LMFDB - Embedded newform 102.10.a.h.1.3

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)

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")

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);

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:	$1$
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} - x^{3} - 520688x^{2} - 146431260x - 953767152 $ x^4 - x^3 - 520688x^2 - 146431260x - 953767152
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{5}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-6.67167$ 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)

$f(q)$	$=$	\(q-16.0000 q^{2} -81.0000 q^{3} +256.000 q^{4} +901.022 q^{5} +1296.00 q^{6} -1949.06 q^{7} -4096.00 q^{8} +6561.00 q^{9} -14416.4 q^{10} +25996.5 q^{11} -20736.0 q^{12} -110290. q^{13} +31185.0 q^{14} -72982.8 q^{15} +65536.0 q^{16} -83521.0 q^{17} -104976. q^{18} +116465. q^{19} +230662. q^{20} +157874. q^{21} -415944. q^{22} -287617. q^{23} +331776. q^{24} -1.14128e6 q^{25} +1.76463e6 q^{26} -531441. q^{27} -498960. q^{28} +6.95263e6 q^{29} +1.16772e6 q^{30} +6.21369e6 q^{31} -1.04858e6 q^{32} -2.10572e6 q^{33} +1.33634e6 q^{34} -1.75615e6 q^{35} +1.67962e6 q^{36} +1.41015e7 q^{37} -1.86344e6 q^{38} +8.93346e6 q^{39} -3.69059e6 q^{40} -7.62188e6 q^{41} -2.52599e6 q^{42} -1.02031e7 q^{43} +6.65510e6 q^{44} +5.91161e6 q^{45} +4.60187e6 q^{46} -5.18233e7 q^{47} -5.30842e6 q^{48} -3.65548e7 q^{49} +1.82605e7 q^{50} +6.76520e6 q^{51} -2.82342e7 q^{52} +2.75093e7 q^{53} +8.50306e6 q^{54} +2.34234e7 q^{55} +7.98337e6 q^{56} -9.43365e6 q^{57} -1.11242e8 q^{58} -4.46972e7 q^{59} -1.86836e7 q^{60} +3.36778e7 q^{61} -9.94191e7 q^{62} -1.27878e7 q^{63} +1.67772e7 q^{64} -9.93734e7 q^{65} +3.36915e7 q^{66} -7.61270e7 q^{67} -2.13814e7 q^{68} +2.32970e7 q^{69} +2.80984e7 q^{70} -7.55178e7 q^{71} -2.68739e7 q^{72} -4.10228e8 q^{73} -2.25624e8 q^{74} +9.24440e7 q^{75} +2.98150e7 q^{76} -5.06689e7 q^{77} -1.42935e8 q^{78} +3.46554e8 q^{79} +5.90494e7 q^{80} +4.30467e7 q^{81} +1.21950e8 q^{82} -7.32010e8 q^{83} +4.04158e7 q^{84} -7.52543e7 q^{85} +1.63250e8 q^{86} -5.63163e8 q^{87} -1.06482e8 q^{88} -1.11010e9 q^{89} -9.45857e7 q^{90} +2.14962e8 q^{91} -7.36300e7 q^{92} -5.03309e8 q^{93} +8.29173e8 q^{94} +1.04937e8 q^{95} +8.49347e7 q^{96} -7.90680e8 q^{97} +5.84876e8 q^{98} +1.70563e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 64 q^{2} - 324 q^{3} + 1024 q^{4} - 942 q^{5} + 5184 q^{6} - 2084 q^{7} - 16384 q^{8} + 26244 q^{9} + 15072 q^{10} - 68450 q^{11} - 82944 q^{12} + 64722 q^{13} + 33344 q^{14} + 76302 q^{15} + 262144 q^{16}+ \cdots - 449100450 q^{99}+O(q^{100}) $ 4 * q - 64 * q^2 - 324 * q^3 + 1024 * q^4 - 942 * q^5 + 5184 * q^6 - 2084 * q^7 - 16384 * q^8 + 26244 * q^9 + 15072 * q^10 - 68450 * q^11 - 82944 * q^12 + 64722 * q^13 + 33344 * q^14 + 76302 * q^15 + 262144 * q^16 - 334084 * q^17 - 419904 * q^18 - 203854 * q^19 - 241152 * q^20 + 168804 * q^21 + 1095200 * q^22 + 2505834 * q^23 + 1327104 * q^24 + 6830638 * q^25 - 1035552 * q^26 - 2125764 * q^27 - 533504 * q^28 - 885976 * q^29 - 1220832 * q^30 + 11921296 * q^31 - 4194304 * q^32 + 5544450 * q^33 + 5345344 * q^34 + 38217208 * q^35 + 6718464 * q^36 + 14106124 * q^37 + 3261664 * q^38 - 5242482 * q^39 + 3858432 * q^40 - 14158146 * q^41 - 2700864 * q^42 + 26846790 * q^43 - 17523200 * q^44 - 6180462 * q^45 - 40093344 * q^46 - 35033332 * q^47 - 21233664 * q^48 + 46195148 * q^49 - 109290208 * q^50 + 27060804 * q^51 + 16568832 * q^52 - 95616880 * q^53 + 34012224 * q^54 - 216054070 * q^55 + 8536064 * q^56 + 16512174 * q^57 + 14175616 * q^58 - 102623436 * q^59 + 19533312 * q^60 - 196381204 * q^61 - 190740736 * q^62 - 13673124 * q^63 + 67108864 * q^64 - 748875142 * q^65 - 88711200 * q^66 + 44116808 * q^67 - 85525504 * q^68 - 202972554 * q^69 - 611475328 * q^70 - 391106100 * q^71 - 107495424 * q^72 - 325868288 * q^73 - 225697984 * q^74 - 553281678 * q^75 - 52186624 * q^76 - 1690587600 * q^77 + 83879712 * q^78 + 108839048 * q^79 - 61734912 * q^80 + 172186884 * q^81 + 226530336 * q^82 - 319973836 * q^83 + 43213824 * q^84 + 78676782 * q^85 - 429548640 * q^86 + 71764056 * q^87 + 280371200 * q^88 - 829727740 * q^89 + 98887392 * q^90 - 1890352424 * q^91 + 641493504 * q^92 - 965624976 * q^93 + 560533312 * q^94 - 571320138 * q^95 + 339738624 * q^96 - 354724644 * q^97 - 739122368 * q^98 - 449100450 * 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
$5$	901.022	0.644719	0.322360	−	0.946617i	$-0.395524\pi$
$5$	901.022	0.644719	0.322360	+	0.946617i	$0.395524\pi$
$6$	1296.00	0.408248
$7$	−1949.06	−0.306821	−0.153410	−	0.988163i	$-0.549026\pi$
$7$	−1949.06	−0.306821	−0.153410	+	0.988163i	$0.549026\pi$
$8$	−4096.00	−0.353553
$9$	6561.00	0.333333
$10$	−14416.4	−0.455885
$11$	25996.5	0.535362	0.267681	−	0.963508i	$-0.413743\pi$
$11$	25996.5	0.535362	0.267681	+	0.963508i	$0.413743\pi$
$12$	−20736.0	−0.288675
$13$	−110290.	−1.07100	−0.535500	−	0.844535i	$-0.679877\pi$
$13$	−110290.	−1.07100	−0.535500	+	0.844535i	$0.679877\pi$
$14$	31185.0	0.216955
$15$	−72982.8	−0.372229
$16$	65536.0	0.250000
$17$	−83521.0	−0.242536
$17$	−83521.0	−0.242536
$18$	−104976.	−0.235702
$19$	116465.	0.205024	0.102512	−	0.994732i	$-0.467312\pi$
$19$	116465.	0.205024	0.102512	+	0.994732i	$0.467312\pi$
$20$	230662.	0.322360
$21$	157874.	0.177143
$22$	−415944.	−0.378558
$23$	−287617.	−0.214309	−0.107154	−	0.994242i	$-0.534174\pi$
$23$	−287617.	−0.214309	−0.107154	+	0.994242i	$0.534174\pi$
$24$	331776.	0.204124
$25$	−1.14128e6	−0.584337
$26$	1.76463e6	0.757312
$27$	−531441.	−0.192450
$28$	−498960.	−0.153410
$29$	6.95263e6	1.82540	0.912701	−	0.408629i	$-0.133993\pi$
$29$	6.95263e6	1.82540	0.912701	+	0.408629i	$0.133993\pi$
$30$	1.16772e6	0.263205
$31$	6.21369e6	1.20843	0.604216	−	0.796821i	$-0.293486\pi$
$31$	6.21369e6	1.20843	0.604216	+	0.796821i	$0.293486\pi$
$32$	−1.04858e6	−0.176777
$33$	−2.10572e6	−0.309092
$34$	1.33634e6	0.171499
$35$	−1.75615e6	−0.197813
$36$	1.67962e6	0.166667
$37$	1.41015e7	1.23697	0.618483	−	0.785798i	$-0.287748\pi$
$37$	1.41015e7	1.23697	0.618483	+	0.785798i	$0.287748\pi$
$38$	−1.86344e6	−0.144974
$39$	8.93346e6	0.618343
$40$	−3.69059e6	−0.227943
$41$	−7.62188e6	−0.421245	−0.210623	−	0.977567i	$-0.567549\pi$
$41$	−7.62188e6	−0.421245	−0.210623	+	0.977567i	$0.567549\pi$
$42$	−2.52599e6	−0.125259
$43$	−1.02031e7	−0.455119	−0.227559	−	0.973764i	$-0.573075\pi$
$43$	−1.02031e7	−0.455119	−0.227559	+	0.973764i	$0.573075\pi$
$44$	6.65510e6	0.267681
$45$	5.91161e6	0.214906
