LMFDB - Embedded newform 29.16.b.a.28.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,16,Mod(28,29)]

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([1]))

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("29.28");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	29.b (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$41.3811164790$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			28.18
Character	$\chi$	$=$	29.28
Dual form			29.16.b.a.28.19

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.1196i q^{2} -4604.16i q^{3} +32665.6 q^{4} +98965.0 q^{5} -46592.0 q^{6} -632277. q^{7} -662159. i q^{8} -6.84936e6 q^{9} +O(q^{10})$	\(q-10.1196i q^{2} -4604.16i q^{3} +32665.6 q^{4} +98965.0 q^{5} -46592.0 q^{6} -632277. q^{7} -662159. i q^{8} -6.84936e6 q^{9} -1.00148e6i q^{10} -2.29375e7i q^{11} -1.50398e8i q^{12} -3.60728e8 q^{13} +6.39836e6i q^{14} -4.55651e8i q^{15} +1.06369e9 q^{16} -1.04308e9i q^{17} +6.93124e7i q^{18} -4.76574e9i q^{19} +3.23275e9 q^{20} +2.91110e9i q^{21} -2.32118e8 q^{22} +2.47201e10 q^{23} -3.04868e9 q^{24} -2.07235e10 q^{25} +3.65040e9i q^{26} -3.45291e10i q^{27} -2.06537e10 q^{28} +(-8.19484e10 + 4.37454e10i) q^{29} -4.61098e9 q^{30} +1.81010e11i q^{31} -3.24616e10i q^{32} -1.05608e11 q^{33} -1.05555e10 q^{34} -6.25733e10 q^{35} -2.23738e11 q^{36} -1.08171e12i q^{37} -4.82272e10 q^{38} +1.66085e12i q^{39} -6.55305e10i q^{40} -1.29165e12i q^{41} +2.94590e10 q^{42} -2.10835e12i q^{43} -7.49268e11i q^{44} -6.77847e11 q^{45} -2.50156e11i q^{46} +2.66518e12i q^{47} -4.89738e12i q^{48} -4.34779e12 q^{49} +2.09713e11i q^{50} -4.80251e12 q^{51} -1.17834e13 q^{52} +2.79041e12 q^{53} -3.49419e11 q^{54} -2.27001e12i q^{55} +4.18667e11i q^{56} -2.19422e13 q^{57} +(4.42683e11 + 8.29281e11i) q^{58} -2.26657e13 q^{59} -1.48841e13i q^{60} +1.11295e13i q^{61} +1.83174e12 q^{62} +4.33069e12 q^{63} +3.45263e13 q^{64} -3.56994e13 q^{65} +1.06871e12i q^{66} -1.28184e13 q^{67} -3.40728e13i q^{68} -1.13815e14i q^{69} +6.33213e11i q^{70} +2.16100e13 q^{71} +4.53536e12i q^{72} +5.22494e13i q^{73} -1.09464e13 q^{74} +9.54143e13i q^{75} -1.55676e14i q^{76} +1.45029e13i q^{77} +1.68070e13 q^{78} +1.17471e14i q^{79} +1.05268e14 q^{80} -2.57258e14 q^{81} -1.30709e13 q^{82} +1.31752e14 q^{83} +9.50929e13i q^{84} -1.03228e14i q^{85} -2.13356e13 q^{86} +(2.01410e14 + 3.77303e14i) q^{87} -1.51883e13 q^{88} +7.95016e14i q^{89} +6.85951e12i q^{90} +2.28080e14 q^{91} +8.07497e14 q^{92} +8.33398e14 q^{93} +2.69705e13 q^{94} -4.71642e14i q^{95} -1.49458e14 q^{96} +3.46892e14i q^{97} +4.39977e13i q^{98} +1.57107e14i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 508108 q^{4} + 470082 q^{5} + 1112016 q^{6} - 4820620 q^{7} - 167460710 q^{9}+O(q^{10}) $ 36 * q - 508108 * q^4 + 470082 * q^5 + 1112016 * q^6 - 4820620 * q^7 - 167460710 * q^9	\( 36 q - 508108 q^{4} + 470082 q^{5} + 1112016 q^{6} - 4820620 q^{7} - 167460710 q^{9} + 133305618 q^{13} + 5626041364 q^{16} - 30737731548 q^{20} - 51638088984 q^{22} - 23459433564 q^{23} - 13473060100 q^{24} + 169887741474 q^{25} + 281303298768 q^{28} - 85550328684 q^{29} - 681215606256 q^{30} + 831111242422 q^{33} - 449988200584 q^{34} + 726838987044 q^{35} + 1809260484664 q^{36} - 2518300733088 q^{38} - 5363921425320 q^{42} - 16561773855556 q^{45} + 29824615981340 q^{49} + 1184881612900 q^{51} + 21527128606228 q^{52} - 40200435711486 q^{53} + 9043904345168 q^{54} + 42099004809572 q^{57} - 3461494533632 q^{58} - 50458797940572 q^{59} - 298531808710416 q^{62} + 159779590145904 q^{63} - 71569159267548 q^{64} + 92095395748902 q^{65} + 130146715692752 q^{67} - 178710878083152 q^{71} - 205323946615296 q^{74} + 13818320315976 q^{78} + 857820862108188 q^{80} + 126746036597568 q^{81} + 249211917251112 q^{82} - 541736282848188 q^{83} + 630538772195064 q^{86} - 633552108095260 q^{87} + 969723837884556 q^{88} - 962583563732444 q^{91} + 22\!\cdots\!64 q^{92}+ \cdots + 40\!\cdots\!64 q^{96}+O(q^{100}) \) 36 * q - 508108 * q^4 + 470082 * q^5 + 1112016 * q^6 - 4820620 * q^7 - 167460710 * q^9 + 133305618 * q^13 + 5626041364 * q^16 - 30737731548 * q^20 - 51638088984 * q^22 - 23459433564 * q^23 - 13473060100 * q^24 + 169887741474 * q^25 + 281303298768 * q^28 - 85550328684 * q^29 - 681215606256 * q^30 + 831111242422 * q^33 - 449988200584 * q^34 + 726838987044 * q^35 + 1809260484664 * q^36 - 2518300733088 * q^38 - 5363921425320 * q^42 - 16561773855556 * q^45 + 29824615981340 * q^49 + 1184881612900 * q^51 + 21527128606228 * q^52 - 40200435711486 * q^53 + 9043904345168 * q^54 + 42099004809572 * q^57 - 3461494533632 * q^58 - 50458797940572 * q^59 - 298531808710416 * q^62 + 159779590145904 * q^63 - 71569159267548 * q^64 + 92095395748902 * q^65 + 130146715692752 * q^67 - 178710878083152 * q^71 - 205323946615296 * q^74 + 13818320315976 * q^78 + 857820862108188 * q^80 + 126746036597568 * q^81 + 249211917251112 * q^82 - 541736282848188 * q^83 + 630538772195064 * q^86 - 633552108095260 * q^87 + 969723837884556 * q^88 - 962583563732444 * q^91 + 2248076163071664 * q^92 - 212103831463414 * q^93 - 5356847193577464 * q^94 + 4021088569901964 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	10.1196i		−	0.0559032i	−0.999609	−	0.0279516i	$-0.991102\pi$
$2$		−	10.1196i		−	0.0559032i	0.999609	−	0.0279516i	$-0.00889842\pi$
$3$		−	4604.16i		−	1.21546i	−0.794144	−	0.607730i	$-0.792080\pi$
$3$		−	4604.16i		−	1.21546i	0.794144	−	0.607730i	$-0.207920\pi$
$4$	32665.6			0.996875
$5$	98965.0			0.566509			0.283254	−	0.959045i	$-0.408586\pi$
$5$	98965.0			0.566509			0.283254	+	0.959045i	$0.408586\pi$
$6$	−46592.0			−0.0679481
$7$	−632277.			−0.290183			−0.145091	−	0.989418i	$-0.546348\pi$
$7$	−632277.			−0.290183			−0.145091	+	0.989418i	$0.546348\pi$
$8$		−	662159.i		−	0.111632i
$9$	−6.84936e6			−0.477344
$10$		−	1.00148e6i		−	0.0316696i
$11$		−	2.29375e7i		−	0.354896i	−0.984130	−	0.177448i	$-0.943216\pi$
$11$		−	2.29375e7i		−	0.354896i	0.984130	−	0.177448i	$-0.0567842\pi$
$12$		−	1.50398e8i		−	1.21166i
$13$	−3.60728e8			−1.59443			−0.797213	−	0.603698i	$-0.793693\pi$
$13$	−3.60728e8			−1.59443			−0.797213	+	0.603698i	$0.793693\pi$
$14$			6.39836e6i			0.0162221i
$15$		−	4.55651e8i		−	0.688569i
$16$	1.06369e9			0.990634
$17$		−	1.04308e9i		−	0.616525i	−0.951301	−	0.308263i	$-0.900252\pi$
$17$		−	1.04308e9i		−	0.616525i	0.951301	−	0.308263i	$-0.0997476\pi$
$18$			6.93124e7i			0.0266850i
$19$		−	4.76574e9i		−	1.22315i	−0.791188	−	0.611573i	$-0.790537\pi$
$19$		−	4.76574e9i		−	1.22315i	0.791188	−	0.611573i	$-0.209463\pi$
$20$	3.23275e9			0.564738
$21$			2.91110e9i			0.352706i
$22$	−2.32118e8			−0.0198398
$23$	2.47201e10			1.51388			0.756940	−	0.653484i	$-0.226693\pi$
$23$	2.47201e10			1.51388			0.756940	+	0.653484i	$0.226693\pi$
$24$	−3.04868e9			−0.135684
$25$	−2.07235e10			−0.679068
$26$			3.65040e9i			0.0891334i
$27$		−	3.45291e10i		−	0.635268i
$28$	−2.06537e10			−0.289276
$29$	−8.19484e10	+	4.37454e10i	−0.882176	+	0.470920i
$29$	−8.19484e10	+	4.37454e10i	−0.882176	+	0.470920i
$30$	−4.61098e9			−0.0384932
$31$			1.81010e11i			1.18165i	0.806799	+	0.590826i	$0.201198\pi$
$31$			1.81010e11i			1.18165i	−0.806799	+	0.590826i	$0.798802\pi$
$32$		−	3.24616e10i		−	0.167011i
$33$	−1.05608e11			−0.431363
$34$	−1.05555e10			−0.0344657
$35$	−6.25733e10			−0.164391
$36$	−2.23738e11			−0.475852
$37$		−	1.08171e12i		−	1.87325i	−0.350331	−	0.936626i	$-0.613931\pi$
$37$		−	1.08171e12i		−	1.87325i	0.350331	−	0.936626i	$-0.386069\pi$
$38$	−4.82272e10			−0.0683777
$39$			1.66085e12i			1.93796i
