LMFDB - Embedded newform 29.16.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,16,Mod(1,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	29.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:	$41.3811164790$
Analytic rank:	$0$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 505005 x^{17} - 8736364 x^{16} + 105356631548 x^{15} + 3420215362096 x^{14} + \cdots - 44\!\cdots\!16 $ x^19 - 505005x^17 - 8736364x^16 + 105356631548x^15 + 3420215362096x^14 - 11728115084600096x^13 - 526667384321784320x^12 + 752639041053026643200x^11 + 40754151979122502310912x^10 - 28214216503608778938845184x^9 - 1695908354434496093367894016x^8 + 602673095240440629989514543104x^7 + 38350831066057179894641242144768x^6 - 6885716108325545063604182908403712x^5 - 456772325113502009511188321406025728x^4 + 36920835566283148767251922402968338432x^3 + 2536352111314177920131172586486147055616x^2 - 64060563711600166379571072317272711233536*x - 4498782094616840134153644664240655371862016
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{43}\cdot 3^{6}\cdot 5^{5}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-245.307$ of defining polynomial
Character	$\chi$	$=$	29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-245.307 q^{2} -5730.81 q^{3} +27407.6 q^{4} +9338.19 q^{5} +1.40581e6 q^{6} -2.46876e6 q^{7} +1.31495e6 q^{8} +1.84933e7 q^{9} +O(q^{10})$	\(q-245.307 q^{2} -5730.81 q^{3} +27407.6 q^{4} +9338.19 q^{5} +1.40581e6 q^{6} -2.46876e6 q^{7} +1.31495e6 q^{8} +1.84933e7 q^{9} -2.29072e6 q^{10} +5.91587e7 q^{11} -1.57068e8 q^{12} -4.35199e7 q^{13} +6.05604e8 q^{14} -5.35154e7 q^{15} -1.22066e9 q^{16} -3.03579e9 q^{17} -4.53653e9 q^{18} -3.99101e9 q^{19} +2.55937e8 q^{20} +1.41480e10 q^{21} -1.45120e10 q^{22} -1.39703e10 q^{23} -7.53570e9 q^{24} -3.04304e10 q^{25} +1.06757e10 q^{26} -2.37504e10 q^{27} -6.76627e10 q^{28} -1.72499e10 q^{29} +1.31277e10 q^{30} -5.05812e10 q^{31} +2.56348e11 q^{32} -3.39027e11 q^{33} +7.44701e11 q^{34} -2.30537e10 q^{35} +5.06856e11 q^{36} -6.03065e11 q^{37} +9.79024e11 q^{38} +2.49404e11 q^{39} +1.22792e10 q^{40} +9.07845e10 q^{41} -3.47060e12 q^{42} -2.93108e12 q^{43} +1.62140e12 q^{44} +1.72693e11 q^{45} +3.42703e12 q^{46} +3.26530e12 q^{47} +6.99535e12 q^{48} +1.34720e12 q^{49} +7.46479e12 q^{50} +1.73975e13 q^{51} -1.19278e12 q^{52} -1.26049e12 q^{53} +5.82615e12 q^{54} +5.52435e11 q^{55} -3.24628e12 q^{56} +2.28717e13 q^{57} +4.23152e12 q^{58} -1.35616e13 q^{59} -1.46673e12 q^{60} +1.32108e12 q^{61} +1.24079e13 q^{62} -4.56553e13 q^{63} -2.28855e13 q^{64} -4.06397e11 q^{65} +8.31657e13 q^{66} -6.83216e13 q^{67} -8.32037e13 q^{68} +8.00614e13 q^{69} +5.65524e12 q^{70} -6.25893e13 q^{71} +2.43176e13 q^{72} -8.45395e13 q^{73} +1.47936e14 q^{74} +1.74391e14 q^{75} -1.09384e14 q^{76} -1.46048e14 q^{77} -6.11806e13 q^{78} +1.46351e14 q^{79} -1.13987e13 q^{80} -1.29249e14 q^{81} -2.22701e13 q^{82} -2.17204e14 q^{83} +3.87762e14 q^{84} -2.83488e13 q^{85} +7.19014e14 q^{86} +9.88557e13 q^{87} +7.77904e13 q^{88} +5.98532e13 q^{89} -4.23629e13 q^{90} +1.07440e14 q^{91} -3.82894e14 q^{92} +2.89871e14 q^{93} -8.01002e14 q^{94} -3.72689e13 q^{95} -1.46908e15 q^{96} -9.17400e14 q^{97} -3.30477e14 q^{98} +1.09404e15 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 9908 q^{3} + 387418 q^{4} + 230490 q^{5} + 1566838 q^{6} + 2882024 q^{7} + 26209092 q^{8} + 93022899 q^{9}+O(q^{10}) $ 19 * q + 9908 * q^3 + 387418 * q^4 + 230490 * q^5 + 1566838 * q^6 + 2882024 * q^7 + 26209092 * q^8 + 93022899 * q^9	\( 19 q + 9908 q^{3} + 387418 q^{4} + 230490 q^{5} + 1566838 q^{6} + 2882024 q^{7} + 26209092 q^{8} + 93022899 q^{9} - 46518144 q^{10} + 56910992 q^{11} + 907194664 q^{12} + 377780326 q^{13} + 1552762656 q^{14} + 2058712006 q^{15} + 9746645474 q^{16} - 797562458 q^{17} - 2812146948 q^{18} + 5568901154 q^{19} - 6814671874 q^{20} - 19358601528 q^{21} - 43431230566 q^{22} - 22787265900 q^{23} - 32333767894 q^{24} + 113218218877 q^{25} - 60020783208 q^{26} + 115546592594 q^{27} + 171573547692 q^{28} - 327747649871 q^{29} - 152869385454 q^{30} + 190165645448 q^{31} + 1523182591996 q^{32} + 1432316120556 q^{33} + 781895976484 q^{34} + 1076956461508 q^{35} + 4124169333892 q^{36} + 1157558623486 q^{37} + 454200349888 q^{38} - 3276695149790 q^{39} + 1497234313960 q^{40} - 327181726714 q^{41} + 14801498493780 q^{42} + 3969726268184 q^{43} + 9884551144664 q^{44} + 13723027476954 q^{45} + 4360233976812 q^{46} + 17801533447516 q^{47} + 44888708498560 q^{48} + 26274460777219 q^{49} + 49590112735028 q^{50} + 48299925405108 q^{51} + 38417786090034 q^{52} + 42945469924134 q^{53} + 78537259690434 q^{54} + 43646306609786 q^{55} + 153497246476960 q^{56} + 87149617056284 q^{57} + 76276585694640 q^{59} + 137931874827396 q^{60} + 75095043245982 q^{61} + 45115853357766 q^{62} + 77728938376620 q^{63} + 263521279152786 q^{64} + 25707147233724 q^{65} - 97128209185404 q^{66} + 39919578800676 q^{67} + 172949157314596 q^{68} + 61328545437264 q^{69} + 524547167494056 q^{70} + 128037096114140 q^{71} + 307467488440744 q^{72} + 333487363889334 q^{73} + 220493893416424 q^{74} - 68218174510546 q^{75} + 354934779140576 q^{76} - 692163369062472 q^{77} - 818320982346402 q^{78} + 213267241183292 q^{79} - 452775952882810 q^{80} + 48823702443271 q^{81} - 17\!\cdots\!96 q^{82}+ \cdots - 233858833882834 q^{99}+O(q^{100}) \) 19 * q + 9908 * q^3 + 387418 * q^4 + 230490 * q^5 + 1566838 * q^6 + 2882024 * q^7 + 26209092 * q^8 + 93022899 * q^9 - 46518144 * q^10 + 56910992 * q^11 + 907194664 * q^12 + 377780326 * q^13 + 1552762656 * q^14 + 2058712006 * q^15 + 9746645474 * q^16 - 797562458 * q^17 - 2812146948 * q^18 + 5568901154 * q^19 - 6814671874 * q^20 - 19358601528 * q^21 - 43431230566 * q^22 - 22787265900 * q^23 - 32333767894 * q^24 + 113218218877 * q^25 - 60020783208 * q^26 + 115546592594 * q^27 + 171573547692 * q^28 - 327747649871 * q^29 - 152869385454 * q^30 + 190165645448 * q^31 + 1523182591996 * q^32 + 1432316120556 * q^33 + 781895976484 * q^34 + 1076956461508 * q^35 + 4124169333892 * q^36 + 1157558623486 * q^37 + 454200349888 * q^38 - 3276695149790 * q^39 + 1497234313960 * q^40 - 327181726714 * q^41 + 14801498493780 * q^42 + 3969726268184 * q^43 + 9884551144664 * q^44 + 13723027476954 * q^45 + 4360233976812 * q^46 + 17801533447516 * q^47 + 44888708498560 * q^48 + 26274460777219 * q^49 + 49590112735028 * q^50 + 48299925405108 * q^51 + 38417786090034 * q^52 + 42945469924134 * q^53 + 78537259690434 * q^54 + 43646306609786 * q^55 + 153497246476960 * q^56 + 87149617056284 * q^57 + 76276585694640 * q^59 + 137931874827396 * q^60 + 75095043245982 * q^61 + 45115853357766 * q^62 + 77728938376620 * q^63 + 263521279152786 * q^64 + 25707147233724 * q^65 - 97128209185404 * q^66 + 39919578800676 * q^67 + 172949157314596 * q^68 + 61328545437264 * q^69 + 524547167494056 * q^70 + 128037096114140 * q^71 + 307467488440744 * q^72 + 333487363889334 * q^73 + 220493893416424 * q^74 - 68218174510546 * q^75 + 354934779140576 * q^76 - 692163369062472 * q^77 - 818320982346402 * q^78 + 213267241183292 * q^79 - 452775952882810 * q^80 + 48823702443271 * q^81 - 1736995581874796 * q^82 - 66633324408168 * q^83 - 2217716778602152 * q^84 - 1419457827450068 * q^85 - 1364891612086326 * q^86 - 170911774469572 * q^87 - 4325342725143834 * q^88 - 2341312102493090 * q^89 - 6182213358743320 * q^90 + 852022408820524 * q^91 - 3781297333622004 * q^92 - 3548745569232820 * q^93 - 914001881049618 * q^94 - 4053850425835916 * q^95 - 775984072309158 * q^96 - 686179834828282 * q^97 - 5170682580897840 * q^98 - 233858833882834 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−245.307	−1.35514	−0.677572	−	0.735457i	$-0.736968\pi$
