LMFDB - Embedded newform 285.10.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,10,Mod(1,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("285.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$N$	$=$	$285 = 3 \cdot 5 \cdot 19$
Weight:	$k$	$=$	$10$
Character orbit:	$[\chi]$	$=$	285.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:	$146.785213307$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{12} - 3 x^{11} - 4398 x^{10} + 4080 x^{9} + 7026370 x^{8} + 7294322 x^{7} - 5023445596 x^{6} + \cdots + 49\!\cdots\!00$ x^12 - 3x^11 - 4398x^10 + 4080x^9 + 7026370x^8 + 7294322x^7 - 5023445596x^6 - 14095608472x^5 + 1618065377925x^4 + 6513052039465x^3 - 200178138151710x^2 - 846933501654000*x + 4998249308239200
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$2^{13}\cdot 3^{6}\cdot 5^{2}$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-14.0719$ of defining polynomial
Character	$\chi$	$=$	285.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-17.0719 q^{2} -81.0000 q^{3} -220.549 q^{4} +625.000 q^{5} +1382.83 q^{6} +11804.8 q^{7} +12506.0 q^{8} +6561.00 q^{9} -10670.0 q^{10} +10723.5 q^{11} +17864.5 q^{12} +55804.2 q^{13} -201531. q^{14} -50625.0 q^{15} -100581. q^{16} +39049.4 q^{17} -112009. q^{18} +130321. q^{19} -137843. q^{20} -956188. q^{21} -183072. q^{22} +85590.2 q^{23} -1.01299e6 q^{24} +390625. q^{25} -952685. q^{26} -531441. q^{27} -2.60354e6 q^{28} -4.91333e6 q^{29} +864266. q^{30} -7.66372e6 q^{31} -4.68598e6 q^{32} -868607. q^{33} -666649. q^{34} +7.37800e6 q^{35} -1.44702e6 q^{36} -1.74637e7 q^{37} -2.22483e6 q^{38} -4.52014e6 q^{39} +7.81627e6 q^{40} +2.56765e7 q^{41} +1.63240e7 q^{42} -3.52977e7 q^{43} -2.36507e6 q^{44} +4.10062e6 q^{45} -1.46119e6 q^{46} -9.69853e6 q^{47} +8.14703e6 q^{48} +9.89996e7 q^{49} -6.66872e6 q^{50} -3.16300e6 q^{51} -1.23076e7 q^{52} -6.79387e7 q^{53} +9.07272e6 q^{54} +6.70222e6 q^{55} +1.47631e8 q^{56} -1.05560e7 q^{57} +8.38799e7 q^{58} -2.56493e7 q^{59} +1.11653e7 q^{60} -7.01660e6 q^{61} +1.30835e8 q^{62} +7.74513e7 q^{63} +1.31496e8 q^{64} +3.48776e7 q^{65} +1.48288e7 q^{66} -1.24277e8 q^{67} -8.61233e6 q^{68} -6.93281e6 q^{69} -1.25957e8 q^{70} +6.68509e7 q^{71} +8.20520e7 q^{72} +4.31812e8 q^{73} +2.98138e8 q^{74} -3.16406e7 q^{75} -2.87422e7 q^{76} +1.26589e8 q^{77} +7.71675e7 q^{78} -1.81702e8 q^{79} -6.28629e7 q^{80} +4.30467e7 q^{81} -4.38346e8 q^{82} -6.01036e8 q^{83} +2.10887e8 q^{84} +2.44059e7 q^{85} +6.02600e8 q^{86} +3.97979e8 q^{87} +1.34109e8 q^{88} -4.69609e8 q^{89} -7.00056e7 q^{90} +6.58757e8 q^{91} -1.88769e7 q^{92} +6.20762e8 q^{93} +1.65573e8 q^{94} +8.14506e7 q^{95} +3.79565e8 q^{96} -3.63557e8 q^{97} -1.69011e9 q^{98} +7.03572e7 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$12 q - 33 q^{2} - 972 q^{3} + 2751 q^{4} + 7500 q^{5} + 2673 q^{6} - 3450 q^{7} - 18327 q^{8} + 78732 q^{9} - 20625 q^{10} - 8180 q^{11} - 222831 q^{12} - 54754 q^{13} - 198168 q^{14} - 607500 q^{15} + 319475 q^{16}+ \cdots - 53668980 q^{99}+O(q^{100})$ 12 * q - 33 * q^2 - 972 * q^3 + 2751 * q^4 + 7500 * q^5 + 2673 * q^6 - 3450 * q^7 - 18327 * q^8 + 78732 * q^9 - 20625 * q^10 - 8180 * q^11 - 222831 * q^12 - 54754 * q^13 - 198168 * q^14 - 607500 * q^15 + 319475 * q^16 + 622056 * q^17 - 216513 * q^18 + 1563852 * q^19 + 1719375 * q^20 + 279450 * q^21 + 1080046 * q^22 - 260950 * q^23 + 1484487 * q^24 + 4687500 * q^25 + 138408 * q^26 - 6377292 * q^27 - 10403256 * q^28 - 13341236 * q^29 + 1670625 * q^30 - 25146168 * q^31 - 20499967 * q^32 + 662580 * q^33 - 35204664 * q^34 - 2156250 * q^35 + 18049311 * q^36 - 13452262 * q^37 - 4300593 * q^38 + 4435074 * q^39 - 11454375 * q^40 - 15407528 * q^41 + 16051608 * q^42 - 9479442 * q^43 - 19754122 * q^44 + 49207500 * q^45 - 40375204 * q^46 + 14425082 * q^47 - 25877475 * q^48 - 11054488 * q^49 - 12890625 * q^50 - 50386536 * q^51 + 41921168 * q^52 - 49133618 * q^53 + 17537553 * q^54 - 5112500 * q^55 - 95483884 * q^56 - 126672012 * q^57 + 237527692 * q^58 - 88347684 * q^59 - 139269375 * q^60 - 178983832 * q^61 + 299493054 * q^62 - 22635450 * q^63 + 342342499 * q^64 - 34221250 * q^65 - 87483726 * q^66 - 11418912 * q^67 + 369530944 * q^68 + 21136950 * q^69 - 123855000 * q^70 - 175745456 * q^71 - 120243447 * q^72 + 216614468 * q^73 + 183691428 * q^74 - 379687500 * q^75 + 358513071 * q^76 + 605840856 * q^77 - 11211048 * q^78 - 125678224 * q^79 + 199671875 * q^80 + 516560652 * q^81 + 857111058 * q^82 + 759016846 * q^83 + 842663736 * q^84 + 388785000 * q^85 + 290528982 * q^86 + 1080640116 * q^87 + 2351936450 * q^88 + 308917100 * q^89 - 135320625 * q^90 + 609006592 * q^91 + 3006293692 * q^92 + 2036839608 * q^93 + 840979428 * q^94 + 977407500 * q^95 + 1660497327 * q^96 + 565359698 * q^97 - 348280833 * q^98 - 53668980 * q^99

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

)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$\alpha_n$			$\theta_n$
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$\alpha_p$			$\theta_p$

