LMFDB - Embedded newform 29.10.a.a.1.7

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			1.7
Root			$-24.3559$ 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)

$f(q)$	$=$	$q+24.3559 q^{2} +100.461 q^{3} +81.2084 q^{4} -2213.18 q^{5} +2446.80 q^{6} -1575.25 q^{7} -10492.3 q^{8} -9590.68 q^{9} +O(q^{10})$	\(q+24.3559 q^{2} +100.461 q^{3} +81.2084 q^{4} -2213.18 q^{5} +2446.80 q^{6} -1575.25 q^{7} -10492.3 q^{8} -9590.68 q^{9} -53903.9 q^{10} -60678.9 q^{11} +8158.23 q^{12} +169843. q^{13} -38366.5 q^{14} -222337. q^{15} -297128. q^{16} +508356. q^{17} -233589. q^{18} -418524. q^{19} -179729. q^{20} -158250. q^{21} -1.47789e6 q^{22} -541114. q^{23} -1.05406e6 q^{24} +2.94504e6 q^{25} +4.13668e6 q^{26} -2.94085e6 q^{27} -127923. q^{28} -707281. q^{29} -5.41522e6 q^{30} -6.62773e6 q^{31} -1.86475e6 q^{32} -6.09584e6 q^{33} +1.23815e7 q^{34} +3.48631e6 q^{35} -778844. q^{36} -1.32108e7 q^{37} -1.01935e7 q^{38} +1.70625e7 q^{39} +2.32214e7 q^{40} +3.08944e7 q^{41} -3.85432e6 q^{42} -2.17269e7 q^{43} -4.92764e6 q^{44} +2.12259e7 q^{45} -1.31793e7 q^{46} +5.44016e7 q^{47} -2.98496e7 q^{48} -3.78722e7 q^{49} +7.17291e7 q^{50} +5.10697e7 q^{51} +1.37927e7 q^{52} -4.58294e6 q^{53} -7.16269e7 q^{54} +1.34293e8 q^{55} +1.65280e7 q^{56} -4.20451e7 q^{57} -1.72264e7 q^{58} +2.84982e7 q^{59} -1.80556e7 q^{60} -6.28415e7 q^{61} -1.61424e8 q^{62} +1.51077e7 q^{63} +1.06712e8 q^{64} -3.75894e8 q^{65} -1.48469e8 q^{66} -2.22931e8 q^{67} +4.12828e7 q^{68} -5.43606e7 q^{69} +8.49120e7 q^{70} -2.72133e8 q^{71} +1.00628e8 q^{72} +2.97447e8 q^{73} -3.21760e8 q^{74} +2.95861e8 q^{75} -3.39876e7 q^{76} +9.55843e7 q^{77} +4.15573e8 q^{78} -1.70482e8 q^{79} +6.57598e8 q^{80} -1.06666e8 q^{81} +7.52459e8 q^{82} -3.53366e7 q^{83} -1.28512e7 q^{84} -1.12508e9 q^{85} -5.29178e8 q^{86} -7.10538e7 q^{87} +6.36662e8 q^{88} +2.52276e7 q^{89} +5.16976e8 q^{90} -2.67545e8 q^{91} -4.39429e7 q^{92} -6.65825e8 q^{93} +1.32500e9 q^{94} +9.26269e8 q^{95} -1.87334e8 q^{96} -7.85122e8 q^{97} -9.22410e8 q^{98} +5.81953e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	24.3559	1.07639	0.538194	−	0.842821i	$-0.319107\pi$
$2$	24.3559	1.07639	0.538194	+	0.842821i	$0.319107\pi$
$3$	100.461	0.716061	0.358030	−	0.933710i	$-0.383448\pi$
$3$	100.461	0.716061	0.358030	+	0.933710i	$0.383448\pi$
$4$	81.2084	0.158610
$5$	−2213.18	−1.58362	−0.791812	−	0.610765i	$-0.790862\pi$
$5$	−2213.18	−1.58362	−0.791812	+	0.610765i	$0.790862\pi$
$6$	2446.80	0.770759
$7$	−1575.25	−0.247975	−0.123987	−	0.992284i	$-0.539568\pi$
$7$	−1575.25	−0.247975	−0.123987	+	0.992284i	$0.539568\pi$
$8$	−10492.3	−0.905662
$9$	−9590.68	−0.487257
$10$	−53903.9	−1.70459
$11$	−60678.9	−1.24960	−0.624800	−	0.780785i	$-0.714819\pi$
$11$	−60678.9	−1.24960	−0.624800	+	0.780785i	$0.714819\pi$
$12$	8158.23	0.113574
$13$	169843.	1.64931	0.824656	−	0.565634i	$-0.191369\pi$
$13$	169843.	1.64931	0.824656	+	0.565634i	$0.191369\pi$
$14$	−38366.5	−0.266917
$15$	−222337.	−1.13397
$16$	−297128.	−1.13345
$17$	508356.	1.47621	0.738105	−	0.674686i	$-0.235721\pi$
$17$	508356.	1.47621	0.738105	+	0.674686i	$0.235721\pi$
$18$	−233589.	−0.524477
$19$	−418524.	−0.736765	−0.368382	−	0.929674i	$-0.620088\pi$
$19$	−418524.	−0.736765	−0.368382	+	0.929674i	$0.620088\pi$
$20$	−179729.	−0.251179
$21$	−158250.	−0.177565
$22$	−1.47789e6	−1.34505
$23$	−541114.	−0.403193	−0.201597	−	0.979469i	$-0.564613\pi$
$23$	−541114.	−0.403193	−0.201597	+	0.979469i	$0.564613\pi$
$24$	−1.05406e6	−0.648509
$25$	2.94504e6	1.50786
$26$	4.13668e6	1.77530
$27$	−2.94085e6	−1.06497
$28$	−127923.	−0.0393313
$29$	−707281.	−0.185695
$29$	−707281.	−0.185695
$30$	−5.41522e6	−1.22059
$31$	−6.62773e6	−1.28895	−0.644476	−	0.764624i	$-0.722925\pi$
$31$	−6.62773e6	−1.28895	−0.644476	+	0.764624i	$0.722925\pi$
$32$	−1.86475e6	−0.314373
$33$	−6.09584e6	−0.894789
$34$	1.23815e7	1.58897
$35$	3.48631e6	0.392698
$36$	−778844.	−0.0772839
$37$	−1.32108e7	−1.15883	−0.579417	−	0.815032i	$-0.696720\pi$
$37$	−1.32108e7	−1.15883	−0.579417	+	0.815032i	$0.696720\pi$
$38$	−1.01935e7	−0.793045
$39$	1.70625e7	1.18101
$40$	2.32214e7	1.43423
$41$	3.08944e7	1.70747	0.853733	−	0.520712i	$-0.174333\pi$
$41$	3.08944e7	1.70747	0.853733	+	0.520712i	$0.174333\pi$
$42$	−3.85432e6	−0.191129
$43$	−2.17269e7	−0.969147	−0.484574	−	0.874750i	$-0.661025\pi$
$43$	−2.17269e7	−0.969147	−0.484574	+	0.874750i	$0.661025\pi$
$44$	−4.92764e6	−0.198199
$45$	2.12259e7	0.771632
$46$	−1.31793e7	−0.433992
$47$	5.44016e7	1.62619	0.813095	−	0.582131i	$-0.197781\pi$
$47$	5.44016e7	1.62619	0.813095	+	0.582131i	$0.197781\pi$
$48$	−2.98496e7	−0.811621
$49$	−3.78722e7	−0.938509
$50$	7.17291e7	1.62304
$51$	5.10697e7	1.05706
$52$	1.37927e7	0.261598
$53$	−4.58294e6	−0.0797817	−0.0398908	−	0.999204i	$-0.512701\pi$
$53$	−4.58294e6	−0.0797817	−0.0398908	+	0.999204i	$0.512701\pi$
$54$	−7.16269e7	−1.14632
$55$	1.34293e8	1.97890
$56$	1.65280e7	0.224581
$57$	−4.20451e7	−0.527568
$58$	−1.72264e7	−0.199880
$59$	2.84982e7	0.306184	0.153092	−	0.988212i	$-0.451077\pi$
$59$	2.84982e7	0.306184	0.153092	+	0.988212i	$0.451077\pi$
$60$	−1.80556e7	−0.179859
$61$	−6.28415e7	−0.581115	−0.290558	−	0.956857i	$-0.593841\pi$
$61$	−6.28415e7	−0.581115	−0.290558	+	0.956857i	$0.593841\pi$
$62$	−1.61424e8	−1.38741
$63$	1.51077e7	0.120827
$64$	1.06712e8	0.795066
$65$	−3.75894e8	−2.61189
$66$	−1.48469e8	−0.963140
$67$	−2.22931e8	−1.35156	−0.675779	−	0.737104i	$-0.736193\pi$
$67$	−2.22931e8	−1.35156	−0.675779	+	0.737104i	$0.736193\pi$
$68$	4.12828e7	0.234142
$69$	−5.43606e7	−0.288711
$70$	8.49120e7	0.422696
$71$	−2.72133e8	−1.27092	−0.635460	−	0.772134i	$-0.719190\pi$
$71$	−2.72133e8	−1.27092	−0.635460	+	0.772134i	$0.719190\pi$
$72$	1.00628e8	0.441290
$73$	2.97447e8	1.22590	0.612952	−	0.790120i	$-0.289982\pi$
$73$	2.97447e8	1.22590	0.612952	+	0.790120i	$0.289982\pi$
$74$	−3.21760e8	−1.24735
$75$	2.95861e8	1.07972
$76$	−3.39876e7	−0.116858
$77$	9.55843e7	0.309869
$78$	4.15573e8	1.27122
$79$	−1.70482e8	−0.492445	−0.246223	−	0.969213i	$-0.579189\pi$
