LMFDB - Embedded newform 29.10.a.a.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,10,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, 10, names="a")

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

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 10 $
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:	$14.9360392488$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 2901 x^{7} - 4592 x^{6} + 2830996 x^{5} + 7409504 x^{4} - 1038861888 x^{3} - 2974719488 x^{2} + \cdots + 456378417152 $ x^9 - 2901x^7 - 4592x^6 + 2830996x^5 + 7409504x^4 - 1038861888x^3 - 2974719488x^2 + 115773751296*x + 456378417152
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{2}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-30.2923$ 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)

$f(q)$	$=$	$q+30.2923 q^{2} -209.271 q^{3} +405.624 q^{4} +2211.65 q^{5} -6339.31 q^{6} -7440.75 q^{7} -3222.36 q^{8} +24111.4 q^{9} +O(q^{10})$	\(q+30.2923 q^{2} -209.271 q^{3} +405.624 q^{4} +2211.65 q^{5} -6339.31 q^{6} -7440.75 q^{7} -3222.36 q^{8} +24111.4 q^{9} +66995.9 q^{10} -58617.9 q^{11} -84885.5 q^{12} -87085.1 q^{13} -225398. q^{14} -462834. q^{15} -305293. q^{16} +265141. q^{17} +730391. q^{18} -1.07169e6 q^{19} +897098. q^{20} +1.55714e6 q^{21} -1.77567e6 q^{22} +90729.0 q^{23} +674347. q^{24} +2.93826e6 q^{25} -2.63801e6 q^{26} -926742. q^{27} -3.01815e6 q^{28} -707281. q^{29} -1.40203e7 q^{30} +5.97407e6 q^{31} -7.59817e6 q^{32} +1.22670e7 q^{33} +8.03173e6 q^{34} -1.64563e7 q^{35} +9.78019e6 q^{36} -7.79633e6 q^{37} -3.24639e7 q^{38} +1.82244e7 q^{39} -7.12673e6 q^{40} +2.38054e7 q^{41} +4.71692e7 q^{42} +1.27778e7 q^{43} -2.37768e7 q^{44} +5.33260e7 q^{45} +2.74839e6 q^{46} +3.56871e6 q^{47} +6.38889e7 q^{48} +1.50112e7 q^{49} +8.90066e7 q^{50} -5.54864e7 q^{51} -3.53239e7 q^{52} -1.08582e8 q^{53} -2.80732e7 q^{54} -1.29642e8 q^{55} +2.39768e7 q^{56} +2.24273e8 q^{57} -2.14252e7 q^{58} -1.52685e8 q^{59} -1.87737e8 q^{60} +5.18800e7 q^{61} +1.80968e8 q^{62} -1.79407e8 q^{63} -7.38564e7 q^{64} -1.92602e8 q^{65} +3.71597e8 q^{66} +1.59257e8 q^{67} +1.07548e8 q^{68} -1.89870e7 q^{69} -4.98500e8 q^{70} +1.43665e8 q^{71} -7.76957e7 q^{72} +4.78152e7 q^{73} -2.36169e8 q^{74} -6.14892e8 q^{75} -4.34702e8 q^{76} +4.36161e8 q^{77} +5.52060e8 q^{78} +1.51075e8 q^{79} -6.75199e8 q^{80} -2.80645e8 q^{81} +7.21121e8 q^{82} -2.73363e8 q^{83} +6.31612e8 q^{84} +5.86398e8 q^{85} +3.87069e8 q^{86} +1.48014e8 q^{87} +1.88888e8 q^{88} -6.68887e8 q^{89} +1.61537e9 q^{90} +6.47979e8 q^{91} +3.68019e7 q^{92} -1.25020e9 q^{93} +1.08104e8 q^{94} -2.37019e9 q^{95} +1.59008e9 q^{96} -6.85222e8 q^{97} +4.54724e8 q^{98} -1.41336e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 244 q^{3} + 1194 q^{4} - 738 q^{5} - 2330 q^{6} - 7128 q^{7} - 13776 q^{8} + 33017 q^{9}+O(q^{10}) $ 9 * q - 244 * q^3 + 1194 * q^4 - 738 * q^5 - 2330 * q^6 - 7128 * q^7 - 13776 * q^8 + 33017 * q^9	\( 9 q - 244 q^{3} + 1194 q^{4} - 738 q^{5} - 2330 q^{6} - 7128 q^{7} - 13776 q^{8} + 33017 q^{9} + 37812 q^{10} - 59512 q^{11} - 127348 q^{12} - 165758 q^{13} - 406080 q^{14} - 693178 q^{15} - 1044958 q^{16} - 394814 q^{17} - 1676576 q^{18} - 2256606 q^{19} - 2237578 q^{20} - 1750168 q^{21} - 5311718 q^{22} - 1699500 q^{23} - 4446318 q^{24} - 983481 q^{25} - 4264740 q^{26} - 6987958 q^{27} - 8491636 q^{28} - 6365529 q^{29} - 16907854 q^{30} - 11929632 q^{31} - 1346192 q^{32} + 1750252 q^{33} + 8655764 q^{34} - 3275324 q^{35} + 29848532 q^{36} + 14454898 q^{37} + 14709736 q^{38} + 41155042 q^{39} + 45167060 q^{40} + 52495202 q^{41} + 103102340 q^{42} + 21819888 q^{43} + 70837004 q^{44} + 61248326 q^{45} + 20628012 q^{46} + 44968948 q^{47} + 122982540 q^{48} - 26826775 q^{49} + 155997680 q^{50} - 28882428 q^{51} + 29562122 q^{52} - 111394302 q^{53} + 70575802 q^{54} - 173560742 q^{55} + 67419136 q^{56} + 85769252 q^{57} - 236142720 q^{59} - 47991000 q^{60} - 241129054 q^{61} + 261343278 q^{62} - 328513060 q^{63} - 333112958 q^{64} - 625660884 q^{65} + 223958776 q^{66} - 672046492 q^{67} - 63179948 q^{68} - 705827600 q^{69} - 366389016 q^{70} - 475841956 q^{71} - 18937608 q^{72} - 424813822 q^{73} - 532689728 q^{74} - 913708498 q^{75} - 552478056 q^{76} - 182224776 q^{77} + 928127886 q^{78} - 170801148 q^{79} + 562655678 q^{80} - 914585851 q^{81} + 1468192652 q^{82} - 468898296 q^{83} + 952386216 q^{84} - 271552972 q^{85} + 1462277802 q^{86} + 172576564 q^{87} + 1176890862 q^{88} - 676036598 q^{89} + 4017858752 q^{90} + 9763884 q^{91} + 2724990708 q^{92} - 858755220 q^{93} + 2429128614 q^{94} + 69331732 q^{95} + 3111862050 q^{96} + 170708754 q^{97} + 3278517600 q^{98} + 305494078 q^{99}+O(q^{100}) \) 9 * q - 244 * q^3 + 1194 * q^4 - 738 * q^5 - 2330 * q^6 - 7128 * q^7 - 13776 * q^8 + 33017 * q^9 + 37812 * q^10 - 59512 * q^11 - 127348 * q^12 - 165758 * q^13 - 406080 * q^14 - 693178 * q^15 - 1044958 * q^16 - 394814 * q^17 - 1676576 * q^18 - 2256606 * q^19 - 2237578 * q^20 - 1750168 * q^21 - 5311718 * q^22 - 1699500 * q^23 - 4446318 * q^24 - 983481 * q^25 - 4264740 * q^26 - 6987958 * q^27 - 8491636 * q^28 - 6365529 * q^29 - 16907854 * q^30 - 11929632 * q^31 - 1346192 * q^32 + 1750252 * q^33 + 8655764 * q^34 - 3275324 * q^35 + 29848532 * q^36 + 14454898 * q^37 + 14709736 * q^38 + 41155042 * q^39 + 45167060 * q^40 + 52495202 * q^41 + 103102340 * q^42 + 21819888 * q^43 + 70837004 * q^44 + 61248326 * q^45 + 20628012 * q^46 + 44968948 * q^47 + 122982540 * q^48 - 26826775 * q^49 + 155997680 * q^50 - 28882428 * q^51 + 29562122 * q^52 - 111394302 * q^53 + 70575802 * q^54 - 173560742 * q^55 + 67419136 * q^56 + 85769252 * q^57 - 236142720 * q^59 - 47991000 * q^60 - 241129054 * q^61 + 261343278 * q^62 - 328513060 * q^63 - 333112958 * q^64 - 625660884 * q^65 + 223958776 * q^66 - 672046492 * q^67 - 63179948 * q^68 - 705827600 * q^69 - 366389016 * q^70 - 475841956 * q^71 - 18937608 * q^72 - 424813822 * q^73 - 532689728 * q^74 - 913708498 * q^75 - 552478056 * q^76 - 182224776 * q^77 + 928127886 * q^78 - 170801148 * q^79 + 562655678 * q^80 - 914585851 * q^81 + 1468192652 * q^82 - 468898296 * q^83 + 952386216 * q^84 - 271552972 * q^85 + 1462277802 * q^86 + 172576564 * q^87 + 1176890862 * q^88 - 676036598 * q^89 + 4017858752 * q^90 + 9763884 * q^91 + 2724990708 * q^92 - 858755220 * q^93 + 2429128614 * q^94 + 69331732 * q^95 + 3111862050 * q^96 + 170708754 * q^97 + 3278517600 * q^98 + 305494078 * 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 $

$2$	30.2923	1.33874	0.669372	−	0.742927i	$-0.266563\pi$
$2$	30.2923	1.33874	0.669372	+	0.742927i	$0.266563\pi$
$3$	−209.271	−1.49164	−0.745820	−	0.666148i	$-0.767942\pi$
$3$	−209.271	−1.49164	−0.745820	+	0.666148i	$0.767942\pi$
$4$	405.624	0.792235
$5$	2211.65	1.58253	0.791263	−	0.611476i	$-0.209424\pi$
$5$	2211.65	1.58253	0.791263	+	0.611476i	$0.209424\pi$
$6$	−6339.31	−1.99692
$7$	−7440.75	−1.17132	−0.585660	−	0.810557i	$-0.699165\pi$
$7$	−7440.75	−1.17132	−0.585660	+	0.810557i	$0.699165\pi$