$2$	−17.0719	−0.754480	−0.377240	−	0.926116i	$-0.623127\pi$
$2$	−17.0719	−0.754480	−0.377240	+	0.926116i	$0.623127\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	−220.549	−0.430761
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	1382.83	0.435599
$7$	11804.8	1.85831	0.929153	−	0.369695i	$-0.120538\pi$
$7$	11804.8	1.85831	0.929153	+	0.369695i	$0.120538\pi$
$8$	12506.0	1.07948
$9$	6561.00	0.333333
$10$	−10670.0	−0.337413
$11$	10723.5	0.220837	0.110418	−	0.993885i	$-0.464781\pi$
$11$	10723.5	0.220837	0.110418	+	0.993885i	$0.464781\pi$
$12$	17864.5	0.248700
$13$	55804.2	0.541903	0.270952	−	0.962593i	$-0.412662\pi$
$13$	55804.2	0.541903	0.270952	+	0.962593i	$0.412662\pi$
$14$	−201531.	−1.40205
$15$	−50625.0	−0.258199
$16$	−100581.	−0.383685
$17$	39049.4	0.113395	0.0566976	−	0.998391i	$-0.481943\pi$
$17$	39049.4	0.113395	0.0566976	+	0.998391i	$0.481943\pi$
$18$	−112009.	−0.251493
$19$	130321.	0.229416
$19$	130321.	0.229416
$20$	−137843.	−0.192642
$21$	−956188.	−1.07289
$22$	−183072.	−0.166617
$23$	85590.2	0.0637748	0.0318874	−	0.999491i	$-0.489848\pi$
$23$	85590.2	0.0637748	0.0318874	+	0.999491i	$0.489848\pi$
$24$	−1.01299e6	−0.623238
$25$	390625.	0.200000
$26$	−952685.	−0.408855
$27$	−531441.	−0.192450
$28$	−2.60354e6	−0.800485
$29$	−4.91333e6	−1.28998	−0.644992	−	0.764189i	$-0.723139\pi$
$29$	−4.91333e6	−1.28998	−0.644992	+	0.764189i	$0.723139\pi$
$30$	864266.	0.194806
$31$	−7.66372e6	−1.49043	−0.745216	−	0.666823i	$-0.767654\pi$
$31$	−7.66372e6	−1.49043	−0.745216	+	0.666823i	$0.767654\pi$
$32$	−4.68598e6	−0.789997
$33$	−868607.	−0.127500
$34$	−666649.	−0.0855543
$35$	7.37800e6	0.831060
$36$	−1.44702e6	−0.143587
$37$	−1.74637e7	−1.53189	−0.765944	−	0.642907i	$-0.777728\pi$
$37$	−1.74637e7	−1.53189	−0.765944	+	0.642907i	$0.777728\pi$
$38$	−2.22483e6	−0.173089
$39$	−4.52014e6	−0.312868
$40$	7.81627e6	0.482758
$41$	2.56765e7	1.41908	0.709541	−	0.704664i	$-0.248902\pi$
$41$	2.56765e7	1.41908	0.709541	+	0.704664i	$0.248902\pi$
$42$	1.63240e7	0.809476
$43$	−3.52977e7	−1.57449	−0.787243	−	0.616643i	$-0.788492\pi$
$43$	−3.52977e7	−1.57449	−0.787243	+	0.616643i	$0.788492\pi$
$44$	−2.36507e6	−0.0951278
$45$	4.10062e6	0.149071
$46$	−1.46119e6	−0.0481168
$47$	−9.69853e6	−0.289912	−0.144956	−	0.989438i	$-0.546304\pi$
$47$	−9.69853e6	−0.289912	−0.144956	+	0.989438i	$0.546304\pi$
$48$	8.14703e6	0.221520
$49$	9.89996e7	2.45330
$50$	−6.66872e6	−0.150896
$51$	−3.16300e6	−0.0654687
$52$	−1.23076e7	−0.233431
$53$	−6.79387e7	−1.18270	−0.591352	−	0.806414i	$-0.701406\pi$
$53$	−6.79387e7	−1.18270	−0.591352	+	0.806414i	$0.701406\pi$
$54$	9.07272e6	0.145200
$55$	6.70222e6	0.0987612
$56$	1.47631e8	2.00600
$57$	−1.05560e7	−0.132453
$58$	8.38799e7	0.973267
$59$	−2.56493e7	−0.275576	−0.137788	−	0.990462i	$-0.543999\pi$
$59$	−2.56493e7	−0.275576	−0.137788	+	0.990462i	$0.543999\pi$
$60$	1.11653e7	0.111222
$61$	−7.01660e6	−0.0648847	−0.0324424	−	0.999474i	$-0.510329\pi$
$61$	−7.01660e6	−0.0648847	−0.0324424	+	0.999474i	$0.510329\pi$
$62$	1.30835e8	1.12450
$63$	7.74513e7	0.619435
$64$	1.31496e8	0.979721
$65$	3.48776e7	0.242347
$66$	1.48288e7	0.0961963
$67$	−1.24277e8	−0.753451	−0.376725	−	0.926325i	$-0.622950\pi$
$67$	−1.24277e8	−0.753451	−0.376725	+	0.926325i	$0.622950\pi$
$68$	−8.61233e6	−0.0488462
$69$	−6.93281e6	−0.0368204
$70$	−1.25957e8	−0.627018
$71$	6.68509e7	0.312208	0.156104	−	0.987741i	$-0.450106\pi$
$71$	6.68509e7	0.312208	0.156104	+	0.987741i	$0.450106\pi$
$72$	8.20520e7	0.359827
$73$	4.31812e8	1.77968	0.889839	−	0.456275i	$-0.150817\pi$
$73$	4.31812e8	1.77968	0.889839	+	0.456275i	$0.150817\pi$
$74$	2.98138e8	1.15578
$75$	−3.16406e7	−0.115470
$76$	−2.87422e7	−0.0988233
$77$	1.26589e8	0.410382
$78$	7.71675e7	0.236053
$79$	−1.81702e8	−0.524853	−0.262427	−	0.964952i	$-0.584523\pi$
$79$	−1.81702e8	−0.524853	−0.262427	+	0.964952i	$0.584523\pi$
$80$	−6.28629e7	−0.171589
$81$	4.30467e7	0.111111
$82$	−4.38346e8	−1.07067
$83$	−6.01036e8	−1.39011	−0.695055	−	0.718956i	$-0.744620\pi$
$83$	−6.01036e8	−1.39011	−0.695055	+	0.718956i	$0.744620\pi$
$84$	2.10887e8	0.462160
$85$	2.44059e7	0.0507118
$86$	6.02600e8	1.18792
$87$	3.97979e8	0.744773
$88$	1.34109e8	0.238389
$89$	−4.69609e8	−0.793380	−0.396690	−	0.917953i	$-0.629841\pi$
$89$	−4.69609e8	−0.793380	−0.396690	+	0.917953i	$0.629841\pi$
$90$	−7.00056e7	−0.112471
$91$	6.58757e8	1.00702
$92$	−1.88769e7	−0.0274717
$93$	6.20762e8	0.860501
$94$	1.65573e8	0.218732
$95$	8.14506e7	0.102598
$96$	3.79565e8	0.456105
$97$	−3.63557e8	−0.416966	−0.208483	−	0.978026i	$-0.566853\pi$
$97$	−3.63557e8	−0.416966	−0.208483	+	0.978026i	$0.566853\pi$
$98$	−1.69011e9	−1.85097
$99$	7.03572e7	0.0736123
$100$	−8.61521e7	−0.0861521
$101$	−1.10033e9	−1.05215	−0.526074	−	0.850439i	$-0.676336\pi$
$101$	−1.10033e9	−1.05215	−0.526074	+	0.850439i	$0.676336\pi$
$102$	5.39985e7	0.0493948
$103$	−4.43205e8	−0.388005	−0.194002	−	0.981001i	$-0.562147\pi$
$103$	−4.43205e8	−0.388005	−0.194002	+	0.981001i	$0.562147\pi$
$104$	6.97889e8	0.584974
$105$	−5.97618e8	−0.479813
$106$	1.15984e9	0.892326
$107$	−1.53314e9	−1.13072	−0.565360	−	0.824844i	$-0.691263\pi$
$107$	−1.53314e9	−1.13072	−0.565360	+	0.824844i	$0.691263\pi$
$108$	1.17209e8	0.0828999
$109$	−1.91067e9	−1.29648	−0.648240	−	0.761436i	$-0.724495\pi$
$109$	−1.91067e9	−1.29648	−0.648240	+	0.761436i	$0.724495\pi$
$110$	−1.14420e8	−0.0745133
$111$	1.41456e9	0.884436
$112$	−1.18733e9	−0.713004
$113$	1.84040e9	1.06184	0.530919	−	0.847423i	$-0.321847\pi$
$113$	1.84040e9	1.06184	0.530919	+	0.847423i	$0.321847\pi$
$114$	1.80211e8	0.0999333
$115$	5.34939e7	0.0285209
$116$	1.08363e9	0.555675
$117$	3.66131e8	0.180634
$118$	4.37883e8	0.207916
$119$	4.60970e8	0.210723
$120$	−6.33118e8	−0.278720
$121$	−2.24295e9	−0.951231
$122$	1.19787e8	0.0489542
$123$	−2.07979e9	−0.819308
$124$	1.69023e9	0.642020
$125$	2.44141e8	0.0894427
$126$	−1.32224e9	−0.467351
$127$	1.51876e9	0.518049	0.259025	−	0.965871i	$-0.416599\pi$
$127$	1.51876e9	0.518049	0.259025	+	0.965871i	$0.416599\pi$
$128$	1.54333e8	0.0508177
$129$	2.85912e9	0.909030
$130$	−5.95428e8	−0.182845
$131$	5.54699e9	1.64565	0.822823	−	0.568298i	$-0.192398\pi$
$131$	5.54699e9	1.64565	0.822823	+	0.568298i	$0.192398\pi$
$132$	1.91571e8	0.0549221
$133$	1.53841e9	0.426325
$134$	2.12165e9	0.568463
$135$	−3.32151e8	−0.0860663
$136$	4.88353e8	0.122408