$2$	−245.307	−1.35514	−0.677572	+	0.735457i	$0.736968\pi$
$3$	−5730.81	−1.51289	−0.756443	−	0.654059i	$-0.773065\pi$
$3$	−5730.81	−1.51289	−0.756443	+	0.654059i	$0.773065\pi$
$4$	27407.6	0.836413
$5$	9338.19	0.0534549	0.0267275	−	0.999643i	$-0.491491\pi$
$5$	9338.19	0.0534549	0.0267275	+	0.999643i	$0.491491\pi$
$6$	1.40581e6	2.05018
$7$	−2.46876e6	−1.13303	−0.566517	−	0.824050i	$-0.691709\pi$
$7$	−2.46876e6	−1.13303	−0.566517	+	0.824050i	$0.691709\pi$
$8$	1.31495e6	0.221683
$9$	1.84933e7	1.28883
$10$	−2.29072e6	−0.0724391
$11$	5.91587e7	0.915320	0.457660	−	0.889127i	$-0.348688\pi$
$11$	5.91587e7	0.915320	0.457660	+	0.889127i	$0.348688\pi$
$12$	−1.57068e8	−1.26540
$13$	−4.35199e7	−0.192359	−0.0961795	−	0.995364i	$-0.530662\pi$
$13$	−4.35199e7	−0.192359	−0.0961795	+	0.995364i	$0.530662\pi$
$14$	6.05604e8	1.53542
$15$	−5.35154e7	−0.0808712
$16$	−1.22066e9	−1.13683
$17$	−3.03579e9	−1.79434	−0.897170	−	0.441686i	$-0.854381\pi$
$17$	−3.03579e9	−1.79434	−0.897170	+	0.441686i	$0.854381\pi$
$18$	−4.53653e9	−1.74654
$19$	−3.99101e9	−1.02431	−0.512155	−	0.858893i	$-0.671153\pi$
$19$	−3.99101e9	−1.02431	−0.512155	+	0.858893i	$0.671153\pi$
$20$	2.55937e8	0.0447104
$21$	1.41480e10	1.71415
$22$	−1.45120e10	−1.24039
$23$	−1.39703e10	−0.855556	−0.427778	−	0.903884i	$-0.640704\pi$
$23$	−1.39703e10	−0.855556	−0.427778	+	0.903884i	$0.640704\pi$
$24$	−7.53570e9	−0.335382
$25$	−3.04304e10	−0.997143
$26$	1.06757e10	0.260674
$27$	−2.37504e10	−0.436962
$28$	−6.76627e10	−0.947685
$29$	−1.72499e10	−0.185695
$29$	−1.72499e10	−0.185695
$30$	1.31277e10	0.109592
$31$	−5.05812e10	−0.330200	−0.165100	−	0.986277i	$-0.552795\pi$
$31$	−5.05812e10	−0.330200	−0.165100	+	0.986277i	$0.552795\pi$
$32$	2.56348e11	1.31888
$33$	−3.39027e11	−1.38478
$34$	7.44701e11	2.43159
$35$	−2.30537e10	−0.0605662
$36$	5.06856e11	1.07799
$37$	−6.03065e11	−1.04436	−0.522181	−	0.852835i	$-0.674882\pi$
$37$	−6.03065e11	−1.04436	−0.522181	+	0.852835i	$0.674882\pi$
$38$	9.79024e11	1.38809
$39$	2.49404e11	0.291017
$40$	1.22792e10	0.0118501
$41$	9.07845e10	0.0728002	0.0364001	−	0.999337i	$-0.488411\pi$
$41$	9.07845e10	0.0728002	0.0364001	+	0.999337i	$0.488411\pi$
$42$	−3.47060e12	−2.32292
$43$	−2.93108e12	−1.64442	−0.822212	−	0.569182i	$-0.807260\pi$
$43$	−2.93108e12	−1.64442	−0.822212	+	0.569182i	$0.807260\pi$
$44$	1.62140e12	0.765586
$45$	1.72693e11	0.0688941
$46$	3.42703e12	1.15940
$47$	3.26530e12	0.940134	0.470067	−	0.882631i	$-0.344230\pi$
$47$	3.26530e12	0.940134	0.470067	+	0.882631i	$0.344230\pi$
$48$	6.99535e12	1.71989
$49$	1.34720e12	0.283766
$50$	7.46479e12	1.35127
$51$	1.73975e13	2.71463
$52$	−1.19278e12	−0.160892
$53$	−1.26049e12	−0.147390	−0.0736952	−	0.997281i	$-0.523479\pi$
$53$	−1.26049e12	−0.147390	−0.0736952	+	0.997281i	$0.523479\pi$
$54$	5.82615e12	0.592146
$55$	5.52435e11	0.0489284
$56$	−3.24628e12	−0.251175
$57$	2.28717e13	1.54966
$58$	4.23152e12	0.251644
$59$	−1.35616e13	−0.709448	−0.354724	−	0.934971i	$-0.615425\pi$
$59$	−1.35616e13	−0.709448	−0.354724	+	0.934971i	$0.615425\pi$
$60$	−1.46673e12	−0.0676418
$61$	1.32108e12	0.0538215	0.0269108	−	0.999638i	$-0.491433\pi$
$61$	1.32108e12	0.0538215	0.0269108	+	0.999638i	$0.491433\pi$
$62$	1.24079e13	0.447468
$63$	−4.56553e13	−1.46028
$64$	−2.28855e13	−0.650444
$65$	−4.06397e11	−0.0102825
$66$	8.31657e13	1.87657
$67$	−6.83216e13	−1.37720	−0.688600	−	0.725141i	$-0.741774\pi$
$67$	−6.83216e13	−1.37720	−0.688600	+	0.725141i	$0.741774\pi$
$68$	−8.32037e13	−1.50081
$69$	8.00614e13	1.29436
$70$	5.65524e12	0.0820759
$71$	−6.25893e13	−0.816700	−0.408350	−	0.912826i	$-0.633896\pi$
$71$	−6.25893e13	−0.816700	−0.408350	+	0.912826i	$0.633896\pi$
$72$	2.43176e13	0.285711
$73$	−8.45395e13	−0.895650	−0.447825	−	0.894121i	$-0.647801\pi$
$73$	−8.45395e13	−0.895650	−0.447825	+	0.894121i	$0.647801\pi$
$74$	1.47936e14	1.41526
$75$	1.74391e14	1.50856
$76$	−1.09384e14	−0.856746
$77$	−1.46048e14	−1.03709
$78$	−6.11806e13	−0.394370
$79$	1.46351e14	0.857419	0.428709	−	0.903443i	$-0.358968\pi$
$79$	1.46351e14	0.857419	0.428709	+	0.903443i	$0.358968\pi$
$80$	−1.13987e13	−0.0607689
$81$	−1.29249e14	−0.627753
$82$	−2.22701e13	−0.0986547
$83$	−2.17204e14	−0.878583	−0.439292	−	0.898344i	$-0.644771\pi$
$83$	−2.17204e14	−0.878583	−0.439292	+	0.898344i	$0.644771\pi$
$84$	3.87762e14	1.43374
$85$	−2.83488e13	−0.0959163
$86$	7.19014e14	2.22843
$87$	9.88557e13	0.280936
$88$	7.77904e13	0.202911
$89$	5.98532e13	0.143437	0.0717186	−	0.997425i	$-0.477152\pi$
$89$	5.98532e13	0.143437	0.0717186	+	0.997425i	$0.477152\pi$
$90$	−4.23629e13	−0.0933614
$91$	1.07440e14	0.217949
$92$	−3.82894e14	−0.715599
$93$	2.89871e14	0.499555
$94$	−8.01002e14	−1.27402
$95$	−3.72689e13	−0.0547544
$96$	−1.46908e15	−1.99531
$97$	−9.17400e14	−1.15285	−0.576423	−	0.817152i	$-0.695552\pi$
$97$	−9.17400e14	−1.15285	−0.576423	+	0.817152i	$0.695552\pi$
$98$	−3.30477e14	−0.384544
$99$	1.09404e15	1.17969
$100$	−8.34023e14	−0.834023
$101$	−1.83188e15	−1.70015	−0.850074	−	0.526664i	$-0.823443\pi$
$101$	−1.83188e15	−1.70015	−0.850074	+	0.526664i	$0.823443\pi$
$102$	−4.26774e15	−3.67872
$103$	1.48960e15	1.19341	0.596706	−	0.802460i	$-0.296476\pi$
$103$	1.48960e15	1.19341	0.596706	+	0.802460i	$0.296476\pi$
$104$	−5.72263e13	−0.0426428
$105$	1.32116e14	0.0916299
$106$	3.09206e14	0.199735
$107$	−3.79544e13	−0.0228499	−0.0114249	−	0.999935i	$-0.503637\pi$
$107$	−3.79544e13	−0.0228499	−0.0114249	+	0.999935i	$0.503637\pi$
$108$	−6.50942e14	−0.365481
$109$	3.79003e15	1.98584	0.992918	−	0.118801i	$-0.0379051\pi$
$109$	3.79003e15	1.98584	0.992918	+	0.118801i	$0.0379051\pi$
$110$	−1.35516e14	−0.0663050
$111$	3.45605e15	1.58000
$112$	3.01351e15	1.28806
$113$	−2.73812e15	−1.09487	−0.547437	−	0.836847i	$-0.684397\pi$
$113$	−2.73812e15	−1.09487	−0.547437	+	0.836847i	$0.684397\pi$
$114$	−5.61060e15	−2.10002
$115$	−1.30458e14	−0.0457337
$116$	−4.72778e14	−0.155318
$117$	−8.04824e14	−0.247917
$118$	3.32676e15	0.961404
$119$	7.49462e15	2.03305
$120$	−7.03698e13	−0.0179278
$121$	−6.77502e14	−0.162189
$122$	−3.24071e14	−0.0729359
$123$	−5.20268e14	−0.110138
$124$	−1.38631e15	−0.276184
$125$	−5.69144e14	−0.106757
$126$	1.11996e16	1.97889
$127$	8.08500e15	1.34633	0.673166	−	0.739491i	$-0.264934\pi$
$127$	8.08500e15	1.34633	0.673166	+	0.739491i	$0.264934\pi$
$128$	−2.78604e15	−0.437434
$129$	1.67974e16	2.48783
$130$	9.96921e13	0.0139343
$131$	−6.65017e15	−0.877602	−0.438801	−	0.898584i	$-0.644597\pi$
$131$	−6.65017e15	−0.877602	−0.438801	+	0.898584i	$0.644597\pi$
$132$	−9.29191e15	−1.15825
$133$	9.85284e15	1.16058
$134$	1.67598e16	1.86630
$135$	−2.21786e14	−0.0233578
$136$	−3.99190e15	−0.397775
$137$	7.77853e15	0.733658	0.366829	−	0.930288i	$-0.380443\pi$
$137$	7.77853e15	0.733658	0.366829	+	0.930288i	$0.380443\pi$
$138$	−1.96396e16	−1.75404
$139$	9.84251e15	0.832712	0.416356	−	0.909202i	$-0.363307\pi$
$139$	9.84251e15	0.832712	0.416356	+	0.909202i	$0.363307\pi$
