LMFDB - Embedded newform 29.16.b.a.28.6

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			28.6
Character	$\chi$	$=$	29.28
Dual form			29.16.b.a.28.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-255.661i q^{2} +4338.48i q^{3} -32594.8 q^{4} -284737. q^{5} +1.10918e6 q^{6} -3.50246e6 q^{7} -44288.6i q^{8} -4.47354e6 q^{9} +O(q^{10})$	\(q-255.661i q^{2} +4338.48i q^{3} -32594.8 q^{4} -284737. q^{5} +1.10918e6 q^{6} -3.50246e6 q^{7} -44288.6i q^{8} -4.47354e6 q^{9} +7.27962e7i q^{10} -3.04941e7i q^{11} -1.41412e8i q^{12} -4.29015e8 q^{13} +8.95444e8i q^{14} -1.23533e9i q^{15} -1.07939e9 q^{16} +2.53498e9i q^{17} +1.14371e9i q^{18} -4.65883e9i q^{19} +9.28093e9 q^{20} -1.51954e10i q^{21} -7.79616e9 q^{22} +5.54895e9 q^{23} +1.92146e8 q^{24} +5.05575e10 q^{25} +1.09683e11i q^{26} +4.28441e10i q^{27} +1.14162e11 q^{28} +(6.49672e10 + 6.63961e10i) q^{29} -3.15825e11 q^{30} -8.17168e10i q^{31} +2.74507e11i q^{32} +1.32298e11 q^{33} +6.48096e11 q^{34} +9.97279e11 q^{35} +1.45814e11 q^{36} -3.34605e11i q^{37} -1.19108e12 q^{38} -1.86128e12i q^{39} +1.26106e10i q^{40} -4.52645e11i q^{41} -3.88487e12 q^{42} +6.62585e11i q^{43} +9.93947e11i q^{44} +1.27378e12 q^{45} -1.41865e12i q^{46} -4.60853e12i q^{47} -4.68291e12i q^{48} +7.51966e12 q^{49} -1.29256e13i q^{50} -1.09980e13 q^{51} +1.39837e13 q^{52} -2.69409e12 q^{53} +1.09536e13 q^{54} +8.68279e12i q^{55} +1.55119e11i q^{56} +2.02123e13 q^{57} +(1.69749e13 - 1.66096e13i) q^{58} -3.38176e13 q^{59} +4.02652e13i q^{60} +2.05845e13i q^{61} -2.08918e13 q^{62} +1.56684e13 q^{63} +3.48114e13 q^{64} +1.22157e14 q^{65} -3.38235e13i q^{66} -3.33094e13 q^{67} -8.26270e13i q^{68} +2.40740e13i q^{69} -2.54966e14i q^{70} +8.83696e13 q^{71} +1.98127e11i q^{72} +1.19616e14i q^{73} -8.55456e13 q^{74} +2.19343e14i q^{75} +1.51854e14i q^{76} +1.06804e14i q^{77} -4.75857e14 q^{78} -2.60180e14i q^{79} +3.07342e14 q^{80} -2.50069e14 q^{81} -1.15724e14 q^{82} -1.84704e14 q^{83} +4.95289e14i q^{84} -7.21801e14i q^{85} +1.69397e14 q^{86} +(-2.88059e14 + 2.81859e14i) q^{87} -1.35054e12 q^{88} +8.68945e13i q^{89} -3.25657e14i q^{90} +1.50261e15 q^{91} -1.80867e14 q^{92} +3.54527e14 q^{93} -1.17822e15 q^{94} +1.32654e15i q^{95} -1.19094e15 q^{96} +7.72413e14i q^{97} -1.92249e15i q^{98} +1.36416e14i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	255.661i		−	1.41234i	−0.708041	−	0.706172i	$-0.750421\pi$
$2$		−	255.661i		−	1.41234i	0.708041	−	0.706172i	$-0.249579\pi$
$3$			4338.48i			1.14532i	0.819791	+	0.572662i	$0.194089\pi$
$3$			4338.48i			1.14532i	−0.819791	+	0.572662i	$0.805911\pi$
$4$	−32594.8			−0.994713
$5$	−284737.			−1.62993			−0.814964	−	0.579511i	$-0.803244\pi$
$5$	−284737.			−1.62993			−0.814964	+	0.579511i	$0.803244\pi$
$6$	1.10918e6			1.61759
$7$	−3.50246e6			−1.60745			−0.803725	−	0.595000i	$-0.797152\pi$
$7$	−3.50246e6			−1.60745			−0.803725	+	0.595000i	$0.797152\pi$
$8$		−	44288.6i		−	0.00746650i
$9$	−4.47354e6			−0.311769
$10$			7.27962e7i			2.30202i
