LMFDB - Embedded newform 29.16.a.b.1.3

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			1.3
Root			$-288.415$ 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)

$f(q)$	$=$	$q-288.415 q^{2} +2292.83 q^{3} +50415.0 q^{4} -130035. q^{5} -661285. q^{6} -2.37154e6 q^{7} -5.08966e6 q^{8} -9.09186e6 q^{9} +O(q^{10})$	\(q-288.415 q^{2} +2292.83 q^{3} +50415.0 q^{4} -130035. q^{5} -661285. q^{6} -2.37154e6 q^{7} -5.08966e6 q^{8} -9.09186e6 q^{9} +3.75041e7 q^{10} -6.52735e7 q^{11} +1.15593e8 q^{12} +1.63150e8 q^{13} +6.83987e8 q^{14} -2.98148e8 q^{15} -1.84066e8 q^{16} +2.09698e9 q^{17} +2.62222e9 q^{18} -5.84902e9 q^{19} -6.55573e9 q^{20} -5.43753e9 q^{21} +1.88258e10 q^{22} -2.93558e10 q^{23} -1.16697e10 q^{24} -1.36084e10 q^{25} -4.70550e10 q^{26} -5.37456e10 q^{27} -1.19561e11 q^{28} -1.72499e10 q^{29} +8.59904e10 q^{30} +1.68511e11 q^{31} +2.19865e11 q^{32} -1.49661e11 q^{33} -6.04799e11 q^{34} +3.08384e11 q^{35} -4.58366e11 q^{36} -2.70459e11 q^{37} +1.68694e12 q^{38} +3.74076e11 q^{39} +6.61836e11 q^{40} -2.20706e12 q^{41} +1.56826e12 q^{42} +3.01158e12 q^{43} -3.29077e12 q^{44} +1.18226e12 q^{45} +8.46665e12 q^{46} +1.96954e12 q^{47} -4.22032e11 q^{48} +8.76635e11 q^{49} +3.92486e12 q^{50} +4.80801e12 q^{51} +8.22523e12 q^{52} -3.23021e12 q^{53} +1.55010e13 q^{54} +8.48786e12 q^{55} +1.20703e13 q^{56} -1.34108e13 q^{57} +4.97512e12 q^{58} -2.03859e13 q^{59} -1.50312e13 q^{60} +1.45122e13 q^{61} -4.86010e13 q^{62} +2.15617e13 q^{63} -5.73809e13 q^{64} -2.12153e13 q^{65} +4.31644e13 q^{66} +1.66961e13 q^{67} +1.05719e14 q^{68} -6.73078e13 q^{69} -8.89424e13 q^{70} +6.64010e13 q^{71} +4.62745e13 q^{72} +1.21338e14 q^{73} +7.80044e13 q^{74} -3.12017e13 q^{75} -2.94879e14 q^{76} +1.54799e14 q^{77} -1.07889e14 q^{78} +1.50874e14 q^{79} +2.39351e13 q^{80} +7.22890e12 q^{81} +6.36550e14 q^{82} +2.23112e14 q^{83} -2.74133e14 q^{84} -2.72681e14 q^{85} -8.68584e14 q^{86} -3.95510e13 q^{87} +3.32220e14 q^{88} +1.48284e14 q^{89} -3.40982e14 q^{90} -3.86918e14 q^{91} -1.47997e15 q^{92} +3.86366e14 q^{93} -5.68045e14 q^{94} +7.60579e14 q^{95} +5.04113e14 q^{96} +4.67038e14 q^{97} -2.52835e14 q^{98} +5.93457e14 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−288.415	−1.59328	−0.796641	−	0.604453i	$-0.793392\pi$
$2$	−288.415	−1.59328	−0.796641	+	0.604453i	$0.793392\pi$
$3$	2292.83	0.605287	0.302644	−	0.953104i	$-0.402131\pi$
$3$	2292.83	0.605287	0.302644	+	0.953104i	$0.402131\pi$
$4$	50415.0	1.53854
$5$	−130035.	−0.744366	−0.372183	−	0.928159i	$-0.621391\pi$
$5$	−130035.	−0.744366	−0.372183	+	0.928159i	$0.621391\pi$
$6$	−661285.	−0.964393
$7$	−2.37154e6	−1.08842	−0.544208	−	0.838950i	$-0.683170\pi$
$7$	−2.37154e6	−1.08842	−0.544208	+	0.838950i	$0.683170\pi$
$8$	−5.08966e6	−0.858053
$9$	−9.09186e6	−0.633627
$10$	3.75041e7	1.18598
$11$	−6.52735e7	−1.00993	−0.504966	−	0.863139i	$-0.668495\pi$
$11$	−6.52735e7	−1.00993	−0.504966	+	0.863139i	$0.668495\pi$
$12$	1.15593e8	0.931262
$13$	1.63150e8	0.721129	0.360565	−	0.932734i	$-0.382584\pi$
$13$	1.63150e8	0.721129	0.360565	+	0.932734i	$0.382584\pi$
$14$	6.83987e8	1.73415
$15$	−2.98148e8	−0.450555
$16$	−1.84066e8	−0.171425
$17$	2.09698e9	1.23944	0.619722	−	0.784821i	$-0.287245\pi$
$17$	2.09698e9	1.23944	0.619722	+	0.784821i	$0.287245\pi$
$18$	2.62222e9	1.00955
$19$	−5.84902e9	−1.50117	−0.750587	−	0.660771i	$-0.770229\pi$
$19$	−5.84902e9	−1.50117	−0.750587	+	0.660771i	$0.770229\pi$
$20$	−6.55573e9	−1.14524
$21$	−5.43753e9	−0.658805
$22$	1.88258e10	1.60910
$23$	−2.93558e10	−1.79778	−0.898888	−	0.438179i	$-0.855624\pi$
$23$	−2.93558e10	−1.79778	−0.898888	+	0.438179i	$0.855624\pi$
$24$	−1.16697e10	−0.519369
$25$	−1.36084e10	−0.445920
$26$	−4.70550e10	−1.14896
$27$	−5.37456e10	−0.988814
$28$	−1.19561e11	−1.67458
$29$	−1.72499e10	−0.185695
$29$	−1.72499e10	−0.185695
$30$	8.59904e10	0.717861
$31$	1.68511e11	1.10006	0.550028	−	0.835146i	$-0.314617\pi$
$31$	1.68511e11	1.10006	0.550028	+	0.835146i	$0.314617\pi$
$32$	2.19865e11	1.13118
$33$	−1.49661e11	−0.611299
$34$	−6.04799e11	−1.97478
$35$	3.08384e11	0.810179
$36$	−4.58366e11	−0.974863
$37$	−2.70459e11	−0.468370	−0.234185	−	0.972192i	$-0.575242\pi$
$37$	−2.70459e11	−0.468370	−0.234185	+	0.972192i	$0.575242\pi$
$38$	1.68694e12	2.39179
$39$	3.74076e11	0.436490
$40$	6.61836e11	0.638705
$41$	−2.20706e12	−1.76985	−0.884924	−	0.465736i	$-0.845790\pi$
$41$	−2.20706e12	−1.76985	−0.884924	+	0.465736i	$0.845790\pi$
$42$	1.56826e12	1.04966
$43$	3.01158e12	1.68959	0.844794	−	0.535091i	$-0.179723\pi$
$43$	3.01158e12	1.68959	0.844794	+	0.535091i	$0.179723\pi$
$44$	−3.29077e12	−1.55382
$45$	1.18226e12	0.471650
$46$	8.46665e12	2.86436
$47$	1.96954e12	0.567063	0.283532	−	0.958963i	$-0.408494\pi$
$47$	1.96954e12	0.567063	0.283532	+	0.958963i	$0.408494\pi$
$48$	−4.22032e11	−0.103762
$49$	8.76635e11	0.184650
$50$	3.92486e12	0.710476
$51$	4.80801e12	0.750220
$52$	8.22523e12	1.10949
$53$	−3.23021e12	−0.377713	−0.188856	−	0.982005i	$-0.560478\pi$
$53$	−3.23021e12	−0.377713	−0.188856	+	0.982005i	$0.560478\pi$
$54$	1.55010e13	1.57546
$55$	8.48786e12	0.751758
$56$	1.20703e13	0.933919
$57$	−1.34108e13	−0.908642
$58$	4.97512e12	0.295865
$59$	−2.03859e13	−1.06645	−0.533223	−	0.845975i	$-0.679019\pi$
$59$	−2.03859e13	−1.06645	−0.533223	+	0.845975i	$0.679019\pi$
$60$	−1.50312e13	−0.693199
$61$	1.45122e13	0.591233	0.295616	−	0.955307i	$-0.404475\pi$
$61$	1.45122e13	0.591233	0.295616	+	0.955307i	$0.404475\pi$
$62$	−4.86010e13	−1.75270
$63$	2.15617e13	0.689650
$64$	−5.73809e13	−1.63086
$65$	−2.12153e13	−0.536784
$66$	4.31644e13	0.973971
$67$	1.66961e13	0.336553	0.168276	−	0.985740i	$-0.446180\pi$
$67$	1.66961e13	0.336553	0.168276	+	0.985740i	$0.446180\pi$
$68$	1.05719e14	1.90694
$69$	−6.73078e13	−1.08817
$70$	−8.89424e13	−1.29084
$71$	6.64010e13	0.866438	0.433219	−	0.901289i	$-0.357378\pi$
$71$	6.64010e13	0.866438	0.433219	+	0.901289i	$0.357378\pi$
$72$	4.62745e13	0.543685
$73$	1.21338e14	1.28551	0.642757	−	0.766070i	$-0.277791\pi$
$73$	1.21338e14	1.28551	0.642757	+	0.766070i	$0.277791\pi$
