LMFDB - Embedded newform 102.10.a.i.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [102,10,Mod(1,102)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("102.1"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(102, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 10, names="a")

Level:	$N$	$=$	$102 = 2 \cdot 3 \cdot 17$
Weight:	$k$	$=$	$10$
Character orbit:	$[\chi]$	$=$	102.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,64,324] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$52.5336552887$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{4} - 1502266x^{2} - 135577497x + 425775023262$ x^4 - 1502266x^2 - 135577497x + 425775023262
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$2^{6}\cdot 3$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-747.335$ of defining polynomial
Character	$\chi$	$=$	102.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+16.0000 q^{2} +81.0000 q^{3} +256.000 q^{4} +1842.42 q^{5} +1296.00 q^{6} -4706.68 q^{7} +4096.00 q^{8} +6561.00 q^{9} +29478.7 q^{10} +22720.2 q^{11} +20736.0 q^{12} +11385.1 q^{13} -75306.8 q^{14} +149236. q^{15} +65536.0 q^{16} +83521.0 q^{17} +104976. q^{18} +523587. q^{19} +471658. q^{20} -381241. q^{21} +363522. q^{22} +1.58895e6 q^{23} +331776. q^{24} +1.44137e6 q^{25} +182162. q^{26} +531441. q^{27} -1.20491e6 q^{28} +2.02281e6 q^{29} +2.38777e6 q^{30} -9.22058e6 q^{31} +1.04858e6 q^{32} +1.84033e6 q^{33} +1.33634e6 q^{34} -8.67166e6 q^{35} +1.67962e6 q^{36} -2.94408e6 q^{37} +8.37739e6 q^{38} +922193. q^{39} +7.54654e6 q^{40} +2.75165e7 q^{41} -6.09985e6 q^{42} -8.43166e6 q^{43} +5.81636e6 q^{44} +1.20881e7 q^{45} +2.54232e7 q^{46} +4.11237e7 q^{47} +5.30842e6 q^{48} -1.82008e7 q^{49} +2.30619e7 q^{50} +6.76520e6 q^{51} +2.91459e6 q^{52} -2.85885e7 q^{53} +8.50306e6 q^{54} +4.18600e7 q^{55} -1.92785e7 q^{56} +4.24105e7 q^{57} +3.23649e7 q^{58} +8.35446e7 q^{59} +3.82043e7 q^{60} -1.27674e8 q^{61} -1.47529e8 q^{62} -3.08805e7 q^{63} +1.67772e7 q^{64} +2.09761e7 q^{65} +2.94453e7 q^{66} +1.40982e8 q^{67} +2.13814e7 q^{68} +1.28705e8 q^{69} -1.38747e8 q^{70} +7.71872e7 q^{71} +2.68739e7 q^{72} -6.55896e7 q^{73} -4.71053e7 q^{74} +1.16751e8 q^{75} +1.34038e8 q^{76} -1.06936e8 q^{77} +1.47551e7 q^{78} +2.78910e8 q^{79} +1.20745e8 q^{80} +4.30467e7 q^{81} +4.40264e8 q^{82} -1.06724e8 q^{83} -9.75976e7 q^{84} +1.53880e8 q^{85} -1.34907e8 q^{86} +1.63848e8 q^{87} +9.30617e7 q^{88} +5.19026e8 q^{89} +1.93409e8 q^{90} -5.35860e7 q^{91} +4.06771e8 q^{92} -7.46867e8 q^{93} +6.57979e8 q^{94} +9.64664e8 q^{95} +8.49347e7 q^{96} -5.03657e8 q^{97} -2.91213e8 q^{98} +1.49067e8 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q + 64 q^{2} + 324 q^{3} + 1024 q^{4} + 942 q^{5} + 5184 q^{6} + 5088 q^{7} + 16384 q^{8} + 26244 q^{9} + 15072 q^{10} - 20822 q^{11} + 82944 q^{12} + 260722 q^{13} + 81408 q^{14} + 76302 q^{15} + 262144 q^{16}+ \cdots - 136613142 q^{99}+O(q^{100})$ 4 * q + 64 * q^2 + 324 * q^3 + 1024 * q^4 + 942 * q^5 + 5184 * q^6 + 5088 * q^7 + 16384 * q^8 + 26244 * q^9 + 15072 * q^10 - 20822 * q^11 + 82944 * q^12 + 260722 * q^13 + 81408 * q^14 + 76302 * q^15 + 262144 * q^16 + 334084 * q^17 + 419904 * q^18 + 1127114 * q^19 + 241152 * q^20 + 412128 * q^21 - 333152 * q^22 + 342858 * q^23 + 1327104 * q^24 + 3673510 * q^25 + 4171552 * q^26 + 2125764 * q^27 + 1302528 * q^28 + 3453272 * q^29 + 1220832 * q^30 + 8734524 * q^31 + 4194304 * q^32 - 1686582 * q^33 + 5345344 * q^34 + 19894600 * q^35 + 6718464 * q^36 + 4427508 * q^37 + 18033824 * q^38 + 21118482 * q^39 + 3858432 * q^40 - 12694878 * q^41 + 6594048 * q^42 + 11513590 * q^43 - 5330432 * q^44 + 6180462 * q^45 + 5485728 * q^46 - 1620412 * q^47 + 21233664 * q^48 + 37347556 * q^49 + 58776160 * q^50 + 27060804 * q^51 + 66744832 * q^52 + 42954392 * q^53 + 34012224 * q^54 + 147527674 * q^55 + 20840448 * q^56 + 91296234 * q^57 + 55252352 * q^58 - 30959244 * q^59 + 19533312 * q^60 - 52264348 * q^61 + 139752384 * q^62 + 33382368 * q^63 + 67108864 * q^64 - 168445258 * q^65 - 26985312 * q^66 + 268395776 * q^67 + 85525504 * q^68 + 27771498 * q^69 + 318313600 * q^70 + 405104640 * q^71 + 107495424 * q^72 + 80652312 * q^73 + 70840128 * q^74 + 297554310 * q^75 + 288541184 * q^76 + 467201496 * q^77 + 337895712 * q^78 - 153459652 * q^79 + 61734912 * q^80 + 172186884 * q^81 - 203118048 * q^82 + 963057596 * q^83 + 105504768 * q^84 + 78676782 * q^85 + 184217440 * q^86 + 279715032 * q^87 - 85286912 * q^88 + 1052288804 * q^89 + 98887392 * q^90 - 369963848 * q^91 + 87771648 * q^92 + 707496444 * q^93 - 25926592 * q^94 - 870496374 * q^95 + 339738624 * q^96 + 340518220 * q^97 + 597560896 * q^98 - 136613142 * 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

)

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

$2$	16.0000	0.707107
$2$	16.0000	0.707107
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	256.000	0.500000
$5$	1842.42	1.31833	0.659163	−	0.752000i	$-0.270911\pi$
$5$	1842.42	1.31833	0.659163	+	0.752000i	$0.270911\pi$
$6$	1296.00	0.408248
$7$	−4706.68	−0.740923	−0.370462	−	0.928848i	$-0.620800\pi$
$7$	−4706.68	−0.740923	−0.370462	+	0.928848i	$0.620800\pi$
$8$	4096.00	0.353553
$9$	6561.00	0.333333
$10$	29478.7	0.932197
$11$	22720.2	0.467890	0.233945	−	0.972250i	$-0.424836\pi$
$11$	22720.2	0.467890	0.233945	+	0.972250i	$0.424836\pi$
$12$	20736.0	0.288675
$13$	11385.1	0.110558	0.0552792	−	0.998471i	$-0.482395\pi$
$13$	11385.1	0.110558	0.0552792	+	0.998471i	$0.482395\pi$
$14$	−75306.8	−0.523912
$15$	149236.	0.761136
$16$	65536.0	0.250000
$17$	83521.0	0.242536
$17$	83521.0	0.242536
$18$	104976.	0.235702
$19$	523587.	0.921716	0.460858	−	0.887474i	$-0.347542\pi$
$19$	523587.	0.921716	0.460858	+	0.887474i	$0.347542\pi$
$20$	471658.	0.659163
$21$	−381241.	−0.427772
$22$	363522.	0.330848
$23$	1.58895e6	1.18395	0.591977	−	0.805955i	$-0.298348\pi$
$23$	1.58895e6	1.18395	0.591977	+	0.805955i	$0.298348\pi$
$24$	331776.	0.204124
$25$	1.44137e6	0.737982
$26$	182162.	0.0781766
$27$	531441.	0.192450
$28$	−1.20491e6	−0.370462
$29$	2.02281e6	0.531085	0.265542	−	0.964099i	$-0.414449\pi$
