LMFDB - Embedded newform 177.14.a.b.1.16

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			1.16
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)

$f(q)$	$=$	$q+13.8965 q^{2} -729.000 q^{3} -7998.89 q^{4} +24353.7 q^{5} -10130.5 q^{6} -38818.7 q^{7} -224997. q^{8} +531441. q^{9} +O(q^{10})$	\(q+13.8965 q^{2} -729.000 q^{3} -7998.89 q^{4} +24353.7 q^{5} -10130.5 q^{6} -38818.7 q^{7} -224997. q^{8} +531441. q^{9} +338431. q^{10} +1.36078e6 q^{11} +5.83119e6 q^{12} -1.15964e7 q^{13} -539443. q^{14} -1.77538e7 q^{15} +6.24002e7 q^{16} +5.54118e7 q^{17} +7.38517e6 q^{18} -2.71265e8 q^{19} -1.94802e8 q^{20} +2.82988e7 q^{21} +1.89101e7 q^{22} +4.08870e8 q^{23} +1.64022e8 q^{24} -6.27602e8 q^{25} -1.61149e8 q^{26} -3.87420e8 q^{27} +3.10506e8 q^{28} -1.59049e9 q^{29} -2.46716e8 q^{30} +4.27743e9 q^{31} +2.71032e9 q^{32} -9.92012e8 q^{33} +7.70030e8 q^{34} -9.45377e8 q^{35} -4.25094e9 q^{36} +2.54759e9 q^{37} -3.76963e9 q^{38} +8.45374e9 q^{39} -5.47949e9 q^{40} -2.20088e10 q^{41} +3.93254e8 q^{42} +5.67278e10 q^{43} -1.08848e10 q^{44} +1.29425e10 q^{45} +5.68186e9 q^{46} +5.63077e10 q^{47} -4.54898e10 q^{48} -9.53821e10 q^{49} -8.72146e9 q^{50} -4.03952e10 q^{51} +9.27579e10 q^{52} +9.18905e10 q^{53} -5.38379e9 q^{54} +3.31401e10 q^{55} +8.73407e9 q^{56} +1.97752e11 q^{57} -2.21022e10 q^{58} -4.21805e10 q^{59} +1.42011e11 q^{60} +3.59239e11 q^{61} +5.94413e10 q^{62} -2.06298e10 q^{63} -4.73519e11 q^{64} -2.82414e11 q^{65} -1.37855e10 q^{66} +4.39295e10 q^{67} -4.43233e11 q^{68} -2.98066e11 q^{69} -1.31374e10 q^{70} +1.08282e12 q^{71} -1.19572e11 q^{72} -1.32180e12 q^{73} +3.54025e10 q^{74} +4.57522e11 q^{75} +2.16982e12 q^{76} -5.28238e10 q^{77} +1.17477e11 q^{78} +3.85896e12 q^{79} +1.51967e12 q^{80} +2.82430e11 q^{81} -3.05845e11 q^{82} +2.36000e12 q^{83} -2.26359e11 q^{84} +1.34948e12 q^{85} +7.88317e11 q^{86} +1.15947e12 q^{87} -3.06172e11 q^{88} +6.93420e12 q^{89} +1.79856e11 q^{90} +4.50155e11 q^{91} -3.27051e12 q^{92} -3.11825e12 q^{93} +7.82480e11 q^{94} -6.60630e12 q^{95} -1.97582e12 q^{96} +7.40111e12 q^{97} -1.32548e12 q^{98} +7.23177e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	13.8965	0.153536	0.0767680	−	0.997049i	$-0.475540\pi$
$2$	13.8965	0.153536	0.0767680	+	0.997049i	$0.475540\pi$
$3$	−729.000	−0.577350
$3$	−729.000	−0.577350
$4$	−7998.89	−0.976427
$5$	24353.7	0.697043	0.348521	−	0.937301i	$-0.386684\pi$
$5$	24353.7	0.697043	0.348521	+	0.937301i	$0.386684\pi$
$6$	−10130.5	−0.0886441
$7$	−38818.7	−0.124711	−0.0623553	−	0.998054i	$-0.519861\pi$
$7$	−38818.7	−0.124711	−0.0623553	+	0.998054i	$0.519861\pi$
$8$	−224997.	−0.303453
$9$	531441.	0.333333
$10$	338431.	0.107021
$11$	1.36078e6	0.231599	0.115800	−	0.993273i	$-0.463057\pi$
$11$	1.36078e6	0.231599	0.115800	+	0.993273i	$0.463057\pi$
$12$	5.83119e6	0.563740
$13$	−1.15964e7	−0.666330	−0.333165	−	0.942868i	$-0.608117\pi$
$13$	−1.15964e7	−0.666330	−0.333165	+	0.942868i	$0.608117\pi$
$14$	−539443.	−0.0191476
$15$	−1.77538e7	−0.402438
$16$	6.24002e7	0.929836
$17$	5.54118e7	0.556781	0.278391	−	0.960468i	$-0.410199\pi$
$17$	5.54118e7	0.556781	0.278391	+	0.960468i	$0.410199\pi$
$18$	7.38517e6	0.0511787
$19$	−2.71265e8	−1.32280	−0.661401	−	0.750032i	$-0.730038\pi$
$19$	−2.71265e8	−1.32280	−0.661401	+	0.750032i	$0.730038\pi$
$20$	−1.94802e8	−0.680611
$21$	2.82988e7	0.0720017
$22$	1.89101e7	0.0355588
$23$	4.08870e8	0.575910	0.287955	−	0.957644i	$-0.407025\pi$
$23$	4.08870e8	0.575910	0.287955	+	0.957644i	$0.407025\pi$
$24$	1.64022e8	0.175198
$25$	−6.27602e8	−0.514131
$26$	−1.61149e8	−0.102306
$27$	−3.87420e8	−0.192450
$28$	3.10506e8	0.121771
$29$	−1.59049e9	−0.496528	−0.248264	−	0.968692i	$-0.579860\pi$
$29$	−1.59049e9	−0.496528	−0.248264	+	0.968692i	$0.579860\pi$
$30$	−2.46716e8	−0.0617887
$31$	4.27743e9	0.865630	0.432815	−	0.901483i	$-0.357520\pi$
$31$	4.27743e9	0.865630	0.432815	+	0.901483i	$0.357520\pi$
$32$	2.71032e9	0.446216
$33$	−9.92012e8	−0.133714
$34$	7.70030e8	0.0854860
$35$	−9.45377e8	−0.0869286
$36$	−4.25094e9	−0.325476
$37$	2.54759e9	0.163237	0.0816184	−	0.996664i	$-0.473991\pi$
$37$	2.54759e9	0.163237	0.0816184	+	0.996664i	$0.473991\pi$
$38$	−3.76963e9	−0.203098
$39$	8.45374e9	0.384706
$40$	−5.47949e9	−0.211519
$41$	−2.20088e10	−0.723604	−0.361802	−	0.932255i	$-0.617838\pi$
$41$	−2.20088e10	−0.723604	−0.361802	+	0.932255i	$0.617838\pi$
$42$	3.93254e8	0.0110549
$43$	5.67278e10	1.36852	0.684259	−	0.729239i	$-0.260126\pi$
$43$	5.67278e10	1.36852	0.684259	+	0.729239i	$0.260126\pi$
$44$	−1.08848e10	−0.226140
$45$	1.29425e10	0.232348
$46$	5.68186e9	0.0884229
$47$	5.63077e10	0.761960	0.380980	−	0.924583i	$-0.375587\pi$
$47$	5.63077e10	0.761960	0.380980	+	0.924583i	$0.375587\pi$
$48$	−4.54898e10	−0.536841
$49$	−9.53821e10	−0.984447
$50$	−8.72146e9	−0.0789377
$51$	−4.03952e10	−0.321458
$52$	9.27579e10	0.650623
$53$	9.18905e10	0.569479	0.284739	−	0.958605i	$-0.408093\pi$
$53$	9.18905e10	0.569479	0.284739	+	0.958605i	$0.408093\pi$
$54$	−5.38379e9	−0.0295480
$55$	3.31401e10	0.161434
$56$	8.73407e9	0.0378438
$57$	1.97752e11	0.763721
$58$	−2.21022e10	−0.0762349
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	1.42011e11	0.392951
$61$	3.59239e11	0.892769	0.446384	−	0.894841i	$-0.352711\pi$
$61$	3.59239e11	0.892769	0.446384	+	0.894841i	$0.352711\pi$
$62$	5.94413e10	0.132905
$63$	−2.06298e10	−0.0415702
$64$	−4.73519e11	−0.861326
$65$	−2.82414e11	−0.464461
$66$	−1.37855e10	−0.0205299
$67$	4.39295e10	0.0593294	0.0296647	−	0.999560i	$-0.490556\pi$
$67$	4.39295e10	0.0593294	0.0296647	+	0.999560i	$0.490556\pi$
$68$	−4.43233e11	−0.543656
$69$	−2.98066e11	−0.332502
$70$	−1.31374e10	−0.0133467
$71$	1.08282e12	1.00317	0.501586	−	0.865108i	$-0.332750\pi$
$71$	1.08282e12	1.00317	0.501586	+	0.865108i	$0.332750\pi$
$72$	−1.19572e11	−0.101151
$73$	−1.32180e12	−1.02227	−0.511136	−	0.859500i	$-0.670775\pi$
$73$	−1.32180e12	−1.02227	−0.511136	+	0.859500i	$0.670775\pi$
$74$	3.54025e10	0.0250627
$75$	4.57522e11	0.296834
$76$	2.16982e12	1.29162
$77$	−5.28238e10	−0.0288829
$78$	1.17477e11	0.0590662
$79$	3.85896e12	1.78605	0.893027	−	0.450003i	$-0.148577\pi$