$74$	7.80044e13	0.746245
$75$	−3.12017e13	−0.269910
$76$	−2.94879e14	−2.30962
$77$	1.54799e14	1.09923
$78$	−1.07889e14	−0.695452
$79$	1.50874e14	0.883914	0.441957	−	0.897036i	$-0.354284\pi$
$79$	1.50874e14	0.883914	0.441957	+	0.897036i	$0.354284\pi$
$80$	2.39351e13	0.127603
$81$	7.22890e12	0.0351103
$82$	6.36550e14	2.81986
$83$	2.23112e14	0.902481	0.451241	−	0.892402i	$-0.350982\pi$
$83$	2.23112e14	0.902481	0.451241	+	0.892402i	$0.350982\pi$
$84$	−2.74133e14	−1.01360
$85$	−2.72681e14	−0.922600
$86$	−8.68584e14	−2.69199
$87$	−3.95510e13	−0.112399
$88$	3.32220e14	0.866574
$89$	1.48284e14	0.355361	0.177680	−	0.984088i	$-0.443141\pi$
$89$	1.48284e14	0.355361	0.177680	+	0.984088i	$0.443141\pi$
$90$	−3.40982e14	−0.751471
$91$	−3.86918e14	−0.784889
$92$	−1.47997e15	−2.76596
$93$	3.86366e14	0.665851
$94$	−5.68045e14	−0.903491
$95$	7.60579e14	1.11742
$96$	5.04113e14	0.684690
$97$	4.67038e14	0.586900	0.293450	−	0.955974i	$-0.405197\pi$
$97$	4.67038e14	0.586900	0.293450	+	0.955974i	$0.405197\pi$
$98$	−2.52835e14	−0.294199
$99$	5.93457e14	0.639920
$100$	−6.86068e14	−0.686068
$101$	4.09738e14	0.380274	0.190137	−	0.981758i	$-0.439107\pi$
$101$	4.09738e14	0.380274	0.190137	+	0.981758i	$0.439107\pi$
$102$	−1.38670e15	−1.19531
$103$	2.96968e14	0.237920	0.118960	−	0.992899i	$-0.462044\pi$
$103$	2.96968e14	0.237920	0.118960	+	0.992899i	$0.462044\pi$
$104$	−8.30380e14	−0.618767
$105$	7.07070e14	0.490391
$106$	9.31639e14	0.601802
$107$	−1.14390e15	−0.688669	−0.344335	−	0.938847i	$-0.611895\pi$
$107$	−1.14390e15	−0.688669	−0.344335	+	0.938847i	$0.611895\pi$
$108$	−2.70959e15	−1.52133
$109$	−6.12997e14	−0.321188	−0.160594	−	0.987021i	$-0.551341\pi$
$109$	−6.12997e14	−0.321188	−0.160594	+	0.987021i	$0.551341\pi$
$110$	−2.44802e15	−1.19776
$111$	−6.20116e14	−0.283498
$112$	4.36521e14	0.186582
$113$	−2.11600e15	−0.846111	−0.423055	−	0.906104i	$-0.639042\pi$
$113$	−2.11600e15	−0.846111	−0.423055	+	0.906104i	$0.639042\pi$
$114$	3.86787e15	1.44772
$115$	3.81729e15	1.33820
$116$	−8.69653e14	−0.285701
$117$	−1.48334e15	−0.456927
$118$	5.87958e15	1.69915
$119$	−4.97307e15	−1.34903
$120$	1.51747e15	0.386600
$121$	8.33836e13	0.0199614
$122$	−4.18552e15	−0.942000
$123$	−5.06041e15	−1.07127
$124$	8.49548e15	1.69249
$125$	5.73793e15	1.07629
$126$	−6.21871e15	−1.09881
$127$	1.00346e16	1.67098	0.835491	−	0.549504i	$-0.185183\pi$
$127$	1.00346e16	1.67098	0.835491	+	0.549504i	$0.185183\pi$
$128$	9.34496e15	1.46724
$129$	6.90503e15	1.02269
$130$	6.11881e15	0.855247
$131$	1.46025e16	1.92705	0.963523	−	0.267626i	$-0.0862392\pi$
$131$	1.46025e16	1.92705	0.963523	+	0.267626i	$0.0862392\pi$
$132$	−7.54515e15	−0.940510
$133$	1.38712e16	1.63390
$134$	−4.81539e15	−0.536223
$135$	6.98882e15	0.736039
$136$	−1.06729e16	−1.06351
$137$	−1.50730e16	−1.42165	−0.710827	−	0.703367i	$-0.751679\pi$
$137$	−1.50730e16	−1.42165	−0.710827	+	0.703367i	$0.751679\pi$
$138$	1.94126e16	1.73376
$139$	4.11937e15	0.348514	0.174257	−	0.984700i	$-0.444248\pi$
$139$	4.11937e15	0.348514	0.174257	+	0.984700i	$0.444248\pi$
$140$	1.55472e16	1.24650
$141$	4.51582e15	0.343236
$142$	−1.91510e16	−1.38048
$143$	−1.06494e16	−0.728291
$144$	1.67351e15	0.108620
$145$	2.24309e15	0.138225
$146$	−3.49958e16	−2.04819
$147$	2.00997e15	0.111766
$148$	−1.36352e16	−0.720608
$149$	−1.96409e16	−0.986882	−0.493441	−	0.869779i	$-0.664261\pi$
$149$	−1.96409e16	−0.986882	−0.493441	+	0.869779i	$0.664261\pi$
$150$	8.99902e15	0.430042
$151$	−4.91094e15	−0.223274	−0.111637	−	0.993749i	$-0.535609\pi$
$151$	−4.91094e15	−0.223274	−0.111637	+	0.993749i	$0.535609\pi$
$152$	2.97695e16	1.28809
$153$	−1.90654e16	−0.785346
$154$	−4.46462e16	−1.75138
$155$	−2.19124e16	−0.818844
$156$	1.88590e16	0.671560
$157$	3.42812e16	1.16361	0.581806	−	0.813328i	$-0.302346\pi$
$157$	3.42812e16	1.16361	0.581806	+	0.813328i	$0.302346\pi$
$158$	−4.35142e16	−1.40832
$159$	−7.40630e15	−0.228625
$160$	−2.85903e16	−0.842012
$161$	6.96185e16	1.95673
$162$	−2.08492e15	−0.0559406
$163$	−1.03791e16	−0.265921	−0.132960	−	0.991121i	$-0.542448\pi$
$163$	−1.03791e16	−0.265921	−0.132960	+	0.991121i	$0.542448\pi$
$164$	−1.11269e17	−2.72299
$165$	1.94612e16	0.455030
$166$	−6.43489e16	−1.43791
$167$	−6.77452e16	−1.44712	−0.723560	−	0.690261i	$-0.757496\pi$
$167$	−6.77452e16	−1.44712	−0.723560	+	0.690261i	$0.757496\pi$
$168$	2.76752e16	0.565289
$169$	−2.45678e16	−0.479973
$170$	7.86453e16	1.46996
$171$	5.31784e16	0.951185
$172$	1.51829e17	2.59951
$173$	−1.16358e17	−1.90744	−0.953722	−	0.300688i	$-0.902784\pi$
$173$	−1.16358e17	−1.90744	−0.953722	+	0.300688i	$0.902784\pi$
$174$	1.14071e16	0.179083
$175$	3.22728e16	0.485346
$176$	1.20147e16	0.173128
$177$	−4.67413e16	−0.645507
$178$	−4.27673e16	−0.566189
$179$	1.35642e17	1.72186	0.860929	−	0.508725i	$-0.169883\pi$
$179$	1.35642e17	1.72186	0.860929	+	0.508725i	$0.169883\pi$
$180$	5.96038e16	0.725655
$181$	−3.36643e16	−0.393170	−0.196585	−	0.980487i	$-0.562985\pi$
$181$	−3.36643e16	−0.393170	−0.196585	+	0.980487i	$0.562985\pi$
$182$	1.11593e17	1.25055
$183$	3.32739e16	0.357866
$184$	1.49411e17	1.54259
$185$	3.51693e16	0.348638
$186$	−1.11434e17	−1.06089
$187$	−1.36877e17	−1.25175
$188$	9.92946e16	0.872452
$189$	1.27460e17	1.07624
$190$	−2.19362e17	−1.78037
$191$	−1.52345e17	−1.18871	−0.594357	−	0.804201i	$-0.702594\pi$
$191$	−1.52345e17	−1.18871	−0.594357	+	0.804201i	$0.702594\pi$
$192$	−1.31565e17	−0.987142
$193$	1.08661e17	0.784143	0.392071	−	0.919935i	$-0.371759\pi$
$193$	1.08661e17	0.784143	0.392071	+	0.919935i	$0.371759\pi$
$194$	−1.34701e17	−0.935097
$195$	−4.86430e16	−0.324908
$196$	4.41956e16	0.284092
$197$	−1.37064e17	−0.848058	−0.424029	−	0.905649i	$-0.639385\pi$
$197$	−1.37064e17	−0.848058	−0.424029	+	0.905649i	$0.639385\pi$
$198$	−1.71162e17	−1.01957
$199$	−6.60987e15	−0.0379136	−0.0189568	−	0.999820i	$-0.506034\pi$
$199$	−6.60987e15	−0.0379136	−0.0189568	+	0.999820i	$0.506034\pi$
$200$	6.92621e16	0.382623
$201$	3.82812e16	0.203711
$202$	−1.18175e17	−0.605883
$203$	4.09088e16	0.202114
$204$	2.42396e17	1.15425
$205$	2.86996e17	1.31741