$79$	−1.70482e8	−0.492445	−0.246223	+	0.969213i	$0.579189\pi$
$80$	6.57598e8	1.79496
$81$	−1.06666e8	−0.275323
$82$	7.52459e8	1.83789
$83$	−3.53366e7	−0.0817286	−0.0408643	−	0.999165i	$-0.513011\pi$
$83$	−3.53366e7	−0.0817286	−0.0408643	+	0.999165i	$0.513011\pi$
$84$	−1.28512e7	−0.0281636
$85$	−1.12508e9	−2.33776
$86$	−5.29178e8	−1.04318
$87$	−7.10538e7	−0.132969
$88$	6.36662e8	1.13171
$89$	2.52276e7	0.0426207	0.0213103	−	0.999773i	$-0.493216\pi$
$89$	2.52276e7	0.0426207	0.0213103	+	0.999773i	$0.493216\pi$
$90$	5.16976e8	0.830575
$91$	−2.67545e8	−0.408988
$92$	−4.39429e7	−0.0639505
$93$	−6.65825e8	−0.922968
$94$	1.32500e9	1.75041
$95$	9.26269e8	1.16676
$96$	−1.87334e8	−0.225110
$97$	−7.85122e8	−0.900460	−0.450230	−	0.892913i	$-0.648658\pi$
$97$	−7.85122e8	−0.900460	−0.450230	+	0.892913i	$0.648658\pi$
$98$	−9.22410e8	−1.01020
$99$	5.81953e8	0.608876
$100$	2.39162e8	0.239162
$101$	3.60554e7	0.0344766	0.0172383	−	0.999851i	$-0.494513\pi$
$101$	3.60554e7	0.0344766	0.0172383	+	0.999851i	$0.494513\pi$
$102$	1.24385e9	1.13780
$103$	7.08796e7	0.0620517	0.0310259	−	0.999519i	$-0.490123\pi$
$103$	7.08796e7	0.0620517	0.0310259	+	0.999519i	$0.490123\pi$
$104$	−1.78205e9	−1.49372
$105$	3.50236e8	0.281196
$106$	−1.11622e8	−0.0858760
$107$	−1.27630e9	−0.941297	−0.470649	−	0.882321i	$-0.655980\pi$
$107$	−1.27630e9	−0.941297	−0.470649	+	0.882321i	$0.655980\pi$
$108$	−2.38822e8	−0.168914
$109$	1.54005e9	1.04500	0.522500	−	0.852639i	$-0.324999\pi$
$109$	1.54005e9	1.04500	0.522500	+	0.852639i	$0.324999\pi$
$110$	3.27083e9	2.13006
$111$	−1.32716e9	−0.829795
$112$	4.68050e8	0.281068
$113$	−1.73234e9	−0.999494	−0.499747	−	0.866171i	$-0.666574\pi$
$113$	−1.73234e9	−0.999494	−0.499747	+	0.866171i	$0.666574\pi$
$114$	−1.02405e9	−0.567868
$115$	1.19758e9	0.638506
$116$	−5.74371e7	−0.0294532
$117$	−1.62891e9	−0.803639
$118$	6.94098e8	0.329573
$119$	−8.00786e8	−0.366063
$120$	2.33283e9	1.02699
$121$	1.32399e9	0.561500
$122$	−1.53056e9	−0.625505
$123$	3.10366e9	1.22265
$124$	−5.38227e8	−0.204441
$125$	−2.19529e9	−0.804262
$126$	3.67961e8	0.130057
$127$	−4.31555e9	−1.47204	−0.736020	−	0.676960i	$-0.763297\pi$
$127$	−4.31555e9	−1.47204	−0.736020	+	0.676960i	$0.763297\pi$
$128$	3.55381e9	1.17017
$129$	−2.18270e9	−0.693968
$130$	−9.15521e9	−2.81141
$131$	3.65866e9	1.08543	0.542715	−	0.839917i	$-0.317396\pi$
$131$	3.65866e9	1.08543	0.542715	+	0.839917i	$0.317396\pi$
$132$	−4.95033e8	−0.141923
$133$	6.59278e8	0.182699
$134$	−5.42969e9	−1.45480
$135$	6.50863e9	1.68651
$136$	−5.33383e9	−1.33695
$137$	4.87699e9	1.18279	0.591397	−	0.806381i	$-0.298577\pi$
$137$	4.87699e9	1.18279	0.591397	+	0.806381i	$0.298577\pi$
$138$	−1.32400e9	−0.310765
$139$	−3.17975e9	−0.722481	−0.361241	−	0.932473i	$-0.617647\pi$
$139$	−3.17975e9	−0.722481	−0.361241	+	0.932473i	$0.617647\pi$
$140$	2.83117e8	0.0622859
$141$	5.46521e9	1.16445
$142$	−6.62803e9	−1.36800
$143$	−1.03059e10	−2.06098
$144$	2.84966e9	0.552283
$145$	1.56534e9	0.294071
$146$	7.24458e9	1.31955
$147$	−3.80466e9	−0.672029
$148$	−1.07283e9	−0.183803
$149$	−1.94311e9	−0.322968	−0.161484	−	0.986875i	$-0.551628\pi$
$149$	−1.94311e9	−0.322968	−0.161484	+	0.986875i	$0.551628\pi$
$150$	7.20594e9	1.16220
$151$	2.72664e9	0.426808	0.213404	−	0.976964i	$-0.431545\pi$
$151$	2.72664e9	0.426808	0.213404	+	0.976964i	$0.431545\pi$
$152$	4.39128e9	0.667260
$153$	−4.87548e9	−0.719294
$154$	2.32804e9	0.333539
$155$	1.46684e10	2.04122
$156$	1.38562e9	0.187320
$157$	3.49578e9	0.459193	0.229596	−	0.973286i	$-0.426259\pi$
$157$	3.49578e9	0.459193	0.229596	+	0.973286i	$0.426259\pi$
$158$	−4.15225e9	−0.530062
$159$	−4.60405e8	−0.0571285
$160$	4.12702e9	0.497848
$161$	8.52387e8	0.0999817
$162$	−2.59794e9	−0.296355
$163$	−5.30051e9	−0.588130	−0.294065	−	0.955785i	$-0.595008\pi$
$163$	−5.30051e9	−0.588130	−0.294065	+	0.955785i	$0.595008\pi$
$164$	2.50888e9	0.270821
$165$	1.34912e10	1.41701
$166$	−8.60655e8	−0.0879716
$167$	3.77890e9	0.375959	0.187980	−	0.982173i	$-0.439806\pi$
$167$	3.77890e9	0.375959	0.187980	+	0.982173i	$0.439806\pi$
$168$	1.66041e9	0.160814
$169$	1.82422e10	1.72023
$170$	−2.74024e10	−2.51634
$171$	4.01393e9	0.358994
$172$	−1.76441e9	−0.153717
$173$	−3.15939e9	−0.268161	−0.134081	−	0.990970i	$-0.542808\pi$
$173$	−3.15939e9	−0.268161	−0.134081	+	0.990970i	$0.542808\pi$
$174$	−1.73058e9	−0.143126
$175$	−4.63917e9	−0.373912
$176$	1.80294e10	1.41636
$177$	2.86294e9	0.219247
$178$	6.14440e8	0.0458764
$179$	5.53361e9	0.402875	0.201437	−	0.979501i	$-0.435439\pi$
$179$	5.53361e9	0.402875	0.201437	+	0.979501i	$0.435439\pi$
$180$	1.72372e9	0.122389
$181$	−2.23326e10	−1.54663	−0.773313	−	0.634025i	$-0.781402\pi$
$181$	−2.23326e10	−1.54663	−0.773313	+	0.634025i	$0.781402\pi$
$182$	−6.51629e9	−0.440229
$183$	−6.31309e9	−0.416114
$184$	5.67753e9	0.365157
$185$	2.92379e10	1.83516
$186$	−1.62167e10	−0.993471
$187$	−3.08465e10	−1.84467
$188$	4.41787e9	0.257930
$189$	4.63256e9	0.264085
$190$	2.25601e10	1.25588
$191$	−2.26102e9	−0.122929	−0.0614644	−	0.998109i	$-0.519577\pi$
$191$	−2.26102e9	−0.122929	−0.0614644	+	0.998109i	$0.519577\pi$
$192$	1.07203e10	0.569315
$193$	−2.29730e10	−1.19182	−0.595908	−	0.803053i	$-0.703208\pi$
$193$	−2.29730e10	−1.19182	−0.595908	+	0.803053i	$0.703208\pi$
$194$	−1.91223e10	−0.969244
$195$	−3.77625e10	−1.87027
$196$	−3.07554e9	−0.148857
$197$	1.92736e10	0.911728	0.455864	−	0.890049i	$-0.349330\pi$
$197$	1.92736e10	0.911728	0.455864	+	0.890049i	$0.349330\pi$
$198$	1.41740e10	0.655387
$199$	2.34419e10	1.05963	0.529815	−	0.848113i	$-0.322261\pi$
$199$	2.34419e10	1.05963	0.529815	+	0.848113i	$0.322261\pi$
$200$	−3.09003e10	−1.36561
$201$	−2.23958e10	−0.967797
$202$	8.78161e8	0.0371102
$203$	1.11414e9	0.0460477
$204$	4.14729e9	0.167660
$205$	−6.83748e10	−2.70398
$206$	1.72633e9	0.0667917
$207$	5.18965e9	0.196459
$208$	−5.04651e10	−1.86942
$209$	2.53956e10	0.920661
$210$	8.53030e9	0.302676
$211$	−9.48128e9	−0.329303	−0.164652	−	0.986352i	$-0.552650\pi$
$211$	−9.48128e9	−0.329303	−0.164652	+	0.986352i	$0.552650\pi$
