LMFDB - Embedded newform 177.14.a.b.1.13

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			1.13
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-57.5851 q^{2} -729.000 q^{3} -4875.95 q^{4} +31633.2 q^{5} +41979.6 q^{6} +267144. q^{7} +752520. q^{8} +531441. q^{9} +O(q^{10})$	\(q-57.5851 q^{2} -729.000 q^{3} -4875.95 q^{4} +31633.2 q^{5} +41979.6 q^{6} +267144. q^{7} +752520. q^{8} +531441. q^{9} -1.82160e6 q^{10} +3.70473e6 q^{11} +3.55457e6 q^{12} +3.03857e7 q^{13} -1.53835e7 q^{14} -2.30606e7 q^{15} -3.39015e6 q^{16} +5.25313e6 q^{17} -3.06031e7 q^{18} -1.93452e8 q^{19} -1.54242e8 q^{20} -1.94748e8 q^{21} -2.13337e8 q^{22} -1.22257e8 q^{23} -5.48587e8 q^{24} -2.20043e8 q^{25} -1.74976e9 q^{26} -3.87420e8 q^{27} -1.30258e9 q^{28} +8.14387e8 q^{29} +1.32795e9 q^{30} +1.38541e9 q^{31} -5.96942e9 q^{32} -2.70075e9 q^{33} -3.02502e8 q^{34} +8.45061e9 q^{35} -2.59128e9 q^{36} -2.86691e10 q^{37} +1.11400e10 q^{38} -2.21512e10 q^{39} +2.38046e10 q^{40} -1.17360e10 q^{41} +1.12146e10 q^{42} -2.19728e10 q^{43} -1.80641e10 q^{44} +1.68112e10 q^{45} +7.04019e9 q^{46} -4.74856e10 q^{47} +2.47142e9 q^{48} -2.55232e10 q^{49} +1.26712e10 q^{50} -3.82953e9 q^{51} -1.48159e11 q^{52} -1.45553e11 q^{53} +2.23097e10 q^{54} +1.17193e11 q^{55} +2.01031e11 q^{56} +1.41026e11 q^{57} -4.68966e10 q^{58} -4.21805e10 q^{59} +1.12442e11 q^{60} -5.68197e10 q^{61} -7.97793e10 q^{62} +1.41971e11 q^{63} +3.71522e11 q^{64} +9.61197e11 q^{65} +1.55523e11 q^{66} +6.47814e11 q^{67} -2.56140e10 q^{68} +8.91254e10 q^{69} -4.86630e11 q^{70} -1.68243e11 q^{71} +3.99920e11 q^{72} -6.75444e11 q^{73} +1.65091e12 q^{74} +1.60411e11 q^{75} +9.43262e11 q^{76} +9.89696e11 q^{77} +1.27558e12 q^{78} -1.56297e11 q^{79} -1.07241e11 q^{80} +2.82430e11 q^{81} +6.75817e11 q^{82} -3.56084e12 q^{83} +9.49581e11 q^{84} +1.66173e11 q^{85} +1.26531e12 q^{86} -5.93688e11 q^{87} +2.78788e12 q^{88} -6.47668e12 q^{89} -9.68074e11 q^{90} +8.11735e12 q^{91} +5.96120e11 q^{92} -1.00997e12 q^{93} +2.73446e12 q^{94} -6.11950e12 q^{95} +4.35171e12 q^{96} -1.96982e12 q^{97} +1.46976e12 q^{98} +1.96885e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−57.5851	−0.636232	−0.318116	−	0.948052i	$-0.603050\pi$
$2$	−57.5851	−0.636232	−0.318116	+	0.948052i	$0.603050\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	−4875.95	−0.595209
$5$	31633.2	0.905395	0.452698	−	0.891664i	$-0.350462\pi$
$5$	31633.2	0.905395	0.452698	+	0.891664i	$0.350462\pi$
$6$	41979.6	0.367329
$7$	267144.	0.858238	0.429119	−	0.903248i	$-0.358824\pi$
$7$	267144.	0.858238	0.429119	+	0.903248i	$0.358824\pi$
$8$	752520.	1.01492
$9$	531441.	0.333333
$10$	−1.82160e6	−0.576041
$11$	3.70473e6	0.630528	0.315264	−	0.949004i	$-0.397907\pi$
$11$	3.70473e6	0.630528	0.315264	+	0.949004i	$0.397907\pi$
$12$	3.55457e6	0.343644
$13$	3.03857e7	1.74597	0.872986	−	0.487745i	$-0.162180\pi$
$13$	3.03857e7	1.74597	0.872986	+	0.487745i	$0.162180\pi$
$14$	−1.53835e7	−0.546038
$15$	−2.30606e7	−0.522730
$16$	−3.39015e6	−0.0505172
$17$	5.25313e6	0.0527837	0.0263919	−	0.999652i	$-0.491598\pi$
$17$	5.25313e6	0.0527837	0.0263919	+	0.999652i	$0.491598\pi$
$18$	−3.06031e7	−0.212077
$19$	−1.93452e8	−0.943354	−0.471677	−	0.881771i	$-0.656351\pi$
$19$	−1.93452e8	−0.943354	−0.471677	+	0.881771i	$0.656351\pi$
$20$	−1.54242e8	−0.538899
$21$	−1.94748e8	−0.495504
$22$	−2.13337e8	−0.401162
$23$	−1.22257e8	−0.172204	−0.0861020	−	0.996286i	$-0.527441\pi$
$23$	−1.22257e8	−0.172204	−0.0861020	+	0.996286i	$0.527441\pi$
$24$	−5.48587e8	−0.585966
$25$	−2.20043e8	−0.180259
$26$	−1.74976e9	−1.11084
$27$	−3.87420e8	−0.192450
$28$	−1.30258e9	−0.510831
$29$	8.14387e8	0.254240	0.127120	−	0.991887i	$-0.459427\pi$
$29$	8.14387e8	0.254240	0.127120	+	0.991887i	$0.459427\pi$
$30$	1.32795e9	0.332578
$31$	1.38541e9	0.280368	0.140184	−	0.990125i	$-0.455231\pi$
$31$	1.38541e9	0.280368	0.140184	+	0.990125i	$0.455231\pi$
$32$	−5.96942e9	−0.982782
$33$	−2.70075e9	−0.364035
$34$	−3.02502e8	−0.0335827
$35$	8.45061e9	0.777045
$36$	−2.59128e9	−0.198403
$37$	−2.86691e10	−1.83697	−0.918487	−	0.395452i	$-0.870588\pi$
$37$	−2.86691e10	−1.83697	−0.918487	+	0.395452i	$0.870588\pi$
$38$	1.11400e10	0.600192
$39$	−2.21512e10	−1.00804
$40$	2.38046e10	0.918906
$41$	−1.17360e10	−0.385855	−0.192927	−	0.981213i	$-0.561798\pi$
$41$	−1.17360e10	−0.385855	−0.192927	+	0.981213i	$0.561798\pi$
$42$	1.12146e10	0.315255
$43$	−2.19728e10	−0.530078	−0.265039	−	0.964238i	$-0.585385\pi$
$43$	−2.19728e10	−0.530078	−0.265039	+	0.964238i	$0.585385\pi$
$44$	−1.80641e10	−0.375296
$45$	1.68112e10	0.301798
$46$	7.04019e9	0.109562
$47$	−4.74856e10	−0.642578	−0.321289	−	0.946981i	$-0.604116\pi$
$47$	−4.74856e10	−0.642578	−0.321289	+	0.946981i	$0.604116\pi$
$48$	2.47142e9	0.0291661
$49$	−2.55232e10	−0.263428
$50$	1.26712e10	0.114687
$51$	−3.82953e9	−0.0304747
$52$	−1.48159e11	−1.03922
$53$	−1.45553e11	−0.902042	−0.451021	−	0.892513i	$-0.648940\pi$
$53$	−1.45553e11	−0.902042	−0.451021	+	0.892513i	$0.648940\pi$
$54$	2.23097e10	0.122443
$55$	1.17193e11	0.570877
$56$	2.01031e11	0.871045
$57$	1.41026e11	0.544645
$58$	−4.68966e10	−0.161755
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	1.12442e11	0.311134
$61$	−5.68197e10	−0.141207	−0.0706033	−	0.997504i	$-0.522492\pi$
$61$	−5.68197e10	−0.141207	−0.0706033	+	0.997504i	$0.522492\pi$
$62$	−7.97793e10	−0.178379
$63$	1.41971e11	0.286079
$64$	3.71522e11	0.675794
$65$	9.61197e11	1.58080
$66$	1.55523e11	0.231611
$67$	6.47814e11	0.874912	0.437456	−	0.899240i	$-0.355880\pi$
$67$	6.47814e11	0.874912	0.437456	+	0.899240i	$0.355880\pi$
$68$	−2.56140e10	−0.0314173
$69$	8.91254e10	0.0994220
$70$	−4.86630e11	−0.494381
$71$	−1.68243e11	−0.155868	−0.0779340	−	0.996959i	$-0.524832\pi$
$71$	−1.68243e11	−0.155868	−0.0779340	+	0.996959i	$0.524832\pi$
$72$	3.99920e11	0.338308
$73$	−6.75444e11	−0.522385	−0.261193	−	0.965287i	$-0.584116\pi$
$73$	−6.75444e11	−0.522385	−0.261193	+	0.965287i	$0.584116\pi$
$74$	1.65091e12	1.16874
$75$	1.60411e11	0.104073
$76$	9.43262e11	0.561493
$77$	9.89696e11	0.541143
$78$	1.27558e12	0.641346
