LMFDB - Embedded newform 105.8.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,8,Mod(1,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("105.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$N$	$=$	$105 = 3 \cdot 5 \cdot 7$
Weight:	$k$	$=$	$8$
Character orbit:	$[\chi]$	$=$	105.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:	$32.8004276758$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{2} - 2$ x^2 - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$2^{2}$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	105.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-17.3137 q^{2} +27.0000 q^{3} +171.765 q^{4} +125.000 q^{5} -467.470 q^{6} +343.000 q^{7} -757.726 q^{8} +729.000 q^{9} -2164.21 q^{10} -6025.40 q^{11} +4637.64 q^{12} -628.668 q^{13} -5938.60 q^{14} +3375.00 q^{15} -8866.81 q^{16} -9453.79 q^{17} -12621.7 q^{18} -3239.07 q^{19} +21470.6 q^{20} +9261.00 q^{21} +104322. q^{22} -15467.1 q^{23} -20458.6 q^{24} +15625.0 q^{25} +10884.6 q^{26} +19683.0 q^{27} +58915.2 q^{28} +44459.0 q^{29} -58433.8 q^{30} +163312. q^{31} +250506. q^{32} -162686. q^{33} +163680. q^{34} +42875.0 q^{35} +125216. q^{36} +214874. q^{37} +56080.3 q^{38} -16974.0 q^{39} -94715.7 q^{40} -549784. q^{41} -160342. q^{42} -718371. q^{43} -1.03495e6 q^{44} +91125.0 q^{45} +267792. q^{46} -847994. q^{47} -239404. q^{48} +117649. q^{49} -270527. q^{50} -255252. q^{51} -107983. q^{52} -2.07211e6 q^{53} -340786. q^{54} -753175. q^{55} -259900. q^{56} -87454.9 q^{57} -769750. q^{58} -686310. q^{59} +579705. q^{60} +1.88974e6 q^{61} -2.82753e6 q^{62} +250047. q^{63} -3.20224e6 q^{64} -78583.5 q^{65} +2.81670e6 q^{66} -243851. q^{67} -1.62382e6 q^{68} -417611. q^{69} -742325. q^{70} -1.12944e6 q^{71} -552382. q^{72} +2.61957e6 q^{73} -3.72026e6 q^{74} +421875. q^{75} -556357. q^{76} -2.06671e6 q^{77} +293883. q^{78} -132486. q^{79} -1.10835e6 q^{80} +531441. q^{81} +9.51879e6 q^{82} -7.53836e6 q^{83} +1.59071e6 q^{84} -1.18172e6 q^{85} +1.24377e7 q^{86} +1.20039e6 q^{87} +4.56560e6 q^{88} -2.53142e6 q^{89} -1.57771e6 q^{90} -215633. q^{91} -2.65669e6 q^{92} +4.40942e6 q^{93} +1.46819e7 q^{94} -404884. q^{95} +6.76367e6 q^{96} -1.75138e7 q^{97} -2.03694e6 q^{98} -4.39252e6 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q - 12 q^{2} + 54 q^{3} + 72 q^{4} + 250 q^{5} - 324 q^{6} + 686 q^{7} - 1968 q^{8} + 1458 q^{9} - 1500 q^{10} - 10976 q^{11} + 1944 q^{12} - 2796 q^{13} - 4116 q^{14} + 6750 q^{15} - 2528 q^{16} - 8284 q^{17}+ \cdots - 8001504 q^{99}+O(q^{100})$ 2 * q - 12 * q^2 + 54 * q^3 + 72 * q^4 + 250 * q^5 - 324 * q^6 + 686 * q^7 - 1968 * q^8 + 1458 * q^9 - 1500 * q^10 - 10976 * q^11 + 1944 * q^12 - 2796 * q^13 - 4116 * q^14 + 6750 * q^15 - 2528 * q^16 - 8284 * q^17 - 8748 * q^18 - 8096 * q^19 + 9000 * q^20 + 18522 * q^21 + 78016 * q^22 - 90976 * q^23 - 53136 * q^24 + 31250 * q^25 - 632 * q^26 + 39366 * q^27 + 24696 * q^28 - 12532 * q^29 - 40500 * q^30 - 117960 * q^31 + 439104 * q^32 - 296352 * q^33 + 169896 * q^34 + 85750 * q^35 + 52488 * q^36 - 174212 * q^37 + 30272 * q^38 - 75492 * q^39 - 246000 * q^40 - 492700 * q^41 - 111132 * q^42 - 661176 * q^43 - 541056 * q^44 + 182250 * q^45 - 133440 * q^46 - 1675408 * q^47 - 68256 * q^48 + 235298 * q^49 - 187500 * q^50 - 223668 * q^51 + 108240 * q^52 - 555436 * q^53 - 236196 * q^54 - 1372000 * q^55 - 675024 * q^56 - 218592 * q^57 - 1072584 * q^58 - 3121176 * q^59 + 243000 * q^60 - 511588 * q^61 - 4322128 * q^62 + 500094 * q^63 - 3011456 * q^64 - 349500 * q^65 + 2106432 * q^66 - 252728 * q^67 - 1740528 * q^68 - 2456352 * q^69 - 514500 * q^70 - 1099336 * q^71 - 1434672 * q^72 + 5012588 * q^73 - 5787752 * q^74 + 843750 * q^75 - 71808 * q^76 - 3764768 * q^77 - 17064 * q^78 + 83648 * q^79 - 316000 * q^80 + 1062882 * q^81 + 9822120 * q^82 - 4404184 * q^83 + 666792 * q^84 - 1035500 * q^85 + 12741584 * q^86 - 338364 * q^87 + 10557184 * q^88 - 4381564 * q^89 - 1093500 * q^90 - 959028 * q^91 + 4876416 * q^92 - 3184920 * q^93 + 10285280 * q^94 - 1012000 * q^95 + 11855808 * q^96 - 8539828 * q^97 - 1411788 * q^98 - 8001504 * 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

)

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

$2$	−17.3137	−1.53033	−0.765165	−	0.643834i	$-0.777343\pi$
$2$	−17.3137	−1.53033	−0.765165	+	0.643834i	$0.777343\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	171.765	1.34191
$5$	125.000	0.447214
$5$	125.000	0.447214
$6$	−467.470	−0.883536
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	−757.726	−0.523235
$9$	729.000	0.333333
$10$	−2164.21	−0.684384
$11$	−6025.40	−1.36493	−0.682467	−	0.730917i	$-0.739093\pi$
$11$	−6025.40	−1.36493	−0.682467	+	0.730917i	$0.739093\pi$
$12$	4637.64	0.774752
$13$	−628.668	−0.0793633	−0.0396816	−	0.999212i	$-0.512634\pi$
$13$	−628.668	−0.0793633	−0.0396816	+	0.999212i	$0.512634\pi$
$14$	−5938.60	−0.578410
$15$	3375.00	0.258199
$16$	−8866.81	−0.541187
$17$	−9453.79	−0.466697	−0.233348	−	0.972393i	$-0.574968\pi$
$17$	−9453.79	−0.466697	−0.233348	+	0.972393i	$0.574968\pi$
$18$	−12621.7	−0.510110
$19$	−3239.07	−0.108338	−0.0541692	−	0.998532i	$-0.517251\pi$
$19$	−3239.07	−0.108338	−0.0541692	+	0.998532i	$0.517251\pi$
$20$	21470.6	0.600120
$21$	9261.00	0.218218
$22$	104322.	2.08880
$23$	−15467.1	−0.265070	−0.132535	−	0.991178i	$-0.542312\pi$
$23$	−15467.1	−0.265070	−0.132535	+	0.991178i	$0.542312\pi$
$24$	−20458.6	−0.302090
$25$	15625.0	0.200000
$26$	10884.6	0.121452
$27$	19683.0	0.192450
$28$	58915.2	0.507194
$29$	44459.0	0.338506	0.169253	−	0.985573i	$-0.445864\pi$
$29$	44459.0	0.338506	0.169253	+	0.985573i	$0.445864\pi$
$30$	−58433.8	−0.395130
$31$	163312.	0.984581	0.492291	−	0.870431i	$-0.336160\pi$
$31$	163312.	0.984581	0.492291	+	0.870431i	$0.336160\pi$
$32$	250506.	1.35143
$33$	−162686.	−0.788045
$34$	163680.	0.714200
$35$	42875.0	0.169031
$36$	125216.	0.447303
$37$	214874.	0.697393	0.348696	−	0.937236i	$-0.386624\pi$
