LMFDB - Embedded newform 29.10.a.a.1.5

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			1.5
Root			$-4.12402$ 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)

$f(q)$	$=$	$q+4.12402 q^{2} +158.305 q^{3} -494.992 q^{4} +522.723 q^{5} +652.853 q^{6} -9369.41 q^{7} -4152.85 q^{8} +5377.54 q^{9} +O(q^{10})$	\(q+4.12402 q^{2} +158.305 q^{3} -494.992 q^{4} +522.723 q^{5} +652.853 q^{6} -9369.41 q^{7} -4152.85 q^{8} +5377.54 q^{9} +2155.72 q^{10} -6957.32 q^{11} -78359.9 q^{12} -77404.1 q^{13} -38639.6 q^{14} +82749.7 q^{15} +236310. q^{16} +2734.04 q^{17} +22177.1 q^{18} -81749.2 q^{19} -258744. q^{20} -1.48323e6 q^{21} -28692.1 q^{22} -1.95071e6 q^{23} -657418. q^{24} -1.67989e6 q^{25} -319216. q^{26} -2.26463e6 q^{27} +4.63779e6 q^{28} -707281. q^{29} +341261. q^{30} +2.30422e6 q^{31} +3.10081e6 q^{32} -1.10138e6 q^{33} +11275.2 q^{34} -4.89760e6 q^{35} -2.66184e6 q^{36} +1.66645e7 q^{37} -337135. q^{38} -1.22535e7 q^{39} -2.17079e6 q^{40} +2.60123e6 q^{41} -6.11685e6 q^{42} +2.23061e7 q^{43} +3.44382e6 q^{44} +2.81096e6 q^{45} -8.04477e6 q^{46} -1.13465e7 q^{47} +3.74091e7 q^{48} +4.74322e7 q^{49} -6.92788e6 q^{50} +432813. q^{51} +3.83144e7 q^{52} +6.78763e7 q^{53} -9.33937e6 q^{54} -3.63675e6 q^{55} +3.89098e7 q^{56} -1.29413e7 q^{57} -2.91684e6 q^{58} -1.61848e8 q^{59} -4.09605e7 q^{60} -5.64355e7 q^{61} +9.50265e6 q^{62} -5.03843e7 q^{63} -1.08203e8 q^{64} -4.04609e7 q^{65} -4.54211e6 q^{66} -3.70760e7 q^{67} -1.35333e6 q^{68} -3.08808e8 q^{69} -2.01978e7 q^{70} +2.62158e8 q^{71} -2.23321e7 q^{72} +1.99967e8 q^{73} +6.87247e7 q^{74} -2.65935e8 q^{75} +4.04652e7 q^{76} +6.51860e7 q^{77} -5.05335e7 q^{78} +1.16097e8 q^{79} +1.23524e8 q^{80} -4.64349e8 q^{81} +1.07275e7 q^{82} -3.04414e8 q^{83} +7.34186e8 q^{84} +1.42915e6 q^{85} +9.19907e7 q^{86} -1.11966e8 q^{87} +2.88927e7 q^{88} -3.86314e8 q^{89} +1.15924e7 q^{90} +7.25230e8 q^{91} +9.65588e8 q^{92} +3.64770e8 q^{93} -4.67932e7 q^{94} -4.27322e7 q^{95} +4.90874e8 q^{96} -1.61913e9 q^{97} +1.95611e8 q^{98} -3.74132e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	4.12402	0.182258	0.0911288	−	0.995839i	$-0.470953\pi$
$2$	4.12402	0.182258	0.0911288	+	0.995839i	$0.470953\pi$
$3$	158.305	1.12836	0.564182	−	0.825650i	$-0.309191\pi$
$3$	158.305	1.12836	0.564182	+	0.825650i	$0.309191\pi$
$4$	−494.992	−0.966782
$5$	522.723	0.374030	0.187015	−	0.982357i	$-0.440119\pi$
$5$	522.723	0.374030	0.187015	+	0.982357i	$0.440119\pi$
$6$	652.853	0.205653
$7$	−9369.41	−1.47493	−0.737464	−	0.675386i	$-0.763977\pi$
$7$	−9369.41	−1.47493	−0.737464	+	0.675386i	$0.763977\pi$
$8$	−4152.85	−0.358461
$9$	5377.54	0.273207
$10$	2155.72	0.0681698
$11$	−6957.32	−0.143276	−0.0716382	−	0.997431i	$-0.522823\pi$
$11$	−6957.32	−0.143276	−0.0716382	+	0.997431i	$0.522823\pi$
$12$	−78359.9	−1.09088
$13$	−77404.1	−0.751655	−0.375828	−	0.926690i	$-0.622642\pi$
$13$	−77404.1	−0.751655	−0.375828	+	0.926690i	$0.622642\pi$
$14$	−38639.6	−0.268817
$15$	82749.7	0.422042
$16$	236310.	0.901450
$17$	2734.04	0.00793935	0.00396968	−	0.999992i	$-0.498736\pi$
$17$	2734.04	0.00793935	0.00396968	+	0.999992i	$0.498736\pi$
$18$	22177.1	0.0497941
$19$	−81749.2	−0.143910	−0.0719552	−	0.997408i	$-0.522924\pi$
$19$	−81749.2	−0.143910	−0.0719552	+	0.997408i	$0.522924\pi$
$20$	−258744.	−0.361605
$21$	−1.48323e6	−1.66426
$22$	−28692.1	−0.0261132
$23$	−1.95071e6	−1.45351	−0.726755	−	0.686897i	$-0.758972\pi$
$23$	−1.95071e6	−1.45351	−0.726755	+	0.686897i	$0.758972\pi$
$24$	−657418.	−0.404475
$25$	−1.67989e6	−0.860102
$26$	−319216.	−0.136995
$27$	−2.26463e6	−0.820087
$28$	4.63779e6	1.42593
$29$	−707281.	−0.185695
$29$	−707281.	−0.185695
$30$	341261.	0.0769204
$31$	2.30422e6	0.448122	0.224061	−	0.974575i	$-0.428068\pi$
$31$	2.30422e6	0.448122	0.224061	+	0.974575i	$0.428068\pi$
$32$	3.10081e6	0.522757
$33$	−1.10138e6	−0.161668
$34$	11275.2	0.00144701
$35$	−4.89760e6	−0.551667
$36$	−2.66184e6	−0.264132
$37$	1.66645e7	1.46179	0.730894	−	0.682491i	$-0.239103\pi$
$37$	1.66645e7	1.46179	0.730894	+	0.682491i	$0.239103\pi$
$38$	−337135.	−0.0262288
$39$	−1.22535e7	−0.848141
$40$	−2.17079e6	−0.134075
$41$	2.60123e6	0.143764	0.0718822	−	0.997413i	$-0.477099\pi$
$41$	2.60123e6	0.143764	0.0718822	+	0.997413i	$0.477099\pi$
$42$	−6.11685e6	−0.303324
$43$	2.23061e7	0.994983	0.497491	−	0.867469i	$-0.334255\pi$
$43$	2.23061e7	0.994983	0.497491	+	0.867469i	$0.334255\pi$
$44$	3.44382e6	0.138517
$45$	2.81096e6	0.102188
$46$	−8.04477e6	−0.264913
$47$	−1.13465e7	−0.339173	−0.169587	−	0.985515i	$-0.554243\pi$
$47$	−1.13465e7	−0.339173	−0.169587	+	0.985515i	$0.554243\pi$
$48$	3.74091e7	1.01716
$49$	4.74322e7	1.17542
$50$	−6.92788e6	−0.156760
$51$	432813.	0.00895849
$52$	3.83144e7	0.726687
$53$	6.78763e7	1.18162	0.590809	−	0.806812i	$-0.298809\pi$
$53$	6.78763e7	1.18162	0.590809	+	0.806812i	$0.298809\pi$
$54$	−9.33937e6	−0.149467
$55$	−3.63675e6	−0.0535897
$56$	3.89098e7	0.528704
$57$	−1.29413e7	−0.162384
$58$	−2.91684e6	−0.0338444
$59$	−1.61848e8	−1.73890	−0.869448	−	0.494024i	$-0.835526\pi$
$59$	−1.61848e8	−1.73890	−0.869448	+	0.494024i	$0.835526\pi$
$60$	−4.09605e7	−0.408023
$61$	−5.64355e7	−0.521877	−0.260939	−	0.965355i	$-0.584032\pi$
$61$	−5.64355e7	−0.521877	−0.260939	+	0.965355i	$0.584032\pi$
$62$	9.50265e6	0.0816737
$63$	−5.03843e7	−0.402961
$64$	−1.08203e8	−0.806174
$65$	−4.04609e7	−0.281141
$66$	−4.54211e6	−0.0294652
$67$	−3.70760e7	−0.224779	−0.112390	−	0.993664i	$-0.535850\pi$
$67$	−3.70760e7	−0.224779	−0.112390	+	0.993664i	$0.535850\pi$
$68$	−1.35333e6	−0.00767563
$69$	−3.08808e8	−1.64009
$70$	−2.01978e7	−0.100546
$71$	2.62158e8	1.22434	0.612168	−	0.790728i	$-0.290298\pi$
$71$	2.62158e8	1.22434	0.612168	+	0.790728i	$0.290298\pi$
$72$	−2.23321e7	−0.0979341
$73$	1.99967e8	0.824147	0.412074	−	0.911151i	$-0.364805\pi$
$73$	1.99967e8	0.824147	0.412074	+	0.911151i	$0.364805\pi$
$74$	6.87247e7	0.266422
$75$	−2.65935e8	−0.970508
$76$	4.04652e7	0.139130
$77$	6.51860e7	0.211323
$78$	−5.05335e7	−0.154580
$79$	1.16097e8	0.335350	0.167675	−	0.985842i	$-0.446374\pi$
