LMFDB - Embedded newform 177.14.a.b.1.26

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			1.26
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)

$f(q)$	$=$	$q+135.969 q^{2} -729.000 q^{3} +10295.5 q^{4} +14871.0 q^{5} -99121.2 q^{6} +565878. q^{7} +286008. q^{8} +531441. q^{9} +O(q^{10})$	\(q+135.969 q^{2} -729.000 q^{3} +10295.5 q^{4} +14871.0 q^{5} -99121.2 q^{6} +565878. q^{7} +286008. q^{8} +531441. q^{9} +2.02200e6 q^{10} -4.62572e6 q^{11} -7.50541e6 q^{12} +5.26047e6 q^{13} +7.69417e7 q^{14} -1.08410e7 q^{15} -4.54525e7 q^{16} -1.51921e7 q^{17} +7.22593e7 q^{18} -3.97961e8 q^{19} +1.53105e8 q^{20} -4.12525e8 q^{21} -6.28953e8 q^{22} -4.87481e8 q^{23} -2.08500e8 q^{24} -9.99555e8 q^{25} +7.15259e8 q^{26} -3.87420e8 q^{27} +5.82599e9 q^{28} -1.57531e9 q^{29} -1.47404e9 q^{30} -1.56196e9 q^{31} -8.52309e9 q^{32} +3.37215e9 q^{33} -2.06566e9 q^{34} +8.41520e9 q^{35} +5.47144e9 q^{36} +1.75573e10 q^{37} -5.41102e10 q^{38} -3.83488e9 q^{39} +4.25324e9 q^{40} -6.99606e9 q^{41} -5.60905e10 q^{42} -1.31585e10 q^{43} -4.76241e10 q^{44} +7.90308e9 q^{45} -6.62821e10 q^{46} -5.20639e10 q^{47} +3.31348e10 q^{48} +2.23329e11 q^{49} -1.35908e11 q^{50} +1.10751e10 q^{51} +5.41591e10 q^{52} +6.95021e10 q^{53} -5.26771e10 q^{54} -6.87893e10 q^{55} +1.61846e11 q^{56} +2.90113e11 q^{57} -2.14193e11 q^{58} -4.21805e10 q^{59} -1.11613e11 q^{60} +2.59847e11 q^{61} -2.12378e11 q^{62} +3.00731e11 q^{63} -7.86527e11 q^{64} +7.82287e10 q^{65} +4.58507e11 q^{66} -5.43093e11 q^{67} -1.56410e11 q^{68} +3.55373e11 q^{69} +1.14420e12 q^{70} -6.68077e10 q^{71} +1.51996e11 q^{72} -1.85167e12 q^{73} +2.38724e12 q^{74} +7.28676e11 q^{75} -4.09720e12 q^{76} -2.61759e12 q^{77} -5.21424e11 q^{78} -3.02475e12 q^{79} -6.75926e11 q^{80} +2.82430e11 q^{81} -9.51245e11 q^{82} -1.94134e12 q^{83} -4.24715e12 q^{84} -2.25923e11 q^{85} -1.78915e12 q^{86} +1.14840e12 q^{87} -1.32299e12 q^{88} +8.67857e12 q^{89} +1.07457e12 q^{90} +2.97678e12 q^{91} -5.01885e12 q^{92} +1.13867e12 q^{93} -7.07907e12 q^{94} -5.91809e12 q^{95} +6.21333e12 q^{96} +1.35337e13 q^{97} +3.03657e13 q^{98} -2.45830e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	135.969	1.50226	0.751128	−	0.660157i	$-0.229510\pi$
$2$	135.969	1.50226	0.751128	+	0.660157i	$0.229510\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	10295.5	1.25677
$5$	14871.0	0.425634	0.212817	−	0.977092i	$-0.431736\pi$
$5$	14871.0	0.425634	0.212817	+	0.977092i	$0.431736\pi$
$6$	−99121.2	−0.867328
$7$	565878.	1.81796	0.908982	−	0.416834i	$-0.136861\pi$
$7$	565878.	1.81796	0.908982	+	0.416834i	$0.136861\pi$
$8$	286008.	0.385739
$9$	531441.	0.333333
$10$	2.02200e6	0.639412
$11$	−4.62572e6	−0.787276	−0.393638	−	0.919265i	$-0.628784\pi$
$11$	−4.62572e6	−0.787276	−0.393638	+	0.919265i	$0.628784\pi$
$12$	−7.50541e6	−0.725598
$13$	5.26047e6	0.302268	0.151134	−	0.988513i	$-0.451707\pi$
$13$	5.26047e6	0.302268	0.151134	+	0.988513i	$0.451707\pi$
$14$	7.69417e7	2.73105
$15$	−1.08410e7	−0.245740
$16$	−4.54525e7	−0.677294
$17$	−1.51921e7	−0.152651	−0.0763257	−	0.997083i	$-0.524319\pi$
$17$	−1.51921e7	−0.152651	−0.0763257	+	0.997083i	$0.524319\pi$
$18$	7.22593e7	0.500752
$19$	−3.97961e8	−1.94063	−0.970313	−	0.241853i	$-0.922245\pi$
$19$	−3.97961e8	−1.94063	−0.970313	+	0.241853i	$0.922245\pi$
$20$	1.53105e8	0.534926
$21$	−4.12525e8	−1.04960
$22$	−6.28953e8	−1.18269
$23$	−4.87481e8	−0.686636	−0.343318	−	0.939219i	$-0.611551\pi$
$23$	−4.87481e8	−0.686636	−0.343318	+	0.939219i	$0.611551\pi$
$24$	−2.08500e8	−0.222706
$25$	−9.99555e8	−0.818836
$26$	7.15259e8	0.454085
$27$	−3.87420e8	−0.192450
$28$	5.82599e9	2.28477
$29$	−1.57531e9	−0.491790	−0.245895	−	0.969297i	$-0.579082\pi$
$29$	−1.57531e9	−0.491790	−0.245895	+	0.969297i	$0.579082\pi$
$30$	−1.47404e9	−0.369164
$31$	−1.56196e9	−0.316097	−0.158048	−	0.987431i	$-0.550520\pi$
$31$	−1.56196e9	−0.316097	−0.158048	+	0.987431i	$0.550520\pi$
$32$	−8.52309e9	−1.40321
$33$	3.37215e9	0.454534
$34$	−2.06566e9	−0.229322
$35$	8.41520e9	0.773788
$36$	5.47144e9	0.418924
$37$	1.75573e10	1.12498	0.562491	−	0.826804i	$-0.309843\pi$
$37$	1.75573e10	1.12498	0.562491	+	0.826804i	$0.309843\pi$
$38$	−5.41102e10	−2.91532
$39$	−3.83488e9	−0.174515
$40$	4.25324e9	0.164184
$41$	−6.99606e9	−0.230016	−0.115008	−	0.993365i	$-0.536689\pi$
$41$	−6.99606e9	−0.230016	−0.115008	+	0.993365i	$0.536689\pi$
$42$	−5.60905e10	−1.57677
$43$	−1.31585e10	−0.317440	−0.158720	−	0.987324i	$-0.550737\pi$
$43$	−1.31585e10	−0.317440	−0.158720	+	0.987324i	$0.550737\pi$
$44$	−4.76241e10	−0.989428
$45$	7.90308e9	0.141878
$46$	−6.62821e10	−1.03150
$47$	−5.20639e10	−0.704532	−0.352266	−	0.935900i	$-0.614589\pi$
$47$	−5.20639e10	−0.704532	−0.352266	+	0.935900i	$0.614589\pi$
$48$	3.31348e10	0.391036
$49$	2.23329e11	2.30500
$50$	−1.35908e11	−1.23010
$51$	1.10751e10	0.0881334
$52$	5.41591e10	0.379883
$53$	6.95021e10	0.430730	0.215365	−	0.976534i	$-0.430906\pi$
$53$	6.95021e10	0.430730	0.215365	+	0.976534i	$0.430906\pi$
$54$	−5.26771e10	−0.289109
$55$	−6.87893e10	−0.335092
$56$	1.61846e11	0.701260
$57$	2.90113e11	1.12042
$58$	−2.14193e11	−0.738794
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	−1.11613e11	−0.308839
$61$	2.59847e11	0.645765	0.322883	−	0.946439i	$-0.395348\pi$
$61$	2.59847e11	0.645765	0.322883	+	0.946439i	$0.395348\pi$
$62$	−2.12378e11	−0.474858
$63$	3.00731e11	0.605988
$64$	−7.86527e11	−1.43068
$65$	7.82287e10	0.128656
$66$	4.58507e11	0.682827
$67$	−5.43093e11	−0.733479	−0.366739	−	0.930324i	$-0.619526\pi$
$67$	−5.43093e11	−0.733479	−0.366739	+	0.930324i	$0.619526\pi$
$68$	−1.56410e11	−0.191848
$69$	3.55373e11	0.396429
$70$	1.14420e12	1.16243
$71$	−6.68077e10	−0.0618938	−0.0309469	−	0.999521i	$-0.509852\pi$
$71$	−6.68077e10	−0.0618938	−0.0309469	+	0.999521i	$0.509852\pi$
$72$	1.51996e11	0.128580
$73$	−1.85167e12	−1.43207	−0.716035	−	0.698064i	$-0.754045\pi$
$73$	−1.85167e12	−1.43207	−0.716035	+	0.698064i	$0.754045\pi$
$74$	2.38724e12	1.69001
$75$	7.28676e11	0.472755
$76$	−4.09720e12	−2.43893
$77$	−2.61759e12	−1.43124
$78$	−5.21424e11	−0.262166
