LMFDB - Embedded newform 210.8.a.m.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [210,8,Mod(1,210)] 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("210.1"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(210, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	210.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,16,-54,128,-250,-432,686] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$65.6008553517$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{60349}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 15087 $ x^2 - x - 15087
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-122.330$ of defining polynomial
Character	$\chi$	$=$	210.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -125.000 q^{5} -216.000 q^{6} +343.000 q^{7} +512.000 q^{8} +729.000 q^{9} -1000.00 q^{10} +3519.96 q^{11} -1728.00 q^{12} +6677.73 q^{13} +2744.00 q^{14} +3375.00 q^{15} +4096.00 q^{16} -18721.7 q^{17} +5832.00 q^{18} -50642.7 q^{19} -8000.00 q^{20} -9261.00 q^{21} +28159.7 q^{22} -28131.4 q^{23} -13824.0 q^{24} +15625.0 q^{25} +53421.9 q^{26} -19683.0 q^{27} +21952.0 q^{28} +112339. q^{29} +27000.0 q^{30} +60246.1 q^{31} +32768.0 q^{32} -95039.0 q^{33} -149774. q^{34} -42875.0 q^{35} +46656.0 q^{36} +295052. q^{37} -405142. q^{38} -180299. q^{39} -64000.0 q^{40} +517347. q^{41} -74088.0 q^{42} +619634. q^{43} +225278. q^{44} -91125.0 q^{45} -225051. q^{46} +276014. q^{47} -110592. q^{48} +117649. q^{49} +125000. q^{50} +505486. q^{51} +427375. q^{52} +352657. q^{53} -157464. q^{54} -439995. q^{55} +175616. q^{56} +1.36735e6 q^{57} +898709. q^{58} +1.58099e6 q^{59} +216000. q^{60} -1.87269e6 q^{61} +481968. q^{62} +250047. q^{63} +262144. q^{64} -834717. q^{65} -760312. q^{66} -1.31755e6 q^{67} -1.19819e6 q^{68} +759548. q^{69} -343000. q^{70} +2.80545e6 q^{71} +373248. q^{72} +2.87230e6 q^{73} +2.36042e6 q^{74} -421875. q^{75} -3.24114e6 q^{76} +1.20735e6 q^{77} -1.44239e6 q^{78} +3.67436e6 q^{79} -512000. q^{80} +531441. q^{81} +4.13877e6 q^{82} +5.26388e6 q^{83} -592704. q^{84} +2.34021e6 q^{85} +4.95707e6 q^{86} -3.03314e6 q^{87} +1.80222e6 q^{88} +6.56307e6 q^{89} -729000. q^{90} +2.29046e6 q^{91} -1.80041e6 q^{92} -1.62664e6 q^{93} +2.20811e6 q^{94} +6.33034e6 q^{95} -884736. q^{96} -6.95052e6 q^{97} +941192. q^{98} +2.56605e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 16 q^{2} - 54 q^{3} + 128 q^{4} - 250 q^{5} - 432 q^{6} + 686 q^{7} + 1024 q^{8} + 1458 q^{9} - 2000 q^{10} + 4092 q^{11} - 3456 q^{12} - 7280 q^{13} + 5488 q^{14} + 6750 q^{15} + 8192 q^{16} - 13860 q^{17}+ \cdots + 2983068 q^{99}+O(q^{100}) $ 2 * q + 16 * q^2 - 54 * q^3 + 128 * q^4 - 250 * q^5 - 432 * q^6 + 686 * q^7 + 1024 * q^8 + 1458 * q^9 - 2000 * q^10 + 4092 * q^11 - 3456 * q^12 - 7280 * q^13 + 5488 * q^14 + 6750 * q^15 + 8192 * q^16 - 13860 * q^17 + 11664 * q^18 - 4004 * q^19 - 16000 * q^20 - 18522 * q^21 + 32736 * q^22 - 9096 * q^23 - 27648 * q^24 + 31250 * q^25 - 58240 * q^26 - 39366 * q^27 + 43904 * q^28 - 34740 * q^29 + 54000 * q^30 - 29852 * q^31 + 65536 * q^32 - 110484 * q^33 - 110880 * q^34 - 85750 * q^35 + 93312 * q^36 + 442708 * q^37 - 32032 * q^38 + 196560 * q^39 - 128000 * q^40 + 162108 * q^41 - 148176 * q^42 + 1091872 * q^43 + 261888 * q^44 - 182250 * q^45 - 72768 * q^46 + 1630968 * q^47 - 221184 * q^48 + 235298 * q^49 + 250000 * q^50 + 374220 * q^51 - 465920 * q^52 + 2146848 * q^53 - 314928 * q^54 - 511500 * q^55 + 351232 * q^56 + 108108 * q^57 - 277920 * q^58 + 2106624 * q^59 + 432000 * q^60 - 1528532 * q^61 - 238816 * q^62 + 500094 * q^63 + 524288 * q^64 + 910000 * q^65 - 883872 * q^66 + 1987240 * q^67 - 887040 * q^68 + 245592 * q^69 - 686000 * q^70 + 5059644 * q^71 + 746496 * q^72 - 1321568 * q^73 + 3541664 * q^74 - 843750 * q^75 - 256256 * q^76 + 1403556 * q^77 + 1572480 * q^78 + 11493496 * q^79 - 1024000 * q^80 + 1062882 * q^81 + 1296864 * q^82 + 4920816 * q^83 - 1185408 * q^84 + 1732500 * q^85 + 8734976 * q^86 + 937980 * q^87 + 2095104 * q^88 + 12159228 * q^89 - 1458000 * q^90 - 2497040 * q^91 - 582144 * q^92 + 806004 * q^93 + 13047744 * q^94 + 500500 * q^95 - 1769472 * q^96 + 4037080 * q^97 + 1882384 * q^98 + 2983068 * 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 $

$2$	8.00000	0.707107
$2$	8.00000	0.707107
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	64.0000	0.500000
$5$	−125.000	−0.447214
$5$	−125.000	−0.447214
$6$	−216.000	−0.408248
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	512.000	0.353553
$9$	729.000	0.333333
$10$	−1000.00	−0.316228
$11$	3519.96	0.797377	0.398688	−	0.917086i	$-0.369466\pi$
$11$	3519.96	0.797377	0.398688	+	0.917086i	$0.369466\pi$
$12$	−1728.00	−0.288675
$13$	6677.73	0.843000	0.421500	−	0.906828i	$-0.361504\pi$
$13$	6677.73	0.843000	0.421500	+	0.906828i	$0.361504\pi$
$14$	2744.00	0.267261
$15$	3375.00	0.258199
$16$	4096.00	0.250000
$17$	−18721.7	−0.924217	−0.462109	−	0.886823i	$-0.652907\pi$
$17$	−18721.7	−0.924217	−0.462109	+	0.886823i	$0.652907\pi$
$18$	5832.00	0.235702
$19$	−50642.7	−1.69387	−0.846934	−	0.531698i	$-0.821554\pi$
$19$	−50642.7	−1.69387	−0.846934	+	0.531698i	$0.821554\pi$
$20$	−8000.00	−0.223607
$21$	−9261.00	−0.218218
$22$	28159.7	0.563831
$23$	−28131.4	−0.482107	−0.241054	−	0.970512i	$-0.577493\pi$
$23$	−28131.4	−0.482107	−0.241054	+	0.970512i	$0.577493\pi$
$24$	−13824.0	−0.204124
$25$	15625.0	0.200000
$26$	53421.9	0.596091
$27$	−19683.0	−0.192450
$28$	21952.0	0.188982
$29$	112339.	0.855335	0.427667	−	0.903936i	$-0.359335\pi$
$29$	112339.	0.855335	0.427667	+	0.903936i	$0.359335\pi$
$30$	27000.0	0.182574
$31$	60246.1	0.363214	0.181607	−	0.983371i	$-0.441870\pi$
$31$	60246.1	0.363214	0.181607	+	0.983371i	$0.441870\pi$
$32$	32768.0	0.176777
$33$	−95039.0	−0.460366
$34$	−149774.	−0.653520
$35$	−42875.0	−0.169031
$36$	46656.0	0.166667
$37$	295052.	0.957619	0.478809	−	0.877919i	$-0.341068\pi$
$37$	295052.	0.957619	0.478809	+	0.877919i	$0.341068\pi$
$38$	−405142.	−1.19775
$39$	−180299.	−0.486706
$40$	−64000.0	−0.158114
$41$	517347.	1.17230	0.586149	−	0.810203i	$-0.300643\pi$
$41$	517347.	1.17230	0.586149	+	0.810203i	$0.300643\pi$
$42$	−74088.0	−0.154303
$43$	619634.	1.18849	0.594245	−	0.804284i	$-0.297451\pi$
$43$	619634.	1.18849	0.594245	+	0.804284i	$0.297451\pi$
$44$	225278.	0.398688
$45$	−91125.0	−0.149071
$46$	−225051.	−0.340901