$11$		−	3.04941e7i		−	0.471813i	−0.971776	−	0.235907i	$-0.924194\pi$
$11$		−	3.04941e7i		−	0.471813i	0.971776	−	0.235907i	$-0.0758060\pi$
$12$		−	1.41412e8i		−	1.13927i
$13$	−4.29015e8			−1.89626			−0.948130	−	0.317883i	$-0.897028\pi$
$13$	−4.29015e8			−1.89626			−0.948130	+	0.317883i	$0.897028\pi$
$14$			8.95444e8i			2.27027i
$15$		−	1.23533e9i		−	1.86680i
$16$	−1.07939e9			−1.00526
$17$			2.53498e9i			1.49833i	0.662385	+	0.749164i	$0.269545\pi$
$17$			2.53498e9i			1.49833i	−0.662385	+	0.749164i	$0.730455\pi$
$18$			1.14371e9i			0.440325i
$19$		−	4.65883e9i		−	1.19571i	−0.801605	−	0.597854i	$-0.796020\pi$
$19$		−	4.65883e9i		−	1.19571i	0.801605	−	0.597854i	$-0.203980\pi$
$20$	9.28093e9			1.62131
$21$		−	1.51954e10i		−	1.84105i
$22$	−7.79616e9			−0.666362
$23$	5.54895e9			0.339823			0.169911	−	0.985459i	$-0.445652\pi$
$23$	5.54895e9			0.339823			0.169911	+	0.985459i	$0.445652\pi$
$24$	1.92146e8			0.00855157
$25$	5.05575e10			1.65667
$26$			1.09683e11i			2.67817i
$27$			4.28441e10i			0.788248i
$28$	1.14162e11			1.59895
$29$	6.49672e10	+	6.63961e10i	0.699374	+	0.714756i
$29$	6.49672e10	+	6.63961e10i	0.699374	+	0.714756i
$30$	−3.15825e11			−2.63656
$31$		−	8.17168e10i		−	0.533456i	−0.963772	−	0.266728i	$-0.914057\pi$
$31$		−	8.17168e10i		−	0.533456i	0.963772	−	0.266728i	$-0.0859426\pi$
$32$			2.74507e11i			1.41230i
$33$	1.32298e11			0.540380
$34$	6.48096e11			2.11615
$35$	9.97279e11			2.62003
$36$	1.45814e11			0.310121
$37$		−	3.34605e11i		−	0.579454i	−0.957109	−	0.289727i	$-0.906435\pi$
$37$		−	3.34605e11i		−	0.579454i	0.957109	−	0.289727i	$-0.0935646\pi$
$38$	−1.19108e12			−1.68875
$39$		−	1.86128e12i		−	2.17183i
$40$			1.26106e10i			0.0121699i
$41$		−	4.52645e11i		−	0.362977i	−0.983393	−	0.181488i	$-0.941908\pi$
$41$		−	4.52645e11i		−	0.362977i	0.983393	−	0.181488i	$-0.0580915\pi$
$42$	−3.88487e12			−2.60020
$43$			6.62585e11i			0.371730i	0.982575	+	0.185865i	$0.0595088\pi$
$43$			6.62585e11i			0.371730i	−0.982575	+	0.185865i	$0.940491\pi$
$44$			9.93947e11i			0.469319i
$45$	1.27378e12			0.508161
$46$		−	1.41865e12i		−	0.479946i
$47$		−	4.60853e12i		−	1.32687i	−0.748234	−	0.663435i	$-0.769098\pi$
$47$		−	4.60853e12i		−	1.32687i	0.748234	−	0.663435i	$-0.230902\pi$
$48$		−	4.68291e12i		−	1.15135i
$49$	7.51966e12			1.58390
$50$		−	1.29256e13i		−	2.33978i
$51$	−1.09980e13			−1.71607
$52$	1.39837e13			1.88623
$53$	−2.69409e12			−0.315024			−0.157512	−	0.987517i	$-0.550347\pi$
$53$	−2.69409e12			−0.315024			−0.157512	+	0.987517i	$0.550347\pi$
$54$	1.09536e13			1.11328
$55$			8.68279e12i			0.769022i
$56$			1.55119e11i			0.0120020i
$57$	2.02123e13			1.36947
$58$	1.69749e13	−	1.66096e13i	1.00948	−	0.987756i
$59$	−3.38176e13			−1.76910			−0.884550	−	0.466445i	$-0.845535\pi$
$59$	−3.38176e13			−1.76910			−0.884550	+	0.466445i	$0.845535\pi$
$60$			4.02652e13i			1.85693i
$61$			2.05845e13i			0.838622i	0.907843	+	0.419311i	$0.137728\pi$
$61$			2.05845e13i			0.838622i	−0.907843	+	0.419311i	$0.862272\pi$
$62$	−2.08918e13			−0.753423