$79$	−3.02475e12	−1.39995	−0.699976	−	0.714167i	$-0.746806\pi$
$79$	−3.02475e12	−1.39995	−0.699976	+	0.714167i	$0.746806\pi$
$80$	−6.75926e11	−0.288280
$81$	2.82430e11	0.111111
$82$	−9.51245e11	−0.345543
$83$	−1.94134e12	−0.651771	−0.325885	−	0.945409i	$-0.605662\pi$
$83$	−1.94134e12	−0.651771	−0.325885	+	0.945409i	$0.605662\pi$
$84$	−4.24715e12	−1.31911
$85$	−2.25923e11	−0.0649737
$86$	−1.78915e12	−0.476876
$87$	1.14840e12	0.283935
$88$	−1.32299e12	−0.303683
$89$	8.67857e12	1.85103	0.925514	−	0.378713i	$-0.123633\pi$
$89$	8.67857e12	1.85103	0.925514	+	0.378713i	$0.123633\pi$
$90$	1.07457e12	0.213137
$91$	2.97678e12	0.549513
$92$	−5.01885e12	−0.862945
$93$	1.13867e12	0.182499
$94$	−7.07907e12	−1.05839
$95$	−5.91809e12	−0.825997
$96$	6.21333e12	0.810143
$97$	1.35337e13	1.64968	0.824841	−	0.565365i	$-0.191265\pi$
$97$	1.35337e13	1.64968	0.824841	+	0.565365i	$0.191265\pi$
$98$	3.03657e13	3.46269
$99$	−2.45830e12	−0.262425
$100$	−1.02909e13	−1.02909
$101$	4.79551e12	0.449517	0.224758	−	0.974415i	$-0.427841\pi$
$101$	4.79551e12	0.449517	0.224758	+	0.974415i	$0.427841\pi$
$102$	1.50586e12	0.132399
$103$	−1.61695e13	−1.33430	−0.667152	−	0.744921i	$-0.732487\pi$
$103$	−1.61695e13	−1.33430	−0.667152	+	0.744921i	$0.732487\pi$
$104$	1.50454e12	0.116597
$105$	−6.13468e12	−0.446747
$106$	9.45012e12	0.647067
$107$	−7.73534e12	−0.498293	−0.249147	−	0.968466i	$-0.580150\pi$
$107$	−7.73534e12	−0.498293	−0.249147	+	0.968466i	$0.580150\pi$
$108$	−3.98868e12	−0.241866
$109$	9.72348e12	0.555328	0.277664	−	0.960678i	$-0.410440\pi$
$109$	9.72348e12	0.555328	0.277664	+	0.960678i	$0.410440\pi$
$110$	−9.35320e12	−0.503394
$111$	−1.27992e13	−0.649508
$112$	−2.57205e13	−1.23130
$113$	−6.76629e12	−0.305732	−0.152866	−	0.988247i	$-0.548850\pi$
$113$	−6.76629e12	−0.305732	−0.152866	+	0.988247i	$0.548850\pi$
$114$	3.94463e13	1.68316
$115$	−7.24935e12	−0.292256
$116$	−1.62186e13	−0.618068
$117$	2.79563e12	0.100756
$118$	−5.73523e12	−0.195577
$119$	−8.59690e12	−0.277515
$120$	−3.10061e12	−0.0947915
$121$	−1.31254e13	−0.380196
$122$	3.53311e13	0.970104
$123$	5.10013e12	0.132800
$124$	−1.60812e13	−0.397262
$125$	−3.30176e13	−0.774159
$126$	4.08900e13	0.910350
$127$	−1.62713e13	−0.344111	−0.172056	−	0.985087i	$-0.555041\pi$
$127$	−1.62713e13	−0.344111	−0.172056	+	0.985087i	$0.555041\pi$
$128$	−3.71219e13	−0.746045
$129$	9.59256e12	0.183274
$130$	1.06367e13	0.193274
$131$	3.68844e13	0.637646	0.318823	−	0.947814i	$-0.396712\pi$
$131$	3.68844e13	0.637646	0.318823	+	0.947814i	$0.396712\pi$
$132$	3.47179e13	0.571246
$133$	−2.25197e14	−3.52799
$134$	−7.38436e13	−1.10187
$135$	−5.76135e12	−0.0819133
$136$	−4.34508e12	−0.0588836
$137$	−8.38489e13	−1.08346	−0.541731	−	0.840552i	$-0.682231\pi$
$137$	−8.38489e13	−1.08346	−0.541731	+	0.840552i	$0.682231\pi$
$138$	4.83197e13	0.595538
$139$	5.02041e13	0.590395	0.295198	−	0.955436i	$-0.404615\pi$
$139$	5.02041e13	0.590395	0.295198	+	0.955436i	$0.404615\pi$
$140$	8.66385e13	0.972476
$141$	3.79546e13	0.406762
$142$	−9.08376e12	−0.0929804
$143$	−2.43335e13	−0.237969
$144$	−2.41553e13	−0.225765
$145$	−2.34265e13	−0.209322
$146$	−2.51769e14	−2.15134
$147$	−1.62807e14	−1.33079
$148$	1.80760e14	1.41385
$149$	−4.88234e13	−0.365525	−0.182763	−	0.983157i	$-0.558504\pi$
$149$	−4.88234e13	−0.365525	−0.182763	+	0.983157i	$0.558504\pi$
$150$	9.90771e13	0.710199
$151$	5.71890e13	0.392611	0.196306	−	0.980543i	$-0.437106\pi$
$151$	5.71890e13	0.392611	0.196306	+	0.980543i	$0.437106\pi$
$152$	−1.13820e14	−0.748575
$153$	−8.07373e12	−0.0508838
$154$	−3.55911e14	−2.15009
$155$	−2.32280e13	−0.134542
$156$	−3.94820e13	−0.219325
$157$	−2.76850e14	−1.47535	−0.737677	−	0.675153i	$-0.764077\pi$
$157$	−2.76850e14	−1.47535	−0.737677	+	0.675153i	$0.764077\pi$
$158$	−4.11271e14	−2.10309
$159$	−5.06671e13	−0.248682
$160$	−1.26747e14	−0.597254
$161$	−2.75855e14	−1.24828
$162$	3.84016e13	0.166917
$163$	−3.15453e14	−1.31739	−0.658697	−	0.752409i	$-0.728892\pi$
$163$	−3.15453e14	−1.31739	−0.658697	+	0.752409i	$0.728892\pi$
$164$	−7.20278e13	−0.289078
$165$	5.01474e13	0.193465
$166$	−2.63962e14	−0.979127
$167$	−3.00029e14	−1.07030	−0.535151	−	0.844757i	$-0.679745\pi$
$167$	−3.00029e14	−1.07030	−0.535151	+	0.844757i	$0.679745\pi$
$168$	−1.17986e14	−0.404873
$169$	−2.75203e14	−0.908634
$170$	−3.07185e13	−0.0976071
$171$	−2.11493e14	−0.646875
$172$	−1.35473e14	−0.398950
$173$	6.53186e14	1.85241	0.926205	−	0.377020i	$-0.123051\pi$
$173$	6.53186e14	1.85241	0.926205	+	0.377020i	$0.123051\pi$
$174$	1.56147e14	0.426543
$175$	−5.65626e14	−1.48861
$176$	2.10250e14	0.533218
$177$	3.07496e13	0.0751646
$178$	1.18001e15	2.78072
$179$	6.99007e14	1.58832	0.794158	−	0.607712i	$-0.207912\pi$
$179$	6.99007e14	1.58832	0.794158	+	0.607712i	$0.207912\pi$
$180$	8.13661e13	0.178309
$181$	−6.16173e14	−1.30254	−0.651272	−	0.758845i	$-0.725764\pi$
$181$	−6.16173e14	−1.30254	−0.651272	+	0.758845i	$0.725764\pi$
$182$	4.04749e14	0.825510
$183$	−1.89429e14	−0.372833
$184$	−1.39423e14	−0.264862
$185$	2.61095e14	0.478831
$186$	1.54824e14	0.274160
$187$	7.02746e13	0.120179
$188$	−5.36024e14	−0.885437
$189$	−2.19233e14	−0.349867
$190$	−8.04675e14	−1.24086
$191$	−2.56210e13	−0.0381837	−0.0190919	−	0.999818i	$-0.506078\pi$
$191$	−2.56210e13	−0.0381837	−0.0190919	+	0.999818i	$0.506078\pi$
$192$	5.73378e14	0.826006
$193$	1.06399e15	1.48189	0.740946	−	0.671565i	$-0.234377\pi$
$193$	1.06399e15	1.48189	0.740946	+	0.671565i	$0.234377\pi$
$194$	1.84016e15	2.47824
$195$	−5.70287e13	−0.0742794
$196$	2.29928e15	2.89686
$197$	−1.40757e14	−0.171569	−0.0857846	−	0.996314i	$-0.527340\pi$
$197$	−1.40757e14	−0.171569	−0.0857846	+	0.996314i	$0.527340\pi$
$198$	−3.34252e14	−0.394230
$199$	−3.44792e14	−0.393561	−0.196780	−	0.980448i	$-0.563049\pi$
$199$	−3.44792e14	−0.393561	−0.196780	+	0.980448i	$0.563049\pi$
$200$	−2.85881e14	−0.315857
$201$	3.95914e14	0.423474
$202$	6.52039e14	0.675289
$203$	−8.91434e14	−0.894056
$204$	1.14023e14	0.110764
$205$	−1.04039e14	−0.0979028
$206$	−2.19855e15	−2.00447
$207$	−2.59067e14	−0.228879
