LMFDB - Embedded newform 11.14.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,14,Mod(1,11)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(11, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("11.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	11.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:	$11.7954021847$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 1179x^{3} + 1520x^{2} + 251749x + 900864 $ x^5 - x^4 - 1179x^3 + 1520x^2 + 251749*x + 900864
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-3.95876$ of defining polynomial
Character	$\chi$	$=$	11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.83503 q^{2} +2253.71 q^{3} -8177.29 q^{4} -38770.4 q^{5} +8643.04 q^{6} -547112. q^{7} -62776.7 q^{8} +3.48488e6 q^{9} +O(q^{10})$	\(q+3.83503 q^{2} +2253.71 q^{3} -8177.29 q^{4} -38770.4 q^{5} +8643.04 q^{6} -547112. q^{7} -62776.7 q^{8} +3.48488e6 q^{9} -148686. q^{10} -1.77156e6 q^{11} -1.84292e7 q^{12} -7.21817e6 q^{13} -2.09819e6 q^{14} -8.73772e7 q^{15} +6.67476e7 q^{16} -1.23211e8 q^{17} +1.33646e7 q^{18} +1.60970e8 q^{19} +3.17037e8 q^{20} -1.23303e9 q^{21} -6.79399e6 q^{22} +1.39369e8 q^{23} -1.41480e8 q^{24} +2.82441e8 q^{25} -2.76819e7 q^{26} +4.26076e9 q^{27} +4.47389e9 q^{28} -5.47206e8 q^{29} -3.35094e8 q^{30} -5.05330e9 q^{31} +7.70246e8 q^{32} -3.99258e9 q^{33} -4.72519e8 q^{34} +2.12117e10 q^{35} -2.84969e10 q^{36} +5.97469e9 q^{37} +6.17326e8 q^{38} -1.62677e10 q^{39} +2.43388e9 q^{40} -8.53804e9 q^{41} -4.72870e9 q^{42} +2.90995e10 q^{43} +1.44866e10 q^{44} -1.35110e11 q^{45} +5.34485e8 q^{46} -1.01229e11 q^{47} +1.50430e11 q^{48} +2.02442e11 q^{49} +1.08317e9 q^{50} -2.77682e11 q^{51} +5.90251e10 q^{52} +2.46770e11 q^{53} +1.63401e10 q^{54} +6.86841e10 q^{55} +3.43459e10 q^{56} +3.62780e11 q^{57} -2.09855e9 q^{58} -2.51941e11 q^{59} +7.14509e11 q^{60} -3.46262e11 q^{61} -1.93796e10 q^{62} -1.90662e12 q^{63} -5.43843e11 q^{64} +2.79851e11 q^{65} -1.53117e10 q^{66} +5.98044e11 q^{67} +1.00753e12 q^{68} +3.14098e11 q^{69} +8.13476e10 q^{70} +2.96902e11 q^{71} -2.18769e11 q^{72} -2.52115e12 q^{73} +2.29131e10 q^{74} +6.36539e11 q^{75} -1.31630e12 q^{76} +9.69241e11 q^{77} -6.23869e10 q^{78} -1.34081e12 q^{79} -2.58783e12 q^{80} +4.04649e12 q^{81} -3.27436e10 q^{82} -2.88598e12 q^{83} +1.00828e13 q^{84} +4.77695e12 q^{85} +1.11597e11 q^{86} -1.23324e12 q^{87} +1.11213e11 q^{88} +7.16846e11 q^{89} -5.18151e11 q^{90} +3.94914e12 q^{91} -1.13966e12 q^{92} -1.13887e13 q^{93} -3.88216e11 q^{94} -6.24089e12 q^{95} +1.73591e12 q^{96} -2.38697e12 q^{97} +7.76371e11 q^{98} -6.17367e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 64 q^{2} + 480 q^{3} - 2400 q^{4} - 454 q^{5} + 79548 q^{6} - 313920 q^{7} - 255168 q^{8} + 1321749 q^{9}+O(q^{10}) $ 5 * q - 64 * q^2 + 480 * q^3 - 2400 * q^4 - 454 * q^5 + 79548 * q^6 - 313920 * q^7 - 255168 * q^8 + 1321749 * q^9	\( 5 q - 64 q^{2} + 480 q^{3} - 2400 q^{4} - 454 q^{5} + 79548 q^{6} - 313920 q^{7} - 255168 q^{8} + 1321749 q^{9} - 3535724 q^{10} - 8857805 q^{11} - 29768880 q^{12} - 36339498 q^{13} - 64558312 q^{14} - 162945300 q^{15} - 128942592 q^{16} - 309078454 q^{17} - 302859828 q^{18} - 147232948 q^{19} - 62530256 q^{20} - 859909128 q^{21} + 113379904 q^{22} + 677905444 q^{23} + 755940096 q^{24} + 1540265631 q^{25} + 1643160872 q^{26} + 5029885620 q^{27} + 6948937120 q^{28} + 2368825878 q^{29} + 7601916540 q^{30} - 83363076 q^{31} + 10024391680 q^{32} - 850349280 q^{33} + 7463914000 q^{34} + 591040520 q^{35} - 15037063632 q^{36} - 32935650382 q^{37} - 25107474384 q^{38} - 54599307000 q^{39} - 27853580928 q^{40} - 70273827286 q^{41} - 18264520200 q^{42} - 54501240436 q^{43} + 4251746400 q^{44} - 118334367738 q^{45} - 9391823524 q^{46} - 45017434472 q^{47} + 236995825920 q^{48} + 77867671053 q^{49} + 252640243516 q^{50} - 14973171168 q^{51} + 370262207008 q^{52} + 242684257518 q^{53} + 386371416420 q^{54} + 804288694 q^{55} + 508508098560 q^{56} - 78232137120 q^{57} + 338805253176 q^{58} - 384712501184 q^{59} + 607819216080 q^{60} - 795317095690 q^{61} + 567054167132 q^{62} - 1777323941640 q^{63} - 502608203776 q^{64} - 1104664950268 q^{65} - 140924134428 q^{66} - 1005952134296 q^{67} + 9188915584 q^{68} - 2334490276524 q^{69} - 50031562280 q^{70} - 1427050574148 q^{71} + 714622284864 q^{72} - 4111049036406 q^{73} + 2579474987436 q^{74} - 584109490620 q^{75} + 1028633987648 q^{76} + 556128429120 q^{77} + 4554998846160 q^{78} - 3666957194024 q^{79} + 1569918525184 q^{80} + 4090930814781 q^{81} + 4301648616232 q^{82} + 2718055516116 q^{83} + 8581863439392 q^{84} + 1506197091796 q^{85} + 6558172582872 q^{86} + 3556682104680 q^{87} + 452045677248 q^{88} + 7963494884214 q^{89} - 4671771563808 q^{90} - 604892444560 q^{91} + 6414213002576 q^{92} + 361484424660 q^{93} - 9832269652768 q^{94} - 5225122758984 q^{95} - 12178790559744 q^{96} - 13542719272730 q^{97} - 8557591646352 q^{98} - 2341558980189 q^{99}+O(q^{100}) \) 5 * q - 64 * q^2 + 480 * q^3 - 2400 * q^4 - 454 * q^5 + 79548 * q^6 - 313920 * q^7 - 255168 * q^8 + 1321749 * q^9 - 3535724 * q^10 - 8857805 * q^11 - 29768880 * q^12 - 36339498 * q^13 - 64558312 * q^14 - 162945300 * q^15 - 128942592 * q^16 - 309078454 * q^17 - 302859828 * q^18 - 147232948 * q^19 - 62530256 * q^20 - 859909128 * q^21 + 113379904 * q^22 + 677905444 * q^23 + 755940096 * q^24 + 1540265631 * q^25 + 1643160872 * q^26 + 5029885620 * q^27 + 6948937120 * q^28 + 2368825878 * q^29 + 7601916540 * q^30 - 83363076 * q^31 + 10024391680 * q^32 - 850349280 * q^33 + 7463914000 * q^34 + 591040520 * q^35 - 15037063632 * q^36 - 32935650382 * q^37 - 25107474384 * q^38 - 54599307000 * q^39 - 27853580928 * q^40 - 70273827286 * q^41 - 18264520200 * q^42 - 54501240436 * q^43 + 4251746400 * q^44 - 118334367738 * q^45 - 9391823524 * q^46 - 45017434472 * q^47 + 236995825920 * q^48 + 77867671053 * q^49 + 252640243516 * q^50 - 14973171168 * q^51 + 370262207008 * q^52 + 242684257518 * q^53 + 386371416420 * q^54 + 804288694 * q^55 + 508508098560 * q^56 - 78232137120 * q^57 + 338805253176 * q^58 - 384712501184 * q^59 + 607819216080 * q^60 - 795317095690 * q^61 + 567054167132 * q^62 - 1777323941640 * q^63 - 502608203776 * q^64 - 1104664950268 * q^65 - 140924134428 * q^66 - 1005952134296 * q^67 + 9188915584 * q^68 - 2334490276524 * q^69 - 50031562280 * q^70 - 1427050574148 * q^71 + 714622284864 * q^72 - 4111049036406 * q^73 + 2579474987436 * q^74 - 584109490620 * q^75 + 1028633987648 * q^76 + 556128429120 * q^77 + 4554998846160 * q^78 - 3666957194024 * q^79 + 1569918525184 * q^80 + 4090930814781 * q^81 + 4301648616232 * q^82 + 2718055516116 * q^83 + 8581863439392 * q^84 + 1506197091796 * q^85 + 6558172582872 * q^86 + 3556682104680 * q^87 + 452045677248 * q^88 + 7963494884214 * q^89 - 4671771563808 * q^90 - 604892444560 * q^91 + 6414213002576 * q^92 + 361484424660 * q^93 - 9832269652768 * q^94 - 5225122758984 * q^95 - 12178790559744 * q^96 - 13542719272730 * q^97 - 8557591646352 * q^98 - 2341558980189 * 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 $

$2$	3.83503	0.0423715	0.0211857	−	0.999776i	$-0.493256\pi$
$2$	3.83503	0.0423715	0.0211857	+	0.999776i	$0.493256\pi$
$3$	2253.71	1.78488	0.892441	−	0.451164i	$-0.148991\pi$
