LMFDB - Embedded newform 105.10.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,10,Mod(1,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("105.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	105.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$54.0787627972$
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} - 988x^{2} - 844x + 192256 $ x^4 - x^3 - 988x^2 - 844x + 192256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 5^{2} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-24.8635$ of defining polynomial
Character	$\chi$	$=$	105.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+16.5158 q^{2} -81.0000 q^{3} -239.228 q^{4} +625.000 q^{5} -1337.78 q^{6} +2401.00 q^{7} -12407.1 q^{8} +6561.00 q^{9} +10322.4 q^{10} -12829.4 q^{11} +19377.5 q^{12} +138879. q^{13} +39654.5 q^{14} -50625.0 q^{15} -82429.1 q^{16} +207978. q^{17} +108360. q^{18} -912465. q^{19} -149518. q^{20} -194481. q^{21} -211888. q^{22} +1.26892e6 q^{23} +1.00498e6 q^{24} +390625. q^{25} +2.29369e6 q^{26} -531441. q^{27} -574387. q^{28} -2.77726e6 q^{29} -836113. q^{30} -6.41934e6 q^{31} +4.99107e6 q^{32} +1.03918e6 q^{33} +3.43492e6 q^{34} +1.50062e6 q^{35} -1.56958e6 q^{36} +1.15749e7 q^{37} -1.50701e7 q^{38} -1.12492e7 q^{39} -7.75446e6 q^{40} -1.40653e7 q^{41} -3.21201e6 q^{42} -2.63525e7 q^{43} +3.06916e6 q^{44} +4.10062e6 q^{45} +2.09573e7 q^{46} -5.53931e7 q^{47} +6.67676e6 q^{48} +5.76480e6 q^{49} +6.45149e6 q^{50} -1.68462e7 q^{51} -3.32236e7 q^{52} -7.98630e7 q^{53} -8.77718e6 q^{54} -8.01838e6 q^{55} -2.97895e7 q^{56} +7.39097e7 q^{57} -4.58686e7 q^{58} +1.37206e7 q^{59} +1.21109e7 q^{60} -1.81995e8 q^{61} -1.06021e8 q^{62} +1.57530e7 q^{63} +1.24635e8 q^{64} +8.67991e7 q^{65} +1.71629e7 q^{66} +2.08956e8 q^{67} -4.97541e7 q^{68} -1.02783e8 q^{69} +2.47840e7 q^{70} -3.88941e8 q^{71} -8.14032e7 q^{72} +1.76298e8 q^{73} +1.91168e8 q^{74} -3.16406e7 q^{75} +2.18287e8 q^{76} -3.08034e7 q^{77} -1.85789e8 q^{78} -5.61309e8 q^{79} -5.15182e7 q^{80} +4.30467e7 q^{81} -2.32299e8 q^{82} -1.35162e8 q^{83} +4.65253e7 q^{84} +1.29986e8 q^{85} -4.35233e8 q^{86} +2.24958e8 q^{87} +1.59176e8 q^{88} +8.20451e8 q^{89} +6.77251e7 q^{90} +3.33447e8 q^{91} -3.03562e8 q^{92} +5.19967e8 q^{93} -9.14862e8 q^{94} -5.70291e8 q^{95} -4.04277e8 q^{96} +3.19499e8 q^{97} +9.52103e7 q^{98} -8.41738e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 41 q^{2} - 324 q^{3} + 501 q^{4} + 2500 q^{5} + 3321 q^{6} + 9604 q^{7} - 29367 q^{8} + 26244 q^{9} - 25625 q^{10} - 32854 q^{11} - 40581 q^{12} - 133882 q^{13} - 98441 q^{14} - 202500 q^{15} - 90479 q^{16}+ \cdots - 215555094 q^{99}+O(q^{100}) $ 4 * q - 41 * q^2 - 324 * q^3 + 501 * q^4 + 2500 * q^5 + 3321 * q^6 + 9604 * q^7 - 29367 * q^8 + 26244 * q^9 - 25625 * q^10 - 32854 * q^11 - 40581 * q^12 - 133882 * q^13 - 98441 * q^14 - 202500 * q^15 - 90479 * q^16 + 334344 * q^17 - 269001 * q^18 + 72046 * q^19 + 313125 * q^20 - 777924 * q^21 + 990556 * q^22 + 47460 * q^23 + 2378727 * q^24 + 1562500 * q^25 + 4203458 * q^26 - 2125764 * q^27 + 1202901 * q^28 + 7010312 * q^29 + 2075625 * q^30 - 3711690 * q^31 + 18115265 * q^32 + 2661174 * q^33 + 12757214 * q^34 + 6002500 * q^35 + 3287061 * q^36 + 5222716 * q^37 - 759964 * q^38 + 10844442 * q^39 - 18354375 * q^40 - 5689292 * q^41 + 7973721 * q^42 - 71286384 * q^43 + 6098004 * q^44 + 16402500 * q^45 + 13833560 * q^46 - 100832160 * q^47 + 7328799 * q^48 + 23059204 * q^49 - 16015625 * q^50 - 27081864 * q^51 - 7238698 * q^52 - 149250454 * q^53 + 21789081 * q^54 - 20533750 * q^55 - 70510167 * q^56 - 5835726 * q^57 - 191838758 * q^58 + 24779068 * q^59 - 25363125 * q^60 - 301336048 * q^61 - 107946280 * q^62 + 63011844 * q^63 - 71492607 * q^64 - 83676250 * q^65 - 80235036 * q^66 - 10978016 * q^67 - 527886134 * q^68 - 3844260 * q^69 - 61525625 * q^70 - 507837170 * q^71 - 192676887 * q^72 - 158796526 * q^73 - 252589374 * q^74 - 126562500 * q^75 - 604814036 * q^76 - 78882454 * q^77 - 340480098 * q^78 - 36676584 * q^79 - 56549375 * q^80 + 172186884 * q^81 - 1841487282 * q^82 + 201009048 * q^83 - 97434981 * q^84 + 208965000 * q^85 + 162200156 * q^86 - 567835272 * q^87 - 1446483548 * q^88 + 161323024 * q^89 - 168125625 * q^90 - 321450682 * q^91 + 563662840 * q^92 + 300646890 * q^93 - 918128840 * q^94 + 45028750 * q^95 - 1467336465 * q^96 - 1913030882 * q^97 - 236356841 * q^98 - 215555094 * 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 $

$2$	16.5158	0.729902	0.364951	−	0.931027i	$-0.381086\pi$
$2$	16.5158	0.729902	0.364951	+	0.931027i	$0.381086\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	−239.228	−0.467242
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	−1337.78	−0.421409
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	−12407.1	−1.07094
$9$	6561.00	0.333333
$10$	10322.4	0.326422
$11$	−12829.4	−0.264204	−0.132102	−	0.991236i	$-0.542173\pi$
$11$	−12829.4	−0.264204	−0.132102	+	0.991236i	$0.542173\pi$
$12$	19377.5	0.269763
$13$	138879.	1.34862	0.674311	−	0.738448i	$-0.264441\pi$
$13$	138879.	1.34862	0.674311	+	0.738448i	$0.264441\pi$
$14$	39654.5	0.275877
$15$	−50625.0	−0.258199
$16$	−82429.1	−0.314442
$17$	207978.	0.603944	0.301972	−	0.953317i	$-0.402355\pi$
$17$	207978.	0.603944	0.301972	+	0.953317i	$0.402355\pi$
$18$	108360.	0.243301
$19$	−912465.	−1.60629	−0.803147	−	0.595781i	$-0.796843\pi$
$19$	−912465.	−1.60629	−0.803147	+	0.595781i	$0.796843\pi$
$20$	−149518.	−0.208957
$21$	−194481.	−0.218218
$22$	−211888.	−0.192843
$23$	1.26892e6	0.945498	0.472749	−	0.881197i	$-0.343262\pi$
$23$	1.26892e6	0.945498	0.472749	+	0.881197i	$0.343262\pi$
$24$	1.00498e6	0.618310
$25$	390625.	0.200000
$26$	2.29369e6	0.984362
$27$	−531441.	−0.192450
$28$	−574387.	−0.176601
$29$	−2.77726e6	−0.729163	−0.364582	−	0.931171i	$-0.618788\pi$
$29$	−2.77726e6	−0.729163	−0.364582	+	0.931171i	$0.618788\pi$
$30$	−836113.	−0.188460
$31$	−6.41934e6	−1.24843	−0.624213	−	0.781254i	$-0.714580\pi$
$31$	−6.41934e6	−1.24843	−0.624213	+	0.781254i	$0.714580\pi$
$32$	4.99107e6	0.841432
$33$	1.03918e6	0.152538
$34$	3.43492e6	0.440820
$35$	1.50062e6	0.169031
$36$	−1.56958e6	−0.155747
$37$	1.15749e7	1.01533	0.507667	−	0.861554i	$-0.330508\pi$
$37$	1.15749e7	1.01533	0.507667	+	0.861554i	$0.330508\pi$
$38$	−1.50701e7	−1.17244
$39$	−1.12492e7	−0.778627
$40$	−7.75446e6	−0.478941
$41$	−1.40653e7	−0.777357	−0.388679	−	0.921373i	$-0.627068\pi$
$41$	−1.40653e7	−0.777357	−0.388679	+	0.921373i	$0.627068\pi$
$42$	−3.21201e6	−0.159278
$43$	−2.63525e7	−1.17548	−0.587738	−	0.809051i	$-0.699982\pi$