$208$	−2.39101e14	−0.204725
$209$	1.84086e15	1.52781
$210$	−8.34124e14	−0.671128
$211$	1.32674e15	1.03502	0.517511	−	0.855676i	$-0.326859\pi$
$211$	1.32674e15	1.03502	0.517511	+	0.855676i	$0.326859\pi$
$212$	7.15558e14	0.541330
$213$	4.87028e13	0.0357344
$214$	−1.05176e15	−0.748564
$215$	−1.95681e14	−0.135113
$216$	−1.10805e14	−0.0742355
$217$	−8.83881e14	−0.574653
$218$	1.32209e15	0.834244
$219$	1.34987e15	0.826807
$220$	−7.08220e14	−0.421134
$221$	−7.99178e13	−0.0461417
$222$	−1.74030e15	−0.975728
$223$	−6.06277e14	−0.330133	−0.165067	−	0.986282i	$-0.552784\pi$
$223$	−6.06277e14	−0.330133	−0.165067	+	0.986282i	$0.552784\pi$
$224$	−4.82303e15	−2.55098
$225$	−5.31205e14	−0.272945
$226$	−9.20003e14	−0.459287
$227$	1.97893e14	0.0959982	0.0479991	−	0.998847i	$-0.484716\pi$
$227$	1.97893e14	0.0959982	0.0479991	+	0.998847i	$0.484716\pi$
$228$	2.98686e15	1.40811
$229$	6.98153e12	0.00319904	0.00159952	−	0.999999i	$-0.499491\pi$
$229$	6.98153e12	0.00319904	0.00159952	+	0.999999i	$0.499491\pi$
$230$	−9.85684e14	−0.439043
$231$	1.90823e15	0.826327
$232$	−4.50552e14	−0.189702
$233$	2.12000e15	0.868006	0.434003	−	0.900911i	$-0.357101\pi$
$233$	2.12000e15	0.868006	0.434003	+	0.900911i	$0.357101\pi$
$234$	3.80118e14	0.151362
$235$	−7.74245e14	−0.299873
$236$	−4.34269e14	−0.163618
$237$	2.20504e15	0.808262
$238$	−1.16891e15	−0.416899
$239$	−1.05429e14	−0.0365908	−0.0182954	−	0.999833i	$-0.505824\pi$
$239$	−1.05429e14	−0.0365908	−0.0182954	+	0.999833i	$0.505824\pi$
$240$	4.92750e14	0.166438
$241$	1.15218e15	0.378800	0.189400	−	0.981900i	$-0.439346\pi$
$241$	1.15218e15	0.378800	0.189400	+	0.981900i	$0.439346\pi$
$242$	−1.78464e15	−0.571152
$243$	−2.05891e14	−0.0641500
$244$	2.67526e15	0.811580
$245$	3.32113e15	0.981085
$246$	6.93458e14	0.199500
$247$	−2.09346e15	−0.586590
$248$	−4.46734e14	−0.121931
$249$	1.41524e15	0.376300
$250$	−4.48936e15	−1.16298
$251$	−6.21250e15	−1.56815	−0.784074	−	0.620667i	$-0.786862\pi$
$251$	−6.21250e15	−1.56815	−0.784074	+	0.620667i	$0.786862\pi$
$252$	3.09617e15	0.761590
$253$	2.25495e15	0.540572
$254$	−2.21239e15	−0.516943
$255$	1.64698e14	0.0375126
$256$	1.39582e15	0.309933
$257$	−4.13075e15	−0.894260	−0.447130	−	0.894469i	$-0.647554\pi$
$257$	−4.13075e15	−0.894260	−0.447130	+	0.894469i	$0.647554\pi$
$258$	1.30429e15	0.275325
$259$	9.93526e15	2.04518
$260$	8.05402e14	0.161691
$261$	−8.37185e14	−0.163930
$262$	5.01513e15	0.957907
$263$	8.18774e15	1.52564	0.762819	−	0.646612i	$-0.223815\pi$
$263$	8.18774e15	1.52564	0.762819	+	0.646612i	$0.223815\pi$
$264$	9.64463e14	0.175332
$265$	1.03357e15	0.183333
$266$	−3.06198e16	−5.29994
$267$	−6.32668e15	−1.06869
$268$	−5.59140e15	−0.921817
$269$	5.14918e15	0.828607	0.414304	−	0.910139i	$-0.364025\pi$
$269$	5.14918e15	0.828607	0.414304	+	0.910139i	$0.364025\pi$
$270$	−7.83363e14	−0.123055
$271$	−4.11649e15	−0.631287	−0.315643	−	0.948878i	$-0.602220\pi$
$271$	−4.11649e15	−0.631287	−0.315643	+	0.948878i	$0.602220\pi$
$272$	6.90520e14	0.103390
$273$	−2.17008e15	−0.317262
$274$	−1.14008e16	−1.62764
$275$	4.62366e15	0.644650
$276$	3.65874e15	0.498222
$277$	−1.25002e16	−1.66264	−0.831320	−	0.555794i	$-0.812414\pi$
$277$	−1.25002e16	−1.66264	−0.831320	+	0.555794i	$0.812414\pi$
$278$	6.82618e15	0.886924
$279$	−8.30092e14	−0.105366
$280$	2.40681e15	0.298480
$281$	7.37677e15	0.893872	0.446936	−	0.894566i	$-0.352515\pi$
$281$	7.37677e15	0.893872	0.446936	+	0.894566i	$0.352515\pi$
$282$	5.16064e15	0.611061
$283$	−3.40405e15	−0.393898	−0.196949	−	0.980414i	$-0.563103\pi$
$283$	−3.40405e15	−0.393898	−0.196949	+	0.980414i	$0.563103\pi$
$284$	−6.87818e14	−0.0777865
$285$	4.31429e15	0.476889
$286$	−3.30859e15	−0.357490
$287$	−3.95892e15	−0.418161
$288$	−4.52952e15	−0.467736
$289$	−9.67378e15	−0.976698
$290$	−3.18527e15	−0.314456
$291$	−9.86606e15	−0.952444
$292$	−1.90638e16	−1.79979
$293$	1.95473e16	1.80487	0.902436	−	0.430823i	$-0.141777\pi$
$293$	1.95473e16	1.80487	0.902436	+	0.430823i	$0.141777\pi$
$294$	−2.21366e16	−1.99919
$295$	−6.27269e14	−0.0554129
$296$	5.02152e15	0.433949
$297$	1.79210e15	0.151511
$298$	−6.63845e15	−0.549112
$299$	−2.56438e15	−0.207548
$300$	7.50207e15	0.594146
$301$	−7.44611e15	−0.577095
$302$	7.77592e15	0.589802
$303$	−3.49593e15	−0.259529
$304$	1.80883e16	1.31438
$305$	3.86420e15	0.274860
$306$	−1.09777e15	−0.0764405
$307$	6.42196e15	0.437792	0.218896	−	0.975748i	$-0.429754\pi$
$307$	6.42196e15	0.437792	0.218896	+	0.975748i	$0.429754\pi$
$308$	−2.69494e16	−1.79874
$309$	1.17876e16	0.770361
$310$	−3.15829e15	−0.202116
$311$	−2.28056e16	−1.42922	−0.714609	−	0.699524i	$-0.753395\pi$
$311$	−2.28056e16	−1.42922	−0.714609	+	0.699524i	$0.753395\pi$
$312$	−1.09681e15	−0.0673171
$313$	1.02591e16	0.616697	0.308348	−	0.951274i	$-0.400224\pi$
$313$	1.02591e16	0.616697	0.308348	+	0.951274i	$0.400224\pi$
$314$	−3.76429e16	−2.21636
$315$	4.47218e15	0.257929
$316$	−3.11412e16	−1.75942
$317$	−7.74301e15	−0.428573	−0.214286	−	0.976771i	$-0.568743\pi$
$317$	−7.74301e15	−0.428573	−0.214286	+	0.976771i	$0.568743\pi$
$318$	−6.88913e15	−0.373584
$319$	7.28695e15	0.387174
$320$	−1.16965e16	−0.608948
$321$	5.63907e15	0.287690
$322$	−3.75076e16	−1.87524
$323$	6.04588e15	0.296239
$324$	2.90775e15	0.139641
$325$	−5.25813e15	−0.247508
$326$	−4.28917e16	−1.97906
$327$	−7.08841e15	−0.320619
$328$	−2.00093e15	−0.0887262
$329$	−2.94618e16	−1.28082
$330$	6.81848e15	0.290634
$331$	−9.29633e15	−0.388535	−0.194267	−	0.980949i	$-0.562233\pi$
$331$	−9.29633e15	−0.388535	−0.194267	+	0.980949i	$0.562233\pi$
$332$	−1.99871e16	−0.819128
$333$	9.33065e15	0.374994
$334$	−4.07946e16	−1.60787
$335$	−8.07636e15	−0.312194
$336$	1.87503e16	0.710890
$337$	7.32755e15	0.272499	0.136249	−	0.990675i	$-0.456495\pi$
$337$	7.32755e15	0.272499	0.136249	+	0.990675i	$0.456495\pi$
$338$	−3.74189e16	−1.36500
$339$	4.93262e15	0.176514
$340$	−2.32599e15	−0.0816572
$341$	7.22521e15	0.248855
$342$	−2.87564e16	−0.971772
$343$	7.15495e16	2.37244
$344$	−3.76344e15	−0.122449
$345$	5.28477e15	0.168734
$346$	8.88128e16	2.78279
$347$	2.29537e16	0.705847	0.352924	−	0.935652i	$-0.385188\pi$