$79$	3.85896e12	1.78605	0.893027	+	0.450003i	$0.148577\pi$
$80$	1.51967e12	0.648135
$81$	2.82430e11	0.111111
$82$	−3.05845e11	−0.111099
$83$	2.36000e12	0.792328	0.396164	−	0.918180i	$-0.370341\pi$
$83$	2.36000e12	0.792328	0.396164	+	0.918180i	$0.370341\pi$
$84$	−2.26359e11	−0.0703044
$85$	1.34948e12	0.388100
$86$	7.88317e11	0.210117
$87$	1.15947e12	0.286671
$88$	−3.06172e11	−0.0702794
$89$	6.93420e12	1.47898	0.739488	−	0.673169i	$-0.235067\pi$
$89$	6.93420e12	1.47898	0.739488	+	0.673169i	$0.235067\pi$
$90$	1.79856e11	0.0356737
$91$	4.50155e11	0.0830984
$92$	−3.27051e12	−0.562334
$93$	−3.11825e12	−0.499772
$94$	7.82480e11	0.116988
$95$	−6.60630e12	−0.922050
$96$	−1.97582e12	−0.257623
$97$	7.40111e12	0.902153	0.451077	−	0.892485i	$-0.351040\pi$
$97$	7.40111e12	0.902153	0.451077	+	0.892485i	$0.351040\pi$
$98$	−1.32548e12	−0.151148
$99$	7.23177e11	0.0771997
$100$	5.02012e12	0.502012
$101$	−2.00378e13	−1.87829	−0.939143	−	0.343525i	$-0.888379\pi$
$101$	−2.00378e13	−1.87829	−0.939143	+	0.343525i	$0.888379\pi$
$102$	−5.61352e11	−0.0493553
$103$	−1.59804e13	−1.31870	−0.659348	−	0.751837i	$-0.729168\pi$
$103$	−1.59804e13	−1.31870	−0.659348	+	0.751837i	$0.729168\pi$
$104$	2.60914e12	0.202200
$105$	6.89180e11	0.0501883
$106$	1.27696e12	0.0874355
$107$	1.55246e13	1.00006	0.500030	−	0.866008i	$-0.333322\pi$
$107$	1.55246e13	1.00006	0.500030	+	0.866008i	$0.333322\pi$
$108$	3.09893e12	0.187913
$109$	−1.02224e13	−0.583822	−0.291911	−	0.956446i	$-0.594291\pi$
$109$	−1.02224e13	−0.583822	−0.291911	+	0.956446i	$0.594291\pi$
$110$	4.60531e11	0.0247860
$111$	−1.85719e12	−0.0942448
$112$	−2.42229e12	−0.115960
$113$	6.47437e12	0.292542	0.146271	−	0.989245i	$-0.453273\pi$
$113$	6.47437e12	0.292542	0.146271	+	0.989245i	$0.453273\pi$
$114$	2.74806e12	0.117259
$115$	9.95749e12	0.401434
$116$	1.27221e13	0.484823
$117$	−6.16278e12	−0.222110
$118$	−5.86162e11	−0.0199887
$119$	−2.15101e12	−0.0694365
$120$	3.99455e12	0.122121
$121$	−3.26710e13	−0.946362
$122$	4.99216e12	0.137072
$123$	1.60444e13	0.417773
$124$	−3.42147e13	−0.845224
$125$	−4.50130e13	−1.05541
$126$	−2.86682e11	−0.00638252
$127$	4.51014e13	0.953818	0.476909	−	0.878953i	$-0.341757\pi$
$127$	4.51014e13	0.953818	0.476909	+	0.878953i	$0.341757\pi$
$128$	−2.87832e13	−0.578460
$129$	−4.13545e13	−0.790115
$130$	−3.92456e12	−0.0713114
$131$	−1.10706e14	−1.91384	−0.956921	−	0.290349i	$-0.906228\pi$
$131$	−1.10706e14	−1.91384	−0.956921	+	0.290349i	$0.906228\pi$
$132$	7.93499e12	0.130562
$133$	1.05301e13	0.164968
$134$	6.10466e11	0.00910920
$135$	−9.43511e12	−0.134146
$136$	−1.24675e13	−0.168957
$137$	−2.16910e13	−0.280283	−0.140141	−	0.990131i	$-0.544756\pi$
$137$	−2.16910e13	−0.280283	−0.140141	+	0.990131i	$0.544756\pi$
$138$	−4.14208e12	−0.0510510
$139$	−2.55160e12	−0.0300065	−0.0150033	−	0.999887i	$-0.504776\pi$
$139$	−2.55160e12	−0.0300065	−0.0150033	+	0.999887i	$0.504776\pi$
$140$	7.56196e12	0.0848794
$141$	−4.10483e13	−0.439918
$142$	1.50473e13	0.154023
$143$	−1.57801e13	−0.154321
$144$	3.31620e13	0.309945
$145$	−3.87343e13	−0.346101
$146$	−1.83683e13	−0.156955
$147$	6.95336e13	0.568371
$148$	−2.03779e13	−0.159389
$149$	−2.46245e14	−1.84356	−0.921778	−	0.387718i	$-0.873263\pi$
$149$	−2.46245e14	−1.84356	−0.921778	+	0.387718i	$0.873263\pi$
$150$	6.35795e12	0.0455747
$151$	−4.30791e12	−0.0295744	−0.0147872	−	0.999891i	$-0.504707\pi$
$151$	−4.30791e12	−0.0295744	−0.0147872	+	0.999891i	$0.504707\pi$
$152$	6.10337e13	0.401408
$153$	2.94481e13	0.185594
$154$	−7.34066e11	−0.00443456
$155$	1.04171e14	0.603381
$156$	−6.76205e13	−0.375637
$157$	3.29080e14	1.75370	0.876848	−	0.480768i	$-0.159642\pi$
$157$	3.29080e14	1.75370	0.876848	+	0.480768i	$0.159642\pi$
$158$	5.36261e13	0.274224
$159$	−6.69882e13	−0.328789
$160$	6.60062e13	0.311032
$161$	−1.58718e13	−0.0718220
$162$	3.92478e12	0.0170596
$163$	3.19545e14	1.33448	0.667242	−	0.744841i	$-0.267475\pi$
$163$	3.19545e14	1.33448	0.667242	+	0.744841i	$0.267475\pi$
$164$	1.76046e14	0.706546
$165$	−2.41591e13	−0.0932042
$166$	3.27958e13	0.121651
$167$	−5.27737e14	−1.88261	−0.941305	−	0.337558i	$-0.890399\pi$
$167$	−5.27737e14	−1.88261	−0.941305	+	0.337558i	$0.890399\pi$
$168$	−6.36713e12	−0.0218491
$169$	−1.68400e14	−0.556004
$170$	1.87531e13	0.0595874
$171$	−1.44161e14	−0.440934
$172$	−4.53759e14	−1.33626
$173$	−3.81682e12	−0.0108244	−0.00541218	−	0.999985i	$-0.501723\pi$
$173$	−3.81682e12	−0.0108244	−0.00541218	+	0.999985i	$0.501723\pi$
$174$	1.61125e13	0.0440143
$175$	2.43627e13	0.0641176
$176$	8.49133e13	0.215349
$177$	3.07496e13	0.0751646
$178$	9.63611e13	0.227076
$179$	−3.62969e14	−0.824754	−0.412377	−	0.911013i	$-0.635301\pi$
$179$	−3.62969e14	−0.824754	−0.412377	+	0.911013i	$0.635301\pi$
$180$	−1.03526e14	−0.226870
$181$	8.98134e14	1.89859	0.949294	−	0.314391i	$-0.101800\pi$
$181$	8.98134e14	1.89859	0.949294	+	0.314391i	$0.101800\pi$
$182$	6.25557e12	0.0127586
$183$	−2.61885e14	−0.515440
$184$	−9.19944e13	−0.174761
$185$	6.20431e13	0.113783
$186$	−4.33327e13	−0.0767329
$187$	7.54036e13	0.128950
$188$	−4.50399e14	−0.743998
$189$	1.50391e13	0.0240006
$190$	−9.18043e13	−0.141568
$191$	−1.10232e15	−1.64283	−0.821414	−	0.570332i	$-0.806815\pi$
$191$	−1.10232e15	−1.64283	−0.821414	+	0.570332i	$0.806815\pi$
$192$	3.45195e14	0.497287
$193$	6.46237e14	0.900056	0.450028	−	0.893015i	$-0.351414\pi$
$193$	6.46237e14	0.900056	0.450028	+	0.893015i	$0.351414\pi$
$194$	1.02849e14	0.138513
$195$	2.05880e14	0.268157
$196$	7.62951e14	0.961241
$197$	−3.86799e14	−0.471471	−0.235735	−	0.971817i	$-0.575750\pi$
$197$	−3.86799e14	−0.471471	−0.235735	+	0.971817i	$0.575750\pi$
$198$	1.00496e13	0.0118529
$199$	−9.34386e14	−1.06655	−0.533275	−	0.845942i	$-0.679039\pi$
$199$	−9.34386e14	−1.06655	−0.533275	+	0.845942i	$0.679039\pi$
$200$	1.41208e14	0.156015
$201$	−3.20246e13	−0.0342539
$202$	−2.78456e14	−0.288385
$203$	6.17407e13	0.0619223
$204$	3.23117e14	0.313880
$205$	−5.35994e14	−0.504383
$206$	−2.22071e14	−0.202467
$207$	2.17290e14	0.191970
$208$	−7.23615e14	−0.619578
$209$	−3.69133e14	−0.306360
$210$	9.57718e12	0.00770571
