LMFDB - Embedded newform 29.10.a.a.1.2

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			1.2
Root			$33.5115$ 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)

$f(q)$	$=$	$q-33.5115 q^{2} -215.845 q^{3} +611.021 q^{4} -1510.04 q^{5} +7233.29 q^{6} +2235.57 q^{7} -3318.35 q^{8} +26906.1 q^{9} +O(q^{10})$	\(q-33.5115 q^{2} -215.845 q^{3} +611.021 q^{4} -1510.04 q^{5} +7233.29 q^{6} +2235.57 q^{7} -3318.35 q^{8} +26906.1 q^{9} +50603.9 q^{10} +49368.8 q^{11} -131886. q^{12} +2621.69 q^{13} -74917.2 q^{14} +325936. q^{15} -201640. q^{16} +129972. q^{17} -901663. q^{18} -849850. q^{19} -922669. q^{20} -482536. q^{21} -1.65442e6 q^{22} +2.40490e6 q^{23} +716250. q^{24} +327108. q^{25} -87856.7 q^{26} -1.55907e6 q^{27} +1.36598e6 q^{28} -707281. q^{29} -1.09226e7 q^{30} -2.51437e6 q^{31} +8.45625e6 q^{32} -1.06560e7 q^{33} -4.35556e6 q^{34} -3.37580e6 q^{35} +1.64402e7 q^{36} +9.65069e6 q^{37} +2.84798e7 q^{38} -565878. q^{39} +5.01086e6 q^{40} +2.02993e7 q^{41} +1.61705e7 q^{42} +3.12314e7 q^{43} +3.01654e7 q^{44} -4.06294e7 q^{45} -8.05918e7 q^{46} -3.68899e7 q^{47} +4.35230e7 q^{48} -3.53558e7 q^{49} -1.09619e7 q^{50} -2.80538e7 q^{51} +1.60191e6 q^{52} -2.34695e7 q^{53} +5.22466e7 q^{54} -7.45490e7 q^{55} -7.41840e6 q^{56} +1.83436e8 q^{57} +2.37021e7 q^{58} -5.09173e7 q^{59} +1.99154e8 q^{60} -1.82091e8 q^{61} +8.42603e7 q^{62} +6.01503e7 q^{63} -1.80142e8 q^{64} -3.95887e6 q^{65} +3.57099e8 q^{66} -1.76459e8 q^{67} +7.94157e7 q^{68} -5.19086e8 q^{69} +1.13128e8 q^{70} +2.83059e7 q^{71} -8.92839e7 q^{72} +1.91595e8 q^{73} -3.23409e8 q^{74} -7.06046e7 q^{75} -5.19277e8 q^{76} +1.10367e8 q^{77} +1.89634e7 q^{78} +5.15663e8 q^{79} +3.04485e8 q^{80} -1.93076e8 q^{81} -6.80259e8 q^{82} -2.13499e8 q^{83} -2.94840e8 q^{84} -1.96264e8 q^{85} -1.04661e9 q^{86} +1.52663e8 q^{87} -1.63823e8 q^{88} +2.43874e8 q^{89} +1.36155e9 q^{90} +5.86096e6 q^{91} +1.46945e9 q^{92} +5.42714e8 q^{93} +1.23624e9 q^{94} +1.28331e9 q^{95} -1.82524e9 q^{96} +4.29900e8 q^{97} +1.18483e9 q^{98} +1.32832e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−33.5115	−1.48101	−0.740507	−	0.672049i	$-0.765414\pi$
$2$	−33.5115	−1.48101	−0.740507	+	0.672049i	$0.765414\pi$
$3$	−215.845	−1.53850	−0.769248	−	0.638950i	$-0.779369\pi$
$3$	−215.845	−1.53850	−0.769248	+	0.638950i	$0.779369\pi$
$4$	611.021	1.19340
$5$	−1510.04	−1.08050	−0.540250	−	0.841505i	$-0.681670\pi$
$5$	−1510.04	−1.08050	−0.540250	+	0.841505i	$0.681670\pi$
$6$	7233.29	2.27853
$7$	2235.57	0.351922	0.175961	−	0.984397i	$-0.443697\pi$
$7$	2235.57	0.351922	0.175961	+	0.984397i	$0.443697\pi$
$8$	−3318.35	−0.286429
$9$	26906.1	1.36697
$10$	50603.9	1.60023
$11$	49368.8	1.01668	0.508341	−	0.861156i	$-0.330259\pi$
$11$	49368.8	1.01668	0.508341	+	0.861156i	$0.330259\pi$
$12$	−131886.	−1.83604
$13$	2621.69	0.0254587	0.0127293	−	0.999919i	$-0.495948\pi$
$13$	2621.69	0.0254587	0.0127293	+	0.999919i	$0.495948\pi$
$14$	−74917.2	−0.521201
$15$	325936.	1.66234
$16$	−201640.	−0.769195
$17$	129972.	0.377424	0.188712	−	0.982032i	$-0.439569\pi$
$17$	129972.	0.377424	0.188712	+	0.982032i	$0.439569\pi$
$18$	−901663.	−2.02450
$19$	−849850.	−1.49607	−0.748034	−	0.663661i	$-0.769002\pi$
$19$	−849850.	−1.49607	−0.748034	+	0.663661i	$0.769002\pi$
$20$	−922669.	−1.28947
$21$	−482536.	−0.541431
$22$	−1.65442e6	−1.50572
$23$	2.40490e6	1.79193	0.895967	−	0.444121i	$-0.146484\pi$
$23$	2.40490e6	1.79193	0.895967	+	0.444121i	$0.146484\pi$
$24$	716250.	0.440671
$25$	327108.	0.167479
$26$	−87856.7	−0.0377047
$27$	−1.55907e6	−0.564583
$28$	1.36598e6	0.419984
$29$	−707281.	−0.185695
$29$	−707281.	−0.185695
$30$	−1.09226e7	−2.46195
$31$	−2.51437e6	−0.488992	−0.244496	−	0.969650i	$-0.578622\pi$
$31$	−2.51437e6	−0.488992	−0.244496	+	0.969650i	$0.578622\pi$
$32$	8.45625e6	1.42562
$33$	−1.06560e7	−1.56416
$34$	−4.35556e6	−0.558971
$35$	−3.37580e6	−0.380252
$36$	1.64402e7	1.63134
$37$	9.65069e6	0.846546	0.423273	−	0.906002i	$-0.360881\pi$
$37$	9.65069e6	0.846546	0.423273	+	0.906002i	$0.360881\pi$
$38$	2.84798e7	2.21570
$39$	−565878.	−0.0391681
$40$	5.01086e6	0.309487
$41$	2.02993e7	1.12190	0.560948	−	0.827851i	$-0.310437\pi$
$41$	2.02993e7	1.12190	0.560948	+	0.827851i	$0.310437\pi$
$42$	1.61705e7	0.801866
$43$	3.12314e7	1.39310	0.696551	−	0.717508i	$-0.254717\pi$
$43$	3.12314e7	1.39310	0.696551	+	0.717508i	$0.254717\pi$
$44$	3.01654e7	1.21331
$45$	−4.06294e7	−1.47701
$46$	−8.05918e7	−2.65388
$47$	−3.68899e7	−1.10272	−0.551362	−	0.834266i	$-0.685892\pi$
$47$	−3.68899e7	−1.10272	−0.551362	+	0.834266i	$0.685892\pi$
$48$	4.35230e7	1.18340
$49$	−3.53558e7	−0.876151
$50$	−1.09619e7	−0.248039
$51$	−2.80538e7	−0.580666
$52$	1.60191e6	0.0303824
$53$	−2.34695e7	−0.408567	−0.204283	−	0.978912i	$-0.565486\pi$
$53$	−2.34695e7	−0.408567	−0.204283	+	0.978912i	$0.565486\pi$
$54$	5.22466e7	0.836154
$55$	−7.45490e7	−1.09852
$56$	−7.41840e6	−0.100801
$57$	1.83436e8	2.30169
$58$	2.37021e7	0.275017
$59$	−5.09173e7	−0.547056	−0.273528	−	0.961864i	$-0.588191\pi$
$59$	−5.09173e7	−0.547056	−0.273528	+	0.961864i	$0.588191\pi$
$60$	1.99154e8	1.98384
$61$	−1.82091e8	−1.68385	−0.841925	−	0.539594i	$-0.818578\pi$
$61$	−1.82091e8	−1.68385	−0.841925	+	0.539594i	$0.818578\pi$
$62$	8.42603e7	0.724203
$63$	6.01503e7	0.481067
$64$	−1.80142e8	−1.34216
$65$	−3.95887e6	−0.0275081
$66$	3.57099e8	2.31654
$67$	−1.76459e8	−1.06981	−0.534906	−	0.844912i	$-0.679653\pi$
$67$	−1.76459e8	−1.06981	−0.534906	+	0.844912i	$0.679653\pi$
$68$	7.94157e7	0.450419
$69$	−5.19086e8	−2.75688
$70$	1.13128e8	0.563158
$71$	2.83059e7	0.132195	0.0660974	−	0.997813i	$-0.478945\pi$
$71$	2.83059e7	0.132195	0.0660974	+	0.997813i	$0.478945\pi$
$72$	−8.92839e7	−0.391540
$73$	1.91595e8	0.789646	0.394823	−	0.918757i	$-0.370806\pi$
$73$	1.91595e8	0.789646	0.394823	+	0.918757i	$0.370806\pi$
$74$	−3.23409e8	−1.25375
$75$	−7.06046e7	−0.257666
$76$	−5.19277e8	−1.78541
$77$	1.10367e8	0.357793
$78$	1.89634e7	0.0580085
$79$	5.15663e8	1.48951	0.744756	−	0.667337i	$-0.232566\pi$
