LMFDB - Embedded newform 177.14.a.b.1.12

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			1.12
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)

$f(q)$	$=$	$q-63.8588 q^{2} -729.000 q^{3} -4114.05 q^{4} +18414.6 q^{5} +46553.1 q^{6} +120263. q^{7} +785850. q^{8} +531441. q^{9} +O(q^{10})$	\(q-63.8588 q^{2} -729.000 q^{3} -4114.05 q^{4} +18414.6 q^{5} +46553.1 q^{6} +120263. q^{7} +785850. q^{8} +531441. q^{9} -1.17593e6 q^{10} -3.91572e6 q^{11} +2.99914e6 q^{12} -9.55466e6 q^{13} -7.67982e6 q^{14} -1.34242e7 q^{15} -1.64811e7 q^{16} +4.69357e6 q^{17} -3.39372e7 q^{18} +3.61757e8 q^{19} -7.57586e7 q^{20} -8.76714e7 q^{21} +2.50053e8 q^{22} +1.17374e9 q^{23} -5.72885e8 q^{24} -8.81606e8 q^{25} +6.10149e8 q^{26} -3.87420e8 q^{27} -4.94766e8 q^{28} -4.59818e9 q^{29} +8.57256e8 q^{30} -5.94328e9 q^{31} -5.38522e9 q^{32} +2.85456e9 q^{33} -2.99726e8 q^{34} +2.21459e9 q^{35} -2.18638e9 q^{36} -1.48917e10 q^{37} -2.31014e10 q^{38} +6.96535e9 q^{39} +1.44711e10 q^{40} -1.83734e10 q^{41} +5.59859e9 q^{42} +1.62479e10 q^{43} +1.61095e10 q^{44} +9.78627e9 q^{45} -7.49535e10 q^{46} +1.36551e9 q^{47} +1.20147e10 q^{48} -8.24259e10 q^{49} +5.62983e10 q^{50} -3.42161e9 q^{51} +3.93084e10 q^{52} +1.60234e11 q^{53} +2.47402e10 q^{54} -7.21065e10 q^{55} +9.45083e10 q^{56} -2.63721e11 q^{57} +2.93635e11 q^{58} -4.21805e10 q^{59} +5.52280e10 q^{60} +2.01713e11 q^{61} +3.79531e11 q^{62} +6.39124e10 q^{63} +4.78907e11 q^{64} -1.75945e11 q^{65} -1.82289e11 q^{66} +5.67639e11 q^{67} -1.93096e10 q^{68} -8.55654e11 q^{69} -1.41421e11 q^{70} -2.83595e11 q^{71} +4.17633e11 q^{72} +2.34947e12 q^{73} +9.50965e11 q^{74} +6.42690e11 q^{75} -1.48829e12 q^{76} -4.70915e11 q^{77} -4.44799e11 q^{78} +1.78071e12 q^{79} -3.03493e11 q^{80} +2.82430e11 q^{81} +1.17330e12 q^{82} +1.42768e12 q^{83} +3.60685e11 q^{84} +8.64303e10 q^{85} -1.03757e12 q^{86} +3.35208e12 q^{87} -3.07717e12 q^{88} -5.50543e12 q^{89} -6.24940e11 q^{90} -1.14907e12 q^{91} -4.82882e12 q^{92} +4.33265e12 q^{93} -8.72001e10 q^{94} +6.66162e12 q^{95} +3.92582e12 q^{96} +1.04921e13 q^{97} +5.26362e12 q^{98} -2.08097e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−63.8588	−0.705547	−0.352773	−	0.935709i	$-0.614761\pi$
$2$	−63.8588	−0.705547	−0.352773	+	0.935709i	$0.614761\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	−4114.05	−0.502204
$5$	18414.6	0.527057	0.263528	−	0.964652i	$-0.415114\pi$
$5$	18414.6	0.527057	0.263528	+	0.964652i	$0.415114\pi$
$6$	46553.1	0.407348
$7$	120263.	0.386361	0.193180	−	0.981163i	$-0.438120\pi$
$7$	120263.	0.386361	0.193180	+	0.981163i	$0.438120\pi$
$8$	785850.	1.05988
$9$	531441.	0.333333
$10$	−1.17593e6	−0.371863
$11$	−3.91572e6	−0.666437	−0.333219	−	0.942850i	$-0.608135\pi$
$11$	−3.91572e6	−0.666437	−0.333219	+	0.942850i	$0.608135\pi$
$12$	2.99914e6	0.289947
$13$	−9.55466e6	−0.549014	−0.274507	−	0.961585i	$-0.588515\pi$
$13$	−9.55466e6	−0.549014	−0.274507	+	0.961585i	$0.588515\pi$
$14$	−7.67982e6	−0.272596
$15$	−1.34242e7	−0.304296
$16$	−1.64811e7	−0.245588
$17$	4.69357e6	0.0471613	0.0235806	−	0.999722i	$-0.492493\pi$
$17$	4.69357e6	0.0471613	0.0235806	+	0.999722i	$0.492493\pi$
$18$	−3.39372e7	−0.235182
$19$	3.61757e8	1.76408	0.882041	−	0.471172i	$-0.156169\pi$
$19$	3.61757e8	1.76408	0.882041	+	0.471172i	$0.156169\pi$
$20$	−7.57586e7	−0.264690
$21$	−8.76714e7	−0.223066
$22$	2.50053e8	0.470203
$23$	1.17374e9	1.65326	0.826628	−	0.562749i	$-0.190256\pi$
$23$	1.17374e9	1.65326	0.826628	+	0.562749i	$0.190256\pi$
$24$	−5.72885e8	−0.611919
$25$	−8.81606e8	−0.722211
$26$	6.10149e8	0.387355
$27$	−3.87420e8	−0.192450
$28$	−4.94766e8	−0.194032
$29$	−4.59818e9	−1.43549	−0.717744	−	0.696307i	$-0.754825\pi$
$29$	−4.59818e9	−1.43549	−0.717744	+	0.696307i	$0.754825\pi$
$30$	8.57256e8	0.214695
$31$	−5.94328e9	−1.20275	−0.601375	−	0.798967i	$-0.705380\pi$
$31$	−5.94328e9	−1.20275	−0.601375	+	0.798967i	$0.705380\pi$
$32$	−5.38522e9	−0.886601
$33$	2.85456e9	0.384768
$34$	−2.99726e8	−0.0332745
$35$	2.21459e9	0.203634
$36$	−2.18638e9	−0.167401
$37$	−1.48917e10	−0.954185	−0.477093	−	0.878853i	$-0.658309\pi$
$37$	−1.48917e10	−0.954185	−0.477093	+	0.878853i	$0.658309\pi$
$38$	−2.31014e10	−1.24464
$39$	6.96535e9	0.316973
$40$	1.44711e10	0.558614
$41$	−1.83734e10	−0.604080	−0.302040	−	0.953295i	$-0.597668\pi$
$41$	−1.83734e10	−0.604080	−0.302040	+	0.953295i	$0.597668\pi$
$42$	5.59859e9	0.157383
$43$	1.62479e10	0.391970	0.195985	−	0.980607i	$-0.437210\pi$
$43$	1.62479e10	0.391970	0.195985	+	0.980607i	$0.437210\pi$
$44$	1.61095e10	0.334687
$45$	9.78627e9	0.175686
$46$	−7.49535e10	−1.16645
$47$	1.36551e9	0.0184782	0.00923911	−	0.999957i	$-0.497059\pi$
$47$	1.36551e9	0.0184782	0.00923911	+	0.999957i	$0.497059\pi$
$48$	1.20147e10	0.141790
$49$	−8.24259e10	−0.850725
$50$	5.62983e10	0.509554
$51$	−3.42161e9	−0.0272286
$52$	3.93084e10	0.275717
$53$	1.60234e11	0.993026	0.496513	−	0.868029i	$-0.334614\pi$
$53$	1.60234e11	0.993026	0.496513	+	0.868029i	$0.334614\pi$
$54$	2.47402e10	0.135783
$55$	−7.21065e10	−0.351250
$56$	9.45083e10	0.409494
$57$	−2.63721e11	−1.01849
$58$	2.93635e11	1.01280
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	5.52280e10	0.152819
$61$	2.01713e11	0.501291	0.250646	−	0.968079i	$-0.419357\pi$
$61$	2.01713e11	0.501291	0.250646	+	0.968079i	$0.419357\pi$
$62$	3.79531e11	0.848596
$63$	6.39124e10	0.128787
$64$	4.78907e11	0.871127
$65$	−1.75945e11	−0.289362
$66$	−1.82289e11	−0.271472
$67$	5.67639e11	0.766631	0.383315	−	0.923618i	$-0.374782\pi$
$67$	5.67639e11	0.766631	0.383315	+	0.923618i	$0.374782\pi$
$68$	−1.93096e10	−0.0236846
$69$	−8.55654e11	−0.954507
$70$	−1.41421e11	−0.143673
$71$	−2.83595e11	−0.262736	−0.131368	−	0.991334i	$-0.541937\pi$
$71$	−2.83595e11	−0.262736	−0.131368	+	0.991334i	$0.541937\pi$
$72$	4.17633e11	0.353292
$73$	2.34947e12	1.81707	0.908534	−	0.417812i	$-0.137203\pi$
$73$	2.34947e12	1.81707	0.908534	+	0.417812i	$0.137203\pi$
$74$	9.50965e11	0.673222
$75$	6.42690e11	0.416969
$76$	−1.48829e12	−0.885929
$77$	−4.70915e11	−0.257485
$78$	−4.44799e11	−0.223640
