LMFDB - Embedded newform 14.12.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,12,Mod(1,14)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(14, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("14.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	14.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:	$10.7568045278$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{153169}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 38292 $ x^2 - x - 38292
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$196.184$ of defining polynomial
Character	$\chi$	$=$	14.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-32.0000 q^{2} -216.368 q^{3} +1024.00 q^{4} -8085.73 q^{5} +6923.78 q^{6} -16807.0 q^{7} -32768.0 q^{8} -130332. q^{9} +O(q^{10})$	\(q-32.0000 q^{2} -216.368 q^{3} +1024.00 q^{4} -8085.73 q^{5} +6923.78 q^{6} -16807.0 q^{7} -32768.0 q^{8} -130332. q^{9} +258743. q^{10} +929186. q^{11} -221561. q^{12} +777193. q^{13} +537824. q^{14} +1.74949e6 q^{15} +1.04858e6 q^{16} +3.10322e6 q^{17} +4.17062e6 q^{18} +1.72132e7 q^{19} -8.27979e6 q^{20} +3.63650e6 q^{21} -2.97340e7 q^{22} -4.28822e7 q^{23} +7.08995e6 q^{24} +1.65509e7 q^{25} -2.48702e7 q^{26} +6.65286e7 q^{27} -1.72104e7 q^{28} -8.18166e7 q^{29} -5.59838e7 q^{30} +6.67578e7 q^{31} -3.35544e7 q^{32} -2.01046e8 q^{33} -9.93031e7 q^{34} +1.35897e8 q^{35} -1.33460e8 q^{36} +7.15862e8 q^{37} -5.50822e8 q^{38} -1.68160e8 q^{39} +2.64953e8 q^{40} +7.58605e8 q^{41} -1.16368e8 q^{42} -2.01326e8 q^{43} +9.51487e8 q^{44} +1.05383e9 q^{45} +1.37223e9 q^{46} -7.54720e8 q^{47} -2.26878e8 q^{48} +2.82475e8 q^{49} -5.29629e8 q^{50} -6.71439e8 q^{51} +7.95845e8 q^{52} -1.49545e9 q^{53} -2.12892e9 q^{54} -7.51315e9 q^{55} +5.50732e8 q^{56} -3.72438e9 q^{57} +2.61813e9 q^{58} +3.20003e9 q^{59} +1.79148e9 q^{60} -4.59693e9 q^{61} -2.13625e9 q^{62} +2.19049e9 q^{63} +1.07374e9 q^{64} -6.28417e9 q^{65} +6.43348e9 q^{66} +8.85803e9 q^{67} +3.17770e9 q^{68} +9.27834e9 q^{69} -4.34870e9 q^{70} -4.38392e9 q^{71} +4.27071e9 q^{72} +2.72701e10 q^{73} -2.29076e10 q^{74} -3.58109e9 q^{75} +1.76263e10 q^{76} -1.56168e10 q^{77} +5.38111e9 q^{78} +4.19225e10 q^{79} -8.47850e9 q^{80} +8.69322e9 q^{81} -2.42753e10 q^{82} -4.75219e10 q^{83} +3.72377e9 q^{84} -2.50918e10 q^{85} +6.44242e9 q^{86} +1.77025e10 q^{87} -3.04476e10 q^{88} +1.00263e11 q^{89} -3.37225e10 q^{90} -1.30623e10 q^{91} -4.39114e10 q^{92} -1.44443e10 q^{93} +2.41510e10 q^{94} -1.39181e11 q^{95} +7.26011e9 q^{96} +5.11389e10 q^{97} -9.03921e9 q^{98} -1.21103e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 64 q^{2} + 350 q^{3} + 2048 q^{4} + 266 q^{5} - 11200 q^{6} - 33614 q^{7} - 65536 q^{8} + 13294 q^{9}+O(q^{10}) $ 2 * q - 64 * q^2 + 350 * q^3 + 2048 * q^4 + 266 * q^5 - 11200 * q^6 - 33614 * q^7 - 65536 * q^8 + 13294 * q^9	\( 2 q - 64 q^{2} + 350 q^{3} + 2048 q^{4} + 266 q^{5} - 11200 q^{6} - 33614 q^{7} - 65536 q^{8} + 13294 q^{9} - 8512 q^{10} + 773500 q^{11} + 358400 q^{12} + 3275622 q^{13} + 1075648 q^{14} + 6479648 q^{15} + 2097152 q^{16} + 9376528 q^{17} - 425408 q^{18} + 1741642 q^{19} + 272384 q^{20} - 5882450 q^{21} - 24752000 q^{22} - 11993072 q^{23} - 11468800 q^{24} + 37474186 q^{25} - 104819904 q^{26} + 47543300 q^{27} - 34420736 q^{28} - 23355904 q^{29} - 207348736 q^{30} + 142349508 q^{31} - 67108864 q^{32} - 289221968 q^{33} - 300048896 q^{34} - 4470662 q^{35} + 13613056 q^{36} + 530129728 q^{37} - 55732544 q^{38} + 1246871112 q^{39} - 8716288 q^{40} - 206465112 q^{41} + 188238400 q^{42} + 1036645444 q^{43} + 792064000 q^{44} + 2253352402 q^{45} + 383778304 q^{46} - 2847603444 q^{47} + 367001600 q^{48} + 564950498 q^{49} - 1199173952 q^{50} + 2881561300 q^{51} + 3354236928 q^{52} - 4876085316 q^{53} - 1521385600 q^{54} - 8813398328 q^{55} + 1101463552 q^{56} - 12486968516 q^{57} + 747388928 q^{58} - 6723217942 q^{59} + 6635159552 q^{60} - 9724278438 q^{61} - 4555184256 q^{62} - 223432258 q^{63} + 2147483648 q^{64} + 14582040228 q^{65} + 9255102976 q^{66} + 8448611288 q^{67} + 9601564672 q^{68} + 26772956224 q^{69} + 143061184 q^{70} - 26281683512 q^{71} - 435617792 q^{72} + 61139797628 q^{73} - 16964151296 q^{74} + 8269186618 q^{75} + 1783441408 q^{76} - 13000214500 q^{77} - 39899875584 q^{78} + 37890465096 q^{79} + 278921216 q^{80} - 27502341218 q^{81} + 6606883584 q^{82} - 46563770750 q^{83} - 6023628800 q^{84} + 27301125124 q^{85} - 33172654208 q^{86} + 50812775132 q^{87} - 25346048000 q^{88} + 80689325220 q^{89} - 72107276864 q^{90} - 55053378954 q^{91} - 12280905728 q^{92} + 28368494568 q^{93} + 91123310208 q^{94} - 268395234800 q^{95} - 11744051200 q^{96} - 9944168416 q^{97} - 18078415936 q^{98} - 143463109300 q^{99}+O(q^{100}) \) 2 * q - 64 * q^2 + 350 * q^3 + 2048 * q^4 + 266 * q^5 - 11200 * q^6 - 33614 * q^7 - 65536 * q^8 + 13294 * q^9 - 8512 * q^10 + 773500 * q^11 + 358400 * q^12 + 3275622 * q^13 + 1075648 * q^14 + 6479648 * q^15 + 2097152 * q^16 + 9376528 * q^17 - 425408 * q^18 + 1741642 * q^19 + 272384 * q^20 - 5882450 * q^21 - 24752000 * q^22 - 11993072 * q^23 - 11468800 * q^24 + 37474186 * q^25 - 104819904 * q^26 + 47543300 * q^27 - 34420736 * q^28 - 23355904 * q^29 - 207348736 * q^30 + 142349508 * q^31 - 67108864 * q^32 - 289221968 * q^33 - 300048896 * q^34 - 4470662 * q^35 + 13613056 * q^36 + 530129728 * q^37 - 55732544 * q^38 + 1246871112 * q^39 - 8716288 * q^40 - 206465112 * q^41 + 188238400 * q^42 + 1036645444 * q^43 + 792064000 * q^44 + 2253352402 * q^45 + 383778304 * q^46 - 2847603444 * q^47 + 367001600 * q^48 + 564950498 * q^49 - 1199173952 * q^50 + 2881561300 * q^51 + 3354236928 * q^52 - 4876085316 * q^53 - 1521385600 * q^54 - 8813398328 * q^55 + 1101463552 * q^56 - 12486968516 * q^57 + 747388928 * q^58 - 6723217942 * q^59 + 6635159552 * q^60 - 9724278438 * q^61 - 4555184256 * q^62 - 223432258 * q^63 + 2147483648 * q^64 + 14582040228 * q^65 + 9255102976 * q^66 + 8448611288 * q^67 + 9601564672 * q^68 + 26772956224 * q^69 + 143061184 * q^70 - 26281683512 * q^71 - 435617792 * q^72 + 61139797628 * q^73 - 16964151296 * q^74 + 8269186618 * q^75 + 1783441408 * q^76 - 13000214500 * q^77 - 39899875584 * q^78 + 37890465096 * q^79 + 278921216 * q^80 - 27502341218 * q^81 + 6606883584 * q^82 - 46563770750 * q^83 - 6023628800 * q^84 + 27301125124 * q^85 - 33172654208 * q^86 + 50812775132 * q^87 - 25346048000 * q^88 + 80689325220 * q^89 - 72107276864 * q^90 - 55053378954 * q^91 - 12280905728 * q^92 + 28368494568 * q^93 + 91123310208 * q^94 - 268395234800 * q^95 - 11744051200 * q^96 - 9944168416 * q^97 - 18078415936 * q^98 - 143463109300 * 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 $

$2$	−32.0000	−0.707107
$2$	−32.0000	−0.707107
$3$	−216.368	−0.514075	−0.257037	−	0.966401i	$-0.582746\pi$
$3$	−216.368	−0.514075	−0.257037	+	0.966401i	$0.582746\pi$
$4$	1024.00	0.500000
$5$	−8085.73	−1.15714	−0.578568	−	0.815634i	$-0.696388\pi$
$5$	−8085.73	−1.15714	−0.578568	+	0.815634i	$0.696388\pi$
$6$	6923.78	0.363506
$7$	−16807.0	−0.377964
$7$	−16807.0	−0.377964
$8$	−32768.0	−0.353553
$9$	−130332.	−0.735727
$10$	258743.	0.818218
$11$	929186.	1.73957	0.869787	−	0.493427i	$-0.164256\pi$