$29$	2.02281e6	0.531085	0.265542	+	0.964099i	$0.414449\pi$
$30$	2.38777e6	0.538204
$31$	−9.22058e6	−1.79321	−0.896604	−	0.442833i	$-0.853973\pi$
$31$	−9.22058e6	−1.79321	−0.896604	+	0.442833i	$0.853973\pi$
$32$	1.04858e6	0.176777
$33$	1.84033e6	0.270137
$34$	1.33634e6	0.171499
$35$	−8.67166e6	−0.976778
$36$	1.67962e6	0.166667
$37$	−2.94408e6	−0.258251	−0.129125	−	0.991628i	$-0.541217\pi$
$37$	−2.94408e6	−0.258251	−0.129125	+	0.991628i	$0.541217\pi$
$38$	8.37739e6	0.651752
$39$	922193.	0.0638309
$40$	7.54654e6	0.466098
$41$	2.75165e7	1.52078	0.760389	−	0.649468i	$-0.225008\pi$
$41$	2.75165e7	1.52078	0.760389	+	0.649468i	$0.225008\pi$
$42$	−6.09985e6	−0.302481
$43$	−8.43166e6	−0.376101	−0.188051	−	0.982159i	$-0.560217\pi$
$43$	−8.43166e6	−0.376101	−0.188051	+	0.982159i	$0.560217\pi$
$44$	5.81636e6	0.233945
$45$	1.20881e7	0.439442
$46$	2.54232e7	0.837182
$47$	4.11237e7	1.22928	0.614642	−	0.788806i	$-0.289301\pi$
$47$	4.11237e7	1.22928	0.614642	+	0.788806i	$0.289301\pi$
$48$	5.30842e6	0.144338
$49$	−1.82008e7	−0.451033
$50$	2.30619e7	0.521832
$51$	6.76520e6	0.140028
$52$	2.91459e6	0.0552792
$53$	−2.85885e7	−0.497680	−0.248840	−	0.968545i	$-0.580049\pi$
$53$	−2.85885e7	−0.497680	−0.248840	+	0.968545i	$0.580049\pi$
$54$	8.50306e6	0.136083
$55$	4.18600e7	0.616832
$56$	−1.92785e7	−0.261956
$57$	4.24105e7	0.532153
$58$	3.23649e7	0.375534
$59$	8.35446e7	0.897604	0.448802	−	0.893631i	$-0.351851\pi$
$59$	8.35446e7	0.897604	0.448802	+	0.893631i	$0.351851\pi$
$60$	3.82043e7	0.380568
$61$	−1.27674e8	−1.18064	−0.590320	−	0.807169i	$-0.700998\pi$
$61$	−1.27674e8	−1.18064	−0.590320	+	0.807169i	$0.700998\pi$
$62$	−1.47529e8	−1.26799
$63$	−3.08805e7	−0.246974
$64$	1.67772e7	0.125000
$65$	2.09761e7	0.145752
$66$	2.94453e7	0.191015
$67$	1.40982e8	0.854726	0.427363	−	0.904080i	$-0.359443\pi$
$67$	1.40982e8	0.854726	0.427363	+	0.904080i	$0.359443\pi$
$68$	2.13814e7	0.121268
$69$	1.28705e8	0.683556
$70$	−1.38747e8	−0.690686
$71$	7.71872e7	0.360481	0.180241	−	0.983623i	$-0.442312\pi$
$71$	7.71872e7	0.360481	0.180241	+	0.983623i	$0.442312\pi$
$72$	2.68739e7	0.117851
$73$	−6.55896e7	−0.270322	−0.135161	−	0.990824i	$-0.543155\pi$
$73$	−6.55896e7	−0.270322	−0.135161	+	0.990824i	$0.543155\pi$
$74$	−4.71053e7	−0.182611
$75$	1.16751e8	0.426074
$76$	1.34038e8	0.460858
$77$	−1.06936e8	−0.346671
$78$	1.47551e7	0.0451353
$79$	2.78910e8	0.805641	0.402820	−	0.915279i	$-0.368030\pi$
$79$	2.78910e8	0.805641	0.402820	+	0.915279i	$0.368030\pi$
$80$	1.20745e8	0.329581
$81$	4.30467e7	0.111111
$82$	4.40264e8	1.07535
$83$	−1.06724e8	−0.246836	−0.123418	−	0.992355i	$-0.539386\pi$
$83$	−1.06724e8	−0.246836	−0.123418	+	0.992355i	$0.539386\pi$
$84$	−9.75976e7	−0.213886
$85$	1.53880e8	0.319741
$86$	−1.34907e8	−0.265944
$87$	1.63848e8	0.306622
$88$	9.30617e7	0.165424
$89$	5.19026e8	0.876868	0.438434	−	0.898763i	$-0.355533\pi$
$89$	5.19026e8	0.876868	0.438434	+	0.898763i	$0.355533\pi$
$90$	1.93409e8	0.310732
$91$	−5.35860e7	−0.0819153
$92$	4.06771e8	0.591977
$93$	−7.46867e8	−1.03531
$94$	6.57979e8	0.869235
$95$	9.64664e8	1.21512
$96$	8.49347e7	0.102062
$97$	−5.03657e8	−0.577647	−0.288823	−	0.957382i	$-0.593264\pi$
$97$	−5.03657e8	−0.577647	−0.288823	+	0.957382i	$0.593264\pi$
$98$	−2.91213e8	−0.318928
$99$	1.49067e8	0.155963
$100$	3.68991e8	0.368991
$101$	7.78837e7	0.0744733	0.0372366	−	0.999306i	$-0.488144\pi$
$101$	7.78837e7	0.0744733	0.0372366	+	0.999306i	$0.488144\pi$
$102$	1.08243e8	0.0990148
$103$	−9.98786e8	−0.874390	−0.437195	−	0.899367i	$-0.644028\pi$
$103$	−9.98786e8	−0.874390	−0.437195	+	0.899367i	$0.644028\pi$
$104$	4.66334e7	0.0390883
$105$	−7.02404e8	−0.563943
$106$	−4.57416e8	−0.351913
$107$	1.16801e8	0.0861431	0.0430715	−	0.999072i	$-0.486286\pi$
$107$	1.16801e8	0.0861431	0.0430715	+	0.999072i	$0.486286\pi$
$108$	1.36049e8	0.0962250
$109$	−6.41849e8	−0.435526	−0.217763	−	0.976002i	$-0.569876\pi$
$109$	−6.41849e8	−0.435526	−0.217763	+	0.976002i	$0.569876\pi$
$110$	6.69760e8	0.436166
$111$	−2.38471e8	−0.149101
$112$	−3.08457e8	−0.185231
$113$	7.45533e8	0.430144	0.215072	−	0.976598i	$-0.431001\pi$
$113$	7.45533e8	0.430144	0.215072	+	0.976598i	$0.431001\pi$
$114$	6.78568e8	0.376289
$115$	2.92751e9	1.56084
$116$	5.17839e8	0.265542
$117$	7.46976e7	0.0368528
$118$	1.33671e9	0.634702
$119$	−3.93106e8	−0.179700
$120$	6.11269e8	0.269102
$121$	−1.84174e9	−0.781079
$122$	−2.04278e9	−0.834838
$123$	2.22884e9	0.878022
$124$	−2.36047e9	−0.896604
$125$	−9.42863e8	−0.345425
$126$	−4.94088e8	−0.174637
$127$	−1.05616e9	−0.360257	−0.180128	−	0.983643i	$-0.557651\pi$
$127$	−1.05616e9	−0.360257	−0.180128	+	0.983643i	$0.557651\pi$
$128$	2.68435e8	0.0883883
$129$	−6.82964e8	−0.217142
$130$	3.35617e8	0.103062
$131$	4.56700e9	1.35491	0.677455	−	0.735564i	$-0.263083\pi$
$131$	4.56700e9	1.35491	0.677455	+	0.735564i	$0.263083\pi$
$132$	4.71125e8	0.135068
$133$	−2.46435e9	−0.682921
$134$	2.25571e9	0.604383
$135$	9.79135e8	0.253712
$136$	3.42102e8	0.0857493
$137$	−1.67144e9	−0.405366	−0.202683	−	0.979244i	$-0.564966\pi$
$137$	−1.67144e9	−0.405366	−0.202683	+	0.979244i	$0.564966\pi$
$138$	2.05928e9	0.483347
$139$	−7.65389e9	−1.73906	−0.869532	−	0.493877i	$-0.835579\pi$
$139$	−7.65389e9	−1.73906	−0.869532	+	0.493877i	$0.835579\pi$
$140$	−2.21994e9	−0.488389
$141$	3.33102e9	0.709727
$142$	1.23500e9	0.254899
$143$	2.58671e8	0.0517292
$144$	4.29982e8	0.0833333
$145$	3.72686e9	0.700143
$146$	−1.04943e9	−0.191147
$147$	−1.47426e9	−0.260404
$148$	−7.53685e8	−0.129125
$149$	−1.06850e10	−1.77598	−0.887990	−	0.459863i	$-0.847898\pi$
$149$	−1.06850e10	−1.77598	−0.887990	+	0.459863i	$0.847898\pi$
$150$	1.86802e9	0.301280
$151$	9.03596e8	0.141442	0.0707210	−	0.997496i	$-0.477470\pi$
$151$	9.03596e8	0.141442	0.0707210	+	0.997496i	$0.477470\pi$
$152$	2.14461e9	0.325876
$153$	5.47981e8	0.0808452
$154$	−1.71098e9	−0.245133
$155$	−1.69881e10	−2.36403
$156$	2.36081e8	0.0319155
$157$	−3.53273e9	−0.464047	−0.232023	−	0.972710i	$-0.574535\pi$
$157$	−3.53273e9	−0.464047	−0.232023	+	0.972710i	$0.574535\pi$
$158$	4.46255e9	0.569674
$159$	−2.31567e9	−0.287336
$160$	1.93191e9	0.233049
$161$	−7.47867e9	−0.877219