$47$	276014.	0.387783	0.193891	−	0.981023i	$-0.437889\pi$
$47$	276014.	0.387783	0.193891	+	0.981023i	$0.437889\pi$
$48$	−110592.	−0.144338
$49$	117649.	0.142857
$50$	125000.	0.141421
$51$	505486.	0.533597
$52$	427375.	0.421500
$53$	352657.	0.325377	0.162688	−	0.986678i	$-0.447983\pi$
$53$	352657.	0.325377	0.162688	+	0.986678i	$0.447983\pi$
$54$	−157464.	−0.136083
$55$	−439995.	−0.356598
$56$	175616.	0.133631
$57$	1.36735e6	0.977955
$58$	898709.	0.604813
$59$	1.58099e6	1.00218	0.501092	−	0.865394i	$-0.332932\pi$
$59$	1.58099e6	1.00218	0.501092	+	0.865394i	$0.332932\pi$
$60$	216000.	0.129099
$61$	−1.87269e6	−1.05636	−0.528178	−	0.849134i	$-0.677125\pi$
$61$	−1.87269e6	−1.05636	−0.528178	+	0.849134i	$0.677125\pi$
$62$	481968.	0.256831
$63$	250047.	0.125988
$64$	262144.	0.125000
$65$	−834717.	−0.377001
$66$	−760312.	−0.325528
$67$	−1.31755e6	−0.535188	−0.267594	−	0.963532i	$-0.586229\pi$
$67$	−1.31755e6	−0.535188	−0.267594	+	0.963532i	$0.586229\pi$
$68$	−1.19819e6	−0.462109
$69$	759548.	0.278345
$70$	−343000.	−0.119523
$71$	2.80545e6	0.930248	0.465124	−	0.885246i	$-0.346010\pi$
$71$	2.80545e6	0.930248	0.465124	+	0.885246i	$0.346010\pi$
$72$	373248.	0.117851
$73$	2.87230e6	0.864172	0.432086	−	0.901832i	$-0.357778\pi$
$73$	2.87230e6	0.864172	0.432086	+	0.901832i	$0.357778\pi$
$74$	2.36042e6	0.677139
$75$	−421875.	−0.115470
$76$	−3.24114e6	−0.846934
$77$	1.20735e6	0.301380
$78$	−1.44239e6	−0.344153
$79$	3.67436e6	0.838468	0.419234	−	0.907878i	$-0.362299\pi$
$79$	3.67436e6	0.838468	0.419234	+	0.907878i	$0.362299\pi$
$80$	−512000.	−0.111803
$81$	531441.	0.111111
$82$	4.13877e6	0.828940
$83$	5.26388e6	1.01049	0.505246	−	0.862975i	$-0.331402\pi$
$83$	5.26388e6	1.01049	0.505246	+	0.862975i	$0.331402\pi$
$84$	−592704.	−0.109109
$85$	2.34021e6	0.413322
$86$	4.95707e6	0.840390
$87$	−3.03314e6	−0.493828
$88$	1.80222e6	0.281915
$89$	6.56307e6	0.986830	0.493415	−	0.869794i	$-0.335748\pi$
$89$	6.56307e6	0.986830	0.493415	+	0.869794i	$0.335748\pi$
$90$	−729000.	−0.105409
$91$	2.29046e6	0.318624
$92$	−1.80041e6	−0.241054
$93$	−1.62664e6	−0.209702
$94$	2.20811e6	0.274204
$95$	6.33034e6	0.757521
$96$	−884736.	−0.102062
$97$	−6.95052e6	−0.773243	−0.386622	−	0.922238i	$-0.626358\pi$
$97$	−6.95052e6	−0.773243	−0.386622	+	0.922238i	$0.626358\pi$
$98$	941192.	0.101015
$99$	2.56605e6	0.265792
$100$	1.00000e6	0.100000
$101$	1.69564e6	0.163761	0.0818803	−	0.996642i	$-0.473907\pi$
$101$	1.69564e6	0.163761	0.0818803	+	0.996642i	$0.473907\pi$
$102$	4.04389e6	0.377310
$103$	1.22518e7	1.10476	0.552381	−	0.833592i	$-0.313719\pi$
$103$	1.22518e7	1.10476	0.552381	+	0.833592i	$0.313719\pi$
$104$	3.41900e6	0.298045
$105$	1.15762e6	0.0975900
$106$	2.82125e6	0.230076
$107$	−5.83900e6	−0.460782	−0.230391	−	0.973098i	$-0.574001\pi$
$107$	−5.83900e6	−0.460782	−0.230391	+	0.973098i	$0.574001\pi$
$108$	−1.25971e6	−0.0962250
$109$	5.52553e6	0.408678	0.204339	−	0.978900i	$-0.434496\pi$
$109$	5.52553e6	0.408678	0.204339	+	0.978900i	$0.434496\pi$
$110$	−3.51996e6	−0.252153
$111$	−7.96641e6	−0.552881
$112$	1.40493e6	0.0944911
$113$	−8.70717e6	−0.567679	−0.283839	−	0.958872i	$-0.591608\pi$
$113$	−8.70717e6	−0.567679	−0.283839	+	0.958872i	$0.591608\pi$
$114$	1.09388e7	0.691519
$115$	3.51642e6	0.215605
$116$	7.18967e6	0.427667
$117$	4.86807e6	0.281000
$118$	1.26479e7	0.708651
$119$	−6.42154e6	−0.349321
$120$	1.72800e6	0.0912871
$121$	−7.09704e6	−0.364190
$122$	−1.49815e7	−0.746957
$123$	−1.39684e7	−0.676827
$124$	3.85575e6	0.181607
$125$	−1.95312e6	−0.0894427
$126$	2.00038e6	0.0890871
$127$	3.61042e7	1.56403	0.782013	−	0.623262i	$-0.214193\pi$
$127$	3.61042e7	1.56403	0.782013	+	0.623262i	$0.214193\pi$
$128$	2.09715e6	0.0883883
$129$	−1.67301e7	−0.686175
$130$	−6.67773e6	−0.266580
$131$	−4.44686e7	−1.72824	−0.864119	−	0.503287i	$-0.832124\pi$
$131$	−4.44686e7	−1.72824	−0.864119	+	0.503287i	$0.832124\pi$
$132$	−6.08249e6	−0.230183
$133$	−1.73705e7	−0.640222
$134$	−1.05404e7	−0.378435
$135$	2.46038e6	0.0860663
$136$	−9.58551e6	−0.326760
$137$	2.85208e7	0.947631	0.473815	−	0.880624i	$-0.342876\pi$
$137$	2.85208e7	0.947631	0.473815	+	0.880624i	$0.342876\pi$
$138$	6.07638e6	0.196820
$139$	−1.21196e7	−0.382770	−0.191385	−	0.981515i	$-0.561298\pi$
$139$	−1.21196e7	−0.382770	−0.191385	+	0.981515i	$0.561298\pi$
$140$	−2.74400e6	−0.0845154
$141$	−7.45238e6	−0.223886
$142$	2.24436e7	0.657785
$143$	2.35054e7	0.672188
$144$	2.98598e6	0.0833333
$145$	−1.40423e7	−0.382517
$146$	2.29784e7	0.611062
$147$	−3.17652e6	−0.0824786
$148$	1.88833e7	0.478809
$149$	4.58417e7	1.13529	0.567647	−	0.823272i	$-0.307854\pi$
$149$	4.58417e7	1.13529	0.567647	+	0.823272i	$0.307854\pi$
$150$	−3.37500e6	−0.0816497
$151$	−1.29270e7	−0.305548	−0.152774	−	0.988261i	$-0.548821\pi$
$151$	−1.29270e7	−0.305548	−0.152774	+	0.988261i	$0.548821\pi$
$152$	−2.59291e7	−0.598873
$153$	−1.36481e7	−0.308072
$154$	9.65878e6	0.213108
$155$	−7.53076e6	−0.162434
$156$	−1.15391e7	−0.243353
$157$	−2.72032e7	−0.561012	−0.280506	−	0.959852i	$-0.590502\pi$
$157$	−2.72032e7	−0.561012	−0.280506	+	0.959852i	$0.590502\pi$
$158$	2.93949e7	0.592887
$159$	−9.52173e6	−0.187856
$160$	−4.09600e6	−0.0790569
$161$	−9.64907e6	−0.182219
$162$	4.25153e6	0.0785674
$163$	8.01738e7	1.45003	0.725013	−	0.688735i	$-0.241834\pi$
$163$	8.01738e7	1.45003	0.725013	+	0.688735i	$0.241834\pi$
$164$	3.31102e7	0.586149
$165$	1.18799e7	0.205882
$166$	4.21111e7	0.714526
$167$	−4.62354e7	−0.768188	−0.384094	−	0.923294i	$-0.625486\pi$
$167$	−4.62354e7	−0.768188	−0.384094	+	0.923294i	$0.625486\pi$
$168$	−4.74163e6	−0.0771517
$169$	−1.81564e7	−0.289352
$170$	1.87217e7	0.292263
$171$	−3.69186e7	−0.564623
$172$	3.96566e7	0.594245
$173$	8.09446e7	1.18857	0.594287	−	0.804253i	$-0.297434\pi$
$173$	8.09446e7	1.18857	0.594287	+	0.804253i	$0.297434\pi$
$174$	−2.42651e7	−0.349189
$175$	5.35938e6	0.0755929
$176$	1.44178e7	0.199344
$177$	−4.26867e7	−0.578611
$178$	5.25046e7	0.697794
$179$	1.50560e7	0.196212	0.0981058	−	0.995176i	$-0.468722\pi$
$179$	1.50560e7	0.196212	0.0981058	+	0.995176i	$0.468722\pi$
$180$	−5.83200e6	−0.0745356
$181$	7.88125e7	0.987916	0.493958	−	0.869486i	$-0.335550\pi$
$181$	7.88125e7	0.987916	0.493958	+	0.869486i	$0.335550\pi$
$182$	1.83237e7	0.225301
$183$	5.05625e7	0.609888
$184$	−1.44033e7	−0.170451
$185$	−3.68815e7	−0.428260
$186$	−1.30131e7	−0.148282
