LMFDB - Embedded newform 29.16.b.a.28.2

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			28.2
Character	$\chi$	$=$	29.28
Dual form			29.16.b.a.28.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-327.159i q^{2} -2163.79i q^{3} -74264.8 q^{4} +235169. q^{5} -707903. q^{6} +2.51260e6 q^{7} +1.35760e7i q^{8} +9.66691e6 q^{9} +O(q^{10})$	\(q-327.159i q^{2} -2163.79i q^{3} -74264.8 q^{4} +235169. q^{5} -707903. q^{6} +2.51260e6 q^{7} +1.35760e7i q^{8} +9.66691e6 q^{9} -7.69374e7i q^{10} -7.17284e7i q^{11} +1.60694e8i q^{12} -4.51020e8 q^{13} -8.22019e8i q^{14} -5.08856e8i q^{15} +2.00801e9 q^{16} +1.32955e9i q^{17} -3.16261e9i q^{18} +3.49440e8i q^{19} -1.74648e10 q^{20} -5.43674e9i q^{21} -2.34666e10 q^{22} -2.49620e10 q^{23} +2.93757e10 q^{24} +2.47867e10 q^{25} +1.47555e11i q^{26} -5.19652e10i q^{27} -1.86598e11 q^{28} +(-2.92440e10 - 8.81702e10i) q^{29} -1.66477e11 q^{30} -2.04746e11i q^{31} -2.12079e11i q^{32} -1.55205e11 q^{33} +4.34975e11 q^{34} +5.90884e11 q^{35} -7.17912e11 q^{36} -7.75922e11i q^{37} +1.14322e11 q^{38} +9.75913e11i q^{39} +3.19266e12i q^{40} -9.31848e11i q^{41} -1.77868e12 q^{42} +1.23664e12i q^{43} +5.32690e12i q^{44} +2.27335e12 q^{45} +8.16653e12i q^{46} -2.93435e12i q^{47} -4.34492e12i q^{48} +1.56559e12 q^{49} -8.10917e12i q^{50} +2.87688e12 q^{51} +3.34949e13 q^{52} -8.73122e12 q^{53} -1.70009e13 q^{54} -1.68683e13i q^{55} +3.41112e13i q^{56} +7.56115e11 q^{57} +(-2.88456e13 + 9.56744e12i) q^{58} -2.99957e12 q^{59} +3.77901e13i q^{60} +4.29433e13i q^{61} -6.69844e13 q^{62} +2.42891e13 q^{63} -3.58492e12 q^{64} -1.06066e14 q^{65} +5.07768e13i q^{66} +5.77645e13 q^{67} -9.87391e13i q^{68} +5.40126e13i q^{69} -1.93313e14i q^{70} +4.14492e13 q^{71} +1.31238e14i q^{72} +5.77169e12i q^{73} -2.53850e14 q^{74} -5.36332e13i q^{75} -2.59511e13i q^{76} -1.80225e14i q^{77} +3.19279e14 q^{78} +5.65194e13i q^{79} +4.72221e14 q^{80} +2.62676e13 q^{81} -3.04862e14 q^{82} +1.19422e14 q^{83} +4.03759e14i q^{84} +3.12669e14i q^{85} +4.04578e14 q^{86} +(-1.90782e14 + 6.32780e13i) q^{87} +9.73788e14 q^{88} -6.03893e14i q^{89} -7.43747e14i q^{90} -1.13323e15 q^{91} +1.85380e15 q^{92} -4.43027e14 q^{93} -9.60000e14 q^{94} +8.21772e13i q^{95} -4.58895e14 q^{96} +5.20879e14i q^{97} -5.12196e14i q^{98} -6.93392e14i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	327.159i		−	1.80731i	−0.428257	−	0.903657i	$-0.640872\pi$
$2$		−	327.159i		−	1.80731i	0.428257	−	0.903657i	$-0.359128\pi$
$3$		−	2163.79i		−	0.571224i	−0.958345	−	0.285612i	$-0.907803\pi$
$3$		−	2163.79i		−	0.571224i	0.958345	−	0.285612i	$-0.0921968\pi$
$4$	−74264.8			−2.26638
$5$	235169.			1.34618			0.673092	−	0.739559i	$-0.264966\pi$
$5$	235169.			1.34618			0.673092	+	0.739559i	$0.264966\pi$
$6$	−707903.			−1.03238
$7$	2.51260e6			1.15316			0.576578	−	0.817042i	$-0.304388\pi$
$7$	2.51260e6			1.15316			0.576578	+	0.817042i	$0.304388\pi$
$8$			1.35760e7i			2.28875i
$9$	9.66691e6			0.673704
$10$		−	7.69374e7i		−	2.43298i
$11$		−	7.17284e7i		−	1.10980i	−0.831916	−	0.554902i	$-0.812756\pi$
$11$		−	7.17284e7i		−	1.10980i	0.831916	−	0.554902i	$-0.187244\pi$
$12$			1.60694e8i			1.29461i
$13$	−4.51020e8			−1.99352			−0.996760	−	0.0804354i	$-0.974369\pi$
$13$	−4.51020e8			−1.99352			−0.996760	+	0.0804354i	$0.974369\pi$
$14$		−	8.22019e8i		−	2.08411i
$15$		−	5.08856e8i		−	0.768972i
$16$	2.00801e9			1.87011
$17$			1.32955e9i			0.785849i	0.919571	+	0.392925i	$0.128537\pi$
$17$			1.32955e9i			0.785849i	−0.919571	+	0.392925i	$0.871463\pi$
$18$		−	3.16261e9i		−	1.21759i
$19$			3.49440e8i			0.0896851i	0.998994	+	0.0448425i	$0.0142786\pi$
$19$			3.49440e8i			0.0896851i	−0.998994	+	0.0448425i	$0.985721\pi$
$20$	−1.74648e10			−3.05097
$21$		−	5.43674e9i		−	0.658709i
$22$	−2.34666e10			−2.00576
$23$	−2.49620e10			−1.52869			−0.764347	−	0.644805i	$-0.776938\pi$
$23$	−2.49620e10			−1.52869			−0.764347	+	0.644805i	$0.776938\pi$
$24$	2.93757e10			1.30739
$25$	2.47867e10			0.812209
$26$			1.47555e11i			3.60292i
$27$		−	5.19652e10i		−	0.956059i
$28$	−1.86598e11			−2.61349
$29$	−2.92440e10	−	8.81702e10i	−0.314813	−	0.949154i
$29$	−2.92440e10	−	8.81702e10i	−0.314813	−	0.949154i
$30$	−1.66477e11			−1.38977
$31$		−	2.04746e11i		−	1.33660i	−0.743891	−	0.668301i	$-0.767022\pi$
$31$		−	2.04746e11i		−	1.33660i	0.743891	−	0.668301i	$-0.232978\pi$
$32$		−	2.12079e11i		−	1.09112i
$33$	−1.55205e11			−0.633946
$34$	4.34975e11			1.42028
$35$	5.90884e11			1.55236
$36$	−7.17912e11			−1.52687
$37$		−	7.75922e11i		−	1.34371i	−0.740684	−	0.671854i	$-0.765498\pi$
$37$		−	7.75922e11i		−	1.34371i	0.740684	−	0.671854i	$-0.234502\pi$
$38$	1.14322e11			0.162089
$39$			9.75913e11i			1.13875i
$40$			3.19266e12i			3.08108i
$41$		−	9.31848e11i		−	0.747250i	−0.927580	−	0.373625i	$-0.878115\pi$
$41$		−	9.31848e11i		−	0.747250i	0.927580	−	0.373625i	$-0.121885\pi$
$42$	−1.77868e12			−1.19049
$43$			1.23664e12i			0.693794i	0.937903	+	0.346897i	$0.112765\pi$
$43$			1.23664e12i			0.693794i	−0.937903	+	0.346897i	$0.887235\pi$
$44$			5.32690e12i			2.51524i
$45$	2.27335e12			0.906929
$46$			8.16653e12i			2.76283i
$47$		−	2.93435e12i		−	0.844848i	−0.906398	−	0.422424i	$-0.861179\pi$
$47$		−	2.93435e12i		−	0.844848i	0.906398	−	0.422424i	$-0.138821\pi$
$48$		−	4.34492e12i		−	1.06825i
$49$	1.56559e12			0.329767
$50$		−	8.10917e12i		−	1.46792i
$51$	2.87688e12			0.448896
$52$	3.34949e13			4.51808
$53$	−8.73122e12			−1.02095			−0.510477	−	0.859892i	$-0.670531\pi$
$53$	−8.73122e12			−1.02095			−0.510477	+	0.859892i	$0.670531\pi$
$54$	−1.70009e13			−1.72790
$55$		−	1.68683e13i		−	1.49400i
$56$			3.41112e13i			2.63929i
$57$	7.56115e11			0.0512302
$58$	−2.88456e13	+	9.56744e12i	−1.71542	+	0.568965i
$59$	−2.99957e12			−0.156917			−0.0784584	−	0.996917i	$-0.525000\pi$
$59$	−2.99957e12			−0.156917			−0.0784584	+	0.996917i	$0.525000\pi$
$60$			3.77901e13i			1.74278i
$61$			4.29433e13i			1.74953i	0.484547	+	0.874765i	$0.338984\pi$
$61$			4.29433e13i			1.74953i	−0.484547	+	0.874765i	$0.661016\pi$
$62$	−6.69844e13			−2.41566
$63$	2.42891e13			0.776885
$64$	−3.58492e12			−0.101890
$65$	−1.06066e14			−2.68364
$66$			5.07768e13i			1.14574i
$67$	5.77645e13			1.16439			0.582197	−	0.813048i	$-0.302193\pi$
$67$	5.77645e13			1.16439			0.582197	+	0.813048i	$0.302193\pi$
$68$		−	9.87391e13i		−	1.78103i
$69$			5.40126e13i			0.873226i
$70$		−	1.93313e14i		−	2.80560i
$71$	4.14492e13			0.540852			0.270426	−	0.962741i	$-0.412835\pi$
$71$	4.14492e13			0.540852			0.270426	+	0.962741i	$0.412835\pi$
$72$			1.31238e14i			1.54194i
$73$			5.77169e12i			0.0611479i	0.999533	+	0.0305740i	$0.00973351\pi$
$73$			5.77169e12i			0.0611479i	−0.999533	+	0.0305740i	$0.990266\pi$
$74$	−2.53850e14			−2.42850
$75$		−	5.36332e13i		−	0.463953i
$76$		−	2.59511e13i		−	0.203261i
$77$		−	1.80225e14i		−	1.27978i