$37$	214874.	0.697393	0.348696	+	0.937236i	$0.386624\pi$
$38$	56080.3	0.165794
$39$	−16974.0	−0.0458204
$40$	−94715.7	−0.233998
$41$	−549784.	−1.24580	−0.622900	−	0.782301i	$-0.714046\pi$
$41$	−549784.	−1.24580	−0.622900	+	0.782301i	$0.714046\pi$
$42$	−160342.	−0.333945
$43$	−718371.	−1.37787	−0.688937	−	0.724822i	$-0.741922\pi$
$43$	−718371.	−1.37787	−0.688937	+	0.724822i	$0.741922\pi$
$44$	−1.03495e6	−1.83162
$45$	91125.0	0.149071
$46$	267792.	0.405645
$47$	−847994.	−1.19138	−0.595690	−	0.803215i	$-0.703121\pi$
$47$	−847994.	−1.19138	−0.595690	+	0.803215i	$0.703121\pi$
$48$	−239404.	−0.312455
$49$	117649.	0.142857
$50$	−270527.	−0.306066
$51$	−255252.	−0.269447
$52$	−107983.	−0.106498
$53$	−2.07211e6	−1.91182	−0.955911	−	0.293655i	$-0.905128\pi$
$53$	−2.07211e6	−1.91182	−0.955911	+	0.293655i	$0.905128\pi$
$54$	−340786.	−0.294512
$55$	−753175.	−0.610417
$56$	−259900.	−0.197764
$57$	−87454.9	−0.0625492
$58$	−769750.	−0.518026
$59$	−686310.	−0.435049	−0.217525	−	0.976055i	$-0.569798\pi$
$59$	−686310.	−0.435049	−0.217525	+	0.976055i	$0.569798\pi$
$60$	579705.	0.346480
$61$	1.88974e6	1.06598	0.532989	−	0.846122i	$-0.321069\pi$
$61$	1.88974e6	1.06598	0.532989	+	0.846122i	$0.321069\pi$
$62$	−2.82753e6	−1.50673
$63$	250047.	0.125988
$64$	−3.20224e6	−1.52695
$65$	−78583.5	−0.0354923
$66$	2.81670e6	1.20597
$67$	−243851.	−0.0990520	−0.0495260	−	0.998773i	$-0.515771\pi$
$67$	−243851.	−0.0990520	−0.0495260	+	0.998773i	$0.515771\pi$
$68$	−1.62382e6	−0.626265
$69$	−417611.	−0.153038
$70$	−742325.	−0.258673
$71$	−1.12944e6	−0.374506	−0.187253	−	0.982312i	$-0.559958\pi$
$71$	−1.12944e6	−0.374506	−0.187253	+	0.982312i	$0.559958\pi$
$72$	−552382.	−0.174412
$73$	2.61957e6	0.788133	0.394066	−	0.919082i	$-0.371068\pi$
$73$	2.61957e6	0.788133	0.394066	+	0.919082i	$0.371068\pi$
$74$	−3.72026e6	−1.06724
$75$	421875.	0.115470
$76$	−556357.	−0.145380
$77$	−2.06671e6	−0.515896
$78$	293883.	0.0701203
$79$	−132486.	−0.0302326	−0.0151163	−	0.999886i	$-0.504812\pi$
$79$	−132486.	−0.0302326	−0.0151163	+	0.999886i	$0.504812\pi$
$80$	−1.10835e6	−0.242026
$81$	531441.	0.111111
$82$	9.51879e6	1.90649
$83$	−7.53836e6	−1.44712	−0.723558	−	0.690263i	$-0.757495\pi$
$83$	−7.53836e6	−1.44712	−0.723558	+	0.690263i	$0.757495\pi$
$84$	1.59071e6	0.292829
$85$	−1.18172e6	−0.208713
$86$	1.24377e7	2.10860
$87$	1.20039e6	0.195437
$88$	4.56560e6	0.714182
$89$	−2.53142e6	−0.380626	−0.190313	−	0.981723i	$-0.560950\pi$
$89$	−2.53142e6	−0.380626	−0.190313	+	0.981723i	$0.560950\pi$
$90$	−1.57771e6	−0.228128
$91$	−215633.	−0.0299965
$92$	−2.65669e6	−0.355700
$93$	4.40942e6	0.568448
$94$	1.46819e7	1.82320
$95$	−404884.	−0.0484504
$96$	6.76367e6	0.780249
$97$	−1.75138e7	−1.94840	−0.974202	−	0.225678i	$-0.927540\pi$
$97$	−1.75138e7	−1.94840	−0.974202	+	0.225678i	$0.927540\pi$
$98$	−2.03694e6	−0.218619
$99$	−4.39252e6	−0.454978
$100$	2.68382e6	0.268382
$101$	7.98039e6	0.770725	0.385362	−	0.922765i	$-0.374076\pi$
$101$	7.98039e6	0.770725	0.385362	+	0.922765i	$0.374076\pi$
$102$	4.41936e6	0.412343
$103$	5.45521e6	0.491905	0.245952	−	0.969282i	$-0.420899\pi$
$103$	5.45521e6	0.491905	0.245952	+	0.969282i	$0.420899\pi$
$104$	476358.	0.0415257
$105$	1.15762e6	0.0975900
$106$	3.58759e7	2.92572
$107$	−5.88346e6	−0.464290	−0.232145	−	0.972681i	$-0.574574\pi$
$107$	−5.88346e6	−0.464290	−0.232145	+	0.972681i	$0.574574\pi$
$108$	3.38084e6	0.258251
$109$	−7.47026e6	−0.552514	−0.276257	−	0.961084i	$-0.589094\pi$
$109$	−7.47026e6	−0.552514	−0.276257	+	0.961084i	$0.589094\pi$
$110$	1.30403e7	0.934139
$111$	5.80159e6	0.402640
$112$	−3.04132e6	−0.204550
$113$	8.22846e6	0.536468	0.268234	−	0.963354i	$-0.413560\pi$
$113$	8.22846e6	0.536468	0.268234	+	0.963354i	$0.413560\pi$
$114$	1.51417e6	0.0957210
$115$	−1.93338e6	−0.118543
$116$	7.63648e6	0.454245
$117$	−458299.	−0.0264544
$118$	1.18826e7	0.665769
$119$	−3.24265e6	−0.176395
$120$	−2.55732e6	−0.135099
$121$	1.68183e7	0.863044
$122$	−3.27185e7	−1.63130
$123$	−1.48442e7	−0.719263
$124$	2.80512e7	1.32122
$125$	1.95312e6	0.0894427
$126$	−4.32924e6	−0.192803
$127$	−1.66768e7	−0.722436	−0.361218	−	0.932481i	$-0.617639\pi$
$127$	−1.66768e7	−0.722436	−0.361218	+	0.932481i	$0.617639\pi$
$128$	2.33779e7	0.985303
$129$	−1.93960e7	−0.795515
$130$	1.36057e6	0.0543150
$131$	−3.05686e7	−1.18803	−0.594013	−	0.804455i	$-0.702457\pi$
$131$	−3.05686e7	−1.18803	−0.594013	+	0.804455i	$0.702457\pi$
$132$	−2.79437e7	−1.05749
$133$	−1.11100e6	−0.0409481
$134$	4.22197e6	0.151582
$135$	2.46038e6	0.0860663
$136$	7.16338e6	0.244192
$137$	−4.42073e7	−1.46883	−0.734416	−	0.678700i	$-0.762544\pi$
$137$	−4.42073e7	−1.46883	−0.734416	+	0.678700i	$0.762544\pi$
$138$	7.23040e6	0.234199
$139$	−3.27555e7	−1.03451	−0.517253	−	0.855833i	$-0.673045\pi$
$139$	−3.27555e7	−1.03451	−0.517253	+	0.855833i	$0.673045\pi$
$140$	7.36440e6	0.226824
$141$	−2.28958e7	−0.687843
$142$	1.95548e7	0.573118
$143$	3.78798e6	0.108326
$144$	−6.46391e6	−0.180396
$145$	5.55738e6	0.151385
$146$	−4.53544e7	−1.20610
$147$	3.17652e6	0.0824786
$148$	3.69077e7	0.935839
$149$	4.93438e7	1.22203	0.611014	−	0.791620i	$-0.290762\pi$
$149$	4.93438e7	1.22203	0.611014	+	0.791620i	$0.290762\pi$
$150$	−7.30422e6	−0.176707
$151$	4.30468e7	1.01747	0.508735	−	0.860923i	$-0.330113\pi$
$151$	4.30468e7	1.01747	0.508735	+	0.860923i	$0.330113\pi$
$152$	2.45433e6	0.0566865
$153$	−6.89181e6	−0.155566
$154$	3.57825e7	0.789492
$155$	2.04140e7	0.440318
$156$	−2.91554e6	−0.0614869
$157$	−2.00654e7	−0.413808	−0.206904	−	0.978361i	$-0.566339\pi$
$157$	−2.00654e7	−0.413808	−0.206904	+	0.978361i	$0.566339\pi$
$158$	2.29383e6	0.0462659
$159$	−5.59470e7	−1.10379
$160$	3.13133e7	0.604378
$161$	−5.30521e6	−0.100187
$162$	−9.20121e6	−0.170037
$163$	344989.	0.00623949	0.00311974	−	0.999995i	$-0.499007\pi$
$163$	344989.	0.00623949	0.00311974	+	0.999995i	$0.499007\pi$
$164$	−9.44333e7	−1.67175
$165$	−2.03357e7	−0.352424
$166$	1.30517e8	2.21457