$212$	−3.72173e8	−0.0126542
$213$	−2.73386e10	−0.910056
$214$	−3.10855e10	−1.01320
$215$	4.80856e10	1.53476
$216$	3.08563e10	0.964499
$217$	1.04403e10	0.319628
$218$	3.75093e10	1.12482
$219$	2.98817e10	0.877822
$220$	1.09058e10	0.313873
$221$	8.63408e10	2.43473
$222$	−3.23242e10	−0.893181
$223$	6.82860e10	1.84910	0.924548	−	0.381064i	$-0.124442\pi$
$223$	6.82860e10	1.84910	0.924548	+	0.381064i	$0.124442\pi$
$224$	2.93744e9	0.0779565
$225$	−2.82450e10	−0.734717
$226$	−4.21927e10	−1.07584
$227$	1.76762e10	0.441847	0.220923	−	0.975291i	$-0.429093\pi$
$227$	1.76762e10	0.441847	0.220923	+	0.975291i	$0.429093\pi$
$228$	−3.41442e9	−0.0836777
$229$	4.44893e10	1.06904	0.534522	−	0.845154i	$-0.320492\pi$
$229$	4.44893e10	1.06904	0.534522	+	0.845154i	$0.320492\pi$
$230$	2.91682e10	0.687280
$231$	9.60245e9	0.221885
$232$	7.42101e9	0.168177
$233$	−1.92432e10	−0.427736	−0.213868	−	0.976863i	$-0.568606\pi$
$233$	−1.92432e10	−0.427736	−0.213868	+	0.976863i	$0.568606\pi$
$234$	−3.96736e10	−0.865027
$235$	−1.20401e11	−2.57527
$236$	2.31429e9	0.0485639
$237$	−1.71268e10	−0.352621
$238$	−1.95038e10	−0.394025
$239$	4.91269e10	0.973933	0.486967	−	0.873421i	$-0.338103\pi$
$239$	4.91269e10	0.973933	0.486967	+	0.873421i	$0.338103\pi$
$240$	6.60626e10	1.28530
$241$	6.82587e9	0.130341	0.0651706	−	0.997874i	$-0.479241\pi$
$241$	6.82587e9	0.130341	0.0651706	+	0.997874i	$0.479241\pi$
$242$	3.22469e10	0.604391
$243$	4.71690e10	0.867818
$244$	−5.10326e9	−0.0921708
$245$	8.38180e10	1.48624
$246$	7.55924e10	1.31604
$247$	−7.10834e10	−1.21516
$248$	6.95401e10	1.16735
$249$	−3.54994e9	−0.0585226
$250$	−5.34683e10	−0.865698
$251$	−1.07483e11	−1.70927	−0.854633	−	0.519232i	$-0.826218\pi$
$251$	−1.07483e11	−1.70927	−0.854633	+	0.519232i	$0.826218\pi$
$252$	1.22687e9	0.0191644
$253$	3.28342e10	0.503830
$254$	−1.05109e11	−1.58448
$255$	−1.13027e11	−1.67398
$256$	3.19197e10	0.464493
$257$	−7.99962e10	−1.14385	−0.571927	−	0.820305i	$-0.693804\pi$
$257$	−7.99962e10	−1.14385	−0.571927	+	0.820305i	$0.693804\pi$
$258$	−5.31615e10	−0.746979
$259$	2.08102e10	0.287361
$260$	−3.05257e10	−0.414272
$261$	6.78331e9	0.0904814
$262$	8.91099e10	1.16834
$263$	1.95262e10	0.251661	0.125831	−	0.992052i	$-0.459840\pi$
$263$	1.95262e10	0.251661	0.125831	+	0.992052i	$0.459840\pi$
$264$	6.39594e10	0.810376
$265$	1.01429e10	0.126344
$266$	1.60573e10	0.196655
$267$	2.53438e9	0.0305190
$268$	−1.81039e10	−0.214371
$269$	8.62787e10	1.00466	0.502329	−	0.864676i	$-0.332477\pi$
$269$	8.62787e10	1.00466	0.502329	+	0.864676i	$0.332477\pi$
$270$	1.58523e11	1.81533
$271$	2.21299e10	0.249240	0.124620	−	0.992205i	$-0.460229\pi$
$271$	2.21299e10	0.249240	0.124620	+	0.992205i	$0.460229\pi$
$272$	−1.51047e11	−1.67321
$273$	−2.68777e10	−0.292860
$274$	1.18783e11	1.27314
$275$	−1.78702e11	−1.88422
$276$	−4.41453e9	−0.0457924
$277$	−1.59269e10	−0.162544	−0.0812722	−	0.996692i	$-0.525898\pi$
$277$	−1.59269e10	−0.162544	−0.0812722	+	0.996692i	$0.525898\pi$
$278$	−7.74456e10	−0.777670
$279$	6.35644e10	0.628051
$280$	−3.65794e10	−0.355652
$281$	−8.40158e10	−0.803864	−0.401932	−	0.915670i	$-0.631661\pi$
$281$	−8.40158e10	−0.803864	−0.401932	+	0.915670i	$0.631661\pi$
$282$	1.33110e11	1.25340
$283$	−9.71373e10	−0.900217	−0.450108	−	0.892974i	$-0.648615\pi$
$283$	−9.71373e10	−0.900217	−0.450108	+	0.892974i	$0.648615\pi$
$284$	−2.20995e10	−0.201581
$285$	9.30534e10	0.835469
$286$	−2.51009e11	−2.21841
$287$	−4.86662e10	−0.423408
$288$	1.78842e10	0.153180
$289$	1.39838e11	1.17919
$290$	3.81252e10	0.316535
$291$	−7.88738e10	−0.644784
$292$	2.41552e10	0.194441
$293$	6.11579e9	0.0484784	0.0242392	−	0.999706i	$-0.492284\pi$
$293$	6.11579e9	0.0484784	0.0242392	+	0.999706i	$0.492284\pi$
$294$	−9.26658e10	−0.723364
$295$	−6.30716e10	−0.484881
$296$	1.38612e11	1.04951
$297$	1.78448e11	1.33078
$298$	−4.73261e10	−0.347639
$299$	−9.19044e10	−0.664992
$300$	2.40264e10	0.171255
$301$	3.42252e10	0.240324
$302$	6.64098e10	0.459411
$303$	3.62214e9	0.0246873
$304$	1.24355e11	0.835088
$305$	1.39080e11	0.920268
$306$	−1.18747e11	−0.774239
$307$	−1.90822e11	−1.22604	−0.613022	−	0.790065i	$-0.710046\pi$
$307$	−1.90822e11	−1.22604	−0.613022	+	0.790065i	$0.710046\pi$
$308$	7.76224e9	0.0491484
$309$	7.12060e9	0.0444328
$310$	3.57261e11	2.19714
$311$	−1.27181e11	−0.770903	−0.385452	−	0.922728i	$-0.625954\pi$
$311$	−1.27181e11	−0.770903	−0.385452	+	0.922728i	$0.625954\pi$
$312$	−1.79025e11	−1.06959
$313$	−2.76470e11	−1.62817	−0.814084	−	0.580747i	$-0.802761\pi$
$313$	−2.76470e11	−1.62817	−0.814084	+	0.580747i	$0.802761\pi$
$314$	8.51427e10	0.494269
$315$	−3.34360e10	−0.191345
$316$	−1.38446e10	−0.0781068
$317$	−2.70980e11	−1.50720	−0.753600	−	0.657333i	$-0.771684\pi$
$317$	−2.70980e11	−1.50720	−0.753600	+	0.657333i	$0.771684\pi$
$318$	−1.12136e10	−0.0614924
$319$	4.29171e10	0.232045
$320$	−2.36173e11	−1.25908
$321$	−1.28218e11	−0.674026
$322$	2.07606e10	0.107619
$323$	−2.12759e11	−1.08762
$324$	−8.66216e9	−0.0436691
$325$	5.00195e11	2.48694
$326$	−1.29098e11	−0.633056
$327$	1.54714e11	0.748283
$328$	−3.24153e11	−1.54639
$329$	−8.56959e10	−0.403254
$330$	3.28590e11	1.52525
$331$	−5.53815e10	−0.253594	−0.126797	−	0.991929i	$-0.540470\pi$
$331$	−5.53815e10	−0.253594	−0.126797	+	0.991929i	$0.540470\pi$
$332$	−2.86963e9	−0.0129630
$333$	1.26700e11	0.564650
$334$	9.20383e10	0.404678
$335$	4.93387e11	2.14036
$336$	4.70205e10	0.201261
$337$	3.48911e11	1.47360	0.736802	−	0.676109i	$-0.236335\pi$
$337$	3.48911e11	1.47360	0.736802	+	0.676109i	$0.236335\pi$
$338$	4.44305e11	1.85164
$339$	−1.74032e11	−0.715699
$340$	−9.13662e10	−0.370792
$341$	4.02163e11	1.61067
$342$	9.77627e10	0.386417
$343$	1.23225e11	0.480701
$344$	2.27965e11	0.877720
$345$	1.20310e11	0.457209
$346$	−7.69497e10	−0.288645
$347$	−2.61067e11	−0.966652	−0.483326	−	0.875440i	$-0.660571\pi$
$347$	−2.61067e11	−0.966652	−0.483326	+	0.875440i	$0.660571\pi$
$348$	−5.77016e9	−0.0210902
$349$	−6.20656e10	−0.223942	−0.111971	−	0.993711i	$-0.535716\pi$
