−1.08395
$411$	9.08262e15	0.0929478
$412$	2.66100e16	0.268048
$413$	1.74231e16	0.172763
$414$	2.14127e16	0.209011
$415$	−1.39421e16	−0.133972
$416$	−8.99646e16	−0.851069
$417$	1.08223e16	0.100795
$418$	2.90869e16	0.266718
$419$	−7.54584e16	−0.681266	−0.340633	−	0.940196i	$-0.610641\pi$
$419$	−7.54584e16	−0.681266	−0.340633	+	0.940196i	$0.610641\pi$
$420$	5.38016e16	0.478272
$421$	1.61204e16	0.141105	0.0705525	−	0.997508i	$-0.477524\pi$
$421$	1.61204e16	0.141105	0.0705525	+	0.997508i	$0.477524\pi$
$422$	1.25406e17	1.08091
$423$	3.74174e16	0.317586
$424$	1.71247e17	1.43135
$425$	1.19413e16	0.0982931
$426$	1.54561e16	0.125296
$427$	−1.85431e17	−1.48048
$428$	−4.14510e16	−0.325949
$429$	2.50234e16	0.193809
$430$	−5.27713e15	−0.0402581
$431$	2.11458e16	0.158899	0.0794496	−	0.996839i	$-0.474684\pi$
$431$	2.11458e16	0.158899	0.0794496	+	0.996839i	$0.474684\pi$
$432$	−2.36090e15	−0.0174756
$433$	−1.96271e17	−1.43115	−0.715574	−	0.698537i	$-0.753835\pi$
$433$	−1.96271e17	−1.43115	−0.715574	+	0.698537i	$0.753835\pi$
$434$	−1.45608e16	−0.104593
$435$	−5.34275e16	−0.378081
$436$	−1.94966e16	−0.135924
$437$	1.76444e17	1.21193
$438$	7.90572e15	0.0535007
$439$	1.63153e17	1.08786	0.543932	−	0.839129i	$-0.316935\pi$
$439$	1.63153e17	1.08786	0.543932	+	0.839129i	$0.316935\pi$
$440$	5.64931e16	0.371153
$441$	3.91829e16	0.253656
$442$	7.51704e16	0.479515
$443$	9.43420e16	0.593036	0.296518	−	0.955027i	$-0.404175\pi$
$443$	9.43420e16	0.593036	0.296518	+	0.955027i	$0.404175\pi$
$444$	1.40079e16	0.0867726
$445$	−1.44222e16	−0.0880424
$446$	1.27334e17	0.766068
$447$	−2.83869e16	−0.168314
$448$	−1.15217e17	−0.673303
$449$	8.35783e16	0.481385	0.240692	−	0.970601i	$-0.422626\pi$
$449$	8.35783e16	0.481385	0.240692	+	0.970601i	$0.422626\pi$
$450$	−3.42592e15	−0.0194490
$451$	1.40822e17	0.787995
$452$	1.92588e17	1.06226
$453$	−8.39639e16	−0.456514
$454$	1.95366e17	1.04709
$455$	−1.98295e17	−1.04770
$456$	1.21501e17	0.632858
$457$	2.88918e17	1.48361	0.741805	−	0.670615i	$-0.233970\pi$
$457$	2.88918e17	1.48361	0.741805	+	0.670615i	$0.233970\pi$
$458$	−1.26851e16	−0.0642196
$459$	3.79894e16	0.189618
$460$	1.35994e17	0.669257
$461$	2.60150e16	0.126232	0.0631159	−	0.998006i	$-0.479896\pi$
$461$	2.60150e16	0.126232	0.0631159	+	0.998006i	$0.479896\pi$
$462$	3.77829e16	0.180768
$463$	8.30710e16	0.391898	0.195949	−	0.980614i	$-0.437221\pi$
$463$	8.30710e16	0.391898	0.195949	+	0.980614i	$0.437221\pi$
$464$	−1.34725e16	−0.0626731
$465$	1.60928e16	0.0738223
$466$	8.34504e16	0.377503
$467$	−2.52906e17	−1.12824	−0.564118	−	0.825694i	$-0.690784\pi$
$467$	−2.52906e17	−1.12824	−0.564118	+	0.825694i	$0.690784\pi$
$468$	4.14803e16	0.182492
$469$	8.13444e16	0.352943
$470$	−1.23553e17	−0.528711
$471$	−1.04588e17	−0.441413
$472$	3.03263e16	0.126240
$473$	7.12798e15	0.0292664
$474$	−7.56564e16	−0.306398
$475$	−2.82302e16	−0.112773
$476$	−2.18305e17	−0.860238
$477$	−1.26582e17	−0.492041
$478$	−1.61466e17	−0.619157
$479$	−4.06289e16	−0.153693	−0.0768466	−	0.997043i	$-0.524485\pi$
$479$	−4.06289e16	−0.153693	−0.0768466	+	0.997043i	$0.524485\pi$
$480$	1.50130e17	0.560273
$481$	−5.16284e16	−0.190084
$482$	−2.00598e17	−0.728652
$483$	2.29195e17	0.821389
$484$	1.55788e17	0.550858
$485$	2.23697e17	0.780438
$486$	−1.08991e16	−0.0375192
$487$	1.91152e17	0.649293	0.324647	−	0.945835i	$-0.394755\pi$
$487$	1.91152e17	0.649293	0.324647	+	0.945835i	$0.394755\pi$
$488$	−3.22758e17	−1.08180
$489$	6.81913e14	0.00225539
$490$	−1.29383e17	−0.422282
$491$	2.73363e17	0.880461	0.440231	−	0.897885i	$-0.354897\pi$
$491$	2.73363e17	0.880461	0.440231	+	0.897885i	$0.354897\pi$
$492$	2.33435e17	0.741981
$493$	2.16787e17	0.680030
$494$	−1.77709e17	−0.550154
$495$	−4.17583e16	−0.127588
$496$	4.05802e15	0.0122372
$497$	1.65438e17	0.492401
$498$	−1.62301e16	−0.0476795
$499$	2.57000e17	0.745211	0.372605	−	0.927990i	$-0.378465\pi$
$499$	2.57000e17	0.745211	0.372605	+	0.927990i	$0.378465\pi$
$500$	−2.39863e17	−0.686528
