LMFDB - Embedded newform 29.10.a.a.1.4

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			1.4
Root			$15.4003$ 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)

$f(q)$	$=$	$q-15.4003 q^{2} -207.293 q^{3} -274.831 q^{4} +1546.00 q^{5} +3192.38 q^{6} +3958.22 q^{7} +12117.4 q^{8} +23287.4 q^{9} +O(q^{10})$	\(q-15.4003 q^{2} -207.293 q^{3} -274.831 q^{4} +1546.00 q^{5} +3192.38 q^{6} +3958.22 q^{7} +12117.4 q^{8} +23287.4 q^{9} -23808.9 q^{10} -22657.1 q^{11} +56970.5 q^{12} -60218.4 q^{13} -60957.7 q^{14} -320475. q^{15} -45898.7 q^{16} +5542.42 q^{17} -358633. q^{18} +832454. q^{19} -424888. q^{20} -820511. q^{21} +348926. q^{22} -1.66666e6 q^{23} -2.51186e6 q^{24} +436991. q^{25} +927382. q^{26} -747173. q^{27} -1.08784e6 q^{28} -707281. q^{29} +4.93541e6 q^{30} -7.33478e6 q^{31} -5.49727e6 q^{32} +4.69666e6 q^{33} -85355.0 q^{34} +6.11940e6 q^{35} -6.40010e6 q^{36} +1.86401e7 q^{37} -1.28200e7 q^{38} +1.24829e7 q^{39} +1.87335e7 q^{40} -4.20403e6 q^{41} +1.26361e7 q^{42} -2.70316e7 q^{43} +6.22686e6 q^{44} +3.60024e7 q^{45} +2.56670e7 q^{46} +2.31538e6 q^{47} +9.51448e6 q^{48} -2.46861e7 q^{49} -6.72979e6 q^{50} -1.14891e6 q^{51} +1.65499e7 q^{52} -2.48108e7 q^{53} +1.15067e7 q^{54} -3.50278e7 q^{55} +4.79634e7 q^{56} -1.72562e8 q^{57} +1.08923e7 q^{58} -1.25543e8 q^{59} +8.80764e7 q^{60} +3.97338e7 q^{61} +1.12958e8 q^{62} +9.21767e7 q^{63} +1.08160e8 q^{64} -9.30977e7 q^{65} -7.23299e7 q^{66} -2.81728e8 q^{67} -1.52323e6 q^{68} +3.45486e8 q^{69} -9.42406e7 q^{70} -2.53917e7 q^{71} +2.82184e8 q^{72} +1.94855e7 q^{73} -2.87064e8 q^{74} -9.05851e7 q^{75} -2.28784e8 q^{76} -8.96816e7 q^{77} -1.92240e8 q^{78} -5.92481e8 q^{79} -7.09594e7 q^{80} -3.03483e8 q^{81} +6.47433e7 q^{82} -8.55323e7 q^{83} +2.25502e8 q^{84} +8.56859e6 q^{85} +4.16295e8 q^{86} +1.46614e8 q^{87} -2.74546e8 q^{88} +9.41706e8 q^{89} -5.54447e8 q^{90} -2.38358e8 q^{91} +4.58048e8 q^{92} +1.52045e9 q^{93} -3.56576e7 q^{94} +1.28697e9 q^{95} +1.13955e9 q^{96} +5.83360e7 q^{97} +3.80174e8 q^{98} -5.27625e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−15.4003	−0.680604	−0.340302	−	0.940316i	$-0.610529\pi$
$2$	−15.4003	−0.680604	−0.340302	+	0.940316i	$0.610529\pi$
$3$	−207.293	−1.47754	−0.738770	−	0.673958i	$-0.764593\pi$
$3$	−207.293	−1.47754	−0.738770	+	0.673958i	$0.764593\pi$
$4$	−274.831	−0.536779
$5$	1546.00	1.10623	0.553114	−	0.833106i	$-0.313439\pi$
$5$	1546.00	1.10623	0.553114	+	0.833106i	$0.313439\pi$
$6$	3192.38	1.00562
$7$	3958.22	0.623101	0.311550	−	0.950230i	$-0.399152\pi$
$7$	3958.22	0.623101	0.311550	+	0.950230i	$0.399152\pi$
$8$	12117.4	1.04594
$9$	23287.4	1.18312
$10$	−23808.9	−0.752902
$11$	−22657.1	−0.466591	−0.233296	−	0.972406i	$-0.574951\pi$
$11$	−22657.1	−0.466591	−0.233296	+	0.972406i	$0.574951\pi$
$12$	56970.5	0.793112
$13$	−60218.4	−0.584769	−0.292384	−	0.956301i	$-0.594449\pi$
$13$	−60218.4	−0.584769	−0.292384	+	0.956301i	$0.594449\pi$
$14$	−60957.7	−0.424085
$15$	−320475.	−1.63450
$16$	−45898.7	−0.175090
$17$	5542.42	0.0160946	0.00804729	−	0.999968i	$-0.497438\pi$
$17$	5542.42	0.0160946	0.00804729	+	0.999968i	$0.497438\pi$
$18$	−358633.	−0.805238
$19$	832454.	1.46544	0.732721	−	0.680529i	$-0.238250\pi$
$19$	832454.	1.46544	0.732721	+	0.680529i	$0.238250\pi$
$20$	−424888.	−0.593799
$21$	−820511.	−0.920656
$22$	348926.	0.317564
$23$	−1.66666e6	−1.24185	−0.620927	−	0.783868i	$-0.713244\pi$
$23$	−1.66666e6	−1.24185	−0.620927	+	0.783868i	$0.713244\pi$
$24$	−2.51186e6	−1.54541
$25$	436991.	0.223739
$26$	927382.	0.397996
$27$	−747173.	−0.270573
$28$	−1.08784e6	−0.334467
$29$	−707281.	−0.185695
$29$	−707281.	−0.185695
$30$	4.93541e6	1.11244
$31$	−7.33478e6	−1.42646	−0.713230	−	0.700930i	$-0.752769\pi$
$31$	−7.33478e6	−1.42646	−0.713230	+	0.700930i	$0.752769\pi$
$32$	−5.49727e6	−0.926770
$33$	4.69666e6	0.689407
$34$	−85355.0	−0.0109540
$35$	6.11940e6	0.689291
$36$	−6.40010e6	−0.635076
$37$	1.86401e7	1.63509	0.817544	−	0.575866i	$-0.195335\pi$
$37$	1.86401e7	1.63509	0.817544	+	0.575866i	$0.195335\pi$
$38$	−1.28200e7	−0.997386
$39$	1.24829e7	0.864019
$40$	1.87335e7	1.15704
$41$	−4.20403e6	−0.232348	−0.116174	−	0.993229i	$-0.537063\pi$
$41$	−4.20403e6	−0.232348	−0.116174	+	0.993229i	$0.537063\pi$
$42$	1.26361e7	0.626602
$43$	−2.70316e7	−1.20577	−0.602884	−	0.797829i	$-0.705982\pi$
$43$	−2.70316e7	−1.20577	−0.602884	+	0.797829i	$0.705982\pi$
$44$	6.22686e6	0.250456
$45$	3.60024e7	1.30880
$46$	2.56670e7	0.845211
$47$	2.31538e6	0.0692122	0.0346061	−	0.999401i	$-0.488982\pi$
$47$	2.31538e6	0.0692122	0.0346061	+	0.999401i	$0.488982\pi$
$48$	9.51448e6	0.258702
$49$	−2.46861e7	−0.611745
$50$	−6.72979e6	−0.152278
$51$	−1.14891e6	−0.0237804
$52$	1.65499e7	0.313892
$53$	−2.48108e7	−0.431916	−0.215958	−	0.976403i	$-0.569287\pi$
$53$	−2.48108e7	−0.431916	−0.215958	+	0.976403i	$0.569287\pi$
$54$	1.15067e7	0.184153
$55$	−3.50278e7	−0.516156
$56$	4.79634e7	0.651724
$57$	−1.72562e8	−2.16525
$58$	1.08923e7	0.126385
$59$	−1.25543e8	−1.34883	−0.674416	−	0.738351i	$-0.735605\pi$
$59$	−1.25543e8	−1.34883	−0.674416	+	0.738351i	$0.735605\pi$
$60$	8.80764e7	0.877362
$61$	3.97338e7	0.367431	0.183715	−	0.982979i	$-0.441188\pi$
$61$	3.97338e7	0.367431	0.183715	+	0.982979i	$0.441188\pi$
$62$	1.12958e8	0.970854
$63$	9.21767e7	0.737205
$64$	1.08160e8	0.805853
$65$	−9.30977e7	−0.646887
$66$	−7.23299e7	−0.469213
$67$	−2.81728e8	−1.70802	−0.854011	−	0.520255i	$-0.825837\pi$
$67$	−2.81728e8	−1.70802	−0.854011	+	0.520255i	$0.825837\pi$
$68$	−1.52323e6	−0.00863923
$69$	3.45486e8	1.83489
$70$	−9.42406e7	−0.469134
$71$	−2.53917e7	−0.118585	−0.0592923	−	0.998241i	$-0.518884\pi$
$71$	−2.53917e7	−0.118585	−0.0592923	+	0.998241i	$0.518884\pi$
$72$	2.82184e8	1.23747
$73$	1.94855e7	0.0803079	0.0401540	−	0.999194i	$-0.487215\pi$
$73$	1.94855e7	0.0803079	0.0401540	+	0.999194i	$0.487215\pi$
$74$	−2.87064e8	−1.11285
$75$	−9.05851e7	−0.330584
$76$	−2.28784e8	−0.786619
$77$	−8.96816e7	−0.290733
$78$	−1.92240e8	−0.588055
$79$	−5.92481e8	−1.71140	−0.855702	−	0.517468i	$-0.826875\pi$