$206$	−8.56500e16	−0.379073
$207$	2.66899e17	1.13912
$208$	−3.00305e16	−0.123620
$209$	3.81786e17	1.51608
$210$	−2.03929e17	−0.781331
$211$	−9.46629e16	−0.349995	−0.174997	−	0.984569i	$-0.555992\pi$
$211$	−9.46629e16	−0.349995	−0.174997	+	0.984569i	$0.555992\pi$
$212$	−1.62851e17	−0.581128
$213$	1.52246e17	0.524444
$214$	3.29918e17	1.09724
$215$	−3.91612e17	−1.25767
$216$	2.73547e17	0.848455
$217$	−3.99630e17	−1.19732
$218$	1.76797e17	0.511743
$219$	2.78208e17	0.778106
$220$	4.27916e17	1.15661
$221$	3.42123e17	0.893800
$222$	1.78851e17	0.451693
$223$	−3.96315e17	−0.967730	−0.483865	−	0.875143i	$-0.660767\pi$
$223$	−3.96315e17	−0.967730	−0.483865	+	0.875143i	$0.660767\pi$
$224$	−5.21420e17	−1.23120
$225$	1.23726e17	0.282547
$226$	6.10285e17	1.34809
$227$	−6.73972e17	−1.44028	−0.720141	−	0.693827i	$-0.755923\pi$
$227$	−6.73972e17	−1.44028	−0.720141	+	0.693827i	$0.755923\pi$
$228$	−6.76105e17	−1.39799
$229$	1.97565e17	0.395315	0.197658	−	0.980271i	$-0.436667\pi$
$229$	1.97565e17	0.395315	0.197658	+	0.980271i	$0.436667\pi$
$230$	−1.10096e18	−2.13213
$231$	3.54926e17	0.665347
$232$	8.77960e16	0.159336
$233$	6.31312e17	1.10936	0.554682	−	0.832062i	$-0.312840\pi$
$233$	6.31312e17	1.10936	0.554682	+	0.832062i	$0.312840\pi$
$234$	4.27817e17	0.728013
$235$	−2.56110e17	−0.422102
$236$	−1.02775e18	−1.64078
$237$	3.45927e17	0.535022
$238$	1.43431e18	2.14939
$239$	5.66717e17	0.822966	0.411483	−	0.911417i	$-0.365011\pi$
$239$	5.66717e17	0.822966	0.411483	+	0.911417i	$0.365011\pi$
$240$	5.48791e16	0.0772365
$241$	−5.96748e16	−0.0814073	−0.0407037	−	0.999171i	$-0.512960\pi$
$241$	−5.96748e16	−0.0814073	−0.0407037	+	0.999171i	$0.512960\pi$
$242$	−2.40491e16	−0.0318041
$243$	7.87765e17	1.01007
$244$	7.31631e17	0.909638
$245$	−1.13994e17	−0.137447
$246$	1.45950e18	1.70683
$247$	−9.54270e17	−1.08254
$248$	−8.57663e17	−0.943907
$249$	5.11558e17	0.546261
$250$	−1.65490e18	−1.71484
$251$	−4.54772e17	−0.457342	−0.228671	−	0.973504i	$-0.573438\pi$
$251$	−4.54772e17	−0.457342	−0.228671	+	0.973504i	$0.573438\pi$
$252$	1.08703e18	1.06106
$253$	1.91616e18	1.81563
$254$	−2.89412e18	−2.66234
$255$	−6.25211e17	−0.558438
$256$	−8.14963e17	−0.706868
$257$	−9.78517e17	−0.824270	−0.412135	−	0.911123i	$-0.635217\pi$
$257$	−9.78517e17	−0.824270	−0.412135	+	0.911123i	$0.635217\pi$
$258$	−1.99151e18	−1.62943
$259$	6.41405e17	0.509781
$260$	−1.06957e18	−0.825866
$261$	1.56833e17	0.117662
$262$	−4.21157e18	−3.07033
$263$	2.50058e18	1.77163	0.885815	−	0.464038i	$-0.153600\pi$
$263$	2.50058e18	1.77163	0.885815	+	0.464038i	$0.153600\pi$
$264$	7.61723e17	0.524527
$265$	4.20041e17	0.281156
$266$	−4.00065e18	−2.60327
$267$	3.39989e17	0.215095
$268$	8.41733e17	0.517801
$269$	1.10948e18	0.663706	0.331853	−	0.943331i	$-0.392326\pi$
$269$	1.10948e18	0.663706	0.331853	+	0.943331i	$0.392326\pi$
$270$	−2.01568e18	−1.17272
$271$	−2.82773e16	−0.0160018	−0.00800088	−	0.999968i	$-0.502547\pi$
$271$	−2.82773e16	−0.0160018	−0.00800088	+	0.999968i	$0.502547\pi$
$272$	−3.85983e17	−0.212472
$273$	−8.87135e17	−0.475083
$274$	4.34726e18	2.26510
$275$	8.88268e17	0.450349
$276$	−3.39332e18	−1.67420
$277$	2.01748e17	0.0968747	0.0484373	−	0.998826i	$-0.484576\pi$
$277$	2.01748e17	0.0968747	0.0484373	+	0.998826i	$0.484576\pi$
$278$	−1.18809e18	−0.555280
$279$	−1.53208e18	−0.697026
$280$	−1.56957e18	−0.695177
$281$	−3.62128e18	−1.56158	−0.780792	−	0.624791i	$-0.785184\pi$
$281$	−3.62128e18	−1.56158	−0.780792	+	0.624791i	$0.785184\pi$
$282$	−1.30243e18	−0.546872
$283$	3.04662e18	1.24572	0.622860	−	0.782333i	$-0.285970\pi$
$283$	3.04662e18	1.24572	0.622860	+	0.782333i	$0.285970\pi$
$284$	3.34761e18	1.33305
$285$	1.74388e18	0.676362
$286$	3.07144e18	1.16037
$287$	5.23414e18	1.92633
$288$	−1.99899e18	−0.716747
$289$	1.53490e18	0.536223
$290$	−6.46941e17	−0.220232
$291$	1.07084e18	0.355243
$292$	6.11728e18	1.97782
$293$	−1.07346e18	−0.338281	−0.169140	−	0.985592i	$-0.554099\pi$
$293$	−1.07346e18	−0.338281	−0.169140	+	0.985592i	$0.554099\pi$
$294$	−5.79706e17	−0.178075
$295$	2.65088e18	0.793826
$296$	1.37655e18	0.401886
$297$	3.50816e18	0.998634
$298$	5.66474e18	1.57238
$299$	−4.78941e18	−1.29643
$300$	−1.57303e18	−0.415268
$301$	−7.14208e18	−1.83898
$302$	1.41639e18	0.355738
$303$	9.39459e17	0.230175
$304$	1.07661e18	0.257339
$305$	−1.88709e18	−0.440093
$306$	5.49875e18	1.25128
$307$	−9.20477e15	−0.00204397	−0.00102199	−	0.999999i	$-0.500325\pi$
$307$	−9.20477e15	−0.00204397	−0.00102199	+	0.999999i	$0.500325\pi$
$308$	7.80418e18	1.69121
$309$	6.80897e17	0.144010
$310$	6.31985e18	1.30465
$311$	2.30476e18	0.464432	0.232216	−	0.972664i	$-0.425402\pi$
$311$	2.30476e18	0.464432	0.232216	+	0.972664i	$0.425402\pi$
$312$	−1.90392e18	−0.374532
$313$	1.98962e18	0.382110	0.191055	−	0.981579i	$-0.438809\pi$
$313$	1.98962e18	0.382110	0.191055	+	0.981579i	$0.438809\pi$
$314$	−9.88719e18	−1.85396
$315$	−2.80378e18	−0.513352
$316$	7.60630e18	1.35994
$317$	−1.77657e18	−0.310198	−0.155099	−	0.987899i	$-0.549570\pi$
$317$	−1.77657e18	−0.310198	−0.155099	+	0.987899i	$0.549570\pi$
$318$	2.13609e18	0.364263
$319$	1.12596e18	0.187540
$320$	7.46155e18	1.21396
$321$	−2.62277e18	−0.416843
$322$	−2.00790e19	−3.11762
$323$	−1.22653e19	−1.86062
$324$	3.64445e17	0.0540187
$325$	−2.22022e18	−0.321566
$326$	2.99348e18	0.423687
$327$	−1.40550e18	−0.194411
$328$	1.12332e19	1.51862
$329$	−4.67085e18	−0.617201
$330$	−5.61289e18	−0.724990
$331$	−1.22738e19	−1.54977	−0.774885	−	0.632102i	$-0.782193\pi$
$331$	−1.22738e19	−1.54977	−0.774885	+	0.632102i	$0.782193\pi$
$332$	1.12482e19	1.38851
$333$	2.45898e18	0.296772
$334$	1.95387e19	2.30567
$335$	−2.17108e18	−0.250518
$336$	1.00087e18	0.112936
$337$	−5.33474e18	−0.588693	−0.294347	−	0.955699i	$-0.595102\pi$
$337$	−5.33474e18	−0.588693	−0.294347	+	0.955699i	$0.595102\pi$
$338$	7.08572e18	0.764731
$339$	−4.85162e18	−0.512140
$340$	−1.37472e19	−1.41946
$341$	−1.09993e19	−1.11098
$342$	−1.53374e19	−1.51550
$343$	9.18005e18	0.887440
$344$	−1.53279e19	−1.44976
$345$	8.75239e18	0.809997
$346$	3.35595e19	3.03910