$79$	5.15663e8	1.48951	0.744756	+	0.667337i	$0.232566\pi$
$80$	3.04485e8	0.831115
$81$	−1.93076e8	−0.498362
$82$	−6.80259e8	−1.66154
$83$	−2.13499e8	−0.493792	−0.246896	−	0.969042i	$-0.579411\pi$
$83$	−2.13499e8	−0.493792	−0.246896	+	0.969042i	$0.579411\pi$
$84$	−2.94840e8	−0.646144
$85$	−1.96264e8	−0.407807
$86$	−1.04661e9	−2.06320
$87$	1.52663e8	0.285692
$88$	−1.63823e8	−0.291208
$89$	2.43874e8	0.412012	0.206006	−	0.978551i	$-0.433953\pi$
$89$	2.43874e8	0.412012	0.206006	+	0.978551i	$0.433953\pi$
$90$	1.36155e9	2.18747
$91$	5.86096e6	0.00895947
$92$	1.46945e9	2.13849
$93$	5.42714e8	0.752312
$94$	1.23624e9	1.63315
$95$	1.28331e9	1.61650
$96$	−1.82524e9	−2.19331
$97$	4.29900e8	0.493055	0.246527	−	0.969136i	$-0.420710\pi$
$97$	4.29900e8	0.493055	0.246527	+	0.969136i	$0.420710\pi$
$98$	1.18483e9	1.29759
$99$	1.32832e9	1.38977
$100$	1.99870e8	0.199870
$101$	−8.51087e8	−0.813819	−0.406909	−	0.913468i	$-0.633394\pi$
$101$	−8.51087e8	−0.813819	−0.406909	+	0.913468i	$0.633394\pi$
$102$	9.40126e8	0.859974
$103$	−1.96855e9	−1.72337	−0.861684	−	0.507445i	$-0.830590\pi$
$103$	−1.96855e9	−1.72337	−0.861684	+	0.507445i	$0.830590\pi$
$104$	−8.69969e6	−0.00729212
$105$	7.28651e8	0.585016
$106$	7.86499e8	0.605093
$107$	−2.35820e9	−1.73922	−0.869608	−	0.493743i	$-0.835628\pi$
$107$	−2.35820e9	−1.73922	−0.869608	+	0.493743i	$0.835628\pi$
$108$	−9.52622e8	−0.673773
$109$	2.46807e9	1.67470	0.837352	−	0.546664i	$-0.184102\pi$
$109$	2.46807e9	1.67470	0.837352	+	0.546664i	$0.184102\pi$
$110$	2.49825e9	1.62693
$111$	−2.08305e9	−1.30241
$112$	−4.50779e8	−0.270697
$113$	1.63593e9	0.943868	0.471934	−	0.881634i	$-0.343556\pi$
$113$	1.63593e9	0.943868	0.471934	+	0.881634i	$0.343556\pi$
$114$	−6.14722e9	−3.40884
$115$	−3.63151e9	−1.93618
$116$	−4.32164e8	−0.221609
$117$	7.05394e7	0.0348013
$118$	1.70632e9	0.810197
$119$	2.90561e8	0.132824
$120$	−1.08157e9	−0.476144
$121$	7.93263e7	0.0336421
$122$	6.10213e9	2.49380
$123$	−4.38150e9	−1.72603
$124$	−1.53633e9	−0.583563
$125$	2.45536e9	0.899538
$126$	−2.01573e9	−0.712467
$127$	−4.12308e9	−1.40639	−0.703194	−	0.710998i	$-0.748243\pi$
$127$	−4.12308e9	−1.40639	−0.703194	+	0.710998i	$0.748243\pi$
$128$	1.70724e9	0.562145
$129$	−6.74113e9	−2.14328
$130$	1.32668e8	0.0407399
$131$	1.16336e9	0.345137	0.172569	−	0.984997i	$-0.444793\pi$
$131$	1.16336e9	0.345137	0.172569	+	0.984997i	$0.444793\pi$
$132$	−6.51104e9	−1.86667
$133$	−1.89990e9	−0.526499
$134$	5.91341e9	1.58441
$135$	2.35426e9	0.610031
$136$	−4.31293e8	−0.108105
$137$	2.51602e9	0.610198	0.305099	−	0.952321i	$-0.401310\pi$
$137$	2.51602e9	0.610198	0.305099	+	0.952321i	$0.401310\pi$
$138$	1.73953e10	4.08298
$139$	−5.14223e9	−1.16838	−0.584191	−	0.811617i	$-0.698588\pi$
$139$	−5.14223e9	−1.16838	−0.584191	+	0.811617i	$0.698588\pi$
$140$	−2.06269e9	−0.453793
$141$	7.96249e9	1.69654
$142$	−9.48573e8	−0.195782
$143$	1.29430e8	0.0258834
$144$	−5.42534e9	−1.05147
$145$	1.06803e9	0.200644
$146$	−6.42065e9	−1.16948
$147$	7.63138e9	1.34795
$148$	5.89677e9	1.01027
$149$	−8.71023e9	−1.44774	−0.723872	−	0.689935i	$-0.757639\pi$
$149$	−8.71023e9	−1.44774	−0.723872	+	0.689935i	$0.757639\pi$
$150$	2.36607e9	0.381607
$151$	−8.20947e9	−1.28505	−0.642524	−	0.766266i	$-0.722113\pi$
$151$	−8.20947e9	−1.28505	−0.642524	+	0.766266i	$0.722113\pi$
$152$	2.82010e9	0.428518
$153$	3.49704e9	0.515928
$154$	−3.69857e9	−0.529896
$155$	3.79681e9	0.528355
$156$	−3.45764e8	−0.0467432
$157$	1.20586e10	1.58397	0.791987	−	0.610537i	$-0.209047\pi$
$157$	1.20586e10	1.58397	0.791987	+	0.610537i	$0.209047\pi$
$158$	−1.72806e10	−2.20599
$159$	5.06578e9	0.628578
$160$	−1.27693e10	−1.54038
$161$	5.37632e9	0.630621
$162$	6.47026e9	0.738081
$163$	−1.51539e10	−1.68144	−0.840720	−	0.541470i	$-0.817868\pi$
$163$	−1.51539e10	−1.68144	−0.840720	+	0.541470i	$0.817868\pi$
$164$	1.24033e10	1.33887
$165$	1.60910e10	1.69008
$166$	7.15467e9	0.731313
$167$	5.06407e9	0.503820	0.251910	−	0.967751i	$-0.418941\pi$
$167$	5.06407e9	0.503820	0.251910	+	0.967751i	$0.418941\pi$
$168$	1.60122e9	0.155082
$169$	−1.05976e10	−0.999352
$170$	6.57709e9	0.603968
$171$	−2.28661e10	−2.04508
$172$	1.90830e10	1.66253
$173$	3.88496e9	0.329746	0.164873	−	0.986315i	$-0.447279\pi$
$173$	3.88496e9	0.329746	0.164873	+	0.986315i	$0.447279\pi$
$174$	−5.11597e9	−0.423113
$175$	7.31272e8	0.0589397
$176$	−9.95471e9	−0.782027
$177$	1.09903e10	0.841643
$178$	−8.17257e9	−0.610195
$179$	1.57795e10	1.14883	0.574415	−	0.818564i	$-0.305230\pi$
$179$	1.57795e10	1.14883	0.574415	+	0.818564i	$0.305230\pi$
$180$	−2.48254e10	−1.76267
$181$	7.07224e9	0.489782	0.244891	−	0.969551i	$-0.421248\pi$
$181$	7.07224e9	0.489782	0.244891	+	0.969551i	$0.421248\pi$
$182$	−1.96410e8	−0.0132691
$183$	3.93034e10	2.59060
$184$	−7.98031e9	−0.513262
$185$	−1.45730e10	−0.914692
$186$	−1.81872e10	−1.11418
$187$	6.41656e9	0.383721
$188$	−2.25405e10	−1.31599
$189$	−3.48540e9	−0.198689
$190$	−4.30057e10	−2.39406
$191$	2.97722e9	0.161868	0.0809340	−	0.996719i	$-0.474210\pi$
$191$	2.97722e9	0.161868	0.0809340	+	0.996719i	$0.474210\pi$
$192$	3.88828e10	2.06491
$193$	1.29537e10	0.672025	0.336012	−	0.941858i	$-0.390922\pi$
$193$	1.29537e10	0.672025	0.336012	+	0.941858i	$0.390922\pi$
$194$	−1.44066e10	−0.730221
$195$	8.54501e8	0.0423211
$196$	−2.16032e10	−1.04560
$197$	−1.47967e10	−0.699948	−0.349974	−	0.936760i	$-0.613810\pi$
$197$	−1.47967e10	−0.699948	−0.349974	+	0.936760i	$0.613810\pi$
$198$	−4.45140e10	−2.05827
$199$	2.68070e10	1.21174	0.605869	−	0.795564i	$-0.292825\pi$
$199$	2.68070e10	1.21174	0.605869	+	0.795564i	$0.292825\pi$
$200$	−1.08546e9	−0.0479710
$201$	3.80878e10	1.64590
$202$	2.85212e10	1.20528
$203$	−1.58117e9	−0.0653503
$204$	−1.71415e10	−0.692967
$205$	−3.06528e10	−1.21221
$206$	6.59689e10	2.55233
$207$	6.47064e10	2.44952
$208$	−5.28637e8	−0.0195827
$209$	−4.19560e10	−1.52102
$210$	−2.44182e10	−0.866416
$211$	−1.62028e10	−0.562755	−0.281377	−	0.959597i	$-0.590791\pi$