$347$	2.29537e16	0.705847	0.352924	+	0.935652i	$0.385188\pi$
$348$	1.18234e16	0.356842
$349$	3.23120e15	0.0957190	0.0478595	−	0.998854i	$-0.484760\pi$
$349$	3.23120e15	0.0957190	0.0478595	+	0.998854i	$0.484760\pi$
$350$	−7.69074e16	−2.23628
$351$	−2.03801e15	−0.0581716
$352$	3.94255e16	1.10471
$353$	−8.68610e15	−0.238940	−0.119470	−	0.992838i	$-0.538120\pi$
$353$	−8.68610e15	−0.238940	−0.119470	+	0.992838i	$0.538120\pi$
$354$	4.18098e15	0.112916
$355$	−9.93501e14	−0.0263441
$356$	8.93501e16	2.32632
$357$	6.26714e15	0.160223
$358$	9.50430e16	2.38606
$359$	−7.07510e16	−1.74429	−0.872146	−	0.489247i	$-0.837272\pi$
$359$	−7.07510e16	−1.74429	−0.872146	+	0.489247i	$0.837272\pi$
$360$	2.26035e15	0.0547279
$361$	1.16320e17	2.76603
$362$	−8.37803e16	−1.95675
$363$	9.56842e15	0.219506
$364$	3.06474e16	0.690614
$365$	−2.75362e16	−0.609538
$366$	−2.57564e16	−0.560090
$367$	−1.25852e16	−0.268864	−0.134432	−	0.990923i	$-0.542921\pi$
$367$	−1.25852e16	−0.268864	−0.134432	+	0.990923i	$0.542921\pi$
$368$	2.21572e16	0.465055
$369$	−3.71799e15	−0.0766721
$370$	3.55007e16	0.719326
$371$	3.93297e16	0.783052
$372$	1.17232e16	0.229359
$373$	−4.62444e16	−0.889101	−0.444551	−	0.895754i	$-0.646637\pi$
$373$	−4.62444e16	−0.889101	−0.444551	+	0.895754i	$0.646637\pi$
$374$	9.55515e15	0.180539
$375$	2.40698e16	0.446961
$376$	−1.48907e16	−0.271766
$377$	−8.28688e15	−0.148652
$378$	−2.98088e16	−0.525591
$379$	1.98196e15	0.0343510	0.0171755	−	0.999852i	$-0.494533\pi$
$379$	1.98196e15	0.0343510	0.0171755	+	0.999852i	$0.494533\pi$
$380$	−6.09296e16	−1.03809
$381$	1.18618e16	0.198673
$382$	−3.48365e15	−0.0573618
$383$	−5.23532e16	−0.847522	−0.423761	−	0.905774i	$-0.639290\pi$
$383$	−5.23532e16	−0.847522	−0.423761	+	0.905774i	$0.639290\pi$
$384$	2.70618e16	0.430729
$385$	−3.89264e16	−0.609185
$386$	1.44670e17	2.22618
$387$	−6.99297e15	−0.105813
$388$	1.39336e17	2.07327
$389$	−8.86587e16	−1.29733	−0.648663	−	0.761076i	$-0.724671\pi$
$389$	−8.86587e16	−1.29733	−0.648663	+	0.761076i	$0.724671\pi$
$390$	−7.75412e15	−0.111587
$391$	7.40587e15	0.104816
$392$	6.38739e16	0.889127
$393$	−2.68887e16	−0.368145
$394$	−1.91385e16	−0.257741
$395$	−4.49812e16	−0.595867
$396$	−2.53094e16	−0.329809
$397$	2.67985e16	0.343536	0.171768	−	0.985137i	$-0.445052\pi$
$397$	2.67985e16	0.343536	0.171768	+	0.985137i	$0.445052\pi$
$398$	−4.68809e16	−0.591229
$399$	1.64169e17	2.03689
$400$	4.54322e16	0.554593
$401$	−6.51571e13	−0.000782571 0	−0.000391285	−	1.00000i	$-0.500125\pi$
$401$	−6.51571e13	−0.000782571 0	−0.000391285		1.00000i	$0.500125\pi$
$402$	5.38320e16	0.636167
$403$	−8.21667e15	−0.0955461
$404$	4.93721e16	0.564941
$405$	4.20002e15	0.0472927
$406$	−1.21207e17	−1.34310
$407$	−8.12150e16	−0.885671
$408$	3.16756e15	0.0339965
$409$	1.32374e17	1.39830	0.699152	−	0.714973i	$-0.253561\pi$
$409$	1.32374e17	1.39830	0.699152	+	0.714973i	$0.253561\pi$
$410$	−1.41460e16	−0.147075
$411$	6.11259e16	0.625537
$412$	−1.66473e17	−1.67692
$413$	−2.38690e16	−0.236679
$414$	−3.52250e16	−0.343834
$415$	−2.88698e16	−0.277416
$416$	−4.48355e16	−0.424146
$417$	−3.65988e16	−0.340865
$418$	2.50299e17	2.29516
$419$	−1.23619e17	−1.11607	−0.558037	−	0.829816i	$-0.688445\pi$
$419$	−1.23619e17	−1.11607	−0.558037	+	0.829816i	$0.688445\pi$
$420$	−6.31595e16	−0.561459
$421$	−4.71407e16	−0.412631	−0.206316	−	0.978485i	$-0.566147\pi$
$421$	−4.71407e16	−0.412631	−0.206316	+	0.978485i	$0.566147\pi$
$422$	1.80395e17	1.55487
$423$	−2.76689e16	−0.234844
$424$	1.98782e16	0.166149
$425$	1.51854e16	0.124996
$426$	6.62206e15	0.0536823
$427$	1.47042e17	1.17398
$428$	−7.96391e16	−0.626242
$429$	1.77391e16	0.137391
$430$	−2.66065e16	−0.202975
$431$	2.08591e17	1.56745	0.783724	−	0.621109i	$-0.213318\pi$
$431$	2.08591e17	1.56745	0.783724	+	0.621109i	$0.213318\pi$
$432$	1.76092e16	0.130345
$433$	−1.03061e17	−0.751486	−0.375743	−	0.926724i	$-0.622613\pi$
$433$	−1.03061e17	−0.751486	−0.375743	+	0.926724i	$0.622613\pi$
$434$	−1.20180e17	−0.863276
$435$	1.70779e16	0.120852
$436$	1.00108e17	0.697921
$437$	1.93998e17	1.33250
$438$	1.83540e17	1.24208
$439$	1.18132e17	0.787674	0.393837	−	0.919180i	$-0.371147\pi$
$439$	1.18132e17	0.787674	0.393837	+	0.919180i	$0.371147\pi$
$440$	−1.96743e16	−0.129258
$441$	1.18686e17	0.768332
$442$	−1.08663e16	−0.0693167
$443$	−2.29589e15	−0.0144320	−0.00721600	−	0.999974i	$-0.502297\pi$
$443$	−2.29589e15	−0.0144320	−0.00721600	+	0.999974i	$0.502297\pi$
$444$	−1.31774e17	−0.816285
$445$	1.29059e17	0.787861
$446$	−8.24347e16	−0.495945
$447$	3.55923e16	0.211036
$448$	−4.45078e17	−2.60093
$449$	4.08517e16	0.235293	0.117646	−	0.993056i	$-0.462465\pi$
$449$	4.08517e16	0.235293	0.117646	+	0.993056i	$0.462465\pi$
$450$	−7.22272e16	−0.410034
$451$	3.23618e16	0.181086
$452$	−6.96622e16	−0.384235
$453$	−4.16908e16	−0.226674
$454$	2.69073e16	0.144214
$455$	4.42679e16	0.233892
$456$	8.29748e16	0.432190
$457$	6.51232e16	0.334411	0.167205	−	0.985922i	$-0.446526\pi$
$457$	6.51232e16	0.334411	0.167205	+	0.985922i	$0.446526\pi$
$458$	9.49270e14	0.00480578
$459$	5.88575e15	0.0293778
$460$	−7.46355e16	−0.367299
$461$	4.89765e16	0.237646	0.118823	−	0.992915i	$-0.462088\pi$
$461$	4.89765e16	0.237646	0.118823	+	0.992915i	$0.462088\pi$
$462$	2.59459e17	1.24135
$463$	8.92606e16	0.421098	0.210549	−	0.977583i	$-0.432475\pi$
$463$	8.92606e16	0.421098	0.210549	+	0.977583i	$0.432475\pi$
$464$	7.16018e16	0.333086
$465$	1.69332e16	0.0776776
$466$	2.88254e17	1.30397
$467$	4.15893e16	0.185533	0.0927666	−	0.995688i	$-0.470429\pi$
$467$	4.15893e16	0.185533	0.0927666	+	0.995688i	$0.470429\pi$
$468$	2.87824e16	0.126628
$469$	−3.07324e17	−1.33344
$470$	−1.05273e17	−0.450486
$471$	2.01824e17	0.851796
$472$	−1.20640e16	−0.0502189
$473$	6.08676e16	0.249913
$474$	2.99816e17	1.21422
$475$	3.97784e17	1.58905
$476$	−8.85092e16	−0.348773
$477$	3.69363e16	0.143577
$478$	−1.43350e16	−0.0549688
$479$	4.68087e17	1.77070	0.885351	−	0.464923i	$-0.153918\pi$
$479$	4.68087e17	1.77070	0.885351	+	0.464923i	$0.153918\pi$
$480$	9.23988e16	0.344825