$40$		−	6.55305e10i		−	0.0632403i
$41$		−	1.29165e12i		−	1.03578i	−0.855448	−	0.517889i	$-0.826718\pi$
$41$		−	1.29165e12i		−	1.03578i	0.855448	−	0.517889i	$-0.173282\pi$
$42$	2.94590e10			0.0197174
$43$		−	2.10835e12i		−	1.18285i	−0.806360	−	0.591425i	$-0.798566\pi$
$43$		−	2.10835e12i		−	1.18285i	0.806360	−	0.591425i	$-0.201434\pi$
$44$		−	7.49268e11i		−	0.353787i
$45$	−6.77847e11			−0.270419
$46$		−	2.50156e11i		−	0.0846307i
$47$			2.66518e12i			0.767349i	0.923468	+	0.383675i	$0.125342\pi$
$47$			2.66518e12i			0.767349i	−0.923468	+	0.383675i	$0.874658\pi$
$48$		−	4.89738e12i		−	1.20408i
$49$	−4.34779e12			−0.915794
$50$			2.09713e11i			0.0379620i
$51$	−4.80251e12			−0.749362
$52$	−1.17834e13			−1.58944
$53$	2.79041e12			0.326287			0.163143	−	0.986602i	$-0.447837\pi$
$53$	2.79041e12			0.326287			0.163143	+	0.986602i	$0.447837\pi$
$54$	−3.49419e11			−0.0355135
$55$		−	2.27001e12i		−	0.201052i
$56$			4.18667e11i			0.0323936i
$57$	−2.19422e13			−1.48669
$58$	4.42683e11	+	8.29281e11i	0.0263259	+	0.0493164i
$59$	−2.26657e13			−1.18571			−0.592855	−	0.805309i	$-0.701999\pi$
$59$	−2.26657e13			−1.18571			−0.592855	+	0.805309i	$0.701999\pi$
$60$		−	1.48841e13i		−	0.686417i
$61$			1.11295e13i			0.453421i	0.973962	+	0.226710i	$0.0727971\pi$
$61$			1.11295e13i			0.453421i	−0.973962	+	0.226710i	$0.927203\pi$
$62$	1.83174e12			0.0660580
$63$	4.33069e12			0.138517
$64$	3.45263e13			0.981298
$65$	−3.56994e13			−0.903256
$66$			1.06871e12i			0.0241145i
$67$	−1.28184e13			−0.258388			−0.129194	−	0.991619i	$-0.541239\pi$
$67$	−1.28184e13			−0.258388			−0.129194	+	0.991619i	$0.541239\pi$
$68$		−	3.40728e13i		−	0.614599i
$69$		−	1.13815e14i		−	1.84006i
$70$			6.33213e11i			0.00918999i
$71$	2.16100e13			0.281980			0.140990	−	0.990011i	$-0.454971\pi$
$71$	2.16100e13			0.281980			0.140990	+	0.990011i	$0.454971\pi$
$72$			4.53536e12i			0.0532866i
$73$			5.22494e13i			0.553554i	0.960934	+	0.276777i	$0.0892664\pi$
$73$			5.22494e13i			0.553554i	−0.960934	+	0.276777i	$0.910734\pi$
$74$	−1.09464e13			−0.104721
$75$			9.54143e13i			0.825380i
$76$		−	1.55676e14i		−	1.21932i
$77$			1.45029e13i			0.102985i
$78$	1.68070e13			0.108338
$79$			1.17471e14i			0.688220i	0.938929	+	0.344110i	$0.111819\pi$
$79$			1.17471e14i			0.688220i	−0.938929	+	0.344110i	$0.888181\pi$
$80$	1.05268e14			0.561203
$81$	−2.57258e14			−1.24949
$82$	−1.30709e13			−0.0579033
$83$	1.31752e14			0.532934			0.266467	−	0.963844i	$-0.414144\pi$
$83$	1.31752e14			0.532934			0.266467	+	0.963844i	$0.414144\pi$
$84$			9.50929e13i			0.351604i
$85$		−	1.03228e14i		−	0.349267i
$86$	−2.13356e13			−0.0661250
$87$	2.01410e14	+	3.77303e14i	0.572384	+	1.07225i
$88$	−1.51883e13			−0.0396177
$89$			7.95016e14i			1.90524i	0.304156	+	0.952622i	$0.401626\pi$
$89$			7.95016e14i			1.90524i	−0.304156	+	0.952622i	$0.598374\pi$
$90$			6.85951e12i			0.0151173i
$91$	2.28080e14			0.462675
$92$	8.07497e14			1.50915
$93$	8.33398e14			1.43625
$94$	2.69705e13			0.0428972
$95$		−	4.71642e14i		−	0.692923i
$96$	−1.49458e14			−0.202995
$97$			3.46892e14i			0.435920i	0.975958	+	0.217960i	$0.0699402\pi$
$97$			3.46892e14i			0.435920i	−0.975958	+	0.217960i	$0.930060\pi$
$98$			4.39977e13i			0.0511958i
$99$			1.57107e14i			0.169408i
$100$	−6.76946e14			−0.676946
$101$		−	1.77795e15i		−	1.65010i	−0.565059	−	0.825050i	$-0.691147\pi$
$101$		−	1.77795e15i		−	1.65010i	0.565059	−	0.825050i	$-0.308853\pi$
$102$			4.85992e13i			0.0418917i
$103$	1.21845e15			0.976175			0.488088	−	0.872795i	$-0.337695\pi$
$103$	1.21845e15			0.976175			0.488088	+	0.872795i	$0.337695\pi$
$104$			2.38859e14i			0.177988i
$105$			2.88097e14i			0.199811i
$106$		−	2.82377e13i		−	0.0182405i
$107$	2.32426e14			0.139928			0.0699642	−	0.997550i	$-0.477712\pi$
$107$	2.32426e14			0.139928			0.0699642	+	0.997550i	$0.477712\pi$
$108$		−	1.12791e15i		−	0.633283i
$109$	1.93980e15			1.01639			0.508193	−	0.861243i	$-0.330314\pi$
$109$	1.93980e15			1.01639			0.508193	+	0.861243i	$0.330314\pi$
$110$	−2.29715e13			−0.0112394
$111$	−4.98034e15			−2.27686
$112$	−6.72544e14			−0.287465
$113$			1.33531e15i			0.533943i	0.963704	+	0.266972i	$0.0860230\pi$
$113$			1.33531e15i			0.533943i	−0.963704	+	0.266972i	$0.913977\pi$
$114$			2.22045e14i			0.0831104i
$115$	2.44643e15			0.857627
$116$	−2.67689e15	+	1.42897e15i	−0.879419	+	0.469448i
$117$	2.47075e15			0.761089
$118$			2.29366e14i			0.0662849i
$119$			6.59516e14i			0.178905i
$120$	−3.01713e14			−0.0768660
$121$	3.65112e15			0.874048
$122$	1.12625e14			0.0253476
$123$	−5.94697e15			−1.25895
$124$			5.91279e15i			1.17796i
$125$	−5.07107e15			−0.951207
$126$		−	4.38246e13i		−	0.00774354i
$127$		−	7.51956e15i		−	1.25217i	−0.779753	−	0.626087i	$-0.784656\pi$
$127$		−	7.51956e15i		−	1.25217i	0.779753	−	0.626087i	$-0.215344\pi$
$128$		−	1.41309e15i		−	0.221869i
$129$	−9.70718e15			−1.43771
$130$			3.61262e14i			0.0504949i
$131$		−	1.21212e16i		−	1.59960i	−0.600264	−	0.799802i	$-0.704938\pi$
$131$		−	1.21212e16i		−	1.59960i	0.600264	−	0.799802i	$-0.295062\pi$
$132$	−3.44975e15			−0.430014
$133$			3.01327e15i			0.354936i
$134$			1.29716e14i			0.0144447i
$135$		−	3.41717e15i		−	0.359885i
$136$	−6.90685e14			−0.0688237
$137$		−	1.52785e16i		−	1.44104i	−0.693432	−	0.720522i	$-0.743902\pi$
$137$		−	1.52785e16i		−	1.44104i	0.693432	−	0.720522i	$-0.256098\pi$
$138$	−1.15176e15			−0.102865
$139$	−5.66800e15			−0.479534			−0.239767	−	0.970831i	$-0.577071\pi$
$139$	−5.66800e15			−0.479534			−0.239767	+	0.970831i	$0.577071\pi$
$140$	−2.04399e15			−0.163877
$141$	1.22709e16			0.932683
$142$		−	2.18684e14i		−	0.0157636i
$143$			8.27421e15i			0.565856i
$144$	−7.28556e15			−0.472873
$145$	−8.11002e15	+	4.32926e15i	−0.499760	+	0.266780i
$146$	5.28741e14			0.0309454
$147$			2.00179e16i			1.11311i
$148$		−	3.53346e16i		−	1.86740i
$149$	2.12500e16			1.06773			0.533865	−	0.845570i	$-0.320739\pi$
$149$	2.12500e16			1.06773			0.533865	+	0.845570i	$0.320739\pi$
$150$	9.65550e14			0.0461413
$151$	3.12874e16			1.42247			0.711233	−	0.702956i	$-0.248137\pi$
$151$	3.12874e16			1.42247			0.711233	+	0.702956i	$0.248137\pi$
$152$	−3.15568e15			−0.136542
$153$			7.14443e15i			0.294294i
$154$	1.46763e14			0.00575718
$155$			1.79136e16i			0.669416i
$156$			5.42526e16i			1.93191i
$157$			2.23841e16i			0.759787i	0.925030	+	0.379894i	$0.124039\pi$
$157$			2.23841e16i			0.759787i	−0.925030	+	0.379894i	$0.875961\pi$
$158$	1.18875e15			0.0384737
$159$		−	1.28475e16i		−	0.396589i
$160$		−	3.21257e15i		−	0.0946133i
$161$	−1.56299e16			−0.439302
$162$			2.60334e15i			0.0698502i
$163$			2.25776e16i			0.578456i	0.957260	+	0.289228i	$0.0933986\pi$
$163$			2.25776e16i			0.578456i	−0.957260	+	0.289228i	$0.906601\pi$
$164$		−	4.21926e16i		−	1.03254i
$165$	−1.04515e16			−0.244371
$166$		−	1.33328e15i		−	0.0297927i
$167$	−1.94925e16			−0.416384			−0.208192	−	0.978088i	$-0.566758\pi$
$167$	−1.94925e16			−0.416384			−0.208192	+	0.978088i	$0.566758\pi$
$168$	1.92761e15			0.0393731
$169$	7.89386e16			1.54219
$170$	−1.04463e15			−0.0195251
$171$			3.26423e16i			0.583861i
$172$		−	6.88706e16i		−	1.17915i
$173$	4.48461e16			0.735155			0.367578	−	0.929993i	$-0.380187\pi$
$173$	4.48461e16			0.735155			0.367578	+	0.929993i	$0.380187\pi$
$174$	3.81814e15	−	2.03818e15i	0.0599421	−	0.0319981i
$175$	1.31030e16			0.197054
$176$		−	2.43983e16i		−	0.351573i
$177$			1.04356e17i			1.44118i
$178$	8.04520e15			0.106509
$179$	7.85345e15			0.0996926			0.0498463	−	0.998757i	$-0.484127\pi$
$179$	7.85345e15			0.0996926			0.0498463	+	0.998757i	$0.484127\pi$