$211$	−1.62028e10	−0.562755	−0.281377	+	0.959597i	$0.590791\pi$
$212$	−1.43404e10	−0.487584
$213$	−6.10969e9	−0.203381
$214$	7.90268e10	2.57580
$215$	−4.71607e10	−1.50525
$216$	5.17353e9	0.161713
$217$	−5.62104e9	−0.172087
$218$	−8.27087e10	−2.48026
$219$	−4.13549e10	−1.21487
$220$	−4.55510e10	−1.31098
$221$	3.40746e8	0.00960873
$222$	6.98062e10	1.92888
$223$	−1.25197e10	−0.339018	−0.169509	−	0.985529i	$-0.554218\pi$
$223$	−1.25197e10	−0.339018	−0.169509	+	0.985529i	$0.554218\pi$
$224$	1.89045e10	0.501706
$225$	8.80119e9	0.228939
$226$	−5.48224e10	−1.39788
$227$	−3.85527e10	−0.963693	−0.481846	−	0.876256i	$-0.660034\pi$
$227$	−3.85527e10	−0.963693	−0.481846	+	0.876256i	$0.660034\pi$
$228$	1.12083e11	2.74684
$229$	−3.10216e10	−0.745426	−0.372713	−	0.927947i	$-0.621572\pi$
$229$	−3.10216e10	−0.745426	−0.372713	+	0.927947i	$0.621572\pi$
$230$	1.21697e11	2.86751
$231$	−2.38222e10	−0.550463
$232$	2.34701e9	0.0531886
$233$	4.95778e10	1.10201	0.551006	−	0.834502i	$-0.314244\pi$
$233$	4.95778e10	1.10201	0.551006	+	0.834502i	$0.314244\pi$
$234$	−2.36388e9	−0.0515412
$235$	5.57053e10	1.19149
$236$	−3.11116e10	−0.652857
$237$	−1.11303e11	−2.29161
$238$	−9.73715e9	−0.196714
$239$	−4.76517e10	−0.944687	−0.472344	−	0.881415i	$-0.656592\pi$
$239$	−4.76517e10	−0.944687	−0.472344	+	0.881415i	$0.656592\pi$
$240$	−6.57216e10	−1.27867
$241$	2.05567e10	0.392534	0.196267	−	0.980551i	$-0.437118\pi$
$241$	2.05567e10	0.392534	0.196267	+	0.980551i	$0.437118\pi$
$242$	−2.65834e9	−0.0498244
$243$	7.23615e10	1.33131
$244$	−1.11261e11	−2.00951
$245$	5.33889e10	0.946681
$246$	1.46831e11	2.55628
$247$	−2.22804e9	−0.0380879
$248$	8.34357e9	0.140062
$249$	4.60827e10	0.759698
$250$	−8.22827e10	−1.33223
$251$	−8.51191e10	−1.35362	−0.676808	−	0.736160i	$-0.736637\pi$
$251$	−8.51191e10	−1.35362	−0.676808	+	0.736160i	$0.736637\pi$
$252$	3.67531e10	0.574106
$253$	1.18727e11	1.82183
$254$	1.38171e11	2.08288
$255$	4.23625e10	0.627409
$256$	3.50208e10	0.509619
$257$	−2.87247e10	−0.410729	−0.205365	−	0.978686i	$-0.565838\pi$
$257$	−2.87247e10	−0.410729	−0.205365	+	0.978686i	$0.565838\pi$
$258$	2.25906e11	3.17423
$259$	2.15748e10	0.297918
$260$	−2.41895e9	−0.0328282
$261$	−1.90302e10	−0.253840
$262$	−3.89858e10	−0.511153
$263$	1.19144e11	1.53558	0.767791	−	0.640700i	$-0.221356\pi$
$263$	1.19144e11	1.53558	0.767791	+	0.640700i	$0.221356\pi$
$264$	3.53604e10	0.448022
$265$	3.54400e10	0.441456
$266$	6.36684e10	0.779752
$267$	−5.26389e10	−0.633879
$268$	−1.07820e11	−1.27671
$269$	−8.48513e10	−0.988037	−0.494018	−	0.869452i	$-0.664472\pi$
$269$	−8.48513e10	−0.988037	−0.494018	+	0.869452i	$0.664472\pi$
$270$	−7.88947e10	−0.903464
$271$	−1.45259e11	−1.63600	−0.817999	−	0.575220i	$-0.804916\pi$
$271$	−1.45259e11	−1.63600	−0.817999	+	0.575220i	$0.804916\pi$
$272$	−2.62076e10	−0.290313
$273$	−1.26506e9	−0.0137841
$274$	−8.43155e10	−0.903712
$275$	1.61489e10	0.170273
$276$	−3.17172e11	−3.29007
$277$	−1.02115e11	−1.04215	−0.521076	−	0.853510i	$-0.674469\pi$
$277$	−1.02115e11	−1.04215	−0.521076	+	0.853510i	$0.674469\pi$
$278$	1.72324e11	1.73039
$279$	−6.76518e10	−0.668437
$280$	1.12021e10	0.108915
$281$	−2.64878e10	−0.253435	−0.126718	−	0.991939i	$-0.540444\pi$
$281$	−2.64878e10	−0.253435	−0.126718	+	0.991939i	$0.540444\pi$
$282$	−2.66835e11	−2.51259
$283$	−7.40820e10	−0.686552	−0.343276	−	0.939235i	$-0.611537\pi$
$283$	−7.40820e10	−0.686552	−0.343276	+	0.939235i	$0.611537\pi$
$284$	1.72955e10	0.157761
$285$	−2.76996e11	−2.48698
$286$	−4.33738e9	−0.0383336
$287$	4.53804e10	0.394820
$288$	2.27525e11	1.94878
$289$	−1.01695e11	−0.857551
$290$	−3.57911e10	−0.297156
$291$	−9.27919e10	−0.758563
$292$	1.17069e11	0.942364
$293$	−9.17114e10	−0.726974	−0.363487	−	0.931599i	$-0.618414\pi$
$293$	−9.17114e10	−0.726974	−0.363487	+	0.931599i	$0.618414\pi$
$294$	−2.55739e11	−1.99634
$295$	7.68874e10	0.591093
$296$	−3.20244e10	−0.242476
$297$	−7.69691e10	−0.574001
$298$	2.91893e11	2.14413
$299$	6.30490e9	0.0456203
$300$	−4.31409e10	−0.307499
$301$	6.98198e10	0.490263
$302$	2.75112e11	1.90317
$303$	1.83703e11	1.25206
$304$	1.71364e11	1.15077
$305$	2.74965e11	1.81940
$306$	−1.17191e11	−0.764096
$307$	−4.19912e10	−0.269796	−0.134898	−	0.990860i	$-0.543071\pi$
$307$	−4.19912e10	−0.269796	−0.134898	+	0.990860i	$0.543071\pi$
$308$	6.74367e10	0.426990
$309$	4.24901e11	2.65140
$310$	−1.27237e11	−0.782501
$311$	−5.96708e10	−0.361693	−0.180847	−	0.983511i	$-0.557884\pi$
$311$	−5.96708e10	−0.361693	−0.180847	+	0.983511i	$0.557884\pi$
$312$	1.87778e9	0.0112189
$313$	1.66402e11	0.979963	0.489982	−	0.871733i	$-0.337003\pi$
$313$	1.66402e11	0.979963	0.489982	+	0.871733i	$0.337003\pi$
$314$	−4.04102e11	−2.34589
$315$	−9.08297e10	−0.519793
$316$	3.15081e11	1.77759
$317$	−1.03546e10	−0.0575927	−0.0287963	−	0.999585i	$-0.509167\pi$
$317$	−1.03546e10	−0.0575927	−0.0287963	+	0.999585i	$0.509167\pi$
$318$	−1.69762e11	−0.930933
$319$	−3.49176e10	−0.188793
$320$	2.72023e11	1.45021
$321$	5.09006e11	2.67578
$322$	−1.80168e11	−0.933958
$323$	−1.10457e11	−0.564652
$324$	−1.17973e11	−0.594746
$325$	8.57575e8	0.00426380
$326$	5.07832e11	2.49024
$327$	−5.32721e11	−2.57653
$328$	−6.73601e10	−0.321344
$329$	−8.24698e10	−0.388073
$330$	−5.39235e11	−2.50302
$331$	1.37375e11	0.629043	0.314522	−	0.949250i	$-0.398156\pi$
$331$	1.37375e11	0.629043	0.314522	+	0.949250i	$0.398156\pi$
$332$	−1.30452e11	−0.589292
$333$	2.59662e11	1.15720
$334$	−1.69705e11	−0.746164
$335$	2.66461e11	1.15593
$336$	9.72985e10	0.416466
$337$	−3.47419e11	−1.46730	−0.733650	−	0.679527i	$-0.762185\pi$
$337$	−3.47419e11	−1.46730	−0.733650	+	0.679527i	$0.762185\pi$
$338$	3.55142e11	1.48005
$339$	−3.53107e11	−1.45214
$340$	−1.19921e11	−0.486677
$341$	−1.24131e11	−0.497149
$342$	7.66279e11	3.02879
$343$	−1.69254e11	−0.660259
$344$	−1.03637e11	−0.399025
$345$	7.83842e11	2.97881
$346$	−1.30191e11	−0.488358
$347$	−2.56057e11	−0.948099	−0.474049	−	0.880498i	$-0.657208\pi$
$347$	−2.56057e11	−0.948099	−0.474049	+	0.880498i	$0.657208\pi$
$348$	9.32804e10	0.340945
