LMFDB - Embedded newform 169.10.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,10,Mod(1,169)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(169, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("169.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	169.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:	$87.0410563117$
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} - 1602x^{2} + 1544x + 342272 $ x^4 - x^3 - 1602x^2 + 1544x + 342272
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 13)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$36.6235$ of defining polynomial
Character	$\chi$	$=$	169.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+44.6235 q^{2} -51.0278 q^{3} +1479.26 q^{4} -151.187 q^{5} -2277.04 q^{6} -5436.58 q^{7} +43162.5 q^{8} -17079.2 q^{9} -6746.48 q^{10} -33841.6 q^{11} -75483.2 q^{12} -242599. q^{14} +7714.72 q^{15} +1.16868e6 q^{16} -588951. q^{17} -762133. q^{18} +123244. q^{19} -223644. q^{20} +277417. q^{21} -1.51013e6 q^{22} -1.55650e6 q^{23} -2.20248e6 q^{24} -1.93027e6 q^{25} +1.87589e6 q^{27} -8.04211e6 q^{28} +273935. q^{29} +344258. q^{30} +5.07992e6 q^{31} +3.00515e7 q^{32} +1.72686e6 q^{33} -2.62811e7 q^{34} +821938. q^{35} -2.52645e7 q^{36} -8.27832e6 q^{37} +5.49960e6 q^{38} -6.52559e6 q^{40} -1.69055e7 q^{41} +1.23793e7 q^{42} -1.23150e7 q^{43} -5.00604e7 q^{44} +2.58214e6 q^{45} -6.94565e7 q^{46} +3.71528e7 q^{47} -5.96352e7 q^{48} -1.07972e7 q^{49} -8.61353e7 q^{50} +3.00528e7 q^{51} -5.85375e7 q^{53} +8.37089e7 q^{54} +5.11640e6 q^{55} -2.34656e8 q^{56} -6.28889e6 q^{57} +1.22239e7 q^{58} +2.83630e7 q^{59} +1.14121e7 q^{60} +2.89102e7 q^{61} +2.26684e8 q^{62} +9.28523e7 q^{63} +7.42638e8 q^{64} +7.70586e7 q^{66} +9.52452e7 q^{67} -8.71211e8 q^{68} +7.94247e7 q^{69} +3.66778e7 q^{70} +1.35041e7 q^{71} -7.37179e8 q^{72} +1.20684e8 q^{73} -3.69408e8 q^{74} +9.84972e7 q^{75} +1.82310e8 q^{76} +1.83983e8 q^{77} +2.80552e8 q^{79} -1.76689e8 q^{80} +2.40447e8 q^{81} -7.54385e8 q^{82} -5.16031e8 q^{83} +4.10371e8 q^{84} +8.90415e7 q^{85} -5.49538e8 q^{86} -1.39783e7 q^{87} -1.46069e9 q^{88} -1.00683e9 q^{89} +1.15224e8 q^{90} -2.30247e9 q^{92} -2.59217e8 q^{93} +1.65789e9 q^{94} -1.86329e7 q^{95} -1.53346e9 q^{96} -1.99014e8 q^{97} -4.81809e8 q^{98} +5.77986e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 33 q^{2} - 163 q^{3} + 1429 q^{4} - 471 q^{5} + 4529 q^{6} + 11241 q^{7} + 45543 q^{8} - 29953 q^{9} - 67831 q^{10} + 40140 q^{11} - 155479 q^{12} - 277653 q^{14} - 83307 q^{15} + 726609 q^{16} + 78717 q^{17}+ \cdots - 2132181050 q^{99}+O(q^{100}) $ 4 * q + 33 * q^2 - 163 * q^3 + 1429 * q^4 - 471 * q^5 + 4529 * q^6 + 11241 * q^7 + 45543 * q^8 - 29953 * q^9 - 67831 * q^10 + 40140 * q^11 - 155479 * q^12 - 277653 * q^14 - 83307 * q^15 + 726609 * q^16 + 78717 * q^17 - 1691026 * q^18 - 209664 * q^19 - 870843 * q^20 - 1138431 * q^21 + 1364090 * q^22 - 4257444 * q^23 - 3561573 * q^24 - 2900157 * q^25 - 2077801 * q^27 - 4035181 * q^28 - 1647936 * q^29 - 744143 * q^30 + 11366002 * q^31 + 29458959 * q^32 + 14413222 * q^33 - 26257659 * q^34 - 13789797 * q^35 - 11587714 * q^36 - 4636891 * q^37 + 25172466 * q^38 + 22536791 * q^40 - 13859538 * q^41 + 75564923 * q^42 - 33368081 * q^43 - 66489222 * q^44 + 17423928 * q^45 - 71369332 * q^46 + 3943005 * q^47 - 620787 * q^48 + 23294923 * q^49 + 4217748 * q^50 - 19664471 * q^51 - 171019326 * q^53 + 64946915 * q^54 - 121160538 * q^55 - 281552967 * q^56 + 47829030 * q^57 - 79964734 * q^58 + 63389388 * q^59 - 37708135 * q^60 + 77050190 * q^61 - 95878740 * q^62 + 155695476 * q^63 + 768962465 * q^64 - 42396374 * q^66 + 41174072 * q^67 - 717615423 * q^68 + 546642556 * q^69 - 409056389 * q^70 - 252460989 * q^71 - 562579254 * q^72 - 594415068 * q^73 - 957058539 * q^74 + 533318748 * q^75 + 326897170 * q^76 + 561950454 * q^77 + 115998984 * q^79 + 509107233 * q^80 + 437803700 * q^81 - 875148240 * q^82 + 79577862 * q^83 - 108899441 * q^84 - 549463469 * q^85 + 589924887 * q^86 - 1087526510 * q^87 - 2327564370 * q^88 + 1152240276 * q^89 + 877550038 * q^90 - 4213481460 * q^92 - 1618266556 * q^93 + 1859909503 * q^94 - 1273705170 * q^95 - 3171454029 * q^96 - 1049098084 * q^97 - 420532254 * q^98 - 2132181050 * 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 $

$2$	44.6235	1.97210	0.986050	−	0.166451i	$-0.0532307\pi$
$2$	44.6235	1.97210	0.986050	+	0.166451i	$0.0532307\pi$
$3$	−51.0278	−0.363715	−0.181857	−	0.983325i	$-0.558211\pi$
$3$	−51.0278	−0.363715	−0.181857	+	0.983325i	$0.558211\pi$
$4$	1479.26	2.88918
$5$	−151.187	−0.108180	−0.0540902	−	0.998536i	$-0.517226\pi$
$5$	−151.187	−0.108180	−0.0540902	+	0.998536i	$0.517226\pi$
$6$	−2277.04	−0.717282
$7$	−5436.58	−0.855824	−0.427912	−	0.903820i	$-0.640751\pi$
$7$	−5436.58	−0.855824	−0.427912	+	0.903820i	$0.640751\pi$
$8$	43162.5	3.72564
$9$	−17079.2	−0.867712
$10$	−6746.48	−0.213342
$11$	−33841.6	−0.696921	−0.348461	−	0.937323i	$-0.613295\pi$
$11$	−33841.6	−0.696921	−0.348461	+	0.937323i	$0.613295\pi$
$12$	−75483.2	−1.05084
$13$	0	0
$13$	0	0
$14$	−242599.	−1.68777
$15$	7714.72	0.0393468
$16$	1.16868e6	4.45816
$17$	−588951.	−1.71025	−0.855124	−	0.518424i	$-0.826519\pi$
$17$	−588951.	−1.71025	−0.855124	+	0.518424i	$0.826519\pi$
$18$	−762133.	−1.71121
$19$	123244.	0.216958	0.108479	−	0.994099i	$-0.465402\pi$
$19$	123244.	0.216958	0.108479	+	0.994099i	$0.465402\pi$
$20$	−223644.	−0.312552
$21$	277417.	0.311276
$22$	−1.51013e6	−1.37440
$23$	−1.55650e6	−1.15978	−0.579888	−	0.814696i	$-0.696904\pi$
$23$	−1.55650e6	−1.15978	−0.579888	+	0.814696i	$0.696904\pi$
$24$	−2.20248e6	−1.35507
$25$	−1.93027e6	−0.988297
$26$	0	0
$27$	1.87589e6	0.679314
$28$	−8.04211e6	−2.47263
$29$	273935.	0.0719211	0.0359606	−	0.999353i	$-0.488551\pi$
$29$	273935.	0.0719211	0.0359606	+	0.999353i	$0.488551\pi$
$30$	344258.	0.0775958
$31$	5.07992e6	0.987936	0.493968	−	0.869480i	$-0.335546\pi$
$31$	5.07992e6	0.987936	0.493968	+	0.869480i	$0.335546\pi$
$32$	3.00515e7	5.06630
$33$	1.72686e6	0.253480
$34$	−2.62811e7	−3.37278
$35$	821938.	0.0925834
$36$	−2.52645e7	−2.50697
$37$	−8.27832e6	−0.726164	−0.363082	−	0.931757i	$-0.618275\pi$
$37$	−8.27832e6	−0.726164	−0.363082	+	0.931757i	$0.618275\pi$
$38$	5.49960e6	0.427863
$39$	0	0
$40$	−6.52559e6	−0.403041
$41$	−1.69055e7	−0.934333	−0.467167	−	0.884169i	$-0.654725\pi$