$46$	4.60187e6	0.151539
$47$	−5.18233e7	−1.54912	−0.774560	−	0.632500i	$-0.782029\pi$
$47$	−5.18233e7	−1.54912	−0.774560	+	0.632500i	$0.782029\pi$
$48$	−5.30842e6	−0.144338
$49$	−3.65548e7	−0.905861
$50$	1.82605e7	0.413189
$51$	6.76520e6	0.140028
$52$	−2.82342e7	−0.535500
$53$	2.75093e7	0.478893	0.239446	−	0.970910i	$-0.423034\pi$
$53$	2.75093e7	0.478893	0.239446	+	0.970910i	$0.423034\pi$
$54$	8.50306e6	0.136083
$55$	2.34234e7	0.345158
$56$	7.98337e6	0.108478
$57$	−9.43365e6	−0.118370
$58$	−1.11242e8	−1.29075
$59$	−4.46972e7	−0.480227	−0.240113	−	0.970745i	$-0.577185\pi$
$59$	−4.46972e7	−0.480227	−0.240113	+	0.970745i	$0.577185\pi$
$60$	−1.86836e7	−0.186114
$61$	3.36778e7	0.311430	0.155715	−	0.987802i	$-0.450232\pi$
$61$	3.36778e7	0.311430	0.155715	+	0.987802i	$0.450232\pi$
$62$	−9.94191e7	−0.854491
$63$	−1.27878e7	−0.102274
$64$	1.67772e7	0.125000
$65$	−9.93734e7	−0.690495
$66$	3.36915e7	0.218561
$67$	−7.61270e7	−0.461533	−0.230766	−	0.973009i	$-0.574123\pi$
$67$	−7.61270e7	−0.461533	−0.230766	+	0.973009i	$0.574123\pi$
$68$	−2.13814e7	−0.121268
$69$	2.32970e7	0.123731
$70$	2.80984e7	0.139875
$71$	−7.55178e7	−0.352685	−0.176342	−	0.984329i	$-0.556427\pi$
$71$	−7.55178e7	−0.352685	−0.176342	+	0.984329i	$0.556427\pi$
$72$	−2.68739e7	−0.117851
$73$	−4.10228e8	−1.69072	−0.845361	−	0.534196i	$-0.820615\pi$
$73$	−4.10228e8	−1.69072	−0.845361	+	0.534196i	$0.820615\pi$
$74$	−2.25624e8	−0.874667
$75$	9.24440e7	0.337367
$76$	2.98150e7	0.102512
$77$	−5.06689e7	−0.164260
$78$	−1.42935e8	−0.437234
$79$	3.46554e8	1.00104	0.500518	−	0.865726i	$-0.333143\pi$
$79$	3.46554e8	1.00104	0.500518	+	0.865726i	$0.333143\pi$
$80$	5.90494e7	0.161180
$81$	4.30467e7	0.111111
$82$	1.21950e8	0.297865
$83$	−7.32010e8	−1.69303	−0.846517	−	0.532362i	$-0.821305\pi$
$83$	−7.32010e8	−1.69303	−0.846517	+	0.532362i	$0.821305\pi$
$84$	4.04158e7	0.0885716
$85$	−7.52543e7	−0.156367
$86$	1.63250e8	0.321817
$87$	−5.63163e8	−1.05390
$88$	−1.06482e8	−0.189279
$89$	−1.11010e9	−1.87545	−0.937727	−	0.347374i	$-0.887074\pi$
$89$	−1.11010e9	−1.87545	−0.937727	+	0.347374i	$0.887074\pi$
$90$	−9.45857e7	−0.151962
$91$	2.14962e8	0.328605
$92$	−7.36300e7	−0.107154
$93$	−5.03309e8	−0.697689
$94$	8.29173e8	1.09539
$95$	1.04937e8	0.132183
$96$	8.49347e7	0.102062
$97$	−7.90680e8	−0.906834	−0.453417	−	0.891298i	$-0.649795\pi$
$97$	−7.90680e8	−0.906834	−0.453417	+	0.891298i	$0.649795\pi$
$98$	5.84876e8	0.640540
$99$	1.70563e8	0.178454
$100$	−2.92169e8	−0.292169
$101$	−5.38074e8	−0.514512	−0.257256	−	0.966343i	$-0.582818\pi$
$101$	−5.38074e8	−0.514512	−0.257256	+	0.966343i	$0.582818\pi$
$102$	−1.08243e8	−0.0990148
$103$	5.70585e8	0.499520	0.249760	−	0.968308i	$-0.419648\pi$
$103$	5.70585e8	0.499520	0.249760	+	0.968308i	$0.419648\pi$
$104$	4.51746e8	0.378656
$105$	1.42248e8	0.114208
$106$	−4.40149e8	−0.338628
$107$	−6.82999e8	−0.503725	−0.251862	−	0.967763i	$-0.581043\pi$
$107$	−6.82999e8	−0.503725	−0.251862	+	0.967763i	$0.581043\pi$
$108$	−1.36049e8	−0.0962250
$109$	5.78817e8	0.392755	0.196378	−	0.980528i	$-0.437082\pi$
$109$	5.78817e8	0.392755	0.196378	+	0.980528i	$0.437082\pi$
$110$	−3.74775e8	−0.244064
$111$	−1.14222e9	−0.714162
$112$	−1.27734e8	−0.0767052
$113$	−1.01384e9	−0.584946	−0.292473	−	0.956274i	$-0.594478\pi$
$113$	−1.01384e9	−0.584946	−0.292473	+	0.956274i	$0.594478\pi$
$114$	1.50938e8	0.0837005
$115$	−2.59149e8	−0.138169
$116$	1.77987e9	0.912701
$117$	−7.23611e8	−0.357000
$118$	7.15156e8	0.339572
$119$	1.62788e8	0.0744150
$120$	2.98938e8	0.131603
$121$	−1.68213e9	−0.713387
$122$	−5.38845e8	−0.220214
$123$	6.17372e8	0.243206
$124$	1.59071e9	0.604216
$125$	−2.78813e9	−1.02145
$126$	2.04605e8	0.0723184
$127$	3.67739e9	1.25436	0.627181	−	0.778873i	$-0.284208\pi$
$127$	3.67739e9	1.25436	0.627181	+	0.778873i	$0.284208\pi$
$128$	−2.68435e8	−0.0883883
$129$	8.26452e8	0.262763
$130$	1.58998e9	0.488253
$131$	3.08555e9	0.915403	0.457702	−	0.889106i	$-0.348673\pi$
$131$	3.08555e9	0.915403	0.457702	+	0.889106i	$0.348673\pi$
$132$	−5.39063e8	−0.154546
$133$	−2.26997e8	−0.0629055
$134$	1.21803e9	0.326353
$135$	−4.78840e8	−0.124076
$136$	3.42102e8	0.0857493
$137$	2.35433e9	0.570986	0.285493	−	0.958381i	$-0.407843\pi$
$137$	2.35433e9	0.570986	0.285493	+	0.958381i	$0.407843\pi$
$138$	−3.72752e8	−0.0874911
$139$	2.80837e9	0.638099	0.319050	−	0.947738i	$-0.396636\pi$
$139$	2.80837e9	0.638099	0.319050	+	0.947738i	$0.396636\pi$
$140$	−4.49575e8	−0.0989067
$141$	4.19769e9	0.894385
$142$	1.20828e9	0.249386
$143$	−2.86715e9	−0.573373
$144$	4.29982e8	0.0833333
$145$	6.26448e9	1.17687
$146$	6.56364e9	1.19552
$147$	2.96094e9	0.522999
$148$	3.60998e9	0.618483
$149$	−5.55931e9	−0.924023	−0.462011	−	0.886874i	$-0.652872\pi$
$149$	−5.55931e9	−0.924023	−0.462011	+	0.886874i	$0.652872\pi$
$150$	−1.47910e9	−0.238555
$151$	−8.79579e9	−1.37682	−0.688412	−	0.725320i	$-0.741692\pi$
$151$	−8.79579e9	−1.37682	−0.688412	+	0.725320i	$0.741692\pi$
$152$	−4.77040e8	−0.0724868
$153$	−5.47981e8	−0.0808452
$154$	8.10702e8	0.116150
$155$	5.59868e9	0.779099
$156$	2.28697e9	0.309171
$157$	2.22627e9	0.292435	0.146218	−	0.989252i	$-0.453290\pi$
$157$	2.22627e9	0.292435	0.146218	+	0.989252i	$0.453290\pi$
$158$	−5.54487e9	−0.707839
$159$	−2.22825e9	−0.276489
$160$	−9.44790e8	−0.113971
$161$	5.60584e8	0.0657543
$162$	−6.88748e8	−0.0785674
$163$	4.52424e9	0.501997	0.250999	−	0.967987i	$-0.419241\pi$
$163$	4.52424e9	0.501997	0.250999	+	0.967987i	$0.419241\pi$
$164$	−1.95120e9	−0.210623
$165$	−1.89730e9	−0.199277
$166$	1.17122e10	1.19716
$167$	1.76082e8	0.0175182	0.00875912	−	0.999962i	$-0.497212\pi$
$167$	1.76082e8	0.0175182	0.00875912	+	0.999962i	$0.497212\pi$
$168$	−6.46653e8	−0.0626296
$169$	1.55931e9	0.147042
$170$	1.20407e9	0.110568
$171$	7.64126e8	0.0683412
$172$	−2.61200e9	−0.227559
$173$	−1.90271e10	−1.61497	−0.807486	−	0.589886i	$-0.799173\pi$
$173$	−1.90271e10	−1.61497	−0.807486	+	0.589886i	$0.799173\pi$
$174$	9.01061e9	0.745217
$175$	2.22444e9	0.179287
$176$	1.70371e9	0.133841
$177$	3.62048e9	0.277259
$178$	1.77616e10	1.32615
$179$	−1.15308e10	−0.839503	−0.419751	−	0.907639i	$-0.637883\pi$
$179$	−1.15308e10	−0.839503	−0.419751	+	0.907639i	$0.637883\pi$
$180$	1.51337e9	0.107453
$181$	−5.07036e8	−0.0351144	−0.0175572	−	0.999846i	$-0.505589\pi$
$181$	−5.07036e8	−0.0351144	−0.0175572	+	0.999846i	$0.505589\pi$
$182$	−3.43939e9	−0.232359
$183$	−2.72790e9	−0.179804
$184$	1.17808e9	0.0757695
$185$	1.27058e10	0.797495
$186$	8.05295e9	0.493340
$187$	−2.17125e9	−0.129844
$188$	−1.32668e10	−0.774560