$347$	−4.90234e18	−0.434443	−0.217221	−	0.976122i	$-0.569699\pi$
$347$	−4.90234e18	−0.434443	−0.217221	+	0.976122i	$0.569699\pi$
$348$	−1.99396e18	−0.172931
$349$	1.46406e19	1.24270	0.621351	−	0.783532i	$-0.286584\pi$
$349$	1.46406e19	1.24270	0.621351	+	0.783532i	$0.286584\pi$
$350$	−9.30796e18	−0.773293
$351$	−8.76862e18	−0.713063
$352$	−1.43514e19	−1.14242
$353$	−1.47068e19	−1.14606	−0.573031	−	0.819534i	$-0.694232\pi$
$353$	−1.47068e19	−1.14606	−0.573031	+	0.819534i	$0.694232\pi$
$354$	1.34809e19	1.02847
$355$	−8.63448e18	−0.644946
$356$	7.47574e18	0.546738
$357$	−1.14024e19	−0.816552
$358$	−3.91212e19	−2.74340
$359$	9.22544e18	0.633547	0.316773	−	0.948501i	$-0.397401\pi$
$359$	9.22544e18	0.633547	0.316773	+	0.948501i	$0.397401\pi$
$360$	−6.01732e18	−0.404701
$361$	1.90299e19	1.25352
$362$	9.70928e18	0.626430
$363$	1.91184e17	0.0120824
$364$	−1.95065e19	−1.20759
$365$	−1.57783e19	−0.956892
$366$	−9.59667e18	−0.570181
$367$	−3.30439e19	−1.92352	−0.961759	−	0.273897i	$-0.911687\pi$
$367$	−3.30439e19	−1.92352	−0.961759	+	0.273897i	$0.911687\pi$
$368$	5.40342e18	0.308184
$369$	2.00663e19	1.12142
$370$	−1.01433e19	−0.555479
$371$	7.66056e18	0.411108
$372$	1.94787e19	1.02444
$373$	−1.93979e18	−0.0999859	−0.0499929	−	0.998750i	$-0.515920\pi$
$373$	−1.93979e18	−0.0999859	−0.0499929	+	0.998750i	$0.515920\pi$
$374$	3.94774e19	1.99440
$375$	1.31561e19	0.651467
$376$	−1.00243e19	−0.486570
$377$	−2.81432e18	−0.133910
$378$	−3.67613e19	−1.71475
$379$	2.55034e19	1.16628	0.583141	−	0.812371i	$-0.301823\pi$
$379$	2.55034e19	1.16628	0.583141	+	0.812371i	$0.301823\pi$
$380$	3.83446e19	1.71920
$381$	2.30076e19	1.01142
$382$	4.39385e19	1.89396
$383$	−1.72448e18	−0.0728898	−0.0364449	−	0.999336i	$-0.511603\pi$
$383$	−1.72448e18	−0.0728898	−0.0364449	+	0.999336i	$0.511603\pi$
$384$	2.14264e19	0.888105
$385$	−2.01293e19	−0.818226
$386$	−3.13395e19	−1.24936
$387$	−2.73809e19	−1.07057
$388$	2.35457e19	0.902972
$389$	−2.29268e19	−0.862427	−0.431214	−	0.902250i	$-0.641914\pi$
$389$	−2.29268e19	−0.862427	−0.431214	+	0.902250i	$0.641914\pi$
$390$	1.40294e19	0.517670
$391$	−6.15585e19	−2.22824
$392$	−4.46178e18	−0.158439
$393$	3.34810e19	1.16642
$394$	3.95312e19	1.35120
$395$	−1.96189e19	−0.657955
$396$	2.99192e19	0.984545
$397$	6.81776e18	0.220147	0.110074	−	0.993923i	$-0.464891\pi$
$397$	6.81776e18	0.220147	0.110074	+	0.993923i	$0.464891\pi$
$398$	1.90638e18	0.0604070
$399$	3.18042e19	0.988981
$400$	2.50485e18	0.0764419
$401$	5.63171e19	1.68678	0.843388	−	0.537305i	$-0.180558\pi$
$401$	5.63171e19	1.68678	0.843388	+	0.537305i	$0.180558\pi$
$402$	−1.10409e19	−0.324569
$403$	2.74926e19	0.793283
$404$	2.06570e19	0.585068
$405$	−9.40012e17	−0.0261349
$406$	−1.17987e19	−0.322024
$407$	1.76538e19	0.473022
$408$	−2.44711e19	−0.643729
$409$	−5.24429e19	−1.35445	−0.677223	−	0.735778i	$-0.736817\pi$
$409$	−5.24429e19	−1.35445	−0.677223	+	0.735778i	$0.736817\pi$
$410$	−8.27739e19	−2.09901
$411$	−3.45597e19	−0.860510
$412$	1.49717e19	0.366050
$413$	4.83459e19	1.16074
$414$	−7.69775e19	−1.81494
$415$	−2.90125e19	−0.671776
$416$	3.58711e19	0.815728
$417$	9.44500e18	0.210951
$418$	−1.10113e20	−2.41555
$419$	4.96411e19	1.06964	0.534819	−	0.844967i	$-0.320380\pi$
$419$	4.96411e19	1.06964	0.534819	+	0.844967i	$0.320380\pi$
$420$	3.56470e19	0.754489
$421$	−2.39797e19	−0.498572	−0.249286	−	0.968430i	$-0.580196\pi$
$421$	−2.39797e19	−0.498572	−0.249286	+	0.968430i	$0.580196\pi$
$422$	2.73022e19	0.557640
$423$	−1.79068e19	−0.359307
$424$	1.64407e19	0.324097
$425$	−2.85365e19	−0.552693
$426$	−4.39100e19	−0.835586
$427$	−3.44162e19	−0.643507
$428$	−5.76699e19	−1.05955
$429$	−2.44172e19	−0.440825
$430$	1.12947e20	2.00382
$431$	−3.88162e18	−0.0676758	−0.0338379	−	0.999427i	$-0.510773\pi$
$431$	−3.88162e18	−0.0676758	−0.0338379	+	0.999427i	$0.510773\pi$
$432$	9.89276e18	0.169508
$433$	1.60711e19	0.270636	0.135318	−	0.990802i	$-0.456794\pi$
$433$	1.60711e19	0.270636	0.135318	+	0.990802i	$0.456794\pi$
$434$	1.15259e20	1.90767
$435$	5.14302e18	0.0836660
$436$	−3.09043e19	−0.494163
$437$	1.71703e20	2.69877
$438$	−8.02392e19	−1.23974
$439$	8.45647e19	1.28442	0.642208	−	0.766531i	$-0.278019\pi$
$439$	8.45647e19	1.28442	0.642208	+	0.766531i	$0.278019\pi$
$440$	−4.32003e19	−0.645048
$441$	−7.97024e18	−0.116999
$442$	−9.86733e19	−1.42407
$443$	2.52830e19	0.358757	0.179378	−	0.983780i	$-0.442591\pi$
$443$	2.52830e19	0.358757	0.179378	+	0.983780i	$0.442591\pi$
$444$	−3.12632e19	−0.436175
$445$	−1.92822e19	−0.264518
$446$	1.14303e20	1.54187
$447$	−4.50333e19	−0.597347
$448$	1.36081e20	1.77506
$449$	−3.39392e19	−0.435365	−0.217683	−	0.976020i	$-0.569850\pi$
$449$	−3.39392e19	−0.435365	−0.217683	+	0.976020i	$0.569850\pi$
$450$	−3.56843e19	−0.450177
$451$	1.44063e20	1.78742
$452$	−1.06678e20	−1.30178
$453$	−1.12599e19	−0.135145
$454$	1.94383e20	2.29478
$455$	5.03129e19	0.584244
$456$	6.82564e19	0.779663
$457$	4.00914e19	0.450484	0.225242	−	0.974303i	$-0.427683\pi$
$457$	4.00914e19	0.450484	0.225242	+	0.974303i	$0.427683\pi$
$458$	−5.69806e19	−0.629848
$459$	−1.12703e20	−1.22558
$460$	1.92449e20	2.05888
$461$	−1.51190e20	−1.59135	−0.795676	−	0.605722i	$-0.792884\pi$
$461$	−1.51190e20	−1.59135	−0.795676	+	0.605722i	$0.792884\pi$
$462$	−1.02366e20	−1.06009
$463$	1.85124e20	1.88627	0.943136	−	0.332407i	$-0.107861\pi$
$463$	1.85124e20	1.88627	0.943136	+	0.332407i	$0.107861\pi$
$464$	3.17512e18	0.0318329
$465$	−5.02412e19	−0.495636
$466$	−1.82080e20	−1.76753
$467$	−5.09324e19	−0.486539	−0.243270	−	0.969959i	$-0.578220\pi$
$467$	−5.09324e19	−0.486539	−0.243270	+	0.969959i	$0.578220\pi$
$468$	−7.47826e19	−0.703002
$469$	−3.95954e19	−0.366309
$470$	7.38659e19	0.672528
$471$	7.86007e19	0.704320
$472$	1.03757e20	0.915068
$473$	−1.96576e20	−1.70637
$474$	−9.97704e19	−0.852441
$475$	7.95958e19	0.669404
$476$	−2.50717e20	−2.07555
$477$	2.93686e19	0.239329
$478$	−1.63449e20	−1.31122
$479$	−1.74644e20	−1.37923	−0.689616	−	0.724175i	$-0.742221\pi$
$479$	−1.74644e20	−1.37923	−0.689616	+	0.724175i	$0.742221\pi$