$137$	6.74188e8	0.163508	0.0817539	−	0.996653i	$-0.473948\pi$
$137$	6.74188e8	0.163508	0.0817539	+	0.996653i	$0.473948\pi$
$138$	1.18356e8	0.0277802
$139$	3.90541e9	0.887360	0.443680	−	0.896185i	$-0.353673\pi$
$139$	3.90541e9	0.887360	0.443680	+	0.896185i	$0.353673\pi$
$140$	−1.62721e9	−0.357988
$141$	7.85581e8	0.167381
$142$	−1.14127e9	−0.235555
$143$	5.98419e8	0.119672
$144$	−6.59909e8	−0.127895
$145$	−3.07083e9	−0.576899
$146$	−7.37185e9	−1.34273
$147$	−8.01897e9	−1.41641
$148$	3.85160e9	0.659877
$149$	−3.80714e9	−0.632791	−0.316396	−	0.948627i	$-0.602473\pi$
$149$	−3.80714e9	−0.632791	−0.316396	+	0.948627i	$0.602473\pi$
$150$	5.40166e8	0.0871198
$151$	−5.03611e9	−0.788314	−0.394157	−	0.919043i	$-0.628963\pi$
$151$	−5.03611e9	−0.788314	−0.394157	+	0.919043i	$0.628963\pi$
$152$	1.62980e9	0.247650
$153$	2.56203e8	0.0377984
$154$	−2.16112e9	−0.309625
$155$	−4.78983e9	−0.666542
$156$	9.96914e8	0.134771
$157$	−1.27343e10	−1.67273	−0.836363	−	0.548175i	$-0.815323\pi$
$157$	−1.27343e10	−1.67273	−0.836363	+	0.548175i	$0.815323\pi$
$158$	3.10200e9	0.395991
$159$	5.50304e9	0.682834
$160$	−2.92874e9	−0.353298
$161$	1.01038e9	0.118513
$162$	−7.34890e8	−0.0838311
$163$	−7.30036e9	−0.810028	−0.405014	−	0.914310i	$-0.632733\pi$
$163$	−7.30036e9	−0.810028	−0.405014	+	0.914310i	$0.632733\pi$
$164$	−5.66293e9	−0.611285
$165$	−5.42880e8	−0.0570198
$166$	1.02608e10	1.04881
$167$	−1.73438e9	−0.172552	−0.0862758	−	0.996271i	$-0.527497\pi$
$167$	−1.73438e9	−0.172552	−0.0862758	+	0.996271i	$0.527497\pi$
$168$	−1.19581e10	−1.15817
$169$	−7.49039e9	−0.706341
$170$	−4.16655e8	−0.0382611
$171$	8.55036e8	0.0764719
$172$	7.78489e9	0.678226
$173$	−5.91992e9	−0.502468	−0.251234	−	0.967926i	$-0.580836\pi$
$173$	−5.91992e9	−0.502468	−0.251234	+	0.967926i	$0.580836\pi$
$174$	−6.79427e9	−0.561916
$175$	4.61125e9	0.371661
$176$	−1.07858e9	−0.0847317
$177$	2.07759e9	0.159104
$178$	8.01713e9	0.598589
$179$	1.13075e10	0.823241	0.411620	−	0.911355i	$-0.364963\pi$
$179$	1.13075e10	0.823241	0.411620	+	0.911355i	$0.364963\pi$
$180$	−9.04391e8	−0.0642140
$181$	−1.96730e10	−1.36244	−0.681219	−	0.732080i	$-0.738550\pi$
$181$	−1.96730e10	−1.36244	−0.681219	+	0.732080i	$0.738550\pi$
$182$	−1.12463e10	−0.759778
$183$	5.68344e8	0.0374612
$184$	1.07039e9	0.0688436
$185$	−1.09148e10	−0.685082
$186$	−1.05976e10	−0.649231
$187$	4.18748e8	0.0250418
$188$	2.13901e9	0.124883
$189$	−6.27355e9	−0.357631
$190$	−1.39052e9	−0.0774080
$191$	−8.57929e9	−0.466446	−0.233223	−	0.972423i	$-0.574927\pi$
$191$	−8.57929e9	−0.466446	−0.233223	+	0.972423i	$0.574927\pi$
$192$	−1.06512e10	−0.565642
$193$	2.00369e10	1.03949	0.519747	−	0.854320i	$-0.326026\pi$
$193$	2.00369e10	1.03949	0.519747	+	0.854320i	$0.326026\pi$
$194$	6.20663e9	0.314592
$195$	−2.82509e9	−0.139919
$196$	−2.18343e10	−1.05679
$197$	−9.28019e9	−0.438994	−0.219497	−	0.975613i	$-0.570442\pi$
$197$	−9.28019e9	−0.438994	−0.219497	+	0.975613i	$0.570442\pi$
$198$	−1.20113e9	−0.0555389
$199$	3.12211e10	1.41127	0.705635	−	0.708576i	$-0.250662\pi$
$199$	3.12211e10	1.41127	0.705635	+	0.708576i	$0.250662\pi$
$200$	4.88517e9	0.215896
$201$	1.00665e10	0.435005
$202$	1.87847e10	0.793824
$203$	−5.80008e10	−2.39719
$204$	6.97599e8	0.0282013
$205$	1.60478e10	0.634633
$206$	7.56636e9	0.292742
$207$	5.61557e8	0.0212583
$208$	−5.61282e9	−0.207920
$209$	1.39750e9	0.0506634
$210$	1.02025e10	0.362009
$211$	2.95630e10	1.02678	0.513391	−	0.858155i	$-0.328389\pi$
$211$	2.95630e10	1.02678	0.513391	+	0.858155i	$0.328389\pi$
$212$	1.49838e10	0.509462
$213$	−5.41492e9	−0.180254
$214$	2.61737e10	0.853105
$215$	−2.20611e10	−0.704131
$216$	−6.64622e9	−0.207746
$217$	−9.04687e10	−2.76968
$218$	3.26188e10	0.978167
$219$	−3.49767e10	−1.02750
$220$	−1.47817e9	−0.0425424
$221$	2.17912e9	0.0614492
$222$	−2.41492e10	−0.667289
$223$	3.58409e10	0.970527	0.485263	−	0.874368i	$-0.338724\pi$
$223$	3.58409e10	0.970527	0.485263	+	0.874368i	$0.338724\pi$
$224$	−5.53171e10	−1.46806
$225$	2.56289e9	0.0666667
$226$	−3.14191e10	−0.801135
$227$	−7.63678e10	−1.90895	−0.954474	−	0.298296i	$-0.903582\pi$
$227$	−7.63678e10	−1.90895	−0.954474	+	0.298296i	$0.903582\pi$
$228$	2.32812e9	0.0570556
$229$	−7.53272e10	−1.81006	−0.905028	−	0.425351i	$-0.860151\pi$
$229$	−7.53272e10	−1.81006	−0.905028	+	0.425351i	$0.860151\pi$
$230$	−9.13244e8	−0.0215185
$231$	−1.02537e10	−0.236934
$232$	−6.14462e10	−1.39251
$233$	5.23818e10	1.16434	0.582168	−	0.813068i	$-0.302205\pi$
$233$	5.23818e10	1.16434	0.582168	+	0.813068i	$0.302205\pi$
$234$	−6.25057e9	−0.136285
$235$	−6.06158e9	−0.129652
$236$	5.65694e9	0.118707
$237$	1.47179e10	0.303024
$238$	−7.86965e9	−0.158986
$239$	−2.49810e10	−0.495243	−0.247622	−	0.968857i	$-0.579649\pi$
$239$	−2.49810e10	−0.495243	−0.247622	+	0.968857i	$0.579649\pi$
$240$	5.09189e9	0.0990669
$241$	8.94691e10	1.70843	0.854213	−	0.519923i	$-0.174039\pi$
$241$	8.94691e10	1.70843	0.854213	+	0.519923i	$0.174039\pi$
$242$	3.82915e10	0.717684
$243$	−3.48678e9	−0.0641500
$244$	1.54751e9	0.0279498
$245$	6.18748e10	1.09715
$246$	3.55061e10	0.618151
$247$	7.27246e9	0.124321
$248$	−9.58427e10	−1.60889
$249$	4.86840e10	0.802581
$250$	−4.16795e9	−0.0674827
$251$	−3.78202e8	−0.00601440	−0.00300720	−	0.999995i	$-0.500957\pi$
$251$	−3.78202e8	−0.00601440	−0.00300720	+	0.999995i	$0.500957\pi$
$252$	−1.70818e10	−0.266828
$253$	9.17831e8	0.0140838
$254$	−2.59281e10	−0.390858
$255$	−1.97688e9	−0.0292785
$256$	−6.99607e10	−1.01806
$257$	−6.92550e10	−0.990266	−0.495133	−	0.868817i	$-0.664881\pi$
$257$	−6.92550e10	−0.990266	−0.495133	+	0.868817i	$0.664881\pi$
$258$	−4.88106e10	−0.685844
$259$	−2.06155e11	−2.84672
$260$	−7.69224e9	−0.104393
$261$	−3.22363e10	−0.429995
$262$	−9.46977e10	−1.24161
$263$	1.22467e11	1.57840	0.789200	−	0.614136i	$-0.210495\pi$
$263$	1.22467e11	1.57840	0.789200	+	0.614136i	$0.210495\pi$
$264$	−1.08628e10	−0.137634
$265$	−4.24617e10	−0.528921
$266$	−2.62637e10	−0.321653
$267$	3.80383e10	0.458058
$268$	2.74093e10	0.324557
$269$	−2.06902e10	−0.240924	−0.120462	−	0.992718i	$-0.538438\pi$
$269$	−2.06902e10	−0.240924	−0.120462	+	0.992718i	$0.538438\pi$
$270$	5.67045e9	0.0649353
$271$	−3.14415e10	−0.354113	−0.177057	−	0.984201i	$-0.556658\pi$
$271$	−3.14415e10	−0.354113	−0.177057	+	0.984201i	$0.556658\pi$
$272$	−3.92761e9	−0.0435080
$273$	−5.33593e10	−0.581405