$11$	929186.	1.73957	0.869787	+	0.493427i	$0.164256\pi$
$12$	−221561.	−0.257037
$13$	777193.	0.580551	0.290275	−	0.956943i	$-0.406253\pi$
$13$	777193.	0.580551	0.290275	+	0.956943i	$0.406253\pi$
$14$	537824.	0.267261
$15$	1.74949e6	0.594854
$16$	1.04858e6	0.250000
$17$	3.10322e6	0.530083	0.265042	−	0.964237i	$-0.414614\pi$
$17$	3.10322e6	0.530083	0.265042	+	0.964237i	$0.414614\pi$
$18$	4.17062e6	0.520238
$19$	1.72132e7	1.59484	0.797418	−	0.603427i	$-0.206198\pi$
$19$	1.72132e7	1.59484	0.797418	+	0.603427i	$0.206198\pi$
$20$	−8.27979e6	−0.578568
$21$	3.63650e6	0.194302
$22$	−2.97340e7	−1.23006
$23$	−4.28822e7	−1.38923	−0.694615	−	0.719382i	$-0.744425\pi$
$23$	−4.28822e7	−1.38923	−0.694615	+	0.719382i	$0.744425\pi$
$24$	7.08995e6	0.181753
$25$	1.65509e7	0.338963
$26$	−2.48702e7	−0.410511
$27$	6.65286e7	0.892294
$28$	−1.72104e7	−0.188982
$29$	−8.18166e7	−0.740717	−0.370359	−	0.928889i	$-0.620765\pi$
$29$	−8.18166e7	−0.740717	−0.370359	+	0.928889i	$0.620765\pi$
$30$	−5.59838e7	−0.420625
$31$	6.67578e7	0.418806	0.209403	−	0.977829i	$-0.432848\pi$
$31$	6.67578e7	0.418806	0.209403	+	0.977829i	$0.432848\pi$
$32$	−3.35544e7	−0.176777
$33$	−2.01046e8	−0.894271
$34$	−9.93031e7	−0.374825
$35$	1.35897e8	0.437356
$36$	−1.33460e8	−0.367864
$37$	7.15862e8	1.69715	0.848574	−	0.529076i	$-0.177461\pi$
$37$	7.15862e8	1.69715	0.848574	+	0.529076i	$0.177461\pi$
$38$	−5.50822e8	−1.12772
$39$	−1.68160e8	−0.298447
$40$	2.64953e8	0.409109
$41$	7.58605e8	1.02260	0.511298	−	0.859403i	$-0.329165\pi$
$41$	7.58605e8	1.02260	0.511298	+	0.859403i	$0.329165\pi$
$42$	−1.16368e8	−0.137392
$43$	−2.01326e8	−0.208844	−0.104422	−	0.994533i	$-0.533299\pi$
$43$	−2.01326e8	−0.208844	−0.104422	+	0.994533i	$0.533299\pi$
$44$	9.51487e8	0.869787
$45$	1.05383e9	0.851336
$46$	1.37223e9	0.982333
$47$	−7.54720e8	−0.480007	−0.240003	−	0.970772i	$-0.577149\pi$
$47$	−7.54720e8	−0.480007	−0.240003	+	0.970772i	$0.577149\pi$
$48$	−2.26878e8	−0.128519
$49$	2.82475e8	0.142857
$50$	−5.29629e8	−0.239683
$51$	−6.71439e8	−0.272502
$52$	7.95845e8	0.290275
$53$	−1.49545e9	−0.491197	−0.245598	−	0.969372i	$-0.578984\pi$
$53$	−1.49545e9	−0.491197	−0.245598	+	0.969372i	$0.578984\pi$
$54$	−2.12892e9	−0.630947
$55$	−7.51315e9	−2.01292
$56$	5.50732e8	0.133631
$57$	−3.72438e9	−0.819866
$58$	2.61813e9	0.523766
$59$	3.20003e9	0.582730	0.291365	−	0.956612i	$-0.405891\pi$
$59$	3.20003e9	0.582730	0.291365	+	0.956612i	$0.405891\pi$
$60$	1.79148e9	0.297427
$61$	−4.59693e9	−0.696873	−0.348437	−	0.937332i	$-0.613287\pi$
$61$	−4.59693e9	−0.696873	−0.348437	+	0.937332i	$0.613287\pi$
$62$	−2.13625e9	−0.296140
$63$	2.19049e9	0.278079
$64$	1.07374e9	0.125000
$65$	−6.28417e9	−0.671776
$66$	6.43348e9	0.632345
$67$	8.85803e9	0.801541	0.400770	−	0.916179i	$-0.368743\pi$
$67$	8.85803e9	0.801541	0.400770	+	0.916179i	$0.368743\pi$
$68$	3.17770e9	0.265042
$69$	9.27834e9	0.714168
$70$	−4.34870e9	−0.309257
$71$	−4.38392e9	−0.288364	−0.144182	−	0.989551i	$-0.546055\pi$
$71$	−4.38392e9	−0.288364	−0.144182	+	0.989551i	$0.546055\pi$
$72$	4.27071e9	0.260119
$73$	2.72701e10	1.53961	0.769804	−	0.638280i	$-0.220354\pi$
$73$	2.72701e10	1.53961	0.769804	+	0.638280i	$0.220354\pi$
$74$	−2.29076e10	−1.20007
$75$	−3.58109e9	−0.174252
$76$	1.76263e10	0.797418
$77$	−1.56168e10	−0.657497
$78$	5.38111e9	0.211034
$79$	4.19225e10	1.53284	0.766422	−	0.642338i	$-0.222035\pi$
$79$	4.19225e10	1.53284	0.766422	+	0.642338i	$0.222035\pi$
$80$	−8.47850e9	−0.289284
$81$	8.69322e9	0.277021
$82$	−2.42753e10	−0.723085
$83$	−4.75219e10	−1.32423	−0.662116	−	0.749401i	$-0.730341\pi$
$83$	−4.75219e10	−1.32423	−0.662116	+	0.749401i	$0.730341\pi$
$84$	3.72377e9	0.0971510
$85$	−2.50918e10	−0.613378
$86$	6.44242e9	0.147675
$87$	1.77025e10	0.380784
$88$	−3.04476e10	−0.615032
$89$	1.00263e11	1.90325	0.951626	−	0.307257i	$-0.0994112\pi$
$89$	1.00263e11	1.90325	0.951626	+	0.307257i	$0.0994112\pi$
$90$	−3.37225e10	−0.601985
$91$	−1.30623e10	−0.219428
$92$	−4.39114e10	−0.694615
$93$	−1.44443e10	−0.215297
$94$	2.41510e10	0.339416
$95$	−1.39181e11	−1.84544
$96$	7.26011e9	0.0908765
$97$	5.11389e10	0.604654	0.302327	−	0.953204i	$-0.402237\pi$
$97$	5.11389e10	0.604654	0.302327	+	0.953204i	$0.402237\pi$
$98$	−9.03921e9	−0.101015
$99$	−1.21103e11	−1.27985
$100$	1.69481e10	0.169481
$101$	1.25542e11	1.18856	0.594282	−	0.804257i	$-0.297436\pi$
$101$	1.25542e11	1.18856	0.594282	+	0.804257i	$0.297436\pi$
$102$	2.14860e10	0.192688
$103$	1.16672e11	0.991661	0.495830	−	0.868419i	$-0.334864\pi$
$103$	1.16672e11	0.991661	0.495830	+	0.868419i	$0.334864\pi$
$104$	−2.54670e10	−0.205256
$105$	−2.94037e10	−0.224834
$106$	4.78545e10	0.347329
$107$	−1.08213e11	−0.745880	−0.372940	−	0.927855i	$-0.621650\pi$
$107$	−1.08213e11	−0.745880	−0.372940	+	0.927855i	$0.621650\pi$
$108$	6.81253e10	0.446147
$109$	−1.19991e11	−0.746970	−0.373485	−	0.927636i	$-0.621837\pi$
$109$	−1.19991e11	−0.746970	−0.373485	+	0.927636i	$0.621837\pi$
$110$	2.40421e11	1.42335
$111$	−1.54890e11	−0.872462
$112$	−1.76234e10	−0.0944911
$113$	3.34040e10	0.170556	0.0852781	−	0.996357i	$-0.472822\pi$
$113$	3.34040e10	0.170556	0.0852781	+	0.996357i	$0.472822\pi$
$114$	1.19180e11	0.579732
$115$	3.46734e11	1.60753
$116$	−8.37802e10	−0.370359
$117$	−1.01293e11	−0.427127
$118$	−1.02401e11	−0.412053
$119$	−5.21559e10	−0.200353
$120$	−5.73274e10	−0.210313
$121$	5.78075e11	2.02612
$122$	1.47102e11	0.492764
$123$	−1.64138e11	−0.525691
$124$	6.83600e10	0.209403
$125$	2.60985e11	0.764910
$126$	−7.00956e10	−0.196631
$127$	−4.86962e11	−1.30790	−0.653951	−	0.756537i	$-0.726890\pi$
$127$	−4.86962e11	−1.30790	−0.653951	+	0.756537i	$0.726890\pi$
$128$	−3.43597e10	−0.0883883
$129$	4.35605e10	0.107362
$130$	2.01093e11	0.475017
$131$	−7.44729e11	−1.68658	−0.843289	−	0.537461i	$-0.819383\pi$
$131$	−7.44729e11	−1.68658	−0.843289	+	0.537461i	$0.819383\pi$
$132$	−2.05871e11	−0.447136
$133$	−2.89302e11	−0.602792
$134$	−2.83457e11	−0.566775
$135$	−5.37932e11	−1.03250
$136$	−1.01686e11	−0.187413
$137$	−2.34778e11	−0.415618	−0.207809	−	0.978169i	$-0.566633\pi$
$137$	−2.34778e11	−0.415618	−0.207809	+	0.978169i	$0.566633\pi$
$138$	−2.96907e11	−0.504993
$139$	1.33863e11	0.218816	0.109408	−	0.993997i	$-0.465105\pi$
$139$	1.33863e11	0.218816	0.109408	+	0.993997i	$0.465105\pi$
$140$	1.39158e11	0.218678
$141$	1.63297e11	0.246759
$142$	1.40285e11	0.203904
$143$	7.22157e11	1.00991
$144$	−1.36663e11	−0.183932
$145$	6.61547e11	0.857110
$146$	−8.72642e11	−1.08867
$147$	−6.11186e10	−0.0734393
$148$	7.33043e11	0.848574
$149$	1.27265e12	1.41966	0.709828	−	0.704375i	$-0.248773\pi$
$149$	1.27265e12	1.41966	0.709828	+	0.704375i	$0.248773\pi$
$150$	1.14595e11	0.123215
$151$	1.33403e12	1.38291	0.691455	−	0.722420i	$-0.256970\pi$
$151$	1.33403e12	1.38291	0.691455	+	0.722420i	$0.256970\pi$
$152$	−5.64041e11	−0.563860
$153$	−4.04449e11	−0.389996
$154$	4.99739e11	0.464921
$155$	−5.39785e11	−0.484615
$156$	−1.72196e11	−0.149223
$157$	6.10205e11	0.510537	0.255269	−	0.966870i	$-0.417836\pi$
$157$	6.10205e11	0.510537	0.255269	+	0.966870i	$0.417836\pi$
$158$	−1.34152e12	−1.08388
$159$	3.23568e11	0.252512
$160$	2.71312e11	0.204555