$480$	−6.55525e19	−0.509660
$481$	−4.41256e19	−0.337755
$482$	1.72111e19	0.129705
$483$	1.59623e20	1.18438
$484$	4.20379e18	0.0307115
$485$	−6.07314e19	−0.436868
$486$	−2.27203e20	−1.60932
$487$	3.13176e19	0.218434	0.109217	−	0.994018i	$-0.465166\pi$
$487$	3.13176e19	0.218434	0.109217	+	0.994018i	$0.465166\pi$
$488$	−7.38620e19	−0.507309
$489$	−2.37975e19	−0.160959
$490$	3.28774e19	0.218991
$491$	2.28250e20	1.49727	0.748636	−	0.662982i	$-0.230709\pi$
$491$	2.28250e20	1.49727	0.748636	+	0.662982i	$0.230709\pi$
$492$	−2.55121e20	−1.64819
$493$	−3.61726e19	−0.230159
$494$	2.75226e20	1.72479
$495$	−7.71704e19	−0.476334
$496$	−3.10172e19	−0.188577
$497$	−1.57473e20	−0.943045
$498$	−1.47541e20	−0.870347
$499$	1.26101e20	0.732765	0.366383	−	0.930464i	$-0.380596\pi$
$499$	1.26101e20	0.732765	0.366383	+	0.930464i	$0.380596\pi$
$500$	2.89278e20	1.65592
$501$	−1.55328e20	−0.875924
$502$	1.31163e20	0.728674
$503$	−7.00346e19	−0.383312	−0.191656	−	0.981462i	$-0.561386\pi$
$503$	−7.00346e19	−0.383312	−0.191656	+	0.981462i	$0.561386\pi$
$504$	−1.09742e20	−0.591756
$505$	−5.32804e19	−0.283063
$506$	−5.52648e20	−2.89281
$507$	−5.63298e19	−0.290521
$508$	5.05894e20	2.57088
$509$	−1.40973e19	−0.0705914	−0.0352957	−	0.999377i	$-0.511237\pi$
$509$	−1.40973e19	−0.0705914	−0.0352957	+	0.999377i	$0.511237\pi$
$510$	1.80320e20	0.889749
$511$	−2.87759e20	−1.39917
$512$	−7.11681e19	−0.341005
$513$	3.14359e20	1.48438
$514$	2.82219e20	1.31329
$515$	−3.86164e19	−0.177099
$516$	3.48117e20	1.57345
$517$	−1.28559e20	−0.572695
$518$	−1.84991e20	−0.812225
$519$	−2.66790e20	−1.15455
$520$	1.07979e20	0.460589
$521$	3.82168e20	1.60684	0.803418	−	0.595416i	$-0.203013\pi$
$521$	3.82168e20	1.60684	0.803418	+	0.595416i	$0.203013\pi$
$522$	−4.52331e19	−0.187468
$523$	−1.06399e20	−0.434686	−0.217343	−	0.976095i	$-0.569739\pi$
$523$	−1.06399e20	−0.434686	−0.217343	+	0.976095i	$0.569739\pi$
$524$	7.36185e20	2.96485
$525$	7.39960e19	0.293774
$526$	−7.21205e20	−2.82270
$527$	3.53364e20	1.36346
$528$	2.75475e19	0.104792
$529$	5.95129e20	2.23200
$530$	−1.21146e20	−0.447961
$531$	1.85345e20	0.675729
$532$	6.99316e20	2.51383
$533$	−3.60083e20	−1.27629
$534$	−9.80579e19	−0.342707
$535$	1.48748e20	0.512622
$536$	−8.49773e19	−0.288780
$537$	3.11004e20	1.04222
$538$	−3.19989e20	−1.05747
$539$	−5.72211e19	−0.186483
$540$	3.52342e20	1.13243
$541$	−4.17549e20	−1.32351	−0.661756	−	0.749719i	$-0.730188\pi$
$541$	−4.17549e20	−1.32351	−0.661756	+	0.749719i	$0.730188\pi$
$542$	8.15558e18	0.0254953
$543$	−7.71864e19	−0.237981
$544$	4.61053e20	1.40204
$545$	7.97113e19	0.239081
$546$	2.55863e20	0.756941
$547$	1.83253e20	0.534745	0.267373	−	0.963593i	$-0.413845\pi$
$547$	1.83253e20	0.534745	0.267373	+	0.963593i	$0.413845\pi$
$548$	−7.59903e20	−2.18728
$549$	−1.31942e20	−0.374621
$550$	−2.56190e20	−0.717532
$551$	1.00895e20	0.278761
$552$	3.42574e20	0.933708
$553$	−3.57803e20	−0.962066
$554$	−5.81870e19	−0.154349
$555$	8.06370e19	0.211027
$556$	2.07678e20	0.536204
$557$	−1.19881e20	−0.305378	−0.152689	−	0.988274i	$-0.548793\pi$
$557$	−1.19881e20	−0.305378	−0.152689	+	0.988274i	$0.548793\pi$
$558$	4.41873e20	1.11056
$559$	4.91341e20	1.21841
$560$	−5.67631e19	−0.138885
$561$	−3.13836e20	−0.757671
$562$	1.04443e21	2.48804
$563$	1.83342e20	0.430972	0.215486	−	0.976507i	$-0.430866\pi$
$563$	1.83342e20	0.430972	0.215486	+	0.976507i	$0.430866\pi$
$564$	2.27665e20	0.528084
$565$	2.75155e20	0.629816
$566$	−8.78691e20	−1.98478
$567$	−1.71436e19	−0.0382146
$568$	−3.37959e20	−0.743449
$569$	5.71422e20	1.24055	0.620276	−	0.784384i	$-0.287021\pi$
$569$	5.71422e20	1.24055	0.620276	+	0.784384i	$0.287021\pi$
$570$	−5.02959e20	−1.07763
$571$	−1.14764e20	−0.242681	−0.121341	−	0.992611i	$-0.538719\pi$
$571$	−1.14764e20	−0.242681	−0.121341	+	0.992611i	$0.538719\pi$
$572$	−5.36890e20	−1.12051
$573$	−3.49300e20	−0.719514
$574$	−1.50960e21	−3.06919
$575$	3.99486e20	0.801664
$576$	5.21699e20	1.03336
$577$	4.12547e20	0.806593	0.403296	−	0.915069i	$-0.367864\pi$
$577$	4.12547e20	0.806593	0.403296	+	0.915069i	$0.367864\pi$
$578$	−4.42687e20	−0.854354
$579$	2.49142e20	0.474632
$580$	1.13086e20	0.212666
$581$	−5.29120e20	−0.982275
$582$	−3.08845e20	−0.566002
$583$	2.10847e20	0.381464
$584$	−6.17571e20	−1.10304
$585$	1.92887e20	0.340121
$586$	3.09601e20	0.538977
$587$	−6.11668e20	−1.05131	−0.525654	−	0.850698i	$-0.676179\pi$
$587$	−6.11668e20	−1.05131	−0.525654	+	0.850698i	$0.676179\pi$
$588$	1.01333e20	0.171957
$589$	−9.85623e20	−1.65138
$590$	−7.64553e20	−1.26479
$591$	−3.14263e20	−0.513319
$592$	4.97825e19	0.0802904
$593$	−3.02071e20	−0.481060	−0.240530	−	0.970642i	$-0.577321\pi$
$593$	−3.02071e20	−0.481060	−0.240530	+	0.970642i	$0.577321\pi$
$594$	−1.01181e21	−1.59111
$595$	6.46674e20	1.00417
$596$	−9.90199e20	−1.51836
$597$	−1.51553e19	−0.0229486
$598$	1.38134e21	2.06557
$599$	−4.06549e20	−0.600360	−0.300180	−	0.953883i	$-0.597047\pi$
$599$	−4.06549e20	−0.600360	−0.300180	+	0.953883i	$0.597047\pi$
$600$	1.58806e20	0.231597
$601$	1.19609e21	1.72269	0.861344	−	0.508023i	$-0.169623\pi$
$601$	1.19609e21	1.72269	0.861344	+	0.508023i	$0.169623\pi$
$602$	2.05988e21	2.93001
$603$	−1.51798e20	−0.213249
$604$	−2.47585e20	−0.343517
$605$	−1.08428e19	−0.0148586
$606$	−2.70954e20	−0.366733
$607$	−7.32649e20	−0.979446	−0.489723	−	0.871878i	$-0.662902\pi$
$607$	−7.32649e20	−0.979446	−0.489723	+	0.871878i	$0.662902\pi$
$608$	−1.28600e21	−1.69810
$609$	9.37967e19	0.122337
$610$	5.44265e20	0.701192
$611$	3.21332e20	0.408926
$612$	−9.61184e20	−1.20829
$613$	−8.41095e20	−1.04446	−0.522230	−	0.852805i	$-0.674900\pi$
$613$	−8.41095e20	−1.04446	−0.522230	+	0.852805i	$0.674900\pi$
$614$	2.65479e18	0.00325662
$615$	6.58032e20	0.797414
$616$	−7.87873e20	−0.943194
$617$	3.50865e20	0.414956	0.207478	−	0.978240i	$-0.433474\pi$
$617$	3.50865e20	0.414956	0.207478	+	0.978240i	$0.433474\pi$
$618$	−1.96381e20	−0.229448
$619$	6.26169e20	0.722790	0.361395	−	0.932413i	$-0.382301\pi$
$619$	6.26169e20	0.722790	0.361395	+	0.932413i	$0.382301\pi$
$620$	−1.10471e21	−1.25983