$78$	3.19279e14			2.05807
$79$			5.65194e13i			0.331127i	0.986199	+	0.165563i	$0.0529442\pi$
$79$			5.65194e13i			0.331127i	−0.986199	+	0.165563i	$0.947056\pi$
$80$	4.72221e14			2.51751
$81$	2.62676e13			0.127580
$82$	−3.04862e14			−1.35052
$83$	1.19422e14			0.483058			0.241529	−	0.970394i	$-0.422351\pi$
$83$	1.19422e14			0.483058			0.241529	+	0.970394i	$0.422351\pi$
$84$			4.03759e14i			1.49289i
$85$			3.12669e14i			1.05790i
$86$	4.04578e14			1.25390
$87$	−1.90782e14	+	6.32780e13i	−0.542179	+	0.179828i
$88$	9.73788e14			2.54006
$89$		−	6.03893e14i		−	1.44722i	−0.690209	−	0.723610i	$-0.742481\pi$
$89$		−	6.03893e14i		−	1.44722i	0.690209	−	0.723610i	$-0.257519\pi$
$90$		−	7.43747e14i		−	1.63910i
$91$	−1.13323e15			−2.29884
$92$	1.85380e15			3.46460
$93$	−4.43027e14			−0.763499
$94$	−9.60000e14			−1.52691
$95$			8.21772e13i			0.120733i
$96$	−4.58895e14			−0.623274
$97$			5.20879e14i			0.654560i	0.944927	+	0.327280i	$0.106132\pi$
$97$			5.20879e14i			0.654560i	−0.944927	+	0.327280i	$0.893868\pi$
$98$		−	5.12196e14i		−	0.595993i
$99$		−	6.93392e14i		−	0.747679i
$100$	−1.84078e15			−1.84078
$101$			1.58634e14i			0.147227i	0.997287	+	0.0736134i	$0.0234531\pi$
$101$			1.58634e14i			0.147227i	−0.997287	+	0.0736134i	$0.976547\pi$
$102$		−	9.41196e14i		−	0.811295i
$103$	1.58250e15			1.26784			0.633920	−	0.773398i	$-0.281445\pi$
$103$	1.58250e15			1.26784			0.633920	+	0.773398i	$0.281445\pi$
$104$		−	6.12307e15i		−	4.56267i
$105$		−	1.27855e15i		−	0.886744i
$106$			2.85650e15i			1.84518i
$107$	4.49153e14			0.270406			0.135203	−	0.990818i	$-0.456831\pi$
$107$	4.49153e14			0.270406			0.135203	+	0.990818i	$0.456831\pi$
$108$			3.85919e15i			2.16680i
$109$	−4.05225e14			−0.212323			−0.106162	−	0.994349i	$-0.533856\pi$
$109$	−4.05225e14			−0.212323			−0.106162	+	0.994349i	$0.533856\pi$
$110$	−5.51860e15			−2.70012
$111$	−1.67893e15			−0.767558
$112$	5.04533e15			2.15652
$113$		−	3.22452e15i		−	1.28937i	−0.764449	−	0.644684i	$-0.776989\pi$
$113$		−	3.22452e15i		−	1.28937i	0.764449	−	0.644684i	$-0.223011\pi$
$114$		−	2.47370e14i		−	0.0925891i
$115$	−5.87027e15			−2.05790
$116$	2.17180e15	+	6.54794e15i	0.713486	+	2.15115i
$117$	−4.35997e15			−1.34304
$118$			9.81337e14i			0.283598i
$119$			3.34064e15i			0.906206i
$120$	6.90825e15			1.75998
$121$	−9.67716e14			−0.231663
$122$	1.40493e16			3.16195
$123$	−2.01632e15			−0.426847
$124$			1.52054e16i			3.02925i
$125$	−1.34773e15			−0.252801
$126$		−	7.94638e15i		−	1.40407i
$127$		−	5.35389e15i		−	0.891541i	−0.895147	−	0.445771i	$-0.852930\pi$
$127$		−	5.35389e15i		−	0.891541i	0.895147	−	0.445771i	$-0.147070\pi$
$128$		−	5.77657e15i		−	0.906974i
$129$	2.67584e15			0.396312
$130$			3.47003e16i			4.85018i
$131$		−	7.30720e14i		−	0.0964309i	−0.998837	−	0.0482155i	$-0.984647\pi$
$131$		−	7.30720e14i		−	0.0964309i	0.998837	−	0.0482155i	$-0.0153534\pi$
$132$	1.15263e16			1.43676
$133$			8.78002e14i			0.103421i
$134$		−	1.88982e16i		−	2.10442i
$135$		−	1.22206e16i		−	1.28703i
$136$	−1.80501e16			−1.79861
$137$			1.35058e15i			0.127384i	0.997970	+	0.0636920i	$0.0202875\pi$
$137$			1.35058e15i			0.127384i	−0.997970	+	0.0636920i	$0.979712\pi$
$138$	1.76707e16			1.57819
$139$	3.09087e15			0.261499			0.130750	−	0.991415i	$-0.458262\pi$
$139$	3.09087e15			0.261499			0.130750	+	0.991415i	$0.458262\pi$
$140$	−4.38819e16			−3.51824
$141$	−6.34933e15			−0.482597
$142$		−	1.35605e16i		−	0.977489i
$143$			3.23509e16i			2.21241i
$144$	1.94113e16			1.25990
$145$	−6.87727e15	−	2.07348e16i	−0.423795	−	1.27773i
$146$	1.88826e15			0.110513
$147$		−	3.38761e15i		−	0.188371i
$148$			5.76237e16i			3.04536i
$149$	3.06651e16			1.54080			0.770402	−	0.637558i	$-0.220055\pi$
$149$	3.06651e16			1.54080			0.770402	+	0.637558i	$0.220055\pi$
$150$	−1.75466e16			−0.838509
$151$	−6.06041e14			−0.0275534			−0.0137767	−	0.999905i	$-0.504385\pi$
$151$	−6.06041e14			−0.0275534			−0.0137767	+	0.999905i	$0.504385\pi$
$152$	−4.74401e15			−0.205267
$153$			1.28527e16i			0.529429i
$154$	−5.89621e16			−2.31296
$155$		−	4.81498e16i		−	1.79931i
$156$		−	7.24760e16i		−	2.58083i
$157$			2.17662e16i			0.738813i	0.929268	+	0.369406i	$0.120439\pi$
$157$			2.17662e16i			0.738813i	−0.929268	+	0.369406i	$0.879561\pi$
$158$	1.84908e16			0.598450
$159$			1.88925e16i			0.583193i
$160$		−	4.98743e16i		−	1.46885i
$161$	−6.27195e16			−1.76282
$162$		−	8.59369e15i		−	0.230578i
$163$		−	3.94701e16i		−	1.01126i	−0.862752	−	0.505628i	$-0.831261\pi$
$163$		−	3.94701e16i		−	1.01126i	0.862752	−	0.505628i	$-0.168739\pi$
$164$			6.92035e16i			1.69355i
$165$	−3.64994e16			−0.853407
$166$		−	3.90700e16i		−	0.873037i
$167$	−1.76634e16			−0.377312			−0.188656	−	0.982043i	$-0.560413\pi$
$167$	−1.76634e16			−0.377312			−0.188656	+	0.982043i	$0.560413\pi$
$168$	7.38095e16			1.50762
$169$	1.52233e17			2.97412
$170$	1.02293e17			1.91195
$171$			3.37800e15i			0.0604212i
$172$		−	9.18390e16i		−	1.57240i
$173$	8.81767e16			1.44547			0.722733	−	0.691127i	$-0.242885\pi$
$173$	8.81767e16			1.44547			0.722733	+	0.691127i	$0.242885\pi$
$174$	2.07019e16	+	6.24160e16i	0.325006	+	0.979888i
$175$	6.22789e16			0.936603
$176$		−	1.44032e17i		−	2.07545i
$177$			6.49045e15i			0.0896346i
$178$	−1.97569e17			−2.61558
$179$	1.26571e16			0.160670			0.0803352	−	0.996768i	$-0.474401\pi$
$179$	1.26571e16			0.160670			0.0803352	+	0.996768i	$0.474401\pi$
$180$	−1.68830e17			−2.05545
$181$	−2.79960e16			−0.326969			−0.163484	−	0.986546i	$-0.552273\pi$
$181$	−2.79960e16			−0.326969			−0.163484	+	0.986546i	$0.552273\pi$
$182$			3.70747e17i			4.15472i
$183$	9.29203e16			0.999373
$184$		−	3.38885e17i		−	3.49880i
$185$		−	1.82472e17i		−	1.80888i
$186$			1.44940e17i			1.37988i
$187$	9.53668e16			0.872138
$188$			2.17919e17i			1.91475i
$189$		−	1.30568e17i		−	1.10248i
$190$	2.68850e16			0.218202
$191$			1.90007e17i			1.48259i	0.671181	+	0.741293i	$0.265787\pi$
$191$			1.90007e17i			1.48259i	−0.671181	+	0.741293i	$0.734213\pi$
$192$			7.75703e15i			0.0582018i
$193$			4.58576e16i			0.330926i	0.986216	+	0.165463i	$0.0529119\pi$
$193$			4.58576e16i			0.330926i	−0.986216	+	0.165463i	$0.947088\pi$
$194$	1.70410e17			1.18299
$195$			2.29504e17i			1.53296i
$196$	−1.16268e17			−0.747378
$197$	2.76867e16			0.171306			0.0856532	−	0.996325i	$-0.472702\pi$
$197$	2.76867e16			0.171306			0.0856532	+	0.996325i	$0.472702\pi$
$198$	−2.26849e17			−1.35129
$199$	2.11201e17			1.21143			0.605715	−	0.795682i	$-0.292887\pi$
$199$	2.11201e17			1.21143			0.605715	+	0.795682i	$0.292887\pi$
$200$			3.36505e17i			1.85894i
$201$		−	1.24990e17i		−	0.665129i
$202$	5.18986e16			0.266085
$203$	−7.34785e16	−	2.21536e17i	−0.363028	−	1.09452i
$204$	−2.13651e17			−1.01737
$205$		−	2.19141e17i		−	1.00594i
$206$		−	5.17729e17i		−	2.29139i
$207$	−2.41305e17			−1.02989
$208$	−9.05654e17			−3.72810