$187$	−6.58997e7	−0.736949
$188$	1.76649e7	0.193891
$189$	−6.75127e6	−0.0727393
$190$	5.06427e7	0.535648
$191$	−7.60345e7	−0.789576	−0.394788	−	0.918772i	$-0.629182\pi$
$191$	−7.60345e7	−0.789576	−0.394788	+	0.918772i	$0.629182\pi$
$192$	−7.07789e6	−0.0721688
$193$	−1.10481e8	−1.10620	−0.553102	−	0.833113i	$-0.686556\pi$
$193$	−1.10481e8	−1.10620	−0.553102	+	0.833113i	$0.686556\pi$
$194$	−5.56042e7	−0.546766
$195$	2.25374e7	0.217662
$196$	7.52954e6	0.0714286
$197$	5.49344e7	0.511932	0.255966	−	0.966686i	$-0.417606\pi$
$197$	5.49344e7	0.511932	0.255966	+	0.966686i	$0.417606\pi$
$198$	2.05284e7	0.187944
$199$	1.82083e8	1.63789	0.818945	−	0.573873i	$-0.194560\pi$
$199$	1.82083e8	1.63789	0.818945	+	0.573873i	$0.194560\pi$
$200$	8.00000e6	0.0707107
$201$	3.55739e7	0.308991
$202$	1.35651e7	0.115796
$203$	3.85322e7	0.323286
$204$	3.23511e7	0.266798
$205$	−6.46683e7	−0.524268
$206$	9.80143e7	0.781185
$207$	−2.05078e7	−0.160702
$208$	2.73520e7	0.210750
$209$	−1.78261e8	−1.35065
$210$	9.26100e6	0.0690066
$211$	−1.05968e8	−0.776582	−0.388291	−	0.921537i	$-0.626935\pi$
$211$	−1.05968e8	−0.776582	−0.388291	+	0.921537i	$0.626935\pi$
$212$	2.25700e7	0.162688
$213$	−7.57472e7	−0.537079
$214$	−4.67120e7	−0.325822
$215$	−7.74543e7	−0.531509
$216$	−1.00777e7	−0.0680414
$217$	2.06644e7	0.137282
$218$	4.42042e7	0.288979
$219$	−7.75522e7	−0.498930
$220$	−2.81597e7	−0.178299
$221$	−1.25019e8	−0.779115
$222$	−6.37313e7	−0.390946
$223$	−1.28916e8	−0.778467	−0.389234	−	0.921139i	$-0.627260\pi$
$223$	−1.28916e8	−0.778467	−0.389234	+	0.921139i	$0.627260\pi$
$224$	1.12394e7	0.0668153
$225$	1.13906e7	0.0666667
$226$	−6.96574e7	−0.401409
$227$	−1.86514e8	−1.05833	−0.529165	−	0.848519i	$-0.677495\pi$
$227$	−1.86514e8	−1.05833	−0.529165	+	0.848519i	$0.677495\pi$
$228$	8.75107e7	0.488978
$229$	−2.18056e8	−1.19990	−0.599948	−	0.800039i	$-0.704812\pi$
$229$	−2.18056e8	−1.19990	−0.599948	+	0.800039i	$0.704812\pi$
$230$	2.81314e7	0.152456
$231$	−3.25984e7	−0.174002
$232$	5.75174e7	0.302407
$233$	3.05352e8	1.58145	0.790724	−	0.612172i	$-0.209704\pi$
$233$	3.05352e8	1.58145	0.790724	+	0.612172i	$0.209704\pi$
$234$	3.89445e7	0.198697
$235$	−3.45017e7	−0.173422
$236$	1.01183e8	0.501092
$237$	−9.92077e7	−0.484090
$238$	−5.13723e7	−0.247007
$239$	4.18715e7	0.198393	0.0991963	−	0.995068i	$-0.468373\pi$
$239$	4.18715e7	0.198393	0.0991963	+	0.995068i	$0.468373\pi$
$240$	1.38240e7	0.0645497
$241$	1.08957e6	0.00501412	0.00250706	−	0.999997i	$-0.499202\pi$
$241$	1.08957e6	0.00501412	0.00250706	+	0.999997i	$0.499202\pi$
$242$	−5.67763e7	−0.257521
$243$	−1.43489e7	−0.0641500
$244$	−1.19852e8	−0.528178
$245$	−1.47061e7	−0.0638877
$246$	−1.11747e8	−0.478589
$247$	−3.38179e8	−1.42793
$248$	3.08460e7	0.128416
$249$	−1.42125e8	−0.583408
$250$	−1.56250e7	−0.0632456
$251$	−2.67474e8	−1.06764	−0.533819	−	0.845599i	$-0.679243\pi$
$251$	−2.67474e8	−1.06764	−0.533819	+	0.845599i	$0.679243\pi$
$252$	1.60030e7	0.0629941
$253$	−9.90214e7	−0.384421
$254$	2.88833e8	1.10593
$255$	−6.31857e7	−0.238632
$256$	1.67772e7	0.0625000
$257$	−2.01059e8	−0.738852	−0.369426	−	0.929260i	$-0.620446\pi$
$257$	−2.01059e8	−0.738852	−0.369426	+	0.929260i	$0.620446\pi$
$258$	−1.33841e8	−0.485199
$259$	1.01203e8	0.361946
$260$	−5.34219e7	−0.188500
$261$	8.18949e7	0.285112
$262$	−3.55749e8	−1.22205
$263$	−1.06890e8	−0.362321	−0.181161	−	0.983454i	$-0.557985\pi$
$263$	−1.06890e8	−0.362321	−0.181161	+	0.983454i	$0.557985\pi$
$264$	−4.86600e7	−0.162764
$265$	−4.40821e7	−0.145513
$266$	−1.38964e8	−0.452705
$267$	−1.77203e8	−0.569746
$268$	−8.43234e7	−0.267594
$269$	1.24137e8	0.388837	0.194419	−	0.980919i	$-0.437718\pi$
$269$	1.24137e8	0.388837	0.194419	+	0.980919i	$0.437718\pi$
$270$	1.96830e7	0.0608581
$271$	−5.64382e8	−1.72258	−0.861292	−	0.508110i	$-0.830344\pi$
$271$	−5.64382e8	−1.72258	−0.861292	+	0.508110i	$0.830344\pi$
$272$	−7.66841e7	−0.231054
$273$	−6.18425e7	−0.183958
$274$	2.28166e8	0.670076
$275$	5.49994e7	0.159475
$276$	4.86110e7	0.139172
$277$	−6.37061e7	−0.180095	−0.0900475	−	0.995937i	$-0.528702\pi$
$277$	−6.37061e7	−0.180095	−0.0900475	+	0.995937i	$0.528702\pi$
$278$	−9.69571e7	−0.270659
$279$	4.39194e7	0.121071
$280$	−2.19520e7	−0.0597614
$281$	5.79899e8	1.55912	0.779561	−	0.626327i	$-0.215442\pi$
$281$	5.79899e8	1.55912	0.779561	+	0.626327i	$0.215442\pi$
$282$	−5.96190e7	−0.158312
$283$	−7.37071e7	−0.193311	−0.0966555	−	0.995318i	$-0.530815\pi$
$283$	−7.37071e7	−0.193311	−0.0966555	+	0.995318i	$0.530815\pi$
$284$	1.79549e8	0.465124
$285$	−1.70919e8	−0.437355
$286$	1.88043e8	0.475309
$287$	1.77450e8	0.443087
$288$	2.38879e7	0.0589256
$289$	−5.98368e7	−0.145823
$290$	−1.12339e8	−0.270481
$291$	1.87664e8	0.446432
$292$	1.83827e8	0.432086
$293$	2.11635e8	0.491530	0.245765	−	0.969329i	$-0.420961\pi$
$293$	2.11635e8	0.491530	0.245765	+	0.969329i	$0.420961\pi$
$294$	−2.54122e7	−0.0583212
$295$	−1.97624e8	−0.448190
$296$	1.51067e8	0.338569
$297$	−6.92834e7	−0.153455
$298$	3.66733e8	0.802774
$299$	−1.87854e8	−0.406416
$300$	−2.70000e7	−0.0577350
$301$	2.12534e8	0.449207
$302$	−1.03416e8	−0.216055
$303$	−4.57823e7	−0.0945472
$304$	−2.07433e8	−0.423467
$305$	2.34086e8	0.472417
$306$	−1.09185e8	−0.217840
$307$	−6.01634e8	−1.18672	−0.593359	−	0.804938i	$-0.702199\pi$
$307$	−6.01634e8	−1.18672	−0.593359	+	0.804938i	$0.702199\pi$
$308$	7.72702e7	0.150690
$309$	−3.30798e8	−0.637835
$310$	−6.02461e7	−0.114858
$311$	1.02466e9	1.93161	0.965807	−	0.259263i	$-0.0834796\pi$
$311$	1.02466e9	1.93161	0.965807	+	0.259263i	$0.0834796\pi$
$312$	−9.23130e7	−0.172077
$313$	−3.64643e8	−0.672144	−0.336072	−	0.941836i	$-0.609099\pi$
$313$	−3.64643e8	−0.672144	−0.336072	+	0.941836i	$0.609099\pi$
$314$	−2.17626e8	−0.396695
$315$	−3.12559e7	−0.0563436
$316$	2.35159e8	0.419234
$317$	2.45967e8	0.433680	0.216840	−	0.976207i	$-0.430425\pi$
$317$	2.45967e8	0.433680	0.216840	+	0.976207i	$0.430425\pi$
$318$	−7.61738e7	−0.132834
$319$	3.95428e8	0.682024
$320$	−3.27680e7	−0.0559017
$321$	1.57653e8	0.266033
$322$	−7.71925e7	−0.128849
$323$	9.48118e8	1.56550
$324$	3.40122e7	0.0555556
$325$	1.04340e8	0.168600
$326$	6.41390e8	1.02532
$327$	−1.49189e8	−0.235950
$328$	2.64882e8	0.414470
$329$	9.46728e7	0.146568
$330$	9.50390e7	0.145580
$331$	−1.28738e9	−1.95123	−0.975617	−	0.219478i	$-0.929565\pi$
$331$	−1.28738e9	−1.95123	−0.975617	+	0.219478i	$0.929565\pi$