$180$	−2.21423e16			−0.269574
$181$	9.49927e16			1.10943			0.554716	−	0.832040i	$-0.312827\pi$
$181$	9.49927e16			1.10943			0.554716	+	0.832040i	$0.312827\pi$
$182$		−	2.30806e15i		−	0.0258650i
$183$	5.12419e16			0.551115
$184$		−	1.63686e16i		−	0.168997i
$185$		−	1.07051e17i		−	1.06121i
$186$		−	8.43361e15i		−	0.0802909i
$187$	−2.39257e16			−0.218803
$188$			8.70598e16i			0.764951i
$189$			2.18319e16i			0.184344i
$190$	−4.77280e15			−0.0387366
$191$			8.35970e15i			0.0652290i	0.999468	+	0.0326145i	$0.0103834\pi$
$191$			8.35970e15i			0.0652290i	−0.999468	+	0.0326145i	$0.989617\pi$
$192$		−	1.58965e17i		−	1.19273i
$193$			4.50001e16i			0.324738i	0.986730	+	0.162369i	$0.0519135\pi$
$193$			4.50001e16i			0.324738i	−0.986730	+	0.162369i	$0.948086\pi$
$194$	3.51039e15			0.0243693
$195$			1.64366e17i			1.09787i
$196$	−1.42023e17			−0.912932
$197$	5.27797e16			0.326566			0.163283	−	0.986579i	$-0.447792\pi$
$197$	5.27797e16			0.326566			0.163283	+	0.986579i	$0.447792\pi$
$198$	1.58986e15			0.00947042
$199$	−2.56971e17			−1.47396			−0.736982	−	0.675912i	$-0.763750\pi$
$199$	−2.56971e17			−1.47396			−0.736982	+	0.675912i	$0.763750\pi$
$200$			1.37222e16i			0.0758054i
$201$			5.90178e16i			0.314060i
$202$	−1.79921e16			−0.0922458
$203$	5.18140e16	−	2.76592e16i	0.255992	−	0.136653i
$204$	−1.56877e17			−0.747020
$205$		−	1.27828e17i		−	0.586778i
$206$		−	1.23301e16i		−	0.0545713i
$207$	−1.69317e17			−0.722641
$208$	−3.83701e17			−1.57949
$209$	−1.09314e17			−0.434090
$210$	2.91541e15			0.0111701
$211$		−	1.85294e17i		−	0.685082i	−0.939503	−	0.342541i	$-0.888712\pi$
$211$		−	1.85294e17i		−	0.685082i	0.939503	−	0.342541i	$-0.111288\pi$
$212$	9.11505e16			0.325267
$213$		−	9.94961e16i		−	0.342735i
$214$		−	2.35204e15i		−	0.00782243i
$215$		−	2.08653e17i		−	0.670095i
$216$	−2.28637e16			−0.0709160
$217$		−	1.14448e17i		−	0.342895i
$218$		−	1.96299e16i		−	0.0568192i
$219$	2.40565e17			0.672823
$220$		−	7.41514e16i		−	0.200424i
$221$			3.76268e17i			0.983004i
$222$			5.03988e16i			0.127284i
$223$	3.99375e17			0.975202			0.487601	−	0.873066i	$-0.337872\pi$
$223$	3.99375e17			0.975202			0.487601	+	0.873066i	$0.337872\pi$
$224$			2.05247e16i			0.0484638i
$225$	1.41943e17			0.324149
$226$	1.35128e16			0.0298491
$227$	1.19538e17			0.255453			0.127726	−	0.991809i	$-0.459232\pi$
$227$	1.19538e17			0.255453			0.127726	+	0.991809i	$0.459232\pi$
$228$	−7.16756e17			−1.48204
$229$		−	6.85655e17i		−	1.37195i	−0.727623	−	0.685977i	$-0.759375\pi$
$229$		−	6.85655e17i		−	1.37195i	0.727623	−	0.685977i	$-0.240625\pi$
$230$		−	2.47567e16i		−	0.0479440i
$231$	6.67735e16			0.125174
$232$	2.89664e16	+	5.42628e16i	0.0525695	+	0.0984787i
$233$	7.01570e17			1.23282			0.616412	−	0.787424i	$-0.288585\pi$
$233$	7.01570e17			1.23282			0.616412	+	0.787424i	$0.288585\pi$
$234$		−	2.50029e16i		−	0.0425473i
$235$			2.63760e17i			0.434710i
$236$	−7.40388e17			−1.18200
$237$	5.40855e17			0.836504
$238$	6.67400e15			0.0100014
$239$	−7.69920e16			−0.111805			−0.0559025	−	0.998436i	$-0.517804\pi$
$239$	−7.69920e16			−0.111805			−0.0559025	+	0.998436i	$0.517804\pi$
$240$		−	4.84669e17i		−	0.682120i
$241$	−3.81931e16			−0.0521023			−0.0260511	−	0.999661i	$-0.508293\pi$
$241$	−3.81931e16			−0.0521023			−0.0260511	+	0.999661i	$0.508293\pi$
$242$		−	3.69477e16i		−	0.0488621i
$243$			6.89003e17i			0.883433i
$244$			3.63551e17i			0.452004i
$245$	−4.30279e17			−0.518805
$246$			6.01807e16i			0.0703791i
$247$			1.71913e18i			1.95022i
$248$	1.19857e17			0.131910
$249$		−	6.06609e17i		−	0.647760i
$250$			5.13170e16i			0.0531755i
$251$			9.76130e17i			0.981646i	0.871259	+	0.490823i	$0.163304\pi$
$251$			9.76130e17i			0.981646i	−0.871259	+	0.490823i	$0.836696\pi$
$252$	1.41465e17			0.138084
$253$		−	5.67018e17i		−	0.537271i
$254$	−7.60946e16			−0.0700004
$255$	−4.75280e17			−0.424520
$256$	1.11706e18			0.968895
$257$	2.16354e18			1.82249			0.911247	−	0.411860i	$-0.135121\pi$
$257$	2.16354e18			1.82249			0.911247	+	0.411860i	$0.135121\pi$
$258$			9.82323e16i			0.0803724i
$259$			6.83937e17i			0.543586i
$260$	−1.16614e18			−0.900434
$261$	5.61294e17	−	2.99628e17i	0.421101	−	0.224791i
$262$	−1.22662e17			−0.0894229
$263$		−	7.57691e17i		−	0.536814i	−0.963306	−	0.268407i	$-0.913503\pi$
$263$		−	7.57691e17i		−	0.536814i	0.963306	−	0.268407i	$-0.0864972\pi$
$264$			6.99293e16i			0.0481537i
$265$	2.76153e17			0.184844
$266$	3.04929e16			0.0198420
$267$	3.66038e18			2.31575
$268$	−4.18720e17			−0.257580
$269$			2.80037e18i			1.67522i	0.546265	+	0.837612i	$0.316049\pi$
$269$			2.80037e18i			1.67522i	−0.546265	+	0.837612i	$0.683951\pi$
$270$	−3.45803e16			−0.0201187
$271$			6.01124e17i			0.340169i	0.985430	+	0.170084i	$0.0544040\pi$
$271$			6.01124e17i			0.340169i	−0.985430	+	0.170084i	$0.945596\pi$
$272$		−	1.10951e18i		−	0.610751i
$273$		−	1.05012e18i		−	0.562363i
$274$	−1.54612e17			−0.0805589
$275$			4.75346e17i			0.240999i
$276$		−	3.71784e18i		−	1.83431i
$277$	−7.69615e17			−0.369552			−0.184776	−	0.982781i	$-0.559156\pi$
$277$	−7.69615e17			−0.369552			−0.184776	+	0.982781i	$0.559156\pi$
$278$			5.73577e16i			0.0268074i
$279$		−	1.23980e18i		−	0.564054i
$280$			4.14334e16i			0.0183513i
$281$	−2.91303e18			−1.25617			−0.628084	−	0.778146i	$-0.716160\pi$
$281$	−2.91303e18			−1.25617			−0.628084	+	0.778146i	$0.716160\pi$
$282$		−	1.24176e17i		−	0.0521399i
$283$	1.46768e18			0.600113			0.300057	−	0.953921i	$-0.402994\pi$
$283$	1.46768e18			0.600113			0.300057	+	0.953921i	$0.402994\pi$
$284$	7.05905e17			0.281099
$285$	−2.17151e18			−0.842220
$286$	8.37313e16			0.0316331
$287$			8.16682e17i			0.300565i
$288$			2.22341e17i			0.0797217i
$289$	1.77441e18			0.619897
$290$	4.38102e16	+	8.20698e16i	0.0149139	+	0.0279382i
$291$	1.59715e18			0.529843
$292$			1.70676e18i			0.551824i
$293$		−	2.99945e18i		−	0.945223i	−0.881271	−	0.472611i	$-0.843311\pi$
$293$		−	2.99945e18i		−	0.945223i	0.881271	−	0.472611i	$-0.156689\pi$
$294$	2.02572e17			0.0622264
$295$	−2.24311e18			−0.671715
$296$	−7.16261e17			−0.209114
$297$	−7.92013e17			−0.225454
$298$		−	2.15040e17i		−	0.0596895i
$299$	−8.91723e18			−2.41377
$300$			3.11676e18i			0.822800i
$301$			1.33306e18i			0.343243i
$302$		−	3.16614e17i		−	0.0795204i
$303$	−8.18598e18			−2.00563
$304$		−	5.06925e18i		−	1.21169i
$305$			1.10143e18i			0.256867i
$306$	7.22985e16			0.0164520
$307$			6.52587e18i			1.44911i	0.689218	+	0.724554i	$0.257954\pi$
$307$			6.52587e18i			1.44911i	−0.689218	+	0.724554i	$0.742046\pi$
$308$			4.73745e17i			0.102663i
$309$		−	5.60993e18i		−	1.18650i
$310$	1.81278e17			0.0374225
$311$			8.48989e17i			0.171080i	0.996335	+	0.0855400i	$0.0272615\pi$
$311$			8.48989e17i			0.171080i	−0.996335	+	0.0855400i	$0.972738\pi$
$312$	1.09974e18			0.216338
$313$	5.08132e18			0.975875			0.487938	−	0.872879i	$-0.337749\pi$
$313$	5.08132e18			0.975875			0.487938	+	0.872879i	$0.337749\pi$
$314$	2.26517e17			0.0424745
$315$	4.28587e17			0.0784711
$316$			3.83726e18i			0.686070i
$317$		−	8.78395e18i		−	1.53372i	−0.641816	−	0.766859i	$-0.721819\pi$
$317$		−	8.78395e18i		−	1.53372i	0.641816	−	0.766859i	$-0.278181\pi$
$318$	−1.30011e17			−0.0221706
$319$	1.00341e18	+	1.87969e18i	0.167128	+	0.313081i
$320$	3.41690e18			0.555914
$321$		−	1.07012e18i		−	0.170077i
$322$			1.58168e17i			0.0245584i
$323$	−4.97105e18			−0.754101
$324$	−8.40349e18			−1.24558
$325$	7.47554e18			1.08272
$326$	2.28475e17			0.0323375
$327$		−	8.93116e18i		−	1.23538i
$328$	−8.55279e17			−0.115626
$329$		−	1.68513e18i		−	0.222672i