$189$	1.03581e9	0.0590477
$190$	−1.67900e9	−0.0934672
$191$	−1.57949e10	−0.858752	−0.429376	−	0.903126i	$-0.641266\pi$
$191$	−1.57949e10	−0.858752	−0.429376	+	0.903126i	$0.641266\pi$
$192$	−1.35895e9	−0.0721688
$193$	−2.43748e10	−1.26454	−0.632272	−	0.774746i	$-0.717878\pi$
$193$	−2.43748e10	−1.26454	−0.632272	+	0.774746i	$0.717878\pi$
$194$	1.26509e10	0.641229
$195$	8.04925e9	0.398657
$196$	−9.35802e9	−0.452930
$197$	−2.45125e10	−1.15955	−0.579775	−	0.814777i	$-0.696860\pi$
$197$	−2.45125e10	−1.15955	−0.579775	+	0.814777i	$0.696860\pi$
$198$	−2.72901e9	−0.126186
$199$	1.29044e10	0.583311	0.291655	−	0.956523i	$-0.405794\pi$
$199$	1.29044e10	0.583311	0.291655	+	0.956523i	$0.405794\pi$
$200$	4.67470e9	0.206594
$201$	6.16629e9	0.266466
$202$	8.60918e9	0.363815
$203$	−1.35511e10	−0.560071
$204$	1.73189e9	0.0700140
$205$	−6.86749e9	−0.271585
$206$	−9.12936e9	−0.353214
$207$	−1.88706e9	−0.0714362
$208$	−7.22794e9	−0.267750
$209$	3.02768e9	0.109762
$210$	−2.27597e9	−0.0807569
$211$	3.25664e10	1.13109	0.565547	−	0.824716i	$-0.308665\pi$
$211$	3.25664e10	1.13109	0.565547	+	0.824716i	$0.308665\pi$
$212$	7.04238e9	0.239446
$213$	6.11694e9	0.203623
$214$	1.09280e10	0.356187
$215$	−9.19323e9	−0.293424
$216$	2.17678e9	0.0680414
$217$	−1.21109e10	−0.370772
$218$	−9.26107e9	−0.277720
$219$	3.32284e10	0.976139
$220$	5.99640e9	0.172579
$221$	9.21150e9	0.259756
$222$	1.82755e10	0.504989
$223$	2.62532e10	0.710903	0.355451	−	0.934695i	$-0.384327\pi$
$223$	2.62532e10	0.710903	0.355451	+	0.934695i	$0.384327\pi$
$224$	2.04374e9	0.0542388
$225$	−7.48796e9	−0.194779
$226$	1.62214e10	0.413619
$227$	−1.97689e10	−0.494158	−0.247079	−	0.968995i	$-0.579471\pi$
$227$	−1.97689e10	−0.494158	−0.247079	+	0.968995i	$0.579471\pi$
$228$	−2.41502e9	−0.0591852
$229$	−3.36452e10	−0.808468	−0.404234	−	0.914656i	$-0.632462\pi$
$229$	−3.36452e10	−0.808468	−0.404234	+	0.914656i	$0.632462\pi$
$230$	4.14639e9	0.0977001
$231$	4.10418e9	0.0948358
$232$	−2.84780e10	−0.645377
$233$	4.57811e9	0.101762	0.0508808	−	0.998705i	$-0.483797\pi$
$233$	4.57811e9	0.101762	0.0508808	+	0.998705i	$0.483797\pi$
$234$	1.15778e10	0.252437
$235$	−4.66940e10	−0.998747
$236$	−1.14425e10	−0.240113
$237$	−2.80709e10	−0.577948
$238$	−2.60460e9	−0.0526194
$239$	−2.38479e9	−0.0472781	−0.0236391	−	0.999721i	$-0.507525\pi$
$239$	−2.38479e9	−0.0472781	−0.0236391	+	0.999721i	$0.507525\pi$
$240$	−4.78300e9	−0.0930572
$241$	5.01161e9	0.0956975	0.0478487	−	0.998855i	$-0.484763\pi$
$241$	5.01161e9	0.0956975	0.0478487	+	0.998855i	$0.484763\pi$
$242$	2.69141e10	0.504441
$243$	−3.48678e9	−0.0641500
$244$	8.62153e9	0.155715
$245$	−3.29366e10	−0.584026
$246$	−9.87796e9	−0.171973
$247$	−1.28449e10	−0.219580
$248$	−2.54513e10	−0.427245
$249$	5.92928e10	0.977474
$250$	4.46101e10	0.722276
$251$	−3.75043e10	−0.596416	−0.298208	−	0.954501i	$-0.596389\pi$
$251$	−3.75043e10	−0.596416	−0.298208	+	0.954501i	$0.596389\pi$
$252$	−3.27368e9	−0.0511368
$253$	−7.47704e9	−0.114733
$254$	−5.88383e10	−0.886969
$255$	6.09560e9	0.0902787
$256$	4.29497e9	0.0625000
$257$	−1.37923e11	−1.97214	−0.986069	−	0.166334i	$-0.946807\pi$
$257$	−1.37923e11	−1.97214	−0.986069	+	0.166334i	$0.946807\pi$
$258$	−1.32232e10	−0.185801
$259$	−2.74847e10	−0.379527
$260$	−2.54396e10	−0.345247
$261$	4.56162e10	0.608467
$262$	−4.93689e10	−0.647288
$263$	7.87614e10	1.01511	0.507554	−	0.861620i	$-0.330550\pi$
$263$	7.87614e10	1.01511	0.507554	+	0.861620i	$0.330550\pi$
$264$	8.62501e9	0.109280
$265$	2.47865e10	0.308751
$266$	3.63196e9	0.0444809
$267$	8.99179e10	1.08279
$268$	−1.94885e10	−0.230766
$269$	−5.59249e10	−0.651209	−0.325604	−	0.945506i	$-0.605568\pi$
$269$	−5.59249e10	−0.651209	−0.325604	+	0.945506i	$0.605568\pi$
$270$	7.66144e9	0.0877351
$271$	−1.74154e11	−1.96142	−0.980711	−	0.195464i	$-0.937379\pi$
$271$	−1.74154e11	−1.96142	−0.980711	+	0.195464i	$0.937379\pi$
$272$	−5.47363e9	−0.0606339
$273$	−1.74119e10	−0.189720
$274$	−3.76694e10	−0.403748
$275$	−2.96694e10	−0.312832
$276$	5.96403e9	0.0618655
$277$	7.82075e10	0.798159	0.399080	−	0.916916i	$-0.369330\pi$
$277$	7.82075e10	0.798159	0.399080	+	0.916916i	$0.369330\pi$
$278$	−4.49340e10	−0.451204
$279$	4.07680e10	0.402811
$280$	7.19319e9	0.0699376
$281$	6.59729e9	0.0631229	0.0315614	−	0.999502i	$-0.489952\pi$
$281$	6.59729e9	0.0631229	0.0315614	+	0.999502i	$0.489952\pi$
$282$	−6.71631e10	−0.632426
$283$	−5.51464e10	−0.511067	−0.255534	−	0.966800i	$-0.582251\pi$
$283$	−5.51464e10	−0.511067	−0.255534	+	0.966800i	$0.582251\pi$
$284$	−1.93326e10	−0.176342
$285$	−8.49993e9	−0.0763156
$286$	4.58743e10	0.405436
$287$	1.48555e10	0.129247
$288$	−6.87971e9	−0.0589256
$289$	6.97576e9	0.0588235
$290$	−1.00232e11	−0.832173
$291$	6.40451e10	0.523561
$292$	−1.05018e11	−0.845361
$293$	−3.43875e10	−0.272581	−0.136291	−	0.990669i	$-0.543518\pi$
$293$	−3.43875e10	−0.272581	−0.136291	+	0.990669i	$0.543518\pi$
$294$	−4.73750e10	−0.369816
$295$	−4.02732e10	−0.309611
$296$	−5.77597e10	−0.437333
$297$	−1.38156e10	−0.103031
$298$	8.89490e10	0.653383
$299$	3.17212e10	0.229525
$300$	2.36657e10	0.168684
$301$	1.98865e10	0.139640
$302$	1.40733e11	0.973562
$303$	4.35840e10	0.297054
$304$	7.63264e9	0.0512559
$305$	3.03445e10	0.200785
$306$	8.76770e9	0.0571662
$307$	2.53914e11	1.63141	0.815707	−	0.578465i	$-0.196348\pi$
$307$	2.53914e11	1.63141	0.815707	+	0.578465i	$0.196348\pi$
$308$	−1.29712e10	−0.0821302
$309$	−4.62174e10	−0.288398
$310$	−8.95788e10	−0.550906
$311$	−2.55183e10	−0.154679	−0.0773393	−	0.997005i	$-0.524642\pi$
$311$	−2.55183e10	−0.154679	−0.0773393	+	0.997005i	$0.524642\pi$
$312$	−3.65915e10	−0.218617
$313$	5.48416e10	0.322969	0.161484	−	0.986875i	$-0.448372\pi$
$313$	5.48416e10	0.322969	0.161484	+	0.986875i	$0.448372\pi$
$314$	−3.56204e10	−0.206783
$315$	−1.15221e10	−0.0659378
$316$	8.87179e10	0.500518
$317$	2.24499e11	1.24867	0.624336	−	0.781156i	$-0.285370\pi$
$317$	2.24499e11	1.24867	0.624336	+	0.781156i	$0.285370\pi$
$318$	3.56520e10	0.195507
$319$	1.80744e11	0.977251
$320$	1.51166e10	0.0805899
$321$	5.53229e10	0.290826
$322$	−8.96935e9	−0.0464953
$323$	−9.72726e9	−0.0497255
$324$	1.10200e10	0.0555556
$325$	1.25872e11	0.625826
$326$	−7.23878e10	−0.354966
$327$	−4.68842e10	−0.226757
$328$	3.12192e10	0.148933
$329$	1.01007e11	0.475302
$330$	3.03568e10	0.140910
$331$	2.56771e11	1.17576	0.587881	−	0.808947i	$-0.299962\pi$
$331$	2.56771e11	1.17576	0.587881	+	0.808947i	$0.299962\pi$
$332$	−1.87395e11	−0.846517
$333$	9.25199e10	0.412322
$334$	−2.81731e9	−0.0123873
$335$	−6.85922e10	−0.297559