$209$	2.50647e16			0.0995328
$210$	−4.18289e17			−1.60262
$211$			4.99204e17i			1.84569i	0.385167	+	0.922847i	$0.374144\pi$
$211$			4.99204e17i			1.84569i	−0.385167	+	0.922847i	$0.625856\pi$
$212$	6.48423e17			2.31387
$213$		−	8.96874e16i		−	0.308947i
$214$		−	1.46944e17i		−	0.488708i
$215$			2.90819e17i			0.933974i
$216$	7.05483e17			2.18818
$217$		−	5.14444e17i		−	1.54131i
$218$			1.32573e17i			0.383735i
$219$	1.24887e16			0.0349291
$220$			1.25272e18i			3.38597i
$221$		−	5.99655e17i		−	1.56661i
$222$			5.49278e17i			1.38722i
$223$	−1.26404e17			−0.308655			−0.154328	−	0.988020i	$-0.549321\pi$
$223$	−1.26404e17			−0.308655			−0.154328	+	0.988020i	$0.549321\pi$
$224$		−	5.32869e17i		−	1.25823i
$225$	2.39610e17			0.547188
$226$	−1.05493e18			−2.33029
$227$	−4.35843e16			−0.0931400			−0.0465700	−	0.998915i	$-0.514829\pi$
$227$	−4.35843e16			−0.0931400			−0.0465700	+	0.998915i	$0.514829\pi$
$228$	−5.61527e16			−0.116107
$229$		−	5.46694e16i		−	0.109390i	−0.998503	−	0.0546951i	$-0.982581\pi$
$229$		−	5.46694e16i		−	0.109390i	0.998503	−	0.0546951i	$-0.0174187\pi$
$230$			1.92051e18i			3.71927i
$231$	−3.89969e17			−0.731038
$232$	1.19700e18	−	3.97018e17i	2.17238	−	0.720528i
$233$	−3.80048e17			−0.667835			−0.333918	−	0.942602i	$-0.608371\pi$
$233$	−3.80048e17			−0.667835			−0.333918	+	0.942602i	$0.608371\pi$
$234$			1.42640e18i			2.42730i
$235$		−	6.90068e17i		−	1.13732i
$236$	2.22763e17			0.355634
$237$	1.22296e17			0.189147
$238$	1.09292e18			1.63780
$239$	2.99102e17			0.434346			0.217173	−	0.976133i	$-0.430316\pi$
$239$	2.99102e17			0.434346			0.217173	+	0.976133i	$0.430316\pi$
$240$		−	1.02179e18i		−	1.43806i
$241$	5.50081e17			0.750411			0.375205	−	0.926942i	$-0.377572\pi$
$241$	5.50081e17			0.750411			0.375205	+	0.926942i	$0.377572\pi$
$242$			3.16597e17i			0.418689i
$243$		−	8.02482e17i		−	1.02894i
$244$		−	3.18918e18i		−	3.96511i
$245$	3.68177e17			0.443927
$246$			6.59658e17i			0.771446i
$247$		−	1.57604e17i		−	0.178789i
$248$	2.77964e18			3.05915
$249$		−	2.58405e17i		−	0.275934i
$250$			4.40922e17i			0.456890i
$251$		−	1.15107e18i		−	1.15757i	−0.815480	−	0.578786i	$-0.803527\pi$
$251$		−	1.15107e18i		−	1.15757i	0.815480	−	0.578786i	$-0.196473\pi$
$252$	−1.80382e18			−1.76072
$253$			1.79048e18i			1.69655i
$254$	−1.75157e18			−1.61129
$255$	6.76551e17			0.604296
$256$	−2.00732e18			−1.74108
$257$	−1.74711e18			−1.47171			−0.735853	−	0.677141i	$-0.763219\pi$
$257$	−1.74711e18			−1.47171			−0.735853	+	0.677141i	$0.763219\pi$
$258$		−	8.75423e17i		−	0.716259i
$259$		−	1.94958e18i		−	1.54950i
$260$	7.87695e18			6.08216
$261$	−2.82699e17	−	8.52333e17i	−0.212090	−	0.639448i
$262$	−2.39061e17			−0.174281
$263$			1.12024e18i			0.793672i	0.917889	+	0.396836i	$0.129892\pi$
$263$			1.12024e18i			0.793672i	−0.917889	+	0.396836i	$0.870108\pi$
$264$		−	2.10708e18i		−	1.45094i
$265$	−2.05331e18			−1.37439
$266$	2.87246e17			0.186914
$267$	−1.30670e18			−0.826687
$268$	−4.28987e18			−2.63896
$269$		−	9.86319e17i		−	0.590031i	−0.955492	−	0.295016i	$-0.904675\pi$
$269$		−	9.86319e17i		−	0.590031i	0.955492	−	0.295016i	$-0.0953249\pi$
$270$	−3.99807e18			−2.32607
$271$			2.35022e18i			1.32996i	0.746861	+	0.664980i	$0.231560\pi$
$271$			2.35022e18i			1.32996i	−0.746861	+	0.664980i	$0.768440\pi$
$272$			2.66976e18i			1.46962i
$273$			2.45208e18i			1.31315i
$274$	4.41853e17			0.230223
$275$		−	1.77791e18i		−	0.901392i
$276$		−	4.01123e18i		−	1.97906i
$277$	−2.17959e18			−1.04659			−0.523296	−	0.852151i	$-0.675298\pi$
$277$	−2.17959e18			−1.04659			−0.523296	+	0.852151i	$0.675298\pi$
$278$		−	1.01121e18i		−	0.472611i
$279$		−	1.97926e18i		−	0.900474i
$280$			8.02187e18i			3.55296i
$281$	1.10254e18			0.475441			0.237721	−	0.971334i	$-0.423600\pi$
$281$	1.10254e18			0.475441			0.237721	+	0.971334i	$0.423600\pi$
$282$			2.07724e18i			0.872204i
$283$	1.44966e17			0.0592744			0.0296372	−	0.999561i	$-0.490565\pi$
$283$	1.44966e17			0.0592744			0.0296372	+	0.999561i	$0.490565\pi$
$284$	−3.07822e18			−1.22578
$285$	1.77814e17			0.0689653
$286$	1.05839e19			3.99853
$287$		−	2.34136e18i		−	0.861695i
$288$		−	2.05015e18i		−	0.735092i
$289$	1.09471e18			0.382441
$290$	−6.78359e18	+	2.24996e18i	−2.30927	+	0.765931i
$291$	1.12707e18			0.373900
$292$		−	4.28634e17i		−	0.138585i
$293$		−	2.55227e18i		−	0.804304i	−0.915573	−	0.402152i	$-0.868262\pi$
$293$		−	2.55227e18i		−	0.804304i	0.915573	−	0.402152i	$-0.131738\pi$
$294$	−1.10829e18			−0.340445
$295$	−7.05405e17			−0.211239
$296$	1.05340e19			3.07541
$297$	−3.72738e18			−1.06104
$298$		−	1.00324e19i		−	2.78472i
$299$	1.12584e19			3.04748
$300$			3.98306e18i			1.05150i
$301$			3.10719e18i			0.800053i
$302$			1.98271e17i			0.0497976i
$303$	3.43252e17			0.0840994
$304$			7.01679e17i			0.167721i
$305$			1.00989e19i			2.35519i
$306$	4.20487e18			0.956845
$307$		−	2.33832e18i		−	0.519238i	−0.965711	−	0.259619i	$-0.916403\pi$
$307$		−	2.33832e18i		−	0.519238i	0.965711	−	0.259619i	$-0.0835969\pi$
$308$			1.33844e19i			2.90046i
$309$		−	3.42420e18i		−	0.724221i
$310$	−1.57526e19			−3.25192
$311$			3.07645e18i			0.619936i	0.950747	+	0.309968i	$0.100318\pi$
$311$			3.07645e18i			0.619936i	−0.950747	+	0.309968i	$0.899682\pi$
$312$	−1.32490e19			−2.60630
$313$	5.67516e18			1.08992			0.544961	−	0.838461i	$-0.316545\pi$
$313$	5.67516e18			1.08992			0.544961	+	0.838461i	$0.316545\pi$
$314$	7.12099e18			1.33527
$315$	5.71202e18			1.04583
$316$		−	4.19740e18i		−	0.750460i
$317$			5.76163e18i			1.00601i	0.864284	+	0.503004i	$0.167772\pi$
$317$			5.76163e18i			1.00601i	−0.864284	+	0.503004i	$0.832228\pi$
$318$	6.18086e18			1.05401
$319$	−6.32430e18	+	2.09763e18i	−1.05337	+	0.349380i
$320$	−8.43061e17			−0.137162
$321$		−	9.71874e17i		−	0.154462i
$322$			2.05192e19i			3.18597i
$323$	−4.64599e17			−0.0704789
$324$	−1.95076e18			−0.289146
$325$	−1.11793e19			−1.61915
$326$	−1.29130e19			−1.82766
$327$			8.76823e17i			0.121284i
$328$	1.26508e19			1.71027
$329$		−	7.37285e18i		−	0.974241i
$330$			1.19411e19i			1.54237i
$331$		−	8.00495e18i		−	1.01076i	−0.862896	−	0.505381i	$-0.831352\pi$
$331$		−	8.00495e18i		−	1.01076i	0.862896	−	0.505381i	$-0.168648\pi$
$332$	−8.86886e18			−1.09479
$333$		−	7.50077e18i		−	0.905261i
$334$			5.77873e18i			0.681920i
$335$	1.35844e19			1.56749
$336$		−	1.09170e19i		−	1.23186i
$337$			2.22591e18i			0.245631i	0.992429	+	0.122816i	$0.0391924\pi$
$337$			2.22591e18i			0.245631i	−0.992429	+	0.122816i	$0.960808\pi$
$338$		−	4.98044e19i		−	5.37517i
$339$	−6.97719e18			−0.736517
$340$		−	2.32203e19i		−	2.39760i
$341$	−1.46861e19			−1.48337
$342$	1.10514e18			0.109200
$343$	−7.99502e18			−0.772883
$344$	−1.67887e19			−1.58792
$345$			1.27021e19i			1.17552i
$346$		−	2.88478e19i		−	2.61241i
$347$	6.46966e18			0.573337			0.286669	−	0.958030i	$-0.407452\pi$