$79$	−1.56297e11	−0.0723393	−0.0361696	−	0.999346i	$-0.511516\pi$
$79$	−1.56297e11	−0.0723393	−0.0361696	+	0.999346i	$0.511516\pi$
$80$	−1.07241e11	−0.0457380
$81$	2.82430e11	0.111111
$82$	6.75817e11	0.245493
$83$	−3.56084e12	−1.19549	−0.597743	−	0.801687i	$-0.703936\pi$
$83$	−3.56084e12	−1.19549	−0.597743	+	0.801687i	$0.703936\pi$
$84$	9.49581e11	0.294928
$85$	1.66173e11	0.0477901
$86$	1.26531e12	0.337253
$87$	−5.93688e11	−0.146785
$88$	2.78788e12	0.639937
$89$	−6.47668e12	−1.38139	−0.690697	−	0.723144i	$-0.742696\pi$
$89$	−6.47668e12	−1.38139	−0.690697	+	0.723144i	$0.742696\pi$
$90$	−9.68074e11	−0.192014
$91$	8.11735e12	1.49846
$92$	5.96120e11	0.102497
$93$	−1.00997e12	−0.161871
$94$	2.73446e12	0.408828
$95$	−6.11950e12	−0.854108
$96$	4.35171e12	0.567410
$97$	−1.96982e12	−0.240110	−0.120055	−	0.992767i	$-0.538307\pi$
$97$	−1.96982e12	−0.240110	−0.120055	+	0.992767i	$0.538307\pi$
$98$	1.46976e12	0.167601
$99$	1.96885e12	0.210176
$100$	1.07292e12	0.107292
$101$	−1.43041e13	−1.34082	−0.670411	−	0.741990i	$-0.733882\pi$
$101$	−1.43041e13	−1.34082	−0.670411	+	0.741990i	$0.733882\pi$
$102$	2.20524e11	0.0193890
$103$	−2.57948e12	−0.212858	−0.106429	−	0.994320i	$-0.533942\pi$
$103$	−2.57948e12	−0.212858	−0.106429	+	0.994320i	$0.533942\pi$
$104$	2.28658e13	1.77203
$105$	−6.16050e12	−0.448627
$106$	8.38167e12	0.573908
$107$	5.39263e12	0.347381	0.173690	−	0.984800i	$-0.444431\pi$
$107$	5.39263e12	0.347381	0.173690	+	0.984800i	$0.444431\pi$
$108$	1.88904e12	0.114548
$109$	3.47738e13	1.98600	0.993002	−	0.118097i	$-0.0376794\pi$
$109$	3.47738e13	1.98600	0.993002	+	0.118097i	$0.0376794\pi$
$110$	−6.74855e12	−0.363210
$111$	2.08998e13	1.06058
$112$	−9.05657e11	−0.0433557
$113$	7.73249e12	0.349389	0.174695	−	0.984623i	$-0.444106\pi$
$113$	7.73249e12	0.349389	0.174695	+	0.984623i	$0.444106\pi$
$114$	−8.12102e12	−0.346521
$115$	−3.86738e12	−0.155913
$116$	−3.97091e12	−0.151326
$117$	1.61482e13	0.581991
$118$	2.42897e12	0.0828303
$119$	1.40334e12	0.0453010
$120$	−1.73536e13	−0.530531
$121$	−2.07977e13	−0.602435
$122$	3.27197e12	0.0898402
$123$	8.55552e12	0.222773
$124$	−6.75522e12	−0.166878
$125$	−4.55754e13	−1.06860
$126$	−8.17543e12	−0.182013
$127$	2.67212e13	0.565109	0.282555	−	0.959251i	$-0.408818\pi$
$127$	2.67212e13	0.565109	0.282555	+	0.959251i	$0.408818\pi$
$128$	2.75073e13	0.552820
$129$	1.60182e13	0.306041
$130$	−5.53507e13	−1.00575
$131$	−3.15424e13	−0.545294	−0.272647	−	0.962114i	$-0.587899\pi$
$131$	−3.15424e13	−0.545294	−0.272647	+	0.962114i	$0.587899\pi$
$132$	1.31687e13	0.216677
$133$	−5.16795e13	−0.809622
$134$	−3.73045e13	−0.556647
$135$	−1.22554e13	−0.174243
$136$	3.95308e12	0.0535714
$137$	−8.10965e13	−1.04790	−0.523948	−	0.851750i	$-0.675541\pi$
$137$	−8.10965e13	−1.04790	−0.523948	+	0.851750i	$0.675541\pi$
$138$	−5.13230e12	−0.0632554
$139$	−1.15642e14	−1.35994	−0.679971	−	0.733239i	$-0.738008\pi$
$139$	−1.15642e14	−1.35994	−0.679971	+	0.733239i	$0.738008\pi$
$140$	−4.12048e13	−0.462504
$141$	3.46170e13	0.370992
$142$	9.68828e12	0.0991682
$143$	1.12571e14	1.10088
$144$	−1.80166e12	−0.0168391
$145$	2.57617e13	0.230188
$146$	3.88956e13	0.332358
$147$	1.86064e13	0.152090
$148$	1.39789e14	1.09338
$149$	2.57327e14	1.92653	0.963264	−	0.268557i	$-0.0865467\pi$
$149$	2.57327e14	1.92653	0.963264	+	0.268557i	$0.0865467\pi$
$150$	−9.23731e12	−0.0662144
$151$	−2.08141e13	−0.142892	−0.0714458	−	0.997444i	$-0.522761\pi$
$151$	−2.08141e13	−0.142892	−0.0714458	+	0.997444i	$0.522761\pi$
$152$	−1.45576e14	−0.957431
$153$	2.79173e12	0.0175946
$154$	−5.69918e13	−0.344292
$155$	4.38251e13	0.253844
$156$	1.08008e14	0.599993
$157$	−1.21070e14	−0.645191	−0.322595	−	0.946537i	$-0.604555\pi$
$157$	−1.21070e14	−0.645191	−0.322595	+	0.946537i	$0.604555\pi$
$158$	9.00037e12	0.0460245
$159$	1.06108e14	0.520794
$160$	−1.88832e14	−0.889806
$161$	−3.26602e13	−0.147792
$162$	−1.62637e13	−0.0706924
$163$	−9.75359e13	−0.407329	−0.203664	−	0.979041i	$-0.565285\pi$
$163$	−9.75359e13	−0.407329	−0.203664	+	0.979041i	$0.565285\pi$
$164$	5.72240e13	0.229664
$165$	−8.54334e13	−0.329596
$166$	2.05051e14	0.760607
$167$	−3.90228e13	−0.139207	−0.0696036	−	0.997575i	$-0.522173\pi$
$167$	−3.90228e13	−0.139207	−0.0696036	+	0.997575i	$0.522173\pi$
$168$	−1.46552e14	−0.502898
$169$	6.20415e14	2.04842
$170$	−9.56911e12	−0.0304056
$171$	−1.02808e14	−0.314451
$172$	1.07138e14	0.315507
$173$	−3.31154e14	−0.939141	−0.469570	−	0.882895i	$-0.655591\pi$
$173$	−3.31154e14	−0.939141	−0.469570	+	0.882895i	$0.655591\pi$
$174$	3.41876e13	0.0933896
$175$	−5.87831e13	−0.154705
$176$	−1.25596e13	−0.0318525
$177$	3.07496e13	0.0751646
$178$	3.72961e14	0.878887
$179$	1.86211e14	0.423116	0.211558	−	0.977365i	$-0.432146\pi$
$179$	1.86211e14	0.423116	0.211558	+	0.977365i	$0.432146\pi$
$180$	−8.19705e13	−0.179633
$181$	−7.41190e13	−0.156682	−0.0783409	−	0.996927i	$-0.524962\pi$
$181$	−7.41190e13	−0.156682	−0.0783409	+	0.996927i	$0.524962\pi$
$182$	−4.67438e14	−0.953368
$183$	4.14216e13	0.0815257
$184$	−9.20009e13	−0.174774
$185$	−9.06896e14	−1.66319
$186$	5.81591e13	0.102987
$187$	1.94614e13	0.0332816
$188$	2.31537e14	0.382468
$189$	−1.03497e14	−0.165168
$190$	3.52392e14	0.543411
$191$	−1.00935e15	−1.50426	−0.752130	−	0.659015i	$-0.770973\pi$
$191$	−1.00935e15	−1.50426	−0.752130	+	0.659015i	$0.770973\pi$
$192$	−2.70839e14	−0.390170
$193$	1.02739e15	1.43091	0.715456	−	0.698658i	$-0.246219\pi$
$193$	1.02739e15	1.43091	0.715456	+	0.698658i	$0.246219\pi$
$194$	1.13432e14	0.152765
$195$	−7.00713e14	−0.912672
$196$	1.24450e14	0.156795
$197$	−3.08783e14	−0.376376	−0.188188	−	0.982133i	$-0.560261\pi$
$197$	−3.08783e14	−0.376376	−0.188188	+	0.982133i	$0.560261\pi$
$198$	−1.13376e14	−0.133721
$199$	−2.31325e14	−0.264045	−0.132023	−	0.991247i	$-0.542147\pi$
$199$	−2.31325e14	−0.264045	−0.132023	+	0.991247i	$0.542147\pi$
$200$	−1.65587e14	−0.182949
$201$	−4.72257e14	−0.505130
$202$	8.23702e14	0.853073
$203$	2.17558e14	0.218198
$204$	1.86726e13	0.0181388
$205$	−3.71246e14	−0.349351
$206$	1.48540e14	0.135427
$207$	−6.49724e13	−0.0574013
$208$	−1.03012e14	−0.0882016