$481$	9.23594e16	0.340046
$482$	1.56660e17	0.569054
$483$	2.01098e17	0.720695
$484$	−1.35132e17	−0.477820
$485$	2.01260e17	0.702161
$486$	−2.79947e16	−0.0963698
$487$	−2.08265e17	−0.707423	−0.353711	−	0.935355i	$-0.615080\pi$
$487$	−2.08265e17	−0.707423	−0.353711	+	0.935355i	$0.615080\pi$
$488$	7.43185e16	0.249097
$489$	2.29965e17	0.760597
$490$	4.51570e17	1.47384
$491$	2.86763e17	0.923620	0.461810	−	0.886979i	$-0.347200\pi$
$491$	2.86763e17	0.923620	0.461810	+	0.886979i	$0.347200\pi$
$492$	5.25083e16	0.166899
$493$	2.39323e16	0.0750724
$494$	−2.84645e17	−0.881208
$495$	−3.65575e16	−0.111697
$496$	7.09951e16	0.214091
$497$	−3.78050e16	−0.112521
$498$	1.92428e17	0.565299
$499$	2.29879e17	0.666570	0.333285	−	0.942826i	$-0.391843\pi$
$499$	2.29879e17	0.666570	0.333285	+	0.942826i	$0.391843\pi$
$500$	−3.39932e17	−0.972942
$501$	2.18721e17	0.617939
$502$	−8.44705e17	−2.35576
$503$	−6.27418e16	−0.172729	−0.0863645	−	0.996264i	$-0.527525\pi$
$503$	−6.27418e16	−0.172729	−0.0863645	+	0.996264i	$0.527525\pi$
$504$	8.60114e16	0.233753
$505$	7.13143e16	0.191330
$506$	3.06603e17	0.812078
$507$	2.00623e17	0.524600
$508$	−1.67521e17	−0.432470
$509$	−5.60617e17	−1.42890	−0.714448	−	0.699689i	$-0.753322\pi$
$509$	−5.60617e17	−1.42890	−0.714448	+	0.699689i	$0.753322\pi$
$510$	2.23938e16	0.0563535
$511$	−1.04782e18	−2.60345
$512$	4.93890e17	1.21164
$513$	1.54178e17	0.373474
$514$	−5.61653e17	−1.34341
$515$	−2.40458e17	−0.567926
$516$	9.87600e16	0.230334
$517$	2.40833e17	0.554662
$518$	1.35088e18	3.07238
$519$	−4.76173e17	−1.06949
$520$	2.23740e16	0.0496275
$521$	6.89016e17	1.50933	0.754665	−	0.656111i	$-0.227800\pi$
$521$	6.89016e17	1.50933	0.754665	+	0.656111i	$0.227800\pi$
$522$	−1.13831e17	−0.246265
$523$	5.75513e17	1.22969	0.614843	−	0.788650i	$-0.289219\pi$
$523$	5.75513e17	1.22969	0.614843	+	0.788650i	$0.289219\pi$
$524$	3.79743e17	0.801376
$525$	4.12341e17	0.859452
$526$	1.11328e18	2.29190
$527$	2.37296e16	0.0482526
$528$	−1.53273e17	−0.307853
$529$	−2.66399e17	−0.528531
$530$	1.40533e17	0.275414
$531$	−2.24165e16	−0.0433963
$532$	−2.31851e18	−4.43388
$533$	−3.68026e16	−0.0695266
$534$	−8.60230e17	−1.60545
$535$	−1.15033e17	−0.212091
$536$	−1.55329e17	−0.282931
$537$	−5.09576e17	−0.917014
$538$	7.00128e17	1.24478
$539$	−1.03306e18	−1.81467
$540$	−5.93159e16	−0.102946
$541$	−3.16351e17	−0.542483	−0.271242	−	0.962511i	$-0.587434\pi$
$541$	−3.16351e17	−0.542483	−0.271242	+	0.962511i	$0.587434\pi$
$542$	−5.59714e17	−0.948354
$543$	4.49190e17	0.752024
$544$	1.29484e17	0.214202
$545$	1.44598e17	0.236366
$546$	−2.95062e17	−0.476608
$547$	−7.69801e17	−1.22874	−0.614372	−	0.789017i	$-0.710590\pi$
$547$	−7.69801e17	−1.22874	−0.614372	+	0.789017i	$0.710590\pi$
$548$	−8.63266e17	−1.36167
$549$	1.38094e17	0.215255
$550$	6.28674e17	0.968429
$551$	6.26912e17	0.954380
$552$	1.01640e17	0.152918
$553$	−1.71164e18	−2.54506
$554$	−1.69963e18	−2.49771
$555$	−1.90338e17	−0.276453
$556$	5.16875e17	0.741993
$557$	−1.14266e18	−1.62128	−0.810640	−	0.585545i	$-0.800881\pi$
$557$	−1.14266e18	−1.62128	−0.810640	+	0.585545i	$0.800881\pi$
$558$	−1.12866e17	−0.158286
$559$	−6.92200e16	−0.0959521
$560$	−3.82491e17	−0.524082
$561$	−5.12302e16	−0.0693853
$562$	1.00301e18	1.34282
$563$	1.48837e18	1.96972	0.984862	−	0.173342i	$-0.0554567\pi$
$563$	1.48837e18	1.96972	0.984862	+	0.173342i	$0.0554567\pi$
$564$	3.90761e17	0.511208
$565$	−1.00622e17	−0.130130
$566$	−4.62844e17	−0.591736
$567$	1.59821e17	0.201996
$568$	−1.91076e16	−0.0238749
$569$	9.23281e17	1.14052	0.570262	−	0.821463i	$-0.306842\pi$
$569$	9.23281e17	1.14052	0.570262	+	0.821463i	$0.306842\pi$
$570$	5.86608e17	0.716410
$571$	−1.34961e18	−1.62957	−0.814785	−	0.579763i	$-0.803145\pi$
$571$	−1.34961e18	−1.62957	−0.814785	+	0.579763i	$0.803145\pi$
$572$	−2.50525e17	−0.299073
$573$	1.86777e16	0.0220454
$574$	−5.38289e17	−0.628186
$575$	4.87264e17	0.562242
$576$	−4.17993e17	−0.476895
$577$	−1.33052e18	−1.50099	−0.750494	−	0.660877i	$-0.770184\pi$
$577$	−1.33052e18	−1.50099	−0.750494	+	0.660877i	$0.770184\pi$
$578$	−1.31533e18	−1.46725
$579$	−7.75651e17	−0.855571
$580$	−2.41187e17	−0.263071
$581$	−1.09856e18	−1.18490
$582$	−1.34148e18	−1.43081
$583$	−3.21498e17	−0.339103
$584$	−5.29592e17	−0.552406
$585$	4.15739e16	0.0428853
$586$	2.65782e18	2.71138
$587$	9.34700e17	0.943028	0.471514	−	0.881859i	$-0.343708\pi$
$587$	9.34700e17	0.943028	0.471514	+	0.881859i	$0.343708\pi$
$588$	−1.67617e18	−1.67250
$589$	6.21600e17	0.613426
$590$	−8.52889e16	−0.0832443
$591$	1.02612e17	0.0990555
$592$	−7.98021e17	−0.761944
$593$	1.21818e18	1.15042	0.575212	−	0.818005i	$-0.304920\pi$
$593$	1.21818e18	1.15042	0.575212	+	0.818005i	$0.304920\pi$
$594$	2.43669e17	0.227609
$595$	−1.27845e17	−0.118120
$596$	−5.02661e17	−0.459382
$597$	2.51353e17	0.227222
$598$	−3.48675e17	−0.311791
$599$	−1.11415e18	−0.985528	−0.492764	−	0.870163i	$-0.664013\pi$
$599$	−1.11415e18	−0.985528	−0.492764	+	0.870163i	$0.664013\pi$
$600$	2.08407e17	0.182360
$601$	3.61425e17	0.312848	0.156424	−	0.987690i	$-0.450003\pi$
$601$	3.61425e17	0.312848	0.156424	+	0.987690i	$0.450003\pi$
$602$	−1.01244e18	−0.866944
$603$	−2.88622e17	−0.244493
$604$	5.88789e17	0.493423
$605$	−1.95188e17	−0.161824
$606$	−4.75337e17	−0.389879
$607$	2.38616e18	1.93630	0.968149	−	0.250373i	$-0.0805532\pi$
$607$	2.38616e18	1.93630	0.968149	+	0.250373i	$0.0805532\pi$
$608$	3.39186e18	2.72310
$609$	6.49855e17	0.516184
$610$	5.25411e17	0.412910
$611$	−2.73881e17	−0.212958
$612$	−8.31229e16	−0.0639494
$613$	2.91648e17	0.222006	0.111003	−	0.993820i	$-0.464594\pi$
$613$	2.91648e17	0.222006	0.111003	+	0.993820i	$0.464594\pi$
$614$	8.73185e17	0.657676
$615$	7.58443e16	0.0565242
$616$	−7.48653e17	−0.552085
$617$	−4.54503e16	−0.0331653	−0.0165826	−	0.999862i	$-0.505279\pi$
$617$	−4.54503e16	−0.0331653	−0.0165826	+	0.999862i	$0.505279\pi$
$618$	1.60274e18	1.15728
$619$	2.89647e17	0.206957	0.103479	−	0.994632i	$-0.467003\pi$
$619$	2.89647e17	0.206957	0.103479	+	0.994632i	$0.467003\pi$
$620$	−2.39144e17	−0.169088
$621$	1.88860e17	0.132143