$332$	3.36889e8	0.505246
$333$	2.15093e8	0.319206
$334$	−3.69883e8	−0.543191
$335$	1.64694e8	0.239343
$336$	−3.79331e7	−0.0545545
$337$	−4.49735e8	−0.640106	−0.320053	−	0.947400i	$-0.603701\pi$
$337$	−4.49735e8	−0.640106	−0.320053	+	0.947400i	$0.603701\pi$
$338$	−1.45251e8	−0.204602
$339$	2.35094e8	0.327749
$340$	1.49774e8	0.206661
$341$	2.12064e8	0.289619
$342$	−2.95348e8	−0.399249
$343$	4.03536e7	0.0539949
$344$	3.17253e8	0.420195
$345$	−9.49434e7	−0.124480
$346$	6.47556e8	0.840449
$347$	7.51045e8	0.964967	0.482484	−	0.875905i	$-0.339735\pi$
$347$	7.51045e8	0.964967	0.482484	+	0.875905i	$0.339735\pi$
$348$	−1.94121e8	−0.246914
$349$	3.43593e8	0.432668	0.216334	−	0.976319i	$-0.430590\pi$
$349$	3.43593e8	0.432668	0.216334	+	0.976319i	$0.430590\pi$
$350$	4.28750e7	0.0534522
$351$	−1.31438e8	−0.162235
$352$	1.15342e8	0.140958
$353$	9.80245e8	1.18611	0.593053	−	0.805164i	$-0.297923\pi$
$353$	9.80245e8	1.18611	0.593053	+	0.805164i	$0.297923\pi$
$354$	−3.41494e8	−0.409140
$355$	−3.50682e8	−0.416020
$356$	4.20037e8	0.493415
$357$	1.73382e8	0.201681
$358$	1.20448e8	0.138743
$359$	−1.32862e9	−1.51555	−0.757776	−	0.652515i	$-0.773714\pi$
$359$	−1.32862e9	−1.51555	−0.757776	+	0.652515i	$0.773714\pi$
$360$	−4.66560e7	−0.0527046
$361$	1.67082e9	1.86919
$362$	6.30500e8	0.698562
$363$	1.91620e8	0.210265
$364$	1.46590e8	0.159312
$365$	−3.59038e8	−0.386470
$366$	4.04500e8	0.431256
$367$	2.38105e8	0.251442	0.125721	−	0.992066i	$-0.459876\pi$
$367$	2.38105e8	0.251442	0.125721	+	0.992066i	$0.459876\pi$
$368$	−1.15226e8	−0.120527
$369$	3.77146e8	0.390766
$370$	−2.95052e8	−0.302826
$371$	1.20961e8	0.122981
$372$	−1.04105e8	−0.104851
$373$	9.10450e8	0.908396	0.454198	−	0.890901i	$-0.349926\pi$
$373$	9.10450e8	0.908396	0.454198	+	0.890901i	$0.349926\pi$
$374$	−5.27197e8	−0.521102
$375$	5.27344e7	0.0516398
$376$	1.41319e8	0.137102
$377$	7.50168e8	0.721047
$378$	−5.40102e7	−0.0514344
$379$	−1.02823e9	−0.970182	−0.485091	−	0.874464i	$-0.661213\pi$
$379$	−1.02823e9	−0.970182	−0.485091	+	0.874464i	$0.661213\pi$
$380$	4.05142e8	0.378760
$381$	−9.74812e8	−0.902991
$382$	−6.08276e8	−0.558315
$383$	6.41610e7	0.0583546	0.0291773	−	0.999574i	$-0.490711\pi$
$383$	6.41610e7	0.0583546	0.0291773	+	0.999574i	$0.490711\pi$
$384$	−5.66231e7	−0.0510310
$385$	−1.50918e8	−0.134781
$386$	−8.83845e8	−0.782205
$387$	4.51713e8	0.396164
$388$	−4.44833e8	−0.386622
$389$	9.49774e8	0.818082	0.409041	−	0.912516i	$-0.365863\pi$
$389$	9.49774e8	0.818082	0.409041	+	0.912516i	$0.365863\pi$
$390$	1.80299e8	0.153910
$391$	5.26667e8	0.445572
$392$	6.02363e7	0.0505076
$393$	1.20065e9	0.997799
$394$	4.39475e8	0.361991
$395$	−4.59295e8	−0.374974
$396$	1.64227e8	0.132896
$397$	2.27174e8	0.182218	0.0911092	−	0.995841i	$-0.470959\pi$
$397$	2.27174e8	0.182218	0.0911092	+	0.995841i	$0.470959\pi$
$398$	1.45667e9	1.15816
$399$	4.69002e8	0.369632
$400$	6.40000e7	0.0500000
$401$	−2.41936e8	−0.187368	−0.0936838	−	0.995602i	$-0.529864\pi$
$401$	−2.41936e8	−0.187368	−0.0936838	+	0.995602i	$0.529864\pi$
$402$	2.84591e8	0.218489
$403$	4.02307e8	0.306189
$404$	1.08521e8	0.0818803
$405$	−6.64301e7	−0.0496904
$406$	3.08257e8	0.228598
$407$	1.03857e9	0.763583
$408$	2.58809e8	0.188655
$409$	−2.31304e9	−1.67167	−0.835835	−	0.548980i	$-0.815016\pi$
$409$	−2.31304e9	−1.67167	−0.835835	+	0.548980i	$0.815016\pi$
$410$	−5.17347e8	−0.370713
$411$	−7.70061e8	−0.547115
$412$	7.84114e8	0.552381
$413$	5.42280e8	0.378790
$414$	−1.64062e8	−0.113634
$415$	−6.57985e8	−0.451906
$416$	2.18816e8	0.149023
$417$	3.27230e8	0.220992
$418$	−1.42608e9	−0.955055
$419$	2.81742e9	1.87113	0.935563	−	0.353161i	$-0.114893\pi$
$419$	2.81742e9	1.87113	0.935563	+	0.353161i	$0.114893\pi$
$420$	7.40880e7	0.0487950
$421$	−3.19306e8	−0.208555	−0.104277	−	0.994548i	$-0.533253\pi$
$421$	−3.19306e8	−0.208555	−0.104277	+	0.994548i	$0.533253\pi$
$422$	−8.47747e8	−0.549127
$423$	2.01214e8	0.129261
$424$	1.80560e8	0.115038
$425$	−2.92527e8	−0.184843
$426$	−6.05978e8	−0.379772
$427$	−6.42331e8	−0.399265
$428$	−3.73696e8	−0.230391
$429$	−6.34645e8	−0.388088
$430$	−6.19634e8	−0.375834
$431$	2.18418e8	0.131407	0.0657035	−	0.997839i	$-0.479071\pi$
$431$	2.18418e8	0.131407	0.0657035	+	0.997839i	$0.479071\pi$
$432$	−8.06216e7	−0.0481125
$433$	−1.85135e8	−0.109593	−0.0547963	−	0.998498i	$-0.517451\pi$
$433$	−1.85135e8	−0.109593	−0.0547963	+	0.998498i	$0.517451\pi$
$434$	1.65315e8	0.0970731
$435$	3.79143e8	0.220847
$436$	3.53634e8	0.204339
$437$	1.42465e9	0.816626
$438$	−6.20417e8	−0.352797
$439$	−1.14067e9	−0.643480	−0.321740	−	0.946828i	$-0.604268\pi$
$439$	−1.14067e9	−0.643480	−0.321740	+	0.946828i	$0.604268\pi$
$440$	−2.25278e8	−0.126076
$441$	8.57661e7	0.0476190
$442$	−1.00015e9	−0.550917
$443$	1.64332e9	0.898070	0.449035	−	0.893514i	$-0.351768\pi$
$443$	1.64332e9	0.898070	0.449035	+	0.893514i	$0.351768\pi$
$444$	−5.09850e8	−0.276441
$445$	−8.20384e8	−0.441324
$446$	−1.03133e9	−0.550460
$447$	−1.23772e9	−0.655462
$448$	8.99154e7	0.0472456
$449$	1.28514e9	0.670023	0.335011	−	0.942214i	$-0.391260\pi$
$449$	1.28514e9	0.670023	0.335011	+	0.942214i	$0.391260\pi$
$450$	9.11250e7	0.0471405
$451$	1.82104e9	0.934764
$452$	−5.57259e8	−0.283839
$453$	3.49030e8	0.176408
$454$	−1.49211e9	−0.748352
$455$	−2.86308e8	−0.142493
$456$	7.00085e8	0.345759
$457$	3.90828e9	1.91549	0.957744	−	0.287622i	$-0.0928648\pi$
$457$	3.90828e9	1.91549	0.957744	+	0.287622i	$0.0928648\pi$
$458$	−1.74445e9	−0.848454
$459$	3.68499e8	0.177866
$460$	2.25051e8	0.107802
$461$	1.09634e9	0.521183	0.260592	−	0.965449i	$-0.416082\pi$
$461$	1.09634e9	0.521183	0.260592	+	0.965449i	$0.416082\pi$
$462$	−2.60787e8	−0.123038
$463$	−1.19341e9	−0.558801	−0.279400	−	0.960175i	$-0.590136\pi$
$463$	−1.19341e9	−0.558801	−0.279400	+	0.960175i	$0.590136\pi$
$464$	4.60139e8	0.213834
$465$	2.03330e8	0.0937815
$466$	2.44282e9	1.11825
$467$	−601931.	−0.000273488 0	−0.000136744	−	1.00000i	$-0.500044\pi$
$467$	−601931.	−0.000273488 0	−0.000136744		1.00000i	$0.500044\pi$
$468$	3.11556e8	0.140500
$469$	−4.51920e8	−0.202282
$470$	−2.76014e8	−0.122628
$471$	7.34488e8	0.323900
$472$	8.09467e8	0.354325
$473$	2.18109e9	0.947675
$474$	−7.93661e8	−0.342303
$475$	−7.91293e8	−0.338774
$476$	−4.10979e8	−0.174661
$477$	2.57087e8	0.108459
$478$	3.34972e8	0.140285
$479$	−2.69852e9	−1.12189	−0.560947	−	0.827852i	$-0.689563\pi$