$79$	−5.92481e8	−1.71140	−0.855702	+	0.517468i	$0.826875\pi$
$80$	−7.09594e7	−0.193689
$81$	−3.03483e8	−0.783342
$82$	6.47433e7	0.158137
$83$	−8.55323e7	−0.197824	−0.0989119	−	0.995096i	$-0.531536\pi$
$83$	−8.55323e7	−0.197824	−0.0989119	+	0.995096i	$0.531536\pi$
$84$	2.25502e8	0.494189
$85$	8.56859e6	0.0178043
$86$	4.16295e8	0.820650
$87$	1.46614e8	0.274372
$88$	−2.74546e8	−0.488025
$89$	9.41706e8	1.59096	0.795482	−	0.605977i	$-0.207218\pi$
$89$	9.41706e8	1.59096	0.795482	+	0.605977i	$0.207218\pi$
$90$	−5.54447e8	−0.890777
$91$	−2.38358e8	−0.364370
$92$	4.58048e8	0.666601
$93$	1.52045e9	2.10765
$94$	−3.56576e7	−0.0471061
$95$	1.28697e9	1.62111
$96$	1.13955e9	1.36934
$97$	5.83360e7	0.0669058	0.0334529	−	0.999440i	$-0.489350\pi$
$97$	5.83360e7	0.0669058	0.0334529	+	0.999440i	$0.489350\pi$
$98$	3.80174e8	0.416356
$99$	−5.27625e8	−0.552035
$100$	−1.20098e8	−0.120098
$101$	4.25382e8	0.406755	0.203377	−	0.979100i	$-0.434808\pi$
$101$	4.25382e8	0.406755	0.203377	+	0.979100i	$0.434808\pi$
$102$	1.76935e7	0.0161850
$103$	1.30643e8	0.114372	0.0571860	−	0.998364i	$-0.481787\pi$
$103$	1.30643e8	0.114372	0.0571860	+	0.998364i	$0.481787\pi$
$104$	−7.29693e8	−0.611632
$105$	−1.26851e9	−1.01846
$106$	3.82094e8	0.293964
$107$	−1.17614e8	−0.0867426	−0.0433713	−	0.999059i	$-0.513810\pi$
$107$	−1.17614e8	−0.0867426	−0.0433713	+	0.999059i	$0.513810\pi$
$108$	2.05346e8	0.145238
$109$	−3.17965e8	−0.215755	−0.107877	−	0.994164i	$-0.534405\pi$
$109$	−3.17965e8	−0.215755	−0.107877	+	0.994164i	$0.534405\pi$
$110$	5.39439e8	0.351298
$111$	−3.86397e9	−2.41591
$112$	−1.81677e8	−0.109099
$113$	1.72545e9	0.995520	0.497760	−	0.867315i	$-0.334156\pi$
$113$	1.72545e9	0.995520	0.497760	+	0.867315i	$0.334156\pi$
$114$	2.65751e9	1.47368
$115$	−2.57665e9	−1.37377
$116$	1.94383e8	0.0996773
$117$	−1.40233e9	−0.691854
$118$	1.93340e9	0.918020
$119$	2.19381e7	0.0100285
$120$	−3.88333e9	−1.70958
$121$	−1.84460e9	−0.782292
$122$	−6.11912e8	−0.250075
$123$	8.71466e8	0.343303
$124$	2.01582e9	0.765694
$125$	−2.34394e9	−0.858721
$126$	−1.41955e9	−0.501745
$127$	−3.28989e9	−1.12218	−0.561092	−	0.827754i	$-0.689619\pi$
$127$	−3.28989e9	−1.12218	−0.561092	+	0.827754i	$0.689619\pi$
$128$	1.14891e9	0.378304
$129$	5.60346e9	1.78157
$130$	1.43373e9	0.440274
$131$	−5.91876e9	−1.75594	−0.877970	−	0.478715i	$-0.841103\pi$
$131$	−5.91876e9	−1.75594	−0.877970	+	0.478715i	$0.841103\pi$
$132$	−1.29079e9	−0.370059
$133$	3.29503e9	0.913119
$134$	4.33869e9	1.16249
$135$	−1.15513e9	−0.299315
$136$	6.71599e7	0.0168339
$137$	4.07090e9	0.987296	0.493648	−	0.869662i	$-0.335663\pi$
$137$	4.07090e9	0.987296	0.493648	+	0.869662i	$0.335663\pi$
$138$	−5.32059e9	−1.24883
$139$	−1.65106e9	−0.375142	−0.187571	−	0.982251i	$-0.560061\pi$
$139$	−1.65106e9	−0.375142	−0.187571	+	0.982251i	$0.560061\pi$
$140$	−1.68180e9	−0.369997
$141$	−4.79963e8	−0.102264
$142$	3.91039e8	0.0807091
$143$	1.36437e9	0.272848
$144$	−1.06886e9	−0.207153
$145$	−1.09346e9	−0.205421
$146$	−3.00082e8	−0.0546579
$147$	5.11727e9	0.903878
$148$	−5.12288e9	−0.877680
$149$	1.09621e9	0.182203	0.0911014	−	0.995842i	$-0.470961\pi$
$149$	1.09621e9	0.182203	0.0911014	+	0.995842i	$0.470961\pi$
$150$	1.39504e9	0.224996
$151$	7.42003e9	1.16147	0.580737	−	0.814091i	$-0.302764\pi$
$151$	7.42003e9	1.16147	0.580737	+	0.814091i	$0.302764\pi$
$152$	1.00872e10	1.53276
$153$	1.29069e8	0.0190419
$154$	1.38112e9	0.197874
$155$	−1.13396e10	−1.57799
$156$	−3.43067e9	−0.463787
$157$	−1.06087e10	−1.39353	−0.696763	−	0.717302i	$-0.745377\pi$
$157$	−1.06087e10	−1.39353	−0.696763	+	0.717302i	$0.745377\pi$
$158$	9.12439e9	1.16479
$159$	5.14311e9	0.638173
$160$	−8.49878e9	−1.02522
$161$	−6.59699e9	−0.773801
$162$	4.67372e9	0.533145
$163$	1.08213e10	1.20071	0.600353	−	0.799735i	$-0.295027\pi$
$163$	1.08213e10	1.20071	0.600353	+	0.799735i	$0.295027\pi$
$164$	1.15540e9	0.124719
$165$	7.26103e9	0.762641
$166$	1.31722e9	0.134640
$167$	1.93867e10	1.92876	0.964382	−	0.264514i	$-0.0852117\pi$
$167$	1.93867e10	1.92876	0.964382	+	0.264514i	$0.0852117\pi$
$168$	−9.94248e9	−0.962948
$169$	−6.97824e9	−0.658045
$170$	−1.31959e8	−0.0121176
$171$	1.93857e10	1.73380
$172$	7.42911e9	0.647231
$173$	5.01394e9	0.425570	0.212785	−	0.977099i	$-0.431747\pi$
$173$	5.01394e9	0.425570	0.212785	+	0.977099i	$0.431747\pi$
$174$	−2.25791e9	−0.186739
$175$	1.72970e9	0.139412
$176$	1.03993e9	0.0816953
$177$	2.60242e10	1.99295
$178$	−1.45026e10	−1.08282
$179$	−1.65570e10	−1.20543	−0.602717	−	0.797955i	$-0.705915\pi$
$179$	−1.65570e10	−1.20543	−0.602717	+	0.797955i	$0.705915\pi$
$180$	−9.89456e9	−0.702538
$181$	−2.74840e10	−1.90338	−0.951691	−	0.307058i	$-0.900656\pi$
$181$	−2.74840e10	−1.90338	−0.951691	+	0.307058i	$0.900656\pi$
$182$	3.67078e9	0.247991
$183$	−8.23654e9	−0.542894
$184$	−2.01956e10	−1.29890
$185$	2.88176e10	1.80878
$186$	−2.34154e10	−1.43448
$187$	−1.25575e8	−0.00750959
$188$	−6.36338e8	−0.0371516
$189$	−2.95747e9	−0.168594
$190$	−1.98198e10	−1.10334
$191$	−2.99580e10	−1.62878	−0.814391	−	0.580316i	$-0.802929\pi$
$191$	−2.99580e10	−1.62878	−0.814391	+	0.580316i	$0.802929\pi$
$192$	−2.24208e10	−1.19068
$193$	1.12672e10	0.584531	0.292266	−	0.956337i	$-0.405591\pi$
$193$	1.12672e10	0.584531	0.292266	+	0.956337i	$0.405591\pi$
$194$	−8.98392e8	−0.0455363
$195$	1.92985e10	0.955802
$196$	6.78451e9	0.328372
$197$	2.69790e9	0.127623	0.0638113	−	0.997962i	$-0.479674\pi$
$197$	2.69790e9	0.127623	0.0638113	+	0.997962i	$0.479674\pi$
$198$	8.12558e9	0.375717
$199$	3.36839e10	1.52259	0.761296	−	0.648405i	$-0.224564\pi$
$199$	3.36839e10	1.52259	0.761296	+	0.648405i	$0.224564\pi$
$200$	5.29520e9	0.234017
$201$	5.84003e10	2.52367
$202$	−6.55101e9	−0.276839
$203$	−2.79957e9	−0.115707
$204$	3.15755e8	0.0127648
$205$	−6.49942e9	−0.257029
$206$	−2.01195e9	−0.0778421
$207$	−3.88121e10	−1.46927
$208$	2.76395e9	0.102387
$209$	−1.88610e10	−0.683763
$210$	1.95354e10	0.693164
$211$	−3.90404e10	−1.35595	−0.677975	−	0.735085i	$-0.737142\pi$
$211$	−3.90404e10	−1.35595	−0.677975	+	0.735085i	$0.737142\pi$