$622$	−3.10084e18	−2.14705
$623$	4.91101e18	3.36510
$624$	1.74305e17	0.118198
$625$	7.29154e17	0.489327
$626$	1.39492e18	0.926436
$627$	−1.34198e18	−0.882081
$628$	−2.85030e18	−1.85419
$629$	−2.66732e17	−0.171730
$630$	6.08077e17	0.387476
$631$	2.35931e17	0.148797	0.0743985	−	0.997229i	$-0.476296\pi$
$631$	2.35931e17	0.148797	0.0743985	+	0.997229i	$0.476296\pi$
$632$	−8.65102e17	−0.540016
$633$	−9.67193e17	−0.597570
$634$	−1.05281e18	−0.643826
$635$	−2.41972e17	−0.146466
$636$	−5.21642e17	−0.312537
$637$	1.17481e18	0.696728
$638$	9.90797e17	0.581635
$639$	−3.55044e16	−0.0206313
$640$	−5.52041e17	−0.317542
$641$	−1.76804e18	−1.00673	−0.503367	−	0.864073i	$-0.667906\pi$
$641$	−1.76804e18	−1.00673	−0.503367	+	0.864073i	$0.667906\pi$
$642$	7.66736e17	0.432184
$643$	2.14562e18	1.19724	0.598619	−	0.801034i	$-0.295716\pi$
$643$	2.14562e18	1.19724	0.598619	+	0.801034i	$0.295716\pi$
$644$	−2.84006e18	−1.56880
$645$	1.42651e17	0.0780078
$646$	8.22050e17	0.445027
$647$	1.42552e18	0.764004	0.382002	−	0.924162i	$-0.375235\pi$
$647$	1.42552e18	0.764004	0.382002	+	0.924162i	$0.375235\pi$
$648$	8.07771e16	0.0428599
$649$	1.95115e17	0.102495
$650$	−7.14941e17	−0.371821
$651$	6.44349e17	0.331776
$652$	−3.24774e18	−1.65566
$653$	1.78117e18	0.899022	0.449511	−	0.893275i	$-0.351598\pi$
$653$	1.78117e18	0.899022	0.449511	+	0.893275i	$0.351598\pi$
$654$	−9.63802e17	−0.481651
$655$	5.48510e17	0.271404
$656$	3.17988e17	0.155789
$657$	−9.84052e17	−0.477357
$658$	−4.00589e18	−1.92411
$659$	−2.32577e18	−1.10615	−0.553073	−	0.833133i	$-0.686545\pi$
$659$	−2.32577e18	−1.10615	−0.553073	+	0.833133i	$0.686545\pi$
$660$	5.16292e17	0.243142
$661$	−9.94481e17	−0.463753	−0.231877	−	0.972745i	$-0.574487\pi$
$661$	−9.94481e17	−0.463753	−0.231877	+	0.972745i	$0.574487\pi$
$662$	−1.26401e18	−0.583679
$663$	5.82601e16	0.0266399
$664$	−5.55240e17	−0.251413
$665$	−3.34892e18	−1.50163
$666$	1.26868e18	0.563337
$667$	7.67934e17	0.337680
$668$	−3.08894e18	−1.34513
$669$	4.41976e17	0.190603
$670$	−1.09813e18	−0.468995
$671$	−1.20198e18	−0.508396
$672$	3.51599e18	1.47281
$673$	−3.17780e18	−1.31834	−0.659171	−	0.751993i	$-0.729093\pi$
$673$	−3.17780e18	−1.31834	−0.659171	+	0.751993i	$0.729093\pi$
$674$	9.96318e17	0.409363
$675$	3.87248e17	0.157585
$676$	−2.83334e18	−1.14195
$677$	−5.69548e17	−0.227355	−0.113677	−	0.993518i	$-0.536263\pi$
$677$	−5.69548e17	−0.227355	−0.113677	+	0.993518i	$0.536263\pi$
$678$	6.70682e17	0.265170
$679$	7.65842e18	2.99906
$680$	−6.46158e16	−0.0250629
$681$	−1.44264e17	−0.0554246
$682$	9.82403e17	0.373845
$683$	1.48896e18	0.561240	0.280620	−	0.959819i	$-0.409460\pi$
$683$	1.48896e18	0.561240	0.280620	+	0.959819i	$0.409460\pi$
$684$	−2.17742e18	−0.812975
$685$	−1.24692e18	−0.461159
$686$	9.72849e18	3.56401
$687$	−5.08954e15	−0.00184697
$688$	5.98087e17	0.215000
$689$	3.65614e17	0.130196
$690$	7.18564e17	0.253481
$691$	7.16340e17	0.250330	0.125165	−	0.992136i	$-0.460054\pi$
$691$	7.16340e17	0.250330	0.125165	+	0.992136i	$0.460054\pi$
$692$	6.72487e18	2.32806
$693$	−1.39110e18	−0.477080
$694$	3.12098e18	1.06036
$695$	7.46587e17	0.251292
$696$	3.28452e17	0.109525
$697$	1.06285e17	0.0351123
$698$	4.39342e17	0.143794
$699$	−1.54548e18	−0.501144
$700$	−5.82340e18	−1.87085
$701$	4.63839e17	0.147639	0.0738194	−	0.997272i	$-0.476481\pi$
$701$	4.63839e17	0.147639	0.0738194	+	0.997272i	$0.476481\pi$
$702$	−2.77106e17	−0.0873886
$703$	−6.98710e18	−2.18317
$704$	3.63826e18	1.12634
$705$	5.64425e17	0.173132
$706$	−1.18104e18	−0.358950
$707$	2.71367e18	0.817206
$708$	3.16582e17	0.0944649
$709$	1.35381e18	0.400273	0.200137	−	0.979768i	$-0.435861\pi$
$709$	1.35381e18	0.400273	0.200137	+	0.979768i	$0.435861\pi$
$710$	−1.35085e17	−0.0395756
$711$	−1.60747e18	−0.466650
$712$	2.48214e18	0.714014
$713$	7.61427e17	0.217043
$714$	8.52134e17	0.240696
$715$	−3.61864e17	−0.101288
$716$	7.19661e18	1.99615
$717$	7.68575e16	0.0211257
$718$	−9.61993e18	−2.62037
$719$	−5.27709e18	−1.42448	−0.712241	−	0.701935i	$-0.752320\pi$
$719$	−5.27709e18	−1.42448	−0.712241	+	0.701935i	$0.752320\pi$
$720$	−3.59215e17	−0.0960932
$721$	−9.14997e18	−2.42572
$722$	1.58158e19	4.15528
$723$	−8.39940e17	−0.218700
$724$	−6.34380e18	−1.63700
$725$	1.57461e18	0.402695
$726$	1.30101e18	0.329755
$727$	−5.98563e18	−1.50361	−0.751807	−	0.659383i	$-0.770818\pi$
$727$	−5.98563e18	−1.50361	−0.751807	+	0.659383i	$0.770818\pi$
$728$	8.51384e17	0.211969
$729$	1.50095e17	0.0370370
$730$	−3.74407e18	−0.915683
$731$	1.99906e17	0.0484577
$732$	−1.95026e18	−0.468566
$733$	−4.14828e18	−0.987853	−0.493926	−	0.869504i	$-0.664439\pi$
$733$	−4.14828e18	−0.987853	−0.493926	+	0.869504i	$0.664439\pi$
$734$	−1.71120e18	−0.403902
$735$	−2.42111e18	−0.566430
$736$	4.15484e18	0.963493
$737$	2.51220e18	0.577451
$738$	−5.05531e17	−0.115181
$739$	6.15980e17	0.139116	0.0695582	−	0.997578i	$-0.477841\pi$
$739$	6.15980e17	0.139116	0.0695582	+	0.997578i	$0.477841\pi$
$740$	2.68810e18	0.601782
$741$	1.52613e18	0.338668
$742$	5.34761e18	1.17634
$743$	−6.92666e18	−1.51042	−0.755208	−	0.655486i	$-0.772464\pi$
$743$	−6.92666e18	−1.51042	−0.755208	+	0.655486i	$0.772464\pi$
$744$	3.25669e17	0.0703968
$745$	−7.26055e17	−0.155580
$746$	−6.28778e18	−1.33566
$747$	−1.03171e18	−0.217257
$748$	7.23511e17	0.151038
$749$	−4.37726e18	−0.905880
$750$	3.27274e18	0.671449
$751$	6.62067e18	1.34661	0.673306	−	0.739364i	$-0.264874\pi$
$751$	6.62067e18	1.34661	0.673306	+	0.739364i	$0.264874\pi$
$752$	2.36643e18	0.477176
$753$	4.52891e18	0.905371
$754$	−1.12676e18	−0.223314
$755$	8.50461e17	0.167109
$756$	−2.25711e18	−0.439704
$757$	7.56413e18	1.46095	0.730476	−	0.682939i	$-0.239298\pi$
$757$	7.56413e18	1.46095	0.730476	+	0.682939i	$0.239298\pi$
$758$	2.69484e17	0.0516040
$759$	−1.64386e18	−0.312099
$760$	−1.69262e18	−0.318619
$761$	−4.11641e18	−0.768277	−0.384139	−	0.923275i	$-0.625502\pi$
$761$	−4.11641e18	−0.768277	−0.384139	+	0.923275i	$0.625502\pi$
$762$	1.61283e18	0.298457
$763$	5.50230e18	1.00957
$764$	−2.63780e17	−0.0479883
$765$	−1.20065e17	−0.0216579
$766$	−7.11839e18	−1.27320