$274$	−1.15097e10	−0.123363
$275$	4.18889e9	0.0441674
$276$	1.52903e9	0.0158608
$277$	1.81200e11	1.84926	0.924631	−	0.380865i	$-0.124374\pi$
$277$	1.81200e11	1.84926	0.924631	+	0.380865i	$0.124374\pi$
$278$	−6.66729e10	−0.669495
$279$	−5.02817e10	−0.496811
$280$	9.22694e10	0.897112
$281$	1.51008e11	1.44485	0.722423	−	0.691451i	$-0.243028\pi$
$281$	1.51008e11	1.44485	0.722423	+	0.691451i	$0.243028\pi$
$282$	−1.34114e10	−0.126285
$283$	−2.02089e11	−1.87285	−0.936425	−	0.350867i	$-0.885887\pi$
$283$	−2.02089e11	−1.87285	−0.936425	+	0.350867i	$0.885887\pi$
$284$	−1.47439e10	−0.134487
$285$	−6.59750e9	−0.0592349
$286$	−1.02162e10	−0.0902902
$287$	3.03105e11	2.63709
$288$	−3.07447e10	−0.263332
$289$	−1.17063e11	−0.987142
$290$	5.24249e10	0.435258
$291$	2.94482e10	0.240735
$292$	−9.52358e10	−0.766615
$293$	1.59940e11	1.26781	0.633905	−	0.773411i	$-0.281451\pi$
$293$	1.59940e11	1.26781	0.633905	+	0.773411i	$0.281451\pi$
$294$	1.36899e11	1.06866
$295$	−1.60308e10	−0.123241
$296$	−2.18401e11	−1.65364
$297$	−5.69893e9	−0.0425001
$298$	6.49952e10	0.477428
$299$	4.77629e9	0.0345598
$300$	6.97832e9	0.0497400
$301$	−4.16682e11	−2.92588
$302$	8.59761e10	0.594766
$303$	8.91267e10	0.607458
$304$	−1.31078e10	−0.0880233
$305$	−4.38537e9	−0.0290173
$306$	−4.37388e9	−0.0285181
$307$	−2.20955e11	−1.41965	−0.709826	−	0.704378i	$-0.751226\pi$
$307$	−2.20955e11	−1.41965	−0.709826	+	0.704378i	$0.751226\pi$
$308$	−2.79192e10	−0.176777
$309$	3.58996e10	0.224015
$310$	8.17716e10	0.502892
$311$	−8.57467e10	−0.519752	−0.259876	−	0.965642i	$-0.583682\pi$
$311$	−8.57467e10	−0.519752	−0.259876	+	0.965642i	$0.583682\pi$
$312$	−5.65290e10	−0.337735
$313$	−1.99701e11	−1.17606	−0.588031	−	0.808838i	$-0.700097\pi$
$313$	−1.99701e11	−1.17606	−0.588031	+	0.808838i	$0.700097\pi$
$314$	2.17398e11	1.26204
$315$	4.84070e10	0.277020
$316$	4.00743e10	0.226086
$317$	1.01674e11	0.565513	0.282757	−	0.959192i	$-0.408751\pi$
$317$	1.01674e11	0.565513	0.282757	+	0.959192i	$0.408751\pi$
$318$	−9.39474e10	−0.515184
$319$	−5.26883e10	−0.284876
$320$	8.21850e10	0.438145
$321$	1.24184e11	0.652821
$322$	−1.72490e10	−0.0894157
$323$	5.08896e9	0.0260146
$324$	−9.49393e9	−0.0478623
$325$	2.17985e10	0.108381
$326$	1.24631e11	0.611150
$327$	1.54764e11	0.748523
$328$	3.21110e11	1.53187
$329$	−1.14489e11	−0.538745
$330$	9.26800e9	0.0430203
$331$	6.55209e10	0.300022	0.150011	−	0.988684i	$-0.452069\pi$
$331$	6.55209e10	0.300022	0.150011	+	0.988684i	$0.452069\pi$
$332$	1.32558e11	0.598805
$333$	−1.14579e11	−0.510630
$334$	2.96091e10	0.130187
$335$	−7.76732e10	−0.336953
$336$	9.61740e10	0.411653
$337$	−1.63149e11	−0.689050	−0.344525	−	0.938777i	$-0.611960\pi$
$337$	−1.63149e11	−0.689050	−0.344525	+	0.938777i	$0.611960\pi$
$338$	1.27875e11	0.532920
$339$	−1.49072e11	−0.613052
$340$	−5.38271e9	−0.0218447
$341$	−8.21823e10	−0.329142
$342$	−1.45971e10	−0.0576965
$343$	6.92304e11	2.70068
$344$	−4.41434e11	−1.69962
$345$	−4.33301e9	−0.0164666
$346$	1.01064e11	0.379102
$347$	4.60263e11	1.70421	0.852105	−	0.523370i	$-0.175325\pi$
$347$	4.60263e11	1.70421	0.852105	+	0.523370i	$0.175325\pi$
$348$	−8.77741e10	−0.320819
$349$	−1.56693e11	−0.565372	−0.282686	−	0.959212i	$-0.591225\pi$
$349$	−1.56693e11	−0.565372	−0.282686	+	0.959212i	$0.591225\pi$
$350$	−7.87229e10	−0.280411
$351$	−2.96566e10	−0.104289
$352$	−5.02504e10	−0.174461
$353$	1.39647e11	0.478680	0.239340	−	0.970936i	$-0.423069\pi$
$353$	1.39647e11	0.478680	0.239340	+	0.970936i	$0.423069\pi$
$354$	−3.54685e10	−0.120041
$355$	4.17818e10	0.139624
$356$	1.03572e11	0.341757
$357$	−3.73386e10	−0.121661
$358$	−1.93040e11	−0.621118
$359$	3.87102e11	1.22999	0.614993	−	0.788533i	$-0.289159\pi$
$359$	3.87102e11	1.22999	0.614993	+	0.788533i	$0.289159\pi$
$360$	5.12825e10	0.160919
$361$	1.69836e10	0.0526316
$362$	3.35856e11	1.02793
$363$	1.81679e11	0.549194
$364$	−1.45289e11	−0.433786
$365$	2.69882e11	0.795896
$366$	−9.70273e9	−0.0282637
$367$	3.70839e11	1.06706	0.533529	−	0.845782i	$-0.320866\pi$
$367$	3.70839e11	1.06706	0.533529	+	0.845782i	$0.320866\pi$
$368$	−8.60872e9	−0.0244694
$369$	1.68463e11	0.473028
$370$	1.86336e11	0.516880
$371$	−8.02003e11	−2.19783
$372$	−1.36909e11	−0.370670
$373$	−1.58356e11	−0.423590	−0.211795	−	0.977314i	$-0.567931\pi$
$373$	−1.58356e11	−0.423590	−0.211795	+	0.977314i	$0.567931\pi$
$374$	−7.14884e9	−0.0188935
$375$	−1.97754e10	−0.0516398
$376$	−1.21290e11	−0.312954
$377$	−2.74184e11	−0.699047
$378$	1.07102e11	0.269825
$379$	−5.77139e11	−1.43682	−0.718412	−	0.695617i	$-0.755131\pi$
$379$	−5.77139e11	−1.43682	−0.718412	+	0.695617i	$0.755131\pi$
$380$	−1.79639e10	−0.0441951
$381$	−1.23019e11	−0.299096
$382$	1.46465e11	0.351924
$383$	3.76018e11	0.892923	0.446461	−	0.894803i	$-0.352684\pi$
$383$	3.76018e11	0.892923	0.446461	+	0.894803i	$0.352684\pi$
$384$	−1.25010e10	−0.0293396
$385$	7.91183e10	0.183529
$386$	−3.42068e11	−0.784277
$387$	−2.31588e11	−0.524828
$388$	8.01824e10	0.179612
$389$	7.59614e11	1.68198	0.840988	−	0.541053i	$-0.181974\pi$
$389$	7.59614e11	1.68198	0.840988	+	0.541053i	$0.181974\pi$
$390$	4.82297e10	0.105566
$391$	3.34225e9	0.00723175
$392$	1.23809e12	2.64829
$393$	−4.49306e11	−0.950114
$394$	1.58431e11	0.331212
$395$	−1.13564e11	−0.234721
$396$	−1.55172e10	−0.0317093
$397$	4.42109e11	0.893248	0.446624	−	0.894722i	$-0.352626\pi$
$397$	4.42109e11	0.893248	0.446624	+	0.894722i	$0.352626\pi$
$398$	−5.33005e11	−1.06477
$399$	−1.24611e11	−0.246139
$400$	−3.92893e10	−0.0767369
$401$	2.21483e11	0.427752	0.213876	−	0.976861i	$-0.431391\pi$
$401$	2.21483e11	0.427752	0.213876	+	0.976861i	$0.431391\pi$
$402$	−1.71854e11	−0.328202
$403$	−4.27668e11	−0.807670
$404$	2.42677e11	0.453224
$405$	2.69042e10	0.0496904
$406$	9.90185e11	1.80863
$407$	−1.87272e11	−0.338297
$408$	−3.95566e10	−0.0706721
$409$	−1.65746e11	−0.292879	−0.146439	−	0.989220i	$-0.546781\pi$
$409$	−1.65746e11	−0.292879	−0.146439	+	0.989220i	$0.546781\pi$
$410$	−2.73967e11	−0.478818
$411$	−5.46092e10	−0.0944012
$412$	9.77486e10	0.167137
$413$	−3.02785e11	−0.512105
$414$	−9.58687e9	−0.0160389
$415$	−3.75648e11	−0.621676
$416$	−2.61497e11	−0.428102
$417$	−3.16338e11	−0.512318
$418$	−2.38581e10	−0.0382245
$419$	1.50545e11	0.238619	0.119309	−	0.992857i	$-0.461932\pi$
$419$	1.50545e11	0.238619	0.119309	+	0.992857i	$0.461932\pi$
$420$	1.31804e11	0.206684