$349$	6.68346e10	0.241150	0.120575	−	0.992704i	$-0.461526\pi$
$349$	6.68346e10	0.241150	0.120575	+	0.992704i	$0.461526\pi$
$350$	−2.45060e10	−0.0872904
$351$	−4.08738e9	−0.0143735
$352$	4.17475e11	1.44940
$353$	1.94329e11	0.666120	0.333060	−	0.942906i	$-0.391919\pi$
$353$	1.94329e11	0.666120	0.333060	+	0.942906i	$0.391919\pi$
$354$	−3.68300e11	−1.24648
$355$	−4.27431e10	−0.142836
$356$	1.49012e11	0.491695
$357$	−6.27162e10	−0.204349
$358$	−5.28796e11	−1.70143
$359$	−3.99142e11	−1.26824	−0.634121	−	0.773234i	$-0.718638\pi$
$359$	−3.99142e11	−1.26824	−0.634121	+	0.773234i	$0.718638\pi$
$360$	1.34823e11	0.423059
$361$	3.99558e11	1.23822
$362$	−2.37001e11	−0.725374
$363$	−1.71222e10	−0.0517582
$364$	3.58117e9	0.0106922
$365$	−2.89318e11	−0.853212
$366$	−1.31712e12	−3.83671
$367$	−4.37272e11	−1.25821	−0.629107	−	0.777319i	$-0.716579\pi$
$367$	−4.37272e11	−1.25821	−0.629107	+	0.777319i	$0.716579\pi$
$368$	−4.84924e11	−1.37835
$369$	5.46174e11	1.53360
$370$	4.88362e11	1.35467
$371$	−5.24677e10	−0.143784
$372$	3.31610e11	0.897810
$373$	4.23809e11	1.13365	0.566827	−	0.823837i	$-0.308171\pi$
$373$	4.23809e11	1.13365	0.566827	+	0.823837i	$0.308171\pi$
$374$	−2.15029e11	−0.568295
$375$	−5.29977e11	−1.38394
$376$	1.22414e11	0.315852
$377$	−1.85427e9	−0.00472756
$378$	1.16801e11	0.294261
$379$	2.91331e11	0.725289	0.362644	−	0.931928i	$-0.381874\pi$
$379$	2.91331e11	0.725289	0.362644	+	0.931928i	$0.381874\pi$
$380$	7.84130e11	1.92913
$381$	8.89947e11	2.16372
$382$	−9.97712e10	−0.239729
$383$	−4.56241e10	−0.108343	−0.0541713	−	0.998532i	$-0.517252\pi$
$383$	−4.56241e10	−0.108343	−0.0541713	+	0.998532i	$0.517252\pi$
$384$	−3.68498e11	−0.864858
$385$	−1.66659e11	−0.386595
$386$	−4.34097e11	−0.995278
$387$	8.40313e11	1.90433
$388$	2.62678e11	0.588412
$389$	−3.61185e11	−0.799754	−0.399877	−	0.916569i	$-0.630947\pi$
$389$	−3.61185e11	−0.799754	−0.399877	+	0.916569i	$0.630947\pi$
$390$	−2.86356e10	−0.0626781
$391$	3.12570e11	0.676320
$392$	1.17323e11	0.250955
$393$	−2.51105e11	−0.530992
$394$	4.95858e11	1.03663
$395$	−7.78674e11	−1.60942
$396$	8.11632e11	1.65856
$397$	−6.83981e10	−0.138193	−0.0690966	−	0.997610i	$-0.522012\pi$
$397$	−6.83981e10	−0.138193	−0.0690966	+	0.997610i	$0.522012\pi$
$398$	−8.98342e11	−1.79460
$399$	4.10083e11	0.810017
$400$	−6.59580e10	−0.128824
$401$	−7.17456e11	−1.38562	−0.692812	−	0.721118i	$-0.743629\pi$
$401$	−7.17456e11	−1.38562	−0.692812	+	0.721118i	$0.743629\pi$
$402$	−1.27638e12	−2.43760
$403$	−6.59189e9	−0.0124491
$404$	−5.20032e11	−0.971212
$405$	2.91553e11	0.538480
$406$	5.29875e10	0.0967847
$407$	4.76442e11	0.860668
$408$	9.30925e10	0.166320
$409$	−2.41453e11	−0.426657	−0.213328	−	0.976981i	$-0.568430\pi$
$409$	−2.41453e11	−0.426657	−0.213328	+	0.976981i	$0.568430\pi$
$410$	1.02722e12	1.79530
$411$	−5.43070e11	−0.938788
$412$	−1.20282e12	−2.05667
$413$	−1.13829e11	−0.192521
$414$	−2.16841e12	−3.62777
$415$	3.22393e11	0.533543
$416$	2.21697e10	0.0362944
$417$	1.10992e12	1.79755
$418$	1.40601e12	2.25266
$419$	−2.81074e11	−0.445510	−0.222755	−	0.974874i	$-0.571505\pi$
$419$	−2.81074e11	−0.445510	−0.222755	+	0.974874i	$0.571505\pi$
$420$	4.45221e11	0.698158
$421$	4.83480e11	0.750082	0.375041	−	0.927008i	$-0.377629\pi$
$421$	4.83480e11	0.750082	0.375041	+	0.927008i	$0.377629\pi$
$422$	5.42980e11	0.833447
$423$	−9.92562e11	−1.50739
$424$	7.78802e10	0.117026
$425$	4.25149e10	0.0632108
$426$	2.04745e11	0.301210
$427$	−4.07076e11	−0.592584
$428$	−1.44091e12	−2.07558
$429$	−2.79367e10	−0.0398215
$430$	1.58043e12	2.22929
$431$	7.21047e11	1.00650	0.503252	−	0.864140i	$-0.332137\pi$
$431$	7.21047e11	1.00650	0.503252	+	0.864140i	$0.332137\pi$
$432$	3.14370e11	0.434274
$433$	2.07356e11	0.283479	0.141739	−	0.989904i	$-0.454731\pi$
$433$	2.07356e11	0.283479	0.141739	+	0.989904i	$0.454731\pi$
$434$	1.88370e11	0.254863
$435$	−2.30528e11	−0.308690
$436$	1.50804e12	1.99859
$437$	−2.04380e12	−2.68085
$438$	1.38587e12	1.79923
$439$	2.27692e11	0.292589	0.146295	−	0.989241i	$-0.453265\pi$
$439$	2.27692e11	0.292589	0.146295	+	0.989241i	$0.453265\pi$
$440$	2.47380e11	0.314650
$441$	−9.51287e11	−1.19767
$442$	−1.14189e10	−0.0142307
$443$	−3.03365e11	−0.374239	−0.187120	−	0.982337i	$-0.559915\pi$
$443$	−3.03365e11	−0.374239	−0.187120	+	0.982337i	$0.559915\pi$
$444$	−1.27279e12	−1.55429
$445$	−3.68260e11	−0.445179
$446$	4.19555e11	0.502091
$447$	1.88006e12	2.22735
$448$	−4.02720e11	−0.472337
$449$	−1.77878e11	−0.206545	−0.103272	−	0.994653i	$-0.532931\pi$
$449$	−1.77878e11	−0.206545	−0.103272	+	0.994653i	$0.532931\pi$
$450$	−2.94941e11	−0.339062
$451$	1.00215e12	1.14061
$452$	9.99587e11	1.12641
$453$	1.77197e12	1.97704
$454$	1.29196e12	1.42724
$455$	−8.85031e9	−0.00968071
$456$	−6.08705e11	−0.659273
$457$	2.10431e11	0.225677	0.112838	−	0.993613i	$-0.464006\pi$
$457$	2.10431e11	0.225677	0.112838	+	0.993613i	$0.464006\pi$
$458$	1.03958e12	1.10399
$459$	−2.02635e11	−0.213087
$460$	−2.21893e12	−2.31064
$461$	2.72519e11	0.281024	0.140512	−	0.990079i	$-0.455125\pi$
$461$	2.72519e11	0.281024	0.140512	+	0.990079i	$0.455125\pi$
$462$	7.98318e11	0.815243
$463$	7.76739e10	0.0785527	0.0392763	−	0.999228i	$-0.487495\pi$
$463$	7.76739e10	0.0785527	0.0392763	+	0.999228i	$0.487495\pi$
$464$	1.42616e11	0.142836
$465$	−8.19522e11	−0.812873
$466$	−1.66143e12	−1.63209
$467$	−1.67836e12	−1.63290	−0.816450	−	0.577416i	$-0.804061\pi$
$467$	−1.67836e12	−1.63290	−0.816450	+	0.577416i	$0.804061\pi$
$468$	4.31010e10	0.0415319
$469$	−3.94486e11	−0.376490
$470$	−1.86677e12	−1.76462
$471$	−2.60279e12	−2.43694
$472$	1.68962e11	0.156693
$473$	1.54185e12	1.41634
$474$	3.72994e12	3.39390
$475$	−2.77993e11	−0.250560
$476$	1.77539e11	0.158512
$477$	−6.31473e11	−0.558499
$478$	1.59688e12	1.39909
$479$	1.71530e12	1.48878	0.744389	−	0.667747i	$-0.232741\pi$
$479$	1.71530e12	1.48878	0.744389	+	0.667747i	$0.232741\pi$
$480$	2.75619e12	2.36987
$481$	2.53011e10	0.0215519
$482$	−6.88887e11	−0.581348
$483$	−1.16045e12	−0.970208