$161$	7.20721e11	0.525079
$162$	−2.78183e11	−0.195884
$163$	−1.54010e12	−1.04837	−0.524186	−	0.851604i	$-0.675631\pi$
$163$	−1.54010e12	−1.04837	−0.524186	+	0.851604i	$0.675631\pi$
$164$	7.76811e11	0.511298
$165$	1.62561e12	1.03479
$166$	1.52070e12	0.936373
$167$	1.12857e12	0.672337	0.336168	−	0.941802i	$-0.390869\pi$
$167$	1.12857e12	0.672337	0.336168	+	0.941802i	$0.390869\pi$
$168$	−1.19161e11	−0.0686961
$169$	−1.18813e12	−0.662961
$170$	8.02938e11	0.433724
$171$	−2.24343e12	−1.17336
$172$	−2.06158e11	−0.104422
$173$	−3.57186e12	−1.75243	−0.876214	−	0.481922i	$-0.839939\pi$
$173$	−3.57186e12	−1.75243	−0.876214	+	0.481922i	$0.839939\pi$
$174$	−5.66480e11	−0.269255
$175$	−2.78171e11	−0.128116
$176$	9.74322e11	0.434894
$177$	−6.92384e11	−0.299567
$178$	−3.20842e12	−1.34580
$179$	6.57394e10	0.0267383	0.0133691	−	0.999911i	$-0.495744\pi$
$179$	6.57394e10	0.0267383	0.0133691	+	0.999911i	$0.495744\pi$
$180$	1.07912e12	0.425668
$181$	3.13838e12	1.20081	0.600404	−	0.799697i	$-0.295006\pi$
$181$	3.13838e12	1.20081	0.600404	+	0.799697i	$0.295006\pi$
$182$	4.17993e11	0.155159
$183$	9.94629e11	0.358245
$184$	1.40516e12	0.491167
$185$	−5.78827e12	−1.96383
$186$	4.62216e11	0.152238
$187$	2.88347e12	0.922119
$188$	−7.72833e11	−0.240003
$189$	−1.11815e12	−0.337255
$190$	4.45380e12	1.30492
$191$	−6.05638e12	−1.72397	−0.861985	−	0.506935i	$-0.830779\pi$
$191$	−6.05638e12	−1.72397	−0.861985	+	0.506935i	$0.830779\pi$
$192$	−2.32323e11	−0.0642594
$193$	−1.00768e12	−0.270867	−0.135433	−	0.990786i	$-0.543243\pi$
$193$	−1.00768e12	−0.270867	−0.135433	+	0.990786i	$0.543243\pi$
$194$	−1.63645e12	−0.427555
$195$	1.35969e12	0.345343
$196$	2.89255e11	0.0714286
$197$	2.07465e12	0.498173	0.249087	−	0.968481i	$-0.419870\pi$
$197$	2.07465e12	0.498173	0.249087	+	0.968481i	$0.419870\pi$
$198$	3.87528e12	0.904992
$199$	5.90684e11	0.134172	0.0670862	−	0.997747i	$-0.478630\pi$
$199$	5.90684e11	0.134172	0.0670862	+	0.997747i	$0.478630\pi$
$200$	−5.42340e11	−0.119841
$201$	−1.91659e12	−0.412052
$202$	−4.01735e12	−0.840442
$203$	1.37509e12	0.279965
$204$	−6.87553e11	−0.136251
$205$	−6.13387e12	−1.18328
$206$	−3.73351e12	−0.701210
$207$	5.58892e12	1.02209
$208$	8.14945e11	0.145138
$209$	1.59942e13	2.77434
$210$	9.40920e11	0.158981
$211$	5.15896e12	0.849198	0.424599	−	0.905382i	$-0.360415\pi$
$211$	5.15896e12	0.849198	0.424599	+	0.905382i	$0.360415\pi$
$212$	−1.53134e12	−0.245598
$213$	9.48540e11	0.148241
$214$	3.46282e12	0.527417
$215$	1.62787e12	0.241661
$216$	−2.18001e12	−0.315473
$217$	−1.12200e12	−0.158294
$218$	3.83971e12	0.528188
$219$	−5.90037e12	−0.791474
$220$	−7.69346e12	−1.00646
$221$	2.41180e12	0.307740
$222$	4.95647e12	0.616924
$223$	−4.00273e12	−0.486049	−0.243024	−	0.970020i	$-0.578139\pi$
$223$	−4.00273e12	−0.486049	−0.243024	+	0.970020i	$0.578139\pi$
$224$	5.63949e11	0.0668153
$225$	−2.15711e12	−0.249384
$226$	−1.06893e12	−0.120601
$227$	9.20423e12	1.01355	0.506775	−	0.862078i	$-0.330838\pi$
$227$	9.20423e12	1.01355	0.506775	+	0.862078i	$0.330838\pi$
$228$	−3.81377e12	−0.409933
$229$	−5.19626e12	−0.545250	−0.272625	−	0.962120i	$-0.587892\pi$
$229$	−5.19626e12	−0.545250	−0.272625	+	0.962120i	$0.587892\pi$
$230$	−1.10955e13	−1.13669
$231$	3.37898e12	0.338003
$232$	2.68097e12	0.261883
$233$	−3.83092e12	−0.365464	−0.182732	−	0.983163i	$-0.558494\pi$
$233$	−3.83092e12	−0.365464	−0.182732	+	0.983163i	$0.558494\pi$
$234$	3.24137e12	0.302024
$235$	6.10246e12	0.555433
$236$	3.27683e12	0.291365
$237$	−9.07069e12	−0.787996
$238$	1.66899e12	0.141671
$239$	8.35803e12	0.693291	0.346646	−	0.937996i	$-0.387321\pi$
$239$	8.35803e12	0.693291	0.346646	+	0.937996i	$0.387321\pi$
$240$	1.83448e12	0.148714
$241$	−2.46542e13	−1.95342	−0.976712	−	0.214557i	$-0.931169\pi$
$241$	−2.46542e13	−1.95342	−0.976712	+	0.214557i	$0.931169\pi$
$242$	−1.84984e13	−1.43268
$243$	−1.36663e13	−1.03470
$244$	−4.70726e12	−0.348437
$245$	−2.28402e12	−0.165305
$246$	5.25241e12	0.371720
$247$	1.33780e13	0.925884
$248$	−2.18752e12	−0.148070
$249$	1.02822e13	0.680754
$250$	−8.35152e12	−0.540873
$251$	2.41509e13	1.53013	0.765066	−	0.643952i	$-0.222707\pi$
$251$	2.41509e13	1.53013	0.765066	+	0.643952i	$0.222707\pi$
$252$	2.24306e12	0.139039
$253$	−3.98455e13	−2.41667
$254$	1.55828e13	0.924826
$255$	5.42907e12	0.315322
$256$	1.09951e12	0.0625000
$257$	2.85094e12	0.158619	0.0793096	−	0.996850i	$-0.474728\pi$
$257$	2.85094e12	0.158619	0.0793096	+	0.996850i	$0.474728\pi$
$258$	−1.39394e12	−0.0759161
$259$	−1.20315e13	−0.641462
$260$	−6.43499e12	−0.335888
$261$	1.06633e13	0.544966
$262$	2.38313e13	1.19259
$263$	9.46986e12	0.464074	0.232037	−	0.972707i	$-0.425461\pi$
$263$	9.46986e12	0.464074	0.232037	+	0.972707i	$0.425461\pi$
$264$	6.58788e12	0.316173
$265$	1.20918e13	0.568381
$266$	9.25766e12	0.426238
$267$	−2.16938e13	−0.978414
$268$	9.07062e12	0.400770
$269$	3.35397e13	1.45185	0.725924	−	0.687775i	$-0.241413\pi$
$269$	3.35397e13	1.45185	0.725924	+	0.687775i	$0.241413\pi$
$270$	1.72138e13	0.730091
$271$	−1.21626e13	−0.505468	−0.252734	−	0.967536i	$-0.581330\pi$
$271$	−1.21626e13	−0.505468	−0.252734	+	0.967536i	$0.581330\pi$
$272$	3.25397e12	0.132521
$273$	2.82626e12	0.112802
$274$	7.51290e12	0.293886
$275$	1.53789e13	0.589651
$276$	9.50102e12	0.357084
$277$	−4.20565e13	−1.54951	−0.774756	−	0.632260i	$-0.782127\pi$
$277$	−4.20565e13	−1.54951	−0.774756	+	0.632260i	$0.782127\pi$
$278$	−4.28361e12	−0.154726
$279$	−8.70066e12	−0.308127
$280$	−4.45307e12	−0.154629
$281$	1.32290e13	0.450444	0.225222	−	0.974307i	$-0.427689\pi$
$281$	1.32290e13	0.450444	0.225222	+	0.974307i	$0.427689\pi$
$282$	−5.22551e12	−0.174485
$283$	1.15055e13	0.376773	0.188386	−	0.982095i	$-0.439674\pi$
$283$	1.15055e13	0.376773	0.188386	+	0.982095i	$0.439674\pi$
$284$	−4.48913e12	−0.144182
$285$	3.01144e13	0.948696
$286$	−2.31090e13	−0.714115
$287$	−1.27499e13	−0.386505
$288$	4.37321e12	0.130059
$289$	−2.46419e13	−0.719012
$290$	−2.11695e13	−0.606068
$291$	−1.10648e13	−0.310838
$292$	2.79245e13	0.769804
$293$	−4.65329e13	−1.25889	−0.629445	−	0.777045i	$-0.716718\pi$
$293$	−4.65329e13	−1.25889	−0.629445	+	0.777045i	$0.716718\pi$
$294$	1.95580e12	0.0519294
$295$	−2.58746e13	−0.674298
$296$	−2.34574e13	−0.600033
$297$	6.18175e13	1.55221
$298$	−4.07247e13	−1.00385
$299$	−3.33277e13	−0.806518
$300$	−3.66704e12	−0.0871261
$301$	3.38368e12	0.0789358
$302$	−4.26891e13	−0.977865
$303$	−2.71634e13	−0.611011
$304$	1.80493e13	0.398709
$305$	3.71695e13	0.806377
$306$	1.29424e13	0.275769
$307$	2.04296e13	0.427561	0.213780	−	0.976882i	$-0.431422\pi$
$307$	2.04296e13	0.427561	0.213780	+	0.976882i	$0.431422\pi$
$308$	−1.59916e13	−0.328749
$309$	−2.52442e13	−0.509788
$310$	1.72731e13	0.342674
$311$	2.12127e13	0.413440	0.206720	−	0.978400i	$-0.433721\pi$
$311$	2.12127e13	0.413440	0.206720	+	0.978400i	$0.433721\pi$
$312$	5.51026e12	0.105517
$313$	4.81885e13	0.906671	0.453335	−	0.891340i	$-0.350234\pi$
$313$	4.81885e13	0.906671	0.453335	+	0.891340i	$0.350234\pi$
$314$	−1.95266e13	−0.361005
$315$	−1.77117e13	−0.321775
$316$	4.29286e13	0.766422
$317$	6.51596e13	1.14328	0.571640	−	0.820505i	$-0.306308\pi$
$317$	6.51596e13	1.14328	0.571640	+	0.820505i	$0.306308\pi$