$349$	−6.20656e10	−0.223942	−0.111971	+	0.993711i	$0.535716\pi$
$350$	−1.12991e11	−0.402474
$351$	−4.99483e11	−1.75646
$352$	1.13151e11	0.392840
$353$	1.63816e11	0.561526	0.280763	−	0.959777i	$-0.409412\pi$
$353$	1.63816e11	0.561526	0.280763	+	0.959777i	$0.409412\pi$
$354$	6.97295e10	0.235994
$355$	6.02279e11	2.01266
$356$	2.04869e9	0.00676007
$357$	−8.04474e10	−0.262123
$358$	1.34776e11	0.433649
$359$	2.44825e11	0.777912	0.388956	−	0.921256i	$-0.372836\pi$
$359$	2.44825e11	0.777912	0.388956	+	0.921256i	$0.372836\pi$
$360$	−2.22709e11	−0.698837
$361$	−1.47526e11	−0.457177
$362$	−5.43929e11	−1.66477
$363$	1.33008e11	0.402068
$364$	−2.17269e10	−0.0648696
$365$	−6.58304e11	−1.94137
$366$	−1.53761e11	−0.447900
$367$	−4.19390e11	−1.20676	−0.603380	−	0.797454i	$-0.706180\pi$
$367$	−4.19390e11	−1.20676	−0.603380	+	0.797454i	$0.706180\pi$
$368$	1.60780e11	0.457000
$369$	−2.96298e11	−0.831975
$370$	7.12113e11	1.97534
$371$	7.21927e9	0.0197838
$372$	−5.40705e10	−0.146392
$373$	2.68648e11	0.718611	0.359305	−	0.933220i	$-0.383014\pi$
$373$	2.68648e11	0.718611	0.359305	+	0.933220i	$0.383014\pi$
$374$	−7.51294e11	−1.98558
$375$	−2.20540e11	−0.575901
$376$	−5.70798e11	−1.47278
$377$	−1.20127e11	−0.306270
$378$	1.12830e11	0.284257
$379$	4.18554e11	1.04202	0.521009	−	0.853551i	$-0.325556\pi$
$379$	4.18554e11	1.04202	0.521009	+	0.853551i	$0.325556\pi$
$380$	7.52208e10	0.185060
$381$	−4.33542e11	−1.05407
$382$	−5.50690e10	−0.132319
$383$	−2.61122e11	−0.620083	−0.310041	−	0.950723i	$-0.600343\pi$
$383$	−2.61122e11	−0.620083	−0.310041	+	0.950723i	$0.600343\pi$
$384$	3.57018e11	0.837914
$385$	−2.11545e11	−0.490716
$386$	−5.59527e11	−1.28286
$387$	2.08376e11	0.472224
$388$	−6.37585e10	−0.142822
$389$	3.59930e11	0.796974	0.398487	−	0.917174i	$-0.369535\pi$
$389$	3.59930e11	0.796974	0.398487	+	0.917174i	$0.369535\pi$
$390$	−9.19738e11	−2.01314
$391$	−2.75078e11	−0.595198
$392$	3.97367e11	0.849971
$393$	3.67551e11	0.777233
$394$	4.69426e11	0.981372
$395$	3.77309e11	0.779847
$396$	4.72594e10	0.0965739
$397$	5.61304e11	1.13407	0.567037	−	0.823693i	$-0.308090\pi$
$397$	5.61304e11	1.13407	0.567037	+	0.823693i	$0.308090\pi$
$398$	5.70948e11	1.14057
$399$	6.62314e10	0.130824
$400$	−8.75055e11	−1.70909
$401$	2.69326e11	0.520149	0.260075	−	0.965589i	$-0.416253\pi$
$401$	2.69326e11	0.520149	0.260075	+	0.965589i	$0.416253\pi$
$402$	−5.45469e11	−1.04173
$403$	−1.12567e12	−2.12589
$404$	2.92800e9	0.00546833
$405$	2.36071e11	0.436008
$406$	2.71359e10	0.0495652
$407$	8.01617e11	1.44808
$408$	−5.35839e11	−0.957335
$409$	1.43250e11	0.253128	0.126564	−	0.991958i	$-0.459605\pi$
$409$	1.43250e11	0.253128	0.126564	+	0.991958i	$0.459605\pi$
$410$	−1.66533e12	−2.91053
$411$	4.89945e11	0.846952
$412$	5.75602e9	0.00984203
$413$	−4.48917e10	−0.0759260
$414$	1.26398e11	0.211466
$415$	7.82064e10	0.129427
$416$	−3.16715e11	−0.518499
$417$	−3.19440e11	−0.517340
$418$	6.18532e11	0.990988
$419$	9.83015e11	1.55811	0.779053	−	0.626958i	$-0.215700\pi$
$419$	9.83015e11	1.55811	0.779053	+	0.626958i	$0.215700\pi$
$420$	2.84421e10	0.0446005
$421$	4.46349e11	0.692477	0.346238	−	0.938147i	$-0.387459\pi$
$421$	4.46349e11	0.692477	0.346238	+	0.938147i	$0.387459\pi$
$422$	−2.30925e11	−0.354458
$423$	−5.21749e11	−0.792373
$424$	4.80856e10	0.0722552
$425$	1.49713e12	2.22592
$426$	−6.65856e11	−0.979573
$427$	9.89909e10	0.144102
$428$	−1.03646e11	−0.149299
$429$	−1.03534e12	−1.47579
$430$	1.17117e12	1.65200
$431$	5.92430e11	0.826969	0.413485	−	0.910511i	$-0.364312\pi$
$431$	5.92430e11	0.826969	0.413485	+	0.910511i	$0.364312\pi$
$432$	8.73808e11	1.20709
$433$	6.25587e11	0.855248	0.427624	−	0.903957i	$-0.359351\pi$
$433$	6.25587e11	0.855248	0.427624	+	0.903957i	$0.359351\pi$
$434$	2.54283e11	0.344043
$435$	1.57255e11	0.210573
$436$	1.25065e11	0.165748
$437$	2.26469e11	0.297059
$438$	7.27794e11	0.944877
$439$	−7.82327e10	−0.100530	−0.0502652	−	0.998736i	$-0.516007\pi$
$439$	−7.82327e10	−0.100530	−0.0502652	+	0.998736i	$0.516007\pi$
$440$	−1.40905e12	−1.79221
$441$	3.63220e11	0.457295
$442$	2.10291e12	2.62071
$443$	−1.09899e12	−1.35575	−0.677873	−	0.735179i	$-0.737098\pi$
$443$	−1.09899e12	−1.35575	−0.677873	+	0.735179i	$0.737098\pi$
$444$	−1.07777e11	−0.131614
$445$	−5.58332e10	−0.0674951
$446$	1.66316e12	1.99034
$447$	−1.95206e11	−0.231265
$448$	−1.68098e11	−0.197156
$449$	−1.05130e12	−1.22073	−0.610363	−	0.792122i	$-0.708976\pi$
$449$	−1.05130e12	−1.22073	−0.610363	+	0.792122i	$0.708976\pi$
$450$	−6.87931e11	−0.790840
$451$	−1.87464e12	−2.13365
$452$	−1.40681e11	−0.158530
$453$	2.73920e11	0.305620
$454$	4.30518e11	0.475598
$455$	5.92125e11	0.647682
$456$	4.41150e11	0.477798
$457$	−6.09881e11	−0.654067	−0.327034	−	0.945013i	$-0.606049\pi$
$457$	−6.09881e11	−0.654067	−0.327034	+	0.945013i	$0.606049\pi$
$458$	1.08358e12	1.15071
$459$	−1.49500e12	−1.57211
$460$	9.72537e10	0.101273
$461$	−1.33133e12	−1.37288	−0.686438	−	0.727189i	$-0.740827\pi$
$461$	−1.33133e12	−1.37288	−0.686438	+	0.727189i	$0.740827\pi$
$462$	2.33876e11	0.238834
$463$	1.44868e12	1.46507	0.732535	−	0.680730i	$-0.238337\pi$
$463$	1.44868e12	1.46507	0.732535	+	0.680730i	$0.238337\pi$
$464$	2.10153e11	0.210477
$465$	1.47359e12	1.46163
$466$	−4.68685e11	−0.460410
$467$	1.85556e11	0.180530	0.0902652	−	0.995918i	$-0.471229\pi$
$467$	1.85556e11	0.180530	0.0902652	+	0.995918i	$0.471229\pi$
$468$	−1.32281e11	−0.127465
$469$	3.51172e11	0.335152
$470$	−2.93246e12	−2.77199
$471$	3.51187e11	0.328810
$472$	−2.99012e11	−0.277300
$473$	1.31837e12	1.21105
$474$	−4.17137e11	−0.379556
$475$	−1.23257e12	−1.11094
$476$	−6.50305e10	−0.0580612
$477$	4.39536e10	0.0388742
$478$	1.19653e12	1.04833
$479$	−1.56593e12	−1.35914	−0.679569	−	0.733612i	$-0.737833\pi$
$479$	−1.56593e12	−1.35914	−0.679569	+	0.733612i	$0.737833\pi$
$480$	4.14603e11	0.356490
$481$	−2.24376e12	−1.91128
$482$	1.66250e11	0.140298
$483$	8.56313e10	0.0715930
$484$	1.07519e11	0.0890595
$485$	1.73762e12	1.42599
$486$	1.14884e12	0.934109
$487$	−2.10160e12	−1.69305	−0.846524	−	0.532350i	$-0.821309\pi$