$79$	1.78071e12	0.824170	0.412085	−	0.911145i	$-0.364801\pi$
$79$	1.78071e12	0.824170	0.412085	+	0.911145i	$0.364801\pi$
$80$	−3.03493e11	−0.129439
$81$	2.82430e11	0.111111
$82$	1.17330e12	0.426207
$83$	1.42768e12	0.479319	0.239659	−	0.970857i	$-0.422964\pi$
$83$	1.42768e12	0.479319	0.239659	+	0.970857i	$0.422964\pi$
$84$	3.60685e11	0.112024
$85$	8.64303e10	0.0248567
$86$	−1.03757e12	−0.276553
$87$	3.35208e12	0.828779
$88$	−3.07717e12	−0.706340
$89$	−5.50543e12	−1.17424	−0.587119	−	0.809500i	$-0.699738\pi$
$89$	−5.50543e12	−1.17424	−0.587119	+	0.809500i	$0.699738\pi$
$90$	−6.24940e11	−0.123954
$91$	−1.14907e12	−0.212118
$92$	−4.82882e12	−0.830271
$93$	4.33265e12	0.694408
$94$	−8.72001e10	−0.0130372
$95$	6.66162e12	0.929771
$96$	3.92582e12	0.511880
$97$	1.04921e13	1.27893	0.639465	−	0.768820i	$-0.279156\pi$
$97$	1.04921e13	1.27893	0.639465	+	0.768820i	$0.279156\pi$
$98$	5.26362e12	0.600227
$99$	−2.08097e12	−0.222146
$100$	3.62697e12	0.362697
$101$	1.03017e13	0.965648	0.482824	−	0.875717i	$-0.339611\pi$
$101$	1.03017e13	0.965648	0.482824	+	0.875717i	$0.339611\pi$
$102$	2.18500e11	0.0192110
$103$	1.10824e13	0.914518	0.457259	−	0.889334i	$-0.348831\pi$
$103$	1.10824e13	0.914518	0.457259	+	0.889334i	$0.348831\pi$
$104$	−7.50853e12	−0.581886
$105$	−1.61443e12	−0.117568
$106$	−1.02323e13	−0.700626
$107$	−8.17553e11	−0.0526649	−0.0263325	−	0.999653i	$-0.508383\pi$
$107$	−8.17553e11	−0.0526649	−0.0263325	+	0.999653i	$0.508383\pi$
$108$	1.59387e12	0.0966491
$109$	−1.99066e13	−1.13691	−0.568455	−	0.822715i	$-0.692458\pi$
$109$	−1.99066e13	−1.13691	−0.568455	+	0.822715i	$0.692458\pi$
$110$	4.60463e12	0.247824
$111$	1.08560e13	0.550899
$112$	−1.98206e12	−0.0948855
$113$	1.70793e12	0.0771723	0.0385861	−	0.999255i	$-0.487715\pi$
$113$	1.70793e12	0.0771723	0.0385861	+	0.999255i	$0.487715\pi$
$114$	1.68409e13	0.718595
$115$	2.16139e13	0.871359
$116$	1.89172e13	0.720907
$117$	−5.07774e12	−0.183005
$118$	2.69360e12	0.0918544
$119$	5.64461e11	0.0182213
$120$	−1.05494e13	−0.322516
$121$	−1.91898e13	−0.555861
$122$	−1.28812e13	−0.353684
$123$	1.33942e13	0.348766
$124$	2.44510e13	0.604025
$125$	−3.87132e13	−0.907703
$126$	−4.08137e12	−0.0908652
$127$	−3.27440e13	−0.692479	−0.346240	−	0.938146i	$-0.612542\pi$
$127$	−3.27440e13	−0.692479	−0.346240	+	0.938146i	$0.612542\pi$
$128$	1.35333e13	0.271981
$129$	−1.18447e13	−0.226304
$130$	1.12357e13	0.204158
$131$	−4.51213e13	−0.780043	−0.390022	−	0.920806i	$-0.627532\pi$
$131$	−4.51213e13	−0.780043	−0.390022	+	0.920806i	$0.627532\pi$
$132$	−1.17438e13	−0.193232
$133$	4.35058e13	0.681572
$134$	−3.62488e13	−0.540894
$135$	−7.13419e12	−0.101432
$136$	3.68844e12	0.0499851
$137$	−1.29786e14	−1.67705	−0.838524	−	0.544865i	$-0.816581\pi$
$137$	−1.29786e14	−1.67705	−0.838524	+	0.544865i	$0.816581\pi$
$138$	5.46411e13	0.673450
$139$	8.14124e13	0.957402	0.478701	−	0.877978i	$-0.341108\pi$
$139$	8.14124e13	0.957402	0.478701	+	0.877978i	$0.341108\pi$
$140$	−9.11093e12	−0.102266
$141$	−9.95459e11	−0.0106684
$142$	1.81100e13	0.185372
$143$	3.74134e13	0.365884
$144$	−8.75874e12	−0.0818626
$145$	−8.46737e13	−0.756583
$146$	−1.50034e14	−1.28203
$147$	6.00885e13	0.491166
$148$	6.12652e13	0.479195
$149$	8.63226e13	0.646270	0.323135	−	0.946353i	$-0.395263\pi$
$149$	8.63226e13	0.646270	0.323135	+	0.946353i	$0.395263\pi$
$150$	−4.10414e13	−0.294191
$151$	2.12012e14	1.45550	0.727748	−	0.685845i	$-0.240567\pi$
$151$	2.12012e14	1.45550	0.727748	+	0.685845i	$0.240567\pi$
$152$	2.84287e14	1.86971
$153$	2.49436e12	0.0157204
$154$	3.00720e13	0.181668
$155$	−1.09443e14	−0.633917
$156$	−2.86558e13	−0.159185
$157$	−1.66693e14	−0.888321	−0.444161	−	0.895947i	$-0.646498\pi$
$157$	−1.66693e14	−0.888321	−0.444161	+	0.895947i	$0.646498\pi$
$158$	−1.13714e14	−0.581491
$159$	−1.16810e14	−0.573324
$160$	−9.91666e13	−0.467289
$161$	1.41157e14	0.638753
$162$	−1.80356e13	−0.0783941
$163$	−4.64988e13	−0.194188	−0.0970940	−	0.995275i	$-0.530955\pi$
$163$	−4.64988e13	−0.194188	−0.0970940	+	0.995275i	$0.530955\pi$
$164$	7.55891e13	0.303371
$165$	5.25656e13	0.202794
$166$	−9.11702e13	−0.338182
$167$	3.31583e14	1.18287	0.591433	−	0.806354i	$-0.298562\pi$
$167$	3.31583e14	1.18287	0.591433	+	0.806354i	$0.298562\pi$
$168$	−6.88965e13	−0.236422
$169$	−2.11584e14	−0.698584
$170$	−5.51933e12	−0.0175375
$171$	1.92253e14	0.588027
$172$	−6.68448e13	−0.196849
$173$	6.09235e13	0.172777	0.0863883	−	0.996262i	$-0.472467\pi$
$173$	6.09235e13	0.172777	0.0863883	+	0.996262i	$0.472467\pi$
$174$	−2.14060e14	−0.584743
$175$	−1.06024e14	−0.279034
$176$	6.45355e13	0.163669
$177$	3.07496e13	0.0751646
$178$	3.51570e14	0.828481
$179$	2.22302e14	0.505125	0.252563	−	0.967581i	$-0.418727\pi$
$179$	2.22302e14	0.505125	0.252563	+	0.967581i	$0.418727\pi$
$180$	−4.02612e13	−0.0882299
$181$	−3.90444e14	−0.825368	−0.412684	−	0.910874i	$-0.635409\pi$
$181$	−3.90444e14	−0.825368	−0.412684	+	0.910874i	$0.635409\pi$
$182$	7.33781e13	0.149659
$183$	−1.47049e14	−0.289421
$184$	9.22381e14	1.75224
$185$	−2.74224e14	−0.502910
$186$	−2.76678e14	−0.489937
$187$	−1.83787e13	−0.0314300
$188$	−5.61779e12	−0.00927983
$189$	−4.65922e13	−0.0743552
$190$	−4.25403e14	−0.655997
$191$	−2.60963e14	−0.388922	−0.194461	−	0.980910i	$-0.562296\pi$
$191$	−2.60963e14	−0.388922	−0.194461	+	0.980910i	$0.562296\pi$
$192$	−3.49123e14	−0.502945
$193$	1.06191e14	0.147899	0.0739496	−	0.997262i	$-0.476440\pi$
$193$	1.06191e14	0.147899	0.0739496	+	0.997262i	$0.476440\pi$
$194$	−6.70014e14	−0.902345
$195$	1.28264e14	0.167063
$196$	3.39105e14	0.427237
$197$	−7.48053e14	−0.911804	−0.455902	−	0.890030i	$-0.650683\pi$
$197$	−7.48053e14	−0.911804	−0.455902	+	0.890030i	$0.650683\pi$
$198$	1.32889e14	0.156734
$199$	−9.12192e14	−1.04122	−0.520608	−	0.853796i	$-0.674295\pi$
$199$	−9.12192e14	−1.04122	−0.520608	+	0.853796i	$0.674295\pi$
$200$	−6.92810e14	−0.765454
$201$	−4.13809e14	−0.442614
$202$	−6.57853e14	−0.681310
$203$	−5.52989e14	−0.554616
$204$	1.40767e13	0.0136743
$205$	−3.38339e14	−0.318384
$206$	−7.07710e14	−0.645235
$207$	6.23772e14	0.551085
$208$	1.57472e14	0.134831
$209$	−1.41654e15	−1.17565