$140$	−6.31847e14	−0.0506584
$141$	−1.87128e16	−1.42232
$142$	1.53536e16	1.10674
$143$	−2.57458e15	−0.176070
$144$	−2.25739e16	−1.46517
$145$	−1.61083e14	−0.00992633
$146$	2.07381e16	1.21373
$147$	−7.72054e15	−0.429306
$148$	−1.65286e16	−0.873519
$149$	−9.85978e15	−0.495416	−0.247708	−	0.968835i	$-0.579677\pi$
$149$	−9.85978e15	−0.495416	−0.247708	+	0.968835i	$0.579677\pi$
$150$	−4.27793e16	−2.04432
$151$	3.42135e16	1.55550	0.777750	−	0.628573i	$-0.216361\pi$
$151$	3.42135e16	1.55550	0.777750	+	0.628573i	$0.216361\pi$
$152$	−5.24797e15	−0.227072
$153$	−5.61416e16	−2.31259
$154$	3.58267e16	1.40540
$155$	−4.72337e14	−0.0176508
$156$	6.83556e15	0.243411
$157$	−2.25208e16	−0.764428	−0.382214	−	0.924074i	$-0.624838\pi$
$157$	−2.25208e16	−0.764428	−0.382214	+	0.924074i	$0.624838\pi$
$158$	−3.59010e16	−1.16192
$159$	7.22360e15	0.222985
$160$	2.39383e15	0.0705006
$161$	3.44894e16	0.969374
$162$	3.17056e16	0.850695
$163$	−5.33199e15	−0.136610	−0.0683050	−	0.997664i	$-0.521759\pi$
$163$	−5.33199e15	−0.136610	−0.0683050	+	0.997664i	$0.521759\pi$
$164$	2.48818e15	0.0608911
$165$	−3.16590e15	−0.0740231
$166$	5.32818e16	1.19061
$167$	−1.00014e15	−0.0213642	−0.0106821	−	0.999943i	$-0.503400\pi$
$167$	−1.00014e15	−0.0213642	−0.0106821	+	0.999943i	$0.503400\pi$
$168$	1.86038e16	0.379999
$169$	−4.92919e16	−0.962998
$170$	6.95416e15	0.129980
$171$	−7.38068e16	−1.32016
$172$	−8.03337e16	−1.37542
$173$	1.00195e16	0.164248	0.0821242	−	0.996622i	$-0.473830\pi$
$173$	1.00195e16	0.164248	0.0821242	+	0.996622i	$0.473830\pi$
$174$	−2.42500e16	−0.380709
$175$	7.51252e16	1.12980
$176$	−7.22125e16	−1.04056
$177$	7.77189e16	1.07331
$178$	−1.46824e16	−0.194378
$179$	−5.70550e16	−0.724262	−0.362131	−	0.932127i	$-0.617951\pi$
$179$	−5.70550e16	−0.724262	−0.362131	+	0.932127i	$0.617951\pi$
$180$	4.73311e15	0.0576240
$181$	7.23122e16	0.844544	0.422272	−	0.906469i	$-0.361233\pi$
$181$	7.23122e16	0.844544	0.422272	+	0.906469i	$0.361233\pi$
$182$	−2.63558e16	−0.295353
$183$	−7.57086e15	−0.0814258
$184$	−1.83703e16	−0.189662
$185$	−5.63154e15	−0.0558263
$186$	−7.11075e16	−0.676969
$187$	−1.79593e17	−1.64240
$188$	8.94941e16	0.786340
$189$	5.86341e16	0.495093
$190$	9.14232e15	0.0742001
$191$	2.46393e16	0.192255	0.0961276	−	0.995369i	$-0.469354\pi$
$191$	2.46393e16	0.192255	0.0961276	+	0.995369i	$0.469354\pi$
$192$	1.31152e17	0.984048
$193$	−1.91476e17	−1.38177	−0.690884	−	0.722966i	$-0.742778\pi$
$193$	−1.91476e17	−1.38177	−0.690884	+	0.722966i	$0.742778\pi$
$194$	2.25045e17	1.56227
$195$	2.32898e15	0.0155563
$196$	3.69235e16	0.237346
$197$	−2.87172e16	−0.177683	−0.0888415	−	0.996046i	$-0.528316\pi$
$197$	−2.87172e16	−0.177683	−0.0888415	+	0.996046i	$0.528316\pi$
$198$	−2.68375e17	−1.59865
$199$	1.57001e17	0.900540	0.450270	−	0.892892i	$-0.351328\pi$
$199$	1.57001e17	0.900540	0.450270	+	0.892892i	$0.351328\pi$
$200$	−4.00143e16	−0.221050
$201$	3.91538e17	2.08355
$202$	4.49373e17	2.30394
$203$	4.25857e16	0.210399
$204$	4.76824e17	2.27056
$205$	8.47763e14	0.00389153
$206$	−3.65409e17	−1.61724
$207$	−2.58357e17	−1.10266
$208$	5.31229e16	0.218679
$209$	−2.36103e17	−0.937572
$210$	−3.24091e16	−0.124172
$211$	−3.41918e17	−1.26417	−0.632083	−	0.774901i	$-0.717800\pi$
$211$	−3.41918e17	−1.26417	−0.632083	+	0.774901i	$0.717800\pi$
$212$	−3.45469e16	−0.123279
$213$	3.58687e17	1.23557
$214$	9.31049e15	0.0309649
$215$	−2.73709e16	−0.0879025
$216$	−3.12305e16	−0.0968671
$217$	1.24873e17	0.374128
$218$	−9.29720e17	−2.69109
$219$	4.84480e17	1.35502
$220$	1.51409e16	0.0409244
$221$	1.32117e17	0.345157
$222$	−8.47794e17	−2.14113
$223$	7.33630e17	1.79139	0.895696	−	0.444667i	$-0.146678\pi$
$223$	7.33630e17	1.79139	0.895696	+	0.444667i	$0.146678\pi$
$224$	−6.32861e17	−1.49433
$225$	−5.62757e17	−1.28514
$226$	6.71681e17	1.48371
$227$	7.70400e17	1.64635	0.823175	−	0.567787i	$-0.192200\pi$
$227$	7.70400e17	1.64635	0.823175	+	0.567787i	$0.192200\pi$
$228$	6.26859e17	1.29616
$229$	1.59741e17	0.319633	0.159816	−	0.987147i	$-0.448910\pi$
$229$	1.59741e17	0.319633	0.159816	+	0.987147i	$0.448910\pi$
$230$	3.20022e16	0.0619757
$231$	8.36975e17	1.56900
$232$	−2.26827e16	−0.0411656
$233$	−3.21155e17	−0.564345	−0.282173	−	0.959364i	$-0.591055\pi$
$233$	−3.21155e17	−0.564345	−0.282173	+	0.959364i	$0.591055\pi$
$234$	1.97429e17	0.335964
$235$	3.04920e16	0.0502548
$236$	−3.71691e17	−0.593392
$237$	−8.38710e17	−1.29718
$238$	−1.83848e18	−2.75507
$239$	6.66352e17	0.967653	0.483826	−	0.875164i	$-0.339247\pi$
$239$	6.66352e17	0.967653	0.483826	+	0.875164i	$0.339247\pi$
$240$	6.53240e16	0.0919365
$241$	2.95411e17	0.402995	0.201497	−	0.979489i	$-0.435419\pi$
$241$	2.95411e17	0.402995	0.201497	+	0.979489i	$0.435419\pi$
$242$	1.66196e17	0.219789
$243$	1.08149e18	1.38668
$244$	3.62077e16	0.0450170
$245$	1.25804e16	0.0151687
$246$	1.27626e17	0.149253
$247$	1.73688e17	0.197035
$248$	−6.65116e16	−0.0731998
$249$	1.24476e18	1.32920
$250$	1.39615e17	0.144671
$251$	1.16584e18	1.17242	0.586212	−	0.810158i	$-0.300619\pi$
$251$	1.16584e18	1.17242	0.586212	+	0.810158i	$0.300619\pi$
$252$	−1.25130e18	−1.22140
$253$	−8.26467e17	−0.783108
$254$	−1.98331e18	−1.82447
$255$	1.62461e17	0.145110
$256$	1.43335e18	1.24323
$257$	9.22817e17	0.777351	0.388675	−	0.921375i	$-0.372933\pi$
$257$	9.22817e17	0.777351	0.388675	+	0.921375i	$0.372933\pi$
$258$	−4.12053e18	−3.37136
$259$	1.48882e18	1.18330
$260$	−1.11384e16	−0.00860045
$261$	−3.19006e17	−0.239329
$262$	1.63133e18	1.18928
$263$	−2.03447e18	−1.44140	−0.720699	−	0.693248i	$-0.756179\pi$
$263$	−2.03447e18	−1.44140	−0.720699	+	0.693248i	$0.756179\pi$
$264$	−4.45802e17	−0.306982
$265$	−1.17707e16	−0.00787874
$266$	−2.41697e18	−1.57275
$267$	−3.43007e17	−0.217004
$268$	−1.87253e18	−1.15191
$269$	−2.60508e18	−1.55840	−0.779201	−	0.626774i	$-0.784375\pi$
$269$	−2.60508e18	−1.55840	−0.779201	+	0.626774i	$0.784375\pi$
$270$	5.44057e16	0.0316531
$271$	8.56279e17	0.484558	0.242279	−	0.970207i	$-0.422105\pi$
$271$	8.56279e17	0.484558	0.242279	+	0.970207i	$0.422105\pi$
$272$	3.70566e18	2.03985
$273$	−6.15718e17	−0.329733
$274$	−1.90813e18	−0.994211
$275$	−1.80022e18	−0.912705
$276$	2.19429e18	1.08262
$277$	−2.76150e18	−1.32601	−0.663005	−	0.748615i	$-0.730719\pi$
$277$	−2.76150e18	−1.32601	−0.663005	+	0.748615i	$0.730719\pi$
$278$	−2.41444e18	−1.12844
$279$	−9.35412e17	−0.425570
$280$	−3.03144e16	−0.0134265
$281$	−3.13921e18	−1.35370	−0.676850	−	0.736121i	$-0.736656\pi$
$281$	−3.13921e18	−1.35370	−0.676850	+	0.736121i	$0.736656\pi$
$282$	4.59039e18	1.92744
$283$	−3.22792e18	−1.31985	−0.659924	−	0.751332i	$-0.729412\pi$
$283$	−3.22792e18	−1.31985	−0.659924	+	0.751332i	$0.729412\pi$
$284$	−1.71542e18	−0.683098
$285$	2.13581e17	0.0828372
$286$	6.31562e17	0.238600
$287$	−2.24125e17	−0.0824851
$288$	4.74071e18	1.69981
$289$	6.35359e18	2.21965
$290$	3.95147e16	0.0134516
$291$	5.25745e18	1.74412
$292$	−2.31702e18	−0.749133
$293$	2.11816e18	0.667501	0.333751	−	0.942661i	$-0.391686\pi$
$293$	2.11816e18	0.667501	0.333751	+	0.942661i	$0.391686\pi$
$294$	1.89390e18	0.581772
$295$	−1.26641e17	−0.0379235
$296$	−7.92998e17	−0.231518
$297$	−1.40504e18	−0.399960
$298$	2.41867e18	0.671360
$299$	6.07988e17	0.164574
$300$	4.77963e18	1.26178
$301$	7.23611e18	1.86319
$302$	−8.39281e18	−2.10793