$211$	−1.79964e15	−1.40395	−0.701974	−	0.712203i	$-0.747698\pi$
$211$	−1.79964e15	−1.40395	−0.701974	+	0.712203i	$0.747698\pi$
$212$	−7.35022e14	−0.556054
$213$	−7.89372e14	−0.579181
$214$	2.15738e14	0.153545
$215$	1.38153e15	0.953916
$216$	8.71683e13	0.0583995
$217$	−1.66044e14	−0.107953
$218$	−1.42055e14	−0.0896376
$219$	9.63590e14	0.590209
$220$	−2.65084e14	−0.157629
$221$	−6.42575e14	−0.371000
$222$	−2.58084e13	−0.0144700
$223$	−1.32027e15	−0.718919	−0.359460	−	0.933161i	$-0.617039\pi$
$223$	−1.32027e15	−0.718919	−0.359460	+	0.933161i	$0.617039\pi$
$224$	−1.05211e14	−0.0556479
$225$	−3.33533e14	−0.171377
$226$	8.99711e13	0.0449157
$227$	−3.28120e15	−1.59171	−0.795857	−	0.605484i	$-0.792979\pi$
$227$	−3.28120e15	−1.59171	−0.795857	+	0.605484i	$0.792979\pi$
$228$	−1.58180e15	−0.745717
$229$	1.93024e15	0.884466	0.442233	−	0.896900i	$-0.354186\pi$
$229$	1.93024e15	0.884466	0.442233	+	0.896900i	$0.354186\pi$
$230$	1.38374e14	0.0616345
$231$	3.85086e13	0.0166755
$232$	3.57855e14	0.150673
$233$	−8.79348e14	−0.360037	−0.180019	−	0.983663i	$-0.557616\pi$
$233$	−8.79348e14	−0.360037	−0.180019	+	0.983663i	$0.557616\pi$
$234$	−8.56410e13	−0.0341019
$235$	1.37130e15	0.531119
$236$	3.37397e14	0.127120
$237$	−2.81318e15	−1.03118
$238$	−2.98915e13	−0.0106610
$239$	5.01331e15	1.73996	0.869979	−	0.493090i	$-0.164132\pi$
$239$	5.01331e15	1.73996	0.869979	+	0.493090i	$0.164132\pi$
$240$	−1.10784e15	−0.374201
$241$	−4.43682e15	−1.45868	−0.729342	−	0.684149i	$-0.760174\pi$
$241$	−4.43682e15	−1.45868	−0.729342	+	0.684149i	$0.760174\pi$
$242$	−4.54012e14	−0.145301
$243$	−2.05891e14	−0.0641500
$244$	−2.87351e15	−0.871723
$245$	−2.32291e15	−0.686202
$246$	2.22961e14	0.0641432
$247$	3.14568e15	0.881423
$248$	−9.62408e14	−0.262678
$249$	−1.72044e15	−0.457451
$250$	−6.25523e14	−0.162044
$251$	−5.84508e15	−1.47541	−0.737703	−	0.675126i	$-0.764089\pi$
$251$	−5.84508e15	−1.47541	−0.737703	+	0.675126i	$0.764089\pi$
$252$	1.65016e14	0.0405902
$253$	5.56384e14	0.133380
$254$	6.26751e14	0.146445
$255$	−9.83772e14	−0.224070
$256$	3.47908e15	0.772511
$257$	5.19068e15	1.12372	0.561861	−	0.827232i	$-0.310086\pi$
$257$	5.19068e15	1.12372	0.561861	+	0.827232i	$0.310086\pi$
$258$	−5.74683e14	−0.121311
$259$	−9.88939e13	−0.0203573
$260$	2.25900e15	0.453512
$261$	−8.45251e14	−0.165509
$262$	−1.53842e15	−0.293844
$263$	−6.11545e15	−1.13951	−0.569753	−	0.821816i	$-0.692961\pi$
$263$	−6.11545e15	−1.13951	−0.569753	+	0.821816i	$0.692961\pi$
$264$	2.23199e14	0.0405758
$265$	2.23787e15	0.396951
$266$	1.46332e14	0.0253285
$267$	−5.05503e15	−0.853888
$268$	−3.51387e14	−0.0579308
$269$	3.18527e14	0.0512574	0.0256287	−	0.999672i	$-0.491841\pi$
$269$	3.18527e14	0.0512574	0.0256287	+	0.999672i	$0.491841\pi$
$270$	−1.31115e14	−0.0205962
$271$	−6.01257e15	−0.922061	−0.461030	−	0.887384i	$-0.652520\pi$
$271$	−6.01257e15	−0.922061	−0.461030	+	0.887384i	$0.652520\pi$
$272$	3.45771e15	0.517715
$273$	−3.28163e14	−0.0479769
$274$	−3.01429e14	−0.0430335
$275$	−8.54031e14	−0.119072
$276$	2.38420e15	0.324663
$277$	1.03755e16	1.38004	0.690018	−	0.723792i	$-0.257603\pi$
$277$	1.03755e16	1.38004	0.690018	+	0.723792i	$0.257603\pi$
$278$	−3.54583e13	−0.00460708
$279$	2.27320e15	0.288543
$280$	2.12707e14	0.0263787
$281$	−7.04622e15	−0.853817	−0.426909	−	0.904295i	$-0.640397\pi$
$281$	−7.04622e15	−0.853817	−0.426909	+	0.904295i	$0.640397\pi$
$282$	−5.70428e14	−0.0675432
$283$	−1.07690e16	−1.24613	−0.623064	−	0.782171i	$-0.714113\pi$
$283$	−1.07690e16	−1.24613	−0.623064	+	0.782171i	$0.714113\pi$
$284$	−8.66132e15	−0.979523
$285$	4.81599e15	0.532346
$286$	−2.19289e14	−0.0236939
$287$	8.54351e14	0.0902410
$288$	1.44037e15	0.148739
$289$	−6.83411e15	−0.689995
$290$	−5.38270e14	−0.0531390
$291$	−5.39541e15	−0.520859
$292$	1.05729e16	0.998173
$293$	3.33512e15	0.307944	0.153972	−	0.988075i	$-0.450793\pi$
$293$	3.33512e15	0.307944	0.153972	+	0.988075i	$0.450793\pi$
$294$	9.66273e14	0.0872654
$295$	−1.02725e15	−0.0907472
$296$	−5.73198e14	−0.0495346
$297$	−5.27196e14	−0.0445713
$298$	−3.42194e15	−0.283052
$299$	−4.74140e15	−0.383746
$300$	−3.65966e15	−0.289837
$301$	−2.20210e15	−0.170669
$302$	−5.98648e13	−0.00454074
$303$	1.46076e16	1.08443
$304$	−1.69270e16	−1.22999
$305$	8.74878e15	0.622298
$306$	4.09226e14	0.0284953
$307$	−2.20366e16	−1.50226	−0.751129	−	0.660155i	$-0.770490\pi$
$307$	−2.20366e16	−1.50226	−0.751129	+	0.660155i	$0.770490\pi$
$308$	4.22532e14	0.0282020
$309$	1.16497e16	0.761350
$310$	1.44761e15	0.0926407
$311$	−1.56660e15	−0.0981785	−0.0490892	−	0.998794i	$-0.515632\pi$
$311$	−1.56660e15	−0.0981785	−0.0490892	+	0.998794i	$0.515632\pi$
$312$	−1.90206e15	−0.116740
$313$	−2.15251e16	−1.29392	−0.646959	−	0.762525i	$-0.723959\pi$
$313$	−2.15251e16	−1.29392	−0.646959	+	0.762525i	$0.723959\pi$
$314$	4.57306e15	0.269256
$315$	−5.02412e14	−0.0289762
$316$	−3.08674e16	−1.74395
$317$	−6.47131e15	−0.358185	−0.179092	−	0.983832i	$-0.557316\pi$
$317$	−6.47131e15	−0.358185	−0.179092	+	0.983832i	$0.557316\pi$
$318$	−9.30901e14	−0.0504809
$319$	−2.16431e15	−0.114995
$320$	−1.15319e16	−0.600381
$321$	−1.13174e16	−0.577385
$322$	−2.20562e14	−0.0110273
$323$	−1.50313e16	−0.736512
$324$	−2.25912e15	−0.108492
$325$	7.27789e15	0.342581
$326$	4.44056e15	0.204891
$327$	7.45212e15	0.337070
$328$	4.95190e15	0.219579
$329$	−2.18579e15	−0.0950245
$330$	−3.35727e14	−0.0143102
$331$	−2.15691e16	−0.901467	−0.450734	−	0.892658i	$-0.648838\pi$
$331$	−2.15691e16	−0.901467	−0.450734	+	0.892658i	$0.648838\pi$
$332$	−1.88774e16	−0.773650
$333$	1.35389e15	0.0544122
$334$	−7.33369e15	−0.289048
$335$	1.06985e15	0.0413552
$336$	1.76585e15	0.0669497
$337$	−3.91853e16	−1.45723	−0.728617	−	0.684922i	$-0.759836\pi$
$337$	−3.91853e16	−1.45723	−0.728617	+	0.684922i	$0.759836\pi$
$338$	−2.34017e15	−0.0853666
$339$	−4.71982e15	−0.168899
$340$	−1.07944e16	−0.378951
$341$	5.82066e15	0.200479
$342$	−2.00334e15	−0.0676993
$343$	7.46371e15	0.247482
$344$	−1.27636e16	−0.415281
$345$	−7.25901e15	−0.231768
$346$	−5.30404e13	−0.00166193
$347$	2.89306e16	0.889643	0.444822	−	0.895619i	$-0.353267\pi$