$330$			1.05765e17i			0.0136611i
$331$			1.80252e18i			0.227599i	0.993504	+	0.113799i	$0.0363021\pi$
$331$			1.80252e18i			0.227599i	−0.993504	+	0.113799i	$0.963698\pi$
$332$	4.30377e18			0.531268
$333$			7.40899e18i			0.894185i
$334$			1.97256e17i			0.0232772i
$335$	−1.26857e18			−0.146379
$336$			3.09650e18i			0.349403i
$337$		−	6.62866e18i		−	0.731479i	−0.930717	−	0.365739i	$-0.880816\pi$
$337$		−	6.62866e18i		−	0.731479i	0.930717	−	0.365739i	$-0.119184\pi$
$338$		−	7.98823e17i		−	0.0862135i
$339$	6.14800e18			0.648987
$340$		−	3.37202e18i		−	0.348175i
$341$	4.15192e18			0.419364
$342$	3.30325e17			0.0326397
$343$	5.75078e18			0.555931
$344$	−1.39606e18			−0.132043
$345$		−	1.12637e19i		−	1.04241i
$346$		−	4.53823e17i		−	0.0410975i
$347$	−1.95830e18			−0.173544			−0.0867718	−	0.996228i	$-0.527655\pi$
$347$	−1.95830e18			−0.173544			−0.0867718	+	0.996228i	$0.527655\pi$
$348$	6.57919e18	+	1.23248e19i	0.570595	+	1.06890i
$349$	5.33974e18			0.453242			0.226621	−	0.973983i	$-0.427232\pi$
$349$	5.33974e18			0.453242			0.226621	+	0.973983i	$0.427232\pi$
$350$		−	1.32596e17i		−	0.0110159i
$351$			1.24556e19i			1.01289i
$352$	−7.44590e17			−0.0592717
$353$	−1.34692e19			−1.04962			−0.524808	−	0.851221i	$-0.675863\pi$
$353$	−1.34692e19			−1.04962			−0.524808	+	0.851221i	$0.675863\pi$
$354$	1.05604e18			0.0805667
$355$	2.13864e18			0.159744
$356$			2.59697e19i			1.89929i
$357$	3.03651e18			0.217452
$358$		−	7.94734e16i		−	0.00557313i
$359$			3.34908e18i			0.229994i	0.993366	+	0.114997i	$0.0366859\pi$
$359$			3.34908e18i			0.229994i	−0.993366	+	0.114997i	$0.963314\pi$
$360$			4.48842e17i			0.0301873i
$361$	−7.53115e18			−0.496087
$362$		−	9.61283e17i		−	0.0620207i
$363$		−	1.68103e19i		−	1.06237i
$364$	7.45036e18			0.461229
$365$			5.17087e18i			0.313593i
$366$		−	5.18545e17i		−	0.0308091i
$367$			2.27810e19i			1.32610i	0.748574	+	0.663051i	$0.230739\pi$
$367$			2.27810e19i			1.32610i	−0.748574	+	0.663051i	$0.769261\pi$
$368$	2.62944e19			1.49970
$369$			8.84699e18i			0.494422i
$370$	−1.08331e18			−0.0593252
$371$	−1.76431e18			−0.0946829
$372$	2.72234e19			1.43176
$373$	−1.33331e19			−0.687251			−0.343625	−	0.939107i	$-0.611655\pi$
$373$	−1.33331e19			−0.687251			−0.343625	+	0.939107i	$0.611655\pi$
$374$			2.42117e17i			0.0122318i
$375$			2.33480e19i			1.15615i
$376$	1.76477e18			0.0856604
$377$	2.95610e19	−	1.57802e19i	1.40656	−	0.750847i
$378$	2.20929e17			0.0103054
$379$		−	2.40118e19i		−	1.09807i	−0.835799	−	0.549035i	$-0.814995\pi$
$379$		−	2.40118e19i		−	1.09807i	0.835799	−	0.549035i	$-0.185005\pi$
$380$		−	1.54065e19i		−	0.690758i
$381$	−3.46212e19			−1.52197
$382$	8.45964e16			0.00364650
$383$	6.82590e18			0.288516			0.144258	−	0.989540i	$-0.453921\pi$
$383$	6.82590e18			0.288516			0.144258	+	0.989540i	$0.453921\pi$
$384$	−6.50611e18			−0.269673
$385$			1.43528e18i			0.0583419i
$386$	4.55381e17			0.0181539
$387$			1.44409e19i			0.564626i
$388$			1.13314e19i			0.434557i
$389$		−	3.83636e19i		−	1.44310i	−0.692360	−	0.721552i	$-0.743429\pi$
$389$		−	3.83636e19i		−	1.44310i	0.692360	−	0.721552i	$-0.256571\pi$
$390$	1.66331e18			0.0613745
$391$		−	2.57851e19i		−	0.933346i
$392$			2.87893e18i			0.102232i
$393$	−5.58081e19			−1.94425
$394$		−	5.34107e17i		−	0.0182561i
$395$			1.16255e19i			0.389883i
$396$			5.13201e18i			0.168878i
$397$	3.21164e19			1.03705			0.518523	−	0.855063i	$-0.326482\pi$
$397$	3.21164e19			1.03705			0.518523	+	0.855063i	$0.326482\pi$
$398$			2.60044e18i			0.0823992i
$399$	1.38736e19			0.431411
$400$	−2.20433e19			−0.672708
$401$	−1.04029e19			−0.311582			−0.155791	−	0.987790i	$-0.549793\pi$
$401$	−1.04029e19			−0.311582			−0.155791	+	0.987790i	$0.549793\pi$
$402$	5.97233e17			0.0175569
$403$		−	6.52953e19i		−	1.88406i
$404$		−	5.80780e19i		−	1.64494i
$405$	−2.54596e19			−0.707845
$406$	−2.79898e17	−	5.24335e17i	−0.00763933	−	0.0143108i
$407$	−2.48117e19			−0.664810
$408$			3.18002e18i			0.0836525i
$409$			4.23181e19i			1.09295i	0.837475	+	0.546476i	$0.184031\pi$
$409$			4.23181e19i			1.09295i	−0.837475	+	0.546476i	$0.815969\pi$
$410$	−1.29357e18			−0.0328027
$411$	−7.03448e19			−1.75153
$412$	3.98013e19			0.973125
$413$	1.43310e19			0.344073
$414$			1.71341e18i			0.0403979i
$415$	1.30389e19			0.301912
$416$			1.17098e19i			0.266287i
$417$			2.60964e19i			0.582854i
$418$			1.10621e18i			0.0242670i
$419$	−7.32807e19			−1.57901			−0.789504	−	0.613746i	$-0.789662\pi$
$419$	−7.32807e19			−1.57901			−0.789504	+	0.613746i	$0.789662\pi$
$420$			9.41087e18i			0.199187i
$421$			7.50338e19i			1.56006i	0.625742	+	0.780030i	$0.284796\pi$
$421$			7.50338e19i			1.56006i	−0.625742	+	0.780030i	$0.715204\pi$
$422$	−1.87509e18			−0.0382982
$423$		−	1.82548e19i		−	0.366289i
$424$		−	1.84770e18i		−	0.0364239i
$425$			2.16163e19i			0.418662i
$426$	−1.00686e18			−0.0191600
$427$		−	7.03692e18i		−	0.131575i
$428$	7.59232e18			0.139491
$429$	3.80957e19			0.687776
$430$	−2.11148e18			−0.0374604
$431$	−7.53515e19			−1.31375			−0.656875	−	0.754000i	$-0.728122\pi$
$431$	−7.53515e19			−1.31375			−0.656875	+	0.754000i	$0.728122\pi$
$432$		−	3.67281e19i		−	0.629318i
$433$		−	5.20958e18i		−	0.0877291i	−0.999037	−	0.0438645i	$-0.986033\pi$
$433$		−	5.20958e18i		−	0.0877291i	0.999037	−	0.0438645i	$-0.0139670\pi$
$434$	−1.15817e18			−0.0191689
$435$	1.99326e19	+	3.73398e19i	0.324261	+	0.607439i
$436$	6.33648e19			1.01321
$437$		−	1.17810e20i		−	1.85170i
$438$		−	2.43441e18i		−	0.0376129i
$439$	7.34701e19			1.11590			0.557952	−	0.829873i	$-0.311587\pi$
$439$	7.34701e19			1.11590			0.557952	+	0.829873i	$0.311587\pi$
$440$	−1.50311e18			−0.0224438
$441$	2.97796e19			0.437148
$442$	3.80766e18			0.0549530
$443$			6.48166e19i			0.919725i	0.887990	+	0.459862i	$0.152101\pi$
$443$			6.48166e19i			0.919725i	−0.887990	+	0.459862i	$0.847899\pi$
$444$	−1.62686e20			−2.26975
$445$			7.86788e19i			1.07934i
$446$		−	4.04150e18i		−	0.0545169i
$447$		−	9.78383e19i		−	1.29778i
$448$	−2.18302e19			−0.284756
$449$			2.23926e19i			0.287248i	0.989632	+	0.143624i	$0.0458756\pi$
$449$			2.23926e19i			0.287248i	−0.989632	+	0.143624i	$0.954124\pi$
$450$		−	1.43640e18i		−	0.0181209i
$451$	−2.96273e19			−0.367594
$452$			4.36188e19i			0.532275i
$453$		−	1.44052e20i		−	1.72895i
$454$		−	1.20967e18i		−	0.0142806i
$455$	2.25719e19			0.262110
$456$			1.45292e19i			0.165961i
$457$	1.14115e20			1.28224			0.641121	−	0.767440i	$-0.278470\pi$
$457$	1.14115e20			1.28224			0.641121	+	0.767440i	$0.278470\pi$
$458$	−6.93852e18			−0.0766966
$459$	−3.60166e19			−0.391659
$460$	7.99139e19			0.854946
$461$			1.15515e19i			0.121585i	0.998150	+	0.0607926i	$0.0193628\pi$
$461$			1.15515e19i			0.121585i	−0.998150	+	0.0607926i	$0.980637\pi$
$462$		−	6.75718e17i		−	0.00699762i
$463$	1.12459e20			1.14587			0.572936	−	0.819600i	$-0.305804\pi$
$463$	1.12459e20			1.14587			0.572936	+	0.819600i	$0.305804\pi$
$464$	−8.71673e19	+	4.65313e19i	−0.873914	+	0.466509i
$465$	8.24772e19			0.813649
$466$		−	7.09957e18i		−	0.0689188i
$467$		−	7.81438e19i		−	0.746479i	−0.927735	−	0.373240i	$-0.878247\pi$
$467$		−	7.81438e19i		−	0.746479i	0.927735	−	0.373240i	$-0.121753\pi$
$468$	8.07086e19			0.758711
$469$	8.10476e18			0.0749797
$470$	2.66913e18			0.0243017
$471$	1.03060e20			0.923491
$472$			1.50083e19i			0.132363i
$473$	−4.83604e19			−0.419789
$474$		−	5.47321e18i		−	0.0467632i
$475$			9.87628e19i			0.830599i
$476$			2.15435e19i			0.178346i
$477$	−1.91126e19			−0.155751
$478$			7.79124e17i			0.00625025i
$479$		−	7.89022e19i		−	0.623122i	−0.950226	−	0.311561i	$-0.899148\pi$