$209$	−7.16687e14	−0.594811
$210$	3.54753e14	0.285431
$211$	−1.97669e15	−1.54206	−0.771031	−	0.636798i	$-0.780259\pi$
$211$	−1.97669e15	−1.54206	−0.771031	+	0.636798i	$0.780259\pi$
$212$	7.09708e14	0.536904
$213$	1.22649e14	0.0899905
$214$	−3.10535e14	−0.221015
$215$	−6.95069e14	−0.479930
$216$	−2.91542e14	−0.195322
$217$	3.70105e14	0.240623
$218$	−2.00245e15	−1.26356
$219$	4.92399e14	0.301599
$220$	−5.71425e14	−0.339791
$221$	1.59620e14	0.0921589
$222$	−1.20352e15	−0.674773
$223$	−1.00091e15	−0.545023	−0.272511	−	0.962153i	$-0.587854\pi$
$223$	−1.00091e15	−0.545023	−0.272511	+	0.962153i	$0.587854\pi$
$224$	−1.59469e15	−0.843461
$225$	−1.16940e14	−0.0600864
$226$	−4.45277e14	−0.222293
$227$	−3.14480e15	−1.52555	−0.762773	−	0.646667i	$-0.776163\pi$
$227$	−3.14480e15	−1.52555	−0.762773	+	0.646667i	$0.776163\pi$
$228$	−6.87638e14	−0.324178
$229$	−1.80493e15	−0.827044	−0.413522	−	0.910494i	$-0.635702\pi$
$229$	−1.80493e15	−0.827044	−0.413522	+	0.910494i	$0.635702\pi$
$230$	2.22704e14	0.0991966
$231$	−7.21488e14	−0.312429
$232$	6.12842e14	0.258034
$233$	1.72121e15	0.704727	0.352363	−	0.935863i	$-0.385378\pi$
$233$	1.72121e15	0.704727	0.352363	+	0.935863i	$0.385378\pi$
$234$	−9.29896e14	−0.370281
$235$	−1.50212e15	−0.581787
$236$	2.05670e14	0.0774896
$237$	1.13940e14	0.0417651
$238$	−8.08115e13	−0.0288219
$239$	−3.39273e15	−1.17751	−0.588753	−	0.808313i	$-0.700381\pi$
$239$	−3.39273e15	−1.17751	−0.588753	+	0.808313i	$0.700381\pi$
$240$	7.81789e13	0.0264068
$241$	2.85588e15	0.938920	0.469460	−	0.882954i	$-0.344449\pi$
$241$	2.85588e15	0.938920	0.469460	+	0.882954i	$0.344449\pi$
$242$	1.19764e15	0.383288
$243$	−2.05891e14	−0.0641500
$244$	2.77050e14	0.0840475
$245$	−8.07382e14	−0.238506
$246$	−4.92671e14	−0.141735
$247$	−5.87817e15	−1.64707
$248$	1.04255e15	0.284552
$249$	2.59585e15	0.690215
$250$	2.62447e15	0.679878
$251$	6.96415e15	1.75788	0.878939	−	0.476934i	$-0.158252\pi$
$251$	6.96415e15	1.75788	0.878939	+	0.476934i	$0.158252\pi$
$252$	−6.92244e14	−0.170277
$253$	−4.52930e14	−0.108579
$254$	−1.53875e15	−0.359540
$255$	−1.21140e14	−0.0275916
$256$	−4.62752e15	−1.02752
$257$	−8.23785e14	−0.178340	−0.0891700	−	0.996016i	$-0.528421\pi$
$257$	−8.23785e14	−0.178340	−0.0891700	+	0.996016i	$0.528421\pi$
$258$	−9.22408e14	−0.194713
$259$	−7.65877e15	−1.57656
$260$	−4.68675e15	−0.940904
$261$	4.32798e14	0.0847466
$262$	1.81637e15	0.346934
$263$	−6.43801e14	−0.119961	−0.0599804	−	0.998200i	$-0.519104\pi$
$263$	−6.43801e14	−0.119961	−0.0599804	+	0.998200i	$0.519104\pi$
$264$	−2.03237e15	−0.369468
$265$	−4.60430e15	−0.816705
$266$	2.97597e15	0.515107
$267$	4.72150e15	0.797548
$268$	−3.15871e15	−0.520755
$269$	3.19797e15	0.514617	0.257308	−	0.966329i	$-0.417164\pi$
$269$	3.19797e15	0.514617	0.257308	+	0.966329i	$0.417164\pi$
$270$	7.05726e14	0.110859
$271$	−4.06076e15	−0.622740	−0.311370	−	0.950289i	$-0.600788\pi$
$271$	−4.06076e15	−0.622740	−0.311370	+	0.950289i	$0.600788\pi$
$272$	−1.78089e13	−0.00266648
$273$	−5.91755e15	−0.865136
$274$	4.66995e15	0.666705
$275$	−8.15201e14	−0.113659
$276$	−4.34571e14	−0.0591769
$277$	−1.06729e16	−1.41960	−0.709798	−	0.704405i	$-0.751214\pi$
$277$	−1.06729e16	−1.41960	−0.709798	+	0.704405i	$0.751214\pi$
$278$	6.65927e15	0.865238
$279$	7.36266e14	0.0934561
$280$	6.35925e15	0.788640
$281$	2.65538e15	0.321762	0.160881	−	0.986974i	$-0.448566\pi$
$281$	2.65538e15	0.321762	0.160881	+	0.986974i	$0.448566\pi$
$282$	−1.99342e15	−0.236037
$283$	−2.80805e15	−0.324932	−0.162466	−	0.986714i	$-0.551945\pi$
$283$	−2.80805e15	−0.324932	−0.162466	+	0.986714i	$0.551945\pi$
$284$	8.20344e14	0.0927741
$285$	4.46112e15	0.493119
$286$	−6.48241e15	−0.700418
$287$	−3.13519e15	−0.331155
$288$	−3.17239e15	−0.327594
$289$	−9.87698e15	−0.997214
$290$	−1.48349e15	−0.146453
$291$	1.43600e15	0.138627
$292$	3.29343e15	0.310929
$293$	1.12425e16	1.03806	0.519032	−	0.854755i	$-0.326293\pi$
$293$	1.12425e16	1.03806	0.519032	+	0.854755i	$0.326293\pi$
$294$	−1.07145e15	−0.0967645
$295$	−1.33431e15	−0.117872
$296$	−2.15741e16	−1.86439
$297$	−1.43529e15	−0.121345
$298$	−1.48182e16	−1.22572
$299$	−3.71487e15	−0.300663
$300$	−7.82159e14	−0.0619451
$301$	−5.86989e15	−0.454933
$302$	1.19858e15	0.0909122
$303$	1.04277e16	0.774123
$304$	6.55831e14	0.0476555
$305$	−1.79739e15	−0.127848
$306$	−1.60762e14	−0.0111942
$307$	2.19317e16	1.49511	0.747555	−	0.664200i	$-0.231228\pi$
$307$	2.19317e16	1.49511	0.747555	+	0.664200i	$0.231228\pi$
$308$	−4.82571e15	−0.322093
$309$	1.88044e15	0.122894
$310$	−2.52368e15	−0.161504
$311$	−2.42365e16	−1.51889	−0.759446	−	0.650570i	$-0.774530\pi$
$311$	−2.42365e16	−1.51889	−0.759446	+	0.650570i	$0.774530\pi$
$312$	−1.66692e16	−1.02308
$313$	1.66454e16	1.00059	0.500295	−	0.865855i	$-0.333225\pi$
$313$	1.66454e16	1.00059	0.500295	+	0.865855i	$0.333225\pi$
$314$	6.97182e15	0.410491
$315$	4.49100e15	0.259015
$316$	7.62096e14	0.0430570
$317$	2.78403e16	1.54095	0.770474	−	0.637471i	$-0.220019\pi$
$317$	2.78403e16	1.54095	0.770474	+	0.637471i	$0.220019\pi$
$318$	−6.11024e15	−0.331346
$319$	3.01708e15	0.160305
$320$	1.17524e16	0.611861
$321$	−3.93123e15	−0.200560
$322$	1.88074e15	0.0940300
$323$	−1.01623e15	−0.0497937
$324$	−1.37711e15	−0.0661343
$325$	−6.68616e15	−0.314728
$326$	5.61662e15	0.259156
$327$	−2.53501e16	−1.14662
$328$	−8.83154e15	−0.391613
$329$	−1.26855e16	−0.551485
$330$	4.91969e15	0.209699
$331$	−3.38160e16	−1.41332	−0.706661	−	0.707553i	$-0.749799\pi$
$331$	−3.38160e16	−1.41332	−0.706661	+	0.707553i	$0.749799\pi$
$332$	1.73625e16	0.711565
$333$	−1.52359e16	−0.612325
$334$	2.24713e15	0.0885680
$335$	2.04924e16	0.792141
$336$	6.60224e14	0.0250314
$337$	−9.87424e15	−0.367206	−0.183603	−	0.983001i	$-0.558776\pi$
$337$	−9.87424e15	−0.367206	−0.183603	+	0.983001i	$0.558776\pi$
$338$	−3.57267e16	−1.30327
$339$	−5.63699e15	−0.201720
$340$	−8.10253e14	−0.0284451
$341$	5.13259e15	0.176780
$342$	5.92023e15	0.200064
$343$	−3.27017e16	−1.08432
$344$	−1.65349e16	−0.537988
$345$	2.81932e15	0.0900162
$346$	1.90696e16	0.597511
$347$	4.99385e16	1.53566	0.767828	−	0.640656i	$-0.221337\pi$