$347$	2.89306e16	0.889643	0.444822	+	0.895619i	$0.353267\pi$
$348$	−9.27444e15	−0.279913
$349$	3.06220e16	0.907129	0.453564	−	0.891224i	$-0.350152\pi$
$349$	3.06220e16	0.907129	0.453564	+	0.891224i	$0.350152\pi$
$350$	3.38556e14	0.00984436
$351$	4.49266e15	0.128235
$352$	3.68816e15	0.103343
$353$	1.03669e16	0.285176	0.142588	−	0.989782i	$-0.454458\pi$
$353$	1.03669e16	0.285176	0.142588	+	0.989782i	$0.454458\pi$
$354$	4.27312e14	0.0115405
$355$	2.63705e16	0.699253
$356$	−5.54659e16	−1.44411
$357$	1.56809e15	0.0400892
$358$	−5.04399e15	−0.126630
$359$	2.74116e16	0.675802	0.337901	−	0.941182i	$-0.390283\pi$
$359$	2.74116e16	0.675802	0.337901	+	0.941182i	$0.390283\pi$
$360$	−2.91203e15	−0.0705065
$361$	3.15316e16	0.749807
$362$	1.24809e16	0.291502
$363$	2.38171e16	0.546382
$364$	−3.60074e15	−0.0811395
$365$	−3.21906e16	−0.712567
$366$	−3.63928e15	−0.0791386
$367$	6.96728e16	1.48845	0.744225	−	0.667929i	$-0.232819\pi$
$367$	6.96728e16	1.48845	0.744225	+	0.667929i	$0.232819\pi$
$368$	2.55136e16	0.535501
$369$	−1.16964e16	−0.241201
$370$	8.62182e14	0.0174698
$371$	−3.56707e15	−0.0710200
$372$	2.49425e16	0.487990
$373$	−1.91725e16	−0.368613	−0.184306	−	0.982869i	$-0.559004\pi$
$373$	−1.91725e16	−0.368613	−0.184306	+	0.982869i	$0.559004\pi$
$374$	1.04785e15	0.0197985
$375$	3.28145e16	0.609344
$376$	−1.26690e16	−0.231219
$377$	1.84439e16	0.330852
$378$	2.08991e14	0.00368495
$379$	5.15368e16	0.893229	0.446615	−	0.894726i	$-0.352630\pi$
$379$	5.15368e16	0.893229	0.446615	+	0.894726i	$0.352630\pi$
$380$	5.28430e16	0.900314
$381$	−3.28789e16	−0.550687
$382$	−1.53184e16	−0.252233
$383$	−4.94719e16	−0.800879	−0.400439	−	0.916323i	$-0.631143\pi$
$383$	−4.94719e16	−0.800879	−0.400439	+	0.916323i	$0.631143\pi$
$384$	2.09829e16	0.333974
$385$	−1.28645e15	−0.0201326
$386$	8.98043e15	0.138191
$387$	3.01475e16	0.456173
$388$	−5.92006e16	−0.880887
$389$	−1.24941e17	−1.82824	−0.914118	−	0.405449i	$-0.867115\pi$
$389$	−1.24941e17	−1.82824	−0.914118	+	0.405449i	$0.867115\pi$
$390$	2.86100e15	0.0411717
$391$	2.26562e16	0.320656
$392$	2.14606e16	0.298733
$393$	8.07043e16	1.10496
$394$	−5.37515e15	−0.0723877
$395$	9.39799e16	1.24496
$396$	−5.78461e15	−0.0753799
$397$	2.53071e16	0.324417	0.162209	−	0.986756i	$-0.448138\pi$
$397$	2.53071e16	0.324417	0.162209	+	0.986756i	$0.448138\pi$
$398$	−1.29847e16	−0.163754
$399$	−7.67647e15	−0.0952440
$400$	−3.91625e16	−0.478058
$401$	1.02781e17	1.23445	0.617225	−	0.786786i	$-0.288257\pi$
$401$	1.02781e17	1.23445	0.617225	+	0.786786i	$0.288257\pi$
$402$	−4.45030e14	−0.00525920
$403$	−4.96026e16	−0.576795
$404$	1.60280e17	1.83401
$405$	6.87820e15	0.0774492
$406$	8.57979e14	0.00950730
$407$	3.46672e15	0.0378055
$408$	9.08879e15	0.0975472
$409$	6.97930e16	0.737243	0.368621	−	0.929580i	$-0.379830\pi$
$409$	6.97930e16	0.737243	0.368621	+	0.929580i	$0.379830\pi$
$410$	−7.44844e15	−0.0774409
$411$	1.58128e16	0.161821
$412$	1.27825e17	1.28761
$413$	1.63739e15	0.0162359
$414$	3.01957e15	0.0294743
$415$	5.74747e16	0.552286
$416$	−3.14298e16	−0.297327
$417$	1.86011e15	0.0173243
$418$	−5.12965e15	−0.0470373
$419$	−3.26386e16	−0.294673	−0.147337	−	0.989086i	$-0.547070\pi$
$419$	−3.26386e16	−0.294673	−0.147337	+	0.989086i	$0.547070\pi$
$420$	−5.51267e15	−0.0490052
$421$	2.87811e16	0.251926	0.125963	−	0.992035i	$-0.459798\pi$
$421$	2.87811e16	0.251926	0.125963	+	0.992035i	$0.459798\pi$
$422$	−2.50087e16	−0.215556
$423$	2.99242e16	0.253987
$424$	−2.06750e16	−0.172810
$425$	−3.47766e16	−0.286259
$426$	−1.09695e16	−0.0889252
$427$	−1.39452e16	−0.111338
$428$	−1.24180e17	−0.976486
$429$	1.15037e16	0.0890976
$430$	1.91984e16	0.146460
$431$	1.50455e17	1.13059	0.565294	−	0.824890i	$-0.308763\pi$
$431$	1.50455e17	1.13059	0.565294	+	0.824890i	$0.308763\pi$
$432$	−2.41751e16	−0.178947
$433$	−1.33321e17	−0.972139	−0.486069	−	0.873920i	$-0.661570\pi$
$433$	−1.33321e17	−0.972139	−0.486069	+	0.873920i	$0.661570\pi$
$434$	−2.30743e15	−0.0165747
$435$	2.82373e16	0.199822
$436$	8.17677e16	0.570059
$437$	−1.10912e17	−0.761815
$438$	1.33905e16	0.0906183
$439$	−8.30528e16	−0.553777	−0.276889	−	0.960902i	$-0.589303\pi$
$439$	−8.30528e16	−0.553777	−0.276889	+	0.960902i	$0.589303\pi$
$440$	−7.45641e15	−0.0489877
$441$	−5.06900e16	−0.328149
$442$	−8.92954e15	−0.0569619
$443$	2.44860e17	1.53920	0.769598	−	0.638529i	$-0.220457\pi$
$443$	2.44860e17	1.53920	0.769598	+	0.638529i	$0.220457\pi$
$444$	1.48555e16	0.0920231
$445$	1.68873e17	1.03091
$446$	−1.83471e16	−0.110380
$447$	1.79512e17	1.06438
$448$	1.83814e16	0.107416
$449$	1.59805e17	0.920426	0.460213	−	0.887809i	$-0.347773\pi$
$449$	1.59805e17	0.920426	0.460213	+	0.887809i	$0.347773\pi$
$450$	−4.63494e15	−0.0263126
$451$	−2.99492e16	−0.167586
$452$	−5.17878e16	−0.285645
$453$	3.14046e15	0.0170748
$454$	−4.55972e16	−0.244385
$455$	1.09629e16	0.0579232
$456$	−4.44935e16	−0.231753
$457$	1.95607e17	1.00445	0.502225	−	0.864737i	$-0.332515\pi$
$457$	1.95607e17	1.00445	0.502225	+	0.864737i	$0.332515\pi$
$458$	2.68236e16	0.135797
$459$	−2.14677e16	−0.107153
$460$	−7.96488e16	−0.391971
$461$	1.23844e17	0.600924	0.300462	−	0.953794i	$-0.402859\pi$
$461$	1.23844e17	0.600924	0.300462	+	0.953794i	$0.402859\pi$
$462$	5.35134e14	0.00256029
$463$	−3.31348e17	−1.56318	−0.781589	−	0.623794i	$-0.785591\pi$
$463$	−3.31348e17	−1.56318	−0.781589	+	0.623794i	$0.785591\pi$
$464$	−9.92469e16	−0.461690
$465$	−7.59408e16	−0.348362
$466$	−1.22199e16	−0.0552787
$467$	−1.40310e17	−0.625934	−0.312967	−	0.949764i	$-0.601323\pi$
$467$	−1.40310e17	−0.625934	−0.312967	+	0.949764i	$0.601323\pi$
$468$	4.92954e16	0.216874
$469$	−1.70529e15	−0.00739901
$470$	1.90563e16	0.0815458
$471$	−2.39900e17	−1.01250
$472$	9.49047e15	0.0395062
$473$	7.71943e16	0.316948
$474$	−3.90934e16	−0.158323
$475$	1.70246e17	0.680094
$476$	1.72057e16	0.0677997
$477$	4.88344e16	0.189826
$478$	6.96675e16	0.267146
$479$	−1.51804e17	−0.574253	−0.287126	−	0.957893i	$-0.592700\pi$
$479$	−1.51804e17	−0.574253	−0.287126	+	0.957893i	$0.592700\pi$
$480$	−4.81185e16	−0.179574
$481$	−2.95427e16	−0.108770
$482$	−6.16563e16	−0.223961
$483$	1.15705e16	0.0414665