$318$	−1.03542e13	−0.178553
$319$	−7.60229e13	−1.28853
$320$	−8.68199e12	−0.144642
$321$	2.34139e13	0.383438
$322$	−2.30631e13	−0.371287
$323$	5.34163e13	0.845396
$324$	8.90186e12	0.138511
$325$	1.28632e13	0.196785
$326$	4.92831e13	0.741312
$327$	2.59622e13	0.383999
$328$	−2.48580e13	−0.361542
$329$	1.26846e13	0.181426
$330$	−5.20194e13	−0.731709
$331$	4.98098e13	0.689066	0.344533	−	0.938774i	$-0.388037\pi$
$331$	4.98098e13	0.689066	0.344533	+	0.938774i	$0.388037\pi$
$332$	−4.86624e13	−0.662116
$333$	−9.32996e13	−1.24864
$334$	−3.61142e13	−0.475414
$335$	−7.16236e13	−0.927491
$336$	3.81315e12	0.0485755
$337$	1.01341e14	1.27005	0.635027	−	0.772490i	$-0.280989\pi$
$337$	1.01341e14	1.27005	0.635027	+	0.772490i	$0.280989\pi$
$338$	3.80202e13	0.468784
$339$	−7.22757e12	−0.0876786
$340$	−2.56940e13	−0.306689
$341$	6.20304e13	0.728544
$342$	7.17896e13	0.829694
$343$	−4.74756e12	−0.0539949
$344$	6.59704e12	0.0738376
$345$	−7.50222e13	−0.826389
$346$	1.14299e14	1.23915
$347$	1.62699e12	0.0173609	0.00868047	−	0.999962i	$-0.497237\pi$
$347$	1.62699e12	0.0173609	0.00868047	+	0.999962i	$0.497237\pi$
$348$	1.81274e13	0.190392
$349$	6.47625e13	0.669551	0.334775	−	0.942298i	$-0.391340\pi$
$349$	6.47625e13	0.669551	0.334775	+	0.942298i	$0.391340\pi$
$350$	8.90148e12	0.0905916
$351$	5.17055e13	0.518022
$352$	−3.11783e13	−0.307516
$353$	−1.37883e14	−1.33891	−0.669454	−	0.742854i	$-0.733472\pi$
$353$	−1.37883e14	−1.33891	−0.669454	+	0.742854i	$0.733472\pi$
$354$	2.21563e13	0.211826
$355$	3.54472e13	0.333676
$356$	1.02670e14	0.951626
$357$	1.12849e13	0.102996
$358$	−2.10366e12	−0.0189068
$359$	−2.23933e13	−0.198197	−0.0990987	−	0.995078i	$-0.531596\pi$
$359$	−2.23933e13	−0.198197	−0.0990987	+	0.995078i	$0.531596\pi$
$360$	−3.45318e13	−0.300993
$361$	1.79803e14	1.54350
$362$	−1.00428e14	−0.849099
$363$	−1.25077e14	−1.04158
$364$	−1.33758e13	−0.109714
$365$	−2.20498e14	−1.78154
$366$	−3.18281e13	−0.253318
$367$	−7.83559e13	−0.614339	−0.307170	−	0.951655i	$-0.599382\pi$
$367$	−7.83559e13	−0.614339	−0.307170	+	0.951655i	$0.599382\pi$
$368$	−4.49652e13	−0.347307
$369$	−9.88703e13	−0.752352
$370$	1.85225e14	1.38864
$371$	2.51341e13	0.185655
$372$	−1.47909e13	−0.107649
$373$	−6.45937e13	−0.463225	−0.231612	−	0.972808i	$-0.574400\pi$
$373$	−6.45937e13	−0.463225	−0.231612	+	0.972808i	$0.574400\pi$
$374$	−9.22711e13	−0.652037
$375$	−5.64688e13	−0.393221
$376$	2.47307e13	0.169708
$377$	−6.35872e13	−0.430024
$378$	3.57807e13	0.238476
$379$	−1.15994e14	−0.761937	−0.380968	−	0.924588i	$-0.624409\pi$
$379$	−1.15994e14	−0.761937	−0.380968	+	0.924588i	$0.624409\pi$
$380$	−1.42521e14	−0.922721
$381$	1.05363e14	0.672359
$382$	1.93804e14	1.21903
$383$	−8.62171e13	−0.534564	−0.267282	−	0.963618i	$-0.586126\pi$
$383$	−8.62171e13	−0.534564	−0.267282	+	0.963618i	$0.586126\pi$
$384$	7.43435e12	0.0454382
$385$	1.26273e14	0.760813
$386$	3.22456e13	0.191532
$387$	2.62392e13	0.153652
$388$	5.23663e13	0.302327
$389$	2.15803e14	1.22838	0.614192	−	0.789157i	$-0.289482\pi$
$389$	2.15803e14	1.22838	0.614192	+	0.789157i	$0.289482\pi$
$390$	−4.35102e13	−0.244194
$391$	−1.33073e14	−0.736407
$392$	−9.25615e12	−0.0505076
$393$	1.61136e14	0.867027
$394$	−6.63888e13	−0.352262
$395$	−3.38974e14	−1.77371
$396$	−1.24009e14	−0.639926
$397$	−5.69378e13	−0.289770	−0.144885	−	0.989449i	$-0.546281\pi$
$397$	−5.69378e13	−0.289770	−0.144885	+	0.989449i	$0.546281\pi$
$398$	−1.89019e13	−0.0948742
$399$	6.25957e13	0.309880
$400$	1.73549e13	0.0847407
$401$	1.74820e14	0.841970	0.420985	−	0.907067i	$-0.361684\pi$
$401$	1.74820e14	0.841970	0.420985	+	0.907067i	$0.361684\pi$
$402$	6.13310e13	0.291365
$403$	5.18836e13	0.243138
$404$	1.28555e14	0.594282
$405$	−7.02911e13	−0.320551
$406$	−4.40029e13	−0.197965
$407$	6.65169e14	2.95232
$408$	2.20017e13	0.0963441
$409$	−1.66731e14	−0.720341	−0.360171	−	0.932886i	$-0.617282\pi$
$409$	−1.66731e14	−0.720341	−0.360171	+	0.932886i	$0.617282\pi$
$410$	1.96284e14	0.836707
$411$	5.07985e13	0.213659
$412$	1.19472e14	0.495830
$413$	−5.37829e13	−0.220251
$414$	−1.78845e14	−0.722729
$415$	3.84249e14	1.53232
$416$	−2.60783e13	−0.102628
$417$	−2.89637e13	−0.112488
$418$	−5.11816e14	−1.96175
$419$	2.84625e14	1.07670	0.538352	−	0.842720i	$-0.319047\pi$
$419$	2.84625e14	1.07670	0.538352	+	0.842720i	$0.319047\pi$
$420$	−3.01094e13	−0.112417
$421$	1.70922e14	0.629865	0.314932	−	0.949114i	$-0.398018\pi$
$421$	1.70922e14	0.629865	0.314932	+	0.949114i	$0.398018\pi$
$422$	−1.65087e14	−0.600473
$423$	9.83640e13	0.353154
$424$	4.90030e13	0.173664
$425$	5.13612e13	0.179678
$426$	−3.03533e13	−0.104822
$427$	7.72606e13	0.263393
$428$	−1.10810e14	−0.372940
$429$	−1.56252e14	−0.519170
$430$	−5.20917e13	−0.170880
$431$	1.07374e13	0.0347755	0.0173877	−	0.999849i	$-0.494465\pi$
$431$	1.07374e13	0.0347755	0.0173877	+	0.999849i	$0.494465\pi$
$432$	6.97603e13	0.223073
$433$	7.58226e13	0.239395	0.119697	−	0.992810i	$-0.461808\pi$
$433$	7.58226e13	0.239395	0.119697	+	0.992810i	$0.461808\pi$
$434$	3.59039e13	0.111931
$435$	−1.43138e14	−0.440619
$436$	−1.22871e14	−0.373485
$437$	−7.38139e14	−2.21559
$438$	1.88812e14	0.559657
$439$	−8.52215e13	−0.249456	−0.124728	−	0.992191i	$-0.539806\pi$
$439$	−8.52215e13	−0.249456	−0.124728	+	0.992191i	$0.539806\pi$
$440$	2.46191e14	0.711676
$441$	−3.68155e13	−0.105104
$442$	−7.71777e13	−0.217605
$443$	−5.52093e14	−1.53742	−0.768708	−	0.639599i	$-0.779100\pi$
$443$	−5.52093e14	−1.53742	−0.768708	+	0.639599i	$0.779100\pi$
$444$	−1.58607e14	−0.436231
$445$	−8.10701e14	−2.20232
$446$	1.28087e14	0.343688
$447$	−2.75360e14	−0.729810
$448$	−1.80464e13	−0.0472456
$449$	5.57248e14	1.44110	0.720549	−	0.693404i	$-0.243890\pi$
$449$	5.57248e14	1.44110	0.720549	+	0.693404i	$0.243890\pi$
$450$	6.90275e13	0.176341
$451$	7.04885e14	1.77888
$452$	3.42057e13	0.0852781
$453$	−2.88642e14	−0.710919
$454$	−2.94535e14	−0.716688
$455$	1.05618e14	0.253907
$456$	1.22041e14	0.289866
$457$	4.61614e14	1.08328	0.541639	−	0.840611i	$-0.317804\pi$
$457$	4.61614e14	1.08328	0.541639	+	0.840611i	$0.317804\pi$
$458$	1.66280e14	0.385550
$459$	2.06453e14	0.472990
$460$	3.55056e14	0.803763
$461$	−4.68571e14	−1.04814	−0.524071	−	0.851675i	$-0.675587\pi$
$461$	−4.68571e14	−1.04814	−0.524071	+	0.851675i	$0.675587\pi$
$462$	−1.08128e14	−0.239004
$463$	−8.59462e14	−1.87729	−0.938645	−	0.344885i	$-0.887918\pi$
$463$	−8.59462e14	−1.87729	−0.938645	+	0.344885i	$0.887918\pi$
$464$	−8.57909e13	−0.185179
$465$	1.16792e14	0.249128
$466$	1.22589e14	0.258422
$467$	4.29547e14	0.894887	0.447443	−	0.894312i	$-0.352335\pi$
$467$	4.29547e14	0.894887	0.447443	+	0.894312i	$0.352335\pi$
$468$	−1.03724e14	−0.213563
$469$	−1.48877e14	−0.302954
$470$	−1.95279e14	−0.392750
$471$	−1.32029e14	−0.262454
$472$	−1.04858e14	−0.206026
$473$	−1.87069e14	−0.363300
$474$	2.90262e14	0.557198
$475$	2.84894e14	0.540590
$476$	−5.34076e13	−0.100176
$477$	1.94905e14	0.361387
$478$	−2.67457e14	−0.490231
$479$	4.15085e14	0.752128	0.376064	−	0.926594i	$-0.377277\pi$
$479$	4.15085e14	0.752128	0.376064	+	0.926594i	$0.377277\pi$
$480$	−5.87033e13	−0.105156
$481$	5.56363e14	0.985281
$482$	7.88933e14	1.38128