$3$	2253.71	1.78488	0.892441	+	0.451164i	$0.148991\pi$
$4$	−8177.29	−0.998205
$5$	−38770.4	−1.10967	−0.554837	−	0.831959i	$-0.687219\pi$
$5$	−38770.4	−1.10967	−0.554837	+	0.831959i	$0.687219\pi$
$6$	8643.04	0.0756281
$7$	−547112.	−1.75768	−0.878838	−	0.477121i	$-0.841680\pi$
$7$	−547112.	−1.75768	−0.878838	+	0.477121i	$0.841680\pi$
$8$	−62776.7	−0.0846669
$9$	3.48488e6	2.18580
$10$	−148686.	−0.0470185
$11$	−1.77156e6	−0.301511
$11$	−1.77156e6	−0.301511
$12$	−1.84292e7	−1.78168
$13$	−7.21817e6	−0.414759	−0.207379	−	0.978261i	$-0.566493\pi$
$13$	−7.21817e6	−0.414759	−0.207379	+	0.978261i	$0.566493\pi$
$14$	−2.09819e6	−0.0744753
$15$	−8.73772e7	−1.98064
$16$	6.67476e7	0.994617
$17$	−1.23211e8	−1.23803	−0.619017	−	0.785378i	$-0.712469\pi$
$17$	−1.23211e8	−1.23803	−0.619017	+	0.785378i	$0.712469\pi$
$18$	1.33646e7	0.0926158
$19$	1.60970e8	0.784960	0.392480	−	0.919761i	$-0.371617\pi$
$19$	1.60970e8	0.784960	0.392480	+	0.919761i	$0.371617\pi$
$20$	3.17037e8	1.10768
$21$	−1.23303e9	−3.13724
$22$	−6.79399e6	−0.0127755
$23$	1.39369e8	0.196307	0.0981536	−	0.995171i	$-0.468706\pi$
$23$	1.39369e8	0.196307	0.0981536	+	0.995171i	$0.468706\pi$
$24$	−1.41480e8	−0.151120
$25$	2.82441e8	0.231375
$26$	−2.76819e7	−0.0175739
$27$	4.26076e9	2.11652
$28$	4.47389e9	1.75452
$29$	−5.47206e8	−0.170830	−0.0854149	−	0.996345i	$-0.527222\pi$
$29$	−5.47206e8	−0.170830	−0.0854149	+	0.996345i	$0.527222\pi$
$30$	−3.35094e8	−0.0839225
$31$	−5.05330e9	−1.02264	−0.511322	−	0.859389i	$-0.670844\pi$
$31$	−5.05330e9	−1.02264	−0.511322	+	0.859389i	$0.670844\pi$
$32$	7.70246e8	0.126810
$33$	−3.99258e9	−0.538162
$34$	−4.72519e8	−0.0524573
$35$	2.12117e10	1.95045
$36$	−2.84969e10	−2.18188
$37$	5.97469e9	0.382828	0.191414	−	0.981509i	$-0.438693\pi$
$37$	5.97469e9	0.382828	0.191414	+	0.981509i	$0.438693\pi$
$38$	6.17326e8	0.0332599
$39$	−1.62677e10	−0.740295
$40$	2.43388e9	0.0939526
$41$	−8.53804e9	−0.280713	−0.140357	−	0.990101i	$-0.544825\pi$
$41$	−8.53804e9	−0.280713	−0.140357	+	0.990101i	$0.544825\pi$
$42$	−4.72870e9	−0.132930
$43$	2.90995e10	0.702005	0.351002	−	0.936375i	$-0.385841\pi$
$43$	2.90995e10	0.702005	0.351002	+	0.936375i	$0.385841\pi$
$44$	1.44866e10	0.300970
$45$	−1.35110e11	−2.42553
$46$	5.34485e8	0.00831783
$47$	−1.01229e11	−1.36984	−0.684918	−	0.728620i	$-0.740162\pi$
$47$	−1.01229e11	−1.36984	−0.684918	+	0.728620i	$0.740162\pi$
$48$	1.50430e11	1.77527
$49$	2.02442e11	2.08942
$50$	1.08317e9	0.00980371
$51$	−2.77682e11	−2.20974
$52$	5.90251e10	0.414014
$53$	2.46770e11	1.52932	0.764660	−	0.644434i	$-0.222907\pi$
$53$	2.46770e11	1.52932	0.764660	+	0.644434i	$0.222907\pi$
$54$	1.63401e10	0.0896801
$55$	6.86841e10	0.334579
$56$	3.43459e10	0.148817
$57$	3.62780e11	1.40106
$58$	−2.09855e9	−0.00723832
$59$	−2.51941e11	−0.777607	−0.388804	−	0.921321i	$-0.627112\pi$
$59$	−2.51941e11	−0.777607	−0.388804	+	0.921321i	$0.627112\pi$
$60$	7.14509e11	1.97708
$61$	−3.46262e11	−0.860521	−0.430260	−	0.902705i	$-0.641578\pi$
$61$	−3.46262e11	−0.860521	−0.430260	+	0.902705i	$0.641578\pi$
$62$	−1.93796e10	−0.0433309
$63$	−1.90662e12	−3.84193
$64$	−5.43843e11	−0.989244
$65$	2.79851e11	0.460247
$66$	−1.53117e10	−0.0228027
$67$	5.98044e11	0.807694	0.403847	−	0.914827i	$-0.367673\pi$
$67$	5.98044e11	0.807694	0.403847	+	0.914827i	$0.367673\pi$
$68$	1.00753e12	1.23581
$69$	3.14098e11	0.350385
$70$	8.13476e10	0.0826433
$71$	2.96902e11	0.275064	0.137532	−	0.990497i	$-0.456083\pi$
$71$	2.96902e11	0.275064	0.137532	+	0.990497i	$0.456083\pi$
$72$	−2.18769e11	−0.185065
$73$	−2.52115e12	−1.94985	−0.974924	−	0.222537i	$-0.928566\pi$
$73$	−2.52115e12	−1.94985	−0.974924	+	0.222537i	$0.928566\pi$
$74$	2.29131e10	0.0162210
$75$	6.36539e11	0.412978
$76$	−1.31630e12	−0.783551
$77$	9.69241e11	0.529959
$78$	−6.23869e10	−0.0313674
$79$	−1.34081e12	−0.620572	−0.310286	−	0.950643i	$-0.600425\pi$
$79$	−1.34081e12	−0.620572	−0.310286	+	0.950643i	$0.600425\pi$
$80$	−2.58783e12	−1.10370
$81$	4.04649e12	1.59194
$82$	−3.27436e10	−0.0118942
$83$	−2.88598e12	−0.968915	−0.484457	−	0.874815i	$-0.660983\pi$
$83$	−2.88598e12	−0.968915	−0.484457	+	0.874815i	$0.660983\pi$
$84$	1.00828e13	3.13161
$85$	4.77695e12	1.37381
$86$	1.11597e11	0.0297450
$87$	−1.23324e12	−0.304911
$88$	1.11213e11	0.0255280
$89$	7.16846e11	0.152894	0.0764471	−	0.997074i	$-0.475642\pi$
$89$	7.16846e11	0.152894	0.0764471	+	0.997074i	$0.475642\pi$
$90$	−5.18151e11	−0.102773
$91$	3.94914e12	0.729011
$92$	−1.13966e12	−0.195955
$93$	−1.13887e13	−1.82530
$94$	−3.88216e11	−0.0580420
$95$	−6.24089e12	−0.871049
$96$	1.73591e12	0.226341
$97$	−2.38697e12	−0.290958	−0.145479	−	0.989361i	$-0.546472\pi$
$97$	−2.38697e12	−0.290958	−0.145479	+	0.989361i	$0.546472\pi$
$98$	7.76371e11	0.0885319
$99$	−6.17367e12	−0.659045
$100$	−2.30960e12	−0.230960
$101$	−7.73740e12	−0.725281	−0.362640	−	0.931929i	$-0.618125\pi$
$101$	−7.73740e12	−0.725281	−0.362640	+	0.931929i	$0.618125\pi$
$102$	−1.06492e12	−0.0936301
$103$	−1.12020e13	−0.924390	−0.462195	−	0.886778i	$-0.652938\pi$
$103$	−1.12020e13	−0.924390	−0.462195	+	0.886778i	$0.652938\pi$
$104$	4.53133e11	0.0351163
$105$	4.78051e13	3.48132
$106$	9.46368e11	0.0647996
$107$	1.38099e13	0.889602	0.444801	−	0.895629i	$-0.353274\pi$
$107$	1.38099e13	0.889602	0.444801	+	0.895629i	$0.353274\pi$
$108$	−3.48415e13	−2.11272
$109$	−7.60663e12	−0.434430	−0.217215	−	0.976124i	$-0.569697\pi$
$109$	−7.60663e12	−0.434430	−0.217215	+	0.976124i	$0.569697\pi$
$110$	2.63406e11	0.0141766
$111$	1.34652e13	0.683303
$112$	−3.65184e13	−1.74821
$113$	2.21910e13	1.00269	0.501345	−	0.865247i	$-0.332839\pi$
$113$	2.21910e13	1.00269	0.501345	+	0.865247i	$0.332839\pi$
$114$	1.39127e12	0.0593650
$115$	−5.40340e12	−0.217837
$116$	4.47466e12	0.170523
$117$	−2.51544e13	−0.906581
$118$	−9.66200e11	−0.0329484
$119$	6.74103e13	2.17606
$120$	5.48525e12	0.167694
$121$	3.13843e12	0.0909091
$122$	−1.32793e12	−0.0364615
$123$	−1.92422e13	−0.501040
$124$	4.13223e13	1.02081
$125$	3.63768e13	0.852922
$126$	−7.31193e12	−0.162788
$127$	−2.50632e13	−0.530044	−0.265022	−	0.964242i	$-0.585379\pi$
$127$	−2.50632e13	−0.530044	−0.265022	+	0.964242i	$0.585379\pi$
$128$	−8.39551e12	−0.168726
$129$	6.55817e13	1.25300
$130$	1.07324e12	0.0195013
$131$	1.71888e13	0.297154	0.148577	−	0.988901i	$-0.452531\pi$
$131$	1.71888e13	0.297154	0.148577	+	0.988901i	$0.452531\pi$
$132$	3.26485e13	0.537196
$133$	−8.80687e13	−1.37970
$134$	2.29351e12	0.0342232
$135$	−1.65191e14	−2.34865
$136$	7.73479e12	0.104820
$137$	7.06802e13	0.913301	0.456650	−	0.889646i	$-0.349049\pi$
$137$	7.06802e13	0.913301	0.456650	+	0.889646i	$0.349049\pi$
$138$	1.20457e12	0.0148463
$139$	−6.09540e13	−0.716813	−0.358406	−	0.933566i	$-0.616680\pi$
$139$	−6.09540e13	−0.716813	−0.358406	+	0.933566i	$0.616680\pi$
$140$	−1.73455e14	−1.94694
$141$	−2.28141e14	−2.44500
$142$	1.13863e12	0.0116549
$143$	1.27874e13	0.125054
$144$	2.32607e14	2.17404
$145$	2.12154e13	0.189565
$146$	−9.66870e12	−0.0826180
$147$	4.56245e14	3.72937
$148$	−4.88568e13	−0.382141
$149$	3.73295e13	0.279474	0.139737	−	0.990189i	$-0.455374\pi$
$149$	3.73295e13	0.279474	0.139737	+	0.990189i	$0.455374\pi$
$150$	2.44114e12	0.0174985
$151$	−2.07798e14	−1.42657	−0.713284	−	0.700876i	$-0.752793\pi$
$151$	−2.07798e14	−1.42657	−0.713284	+	0.700876i	$0.752793\pi$