$303$	1.04981e19	2.57213
$304$	4.87166e18	1.16446
$305$	1.23365e16	0.00287702
$306$	1.37719e19	3.13389
$307$	8.50325e18	1.88820	0.944098	−	0.329665i	$-0.106936\pi$
$307$	8.50325e18	1.88820	0.944098	+	0.329665i	$0.106936\pi$
$308$	−4.00283e18	−0.867435
$309$	−8.53661e18	−1.80550
$310$	1.15868e17	0.0239194
$311$	−6.25998e18	−1.26145	−0.630725	−	0.776006i	$-0.717242\pi$
$311$	−6.25998e18	−1.26145	−0.630725	+	0.776006i	$0.717242\pi$
$312$	3.27953e17	0.0645137
$313$	−6.22166e18	−1.19488	−0.597439	−	0.801914i	$-0.703815\pi$
$313$	−6.22166e18	−1.19488	−0.597439	+	0.801914i	$0.703815\pi$
$314$	5.52451e18	1.03591
$315$	−4.26338e17	−0.0780594
$316$	4.01113e18	0.717156
$317$	−3.83629e18	−0.669833	−0.334916	−	0.942248i	$-0.608708\pi$
$317$	−3.83629e18	−0.669833	−0.334916	+	0.942248i	$0.608708\pi$
$318$	−1.77200e18	−0.302176
$319$	−1.02048e18	−0.169971
$320$	−2.13709e17	−0.0347694
$321$	2.17509e17	0.0345693
$322$	−8.46049e18	−1.31364
$323$	1.21159e19	1.83796
$324$	−3.54240e18	−0.525061
$325$	1.32433e18	0.191809
$326$	1.30798e18	0.185126
$327$	−2.17199e19	−3.00435
$328$	1.19377e17	0.0161386
$329$	−8.06124e18	−1.06520
$330$	7.76617e17	0.100312
$331$	−7.84942e18	−0.991123	−0.495561	−	0.868573i	$-0.665038\pi$
$331$	−7.84942e18	−0.991123	−0.495561	+	0.868573i	$0.665038\pi$
$332$	−5.95305e18	−0.734859
$333$	−1.11526e19	−1.34600
$334$	2.45342e17	0.0289516
$335$	−6.38000e17	−0.0736181
$336$	−1.72698e19	−1.94869
$337$	−4.82675e18	−0.532636	−0.266318	−	0.963885i	$-0.585807\pi$
$337$	−4.82675e18	−0.532636	−0.266318	+	0.963885i	$0.585807\pi$
$338$	1.20917e19	1.30500
$339$	1.56916e19	1.65642
$340$	−7.76972e17	−0.0802257
$341$	−2.99232e18	−0.302239
$342$	1.81053e19	1.78900
$343$	8.39467e18	0.811517
$344$	−3.85421e18	−0.364541
$345$	7.47628e17	0.0691899
$346$	−2.45786e18	−0.222580
$347$	6.90458e18	0.611880	0.305940	−	0.952051i	$-0.401029\pi$
$347$	6.90458e18	0.611880	0.305940	+	0.952051i	$0.401029\pi$
$348$	2.70940e18	0.234979
$349$	1.16299e17	0.00987153	0.00493576	−	0.999988i	$-0.498429\pi$
$349$	1.16299e17	0.00987153	0.00493576	+	0.999988i	$0.498429\pi$
$350$	−1.84287e19	−1.53104
$351$	1.03362e18	0.0840535
$352$	1.51652e19	1.20720
$353$	2.17380e19	1.69398	0.846991	−	0.531607i	$-0.178412\pi$
$353$	2.17380e19	1.69398	0.846991	+	0.531607i	$0.178412\pi$
$354$	−1.90650e19	−1.45449
$355$	−5.84471e17	−0.0436566
$356$	1.64043e18	0.119973
$357$	−4.29503e19	−3.07577
$358$	1.39960e19	0.981479
$359$	−1.92033e19	−1.31876	−0.659381	−	0.751809i	$-0.729182\pi$
$359$	−1.92033e19	−1.31876	−0.659381	+	0.751809i	$0.729182\pi$
$360$	2.27083e17	0.0152727
$361$	7.47072e17	0.0492106
$362$	−1.77387e19	−1.14448
$363$	3.88263e18	0.245373
$364$	2.94467e18	0.182296
$365$	−7.89446e17	−0.0478769
$366$	1.85719e18	0.110344
$367$	−1.99804e19	−1.16308	−0.581538	−	0.813520i	$-0.697549\pi$
$367$	−1.99804e19	−1.16308	−0.581538	+	0.813520i	$0.697549\pi$
$368$	1.70530e19	0.972618
$369$	1.67890e18	0.0938268
$370$	1.38146e18	0.0756527
$371$	3.11183e18	0.166998
$372$	7.94468e18	0.417834
$373$	−9.80493e17	−0.0505392	−0.0252696	−	0.999681i	$-0.508044\pi$
$373$	−9.80493e17	−0.0505392	−0.0252696	+	0.999681i	$0.508044\pi$
$374$	4.40555e19	2.22568
$375$	3.26165e18	0.161511
$376$	4.29370e18	0.208412
$377$	7.50712e17	0.0357202
$378$	−1.43834e19	−0.670921
$379$	1.84051e19	0.841673	0.420836	−	0.907137i	$-0.361737\pi$
$379$	1.84051e19	0.841673	0.420836	+	0.907137i	$0.361737\pi$
$380$	−1.02145e18	−0.0457973
$381$	−4.63336e19	−2.03685
$382$	−6.04420e18	−0.260533
$383$	3.40952e19	1.44113	0.720563	−	0.693389i	$-0.243883\pi$
$383$	3.40952e19	1.44113	0.720563	+	0.693389i	$0.243883\pi$
$384$	1.59663e19	0.661788
$385$	−1.36383e18	−0.0554375
$386$	4.69705e19	1.87249
$387$	−5.42051e19	−2.11938
$388$	−2.51437e19	−0.964255
$389$	2.00905e19	0.755733	0.377866	−	0.925860i	$-0.376658\pi$
$389$	2.00905e19	0.755733	0.377866	+	0.925860i	$0.376658\pi$
$390$	−5.71316e17	−0.0210810
$391$	4.24110e19	1.53516
$392$	1.77149e18	0.0629063
$393$	3.81108e19	1.32771
$394$	7.04454e18	0.240786
$395$	1.36665e18	0.0458332
$396$	2.99849e19	0.986708
$397$	−3.51427e19	−1.13477	−0.567383	−	0.823454i	$-0.692044\pi$
$397$	−3.51427e19	−1.13477	−0.567383	+	0.823454i	$0.692044\pi$
$398$	−3.85134e19	−1.22036
$399$	−5.64648e19	−1.75582
$400$	3.71451e19	1.13358
$401$	4.49194e19	1.34540	0.672699	−	0.739916i	$-0.265135\pi$
$401$	4.49194e19	1.34540	0.672699	+	0.739916i	$0.265135\pi$
$402$	−9.60471e19	−2.82351
$403$	2.20129e18	0.0635169
$404$	−5.02074e19	−1.42203
$405$	−1.20695e18	−0.0335565
$406$	−1.04466e19	−0.285121
$407$	−3.56765e19	−0.955926
$408$	2.28768e19	0.601789
$409$	−5.34707e19	−1.38099	−0.690495	−	0.723337i	$-0.742607\pi$
$409$	−5.34707e19	−1.38099	−0.690495	+	0.723337i	$0.742607\pi$
$410$	−2.07962e17	−0.00527358
$411$	−4.45773e19	−1.10994
$412$	4.08263e19	0.998185
$413$	3.34803e19	0.803829
$414$	6.33769e19	1.49427
$415$	−2.02830e18	−0.0469646
$416$	−1.11562e19	−0.253698
$417$	−5.64056e19	−1.25980
$418$	5.79178e19	1.27054
$419$	6.63751e19	1.43021	0.715106	−	0.699016i	$-0.246378\pi$
$419$	6.63751e19	1.43021	0.715106	+	0.699016i	$0.246378\pi$
$420$	3.62099e18	0.0766405
$421$	7.71622e19	1.60431	0.802156	−	0.597114i	$-0.203686\pi$
$421$	7.71622e19	1.60431	0.802156	+	0.597114i	$0.203686\pi$
$422$	8.38750e19	1.71313
$423$	6.03861e19	1.21167
$424$	−1.65747e18	−0.0326740
$425$	9.23802e19	1.78921
$426$	−8.79885e19	−1.67438
$427$	−3.26143e18	−0.0609816
$428$	−1.04024e18	−0.0191119
$429$	1.47544e19	0.266374
$430$	6.71429e18	0.119121
$431$	−9.08366e19	−1.58373	−0.791865	−	0.610696i	$-0.790890\pi$
$431$	−9.08366e19	−1.58373	−0.791865	+	0.610696i	$0.790890\pi$
$432$	2.89912e19	0.496750
$433$	−7.16825e19	−1.20713	−0.603565	−	0.797314i	$-0.706254\pi$
$433$	−7.16825e19	−1.20713	−0.603565	+	0.797314i	$0.706254\pi$
$434$	−3.06322e19	−0.506997
$435$	9.23134e17	0.0150174
$436$	1.03875e20	1.66098
$437$	5.57559e19	0.876354
$438$	−1.18846e20	−1.83624
$439$	2.01598e18	0.0306198	0.0153099	−	0.999883i	$-0.495127\pi$
$439$	2.01598e18	0.0306198	0.0153099	+	0.999883i	$0.495127\pi$
$440$	7.26422e17	0.0108466
$441$	2.49141e19	0.365726
$442$	−3.24093e19	−0.467738
$443$	2.62507e19	0.372489	0.186245	−	0.982503i	$-0.440368\pi$
$443$	2.62507e19	0.372489	0.186245	+	0.982503i	$0.440368\pi$
$444$	9.47220e19	1.32153
$445$	5.58920e17	0.00766743
$446$	−1.79965e20	−2.42759
$447$	5.65045e19	0.749508
$448$	5.64986e19	0.736975
$449$	−1.09859e18	−0.0140925	−0.00704624	−	0.999975i	$-0.502243\pi$
$449$	−1.09859e18	−0.0140925	−0.00704624	+	0.999975i	$0.502243\pi$
$450$	1.38048e20	1.74155
$451$	5.37069e18	0.0666355
$452$	−7.50453e19	−0.915768
$453$	−1.96071e20	−2.35330
$454$	−1.88985e20	−2.23104
$455$	1.00330e18	0.0116505
$456$	3.00751e19	0.343535
$457$	1.44285e20	1.62125	0.810624	−	0.585567i	$-0.199128\pi$
$457$	1.44285e20	1.62125	0.810624	+	0.585567i	$0.199128\pi$
$458$	−3.91857e19	−0.433148
$459$	7.21013e19	0.784058
$460$	−3.57553e18	−0.0382523
$461$	1.01999e20	1.07359	0.536797	−	0.843712i	$-0.319634\pi$
$461$	1.01999e20	1.07359	0.536797	+	0.843712i	$0.319634\pi$
$462$	−2.05316e20	−2.12622
$463$	−1.29024e20	−1.31466	−0.657331	−	0.753602i	$-0.728314\pi$
$463$	−1.29024e20	−1.31466	−0.657331	+	0.753602i	$0.728314\pi$
$464$	2.10562e19	0.211103
$465$	2.70687e18	0.0267037
$466$	7.87815e19	0.764769