$347$	6.46966e18			0.573337			0.286669	+	0.958030i	$0.407452\pi$
$348$	1.41684e19	−	4.69933e18i	1.22879	−	0.407560i
$349$	9.75878e17			0.0828333			0.0414166	−	0.999142i	$-0.486813\pi$
$349$	9.75878e17			0.0828333			0.0414166	+	0.999142i	$0.486813\pi$
$350$		−	2.03751e19i		−	1.69274i
$351$			2.34374e19i			1.90592i
$352$	−1.52121e19			−1.21093
$353$	2.03484e19			1.58569			0.792847	−	0.609421i	$-0.208598\pi$
$353$	2.03484e19			1.58569			0.792847	+	0.609421i	$0.208598\pi$
$354$	2.12341e18			0.161998
$355$	9.74755e18			0.728086
$356$			4.48480e19i			3.27996i
$357$	7.22844e18			0.517646
$358$		−	4.14088e18i		−	0.290382i
$359$			7.87831e18i			0.541034i	0.962715	+	0.270517i	$0.0871947\pi$
$359$			7.87831e18i			0.541034i	−0.962715	+	0.270517i	$0.912805\pi$
$360$			3.08632e19i			2.07573i
$361$	1.50590e19			0.991957
$362$			9.15913e18i			0.590935i
$363$			2.09394e18i			0.132332i
$364$	8.41593e19			5.21005
$365$			1.35732e18i			0.0823163i
$366$		−	3.03997e19i		−	1.80618i
$367$			2.06114e19i			1.19981i	0.800072	+	0.599904i	$0.204794\pi$
$367$			2.06114e19i			1.19981i	−0.800072	+	0.599904i	$0.795206\pi$
$368$	−5.01240e19			−2.85882
$369$		−	9.00809e18i		−	0.503425i
$370$	−5.96974e19			−3.26921
$371$	−2.19381e19			−1.17732
$372$	3.29013e19			1.73038
$373$	−3.40029e17			−0.0175267			−0.00876335	−	0.999962i	$-0.502789\pi$
$373$	−3.40029e17			−0.0175267			−0.00876335	+	0.999962i	$0.502789\pi$
$374$		−	3.12001e19i		−	1.57623i
$375$			2.91621e18i			0.144406i
$376$	3.98369e19			1.93365
$377$	1.31896e19	+	3.97665e19i	0.627585	+	1.89216i
$378$	−4.27164e19			−1.99254
$379$		−	2.05464e19i		−	0.939598i	−0.882773	−	0.469799i	$-0.844326\pi$
$379$		−	2.05464e19i		−	0.939598i	0.882773	−	0.469799i	$-0.155674\pi$
$380$		−	6.10288e18i		−	0.273626i
$381$	−1.15847e19			−0.509269
$382$	6.21625e19			2.67950
$383$	−1.59681e19			−0.674934			−0.337467	−	0.941337i	$-0.609570\pi$
$383$	−1.59681e19			−0.674934			−0.337467	+	0.941337i	$0.609570\pi$
$384$	−1.24993e19			−0.518085
$385$		−	4.23832e19i		−	1.72281i
$386$	1.50027e19			0.598087
$387$			1.19545e19i			0.467412i
$388$		−	3.86830e19i		−	1.48348i
$389$			1.23416e19i			0.464248i	0.972686	+	0.232124i	$0.0745676\pi$
$389$			1.23416e19i			0.464248i	−0.972686	+	0.232124i	$0.925432\pi$
$390$	7.50843e19			2.77054
$391$		−	3.31883e19i		−	1.20132i
$392$			2.12545e19i			0.754755i
$393$	−1.58113e18			−0.0550836
$394$		−	9.05793e18i		−	0.309605i
$395$			1.32916e19i			0.445757i
$396$			5.14946e19i			1.69453i
$397$	−1.49827e19			−0.483793			−0.241897	−	0.970302i	$-0.577769\pi$
$397$	−1.49827e19			−0.483793			−0.241897	+	0.970302i	$0.577769\pi$
$398$		−	6.90963e19i		−	2.18943i
$399$	1.89981e18			0.0590764
$400$	4.97719e19			1.51892
$401$	−5.42271e19			−1.62418			−0.812089	−	0.583533i	$-0.801670\pi$
$401$	−5.42271e19			−1.62418			−0.812089	+	0.583533i	$0.801670\pi$
$402$	−4.08917e19			−1.20210
$403$			9.23444e19i			2.66454i
$404$		−	1.17809e19i		−	0.333672i
$405$	6.17732e18			0.171746
$406$	−7.24775e19	+	2.40391e19i	−1.97814	+	0.656105i
$407$	−5.56556e19			−1.49125
$408$			3.90567e19i			1.02741i
$409$		−	5.51035e19i		−	1.42316i	−0.702604	−	0.711581i	$-0.747980\pi$
$409$		−	5.51035e19i		−	1.42316i	0.702604	−	0.711581i	$-0.252020\pi$
$410$	−7.16940e19			−1.81804
$411$	2.92236e18			0.0727647
$412$	−1.17524e20			−2.87341
$413$	−7.53673e18			−0.180949
$414$			7.89451e19i			1.86133i
$415$	2.80843e19			0.650284
$416$			9.56518e19i			2.17517i
$417$		−	6.68801e18i		−	0.149374i
$418$		−	8.20015e18i		−	0.179887i
$419$	−5.59770e19			−1.20616			−0.603079	−	0.797681i	$-0.706060\pi$
$419$	−5.59770e19			−1.20616			−0.603079	+	0.797681i	$0.706060\pi$
$420$			9.49513e19i			2.00970i
$421$		−	6.28392e19i		−	1.30652i	−0.757135	−	0.653258i	$-0.773402\pi$
$421$		−	6.28392e19i		−	1.30652i	0.757135	−	0.653258i	$-0.226598\pi$
$422$	1.63319e20			3.33575
$423$		−	2.83661e19i		−	0.569177i
$424$		−	1.18535e20i		−	2.33671i
$425$			3.29552e19i			0.638274i
$426$	−2.93420e19			−0.558365
$427$			1.07899e20i			2.01748i
$428$	−3.33563e19			−0.612843
$429$	7.00007e19			1.26378
$430$	9.51441e19			1.68798
$431$	5.94346e19			1.03624			0.518120	−	0.855308i	$-0.326632\pi$
$431$	5.94346e19			1.03624			0.518120	+	0.855308i	$0.326632\pi$
$432$		−	1.04347e20i		−	1.78793i
$433$			4.78947e19i			0.806544i	0.915080	+	0.403272i	$0.132127\pi$
$433$			4.78947e19i			0.806544i	−0.915080	+	0.403272i	$0.867873\pi$
$434$	−1.68305e20			−2.78563
$435$	−4.48659e19	+	1.48810e19i	−0.729872	+	0.242082i
$436$	3.00940e19			0.481206
$437$		−	8.72271e18i		−	0.137101i
$438$		−	4.08580e18i		−	0.0631279i
$439$	7.83901e19			1.19063			0.595315	−	0.803492i	$-0.297027\pi$
$439$	7.83901e19			1.19063			0.595315	+	0.803492i	$0.297027\pi$
$440$	2.29004e20			3.41939
$441$	1.51344e19			0.222165
$442$	−1.96183e20			−2.83135
$443$		−	6.22916e19i		−	0.883897i	−0.897041	−	0.441948i	$-0.854287\pi$
$443$		−	6.22916e19i		−	0.883897i	0.897041	−	0.441948i	$-0.145713\pi$
$444$	1.24686e20			1.73958
$445$		−	1.42017e20i		−	1.94822i
$446$			4.13541e19i			0.557837i
$447$		−	6.63529e19i		−	0.880144i
$448$	−9.00748e18			−0.117495
$449$			3.96064e19i			0.508063i	0.967196	+	0.254031i	$0.0817567\pi$
$449$			3.96064e19i			0.508063i	−0.967196	+	0.254031i	$0.918243\pi$
$450$		−	7.83906e19i		−	0.988941i
$451$	−6.68399e19			−0.829301
$452$			2.39468e20i			2.92220i
$453$			1.31135e18i			0.0157391i
$454$			1.42590e19i			0.168333i
$455$	−2.66500e20			−3.09466
$456$			1.02651e19i			0.117253i
$457$	−1.05440e20			−1.18477			−0.592384	−	0.805655i	$-0.701813\pi$
$457$	−1.05440e20			−1.18477			−0.592384	+	0.805655i	$0.701813\pi$
$458$	−1.78856e19			−0.197702
$459$	6.90906e19			0.751318
$460$	4.35955e20			4.66399
$461$		−	1.39084e20i		−	1.46393i	−0.681341	−	0.731966i	$-0.738603\pi$
$461$		−	1.39084e20i		−	1.46393i	0.681341	−	0.731966i	$-0.261397\pi$
$462$			1.27582e20i			1.32121i
$463$	1.69920e20			1.73136			0.865681	−	0.500596i	$-0.166886\pi$
$463$	1.69920e20			1.73136			0.865681	+	0.500596i	$0.166886\pi$
$464$	−5.87224e19	−	1.77047e20i	−0.588734	−	1.77502i
$465$	−1.04186e20			−1.02781
$466$			1.24336e20i			1.20699i
$467$		−	1.35865e20i		−	1.29787i	−0.760845	−	0.648933i	$-0.775215\pi$
$467$		−	1.35865e20i		−	1.29787i	0.760845	−	0.648933i	$-0.224785\pi$
$468$	3.23792e20			3.04385
$469$	1.45139e20			1.34273
$470$	−2.25762e20			−2.05549
$471$	4.70974e19			0.422027
$472$		−	4.07224e19i		−	0.359144i
$473$	8.87024e19			0.769975
$474$		−	4.00103e19i		−	0.341849i
$475$			8.66144e18i			0.0728430i
$476$		−	2.48092e20i		−	2.05381i
$477$	−8.44039e19			−0.687820
$478$		−	9.78539e19i		−	0.784999i
$479$			3.91138e19i			0.308897i	0.988001	+	0.154449i	$0.0493601\pi$
$479$			3.91138e19i			0.308897i	−0.988001	+	0.154449i	$0.950640\pi$
$480$	−1.07918e20			−0.839041
$481$			3.49956e20i			2.67871i
$482$		−	1.79964e20i		−	1.35623i