$210$	1.03096e14	0.0829498
$211$	1.88689e15	1.47201	0.736005	−	0.676976i	$-0.236710\pi$
$211$	1.88689e15	1.47201	0.736005	+	0.676976i	$0.236710\pi$
$212$	−6.59209e14	−0.498701
$213$	2.06741e14	0.151691
$214$	5.22080e13	0.0371576
$215$	2.99199e14	0.206590
$216$	−3.04454e14	−0.203973
$217$	−7.14754e14	−0.464695
$218$	1.27121e15	0.802143
$219$	−1.71276e15	−1.04908
$220$	2.96650e14	0.176399
$221$	−4.48455e13	−0.0258922
$222$	−6.93254e14	−0.388685
$223$	6.28777e14	0.342385	0.171193	−	0.985238i	$-0.445238\pi$
$223$	6.28777e14	0.342385	0.171193	+	0.985238i	$0.445238\pi$
$224$	−6.47640e14	−0.342548
$225$	−4.68521e14	−0.240737
$226$	−1.09067e14	−0.0544487
$227$	1.17064e15	0.567879	0.283939	−	0.958842i	$-0.408359\pi$
$227$	1.17064e15	0.567879	0.283939	+	0.958842i	$0.408359\pi$
$228$	1.08496e15	0.511491
$229$	−2.26275e14	−0.103683	−0.0518414	−	0.998655i	$-0.516509\pi$
$229$	−2.26275e14	−0.103683	−0.0518414	+	0.998655i	$0.516509\pi$
$230$	−1.38024e15	−0.614785
$231$	3.43297e14	0.148659
$232$	−3.61348e15	−1.52144
$233$	−2.85646e15	−1.16954	−0.584770	−	0.811199i	$-0.698815\pi$
$233$	−2.85646e15	−1.16954	−0.584770	+	0.811199i	$0.698815\pi$
$234$	3.24258e14	0.129118
$235$	2.51454e13	0.00973906
$236$	1.73533e14	0.0653813
$237$	−1.29814e15	−0.475835
$238$	−3.60458e13	−0.0128560
$239$	1.01593e15	0.352596	0.176298	−	0.984337i	$-0.443588\pi$
$239$	1.01593e15	0.352596	0.176298	+	0.984337i	$0.443588\pi$
$240$	2.21247e14	0.0747315
$241$	−8.99146e14	−0.295610	−0.147805	−	0.989016i	$-0.547221\pi$
$241$	−8.99146e14	−0.295610	−0.147805	+	0.989016i	$0.547221\pi$
$242$	1.22544e15	0.392186
$243$	−2.05891e14	−0.0641500
$244$	−8.29858e14	−0.251750
$245$	−1.51784e15	−0.448380
$246$	−8.55338e14	−0.246071
$247$	−3.45647e15	−0.968506
$248$	−4.67053e15	−1.27476
$249$	−1.04078e15	−0.276735
$250$	2.47218e15	0.640427
$251$	−6.61525e15	−1.66981	−0.834905	−	0.550393i	$-0.814478\pi$
$251$	−6.61525e15	−1.66981	−0.834905	+	0.550393i	$0.814478\pi$
$252$	−2.62939e14	−0.0646773
$253$	−4.59603e15	−1.10179
$254$	2.09099e15	0.488577
$255$	−6.30077e13	−0.0143510
$256$	−4.78742e15	−1.06302
$257$	2.15487e15	0.466504	0.233252	−	0.972416i	$-0.425063\pi$
$257$	2.15487e15	0.466504	0.233252	+	0.972416i	$0.425063\pi$
$258$	7.56391e14	0.159668
$259$	−1.79091e15	−0.368660
$260$	7.23848e14	0.145318
$261$	−2.44366e15	−0.478496
$262$	2.88140e15	0.550357
$263$	6.52155e15	1.21517	0.607587	−	0.794253i	$-0.292137\pi$
$263$	6.52155e15	1.21517	0.607587	+	0.794253i	$0.292137\pi$
$264$	2.24326e15	0.407806
$265$	2.95064e15	0.523381
$266$	−2.77823e15	−0.480881
$267$	4.01346e15	0.677947
$268$	−2.33530e15	−0.385005
$269$	−5.06945e15	−0.815776	−0.407888	−	0.913032i	$-0.633735\pi$
$269$	−5.06945e15	−0.815776	−0.407888	+	0.913032i	$0.633735\pi$
$270$	4.55581e14	0.0715651
$271$	−1.22251e16	−1.87478	−0.937392	−	0.348275i	$-0.886767\pi$
$271$	−1.22251e16	−1.87478	−0.937392	+	0.348275i	$0.886767\pi$
$272$	−7.73553e13	−0.0115822
$273$	8.37670e14	0.122466
$274$	8.28800e15	1.18324
$275$	3.45212e15	0.481309
$276$	3.52021e15	0.479357
$277$	−2.00845e15	−0.267142	−0.133571	−	0.991039i	$-0.542644\pi$
$277$	−2.00845e15	−0.267142	−0.133571	+	0.991039i	$0.542644\pi$
$278$	−5.19890e15	−0.675492
$279$	−3.15850e15	−0.400917
$280$	1.74033e15	0.215827
$281$	3.49015e15	0.422915	0.211457	−	0.977387i	$-0.432179\pi$
$281$	3.49015e15	0.422915	0.211457	+	0.977387i	$0.432179\pi$
$282$	6.35688e13	0.00752706
$283$	1.96381e15	0.227242	0.113621	−	0.993524i	$-0.463755\pi$
$283$	1.96381e15	0.227242	0.113621	+	0.993524i	$0.463755\pi$
$284$	1.16673e15	0.131947
$285$	−4.85632e15	−0.536804
$286$	−2.38917e15	−0.258148
$287$	−2.20963e15	−0.233393
$288$	−2.86193e15	−0.295534
$289$	−9.88255e15	−0.997776
$290$	5.40716e15	0.533805
$291$	−7.64875e15	−0.738390
$292$	−9.66584e15	−0.912538
$293$	1.34590e16	1.24272	0.621358	−	0.783526i	$-0.286581\pi$
$293$	1.34590e16	1.24272	0.621358	+	0.783526i	$0.286581\pi$
$294$	−3.83718e15	−0.346541
$295$	−7.76738e14	−0.0686169
$296$	−1.17026e16	−1.01132
$297$	1.51703e15	0.128256
$298$	−5.51246e15	−0.455974
$299$	−1.12147e16	−0.907660
$300$	−2.64406e15	−0.209403
$301$	1.95402e15	0.151442
$302$	−1.35389e16	−1.02692
$303$	−7.50992e15	−0.557517
$304$	−5.96216e15	−0.433237
$305$	3.71446e15	0.264209
$306$	−1.59287e14	−0.0110915
$307$	−1.54157e16	−1.05090	−0.525452	−	0.850823i	$-0.676104\pi$
$307$	−1.54157e16	−1.05090	−0.525452	+	0.850823i	$0.676104\pi$
$308$	1.93737e15	0.129310
$309$	−8.07908e15	−0.527997
$310$	6.98891e15	0.447258
$311$	2.06399e16	1.29349	0.646747	−	0.762705i	$-0.276129\pi$
$311$	2.06399e16	1.29349	0.646747	+	0.762705i	$0.276129\pi$
$312$	5.47372e15	0.335952
$313$	1.07125e16	0.643948	0.321974	−	0.946748i	$-0.395654\pi$
$313$	1.07125e16	0.643948	0.321974	+	0.946748i	$0.395654\pi$
$314$	1.06448e16	0.626752
$315$	1.17692e15	0.0678780
$316$	−7.32593e15	−0.413901
$317$	7.10976e15	0.393523	0.196761	−	0.980451i	$-0.436958\pi$
$317$	7.10976e15	0.393523	0.196761	+	0.980451i	$0.436958\pi$
$318$	7.45937e15	0.404507
$319$	1.80052e16	0.956663
$320$	8.81888e15	0.459133
$321$	5.95996e14	0.0304061
$322$	−9.01409e15	−0.450670
$323$	1.69793e15	0.0831964
$324$	−1.16193e15	−0.0558004
$325$	8.42344e15	0.396504
$326$	2.96936e15	0.137009
$327$	1.45119e16	0.656395
$328$	−1.44387e16	−0.640249
$329$	1.64220e14	0.00713926
$330$	−3.35678e15	−0.143081
$331$	−4.63238e16	−1.93607	−0.968037	−	0.250806i	$-0.919304\pi$
$331$	−4.63238e16	−1.93607	−0.968037	+	0.250806i	$0.919304\pi$
$332$	−5.87356e15	−0.240716
$333$	−7.91405e15	−0.318062
$334$	−2.11745e16	−0.834567
$335$	1.04529e16	0.404058
$336$	1.44492e15	0.0547822
$337$	1.40598e16	0.522860	0.261430	−	0.965222i	$-0.415806\pi$
$337$	1.40598e16	0.522860	0.261430	+	0.965222i	$0.415806\pi$
$338$	1.35115e16	0.492883
$339$	−1.24508e15	−0.0445554
$340$	−3.55579e14	−0.0124831
$341$	2.32722e16	0.801557
$342$	−1.22770e16	−0.414881
$343$	−2.15649e16	−0.715048
$344$	1.27684e16	0.415439
$345$	−1.57565e16	−0.503079
$346$	−3.89050e15	−0.121902
$347$	−3.96808e16	−1.22022	−0.610111	−	0.792316i	$-0.708875\pi$