$162$	6.88748e8	0.0785674
$163$	−9.95354e9	−1.10442	−0.552209	−	0.833706i	$-0.686215\pi$
$163$	−9.95354e9	−1.10442	−0.552209	+	0.833706i	$0.686215\pi$
$164$	7.04422e9	0.760389
$165$	3.39066e9	0.356128
$166$	−1.70758e9	−0.174540
$167$	−1.98167e9	−0.197155	−0.0985774	−	0.995129i	$-0.531429\pi$
$167$	−1.98167e9	−0.197155	−0.0985774	+	0.995129i	$0.531429\pi$
$168$	−1.56156e9	−0.151240
$169$	−1.04749e10	−0.987777
$170$	2.46209e9	0.226091
$171$	3.43525e9	0.307239
$172$	−2.15850e9	−0.188051
$173$	−7.64973e9	−0.649290	−0.324645	−	0.945836i	$-0.605245\pi$
$173$	−7.64973e9	−0.649290	−0.324645	+	0.945836i	$0.605245\pi$
$174$	2.62156e9	0.216814
$175$	−6.78407e9	−0.546788
$176$	1.48899e9	0.116973
$177$	6.76712e9	0.518232
$178$	8.30442e9	0.620039
$179$	−1.49195e10	−1.08621	−0.543106	−	0.839664i	$-0.682752\pi$
$179$	−1.49195e10	−1.08621	−0.543106	+	0.839664i	$0.682752\pi$
$180$	3.09455e9	0.219721
$181$	−7.92926e8	−0.0549135	−0.0274568	−	0.999623i	$-0.508741\pi$
$181$	−7.92926e8	−0.0549135	−0.0274568	+	0.999623i	$0.508741\pi$
$182$	−8.57376e8	−0.0579229
$183$	−1.03416e10	−0.681643
$184$	6.50834e9	0.418591
$185$	−5.42422e9	−0.340459
$186$	−1.19499e10	−0.732074
$187$	1.89761e9	0.113480
$188$	1.05277e10	0.614642
$189$	−2.50132e9	−0.142591
$190$	1.54346e10	0.859221
$191$	−2.90951e10	−1.58187	−0.790933	−	0.611902i	$-0.790405\pi$
$191$	−2.90951e10	−1.58187	−0.790933	+	0.611902i	$0.790405\pi$
$192$	1.35895e9	0.0721688
$193$	−2.40531e10	−1.24785	−0.623926	−	0.781484i	$-0.714463\pi$
$193$	−2.40531e10	−1.24785	−0.623926	+	0.781484i	$0.714463\pi$
$194$	−8.05852e9	−0.408458
$195$	1.69906e9	0.0841499
$196$	−4.65941e9	−0.225516
$197$	−1.95453e10	−0.924577	−0.462289	−	0.886729i	$-0.652972\pi$
$197$	−1.95453e10	−0.924577	−0.462289	+	0.886729i	$0.652972\pi$
$198$	2.38507e9	0.110283
$199$	2.68267e10	1.21263	0.606316	−	0.795224i	$-0.292647\pi$
$199$	2.68267e10	1.21263	0.606316	+	0.795224i	$0.292647\pi$
$200$	5.90386e9	0.260916
$201$	1.14195e10	0.493476
$202$	1.24614e9	0.0526606
$203$	−9.52071e9	−0.393493
$204$	1.73189e9	0.0700140
$205$	5.06968e10	2.00488
$206$	−1.59806e10	−0.618287
$207$	1.04251e10	0.394651
$208$	7.46134e8	0.0276396
$209$	1.18960e10	0.431262
$210$	−1.12385e10	−0.398768
$211$	5.00514e10	1.73838	0.869191	−	0.494477i	$-0.164640\pi$
$211$	5.00514e10	1.73838	0.869191	+	0.494477i	$0.164640\pi$
$212$	−7.31866e9	−0.248840
$213$	6.25216e9	0.208124
$214$	1.86882e9	0.0609124
$215$	−1.55346e10	−0.495824
$216$	2.17678e9	0.0680414
$217$	4.33983e10	1.32863
$218$	−1.02696e10	−0.307963
$219$	−5.31276e9	−0.156071
$220$	1.07162e10	0.308416
$221$	9.50895e8	0.0268143
$222$	−3.81553e9	−0.105431
$223$	7.47280e9	0.202354	0.101177	−	0.994868i	$-0.467739\pi$
$223$	7.47280e9	0.202354	0.101177	+	0.994868i	$0.467739\pi$
$224$	−4.93531e9	−0.130978
$225$	9.45684e9	0.245994
$226$	1.19285e10	0.304158
$227$	−3.05696e10	−0.764141	−0.382070	−	0.924133i	$-0.624789\pi$
$227$	−3.05696e10	−0.764141	−0.382070	+	0.924133i	$0.624789\pi$
$228$	1.08571e10	0.266077
$229$	4.56008e10	1.09575	0.547877	−	0.836559i	$-0.315436\pi$
$229$	4.56008e10	1.09575	0.547877	+	0.836559i	$0.315436\pi$
$230$	4.68401e10	1.10368
$231$	−8.66185e9	−0.200151
$232$	8.28543e9	0.187767
$233$	6.06866e10	1.34893	0.674467	−	0.738305i	$-0.264373\pi$
$233$	6.06866e10	1.34893	0.674467	+	0.738305i	$0.264373\pi$
$234$	1.19516e9	0.0260589
$235$	7.57670e10	1.62060
$236$	2.13874e10	0.448802
$237$	2.25917e10	0.465137
$238$	−6.28970e9	−0.127067
$239$	−8.33322e10	−1.65205	−0.826023	−	0.563636i	$-0.809402\pi$
$239$	−8.33322e10	−1.65205	−0.826023	+	0.563636i	$0.809402\pi$
$240$	9.78031e9	0.190284
$241$	−3.39371e10	−0.648033	−0.324017	−	0.946051i	$-0.605033\pi$
$241$	−3.39371e10	−0.648033	−0.324017	+	0.946051i	$0.605033\pi$
$242$	−2.94679e10	−0.552306
$243$	3.48678e9	0.0641500
$244$	−3.26845e10	−0.590320
$245$	−3.35334e10	−0.594608
$246$	3.56614e10	0.620855
$247$	5.96109e9	0.101903
$248$	−3.77675e10	−0.633995
$249$	−8.64461e9	−0.142511
$250$	−1.50858e10	−0.244252
$251$	5.27511e10	0.838880	0.419440	−	0.907783i	$-0.362226\pi$
$251$	5.27511e10	0.838880	0.419440	+	0.907783i	$0.362226\pi$
$252$	−7.90541e9	−0.123487
$253$	3.61012e10	0.553961
$254$	−1.68985e10	−0.254740
$255$	1.24643e10	0.184603
$256$	4.29497e9	0.0625000
$257$	5.27283e10	0.753954	0.376977	−	0.926223i	$-0.376964\pi$
$257$	5.27283e10	0.753954	0.376977	+	0.926223i	$0.376964\pi$
$258$	−1.09274e10	−0.153543
$259$	1.38568e10	0.191344
$260$	5.36988e9	0.0728760
$261$	1.32717e10	0.177028
$262$	7.30721e10	0.958066
$263$	1.27039e11	1.63733	0.818666	−	0.574270i	$-0.194714\pi$
$263$	1.27039e11	1.63733	0.818666	+	0.574270i	$0.194714\pi$
$264$	7.53800e9	0.0955077
$265$	−5.26720e10	−0.656105
$266$	−3.94296e10	−0.482898
$267$	4.20411e10	0.506260
$268$	3.60914e10	0.427363
$269$	−5.11763e10	−0.595914	−0.297957	−	0.954579i	$-0.596305\pi$
$269$	−5.11763e10	−0.595914	−0.297957	+	0.954579i	$0.596305\pi$
$270$	1.56662e10	0.179401
$271$	−1.20074e11	−1.35234	−0.676172	−	0.736744i	$-0.736362\pi$
$271$	−1.20074e11	−1.35234	−0.676172	+	0.736744i	$0.736362\pi$
$272$	5.47363e9	0.0606339
$273$	−4.34046e9	−0.0472938
$274$	−2.67430e10	−0.286637
$275$	3.27482e10	0.345295
$276$	3.29485e10	0.341778
$277$	1.81854e11	1.85594	0.927972	−	0.372649i	$-0.121550\pi$
$277$	1.81854e11	1.85594	0.927972	+	0.372649i	$0.121550\pi$
$278$	−1.22462e11	−1.22970
$279$	−6.04962e10	−0.597736
$280$	−3.55191e10	−0.345343
$281$	−1.15809e10	−0.110806	−0.0554030	−	0.998464i	$-0.517644\pi$
$281$	−1.15809e10	−0.110806	−0.0554030	+	0.998464i	$0.517644\pi$
$282$	5.32963e10	0.501853
$283$	−1.57674e11	−1.46124	−0.730619	−	0.682785i	$-0.760768\pi$
$283$	−1.57674e11	−1.46124	−0.730619	+	0.682785i	$0.760768\pi$
$284$	1.97599e10	0.180241
$285$	7.81378e10	0.701551
$286$	4.13874e9	0.0365781
$287$	−1.29511e11	−1.12678
$288$	6.87971e9	0.0589256
$289$	6.97576e9	0.0588235
$290$	5.96297e10	0.495076
$291$	−4.07962e10	−0.333504
$292$	−1.67909e10	−0.135161
$293$	−1.66582e11	−1.32045	−0.660227	−	0.751066i	$-0.729540\pi$
$293$	−1.66582e11	−1.32045	−0.660227	+	0.751066i	$0.729540\pi$
$294$	−2.35882e10	−0.184133