$43$	−2.63525e7	−1.17548	−0.587738	+	0.809051i	$0.699982\pi$
$44$	3.06916e6	0.123447
$45$	4.10062e6	0.149071
$46$	2.09573e7	0.690121
$47$	−5.53931e7	−1.65583	−0.827914	−	0.560855i	$-0.810473\pi$
$47$	−5.53931e7	−1.65583	−0.827914	+	0.560855i	$0.810473\pi$
$48$	6.67676e6	0.181543
$49$	5.76480e6	0.142857
$50$	6.45149e6	0.145980
$51$	−1.68462e7	−0.348687
$52$	−3.32236e7	−0.630133
$53$	−7.98630e7	−1.39029	−0.695143	−	0.718871i	$-0.744659\pi$
$53$	−7.98630e7	−1.39029	−0.695143	+	0.718871i	$0.744659\pi$
$54$	−8.77718e6	−0.140470
$55$	−8.01838e6	−0.118156
$56$	−2.97895e7	−0.404779
$57$	7.39097e7	0.927394
$58$	−4.58686e7	−0.532218
$59$	1.37206e7	0.147414	0.0737071	−	0.997280i	$-0.476517\pi$
$59$	1.37206e7	0.147414	0.0737071	+	0.997280i	$0.476517\pi$
$60$	1.21109e7	0.120641
$61$	−1.81995e8	−1.68297	−0.841484	−	0.540282i	$-0.818317\pi$
$61$	−1.81995e8	−1.68297	−0.841484	+	0.540282i	$0.818317\pi$
$62$	−1.06021e8	−0.911229
$63$	1.57530e7	0.125988
$64$	1.24635e8	0.928605
$65$	8.67991e7	0.603122
$66$	1.71629e7	0.111338
$67$	2.08956e8	1.26683	0.633416	−	0.773812i	$-0.281652\pi$
$67$	2.08956e8	1.26683	0.633416	+	0.773812i	$0.281652\pi$
$68$	−4.97541e7	−0.282188
$69$	−1.02783e8	−0.545883
$70$	2.47840e7	0.123376
$71$	−3.88941e8	−1.81644	−0.908221	−	0.418492i	$-0.862559\pi$
$71$	−3.88941e8	−1.81644	−0.908221	+	0.418492i	$0.862559\pi$
$72$	−8.14032e7	−0.356981
$73$	1.76298e8	0.726598	0.363299	−	0.931673i	$-0.381650\pi$
$73$	1.76298e8	0.726598	0.363299	+	0.931673i	$0.381650\pi$
$74$	1.91168e8	0.741094
$75$	−3.16406e7	−0.115470
$76$	2.18287e8	0.750529
$77$	−3.08034e7	−0.0998598
$78$	−1.85789e8	−0.568322
$79$	−5.61309e8	−1.62136	−0.810681	−	0.585488i	$-0.800903\pi$
$79$	−5.61309e8	−1.62136	−0.810681	+	0.585488i	$0.800903\pi$
$80$	−5.15182e7	−0.140623
$81$	4.30467e7	0.111111
$82$	−2.32299e8	−0.567395
$83$	−1.35162e8	−0.312610	−0.156305	−	0.987709i	$-0.549958\pi$
$83$	−1.35162e8	−0.312610	−0.156305	+	0.987709i	$0.549958\pi$
$84$	4.65253e7	0.101961
$85$	1.29986e8	0.270092
$86$	−4.35233e8	−0.857983
$87$	2.24958e8	0.420983
$88$	1.59176e8	0.282948
$89$	8.20451e8	1.38611	0.693055	−	0.720885i	$-0.256264\pi$
$89$	8.20451e8	1.38611	0.693055	+	0.720885i	$0.256264\pi$
$90$	6.77251e7	0.108807
$91$	3.33447e8	0.509731
$92$	−3.03562e8	−0.441777
$93$	5.19967e8	0.720779
$94$	−9.14862e8	−1.20859
$95$	−5.70291e8	−0.718357
$96$	−4.04277e8	−0.485801
$97$	3.19499e8	0.366435	0.183218	−	0.983072i	$-0.441349\pi$
$97$	3.19499e8	0.366435	0.183218	+	0.983072i	$0.441349\pi$
$98$	9.52103e7	0.104272
$99$	−8.41738e7	−0.0880681
$100$	−9.34485e7	−0.0934485
$101$	9.52392e8	0.910687	0.455344	−	0.890316i	$-0.349516\pi$
$101$	9.52392e8	0.910687	0.455344	+	0.890316i	$0.349516\pi$
$102$	−2.78229e8	−0.254508
$103$	−1.28829e9	−1.12784	−0.563919	−	0.825830i	$-0.690707\pi$
$103$	−1.28829e9	−1.12784	−0.563919	+	0.825830i	$0.690707\pi$
$104$	−1.72308e9	−1.44430
$105$	−1.21551e8	−0.0975900
$106$	−1.31900e9	−1.01477
$107$	−1.23774e9	−0.912858	−0.456429	−	0.889760i	$-0.650872\pi$
$107$	−1.23774e9	−0.912858	−0.456429	+	0.889760i	$0.650872\pi$
$108$	1.27136e8	0.0899208
$109$	−1.59578e9	−1.08281	−0.541406	−	0.840761i	$-0.682108\pi$
$109$	−1.59578e9	−1.08281	−0.541406	+	0.840761i	$0.682108\pi$
$110$	−1.32430e8	−0.0862421
$111$	−9.37565e8	−0.586203
$112$	−1.97912e8	−0.118848
$113$	1.42100e9	0.819865	0.409933	−	0.912116i	$-0.365552\pi$
$113$	1.42100e9	0.819865	0.409933	+	0.912116i	$0.365552\pi$
$114$	1.22068e9	0.676907
$115$	7.93078e8	0.422839
$116$	6.64398e8	0.340696
$117$	9.11182e8	0.449540
$118$	2.26607e8	0.107598
$119$	4.99354e8	0.228269
$120$	6.28111e8	0.276517
$121$	−2.19335e9	−0.930196
$122$	−3.00580e9	−1.22840
$123$	1.13929e9	0.448807
$124$	1.53569e9	0.583318
$125$	2.44141e8	0.0894427
$126$	2.60173e8	0.0919591
$127$	4.80189e9	1.63793	0.818965	−	0.573843i	$-0.194548\pi$
$127$	4.80189e9	1.63793	0.818965	+	0.573843i	$0.194548\pi$
$128$	−4.96976e8	−0.163640
$129$	2.13455e9	0.678662
$130$	1.43356e9	0.440220
$131$	−6.54474e9	−1.94165	−0.970826	−	0.239785i	$-0.922923\pi$
$131$	−6.54474e9	−1.94165	−0.970826	+	0.239785i	$0.922923\pi$
$132$	−2.48602e8	−0.0712724
$133$	−2.19083e9	−0.607122
$134$	3.45108e9	0.924664
$135$	−3.32151e8	−0.0860663
$136$	−2.58041e9	−0.646790
$137$	−3.81152e9	−0.924392	−0.462196	−	0.886778i	$-0.652938\pi$
$137$	−3.81152e9	−0.924392	−0.462196	+	0.886778i	$0.652938\pi$
$138$	−1.69754e9	−0.398442
$139$	6.86569e9	1.55997	0.779987	−	0.625795i	$-0.215225\pi$
$139$	6.86569e9	1.55997	0.779987	+	0.625795i	$0.215225\pi$
$140$	−3.58992e8	−0.0789784
$141$	4.48684e9	0.955993
$142$	−6.42368e9	−1.32582
$143$	−1.78173e9	−0.356311
$144$	−5.40817e8	−0.104814
$145$	−1.73578e9	−0.326092
$146$	2.91170e9	0.530346
$147$	−4.66949e8	−0.0824786
$148$	−2.76904e9	−0.474407
$149$	3.04735e9	0.506505	0.253253	−	0.967400i	$-0.418500\pi$
$149$	3.04735e9	0.506505	0.253253	+	0.967400i	$0.418500\pi$
$150$	−5.22570e8	−0.0842819
$151$	2.10650e9	0.329736	0.164868	−	0.986316i	$-0.447280\pi$
$151$	2.10650e9	0.329736	0.164868	+	0.986316i	$0.447280\pi$
$152$	1.13211e10	1.72025
$153$	1.36454e9	0.201315
$154$	−5.08743e8	−0.0728879
$155$	−4.01209e9	−0.558313
$156$	2.69112e9	0.363807
$157$	4.75713e9	0.624879	0.312440	−	0.949938i	$-0.398854\pi$
$157$	4.75713e9	0.624879	0.312440	+	0.949938i	$0.398854\pi$
$158$	−9.27047e9	−1.18344
$159$	6.46891e9	0.802682
$160$	3.11942e9	0.376300
$161$	3.04669e9	0.357365
$162$	7.10951e8	0.0811003
$163$	7.05765e9	0.783098	0.391549	−	0.920157i	$-0.371939\pi$
$163$	7.05765e9	0.783098	0.391549	+	0.920157i	$0.371939\pi$
$164$	3.36481e9	0.363214
$165$	6.49489e8	0.0682172
$166$	−2.23231e9	−0.228175
$167$	1.50182e10	1.49415	0.747074	−	0.664741i	$-0.231458\pi$
$167$	1.50182e10	1.49415	0.747074	+	0.664741i	$0.231458\pi$
$168$	2.41295e9	0.233699
$169$	8.68274e9	0.818779
$170$	2.14682e9	0.197141
$171$	−5.98668e9	−0.535431
$172$	6.30426e9	0.549233
$173$	4.19710e9	0.356239	0.178120	−	0.984009i	$-0.442999\pi$
$173$	4.19710e9	0.356239	0.178120	+	0.984009i	$0.442999\pi$
$174$	3.71536e9	0.307276
$175$	9.37891e8	0.0755929
$176$	1.05752e9	0.0830769
$177$	−1.11137e9	−0.0851096
$178$	1.35504e10	1.01172
$179$	2.00503e10	1.45976	0.729881	−	0.683574i	$-0.239575\pi$
$179$	2.00503e10	1.45976	0.729881	+	0.683574i	$0.239575\pi$
$180$	−9.80985e8	−0.0696524
$181$	−6.79500e9	−0.470583	−0.235291	−	0.971925i	$-0.575604\pi$
$181$	−6.79500e9	−0.470583	−0.235291	+	0.971925i	$0.575604\pi$
$182$	5.50715e9	0.372054
$183$	1.47416e10	0.971662
$184$	−1.57437e10	−1.01257
$185$	7.23430e9	0.454071
$186$	8.58767e9	0.526099