$347$	−3.96808e16	−1.22022	−0.610111	+	0.792316i	$0.708875\pi$
$348$	−1.37906e16	−0.416216
$349$	−4.08458e16	−1.20999	−0.604996	−	0.796229i	$-0.706825\pi$
$349$	−4.08458e16	−1.20999	−0.604996	+	0.796229i	$0.706825\pi$
$350$	6.77057e15	0.196872
$351$	3.70167e15	0.105658
$352$	2.10870e16	0.590864
$353$	5.54402e16	1.52507	0.762534	−	0.646948i	$-0.223955\pi$
$353$	5.54402e16	1.52507	0.762534	+	0.646948i	$0.223955\pi$
$354$	−1.96363e15	−0.0530321
$355$	−5.22229e15	−0.138477
$356$	2.26496e16	0.589707
$357$	−4.11492e14	−0.0105201
$358$	−1.41960e16	−0.356390
$359$	−7.48019e16	−1.84416	−0.922080	−	0.386998i	$-0.873512\pi$
$359$	−7.48019e16	−1.84416	−0.922080	+	0.386998i	$0.873512\pi$
$360$	7.69054e15	0.186205
$361$	8.88153e16	2.11199
$362$	2.49333e16	0.582336
$363$	1.39894e16	0.320927
$364$	4.72732e15	0.106526
$365$	4.32645e16	0.957697
$366$	9.39036e15	0.204200
$367$	2.69332e16	0.575384	0.287692	−	0.957723i	$-0.407112\pi$
$367$	2.69332e16	0.575384	0.287692	+	0.957723i	$0.407112\pi$
$368$	−1.93445e16	−0.406019
$369$	−9.76438e15	−0.201360
$370$	1.75116e16	0.354826
$371$	1.92701e16	0.383666
$372$	−1.78248e16	−0.348734
$373$	5.13785e15	0.0987812	0.0493906	−	0.998780i	$-0.484272\pi$
$373$	5.13785e15	0.0987812	0.0493906	+	0.998780i	$0.484272\pi$
$374$	1.17364e15	0.0221754
$375$	2.82219e16	0.524063
$376$	1.07309e15	0.0195846
$377$	4.39341e16	0.788103
$378$	2.97532e15	0.0524611
$379$	−5.72424e15	−0.0992117	−0.0496058	−	0.998769i	$-0.515797\pi$
$379$	−5.72424e15	−0.0992117	−0.0496058	+	0.998769i	$0.515797\pi$
$380$	−2.74062e16	−0.466935
$381$	2.38703e16	0.399803
$382$	1.66648e16	0.274403
$383$	−6.23726e16	−1.00972	−0.504861	−	0.863201i	$-0.668456\pi$
$383$	−6.23726e16	−1.00972	−0.504861	+	0.863201i	$0.668456\pi$
$384$	−9.86576e15	−0.157028
$385$	−8.67170e15	−0.135709
$386$	−6.78124e15	−0.104350
$387$	8.63481e15	0.130657
$388$	−4.31651e16	−0.642283
$389$	−1.15033e15	−0.0168325	−0.00841625	−	0.999965i	$-0.502679\pi$
$389$	−1.15033e15	−0.0168325	−0.00841625	+	0.999965i	$0.502679\pi$
$390$	−8.19079e15	−0.117871
$391$	5.50902e15	0.0779696
$392$	−6.47744e16	−0.901663
$393$	3.28935e16	0.450358
$394$	4.77697e16	0.643321
$395$	3.27910e16	0.434384
$396$	8.56124e15	0.111562
$397$	−7.66690e16	−0.982837	−0.491418	−	0.870924i	$-0.663521\pi$
$397$	−7.66690e16	−0.982837	−0.491418	+	0.870924i	$0.663521\pi$
$398$	5.82515e16	0.734627
$399$	−3.17158e16	−0.393506
$400$	1.45298e16	0.177366
$401$	2.78495e16	0.334487	0.167243	−	0.985916i	$-0.446513\pi$
$401$	2.78495e16	0.334487	0.167243	+	0.985916i	$0.446513\pi$
$402$	2.64254e16	0.312285
$403$	5.67860e16	0.660327
$404$	−4.23816e16	−0.484952
$405$	5.20083e15	0.0585618
$406$	3.53132e16	0.391308
$407$	5.83117e16	0.635905
$408$	−2.68887e15	−0.0288589
$409$	−8.47371e16	−0.895101	−0.447550	−	0.894259i	$-0.647703\pi$
$409$	−8.47371e16	−0.895101	−0.447550	+	0.894259i	$0.647703\pi$
$410$	2.16059e16	0.224635
$411$	9.46143e16	0.968244
$412$	−4.55936e16	−0.459274
$413$	−5.07274e15	−0.0502999
$414$	−3.98333e16	−0.388816
$415$	2.62902e16	0.252628
$416$	5.14539e16	0.486757
$417$	−5.93496e16	−0.552756
$418$	9.04586e16	0.829476
$419$	−2.15791e16	−0.194824	−0.0974118	−	0.995244i	$-0.531056\pi$
$419$	−2.15791e16	−0.194824	−0.0974118	+	0.995244i	$0.531056\pi$
$420$	6.64186e15	0.0590432
$421$	−5.87309e15	−0.0514083	−0.0257042	−	0.999670i	$-0.508183\pi$
$421$	−5.87309e15	−0.0514083	−0.0257042	+	0.999670i	$0.508183\pi$
$422$	−1.20495e17	−1.03857
$423$	7.25690e14	0.00615940
$424$	1.25920e17	1.05248
$425$	−4.13788e15	−0.0340604
$426$	−1.32022e16	−0.107025
$427$	2.42585e16	0.193679
$428$	3.36346e15	0.0264485
$429$	−2.72744e16	−0.211243
$430$	−1.91065e16	−0.145759
$431$	2.09721e17	1.57594	0.787970	−	0.615713i	$-0.211132\pi$
$431$	2.09721e17	1.57594	0.787970	+	0.615713i	$0.211132\pi$
$432$	6.38512e15	0.0472634
$433$	−1.91663e17	−1.39755	−0.698775	−	0.715342i	$-0.746271\pi$
$433$	−1.91663e17	−1.39755	−0.698775	+	0.715342i	$0.746271\pi$
$434$	4.56433e16	0.327864
$435$	6.17272e16	0.436814
$436$	8.18970e16	0.570960
$437$	4.24608e17	2.91648
$438$	1.09375e17	0.740178
$439$	5.54766e16	0.369905	0.184952	−	0.982747i	$-0.440787\pi$
$439$	5.54766e16	0.369905	0.184952	+	0.982747i	$0.440787\pi$
$440$	−5.66648e16	−0.372281
$441$	−4.38045e16	−0.283575
$442$	2.86378e15	0.0182682
$443$	−1.61504e17	−1.01521	−0.507607	−	0.861589i	$-0.669470\pi$
$443$	−1.61504e17	−1.01521	−0.507607	+	0.861589i	$0.669470\pi$
$444$	−4.46623e16	−0.276664
$445$	−1.01380e17	−0.618890
$446$	−4.01529e16	−0.241569
$447$	−6.29292e16	−0.373124
$448$	5.75946e16	0.336569
$449$	−8.58276e16	−0.494340	−0.247170	−	0.968972i	$-0.579501\pi$
$449$	−8.58276e16	−0.494340	−0.247170	+	0.968972i	$0.579501\pi$
$450$	2.99192e16	0.169851
$451$	7.19451e16	0.402581
$452$	−7.02653e15	−0.0387562
$453$	−1.54557e17	−0.840331
$454$	−7.47557e16	−0.400665
$455$	−2.11596e16	−0.111798
$456$	−2.07245e17	−1.07948
$457$	−2.08369e17	−1.06998	−0.534992	−	0.844857i	$-0.679686\pi$
$457$	−2.08369e17	−1.06998	−0.534992	+	0.844857i	$0.679686\pi$
$458$	1.44497e16	0.0731531
$459$	−1.81839e15	−0.00907619
$460$	−8.89207e16	−0.437600
$461$	8.06039e16	0.391111	0.195555	−	0.980693i	$-0.437349\pi$
$461$	8.06039e16	0.391111	0.195555	+	0.980693i	$0.437349\pi$
$462$	−2.19225e16	−0.104886
$463$	−3.05515e17	−1.44131	−0.720653	−	0.693296i	$-0.756158\pi$
$463$	−3.05515e17	−1.44131	−0.720653	+	0.693296i	$0.756158\pi$
$464$	7.57832e16	0.352538
$465$	7.97841e16	0.365992
$466$	1.82410e17	0.825165
$467$	−3.37157e16	−0.150408	−0.0752042	−	0.997168i	$-0.523961\pi$
$467$	−3.37157e16	−0.150408	−0.0752042	+	0.997168i	$0.523961\pi$
$468$	2.08901e16	0.0919056
$469$	6.82657e16	0.296196
$470$	−1.60575e15	−0.00687137
$471$	1.21519e17	0.512873
$472$	−3.31476e16	−0.137984
$473$	−6.36224e16	−0.261224
$474$	8.28975e16	0.335724
$475$	−3.18927e17	−1.27404
$476$	−2.32222e15	−0.00915079
$477$	8.51547e16	0.331009
$478$	−6.48760e16	−0.248773
$479$	1.85402e17	0.701350	0.350675	−	0.936497i	$-0.385952\pi$
$479$	1.85402e17	0.701350	0.350675	+	0.936497i	$0.385952\pi$
$480$	7.22925e16	0.269790
$481$	1.42285e17	0.523861
$482$	5.74184e16	0.208567