$8$	−3222.36	−0.278144
$9$	24111.4	1.22499
$10$	66995.9	2.11860
$11$	−58617.9	−1.20715	−0.603577	−	0.797304i	$-0.706259\pi$
$11$	−58617.9	−1.20715	−0.603577	+	0.797304i	$0.706259\pi$
$12$	−84885.5	−1.18173
$13$	−87085.1	−0.845666	−0.422833	−	0.906208i	$-0.638964\pi$
$13$	−87085.1	−0.845666	−0.422833	+	0.906208i	$0.638964\pi$
$14$	−225398.	−1.56810
$15$	−462834.	−2.36056
$16$	−305293.	−1.16460
$17$	265141.	0.769940	0.384970	−	0.922929i	$-0.374212\pi$
$17$	265141.	0.769940	0.384970	+	0.922929i	$0.374212\pi$
$18$	730391.	1.63994
$19$	−1.07169e6	−1.88659	−0.943293	−	0.331963i	$-0.892289\pi$
$19$	−1.07169e6	−1.88659	−0.943293	+	0.331963i	$0.892289\pi$
$20$	897098.	1.25373
$21$	1.55714e6	1.74719
$22$	−1.77567e6	−1.61607
$23$	90729.0	0.0676038	0.0338019	−	0.999429i	$-0.489238\pi$
$23$	90729.0	0.0676038	0.0338019	+	0.999429i	$0.489238\pi$
$24$	674347.	0.414890
$25$	2.93826e6	1.50439
$26$	−2.63801e6	−1.13213
$27$	−926742.	−0.335600
$28$	−3.01815e6	−0.927961
$29$	−707281.	−0.185695
$29$	−707281.	−0.185695
$30$	−1.40203e7	−3.16018
$31$	5.97407e6	1.16183	0.580915	−	0.813964i	$-0.302695\pi$
$31$	5.97407e6	1.16183	0.580915	+	0.813964i	$0.302695\pi$
$32$	−7.59817e6	−1.28096
$33$	1.22670e7	1.80064
$34$	8.03173e6	1.03075
$35$	−1.64563e7	−1.85364
$36$	9.78019e6	0.970478
$37$	−7.79633e6	−0.683884	−0.341942	−	0.939721i	$-0.611085\pi$
$37$	−7.79633e6	−0.683884	−0.341942	+	0.939721i	$0.611085\pi$
$38$	−3.24639e7	−2.52565
$39$	1.82244e7	1.26143
$40$	−7.12673e6	−0.440170
$41$	2.38054e7	1.31567	0.657837	−	0.753160i	$-0.271471\pi$
$41$	2.38054e7	1.31567	0.657837	+	0.753160i	$0.271471\pi$
$42$	4.71692e7	2.33904
$43$	1.27778e7	0.569965	0.284983	−	0.958533i	$-0.408012\pi$
$43$	1.27778e7	0.569965	0.284983	+	0.958533i	$0.408012\pi$
$44$	−2.37768e7	−0.956351
$45$	5.33260e7	1.93857
$46$	2.74839e6	0.0905041
$47$	3.56871e6	0.106677	0.0533385	−	0.998576i	$-0.483014\pi$
$47$	3.56871e6	0.106677	0.0533385	+	0.998576i	$0.483014\pi$
$48$	6.38889e7	1.73716
$49$	1.50112e7	0.371992
$50$	8.90066e7	2.01399
$51$	−5.54864e7	−1.14847
$52$	−3.53239e7	−0.669967
$53$	−1.08582e8	−1.89024	−0.945118	−	0.326728i	$-0.894054\pi$
$53$	−1.08582e8	−1.89024	−0.945118	+	0.326728i	$0.894054\pi$
$54$	−2.80732e7	−0.449283
$55$	−1.29642e8	−1.91035
$56$	2.39768e7	0.325795
$57$	2.24273e8	2.81410
$58$	−2.14252e7	−0.248599
$59$	−1.52685e8	−1.64045	−0.820223	−	0.572043i	$-0.806151\pi$
$59$	−1.52685e8	−1.64045	−0.820223	+	0.572043i	$0.806151\pi$
$60$	−1.87737e8	−1.87012
$61$	5.18800e7	0.479751	0.239876	−	0.970804i	$-0.422893\pi$
$61$	5.18800e7	0.479751	0.239876	+	0.970804i	$0.422893\pi$
$62$	1.80968e8	1.55539
$63$	−1.79407e8	−1.43485
$64$	−7.38564e7	−0.550273
$65$	−1.92602e8	−1.33829
$66$	3.71597e8	2.41060
$67$	1.59257e8	0.965521	0.482761	−	0.875752i	$-0.339634\pi$
$67$	1.59257e8	0.965521	0.482761	+	0.875752i	$0.339634\pi$
$68$	1.07548e8	0.609973
$69$	−1.89870e7	−0.100840
$70$	−4.98500e8	−2.48156
$71$	1.43665e8	0.670946	0.335473	−	0.942050i	$-0.391104\pi$
$71$	1.43665e8	0.670946	0.335473	+	0.942050i	$0.391104\pi$
$72$	−7.76957e7	−0.340723
$73$	4.78152e7	0.197066	0.0985332	−	0.995134i	$-0.468585\pi$
$73$	4.78152e7	0.197066	0.0985332	+	0.995134i	$0.468585\pi$
$74$	−2.36169e8	−0.915546
$75$	−6.14892e8	−2.24400
$76$	−4.34702e8	−1.49462
$77$	4.36161e8	1.41397
$78$	5.52060e8	1.68873
$79$	1.51075e8	0.436387	0.218193	−	0.975906i	$-0.429984\pi$
$79$	1.51075e8	0.436387	0.218193	+	0.975906i	$0.429984\pi$
$80$	−6.75199e8	−1.84301
$81$	−2.80645e8	−0.724393
$82$	7.21121e8	1.76135
$83$	−2.73363e8	−0.632250	−0.316125	−	0.948718i	$-0.602382\pi$
$83$	−2.73363e8	−0.632250	−0.316125	+	0.948718i	$0.602382\pi$
$84$	6.31612e8	1.38418
$85$	5.86398e8	1.21845
$86$	3.87069e8	0.763037
$87$	1.48014e8	0.276990
$88$	1.88888e8	0.335763
$89$	−6.68887e8	−1.13005	−0.565025	−	0.825074i	$-0.691133\pi$
$89$	−6.68887e8	−1.13005	−0.565025	+	0.825074i	$0.691133\pi$
$90$	1.61537e9	2.59525
$91$	6.47979e8	0.990546
$92$	3.68019e7	0.0535581
$93$	−1.25020e9	−1.73303
$94$	1.08104e8	0.142813
$95$	−2.37019e9	−2.98557
$96$	1.59008e9	1.91072
$97$	−6.85222e8	−0.785885	−0.392942	−	0.919563i	$-0.628543\pi$
$97$	−6.85222e8	−0.785885	−0.392942	+	0.919563i	$0.628543\pi$
$98$	4.54724e8	0.498002
$99$	−1.41336e9	−1.47875
$100$	1.19183e9	1.19183
$101$	1.38644e9	1.32573	0.662864	−	0.748740i	$-0.269341\pi$
$101$	1.38644e9	1.32573	0.662864	+	0.748740i	$0.269341\pi$
$102$	−1.68081e9	−1.53751
$103$	−1.15136e7	−0.0100796	−0.00503979	−	0.999987i	$-0.501604\pi$
$103$	−1.15136e7	−0.0100796	−0.00503979	+	0.999987i	$0.501604\pi$
$104$	2.80620e8	0.235217
$105$	3.44383e9	2.76497
$106$	−3.28920e9	−2.53054
$107$	5.07640e8	0.374394	0.187197	−	0.982322i	$-0.440060\pi$
$107$	5.07640e8	0.374394	0.187197	+	0.982322i	$0.440060\pi$
$108$	−3.75909e8	−0.265874
$109$	1.45185e8	0.0985150	0.0492575	−	0.998786i	$-0.484315\pi$
$109$	1.45185e8	0.0985150	0.0492575	+	0.998786i	$0.484315\pi$
$110$	−3.92716e9	−2.55747
$111$	1.63155e9	1.02011
$112$	2.27161e9	1.36412
$113$	−1.74742e9	−1.00819	−0.504097	−	0.863647i	$-0.668174\pi$
$113$	−1.74742e9	−1.00819	−0.504097	+	0.863647i	$0.668174\pi$
$114$	6.79375e9	3.76736
$115$	2.00661e8	0.106985
$116$	−2.86890e8	−0.147114
$117$	−2.09975e9	−1.03593
$118$	−4.62518e9	−2.19614
$119$	−1.97285e9	−0.901846
$120$	1.49142e9	0.656574
$121$	1.07811e9	0.457223
$122$	1.57157e9	0.642264
$123$	−4.98179e9	−1.96251
$124$	2.42323e9	0.920442
$125$	2.17876e9	0.798206
$126$	−5.43466e9	−1.92090
$127$	4.30232e9	1.46753	0.733763	−	0.679406i	$-0.237762\pi$
$127$	4.30232e9	1.46753	0.733763	+	0.679406i	$0.237762\pi$
$128$	1.65298e9	0.544281
$129$	−2.67403e9	−0.850182
$130$	−5.83435e9	−1.79163
$131$	−4.32842e9	−1.28413	−0.642064	−	0.766651i	$-0.721922\pi$
$131$	−4.32842e9	−1.28413	−0.642064	+	0.766651i	$0.721922\pi$
$132$	4.97581e9	1.42653
$133$	7.97415e9	2.20980
$134$	4.82426e9	1.29259
$135$	−2.04963e9	−0.531096
$136$	−8.54380e8	−0.214154
$137$	1.72285e9	0.417835	0.208918	−	0.977933i	$-0.433006\pi$
$137$	1.72285e9	0.417835	0.208918	+	0.977933i	$0.433006\pi$
$138$	−5.75159e8	−0.135000
$139$	−6.18663e9	−1.40568	−0.702841	−	0.711347i	$-0.748086\pi$
$139$	−6.18663e9	−1.40568	−0.702841	+	0.711347i	$0.748086\pi$
$140$	−6.67509e9	−1.46852
$141$	−7.46828e8	−0.159123
$142$	4.35193e9	0.898224
$143$	5.10475e9	1.02085
$144$	−7.36104e9	−1.42662
$145$	−1.56426e9	−0.293868
$146$	1.44843e9	0.263822
$147$	−3.14141e9	−0.554877
$148$	−3.16238e9	−0.541797
$149$	−1.14663e10	−1.90583	−0.952916	−	0.303235i	$-0.901933\pi$
$149$	−1.14663e10	−1.90583	−0.952916	+	0.303235i	$0.901933\pi$
$150$	−1.86265e10	−3.00415
$151$	−8.80916e8	−0.137892	−0.0689458	−	0.997620i	$-0.521964\pi$
$151$	−8.80916e8	−0.137892	−0.0689458	+	0.997620i	$0.521964\pi$
$152$	3.45336e9	0.524742
$153$	6.39293e9	0.943166
$154$	1.32123e10	1.89294
$155$	1.32125e10	1.83862
$156$	7.39227e9	0.999348
$157$	−3.57364e8	−0.0469421	−0.0234711	−	0.999725i	$-0.507472\pi$
$157$	−3.57364e8	−0.0469421	−0.0234711	+	0.999725i	$0.507472\pi$