$167$	−3.11874e7	−0.518169	−0.259085	−	0.965855i	$-0.583421\pi$
$167$	−3.11874e7	−0.518169	−0.259085	+	0.965855i	$0.583421\pi$
$168$	−7.01730e6	−0.114179
$169$	−6.23533e7	−0.993701
$170$	2.04600e7	0.319400
$171$	−2.36128e6	−0.0361128
$172$	−1.23391e8	−1.84898
$173$	−3.52528e7	−0.517646	−0.258823	−	0.965925i	$-0.583335\pi$
$173$	−3.52528e7	−0.517646	−0.258823	+	0.965925i	$0.583335\pi$
$174$	−2.07833e7	−0.299083
$175$	5.35938e6	0.0755929
$176$	5.34261e7	0.738685
$177$	−1.85304e7	−0.251176
$178$	4.38282e7	0.582483
$179$	1.02247e8	1.33249	0.666246	−	0.745732i	$-0.267900\pi$
$179$	1.02247e8	1.33249	0.666246	+	0.745732i	$0.267900\pi$
$180$	1.56520e7	0.200040
$181$	−5.21416e7	−0.653596	−0.326798	−	0.945094i	$-0.605970\pi$
$181$	−5.21416e7	−0.653596	−0.326798	+	0.945094i	$0.605970\pi$
$182$	3.73341e6	0.0459045
$183$	5.10231e7	0.615443
$184$	1.17198e7	0.138694
$185$	2.68592e7	0.311884
$186$	−7.63434e7	−0.869913
$187$	5.69629e7	0.637010
$188$	−1.45655e8	−1.59872
$189$	6.75127e6	0.0727393
$190$	7.01004e6	0.0741452
$191$	1.44401e8	1.49953	0.749764	−	0.661705i	$-0.230167\pi$
$191$	1.44401e8	1.49953	0.749764	+	0.661705i	$0.230167\pi$
$192$	−8.64605e7	−0.881584
$193$	−3.75823e7	−0.376299	−0.188149	−	0.982140i	$-0.560249\pi$
$193$	−3.75823e7	−0.376299	−0.188149	+	0.982140i	$0.560249\pi$
$194$	3.03229e8	2.98170
$195$	−2.12175e6	−0.0204915
$196$	2.02079e7	0.191701
$197$	1.16331e8	1.08408	0.542042	−	0.840351i	$-0.317651\pi$
$197$	1.16331e8	1.08408	0.542042	+	0.840351i	$0.317651\pi$
$198$	7.60508e7	0.696266
$199$	−1.04716e8	−0.941952	−0.470976	−	0.882146i	$-0.656098\pi$
$199$	−1.04716e8	−0.941952	−0.470976	+	0.882146i	$0.656098\pi$
$200$	−1.18395e7	−0.104647
$201$	−6.58398e6	−0.0571877
$202$	−1.38170e8	−1.17946
$203$	1.52494e7	0.127943
$204$	−4.38433e7	−0.361574
$205$	−6.87230e7	−0.557139
$206$	−9.44498e7	−0.752776
$207$	−1.12755e7	−0.0883567
$208$	5.57428e6	0.0429504
$209$	1.95167e7	0.147875
$210$	−2.00428e7	−0.149345
$211$	2.01137e8	1.47402	0.737010	−	0.675882i	$-0.236237\pi$
$211$	2.01137e8	1.47402	0.737010	+	0.675882i	$0.236237\pi$
$212$	−3.55915e8	−2.56549
$213$	−3.04949e7	−0.216221
$214$	1.01864e8	0.710517
$215$	−8.97964e7	−0.616204
$216$	−1.49143e7	−0.100697
$217$	5.60159e7	0.372137
$218$	1.29338e8	0.845528
$219$	7.07283e7	0.455029
$220$	−1.29369e8	−0.819125
$221$	5.94329e6	0.0370386
$222$	−1.00447e8	−0.616172
$223$	−2.75457e8	−1.66336	−0.831681	−	0.555254i	$-0.812621\pi$
$223$	−2.75457e8	−1.66336	−0.831681	+	0.555254i	$0.812621\pi$
$224$	8.59237e7	0.510793
$225$	1.13906e7	0.0666667
$226$	−1.42465e8	−0.820974
$227$	−2.52670e8	−1.43371	−0.716857	−	0.697220i	$-0.754420\pi$
$227$	−2.52670e8	−1.43371	−0.716857	+	0.697220i	$0.754420\pi$
$228$	−1.50216e7	−0.0839355
$229$	6.00808e7	0.330607	0.165303	−	0.986243i	$-0.447140\pi$
$229$	6.00808e7	0.330607	0.165303	+	0.986243i	$0.447140\pi$
$230$	3.34741e7	0.181410
$231$	−5.58012e7	−0.297853
$232$	−3.36877e7	−0.177119
$233$	−2.25412e8	−1.16743	−0.583716	−	0.811958i	$-0.698402\pi$
$233$	−2.25412e8	−1.16743	−0.583716	+	0.811958i	$0.698402\pi$
$234$	7.93485e6	0.0404840
$235$	−1.05999e8	−0.532801
$236$	−1.17884e8	−0.583797
$237$	−3.57713e6	−0.0174548
$238$	5.61423e7	0.269942
$239$	2.80211e8	1.32768	0.663839	−	0.747875i	$-0.268926\pi$
$239$	2.80211e8	1.32768	0.663839	+	0.747875i	$0.268926\pi$
$240$	−2.99255e7	−0.139734
$241$	2.24227e6	0.0103188	0.00515939	−	0.999987i	$-0.498358\pi$
$241$	2.24227e6	0.0103188	0.00515939	+	0.999987i	$0.498358\pi$
$242$	−2.91187e8	−1.32074
$243$	1.43489e7	0.0641500
$244$	3.24591e8	1.43045
$245$	1.47061e7	0.0638877
$246$	2.57007e8	1.10071
$247$	2.03630e6	0.00859809
$248$	−1.23746e8	−0.515168
$249$	−2.03536e8	−0.835493
$250$	−3.38158e7	−0.136877
$251$	−3.57258e8	−1.42601	−0.713007	−	0.701157i	$-0.752667\pi$
$251$	−3.57258e8	−1.42601	−0.713007	+	0.701157i	$0.752667\pi$
$252$	4.29492e7	0.169065
$253$	9.31953e7	0.361803
$254$	2.88737e8	1.10557
$255$	−3.19065e7	−0.120501
$256$	5.12936e6	0.0191083
$257$	4.15303e8	1.52616	0.763079	−	0.646306i	$-0.223687\pi$
$257$	4.15303e8	1.52616	0.763079	+	0.646306i	$0.223687\pi$
$258$	3.35817e8	1.21740
$259$	7.37017e7	0.263590
$260$	−1.34979e7	−0.0476275
$261$	3.24106e7	0.112835
$262$	5.29256e8	1.81807
$263$	−2.52721e8	−0.856635	−0.428317	−	0.903628i	$-0.640893\pi$
$263$	−2.52721e8	−0.856635	−0.428317	+	0.903628i	$0.640893\pi$
$264$	1.23271e8	0.412333
$265$	−2.59014e8	−0.854993
$266$	1.92355e7	0.0626641
$267$	−6.83482e7	−0.219754
$268$	−4.18850e7	−0.132919
$269$	−1.43349e8	−0.449015	−0.224507	−	0.974472i	$-0.572077\pi$
$269$	−1.43349e8	−0.449015	−0.224507	+	0.974472i	$0.572077\pi$
$270$	−4.25982e7	−0.131710
$271$	2.71250e8	0.827900	0.413950	−	0.910300i	$-0.364149\pi$
$271$	2.71250e8	0.827900	0.413950	+	0.910300i	$0.364149\pi$
$272$	8.38249e7	0.252570
$273$	−5.82209e6	−0.0173185
$274$	7.65393e8	2.24780
$275$	−9.41469e7	−0.272987
$276$	−7.17307e7	−0.205364
$277$	3.51479e8	0.993619	0.496810	−	0.867860i	$-0.334505\pi$
$277$	3.51479e8	0.993619	0.496810	+	0.867860i	$0.334505\pi$
$278$	5.67120e8	1.58314
$279$	1.19054e8	0.328194
$280$	−3.24875e7	−0.0884429
$281$	−1.15053e8	−0.309334	−0.154667	−	0.987967i	$-0.549430\pi$
$281$	−1.15053e8	−0.309334	−0.154667	+	0.987967i	$0.549430\pi$
$282$	3.96412e8	1.05263
$283$	6.58900e8	1.72809	0.864046	−	0.503413i	$-0.167923\pi$
$283$	6.58900e8	1.72809	0.864046	+	0.503413i	$0.167923\pi$
$284$	−1.93998e8	−0.502553
$285$	−1.09319e7	−0.0279729
$286$	−6.55839e7	−0.165774
$287$	−1.88576e8	−0.470868
$288$	1.82619e8	0.450477
$289$	−3.20965e8	−0.782194
$290$	−9.62188e7	−0.231668
$291$	−4.72872e8	−1.12491
$292$	4.49949e8	1.05760
$293$	5.98337e8	1.38966	0.694831	−	0.719174i	$-0.255479\pi$
$293$	5.98337e8	1.38966	0.694831	+	0.719174i	$0.255479\pi$
$294$	−5.49974e7	−0.126219
$295$	−8.57887e7	−0.194560
$296$	−1.62815e8	−0.364901
$297$	−1.18598e8	−0.262682
$298$	−8.54325e8	−1.87011
$299$	9.72365e6	0.0210368
$300$	7.24631e7	0.154950
$301$	−2.46401e8	−0.520787
$302$	−7.45301e8	−1.55707