$483$			1.35712e20i			1.00696i
$484$	7.18672e19			0.525038
$485$			1.22494e20i			0.881157i
$486$	−2.62539e20			−1.85961
$487$	−1.79076e18			−0.0124902			−0.00624512	−	0.999980i	$-0.501988\pi$
$487$	−1.79076e18			−0.0124902			−0.00624512	+	0.999980i	$0.501988\pi$
$488$	−5.83000e20			−4.00424
$489$	−8.54051e19			−0.577653
$490$		−	1.20452e20i		−	0.802315i
$491$			1.22992e20i			0.806799i	0.915024	+	0.403399i	$0.132171\pi$
$491$			1.22992e20i			0.806799i	−0.915024	+	0.403399i	$0.867829\pi$
$492$	1.49742e20			0.967398
$493$	1.17227e20	−	3.88815e19i	0.745892	−	0.247395i
$494$	−5.15616e19			−0.323128
$495$		−	1.63064e20i		−	1.00651i
$496$		−	4.11132e20i		−	2.49959i
$497$	1.04145e20			0.623686
$498$	−8.45393e19			−0.498699
$499$	−7.83398e19			−0.455227			−0.227614	−	0.973751i	$-0.573092\pi$
$499$	−7.83398e19			−0.455227			−0.227614	+	0.973751i	$0.573092\pi$
$500$	1.00089e20			0.572944
$501$			3.82199e19i			0.215529i
$502$	−3.76582e20			−2.09210
$503$		−	1.94868e20i		−	1.06655i	−0.845943	−	0.533274i	$-0.820961\pi$
$503$		−	1.94868e20i		−	1.06655i	0.845943	−	0.533274i	$-0.179039\pi$
$504$			3.29750e20i			1.77810i
$505$			3.73058e19i			0.198194i
$506$	5.85772e20			3.06620
$507$		−	3.29401e20i		−	1.69889i
$508$			3.97606e20i			2.02057i
$509$	2.58584e20			1.29485			0.647423	−	0.762131i	$-0.275847\pi$
$509$	2.58584e20			1.29485			0.647423	+	0.762131i	$0.275847\pi$
$510$		−	2.21340e20i		−	1.09215i
$511$			1.45019e19i			0.0705130i
$512$			4.67427e20i			2.23970i
$513$	1.81587e19			0.0857442
$514$			5.71581e20i			2.65983i
$515$	3.72154e20			1.70675
$516$	−1.98721e20			−0.898194
$517$	−2.10477e20			−0.937615
$518$	−6.37822e20			−2.80044
$519$		−	1.90796e20i		−	0.825685i
$520$		−	1.43995e21i		−	6.14219i
$521$	1.57085e20			0.660466			0.330233	−	0.943899i	$-0.392873\pi$
$521$	1.57085e20			0.660466			0.330233	+	0.943899i	$0.392873\pi$
$522$	−2.78848e20	+	9.24876e19i	−1.15568	+	0.383314i
$523$	−2.90825e20			−1.18814			−0.594071	−	0.804412i	$-0.702480\pi$
$523$	−2.90825e20			−1.18814			−0.594071	+	0.804412i	$0.702480\pi$
$524$			5.42668e19i			0.218549i
$525$		−	1.34759e20i		−	0.535010i
$526$	3.66495e20			1.43441
$527$	2.72221e20			1.05037
$528$	−3.11654e20			−1.18555
$529$	3.56466e20			1.33690
$530$			6.71758e20i			2.48395i
$531$	−2.89966e19			−0.105715
$532$		−	6.52046e19i		−	0.234391i
$533$			4.20282e20i			1.48966i
$534$			4.27498e20i			1.49408i
$535$	1.05627e20			0.364016
$536$			7.84214e20i			2.66501i
$537$		−	2.73873e19i		−	0.0917787i
$538$	−3.22683e20			−1.06637
$539$		−	1.12297e20i		−	0.365977i
$540$			9.07560e20i			2.91690i
$541$		−	5.99080e20i		−	1.89892i	−0.313895	−	0.949458i	$-0.601634\pi$
$541$		−	5.99080e20i		−	1.89892i	0.313895	−	0.949458i	$-0.398366\pi$
$542$	7.68895e20			2.40366
$543$			6.05775e19i			0.186772i
$544$	2.81971e20			0.857456
$545$	−9.52962e19			−0.285826
$546$	8.02219e20			2.37327
$547$	−2.28999e19			−0.0668235			−0.0334117	−	0.999442i	$-0.510637\pi$
$547$	−2.28999e19			−0.0668235			−0.0334117	+	0.999442i	$0.510637\pi$
$548$		−	1.00300e20i		−	0.288701i
$549$			4.15129e20i			1.17866i
$550$	−5.81658e20			−1.62910
$551$	3.08101e19	−	1.02190e19i	0.0851249	−	0.0282340i
$552$	−7.33277e20			−1.99860
$553$			1.42011e20i			0.381840i
$554$			7.13073e20i			1.89152i
$555$	−3.94832e20			−1.03327
$556$	−2.29543e20			−0.592657
$557$	4.96235e20			1.26408			0.632039	−	0.774937i	$-0.282218\pi$
$557$	4.96235e20			1.26408			0.632039	+	0.774937i	$0.282218\pi$
$558$	−6.47532e20			−1.62744
$559$		−	5.57750e20i		−	1.38309i
$560$	1.18650e21			2.90308
$561$		−	2.06354e20i		−	0.498186i
$562$		−	3.60705e20i		−	0.859271i
$563$			7.15855e20i			1.68272i	0.540475	+	0.841360i	$0.318245\pi$
$563$			7.15855e20i			1.68272i	−0.540475	+	0.841360i	$0.681755\pi$
$564$	4.71532e20			1.09375
$565$		−	7.58306e20i		−	1.73572i
$566$		−	4.74268e19i		−	0.107127i
$567$	6.60000e19			0.147120
$568$			5.62716e20i			1.23788i
$569$		−	1.89760e20i		−	0.411967i	−0.978555	−	0.205984i	$-0.933961\pi$
$569$		−	1.89760e20i		−	0.411967i	0.978555	−	0.205984i	$-0.0660394\pi$
$570$		−	5.81735e19i		−	0.124642i
$571$	1.16175e20			0.245665			0.122832	−	0.992427i	$-0.460802\pi$
$571$	1.16175e20			0.245665			0.122832	+	0.992427i	$0.460802\pi$
$572$		−	2.40254e21i		−	5.01418i
$573$	4.11136e20			0.846888
$574$	−7.65996e20			−1.55735
$575$	−6.18724e20			−1.24162
$576$	−3.46551e19			−0.0686435
$577$		−	7.40630e20i		−	1.44805i	−0.689775	−	0.724024i	$-0.742291\pi$
$577$		−	7.40630e20i		−	1.44805i	0.689775	−	0.724024i	$-0.257709\pi$
$578$		−	3.58143e20i		−	0.691191i
$579$	9.92262e19			0.189033
$580$	5.10740e20	+	1.53987e21i	0.960483	+	2.89584i
$581$	3.00060e20			0.557040
$582$		−	3.68732e20i		−	0.675754i
$583$			6.26277e20i			1.13306i
$584$	−7.83568e19			−0.139952
$585$	−1.02533e21			−1.80798
$586$	−8.34999e20			−1.45363
$587$	−3.25073e19			−0.0558721			−0.0279360	−	0.999610i	$-0.508893\pi$
$587$	−3.25073e19			−0.0558721			−0.0279360	+	0.999610i	$0.508893\pi$
$588$			2.51580e20i			0.426920i
$589$	7.15463e19			0.119873
$590$			2.30780e20i			0.381775i
$591$		−	5.99082e19i		−	0.0978543i
$592$		−	1.55806e21i		−	2.51288i
$593$	−9.11421e20			−1.45147			−0.725736	−	0.687973i	$-0.758501\pi$
$593$	−9.11421e20			−1.45147			−0.725736	+	0.687973i	$0.758501\pi$
$594$			1.21945e21i			1.91763i
$595$			7.85612e20i			1.21992i
$596$	−2.27734e21			−3.49205
$597$		−	4.56996e20i		−	0.691998i
$598$		−	3.68327e21i		−	5.50775i
$599$			4.11734e20i			0.608017i	0.952669	+	0.304008i	$0.0983251\pi$
$599$			4.11734e20i			0.608017i	−0.952669	+	0.304008i	$0.901675\pi$
$600$	7.28127e20			1.06187
$601$		−	1.02932e20i		−	0.148250i	−0.997249	−	0.0741248i	$-0.976384\pi$
$601$		−	1.02932e20i		−	0.148250i	0.997249	−	0.0741248i	$-0.0236163\pi$
$602$	1.01654e21			1.44595
$603$	5.58404e20			0.784456
$604$	4.50075e19			0.0624465
$605$	−2.27576e20			−0.311861
$606$		−	1.12298e20i		−	0.151994i
$607$			5.96092e20i			0.796889i	0.917192	+	0.398445i	$0.130450\pi$
$607$			5.96092e20i			0.796889i	−0.917192	+	0.398445i	$0.869550\pi$
$608$	7.41088e19			0.0978573
$609$	−4.79358e20	+	1.58992e20i	−0.625217	+	0.207370i
$610$	3.30395e21			4.25656
$611$			1.32345e21i			1.68422i
$612$		−	9.54502e20i		−	1.19989i
$613$	−8.45979e20			−1.05052			−0.525262	−	0.850941i	$-0.676033\pi$
$613$	−8.45979e20			−1.05052			−0.525262	+	0.850941i	$0.676033\pi$
$614$	−7.65002e20			−0.938426
$615$	−4.74176e20			−0.574614
$616$	2.44674e21			2.92909
$617$		−	4.79571e20i		−	0.567172i	−0.958947	−	0.283586i	$-0.908476\pi$
$617$		−	4.79571e20i		−	0.567172i	0.958947	−	0.283586i	$-0.0915241\pi$
$618$	−1.12026e21			−1.30889
$619$			4.08621e20i			0.471673i	0.971793	+	0.235836i	$0.0757829\pi$
$619$			4.08621e20i			0.471673i	−0.971793	+	0.235836i	$0.924217\pi$
$620$			3.57583e21i			4.07793i
$621$			1.29716e21i			1.46152i