$483$	−1.02903e17	−0.368784
$484$	7.89480e16	0.279156
$485$	1.93208e17	0.674068
$486$	1.31480e16	0.0452609
$487$	−5.28050e17	−1.79365	−0.896824	−	0.442388i	$-0.854131\pi$
$487$	−5.28050e17	−1.79365	−0.896824	+	0.442388i	$0.854131\pi$
$488$	1.58516e17	0.531306
$489$	3.38976e16	0.112115
$490$	9.69275e16	0.316353
$491$	9.57612e16	0.308432	0.154216	−	0.988037i	$-0.450715\pi$
$491$	9.57612e16	0.308432	0.154216	+	0.988037i	$0.450715\pi$
$492$	−5.51045e16	−0.175151
$493$	−2.15819e16	−0.0676994
$494$	2.20726e17	0.683326
$495$	−3.83203e16	−0.117083
$496$	9.79519e16	0.295381
$497$	−3.41059e16	−0.101511
$498$	6.64631e16	0.195249
$499$	−1.14773e17	−0.332801	−0.166401	−	0.986058i	$-0.553215\pi$
$499$	−1.14773e17	−0.332801	−0.166401	+	0.986058i	$0.553215\pi$
$500$	1.59268e17	0.455852
$501$	−2.41724e17	−0.682928
$502$	4.22442e17	1.17813
$503$	9.36677e16	0.257868	0.128934	−	0.991653i	$-0.458844\pi$
$503$	9.36677e16	0.257868	0.128934	+	0.991653i	$0.458844\pi$
$504$	5.02256e16	0.136498
$505$	1.89701e17	0.508951
$506$	2.93497e17	0.777365
$507$	1.54244e17	0.403327
$508$	1.34710e17	0.347766
$509$	−6.74000e17	−1.71789	−0.858943	−	0.512071i	$-0.828879\pi$
$509$	−6.74000e17	−1.71789	−0.858943	+	0.512071i	$0.828879\pi$
$510$	4.02359e15	0.0101253
$511$	2.82553e17	0.702044
$512$	1.94855e17	0.478031
$513$	−1.40152e17	−0.339498
$514$	−1.37607e17	−0.329141
$515$	2.04078e17	0.482003
$516$	4.87299e16	0.113651
$517$	−5.34697e15	−0.0123146
$518$	1.14365e17	0.260107
$519$	−4.44132e16	−0.0997526
$520$	−1.38267e17	−0.306687
$521$	4.53485e17	0.993385	0.496693	−	0.867927i	$-0.334548\pi$
$521$	4.53485e17	0.993385	0.496693	+	0.867927i	$0.334548\pi$
$522$	1.56049e17	0.337601
$523$	8.66889e17	1.85226	0.926132	−	0.377201i	$-0.123113\pi$
$523$	8.66889e17	1.85226	0.926132	+	0.377201i	$0.123113\pi$
$524$	1.85632e17	0.391740
$525$	7.72916e16	0.161100
$526$	−4.16459e17	−0.857363
$527$	−2.78952e16	−0.0567232
$528$	−4.70464e16	−0.0944943
$529$	8.73622e17	1.73325
$530$	−1.88424e17	−0.369270
$531$	−2.24165e16	−0.0433963
$532$	−1.78985e17	−0.342288
$533$	1.75552e17	0.331648
$534$	−2.56295e17	−0.478323
$535$	−1.50549e16	−0.0277574
$536$	4.46079e17	0.812533
$537$	−1.62058e17	−0.291634
$538$	3.23729e17	0.575568
$539$	3.22757e17	0.566955
$540$	2.93504e16	0.0509396
$541$	−6.69887e17	−1.14873	−0.574367	−	0.818598i	$-0.694752\pi$
$541$	−6.69887e17	−1.14873	−0.574367	+	0.818598i	$0.694752\pi$
$542$	7.80679e17	1.32275
$543$	2.84633e17	0.476526
$544$	−2.52759e16	−0.0418132
$545$	−3.66573e17	−0.599215
$546$	−5.34926e16	−0.0864056
$547$	7.81136e17	1.24683	0.623417	−	0.781889i	$-0.285744\pi$
$547$	7.81136e17	1.24683	0.623417	+	0.781889i	$0.285744\pi$
$548$	5.33948e17	0.842220
$549$	1.07199e17	0.167097
$550$	−2.20448e17	−0.339586
$551$	−1.66343e18	−2.53232
$552$	−6.72416e17	−1.01166
$553$	2.14153e17	0.318427
$554$	1.28257e17	0.188481
$555$	1.99910e17	0.290355
$556$	−3.34935e17	−0.480811
$557$	4.27554e17	0.606642	0.303321	−	0.952888i	$-0.401905\pi$
$557$	4.27554e17	0.606642	0.303321	+	0.952888i	$0.401905\pi$
$558$	2.01698e17	0.282865
$559$	−1.55243e17	−0.215197
$560$	−3.64989e16	−0.0500100
$561$	1.33981e16	0.0181461
$562$	−2.22877e17	−0.298386
$563$	8.65471e16	0.114538	0.0572688	−	0.998359i	$-0.481761\pi$
$563$	8.65471e16	0.114538	0.0572688	+	0.998359i	$0.481761\pi$
$564$	4.09537e15	0.00535771
$565$	3.14509e16	0.0406742
$566$	−1.25407e17	−0.160330
$567$	3.39657e16	0.0429290
$568$	−2.22863e17	−0.278467
$569$	−1.27671e16	−0.0157712	−0.00788558	−	0.999969i	$-0.502510\pi$
$569$	−1.27671e16	−0.0157712	−0.00788558	+	0.999969i	$0.502510\pi$
$570$	3.10119e17	0.378740
$571$	−1.88068e17	−0.227080	−0.113540	−	0.993533i	$-0.536219\pi$
$571$	−1.88068e17	−0.227080	−0.113540	+	0.993533i	$0.536219\pi$
$572$	−1.53921e17	−0.183748
$573$	1.90242e17	0.224544
$574$	1.41104e17	0.164670
$575$	−1.03477e18	−1.19400
$576$	2.54511e17	0.290376
$577$	1.05926e18	1.19498	0.597491	−	0.801876i	$-0.296164\pi$
$577$	1.05926e18	1.19498	0.597491	+	0.801876i	$0.296164\pi$
$578$	6.31088e17	0.703978
$579$	−7.74133e16	−0.0853896
$580$	3.48352e17	0.379959
$581$	1.71697e17	0.185190
$582$	4.88440e17	0.520969
$583$	−6.27430e17	−0.661789
$584$	1.84633e18	1.92586
$585$	−9.35045e16	−0.0964538
$586$	−8.59474e17	−0.876795
$587$	1.21775e18	1.22860	0.614301	−	0.789072i	$-0.289438\pi$
$587$	1.21775e18	1.22860	0.614301	+	0.789072i	$0.289438\pi$
$588$	−2.47207e17	−0.246666
$589$	−2.15003e18	−2.12175
$590$	4.96015e16	0.0484125
$591$	5.45330e17	0.526430
$592$	2.45432e17	0.234336
$593$	−5.86979e17	−0.554328	−0.277164	−	0.960823i	$-0.589395\pi$
$593$	−5.86979e17	−0.554328	−0.277164	+	0.960823i	$0.589395\pi$
$594$	−9.68758e16	−0.0904906
$595$	1.03943e16	0.00960364
$596$	−3.55136e17	−0.324559
$597$	6.64988e17	0.601147
$598$	7.16155e17	0.640397
$599$	−1.74292e18	−1.54171	−0.770854	−	0.637012i	$-0.780170\pi$
$599$	−1.74292e18	−1.54171	−0.770854	+	0.637012i	$0.780170\pi$
$600$	5.05058e17	0.441935
$601$	−6.26376e17	−0.542189	−0.271095	−	0.962553i	$-0.587386\pi$
$601$	−6.26376e17	−0.542189	−0.271095	+	0.962553i	$0.587386\pi$
$602$	−1.24781e17	−0.106849
$603$	3.01667e17	0.255544
$604$	−8.72230e17	−0.730955
$605$	−3.53373e17	−0.292970
$606$	4.79575e17	0.393354
$607$	−1.70636e18	−1.38466	−0.692331	−	0.721580i	$-0.743416\pi$
$607$	−1.70636e18	−1.38466	−0.692331	+	0.721580i	$0.743416\pi$
$608$	−1.94814e18	−1.56404
$609$	4.03129e17	0.320208
$610$	−2.37201e17	−0.186412
$611$	−1.30470e16	−0.0101448
$612$	−1.02619e16	−0.00789485
$613$	−3.36839e17	−0.256407	−0.128203	−	0.991748i	$-0.540921\pi$
$613$	−3.36839e17	−0.256407	−0.128203	+	0.991748i	$0.540921\pi$
$614$	9.84427e17	0.741462
$615$	2.46649e17	0.183819
$616$	−3.70068e17	−0.272902
$617$	−3.34927e17	−0.244397	−0.122199	−	0.992506i	$-0.538995\pi$
$617$	−3.34927e17	−0.244397	−0.122199	+	0.992506i	$0.538995\pi$
$618$	5.15920e17	0.372527
$619$	−2.03089e18	−1.45110	−0.725550	−	0.688169i	$-0.758415\pi$
$619$	−2.03089e18	−1.45110	−0.725550	+	0.688169i	$0.758415\pi$
$620$	4.50255e17	0.318356
$621$	−4.54730e17	−0.318169
$622$	−1.31804e18	−0.912621
$623$	−6.62097e17	−0.453680