$303$	2.15470e8	0.444978
$304$	2.87202e7	0.0586314
$305$	2.36218e8	0.476720
$306$	1.19323e8	0.238067
$307$	−3.68389e7	−0.0726645	−0.0363322	−	0.999340i	$-0.511567\pi$
$307$	−3.68389e7	−0.0726645	−0.0363322	+	0.999340i	$0.511567\pi$
$308$	−3.54988e8	−0.692287
$309$	1.47291e8	0.284001
$310$	−3.53441e8	−0.673832
$311$	2.16416e8	0.407969	0.203985	−	0.978974i	$-0.434611\pi$
$311$	2.16416e8	0.407969	0.203985	+	0.978974i	$0.434611\pi$
$312$	1.28617e7	0.0239749
$313$	1.82287e8	0.336008	0.168004	−	0.985786i	$-0.446268\pi$
$313$	1.82287e8	0.336008	0.168004	+	0.985786i	$0.446268\pi$
$314$	3.47406e8	0.633262
$315$	3.12559e7	0.0563436
$316$	−2.27564e7	−0.0405695
$317$	8.62583e8	1.52087	0.760437	−	0.649411i	$-0.224985\pi$
$317$	8.62583e8	1.52087	0.760437	+	0.649411i	$0.224985\pi$
$318$	9.68650e8	1.68917
$319$	−2.67883e8	−0.462039
$320$	−4.00280e8	−0.682872
$321$	−1.58853e8	−0.268058
$322$	9.18528e7	0.153319
$323$	3.06215e7	0.0505612
$324$	9.12827e7	0.149101
$325$	−9.82293e6	−0.0158727
$326$	−5.97304e6	−0.00954847
$327$	−2.01697e8	−0.318994
$328$	4.16585e8	0.651847
$329$	−2.90862e8	−0.450299
$330$	3.52087e8	0.539326
$331$	−2.10328e8	−0.318785	−0.159393	−	0.987215i	$-0.550954\pi$
$331$	−2.10328e8	−0.318785	−0.159393	+	0.987215i	$0.550954\pi$
$332$	−1.29482e9	−1.94190
$333$	1.56643e8	0.232464
$334$	5.39970e8	0.792970
$335$	−3.04814e7	−0.0442974
$336$	−8.21155e7	−0.118097
$337$	−1.21931e9	−1.73544	−0.867719	−	0.497055i	$-0.834415\pi$
$337$	−1.21931e9	−1.73544	−0.867719	+	0.497055i	$0.834415\pi$
$338$	1.07957e9	1.52069
$339$	2.22168e8	0.309730
$340$	−2.02978e8	−0.280074
$341$	−9.84019e8	−1.34389
$342$	4.08825e7	0.0552645
$343$	4.03536e7	0.0539949
$344$	5.44328e8	0.720952
$345$	−5.22014e7	−0.0684408
$346$	6.10357e8	0.792169
$347$	4.29491e8	0.551824	0.275912	−	0.961183i	$-0.411020\pi$
$347$	4.29491e8	0.551824	0.275912	+	0.961183i	$0.411020\pi$
$348$	2.06185e8	0.262259
$349$	4.92205e8	0.619807	0.309904	−	0.950768i	$-0.399703\pi$
$349$	4.92205e8	0.619807	0.309904	+	0.950768i	$0.399703\pi$
$350$	−9.27907e7	−0.115682
$351$	−1.23741e7	−0.0152735
$352$	−1.50940e9	−1.84461
$353$	8.39592e8	1.01591	0.507957	−	0.861382i	$-0.330401\pi$
$353$	8.39592e8	1.01591	0.507957	+	0.861382i	$0.330401\pi$
$354$	3.20829e8	0.384382
$355$	−1.41180e8	−0.167484
$356$	−4.34807e8	−0.510766
$357$	−8.75515e7	−0.101842
$358$	−1.77027e9	−2.03915
$359$	−1.59128e8	−0.181517	−0.0907584	−	0.995873i	$-0.528929\pi$
$359$	−1.59128e8	−0.181517	−0.0907584	+	0.995873i	$0.528929\pi$
$360$	−6.90478e7	−0.0779993
$361$	−8.83380e8	−0.988263
$362$	9.02764e8	1.00022
$363$	4.54094e8	0.498279
$364$	−3.70381e7	−0.0402526
$365$	3.27446e8	0.352464
$366$	−8.83399e8	−0.941831
$367$	3.09960e8	0.327322	0.163661	−	0.986517i	$-0.447670\pi$
$367$	3.09960e8	0.327322	0.163661	+	0.986517i	$0.447670\pi$
$368$	1.37144e8	0.143453
$369$	−4.00792e8	−0.415267
$370$	−4.65033e8	−0.477285
$371$	−7.10734e8	−0.722601
$372$	7.57381e8	0.762806
$373$	−1.80234e9	−1.79827	−0.899137	−	0.437667i	$-0.855805\pi$
$373$	−1.80234e9	−1.79827	−0.899137	+	0.437667i	$0.855805\pi$
$374$	−9.86238e8	−0.974835
$375$	5.27344e7	0.0516398
$376$	6.42547e8	0.623372
$377$	−2.79500e7	−0.0268650
$378$	−1.16890e8	−0.111315
$379$	−3.82836e8	−0.361223	−0.180611	−	0.983555i	$-0.557808\pi$
$379$	−3.82836e8	−0.361223	−0.180611	+	0.983555i	$0.557808\pi$
$380$	−6.95447e7	−0.0650161
$381$	−4.50273e8	−0.417098
$382$	−2.50013e9	−2.29477
$383$	1.86168e9	1.69320	0.846600	−	0.532230i	$-0.178646\pi$
$383$	1.86168e9	1.69320	0.846600	+	0.532230i	$0.178646\pi$
$384$	6.31202e8	0.568865
$385$	−2.58339e8	−0.230716
$386$	6.50689e8	0.575862
$387$	−5.23692e8	−0.459291
$388$	−3.00825e9	−2.61458
$389$	3.85900e8	0.332393	0.166196	−	0.986093i	$-0.446851\pi$
$389$	3.85900e8	0.332393	0.166196	+	0.986093i	$0.446851\pi$
$390$	3.67354e7	0.0313588
$391$	1.46222e8	0.123707
$392$	−8.91457e7	−0.0747479
$393$	−8.25353e8	−0.685908
$394$	−2.01412e9	−1.65901
$395$	−1.65608e7	−0.0135205
$396$	−7.54479e8	−0.610539
$397$	3.79655e8	0.304525	0.152262	−	0.988340i	$-0.451344\pi$
$397$	3.79655e8	0.304525	0.152262	+	0.988340i	$0.451344\pi$
$398$	1.81303e9	1.44150
$399$	−2.99970e7	−0.0236414
$400$	−1.38544e8	−0.108237
$401$	1.80210e7	0.0139564	0.00697821	−	0.999976i	$-0.497779\pi$
$401$	1.80210e7	0.0139564	0.00697821	+	0.999976i	$0.497779\pi$
$402$	1.13993e8	0.0875160
$403$	−1.02669e8	−0.0781396
$404$	1.37075e9	1.03424
$405$	6.64301e7	0.0496904
$406$	−2.64024e8	−0.195796
$407$	−1.29470e9	−0.951895
$408$	1.93411e8	0.140984
$409$	−1.39088e9	−1.00521	−0.502605	−	0.864516i	$-0.667625\pi$
$409$	−1.39088e9	−1.00521	−0.502605	+	0.864516i	$0.667625\pi$
$410$	1.18985e9	0.852606
$411$	−1.19360e9	−0.848031
$412$	9.37011e8	0.660092
$413$	−2.35404e8	−0.164433
$414$	1.95221e8	0.135215
$415$	−9.42295e8	−0.647170
$416$	−1.57485e8	−0.107254
$417$	−8.84399e8	−0.597272
$418$	−3.37906e8	−0.226297
$419$	−3.32765e8	−0.220998	−0.110499	−	0.993876i	$-0.535245\pi$
$419$	−3.32765e8	−0.220998	−0.110499	+	0.993876i	$0.535245\pi$
$420$	1.98839e8	0.130957
$421$	2.85745e9	1.86634	0.933172	−	0.359429i	$-0.117029\pi$
$421$	2.85745e9	1.86634	0.933172	+	0.359429i	$0.117029\pi$
$422$	−3.48243e9	−2.25574
$423$	−6.18187e8	−0.397127
$424$	1.57009e9	1.00033
$425$	−1.47715e8	−0.0933393
$426$	5.27979e8	0.330890
$427$	6.48182e8	0.402902
$428$	−1.01057e9	−0.623036
$429$	1.02275e8	0.0625418
$430$	1.55471e9	0.942995
$431$	1.95001e9	1.17318	0.586592	−	0.809883i	$-0.300469\pi$
$431$	1.95001e9	1.17318	0.586592	+	0.809883i	$0.300469\pi$
$432$	−1.74525e8	−0.104152
$433$	1.51441e9	0.896472	0.448236	−	0.893915i	$-0.352052\pi$
$433$	1.51441e9	0.896472	0.448236	+	0.893915i	$0.352052\pi$
$434$	−9.69843e8	−0.569492
$435$	1.50049e8	0.0874020
$436$	−1.28313e9	−0.741424
$437$	5.00989e7	0.0287173
$438$	−1.22457e9	−0.696344
$439$	1.21673e9	0.686383	0.343192	−	0.939265i	$-0.388492\pi$
$439$	1.21673e9	0.686383	0.343192	+	0.939265i	$0.388492\pi$
$440$	5.70700e8	0.319392