$336$	1.03464e10	0.0442858
$337$	1.12141e11	0.473618	0.236809	−	0.971556i	$-0.423898\pi$
$337$	1.12141e11	0.473618	0.236809	+	0.971556i	$0.423898\pi$
$338$	−2.49490e10	−0.103975
$339$	8.21209e10	0.337718
$340$	−1.92651e10	−0.0781837
$341$	1.61534e11	0.646949
$342$	−1.22260e10	−0.0483245
$343$	1.49899e11	0.584758
$344$	4.17919e10	0.160909
$345$	2.09911e10	0.0797718
$346$	3.04434e11	1.14196
$347$	3.79942e10	0.140681	0.0703404	−	0.997523i	$-0.477591\pi$
$347$	3.79942e10	0.140681	0.0703404	+	0.997523i	$0.477591\pi$
$348$	−1.44170e11	−0.526948
$349$	2.71952e11	0.981246	0.490623	−	0.871372i	$-0.336769\pi$
$349$	2.71952e11	0.981246	0.490623	+	0.871372i	$0.336769\pi$
$350$	−3.55910e10	−0.126775
$351$	5.86125e10	0.206114
$352$	−2.72593e10	−0.0946396
$353$	3.27883e11	1.12391	0.561956	−	0.827167i	$-0.310049\pi$
$353$	3.27883e11	1.12391	0.561956	+	0.827167i	$0.310049\pi$
$354$	−5.79276e10	−0.196052
$355$	−6.80432e10	−0.227383
$356$	−2.84185e11	−0.937727
$357$	−1.31858e10	−0.0429635
$358$	1.84493e11	0.593618
$359$	−7.16409e10	−0.227633	−0.113817	−	0.993502i	$-0.536308\pi$
$359$	−7.16409e10	−0.227633	−0.113817	+	0.993502i	$0.536308\pi$
$360$	−2.42139e10	−0.0759809
$361$	−3.09124e11	−0.957965
$362$	8.11257e9	0.0248296
$363$	1.36253e11	0.411874
$364$	5.50302e10	0.164303
$365$	−3.69624e11	−1.09004
$366$	4.36465e10	0.127141
$367$	2.69983e11	0.776853	0.388427	−	0.921480i	$-0.373019\pi$
$367$	2.69983e11	0.776853	0.388427	+	0.921480i	$0.373019\pi$
$368$	−1.88493e10	−0.0535771
$369$	−5.00072e10	−0.140415
$370$	−2.03292e11	−0.563914
$371$	−5.36174e10	−0.146934
$372$	−1.28847e11	−0.348844
$373$	−2.51049e11	−0.671534	−0.335767	−	0.941945i	$-0.608995\pi$
$373$	−2.51049e11	−0.671534	−0.335767	+	0.941945i	$0.608995\pi$
$374$	3.47401e10	0.0918139
$375$	2.25839e11	0.589736
$376$	2.12268e11	0.547697
$377$	−7.66804e11	−1.95501
$378$	−1.65730e10	−0.0417530
$379$	4.28602e11	1.06703	0.533516	−	0.845790i	$-0.320870\pi$
$379$	4.28602e11	1.06703	0.533516	+	0.845790i	$0.320870\pi$
$380$	2.68640e10	0.0660913
$381$	−2.97869e11	−0.724207
$382$	2.52719e11	0.607229
$383$	3.82563e11	0.908467	0.454233	−	0.890883i	$-0.349913\pi$
$383$	3.82563e11	0.908467	0.454233	+	0.890883i	$0.349913\pi$
$384$	2.17433e10	0.0510310
$385$	−4.56538e10	−0.105902
$386$	3.89998e11	0.894168
$387$	−6.69426e10	−0.151706
$388$	−2.02414e11	−0.453417
$389$	6.42384e11	1.42240	0.711200	−	0.702990i	$-0.248152\pi$
$389$	6.42384e11	1.42240	0.711200	+	0.702990i	$0.248152\pi$
$390$	−1.28788e11	−0.281893
$391$	2.40221e10	0.0519775
$392$	1.49728e11	0.320270
$393$	−2.49930e11	−0.528508
$394$	3.92200e11	0.819926
$395$	3.12253e11	0.645387
$396$	4.36641e10	0.0892271
$397$	−7.12935e11	−1.44043	−0.720216	−	0.693750i	$-0.755957\pi$
$397$	−7.12935e11	−1.44043	−0.720216	+	0.693750i	$0.755957\pi$
$398$	−2.06471e11	−0.412463
$399$	1.83868e10	0.0363185
$400$	−7.47952e10	−0.146084
$401$	6.99689e11	1.35131	0.675656	−	0.737217i	$-0.263861\pi$
$401$	6.99689e11	1.35131	0.675656	+	0.737217i	$0.263861\pi$
$402$	−9.86606e10	−0.188420
$403$	−6.85306e11	−1.29423
$404$	−1.37747e11	−0.257256
$405$	3.87861e10	0.0716354
$406$	2.16818e11	0.396030
$407$	3.66590e11	0.662225
$408$	−2.77103e10	−0.0495074
$409$	−8.73573e11	−1.54363	−0.771817	−	0.635844i	$-0.780652\pi$
$409$	−8.73573e11	−1.54363	−0.771817	+	0.635844i	$0.780652\pi$
$410$	1.09880e11	0.192039
$411$	−1.90701e11	−0.329659
$412$	1.46070e11	0.249760
$413$	8.71178e10	0.147344
$414$	3.01929e10	0.0505130
$415$	−6.59557e11	−1.09153
$416$	1.15647e11	0.189328
$417$	−2.27478e11	−0.368407
$418$	−4.84429e10	−0.0776134
$419$	−8.22467e11	−1.30363	−0.651816	−	0.758377i	$-0.725993\pi$
$419$	−8.22467e11	−1.30363	−0.651816	+	0.758377i	$0.725993\pi$
$420$	3.64155e10	0.0571038
$421$	−5.36358e8	−0.000832118 0	−0.000416059	−	1.00000i	$-0.500132\pi$
$421$	−5.36358e8	−0.000832118 0	−0.000416059		1.00000i	$0.500132\pi$
$422$	−5.21063e11	−0.799805
$423$	−3.40013e11	−0.516373
$424$	−1.12678e11	−0.169314
$425$	9.53212e10	0.141723
$426$	−9.78711e10	−0.143983
$427$	−6.56403e10	−0.0955531
$428$	−1.74848e11	−0.251862
$429$	2.32239e11	0.331037
$430$	1.47092e11	0.207482
$431$	1.45550e11	0.203172	0.101586	−	0.994827i	$-0.467608\pi$
$431$	1.45550e11	0.203172	0.101586	+	0.994827i	$0.467608\pi$
$432$	−3.48285e10	−0.0481125
$433$	−1.25589e11	−0.171695	−0.0858475	−	0.996308i	$-0.527360\pi$
$433$	−1.25589e11	−0.171695	−0.0858475	+	0.996308i	$0.527360\pi$
$434$	1.93774e11	0.262176
$435$	−5.07423e11	−0.679467
$436$	1.48177e11	0.196378
$437$	−3.34973e10	−0.0439383
$438$	−5.31655e11	−0.690234
$439$	−1.32851e12	−1.70716	−0.853582	−	0.520958i	$-0.825575\pi$
$439$	−1.32851e12	−1.70716	−0.853582	+	0.520958i	$0.825575\pi$
$440$	−9.59424e10	−0.122032
$441$	−2.39836e11	−0.301954
$442$	−1.47384e11	−0.183675
$443$	−3.17602e11	−0.391801	−0.195901	−	0.980624i	$-0.562763\pi$
$443$	−3.17602e11	−0.391801	−0.195901	+	0.980624i	$0.562763\pi$
$444$	−2.92409e11	−0.357081
$445$	−1.00022e12	−1.20914
$446$	−4.20051e11	−0.502684
$447$	4.50304e11	0.533485
$448$	−3.26999e10	−0.0383526
$449$	−5.01367e11	−0.582166	−0.291083	−	0.956698i	$-0.594016\pi$
$449$	−5.01367e11	−0.582166	−0.291083	+	0.956698i	$0.594016\pi$
$450$	1.19807e11	0.137730
$451$	−1.98142e11	−0.225519
$452$	−2.59542e11	−0.292473
$453$	7.12459e11	0.794910
$454$	3.16302e11	0.349422
$455$	1.93685e11	0.211858
$456$	3.86402e10	0.0418502
$457$	−3.23430e11	−0.346863	−0.173431	−	0.984846i	$-0.555485\pi$
$457$	−3.23430e11	−0.346863	−0.173431	+	0.984846i	$0.555485\pi$
$458$	5.38323e11	0.571673
$459$	4.43865e10	0.0466760
$460$	−6.63423e10	−0.0690844
$461$	1.34674e12	1.38876	0.694381	−	0.719607i	$-0.255678\pi$
$461$	1.34674e12	1.38876	0.694381	+	0.719607i	$0.255678\pi$
$462$	−6.56668e10	−0.0670590
$463$	−7.31716e11	−0.739994	−0.369997	−	0.929033i	$-0.620641\pi$
$463$	−7.31716e11	−0.739994	−0.369997	+	0.929033i	$0.620641\pi$
$464$	4.55648e11	0.456350
$465$	−4.53493e11	−0.449813
$466$	−7.32497e10	−0.0719564
$467$	1.60468e12	1.56122	0.780608	−	0.625021i	$-0.214910\pi$
$467$	1.60468e12	1.56122	0.780608	+	0.625021i	$0.214910\pi$
$468$	−1.85244e11	−0.178500
$469$	1.48377e11	0.141608
$470$	7.47104e11	0.706221
$471$	−1.80328e11	−0.168838
$472$	1.83080e11	0.169786
$473$	−2.65245e11	−0.243653
$474$	4.49135e11	0.408671
$475$	−1.32919e11	−0.119803
$476$	4.16737e10	0.0372075
$477$	1.80488e11	0.159631
$478$	3.81567e10	0.0334307
$479$	−2.96397e11	−0.257255	−0.128628	−	0.991693i	$-0.541057\pi$
$479$	−2.96397e11	−0.257255	−0.128628	+	0.991693i	$0.541057\pi$