$41$	−1.69055e7	−0.934333	−0.467167	+	0.884169i	$0.654725\pi$
$42$	1.23793e7	0.613867
$43$	−1.23150e7	−0.549320	−0.274660	−	0.961541i	$-0.588565\pi$
$43$	−1.23150e7	−0.549320	−0.274660	+	0.961541i	$0.588565\pi$
$44$	−5.00604e7	−2.01353
$45$	2.58214e6	0.0938693
$46$	−6.94565e7	−2.28719
$47$	3.71528e7	1.11058	0.555292	−	0.831655i	$-0.312606\pi$
$47$	3.71528e7	1.11058	0.555292	+	0.831655i	$0.312606\pi$
$48$	−5.96352e7	−1.62150
$49$	−1.07972e7	−0.267565
$50$	−8.61353e7	−1.94902
$51$	3.00528e7	0.622042
$52$	0	0
$53$	−5.85375e7	−1.01904	−0.509521	−	0.860458i	$-0.670178\pi$
$53$	−5.85375e7	−1.01904	−0.509521	+	0.860458i	$0.670178\pi$
$54$	8.37089e7	1.33968
$55$	5.11640e6	0.0753932
$56$	−2.34656e8	−3.18850
$57$	−6.28889e6	−0.0789109
$58$	1.22239e7	0.141836
$59$	2.83630e7	0.304732	0.152366	−	0.988324i	$-0.451311\pi$
$59$	2.83630e7	0.304732	0.152366	+	0.988324i	$0.451311\pi$
$60$	1.14121e7	0.113680
$61$	2.89102e7	0.267342	0.133671	−	0.991026i	$-0.457323\pi$
$61$	2.89102e7	0.267342	0.133671	+	0.991026i	$0.457323\pi$
$62$	2.26684e8	1.94831
$63$	9.28523e7	0.742609
$64$	7.42638e8	5.53308
$65$	0	0
$66$	7.70586e7	0.499889
$67$	9.52452e7	0.577439	0.288720	−	0.957414i	$-0.406770\pi$
$67$	9.52452e7	0.577439	0.288720	+	0.957414i	$0.406770\pi$
$68$	−8.71211e8	−4.94121
$69$	7.94247e7	0.421827
$70$	3.66778e7	0.182584
$71$	1.35041e7	0.0630671	0.0315335	−	0.999503i	$-0.489961\pi$
$71$	1.35041e7	0.0630671	0.0315335	+	0.999503i	$0.489961\pi$
$72$	−7.37179e8	−3.23278
$73$	1.20684e8	0.497390	0.248695	−	0.968582i	$-0.419998\pi$
$73$	1.20684e8	0.497390	0.248695	+	0.968582i	$0.419998\pi$
$74$	−3.69408e8	−1.43207
$75$	9.84972e7	0.359458
$76$	1.82310e8	0.626831
$77$	1.83983e8	0.596442
$78$	0	0
$79$	2.80552e8	0.810386	0.405193	−	0.914231i	$-0.367204\pi$
$79$	2.80552e8	0.810386	0.405193	+	0.914231i	$0.367204\pi$
$80$	−1.76689e8	−0.482286
$81$	2.40447e8	0.620635
$82$	−7.54385e8	−1.84260
$83$	−5.16031e8	−1.19350	−0.596752	−	0.802426i	$-0.703542\pi$
$83$	−5.16031e8	−1.19350	−0.596752	+	0.802426i	$0.703542\pi$
$84$	4.10371e8	0.899331
$85$	8.90415e7	0.185015
$86$	−5.49538e8	−1.08331
$87$	−1.39783e7	−0.0261588
$88$	−1.46069e9	−2.59648
$89$	−1.00683e9	−1.70099	−0.850497	−	0.525980i	$-0.823699\pi$
$89$	−1.00683e9	−1.70099	−0.850497	+	0.525980i	$0.823699\pi$
$90$	1.15224e8	0.185120
$91$	0	0
$92$	−2.30247e9	−3.35080
$93$	−2.59217e8	−0.359327
$94$	1.65789e9	2.19018
$95$	−1.86329e7	−0.0234706
$96$	−1.53346e9	−1.84269
$97$	−1.99014e8	−0.228250	−0.114125	−	0.993466i	$-0.536406\pi$
$97$	−1.99014e8	−0.228250	−0.114125	+	0.993466i	$0.536406\pi$
$98$	−4.81809e8	−0.527664
$99$	5.77986e8	0.604727
$100$	−2.85536e9	−2.85536
$101$	−6.11325e8	−0.584556	−0.292278	−	0.956333i	$-0.594413\pi$
$101$	−6.11325e8	−0.584556	−0.292278	+	0.956333i	$0.594413\pi$
$102$	1.34106e9	1.22673
$103$	−1.23832e9	−1.08409	−0.542047	−	0.840348i	$-0.682351\pi$
$103$	−1.23832e9	−1.08409	−0.542047	+	0.840348i	$0.682351\pi$
$104$	0	0
$105$	−4.19417e7	−0.0336739
$106$	−2.61215e9	−2.00965
$107$	1.86278e8	0.137383	0.0686917	−	0.997638i	$-0.478118\pi$
$107$	1.86278e8	0.137383	0.0686917	+	0.997638i	$0.478118\pi$
$108$	2.77493e9	1.96266
$109$	1.79600e9	1.21868	0.609338	−	0.792911i	$-0.291435\pi$
$109$	1.79600e9	1.21868	0.609338	+	0.792911i	$0.291435\pi$
$110$	2.28312e8	0.148683
$111$	4.22424e8	0.264116
$112$	−6.35363e9	−3.81541
$113$	1.28965e9	0.744081	0.372041	−	0.928216i	$-0.378658\pi$
$113$	1.28965e9	0.744081	0.372041	+	0.928216i	$0.378658\pi$
$114$	−2.80632e8	−0.155620
$115$	2.35322e8	0.125465
$116$	4.05221e8	0.207793
$117$	0	0
$118$	1.26566e9	0.600961
$119$	3.20188e9	1.46367
$120$	3.32986e8	0.146592
$121$	−1.21269e9	−0.514301
$122$	1.29008e9	0.527225
$123$	8.62652e8	0.339831
$124$	7.51451e9	2.85432
$125$	5.87117e8	0.215095
$126$	4.14340e9	1.46450
$127$	2.03329e9	0.693558	0.346779	−	0.937947i	$-0.387275\pi$
$127$	2.03329e9	0.693558	0.346779	+	0.937947i	$0.387275\pi$
$128$	1.77528e10	5.84549
$129$	6.28406e8	0.199796
$130$	0	0
$131$	−1.89177e8	−0.0561237	−0.0280619	−	0.999606i	$-0.508934\pi$
$131$	−1.89177e8	−0.0561237	−0.0280619	+	0.999606i	$0.508934\pi$
$132$	2.55447e9	0.732350
$133$	−6.70028e8	−0.185678
$134$	4.25017e9	1.13877
$135$	−2.83610e8	−0.0734884
$136$	−2.54206e10	−6.37177
$137$	−4.31369e9	−1.04618	−0.523090	−	0.852277i	$-0.675221\pi$
$137$	−4.31369e9	−1.04618	−0.523090	+	0.852277i	$0.675221\pi$
$138$	3.54421e9	0.831885
$139$	−4.25633e9	−0.967094	−0.483547	−	0.875318i	$-0.660652\pi$
$139$	−4.25633e9	−0.967094	−0.483547	+	0.875318i	$0.660652\pi$
$140$	1.21586e9	0.267490
$141$	−1.89583e9	−0.403936
$142$	6.02600e8	0.124375
$143$	0	0
$144$	−1.99601e10	−3.86840
$145$	−4.14153e7	−0.00778045
$146$	5.38535e9	0.980903
$147$	5.50957e8	0.0973172
$148$	−1.22458e10	−2.09801
$149$	−4.12743e9	−0.686027	−0.343013	−	0.939330i	$-0.611448\pi$
$149$	−4.12743e9	−0.686027	−0.343013	+	0.939330i	$0.611448\pi$
$150$	4.39529e9	0.708887
$151$	2.08019e9	0.325617	0.162808	−	0.986658i	$-0.447945\pi$
$151$	2.08019e9	0.325617	0.162808	+	0.986658i	$0.447945\pi$
$152$	5.31953e9	0.808309
$153$	1.00588e10	1.48400
$154$	8.20995e9	1.17624
$155$	−7.68015e8	−0.106875
$156$	0	0
$157$	8.58336e9	1.12748	0.563740	−	0.825952i	$-0.309362\pi$
$157$	8.58336e9	1.12748	0.563740	+	0.825952i	$0.309362\pi$
$158$	1.25192e10	1.59816
$159$	2.98704e9	0.370641
$160$	−4.54338e9	−0.548074
$161$	8.46204e9	0.992564
$162$	1.07296e10	1.22395
$163$	1.61852e10	1.79586	0.897931	−	0.440136i	$-0.145070\pi$
$163$	1.61852e10	1.79586	0.897931	+	0.440136i	$0.145070\pi$
$164$	−2.50077e10	−2.69945
$165$	−2.61078e8	−0.0274216
$166$	−2.30271e10	−2.35371
$167$	−6.45435e9	−0.642138	−0.321069	−	0.947056i	$-0.604042\pi$
$167$	−6.45435e9	−0.642138	−0.321069	+	0.947056i	$0.604042\pi$
$168$	1.19740e10	1.15970
$169$	0	0
$170$	3.97335e9	0.364868
$171$	−2.10491e9	−0.188257
$172$	−1.82170e10	−1.58708
$173$	1.10049e10	0.934067	0.467033	−	0.884240i	$-0.345323\pi$
$173$	1.10049e10	0.934067	0.467033	+	0.884240i	$0.345323\pi$
$174$	−6.23760e8	−0.0515877
$175$	1.04941e10	0.845809
$176$	−3.95500e10	−3.10699
$177$	−1.44730e9	−0.110835
$178$	−4.49285e10	−3.35453
$179$	6.52622e7	0.00475142	0.00237571	−	0.999997i	$-0.499244\pi$
$179$	6.52622e7	0.00475142	0.00237571	+	0.999997i	$0.499244\pi$
$180$	3.81965e9	0.271205
$181$	1.03390e10	0.716017	0.358008	−	0.933718i	$-0.383456\pi$