$767$	−2.21889e17	−0.0393520
$768$	−1.01755e18	−0.178940
$769$	−2.29337e18	−0.399902	−0.199951	−	0.979806i	$-0.564078\pi$
$769$	−2.29337e18	−0.399902	−0.199951	+	0.979806i	$0.564078\pi$
$770$	−5.29277e18	−0.915152
$771$	3.01132e18	0.516301
$772$	1.09543e19	1.86240
$773$	6.93298e18	1.16884	0.584418	−	0.811453i	$-0.301323\pi$
$773$	6.93298e18	1.16884	0.584418	+	0.811453i	$0.301323\pi$
$774$	−9.50825e17	−0.158959
$775$	1.56127e18	0.258831
$776$	3.87075e18	0.636346
$777$	−7.24281e18	−1.18078
$778$	−1.20548e19	−1.94892
$779$	2.78416e18	0.446376
$780$	−5.87138e17	−0.0933524
$781$	3.09034e17	0.0487276
$782$	1.00697e18	0.157460
$783$	6.10308e17	0.0946450
$784$	−1.01508e19	−1.56116
$785$	−4.11705e18	−0.627961
$786$	−3.65603e18	−0.553048
$787$	4.83511e18	0.725388	0.362694	−	0.931908i	$-0.381857\pi$
$787$	4.83511e18	0.725388	0.362694	+	0.931908i	$0.381857\pi$
$788$	−1.44916e18	−0.215624
$789$	−5.96886e18	−0.880828
$790$	−6.11603e18	−0.895145
$791$	−3.82889e18	−0.555810
$792$	−7.03093e17	−0.101228
$793$	1.36692e18	0.195194
$794$	3.64376e18	0.516080
$795$	−7.53472e17	−0.105848
$796$	−3.54980e18	−0.494616
$797$	−7.75098e18	−1.07122	−0.535608	−	0.844466i	$-0.679918\pi$
$797$	−7.75098e18	−1.07122	−0.535608	+	0.844466i	$0.679918\pi$
$798$	2.23218e19	3.05992
$799$	7.90963e17	0.107548
$800$	8.51930e18	1.14900
$801$	4.61215e18	0.617010
$802$	−8.85933e15	−0.00117562
$803$	8.56530e18	1.12744
$804$	4.07613e18	0.532211
$805$	−4.10225e18	−0.531311
$806$	−1.11721e18	−0.143535
$807$	−3.75376e18	−0.478397
$808$	1.37156e18	0.173396
$809$	2.73804e18	0.343379	0.171690	−	0.985151i	$-0.445077\pi$
$809$	2.73804e18	0.343379	0.171690	+	0.985151i	$0.445077\pi$
$810$	5.71072e17	0.0710457
$811$	7.68808e18	0.948817	0.474409	−	0.880305i	$-0.342662\pi$
$811$	7.68808e18	0.948817	0.474409	+	0.880305i	$0.342662\pi$
$812$	−9.17774e18	−1.12363
$813$	3.00092e18	0.364473
$814$	−1.10427e19	−1.33051
$815$	−4.69112e18	−0.560728
$816$	−5.03389e17	−0.0596922
$817$	5.23657e18	0.616033
$818$	1.79987e19	2.10061
$819$	1.58198e18	0.183171
$820$	−1.07113e18	−0.123042
$821$	1.43822e18	0.163906	0.0819531	−	0.996636i	$-0.473884\pi$
$821$	1.43822e18	0.163906	0.0819531	+	0.996636i	$0.473884\pi$
$822$	8.31121e18	0.939717
$823$	−1.62002e19	−1.81728	−0.908638	−	0.417585i	$-0.862877\pi$
$823$	−1.62002e19	−1.81728	−0.908638	+	0.417585i	$0.862877\pi$
$824$	−4.62461e18	−0.514693
$825$	−3.37065e18	−0.372189
$826$	−3.24544e18	−0.355552
$827$	6.73674e18	0.732258	0.366129	−	0.930564i	$-0.380683\pi$
$827$	6.73674e18	0.732258	0.366129	+	0.930564i	$0.380683\pi$
$828$	−2.66722e18	−0.287648
$829$	−1.81891e19	−1.94629	−0.973143	−	0.230202i	$-0.926061\pi$
$829$	−1.81891e19	−1.94629	−0.973143	+	0.230202i	$0.926061\pi$
$830$	−3.92539e18	−0.416750
$831$	9.11264e18	0.959926
$832$	−4.13750e18	−0.432451
$833$	−3.39284e18	−0.351861
$834$	−4.97629e18	−0.512066
$835$	−4.46175e18	−0.455557
$836$	1.89525e19	1.92011
$837$	6.05137e17	0.0608328
$838$	−1.68083e19	−1.67663
$839$	−3.98479e18	−0.394414	−0.197207	−	0.980362i	$-0.563187\pi$
$839$	−3.98479e18	−0.394414	−0.197207	+	0.980362i	$0.563187\pi$
$840$	−1.75457e18	−0.172328
$841$	−7.77902e18	−0.758143
$842$	−6.40965e18	−0.619878
$843$	−5.37767e18	−0.516077
$844$	1.36594e19	1.30079
$845$	−4.09255e18	−0.386746
$846$	−3.76211e18	−0.352796
$847$	−7.42737e18	−0.691183
$848$	−3.15904e18	−0.291731
$849$	2.48155e18	0.227417
$850$	2.06474e18	0.187777
$851$	−8.55882e18	−0.772453
$852$	5.01419e17	0.0449101
$853$	1.39064e19	1.23608	0.618038	−	0.786148i	$-0.287928\pi$
$853$	1.39064e19	1.23608	0.618038	+	0.786148i	$0.287928\pi$
$854$	1.99931e19	1.76362
$855$	−3.14512e18	−0.275332
$856$	−2.21237e18	−0.192211
$857$	1.31755e19	1.13603	0.568016	−	0.823017i	$-0.307711\pi$
$857$	1.31755e19	1.13603	0.568016	+	0.823017i	$0.307711\pi$
$858$	2.41196e18	0.206397
$859$	−1.38259e19	−1.17419	−0.587094	−	0.809518i	$-0.699728\pi$
$859$	−1.38259e19	−1.17419	−0.587094	+	0.809518i	$0.699728\pi$
$860$	−2.01463e18	−0.169807
$861$	2.88605e18	0.241426
$862$	2.83618e19	2.35471
$863$	8.08219e18	0.665977	0.332988	−	0.942931i	$-0.391943\pi$
$863$	8.08219e18	0.665977	0.332988	+	0.942931i	$0.391943\pi$
$864$	3.30202e18	0.270048
$865$	9.71356e18	0.788449
$866$	−1.40130e19	−1.12892
$867$	7.05218e18	0.563897
$868$	−9.09998e18	−0.722208
$869$	1.39916e19	1.10215
$870$	2.32206e18	0.181551
$871$	−2.85692e18	−0.221708
$872$	2.78099e18	0.214211
$873$	7.19236e18	0.549894
$874$	2.63777e19	2.00176
$875$	−1.86839e19	−1.40739
$876$	1.38975e19	1.03911
$877$	4.56723e18	0.338966	0.169483	−	0.985533i	$-0.445790\pi$
$877$	4.56723e18	0.338966	0.169483	+	0.985533i	$0.445790\pi$
$878$	1.60622e19	1.18329
$879$	−1.42500e19	−1.04204
$880$	3.12664e18	0.226956
$881$	−1.77081e19	−1.27594	−0.637968	−	0.770063i	$-0.720225\pi$
$881$	−1.77081e19	−1.27594	−0.637968	+	0.770063i	$0.720225\pi$
$882$	1.61376e19	1.15423
$883$	2.48878e18	0.176702	0.0883510	−	0.996089i	$-0.471840\pi$
$883$	2.48878e18	0.176702	0.0883510	+	0.996089i	$0.471840\pi$
$884$	−8.22792e17	−0.0579897
$885$	4.57279e17	0.0319926
$886$	−3.12169e17	−0.0216806
$887$	1.81625e18	0.125219	0.0626096	−	0.998038i	$-0.480058\pi$
$887$	1.81625e18	0.125219	0.0626096	+	0.998038i	$0.480058\pi$
$888$	−3.66069e18	−0.250541
$889$	−9.20759e18	−0.625582
$890$	1.75480e19	1.18357
$891$	−1.30644e18	−0.0874751
$892$	−6.24191e18	−0.414903
$893$	2.07194e19	1.36723
$894$	4.83943e18	0.317030
$895$	1.03950e19	0.676041
$896$	−2.10065e19	−1.35628
$897$	1.86943e18	0.119828
$898$	5.55455e18	0.353470
$899$	2.46058e18	0.155453
$900$	−5.46901e18	−0.343030
$901$	−1.05589e18	−0.0657515
$902$	4.40020e18	0.272038
$903$	5.42822e18	0.333186
$904$	−1.93521e18	−0.117933
$905$	−9.16314e18	−0.554407
$906$	−5.66864e18	−0.340523
$907$	1.81223e19	1.08085	0.540425	−	0.841392i	$-0.318264\pi$
$907$	1.81223e19	1.08085	0.540425	+	0.841392i	$0.318264\pi$
$908$	2.03741e18	0.120648
$909$	2.54853e18	0.149839
$910$	6.01905e18	0.351365
$911$	−1.77373e19	−1.02806	−0.514029	−	0.857773i	$-0.671848\pi$
$911$	−1.77373e19	−1.02806	−0.514029	+	0.857773i	$0.671848\pi$