$501$	−2.22203e17	−0.627776
$502$	−8.53604e15	−0.0238058
$503$	−6.49415e17	−1.78785	−0.893923	−	0.448220i	$-0.852058\pi$
$503$	−6.49415e17	−1.78785	−0.893923	+	0.448220i	$0.852058\pi$
$504$	1.57825e17	0.428921
$505$	2.74466e15	0.00736366
$506$	9.55035e16	0.252954
$507$	6.79131e16	0.177583
$508$	−2.09055e17	−0.539694
$509$	−1.17905e17	−0.300514	−0.150257	−	0.988647i	$-0.548010\pi$
$509$	−1.17905e17	−0.300514	−0.150257	+	0.988647i	$0.548010\pi$
$510$	−1.25442e17	−0.315672
$511$	8.46205e16	0.210252
$512$	7.37489e16	0.180926
$513$	−8.98101e16	−0.217552
$514$	−3.39660e17	−0.812427
$515$	1.63666e17	0.386554
$516$	1.18157e16	0.0275574
$517$	1.66887e17	0.384356
$518$	−7.79539e16	−0.177294
$519$	−1.59605e17	−0.358475
$520$	−3.45150e17	−0.765571
$521$	3.63292e17	0.795811	0.397906	−	0.917426i	$-0.369737\pi$
$521$	3.63292e17	0.795811	0.397906	+	0.917426i	$0.369737\pi$
$522$	−6.21956e16	−0.134556
$523$	3.36655e17	0.719323	0.359662	−	0.933083i	$-0.382892\pi$
$523$	3.36655e17	0.719323	0.359662	+	0.933083i	$0.382892\pi$
$524$	5.80782e16	0.122563
$525$	−3.66701e16	−0.0764322
$526$	−2.88093e17	−0.593096
$527$	−6.52980e16	−0.132779
$528$	−1.05299e16	−0.0211497
$529$	7.52972e16	0.149388
$530$	4.17975e17	0.819139
$531$	−2.24165e16	−0.0433963
$532$	5.16091e17	0.986963
$533$	−8.60366e17	−1.62539
$534$	−1.67891e16	−0.0313335
$535$	−2.54946e17	−0.470054
$536$	1.41587e17	0.257900
$537$	−9.25810e16	−0.166605
$538$	3.64714e17	0.648437
$539$	1.74761e17	0.306986
$540$	−6.92209e16	−0.120137
$541$	6.16378e17	1.05698	0.528488	−	0.848941i	$-0.322759\pi$
$541$	6.16378e17	1.05698	0.528488	+	0.848941i	$0.322759\pi$
$542$	5.50824e17	0.933291
$543$	6.50496e17	1.08904
$544$	−6.09166e17	−1.00773
$545$	−1.19914e17	−0.196017
$546$	−2.30838e17	−0.372868
$547$	2.56338e17	0.409163	0.204581	−	0.978850i	$-0.434417\pi$
$547$	2.56338e17	0.409163	0.204581	+	0.978850i	$0.434417\pi$
$548$	6.71513e16	0.105921
$549$	2.38575e17	0.371881
$550$	−1.52801e16	−0.0235380
$551$	−5.12503e17	−0.780209
$552$	3.98933e17	0.600200
$553$	−8.09804e17	−1.20411
$554$	−6.84007e17	−1.00519
$555$	8.61559e16	0.125135
$556$	8.00137e16	0.114863
$557$	6.80740e17	0.965878	0.482939	−	0.875654i	$-0.339569\pi$
$557$	6.80740e17	0.965878	0.482939	+	0.875654i	$0.339569\pi$
$558$	1.87338e16	0.0262727
$559$	−4.35490e16	−0.0603673
$560$	8.34433e16	0.114332
$561$	1.69438e17	0.229484
$562$	−2.54634e17	−0.340903
$563$	−3.41798e17	−0.452340	−0.226170	−	0.974088i	$-0.572621\pi$
$563$	−3.41798e17	−0.452340	−0.226170	+	0.974088i	$0.572621\pi$
$564$	2.76642e17	0.361912
$565$	1.18452e18	1.53189
$566$	2.56216e17	0.327566
$567$	−1.16660e17	−0.147446
$568$	2.87959e17	0.359804
$569$	1.11798e18	1.38103	0.690516	−	0.723318i	$-0.257384\pi$
$569$	1.11798e18	1.38103	0.690516	+	0.723318i	$0.257384\pi$
$570$	2.96555e17	0.362175
$571$	−2.93875e17	−0.354836	−0.177418	−	0.984136i	$-0.556774\pi$
$571$	−2.93875e17	−0.354836	−0.177418	+	0.984136i	$0.556774\pi$
$572$	1.85008e17	0.220859
$573$	7.59573e17	0.896530
$574$	−1.29907e18	−1.51602
$575$	−9.26906e16	−0.106953
$576$	1.48238e17	0.169127
$577$	−8.64918e17	−0.975735	−0.487868	−	0.872918i	$-0.662225\pi$
$577$	−8.64918e17	−0.975735	−0.487868	+	0.872918i	$0.662225\pi$
$578$	−1.53172e16	−0.0170863
$579$	−6.86200e17	−0.756903
$580$	−3.95010e17	−0.430850
$581$	−1.73723e17	−0.187375
$582$	2.60408e17	0.277751
$583$	−5.64571e17	−0.595488
$584$	1.47289e17	0.153634
$585$	2.55126e17	0.263173
$586$	−9.75027e17	−0.994677
$587$	−1.34860e17	−0.136061	−0.0680306	−	0.997683i	$-0.521672\pi$
$587$	−1.34860e17	−0.136061	−0.0680306	+	0.997683i	$0.521672\pi$
$588$	2.89694e17	0.289059
$589$	1.54370e17	0.152340
$590$	7.40197e16	0.0722452
$591$	1.05734e18	1.02070
$592$	2.17254e16	0.0207433
$593$	2.81323e17	0.265675	0.132837	−	0.991138i	$-0.457591\pi$
$593$	2.81323e17	0.265675	0.132837	+	0.991138i	$0.457591\pi$
$594$	−4.86113e16	−0.0454073
$595$	−1.34269e18	−1.24056
$596$	−2.09875e17	−0.191805
$597$	−6.65741e17	−0.601828
$598$	−5.83487e17	−0.521763