$484$	2.61331e17	0.924053
$485$	1.80244e17	0.628840
$486$	−2.86116e15	−0.00984934
$487$	4.89834e17	1.66384	0.831918	−	0.554898i	$-0.187243\pi$
$487$	4.89834e17	1.66384	0.831918	+	0.554898i	$0.187243\pi$
$488$	−8.08274e16	−0.270913
$489$	−2.32949e17	−0.770464
$490$	−3.22802e16	−0.105357
$491$	−2.84885e17	−0.917573	−0.458786	−	0.888547i	$-0.651716\pi$
$491$	−2.84885e17	−0.917573	−0.458786	+	0.888547i	$0.651716\pi$
$492$	−1.28337e17	−0.407924
$493$	−8.81319e16	−0.276457
$494$	4.37139e16	0.135330
$495$	1.76120e16	0.0538115
$496$	2.66913e17	0.804893
$497$	−4.20334e16	−0.125106
$498$	−2.39081e16	−0.0702351
$499$	5.65300e17	1.63918	0.819588	−	0.572953i	$-0.194202\pi$
$499$	5.65300e17	1.63918	0.819588	+	0.572953i	$0.194202\pi$
$500$	3.60054e17	1.03053
$501$	3.84720e17	1.08693
$502$	−8.12261e16	−0.226528
$503$	−5.71067e17	−1.57215	−0.786076	−	0.618129i	$-0.787891\pi$
$503$	−5.71067e17	−1.57215	−0.786076	+	0.618129i	$0.787891\pi$
$504$	4.64164e15	0.0126146
$505$	−4.87995e17	−1.30925
$506$	7.73179e15	0.0204787
$507$	1.22763e17	0.321009
$508$	−3.60761e17	−0.931333
$509$	7.01987e16	0.178922	0.0894610	−	0.995990i	$-0.471486\pi$
$509$	7.01987e16	0.178922	0.0894610	+	0.995990i	$0.471486\pi$
$510$	−1.36710e16	−0.0344028
$511$	5.13104e16	0.127488
$512$	2.84139e17	0.697069
$513$	1.05094e17	0.254574
$514$	7.21322e16	0.172532
$515$	−3.89181e17	−0.919188
$516$	3.30790e17	0.771489
$517$	7.66227e16	0.176469
$518$	−1.37428e15	−0.00312559
$519$	2.78246e15	0.00624945
$520$	6.35421e16	0.140942
$521$	6.14491e17	1.34608	0.673039	−	0.739607i	$-0.264989\pi$
$521$	6.14491e17	1.34608	0.673039	+	0.739607i	$0.264989\pi$
$522$	−1.17460e16	−0.0254116
$523$	−8.44488e16	−0.180440	−0.0902199	−	0.995922i	$-0.528757\pi$
$523$	−8.44488e16	−0.180440	−0.0902199	+	0.995922i	$0.528757\pi$
$524$	8.85521e17	1.86873
$525$	−1.77604e16	−0.0370183
$526$	−8.49834e16	−0.174955
$527$	2.37020e17	0.481966
$528$	−6.19018e16	−0.124332
$529$	−3.36862e17	−0.668328
$530$	3.10986e16	0.0609463
$531$	−2.24165e16	−0.0433963
$532$	−8.42294e16	−0.161079
$533$	2.55221e17	0.482159
$534$	−7.02472e16	−0.131103
$535$	3.78081e17	0.697085
$536$	−9.88399e15	−0.0180037
$537$	2.64604e17	0.476172
$538$	4.42641e15	0.00786985
$539$	−1.29795e17	−0.227997
$540$	7.54704e16	0.130984
$541$	6.19069e17	1.06159	0.530795	−	0.847500i	$-0.321893\pi$
$541$	6.19069e17	1.06159	0.530795	+	0.847500i	$0.321893\pi$
$542$	−8.35536e16	−0.141569
$543$	−6.54740e17	−1.09615
$544$	1.50184e17	0.248445
$545$	−2.48953e17	−0.406949
$546$	−4.56031e15	−0.00736618
$547$	−5.32724e17	−0.850325	−0.425162	−	0.905117i	$-0.639783\pi$
$547$	−5.32724e17	−0.850325	−0.425162	+	0.905117i	$0.639783\pi$
$548$	1.73504e17	0.273676
$549$	1.90914e17	0.297590
$550$	−1.18680e16	−0.0182819
$551$	4.31444e17	0.656809
$552$	6.70639e16	0.100899
$553$	−1.49800e17	−0.222740
$554$	1.44183e17	0.211885
$555$	−4.52294e16	−0.0656926
$556$	2.04099e16	0.0292992
$557$	9.18552e17	1.30330	0.651651	−	0.758519i	$-0.274077\pi$
$557$	9.18552e17	1.30330	0.651651	+	0.758519i	$0.274077\pi$
$558$	3.15895e16	0.0443018
$559$	−6.57835e17	−0.911885
$560$	−5.89917e16	−0.0808293
$561$	−5.49692e16	−0.0744493
$562$	−9.79177e16	−0.131092
$563$	−2.89698e17	−0.383391	−0.191695	−	0.981454i	$-0.561399\pi$
$563$	−2.89698e17	−0.383391	−0.191695	+	0.981454i	$0.561399\pi$
$564$	3.28341e17	0.429547
$565$	1.57675e17	0.203914
$566$	−1.49651e17	−0.191326
$567$	−1.09635e16	−0.0138567
$568$	−2.43630e17	−0.304415
$569$	−2.60065e17	−0.321257	−0.160628	−	0.987015i	$-0.551352\pi$
$569$	−2.60065e17	−0.321257	−0.160628	+	0.987015i	$0.551352\pi$
$570$	6.69254e16	0.0817343
$571$	−1.01888e18	−1.23024	−0.615120	−	0.788434i	$-0.710892\pi$
$571$	−1.01888e18	−1.23024	−0.615120	+	0.788434i	$0.710892\pi$
$572$	1.26224e17	0.150684
$573$	8.03594e17	0.948487
$574$	1.18725e16	0.0138552
$575$	−2.56608e17	−0.296093
$576$	−2.51647e17	−0.287109
$577$	−4.83795e17	−0.545781	−0.272891	−	0.962045i	$-0.587980\pi$
$577$	−4.83795e17	−0.545781	−0.272891	+	0.962045i	$0.587980\pi$
$578$	−9.49701e16	−0.105939
$579$	−4.71107e17	−0.519647
$580$	3.09831e17	0.337943
$581$	−9.16121e16	−0.0988117
$582$	−7.49772e16	−0.0799705
$583$	1.25043e17	0.131891
$584$	2.97400e17	0.310211
$585$	−1.50086e17	−0.154820
$586$	4.63464e16	0.0472805
$587$	5.91386e17	0.596655	0.298327	−	0.954464i	$-0.403571\pi$
$587$	5.91386e17	0.596655	0.298327	+	0.954464i	$0.403571\pi$
$588$	−5.56191e17	−0.554973
$589$	−1.16032e18	−1.14506
$590$	−1.42752e16	−0.0139330
$591$	2.81976e17	0.272204
$592$	1.58970e17	0.151783
$593$	−7.32000e17	−0.691283	−0.345641	−	0.938367i	$-0.612339\pi$
$593$	−7.32000e17	−0.691283	−0.345641	+	0.938367i	$0.612339\pi$
$594$	−7.32617e15	−0.00684329
$595$	−5.23851e16	−0.0484002
$596$	1.96968e18	1.80010
$597$	6.81168e17	0.615773
$598$	−6.58888e16	−0.0589188
$599$	7.83545e17	0.693090	0.346545	−	0.938033i	$-0.387355\pi$
$599$	7.83545e17	0.693090	0.346545	+	0.938033i	$0.387355\pi$
$600$	−1.02941e17	−0.0900750
$601$	−8.06682e17	−0.698262	−0.349131	−	0.937074i	$-0.613523\pi$
$601$	−8.06682e17	−0.698262	−0.349131	+	0.937074i	$0.613523\pi$
$602$	−3.06014e16	−0.0262038
$603$	2.33459e16	0.0197765
$604$	3.44585e16	0.0288773
$605$	−7.95658e17	−0.659655
$606$	2.02994e17	0.166499
$607$	−2.22081e17	−0.180213	−0.0901064	−	0.995932i	$-0.528721\pi$
$607$	−2.22081e17	−0.180213	−0.0901064	+	0.995932i	$0.528721\pi$
$608$	−7.35213e17	−0.590256
$609$	−4.50089e16	−0.0357509
$610$	1.21577e17	0.0955451
$611$	−6.52964e17	−0.507717
$612$	−2.35552e17	−0.181219
$613$	1.04901e18	0.798521	0.399261	−	0.916837i	$-0.369267\pi$
$613$	1.04901e18	0.798521	0.399261	+	0.916837i	$0.369267\pi$
$614$	−3.06231e17	−0.230651
$615$	3.90740e17	0.291206
$616$	1.18852e16	0.00876458
$617$	−1.76568e18	−1.28842	−0.644212	−	0.764847i	$-0.722815\pi$
$617$	−1.76568e18	−1.28842	−0.644212	+	0.764847i	$0.722815\pi$
$618$	1.61890e17	0.116895
$619$	−1.93516e18	−1.38270	−0.691351	−	0.722519i	$-0.742984\pi$
$619$	−1.93516e18	−1.38270	−0.691351	+	0.722519i	$0.742984\pi$
$620$	−8.33254e17	−0.589157
$621$	−1.58405e17	−0.110834
$622$	−2.17703e16	−0.0150739
$623$	−2.69176e17	−0.184444