$467$	−1.59891e20	−1.52738	−0.763692	−	0.645581i	$-0.776615\pi$
$467$	−1.59891e20	−1.52738	−0.763692	+	0.645581i	$0.776615\pi$
$468$	−2.20583e19	−0.207361
$469$	1.68669e20	1.56042
$470$	−7.47991e18	−0.0681024
$471$	1.29062e20	1.15649
$472$	−1.78328e19	−0.157273
$473$	−1.73399e20	−1.50517
$474$	2.05742e20	1.75786
$475$	1.21448e20	1.02138
$476$	2.05410e20	1.70047
$477$	−2.33105e19	−0.189961
$478$	−1.63461e20	−1.31131
$479$	−1.40487e20	−1.10948	−0.554739	−	0.832025i	$-0.687182\pi$
$479$	−1.40487e20	−1.10948	−0.554739	+	0.832025i	$0.687182\pi$
$480$	−1.37186e19	−0.106659
$481$	2.62453e19	0.200893
$482$	−7.24665e19	−0.546116
$483$	−1.97652e20	−1.46655
$484$	−1.85687e19	−0.135657
$485$	−8.56686e18	−0.0616252
$486$	−2.65298e20	−1.87915
$487$	4.87971e19	0.340351	0.170175	−	0.985414i	$-0.445567\pi$
$487$	4.87971e19	0.340351	0.170175	+	0.985414i	$0.445567\pi$
$488$	1.73715e18	0.0119313
$489$	3.05566e19	0.206675
$490$	−3.08606e18	−0.0205558
$491$	−1.68198e20	−1.10334	−0.551670	−	0.834062i	$-0.686009\pi$
$491$	−1.68198e20	−1.10334	−0.551670	+	0.834062i	$0.686009\pi$
$492$	−1.42593e19	−0.0921213
$493$	5.23670e19	0.333201
$494$	−4.26070e19	−0.267011
$495$	1.02163e19	0.0630602
$496$	6.17424e19	0.375380
$497$	1.54518e20	0.925348
$498$	−3.05348e20	−1.80125
$499$	2.04576e20	1.18878	0.594389	−	0.804178i	$-0.297394\pi$
$499$	2.04576e20	1.18878	0.594389	+	0.804178i	$0.297394\pi$
$500$	−1.55989e19	−0.0892931
$501$	5.73161e18	0.0323217
$502$	−2.85988e20	−1.58880
$503$	−2.38147e20	−1.30342	−0.651712	−	0.758466i	$-0.725949\pi$
$503$	−2.38147e20	−1.30342	−0.651712	+	0.758466i	$0.725949\pi$
$504$	−6.00343e19	−0.323721
$505$	−1.71064e19	−0.0908812
$506$	2.02738e20	1.06122
$507$	2.82482e20	1.45691
$508$	2.21590e20	1.12609
$509$	3.24980e19	0.162732	0.0813660	−	0.996684i	$-0.474072\pi$
$509$	3.24980e19	0.162732	0.0813660	+	0.996684i	$0.474072\pi$
$510$	−3.98529e19	−0.196645
$511$	2.08707e20	1.01480
$512$	−2.60317e20	−1.24732
$513$	9.47884e19	0.447584
$514$	−2.26374e20	−1.05342
$515$	1.39102e19	0.0637937
$516$	4.60377e20	2.08085
$517$	1.93171e20	0.860524
$518$	−3.65218e20	−1.60354
$519$	−5.74200e19	−0.248489
$520$	−5.34390e17	−0.00227947
$521$	5.95878e19	0.250538	0.125269	−	0.992123i	$-0.460021\pi$
$521$	5.95878e19	0.250538	0.125269	+	0.992123i	$0.460021\pi$
$522$	7.82545e19	0.324325
$523$	2.23293e20	0.912248	0.456124	−	0.889916i	$-0.349237\pi$
$523$	2.23293e20	0.912248	0.456124	+	0.889916i	$0.349237\pi$
$524$	−1.82265e20	−0.734038
$525$	−4.30528e20	−1.70925
$526$	4.99071e20	1.95330
$527$	1.53554e20	0.592491
$528$	4.13836e20	1.57425
$529$	−7.14646e19	−0.268024
$530$	2.88743e18	0.0106768
$531$	−2.50798e20	−0.914355
$532$	2.70043e20	0.970723
$533$	−3.95093e18	−0.0140038
$534$	8.41421e19	0.294072
$535$	−3.54426e17	−0.00122144
$536$	−8.98392e19	−0.305302
$537$	3.26971e20	1.09573
$538$	6.39046e20	2.11186
$539$	7.96984e19	0.259737
$540$	−6.07862e18	−0.0195367
$541$	−2.63493e20	−0.835198	−0.417599	−	0.908631i	$-0.637128\pi$
$541$	−2.63493e20	−0.835198	−0.417599	+	0.908631i	$0.637128\pi$
$542$	−2.10051e20	−0.656645
$543$	−4.14407e20	−1.27770
$544$	−7.78218e20	−2.36652
$545$	3.53920e19	0.106153
$546$	1.51040e20	0.446835
$547$	−3.51471e20	−1.02561	−0.512807	−	0.858504i	$-0.671395\pi$
$547$	−3.51471e20	−1.02561	−0.512807	+	0.858504i	$0.671395\pi$
$548$	2.13191e20	0.613641
$549$	2.44311e19	0.0693666
$550$	4.41607e20	1.23685
$551$	6.88445e19	0.190210
$552$	1.05276e20	0.286938
$553$	−3.61305e20	−0.971484
$554$	6.77415e20	1.79693
$555$	3.22733e19	0.0844589
$556$	2.69760e20	0.696492
$557$	−4.44080e20	−1.13122	−0.565610	−	0.824673i	$-0.691359\pi$
$557$	−4.44080e20	−1.13122	−0.565610	+	0.824673i	$0.691359\pi$
$558$	2.29463e20	0.576709
$559$	1.27560e20	0.316320
$560$	2.81407e19	0.0688533
$561$	1.02921e21	2.48476
$562$	7.70070e20	1.83446
$563$	−3.16690e20	−0.744425	−0.372213	−	0.928147i	$-0.621401\pi$
$563$	−3.16690e20	−0.744425	−0.372213	+	0.928147i	$0.621401\pi$
$564$	−5.12874e20	−1.18964
$565$	−2.55691e19	−0.0585264
$566$	7.91831e20	1.78858
$567$	3.19084e20	0.711265
$568$	−8.23015e19	−0.181049
$569$	1.50676e18	0.00327117	0.00163559	−	0.999999i	$-0.499479\pi$
$569$	1.50676e18	0.00327117	0.00163559	+	0.999999i	$0.499479\pi$
$570$	−5.23929e19	−0.112256
$571$	−1.04862e20	−0.221741	−0.110870	−	0.993835i	$-0.535364\pi$
$571$	−1.04862e20	−0.221741	−0.110870	+	0.993835i	$0.535364\pi$
$572$	−7.05630e19	−0.147267
$573$	−1.41203e20	−0.290860
$574$	5.49794e19	0.111779
$575$	4.25123e20	0.853111
$576$	−4.23227e20	−0.838309
$577$	−5.87583e20	−1.14882	−0.574408	−	0.818569i	$-0.694768\pi$
$577$	−5.87583e20	−1.14882	−0.574408	+	0.818569i	$0.694768\pi$
$578$	−1.55858e21	−3.00795
$579$	1.09731e21	2.09046
$580$	−4.41489e18	−0.00830251
$581$	5.36225e20	0.995465
$582$	−1.28969e21	−2.36354
$583$	−7.45686e19	−0.134909
$584$	−1.11165e20	−0.198551
$585$	−7.51560e18	−0.0132524
$586$	−5.19601e20	−0.904560
$587$	−8.69603e20	−1.49463	−0.747317	−	0.664467i	$-0.768659\pi$
$587$	−8.69603e20	−1.49463	−0.747317	+	0.664467i	$0.768659\pi$
$588$	−2.11601e20	−0.359078
$589$	2.01871e20	0.338227
$590$	3.10659e19	0.0513918
$591$	1.64573e20	0.268814
$592$	7.36136e20	1.18726
$593$	−9.22454e20	−1.46904	−0.734521	−	0.678586i	$-0.762593\pi$
$593$	−9.22454e20	−1.46904	−0.734521	+	0.678586i	$0.762593\pi$
$594$	3.44667e20	0.542003
$595$	6.99862e19	0.108676
$596$	−2.70233e20	−0.414373
$597$	−8.99740e20	−1.36242
$598$	−1.49144e20	−0.223021
$599$	−2.05757e20	−0.303846	−0.151923	−	0.988392i	$-0.548547\pi$
$599$	−2.05757e20	−0.303846	−0.151923	+	0.988392i	$0.548547\pi$
$600$	2.29314e20	0.334423
$601$	1.84230e20	0.265339	0.132670	−	0.991160i	$-0.457645\pi$
$601$	1.84230e20	0.265339	0.132670	+	0.991160i	$0.457645\pi$
$602$	−1.77507e21	−2.52489
$603$	−1.26349e21	−1.77497
$604$	9.37709e20	1.30104
$605$	−6.32664e18	−0.00866978
$606$	−2.57527e21	−3.48561
$607$	6.38802e20	0.853987	0.426994	−	0.904255i	$-0.359573\pi$
$607$	6.38802e20	0.853987	0.426994	+	0.904255i	$0.359573\pi$
$608$	−1.02309e21	−1.35094
$609$	−2.44051e20	−0.318310
$610$	−3.02623e18	−0.00389878
$611$	−1.42106e20	−0.180843
$612$	−1.53871e21	−1.93428
$613$	5.14014e20	0.638295	0.319147	−	0.947705i	$-0.396603\pi$
$613$	5.14014e20	0.638295	0.319147	+	0.947705i	$0.396603\pi$
$614$	−2.08591e21	−2.55878
$615$	−4.85836e18	−0.00588744
$616$	−1.92046e20	−0.229905
$617$	1.07341e21	1.26948	0.634739	−	0.772727i	$-0.281108\pi$
$617$	1.07341e21	1.26948	0.634739	+	0.772727i	$0.281108\pi$
$618$	2.09409e21	2.44671
$619$	1.53796e21	1.77527	0.887634	−	0.460550i	$-0.152348\pi$
$619$	1.53796e21	1.77527	0.887634	+	0.460550i	$0.152348\pi$
$620$	−1.29456e19	−0.0147634
$621$	3.31802e20	0.373845
$622$	1.53562e21	1.70945
$623$	−1.47763e20	−0.162519
$624$	−3.04437e20	−0.330836
$625$	9.23347e20	0.991436
$626$	1.52622e21	1.61923
$627$	1.35306e21	1.41844
$628$	−6.17241e20	−0.639377
$629$	1.83078e21	1.87394
$630$	1.04584e20	0.105782
$631$	6.29451e20	0.629132	0.314566	−	0.949236i	$-0.398141\pi$
$631$	6.29451e20	0.629132	0.314566	+	0.949236i	$0.398141\pi$
$632$	1.92444e20	0.190075
$633$	1.95947e21	1.91254
$634$	9.41068e20	0.907719
$635$	7.54993e19	0.0719681
$636$	1.97982e20	0.186508
$637$	−5.86299e19	−0.0545850
$638$	2.50331e20	0.230335
$639$	−1.15748e21	−1.05258
$640$	−2.60166e19	−0.0233830
$641$	−1.36116e21	−1.20914	−0.604568	−	0.796554i	$-0.706654\pi$