$487$	−2.10160e12	−1.69305	−0.846524	+	0.532350i	$0.821309\pi$
$488$	6.59352e11	0.526294
$489$	−5.32492e11	−0.421137
$490$	2.04146e12	1.59977
$491$	−1.86653e12	−1.44933	−0.724667	−	0.689099i	$-0.758007\pi$
$491$	−1.86653e12	−1.44933	−0.724667	+	0.689099i	$0.758007\pi$
$492$	2.52043e11	0.193924
$493$	−3.59551e11	−0.274125
$494$	−1.73130e12	−1.30798
$495$	−1.28797e12	−0.964231
$496$	1.96928e12	1.46097
$497$	4.28676e11	0.315156
$498$	−8.64618e10	−0.0629930
$499$	3.38151e11	0.244151	0.122075	−	0.992521i	$-0.461045\pi$
$499$	3.38151e11	0.244151	0.122075	+	0.992521i	$0.461045\pi$
$500$	−1.78276e11	−0.127564
$501$	3.79630e11	0.269210
$502$	−2.61785e12	−1.83983
$503$	1.30064e12	0.905947	0.452973	−	0.891524i	$-0.350363\pi$
$503$	1.30064e12	0.905947	0.452973	+	0.891524i	$0.350363\pi$
$504$	−1.58514e11	−0.109429
$505$	−7.97971e10	−0.0545979
$506$	7.99706e11	0.542316
$507$	1.83262e12	1.23179
$508$	−3.50459e11	−0.233480
$509$	2.79225e12	1.84384	0.921921	−	0.387379i	$-0.126619\pi$
$509$	2.79225e12	1.84384	0.921921	+	0.387379i	$0.126619\pi$
$510$	−2.75286e12	−1.80185
$511$	−4.68552e11	−0.303993
$512$	−1.04212e12	−0.670198
$513$	1.23082e12	0.784630
$514$	−1.94838e12	−1.23123
$515$	−1.56869e11	−0.0982665
$516$	−1.77253e11	−0.110070
$517$	−3.30103e12	−2.03209
$518$	5.06852e11	0.309312
$519$	−3.17394e11	−0.192020
$520$	3.94399e12	2.36549
$521$	−3.11544e12	−1.85246	−0.926231	−	0.376956i	$-0.876971\pi$
$521$	−3.11544e12	−1.85246	−0.926231	+	0.376956i	$0.876971\pi$
$522$	1.65213e11	0.0973930
$523$	−7.97590e11	−0.466146	−0.233073	−	0.972459i	$-0.574878\pi$
$523$	−7.97590e11	−0.466146	−0.233073	+	0.972459i	$0.574878\pi$
$524$	2.97114e11	0.172160
$525$	−4.66053e11	−0.267743
$526$	4.75577e11	0.270885
$527$	−3.36925e12	−1.90276
$528$	1.81124e12	1.01420
$529$	−1.50835e12	−0.837435
$530$	2.47039e11	0.135995
$531$	−2.73317e11	−0.149191
$532$	5.35389e10	0.0289779
$533$	5.24720e12	2.81614
$534$	6.17269e10	0.0328503
$535$	2.82469e12	1.49066
$536$	2.33906e12	1.22405
$537$	5.55910e11	0.288483
$538$	2.10139e12	1.08140
$539$	2.29805e12	1.17276
$540$	5.28555e11	0.267497
$541$	2.66102e12	1.33555	0.667776	−	0.744362i	$-0.267246\pi$
$541$	2.66102e12	1.33555	0.667776	+	0.744362i	$0.267246\pi$
$542$	5.38994e11	0.268279
$543$	−2.24354e12	−1.10748
$544$	−9.47956e11	−0.464080
$545$	−3.40841e12	−1.65489
$546$	−6.54630e11	−0.315231
$547$	−2.32575e12	−1.11076	−0.555379	−	0.831597i	$-0.687427\pi$
$547$	−2.32575e12	−1.11076	−0.555379	+	0.831597i	$0.687427\pi$
$548$	3.96052e11	0.187603
$549$	6.02693e11	0.283153
$550$	−4.35245e12	−2.02816
$551$	2.96014e11	0.136814
$552$	5.70368e11	0.261474
$553$	2.68552e11	0.122114
$554$	−3.87913e11	−0.174961
$555$	2.93725e12	1.31408
$556$	−2.58222e11	−0.114593
$557$	−8.52834e11	−0.375419	−0.187709	−	0.982225i	$-0.560106\pi$
$557$	−8.52834e11	−0.375419	−0.187709	+	0.982225i	$0.560106\pi$
$558$	1.54817e12	0.676027
$559$	−3.69017e12	−1.59843
$560$	−1.03588e12	−0.445105
$561$	−3.09886e12	−1.32090
$562$	−2.04628e12	−0.865269
$563$	4.06061e12	1.70335	0.851675	−	0.524070i	$-0.175587\pi$
$563$	4.06061e12	1.70335	0.851675	+	0.524070i	$0.175587\pi$
$564$	4.43821e11	0.184694
$565$	3.83398e12	1.58282
$566$	−2.36586e12	−0.968982
$567$	1.68025e11	0.0682732
$568$	2.85530e12	1.15102
$569$	−2.57557e12	−1.03007	−0.515037	−	0.857168i	$-0.672222\pi$
$569$	−2.57557e12	−1.03007	−0.515037	+	0.857168i	$0.672222\pi$
$570$	2.26640e12	0.899289
$571$	1.16025e12	0.456760	0.228380	−	0.973572i	$-0.426657\pi$
$571$	1.16025e12	0.456760	0.228380	+	0.973572i	$0.426657\pi$
$572$	−8.36926e11	−0.326892
$573$	−2.27143e11	−0.0880244
$574$	−1.18531e12	−0.455751
$575$	−1.59360e12	−0.607960
$576$	−1.02344e12	−0.387401
$577$	4.68066e12	1.75799	0.878993	−	0.476834i	$-0.158216\pi$
$577$	4.68066e12	1.75799	0.878993	+	0.476834i	$0.158216\pi$
$578$	3.40588e12	1.26927
$579$	−2.30788e12	−0.853413
$580$	1.27119e11	0.0466427
$581$	5.56639e10	0.0202666
$582$	−1.92104e12	−0.694037
$583$	2.78088e11	0.0996952
$584$	−3.12090e12	−1.11025
$585$	3.60508e12	1.27266
$586$	1.48955e11	0.0521816
$587$	−2.02367e12	−0.703506	−0.351753	−	0.936093i	$-0.614414\pi$
$587$	−2.02367e12	−0.703506	−0.351753	+	0.936093i	$0.614414\pi$
$588$	−3.08970e11	−0.106591
$589$	2.77386e12	0.949655
$590$	−1.53616e12	−0.521920
$591$	1.93624e12	0.652852
$592$	3.92529e12	1.31348
$593$	−2.18835e12	−0.726727	−0.363363	−	0.931647i	$-0.618372\pi$
$593$	−2.18835e12	−0.726727	−0.363363	+	0.931647i	$0.618372\pi$
$594$	4.34625e12	1.43244
$595$	1.77228e12	0.579705
$596$	−1.57797e11	−0.0512260
$597$	2.35499e12	0.758759
$598$	−2.23841e12	−0.715789
$599$	3.95151e12	1.25413	0.627064	−	0.778968i	$-0.284256\pi$
$599$	3.95151e12	1.25413	0.627064	+	0.778968i	$0.284256\pi$
$600$	−3.10426e12	−0.977862
$601$	−4.59686e12	−1.43723	−0.718614	−	0.695409i	$-0.755223\pi$
$601$	−4.59686e12	−1.43723	−0.718614	+	0.695409i	$0.755223\pi$
$602$	8.33585e11	0.258682
$603$	2.13806e12	0.658556
$604$	2.21426e11	0.0676960
$605$	−2.93022e12	−0.889204
$606$	8.82205e10	0.0265731
$607$	−6.36094e11	−0.190183	−0.0950916	−	0.995469i	$-0.530314\pi$
$607$	−6.36094e11	−0.190183	−0.0950916	+	0.995469i	$0.530314\pi$
$608$	7.80441e11	0.231619
$609$	1.11927e11	0.0329730
$610$	3.38741e12	0.990565
$611$	9.23974e12	2.68210
$612$	−3.95930e11	−0.114087
$613$	1.20615e12	0.345008	0.172504	−	0.985009i	$-0.444814\pi$
$613$	1.20615e12	0.345008	0.172504	+	0.985009i	$0.444814\pi$
$614$	−4.64764e12	−1.31970
$615$	−6.86897e12	−1.93621
$616$	−1.00290e12	−0.280637
$617$	−3.39703e11	−0.0943662	−0.0471831	−	0.998886i	$-0.515024\pi$
$617$	−3.39703e11	−0.0943662	−0.0471831	+	0.998886i	$0.515024\pi$
$618$	1.73428e11	0.0478269
$619$	3.36814e12	0.922110	0.461055	−	0.887372i	$-0.347471\pi$
$619$	3.36814e12	0.922110	0.461055	+	0.887372i	$0.347471\pi$
$620$	1.19119e12	0.323757
$621$	1.59133e12	0.429387
$622$	−3.09760e12	−0.829791
$623$	−3.97397e10	−0.0105689
$624$	−5.06975e12	−1.33862
$625$	−8.93454e11	−0.234214
$626$	−6.73368e12	−1.75254
$627$	2.55125e12	0.659249
$628$	2.83886e11	0.0728326
$629$	−6.71579e12	−1.71068