$624$	5.27515e17	0.357713
$625$	−3.30117e17	−0.221538
$626$	−2.99123e17	−0.198663
$627$	2.69098e17	0.176877
$628$	−2.63228e18	−1.71236
$629$	1.41166e17	0.0908871
$630$	−6.98177e15	−0.00444889
$631$	−2.49142e18	−1.57129	−0.785646	−	0.618676i	$-0.787669\pi$
$631$	−2.49142e18	−1.57129	−0.785646	+	0.618676i	$0.787669\pi$
$632$	−8.68253e17	−0.541983
$633$	1.31194e18	0.810569
$634$	−8.99285e16	−0.0549942
$635$	1.09838e18	0.664852
$636$	5.35831e17	0.321038
$637$	1.10608e18	0.655967
$638$	−3.00764e16	−0.0176559
$639$	5.75452e17	0.334390
$640$	−7.00976e17	−0.403212
$641$	1.72871e18	0.984338	0.492169	−	0.870500i	$-0.336204\pi$
$641$	1.72871e18	0.984338	0.492169	+	0.870500i	$0.336204\pi$
$642$	−1.57273e17	−0.0886494
$643$	−2.00421e18	−1.11834	−0.559168	−	0.829054i	$-0.688879\pi$
$643$	−2.00421e18	−1.11834	−0.559168	+	0.829054i	$0.688879\pi$
$644$	1.26957e17	0.0701290
$645$	−1.00713e18	−0.550744
$646$	−2.08882e17	−0.113081
$647$	−3.24266e18	−1.73790	−0.868949	−	0.494902i	$-0.835204\pi$
$647$	−3.24266e18	−1.73790	−0.868949	+	0.494902i	$0.835204\pi$
$648$	−6.35457e16	−0.0337170
$649$	−5.73986e16	−0.0301516
$650$	1.01137e17	0.0525986
$651$	1.21046e17	0.0623268
$652$	−2.55601e18	−1.30303
$653$	−5.12082e17	−0.258466	−0.129233	−	0.991614i	$-0.541252\pi$
$653$	−5.12082e17	−0.258466	−0.129233	+	0.991614i	$0.541252\pi$
$654$	1.03558e17	0.0517523
$655$	−2.69609e18	−1.33403
$656$	−1.37335e18	−0.672833
$657$	−7.02457e17	−0.340757
$658$	−3.03748e16	−0.0145897
$659$	−1.67138e18	−0.794916	−0.397458	−	0.917620i	$-0.630108\pi$
$659$	−1.67138e18	−0.794916	−0.397458	+	0.917620i	$0.630108\pi$
$660$	1.93246e17	0.0910071
$661$	−2.13110e18	−0.993791	−0.496896	−	0.867810i	$-0.665527\pi$
$661$	−2.13110e18	−0.993791	−0.496896	+	0.867810i	$0.665527\pi$
$662$	−2.99735e17	−0.138408
$663$	4.68437e17	0.214197
$664$	−5.30992e17	−0.240434
$665$	2.56448e17	0.114989
$666$	1.88144e16	0.00835424
$667$	−6.50304e17	−0.285955
$668$	4.22131e18	1.83823
$669$	9.62475e17	0.415068
$670$	1.48671e16	0.00634951
$671$	4.88846e17	0.206764
$672$	7.66987e16	0.0321283
$673$	−6.50658e17	−0.269933	−0.134966	−	0.990850i	$-0.543093\pi$
$673$	−6.50658e17	−0.269933	−0.134966	+	0.990850i	$0.543093\pi$
$674$	−5.44539e17	−0.223738
$675$	2.43146e17	0.0989446
$676$	1.34701e18	0.542897
$677$	6.36618e17	0.254128	0.127064	−	0.991895i	$-0.459445\pi$
$677$	6.36618e17	0.254128	0.127064	+	0.991895i	$0.459445\pi$
$678$	−6.55889e16	−0.0259321
$679$	−2.87301e17	−0.112508
$680$	−3.03629e17	−0.117770
$681$	2.39200e18	0.918977
$682$	8.08868e16	0.0307808
$683$	1.95336e18	0.736288	0.368144	−	0.929769i	$-0.379993\pi$
$683$	1.95336e18	0.736288	0.368144	+	0.929769i	$0.379993\pi$
$684$	1.15313e18	0.430540
$685$	−5.28257e17	−0.195369
$686$	1.03719e17	0.0379973
$687$	−1.40715e18	−0.510647
$688$	3.53983e18	1.27250
$689$	−1.06559e18	−0.379461
$690$	−1.00875e17	−0.0355847
$691$	−4.60580e17	−0.160952	−0.0804762	−	0.996757i	$-0.525644\pi$
$691$	−4.60580e17	−0.160952	−0.0804762	+	0.996757i	$0.525644\pi$
$692$	3.05303e16	0.0105692
$693$	−2.80728e16	−0.00962762
$694$	4.02034e17	0.136592
$695$	−6.21408e16	−0.0209158
$696$	−2.60876e17	−0.0869910
$697$	−1.21955e18	−0.402889
$698$	4.25539e17	0.139277
$699$	6.41045e17	0.207867
$700$	−1.94874e17	−0.0626062
$701$	2.44325e18	0.777679	0.388839	−	0.921306i	$-0.372876\pi$
$701$	2.44325e18	0.777679	0.388839	+	0.921306i	$0.372876\pi$
$702$	6.24323e16	0.0196887
$703$	−6.91071e17	−0.215930
$704$	−6.44357e17	−0.199482
$705$	−9.99678e17	−0.306641
$706$	1.44064e17	0.0437848
$707$	7.77842e17	0.234242
$708$	−2.45963e17	−0.0733927
$709$	−2.57462e18	−0.761223	−0.380612	−	0.924735i	$-0.624287\pi$
$709$	−2.57462e18	−0.761223	−0.380612	+	0.924735i	$0.624287\pi$
$710$	3.66458e17	0.107361
$711$	2.05081e18	0.595351
$712$	−1.56017e18	−0.448799
$713$	1.74891e18	0.498525
$714$	2.17909e16	0.00615513
$715$	−3.84304e17	−0.107569
$716$	2.90335e18	0.805312
$717$	−3.65471e18	−1.00456
$718$	3.80924e17	0.103760
$719$	−4.51699e18	−1.21930	−0.609652	−	0.792669i	$-0.708691\pi$
$719$	−4.51699e18	−1.21930	−0.609652	+	0.792669i	$0.708691\pi$
$720$	8.07617e17	0.216045
$721$	6.20337e17	0.164455
$722$	4.38179e17	0.115122
$723$	3.23444e18	0.842172
$724$	−7.18408e18	−1.85383
$725$	9.98194e17	0.255281
$726$	3.30975e17	0.0838894
$727$	−2.38548e18	−0.599242	−0.299621	−	0.954058i	$-0.596860\pi$
$727$	−2.38548e18	−0.599242	−0.299621	+	0.954058i	$0.596860\pi$
$728$	−1.01283e17	−0.0252164
$729$	1.50095e17	0.0370370
$730$	−4.47337e17	−0.109405
$731$	3.14339e18	0.761965
$732$	2.09479e18	0.503290
$733$	−6.68849e16	−0.0159277	−0.00796383	−	0.999968i	$-0.502535\pi$
$733$	−6.68849e16	−0.0159277	−0.00796383	+	0.999968i	$0.502535\pi$
$734$	9.68208e17	0.228531
$735$	1.69340e18	0.396179
$736$	1.10817e18	0.256980
$737$	5.97786e16	0.0137406
$738$	−1.62538e17	−0.0370331
$739$	1.73606e18	0.392080	0.196040	−	0.980596i	$-0.437192\pi$
$739$	1.73606e18	0.392080	0.196040	+	0.980596i	$0.437192\pi$
$740$	−4.96276e17	−0.111101
$741$	−2.29320e18	−0.508890
$742$	−4.95697e16	−0.0109041
$743$	−8.45764e18	−1.84426	−0.922130	−	0.386880i	$-0.873553\pi$
$743$	−8.45764e18	−1.84426	−0.922130	+	0.386880i	$0.873553\pi$
$744$	7.01595e17	0.151657
$745$	−5.99696e18	−1.28504
$746$	−2.66430e17	−0.0565953
$747$	1.25420e18	0.264109
$748$	−6.03145e17	−0.125910
$749$	−6.02645e17	−0.124718
$750$	4.56006e17	0.0935562
$751$	3.98471e18	0.810471	0.405235	−	0.914212i	$-0.367190\pi$
$751$	3.98471e18	0.810471	0.405235	+	0.914212i	$0.367190\pi$
$752$	3.51362e18	0.708497
$753$	4.26106e18	0.851826
$754$	2.56305e17	0.0507976
$755$	−1.04913e17	−0.0206146
$756$	−1.20296e17	−0.0234348
$757$	8.08563e18	1.56168	0.780838	−	0.624734i	$-0.214793\pi$
$757$	8.08563e18	1.56168	0.780838	+	0.624734i	$0.214793\pi$
$758$	7.16181e17	0.137143
$759$	−4.05604e17	−0.0770071
$760$	1.48639e18	0.279799
$761$	−3.24162e18	−0.605008	−0.302504	−	0.953148i	$-0.597823\pi$
$761$	−3.24162e18	−0.605008	−0.302504	+	0.953148i	$0.597823\pi$
$762$	−4.56901e17	−0.0845503
$763$	3.96819e17	0.0728087
$764$	8.81736e18	1.60410
$765$	7.17170e17	0.129367
$766$	−6.87486e17	−0.122964