$624$	−1.14797e17	−0.0778448
$625$	3.63291e17	0.243800
$626$	−6.84085e17	−0.454336
$627$	1.03266e18	0.678762
$628$	6.85785e17	0.446118
$629$	−6.98952e16	−0.0450006
$630$	−7.51568e16	−0.0478911
$631$	−1.93258e18	−1.21884	−0.609421	−	0.792847i	$-0.708598\pi$
$631$	−1.93258e18	−1.21884	−0.609421	+	0.792847i	$0.708598\pi$
$632$	1.39937e18	0.873517
$633$	−1.37554e18	−0.849865
$634$	−4.54021e17	−0.277649
$635$	−6.02967e17	−0.364976
$636$	4.80564e17	0.287925
$637$	7.87552e17	0.467060
$638$	−1.14979e18	−0.674970
$639$	−1.50714e17	−0.0875786
$640$	2.49210e17	0.143349
$641$	−3.17896e18	−1.81012	−0.905060	−	0.425283i	$-0.860175\pi$
$641$	−3.17896e18	−1.81012	−0.905060	+	0.425283i	$0.860175\pi$
$642$	−3.80596e16	−0.0214529
$643$	1.99242e18	1.11176	0.555879	−	0.831263i	$-0.312382\pi$
$643$	1.99242e18	1.11176	0.555879	+	0.831263i	$0.312382\pi$
$644$	−5.80726e17	−0.320784
$645$	−2.18116e17	−0.119275
$646$	−1.08428e17	−0.0586989
$647$	−1.34205e18	−0.719267	−0.359634	−	0.933094i	$-0.617098\pi$
$647$	−1.34205e18	−0.719267	−0.359634	+	0.933094i	$0.617098\pi$
$648$	2.21947e17	0.117764
$649$	1.65167e17	0.0867628
$650$	−5.37911e17	−0.279752
$651$	5.21056e17	0.268292
$652$	1.91299e17	0.0975220
$653$	−2.21477e18	−1.11787	−0.558937	−	0.829210i	$-0.688791\pi$
$653$	−2.21477e18	−1.11787	−0.558937	+	0.829210i	$0.688791\pi$
$654$	−9.26715e17	−0.463117
$655$	−8.30892e17	−0.411127
$656$	3.02814e17	0.148355
$657$	1.24860e18	0.605689
$658$	−1.04869e16	−0.00503708
$659$	−2.98710e18	−1.42068	−0.710338	−	0.703861i	$-0.751458\pi$
$659$	−2.98710e18	−1.42068	−0.710338	+	0.703861i	$0.751458\pi$
$660$	−2.16258e17	−0.101844
$661$	−1.01538e18	−0.473498	−0.236749	−	0.971571i	$-0.576082\pi$
$661$	−1.01538e18	−0.473498	−0.236749	+	0.971571i	$0.576082\pi$
$662$	2.95818e18	1.36599
$663$	3.26924e16	0.0149489
$664$	1.12194e18	0.508018
$665$	8.01143e17	0.359227
$666$	5.05382e17	0.224407
$667$	−5.39706e18	−2.37323
$668$	−1.36415e18	−0.594040
$669$	−4.58378e17	−0.197676
$670$	−6.67507e17	−0.285082
$671$	−7.89852e17	−0.334079
$672$	4.72129e17	0.197770
$673$	−5.60114e17	−0.232369	−0.116185	−	0.993228i	$-0.537066\pi$
$673$	−5.60114e17	−0.232369	−0.116185	+	0.993228i	$0.537066\pi$
$674$	−8.97843e17	−0.368902
$675$	3.41552e17	0.138990
$676$	8.70466e17	0.350831
$677$	−8.13286e17	−0.324651	−0.162326	−	0.986737i	$-0.551899\pi$
$677$	−8.13286e17	−0.324651	−0.162326	+	0.986737i	$0.551899\pi$
$678$	7.95096e16	0.0314360
$679$	1.26181e18	0.494128
$680$	6.79212e16	0.0263450
$681$	−8.53397e17	−0.327865
$682$	−1.48614e18	−0.565536
$683$	2.98829e18	1.12639	0.563195	−	0.826324i	$-0.309572\pi$
$683$	2.98829e18	1.12639	0.563195	+	0.826324i	$0.309572\pi$
$684$	−7.90937e17	−0.295310
$685$	−2.38996e18	−0.883899
$686$	1.37711e18	0.504500
$687$	1.64955e17	0.0598613
$688$	−2.67784e17	−0.0962631
$689$	−1.53098e18	−0.545185
$690$	1.00619e18	0.354946
$691$	−3.41593e18	−1.19372	−0.596858	−	0.802347i	$-0.703585\pi$
$691$	−3.41593e18	−1.19372	−0.596858	+	0.802347i	$0.703585\pi$
$692$	−2.50642e17	−0.0867690
$693$	−2.50263e17	−0.0858284
$694$	2.53397e18	0.860924
$695$	1.49918e18	0.504605
$696$	2.63423e18	0.878402
$697$	−8.62369e16	−0.0284892
$698$	2.60836e18	0.853705
$699$	2.08236e18	0.675234
$700$	4.36189e17	0.140132
$701$	−6.57222e17	−0.209192	−0.104596	−	0.994515i	$-0.533355\pi$
$701$	−6.57222e17	−0.209192	−0.104596	+	0.994515i	$0.533355\pi$
$702$	−2.36384e17	−0.0745465
$703$	−5.38718e18	−1.68326
$704$	−1.87527e18	−0.580551
$705$	−1.83310e16	−0.00562285
$706$	−3.54035e18	−1.07601
$707$	1.23891e18	0.373089
$708$	−1.26506e17	−0.0377479
$709$	−1.79482e17	−0.0530665	−0.0265333	−	0.999648i	$-0.508447\pi$
$709$	−1.79482e17	−0.0530665	−0.0265333	+	0.999648i	$0.508447\pi$
$710$	3.33489e17	0.0977018
$711$	9.46342e17	0.274723
$712$	−4.32644e18	−1.24455
$713$	−6.97585e18	−1.98845
$714$	2.62774e16	0.00742239
$715$	6.88953e17	0.192841
$716$	−9.14563e17	−0.253676
$717$	−7.40612e17	−0.203571
$718$	4.77676e18	1.30114
$719$	4.97080e18	1.34180	0.670902	−	0.741546i	$-0.265907\pi$
$719$	4.97080e18	1.34180	0.670902	+	0.741546i	$0.265907\pi$
$720$	−1.61289e17	−0.0431462
$721$	1.33280e18	0.353334
$722$	−5.67164e18	−1.49011
$723$	6.55478e17	0.170671
$724$	1.60631e18	0.414503
$725$	4.05379e18	1.03673
$726$	−8.93346e17	−0.226429
$727$	7.59211e17	0.190717	0.0953583	−	0.995443i	$-0.469600\pi$
$727$	7.59211e17	0.190717	0.0953583	+	0.995443i	$0.469600\pi$
$728$	−9.02995e17	−0.224818
$729$	1.50095e17	0.0370370
$730$	−2.76282e18	−0.675700
$731$	7.62608e16	0.0184858
$732$	6.04966e17	0.145348
$733$	6.71055e18	1.59802	0.799010	−	0.601318i	$-0.205357\pi$
$733$	6.71055e18	1.59802	0.799010	+	0.601318i	$0.205357\pi$
$734$	−1.71992e18	−0.405960
$735$	1.10651e18	0.258873
$736$	−6.32083e18	−1.46578
$737$	−2.22272e18	−0.510911
$738$	6.23541e17	0.142069
$739$	−5.57650e18	−1.25943	−0.629713	−	0.776828i	$-0.716827\pi$
$739$	−5.57650e18	−1.25943	−0.629713	+	0.776828i	$0.716827\pi$
$740$	1.12817e18	0.252563
$741$	2.51977e18	0.559167
$742$	−1.23057e18	−0.270694
$743$	8.17239e18	1.78206	0.891029	−	0.453946i	$-0.149984\pi$
$743$	8.17239e18	1.78206	0.891029	+	0.453946i	$0.149984\pi$
$744$	3.40481e18	0.735986
$745$	1.58960e18	0.340621
$746$	−3.28097e17	−0.0696948
$747$	7.58730e17	0.159773
$748$	7.56110e16	0.0157843
$749$	−9.83210e16	−0.0203477
$750$	−1.80222e18	−0.369751
$751$	−5.17756e18	−1.05309	−0.526545	−	0.850147i	$-0.676513\pi$
$751$	−5.17756e18	−1.05309	−0.526545	+	0.850147i	$0.676513\pi$
$752$	−2.25052e16	−0.00453802
$753$	4.82252e18	0.964066
$754$	−2.80558e18	−0.556044
$755$	3.90412e18	0.767129
$756$	1.91683e17	0.0373414
$757$	−9.33308e17	−0.180261	−0.0901305	−	0.995930i	$-0.528728\pi$
$757$	−9.33308e17	−0.180261	−0.0901305	+	0.995930i	$0.528728\pi$
$758$	3.65543e17	0.0699985
$759$	3.35050e18	0.636119
$760$	5.23503e18	0.985441
$761$	6.65862e18	1.24275	0.621375	−	0.783513i	$-0.286574\pi$
$761$	6.65862e18	1.24275	0.621375	+	0.783513i	$0.286574\pi$
$762$	−1.52433e18	−0.282080
$763$	−2.39402e18	−0.439257
$764$	1.07362e18	0.195318
$765$	4.59326e16	0.00828555
$766$	3.98304e18	0.712406