$483$	−1.55941e14	−0.269930
$484$	5.91949e14	1.01306
$485$	−4.13496e14	−0.699667
$486$	4.37321e14	0.731646
$487$	4.01530e14	0.664215	0.332108	−	0.943241i	$-0.392240\pi$
$487$	4.01530e14	0.664215	0.332108	+	0.943241i	$0.392240\pi$
$488$	1.50632e14	0.246382
$489$	3.33228e14	0.538942
$490$	7.30886e13	0.116888
$491$	−7.53913e14	−1.19227	−0.596133	−	0.802886i	$-0.703297\pi$
$491$	−7.53913e14	−1.19227	−0.596133	+	0.802886i	$0.703297\pi$
$492$	−1.68077e14	−0.262846
$493$	−2.53895e14	−0.392642
$494$	−4.28095e14	−0.654699
$495$	9.79203e14	1.48096
$496$	7.00006e13	0.104701
$497$	7.36805e13	0.108991
$498$	−3.29031e14	−0.481366
$499$	3.63198e14	0.525521	0.262761	−	0.964861i	$-0.415367\pi$
$499$	3.63198e14	0.525521	0.262761	+	0.964861i	$0.415367\pi$
$500$	2.67248e14	0.382455
$501$	−2.44186e14	−0.345632
$502$	−7.72830e14	−1.08197
$503$	−1.83946e14	−0.254722	−0.127361	−	0.991856i	$-0.540651\pi$
$503$	−1.83946e14	−0.254722	−0.127361	+	0.991856i	$0.540651\pi$
$504$	−7.17779e13	−0.0983157
$505$	−1.01510e15	−1.37533
$506$	1.27506e15	1.70884
$507$	2.57074e14	0.340812
$508$	−4.98649e14	−0.653951
$509$	−1.03413e15	−1.34162	−0.670808	−	0.741631i	$-0.734052\pi$
$509$	−1.03413e15	−1.34162	−0.670808	+	0.741631i	$0.734052\pi$
$510$	−1.73730e14	−0.222966
$511$	−4.58328e14	−0.581917
$512$	−3.51844e13	−0.0441942
$513$	1.14517e15	1.42306
$514$	−9.12301e13	−0.112161
$515$	−9.43381e14	−1.14749
$516$	4.46059e13	0.0536808
$517$	−7.01275e14	−0.835008
$518$	3.85008e14	0.453582
$519$	7.72836e14	0.900880
$520$	2.05920e14	0.237509
$521$	6.77847e14	0.773614	0.386807	−	0.922161i	$-0.373578\pi$
$521$	6.77847e14	0.773614	0.386807	+	0.922161i	$0.373578\pi$
$522$	−3.41226e14	−0.385349
$523$	2.27928e14	0.254706	0.127353	−	0.991857i	$-0.459352\pi$
$523$	2.27928e14	0.254706	0.127353	+	0.991857i	$0.459352\pi$
$524$	−7.62603e14	−0.843289
$525$	6.01874e13	0.0658611
$526$	−3.03036e14	−0.328150
$527$	2.07164e14	0.222002
$528$	−2.10812e14	−0.223568
$529$	8.86073e14	0.929958
$530$	−3.86939e14	−0.401906
$531$	−4.17065e14	−0.428730
$532$	−2.96245e14	−0.301396
$533$	5.89582e14	0.593669
$534$	6.94200e14	0.691844
$535$	8.74982e14	0.863085
$536$	−2.90260e14	−0.283387
$537$	−1.42239e13	−0.0137455
$538$	−1.07327e15	−1.02661
$539$	2.62472e14	0.248511
$540$	−5.50843e14	−0.516252
$541$	−1.38148e15	−1.28162	−0.640810	−	0.767700i	$-0.721401\pi$
$541$	−1.38148e15	−1.28162	−0.640810	+	0.767700i	$0.721401\pi$
$542$	3.89202e14	0.357420
$543$	−6.79046e14	−0.617305
$544$	−1.04127e14	−0.0937063
$545$	9.70215e14	0.864346
$546$	−9.04403e13	−0.0797632
$547$	−1.69384e15	−1.47891	−0.739455	−	0.673206i	$-0.764917\pi$
$547$	−1.69384e15	−1.47891	−0.739455	+	0.673206i	$0.764917\pi$
$548$	−2.40413e14	−0.207809
$549$	5.99127e14	0.512709
$550$	−4.92124e14	−0.416946
$551$	−1.40832e15	−1.18132
$552$	−3.04033e14	−0.252496
$553$	−7.04591e14	−0.579360
$554$	1.34581e15	1.09567
$555$	1.25240e15	1.00956
$556$	1.37076e14	0.109408
$557$	2.08073e15	1.64442	0.822210	−	0.569185i	$-0.192741\pi$
$557$	2.08073e15	1.64442	0.822210	+	0.569185i	$0.192741\pi$
$558$	2.78421e14	0.217878
$559$	−1.56469e14	−0.121245
$560$	1.42498e14	0.109339
$561$	−6.23891e14	−0.474038
$562$	−4.23326e14	−0.318512
$563$	6.55504e14	0.488404	0.244202	−	0.969724i	$-0.421474\pi$
$563$	6.55504e14	0.488404	0.244202	+	0.969724i	$0.421474\pi$
$564$	1.67216e14	0.123380
$565$	−2.70096e14	−0.197357
$566$	−3.68175e14	−0.266418
$567$	−1.46107e14	−0.104704
$568$	1.43652e14	0.101952
$569$	−9.67393e14	−0.679964	−0.339982	−	0.940432i	$-0.610421\pi$
$569$	−9.67393e14	−0.679964	−0.339982	+	0.940432i	$0.610421\pi$
$570$	−9.63659e14	−0.670829
$571$	1.88719e14	0.130112	0.0650558	−	0.997882i	$-0.479277\pi$
$571$	1.88719e14	0.130112	0.0650558	+	0.997882i	$0.479277\pi$
$572$	7.39488e14	0.504956
$573$	1.31041e15	0.886249
$574$	4.07996e14	0.273300
$575$	−7.09739e14	−0.470897
$576$	−1.39943e14	−0.0919659
$577$	2.57664e15	1.67721	0.838604	−	0.544741i	$-0.183372\pi$
$577$	2.57664e15	1.67721	0.838604	+	0.544741i	$0.183372\pi$
$578$	7.88541e14	0.508418
$579$	2.18029e14	0.139246
$580$	6.77424e14	0.428555
$581$	7.98700e14	0.500513
$582$	3.54075e14	0.219795
$583$	−1.38955e15	−0.854473
$584$	−8.93585e14	−0.544334
$585$	8.19027e14	0.494244
$586$	1.48905e15	0.890170
$587$	−1.09797e13	−0.00650251	−0.00325126	−	0.999995i	$-0.501035\pi$
$587$	−1.09797e13	−0.00650251	−0.00325126	+	0.999995i	$0.501035\pi$
$588$	−6.25855e13	−0.0367196
$589$	1.14911e15	0.667927
$590$	8.27986e14	0.476801
$591$	−4.48888e14	−0.256098
$592$	7.50636e14	0.424287
$593$	−2.85138e13	−0.0159681	−0.00798407	−	0.999968i	$-0.502541\pi$
$593$	−2.85138e13	−0.0159681	−0.00798407	+	0.999968i	$0.502541\pi$
$594$	−1.97816e15	−1.09758
$595$	4.21718e14	0.231835
$596$	1.30319e15	0.709828
$597$	−1.27805e14	−0.0689746
$598$	1.06649e15	0.570294
$599$	−1.59528e15	−0.845260	−0.422630	−	0.906302i	$-0.638893\pi$
$599$	−1.59528e15	−0.845260	−0.422630	+	0.906302i	$0.638893\pi$
$600$	1.17345e14	0.0616074
$601$	1.81502e15	0.944218	0.472109	−	0.881540i	$-0.343493\pi$
$601$	1.81502e15	0.944218	0.472109	+	0.881540i	$0.343493\pi$
$602$	−1.08278e14	−0.0558160
$603$	−1.15448e15	−0.589715
$604$	1.36605e15	0.691455
$605$	−4.67416e15	−2.34449
$606$	8.69227e14	0.432050
$607$	−1.94277e15	−0.956938	−0.478469	−	0.878104i	$-0.658808\pi$
$607$	−1.94277e15	−0.956938	−0.478469	+	0.878104i	$0.658808\pi$
$608$	−5.77578e14	−0.281930
$609$	−2.97526e14	−0.143923
$610$	−1.18943e15	−0.570195
$611$	−5.86562e14	−0.278668
$612$	−4.14156e14	−0.194998
$613$	5.23832e14	0.244433	0.122216	−	0.992503i	$-0.461000\pi$
$613$	5.23832e14	0.244433	0.122216	+	0.992503i	$0.461000\pi$
$614$	−6.53746e14	−0.302331
$615$	1.32717e15	0.608296
$616$	5.11732e14	0.232460
$617$	1.94074e15	0.873772	0.436886	−	0.899517i	$-0.356081\pi$
$617$	1.94074e15	0.873772	0.436886	+	0.899517i	$0.356081\pi$
$618$	8.07813e14	0.360474
$619$	−3.19948e15	−1.41508	−0.707540	−	0.706673i	$-0.750195\pi$
$619$	−3.19948e15	−1.41508	−0.707540	+	0.706673i	$0.750195\pi$
$620$	−5.52740e14	−0.242307
$621$	−2.85289e15	−1.23960
$622$	−6.78805e14	−0.292347
$623$	−1.68512e15	−0.719362
$624$	−1.76328e14	−0.0746116
$625$	−2.91840e15	−1.22407
$626$	−1.54203e15	−0.641113
$627$	−3.46065e15	−1.42622
$628$	6.24850e14	0.255269
$629$	2.22148e15	0.899630
$630$	5.66774e14	0.227529
$631$	1.84535e15	0.734376	0.367188	−	0.930147i	$-0.380321\pi$
$631$	1.84535e15	0.734376	0.367188	+	0.930147i	$0.380321\pi$
$632$	−1.37372e15	−0.541942
$633$	−1.11623e15	−0.436551
$634$	−2.08511e15	−0.808420
$635$	3.93745e15	1.51342
$636$	3.31334e14	0.126256
$637$	2.19538e14	0.0829358
$638$	2.43273e15	0.911130
$639$	5.71364e14	0.212157
$640$	2.77824e14	0.102277
$641$	1.60601e15	0.586178	0.293089	−	0.956085i	$-0.405317\pi$
$641$	1.60601e15	0.586178	0.293089	+	0.956085i	$0.405317\pi$
$642$	−7.49244e14	−0.271132
$643$	5.05967e15	1.81536	0.907678	−	0.419666i	$-0.137853\pi$
$643$	5.05967e15	1.81536	0.907678	+	0.419666i	$0.137853\pi$
$644$	7.38018e14	0.262540
$645$	−3.52218e14	−0.124232
$646$	−1.70932e15	−0.597785
$647$	−9.70805e14	−0.336634	−0.168317	−	0.985733i	$-0.553833\pi$
$647$	−9.70805e14	−0.336634	−0.168317	+	0.985733i	$0.553833\pi$