$212$	6.81877e9	0.231843
$213$	5.26352e9	0.175214
$214$	1.81129e9	0.0590373
$215$	−4.17908e10	−1.33385
$216$	−9.05381e9	−0.283002
$217$	−2.90327e10	−0.888828
$218$	4.89676e9	0.146843
$219$	−4.03921e9	−0.118658
$220$	9.62673e9	0.277062
$221$	−3.33756e8	−0.00941161
$222$	5.95063e10	1.64428
$223$	1.18395e9	0.0320598	0.0160299	−	0.999872i	$-0.494897\pi$
$223$	1.18395e9	0.0320598	0.0160299	+	0.999872i	$0.494897\pi$
$224$	−2.17594e10	−0.577471
$225$	1.01764e10	0.264711
$226$	−2.65725e10	−0.677554
$227$	−2.34636e10	−0.586514	−0.293257	−	0.956034i	$-0.594739\pi$
$227$	−2.34636e10	−0.586514	−0.293257	+	0.956034i	$0.594739\pi$
$228$	4.74253e10	1.16226
$229$	−3.40676e10	−0.818619	−0.409309	−	0.912396i	$-0.634230\pi$
$229$	−3.40676e10	−0.818619	−0.409309	+	0.912396i	$0.634230\pi$
$230$	3.96812e10	0.934995
$231$	1.85904e10	0.429570
$232$	−8.57043e9	−0.194226
$233$	−6.05483e10	−1.34586	−0.672931	−	0.739705i	$-0.734965\pi$
$233$	−6.05483e10	−1.34586	−0.672931	+	0.739705i	$0.734965\pi$
$234$	2.15963e10	0.470878
$235$	3.57958e9	0.0765644
$236$	3.45030e10	0.724025
$237$	1.22817e11	2.52867
$238$	−3.37854e8	−0.00682546
$239$	7.37646e9	0.146237	0.0731185	−	0.997323i	$-0.476705\pi$
$239$	7.37646e9	0.146237	0.0731185	+	0.997323i	$0.476705\pi$
$240$	1.47094e10	0.286183
$241$	−6.41814e10	−1.22555	−0.612777	−	0.790256i	$-0.709948\pi$
$241$	−6.41814e10	−1.22555	−0.612777	+	0.790256i	$0.709948\pi$
$242$	2.84075e10	0.532431
$243$	7.76165e10	1.42799
$244$	−1.09201e10	−0.197229
$245$	−3.81648e10	−0.676730
$246$	−1.34208e10	−0.233653
$247$	−5.01291e10	−0.856946
$248$	−8.88787e10	−1.49199
$249$	1.77303e10	0.292293
$250$	3.60974e10	0.584449
$251$	1.01708e11	1.61743	0.808713	−	0.588203i	$-0.200165\pi$
$251$	1.01708e11	1.61743	0.808713	+	0.588203i	$0.200165\pi$
$252$	−2.53330e10	−0.395716
$253$	3.77616e10	0.579439
$254$	5.06652e10	0.763762
$255$	−1.77621e9	−0.0263065
$256$	−7.30713e10	−1.06333
$257$	1.03674e11	1.48242	0.741208	−	0.671276i	$-0.234253\pi$
$257$	1.03674e11	1.48242	0.741208	+	0.671276i	$0.234253\pi$
$258$	−8.62950e10	−1.21254
$259$	7.37816e10	1.01882
$260$	2.55861e10	0.347235
$261$	−1.64708e10	−0.219701
$262$	9.11507e10	1.19510
$263$	1.21236e11	1.56254	0.781268	−	0.624196i	$-0.214573\pi$
$263$	1.21236e11	1.56254	0.781268	+	0.624196i	$0.214573\pi$
$264$	5.69114e10	0.721077
$265$	−3.83575e10	−0.477797
$266$	−5.07445e10	−0.621472
$267$	−1.95209e11	−2.35071
$268$	7.74275e10	0.916830
$269$	−7.61186e10	−0.886351	−0.443175	−	0.896435i	$-0.646148\pi$
$269$	−7.61186e10	−0.886351	−0.443175	+	0.896435i	$0.646148\pi$
$270$	1.77893e10	0.203715
$271$	−1.01182e11	−1.13957	−0.569787	−	0.821793i	$-0.692974\pi$
$271$	−1.01182e11	−1.13957	−0.569787	+	0.821793i	$0.692974\pi$
$272$	−2.54390e8	−0.00281799
$273$	4.94099e10	0.538371
$274$	−6.26930e10	−0.671957
$275$	−9.90093e9	−0.104395
$276$	−9.49503e10	−0.984930
$277$	1.08999e10	0.111241	0.0556203	−	0.998452i	$-0.482286\pi$
$277$	1.08999e10	0.111241	0.0556203	+	0.998452i	$0.482286\pi$
$278$	2.54268e10	0.255323
$279$	−1.70808e11	−1.68768
$280$	7.41514e10	0.720955
$281$	−6.18982e10	−0.592242	−0.296121	−	0.955150i	$-0.595693\pi$
$281$	−6.18982e10	−0.592242	−0.296121	+	0.955150i	$0.595693\pi$
$282$	7.39157e9	0.0696011
$283$	1.12113e11	1.03900	0.519502	−	0.854469i	$-0.326118\pi$
$283$	1.12113e11	1.03900	0.519502	+	0.854469i	$0.326118\pi$
$284$	6.97841e9	0.0636537
$285$	−2.66781e11	−2.39526
$286$	−2.10118e10	−0.185701
$287$	−1.66404e10	−0.144776
$288$	−1.28017e11	−1.09648
$289$	−1.18557e11	−0.999741
$290$	1.68396e10	0.139810
$291$	−1.20926e10	−0.0988560
$292$	−5.35521e9	−0.0431076
$293$	1.76830e11	1.40169	0.700845	−	0.713314i	$-0.252807\pi$
$293$	1.76830e11	1.40169	0.700845	+	0.713314i	$0.252807\pi$
$294$	−7.88074e10	−0.615183
$295$	−1.94089e11	−1.49212
$296$	2.25870e11	1.71020
$297$	1.69288e10	0.126247
$298$	−1.68819e10	−0.124008
$299$	1.00363e11	0.726198
$300$	2.48956e10	0.177450
$301$	−1.06997e11	−0.751315
$302$	−1.14271e11	−0.790503
$303$	−8.81787e10	−0.600996
$304$	−3.82086e10	−0.256584
$305$	6.14284e10	0.406462
$306$	−1.98770e9	−0.0129600
$307$	−6.54871e10	−0.420758	−0.210379	−	0.977620i	$-0.567470\pi$
$307$	−6.54871e10	−0.420758	−0.210379	+	0.977620i	$0.567470\pi$
$308$	2.46473e10	0.156060
$309$	−2.70815e10	−0.168989
$310$	1.74633e11	1.07399
$311$	8.21809e9	0.0498137	0.0249069	−	0.999690i	$-0.492071\pi$
$311$	8.21809e9	0.0498137	0.0249069	+	0.999690i	$0.492071\pi$
$312$	1.51260e11	0.903710
$313$	3.27979e11	1.93151	0.965754	−	0.259458i	$-0.0835440\pi$
$313$	3.27979e11	1.93151	0.965754	+	0.259458i	$0.0835440\pi$
$314$	1.63378e11	0.948438
$315$	1.42505e11	0.815517
$316$	1.62832e11	0.918646
$317$	−1.22951e11	−0.683857	−0.341929	−	0.939726i	$-0.611080\pi$
$317$	−1.22951e11	−0.683857	−0.341929	+	0.939726i	$0.611080\pi$
$318$	−7.92054e10	−0.434343
$319$	1.60249e10	0.0866439
$320$	1.67215e11	0.891457
$321$	2.43806e10	0.128166
$322$	1.01596e11	0.526651
$323$	4.61381e9	0.0235857
$324$	8.34064e10	0.420481
$325$	−2.63149e10	−0.130836
$326$	−1.66652e11	−0.817205
$327$	6.59120e10	0.318786
$328$	−5.09420e10	−0.243021
$329$	9.16479e9	0.0431262
$330$	−1.11822e11	−0.519056
$331$	3.75660e11	1.72016	0.860081	−	0.510158i	$-0.170413\pi$
$331$	3.75660e11	1.72016	0.860081	+	0.510158i	$0.170413\pi$
$332$	2.35069e10	0.106188
$333$	4.34081e11	1.93451
$334$	−2.98560e11	−1.31272
$335$	−4.35551e11	−1.88946
$336$	3.76604e10	0.161197
$337$	1.35186e11	0.570949	0.285474	−	0.958386i	$-0.407849\pi$
$337$	1.35186e11	0.570949	0.285474	+	0.958386i	$0.407849\pi$
$338$	1.07467e11	0.447868
$339$	−3.57674e11	−1.47092
$340$	−2.35491e9	−0.00955695
$341$	1.66185e11	0.665574
$342$	−2.98546e11	−1.18003
$343$	−2.57441e11	−1.00428
$344$	−3.27553e11	−1.26116
$345$	5.34122e11	2.02981
$346$	−7.72161e10	−0.289645
$347$	−2.54223e11	−0.941309	−0.470654	−	0.882318i	$-0.655982\pi$
$347$	−2.54223e11	−0.941309	−0.470654	+	0.882318i	$0.655982\pi$
$348$	−4.02942e10	−0.147277
$349$	−4.42380e10	−0.159618	−0.0798088	−	0.996810i	$-0.525431\pi$