$63$	1.56684e13			0.501153
$64$	3.48114e13			0.989399
$65$	1.22157e14			3.09077
$66$		−	3.38235e13i		−	0.763201i
$67$	−3.33094e13			−0.671437			−0.335719	−	0.941962i	$-0.608979\pi$
$67$	−3.33094e13			−0.671437			−0.335719	+	0.941962i	$0.608979\pi$
$68$		−	8.26270e13i		−	1.49041i
$69$			2.40740e13i			0.389207i
$70$		−	2.54966e14i		−	3.70038i
$71$	8.83696e13			1.15310			0.576548	−	0.817064i	$-0.304400\pi$
$71$	8.83696e13			1.15310			0.576548	+	0.817064i	$0.304400\pi$
$72$			1.98127e11i			0.00232782i
$73$			1.19616e14i			1.26727i	0.773633	+	0.633634i	$0.218438\pi$
$73$			1.19616e14i			1.26727i	−0.773633	+	0.633634i	$0.781562\pi$
$74$	−8.55456e13			−0.818389
$75$			2.19343e14i			1.89742i
$76$			1.51854e14i			1.18939i
$77$			1.06804e14i			0.758417i
$78$	−4.75857e14			−3.06737
$79$		−	2.60180e14i		−	1.52430i	−0.647400	−	0.762150i	$-0.724144\pi$
$79$		−	2.60180e14i		−	1.52430i	0.647400	−	0.762150i	$-0.275856\pi$
$80$	3.07342e14			1.63850
$81$	−2.50069e14			−1.21457
$82$	−1.15724e14			−0.512648
$83$	−1.84704e14			−0.747121			−0.373561	−	0.927606i	$-0.621863\pi$
$83$	−1.84704e14			−0.747121			−0.373561	+	0.927606i	$0.621863\pi$
$84$			4.95289e14i			1.83132i
$85$		−	7.21801e14i		−	2.44217i
$86$	1.69397e14			0.525011
$87$	−2.88059e14	+	2.81859e14i	−0.818628	+	0.801010i
$88$	−1.35054e12			−0.00352280
$89$			8.68945e13i			0.208241i	0.994565	+	0.104121i	$0.0332028\pi$
$89$			8.68945e13i			0.208241i	−0.994565	+	0.104121i	$0.966797\pi$
$90$		−	3.25657e14i		−	0.717698i
$91$	1.50261e15			3.04814
$92$	−1.80867e14			−0.338026
$93$	3.54527e14			0.610981
$94$	−1.17822e15			−1.87400
$95$			1.32654e15i			1.94892i
$96$	−1.19094e15			−1.61755
$97$			7.72413e14i			0.970647i	0.874335	+	0.485323i	$0.161298\pi$
$97$			7.72413e14i			0.970647i	−0.874335	+	0.485323i	$0.838702\pi$
$98$		−	1.92249e15i		−	2.23701i
$99$			1.36416e14i			0.147097i
$100$	−1.64791e15			−1.64791
$101$		−	1.57894e15i		−	1.46540i	−0.680553	−	0.732699i	$-0.738261\pi$
$101$		−	1.57894e15i		−	1.46540i	0.680553	−	0.732699i	$-0.261739\pi$
$102$			2.81175e15i			2.42368i
$103$	7.07937e14			0.567173			0.283587	−	0.958947i	$-0.408476\pi$
$103$	7.07937e14			0.567173			0.283587	+	0.958947i	$0.408476\pi$
$104$			1.90005e13i			0.0141584i
$105$			4.32668e15i			3.00079i
$106$			6.88775e14i			0.444921i
$107$	2.63643e14			0.158722			0.0793612	−	0.996846i	$-0.474712\pi$
$107$	2.63643e14			0.158722			0.0793612	+	0.996846i	$0.474712\pi$
$108$		−	1.39649e15i		−	0.784081i
$109$	−1.75431e15			−0.919194			−0.459597	−	0.888128i	$-0.652006\pi$
$109$	−1.75431e15			−0.919194			−0.459597	+	0.888128i	$0.652006\pi$
$110$	2.21985e15			1.08612
$111$	1.45168e15			0.663664
$112$	3.78051e15			1.61590
$113$			2.51196e14i			0.100444i	0.998738	+	0.0502220i	$0.0159929\pi$
$113$			2.51196e14i			0.100444i	−0.998738	+	0.0502220i	$0.984007\pi$
$114$		−	5.16750e15i		−	1.93417i
$115$	−1.57999e15			−0.553887
$116$	−2.11759e15	−	2.16417e15i	−0.695677	−	0.710977i
$117$	1.91922e15			0.591195
$118$			8.64585e15i			2.49858i