$479$	−2.69852e9	−1.12189	−0.560947	+	0.827852i	$0.689563\pi$
$480$	1.10592e8	0.0456435
$481$	1.97028e9	0.807272
$482$	8.71655e6	0.00354552
$483$	2.60525e8	0.105204
$484$	−4.54210e8	−0.182095
$485$	8.68815e8	0.345805
$486$	−1.14791e8	−0.0453609
$487$	1.68306e9	0.660312	0.330156	−	0.943926i	$-0.392899\pi$
$487$	1.68306e9	0.660312	0.330156	+	0.943926i	$0.392899\pi$
$488$	−9.58815e8	−0.373478
$489$	−2.16469e9	−0.837173
$490$	−1.17649e8	−0.0451754
$491$	2.82688e8	0.107776	0.0538879	−	0.998547i	$-0.482839\pi$
$491$	2.82688e8	0.107776	0.0538879	+	0.998547i	$0.482839\pi$
$492$	−8.93975e8	−0.338413
$493$	−2.10317e9	−0.790515
$494$	−2.70543e9	−1.00970
$495$	−3.20757e8	−0.118866
$496$	2.46768e8	0.0908035
$497$	9.62270e8	0.351601
$498$	−1.13700e9	−0.412532
$499$	−4.48890e9	−1.61729	−0.808646	−	0.588296i	$-0.799799\pi$
$499$	−4.48890e9	−1.61729	−0.808646	+	0.588296i	$0.799799\pi$
$500$	−1.25000e8	−0.0447214
$501$	1.24836e9	0.443513
$502$	−2.13979e9	−0.754933
$503$	−2.89277e9	−1.01350	−0.506752	−	0.862092i	$-0.669154\pi$
$503$	−2.89277e9	−1.01350	−0.506752	+	0.862092i	$0.669154\pi$
$504$	1.28024e8	0.0445435
$505$	−2.11955e8	−0.0732360
$506$	−7.92171e8	−0.271827
$507$	4.90222e8	0.167057
$508$	2.31067e9	0.782013
$509$	−2.19437e9	−0.737561	−0.368781	−	0.929516i	$-0.620225\pi$
$509$	−2.19437e9	−0.737561	−0.368781	+	0.929516i	$0.620225\pi$
$510$	−5.05486e8	−0.168738
$511$	9.85200e8	0.326626
$512$	1.34218e8	0.0441942
$513$	9.96801e8	0.325985
$514$	−1.60847e9	−0.522447
$515$	−1.53147e9	−0.494065
$516$	−1.07073e9	−0.343088
$517$	9.71558e8	0.309209
$518$	8.09623e8	0.255934
$519$	−2.18550e9	−0.686224
$520$	−4.27375e8	−0.133290
$521$	−4.71788e9	−1.46156	−0.730778	−	0.682615i	$-0.760842\pi$
$521$	−4.71788e9	−1.46156	−0.730778	+	0.682615i	$0.760842\pi$
$522$	6.55159e8	0.201604
$523$	3.42625e9	1.04728	0.523640	−	0.851939i	$-0.324574\pi$
$523$	3.42625e9	1.04728	0.523640	+	0.851939i	$0.324574\pi$
$524$	−2.84599e9	−0.864119
$525$	−1.44703e8	−0.0436436
$526$	−8.55124e8	−0.256200
$527$	−1.12791e9	−0.335689
$528$	−3.89280e8	−0.115091
$529$	−2.61345e9	−0.767572
$530$	−3.52657e8	−0.102893
$531$	1.15254e9	0.334061
$532$	−1.11171e9	−0.320111
$533$	3.45470e9	0.988247
$534$	−1.41762e9	−0.402872
$535$	7.29875e8	0.206068
$536$	−6.74587e8	−0.189217
$537$	−4.06513e8	−0.113283
$538$	9.93095e8	0.274950
$539$	4.14120e8	0.113911
$540$	1.57464e8	0.0430331
$541$	−4.59939e9	−1.24885	−0.624424	−	0.781086i	$-0.714666\pi$
$541$	−4.59939e9	−1.24885	−0.624424	+	0.781086i	$0.714666\pi$
$542$	−4.51505e9	−1.21805
$543$	−2.12794e9	−0.570373
$544$	−6.13473e8	−0.163380
$545$	−6.90691e8	−0.182766
$546$	−4.94740e8	−0.130078
$547$	−2.74928e9	−0.718230	−0.359115	−	0.933293i	$-0.616921\pi$
$547$	−2.74928e9	−0.718230	−0.359115	+	0.933293i	$0.616921\pi$
$548$	1.82533e9	0.473815
$549$	−1.36519e9	−0.352119
$550$	4.39995e8	0.112766
$551$	−5.68914e9	−1.44882
$552$	3.88888e8	0.0984098
$553$	1.26030e9	0.316911
$554$	−5.09649e8	−0.127346
$555$	9.95801e8	0.247256
$556$	−7.75657e8	−0.191385
$557$	7.39183e9	1.81242	0.906210	−	0.422827i	$-0.138962\pi$
$557$	7.39183e9	1.81242	0.906210	+	0.422827i	$0.138962\pi$
$558$	3.51355e8	0.0856104
$559$	4.13775e9	1.00190
$560$	−1.75616e8	−0.0422577
$561$	1.77929e9	0.425478
$562$	4.63919e9	1.10247
$563$	5.44513e9	1.28596	0.642982	−	0.765881i	$-0.277697\pi$
$563$	5.44513e9	1.28596	0.642982	+	0.765881i	$0.277697\pi$
$564$	−4.76952e8	−0.111943
$565$	1.08840e9	0.253874
$566$	−5.89657e8	−0.136692
$567$	1.82284e8	0.0419961
$568$	1.43639e9	0.328892
$569$	−5.67835e9	−1.29220	−0.646100	−	0.763253i	$-0.723601\pi$
$569$	−5.67835e9	−1.29220	−0.646100	+	0.763253i	$0.723601\pi$
$570$	−1.36735e9	−0.309257
$571$	−3.19953e8	−0.0719216	−0.0359608	−	0.999353i	$-0.511449\pi$
$571$	−3.19953e8	−0.0719216	−0.0359608	+	0.999353i	$0.511449\pi$
$572$	1.50434e9	0.336094
$573$	2.05293e9	0.455862
$574$	1.41960e9	0.313310
$575$	−4.39553e8	−0.0964215
$576$	1.91103e8	0.0416667
$577$	−7.51130e9	−1.62780	−0.813898	−	0.581008i	$-0.802658\pi$
$577$	−7.51130e9	−1.62780	−0.813898	+	0.581008i	$0.802658\pi$
$578$	−4.78694e8	−0.103112
$579$	2.98298e9	0.638667
$580$	−8.98709e8	−0.191259
$581$	1.80551e9	0.381930
$582$	1.50131e9	0.315675
$583$	1.24134e9	0.259448
$584$	1.47062e9	0.305531
$585$	−6.08509e8	−0.125667
$586$	1.69308e9	0.347564
$587$	7.32306e9	1.49437	0.747187	−	0.664614i	$-0.231404\pi$
$587$	7.32306e9	1.49437	0.747187	+	0.664614i	$0.231404\pi$
$588$	−2.03297e8	−0.0412393
$589$	−3.05103e9	−0.615237
$590$	−1.58099e9	−0.316918
$591$	−1.48323e9	−0.295564
$592$	1.20853e9	0.239405
$593$	−9.90570e8	−0.195072	−0.0975358	−	0.995232i	$-0.531096\pi$
$593$	−9.90570e8	−0.195072	−0.0975358	+	0.995232i	$0.531096\pi$
$594$	−5.54267e8	−0.108509
$595$	8.02693e8	0.156221
$596$	2.93387e9	0.567647
$597$	−4.91625e9	−0.945636
$598$	−1.50283e9	−0.287380
$599$	−4.28113e9	−0.813889	−0.406944	−	0.913453i	$-0.633406\pi$
$599$	−4.28113e9	−0.813889	−0.406944	+	0.913453i	$0.633406\pi$
$600$	−2.16000e8	−0.0408248
$601$	8.35731e7	0.0157038	0.00785192	−	0.999969i	$-0.497501\pi$
$601$	8.35731e7	0.0157038	0.00785192	+	0.999969i	$0.497501\pi$
$602$	1.70028e9	0.317637
$603$	−9.60496e8	−0.178396
$604$	−8.27330e8	−0.152774
$605$	8.87130e8	0.162871
$606$	−3.66259e8	−0.0668550
$607$	−5.98423e9	−1.08605	−0.543023	−	0.839718i	$-0.682720\pi$
$607$	−5.98423e9	−1.08605	−0.543023	+	0.839718i	$0.682720\pi$
$608$	−1.65946e9	−0.299436
$609$	−1.04037e9	−0.186649
$610$	1.87269e9	0.334049
$611$	1.84315e9	0.326901
$612$	−8.73479e8	−0.154036
$613$	6.68595e9	1.17233	0.586167	−	0.810190i	$-0.300636\pi$
$613$	6.68595e9	1.17233	0.586167	+	0.810190i	$0.300636\pi$
$614$	−4.81307e9	−0.839137
$615$	1.74605e9	0.302686
$616$	6.18162e8	0.106554
$617$	−6.99468e9	−1.19886	−0.599432	−	0.800426i	$-0.704607\pi$
$617$	−6.99468e9	−1.19886	−0.599432	+	0.800426i	$0.704607\pi$
$618$	−2.64638e9	−0.451017
$619$	−1.02850e10	−1.74296	−0.871480	−	0.490431i	$-0.836839\pi$
$619$	−1.02850e10	−1.74296	−0.871480	+	0.490431i	$0.836839\pi$
$620$	−4.81968e8	−0.0812171
$621$	5.53710e8	0.0927816
$622$	8.19731e9	1.36586
$623$	2.25113e9	0.372987
$624$	−7.38504e8	−0.121677
$625$	2.44141e8	0.0400000
$626$	−2.91714e9	−0.475277
$627$	4.81303e9	0.779799
$628$	−1.74101e9	−0.280506
$629$	−5.52388e9	−0.885048
$630$	−2.50047e8	−0.0398410
$631$	4.35280e9	0.689709	0.344855	−	0.938656i	$-0.387928\pi$