$621$	1.57775e21	1.77767
$622$	−6.64726e20	−0.739971
$623$	−3.51661e20	−0.386780
$624$	−6.88547e19	−0.0748255
$625$	−3.30839e20	−0.355235
$626$	−5.73836e20	−0.608808
$627$	8.75369e20	0.917666
$628$	1.72829e21	1.79027
$629$	−5.67148e20	−0.580519
$630$	8.08652e20	0.817913
$631$	3.98812e20	0.398610	0.199305	−	0.979938i	$-0.436132\pi$
$631$	3.98812e20	0.398610	0.199305	+	0.979938i	$0.436132\pi$
$632$	−7.67895e20	−0.758445
$633$	−2.17046e20	−0.211847
$634$	5.12390e20	0.494232
$635$	−1.30485e21	−1.24382
$636$	−3.73389e20	−0.351749
$637$	1.43023e20	0.133156
$638$	−3.24743e20	−0.298803
$639$	−6.03709e20	−0.548998
$640$	−1.21517e21	−1.09217
$641$	1.61848e21	1.43771	0.718854	−	0.695161i	$-0.244667\pi$
$641$	1.61848e21	1.43771	0.718854	+	0.695161i	$0.244667\pi$
$642$	7.56445e20	0.664148
$643$	−9.95134e20	−0.863574	−0.431787	−	0.901976i	$-0.642117\pi$
$643$	−9.95134e20	−0.863574	−0.431787	+	0.901976i	$0.642117\pi$
$644$	3.50982e21	3.01051
$645$	−8.97898e20	−0.761253
$646$	3.53748e21	2.96449
$647$	1.86187e21	1.54230	0.771149	−	0.636655i	$-0.219682\pi$
$647$	1.86187e21	1.54230	0.771149	+	0.636655i	$0.219682\pi$
$648$	−3.67926e19	−0.0301265
$649$	1.33066e21	1.07704
$650$	6.40343e20	0.512345
$651$	−9.16282e20	−0.724723
$652$	−5.23262e20	−0.409131
$653$	1.28474e20	0.0993037	0.0496518	−	0.998767i	$-0.484189\pi$
$653$	1.28474e20	0.0993037	0.0496518	+	0.998767i	$0.484189\pi$
$654$	4.05366e20	0.309752
$655$	−1.89884e21	−1.43443
$656$	4.06246e20	0.303397
$657$	−1.10319e21	−0.814536
$658$	1.34714e21	0.983374
$659$	7.98584e20	0.576341	0.288171	−	0.957579i	$-0.406953\pi$
$659$	7.98584e20	0.576341	0.288171	+	0.957579i	$0.406953\pi$
$660$	9.81136e20	0.700084
$661$	−1.30854e21	−0.923158	−0.461579	−	0.887099i	$-0.652717\pi$
$661$	−1.30854e21	−0.923158	−0.461579	+	0.887099i	$0.652717\pi$
$662$	3.53993e21	2.46922
$663$	7.84428e20	0.541006
$664$	−1.13557e21	−0.774377
$665$	−1.80374e21	−1.21622
$666$	−7.09205e20	−0.472841
$667$	5.06384e20	0.333838
$668$	−3.41537e21	−2.22646
$669$	−9.08682e20	−0.585755
$670$	6.26171e20	0.399146
$671$	−9.47260e20	−0.597104
$672$	−1.19552e21	−0.745228
$673$	−2.68452e21	−1.65483	−0.827417	−	0.561588i	$-0.810191\pi$
$673$	−2.68452e21	−1.65483	−0.827417	+	0.561588i	$0.810191\pi$
$674$	1.53862e21	0.937954
$675$	7.31391e20	0.440932
$676$	−1.23859e21	−0.738459
$677$	1.09505e21	0.645683	0.322841	−	0.946453i	$-0.395362\pi$
$677$	1.09505e21	0.645683	0.322841	+	0.946453i	$0.395362\pi$
$678$	1.39928e21	0.815984
$679$	−1.10760e21	−0.638792
$680$	1.38786e21	0.791639
$681$	−1.54530e21	−0.871785
$682$	3.17236e21	1.77011
$683$	1.54857e21	0.854622	0.427311	−	0.904105i	$-0.359461\pi$
$683$	1.54857e21	0.854622	0.427311	+	0.904105i	$0.359461\pi$
$684$	2.68099e21	1.46344
$685$	1.96002e21	1.05823
$686$	−2.64766e21	−1.41394
$687$	4.52982e20	0.239279
$688$	−5.54331e20	−0.289638
$689$	−5.27010e20	−0.272380
$690$	−2.52432e21	−1.29055
$691$	−1.47834e21	−0.747634	−0.373817	−	0.927503i	$-0.621951\pi$
$691$	−1.47834e21	−0.747634	−0.373817	+	0.927503i	$0.621951\pi$
$692$	−5.86621e21	−2.93469
$693$	−1.40741e21	−0.696499
$694$	1.41391e21	0.692189
$695$	−5.35664e20	−0.259422
$696$	2.01301e20	0.0964443
$697$	−4.62817e21	−2.19363
$698$	−4.22256e21	−1.97998
$699$	1.44749e21	0.671485
$700$	1.62704e21	0.746727
$701$	3.13515e21	1.42355	0.711776	−	0.702406i	$-0.247891\pi$
$701$	3.13515e21	1.42355	0.711776	+	0.702406i	$0.247891\pi$
$702$	2.52900e21	1.13611
$703$	1.58192e21	0.703105
$704$	3.74546e21	1.64706
$705$	−5.87216e20	−0.255493
$706$	4.24166e21	1.82600
$707$	−9.71710e20	−0.413896
$708$	−2.35646e21	−0.993141
$709$	4.28977e21	1.78891	0.894453	−	0.447162i	$-0.147565\pi$
$709$	4.28977e21	1.78891	0.894453	+	0.447162i	$0.147565\pi$
$710$	2.49031e21	1.02758
$711$	−1.37172e21	−0.560072
$712$	−7.54715e20	−0.304918
$713$	−4.94677e21	−1.97765
$714$	3.28861e21	1.30100
$715$	1.38480e21	0.542115
$716$	6.83841e21	2.64916
$717$	1.29938e21	0.498131
$718$	−2.66075e21	−1.00942
$719$	−3.42008e21	−1.28401	−0.642006	−	0.766700i	$-0.721898\pi$
$719$	−3.42008e21	−1.28401	−0.642006	+	0.766700i	$0.721898\pi$
$720$	−2.17615e20	−0.0808527
$721$	−7.04272e20	−0.258956
$722$	−5.48851e21	−1.99722
$723$	−1.36824e20	−0.0492748
$724$	−1.69719e21	−0.604909
$725$	2.34743e20	0.0828053
$726$	−5.51403e19	−0.0192506
$727$	−4.18516e21	−1.44612	−0.723060	−	0.690786i	$-0.757265\pi$
$727$	−4.18516e21	−1.44612	−0.723060	+	0.690786i	$0.757265\pi$
$728$	1.96928e21	0.673476
$729$	1.70248e21	0.576270
$730$	4.55069e21	1.52460
$731$	6.31522e21	2.09415
$732$	1.67750e21	0.550592
$733$	−1.09203e20	−0.0354777	−0.0177389	−	0.999843i	$-0.505647\pi$
$733$	−1.09203e20	−0.0354777	−0.0177389	+	0.999843i	$0.505647\pi$
$734$	9.53036e21	3.06470
$735$	−2.61367e20	−0.0831948
$736$	−6.45433e21	−2.03361
$737$	−1.08981e21	−0.339895
$738$	−5.78742e21	−1.78674
$739$	−1.86181e21	−0.568988	−0.284494	−	0.958678i	$-0.591826\pi$
$739$	−1.86181e21	−0.568988	−0.284494	+	0.958678i	$0.591826\pi$
$740$	1.77306e21	0.536396
$741$	−2.18798e21	−0.655248
$742$	−2.20942e21	−0.655011
$743$	3.68256e21	1.08077	0.540386	−	0.841417i	$-0.318278\pi$
$743$	3.68256e21	1.08077	0.540386	+	0.841417i	$0.318278\pi$
$744$	−1.96647e21	−0.571335
$745$	2.55402e21	0.734601
$746$	5.59464e20	0.159306
$747$	−2.02851e21	−0.571836
$748$	−6.90067e21	−1.92588
$749$	2.71281e21	0.749559
$750$	−3.79441e21	−1.03797
$751$	−5.31785e21	−1.44025	−0.720123	−	0.693847i	$-0.755915\pi$
$751$	−5.31785e21	−1.44025	−0.720123	+	0.693847i	$0.755915\pi$
$752$	−3.62527e20	−0.0972089
$753$	−1.04271e21	−0.276823
$754$	8.11693e20	0.213357
$755$	6.38596e20	0.166197
$756$	6.42589e21	1.65584
$757$	−6.27857e21	−1.60192	−0.800961	−	0.598716i	$-0.795678\pi$
$757$	−6.27857e21	−1.60192	−0.800961	+	0.598716i	$0.795678\pi$
$758$	−7.35555e21	−1.85822
$759$	4.39342e21	1.09898
$760$	−3.87109e21	−0.958807
$761$	−4.65754e20	−0.114228	−0.0571139	−	0.998368i	$-0.518190\pi$
$761$	−4.65754e20	−0.114228	−0.0571139	+	0.998368i	$0.518190\pi$
$762$	−6.63572e21	−1.61148
$763$	1.45375e21	0.349587
$764$	−7.68047e21	−1.82889
$765$	2.47918e21	0.584584