$158$	4.57642e9	0.584210
$159$	2.27231e10	2.81955
$160$	−1.68045e10	−2.02714
$161$	−6.75092e8	−0.0791857
$162$	−8.50138e9	−0.969777
$163$	1.26763e10	1.40653	0.703266	−	0.710927i	$-0.251724\pi$
$163$	1.26763e10	1.40653	0.703266	+	0.710927i	$0.251724\pi$
$164$	9.65606e9	1.04232
$165$	2.71303e10	2.84956
$166$	−8.28081e9	−0.846421
$167$	1.37720e9	0.137017	0.0685085	−	0.997651i	$-0.478176\pi$
$167$	1.37720e9	0.137017	0.0685085	+	0.997651i	$0.478176\pi$
$168$	−5.01765e9	−0.485969
$169$	−3.02068e9	−0.284849
$170$	1.77634e10	1.63119
$171$	−2.58399e10	−2.31104
$172$	5.18299e9	0.451546
$173$	−4.16391e9	−0.353422	−0.176711	−	0.984263i	$-0.556546\pi$
$173$	−4.16391e9	−0.353422	−0.176711	+	0.984263i	$0.556546\pi$
$174$	4.48367e9	0.370819
$175$	−2.18628e10	−1.76212
$176$	1.78956e10	1.40585
$177$	3.19526e10	2.44695
$178$	−2.02621e10	−1.51285
$179$	2.48475e10	1.80902	0.904511	−	0.426451i	$-0.140236\pi$
$179$	2.48475e10	1.80902	0.904511	+	0.426451i	$0.140236\pi$
$180$	2.16303e10	1.53581
$181$	−1.57169e10	−1.08846	−0.544230	−	0.838936i	$-0.683178\pi$
$181$	−1.57169e10	−1.08846	−0.544230	+	0.838936i	$0.683178\pi$
$182$	1.96288e10	1.32609
$183$	−1.08570e10	−0.715615
$184$	−2.92362e8	−0.0188036
$185$	−1.72427e10	−1.08226
$186$	−3.78714e10	−2.32008
$187$	−1.55420e10	−0.929436
$188$	1.44755e9	0.0845132
$189$	6.89566e9	0.393095
$190$	−7.17986e10	−3.99691
$191$	−2.38332e10	−1.29578	−0.647890	−	0.761734i	$-0.724348\pi$
$191$	−2.38332e10	−1.29578	−0.647890	+	0.761734i	$0.724348\pi$
$192$	1.54560e10	0.820808
$193$	−1.77863e10	−0.922737	−0.461368	−	0.887209i	$-0.652641\pi$
$193$	−1.77863e10	−0.922737	−0.461368	+	0.887209i	$0.652641\pi$
$194$	−2.07570e10	−1.05210
$195$	4.03060e10	1.99624
$196$	6.08891e9	0.294705
$197$	−9.37236e9	−0.443354	−0.221677	−	0.975120i	$-0.571153\pi$
$197$	−9.37236e9	−0.443354	−0.221677	+	0.975120i	$0.571153\pi$
$198$	−4.28140e10	−1.97967
$199$	−3.61961e10	−1.63615	−0.818076	−	0.575110i	$-0.804959\pi$
$199$	−3.61961e10	−1.63615	−0.818076	+	0.575110i	$0.804959\pi$
$200$	−9.46812e9	−0.418436
$201$	−3.33279e10	−1.44021
$202$	4.19984e10	1.77481
$203$	5.26270e9	0.217509
$204$	−2.25066e10	−0.909860
$205$	5.26492e10	2.08209
$206$	−3.48772e8	−0.0134940
$207$	2.18761e9	0.0828138
$208$	2.65864e10	0.984861
$209$	6.28200e10	2.27740
$210$	1.04322e11	3.70159
$211$	−3.83364e8	−0.0133150	−0.00665748	−	0.999978i	$-0.502119\pi$
$211$	−3.83364e8	−0.0133150	−0.00665748	+	0.999978i	$0.502119\pi$
$212$	−4.40435e10	−1.49751
$213$	−3.00649e10	−1.00081
$214$	1.53776e10	0.501218
$215$	2.82600e10	0.901984
$216$	2.98630e9	0.0933451
$217$	−4.44516e10	−1.36087
$218$	4.39799e9	0.131886
$219$	−1.00063e10	−0.293952
$220$	−5.25860e10	−1.51345
$221$	−2.30898e10	−0.651112
$222$	4.94234e10	1.36566
$223$	2.46364e10	0.667121	0.333561	−	0.942729i	$-0.391750\pi$
$223$	2.46364e10	0.667121	0.333561	+	0.942729i	$0.391750\pi$
$224$	5.65361e10	1.50041
$225$	7.08456e10	1.84286
$226$	−5.29333e10	−1.34971
$227$	−6.02091e10	−1.50503	−0.752516	−	0.658573i	$-0.771160\pi$
$227$	−6.02091e10	−1.50503	−0.752516	+	0.658573i	$0.771160\pi$
$228$	9.09706e10	2.22943
$229$	−1.98904e10	−0.477951	−0.238976	−	0.971026i	$-0.576812\pi$
$229$	−1.98904e10	−0.477951	−0.238976	+	0.971026i	$0.576812\pi$
$230$	6.07847e9	0.143225
$231$	−9.12760e10	−2.10913
$232$	2.27911e9	0.0516500
$233$	5.23732e10	1.16415	0.582073	−	0.813137i	$-0.302242\pi$
$233$	5.23732e10	1.16415	0.582073	+	0.813137i	$0.302242\pi$
$234$	−6.36062e10	−1.38685
$235$	7.89272e9	0.168819
$236$	−6.19327e10	−1.29962
$237$	−3.16157e10	−0.650931
$238$	−5.97621e10	−1.20734
$239$	8.19040e8	0.0162373	0.00811867	−	0.999967i	$-0.497416\pi$
$239$	8.19040e8	0.0162373	0.00811867	+	0.999967i	$0.497416\pi$
$240$	1.41300e11	2.74910
$241$	−4.06753e10	−0.776702	−0.388351	−	0.921512i	$-0.626955\pi$
$241$	−4.06753e10	−0.776702	−0.388351	+	0.921512i	$0.626955\pi$
$242$	3.26584e10	0.612105
$243$	7.69719e10	1.41613
$244$	2.10438e10	0.380076
$245$	3.31995e10	0.588687
$246$	−1.50910e11	−2.62730
$247$	9.33279e10	1.59542
$248$	−1.92506e10	−0.323156
$249$	5.72071e10	0.943089
$250$	6.59998e10	1.06859
$251$	5.50603e10	0.875603	0.437801	−	0.899072i	$-0.355757\pi$
$251$	5.50603e10	0.875603	0.437801	+	0.899072i	$0.355757\pi$
$252$	−7.27720e10	−1.13674
$253$	−5.31834e9	−0.0816082
$254$	1.30327e11	1.96464
$255$	−1.22716e11	−1.81749
$256$	8.78871e10	1.27893
$257$	2.09734e9	0.0299895	0.0149948	−	0.999888i	$-0.495227\pi$
$257$	2.09734e9	0.0299895	0.0149948	+	0.999888i	$0.495227\pi$
$258$	−8.10025e10	−1.13818
$259$	5.80106e10	0.801048
$260$	−7.81239e10	−1.06024
$261$	−1.70536e10	−0.227474
$262$	−1.31118e11	−1.71912
$263$	1.83650e10	0.236696	0.118348	−	0.992972i	$-0.462240\pi$
$263$	1.83650e10	0.236696	0.118348	+	0.992972i	$0.462240\pi$
$264$	−3.95288e10	−0.500837
$265$	−2.40145e11	−2.99135
$266$	2.41556e11	2.95835
$267$	1.39979e11	1.68563
$268$	6.45985e10	0.764920
$269$	3.05798e10	0.356082	0.178041	−	0.984023i	$-0.443024\pi$
$269$	3.05798e10	0.356082	0.178041	+	0.984023i	$0.443024\pi$
$270$	−6.20880e10	−0.711001
$271$	−3.46475e10	−0.390220	−0.195110	−	0.980781i	$-0.562506\pi$
$271$	−3.46475e10	−0.390220	−0.195110	+	0.980781i	$0.562506\pi$
$272$	−8.09455e10	−0.896670
$273$	−1.35603e11	−1.47754
$274$	5.21891e10	0.559374
$275$	−1.72234e11	−1.81603
$276$	−7.70158e9	−0.0798893
$277$	−1.19720e10	−0.122182	−0.0610912	−	0.998132i	$-0.519458\pi$
$277$	−1.19720e10	−0.122182	−0.0610912	+	0.998132i	$0.519458\pi$
$278$	−1.87407e11	−1.88185
$279$	1.44043e11	1.42323
$280$	5.30282e10	0.515580
$281$	7.68408e10	0.735213	0.367607	−	0.929981i	$-0.380177\pi$
$281$	7.68408e10	0.735213	0.367607	+	0.929981i	$0.380177\pi$
$282$	−2.26231e10	−0.213026
$283$	7.54873e10	0.699576	0.349788	−	0.936829i	$-0.386254\pi$
$283$	7.54873e10	0.699576	0.349788	+	0.936829i	$0.386254\pi$
$284$	5.82739e10	0.531547
$285$	4.96013e11	4.45339
$286$	1.54635e11	1.36666
$287$	−1.77130e11	−1.54108
$288$	−1.83203e11	−1.56915
$289$	−4.82882e10	−0.407193
$290$	−4.73849e10	−0.393414
$291$	1.43397e11	1.17226
$292$	1.93950e10	0.156123
$293$	−9.74301e10	−0.772305	−0.386152	−	0.922435i	$-0.626196\pi$
$293$	−9.74301e10	−0.772305	−0.386152	+	0.922435i	$0.626196\pi$
$294$	−9.51607e10	−0.742839
$295$	−3.37685e11	−2.59605
$296$	2.51226e10	0.190218
$297$	5.43237e10	0.405121
$298$	−3.47340e11	−2.55142
$299$	−7.90115e9	−0.0571702
$300$	−2.49415e11	−1.77778
$301$	−9.50765e10	−0.667612
$302$	−2.66850e10	−0.184602
$303$	−2.90142e11	−1.97751
$304$	3.27178e11	2.19711
$305$	1.14740e11	0.759218
$306$	1.93657e11	1.26266
$307$	8.62128e10	0.553923	0.276961	−	0.960881i	$-0.410673\pi$
$307$	8.62128e10	0.553923	0.276961	+	0.960881i	$0.410673\pi$
$308$	1.76918e11	1.12019
$309$	2.40946e9	0.0150351
$310$	4.00238e11	2.46145
$311$	−8.90604e10	−0.539837	−0.269919	−	0.962883i	$-0.586997\pi$
$311$	−8.90604e10	−0.539837	−0.269919	+	0.962883i	$0.586997\pi$
$312$	−5.87256e10	−0.350858
$313$	−1.19988e11	−0.706627	−0.353313	−	0.935505i	$-0.614945\pi$
$313$	−1.19988e11	−0.706627	−0.353313	+	0.935505i	$0.614945\pi$