$79$	1.16097e8	0.335350	0.167675	+	0.985842i	$0.446374\pi$
$80$	1.23524e8	0.337169
$81$	−4.64349e8	−1.19856
$82$	1.07275e7	0.0262022
$83$	−3.04414e8	−0.704066	−0.352033	−	0.935988i	$-0.614510\pi$
$83$	−3.04414e8	−0.704066	−0.352033	+	0.935988i	$0.614510\pi$
$84$	7.34186e8	1.60897
$85$	1.42915e6	0.00296956
$86$	9.19907e7	0.181343
$87$	−1.11966e8	−0.209532
$88$	2.88927e7	0.0513590
$89$	−3.86314e8	−0.652658	−0.326329	−	0.945256i	$-0.605812\pi$
$89$	−3.86314e8	−0.652658	−0.326329	+	0.945256i	$0.605812\pi$
$90$	1.15924e7	0.0186245
$91$	7.25230e8	1.10864
$92$	9.65588e8	1.40523
$93$	3.64770e8	0.505646
$94$	−4.67932e7	−0.0618169
$95$	−4.27322e7	−0.0538268
$96$	4.90874e8	0.589861
$97$	−1.61913e9	−1.85699	−0.928496	−	0.371342i	$-0.878898\pi$
$97$	−1.61913e9	−1.85699	−0.928496	+	0.371342i	$0.878898\pi$
$98$	1.95611e8	0.214228
$99$	−3.74132e7	−0.0391442
$100$	8.31531e8	0.831531
$101$	−9.22738e8	−0.882332	−0.441166	−	0.897425i	$-0.645435\pi$
$101$	−9.22738e8	−0.882332	−0.441166	+	0.897425i	$0.645435\pi$
$102$	1.78493e6	0.00163275
$103$	8.72296e8	0.763653	0.381827	−	0.924234i	$-0.375295\pi$
$103$	8.72296e8	0.763653	0.381827	+	0.924234i	$0.375295\pi$
$104$	3.21448e8	0.269439
$105$	−7.75316e8	−0.622482
$106$	2.79923e8	0.215359
$107$	−3.62722e8	−0.267514	−0.133757	−	0.991014i	$-0.542704\pi$
$107$	−3.62722e8	−0.267514	−0.133757	+	0.991014i	$0.542704\pi$
$108$	1.12097e9	0.792846
$109$	−7.27651e8	−0.493747	−0.246873	−	0.969048i	$-0.579403\pi$
$109$	−7.27651e8	−0.493747	−0.246873	+	0.969048i	$0.579403\pi$
$110$	−1.49980e7	−0.00976712
$111$	2.63808e9	1.64943
$112$	−2.21408e9	−1.32957
$113$	2.51672e9	1.45205	0.726027	−	0.687666i	$-0.241365\pi$
$113$	2.51672e9	1.45205	0.726027	+	0.687666i	$0.241365\pi$
$114$	−5.33703e7	−0.0295956
$115$	−1.01968e9	−0.543656
$116$	3.50099e8	0.179527
$117$	−4.16243e8	−0.205358
$118$	−6.67465e8	−0.316927
$119$	−2.56164e7	−0.0117100
$120$	−3.43647e8	−0.151286
$121$	−2.30954e9	−0.979472
$122$	−2.32741e8	−0.0951161
$123$	4.11788e8	0.162219
$124$	−1.14057e9	−0.433237
$125$	−1.89906e9	−0.695734
$126$	−2.07786e8	−0.0734427
$127$	−4.09762e9	−1.39770	−0.698852	−	0.715267i	$-0.746305\pi$
$127$	−4.09762e9	−1.39770	−0.698852	+	0.715267i	$0.746305\pi$
$128$	−2.03384e9	−0.669688
$129$	3.53117e9	1.12270
$130$	−1.66861e8	−0.0512402
$131$	1.27234e8	0.0377471	0.0188735	−	0.999822i	$-0.493992\pi$
$131$	1.27234e8	0.0377471	0.0188735	+	0.999822i	$0.493992\pi$
$132$	5.45175e8	0.156298
$133$	7.65942e8	0.212258
$134$	−1.52902e8	−0.0409677
$135$	−1.18377e9	−0.306737
$136$	−1.13541e7	−0.00284595
$137$	−6.98179e9	−1.69326	−0.846631	−	0.532181i	$-0.821373\pi$
$137$	−6.98179e9	−1.69326	−0.846631	+	0.532181i	$0.821373\pi$
$138$	−1.27353e9	−0.298919
$139$	3.75451e9	0.853075	0.426537	−	0.904470i	$-0.359733\pi$
$139$	3.75451e9	0.853075	0.426537	+	0.904470i	$0.359733\pi$
$140$	2.42428e9	0.533342
$141$	−1.79621e9	−0.382711
$142$	1.08114e9	0.223144
$143$	5.38525e8	0.107695
$144$	1.27076e9	0.246283
$145$	−3.69712e8	−0.0694556
$146$	8.24666e8	0.150207
$147$	7.50877e9	1.32630
$148$	−8.24880e9	−1.41323
$149$	1.02977e9	0.171160	0.0855802	−	0.996331i	$-0.472726\pi$
$149$	1.02977e9	0.171160	0.0855802	+	0.996331i	$0.472726\pi$
$150$	−1.09672e9	−0.176882
$151$	4.67094e9	0.731153	0.365577	−	0.930781i	$-0.380872\pi$
$151$	4.67094e9	0.731153	0.365577	+	0.930781i	$0.380872\pi$
$152$	3.39493e8	0.0515863
$153$	1.47024e7	0.00216909
$154$	2.68828e8	0.0385151
$155$	1.20447e9	0.167611
$156$	6.06537e9	0.819968
$157$	3.25207e9	0.427180	0.213590	−	0.976923i	$-0.431484\pi$
$157$	3.25207e9	0.427180	0.213590	+	0.976923i	$0.431484\pi$
$158$	4.78786e8	0.0611201
$159$	1.07452e10	1.33330
$160$	1.62086e9	0.195527
$161$	1.82770e10	2.14382
$162$	−1.91498e9	−0.218448
$163$	−8.55118e9	−0.948815	−0.474408	−	0.880305i	$-0.657338\pi$
$163$	−8.55118e9	−0.948815	−0.474408	+	0.880305i	$0.657338\pi$
$164$	−1.28759e9	−0.138989
$165$	−5.75716e8	−0.0604687
$166$	−1.25541e9	−0.128321
$167$	−1.81205e10	−1.80279	−0.901395	−	0.432998i	$-0.857456\pi$
$167$	−1.81205e10	−1.80279	−0.901395	+	0.432998i	$0.857456\pi$
$168$	6.15962e9	0.596571
$169$	−4.61311e9	−0.435015
$170$	5.89382e6	0.000541224 0
$171$	−4.39609e8	−0.0393174
$172$	−1.10414e10	−0.961932
$173$	1.37502e10	1.16708	0.583540	−	0.812084i	$-0.301667\pi$
$173$	1.37502e10	1.16708	0.583540	+	0.812084i	$0.301667\pi$
$174$	−4.61751e8	−0.0381888
$175$	1.57395e10	1.26859
$176$	−1.64408e9	−0.129157
$177$	−2.56214e10	−1.96211
$178$	−1.59317e9	−0.118952
$179$	−5.63278e9	−0.410095	−0.205047	−	0.978752i	$-0.565735\pi$
$179$	−5.63278e9	−0.410095	−0.205047	+	0.978752i	$0.565735\pi$
$180$	−1.39140e9	−0.0987932
$181$	1.20236e10	0.832682	0.416341	−	0.909209i	$-0.363312\pi$
$181$	1.20236e10	0.832682	0.416341	+	0.909209i	$0.363312\pi$
$182$	2.99086e9	0.202058
$183$	−8.93404e9	−0.588868
$184$	8.10102e9	0.521026
$185$	8.71091e9	0.546752
$186$	1.50432e9	0.0921577
$187$	−1.90216e7	−0.00113752
$188$	5.61644e9	0.327907
$189$	2.12182e10	1.20957
$190$	−1.76228e8	−0.00981034
$191$	1.52703e10	0.830227	0.415114	−	0.909770i	$-0.363742\pi$
$191$	1.52703e10	0.830227	0.415114	+	0.909770i	$0.363742\pi$
$192$	−1.71291e10	−0.909658
$193$	−3.43295e10	−1.78098	−0.890490	−	0.455003i	$-0.849638\pi$
$193$	−3.43295e10	−1.78098	−0.890490	+	0.455003i	$0.849638\pi$
$194$	−6.67734e9	−0.338451
$195$	−6.40516e9	−0.317230
$196$	−2.34786e10	−1.13637
$197$	2.47328e10	1.16997	0.584987	−	0.811043i	$-0.301100\pi$
$197$	2.47328e10	1.16997	0.584987	+	0.811043i	$0.301100\pi$
$198$	−1.54293e8	−0.00713432
$199$	−2.85056e10	−1.28852	−0.644259	−	0.764807i	$-0.722834\pi$
$199$	−2.85056e10	−1.28852	−0.644259	+	0.764807i	$0.722834\pi$
$200$	6.97632e9	0.308313
$201$	−5.86932e9	−0.253633
$202$	−3.80539e9	−0.160812
$203$	6.62681e9	0.273887
$204$	−2.14239e8	−0.00866091
$205$	1.35972e9	0.0537722
$206$	3.59736e9	0.139182
$207$	−1.04900e10	−0.397109
$208$	−1.82913e10	−0.677580
$209$	5.68756e8	0.0206190
$210$	−3.19742e9	−0.113452
$211$	−4.54536e10	−1.57869	−0.789347	−	0.613948i	$-0.789580\pi$