$766$	4.97365e20	0.116134
$767$	−3.32596e21	−0.769046
$768$	−1.86857e21	−0.427858
$769$	6.69221e20	0.151748	0.0758739	−	0.997117i	$-0.475825\pi$
$769$	6.69221e20	0.151748	0.0758739	+	0.997117i	$0.475825\pi$
$770$	5.80558e21	1.30366
$771$	−2.24357e21	−0.498921
$772$	5.47816e21	1.20644
$773$	2.36232e21	0.515220	0.257610	−	0.966249i	$-0.417065\pi$
$773$	2.36232e21	0.515220	0.257610	+	0.966249i	$0.417065\pi$
$774$	7.89704e21	1.70572
$775$	−2.29316e21	−0.490537
$776$	−2.37707e21	−0.503591
$777$	1.47063e21	0.308564
$778$	6.61244e21	1.37409
$779$	1.29092e22	2.65685
$780$	−2.45234e21	−0.499886
$781$	−4.33423e21	−0.875042
$782$	1.77544e22	3.55022
$783$	9.27105e20	0.183618
$784$	−1.61359e20	−0.0316536
$785$	−4.45776e21	−0.866152
$786$	−9.65640e21	−1.85843
$787$	8.28193e20	0.157878	0.0789389	−	0.996879i	$-0.474847\pi$
$787$	8.28193e20	0.157878	0.0789389	+	0.996879i	$0.474847\pi$
$788$	−6.91007e21	−1.30478
$789$	5.73340e21	1.07235
$790$	5.65838e21	1.04831
$791$	5.01818e21	0.920921
$792$	−3.02050e21	−0.549085
$793$	2.36767e21	0.426355
$794$	−1.96634e21	−0.350756
$795$	9.63081e20	0.170180
$796$	−3.33237e20	−0.0583317
$797$	−4.79558e21	−0.831579	−0.415789	−	0.909461i	$-0.636495\pi$
$797$	−4.79558e21	−0.831579	−0.415789	+	0.909461i	$0.636495\pi$
$798$	−9.17280e21	−1.57572
$799$	4.13009e21	0.702844
$800$	−2.99202e21	−0.504416
$801$	−1.34818e21	−0.225166
$802$	−1.62427e22	−2.68751
$803$	−7.92018e21	−1.29828
$804$	1.92995e21	0.313419
$805$	−9.05286e21	−1.45652
$806$	−7.92927e21	−1.26392
$807$	2.54384e21	0.401733
$808$	−2.08543e21	−0.326295
$809$	2.09962e21	0.325482	0.162741	−	0.986669i	$-0.447966\pi$
$809$	2.09962e21	0.325482	0.162741	+	0.986669i	$0.447966\pi$
$810$	2.71113e20	0.0416402
$811$	2.38357e21	0.362720	0.181360	−	0.983417i	$-0.441950\pi$
$811$	2.38357e21	0.362720	0.181360	+	0.983417i	$0.441950\pi$
$812$	2.06242e21	0.310961
$813$	−6.48349e19	−0.00968567
$814$	−5.09162e21	−0.753656
$815$	1.34965e21	0.197942
$816$	−8.84993e20	−0.128607
$817$	−1.76148e22	−2.53637
$818$	1.51253e22	2.15801
$819$	3.51780e21	0.497327
$820$	1.44689e22	2.02690
$821$	−3.85472e21	−0.535080	−0.267540	−	0.963547i	$-0.586211\pi$
$821$	−3.85472e21	−0.535080	−0.267540	+	0.963547i	$0.586211\pi$
$822$	9.96751e21	1.37103
$823$	1.21563e22	1.65693	0.828464	−	0.560042i	$-0.189215\pi$
$823$	1.21563e22	1.65693	0.828464	+	0.560042i	$0.189215\pi$
$824$	−1.51147e21	−0.204148
$825$	2.03664e21	0.272590
$826$	−1.39437e22	−1.84938
$827$	1.35131e22	1.77608	0.888042	−	0.459762i	$-0.152065\pi$
$827$	1.35131e22	1.77608	0.888042	+	0.459762i	$0.152065\pi$
$828$	1.34557e22	1.75259
$829$	5.85728e21	0.756026	0.378013	−	0.925800i	$-0.376607\pi$
$829$	5.85728e21	0.756026	0.378013	+	0.925800i	$0.376607\pi$
$830$	8.36763e21	1.07033
$831$	4.62572e20	0.0586370
$832$	−9.36173e21	−1.17606
$833$	1.83829e21	0.228863
$834$	−2.72408e21	−0.336104
$835$	8.80926e21	1.07719
$836$	1.92478e22	2.33256
$837$	−9.05671e21	−1.08775
$838$	−1.43172e22	−1.70423
$839$	1.25317e22	1.47841	0.739207	−	0.673478i	$-0.235200\pi$
$839$	1.25317e22	1.47841	0.739207	+	0.673478i	$0.235200\pi$
$840$	−3.59875e21	−0.420782
$841$	2.97558e20	0.0344828
$842$	6.91609e21	0.794365
$843$	−8.30298e21	−0.945207
$844$	−4.77243e21	−0.538482
$845$	3.19469e21	0.357275
$846$	5.16458e21	0.572476
$847$	−1.97747e20	−0.0217263
$848$	5.94573e20	0.0647495
$849$	6.98538e21	0.754019
$850$	8.23035e21	0.880595
$851$	7.93955e21	0.842024
$852$	7.67549e21	0.806880
$853$	−1.33798e22	−1.39422	−0.697110	−	0.716964i	$-0.745531\pi$
$853$	−1.33798e22	−1.39422	−0.697110	+	0.716964i	$0.745531\pi$
$854$	9.92613e21	1.02529
$855$	−6.91508e21	−0.708029
$856$	5.82208e21	0.590915
$857$	1.21543e22	1.22285	0.611427	−	0.791300i	$-0.290596\pi$
$857$	1.21543e22	1.22285	0.611427	+	0.791300i	$0.290596\pi$
$858$	7.04229e21	0.702359
$859$	1.28735e22	1.27276	0.636380	−	0.771375i	$-0.280431\pi$
$859$	1.28735e22	1.27276	0.636380	+	0.771375i	$0.280431\pi$
$860$	−1.97431e22	−1.93498
$861$	1.20010e22	1.16598
$862$	1.11952e21	0.107827
$863$	1.28297e22	1.22499	0.612497	−	0.790473i	$-0.290165\pi$
$863$	1.28297e22	1.22499	0.612497	+	0.790473i	$0.290165\pi$
$864$	−1.18168e22	−1.11853
$865$	1.51307e22	1.41984
$866$	−4.63513e21	−0.431199
$867$	3.51925e21	0.324569
$868$	−2.01474e22	−1.84213
$869$	−9.84805e21	−0.892692
$870$	−1.48332e21	−0.133303
$871$	2.72397e21	0.242698
$872$	3.11995e21	0.275597
$873$	−4.24624e21	−0.371876
$874$	−4.95216e22	−4.29991
$875$	−1.36077e22	−1.17145
$876$	1.40259e22	1.19715
$877$	1.28837e22	1.09029	0.545146	−	0.838341i	$-0.316474\pi$
$877$	1.28837e22	1.09029	0.545146	+	0.838341i	$0.316474\pi$
$878$	−2.43897e22	−2.04643
$879$	−2.46125e21	−0.204757
$880$	−1.56233e21	−0.128870
$881$	1.71596e22	1.40342	0.701710	−	0.712463i	$-0.252420\pi$
$881$	1.71596e22	1.40342	0.701710	+	0.712463i	$0.252420\pi$
$882$	2.29874e21	0.186412
$883$	1.51268e22	1.21630	0.608150	−	0.793822i	$-0.291912\pi$
$883$	1.51268e22	1.21630	0.608150	+	0.793822i	$0.291912\pi$
$884$	1.72481e22	1.37515
$885$	6.07801e21	0.480493
$886$	−7.29198e21	−0.571600
$887$	−7.75246e21	−0.602576	−0.301288	−	0.953533i	$-0.597417\pi$
$887$	−7.75246e21	−0.602576	−0.301288	+	0.953533i	$0.597417\pi$
$888$	3.15618e21	0.243257
$889$	−2.37974e22	−1.81872
$890$	5.56126e21	0.421452
$891$	−4.71856e20	−0.0354590
$892$	−1.99802e22	−1.48890
$893$	−1.15199e22	−0.851261
$894$	1.29883e22	0.951742
$895$	−1.76383e22	−1.28169
$896$	−2.21619e22	−1.59697
$897$	−1.09813e22	−0.784712
$898$	9.78855e21	0.693659
$899$	−2.90679e21	−0.204275
$900$	6.23763e21	0.434711
$901$	−6.77368e21	−0.468154
$902$	−4.15498e22	−2.84787
$903$	−1.63755e22	−1.11311
$904$	1.07697e22	0.726008
$905$	4.37755e21	0.292662
$906$	3.24753e21	0.215324
$907$	1.75320e22	1.15286	0.576429	−	0.817147i	$-0.304446\pi$
$907$	1.75320e22	1.15286	0.576429	+	0.817147i	$0.304446\pi$
$908$	−3.39783e22	−2.21594
$909$	−3.72528e21	−0.240952
$910$	−1.45110e22	−0.930865
$911$	2.81184e20	0.0178897	0.00894484	−	0.999960i	$-0.497153\pi$
$911$	2.81184e20	0.0178897	0.00894484	+	0.999960i	$0.497153\pi$