$631$	4.35280e9	0.689709	0.344855	+	0.938656i	$0.387928\pi$
$632$	1.88127e9	0.296443
$633$	2.86115e9	0.448360
$634$	1.96773e9	0.306658
$635$	−4.51302e9	−0.699454
$636$	−6.09391e8	−0.0939282
$637$	7.85629e8	0.120429
$638$	3.16342e9	0.482264
$639$	2.04518e9	0.310083
$640$	−2.62144e8	−0.0395285
$641$	−3.86890e9	−0.580209	−0.290104	−	0.956995i	$-0.593690\pi$
$641$	−3.86890e9	−0.580209	−0.290104	+	0.956995i	$0.593690\pi$
$642$	1.26122e9	0.188113
$643$	1.13220e10	1.67952	0.839761	−	0.542957i	$-0.182695\pi$
$643$	1.13220e10	1.67952	0.839761	+	0.542957i	$0.182695\pi$
$644$	−6.17540e8	−0.0911097
$645$	2.09127e9	0.306867
$646$	7.58494e9	1.10698
$647$	−1.21102e10	−1.75787	−0.878936	−	0.476939i	$-0.841746\pi$
$647$	−1.21102e10	−1.75787	−0.878936	+	0.476939i	$0.841746\pi$
$648$	2.72098e8	0.0392837
$649$	5.56503e9	0.799118
$650$	8.34717e8	0.119218
$651$	−5.57939e8	−0.0792598
$652$	5.13112e9	0.725013
$653$	−7.39788e9	−1.03971	−0.519854	−	0.854255i	$-0.674014\pi$
$653$	−7.39788e9	−1.03971	−0.519854	+	0.854255i	$0.674014\pi$
$654$	−1.19351e9	−0.166842
$655$	5.55857e9	0.772892
$656$	2.11905e9	0.293075
$657$	2.09391e9	0.288057
$658$	7.57382e8	0.103639
$659$	−3.57740e9	−0.486932	−0.243466	−	0.969909i	$-0.578284\pi$
$659$	−3.57740e9	−0.486932	−0.243466	+	0.969909i	$0.578284\pi$
$660$	7.60312e8	0.102941
$661$	5.65356e9	0.761407	0.380703	−	0.924697i	$-0.375682\pi$
$661$	5.65356e9	0.761407	0.380703	+	0.924697i	$0.375682\pi$
$662$	−1.02991e10	−1.37973
$663$	3.37550e9	0.449822
$664$	2.69511e9	0.357263
$665$	2.17131e9	0.286316
$666$	1.72074e9	0.225713
$667$	−3.16024e9	−0.412363
$668$	−2.95907e9	−0.384094
$669$	3.48074e9	0.449448
$670$	1.31755e9	0.169241
$671$	−6.59178e9	−0.842314
$672$	−3.03464e8	−0.0385758
$673$	6.36080e9	0.804376	0.402188	−	0.915557i	$-0.368250\pi$
$673$	6.36080e9	0.804376	0.402188	+	0.915557i	$0.368250\pi$
$674$	−3.59788e9	−0.452623
$675$	−3.07547e8	−0.0384900
$676$	−1.16201e9	−0.144676
$677$	1.44945e10	1.79532	0.897660	−	0.440688i	$-0.145265\pi$
$677$	1.44945e10	1.79532	0.897660	+	0.440688i	$0.145265\pi$
$678$	1.88075e9	0.231754
$679$	−2.38403e9	−0.292258
$680$	1.19819e9	0.146132
$681$	5.03588e9	0.611027
$682$	1.69651e9	0.204791
$683$	−2.75173e9	−0.330471	−0.165235	−	0.986254i	$-0.552838\pi$
$683$	−2.75173e9	−0.330471	−0.165235	+	0.986254i	$0.552838\pi$
$684$	−2.36279e9	−0.282311
$685$	−3.56510e9	−0.423793
$686$	3.22829e8	0.0381802
$687$	5.88751e9	0.692760
$688$	2.53802e9	0.297123
$689$	2.35495e9	0.274292
$690$	−7.59548e8	−0.0880204
$691$	−7.78827e9	−0.897982	−0.448991	−	0.893536i	$-0.648217\pi$
$691$	−7.78827e9	−0.897982	−0.448991	+	0.893536i	$0.648217\pi$
$692$	5.18045e9	0.594287
$693$	8.80156e8	0.100460
$694$	6.00836e9	0.682335
$695$	1.51496e9	0.171180
$696$	−1.55297e9	−0.174595
$697$	−9.68561e9	−1.08346
$698$	2.74874e9	0.305943
$699$	−8.24451e9	−0.913050
$700$	3.43000e8	0.0377964
$701$	2.68202e9	0.294069	0.147034	−	0.989131i	$-0.453027\pi$
$701$	2.68202e9	0.294069	0.147034	+	0.989131i	$0.453027\pi$
$702$	−1.05150e9	−0.114718
$703$	−1.49422e10	−1.62208
$704$	9.22737e8	0.0996721
$705$	9.31547e8	0.100125
$706$	7.84196e9	0.838703
$707$	5.81605e8	0.0618957
$708$	−2.73195e9	−0.289305
$709$	2.19067e8	0.0230842	0.0115421	−	0.999933i	$-0.496326\pi$
$709$	2.19067e8	0.0230842	0.0115421	+	0.999933i	$0.496326\pi$
$710$	−2.80545e9	−0.294170
$711$	2.67861e9	0.279489
$712$	3.36029e9	0.348897
$713$	−1.69481e9	−0.175108
$714$	1.38705e9	0.142610
$715$	−2.93817e9	−0.300612
$716$	9.63586e8	0.0981058
$717$	−1.13053e9	−0.114542
$718$	−1.06290e10	−1.07166
$719$	−1.29846e10	−1.30279	−0.651397	−	0.758737i	$-0.725817\pi$
$719$	−1.29846e10	−1.30279	−0.651397	+	0.758737i	$0.725817\pi$
$720$	−3.73248e8	−0.0372678
$721$	4.20236e9	0.417561
$722$	1.33665e10	1.32172
$723$	−2.94184e7	−0.00289491
$724$	5.04400e9	0.493958
$725$	1.75529e9	0.171067
$726$	1.53296e9	0.148680
$727$	6.39689e9	0.617445	0.308723	−	0.951152i	$-0.400098\pi$
$727$	6.39689e9	0.617445	0.308723	+	0.951152i	$0.400098\pi$
$728$	1.17272e9	0.112651
$729$	3.87420e8	0.0370370
$730$	−2.87230e9	−0.273275
$731$	−1.16006e10	−1.09842
$732$	3.23600e9	0.304944
$733$	1.48516e10	1.39287	0.696435	−	0.717620i	$-0.254769\pi$
$733$	1.48516e10	1.39287	0.696435	+	0.717620i	$0.254769\pi$
$734$	1.90484e9	0.177796
$735$	3.97065e8	0.0368856
$736$	−9.21809e8	−0.0852254
$737$	−4.63773e9	−0.426746
$738$	3.01717e9	0.276313
$739$	−2.79353e9	−0.254624	−0.127312	−	0.991863i	$-0.540635\pi$
$739$	−2.79353e9	−0.254624	−0.127312	+	0.991863i	$0.540635\pi$
$740$	−2.36042e9	−0.214130
$741$	9.13083e9	0.824416
$742$	9.67690e8	0.0869606
$743$	1.54292e10	1.38001	0.690006	−	0.723803i	$-0.257608\pi$
$743$	1.54292e10	1.38001	0.690006	+	0.723803i	$0.257608\pi$
$744$	−8.32842e8	−0.0741408
$745$	−5.73021e9	−0.507719
$746$	7.28360e9	0.642333
$747$	3.83737e9	0.336831
$748$	−4.21758e9	−0.368475
$749$	−2.00278e9	−0.174159
$750$	4.21875e8	0.0365148
$751$	−1.14294e10	−0.984652	−0.492326	−	0.870411i	$-0.663853\pi$
$751$	−1.14294e10	−0.984652	−0.492326	+	0.870411i	$0.663853\pi$
$752$	1.13055e9	0.0969457
$753$	7.22180e9	0.616401
$754$	6.00134e9	0.509857
$755$	1.61588e9	0.136645
$756$	−4.32081e8	−0.0363696
$757$	2.06161e10	1.72731	0.863657	−	0.504079i	$-0.168168\pi$
$757$	2.06161e10	1.72731	0.863657	+	0.504079i	$0.168168\pi$
$758$	−8.22584e9	−0.686022
$759$	2.67358e9	0.221946
$760$	3.24114e9	0.267824
$761$	−3.18960e9	−0.262355	−0.131178	−	0.991359i	$-0.541876\pi$
$761$	−3.18960e9	−0.262355	−0.131178	+	0.991359i	$0.541876\pi$
$762$	−7.79850e9	−0.638511
$763$	1.89526e9	0.154466
$764$	−4.86621e9	−0.394788
$765$	1.70601e9	0.137774
$766$	5.13288e8	0.0412629
$767$	1.05574e10	0.844840
$768$	−4.52985e8	−0.0360844
$769$	−1.12671e10	−0.893453	−0.446726	−	0.894671i	$-0.647410\pi$
$769$	−1.12671e10	−0.893453	−0.446726	+	0.894671i	$0.647410\pi$
$770$	−1.20735e9	−0.0953048
$771$	5.42859e9	0.426577
$772$	−7.07076e9	−0.553102
$773$	1.17514e10	0.915084	0.457542	−	0.889188i	$-0.348730\pi$
$773$	1.17514e10	0.915084	0.457542	+	0.889188i	$0.348730\pi$
$774$	3.61371e9	0.280130
$775$	9.41345e8	0.0726428
$776$	−3.55867e9	−0.273383
$777$	−2.73248e9	−0.208970
$778$	7.59819e9	0.578471
$779$	−2.61999e10	−1.98572
$780$	1.44239e9	0.108831
$781$	9.87509e9	0.741758
$782$	4.21334e9	0.315067
$783$	−2.21116e9	−0.164609
$784$	4.81890e8	0.0357143