$152$	−1.01052e13	−0.0664601
$153$	−4.29376e14	−2.70610
$154$	3.71707e12	0.0224551
$155$	1.95919e14	1.13480
$156$	1.33025e14	0.738966
$157$	−9.79751e13	−0.522117	−0.261059	−	0.965323i	$-0.584072\pi$
$157$	−9.79751e13	−0.522117	−0.261059	+	0.965323i	$0.584072\pi$
$158$	−5.14206e12	−0.0262946
$159$	5.56147e14	2.72966
$160$	−2.98627e13	−0.140718
$161$	−7.62506e13	−0.345044
$162$	1.55184e13	0.0674527
$163$	5.61032e13	0.234298	0.117149	−	0.993114i	$-0.462625\pi$
$163$	5.61032e13	0.234298	0.117149	+	0.993114i	$0.462625\pi$
$164$	6.98180e13	0.280209
$165$	1.54794e14	0.597184
$166$	−1.10678e13	−0.0410544
$167$	−4.93523e14	−1.76056	−0.880279	−	0.474456i	$-0.842645\pi$
$167$	−4.93523e14	−1.76056	−0.880279	+	0.474456i	$0.842645\pi$
$168$	7.74055e13	0.265621
$169$	−2.50773e14	−0.827975
$170$	1.83197e13	0.0582105
$171$	5.60962e14	1.71577
$172$	−2.37955e14	−0.700744
$173$	4.28104e14	1.21409	0.607043	−	0.794669i	$-0.292356\pi$
$173$	4.28104e14	1.21409	0.607043	+	0.794669i	$0.292356\pi$
$174$	−4.72952e12	−0.0129195
$175$	−1.54526e14	−0.406683
$176$	−1.18247e14	−0.299888
$177$	−5.67801e14	−1.38794
$178$	2.74913e12	0.00647835
$179$	−6.06066e12	−0.0137713	−0.00688566	−	0.999976i	$-0.502192\pi$
$179$	−6.06066e12	−0.0137713	−0.00688566	+	0.999976i	$0.502192\pi$
$180$	1.10483e15	2.42117
$181$	−5.20330e14	−1.09994	−0.549969	−	0.835185i	$-0.685360\pi$
$181$	−5.20330e14	−1.09994	−0.549969	+	0.835185i	$0.685360\pi$
$182$	1.51451e13	0.0308893
$183$	−7.80374e14	−1.53593
$184$	−8.74915e12	−0.0166207
$185$	−2.31641e14	−0.424814
$186$	−4.36759e13	−0.0773406
$187$	2.18276e14	0.373281
$188$	8.27779e14	1.36738
$189$	−2.33111e15	−3.72016
$190$	−2.39340e13	−0.0369077
$191$	2.33586e14	0.348121	0.174061	−	0.984735i	$-0.444311\pi$
$191$	2.33586e14	0.348121	0.174061	+	0.984735i	$0.444311\pi$
$192$	−1.22566e15	−1.76568
$193$	1.30013e15	1.81078	0.905389	−	0.424584i	$-0.139580\pi$
$193$	1.30013e15	1.81078	0.905389	+	0.424584i	$0.139580\pi$
$194$	−9.15409e12	−0.0123283
$195$	6.30703e14	0.821486
$196$	−1.65543e15	−2.08567
$197$	1.44441e15	1.76060	0.880301	−	0.474415i	$-0.157340\pi$
$197$	1.44441e15	1.76060	0.880301	+	0.474415i	$0.157340\pi$
$198$	−2.36762e13	−0.0279247
$199$	1.99781e14	0.228039	0.114020	−	0.993479i	$-0.463627\pi$
$199$	1.99781e14	0.228039	0.114020	+	0.993479i	$0.463627\pi$
$200$	−1.77307e13	−0.0195898
$201$	1.34782e15	1.44164
$202$	−2.96732e13	−0.0307312
$203$	2.99383e14	0.300263
$204$	2.27069e15	2.20578
$205$	3.31023e14	0.311500
$206$	−4.29601e13	−0.0391678
$207$	4.85685e14	0.429089
$208$	−4.81796e14	−0.412526
$209$	−2.85169e14	−0.236674
$210$	1.83334e14	0.147508
$211$	4.66995e12	0.00364314	0.00182157	−	0.999998i	$-0.499420\pi$
$211$	4.66995e12	0.00364314	0.00182157	+	0.999998i	$0.499420\pi$
$212$	−2.01791e15	−1.52657
$213$	6.69130e14	0.490956
$214$	5.29613e13	0.0376937
$215$	−1.12820e15	−0.778996
$216$	−2.67476e14	−0.179199
$217$	2.76472e15	1.79748
$218$	−2.91716e13	−0.0184075
$219$	−5.68195e15	−3.48025
$220$	−5.61650e14	−0.333978
$221$	8.89360e14	0.513485
$222$	5.16394e13	0.0289526
$223$	2.03028e15	1.10554	0.552769	−	0.833335i	$-0.313571\pi$
$223$	2.03028e15	1.10554	0.552769	+	0.833335i	$0.313571\pi$
$224$	−4.21410e14	−0.222891
$225$	9.84271e14	0.505741
$226$	8.51031e13	0.0424855
$227$	1.79073e15	0.868684	0.434342	−	0.900748i	$-0.356981\pi$
$227$	1.79073e15	0.868684	0.434342	+	0.900748i	$0.356981\pi$
$228$	−2.96656e15	−1.39855
$229$	1.32298e15	0.606208	0.303104	−	0.952957i	$-0.401977\pi$
$229$	1.32298e15	0.606208	0.303104	+	0.952957i	$0.401977\pi$
$230$	−2.07222e13	−0.00923007
$231$	2.18439e15	0.945914
$232$	3.43518e13	0.0144636
$233$	−2.95208e15	−1.20869	−0.604344	−	0.796724i	$-0.706565\pi$
$233$	−2.95208e15	−1.20869	−0.604344	+	0.796724i	$0.706565\pi$
$234$	−9.64680e13	−0.0384132
$235$	3.92469e15	1.52007
$236$	2.06019e15	0.776211
$237$	−3.02180e15	−1.10765
$238$	2.58520e14	0.0922029
$239$	−3.89609e15	−1.35221	−0.676103	−	0.736807i	$-0.736332\pi$
$239$	−3.89609e15	−1.35221	−0.676103	+	0.736807i	$0.736332\pi$
$240$	−5.83222e15	−1.96998
$241$	−2.98562e15	−0.981576	−0.490788	−	0.871279i	$-0.663291\pi$
$241$	−2.98562e15	−0.981576	−0.490788	+	0.871279i	$0.663291\pi$
$242$	1.20360e13	0.00385195
$243$	2.32657e15	0.724896
$244$	2.83149e15	0.858976
$245$	−7.84876e15	−2.31858
$246$	−7.37946e13	−0.0212298
$247$	−1.16191e15	−0.325569
$248$	3.17230e14	0.0865841
$249$	−6.50416e15	−1.72940
$250$	1.39506e14	0.0361396
$251$	4.57193e15	1.15404	0.577020	−	0.816730i	$-0.304216\pi$
$251$	4.57193e15	1.15404	0.577020	+	0.816730i	$0.304216\pi$
$252$	1.55910e16	3.83504
$253$	−2.46901e14	−0.0591888
$254$	−9.61181e13	−0.0224588
$255$	1.07658e16	2.45209
$256$	4.42296e15	0.982095
$257$	3.93529e15	0.851944	0.425972	−	0.904736i	$-0.359932\pi$
$257$	3.93529e15	0.851944	0.425972	+	0.904736i	$0.359932\pi$
$258$	2.51508e14	0.0530913
$259$	−3.26882e15	−0.672888
$260$	−2.28843e15	−0.459420
$261$	−1.90695e15	−0.373401
$262$	6.59195e13	0.0125909
$263$	6.53606e14	0.121788	0.0608939	−	0.998144i	$-0.480605\pi$
$263$	6.53606e14	0.121788	0.0608939	+	0.998144i	$0.480605\pi$
$264$	2.50641e14	0.0455645
$265$	−9.56736e15	−1.69705
$266$	−3.37746e14	−0.0584601
$267$	1.61556e15	0.272898
$268$	−4.89038e15	−0.806244
$269$	8.75312e15	1.40855	0.704277	−	0.709926i	$-0.251272\pi$
$269$	8.75312e15	1.40855	0.704277	+	0.709926i	$0.251272\pi$
$270$	−6.33513e14	−0.0995156
$271$	6.97017e15	1.06891	0.534457	−	0.845196i	$-0.320516\pi$
$271$	6.97017e15	1.06891	0.534457	+	0.845196i	$0.320516\pi$
$272$	−8.22406e15	−1.23137
$273$	8.90022e15	1.30120
$274$	2.71060e14	0.0386979
$275$	−5.00361e14	−0.0697623
$276$	−2.56847e15	−0.349756
$277$	−5.76466e15	−0.766753	−0.383376	−	0.923592i	$-0.625239\pi$
$277$	−5.76466e15	−0.766753	−0.383376	+	0.923592i	$0.625239\pi$
$278$	−2.33760e14	−0.0303724
$279$	−1.76101e16	−2.23530
$280$	−1.33160e15	−0.165138
$281$	−7.68618e15	−0.931364	−0.465682	−	0.884952i	$-0.654191\pi$
$281$	−7.68618e15	−0.931364	−0.465682	+	0.884952i	$0.654191\pi$
$282$	−8.74925e14	−0.103598
$283$	1.54050e16	1.78258	0.891292	−	0.453430i	$-0.149800\pi$
$283$	1.54050e16	1.78258	0.891292	+	0.453430i	$0.149800\pi$
$284$	−2.42785e15	−0.274570
$285$	−1.40651e16	−1.55472
$286$	4.90402e13	0.00529874
$287$	4.67126e15	0.493403
$288$	2.68421e15	0.277182
$289$	5.27643e15	0.532726
$290$	8.13616e13	0.00803217
$291$	−5.37953e15	−0.519325
$292$	2.06162e16	1.94635
$293$	−8.82884e15	−0.815199	−0.407600	−	0.913161i	$-0.633634\pi$
$293$	−8.82884e15	−0.815199	−0.407600	+	0.913161i	$0.633634\pi$
$294$	1.74971e15	0.158019
$295$	9.76784e15	0.862890
$296$	−3.75071e14	−0.0324129
$297$	−7.54819e15	−0.638155
$298$	1.43160e14	0.0118417
$299$	−1.00599e15	−0.0814201
$300$	−5.20516e15	−0.412236
$301$	−1.59207e16	−1.23390
$302$	−7.96913e14	−0.0604458
$303$	−1.74378e16	−1.29454
$304$	1.07444e16	0.780735
$305$	1.34247e16	0.954897
$306$	−1.64667e15	−0.114661
$307$	1.50612e16	1.02674	0.513370	−	0.858168i	$-0.328397\pi$
$307$	1.50612e16	1.02674	0.513370	+	0.858168i	$0.328397\pi$
$308$	−7.92577e15	−0.529008
$309$	−2.52461e16	−1.64993
$310$	7.51353e14	0.0480832
$311$	7.78678e15	0.487995	0.243997	−	0.969776i	$-0.421541\pi$
$311$	7.78678e15	0.487995	0.243997	+	0.969776i	$0.421541\pi$
$312$	1.02123e15	0.0626785