$119$		−	8.87865e15i		−	2.40849i
$120$	−5.47109e13			−0.0139385
$121$	3.24736e15			0.777392
$122$	5.26266e15			1.18442
$123$	1.96379e15			0.415726
$124$			2.66354e15i			0.530636i
$125$	−5.70611e15			−1.07032
$126$		−	4.00580e15i		−	0.707800i
$127$			1.22991e15i			0.204807i	0.994743	+	0.102403i	$0.0326532\pi$
$127$			1.22991e15i			0.204807i	−0.994743	+	0.102403i	$0.967347\pi$
$128$			9.51078e13i			0.0149328i
$129$	−2.87461e15			−0.425752
$130$		−	3.12307e16i		−	4.36523i
$131$			1.08083e15i			0.142633i	0.997454	+	0.0713167i	$0.0227201\pi$
$131$			1.08083e15i			0.142633i	−0.997454	+	0.0713167i	$0.977280\pi$
$132$	−4.31222e15			−0.537523
$133$			1.63174e16i			1.92204i
$134$			8.51592e15i			0.948300i
$135$		−	1.21993e16i		−	1.28479i
$136$	1.12271e14			0.0111873
$137$		−	1.43621e15i		−	0.135461i	−0.997704	−	0.0677306i	$-0.978424\pi$
$137$		−	1.43621e15i		−	0.135461i	0.997704	−	0.0677306i	$-0.0215758\pi$
$138$	6.15481e15			0.549694
$139$	−6.62115e15			−0.560173			−0.280087	−	0.959975i	$-0.590363\pi$
$139$	−6.62115e15			−0.560173			−0.280087	+	0.959975i	$0.590363\pi$
$140$	−3.25061e16			−2.60618
$141$	1.99940e16			1.51970
$142$		−	2.25927e16i		−	1.62857i
$143$			1.30824e16i			0.894681i
$144$	4.82869e15			0.313408
$145$	−1.84986e16	−	1.89054e16i	−1.13993	−	1.16500i
$146$	3.05813e16			1.78982
$147$			3.26239e16i			1.81408i
$148$			1.09064e16i			0.576391i
$149$	8.23421e15			0.413738			0.206869	−	0.978369i	$-0.433673\pi$
$149$	8.23421e15			0.413738			0.206869	+	0.978369i	$0.433673\pi$
$150$	5.60775e16			2.67981
$151$	1.47222e14			0.00669336			0.00334668	−	0.999994i	$-0.498935\pi$
$151$	1.47222e14			0.00669336			0.00334668	+	0.999994i	$0.498935\pi$
$152$	−2.06333e14			−0.00892776
$153$		−	1.13403e16i		−	0.467132i
$154$	2.73057e16			1.07114
$155$			2.32678e16i			0.869496i
$156$			6.06679e16i			2.16035i
$157$		−	4.97202e15i		−	0.168766i	−0.996433	−	0.0843831i	$-0.973108\pi$
$157$		−	4.97202e15i		−	0.168766i	0.996433	−	0.0843831i	$-0.0268919\pi$
$158$	−6.65180e16			−2.15283
$159$		−	1.16883e16i		−	0.360804i
$160$		−	7.81622e16i		−	2.30195i
$161$	−1.94350e16			−0.546248
$162$			6.39330e16i			1.71539i
$163$			4.21642e16i			1.08028i	0.841575	+	0.540140i	$0.181629\pi$
$163$			4.21642e16i			1.08028i	−0.841575	+	0.540140i	$0.818371\pi$
$164$			1.47539e16i			0.361058i
$165$	−3.76701e16			−0.880780
$166$			4.72218e16i			1.05519i
$167$	3.03047e16			0.647347			0.323673	−	0.946169i	$-0.395082\pi$
$167$	3.03047e16			0.647347			0.323673	+	0.946169i	$0.395082\pi$
$168$	−6.72982e14			−0.0137462
$169$	1.32868e17			2.59580
$170$	−1.84537e17			−3.44918
$171$			2.08415e16i			0.372784i
$172$		−	2.15968e16i		−	0.369765i
$173$	−8.63150e16			−1.41495			−0.707474	−	0.706739i	$-0.750165\pi$
$173$	−8.63150e16			−1.41495			−0.707474	+	0.706739i	$0.750165\pi$
$174$	7.20606e16	+	7.36455e16i	1.13130	+	1.15618i
$175$	−1.77076e17			−2.66301
$176$			3.29149e16i			0.474294i
$177$		−	1.46717e17i		−	2.02619i
$178$	2.22156e16			0.294108