$349$	−4.42380e10	−0.159618	−0.0798088	+	0.996810i	$0.525431\pi$
$350$	−2.66379e10	−0.0948844
$351$	4.49936e10	0.158223
$352$	1.24552e11	0.432423
$353$	−2.56826e10	−0.0880345	−0.0440172	−	0.999031i	$-0.514016\pi$
$353$	−2.56826e10	−0.0880345	−0.0440172	+	0.999031i	$0.514016\pi$
$354$	−4.00780e11	−1.35641
$355$	−3.92555e10	−0.131182
$356$	−2.58810e11	−0.853996
$357$	−4.54762e9	−0.0148176
$358$	2.54983e11	0.820423
$359$	−2.97776e10	−0.0946160	−0.0473080	−	0.998880i	$-0.515064\pi$
$359$	−2.97776e10	−0.0946160	−0.0473080	+	0.998880i	$0.515064\pi$
$360$	4.36256e11	1.36893
$361$	3.70292e11	1.14752
$362$	4.23261e11	1.29545
$363$	3.82374e11	1.15587
$364$	6.55080e10	0.195586
$365$	3.01246e10	0.0888388
$366$	1.26845e11	0.369495
$367$	−2.75687e11	−0.793268	−0.396634	−	0.917977i	$-0.629822\pi$
$367$	−2.75687e11	−0.793268	−0.396634	+	0.917977i	$0.629822\pi$
$368$	7.64974e10	0.217436
$369$	−9.79010e10	−0.274896
$370$	−4.43800e11	−1.23106
$371$	−9.82065e10	−0.269127
$372$	−4.17866e11	−1.13134
$373$	−2.48124e11	−0.663710	−0.331855	−	0.943330i	$-0.607674\pi$
$373$	−2.48124e11	−0.663710	−0.331855	+	0.943330i	$0.607674\pi$
$374$	1.93389e9	0.00511106
$375$	4.85883e11	1.26879
$376$	2.80565e10	0.0723916
$377$	4.25913e10	0.108589
$378$	4.55459e10	0.114746
$379$	−2.18518e11	−0.544016	−0.272008	−	0.962295i	$-0.587688\pi$
$379$	−2.18518e11	−0.544016	−0.272008	+	0.962295i	$0.587688\pi$
$380$	−3.53700e11	−0.870179
$381$	6.81970e11	1.65807
$382$	4.61363e11	1.10856
$383$	−4.48827e11	−1.06582	−0.532911	−	0.846171i	$-0.678902\pi$
$383$	−4.48827e11	−1.06582	−0.532911	+	0.846171i	$0.678902\pi$
$384$	−2.38161e11	−0.558959
$385$	−1.38648e11	−0.321617
$386$	−1.73518e11	−0.397834
$387$	−6.29496e11	−1.42657
$388$	−1.60325e10	−0.0359136
$389$	7.28717e11	1.61356	0.806781	−	0.590850i	$-0.201207\pi$
$389$	7.28717e11	1.61356	0.806781	+	0.590850i	$0.201207\pi$
$390$	−2.97203e11	−0.650522
$391$	−9.23732e9	−0.0199871
$392$	−2.99132e11	−0.639847
$393$	1.22692e12	2.59447
$394$	−4.15485e10	−0.0868604
$395$	−9.15976e11	−1.89320
$396$	1.45008e11	0.296321
$397$	−9.30288e9	−0.0187958	−0.00939788	−	0.999956i	$-0.502991\pi$
$397$	−9.30288e9	−0.0187958	−0.00939788	+	0.999956i	$0.502991\pi$
$398$	−5.18742e11	−1.03628
$399$	−6.83037e11	−1.34917
$400$	−2.00573e10	−0.0391744
$401$	4.65633e11	0.899278	0.449639	−	0.893210i	$-0.351553\pi$
$401$	4.65633e11	0.899278	0.449639	+	0.893210i	$0.351553\pi$
$402$	−8.99381e11	−1.71762
$403$	4.41689e11	0.834150
$404$	−1.16908e11	−0.218337
$405$	−4.69184e11	−0.866554
$406$	4.31142e10	0.0787505
$407$	−4.22331e11	−0.762918
$408$	−1.39218e10	−0.0248728
$409$	1.38225e11	0.244249	0.122125	−	0.992515i	$-0.461029\pi$
$409$	1.38225e11	0.244249	0.122125	+	0.992515i	$0.461029\pi$
$410$	1.00093e11	0.174935
$411$	−8.43869e11	−1.45877
$412$	−3.59048e10	−0.0613925
$413$	−4.96926e11	−0.840459
$414$	5.97719e11	0.999989
$415$	−1.32233e11	−0.218838
$416$	3.31037e11	0.541947
$417$	3.42253e11	0.554287
$418$	2.90465e11	0.465372
$419$	8.14126e11	1.29041	0.645206	−	0.764009i	$-0.276772\pi$
$419$	8.14126e11	1.29041	0.645206	+	0.764009i	$0.276772\pi$
$420$	3.48625e11	0.546685
$421$	6.26961e11	0.972682	0.486341	−	0.873769i	$-0.338331\pi$
$421$	6.26961e11	0.972682	0.486341	+	0.873769i	$0.338331\pi$
$422$	6.01235e11	0.922864
$423$	5.39193e10	0.0818866
$424$	−3.00643e11	−0.451757
$425$	2.42199e9	0.00360099
$426$	−8.10597e10	−0.119251
$427$	1.57275e11	0.228946
$428$	3.23240e10	0.0465616
$429$	−2.82825e11	−0.403144
$430$	6.43591e11	0.907825
$431$	1.05646e11	0.147471	0.0737356	−	0.997278i	$-0.476508\pi$
$431$	1.05646e11	0.147471	0.0737356	+	0.997278i	$0.476508\pi$
$432$	3.42943e10	0.0473745
$433$	5.56220e11	0.760416	0.380208	−	0.924901i	$-0.375852\pi$
$433$	5.56220e11	0.760416	0.380208	+	0.924901i	$0.375852\pi$
$434$	4.47112e11	0.604940
$435$	2.26666e11	0.303518
$436$	8.73866e10	0.115813
$437$	−1.38741e12	−1.81987
$438$	6.22050e10	0.0807591
$439$	1.21419e12	1.56025	0.780127	−	0.625621i	$-0.215155\pi$
$439$	1.21419e12	1.56025	0.780127	+	0.625621i	$0.215155\pi$
$440$	−4.24447e11	−0.539867
$441$	−5.74877e11	−0.723771
$442$	5.13994e9	0.00640557
$443$	−9.56779e11	−1.18031	−0.590154	−	0.807291i	$-0.700933\pi$
$443$	−9.56779e11	−1.18031	−0.590154	+	0.807291i	$0.700933\pi$
$444$	1.06194e12	1.29681
$445$	1.45588e12	1.75997
$446$	−1.82331e10	−0.0218200
$447$	−2.27236e11	−0.269212
$448$	4.28120e11	0.502128
$449$	1.05651e12	1.22678	0.613388	−	0.789781i	$-0.289806\pi$
$449$	1.05651e12	1.22678	0.613388	+	0.789781i	$0.289806\pi$
$450$	−1.56719e11	−0.180163
$451$	9.52509e10	0.108411
$452$	−4.74207e11	−0.534374
$453$	−1.53812e12	−1.71612
$454$	3.61346e11	0.399183
$455$	−3.68501e11	−0.403076
$456$	−2.09101e12	−2.26472
$457$	−6.18622e11	−0.663442	−0.331721	−	0.943378i	$-0.607629\pi$
$457$	−6.18622e11	−0.663442	−0.331721	+	0.943378i	$0.607629\pi$
$458$	5.24651e11	0.557155
$459$	−4.14115e9	−0.00435476
$460$	7.08143e11	0.737413
$461$	−5.66710e10	−0.0584395	−0.0292198	−	0.999573i	$-0.509302\pi$
$461$	−5.66710e10	−0.0584395	−0.0292198	+	0.999573i	$0.509302\pi$
$462$	−2.86297e11	−0.292367
$463$	2.64517e11	0.267509	0.133755	−	0.991014i	$-0.457297\pi$
$463$	2.64517e11	0.267509	0.133755	+	0.991014i	$0.457297\pi$
$464$	3.24633e10	0.0325133
$465$	2.35062e12	2.33154
$466$	9.32462e11	0.915998
$467$	−2.81110e11	−0.273496	−0.136748	−	0.990606i	$-0.543665\pi$
$467$	−2.81110e11	−0.273496	−0.136748	+	0.990606i	$0.543665\pi$
$468$	3.85404e11	0.371373
$469$	−1.11514e12	−1.06427
$470$	−5.51266e10	−0.0521100
$471$	2.19912e12	2.05899
$472$	−1.52126e12	−1.41079
$473$	6.12457e11	0.562601
$474$	−1.89142e12	−1.72102
$475$	3.63774e11	0.327877
$476$	−6.02927e9	−0.00538311
$477$	−5.77780e11	−0.511010
$478$	−1.13600e11	−0.0995294
$479$	−1.90719e12	−1.65533	−0.827666	−	0.561221i	$-0.810332\pi$
$479$	−1.90719e12	−1.65533	−0.827666	+	0.561221i	$0.810332\pi$
$480$	1.76174e12	1.51480
$481$	−1.12248e12	−0.956149
$482$	9.88413e11	0.834116
$483$	1.36751e12	1.14332
$484$	5.06954e11	0.419918
$485$	9.01874e10	0.0740130
$486$	−1.19532e12	−0.971896