$480$	7.65280e10	0.0658014
$481$	−1.55525e12	−1.32479
$482$	−8.01857e10	−0.0676683
$483$	−4.54073e10	−0.0379633
$484$	−4.30625e11	−0.356694
$485$	−7.12420e11	−0.584653
$486$	5.57886e10	0.0453609
$487$	4.65516e11	0.375020	0.187510	−	0.982263i	$-0.439958\pi$
$487$	4.65516e11	0.375020	0.187510	+	0.982263i	$0.439958\pi$
$488$	−1.37944e11	−0.110107
$489$	−3.66463e11	−0.289828
$490$	5.26986e11	0.412969
$491$	2.92693e11	0.227272	0.113636	−	0.993522i	$-0.463750\pi$
$491$	2.92693e11	0.227272	0.113636	+	0.993522i	$0.463750\pi$
$492$	1.58047e11	0.121603
$493$	−5.80691e11	−0.442725
$494$	2.05518e11	0.155267
$495$	1.53681e11	0.115053
$496$	4.07221e11	0.302108
$497$	1.47189e11	0.108211
$498$	−9.48685e11	−0.691178
$499$	1.78163e12	1.28637	0.643185	−	0.765711i	$-0.277613\pi$
$499$	1.78163e12	1.28637	0.643185	+	0.765711i	$0.277613\pi$
$500$	−7.13762e11	−0.510726
$501$	−1.42626e10	−0.0101142
$502$	6.00069e11	0.421730
$503$	1.95659e12	1.36283	0.681417	−	0.731895i	$-0.261364\pi$
$503$	1.95659e12	1.36283	0.681417	+	0.731895i	$0.261364\pi$
$504$	5.23789e10	0.0361592
$505$	−4.84816e11	−0.331716
$506$	1.19633e11	0.0811283
$507$	−1.26304e11	−0.0848950
$508$	9.41412e11	0.627181
$509$	4.54550e11	0.300159	0.150080	−	0.988674i	$-0.452047\pi$
$509$	4.54550e11	0.300159	0.150080	+	0.988674i	$0.452047\pi$
$510$	−9.75295e10	−0.0638367
$511$	7.99560e11	0.518749
$512$	−6.87195e10	−0.0441942
$513$	−6.18942e10	−0.0394568
$514$	2.20677e12	1.39451
$515$	5.14110e11	0.322050
$516$	2.11572e11	0.131381
$517$	−1.34723e12	−0.829340
$518$	4.39756e11	0.268366
$519$	1.54120e12	0.932405
$520$	4.07034e11	0.244127
$521$	6.91402e11	0.411113	0.205556	−	0.978645i	$-0.434100\pi$
$521$	6.91402e11	0.411113	0.205556	+	0.978645i	$0.434100\pi$
$522$	−7.29860e11	−0.430251
$523$	−1.96595e12	−1.14899	−0.574493	−	0.818510i	$-0.694801\pi$
$523$	−1.96595e12	−1.14899	−0.574493	+	0.818510i	$0.694801\pi$
$524$	7.89902e11	0.457702
$525$	−1.80179e11	−0.103511
$526$	−1.26018e12	−0.717790
$527$	−5.18974e11	−0.293088
$528$	−1.38000e11	−0.0772729
$529$	−1.71843e12	−0.954072
$530$	−3.96584e11	−0.218320
$531$	−2.93259e11	−0.160076
$532$	−5.81114e10	−0.0314528
$533$	8.40615e11	0.451154
$534$	−1.43869e12	−0.765651
$535$	−6.15397e11	−0.324761
$536$	3.11816e11	0.163176
$537$	9.33998e11	0.484687
$538$	8.94799e11	0.460474
$539$	−9.50296e11	−0.484964
$540$	−1.22583e11	−0.0620381
$541$	6.17722e11	0.310031	0.155015	−	0.987912i	$-0.450457\pi$
$541$	6.17722e11	0.310031	0.155015	+	0.987912i	$0.450457\pi$
$542$	2.78646e12	1.38693
$543$	4.10699e10	0.0202733
$544$	8.75781e10	0.0428746
$545$	5.21527e11	0.253217
$546$	2.78590e11	0.134153
$547$	−1.45929e12	−0.696946	−0.348473	−	0.937319i	$-0.613300\pi$
$547$	−1.45929e12	−0.696946	−0.348473	+	0.937319i	$0.613300\pi$
$548$	6.02710e11	0.285493
$549$	2.20960e11	0.103810
$550$	4.74710e11	0.221206
$551$	8.09737e11	0.374250
$552$	−9.54245e10	−0.0437455
$553$	−6.75457e11	−0.307139
$554$	−1.25132e12	−0.564384
$555$	−1.02917e12	−0.460434
$556$	7.18944e11	0.319050
$557$	−2.73089e12	−1.20214	−0.601072	−	0.799195i	$-0.705259\pi$
$557$	−2.73089e12	−1.20214	−0.601072	+	0.799195i	$0.705259\pi$
$558$	−6.52289e11	−0.284830
$559$	1.12530e12	0.487432
$560$	−1.15091e11	−0.0494533
$561$	1.75872e11	0.0749657
$562$	−1.05557e11	−0.0446346
$563$	−1.46442e12	−0.614297	−0.307148	−	0.951662i	$-0.599375\pi$
$563$	−1.46442e12	−0.614297	−0.307148	+	0.951662i	$0.599375\pi$
$564$	1.07461e12	0.447192
$565$	−9.13490e11	−0.377126
$566$	8.82342e11	0.361379
$567$	−8.39008e10	−0.0340912
$568$	3.09321e11	0.124693
$569$	1.20243e12	0.480898	0.240449	−	0.970662i	$-0.422705\pi$
$569$	1.20243e12	0.480898	0.240449	+	0.970662i	$0.422705\pi$
$570$	1.35999e11	0.0539633
$571$	2.17441e12	0.856010	0.428005	−	0.903776i	$-0.359217\pi$
$571$	2.17441e12	0.856010	0.428005	+	0.903776i	$0.359217\pi$
$572$	−7.33989e11	−0.286687
$573$	1.27939e12	0.495801
$574$	−2.37689e11	−0.0913913
$575$	3.28253e11	0.125228
$576$	1.10075e11	0.0416667
$577$	−2.34293e12	−0.879972	−0.439986	−	0.898005i	$-0.645017\pi$
$577$	−2.34293e12	−0.879972	−0.439986	+	0.898005i	$0.645017\pi$
$578$	−1.11612e11	−0.0415945
$579$	1.97436e12	0.730085
$580$	1.60371e12	0.588435
$581$	1.42673e12	0.519458
$582$	−1.02472e12	−0.370214
$583$	7.15145e11	0.256381
$584$	1.68029e12	0.597760
$585$	−6.51989e11	−0.230165
$586$	5.50200e11	0.192744
$587$	3.53091e12	1.22748	0.613740	−	0.789508i	$-0.289664\pi$
$587$	3.53091e12	1.22748	0.613740	+	0.789508i	$0.289664\pi$
$588$	7.57999e11	0.261500
$589$	7.23677e11	0.247757
$590$	6.44371e11	0.218928
$591$	1.98551e12	0.669467
$592$	9.24156e11	0.309241
$593$	−2.00254e12	−0.665021	−0.332510	−	0.943100i	$-0.607896\pi$
$593$	−2.00254e12	−0.665021	−0.332510	+	0.943100i	$0.607896\pi$
$594$	2.21050e11	0.0728536
$595$	1.46675e11	0.0479768
$596$	−1.42318e12	−0.462011
$597$	−1.04526e12	−0.336775
$598$	−5.07539e11	−0.162298
$599$	2.63623e12	0.836686	0.418343	−	0.908289i	$-0.362611\pi$
$599$	2.63623e12	0.836686	0.418343	+	0.908289i	$0.362611\pi$
$600$	−3.78651e11	−0.119277
$601$	3.41223e12	1.06685	0.533425	−	0.845847i	$-0.320904\pi$
$601$	3.41223e12	1.06685	0.533425	+	0.845847i	$0.320904\pi$
$602$	−3.18184e11	−0.0987403
$603$	−4.99470e11	−0.153844
$604$	−2.25172e12	−0.688412
$605$	−1.51564e12	−0.459934
$606$	−6.97343e11	−0.210049
$607$	1.20751e12	0.361028	0.180514	−	0.983572i	$-0.442224\pi$
$607$	1.20751e12	0.361028	0.180514	+	0.983572i	$0.442224\pi$
$608$	−1.22122e11	−0.0362434
$609$	1.09764e12	0.323357
$610$	−4.85512e11	−0.141976
$611$	5.71558e12	1.65911
$612$	−1.40283e11	−0.0404226
$613$	−2.91601e12	−0.834099	−0.417049	−	0.908884i	$-0.636936\pi$
$613$	−2.91601e12	−0.834099	−0.417049	+	0.908884i	$0.636936\pi$
$614$	−4.06263e12	−1.15358
$615$	5.56266e11	0.156800
$616$	2.07540e11	0.0580748
$617$	−5.62865e11	−0.156358	−0.0781792	−	0.996939i	$-0.524911\pi$
$617$	−5.62865e11	−0.156358	−0.0781792	+	0.996939i	$0.524911\pi$
$618$	7.39478e11	0.203928
$619$	−2.45987e12	−0.673447	−0.336724	−	0.941604i	$-0.609319\pi$
$619$	−2.45987e12	−0.673447	−0.336724	+	0.941604i	$0.609319\pi$
$620$	1.43326e12	0.389550
$621$	1.52852e11	0.0412437
$622$	4.08293e11	0.109374
$623$	2.16365e12	0.575428
$624$	5.85463e11	0.154586
$625$	−2.83098e11	−0.0742125
$626$	−8.77466e11	−0.228373
$627$	−2.45242e11	−0.0633710
$628$	5.69926e11	0.146218
$629$	−1.17777e12	−0.300008
$630$	1.84354e11	0.0466250
$631$	−3.46216e12	−0.869390	−0.434695	−	0.900578i	$-0.643144\pi$
$631$	−3.46216e12	−0.869390	−0.434695	+	0.900578i	$0.643144\pi$
$632$	−1.41949e12	−0.353920