$479$		−	7.89022e19i		−	0.623122i	0.950226	−	0.311561i	$-0.100852\pi$
$480$	−1.47912e19			−0.114999
$481$			3.90201e20i			2.98676i
$482$			3.86497e17i			0.00291268i
$483$			7.19627e19i			0.533954i
$484$	1.19266e20			0.871317
$485$			3.43302e19i			0.246952i
$486$	6.97240e18			0.0493867
$487$	8.30789e19			0.579460			0.289730	−	0.957108i	$-0.406434\pi$
$487$	8.30789e19			0.579460			0.289730	+	0.957108i	$0.406434\pi$
$488$	7.36949e18			0.0506161
$489$	1.03951e20			0.703090
$490$			4.35423e18i			0.0290028i
$491$		−	2.78515e20i		−	1.82700i	−0.406843	−	0.913498i	$-0.633370\pi$
$491$		−	2.78515e20i		−	1.82700i	0.406843	−	0.913498i	$-0.366630\pi$
$492$	−1.94261e20			−1.25501
$493$	4.56299e19	+	8.54787e19i	0.290334	+	0.543884i
$494$	1.73969e19			0.109023
$495$			1.55481e19i			0.0959709i
$496$			1.92538e20i			1.17058i
$497$	−1.36635e19			−0.0818258
$498$	−6.13861e18			−0.0362118
$499$	1.46752e20			0.852765			0.426383	−	0.904543i	$-0.359788\pi$
$499$	1.46752e20			0.852765			0.426383	+	0.904543i	$0.359788\pi$
$500$	−1.65650e20			−0.948234
$501$			8.97466e19i			0.506099i
$502$	9.87800e18			0.0548771
$503$			3.43361e20i			1.87928i	0.342168	+	0.939639i	$0.388839\pi$
$503$			3.43361e20i			1.87928i	−0.342168	+	0.939639i	$0.611161\pi$
$504$		−	2.86760e18i		−	0.0154629i
$505$		−	1.75955e20i		−	0.934797i
$506$	−5.73797e18			−0.0300351
$507$		−	3.63446e20i		−	1.87448i
$508$		−	2.45631e20i		−	1.24826i
$509$	−2.70613e20			−1.35508			−0.677541	−	0.735485i	$-0.736954\pi$
$509$	−2.70613e20			−1.35508			−0.677541	+	0.735485i	$0.736954\pi$
$510$			4.80962e18i			0.0237320i
$511$		−	3.30361e19i		−	0.160632i
$512$		−	5.76084e19i		−	0.276033i
$513$	−1.64557e20			−0.777026
$514$		−	2.18940e19i		−	0.101883i
$515$	1.20584e20			0.553012
$516$	−3.17091e20			−1.43321
$517$	6.11327e19			0.272330
$518$	6.92114e18			0.0303882
$519$		−	2.06479e20i		−	0.893552i
$520$			2.36387e19i			0.100832i
$521$	−3.61608e20			−1.52039			−0.760195	−	0.649695i	$-0.774897\pi$
$521$	−3.61608e20			−1.52039			−0.760195	+	0.649695i	$0.774897\pi$
$522$	−3.03210e18	−	5.68004e18i	−0.0125665	−	0.0235409i
$523$	−3.50695e19			−0.143274			−0.0716370	−	0.997431i	$-0.522822\pi$
$523$	−3.50695e19			−0.143274			−0.0716370	+	0.997431i	$0.522822\pi$
$524$		−	3.95948e20i		−	1.59460i
$525$		−	6.03282e19i		−	0.239511i
$526$	−7.66749e18			−0.0300096
$527$	1.88808e20			0.728518
$528$	−1.12334e20			−0.427323
$529$	3.44448e20			1.29183
$530$		−	2.79455e18i		−	0.0103334i
$531$	1.55245e20			0.565991
$532$			9.84301e19i			0.353827i
$533$			4.65935e20i			1.65147i
$534$		−	3.70414e19i		−	0.129458i
$535$	2.30020e19			0.0792706
$536$			8.48779e18i			0.0288442i
$537$		−	3.61585e19i		−	0.121172i
$538$	2.83385e19			0.0936503
$539$			9.97276e19i			0.325012i
$540$		−	1.11624e20i		−	0.358760i
$541$			2.03258e20i			0.644271i	0.946693	+	0.322136i	$0.104401\pi$
$541$			2.03258e20i			0.644271i	−0.946693	+	0.322136i	$0.895599\pi$
$542$	6.08311e18			0.0190165
$543$		−	4.37361e20i		−	1.34847i
$544$	−3.38601e19			−0.102967
$545$	1.91973e20			0.575792
$546$	−1.06267e19			−0.0314379
$547$	−4.65786e20			−1.35919			−0.679597	−	0.733585i	$-0.737845\pi$
$547$	−4.65786e20			−1.35919			−0.679597	+	0.733585i	$0.737845\pi$
$548$		−	4.99082e20i		−	1.43654i
$549$		−	7.62299e19i		−	0.216438i
$550$	4.81029e18			0.0134726
$551$	2.08479e20	+	3.90545e20i	0.576004	+	1.07903i
$552$	−7.53638e19			−0.205409
$553$		−	7.42742e19i		−	0.199710i
$554$			7.78816e18i			0.0206591i
$555$	−4.92880e20			−1.28986
$556$	−1.85149e20			−0.478035
$557$	−5.95663e20			−1.51735			−0.758676	−	0.651468i	$-0.774153\pi$
$557$	−5.95663e20			−1.51735			−0.758676	+	0.651468i	$0.774153\pi$
$558$	−1.25462e19			−0.0315324
$559$			7.60541e20i			1.88597i
$560$	−6.65583e19			−0.162852
$561$			1.10158e20i			0.265946i
$562$			2.94785e19i			0.0702237i
$563$			7.84690e19i			0.184453i	0.995738	+	0.0922263i	$0.0293983\pi$
$563$			7.84690e19i			0.184453i	−0.995738	+	0.0922263i	$0.970602\pi$
$564$	4.00837e20			0.929768
$565$			1.32149e20i			0.302484i
$566$		−	1.48523e19i		−	0.0335482i
$567$	1.62658e20			0.362580
$568$		−	1.43093e19i		−	0.0314779i
$569$		−	4.46439e20i		−	0.969215i	−0.874732	−	0.484608i	$-0.838962\pi$
$569$		−	4.46439e20i		−	0.969215i	0.874732	−	0.484608i	$-0.161038\pi$
$570$			2.19747e19i			0.0470828i
$571$	1.64304e20			0.347439			0.173719	−	0.984795i	$-0.444421\pi$
$571$	1.64304e20			0.347439			0.173719	+	0.984795i	$0.444421\pi$
$572$			2.70282e20i			0.564088i
$573$	3.84894e19			0.0792832
$574$	8.26445e18			0.0168025
$575$	−5.12287e20			−1.02803
$576$	−2.36483e20			−0.468416
$577$		−	6.38163e20i		−	1.24771i	−0.781541	−	0.623854i	$-0.785566\pi$
$577$		−	6.38163e20i		−	1.24771i	0.781541	−	0.623854i	$-0.214434\pi$
$578$		−	1.79562e19i		−	0.0346542i
$579$	2.07187e20			0.394707
$580$	−2.64919e20	+	1.41418e20i	−0.498199	+	0.265946i
$581$	−8.33040e19			−0.154648
$582$		−	1.61624e19i		−	0.0296199i
$583$		−	6.40052e19i		−	0.115798i
$584$	3.45974e19			0.0617942
$585$	2.44518e20			0.431164
$586$	−3.03531e19			−0.0528409
$587$	3.00944e20			0.517250			0.258625	−	0.965978i	$-0.416731\pi$
$587$	3.00944e20			0.517250			0.258625	+	0.965978i	$0.416731\pi$
$588$			6.53897e20i			1.10963i
$589$	8.62646e20			1.44533
$590$			2.26992e19i			0.0375510i
$591$		−	2.43006e20i		−	0.396928i
$592$		−	1.15059e21i		−	1.85571i
$593$	7.11973e20			1.13384			0.566922	−	0.823771i	$-0.308134\pi$
$593$	7.11973e20			1.13384			0.566922	+	0.823771i	$0.308134\pi$
$594$			8.01481e18i			0.0126036i
$595$			6.52690e19i			0.101351i
$596$	6.94143e20			1.06439
$597$			1.18314e21i			1.79154i
$598$			9.02383e19i			0.134937i
$599$			4.55540e20i			0.672706i	0.941736	+	0.336353i	$0.109194\pi$
$599$			4.55540e20i			0.672706i	−0.941736	+	0.336353i	$0.890806\pi$
$600$	6.31794e19			0.0921385
$601$			8.13175e20i			1.17119i	0.810605	+	0.585593i	$0.199138\pi$
$601$			8.13175e20i			1.17119i	−0.810605	+	0.585593i	$0.800862\pi$
$602$	1.34900e19			0.0191884
$603$	8.77976e19			0.123340
$604$	1.02202e21			1.41802
$605$	3.61333e20			0.495156
$606$			8.28385e19i			0.112121i
$607$		−	1.12163e21i		−	1.49946i	−0.661744	−	0.749730i	$-0.730183\pi$
$607$		−	1.12163e21i		−	1.49946i	0.661744	−	0.749730i	$-0.269817\pi$
$608$	−1.54704e20			−0.204279
$609$	−1.27347e20	−	2.38560e20i	−0.166096	−	0.311149i
$610$	1.11460e19			0.0143597
$611$		−	9.61405e20i		−	1.22348i
$612$			2.33377e20i			0.293375i
$613$	1.16051e21			1.44110			0.720551	−	0.693402i	$-0.243889\pi$
$613$	1.16051e21			1.44110			0.720551	+	0.693402i	$0.243889\pi$
$614$	6.60389e19			0.0810097
$615$	−5.88542e20			−0.713205
$616$	9.60320e18			0.0114964
$617$		−	6.39180e20i		−	0.755934i	−0.925819	−	0.377967i	$-0.876623\pi$
$617$		−	6.39180e20i		−	0.755934i	0.925819	−	0.377967i	$-0.123377\pi$
$618$	−5.67699e19			−0.0663292
$619$			9.33837e20i			1.07793i	0.842327	+	0.538966i	$0.181185\pi$
$619$			9.33837e20i			1.07793i	−0.842327	+	0.538966i	$0.818815\pi$
$620$			5.85160e20i			0.667324i
$621$		−	8.53563e20i		−	0.961720i
$622$	8.59139e18			0.00956391
$623$		−	5.02670e20i		−	0.552870i
$624$			1.76662e21i			1.91981i
$625$	1.30572e20			0.140201
$626$		−	5.14207e19i		−	0.0545545i
$627$			5.03301e20i			0.527619i
$628$			7.31190e20i			0.757413i
$629$	−1.12831e21			−1.15491
$630$		−	4.33711e18i		−	0.00438678i
$631$	−1.11871e21			−1.11814			−0.559072	−	0.829119i	$-0.688843\pi$
$631$	−1.11871e21			−1.11814			−0.559072	+	0.829119i	$0.688843\pi$
$632$	7.77844e19			0.0768271
$633$	−8.53122e20			−0.832690
$634$	−8.88896e19			−0.0857396
$635$		−	7.44173e20i		−	0.709367i