$211$	−4.54536e10	−1.57869	−0.789347	+	0.613948i	$0.789580\pi$
$212$	−3.35983e10	−1.14237
$213$	4.15010e10	1.38150
$214$	−1.49587e9	−0.0487565
$215$	1.16599e10	0.372153
$216$	9.40468e9	0.293969
$217$	−2.15892e10	−0.660949
$218$	−3.00085e9	−0.0899890
$219$	3.16558e10	0.929939
$220$	1.80016e9	0.0518096
$221$	−2.11626e8	−0.00596766
$222$	1.08795e10	0.300621
$223$	−2.69451e10	−0.729639	−0.364819	−	0.931078i	$-0.618869\pi$
$223$	−2.69451e10	−0.729639	−0.364819	+	0.931078i	$0.618869\pi$
$224$	−2.90527e10	−0.771029
$225$	−9.03365e9	−0.234986
$226$	1.03790e10	0.264648
$227$	7.81792e10	1.95423	0.977113	−	0.212720i	$-0.0682321\pi$
$227$	7.81792e10	1.95423	0.977113	+	0.212720i	$0.0682321\pi$
$228$	6.40586e9	0.156989
$229$	1.30162e9	0.0312769	0.0156385	−	0.999878i	$-0.495022\pi$
$229$	1.30162e9	0.0312769	0.0156385	+	0.999878i	$0.495022\pi$
$230$	−4.20518e9	−0.0990854
$231$	1.03193e10	0.238449
$232$	2.93723e9	0.0665645
$233$	8.22007e10	1.82715	0.913574	−	0.406673i	$-0.133311\pi$
$233$	8.22007e10	1.82715	0.913574	+	0.406673i	$0.133311\pi$
$234$	−1.71659e9	−0.0374280
$235$	−5.93108e9	−0.126861
$236$	8.01136e10	1.68113
$237$	1.83787e10	0.378398
$238$	−1.05642e8	−0.00213423
$239$	−2.06826e10	−0.410029	−0.205014	−	0.978759i	$-0.565724\pi$
$239$	−2.06826e10	−0.410029	−0.205014	+	0.978759i	$0.565724\pi$
$240$	1.95546e10	0.380450
$241$	3.88025e10	0.740940	0.370470	−	0.928845i	$-0.379197\pi$
$241$	3.88025e10	0.740940	0.370470	+	0.928845i	$0.379197\pi$
$242$	−9.52460e9	−0.178516
$243$	−2.89341e10	−0.532331
$244$	2.79352e10	0.504542
$245$	2.47939e10	0.439640
$246$	1.69822e9	0.0295656
$247$	6.32772e9	0.108171
$248$	−9.56910e9	−0.160634
$249$	−4.81903e10	−0.794443
$250$	−7.83174e9	−0.126803
$251$	−2.18093e10	−0.346825	−0.173413	−	0.984849i	$-0.555479\pi$
$251$	−2.18093e10	−0.346825	−0.173413	+	0.984849i	$0.555479\pi$
$252$	2.49399e10	0.389576
$253$	1.35717e10	0.208254
$254$	−1.68987e10	−0.254742
$255$	2.26241e8	0.00335074
$256$	4.70122e10	0.684118
$257$	−8.98583e10	−1.28487	−0.642435	−	0.766340i	$-0.722076\pi$
$257$	−8.98583e10	−1.28487	−0.642435	+	0.766340i	$0.722076\pi$
$258$	1.45626e10	0.204621
$259$	−1.56136e11	−2.15603
$260$	2.00278e10	0.271803
$261$	−3.80343e9	−0.0507333
$262$	5.24717e8	0.00687969
$263$	−1.16481e11	−1.50125	−0.750625	−	0.660728i	$-0.770248\pi$
$263$	−1.16481e11	−1.50125	−0.750625	+	0.660728i	$0.770248\pi$
$264$	4.57387e9	0.0579517
$265$	3.54805e10	0.441960
$266$	3.15876e9	0.0386856
$267$	−6.11555e10	−0.736436
$268$	1.83523e10	0.217313
$269$	−5.89686e8	−0.00686650	−0.00343325	−	0.999994i	$-0.501093\pi$
$269$	−5.89686e8	−0.00686650	−0.00343325	+	0.999994i	$0.501093\pi$
$270$	−4.88190e9	−0.0559052
$271$	−1.04534e11	−1.17733	−0.588664	−	0.808378i	$-0.700346\pi$
$271$	−1.04534e11	−1.17733	−0.588664	+	0.808378i	$0.700346\pi$
$272$	6.46081e8	0.00715693
$273$	1.14808e11	1.25095
$274$	−2.87930e10	−0.308610
$275$	1.16875e10	0.123232
$276$	1.52858e11	1.58561
$277$	1.61484e11	1.64805	0.824027	−	0.566551i	$-0.191722\pi$
$277$	1.61484e11	1.64805	0.824027	+	0.566551i	$0.191722\pi$
$278$	1.54837e10	0.155479
$279$	1.23910e10	0.122430
$280$	2.03390e10	0.197751
$281$	1.49725e10	0.143257	0.0716286	−	0.997431i	$-0.477180\pi$
$281$	1.49725e10	0.143257	0.0716286	+	0.997431i	$0.477180\pi$
$282$	−7.40761e9	−0.0697520
$283$	9.20857e10	0.853401	0.426700	−	0.904393i	$-0.359676\pi$
$283$	9.20857e10	0.853401	0.426700	+	0.904393i	$0.359676\pi$
$284$	−1.29766e11	−1.18367
$285$	−6.76472e9	−0.0607363
$286$	2.22089e9	0.0196281
$287$	−2.43720e10	−0.212042
$288$	1.66747e10	0.142821
$289$	−1.18580e11	−0.999937
$290$	−1.52470e9	−0.0126588
$291$	−2.56317e11	−2.09536
$292$	−9.89820e10	−0.796771
$293$	8.43777e9	0.0668842	0.0334421	−	0.999441i	$-0.489353\pi$
$293$	8.43777e9	0.0668842	0.0334421	+	0.999441i	$0.489353\pi$
$294$	3.09663e10	0.241728
$295$	−8.46017e10	−0.650399
$296$	−6.92052e10	−0.523994
$297$	1.57558e10	0.117499
$298$	4.24680e9	0.0311953
$299$	1.50993e11	1.09254
$300$	1.31636e11	0.938270
$301$	−2.08995e11	−1.46753
$302$	1.92630e10	0.133258
$303$	−1.46074e11	−0.995593
$304$	−1.93181e10	−0.129728
$305$	−2.95001e10	−0.195198
$306$	6.06330e7	0.000395333 0
$307$	1.26786e10	0.0814609	0.0407305	−	0.999170i	$-0.487032\pi$
$307$	1.26786e10	0.0814609	0.0407305	+	0.999170i	$0.487032\pi$
$308$	−3.22666e10	−0.204303
$309$	1.38089e11	0.861679
$310$	4.96725e9	0.0305484
$311$	2.02908e9	0.0122992	0.00614959	−	0.999981i	$-0.498043\pi$
$311$	2.02908e9	0.0122992	0.00614959	+	0.999981i	$0.498043\pi$
$312$	5.08869e10	0.304025
$313$	1.26606e10	0.0745596	0.0372798	−	0.999305i	$-0.488131\pi$
$313$	1.26606e10	0.0745596	0.0372798	+	0.999305i	$0.488131\pi$
$314$	1.34116e10	0.0778568
$315$	−2.63370e10	−0.150719
$316$	−5.74671e10	−0.324211
$317$	9.15618e10	0.509270	0.254635	−	0.967037i	$-0.418045\pi$
$317$	9.15618e10	0.509270	0.254635	+	0.967037i	$0.418045\pi$
$318$	4.43133e10	0.243003
$319$	4.92078e9	0.0266058
$320$	−5.65600e10	−0.301533
$321$	−5.74208e10	−0.301854
$322$	7.53748e10	0.390728
$323$	−2.23506e8	−0.00114256
$324$	2.29849e11	1.15875
$325$	1.30030e11	0.646500
$326$	−3.52652e10	−0.172929
$327$	−1.15191e11	−0.557126
$328$	−1.08025e10	−0.0515339
$329$	1.06310e11	0.500257
$330$	−2.37426e9	−0.0110209
$331$	3.02057e11	1.38313	0.691565	−	0.722315i	$-0.256922\pi$
$331$	3.02057e11	1.38313	0.691565	+	0.722315i	$0.256922\pi$
$332$	1.50683e11	0.680679
$333$	8.96139e10	0.399371
$334$	−7.47291e10	−0.328572
$335$	−1.93805e10	−0.0840742
$336$	−3.50501e11	−1.50025
$337$	3.32998e11	1.40639	0.703196	−	0.710996i	$-0.251756\pi$
$337$	3.32998e11	1.40639	0.703196	+	0.710996i	$0.251756\pi$
$338$	−1.90246e10	−0.0792847
$339$	3.98411e11	1.63845
$340$	−7.07417e8	−0.00287091
$341$	−1.60312e10	−0.0642054
$342$	−1.81296e9	−0.00716589
$343$	−6.63227e10	−0.258725
$344$	−9.26340e10	−0.356662
$345$	−1.61421e11	−0.613442
$346$	5.67060e10	0.212709
$347$	−2.46311e11	−0.912015	−0.456007	−	0.889976i	$-0.650721\pi$
$347$	−2.46311e11	−0.912015	−0.456007	+	0.889976i	$0.650721\pi$
$348$	5.54225e10	0.202572
$349$	3.33319e11	1.20267	0.601335	−	0.798997i	$-0.294636\pi$