$622$	1.00649e21			1.12042
$623$		−	1.51734e21i		−	1.66887i
$624$			1.95965e21i			2.12958i
$625$	−1.07337e21			−1.15253
$626$		−	1.85668e21i		−	1.96983i
$627$		−	5.42349e19i		−	0.0568555i
$628$		−	1.61646e21i		−	1.67443i
$629$	1.03163e21			1.05595
$630$		−	1.86874e21i		−	1.89014i
$631$	−1.92987e21			−1.92889			−0.964447	−	0.264275i	$-0.914867\pi$
$631$	−1.92987e21			−1.92889			−0.964447	+	0.264275i	$0.914867\pi$
$632$	−7.67310e20			−0.757867
$633$	1.08017e21			1.05430
$634$	1.88497e21			1.81817
$635$		−	1.25907e21i		−	1.20018i
$636$		−	1.40305e21i		−	1.32174i
$637$	−7.06112e20			−0.657397
$638$	6.86257e20	+	2.06905e21i	0.631439	+	1.90378i
$639$	4.00686e20			0.364374
$640$		−	1.35847e21i		−	1.22095i
$641$			5.62278e20i			0.499477i	0.968313	+	0.249739i	$0.0803447\pi$
$641$			5.62278e20i			0.499477i	−0.968313	+	0.249739i	$0.919655\pi$
$642$	−3.17957e20			−0.279162
$643$	−1.15662e21			−1.00371			−0.501857	−	0.864951i	$-0.667350\pi$
$643$	−1.15662e21			−1.00371			−0.501857	+	0.864951i	$0.667350\pi$
$644$	4.65785e21			3.99523
$645$	6.29273e20			0.533508
$646$			1.51998e20i			0.127378i
$647$	1.67194e21			1.38496			0.692482	−	0.721435i	$-0.256517\pi$
$647$	1.67194e21			1.38496			0.692482	+	0.721435i	$0.256517\pi$
$648$			3.56611e20i			0.291999i
$649$			2.15155e20i			0.174147i
$650$			3.65740e21i			2.92632i
$651$	−1.11315e21			−0.880433
$652$			2.93124e21i			2.29189i
$653$		−	2.32854e21i		−	1.79985i	−0.436048	−	0.899923i	$-0.643622\pi$
$653$		−	2.32854e21i		−	1.79985i	0.436048	−	0.899923i	$-0.356378\pi$
$654$	2.86860e20			0.219198
$655$		−	1.71842e20i		−	0.129814i
$656$		−	1.87116e21i		−	1.39744i
$657$			5.57944e19i			0.0411956i
$658$	−2.41209e21			−1.76076
$659$			8.29636e20i			0.598752i	0.954135	+	0.299376i	$0.0967784\pi$
$659$			8.29636e20i			0.598752i	−0.954135	+	0.299376i	$0.903222\pi$
$660$	2.71062e21			1.93415
$661$	−1.11973e20			−0.0789958			−0.0394979	−	0.999220i	$-0.512576\pi$
$661$	−1.11973e20			−0.0789958			−0.0394979	+	0.999220i	$0.512576\pi$
$662$	−2.61889e21			−1.82676
$663$	−1.29753e21			−0.894882
$664$			1.62128e21i			1.10560i
$665$			2.06478e20i			0.139223i
$666$	−2.45394e21			−1.63609
$667$	7.29989e20	+	2.20090e21i	0.481252	+	1.45097i
$668$	1.31177e21			0.855132
$669$			2.73511e20i			0.176311i
$670$		−	4.44425e21i		−	2.83294i
$671$	3.08025e21			1.94163
$672$	−1.15302e21			−0.718732
$673$	4.93200e20			0.304025			0.152013	−	0.988379i	$-0.451425\pi$
$673$	4.93200e20			0.304025			0.152013	+	0.988379i	$0.451425\pi$
$674$	7.28227e20			0.443933
$675$		−	1.28804e21i		−	0.776520i
$676$	−1.13056e22			−6.74050
$677$		−	9.22814e20i		−	0.544126i	−0.962279	−	0.272063i	$-0.912294\pi$
$677$		−	9.22814e20i		−	0.544126i	0.962279	−	0.272063i	$-0.0877059\pi$
$678$			2.28265e21i			1.33112i
$679$			1.30876e21i			0.754809i
$680$	−4.24481e21			−2.42126
$681$			9.43074e19i			0.0532038i
$682$			4.80468e21i			2.68091i
$683$	−2.54799e21			−1.40619			−0.703093	−	0.711098i	$-0.748198\pi$
$683$	−2.54799e21			−1.40619			−0.703093	+	0.711098i	$0.748198\pi$
$684$		−	2.50867e20i		−	0.136937i
$685$			3.17613e20i			0.171482i
$686$			2.61564e21i			1.39684i
$687$	−1.18293e20			−0.0624863
$688$			2.48319e21i			1.29747i
$689$	3.93795e21			2.03529
$690$	4.15559e21			2.12454
$691$	2.67015e21			1.35036			0.675182	−	0.737651i	$-0.264065\pi$
$691$	2.67015e21			1.35036			0.675182	+	0.737651i	$0.264065\pi$
$692$	−6.54843e21			−3.27598
$693$		−	1.74222e21i		−	0.862189i
$694$		−	2.11660e21i		−	1.03620i
$695$	7.26876e20			0.352026
$696$	−8.59065e20	−	2.59006e21i	−0.411582	−	1.24091i
$697$	1.23894e21			0.587226
$698$		−	3.19267e20i		−	0.149706i
$699$			8.22346e20i			0.381483i
$700$	−4.62513e21			−2.12270
$701$	−3.48455e21			−1.58220			−0.791099	−	0.611688i	$-0.790491\pi$
$701$	−3.48455e21			−1.58220			−0.791099	+	0.611688i	$0.790491\pi$
$702$	7.66773e21			3.44460
$703$	2.71138e20			0.120511
$704$			2.57141e20i			0.113078i
$705$	−1.49316e21			−0.649664
$706$		−	6.65715e21i		−	2.86585i
$707$			3.98584e20i			0.169775i
$708$		−	4.82013e20i		−	0.203146i
$709$	−1.65286e21			−0.689269			−0.344634	−	0.938737i	$-0.611997\pi$
$709$	−1.65286e21			−0.689269			−0.344634	+	0.938737i	$0.611997\pi$
$710$		−	3.18899e21i		−	1.31588i
$711$			5.46368e20i			0.223081i
$712$	8.19848e21			3.31233
$713$			5.11086e21i			2.04326i
$714$		−	2.36485e21i		−	0.935549i
$715$			7.60792e21i			2.97832i
$716$	−9.39976e20			−0.364141
$717$		−	6.47195e20i		−	0.248108i
$718$	2.57746e21			0.977819
$719$	−2.42457e20			−0.0910267			−0.0455133	−	0.998964i	$-0.514492\pi$
$719$	−2.42457e20			−0.0910267			−0.0455133	+	0.998964i	$0.514492\pi$
$720$	4.56492e21			1.69605
$721$	3.97619e21			1.46202
$722$		−	4.92669e21i		−	1.79278i
$723$		−	1.19026e21i		−	0.428652i
$724$	2.07912e21			0.741037
$725$	−7.24862e20	−	2.18544e21i	−0.255694	−	0.770911i
$726$	6.85049e20			0.239165
$727$			3.97979e21i			1.37516i	0.726110	+	0.687578i	$0.241326\pi$
$727$			3.97979e21i			1.37516i	−0.726110	+	0.687578i	$0.758674\pi$
$728$		−	1.53848e22i		−	5.26147i
$729$	−1.35949e21			−0.460172
$730$	4.44059e20			0.148771
$731$	−1.64418e21			−0.545218
$732$	−6.90071e21			−2.26496
$733$		−	2.41996e21i		−	0.786192i	−0.919497	−	0.393096i	$-0.871404\pi$
$733$		−	2.41996e21i		−	0.786192i	0.919497	−	0.393096i	$-0.128596\pi$
$734$	6.74319e21			2.16843
$735$		−	7.96659e20i		−	0.253582i
$736$			5.29391e21i			1.66799i
$737$		−	4.14335e21i		−	1.29225i
$738$	−2.94707e21			−0.909847
$739$			6.28024e21i			1.91930i	0.281196	+	0.959650i	$0.409269\pi$
$739$			6.28024e21i			1.91930i	−0.281196	+	0.959650i	$0.590731\pi$
$740$			1.35513e22i			4.09961i
$741$	−3.41023e20			−0.102128
$742$			7.17723e21i			2.12778i
$743$			1.61237e21i			0.473204i	0.971607	+	0.236602i	$0.0760337\pi$
$743$			1.61237e21i			0.473204i	−0.971607	+	0.236602i	$0.923966\pi$
$744$		−	6.01456e21i		−	1.74746i
$745$	7.21147e21			2.07421
$746$			1.11244e20i			0.0316762i
$747$	1.15444e21			0.325438
$748$	−7.08240e21			−1.97660
$749$	1.12854e21			0.311820
$750$	9.54064e20			0.260987
$751$		−	4.01567e21i		−	1.08757i	−0.839223	−	0.543787i	$-0.816990\pi$
$751$		−	4.01567e21i		−	1.08757i	0.839223	−	0.543787i	$-0.183010\pi$
$752$		−	5.89222e21i		−	1.57996i
$753$	−2.49067e21			−0.661232
$754$	1.30100e22	−	4.31510e21i	3.41972	−	1.13424i
$755$	−1.42522e20			−0.0370919
$756$			9.69659e21i			2.49865i
$757$			2.70758e21i			0.690816i	0.938453	+	0.345408i	$0.112259\pi$
$757$			2.70758e21i			0.690816i	−0.938453	+	0.345408i	$0.887741\pi$
$758$	−6.72194e21			−1.69815
$759$	3.87423e21			0.969109
$760$	−1.11564e21			−0.276327
$761$	4.07331e21			0.998993			0.499496	−	0.866316i	$-0.333518\pi$
$761$	4.07331e21			0.998993			0.499496	+	0.866316i	$0.333518\pi$
$762$			3.79004e21i			0.920410i
$763$	−1.01817e21			−0.244842
$764$		−	1.41109e22i		−	3.36011i
$765$			3.02255e21i			0.712709i