$636$		−	4.19671e20i		−	0.395349i
$637$	1.56837e21			1.46017
$638$	1.90217e19	−	1.01541e19i	0.0175022	−	0.00934297i
$639$	−1.48015e20			−0.134601
$640$		−	1.39847e20i		−	0.125691i
$641$			1.46686e21i			1.30303i	0.758636	+	0.651514i	$0.225866\pi$
$641$			1.46686e21i			1.30303i	−0.758636	+	0.651514i	$0.774134\pi$
$642$	−1.08292e19			−0.00950786
$643$	5.78279e20			0.501828			0.250914	−	0.968009i	$-0.419269\pi$
$643$	5.78279e20			0.501828			0.250914	+	0.968009i	$0.419269\pi$
$644$	−5.10562e20			−0.437929
$645$	−9.60672e20			−0.814474
$646$			5.03048e19i			0.0421566i
$647$	−1.46636e21			−1.21467			−0.607335	−	0.794446i	$-0.707761\pi$
$647$	−1.46636e21			−1.21467			−0.607335	+	0.794446i	$0.707761\pi$
$648$			1.70346e20i			0.139482i
$649$			5.19895e20i			0.420804i
$650$		−	7.56491e19i		−	0.0605276i
$651$	−5.26938e20			−0.416775
$652$			7.37510e20i			0.576648i
$653$		−	1.58007e21i		−	1.22132i	−0.791894	−	0.610659i	$-0.790905\pi$
$653$		−	1.58007e21i		−	1.22132i	0.791894	−	0.610659i	$-0.209095\pi$
$654$	−9.03793e19			−0.0690615
$655$		−	1.19958e21i		−	0.906190i
$656$		−	1.37391e21i		−	1.02608i
$657$		−	3.57875e20i		−	0.264236i
$658$	−1.70528e19			−0.0124480
$659$			5.62163e20i			0.405716i	0.979208	+	0.202858i	$0.0650229\pi$
$659$			5.62163e20i			0.405716i	−0.979208	+	0.202858i	$0.934977\pi$
$660$	−3.41405e20			−0.243607
$661$	−9.60861e20			−0.677875			−0.338938	−	0.940809i	$-0.610068\pi$
$661$	−9.60861e20			−0.677875			−0.338938	+	0.940809i	$0.610068\pi$
$662$	1.82407e19			0.0127235
$663$	1.73240e21			1.19480
$664$		−	8.72410e19i		−	0.0594922i
$665$			2.98208e20i			0.201074i
$666$	7.49757e19			0.0499877
$667$	−2.02577e21	+	1.08139e21i	−1.33551	+	0.712916i
$668$	−6.36735e20			−0.415083
$669$		−	1.83879e21i		−	1.18532i
$670$			1.28374e19i			0.00818304i
$671$	2.55283e20			0.160917
$672$	9.44991e19			0.0589058
$673$	2.01361e21			1.24126			0.620630	−	0.784104i	$-0.286877\pi$
$673$	2.01361e21			1.24126			0.620630	+	0.784104i	$0.286877\pi$
$674$	−6.70791e19			−0.0408920
$675$			7.15564e20i			0.431390i
$676$	2.57858e21			1.53737
$677$		−	6.96292e20i		−	0.410560i	−0.978703	−	0.205280i	$-0.934190\pi$
$677$		−	6.96292e20i		−	0.410560i	0.978703	−	0.205280i	$-0.0658105\pi$
$678$		−	6.22150e19i		−	0.0362804i
$679$		−	2.19332e20i		−	0.126496i
$680$	−6.83536e19			−0.0389892
$681$		−	5.50370e20i		−	0.310492i
$682$		−	4.20156e19i		−	0.0234438i
$683$	−1.04814e21			−0.578448			−0.289224	−	0.957261i	$-0.593397\pi$
$683$	−1.04814e21			−0.578448			−0.289224	+	0.957261i	$0.593397\pi$
$684$			1.06628e21i			0.582036i
$685$		−	1.51204e21i		−	0.816365i
$686$		−	5.81953e19i		−	0.0310783i
$687$	−3.15686e21			−1.66756
$688$		−	2.24262e21i		−	1.17177i
$689$	−1.00658e21			−0.520240
$690$	−1.13984e20			−0.0582741
$691$	−5.53195e20			−0.279765			−0.139882	−	0.990168i	$-0.544672\pi$
$691$	−5.53195e20			−0.279765			−0.139882	+	0.990168i	$0.544672\pi$
$692$	1.46493e21			0.732858
$693$		−	9.93354e19i		−	0.0491592i
$694$			1.98171e19i			0.00970163i
$695$	−5.60934e20			−0.271660
$696$	2.49835e20	−	1.33366e20i	0.119697	−	0.0638962i
$697$	−1.34730e21			−0.638584
$698$		−	5.40358e19i		−	0.0253376i
$699$		−	3.23014e21i		−	1.49845i
$700$	4.28017e20			0.196438
$701$	3.21985e21			1.46201			0.731005	−	0.682372i	$-0.239052\pi$
$701$	3.21985e21			1.46201			0.731005	+	0.682372i	$0.239052\pi$
$702$	1.26045e20			0.0566236
$703$	−5.15513e21			−2.29126
$704$		−	7.91949e20i		−	0.348259i
$705$	1.21439e21			0.528373
$706$			1.36302e20i			0.0586768i
$707$			1.12416e21i			0.478831i
$708$			3.40886e21i			1.43668i
$709$	−1.42733e21			−0.595218			−0.297609	−	0.954688i	$-0.596189\pi$
$709$	−1.42733e21			−0.595218			−0.297609	+	0.954688i	$0.596189\pi$
$710$		−	2.16421e19i		−	0.00893020i
$711$		−	8.04601e20i		−	0.328518i
$712$	5.26427e20			0.212685
$713$			4.47458e21i			1.78888i
$714$		−	3.07282e19i		−	0.0121563i
$715$			8.18857e20i			0.320563i
$716$	2.56538e20			0.0993811
$717$			3.54483e20i			0.135895i
$718$	3.38911e19			0.0128574
$719$	3.52622e20			0.132386			0.0661931	−	0.997807i	$-0.478915\pi$
$719$	3.52622e20			0.132386			0.0661931	+	0.997807i	$0.478915\pi$
$720$	−7.21016e20			−0.267887
$721$	−7.70396e20			−0.283269
$722$			7.62119e19i			0.0277328i
$723$			1.75847e20i			0.0633283i
$724$	3.10299e21			1.10596
$725$	1.69826e21	−	9.06557e20i	0.599057	−	0.319786i
$726$	−1.70113e20			−0.0593899
$727$			3.57655e21i			1.23582i	0.786248	+	0.617911i	$0.212021\pi$
$727$			3.57655e21i			1.23582i	−0.786248	+	0.617911i	$0.787979\pi$
$728$		−	1.51025e20i		−	0.0516492i
$729$	−5.19098e20			−0.175709
$730$	5.23269e19			0.0175309
$731$	−2.19918e21			−0.729257
$732$	1.67385e21			0.549393
$733$			5.56389e20i			0.180758i	0.995907	+	0.0903792i	$0.0288079\pi$
$733$			5.56389e20i			0.180758i	−0.995907	+	0.0903792i	$0.971192\pi$
$734$	2.30533e20			0.0741333
$735$			1.98107e21i			0.630587i
$736$		−	8.02455e20i		−	0.252835i
$737$			2.94022e20i			0.0917009i
$738$	8.95276e19			0.0276398
$739$		−	4.38827e20i		−	0.134110i	−0.997749	−	0.0670548i	$-0.978640\pi$
$739$		−	4.38827e20i		−	0.134110i	0.997749	−	0.0670548i	$-0.0213602\pi$
$740$		−	3.49688e21i		−	1.05790i
$741$	7.91517e21			2.37041
$742$			1.78541e19i			0.00529307i
$743$			4.18481e21i			1.22817i	0.789239	+	0.614087i	$0.210475\pi$
$743$			4.18481e21i			1.22817i	−0.789239	+	0.614087i	$0.789525\pi$
$744$		−	5.51841e20i		−	0.160331i
$745$	2.10301e21			0.604879
$746$			1.34925e20i			0.0384195i
$747$	−9.02420e20			−0.254392
$748$	−7.81547e20			−0.218119
$749$	−1.46957e20			−0.0406048
$750$	2.36272e20			0.0646326
$751$		−	1.54618e21i		−	0.418757i	−0.977835	−	0.209378i	$-0.932856\pi$
$751$		−	1.54618e21i		−	0.418757i	0.977835	−	0.209378i	$-0.0671440\pi$
$752$			2.83492e21i			0.760163i
$753$	4.49426e21			1.19315
$754$	−1.59688e20	−	2.99144e20i	−0.0419747	−	0.0786314i
$755$	3.09636e21			0.805840
$756$			7.13153e20i			0.183768i
$757$			4.45250e20i			0.113602i	0.998386	+	0.0568009i	$0.0180900\pi$
$757$			4.45250e20i			0.113602i	−0.998386	+	0.0568009i	$0.981910\pi$
$758$	−2.42988e20			−0.0613856
$759$	−2.61064e21			−0.653031
$760$	−3.12302e20			−0.0773521
$761$	2.49136e20			0.0611015			0.0305508	−	0.999533i	$-0.490274\pi$
$761$	2.49136e20			0.0611015			0.0305508	+	0.999533i	$0.490274\pi$
$762$			3.50351e20i			0.0850828i
$763$	−1.22649e21			−0.294938
$764$			2.73075e20i			0.0650251i
$765$			7.07049e20i			0.166720i
$766$		−	6.90751e19i		−	0.0161289i
$767$	8.17613e21			1.89053
$768$		−	5.14312e21i		−	1.17765i
$769$			4.92591e21i			1.11696i	0.829517	+	0.558481i	$0.188616\pi$
$769$			4.92591e21i			1.11696i	−0.829517	+	0.558481i	$0.811384\pi$
$770$	1.45244e19			0.00326149
$771$		−	9.96127e21i		−	2.21517i
$772$			1.46995e21i			0.323723i
$773$		−	5.06935e21i		−	1.10562i	−0.833307	−	0.552810i	$-0.813555\pi$
$773$		−	5.06935e21i		−	1.10562i	0.833307	−	0.552810i	$-0.186445\pi$
$774$	1.46135e20			0.0315644
$775$		−	3.75116e21i		−	0.802421i
$776$	2.29698e20			0.0486624
$777$	3.14895e21			0.660707
$778$	−3.88223e20			−0.0806741
$779$	−6.15568e21			−1.26691
$780$			5.36911e21i			1.09444i
$781$		−	4.95681e20i		−	0.100074i
$782$	−2.60933e20			−0.0521770
$783$	1.51049e21	+	2.82960e21i	0.299160	+	0.560418i
$784$	−4.62468e21			−0.907217
$785$			2.21524e21i			0.430426i
$786$			5.64753e20i			0.108690i
$787$	−4.96882e21			−0.947203			−0.473601	−	0.880739i	$-0.657046\pi$
$787$	−4.96882e21			−0.947203			−0.473601	+	0.880739i	$0.657046\pi$
$788$	1.72408e21			0.325545
$789$	−3.48853e21			−0.652476
$790$	1.17645e20			0.0217957
$791$		−	8.44288e20i		−	0.154941i