$295$	1.53924e11	1.18333
$296$	−1.20590e10	−0.0913055
$297$	1.20744e10	0.0900456
$298$	−1.70961e11	−1.25581
$299$	1.80904e10	0.130896
$300$	2.98883e10	0.213037
$301$	3.96851e10	0.278662
$302$	1.44575e10	0.100015
$303$	6.30858e9	0.0429972
$304$	3.43138e10	0.230429
$305$	−2.35228e11	−1.55647
$306$	8.76770e9	0.0571662
$307$	5.29467e10	0.340186	0.170093	−	0.985428i	$-0.445593\pi$
$307$	5.29467e10	0.340186	0.170093	+	0.985428i	$0.445593\pi$
$308$	−2.73757e10	−0.173335
$309$	−8.09017e10	−0.504829
$310$	−2.71810e11	−1.67162
$311$	−1.85494e11	−1.12437	−0.562183	−	0.827013i	$-0.690039\pi$
$311$	−1.85494e11	−1.12437	−0.562183	+	0.827013i	$0.690039\pi$
$312$	3.77730e9	0.0225676
$313$	−8.70761e9	−0.0512802	−0.0256401	−	0.999671i	$-0.508162\pi$
$313$	−8.70761e9	−0.0512802	−0.0256401	+	0.999671i	$0.508162\pi$
$314$	−5.65237e10	−0.328131
$315$	−5.68947e10	−0.325593
$316$	7.14008e10	0.402820
$317$	1.13116e11	0.629152	0.314576	−	0.949232i	$-0.398138\pi$
$317$	1.13116e11	0.629152	0.314576	+	0.949232i	$0.398138\pi$
$318$	−3.70507e10	−0.203177
$319$	4.59585e10	0.248490
$320$	3.09106e10	0.164791
$321$	9.46090e9	0.0497347
$322$	−1.19659e11	−0.620288
$323$	4.37305e10	0.223549
$324$	1.10200e10	0.0555556
$325$	1.64102e10	0.0815901
$326$	−1.59257e11	−0.780941
$327$	−5.19898e10	−0.251451
$328$	1.12708e11	0.537676
$329$	−1.93556e11	−0.910805
$330$	5.42505e10	0.251821
$331$	9.98136e10	0.457050	0.228525	−	0.973538i	$-0.426610\pi$
$331$	9.98136e10	0.457050	0.228525	+	0.973538i	$0.426610\pi$
$332$	−2.73212e10	−0.123418
$333$	−1.93161e10	−0.0860836
$334$	−3.17067e10	−0.139409
$335$	2.59747e11	1.12681
$336$	−2.49850e10	−0.106943
$337$	1.96168e9	0.00828503	0.00414252	−	0.999991i	$-0.498681\pi$
$337$	1.96168e9	0.00828503	0.00414252	+	0.999991i	$0.498681\pi$
$338$	−1.67598e11	−0.698464
$339$	6.03882e10	0.248344
$340$	3.93934e10	0.159870
$341$	−2.09493e11	−0.839025
$342$	5.49640e10	0.217251
$343$	2.75597e11	1.07510
$344$	−3.45361e10	−0.132972
$345$	2.37128e11	0.901150
$346$	−1.22396e11	−0.459117
$347$	4.01242e11	1.48567	0.742837	−	0.669473i	$-0.233480\pi$
$347$	4.01242e11	1.48567	0.742837	+	0.669473i	$0.233480\pi$
$348$	4.19450e10	0.153311
$349$	2.40412e11	0.867443	0.433722	−	0.901047i	$-0.357200\pi$
$349$	2.40412e11	0.867443	0.433722	+	0.901047i	$0.357200\pi$
$350$	−1.08545e11	−0.386638
$351$	6.05051e9	0.0212770
$352$	2.38238e10	0.0827121
$353$	1.29986e11	0.445565	0.222783	−	0.974868i	$-0.428486\pi$
$353$	1.29986e11	0.445565	0.222783	+	0.974868i	$0.428486\pi$
$354$	1.08274e11	0.366445
$355$	1.42211e11	0.475232
$356$	1.32871e11	0.438434
$357$	−3.18416e10	−0.103750
$358$	−2.38712e11	−0.768068
$359$	8.71259e10	0.276836	0.138418	−	0.990374i	$-0.455798\pi$
$359$	8.71259e10	0.276836	0.138418	+	0.990374i	$0.455798\pi$
$360$	4.95128e10	0.155366
$361$	−4.85447e10	−0.150439
$362$	−1.26868e10	−0.0388297
$363$	−1.49181e11	−0.450956
$364$	−1.37180e10	−0.0409576
$365$	−1.20843e11	−0.356373
$366$	−1.65465e11	−0.481994
$367$	−2.09905e11	−0.603985	−0.301993	−	0.953310i	$-0.597652\pi$
$367$	−2.09905e11	−0.603985	−0.301993	+	0.953310i	$0.597652\pi$
$368$	1.04133e11	0.295989
$369$	1.80536e11	0.506926
$370$	−8.67875e10	−0.240741
$371$	1.34557e11	0.368743
$372$	−1.91198e11	−0.517655
$373$	−2.47415e11	−0.661814	−0.330907	−	0.943663i	$-0.607355\pi$
$373$	−2.47415e11	−0.661814	−0.330907	+	0.943663i	$0.607355\pi$
$374$	3.03618e10	0.0802425
$375$	−7.63719e10	−0.199431
$376$	1.68443e11	0.434617
$377$	2.30299e10	0.0587159
$378$	−4.00211e10	−0.100827
$379$	−1.60649e11	−0.399946	−0.199973	−	0.979801i	$-0.564085\pi$
$379$	−1.60649e11	−0.399946	−0.199973	+	0.979801i	$0.564085\pi$
$380$	2.46954e11	0.607561
$381$	−8.55488e10	−0.207994
$382$	−4.65522e11	−1.11855
$383$	−1.89236e11	−0.449376	−0.224688	−	0.974431i	$-0.572136\pi$
$383$	−1.89236e11	−0.449376	−0.224688	+	0.974431i	$0.572136\pi$
$384$	2.17433e10	0.0510310
$385$	−1.97021e11	−0.457025
$386$	−3.84849e11	−0.882364
$387$	−5.53201e10	−0.125367
$388$	−1.28936e11	−0.288823
$389$	−5.23103e11	−1.15828	−0.579141	−	0.815227i	$-0.696612\pi$
$389$	−5.23103e11	−1.15828	−0.579141	+	0.815227i	$0.696612\pi$
$390$	2.71850e10	0.0595030
$391$	1.32711e11	0.287151
$392$	−7.45505e10	−0.159464
$393$	3.69927e11	0.782258
$394$	−3.12724e11	−0.653775
$395$	5.13867e11	1.06210
$396$	3.81611e10	0.0779817
$397$	−1.03285e11	−0.208679	−0.104339	−	0.994542i	$-0.533273\pi$
$397$	−1.03285e11	−0.208679	−0.104339	+	0.994542i	$0.533273\pi$
$398$	4.29227e11	0.857460
$399$	−1.99613e11	−0.394285
$400$	9.44617e10	0.184496
$401$	−6.26999e11	−1.21092	−0.605462	−	0.795874i	$-0.707012\pi$
$401$	−6.26999e11	−1.21092	−0.605462	+	0.795874i	$0.707012\pi$
$402$	1.82713e11	0.348941
$403$	−1.04977e11	−0.198254
$404$	1.99382e10	0.0372366
$405$	7.93100e10	0.146481
$406$	−1.52331e11	−0.278242
$407$	−6.68900e10	−0.120833
$408$	2.77103e10	0.0495074
$409$	−7.75508e11	−1.37035	−0.685175	−	0.728379i	$-0.740274\pi$
$409$	−7.75508e11	−1.37035	−0.685175	+	0.728379i	$0.740274\pi$
$410$	8.11149e11	1.41766
$411$	−1.35386e11	−0.234038
$412$	−2.55689e11	−0.437195
$413$	−3.93218e11	−0.665055
$414$	1.66802e11	0.279061
$415$	−1.96629e11	−0.325410
$416$	1.19381e10	0.0195441
$417$	−6.19965e11	−1.00405
$418$	1.90335e11	0.304949
$419$	3.75763e11	0.595595	0.297798	−	0.954629i	$-0.403748\pi$
$419$	3.75763e11	0.595595	0.297798	+	0.954629i	$0.403748\pi$
$420$	−1.79815e11	−0.281972
$421$	2.03242e11	0.315314	0.157657	−	0.987494i	$-0.449606\pi$
$421$	2.03242e11	0.315314	0.157657	+	0.987494i	$0.449606\pi$
$422$	8.00822e11	1.22922
$423$	2.69813e11	0.409761
$424$	−1.17099e11	−0.175957
$425$	1.20385e11	0.178987
$426$	1.00035e11	0.147166
$427$	6.00919e11	0.874763
$428$	2.99011e10	0.0430715
$429$	2.09524e10	0.0298659
$430$	−2.48554e11	−0.350601
$431$	1.02073e12	1.42483	0.712414	−	0.701759i	$-0.247602\pi$
$431$	1.02073e12	1.42483	0.712414	+	0.701759i	$0.247602\pi$
$432$	3.48285e10	0.0481125
$433$	−9.21908e11	−1.26035	−0.630176	−	0.776452i	$-0.717017\pi$
$433$	−9.21908e11	−1.26035	−0.630176	+	0.776452i	$0.717017\pi$
$434$	6.94373e11	0.939483
$435$	3.01875e11	0.404228
$436$	−1.64313e11	−0.217763
$437$	8.31953e11	1.09127