$349$	3.33319e11	1.20267	0.601335	+	0.798997i	$0.294636\pi$
$350$	6.49101e10	0.231210
$351$	1.75291e11	0.616423
$352$	−2.15733e10	−0.0748988
$353$	−8.64349e10	−0.296280	−0.148140	−	0.988966i	$-0.547329\pi$
$353$	−8.64349e10	−0.296280	−0.148140	+	0.988966i	$0.547329\pi$
$354$	−1.05663e11	−0.357609
$355$	1.37036e11	0.457938
$356$	1.91223e11	0.630978
$357$	−4.05520e9	−0.0132131
$358$	−2.32297e10	−0.0747428
$359$	2.79903e11	0.889371	0.444685	−	0.895687i	$-0.353315\pi$
$359$	2.79903e11	0.889371	0.444685	+	0.895687i	$0.353315\pi$
$360$	−1.16735e10	−0.0366303
$361$	−3.16005e11	−0.979290
$362$	4.95853e10	0.151763
$363$	−3.65613e11	−1.10520
$364$	−3.58984e11	−1.07181
$365$	1.04527e11	0.308256
$366$	−3.68441e10	−0.107326
$367$	8.93592e10	0.257124	0.128562	−	0.991701i	$-0.458964\pi$
$367$	8.93592e10	0.257124	0.128562	+	0.991701i	$0.458964\pi$
$368$	−4.60972e11	−1.31027
$369$	1.39882e10	0.0392775
$370$	3.59239e10	0.0996497
$371$	−6.35961e11	−1.74280
$372$	−1.80559e11	−0.488849
$373$	2.82322e11	0.755188	0.377594	−	0.925971i	$-0.376751\pi$
$373$	2.82322e11	0.755188	0.377594	+	0.925971i	$0.376751\pi$
$374$	−7.84455e7	−0.000207322 0
$375$	−3.00631e11	−0.785041
$376$	4.71204e10	0.121580
$377$	5.47464e10	0.139579
$378$	8.75044e10	0.220453
$379$	2.45036e11	0.610034	0.305017	−	0.952347i	$-0.401338\pi$
$379$	2.45036e11	0.610034	0.305017	+	0.952347i	$0.401338\pi$
$380$	2.11521e10	0.0520388
$381$	−6.48675e11	−1.57712
$382$	6.29749e10	0.151315
$383$	4.51310e11	1.07172	0.535859	−	0.844307i	$-0.319988\pi$
$383$	4.51310e11	1.07172	0.535859	+	0.844307i	$0.319988\pi$
$384$	−3.21968e11	−0.755653
$385$	3.40742e10	0.0790410
$386$	−1.41575e11	−0.324597
$387$	1.19952e11	0.271836
$388$	8.01459e11	1.79531
$389$	−3.83675e11	−0.849552	−0.424776	−	0.905298i	$-0.639647\pi$
$389$	−3.83675e11	−0.849552	−0.424776	+	0.905298i	$0.639647\pi$
$390$	−2.64150e10	−0.0578176
$391$	−5.33333e9	−0.0115399
$392$	−1.96979e11	−0.421340
$393$	2.01419e10	0.0425925
$394$	1.01999e11	0.213236
$395$	6.06865e10	0.125431
$396$	1.85193e10	0.0378439
$397$	1.81989e10	0.0367695	0.0183848	−	0.999831i	$-0.494148\pi$
$397$	1.81989e10	0.0367695	0.0183848	+	0.999831i	$0.494148\pi$
$398$	−1.17557e11	−0.234842
$399$	1.21253e11	0.239504
$400$	−3.96973e11	−0.775339
$401$	−9.54413e11	−1.84326	−0.921630	−	0.388070i	$-0.873142\pi$
$401$	−9.54413e11	−1.84326	−0.921630	+	0.388070i	$0.873142\pi$
$402$	−2.42052e10	−0.0462265
$403$	−1.78356e11	−0.336834
$404$	4.56748e11	0.853023
$405$	−2.42726e11	−0.448299
$406$	2.73291e10	0.0499180
$407$	−1.15940e11	−0.209440
$408$	−1.79741e9	−0.00321127
$409$	7.03746e11	1.24354	0.621772	−	0.783198i	$-0.286413\pi$
$409$	7.03746e11	1.24354	0.621772	+	0.783198i	$0.286413\pi$
$410$	5.60752e9	0.00980039
$411$	−1.10525e12	−1.91062
$412$	−4.31780e11	−0.738286
$413$	1.51642e12	2.56475
$414$	−4.32611e10	−0.0723762
$415$	−1.59124e11	−0.263342
$416$	−2.40015e11	−0.392933
$417$	5.94359e11	0.962580
$418$	2.34556e9	0.00375797
$419$	3.47899e11	0.551430	0.275715	−	0.961239i	$-0.411085\pi$
$419$	3.47899e11	0.551430	0.275715	+	0.961239i	$0.411085\pi$
$420$	3.83776e11	0.601805
$421$	1.39031e11	0.215696	0.107848	−	0.994167i	$-0.465604\pi$
$421$	1.39031e11	0.215696	0.107848	+	0.994167i	$0.465604\pi$
$422$	−1.87452e11	−0.287729
$423$	−6.10162e10	−0.0926646
$424$	−2.81880e11	−0.423564
$425$	−4.59288e9	−0.00682865
$426$	1.71151e11	0.251788
$427$	5.28768e11	0.769732
$428$	1.79545e11	0.258628
$429$	8.52513e10	0.121519
$430$	4.80856e10	0.0678277
$431$	5.92859e11	0.827567	0.413784	−	0.910375i	$-0.364207\pi$
$431$	5.92859e11	0.827567	0.413784	+	0.910375i	$0.364207\pi$
$432$	−5.35154e11	−0.739268
$433$	1.29106e12	1.76502	0.882510	−	0.470293i	$-0.155852\pi$
$433$	1.29106e12	1.76502	0.882510	+	0.470293i	$0.155852\pi$
$434$	−8.90342e10	−0.120463
$435$	−5.85273e10	−0.0783713
$436$	3.60182e11	0.477345
$437$	1.59469e11	0.209175
$438$	1.30549e11	0.169488
$439$	−1.17707e12	−1.51256	−0.756282	−	0.654246i	$-0.772986\pi$
$439$	−1.17707e12	−1.51256	−0.756282	+	0.654246i	$0.772986\pi$
$440$	1.51029e10	0.0192098
$441$	2.55069e11	0.321132
$442$	−8.72749e8	−0.00108765
$443$	−5.68412e11	−0.701207	−0.350603	−	0.936524i	$-0.614023\pi$
$443$	−5.68412e11	−0.701207	−0.350603	+	0.936524i	$0.614023\pi$
$444$	−1.30583e12	−1.59464
$445$	−2.01935e11	−0.244113
$446$	−1.11122e11	−0.132982
$447$	1.63018e11	0.193131
$448$	1.01380e12	1.18905
$449$	8.74039e11	1.01490	0.507449	−	0.861682i	$-0.330589\pi$
$449$	8.74039e11	1.01490	0.507449	+	0.861682i	$0.330589\pi$
$450$	−3.72549e10	−0.0428280
$451$	−1.80976e10	−0.0205981
$452$	−1.24576e12	−1.40382
$453$	7.39434e11	0.825007
$454$	3.22412e11	0.356173
$455$	3.79094e11	0.414664
$456$	5.37434e10	0.0582081
$457$	4.43966e11	0.476131	0.238066	−	0.971249i	$-0.423487\pi$
$457$	4.43966e11	0.476131	0.238066	+	0.971249i	$0.423487\pi$
$458$	5.36790e9	0.00570046
$459$	−6.19159e9	−0.00651096
$460$	5.04735e11	0.525597
$461$	7.42537e11	0.765709	0.382854	−	0.923809i	$-0.374941\pi$
$461$	7.42537e11	0.765709	0.382854	+	0.923809i	$0.374941\pi$
$462$	4.25569e10	0.0434591
$463$	−5.15880e11	−0.521716	−0.260858	−	0.965377i	$-0.584005\pi$
$463$	−5.15880e11	−0.521716	−0.260858	+	0.965377i	$0.584005\pi$
$464$	−1.67137e11	−0.167395
$465$	1.90674e11	0.189127
$466$	3.38997e11	0.333011
$467$	−1.95165e12	−1.89879	−0.949394	−	0.314087i	$-0.898302\pi$
$467$	−1.95165e12	−1.89879	−0.949394	+	0.314087i	$0.898302\pi$
$468$	2.06037e11	0.198536
$469$	3.47380e11	0.331533
$470$	−2.44599e10	−0.0231214
$471$	5.14819e11	0.482015
$472$	6.72132e11	0.623326
$473$	−1.55191e11	−0.142558
$474$	7.57943e10	0.0689658
$475$	1.37329e11	0.123778
$476$	1.26799e10	0.0113210
$477$	3.65007e11	0.322826
$478$	−8.52953e10	−0.0747308
$479$	−1.61869e12	−1.40492	−0.702462	−	0.711722i	$-0.747916\pi$
$479$	−1.61869e12	−1.40492	−0.702462	+	0.711722i	$0.747916\pi$
$480$	2.56591e11	0.220625
$481$	−1.28990e12	−1.09876
$482$	1.60022e11	0.135042
$483$	2.89335e12	2.41902
$484$	1.14321e12	0.946936
$485$	−8.46358e11	−0.694570
$486$	−1.19325e11	−0.0970213