$314$	−1.08254e10	−0.0628435
$315$	−3.96785e11	−2.27069
$316$	6.12798e10	0.345721
$317$	2.93546e11	1.63271	0.816355	−	0.577550i	$-0.195991\pi$
$317$	2.93546e11	1.63271	0.816355	+	0.577550i	$0.195991\pi$
$318$	6.88334e11	3.77466
$319$	4.14593e10	0.224163
$320$	−1.63344e11	−0.870821
$321$	−1.06235e11	−0.558461
$322$	−2.04501e10	−0.106009
$323$	−2.84148e11	−1.45256
$324$	−1.13836e11	−0.573890
$325$	−2.55878e11	−1.27221
$326$	3.83996e11	1.88299
$327$	−3.03830e10	−0.146949
$328$	−7.67097e10	−0.365947
$329$	−2.65539e10	−0.124953
$330$	8.21841e11	3.81483
$331$	−2.97594e11	−1.36269	−0.681346	−	0.731961i	$-0.738605\pi$
$331$	−2.97594e11	−1.36269	−0.681346	+	0.731961i	$0.738605\pi$
$332$	−1.10883e11	−0.500891
$333$	−1.87981e11	−0.837750
$334$	4.17187e10	0.183431
$335$	3.52220e11	1.52796
$336$	−4.75382e11	−2.03477
$337$	1.57237e11	0.664078	0.332039	−	0.943266i	$-0.392263\pi$
$337$	1.57237e11	0.664078	0.332039	+	0.943266i	$0.392263\pi$
$338$	−9.15034e10	−0.381340
$339$	3.65684e11	1.50386
$340$	2.37857e11	0.965298
$341$	−3.50187e11	−1.40251
$342$	−7.82750e11	−3.09389
$343$	1.88567e11	0.735599
$344$	−4.11747e10	−0.158532
$345$	−4.19925e10	−0.159583
$346$	−1.26134e11	−0.473142
$347$	3.50291e10	0.129702	0.0648510	−	0.997895i	$-0.479343\pi$
$347$	3.50291e10	0.129702	0.0648510	+	0.997895i	$0.479343\pi$
$348$	6.00379e10	0.219442
$349$	2.19825e11	0.793162	0.396581	−	0.918000i	$-0.370197\pi$
$349$	2.19825e11	0.793162	0.396581	+	0.918000i	$0.370197\pi$
$350$	−6.62276e11	−2.35903
$351$	8.07055e10	0.283806
$352$	4.45389e11	1.54631
$353$	2.13099e11	0.730459	0.365230	−	0.930917i	$-0.380990\pi$
$353$	2.13099e11	0.730459	0.365230	+	0.930917i	$0.380990\pi$
$354$	9.67917e11	3.27585
$355$	3.17735e11	1.06179
$356$	−2.71317e11	−0.895265
$357$	4.12860e11	1.34523
$358$	7.52688e11	2.42182
$359$	−4.43984e11	−1.41072	−0.705362	−	0.708847i	$-0.749215\pi$
$359$	−4.43984e11	−1.41072	−0.705362	+	0.708847i	$0.749215\pi$
$360$	−1.71836e11	−0.539202
$361$	8.25823e11	2.55920
$362$	−4.76101e11	−1.45717
$363$	−2.25617e11	−0.682012
$364$	2.62836e11	0.784746
$365$	1.05750e11	0.311863
$366$	−3.28883e11	−0.958026
$367$	−4.36744e11	−1.25669	−0.628347	−	0.777933i	$-0.716268\pi$
$367$	−4.36744e11	−1.25669	−0.628347	+	0.777933i	$0.716268\pi$
$368$	−2.76989e10	−0.0787312
$369$	5.73983e11	1.61168
$370$	−5.22322e11	−1.44888
$371$	8.07931e11	2.21407
$372$	−5.07112e11	−1.37297
$373$	1.94323e11	0.519798	0.259899	−	0.965636i	$-0.416311\pi$
$373$	1.94323e11	0.519798	0.259899	+	0.965636i	$0.416311\pi$
$374$	−4.70803e11	−1.24428
$375$	−4.55952e11	−1.19064
$376$	−1.14997e10	−0.0296715
$377$	6.15937e10	0.157036
$378$	2.08886e11	0.526254
$379$	−7.33461e10	−0.182600	−0.0912999	−	0.995823i	$-0.529102\pi$
$379$	−7.33461e10	−0.182600	−0.0912999	+	0.995823i	$0.529102\pi$
$380$	−9.61408e11	−2.36527
$381$	−9.00351e11	−2.18902
$382$	−7.21961e11	−1.73472
$383$	−2.45549e11	−0.583102	−0.291551	−	0.956555i	$-0.594171\pi$
$383$	−2.45549e11	−0.583102	−0.291551	+	0.956555i	$0.594171\pi$
$384$	−3.45921e11	−0.811871
$385$	9.64635e11	2.23764
$386$	−5.38788e11	−1.23531
$387$	3.08091e11	0.698200
$388$	−2.77943e11	−0.622605
$389$	−1.40940e11	−0.312077	−0.156038	−	0.987751i	$-0.549872\pi$
$389$	−1.40940e11	−0.312077	−0.156038	+	0.987751i	$0.549872\pi$
$390$	1.22096e12	2.67246
$391$	2.40560e10	0.0520508
$392$	−4.83715e10	−0.103467
$393$	9.05814e11	1.91546
$394$	−2.83910e11	−0.593538
$395$	3.34125e11	0.690593
$396$	−5.73294e11	−1.17152
$397$	−4.91707e11	−0.993457	−0.496729	−	0.867906i	$-0.665466\pi$
$397$	−4.91707e11	−0.993457	−0.496729	+	0.867906i	$0.665466\pi$
$398$	−1.09647e12	−2.19039
$399$	−1.66876e12	−3.29622
$400$	−8.97028e11	−1.75201
$401$	8.76151e11	1.69211	0.846057	−	0.533093i	$-0.178970\pi$
$401$	8.76151e11	1.69211	0.846057	+	0.533093i	$0.178970\pi$
$402$	−1.00958e12	−1.92807
$403$	−5.20252e11	−0.982520
$404$	5.62373e11	1.05029
$405$	−6.20687e11	−1.14637
$406$	1.59419e11	0.291189
$407$	4.57005e11	0.825554
$408$	1.78797e11	0.319440
$409$	2.79101e11	0.493180	0.246590	−	0.969120i	$-0.420690\pi$
$409$	2.79101e11	0.493180	0.246590	+	0.969120i	$0.420690\pi$
$410$	1.59487e12	2.78738
$411$	−3.60543e11	−0.623260
$412$	−4.67018e9	−0.00798539
$413$	1.13609e12	1.92149
$414$	6.62677e10	0.110866
$415$	−6.04583e11	−1.00055
$416$	6.61688e11	1.08326
$417$	1.29468e12	2.09677
$418$	1.90296e12	3.04886
$419$	−7.04129e11	−1.11606	−0.558032	−	0.829819i	$-0.688443\pi$
$419$	−7.04129e11	−1.11606	−0.558032	+	0.829819i	$0.688443\pi$
$420$	1.39690e12	2.19051
$421$	2.16565e10	0.0335984	0.0167992	−	0.999859i	$-0.494652\pi$
$421$	2.16565e10	0.0335984	0.0167992	+	0.999859i	$0.494652\pi$
$422$	−1.16130e10	−0.0178253
$423$	8.60466e10	0.130678
$424$	3.49890e11	0.525757
$425$	7.79052e11	1.15829
$426$	−9.10734e11	−1.33983
$427$	−3.86026e11	−0.561942
$428$	2.05911e11	0.296608
$429$	−1.06828e12	−1.52274
$430$	8.56061e11	1.20753
$431$	−1.17090e12	−1.63445	−0.817224	−	0.576320i	$-0.804488\pi$
$431$	−1.17090e12	−1.63445	−0.817224	+	0.576320i	$0.804488\pi$
$432$	2.82928e11	0.390839
$433$	1.75572e10	0.0240026	0.0120013	−	0.999928i	$-0.496180\pi$
$433$	1.75572e10	0.0240026	0.0120013	+	0.999928i	$0.496180\pi$
$434$	−1.34654e12	−1.82186
$435$	3.27354e11	0.438344
$436$	5.88906e10	0.0780471
$437$	−9.72330e10	−0.127540
$438$	−3.03115e11	−0.393527
$439$	−3.20997e11	−0.412487	−0.206244	−	0.978501i	$-0.566124\pi$
$439$	−3.20997e11	−0.412487	−0.206244	+	0.978501i	$0.566124\pi$
$440$	4.17754e11	0.531353
$441$	3.61942e11	0.455685
$442$	−6.99444e11	−0.871672
$443$	5.09771e11	0.628867	0.314433	−	0.949280i	$-0.398186\pi$
$443$	5.09771e11	0.628867	0.314433	+	0.949280i	$0.398186\pi$
$444$	6.61796e11	0.808166
$445$	−1.47934e12	−1.78833
$446$	7.46292e11	0.893104
$447$	2.39956e12	2.84281
$448$	5.49547e11	0.644546
$449$	1.41978e12	1.64859	0.824297	−	0.566158i	$-0.191571\pi$
$449$	1.41978e12	1.64859	0.824297	+	0.566158i	$0.191571\pi$
$450$	2.14608e12	2.46711
$451$	−1.39542e12	−1.58822
$452$	−7.08795e11	−0.798726
$453$	1.84350e11	0.205685
$454$	−1.82387e12	−2.01485
$455$	1.43310e12	1.56756
$456$	−7.22689e11	−0.782725
$457$	1.66458e12	1.78518	0.892591	−	0.450867i	$-0.148885\pi$
$457$	1.66458e12	1.78518	0.892591	+	0.450867i	$0.148885\pi$
$458$	−6.02526e11	−0.639854
$459$	−2.45717e11	−0.258392
$460$	8.13928e10	0.0847570
$461$	1.01161e12	1.04318	0.521591	−	0.853196i	$-0.325339\pi$
$461$	1.01161e12	1.04318	0.521591	+	0.853196i	$0.325339\pi$
$462$	−2.76496e12	−2.82358
$463$	1.02470e12	1.03629	0.518144	−	0.855293i	$-0.326623\pi$
$463$	1.02470e12	1.03629	0.518144	+	0.855293i	$0.326623\pi$
$464$	2.15928e11	0.216261
$465$	−2.76500e12	−2.74256
$466$	1.58650e12	1.55849
$467$	2.88969e11	0.281141	0.140571	−	0.990071i	$-0.455106\pi$
$467$	2.88969e11	0.281141	0.140571	+	0.990071i	$0.455106\pi$
$468$	−8.51709e11	−0.820701
$469$	−1.18499e12	−1.13093
$470$	2.39089e11	0.226005
$471$	7.47861e10	0.0700207
$472$	4.92006e11	0.456280
$473$	−7.49008e11	−0.688036
$474$	−9.57713e11	−0.871430