$767$	4.89140e17	0.0867488
$768$	−2.53625e18	−0.446009
$769$	−7.85230e18	−1.36923	−0.684614	−	0.728906i	$-0.740029\pi$
$769$	−7.85230e18	−1.36923	−0.684614	+	0.728906i	$0.740029\pi$
$770$	−1.78772e16	−0.00309108
$771$	−3.78400e18	−0.648781
$772$	−5.16918e18	−0.878838
$773$	−2.39859e18	−0.404379	−0.202190	−	0.979346i	$-0.564806\pi$
$773$	−2.39859e18	−0.404379	−0.202190	+	0.979346i	$0.564806\pi$
$774$	4.18944e17	0.0700390
$775$	−2.68452e18	−0.445047
$776$	−1.66522e18	−0.273761
$777$	7.20937e16	0.0117533
$778$	−1.73624e18	−0.280700
$779$	5.97021e18	0.957185
$780$	−1.64681e18	−0.261835
$781$	1.47348e18	0.232334
$782$	3.14842e17	0.0492322
$783$	6.16188e17	0.0955569
$784$	−5.95187e18	−0.915374
$785$	8.01432e18	1.22240
$786$	1.12151e18	0.169651
$787$	9.20950e18	1.38166	0.690829	−	0.723019i	$-0.257246\pi$
$787$	9.20950e18	1.38166	0.690829	+	0.723019i	$0.257246\pi$
$788$	3.09396e18	0.460357
$789$	4.45817e18	0.657894
$790$	1.30599e18	0.191146
$791$	−2.51326e17	−0.0364830
$792$	−1.62712e17	−0.0234265
$793$	−4.16586e18	−0.594879
$794$	3.51680e17	0.0498097
$795$	−1.63141e18	−0.229180
$796$	7.47405e18	1.04141
$797$	1.04263e19	1.44096	0.720480	−	0.693476i	$-0.243921\pi$
$797$	1.04263e19	1.44096	0.720480	+	0.693476i	$0.243921\pi$
$798$	−1.06676e17	−0.0146234
$799$	3.12012e18	0.424245
$800$	−1.70100e18	−0.229414
$801$	3.68512e18	0.492992
$802$	1.42829e18	0.189533
$803$	−1.79868e18	−0.236757
$804$	2.56161e17	0.0334464
$805$	−3.86536e17	−0.0500630
$806$	−6.89302e17	−0.0885588
$807$	−2.32206e17	−0.0295934
$808$	4.50844e18	0.569971
$809$	−2.88620e18	−0.361961	−0.180980	−	0.983487i	$-0.557927\pi$
$809$	−2.88620e18	−0.361961	−0.180980	+	0.983487i	$0.557927\pi$
$810$	9.55828e16	0.0118912
$811$	−4.80075e18	−0.592480	−0.296240	−	0.955114i	$-0.595733\pi$
$811$	−4.80075e18	−0.592480	−0.296240	+	0.955114i	$0.595733\pi$
$812$	−4.93857e17	−0.0604626
$813$	4.38316e18	0.532352
$814$	4.81752e16	0.00580450
$815$	7.78211e18	0.930192
$816$	−2.52067e18	−0.298903
$817$	−1.53882e19	−1.81028
$818$	9.69878e17	0.113193
$819$	2.39231e17	0.0276995
$820$	4.28736e18	0.492493
$821$	7.45932e18	0.850097	0.425049	−	0.905171i	$-0.360257\pi$
$821$	7.45932e18	0.850097	0.425049	+	0.905171i	$0.360257\pi$
$822$	2.19742e17	0.0248454
$823$	−2.96531e18	−0.332637	−0.166319	−	0.986072i	$-0.553188\pi$
$823$	−2.96531e18	−0.332637	−0.166319	+	0.986072i	$0.553188\pi$
$824$	3.59553e18	0.400162
$825$	6.22588e17	0.0687465
$826$	2.27540e16	0.00249280
$827$	−1.18918e19	−1.29259	−0.646297	−	0.763086i	$-0.723683\pi$
$827$	−1.18918e19	−1.29259	−0.646297	+	0.763086i	$0.723683\pi$
$828$	−1.73808e18	−0.187445
$829$	−1.07442e17	−0.0114966	−0.00574828	−	0.999983i	$-0.501830\pi$
$829$	−1.07442e17	−0.0114966	−0.00574828	+	0.999983i	$0.501830\pi$
$830$	7.98697e17	0.0847958
$831$	−7.56374e18	−0.796764
$832$	5.49109e18	0.573927
$833$	−5.28530e18	−0.548122
$834$	2.58491e16	0.00265990
$835$	−1.28523e19	−1.31226
$836$	2.95265e18	0.299138
$837$	−1.65716e18	−0.166591
$838$	−4.53562e17	−0.0452430
$839$	1.14969e19	1.13796	0.568980	−	0.822351i	$-0.307338\pi$
$839$	1.14969e19	1.13796	0.568980	+	0.822351i	$0.307338\pi$
$840$	−1.55063e17	−0.0152298
$841$	−7.73097e18	−0.753460
$842$	3.99956e17	0.0386798
$843$	5.13669e18	0.492952
$844$	1.43952e19	1.37085
$845$	−4.10115e18	−0.387559
$846$	4.15842e17	0.0389961
$847$	1.26824e18	0.118021
$848$	5.73399e18	0.529522
$849$	7.85059e18	0.719453
$850$	−4.83272e17	−0.0439510
$851$	1.04163e18	0.0940096
$852$	6.31410e18	0.565528
$853$	−1.05334e19	−0.936263	−0.468132	−	0.883659i	$-0.655073\pi$
$853$	−1.05334e19	−0.936263	−0.468132	+	0.883659i	$0.655073\pi$
$854$	−1.93789e17	−0.0170943
$855$	−3.51086e18	−0.307350
$856$	−3.49299e18	−0.303471
$857$	−1.72922e19	−1.49099	−0.745496	−	0.666510i	$-0.767787\pi$
$857$	−1.72922e19	−1.49099	−0.745496	+	0.666510i	$0.767787\pi$
$858$	1.59861e17	0.0136797
$859$	−8.32639e18	−0.707134	−0.353567	−	0.935409i	$-0.615031\pi$
$859$	−8.32639e18	−0.707134	−0.353567	+	0.935409i	$0.615031\pi$
$860$	−1.10507e19	−0.931429
$861$	−6.22822e17	−0.0521007
$862$	2.09080e18	0.173586
$863$	2.25124e19	1.85504	0.927518	−	0.373778i	$-0.121938\pi$
$863$	2.25124e19	1.85504	0.927518	+	0.373778i	$0.121938\pi$
$864$	−1.05003e18	−0.0858743
$865$	−9.29536e16	−0.00754504
$866$	−1.85270e18	−0.149258
$867$	4.98206e18	0.398369
$868$	1.32817e18	0.105408
$869$	5.25122e18	0.413648
$870$	3.92399e17	0.0306798
$871$	−5.09422e17	−0.0395330
$872$	2.30000e18	0.177162
$873$	3.93325e18	0.300718
$874$	−1.54129e18	−0.116966
$875$	1.74734e18	0.131621
$876$	−7.70765e18	−0.576295
$877$	1.31518e19	0.976085	0.488043	−	0.872820i	$-0.337711\pi$
$877$	1.31518e19	0.976085	0.488043	+	0.872820i	$0.337711\pi$
$878$	−1.15414e18	−0.0850248
$879$	−2.43130e18	−0.177791
$880$	2.06795e18	0.150108
$881$	−8.20418e18	−0.591142	−0.295571	−	0.955321i	$-0.595510\pi$
$881$	−8.20418e18	−0.591142	−0.295571	+	0.955321i	$0.595510\pi$
$882$	−7.04413e17	−0.0503827
$883$	−9.12088e18	−0.647578	−0.323789	−	0.946129i	$-0.604957\pi$
$883$	−9.12088e18	−0.647578	−0.323789	+	0.946129i	$0.604957\pi$
$884$	5.13988e18	0.362254
$885$	7.48866e17	0.0523929
$886$	3.40270e18	0.236322
$887$	2.61506e19	1.80293	0.901463	−	0.432856i	$-0.142494\pi$
$887$	2.61506e19	1.80293	0.901463	+	0.432856i	$0.142494\pi$
$888$	4.17862e17	0.0285988
$889$	−1.75077e18	−0.118951
$890$	2.34675e18	0.158282
$891$	3.84326e17	0.0257332
$892$	1.05607e19	0.701972
$893$	−1.52743e19	−1.00792
$894$	2.49459e18	0.163420
$895$	−8.83962e18	−0.574889
$896$	1.11732e18	0.0721401
$897$	3.45648e18	0.221556
$898$	2.22073e18	0.141319
$899$	−6.80321e18	−0.429809
$900$	2.66790e18	0.167337
$901$	5.09182e18	0.317075
$902$	−4.16189e17	−0.0257305
$903$	1.60533e18	0.0985357
$904$	−1.45671e18	−0.0887725
$905$	2.18729e19	1.32340
$906$	4.36414e16	0.00262160
$907$	1.77331e19	1.05764	0.528819	−	0.848735i	$-0.322635\pi$
$907$	1.77331e19	1.05764	0.528819	+	0.848735i	$0.322635\pi$
$908$	2.62460e19	1.55419
$909$	−1.06489e19	−0.626096
$910$	1.52346e17	0.00889329
$911$	−2.37437e19	−1.37619	−0.688096	−	0.725620i	$-0.741553\pi$
$911$	−2.37437e19	−1.37619	−0.688096	+	0.725620i	$0.741553\pi$