$785$	3.40041e9	0.250892
$786$	9.60521e9	0.705550
$787$	−2.56624e10	−1.87666	−0.938329	−	0.345744i	$-0.887626\pi$
$787$	−2.56624e10	−1.87666	−0.938329	+	0.345744i	$0.887626\pi$
$788$	3.51580e9	0.255966
$789$	2.88604e9	0.209186
$790$	−3.67436e9	−0.265147
$791$	−2.98656e9	−0.214562
$792$	1.31382e9	0.0939718
$793$	−1.25053e10	−0.890508
$794$	1.81739e9	0.128848
$795$	1.19022e9	0.0840119
$796$	1.16533e10	0.818945
$797$	4.18152e9	0.292570	0.146285	−	0.989242i	$-0.453268\pi$
$797$	4.18152e9	0.292570	0.146285	+	0.989242i	$0.453268\pi$
$798$	3.75202e9	0.261370
$799$	−5.16745e9	−0.358395
$800$	5.12000e8	0.0353553
$801$	4.78448e9	0.328943
$802$	−1.93549e9	−0.132489
$803$	1.01104e10	0.689071
$804$	2.27673e9	0.154495
$805$	1.20613e9	0.0814910
$806$	3.21846e9	0.216509
$807$	−3.35170e9	−0.224495
$808$	8.68169e8	0.0578981
$809$	2.07425e10	1.37734	0.688672	−	0.725073i	$-0.258194\pi$
$809$	2.07425e10	1.37734	0.688672	+	0.725073i	$0.258194\pi$
$810$	−5.31441e8	−0.0351364
$811$	1.07679e10	0.708857	0.354429	−	0.935083i	$-0.384675\pi$
$811$	1.07679e10	0.708857	0.354429	+	0.935083i	$0.384675\pi$
$812$	2.46606e9	0.161643
$813$	1.52383e10	0.994535
$814$	8.30858e9	0.539935
$815$	−1.00217e10	−0.648472
$816$	2.07047e9	0.133399
$817$	−3.13800e10	−2.01315
$818$	−1.85043e10	−1.18205
$819$	1.66975e9	0.106208
$820$	−4.13877e9	−0.262134
$821$	−8.99808e9	−0.567478	−0.283739	−	0.958902i	$-0.591575\pi$
$821$	−8.99808e9	−0.567478	−0.283739	+	0.958902i	$0.591575\pi$
$822$	−6.16048e9	−0.386869
$823$	2.65950e10	1.66303	0.831517	−	0.555499i	$-0.187473\pi$
$823$	2.65950e10	1.66303	0.831517	+	0.555499i	$0.187473\pi$
$824$	6.27291e9	0.390593
$825$	−1.48498e9	−0.0920731
$826$	4.33824e9	0.267845
$827$	−1.71850e8	−0.0105653	−0.00528264	−	0.999986i	$-0.501682\pi$
$827$	−1.71850e8	−0.0105653	−0.00528264	+	0.999986i	$0.501682\pi$
$828$	−1.31250e9	−0.0803512
$829$	−2.04622e10	−1.24742	−0.623709	−	0.781656i	$-0.714375\pi$
$829$	−2.04622e10	−1.24742	−0.623709	+	0.781656i	$0.714375\pi$
$830$	−5.26388e9	−0.319546
$831$	1.72006e9	0.103978
$832$	1.75053e9	0.105375
$833$	−2.20259e9	−0.132031
$834$	2.61784e9	0.156265
$835$	5.77943e9	0.343544
$836$	−1.14087e10	−0.675326
$837$	−1.18582e9	−0.0699006
$838$	2.25394e10	1.32309
$839$	1.65787e9	0.0969135	0.0484567	−	0.998825i	$-0.484570\pi$
$839$	1.65787e9	0.0969135	0.0484567	+	0.998825i	$0.484570\pi$
$840$	5.92704e8	0.0345033
$841$	−4.62990e9	−0.268402
$842$	−2.55445e9	−0.147471
$843$	−1.56573e10	−0.900159
$844$	−6.78197e9	−0.388291
$845$	2.26955e9	0.129402
$846$	1.60971e9	0.0914013
$847$	−2.43428e9	−0.137651
$848$	1.44448e9	0.0813442
$849$	1.99009e9	0.111608
$850$	−2.34021e9	−0.130704
$851$	−8.30023e9	−0.461675
$852$	−4.84782e9	−0.268539
$853$	−9.42074e8	−0.0519713	−0.0259856	−	0.999662i	$-0.508272\pi$
$853$	−9.42074e8	−0.0519713	−0.0259856	+	0.999662i	$0.508272\pi$
$854$	−5.13865e9	−0.282323
$855$	4.61482e9	0.252507
$856$	−2.98957e9	−0.162911
$857$	6.47349e9	0.351322	0.175661	−	0.984451i	$-0.443794\pi$
$857$	6.47349e9	0.351322	0.175661	+	0.984451i	$0.443794\pi$
$858$	−5.07716e9	−0.274420
$859$	1.69921e10	0.914685	0.457342	−	0.889291i	$-0.348801\pi$
$859$	1.69921e10	0.914685	0.457342	+	0.889291i	$0.348801\pi$
$860$	−4.95707e9	−0.265755
$861$	−4.79115e9	−0.255817
$862$	1.74735e9	0.0929187
$863$	−1.78341e10	−0.944527	−0.472263	−	0.881457i	$-0.656563\pi$
$863$	−1.78341e10	−0.944527	−0.472263	+	0.881457i	$0.656563\pi$
$864$	−6.44973e8	−0.0340207
$865$	−1.01181e10	−0.531546
$866$	−1.48108e9	−0.0774937
$867$	1.61559e9	0.0841909
$868$	1.32252e9	0.0686410
$869$	1.29336e10	0.668575
$870$	3.03314e9	0.156162
$871$	−8.79826e9	−0.451163
$872$	2.82907e9	0.144489
$873$	−5.06693e9	−0.257748
$874$	1.13972e10	0.577442
$875$	−6.69922e8	−0.0338062
$876$	−4.96334e9	−0.249465
$877$	−2.85639e9	−0.142995	−0.0714973	−	0.997441i	$-0.522778\pi$
$877$	−2.85639e9	−0.142995	−0.0714973	+	0.997441i	$0.522778\pi$
$878$	−9.12538e9	−0.455009
$879$	−5.71413e9	−0.283785
$880$	−1.80222e9	−0.0891494
$881$	3.45454e10	1.70206	0.851029	−	0.525118i	$-0.175979\pi$
$881$	3.45454e10	1.70206	0.851029	+	0.525118i	$0.175979\pi$
$882$	6.86129e8	0.0336718
$883$	−1.10261e10	−0.538964	−0.269482	−	0.963005i	$-0.586853\pi$
$883$	−1.10261e10	−0.538964	−0.269482	+	0.963005i	$0.586853\pi$
$884$	−8.00118e9	−0.389557
$885$	5.33584e9	0.258763
$886$	1.31466e10	0.635031
$887$	−1.39915e10	−0.673180	−0.336590	−	0.941651i	$-0.609274\pi$
$887$	−1.39915e10	−0.673180	−0.336590	+	0.941651i	$0.609274\pi$
$888$	−4.07880e9	−0.195473
$889$	1.23837e10	0.591146
$890$	−6.56307e9	−0.312063
$891$	1.87065e9	0.0885974
$892$	−8.25063e9	−0.389234
$893$	−1.39781e10	−0.656853
$894$	−9.90180e9	−0.463482
$895$	−1.88200e9	−0.0877485
$896$	7.19323e8	0.0334077
$897$	5.07206e9	0.234645
$898$	1.02812e10	0.473778
$899$	6.76796e9	0.310670
$900$	7.29000e8	0.0333333
$901$	−6.60233e9	−0.300719
$902$	1.45683e10	0.660978
$903$	−5.73843e9	−0.259350
$904$	−4.45807e9	−0.200705
$905$	−9.85156e9	−0.441809
$906$	2.79224e9	0.124739
$907$	−3.11910e10	−1.38804	−0.694022	−	0.719953i	$-0.744163\pi$
$907$	−3.11910e10	−1.38804	−0.694022	+	0.719953i	$0.744163\pi$
$908$	−1.19369e10	−0.529165
$909$	1.23612e9	0.0545869
$910$	−2.29046e9	−0.100758
$911$	4.30600e9	0.188695	0.0943474	−	0.995539i	$-0.469924\pi$
$911$	4.30600e9	0.188695	0.0943474	+	0.995539i	$0.469924\pi$
$912$	5.60068e9	0.244489
$913$	1.85287e10	0.805743
$914$	3.12663e10	1.35445
$915$	−6.32031e9	−0.272750
$916$	−1.39556e10	−0.599948
$917$	−1.52527e10	−0.653213
$918$	2.94799e9	0.125770
$919$	9.02176e9	0.383431	0.191715	−	0.981451i	$-0.438595\pi$
$919$	9.02176e9	0.383431	0.191715	+	0.981451i	$0.438595\pi$
$920$	1.80041e9	0.0762279
$921$	1.62441e10	0.685152
$922$	8.77069e9	0.368532
$923$	1.87341e10	0.784199
$924$	−2.08630e9	−0.0870009
$925$	4.61019e9	0.191524
$926$	−9.54729e9	−0.395132
$927$	8.93155e9	0.368254
$928$	3.68111e9	0.151203
$929$	3.36166e10	1.37562	0.687811	−	0.725889i	$-0.258572\pi$
$929$	3.36166e10	1.37562	0.687811	+	0.725889i	$0.258572\pi$
$930$	1.62664e9	0.0663135
$931$	−5.95807e9	−0.241981
$932$	1.95425e10	0.790724
$933$	−2.76659e10	−1.11522
$934$	−4.81545e6	−0.000193385 0
$935$	8.23746e9	0.329574
$936$	2.49245e9	0.0993485
$937$	4.46714e9	0.177395	0.0886975	−	0.996059i	$-0.471730\pi$
$937$	4.46714e9	0.177395	0.0886975	+	0.996059i	$0.471730\pi$
$938$	−3.61536e9	−0.143035
$939$	9.84535e9	0.388062