$187$	−2.66823e9	−0.159565
$188$	1.32516e10	0.773673
$189$	−1.27599e9	−0.0727393
$190$	−9.41881e9	−0.524330
$191$	−9.36304e9	−0.509057	−0.254529	−	0.967065i	$-0.581920\pi$
$191$	−9.36304e9	−0.509057	−0.254529	+	0.967065i	$0.581920\pi$
$192$	−1.00955e10	−0.536130
$193$	−2.10635e10	−1.09276	−0.546378	−	0.837539i	$-0.683994\pi$
$193$	−2.10635e10	−1.09276	−0.546378	+	0.837539i	$0.683994\pi$
$194$	5.27679e9	0.267462
$195$	−7.03072e9	−0.348212
$196$	−1.37910e9	−0.0667489
$197$	−1.42885e10	−0.675911	−0.337955	−	0.941162i	$-0.609735\pi$
$197$	−1.42885e10	−0.675911	−0.337955	+	0.941162i	$0.609735\pi$
$198$	−1.39020e9	−0.0642811
$199$	−4.29602e9	−0.194190	−0.0970952	−	0.995275i	$-0.530955\pi$
$199$	−4.29602e9	−0.194190	−0.0970952	+	0.995275i	$0.530955\pi$
$200$	−4.84654e9	−0.214189
$201$	−1.69255e10	−0.731406
$202$	1.57295e10	0.664713
$203$	−6.66819e9	−0.275598
$204$	4.03008e9	0.162921
$205$	−8.79079e9	−0.347645
$206$	−2.12772e10	−0.823212
$207$	8.32541e9	0.315166
$208$	−1.14476e10	−0.424063
$209$	1.17064e10	0.424390
$210$	−2.00751e9	−0.0712312
$211$	−3.28516e10	−1.14100	−0.570500	−	0.821298i	$-0.693250\pi$
$211$	−3.28516e10	−1.14100	−0.570500	+	0.821298i	$0.693250\pi$
$212$	1.91055e10	0.649601
$213$	3.15042e10	1.04872
$214$	−2.04423e10	−0.666297
$215$	−1.64703e10	−0.525689
$216$	6.59366e9	0.206103
$217$	−1.54128e10	−0.471861
$218$	−2.63556e10	−0.790347
$219$	−1.42801e10	−0.419501
$220$	1.91822e9	0.0552074
$221$	2.88836e10	0.814492
$222$	−1.54846e10	−0.427871
$223$	−3.93927e10	−1.06670	−0.533352	−	0.845893i	$-0.679068\pi$
$223$	−3.93927e10	−1.06670	−0.533352	+	0.845893i	$0.679068\pi$
$224$	1.19836e10	0.318031
$225$	2.56289e9	0.0666667
$226$	2.34690e10	0.598422
$227$	3.23719e10	0.809192	0.404596	−	0.914495i	$-0.367412\pi$
$227$	3.23719e10	0.809192	0.404596	+	0.914495i	$0.367412\pi$
$228$	−1.76813e10	−0.433318
$229$	−5.70687e10	−1.37132	−0.685659	−	0.727923i	$-0.740486\pi$
$229$	−5.70687e10	−1.37132	−0.685659	+	0.727923i	$0.740486\pi$
$230$	1.30983e10	0.308632
$231$	2.49508e9	0.0576541
$232$	3.44578e10	0.780893
$233$	8.67332e8	0.0192790	0.00963948	−	0.999954i	$-0.496932\pi$
$233$	8.67332e8	0.0192790	0.00963948	+	0.999954i	$0.496932\pi$
$234$	1.50489e10	0.328121
$235$	−3.46207e10	−0.740509
$236$	−3.28236e9	−0.0688782
$237$	4.54660e10	0.936094
$238$	8.24724e9	0.166614
$239$	−5.63490e10	−1.11711	−0.558555	−	0.829468i	$-0.688644\pi$
$239$	−5.63490e10	−1.11711	−0.558555	+	0.829468i	$0.688644\pi$
$240$	4.17297e9	0.0811886
$241$	−8.18472e10	−1.56289	−0.781443	−	0.623977i	$-0.785516\pi$
$241$	−8.18472e10	−1.56289	−0.781443	+	0.623977i	$0.785516\pi$
$242$	−3.62250e10	−0.678952
$243$	−3.48678e9	−0.0641500
$244$	4.35384e10	0.786354
$245$	3.60300e9	0.0638877
$246$	1.88162e10	0.327586
$247$	−1.26722e11	−2.16628
$248$	7.96457e10	1.33699
$249$	1.09481e10	0.180486
$250$	4.03218e9	0.0652845
$251$	7.00799e10	1.11445	0.557226	−	0.830361i	$-0.311866\pi$
$251$	7.00799e10	1.11445	0.557226	+	0.830361i	$0.311866\pi$
$252$	−3.76855e9	−0.0588670
$253$	−1.62796e10	−0.249804
$254$	7.93071e10	1.19553
$255$	−1.05289e10	−0.155938
$256$	−7.20212e10	−1.04805
$257$	−2.33185e10	−0.333428	−0.166714	−	0.986005i	$-0.553316\pi$
$257$	−2.33185e10	−0.333428	−0.166714	+	0.986005i	$0.553316\pi$
$258$	3.52539e10	0.495357
$259$	2.77913e10	0.383760
$260$	−2.07648e10	−0.281804
$261$	−1.82216e10	−0.243054
$262$	−1.08092e11	−1.41722
$263$	−6.60786e10	−0.851647	−0.425824	−	0.904806i	$-0.640016\pi$
$263$	−6.60786e10	−0.851647	−0.425824	+	0.904806i	$0.640016\pi$
$264$	−1.28933e10	−0.163360
$265$	−4.99144e10	−0.621755
$266$	−3.61833e10	−0.443140
$267$	−6.64565e10	−0.800271
$268$	−4.99882e10	−0.591918
$269$	9.71447e8	0.0113119	0.00565593	−	0.999984i	$-0.498200\pi$
$269$	9.71447e8	0.0113119	0.00565593	+	0.999984i	$0.498200\pi$
$270$	−5.48574e9	−0.0628200
$271$	5.78835e10	0.651918	0.325959	−	0.945384i	$-0.394313\pi$
$271$	5.78835e10	0.651918	0.325959	+	0.945384i	$0.394313\pi$
$272$	−1.71434e10	−0.189905
$273$	−2.70092e10	−0.294293
$274$	−6.29504e10	−0.674716
$275$	−5.01149e9	−0.0528408
$276$	2.45886e10	0.255060
$277$	6.14358e10	0.626993	0.313496	−	0.949589i	$-0.398500\pi$
$277$	6.14358e10	0.626993	0.313496	+	0.949589i	$0.398500\pi$
$278$	1.13392e11	1.13863
$279$	−4.21173e10	−0.416142
$280$	−1.86185e10	−0.181023
$281$	2.52020e10	0.241133	0.120567	−	0.992705i	$-0.461529\pi$
$281$	2.52020e10	0.241133	0.120567	+	0.992705i	$0.461529\pi$
$282$	7.41038e10	0.697782
$283$	1.03229e11	0.956674	0.478337	−	0.878176i	$-0.341240\pi$
$283$	1.03229e11	0.956674	0.478337	+	0.878176i	$0.341240\pi$
$284$	9.30457e10	0.848718
$285$	4.61935e10	0.414743
$286$	−2.94267e10	−0.260073
$287$	−3.37707e10	−0.293813
$288$	3.27464e10	0.280477
$289$	−7.53331e10	−0.635252
$290$	−2.86679e10	−0.238015
$291$	−2.58794e10	−0.211561
$292$	−4.21754e10	−0.339497
$293$	1.83294e11	1.45293	0.726465	−	0.687203i	$-0.241162\pi$
$293$	1.83294e11	1.45293	0.726465	+	0.687203i	$0.241162\pi$
$294$	−7.71204e9	−0.0602013
$295$	8.57538e9	0.0659256
$296$	−1.43611e11	−1.08736
$297$	6.81808e9	0.0508461
$298$	5.03294e10	0.369699
$299$	1.76226e11	1.27512
$300$	7.56933e9	0.0539525
$301$	−6.32724e10	−0.444288
$302$	3.47906e10	0.240675
$303$	−7.71437e10	−0.525786
$304$	7.52137e10	0.505087
$305$	−1.13747e11	−0.752646
$306$	2.25365e10	0.146940
$307$	−2.56233e11	−1.64631	−0.823157	−	0.567814i	$-0.807789\pi$
$307$	−2.56233e11	−1.64631	−0.823157	+	0.567814i	$0.807789\pi$
$308$	7.36904e9	0.0466587
$309$	1.04352e11	0.651158
$310$	−6.62629e10	−0.407514
$311$	−2.87707e10	−0.174393	−0.0871963	−	0.996191i	$-0.527791\pi$
$311$	−2.87707e10	−0.174393	−0.0871963	+	0.996191i	$0.527791\pi$
$312$	1.39570e11	0.833866
$313$	−9.72372e10	−0.572641	−0.286321	−	0.958134i	$-0.592432\pi$
$313$	−9.72372e10	−0.572641	−0.286321	+	0.958134i	$0.592432\pi$
$314$	7.85678e10	0.456101
$315$	9.84560e9	0.0563436
$316$	1.34281e11	0.757569
$317$	−1.55562e11	−0.865241	−0.432620	−	0.901576i	$-0.642411\pi$
$317$	−1.55562e11	−0.865241	−0.432620	+	0.901576i	$0.642411\pi$
$318$	1.06839e11	0.585880
$319$	3.56306e10	0.192648
$320$	7.78971e10	0.415285
$321$	1.00257e11	0.527039
$322$	5.03185e10	0.260841
$323$	−1.89772e11	−0.970112
$324$	−1.02980e10	−0.0519158
$325$	5.42494e10	0.269724
$326$	1.16563e11	0.571585
$327$	1.29258e11	0.625162
$328$	1.74510e11	0.832506
$329$	−1.32999e11	−0.625844
$330$	1.07268e10	0.0497919
$331$	−8.53724e10	−0.390923	−0.195462	−	0.980711i	$-0.562621\pi$
$331$	−8.53724e10	−0.390923	−0.195462	+	0.980711i	$0.562621\pi$
$332$	3.23346e10	0.146065
$333$	7.59428e10	0.338444