$179$	−1.17746e16			−0.149468			−0.0747340	−	0.997204i	$-0.523811\pi$
$179$	−1.17746e16			−0.149468			−0.0747340	+	0.997204i	$0.523811\pi$
$180$	−4.15186e16			−0.505475
$181$	−2.96316e16			−0.346072			−0.173036	−	0.984916i	$-0.555358\pi$
$181$	−2.96316e16			−0.346072			−0.173036	+	0.984916i	$0.555358\pi$
$182$		−	3.84159e17i		−	4.30503i
$183$	−8.93054e16			−0.960494
$184$		−	2.45756e14i		−	0.00253729i
$185$			9.52743e16i			0.944470i
$186$		−	9.06389e16i		−	0.862914i
$187$	7.73017e16			0.706931
$188$			1.50214e17i			1.31986i
$189$		−	1.50060e17i		−	1.26707i
$190$	3.39145e17			2.75254
$191$		−	1.16121e17i		−	0.906070i	−0.891493	−	0.453035i	$-0.850341\pi$
$191$		−	1.16121e17i		−	0.906070i	0.891493	−	0.453035i	$-0.149659\pi$
$192$			1.51029e17i			1.13318i
$193$			6.10297e16i			0.440414i	0.975453	+	0.220207i	$0.0706733\pi$
$193$			6.10297e16i			0.440414i	−0.975453	+	0.220207i	$0.929327\pi$
$194$	1.97476e17			1.37089
$195$			5.29974e17i			3.53993i
$196$	−2.45101e17			−1.57553
$197$	1.45021e17			0.897290			0.448645	−	0.893710i	$-0.351907\pi$
$197$	1.45021e17			0.897290			0.448645	+	0.893710i	$0.351907\pi$
$198$	3.48764e16			0.207751
$199$	−6.54787e16			−0.375579			−0.187790	−	0.982209i	$-0.560132\pi$
$199$	−6.54787e16			−0.375579			−0.187790	+	0.982209i	$0.560132\pi$
$200$		−	2.23912e15i		−	0.0123695i
$201$		−	1.44512e17i		−	0.769014i
$202$	−4.03674e17			−2.06964
$203$	−2.27545e17	−	2.32550e17i	−1.12421	−	1.14894i
$204$	3.58476e17			1.70700
$205$			1.28885e17i			0.591627i
$206$		−	1.80992e17i		−	0.801043i
$207$	−2.48235e16			−0.105946
$208$	4.63074e17			1.90623
$209$	−1.42067e17			−0.564151
$210$	1.10617e18			4.23814
$211$			2.41220e17i			0.891855i	0.895069	+	0.445927i	$0.147126\pi$
$211$			2.41220e17i			0.891855i	−0.895069	+	0.445927i	$0.852874\pi$
$212$	8.78132e16			0.313358
$213$			3.83390e17i			1.32067i
$214$		−	6.74034e16i		−	0.224171i
$215$		−	1.88662e17i		−	0.605894i
$216$	1.89751e15			0.00588546
$217$			2.86210e17i			0.857505i
$218$			4.48509e17i			1.29822i
$219$	−5.18953e17			−1.45143
$220$		−	2.83013e17i		−	0.764957i
$221$		−	1.08754e18i		−	2.84122i
$222$		−	3.71138e17i		−	0.937321i
$223$	−1.83091e17			−0.447074			−0.223537	−	0.974695i	$-0.571760\pi$
$223$	−1.83091e17			−0.447074			−0.223537	+	0.974695i	$0.571760\pi$
$224$		−	9.61448e17i		−	2.27021i
$225$	−2.26171e17			−0.516498
$226$	6.42211e16			0.141861
$227$	7.58957e17			1.62190			0.810948	−	0.585118i	$-0.198952\pi$
$227$	7.58957e17			1.62190			0.810948	+	0.585118i	$0.198952\pi$
$228$	−6.58814e17			−1.36223
$229$		−	4.15449e17i		−	0.831288i	−0.909527	−	0.415644i	$-0.863556\pi$
$229$		−	4.15449e17i		−	0.831288i	0.909527	−	0.415644i	$-0.136444\pi$
$230$			4.03943e17i			0.782278i
$231$	−4.63368e17			−0.868634
$232$	2.94059e15	−	2.87731e15i	0.00533673	−	0.00522188i
$233$	−6.19581e17			−1.08875			−0.544376	−	0.838841i	$-0.683234\pi$
$233$	−6.19581e17			−1.08875			−0.544376	+	0.838841i	$0.683234\pi$
$234$		−	4.90670e17i		−	0.834970i
$235$			1.31222e18i			2.16270i