$792$	1.04030e20			0.0189112
$793$		−	4.01471e21i		−	0.722946i
$794$		−	3.25004e20i		−	0.0579742i
$795$		−	1.27145e21i		−	0.224671i
$796$	−8.39413e21			−1.46936
$797$			8.87124e21i			1.53832i	0.639056	+	0.769160i	$0.279325\pi$
$797$			8.87124e21i			1.53832i	−0.639056	+	0.769160i	$0.720675\pi$
$798$		−	1.40394e20i		−	0.0241172i
$799$	2.78000e21			0.473090
$800$			6.72719e20i			0.113412i
$801$		−	5.44535e21i		−	0.909456i
$802$			1.05273e20i			0.0174184i
$803$	1.19847e21			0.196454
$804$			1.92785e21i			0.313078i
$805$	−1.54682e21			−0.248869
$806$	−6.60759e20			−0.105325
$807$	1.28933e22			2.03617
$808$	−1.17729e21			−0.184203
$809$			8.33384e21i			1.29191i	0.763377	+	0.645953i	$0.223540\pi$
$809$			8.33384e21i			1.29191i	−0.763377	+	0.645953i	$0.776460\pi$
$810$			2.57639e20i			0.0395708i
$811$	−1.17700e22			−1.79110			−0.895551	−	0.444958i	$-0.853218\pi$
$811$	−1.17700e22			−1.79110			−0.895551	+	0.444958i	$0.853218\pi$
$812$	1.69254e21	−	9.03503e20i	0.255192	−	0.136226i
$813$	2.76767e21			0.413462
$814$			2.51083e20i			0.0371650i
$815$			2.23439e21i			0.327700i
$816$	−5.10836e21			−0.742344
$817$	−1.00479e22			−1.44680
$818$	4.28240e20			0.0610995
$819$	−1.56220e21			−0.220855
$820$		−	4.17559e21i		−	0.584944i
$821$	2.99107e21			0.415196			0.207598	−	0.978214i	$-0.433435\pi$
$821$	2.99107e21			0.415196			0.207598	+	0.978214i	$0.433435\pi$
$822$			7.11858e20i			0.0979162i
$823$		−	1.28737e22i		−	1.75471i	−0.479839	−	0.877357i	$-0.659305\pi$
$823$		−	1.28737e22i		−	1.75471i	0.479839	−	0.877357i	$-0.340695\pi$
$824$		−	8.06806e20i		−	0.108972i
$825$	2.18857e21			0.292924
$826$		−	1.45023e20i		−	0.0192348i
$827$			4.98206e21i			0.654814i	0.944883	+	0.327407i	$0.106175\pi$
$827$			4.98206e21i			0.654814i	−0.944883	+	0.327407i	$0.893825\pi$
$828$	−5.53084e21			−0.720383
$829$		−	5.63716e21i		−	0.727615i	−0.931474	−	0.363807i	$-0.881477\pi$
$829$		−	5.63716e21i		−	0.727615i	0.931474	−	0.363807i	$-0.118523\pi$
$830$		−	1.31948e20i		−	0.0168778i
$831$			3.54343e21i			0.449175i
$832$	−1.24546e22			−1.56461
$833$			4.53509e21i			0.564610i
$834$	2.64084e20			0.0325834
$835$	−1.92908e21			−0.235885
$836$	−3.57082e21			−0.432734
$837$	6.25011e21			0.750665
$838$			7.41568e20i			0.0882715i
$839$		−	4.15072e21i		−	0.489676i	−0.969564	−	0.244838i	$-0.921265\pi$
$839$		−	4.15072e21i		−	0.489676i	0.969564	−	0.244838i	$-0.0787348\pi$
$840$	1.90766e20			0.0223052
$841$	4.80188e21	−	7.16972e21i	0.556469	−	0.830868i
$842$	7.59309e20			0.0872123
$843$			1.34120e22i			1.52682i
$844$		−	6.05273e21i		−	0.682941i
$845$	7.81216e21			0.873667
$846$	−1.84730e20			−0.0204767
$847$	−2.30852e21			−0.253634
$848$	2.96812e21			0.323231
$849$		−	6.75743e21i		−	0.729414i
$850$	2.18747e20			0.0234046
$851$		−	2.67399e22i		−	2.83588i
$852$		−	3.25010e21i		−	0.341664i
$853$			1.00988e22i			1.05233i	0.850383	+	0.526164i	$0.176370\pi$
$853$			1.00988e22i			1.05233i	−0.850383	+	0.526164i	$0.823630\pi$
$854$	−7.12104e19			−0.00735546
$855$			3.23044e21i			0.330762i
$856$		−	1.53903e20i		−	0.0156204i
$857$	−1.56418e22			−1.57373			−0.786865	−	0.617126i	$-0.788297\pi$
$857$	−1.56418e22			−1.57373			−0.786865	+	0.617126i	$0.788297\pi$
$858$		−	3.85512e20i		−	0.0384488i
$859$			1.45748e22i			1.44097i	0.693470	+	0.720485i	$0.256081\pi$
$859$			1.45748e22i			1.44097i	−0.693470	+	0.720485i	$0.743919\pi$
$860$		−	6.81578e21i		−	0.668001i
$861$	3.76013e21			0.365325
$862$			7.62524e20i			0.0734428i
$863$	1.31318e21			0.125384			0.0626919	−	0.998033i	$-0.480031\pi$
$863$	1.31318e21			0.125384			0.0626919	+	0.998033i	$0.480031\pi$
$864$	−1.12087e21			−0.106097
$865$	4.43820e21			0.416472
$866$	−5.27186e19			−0.00490433
$867$		−	8.16965e21i		−	0.753460i
$868$		−	3.73852e21i		−	0.341824i
$869$	2.69450e21			0.244247
$870$	3.77862e20	−	2.01709e20i	0.0339578	−	0.0181272i
$871$	4.62394e21			0.411980
$872$		−	1.28446e21i		−	0.113461i
$873$		−	2.37599e21i		−	0.208083i
$874$	−1.19218e21			−0.103516
$875$	3.20632e21			0.276024
$876$	7.85819e21			0.670721
$877$	4.61558e21			0.390597			0.195299	−	0.980744i	$-0.437432\pi$
$877$	4.61558e21			0.390597			0.195299	+	0.980744i	$0.437432\pi$
$878$		−	7.43484e20i		−	0.0623825i
$879$	−1.38099e22			−1.14888
$880$		−	2.41458e21i		−	0.199169i
$881$			1.41557e22i			1.15774i	0.815420	+	0.578870i	$0.196506\pi$
$881$			1.41557e22i			1.15774i	−0.815420	+	0.578870i	$0.803494\pi$
$882$		−	3.01356e20i		−	0.0244380i
$883$	−4.25918e21			−0.342468			−0.171234	−	0.985230i	$-0.554775\pi$
$883$	−4.25918e21			−0.342468			−0.171234	+	0.985230i	$0.554775\pi$
$884$			1.22910e22i			0.979932i
$885$			1.03276e22i			0.816443i
$886$	6.55914e20			0.0514155
$887$		−	9.03950e21i		−	0.702615i	−0.936260	−	0.351307i	$-0.885737\pi$
$887$		−	9.03950e21i		−	0.702615i	0.936260	−	0.351307i	$-0.114263\pi$
$888$			3.29778e21i			0.254170i
$889$			4.75444e21i			0.363359i
$890$	7.96194e20			0.0603384
$891$			5.90087e21i			0.443438i
$892$	1.30458e22			0.972155
$893$	1.27016e22			0.938580
$894$	−9.90079e20			−0.0725502
$895$	7.77217e20			0.0564767
$896$			8.93466e20i			0.0643825i
$897$			4.10563e22i			2.93384i
$898$	2.26603e20			0.0160581
$899$	−7.91834e21	−	1.48335e22i	−0.556463	−	1.04242i
$900$	4.63664e21			0.323136
$901$		−	2.91063e21i		−	0.201164i
$902$			2.99815e20i			0.0205497i
$903$	6.13763e21			0.417198
$904$	8.84190e20			0.0596050
$905$	9.40095e21			0.628503
$906$	−1.45774e21			−0.0966539
$907$		−	1.92097e22i		−	1.26318i	−0.775303	−	0.631590i	$-0.782403\pi$
$907$		−	1.92097e22i		−	1.26318i	0.775303	−	0.631590i	$-0.217597\pi$
$908$	3.90476e21			0.254654
$909$			1.21779e22i			0.787665i
$910$		−	2.28418e20i		−	0.0146528i
$911$			2.11258e22i			1.34408i	0.740514	+	0.672041i	$0.234582\pi$
$911$			2.11258e22i			1.34408i	−0.740514	+	0.672041i	$0.765418\pi$
$912$	−2.33396e22			−1.47276
$913$		−	3.02208e21i		−	0.189136i
$914$		−	1.15479e21i		−	0.0716814i
$915$	5.07116e21			0.312211
$916$		−	2.23973e22i		−	1.36767i
$917$			7.66398e21i			0.464178i
$918$			3.64472e20i			0.0218950i
$919$	7.06742e21			0.421109			0.210554	−	0.977582i	$-0.432473\pi$
$919$	7.06742e21			0.421109			0.210554	+	0.977582i	$0.432473\pi$
$920$		−	1.61992e21i		−	0.0957382i
$921$	3.00461e22			1.76133
$922$	1.16896e20			0.00679700
$923$	−7.79534e21			−0.449596
$924$	2.18120e21			0.124783
$925$			2.24167e22i			1.27206i
$926$		−	1.13803e21i		−	0.0640579i
$927$	−8.34559e21			−0.465971
$928$	1.42005e21	+	2.66018e21i	0.0786489	+	0.147333i
$929$	3.62660e22			1.99242			0.996212	−	0.0869607i	$-0.0277155\pi$
$929$	3.62660e22			1.99242			0.996212	+	0.0869607i	$0.0277155\pi$
$930$		−	8.34632e20i		−	0.0454855i
$931$			2.07204e22i			1.12015i
$932$	2.29172e22			1.22897
$933$	3.90888e21			0.207941
$934$	−7.90780e20			−0.0417305
$935$	−2.36781e21			−0.123954
$936$		−	1.63603e21i		−	0.0849616i
$937$	−2.32796e22			−1.19930			−0.599652	−	0.800261i	$-0.704694\pi$
$937$	−2.32796e22			−1.19930			−0.599652	+	0.800261i	$0.704694\pi$
$938$		−	8.20165e19i		−	0.00419160i
$939$		−	2.33952e22i		−	1.18614i
$940$			8.61587e21i			0.433352i
$941$	3.84440e21			0.191826			0.0959128	−	0.995390i	$-0.469423\pi$
$941$	3.84440e21			0.191826			0.0959128	+	0.995390i	$0.469423\pi$
$942$		−	1.04292e21i		−	0.0516261i
$943$		−	3.19298e22i		−	1.56804i
$944$	−2.41091e22			−1.17460
$945$			2.16060e21i			0.104432i
$946$			4.89386e20i			0.0234675i
$947$		−	2.83462e22i		−	1.34856i	−0.738476	−	0.674280i	$-0.764454\pi$
$947$		−	2.83462e22i		−	1.34856i	0.738476	−	0.674280i	$-0.235546\pi$
$948$	1.76674e22			0.833890