$181$	1.03390e10	0.716017	0.358008	+	0.933718i	$0.383456\pi$
$182$	0	0
$183$	−1.47522e9	−0.0972363
$184$	−6.71824e10	−4.32091
$185$	1.25157e9	0.0785566
$186$	−1.15672e10	−0.708629
$187$	1.99310e10	1.19191
$188$	5.49587e10	3.20868
$189$	−1.01984e10	−0.581374
$190$	−8.31466e8	−0.0462864
$191$	−9.97341e9	−0.542243	−0.271121	−	0.962545i	$-0.587394\pi$
$191$	−9.97341e9	−0.542243	−0.271121	+	0.962545i	$0.587394\pi$
$192$	−3.78952e10	−2.01246
$193$	−1.88609e10	−0.978488	−0.489244	−	0.872147i	$-0.662727\pi$
$193$	−1.88609e10	−0.978488	−0.489244	+	0.872147i	$0.662727\pi$
$194$	−8.88071e9	−0.450132
$195$	0	0
$196$	−1.59718e10	−0.773041
$197$	2.53795e10	1.20056	0.600282	−	0.799789i	$-0.295055\pi$
$197$	2.53795e10	1.20056	0.600282	+	0.799789i	$0.295055\pi$
$198$	2.57918e10	1.19258
$199$	−2.16921e10	−0.980535	−0.490267	−	0.871572i	$-0.663101\pi$
$199$	−2.16921e10	−0.980535	−0.490267	+	0.871572i	$0.663101\pi$
$200$	−8.33151e10	−3.68204
$201$	−4.86015e9	−0.210023
$202$	−2.72795e10	−1.15280
$203$	−1.48927e9	−0.0615519
$204$	4.44559e10	1.79719
$205$	2.55589e9	0.101076
$206$	−5.52584e10	−2.13794
$207$	2.65837e10	1.00635
$208$	0	0
$209$	−4.17079e9	−0.151203
$210$	−1.87158e9	−0.0664084
$211$	3.18579e10	1.10649	0.553243	−	0.833020i	$-0.313390\pi$
$211$	3.18579e10	1.10649	0.553243	+	0.833020i	$0.313390\pi$
$212$	−8.65920e10	−2.94419
$213$	−6.89083e8	−0.0229384
$214$	8.31237e9	0.270934
$215$	1.86186e9	0.0594257
$216$	8.09681e10	2.53088
$217$	−2.76174e10	−0.845500
$218$	8.01440e10	2.40335
$219$	−6.15824e9	−0.180908
$220$	7.56847e9	0.217824
$221$	0	0
$222$	1.88501e10	0.520864
$223$	5.26237e10	1.42498	0.712491	−	0.701681i	$-0.247567\pi$
$223$	5.26237e10	1.42498	0.712491	+	0.701681i	$0.247567\pi$
$224$	−1.63377e11	−4.33586
$225$	3.29674e10	0.857557
$226$	5.75489e10	1.46740
$227$	−6.75026e10	−1.68735	−0.843673	−	0.536857i	$-0.819612\pi$
$227$	−6.75026e10	−1.68735	−0.843673	+	0.536857i	$0.819612\pi$
$228$	−9.30289e9	−0.227987
$229$	1.69036e10	0.406180	0.203090	−	0.979160i	$-0.434902\pi$
$229$	1.69036e10	0.406180	0.203090	+	0.979160i	$0.434902\pi$
$230$	1.05009e10	0.247429
$231$	−9.38822e9	−0.216935
$232$	1.18237e10	0.267953
$233$	2.65324e10	0.589760	0.294880	−	0.955534i	$-0.404720\pi$
$233$	2.65324e10	0.589760	0.294880	+	0.955534i	$0.404720\pi$
$234$	0	0
$235$	−5.61701e9	−0.120143
$236$	4.19561e10	0.880423
$237$	−1.43160e10	−0.294749
$238$	1.42879e11	2.88651
$239$	3.72393e10	0.738262	0.369131	−	0.929377i	$-0.379655\pi$
$239$	3.72393e10	0.738262	0.369131	+	0.929377i	$0.379655\pi$
$240$	9.01604e9	0.175414
$241$	3.55835e10	0.679472	0.339736	−	0.940521i	$-0.389662\pi$
$241$	3.55835e10	0.679472	0.339736	+	0.940521i	$0.389662\pi$
$242$	−5.41147e10	−1.01425
$243$	−4.91926e10	−0.905048
$244$	4.27657e10	0.772399
$245$	1.63239e9	0.0289452
$246$	3.84946e10	0.670180
$247$	0	0
$248$	2.19262e11	3.68070
$249$	2.63319e10	0.434095
$250$	2.61992e10	0.424188
$251$	−9.97075e10	−1.58561	−0.792805	−	0.609476i	$-0.791380\pi$
$251$	−9.97075e10	−1.58561	−0.792805	+	0.609476i	$0.791380\pi$
$252$	1.37353e11	2.14553
$253$	5.26744e10	0.808272
$254$	9.07326e10	1.36776
$255$	−4.54359e9	−0.0672927
$256$	4.11960e11	5.99481
$257$	5.47306e10	0.782584	0.391292	−	0.920267i	$-0.372028\pi$
$257$	5.47306e10	0.782584	0.391292	+	0.920267i	$0.372028\pi$
$258$	2.80417e10	0.394017
$259$	4.50058e10	0.621469
$260$	0	0
$261$	−4.67858e9	−0.0624068
$262$	−8.44172e9	−0.110682
$263$	9.60519e10	1.23796	0.618978	−	0.785408i	$-0.287547\pi$
$263$	9.60519e10	1.23796	0.618978	+	0.785408i	$0.287547\pi$
$264$	7.45356e10	0.944378
$265$	8.85008e9	0.110240
$266$	−2.98990e10	−0.366176
$267$	5.13765e10	0.618677
$268$	1.40892e11	1.66832
$269$	−1.50514e11	−1.75264	−0.876319	−	0.481731i	$-0.840008\pi$
$269$	−1.50514e11	−1.75264	−0.876319	+	0.481731i	$0.840008\pi$
$270$	−1.26557e10	−0.144927
$271$	−1.10945e11	−1.24953	−0.624765	−	0.780813i	$-0.714805\pi$
$271$	−1.10945e11	−1.24953	−0.624765	+	0.780813i	$0.714805\pi$
$272$	−6.88296e11	−7.62457
$273$	0	0
$274$	−1.92492e11	−2.06317
$275$	6.53233e10	0.688765
$276$	1.17490e11	1.21873
$277$	6.50996e10	0.664384	0.332192	−	0.943212i	$-0.392212\pi$
$277$	6.50996e10	0.664384	0.332192	+	0.943212i	$0.392212\pi$
$278$	−1.89932e11	−1.90721
$279$	−8.67607e10	−0.857244
$280$	3.54769e10	0.344933
$281$	5.78359e10	0.553375	0.276687	−	0.960960i	$-0.410763\pi$
$281$	5.78359e10	0.553375	0.276687	+	0.960960i	$0.410763\pi$
$282$	−8.45985e10	−0.796602
$283$	2.07928e10	0.192696	0.0963482	−	0.995348i	$-0.469284\pi$
$283$	2.07928e10	0.192696	0.0963482	+	0.995348i	$0.469284\pi$
$284$	1.99760e10	0.182212
$285$	9.50796e8	0.00853661
$286$	0	0
$287$	9.19083e10	0.799625
$288$	−5.13254e11	−4.39609
$289$	2.28275e11	1.92495
$290$	−1.84810e9	−0.0153438
$291$	1.01552e10	0.0830179
$292$	1.78523e11	1.43705
$293$	−8.15549e10	−0.646466	−0.323233	−	0.946319i	$-0.604770\pi$
$293$	−8.15549e10	−0.646466	−0.323233	+	0.946319i	$0.604770\pi$
$294$	2.45856e10	0.191919
$295$	−4.28810e9	−0.0329660
$296$	−3.57313e11	−2.70543
$297$	−6.34831e10	−0.473428
$298$	−1.84180e11	−1.35291
$299$	0	0
$300$	1.45703e11	1.03854
$301$	6.69514e10	0.470122
$302$	9.28254e10	0.642148
$303$	3.11945e10	0.212611
$304$	1.44033e11	0.967235
$305$	−4.37084e9	−0.0289212
$306$	4.48859e11	2.92660
$307$	−2.41080e11	−1.54895	−0.774477	−	0.632603i	$-0.781987\pi$
$307$	−2.41080e11	−1.54895	−0.774477	+	0.632603i	$0.781987\pi$
$308$	2.72158e11	1.72323
$309$	6.31889e10	0.394301
$310$	−3.42716e10	−0.210769
$311$	6.46351e10	0.391784	0.195892	−	0.980625i	$-0.437240\pi$
$311$	6.46351e10	0.391784	0.195892	+	0.980625i	$0.437240\pi$
$312$	0	0
$313$	−2.64577e11	−1.55812	−0.779062	−	0.626947i	$-0.784304\pi$
$313$	−2.64577e11	−1.55812	−0.779062	+	0.626947i	$0.784304\pi$
$314$	3.83020e11	2.22350
$315$	−1.40380e10	−0.0803357
$316$	4.15009e11	2.34135
$317$	2.92101e11	1.62468	0.812338	−	0.583187i	$-0.198195\pi$
$317$	2.92101e11	1.62468	0.812338	+	0.583187i	$0.198195\pi$
$318$	1.33292e11	0.730941
$319$	−9.27039e9	−0.0501234
$320$	−1.12277e11	−0.598571
$321$	−9.50534e9	−0.0499684
$322$	3.77606e11	1.95743
$323$	−7.25849e10	−0.371052
$324$	3.55683e11	1.79312
$325$	0	0
$326$	7.22239e11	3.54162
$327$	−9.16461e10	−0.443250
$328$	−7.29685e11	−3.48099
$329$	−2.01984e11	−0.950466
$330$	−1.16502e10	−0.0540781
$331$	−6.47388e8	−0.00296441	−0.00148221	−	0.999999i	$-0.500472\pi$
$331$	−6.47388e8	−0.00296441	−0.00148221	+	0.999999i	$0.500472\pi$