$648$	−2.84860e14	−0.0979418
$649$	2.97342e15	1.01370
$650$	−4.11624e14	−0.139148
$651$	2.42765e14	0.0813748
$652$	−1.57706e15	−0.524186
$653$	−4.87338e14	−0.160623	−0.0803115	−	0.996770i	$-0.525592\pi$
$653$	−4.87338e14	−0.160623	−0.0803115	+	0.996770i	$0.525592\pi$
$654$	−8.30792e14	−0.271528
$655$	6.02168e15	1.95160
$656$	7.95455e14	0.255649
$657$	−3.55416e15	−1.13273
$658$	−4.05906e14	−0.128287
$659$	−1.24361e15	−0.389775	−0.194887	−	0.980826i	$-0.562434\pi$
$659$	−1.24361e15	−0.389775	−0.194887	+	0.980826i	$0.562434\pi$
$660$	1.66462e15	0.517397
$661$	−4.32731e15	−1.33386	−0.666930	−	0.745121i	$-0.732392\pi$
$661$	−4.32731e15	−1.33386	−0.666930	+	0.745121i	$0.732392\pi$
$662$	−1.59391e15	−0.487243
$663$	−5.21837e14	−0.158201
$664$	1.55720e15	0.468187
$665$	2.33922e15	0.697512
$666$	2.98559e15	0.882921
$667$	3.50848e15	1.02903
$668$	1.15565e15	0.336168
$669$	8.66063e14	0.249865
$670$	2.29196e15	0.655835
$671$	−4.27141e15	−1.21226
$672$	−1.22021e14	−0.0343481
$673$	5.35005e15	1.49374	0.746869	−	0.664971i	$-0.231556\pi$
$673$	5.35005e15	1.49374	0.746869	+	0.664971i	$0.231556\pi$
$674$	−3.24292e15	−0.898063
$675$	1.10111e15	0.302454
$676$	−1.21665e15	−0.331480
$677$	2.64289e15	0.714234	0.357117	−	0.934060i	$-0.383760\pi$
$677$	2.64289e15	0.714234	0.357117	+	0.934060i	$0.383760\pi$
$678$	2.31282e14	0.0619982
$679$	−8.59492e14	−0.228538
$680$	8.22209e14	0.216862
$681$	−1.99150e15	−0.521041
$682$	−1.98497e15	−0.515158
$683$	3.61158e15	0.929787	0.464894	−	0.885367i	$-0.346093\pi$
$683$	3.61158e15	0.929787	0.464894	+	0.885367i	$0.346093\pi$
$684$	−2.29727e15	−0.586682
$685$	1.89835e15	0.480926
$686$	1.51922e14	0.0381802
$687$	1.12431e15	0.280299
$688$	−2.11105e14	−0.0522111
$689$	−1.16225e15	−0.285165
$690$	2.40071e15	0.584345
$691$	−5.42252e15	−1.30940	−0.654700	−	0.755889i	$-0.727205\pi$
$691$	−5.42252e15	−1.30940	−0.654700	+	0.755889i	$0.727205\pi$
$692$	−3.65758e15	−0.876214
$693$	2.03537e15	0.483739
$694$	−5.20637e13	−0.0122760
$695$	−1.08238e15	−0.253200
$696$	−5.80076e14	−0.134628
$697$	2.35412e15	0.542061
$698$	−2.07240e15	−0.473444
$699$	8.28888e14	0.187876
$700$	−2.84847e14	−0.0640579
$701$	−2.11026e15	−0.470855	−0.235427	−	0.971892i	$-0.575649\pi$
$701$	−2.11026e15	−0.470855	−0.235427	+	0.971892i	$0.575649\pi$
$702$	−1.65458e15	−0.366297
$703$	1.23223e16	2.70668
$704$	9.97706e14	0.217447
$705$	−1.32038e15	−0.285534
$706$	4.41226e15	0.946751
$707$	−2.10999e15	−0.449235
$708$	−7.09001e14	−0.149783
$709$	−9.03782e15	−1.89456	−0.947282	−	0.320401i	$-0.896182\pi$
$709$	−9.03782e15	−1.89456	−0.947282	+	0.320401i	$0.896182\pi$
$710$	−1.13431e15	−0.235945
$711$	−5.46383e15	−1.12775
$712$	−3.28542e15	−0.672902
$713$	−2.86272e15	−0.581817
$714$	−3.61116e14	−0.0728293
$715$	−5.83916e15	−1.16860
$716$	6.73171e13	0.0133691
$717$	−1.80841e15	−0.356404
$718$	7.16584e14	0.140147
$719$	−3.12729e15	−0.606959	−0.303479	−	0.952838i	$-0.598148\pi$
$719$	−3.12729e15	−0.606959	−0.303479	+	0.952838i	$0.598148\pi$
$720$	1.10502e15	0.212834
$721$	−1.96091e15	−0.374812
$722$	−5.75371e15	−1.09142
$723$	5.33437e15	1.00421
$724$	3.21370e15	0.600404
$725$	−1.35414e15	−0.251075
$726$	4.00247e15	0.736506
$727$	6.29576e14	0.114976	0.0574882	−	0.998346i	$-0.481691\pi$
$727$	6.29576e14	0.114976	0.0574882	+	0.998346i	$0.481691\pi$
$728$	4.28025e14	0.0775794
$729$	1.41697e15	0.254894
$730$	7.05595e15	1.25974
$731$	−6.24759e14	−0.110705
$732$	1.01850e15	0.179123
$733$	−5.71901e14	−0.0998272	−0.0499136	−	0.998754i	$-0.515895\pi$
$733$	−5.71901e14	−0.0998272	−0.0499136	+	0.998754i	$0.515895\pi$
$734$	2.50739e15	0.434403
$735$	4.94189e14	0.0849792
$736$	1.43889e15	0.245583
$737$	8.23076e15	1.39434
$738$	3.16385e15	0.531993
$739$	−7.10258e15	−1.18542	−0.592709	−	0.805417i	$-0.701942\pi$
$739$	−7.10258e15	−1.18542	−0.592709	+	0.805417i	$0.701942\pi$
$740$	−5.92719e15	−0.981916
$741$	−2.89456e15	−0.475974
$742$	−8.04290e14	−0.131278
$743$	2.02324e15	0.327800	0.163900	−	0.986477i	$-0.447593\pi$
$743$	2.02324e15	0.327800	0.163900	+	0.986477i	$0.447593\pi$
$744$	4.73309e14	0.0761191
$745$	−1.02903e16	−1.64273
$746$	2.06700e15	0.327549
$747$	6.19361e15	0.974273
$748$	2.95268e15	0.461059
$749$	1.81874e15	0.281916
$750$	1.80700e15	0.278049
$751$	1.11790e15	0.170759	0.0853793	−	0.996349i	$-0.472790\pi$
$751$	1.11790e15	0.170759	0.0853793	+	0.996349i	$0.472790\pi$
$752$	−7.91381e14	−0.120002
$753$	−5.22549e15	−0.786602
$754$	2.03479e15	0.304073
$755$	−1.07866e16	−1.60021
$756$	−1.14498e15	−0.168628
$757$	−1.66402e15	−0.243294	−0.121647	−	0.992573i	$-0.538818\pi$
$757$	−1.66402e15	−0.243294	−0.121647	+	0.992573i	$0.538818\pi$
$758$	3.71180e15	0.538770
$759$	8.62131e15	1.24235
$760$	4.56069e15	0.652462
$761$	−4.11155e15	−0.583969	−0.291984	−	0.956423i	$-0.594316\pi$
$761$	−4.11155e15	−0.583969	−0.291984	+	0.956423i	$0.594316\pi$
$762$	−3.37162e15	−0.475430
$763$	2.01669e15	0.282328
$764$	−6.20173e15	−0.861985
$765$	3.27026e15	0.451279
$766$	2.75895e15	0.377994
$767$	2.48704e15	0.338304
$768$	−2.37899e14	−0.0321297
$769$	4.51069e15	0.604851	0.302425	−	0.953173i	$-0.402204\pi$
$769$	4.51069e15	0.604851	0.302425	+	0.953173i	$0.402204\pi$
$770$	−4.04075e15	−0.537976
$771$	−6.16852e14	−0.0815422
$772$	−1.03186e15	−0.135433
$773$	1.07683e16	1.40334	0.701668	−	0.712504i	$-0.252439\pi$
$773$	1.07683e16	1.40334	0.701668	+	0.712504i	$0.252439\pi$
$774$	−8.39653e14	−0.108649
$775$	1.10490e15	0.141959
$776$	−1.67572e15	−0.213778
$777$	2.60323e15	0.329759
$778$	−6.90569e15	−0.868599
$779$	1.30580e16	1.63087
$780$	1.39233e15	0.172672
$781$	−4.07347e15	−0.501631
$782$	4.25834e15	0.520718
$783$	−5.44314e15	−0.660937
$784$	2.96197e14	0.0357143
$785$	−4.93395e15	−0.590761
$786$	−5.15634e15	−0.613081
$787$	1.46938e16	1.73489	0.867447	−	0.497530i	$-0.165760\pi$
$787$	1.46938e16	1.73489	0.867447	+	0.497530i	$0.165760\pi$
$788$	2.12444e15	0.249087
$789$	−2.04898e15	−0.238569
$790$	1.08472e16	1.25420
$791$	−5.61422e14	−0.0644642
$792$	3.96829e15	0.452496
$793$	−3.57270e15	−0.404570
$794$	1.82201e15	0.204898
$795$	−2.61629e15	−0.292190
$796$	6.04860e14	0.0670862
$797$	1.95115e15	0.214917	0.107458	−	0.994210i	$-0.465729\pi$
$797$	1.95115e15	0.214917	0.107458	+	0.994210i	$0.465729\pi$
$798$	−2.00306e15	−0.219118
$799$	−2.34206e15	−0.254443
$800$	−5.55356e14	−0.0599207
$801$	−1.30675e16	−1.40027
$802$	−5.59424e15	−0.595363
$803$	2.53390e16	2.67826
$804$	−1.96259e15	−0.206026
$805$	−5.82756e15	−0.607588
$806$	−1.66028e15	−0.171924
$807$	−7.25691e15	−0.746358
$808$	−4.11377e15	−0.420221
$809$	2.18113e15	0.221292	0.110646	−	0.993860i	$-0.464708\pi$
$809$	2.18113e15	0.221292	0.110646	+	0.993860i	$0.464708\pi$
$810$	2.24931e15	0.226664
$811$	−1.61777e16	−1.61921	−0.809604	−	0.586977i	$-0.800318\pi$
$811$	−1.61777e16	−1.61921	−0.809604	+	0.586977i	$0.800318\pi$
$812$	1.40809e15	0.139982
$813$	2.63159e15	0.259849
$814$	−2.12854e16	−2.08760
$815$	1.24528e16	1.21311
$816$	−7.04054e14	−0.0681256
$817$	−3.46546e15	−0.333073
$818$	5.33539e15	0.509358
$819$	1.70243e15	0.161439
$820$	−6.28109e15	−0.591641
$821$	1.81865e16	1.70162	0.850810	−	0.525473i	$-0.176112\pi$
$821$	1.81865e16	1.70162	0.850810	+	0.525473i	$0.176112\pi$