$475$	−3.14889e12	−2.83815
$476$	−8.00236e11	−0.714474
$477$	−2.61807e12	−2.31552
$478$	2.48106e10	0.0217376
$479$	2.44109e9	0.00211872	0.00105936	−	0.999999i	$-0.499663\pi$
$479$	2.44109e9	0.00211872	0.00105936	+	0.999999i	$0.499663\pi$
$480$	3.51669e12	3.02377
$481$	6.78945e11	0.578338
$482$	−1.23215e12	−1.03980
$483$	1.41277e11	0.118116
$484$	4.37307e11	0.362228
$485$	−1.51547e12	−1.24368
$486$	2.33166e12	1.89584
$487$	2.04582e12	1.64811	0.824057	−	0.566507i	$-0.191706\pi$
$487$	2.04582e12	1.64811	0.824057	+	0.566507i	$0.191706\pi$
$488$	−1.67176e11	−0.133440
$489$	−2.65279e12	−2.09804
$490$	1.00569e12	0.788100
$491$	−1.15315e12	−0.895403	−0.447702	−	0.894183i	$-0.647757\pi$
$491$	−1.15315e12	−0.895403	−0.447702	+	0.894183i	$0.647757\pi$
$492$	−2.02074e12	−1.55477
$493$	−1.87529e11	−0.142974
$494$	2.82712e12	2.13586
$495$	−3.12586e12	−2.34016
$496$	−1.82384e12	−1.35306
$497$	−1.06897e12	−0.785892
$498$	1.73294e12	1.26255
$499$	1.31320e12	0.948154	0.474077	−	0.880483i	$-0.342782\pi$
$499$	1.31320e12	0.948154	0.474077	+	0.880483i	$0.342782\pi$
$500$	8.83760e11	0.632367
$501$	−2.88209e11	−0.204380
$502$	1.66790e12	1.17221
$503$	1.30574e12	0.909493	0.454747	−	0.890621i	$-0.349730\pi$
$503$	1.30574e12	0.909493	0.454747	+	0.890621i	$0.349730\pi$
$504$	5.78115e11	0.399095
$505$	3.06631e12	2.09800
$506$	−1.61105e11	−0.109253
$507$	6.32141e11	0.424892
$508$	1.74512e12	1.16263
$509$	−5.88476e11	−0.388596	−0.194298	−	0.980943i	$-0.562243\pi$
$509$	−5.88476e11	−0.388596	−0.194298	+	0.980943i	$0.562243\pi$
$510$	−3.71736e12	−2.43315
$511$	−3.55781e11	−0.230828
$512$	1.81598e12	1.16787
$513$	9.93177e11	0.633138
$514$	6.35332e10	0.0401483
$515$	−2.54639e10	−0.0159512
$516$	−1.08465e12	−0.673544
$517$	−2.09190e11	−0.128776
$518$	1.75728e12	1.07240
$519$	8.71386e11	0.527179
$520$	6.20632e11	0.372237
$521$	−5.24300e11	−0.311753	−0.155876	−	0.987777i	$-0.549820\pi$
$521$	−5.24300e11	−0.311753	−0.155876	+	0.987777i	$0.549820\pi$
$522$	−5.16592e11	−0.304530
$523$	1.15598e12	0.675604	0.337802	−	0.941217i	$-0.390317\pi$
$523$	1.15598e12	0.675604	0.337802	+	0.941217i	$0.390317\pi$
$524$	−1.75571e12	−1.01733
$525$	4.57526e12	2.62845
$526$	5.56319e11	0.316875
$527$	1.58397e12	0.894538
$528$	−3.74503e12	−2.09702
$529$	−1.79292e12	−0.995430
$530$	−7.27455e12	−4.00465
$531$	−3.68145e12	−2.00953
$532$	3.23451e12	1.75068
$533$	−2.07310e12	−1.11262
$534$	4.24028e12	2.25662
$535$	1.12272e12	0.592489
$536$	−5.13184e11	−0.268554
$537$	−5.19986e12	−2.69841
$538$	9.26334e11	0.476702
$539$	−8.79925e11	−0.449052
$540$	−8.31379e11	−0.420753
$541$	2.73327e12	1.37181	0.685907	−	0.727689i	$-0.259406\pi$
$541$	2.73327e12	1.37181	0.685907	+	0.727689i	$0.259406\pi$
$542$	−1.04955e12	−0.522405
$543$	3.28909e12	1.62359
$544$	−2.01459e12	−0.986258
$545$	3.21098e11	0.155903
$546$	−4.10774e12	−1.97804
$547$	3.03604e11	0.144999	0.0724995	−	0.997368i	$-0.476902\pi$
$547$	3.03604e11	0.144999	0.0724995	+	0.997368i	$0.476902\pi$
$548$	6.98830e11	0.331024
$549$	1.25090e12	0.587689
$550$	−5.21738e12	−2.43120
$551$	7.57983e11	0.350330
$552$	6.11829e10	0.0280481
$553$	−1.12411e12	−0.511149
$554$	−3.62661e11	−0.163571
$555$	3.60841e12	1.61435
$556$	−2.50945e12	−1.11363
$557$	−2.82781e12	−1.24480	−0.622402	−	0.782697i	$-0.713843\pi$
$557$	−2.82781e12	−1.24480	−0.622402	+	0.782697i	$0.713843\pi$
$558$	4.36340e12	1.90534
$559$	−1.11276e12	−0.482000
$560$	5.02399e12	2.15875
$561$	3.25249e12	1.38638
$562$	2.32768e12	0.984262
$563$	−4.36631e12	−1.83158	−0.915791	−	0.401655i	$-0.868435\pi$
$563$	−4.36631e12	−1.83158	−0.915791	+	0.401655i	$0.868435\pi$
$564$	−3.02932e11	−0.126063
$565$	−3.86467e12	−1.59549
$566$	2.28669e12	0.936554
$567$	2.08821e12	0.848497
$568$	−4.62939e11	−0.186619
$569$	2.37947e12	0.951646	0.475823	−	0.879541i	$-0.342150\pi$
$569$	2.37947e12	0.951646	0.475823	+	0.879541i	$0.342150\pi$
$570$	1.50254e13	5.96195
$571$	−3.11148e12	−1.22491	−0.612455	−	0.790505i	$-0.709818\pi$
$571$	−3.11148e12	−1.22491	−0.612455	+	0.790505i	$0.709818\pi$
$572$	2.07061e12	0.808753
$573$	4.98759e12	1.93284
$574$	−5.36569e12	−2.06311
$575$	2.66585e11	0.101702
$576$	−1.78078e12	−0.674077
$577$	−2.82937e12	−1.06267	−0.531335	−	0.847162i	$-0.678309\pi$
$577$	−2.82937e12	−1.06267	−0.531335	+	0.847162i	$0.678309\pi$
$578$	−1.46276e12	−0.545127
$579$	3.72216e12	1.37639
$580$	−6.34500e11	−0.232812
$581$	2.03403e12	0.740568
$582$	4.34384e12	1.56935
$583$	6.36484e12	2.28181
$584$	−1.54078e11	−0.0548128
$585$	−4.64390e12	−1.63939
$586$	−2.95138e12	−1.03392
$587$	5.72820e12	1.99135	0.995673	−	0.0929232i	$-0.0296211\pi$
$587$	5.72820e12	1.99135	0.995673	+	0.0929232i	$0.0296211\pi$
$588$	−1.27423e12	−0.439594
$589$	−6.40232e12	−2.19189
$590$	−1.02293e13	−3.47544
$591$	1.96136e12	0.661325
$592$	2.38016e12	0.796451
$593$	−7.22977e11	−0.240093	−0.120046	−	0.992768i	$-0.538304\pi$
$593$	−7.22977e11	−0.240093	−0.120046	+	0.992768i	$0.538304\pi$
$594$	1.64559e12	0.542354
$595$	−4.36324e12	−1.42719
$596$	−4.65101e12	−1.50987
$597$	7.57481e12	2.44055
$598$	−2.39344e11	−0.0765363
$599$	−4.17554e12	−1.32523	−0.662617	−	0.748959i	$-0.730554\pi$
$599$	−4.17554e12	−1.32523	−0.662617	+	0.748959i	$0.730554\pi$
$600$	1.98141e12	0.624155
$601$	2.84889e12	0.890718	0.445359	−	0.895352i	$-0.353076\pi$
$601$	2.84889e12	0.890718	0.445359	+	0.895352i	$0.353076\pi$
$602$	−2.88009e12	−0.893761
$603$	3.83991e12	1.18275
$604$	−3.57321e11	−0.109243
$605$	2.38439e12	0.723567
$606$	−8.78906e12	−2.64738
$607$	1.82971e12	0.547057	0.273528	−	0.961864i	$-0.411809\pi$
$607$	1.82971e12	0.547057	0.273528	+	0.961864i	$0.411809\pi$
$608$	8.14285e12	2.41663
$609$	−1.10133e12	−0.324445
$610$	3.47575e12	1.01640
$611$	−3.10781e11	−0.0902131
$612$	2.59313e12	0.747210
$613$	−6.03104e11	−0.172512	−0.0862562	−	0.996273i	$-0.527490\pi$
$613$	−6.03104e11	−0.172512	−0.0862562	+	0.996273i	$0.527490\pi$
$614$	2.61159e12	0.741561
$615$	−1.10180e13	−3.10573
$616$	−1.40547e12	−0.393286
$617$	−2.56407e12	−0.712274	−0.356137	−	0.934434i	$-0.615906\pi$
$617$	−2.56407e12	−0.712274	−0.356137	+	0.934434i	$0.615906\pi$
$618$	7.29880e10	0.0201281
$619$	−9.71725e11	−0.266033	−0.133017	−	0.991114i	$-0.542466\pi$
$619$	−9.71725e11	−0.266033	−0.133017	+	0.991114i	$0.542466\pi$
$620$	5.35932e12	1.45662
$621$	−8.40824e10	−0.0226878
$622$	−2.69785e12	−0.722704
$623$	4.97702e12	1.32365
$624$	−5.56378e12	−1.46906
$625$	−9.20127e11	−0.241206
$626$	−3.63473e12	−0.945992
$627$	−1.31464e13	−3.39706
$628$	−1.44956e11	−0.0371892
$629$	−2.06713e12	−0.526550
$630$	−1.20195e13	−3.03987
$631$	−2.65560e12	−0.666854	−0.333427	−	0.942776i	$-0.608205\pi$
$631$	−2.65560e12	−0.666854	−0.333427	+	0.942776i	$0.608205\pi$
$632$	−4.86819e11	−0.121378
$633$	8.02270e10	0.0198611
$634$	8.89218e12	2.18578
$635$	9.51520e12	2.32240
$636$	9.21703e12	2.23375
$637$	−1.30725e12	−0.314581
$638$	1.25590e12	0.300097
$639$	3.46396e12	0.821900
$640$	3.65581e12	0.861339
$641$	−9.22283e11	−0.215776	−0.107888	−	0.994163i	$-0.534409\pi$