$332$	−7.63342e11	−3.44824
$333$	1.41387e11	0.630101
$334$	−2.88016e11	−1.26636
$335$	−1.43998e10	−0.0624676
$336$	3.24211e11	1.38772
$337$	1.60029e11	0.675874	0.337937	−	0.941169i	$-0.390271\pi$
$337$	1.60029e11	0.675874	0.337937	+	0.941169i	$0.390271\pi$
$338$	0	0
$339$	−6.58082e10	−0.270633
$340$	1.31715e11	0.534542
$341$	−1.71912e11	−0.688514
$342$	−9.39286e10	−0.371262
$343$	2.78085e11	1.08481
$344$	−5.31545e11	−2.04657
$345$	−1.20080e10	−0.0456334
$346$	4.91077e11	1.84207
$347$	−2.61745e11	−0.969160	−0.484580	−	0.874747i	$-0.661027\pi$
$347$	−2.61745e11	−0.969160	−0.484580	+	0.874747i	$0.661027\pi$
$348$	−2.06775e10	−0.0755773
$349$	−2.80466e11	−1.01196	−0.505982	−	0.862544i	$-0.668870\pi$
$349$	−2.80466e11	−1.01196	−0.505982	+	0.862544i	$0.668870\pi$
$350$	4.68282e11	1.66802
$351$	0	0
$352$	−1.01699e12	−3.53081
$353$	3.94018e11	1.35061	0.675304	−	0.737539i	$-0.264012\pi$
$353$	3.94018e11	1.35061	0.675304	+	0.737539i	$0.264012\pi$
$354$	−6.45835e10	−0.218578
$355$	−2.04164e9	−0.00682262
$356$	−1.48937e12	−4.91447
$357$	−1.63385e11	−0.532359
$358$	2.91223e9	0.00937027
$359$	5.24181e10	0.166554	0.0832772	−	0.996526i	$-0.473461\pi$
$359$	5.24181e10	0.166554	0.0832772	+	0.996526i	$0.473461\pi$
$360$	1.11452e11	0.349724
$361$	−3.07499e11	−0.952929
$362$	4.61361e11	1.41206
$363$	6.18811e10	0.187059
$364$	0	0
$365$	−1.82458e10	−0.0538078
$366$	−6.58297e10	−0.191760
$367$	2.64041e11	0.759755	0.379877	−	0.925037i	$-0.375966\pi$
$367$	2.64041e11	0.759755	0.379877	+	0.925037i	$0.375966\pi$
$368$	−1.81905e12	−5.17047
$369$	2.88733e11	0.810732
$370$	5.58495e10	0.154921
$371$	3.18244e11	0.872122
$372$	−3.83449e11	−1.03816
$373$	3.07202e11	0.821740	0.410870	−	0.911694i	$-0.365225\pi$
$373$	3.07202e11	0.821740	0.410870	+	0.911694i	$0.365225\pi$
$374$	8.89393e11	2.35056
$375$	−2.99593e10	−0.0782331
$376$	1.60361e12	4.13764
$377$	0	0
$378$	−4.55090e11	−1.14653
$379$	−3.79660e11	−0.945188	−0.472594	−	0.881280i	$-0.656682\pi$
$379$	−3.79660e11	−0.945188	−0.472594	+	0.881280i	$0.656682\pi$
$380$	−2.75629e10	−0.0678107
$381$	−1.03754e11	−0.252257
$382$	−4.45049e11	−1.06936
$383$	1.09927e11	0.261041	0.130521	−	0.991446i	$-0.458335\pi$
$383$	1.09927e11	0.261041	0.130521	+	0.991446i	$0.458335\pi$
$384$	−9.05884e11	−2.12609
$385$	−2.78157e10	−0.0645233
$386$	−8.41641e11	−1.92968
$387$	2.10330e11	0.476652
$388$	−2.94393e11	−0.659455
$389$	−5.71954e11	−1.26645	−0.633225	−	0.773968i	$-0.718269\pi$
$389$	−5.71954e11	−1.26645	−0.633225	+	0.773968i	$0.718269\pi$
$390$	0	0
$391$	9.16702e11	1.98350
$392$	−4.66034e11	−0.996851
$393$	9.65326e9	0.0204130
$394$	1.13252e12	2.36763
$395$	−4.24158e10	−0.0876678
$396$	8.54991e11	1.74716
$397$	−3.88595e11	−0.785127	−0.392563	−	0.919725i	$-0.628412\pi$
$397$	−3.88595e11	−0.785127	−0.392563	+	0.919725i	$0.628412\pi$
$398$	−9.67978e11	−1.93371
$399$	3.41900e10	0.0675339
$400$	−2.25587e12	−4.40599
$401$	−2.52996e11	−0.488612	−0.244306	−	0.969698i	$-0.578560\pi$
$401$	−2.52996e11	−0.488612	−0.244306	+	0.969698i	$0.578560\pi$
$402$	−2.16877e11	−0.414187
$403$	0	0
$404$	−9.04307e11	−1.68888
$405$	−3.63523e10	−0.0671405
$406$	−6.64565e10	−0.121386
$407$	2.80151e11	0.506079
$408$	1.29716e12	2.31751
$409$	3.00728e11	0.531397	0.265699	−	0.964056i	$-0.414397\pi$
$409$	3.00728e11	0.531397	0.265699	+	0.964056i	$0.414397\pi$
$410$	1.14053e11	0.199333
$411$	2.20118e11	0.380511
$412$	−1.83180e12	−3.13214
$413$	−1.54198e11	−0.260797
$414$	1.18626e12	1.98462
$415$	7.80169e10	0.129114
$416$	0	0
$417$	2.17191e11	0.351746
$418$	−1.86115e11	−0.298187
$419$	−6.65230e11	−1.05441	−0.527204	−	0.849739i	$-0.676760\pi$
$419$	−6.65230e11	−1.05441	−0.527204	+	0.849739i	$0.676760\pi$
$420$	−6.20426e10	−0.0972899
$421$	−3.52570e11	−0.546986	−0.273493	−	0.961874i	$-0.588179\pi$
$421$	−3.52570e11	−0.546986	−0.273493	+	0.961874i	$0.588179\pi$
$422$	1.42161e12	2.18210
$423$	−6.34540e11	−0.963667
$424$	−2.52662e12	−3.79659
$425$	1.13683e12	1.69023
$426$	−3.07493e10	−0.0452368
$427$	−1.57173e11	−0.228798
$428$	2.75553e11	0.396925
$429$	0	0
$430$	8.30828e10	0.117193
$431$	7.16673e10	0.100040	0.0500200	−	0.998748i	$-0.484072\pi$
$431$	7.16673e10	0.100040	0.0500200	+	0.998748i	$0.484072\pi$
$432$	2.19232e12	3.02849
$433$	−7.54601e11	−1.03163	−0.515813	−	0.856701i	$-0.672510\pi$
$433$	−7.54601e11	−1.03163	−0.515813	+	0.856701i	$0.672510\pi$
$434$	−1.23238e12	−1.66741
$435$	2.11333e9	0.00282987
$436$	2.65675e12	3.52097
$437$	−1.91830e11	−0.251623
$438$	−2.74802e11	−0.356769
$439$	−9.89110e11	−1.27102	−0.635512	−	0.772091i	$-0.719211\pi$
$439$	−9.89110e11	−1.27102	−0.635512	+	0.772091i	$0.719211\pi$
$440$	2.20836e11	0.280888
$441$	1.84407e11	0.232169
$442$	0	0
$443$	−1.32070e12	−1.62925	−0.814627	−	0.579986i	$-0.803058\pi$
$443$	−1.32070e12	−1.62925	−0.814627	+	0.579986i	$0.803058\pi$
$444$	6.24875e11	0.763079
$445$	1.52220e11	0.184014
$446$	2.34825e12	2.81021
$447$	2.10613e11	0.249518
$448$	−4.03741e12	−4.73535
$449$	1.47544e11	0.171322	0.0856608	−	0.996324i	$-0.472700\pi$
$449$	1.47544e11	0.171322	0.0856608	+	0.996324i	$0.472700\pi$
$450$	1.47112e12	1.69119
$451$	5.72110e11	0.651156
$452$	1.90773e12	2.14978
$453$	−1.06147e11	−0.118432
$454$	−3.01221e12	−3.32762
$455$	0	0
$456$	−2.71444e11	−0.293994
$457$	−8.62112e11	−0.924572	−0.462286	−	0.886731i	$-0.652971\pi$
$457$	−8.62112e11	−0.924572	−0.462286	+	0.886731i	$0.652971\pi$
$458$	7.54296e11	0.801027
$459$	−1.10481e12	−1.16180
$460$	3.48102e11	0.362490
$461$	−1.10935e12	−1.14396	−0.571982	−	0.820266i	$-0.693825\pi$
$461$	−1.10935e12	−1.14396	−0.571982	+	0.820266i	$0.693825\pi$
$462$	−4.18935e11	−0.427817
$463$	5.23314e11	0.529234	0.264617	−	0.964354i	$-0.414754\pi$
$463$	5.23314e11	0.529234	0.264617	+	0.964354i	$0.414754\pi$
$464$	3.20143e11	0.320636
$465$	3.91901e10	0.0388721
$466$	1.18397e12	1.16306
$467$	−5.66414e11	−0.551071	−0.275536	−	0.961291i	$-0.588855\pi$
$467$	−5.66414e11	−0.551071	−0.275536	+	0.961291i	$0.588855\pi$
$468$	0	0
$469$	−5.17808e11	−0.494187
$470$	−2.50651e11	−0.236935
$471$	−4.37990e11	−0.410081
$472$	1.22422e12	1.13532
$473$	4.16759e11	0.382833
$474$	−6.38828e11	−0.581275
$475$	−2.37895e11	−0.214419
$476$	4.73641e12	4.22881
$477$	9.99771e11	0.884235
$478$	1.66175e12	1.45593
$479$	1.28230e12	1.11296	0.556480	−	0.830861i	$-0.312152\pi$