$441$	8.57661e7	0.0476190
$442$	−1.02900e8	−0.0566812
$443$	2.35309e9	1.28596	0.642978	−	0.765884i	$-0.277699\pi$
$443$	2.35309e9	1.28596	0.642978	+	0.765884i	$0.277699\pi$
$444$	9.96508e8	0.540307
$445$	−3.16427e8	−0.170221
$446$	4.76918e9	2.54549
$447$	1.33228e9	0.705538
$448$	−1.09837e9	−0.577132
$449$	−2.19434e9	−1.14404	−0.572022	−	0.820238i	$-0.693841\pi$
$449$	−2.19434e9	−1.14404	−0.572022	+	0.820238i	$0.693841\pi$
$450$	−1.97214e8	−0.102022
$451$	3.31267e9	1.70043
$452$	1.41336e9	0.719892
$453$	1.16226e9	0.587437
$454$	4.37465e9	2.19406
$455$	−2.69541e7	−0.0134148
$456$	6.62668e7	0.0327280
$457$	3.57722e9	1.75323	0.876614	−	0.481194i	$-0.159797\pi$
$457$	3.57722e9	1.75323	0.876614	+	0.481194i	$0.159797\pi$
$458$	−1.04022e9	−0.505938
$459$	−1.86079e8	−0.0898158
$460$	−3.32087e8	−0.159074
$461$	1.75219e9	0.832967	0.416484	−	0.909143i	$-0.363262\pi$
$461$	1.75219e9	0.832967	0.416484	+	0.909143i	$0.363262\pi$
$462$	9.66126e8	0.455813
$463$	−1.79793e9	−0.841861	−0.420931	−	0.907093i	$-0.638296\pi$
$463$	−1.79793e9	−0.841861	−0.420931	+	0.907093i	$0.638296\pi$
$464$	−3.94210e8	−0.183195
$465$	5.51177e8	0.254218
$466$	3.90272e9	1.78656
$467$	7.91121e8	0.359446	0.179723	−	0.983717i	$-0.442480\pi$
$467$	7.91121e8	0.359446	0.179723	+	0.983717i	$0.442480\pi$
$468$	−7.87195e7	−0.0354995
$469$	−8.36410e7	−0.0374381
$470$	1.83524e9	0.815362
$471$	−5.41765e8	−0.238912
$472$	5.20035e8	0.227633
$473$	4.32847e9	1.88071
$474$	6.19334e7	0.0267116
$475$	−5.06105e7	−0.0216677
$476$	−5.56972e8	−0.236706
$477$	−1.51057e9	−0.637274
$478$	−4.85150e9	−2.03179
$479$	−2.30735e9	−0.959266	−0.479633	−	0.877469i	$-0.659230\pi$
$479$	−2.30735e9	−0.959266	−0.479633	+	0.877469i	$0.659230\pi$
$480$	8.45459e8	0.348938
$481$	−1.35084e8	−0.0553474
$482$	−3.88220e7	−0.0157911
$483$	−1.43241e8	−0.0578430
$484$	2.88878e9	1.15813
$485$	−2.18922e9	−0.871353
$486$	−2.48433e8	−0.0981707
$487$	−1.33253e9	−0.522789	−0.261394	−	0.965232i	$-0.584182\pi$
$487$	−1.33253e9	−0.522789	−0.261394	+	0.965232i	$0.584182\pi$
$488$	−1.43191e9	−0.557758
$489$	9.31471e6	0.00360237
$490$	−2.54618e8	−0.0977692
$491$	4.43731e9	1.69174	0.845871	−	0.533387i	$-0.179081\pi$
$491$	4.43731e9	1.69174	0.845871	+	0.533387i	$0.179081\pi$
$492$	−2.54970e9	−0.965186
$493$	−4.20306e8	−0.157980
$494$	−3.52559e7	−0.0131579
$495$	−5.49065e8	−0.203472
$496$	−1.44805e9	−0.532843
$497$	−3.87398e8	−0.141550
$498$	3.52396e9	1.27858
$499$	2.41786e9	0.871123	0.435561	−	0.900159i	$-0.356550\pi$
$499$	2.41786e9	0.871123	0.435561	+	0.900159i	$0.356550\pi$
$500$	3.35478e8	0.120024
$501$	−8.42060e8	−0.299165
$502$	6.18546e9	2.18227
$503$	−3.01913e9	−1.05778	−0.528888	−	0.848691i	$-0.677391\pi$
$503$	−3.01913e9	−1.05778	−0.528888	+	0.848691i	$0.677391\pi$
$504$	−1.89467e8	−0.0659215
$505$	9.97548e8	0.344678
$506$	−1.61356e9	−0.553678
$507$	−1.68354e9	−0.573714
$508$	−2.86448e9	−0.969444
$509$	−3.16242e9	−1.06294	−0.531468	−	0.847078i	$-0.678360\pi$
$509$	−3.16242e9	−1.06294	−0.531468	+	0.847078i	$0.678360\pi$
$510$	5.52420e8	0.184406
$511$	8.98511e8	0.297886
$512$	−3.08117e9	−1.01455
$513$	−6.37546e7	−0.0208497
$514$	−7.19044e9	−2.33552
$515$	6.81901e8	0.219986
$516$	−3.33155e9	−1.06751
$517$	5.10950e9	1.62615
$518$	−1.27605e9	−0.403379
$519$	−9.51826e8	−0.298863
$520$	5.95447e7	0.0185708
$521$	3.23968e9	1.00362	0.501811	−	0.864977i	$-0.332667\pi$
$521$	3.23968e9	1.00362	0.501811	+	0.864977i	$0.332667\pi$
$522$	−5.61148e8	−0.172675
$523$	−4.98015e9	−1.52225	−0.761127	−	0.648603i	$-0.775353\pi$
$523$	−4.98015e9	−1.52225	−0.761127	+	0.648603i	$0.775353\pi$
$524$	−5.25060e9	−1.59423
$525$	1.44703e8	0.0436436
$526$	4.37553e9	1.31093
$527$	−1.54391e9	−0.459501
$528$	1.44250e9	0.426480
$529$	−3.16560e9	−0.929738
$530$	4.48449e9	1.30842
$531$	−5.00320e8	−0.145016
$532$	−1.90831e8	−0.0549487
$533$	3.45631e8	0.0988708
$534$	1.18336e9	0.336297
$535$	−7.35432e8	−0.207637
$536$	1.84772e8	0.0518275
$537$	2.76067e9	0.769315
$538$	2.48190e9	0.687141
$539$	−7.08882e8	−0.194991
$540$	4.22605e8	0.115493
$541$	4.92830e9	1.33816	0.669078	−	0.743192i	$-0.266689\pi$
$541$	4.92830e9	1.33816	0.669078	+	0.743192i	$0.266689\pi$
$542$	−4.69635e9	−1.26696
$543$	−1.40782e9	−0.377354
$544$	−2.36823e9	−0.630708
$545$	−9.33782e8	−0.247092
$546$	1.00802e8	0.0265030
$547$	−1.70408e9	−0.445178	−0.222589	−	0.974912i	$-0.571451\pi$
$547$	−1.70408e9	−0.445178	−0.222589	+	0.974912i	$0.571451\pi$
$548$	−7.59325e9	−1.97104
$549$	1.37762e9	0.355326
$550$	1.63003e9	0.417760
$551$	−1.44006e8	−0.0366733
$552$	3.16435e8	0.0800751
$553$	−4.54428e7	−0.0114269
$554$	−6.08540e9	−1.52057
$555$	7.25199e8	0.180066
$556$	−5.62624e9	−1.38821
$557$	4.37024e9	1.07155	0.535774	−	0.844361i	$-0.320020\pi$
$557$	4.37024e9	1.07155	0.535774	+	0.844361i	$0.320020\pi$
$558$	−2.06127e9	−0.502245
$559$	4.51617e8	0.109352
$560$	−3.80165e8	−0.0914773
$561$	1.53800e9	0.367778
$562$	1.99200e9	0.473383
$563$	−2.41766e9	−0.570974	−0.285487	−	0.958383i	$-0.592155\pi$
$563$	−2.41766e9	−0.570974	−0.285487	+	0.958383i	$0.592155\pi$
$564$	−3.93269e9	−0.923024
$565$	1.02856e9	0.239916
$566$	−1.14080e10	−2.64455
$567$	1.82284e8	0.0419961
$568$	8.55805e8	0.195955
$569$	4.41532e9	1.00478	0.502388	−	0.864642i	$-0.332455\pi$
$569$	4.41532e9	1.00478	0.502388	+	0.864642i	$0.332455\pi$
$570$	1.89271e8	0.0428077
$571$	−5.60339e9	−1.25958	−0.629788	−	0.776767i	$-0.716858\pi$
$571$	−5.60339e9	−1.25958	−0.629788	+	0.776767i	$0.716858\pi$
$572$	6.50640e8	0.145363
$573$	3.89884e9	0.865753
$574$	3.26495e9	0.720584
$575$	−2.41673e8	−0.0530140
$576$	−2.33443e9	−0.508983
$577$	6.17027e9	1.33718	0.668589	−	0.743632i	$-0.266899\pi$
$577$	6.17027e9	1.33718	0.668589	+	0.743632i	$0.266899\pi$
$578$	5.55709e9	1.19702
$579$	−1.01472e9	−0.217256
$580$	9.54560e8	0.203145
$581$	−2.58566e9	−0.546959
$582$	8.18717e9	1.72149
$583$	1.24853e10	2.60951
$584$	−1.98491e9	−0.412379
$585$	−5.72874e7	−0.0118308
$586$	−1.03594e10	−2.12664