$347$	4.99385e16	1.53566	0.767828	+	0.640656i	$0.221337\pi$
$348$	2.89479e15	0.0873680
$349$	−1.42517e16	−0.422183	−0.211091	−	0.977466i	$-0.567702\pi$
$349$	−1.42517e16	−0.422183	−0.211091	+	0.977466i	$0.567702\pi$
$350$	3.38503e15	0.0984285
$351$	−1.17720e16	−0.336013
$352$	−2.21151e16	−0.619672
$353$	3.05197e16	0.839547	0.419773	−	0.907629i	$-0.362110\pi$
$353$	3.05197e16	0.839547	0.419773	+	0.907629i	$0.362110\pi$
$354$	−1.77072e15	−0.0478221
$355$	−5.32206e15	−0.141122
$356$	3.15800e16	0.822218
$357$	−1.02303e15	−0.0261545
$358$	−1.07230e16	−0.269200
$359$	2.10998e16	0.520192	0.260096	−	0.965583i	$-0.416246\pi$
$359$	2.10998e16	0.520192	0.260096	+	0.965583i	$0.416246\pi$
$360$	1.26507e16	0.306302
$361$	−4.62936e15	−0.110084
$362$	4.26815e15	0.0996860
$363$	1.51615e16	0.347816
$364$	−3.95798e16	−0.891897
$365$	−2.13665e16	−0.472965
$366$	−2.38527e15	−0.0518692
$367$	−2.42514e16	−0.518092	−0.259046	−	0.965865i	$-0.583408\pi$
$367$	−2.42514e16	−0.518092	−0.259046	+	0.965865i	$0.583408\pi$
$368$	4.14470e14	0.00869926
$369$	−6.23697e15	−0.128618
$370$	5.22237e16	1.05817
$371$	−3.88835e16	−0.774167
$372$	4.92455e15	0.0963469
$373$	1.03626e17	1.99232	0.996161	−	0.0875416i	$-0.0279011\pi$
$373$	1.03626e17	1.99232	0.996161	+	0.0875416i	$0.0279011\pi$
$374$	−1.12069e15	−0.0211748
$375$	3.32245e16	0.616957
$376$	−3.57338e16	−0.652167
$377$	2.47457e16	0.443896
$378$	5.95989e15	0.105085
$379$	1.68371e16	0.291818	0.145909	−	0.989298i	$-0.453389\pi$
$379$	1.68371e16	0.291818	0.145909	+	0.989298i	$0.453389\pi$
$380$	2.98384e16	0.508373
$381$	−1.94798e16	−0.326266
$382$	5.81233e16	0.957058
$383$	8.78160e16	1.42161	0.710807	−	0.703387i	$-0.248330\pi$
$383$	8.78160e16	1.42161	0.710807	+	0.703387i	$0.248330\pi$
$384$	−2.00529e16	−0.319171
$385$	3.13073e16	0.489948
$386$	−5.91624e16	−0.910391
$387$	−1.16772e16	−0.176693
$388$	9.60474e15	0.142915
$389$	3.56286e15	0.0521347	0.0260673	−	0.999660i	$-0.491702\pi$
$389$	3.56286e15	0.0521347	0.0260673	+	0.999660i	$0.491702\pi$
$390$	4.03506e16	0.580671
$391$	−6.42232e14	−0.00908956
$392$	−1.92067e16	−0.267359
$393$	2.29944e16	0.314826
$394$	1.77813e16	0.239463
$395$	−4.94417e15	−0.0654956
$396$	−9.60000e15	−0.125099
$397$	−8.74066e15	−0.112048	−0.0560242	−	0.998429i	$-0.517842\pi$
$397$	−8.74066e15	−0.112048	−0.0560242	+	0.998429i	$0.517842\pi$
$398$	1.33209e16	0.167994
$399$	3.76743e16	0.467435
$400$	7.45979e14	0.00910619
$401$	9.14289e16	1.09811	0.549054	−	0.835787i	$-0.314988\pi$
$401$	9.14289e16	1.09811	0.549054	+	0.835787i	$0.314988\pi$
$402$	2.71950e16	0.321380
$403$	4.20968e16	0.489515
$404$	6.97460e16	0.798069
$405$	8.93415e15	0.100599
$406$	−1.25281e16	−0.138825
$407$	−1.06211e17	−1.15826
$408$	−2.88180e15	−0.0309295
$409$	3.81780e15	0.0403284	0.0201642	−	0.999797i	$-0.493581\pi$
$409$	3.81780e15	0.0403284	0.0201642	+	0.999797i	$0.493581\pi$
$410$	2.13783e16	0.222268
$411$	5.91193e16	0.605003
$412$	1.25774e16	0.126695
$413$	−1.12683e16	−0.111733
$414$	3.74145e15	0.0365205
$415$	−1.12641e17	−1.08239
$416$	−1.81385e17	−1.71591
$417$	8.43032e16	0.785163
$418$	4.12705e16	0.378438
$419$	5.77997e16	0.521837	0.260918	−	0.965361i	$-0.415975\pi$
$419$	5.77997e16	0.521837	0.260918	+	0.965361i	$0.415975\pi$
$420$	3.00383e16	0.267027
$421$	−3.64550e15	−0.0319097	−0.0159549	−	0.999873i	$-0.505079\pi$
$421$	−3.64550e15	−0.0319097	−0.0159549	+	0.999873i	$0.505079\pi$
$422$	1.13828e17	0.981109
$423$	−2.52358e16	−0.214193
$424$	−1.09531e17	−0.915503
$425$	−1.15591e15	−0.00951475
$426$	−7.06276e15	−0.0572548
$427$	−1.51790e16	−0.121189
$428$	−2.62942e16	−0.206764
$429$	−8.20641e16	−0.635596
$430$	4.00257e16	0.305347
$431$	−8.89222e16	−0.668202	−0.334101	−	0.942537i	$-0.608433\pi$
$431$	−8.89222e16	−0.668202	−0.334101	+	0.942537i	$0.608433\pi$
$432$	1.31341e15	0.00972203
$433$	−3.07518e15	−0.0224233	−0.0112116	−	0.999937i	$-0.503569\pi$
$433$	−3.07518e15	−0.0224233	−0.0112116	+	0.999937i	$0.503569\pi$
$434$	−2.13125e16	−0.153092
$435$	−1.87803e16	−0.132899
$436$	−1.69555e17	−1.18209
$437$	2.36509e16	0.162449
$438$	−2.83549e16	−0.191887
$439$	5.16973e16	0.344706	0.172353	−	0.985035i	$-0.444863\pi$
$439$	5.16973e16	0.344706	0.172353	+	0.985035i	$0.444863\pi$
$440$	8.81897e16	0.579396
$441$	−1.35641e16	−0.0878092
$442$	−9.19173e15	−0.0586344
$443$	−3.39507e16	−0.213415	−0.106707	−	0.994290i	$-0.534031\pi$
$443$	−3.39507e16	−0.213415	−0.106707	+	0.994290i	$0.534031\pi$
$444$	−1.01906e17	−0.631265
$445$	−2.04878e17	−1.25071
$446$	5.76377e16	0.346761
$447$	−1.87592e17	−1.11228
$448$	9.92497e16	0.579992
$449$	4.80872e16	0.276967	0.138484	−	0.990365i	$-0.455777\pi$
$449$	4.80872e16	0.276967	0.138484	+	0.990365i	$0.455777\pi$
$450$	6.73400e15	0.0382289
$451$	−4.34786e16	−0.243292
$452$	−3.77033e16	−0.207960
$453$	1.51734e16	0.0824985
$454$	1.81094e17	0.970601
$455$	2.56778e17	1.35670
$456$	1.06125e17	0.552773
$457$	3.55915e17	1.82764	0.913821	−	0.406117i	$-0.133117\pi$
$457$	3.55915e17	1.82764	0.913821	+	0.406117i	$0.133117\pi$
$458$	1.03937e17	0.526192
$459$	−2.03517e15	−0.0101582
$460$	1.88572e16	0.0928006
$461$	−3.24418e17	−1.57416	−0.787081	−	0.616850i	$-0.788409\pi$
$461$	−3.24418e17	−1.57416	−0.787081	+	0.616850i	$0.788409\pi$
$462$	4.15470e16	0.198777
$463$	1.39573e17	0.658451	0.329226	−	0.944251i	$-0.393212\pi$
$463$	1.39573e17	0.658451	0.329226	+	0.944251i	$0.393212\pi$
$464$	−2.76089e15	−0.0128435
$465$	−3.19485e16	−0.146557
$466$	−9.91162e16	−0.448370
$467$	−6.92696e16	−0.309017	−0.154509	−	0.987991i	$-0.549379\pi$
$467$	−6.92696e16	−0.309017	−0.154509	+	0.987991i	$0.549379\pi$
$468$	−7.87379e16	−0.346406
$469$	1.73059e17	0.750882
$470$	8.64998e16	0.370151
$471$	8.82599e16	0.372501
$472$	−3.17417e16	−0.132132
$473$	−8.14032e16	−0.334229
$474$	−6.56127e15	−0.0265723
$475$	4.25678e16	0.170048
$476$	−6.84262e15	−0.0269635
$477$	−7.73526e16	−0.300681
$478$	1.95371e17	0.749167
$479$	1.85239e17	0.700730	0.350365	−	0.936613i	$-0.386058\pi$
$479$	1.85239e17	0.700730	0.350365	+	0.936613i	$0.386058\pi$
$480$	1.37658e17	0.513730
$481$	−8.71131e17	−3.20730