$912$	2.46848e21	0.155764
$913$	−1.45633e22	−0.911444
$914$	−1.15629e22	−0.717747
$915$	−4.32678e21	−0.266383
$916$	9.96024e21	0.608210
$917$	−3.46304e22	−2.09743
$918$	3.25053e22	1.95269
$919$	−5.35010e21	−0.318783	−0.159392	−	0.987215i	$-0.550953\pi$
$919$	−5.35010e21	−0.318783	−0.159392	+	0.987215i	$0.550953\pi$
$920$	−1.94287e22	−1.14825
$921$	−2.11049e19	−0.00123719
$922$	4.36054e22	2.53547
$923$	1.08334e22	0.624813
$924$	1.78936e22	1.02367
$925$	3.68052e21	0.208856
$926$	−5.33924e22	−3.00536
$927$	−2.69999e21	−0.150753
$928$	−3.79265e21	−0.210055
$929$	−1.28681e22	−0.706962	−0.353481	−	0.935442i	$-0.615002\pi$
$929$	−1.28681e22	−0.706962	−0.353481	+	0.935442i	$0.615002\pi$
$930$	1.44903e22	0.789688
$931$	−5.12746e21	−0.277191
$932$	3.18276e22	1.70681
$933$	5.28441e21	0.281115
$934$	1.46897e22	0.775193
$935$	1.77989e22	0.931763
$936$	7.54970e21	0.392067
$937$	−3.20975e22	−1.65358	−0.826788	−	0.562514i	$-0.809834\pi$
$937$	−3.20975e22	−1.65358	−0.826788	+	0.562514i	$0.809834\pi$
$938$	1.14199e22	0.583634
$939$	4.56186e21	0.231286
$940$	−1.29118e22	−0.649423
$941$	−6.67762e21	−0.333196	−0.166598	−	0.986025i	$-0.553278\pi$
$941$	−6.67762e21	−0.333196	−0.166598	+	0.986025i	$0.553278\pi$
$942$	−2.26696e22	−1.12218
$943$	6.47902e22	3.18179
$944$	3.75235e21	0.182816
$945$	−1.65743e22	−0.801117
$946$	5.66955e22	2.71873
$947$	−3.41838e22	−1.62628	−0.813139	−	0.582069i	$-0.802243\pi$
$947$	−3.41838e22	−1.62628	−0.813139	+	0.582069i	$0.802243\pi$
$948$	1.74399e22	0.823155
$949$	1.97964e22	0.927022
$950$	−2.29566e22	−1.06655
$951$	−4.07337e21	−0.187759
$952$	2.53112e22	1.15754
$953$	1.03966e22	0.471732	0.235866	−	0.971786i	$-0.424207\pi$
$953$	1.03966e22	0.471732	0.235866	+	0.971786i	$0.424207\pi$
$954$	−8.47033e21	−0.381318
$955$	1.98102e22	0.884838
$956$	2.85710e22	1.26617
$957$	2.58163e21	0.113515
$958$	5.03699e22	2.19751
$959$	3.57461e22	1.54735
$960$	1.71080e22	0.734794
$961$	4.93063e21	0.210125
$962$	1.27265e22	0.538139
$963$	1.04002e22	0.436359
$964$	−3.00851e21	−0.125249
$965$	−1.41298e22	−0.583689
$966$	−4.60376e22	−1.88705
$967$	−3.43817e22	−1.39839	−0.699196	−	0.714930i	$-0.746459\pi$
$967$	−3.43817e22	−1.39839	−0.699196	+	0.714930i	$0.746459\pi$
$968$	−4.24394e20	−0.0171279
$969$	−2.81221e22	−1.12621
$970$	1.75158e22	0.696054
$971$	1.34470e22	0.530252	0.265126	−	0.964214i	$-0.414586\pi$
$971$	1.34470e22	0.530252	0.265126	+	0.964214i	$0.414586\pi$
$972$	3.97152e22	1.55403
$973$	−9.76925e21	−0.379328
$974$	−9.03244e21	−0.348027
$975$	−5.09057e21	−0.194640
$976$	−2.67120e21	−0.101352
$977$	2.56506e22	0.965802	0.482901	−	0.875675i	$-0.339583\pi$
$977$	2.56506e22	0.965802	0.482901	+	0.875675i	$0.339583\pi$
$978$	6.86354e21	0.256452
$979$	−9.67902e21	−0.358890
$980$	−5.74699e21	−0.211468
$981$	5.57328e21	0.203514
$982$	−6.58308e22	−2.38557
$983$	−1.11940e22	−0.402564	−0.201282	−	0.979533i	$-0.564511\pi$
$983$	−1.11940e22	−0.402564	−0.201282	+	0.979533i	$0.564511\pi$
$984$	2.57558e22	0.919203
$985$	1.78231e22	0.631265
$986$	1.04327e22	0.366708
$987$	−1.07094e22	−0.373584
$988$	−4.81096e22	−1.66554
$989$	−8.84074e22	−3.03750
$990$	2.22571e22	0.758934
$991$	3.23707e22	1.09547	0.547734	−	0.836653i	$-0.315491\pi$
$991$	3.23707e22	1.09547	0.547734	+	0.836653i	$0.315491\pi$
$992$	3.70497e22	1.24436
$993$	−2.81416e22	−0.938057
$994$	4.54174e22	1.50254
$995$	8.59516e20	0.0282215
$996$	2.57902e22	0.840446
$997$	−3.35239e22	−1.08428	−0.542139	−	0.840289i	$-0.682385\pi$
$997$	−3.35239e22	−1.08428	−0.542139	+	0.840289i	$0.682385\pi$
$998$	−3.63694e22	−1.16750
$999$	1.45360e22	0.463131

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.16.a.b.1.3	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.16.a.b.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-288.415 q^{2} +2292.83 q^{3} +50415.0 q^{4} -130035. q^{5} -661285. q^{6} -2.37154e6 q^{7} -5.08966e6 q^{8} -9.09186e6 q^{9} +O(q^{10})\)	\(q-288.415 q^{2} +2292.83 q^{3} +50415.0 q^{4} -130035. q^{5} -661285. q^{6} -2.37154e6 q^{7} -5.08966e6 q^{8} -9.09186e6 q^{9} +3.75041e7 q^{10} -6.52735e7 q^{11} +1.15593e8 q^{12} +1.63150e8 q^{13} +6.83987e8 q^{14} -2.98148e8 q^{15} -1.84066e8 q^{16} +2.09698e9 q^{17} +2.62222e9 q^{18} -5.84902e9 q^{19} -6.55573e9 q^{20} -5.43753e9 q^{21} +1.88258e10 q^{22} -2.93558e10 q^{23} -1.16697e10 q^{24} -1.36084e10 q^{25} -4.70550e10 q^{26} -5.37456e10 q^{27} -1.19561e11 q^{28} -1.72499e10 q^{29} +8.59904e10 q^{30} +1.68511e11 q^{31} +2.19865e11 q^{32} -1.49661e11 q^{33} -6.04799e11 q^{34} +3.08384e11 q^{35} -4.58366e11 q^{36} -2.70459e11 q^{37} +1.68694e12 q^{38} +3.74076e11 q^{39} +6.61836e11 q^{40} -2.20706e12 q^{41} +1.56826e12 q^{42} +3.01158e12 q^{43} -3.29077e12 q^{44} +1.18226e12 q^{45} +8.46665e12 q^{46} +1.96954e12 q^{47} -4.22032e11 q^{48} +8.76635e11 q^{49} +3.92486e12 q^{50} +4.80801e12 q^{51} +8.22523e12 q^{52} -3.23021e12 q^{53} +1.55010e13 q^{54} +8.48786e12 q^{55} +1.20703e13 q^{56} -1.34108e13 q^{57} +4.97512e12 q^{58} -2.03859e13 q^{59} -1.50312e13 q^{60} +1.45122e13 q^{61} -4.86010e13 q^{62} +2.15617e13 q^{63} -5.73809e13 q^{64} -2.12153e13 q^{65} +4.31644e13 q^{66} +1.66961e13 q^{67} +1.05719e14 q^{68} -6.73078e13 q^{69} -8.89424e13 q^{70} +6.64010e13 q^{71} +4.62745e13 q^{72} +1.21338e14 q^{73} +7.80044e13 q^{74} -3.12017e13 q^{75} -2.94879e14 q^{76} +1.54799e14 q^{77} -1.07889e14 q^{78} +1.50874e14 q^{79} +2.39351e13 q^{80} +7.22890e12 q^{81} +6.36550e14 q^{82} +2.23112e14 q^{83} -2.74133e14 q^{84} -2.72681e14 q^{85} -8.68584e14 q^{86} -3.95510e13 q^{87} +3.32220e14 q^{88} +1.48284e14 q^{89} -3.40982e14 q^{90} -3.86918e14 q^{91} -1.47997e15 q^{92} +3.86366e14 q^{93} -5.68045e14 q^{94} +7.60579e14 q^{95} +5.04113e14 q^{96} +4.67038e14 q^{97} -2.52835e14 q^{98} +5.93457e14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 9908 q^{3} + 387418 q^{4} + 230490 q^{5} + 1566838 q^{6} + 2882024 q^{7} + 26209092 q^{8} + 93022899 q^{9}+O(q^{10}) \) 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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