$587$	−8.17721e9	−1.66868	−0.834338	−	0.551254i	$-0.814150\pi$
$587$	−8.17721e9	−1.66868	−0.834338	+	0.551254i	$0.814150\pi$
$588$	5.45614e8	0.110679
$589$	−5.28978e8	−0.106668
$590$	1.48532e9	0.297741
$591$	3.14093e9	0.625896
$592$	−1.90525e9	−0.377420
$593$	4.01515e9	0.790698	0.395349	−	0.918531i	$-0.370624\pi$
$593$	4.01515e9	0.790698	0.395349	+	0.918531i	$0.370624\pi$
$594$	2.05337e9	0.401990
$595$	−4.05331e8	−0.0788861
$596$	8.47552e9	1.63985
$597$	−2.82734e9	−0.543836
$598$	−1.68352e8	−0.0321933
$599$	−5.38280e9	−1.02333	−0.511664	−	0.859186i	$-0.670971\pi$
$599$	−5.38280e9	−1.02333	−0.511664	+	0.859186i	$0.670971\pi$
$600$	−3.19666e8	−0.0604180
$601$	8.50523e9	1.59818	0.799089	−	0.601212i	$-0.205315\pi$
$601$	8.50523e9	1.59818	0.799089	+	0.601212i	$0.205315\pi$
$602$	4.26612e9	0.796976
$603$	−1.77768e8	−0.0330173
$604$	7.39392e9	1.36535
$605$	2.10229e9	0.385965
$606$	−3.73059e9	−0.680963
$607$	1.01613e10	1.84412	0.922062	−	0.387041i	$-0.126503\pi$
$607$	1.01613e10	1.84412	0.922062	+	0.387041i	$0.126503\pi$
$608$	−8.11407e8	−0.146412
$609$	4.11735e8	0.0738681
$610$	−4.08981e9	−0.729539
$611$	5.33106e8	0.0945518
$612$	−1.18377e9	−0.208755
$613$	−5.37485e8	−0.0942441	−0.0471221	−	0.998889i	$-0.515005\pi$
$613$	−5.37485e8	−0.0942441	−0.0471221	+	0.998889i	$0.515005\pi$
$614$	6.37818e8	0.111201
$615$	−1.85552e9	−0.321664
$616$	1.56600e9	0.269935
$617$	−7.57829e9	−1.29889	−0.649446	−	0.760407i	$-0.724999\pi$
$617$	−7.57829e9	−1.29889	−0.649446	+	0.760407i	$0.724999\pi$
$618$	−2.55015e9	−0.434616
$619$	−7.53812e8	−0.127746	−0.0638728	−	0.997958i	$-0.520345\pi$
$619$	−7.53812e8	−0.127746	−0.0638728	+	0.997958i	$0.520345\pi$
$620$	3.50640e9	0.590867
$621$	−3.04438e8	−0.0510128
$622$	−3.74696e9	−0.624328
$623$	−8.68275e8	−0.143863
$624$	1.50506e8	0.0247974
$625$	2.44141e8	0.0400000
$626$	−3.15606e9	−0.514204
$627$	5.26951e8	0.0853756
$628$	−3.44652e9	−0.555293
$629$	−2.03137e9	−0.325471
$630$	−5.41155e8	−0.0862243
$631$	6.58609e8	0.104358	0.0521789	−	0.998638i	$-0.483383\pi$
$631$	6.58609e8	0.104358	0.0521789	+	0.998638i	$0.483383\pi$
$632$	1.00388e8	0.0158188
$633$	5.43070e9	0.851026
$634$	−1.49345e10	−2.32744
$635$	−2.08460e9	−0.323083
$636$	−9.60971e9	−1.48119
$637$	−7.39621e7	−0.0113376
$638$	4.63805e9	0.707072
$639$	−8.23361e8	−0.124835
$640$	2.92223e9	0.440641
$641$	−7.38378e9	−1.10733	−0.553663	−	0.832741i	$-0.686771\pi$
$641$	−7.38378e9	−1.10733	−0.553663	+	0.832741i	$0.686771\pi$
$642$	2.75034e9	0.410217
$643$	1.70284e9	0.252601	0.126301	−	0.991992i	$-0.459690\pi$
$643$	1.70284e9	0.252601	0.126301	+	0.991992i	$0.459690\pi$
$644$	−9.11246e8	−0.134442
$645$	−2.42450e9	−0.355765
$646$	−5.30171e8	−0.0773753
$647$	4.71645e9	0.684622	0.342311	−	0.939587i	$-0.388790\pi$
$647$	4.71645e9	0.684622	0.342311	+	0.939587i	$0.388790\pi$
$648$	−4.02687e8	−0.0581373
$649$	4.13529e9	0.593813
$650$	1.70071e8	0.0242904
$651$	1.51243e9	0.214853
$652$	5.92569e7	0.00837283
$653$	−1.23963e9	−0.174220	−0.0871099	−	0.996199i	$-0.527763\pi$
$653$	−1.23963e9	−0.174220	−0.0871099	+	0.996199i	$0.527763\pi$
$654$	3.49212e9	0.488166
$655$	−3.82108e9	−0.531302
$656$	4.87483e9	0.674211
$657$	1.90966e9	0.262711
$658$	5.03590e9	0.689106
$659$	−1.40452e10	−1.91173	−0.955867	−	0.293799i	$-0.905080\pi$
$659$	−1.40452e10	−1.91173	−0.955867	+	0.293799i	$0.905080\pi$
$660$	−3.49296e9	−0.472922
$661$	4.20603e9	0.566458	0.283229	−	0.959052i	$-0.408594\pi$
$661$	4.20603e9	0.566458	0.283229	+	0.959052i	$0.408594\pi$
$662$	3.64155e9	0.487847
$663$	1.60469e8	0.0213842
$664$	5.71201e9	0.757183
$665$	−1.38875e8	−0.0183125
$666$	−2.71207e9	−0.355747
$667$	−6.87651e8	−0.0897279
$668$	−5.35689e9	−0.695337
$669$	−7.43734e9	−0.960342
$670$	5.27746e8	0.0677896
$671$	−1.13865e10	−1.45499
$672$	2.31994e9	0.294906
$673$	7.56778e9	0.957009	0.478504	−	0.878085i	$-0.341179\pi$
$673$	7.56778e9	0.957009	0.478504	+	0.878085i	$0.341179\pi$
$674$	2.11108e10	2.65579
$675$	3.07547e8	0.0384900
$676$	−1.07101e10	−1.33346
$677$	1.04426e10	1.29344	0.646721	−	0.762727i	$-0.276140\pi$
$677$	1.04426e10	1.29344	0.646721	+	0.762727i	$0.276140\pi$
$678$	−3.84656e9	−0.473989
$679$	−6.00723e9	−0.736427
$680$	8.95422e8	0.109206
$681$	−6.82208e9	−0.827756
$682$	1.70370e10	2.05659
$683$	−1.06039e10	−1.27349	−0.636744	−	0.771076i	$-0.719719\pi$
$683$	−1.06039e10	−1.27349	−0.636744	+	0.771076i	$0.719719\pi$
$684$	−4.05584e8	−0.0484602
$685$	−5.52591e9	−0.656882
$686$	−6.98671e8	−0.0826301
$687$	1.62218e9	0.190876
$688$	6.36966e9	0.745687
$689$	1.30267e9	0.151728
$690$	9.03799e8	0.104737
$691$	−4.46875e9	−0.515244	−0.257622	−	0.966246i	$-0.582939\pi$
$691$	−4.46875e9	−0.515244	−0.257622	+	0.966246i	$0.582939\pi$
$692$	−6.05518e9	−0.694634
$693$	−1.50663e9	−0.171965
$694$	−7.43608e9	−0.844473
$695$	−4.09444e9	−0.462645
$696$	−9.09569e8	−0.102259
$697$	5.19754e9	0.581411
$698$	−8.52189e9	−0.948510
$699$	−6.08613e9	−0.674017
$700$	9.20550e8	0.101439
$701$	−1.65190e9	−0.181122	−0.0905610	−	0.995891i	$-0.528866\pi$
$701$	−1.65190e9	−0.181122	−0.0905610	+	0.995891i	$0.528866\pi$
$702$	2.14241e8	0.0233734
$703$	−6.95991e8	−0.0755545
$704$	1.92948e10	2.08418
$705$	−2.86198e9	−0.307613
$706$	−1.45365e10	−1.55468
$707$	2.73727e9	0.291306
$708$	−3.18286e9	−0.337055
$709$	1.15694e10	1.21913	0.609565	−	0.792736i	$-0.291344\pi$
$709$	1.15694e10	1.21913	0.609565	+	0.792736i	$0.291344\pi$
$710$	2.44435e9	0.256306
$711$	−9.65825e7	−0.0100775
$712$	1.91812e9	0.199157
$713$	−2.52595e9	−0.260983
$714$	1.51584e9	0.155851
$715$	4.73497e8	0.0484447
$716$	1.75624e10	1.78809
$717$	7.56570e9	0.766536
$718$	2.75510e9	0.277781
$719$	−4.84395e9	−0.486014	−0.243007	−	0.970025i	$-0.578134\pi$
$719$	−4.84395e9	−0.486014	−0.243007	+	0.970025i	$0.578134\pi$
$720$	−8.07988e8	−0.0806754
$721$	1.87114e9	0.185922
$722$	1.52946e10	1.51237
$723$	6.05413e7	0.00595755
$724$	−8.95607e9	−0.877067
$725$	6.94672e8	0.0677013
$726$	−7.86205e9	−0.762531