$479$	1.28230e12	1.11296	0.556480	+	0.830861i	$0.312152\pi$
$480$	2.31839e11	0.199343
$481$	0	0
$482$	1.58786e12	1.33999
$483$	−4.31799e11	−0.361010
$484$	−1.79389e12	−1.48591
$485$	3.00883e10	0.0246922
$486$	−2.19515e12	−1.78485
$487$	−2.27286e12	−1.83102	−0.915510	−	0.402295i	$-0.868213\pi$
$487$	−2.27286e12	−1.83102	−0.915510	+	0.402295i	$0.868213\pi$
$488$	1.24784e12	0.996022
$489$	−8.25893e11	−0.653182
$490$	7.28431e10	0.0570829
$491$	−1.15965e12	−0.900449	−0.450225	−	0.892915i	$-0.648656\pi$
$491$	−1.15965e12	−0.900449	−0.450225	+	0.892915i	$0.648656\pi$
$492$	1.27609e12	0.981831
$493$	−1.61334e11	−0.123003
$494$	0	0
$495$	−8.73838e10	−0.0654195
$496$	5.93680e12	4.40438
$497$	−7.34160e10	−0.0539743
$498$	1.17502e12	0.856079
$499$	6.99224e11	0.504852	0.252426	−	0.967616i	$-0.418772\pi$
$499$	6.99224e11	0.504852	0.252426	+	0.967616i	$0.418772\pi$
$500$	8.68498e11	0.621446
$501$	3.29351e11	0.233555
$502$	−4.44930e12	−3.12698
$503$	2.07525e12	1.44549	0.722745	−	0.691115i	$-0.242880\pi$
$503$	2.07525e12	1.44549	0.722745	+	0.691115i	$0.242880\pi$
$504$	4.00773e12	2.76670
$505$	9.24241e10	0.0632374
$506$	2.35052e12	1.59399
$507$	0	0
$508$	3.00776e12	2.00381
$509$	−1.59826e12	−1.05540	−0.527700	−	0.849431i	$-0.676945\pi$
$509$	−1.59826e12	−1.05540	−0.527700	+	0.849431i	$0.676945\pi$
$510$	−2.02751e11	−0.132708
$511$	−6.56109e11	−0.425678
$512$	9.29369e12	5.97687
$513$	2.31193e11	0.147383
$514$	2.44227e12	1.54333
$515$	1.87218e11	0.117278
$516$	9.29575e11	0.577246
$517$	−1.25731e12	−0.773990
$518$	2.00832e12	1.22560
$519$	−5.61555e11	−0.339734
$520$	0	0
$521$	3.94430e11	0.234531	0.117265	−	0.993101i	$-0.462587\pi$
$521$	3.94430e11	0.234531	0.117265	+	0.993101i	$0.462587\pi$
$522$	−2.08775e11	−0.123072
$523$	−3.33919e12	−1.95157	−0.975783	−	0.218742i	$-0.929805\pi$
$523$	−3.33919e12	−1.95157	−0.975783	+	0.218742i	$0.929805\pi$
$524$	−2.79841e11	−0.162151
$525$	−5.35488e11	−0.307633
$526$	4.28618e12	2.44137
$527$	−2.99182e12	−1.68962
$528$	2.01815e12	1.13006
$529$	6.21539e11	0.345079
$530$	3.94922e11	0.217405
$531$	−4.84416e11	−0.264419
$532$	−9.91145e11	−0.536457
$533$	0	0
$534$	2.29260e12	1.22009
$535$	−2.81627e10	−0.0148622
$536$	4.11102e12	2.15133
$537$	−3.33019e9	−0.00172816
$538$	−6.71648e12	−3.45638
$539$	3.65394e11	0.186471
$540$	−4.19532e11	−0.212321
$541$	4.98286e11	0.250087	0.125043	−	0.992151i	$-0.460093\pi$
$541$	4.98286e11	0.250087	0.125043	+	0.992151i	$0.460093\pi$
$542$	−4.95077e12	−2.46420
$543$	−5.27574e11	−0.260426
$544$	−1.76988e13	−8.66463
$545$	−2.71532e11	−0.131837
$546$	0	0
$547$	−3.77955e12	−1.80508	−0.902542	−	0.430602i	$-0.858301\pi$
$547$	−3.77955e12	−1.80508	−0.902542	+	0.430602i	$0.858301\pi$
$548$	−6.38106e12	−3.02260
$549$	−4.93763e11	−0.231976
$550$	2.91496e12	1.35831
$551$	3.37610e10	0.0156039
$552$	3.42817e12	1.57158
$553$	−1.52525e12	−0.693548
$554$	2.90497e12	1.31023
$555$	−6.38649e10	−0.0285722
$556$	−6.29621e12	−2.79411
$557$	2.05347e12	0.903941	0.451971	−	0.892033i	$-0.350721\pi$
$557$	2.05347e12	0.903941	0.451971	+	0.892033i	$0.350721\pi$
$558$	−3.87157e12	−1.69057
$559$	0	0
$560$	9.60584e11	0.412752
$561$	−1.01704e12	−0.433514
$562$	2.58084e12	1.09131
$563$	−2.31654e12	−0.971745	−0.485872	−	0.874030i	$-0.661498\pi$
$563$	−2.31654e12	−0.971745	−0.485872	+	0.874030i	$0.661498\pi$
$564$	−2.80442e12	−1.16704
$565$	−1.94978e11	−0.0804950
$566$	9.27847e11	0.380016
$567$	−1.30721e12	−0.531155
$568$	5.82870e11	0.234965
$569$	−2.21221e11	−0.0884752	−0.0442376	−	0.999021i	$-0.514086\pi$
$569$	−2.21221e11	−0.0884752	−0.0442376	+	0.999021i	$0.514086\pi$
$570$	4.24278e10	0.0168350
$571$	−1.76805e12	−0.696038	−0.348019	−	0.937487i	$-0.613146\pi$
$571$	−1.76805e12	−0.696038	−0.348019	+	0.937487i	$0.613146\pi$
$572$	0	0
$573$	5.08921e11	0.197222
$574$	4.10127e12	1.57694
$575$	3.00446e12	1.14620
$576$	−1.26836e13	−4.80112
$577$	9.40605e10	0.0353278	0.0176639	−	0.999844i	$-0.494377\pi$
$577$	9.40605e10	0.0353278	0.0176639	+	0.999844i	$0.494377\pi$
$578$	1.01865e13	3.79619
$579$	9.62432e11	0.355890
$580$	−6.12639e10	−0.0224791
$581$	2.80544e12	1.02143
$582$	4.53163e11	0.163720
$583$	1.98100e12	0.710192
$584$	5.20902e12	1.85310
$585$	0	0
$586$	−3.63926e12	−1.27489
$587$	−3.14652e12	−1.09385	−0.546927	−	0.837181i	$-0.684202\pi$
$587$	−3.14652e12	−1.09385	−0.546927	+	0.837181i	$0.684202\pi$
$588$	8.15008e11	0.281167
$589$	6.26071e11	0.214341
$590$	−1.91350e11	−0.0650122
$591$	−1.29506e12	−0.436663
$592$	−9.67472e12	−3.23736
$593$	−2.16558e12	−0.719165	−0.359583	−	0.933113i	$-0.617081\pi$
$593$	−2.16558e12	−0.719165	−0.359583	+	0.933113i	$0.617081\pi$
$594$	−2.83284e12	−0.933648
$595$	−4.84081e11	−0.158340
$596$	−6.10553e12	−1.98205
$597$	1.10690e12	0.356635
$598$	0	0
$599$	−2.13023e12	−0.676094	−0.338047	−	0.941129i	$-0.609766\pi$
$599$	−2.13023e12	−0.676094	−0.338047	+	0.941129i	$0.609766\pi$
$600$	4.25138e12	1.33921
$601$	−5.30559e12	−1.65882	−0.829409	−	0.558641i	$-0.811323\pi$
$601$	−5.30559e12	−1.65882	−0.829409	+	0.558641i	$0.811323\pi$
$602$	2.98761e12	0.927127
$603$	−1.62671e12	−0.501051
$604$	3.07714e12	0.940764
$605$	1.83343e11	0.0556373
$606$	1.39201e12	0.419291
$607$	4.05342e12	1.21191	0.605957	−	0.795497i	$-0.292790\pi$
$607$	4.05342e12	1.21191	0.605957	+	0.795497i	$0.292790\pi$
$608$	3.70368e12	1.09918
$609$	7.59941e10	0.0223873
$610$	−1.95042e11	−0.0570354
$611$	0	0
$612$	1.48796e13	4.28754
$613$	1.53536e12	0.439175	0.219588	−	0.975593i	$-0.429529\pi$
$613$	1.53536e12	0.439175	0.219588	+	0.975593i	$0.429529\pi$
$614$	−1.07578e13	−3.05469
$615$	−1.30421e11	−0.0367630
$616$	7.94114e12	2.22213
$617$	−3.50959e12	−0.974930	−0.487465	−	0.873143i	$-0.662078\pi$
$617$	−3.50959e12	−0.974930	−0.487465	+	0.873143i	$0.662078\pi$
$618$	2.81971e12	0.777601
$619$	2.16976e11	0.0594023	0.0297012	−	0.999559i	$-0.490544\pi$
$619$	2.16976e11	0.0594023	0.0297012	+	0.999559i	$0.490544\pi$
$620$	−1.13609e12	−0.308782
$621$	−2.91982e12	−0.787852
$622$	2.88425e12	0.772638
$623$	5.47373e12	1.45575
$624$	0	0
$625$	3.68129e12	0.965028
$626$	−1.18063e13	−3.07278
$627$	2.12826e11	0.0549947
$628$	1.26970e13	3.25749
$629$	4.87552e12	1.24192
$630$	−6.26426e11	−0.158430
$631$	−5.59463e12	−1.40488	−0.702441	−	0.711742i	$-0.747906\pi$
$631$	−5.59463e12	−1.40488	−0.702441	+	0.711742i	$0.747906\pi$
$632$	1.21093e13	3.01921
$633$	−1.62564e12	−0.402445