$421$	1.11582e12	1.73111	0.865553	−	0.500817i	$-0.166967\pi$
$421$	1.11582e12	1.73111	0.865553	+	0.500817i	$0.166967\pi$
$422$	−5.04698e11	−0.774686
$423$	−6.36321e10	−0.0966372
$424$	−8.49643e11	−1.27670
$425$	1.52537e10	0.0226790
$426$	9.24431e10	0.135998
$427$	−8.28295e10	−0.120576
$428$	3.38133e11	0.487070
$429$	−4.84719e10	−0.0690928
$430$	3.76625e11	0.531253
$431$	5.20796e11	0.726976	0.363488	−	0.931599i	$-0.381586\pi$
$431$	5.20796e11	0.726976	0.363488	+	0.931599i	$0.381586\pi$
$432$	5.34527e10	0.0738401
$433$	−7.81289e11	−1.06811	−0.534055	−	0.845450i	$-0.679333\pi$
$433$	−7.81289e11	−1.06811	−0.534055	+	0.845450i	$0.679333\pi$
$434$	1.54447e12	2.08967
$435$	2.48737e11	0.333073
$436$	4.21397e11	0.558472
$437$	1.11542e10	0.0146309
$438$	5.97120e11	0.775226
$439$	−5.76901e11	−0.741328	−0.370664	−	0.928767i	$-0.620870\pi$
$439$	−5.76901e11	−0.741328	−0.370664	+	0.928767i	$0.620870\pi$
$440$	8.38181e10	0.106611
$441$	6.49536e11	0.817767
$442$	−3.72018e10	−0.0463622
$443$	−1.06242e11	−0.131063	−0.0655314	−	0.997851i	$-0.520874\pi$
$443$	−1.06242e11	−0.131063	−0.0655314	+	0.997851i	$0.520874\pi$
$444$	−3.11979e11	−0.380980
$445$	−2.93506e11	−0.354810
$446$	−6.11874e11	−0.732243
$447$	3.08378e11	0.365342
$448$	1.55228e12	1.82062
$449$	3.68568e11	0.427966	0.213983	−	0.976837i	$-0.431356\pi$
$449$	3.68568e11	0.427966	0.213983	+	0.976837i	$0.431356\pi$
$450$	−4.37535e10	−0.0502986
$451$	2.75343e11	0.313386
$452$	−4.05898e11	−0.457398
$453$	4.07925e11	0.455133
$454$	1.30375e12	1.44026
$455$	4.11723e11	0.450354
$456$	−1.32014e11	−0.142981
$457$	−6.92422e11	−0.742588	−0.371294	−	0.928515i	$-0.621086\pi$
$457$	−6.92422e11	−0.742588	−0.371294	+	0.928515i	$0.621086\pi$
$458$	1.28598e12	1.36565
$459$	−2.07525e10	−0.0218229
$460$	−1.17980e10	−0.0122857
$461$	1.23633e11	0.127491	0.0637455	−	0.997966i	$-0.479695\pi$
$461$	1.23633e11	0.127491	0.0637455	+	0.997966i	$0.479695\pi$
$462$	1.75051e11	0.178762
$463$	−5.65668e11	−0.572067	−0.286033	−	0.958220i	$-0.592337\pi$
$463$	−5.65668e11	−0.572067	−0.286033	+	0.958220i	$0.592337\pi$
$464$	4.94185e11	0.494947
$465$	3.87976e11	0.384828
$466$	−8.94257e11	−0.878468
$467$	1.11034e12	1.08026	0.540130	−	0.841582i	$-0.318375\pi$
$467$	1.11034e12	1.08026	0.540130	+	0.841582i	$0.318375\pi$
$468$	−8.07501e10	−0.0778102
$469$	−1.46707e12	−1.40014
$470$	1.03483e11	0.0978201
$471$	1.03147e12	0.965749
$472$	−3.20771e11	−0.297479
$473$	−3.78517e11	−0.347704
$474$	−2.51262e11	−0.228625
$475$	5.09066e10	0.0458831
$476$	−1.01667e11	−0.0907711
$477$	−4.45746e11	−0.394235
$478$	4.26473e11	0.373651
$479$	−4.59356e11	−0.398694	−0.199347	−	0.979929i	$-0.563882\pi$
$479$	−4.59356e11	−0.398694	−0.199347	+	0.979929i	$0.563882\pi$
$480$	2.37228e11	0.203976
$481$	−9.74545e11	−0.830136
$482$	−1.52741e12	−1.28897
$483$	−8.18404e10	−0.0684236
$484$	4.94682e11	0.409753
$485$	−2.27223e11	−0.186473
$486$	5.95261e10	0.0483999
$487$	2.77447e11	0.223511	0.111756	−	0.993736i	$-0.464353\pi$
$487$	2.77447e11	0.223511	0.111756	+	0.993736i	$0.464353\pi$
$488$	−8.77498e10	−0.0700417
$489$	5.91329e11	0.467670
$490$	−1.05632e12	−0.827777
$491$	−8.86757e11	−0.688554	−0.344277	−	0.938868i	$-0.611876\pi$
$491$	−8.86757e11	−0.688554	−0.344277	+	0.938868i	$0.611876\pi$
$492$	4.58697e11	0.352926
$493$	−1.91863e11	−0.146278
$494$	−1.24155e11	−0.0937978
$495$	4.39733e10	0.0329204
$496$	7.70822e11	0.571856
$497$	7.89161e11	0.580179
$498$	−8.31129e11	−0.605531
$499$	−6.77785e11	−0.489372	−0.244686	−	0.969602i	$-0.578685\pi$
$499$	−6.77785e11	−0.489372	−0.244686	+	0.969602i	$0.578685\pi$
$500$	−5.38451e10	−0.0385284
$501$	1.40484e11	0.0996228
$502$	6.45664e9	0.00453774
$503$	−8.11800e11	−0.565449	−0.282724	−	0.959201i	$-0.591238\pi$
$503$	−8.11800e11	−0.565449	−0.282724	+	0.959201i	$0.591238\pi$
$504$	9.68608e11	0.668668
$505$	−6.87706e11	−0.470535
$506$	−1.56691e10	−0.0106260
$507$	6.06722e11	0.407806
$508$	−3.34961e11	−0.223155
$509$	1.61730e11	0.106797	0.0533986	−	0.998573i	$-0.482995\pi$
$509$	1.61730e11	0.106797	0.0533986	+	0.998573i	$0.482995\pi$
$510$	3.37491e10	0.0220900
$511$	5.09745e12	3.30719
$512$	1.11535e12	0.717290
$513$	−6.92579e10	−0.0441511
$514$	1.18232e12	0.747136
$515$	−2.77003e11	−0.173521
$516$	−6.30576e11	−0.391574
$517$	−1.04003e11	−0.0640232
$518$	3.51946e12	2.14779
$519$	4.79513e11	0.290100
$520$	4.36181e11	0.261608
$521$	−2.87943e12	−1.71213	−0.856065	−	0.516868i	$-0.827098\pi$
$521$	−2.87943e12	−1.71213	−0.856065	+	0.516868i	$0.827098\pi$
$522$	5.50336e11	0.324422
$523$	−1.88151e12	−1.09963	−0.549817	−	0.835285i	$-0.685303\pi$
$523$	−1.88151e12	−1.09963	−0.549817	+	0.835285i	$0.685303\pi$
$524$	−1.22338e12	−0.708879
$525$	−3.73511e11	−0.214579
$526$	−2.09074e12	−1.19087
$527$	−2.99264e11	−0.169008
$528$	8.73651e10	0.0489199
$529$	−1.79383e12	−0.995933
$530$	7.24903e11	0.399060
$531$	−1.68285e11	−0.0918587
$532$	−3.39296e11	−0.183644
$533$	1.43285e12	0.769006
$534$	−6.49388e11	−0.345596
$535$	−9.58213e11	−0.505673
$536$	−1.55421e12	−0.813335
$537$	−9.15905e11	−0.475298
$538$	3.53222e11	0.181772
$539$	1.06163e12	0.541779
$540$	7.32556e10	0.0370740
$541$	−1.62100e12	−0.813568	−0.406784	−	0.913524i	$-0.633350\pi$
$541$	−1.62100e12	−0.813568	−0.406784	+	0.913524i	$0.633350\pi$
$542$	5.36767e11	0.267171
$543$	1.59351e12	0.786604
$544$	−1.82985e11	−0.0895819
$545$	−1.19417e12	−0.579803
$546$	9.10946e11	0.438658
$547$	1.76631e12	0.843575	0.421787	−	0.906695i	$-0.361403\pi$
$547$	1.76631e12	0.843575	0.421787	+	0.906695i	$0.361403\pi$
$548$	−1.48692e11	−0.0704327
$549$	−4.60359e10	−0.0216282
$550$	−7.15123e10	−0.0333234
$551$	−6.40309e11	−0.295943
$552$	−8.67019e10	−0.0397469
$553$	−2.14496e12	−0.975338
$554$	−3.09343e12	−1.39523
$555$	8.84097e11	0.395532
$556$	−8.61336e11	−0.382240
$557$	2.60533e12	1.14687	0.573435	−	0.819251i	$-0.305610\pi$
$557$	2.60533e12	1.14687	0.573435	+	0.819251i	$0.305610\pi$
$558$	8.58405e11	0.374834
$559$	−1.96976e12	−0.853219
$560$	−7.42084e11	−0.318865
$561$	−3.39186e10	−0.0144579
$562$	−2.57800e12	−1.09011
$563$	4.01223e12	1.68306	0.841528	−	0.540214i	$-0.181657\pi$
$563$	4.01223e12	1.68306	0.841528	+	0.540214i	$0.181657\pi$
$564$	−1.73260e11	−0.0721010
$565$	1.15025e12	0.474868
$566$	3.45004e12	1.41303
$567$	5.08158e11	0.206478
$568$	8.36039e11	0.337023
$569$	−3.21451e12	−1.28561	−0.642806	−	0.766029i	$-0.722230\pi$