$641$	−9.22283e11	−0.215776	−0.107888	+	0.994163i	$0.534409\pi$
$642$	−3.21809e12	−0.747637
$643$	−2.12043e12	−0.489186	−0.244593	−	0.969626i	$-0.578654\pi$
$643$	−2.12043e12	−0.489186	−0.244593	+	0.969626i	$0.578654\pi$
$644$	−2.73834e11	−0.0627337
$645$	−5.91400e12	−1.34544
$646$	−8.60750e12	−1.94460
$647$	−1.39399e12	−0.312745	−0.156373	−	0.987698i	$-0.549980\pi$
$647$	−1.39399e12	−0.312745	−0.156373	+	0.987698i	$0.549980\pi$
$648$	9.04339e11	0.201485
$649$	8.95007e12	1.98027
$650$	−7.75115e12	−1.70316
$651$	9.30243e12	2.02993
$652$	5.14183e12	1.11430
$653$	3.96199e12	0.852714	0.426357	−	0.904555i	$-0.359797\pi$
$653$	3.96199e12	0.852714	0.426357	+	0.904555i	$0.359797\pi$
$654$	−9.20372e11	−0.196727
$655$	−9.57294e12	−2.03217
$656$	−7.26762e12	−1.53223
$657$	1.15289e12	0.241404
$658$	−8.04378e11	−0.167280
$659$	−1.89309e12	−0.391010	−0.195505	−	0.980703i	$-0.562635\pi$
$659$	−1.89309e12	−0.391010	−0.195505	+	0.980703i	$0.562635\pi$
$660$	1.10047e13	2.25752
$661$	−8.02349e12	−1.63477	−0.817385	−	0.576092i	$-0.804577\pi$
$661$	−8.02349e12	−1.63477	−0.817385	+	0.576092i	$0.804577\pi$
$662$	−9.01481e12	−1.82430
$663$	4.83204e12	0.971224
$664$	8.80876e11	0.175856
$665$	1.76360e13	3.49706
$666$	−5.69437e12	−1.12153
$667$	−6.41709e10	−0.0125537
$668$	5.58628e11	0.108550
$669$	−5.15568e12	−0.995104
$670$	1.06696e13	2.04555
$671$	−3.04110e12	−0.579134
$672$	−1.18314e13	−2.23807
$673$	−5.04431e12	−0.947837	−0.473919	−	0.880569i	$-0.657161\pi$
$673$	−5.04431e12	−0.947837	−0.473919	+	0.880569i	$0.657161\pi$
$674$	4.76306e12	0.889030
$675$	−2.72301e12	−0.504873
$676$	−1.22526e12	−0.225667
$677$	−3.09729e12	−0.566674	−0.283337	−	0.959020i	$-0.591441\pi$
$677$	−3.09729e12	−0.566674	−0.283337	+	0.959020i	$0.591441\pi$
$678$	1.10774e13	2.01328
$679$	5.09857e12	0.920523
$680$	−1.88959e12	−0.338904
$681$	1.26000e13	2.24497
$682$	−1.06080e13	−1.87760
$683$	8.84640e11	0.155551	0.0777756	−	0.996971i	$-0.475218\pi$
$683$	8.84640e11	0.155551	0.0777756	+	0.996971i	$0.475218\pi$
$684$	−1.04813e13	−1.83089
$685$	3.81034e12	0.661235
$686$	5.71212e12	0.984779
$687$	4.16248e12	0.712931
$688$	−3.90097e12	−0.663781
$689$	9.45587e12	1.59851
$690$	−1.27205e12	−0.213640
$691$	−6.81114e12	−1.13650	−0.568249	−	0.822856i	$-0.692379\pi$
$691$	−6.81114e12	−1.13650	−0.568249	+	0.822856i	$0.692379\pi$
$692$	−1.68898e12	−0.279994
$693$	1.05165e13	1.73209
$694$	1.06111e12	0.173638
$695$	−1.36826e13	−2.22453
$696$	−4.76953e11	−0.0770432
$697$	6.31179e12	1.01299
$698$	6.65900e12	1.06184
$699$	−1.09602e13	−1.73648
$700$	−8.86810e12	−1.39601
$701$	4.81153e12	0.752578	0.376289	−	0.926502i	$-0.377200\pi$
$701$	4.81153e12	0.752578	0.376289	+	0.926502i	$0.377200\pi$
$702$	2.44476e12	0.379943
$703$	8.35522e12	1.29021
$704$	4.32930e12	0.664265
$705$	−1.65172e12	−0.251817
$706$	6.45527e12	0.977898
$707$	−1.03161e13	−1.55285
$708$	1.29607e13	1.93856
$709$	−9.13128e12	−1.35714	−0.678568	−	0.734537i	$-0.737399\pi$
$709$	−9.13128e12	−1.35714	−0.678568	+	0.734537i	$0.737399\pi$
$710$	9.62494e12	1.42146
$711$	3.64264e12	0.534568
$712$	2.15539e12	0.314316
$713$	5.42021e11	0.0785440
$714$	1.25065e13	1.80092
$715$	1.12899e13	1.61552
$716$	1.00787e13	1.43317
$717$	−1.71402e11	−0.0242202
$718$	−1.34493e13	−1.88860
$719$	6.61445e12	0.923025	0.461513	−	0.887134i	$-0.347307\pi$
$719$	6.61445e12	0.923025	0.461513	+	0.887134i	$0.347307\pi$
$720$	−1.62800e13	−2.25766
$721$	8.56696e10	0.0118064
$722$	2.50161e13	3.42612
$723$	8.51217e12	1.15856
$724$	−6.37515e12	−0.862317
$725$	−2.07817e12	−0.279358
$726$	−6.83446e12	−0.913039
$727$	8.11338e12	1.07720	0.538600	−	0.842561i	$-0.318953\pi$
$727$	8.11338e12	1.07720	0.538600	+	0.842561i	$0.318953\pi$
$728$	−2.08802e12	−0.275514
$729$	−1.05841e13	−1.38797
$730$	3.20342e12	0.417504
$731$	3.38792e12	0.438839
$732$	−4.40386e12	−0.566936
$733$	5.89467e12	0.754208	0.377104	−	0.926171i	$-0.376920\pi$
$733$	5.89467e12	0.754208	0.377104	+	0.926171i	$0.376920\pi$
$734$	−1.32300e13	−1.68239
$735$	−6.94770e12	−0.878108
$736$	−6.89374e11	−0.0865974
$737$	−9.33531e12	−1.16553
$738$	1.73873e13	2.15763
$739$	7.12315e12	0.878561	0.439280	−	0.898350i	$-0.355233\pi$
$739$	7.12315e12	0.878561	0.439280	+	0.898350i	$0.355233\pi$
$740$	−6.99408e12	−0.857408
$741$	−1.95308e13	−2.37979
$742$	2.44741e13	2.96408
$743$	5.13641e12	0.618316	0.309158	−	0.951011i	$-0.399953\pi$
$743$	5.13641e12	0.618316	0.309158	+	0.951011i	$0.399953\pi$
$744$	4.02860e12	0.482032
$745$	−2.53594e13	−3.01603
$746$	5.88650e12	0.695877
$747$	−6.59118e12	−0.774499
$748$	−6.30421e12	−0.736332
$749$	−3.77723e12	−0.438536
$750$	−1.38119e13	−1.59396
$751$	−8.42233e12	−0.966168	−0.483084	−	0.875574i	$-0.660483\pi$
$751$	−8.42233e12	−0.966168	−0.483084	+	0.875574i	$0.660483\pi$
$752$	−1.08950e12	−0.124236
$753$	−1.15225e13	−1.30608
$754$	1.86581e12	0.210231
$755$	−1.94827e12	−0.218217
$756$	2.79705e12	0.311424
$757$	−1.45922e13	−1.61506	−0.807531	−	0.589825i	$-0.799197\pi$
$757$	−1.45922e13	−1.61506	−0.807531	+	0.589825i	$0.799197\pi$
$758$	−2.22182e12	−0.244454
$759$	1.11298e12	0.121730
$760$	7.63761e12	0.830417
$761$	−8.95202e12	−0.967587	−0.483794	−	0.875182i	$-0.660741\pi$
$761$	−8.95202e12	−0.967587	−0.483794	+	0.875182i	$0.660741\pi$
$762$	−2.72737e13	−2.93053
$763$	−1.08029e12	−0.115393
$764$	−9.66731e12	−1.02656
$765$	1.41389e13	1.49258
$766$	−7.43826e12	−0.780624
$767$	1.32966e13	1.38727
$768$	−1.83922e13	−1.90770
$769$	1.50826e13	1.55527	0.777636	−	0.628714i	$-0.216419\pi$
$769$	1.50826e13	1.55527	0.777636	+	0.628714i	$0.216419\pi$
$770$	2.92210e13	2.99562
$771$	−4.38912e11	−0.0447335
$772$	−7.21456e12	−0.731024
$773$	−8.72664e12	−0.879102	−0.439551	−	0.898218i	$-0.644862\pi$
$773$	−8.72664e12	−0.879102	−0.439551	+	0.898218i	$0.644862\pi$
$774$	9.33280e12	0.934711
$775$	1.75533e13	1.74784
$776$	2.20803e12	0.218589
$777$	−1.21399e13	−1.19487
$778$	−4.26940e12	−0.417791
$779$	−2.55119e13	−2.48213
$780$	1.63491e13	1.58149
$781$	−8.42132e12	−0.809935
$782$	7.28711e11	0.0696827
$783$	6.55467e11	0.0623194
$784$	−4.58281e12	−0.433221
$785$	−7.90364e11	−0.0742871
$786$	2.74392e13	2.56431
$787$	1.11445e13	1.03556	0.517781	−	0.855513i	$-0.326758\pi$
$787$	1.11445e13	1.03556	0.517781	+	0.855513i	$0.326758\pi$
$788$	−3.80166e12	−0.351241
$789$	−3.84327e12	−0.353065
$790$	1.01214e13	0.924527
$791$	1.30021e13	1.18092
$792$	4.55436e12	0.411305
$793$	−4.51798e12	−0.405709
$794$	−1.48949e13	−1.32998
$795$	5.02554e13	4.46201
$796$	−1.46820e13	−1.29622
$797$	1.72940e13	1.51822	0.759109	−	0.650964i	$-0.225635\pi$
$797$	1.72940e13	1.51822	0.759109	+	0.650964i	$0.225635\pi$
$798$	−5.05506e13	−4.41279
$799$	9.46210e11	0.0821348
$800$	−2.23254e13	−1.92705
$801$	−1.61278e13	−1.38430
$802$	2.65407e13	2.26531
$803$	−2.80282e12	−0.237890
$804$	−1.35186e13	−1.14098
$805$	−1.49307e12	−0.125313
$806$	−1.57596e13	−1.31534
$807$	−6.39948e12	−0.531146
$808$	−4.46760e12	−0.368743
$809$	−6.61839e12	−0.543231	−0.271615	−	0.962406i	$-0.587558\pi$