$599$	9.72310e17	0.860064	0.430032	−	0.902814i	$-0.358502\pi$
$599$	9.72310e17	0.860064	0.430032	+	0.902814i	$0.358502\pi$
$600$	−6.38273e16	−0.0558501
$601$	−7.39160e17	−0.639815	−0.319908	−	0.947449i	$-0.603652\pi$
$601$	−7.39160e17	−0.639815	−0.319908	+	0.947449i	$0.603652\pi$
$602$	−6.57548e16	−0.0563054
$603$	−1.04657e17	−0.0886558
$604$	−6.20778e17	−0.520231
$605$	9.58181e17	0.794397
$606$	3.19509e15	0.00262066
$607$	−7.29265e17	−0.591778	−0.295889	−	0.955222i	$-0.595616\pi$
$607$	−7.29265e17	−0.591778	−0.295889	+	0.955222i	$0.595616\pi$
$608$	1.44012e18	1.15618
$609$	−6.65724e17	−0.528788
$610$	−7.87780e17	−0.619100
$611$	−1.01961e18	−0.792806
$612$	2.80870e17	0.216083
$613$	−5.44643e17	−0.414590	−0.207295	−	0.978278i	$-0.566466\pi$
$613$	−5.44643e17	−0.414590	−0.207295	+	0.978278i	$0.566466\pi$
$614$	8.62432e17	0.649576
$615$	1.43575e18	1.07002
$616$	7.03922e17	0.519099
$617$	4.00338e17	0.292128	0.146064	−	0.989275i	$-0.453339\pi$
$617$	4.00338e17	0.292128	0.146064	+	0.989275i	$0.453339\pi$
$618$	1.90525e17	0.137571
$619$	−2.37123e18	−1.69428	−0.847140	−	0.531370i	$-0.821677\pi$
$619$	−2.37123e18	−1.69428	−0.847140	+	0.531370i	$0.821677\pi$
$620$	1.18980e17	0.0841257
$621$	−2.94881e17	−0.206325
$622$	−1.35913e17	−0.0941071
$623$	−1.79705e17	−0.123137
$624$	6.43336e16	0.0436252
$625$	−1.32663e18	−0.890287
$626$	−5.47956e17	−0.363925
$627$	−4.00566e17	−0.263290
$628$	−7.73258e17	−0.503022
$629$	−3.49585e17	−0.225073
$630$	3.85215e17	0.245465
$631$	−1.48994e18	−0.939676	−0.469838	−	0.882753i	$-0.655688\pi$
$631$	−1.48994e18	−0.939676	−0.469838	+	0.882753i	$0.655688\pi$
$632$	−1.40953e18	−0.879861
$633$	−1.72701e18	−1.06702
$634$	4.17153e17	0.255103
$635$	−1.28580e18	−0.778297
$636$	−9.35866e17	−0.560715
$637$	−1.06772e18	−0.633214
$638$	−2.77401e17	−0.162845
$639$	−2.12852e17	−0.123686
$640$	1.19757e18	0.688861
$641$	1.23302e18	0.702088	0.351044	−	0.936359i	$-0.385827\pi$
$641$	1.23302e18	0.702088	0.351044	+	0.936359i	$0.385827\pi$
$642$	−2.96786e17	−0.167288
$643$	−2.58757e18	−1.44385	−0.721924	−	0.691972i	$-0.756742\pi$
$643$	−2.58757e18	−1.44385	−0.721924	+	0.691972i	$0.756742\pi$
$644$	1.69453e18	0.936031
$645$	7.26732e16	0.0397408
$646$	−1.20330e18	−0.651422
$647$	1.27248e18	0.681984	0.340992	−	0.940066i	$-0.389237\pi$
$647$	1.27248e18	0.681984	0.340992	+	0.940066i	$0.389237\pi$
$648$	−2.03057e17	−0.107741
$649$	−9.99806e16	−0.0525200
$650$	9.33551e16	0.0485514
$651$	2.00521e17	0.103249
$652$	5.04165e15	0.00257018
$653$	−5.94769e17	−0.300201	−0.150101	−	0.988671i	$-0.547960\pi$
$653$	−5.94769e17	−0.300201	−0.150101	+	0.988671i	$0.547960\pi$
$654$	−1.39594e17	−0.0697608
$655$	3.57212e17	0.176749
$656$	3.62045e17	0.177373
$657$	−1.08872e17	−0.0528132
$658$	−1.53951e18	−0.739461
$659$	1.13181e18	0.538294	0.269147	−	0.963099i	$-0.413258\pi$
$659$	1.13181e18	0.538294	0.269147	+	0.963099i	$0.413258\pi$
$660$	−3.08735e17	−0.145395
$661$	−5.06120e17	−0.236017	−0.118009	−	0.993013i	$-0.537651\pi$
$661$	−5.06120e17	−0.236017	−0.118009	+	0.993013i	$0.537651\pi$
$662$	9.56085e17	0.441489
$663$	−1.03520e18	−0.473353
$664$	−3.02379e17	−0.136917
$665$	3.17424e18	1.42331
$666$	1.00295e17	0.0445346
$667$	−1.68274e18	−0.739946
$668$	−1.64283e18	−0.715396
$669$	−1.75356e18	−0.756224
$670$	3.45581e17	0.147592
$671$	1.06408e18	0.450067
$672$	1.87067e18	0.783603
$673$	7.45977e17	0.309476	0.154738	−	0.987956i	$-0.450547\pi$
$673$	7.45977e17	0.309476	0.154738	+	0.987956i	$0.450547\pi$
$674$	−6.90502e17	−0.283711
$675$	4.71796e16	0.0191990
$676$	5.02108e17	0.202369
$677$	−1.68066e18	−0.670895	−0.335448	−	0.942059i	$-0.608888\pi$
$677$	−1.68066e18	−0.670895	−0.335448	+	0.942059i	$0.608888\pi$
$678$	1.37891e18	0.545185
$679$	2.78733e18	1.09153
$680$	−2.33707e18	−0.906491
$681$	−2.69045e18	−1.03364
$682$	8.35555e16	0.0317963
$683$	−8.15123e16	−0.0307248	−0.0153624	−	0.999882i	$-0.504890\pi$
$683$	−8.15123e16	−0.0307248	−0.0153624	+	0.999882i	$0.504890\pi$