$767$	4.03021e17	0.0714755
$768$	3.49003e18	0.613736
$769$	−5.49304e18	−0.957836	−0.478918	−	0.877860i	$-0.658971\pi$
$769$	−5.49304e18	−0.957836	−0.478918	+	0.877860i	$0.658971\pi$
$770$	5.53765e17	0.0957493
$771$	−1.57090e18	−0.269336
$772$	−4.36876e17	−0.0742755
$773$	−4.56545e18	−0.769692	−0.384846	−	0.922981i	$-0.625745\pi$
$773$	−4.56545e18	−0.769692	−0.384846	+	0.922981i	$0.625745\pi$
$774$	−5.51409e17	−0.0921844
$775$	5.23963e18	0.868639
$776$	8.24523e18	1.35551
$777$	1.30557e18	0.212846
$778$	7.34584e16	0.0118761
$779$	−6.64671e18	−1.06565
$780$	−5.27685e17	−0.0838996
$781$	1.11048e18	0.175097
$782$	−3.51799e17	−0.0550112
$783$	1.78143e18	0.276260
$784$	1.35847e18	0.208928
$785$	−3.06959e18	−0.468196
$786$	−2.10054e18	−0.317749
$787$	−8.58589e18	−1.28810	−0.644050	−	0.764983i	$-0.722747\pi$
$787$	−8.58589e18	−1.28810	−0.644050	+	0.764983i	$0.722747\pi$
$788$	3.07753e18	0.457911
$789$	−4.75421e18	−0.701581
$790$	−2.09400e18	−0.306478
$791$	2.05401e17	0.0298163
$792$	−1.63533e18	−0.235447
$793$	−1.92730e18	−0.275216
$794$	4.89599e18	0.693437
$795$	−2.15101e18	−0.302174
$796$	3.75280e18	0.522903
$797$	6.84451e18	0.945939	0.472970	−	0.881079i	$-0.343182\pi$
$797$	6.84451e18	0.945939	0.472970	+	0.881079i	$0.343182\pi$
$798$	2.02533e18	0.277637
$799$	6.40914e15	0.000871456 0
$800$	4.74764e18	0.640313
$801$	−2.92581e18	−0.391413
$802$	−1.77843e18	−0.235996
$803$	−9.19986e18	−1.21096
$804$	1.70243e18	0.222283
$805$	2.59934e18	0.336659
$806$	−3.62629e18	−0.465891
$807$	3.69563e18	0.470989
$808$	8.09557e18	1.02347
$809$	1.01211e19	1.26930	0.634650	−	0.772800i	$-0.281144\pi$
$809$	1.01211e19	1.26930	0.634650	+	0.772800i	$0.281144\pi$
$810$	−3.32119e17	−0.0413181
$811$	−5.21041e18	−0.643037	−0.321519	−	0.946903i	$-0.604193\pi$
$811$	−5.21041e18	−0.643037	−0.321519	+	0.946903i	$0.604193\pi$
$812$	2.27503e18	0.278530
$813$	8.91208e18	1.08241
$814$	−3.72372e18	−0.448661
$815$	−8.56257e17	−0.102348
$816$	5.63920e16	0.00668700
$817$	5.87781e18	0.691468
$818$	5.41121e18	0.631536
$819$	−6.10662e17	−0.0707058
$820$	1.39194e18	0.159894
$821$	2.25361e18	0.256831	0.128416	−	0.991720i	$-0.459011\pi$
$821$	2.25361e18	0.256831	0.128416	+	0.991720i	$0.459011\pi$
$822$	−6.04195e18	−0.683141
$823$	1.04493e19	1.17217	0.586085	−	0.810250i	$-0.300669\pi$
$823$	1.04493e19	1.17217	0.586085	+	0.810250i	$0.300669\pi$
$824$	8.70911e18	0.969275
$825$	−2.51660e18	−0.277884
$826$	3.23939e17	0.0354889
$827$	1.23524e19	1.34265	0.671327	−	0.741162i	$-0.265725\pi$
$827$	1.23524e19	1.34265	0.671327	+	0.741162i	$0.265725\pi$
$828$	−2.56623e18	−0.276757
$829$	−7.88948e18	−0.844197	−0.422098	−	0.906550i	$-0.638706\pi$
$829$	−7.88948e18	−0.844197	−0.422098	+	0.906550i	$0.638706\pi$
$830$	−1.67886e18	−0.178241
$831$	1.46416e18	0.154235
$832$	−4.57579e18	−0.478261
$833$	−3.86872e17	−0.0401213
$834$	3.79000e18	0.389995
$835$	6.10597e18	0.623437
$836$	5.82772e18	0.590416
$837$	2.30255e18	0.231469
$838$	1.37801e18	0.137457
$839$	1.36386e19	1.34995	0.674975	−	0.737841i	$-0.264155\pi$
$839$	1.36386e19	1.34995	0.674975	+	0.737841i	$0.264155\pi$
$840$	−1.26870e18	−0.124608
$841$	1.08827e19	1.06062
$842$	3.75049e17	0.0362710
$843$	−2.54432e18	−0.244170
$844$	−7.76277e18	−0.739249
$845$	−3.89623e18	−0.368193
$846$	−4.63417e16	−0.00434575
$847$	−2.30782e18	−0.214763
$848$	−2.64083e18	−0.243875
$849$	−1.43162e18	−0.131198
$850$	2.64240e17	0.0240312
$851$	−1.74789e19	−1.57751
$852$	−8.50543e17	−0.0761796
$853$	4.63570e18	0.412047	0.206023	−	0.978547i	$-0.433948\pi$
$853$	4.63570e18	0.412047	0.206023	+	0.978547i	$0.433948\pi$
$854$	−1.54912e18	−0.136650
$855$	3.54026e18	0.309924
$856$	−6.42474e17	−0.0558182
$857$	6.54102e18	0.563988	0.281994	−	0.959416i	$-0.409004\pi$
$857$	6.54102e18	0.563988	0.281994	+	0.959416i	$0.409004\pi$
$858$	1.74171e18	0.149042
$859$	4.55967e18	0.387238	0.193619	−	0.981077i	$-0.437977\pi$
$859$	4.55967e18	0.387238	0.193619	+	0.981077i	$0.437977\pi$
$860$	−1.23092e18	−0.103750
$861$	1.61082e18	0.134749
$862$	−1.33925e19	−1.11190
$863$	−1.50526e19	−1.24035	−0.620173	−	0.784465i	$-0.712937\pi$
$863$	−1.50526e19	−1.24035	−0.620173	+	0.784465i	$0.712937\pi$
$864$	2.08634e18	0.170627
$865$	1.12188e18	0.0910631
$866$	1.22394e19	0.986037
$867$	7.20438e18	0.576066
$868$	2.94054e18	0.233372
$869$	−6.97276e18	−0.549258
$870$	−3.94182e18	−0.308192
$871$	−5.42360e18	−0.420891
$872$	−1.56436e19	−1.20498
$873$	5.57594e18	0.426310
$874$	−2.71150e19	−2.05771
$875$	−4.65574e18	−0.350701
$876$	7.04639e18	0.526854
$877$	7.32647e18	0.543748	0.271874	−	0.962333i	$-0.412357\pi$
$877$	7.32647e18	0.543748	0.271874	+	0.962333i	$0.412357\pi$
$878$	−3.54267e18	−0.260985
$879$	−9.81159e18	−0.717483
$880$	1.18840e18	0.0862628
$881$	−7.90227e18	−0.569388	−0.284694	−	0.958618i	$-0.591892\pi$
$881$	−7.90227e18	−0.569388	−0.284694	+	0.958618i	$0.591892\pi$
$882$	2.79730e18	0.200076
$883$	1.84667e19	1.31113	0.655563	−	0.755140i	$-0.272431\pi$
$883$	1.84667e19	1.31113	0.655563	+	0.755140i	$0.272431\pi$
$884$	1.84497e17	0.0130032
$885$	5.66242e17	0.0396160
$886$	1.03134e19	0.716281
$887$	1.78491e19	1.23059	0.615295	−	0.788297i	$-0.289037\pi$
$887$	1.78491e19	1.23059	0.615295	+	0.788297i	$0.289037\pi$
$888$	8.53122e18	0.583884
$889$	−3.93787e18	−0.267547
$890$	6.47403e18	0.436656
$891$	−1.10592e18	−0.0740486
$892$	−2.58682e18	−0.171947
$893$	4.93984e17	0.0325971
$894$	4.01858e18	0.263257
$895$	4.09361e18	0.266230
$896$	1.62755e18	0.105083
$897$	8.17549e18	0.524038
$898$	5.48085e18	0.348780
$899$	2.73283e19	1.72653
$900$	1.92752e18	0.120899
$901$	7.52068e17	0.0468323
$902$	−4.59433e18	−0.284040
$903$	−1.42448e18	−0.0874350
$904$	1.34218e18	0.0817930
$905$	−7.18986e18	−0.435016
$906$	9.86982e18	0.592893
$907$	−1.78793e18	−0.106636	−0.0533178	−	0.998578i	$-0.516980\pi$
$907$	−1.78793e18	−0.106636	−0.0533178	+	0.998578i	$0.516980\pi$
$908$	−4.81608e18	−0.285191
$909$	5.47473e18	0.321883
$910$	1.35123e18	0.0788787
$911$	1.31518e19	0.762283	0.381142	−	0.924517i	$-0.375531\pi$
$911$	1.31518e19	0.762283	0.381142	+	0.924517i	$0.375531\pi$