$482$	−1.64456e17	−0.597371
$483$	2.38093e16	0.0853277
$484$	1.01408e17	0.358575
$485$	−6.23117e16	−0.217394
$486$	1.18563e16	0.0408143
$487$	2.70563e17	0.919030	0.459515	−	0.888170i	$-0.348023\pi$
$487$	2.70563e17	0.919030	0.459515	+	0.888170i	$0.348023\pi$
$488$	−4.27580e16	−0.143314
$489$	7.11037e16	0.235171
$490$	4.64932e16	0.151745
$491$	5.77957e17	1.86151	0.930755	−	0.365642i	$-0.119151\pi$
$491$	5.77957e17	1.86151	0.930755	+	0.365642i	$0.119151\pi$
$492$	−4.17163e16	−0.132597
$493$	4.27808e15	0.0134197
$494$	3.38495e17	1.04792
$495$	6.22809e16	0.190292
$496$	−4.69676e15	−0.0141634
$497$	−4.49450e16	−0.133772
$498$	−1.49483e17	−0.439137
$499$	−1.12887e17	−0.327333	−0.163667	−	0.986516i	$-0.552332\pi$
$499$	−1.12887e17	−0.327333	−0.163667	+	0.986516i	$0.552332\pi$
$500$	2.22224e17	0.636041
$501$	2.84476e16	0.0803713
$502$	−4.01031e17	−1.11842
$503$	5.92794e17	1.63197	0.815985	−	0.578073i	$-0.196195\pi$
$503$	5.92794e17	1.63197	0.815985	+	0.578073i	$0.196195\pi$
$504$	1.06836e17	0.290348
$505$	−4.52484e17	−1.21397
$506$	2.60820e16	0.0690817
$507$	−4.52283e17	−1.18266
$508$	−1.30291e17	−0.336358
$509$	1.88535e17	0.480537	0.240269	−	0.970706i	$-0.422765\pi$
$509$	1.88535e17	0.480537	0.240269	+	0.970706i	$0.422765\pi$
$510$	6.97588e15	0.0175547
$511$	−1.80441e17	−0.448331
$512$	4.11363e16	0.100918
$513$	7.49472e16	0.181548
$514$	4.74378e16	0.113466
$515$	−8.15972e16	−0.192721
$516$	−7.81038e16	−0.182158
$517$	−1.75921e17	−0.405163
$518$	4.41031e17	1.00306
$519$	2.41412e17	0.542213
$520$	7.23320e17	1.60438
$521$	2.58570e17	0.566412	0.283206	−	0.959059i	$-0.408602\pi$
$521$	2.58570e17	0.566412	0.283206	+	0.959059i	$0.408602\pi$
$522$	−2.49228e16	−0.0539185
$523$	−2.33350e17	−0.498594	−0.249297	−	0.968427i	$-0.580199\pi$
$523$	−2.33350e17	−0.498594	−0.249297	+	0.968427i	$0.580199\pi$
$524$	1.53799e17	0.324564
$525$	4.28529e16	0.0893192
$526$	3.70734e16	0.0763228
$527$	7.27776e15	0.0147989
$528$	9.15594e15	0.0183900
$529$	−4.89090e17	−0.970346
$530$	2.65139e17	0.519614
$531$	−2.24165e16	−0.0433963
$532$	2.51987e17	0.481894
$533$	−3.56605e17	−0.673691
$534$	−2.71888e17	−0.507426
$535$	1.70586e17	0.314517
$536$	4.87493e17	0.887968
$537$	−1.35748e17	−0.244286
$538$	−1.84155e17	−0.327416
$539$	−9.45568e16	−0.166099
$540$	5.97565e16	0.103711
$541$	1.90903e17	0.327364	0.163682	−	0.986513i	$-0.447663\pi$
$541$	1.90903e17	0.327364	0.163682	+	0.986513i	$0.447663\pi$
$542$	2.33839e17	0.396207
$543$	5.40327e16	0.0904603
$544$	−3.13581e16	−0.0518749
$545$	1.10001e18	1.79812
$546$	3.40763e17	0.550427
$547$	9.96223e17	1.59015	0.795076	−	0.606509i	$-0.207431\pi$
$547$	9.96223e17	1.59015	0.795076	+	0.606509i	$0.207431\pi$
$548$	3.95423e17	0.623717
$549$	−3.01963e16	−0.0470689
$550$	4.69434e16	0.0723132
$551$	−1.57545e17	−0.239838
$552$	6.70686e16	0.100906
$553$	−4.17537e16	−0.0620843
$554$	6.14602e17	0.903192
$555$	6.61127e17	0.960242
$556$	5.63866e17	0.809450
$557$	−3.59072e17	−0.509474	−0.254737	−	0.967010i	$-0.581989\pi$
$557$	−3.59072e17	−0.509474	−0.254737	+	0.967010i	$0.581989\pi$
$558$	−4.23980e16	−0.0594597
$559$	−6.67658e17	−0.925502
$560$	−2.86488e16	−0.0392541
$561$	−1.41874e16	−0.0192151
$562$	−1.52910e17	−0.204715
$563$	−5.87386e17	−0.777354	−0.388677	−	0.921374i	$-0.627068\pi$
$563$	−5.87386e17	−0.777354	−0.388677	+	0.921374i	$0.627068\pi$
$564$	−1.68791e17	−0.220818
$565$	2.44604e17	0.316336
$566$	1.61702e17	0.206732
$567$	7.54493e16	0.0953598
$568$	−1.26606e17	−0.158194
$569$	7.28452e17	0.899852	0.449926	−	0.893066i	$-0.351450\pi$
$569$	7.28452e17	0.899852	0.449926	+	0.893066i	$0.351450\pi$
$570$	−2.56894e17	−0.313738
$571$	5.87647e17	0.709548	0.354774	−	0.934952i	$-0.384558\pi$
$571$	5.87647e17	0.709548	0.354774	+	0.934952i	$0.384558\pi$
$572$	−5.48890e17	−0.655256
$573$	7.35813e17	0.868485
$574$	1.80540e17	0.210691
$575$	2.69018e16	0.0310414
$576$	1.97442e17	0.225265
$577$	−1.49386e17	−0.168526	−0.0842632	−	0.996444i	$-0.526854\pi$
$577$	−1.49386e17	−0.168526	−0.0842632	+	0.996444i	$0.526854\pi$
$578$	5.68767e17	0.634459
$579$	−7.48967e17	−0.826137
$580$	−1.25613e17	−0.137010
$581$	−9.51256e17	−1.02601
$582$	−8.26921e16	−0.0881992
$583$	−5.39233e17	−0.568763
$584$	−5.08285e17	−0.530181
$585$	5.10819e17	0.526932
$586$	−6.47402e17	−0.660449
$587$	−7.84995e17	−0.791989	−0.395994	−	0.918253i	$-0.629600\pi$
$587$	−7.84995e17	−0.791989	−0.395994	+	0.918253i	$0.629600\pi$
$588$	−9.07242e16	−0.0905254
$589$	−2.68011e17	−0.264486
$590$	7.68362e16	0.0749942
$591$	2.25103e17	0.217301
$592$	9.71925e16	0.0927987
$593$	−6.68703e17	−0.631506	−0.315753	−	0.948841i	$-0.602257\pi$
$593$	−6.68703e17	−0.631506	−0.315753	+	0.948841i	$0.602257\pi$
$594$	8.26513e16	0.0772036
$595$	4.43921e16	0.0410153
$596$	−1.25472e18	−1.14669
$597$	1.68636e17	0.152446
$598$	2.13921e17	0.191292
$599$	−9.64228e17	−0.852914	−0.426457	−	0.904508i	$-0.640238\pi$
$599$	−9.64228e17	−0.852914	−0.426457	+	0.904508i	$0.640238\pi$
$600$	1.20713e17	0.105626
$601$	−1.13508e18	−0.982523	−0.491261	−	0.871012i	$-0.663464\pi$
$601$	−1.13508e18	−0.982523	−0.491261	+	0.871012i	$0.663464\pi$
$602$	3.38018e17	0.289443
$603$	3.44275e17	0.291637
$604$	1.01488e17	0.0850503
$605$	−6.57897e17	−0.545441
$606$	−6.00479e17	−0.492522
$607$	−1.14450e18	−0.928733	−0.464367	−	0.885643i	$-0.653718\pi$
$607$	−1.14450e18	−0.928733	−0.464367	+	0.885643i	$0.653718\pi$
$608$	1.15480e18	0.927111
$609$	−1.58600e17	−0.125977
$610$	1.03503e17	0.0813409
$611$	−1.44288e18	−1.12192
$612$	−1.36123e16	−0.0104724
$613$	2.91443e17	0.221851	0.110925	−	0.993829i	$-0.464619\pi$
$613$	2.91443e17	0.221851	0.110925	+	0.993829i	$0.464619\pi$
$614$	−1.26294e18	−0.951236
$615$	2.70638e17	0.201698
$616$	7.44766e17	0.549218
$617$	−4.37683e17	−0.319379	−0.159689	−	0.987167i	$-0.551049\pi$
$617$	−4.37683e17	−0.319379	−0.159689	+	0.987167i	$0.551049\pi$
$618$	−1.08285e17	−0.0781888
$619$	−5.87911e17	−0.420071	−0.210036	−	0.977694i	$-0.567358\pi$
$619$	−5.87911e17	−0.420071	−0.210036	+	0.977694i	$0.567358\pi$
$620$	−2.13689e17	−0.151090
$621$	4.73649e16	0.0331407
$622$	1.39566e18	0.966368