$684$	−6.64001e17	−0.247916
$685$	4.13017e17	0.152749
$686$	5.06399e17	0.185518
$687$	1.74691e17	0.0633944
$688$	1.83256e16	0.00658768
$689$	3.44930e18	1.22830
$690$	9.73704e17	0.343485
$691$	−4.27942e17	−0.149547	−0.0747734	−	0.997201i	$-0.523823\pi$
$691$	−4.27942e17	−0.149547	−0.0747734	+	0.997201i	$0.523823\pi$
$692$	−1.18002e18	−0.408507
$693$	−5.20321e17	−0.178446
$694$	1.29771e18	0.440902
$695$	4.92128e17	0.165644
$696$	−1.15875e18	−0.386393
$697$	−5.82569e18	−1.92457
$698$	−1.05697e18	−0.345942
$699$	−1.14922e18	−0.372652
$700$	−2.71116e17	−0.0871000
$701$	2.89387e18	0.921110	0.460555	−	0.887631i	$-0.347650\pi$
$701$	2.89387e18	0.921110	0.460555	+	0.887631i	$0.347650\pi$
$702$	2.96995e17	0.0936609
$703$	8.26449e17	0.258230
$704$	6.61162e17	0.204685
$705$	1.70149e18	0.521917
$706$	−1.89454e18	−0.575802
$707$	3.41993e16	0.0102989
$708$	−1.65734e17	−0.0494532
$709$	−2.73955e18	−0.809988	−0.404994	−	0.914319i	$-0.632726\pi$
$709$	−2.73955e18	−0.809988	−0.404994	+	0.914319i	$0.632726\pi$
$710$	7.02841e17	0.205910
$711$	1.04189e18	0.302461
$712$	−3.12792e17	−0.0899779
$713$	5.06856e17	0.144478
$714$	−1.56305e18	−0.441503
$715$	1.13790e18	0.318503
$716$	−6.84487e17	−0.189859
$717$	2.22361e18	0.611200
$718$	−2.34407e17	−0.0638500
$719$	−1.31729e18	−0.355585	−0.177793	−	0.984068i	$-0.556896\pi$
$719$	−1.31729e18	−0.355585	−0.177793	+	0.984068i	$0.556896\pi$
$720$	−1.07358e17	−0.0287192
$721$	2.03932e18	0.540639
$722$	6.18583e17	0.162520
$723$	2.76250e18	0.719288
$724$	4.80936e18	1.24104
$725$	2.69231e17	0.0688538
$726$	1.11543e18	0.282719
$727$	−6.78555e18	−1.70456	−0.852278	−	0.523088i	$-0.824780\pi$
$727$	−6.78555e18	−1.70456	−0.852278	+	0.523088i	$0.824780\pi$
$728$	−4.30068e18	−1.07074
$729$	1.50095e17	0.0370370
$730$	3.59499e17	0.0879223
$731$	−2.94878e17	−0.0714792
$732$	1.76388e18	0.423785
$733$	−5.28441e18	−1.25841	−0.629203	−	0.777241i	$-0.716619\pi$
$733$	−5.28441e18	−1.25841	−0.629203	+	0.777241i	$0.716619\pi$
$734$	−3.85282e18	−0.909398
$735$	1.78178e18	0.416855
$736$	4.72847e18	1.09651
$737$	−4.66786e17	−0.107295
$738$	1.67138e18	0.380809
$739$	−5.56521e18	−1.25688	−0.628439	−	0.777859i	$-0.716306\pi$
$739$	−5.56521e18	−1.25688	−0.628439	+	0.777859i	$0.716306\pi$
$740$	6.36983e17	0.142601
$741$	2.44729e18	0.543084
$742$	5.20811e18	1.14566
$743$	5.01347e18	1.09323	0.546614	−	0.837385i	$-0.315916\pi$
$743$	5.01347e18	1.09323	0.546614	+	0.837385i	$0.315916\pi$
$744$	3.49024e17	0.0754452
$745$	−1.29085e18	−0.276604
$746$	1.44238e18	0.306392
$747$	2.23511e17	0.0470668
$748$	1.25272e18	0.261513
$749$	−3.17671e18	−0.657423
$750$	−1.71740e18	−0.352349
$751$	−5.55282e18	−1.12942	−0.564708	−	0.825291i	$-0.691011\pi$
$751$	−5.55282e18	−1.12942	−0.564708	+	0.825291i	$0.691011\pi$
$752$	4.29056e17	0.0865163
$753$	1.17553e17	0.0234999
$754$	1.69481e18	0.335897
$755$	−3.81812e18	−0.750229
$756$	−8.62515e17	−0.168025
$757$	−2.69428e18	−0.520379	−0.260189	−	0.965558i	$-0.583785\pi$
$757$	−2.69428e18	−0.520379	−0.260189	+	0.965558i	$0.583785\pi$
$758$	1.91559e16	0.00366819
$759$	−1.31521e18	−0.249703
$760$	5.52503e18	1.04003
$761$	6.36065e18	1.18714	0.593569	−	0.804783i	$-0.297718\pi$
$761$	6.36065e18	1.18714	0.593569	+	0.804783i	$0.297718\pi$
$762$	−1.49682e18	−0.276989
$763$	−1.49417e18	−0.274152
$764$	5.61582e18	1.02166
$765$	1.72750e18	0.311616
$766$	3.38687e18	0.605776
$767$	6.10840e17	0.108332
$768$	3.05990e18	0.538096
$769$	−4.04769e18	−0.705806	−0.352903	−	0.935660i	$-0.614806\pi$
$769$	−4.04769e18	−0.705806	−0.352903	+	0.935660i	$0.614806\pi$
$770$	1.71811e18	0.297072
$771$	4.67758e18	0.801987
$772$	−5.07334e18	−0.862545
$773$	−5.86398e18	−0.988611	−0.494306	−	0.869288i	$-0.664578\pi$
$773$	−5.86398e18	−0.988611	−0.494306	+	0.869288i	$0.664578\pi$
$774$	8.45998e16	0.0141434
$775$	−8.10945e16	−0.0134441
$776$	4.85159e18	0.797595
$777$	1.07353e18	0.175016
$778$	3.73238e18	0.603418
$779$	1.37724e19	2.20809
$780$	1.88624e18	0.299904