$641$	−1.36116e21	−1.20914	−0.604568	+	0.796554i	$0.706654\pi$
$642$	−5.33566e19	−0.0468463
$643$	−1.20180e21	−1.04292	−0.521458	−	0.853277i	$-0.674612\pi$
$643$	−1.20180e21	−1.04292	−0.521458	+	0.853277i	$0.674612\pi$
$644$	9.45271e20	0.810798
$645$	1.56858e20	0.132987
$646$	−2.97211e21	−2.49070
$647$	2.12515e21	1.76039	0.880194	−	0.474614i	$-0.157412\pi$
$647$	2.12515e21	1.76039	0.880194	+	0.474614i	$0.157412\pi$
$648$	−1.69955e20	−0.139162
$649$	−8.02285e20	−0.649372
$650$	−3.24867e20	−0.259929
$651$	−7.15622e20	−0.566013
$652$	−1.46137e20	−0.114262
$653$	−8.52380e20	−0.658847	−0.329423	−	0.944182i	$-0.606854\pi$
$653$	−8.52380e20	−0.658847	−0.329423	+	0.944182i	$0.606854\pi$
$654$	5.32805e21	4.07132
$655$	−6.21005e19	−0.0469122
$656$	−1.10817e20	−0.0827612
$657$	−1.56341e21	−1.15434
$658$	1.97748e21	1.44350
$659$	−3.51471e20	−0.253658	−0.126829	−	0.991925i	$-0.540480\pi$
$659$	−3.51471e20	−0.253658	−0.126829	+	0.991925i	$0.540480\pi$
$660$	−8.67696e19	−0.0619139
$661$	−2.12143e21	−1.49664	−0.748322	−	0.663336i	$-0.769140\pi$
$661$	−2.12143e21	−1.49664	−0.748322	+	0.663336i	$0.769140\pi$
$662$	1.92552e21	1.34311
$663$	−7.57138e20	−0.522184
$664$	−2.85612e20	−0.194767
$665$	9.20077e19	0.0620386
$666$	2.73582e21	1.82403
$667$	2.40987e20	0.158873
$668$	−2.74114e19	−0.0178693
$669$	−4.20429e21	−2.71017
$670$	1.56506e20	0.0997631
$671$	7.81534e19	0.0492639
$672$	3.62680e21	2.26076
$673$	−1.35496e21	−0.835241	−0.417621	−	0.908621i	$-0.637136\pi$
$673$	−1.35496e21	−0.835241	−0.417621	+	0.908621i	$0.637136\pi$
$674$	1.18404e21	0.721798
$675$	7.22735e20	0.435713
$676$	−1.35097e21	−0.805464
$677$	1.43638e21	0.846946	0.423473	−	0.905909i	$-0.360811\pi$
$677$	1.43638e21	0.846946	0.423473	+	0.905909i	$0.360811\pi$
$678$	−3.84927e21	−2.24469
$679$	2.26484e21	1.30621
$680$	−3.72771e19	−0.0212630
$681$	−4.41501e21	−2.49074
$682$	7.34037e20	0.409577
$683$	−2.30362e21	−1.27132	−0.635660	−	0.771969i	$-0.719272\pi$
$683$	−2.30362e21	−1.27132	−0.635660	+	0.771969i	$0.719272\pi$
$684$	−2.02287e21	−1.10420
$685$	7.26374e19	0.0392176
$686$	−2.05927e21	−1.09972
$687$	−9.15448e20	−0.483568
$688$	3.57784e21	1.86942
$689$	5.48562e19	0.0283519
$690$	−1.83399e20	−0.0937622
$691$	2.57739e21	1.30345	0.651725	−	0.758456i	$-0.274046\pi$
$691$	2.57739e21	1.30345	0.651725	+	0.758456i	$0.274046\pi$
$692$	2.74611e20	0.137380
$693$	−2.70091e21	−1.33663
$694$	−1.69374e21	−0.829185
$695$	9.19113e19	0.0445126
$696$	1.29990e20	0.0622788
$697$	−2.75602e20	−0.130628
$698$	−2.85289e19	−0.0133773
$699$	1.84048e21	0.853791
$700$	2.05900e21	0.944977
$701$	−1.40683e21	−0.638787	−0.319393	−	0.947622i	$-0.603479\pi$
$701$	−1.40683e21	−0.638787	−0.319393	+	0.947622i	$0.603479\pi$
$702$	−2.53553e20	−0.113905
$703$	2.40684e21	1.06975
$704$	−1.35387e21	−0.595365
$705$	−1.74744e20	−0.0760298
$706$	−5.33248e21	−2.29559
$707$	4.52246e21	1.92633
$708$	2.13009e21	0.897735
$709$	−2.64159e21	−1.10159	−0.550793	−	0.834642i	$-0.685675\pi$
$709$	−2.64159e21	−1.10159	−0.550793	+	0.834642i	$0.685675\pi$
$710$	1.43375e20	0.0591610
$711$	2.70651e21	1.10506
$712$	7.87037e19	0.0317977
$713$	7.06638e20	0.282504
$714$	1.05360e22	4.16811
$715$	−2.40419e19	−0.00941181
$716$	−1.56374e21	−0.605782
$717$	−3.81874e21	−1.46395
$718$	4.71069e21	1.78711
$719$	5.00999e20	0.188092	0.0940460	−	0.995568i	$-0.470020\pi$
$719$	5.00999e20	0.188092	0.0940460	+	0.995568i	$0.470020\pi$
$720$	−2.10800e20	−0.0783206
$721$	−3.67746e21	−1.35218
$722$	−1.83262e20	−0.0666874
$723$	−1.69295e21	−0.609685
$724$	1.98190e21	0.706388
$725$	5.24920e20	0.185165
$726$	−9.52437e20	−0.332515
$727$	−4.61210e21	−1.59364	−0.796821	−	0.604215i	$-0.793487\pi$
$727$	−4.61210e21	−1.59364	−0.796821	+	0.604215i	$0.793487\pi$
$728$	1.41278e20	0.0483157
$729$	−4.34325e21	−1.47014
$730$	1.93657e20	0.0648800
$731$	8.89813e21	2.95065
$732$	−2.07499e20	−0.0681057
$733$	4.07254e21	1.32308	0.661540	−	0.749910i	$-0.269903\pi$
$733$	4.07254e21	1.32308	0.661540	+	0.749910i	$0.269903\pi$
$734$	4.90132e21	1.57613
$735$	−7.20958e19	−0.0229485
$736$	−3.58127e21	−1.12837
$737$	−4.04182e21	−1.26058
$738$	−4.11846e20	−0.127149
$739$	−4.94874e20	−0.151238	−0.0756191	−	0.997137i	$-0.524093\pi$
$739$	−4.94874e20	−0.151238	−0.0756191	+	0.997137i	$0.524093\pi$
$740$	−1.54347e20	−0.0466939
$741$	−9.95375e20	−0.298092
$742$	−7.63355e20	−0.226307
$743$	4.19354e21	1.23074	0.615368	−	0.788240i	$-0.289007\pi$
$743$	4.19354e21	1.23074	0.615368	+	0.788240i	$0.289007\pi$
$744$	3.81165e20	0.110743
$745$	−9.20725e19	−0.0264824
$746$	2.40522e20	0.0684879
$747$	−4.01682e21	−1.13234
$748$	−4.92222e21	−1.37372
$749$	9.37002e19	0.0258897
$750$	−8.00107e20	−0.218871
$751$	−1.76920e21	−0.479157	−0.239578	−	0.970877i	$-0.577009\pi$
$751$	−1.76920e21	−0.479157	−0.239578	+	0.970877i	$0.577009\pi$
$752$	−3.98582e21	−1.06877
$753$	−6.68118e21	−1.77374
$754$	−1.84155e20	−0.0484059
$755$	3.19492e20	0.0831492
$756$	1.60702e21	0.414102
$757$	6.62845e21	1.69119	0.845596	−	0.533824i	$-0.179245\pi$
$757$	6.62845e21	1.69119	0.845596	+	0.533824i	$0.179245\pi$
$758$	−4.51489e21	−1.14059
$759$	4.73632e21	1.18475
$760$	−4.90065e19	−0.0121381
$761$	4.85433e21	1.19054	0.595271	−	0.803525i	$-0.297045\pi$
$761$	4.85433e21	1.19054	0.595271	+	0.803525i	$0.297045\pi$
$762$	1.13660e22	2.76022
$763$	−9.35665e21	−2.25002
$764$	6.75304e20	0.160805
$765$	−5.24261e20	−0.123619
$766$	−8.36379e21	−1.95293
$767$	5.90199e20	0.136469
$768$	−8.21423e21	−1.88087
$769$	−2.52658e21	−0.572908	−0.286454	−	0.958094i	$-0.592477\pi$
$769$	−2.52658e21	−0.572908	−0.286454	+	0.958094i	$0.592477\pi$
$770$	3.34557e20	0.0751258
$771$	−5.28849e21	−1.17604
$772$	−5.24790e21	−1.15573
$773$	2.67204e21	0.582769	0.291384	−	0.956606i	$-0.405884\pi$
$773$	2.67204e21	0.582769	0.291384	+	0.956606i	$0.405884\pi$
$774$	1.32969e22	2.87206
$775$	1.53921e21	0.329256
$776$	−1.20633e21	−0.255567
$777$	−8.53215e21	−1.79020
$778$	−4.92834e21	−1.02413
$779$	−3.62322e20	−0.0745700
$780$	6.38318e19	0.0130115
$781$	−3.70270e21	−0.747542
$782$	−1.04037e22	−2.08036
$783$	4.09692e20	0.0811418
$784$	−1.64447e21	−0.322593
$785$	−2.10303e20	−0.0408624
$786$	−9.34886e21	−1.79924
$787$	2.85100e21	0.543484	0.271742	−	0.962370i	$-0.412400\pi$
$787$	2.85100e21	0.543484	0.271742	+	0.962370i	$0.412400\pi$
$788$	−7.87070e20	−0.148616
$789$	1.16592e22	2.18067
$790$	−3.35250e20	−0.0621106
$791$	6.75976e21	1.24053
$792$	1.43860e21	0.261517
$793$	−5.74933e19	−0.0103531
$794$	8.62076e21	1.53777
$795$	6.74554e19	0.0119196
$796$	4.30301e21	0.753224
$797$	6.60053e21	1.14457	0.572284	−	0.820056i	$-0.306058\pi$
$797$	6.60053e21	1.14457	0.572284	+	0.820056i	$0.306058\pi$
$798$	1.38512e22	2.37939
$799$	−9.91277e21	−1.68692
$800$	−7.80076e21	−1.31511
$801$	1.10688e21	0.184866
$802$	−1.10190e22	−1.82321
$803$	−5.00124e21	−0.819806
$804$	1.07311e22	1.74271
$805$	3.22069e20	0.0518178
$806$	−5.39992e20	−0.0860745
$807$	1.49292e22	2.35769
$808$	−2.40882e21	−0.376894
$809$	3.23520e21	0.501519	0.250759	−	0.968049i	$-0.419320\pi$
$809$	3.23520e21	0.501519	0.250759	+	0.968049i	$0.419320\pi$
$810$	2.96073e20	0.0454738
$811$	5.71009e21	0.868933	0.434467	−	0.900688i	$-0.356937\pi$
$811$	5.71009e21	0.868933	0.434467	+	0.900688i	$0.356937\pi$
$812$	1.16717e21	0.175981
$813$	−4.90717e21	−0.733081