$313$	−2.32642e16	−1.39846	−0.699230	−	0.714897i	$-0.746474\pi$
$313$	−2.32642e16	−1.39846	−0.699230	+	0.714897i	$0.746474\pi$
$314$	−3.75737e14	−0.0221229
$315$	7.39203e16	4.26329
$316$	1.09642e16	0.619458
$317$	−1.55912e16	−0.862966	−0.431483	−	0.902121i	$-0.642010\pi$
$317$	−1.55912e16	−0.862966	−0.431483	+	0.902121i	$0.642010\pi$
$318$	2.13284e15	0.115660
$319$	9.69409e14	0.0515071
$320$	2.10850e16	1.09774
$321$	3.11235e16	1.58783
$322$	−2.92423e14	−0.0146200
$323$	−1.98334e16	−0.971807
$324$	−3.30893e16	−1.58908
$325$	−2.03870e15	−0.0959649
$326$	2.15157e14	0.00992754
$327$	−1.71431e16	−0.775407
$328$	5.35990e14	0.0237671
$329$	5.53835e16	2.40773
$330$	5.93639e14	0.0253036
$331$	1.78827e16	0.747397	0.373699	−	0.927550i	$-0.378089\pi$
$331$	1.78827e16	0.747397	0.373699	+	0.927550i	$0.378089\pi$
$332$	2.35995e16	0.967175
$333$	2.08210e16	0.836787
$334$	−1.89268e15	−0.0745975
$335$	−2.31864e16	−0.896276
$336$	−8.23018e16	−3.12036
$337$	−4.37220e16	−1.62594	−0.812972	−	0.582302i	$-0.802152\pi$
$337$	−4.37220e16	−1.62594	−0.812972	+	0.582302i	$0.802152\pi$
$338$	−9.61722e14	−0.0350825
$339$	5.00120e16	1.78968
$340$	−3.90625e16	−1.37135
$341$	8.95224e15	0.308339
$342$	2.15131e15	0.0726997
$343$	−5.77493e16	−1.91485
$344$	−1.82677e15	−0.0594366
$345$	−1.21777e16	−0.388813
$346$	1.64179e15	0.0514426
$347$	3.57002e16	1.09781	0.548907	−	0.835883i	$-0.315044\pi$
$347$	3.57002e16	1.09781	0.548907	+	0.835883i	$0.315044\pi$
$348$	1.00846e16	0.304364
$349$	−2.43509e15	−0.0721356	−0.0360678	−	0.999349i	$-0.511483\pi$
$349$	−2.43509e15	−0.0721356	−0.0360678	+	0.999349i	$0.511483\pi$
$350$	−5.92613e14	−0.0172317
$351$	−3.07549e16	−0.877845
$352$	−1.36454e15	−0.0382347
$353$	−6.00460e16	−1.65177	−0.825883	−	0.563841i	$-0.809323\pi$
$353$	−6.00460e16	−1.65177	−0.825883	+	0.563841i	$0.809323\pi$
$354$	−2.17753e15	−0.0588090
$355$	−1.15110e16	−0.305231
$356$	−5.86186e15	−0.152620
$357$	1.51923e17	3.88401
$358$	−2.32428e13	−0.000583511 0
$359$	−3.11924e16	−0.769014	−0.384507	−	0.923122i	$-0.625629\pi$
$359$	−3.11924e16	−0.769014	−0.384507	+	0.923122i	$0.625629\pi$
$360$	8.48177e15	0.205362
$361$	−1.61415e16	−0.383838
$362$	−1.99548e15	−0.0466060
$363$	7.07310e15	0.162262
$364$	−3.22933e16	−0.727702
$365$	9.77462e16	2.16370
$366$	−2.99276e15	−0.0650796
$367$	−3.62115e16	−0.773602	−0.386801	−	0.922163i	$-0.626420\pi$
$367$	−3.62115e16	−0.773602	−0.386801	+	0.922163i	$0.626420\pi$
$368$	9.30257e15	0.195251
$369$	−2.97540e16	−0.613584
$370$	−8.88350e14	−0.0180000
$371$	−1.35010e17	−2.68805
$372$	9.31285e16	1.82202
$373$	6.17772e16	1.18774	0.593870	−	0.804561i	$-0.297599\pi$
$373$	6.17772e16	1.18774	0.593870	+	0.804561i	$0.297599\pi$
$374$	8.37095e14	0.0158165
$375$	8.19827e16	1.52237
$376$	6.35482e15	0.115980
$377$	3.94983e15	0.0708532
$378$	−8.93987e15	−0.157628
$379$	−1.42637e16	−0.247217	−0.123609	−	0.992331i	$-0.539447\pi$
$379$	−1.42637e16	−0.247217	−0.123609	+	0.992331i	$0.539447\pi$
$380$	5.10335e16	0.869486
$381$	−5.64851e16	−0.946067
$382$	8.95810e14	0.0147504
$383$	−9.56166e16	−1.54789	−0.773947	−	0.633250i	$-0.781721\pi$
$383$	−9.56166e16	−1.54789	−0.773947	+	0.633250i	$0.781721\pi$
$384$	−1.89210e16	−0.301156
$385$	−3.75779e16	−0.588081
$386$	4.98604e15	0.0767253
$387$	1.01408e17	1.53445
$388$	1.95189e16	0.290435
$389$	1.20563e17	1.76418	0.882088	−	0.471084i	$-0.156137\pi$
$389$	1.20563e17	1.76418	0.882088	+	0.471084i	$0.156137\pi$
$390$	2.41876e15	0.0348076
$391$	−1.71719e16	−0.243035
$392$	−1.27086e16	−0.176905
$393$	3.87385e16	0.530385
$394$	5.53937e15	0.0745993
$395$	5.19839e16	0.688633
$396$	5.04839e16	0.657862
$397$	−8.02804e16	−1.02913	−0.514566	−	0.857450i	$-0.672047\pi$
$397$	−8.02804e16	−1.02913	−0.514566	+	0.857450i	$0.672047\pi$
$398$	7.66166e14	0.00966235
$399$	−1.98481e17	−2.46261
$400$	1.88522e16	0.230130
$401$	1.64236e16	0.197256	0.0986281	−	0.995124i	$-0.468555\pi$
$401$	1.64236e16	0.197256	0.0986281	+	0.995124i	$0.468555\pi$
$402$	5.16891e15	0.0610843
$403$	3.64756e16	0.424150
$404$	6.32710e16	0.723979
$405$	−1.56884e17	−1.76653
$406$	1.14814e15	0.0127226
$407$	−1.05845e16	−0.115427
$408$	1.74320e16	0.187092
$409$	−1.68743e17	−1.78247	−0.891237	−	0.453537i	$-0.850162\pi$
$409$	−1.68743e17	−1.78247	−0.891237	+	0.453537i	$0.850162\pi$
$410$	1.26948e15	0.0131987
$411$	1.59292e17	1.63013
$412$	9.16023e16	0.922730
$413$	1.37840e17	1.36678
$414$	1.86262e15	0.0181811
$415$	1.11891e17	1.07518
$416$	−5.55977e15	−0.0525957
$417$	−1.37372e17	−1.27943
$418$	−1.09363e15	−0.0100282
$419$	−1.05138e17	−0.949221	−0.474610	−	0.880196i	$-0.657411\pi$
$419$	−1.05138e17	−0.949221	−0.474610	+	0.880196i	$0.657411\pi$
$420$	−3.90916e17	−3.47507
$421$	−5.81731e16	−0.509200	−0.254600	−	0.967046i	$-0.581944\pi$
$421$	−5.81731e16	−0.509200	−0.254600	+	0.967046i	$0.581944\pi$
$422$	1.79094e13	0.000154365 0
$423$	−3.52771e17	−2.99419
$424$	−1.54914e16	−0.129483
$425$	−3.47999e16	−0.286450
$426$	2.56613e15	0.0208026
$427$	1.89444e17	1.51252
$428$	−1.12928e17	−0.888005
$429$	2.88191e16	0.223207
$430$	−4.32667e15	−0.0330072
$431$	2.05073e17	1.54101	0.770505	−	0.637434i	$-0.220004\pi$
$431$	2.05073e17	1.54101	0.770505	+	0.637434i	$0.220004\pi$
$432$	2.84396e17	2.10513
$433$	2.98757e16	0.217845	0.108922	−	0.994050i	$-0.465260\pi$
$433$	2.98757e16	0.217845	0.108922	+	0.994050i	$0.465260\pi$
$434$	1.06028e16	0.0761617
$435$	4.78133e16	0.338352
$436$	6.22016e16	0.433650
$437$	2.24343e16	0.154093
$438$	−2.17904e16	−0.147463
$439$	−1.18048e17	−0.787119	−0.393559	−	0.919299i	$-0.628756\pi$
$439$	−1.18048e17	−0.787119	−0.393559	+	0.919299i	$0.628756\pi$
$440$	−4.31176e15	−0.0283278
$441$	7.05486e17	4.56707
$442$	3.41072e15	0.0217571
$443$	1.63238e17	1.02611	0.513057	−	0.858354i	$-0.328513\pi$
$443$	1.63238e17	1.02611	0.513057	+	0.858354i	$0.328513\pi$
$444$	−1.10109e17	−0.682076
$445$	−2.77924e16	−0.169663
$446$	7.78617e15	0.0468433
$447$	8.41297e16	0.498828
$448$	2.97543e17	1.73877
$449$	−3.14931e17	−1.81390	−0.906951	−	0.421237i	$-0.861596\pi$
$449$	−3.14931e17	−1.81390	−0.906951	+	0.421237i	$0.861596\pi$
$450$	3.77471e15	0.0214290
$451$	1.51257e16	0.0846382
$452$	−1.81462e17	−1.00089
$453$	−4.68317e17	−2.54625
$454$	6.86750e15	0.0368074
$455$	−1.53110e17	−0.808964
$456$	−2.27741e16	−0.118623
$457$	2.77435e17	1.42464	0.712321	−	0.701854i	$-0.247644\pi$
$457$	2.77435e17	1.42464	0.712321	+	0.701854i	$0.247644\pi$
$458$	5.07366e15	0.0256859
$459$	−5.24973e17	−2.62032
$460$	4.41852e16	0.217446
$461$	1.49245e17	0.724175	0.362087	−	0.932144i	$-0.382064\pi$
$461$	1.49245e17	0.724175	0.362087	+	0.932144i	$0.382064\pi$
$462$	8.37719e15	0.0400798
$463$	5.09086e16	0.240168	0.120084	−	0.992764i	$-0.461684\pi$
$463$	5.09086e16	0.240168	0.120084	+	0.992764i	$0.461684\pi$
$464$	−3.65247e16	−0.169910
$465$	4.41543e17	2.02549
$466$	−1.13213e16	−0.0512139
$467$	6.52033e16	0.290877	0.145439	−	0.989367i	$-0.453541\pi$
$467$	6.52033e16	0.290877	0.145439	+	0.989367i	$0.453541\pi$
$468$	2.05695e17	0.904953
$469$	−3.27197e17	−1.41966
$470$	1.50513e16	0.0644077
$471$	−2.20807e17	−0.931917
$472$	1.58160e16	0.0658376
$473$	−5.15515e16	−0.211662
$474$	−1.15887e16	−0.0469327
$475$	4.54646e16	0.181620
$476$	−5.51234e17	−2.17215
$477$	8.59962e17	3.34280
$478$	−1.49416e16	−0.0572950