$236$	1.10228e18			1.75975
$237$	1.12879e18			1.74582
$238$	−2.26993e18			−3.40161
$239$	−4.60794e17			−0.669148			−0.334574	−	0.942369i	$-0.608592\pi$
$239$	−4.60794e17			−0.669148			−0.334574	+	0.942369i	$0.608592\pi$
$240$			1.33340e18i			1.87661i
$241$	8.18256e17			1.11625			0.558125	−	0.829757i	$-0.311521\pi$
$241$	8.18256e17			1.11625			0.558125	+	0.829757i	$0.311521\pi$
$242$		−	8.30225e17i		−	1.09794i
$243$		−	4.70154e17i		−	0.602828i
$244$		−	6.70946e17i		−	0.834188i
$245$	−2.14112e18			−2.58164
$246$		−	5.02066e17i		−	0.587148i
$247$			1.99871e18i			2.26737i
$248$	−3.61913e15			−0.00398305
$249$		−	8.01337e17i		−	0.855697i
$250$			1.45883e18i			1.51166i
$251$			1.08138e18i			1.08749i	0.839251	+	0.543744i	$0.182994\pi$
$251$			1.08138e18i			1.08749i	−0.839251	+	0.543744i	$0.817006\pi$
$252$	−5.10708e17			−0.498504
$253$		−	1.69210e17i		−	0.160333i
$254$	3.14439e17			0.289257
$255$	3.13152e18			2.79708
$256$	1.16501e18			1.01049
$257$	−8.05626e17			−0.678633			−0.339316	−	0.940672i	$-0.610196\pi$
$257$	−8.05626e17			−0.678633			−0.339316	+	0.940672i	$0.610196\pi$
$258$			7.34928e17i			0.601308i
$259$			1.17194e18i			0.931445i
$260$	−3.98166e18			−3.07443
$261$	−2.90634e17	−	2.97026e17i	−0.218043	−	0.222839i
$262$	2.76326e17			0.201447
$263$		−	1.03685e18i		−	0.734598i	−0.930103	−	0.367299i	$-0.880283\pi$
$263$		−	1.03685e18i		−	0.734598i	0.930103	−	0.367299i	$-0.119717\pi$
$264$		−	5.85930e15i		−	0.00403475i
$265$	7.67107e17			0.513466
$266$	4.17172e18			2.71458
$267$	−3.76990e17			−0.238504
$268$	1.08571e18			0.667888
$269$			1.61232e18i			0.964517i	0.876029	+	0.482258i	$0.160183\pi$
$269$			1.61232e18i			0.964517i	−0.876029	+	0.482258i	$0.839817\pi$
$270$	−3.11889e18			−1.81456
$271$		−	1.31680e18i		−	0.745161i	−0.928000	−	0.372581i	$-0.878473\pi$
$271$		−	1.31680e18i		−	0.745161i	0.928000	−	0.372581i	$-0.121527\pi$
$272$		−	2.73622e18i		−	1.50621i
$273$			6.51905e18i			3.49112i
$274$	−3.67185e17			−0.191318
$275$		−	1.54170e18i		−	0.781638i
$276$		−	7.84688e17i		−	0.387150i
$277$	1.44382e18			0.693288			0.346644	−	0.937997i	$-0.387321\pi$
$277$	1.44382e18			0.693288			0.346644	+	0.937997i	$0.387321\pi$
$278$			1.69277e18i			0.791157i
$279$			3.65564e17i			0.166315i
$280$		−	4.41681e16i		−	0.0195625i
$281$	−2.98339e17			−0.128651			−0.0643253	−	0.997929i	$-0.520490\pi$
$281$	−2.98339e17			−0.128651			−0.0643253	+	0.997929i	$0.520490\pi$
$282$		−	5.11170e18i		−	2.14633i
$283$	2.93558e18			1.20032			0.600158	−	0.799882i	$-0.295104\pi$
$283$	2.93558e18			1.20032			0.600158	+	0.799882i	$0.295104\pi$
$284$	−2.88039e18			−1.14700
$285$	−5.75518e18			−2.23214
$286$	3.34467e18			1.26360
$287$			1.58537e18i			0.583468i
$288$		−	1.22802e18i		−	0.440312i
$289$	−3.56368e18			−1.24499
$290$	−4.83339e18	+	4.72937e18i	−1.64538	+	1.60997i
$291$	−3.35110e18			−1.11171
$292$		−	3.89886e18i		−	1.26057i
$293$			4.16973e17i			0.131402i	0.997839	+	0.0657008i	$0.0209283\pi$
$293$			4.16973e17i			0.131402i	−0.997839	+	0.0657008i	$0.979072\pi$