$781$	−9.49348e17	−0.149690
$782$	−3.95089e18	−0.617805
$783$	8.56517e17	0.132826
$784$	4.49300e17	0.0691006
$785$	−4.75595e18	−0.725412
$786$	4.15835e17	0.0629035
$787$	−3.23596e18	−0.485476	−0.242738	−	0.970092i	$-0.578045\pi$
$787$	−3.23596e18	−0.485476	−0.242738	+	0.970092i	$0.578045\pi$
$788$	7.81734e18	1.16316
$789$	3.96742e18	0.585474
$790$	−3.44035e18	−0.503531
$791$	1.47595e19	2.14252
$792$	−9.05663e17	−0.130393
$793$	−6.50108e18	−0.928345
$794$	4.40309e18	0.623626
$795$	−5.75608e18	−0.808613
$796$	−4.92208e18	−0.685826
$797$	−1.27032e19	−1.75564	−0.877819	−	0.478993i	$-0.841002\pi$
$797$	−1.27032e19	−1.75564	−0.877819	+	0.478993i	$0.841002\pi$
$798$	3.69517e18	0.506542
$799$	−6.90397e18	−0.938739
$800$	−7.56532e17	−0.102033
$801$	2.31208e17	0.0309308
$802$	7.52961e18	0.999170
$803$	−4.85586e17	−0.0639168
$804$	−7.73772e17	−0.101030
$805$	1.04222e19	1.34986
$806$	−5.10490e17	−0.0655857
$807$	−5.02260e18	−0.640104
$808$	5.95267e16	0.00752555
$809$	3.77318e18	0.473197	0.236599	−	0.971607i	$-0.423967\pi$
$809$	3.77318e18	0.473197	0.236599	+	0.971607i	$0.423967\pi$
$810$	−4.95616e17	−0.0616585
$811$	−4.85204e18	−0.598809	−0.299405	−	0.954126i	$-0.596788\pi$
$811$	−4.85204e18	−0.598809	−0.299405	+	0.954126i	$0.596788\pi$
$812$	−4.92195e18	−0.602592
$813$	−7.58558e18	−0.921298
$814$	4.47330e17	0.0538976
$815$	3.10088e16	0.00370647
$816$	4.35614e17	0.0516554
$817$	6.97117e17	0.0820091
$818$	9.33544e18	1.08953
$819$	3.17895e18	0.368077
$820$	1.06151e19	1.21936
$821$	−3.20579e18	−0.365346	−0.182673	−	0.983174i	$-0.558475\pi$
$821$	−3.20579e18	−0.365346	−0.182673	+	0.983174i	$0.558475\pi$
$822$	4.80798e17	0.0543620
$823$	−1.19960e19	−1.34567	−0.672834	−	0.739794i	$-0.734923\pi$
$823$	−1.19960e19	−1.34567	−0.672834	+	0.739794i	$0.734923\pi$
$824$	3.54961e18	0.395052
$825$	2.10427e17	0.0232355
$826$	9.22309e17	0.101043
$827$	7.99788e18	0.869339	0.434669	−	0.900590i	$-0.356865\pi$
$827$	7.99788e18	0.869339	0.434669	+	0.900590i	$0.356865\pi$
$828$	−2.18017e18	−0.235122
$829$	−4.06021e18	−0.434454	−0.217227	−	0.976121i	$-0.569701\pi$
$829$	−4.06021e18	−0.434454	−0.217227	+	0.976121i	$0.569701\pi$
$830$	−7.38038e17	−0.0783558
$831$	9.41969e18	0.992270
$832$	−4.03943e18	−0.422200
$833$	−7.22972e18	−0.749771
$834$	5.72892e17	0.0589513
$835$	−1.01043e19	−1.03168
$836$	−2.96154e18	−0.300038
$837$	−2.57990e17	−0.0259351
$838$	−3.99447e18	−0.398449
$839$	7.42606e18	0.735031	0.367515	−	0.930017i	$-0.380209\pi$
$839$	7.42606e18	0.735031	0.367515	+	0.930017i	$0.380209\pi$
$840$	7.17683e18	0.704883
$841$	−5.37290e18	−0.523642
$842$	8.53350e17	0.0825275
$843$	3.50665e18	0.336522
$844$	−1.27684e19	−1.21594
$845$	3.08823e18	0.291838
$846$	1.98073e18	0.185745
$847$	1.19392e19	1.11105
$848$	−1.45148e18	−0.134041
$849$	−3.52843e18	−0.323357
$850$	6.32124e17	0.0574883
$851$	2.71355e18	0.244904
$852$	−1.57369e18	−0.140949
$853$	1.36262e19	1.21117	0.605587	−	0.795779i	$-0.292938\pi$
$853$	1.36262e19	1.21117	0.605587	+	0.795779i	$0.292938\pi$
$854$	−9.81599e18	−0.865880
$855$	−4.08396e18	−0.357521
$856$	−5.52932e18	−0.480388
$857$	−3.25642e17	−0.0280779	−0.0140390	−	0.999901i	$-0.504469\pi$
$857$	−3.25642e17	−0.0280779	−0.0140390	+	0.999901i	$0.504469\pi$
$858$	1.32464e18	0.113352
$859$	−1.73799e19	−1.47602	−0.738009	−	0.674790i	$-0.764234\pi$
$859$	−1.73799e19	−1.47602	−0.738009	+	0.674790i	$0.764234\pi$
$860$	5.37301e17	0.0452874
$861$	1.78899e19	1.49654
$862$	1.11937e18	0.0929348
$863$	−1.97071e19	−1.62388	−0.811939	−	0.583743i	$-0.801588\pi$
$863$	−1.97071e19	−1.62388	−0.811939	+	0.583743i	$0.801588\pi$
$864$	−2.40679e18	−0.196834
$865$	−7.25776e18	−0.589112
$866$	−1.03898e19	−0.837029
$867$	2.10938e17	0.0168668
$868$	1.48253e18	0.117659
$869$	4.64698e18	0.366051
$870$	−2.82824e18	−0.221127
$871$	2.85187e18	0.221316
$872$	−2.60073e18	−0.200327
$873$	−3.58617e18	−0.274182
$874$	9.34025e18	0.708817
$875$	−1.83825e19	−1.38469
$876$	−8.04935e17	−0.0601844