$623$	−1.73021e18	−1.18556
$624$	7.50958e16	0.0509232
$625$	−1.17309e18	−0.787247
$626$	−9.58527e17	−0.636607
$627$	5.22465e17	0.343414
$628$	5.90331e17	0.384024
$629$	−1.50602e17	−0.0969623
$630$	−2.58615e17	−0.164794
$631$	−4.53142e17	−0.285788	−0.142894	−	0.989738i	$-0.545641\pi$
$631$	−4.53142e17	−0.285788	−0.142894	+	0.989738i	$0.545641\pi$
$632$	−1.17616e17	−0.0734188
$633$	1.44100e18	0.890310
$634$	−1.60319e18	−0.980401
$635$	8.45278e17	0.511647
$636$	−5.17377e17	−0.309982
$637$	−7.75542e17	−0.459937
$638$	−1.73739e17	−0.101991
$639$	−8.94111e16	−0.0519560
$640$	8.70146e17	0.500521
$641$	−1.30602e18	−0.743659	−0.371830	−	0.928301i	$-0.621269\pi$
$641$	−1.30602e18	−0.743659	−0.371830	+	0.928301i	$0.621269\pi$
$642$	2.26380e17	0.127603
$643$	−2.65976e18	−1.48413	−0.742064	−	0.670329i	$-0.766153\pi$
$643$	−2.65976e18	−1.48413	−0.742064	+	0.670329i	$0.766153\pi$
$644$	1.59250e17	0.0879671
$645$	5.06706e17	0.277088
$646$	5.85196e16	0.0316803
$647$	−1.76549e18	−0.946210	−0.473105	−	0.881006i	$-0.656867\pi$
$647$	−1.76549e18	−0.946210	−0.473105	+	0.881006i	$0.656867\pi$
$648$	2.12534e17	0.112769
$649$	−1.56268e17	−0.0820877
$650$	3.85024e17	0.200240
$651$	−2.69806e17	−0.138924
$652$	4.75581e17	0.242446
$653$	2.17988e18	1.10026	0.550131	−	0.835078i	$-0.314578\pi$
$653$	2.17988e18	1.10026	0.550131	+	0.835078i	$0.314578\pi$
$654$	1.45979e18	0.729516
$655$	−9.97787e17	−0.493707
$656$	3.97867e16	0.0194923
$657$	−3.58959e17	−0.174128
$658$	7.30495e17	0.350872
$659$	1.21068e18	0.575803	0.287901	−	0.957660i	$-0.407042\pi$
$659$	1.21068e18	0.575803	0.287901	+	0.957660i	$0.407042\pi$
$660$	4.16569e17	0.196179
$661$	−3.38669e18	−1.57931	−0.789653	−	0.613553i	$-0.789740\pi$
$661$	−3.38669e18	−1.57931	−0.789653	+	0.613553i	$0.789740\pi$
$662$	1.94730e18	0.899200
$663$	−1.16363e17	−0.0532080
$664$	−2.67960e18	−1.21333
$665$	−1.63479e18	−0.733028
$666$	8.77363e17	0.389580
$667$	−9.95645e16	−0.0437811
$668$	1.90273e17	0.0828574
$669$	7.29666e17	0.314669
$670$	−1.18006e18	−0.503985
$671$	−2.10502e17	−0.0890347
$672$	1.16253e18	0.486972
$673$	−4.57591e18	−1.89836	−0.949181	−	0.314730i	$-0.898086\pi$
$673$	−4.57591e18	−1.89836	−0.949181	+	0.314730i	$0.898086\pi$
$674$	5.68610e17	0.233628
$675$	8.52492e16	0.0346909
$676$	−3.02511e18	−1.21924
$677$	−1.36017e18	−0.542960	−0.271480	−	0.962444i	$-0.587513\pi$
$677$	−1.36017e18	−0.542960	−0.271480	+	0.962444i	$0.587513\pi$
$678$	3.24607e17	0.128341
$679$	−5.26224e17	−0.206071
$680$	1.25049e17	0.0485033
$681$	2.29256e18	0.880774
$682$	−2.95561e17	−0.112473
$683$	−2.69603e18	−1.01623	−0.508113	−	0.861291i	$-0.669657\pi$
$683$	−2.69603e18	−1.01623	−0.508113	+	0.861291i	$0.669657\pi$
$684$	5.01288e17	0.187164
$685$	−2.56534e18	−0.948760
$686$	1.88313e18	0.689880
$687$	1.31579e18	0.477494
$688$	7.44910e16	0.0267780
$689$	−4.42272e18	−1.57494
$690$	−1.62351e17	−0.0572712
$691$	7.32511e17	0.255981	0.127990	−	0.991775i	$-0.459147\pi$
$691$	7.32511e17	0.255981	0.127990	+	0.991775i	$0.459147\pi$
$692$	1.61469e18	0.558985
$693$	5.25965e17	0.180381
$694$	−2.87572e18	−0.977033
$695$	−3.65814e18	−1.23128
$696$	−4.46762e17	−0.148976
$697$	−6.16505e16	−0.0203668
$698$	8.20685e17	0.268606
$699$	−1.25476e18	−0.406874
$700$	2.86624e17	0.0920820
$701$	5.35162e17	0.170340	0.0851702	−	0.996366i	$-0.472857\pi$
$701$	5.35162e17	0.170340	0.0851702	+	0.996366i	$0.472857\pi$
$702$	6.77894e17	0.213782
$703$	5.54609e18	1.73292
$704$	1.37639e18	0.426107
$705$	1.09505e18	0.335895
$706$	−1.75748e18	−0.534146
$707$	−3.82124e18	−1.15074
$708$	−1.49934e17	−0.0447387
$709$	−1.13858e18	−0.336637	−0.168319	−	0.985733i	$-0.553834\pi$
$709$	−1.13858e18	−0.336637	−0.168319	+	0.985733i	$0.553834\pi$
$710$	3.06472e17	0.0897865
$711$	−8.30626e16	−0.0241131
$712$	−4.87383e18	−1.40201
$713$	−1.69377e17	−0.0482805
$714$	5.89116e16	0.0166403
$715$	3.56098e18	0.996735
$716$	−9.07954e17	−0.251843
$717$	2.47330e18	0.679834
$718$	−1.21503e18	−0.330963
$719$	2.78826e18	0.752653	0.376327	−	0.926487i	$-0.377187\pi$
$719$	2.78826e18	0.752653	0.376327	+	0.926487i	$0.377187\pi$
$720$	−5.69924e16	−0.0152460
$721$	−6.89091e17	−0.182683
$722$	2.66582e17	0.0700389
$723$	−2.08193e18	−0.542086
$724$	3.61401e17	0.0932585
$725$	−1.79200e17	−0.0458291
$726$	−8.73077e17	−0.221291
$727$	−6.34339e18	−1.59348	−0.796742	−	0.604319i	$-0.793445\pi$
$727$	−6.34339e18	−1.59348	−0.796742	+	0.604319i	$0.793445\pi$
$728$	6.10846e18	1.52082
$729$	1.50095e17	0.0370370
$730$	1.23039e18	0.300916
$731$	−1.15426e17	−0.0279795
$732$	−2.01970e17	−0.0485248
$733$	−5.37980e18	−1.28112	−0.640561	−	0.767907i	$-0.721298\pi$
$733$	−5.37980e18	−1.28112	−0.640561	+	0.767907i	$0.721298\pi$
$734$	1.39652e18	0.329627
$735$	5.88582e17	0.137702
$736$	7.29804e17	0.169239
$737$	2.39998e18	0.551656
$738$	3.59157e17	0.0818310
$739$	−4.30855e18	−0.973067	−0.486534	−	0.873662i	$-0.661739\pi$
$739$	−4.30855e18	−0.973067	−0.486534	+	0.873662i	$0.661739\pi$
$740$	4.42198e18	0.989944
$741$	4.28519e18	0.950936
$742$	2.23911e18	0.492550
$743$	−4.35573e17	−0.0949804	−0.0474902	−	0.998872i	$-0.515122\pi$
$743$	−4.35573e17	−0.0949804	−0.0474902	+	0.998872i	$0.515122\pi$
$744$	−7.60020e17	−0.164286
$745$	8.14009e18	1.74427
$746$	−5.96729e18	−1.26758
$747$	−1.89238e18	−0.398496
$748$	−9.48930e16	−0.0198095
$749$	1.44061e18	0.298135
$750$	−1.91324e18	−0.392528
$751$	4.25348e18	0.865137	0.432569	−	0.901601i	$-0.357607\pi$
$751$	4.25348e18	0.865137	0.432569	+	0.901601i	$0.357607\pi$
$752$	1.60983e17	0.0324612
$753$	−5.07686e18	−1.01491
$754$	−1.42498e18	−0.282421
$755$	−6.58415e17	−0.129373
$756$	5.04646e17	0.0983095
$757$	6.16432e18	1.19059	0.595294	−	0.803508i	$-0.297036\pi$
$757$	6.16432e18	1.19059	0.595294	+	0.803508i	$0.297036\pi$
$758$	−9.69565e17	−0.185664
$759$	3.30186e17	0.0626883
$760$	−4.60505e18	−0.866854
$761$	6.30534e18	1.17681	0.588407	−	0.808565i	$-0.299755\pi$
$761$	6.30534e18	1.17681	0.588407	+	0.808565i	$0.299755\pi$
$762$	1.12175e18	0.207581
$763$	9.28961e18	1.70446
$764$	4.92152e18	0.895349
$765$	8.83113e16	0.0159300
$766$	−5.05690e18	−0.904476