$814$	8.75170e21	1.29542
$815$	−4.97912e19	−0.00730248
$816$	−2.12364e22	−3.08607
$817$	1.16980e22	1.68440
$818$	1.31167e22	1.87144
$819$	1.98691e21	0.280899
$820$	2.32351e19	0.00325493
$821$	−3.94901e21	−0.548169	−0.274085	−	0.961706i	$-0.588375\pi$
$821$	−3.94901e21	−0.548169	−0.274085	+	0.961706i	$0.588375\pi$
$822$	1.09351e22	1.50413
$823$	−8.37137e21	−1.14103	−0.570516	−	0.821287i	$-0.693257\pi$
$823$	−8.37137e21	−1.14103	−0.570516	+	0.821287i	$0.693257\pi$
$824$	1.95874e21	0.264559
$825$	1.03167e22	1.38082
$826$	−8.21295e21	−1.08930
$827$	6.29375e21	0.827215	0.413607	−	0.910455i	$-0.364269\pi$
$827$	6.29375e21	0.827215	0.413607	+	0.910455i	$0.364269\pi$
$828$	−7.08095e21	−0.922282
$829$	1.14154e21	0.147344	0.0736719	−	0.997283i	$-0.476528\pi$
$829$	1.14154e21	0.147344	0.0736719	+	0.997283i	$0.476528\pi$
$830$	4.97556e20	0.0636438
$831$	1.58256e22	2.00610
$832$	9.95972e20	0.125119
$833$	−4.08981e21	−0.509173
$834$	1.38367e22	1.70721
$835$	−9.33950e18	−0.00114202
$836$	−6.47102e21	−0.784197
$837$	1.20133e21	0.144285
$838$	−1.62823e22	−1.93814
$839$	1.22315e21	0.144300	0.0721500	−	0.997394i	$-0.477014\pi$
$839$	1.22315e21	0.144300	0.0721500	+	0.997394i	$0.477014\pi$
$840$	1.73726e20	0.0203128
$841$	2.97558e20	0.0344828
$842$	−1.89284e22	−2.17407
$843$	1.79902e22	2.04800
$844$	−9.37116e21	−1.05737
$845$	−4.60297e20	−0.0514770
$846$	−1.48131e22	−1.64199
$847$	1.67259e21	0.183765
$848$	1.53862e21	0.167557
$849$	1.84986e22	1.99678
$850$	−2.26615e22	−2.42464
$851$	8.42503e21	0.893511
$852$	9.83075e21	1.03345
$853$	−9.05485e20	−0.0943547	−0.0471774	−	0.998887i	$-0.515023\pi$
$853$	−9.05485e20	−0.0943547	−0.0471774	+	0.998887i	$0.515023\pi$
$854$	8.00052e20	0.0826388
$855$	−6.89222e20	−0.0705689
$856$	−4.99080e19	−0.00506544
$857$	2.37362e20	0.0238811	0.0119406	−	0.999929i	$-0.496199\pi$
$857$	2.37362e20	0.0238811	0.0119406	+	0.999929i	$0.496199\pi$
$858$	−3.61936e21	−0.360975
$859$	8.97043e21	0.886879	0.443440	−	0.896304i	$-0.353758\pi$
$859$	8.97043e21	0.886879	0.443440	+	0.896304i	$0.353758\pi$
$860$	−7.50172e20	−0.0735228
$861$	1.28442e21	0.124791
$862$	2.22829e22	2.14618
$863$	9.96055e21	0.951048	0.475524	−	0.879703i	$-0.342259\pi$
$863$	9.96055e21	0.951048	0.475524	+	0.879703i	$0.342259\pi$
$864$	−6.08838e21	−0.576300
$865$	9.35642e19	0.00877989
$866$	1.75842e22	1.63583
$867$	−3.64112e22	−3.35809
$868$	3.42246e21	0.312925
$869$	8.65794e21	0.784813
$870$	−2.26451e20	−0.0203507
$871$	2.97335e21	0.264917
$872$	4.98368e21	0.440227
$873$	−1.69657e22	−1.48582
$874$	−1.36773e22	−1.18759
$875$	1.40508e21	0.120959
$876$	1.32784e22	1.13335
$877$	6.77124e20	0.0573022	0.0286511	−	0.999589i	$-0.490879\pi$
$877$	6.77124e20	0.0573022	0.0286511	+	0.999589i	$0.490879\pi$
$878$	−4.94535e20	−0.0414943
$879$	−1.21388e22	−1.00985
$880$	−6.74334e20	−0.0556231
$881$	6.51729e21	0.533025	0.266513	−	0.963831i	$-0.414129\pi$
$881$	6.51729e21	0.533025	0.266513	+	0.963831i	$0.414129\pi$
$882$	−6.11160e21	−0.495611
$883$	7.73199e21	0.621708	0.310854	−	0.950458i	$-0.399385\pi$
$883$	7.73199e21	0.621708	0.310854	+	0.950458i	$0.399385\pi$
$884$	3.62101e21	0.288694
$885$	7.25754e20	0.0573739
$886$	−6.43949e21	−0.504776
$887$	−1.07789e22	−0.837817	−0.418908	−	0.908029i	$-0.637587\pi$
$887$	−1.07789e22	−0.837817	−0.418908	+	0.908029i	$0.637587\pi$
$888$	4.54452e21	0.350260
$889$	−1.99599e22	−1.52544
$890$	−1.37107e20	−0.0103905
$891$	−7.64618e21	−0.574595
$892$	2.01070e22	1.49834
$893$	−1.30319e22	−0.962988
$894$	−1.38610e22	−1.01569
$895$	−5.32790e20	−0.0387154
$896$	6.87806e21	0.495628
$897$	−3.48426e21	−0.248982
$898$	2.69492e20	0.0190973
$899$	8.72520e20	0.0613166
$900$	−1.54238e22	−1.07491
$901$	3.82657e21	0.264468
$902$	−1.31747e21	−0.0903007
$903$	−4.14688e22	−2.81879
$904$	−3.60048e21	−0.242715
$905$	6.75265e20	0.0451450
$906$	4.80976e22	3.18905
$907$	2.11962e22	1.39381	0.696904	−	0.717165i	$-0.254560\pi$
$907$	2.11962e22	1.39381	0.696904	+	0.717165i	$0.254560\pi$
$908$	2.11148e22	1.37703
$909$	−3.38774e22	−2.19120
$910$	−2.46115e20	−0.0157880
$911$	−3.04139e22	−1.93501	−0.967506	−	0.252848i	$-0.918633\pi$
$911$	−3.04139e22	−1.93501	−0.967506	+	0.252848i	$0.918633\pi$
$912$	−2.79186e22	−1.76170
$913$	−1.28495e22	−0.804185
$914$	−3.53941e22	−2.19702
$915$	−7.06982e19	−0.00435261
$916$	4.37813e21	0.267345
$917$	1.64176e22	0.994353
$918$	−1.76870e22	−1.06251
$919$	1.67999e22	1.00102	0.500509	−	0.865732i	$-0.333146\pi$
$919$	1.67999e22	1.00102	0.500509	+	0.865732i	$0.333146\pi$
$920$	−1.71545e20	−0.0101384
$921$	−4.87305e22	−2.85663
$922$	−2.50211e22	−1.45487
$923$	2.72388e21	0.157100
$924$	2.29395e22	1.31233
$925$	1.83515e22	1.04138
$926$	3.16506e22	1.78155
$927$	2.75475e22	1.53810
$928$	−4.42197e21	−0.244910
$929$	−8.58632e21	−0.471725	−0.235863	−	0.971786i	$-0.575792\pi$
$929$	−8.58632e21	−0.471725	−0.235863	+	0.971786i	$0.575792\pi$
$930$	−6.64016e20	−0.0361873
$931$	−5.37669e21	−0.290665
$932$	−8.80208e21	−0.472026
$933$	3.58748e22	1.90843
$934$	3.92225e22	2.06982
$935$	−1.67708e21	−0.0877941
$936$	−1.05830e21	−0.0549591
$937$	−2.58164e22	−1.32999	−0.664997	−	0.746846i	$-0.731567\pi$
$937$	−2.58164e22	−1.32999	−0.664997	+	0.746846i	$0.731567\pi$
$938$	−4.13758e22	−2.11459
$939$	3.56551e22	1.80772
$940$	8.35713e20	0.0420338
$941$	1.16782e22	0.582714	0.291357	−	0.956614i	$-0.405893\pi$
$941$	1.16782e22	0.582714	0.291357	+	0.956614i	$0.405893\pi$
$942$	−3.16599e22	−1.56721
$943$	−1.26829e21	−0.0622847
$944$	1.65541e22	0.806519
$945$	5.47536e20	0.0264651
$946$	4.25359e22	2.03973
$947$	2.46099e22	1.17081	0.585403	−	0.810743i	$-0.300936\pi$
$947$	2.46099e22	1.17081	0.585403	+	0.810743i	$0.300936\pi$
$948$	−2.29870e22	−1.08498
$949$	3.67915e21	0.172286
$950$	−2.97921e22	−1.38412
$951$	2.19850e22	1.01338
$952$	9.85503e21	0.450693
$953$	−3.00149e22	−1.36188	−0.680942	−	0.732338i	$-0.738429\pi$
$953$	−3.00149e22	−1.36188	−0.680942	+	0.732338i	$0.738429\pi$
$954$	5.71823e21	0.257424
$955$	2.30087e20	0.0102770
$956$	1.82631e22	0.809358
$957$	5.84817e21	0.257146
$958$	3.44624e22	1.50350
$959$	−1.92033e22	−0.831259
$960$	1.22472e21	0.0526022
$961$	−2.09068e22	−0.890968
$962$	−6.43816e21	−0.272238
$963$	−7.01901e20	−0.0294495
$964$	8.09652e21	0.337070
$965$	−1.78804e21	−0.0738623
$966$	4.84855e22	1.98739
$967$	1.97475e22	0.803181	0.401590	−	0.915819i	$-0.368458\pi$
$967$	1.97475e22	0.803181	0.401590	+	0.915819i	$0.368458\pi$
$968$	−8.90878e20	−0.0359545
$969$	−6.94338e22	−2.78062
$970$	2.10151e21	0.0835110
$971$	−3.15278e22	−1.24322	−0.621611	−	0.783326i	$-0.713522\pi$
$971$	−3.15278e22	−1.24322	−0.621611	+	0.783326i	$0.713522\pi$
$972$	2.96411e22	1.15984
$973$	−2.42988e22	−0.943492
$974$	−1.19703e22	−0.461224
$975$	−7.58946e21	−0.290186
$976$	−1.61259e21	−0.0611857
$977$	3.27607e22	1.23351	0.616757	−	0.787153i	$-0.288446\pi$
$977$	3.27607e22	1.23351	0.616757	+	0.787153i	$0.288446\pi$
$978$	−7.49576e21	−0.280075
$979$	3.54083e21	0.131291
$980$	3.44798e20	0.0126873
$981$	7.00899e22	2.55940
$982$	4.12602e22	1.49518
$983$	−2.53062e22	−0.910073	−0.455036	−	0.890473i	$-0.650374\pi$
$983$	−2.53062e22	−0.910073	−0.455036	+	0.890473i	$0.650374\pi$
$984$	−6.84125e20	−0.0244159
$985$	−2.68167e20	−0.00949803
$986$	−1.28460e22	−0.451534
$987$	4.61974e22	1.61153
$988$	4.76038e21	0.164803