$484$	4.84701e10	0.0401485
$485$	−6.49169e11	−0.532745
$486$	−2.42494e12	−1.97169
$487$	−3.31129e11	−0.266757	−0.133379	−	0.991065i	$-0.542583\pi$
$487$	−3.31129e11	−0.266757	−0.133379	+	0.991065i	$0.542583\pi$
$488$	6.04241e11	0.482304
$489$	3.27090e12	2.58689
$490$	−1.78914e12	−1.40205
$491$	1.42293e12	1.10488	0.552442	−	0.833551i	$-0.313696\pi$
$491$	1.42293e12	1.10488	0.552442	+	0.833551i	$0.313696\pi$
$492$	−2.67719e12	−2.05985
$493$	−9.19268e10	−0.0700860
$494$	7.46651e10	0.0564087
$495$	−2.00582e12	−1.50165
$496$	5.06997e11	0.376130
$497$	6.32797e10	0.0465223
$498$	−1.54430e12	−1.12512
$499$	−1.58091e12	−1.14144	−0.570722	−	0.821143i	$-0.693337\pi$
$499$	−1.58091e12	−1.14144	−0.570722	+	0.821143i	$0.693337\pi$
$500$	1.50028e12	1.07351
$501$	−1.09305e12	−0.775125
$502$	2.85247e12	2.00472
$503$	−9.61329e11	−0.669601	−0.334801	−	0.942289i	$-0.608669\pi$
$503$	−9.61329e11	−0.669601	−0.334801	+	0.942289i	$0.608669\pi$
$504$	−1.99600e11	−0.137792
$505$	1.28518e12	0.879331
$506$	−3.97872e12	−2.69815
$507$	2.28744e12	1.53750
$508$	−2.51929e12	−1.67838
$509$	−1.17863e12	−0.778299	−0.389150	−	0.921175i	$-0.627231\pi$
$509$	−1.17863e12	−0.778299	−0.389150	+	0.921175i	$0.627231\pi$
$510$	−1.41963e12	−0.929202
$511$	4.28325e11	0.277894
$512$	−2.04770e12	−1.31690
$513$	1.32497e12	0.844653
$514$	9.62607e11	0.608296
$515$	2.97259e12	1.86210
$516$	−4.11898e12	−2.55779
$517$	−1.82121e12	−1.12112
$518$	−7.23003e11	−0.441221
$519$	−8.38549e11	−0.507312
$520$	1.31369e10	0.00787913
$521$	2.07049e12	1.23113	0.615565	−	0.788086i	$-0.288928\pi$
$521$	2.07049e12	1.23113	0.615565	+	0.788086i	$0.288928\pi$
$522$	6.37729e11	0.375941
$523$	1.54079e12	0.900507	0.450253	−	0.892901i	$-0.351334\pi$
$523$	1.54079e12	0.900507	0.450253	+	0.892901i	$0.351334\pi$
$524$	7.10835e11	0.411887
$525$	−1.57841e11	−0.0906784
$526$	−3.99271e12	−2.27422
$527$	−3.26798e11	−0.184557
$528$	2.14867e12	1.20315
$529$	3.98239e12	2.21102
$530$	−1.18765e12	−0.653803
$531$	−1.36999e12	−0.747809
$532$	−1.16088e12	−0.628325
$533$	5.32183e10	0.0285620
$534$	1.76401e12	0.938783
$535$	3.56099e12	1.87922
$536$	5.85553e11	0.306425
$537$	−3.40593e12	−1.76747
$538$	2.84349e12	1.46330
$539$	−1.74547e12	−0.890767
$540$	1.43850e12	0.728012
$541$	−2.25534e12	−1.13194	−0.565972	−	0.824425i	$-0.691499\pi$
$541$	−2.25534e12	−1.13194	−0.565972	+	0.824425i	$0.691499\pi$
$542$	4.86786e12	2.42293
$543$	−1.52651e12	−0.753528
$544$	1.09908e12	0.538063
$545$	−3.72689e12	−1.80952
$546$	4.23940e10	0.0204145
$547$	−2.81333e12	−1.34362	−0.671811	−	0.740722i	$-0.734483\pi$
$547$	−2.81333e12	−1.34362	−0.671811	+	0.740722i	$0.734483\pi$
$548$	1.53734e12	0.728211
$549$	−4.89935e12	−2.30177
$550$	−5.41175e11	−0.252177
$551$	6.01083e11	0.277813
$552$	1.72251e12	0.789652
$553$	1.15280e12	0.524192
$554$	3.42203e12	1.54344
$555$	3.14550e12	1.40725
$556$	−3.14201e12	−1.39435
$557$	2.77859e12	1.22314	0.611569	−	0.791191i	$-0.290539\pi$
$557$	2.77859e12	1.22314	0.611569	+	0.791191i	$0.290539\pi$
$558$	2.26712e12	0.989965
$559$	8.18789e10	0.0354665
$560$	6.80697e11	0.292488
$561$	−1.38498e12	−0.590353
$562$	8.87646e11	0.375341
$563$	3.27048e12	1.37190	0.685952	−	0.727647i	$-0.259386\pi$
$563$	3.27048e12	1.37190	0.685952	+	0.727647i	$0.259386\pi$
$564$	4.86525e12	2.02465
$565$	−2.47032e12	−1.01985
$566$	2.48260e12	1.01679
$567$	−4.31634e11	−0.175385
$568$	−9.39289e10	−0.0378645
$569$	5.27658e11	0.211032	0.105516	−	0.994418i	$-0.466351\pi$
$569$	5.27658e11	0.211032	0.105516	+	0.994418i	$0.466351\pi$
$570$	9.28257e12	3.68325
$571$	−4.52545e12	−1.78156	−0.890778	−	0.454439i	$-0.849840\pi$
$571$	−4.52545e12	−1.78156	−0.890778	+	0.454439i	$0.849840\pi$
$572$	7.90842e10	0.0308893
$573$	−6.42619e11	−0.249033
$574$	−1.52076e12	−0.584734
$575$	7.86662e11	0.300112
$576$	−4.84692e12	−1.83470
$577$	−1.28885e12	−0.484075	−0.242038	−	0.970267i	$-0.577816\pi$
$577$	−1.28885e12	−0.484075	−0.242038	+	0.970267i	$0.577816\pi$
$578$	3.40796e12	1.27004
$579$	−2.79599e12	−1.03391
$580$	6.52586e11	0.239448
$581$	−4.77291e11	−0.173776
$582$	3.10960e12	1.12344
$583$	−1.15866e12	−0.415382
$584$	−6.35781e11	−0.226178
$585$	−1.06518e11	−0.0376028
$586$	3.07339e12	1.07666
$587$	4.00387e12	1.39190	0.695951	−	0.718089i	$-0.254983\pi$
$587$	4.00387e12	1.39190	0.695951	+	0.718089i	$0.254983\pi$
$588$	4.66294e12	1.60865
$589$	2.13684e12	0.731565
$590$	−2.57661e12	−0.875417
$591$	3.19378e12	1.07687
$592$	−1.94596e12	−0.651159
$593$	1.61766e12	0.537206	0.268603	−	0.963251i	$-0.413438\pi$
$593$	1.61766e12	0.537206	0.268603	+	0.963251i	$0.413438\pi$
$594$	2.57935e12	0.850103
$595$	−4.38761e11	−0.143516
$596$	−5.32214e12	−1.72774
$597$	−5.78615e12	−1.86425
$598$	−2.11287e11	−0.0675642
$599$	−3.03081e12	−0.961918	−0.480959	−	0.876743i	$-0.659711\pi$
$599$	−3.03081e12	−0.961918	−0.480959	+	0.876743i	$0.659711\pi$
$600$	2.34291e11	0.0738032
$601$	3.22632e12	1.00872	0.504362	−	0.863492i	$-0.331728\pi$
$601$	3.22632e12	1.00872	0.504362	+	0.863492i	$0.331728\pi$
$602$	−2.33977e12	−0.726086
$603$	−4.74782e12	−1.46240
$604$	−5.01616e12	−1.53358
$605$	−1.19786e11	−0.0363503
$606$	−6.15616e12	−1.85431
$607$	−3.99723e12	−1.19512	−0.597558	−	0.801825i	$-0.703862\pi$
$607$	−3.99723e12	−1.19512	−0.597558	+	0.801825i	$0.703862\pi$
$608$	−7.18655e12	−2.13282
$609$	3.41289e11	0.100541
$610$	−9.21449e12	−2.69456
$611$	−9.67137e10	−0.0280739
$612$	2.13677e12	0.615709
$613$	−3.81784e12	−1.09206	−0.546029	−	0.837766i	$-0.683861\pi$
$613$	−3.81784e12	−1.09206	−0.546029	+	0.837766i	$0.683861\pi$
$614$	1.40719e12	0.399571
$615$	6.61625e12	1.86498
$616$	−3.66237e11	−0.102482
$617$	3.23230e12	0.897900	0.448950	−	0.893557i	$-0.351798\pi$
$617$	3.23230e12	0.897900	0.448950	+	0.893557i	$0.351798\pi$
$618$	−1.42391e13	−3.92675
$619$	3.30815e12	0.905685	0.452842	−	0.891591i	$-0.350410\pi$
$619$	3.30815e12	0.905685	0.452842	+	0.891591i	$0.350410\pi$
$620$	2.31993e12	0.630540
$621$	−3.74940e12	−1.01169
$622$	1.99966e12	0.535673