$630$	−8.14364e11	−0.205962
$631$	−9.61309e11	−0.241397	−0.120698	−	0.992689i	$-0.538513\pi$
$631$	−9.61309e11	−0.241397	−0.120698	+	0.992689i	$0.538513\pi$
$632$	1.78875e12	0.445989
$633$	−9.52495e11	−0.235801
$634$	−6.59996e12	−1.62233
$635$	9.55109e12	2.33116
$636$	−3.73887e10	−0.00906116
$637$	−6.43233e12	−1.54789
$638$	1.04528e12	0.249770
$639$	2.60994e12	0.619265
$640$	−7.86523e12	−1.85311
$641$	−2.11380e11	−0.0494542	−0.0247271	−	0.999694i	$-0.507872\pi$
$641$	−2.11380e11	−0.0494542	−0.0247271	+	0.999694i	$0.507872\pi$
$642$	−3.12286e12	−0.725513
$643$	−1.04548e12	−0.241194	−0.120597	−	0.992702i	$-0.538481\pi$
$643$	−1.04548e12	−0.241194	−0.120597	+	0.992702i	$0.538481\pi$
$644$	6.92210e10	0.0158581
$645$	4.83070e12	1.09898
$646$	−5.18193e12	−1.17070
$647$	5.91760e11	0.132763	0.0663813	−	0.997794i	$-0.478855\pi$
$647$	5.91760e11	0.132763	0.0663813	+	0.997794i	$0.478855\pi$
$648$	1.11917e12	0.249350
$649$	−1.72924e12	−0.382608
$650$	1.21827e13	2.67691
$651$	1.04884e12	0.228873
$652$	−4.30446e11	−0.0932833
$653$	−6.95010e12	−1.49583	−0.747914	−	0.663796i	$-0.768945\pi$
$653$	−6.95010e12	−1.49583	−0.747914	+	0.663796i	$0.768945\pi$
$654$	3.76821e12	0.805443
$655$	−8.09728e12	−1.71891
$656$	−9.17958e12	−1.93533
$657$	−2.85272e12	−0.597331
$658$	−2.08720e12	−0.434058
$659$	−4.88531e12	−1.00904	−0.504519	−	0.863401i	$-0.668330\pi$
$659$	−4.88531e12	−1.00904	−0.504519	+	0.863401i	$0.668330\pi$
$660$	1.09560e12	0.224752
$661$	−5.32521e12	−1.08500	−0.542500	−	0.840056i	$-0.682522\pi$
$661$	−5.32521e12	−1.08500	−0.542500	+	0.840056i	$0.682522\pi$
$662$	−1.34886e12	−0.272965
$663$	8.67384e12	1.74341
$664$	3.70763e11	0.0740184
$665$	−1.45910e12	−0.289326
$666$	3.08590e12	0.607782
$667$	3.82719e11	0.0748711
$668$	3.06878e11	0.0596309
$669$	6.86005e12	1.32407
$670$	1.20169e13	2.30386
$671$	3.81316e12	0.726162
$672$	2.95097e11	0.0558216
$673$	−2.69464e12	−0.506328	−0.253164	−	0.967423i	$-0.581471\pi$
$673$	−2.69464e12	−0.506328	−0.253164	+	0.967423i	$0.581471\pi$
$674$	8.49804e12	1.58617
$675$	−8.66093e12	−1.60582
$676$	1.48142e12	0.272846
$677$	−5.90009e12	−1.07947	−0.539734	−	0.841836i	$-0.681475\pi$
$677$	−5.90009e12	−1.07947	−0.539734	+	0.841836i	$0.681475\pi$
$678$	−4.23870e12	−0.770369
$679$	1.23676e12	0.223291
$680$	1.18047e13	2.11722
$681$	1.77576e12	0.316389
$682$	9.79504e12	1.73371
$683$	7.67339e12	1.34925	0.674627	−	0.738158i	$-0.264304\pi$
$683$	7.67339e12	1.34925	0.674627	+	0.738158i	$0.264304\pi$
$684$	3.25965e11	0.0569401
$685$	−1.07937e13	−1.87310
$686$	3.00125e12	0.517421
$687$	4.46942e12	0.765501
$688$	6.45567e12	1.09848
$689$	−7.78382e11	−0.131585
$690$	2.93025e12	0.492134
$691$	−8.36632e12	−1.39599	−0.697997	−	0.716101i	$-0.745925\pi$
$691$	−8.36632e12	−1.39599	−0.697997	+	0.716101i	$0.745925\pi$
$692$	−2.56569e11	−0.0425331
$693$	−9.16719e11	−0.150986
$694$	−6.35852e12	−1.04049
$695$	7.03736e12	1.14414
$696$	7.45518e11	0.120425
$697$	1.57053e13	2.52058
$698$	−1.51166e12	−0.241049
$699$	−1.93318e12	−0.306285
$700$	−3.76739e11	−0.0593062
$701$	−7.10717e11	−0.111164	−0.0555822	−	0.998454i	$-0.517701\pi$
$701$	−7.10717e11	−0.111164	−0.0555822	+	0.998454i	$0.517701\pi$
$702$	−1.21653e13	−1.89063
$703$	5.52903e12	0.853788
$704$	−6.47517e12	−0.993514
$705$	−1.20955e13	−1.84405
$706$	3.98988e12	0.604420
$707$	−5.67961e10	−0.00854932
$708$	2.32495e11	0.0347747
$709$	−5.96922e12	−0.887176	−0.443588	−	0.896231i	$-0.646295\pi$
$709$	−5.96922e12	−0.887176	−0.443588	+	0.896231i	$0.646295\pi$
$710$	1.46690e13	2.16640
$711$	1.63504e12	0.239947
$712$	−2.64695e11	−0.0385999
$713$	3.58635e12	0.519697
$714$	−1.95937e12	−0.282146
$715$	2.28088e13	3.26382
$716$	4.49375e11	0.0639000
$717$	4.93532e12	0.697395
$718$	5.96292e12	0.837334
$719$	9.68339e12	1.35129	0.675643	−	0.737229i	$-0.263866\pi$
$719$	9.68339e12	1.35129	0.675643	+	0.737229i	$0.263866\pi$
$720$	−6.30681e12	−0.874608
$721$	−1.11653e11	−0.0153873
$722$	−3.59311e12	−0.492100
$723$	6.85731e11	0.0933322
$724$	−1.81359e12	−0.245310
$725$	−2.08297e12	−0.280003
$726$	3.23954e12	0.432781
$727$	−1.29591e13	−1.72056	−0.860282	−	0.509819i	$-0.829712\pi$
$727$	−1.29591e13	−1.72056	−0.860282	+	0.509819i	$0.829712\pi$
$728$	2.80716e12	0.370405
$729$	6.83813e12	0.896734
$730$	−1.60336e13	−2.08967
$731$	−1.10450e13	−1.43066
$732$	−5.12676e11	−0.0659999
$733$	−3.93613e12	−0.503618	−0.251809	−	0.967777i	$-0.581025\pi$
$733$	−3.93613e12	−0.503618	−0.251809	+	0.967777i	$0.581025\pi$
$734$	−1.02146e13	−1.29894
$735$	8.42040e12	1.06424
$736$	1.00904e12	0.126753
$737$	1.35272e13	1.68891
$738$	−7.21659e12	−0.895527
$739$	−8.82704e12	−1.08872	−0.544359	−	0.838853i	$-0.683227\pi$
$739$	−8.82704e12	−1.08872	−0.544359	+	0.838853i	$0.683227\pi$
$740$	2.37436e12	0.291074
$741$	−7.14108e12	−0.870125
$742$	1.75832e11	0.0212951
$743$	5.32733e12	0.641299	0.320649	−	0.947198i	$-0.396099\pi$
$743$	5.32733e12	0.641299	0.320649	+	0.947198i	$0.396099\pi$
$744$	6.98604e12	0.835897
$745$	4.30045e12	0.511459
$746$	6.54315e12	0.773504
$747$	3.38902e11	0.0398228
$748$	−2.50500e12	−0.292583
$749$	2.01049e12	0.233418
$750$	−5.37145e12	−0.619892
$751$	−4.52905e12	−0.519550	−0.259775	−	0.965669i	$-0.583648\pi$
$751$	−4.52905e12	−0.519550	−0.259775	+	0.965669i	$0.583648\pi$
$752$	−1.61642e13	−1.84321
$753$	−1.07978e13	−1.22394
$754$	−2.92579e12	−0.329665
$755$	−6.03456e12	−0.675903
$756$	3.76203e11	0.0418865
$757$	−6.14985e12	−0.680664	−0.340332	−	0.940305i	$-0.610539\pi$
$757$	−6.14985e12	−0.680664	−0.340332	+	0.940305i	$0.610539\pi$
$758$	1.01943e13	1.12162
$759$	3.29854e12	0.360773
$760$	−9.71869e12	−1.05669
$761$	−6.25614e12	−0.676201	−0.338100	−	0.941110i	$-0.609784\pi$
$761$	−6.25614e12	−0.676201	−0.338100	+	0.941110i	$0.609784\pi$
$762$	−1.05593e13	−1.13459
$763$	−2.42596e12	−0.259134
$764$	−1.83613e11	−0.0194977
$765$	1.07903e13	1.13909
$766$	−6.35986e12	−0.667449
$767$	4.84022e12	0.504994
$768$	3.20667e12	0.332605
$769$	5.75533e12	0.593474	0.296737	−	0.954959i	$-0.404101\pi$