$479$	2.62267e17	0.992116	0.496058	−	0.868289i	$-0.334780\pi$
$479$	2.62267e17	0.992116	0.496058	+	0.868289i	$0.334780\pi$
$480$	−6.73019e16	−0.251165
$481$	−4.31263e16	−0.158781
$482$	−1.14499e16	−0.0415908
$483$	−1.71847e17	−0.615863
$484$	−2.56638e16	−0.0907459
$485$	9.25436e16	0.322868
$486$	8.92247e15	0.0307149
$487$	−4.97636e17	−1.69034	−0.845169	−	0.534499i	$-0.820500\pi$
$487$	−4.97636e17	−1.69034	−0.845169	+	0.534499i	$0.820500\pi$
$488$	2.17372e16	0.0728576
$489$	1.26440e17	0.418194
$490$	−3.01002e16	−0.0982415
$491$	−4.37919e17	−1.41047	−0.705236	−	0.708973i	$-0.749159\pi$
$491$	−4.37919e17	−1.41047	−0.705236	+	0.708973i	$0.749159\pi$
$492$	1.57349e17	0.500141
$493$	6.74219e16	0.211493
$494$	−4.45596e15	−0.0137948
$495$	2.39356e17	0.731324
$496$	−3.37296e17	−1.01714
$497$	−1.62438e17	−0.483473
$498$	−2.49436e16	−0.0732772
$499$	−8.66285e16	−0.251193	−0.125596	−	0.992081i	$-0.540084\pi$
$499$	−8.66285e16	−0.251193	−0.125596	+	0.992081i	$0.540084\pi$
$500$	−2.97464e17	−0.851391
$501$	−1.11226e18	−3.14239
$502$	1.75335e16	0.0488983
$503$	2.03810e17	0.561090	0.280545	−	0.959841i	$-0.409485\pi$
$503$	2.03810e17	0.561090	0.280545	+	0.959841i	$0.409485\pi$
$504$	1.19691e17	0.325285
$505$	2.99982e17	0.804825
$506$	−9.46873e14	−0.00250792
$507$	−5.65169e17	−1.47784
$508$	2.04949e17	0.529093
$509$	2.52193e16	0.0642787	0.0321394	−	0.999483i	$-0.489768\pi$
$509$	2.52193e16	0.0642787	0.0321394	+	0.999483i	$0.489768\pi$
$510$	4.12873e16	0.103899
$511$	1.37935e18	3.42720
$512$	8.57382e16	0.210339
$513$	6.85856e17	1.66138
$514$	1.50919e16	0.0360981
$515$	4.34307e17	1.02577
$516$	−5.36281e17	−1.25075
$517$	1.79333e17	0.413021
$518$	−1.25360e16	−0.0285112
$519$	9.64821e17	2.16700
$520$	−1.75681e16	−0.0389676
$521$	−7.16618e16	−0.156979	−0.0784897	−	0.996915i	$-0.525010\pi$
$521$	−7.16618e16	−0.156979	−0.0784897	+	0.996915i	$0.525010\pi$
$522$	−7.31319e15	−0.0158215
$523$	3.31232e17	0.707736	0.353868	−	0.935295i	$-0.384866\pi$
$523$	3.31232e17	0.707736	0.353868	+	0.935295i	$0.384866\pi$
$524$	−1.40558e17	−0.296621
$525$	−3.48258e17	−0.725881
$526$	2.50660e15	0.00516033
$527$	6.22624e17	1.26607
$528$	−2.66495e17	−0.535265
$529$	−4.84613e17	−0.961463
$530$	−3.66911e16	−0.0719064
$531$	−8.77983e17	−1.69970
$532$	7.20164e17	1.37723
$533$	6.16290e16	0.116428
$534$	6.19573e15	0.0115631
$535$	−5.35415e17	−0.987168
$536$	−3.75432e16	−0.0683849
$537$	−1.36590e16	−0.0245802
$538$	3.35685e16	0.0596825
$539$	−3.58638e17	−0.629984
$540$	1.35082e18	2.34443
$541$	7.58711e17	1.30105	0.650525	−	0.759485i	$-0.274549\pi$
$541$	7.58711e17	1.30105	0.650525	+	0.759485i	$0.274549\pi$
$542$	2.67308e16	0.0452915
$543$	−1.17267e18	−1.96326
$544$	−9.49029e16	−0.156995
$545$	2.94912e17	0.482076
$546$	3.41326e16	0.0551337
$547$	−9.28087e17	−1.48140	−0.740698	−	0.671839i	$-0.765505\pi$
$547$	−9.28087e17	−1.48140	−0.740698	+	0.671839i	$0.765505\pi$
$548$	−5.77972e17	−0.911661
$549$	−1.20668e18	−1.88093
$550$	−1.91890e15	−0.00295593
$551$	−8.80840e16	−0.134095
$552$	−1.97180e16	−0.0296660
$553$	7.33575e17	1.09076
$554$	−2.21076e16	−0.0324885
$555$	−5.22051e17	−0.758243
$556$	4.98438e17	0.715526
$557$	8.65646e16	0.122823	0.0614117	−	0.998113i	$-0.480440\pi$
$557$	8.65646e16	0.122823	0.0614117	+	0.998113i	$0.480440\pi$
$558$	−6.75354e16	−0.0947129
$559$	−2.10045e17	−0.291163
$560$	1.41583e18	1.93995
$561$	4.91931e17	0.666263
$562$	−2.94767e16	−0.0394633
$563$	−1.38922e18	−1.83851	−0.919257	−	0.393659i	$-0.871209\pi$
$563$	−1.38922e18	−1.83851	−0.919257	+	0.393659i	$0.871209\pi$
$564$	1.86557e18	2.44061
$565$	−8.60354e17	−1.11266
$566$	5.90786e16	0.0755307
$567$	−2.21388e18	−2.79810
$568$	−1.86385e16	−0.0232888
$569$	1.22357e17	0.151147	0.0755733	−	0.997140i	$-0.475921\pi$
$569$	1.22357e17	0.151147	0.0755733	+	0.997140i	$0.475921\pi$
$570$	−5.39402e16	−0.0658758
$571$	6.24145e16	0.0753617	0.0376809	−	0.999290i	$-0.488003\pi$
$571$	6.24145e16	0.0753617	0.0376809	+	0.999290i	$0.488003\pi$
$572$	−1.04567e17	−0.124830
$573$	5.26435e17	0.621355
$574$	1.79144e16	0.0209062
$575$	3.93636e16	0.0454206
$576$	−1.89523e18	−2.16229
$577$	−6.89615e17	−0.777972	−0.388986	−	0.921244i	$-0.627175\pi$
$577$	−6.89615e17	−0.777972	−0.388986	+	0.921244i	$0.627175\pi$
$578$	2.02353e16	0.0225724
$579$	2.93012e18	3.23202
$580$	−1.73484e17	−0.189225
$581$	1.57895e18	1.70304
$582$	−2.06306e16	−0.0220046
$583$	−4.37167e17	−0.461107
$584$	1.58270e17	0.165088
$585$	9.75248e17	1.00601
$586$	−3.38588e16	−0.0345412
$587$	7.44429e16	0.0751061	0.0375531	−	0.999295i	$-0.488044\pi$
$587$	7.44429e16	0.0751061	0.0375531	+	0.999295i	$0.488044\pi$
$588$	−3.73085e18	−3.72268
$589$	−8.13432e17	−0.802735
$590$	3.74600e16	0.0365619
$591$	3.25529e18	3.14247
$592$	3.98796e17	0.380767
$593$	−2.43354e17	−0.229818	−0.114909	−	0.993376i	$-0.536658\pi$
$593$	−2.43354e17	−0.229818	−0.114909	+	0.993376i	$0.536658\pi$
$594$	−2.89475e16	−0.0270396
$595$	−2.61352e18	−2.41472
$596$	−3.05254e17	−0.278972
$597$	4.50248e17	0.407023
$598$	−3.85801e15	−0.00344989
$599$	1.24032e18	1.09713	0.548566	−	0.836107i	$-0.315174\pi$
$599$	1.24032e18	1.09713	0.548566	+	0.836107i	$0.315174\pi$
$600$	−3.99598e16	−0.0349655
$601$	−2.00492e18	−1.73545	−0.867726	−	0.497042i	$-0.834419\pi$
$601$	−2.00492e18	−1.73545	−0.867726	+	0.497042i	$0.834419\pi$
$602$	−6.10562e16	−0.0522820
$603$	2.08411e18	1.76546
$604$	1.69923e18	1.42401
$605$	−1.21678e17	−0.100879
$606$	−6.68746e16	−0.0548516
$607$	5.69411e17	0.462061	0.231030	−	0.972947i	$-0.425790\pi$
$607$	5.69411e17	0.462061	0.231030	+	0.972947i	$0.425790\pi$
$608$	1.23987e17	0.0995410
$609$	6.74721e17	0.535935
$610$	5.14842e16	0.0404604
$611$	7.30688e17	0.568151
$612$	3.51113e18	2.70124
$613$	6.06096e17	0.461369	0.230684	−	0.973029i	$-0.425904\pi$
$613$	6.06096e17	0.461369	0.230684	+	0.973029i	$0.425904\pi$
$614$	5.77601e16	0.0435045
$615$	7.46030e17	0.555991
$616$	−6.08458e16	−0.0448700
$617$	−5.56639e17	−0.406182	−0.203091	−	0.979160i	$-0.565099\pi$
$617$	−5.56639e17	−0.406182	−0.203091	+	0.979160i	$0.565099\pi$
$618$	−9.68196e16	−0.0699098
$619$	−1.13344e18	−0.809858	−0.404929	−	0.914348i	$-0.632704\pi$
$619$	−1.13344e18	−0.809858	−0.404929	+	0.914348i	$0.632704\pi$
$620$	−1.60208e18	−1.13276
$621$	5.93819e17	0.415488
$622$	2.98625e16	0.0206771
$623$	−3.92195e17	−0.268738
$624$	−1.08583e18	−0.736310
$625$	−1.75512e18	−1.17784
$626$	−8.92189e16	−0.0592548
$627$	−6.42687e17	−0.422436
$628$	8.01171e17	0.521180
$629$	−7.36148e17	−0.473954
$630$	2.83486e17	0.180642
$631$	−4.65714e17	−0.293716	−0.146858	−	0.989158i	$-0.546916\pi$
$631$	−4.65714e17	−0.293716	−0.146858	+	0.989158i	$0.546916\pi$
$632$	8.41719e16	0.0525419
$633$	1.05247e16	0.00650258
$634$	−5.97926e16	−0.0365652
$635$	9.71710e17	0.588176
$636$	−4.54777e18	−2.72476
$637$	−1.46126e18	−0.866605
$638$	3.71771e15	0.00218243
$639$	1.03467e18	0.601236
$640$	3.25497e17	0.187231
$641$	−2.74598e18	−1.56358	−0.781790	−	0.623542i	$-0.785693\pi$
$641$	−2.74598e18	−1.56358	−0.781790	+	0.623542i	$0.785693\pi$
$642$	1.19359e17	0.0672789
$643$	1.29604e18	0.723180	0.361590	−	0.932337i	$-0.382234\pi$
$643$	1.29604e18	0.723180	0.361590	+	0.932337i	$0.382234\pi$
$644$	6.23523e17	0.344425
$645$	−2.54263e18	−1.39042
$646$	−7.60615e16	−0.0411769