$623$	5.45196e11	0.144996
$624$	1.14104e11	0.0301279
$625$	−4.34658e12	−1.13943
$626$	−5.57639e12	−1.45134
$627$	9.05600e12	2.34009
$628$	7.36806e12	1.89032
$629$	1.25432e12	0.319507
$630$	3.04384e12	0.769820
$631$	6.09958e11	0.153168	0.0765840	−	0.997063i	$-0.475599\pi$
$631$	6.09958e11	0.153168	0.0765840	+	0.997063i	$0.475599\pi$
$632$	−1.71115e12	−0.426640
$633$	3.49729e12	0.865796
$634$	3.46999e11	0.0852955
$635$	6.22603e12	1.51960
$636$	3.09530e12	0.750146
$637$	−9.26920e10	−0.0223057
$638$	1.17014e12	0.279605
$639$	7.61600e11	0.180706
$640$	−2.57800e12	−0.607398
$641$	3.30981e12	0.774357	0.387179	−	0.922005i	$-0.373450\pi$
$641$	3.30981e12	0.774357	0.387179	+	0.922005i	$0.373450\pi$
$642$	−1.70575e13	−3.96286
$643$	5.75281e12	1.32718	0.663591	−	0.748096i	$-0.269032\pi$
$643$	5.75281e12	1.32718	0.663591	+	0.748096i	$0.269032\pi$
$644$	3.28504e12	0.752584
$645$	1.01794e13	2.31581
$646$	3.70158e12	0.836258
$647$	−5.43496e12	−1.21935	−0.609673	−	0.792653i	$-0.708699\pi$
$647$	−5.43496e12	−1.21935	−0.609673	+	0.792653i	$0.708699\pi$
$648$	6.40694e11	0.142746
$649$	−2.51372e12	−0.556182
$650$	−2.87386e10	−0.00631475
$651$	1.21327e12	0.264755
$652$	−9.25938e12	−2.00663
$653$	1.83587e12	0.395123	0.197561	−	0.980291i	$-0.436698\pi$
$653$	1.83587e12	0.395123	0.197561	+	0.980291i	$0.436698\pi$
$654$	1.78523e13	3.81587
$655$	−1.75672e12	−0.372921
$656$	−4.09314e12	−0.862958
$657$	5.15508e12	1.07942
$658$	2.76369e12	0.574741
$659$	−2.10623e11	−0.0435033	−0.0217516	−	0.999763i	$-0.506924\pi$
$659$	−2.10623e11	−0.0435033	−0.0217516	+	0.999763i	$0.506924\pi$
$660$	9.83196e12	2.01694
$661$	−4.52648e12	−0.922261	−0.461130	−	0.887332i	$-0.652556\pi$
$661$	−4.52648e12	−0.922261	−0.461130	+	0.887332i	$0.652556\pi$
$662$	−4.60363e12	−0.931621
$663$	−7.35484e10	−0.0147830
$664$	7.08465e11	0.141437
$665$	2.86893e12	0.568882
$666$	−8.70167e12	−1.71383
$667$	−1.70094e12	−0.332754
$668$	3.09425e12	0.601259
$669$	2.70232e12	0.521579
$670$	−8.92951e12	−1.71195
$671$	−8.98959e12	−1.71194
$672$	−4.08045e12	−0.771873
$673$	−6.68369e12	−1.25588	−0.627941	−	0.778261i	$-0.716102\pi$
$673$	−6.68369e12	−1.25588	−0.627941	+	0.778261i	$0.716102\pi$
$674$	1.16425e13	2.17309
$675$	−5.09983e11	−0.0945559
$676$	−6.47538e12	−1.19263
$677$	−1.96556e11	−0.0359614	−0.0179807	−	0.999838i	$-0.505724\pi$
$677$	−1.96556e11	−0.0359614	−0.0179807	+	0.999838i	$0.505724\pi$
$678$	1.18332e13	2.15064
$679$	9.61071e11	0.173517
$680$	6.51272e11	0.116808
$681$	8.32141e12	1.48264
$682$	4.15983e12	0.736284
$683$	−3.47573e12	−0.611157	−0.305578	−	0.952167i	$-0.598850\pi$
$683$	−3.47573e12	−0.611157	−0.305578	+	0.952167i	$0.598850\pi$
$684$	−1.39717e13	−2.44060
$685$	−3.79930e12	−0.659319
$686$	5.67194e12	0.977852
$687$	6.69586e12	1.14684
$688$	−6.29749e12	−1.07157
$689$	−6.15298e10	−0.0104016
$690$	−2.62677e13	−4.41166
$691$	1.07487e13	1.79351	0.896756	−	0.442525i	$-0.145917\pi$
$691$	1.07487e13	1.79351	0.896756	+	0.442525i	$0.145917\pi$
$692$	2.37379e12	0.393519
$693$	2.96955e12	0.489092
$694$	8.58085e12	1.40415
$695$	7.76499e12	1.26244
$696$	−5.06590e11	−0.0818305
$697$	2.63834e12	0.423431
$698$	−2.23973e12	−0.357146
$699$	−1.07011e13	−1.69544
$700$	4.46823e11	0.0703386
$701$	−3.24769e12	−0.507976	−0.253988	−	0.967207i	$-0.581742\pi$
$701$	−3.24769e12	−0.507976	−0.253988	+	0.967207i	$0.581742\pi$
$702$	1.36974e11	0.0212874
$703$	−8.20164e12	−1.26649
$704$	−8.89340e12	−1.36455
$705$	−1.20237e13	−1.83311
$706$	−6.51227e12	−0.986532
$707$	−1.90266e12	−0.286401
$708$	6.71528e12	1.00442
$709$	8.38221e12	1.24581	0.622903	−	0.782299i	$-0.285953\pi$
$709$	8.38221e12	1.24581	0.622903	+	0.782299i	$0.285953\pi$
$710$	1.43239e12	0.211543
$711$	1.38745e13	2.03612
$712$	−8.09259e11	−0.118012
$713$	−6.04681e12	−0.876241
$714$	2.10172e12	0.302644
$715$	−1.95444e11	−0.0279670
$716$	9.64163e12	1.37101
$717$	1.02854e13	1.45340
$718$	1.33758e13	1.87828
$719$	6.12344e12	0.854506	0.427253	−	0.904132i	$-0.359481\pi$
$719$	6.12344e12	0.854506	0.427253	+	0.904132i	$0.359481\pi$
$720$	8.19250e12	1.13611
$721$	−4.40082e12	−0.606491
$722$	−1.33898e13	−1.83382
$723$	−4.43706e12	−0.603912
$724$	4.32129e12	0.584507
$725$	−2.31357e11	−0.0311001
$726$	5.73791e11	0.0766547
$727$	5.66461e12	0.752081	0.376041	−	0.926603i	$-0.377285\pi$
$727$	5.66461e12	0.752081	0.376041	+	0.926603i	$0.377285\pi$
$728$	−1.94487e10	−0.00256626
$729$	−1.18186e13	−1.54985
$730$	9.69547e12	1.26362
$731$	4.05921e12	0.525791
$732$	2.40152e13	3.09162
$733$	−3.71010e12	−0.474699	−0.237349	−	0.971424i	$-0.576279\pi$
$733$	−3.71010e12	−0.474699	−0.237349	+	0.971424i	$0.576279\pi$
$734$	1.46537e13	1.86343
$735$	−1.15237e13	−1.45646
$736$	2.03364e13	2.55461
$737$	−8.71156e12	−1.08766
$738$	−1.83031e13	−2.27128
$739$	−3.97920e12	−0.490790	−0.245395	−	0.969423i	$-0.578918\pi$
$739$	−3.97920e12	−0.490790	−0.245395	+	0.969423i	$0.578918\pi$
$740$	−8.90439e12	−1.09159
$741$	4.80912e11	0.0585981
$742$	1.75827e12	0.212946
$743$	8.09600e12	0.974587	0.487294	−	0.873238i	$-0.337984\pi$
$743$	8.09600e12	0.974587	0.487294	+	0.873238i	$0.337984\pi$
$744$	−1.80092e12	−0.215484
$745$	1.31528e13	1.56429
$746$	−1.42025e13	−1.67896
$747$	−5.74442e12	−0.675000
$748$	3.92066e12	0.457933
$749$	−5.27191e12	−0.612069
$750$	1.77603e13	2.04963
$751$	−9.63707e12	−1.10552	−0.552758	−	0.833342i	$-0.686425\pi$
$751$	−9.63707e12	−1.10552	−0.552758	+	0.833342i	$0.686425\pi$
$752$	7.43847e12	0.848210
$753$	1.83725e13	2.08253
$754$	6.21394e10	0.00700158
$755$	1.23967e13	1.38849
$756$	−2.12965e12	−0.237116
$757$	1.02861e13	1.13846	0.569231	−	0.822178i	$-0.307241\pi$
$757$	1.02861e13	1.13846	0.569231	+	0.822178i	$0.307241\pi$
$758$	−9.76296e12	−1.07416
$759$	−2.56266e13	−2.80287
$760$	−4.25848e12	−0.463013
$761$	−5.84763e12	−0.632046	−0.316023	−	0.948752i	$-0.602348\pi$
$761$	−5.84763e12	−0.632046	−0.316023	+	0.948752i	$0.602348\pi$
$762$	−2.98235e13	−3.20450
$763$	5.51754e12	0.589365
$764$	1.81915e12	0.193174
$765$	−5.28068e12	−0.557460