$487$	−1.66357e12	−1.34017	−0.670086	−	0.742283i	$-0.733743\pi$
$487$	−1.66357e12	−1.34017	−0.670086	+	0.742283i	$0.733743\pi$
$488$	2.34369e11	0.187073
$489$	−1.35370e12	−1.07061
$490$	1.02250e11	0.0801278
$491$	7.57345e11	0.588067	0.294034	−	0.955795i	$-0.405002\pi$
$491$	7.57345e11	0.588067	0.294034	+	0.955795i	$0.405002\pi$
$492$	−2.03832e11	−0.156830
$493$	−1.93374e9	−0.00147430
$494$	2.60956e10	0.0197150
$495$	−1.95567e10	−0.0146411
$496$	5.44510e11	0.403960
$497$	−2.45627e12	−1.80581
$498$	−1.98738e11	−0.144793
$499$	−2.29340e12	−1.65588	−0.827938	−	0.560820i	$-0.810486\pi$
$499$	−2.29340e12	−1.65588	−0.827938	+	0.560820i	$0.810486\pi$
$500$	9.40019e11	0.672623
$501$	−2.86856e12	−2.03421
$502$	−8.99421e10	−0.0632115
$503$	−2.45323e12	−1.70877	−0.854383	−	0.519644i	$-0.826065\pi$
$503$	−2.45323e12	−1.70877	−0.854383	+	0.519644i	$0.826065\pi$
$504$	2.09239e11	0.144446
$505$	−4.82336e11	−0.330019
$506$	5.59701e10	0.0379558
$507$	−7.30280e11	−0.490855
$508$	2.02829e12	1.35127
$509$	1.49390e12	0.986488	0.493244	−	0.869891i	$-0.335811\pi$
$509$	1.49390e12	0.986488	0.493244	+	0.869891i	$0.335811\pi$
$510$	9.33023e8	0.000610698 0
$511$	−1.87357e12	−1.21556
$512$	1.23521e12	0.794374
$513$	1.85132e11	0.118019
$514$	−3.70577e11	−0.234177
$515$	4.55969e11	0.285629
$516$	−1.74790e12	−1.08541
$517$	7.89413e10	0.0485956
$518$	−6.43910e11	−0.392953
$519$	2.17672e12	1.31689
$520$	1.68028e11	0.100778
$521$	8.48111e11	0.504293	0.252146	−	0.967689i	$-0.418864\pi$
$521$	8.48111e11	0.504293	0.252146	+	0.967689i	$0.418864\pi$
$522$	−1.56854e10	−0.00924652
$523$	−2.97794e11	−0.174044	−0.0870219	−	0.996206i	$-0.527735\pi$
$523$	−2.97794e11	−0.174044	−0.0870219	+	0.996206i	$0.527735\pi$
$524$	−6.29801e10	−0.0364932
$525$	2.49165e12	1.43143
$526$	−4.80369e11	−0.273614
$527$	6.29984e9	0.00355780
$528$	−2.60267e11	−0.145736
$529$	2.00413e12	1.11269
$530$	1.46322e11	0.0805506
$531$	−8.70345e11	−0.475079
$532$	−3.79136e11	−0.205207
$533$	−2.01346e11	−0.108061
$534$	−2.52206e11	−0.134221
$535$	−1.89603e11	−0.100058
$536$	1.53971e11	0.0805746
$537$	−8.91698e11	−0.462736
$538$	−2.43187e9	−0.00125147
$539$	−3.30001e11	−0.168409
$540$	5.85959e11	0.296548
$541$	2.13446e12	1.07128	0.535638	−	0.844448i	$-0.320071\pi$
$541$	2.13446e12	1.07128	0.535638	+	0.844448i	$0.320071\pi$
$542$	−4.31101e11	−0.214577
$543$	1.90339e12	0.939569
$544$	8.47774e9	0.00415035
$545$	−3.80360e11	−0.184676
$546$	4.73469e11	0.227995
$547$	−2.01671e12	−0.963166	−0.481583	−	0.876401i	$-0.659938\pi$
$547$	−2.01671e12	−0.963166	−0.481583	+	0.876401i	$0.659938\pi$
$548$	3.45593e12	1.63702
$549$	−3.03484e11	−0.142581
$550$	4.81995e10	0.0224600
$551$	5.78197e10	0.0267235
$552$	1.28243e12	0.587908
$553$	−1.08776e12	−0.494618
$554$	6.65964e11	0.300370
$555$	1.37898e12	0.616936
$556$	−1.85846e12	−0.824737
$557$	8.68048e11	0.382116	0.191058	−	0.981579i	$-0.438808\pi$
$557$	8.68048e11	0.382116	0.191058	+	0.981579i	$0.438808\pi$
$558$	5.11008e10	0.0223138
$559$	−1.72658e12	−0.747884
$560$	−1.15735e12	−0.497301
$561$	−3.01122e9	−0.00128354
$562$	6.17469e10	0.0261097
$563$	3.34070e12	1.40136	0.700679	−	0.713476i	$-0.252880\pi$
$563$	3.34070e12	1.40136	0.700679	+	0.713476i	$0.252880\pi$
$564$	8.89111e11	0.369999
$565$	1.31555e12	0.543111
$566$	3.79763e11	0.155539
$567$	4.35067e12	1.76780
$568$	−1.08870e12	−0.438877
$569$	−3.70905e12	−1.48340	−0.741699	−	0.670733i	$-0.765980\pi$
$569$	−3.70905e12	−1.48340	−0.741699	+	0.670733i	$0.765980\pi$
$570$	−2.78978e10	−0.0110696
$571$	−2.27640e12	−0.896162	−0.448081	−	0.893993i	$-0.647892\pi$
$571$	−2.27640e12	−0.896162	−0.448081	+	0.893993i	$0.647892\pi$
$572$	−2.66566e11	−0.104117
$573$	2.41736e12	0.936799
$574$	−1.00511e11	−0.0386463
$575$	3.27697e12	1.25017
$576$	−5.81864e11	−0.220252
$577$	−3.40287e12	−1.27807	−0.639034	−	0.769178i	$-0.720666\pi$
$577$	−3.40287e12	−1.27807	−0.639034	+	0.769178i	$0.720666\pi$
$578$	−4.89028e11	−0.182246
$579$	−5.43453e12	−2.00959
$580$	1.83005e11	0.0671484
$581$	2.85218e12	1.03845
$582$	−1.05706e12	−0.381896
$583$	−4.72237e11	−0.169298
$584$	−8.30433e11	−0.295425
$585$	−2.17580e11	−0.0768099
$586$	3.47975e10	0.0121902
$587$	3.57851e12	1.24403	0.622015	−	0.783005i	$-0.286314\pi$
$587$	3.57851e12	1.24403	0.622015	+	0.783005i	$0.286314\pi$
$588$	−3.71679e12	−1.28224
$589$	−1.88368e11	−0.0644895
$590$	−3.48899e11	−0.118540
$591$	3.91534e12	1.32016
$592$	3.93798e12	1.31773
$593$	2.27900e12	0.756831	0.378416	−	0.925636i	$-0.376469\pi$
$593$	2.27900e12	0.756831	0.378416	+	0.925636i	$0.376469\pi$
$594$	6.49770e10	0.0214151
$595$	−1.33903e10	−0.00437988
$596$	−5.09730e11	−0.165475
$597$	−4.51258e12	−1.45392
$598$	6.22698e11	0.199123
$599$	3.52358e12	1.11831	0.559157	−	0.829062i	$-0.311125\pi$
$599$	3.52358e12	1.11831	0.559157	+	0.829062i	$0.311125\pi$
$600$	1.10439e12	0.347889
$601$	−4.76663e12	−1.49031	−0.745154	−	0.666892i	$-0.767624\pi$
$601$	−4.76663e12	−1.49031	−0.745154	+	0.666892i	$0.767624\pi$
$602$	−8.61899e11	−0.267468
$603$	−1.99378e11	−0.0614113
$604$	−2.31208e12	−0.706866
$605$	−1.20725e12	−0.366352
$606$	−6.02412e11	−0.181454
$607$	−3.10906e11	−0.0929567	−0.0464783	−	0.998919i	$-0.514800\pi$
$607$	−3.10906e11	−0.0929567	−0.0464783	+	0.998919i	$0.514800\pi$
$608$	−2.53489e11	−0.0752302
$609$	1.04906e12	0.309045
$610$	−1.21659e11	−0.0355763
$611$	8.78266e11	0.254941
$612$	−7.27758e9	−0.00209704
$613$	4.98161e12	1.42494	0.712472	−	0.701700i	$-0.247575\pi$
$613$	4.98161e12	1.42494	0.712472	+	0.701700i	$0.247575\pi$
$614$	5.22869e10	0.0148469
$615$	2.15251e11	0.0606747
$616$	−2.70708e11	−0.0757509
$617$	−3.43823e12	−0.955108	−0.477554	−	0.878603i	$-0.658476\pi$
$617$	−3.43823e12	−0.955108	−0.477554	+	0.878603i	$0.658476\pi$
$618$	5.69481e11	0.157048
$619$	4.45272e12	1.21904	0.609519	−	0.792772i	$-0.291363\pi$
$619$	4.45272e12	1.21904	0.609519	+	0.792772i	$0.291363\pi$
$620$	−5.96203e11	−0.162044
$621$	4.41764e12	1.19201
$622$	8.36794e9	0.00224162
$623$	3.61953e12	0.962624
$624$	−2.89561e12	−0.764557
$625$	2.28835e12	0.599877
$626$	5.22124e10	0.0135890