$334$	2.48038e11	1.09058
$335$	1.30598e11	0.566544
$336$	1.60309e10	0.0686169
$337$	−2.95612e11	−1.24850	−0.624248	−	0.781227i	$-0.714594\pi$
$337$	−2.95612e11	−1.24850	−0.624248	+	0.781227i	$0.714594\pi$
$338$	1.43402e11	0.597629
$339$	−1.15101e11	−0.473349
$340$	−3.10963e10	−0.126198
$341$	8.23564e10	0.329840
$342$	−9.88749e10	−0.390813
$343$	1.38413e10	0.0539949
$344$	3.26959e11	1.25887
$345$	−6.42393e10	−0.244126
$346$	6.93185e10	0.260020
$347$	−1.04215e11	−0.385876	−0.192938	−	0.981211i	$-0.561802\pi$
$347$	−1.04215e11	−0.385876	−0.192938	+	0.981211i	$0.561802\pi$
$348$	−5.38162e10	−0.196701
$349$	4.18832e11	1.51121	0.755607	−	0.655025i	$-0.227342\pi$
$349$	4.18832e11	1.51121	0.755607	+	0.655025i	$0.227342\pi$
$350$	1.54900e10	0.0551754
$351$	−7.38057e10	−0.259542
$352$	−6.40325e10	−0.222310
$353$	1.47012e11	0.503925	0.251963	−	0.967737i	$-0.418924\pi$
$353$	1.47012e11	0.503925	0.251963	+	0.967737i	$0.418924\pi$
$354$	−1.83552e10	−0.0621217
$355$	−2.43088e11	−0.812337
$356$	−1.96275e11	−0.647649
$357$	−4.04477e10	−0.131791
$358$	3.31147e11	1.06548
$359$	−5.00405e9	−0.0159000	−0.00794999	−	0.999968i	$-0.502531\pi$
$359$	−5.00405e9	−0.0159000	−0.00794999	+	0.999968i	$0.502531\pi$
$360$	−5.08770e10	−0.159647
$361$	5.09905e11	1.58018
$362$	−1.12225e11	−0.343479
$363$	1.77662e11	0.537049
$364$	−7.97700e10	−0.238168
$365$	1.10186e11	0.324944
$366$	2.43470e11	0.709218
$367$	−1.71677e10	−0.0493987	−0.0246994	−	0.999695i	$-0.507863\pi$
$367$	−1.71677e10	−0.0493987	−0.0246994	+	0.999695i	$0.507863\pi$
$368$	−1.04596e11	−0.297304
$369$	−9.22822e10	−0.259119
$370$	1.19480e11	0.331427
$371$	−1.91751e11	−0.525479
$372$	−1.24391e11	−0.336779
$373$	2.01329e9	0.00538539	0.00269269	−	0.999996i	$-0.499143\pi$
$373$	2.01329e9	0.00538539	0.00269269	+	0.999996i	$0.499143\pi$
$374$	−4.40680e10	−0.116467
$375$	−1.97754e10	−0.0516398
$376$	6.87270e11	1.77330
$377$	−3.85701e11	−0.983365
$378$	−2.10740e10	−0.0530926
$379$	−2.41128e11	−0.600303	−0.300152	−	0.953891i	$-0.597037\pi$
$379$	−2.41128e11	−0.600303	−0.300152	+	0.953891i	$0.597037\pi$
$380$	1.36430e11	0.335647
$381$	−3.88953e11	−0.945660
$382$	−1.54638e11	−0.371562
$383$	−6.60585e10	−0.156868	−0.0784339	−	0.996919i	$-0.524992\pi$
$383$	−6.60585e10	−0.156868	−0.0784339	+	0.996919i	$0.524992\pi$
$384$	4.02551e10	0.0944779
$385$	−1.92521e10	−0.0446587
$386$	−3.47881e11	−0.797606
$387$	−1.72899e11	−0.391826
$388$	−7.64332e10	−0.171214
$389$	3.42911e11	0.759291	0.379645	−	0.925132i	$-0.376046\pi$
$389$	3.42911e11	0.759291	0.379645	+	0.925132i	$0.376046\pi$
$390$	−1.16118e11	−0.254161
$391$	2.63908e11	0.571028
$392$	−7.15247e10	−0.152992
$393$	5.30124e11	1.12101
$394$	−2.35986e11	−0.493349
$395$	−3.50818e11	−0.725095
$396$	2.01367e10	0.0411491
$397$	−1.32157e11	−0.267014	−0.133507	−	0.991048i	$-0.542624\pi$
$397$	−1.32157e11	−0.267014	−0.133507	+	0.991048i	$0.542624\pi$
$398$	−7.09523e10	−0.141740
$399$	1.77457e11	0.350522
$400$	−3.21989e10	−0.0628884
$401$	4.47348e11	0.863965	0.431983	−	0.901882i	$-0.357814\pi$
$401$	4.47348e11	0.863965	0.431983	+	0.901882i	$0.357814\pi$
$402$	−2.79538e11	−0.533855
$403$	−8.91509e11	−1.68365
$404$	−2.27839e11	−0.425512
$405$	2.69042e10	0.0496904
$406$	−1.10131e11	−0.201160
$407$	−1.48499e11	−0.268255
$408$	2.09013e11	0.373424
$409$	2.84409e10	0.0502561	0.0251281	−	0.999684i	$-0.492001\pi$
$409$	2.84409e10	0.0502561	0.0251281	+	0.999684i	$0.492001\pi$
$410$	−1.45187e11	−0.253747
$411$	3.08733e11	0.533698
$412$	3.08196e11	0.526974
$413$	3.29432e10	0.0557173
$414$	1.37501e11	0.230040
$415$	−8.44763e10	−0.139804
$416$	6.93153e11	1.13477
$417$	−5.56121e11	−0.900652
$418$	1.93341e11	0.309763
$419$	−9.96384e9	−0.0157930	−0.00789648	−	0.999969i	$-0.502514\pi$
$419$	−9.96384e9	−0.0157930	−0.00789648	+	0.999969i	$0.502514\pi$
$420$	2.90783e10	0.0455982
$421$	−4.35352e11	−0.675416	−0.337708	−	0.941251i	$-0.609652\pi$
$421$	−4.35352e11	−0.675416	−0.337708	+	0.941251i	$0.609652\pi$
$422$	−5.42571e11	−0.832818
$423$	−3.63434e11	−0.551943
$424$	9.90872e11	1.48892
$425$	8.12413e10	0.120789
$426$	5.20318e11	0.765465
$427$	−4.36971e11	−0.636102
$428$	2.96103e11	0.426526
$429$	1.44320e11	0.205716
$430$	−2.72021e11	−0.383702
$431$	3.83520e11	0.535353	0.267677	−	0.963509i	$-0.413744\pi$
$431$	3.83520e11	0.535353	0.267677	+	0.963509i	$0.413744\pi$
$432$	4.38062e10	0.0605144
$433$	−3.81869e11	−0.522058	−0.261029	−	0.965331i	$-0.584062\pi$
$433$	−3.81869e11	−0.522058	−0.261029	+	0.965331i	$0.584062\pi$
$434$	−2.54556e11	−0.344412
$435$	1.40599e11	0.188269
$436$	3.81755e11	0.505936
$437$	−1.15785e12	−1.51875
$438$	−2.35848e11	−0.306195
$439$	8.63762e11	1.10995	0.554975	−	0.831867i	$-0.312728\pi$
$439$	8.63762e11	1.10995	0.554975	+	0.831867i	$0.312728\pi$
$440$	9.94852e10	0.126538
$441$	3.78229e10	0.0476190
$442$	4.77037e11	0.594499
$443$	−1.14340e12	−1.41053	−0.705265	−	0.708944i	$-0.749172\pi$
$443$	−1.14340e12	−1.41053	−0.705265	+	0.708944i	$0.749172\pi$
$444$	2.24292e11	0.273899
$445$	5.12782e11	0.619887
$446$	−6.50602e11	−0.778590
$447$	−2.46835e11	−0.292431
$448$	2.99249e11	0.350980
$449$	1.52519e12	1.77099	0.885493	−	0.464653i	$-0.153821\pi$
$449$	1.52519e12	1.77099	0.885493	+	0.464653i	$0.153821\pi$
$450$	4.23282e10	0.0486602
$451$	1.80449e11	0.205381
$452$	−3.39944e11	−0.383076
$453$	−1.70627e11	−0.190373
$454$	5.34648e11	0.590632
$455$	2.08405e11	0.227959
$456$	−9.17008e11	−0.993187
$457$	−7.95639e11	−0.853283	−0.426642	−	0.904421i	$-0.640303\pi$
$457$	−7.95639e11	−0.853283	−0.426642	+	0.904421i	$0.640303\pi$
$458$	−9.42535e11	−1.00093
$459$	−1.10528e11	−0.116229
$460$	−1.89726e11	−0.197569
$461$	−1.54880e12	−1.59714	−0.798568	−	0.601905i	$-0.794409\pi$
$461$	−1.54880e12	−1.59714	−0.798568	+	0.601905i	$0.794409\pi$
$462$	4.12082e10	0.0420819
$463$	5.91013e11	0.597699	0.298849	−	0.954300i	$-0.403397\pi$
$463$	5.91013e11	0.597699	0.298849	+	0.954300i	$0.403397\pi$
$464$	2.28927e11	0.229280
$465$	3.24979e11	0.322342
$466$	1.43247e10	0.0140718
$467$	4.98276e11	0.484779	0.242390	−	0.970179i	$-0.422069\pi$
$467$	4.98276e11	0.484779	0.242390	+	0.970179i	$0.422069\pi$
$468$	−2.17980e11	−0.210044
$469$	5.01704e11	0.478817
$470$	−5.71789e11	−0.540499
$471$	−3.85327e11	−0.360774
$472$	−1.70234e11	−0.157872
$473$	3.38087e11	0.310566
$474$	7.50908e11	0.683257
$475$	−3.56432e11	−0.321259
$476$	−1.19460e11	−0.106657
$477$	−5.23981e11	−0.463429
$478$	−9.30650e11	−0.815381
$479$	−5.30502e11	−0.460444	−0.230222	−	0.973138i	$-0.573945\pi$
$479$	−5.30502e11	−0.460444	−0.230222	+	0.973138i	$0.573945\pi$