$633$	−2.63788e12	−0.653038
$634$	−3.59199e12	−0.882944
$635$	3.31341e12	0.808712
$636$	−5.70433e11	−0.138244
$637$	4.03161e12	0.970178
$638$	−2.89191e12	−0.691021
$639$	−4.95472e11	−0.117562
$640$	−2.41866e11	−0.0569857
$641$	−4.24397e12	−0.992912	−0.496456	−	0.868062i	$-0.665366\pi$
$641$	−4.24397e12	−0.992912	−0.496456	+	0.868062i	$0.665366\pi$
$642$	−8.85167e11	−0.205645
$643$	7.91930e12	1.82699	0.913497	−	0.406844i	$-0.133371\pi$
$643$	7.91930e12	1.82699	0.913497	+	0.406844i	$0.133371\pi$
$644$	1.43510e11	0.0328772
$645$	7.44652e11	0.169408
$646$	1.55636e11	0.0351612
$647$	2.49395e11	0.0559523	0.0279762	−	0.999609i	$-0.491094\pi$
$647$	2.49395e11	0.0559523	0.0279762	+	0.999609i	$0.491094\pi$
$648$	−1.76319e11	−0.0392837
$649$	−1.16197e12	−0.257095
$650$	−2.01395e12	−0.442526
$651$	9.80982e11	0.214065
$652$	1.15821e12	0.250999
$653$	1.63163e12	0.351167	0.175583	−	0.984465i	$-0.443819\pi$
$653$	1.63163e12	0.351167	0.175583	+	0.984465i	$0.443819\pi$
$654$	7.50147e11	0.160342
$655$	2.78015e12	0.590178
$656$	−4.99508e11	−0.105311
$657$	−2.69150e12	−0.563574
$658$	−1.61611e12	−0.336090
$659$	−4.22978e12	−0.873641	−0.436820	−	0.899549i	$-0.643896\pi$
$659$	−4.22978e12	−0.873641	−0.436820	+	0.899549i	$0.643896\pi$
$660$	−4.85708e11	−0.0996386
$661$	−2.12817e12	−0.433611	−0.216806	−	0.976215i	$-0.569564\pi$
$661$	−2.12817e12	−0.433611	−0.216806	+	0.976215i	$0.569564\pi$
$662$	−4.10833e12	−0.831390
$663$	−7.46132e11	−0.149970
$664$	2.99831e12	0.598578
$665$	−2.04530e11	−0.0405564
$666$	−1.48032e12	−0.291556
$667$	−1.99970e12	−0.391199
$668$	4.50770e10	0.00875912
$669$	−2.12651e12	−0.410440
$670$	1.09747e12	0.210406
$671$	8.75506e11	0.166728
$672$	−1.65543e11	−0.0313148
$673$	4.23872e12	0.796465	0.398232	−	0.917285i	$-0.369624\pi$
$673$	4.23872e12	0.796465	0.398232	+	0.917285i	$0.369624\pi$
$674$	−1.79425e12	−0.334898
$675$	6.06525e11	0.112456
$676$	3.99184e11	0.0735212
$677$	−7.17586e12	−1.31288	−0.656440	−	0.754378i	$-0.727939\pi$
$677$	−7.17586e12	−1.31288	−0.656440	+	0.754378i	$0.727939\pi$
$678$	−1.31393e12	−0.238803
$679$	1.54109e12	0.278236
$680$	3.08242e11	0.0552842
$681$	1.60128e12	0.285302
$682$	−2.58455e12	−0.457462
$683$	−8.19336e12	−1.44068	−0.720342	−	0.693619i	$-0.756015\pi$
$683$	−8.19336e12	−1.44068	−0.720342	+	0.693619i	$0.756015\pi$
$684$	1.95616e11	0.0341706
$685$	2.12131e12	0.368126
$686$	−2.39839e12	−0.413486
$687$	2.72526e12	0.466769
$688$	−6.68671e11	−0.113780
$689$	−3.03399e12	−0.512894
$690$	−3.35858e11	−0.0564072
$691$	8.75619e12	1.46105	0.730523	−	0.682888i	$-0.239276\pi$
$691$	8.75619e12	1.46105	0.730523	+	0.682888i	$0.239276\pi$
$692$	−4.87094e12	−0.807486
$693$	−3.32438e11	−0.0547535
$694$	−6.07908e11	−0.0994764
$695$	2.53041e12	0.411395
$696$	2.30672e12	0.372608
$697$	6.36587e11	0.102167
$698$	−4.35123e12	−0.693846
$699$	−3.70827e11	−0.0587521
$700$	5.69456e11	0.0896435
$701$	−8.05440e12	−1.25980	−0.629901	−	0.776675i	$-0.716905\pi$
$701$	−8.05440e12	−1.25980	−0.629901	+	0.776675i	$0.716905\pi$
$702$	−9.37799e11	−0.145745
$703$	1.64233e12	0.253607
$704$	4.36149e11	0.0669203
$705$	3.78221e12	0.576627
$706$	−5.24612e12	−0.794725
$707$	1.04874e12	0.157863
$708$	9.26842e11	0.138630
$709$	−5.52069e12	−0.820513	−0.410257	−	0.911970i	$-0.634561\pi$
$709$	−5.52069e12	−0.820513	−0.410257	+	0.911970i	$0.634561\pi$
$710$	1.08869e12	0.160784
$711$	2.27374e12	0.333679
$712$	4.54696e12	0.663073
$713$	−1.78716e12	−0.258977
$714$	2.10973e11	0.0303798
$715$	−2.58336e12	−0.369665
$716$	−2.95189e12	−0.419751
$717$	1.93168e11	0.0272960
$718$	1.14625e12	0.160961
$719$	1.33634e13	1.86483	0.932413	−	0.361393i	$-0.117699\pi$
$719$	1.33634e13	1.86483	0.932413	+	0.361393i	$0.117699\pi$
$720$	3.87423e11	0.0537266
$721$	−1.11211e12	−0.153263
$722$	4.94598e12	0.677384
$723$	−4.05940e11	−0.0552510
$724$	−1.29801e11	−0.0175572
$725$	−7.93493e12	−1.06665
$726$	−2.18004e12	−0.291239
$727$	−2.50036e12	−0.331969	−0.165985	−	0.986128i	$-0.553080\pi$
$727$	−2.50036e12	−0.331969	−0.165985	+	0.986128i	$0.553080\pi$
$728$	−8.80483e11	−0.116180
$729$	2.82430e11	0.0370370
$730$	5.91399e12	0.770775
$731$	8.52174e11	0.110382
$732$	−6.98344e11	−0.0899020
$733$	1.29133e12	0.165222	0.0826110	−	0.996582i	$-0.473674\pi$
$733$	1.29133e12	0.165222	0.0826110	+	0.996582i	$0.473674\pi$
$734$	−4.31973e12	−0.549318
$735$	2.66787e12	0.337187
$736$	3.01588e11	0.0378848
$737$	−1.97904e12	−0.247087
$738$	8.00115e11	0.0992884
$739$	4.95427e12	0.611054	0.305527	−	0.952183i	$-0.401167\pi$
$739$	4.95427e12	0.611054	0.305527	+	0.952183i	$0.401167\pi$
$740$	3.25268e12	0.398748
$741$	1.04043e12	0.126775
$742$	8.57878e11	0.103898
$743$	−6.63545e12	−0.798768	−0.399384	−	0.916784i	$-0.630776\pi$
$743$	−6.63545e12	−0.798768	−0.399384	+	0.916784i	$0.630776\pi$
$744$	2.06155e12	0.246670
$745$	−5.00906e12	−0.595735
$746$	4.01678e12	0.474846
$747$	−4.80272e12	−0.564345
$748$	−5.55841e11	−0.0649222
$749$	1.33121e12	0.154553
$750$	−3.61342e12	−0.417006
$751$	1.26932e13	1.45610	0.728049	−	0.685525i	$-0.240427\pi$
$751$	1.26932e13	1.45610	0.728049	+	0.685525i	$0.240427\pi$
$752$	−3.39629e12	−0.387280
$753$	3.03785e12	0.344341
$754$	1.22689e13	1.38240
$755$	−7.92520e12	−0.887665
$756$	2.65168e11	0.0295239
$757$	3.41823e12	0.378329	0.189165	−	0.981945i	$-0.439422\pi$
$757$	3.41823e12	0.378329	0.189165	+	0.981945i	$0.439422\pi$
$758$	−6.85762e12	−0.754505
$759$	6.05640e11	0.0662410
$760$	−4.29824e11	−0.0467336
$761$	−1.74328e13	−1.88424	−0.942119	−	0.335278i	$-0.891170\pi$
$761$	−1.74328e13	−1.88424	−0.942119	+	0.335278i	$0.891170\pi$
$762$	4.76590e12	0.512092
$763$	−1.12815e12	−0.120506
$764$	−4.04350e12	−0.429376
$765$	−4.93743e11	−0.0521224
$766$	−6.12101e12	−0.642383
$767$	4.92964e12	0.514323
$768$	−3.47892e11	−0.0360844
$769$	−9.93254e12	−1.02422	−0.512108	−	0.858921i	$-0.671135\pi$
$769$	−9.93254e12	−1.02422	−0.512108	+	0.858921i	$0.671135\pi$
$770$	7.30460e11	0.0748839
$771$	1.11718e13	1.13861
$772$	−6.23996e12	−0.632272
$773$	1.05153e13	1.05928	0.529642	−	0.848221i	$-0.322326\pi$
$773$	1.05153e13	1.05928	0.529642	+	0.848221i	$0.322326\pi$
$774$	1.07108e12	0.107272
$775$	−7.09159e12	−0.706132
$776$	3.23863e12	0.320614
$777$	2.22626e12	0.219120
$778$	−1.02782e13	−1.00579
$779$	−8.87681e11	−0.0863652
$780$	2.06061e12	0.199329
$781$	−1.96320e12	−0.188814
$782$	−3.84353e11	−0.0367536
$783$	−3.69491e12	−0.351299
$784$	−2.39565e12	−0.226465
$785$	2.00592e12	0.188539
$786$	3.99888e12	0.373712
$787$	7.04956e12	0.655052	0.327526	−	0.944842i	$-0.393785\pi$