$769$	5.75533e12	0.593474	0.296737	+	0.954959i	$0.404101\pi$
$770$	−5.15237e12	−0.528201
$771$	−8.03646e12	−0.819069
$772$	−1.86560e12	−0.189034
$773$	−4.67836e11	−0.0471288	−0.0235644	−	0.999722i	$-0.507501\pi$
$773$	−4.67836e11	−0.0471288	−0.0235644	+	0.999722i	$0.507501\pi$
$774$	5.07517e12	0.508296
$775$	−1.95189e13	−1.94356
$776$	8.23774e12	0.815512
$777$	2.09061e12	0.205768
$778$	8.76640e12	0.857853
$779$	−1.29300e13	−1.25800
$780$	−3.06663e12	−0.296644
$781$	1.65127e13	1.58814
$782$	−6.69977e12	−0.640663
$783$	2.08001e12	0.197759
$784$	1.12529e13	1.06376
$785$	−7.73678e12	−0.727188
$786$	8.95203e12	0.836604
$787$	−3.26611e12	−0.303490	−0.151745	−	0.988420i	$-0.548489\pi$
$787$	−3.26611e12	−0.303490	−0.151745	+	0.988420i	$0.548489\pi$
$788$	1.56518e12	0.144609
$789$	1.96161e12	0.180205
$790$	9.18968e12	0.839418
$791$	2.72886e12	0.247849
$792$	−6.10602e12	−0.551436
$793$	−1.06732e13	−0.958441
$794$	1.36711e13	1.22070
$795$	1.01896e12	0.0904700
$796$	1.90368e12	0.168068
$797$	7.21893e12	0.633739	0.316869	−	0.948469i	$-0.397368\pi$
$797$	7.21893e12	0.633739	0.316869	+	0.948469i	$0.397368\pi$
$798$	1.61312e12	0.140817
$799$	2.76554e13	2.40060
$800$	−5.49176e12	−0.474031
$801$	−2.41950e11	−0.0207672
$802$	6.55966e12	0.559882
$803$	−1.80488e13	−1.53189
$804$	−1.81873e12	−0.153502
$805$	−1.88649e12	−0.158333
$806$	−2.74168e13	−2.28828
$807$	8.66760e12	0.719396
$808$	−3.78304e11	−0.0312241
$809$	−5.31395e12	−0.436163	−0.218082	−	0.975931i	$-0.569980\pi$
$809$	−5.31395e12	−0.436163	−0.218082	+	0.975931i	$0.569980\pi$
$810$	5.74971e12	0.469314
$811$	2.47114e12	0.200588	0.100294	−	0.994958i	$-0.468022\pi$
$811$	2.47114e12	0.200588	0.100294	+	0.994958i	$0.468022\pi$
$812$	9.04776e10	0.00730364
$813$	2.22318e12	0.178471
$814$	1.95241e13	1.55869
$815$	1.17310e13	0.931376
$816$	−1.51742e13	−1.19812
$817$	9.09323e12	0.714034
$818$	3.48899e12	0.272464
$819$	2.56594e12	0.199282
$820$	−5.55261e12	−0.428879
$821$	−1.31768e13	−1.01220	−0.506100	−	0.862475i	$-0.668914\pi$
$821$	−1.31768e13	−1.01220	−0.506100	+	0.862475i	$0.668914\pi$
$822$	1.19330e13	0.911648
$823$	3.25277e12	0.247147	0.123573	−	0.992335i	$-0.460565\pi$
$823$	3.25277e12	0.247147	0.123573	+	0.992335i	$0.460565\pi$
$824$	−7.43690e11	−0.0561979
$825$	−1.79525e13	−1.34922
$826$	−1.09338e12	−0.0817258
$827$	−2.49083e13	−1.85169	−0.925847	−	0.377899i	$-0.876647\pi$
$827$	−2.49083e13	−1.85169	−0.925847	+	0.377899i	$0.876647\pi$
$828$	4.21443e11	0.0311603
$829$	−5.37114e12	−0.394976	−0.197488	−	0.980305i	$-0.563278\pi$
$829$	−5.37114e12	−0.394976	−0.197488	+	0.980305i	$0.563278\pi$
$830$	1.90478e12	0.139314
$831$	−1.60002e12	−0.116392
$832$	1.81243e13	1.31131
$833$	−1.92526e13	−1.38544
$834$	−7.78023e12	−0.556859
$835$	−8.36338e12	−0.595378
$836$	2.06233e12	0.146026
$837$	1.94911e13	1.37269
$838$	2.39422e13	1.67713
$839$	1.73928e13	1.21183	0.605915	−	0.795530i	$-0.292807\pi$
$839$	1.73928e13	1.21183	0.605915	+	0.795530i	$0.292807\pi$
$840$	−3.67478e12	−0.254668
$841$	5.00246e11	0.0344828
$842$	1.08712e13	0.745373
$843$	−8.44027e12	−0.575615
$844$	−7.69960e11	−0.0522308
$845$	−4.03733e13	−2.72420
$846$	−1.27076e13	−0.852900
$847$	−2.08561e12	−0.139238
$848$	1.36172e12	0.0904288
$849$	−9.75846e12	−0.644610
$850$	3.64639e13	2.39595
$851$	7.14854e12	0.467234
$852$	−2.22012e12	−0.144344
$853$	2.55914e13	1.65510	0.827548	−	0.561395i	$-0.189735\pi$
$853$	2.55914e13	1.65510	0.827548	+	0.561395i	$0.189735\pi$
$854$	2.41101e12	0.155110
$855$	−8.88355e12	−0.568511
$856$	1.33914e13	0.852497
$857$	9.16963e12	0.580682	0.290341	−	0.956923i	$-0.406231\pi$
$857$	9.16963e12	0.580682	0.290341	+	0.956923i	$0.406231\pi$
$858$	−2.52165e13	−1.58852
$859$	−2.27442e12	−0.142528	−0.0712641	−	0.997457i	$-0.522703\pi$
$859$	−2.27442e12	−0.142528	−0.0712641	+	0.997457i	$0.522703\pi$
$860$	3.90495e12	0.243429
$861$	−4.88904e12	−0.303186
$862$	1.44291e13	0.890139
$863$	2.09452e13	1.28540	0.642698	−	0.766120i	$-0.277815\pi$
$863$	2.09452e13	1.28540	0.642698	+	0.766120i	$0.277815\pi$
$864$	5.48394e12	0.334797
$865$	6.99231e12	0.424666
$866$	1.52367e13	0.920579
$867$	1.40482e13	0.844375
$868$	8.47840e11	0.0506962
$869$	1.03447e13	0.615359
$870$	3.83008e12	0.226658
$871$	−3.78634e13	−2.22914
$872$	−1.61587e13	−0.946416
$873$	7.52985e12	0.438755
$874$	5.51585e12	0.319750
$875$	3.45813e12	0.199437
$876$	2.42664e12	0.139231
$877$	−8.04577e12	−0.459272	−0.229636	−	0.973277i	$-0.573754\pi$
$877$	−8.04577e12	−0.459272	−0.229636	+	0.973277i	$0.573754\pi$
$878$	−1.90542e12	−0.108210
$879$	6.14396e11	0.0347135
$880$	−3.99023e13	−2.24298
$881$	1.56243e13	0.873794	0.436897	−	0.899512i	$-0.356078\pi$
$881$	1.56243e13	0.873794	0.436897	+	0.899512i	$0.356078\pi$
$882$	8.84655e12	0.492227
$883$	1.21770e13	0.674087	0.337044	−	0.941489i	$-0.390573\pi$
$883$	1.21770e13	0.674087	0.337044	+	0.941489i	$0.390573\pi$
$884$	7.01160e12	0.386173
$885$	−6.33621e12	−0.347204
$886$	−2.67669e13	−1.45931
$887$	2.50236e13	1.35735	0.678676	−	0.734438i	$-0.262554\pi$
$887$	2.50236e13	1.35735	0.678676	+	0.734438i	$0.262554\pi$
$888$	1.39250e13	0.751513
$889$	6.79805e12	0.365028
$890$	−1.35987e12	−0.0726509
$891$	6.47238e12	0.344044
$892$	5.54539e12	0.293285
$893$	−2.27684e13	−1.19812
$894$	−4.75441e12	−0.248930
$895$	−1.22469e13	−0.638002
$896$	−5.59813e12	−0.290173
$897$	−9.23277e12	−0.476174
$898$	−2.56053e13	−1.31397
$899$	4.68766e12	0.239352
$900$	−2.29373e12	−0.116533
$901$	−2.32977e12	−0.117774
$902$	−4.56584e13	−2.29663
$903$	3.43828e12	0.172087
$904$	1.81762e13	0.905204
$905$	4.94260e13	2.44927
$906$	6.67156e12	0.328966
$907$	1.42304e13	0.698207	0.349103	−	0.937084i	$-0.386486\pi$
$907$	1.42304e13	0.698207	0.349103	+	0.937084i	$0.386486\pi$
$908$	1.43545e12	0.0700814
$909$	−3.45796e11	−0.0167990
$910$	1.44217e13	0.697157
$911$	−3.22836e13	−1.55292	−0.776460	−	0.630167i	$-0.782986\pi$
$911$	−3.22836e13	−1.55292	−0.776460	+	0.630167i	$0.782986\pi$
$912$	1.24928e13	0.597974
$913$	2.14419e12	0.102128
$914$	−1.48542e13	−0.704030
$915$	1.39720e13	0.658968