$809$	−6.61839e12	−0.543231	−0.271615	+	0.962406i	$0.587558\pi$
$810$	−1.88020e13	−1.53470
$811$	4.07466e12	0.330748	0.165374	−	0.986231i	$-0.447117\pi$
$811$	4.07466e12	0.330748	0.165374	+	0.986231i	$0.447117\pi$
$812$	2.13468e12	0.172318
$813$	7.25072e12	0.582068
$814$	1.38437e13	1.10521
$815$	2.80356e13	2.22587
$816$	1.69396e13	1.33751
$817$	−1.36938e13	−1.07529
$818$	8.45460e12	0.660242
$819$	1.56237e13	1.21341
$820$	2.13558e13	1.64950
$821$	−8.72524e12	−0.670244	−0.335122	−	0.942175i	$-0.608778\pi$
$821$	−8.72524e12	−0.670244	−0.335122	+	0.942175i	$0.608778\pi$
$822$	−1.09217e13	−0.834385
$823$	−1.93642e13	−1.47130	−0.735649	−	0.677363i	$-0.763123\pi$
$823$	−1.93642e13	−1.47130	−0.735649	+	0.677363i	$0.763123\pi$
$824$	3.71009e10	0.00280357
$825$	3.60437e13	2.70886
$826$	3.44148e13	2.57238
$827$	3.74443e12	0.278363	0.139181	−	0.990267i	$-0.455553\pi$
$827$	3.74443e12	0.278363	0.139181	+	0.990267i	$0.455553\pi$
$828$	8.87346e11	0.0656080
$829$	3.15284e12	0.231850	0.115925	−	0.993258i	$-0.463017\pi$
$829$	3.15284e12	0.231850	0.115925	+	0.993258i	$0.463017\pi$
$830$	−1.83142e13	−1.33948
$831$	2.50540e12	0.182252
$832$	6.43179e12	0.465347
$833$	3.98009e12	0.286411
$834$	3.92189e13	2.80704
$835$	3.04589e12	0.216833
$836$	2.54813e13	1.80424
$837$	−5.53642e12	−0.389910
$838$	−2.13297e13	−1.49412
$839$	−1.14991e13	−0.801191	−0.400596	−	0.916255i	$-0.631197\pi$
$839$	−1.14991e13	−0.801191	−0.400596	+	0.916255i	$0.631197\pi$
$840$	−1.10973e13	−0.769059
$841$	5.00246e11	0.0344828
$842$	6.56024e11	0.0449796
$843$	−1.60806e13	−1.09667
$844$	−1.55502e11	−0.0105486
$845$	−6.68068e12	−0.450781
$846$	2.60655e12	0.174944
$847$	−8.02194e12	−0.535555
$848$	3.31493e13	2.20137
$849$	−1.57973e13	−1.04352
$850$	2.35993e13	1.55065
$851$	−7.07354e11	−0.0462332
$852$	−1.21950e13	−0.792876
$853$	−9.29074e12	−0.600869	−0.300434	−	0.953802i	$-0.597132\pi$
$853$	−9.29074e12	−0.600869	−0.300434	+	0.953802i	$0.597132\pi$
$854$	−1.16936e13	−0.752297
$855$	−5.71487e13	−3.65728
$856$	−1.63580e12	−0.104135
$857$	8.66196e12	0.548533	0.274266	−	0.961654i	$-0.411565\pi$
$857$	8.66196e12	0.548533	0.274266	+	0.961654i	$0.411565\pi$
$858$	−3.23606e13	−2.03856
$859$	1.48834e13	0.932682	0.466341	−	0.884605i	$-0.345572\pi$
$859$	1.48834e13	0.932682	0.466341	+	0.884605i	$0.345572\pi$
$860$	1.14629e13	0.714584
$861$	3.70683e13	2.29873
$862$	−3.54692e13	−2.18811
$863$	−1.83445e13	−1.12579	−0.562895	−	0.826528i	$-0.690313\pi$
$863$	−1.83445e13	−1.12579	−0.562895	+	0.826528i	$0.690313\pi$
$864$	7.04155e12	0.429889
$865$	−9.20910e12	−0.559300
$866$	5.31847e11	0.0321334
$867$	1.01053e13	0.607385
$868$	−1.80306e13	−1.07813
$869$	−8.85571e12	−0.526786
$870$	9.91630e12	0.586831
$871$	−1.38689e13	−0.816509
$872$	−4.67838e11	−0.0274013
$873$	−1.65217e13	−0.962699
$874$	−2.94541e12	−0.170744
$875$	−1.62116e13	−0.934955
$876$	−4.05881e12	−0.232879
$877$	−7.82882e12	−0.446887	−0.223444	−	0.974717i	$-0.571730\pi$
$877$	−7.82882e12	−0.446887	−0.223444	+	0.974717i	$0.571730\pi$
$878$	−9.72374e12	−0.552215
$879$	2.03893e13	1.15200
$880$	3.95787e13	2.22480
$881$	−7.55920e12	−0.422751	−0.211375	−	0.977405i	$-0.567794\pi$
$881$	−7.55920e12	−0.422751	−0.211375	+	0.977405i	$0.567794\pi$
$882$	1.09641e13	0.610046
$883$	1.91750e12	0.106148	0.0530740	−	0.998591i	$-0.483098\pi$
$883$	1.91750e12	0.106148	0.0530740	+	0.998591i	$0.483098\pi$
$884$	−9.36580e12	−0.515834
$885$	7.06678e13	3.87237
$886$	1.54421e13	0.841891
$887$	−2.17006e13	−1.17711	−0.588553	−	0.808458i	$-0.700302\pi$
$887$	−2.17006e13	−1.17711	−0.588553	+	0.808458i	$0.700302\pi$
$888$	−5.25744e12	−0.283737
$889$	−3.20125e13	−1.71894
$890$	−4.48127e13	−2.39412
$891$	1.64508e13	0.874455
$892$	9.99311e12	0.528517
$893$	−3.82453e12	−0.201255
$894$	7.26883e13	3.80580
$895$	5.49538e13	2.86282
$896$	−1.22994e13	−0.637528
$897$	1.65348e12	0.0852773
$898$	4.30085e13	2.20704
$899$	−4.22534e12	−0.215746
$900$	2.87367e13	1.45998
$901$	−2.87895e13	−1.45537
$902$	−4.22706e13	−2.12622
$903$	1.98968e13	0.995836
$904$	5.63081e12	0.280423
$905$	−3.47602e13	−1.72252
$906$	5.58440e12	0.275359
$907$	−6.27831e12	−0.308042	−0.154021	−	0.988068i	$-0.549222\pi$
$907$	−6.27831e12	−0.308042	−0.154021	+	0.988068i	$0.549222\pi$
$908$	−2.44223e13	−1.19234
$909$	3.34290e13	1.62400
$910$	4.34119e13	2.09857
$911$	−6.54756e12	−0.314954	−0.157477	−	0.987523i	$-0.550336\pi$
$911$	−6.54756e12	−0.314954	−0.157477	+	0.987523i	$0.550336\pi$
$912$	−6.84689e13	−3.27730
$913$	1.60240e13	0.763224
$914$	5.04241e13	2.38990
$915$	−2.40118e13	−1.13248
$916$	−8.06803e12	−0.378650
$917$	3.22067e13	1.50413
$918$	−7.44335e12	−0.345920
$919$	5.20458e12	0.240695	0.120347	−	0.992732i	$-0.461599\pi$
$919$	5.20458e12	0.240695	0.120347	+	0.992732i	$0.461599\pi$
$920$	−6.46601e11	−0.0297571
$921$	−1.80419e13	−0.826253
$922$	3.06441e13	1.39655
$923$	−1.25111e13	−0.567396
$924$	−3.70238e13	−1.67092
$925$	−2.29076e13	−1.02883
$926$	3.10404e13	1.38733
$927$	−2.77608e11	−0.0123474
$928$	5.37404e12	0.237867
$929$	1.65888e13	0.730707	0.365354	−	0.930869i	$-0.380948\pi$
$929$	1.65888e13	0.730707	0.365354	+	0.930869i	$0.380948\pi$
$930$	−8.37583e13	−3.67159
$931$	−1.60873e13	−0.701794
$932$	2.12438e13	0.922277
$933$	1.86378e13	0.805243
$934$	8.75353e12	0.376376
$935$	−3.43734e13	−1.47086
$936$	6.76614e12	0.288138
$937$	−2.58237e12	−0.109443	−0.0547217	−	0.998502i	$-0.517427\pi$
$937$	−2.58237e12	−0.109443	−0.0547217	+	0.998502i	$0.517427\pi$
$938$	−3.58962e13	−1.51403
$939$	2.51101e13	1.05403
$940$	3.20148e12	0.133744
$941$	7.43881e12	0.309279	0.154639	−	0.987971i	$-0.450578\pi$
$941$	7.43881e12	0.309279	0.154639	+	0.987971i	$0.450578\pi$
$942$	2.26544e12	0.0937398
$943$	2.15984e12	0.0889446
$944$	4.66136e13	1.91046
$945$	1.52508e13	0.622083
$946$	−2.26892e13	−0.921104
$947$	1.37002e13	0.553542	0.276771	−	0.960936i	$-0.410736\pi$
$947$	1.37002e13	0.553542	0.276771	+	0.960936i	$0.410736\pi$
$948$	−1.28241e13	−0.515691
$949$	−4.16399e12	−0.166652
$950$	−9.53871e13	−3.79956
$951$	−6.14307e13	−2.43541
$952$	6.35723e12	0.250843
$953$	2.40813e12	0.0945720	0.0472860	−	0.998881i	$-0.484943\pi$
$953$	2.40813e12	0.0945720	0.0472860	+	0.998881i	$0.484943\pi$
$954$	−7.93073e13	−3.09988
$955$	−5.27105e13	−2.05061
$956$	3.32223e11	0.0128638
$957$	−8.67624e12	−0.334370
$958$	7.39463e10	0.00283643
$959$	−1.28193e13	−0.489419
$960$	3.41832e13	1.29895
$961$	9.24984e12	0.349848
$962$	2.05668e13	0.774246
$963$	1.22399e13	0.458628
$964$	−1.64989e13	−0.615331
$965$	−3.93370e13	−1.46025
$966$	4.27962e12	0.158128
$967$	4.50919e13	1.65836	0.829181	−	0.558980i	$-0.188807\pi$
$967$	4.50919e13	1.65836	0.829181	+	0.558980i	$0.188807\pi$
$968$	−3.47405e12	−0.127174
$969$	5.94640e13	2.16669
$970$	−4.59071e13	−1.66497
$971$	−9.35562e12	−0.337743	−0.168871	−	0.985638i	$-0.554012\pi$
$971$	−9.35562e12	−0.337743	−0.168871	+	0.985638i	$0.554012\pi$
$972$	3.12217e13	1.12191
$973$	4.60332e13	1.64650
$974$	6.19726e13	2.20640
$975$	5.35480e13	1.89768
$976$	−1.58386e13	−0.558717