$634$	1.30346e13	3.20402
$635$	−3.07406e11	−0.0750293
$636$	4.41860e12	1.07085
$637$	0	0
$638$	−4.13678e11	−0.0988482
$639$	−2.30638e11	−0.0547240
$640$	−2.68398e12	−0.632367
$641$	−5.59530e12	−1.30907	−0.654534	−	0.756032i	$-0.727135\pi$
$641$	−5.59530e12	−1.30907	−0.654534	+	0.756032i	$0.727135\pi$
$642$	−4.24162e11	−0.0985426
$643$	1.31892e11	0.0304278	0.0152139	−	0.999884i	$-0.495157\pi$
$643$	1.31892e11	0.0304278	0.0152139	+	0.999884i	$0.495157\pi$
$644$	1.25175e13	2.86769
$645$	−9.50066e10	−0.0216140
$646$	−3.23899e12	−0.731752
$647$	−7.90835e11	−0.177426	−0.0887128	−	0.996057i	$-0.528275\pi$
$647$	−7.90835e11	−0.177426	−0.0887128	+	0.996057i	$0.528275\pi$
$648$	1.03783e13	2.31227
$649$	−9.59848e11	−0.212374
$650$	0	0
$651$	1.40925e12	0.307521
$652$	2.39421e13	5.18856
$653$	−8.33141e11	−0.179312	−0.0896560	−	0.995973i	$-0.528577\pi$
$653$	−8.33141e11	−0.179312	−0.0896560	+	0.995973i	$0.528577\pi$
$654$	−4.08957e12	−0.874133
$655$	2.86010e10	0.00607148
$656$	−1.97572e13	−4.16541
$657$	−2.06118e12	−0.431591
$658$	−9.01326e12	−1.87441
$659$	3.45121e12	0.712833	0.356416	−	0.934327i	$-0.383998\pi$
$659$	3.45121e12	0.712833	0.356416	+	0.934327i	$0.383998\pi$
$660$	−3.86202e11	−0.0792259
$661$	−5.01263e12	−1.02131	−0.510656	−	0.859785i	$-0.670598\pi$
$661$	−5.01263e12	−1.02131	−0.510656	+	0.859785i	$0.670598\pi$
$662$	−2.88887e10	−0.00584611
$663$	0	0
$664$	−2.22732e13	−4.44657
$665$	1.01299e11	0.0200867
$666$	6.30918e12	1.24262
$667$	−4.26380e11	−0.0834123
$668$	−9.54765e12	−1.85525
$669$	−2.68527e12	−0.518287
$670$	−6.42570e11	−0.123192
$671$	−9.78368e11	−0.186316
$672$	8.33678e12	1.57702
$673$	−2.19889e12	−0.413176	−0.206588	−	0.978428i	$-0.566236\pi$
$673$	−2.19889e12	−0.413176	−0.206588	+	0.978428i	$0.566236\pi$
$674$	7.14108e12	1.33289
$675$	−3.62097e12	−0.671364
$676$	0	0
$677$	−4.25317e10	−0.00778151	−0.00389075	−	0.999992i	$-0.501238\pi$
$677$	−4.25317e10	−0.00778151	−0.00389075	+	0.999992i	$0.501238\pi$
$678$	−2.93659e12	−0.533716
$679$	1.08196e12	0.195342
$680$	3.84325e12	0.689301
$681$	3.44451e12	0.613713
$682$	−7.67134e12	−1.35782
$683$	9.09442e12	1.59912	0.799561	−	0.600585i	$-0.205065\pi$
$683$	9.09442e12	1.59912	0.799561	+	0.600585i	$0.205065\pi$
$684$	−3.11371e12	−0.543908
$685$	6.52172e11	0.113176
$686$	1.24092e13	2.13936
$687$	−8.62551e11	−0.147734
$688$	−1.43923e13	−2.44896
$689$	0	0
$690$	−5.35837e11	−0.0899937
$691$	6.69654e12	1.11738	0.558688	−	0.829378i	$-0.311305\pi$
$691$	6.69654e12	1.11738	0.558688	+	0.829378i	$0.311305\pi$
$692$	1.62791e13	2.69868
$693$	−3.14227e12	−0.517540
$694$	−1.16800e13	−1.91128
$695$	6.43500e11	0.104621
$696$	−6.03338e11	−0.0974583
$697$	9.95654e12	1.59794
$698$	−1.25154e13	−1.99569
$699$	−1.35389e12	−0.214504
$700$	1.55234e13	2.44369
$701$	−8.97175e12	−1.40329	−0.701643	−	0.712529i	$-0.747550\pi$
$701$	−8.97175e12	−1.40329	−0.701643	+	0.712529i	$0.747550\pi$
$702$	0	0
$703$	−1.02026e12	−0.157547
$704$	−2.51320e13	−3.85612
$705$	2.86624e11	0.0436979
$706$	1.75825e13	2.66353
$707$	3.32352e12	0.500277
$708$	−2.14093e12	−0.320223
$709$	5.56970e12	0.827796	0.413898	−	0.910323i	$-0.364167\pi$
$709$	5.56970e12	0.827796	0.413898	+	0.910323i	$0.364167\pi$
$710$	−9.11050e10	−0.0134549
$711$	−4.79160e12	−0.703181
$712$	−4.34574e13	−6.33730
$713$	−7.90689e12	−1.14578
$714$	−7.29080e12	−1.04986
$715$	0	0
$716$	9.65397e10	0.0137277
$717$	−1.90024e12	−0.268517
$718$	2.33908e12	0.328462
$719$	1.00272e13	1.39927	0.699634	−	0.714502i	$-0.253346\pi$
$719$	1.00272e13	1.39927	0.699634	+	0.714502i	$0.253346\pi$
$720$	3.01770e12	0.418485
$721$	6.73225e12	0.927794
$722$	−1.37217e13	−1.87927
$723$	−1.81574e12	−0.247134
$724$	1.52940e13	2.06870
$725$	−5.28768e11	−0.0710794
$726$	2.76135e12	0.368899
$727$	1.17247e13	1.55668	0.778338	−	0.627845i	$-0.216063\pi$
$727$	1.17247e13	1.55668	0.778338	+	0.627845i	$0.216063\pi$
$728$	0	0
$729$	−2.22252e12	−0.291456
$730$	−8.14192e11	−0.106114
$731$	7.25292e12	0.939474
$732$	−2.18224e12	−0.280933
$733$	6.49737e12	0.831323	0.415661	−	0.909520i	$-0.363550\pi$
$733$	6.49737e12	0.831323	0.415661	+	0.909520i	$0.363550\pi$
$734$	1.17824e13	1.49831
$735$	−8.32973e10	−0.0105278
$736$	−4.67751e13	−5.87577
$737$	−3.22325e12	−0.402430
$738$	1.28843e13	1.59884
$739$	−5.02178e12	−0.619381	−0.309691	−	0.950837i	$-0.600225\pi$
$739$	−5.02178e12	−0.619381	−0.309691	+	0.950837i	$0.600225\pi$
$740$	1.85140e12	0.226964
$741$	0	0
$742$	1.42011e13	1.71991
$743$	3.60670e12	0.434170	0.217085	−	0.976153i	$-0.430345\pi$
$743$	3.60670e12	0.434170	0.217085	+	0.976153i	$0.430345\pi$
$744$	−1.11884e13	−1.33872
$745$	6.24012e11	0.0742146
$746$	1.37084e13	1.62055
$747$	8.81337e12	1.03562
$748$	2.94832e13	3.44363
$749$	−1.01271e12	−0.117576
$750$	−1.33689e12	−0.154283
$751$	1.52152e13	1.74541	0.872707	−	0.488244i	$-0.162362\pi$
$751$	1.52152e13	1.74541	0.872707	+	0.488244i	$0.162362\pi$
$752$	4.34198e13	4.95117
$753$	5.08785e12	0.576710
$754$	0	0
$755$	−3.14497e11	−0.0352253
$756$	−1.50861e13	−1.67969
$757$	1.20577e13	1.33454	0.667272	−	0.744814i	$-0.267462\pi$
$757$	1.20577e13	1.33454	0.667272	+	0.744814i	$0.267462\pi$
$758$	−1.69418e13	−1.86401
$759$	−2.68786e12	−0.293980
$760$	−8.04242e11	−0.0874431
$761$	−9.08606e12	−0.982075	−0.491038	−	0.871138i	$-0.663382\pi$
$761$	−9.08606e12	−0.982075	−0.491038	+	0.871138i	$0.663382\pi$
$762$	−4.62988e12	−0.497476
$763$	−9.76412e12	−1.04297
$764$	−1.47533e13	−1.56663
$765$	−1.52075e12	−0.160540
$766$	4.90532e12	0.514799
$767$	0	0
$768$	−2.10214e13	−2.18040
$769$	−4.28917e12	−0.442288	−0.221144	−	0.975241i	$-0.570979\pi$
$769$	−4.28917e12	−0.442288	−0.221144	+	0.975241i	$0.570979\pi$
$770$	−1.24123e12	−0.127246
$771$	−2.79278e12	−0.284637
$772$	−2.79002e13	−2.82702
$773$	−4.49046e12	−0.452359	−0.226180	−	0.974086i	$-0.572624\pi$
$773$	−4.49046e12	−0.452359	−0.226180	+	0.974086i	$0.572624\pi$
$774$	9.38565e12	0.940005
$775$	−9.80560e12	−0.976375
$776$	−8.58994e12	−0.850379
$777$	−2.29654e12	−0.226037
$778$	−2.55226e13	−2.49756
$779$	−2.08351e12	−0.202711
$780$	0	0
$781$	−4.57000e11	−0.0439528
$782$	4.09065e13	3.91166
$783$	5.13872e11	0.0488570
$784$	−1.26185e13	−1.19285
$785$	−1.29769e12	−0.121971
$786$	4.30762e11	0.0402565
$787$	−3.31359e12	−0.307902	−0.153951	−	0.988078i	$-0.549200\pi$
$787$	−3.31359e12	−0.307902	−0.153951	+	0.988078i	$0.549200\pi$