$877$	−1.41182e19	−1.04781	−0.523905	−	0.851776i	$-0.675525\pi$
$877$	−1.41182e19	−1.04781	−0.523905	+	0.851776i	$0.675525\pi$
$878$	8.63665e18	0.636255
$879$	1.34274e19	0.981895
$880$	−4.78831e17	−0.0347572
$881$	−2.43112e19	−1.75171	−0.875857	−	0.482571i	$-0.839703\pi$
$881$	−2.43112e19	−1.75171	−0.875857	+	0.482571i	$0.839703\pi$
$882$	2.07419e18	0.148355
$883$	4.75021e18	0.337263	0.168631	−	0.985679i	$-0.446065\pi$
$883$	4.75021e18	0.337263	0.168631	+	0.985679i	$0.446065\pi$
$884$	−7.65361e18	−0.539419
$885$	−1.01935e18	−0.0713169
$886$	4.99409e18	0.346846
$887$	4.03966e18	0.278510	0.139255	−	0.990257i	$-0.455529\pi$
$887$	4.03966e18	0.278510	0.139255	+	0.990257i	$0.455529\pi$
$888$	1.86857e18	0.127886
$889$	−1.60215e19	−1.08853
$890$	−7.63454e17	−0.0514930
$891$	6.69443e17	0.0448238
$892$	−1.29647e19	−0.861771
$893$	1.63216e19	1.07703
$894$	−1.50269e18	−0.0984410
$895$	−4.20996e18	−0.273797
$896$	1.49221e19	0.963449
$897$	8.03540e18	0.515059
$898$	4.42430e18	0.281546
$899$	−1.47222e18	−0.0930113
$900$	3.48817e17	0.0218787
$901$	2.33558e19	1.45440
$902$	7.45457e18	0.460872
$903$	9.05531e17	0.0555819
$904$	2.56901e19	1.56557
$905$	2.95802e19	1.78972
$906$	−4.44472e18	−0.267000
$907$	1.36175e19	0.812175	0.406088	−	0.913834i	$-0.366893\pi$
$907$	1.36175e19	0.812175	0.406088	+	0.913834i	$0.366893\pi$
$908$	−1.98915e19	−1.17790
$909$	−4.40007e16	−0.00258698
$910$	−1.04970e19	−0.612766
$911$	2.27922e19	1.32104	0.660522	−	0.750806i	$-0.270335\pi$
$911$	2.27922e19	1.32104	0.660522	+	0.750806i	$0.270335\pi$
$912$	−1.02983e18	−0.0592650
$913$	9.96889e17	0.0569622
$914$	1.52942e19	0.867714
$915$	1.08488e19	0.611145
$916$	1.29156e18	0.0722424
$917$	4.45098e18	0.247204
$918$	2.01101e18	0.110901
$919$	2.16005e19	1.18281	0.591403	−	0.806376i	$-0.298574\pi$
$919$	2.16005e19	1.18281	0.591403	+	0.806376i	$0.298574\pi$
$920$	1.81408e19	0.986360
$921$	−1.18768e19	−0.641229
$922$	1.37713e18	0.0738286
$923$	5.80013e18	0.308764
$924$	−3.84694e18	−0.203351
$925$	−4.34155e17	−0.0227889
$926$	4.39745e18	0.229208
$927$	−2.62379e18	−0.135803
$928$	−1.37344e19	−0.705907
$929$	2.24565e19	1.14614	0.573072	−	0.819505i	$-0.305752\pi$
$929$	2.24565e19	1.14614	0.573072	+	0.819505i	$0.305752\pi$
$930$	8.51889e17	0.0431761
$931$	1.70917e19	0.860223
$932$	−8.49665e18	−0.424663
$933$	1.87170e18	0.0928978
$934$	−1.33878e19	−0.659867
$935$	7.70490e18	0.377130
$936$	5.53323e18	0.268959
$937$	−1.93776e19	−0.935392	−0.467696	−	0.883890i	$-0.654916\pi$
$937$	−1.93776e19	−0.935392	−0.467696	+	0.883890i	$0.654916\pi$
$938$	4.30605e18	0.206424
$939$	7.54609e18	0.359249
$940$	1.25798e19	0.594761
$941$	1.11702e19	0.524481	0.262241	−	0.965003i	$-0.415539\pi$
$941$	1.11702e19	0.524481	0.262241	+	0.965003i	$0.415539\pi$
$942$	−5.53646e18	−0.258167
$943$	4.52201e19	2.09414
$944$	−2.57044e17	−0.0118219
$945$	−5.30493e18	−0.242311
$946$	3.77327e17	0.0171169
$947$	4.05530e18	0.182704	0.0913519	−	0.995819i	$-0.470881\pi$
$947$	4.05530e18	0.182704	0.0913519	+	0.995819i	$0.470881\pi$
$948$	7.70310e18	0.344676
$949$	2.96673e18	0.131840
$950$	−1.49439e18	−0.0659571
$951$	−5.74475e18	−0.251824
$952$	−2.91206e19	−1.26783
$953$	7.00532e17	0.0302917	0.0151459	−	0.999885i	$-0.495179\pi$
$953$	7.00532e17	0.0302917	0.0151459	+	0.999885i	$0.495179\pi$
$954$	−6.70073e18	−0.287778
$955$	3.45403e19	1.47334
$956$	1.64400e19	0.696506
$957$	3.82019e18	0.160752
$958$	−2.15073e18	−0.0898899
$959$	5.14632e18	0.213637
$960$	6.74087e18	0.277941
$961$	−2.39741e19	−0.981839
$962$	−2.73300e18	−0.111174
$963$	4.08713e18	0.165138
$964$	2.04242e19	0.819680
$965$	−3.12038e19	−1.24388
$966$	1.21327e19	0.480402
$967$	−3.90005e19	−1.53390	−0.766952	−	0.641705i	$-0.778227\pi$
$967$	−3.90005e19	−1.53390	−0.766952	+	0.641705i	$0.778227\pi$
$968$	2.07813e19	0.811861
$969$	1.65710e19	0.643051
$970$	1.18416e19	0.456452
$971$	−1.69465e19	−0.648865	−0.324432	−	0.945909i	$-0.605173\pi$
$971$	−1.69465e19	−0.648865	−0.324432	+	0.945909i	$0.605173\pi$
$972$	1.10971e18	0.0422063