$627$	9.00370e10	0.0232657
$628$	−1.60975e12	−0.412990
$629$	4.55614e10	0.0116057
$630$	−1.08614e11	−0.0274698
$631$	−2.30407e12	−0.578580	−0.289290	−	0.957242i	$-0.593419\pi$
$631$	−2.30407e12	−0.578580	−0.289290	+	0.957242i	$0.593419\pi$
$632$	−4.82134e11	−0.120210
$633$	−7.19555e12	−1.78134
$634$	3.77603e11	0.0928182
$635$	−2.14192e12	−0.522783
$636$	−5.31878e12	−1.28901
$637$	−3.67145e12	−0.883507
$638$	2.02934e10	0.00484910
$639$	1.40976e12	0.334497
$640$	−1.06314e12	−0.250483
$641$	−1.89934e12	−0.444368	−0.222184	−	0.975005i	$-0.571319\pi$
$641$	−1.89934e12	−0.444368	−0.222184	+	0.975005i	$0.571319\pi$
$642$	−2.36804e11	−0.0550151
$643$	−4.21739e12	−0.972959	−0.486479	−	0.873692i	$-0.661719\pi$
$643$	−4.21739e12	−0.972959	−0.486479	+	0.873692i	$0.661719\pi$
$644$	−9.04699e12	−2.07261
$645$	1.84582e12	0.419925
$646$	−9.21742e8	−0.000208239 0
$647$	−5.65043e12	−1.26769	−0.633844	−	0.773461i	$-0.718524\pi$
$647$	−5.65043e12	−1.26769	−0.633844	+	0.773461i	$0.718524\pi$
$648$	1.92837e12	0.429639
$649$	1.12603e12	0.249143
$650$	5.36246e11	0.117829
$651$	−3.41768e12	−0.745791
$652$	4.23277e12	0.917298
$653$	5.29385e12	1.13936	0.569681	−	0.821866i	$-0.307067\pi$
$653$	5.29385e12	1.13936	0.569681	+	0.821866i	$0.307067\pi$
$654$	−4.75050e11	−0.101540
$655$	6.65083e10	0.0141185
$656$	6.14696e11	0.129597
$657$	1.07533e12	0.225163
$658$	4.38425e11	0.0911755
$659$	−8.82534e12	−1.82283	−0.911417	−	0.411484i	$-0.865011\pi$
$659$	−8.82534e12	−1.82283	−0.911417	+	0.411484i	$0.865011\pi$
$660$	2.84975e11	0.0584601
$661$	−5.65938e12	−1.15309	−0.576544	−	0.817066i	$-0.695599\pi$
$661$	−5.65938e12	−1.15309	−0.576544	+	0.817066i	$0.695599\pi$
$662$	1.24569e12	0.252086
$663$	−3.35015e10	−0.00673369
$664$	1.26419e12	0.252380
$665$	4.00375e11	0.0793907
$666$	3.69569e11	0.0727884
$667$	1.37970e12	0.269910
$668$	8.96949e12	1.74291
$669$	−4.26555e12	−0.823298
$670$	−7.99254e10	−0.0153232
$671$	3.92640e11	0.0747728
$672$	−4.59920e12	−0.870002
$673$	−3.75371e12	−0.705330	−0.352665	−	0.935750i	$-0.614724\pi$
$673$	−3.75371e12	−0.705330	−0.352665	+	0.935750i	$0.614724\pi$
$674$	1.37329e12	0.256326
$675$	3.80432e12	0.705359
$676$	2.28346e12	0.420564
$677$	6.70236e12	1.22625	0.613125	−	0.789986i	$-0.289912\pi$
$677$	6.70236e12	1.22625	0.613125	+	0.789986i	$0.289912\pi$
$678$	1.64305e12	0.298619
$679$	1.51703e13	2.73893
$680$	−5.93504e9	−0.00106447
$681$	1.23762e13	2.20508
$682$	−6.61130e10	−0.0117019
$683$	8.32872e12	1.46449	0.732243	−	0.681044i	$-0.238474\pi$
$683$	8.32872e12	1.46449	0.732243	+	0.681044i	$0.238474\pi$
$684$	2.17603e11	0.0380113
$685$	−3.64954e12	−0.633330
$686$	−2.73516e11	−0.0471546
$687$	2.06053e11	0.0352918
$688$	5.27115e12	0.896927
$689$	−5.25390e12	−0.888169
$690$	−6.65703e11	−0.111805
$691$	−3.96872e12	−0.662215	−0.331107	−	0.943593i	$-0.607422\pi$
$691$	−3.96872e12	−0.662215	−0.331107	+	0.943593i	$0.607422\pi$
$692$	−6.80623e12	−1.12831
$693$	3.50540e11	0.0577349
$694$	−1.01579e12	−0.166222
$695$	1.96257e12	0.319075
$696$	4.64980e11	0.0751091
$697$	7.11188e9	0.00114140
$698$	1.37462e12	0.219196
$699$	1.30128e13	2.06169
$700$	−7.79095e12	−1.22645
$701$	−2.20618e12	−0.345073	−0.172536	−	0.985003i	$-0.555196\pi$
$701$	−2.20618e12	−0.345073	−0.172536	+	0.985003i	$0.555196\pi$
$702$	7.22905e11	0.112348
$703$	−1.36231e12	−0.210367
$704$	7.52802e11	0.115506
$705$	−9.38920e11	−0.143145
$706$	−3.56459e11	−0.0539993
$707$	8.64551e12	1.30138
$708$	1.26824e13	1.89693
$709$	−9.62495e12	−1.43051	−0.715254	−	0.698864i	$-0.753689\pi$
$709$	−9.62495e12	−1.43051	−0.715254	+	0.698864i	$0.753689\pi$
$710$	5.65139e11	0.0834627
$711$	6.24315e11	0.0916201
$712$	1.60431e12	0.233952
$713$	−4.49487e12	−0.651350
$714$	−1.67237e10	−0.00240819
$715$	2.81499e11	0.0402810
$716$	2.78818e12	0.396472
$717$	−3.27416e12	−0.462662
$718$	1.15433e12	0.162095
$719$	1.24894e12	0.174286	0.0871428	−	0.996196i	$-0.472226\pi$
$719$	1.24894e12	0.174286	0.0871428	+	0.996196i	$0.472226\pi$
$720$	6.64257e11	0.0921170
$721$	−8.17290e12	−1.12633
$722$	−1.30321e12	−0.178483
$723$	6.14263e12	0.836050
$724$	−5.95157e12	−0.805022
$725$	1.18815e12	0.159717
$726$	−1.50779e12	−0.201431
$727$	−4.89456e12	−0.649843	−0.324922	−	0.945741i	$-0.605338\pi$
$727$	−4.89456e12	−0.649843	−0.324922	+	0.945741i	$0.605338\pi$
$728$	−3.01178e12	−0.397403
$729$	4.55936e12	0.597901
$730$	4.31072e11	0.0561819
$731$	6.09858e10	0.00789952
$732$	4.42228e12	0.569307
$733$	−9.85775e12	−1.26128	−0.630638	−	0.776077i	$-0.717207\pi$
$733$	−9.85775e12	−1.26128	−0.630638	+	0.776077i	$0.717207\pi$
$734$	3.68519e11	0.0468627
$735$	3.92500e12	0.496075
$736$	−6.04878e12	−0.759832
$737$	2.57950e11	0.0322056
$738$	5.76876e10	0.00715862
$739$	6.15335e12	0.758947	0.379473	−	0.925203i	$-0.376105\pi$
$739$	6.15335e12	0.758947	0.379473	+	0.925203i	$0.376105\pi$
$740$	−4.31183e12	−0.528590
$741$	1.00171e12	0.122056
$742$	−2.62271e12	−0.317639
$743$	−7.60484e12	−0.915462	−0.457731	−	0.889091i	$-0.651338\pi$
$743$	−7.60484e12	−0.915462	−0.457731	+	0.889091i	$0.651338\pi$
$744$	−1.51484e12	−0.181254
$745$	5.38286e11	0.0640191
$746$	1.16430e12	0.137639
$747$	−1.63700e12	−0.192356
$748$	9.41556e9	0.00109974
$749$	3.39849e12	0.394565
$750$	−1.23981e12	−0.143080
$751$	−8.18052e11	−0.0938428	−0.0469214	−	0.998899i	$-0.514941\pi$
$751$	−8.18052e11	−0.0938428	−0.0469214	+	0.998899i	$0.514941\pi$
$752$	−2.68129e12	−0.305748
$753$	−3.45253e12	−0.391346
$754$	2.25775e11	0.0254393
$755$	2.44161e12	0.273473
$756$	−1.05029e13	−1.16939
$757$	3.23710e12	0.358282	0.179141	−	0.983823i	$-0.442668\pi$
$757$	3.23710e12	0.358282	0.179141	+	0.983823i	$0.442668\pi$
$758$	1.01053e12	0.111183
$759$	2.14848e12	0.234986
$760$	1.77460e11	0.0192948
$761$	1.17749e12	0.127270	0.0636352	−	0.997973i	$-0.479731\pi$
$761$	1.17749e12	0.127270	0.0636352	+	0.997973i	$0.479731\pi$
$762$	−2.67515e12	−0.287442
$763$	6.81767e12	0.728241
$764$	−7.55867e12	−0.802649
$765$	7.68528e9	0.000811304 0
$766$	1.86121e12	0.195329
$767$	1.25277e13	1.30705
$768$	7.44228e12	0.771935