$916$	3.61290e12	0.169561
$917$	−5.76330e12	−0.269159
$918$	−3.64120e13	−1.69220
$919$	7.65321e12	0.353935	0.176968	−	0.984217i	$-0.443371\pi$
$919$	7.65321e12	0.353935	0.176968	+	0.984217i	$0.443371\pi$
$920$	−1.25654e13	−0.578270
$921$	−1.91701e13	−0.877923
$922$	−3.24257e13	−1.47775
$923$	−4.62199e13	−2.09614
$924$	7.79799e11	0.0351932
$925$	−3.89063e13	−1.74736
$926$	3.52839e13	1.57698
$927$	−6.79784e11	−0.0302351
$928$	1.31890e12	0.0583776
$929$	1.59043e13	0.700558	0.350279	−	0.936645i	$-0.386087\pi$
$929$	1.59043e13	0.700558	0.350279	+	0.936645i	$0.386087\pi$
$930$	3.58906e13	1.57328
$931$	1.58504e13	0.691460
$932$	−1.56271e12	−0.0678432
$933$	−1.27767e13	−0.552014
$934$	4.51939e12	0.194321
$935$	6.82689e13	2.92126
$936$	1.70910e13	0.727825
$937$	2.24799e13	0.952722	0.476361	−	0.879250i	$-0.341956\pi$
$937$	2.24799e13	0.952722	0.476361	+	0.879250i	$0.341956\pi$
$938$	8.55310e12	0.360754
$939$	−2.77744e13	−1.16587
$940$	−9.77753e12	−0.408464
$941$	−5.26818e12	−0.219032	−0.109516	−	0.993985i	$-0.534930\pi$
$941$	−5.26818e12	−0.219032	−0.109516	+	0.993985i	$0.534930\pi$
$942$	8.55348e12	0.353927
$943$	−1.67174e13	−0.688438
$944$	−8.46761e12	−0.347046
$945$	−1.02527e13	−0.418211
$946$	3.21099e13	1.30356
$947$	−5.63863e12	−0.227823	−0.113912	−	0.993491i	$-0.536338\pi$
$947$	−5.63863e12	−0.227823	−0.113912	+	0.993491i	$0.536338\pi$
$948$	−1.39084e12	−0.0559292
$949$	5.05193e13	2.02190
$950$	−3.00203e13	−1.19580
$951$	−2.72228e13	−1.07925
$952$	8.40210e12	0.331529
$953$	−5.07222e13	−1.99196	−0.995979	−	0.0895917i	$-0.971444\pi$
$953$	−5.07222e13	−1.99196	−0.995979	+	0.0895917i	$0.971444\pi$
$954$	1.07053e12	0.0418437
$955$	5.00404e12	0.194673
$956$	3.98952e12	0.154476
$957$	4.31147e12	0.166158
$958$	−3.81397e13	−1.46296
$959$	−7.68246e12	−0.293303
$960$	−2.37260e13	−0.901581
$961$	1.74871e13	0.661399
$962$	−5.46488e13	−2.05728
$963$	1.22406e13	0.458654
$964$	5.54318e11	0.0206734
$965$	5.08433e13	1.88739
$966$	2.08562e12	0.0770618
$967$	−4.27613e12	−0.157265	−0.0786324	−	0.996904i	$-0.525055\pi$
$967$	−4.27613e12	−0.157265	−0.0786324	+	0.996904i	$0.525055\pi$
$968$	−1.38917e13	−0.508529
$969$	−2.13739e13	−0.778801
$970$	4.23212e13	1.53492
$971$	−1.12150e13	−0.404868	−0.202434	−	0.979296i	$-0.564885\pi$
$971$	−1.12150e13	−0.404868	−0.202434	+	0.979296i	$0.564885\pi$
$972$	3.83052e12	0.137645
$973$	5.00889e12	0.179157
$974$	−5.11863e13	−1.82238
$975$	5.02499e13	1.78080
$976$	1.86720e13	0.658667
$977$	4.98842e13	1.75161	0.875806	−	0.482664i	$-0.160331\pi$
$977$	4.98842e13	1.75161	0.875806	+	0.482664i	$0.160331\pi$
$978$	−1.29693e13	−0.453306
$979$	−1.53078e12	−0.0532588
$980$	6.80672e12	0.235733
$981$	−1.47702e13	−0.509184
$982$	−4.54610e13	−1.56005
$983$	−4.09483e13	−1.39877	−0.699383	−	0.714748i	$-0.746542\pi$
$983$	−4.09483e13	−1.39877	−0.699383	+	0.714748i	$0.746542\pi$
$984$	−3.25646e13	−1.10731
$985$	−4.26560e13	−1.44383
$986$	−8.75717e12	−0.295065
$987$	−8.60906e12	−0.288754
$988$	−5.77257e12	−0.192736
$989$	1.17567e13	0.390754
$990$	−3.13695e13	−1.03789
$991$	2.36513e13	0.778975	0.389488	−	0.921032i	$-0.372652\pi$
$991$	2.36513e13	0.778975	0.389488	+	0.921032i	$0.372652\pi$
$992$	1.23590e13	0.405212
$993$	−5.56365e12	−0.181589
$994$	1.04408e13	0.339230
$995$	−5.18812e13	−1.67805
$996$	−2.88285e11	−0.00928228
$997$	−2.65134e13	−0.849841	−0.424920	−	0.905231i	$-0.639698\pi$
$997$	−2.65134e13	−0.849841	−0.424920	+	0.905231i	$0.639698\pi$
$998$	8.23596e12	0.262801
$999$	3.88509e13	1.23412

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.10.a.a.1.7	✓	9
3.2	odd	2		261.10.a.b.1.3		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.10.a.a.1.7	✓	9	1.1	even	1	trivial
261.10.a.b.1.3		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)

\(f(q)\)	\(=\)	\(q+24.3559 q^{2} +100.461 q^{3} +81.2084 q^{4} -2213.18 q^{5} +2446.80 q^{6} -1575.25 q^{7} -10492.3 q^{8} -9590.68 q^{9} +O(q^{10})\)	\(q+24.3559 q^{2} +100.461 q^{3} +81.2084 q^{4} -2213.18 q^{5} +2446.80 q^{6} -1575.25 q^{7} -10492.3 q^{8} -9590.68 q^{9} -53903.9 q^{10} -60678.9 q^{11} +8158.23 q^{12} +169843. q^{13} -38366.5 q^{14} -222337. q^{15} -297128. q^{16} +508356. q^{17} -233589. q^{18} -418524. q^{19} -179729. q^{20} -158250. q^{21} -1.47789e6 q^{22} -541114. q^{23} -1.05406e6 q^{24} +2.94504e6 q^{25} +4.13668e6 q^{26} -2.94085e6 q^{27} -127923. q^{28} -707281. q^{29} -5.41522e6 q^{30} -6.62773e6 q^{31} -1.86475e6 q^{32} -6.09584e6 q^{33} +1.23815e7 q^{34} +3.48631e6 q^{35} -778844. q^{36} -1.32108e7 q^{37} -1.01935e7 q^{38} +1.70625e7 q^{39} +2.32214e7 q^{40} +3.08944e7 q^{41} -3.85432e6 q^{42} -2.17269e7 q^{43} -4.92764e6 q^{44} +2.12259e7 q^{45} -1.31793e7 q^{46} +5.44016e7 q^{47} -2.98496e7 q^{48} -3.78722e7 q^{49} +7.17291e7 q^{50} +5.10697e7 q^{51} +1.37927e7 q^{52} -4.58294e6 q^{53} -7.16269e7 q^{54} +1.34293e8 q^{55} +1.65280e7 q^{56} -4.20451e7 q^{57} -1.72264e7 q^{58} +2.84982e7 q^{59} -1.80556e7 q^{60} -6.28415e7 q^{61} -1.61424e8 q^{62} +1.51077e7 q^{63} +1.06712e8 q^{64} -3.75894e8 q^{65} -1.48469e8 q^{66} -2.22931e8 q^{67} +4.12828e7 q^{68} -5.43606e7 q^{69} +8.49120e7 q^{70} -2.72133e8 q^{71} +1.00628e8 q^{72} +2.97447e8 q^{73} -3.21760e8 q^{74} +2.95861e8 q^{75} -3.39876e7 q^{76} +9.55843e7 q^{77} +4.15573e8 q^{78} -1.70482e8 q^{79} +6.57598e8 q^{80} -1.06666e8 q^{81} +7.52459e8 q^{82} -3.53366e7 q^{83} -1.28512e7 q^{84} -1.12508e9 q^{85} -5.29178e8 q^{86} -7.10538e7 q^{87} +6.36662e8 q^{88} +2.52276e7 q^{89} +5.16976e8 q^{90} -2.67545e8 q^{91} -4.39429e7 q^{92} -6.65825e8 q^{93} +1.32500e9 q^{94} +9.26269e8 q^{95} -1.87334e8 q^{96} -7.85122e8 q^{97} -9.22410e8 q^{98} +5.81953e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 244 q^{3} + 1194 q^{4} - 738 q^{5} - 2330 q^{6} - 7128 q^{7} - 13776 q^{8} + 33017 q^{9}+O(q^{10}) \) 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

Varieties

Fields

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Groups

Database

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