$766$			5.22409e21i			1.21982i
$767$	1.35287e21			0.312817
$768$			4.34343e21i			0.994544i
$769$		−	7.92015e21i		−	1.79591i	−0.440083	−	0.897957i	$-0.645051\pi$
$769$		−	7.92015e21i		−	1.79591i	0.440083	−	0.897957i	$-0.354949\pi$
$770$	−1.38660e22			−3.11366
$771$			3.78038e21i			0.840673i
$772$		−	3.40560e21i		−	0.750005i
$773$		−	1.66043e19i		−	0.00362138i	−0.999998	−	0.00181069i	$-0.999424\pi$
$773$		−	1.66043e19i		−	0.00362138i	0.999998	−	0.00181069i	$-0.000576360\pi$
$774$	3.91102e21			0.844760
$775$		−	5.07496e21i		−	1.08560i
$776$	−7.07149e21			−1.49812
$777$	−4.21848e21			−0.885113
$778$	4.03767e21			0.839042
$779$	3.25625e20			0.0670172
$780$		−	1.70441e22i		−	3.47427i
$781$		−	2.97308e21i		−	0.600239i
$782$	−1.08578e22			−2.17117
$783$	−4.58178e21	+	1.51967e21i	−0.907447	+	0.300979i
$784$	3.14372e21			0.616700
$785$			5.11872e21i			0.994577i
$786$			5.17279e20i			0.0995534i
$787$	−7.49421e21			−1.42862			−0.714308	−	0.699831i	$-0.753259\pi$
$787$	−7.49421e21			−1.42862			−0.714308	+	0.699831i	$0.753259\pi$
$788$	−2.05614e21			−0.388246
$789$	2.42396e21			0.453364
$790$	4.34846e21			0.805623
$791$		−	8.10192e21i		−	1.48684i
$792$	9.41353e21			1.71125
$793$		−	1.93683e22i		−	3.48772i
$794$			4.90170e21i			0.874366i
$795$			4.44293e21i			0.785084i
$796$	−1.56848e22			−2.74556
$797$			6.10504e20i			0.105865i	0.998598	+	0.0529323i	$0.0168568\pi$
$797$			6.10504e20i			0.105865i	−0.998598	+	0.0529323i	$0.983143\pi$
$798$		−	6.21540e20i		−	0.106770i
$799$	3.90138e21			0.663923
$800$		−	5.25673e21i		−	0.886218i
$801$		−	5.83778e21i		−	0.974998i
$802$			1.77409e22i			2.93540i
$803$	4.13994e20			0.0678621
$804$			9.28239e21i			1.50744i
$805$	−1.47496e22			−2.37308
$806$	3.02113e22			4.81567
$807$	−2.13419e21			−0.337040
$808$	−2.15363e21			−0.336965
$809$			1.81825e21i			0.281863i	0.990019	+	0.140932i	$0.0450098\pi$
$809$			1.81825e21i			0.281863i	−0.990019	+	0.140932i	$0.954990\pi$
$810$		−	2.02097e21i		−	0.310400i
$811$	1.03501e22			1.57503			0.787513	−	0.616299i	$-0.211369\pi$
$811$	1.03501e22			1.57503			0.787513	+	0.616299i	$0.211369\pi$
$812$	5.45687e21	+	1.64523e22i	0.822760	+	2.48061i
$813$	5.08539e21			0.759705
$814$			1.82082e22i			2.69516i
$815$		−	9.28212e21i		−	1.36134i
$816$	5.77681e21			0.839483
$817$	−4.32132e20			−0.0622230
$818$	−1.80276e22			−2.57210
$819$	−1.09549e22			−1.54874
$820$			1.62745e22i			2.27984i
$821$	−1.06971e22			−1.48489			−0.742445	−	0.669907i	$-0.766334\pi$
$821$	−1.06971e22			−1.48489			−0.742445	+	0.669907i	$0.766334\pi$
$822$		−	9.56077e20i		−	0.131509i
$823$		−	4.45050e21i		−	0.606611i	−0.952893	−	0.303306i	$-0.901910\pi$
$823$		−	4.45050e21i		−	0.606611i	0.952893	−	0.303306i	$-0.0980903\pi$
$824$			2.14841e22i			2.90177i
$825$	−3.84702e21			−0.514897
$826$			2.46571e21i			0.327032i
$827$			1.05576e22i			1.38762i	0.720156	+	0.693812i	$0.244070\pi$
$827$			1.05576e22i			1.38762i	−0.720156	+	0.693812i	$0.755930\pi$
$828$	1.79205e22			2.33412
$829$		−	7.28068e21i		−	0.939752i	−0.882733	−	0.469876i	$-0.844299\pi$
$829$		−	7.28068e21i		−	0.939752i	0.882733	−	0.469876i	$-0.155701\pi$
$830$		−	9.18803e21i		−	1.17527i
$831$			4.71619e21i			0.597838i
$832$	1.61687e21			0.203119
$833$			2.08154e21i			0.259147i
$834$	−2.18804e21			−0.269967
$835$	−4.15387e21			−0.507930
$836$	−1.86143e21			−0.225579
$837$	−1.06397e22			−1.27787
$838$			1.83134e22i			2.17991i
$839$		−	7.55611e21i		−	0.891422i	−0.895177	−	0.445711i	$-0.852951\pi$
$839$		−	7.55611e21i		−	0.891422i	0.895177	−	0.445711i	$-0.147049\pi$
$840$	1.73577e22			2.02954
$841$	−6.91876e21	+	5.15690e21i	−0.801786	+	0.597611i
$842$	−2.05584e22			−2.36129
$843$		−	2.38567e21i		−	0.271583i
$844$		−	3.70733e22i		−	4.18305i
$845$	3.58004e22			4.00371
$846$	−9.28023e21			−1.02868
$847$	−2.43148e21			−0.267144
$848$	−1.75324e22			−1.90929
$849$		−	3.13676e20i		−	0.0338589i
$850$	1.07816e22			1.15356
$851$			1.93685e22i			2.05412i
$852$			6.66062e21i			0.700193i
$853$			1.32017e22i			1.37566i	0.725871	+	0.687831i	$0.241437\pi$
$853$			1.32017e22i			1.37566i	−0.725871	+	0.687831i	$0.758563\pi$
$854$	3.53002e22			3.64622
$855$			7.94400e20i			0.0813380i
$856$			6.09772e21i			0.618892i
$857$	9.64988e21			0.970880			0.485440	−	0.874270i	$-0.338659\pi$
$857$	9.64988e21			0.970880			0.485440	+	0.874270i	$0.338659\pi$
$858$		−	2.29013e22i		−	2.28405i
$859$		−	1.83155e22i		−	1.81080i	−0.424557	−	0.905401i	$-0.639570\pi$
$859$		−	1.83155e22i		−	1.81080i	0.424557	−	0.905401i	$-0.360430\pi$
$860$		−	2.15977e22i		−	2.11674i
$861$	−5.06621e21			−0.492221
$862$		−	1.94446e22i		−	1.87281i
$863$	7.59763e21			0.725433			0.362717	−	0.931899i	$-0.381849\pi$
$863$	7.59763e21			0.725433			0.362717	+	0.931899i	$0.381849\pi$
$864$	−1.10207e22			−1.04318
$865$	2.07364e22			1.94586
$866$	1.56692e22			1.45768
$867$		−	2.36872e21i		−	0.218459i
$868$			3.82051e22i			3.49320i
$869$	4.05404e21			0.367486
$870$	4.86845e21	+	1.46783e22i	0.437518	+	1.31911i
$871$	−2.60529e22			−2.32124
$872$		−	5.50136e21i		−	0.485955i
$873$			5.03530e21i			0.440979i
$874$	−2.85371e21			−0.247784
$875$	−3.38631e21			−0.291519
$876$	−9.27474e20			−0.0791628
$877$	−2.63914e21			−0.223339			−0.111670	−	0.993745i	$-0.535620\pi$
$877$	−2.63914e21			−0.223339			−0.111670	+	0.993745i	$0.535620\pi$
$878$		−	2.56460e22i		−	2.15184i
$879$	−5.52259e21			−0.459437
$880$		−	3.38717e22i		−	2.79394i
$881$		−	5.24190e21i		−	0.428716i	−0.976755	−	0.214358i	$-0.931234\pi$
$881$		−	5.24190e21i		−	0.428716i	0.976755	−	0.214358i	$-0.0687659\pi$
$882$		−	4.95136e21i		−	0.401522i
$883$	3.28609e20			0.0264225			0.0132113	−	0.999913i	$-0.495795\pi$
$883$	3.28609e20			0.0264225			0.0132113	+	0.999913i	$0.495795\pi$
$884$			4.45333e22i			3.55053i
$885$			1.52635e21i			0.120665i
$886$	−2.03792e22			−1.59748
$887$			4.93296e21i			0.383425i	0.981451	+	0.191713i	$0.0614042\pi$
$887$			4.93296e21i			0.383425i	−0.981451	+	0.191713i	$0.938596\pi$
$888$		−	2.27933e22i		−	1.75675i
$889$		−	1.34522e22i		−	1.02809i
$890$	−4.64620e22			−3.52105
$891$		−	1.88414e21i		−	0.141589i
$892$	9.38735e21			0.699531
$893$	1.02538e21			0.0757703
$894$	−2.17079e22			−1.59070
$895$	2.97655e21			0.216292
$896$		−	1.45142e22i		−	1.04588i
$897$		−	2.43607e22i		−	1.74079i
$898$	1.29576e22			0.918229
$899$	−1.80525e22	+	5.98759e21i	−1.26864	+	0.420779i
$900$	−1.77946e22			−1.24014
$901$		−	1.16086e22i		−	0.802315i
$902$			2.18673e22i			1.49881i
$903$	6.72330e21			0.457009
$904$	4.37762e22			2.95104
$905$	−6.58378e21			−0.440160
$906$	4.29018e20			0.0284455
$907$			1.71728e22i			1.12924i	0.825350	+	0.564621i	$0.190978\pi$
$907$			1.71728e22i			1.12924i	−0.825350	+	0.564621i	$0.809022\pi$
$908$	3.23678e21			0.211091
$909$			1.53350e21i			0.0991872i
$910$			8.71879e22i			5.59302i