$487$	3.72536e11	0.300115	0.150058	−	0.988677i	$-0.452054\pi$
$487$	3.72536e11	0.300115	0.150058	+	0.988677i	$0.452054\pi$
$488$	4.81471e11	0.384310
$489$	−2.24319e12	−1.77409
$490$	5.87749e11	0.460585
$491$	−1.79011e12	−1.39000	−0.694998	−	0.719012i	$-0.744595\pi$
$491$	−1.79011e12	−1.39000	−0.694998	+	0.719012i	$0.744595\pi$
$492$	−2.39506e11	−0.184278
$493$	−3.92005e9	−0.00298869
$494$	7.72002e11	0.583240
$495$	−8.15708e11	−0.610677
$496$	3.36657e11	0.249758
$497$	−1.00506e11	−0.0738902
$498$	−2.73051e11	−0.198935
$499$	−5.78422e10	−0.0417631	−0.0208815	−	0.999782i	$-0.506647\pi$
$499$	−5.78422e10	−0.0417631	−0.0208815	+	0.999782i	$0.506647\pi$
$500$	6.44188e11	0.460943
$501$	−4.01872e12	−2.84982
$502$	−1.56634e12	−1.10083
$503$	1.92887e12	1.34353	0.671763	−	0.740766i	$-0.265537\pi$
$503$	1.92887e12	1.34353	0.671763	+	0.740766i	$0.265537\pi$
$504$	1.11694e12	0.771071
$505$	6.57640e11	0.449963
$506$	−5.81539e11	−0.394368
$507$	1.44654e12	0.972288
$508$	9.04162e11	0.602364
$509$	1.43973e12	0.950716	0.475358	−	0.879792i	$-0.342319\pi$
$509$	1.43973e12	0.950716	0.475358	+	0.879792i	$0.342319\pi$
$510$	2.73542e10	0.0179043
$511$	7.71278e10	0.0500399
$512$	5.37079e11	0.345401
$513$	−6.21987e11	−0.396509
$514$	−1.59661e12	−1.00894
$515$	2.01975e11	0.126522
$516$	−1.54000e12	−0.956309
$517$	−5.24598e10	−0.0322938
$518$	−1.13626e12	−0.693416
$519$	−1.03935e12	−0.628797
$520$	−1.12810e12	−0.676604
$521$	−5.70392e11	−0.339159	−0.169580	−	0.985516i	$-0.554241\pi$
$521$	−5.70392e11	−0.339159	−0.169580	+	0.985516i	$0.554241\pi$
$522$	2.53655e11	0.149529
$523$	−7.74760e11	−0.452803	−0.226402	−	0.974034i	$-0.572696\pi$
$523$	−7.74760e11	−0.452803	−0.226402	+	0.974034i	$0.572696\pi$
$524$	1.62666e12	0.942552
$525$	−3.58556e11	−0.205987
$526$	−1.86707e12	−1.06347
$527$	−4.06525e10	−0.0229583
$528$	−2.15570e11	−0.120708
$529$	9.76591e11	0.542203
$530$	5.90717e11	0.325191
$531$	−2.92357e12	−1.59584
$532$	−9.05576e11	−0.490143
$533$	2.53160e11	0.135870
$534$	3.00628e12	1.59990
$535$	−1.81831e11	−0.0959570
$536$	−3.41382e12	−1.78648
$537$	3.43216e12	1.78108
$538$	1.17225e12	0.603253
$539$	5.59316e11	0.285435
$540$	3.17465e11	0.160666
$541$	−2.44001e12	−1.22463	−0.612313	−	0.790615i	$-0.709761\pi$
$541$	−2.44001e12	−1.22463	−0.612313	+	0.790615i	$0.709761\pi$
$542$	1.55824e12	0.775597
$543$	5.69724e12	2.81232
$544$	−3.04682e10	−0.0149160
$545$	−4.91574e11	−0.238674
$546$	−7.60927e11	−0.366417
$547$	2.14873e11	0.102622	0.0513109	−	0.998683i	$-0.483660\pi$
$547$	2.14873e11	0.102622	0.0513109	+	0.998683i	$0.483660\pi$
$548$	−1.11881e12	−0.529960
$549$	9.25297e11	0.434716
$550$	1.52477e11	0.0710515
$551$	−5.88779e11	−0.272126
$552$	4.18641e12	1.91918
$553$	−2.34517e12	−1.06638
$554$	−1.67862e11	−0.0757108
$555$	−5.97370e12	−2.67254
$556$	4.53762e11	0.201368
$557$	−5.57453e11	−0.245392	−0.122696	−	0.992444i	$-0.539154\pi$
$557$	−5.57453e11	−0.245392	−0.122696	+	0.992444i	$0.539154\pi$
$558$	2.63050e12	1.14864
$559$	1.62780e12	0.705095
$560$	−2.80873e11	−0.120688
$561$	2.60309e10	0.0110957
$562$	9.53250e11	0.403082
$563$	3.48512e12	1.46194	0.730971	−	0.682409i	$-0.239068\pi$
$563$	3.48512e12	1.46194	0.730971	+	0.682409i	$0.239068\pi$
$564$	1.31909e11	0.0548930
$565$	2.66755e12	1.10127
$566$	−1.72657e12	−0.707149
$567$	−1.20125e12	−0.488101
$568$	−3.07682e11	−0.124032
$569$	3.49069e11	0.139607	0.0698034	−	0.997561i	$-0.477763\pi$
$569$	3.49069e11	0.139607	0.0698034	+	0.997561i	$0.477763\pi$
$570$	4.10850e12	1.63022
$571$	2.03779e12	0.802226	0.401113	−	0.916029i	$-0.368623\pi$
$571$	2.03779e12	0.802226	0.401113	+	0.916029i	$0.368623\pi$
$572$	−3.74972e11	−0.146459
$573$	6.21009e12	2.40659
$574$	2.56268e11	0.0985350
$575$	−7.28313e11	−0.277852
$576$	2.51876e12	0.953424
$577$	1.32732e12	0.498522	0.249261	−	0.968436i	$-0.419812\pi$
$577$	1.32732e12	0.498522	0.249261	+	0.968436i	$0.419812\pi$
$578$	1.82582e12	0.680427
$579$	−2.33561e12	−0.863668
$580$	3.00515e11	0.110266
$581$	−3.38555e11	−0.123264
$582$	1.86230e11	0.0672817
$583$	5.62140e11	0.201528
$584$	2.36114e11	0.0839970
$585$	−2.16801e12	−0.765348
$586$	−2.72324e12	−0.953995
$587$	3.75909e12	1.30681	0.653403	−	0.757010i	$-0.273341\pi$
$587$	3.75909e12	1.30681	0.653403	+	0.757010i	$0.273341\pi$
$588$	−1.40638e12	−0.485183
$589$	−6.10587e12	−2.09040
$590$	2.98903e12	1.01554
$591$	−5.59256e11	−0.188568
$592$	−8.55558e11	−0.286287
$593$	1.34815e12	0.447705	0.223853	−	0.974623i	$-0.428137\pi$
$593$	1.34815e12	0.447705	0.223853	+	0.974623i	$0.428137\pi$
$594$	−2.60708e11	−0.0859241
$595$	3.39163e10	0.0110939
$596$	−3.01272e11	−0.0978026
$597$	−6.98244e12	−2.24969
$598$	−1.54563e12	−0.494253
$599$	6.21339e12	1.97200	0.986002	−	0.166735i	$-0.0533224\pi$
$599$	6.21339e12	1.97200	0.986002	+	0.166735i	$0.0533224\pi$
$600$	−1.09766e12	−0.345770
$601$	−4.22268e12	−1.32024	−0.660121	−	0.751159i	$-0.729495\pi$
$601$	−4.22268e12	−1.32024	−0.660121	+	0.751159i	$0.729495\pi$
$602$	1.64778e12	0.511347
$603$	−6.56072e12	−2.02080
$604$	−2.03925e12	−0.623455
$605$	−2.85176e12	−0.865393
$606$	1.35798e12	0.409040
$607$	−1.16200e12	−0.347423	−0.173712	−	0.984797i	$-0.555576\pi$
$607$	−1.16200e12	−0.347423	−0.173712	+	0.984797i	$0.555576\pi$
$608$	−4.57622e12	−1.35813
$609$	5.80332e11	0.170962
$610$	−9.46016e11	−0.276640
$611$	−1.39429e11	−0.0404731
$612$	−3.54721e10	−0.0102213
$613$	−5.93205e12	−1.69681	−0.848404	−	0.529349i	$-0.822436\pi$
$613$	−5.93205e12	−1.69681	−0.848404	+	0.529349i	$0.822436\pi$
$614$	1.00852e12	0.286370
$615$	1.34729e12	0.379771
$616$	−1.08671e12	−0.304089
$617$	3.86247e12	1.07296	0.536478	−	0.843914i	$-0.319754\pi$
$617$	3.86247e12	1.07296	0.536478	+	0.843914i	$0.319754\pi$
$618$	4.17063e11	0.115015
$619$	−2.89472e12	−0.792498	−0.396249	−	0.918143i	$-0.629688\pi$
$619$	−2.89472e12	−0.792498	−0.396249	+	0.918143i	$0.629688\pi$
$620$	3.11646e12	0.847031
$621$	1.24528e12	0.336012
$622$	−1.26561e11	−0.0339034
$623$	3.72748e12	0.991331
$624$	−5.72947e11	−0.151281
$625$	−4.47723e12	−1.17368