$727$	−1.17390e10	−1.13308	−0.566541	−	0.824033i	$-0.691719\pi$
$727$	−1.17390e10	−1.13308	−0.566541	+	0.824033i	$0.691719\pi$
$728$	1.63391e8	0.0156952
$729$	3.87420e8	0.0370370
$730$	−5.66930e9	−0.539386
$731$	6.79133e9	0.643049
$732$	8.76395e9	0.825869
$733$	−9.66671e9	−0.906598	−0.453299	−	0.891358i	$-0.649753\pi$
$733$	−9.66671e9	−0.906598	−0.453299	+	0.891358i	$0.649753\pi$
$734$	−5.36656e9	−0.500910
$735$	3.97065e8	0.0368856
$736$	−3.87460e9	−0.358224
$737$	1.46930e9	0.135199
$738$	6.93920e9	0.635495
$739$	−8.77699e9	−0.800000	−0.400000	−	0.916515i	$-0.630990\pi$
$739$	−8.77699e9	−0.800000	−0.400000	+	0.916515i	$0.630990\pi$
$740$	4.61346e9	0.418520
$741$	5.49801e7	0.00496411
$742$	1.23054e10	1.10582
$743$	−1.39551e10	−1.24816	−0.624082	−	0.781359i	$-0.714527\pi$
$743$	−1.39551e10	−1.24816	−0.624082	+	0.781359i	$0.714527\pi$
$744$	−3.34113e9	−0.297432
$745$	6.16798e9	0.546507
$746$	3.12052e10	2.75195
$747$	−5.49547e9	−0.482372
$748$	9.78420e9	0.854810
$749$	−2.01803e9	−0.175485
$750$	−9.13028e8	−0.0790259
$751$	−5.46263e9	−0.470611	−0.235305	−	0.971922i	$-0.575609\pi$
$751$	−5.46263e9	−0.470611	−0.235305	+	0.971922i	$0.575609\pi$
$752$	7.51900e9	0.644760
$753$	−9.64596e9	−0.823309
$754$	4.83917e8	0.0411123
$755$	5.38086e9	0.455027
$756$	1.15963e9	0.0976096
$757$	−9.04842e9	−0.758119	−0.379059	−	0.925372i	$-0.623752\pi$
$757$	−9.04842e9	−0.758119	−0.379059	+	0.925372i	$0.623752\pi$
$758$	6.62830e9	0.552790
$759$	2.51627e9	0.208887
$760$	3.06791e8	0.0253510
$761$	1.02716e10	0.844876	0.422438	−	0.906392i	$-0.361174\pi$
$761$	1.02716e10	0.844876	0.422438	+	0.906392i	$0.361174\pi$
$762$	7.79590e9	0.638298
$763$	−2.56230e9	−0.208831
$764$	2.48030e10	2.01223
$765$	−8.61476e8	−0.0695710
$766$	−3.22325e10	−2.59115
$767$	4.31461e8	0.0345269
$768$	1.38493e8	0.0110322
$769$	−2.37677e9	−0.188471	−0.0942355	−	0.995550i	$-0.530041\pi$
$769$	−2.37677e9	−0.188471	−0.0942355	+	0.995550i	$0.530041\pi$
$770$	4.47281e9	0.353071
$771$	1.12132e10	0.881127
$772$	−6.45531e9	−0.504959
$773$	−2.10182e10	−1.63669	−0.818345	−	0.574727i	$-0.805108\pi$
$773$	−2.10182e10	−1.63669	−0.818345	+	0.574727i	$0.805108\pi$
$774$	9.06706e9	0.702867
$775$	2.55175e9	0.196916
$776$	1.32706e10	1.01947
$777$	1.98995e9	0.152184
$778$	−6.68137e9	−0.508671
$779$	1.78079e9	0.134968
$780$	−3.64442e8	−0.0274978
$781$	6.80532e9	0.511176
$782$	−2.53165e9	−0.189313
$783$	8.75087e8	0.0651456
$784$	−1.04317e9	−0.0773125
$785$	−2.50817e9	−0.185060
$786$	1.42899e10	1.04967
$787$	3.87353e9	0.283266	0.141633	−	0.989919i	$-0.454765\pi$
$787$	3.87353e9	0.283266	0.141633	+	0.989919i	$0.454765\pi$
$788$	1.99815e10	1.45474
$789$	−6.82346e9	−0.494578
$790$	2.86729e8	0.0206908
$791$	2.82236e9	0.202766
$792$	3.32832e9	0.238061
$793$	−1.18802e9	−0.0845995
$794$	−6.57324e9	−0.466023
$795$	−6.99338e9	−0.493631
$796$	−1.79866e10	−1.26401
$797$	−2.09883e10	−1.46849	−0.734247	−	0.678883i	$-0.762465\pi$
$797$	−2.09883e10	−1.46849	−0.734247	+	0.678883i	$0.762465\pi$
$798$	5.19360e8	0.0361791
$799$	8.01675e9	0.556013
$800$	3.91416e9	0.270286
$801$	−1.84540e9	−0.126875
$802$	−3.12010e8	−0.0213579
$803$	−1.57839e10	−1.07575
$804$	−1.13089e9	−0.0767407
$805$	−6.63151e8	−0.0448050
$806$	1.77758e9	0.119579
$807$	−3.87041e9	−0.259239
$808$	−6.04695e9	−0.403270
$809$	1.88503e10	1.25170	0.625849	−	0.779944i	$-0.284753\pi$
$809$	1.88503e10	1.25170	0.625849	+	0.779944i	$0.284753\pi$
$810$	−1.15015e9	−0.0760427
$811$	−3.84352e9	−0.253021	−0.126510	−	0.991965i	$-0.540378\pi$
$811$	−3.84352e9	−0.253021	−0.126510	+	0.991965i	$0.540378\pi$
$812$	2.61931e9	0.171689
$813$	7.32376e9	0.477988
$814$	2.24161e10	1.45671
$815$	4.31236e7	0.00279038
$816$	2.26327e9	0.145821
$817$	2.32685e9	0.149277
$818$	2.40812e10	1.53830
$819$	−1.57197e8	−0.00999883
$820$	−1.18042e10	−0.747630
$821$	1.65030e10	1.04079	0.520394	−	0.853926i	$-0.325785\pi$
$821$	1.65030e10	1.04079	0.520394	+	0.853926i	$0.325785\pi$
$822$	2.06656e10	1.29777
$823$	−6.88244e9	−0.430371	−0.215186	−	0.976573i	$-0.569036\pi$
$823$	−6.88244e9	−0.430371	−0.215186	+	0.976573i	$0.569036\pi$
$824$	−4.13355e9	−0.257382
$825$	−2.54197e9	−0.157609
$826$	4.07572e9	0.251637
$827$	−8.00503e9	−0.492145	−0.246073	−	0.969251i	$-0.579140\pi$
$827$	−8.00503e9	−0.492145	−0.246073	+	0.969251i	$0.579140\pi$
$828$	−1.93673e9	−0.118567
$829$	−8.15406e9	−0.497088	−0.248544	−	0.968621i	$-0.579952\pi$
$829$	−8.15406e9	−0.497088	−0.248544	+	0.968621i	$0.579952\pi$
$830$	1.63146e10	0.990384
$831$	9.48993e9	0.573666
$832$	2.01315e9	0.121184
$833$	−1.11223e9	−0.0666709
$834$	1.53122e10	0.914024
$835$	−3.89843e9	−0.231732
$836$	3.35228e9	0.198435
$837$	3.21447e9	0.189483
$838$	5.76140e9	0.338200
$839$	2.25611e9	0.131885	0.0659423	−	0.997823i	$-0.478995\pi$
$839$	2.25611e9	0.131885	0.0659423	+	0.997823i	$0.478995\pi$
$840$	−8.77162e8	−0.0510625
$841$	−1.52733e10	−0.885413
$842$	−4.94731e10	−2.85612
$843$	−3.10644e9	−0.178594
$844$	3.45482e10	1.97800
$845$	−7.79416e9	−0.444397
$846$	1.07031e10	0.607735
$847$	5.76867e9	0.326200
$848$	1.83730e10	1.03465
$849$	1.77903e10	0.997714
$850$	2.55750e9	0.142840
$851$	−3.32347e9	−0.184858
$852$	−5.23793e9	−0.290149
$853$	3.04625e10	1.68052	0.840259	−	0.542185i	$-0.182403\pi$
$853$	3.04625e10	1.68052	0.840259	+	0.542185i	$0.182403\pi$
$854$	−1.12224e10	−0.616573
$855$	−2.95160e8	−0.0161501
$856$	4.45805e9	0.242933
$857$	6.49074e9	0.352259	0.176129	−	0.984367i	$-0.443642\pi$
$857$	6.49074e9	0.352259	0.176129	+	0.984367i	$0.443642\pi$
$858$	−1.77077e9	−0.0957096
$859$	−1.54195e10	−0.830031	−0.415016	−	0.909814i	$-0.636224\pi$
$859$	−1.54195e10	−0.830031	−0.415016	+	0.909814i	$0.636224\pi$
$860$	−1.54238e10	−0.826890
$861$	−5.09155e9	−0.271856
$862$	−3.37619e10	−1.79536
$863$	−6.95493e9	−0.368345	−0.184173	−	0.982894i	$-0.558961\pi$
$863$	−6.95493e9	−0.368345	−0.184173	+	0.982894i	$0.558961\pi$
$864$	4.93072e9	0.260083
$865$	−4.40660e9	−0.231498
$866$	−2.62201e10	−1.37190