$973$	6.13207e18	0.231672
$974$	1.01188e19	0.379750
$975$	−1.28563e18	−0.0479275
$976$	2.73567e18	0.101307
$977$	5.54794e18	0.204088	0.102044	−	0.994780i	$-0.467462\pi$
$977$	5.54794e18	0.204088	0.102044	+	0.994780i	$0.467462\pi$
$978$	3.60978e16	0.00131910
$979$	1.03122e18	0.0374338
$980$	1.31733e19	0.475036
$981$	1.92240e18	0.0688643
$982$	1.44708e19	0.514952
$983$	−1.85716e19	−0.656525	−0.328263	−	0.944587i	$-0.606463\pi$
$983$	−1.85716e19	−0.656525	−0.328263	+	0.944587i	$0.606463\pi$
$984$	3.11389e19	1.09354
$985$	4.80809e19	1.67740
$986$	1.14758e19	0.397727
$987$	2.12012e19	0.729959
$988$	1.80938e19	0.618883
$989$	2.28890e18	0.0777770
$990$	−2.21052e18	−0.0746217
$991$	−2.96463e18	−0.0994242	−0.0497121	−	0.998764i	$-0.515830\pi$
$991$	−2.96463e18	−0.0994242	−0.0497121	+	0.998764i	$0.515830\pi$
$992$	4.13691e18	0.137832
$993$	−1.31666e19	−0.435815
$994$	8.75763e18	0.287988
$995$	−3.02734e19	−0.989036
$996$	1.65250e18	0.0536359
$997$	−5.55268e19	−1.79054	−0.895270	−	0.445525i	$-0.853017\pi$
$997$	−5.55268e19	−1.79054	−0.895270	+	0.445525i	$0.853017\pi$
$998$	1.36045e19	0.435848
$999$	−1.38120e18	−0.0439623

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.b.1.20	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.b.1.20	✓	31	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:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+52.9360 q^{2} -729.000 q^{3} -5389.78 q^{4} -33150.0 q^{5} -38590.4 q^{6} -413060. q^{7} -718965. q^{8} +531441. q^{9} +O(q^{10})\)	\(q+52.9360 q^{2} -729.000 q^{3} -5389.78 q^{4} -33150.0 q^{5} -38590.4 q^{6} -413060. q^{7} -718965. q^{8} +531441. q^{9} -1.75483e6 q^{10} +2.37030e6 q^{11} +3.92915e6 q^{12} -1.44816e7 q^{13} -2.18658e7 q^{14} +2.41664e7 q^{15} +6.09389e6 q^{16} -9.80573e7 q^{17} +2.81324e7 q^{18} +2.31816e8 q^{19} +1.78671e8 q^{20} +3.01121e8 q^{21} +1.25474e8 q^{22} +7.61140e8 q^{23} +5.24126e8 q^{24} -1.21779e8 q^{25} -7.66597e8 q^{26} -3.87420e8 q^{27} +2.22630e9 q^{28} -2.21082e9 q^{29} +1.27927e9 q^{30} +6.65917e8 q^{31} +6.21235e9 q^{32} -1.72795e9 q^{33} -5.19076e9 q^{34} +1.36930e10 q^{35} -2.86435e9 q^{36} +3.56511e9 q^{37} +1.22714e10 q^{38} +1.05571e10 q^{39} +2.38337e10 q^{40} +5.94111e10 q^{41} +1.59401e10 q^{42} +3.00720e9 q^{43} -1.27754e10 q^{44} -1.76173e10 q^{45} +4.02917e10 q^{46} +7.04075e10 q^{47} -4.44245e9 q^{48} +7.37295e10 q^{49} -6.44648e9 q^{50} +7.14837e10 q^{51} +7.80524e10 q^{52} -2.38186e11 q^{53} -2.05085e10 q^{54} -7.85755e10 q^{55} +2.96976e11 q^{56} -1.68994e11 q^{57} -1.17032e11 q^{58} -4.21805e10 q^{59} -1.30251e11 q^{60} +4.48921e11 q^{61} +3.52510e10 q^{62} -2.19517e11 q^{63} +2.78936e11 q^{64} +4.80064e11 q^{65} -9.14708e10 q^{66} -1.96931e11 q^{67} +5.28507e11 q^{68} -5.54871e11 q^{69} +7.24850e11 q^{70} -4.00518e11 q^{71} -3.82088e11 q^{72} -2.04862e11 q^{73} +1.88723e11 q^{74} +8.87767e10 q^{75} -1.24943e12 q^{76} -9.79076e11 q^{77} +5.58849e11 q^{78} +1.96050e12 q^{79} -2.02013e11 q^{80} +2.82430e11 q^{81} +3.14499e12 q^{82} +4.20575e11 q^{83} -1.62297e12 q^{84} +3.25060e12 q^{85} +1.59189e11 q^{86} +1.61169e12 q^{87} -1.70416e12 q^{88} +4.35059e11 q^{89} -9.32589e11 q^{90} +5.98176e12 q^{91} -4.10237e12 q^{92} -4.85453e11 q^{93} +3.72709e12 q^{94} -7.68469e12 q^{95} -4.52880e12 q^{96} -6.74801e12 q^{97} +3.90295e12 q^{98} +1.25968e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q - 52 q^{2} - 22599 q^{3} + 126886 q^{4} + 33486 q^{5} + 37908 q^{6} - 1135539 q^{7} - 1519749 q^{8} + 16474671 q^{9}+O(q^{10}) \) 31 * q - 52 * q^2 - 22599 * q^3 + 126886 * q^4 + 33486 * q^5 + 37908 * q^6 - 1135539 * q^7 - 1519749 * q^8 + 16474671 * q^9	\( 31 q - 52 q^{2} - 22599 q^{3} + 126886 q^{4} + 33486 q^{5} + 37908 q^{6} - 1135539 q^{7} - 1519749 q^{8} + 16474671 q^{9} - 3854663 q^{10} + 3943968 q^{11} - 92499894 q^{12} - 48510022 q^{13} - 51427459 q^{14} - 24411294 q^{15} + 370110498 q^{16} + 83288419 q^{17} - 27634932 q^{18} - 180425297 q^{19} + 