$480$	−2.52673e11	−0.217257
$481$	1.60750e12	1.36930
$482$	−1.35177e12	−1.14075
$483$	−2.46782e11	−0.206325
$484$	5.24712e11	0.434627
$485$	1.99687e11	0.163875
$486$	−5.75871e10	−0.0468233
$487$	−1.80536e12	−1.45440	−0.727201	−	0.686425i	$-0.759179\pi$
$487$	−1.80536e12	−1.45440	−0.727201	+	0.686425i	$0.759179\pi$
$488$	2.25804e12	1.80236
$489$	−5.71670e11	−0.452122
$490$	5.95065e10	0.0466318
$491$	1.77594e12	1.37900	0.689498	−	0.724288i	$-0.257831\pi$
$491$	1.77594e12	1.37900	0.689498	+	0.724288i	$0.257831\pi$
$492$	−2.72549e11	−0.209702
$493$	−5.77607e11	−0.440374
$494$	−2.09291e12	−1.58117
$495$	−5.26086e10	−0.0393852
$496$	5.29141e11	0.392558
$497$	−9.33848e11	−0.686550
$498$	1.80817e11	0.131737
$499$	−8.84887e11	−0.638904	−0.319452	−	0.947602i	$-0.603499\pi$
$499$	−8.84887e11	−0.638904	−0.319452	+	0.947602i	$0.603499\pi$
$500$	−5.84053e10	−0.0417914
$501$	−1.21647e12	−0.862647
$502$	1.15743e12	0.813442
$503$	2.06604e12	1.43908	0.719538	−	0.694453i	$-0.244354\pi$
$503$	2.06604e12	1.43908	0.719538	+	0.694453i	$0.244354\pi$
$504$	−1.95449e11	−0.134926
$505$	5.95245e11	0.407272
$506$	−2.68870e11	−0.182333
$507$	−7.03302e11	−0.472722
$508$	−1.14875e12	−0.765311
$509$	2.16496e12	1.42962	0.714808	−	0.699320i	$-0.246514\pi$
$509$	2.16496e12	1.42962	0.714808	+	0.699320i	$0.246514\pi$
$510$	−1.73893e11	−0.113819
$511$	4.23291e11	0.274628
$512$	−9.35037e11	−0.601331
$513$	4.84921e11	0.309131
$514$	−3.85124e11	−0.243370
$515$	−8.05183e11	−0.504385
$516$	−5.10645e11	−0.317100
$517$	7.10661e11	0.437477
$518$	4.58995e11	0.280107
$519$	−3.39965e11	−0.205675
$520$	−1.07693e12	−0.645909
$521$	−6.75899e11	−0.401895	−0.200947	−	0.979602i	$-0.564402\pi$
$521$	−6.75899e11	−0.401895	−0.200947	+	0.979602i	$0.564402\pi$
$522$	−3.00944e11	−0.177406
$523$	1.92588e12	1.12557	0.562785	−	0.826603i	$-0.309730\pi$
$523$	1.92588e12	1.12557	0.562785	+	0.826603i	$0.309730\pi$
$524$	1.56569e12	0.907222
$525$	−7.59691e10	−0.0436436
$526$	−1.09134e12	−0.621619
$527$	−1.33508e12	−0.753980
$528$	−8.56589e10	−0.0479645
$529$	−1.90984e11	−0.106034
$530$	−8.24377e11	−0.453821
$531$	9.00209e10	0.0491381
$532$	5.24108e11	0.283673
$533$	−1.95336e12	−1.04836
$534$	−1.09758e12	−0.584120
$535$	−7.73589e11	−0.408242
$536$	−2.59255e12	−1.35671
$537$	−1.62407e12	−0.842794
$538$	1.60442e10	0.00825655
$539$	−7.39590e10	−0.0377435
$540$	7.94598e10	0.0402138
$541$	2.01522e12	1.01143	0.505713	−	0.862702i	$-0.331230\pi$
$541$	2.01522e12	1.01143	0.505713	+	0.862702i	$0.331230\pi$
$542$	9.55992e11	0.475836
$543$	5.50395e11	0.271691
$544$	1.03803e12	0.508178
$545$	−9.97361e11	−0.484248
$546$	−4.46079e11	−0.214805
$547$	2.17077e12	1.03674	0.518372	−	0.855155i	$-0.326538\pi$
$547$	2.17077e12	1.03674	0.518372	+	0.855155i	$0.326538\pi$
$548$	9.11824e11	0.431915
$549$	−1.19407e12	−0.560989
$550$	−8.27688e10	−0.0385687
$551$	2.53415e12	1.17125
$552$	1.27524e12	0.584610
$553$	−1.34770e12	−0.612817
$554$	1.01466e12	0.457643
$555$	−5.85978e11	−0.262158
$556$	−1.64247e12	−0.728886
$557$	1.89893e12	0.835911	0.417955	−	0.908468i	$-0.362747\pi$
$557$	1.89893e12	0.835911	0.417955	+	0.908468i	$0.362747\pi$
$558$	−6.95601e11	−0.303743
$559$	−3.65980e12	−1.58527
$560$	−1.23695e11	−0.0531504
$561$	2.16127e11	0.0921246
$562$	4.16232e11	0.176004
$563$	3.03644e12	1.27373	0.636864	−	0.770976i	$-0.280231\pi$
$563$	3.03644e12	1.27373	0.636864	+	0.770976i	$0.280231\pi$
$564$	−1.07338e12	−0.446681
$565$	8.88128e11	0.366655
$566$	1.70491e12	0.698279
$567$	1.03355e11	0.0419961
$568$	4.82565e12	1.94531
$569$	2.01593e12	0.806252	0.403126	−	0.915144i	$-0.367924\pi$
$569$	2.01593e12	0.806252	0.403126	+	0.915144i	$0.367924\pi$
$570$	7.62924e11	0.302722
$571$	−1.11690e12	−0.439693	−0.219847	−	0.975534i	$-0.570556\pi$
$571$	−1.11690e12	−0.439693	−0.219847	+	0.975534i	$0.570556\pi$
$572$	4.26240e11	0.166484
$573$	7.58406e11	0.293904
$574$	−5.57751e11	−0.214455
$575$	4.95674e11	0.189100
$576$	8.17732e11	0.309535
$577$	1.60868e12	0.604196	0.302098	−	0.953277i	$-0.402313\pi$
$577$	1.60868e12	0.604196	0.302098	+	0.953277i	$0.402313\pi$
$578$	−1.24419e12	−0.463672
$579$	1.70615e12	0.630903
$580$	4.15248e11	0.152364
$581$	−3.24524e11	−0.118156
$582$	−4.27420e11	−0.154419
$583$	1.02460e12	0.367320
$584$	−2.18735e12	−0.778145
$585$	5.69489e11	0.201041
$586$	3.02725e12	1.06050
$587$	1.06147e11	0.0369007	0.0184504	−	0.999830i	$-0.494127\pi$
$587$	1.06147e11	0.0369007	0.0184504	+	0.999830i	$0.494127\pi$
$588$	1.11707e11	0.0385375
$589$	5.85743e12	2.00534
$590$	1.41629e11	0.0481193
$591$	1.15737e12	0.390237
$592$	−9.54107e11	−0.319264
$593$	4.90256e12	1.62808	0.814042	−	0.580807i	$-0.197263\pi$
$593$	4.90256e12	1.62808	0.814042	+	0.580807i	$0.197263\pi$
$594$	1.12606e11	0.0371127
$595$	3.12097e11	0.102085
$596$	−7.29011e11	−0.236661
$597$	3.47978e11	0.112116
$598$	2.91052e12	0.930712
$599$	1.54464e12	0.490238	0.245119	−	0.969493i	$-0.421173\pi$
$599$	1.54464e12	0.490238	0.245119	+	0.969493i	$0.421173\pi$
$600$	3.92570e11	0.123662
$601$	2.64034e12	0.825516	0.412758	−	0.910841i	$-0.364566\pi$
$601$	2.64034e12	0.825516	0.412758	+	0.910841i	$0.364566\pi$
$602$	−1.04499e12	−0.324287
$603$	1.37096e12	0.422277
$604$	−5.03935e11	−0.154066
$605$	−1.37085e12	−0.415996
$606$	−1.27409e12	−0.383772
$607$	3.66339e11	0.109530	0.0547651	−	0.998499i	$-0.482559\pi$
$607$	3.66339e11	0.109530	0.0547651	+	0.998499i	$0.482559\pi$
$608$	−4.55418e12	−1.35159
$609$	5.40123e11	0.159116
$610$	−1.87862e12	−0.549358
$611$	−7.69291e12	−2.23309
$612$	−3.26437e11	−0.0940627
$613$	−4.75554e12	−1.36028	−0.680139	−	0.733083i	$-0.738080\pi$
$613$	−4.75554e12	−1.36028	−0.680139	+	0.733083i	$0.738080\pi$
$614$	−4.23190e12	−1.20165
$615$	7.12054e11	0.200713
$616$	3.82182e11	0.106944
$617$	6.41204e12	1.78120	0.890600	−	0.454787i	$-0.150285\pi$
$617$	6.41204e12	1.78120	0.890600	+	0.454787i	$0.150285\pi$
$618$	1.72345e12	0.475282
$619$	6.76680e12	1.85257	0.926287	−	0.376819i	$-0.122982\pi$
$619$	6.76680e12	1.85257	0.926287	+	0.376819i	$0.122982\pi$
$620$	9.59805e11	0.260868
$621$	−6.74358e11	−0.181961
$622$	−4.75171e11	−0.127290
$623$	1.96990e12	0.523900
$624$	9.27258e11	0.244833
$625$	1.52588e11	0.0400000
$626$	−1.60595e12	−0.417972
$627$	−9.48218e11	−0.245021
$628$	−1.13804e12	−0.291970
$629$	2.40732e12	0.613204
$630$	1.62608e11	0.0411253
$631$	3.44958e12	0.866231	0.433115	−	0.901339i	$-0.357414\pi$
$631$	3.44958e12	0.866231	0.433115	+	0.901339i	$0.357414\pi$
$632$	6.96424e12	1.73639
$633$	2.66098e12	0.658756
$634$	−2.56923e12	−0.631541