$647$	2.62052e18	1.40446	0.702231	−	0.711949i	$-0.252187\pi$
$647$	2.62052e18	1.40446	0.702231	+	0.711949i	$0.252187\pi$
$648$	−2.54025e17	−0.134784
$649$	4.46328e17	0.234457
$650$	−7.81849e15	−0.00406617
$651$	6.23087e18	3.20828
$652$	−4.58772e17	−0.233877
$653$	−3.45256e17	−0.174263	−0.0871317	−	0.996197i	$-0.527770\pi$
$653$	−3.45256e17	−0.174263	−0.0871317	+	0.996197i	$0.527770\pi$
$654$	−6.57444e16	−0.0328551
$655$	−6.66416e17	−0.329744
$656$	−5.69894e17	−0.279202
$657$	−8.78592e18	−4.26199
$658$	2.12397e17	0.102019
$659$	−7.47935e17	−0.355720	−0.177860	−	0.984056i	$-0.556917\pi$
$659$	−7.47935e17	−0.355720	−0.177860	+	0.984056i	$0.556917\pi$
$660$	−1.26580e18	−0.596112
$661$	−1.14572e18	−0.534280	−0.267140	−	0.963658i	$-0.586079\pi$
$661$	−1.14572e18	−0.534280	−0.267140	+	0.963658i	$0.586079\pi$
$662$	6.85807e16	0.0316683
$663$	2.00436e18	0.916510
$664$	1.81172e17	0.0820350
$665$	3.41446e18	1.53102
$666$	7.98493e16	0.0354559
$667$	−7.62637e16	−0.0335351
$668$	4.03568e18	1.75740
$669$	4.57565e18	1.97325
$670$	−8.89205e16	−0.0379766
$671$	6.13425e17	0.259457
$672$	−9.49736e17	−0.397835
$673$	−1.23213e16	−0.00511163	−0.00255581	−	0.999997i	$-0.500814\pi$
$673$	−1.23213e16	−0.00511163	−0.00255581	+	0.999997i	$0.500814\pi$
$674$	−1.67675e17	−0.0688937
$675$	1.20341e18	0.489711
$676$	2.05065e18	0.826489
$677$	−2.25359e18	−0.899597	−0.449798	−	0.893130i	$-0.648504\pi$
$677$	−2.25359e18	−0.899597	−0.449798	+	0.893130i	$0.648504\pi$
$678$	1.91798e17	0.0758316
$679$	1.30594e18	0.511409
$680$	−2.99881e17	−0.116316
$681$	4.03578e18	1.55050
$682$	3.43321e16	0.0130648
$683$	−3.77681e18	−1.42361	−0.711804	−	0.702378i	$-0.752122\pi$
$683$	−3.77681e18	−1.42361	−0.711804	+	0.702378i	$0.752122\pi$
$684$	−4.58715e18	−1.71269
$685$	−2.74030e18	−1.01347
$686$	−2.21470e17	−0.0811350
$687$	2.98161e18	1.08201
$688$	1.94232e18	0.698226
$689$	−1.78123e18	−0.634299
$690$	−4.67018e16	−0.0164746
$691$	−1.03094e18	−0.360267	−0.180134	−	0.983642i	$-0.557653\pi$
$691$	−1.03094e18	−0.360267	−0.180134	+	0.983642i	$0.557653\pi$
$692$	−3.50073e18	−1.21191
$693$	3.37769e18	1.15839
$694$	1.36911e17	0.0465160
$695$	2.36321e18	0.795428
$696$	7.74189e16	0.0258159
$697$	1.05198e18	0.347532
$698$	−9.33864e15	−0.00305649
$699$	−6.65312e18	−2.15736
$700$	1.26361e18	0.405952
$701$	−1.11946e17	−0.0356320	−0.0178160	−	0.999841i	$-0.505671\pi$
$701$	−1.11946e17	−0.0356320	−0.0178160	+	0.999841i	$0.505671\pi$
$702$	−1.17946e17	−0.0371956
$703$	9.61747e17	0.300505
$704$	9.63450e17	0.298268
$705$	8.84510e18	2.71315
$706$	−2.30278e17	−0.0699878
$707$	4.23322e18	1.27481
$708$	4.64308e18	1.38545
$709$	−2.98768e18	−0.883352	−0.441676	−	0.897175i	$-0.645616\pi$
$709$	−2.98768e18	−0.883352	−0.441676	+	0.897175i	$0.645616\pi$
$710$	−4.41450e16	−0.0129331
$711$	−4.67257e18	−1.35645
$712$	−4.50012e16	−0.0129451
$713$	−7.04276e17	−0.200752
$714$	5.82629e17	0.164571
$715$	−4.95774e17	−0.138770
$716$	4.95598e16	0.0137466
$717$	−8.78065e18	−2.41353
$718$	−1.19624e17	−0.0325843
$719$	6.52682e18	1.76183	0.880914	−	0.473276i	$-0.156929\pi$
$719$	6.52682e18	1.76183	0.880914	+	0.473276i	$0.156929\pi$
$720$	−9.01828e18	−2.41247
$721$	6.12876e18	1.62478
$722$	−6.19032e16	−0.0162638
$723$	−6.72872e18	−1.75200
$724$	4.25489e18	1.09796
$725$	−1.54553e17	−0.0395258
$726$	2.71255e16	0.00687528
$727$	5.33700e18	1.34067	0.670337	−	0.742056i	$-0.266149\pi$
$727$	5.33700e18	1.34067	0.670337	+	0.742056i	$0.266149\pi$
$728$	−2.47914e17	−0.0617231
$729$	−1.20799e18	−0.298081
$730$	3.74859e17	0.0916790
$731$	−3.58538e18	−0.869105
$732$	6.38135e18	1.53317
$733$	1.66611e18	0.396760	0.198380	−	0.980125i	$-0.436432\pi$
$733$	1.66611e18	0.396760	0.198380	+	0.980125i	$0.436432\pi$
$734$	−1.38872e17	−0.0327787
$735$	−1.76888e19	−4.13838
$736$	1.07349e17	0.0248938
$737$	−1.05947e18	−0.243529
$738$	−1.14108e17	−0.0259985
$739$	5.14227e17	0.116136	0.0580679	−	0.998313i	$-0.481506\pi$
$739$	5.14227e17	0.116136	0.0580679	+	0.998313i	$0.481506\pi$
$740$	1.89420e18	0.424052
$741$	−2.61861e18	−0.581102
$742$	−5.17769e17	−0.113897
$743$	−1.14447e18	−0.249562	−0.124781	−	0.992184i	$-0.539823\pi$
$743$	−1.14447e18	−0.249562	−0.124781	+	0.992184i	$0.539823\pi$
$744$	7.14943e17	0.154542
$745$	−1.44728e18	−0.310125
$746$	2.36917e17	0.0503263
$747$	−1.00573e19	−2.11786
$748$	−1.78491e18	−0.372611
$749$	−7.55555e18	−1.56363
$750$	3.14406e17	0.0645049
$751$	−4.38866e18	−0.892632	−0.446316	−	0.894875i	$-0.647264\pi$
$751$	−4.38866e18	−0.892632	−0.446316	+	0.894875i	$0.647264\pi$
$752$	−6.75679e18	−1.36246
$753$	1.03038e19	2.05982
$754$	1.51477e16	0.00300215
$755$	8.05643e18	1.58302
$756$	1.90622e19	3.71348
$757$	−3.71011e18	−0.716579	−0.358289	−	0.933611i	$-0.616640\pi$
$757$	−3.71011e18	−0.716579	−0.358289	+	0.933611i	$0.616640\pi$
$758$	−5.47018e16	−0.0104750
$759$	−5.56443e17	−0.105645
$760$	3.91782e17	0.0737490
$761$	−2.58860e18	−0.483130	−0.241565	−	0.970385i	$-0.577661\pi$
$761$	−2.58860e18	−0.483130	−0.241565	+	0.970385i	$0.577661\pi$
$762$	−2.16622e17	−0.0400862
$763$	4.16167e18	0.763587
$764$	−1.91010e18	−0.347496
$765$	1.66471e19	3.00289
$766$	−3.66693e17	−0.0655866
$767$	1.81855e18	0.322519
$768$	9.96807e18	1.75292
$769$	3.63680e18	0.634159	0.317080	−	0.948399i	$-0.397298\pi$
$769$	3.63680e18	0.634159	0.317080	+	0.948399i	$0.397298\pi$
$770$	−1.44112e17	−0.0249179
$771$	8.86899e18	1.52062
$772$	−1.06316e19	−1.80753
$773$	5.56600e18	0.938375	0.469187	−	0.883099i	$-0.344547\pi$
$773$	5.56600e18	0.938375	0.469187	+	0.883099i	$0.344547\pi$
$774$	3.88903e17	0.0650167
$775$	−1.42726e18	−0.236615
$776$	1.49846e17	0.0246345
$777$	−7.36697e18	−1.20102
$778$	4.62363e17	0.0747508
$779$	−1.37437e18	−0.220349
$780$	−5.15745e18	−0.820011
$781$	−5.25980e17	−0.0829349
$782$	−6.58546e16	−0.0102977
$783$	−2.33151e18	−0.361565
$784$	1.35125e19	2.07817
$785$	3.79853e18	0.579380
$786$	1.48563e17	0.0224732
$787$	−1.32018e18	−0.198060	−0.0990302	−	0.995084i	$-0.531574\pi$
$787$	−1.32018e18	−0.198060	−0.0990302	+	0.995084i	$0.531574\pi$
$788$	−1.18114e19	−1.75744
$789$	1.47304e18	0.217377
$790$	1.99360e17	0.0291784
$791$	−1.21410e19	−1.76240
$792$	3.87563e17	0.0557993
$793$	2.49938e18	0.356908
$794$	−3.07878e17	−0.0436059
$795$	−2.15620e19	−3.02903
$796$	−1.63367e18	−0.227630
$797$	−7.29034e18	−1.00756	−0.503778	−	0.863833i	$-0.668057\pi$
$797$	−7.29034e18	−1.00756	−0.503778	+	0.863833i	$0.668057\pi$
$798$	−7.61181e17	−0.104344
$799$	1.24725e19	1.69590
$800$	2.17549e17	0.0293408
$801$	2.49812e18	0.334197
$802$	6.29850e16	0.00835803
$803$	4.46638e18	0.587901
$804$	−1.10215e19	−1.43905
$805$	2.95626e18	0.382887
$806$	1.39885e17	0.0179719
$807$	1.97270e19	2.51410
$808$	4.85728e17	0.0614073
$809$	8.10470e18	1.01642	0.508208	−	0.861234i	$-0.330308\pi$
$809$	8.10470e18	1.01642	0.508208	+	0.861234i	$0.330308\pi$
$810$	−6.01654e17	−0.0748504
$811$	3.12605e18	0.385799	0.192899	−	0.981219i	$-0.438211\pi$
$811$	3.12605e18	0.385799	0.192899	+	0.981219i	$0.438211\pi$
$812$	−2.44814e18	−0.299724
$813$	1.57087e19	1.90789
$814$	−4.05919e16	−0.00489081
$815$	−2.17514e18	−0.259994
$816$	−1.85346e19	−2.19785
$817$	4.68415e18	0.551046
$818$	−6.47133e17	−0.0755261
$819$	1.37623e19	1.59347
$820$	−2.70687e18	−0.310941