$767$	−1.28168e18	−0.227306
$768$	3.37346e18	0.593237
$769$	3.40289e17	0.0593371	0.0296686	−	0.999560i	$-0.490555\pi$
$769$	3.40289e17	0.0593371	0.0296686	+	0.999560i	$0.490555\pi$
$770$	−1.80283e18	−0.311721
$771$	6.00539e17	0.102965
$772$	−5.00950e18	−0.851691
$773$	9.50368e18	1.60223	0.801115	−	0.598510i	$-0.204240\pi$
$773$	9.50368e18	1.60223	0.801115	+	0.598510i	$0.204240\pi$
$774$	6.72435e17	0.112418
$775$	−3.04851e17	−0.0505390
$776$	−1.48233e18	−0.243693
$777$	5.58324e18	0.910228
$778$	−2.05168e17	−0.0331697
$779$	2.27034e18	0.363997
$780$	3.41664e18	0.543231
$781$	−6.23294e17	−0.0982792
$782$	3.69830e16	0.00578307
$783$	−3.15510e17	−0.0489285
$784$	8.65276e16	0.0133076
$785$	−3.82983e18	−0.584153
$786$	−1.32414e18	−0.200302
$787$	−8.58472e16	−0.0128793	−0.00643963	−	0.999979i	$-0.502050\pi$
$787$	−8.58472e16	−0.0128793	−0.00643963	+	0.999979i	$0.502050\pi$
$788$	1.50561e18	0.224023
$789$	4.69331e17	0.0692594
$790$	2.84711e17	0.0416704
$791$	2.06569e18	0.299859
$792$	1.48160e18	0.213312
$793$	−1.72651e18	−0.246543
$794$	5.03332e17	0.0712888
$795$	3.35653e18	0.471525
$796$	1.12793e18	0.157162
$797$	−1.29548e18	−0.179040	−0.0895200	−	0.995985i	$-0.528533\pi$
$797$	−1.29548e18	−0.179040	−0.0895200	+	0.995985i	$0.528533\pi$
$798$	−2.16948e18	−0.297397
$799$	−2.49448e17	−0.0339176
$800$	1.31353e18	0.177156
$801$	−3.44198e18	−0.460465
$802$	−5.26495e18	−0.698651
$803$	−2.50234e18	−0.329379
$804$	2.30270e18	0.300658
$805$	−1.03315e18	−0.133810
$806$	−2.42415e18	−0.311445
$807$	−2.33132e18	−0.297114
$808$	−1.07641e19	−1.36083
$809$	2.98865e18	0.374809	0.187404	−	0.982283i	$-0.439993\pi$
$809$	2.98865e18	0.374809	0.187404	+	0.982283i	$0.439993\pi$
$810$	−5.14474e17	−0.0640046
$811$	−5.04909e17	−0.0623129	−0.0311564	−	0.999515i	$-0.509919\pi$
$811$	−5.04909e17	−0.0623129	−0.0311564	+	0.999515i	$0.509919\pi$
$812$	−1.06080e18	−0.129874
$813$	2.96029e18	0.359539
$814$	6.11619e18	0.736924
$815$	−3.08538e18	−0.368794
$816$	1.29827e16	0.00153949
$817$	4.25067e18	0.500051
$818$	−2.19848e17	−0.0256582
$819$	4.31389e18	0.499487
$820$	1.81018e18	0.207937
$821$	−1.73695e18	−0.197951	−0.0989756	−	0.995090i	$-0.531557\pi$
$821$	−1.73695e18	−0.197951	−0.0989756	+	0.995090i	$0.531557\pi$
$822$	−3.40439e18	−0.384922
$823$	−3.82731e18	−0.429334	−0.214667	−	0.976687i	$-0.568867\pi$
$823$	−3.82731e18	−0.429334	−0.214667	+	0.976687i	$0.568867\pi$
$824$	−1.94111e18	−0.216034
$825$	5.94281e17	0.0656208
$826$	6.48884e17	0.0710881
$827$	−4.13981e18	−0.449982	−0.224991	−	0.974361i	$-0.572235\pi$
$827$	−4.13981e18	−0.449982	−0.224991	+	0.974361i	$0.572235\pi$
$828$	3.16802e17	0.0341658
$829$	1.10335e19	1.18061	0.590307	−	0.807179i	$-0.299007\pi$
$829$	1.10335e19	1.18061	0.590307	+	0.807179i	$0.299007\pi$
$830$	6.48644e18	0.688650
$831$	7.78056e18	0.819604
$832$	1.12890e19	1.17992
$833$	−1.34077e17	−0.0139047
$834$	−4.85461e18	−0.499545
$835$	−1.23442e18	−0.126038
$836$	3.49453e18	0.354037
$837$	−5.36738e17	−0.0539569
$838$	−3.32841e18	−0.332009
$839$	2.68075e18	0.265340	0.132670	−	0.991160i	$-0.457645\pi$
$839$	2.68075e18	0.265340	0.132670	+	0.991160i	$0.457645\pi$
$840$	−4.63590e18	−0.455322
$841$	−9.59740e18	−0.935362
$842$	2.09926e17	0.0203020
$843$	−1.93577e18	−0.185769
$844$	9.63823e18	0.917849
$845$	1.96257e19	1.85463
$846$	1.45321e18	0.136276
$847$	−5.55597e18	−0.517032
$848$	4.93445e17	0.0455686
$849$	2.04707e18	0.187600
$850$	6.65635e16	0.00605359
$851$	3.50500e18	0.316334
$852$	−5.98031e17	−0.0535632
$853$	2.66716e18	0.237072	0.118536	−	0.992950i	$-0.462180\pi$
$853$	2.66716e18	0.237072	0.118536	+	0.992950i	$0.462180\pi$
$854$	8.74086e17	0.0771042
$855$	−3.25216e18	−0.284703
$856$	4.05806e18	0.352565
$857$	1.46804e19	1.26580	0.632898	−	0.774235i	$-0.281865\pi$
$857$	1.46804e19	1.26580	0.632898	+	0.774235i	$0.281865\pi$
$858$	4.72567e18	0.404386
$859$	−7.69268e18	−0.653314	−0.326657	−	0.945143i	$-0.605922\pi$
$859$	−7.69268e18	−0.653314	−0.326657	+	0.945143i	$0.605922\pi$
$860$	3.38913e18	0.285659
$861$	2.28555e18	0.191192
$862$	5.12060e18	0.425132
$863$	4.13923e17	0.0341075	0.0170537	−	0.999855i	$-0.494571\pi$
$863$	4.13923e17	0.0341075	0.0170537	+	0.999855i	$0.494571\pi$
$864$	2.31268e18	0.189137
$865$	−1.04755e19	−0.850294
$866$	1.77084e17	0.0142664
$867$	7.20032e18	0.575742
$868$	−1.80461e18	−0.143221
$869$	−5.79038e17	−0.0456119
$870$	1.08146e18	0.0845545
$871$	1.96843e19	1.52757
$872$	2.61680e19	2.01564
$873$	−1.04684e18	−0.0800366
$874$	−1.36194e18	−0.103355
$875$	−1.21752e19	−0.917114
$876$	−2.40091e18	−0.179515
$877$	−6.24713e18	−0.463642	−0.231821	−	0.972758i	$-0.574468\pi$
$877$	−6.24713e18	−0.463642	−0.231821	+	0.972758i	$0.574468\pi$
$878$	−2.97700e18	−0.219313
$879$	−8.19580e18	−0.599327
$880$	−3.97300e17	−0.0288391
$881$	−3.31160e18	−0.238613	−0.119307	−	0.992857i	$-0.538067\pi$
$881$	−3.31160e18	−0.238613	−0.119307	+	0.992857i	$0.538067\pi$
$882$	7.81091e17	0.0558670
$883$	−2.40266e19	−1.70588	−0.852939	−	0.522011i	$-0.825182\pi$
$883$	−2.40266e19	−1.70588	−0.852939	+	0.522011i	$0.825182\pi$
$884$	−7.78299e17	−0.0548538
$885$	9.72709e17	0.0680537
$886$	1.95506e18	0.135781
$887$	−1.50333e19	−1.03646	−0.518229	−	0.855242i	$-0.673409\pi$
$887$	−1.50333e19	−1.03646	−0.518229	+	0.855242i	$0.673409\pi$
$888$	1.57275e19	1.07640
$889$	7.13841e18	0.484998
$890$	1.17979e19	0.795740
$891$	1.04633e18	0.0700587
$892$	4.88040e18	0.324403
$893$	9.18617e18	0.606178
$894$	1.08025e19	0.707669
$895$	5.89044e18	0.383088
$896$	7.34841e18	0.474451
$897$	2.70814e18	0.173588
$898$	−2.76911e18	−0.176215
$899$	1.12826e18	0.0712808
$900$	5.70194e17	0.0357640
$901$	−7.64606e17	−0.0476131
$902$	2.50372e18	0.154790
$903$	4.27915e18	0.262656
$904$	5.81886e18	0.354603
$905$	−2.34462e18	−0.141859
$906$	−8.73765e17	−0.0524882
$907$	−2.39524e19	−1.42857	−0.714287	−	0.699853i	$-0.753249\pi$
$907$	−2.39524e19	−1.42857	−0.714287	+	0.699853i	$0.753249\pi$
$908$	1.53339e19	0.908018
$909$	−7.60177e18	−0.446940
$910$	−1.47866e19	−0.863175
$911$	2.80901e19	1.62811	0.814057	−	0.580786i	$-0.197255\pi$