$635$	3.00118e12	0.732505
$636$	−1.54754e12	−0.375047
$637$	8.00607e11	0.192660
$638$	5.88467e11	0.140614
$639$	−2.55184e12	−0.605480
$640$	−3.10610e11	−0.0731823
$641$	−1.82522e12	−0.427026	−0.213513	−	0.976940i	$-0.568491\pi$
$641$	−1.82522e12	−0.427026	−0.213513	+	0.976940i	$0.568491\pi$
$642$	1.65583e12	0.384687
$643$	−6.55042e12	−1.51119	−0.755596	−	0.655038i	$-0.772653\pi$
$643$	−6.55042e12	−1.51119	−0.755596	+	0.655038i	$0.772653\pi$
$644$	−7.28853e11	−0.166976
$645$	1.33410e12	0.303507
$646$	−3.13424e12	−0.708087
$647$	−3.47042e12	−0.778596	−0.389298	−	0.921112i	$-0.627282\pi$
$647$	−3.47042e12	−0.778596	−0.389298	+	0.921112i	$0.627282\pi$
$648$	−5.34087e11	−0.118994
$649$	−1.76027e11	−0.0389475
$650$	8.95973e11	0.196872
$651$	1.24844e12	0.272429
$652$	−1.68839e12	−0.365896
$653$	2.16230e12	0.465379	0.232690	−	0.972551i	$-0.425247\pi$
$653$	2.16230e12	0.465379	0.232690	+	0.972551i	$0.425247\pi$
$654$	2.13480e12	0.456307
$655$	−4.09046e12	−0.868333
$656$	1.15939e12	0.244434
$657$	1.15669e12	0.242199
$658$	−2.19658e12	−0.456805
$659$	−3.34439e12	−0.690769	−0.345384	−	0.938461i	$-0.612251\pi$
$659$	−3.34439e12	−0.690769	−0.345384	+	0.938461i	$0.612251\pi$
$660$	−1.55376e11	−0.0318740
$661$	6.80738e11	0.138699	0.0693495	−	0.997592i	$-0.477908\pi$
$661$	6.80738e11	0.138699	0.0693495	+	0.997592i	$0.477908\pi$
$662$	−1.40999e12	−0.285336
$663$	−2.33957e12	−0.470247
$664$	1.67697e12	0.334788
$665$	−1.36927e12	−0.271513
$666$	1.25426e12	0.247031
$667$	−3.52413e12	−0.689422
$668$	−3.59277e12	−0.698129
$669$	3.19081e12	0.615862
$670$	2.15693e12	0.413522
$671$	2.33489e12	0.444647
$672$	−9.70669e11	−0.183615
$673$	−8.90932e12	−1.67408	−0.837041	−	0.547140i	$-0.815716\pi$
$673$	−8.90932e12	−1.67408	−0.837041	+	0.547140i	$0.815716\pi$
$674$	−4.88226e12	−0.911280
$675$	−2.07594e11	−0.0384900
$676$	−2.07716e12	−0.382568
$677$	4.62599e12	0.846362	0.423181	−	0.906045i	$-0.360914\pi$
$677$	4.62599e12	0.846362	0.423181	+	0.906045i	$0.360914\pi$
$678$	−1.90099e12	−0.345499
$679$	7.67118e11	0.138499
$680$	−1.61276e12	−0.289253
$681$	−2.62212e12	−0.467187
$682$	1.36018e12	0.240751
$683$	4.80980e12	0.845734	0.422867	−	0.906192i	$-0.361024\pi$
$683$	4.80980e12	0.845734	0.422867	+	0.906192i	$0.361024\pi$
$684$	1.43218e12	0.250176
$685$	−2.38220e12	−0.413401
$686$	2.28600e11	0.0394110
$687$	4.62256e12	0.791730
$688$	2.17221e12	0.369619
$689$	−1.10913e13	−1.87497
$690$	−1.06096e12	−0.178189
$691$	−1.25914e12	−0.210099	−0.105049	−	0.994467i	$-0.533500\pi$
$691$	−1.25914e12	−0.210099	−0.105049	+	0.994467i	$0.533500\pi$
$692$	−1.00406e12	−0.166450
$693$	−2.02101e11	−0.0332866
$694$	−1.72120e12	−0.281652
$695$	4.29106e12	0.697642
$696$	−2.79108e12	−0.450849
$697$	−2.92526e12	−0.469480
$698$	6.91736e12	1.10304
$699$	−7.02539e10	−0.0111307
$700$	−2.24370e11	−0.0353202
$701$	−8.77170e12	−1.37200	−0.685998	−	0.727603i	$-0.740634\pi$
$701$	−8.77170e12	−1.37200	−0.685998	+	0.727603i	$0.740634\pi$
$702$	−1.21896e12	−0.189441
$703$	−1.05617e13	−1.63092
$704$	−1.59900e12	−0.245341
$705$	2.80428e12	0.427533
$706$	2.42802e12	0.367816
$707$	2.28669e12	0.344208
$708$	2.65871e11	0.0397668
$709$	−3.86988e12	−0.575161	−0.287580	−	0.957756i	$-0.592851\pi$
$709$	−3.86988e12	−0.575161	−0.287580	+	0.957756i	$0.592851\pi$
$710$	−4.01480e12	−0.592927
$711$	−3.68275e12	−0.540454
$712$	−1.01794e13	−1.48445
$713$	−8.14566e12	−1.18038
$714$	−6.68027e11	−0.0961949
$715$	−1.11358e12	−0.159347
$716$	−4.79659e12	−0.682063
$717$	4.56427e12	0.644964
$718$	−8.26459e10	−0.0116054
$719$	3.63696e12	0.507527	0.253763	−	0.967266i	$-0.418332\pi$
$719$	3.63696e12	0.507527	0.253763	+	0.967266i	$0.418332\pi$
$720$	−3.38011e11	−0.0468743
$721$	−3.09319e12	−0.426283
$722$	8.42149e12	1.15338
$723$	6.62963e12	0.902333
$724$	1.62555e12	0.219876
$725$	−1.08487e12	−0.145833
$726$	2.93423e12	0.391993
$727$	8.80402e12	1.16890	0.584449	−	0.811431i	$-0.301311\pi$
$727$	8.80402e12	1.16890	0.584449	+	0.811431i	$0.301311\pi$
$728$	−4.13713e12	−0.545893
$729$	2.82430e11	0.0370370
$730$	1.81981e12	0.237178
$731$	−5.48074e12	−0.709922
$732$	−3.52661e12	−0.454002
$733$	4.46624e12	0.571444	0.285722	−	0.958313i	$-0.407767\pi$
$733$	4.46624e12	0.571444	0.285722	+	0.958313i	$0.407767\pi$
$734$	−2.83539e11	−0.0360563
$735$	−2.91843e11	−0.0368856
$736$	6.33329e12	0.795572
$737$	−2.68079e12	−0.334702
$738$	−1.52412e12	−0.189132
$739$	−6.84484e12	−0.844235	−0.422117	−	0.906541i	$-0.638713\pi$
$739$	−6.84484e12	−0.844235	−0.422117	+	0.906541i	$0.638713\pi$
$740$	−1.73065e12	−0.212161
$741$	1.02645e13	1.25070
$742$	−3.16692e12	−0.383548
$743$	5.65679e11	0.0680958	0.0340479	−	0.999420i	$-0.489160\pi$
$743$	5.65679e11	0.0680958	0.0340479	+	0.999420i	$0.489160\pi$
$744$	−6.45130e12	−0.771914
$745$	1.90459e12	0.226516
$746$	3.32511e10	0.00393081
$747$	−8.86798e11	−0.104203
$748$	6.38316e11	0.0745553
$749$	−2.97182e12	−0.345028
$750$	−3.26607e11	−0.0376920
$751$	−1.09634e13	−1.25766	−0.628831	−	0.777542i	$-0.716466\pi$
$751$	−1.09634e13	−1.25766	−0.628831	+	0.777542i	$0.716466\pi$
$752$	4.56601e12	0.520662
$753$	−5.67647e12	−0.643429
$754$	−6.37016e12	−0.717761
$755$	1.31656e12	0.147462
$756$	3.05253e11	0.0339869
$757$	1.08262e13	1.19824	0.599119	−	0.800660i	$-0.295518\pi$
$757$	1.08262e13	1.19824	0.599119	+	0.800660i	$0.295518\pi$
$758$	−3.98242e12	−0.438163
$759$	1.31864e12	0.144225
$760$	7.07568e12	0.769319
$761$	5.20046e12	0.562097	0.281048	−	0.959694i	$-0.409318\pi$
$761$	5.20046e12	0.562097	0.281048	+	0.959694i	$0.409318\pi$
$762$	−6.42388e12	−0.690239
$763$	−3.83146e12	−0.409265
$764$	2.23990e12	0.237853
$765$	8.52839e11	0.0900307
$766$	−1.09101e12	−0.114498
$767$	1.90550e12	0.198806
$768$	5.83372e12	0.605090
$769$	−5.65047e12	−0.582661	−0.291331	−	0.956622i	$-0.594098\pi$
$769$	−5.65047e12	−0.582661	−0.291331	+	0.956622i	$0.594098\pi$
$770$	−3.17965e11	−0.0325965
$771$	1.88880e12	0.192504
$772$	5.03899e12	0.510582
$773$	7.45376e11	0.0750875	0.0375437	−	0.999295i	$-0.488047\pi$
$773$	7.45376e11	0.0750875	0.0375437	+	0.999295i	$0.488047\pi$
$774$	−2.85556e12	−0.285994
$775$	−2.50756e12	−0.249685
$776$	−3.96407e12	−0.392431
$777$	−2.25109e12	−0.221564
$778$	5.66345e12	0.554208
$779$	1.28341e13	1.24866
$780$	1.68195e12	0.162700
$781$	4.98989e12	0.479911
$782$	4.35865e12	0.416794
$783$	1.47595e12	0.140328
$784$	−4.75187e11	−0.0449203
$785$	2.97320e12	0.279455
$786$	8.75542e12	0.818230
$787$	−1.58169e13	−1.46972	−0.734860	−	0.678218i	$-0.762752\pi$
$787$	−1.58169e13	−1.46972	−0.734860	+	0.678218i	$0.762752\pi$