$438$	−8.50041e10	−0.110359
$439$	4.92301e11	0.632616	0.316308	−	0.948657i	$-0.397557\pi$
$439$	4.92301e11	0.632616	0.316308	+	0.948657i	$0.397557\pi$
$440$	1.71458e11	0.218083
$441$	−1.19415e11	−0.150344
$442$	1.52143e10	0.0189606
$443$	1.51405e12	1.86777	0.933883	−	0.357580i	$-0.116398\pi$
$443$	1.51405e12	1.86777	0.933883	+	0.357580i	$0.116398\pi$
$444$	−6.10485e10	−0.0745506
$445$	9.56262e11	1.15600
$446$	1.19565e11	0.143086
$447$	−8.65488e11	−1.02536
$448$	−7.89649e10	−0.0926154
$449$	−1.28303e12	−1.48980	−0.744901	−	0.667175i	$-0.767503\pi$
$449$	−1.28303e12	−1.48980	−0.744901	+	0.667175i	$0.767503\pi$
$450$	1.51309e11	0.173944
$451$	6.25179e11	0.711558
$452$	1.90856e11	0.215072
$453$	7.31913e10	0.0816615
$454$	−4.89114e11	−0.540329
$455$	−9.87277e10	−0.107991
$456$	1.73713e11	0.188145
$457$	1.05752e12	1.13414	0.567070	−	0.823670i	$-0.308077\pi$
$457$	1.05752e12	1.13414	0.567070	+	0.823670i	$0.308077\pi$
$458$	7.29613e11	0.774815
$459$	4.43865e10	0.0466760
$460$	7.49442e11	0.780419
$461$	1.25776e12	1.29702	0.648508	−	0.761208i	$-0.275393\pi$
$461$	1.25776e12	1.29702	0.648508	+	0.761208i	$0.275393\pi$
$462$	−1.38590e11	−0.141528
$463$	6.39919e11	0.647158	0.323579	−	0.946201i	$-0.395114\pi$
$463$	6.39919e11	0.647158	0.323579	+	0.946201i	$0.395114\pi$
$464$	1.32567e11	0.132771
$465$	−1.37604e12	−1.36487
$466$	9.70985e11	0.953841
$467$	−4.22079e11	−0.410646	−0.205323	−	0.978694i	$-0.565825\pi$
$467$	−4.22079e11	−0.410646	−0.205323	+	0.978694i	$0.565825\pi$
$468$	1.91226e10	0.0184264
$469$	−6.63557e11	−0.633286
$470$	1.21227e12	1.14593
$471$	−2.86151e11	−0.267918
$472$	3.42199e11	0.317351
$473$	−1.91569e11	−0.175974
$474$	3.61467e11	0.328901
$475$	7.54683e11	0.680210
$476$	−1.00635e11	−0.0898501
$477$	−1.87569e11	−0.165893
$478$	−1.33331e12	−1.16817
$479$	1.10730e12	0.961072	0.480536	−	0.876975i	$-0.340442\pi$
$479$	1.10730e12	0.961072	0.480536	+	0.876975i	$0.340442\pi$
$480$	1.56485e11	0.134551
$481$	−3.35186e10	−0.0285518
$482$	−5.42993e11	−0.458229
$483$	−6.05773e11	−0.506463
$484$	−4.71486e11	−0.390539
$485$	−9.27946e11	−0.761526
$486$	5.57886e10	0.0453609
$487$	−2.23395e12	−1.79967	−0.899837	−	0.436226i	$-0.856315\pi$
$487$	−2.23395e12	−1.79967	−0.899837	+	0.436226i	$0.856315\pi$
$488$	−5.22952e11	−0.417419
$489$	−8.06237e11	−0.637636
$490$	−5.36535e11	−0.420451
$491$	−1.88915e11	−0.146690	−0.0733450	−	0.997307i	$-0.523367\pi$
$491$	−1.88915e11	−0.146690	−0.0733450	+	0.997307i	$0.523367\pi$
$492$	5.70582e11	0.439011
$493$	1.68947e11	0.128807
$494$	9.53774e10	0.0720567
$495$	2.74643e11	0.205611
$496$	−6.04280e11	−0.448302
$497$	−3.63295e11	−0.267089
$498$	−1.38314e11	−0.100770
$499$	1.85978e12	1.34279	0.671397	−	0.741098i	$-0.265695\pi$
$499$	1.85978e12	1.34279	0.671397	+	0.741098i	$0.265695\pi$
$500$	−2.41373e11	−0.172712
$501$	−1.60515e11	−0.113827
$502$	8.44018e11	0.593178
$503$	−2.10435e11	−0.146576	−0.0732879	−	0.997311i	$-0.523349\pi$
$503$	−2.10435e11	−0.146576	−0.0732879	+	0.997311i	$0.523349\pi$
$504$	−1.26487e11	−0.0873186
$505$	1.43494e11	0.0981800
$506$	5.77619e11	0.391709
$507$	−8.48465e11	−0.570293
$508$	−2.70377e11	−0.180128
$509$	1.17591e12	0.776504	0.388252	−	0.921553i	$-0.373079\pi$
$509$	1.17591e12	0.776504	0.388252	+	0.921553i	$0.373079\pi$
$510$	1.99429e11	0.130534
$511$	3.08709e11	0.200288
$512$	6.87195e10	0.0441942
$513$	2.78255e11	0.177384
$514$	8.43653e11	0.533126
$515$	−1.84018e12	−1.15273
$516$	−1.74839e11	−0.108571
$517$	9.34337e11	0.575170
$518$	2.21709e11	0.135301
$519$	−6.19628e11	−0.374868
$520$	8.59181e10	0.0515311
$521$	−2.75088e12	−1.63569	−0.817846	−	0.575438i	$-0.804832\pi$
$521$	−2.75088e12	−1.63569	−0.817846	+	0.575438i	$0.804832\pi$
$522$	2.12346e11	0.125178
$523$	1.05531e11	0.0616771	0.0308386	−	0.999524i	$-0.490182\pi$
$523$	1.05531e11	0.0616771	0.0308386	+	0.999524i	$0.490182\pi$
$524$	1.16915e12	0.677455
$525$	−5.49510e11	−0.315688
$526$	2.03263e12	1.15777
$527$	−7.70112e11	−0.434917
$528$	1.20608e11	0.0675342
$529$	7.23609e11	0.401748
$530$	−8.42751e11	−0.463936
$531$	5.48136e11	0.299201
$532$	−6.30874e11	−0.341461
$533$	3.13278e11	0.168135
$534$	6.72658e11	0.357980
$535$	2.15196e11	0.113565
$536$	5.77462e11	0.302191
$537$	−1.20848e12	−0.627125
$538$	−8.18821e11	−0.421375
$539$	−4.13525e11	−0.211034
$540$	2.50659e11	0.126856
$541$	−2.22896e11	−0.111870	−0.0559351	−	0.998434i	$-0.517814\pi$
$541$	−2.22896e11	−0.111870	−0.0559351	+	0.998434i	$0.517814\pi$
$542$	−1.92118e12	−0.956251
$543$	−6.42270e10	−0.0317043
$544$	8.75781e10	0.0428746
$545$	−1.18255e12	−0.574165
$546$	−6.94474e10	−0.0334418
$547$	8.36279e11	0.399400	0.199700	−	0.979857i	$-0.436003\pi$
$547$	8.36279e11	0.399400	0.199700	+	0.979857i	$0.436003\pi$
$548$	−4.27888e11	−0.202683
$549$	−8.37668e11	−0.393547
$550$	5.23971e11	0.244160
$551$	1.05912e12	0.489510
$552$	5.27175e11	0.241674
$553$	−1.31274e12	−0.596918
$554$	2.90967e12	1.31235
$555$	−4.39362e11	−0.196564
$556$	−1.95939e12	−0.869532
$557$	−2.12166e11	−0.0933960	−0.0466980	−	0.998909i	$-0.514870\pi$
$557$	−2.12166e11	−0.0933960	−0.0466980	+	0.998909i	$0.514870\pi$
$558$	−9.67940e11	−0.422663
$559$	−9.59953e10	−0.0415812
$560$	−5.68306e11	−0.244194
$561$	1.53706e11	0.0655178
$562$	−1.85294e11	−0.0783517
$563$	−4.19818e11	−0.176105	−0.0880527	−	0.996116i	$-0.528064\pi$
$563$	−4.19818e11	−0.176105	−0.0880527	+	0.996116i	$0.528064\pi$
$564$	8.52741e11	0.354864
$565$	1.37358e12	0.567070
$566$	−2.52278e12	−1.03325
$567$	−2.02607e11	−0.0823248
$568$	3.16159e11	0.127449
$569$	2.25658e12	0.902497	0.451248	−	0.892398i	$-0.350979\pi$
$569$	2.25658e12	0.902497	0.451248	+	0.892398i	$0.350979\pi$
$570$	1.25021e12	0.496072
$571$	−4.14384e12	−1.63132	−0.815662	−	0.578528i	$-0.803627\pi$
$571$	−4.14384e12	−1.63132	−0.815662	+	0.578528i	$0.803627\pi$
$572$	6.62198e10	0.0258646
$573$	−2.35670e12	−0.913291
$574$	−2.07218e12	−0.796754
$575$	2.29027e12	0.873737
$576$	1.10075e11	0.0416667
$577$	1.03287e12	0.387930	0.193965	−	0.981008i	$-0.437865\pi$
$577$	1.03287e12	0.387930	0.193965	+	0.981008i	$0.437865\pi$
$578$	1.11612e11	0.0415945
$579$	−1.94830e12	−0.720447