$949$		−	1.88478e22i		−	0.882601i
$950$	9.99436e20			0.0464331
$951$	−4.04427e22			−1.86417
$952$	4.36704e20			0.0199715
$953$	−3.02319e22			−1.37173			−0.685865	−	0.727728i	$-0.740576\pi$
$953$	−3.02319e22			−1.37173			−0.685865	+	0.727728i	$0.740576\pi$
$954$			1.93410e20i			0.00870697i
$955$			8.27318e20i			0.0369528i
$956$	−2.51499e21			−0.111456
$957$	8.65441e21	−	4.61986e21i	0.380538	−	0.203137i
$958$	−7.98455e20			−0.0348345
$959$			9.66026e21i			0.418167i
$960$		−	1.57319e22i		−	0.675691i
$961$	−9.29929e21			−0.396300
$962$	3.94866e21			0.166969
$963$	−1.59197e21			−0.0667939
$964$	−1.24760e21			−0.0519395
$965$			4.45343e21i			0.183967i
$966$	7.28231e20			0.0298497
$967$		−	2.87168e22i		−	1.16799i	−0.811759	−	0.583993i	$-0.801490\pi$
$967$		−	2.87168e22i		−	1.16799i	0.811759	−	0.583993i	$-0.198510\pi$
$968$		−	2.41762e21i		−	0.0975714i
$969$			2.28875e22i			0.916579i
$970$	3.47406e20			0.0138054
$971$		−	4.24288e20i		−	0.0167308i	−0.999965	−	0.00836539i	$-0.997337\pi$
$971$		−	4.24288e20i		−	0.0167308i	0.999965	−	0.00836539i	$-0.00266282\pi$
$972$			2.25067e22i			0.880673i
$973$	3.58375e21			0.139152
$974$		−	8.40721e20i		−	0.0323936i
$975$		−	3.44186e22i		−	1.31601i
$976$			1.18383e22i			0.449174i
$977$	7.14516e21			0.269031			0.134516	−	0.990911i	$-0.457052\pi$
$977$	7.14516e21			0.269031			0.134516	+	0.990911i	$0.457052\pi$
$978$		−	1.05193e21i		−	0.0393050i
$979$	1.82357e22			0.676165
$980$	−1.40553e22			−0.517184
$981$	−1.32864e22			−0.485166
$982$	−2.81845e21			−0.102135
$983$			5.19193e22i			1.86714i	0.358394	+	0.933570i	$0.383324\pi$
$983$			5.19193e22i			1.86714i	−0.358394	+	0.933570i	$0.616676\pi$
$984$			3.93784e21i			0.140538i
$985$	5.22335e21			0.185002
$986$	8.65006e20	−	4.61754e20i	0.0304048	−	0.0162306i
$987$	−7.75862e21			−0.270649
$988$			5.61566e22i			1.94412i
$989$		−	5.21187e22i		−	1.79069i
$990$	1.57340e20			0.00536507
$991$	−2.77622e22			−0.939509			−0.469755	−	0.882797i	$-0.655658\pi$
$991$	−2.77622e22			−0.939509			−0.469755	+	0.882797i	$0.655658\pi$
$992$	5.87587e21			0.197349
$993$	8.29907e21			0.276637
$994$			1.38269e20i			0.00457432i
$995$	−2.54312e22			−0.835014
$996$		−	1.98152e22i		−	0.645735i
$997$		−	9.34263e21i		−	0.302173i	−0.988521	−	0.151087i	$-0.951723\pi$
$997$		−	9.34263e21i		−	0.302173i	0.988521	−	0.151087i	$-0.0482772\pi$
$998$		−	1.48506e21i		−	0.0476723i
$999$	−3.73503e22			−1.19002

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.16.b.a.28.18	✓	36
29.28	even	2	inner	29.16.b.a.28.19	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.16.b.a.28.18	✓	36	1.1	even	1	trivial
29.16.b.a.28.19	yes	36	29.28	even	2	inner

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:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	29.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-10.1196i q^{2} -4604.16i q^{3} +32665.6 q^{4} +98965.0 q^{5} -46592.0 q^{6} -632277. q^{7} -662159. i q^{8} -6.84936e6 q^{9} +O(q^{10})\)	\(q-10.1196i q^{2} -4604.16i q^{3} +32665.6 q^{4} +98965.0 q^{5} -46592.0 q^{6} -632277. q^{7} -662159. i q^{8} -6.84936e6 q^{9} -1.00148e6i q^{10} -2.29375e7i q^{11} -1.50398e8i q^{12} -3.60728e8 q^{13} +6.39836e6i q^{14} -4.55651e8i q^{15} +1.06369e9 q^{16} -1.04308e9i q^{17} +6.93124e7i q^{18} -4.76574e9i q^{19} +3.23275e9 q^{20} +2.91110e9i q^{21} -2.32118e8 q^{22} +2.47201e10 q^{23} -3.04868e9 q^{24} -2.07235e10 q^{25} +3.65040e9i q^{26} -3.45291e10i q^{27} -2.06537e10 q^{28} +(-8.19484e10 + 4.37454e10i) q^{29} -4.61098e9 q^{30} +1.81010e11i q^{31} -3.24616e10i q^{32} -1.05608e11 q^{33} -1.05555e10 q^{34} -6.25733e10 q^{35} -2.23738e11 q^{36} -1.08171e12i q^{37} -4.82272e10 q^{38} +1.66085e12i q^{39} -6.55305e10i q^{40} -1.29165e12i q^{41} +2.94590e10 q^{42} -2.10835e12i q^{43} -7.49268e11i q^{44} -6.77847e11 q^{45} -2.50156e11i q^{46} +2.66518e12i q^{47} -4.89738e12i q^{48} -4.34779e12 q^{49} +2.09713e11i q^{50} -4.80251e12 q^{51} -1.17834e13 q^{52} +2.79041e12 q^{53} -3.49419e11 q^{54} -2.27001e12i q^{55} +4.18667e11i q^{56} -2.19422e13 q^{57} +(4.42683e11 + 8.29281e11i) q^{58} -2.26657e13 q^{59} -1.48841e13i q^{60} +1.11295e13i q^{61} +1.83174e12 q^{62} +4.33069e12 q^{63} +3.45263e13 q^{64} -3.56994e13 q^{65} +1.06871e12i q^{66} -1.28184e13 q^{67} -3.40728e13i q^{68} -1.13815e14i q^{69} +6.33213e11i q^{70} +2.16100e13 q^{71} +4.53536e12i q^{72} +5.22494e13i q^{73} -1.09464e13 q^{74} +9.54143e13i q^{75} -1.55676e14i q^{76} +1.45029e13i q^{77} +1.68070e13 q^{78} +1.17471e14i q^{79} +1.05268e14 q^{80} -2.57258e14 q^{81} -1.30709e13 q^{82} +1.31752e14 q^{83} +9.50929e13i q^{84} -1.03228e14i q^{85} -2.13356e13 q^{86} +(2.01410e14 + 3.77303e14i) q^{87} -1.51883e13 q^{88} +7.95016e14i q^{89} +6.85951e12i q^{90} +2.28080e14 q^{91} +8.07497e14 q^{92} +8.33398e14 q^{93} +2.69705e13 q^{94} -4.71642e14i q^{95} -1.49458e14 q^{96} +3.46892e14i q^{97} +4.39977e13i q^{98} +1.57107e14i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 508108 q^{4} + 470082 q^{5} + 1112016 q^{6} - 4820620 q^{7} - 167460710 q^{9}+O(q^{10}) \) 36 * q - 508108 * q^4 + 470082 * q^5 + 1112016 * q^6 - 4820620 * q^7 - 167460710 * q^9	\( 36 q - 508108 q^{4} + 470082 q^{5} + 1112016 q^{6} - 4820620 q^{7} - 167460710 q^{9} + 133305618 q^{13} + 5626041364 q^{16} - 30737731548 q^{20} - 51638088984 q^{22} - 23459433564 q^{23} - 13473060100 q^{24} + 169887741474 q^{25} + 281303298768 q^{28} - 85550328684 q^{29} - 681215606256 q^{30} + 831111242422 q^{33} - 449988200584 q^{34} + 726838987044 q^{35} + 1809260484664 q^{36} - 2518300733088 q^{38} - 5363921425320 q^{42} - 16561773855556 q^{45} + 29824615981340 q^{49} + 1184881612900 q^{51} + 21527128606228 q^{52} - 40200435711486 q^{53} + 9043904345168 q^{54} + 42099004809572 q^{57} - 3461494533632 q^{58} - 50458797940572 q^{59} - 298531808710416 q^{62} + 159779590145904 q^{63} - 71569159267548 q^{64} + 92095395748902 q^{65} + 130146715692752 q^{67} - 178710878083152 q^{71} - 205323946615296 q^{74} + 13818320315976 q^{78} + 857820862108188 q^{80} + 126746036597568 q^{81} + 249211917251112 q^{82} - 541736282848188 q^{83} + 630538772195064 q^{86} - 633552108095260 q^{87} + 969723837884556 q^{88} - 962583563732444 q^{91} + 22\!\cdots\!64 q^{92}+ \cdots + 40\!\cdots\!64 q^{96}+O(q^{100}) \) 36 * q - 508108 * q^4 + 470082 * q^5 + 1112016 * q^6 - 4820620 * q^7 - 167460710 * q^9 + 133305618 * q^13 + 5626041364 * q^16 - 30737731548 * q^20 - 51638088984 * q^22 - 23459433564 * q^23 - 13473060100 * q^24 + 169887741474 * q^25 + 281303298768 * q^28 - 85550328684 * q^29 - 681215606256 * q^30 + 831111242422 * q^33 - 449988200584 * q^34 + 726838987044 * q^35 + 1809260484664 * q^36 - 2518300733088 * q^38 - 5363921425320 * q^42 - 16561773855556 * q^45 + 29824615981340 * q^49 + 1184881612900 * q^51 + 21527128606228 * q^52 - 40200435711486 * q^53 + 9043904345168 * q^54 + 42099004809572 * q^57 - 3461494533632 * q^58 - 50458797940572 * q^59 - 298531808710416 * q^62 + 159779590145904 * q^63 - 71569159267548 * q^64 + 92095395748902 * q^65 + 130146715692752 * q^67 - 178710878083152 * q^71 - 205323946615296 * q^74 + 13818320315976 * q^78 + 857820862108188 * q^80 + 126746036597568 * q^81 + 249211917251112 * q^82 - 541736282848188 * q^83 + 630538772195064 * q^86 - 633552108095260 * q^87 + 969723837884556 * q^88 - 962583563732444 * q^91 + 2248076163071664 * q^92 - 212103831463414 * q^93 - 5356847193577464 * q^94 + 4021088569901964 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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