$912$	4.34642e18	0.250130
$913$	−5.59041e18	−0.319436
$914$	1.33062e19	0.754924
$915$	−2.70784e18	−0.152541
$916$	9.30909e17	0.0520699
$917$	−5.42641e18	−0.301378
$918$	1.16120e17	0.00640368
$919$	−2.87717e19	−1.57549	−0.787743	−	0.616004i	$-0.788750\pi$
$919$	−2.87717e19	−1.57549	−0.787743	+	0.616004i	$0.788750\pi$
$920$	1.69853e19	0.923532
$921$	1.12380e19	0.606740
$922$	−5.14727e18	−0.275947
$923$	2.70965e18	0.144246
$924$	−1.41234e18	−0.0746572
$925$	1.31286e19	0.689123
$926$	1.95098e19	1.01691
$927$	5.88965e18	0.304839
$928$	2.47622e19	1.27271
$929$	9.56512e18	0.488190	0.244095	−	0.969751i	$-0.421509\pi$
$929$	9.56512e18	0.488190	0.244095	+	0.969751i	$0.421509\pi$
$930$	−5.09492e18	−0.258225
$931$	−2.98182e19	−1.50075
$932$	1.17516e19	0.587347
$933$	−1.50465e19	−0.746799
$934$	2.15304e18	0.106120
$935$	−3.38437e17	−0.0165654
$936$	−3.99034e18	−0.193962
$937$	−2.37281e19	−1.14540	−0.572698	−	0.819766i	$-0.694103\pi$
$937$	−2.37281e19	−1.14540	−0.572698	+	0.819766i	$0.694103\pi$
$938$	−4.35937e18	−0.208980
$939$	−7.80938e18	−0.371784
$940$	−1.03449e17	−0.00489099
$941$	5.14891e18	0.241759	0.120880	−	0.992667i	$-0.461429\pi$
$941$	5.14891e18	0.241759	0.120880	+	0.992667i	$0.461429\pi$
$942$	−7.76008e18	−0.361856
$943$	−2.15655e19	−0.998698
$944$	6.95182e17	0.0319728
$945$	−8.57976e17	−0.0391894
$946$	4.06285e18	0.184305
$947$	2.30511e19	1.03852	0.519262	−	0.854615i	$-0.326207\pi$
$947$	2.30511e19	1.03852	0.519262	+	0.854615i	$0.326207\pi$
$948$	5.34060e18	0.238966
$949$	−2.24484e19	−0.997596
$950$	2.03663e19	0.898895
$951$	−5.18302e18	−0.227201
$952$	4.43581e17	0.0193123
$953$	5.07741e18	0.219552	0.109776	−	0.993956i	$-0.464987\pi$
$953$	5.07741e18	0.219552	0.109776	+	0.993956i	$0.464987\pi$
$954$	−5.43788e18	−0.233542
$955$	−4.80554e18	−0.204984
$956$	−4.17959e18	−0.177075
$957$	−1.31258e19	−0.552329
$958$	−1.18396e19	−0.494835
$959$	−1.56084e19	−0.647946
$960$	−6.42896e18	−0.265081
$961$	1.09050e19	0.446607
$962$	−9.08615e18	−0.369609
$963$	−4.34481e17	−0.0175550
$964$	3.69914e18	0.148457
$965$	1.95547e18	0.0779512
$966$	6.57127e18	0.260195
$967$	−4.68899e19	−1.84420	−0.922099	−	0.386954i	$-0.873527\pi$
$967$	−4.68899e19	−1.84420	−0.922099	+	0.386954i	$0.873527\pi$
$968$	−1.50803e19	−0.589143
$969$	−1.23779e18	−0.0480334
$970$	−1.23380e19	−0.475587
$971$	−1.11617e19	−0.427371	−0.213686	−	0.976902i	$-0.568547\pi$
$971$	−1.11617e19	−0.427371	−0.213686	+	0.976902i	$0.568547\pi$
$972$	8.47047e17	0.0322164
$973$	9.79086e18	0.369902
$974$	3.37207e19	1.26550
$975$	−6.14069e18	−0.228922
$976$	−3.32446e18	−0.123111
$977$	−4.19466e19	−1.54306	−0.771529	−	0.636194i	$-0.780508\pi$
$977$	−4.19466e19	−1.54306	−0.771529	+	0.636194i	$0.780508\pi$
$978$	−2.16466e18	−0.0791021
$979$	2.15577e19	0.782557
$980$	6.24448e18	0.225178
$981$	−1.05792e19	−0.378970
$982$	−6.11520e18	−0.217613
$983$	−3.57397e19	−1.26344	−0.631718	−	0.775198i	$-0.717650\pi$
$983$	−3.57397e19	−1.26344	−0.631718	+	0.775198i	$0.717650\pi$
$984$	1.05258e19	0.369648
$985$	−1.37751e19	−0.480573
$986$	1.37820e18	0.0477651
$987$	−1.19716e17	−0.00412185
$988$	1.42201e19	0.486387
$989$	1.90708e19	0.648027
$990$	2.44709e18	0.0826078
$991$	−1.75515e19	−0.588620	−0.294310	−	0.955710i	$-0.595090\pi$
$991$	−1.75515e19	−0.588620	−0.294310	+	0.955710i	$0.595090\pi$
$992$	3.20059e19	1.06636
$993$	3.37700e19	1.11779
$994$	2.17796e18	0.0716207
$995$	−1.67976e19	−0.548780
$996$	4.28183e18	0.138977
$997$	5.23492e18	0.168807	0.0844036	−	0.996432i	$-0.473101\pi$
$997$	5.23492e18	0.168807	0.0844036	+	0.996432i	$0.473101\pi$
$998$	7.32925e18	0.234807
$999$	5.76934e18	0.183633

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.b.1.12	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.b.1.12	✓	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)

\(f(q)\)	\(=\)	\(q-63.8588 q^{2} -729.000 q^{3} -4114.05 q^{4} +18414.6 q^{5} +46553.1 q^{6} +120263. q^{7} +785850. q^{8} +531441. q^{9} +O(q^{10})\)	\(q-63.8588 q^{2} -729.000 q^{3} -4114.05 q^{4} +18414.6 q^{5} +46553.1 q^{6} +120263. q^{7} +785850. q^{8} +531441. q^{9} -1.17593e6 q^{10} -3.91572e6 q^{11} +2.99914e6 q^{12} -9.55466e6 q^{13} -7.67982e6 q^{14} -1.34242e7 q^{15} -1.64811e7 q^{16} +4.69357e6 q^{17} -3.39372e7 q^{18} +3.61757e8 q^{19} -7.57586e7 q^{20} -8.76714e7 q^{21} +2.50053e8 q^{22} +1.17374e9 q^{23} -5.72885e8 q^{24} -8.81606e8 q^{25} +6.10149e8 q^{26} -3.87420e8 q^{27} -4.94766e8 q^{28} -4.59818e9 q^{29} +8.57256e8 q^{30} -5.94328e9 q^{31} -5.38522e9 q^{32} +2.85456e9 q^{33} -2.99726e8 q^{34} +2.21459e9 q^{35} -2.18638e9 q^{36} -1.48917e10 q^{37} -2.31014e10 q^{38} +6.96535e9 q^{39} +1.44711e10 q^{40} -1.83734e10 q^{41} +5.59859e9 q^{42} +1.62479e10 q^{43} +1.61095e10 q^{44} +9.78627e9 q^{45} -7.49535e10 q^{46} +1.36551e9 q^{47} +1.20147e10 q^{48} -8.24259e10 q^{49} +5.62983e10 q^{50} -3.42161e9 q^{51} +3.93084e10 q^{52} +1.60234e11 q^{53} +2.47402e10 q^{54} -7.21065e10 q^{55} +9.45083e10 q^{56} -2.63721e11 q^{57} +2.93635e11 q^{58} -4.21805e10 q^{59} +5.52280e10 q^{60} +2.01713e11 q^{61} +3.79531e11 q^{62} +6.39124e10 q^{63} +4.78907e11 q^{64} -1.75945e11 q^{65} -1.82289e11 q^{66} +5.67639e11 q^{67} -1.93096e10 q^{68} -8.55654e11 q^{69} -1.41421e11 q^{70} -2.83595e11 q^{71} +4.17633e11 q^{72} +2.34947e12 q^{73} +9.50965e11 q^{74} +6.42690e11 q^{75} -1.48829e12 q^{76} -4.70915e11 q^{77} -4.44799e11 q^{78} +1.78071e12 q^{79} -3.03493e11 q^{80} +2.82430e11 q^{81} +1.17330e12 q^{82} +1.42768e12 q^{83} +3.60685e11 q^{84} +8.64303e10 q^{85} -1.03757e12 q^{86} +3.35208e12 q^{87} -3.07717e12 q^{88} -5.50543e12 q^{89} -6.24940e11 q^{90} -1.14907e12 q^{91} -4.82882e12 q^{92} +4.33265e12 q^{93} -8.72001e10 q^{94} +6.66162e12 q^{95} +3.92582e12 q^{96} +1.04921e13 q^{97} +5.26362e12 q^{98} -2.08097e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q - 52 q^{2} - 22599 q^{3} + 126886 q^{4} + 33486 q^{5} + 37908 q^{6} - 1135539 q^{7} - 1519749 q^{8} + 16474671 q^{9}+O(q^{10}) \) 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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