$626$	−5.05098e12	−1.31459
$627$	3.90975e12	1.01029
$628$	2.91560e12	0.748015
$629$	1.03311e11	0.0263160
$630$	−2.19462e12	−0.555044
$631$	4.46252e12	1.12059	0.560297	−	0.828292i	$-0.310687\pi$
$631$	4.46252e12	1.12059	0.560297	+	0.828292i	$0.310687\pi$
$632$	−7.17935e12	−1.79002
$633$	8.09281e12	2.00347
$634$	1.89348e12	0.465436
$635$	−5.08616e12	−1.24139
$636$	−1.41348e12	−0.342558
$637$	1.48656e12	0.357730
$638$	−2.46789e11	−0.0589701
$639$	−5.91306e11	−0.140300
$640$	1.77621e12	0.418490
$641$	2.58707e12	0.605268	0.302634	−	0.953107i	$-0.402134\pi$
$641$	2.58707e12	0.605268	0.302634	+	0.953107i	$0.402134\pi$
$642$	−3.75468e11	−0.0872300
$643$	−3.66867e12	−0.846368	−0.423184	−	0.906044i	$-0.639088\pi$
$643$	−3.66867e12	−0.846368	−0.423184	+	0.906044i	$0.639088\pi$
$644$	1.81305e12	0.415360
$645$	8.66295e12	1.97082
$646$	−7.10541e10	−0.0160525
$647$	−1.39863e12	−0.313786	−0.156893	−	0.987616i	$-0.550148\pi$
$647$	−1.39863e12	−0.313786	−0.156893	+	0.987616i	$0.550148\pi$
$648$	−3.67743e12	−0.819326
$649$	2.84443e12	0.629354
$650$	4.05257e11	0.0890473
$651$	6.01827e12	1.31328
$652$	−2.97404e12	−0.644513
$653$	5.69525e12	1.22575	0.612877	−	0.790178i	$-0.290012\pi$
$653$	5.69525e12	1.22575	0.612877	+	0.790178i	$0.290012\pi$
$654$	−1.01506e12	−0.216967
$655$	−9.15040e12	−1.94247
$656$	1.92959e11	0.0406817
$657$	4.53767e11	0.0950142
$658$	−1.41140e11	−0.0293518
$659$	6.98509e12	1.44274	0.721370	−	0.692550i	$-0.243513\pi$
$659$	6.98509e12	1.44274	0.721370	+	0.692550i	$0.243513\pi$
$660$	−1.99555e12	−0.409370
$661$	−5.29754e12	−1.07936	−0.539682	−	0.841869i	$-0.681455\pi$
$661$	−5.29754e12	−1.07936	−0.539682	+	0.841869i	$0.681455\pi$
$662$	−5.78528e12	−1.17075
$663$	6.91853e10	0.0139060
$664$	−1.03643e12	−0.206911
$665$	5.09412e12	1.01012
$666$	−6.68497e12	−1.31664
$667$	1.17879e12	0.230607
$668$	−5.32805e12	−1.03532
$669$	−2.45424e11	−0.0473696
$670$	6.70762e12	1.28597
$671$	−9.00251e11	−0.171440
$672$	4.51057e12	0.853237
$673$	2.16032e12	0.405929	0.202965	−	0.979186i	$-0.434942\pi$
$673$	2.16032e12	0.405929	0.202965	+	0.979186i	$0.434942\pi$
$674$	−2.08190e12	−0.388590
$675$	−3.26508e11	−0.0605377
$676$	1.91784e12	0.353225
$677$	−7.73764e12	−1.41566	−0.707831	−	0.706382i	$-0.750326\pi$
$677$	−7.73764e12	−1.41566	−0.707831	+	0.706382i	$0.750326\pi$
$678$	5.50829e12	1.00111
$679$	2.30906e11	0.0416891
$680$	1.03829e11	0.0186221
$681$	4.86384e12	0.866597
$682$	−2.55929e12	−0.452992
$683$	−3.00805e12	−0.528923	−0.264461	−	0.964396i	$-0.585194\pi$
$683$	−3.00805e12	−0.528923	−0.264461	+	0.964396i	$0.585194\pi$
$684$	−5.32779e12	−0.930667
$685$	6.29361e12	1.09217
$686$	3.96467e12	0.683516
$687$	7.06197e12	1.20954
$688$	1.24072e12	0.211117
$689$	1.49407e12	0.252571
$690$	−8.22564e12	−1.38149
$691$	−9.43997e12	−1.57514	−0.787571	−	0.616224i	$-0.788662\pi$
$691$	−9.43997e12	−1.57514	−0.787571	+	0.616224i	$0.788662\pi$
$692$	−1.37798e12	−0.228437
$693$	−2.08845e12	−0.343974
$694$	3.91511e12	0.640658
$695$	−2.55254e12	−0.414993
$696$	1.77659e12	0.286976
$697$	−2.33005e10	−0.00373954
$698$	6.81278e11	0.108636
$699$	1.25512e13	1.98856
$700$	−4.75376e11	−0.0748334
$701$	−3.69624e12	−0.578135	−0.289067	−	0.957309i	$-0.593345\pi$
$701$	−3.69624e12	−0.578135	−0.289067	+	0.957309i	$0.593345\pi$
$702$	−6.92915e11	−0.107687
$703$	1.55170e13	2.39613
$704$	−2.45058e12	−0.376004
$705$	−7.42023e11	−0.113127
$706$	3.95520e11	0.0599166
$707$	1.68375e12	0.253449
$708$	−7.15224e12	−1.06978
$709$	−3.08928e12	−0.459144	−0.229572	−	0.973292i	$-0.573733\pi$
$709$	−3.08928e12	−0.459144	−0.229572	+	0.973292i	$0.573733\pi$
$710$	6.04546e11	0.0892827
$711$	−1.37974e13	−2.02480
$712$	1.14111e13	1.66405
$713$	1.22246e13	1.77146
$714$	7.00347e10	0.0100849
$715$	2.10932e12	0.301832
$716$	4.55038e12	0.647051
$717$	−1.52909e12	−0.216071
$718$	4.58584e11	0.0643960
$719$	−1.23477e13	−1.72308	−0.861539	−	0.507692i	$-0.830499\pi$
$719$	−1.23477e13	−1.72308	−0.861539	+	0.507692i	$0.830499\pi$
$720$	−1.65246e12	−0.229158
$721$	5.17115e11	0.0712653
$722$	−5.70260e12	−0.781008
$723$	1.33044e13	1.81080
$724$	7.55344e12	1.02170
$725$	−3.09075e11	−0.0415473
$726$	−5.88867e12	−0.786688
$727$	−7.91650e12	−1.05106	−0.525531	−	0.850774i	$-0.676133\pi$
$727$	−7.91650e12	−1.05106	−0.525531	+	0.850774i	$0.676133\pi$
$728$	−2.88828e12	−0.381108
$729$	−1.01159e13	−1.32657
$730$	−4.63927e11	−0.0604640
$731$	−1.49821e11	−0.0194063
$732$	2.26365e12	0.291414
$733$	−7.02524e12	−0.898863	−0.449431	−	0.893315i	$-0.648373\pi$
$733$	−7.02524e12	−0.898863	−0.449431	+	0.893315i	$0.648373\pi$
$734$	4.24567e12	0.539901
$735$	7.91129e12	0.999895
$736$	9.16206e12	1.15091
$737$	6.38313e12	0.796948
$738$	1.50770e12	0.187095
$739$	−5.62787e12	−0.694136	−0.347068	−	0.937840i	$-0.612823\pi$
$739$	−5.62787e12	−0.694136	−0.347068	+	0.937840i	$0.612823\pi$
$740$	−7.91997e12	−0.970914
$741$	1.03914e13	1.26617
$742$	1.51241e12	0.183169
$743$	−5.57889e11	−0.0671580	−0.0335790	−	0.999436i	$-0.510691\pi$
$743$	−5.57889e11	−0.0671580	−0.0335790	+	0.999436i	$0.510691\pi$
$744$	1.84239e13	2.20447
$745$	1.69474e12	0.201558
$746$	3.82118e12	0.451723
$747$	−1.99183e12	−0.234050
$748$	3.45119e10	0.00403099
$749$	−4.65542e11	−0.0540494
$750$	−7.48275e12	−0.863546
$751$	1.10236e13	1.26457	0.632286	−	0.774735i	$-0.282117\pi$
$751$	1.10236e13	1.26457	0.632286	+	0.774735i	$0.282117\pi$
$752$	−1.06273e11	−0.0121183
$753$	−2.10834e13	−2.38981
$754$	−6.55920e11	−0.0739060
$755$	1.14714e13	1.28485
$756$	8.12804e11	0.0904978
$757$	−7.03280e12	−0.778389	−0.389195	−	0.921156i	$-0.627247\pi$
$757$	−7.03280e12	−0.778389	−0.389195	+	0.921156i	$0.627247\pi$
$758$	3.36525e12	0.370259
$759$	−7.82771e12	−0.856144
$760$	1.55948e13	1.69558
$761$	−1.03885e13	−1.12285	−0.561426	−	0.827527i	$-0.689747\pi$
$761$	−1.03885e13	−1.12285	−0.561426	+	0.827527i	$0.689747\pi$
$762$	−1.05025e13	−1.12849
$763$	−1.25857e12	−0.134437
$764$	8.23339e12	0.874296
$765$	1.99540e11	0.0210647
$766$	6.91208e12	0.725402
$767$	7.55999e12	0.788755
$768$	1.51472e13	1.57111