$912$	1.23398e19	0.710135
$913$	3.21145e18	0.183502
$914$	2.71825e18	0.154219
$915$	−6.37786e18	−0.359284
$916$	−1.54398e19	−0.863617
$917$	4.29744e18	0.238676
$918$	−2.98325e17	−0.0164518
$919$	−2.62075e19	−1.43507	−0.717537	−	0.696520i	$-0.754731\pi$
$919$	−2.62075e19	−1.43507	−0.717537	+	0.696520i	$0.754731\pi$
$920$	−2.24040e18	−0.121816
$921$	1.60647e19	0.867329
$922$	1.72100e18	0.0922635
$923$	−1.25567e19	−0.668443
$924$	−3.08026e17	−0.0162824
$925$	−1.59887e18	−0.0839251
$926$	−4.60458e18	−0.240004
$927$	−8.49263e18	−0.439566
$928$	−4.31073e18	−0.221559
$929$	3.15412e19	1.60982	0.804908	−	0.593400i	$-0.202215\pi$
$929$	3.15412e19	1.60982	0.804908	+	0.593400i	$0.202215\pi$
$930$	−1.05531e18	−0.0534861
$931$	2.58738e19	1.30223
$932$	7.03380e18	0.351550
$933$	1.14205e18	0.0566834
$934$	−1.94981e18	−0.0961034
$935$	1.83635e18	0.0898837
$936$	1.38660e18	0.0673999
$937$	1.49625e19	0.722268	0.361134	−	0.932514i	$-0.382390\pi$
$937$	1.49625e19	0.722268	0.361134	+	0.932514i	$0.382390\pi$
$938$	−2.36975e16	−0.00113601
$939$	1.56918e19	0.747044
$940$	−1.09689e19	−0.518598
$941$	9.51121e18	0.446584	0.223292	−	0.974752i	$-0.428320\pi$
$941$	9.51121e18	0.446584	0.223292	+	0.974752i	$0.428320\pi$
$942$	−3.33376e18	−0.155455
$943$	−8.99873e18	−0.416730
$944$	−2.63207e18	−0.121054
$945$	3.66258e17	0.0167294
$946$	1.07273e18	0.0486629
$947$	−8.69870e18	−0.391904	−0.195952	−	0.980613i	$-0.562780\pi$
$947$	−8.69870e18	−0.391904	−0.195952	+	0.980613i	$0.562780\pi$
$948$	2.25023e19	1.00687
$949$	1.53280e19	0.681170
$950$	2.36583e18	0.104419
$951$	4.71758e18	0.206798
$952$	4.83971e17	0.0210707
$953$	1.69864e18	0.0734509	0.0367254	−	0.999325i	$-0.488307\pi$
$953$	1.69864e18	0.0734509	0.0367254	+	0.999325i	$0.488307\pi$
$954$	6.78627e17	0.0291452
$955$	−2.68456e19	−1.14512
$956$	−4.01009e19	−1.69894
$957$	1.57778e18	0.0663927
$958$	−2.10955e18	−0.0881685
$959$	8.42017e17	0.0349543
$960$	8.40677e18	0.346630
$961$	−6.12112e18	−0.250685
$962$	−4.10540e17	−0.0167000
$963$	8.25042e18	0.333354
$964$	3.54896e19	1.42430
$965$	1.57382e19	0.627377
$966$	1.60790e17	0.00636660
$967$	−2.88013e19	−1.13277	−0.566383	−	0.824142i	$-0.691658\pi$
$967$	−2.88013e19	−1.13277	−0.566383	+	0.824142i	$0.691658\pi$
$968$	7.35086e18	0.287176
$969$	1.09578e19	0.425225
$970$	2.50476e18	0.0965495
$971$	1.27392e19	0.487771	0.243885	−	0.969804i	$-0.421578\pi$
$971$	1.27392e19	0.487771	0.243885	+	0.969804i	$0.421578\pi$
$972$	1.64690e18	0.0626378
$973$	9.90496e16	0.00374213
$974$	6.80697e18	0.255459
$975$	−5.30558e18	−0.197789
$976$	2.24166e19	0.830128
$977$	−3.69962e19	−1.36095	−0.680475	−	0.732771i	$-0.738227\pi$
$977$	−3.69962e19	−1.36095	−0.680475	+	0.732771i	$0.738227\pi$
$978$	−3.23717e18	−0.118294
$979$	9.43595e18	0.342530
$980$	1.85807e19	0.670026
$981$	−5.43260e18	−0.194607
$982$	−3.95891e18	−0.140880
$983$	3.51146e19	1.24134	0.620669	−	0.784072i	$-0.286861\pi$
$983$	3.51146e19	1.24134	0.620669	+	0.784072i	$0.286861\pi$
$984$	−3.60993e18	−0.126774
$985$	−9.41997e18	−0.328635
$986$	−1.22472e18	−0.0424462
$987$	1.59344e18	0.0548624
$988$	−2.51620e19	−0.860645
$989$	2.31943e19	0.788143
$990$	2.44745e17	0.00826200
$991$	−1.08227e19	−0.362957	−0.181478	−	0.983395i	$-0.558088\pi$
$991$	−1.08227e19	−0.362957	−0.181478	+	0.983395i	$0.558088\pi$
$992$	1.15932e19	0.386258
$993$	1.57239e19	0.520462
$994$	−5.84117e17	−0.0192083
$995$	−2.27557e19	−0.743431
$996$	1.37616e19	0.446667
$997$	−2.95468e19	−0.952777	−0.476389	−	0.879235i	$-0.658054\pi$
$997$	−2.95468e19	−0.952777	−0.476389	+	0.879235i	$0.658054\pi$
$998$	7.85569e18	0.251673
$999$	−9.86987e17	−0.0314149

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.b.1.16	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.b.1.16	✓	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)

\(f(q)\)	\(=\)	\(q+13.8965 q^{2} -729.000 q^{3} -7998.89 q^{4} +24353.7 q^{5} -10130.5 q^{6} -38818.7 q^{7} -224997. q^{8} +531441. q^{9} +O(q^{10})\)	\(q+13.8965 q^{2} -729.000 q^{3} -7998.89 q^{4} +24353.7 q^{5} -10130.5 q^{6} -38818.7 q^{7} -224997. q^{8} +531441. q^{9} +338431. q^{10} +1.36078e6 q^{11} +5.83119e6 q^{12} -1.15964e7 q^{13} -539443. q^{14} -1.77538e7 q^{15} +6.24002e7 q^{16} +5.54118e7 q^{17} +7.38517e6 q^{18} -2.71265e8 q^{19} -1.94802e8 q^{20} +2.82988e7 q^{21} +1.89101e7 q^{22} +4.08870e8 q^{23} +1.64022e8 q^{24} -6.27602e8 q^{25} -1.61149e8 q^{26} -3.87420e8 q^{27} +3.10506e8 q^{28} -1.59049e9 q^{29} -2.46716e8 q^{30} +4.27743e9 q^{31} +2.71032e9 q^{32} -9.92012e8 q^{33} +7.70030e8 q^{34} -9.45377e8 q^{35} -4.25094e9 q^{36} +2.54759e9 q^{37} -3.76963e9 q^{38} +8.45374e9 q^{39} -5.47949e9 q^{40} -2.20088e10 q^{41} +3.93254e8 q^{42} +5.67278e10 q^{43} -1.08848e10 q^{44} +1.29425e10 q^{45} +5.68186e9 q^{46} +5.63077e10 q^{47} -4.54898e10 q^{48} -9.53821e10 q^{49} -8.72146e9 q^{50} -4.03952e10 q^{51} +9.27579e10 q^{52} +9.18905e10 q^{53} -5.38379e9 q^{54} +3.31401e10 q^{55} +8.73407e9 q^{56} +1.97752e11 q^{57} -2.21022e10 q^{58} -4.21805e10 q^{59} +1.42011e11 q^{60} +3.59239e11 q^{61} +5.94413e10 q^{62} -2.06298e10 q^{63} -4.73519e11 q^{64} -2.82414e11 q^{65} -1.37855e10 q^{66} +4.39295e10 q^{67} -4.43233e11 q^{68} -2.98066e11 q^{69} -1.31374e10 q^{70} +1.08282e12 q^{71} -1.19572e11 q^{72} -1.32180e12 q^{73} +3.54025e10 q^{74} +4.57522e11 q^{75} +2.16982e12 q^{76} -5.28238e10 q^{77} +1.17477e11 q^{78} +3.85896e12 q^{79} +1.51967e12 q^{80} +2.82430e11 q^{81} -3.05845e11 q^{82} +2.36000e12 q^{83} -2.26359e11 q^{84} +1.34948e12 q^{85} +7.88317e11 q^{86} +1.15947e12 q^{87} -3.06172e11 q^{88} +6.93420e12 q^{89} +1.79856e11 q^{90} +4.50155e11 q^{91} -3.27051e12 q^{92} -3.11825e12 q^{93} +7.82480e11 q^{94} -6.60630e12 q^{95} -1.97582e12 q^{96} +7.40111e12 q^{97} -1.32548e12 q^{98} +7.23177e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q - 52 q^{2} - 22599 q^{3} + 126886 q^{4} + 33486 q^{5} + 37908 q^{6} - 1135539 q^{7} - 1519749 q^{8} + 16474671 q^{9}+O(q^{10}) \) 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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