$822$	−1.62555e15	−0.151080
$823$	−1.04567e16	−0.965378	−0.482689	−	0.875792i	$-0.660340\pi$
$823$	−1.04567e16	−0.965378	−0.482689	+	0.875792i	$0.660340\pi$
$824$	−3.82312e15	−0.350605
$825$	−3.32750e15	−0.303125
$826$	1.72105e15	0.155741
$827$	−2.70872e15	−0.243492	−0.121746	−	0.992561i	$-0.538849\pi$
$827$	−2.70872e15	−0.243492	−0.121746	+	0.992561i	$0.538849\pi$
$828$	5.72305e15	0.511047
$829$	−5.53825e15	−0.491273	−0.245637	−	0.969362i	$-0.578997\pi$
$829$	−5.53825e15	−0.491273	−0.245637	+	0.969362i	$0.578997\pi$
$830$	−1.22960e16	−1.08351
$831$	9.09970e15	0.796565
$832$	8.34504e14	0.0725688
$833$	8.76584e14	0.0757262
$834$	9.26838e14	0.0795409
$835$	−9.12529e15	−0.777985
$836$	1.63781e16	1.38717
$837$	4.44130e15	0.373698
$838$	−9.10801e15	−0.761344
$839$	−1.22159e16	−1.01446	−0.507231	−	0.861810i	$-0.669331\pi$
$839$	−1.22159e16	−1.01446	−0.507231	+	0.861810i	$0.669331\pi$
$840$	9.63502e14	0.0794907
$841$	−5.50655e15	−0.451338
$842$	−5.46951e15	−0.445382
$843$	−2.86232e15	−0.231562
$844$	5.28278e15	0.424599
$845$	9.60692e15	0.767136
$846$	−3.14765e15	−0.249718
$847$	−9.71571e15	−0.765801
$848$	−1.56810e15	−0.122799
$849$	−2.48942e15	−0.193689
$850$	−1.64356e15	−0.127052
$851$	−3.06977e16	−2.35773
$852$	9.71305e14	0.0741204
$853$	1.91918e16	1.45511	0.727556	−	0.686048i	$-0.240656\pi$
$853$	1.91918e16	1.45511	0.727556	+	0.686048i	$0.240656\pi$
$854$	−2.47234e15	−0.186247
$855$	1.81397e16	1.35774
$856$	3.54593e15	0.263709
$857$	−2.25188e16	−1.66399	−0.831994	−	0.554785i	$-0.812801\pi$
$857$	−2.25188e16	−1.66399	−0.831994	+	0.554785i	$0.812801\pi$
$858$	5.00005e15	0.367109
$859$	−1.54652e16	−1.12822	−0.564111	−	0.825699i	$-0.690781\pi$
$859$	−1.54652e16	−1.12822	−0.564111	+	0.825699i	$0.690781\pi$
$860$	1.66693e15	0.120831
$861$	2.75866e15	0.198693
$862$	−3.43596e14	−0.0245900
$863$	5.42996e15	0.386133	0.193067	−	0.981186i	$-0.438157\pi$
$863$	5.42996e15	0.386133	0.193067	+	0.981186i	$0.438157\pi$
$864$	−2.23233e15	−0.157737
$865$	2.88811e16	2.02780
$866$	−2.42632e15	−0.169278
$867$	5.33172e15	0.369626
$868$	−1.14893e15	−0.0791468
$869$	3.89538e16	2.66650
$870$	4.58041e15	0.311565
$871$	6.88439e15	0.465335
$872$	3.93187e15	0.264094
$873$	−6.66503e15	−0.444860
$874$	2.36204e16	1.56666
$875$	−4.38637e15	−0.289109
$876$	−6.04198e15	−0.395737
$877$	4.71598e15	0.306955	0.153477	−	0.988152i	$-0.450953\pi$
$877$	4.71598e15	0.306955	0.153477	+	0.988152i	$0.450953\pi$
$878$	2.72709e15	0.176392
$879$	1.00682e16	0.647164
$880$	−7.87811e15	−0.503231
$881$	5.81396e15	0.369066	0.184533	−	0.982826i	$-0.440923\pi$
$881$	5.81396e15	0.369066	0.184533	+	0.982826i	$0.440923\pi$
$882$	1.17810e15	0.0743197
$883$	−2.78891e16	−1.74844	−0.874219	−	0.485532i	$-0.838626\pi$
$883$	−2.78891e16	−1.74844	−0.874219	+	0.485532i	$0.838626\pi$
$884$	2.46969e15	0.153870
$885$	5.59843e15	0.346640
$886$	1.76670e16	1.08712
$887$	−4.02123e15	−0.245911	−0.122956	−	0.992412i	$-0.539237\pi$
$887$	−4.02123e15	−0.245911	−0.122956	+	0.992412i	$0.539237\pi$
$888$	5.07543e15	0.308462
$889$	8.18438e15	0.494340
$890$	2.59424e16	1.55728
$891$	8.07762e15	0.481899
$892$	−4.09880e15	−0.243024
$893$	−1.29911e16	−0.765533
$894$	8.81152e15	0.516053
$895$	−5.31551e14	−0.0309398
$896$	5.77484e14	0.0334077
$897$	7.21106e15	0.414611
$898$	−1.78319e16	−1.01901
$899$	−5.46189e15	−0.310217
$900$	−2.20888e15	−0.124692
$901$	−4.64072e15	−0.260375
$902$	−2.25563e16	−1.25786
$903$	−7.32121e14	−0.0405789
$904$	−1.09458e15	−0.0603007
$905$	−2.53761e16	−1.38950
$906$	9.23656e15	0.502696
$907$	3.22341e16	1.74372	0.871858	−	0.489759i	$-0.162915\pi$
$907$	3.22341e16	1.74372	0.871858	+	0.489759i	$0.162915\pi$
$908$	9.42513e15	0.506775
$909$	−1.63622e16	−0.874459
$910$	−3.37978e15	−0.179540
$911$	−1.55782e16	−0.822559	−0.411280	−	0.911509i	$-0.634918\pi$
$911$	−1.55782e16	−0.822559	−0.411280	+	0.911509i	$0.634918\pi$
$912$	−3.90530e15	−0.204966
$913$	−4.41567e16	−2.30360
$914$	−1.47717e16	−0.765993
$915$	−8.04230e15	−0.414538
$916$	−5.32097e15	−0.272625
$917$	1.25167e16	0.637466
$918$	−6.60650e15	−0.334454
$919$	4.62791e15	0.232889	0.116445	−	0.993197i	$-0.462850\pi$
$919$	4.62791e15	0.232889	0.116445	+	0.993197i	$0.462850\pi$
$920$	−1.13618e16	−0.568346
$921$	−4.42030e15	−0.219798
$922$	1.49943e16	0.741148
$923$	−3.40715e15	−0.167410
$924$	3.46008e15	0.169001
$925$	1.18482e16	0.575270
$926$	2.75028e16	1.32744
$927$	−1.52061e16	−0.729592
$928$	2.74531e15	0.130942
$929$	−3.72909e15	−0.176814	−0.0884070	−	0.996084i	$-0.528178\pi$
$929$	−3.72909e15	−0.176814	−0.0884070	+	0.996084i	$0.528178\pi$
$930$	−3.73735e15	−0.176160
$931$	4.86230e15	0.227834
$932$	−3.92286e15	−0.182732
$933$	−4.58974e15	−0.212539
$934$	−1.37455e16	−0.632781
$935$	−2.33150e16	−1.06702
$936$	3.31917e15	0.151012
$937$	2.23057e16	1.00890	0.504450	−	0.863441i	$-0.331695\pi$
$937$	2.23057e16	1.00890	0.504450	+	0.863441i	$0.331695\pi$
$938$	4.76406e15	0.214221
$939$	−1.04265e16	−0.466097
$940$	6.24892e15	0.277716
$941$	1.10985e16	0.490368	0.245184	−	0.969477i	$-0.421152\pi$
$941$	1.10985e16	0.490368	0.245184	+	0.969477i	$0.421152\pi$
$942$	4.22492e15	0.185583
$943$	−3.25306e16	−1.42062
$944$	3.35547e15	0.145683
$945$	9.04103e15	0.390250
$946$	5.98621e15	0.256892
$947$	−2.17732e16	−0.928959	−0.464479	−	0.885584i	$-0.653759\pi$
$947$	−2.17732e16	−0.928959	−0.464479	+	0.885584i	$0.653759\pi$
$948$	−9.28838e15	−0.393998
$949$	2.11941e16	0.893821
$950$	−9.11660e15	−0.382255
$951$	−1.40985e16	−0.587731
$952$	1.70904e15	0.0708353
$953$	1.18179e16	0.487001	0.243500	−	0.969901i	$-0.421704\pi$
$953$	1.18179e16	0.487001	0.243500	+	0.969901i	$0.421704\pi$
$954$	−6.23696e15	−0.255539
$955$	4.89702e16	1.99487
$956$	8.55863e15	0.346646
$957$	1.64489e16	0.662402
$958$	−1.32827e16	−0.531835
$959$	3.94591e15	0.157089
$960$	1.87851e15	0.0743568
$961$	−2.09519e16	−0.824602
$962$	−1.78036e16	−0.696699
$963$	1.41036e16	0.548764
$964$	−2.52459e16	−0.976712
$965$	8.14779e15	0.313429
$966$	4.99011e15	0.190869
$967$	−7.39456e15	−0.281233	−0.140617	−	0.990064i	$-0.544908\pi$
$967$	−7.39456e15	−0.281233	−0.140617	+	0.990064i	$0.544908\pi$
$968$	−1.89424e16	−0.716341
$969$	−1.15576e16	−0.434597
$970$	1.32319e16	0.494739
$971$	−1.35867e14	−0.00505138	−0.00252569	−	0.999997i	$-0.500804\pi$
$971$	−1.35867e14	−0.00505138	−0.00252569	+	0.999997i	$0.500804\pi$
$972$	−1.39943e16	−0.517352
$973$	−2.24983e15	−0.0827047
$974$	−1.28490e16	−0.469671
$975$	−2.78320e15	−0.101162
$976$	−4.82023e15	−0.174218
$977$	2.08670e16	0.749963	0.374982	−	0.927032i	$-0.377649\pi$
$977$	2.08670e16	0.749963	0.374982	+	0.927032i	$0.377649\pi$
$978$	−1.06633e16	−0.381090
$979$	9.31632e16	3.31085
$980$	−2.33884e15	−0.0826525
$981$	1.56387e16	0.549566
$982$	2.41252e16	0.843059
$983$	5.85669e15	0.203520	0.101760	−	0.994809i	$-0.467553\pi$
$983$	5.85669e15	0.203520	0.101760	+	0.994809i	$0.467553\pi$
$984$	5.37847e15	0.185860
$985$	−1.67751e16	−0.576454
$986$	8.12465e15	0.277640
$987$	−2.74454e15	−0.0932663
$988$	1.36990e16	0.462942
$989$	8.63329e15	0.290133
$990$	−3.13345e16	−1.04720
$991$	1.01546e16	0.337488	0.168744	−	0.985660i	$-0.446029\pi$