$569$	−3.21451e12	−1.28561	−0.642806	+	0.766029i	$0.722230\pi$
$570$	1.12632e11	0.0446915
$571$	−6.41308e11	−0.252467	−0.126233	−	0.992001i	$-0.540289\pi$
$571$	−6.41308e11	−0.252467	−0.126233	+	0.992001i	$0.540289\pi$
$572$	−1.31981e11	−0.0515501
$573$	6.94922e11	0.269303
$574$	−5.17459e12	−1.98963
$575$	3.34337e10	0.0127550
$576$	8.62745e11	0.326574
$577$	−3.87706e12	−1.45617	−0.728085	−	0.685487i	$-0.759589\pi$
$577$	−3.87706e12	−1.45617	−0.728085	+	0.685487i	$0.759589\pi$
$578$	1.99849e12	0.744778
$579$	−1.62299e12	−0.600152
$580$	6.77270e11	0.248505
$581$	−7.09511e12	−2.58325
$582$	−5.02737e11	−0.181630
$583$	−7.28544e11	−0.261184
$584$	5.40025e12	1.92113
$585$	2.28832e11	0.0807822
$586$	−2.73049e12	−0.956536
$587$	3.11635e12	1.08336	0.541682	−	0.840583i	$-0.317788\pi$
$587$	3.11635e12	1.08336	0.541682	+	0.840583i	$0.317788\pi$
$588$	1.76858e12	0.610136
$589$	−9.98744e11	−0.341929
$590$	2.73677e11	0.0929831
$591$	7.51696e11	0.253453
$592$	1.75650e12	0.587762
$593$	−1.96777e12	−0.653475	−0.326738	−	0.945115i	$-0.605949\pi$
$593$	−1.96777e12	−0.653475	−0.326738	+	0.945115i	$0.605949\pi$
$594$	9.72918e10	0.0320654
$595$	2.88107e11	0.0942382
$596$	8.39663e11	0.272582
$597$	−2.52891e12	−0.814797
$598$	−8.15405e10	−0.0260746
$599$	−2.44774e12	−0.776864	−0.388432	−	0.921477i	$-0.626983\pi$
$599$	−2.44774e12	−0.776864	−0.388432	+	0.921477i	$0.626983\pi$
$600$	−3.95699e11	−0.124648
$601$	8.75163e11	0.273624	0.136812	−	0.990597i	$-0.456314\pi$
$601$	8.75163e11	0.273624	0.136812	+	0.990597i	$0.456314\pi$
$602$	7.11357e12	2.20751
$603$	−8.15383e11	−0.251150
$604$	1.11071e12	0.339574
$605$	−1.40185e12	−0.425403
$606$	−1.52156e12	−0.458314
$607$	−1.87732e12	−0.561293	−0.280647	−	0.959811i	$-0.590549\pi$
$607$	−1.87732e12	−0.561293	−0.280647	+	0.959811i	$0.590549\pi$
$608$	−6.10682e11	−0.181238
$609$	4.69807e12	1.38402
$610$	7.48668e10	0.0218930
$611$	−5.41219e11	−0.157104
$612$	−5.65055e10	−0.0162821
$613$	2.33539e12	0.668017	0.334009	−	0.942570i	$-0.391599\pi$
$613$	2.33539e12	0.668017	0.334009	+	0.942570i	$0.391599\pi$
$614$	3.77213e12	1.07110
$615$	−1.29987e12	−0.366406
$616$	1.58313e12	0.442999
$617$	4.28203e12	1.18951	0.594753	−	0.803909i	$-0.297250\pi$
$617$	4.28203e12	1.18951	0.594753	+	0.803909i	$0.297250\pi$
$618$	−6.12875e11	−0.169014
$619$	−5.25474e12	−1.43861	−0.719305	−	0.694694i	$-0.755540\pi$
$619$	−5.25474e12	−1.43861	−0.719305	+	0.694694i	$0.755540\pi$
$620$	1.05639e12	0.287120
$621$	−4.54862e10	−0.0122735
$622$	1.46386e12	0.392142
$623$	−5.54364e12	−1.47434
$624$	4.54638e11	0.120043
$625$	1.52588e11	0.0400000
$626$	3.40928e12	0.887315
$627$	−1.13198e11	−0.0292505
$628$	2.80853e12	0.720545
$629$	−6.81945e11	−0.173709
$630$	−8.26401e11	−0.209006
$631$	−1.73310e12	−0.435202	−0.217601	−	0.976038i	$-0.569823\pi$
$631$	−1.73310e12	−0.435202	−0.217601	+	0.976038i	$0.569823\pi$
$632$	−2.27237e12	−0.566568
$633$	−2.39461e12	−0.592813
$634$	−1.73577e12	−0.426668
$635$	9.49222e11	0.231679
$636$	−1.21369e12	−0.294138
$637$	5.52459e12	1.32945
$638$	8.99490e11	0.214933
$639$	4.38609e11	0.104069
$640$	9.64583e10	0.0227263
$641$	9.42113e11	0.220415	0.110208	−	0.993909i	$-0.464848\pi$
$641$	9.42113e11	0.220415	0.110208	+	0.993909i	$0.464848\pi$
$642$	−2.12007e12	−0.492540
$643$	1.07698e11	0.0248462	0.0124231	−	0.999923i	$-0.496046\pi$
$643$	1.07698e11	0.0248462	0.0124231	+	0.999923i	$0.496046\pi$
$644$	−2.22838e11	−0.0510508
$645$	1.78695e12	0.406530
$646$	−8.68783e10	−0.0196275
$647$	6.89733e12	1.54743	0.773717	−	0.633532i	$-0.218395\pi$
$647$	6.89733e12	1.54743	0.773717	+	0.633532i	$0.218395\pi$
$648$	5.38343e11	0.119942
$649$	−2.75051e11	−0.0608573
$650$	−3.72143e11	−0.0817710
$651$	7.32796e12	1.59908
$652$	1.61009e12	0.348928
$653$	−6.08371e12	−1.30936	−0.654681	−	0.755906i	$-0.727197\pi$
$653$	−6.08371e12	−1.30936	−0.654681	+	0.755906i	$0.727197\pi$
$654$	−2.64212e12	−0.564745
$655$	3.46687e12	0.735955
$656$	−2.58255e12	−0.544480
$657$	2.83312e12	0.593226
$658$	1.95455e12	0.406472
$659$	−7.58358e12	−1.56635	−0.783177	−	0.621799i	$-0.786402\pi$
$659$	−7.58358e12	−1.56635	−0.783177	+	0.621799i	$0.786402\pi$
$660$	1.19732e11	0.0245619
$661$	−4.44191e12	−0.905030	−0.452515	−	0.891757i	$-0.649473\pi$
$661$	−4.44191e12	−0.905030	−0.452515	+	0.891757i	$0.649473\pi$
$662$	−1.11857e12	−0.226361
$663$	−1.76509e11	−0.0354777
$664$	−7.51658e12	−1.50060
$665$	9.61508e11	0.190658
$666$	1.95608e12	0.385260
$667$	−4.20533e11	−0.0822685
$668$	3.82516e11	0.0743285
$669$	−2.90312e12	−0.560334
$670$	1.32603e12	0.254224
$671$	−7.52428e10	−0.0143289
$672$	4.48068e12	0.847583
$673$	−5.95654e12	−1.11925	−0.559624	−	0.828747i	$-0.689054\pi$
$673$	−5.95654e12	−1.11925	−0.559624	+	0.828747i	$0.689054\pi$
$674$	2.78527e12	0.519874
$675$	−2.07594e11	−0.0384900
$676$	1.65200e12	0.304264
$677$	3.79342e12	0.694036	0.347018	−	0.937858i	$-0.387194\pi$
$677$	3.79342e12	0.694036	0.347018	+	0.937858i	$0.387194\pi$
$678$	2.54495e12	0.462535
$679$	−4.29172e12	−0.774850
$680$	3.05221e11	0.0547424
$681$	6.18579e12	1.10213
$682$	1.40301e12	0.248331
$683$	−8.63237e12	−1.51788	−0.758939	−	0.651162i	$-0.774282\pi$
$683$	−8.63237e12	−1.51788	−0.758939	+	0.651162i	$0.774282\pi$
$684$	−1.88578e11	−0.0329411
$685$	4.21367e11	0.0731229
$686$	−1.18190e13	−2.03761
$687$	6.10150e12	1.04504
$688$	3.55027e12	0.604106
$689$	−3.79127e12	−0.640911
$690$	7.39727e10	0.0124237
$691$	8.23079e12	1.37338	0.686689	−	0.726951i	$-0.259063\pi$
$691$	8.23079e12	1.37338	0.686689	+	0.726951i	$0.259063\pi$
$692$	1.30563e12	0.216443
$693$	8.30552e11	0.136794
$694$	−7.85757e12	−1.28579
$695$	2.44088e12	0.396840
$696$	4.97714e12	0.803967
$697$	1.00265e12	0.160917
$698$	2.67505e12	0.426562
$699$	−4.24292e12	−0.672230
$700$	−1.01701e12	−0.160097
$701$	5.13274e12	0.802819	0.401410	−	0.915899i	$-0.368520\pi$
$701$	5.13274e12	0.802819	0.401410	+	0.915899i	$0.368520\pi$
$702$	5.06296e11	0.0786842
$703$	−2.27588e12	−0.351439
$704$	1.41010e12	0.216359
$705$	4.90988e11	0.0748549
$706$	−2.38404e12	−0.361154
$707$	−1.29892e13	−1.95521
$708$	−4.58212e11	−0.0685357
$709$	3.81960e12	0.567688	0.283844	−	0.958870i	$-0.408390\pi$
$709$	3.81960e12	0.567688	0.283844	+	0.958870i	$0.408390\pi$
$710$	−7.13296e11	−0.105343
$711$	−1.19215e12	−0.174951
$712$	−5.87294e12	−0.856438