$788$	3.75428e13	3.46864
$789$	−4.90132e12	−0.450263
$790$	−1.89274e12	−0.172890
$791$	−7.01131e12	−0.636803
$792$	2.49473e13	2.25300
$793$	0	0
$794$	−1.73405e13	−1.54835
$795$	−4.51600e11	−0.0400961
$796$	−3.20882e13	−2.83294
$797$	8.72292e12	0.765772	0.382886	−	0.923796i	$-0.374930\pi$
$797$	8.72292e12	0.765772	0.382886	+	0.923796i	$0.374930\pi$
$798$	1.52568e12	0.133183
$799$	−2.18812e13	−1.89938
$800$	−5.80074e13	−5.00701
$801$	1.71959e13	1.47597
$802$	−1.12896e13	−0.963592
$803$	−4.08414e12	−0.346642
$804$	−7.18941e12	−0.606794
$805$	−1.27935e12	−0.107376
$806$	0	0
$807$	7.68041e12	0.637460
$808$	−2.63863e13	−2.17785
$809$	1.32412e13	1.08682	0.543411	−	0.839467i	$-0.317132\pi$
$809$	1.32412e13	1.08682	0.543411	+	0.839467i	$0.317132\pi$
$810$	−1.62217e12	−0.132408
$811$	1.09177e13	0.886215	0.443108	−	0.896468i	$-0.353876\pi$
$811$	1.09177e13	0.886215	0.443108	+	0.896468i	$0.353876\pi$
$812$	−2.20301e12	−0.177834
$813$	5.66129e12	0.454473
$814$	1.25013e13	0.998038
$815$	−2.44698e12	−0.194277
$816$	3.51222e13	2.77317
$817$	−1.51775e12	−0.119180
$818$	1.34196e13	1.04797
$819$	0	0
$820$	3.78082e12	0.292028
$821$	2.10770e13	1.61906	0.809532	−	0.587075i	$-0.199721\pi$
$821$	2.10770e13	1.61906	0.809532	+	0.587075i	$0.199721\pi$
$822$	9.82244e12	0.750406
$823$	−2.29237e13	−1.74175	−0.870876	−	0.491503i	$-0.836448\pi$
$823$	−2.29237e13	−1.74175	−0.870876	+	0.491503i	$0.836448\pi$
$824$	−5.34492e13	−4.03895
$825$	−3.33330e12	−0.250514
$826$	−6.88084e12	−0.514317
$827$	−3.15842e11	−0.0234798	−0.0117399	−	0.999931i	$-0.503737\pi$
$827$	−3.15842e11	−0.0234798	−0.0117399	+	0.999931i	$0.503737\pi$
$828$	3.93242e13	2.90752
$829$	1.47916e13	1.08773	0.543864	−	0.839174i	$-0.316961\pi$
$829$	1.47916e13	1.08773	0.543864	+	0.839174i	$0.316961\pi$
$830$	3.48139e12	0.254625
$831$	−3.32189e12	−0.241646
$832$	0	0
$833$	6.35902e12	0.457602
$834$	9.69183e12	0.693679
$835$	9.75811e11	0.0694667
$836$	−6.16967e12	−0.436851
$837$	9.52937e12	0.671119
$838$	−2.96849e13	−2.07940
$839$	1.67083e13	1.16413	0.582067	−	0.813141i	$-0.302244\pi$
$839$	1.67083e13	1.16413	0.582067	+	0.813141i	$0.302244\pi$
$840$	−1.81031e12	−0.125457
$841$	−1.44321e13	−0.994827
$842$	−1.57329e13	−1.07871
$843$	−2.95124e12	−0.201271
$844$	4.71260e13	3.19683
$845$	0	0
$846$	−2.83154e13	−1.90045
$847$	6.59291e12	0.440151
$848$	−6.84116e13	−4.54306
$849$	−1.06101e12	−0.0700865
$850$	5.07295e13	3.33331
$851$	1.28852e13	0.842187
$852$	−1.01933e12	−0.0662731
$853$	−1.47950e13	−0.956850	−0.478425	−	0.878128i	$-0.658792\pi$
$853$	−1.47950e13	−0.956850	−0.478425	+	0.878128i	$0.658792\pi$
$854$	−7.01360e12	−0.451212
$855$	3.18235e11	0.0203657
$856$	8.04021e12	0.511842
$857$	7.22513e12	0.457543	0.228771	−	0.973480i	$-0.426529\pi$
$857$	7.22513e12	0.457543	0.228771	+	0.973480i	$0.426529\pi$
$858$	0	0
$859$	−9.20444e11	−0.0576804	−0.0288402	−	0.999584i	$-0.509181\pi$
$859$	−9.20444e11	−0.0576804	−0.0288402	+	0.999584i	$0.509181\pi$
$860$	2.75417e12	0.171691
$861$	−4.68988e12	−0.290835
$862$	3.19805e12	0.197289
$863$	−2.54308e11	−0.0156067	−0.00780334	−	0.999970i	$-0.502484\pi$
$863$	−2.54308e11	−0.0156067	−0.00780334	+	0.999970i	$0.502484\pi$
$864$	5.63733e13	3.44161
$865$	−1.66379e12	−0.101048
$866$	−3.36730e13	−2.03447
$867$	−1.16484e13	−0.700132
$868$	−4.08532e13	−2.44280
$869$	−9.49433e12	−0.564775
$870$	9.43042e10	0.00558078
$871$	0	0
$872$	7.75200e13	4.54035
$873$	3.39900e12	0.198055
$874$	−8.56013e12	−0.496225
$875$	−3.19191e12	−0.184083
$876$	−9.10962e12	−0.522675
$877$	2.42430e13	1.38385	0.691925	−	0.721970i	$-0.256763\pi$
$877$	2.42430e13	1.38385	0.691925	+	0.721970i	$0.256763\pi$
$878$	−4.41375e13	−2.50659
$879$	4.16156e12	0.235129
$880$	5.97943e12	0.336115
$881$	2.82293e13	1.57873	0.789366	−	0.613923i	$-0.210409\pi$
$881$	2.82293e13	1.57873	0.789366	+	0.613923i	$0.210409\pi$
$882$	8.22890e12	0.457860
$883$	8.84255e12	0.489502	0.244751	−	0.969586i	$-0.421294\pi$
$883$	8.84255e12	0.489502	0.244751	+	0.969586i	$0.421294\pi$
$884$	0	0
$885$	2.18812e11	0.0119902
$886$	−5.89344e13	−3.21305
$887$	−1.51600e13	−0.822323	−0.411161	−	0.911563i	$-0.634877\pi$
$887$	−1.51600e13	−0.822323	−0.411161	+	0.911563i	$0.634877\pi$
$888$	1.82329e13	0.984004
$889$	−1.10541e13	−0.593564
$890$	6.79258e12	0.362894
$891$	−8.13710e12	−0.432534
$892$	7.78440e13	4.11702
$893$	4.57888e12	0.240950
$894$	9.39831e12	0.492074
$895$	−9.86678e9	−0.000514010 0
$896$	−9.65143e13	−5.00271
$897$	0	0
$898$	6.58392e12	0.337863
$899$	1.39157e12	0.0710535
$900$	4.87672e13	2.47763
$901$	3.44757e13	1.74282
$902$	2.55296e13	1.28415
$903$	−3.41638e12	−0.170990
$904$	5.56647e13	2.77218
$905$	−1.56311e12	−0.0774589
$906$	−4.73667e12	−0.233559
$907$	−2.96544e13	−1.45498	−0.727488	−	0.686120i	$-0.759313\pi$
$907$	−2.96544e13	−1.45498	−0.727488	+	0.686120i	$0.759313\pi$
$908$	−9.98538e13	−4.87504
$909$	1.04409e13	0.507226
$910$	0	0
$911$	−7.54006e12	−0.362695	−0.181348	−	0.983419i	$-0.558046\pi$
$911$	−7.54006e12	−0.362695	−0.181348	+	0.983419i	$0.558046\pi$
$912$	−7.34970e12	−0.351798
$913$	1.74633e13	0.831778
$914$	−3.84705e13	−1.82335
$915$	2.23034e11	0.0105191
$916$	2.50047e13	1.17353
$917$	1.02847e12	0.0480321
$918$	−4.93004e13	−2.29118
$919$	−9.55982e12	−0.442109	−0.221055	−	0.975261i	$-0.570950\pi$
$919$	−9.55982e12	−0.442109	−0.221055	+	0.975261i	$0.570950\pi$
$920$	1.01571e13	0.467437
$921$	1.23018e13	0.563377
$922$	−4.95029e13	−2.25601
$923$	0	0
$924$	−1.38876e13	−0.626763
$925$	1.59794e13	0.717665
$926$	2.33521e13	1.04370
$927$	2.11496e13	0.940681
$928$	8.23215e12	0.364374
$929$	1.17249e13	0.516460	0.258230	−	0.966083i	$-0.416861\pi$
$929$	1.17249e13	0.516460	0.258230	+	0.966083i	$0.416861\pi$
$930$	1.74880e12	0.0766597
$931$	−1.33069e12	−0.0580503
$932$	3.92483e13	1.70392
$933$	−3.29819e12	−0.142498
$934$	−2.52754e13	−1.08677
$935$	−3.01331e12	−0.128941
$936$	0	0
$937$	−3.12797e12	−0.132567	−0.0662833	−	0.997801i	$-0.521114\pi$
$937$	−3.12797e12	−0.132567	−0.0662833	+	0.997801i	$0.521114\pi$
$938$	−2.31064e13	−0.974585
$939$	1.35008e13	0.566713
$940$	−8.30901e12	−0.347116
$941$	−4.12131e13	−1.71349	−0.856745	−	0.515740i	$-0.827517\pi$
$941$	−4.12131e13	−1.71349	−0.856745	+	0.515740i	$0.827517\pi$
$942$	−1.95446e13	−0.808721
$943$	2.63135e13	1.08362
$944$	3.31473e13	1.35854
$945$	1.54187e12	0.0628932