$867$	−8.66604e9	−0.451600
$868$	9.62155e9	0.499374
$869$	7.98283e8	0.0412656
$870$	−2.59791e9	−0.133754
$871$	1.53301e8	0.00786109
$872$	5.66041e9	0.289095
$873$	−1.27676e10	−0.649468
$874$	−8.67398e8	−0.0439469
$875$	6.69922e8	0.0338062
$876$	1.21486e10	0.610608
$877$	−2.15955e10	−1.08110	−0.540548	−	0.841313i	$-0.681783\pi$
$877$	−2.15955e10	−1.08110	−0.540548	+	0.841313i	$0.681783\pi$
$878$	−2.10660e10	−1.05039
$879$	1.61551e10	0.802321
$880$	6.67826e9	0.330350
$881$	2.45453e10	1.20935	0.604676	−	0.796471i	$-0.293303\pi$
$881$	2.45453e10	1.20935	0.604676	+	0.796471i	$0.293303\pi$
$882$	−1.48493e9	−0.0728729
$883$	−3.05196e10	−1.49182	−0.745909	−	0.666047i	$-0.767985\pi$
$883$	−3.05196e10	−1.49182	−0.745909	+	0.666047i	$0.767985\pi$
$884$	1.02085e9	0.0497024
$885$	−2.31630e9	−0.112329
$886$	−4.07408e10	−1.96794
$887$	−3.20420e10	−1.54165	−0.770827	−	0.637044i	$-0.780157\pi$
$887$	−3.20420e10	−1.54165	−0.770827	+	0.637044i	$0.780157\pi$
$888$	−4.39602e9	−0.210676
$889$	−5.72014e9	−0.273055
$890$	5.47852e9	0.260494
$891$	−3.20215e9	−0.151659
$892$	−4.73137e10	−2.23208
$893$	2.74671e9	0.129072
$894$	−2.30668e10	−1.07971
$895$	1.27809e10	0.595909
$896$	8.01861e9	0.372410
$897$	2.62539e8	0.0121456
$898$	3.79922e10	1.75076
$899$	7.26068e9	0.333287
$900$	1.95651e9	0.0894607
$901$	1.95893e10	0.892241
$902$	−5.73546e10	−2.60223
$903$	−6.65283e9	−0.300677
$904$	−6.23492e9	−0.280699
$905$	−6.51770e9	−0.292297
$906$	−2.01231e10	−0.898973
$907$	3.57857e10	1.59252	0.796258	−	0.604957i	$-0.206810\pi$
$907$	3.57857e10	1.59252	0.796258	+	0.604957i	$0.206810\pi$
$908$	−4.33997e10	−1.92392
$909$	5.81770e9	0.256908
$910$	4.66676e8	0.0205291
$911$	−2.16444e10	−0.948485	−0.474242	−	0.880394i	$-0.657278\pi$
$911$	−2.16444e10	−0.948485	−0.474242	+	0.880394i	$0.657278\pi$
$912$	7.75446e8	0.0338509
$913$	4.54216e10	1.97522
$914$	−6.19349e10	−2.68302
$915$	6.37788e9	0.275234
$916$	1.03198e10	0.443645
$917$	−1.04850e10	−0.449032
$918$	3.22172e9	0.137448
$919$	−1.39988e10	−0.594957	−0.297478	−	0.954729i	$-0.596146\pi$
$919$	−1.39988e10	−0.594957	−0.297478	+	0.954729i	$0.596146\pi$
$920$	1.46498e9	0.0620259
$921$	−9.94650e8	−0.0419528
$922$	−3.03369e10	−1.27471
$923$	7.10042e8	0.0297220
$924$	−9.58467e9	−0.399692
$925$	3.35740e9	0.139479
$926$	3.11289e10	1.28833
$927$	3.97685e9	0.163968
$928$	1.11373e10	0.457468
$929$	−2.51280e10	−1.02826	−0.514130	−	0.857712i	$-0.671885\pi$
$929$	−2.51280e10	−1.02826	−0.514130	+	0.857712i	$0.671885\pi$
$930$	−9.54292e9	−0.389037
$931$	−3.81073e8	−0.0154769
$932$	−3.87178e10	−1.56659
$933$	5.84323e9	0.235541
$934$	−1.36972e10	−0.550071
$935$	7.12036e9	0.284879
$936$	3.47265e8	0.0138419
$937$	−1.28582e10	−0.510611	−0.255306	−	0.966860i	$-0.582176\pi$
$937$	−1.28582e10	−0.510611	−0.255306	+	0.966860i	$0.582176\pi$
$938$	1.44814e9	0.0572927
$939$	4.92174e9	0.193994
$940$	−1.82069e10	−0.714971
$941$	3.90470e10	1.52765	0.763824	−	0.645424i	$-0.223319\pi$
$941$	3.90470e10	1.52765	0.763824	+	0.645424i	$0.223319\pi$
$942$	9.37997e9	0.365614
$943$	8.50354e9	0.330224
$944$	6.08538e9	0.235443
$945$	8.43909e8	0.0325300
$946$	−7.49419e10	−2.87810
$947$	−4.98341e10	−1.90679	−0.953393	−	0.301731i	$-0.902435\pi$
$947$	−4.98341e10	−1.90679	−0.953393	+	0.301731i	$0.902435\pi$
$948$	−6.14424e8	−0.0234228
$949$	−1.64684e9	−0.0625488
$950$	8.76255e8	0.0331587
$951$	2.32897e10	0.878078
$952$	2.45704e9	0.0922960
$953$	1.99827e10	0.747876	0.373938	−	0.927454i	$-0.378007\pi$
$953$	1.99827e10	0.747876	0.373938	+	0.927454i	$0.378007\pi$
$954$	2.61536e10	0.975240
$955$	1.80502e10	0.670610
$956$	4.81303e10	1.78163
$957$	−7.23285e9	−0.266758
$958$	3.99488e10	1.46799
$959$	−1.51631e10	−0.555166
$960$	−1.08076e10	−0.394256
$961$	−8.41888e8	−0.0306001
$962$	2.33881e9	0.0846998
$963$	−4.28904e9	−0.154763
$964$	3.85143e8	0.0138469
$965$	−4.69779e9	−0.168286
$966$	2.48003e9	0.0885189
$967$	1.31302e10	0.466958	0.233479	−	0.972362i	$-0.424989\pi$
$967$	1.31302e10	0.466958	0.233479	+	0.972362i	$0.424989\pi$
$968$	−1.27437e10	−0.451575
$969$	8.26780e8	0.0291915
$970$	3.79036e10	1.33346
$971$	3.27528e10	1.14810	0.574051	−	0.818819i	$-0.305371\pi$
$971$	3.27528e10	1.14810	0.574051	+	0.818819i	$0.305371\pi$
$972$	2.46463e9	0.0860836
$973$	−1.12351e10	−0.391006
$974$	2.30711e10	0.800040
$975$	−2.65219e8	−0.00916408
$976$	−1.67560e10	−0.576894
$977$	1.96765e10	0.675021	0.337511	−	0.941322i	$-0.390415\pi$
$977$	1.96765e10	0.675021	0.337511	+	0.941322i	$0.390415\pi$
$978$	−1.61272e8	−0.00551281
$979$	1.52528e10	0.519529
$980$	2.52599e9	0.0857315
$981$	−5.44582e9	−0.184171
$982$	−7.68262e10	−2.58892
$983$	1.30579e10	0.438466	0.219233	−	0.975673i	$-0.429644\pi$
$983$	1.30579e10	0.438466	0.219233	+	0.975673i	$0.429644\pi$
$984$	1.12478e10	0.376344
$985$	1.45413e10	0.484817
$986$	7.27706e9	0.241761
$987$	−7.85327e9	−0.259980
$988$	3.49764e8	0.0115379
$989$	1.11111e10	0.365233
$990$	9.50635e9	0.311380
$991$	1.33714e10	0.436435	0.218218	−	0.975900i	$-0.429976\pi$
$991$	1.33714e10	0.436435	0.218218	+	0.975900i	$0.429976\pi$
$992$	4.09106e10	1.33059
$993$	−5.67884e9	−0.184051
$994$	6.70729e9	0.216618
$995$	−1.30895e10	−0.421254
$996$	−3.49602e10	−1.12116
$997$	5.15968e10	1.64888	0.824441	−	0.565948i	$-0.191490\pi$
$997$	5.15968e10	1.64888	0.824441	+	0.565948i	$0.191490\pi$
$998$	−4.18621e10	−1.33311
$999$	4.22936e9	0.134213

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.8.a.c.1.1	✓	2
3.2	odd	2		315.8.a.d.1.2		2
5.4	even	2		525.8.a.f.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.8.a.c.1.1	✓	2	1.1	even	1	trivial
315.8.a.d.1.2		2	3.2	odd	2
525.8.a.f.1.2		2	5.4	even	2

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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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	105.8.a.c.1.1

Level	$105$
Weight	$8$
Character	105.1
Self dual	yes
Analytic conductor	$32.800$
Analytic rank	$1$
Dimension	$2$
CM	no
Inner twists	$1$