$769$	−1.69193e13	−1.74467	−0.872335	−	0.488909i	$-0.837395\pi$
$769$	−1.69193e13	−1.74467	−0.872335	+	0.488909i	$0.837395\pi$
$770$	2.13522e12	0.218894
$771$	−2.14909e13	−2.19033
$772$	−3.09657e12	−0.313764
$773$	−6.76726e12	−0.681718	−0.340859	−	0.940114i	$-0.610718\pi$
$773$	−6.76726e12	−0.681718	−0.340859	+	0.940114i	$0.610718\pi$
$774$	9.69443e12	0.970930
$775$	−3.20523e12	−0.319155
$776$	7.06882e11	0.0699793
$777$	−1.52944e13	−1.50535
$778$	−1.12225e13	−1.09820
$779$	−3.49966e12	−0.340492
$780$	−5.30382e12	−0.513054
$781$	5.75301e11	0.0553306
$782$	1.42257e11	0.0136033
$783$	5.28461e11	0.0502441
$784$	1.13306e12	0.107110
$785$	−1.64011e13	−1.54156
$786$	−1.88949e13	−1.76581
$787$	−1.40500e13	−1.30554	−0.652768	−	0.757558i	$-0.726392\pi$
$787$	−1.40500e13	−1.30554	−0.652768	+	0.757558i	$0.726392\pi$
$788$	−7.41466e11	−0.0685051
$789$	−2.51313e13	−2.30871
$790$	1.41063e13	1.28852
$791$	6.82971e12	0.620309
$792$	−6.39346e12	−0.577394
$793$	−2.39271e12	−0.214862
$794$	1.43267e11	0.0127925
$795$	7.95124e12	0.705965
$796$	−9.25737e12	−0.817295
$797$	−6.87502e11	−0.0603547	−0.0301774	−	0.999545i	$-0.509607\pi$
$797$	−6.87502e11	−0.0603547	−0.0301774	+	0.999545i	$0.509607\pi$
$798$	1.05190e13	0.918249
$799$	1.28328e10	0.00111394
$800$	−2.40226e12	−0.207355
$801$	2.19299e13	1.88231
$802$	−7.17089e12	−0.612052
$803$	−4.41484e11	−0.0374710
$804$	−1.60502e13	−1.35465
$805$	−1.01989e13	−0.856000
$806$	−6.80214e12	−0.567725
$807$	1.57789e13	1.30962
$808$	5.15453e12	0.425440
$809$	2.31429e12	0.189954	0.0949772	−	0.995479i	$-0.469722\pi$
$809$	2.31429e12	0.189954	0.0949772	+	0.995479i	$0.469722\pi$
$810$	7.22558e12	0.589780
$811$	2.07750e13	1.68635	0.843175	−	0.537640i	$-0.180684\pi$
$811$	2.07750e13	1.68635	0.843175	+	0.537640i	$0.180684\pi$
$812$	7.69408e11	0.0621090
$813$	2.09744e13	1.68376
$814$	6.50402e12	0.519245
$815$	1.67298e13	1.32825
$816$	5.27333e10	0.00416370
$817$	−2.25026e13	−1.76698
$818$	−2.12871e12	−0.166237
$819$	−5.55073e12	−0.431095
$820$	1.78624e12	0.137968
$821$	1.17400e13	0.901826	0.450913	−	0.892568i	$-0.351098\pi$
$821$	1.17400e13	0.901826	0.450913	+	0.892568i	$0.351098\pi$
$822$	1.29958e13	0.992844
$823$	5.32682e12	0.404733	0.202367	−	0.979310i	$-0.435137\pi$
$823$	5.32682e12	0.404733	0.202367	+	0.979310i	$0.435137\pi$
$824$	1.58306e12	0.119626
$825$	2.05239e12	0.154247
$826$	7.65281e12	0.572019
$827$	1.19872e13	0.891137	0.445569	−	0.895248i	$-0.353002\pi$
$827$	1.19872e13	0.891137	0.445569	+	0.895248i	$0.353002\pi$
$828$	1.06668e13	0.788672
$829$	8.60218e12	0.632577	0.316288	−	0.948663i	$-0.397563\pi$
$829$	8.60218e12	0.632577	0.316288	+	0.948663i	$0.397563\pi$
$830$	2.03643e12	0.148942
$831$	−2.25947e12	−0.164363
$832$	−6.51321e12	−0.471238
$833$	−1.36821e11	−0.00984578
$834$	−5.27080e12	−0.377250
$835$	2.99718e13	2.13365
$836$	5.18357e12	0.367030
$837$	5.48035e12	0.385961
$838$	−1.25378e13	−0.878259
$839$	−2.40899e13	−1.67844	−0.839222	−	0.543789i	$-0.816989\pi$
$839$	−2.40899e13	−1.67844	−0.839222	+	0.543789i	$0.816989\pi$
$840$	−1.53711e13	−1.06524
$841$	5.00246e11	0.0344828
$842$	−9.65539e12	−0.662011
$843$	1.28311e13	0.875061
$844$	1.07295e13	0.727845
$845$	−1.07884e13	−0.727948
$846$	−8.30374e11	−0.0557323
$847$	−7.30134e12	−0.487447
$848$	1.13878e12	0.0756240
$849$	−2.32402e13	−1.53517
$850$	−3.72993e10	−0.00245085
$851$	−3.10667e13	−2.03054
$852$	−1.44658e12	−0.0940509
$853$	1.41735e13	0.916659	0.458329	−	0.888782i	$-0.348448\pi$
$853$	1.41735e13	0.916659	0.458329	+	0.888782i	$0.348448\pi$
$854$	−2.42208e12	−0.155822
$855$	2.99703e13	1.91798
$856$	−1.42518e12	−0.0907273
$857$	−5.36376e12	−0.339669	−0.169834	−	0.985473i	$-0.554323\pi$
$857$	−5.36376e12	−0.339669	−0.169834	+	0.985473i	$0.554323\pi$
$858$	4.35559e12	0.274381
$859$	−1.25726e13	−0.787870	−0.393935	−	0.919138i	$-0.628887\pi$
$859$	−1.25726e13	−0.787870	−0.393935	+	0.919138i	$0.628887\pi$
$860$	1.14854e13	0.715984
$861$	3.44945e12	0.213912
$862$	−1.62699e12	−0.100369
$863$	7.75614e12	0.475989	0.237994	−	0.971267i	$-0.423510\pi$
$863$	7.75614e12	0.475989	0.237994	+	0.971267i	$0.423510\pi$
$864$	4.10741e12	0.250759
$865$	7.75154e12	0.470778
$866$	−8.56596e12	−0.517542
$867$	2.45761e13	1.47716
$868$	7.97907e12	0.477104
$869$	1.34239e13	0.798527
$870$	−3.49072e12	−0.206576
$871$	1.69652e13	0.998798
$872$	−3.85292e12	−0.225666
$873$	1.35850e12	0.0791579
$874$	2.13666e13	1.23861
$875$	−9.27783e12	−0.535070
$876$	1.11010e12	0.0636932
$877$	−1.47870e12	−0.0844077	−0.0422039	−	0.999109i	$-0.513438\pi$
$877$	−1.47870e12	−0.0844077	−0.0422039	+	0.999109i	$0.513438\pi$
$878$	−1.86988e13	−1.06191
$879$	−3.66557e13	−2.07105
$880$	1.60773e12	0.0903736
$881$	1.94808e13	1.08947	0.544736	−	0.838608i	$-0.316630\pi$
$881$	1.94808e13	1.08947	0.544736	+	0.838608i	$0.316630\pi$
$882$	8.85327e12	0.492601
$883$	6.32492e12	0.350132	0.175066	−	0.984557i	$-0.443986\pi$
$883$	6.32492e12	0.350132	0.175066	+	0.984557i	$0.443986\pi$
$884$	9.17264e10	0.00505195
$885$	4.02334e13	2.20466
$886$	1.47347e13	0.803321
$887$	−1.96859e13	−1.06782	−0.533912	−	0.845540i	$-0.679279\pi$
$887$	−1.96859e13	−1.06782	−0.533912	+	0.845540i	$0.679279\pi$
$888$	−4.68214e13	−2.52689
$889$	−1.30221e13	−0.699234
$890$	−2.24210e13	−1.19784
$891$	6.87603e12	0.365501
$892$	−3.25385e11	−0.0172090
$893$	1.92745e12	0.101426
$894$	3.49951e12	0.183226
$895$	−2.55971e13	−1.33348
$896$	4.54763e12	0.235722
$897$	−2.08046e13	−1.07299
$898$	−1.62706e13	−0.834949
$899$	5.18775e12	0.264887
$900$	−2.79678e12	−0.142091
$901$	−1.37512e11	−0.00695151
$902$	−1.46689e12	−0.0737852
$903$	2.21797e13	1.11010
$904$	2.09080e13	1.04125
$905$	−4.24902e13	−2.10557
$906$	2.36875e13	1.16800
$907$	1.82940e13	0.897583	0.448792	−	0.893636i	$-0.351855\pi$
$907$	1.82940e13	0.897583	0.448792	+	0.893636i	$0.351855\pi$
$908$	6.44852e12	0.314828
$909$	9.90605e12	0.481241
$910$	5.67502e12	0.274335
$911$	3.22004e13	1.54892	0.774459	−	0.632624i	$-0.218022\pi$
$911$	3.22004e13	1.54892	0.774459	+	0.632624i	$0.218022\pi$