$991$	1.01546e16	0.337488	0.168744	+	0.985660i	$0.446029\pi$
$992$	−2.24002e15	−0.0740351
$993$	−1.07772e16	−0.354231
$994$	−2.35778e15	−0.0770686
$995$	−4.77611e15	−0.155256
$996$	1.05290e16	0.340377
$997$	−3.51694e16	−1.13068	−0.565342	−	0.824857i	$-0.691256\pi$
$997$	−3.51694e16	−1.13068	−0.565342	+	0.824857i	$0.691256\pi$
$998$	−1.16223e16	−0.371600
$999$	4.76253e16	1.51436

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.12.a.c.1.1	✓	2
3.2	odd	2		126.12.a.l.1.2		2
4.3	odd	2		112.12.a.c.1.2		2
7.2	even	3		98.12.c.i.67.2		4
7.3	odd	6		98.12.c.k.79.1		4
7.4	even	3		98.12.c.i.79.2		4
7.5	odd	6		98.12.c.k.67.1		4
7.6	odd	2		98.12.a.c.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.12.a.c.1.1	✓	2	1.1	even	1	trivial
98.12.a.c.1.2		2	7.6	odd	2
98.12.c.i.67.2		4	7.2	even	3
98.12.c.i.79.2		4	7.4	even	3
98.12.c.k.67.1		4	7.5	odd	6
98.12.c.k.79.1		4	7.3	odd	6
112.12.a.c.1.2		2	4.3	odd	2
126.12.a.l.1.2		2	3.2	odd	2

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:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	14.a (trivial)

\(f(q)\)	\(=\)	\(q-32.0000 q^{2} -216.368 q^{3} +1024.00 q^{4} -8085.73 q^{5} +6923.78 q^{6} -16807.0 q^{7} -32768.0 q^{8} -130332. q^{9} +O(q^{10})\)	\(q-32.0000 q^{2} -216.368 q^{3} +1024.00 q^{4} -8085.73 q^{5} +6923.78 q^{6} -16807.0 q^{7} -32768.0 q^{8} -130332. q^{9} +258743. q^{10} +929186. q^{11} -221561. q^{12} +777193. q^{13} +537824. q^{14} +1.74949e6 q^{15} +1.04858e6 q^{16} +3.10322e6 q^{17} +4.17062e6 q^{18} +1.72132e7 q^{19} -8.27979e6 q^{20} +3.63650e6 q^{21} -2.97340e7 q^{22} -4.28822e7 q^{23} +7.08995e6 q^{24} +1.65509e7 q^{25} -2.48702e7 q^{26} +6.65286e7 q^{27} -1.72104e7 q^{28} -8.18166e7 q^{29} -5.59838e7 q^{30} +6.67578e7 q^{31} -3.35544e7 q^{32} -2.01046e8 q^{33} -9.93031e7 q^{34} +1.35897e8 q^{35} -1.33460e8 q^{36} +7.15862e8 q^{37} -5.50822e8 q^{38} -1.68160e8 q^{39} +2.64953e8 q^{40} +7.58605e8 q^{41} -1.16368e8 q^{42} -2.01326e8 q^{43} +9.51487e8 q^{44} +1.05383e9 q^{45} +1.37223e9 q^{46} -7.54720e8 q^{47} -2.26878e8 q^{48} +2.82475e8 q^{49} -5.29629e8 q^{50} -6.71439e8 q^{51} +7.95845e8 q^{52} -1.49545e9 q^{53} -2.12892e9 q^{54} -7.51315e9 q^{55} +5.50732e8 q^{56} -3.72438e9 q^{57} +2.61813e9 q^{58} +3.20003e9 q^{59} +1.79148e9 q^{60} -4.59693e9 q^{61} -2.13625e9 q^{62} +2.19049e9 q^{63} +1.07374e9 q^{64} -6.28417e9 q^{65} +6.43348e9 q^{66} +8.85803e9 q^{67} +3.17770e9 q^{68} +9.27834e9 q^{69} -4.34870e9 q^{70} -4.38392e9 q^{71} +4.27071e9 q^{72} +2.72701e10 q^{73} -2.29076e10 q^{74} -3.58109e9 q^{75} +1.76263e10 q^{76} -1.56168e10 q^{77} +5.38111e9 q^{78} +4.19225e10 q^{79} -8.47850e9 q^{80} +8.69322e9 q^{81} -2.42753e10 q^{82} -4.75219e10 q^{83} +3.72377e9 q^{84} -2.50918e10 q^{85} +6.44242e9 q^{86} +1.77025e10 q^{87} -3.04476e10 q^{88} +1.00263e11 q^{89} -3.37225e10 q^{90} -1.30623e10 q^{91} -4.39114e10 q^{92} -1.44443e10 q^{93} +2.41510e10 q^{94} -1.39181e11 q^{95} +7.26011e9 q^{96} +5.11389e10 q^{97} -9.03921e9 q^{98} -1.21103e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 64 q^{2} + 350 q^{3} + 2048 q^{4} + 266 q^{5} - 11200 q^{6} - 33614 q^{7} - 65536 q^{8} + 13294 q^{9}+O(q^{10}) \) 2 * q - 64 * q^2 + 350 * q^3 + 2048 * q^4 + 266 * q^5 - 11200 * q^6 - 33614 * q^7 - 65536 * q^8 + 13294 * q^9	\( 2 q - 64 q^{2} + 350 q^{3} + 2048 q^{4} + 266 q^{5} - 11200 q^{6} - 33614 q^{7} - 65536 q^{8} + 13294 q^{9} - 8512 q^{10} + 773500 q^{11} + 358400 q^{12} + 3275622 q^{13} + 1075648 q^{14} + 6479648 q^{15} + 2097152 q^{16} + 9376528 q^{17} - 425408 q^{18} + 1741642 q^{19} + 272384 q^{20} - 5882450 q^{21} - 24752000 q^{22} - 11993072 q^{23} - 11468800 q^{24} + 37474186 q^{25} - 104819904 q^{26} + 47543300 q^{27} - 34420736 q^{28} - 23355904 q^{29} - 207348736 q^{30} + 142349508 q^{31} - 67108864 q^{32} - 289221968 q^{33} - 300048896 q^{34} - 4470662 q^{35} + 13613056 q^{36} + 530129728 q^{37} - 55732544 q^{38} + 1246871112 q^{39} - 8716288 q^{40} - 206465112 q^{41} + 188238400 q^{42} + 1036645444 q^{43} + 792064000 q^{44} + 2253352402 q^{45} + 383778304 q^{46} - 2847603444 q^{47} + 367001600 q^{48} + 564950498 q^{49} - 1199173952 q^{50} + 2881561300 q^{51} + 3354236928 q^{52} - 4876085316 q^{53} - 1521385600 q^{54} - 8813398328 q^{55} + 1101463552 q^{56} - 12486968516 q^{57} + 747388928 q^{58} - 6723217942 q^{59} + 6635159552 q^{60} - 9724278438 q^{61} - 4555184256 q^{62} - 223432258 q^{63} + 2147483648 q^{64} + 14582040228 q^{65} + 9255102976 q^{66} + 8448611288 q^{67} + 9601564672 q^{68} + 26772956224 q^{69} + 143061184 q^{70} - 26281683512 q^{71} - 435617792 q^{72} + 61139797628 q^{73} - 16964151296 q^{74} + 8269186618 q^{75} + 1783441408 q^{76} - 13000214500 q^{77} - 39899875584 q^{78} + 37890465096 q^{79} + 278921216 q^{80} - 27502341218 q^{81} + 6606883584 q^{82} - 46563770750 q^{83} - 6023628800 q^{84} + 27301125124 q^{85} - 33172654208 q^{86} + 50812775132 q^{87} - 25346048000 q^{88} + 80689325220 q^{89} - 72107276864 q^{90} - 55053378954 q^{91} - 12280905728 q^{92} + 28368494568 q^{93} + 91123310208 q^{94} - 268395234800 q^{95} - 11744051200 q^{96} - 9944168416 q^{97} - 18078415936 q^{98} - 143463109300 q^{99}+O(q^{100}) \) 2 * q - 64 * q^2 + 350 * q^3 + 2048 * q^4 + 266 * q^5 - 11200 * q^6 - 33614 * q^7 - 65536 * q^8 + 13294 * q^9 - 8512 * q^10 + 773500 * q^11 + 358400 * q^12 + 3275622 * q^13 + 1075648 * q^14 + 6479648 * q^15 + 2097152 * q^16 + 9376528 * q^17 - 425408 * q^18 + 1741642 * q^19 + 272384 * q^20 - 5882450 * q^21 - 24752000 * q^22 - 11993072 * q^23 - 11468800 * q^24 + 37474186 * q^25 - 104819904 * q^26 + 47543300 * q^27 - 34420736 * q^28 - 23355904 * q^29 - 207348736 * q^30 + 142349508 * q^31 - 67108864 * q^32 - 289221968 * q^33 - 300048896 * q^34 - 4470662 * q^35 + 13613056 * q^36 + 530129728 * q^37 - 55732544 * q^38 + 1246871112 * q^39 - 8716288 * q^40 - 206465112 * q^41 + 188238400 * q^42 + 1036645444 * q^43 + 792064000 * q^44 + 2253352402 * q^45 + 383778304 * q^46 - 2847603444 * q^47 + 367001600 * q^48 + 564950498 * q^49 - 1199173952 * q^50 + 2881561300 * q^51 + 3354236928 * q^52 - 4876085316 * q^53 - 1521385600 * q^54 - 8813398328 * q^55 + 1101463552 * q^56 - 12486968516 * q^57 + 747388928 * q^58 - 6723217942 * q^59 + 6635159552 * q^60 - 9724278438 * q^61 - 4555184256 * q^62 - 223432258 * q^63 + 2147483648 * q^64 + 14582040228 * q^65 + 9255102976 * q^66 + 8448611288 * q^67 + 9601564672 * q^68 + 26772956224 * q^69 + 143061184 * q^70 - 26281683512 * q^71 - 435617792 * q^72 + 61139797628 * q^73 - 16964151296 * q^74 + 8269186618 * q^75 + 1783441408 * q^76 - 13000214500 * q^77 - 39899875584 * q^78 + 37890465096 * q^79 + 278921216 * q^80 - 27502341218 * q^81 + 6606883584 * q^82 - 46563770750 * q^83 - 6023628800 * q^84 + 27301125124 * q^85 - 33172654208 * q^86 + 50812775132 * q^87 - 25346048000 * q^88 + 80689325220 * q^89 - 72107276864 * q^90 - 55053378954 * q^91 - 12280905728 * q^92 + 28368494568 * q^93 + 91123310208 * q^94 - 268395234800 * q^95 - 11744051200 * q^96 - 9944168416 * q^97 - 18078415936 * q^98 - 143463109300 * q^99

Introduction

L-functions

Modular forms

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