$821$	−9.92532e18	−1.13113	−0.565567	−	0.824702i	$-0.691343\pi$
$821$	−9.92532e18	−1.13113	−0.565567	+	0.824702i	$0.691343\pi$
$822$	6.10891e17	0.0690712
$823$	−1.03980e19	−1.16641	−0.583207	−	0.812323i	$-0.698202\pi$
$823$	−1.03980e19	−1.16641	−0.583207	+	0.812323i	$0.698202\pi$
$824$	7.03227e17	0.0782652
$825$	−1.12767e18	−0.124517
$826$	5.28619e17	0.0579125
$827$	1.39518e19	1.51650	0.758252	−	0.651961i	$-0.226054\pi$
$827$	1.39518e19	1.51650	0.758252	+	0.651961i	$0.226054\pi$
$828$	−3.97159e18	−0.428319
$829$	−1.06229e19	−1.13668	−0.568342	−	0.822793i	$-0.692415\pi$
$829$	−1.06229e19	−1.13668	−0.568342	+	0.822793i	$0.692415\pi$
$830$	4.29103e17	0.0455569
$831$	−1.29919e19	−1.36856
$832$	3.92555e18	0.410297
$833$	−2.49431e19	−2.58677
$834$	−5.26827e17	−0.0542112
$835$	1.91341e19	1.95365
$836$	2.33191e18	0.236249
$837$	−2.15309e19	−2.16445
$838$	−4.03206e17	−0.0402199
$839$	−5.04110e18	−0.498968	−0.249484	−	0.968379i	$-0.580261\pi$
$839$	−5.04110e18	−0.498968	−0.249484	+	0.968379i	$0.580261\pi$
$840$	−3.00104e18	−0.294752
$841$	−9.96119e18	−0.970817
$842$	−2.23095e17	−0.0215756
$843$	−1.73224e19	−1.66237
$844$	−3.81875e16	−0.00363660
$845$	9.72257e18	0.918782
$846$	−1.35288e18	−0.126868
$847$	−1.71707e18	−0.159789
$848$	1.64713e19	1.52109
$849$	3.47184e19	3.18170
$850$	−1.33458e17	−0.0121373
$851$	8.32688e17	0.0751519
$852$	−5.47167e18	−0.490075
$853$	−1.41130e19	−1.25444	−0.627221	−	0.778841i	$-0.715808\pi$
$853$	−1.41130e19	−1.25444	−0.627221	+	0.778841i	$0.715808\pi$
$854$	7.26524e17	0.0640875
$855$	−2.17487e19	−1.90394
$856$	−8.66939e17	−0.0753198
$857$	1.67873e19	1.44745	0.723726	−	0.690087i	$-0.242428\pi$
$857$	1.67873e19	1.44745	0.723726	+	0.690087i	$0.242428\pi$
$858$	1.10522e17	0.00945763
$859$	2.23868e19	1.90124	0.950621	−	0.310354i	$-0.100448\pi$
$859$	2.23868e19	1.90124	0.950621	+	0.310354i	$0.100448\pi$
$860$	9.22560e18	0.777598
$861$	1.05277e19	0.880666
$862$	7.86459e17	0.0652949
$863$	2.33275e19	1.92220	0.961098	−	0.276208i	$-0.0890779\pi$
$863$	2.33275e19	1.92220	0.961098	+	0.276208i	$0.0890779\pi$
$864$	3.28183e18	0.268397
$865$	−1.65978e19	−1.34724
$866$	1.14574e17	0.00923041
$867$	1.18915e19	0.950854
$868$	−2.26079e19	−1.79425
$869$	2.37533e18	0.187110
$870$	1.83365e17	0.0143365
$871$	−4.31678e18	−0.334998
$872$	4.77519e17	0.0367819
$873$	−8.31829e18	−0.635977
$874$	8.60363e16	0.00652916
$875$	−1.99022e19	−1.49916
$876$	4.64629e19	3.47400
$877$	5.49414e18	0.407758	0.203879	−	0.978996i	$-0.434645\pi$
$877$	5.49414e18	0.407758	0.203879	+	0.978996i	$0.434645\pi$
$878$	−4.52719e17	−0.0333514
$879$	−1.98976e19	−1.45503
$880$	4.58450e18	0.332778
$881$	1.86879e19	1.34654	0.673268	−	0.739399i	$-0.264890\pi$
$881$	1.86879e19	1.34654	0.673268	+	0.739399i	$0.264890\pi$
$882$	2.70556e18	0.193513
$883$	−5.00501e18	−0.355353	−0.177677	−	0.984089i	$-0.556858\pi$
$883$	−5.00501e18	−0.355353	−0.177677	+	0.984089i	$0.556858\pi$
$884$	−7.27255e18	−0.512563
$885$	2.20139e19	1.54016
$886$	6.26021e17	0.0434780
$887$	2.09067e19	1.44139	0.720696	−	0.693251i	$-0.243822\pi$
$887$	2.09067e19	1.44139	0.720696	+	0.693251i	$0.243822\pi$
$888$	−8.45301e17	−0.0578531
$889$	1.37124e19	0.931646
$890$	−1.06585e17	−0.00718886
$891$	−7.16860e18	−0.479987
$892$	−1.66022e19	−1.10355
$893$	−1.62949e19	−1.07527
$894$	3.22640e17	0.0211361
$895$	2.34974e17	0.0152817
$896$	4.59328e18	0.296566
$897$	−2.26721e18	−0.145325
$898$	−1.20777e18	−0.0768577
$899$	2.76520e18	0.174698
$900$	−8.04867e18	−0.504833
$901$	−3.04048e19	−1.89335
$902$	5.80073e16	0.00358625
$903$	−3.58805e19	−2.20236
$904$	−1.39308e18	−0.0848947
$905$	2.01734e19	1.22057
$906$	−1.79601e18	−0.107889
$907$	−1.25421e19	−0.748036	−0.374018	−	0.927422i	$-0.622020\pi$
$907$	−1.25421e19	−0.748036	−0.374018	+	0.927422i	$0.622020\pi$
$908$	−1.46433e19	−0.867125
$909$	−2.69639e19	−1.58532
$910$	−5.87181e17	−0.0342770
$911$	2.52897e18	0.146580	0.0732899	−	0.997311i	$-0.476650\pi$
$911$	2.52897e18	0.146580	0.0732899	+	0.997311i	$0.476650\pi$
$912$	2.42147e19	1.39352
$913$	5.11269e18	0.292139
$914$	1.06397e18	0.0603642
$915$	3.02554e19	1.70438
$916$	−1.08184e19	−0.605120
$917$	−9.40419e18	−0.522301
$918$	−2.01329e18	−0.111027
$919$	1.55205e19	0.849877	0.424938	−	0.905222i	$-0.360296\pi$
$919$	1.55205e19	0.849877	0.424938	+	0.905222i	$0.360296\pi$
$920$	3.39208e17	0.0184436
$921$	3.39435e19	1.83261
$922$	5.72358e17	0.0306843
$923$	−2.14309e18	−0.114085
$924$	−1.78624e19	−0.944216
$925$	1.68749e18	0.0885770
$926$	1.95236e17	0.0101763
$927$	−3.90377e19	−2.02053
$928$	−4.21483e17	−0.0216630
$929$	−3.30335e19	−1.68598	−0.842990	−	0.537930i	$-0.819207\pi$
$929$	−3.30335e19	−1.68598	−0.842990	+	0.537930i	$0.819207\pi$
$930$	1.69333e18	0.0858228
$931$	3.25872e19	1.64011
$932$	2.41400e19	1.20652
$933$	1.75491e19	0.871014
$934$	2.50056e17	0.0123249
$935$	−8.46266e18	−0.414220
$936$	1.57911e18	0.0767574
$937$	2.01567e18	0.0973000	0.0486500	−	0.998816i	$-0.484508\pi$
$937$	2.01567e18	0.0973000	0.0486500	+	0.998816i	$0.484508\pi$
$938$	−1.25481e18	−0.0601532
$939$	−5.24307e19	−2.49609
$940$	−3.20933e19	−1.51734
$941$	−2.05315e19	−0.964026	−0.482013	−	0.876164i	$-0.660094\pi$
$941$	−2.05315e19	−0.964026	−0.482013	+	0.876164i	$0.660094\pi$
$942$	−8.46802e17	−0.0394867
$943$	−1.18994e18	−0.0551060
$944$	−1.68165e19	−0.773422
$945$	9.03781e19	4.12816
$946$	−1.97701e17	−0.00896845
$947$	−1.58977e19	−0.716240	−0.358120	−	0.933676i	$-0.616582\pi$
$947$	−1.58977e19	−0.716240	−0.358120	+	0.933676i	$0.616582\pi$
$948$	2.47102e19	1.10566
$949$	1.81981e19	0.808716
$950$	1.74358e17	0.00769552
$951$	−3.51380e19	−1.54029
$952$	−4.23180e18	−0.184240
$953$	1.19313e19	0.515920	0.257960	−	0.966156i	$-0.416950\pi$
$953$	1.19313e19	0.515920	0.257960	+	0.966156i	$0.416950\pi$
$954$	3.29798e18	0.141639
$955$	−9.05623e18	−0.386301
$956$	3.18595e19	1.34978
$957$	2.18476e18	0.0919342
$958$	1.00580e18	0.0420374
$959$	−3.86699e19	−1.60529
$960$	4.75194e19	1.95933
$961$	1.11834e18	0.0458006
$962$	−1.65391e17	−0.00672780
$963$	4.81258e19	1.94450
$964$	2.44143e19	0.979814
$965$	−5.04066e19	−2.00937
$966$	−6.59036e17	−0.0260950
$967$	−3.74553e19	−1.47313	−0.736565	−	0.676367i	$-0.763554\pi$
$967$	−3.74553e19	−1.47313	−0.736565	+	0.676367i	$0.763554\pi$
$968$	−1.97020e17	−0.00769699
$969$	−4.46986e19	−1.73456
$970$	3.54908e17	0.0136804
$971$	1.27351e18	0.0487614	0.0243807	−	0.999703i	$-0.492239\pi$
$971$	1.27351e18	0.0487614	0.0243807	+	0.999703i	$0.492239\pi$
$972$	−1.90251e19	−0.723595
$973$	3.33486e19	1.25992
$974$	−1.90845e18	−0.0716221
$975$	−4.59464e18	−0.171286
$976$	−2.31122e19	−0.855889
$977$	2.14743e19	0.789958	0.394979	−	0.918690i	$-0.370752\pi$
$977$	2.14743e19	0.789958	0.394979	+	0.918690i	$0.370752\pi$
$978$	4.84902e17	0.0177195
$979$	−1.26994e18	−0.0460993
$980$	6.41816e19	2.31441
$981$	−2.65082e19	−0.949579
$982$	−1.67943e18	−0.0597638
$983$	3.33860e19	1.18023	0.590116	−	0.807319i	$-0.299082\pi$
$983$	3.33860e19	1.18023	0.590116	+	0.807319i	$0.299082\pi$
$984$	1.20796e18	0.0424215
$985$	−5.60005e19	−1.95369
$986$	2.58565e17	0.00896127
$987$	1.24818e20	4.29751
$988$	9.50129e18	0.324984
$989$	4.05557e18	0.137809
$990$	9.17936e17	0.0309873
$991$	−2.88574e19	−0.967783	−0.483891	−	0.875128i	$-0.660777\pi$