$766$	1.52893e12	0.160457
$767$	−1.33489e11	−0.0139273
$768$	−7.55906e12	−0.784047
$769$	−9.18691e12	−0.947330	−0.473665	−	0.880705i	$-0.657069\pi$
$769$	−9.18691e12	−0.947330	−0.473665	+	0.880705i	$0.657069\pi$
$770$	5.58500e12	0.572552
$771$	6.20008e12	0.631906
$772$	7.91497e12	0.801995
$773$	−3.93053e12	−0.395953	−0.197976	−	0.980207i	$-0.563437\pi$
$773$	−3.93053e12	−0.395953	−0.197976	+	0.980207i	$0.563437\pi$
$774$	−2.81602e13	−2.82034
$775$	−8.22471e11	−0.0818960
$776$	−1.42656e12	−0.141225
$777$	−4.65680e12	−0.458346
$778$	1.21039e13	1.18445
$779$	−1.72513e13	−1.67843
$780$	5.22119e11	0.0505060
$781$	1.39743e12	0.134400
$782$	−1.04747e13	−1.00164
$783$	1.10270e12	0.104840
$784$	7.12915e12	0.673931
$785$	−1.82090e13	−1.71148
$786$	8.41490e12	0.786407
$787$	−4.49491e12	−0.417671	−0.208835	−	0.977951i	$-0.566967\pi$
$787$	−4.49491e12	−0.417671	−0.208835	+	0.977951i	$0.566967\pi$
$788$	−9.04107e12	−0.835318
$789$	−2.57167e13	−2.36249
$790$	2.60945e13	2.38357
$791$	3.65723e12	0.332168
$792$	−4.40783e12	−0.398072
$793$	−4.77385e11	−0.0428686
$794$	2.29212e12	0.204666
$795$	−7.64955e12	−0.679179
$796$	1.63796e13	1.44609
$797$	−5.72738e12	−0.502798	−0.251399	−	0.967883i	$-0.580891\pi$
$797$	−5.72738e12	−0.502798	−0.251399	+	0.967883i	$0.580891\pi$
$798$	−1.37425e13	−1.19965
$799$	−4.79465e12	−0.416195
$800$	2.76611e12	0.238761
$801$	6.56168e12	0.563208
$802$	2.40430e13	2.05213
$803$	9.45883e12	0.802819
$804$	2.32725e13	1.96422
$805$	−8.11847e12	−0.681386
$806$	2.20904e11	0.0184373
$807$	1.83147e13	1.52009
$808$	2.82421e12	0.233102
$809$	−1.36014e13	−1.11639	−0.558194	−	0.829711i	$-0.688505\pi$
$809$	−1.36014e13	−1.11639	−0.558194	+	0.829711i	$0.688505\pi$
$810$	−9.77038e12	−0.797497
$811$	−2.27735e13	−1.84857	−0.924285	−	0.381702i	$-0.875338\pi$
$811$	−2.27735e13	−1.84857	−0.924285	+	0.381702i	$0.875338\pi$
$812$	−9.66131e11	−0.0779891
$813$	3.13535e13	2.51698
$814$	−1.59663e13	−1.27466
$815$	2.28831e13	1.81680
$816$	5.65677e12	0.446646
$817$	−2.65420e13	−2.08417
$818$	8.09147e12	0.631884
$819$	1.57695e11	0.0122473
$820$	−1.87295e13	−1.44665
$821$	−5.04642e12	−0.387649	−0.193825	−	0.981036i	$-0.562089\pi$
$821$	−5.04642e12	−0.387649	−0.193825	+	0.981036i	$0.562089\pi$
$822$	1.81991e13	1.39036
$823$	2.94615e12	0.223849	0.111925	−	0.993717i	$-0.464298\pi$
$823$	2.94615e12	0.223849	0.111925	+	0.993717i	$0.464298\pi$
$824$	6.53233e12	0.493623
$825$	−3.48566e12	−0.261965
$826$	3.81458e12	0.285126
$827$	−1.52452e12	−0.113334	−0.0566669	−	0.998393i	$-0.518047\pi$
$827$	−1.52452e12	−0.113334	−0.0566669	+	0.998393i	$0.518047\pi$
$828$	3.95370e13	2.92326
$829$	−1.97970e13	−1.45580	−0.727902	−	0.685681i	$-0.759505\pi$
$829$	−1.97970e13	−1.45580	−0.727902	+	0.685681i	$0.759505\pi$
$830$	−1.08039e13	−0.790184
$831$	2.20411e13	1.60335
$832$	−4.72277e11	−0.0341697
$833$	−4.59527e12	−0.330681
$834$	−3.71952e13	−2.66220
$835$	−7.64697e12	−0.544377
$836$	−2.56360e13	−1.81519
$837$	3.92007e12	0.276076
$838$	9.41921e12	0.659807
$839$	−5.19636e12	−0.362052	−0.181026	−	0.983478i	$-0.557942\pi$
$839$	−5.19636e12	−0.362052	−0.181026	+	0.983478i	$0.557942\pi$
$840$	−2.41792e12	−0.167566
$841$	5.00246e11	0.0344828
$842$	−1.62021e13	−1.11088
$843$	5.71726e12	0.389909
$844$	−9.90025e12	−0.671592
$845$	1.60029e13	1.07980
$846$	3.32622e13	2.23247
$847$	1.77339e11	0.0118394
$848$	4.73239e12	0.314268
$849$	1.59902e13	1.05626
$850$	−1.42474e12	−0.0936160
$851$	2.32089e13	1.51695
$852$	−3.73315e12	−0.242715
$853$	1.54707e13	1.00055	0.500275	−	0.865867i	$-0.333232\pi$
$853$	1.54707e13	1.00055	0.500275	+	0.865867i	$0.333232\pi$
$854$	1.36417e13	0.877625
$855$	3.45289e13	2.20971
$856$	7.82534e12	0.498163
$857$	8.83340e12	0.559390	0.279695	−	0.960089i	$-0.409767\pi$
$857$	8.83340e12	0.559390	0.279695	+	0.960089i	$0.409767\pi$
$858$	9.36201e11	0.0589762
$859$	−3.08119e13	−1.93085	−0.965426	−	0.260679i	$-0.916054\pi$
$859$	−3.08119e13	−1.93085	−0.965426	+	0.260679i	$0.916054\pi$
$860$	−2.88162e13	−1.79636
$861$	−9.79513e12	−0.607429
$862$	−2.41634e13	−1.49065
$863$	2.61632e13	1.60562	0.802808	−	0.596237i	$-0.203338\pi$
$863$	2.61632e13	1.60562	0.802808	+	0.596237i	$0.203338\pi$
$864$	−1.31839e13	−0.804879
$865$	−5.86646e12	−0.356290
$866$	−6.94880e12	−0.419836
$867$	2.19504e13	1.31934
$868$	−3.43458e12	−0.205369
$869$	2.54576e13	1.51436
$870$	7.72534e12	0.457173
$871$	−4.62621e11	−0.0272360
$872$	−8.18993e12	−0.479685
$873$	1.15669e13	0.673991
$874$	6.84910e13	3.97038
$875$	5.48912e12	0.316567
$876$	−2.52687e13	−1.44982
$877$	−2.72817e13	−1.55730	−0.778651	−	0.627457i	$-0.784096\pi$
$877$	−2.72817e13	−1.55730	−0.778651	+	0.627457i	$0.784096\pi$
$878$	−7.63031e12	−0.433328
$879$	1.97954e13	1.11845
$880$	1.50321e13	0.844980
$881$	2.33576e12	0.130628	0.0653139	−	0.997865i	$-0.479195\pi$
$881$	2.33576e12	0.130628	0.0653139	+	0.997865i	$0.479195\pi$
$882$	3.18791e13	1.77377
$883$	−1.30068e13	−0.720022	−0.360011	−	0.932948i	$-0.617227\pi$
$883$	−1.30068e13	−0.720022	−0.360011	+	0.932948i	$0.617227\pi$
$884$	2.08203e11	0.0114671
$885$	−1.65958e13	−0.909395
$886$	1.01662e13	0.554253
$887$	2.27159e13	1.23218	0.616089	−	0.787677i	$-0.288716\pi$
$887$	2.27159e13	1.23218	0.616089	+	0.787677i	$0.288716\pi$
$888$	6.91230e12	0.373048
$889$	−9.21742e12	−0.494939
$890$	1.23409e13	0.659316
$891$	−9.53191e12	−0.506676
$892$	−7.64983e12	−0.404585
$893$	3.13509e13	1.64975
$894$	−6.30037e13	−3.29873
$895$	−2.38278e13	−1.24131
$896$	3.81664e12	0.197831
$897$	−1.36088e12	−0.0701866
$898$	5.96096e12	0.305895
$899$	1.77837e12	0.0908035
$900$	5.37772e12	0.273216
$901$	−3.05039e12	−0.154203
$902$	−3.35835e13	−1.68926
$903$	−1.50703e13	−0.754268
$904$	−5.42859e12	−0.270352
$905$	−1.06794e13	−0.529210
$906$	−5.93815e13	−2.92802
$907$	2.42430e13	1.18947	0.594735	−	0.803922i	$-0.297257\pi$
$907$	2.42430e13	1.18947	0.594735	+	0.803922i	$0.297257\pi$
$908$	−2.35565e13	−1.15007
$909$	−2.28994e13	−1.11247
$910$	2.96587e11	0.0143373