$912$	7.92037e12	0.379113
$913$	1.93791e12	0.0923029
$914$	9.52697e12	0.451541
$915$	−1.27337e13	−0.600564
$916$	9.36282e12	0.439417
$917$	−2.34277e13	−1.09413
$918$	6.37749e10	0.00296386
$919$	−1.03091e13	−0.476760	−0.238380	−	0.971172i	$-0.576616\pi$
$919$	−1.03091e13	−0.476760	−0.238380	+	0.971172i	$0.576616\pi$
$920$	−3.12224e13	−1.43688
$921$	1.35750e13	0.621687
$922$	8.72751e11	0.0397742
$923$	1.52905e12	0.0693446
$924$	−5.10921e12	−0.230584
$925$	8.14556e12	0.365833
$926$	−4.07364e12	−0.182068
$927$	3.04235e12	0.135316
$928$	3.88811e12	0.172097
$929$	2.21597e13	0.976096	0.488048	−	0.872817i	$-0.337709\pi$
$929$	2.21597e13	0.976096	0.488048	+	0.872817i	$0.337709\pi$
$930$	−3.62002e13	−1.58686
$931$	−2.05501e13	−0.896478
$932$	1.66405e13	0.722430
$933$	−1.70355e12	−0.0736018
$934$	4.32918e12	0.186142
$935$	−1.94139e11	−0.00830732
$936$	−1.69927e13	−0.723636
$937$	−3.88326e13	−1.64577	−0.822884	−	0.568209i	$-0.807636\pi$
$937$	−3.88326e13	−1.64577	−0.822884	+	0.568209i	$0.807636\pi$
$938$	1.71735e13	0.724346
$939$	−6.79878e13	−2.85388
$940$	−9.83779e11	−0.0410982
$941$	1.41008e13	0.586262	0.293131	−	0.956072i	$-0.405303\pi$
$941$	1.41008e13	0.586262	0.293131	+	0.956072i	$0.405303\pi$
$942$	−3.38670e13	−1.40136
$943$	7.00667e12	0.288542
$944$	5.76226e12	0.236167
$945$	−4.57225e12	−0.186503
$946$	−9.43202e12	−0.382908
$947$	4.54768e12	0.183745	0.0918725	−	0.995771i	$-0.470715\pi$
$947$	4.54768e12	0.183745	0.0918725	+	0.995771i	$0.470715\pi$
$948$	−3.37540e13	−1.35734
$949$	−1.17339e12	−0.0469616
$950$	−5.60224e12	−0.223154
$951$	2.54869e13	1.01043
$952$	2.65834e11	0.0104892
$953$	−2.19885e13	−0.863529	−0.431764	−	0.901986i	$-0.642109\pi$
$953$	−2.19885e13	−0.863529	−0.431764	+	0.901986i	$0.642109\pi$
$954$	8.89798e12	0.347795
$955$	−4.63151e13	−1.80180
$956$	−2.02728e12	−0.0784969
$957$	−3.32185e12	−0.128020
$958$	2.93714e13	1.12662
$959$	1.61135e13	0.615185
$960$	−3.46625e13	−1.31716
$961$	2.73594e13	1.03479
$962$	1.72865e13	0.650758
$963$	−2.73893e12	−0.102627
$964$	1.76390e13	0.657851
$965$	1.74191e13	0.646624
$966$	−2.10601e13	−0.778149
$967$	2.23013e13	0.820185	0.410093	−	0.912044i	$-0.365496\pi$
$967$	2.23013e13	0.820185	0.410093	+	0.912044i	$0.365496\pi$
$968$	−2.23519e13	−0.818229
$969$	−9.56411e11	−0.0348488
$970$	−1.38891e12	−0.0503735
$971$	−2.09688e13	−0.756986	−0.378493	−	0.925604i	$-0.623558\pi$
$971$	−2.09688e13	−0.756986	−0.378493	+	0.925604i	$0.623558\pi$
$972$	−2.13314e13	−0.766516
$973$	−6.53525e12	−0.233751
$974$	−5.73716e12	−0.204259
$975$	5.45489e12	0.193315
$976$	−1.82373e12	−0.0643333
$977$	4.90198e13	1.72126	0.860629	−	0.509232i	$-0.170071\pi$
$977$	4.90198e13	1.72126	0.860629	+	0.509232i	$0.170071\pi$
$978$	3.45458e13	1.20745
$979$	−2.13363e13	−0.742330
$980$	1.04888e13	0.363254
$981$	−7.40459e12	−0.255265
$982$	2.75683e13	0.946036
$983$	1.41129e13	0.482086	0.241043	−	0.970514i	$-0.422511\pi$
$983$	1.41129e13	0.482086	0.241043	+	0.970514i	$0.422511\pi$
$984$	1.05599e13	0.359073
$985$	4.17095e12	0.141180
$986$	6.03700e10	0.00203411
$987$	−1.89980e12	−0.0637206
$988$	1.37770e13	0.459990
$989$	4.50524e13	1.49739
$990$	1.25622e13	0.415629
$991$	2.87585e13	0.947183	0.473592	−	0.880744i	$-0.342957\pi$
$991$	2.87585e13	0.947183	0.473592	+	0.880744i	$0.342957\pi$
$992$	4.03213e13	1.32200
$993$	−7.78718e13	−2.54161
$994$	1.54782e12	0.0502899
$995$	5.20753e13	1.68433
$996$	−4.87282e12	−0.156896
$997$	2.29667e13	0.736156	0.368078	−	0.929795i	$-0.380016\pi$
$997$	2.29667e13	0.736156	0.368078	+	0.929795i	$0.380016\pi$
$998$	8.90788e11	0.0284241
$999$	−1.39274e13	−0.442410

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.10.a.a.1.4	✓	9
3.2	odd	2		261.10.a.b.1.6		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.10.a.a.1.4	✓	9	1.1	even	1	trivial
261.10.a.b.1.6		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)

\(f(q)\)	\(=\)	\(q-15.4003 q^{2} -207.293 q^{3} -274.831 q^{4} +1546.00 q^{5} +3192.38 q^{6} +3958.22 q^{7} +12117.4 q^{8} +23287.4 q^{9} +O(q^{10})\)	\(q-15.4003 q^{2} -207.293 q^{3} -274.831 q^{4} +1546.00 q^{5} +3192.38 q^{6} +3958.22 q^{7} +12117.4 q^{8} +23287.4 q^{9} -23808.9 q^{10} -22657.1 q^{11} +56970.5 q^{12} -60218.4 q^{13} -60957.7 q^{14} -320475. q^{15} -45898.7 q^{16} +5542.42 q^{17} -358633. q^{18} +832454. q^{19} -424888. q^{20} -820511. q^{21} +348926. q^{22} -1.66666e6 q^{23} -2.51186e6 q^{24} +436991. q^{25} +927382. q^{26} -747173. q^{27} -1.08784e6 q^{28} -707281. q^{29} +4.93541e6 q^{30} -7.33478e6 q^{31} -5.49727e6 q^{32} +4.69666e6 q^{33} -85355.0 q^{34} +6.11940e6 q^{35} -6.40010e6 q^{36} +1.86401e7 q^{37} -1.28200e7 q^{38} +1.24829e7 q^{39} +1.87335e7 q^{40} -4.20403e6 q^{41} +1.26361e7 q^{42} -2.70316e7 q^{43} +6.22686e6 q^{44} +3.60024e7 q^{45} +2.56670e7 q^{46} +2.31538e6 q^{47} +9.51448e6 q^{48} -2.46861e7 q^{49} -6.72979e6 q^{50} -1.14891e6 q^{51} +1.65499e7 q^{52} -2.48108e7 q^{53} +1.15067e7 q^{54} -3.50278e7 q^{55} +4.79634e7 q^{56} -1.72562e8 q^{57} +1.08923e7 q^{58} -1.25543e8 q^{59} +8.80764e7 q^{60} +3.97338e7 q^{61} +1.12958e8 q^{62} +9.21767e7 q^{63} +1.08160e8 q^{64} -9.30977e7 q^{65} -7.23299e7 q^{66} -2.81728e8 q^{67} -1.52323e6 q^{68} +3.45486e8 q^{69} -9.42406e7 q^{70} -2.53917e7 q^{71} +2.82184e8 q^{72} +1.94855e7 q^{73} -2.87064e8 q^{74} -9.05851e7 q^{75} -2.28784e8 q^{76} -8.96816e7 q^{77} -1.92240e8 q^{78} -5.92481e8 q^{79} -7.09594e7 q^{80} -3.03483e8 q^{81} +6.47433e7 q^{82} -8.55323e7 q^{83} +2.25502e8 q^{84} +8.56859e6 q^{85} +4.16295e8 q^{86} +1.46614e8 q^{87} -2.74546e8 q^{88} +9.41706e8 q^{89} -5.54447e8 q^{90} -2.38358e8 q^{91} +4.58048e8 q^{92} +1.52045e9 q^{93} -3.56576e7 q^{94} +1.28697e9 q^{95} +1.13955e9 q^{96} +5.83360e7 q^{97} +3.80174e8 q^{98} -5.27625e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 244 q^{3} + 1194 q^{4} - 738 q^{5} - 2330 q^{6} - 7128 q^{7} - 13776 q^{8} + 33017 q^{9}+O(q^{10}) \) 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

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