$788$	3.41822e12	0.315814
$789$	5.35236e12	0.491699
$790$	−5.79404e12	−0.529249
$791$	3.41183e12	0.309880
$792$	1.04436e12	0.0943160
$793$	−2.52752e13	−2.26969
$794$	−2.18269e12	−0.194894
$795$	4.04307e12	0.358971
$796$	1.02773e12	0.0907340
$797$	1.14704e13	1.00697	0.503486	−	0.864003i	$-0.332050\pi$
$797$	1.14704e13	1.00697	0.503486	+	0.864003i	$0.332050\pi$
$798$	2.93085e12	0.255847
$799$	−1.15205e13	−1.00003
$800$	1.94964e12	0.168286
$801$	5.38298e12	0.462037
$802$	7.38832e12	0.630610
$803$	−2.26180e12	−0.191970
$804$	4.04905e12	0.341744
$805$	1.90418e12	0.159818
$806$	−1.47240e13	−1.22890
$807$	−7.86872e10	−0.00653091
$808$	−1.18165e13	−0.975295
$809$	1.12568e13	0.923942	0.461971	−	0.886895i	$-0.347142\pi$
$809$	1.12568e13	0.923942	0.461971	+	0.886895i	$0.347142\pi$
$810$	4.44345e11	0.0362691
$811$	1.67279e13	1.35784	0.678920	−	0.734213i	$-0.262449\pi$
$811$	1.67279e13	1.35784	0.678920	+	0.734213i	$0.262449\pi$
$812$	1.59522e12	0.128771
$813$	−4.68856e12	−0.376385
$814$	−2.45258e12	−0.195800
$815$	4.41103e12	0.350212
$816$	1.38862e12	0.109642
$817$	2.40457e13	1.88816
$818$	4.69725e11	0.0366821
$819$	2.18775e12	0.169910
$820$	2.10300e12	0.162434
$821$	−1.05740e11	−0.00812262	−0.00406131	−	0.999992i	$-0.501293\pi$
$821$	−1.05740e11	−0.00812262	−0.00406131	+	0.999992i	$0.501293\pi$
$822$	5.09898e12	0.389547
$823$	−7.46168e12	−0.566940	−0.283470	−	0.958981i	$-0.591486\pi$
$823$	−7.46168e12	−0.566940	−0.283470	+	0.958981i	$0.591486\pi$
$824$	1.59840e13	1.20785
$825$	4.05931e11	0.0305077
$826$	5.44083e11	0.0406682
$827$	−1.11944e13	−0.832194	−0.416097	−	0.909320i	$-0.636602\pi$
$827$	−1.11944e13	−0.832194	−0.416097	+	0.909320i	$0.636602\pi$
$828$	−1.99167e12	−0.147259
$829$	−8.60493e12	−0.632779	−0.316390	−	0.948629i	$-0.602471\pi$
$829$	−8.60493e12	−0.632779	−0.316390	+	0.948629i	$0.602471\pi$
$830$	−1.39519e12	−0.102043
$831$	−4.97630e12	−0.361994
$832$	1.73092e13	1.25234
$833$	1.19895e12	0.0862777
$834$	−9.18478e12	−0.657388
$835$	9.38637e12	0.668203
$836$	−2.80050e12	−0.198293
$837$	3.41150e12	0.240260
$838$	−1.64561e11	−0.0115273
$839$	−7.30231e11	−0.0508782	−0.0254391	−	0.999676i	$-0.508098\pi$
$839$	−7.30231e11	−0.0508782	−0.0254391	+	0.999676i	$0.508098\pi$
$840$	1.50810e12	0.104513
$841$	−6.79400e12	−0.468321
$842$	−7.19019e12	−0.492988
$843$	−2.04136e12	−0.139218
$844$	7.85903e12	0.533123
$845$	5.42671e12	0.366169
$846$	−6.00241e12	−0.402864
$847$	−5.26624e12	−0.351581
$848$	6.58304e12	0.437165
$849$	−8.36157e12	−0.552336
$850$	1.34177e12	0.0881640
$851$	1.46876e13	0.959995
$852$	−7.53670e12	−0.490008
$853$	4.37580e12	0.283000	0.141500	−	0.989938i	$-0.454807\pi$
$853$	4.37580e12	0.283000	0.141500	+	0.989938i	$0.454807\pi$
$854$	−7.21692e12	−0.464292
$855$	−3.74168e12	−0.239452
$856$	1.53568e13	0.977619
$857$	7.72902e12	0.489453	0.244726	−	0.969592i	$-0.421302\pi$
$857$	7.72902e12	0.489453	0.244726	+	0.969592i	$0.421302\pi$
$858$	2.38356e12	0.150153
$859$	−2.80752e13	−1.75936	−0.879678	−	0.475571i	$-0.842242\pi$
$859$	−2.80752e13	−1.75936	−0.879678	+	0.475571i	$0.842242\pi$
$860$	3.94016e12	0.245624
$861$	2.73543e12	0.169633
$862$	6.33415e12	0.390756
$863$	−2.22338e13	−1.36447	−0.682236	−	0.731132i	$-0.738993\pi$
$863$	−2.22338e13	−1.36447	−0.682236	+	0.731132i	$0.738993\pi$
$864$	−2.65246e12	−0.161934
$865$	2.62319e12	0.159315
$866$	−6.30688e12	−0.381052
$867$	6.10198e12	0.366763
$868$	3.68718e12	0.220473
$869$	7.20126e12	0.428371
$870$	2.32210e12	0.137418
$871$	2.90195e13	1.70848
$872$	1.97990e13	1.15963
$873$	2.09623e12	0.122145
$874$	−1.91228e13	−1.10854
$875$	5.86182e11	0.0338062
$876$	3.41621e12	0.196009
$877$	−1.06207e13	−0.606256	−0.303128	−	0.952950i	$-0.598031\pi$
$877$	−1.06207e13	−0.606256	−0.303128	+	0.952950i	$0.598031\pi$
$878$	1.42657e13	0.810156
$879$	−1.48468e13	−0.838850
$880$	6.60948e11	0.0371531
$881$	1.28159e13	0.716731	0.358365	−	0.933581i	$-0.383334\pi$
$881$	1.28159e13	0.716731	0.358365	+	0.933581i	$0.383334\pi$
$882$	6.24675e11	0.0347573
$883$	−2.93906e12	−0.162699	−0.0813496	−	0.996686i	$-0.525923\pi$
$883$	−2.93906e12	−0.162699	−0.0813496	+	0.996686i	$0.525923\pi$
$884$	−6.90978e12	−0.380565
$885$	−6.94606e11	−0.0380622
$886$	−1.88842e13	−1.02955
$887$	9.57880e12	0.519583	0.259792	−	0.965665i	$-0.416346\pi$
$887$	9.57880e12	0.519583	0.259792	+	0.965665i	$0.416346\pi$
$888$	1.16325e13	0.627790
$889$	1.15293e13	0.619080
$890$	8.46901e12	0.452457
$891$	−5.52264e11	−0.0293560
$892$	9.42384e12	0.498409
$893$	5.05443e13	2.65975
$894$	−4.07668e12	−0.213446
$895$	1.25314e13	0.652826
$896$	−1.19324e12	−0.0618503
$897$	−1.42743e13	−0.736190
$898$	2.51897e13	1.29265
$899$	1.78282e13	0.910307
$900$	−6.13115e11	−0.0311495
$901$	−1.66097e13	−0.839655
$902$	2.98026e12	0.149908
$903$	5.12506e12	0.256510
$904$	−1.76306e13	−0.878030
$905$	−4.24687e12	−0.210451
$906$	−2.81804e12	−0.138954
$907$	−4.48034e12	−0.219826	−0.109913	−	0.993941i	$-0.535057\pi$
$907$	−4.48034e12	−0.219826	−0.109913	+	0.993941i	$0.535057\pi$
$908$	−7.74427e12	−0.378089
$909$	6.24864e12	0.303562
$910$	3.44197e12	0.166388
$911$	−2.29058e13	−1.10183	−0.550913	−	0.834563i	$-0.685720\pi$
$911$	−2.29058e13	−1.10183	−0.550913	+	0.834563i	$0.685720\pi$
$912$	−6.09231e12	−0.291612
$913$	1.73405e12	0.0825930
$914$	−1.31406e13	−0.622814
$915$	9.21351e12	0.434540
$916$	1.36524e13	0.640738
$917$	−1.57139e13	−0.733875
$918$	−1.82546e12	−0.0848359
$919$	−1.89723e13	−0.877407	−0.438703	−	0.898632i	$-0.644562\pi$
$919$	−1.89723e13	−0.877407	−0.438703	+	0.898632i	$0.644562\pi$
$920$	−9.83983e12	−0.452837
$921$	2.07549e13	0.950500
$922$	−2.55797e13	−1.16575
$923$	−5.40156e13	−2.44969
$924$	−5.96893e11	−0.0269384
$925$	4.52144e12	0.203067
$926$	9.76105e12	0.436262
$927$	−8.45249e12	−0.375946
$928$	−1.38615e13	−0.613541
$929$	3.53158e12	0.155560	0.0777800	−	0.996971i	$-0.475217\pi$
$929$	3.53158e12	0.155560	0.0777800	+	0.996971i	$0.475217\pi$
$930$	5.36729e12	0.235278
$931$	−5.26018e12	−0.229471
$932$	−2.07490e11	−0.00900795
$933$	2.33042e12	0.100686
$934$	8.22943e12	0.353841
$935$	−1.66765e12	−0.0713594
$936$	−1.13052e13	−0.481433
$937$	−2.21442e13	−0.938494	−0.469247	−	0.883067i	$-0.655475\pi$
$937$	−2.21442e13	−0.938494	−0.469247	+	0.883067i	$0.655475\pi$
$938$	8.28605e12	0.349490
$939$	7.87621e12	0.330615
$940$	8.28224e12	0.345997
$941$	−2.35256e13	−0.978111	−0.489055	−	0.872253i	$-0.662658\pi$
$941$	−2.35256e13	−0.978111	−0.489055	+	0.872253i	$0.662658\pi$
$942$	−6.36399e12	−0.263330
$943$	−1.78478e13	−0.734989
$944$	−1.13098e12	−0.0463532