$787$	7.04956e12	0.655052	0.327526	+	0.944842i	$0.393785\pi$
$788$	−6.27520e12	−0.579775
$789$	−6.37967e12	−0.586073
$790$	−4.99605e12	−0.456357
$791$	1.97603e12	0.179474
$792$	−6.98626e11	−0.0630931
$793$	−3.71432e12	−0.333541
$794$	1.14070e13	1.01854
$795$	−2.00771e12	−0.178258
$796$	3.30353e12	0.291655
$797$	−4.59176e12	−0.403104	−0.201552	−	0.979478i	$-0.564598\pi$
$797$	−4.59176e12	−0.403104	−0.201552	+	0.979478i	$0.564598\pi$
$798$	−2.94189e11	−0.0256811
$799$	4.32834e12	0.375717
$800$	1.19672e12	0.103297
$801$	−7.28335e12	−0.625151
$802$	−1.11950e13	−0.955521
$803$	−1.06645e13	−0.905149
$804$	1.57857e12	0.133233
$805$	5.05099e11	0.0423931
$806$	1.09649e13	0.915160
$807$	4.52992e12	0.375976
$808$	2.20395e12	0.181907
$809$	−5.10874e12	−0.419320	−0.209660	−	0.977774i	$-0.567236\pi$
$809$	−5.10874e12	−0.419320	−0.209660	+	0.977774i	$0.567236\pi$
$810$	−6.20577e11	−0.0506539
$811$	8.88852e12	0.721499	0.360749	−	0.932663i	$-0.382521\pi$
$811$	8.88852e12	0.721499	0.360749	+	0.932663i	$0.382521\pi$
$812$	−3.46909e12	−0.280036
$813$	1.41065e13	1.13243
$814$	−5.86543e12	−0.468263
$815$	4.07644e12	0.323647
$816$	4.43364e11	0.0350070
$817$	−1.18830e12	−0.0933100
$818$	1.39772e13	1.09151
$819$	1.41036e12	0.109535
$820$	−1.75808e12	−0.135792
$821$	−7.63232e12	−0.586290	−0.293145	−	0.956068i	$-0.594702\pi$
$821$	−7.63232e12	−0.586290	−0.293145	+	0.956068i	$0.594702\pi$
$822$	3.05122e12	0.233104
$823$	−7.82102e12	−0.594243	−0.297121	−	0.954840i	$-0.596027\pi$
$823$	−7.82102e12	−0.594243	−0.297121	+	0.954840i	$0.596027\pi$
$824$	−2.33712e12	−0.176607
$825$	2.40322e12	0.180614
$826$	−1.39388e12	−0.104188
$827$	−1.90083e13	−1.41308	−0.706542	−	0.707671i	$-0.749746\pi$
$827$	−1.90083e13	−1.41308	−0.706542	+	0.707671i	$0.749746\pi$
$828$	−4.83086e11	−0.0357181
$829$	1.50064e13	1.10352	0.551760	−	0.834003i	$-0.313956\pi$
$829$	1.50064e13	1.10352	0.551760	+	0.834003i	$0.313956\pi$
$830$	1.05529e13	0.771829
$831$	−6.33481e12	−0.460818
$832$	−1.85035e12	−0.133875
$833$	3.05309e12	0.219704
$834$	3.63965e12	0.260503
$835$	1.58654e11	0.0112943
$836$	7.75086e11	0.0548809
$837$	−3.30221e12	−0.232563
$838$	1.31595e13	0.921807
$839$	1.90184e13	1.32509	0.662544	−	0.749023i	$-0.269477\pi$
$839$	1.90184e13	1.32509	0.662544	+	0.749023i	$0.269477\pi$
$840$	−5.82649e11	−0.0403785
$841$	3.38320e13	2.33209
$842$	8.58172e9	0.000588396 0
$843$	−5.34380e11	−0.0364440
$844$	8.33701e12	0.565547
$845$	1.40497e12	0.0948011
$846$	5.44021e12	0.365131
$847$	3.27858e12	0.218882
$848$	1.80285e12	0.119723
$849$	4.46686e12	0.295065
$850$	−1.52514e12	−0.100213
$851$	−4.05583e12	−0.265092
$852$	1.56594e12	0.101811
$853$	−1.02067e13	−0.660107	−0.330054	−	0.943962i	$-0.607067\pi$
$853$	−1.02067e13	−0.660107	−0.330054	+	0.943962i	$0.607067\pi$
$854$	1.05024e12	0.0675663
$855$	6.88494e11	0.0440609
$856$	2.79756e12	0.178094
$857$	1.39075e12	0.0880716	0.0440358	−	0.999030i	$-0.485978\pi$
$857$	1.39075e12	0.0880716	0.0440358	+	0.999030i	$0.485978\pi$
$858$	−3.71582e12	−0.234079
$859$	−2.42866e13	−1.52194	−0.760971	−	0.648786i	$-0.775277\pi$
$859$	−2.42866e13	−1.52194	−0.760971	+	0.648786i	$0.775277\pi$
$860$	−2.35347e12	−0.146712
$861$	−1.20330e12	−0.0746207
$862$	−2.32879e12	−0.143664
$863$	2.50537e12	0.153753	0.0768764	−	0.997041i	$-0.475505\pi$
$863$	2.50537e12	0.153753	0.0768764	+	0.997041i	$0.475505\pi$
$864$	5.57256e11	0.0340207
$865$	−1.71438e13	−1.04120
$866$	2.00943e12	0.121407
$867$	−5.65036e11	−0.0339618
$868$	−3.10039e12	−0.185386
$869$	9.00920e12	0.535917
$870$	8.11876e12	0.480456
$871$	8.39603e12	0.494302
$872$	−2.37083e12	−0.138860
$873$	−5.18765e12	−0.302278
$874$	5.35957e11	0.0310691
$875$	5.43425e12	0.313403
$876$	8.50648e12	0.488069
$877$	1.34515e13	0.767845	0.383922	−	0.923365i	$-0.374573\pi$
$877$	1.34515e13	0.767845	0.383922	+	0.923365i	$0.374573\pi$
$878$	2.12562e13	1.20715
$879$	2.78539e12	0.157375
$880$	1.53508e12	0.0862896
$881$	2.43085e13	1.35946	0.679729	−	0.733464i	$-0.262097\pi$
$881$	2.43085e13	1.35946	0.679729	+	0.733464i	$0.262097\pi$
$882$	3.83737e12	0.213513
$883$	5.45854e11	0.0302171	0.0151086	−	0.999886i	$-0.495191\pi$
$883$	5.45854e11	0.0302171	0.0151086	+	0.999886i	$0.495191\pi$
$884$	2.35814e12	0.129878
$885$	3.26213e12	0.178754
$886$	5.08163e12	0.277045
$887$	−2.37122e12	−0.128622	−0.0643111	−	0.997930i	$-0.520485\pi$
$887$	−2.37122e12	−0.128622	−0.0643111	+	0.997930i	$0.520485\pi$
$888$	4.67854e12	0.252494
$889$	−7.16747e12	−0.384865
$890$	1.60036e13	0.854992
$891$	1.11906e12	0.0594847
$892$	6.72082e12	0.355451
$893$	−6.03560e12	−0.317606
$894$	−7.20487e12	−0.377231
$895$	−1.03895e13	−0.541243
$896$	5.23198e11	0.0271194
$897$	−2.56942e12	−0.132516
$898$	8.02187e12	0.411654
$899$	4.32015e13	2.20587
$900$	−1.91692e12	−0.0973896
$901$	−2.29760e12	−0.116148
$902$	3.17028e12	0.159466
$903$	−1.61081e12	−0.0806211
$904$	4.15268e12	0.206809
$905$	−4.56850e11	−0.0226389
$906$	−1.13993e13	−0.562086
$907$	4.55246e12	0.223364	0.111682	−	0.993744i	$-0.464376\pi$
$907$	4.55246e12	0.223364	0.111682	+	0.993744i	$0.464376\pi$
$908$	−5.06083e12	−0.247079
$909$	−3.53030e12	−0.171504
$910$	−3.09896e12	−0.149806
$911$	−2.30228e13	−1.10746	−0.553728	−	0.832698i	$-0.686795\pi$
$911$	−2.30228e13	−1.10746	−0.553728	+	0.832698i	$0.686795\pi$
$912$	−6.18244e11	−0.0295926
$913$	−1.90297e13	−0.906387
$914$	5.17488e12	0.245269
$915$	−2.45790e12	−0.115923
$916$	−8.61316e12	−0.404234
$917$	−6.01395e12	−0.280865
$918$	−7.10184e11	−0.0330049
$919$	2.72003e13	1.25792	0.628961	−	0.777437i	$-0.283480\pi$
$919$	2.72003e13	1.25792	0.628961	+	0.777437i	$0.283480\pi$
$920$	1.06148e12	0.0488500
$921$	−2.05670e13	−0.941897
$922$	−2.15478e13	−0.982004
$923$	8.32883e12	0.377726
$924$	1.05067e12	0.0474179
$925$	−1.60938e13	−0.722805
$926$	1.17075e13	0.523255
$927$	3.74361e12	0.166507
$928$	−7.29036e12	−0.322688
$929$	3.68488e13	1.62313	0.811563	−	0.584265i	$-0.198617\pi$
$929$	3.68488e13	1.62313	0.811563	+	0.584265i	$0.198617\pi$
$930$	7.25589e12	0.318066
$931$	−4.25734e12	−0.185723
$932$	1.17200e12	0.0508808
$933$	2.06698e12	0.0893038
$934$	−2.56749e13	−1.10395
$935$	−1.95635e12	−0.0837132
$936$	2.96391e12	0.126219
$937$	4.24848e13	1.80055	0.900275	−	0.435321i	$-0.143365\pi$
$937$	4.24848e13	1.80055	0.900275	+	0.435321i	$0.143365\pi$
$938$	−2.37402e12	−0.100132
$939$	−4.44217e12	−0.186466
$940$	−1.19537e13	−0.499374
$941$	−3.52687e13	−1.46635	−0.733173	−	0.680043i	$-0.761961\pi$
$941$	−3.52687e13	−1.46635	−0.733173	+	0.680043i	$0.761961\pi$