$991$	−2.88574e19	−0.967783	−0.483891	+	0.875128i	$0.660777\pi$
$992$	−3.89229e18	−0.129682
$993$	4.03024e19	1.33402
$994$	−6.22956e17	−0.0204855
$995$	−7.74559e18	−0.253049
$996$	5.31864e19	1.72629
$997$	−3.03863e18	−0.0979850	−0.0489925	−	0.998799i	$-0.515601\pi$
$997$	−3.03863e18	−0.0979850	−0.0489925	+	0.998799i	$0.515601\pi$
$998$	−3.32223e17	−0.0106434
$999$	2.54567e19	0.810264

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.14.a.a.1.3	✓	5
3.2	odd	2		99.14.a.e.1.3		5
4.3	odd	2		176.14.a.e.1.1		5
11.10	odd	2		121.14.a.b.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.14.a.a.1.3	✓	5	1.1	even	1	trivial
99.14.a.e.1.3		5	3.2	odd	2
121.14.a.b.1.3		5	11.10	odd	2
176.14.a.e.1.1		5	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	11.a (trivial)

\(f(q)\)	\(=\)	\(q+3.83503 q^{2} +2253.71 q^{3} -8177.29 q^{4} -38770.4 q^{5} +8643.04 q^{6} -547112. q^{7} -62776.7 q^{8} +3.48488e6 q^{9} +O(q^{10})\)	\(q+3.83503 q^{2} +2253.71 q^{3} -8177.29 q^{4} -38770.4 q^{5} +8643.04 q^{6} -547112. q^{7} -62776.7 q^{8} +3.48488e6 q^{9} -148686. q^{10} -1.77156e6 q^{11} -1.84292e7 q^{12} -7.21817e6 q^{13} -2.09819e6 q^{14} -8.73772e7 q^{15} +6.67476e7 q^{16} -1.23211e8 q^{17} +1.33646e7 q^{18} +1.60970e8 q^{19} +3.17037e8 q^{20} -1.23303e9 q^{21} -6.79399e6 q^{22} +1.39369e8 q^{23} -1.41480e8 q^{24} +2.82441e8 q^{25} -2.76819e7 q^{26} +4.26076e9 q^{27} +4.47389e9 q^{28} -5.47206e8 q^{29} -3.35094e8 q^{30} -5.05330e9 q^{31} +7.70246e8 q^{32} -3.99258e9 q^{33} -4.72519e8 q^{34} +2.12117e10 q^{35} -2.84969e10 q^{36} +5.97469e9 q^{37} +6.17326e8 q^{38} -1.62677e10 q^{39} +2.43388e9 q^{40} -8.53804e9 q^{41} -4.72870e9 q^{42} +2.90995e10 q^{43} +1.44866e10 q^{44} -1.35110e11 q^{45} +5.34485e8 q^{46} -1.01229e11 q^{47} +1.50430e11 q^{48} +2.02442e11 q^{49} +1.08317e9 q^{50} -2.77682e11 q^{51} +5.90251e10 q^{52} +2.46770e11 q^{53} +1.63401e10 q^{54} +6.86841e10 q^{55} +3.43459e10 q^{56} +3.62780e11 q^{57} -2.09855e9 q^{58} -2.51941e11 q^{59} +7.14509e11 q^{60} -3.46262e11 q^{61} -1.93796e10 q^{62} -1.90662e12 q^{63} -5.43843e11 q^{64} +2.79851e11 q^{65} -1.53117e10 q^{66} +5.98044e11 q^{67} +1.00753e12 q^{68} +3.14098e11 q^{69} +8.13476e10 q^{70} +2.96902e11 q^{71} -2.18769e11 q^{72} -2.52115e12 q^{73} +2.29131e10 q^{74} +6.36539e11 q^{75} -1.31630e12 q^{76} +9.69241e11 q^{77} -6.23869e10 q^{78} -1.34081e12 q^{79} -2.58783e12 q^{80} +4.04649e12 q^{81} -3.27436e10 q^{82} -2.88598e12 q^{83} +1.00828e13 q^{84} +4.77695e12 q^{85} +1.11597e11 q^{86} -1.23324e12 q^{87} +1.11213e11 q^{88} +7.16846e11 q^{89} -5.18151e11 q^{90} +3.94914e12 q^{91} -1.13966e12 q^{92} -1.13887e13 q^{93} -3.88216e11 q^{94} -6.24089e12 q^{95} +1.73591e12 q^{96} -2.38697e12 q^{97} +7.76371e11 q^{98} -6.17367e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 64 q^{2} + 480 q^{3} - 2400 q^{4} - 454 q^{5} + 79548 q^{6} - 313920 q^{7} - 255168 q^{8} + 1321749 q^{9}+O(q^{10}) \) 5 * q - 64 * q^2 + 480 * q^3 - 2400 * q^4 - 454 * q^5 + 79548 * q^6 - 313920 * q^7 - 255168 * q^8 + 1321749 * q^9	\( 5 q - 64 q^{2} + 480 q^{3} - 2400 q^{4} - 454 q^{5} + 79548 q^{6} - 313920 q^{7} - 255168 q^{8} + 1321749 q^{9} - 3535724 q^{10} - 8857805 q^{11} - 29768880 q^{12} - 36339498 q^{13} - 64558312 q^{14} - 162945300 q^{15} - 128942592 q^{16} - 309078454 q^{17} - 302859828 q^{18} - 147232948 q^{19} - 62530256 q^{20} - 859909128 q^{21} + 113379904 q^{22} + 677905444 q^{23} + 755940096 q^{24} + 1540265631 q^{25} + 1643160872 q^{26} + 5029885620 q^{27} + 6948937120 q^{28} + 2368825878 q^{29} + 7601916540 q^{30} - 83363076 q^{31} + 10024391680 q^{32} - 850349280 q^{33} + 7463914000 q^{34} + 591040520 q^{35} - 15037063632 q^{36} - 32935650382 q^{37} - 25107474384 q^{38} - 54599307000 q^{39} - 27853580928 q^{40} - 70273827286 q^{41} - 18264520200 q^{42} - 54501240436 q^{43} + 4251746400 q^{44} - 118334367738 q^{45} - 9391823524 q^{46} - 45017434472 q^{47} + 236995825920 q^{48} + 77867671053 q^{49} + 252640243516 q^{50} - 14973171168 q^{51} + 370262207008 q^{52} + 242684257518 q^{53} + 386371416420 q^{54} + 804288694 q^{55} + 508508098560 q^{56} - 78232137120 q^{57} + 338805253176 q^{58} - 384712501184 q^{59} + 607819216080 q^{60} - 795317095690 q^{61} + 567054167132 q^{62} - 1777323941640 q^{63} - 502608203776 q^{64} - 1104664950268 q^{65} - 140924134428 q^{66} - 1005952134296 q^{67} + 9188915584 q^{68} - 2334490276524 q^{69} - 50031562280 q^{70} - 1427050574148 q^{71} + 714622284864 q^{72} - 4111049036406 q^{73} + 2579474987436 q^{74} - 584109490620 q^{75} + 1028633987648 q^{76} + 556128429120 q^{77} + 4554998846160 q^{78} - 3666957194024 q^{79} + 1569918525184 q^{80} + 4090930814781 q^{81} + 4301648616232 q^{82} + 2718055516116 q^{83} + 8581863439392 q^{84} + 1506197091796 q^{85} + 6558172582872 q^{86} + 3556682104680 q^{87} + 452045677248 q^{88} + 7963494884214 q^{89} - 4671771563808 q^{90} - 604892444560 q^{91} + 6414213002576 q^{92} + 361484424660 q^{93} - 9832269652768 q^{94} - 5225122758984 q^{95} - 12178790559744 q^{96} - 13542719272730 q^{97} - 8557591646352 q^{98} - 2341558980189 q^{99}+O(q^{100}) \) 5 * q - 64 * q^2 + 480 * q^3 - 2400 * q^4 - 454 * q^5 + 79548 * q^6 - 313920 * q^7 - 255168 * q^8 + 1321749 * q^9 - 3535724 * q^10 - 8857805 * q^11 - 29768880 * q^12 - 36339498 * q^13 - 64558312 * q^14 - 162945300 * q^15 - 128942592 * q^16 - 309078454 * q^17 - 302859828 * q^18 - 147232948 * q^19 - 62530256 * q^20 - 859909128 * q^21 + 113379904 * q^22 + 677905444 * q^23 + 755940096 * q^24 + 1540265631 * q^25 + 1643160872 * q^26 + 5029885620 * q^27 + 6948937120 * q^28 + 2368825878 * q^29 + 7601916540 * q^30 - 83363076 * q^31 + 10024391680 * q^32 - 850349280 * q^33 + 7463914000 * q^34 + 591040520 * q^35 - 15037063632 * q^36 - 32935650382 * q^37 - 25107474384 * q^38 - 54599307000 * q^39 - 27853580928 * q^40 - 70273827286 * q^41 - 18264520200 * q^42 - 54501240436 * q^43 + 4251746400 * q^44 - 118334367738 * q^45 - 9391823524 * q^46 - 45017434472 * q^47 + 236995825920 * q^48 + 77867671053 * q^49 + 252640243516 * q^50 - 14973171168 * q^51 + 370262207008 * q^52 + 242684257518 * q^53 + 386371416420 * q^54 + 804288694 * q^55 + 508508098560 * q^56 - 78232137120 * q^57 + 338805253176 * q^58 - 384712501184 * q^59 + 607819216080 * q^60 - 795317095690 * q^61 + 567054167132 * q^62 - 1777323941640 * q^63 - 502608203776 * q^64 - 1104664950268 * q^65 - 140924134428 * q^66 - 1005952134296 * q^67 + 9188915584 * q^68 - 2334490276524 * q^69 - 50031562280 * q^70 - 1427050574148 * q^71 + 714622284864 * q^72 - 4111049036406 * q^73 + 2579474987436 * q^74 - 584109490620 * q^75 + 1028633987648 * q^76 + 556128429120 * q^77 + 4554998846160 * q^78 - 3666957194024 * q^79 + 1569918525184 * q^80 + 4090930814781 * q^81 + 4301648616232 * q^82 + 2718055516116 * q^83 + 8581863439392 * q^84 + 1506197091796 * q^85 + 6558172582872 * q^86 + 3556682104680 * q^87 + 452045677248 * q^88 + 7963494884214 * q^89 - 4671771563808 * q^90 - 604892444560 * q^91 + 6414213002576 * q^92 + 361484424660 * q^93 - 9832269652768 * q^94 - 5225122758984 * q^95 - 12178790559744 * q^96 - 13542719272730 * q^97 - 8557591646352 * q^98 - 2341558980189 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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