$911$			1.64359e22i			1.04570i	0.852425	+	0.522849i	$0.175131\pi$
$911$			1.64359e22i			1.04570i	−0.852425	+	0.522849i	$0.824869\pi$
$912$	1.51829e21			0.0958061
$913$		−	8.56595e21i		−	0.536099i
$914$			3.44956e22i			2.14125i
$915$	2.18519e22			1.34534
$916$			4.06002e21i			0.247920i
$917$		−	1.83601e21i		−	0.111200i
$918$		−	2.26036e22i		−	1.35787i
$919$	2.38784e21			0.142278			0.0711391	−	0.997466i	$-0.477337\pi$
$919$	2.38784e21			0.142278			0.0711391	+	0.997466i	$0.477337\pi$
$920$		−	7.96951e22i		−	4.71002i
$921$	−5.05964e21			−0.296601
$922$	−4.55026e22			−2.64579
$923$	−1.86944e22			−1.07820
$924$	2.89610e22			1.65681
$925$		−	1.92325e22i		−	1.09137i
$926$		−	5.55909e22i		−	3.12911i
$927$	1.52979e22			0.854149
$928$	−1.86990e22	+	6.20204e21i	−1.03564	+	0.343499i
$929$	3.05558e22			1.67871			0.839356	−	0.543582i	$-0.182932\pi$
$929$	3.05558e22			1.67871			0.839356	+	0.543582i	$0.182932\pi$
$930$			3.40854e22i			1.85757i
$931$			5.47079e20i			0.0295752i
$932$	2.82242e22			1.51357
$933$	6.65680e21			0.354122
$934$	−4.44493e22			−2.34565
$935$	2.24273e22			1.17406
$936$		−	5.91912e22i		−	3.07389i
$937$	6.94788e21			0.357936			0.178968	−	0.983855i	$-0.442724\pi$
$937$	6.94788e21			0.357936			0.178968	+	0.983855i	$0.442724\pi$
$938$		−	4.74835e22i		−	2.42673i
$939$		−	1.22799e22i		−	0.622589i
$940$			5.12478e22i			2.57760i
$941$	2.12028e22			1.05796			0.528982	−	0.848633i	$-0.322574\pi$
$941$	2.12028e22			1.05796			0.528982	+	0.848633i	$0.322574\pi$
$942$		−	1.54083e22i		−	0.762736i
$943$			2.32608e22i			1.14232i
$944$	−6.02318e21			−0.293451
$945$		−	3.07054e22i		−	1.48415i
$946$		−	2.90198e22i		−	1.39159i
$947$		−	6.87679e21i		−	0.327161i	−0.986530	−	0.163580i	$-0.947696\pi$
$947$		−	6.87679e21i		−	0.327161i	0.986530	−	0.163580i	$-0.0523043\pi$
$948$	−9.08231e21			−0.428680
$949$		−	2.60315e21i		−	0.121900i
$950$	2.83367e21			0.131650
$951$	1.24670e22			0.574655
$952$	−4.53526e22			−2.07408
$953$	−2.90857e21			−0.131972			−0.0659861	−	0.997821i	$-0.521019\pi$
$953$	−2.90857e21			−0.131972			−0.0659861	+	0.997821i	$0.521019\pi$
$954$			2.76135e22i			1.24311i
$955$			4.46837e22i			1.99583i
$956$	−2.22128e22			−0.984393
$957$	4.53883e21	+	1.36845e22i	0.199574	+	0.601712i
$958$	1.27964e22			0.558274
$959$			3.39345e21i			0.146893i
$960$			1.82421e21i			0.0783503i
$961$	−1.84556e22			−0.786506
$962$	1.14491e23			4.84127
$963$	4.34192e21			0.182173
$964$	−4.08517e22			−1.70072
$965$			1.07843e22i			0.445487i
$966$	4.43993e22			1.81990
$967$			2.37638e22i			0.966535i	0.875473	+	0.483268i	$0.160550\pi$
$967$			2.37638e22i			0.966535i	−0.875473	+	0.483268i	$0.839450\pi$
$968$		−	1.31378e22i		−	0.530220i
$969$			1.00530e21i			0.0402592i
$970$	4.00751e22			1.59253
$971$			8.25082e21i			0.325352i	0.986680	+	0.162676i	$0.0520125\pi$
$971$			8.25082e21i			0.325352i	−0.986680	+	0.162676i	$0.947988\pi$
$972$			5.95962e22i			2.33196i
$973$	7.76613e21			0.301549
$974$			5.85863e20i			0.0225738i
$975$			2.41896e22i			0.924899i
$976$			8.62307e22i			3.27181i
$977$	1.38690e22			0.522199			0.261100	−	0.965312i	$-0.415915\pi$
$977$	1.38690e22			0.522199			0.261100	+	0.965312i	$0.415915\pi$
$978$			2.79410e22i			1.04400i
$979$	−4.33163e22			−1.60613
$980$	−2.73426e22			−1.00611
$981$	−3.91728e21			−0.143043
$982$	4.02379e22			1.45814
$983$			4.26234e22i			1.53284i	0.642340	+	0.766420i	$0.277964\pi$
$983$			4.26234e22i			1.53284i	−0.642340	+	0.766420i	$0.722036\pi$
$984$		−	2.73737e22i		−	0.976946i
$985$	6.51103e21			0.230610
$986$	−1.27204e22	−	3.83518e22i	−0.447121	−	1.34806i
$987$	−1.59533e22			−0.556509
$988$			1.17045e22i			0.405204i
$989$		−	3.08691e22i		−	1.06060i
$990$	−5.33478e22			−1.81908
$991$	−3.97845e22			−1.34636			−0.673181	−	0.739478i	$-0.735073\pi$
$991$	−3.97845e22			−1.34636			−0.673181	+	0.739478i	$0.735073\pi$
$992$	−4.34223e22			−1.45839
$993$	−1.73211e22			−0.577371
$994$		−	3.40720e22i		−	1.12720i
$995$	4.96679e22			1.63081
$996$			1.91904e22i			0.625372i
$997$			1.13283e22i			0.366397i	0.983076	+	0.183199i	$0.0586452\pi$
$997$			1.13283e22i			0.366397i	−0.983076	+	0.183199i	$0.941355\pi$
$998$			2.56296e22i			0.822739i
$999$	−4.03210e22			−1.28466

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.16.b.a.28.2	✓	36
29.28	even	2	inner	29.16.b.a.28.35	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.16.b.a.28.2	✓	36	1.1	even	1	trivial
29.16.b.a.28.35	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)

\(f(q)\)	\(=\)	\(q-327.159i q^{2} -2163.79i q^{3} -74264.8 q^{4} +235169. q^{5} -707903. q^{6} +2.51260e6 q^{7} +1.35760e7i q^{8} +9.66691e6 q^{9} +O(q^{10})\)	\(q-327.159i q^{2} -2163.79i q^{3} -74264.8 q^{4} +235169. q^{5} -707903. q^{6} +2.51260e6 q^{7} +1.35760e7i q^{8} +9.66691e6 q^{9} -7.69374e7i q^{10} -7.17284e7i q^{11} +1.60694e8i q^{12} -4.51020e8 q^{13} -8.22019e8i q^{14} -5.08856e8i q^{15} +2.00801e9 q^{16} +1.32955e9i q^{17} -3.16261e9i q^{18} +3.49440e8i q^{19} -1.74648e10 q^{20} -5.43674e9i q^{21} -2.34666e10 q^{22} -2.49620e10 q^{23} +2.93757e10 q^{24} +2.47867e10 q^{25} +1.47555e11i q^{26} -5.19652e10i q^{27} -1.86598e11 q^{28} +(-2.92440e10 - 8.81702e10i) q^{29} -1.66477e11 q^{30} -2.04746e11i q^{31} -2.12079e11i q^{32} -1.55205e11 q^{33} +4.34975e11 q^{34} +5.90884e11 q^{35} -7.17912e11 q^{36} -7.75922e11i q^{37} +1.14322e11 q^{38} +9.75913e11i q^{39} +3.19266e12i q^{40} -9.31848e11i q^{41} -1.77868e12 q^{42} +1.23664e12i q^{43} +5.32690e12i q^{44} +2.27335e12 q^{45} +8.16653e12i q^{46} -2.93435e12i q^{47} -4.34492e12i q^{48} +1.56559e12 q^{49} -8.10917e12i q^{50} +2.87688e12 q^{51} +3.34949e13 q^{52} -8.73122e12 q^{53} -1.70009e13 q^{54} -1.68683e13i q^{55} +3.41112e13i q^{56} +7.56115e11 q^{57} +(-2.88456e13 + 9.56744e12i) q^{58} -2.99957e12 q^{59} +3.77901e13i q^{60} +4.29433e13i q^{61} -6.69844e13 q^{62} +2.42891e13 q^{63} -3.58492e12 q^{64} -1.06066e14 q^{65} +5.07768e13i q^{66} +5.77645e13 q^{67} -9.87391e13i q^{68} +5.40126e13i q^{69} -1.93313e14i q^{70} +4.14492e13 q^{71} +1.31238e14i q^{72} +5.77169e12i q^{73} -2.53850e14 q^{74} -5.36332e13i q^{75} -2.59511e13i q^{76} -1.80225e14i q^{77} +3.19279e14 q^{78} +5.65194e13i q^{79} +4.72221e14 q^{80} +2.62676e13 q^{81} -3.04862e14 q^{82} +1.19422e14 q^{83} +4.03759e14i q^{84} +3.12669e14i q^{85} +4.04578e14 q^{86} +(-1.90782e14 + 6.32780e13i) q^{87} +9.73788e14 q^{88} -6.03893e14i q^{89} -7.43747e14i q^{90} -1.13323e15 q^{91} +1.85380e15 q^{92} -4.43027e14 q^{93} -9.60000e14 q^{94} +8.21772e13i q^{95} -4.58895e14 q^{96} +5.20879e14i q^{97} -5.12196e14i q^{98} -6.93392e14i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 508108 q^{4} + 470082 q^{5} + 1112016 q^{6} - 4820620 q^{7} - 167460710 q^{9}+O(q^{10}) \) 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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