$713$	−6.55940e11	−0.0950520
$714$	6.37442e11	0.0917907
$715$	3.74012e11	0.0535190
$716$	−2.49386e12	−0.354620
$717$	2.02346e12	0.285929
$718$	−6.60857e12	−0.927999
$719$	−1.11913e13	−1.56172	−0.780859	−	0.624708i	$-0.785218\pi$
$719$	−1.11913e13	−1.56172	−0.780859	+	0.624708i	$0.785218\pi$
$720$	−4.12443e11	−0.0571963
$721$	−5.23194e12	−0.721032
$722$	−2.89942e11	−0.0397094
$723$	−7.24700e12	−0.986360
$724$	4.33887e12	0.586885
$725$	−1.91927e12	−0.257997
$726$	−3.10161e12	−0.414355
$727$	−8.48783e12	−1.12692	−0.563458	−	0.826145i	$-0.690529\pi$
$727$	−8.48783e12	−1.12692	−0.563458	+	0.826145i	$0.690529\pi$
$728$	8.23844e12	1.08706
$729$	2.82430e11	0.0370370
$730$	−4.60741e12	−0.600487
$731$	−1.37836e12	−0.178539
$732$	−1.25348e11	−0.0161368
$733$	4.12823e12	0.528197	0.264098	−	0.964496i	$-0.414926\pi$
$733$	4.12823e12	0.528197	0.264098	+	0.964496i	$0.414926\pi$
$734$	−6.33093e12	−0.805073
$735$	−5.01185e12	−0.633440
$736$	−4.01074e11	−0.0503819
$737$	−1.33269e12	−0.166390
$738$	−2.87599e12	−0.356890
$739$	3.52537e12	0.434815	0.217408	−	0.976081i	$-0.430240\pi$
$739$	3.52537e12	0.434815	0.217408	+	0.976081i	$0.430240\pi$
$740$	2.40725e12	0.295106
$741$	−5.89069e11	−0.0717768
$742$	1.36917e13	1.65821
$743$	−6.43206e12	−0.774284	−0.387142	−	0.922020i	$-0.626538\pi$
$743$	−6.43206e12	−0.774284	−0.387142	+	0.922020i	$0.626538\pi$
$744$	7.76326e12	0.928894
$745$	−2.37946e12	−0.282993
$746$	2.70345e12	0.319590
$747$	−3.94340e12	−0.463370
$748$	−9.23547e10	−0.0107870
$749$	−1.80984e13	−2.10122
$750$	3.37604e11	0.0389612
$751$	1.02373e12	0.117437	0.0587184	−	0.998275i	$-0.481299\pi$
$751$	1.02373e12	0.117437	0.0587184	+	0.998275i	$0.481299\pi$
$752$	9.75485e11	0.111235
$753$	3.06344e10	0.00347242
$754$	4.68085e12	0.527417
$755$	−3.14757e12	−0.352545
$756$	1.38363e12	0.154053
$757$	5.86577e12	0.649222	0.324611	−	0.945848i	$-0.394767\pi$
$757$	5.86577e12	0.649222	0.324611	+	0.945848i	$0.394767\pi$
$758$	9.85287e12	1.08405
$759$	−7.43443e10	−0.00813130
$760$	1.01862e12	0.110752
$761$	6.18495e12	0.668506	0.334253	−	0.942483i	$-0.391516\pi$
$761$	6.18495e12	0.668506	0.334253	+	0.942483i	$0.391516\pi$
$762$	2.10017e12	0.225662
$763$	−2.25550e13	−2.40926
$764$	1.89216e12	0.200926
$765$	1.60127e11	0.0169039
$766$	−6.41934e12	−0.673692
$767$	−1.43134e12	−0.149336
$768$	5.66682e12	0.587779
$769$	−1.87533e11	−0.0193379	−0.00966895	−	0.999953i	$-0.503078\pi$
$769$	−1.87533e11	−0.0193379	−0.00966895	+	0.999953i	$0.503078\pi$
$770$	−1.35070e12	−0.138469
$771$	5.60965e12	0.571731
$772$	−4.41912e12	−0.447773
$773$	−3.37329e12	−0.339818	−0.169909	−	0.985460i	$-0.554347\pi$
$773$	−3.37329e12	−0.339818	−0.169909	+	0.985460i	$0.554347\pi$
$774$	3.95366e12	0.395972
$775$	−2.99364e12	−0.298086
$776$	−4.54666e12	−0.450106
$777$	1.66985e13	1.64355
$778$	−1.29681e13	−1.26902
$779$	3.34618e12	0.325560
$780$	6.23072e11	0.0602715
$781$	7.16879e11	0.0689471
$782$	−5.70586e10	−0.00545621
$783$	2.61114e12	0.248258
$784$	−9.95744e12	−0.941294
$785$	−7.95891e12	−0.748066
$786$	7.67052e12	0.716841
$787$	−3.45820e12	−0.321340	−0.160670	−	0.987008i	$-0.551365\pi$
$787$	−3.45820e12	−0.321340	−0.160670	+	0.987008i	$0.551365\pi$
$788$	2.04674e12	0.189101
$789$	−9.91980e12	−0.911290
$790$	1.93875e12	0.177093
$791$	2.17255e13	1.97322
$792$	8.79889e11	0.0794629
$793$	−3.91556e11	−0.0351612
$794$	−7.54765e12	−0.673937
$795$	3.43940e12	0.305373
$796$	−6.88580e12	−0.607919
$797$	−1.50198e13	−1.31857	−0.659284	−	0.751894i	$-0.729141\pi$
$797$	−1.50198e13	−1.31857	−0.659284	+	0.751894i	$0.729141\pi$
$798$	2.12736e12	0.185707
$799$	−3.78722e11	−0.0328746
$800$	−1.83046e12	−0.157999
$801$	−3.08111e12	−0.264460
$802$	−3.78115e12	−0.322730
$803$	4.63055e12	0.393018
$804$	−2.22015e12	−0.187383
$805$	6.31485e11	0.0530007
$806$	7.30111e12	0.609371
$807$	1.67591e12	0.139097
$808$	−1.37608e13	−1.13577
$809$	−5.19090e12	−0.426063	−0.213032	−	0.977045i	$-0.568334\pi$
$809$	−5.19090e12	−0.426063	−0.213032	+	0.977045i	$0.568334\pi$
$810$	−4.59306e11	−0.0374904
$811$	5.64885e11	0.0458528	0.0229264	−	0.999737i	$-0.492702\pi$
$811$	5.64885e11	0.0458528	0.0229264	+	0.999737i	$0.492702\pi$
$812$	1.27920e13	1.03261
$813$	2.54676e12	0.204447
$814$	3.19710e12	0.255238
$815$	−4.56273e12	−0.362256
$816$	3.18137e11	0.0251193
$817$	−4.60003e12	−0.361212
$818$	2.82960e12	0.220971
$819$	4.32211e12	0.335674
$820$	−3.53933e12	−0.273375
$821$	2.42921e13	1.86604	0.933020	−	0.359826i	$-0.117164\pi$
$821$	2.42921e13	1.86604	0.933020	+	0.359826i	$0.117164\pi$
$822$	9.32284e11	0.0712238
$823$	−1.33695e13	−1.01582	−0.507910	−	0.861410i	$-0.669582\pi$
$823$	−1.33695e13	−1.01582	−0.507910	+	0.861410i	$0.669582\pi$
$824$	−5.54273e12	−0.418843
$825$	−3.39300e11	−0.0255000
$826$	5.16912e12	0.386372
$827$	4.50524e12	0.334922	0.167461	−	0.985879i	$-0.446443\pi$
$827$	4.50524e12	0.334922	0.167461	+	0.985879i	$0.446443\pi$
$828$	−1.23851e11	−0.00915722
$829$	−8.89486e12	−0.654099	−0.327050	−	0.945007i	$-0.606054\pi$
$829$	−8.89486e12	−0.654099	−0.327050	+	0.945007i	$0.606054\pi$
$830$	6.41303e12	0.469042
$831$	−1.46772e13	−1.06767
$832$	7.33803e12	0.530914
$833$	3.86588e12	0.278193
$834$	5.40050e12	0.386533
$835$	−1.08399e12	−0.0771675
$836$	−3.08219e11	−0.0218238
$837$	4.07282e12	0.286834
$838$	−2.57010e12	−0.180033
$839$	1.18724e13	0.827199	0.413599	−	0.910459i	$-0.364271\pi$
$839$	1.18724e13	0.827199	0.413599	+	0.910459i	$0.364271\pi$
$840$	−7.47382e12	−0.517948
$841$	9.63362e12	0.664060
$842$	−1.90492e13	−1.30608
$843$	−1.22317e13	−0.834183
$844$	−6.52011e12	−0.442297
$845$	−4.68149e12	−0.315885
$846$	1.08632e12	0.0729108
$847$	−2.64776e13	−1.76768
$848$	6.83332e12	0.453785
$849$	1.63692e13	1.08129
$850$	−2.60410e11	−0.0171109
$851$	−1.49472e12	−0.0976959
$852$	1.19426e12	0.0776462
$853$	8.65613e12	0.559826	0.279913	−	0.960025i	$-0.409694\pi$
$853$	8.65613e12	0.559826	0.279913	+	0.960025i	$0.409694\pi$
$854$	1.41406e12	0.0909719
$855$	5.34398e11	0.0341993
$856$	−1.91735e13	−1.22059
$857$	−2.58026e12	−0.163399	−0.0816997	−	0.996657i	$-0.526035\pi$
$857$	−2.58026e12	−0.163399	−0.0816997	+	0.996657i	$0.526035\pi$
$858$	8.27509e11	0.0521291
$859$	−1.20094e13	−0.752581	−0.376291	−	0.926502i	$-0.622801\pi$
$859$	−1.20094e13	−0.752581	−0.376291	+	0.926502i	$0.622801\pi$
$860$	4.86556e12	0.303312
$861$	−2.45515e13	−1.52252