$580$	9.54075e11	0.350071
$581$	5.02313e11	0.182887
$582$	−6.52740e11	−0.235823
$583$	−6.49536e11	−0.232860
$584$	−2.68655e11	−0.0955734
$585$	1.37624e11	0.0485840
$586$	−2.66531e12	−0.933702
$587$	5.22320e11	0.181579	0.0907895	−	0.995870i	$-0.471061\pi$
$587$	5.22320e11	0.181579	0.0907895	+	0.995870i	$0.471061\pi$
$588$	−3.77412e11	−0.130202
$589$	−4.82777e12	−1.65283
$590$	2.46278e12	0.836743
$591$	−1.58317e12	−0.533805
$592$	−1.92943e11	−0.0645627
$593$	−1.80456e12	−0.599274	−0.299637	−	0.954053i	$-0.596866\pi$
$593$	−1.80456e12	−0.599274	−0.299637	+	0.954053i	$0.596866\pi$
$594$	1.93191e11	0.0636718
$595$	−7.24265e11	−0.236903
$596$	−2.73537e12	−0.887990
$597$	2.17296e12	0.700113
$598$	2.89446e11	0.0925575
$599$	4.75108e12	1.50790	0.753949	−	0.656933i	$-0.228147\pi$
$599$	4.75108e12	1.50790	0.753949	+	0.656933i	$0.228147\pi$
$600$	4.78213e11	0.150640
$601$	−4.30615e12	−1.34634	−0.673169	−	0.739489i	$-0.735067\pi$
$601$	−4.30615e12	−1.34634	−0.673169	+	0.739489i	$0.735067\pi$
$602$	6.34961e11	0.197044
$603$	9.24983e11	0.284909
$604$	2.31321e11	0.0707210
$605$	−3.39326e12	−1.02972
$606$	1.00937e11	0.0304036
$607$	−2.35745e12	−0.704846	−0.352423	−	0.935841i	$-0.614642\pi$
$607$	−2.35745e12	−0.704846	−0.352423	+	0.935841i	$0.614642\pi$
$608$	5.49020e11	0.162938
$609$	−7.71177e11	−0.227183
$610$	−3.76365e12	−1.10059
$611$	4.68198e11	0.135908
$612$	1.40283e11	0.0404226
$613$	6.89834e12	1.97321	0.986603	−	0.163139i	$-0.0521618\pi$
$613$	6.89834e12	1.97321	0.986603	+	0.163139i	$0.0521618\pi$
$614$	8.47147e11	0.240548
$615$	4.10644e12	1.15752
$616$	−4.38012e11	−0.122567
$617$	−2.85812e12	−0.793959	−0.396979	−	0.917828i	$-0.629942\pi$
$617$	−2.85812e12	−0.793959	−0.396979	+	0.917828i	$0.629942\pi$
$618$	−1.29443e12	−0.356968
$619$	7.92629e11	0.217001	0.108501	−	0.994096i	$-0.465395\pi$
$619$	7.92629e11	0.217001	0.108501	+	0.994096i	$0.465395\pi$
$620$	−4.34897e12	−1.18202
$621$	8.44433e11	0.227852
$622$	−2.96790e12	−0.795048
$623$	−2.44289e12	−0.649692
$624$	6.04368e10	0.0159577
$625$	−4.55232e12	−1.19336
$626$	−1.39322e11	−0.0362606
$627$	9.63573e11	0.248989
$628$	−9.04379e11	−0.232023
$629$	−2.45893e11	−0.0626351
$630$	−9.10316e11	−0.230229
$631$	2.36798e12	0.594629	0.297315	−	0.954780i	$-0.403909\pi$
$631$	2.36798e12	0.594629	0.297315	+	0.954780i	$0.403909\pi$
$632$	1.14241e12	0.284837
$633$	4.05416e12	1.00366
$634$	1.80985e12	0.444878
$635$	−1.94588e12	−0.474936
$636$	−5.92812e11	−0.143668
$637$	−2.07218e11	−0.0498655
$638$	7.35336e11	0.175709
$639$	5.06425e11	0.120160
$640$	4.94570e11	0.116525
$641$	1.68150e12	0.393402	0.196701	−	0.980464i	$-0.436977\pi$
$641$	1.68150e12	0.393402	0.196701	+	0.980464i	$0.436977\pi$
$642$	1.51374e11	0.0351678
$643$	3.24081e11	0.0747661	0.0373831	−	0.999301i	$-0.488098\pi$
$643$	3.24081e11	0.0747661	0.0373831	+	0.999301i	$0.488098\pi$
$644$	−1.91454e12	−0.438610
$645$	−1.25830e12	−0.286264
$646$	6.99688e11	0.158073
$647$	5.21323e12	1.16960	0.584800	−	0.811177i	$-0.301173\pi$
$647$	5.21323e12	1.16960	0.584800	+	0.811177i	$0.301173\pi$
$648$	1.76319e11	0.0392837
$649$	1.89815e12	0.419980
$650$	2.62563e11	0.0576929
$651$	3.51526e12	0.767085
$652$	−2.54811e12	−0.552209
$653$	2.43547e12	0.524171	0.262085	−	0.965045i	$-0.415590\pi$
$653$	2.43547e12	0.524171	0.262085	+	0.965045i	$0.415590\pi$
$654$	−8.31837e11	−0.177803
$655$	8.41432e12	1.78621
$656$	1.80332e12	0.380195
$657$	−4.30333e11	−0.0901075
$658$	−3.09690e12	−0.644036
$659$	6.06001e11	0.125167	0.0625833	−	0.998040i	$-0.480066\pi$
$659$	6.06001e11	0.125167	0.0625833	+	0.998040i	$0.480066\pi$
$660$	8.68008e11	0.178064
$661$	6.77650e12	1.38070	0.690349	−	0.723477i	$-0.257457\pi$
$661$	6.77650e12	1.38070	0.690349	+	0.723477i	$0.257457\pi$
$662$	1.59702e12	0.323183
$663$	7.70225e10	0.0154813
$664$	−4.37140e11	−0.0872698
$665$	−4.54036e12	−0.900312
$666$	−3.09058e11	−0.0608703
$667$	3.21414e12	0.628780
$668$	−5.07308e11	−0.0985774
$669$	6.05297e11	0.116829
$670$	4.15596e12	0.796773
$671$	−2.90077e12	−0.552410
$672$	−3.99760e11	−0.0756202
$673$	6.04180e11	0.113527	0.0567634	−	0.998388i	$-0.481922\pi$
$673$	6.04180e11	0.113527	0.0567634	+	0.998388i	$0.481922\pi$
$674$	3.13869e10	0.00585840
$675$	7.66004e11	0.142025
$676$	−2.68157e12	−0.493888
$677$	2.98303e12	0.545769	0.272885	−	0.962047i	$-0.412022\pi$
$677$	2.98303e12	0.545769	0.272885	+	0.962047i	$0.412022\pi$
$678$	9.66211e11	0.175606
$679$	2.37055e12	0.427992
$680$	6.30294e11	0.113045
$681$	−2.47614e12	−0.441177
$682$	−3.35189e12	−0.593280
$683$	7.12376e12	1.25261	0.626305	−	0.779578i	$-0.284566\pi$
$683$	7.12376e12	1.25261	0.626305	+	0.779578i	$0.284566\pi$
$684$	8.79424e11	0.153619
$685$	−3.07948e12	−0.534405
$686$	4.40955e12	0.760213
$687$	3.69367e12	0.632634
$688$	−5.52577e11	−0.0940253
$689$	−3.25483e11	−0.0550227
$690$	3.79405e12	0.637209
$691$	1.04589e13	1.74515	0.872576	−	0.488479i	$-0.162448\pi$
$691$	1.04589e13	1.74515	0.872576	+	0.488479i	$0.162448\pi$
$692$	−1.95833e12	−0.324645
$693$	−7.01610e11	−0.115557
$694$	6.41987e12	1.05053
$695$	−1.41016e13	−2.29265
$696$	6.71119e11	0.108407
$697$	2.29821e12	0.368843
$698$	3.84659e12	0.613375
$699$	4.91561e12	0.778808
$700$	−1.73672e12	−0.273394
$701$	4.06918e12	0.636467	0.318233	−	0.948012i	$-0.396910\pi$
$701$	4.06918e12	0.636467	0.318233	+	0.948012i	$0.396910\pi$
$702$	9.68081e10	0.0150451
$703$	−1.54148e12	−0.238034
$704$	3.81181e11	0.0584863
$705$	6.13713e12	0.935651
$706$	2.07978e12	0.315062
$707$	−3.66573e11	−0.0551790
$708$	1.73238e12	0.259116
$709$	−1.66533e12	−0.247510	−0.123755	−	0.992313i	$-0.539494\pi$
$709$	−1.66533e12	−0.247510	−0.123755	+	0.992313i	$0.539494\pi$
$710$	2.27538e12	0.336040
$711$	1.82993e12	0.268547
$712$	2.12593e12	0.310020
$713$	−1.46510e13	−2.12308
$714$	−5.09466e11	−0.0733623
$715$	4.76580e11	0.0681959
$716$	−3.81939e12	−0.543106
$717$	−6.74991e12	−0.953809
$718$	1.39401e12	0.195752
$719$	−5.02642e12	−0.701421	−0.350710	−	0.936484i	$-0.614060\pi$
$719$	−5.02642e12	−0.701421	−0.350710	+	0.936484i	$0.614060\pi$
$720$	7.92205e11	0.109860
$721$	4.70096e12	0.647856