$769$	−1.17645e13	−1.21313	−0.606564	−	0.795035i	$-0.707452\pi$
$769$	−1.17645e13	−1.21313	−0.606564	+	0.795035i	$0.707452\pi$
$770$	1.40523e11	0.0144058
$771$	−1.42250e13	−1.44980
$772$	1.69928e13	1.72182
$773$	1.71639e13	1.72905	0.864525	−	0.502590i	$-0.167619\pi$
$773$	1.71639e13	1.72905	0.864525	+	0.502590i	$0.167619\pi$
$774$	4.94683e11	0.0495442
$775$	−3.87083e12	−0.385431
$776$	6.72403e12	0.665659
$777$	−2.47172e13	−2.43279
$778$	−1.58228e12	−0.154837
$779$	−2.12649e11	−0.0206892
$780$	3.17051e12	0.306692
$781$	−1.82392e12	−0.175419
$782$	−2.19948e10	−0.00210324
$783$	1.60173e12	0.152286
$784$	1.12087e13	1.05958
$785$	1.69993e12	0.159778
$786$	8.30654e10	0.00776280
$787$	3.41385e12	0.317219	0.158609	−	0.987341i	$-0.449299\pi$
$787$	3.41385e12	0.317219	0.158609	+	0.987341i	$0.449299\pi$
$788$	−1.22426e13	−1.13111
$789$	−1.84395e13	−1.69396
$790$	2.50272e11	0.0228608
$791$	−2.35802e13	−2.14168
$792$	1.55372e11	0.0140316
$793$	4.36834e12	0.392272
$794$	7.50526e10	0.00670152
$795$	5.61675e12	0.498692
$796$	1.41100e13	1.24572
$797$	−2.07138e13	−1.81843	−0.909217	−	0.416323i	$-0.863319\pi$
$797$	−2.07138e13	−1.81843	−0.909217	+	0.416323i	$0.863319\pi$
$798$	5.00048e11	0.0436514
$799$	−3.10218e10	−0.00269282
$800$	−5.20900e12	−0.449624
$801$	−2.07742e12	−0.178311
$802$	−3.93602e12	−0.335948
$803$	−1.39123e12	−0.118081
$804$	2.90527e12	0.245208
$805$	9.55381e12	0.801854
$806$	−7.35544e11	−0.0613905
$807$	−9.33503e10	−0.00774792
$808$	3.83200e12	0.316282
$809$	1.84610e13	1.51526	0.757628	−	0.652686i	$-0.226358\pi$
$809$	1.84610e13	1.51526	0.757628	+	0.652686i	$0.226358\pi$
$810$	−1.00100e12	−0.0817059
$811$	−1.92728e13	−1.56441	−0.782204	−	0.623022i	$-0.785905\pi$
$811$	−1.92728e13	−1.56441	−0.782204	+	0.623022i	$0.785905\pi$
$812$	−3.28022e12	−0.264789
$813$	−1.65483e13	−1.32845
$814$	−4.78139e11	−0.0381720
$815$	−4.46989e12	−0.354885
$816$	1.02278e11	0.00807563
$817$	−1.82351e12	−0.143188
$818$	2.90226e12	0.226645
$819$	3.89995e12	0.302888
$820$	−6.73052e11	−0.0519860
$821$	−1.14473e13	−0.879345	−0.439673	−	0.898158i	$-0.644905\pi$
$821$	−1.14473e13	−0.879345	−0.439673	+	0.898158i	$0.644905\pi$
$822$	−4.55808e12	−0.348224
$823$	1.52297e13	1.15715	0.578577	−	0.815628i	$-0.303608\pi$
$823$	1.52297e13	1.15715	0.578577	+	0.815628i	$0.303608\pi$
$824$	−3.62252e12	−0.273740
$825$	1.85019e12	0.139051
$826$	6.25375e12	0.467445
$827$	1.05818e13	0.786653	0.393327	−	0.919399i	$-0.371324\pi$
$827$	1.05818e13	0.786653	0.393327	+	0.919399i	$0.371324\pi$
$828$	5.19248e12	0.383918
$829$	1.27259e13	0.935823	0.467911	−	0.883775i	$-0.345007\pi$
$829$	1.27259e13	0.935823	0.467911	+	0.883775i	$0.345007\pi$
$830$	−6.56231e11	−0.0479960
$831$	2.55638e13	1.85961
$832$	8.37533e12	0.605965
$833$	1.29682e11	0.00933204
$834$	2.45115e12	0.175437
$835$	−9.47198e12	−0.674297
$836$	−2.81530e11	−0.0199341
$837$	−5.21821e12	−0.367500
$838$	1.43474e12	0.100502
$839$	6.92247e12	0.482317	0.241158	−	0.970486i	$-0.422473\pi$
$839$	6.92247e12	0.482317	0.241158	+	0.970486i	$0.422473\pi$
$840$	3.21977e12	0.223135
$841$	5.00246e11	0.0344828
$842$	5.73367e11	0.0393123
$843$	2.37023e12	0.161646
$844$	2.24992e13	1.52625
$845$	−2.41138e12	−0.162708
$846$	−2.51632e11	−0.0168888
$847$	2.16391e13	1.44465
$848$	1.60398e13	1.06517
$849$	1.45776e13	0.962947
$850$	−1.89411e10	−0.00124457
$851$	−3.25076e13	−2.12472
$852$	−2.05427e13	−1.33561
$853$	−1.20956e13	−0.782270	−0.391135	−	0.920333i	$-0.627917\pi$
$853$	−1.20956e13	−0.782270	−0.391135	+	0.920333i	$0.627917\pi$
$854$	2.18065e12	0.140289
$855$	−2.29794e11	−0.0147059
$856$	1.50633e12	0.0958934
$857$	2.46234e13	1.55931	0.779657	−	0.626207i	$-0.215393\pi$
$857$	2.46234e13	1.55931	0.779657	+	0.626207i	$0.215393\pi$
$858$	3.51578e11	0.0221477
$859$	−8.88237e12	−0.556621	−0.278311	−	0.960491i	$-0.589774\pi$
$859$	−8.88237e12	−0.556621	−0.278311	+	0.960491i	$0.589774\pi$
$860$	−5.77156e12	−0.359791
$861$	−3.85822e12	−0.239261
$862$	2.44496e12	0.150830
$863$	−5.94885e12	−0.365077	−0.182539	−	0.983199i	$-0.558431\pi$
$863$	−5.94885e12	−0.365077	−0.182539	+	0.983199i	$0.558431\pi$
$864$	−7.02218e12	−0.428706
$865$	7.18753e12	0.436523
$866$	5.32434e12	0.321688
$867$	−1.87719e13	−1.12829
$868$	1.06865e13	0.638993
$869$	−8.07724e11	−0.0480478
$870$	−2.41368e11	−0.0142838
$871$	2.86983e12	0.168957
$872$	3.02183e12	0.176989
$873$	−8.70695e12	−0.507343
$874$	6.57654e11	0.0381238
$875$	1.77930e13	1.02616
$876$	−1.56694e13	−0.899048
$877$	2.38079e13	1.35901	0.679505	−	0.733671i	$-0.262194\pi$
$877$	2.38079e13	1.35901	0.679505	+	0.733671i	$0.262194\pi$
$878$	−4.85427e12	−0.275676
$879$	1.33574e12	0.0754698
$880$	−8.59399e11	−0.0483084
$881$	2.47098e13	1.38190	0.690951	−	0.722902i	$-0.257192\pi$
$881$	2.47098e13	1.38190	0.690951	+	0.722902i	$0.257192\pi$
$882$	1.05191e12	0.0585287
$883$	−1.80865e13	−1.00122	−0.500612	−	0.865672i	$-0.666892\pi$
$883$	−1.80865e13	−1.00122	−0.500612	+	0.865672i	$0.666892\pi$
$884$	1.04753e11	0.00576942
$885$	−1.33929e13	−0.733888
$886$	−2.34414e12	−0.127800
$887$	−3.39122e13	−1.83950	−0.919750	−	0.392504i	$-0.871609\pi$
$887$	−3.39122e13	−1.83950	−0.919750	+	0.392504i	$0.871609\pi$
$888$	−1.09555e13	−0.591256
$889$	3.83923e13	2.06151
$890$	−8.32784e11	−0.0444915
$891$	3.23062e12	0.171726
$892$	1.33376e13	0.705402
$893$	9.27568e11	0.0488106
$894$	6.72291e11	0.0351996
$895$	−2.94438e12	−0.153388
$896$	1.90559e13	0.987742
$897$	2.39030e13	1.23278
$898$	3.60455e12	0.184973
$899$	−1.62973e12	−0.0832142
$900$	4.47159e12	0.227180
$901$	1.85577e11	0.00938128
$902$	−7.46348e10	−0.00375415
$903$	−3.30850e13	−1.65591
$904$	−1.04516e13	−0.520504
$905$	6.28498e12	0.311448
$906$	3.04944e12	0.150364
$907$	1.14178e13	0.560210	0.280105	−	0.959969i	$-0.409631\pi$
$907$	1.14178e13	0.560210	0.280105	+	0.959969i	$0.409631\pi$
$908$	−3.86981e13	−1.88931
$909$	−4.96206e12	−0.241059
$910$	1.56339e12	0.0755756
$911$	−2.87462e13	−1.38276	−0.691382	−	0.722489i	$-0.742998\pi$
$911$	−2.87462e13	−1.38276	−0.691382	+	0.722489i	$0.742998\pi$