$862$	−8.89099e12	−0.548489
$863$	2.57711e13	1.58156	0.790779	−	0.612102i	$-0.209676\pi$
$863$	2.57711e13	1.58156	0.790779	+	0.612102i	$0.209676\pi$
$864$	2.49032e12	0.152035
$865$	−3.69995e12	−0.224710
$866$	1.33381e13	0.805867
$867$	9.48210e12	0.569926
$868$	1.99528e13	1.19307
$869$	−1.94849e12	−0.115907
$870$	−4.24642e12	−0.251296
$871$	−6.93519e12	−0.408297
$872$	−2.38949e13	−1.39952
$873$	−2.38530e12	−0.138989
$874$	−1.90424e11	−0.0110387
$875$	2.88203e12	0.166212
$876$	7.71410e12	0.442605
$877$	−4.15440e12	−0.237143	−0.118571	−	0.992946i	$-0.537831\pi$
$877$	−4.15440e12	−0.237143	−0.118571	+	0.992946i	$0.537831\pi$
$878$	9.84880e12	0.559317
$879$	−1.29552e13	−0.731970
$880$	−6.74113e11	−0.0378932
$881$	2.65371e13	1.48409	0.742047	−	0.670348i	$-0.233855\pi$
$881$	2.65371e13	1.48409	0.742047	+	0.670348i	$0.233855\pi$
$882$	−1.10888e13	−0.616989
$883$	1.41263e13	0.781998	0.390999	−	0.920391i	$-0.372130\pi$
$883$	1.41263e13	0.781998	0.390999	+	0.920391i	$0.372130\pi$
$884$	−4.80604e11	−0.0264699
$885$	1.29850e12	0.0711534
$886$	1.81376e12	0.0988843
$887$	−1.50302e13	−0.815283	−0.407642	−	0.913142i	$-0.633649\pi$
$887$	−1.50302e13	−0.815283	−0.407642	+	0.913142i	$0.633649\pi$
$888$	1.76905e13	0.954731
$889$	1.79286e13	0.962694
$890$	5.01071e12	0.267697
$891$	4.61614e11	0.0245374
$892$	−7.90470e12	−0.418065
$893$	−1.26392e12	−0.0665103
$894$	−5.26461e12	−0.275643
$895$	7.06717e12	0.368164
$896$	1.82187e12	0.0944348
$897$	−3.86880e11	−0.0199531
$898$	−6.29217e12	−0.322892
$899$	3.76544e13	1.92263
$900$	−5.65244e11	−0.0287174
$901$	−2.65297e12	−0.134113
$902$	−4.70063e12	−0.236443
$903$	3.37513e13	1.68926
$904$	2.30160e13	1.14623
$905$	−1.22956e13	−0.609301
$906$	−6.96406e12	−0.343389
$907$	2.29165e13	1.12439	0.562193	−	0.827006i	$-0.309958\pi$
$907$	2.29165e13	1.12439	0.562193	+	0.827006i	$0.309958\pi$
$908$	1.68429e13	0.822299
$909$	−7.21926e12	−0.350716
$910$	−7.02891e12	−0.339783
$911$	−7.02130e12	−0.337742	−0.168871	−	0.985638i	$-0.554012\pi$
$911$	−7.02130e12	−0.337742	−0.168871	+	0.985638i	$0.554012\pi$
$912$	1.06173e12	0.0508203
$913$	−6.44524e12	−0.306988
$914$	1.18210e13	0.560267
$915$	3.55215e11	0.0167532
$916$	1.66134e13	0.779701
$917$	6.54810e13	3.05811
$918$	3.54284e11	0.0164649
$919$	1.14513e13	0.529584	0.264792	−	0.964306i	$-0.414697\pi$
$919$	1.14513e13	0.529584	0.264792	+	0.964306i	$0.414697\pi$
$920$	6.68996e11	0.0307878
$921$	1.78974e13	0.819636
$922$	−2.11065e12	−0.0961893
$923$	3.73056e12	0.169187
$924$	2.26146e12	0.102062
$925$	−6.82174e12	−0.306378
$926$	9.65703e12	0.431613
$927$	−2.90787e12	−0.129335
$928$	2.30238e13	1.01908
$929$	−4.07798e13	−1.79628	−0.898141	−	0.439708i	$-0.855082\pi$
$929$	−4.07798e13	−1.79628	−0.898141	+	0.439708i	$0.855082\pi$
$930$	−6.62350e12	−0.290345
$931$	1.29017e13	0.562826
$932$	−1.15528e13	−0.501550
$933$	6.94548e12	0.300079
$934$	−1.89556e13	−0.815034
$935$	2.61718e11	0.0111990
$936$	4.57885e12	0.194991
$937$	2.76611e12	0.117231	0.0586153	−	0.998281i	$-0.481331\pi$
$937$	2.76611e12	0.117231	0.0586153	+	0.998281i	$0.481331\pi$
$938$	2.50456e13	1.05638
$939$	1.61758e13	0.679000
$940$	1.33688e12	0.0558492
$941$	1.33465e13	0.554900	0.277450	−	0.960740i	$-0.410511\pi$
$941$	1.33465e13	0.554900	0.277450	+	0.960740i	$0.410511\pi$
$942$	−1.76093e13	−0.728638
$943$	2.19765e12	0.0905017
$944$	2.57982e12	0.105734
$945$	−3.92097e12	−0.159938
$946$	6.46201e12	0.262336
$947$	−4.79853e13	−1.93880	−0.969402	−	0.245480i	$-0.921054\pi$
$947$	−4.79853e13	−1.93880	−0.969402	+	0.245480i	$0.921054\pi$
$948$	−3.24602e12	−0.130531
$949$	2.40969e13	0.964413
$950$	−8.69074e11	−0.0346179
$951$	−8.23558e12	−0.326499
$952$	5.76491e12	0.227471
$953$	4.46482e13	1.75342	0.876710	−	0.481020i	$-0.159733\pi$
$953$	4.46482e13	1.75342	0.876710	+	0.481020i	$0.159733\pi$
$954$	7.60974e12	0.297442
$955$	−5.36205e12	−0.208601
$956$	5.50954e12	0.213331
$957$	4.26775e12	0.164473
$958$	7.84209e12	0.300806
$959$	7.95865e12	0.303847
$960$	−6.65698e12	−0.252963
$961$	3.22930e13	1.22139
$962$	1.66374e13	0.626320
$963$	−1.00589e13	−0.376907
$964$	−1.97324e13	−0.735923
$965$	1.25230e13	0.464876
$966$	1.39717e12	0.0516242
$967$	−2.18351e13	−0.803039	−0.401519	−	0.915851i	$-0.631518\pi$
$967$	−2.18351e13	−0.803039	−0.401519	+	0.915851i	$0.631518\pi$
$968$	−2.80504e13	−1.02683
$969$	−4.12206e11	−0.0150196
$970$	3.87914e12	0.140690
$971$	−1.25175e13	−0.451888	−0.225944	−	0.974140i	$-0.572547\pi$
$971$	−1.25175e13	−0.451888	−0.225944	+	0.974140i	$0.572547\pi$
$972$	7.69008e11	0.0276333
$973$	4.61026e13	1.64899
$974$	−4.73655e12	−0.168635
$975$	−1.76568e12	−0.0625736
$976$	7.05734e11	0.0248953
$977$	3.20249e13	1.12451	0.562253	−	0.826965i	$-0.309935\pi$
$977$	3.20249e13	1.12451	0.562253	+	0.826965i	$0.309935\pi$
$978$	−1.00951e13	−0.352847
$979$	−5.03588e12	−0.175208
$980$	−1.36464e13	−0.472609
$981$	−1.25359e13	−0.432160
$982$	1.51386e13	0.519500
$983$	5.40250e13	1.84546	0.922728	−	0.385452i	$-0.125954\pi$
$983$	5.40250e13	1.84546	0.922728	+	0.385452i	$0.125954\pi$
$984$	−2.60099e13	−0.884426
$985$	−5.80012e12	−0.196324
$986$	3.27546e12	0.110364
$987$	9.27363e12	0.311044
$988$	−1.60394e12	−0.0535527
$989$	−3.02114e12	−0.100412
$990$	−7.50708e11	−0.0248378
$991$	−8.74099e12	−0.287892	−0.143946	−	0.989586i	$-0.545979\pi$
$991$	−8.74099e12	−0.287892	−0.143946	+	0.989586i	$0.545979\pi$
$992$	3.59121e13	1.17744
$993$	−5.30719e12	−0.173218
$994$	−1.34725e13	−0.437733
$995$	1.95132e13	0.631139
$996$	−1.07372e13	−0.345720
$997$	−1.29294e13	−0.414429	−0.207214	−	0.978296i	$-0.566440\pi$
$997$	−1.29294e13	−0.414429	−0.207214	+	0.978296i	$0.566440\pi$
$998$	1.15711e13	0.369221
$999$	9.28090e12	0.294812

Display

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a_n

instead) (See

a_n

instead) Display

a_n

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n

up to: 50 250 1000 (See only

a_p

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a_p

) (See only

a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.10.a.c.1.5	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.10.a.c.1.5	✓	12	1.1	even	1	trivial

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	285.10.a.c.1.5

Level	$285$
Weight	$10$
Character	285.1
Self dual	yes
Analytic conductor	$146.785$
Analytic rank	$1$
Dimension	$12$
CM	no
Inner twists	$1$