$722$	−7.76716e11	−0.106376
$723$	−2.74890e12	−0.374142
$724$	−2.02989e11	−0.0274568
$725$	2.91562e12	0.391931
$726$	−2.38690e12	−0.318874
$727$	1.24557e13	1.65373	0.826864	−	0.562401i	$-0.190122\pi$
$727$	1.24557e13	1.65373	0.826864	+	0.562401i	$0.190122\pi$
$728$	−2.19488e11	−0.0289614
$729$	2.82430e11	0.0370370
$730$	−1.93349e12	−0.251994
$731$	−7.04221e11	−0.0912180
$732$	−2.64744e12	−0.340821
$733$	−4.40018e12	−0.562993	−0.281496	−	0.959562i	$-0.590831\pi$
$733$	−4.40018e12	−0.562993	−0.281496	+	0.959562i	$0.590831\pi$
$734$	−3.35849e12	−0.427082
$735$	−2.71621e12	−0.343297
$736$	1.66613e12	0.209296
$737$	3.20313e12	0.399918
$738$	2.88857e12	0.358451
$739$	1.53516e13	1.89345	0.946725	−	0.322042i	$-0.104369\pi$
$739$	1.53516e13	1.89345	0.946725	+	0.322042i	$0.104369\pi$
$740$	−1.38860e12	−0.170229
$741$	4.82848e11	0.0588340
$742$	2.15291e12	0.260741
$743$	−5.98491e12	−0.720456	−0.360228	−	0.932864i	$-0.617301\pi$
$743$	−5.98491e12	−0.720456	−0.360228	+	0.932864i	$0.617301\pi$
$744$	−3.05917e12	−0.366037
$745$	−1.96863e13	−2.34132
$746$	−3.95864e12	−0.467973
$747$	−7.00213e11	−0.0822787
$748$	4.85788e11	0.0567400
$749$	−5.49746e11	−0.0638254
$750$	−1.22195e12	−0.141019
$751$	5.21553e12	0.598300	0.299150	−	0.954206i	$-0.403297\pi$
$751$	5.21553e12	0.598300	0.299150	+	0.954206i	$0.403297\pi$
$752$	2.69508e12	0.307321
$753$	4.27284e12	0.484328
$754$	3.68478e11	0.0415184
$755$	1.66480e12	0.186466
$756$	−6.40338e11	−0.0712954
$757$	−7.20268e12	−0.797192	−0.398596	−	0.917127i	$-0.630502\pi$
$757$	−7.20268e12	−0.797192	−0.398596	+	0.917127i	$0.630502\pi$
$758$	−2.57038e12	−0.282804
$759$	2.92420e12	0.319829
$760$	3.95127e12	0.429611
$761$	1.61306e13	1.74349	0.871746	−	0.489958i	$-0.162988\pi$
$761$	1.61306e13	1.74349	0.871746	+	0.489958i	$0.162988\pi$
$762$	−1.36878e12	−0.147074
$763$	3.02098e12	0.322691
$764$	−7.44835e12	−0.790933
$765$	1.00961e12	0.106580
$766$	−3.02778e12	−0.317757
$767$	9.51164e11	0.0992376
$768$	3.47892e11	0.0360844
$769$	5.44382e12	0.561352	0.280676	−	0.959803i	$-0.409441\pi$
$769$	5.44382e12	0.561352	0.280676	+	0.959803i	$0.409441\pi$
$770$	−3.15234e12	−0.323166
$771$	4.27100e12	0.435296
$772$	−6.15759e12	−0.623926
$773$	6.04146e12	0.608603	0.304302	−	0.952576i	$-0.401577\pi$
$773$	6.04146e12	0.608603	0.304302	+	0.952576i	$0.401577\pi$
$774$	−8.85122e11	−0.0886479
$775$	−1.32903e13	−1.32336
$776$	−2.06298e12	−0.204229
$777$	1.12240e12	0.110473
$778$	−8.36965e12	−0.819029
$779$	1.44073e13	1.40173
$780$	4.34960e11	0.0420750
$781$	1.75371e12	0.168666
$782$	2.12337e12	0.203046
$783$	1.07500e12	0.102207
$784$	−1.19281e12	−0.112758
$785$	−6.50876e12	−0.611765
$786$	5.91884e12	0.553140
$787$	8.60450e12	0.799539	0.399769	−	0.916616i	$-0.369090\pi$
$787$	8.60450e12	0.799539	0.399769	+	0.916616i	$0.369090\pi$
$788$	−5.00359e12	−0.462289
$789$	1.02902e13	0.945314
$790$	8.22188e12	0.751016
$791$	−3.50898e12	−0.318704
$792$	6.10578e11	0.0551414
$793$	−1.45358e12	−0.130530
$794$	−1.65255e12	−0.147558
$795$	−4.26643e12	−0.378802
$796$	6.86764e12	0.606316
$797$	−1.65936e13	−1.45673	−0.728364	−	0.685190i	$-0.759719\pi$
$797$	−1.65936e13	−1.45673	−0.728364	+	0.685190i	$0.759719\pi$
$798$	−3.19380e12	−0.278801
$799$	3.43469e12	0.298145
$800$	1.51139e12	0.130458
$801$	3.40533e12	0.292289
$802$	−1.00320e13	−0.856253
$803$	−1.49021e12	−0.126481
$804$	2.92340e12	0.246738
$805$	−1.37788e13	−1.15646
$806$	−1.67964e12	−0.140187
$807$	−4.14528e12	−0.344051
$808$	3.19012e11	0.0263303
$809$	−1.98766e12	−0.163145	−0.0815724	−	0.996667i	$-0.525994\pi$
$809$	−1.98766e12	−0.163145	−0.0815724	+	0.996667i	$0.525994\pi$
$810$	1.26896e12	0.103577
$811$	−4.87988e12	−0.396110	−0.198055	−	0.980191i	$-0.563462\pi$
$811$	−4.87988e12	−0.396110	−0.198055	+	0.980191i	$0.563462\pi$
$812$	−2.43730e12	−0.196747
$813$	−9.72599e12	−0.780776
$814$	−1.07024e12	−0.0854419
$815$	−1.83386e13	−1.45598
$816$	4.43364e11	0.0350070
$817$	−4.41470e12	−0.346659
$818$	−1.24081e13	−0.968983
$819$	−3.51578e11	−0.0273051
$820$	1.29784e13	1.00244
$821$	−8.52019e12	−0.654493	−0.327246	−	0.944939i	$-0.606121\pi$
$821$	−8.52019e12	−0.654493	−0.327246	+	0.944939i	$0.606121\pi$
$822$	−2.16618e12	−0.165490
$823$	−6.08733e12	−0.462517	−0.231258	−	0.972892i	$-0.574284\pi$
$823$	−6.08733e12	−0.462517	−0.231258	+	0.972892i	$0.574284\pi$
$824$	−4.09103e12	−0.309143
$825$	2.65260e12	0.199356
$826$	−6.29148e12	−0.470265
$827$	9.36596e12	0.696270	0.348135	−	0.937444i	$-0.386815\pi$
$827$	9.36596e12	0.696270	0.348135	+	0.937444i	$0.386815\pi$
$828$	2.66883e12	0.197326
$829$	−3.35583e12	−0.246777	−0.123389	−	0.992358i	$-0.539376\pi$
$829$	−3.35583e12	−0.246777	−0.123389	+	0.992358i	$0.539376\pi$
$830$	−3.14607e12	−0.230100
$831$	1.47302e13	1.07153
$832$	1.91010e11	0.0138198
$833$	−1.52015e12	−0.109392
$834$	−9.91944e12	−0.709970
$835$	−3.65106e12	−0.259914
$836$	3.04537e12	0.215631
$837$	−4.90019e12	−0.345103
$838$	6.01221e12	0.421150
$839$	−1.40575e13	−0.979443	−0.489722	−	0.871879i	$-0.662902\pi$
$839$	−1.40575e13	−0.979443	−0.489722	+	0.871879i	$0.662902\pi$
$840$	−2.87705e12	−0.199384
$841$	−1.04154e13	−0.717949
$842$	3.25187e12	0.222961
$843$	−9.38052e11	−0.0639739
$844$	1.28132e13	0.869191
$845$	−1.92991e13	−1.30221
$846$	4.31700e12	0.289745
$847$	8.66849e12	0.578719
$848$	−1.87358e12	−0.124420
$849$	−1.27716e13	−0.843646
$850$	1.92616e12	0.126563
$851$	−4.67800e12	−0.305757
$852$	1.60055e12	0.104062
$853$	−1.54738e13	−1.00075	−0.500375	−	0.865809i	$-0.666805\pi$
$853$	−1.54738e13	−1.00075	−0.500375	+	0.865809i	$0.666805\pi$
$854$	9.61471e12	0.618551
$855$	6.32916e12	0.405041
$856$	4.78418e11	0.0304562
$857$	−2.12961e13	−1.34861	−0.674306	−	0.738452i	$-0.735557\pi$
$857$	−2.12961e13	−1.34861	−0.674306	+	0.738452i	$0.735557\pi$
$858$	3.35238e11	0.0211184
$859$	−9.74256e12	−0.610525	−0.305263	−	0.952268i	$-0.598744\pi$
$859$	−9.74256e12	−0.610525	−0.305263	+	0.952268i	$0.598744\pi$
$860$	−3.97686e12	−0.247912
$861$	−1.04904e13	−0.650547
$862$	1.63317e13	1.00751
$863$	3.02531e13	1.85661	0.928305	−	0.371820i	$-0.121266\pi$
$863$	3.02531e13	1.85661	0.928305	+	0.371820i	$0.121266\pi$