$294$	8.34068e18			2.56210
$295$	9.62911e18			2.88351
$296$	−1.48192e16			−0.00432650
$297$	1.30649e18			0.371906
$298$		−	2.10517e18i		−	0.584339i
$299$	−2.38059e18			−0.644392
$300$		−	7.14943e18i		−	1.88739i
$301$		−	2.32068e18i		−	0.597538i
$302$		−	3.76389e16i		−	0.00945333i
$303$	6.85021e18			1.67836
$304$			5.02869e18i			1.20200i
$305$		−	5.86116e18i		−	1.36689i
$306$	−2.89928e18			−0.659751
$307$		−	3.81798e18i		−	0.847805i	−0.905708	−	0.423902i	$-0.860660\pi$
$307$		−	3.81798e18i		−	0.847805i	0.905708	−	0.423902i	$-0.139340\pi$
$308$		−	3.48126e18i		−	0.754407i
$309$			3.07138e18i			0.649597i
$310$	5.94868e18			1.22803
$311$		−	1.05766e18i		−	0.213129i	−0.994306	−	0.106565i	$-0.966015\pi$
$311$		−	1.05766e18i		−	0.213129i	0.994306	−	0.106565i	$-0.0339851\pi$
$312$	−8.24334e16			−0.0162160
$313$	−3.82702e18			−0.734984			−0.367492	−	0.930027i	$-0.619783\pi$
$313$	−3.82702e18			−0.734984			−0.367492	+	0.930027i	$0.619783\pi$
$314$	−1.27115e18			−0.238356
$315$	−4.46137e18			−0.816844
$316$			8.48050e18i			1.51624i
$317$		−	5.99098e18i		−	1.04605i	−0.852316	−	0.523026i	$-0.824803\pi$
$317$		−	5.99098e18i		−	1.04605i	0.852316	−	0.523026i	$-0.175197\pi$
$318$	−2.98824e18			−0.509579
$319$	2.02469e18	−	1.98112e18i	0.337231	−	0.329974i
$320$	−9.91208e18			−1.61265
$321$			1.14381e18i			0.181789i
$322$			4.96877e18i			0.771490i
$323$	1.18100e19			1.79156
$324$	8.15094e18			1.20815
$325$	−2.16900e19			−3.14147
$326$	1.07797e19			1.52573
$327$		−	7.61104e18i		−	1.05278i
$328$	−2.00470e16			−0.00271017
$329$			1.61412e19i			2.13288i
$330$			9.63080e18i			1.24396i
$331$		−	6.33970e18i		−	0.800495i	−0.916407	−	0.400248i	$-0.868924\pi$
$331$		−	6.33970e18i		−	0.800495i	0.916407	−	0.400248i	$-0.131076\pi$
$332$	6.02039e18			0.743172
$333$			1.49687e18i			0.180656i
$334$		−	7.74775e18i		−	0.914276i
$335$	9.48441e18			1.09440
$336$			1.64017e19i			1.85073i
$337$		−	1.32020e19i		−	1.45685i	−0.685125	−	0.728425i	$-0.740253\pi$
$337$		−	1.32020e19i		−	1.45685i	0.685125	−	0.728425i	$-0.259747\pi$
$338$		−	3.39693e19i		−	3.66616i
$339$	−1.08981e18			−0.115041
$340$			2.35269e19i			2.42926i
$341$	−2.49188e18			−0.251692
$342$	5.32836e18			0.526499
$343$	−9.70915e18			−0.938588
$344$	2.93450e16			0.00277553
$345$		−	6.85477e18i		−	0.634380i
$346$			2.20674e19i			1.99839i
$347$	1.60030e18			0.141818			0.0709090	−	0.997483i	$-0.477410\pi$
$347$	1.60030e18			0.141818			0.0709090	+	0.997483i	$0.477410\pi$
$348$	9.38920e18	−	9.18714e18i	0.814300	−	0.796776i
$349$	1.12521e18			0.0955087			0.0477543	−	0.998859i	$-0.484794\pi$
$349$	1.12521e18			0.0955087			0.0477543	+	0.998859i	$0.484794\pi$
$350$			4.52714e19i			3.76109i
$351$		−	1.83808e19i		−	1.49472i
$352$	8.37083e18			0.666344
$353$	−2.01863e18			−0.157307			−0.0786533	−	0.996902i	$-0.525062\pi$
$353$	−2.01863e18			−0.157307			−0.0786533	+	0.996902i	$0.525062\pi$
$354$	−3.75099e19			−2.86168
$355$	−2.51621e19			−1.87946
$356$		−	2.83231e18i		−	0.207141i