$911$	3.22431e13	1.55097	0.775486	−	0.631364i	$-0.217505\pi$
$911$	3.22431e13	1.55097	0.775486	+	0.631364i	$0.217505\pi$
$912$	−3.69880e13	−1.77045
$913$	−1.05402e13	−0.502030
$914$	−7.05186e12	−0.334230
$915$	−5.93498e13	−2.79914
$916$	−1.89549e13	−0.889593
$917$	2.60076e12	0.121461
$918$	6.79061e12	0.315585
$919$	3.88807e13	1.79810	0.899052	−	0.437843i	$-0.144257\pi$
$919$	3.88807e13	1.79810	0.899052	+	0.437843i	$0.144257\pi$
$920$	1.20506e13	0.554580
$921$	9.06358e12	0.415080
$922$	−9.13253e12	−0.416200
$923$	7.42092e10	0.00336550
$924$	−1.45559e13	−0.656923
$925$	3.15682e12	0.141779
$926$	−2.60297e12	−0.116338
$927$	−5.29658e13	−2.35579
$928$	−5.98095e12	−0.264731
$929$	−3.63810e13	−1.60252	−0.801262	−	0.598314i	$-0.795837\pi$
$929$	−3.63810e13	−1.60252	−0.801262	+	0.598314i	$0.795837\pi$
$930$	2.74634e13	1.20388
$931$	3.00472e13	1.31078
$932$	3.02931e13	1.31514
$933$	1.28797e13	0.556464
$934$	5.62445e13	2.41835
$935$	−9.68929e12	−0.414610
$936$	−2.34074e11	−0.00996811
$937$	1.80059e13	0.763110	0.381555	−	0.924346i	$-0.375389\pi$
$937$	1.80059e13	0.763110	0.381555	+	0.924346i	$0.375389\pi$
$938$	1.32198e13	0.557587
$939$	−3.59171e13	−1.50767
$940$	3.40371e13	1.42193
$941$	1.84107e13	0.765449	0.382724	−	0.923863i	$-0.374986\pi$
$941$	1.84107e13	0.765449	0.382724	+	0.923863i	$0.374986\pi$
$942$	8.72233e13	3.60914
$943$	4.88177e13	2.01036
$944$	1.02670e13	0.420793
$945$	5.26310e12	0.214683
$946$	−5.16698e13	−2.09762
$947$	−2.12508e13	−0.858618	−0.429309	−	0.903158i	$-0.641243\pi$
$947$	−2.12508e13	−0.858618	−0.429309	+	0.903158i	$0.641243\pi$
$948$	−6.80087e13	−2.73481
$949$	5.02304e11	0.0201033
$950$	9.31596e12	0.371083
$951$	2.23499e12	0.0886061
$952$	−9.64185e11	−0.0380447
$953$	−2.25123e13	−0.884102	−0.442051	−	0.896990i	$-0.645749\pi$
$953$	−2.25123e13	−0.884102	−0.442051	+	0.896990i	$0.645749\pi$
$954$	2.11616e13	0.827144
$955$	−4.49574e12	−0.174898
$956$	−2.91162e13	−1.12739
$957$	7.53679e12	0.290457
$958$	−5.74822e13	−2.20490
$959$	5.62472e12	0.214742
$960$	−5.87147e13	−2.23114
$961$	−2.01176e13	−0.760887
$962$	−8.47878e11	−0.0319187
$963$	−6.34499e13	−2.37746
$964$	1.25606e13	0.468450
$965$	−1.95606e13	−0.726122
$966$	3.88885e13	1.43689
$967$	−4.72675e13	−1.73837	−0.869187	−	0.494483i	$-0.835357\pi$
$967$	−4.72675e13	−1.73837	−0.869187	+	0.494483i	$0.835357\pi$
$968$	−2.63233e11	−0.00963609
$969$	2.38416e13	0.868716
$970$	2.17546e13	0.789003
$971$	5.10718e13	1.84372	0.921859	−	0.387525i	$-0.126670\pi$
$971$	5.10718e13	1.84372	0.921859	+	0.387525i	$0.126670\pi$
$972$	4.42144e13	1.58879
$973$	−1.14958e13	−0.411179
$974$	1.10966e13	0.395071
$975$	−1.85103e11	−0.00655984
$976$	3.67167e13	1.29521
$977$	−4.85655e13	−1.70531	−0.852653	−	0.522477i	$-0.825008\pi$
$977$	−4.85655e13	−1.70531	−0.852653	+	0.522477i	$0.825008\pi$
$978$	−1.09613e14	−3.83122
$979$	1.20397e13	0.418885
$980$	3.26217e13	1.12977
$981$	6.64061e13	2.28927
$982$	−4.76845e13	−1.63635
$983$	4.38934e13	1.49937	0.749684	−	0.661796i	$-0.230206\pi$
$983$	4.38934e13	1.49937	0.749684	+	0.661796i	$0.230206\pi$
$984$	1.45393e13	0.494387
$985$	2.23436e13	0.756293
$986$	3.08061e12	0.103798
$987$	1.78007e13	0.597049
$988$	−1.36138e12	−0.0454541
$989$	7.51083e13	2.49635
$990$	6.72181e13	2.22396
$991$	2.82147e12	0.0929274	0.0464637	−	0.998920i	$-0.485205\pi$
$991$	2.82147e12	0.0929274	0.0464637	+	0.998920i	$0.485205\pi$
$992$	−2.12621e13	−0.697115
$993$	−2.96516e13	−0.967780
$994$	−2.12060e12	−0.0689001
$995$	−4.04797e13	−1.30928
$996$	2.81575e13	0.906624
$997$	−1.57177e13	−0.503805	−0.251902	−	0.967753i	$-0.581056\pi$
$997$	−1.57177e13	−0.503805	−0.251902	+	0.967753i	$0.581056\pi$
$998$	5.29787e13	1.69049
$999$	−1.50461e13	−0.477945

Twists

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

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

\(f(q)\)	\(=\)	\(q-33.5115 q^{2} -215.845 q^{3} +611.021 q^{4} -1510.04 q^{5} +7233.29 q^{6} +2235.57 q^{7} -3318.35 q^{8} +26906.1 q^{9} +O(q^{10})\)	\(q-33.5115 q^{2} -215.845 q^{3} +611.021 q^{4} -1510.04 q^{5} +7233.29 q^{6} +2235.57 q^{7} -3318.35 q^{8} +26906.1 q^{9} +50603.9 q^{10} +49368.8 q^{11} -131886. q^{12} +2621.69 q^{13} -74917.2 q^{14} +325936. q^{15} -201640. q^{16} +129972. q^{17} -901663. q^{18} -849850. q^{19} -922669. q^{20} -482536. q^{21} -1.65442e6 q^{22} +2.40490e6 q^{23} +716250. q^{24} +327108. q^{25} -87856.7 q^{26} -1.55907e6 q^{27} +1.36598e6 q^{28} -707281. q^{29} -1.09226e7 q^{30} -2.51437e6 q^{31} +8.45625e6 q^{32} -1.06560e7 q^{33} -4.35556e6 q^{34} -3.37580e6 q^{35} +1.64402e7 q^{36} +9.65069e6 q^{37} +2.84798e7 q^{38} -565878. q^{39} +5.01086e6 q^{40} +2.02993e7 q^{41} +1.61705e7 q^{42} +3.12314e7 q^{43} +3.01654e7 q^{44} -4.06294e7 q^{45} -8.05918e7 q^{46} -3.68899e7 q^{47} +4.35230e7 q^{48} -3.53558e7 q^{49} -1.09619e7 q^{50} -2.80538e7 q^{51} +1.60191e6 q^{52} -2.34695e7 q^{53} +5.22466e7 q^{54} -7.45490e7 q^{55} -7.41840e6 q^{56} +1.83436e8 q^{57} +2.37021e7 q^{58} -5.09173e7 q^{59} +1.99154e8 q^{60} -1.82091e8 q^{61} +8.42603e7 q^{62} +6.01503e7 q^{63} -1.80142e8 q^{64} -3.95887e6 q^{65} +3.57099e8 q^{66} -1.76459e8 q^{67} +7.94157e7 q^{68} -5.19086e8 q^{69} +1.13128e8 q^{70} +2.83059e7 q^{71} -8.92839e7 q^{72} +1.91595e8 q^{73} -3.23409e8 q^{74} -7.06046e7 q^{75} -5.19277e8 q^{76} +1.10367e8 q^{77} +1.89634e7 q^{78} +5.15663e8 q^{79} +3.04485e8 q^{80} -1.93076e8 q^{81} -6.80259e8 q^{82} -2.13499e8 q^{83} -2.94840e8 q^{84} -1.96264e8 q^{85} -1.04661e9 q^{86} +1.52663e8 q^{87} -1.63823e8 q^{88} +2.43874e8 q^{89} +1.36155e9 q^{90} +5.86096e6 q^{91} +1.46945e9 q^{92} +5.42714e8 q^{93} +1.23624e9 q^{94} +1.28331e9 q^{95} -1.82524e9 q^{96} +4.29900e8 q^{97} +1.18483e9 q^{98} +1.32832e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 244 q^{3} + 1194 q^{4} - 738 q^{5} - 2330 q^{6} - 7128 q^{7} - 13776 q^{8} + 33017 q^{9}+O(q^{10}) \) 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

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more