$942$	2.88525e12	0.119386
$943$	2.19218e12	0.0902764
$944$	−2.92928e12	−0.120057
$945$	9.33290e11	0.0380692
$946$	4.24392e12	0.172289
$947$	−7.57599e12	−0.306101	−0.153050	−	0.988218i	$-0.548910\pi$
$947$	−7.57599e12	−0.306101	−0.153050	+	0.988218i	$0.548910\pi$
$948$	−7.18615e12	−0.288974
$949$	4.52439e13	1.81076
$950$	2.12671e12	0.0847134
$951$	−1.81844e13	−0.720921
$952$	−6.66779e11	−0.0263097
$953$	−3.20452e13	−1.25848	−0.629239	−	0.777212i	$-0.716633\pi$
$953$	−3.20452e13	−1.25848	−0.629239	+	0.777212i	$0.716633\pi$
$954$	−2.88782e12	−0.112876
$955$	−1.42316e13	−0.553654
$956$	−6.10507e11	−0.0236391
$957$	−1.46403e13	−0.564216
$958$	4.74236e12	0.181907
$959$	−4.58875e12	−0.175191
$960$	−1.22445e12	−0.0465286
$961$	1.21704e13	0.460308
$962$	2.48840e13	0.936768
$963$	−4.48116e12	−0.167908
$964$	1.28297e12	0.0478487
$965$	−2.19623e13	−0.815276
$966$	7.26517e11	0.0268441
$967$	−4.96666e13	−1.82661	−0.913305	−	0.407277i	$-0.866478\pi$
$967$	−4.96666e13	−1.82661	−0.913305	+	0.407277i	$0.866478\pi$
$968$	6.89000e12	0.252220
$969$	7.87908e11	0.0287090
$970$	1.13987e13	0.413412
$971$	−3.98179e13	−1.43745	−0.718724	−	0.695296i	$-0.755273\pi$
$971$	−3.98179e13	−1.43745	−0.718724	+	0.695296i	$0.755273\pi$
$972$	−8.92617e11	−0.0320750
$973$	−5.47370e12	−0.195782
$974$	−7.44826e12	−0.265179
$975$	−1.01956e13	−0.361321
$976$	2.20711e12	0.0778574
$977$	1.62538e13	0.570729	0.285365	−	0.958419i	$-0.407885\pi$
$977$	1.62538e13	0.570729	0.285365	+	0.958419i	$0.407885\pi$
$978$	5.86341e12	0.204940
$979$	−2.88587e13	−1.00405
$980$	−8.43178e12	−0.292013
$981$	3.79762e12	0.130918
$982$	−4.68309e12	−0.160705
$983$	3.45100e13	1.17884	0.589419	−	0.807828i	$-0.299357\pi$
$983$	3.45100e13	1.17884	0.589419	+	0.807828i	$0.299357\pi$
$984$	−2.52876e12	−0.0859863
$985$	−2.20863e13	−0.747584
$986$	9.29105e12	0.313054
$987$	−8.18157e12	−0.274416
$988$	−3.28829e12	−0.109790
$989$	2.93459e12	0.0975358
$990$	−2.45890e12	−0.0813546
$991$	−3.69472e12	−0.121689	−0.0608443	−	0.998147i	$-0.519379\pi$
$991$	−3.69472e12	−0.121689	−0.0608443	+	0.998147i	$0.519379\pi$
$992$	−6.51553e12	−0.213623
$993$	−2.07984e13	−0.678827
$994$	−2.35503e12	−0.0765168
$995$	1.16272e13	0.376072
$996$	1.51790e13	0.488737
$997$	−5.00400e13	−1.60394	−0.801971	−	0.597363i	$-0.796215\pi$
$997$	−5.00400e13	−1.60394	−0.801971	+	0.597363i	$0.796215\pi$
$998$	−2.85061e13	−0.909601
$999$	−7.49411e12	−0.238054

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	102.10.a.h.1.3	✓	4
3.2	odd	2		306.10.a.m.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
102.10.a.h.1.3	✓	4	1.1	even	1	trivial
306.10.a.m.1.2		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-16.0000 q^{2} -81.0000 q^{3} +256.000 q^{4} +901.022 q^{5} +1296.00 q^{6} -1949.06 q^{7} -4096.00 q^{8} +6561.00 q^{9} -14416.4 q^{10} +25996.5 q^{11} -20736.0 q^{12} -110290. q^{13} +31185.0 q^{14} -72982.8 q^{15} +65536.0 q^{16} -83521.0 q^{17} -104976. q^{18} +116465. q^{19} +230662. q^{20} +157874. q^{21} -415944. q^{22} -287617. q^{23} +331776. q^{24} -1.14128e6 q^{25} +1.76463e6 q^{26} -531441. q^{27} -498960. q^{28} +6.95263e6 q^{29} +1.16772e6 q^{30} +6.21369e6 q^{31} -1.04858e6 q^{32} -2.10572e6 q^{33} +1.33634e6 q^{34} -1.75615e6 q^{35} +1.67962e6 q^{36} +1.41015e7 q^{37} -1.86344e6 q^{38} +8.93346e6 q^{39} -3.69059e6 q^{40} -7.62188e6 q^{41} -2.52599e6 q^{42} -1.02031e7 q^{43} +6.65510e6 q^{44} +5.91161e6 q^{45} +4.60187e6 q^{46} -5.18233e7 q^{47} -5.30842e6 q^{48} -3.65548e7 q^{49} +1.82605e7 q^{50} +6.76520e6 q^{51} -2.82342e7 q^{52} +2.75093e7 q^{53} +8.50306e6 q^{54} +2.34234e7 q^{55} +7.98337e6 q^{56} -9.43365e6 q^{57} -1.11242e8 q^{58} -4.46972e7 q^{59} -1.86836e7 q^{60} +3.36778e7 q^{61} -9.94191e7 q^{62} -1.27878e7 q^{63} +1.67772e7 q^{64} -9.93734e7 q^{65} +3.36915e7 q^{66} -7.61270e7 q^{67} -2.13814e7 q^{68} +2.32970e7 q^{69} +2.80984e7 q^{70} -7.55178e7 q^{71} -2.68739e7 q^{72} -4.10228e8 q^{73} -2.25624e8 q^{74} +9.24440e7 q^{75} +2.98150e7 q^{76} -5.06689e7 q^{77} -1.42935e8 q^{78} +3.46554e8 q^{79} +5.90494e7 q^{80} +4.30467e7 q^{81} +1.21950e8 q^{82} -7.32010e8 q^{83} +4.04158e7 q^{84} -7.52543e7 q^{85} +1.63250e8 q^{86} -5.63163e8 q^{87} -1.06482e8 q^{88} -1.11010e9 q^{89} -9.45857e7 q^{90} +2.14962e8 q^{91} -7.36300e7 q^{92} -5.03309e8 q^{93} +8.29173e8 q^{94} +1.04937e8 q^{95} +8.49347e7 q^{96} -7.90680e8 q^{97} +5.84876e8 q^{98} +1.70563e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 64 q^{2} - 324 q^{3} + 1024 q^{4} - 942 q^{5} + 5184 q^{6} - 2084 q^{7} - 16384 q^{8} + 26244 q^{9} + 15072 q^{10} - 68450 q^{11} - 82944 q^{12} + 64722 q^{13} + 33344 q^{14} + 76302 q^{15} + 262144 q^{16}+ \cdots - 449100450 q^{99}+O(q^{100}) \) 4 * q - 64 * q^2 - 324 * q^3 + 1024 * q^4 - 942 * q^5 + 5184 * q^6 - 2084 * q^7 - 16384 * q^8 + 26244 * q^9 + 15072 * q^10 - 68450 * q^11 - 82944 * q^12 + 64722 * q^13 + 33344 * q^14 + 76302 * q^15 + 262144 * q^16 - 334084 * q^17 - 419904 * q^18 - 203854 * q^19 - 241152 * q^20 + 168804 * q^21 + 1095200 * q^22 + 2505834 * q^23 + 1327104 * q^24 + 6830638 * q^25 - 1035552 * q^26 - 2125764 * q^27 - 533504 * q^28 - 885976 * q^29 - 1220832 * q^30 + 11921296 * q^31 - 4194304 * q^32 + 5544450 * q^33 + 5345344 * q^34 + 38217208 * q^35 + 6718464 * q^36 + 14106124 * q^37 + 3261664 * q^38 - 5242482 * q^39 + 3858432 * q^40 - 14158146 * q^41 - 2700864 * q^42 + 26846790 * q^43 - 17523200 * q^44 - 6180462 * q^45 - 40093344 * q^46 - 35033332 * q^47 - 21233664 * q^48 + 46195148 * q^49 - 109290208 * q^50 + 27060804 * q^51 + 16568832 * q^52 - 95616880 * q^53 + 34012224 * q^54 - 216054070 * q^55 + 8536064 * q^56 + 16512174 * q^57 + 14175616 * q^58 - 102623436 * q^59 + 19533312 * q^60 - 196381204 * q^61 - 190740736 * q^62 - 13673124 * q^63 + 67108864 * q^64 - 748875142 * q^65 - 88711200 * q^66 + 44116808 * q^67 - 85525504 * q^68 - 202972554 * q^69 - 611475328 * q^70 - 391106100 * q^71 - 107495424 * q^72 - 325868288 * q^73 - 225697984 * q^74 - 553281678 * q^75 - 52186624 * q^76 - 1690587600 * q^77 + 83879712 * q^78 + 108839048 * q^79 - 61734912 * q^80 + 172186884 * q^81 + 226530336 * q^82 - 319973836 * q^83 + 43213824 * q^84 + 78676782 * q^85 - 429548640 * q^86 + 71764056 * q^87 + 280371200 * q^88 - 829727740 * q^89 + 98887392 * q^90 - 1890352424 * q^91 + 641493504 * q^92 - 965624976 * q^93 + 560533312 * q^94 - 571320138 * q^95 + 339738624 * q^96 - 354724644 * q^97 - 739122368 * q^98 - 449100450 * q^99

Introduction

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