$912$	−1.31864e19	−0.758855
$913$	8.98012e18	0.513124
$914$	8.85472e18	0.502371
$915$	−2.81700e18	−0.158690
$916$	7.18782e16	0.00402047
$917$	2.08721e19	1.15922
$918$	8.00277e17	0.0441330
$919$	−1.01122e19	−0.553726	−0.276863	−	0.960909i	$-0.589295\pi$
$919$	−1.01122e19	−0.553726	−0.276863	+	0.960909i	$0.589295\pi$
$920$	−2.07337e18	−0.112734
$921$	−4.68161e18	−0.252759
$922$	6.65926e18	0.357006
$923$	−3.51440e17	−0.0187086
$924$	1.96461e19	1.03851
$925$	−1.75494e19	−0.921175
$926$	1.21366e19	0.632597
$927$	−8.59314e18	−0.444768
$928$	1.34265e19	0.690083
$929$	−3.28679e19	−1.67753	−0.838764	−	0.544496i	$-0.816721\pi$
$929$	−3.28679e19	−1.67753	−0.838764	+	0.544496i	$0.816721\pi$
$930$	2.30239e18	0.116692
$931$	−8.88761e19	−4.47314
$932$	2.18265e19	1.09089
$933$	1.66253e19	0.825159
$934$	5.65484e18	0.278718
$935$	1.04506e18	0.0511522
$936$	7.99573e17	0.0388656
$937$	−2.00980e19	−0.970165	−0.485082	−	0.874468i	$-0.661210\pi$
$937$	−2.00980e19	−0.970165	−0.485082	+	0.874468i	$0.661210\pi$
$938$	−4.17865e19	−2.00317
$939$	−7.47889e18	−0.356050
$940$	−7.97123e18	−0.376872
$941$	−2.11734e19	−0.994163	−0.497082	−	0.867704i	$-0.665595\pi$
$941$	−2.11734e19	−0.994163	−0.497082	+	0.867704i	$0.665595\pi$
$942$	2.74417e19	1.27962
$943$	3.41044e18	0.157937
$944$	1.91721e18	0.0881762
$945$	−3.26022e18	−0.148916
$946$	8.27609e18	0.375433
$947$	1.26414e19	0.569537	0.284768	−	0.958596i	$-0.408083\pi$
$947$	1.26414e19	0.569537	0.284768	+	0.958596i	$0.408083\pi$
$948$	2.27020e19	1.01580
$949$	−9.74064e18	−0.432870
$950$	5.40861e19	2.38717
$951$	5.64466e18	0.247437
$952$	−2.45878e18	−0.107048
$953$	2.34896e19	1.01572	0.507858	−	0.861441i	$-0.330437\pi$
$953$	2.34896e19	1.01572	0.507858	+	0.861441i	$0.330437\pi$
$954$	5.02218e18	0.215689
$955$	−3.81011e17	−0.0162523
$956$	−1.08544e18	−0.0459864
$957$	−5.31219e18	−0.223535
$958$	6.36452e19	2.66005
$959$	−4.74483e19	−1.96970
$960$	8.52673e18	0.351576
$961$	−2.19778e19	−0.900083
$962$	1.25580e19	0.510837
$963$	−4.11088e18	−0.166098
$964$	1.18623e19	0.476065
$965$	1.58227e19	0.630744
$966$	2.73430e19	1.08267
$967$	−1.76101e19	−0.692613	−0.346306	−	0.938121i	$-0.612564\pi$
$967$	−1.76101e19	−0.692613	−0.346306	+	0.938121i	$0.612564\pi$
$968$	−3.75397e18	−0.146656
$969$	−4.40744e18	−0.171034
$970$	2.73651e19	1.05483
$971$	−3.26927e19	−1.25177	−0.625886	−	0.779914i	$-0.715263\pi$
$971$	−3.26927e19	−1.25177	−0.625886	+	0.779914i	$0.715263\pi$
$972$	−2.11975e18	−0.0806220
$973$	2.84094e19	1.07332
$974$	−2.83176e19	−1.06273
$975$	3.83318e18	0.142899
$976$	−1.18107e19	−0.437373
$977$	3.24324e19	1.19307	0.596533	−	0.802589i	$-0.296544\pi$
$977$	3.24324e19	1.19307	0.596533	+	0.802589i	$0.296544\pi$
$978$	3.12681e19	1.14261
$979$	−4.01447e19	−1.45727
$980$	3.41927e19	1.23300
$981$	5.16745e18	0.185109
$982$	3.89908e19	1.38751
$983$	−2.74995e19	−0.972134	−0.486067	−	0.873921i	$-0.661569\pi$
$983$	−2.74995e19	−0.972134	−0.486067	+	0.873921i	$0.661569\pi$
$984$	1.45868e18	0.0512261
$985$	−2.09320e18	−0.0730257
$986$	3.25405e18	0.112778
$987$	2.14777e19	0.739479
$988$	−2.15532e19	−0.737210
$989$	6.41452e18	0.217966
$990$	−4.97067e18	−0.167798
$991$	5.69589e19	1.91022	0.955109	−	0.296254i	$-0.0957377\pi$
$991$	5.69589e19	1.91022	0.955109	+	0.296254i	$0.0957377\pi$
$992$	1.33128e19	0.443550
$993$	6.77703e18	0.224321
$994$	−5.14030e18	−0.169035
$995$	−5.12741e18	−0.167513
$996$	1.45706e19	0.472924
$997$	8.31182e18	0.268026	0.134013	−	0.990980i	$-0.457214\pi$
$997$	8.31182e18	0.268026	0.134013	+	0.990980i	$0.457214\pi$
$998$	3.12563e19	1.00136
$999$	−6.80204e18	−0.216503

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.b.1.26	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.b.1.26	✓	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)

\(f(q)\)	\(=\)	\(q+135.969 q^{2} -729.000 q^{3} +10295.5 q^{4} +14871.0 q^{5} -99121.2 q^{6} +565878. q^{7} +286008. q^{8} +531441. q^{9} +O(q^{10})\)	\(q+135.969 q^{2} -729.000 q^{3} +10295.5 q^{4} +14871.0 q^{5} -99121.2 q^{6} +565878. q^{7} +286008. q^{8} +531441. q^{9} +2.02200e6 q^{10} -4.62572e6 q^{11} -7.50541e6 q^{12} +5.26047e6 q^{13} +7.69417e7 q^{14} -1.08410e7 q^{15} -4.54525e7 q^{16} -1.51921e7 q^{17} +7.22593e7 q^{18} -3.97961e8 q^{19} +1.53105e8 q^{20} -4.12525e8 q^{21} -6.28953e8 q^{22} -4.87481e8 q^{23} -2.08500e8 q^{24} -9.99555e8 q^{25} +7.15259e8 q^{26} -3.87420e8 q^{27} +5.82599e9 q^{28} -1.57531e9 q^{29} -1.47404e9 q^{30} -1.56196e9 q^{31} -8.52309e9 q^{32} +3.37215e9 q^{33} -2.06566e9 q^{34} +8.41520e9 q^{35} +5.47144e9 q^{36} +1.75573e10 q^{37} -5.41102e10 q^{38} -3.83488e9 q^{39} +4.25324e9 q^{40} -6.99606e9 q^{41} -5.60905e10 q^{42} -1.31585e10 q^{43} -4.76241e10 q^{44} +7.90308e9 q^{45} -6.62821e10 q^{46} -5.20639e10 q^{47} +3.31348e10 q^{48} +2.23329e11 q^{49} -1.35908e11 q^{50} +1.10751e10 q^{51} +5.41591e10 q^{52} +6.95021e10 q^{53} -5.26771e10 q^{54} -6.87893e10 q^{55} +1.61846e11 q^{56} +2.90113e11 q^{57} -2.14193e11 q^{58} -4.21805e10 q^{59} -1.11613e11 q^{60} +2.59847e11 q^{61} -2.12378e11 q^{62} +3.00731e11 q^{63} -7.86527e11 q^{64} +7.82287e10 q^{65} +4.58507e11 q^{66} -5.43093e11 q^{67} -1.56410e11 q^{68} +3.55373e11 q^{69} +1.14420e12 q^{70} -6.68077e10 q^{71} +1.51996e11 q^{72} -1.85167e12 q^{73} +2.38724e12 q^{74} +7.28676e11 q^{75} -4.09720e12 q^{76} -2.61759e12 q^{77} -5.21424e11 q^{78} -3.02475e12 q^{79} -6.75926e11 q^{80} +2.82430e11 q^{81} -9.51245e11 q^{82} -1.94134e12 q^{83} -4.24715e12 q^{84} -2.25923e11 q^{85} -1.78915e12 q^{86} +1.14840e12 q^{87} -1.32299e12 q^{88} +8.67857e12 q^{89} +1.07457e12 q^{90} +2.97678e12 q^{91} -5.01885e12 q^{92} +1.13867e12 q^{93} -7.07907e12 q^{94} -5.91809e12 q^{95} +6.21333e12 q^{96} +1.35337e13 q^{97} +3.03657e13 q^{98} -2.45830e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q - 52 q^{2} - 22599 q^{3} + 126886 q^{4} + 33486 q^{5} + 37908 q^{6} - 1135539 q^{7} - 1519749 q^{8} + 16474671 q^{9}+O(q^{10}) \) 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

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