$864$	5.57256e11	0.0340207
$865$	−1.40940e13	−0.855975
$866$	−1.47505e13	−0.891203
$867$	5.65036e11	0.0339618
$868$	1.11100e13	0.664315
$869$	6.33687e12	0.376952
$870$	4.83000e12	0.285832
$871$	1.60509e12	0.0944972
$872$	−2.62902e12	−0.153982
$873$	−3.30449e12	−0.192549
$874$	1.33112e13	0.771645
$875$	4.43775e12	0.255933
$876$	−1.36007e12	−0.0780354
$877$	−1.29745e13	−0.740612	−0.370306	−	0.928910i	$-0.620747\pi$
$877$	−1.29745e13	−0.740612	−0.370306	+	0.928910i	$0.620747\pi$
$878$	7.87681e12	0.447327
$879$	−1.34931e13	−0.762364
$880$	2.74334e12	0.154208
$881$	2.77948e13	1.55443	0.777217	−	0.629233i	$-0.216631\pi$
$881$	2.77948e13	1.55443	0.777217	+	0.629233i	$0.216631\pi$
$882$	−1.91065e12	−0.106309
$883$	3.41003e12	0.188771	0.0943854	−	0.995536i	$-0.469911\pi$
$883$	3.41003e12	0.188771	0.0943854	+	0.995536i	$0.469911\pi$
$884$	2.43429e11	0.0134072
$885$	1.24678e13	0.683198
$886$	2.42247e13	1.32071
$887$	1.46173e13	0.792885	0.396442	−	0.918060i	$-0.370245\pi$
$887$	1.46173e13	0.792885	0.396442	+	0.918060i	$0.370245\pi$
$888$	−9.76775e11	−0.0527153
$889$	4.97100e12	0.266923
$890$	1.53002e13	0.817413
$891$	9.78028e11	0.0519878
$892$	1.91304e12	0.101177
$893$	2.15318e13	1.13305
$894$	−1.38478e13	−0.725041
$895$	−2.74879e13	−1.43198
$896$	−1.26344e12	−0.0654890
$897$	1.46532e12	0.0755729
$898$	−2.05285e13	−1.05345
$899$	−1.86515e13	−0.952346
$900$	2.42095e12	0.122997
$901$	−2.38774e12	−0.120705
$902$	1.00029e13	0.503147
$903$	3.21449e12	0.160886
$904$	3.05370e12	0.152079
$905$	−1.46090e12	−0.0723939
$906$	1.17106e12	0.0577434
$907$	−1.53716e13	−0.754199	−0.377100	−	0.926173i	$-0.623079\pi$
$907$	−1.53716e13	−0.754199	−0.377100	+	0.926173i	$0.623079\pi$
$908$	−7.82582e12	−0.382070
$909$	5.10995e11	0.0248244
$910$	−1.57964e12	−0.0763612
$911$	−1.96370e13	−0.944589	−0.472295	−	0.881441i	$-0.656574\pi$
$911$	−1.96370e13	−0.944589	−0.472295	+	0.881441i	$0.656574\pi$
$912$	2.77942e12	0.133038
$913$	−2.42477e12	−0.115492
$914$	1.69204e13	0.801958
$915$	−1.90535e13	−0.898627
$916$	1.16738e13	0.547877
$917$	−2.14954e13	−1.00388
$918$	7.10184e11	0.0330049
$919$	1.74193e13	0.805582	0.402791	−	0.915292i	$-0.368040\pi$
$919$	1.74193e13	0.805582	0.402791	+	0.915292i	$0.368040\pi$
$920$	1.19911e13	0.551839
$921$	4.28868e12	0.196406
$922$	2.01242e13	0.917128
$923$	8.78784e11	0.0398542
$924$	−2.21743e12	−0.100075
$925$	−4.24351e12	−0.190585
$926$	1.02387e13	0.457610
$927$	−6.55304e12	−0.291463
$928$	2.12107e12	0.0938834
$929$	2.41408e13	1.06336	0.531682	−	0.846944i	$-0.321560\pi$
$929$	2.41408e13	1.06336	0.531682	+	0.846944i	$0.321560\pi$
$930$	−2.20166e13	−0.965112
$931$	−9.52970e12	−0.415724
$932$	1.55358e13	0.674467
$933$	−1.50250e13	−0.649154
$934$	−6.75327e12	−0.290371
$935$	3.49619e12	0.149604
$936$	3.05962e11	0.0130294
$937$	1.77293e13	0.751386	0.375693	−	0.926744i	$-0.377405\pi$
$937$	1.77293e13	0.751386	0.375693	+	0.926744i	$0.377405\pi$
$938$	−1.06169e13	−0.447801
$939$	−7.05316e11	−0.0296066
$940$	1.93963e13	0.810298
$941$	3.01480e13	1.25345	0.626723	−	0.779242i	$-0.284396\pi$
$941$	3.01480e13	1.25345	0.626723	+	0.779242i	$0.284396\pi$
$942$	−4.57842e12	−0.189446
$943$	4.37223e13	1.80053
$944$	5.47518e12	0.224401
$945$	−4.60847e12	−0.187981
$946$	−3.06510e12	−0.124433
$947$	−5.80514e12	−0.234551	−0.117276	−	0.993099i	$-0.537416\pi$
$947$	−5.80514e12	−0.234551	−0.117276	+	0.993099i	$0.537416\pi$
$948$	5.78347e12	0.232568
$949$	−7.46744e11	−0.0298864
$950$	1.20749e13	0.480981
$951$	9.16236e12	0.363241
$952$	−1.61016e12	−0.0635336
$953$	4.65766e13	1.82915	0.914577	−	0.404413i	$-0.132524\pi$
$953$	4.65766e13	1.82915	0.914577	+	0.404413i	$0.132524\pi$
$954$	−3.00111e12	−0.117304
$955$	−5.36053e13	−2.08542
$956$	−2.13330e13	−0.826023
$957$	3.72264e12	0.143465
$958$	1.77168e13	0.679581
$959$	7.86692e12	0.300345
$960$	2.50376e12	0.0951420
$961$	5.85795e13	2.21560
$962$	−5.36298e11	−0.0201892
$963$	7.66333e11	0.0287144
$964$	−8.68789e12	−0.324017
$965$	−4.43158e13	−1.64507
$966$	−9.69236e12	−0.358123
$967$	−3.18508e13	−1.17139	−0.585695	−	0.810531i	$-0.699179\pi$
$967$	−3.18508e13	−1.17139	−0.585695	+	0.810531i	$0.699179\pi$
$968$	−7.54378e12	−0.276153
$969$	3.54217e12	0.129066
$970$	−1.48471e13	−0.538480
$971$	−4.47822e12	−0.161666	−0.0808330	−	0.996728i	$-0.525758\pi$
$971$	−4.47822e12	−0.161666	−0.0808330	+	0.996728i	$0.525758\pi$
$972$	8.92617e11	0.0320750
$973$	3.60244e13	1.28851
$974$	−3.57433e13	−1.27256
$975$	1.32922e12	0.0471061
$976$	−8.36723e12	−0.295160
$977$	2.67219e13	0.938300	0.469150	−	0.883118i	$-0.344560\pi$
$977$	2.67219e13	0.938300	0.469150	+	0.883118i	$0.344560\pi$
$978$	−1.28998e13	−0.450877
$979$	1.17923e13	0.410278
$980$	−8.58456e12	−0.297304
$981$	−4.21117e12	−0.145175
$982$	−3.02265e12	−0.103726
$983$	−3.28908e13	−1.12353	−0.561763	−	0.827298i	$-0.689877\pi$
$983$	−3.28908e13	−1.12353	−0.561763	+	0.827298i	$0.689877\pi$
$984$	9.12931e12	0.310428
$985$	−3.60105e13	−1.21889
$986$	2.70315e12	0.0910803
$987$	−1.56780e13	−0.525853
$988$	1.52604e12	0.0509517
$989$	−1.33975e13	−0.445287
$990$	4.39429e12	0.145389
$991$	1.76149e13	0.580160	0.290080	−	0.957002i	$-0.406318\pi$
$991$	1.76149e13	0.580160	0.290080	+	0.957002i	$0.406318\pi$
$992$	−9.66848e12	−0.316997
$993$	8.08490e12	0.263878
$994$	−5.81272e12	−0.188860
$995$	4.94260e13	1.59864
$996$	−2.21302e12	−0.0712555
$997$	−5.37642e13	−1.72332	−0.861659	−	0.507488i	$-0.830574\pi$
$997$	−5.37642e13	−1.72332	−0.861659	+	0.507488i	$0.830574\pi$
$998$	2.97565e13	0.949499
$999$	−1.56461e12	−0.0497004

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	102.10.a.i.1.4	✓	4
3.2	odd	2		306.10.a.k.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
102.10.a.i.1.4	✓	4	1.1	even	1	trivial
306.10.a.k.1.1		4	3.2	odd	2

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Elliptic curves over $\Q$
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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	102.10.a.i.1.4

Level	$102$
Weight	$10$
Character	102.1
Self dual	yes
Analytic conductor	$52.534$
Analytic rank	$0$
Dimension	$4$
CM	no
Inner twists	$1$