$945$	−7.97494e11	−0.0325300
$946$	5.58378e12	0.226683
$947$	3.85928e13	1.55931	0.779654	−	0.626211i	$-0.215395\pi$
$947$	3.85928e13	1.55931	0.779654	+	0.626211i	$0.215395\pi$
$948$	−1.08767e13	−0.437383
$949$	2.44840e13	0.979905
$950$	−5.88676e12	−0.234488
$951$	1.26005e13	0.499547
$952$	−6.19556e12	−0.244464
$953$	3.03185e13	1.19067	0.595333	−	0.803479i	$-0.297020\pi$
$953$	3.03185e13	1.19067	0.595333	+	0.803479i	$0.297020\pi$
$954$	−8.65398e12	−0.338258
$955$	−5.85190e12	−0.227657
$956$	1.34803e13	0.521961
$957$	−2.88608e12	−0.111225
$958$	−8.76166e12	−0.336079
$959$	−9.15147e12	−0.349387
$960$	−6.30966e12	−0.239765
$961$	1.47683e13	0.558568
$962$	2.65492e13	0.999455
$963$	−8.12083e12	−0.304286
$964$	1.95802e13	0.730247
$965$	−1.31647e13	−0.488695
$966$	−4.07580e12	−0.150597
$967$	2.93197e13	1.07830	0.539150	−	0.842210i	$-0.318745\pi$
$967$	2.93197e13	1.07830	0.539150	+	0.842210i	$0.318745\pi$
$968$	2.72132e13	0.996188
$969$	1.53716e13	0.560094
$970$	3.29799e12	0.119613
$971$	−1.40970e13	−0.508909	−0.254454	−	0.967085i	$-0.581896\pi$
$971$	−1.40970e13	−0.508909	−0.254454	+	0.967085i	$0.581896\pi$
$972$	8.34137e11	0.0299736
$973$	1.64845e13	0.589615
$974$	−2.98170e13	−1.06157
$975$	−4.39420e12	−0.155725
$976$	1.50017e13	0.529196
$977$	1.05548e13	0.370615	0.185307	−	0.982681i	$-0.440672\pi$
$977$	1.05548e13	0.370615	0.185307	+	0.982681i	$0.440672\pi$
$978$	−9.44159e12	−0.330005
$979$	−1.05259e13	−0.366216
$980$	−8.61939e11	−0.0298510
$981$	−1.04699e13	−0.360937
$982$	2.93312e13	1.00653
$983$	−4.57225e13	−1.56185	−0.780924	−	0.624626i	$-0.785251\pi$
$983$	−4.57225e13	−1.56185	−0.780924	+	0.624626i	$0.785251\pi$
$984$	−1.41353e13	−0.480648
$985$	−8.93033e12	−0.302276
$986$	−9.53965e12	−0.321430
$987$	1.07729e13	0.361331
$988$	3.03154e13	1.01218
$989$	−3.34393e13	−1.11141
$990$	−8.68874e11	−0.0287474
$991$	−1.68443e12	−0.0554780	−0.0277390	−	0.999615i	$-0.508831\pi$
$991$	−1.68443e12	−0.0554780	−0.0277390	+	0.999615i	$0.508831\pi$
$992$	−3.20394e13	−1.05047
$993$	6.91517e12	0.225700
$994$	−1.54232e13	−0.501115
$995$	−2.68501e12	−0.0868446
$996$	−2.61910e12	−0.0843306
$997$	−6.00188e12	−0.192380	−0.0961899	−	0.995363i	$-0.530666\pi$
$997$	−6.00188e12	−0.192380	−0.0961899	+	0.995363i	$0.530666\pi$
$998$	−1.46146e13	−0.466338
$999$	−6.15136e12	−0.195401

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.10.a.a.1.4	✓	4
3.2	odd	2		315.10.a.i.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.10.a.a.1.4	✓	4	1.1	even	1	trivial
315.10.a.i.1.1		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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	105.a (trivial)

\(f(q)\)	\(=\)	\(q+16.5158 q^{2} -81.0000 q^{3} -239.228 q^{4} +625.000 q^{5} -1337.78 q^{6} +2401.00 q^{7} -12407.1 q^{8} +6561.00 q^{9} +10322.4 q^{10} -12829.4 q^{11} +19377.5 q^{12} +138879. q^{13} +39654.5 q^{14} -50625.0 q^{15} -82429.1 q^{16} +207978. q^{17} +108360. q^{18} -912465. q^{19} -149518. q^{20} -194481. q^{21} -211888. q^{22} +1.26892e6 q^{23} +1.00498e6 q^{24} +390625. q^{25} +2.29369e6 q^{26} -531441. q^{27} -574387. q^{28} -2.77726e6 q^{29} -836113. q^{30} -6.41934e6 q^{31} +4.99107e6 q^{32} +1.03918e6 q^{33} +3.43492e6 q^{34} +1.50062e6 q^{35} -1.56958e6 q^{36} +1.15749e7 q^{37} -1.50701e7 q^{38} -1.12492e7 q^{39} -7.75446e6 q^{40} -1.40653e7 q^{41} -3.21201e6 q^{42} -2.63525e7 q^{43} +3.06916e6 q^{44} +4.10062e6 q^{45} +2.09573e7 q^{46} -5.53931e7 q^{47} +6.67676e6 q^{48} +5.76480e6 q^{49} +6.45149e6 q^{50} -1.68462e7 q^{51} -3.32236e7 q^{52} -7.98630e7 q^{53} -8.77718e6 q^{54} -8.01838e6 q^{55} -2.97895e7 q^{56} +7.39097e7 q^{57} -4.58686e7 q^{58} +1.37206e7 q^{59} +1.21109e7 q^{60} -1.81995e8 q^{61} -1.06021e8 q^{62} +1.57530e7 q^{63} +1.24635e8 q^{64} +8.67991e7 q^{65} +1.71629e7 q^{66} +2.08956e8 q^{67} -4.97541e7 q^{68} -1.02783e8 q^{69} +2.47840e7 q^{70} -3.88941e8 q^{71} -8.14032e7 q^{72} +1.76298e8 q^{73} +1.91168e8 q^{74} -3.16406e7 q^{75} +2.18287e8 q^{76} -3.08034e7 q^{77} -1.85789e8 q^{78} -5.61309e8 q^{79} -5.15182e7 q^{80} +4.30467e7 q^{81} -2.32299e8 q^{82} -1.35162e8 q^{83} +4.65253e7 q^{84} +1.29986e8 q^{85} -4.35233e8 q^{86} +2.24958e8 q^{87} +1.59176e8 q^{88} +8.20451e8 q^{89} +6.77251e7 q^{90} +3.33447e8 q^{91} -3.03562e8 q^{92} +5.19967e8 q^{93} -9.14862e8 q^{94} -5.70291e8 q^{95} -4.04277e8 q^{96} +3.19499e8 q^{97} +9.52103e7 q^{98} -8.41738e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 41 q^{2} - 324 q^{3} + 501 q^{4} + 2500 q^{5} + 3321 q^{6} + 9604 q^{7} - 29367 q^{8} + 26244 q^{9} - 25625 q^{10} - 32854 q^{11} - 40581 q^{12} - 133882 q^{13} - 98441 q^{14} - 202500 q^{15} - 90479 q^{16}+ \cdots - 215555094 q^{99}+O(q^{100}) \) 4 * q - 41 * q^2 - 324 * q^3 + 501 * q^4 + 2500 * q^5 + 3321 * q^6 + 9604 * q^7 - 29367 * q^8 + 26244 * q^9 - 25625 * q^10 - 32854 * q^11 - 40581 * q^12 - 133882 * q^13 - 98441 * q^14 - 202500 * q^15 - 90479 * q^16 + 334344 * q^17 - 269001 * q^18 + 72046 * q^19 + 313125 * q^20 - 777924 * q^21 + 990556 * q^22 + 47460 * q^23 + 2378727 * q^24 + 1562500 * q^25 + 4203458 * q^26 - 2125764 * q^27 + 1202901 * q^28 + 7010312 * q^29 + 2075625 * q^30 - 3711690 * q^31 + 18115265 * q^32 + 2661174 * q^33 + 12757214 * q^34 + 6002500 * q^35 + 3287061 * q^36 + 5222716 * q^37 - 759964 * q^38 + 10844442 * q^39 - 18354375 * q^40 - 5689292 * q^41 + 7973721 * q^42 - 71286384 * q^43 + 6098004 * q^44 + 16402500 * q^45 + 13833560 * q^46 - 100832160 * q^47 + 7328799 * q^48 + 23059204 * q^49 - 16015625 * q^50 - 27081864 * q^51 - 7238698 * q^52 - 149250454 * q^53 + 21789081 * q^54 - 20533750 * q^55 - 70510167 * q^56 - 5835726 * q^57 - 191838758 * q^58 + 24779068 * q^59 - 25363125 * q^60 - 301336048 * q^61 - 107946280 * q^62 + 63011844 * q^63 - 71492607 * q^64 - 83676250 * q^65 - 80235036 * q^66 - 10978016 * q^67 - 527886134 * q^68 - 3844260 * q^69 - 61525625 * q^70 - 507837170 * q^71 - 192676887 * q^72 - 158796526 * q^73 - 252589374 * q^74 - 126562500 * q^75 - 604814036 * q^76 - 78882454 * q^77 - 340480098 * q^78 - 36676584 * q^79 - 56549375 * q^80 + 172186884 * q^81 - 1841487282 * q^82 + 201009048 * q^83 - 97434981 * q^84 + 208965000 * q^85 + 162200156 * q^86 - 567835272 * q^87 - 1446483548 * q^88 + 161323024 * q^89 - 168125625 * q^90 - 321450682 * q^91 + 563662840 * q^92 + 300646890 * q^93 - 918128840 * q^94 + 45028750 * q^95 - 1467336465 * q^96 - 1913030882 * q^97 - 236356841 * q^98 - 215555094 * q^99

Introduction

L-functions

Modular forms

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