$989$	4.09482e22	1.40690
$990$	−2.50614e21	−0.0854556
$991$	−4.95535e22	−1.67696	−0.838479	−	0.544934i	$-0.816555\pi$
$991$	−4.95535e22	−1.67696	−0.838479	+	0.544934i	$0.816555\pi$
$992$	−1.29664e22	−0.435494
$993$	4.49835e22	1.49946
$994$	−3.79043e22	−1.25398
$995$	1.46610e21	0.0481383
$996$	3.41158e22	1.11176
$997$	−2.02067e22	−0.653554	−0.326777	−	0.945101i	$-0.605963\pi$
$997$	−2.02067e22	−0.653554	−0.326777	+	0.945101i	$0.605963\pi$
$998$	−5.01839e22	−1.61096
$999$	1.43231e22	0.456346

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.16.a.b.1.4	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.16.a.b.1.4	✓	19	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q-245.307 q^{2} -5730.81 q^{3} +27407.6 q^{4} +9338.19 q^{5} +1.40581e6 q^{6} -2.46876e6 q^{7} +1.31495e6 q^{8} +1.84933e7 q^{9} +O(q^{10})\)	\(q-245.307 q^{2} -5730.81 q^{3} +27407.6 q^{4} +9338.19 q^{5} +1.40581e6 q^{6} -2.46876e6 q^{7} +1.31495e6 q^{8} +1.84933e7 q^{9} -2.29072e6 q^{10} +5.91587e7 q^{11} -1.57068e8 q^{12} -4.35199e7 q^{13} +6.05604e8 q^{14} -5.35154e7 q^{15} -1.22066e9 q^{16} -3.03579e9 q^{17} -4.53653e9 q^{18} -3.99101e9 q^{19} +2.55937e8 q^{20} +1.41480e10 q^{21} -1.45120e10 q^{22} -1.39703e10 q^{23} -7.53570e9 q^{24} -3.04304e10 q^{25} +1.06757e10 q^{26} -2.37504e10 q^{27} -6.76627e10 q^{28} -1.72499e10 q^{29} +1.31277e10 q^{30} -5.05812e10 q^{31} +2.56348e11 q^{32} -3.39027e11 q^{33} +7.44701e11 q^{34} -2.30537e10 q^{35} +5.06856e11 q^{36} -6.03065e11 q^{37} +9.79024e11 q^{38} +2.49404e11 q^{39} +1.22792e10 q^{40} +9.07845e10 q^{41} -3.47060e12 q^{42} -2.93108e12 q^{43} +1.62140e12 q^{44} +1.72693e11 q^{45} +3.42703e12 q^{46} +3.26530e12 q^{47} +6.99535e12 q^{48} +1.34720e12 q^{49} +7.46479e12 q^{50} +1.73975e13 q^{51} -1.19278e12 q^{52} -1.26049e12 q^{53} +5.82615e12 q^{54} +5.52435e11 q^{55} -3.24628e12 q^{56} +2.28717e13 q^{57} +4.23152e12 q^{58} -1.35616e13 q^{59} -1.46673e12 q^{60} +1.32108e12 q^{61} +1.24079e13 q^{62} -4.56553e13 q^{63} -2.28855e13 q^{64} -4.06397e11 q^{65} +8.31657e13 q^{66} -6.83216e13 q^{67} -8.32037e13 q^{68} +8.00614e13 q^{69} +5.65524e12 q^{70} -6.25893e13 q^{71} +2.43176e13 q^{72} -8.45395e13 q^{73} +1.47936e14 q^{74} +1.74391e14 q^{75} -1.09384e14 q^{76} -1.46048e14 q^{77} -6.11806e13 q^{78} +1.46351e14 q^{79} -1.13987e13 q^{80} -1.29249e14 q^{81} -2.22701e13 q^{82} -2.17204e14 q^{83} +3.87762e14 q^{84} -2.83488e13 q^{85} +7.19014e14 q^{86} +9.88557e13 q^{87} +7.77904e13 q^{88} +5.98532e13 q^{89} -4.23629e13 q^{90} +1.07440e14 q^{91} -3.82894e14 q^{92} +2.89871e14 q^{93} -8.01002e14 q^{94} -3.72689e13 q^{95} -1.46908e15 q^{96} -9.17400e14 q^{97} -3.30477e14 q^{98} +1.09404e15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 9908 q^{3} + 387418 q^{4} + 230490 q^{5} + 1566838 q^{6} + 2882024 q^{7} + 26209092 q^{8} + 93022899 q^{9}+O(q^{10}) \) 19 * q + 9908 * q^3 + 387418 * q^4 + 230490 * q^5 + 1566838 * q^6 + 2882024 * q^7 + 26209092 * q^8 + 93022899 * q^9	\( 19 q + 9908 q^{3} + 387418 q^{4} + 230490 q^{5} + 1566838 q^{6} + 2882024 q^{7} + 26209092 q^{8} + 93022899 q^{9} - 46518144 q^{10} + 56910992 q^{11} + 907194664 q^{12} + 377780326 q^{13} + 1552762656 q^{14} + 2058712006 q^{15} + 9746645474 q^{16} - 797562458 q^{17} - 2812146948 q^{18} + 5568901154 q^{19} - 6814671874 q^{20} - 19358601528 q^{21} - 43431230566 q^{22} - 22787265900 q^{23} - 32333767894 q^{24} + 113218218877 q^{25} - 60020783208 q^{26} + 115546592594 q^{27} + 171573547692 q^{28} - 327747649871 q^{29} - 152869385454 q^{30} + 190165645448 q^{31} + 1523182591996 q^{32} + 1432316120556 q^{33} + 781895976484 q^{34} + 1076956461508 q^{35} + 4124169333892 q^{36} + 1157558623486 q^{37} + 454200349888 q^{38} - 3276695149790 q^{39} + 1497234313960 q^{40} - 327181726714 q^{41} + 14801498493780 q^{42} + 3969726268184 q^{43} + 9884551144664 q^{44} + 13723027476954 q^{45} + 4360233976812 q^{46} + 17801533447516 q^{47} + 44888708498560 q^{48} + 26274460777219 q^{49} + 49590112735028 q^{50} + 48299925405108 q^{51} + 38417786090034 q^{52} + 42945469924134 q^{53} + 78537259690434 q^{54} + 43646306609786 q^{55} + 153497246476960 q^{56} + 87149617056284 q^{57} + 76276585694640 q^{59} + 137931874827396 q^{60} + 75095043245982 q^{61} + 45115853357766 q^{62} + 77728938376620 q^{63} + 263521279152786 q^{64} + 25707147233724 q^{65} - 97128209185404 q^{66} + 39919578800676 q^{67} + 172949157314596 q^{68} + 61328545437264 q^{69} + 524547167494056 q^{70} + 128037096114140 q^{71} + 307467488440744 q^{72} + 333487363889334 q^{73} + 220493893416424 q^{74} - 68218174510546 q^{75} + 354934779140576 q^{76} - 692163369062472 q^{77} - 818320982346402 q^{78} + 213267241183292 q^{79} - 452775952882810 q^{80} + 48823702443271 q^{81} - 17\!\cdots\!96 q^{82}+ \cdots - 233858833882834 q^{99}+O(q^{100}) \) 19 * q + 9908 * q^3 + 387418 * q^4 + 230490 * q^5 + 1566838 * q^6 + 2882024 * q^7 + 26209092 * q^8 + 93022899 * q^9 - 46518144 * q^10 + 56910992 * q^11 + 907194664 * q^12 + 377780326 * q^13 + 1552762656 * q^14 + 2058712006 * q^15 + 9746645474 * q^16 - 797562458 * q^17 - 2812146948 * q^18 + 5568901154 * q^19 - 6814671874 * q^20 - 19358601528 * q^21 - 43431230566 * q^22 - 22787265900 * q^23 - 32333767894 * q^24 + 113218218877 * q^25 - 60020783208 * q^26 + 115546592594 * q^27 + 171573547692 * q^28 - 327747649871 * q^29 - 152869385454 * q^30 + 190165645448 * q^31 + 1523182591996 * q^32 + 1432316120556 * q^33 + 781895976484 * q^34 + 1076956461508 * q^35 + 4124169333892 * q^36 + 1157558623486 * q^37 + 454200349888 * q^38 - 3276695149790 * q^39 + 1497234313960 * q^40 - 327181726714 * q^41 + 14801498493780 * q^42 + 3969726268184 * q^43 + 9884551144664 * q^44 + 13723027476954 * q^45 + 4360233976812 * q^46 + 17801533447516 * q^47 + 44888708498560 * q^48 + 26274460777219 * q^49 + 49590112735028 * q^50 + 48299925405108 * q^51 + 38417786090034 * q^52 + 42945469924134 * q^53 + 78537259690434 * q^54 + 43646306609786 * q^55 + 153497246476960 * q^56 + 87149617056284 * q^57 + 76276585694640 * q^59 + 137931874827396 * q^60 + 75095043245982 * q^61 + 45115853357766 * q^62 + 77728938376620 * q^63 + 263521279152786 * q^64 + 25707147233724 * q^65 - 97128209185404 * q^66 + 39919578800676 * q^67 + 172949157314596 * q^68 + 61328545437264 * q^69 + 524547167494056 * q^70 + 128037096114140 * q^71 + 307467488440744 * q^72 + 333487363889334 * q^73 + 220493893416424 * q^74 - 68218174510546 * q^75 + 354934779140576 * q^76 - 692163369062472 * q^77 - 818320982346402 * q^78 + 213267241183292 * q^79 - 452775952882810 * q^80 + 48823702443271 * q^81 - 1736995581874796 * q^82 - 66633324408168 * q^83 - 2217716778602152 * q^84 - 1419457827450068 * q^85 - 1364891612086326 * q^86 - 170911774469572 * q^87 - 4325342725143834 * q^88 - 2341312102493090 * q^89 - 6182213358743320 * q^90 + 852022408820524 * q^91 - 3781297333622004 * q^92 - 3548745569232820 * q^93 - 914001881049618 * q^94 - 4053850425835916 * q^95 - 775984072309158 * q^96 - 686179834828282 * q^97 - 5170682580897840 * q^98 - 233858833882834 * q^99

Introduction

L-functions

Modular forms

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Fields

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Groups

Database

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