$912$	−3.05816e12	−0.146381
$913$	2.11791e12	0.100876
$914$	1.83092e12	0.0867785
$915$	−4.67002e12	−0.220254
$916$	−6.44292e11	−0.0302380
$917$	−1.19211e12	−0.0556743
$918$	−2.55342e10	−0.00118667
$919$	1.66611e13	0.770521	0.385261	−	0.922808i	$-0.374112\pi$
$919$	1.66611e13	0.770521	0.385261	+	0.922808i	$0.374112\pi$
$920$	4.23459e12	0.194879
$921$	2.00709e12	0.0919177
$922$	3.06223e12	0.139556
$923$	−2.02921e13	−0.920278
$924$	−5.10797e12	−0.230528
$925$	−2.79945e13	−1.25729
$926$	−2.12750e12	−0.0950867
$927$	4.69080e12	0.208636
$928$	−2.19314e12	−0.0970735
$929$	−1.98262e12	−0.0873312	−0.0436656	−	0.999046i	$-0.513904\pi$
$929$	−1.98262e12	−0.0873312	−0.0436656	+	0.999046i	$0.513904\pi$
$930$	7.86342e11	0.0344697
$931$	−3.87755e12	−0.169155
$932$	−4.06887e13	−1.76645
$933$	3.21213e11	0.0138780
$934$	−8.04865e12	−0.346068
$935$	−9.94303e9	−0.000425467 0
$936$	1.72860e12	0.0736126
$937$	−9.32184e12	−0.395069	−0.197535	−	0.980296i	$-0.563293\pi$
$937$	−9.32184e12	−0.395069	−0.197535	+	0.980296i	$0.563293\pi$
$938$	1.43260e12	0.0604245
$939$	2.00423e12	0.0841304
$940$	2.93584e12	0.122647
$941$	3.81102e13	1.58448	0.792242	−	0.610207i	$-0.208914\pi$
$941$	3.81102e13	1.58448	0.792242	+	0.610207i	$0.208914\pi$
$942$	2.12312e12	0.0878509
$943$	−5.07425e12	−0.208963
$944$	−3.82463e13	−1.56753
$945$	1.10913e13	0.452416
$946$	−6.40009e11	−0.0259822
$947$	−5.46221e12	−0.220695	−0.110348	−	0.993893i	$-0.535196\pi$
$947$	−5.46221e12	−0.220695	−0.110348	+	0.993893i	$0.535196\pi$
$948$	−9.09734e12	−0.365828
$949$	−1.54782e13	−0.619475
$950$	5.66349e11	0.0225594
$951$	1.44947e13	0.574642
$952$	1.06381e11	0.00419757
$953$	2.27780e13	0.894535	0.447267	−	0.894400i	$-0.352397\pi$
$953$	2.27780e13	0.894535	0.447267	+	0.894400i	$0.352397\pi$
$954$	1.50530e12	0.0588375
$955$	7.98212e12	0.310530
$956$	1.02377e13	0.396408
$957$	7.78985e11	0.0300210
$958$	−6.67549e12	−0.256058
$959$	6.54152e13	2.49744
$960$	−8.95375e12	−0.340239
$961$	−2.11302e13	−0.799186
$962$	−5.31957e12	−0.200257
$963$	−1.95055e12	−0.0730868
$964$	−1.92069e13	−0.716327
$965$	−1.79448e13	−0.666140
$966$	1.19322e13	0.440884
$967$	2.26472e13	0.832905	0.416453	−	0.909157i	$-0.363273\pi$
$967$	2.26472e13	0.832905	0.416453	+	0.909157i	$0.363273\pi$
$968$	9.59120e12	0.351102
$969$	−3.53821e10	−0.00128922
$970$	−3.49040e12	−0.126591
$971$	−1.25881e13	−0.454436	−0.227218	−	0.973844i	$-0.572963\pi$
$971$	−1.25881e13	−0.454436	−0.227218	+	0.973844i	$0.572963\pi$
$972$	1.43222e13	0.514648
$973$	−3.51776e13	−1.25822
$974$	−6.86059e12	−0.244257
$975$	2.05844e13	0.729488
$976$	−1.33363e13	−0.470446
$977$	8.69411e12	0.305281	0.152640	−	0.988282i	$-0.451222\pi$
$977$	8.69411e12	0.305281	0.152640	+	0.988282i	$0.451222\pi$
$978$	−5.58266e12	−0.195127
$979$	2.68771e12	0.0935105
$980$	−1.22728e13	−0.425037
$981$	−3.91297e12	−0.134895
$982$	3.12330e12	0.107180
$983$	2.76628e13	0.944943	0.472471	−	0.881346i	$-0.343362\pi$
$983$	2.76628e13	0.944943	0.472471	+	0.881346i	$0.343362\pi$
$984$	−1.71010e12	−0.0581491
$985$	1.29284e13	0.437605
$986$	−7.97476e9	−0.000268702 0
$987$	1.68294e13	0.564472
$988$	−3.13217e12	−0.104578
$989$	−4.35128e13	−1.44622
$990$	−8.06524e10	−0.00266845
$991$	1.15057e13	0.378950	0.189475	−	0.981886i	$-0.439321\pi$
$991$	1.15057e13	0.378950	0.189475	+	0.981886i	$0.439321\pi$
$992$	7.14495e12	0.234259
$993$	4.78172e13	1.56067
$994$	−1.01297e13	−0.329122
$995$	−1.49005e13	−0.481944
$996$	2.38539e13	0.768054
$997$	2.82714e13	0.906190	0.453095	−	0.891462i	$-0.350320\pi$
$997$	2.82714e13	0.906190	0.453095	+	0.891462i	$0.350320\pi$
$998$	−9.45803e12	−0.301796
$999$	−3.77389e13	−1.19879

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.10.a.a.1.5	✓	9
3.2	odd	2		261.10.a.b.1.5		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.10.a.a.1.5	✓	9	1.1	even	1	trivial
261.10.a.b.1.5		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)

\(f(q)\)	\(=\)	\(q+4.12402 q^{2} +158.305 q^{3} -494.992 q^{4} +522.723 q^{5} +652.853 q^{6} -9369.41 q^{7} -4152.85 q^{8} +5377.54 q^{9} +O(q^{10})\)	\(q+4.12402 q^{2} +158.305 q^{3} -494.992 q^{4} +522.723 q^{5} +652.853 q^{6} -9369.41 q^{7} -4152.85 q^{8} +5377.54 q^{9} +2155.72 q^{10} -6957.32 q^{11} -78359.9 q^{12} -77404.1 q^{13} -38639.6 q^{14} +82749.7 q^{15} +236310. q^{16} +2734.04 q^{17} +22177.1 q^{18} -81749.2 q^{19} -258744. q^{20} -1.48323e6 q^{21} -28692.1 q^{22} -1.95071e6 q^{23} -657418. q^{24} -1.67989e6 q^{25} -319216. q^{26} -2.26463e6 q^{27} +4.63779e6 q^{28} -707281. q^{29} +341261. q^{30} +2.30422e6 q^{31} +3.10081e6 q^{32} -1.10138e6 q^{33} +11275.2 q^{34} -4.89760e6 q^{35} -2.66184e6 q^{36} +1.66645e7 q^{37} -337135. q^{38} -1.22535e7 q^{39} -2.17079e6 q^{40} +2.60123e6 q^{41} -6.11685e6 q^{42} +2.23061e7 q^{43} +3.44382e6 q^{44} +2.81096e6 q^{45} -8.04477e6 q^{46} -1.13465e7 q^{47} +3.74091e7 q^{48} +4.74322e7 q^{49} -6.92788e6 q^{50} +432813. q^{51} +3.83144e7 q^{52} +6.78763e7 q^{53} -9.33937e6 q^{54} -3.63675e6 q^{55} +3.89098e7 q^{56} -1.29413e7 q^{57} -2.91684e6 q^{58} -1.61848e8 q^{59} -4.09605e7 q^{60} -5.64355e7 q^{61} +9.50265e6 q^{62} -5.03843e7 q^{63} -1.08203e8 q^{64} -4.04609e7 q^{65} -4.54211e6 q^{66} -3.70760e7 q^{67} -1.35333e6 q^{68} -3.08808e8 q^{69} -2.01978e7 q^{70} +2.62158e8 q^{71} -2.23321e7 q^{72} +1.99967e8 q^{73} +6.87247e7 q^{74} -2.65935e8 q^{75} +4.04652e7 q^{76} +6.51860e7 q^{77} -5.05335e7 q^{78} +1.16097e8 q^{79} +1.23524e8 q^{80} -4.64349e8 q^{81} +1.07275e7 q^{82} -3.04414e8 q^{83} +7.34186e8 q^{84} +1.42915e6 q^{85} +9.19907e7 q^{86} -1.11966e8 q^{87} +2.88927e7 q^{88} -3.86314e8 q^{89} +1.15924e7 q^{90} +7.25230e8 q^{91} +9.65588e8 q^{92} +3.64770e8 q^{93} -4.67932e7 q^{94} -4.27322e7 q^{95} +4.90874e8 q^{96} -1.61913e9 q^{97} +1.95611e8 q^{98} -3.74132e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 244 q^{3} + 1194 q^{4} - 738 q^{5} - 2330 q^{6} - 7128 q^{7} - 13776 q^{8} + 33017 q^{9}+O(q^{10}) \) 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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