$946$	1.85972e13	0.754985
$947$	3.89950e13	1.57556	0.787778	−	0.615959i	$-0.211231\pi$
$947$	3.89950e13	1.57556	0.787778	+	0.615959i	$0.211231\pi$
$948$	−2.11770e13	−0.851583
$949$	0	0
$950$	−1.06157e13	−0.422856
$951$	−1.49053e13	−0.590918
$952$	1.38201e14	5.45312
$953$	−1.29321e13	−0.507869	−0.253935	−	0.967221i	$-0.581725\pi$
$953$	−1.29321e13	−0.507869	−0.253935	+	0.967221i	$0.581725\pi$
$954$	4.46133e13	1.74380
$955$	1.50785e12	0.0586600
$956$	5.50865e13	2.13297
$957$	4.73047e11	0.0182306
$958$	5.72207e13	2.19487
$959$	2.34517e13	0.895347
$960$	5.72924e12	0.217709
$961$	−6.34069e11	−0.0239818
$962$	0	0
$963$	−3.18147e12	−0.119209
$964$	5.26371e13	1.96311
$965$	2.85152e12	0.105853
$966$	−1.92684e13	−0.711948
$967$	−5.25218e12	−0.193161	−0.0965807	−	0.995325i	$-0.530791\pi$
$967$	−5.25218e12	−0.193161	−0.0965807	+	0.995325i	$0.530791\pi$
$968$	−5.23429e13	−1.91610
$969$	3.70385e12	0.134957
$970$	1.34264e12	0.0486954
$971$	−3.59385e13	−1.29740	−0.648699	−	0.761045i	$-0.724686\pi$
$971$	−3.59385e13	−1.29740	−0.648699	+	0.761045i	$0.724686\pi$
$972$	−7.27686e13	−2.61484
$973$	2.31399e13	0.827663
$974$	−1.01423e14	−3.61095
$975$	0	0
$976$	3.37868e13	1.19186
$977$	7.49430e12	0.263151	0.131576	−	0.991306i	$-0.457996\pi$
$977$	7.49430e12	0.263151	0.131576	+	0.991306i	$0.457996\pi$
$978$	−3.68543e13	−1.28814
$979$	3.40729e13	1.18546
$980$	2.41473e12	0.0836279
$981$	−3.06743e13	−1.05746
$982$	−5.17475e13	−1.77578
$983$	4.10408e12	0.140193	0.0700963	−	0.997540i	$-0.477669\pi$
$983$	4.10408e12	0.140193	0.0700963	+	0.997540i	$0.477669\pi$
$984$	3.72342e13	1.26609
$985$	−3.83704e12	−0.129877
$986$	−7.19930e12	−0.242574
$987$	1.03068e13	0.345698
$988$	0	0
$989$	1.91683e13	0.637088
$990$	−3.89937e12	−0.129014
$991$	−5.13439e13	−1.69105	−0.845527	−	0.533933i	$-0.820714\pi$
$991$	−5.13439e13	−1.69105	−0.845527	+	0.533933i	$0.820714\pi$
$992$	1.52659e14	5.00518
$993$	3.30347e10	0.00107820
$994$	−3.27608e12	−0.106443
$995$	3.27956e12	0.106075
$996$	3.89517e13	1.25418
$997$	5.42449e12	0.173872	0.0869362	−	0.996214i	$-0.472292\pi$
$997$	5.42449e12	0.173872	0.0869362	+	0.996214i	$0.472292\pi$
$998$	3.12018e13	0.995618
$999$	−1.55292e13	−0.493293

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.10.a.a.1.4		4
13.12	even	2		13.10.a.a.1.1	✓	4
39.38	odd	2		117.10.a.c.1.4		4
52.51	odd	2		208.10.a.g.1.3		4
65.64	even	2		325.10.a.a.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.a.a.1.1	✓	4	13.12	even	2
117.10.a.c.1.4		4	39.38	odd	2
169.10.a.a.1.4		4	1.1	even	1	trivial
208.10.a.g.1.3		4	52.51	odd	2
325.10.a.a.1.4		4	65.64	even	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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	169.a (trivial)

\(f(q)\)	\(=\)	\(q+44.6235 q^{2} -51.0278 q^{3} +1479.26 q^{4} -151.187 q^{5} -2277.04 q^{6} -5436.58 q^{7} +43162.5 q^{8} -17079.2 q^{9} -6746.48 q^{10} -33841.6 q^{11} -75483.2 q^{12} -242599. q^{14} +7714.72 q^{15} +1.16868e6 q^{16} -588951. q^{17} -762133. q^{18} +123244. q^{19} -223644. q^{20} +277417. q^{21} -1.51013e6 q^{22} -1.55650e6 q^{23} -2.20248e6 q^{24} -1.93027e6 q^{25} +1.87589e6 q^{27} -8.04211e6 q^{28} +273935. q^{29} +344258. q^{30} +5.07992e6 q^{31} +3.00515e7 q^{32} +1.72686e6 q^{33} -2.62811e7 q^{34} +821938. q^{35} -2.52645e7 q^{36} -8.27832e6 q^{37} +5.49960e6 q^{38} -6.52559e6 q^{40} -1.69055e7 q^{41} +1.23793e7 q^{42} -1.23150e7 q^{43} -5.00604e7 q^{44} +2.58214e6 q^{45} -6.94565e7 q^{46} +3.71528e7 q^{47} -5.96352e7 q^{48} -1.07972e7 q^{49} -8.61353e7 q^{50} +3.00528e7 q^{51} -5.85375e7 q^{53} +8.37089e7 q^{54} +5.11640e6 q^{55} -2.34656e8 q^{56} -6.28889e6 q^{57} +1.22239e7 q^{58} +2.83630e7 q^{59} +1.14121e7 q^{60} +2.89102e7 q^{61} +2.26684e8 q^{62} +9.28523e7 q^{63} +7.42638e8 q^{64} +7.70586e7 q^{66} +9.52452e7 q^{67} -8.71211e8 q^{68} +7.94247e7 q^{69} +3.66778e7 q^{70} +1.35041e7 q^{71} -7.37179e8 q^{72} +1.20684e8 q^{73} -3.69408e8 q^{74} +9.84972e7 q^{75} +1.82310e8 q^{76} +1.83983e8 q^{77} +2.80552e8 q^{79} -1.76689e8 q^{80} +2.40447e8 q^{81} -7.54385e8 q^{82} -5.16031e8 q^{83} +4.10371e8 q^{84} +8.90415e7 q^{85} -5.49538e8 q^{86} -1.39783e7 q^{87} -1.46069e9 q^{88} -1.00683e9 q^{89} +1.15224e8 q^{90} -2.30247e9 q^{92} -2.59217e8 q^{93} +1.65789e9 q^{94} -1.86329e7 q^{95} -1.53346e9 q^{96} -1.99014e8 q^{97} -4.81809e8 q^{98} +5.77986e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 33 q^{2} - 163 q^{3} + 1429 q^{4} - 471 q^{5} + 4529 q^{6} + 11241 q^{7} + 45543 q^{8} - 29953 q^{9} - 67831 q^{10} + 40140 q^{11} - 155479 q^{12} - 277653 q^{14} - 83307 q^{15} + 726609 q^{16} + 78717 q^{17}+ \cdots - 2132181050 q^{99}+O(q^{100}) \) 4 * q + 33 * q^2 - 163 * q^3 + 1429 * q^4 - 471 * q^5 + 4529 * q^6 + 11241 * q^7 + 45543 * q^8 - 29953 * q^9 - 67831 * q^10 + 40140 * q^11 - 155479 * q^12 - 277653 * q^14 - 83307 * q^15 + 726609 * q^16 + 78717 * q^17 - 1691026 * q^18 - 209664 * q^19 - 870843 * q^20 - 1138431 * q^21 + 1364090 * q^22 - 4257444 * q^23 - 3561573 * q^24 - 2900157 * q^25 - 2077801 * q^27 - 4035181 * q^28 - 1647936 * q^29 - 744143 * q^30 + 11366002 * q^31 + 29458959 * q^32 + 14413222 * q^33 - 26257659 * q^34 - 13789797 * q^35 - 11587714 * q^36 - 4636891 * q^37 + 25172466 * q^38 + 22536791 * q^40 - 13859538 * q^41 + 75564923 * q^42 - 33368081 * q^43 - 66489222 * q^44 + 17423928 * q^45 - 71369332 * q^46 + 3943005 * q^47 - 620787 * q^48 + 23294923 * q^49 + 4217748 * q^50 - 19664471 * q^51 - 171019326 * q^53 + 64946915 * q^54 - 121160538 * q^55 - 281552967 * q^56 + 47829030 * q^57 - 79964734 * q^58 + 63389388 * q^59 - 37708135 * q^60 + 77050190 * q^61 - 95878740 * q^62 + 155695476 * q^63 + 768962465 * q^64 - 42396374 * q^66 + 41174072 * q^67 - 717615423 * q^68 + 546642556 * q^69 - 409056389 * q^70 - 252460989 * q^71 - 562579254 * q^72 - 594415068 * q^73 - 957058539 * q^74 + 533318748 * q^75 + 326897170 * q^76 + 561950454 * q^77 + 115998984 * q^79 + 509107233 * q^80 + 437803700 * q^81 - 875148240 * q^82 + 79577862 * q^83 - 108899441 * q^84 - 549463469 * q^85 + 589924887 * q^86 - 1087526510 * q^87 - 2327564370 * q^88 + 1152240276 * q^89 + 877550038 * q^90 - 4213481460 * q^92 - 1618266556 * q^93 + 1859909503 * q^94 - 1273705170 * q^95 - 3171454029 * q^96 - 1049098084 * q^97 - 420532254 * q^98 - 2132181050 * q^99

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