$940$	−2.20811e9	−0.0867109
$941$	−2.72193e10	−1.06491	−0.532455	−	0.846459i	$-0.678730\pi$
$941$	−2.72193e10	−1.06491	−0.532455	+	0.846459i	$0.678730\pi$
$942$	5.87590e9	0.229032
$943$	−1.45537e10	−0.565174
$944$	6.47574e9	0.250546
$945$	8.43909e8	0.0325300
$946$	1.74487e10	0.670107
$947$	1.69563e10	0.648793	0.324396	−	0.945921i	$-0.394839\pi$
$947$	1.69563e10	0.648793	0.324396	+	0.945921i	$0.394839\pi$
$948$	−6.34929e9	−0.242045
$949$	1.91805e10	0.728497
$950$	−6.33034e9	−0.239549
$951$	−6.64110e9	−0.250385
$952$	−3.28783e9	−0.123504
$953$	2.92746e10	1.09564	0.547818	−	0.836598i	$-0.315459\pi$
$953$	2.92746e10	1.09564	0.547818	+	0.836598i	$0.315459\pi$
$954$	2.05669e9	0.0766920
$955$	9.50431e9	0.353109
$956$	2.67977e9	0.0991963
$957$	−1.06766e10	−0.393767
$958$	−2.15882e10	−0.793299
$959$	9.78262e9	0.358171
$960$	8.84736e8	0.0322749
$961$	−2.38830e10	−0.868075
$962$	1.57622e10	0.570828
$963$	−4.25663e9	−0.153594
$964$	6.97324e7	0.00250706
$965$	1.38101e10	0.494710
$966$	2.08420e9	0.0743908
$967$	−2.59163e10	−0.921680	−0.460840	−	0.887483i	$-0.652452\pi$
$967$	−2.59163e10	−0.921680	−0.460840	+	0.887483i	$0.652452\pi$
$968$	−3.63368e9	−0.128761
$969$	−2.55992e10	−0.903843
$970$	6.95052e9	0.244521
$971$	−4.70044e10	−1.64767	−0.823837	−	0.566827i	$-0.808171\pi$
$971$	−4.70044e10	−1.64767	−0.823837	+	0.566827i	$0.808171\pi$
$972$	−9.18330e8	−0.0320750
$973$	−4.15704e9	−0.144673
$974$	1.34645e10	0.466911
$975$	−2.81717e9	−0.0973412
$976$	−7.67052e9	−0.264089
$977$	−1.63248e10	−0.560036	−0.280018	−	0.959995i	$-0.590340\pi$
$977$	−1.63248e10	−0.560036	−0.280018	+	0.959995i	$0.590340\pi$
$978$	−1.73175e10	−0.591971
$979$	2.31018e10	0.786875
$980$	−9.41192e8	−0.0319438
$981$	4.02811e9	0.136226
$982$	2.26150e9	0.0762090
$983$	−4.03404e10	−1.35457	−0.677287	−	0.735719i	$-0.736845\pi$
$983$	−4.03404e10	−1.35457	−0.677287	+	0.735719i	$0.736845\pi$
$984$	−7.15180e9	−0.239294
$985$	−6.86680e9	−0.228943
$986$	−1.68254e10	−0.558979
$987$	−2.55616e9	−0.0846211
$988$	−2.16434e10	−0.713965
$989$	−1.74312e10	−0.572980
$990$	−2.56605e9	−0.0840509
$991$	−4.32750e10	−1.41247	−0.706235	−	0.707978i	$-0.749608\pi$
$991$	−4.32750e10	−1.41247	−0.706235	+	0.707978i	$0.749608\pi$
$992$	1.97414e9	0.0642078
$993$	3.47593e10	1.12655
$994$	7.69816e9	0.248619
$995$	−2.27604e10	−0.732486
$996$	−9.09599e9	−0.291704
$997$	−2.29504e10	−0.733428	−0.366714	−	0.930334i	$-0.619517\pi$
$997$	−2.29504e10	−0.733428	−0.366714	+	0.930334i	$0.619517\pi$
$998$	−3.59112e10	−1.14360
$999$	−5.80751e9	−0.184294

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.8.a.m.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.8.a.m.1.2	✓	2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	210.a (trivial)

\(f(q)\)	\(=\)	\(q+8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -125.000 q^{5} -216.000 q^{6} +343.000 q^{7} +512.000 q^{8} +729.000 q^{9} -1000.00 q^{10} +3519.96 q^{11} -1728.00 q^{12} +6677.73 q^{13} +2744.00 q^{14} +3375.00 q^{15} +4096.00 q^{16} -18721.7 q^{17} +5832.00 q^{18} -50642.7 q^{19} -8000.00 q^{20} -9261.00 q^{21} +28159.7 q^{22} -28131.4 q^{23} -13824.0 q^{24} +15625.0 q^{25} +53421.9 q^{26} -19683.0 q^{27} +21952.0 q^{28} +112339. q^{29} +27000.0 q^{30} +60246.1 q^{31} +32768.0 q^{32} -95039.0 q^{33} -149774. q^{34} -42875.0 q^{35} +46656.0 q^{36} +295052. q^{37} -405142. q^{38} -180299. q^{39} -64000.0 q^{40} +517347. q^{41} -74088.0 q^{42} +619634. q^{43} +225278. q^{44} -91125.0 q^{45} -225051. q^{46} +276014. q^{47} -110592. q^{48} +117649. q^{49} +125000. q^{50} +505486. q^{51} +427375. q^{52} +352657. q^{53} -157464. q^{54} -439995. q^{55} +175616. q^{56} +1.36735e6 q^{57} +898709. q^{58} +1.58099e6 q^{59} +216000. q^{60} -1.87269e6 q^{61} +481968. q^{62} +250047. q^{63} +262144. q^{64} -834717. q^{65} -760312. q^{66} -1.31755e6 q^{67} -1.19819e6 q^{68} +759548. q^{69} -343000. q^{70} +2.80545e6 q^{71} +373248. q^{72} +2.87230e6 q^{73} +2.36042e6 q^{74} -421875. q^{75} -3.24114e6 q^{76} +1.20735e6 q^{77} -1.44239e6 q^{78} +3.67436e6 q^{79} -512000. q^{80} +531441. q^{81} +4.13877e6 q^{82} +5.26388e6 q^{83} -592704. q^{84} +2.34021e6 q^{85} +4.95707e6 q^{86} -3.03314e6 q^{87} +1.80222e6 q^{88} +6.56307e6 q^{89} -729000. q^{90} +2.29046e6 q^{91} -1.80041e6 q^{92} -1.62664e6 q^{93} +2.20811e6 q^{94} +6.33034e6 q^{95} -884736. q^{96} -6.95052e6 q^{97} +941192. q^{98} +2.56605e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 16 q^{2} - 54 q^{3} + 128 q^{4} - 250 q^{5} - 432 q^{6} + 686 q^{7} + 1024 q^{8} + 1458 q^{9} - 2000 q^{10} + 4092 q^{11} - 3456 q^{12} - 7280 q^{13} + 5488 q^{14} + 6750 q^{15} + 8192 q^{16} - 13860 q^{17}+ \cdots + 2983068 q^{99}+O(q^{100}) \) 2 * q + 16 * q^2 - 54 * q^3 + 128 * q^4 - 250 * q^5 - 432 * q^6 + 686 * q^7 + 1024 * q^8 + 1458 * q^9 - 2000 * q^10 + 4092 * q^11 - 3456 * q^12 - 7280 * q^13 + 5488 * q^14 + 6750 * q^15 + 8192 * q^16 - 13860 * q^17 + 11664 * q^18 - 4004 * q^19 - 16000 * q^20 - 18522 * q^21 + 32736 * q^22 - 9096 * q^23 - 27648 * q^24 + 31250 * q^25 - 58240 * q^26 - 39366 * q^27 + 43904 * q^28 - 34740 * q^29 + 54000 * q^30 - 29852 * q^31 + 65536 * q^32 - 110484 * q^33 - 110880 * q^34 - 85750 * q^35 + 93312 * q^36 + 442708 * q^37 - 32032 * q^38 + 196560 * q^39 - 128000 * q^40 + 162108 * q^41 - 148176 * q^42 + 1091872 * q^43 + 261888 * q^44 - 182250 * q^45 - 72768 * q^46 + 1630968 * q^47 - 221184 * q^48 + 235298 * q^49 + 250000 * q^50 + 374220 * q^51 - 465920 * q^52 + 2146848 * q^53 - 314928 * q^54 - 511500 * q^55 + 351232 * q^56 + 108108 * q^57 - 277920 * q^58 + 2106624 * q^59 + 432000 * q^60 - 1528532 * q^61 - 238816 * q^62 + 500094 * q^63 + 524288 * q^64 + 910000 * q^65 - 883872 * q^66 + 1987240 * q^67 - 887040 * q^68 + 245592 * q^69 - 686000 * q^70 + 5059644 * q^71 + 746496 * q^72 - 1321568 * q^73 + 3541664 * q^74 - 843750 * q^75 - 256256 * q^76 + 1403556 * q^77 + 1572480 * q^78 + 11493496 * q^79 - 1024000 * q^80 + 1062882 * q^81 + 1296864 * q^82 + 4920816 * q^83 - 1185408 * q^84 + 1732500 * q^85 + 8734976 * q^86 + 937980 * q^87 + 2095104 * q^88 + 12159228 * q^89 - 1458000 * q^90 - 2497040 * q^91 - 582144 * q^92 + 806004 * q^93 + 13047744 * q^94 + 500500 * q^95 - 1769472 * q^96 + 4037080 * q^97 + 1882384 * q^98 + 2983068 * q^99

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