$911$	2.80901e19	1.62811	0.814057	+	0.580786i	$0.197255\pi$
$912$	−4.78101e17	−0.0275139
$913$	−1.31920e19	−0.753788
$914$	−2.04954e19	−1.16280
$915$	1.31030e18	0.0738130
$916$	8.80073e18	0.492264
$917$	−8.42635e18	−0.467992
$918$	1.17195e17	0.00646299
$919$	−2.16751e19	−1.18689	−0.593444	−	0.804875i	$-0.702232\pi$
$919$	−2.16751e19	−1.18689	−0.593444	+	0.804875i	$0.702232\pi$
$920$	−2.91028e18	−0.158239
$921$	−1.59882e19	−0.863202
$922$	1.86817e19	1.00153
$923$	−5.11217e18	−0.272141
$924$	3.51794e18	0.185961
$925$	6.30844e18	0.331132
$926$	−8.03731e18	−0.418928
$927$	−1.37084e18	−0.0709526
$928$	−4.86142e18	−0.249862
$929$	1.63331e19	0.833618	0.416809	−	0.908994i	$-0.363148\pi$
$929$	1.63331e19	0.833618	0.416809	+	0.908994i	$0.363148\pi$
$930$	1.83976e18	0.0932442
$931$	4.93752e18	0.248505
$932$	−8.39255e18	−0.419460
$933$	1.76684e19	0.876933
$934$	3.98890e18	0.196607
$935$	6.15627e17	0.0301330
$936$	1.21518e19	0.590676
$937$	1.37811e19	0.665237	0.332618	−	0.943062i	$-0.392068\pi$
$937$	1.37811e19	0.665237	0.332618	+	0.943062i	$0.392068\pi$
$938$	−9.96565e18	−0.477735
$939$	−1.21345e19	−0.577690
$940$	7.32427e18	0.346285
$941$	9.47490e18	0.444879	0.222440	−	0.974946i	$-0.428598\pi$
$941$	9.47490e18	0.444879	0.222440	+	0.974946i	$0.428598\pi$
$942$	−5.08246e18	−0.236997
$943$	1.43480e18	0.0664457
$944$	1.42998e17	0.00657677
$945$	−3.27394e18	−0.149542
$946$	4.68762e18	0.212647
$947$	−2.78282e18	−0.125375	−0.0626874	−	0.998033i	$-0.519967\pi$
$947$	−2.78282e18	−0.125375	−0.0626874	+	0.998033i	$0.519967\pi$
$948$	−5.55568e17	−0.0248590
$949$	−2.05238e19	−0.912070
$950$	−2.45127e18	−0.108190
$951$	−2.02956e19	−0.889667
$952$	1.05604e18	0.0459770
$953$	−1.09628e19	−0.474041	−0.237021	−	0.971505i	$-0.576171\pi$
$953$	−1.09628e19	−0.474041	−0.237021	+	0.971505i	$0.576171\pi$
$954$	4.45436e18	0.191303
$955$	−3.19288e19	−1.36195
$956$	1.65428e19	0.700862
$957$	−2.19945e18	−0.0925523
$958$	−1.06670e19	−0.445827
$959$	−2.16644e19	−0.899344
$960$	−8.56752e18	−0.353258
$961$	−2.24982e19	−0.921394
$962$	5.01642e19	2.04059
$963$	2.86586e18	0.115794
$964$	−1.39251e19	−0.558854
$965$	3.24996e19	1.29554
$966$	−1.37106e18	−0.0542882
$967$	5.00459e19	1.96832	0.984162	−	0.177271i	$-0.0567268\pi$
$967$	5.00459e19	1.96832	0.984162	+	0.177271i	$0.0567268\pi$
$968$	−1.56507e19	−0.611425
$969$	7.40830e17	0.0287484
$970$	3.58822e18	0.138313
$971$	−1.37541e19	−0.526633	−0.263316	−	0.964710i	$-0.584816\pi$
$971$	−1.37541e19	−0.526633	−0.263316	+	0.964710i	$0.584816\pi$
$972$	1.00392e18	0.0381827
$973$	−3.08931e19	−1.16715
$974$	−1.55804e19	−0.584716
$975$	4.87421e18	0.181708
$976$	1.92627e17	0.00713336
$977$	2.88788e19	1.06234	0.531172	−	0.847264i	$-0.321752\pi$
$977$	2.88788e19	1.06234	0.531172	+	0.847264i	$0.321752\pi$
$978$	−4.09452e18	−0.149624
$979$	−2.39944e19	−0.871008
$980$	3.93676e18	0.141961
$981$	1.84802e19	0.662001
$982$	−3.32817e19	−1.18435
$983$	1.53615e19	0.543044	0.271522	−	0.962432i	$-0.412473\pi$
$983$	1.53615e19	0.543044	0.271522	+	0.962432i	$0.412473\pi$
$984$	6.43820e18	0.226098
$985$	−9.76779e18	−0.340769
$986$	−2.46354e17	−0.00853805
$987$	9.24771e18	0.318400
$988$	2.86617e19	0.980351
$989$	2.68633e18	0.0912816
$990$	−3.58646e18	−0.121070
$991$	−2.66515e19	−0.893806	−0.446903	−	0.894582i	$-0.647473\pi$
$991$	−2.66515e19	−0.893806	−0.446903	+	0.894582i	$0.647473\pi$
$992$	−8.27012e18	−0.275541
$993$	2.46519e19	0.815981
$994$	2.58816e18	0.0851099
$995$	−7.31756e18	−0.239065
$996$	−1.26573e19	−0.410822
$997$	−1.11779e19	−0.360446	−0.180223	−	0.983626i	$-0.557682\pi$
$997$	−1.11779e19	−0.360446	−0.180223	+	0.983626i	$0.557682\pi$
$998$	6.50061e18	0.208260
$999$	1.11070e19	0.353526

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.b.1.13	✓	31

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

\(f(q)\)	\(=\)	\(q-57.5851 q^{2} -729.000 q^{3} -4875.95 q^{4} +31633.2 q^{5} +41979.6 q^{6} +267144. q^{7} +752520. q^{8} +531441. q^{9} +O(q^{10})\)	\(q-57.5851 q^{2} -729.000 q^{3} -4875.95 q^{4} +31633.2 q^{5} +41979.6 q^{6} +267144. q^{7} +752520. q^{8} +531441. q^{9} -1.82160e6 q^{10} +3.70473e6 q^{11} +3.55457e6 q^{12} +3.03857e7 q^{13} -1.53835e7 q^{14} -2.30606e7 q^{15} -3.39015e6 q^{16} +5.25313e6 q^{17} -3.06031e7 q^{18} -1.93452e8 q^{19} -1.54242e8 q^{20} -1.94748e8 q^{21} -2.13337e8 q^{22} -1.22257e8 q^{23} -5.48587e8 q^{24} -2.20043e8 q^{25} -1.74976e9 q^{26} -3.87420e8 q^{27} -1.30258e9 q^{28} +8.14387e8 q^{29} +1.32795e9 q^{30} +1.38541e9 q^{31} -5.96942e9 q^{32} -2.70075e9 q^{33} -3.02502e8 q^{34} +8.45061e9 q^{35} -2.59128e9 q^{36} -2.86691e10 q^{37} +1.11400e10 q^{38} -2.21512e10 q^{39} +2.38046e10 q^{40} -1.17360e10 q^{41} +1.12146e10 q^{42} -2.19728e10 q^{43} -1.80641e10 q^{44} +1.68112e10 q^{45} +7.04019e9 q^{46} -4.74856e10 q^{47} +2.47142e9 q^{48} -2.55232e10 q^{49} +1.26712e10 q^{50} -3.82953e9 q^{51} -1.48159e11 q^{52} -1.45553e11 q^{53} +2.23097e10 q^{54} +1.17193e11 q^{55} +2.01031e11 q^{56} +1.41026e11 q^{57} -4.68966e10 q^{58} -4.21805e10 q^{59} +1.12442e11 q^{60} -5.68197e10 q^{61} -7.97793e10 q^{62} +1.41971e11 q^{63} +3.71522e11 q^{64} +9.61197e11 q^{65} +1.55523e11 q^{66} +6.47814e11 q^{67} -2.56140e10 q^{68} +8.91254e10 q^{69} -4.86630e11 q^{70} -1.68243e11 q^{71} +3.99920e11 q^{72} -6.75444e11 q^{73} +1.65091e12 q^{74} +1.60411e11 q^{75} +9.43262e11 q^{76} +9.89696e11 q^{77} +1.27558e12 q^{78} -1.56297e11 q^{79} -1.07241e11 q^{80} +2.82430e11 q^{81} +6.75817e11 q^{82} -3.56084e12 q^{83} +9.49581e11 q^{84} +1.66173e11 q^{85} +1.26531e12 q^{86} -5.93688e11 q^{87} +2.78788e12 q^{88} -6.47668e12 q^{89} -9.68074e11 q^{90} +8.11735e12 q^{91} +5.96120e11 q^{92} -1.00997e12 q^{93} +2.73446e12 q^{94} -6.11950e12 q^{95} +4.35171e12 q^{96} -1.96982e12 q^{97} +1.46976e12 q^{98} +1.96885e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q - 52 q^{2} - 22599 q^{3} + 126886 q^{4} + 33486 q^{5} + 37908 q^{6} - 1135539 q^{7} - 1519749 q^{8} + 16474671 q^{9}+O(q^{10}) \) 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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