$977$	4.45743e13	1.56516	0.782580	−	0.622550i	$-0.213903\pi$
$977$	4.45743e13	1.56516	0.782580	+	0.622550i	$0.213903\pi$
$978$	−8.03592e13	−2.80874
$979$	3.92087e13	1.36414
$980$	1.34665e13	0.466378
$981$	3.50062e12	0.120680
$982$	−3.49315e13	−1.19872
$983$	−1.73251e13	−0.591813	−0.295907	−	0.955217i	$-0.595622\pi$
$983$	−1.73251e13	−0.591813	−0.295907	+	0.955217i	$0.595622\pi$
$984$	1.60531e13	0.545860
$985$	−2.07283e13	−0.701620
$986$	−5.68069e12	−0.191406
$987$	5.55696e12	0.186385
$988$	3.78561e13	1.26395
$989$	1.15932e12	0.0385318
$990$	−9.46894e13	−3.13287
$991$	3.68113e13	1.21241	0.606206	−	0.795308i	$-0.292691\pi$
$991$	3.68113e13	1.21241	0.606206	+	0.795308i	$0.292691\pi$
$992$	−4.53920e13	−1.48825
$993$	6.22778e13	2.03265
$994$	−3.23817e13	−1.05211
$995$	−8.00531e13	−2.58925
$996$	2.32046e13	0.747148
$997$	3.19481e13	1.02404	0.512020	−	0.858973i	$-0.328897\pi$
$997$	3.19481e13	1.02404	0.512020	+	0.858973i	$0.328897\pi$
$998$	3.97799e13	1.26934
$999$	7.22519e12	0.229512

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.10.a.a.1.8	✓	9
3.2	odd	2		261.10.a.b.1.2		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.10.a.a.1.8	✓	9	1.1	even	1	trivial
261.10.a.b.1.2		9	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q+30.2923 q^{2} -209.271 q^{3} +405.624 q^{4} +2211.65 q^{5} -6339.31 q^{6} -7440.75 q^{7} -3222.36 q^{8} +24111.4 q^{9} +O(q^{10})\)	\(q+30.2923 q^{2} -209.271 q^{3} +405.624 q^{4} +2211.65 q^{5} -6339.31 q^{6} -7440.75 q^{7} -3222.36 q^{8} +24111.4 q^{9} +66995.9 q^{10} -58617.9 q^{11} -84885.5 q^{12} -87085.1 q^{13} -225398. q^{14} -462834. q^{15} -305293. q^{16} +265141. q^{17} +730391. q^{18} -1.07169e6 q^{19} +897098. q^{20} +1.55714e6 q^{21} -1.77567e6 q^{22} +90729.0 q^{23} +674347. q^{24} +2.93826e6 q^{25} -2.63801e6 q^{26} -926742. q^{27} -3.01815e6 q^{28} -707281. q^{29} -1.40203e7 q^{30} +5.97407e6 q^{31} -7.59817e6 q^{32} +1.22670e7 q^{33} +8.03173e6 q^{34} -1.64563e7 q^{35} +9.78019e6 q^{36} -7.79633e6 q^{37} -3.24639e7 q^{38} +1.82244e7 q^{39} -7.12673e6 q^{40} +2.38054e7 q^{41} +4.71692e7 q^{42} +1.27778e7 q^{43} -2.37768e7 q^{44} +5.33260e7 q^{45} +2.74839e6 q^{46} +3.56871e6 q^{47} +6.38889e7 q^{48} +1.50112e7 q^{49} +8.90066e7 q^{50} -5.54864e7 q^{51} -3.53239e7 q^{52} -1.08582e8 q^{53} -2.80732e7 q^{54} -1.29642e8 q^{55} +2.39768e7 q^{56} +2.24273e8 q^{57} -2.14252e7 q^{58} -1.52685e8 q^{59} -1.87737e8 q^{60} +5.18800e7 q^{61} +1.80968e8 q^{62} -1.79407e8 q^{63} -7.38564e7 q^{64} -1.92602e8 q^{65} +3.71597e8 q^{66} +1.59257e8 q^{67} +1.07548e8 q^{68} -1.89870e7 q^{69} -4.98500e8 q^{70} +1.43665e8 q^{71} -7.76957e7 q^{72} +4.78152e7 q^{73} -2.36169e8 q^{74} -6.14892e8 q^{75} -4.34702e8 q^{76} +4.36161e8 q^{77} +5.52060e8 q^{78} +1.51075e8 q^{79} -6.75199e8 q^{80} -2.80645e8 q^{81} +7.21121e8 q^{82} -2.73363e8 q^{83} +6.31612e8 q^{84} +5.86398e8 q^{85} +3.87069e8 q^{86} +1.48014e8 q^{87} +1.88888e8 q^{88} -6.68887e8 q^{89} +1.61537e9 q^{90} +6.47979e8 q^{91} +3.68019e7 q^{92} -1.25020e9 q^{93} +1.08104e8 q^{94} -2.37019e9 q^{95} +1.59008e9 q^{96} -6.85222e8 q^{97} +4.54724e8 q^{98} -1.41336e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 244 q^{3} + 1194 q^{4} - 738 q^{5} - 2330 q^{6} - 7128 q^{7} - 13776 q^{8} + 33017 q^{9}+O(q^{10}) \) 9 * q - 244 * q^3 + 1194 * q^4 - 738 * q^5 - 2330 * q^6 - 7128 * q^7 - 13776 * q^8 + 33017 * q^9	\( 9 q - 244 q^{3} + 1194 q^{4} - 738 q^{5} - 2330 q^{6} - 7128 q^{7} - 13776 q^{8} + 33017 q^{9} + 37812 q^{10} - 59512 q^{11} - 127348 q^{12} - 165758 q^{13} - 406080 q^{14} - 693178 q^{15} - 1044958 q^{16} - 394814 q^{17} - 1676576 q^{18} - 2256606 q^{19} - 2237578 q^{20} - 1750168 q^{21} - 5311718 q^{22} - 1699500 q^{23} - 4446318 q^{24} - 983481 q^{25} - 4264740 q^{26} - 6987958 q^{27} - 8491636 q^{28} - 6365529 q^{29} - 16907854 q^{30} - 11929632 q^{31} - 1346192 q^{32} + 1750252 q^{33} + 8655764 q^{34} - 3275324 q^{35} + 29848532 q^{36} + 14454898 q^{37} + 14709736 q^{38} + 41155042 q^{39} + 45167060 q^{40} + 52495202 q^{41} + 103102340 q^{42} + 21819888 q^{43} + 70837004 q^{44} + 61248326 q^{45} + 20628012 q^{46} + 44968948 q^{47} + 122982540 q^{48} - 26826775 q^{49} + 155997680 q^{50} - 28882428 q^{51} + 29562122 q^{52} - 111394302 q^{53} + 70575802 q^{54} - 173560742 q^{55} + 67419136 q^{56} + 85769252 q^{57} - 236142720 q^{59} - 47991000 q^{60} - 241129054 q^{61} + 261343278 q^{62} - 328513060 q^{63} - 333112958 q^{64} - 625660884 q^{65} + 223958776 q^{66} - 672046492 q^{67} - 63179948 q^{68} - 705827600 q^{69} - 366389016 q^{70} - 475841956 q^{71} - 18937608 q^{72} - 424813822 q^{73} - 532689728 q^{74} - 913708498 q^{75} - 552478056 q^{76} - 182224776 q^{77} + 928127886 q^{78} - 170801148 q^{79} + 562655678 q^{80} - 914585851 q^{81} + 1468192652 q^{82} - 468898296 q^{83} + 952386216 q^{84} - 271552972 q^{85} + 1462277802 q^{86} + 172576564 q^{87} + 1176890862 q^{88} - 676036598 q^{89} + 4017858752 q^{90} + 9763884 q^{91} + 2724990708 q^{92} - 858755220 q^{93} + 2429128614 q^{94} + 69331732 q^{95} + 3111862050 q^{96} + 170708754 q^{97} + 3278517600 q^{98} + 305494078 q^{99}+O(q^{100}) \) 9 * q - 244 * q^3 + 1194 * q^4 - 738 * q^5 - 2330 * q^6 - 7128 * q^7 - 13776 * q^8 + 33017 * q^9 + 37812 * q^10 - 59512 * q^11 - 127348 * q^12 - 165758 * q^13 - 406080 * q^14 - 693178 * q^15 - 1044958 * q^16 - 394814 * q^17 - 1676576 * q^18 - 2256606 * q^19 - 2237578 * q^20 - 1750168 * q^21 - 5311718 * q^22 - 1699500 * q^23 - 4446318 * q^24 - 983481 * q^25 - 4264740 * q^26 - 6987958 * q^27 - 8491636 * q^28 - 6365529 * q^29 - 16907854 * q^30 - 11929632 * q^31 - 1346192 * q^32 + 1750252 * q^33 + 8655764 * q^34 - 3275324 * q^35 + 29848532 * q^36 + 14454898 * q^37 + 14709736 * q^38 + 41155042 * q^39 + 45167060 * q^40 + 52495202 * q^41 + 103102340 * q^42 + 21819888 * q^43 + 70837004 * q^44 + 61248326 * q^45 + 20628012 * q^46 + 44968948 * q^47 + 122982540 * q^48 - 26826775 * q^49 + 155997680 * q^50 - 28882428 * q^51 + 29562122 * q^52 - 111394302 * q^53 + 70575802 * q^54 - 173560742 * q^55 + 67419136 * q^56 + 85769252 * q^57 - 236142720 * q^59 - 47991000 * q^60 - 241129054 * q^61 + 261343278 * q^62 - 328513060 * q^63 - 333112958 * q^64 - 625660884 * q^65 + 223958776 * q^66 - 672046492 * q^67 - 63179948 * q^68 - 705827600 * q^69 - 366389016 * q^70 - 475841956 * q^71 - 18937608 * q^72 - 424813822 * q^73 - 532689728 * q^74 - 913708498 * q^75 - 552478056 * q^76 - 182224776 * q^77 + 928127886 * q^78 - 170801148 * q^79 + 562655678 * q^80 - 914585851 * q^81 + 1468192652 * q^82 - 468898296 * q^83 + 952386216 * q^84 - 271552972 * q^85 + 1462277802 * q^86 + 172576564 * q^87 + 1176890862 * q^88 - 676036598 * q^89 + 4017858752 * q^90 + 9763884 * q^91 + 2724990708 * q^92 - 858755220 * q^93 + 2429128614 * q^94 + 69331732 * q^95 + 3111862050 * q^96 + 170708754 * q^97 + 3278517600 * q^98 + 305494078 * q^99

Introduction

L-functions

Modular forms

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