753620445 q^{20} + 827807931 q^{21} + 2300196142 q^{22} - 1305810279 q^{23} + 1107897021 q^{24} + 8070954867 q^{25} + 464550322 q^{26} - 12010035159 q^{27} - 9887169562 q^{28} + 6248352277 q^{29} + 2810049327 q^{30} - 26730150789 q^{31} - 24001343230 q^{32} - 2875152672 q^{33} - 36571033348 q^{34} + 10255900979 q^{35} + 67432422726 q^{36} - 43284776933 q^{37} - 36293696947 q^{38} + 35363806038 q^{39} - 105980683856 q^{40} - 9961079285 q^{41} + 37490617611 q^{42} - 51755851288 q^{43} - 59623729442 q^{44} + 17795833326 q^{45} - 202287132683 q^{46} - 82747063727 q^{47} - 269810553042 q^{48} + 535277836542 q^{49} + 526974390461 q^{50} - 60717257451 q^{51} + 544982341446 q^{52} + 561701818494 q^{53} + 20145865428 q^{54} - 521861534450 q^{55} - 228056576664 q^{56} + 131530041513 q^{57} + 10555409160 q^{58} - 1307596542871 q^{59} - 549389304405 q^{60} + 618193248201 q^{61} - 1486611437386 q^{62} - 603471981699 q^{63} + 679062548045 q^{64} - 1130583307122 q^{65} - 1676842987518 q^{66} - 4137387490592 q^{67} - 3901389300295 q^{68} + 951935693391 q^{69} - 819291947844 q^{70} - 3766439869810 q^{71} - 807656928309 q^{72} - 2386775553523 q^{73} + 3060770694642 q^{74} - 5883726098043 q^{75} - 847741068784 q^{76} + 1650423006137 q^{77} - 338657184738 q^{78} + 787155757766 q^{79} + 13999832121779 q^{80} + 8755315630911 q^{81} + 10083281915577 q^{82} + 8743877051639 q^{83} + 7207746610698 q^{84} + 15373177520565 q^{85} + 18939443838984 q^{86} - 4555048809933 q^{87} + 39713314506713 q^{88} + 11026795445259 q^{89} - 2048525959383 q^{90} + 23285721962531 q^{91} + 40411079823254 q^{92} + 19486279925181 q^{93} + 35237377585624 q^{94} + 13730236994039 q^{95} + 17496979214670 q^{96} + 10134565481560 q^{97} + 70916776240976 q^{98} + 2095986297888 q^{99}+O(q^{100}) \) 31 * q - 52 * q^2 - 22599 * q^3 + 126886 * q^4 + 33486 * q^5 + 37908 * q^6 - 1135539 * q^7 - 1519749 * q^8 + 16474671 * q^9 - 3854663 * q^10 + 3943968 * q^11 - 92499894 * q^12 - 48510022 * q^13 - 51427459 * q^14 - 24411294 * q^15 + 370110498 * q^16 + 83288419 * q^17 - 27634932 * q^18 - 180425297 * q^19 + 753620445 * q^20 + 827807931 * q^21 + 2300196142 * q^22 - 1305810279 * q^23 + 1107897021 * q^24 + 8070954867 * q^25 + 464550322 * q^26 - 12010035159 * q^27 - 9887169562 * q^28 + 6248352277 * q^29 + 2810049327 * q^30 - 26730150789 * q^31 - 24001343230 * q^32 - 2875152672 * q^33 - 36571033348 * q^34 + 10255900979 * q^35 + 67432422726 * q^36 - 43284776933 * q^37 - 36293696947 * q^38 + 35363806038 * q^39 - 105980683856 * q^40 - 9961079285 * q^41 + 37490617611 * q^42 - 51755851288 * q^43 - 59623729442 * q^44 + 17795833326 * q^45 - 202287132683 * q^46 - 82747063727 * q^47 - 269810553042 * q^48 + 535277836542 * q^49 + 526974390461 * q^50 - 60717257451 * q^51 + 544982341446 * q^52 + 561701818494 * q^53 + 20145865428 * q^54 - 521861534450 * q^55 - 228056576664 * q^56 + 131530041513 * q^57 + 10555409160 * q^58 - 1307596542871 * q^59 - 549389304405 * q^60 + 618193248201 * q^61 - 1486611437386 * q^62 - 603471981699 * q^63 + 679062548045 * q^64 - 1130583307122 * q^65 - 1676842987518 * q^66 - 4137387490592 * q^67 - 3901389300295 * q^68 + 951935693391 * q^69 - 819291947844 * q^70 - 3766439869810 * q^71 - 807656928309 * q^72 - 2386775553523 * q^73 + 3060770694642 * q^74 - 5883726098043 * q^75 - 847741068784 * q^76 + 1650423006137 * q^77 - 338657184738 * q^78 + 787155757766 * q^79 + 13999832121779 * q^80 + 8755315630911 * q^81 + 10083281915577 * q^82 + 8743877051639 * q^83 + 7207746610698 * q^84 + 15373177520565 * q^85 + 18939443838984 * q^86 - 4555048809933 * q^87 + 39713314506713 * q^88 + 11026795445259 * q^89 - 2048525959383 * q^90 + 23285721962531 * q^91 + 40411079823254 * q^92 + 19486279925181 * q^93 + 35237377585624 * q^94 + 13730236994039 * q^95 + 17496979214670 * q^96 + 10134565481560 * q^97 + 70916776240976 * q^98 + 2095986297888 * q^99

Introduction

L-functions

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