$357$	3.85199e19			2.75850
$358$			3.01031e18i			0.211100i
$359$			1.82022e19i			1.25001i	0.780619	+	0.625007i	$0.214904\pi$
$359$			1.82022e19i			1.25001i	−0.780619	+	0.625007i	$0.785096\pi$
$360$		−	5.64141e16i		−	0.00379419i
$361$	−6.52358e18			−0.429717
$362$			7.57567e18i			0.488772i
$363$			1.40886e19i			0.890366i
$364$	−4.89772e19			−3.03203
$365$		−	3.40591e19i		−	2.06556i
$366$			2.28320e19i			1.35655i
$367$			3.05521e19i			1.77847i	0.457454	+	0.889233i	$0.348761\pi$
$367$			3.05521e19i			1.77847i	−0.457454	+	0.889233i	$0.651239\pi$
$368$	−5.98948e18			−0.341610
$369$			2.02493e18i			0.113165i
$370$	2.43580e19			1.33392
$371$	9.43594e18			0.506385
$372$	−1.15557e19			−0.607751
$373$	3.51939e19			1.81406			0.907029	−	0.421067i	$-0.138344\pi$
$373$	3.51939e19			1.81406			0.907029	+	0.421067i	$0.138344\pi$
$374$		−	1.97631e19i		−	0.998430i
$375$		−	2.47559e19i		−	1.22587i
$376$	−2.04105e17			−0.00990708
$377$	−2.78720e19	−	2.84850e19i	−1.32619	−	1.35536i
$378$	−3.83645e19			−1.78954
$379$			2.72016e18i			0.124394i	0.998064	+	0.0621971i	$0.0198107\pi$
$379$			2.72016e18i			0.124394i	−0.998064	+	0.0621971i	$0.980189\pi$
$380$		−	4.32383e19i		−	1.93862i
$381$	−5.33593e18			−0.234570
$382$	−2.96878e19			−1.27968
$383$	4.70140e18			0.198718			0.0993588	−	0.995052i	$-0.468321\pi$
$383$	4.70140e18			0.198718			0.0993588	+	0.995052i	$0.468321\pi$
$384$	−4.12624e17			−0.0171029
$385$		−	3.04111e19i		−	1.23617i
$386$	1.56029e19			0.622016
$387$		−	2.96410e18i		−	0.115894i
$388$		−	2.51766e19i		−	0.965516i
$389$		−	1.27400e19i		−	0.479235i	−0.970867	−	0.239617i	$-0.922978\pi$
$389$		−	1.27400e19i		−	0.479235i	0.970867	−	0.239617i	$-0.0770220\pi$
$390$	1.35494e20			4.99960
$391$			1.40665e19i			0.509166i
$392$		−	3.33035e17i		−	0.0118262i
$393$	−4.68915e18			−0.163362
$394$		−	3.70762e19i		−	1.26728i
$395$			7.40828e19i			2.48450i
$396$		−	4.44646e18i		−	0.146319i
$397$	4.00014e18			0.129165			0.0645827	−	0.997912i	$-0.479428\pi$
$397$	4.00014e18			0.129165			0.0645827	+	0.997912i	$0.479428\pi$
$398$			1.67404e19i			0.530447i
$399$	−7.07926e19			−2.20136
$400$	−5.45712e19			−1.66538
$401$	−7.65409e18			−0.229251			−0.114625	−	0.993409i	$-0.536567\pi$
$401$	−7.65409e18			−0.229251			−0.114625	+	0.993409i	$0.536567\pi$
$402$	−3.69462e19			−1.08611
$403$			3.50578e19i			1.01157i
$404$			5.14652e19i			1.45765i
$405$	7.12039e19			1.97966
$406$	−5.94540e19	+	5.81745e19i	−1.62269	+	1.58777i
$407$	−1.02035e19			−0.273394
$408$			4.87084e17i			0.0128131i
$409$		−	1.60150e19i		−	0.413620i	−0.978381	−	0.206810i	$-0.933692\pi$
$409$		−	1.60150e19i		−	0.413620i	0.978381	−	0.206810i	$-0.0663082\pi$
$410$	3.29509e19			0.835580
$411$	6.23100e18			0.155147
$412$	−2.30751e19			−0.564175
$413$	1.18445e20			2.84374
$414$			6.34640e18i			0.149632i
$415$	5.25921e19			1.21775
$416$		−	1.17768e20i		−	2.67809i
$417$		−	2.87258e19i		−	0.641580i
$418$			3.63210e19i			0.796775i
$419$	6.82194e19			1.46995			0.734976	−	0.678093i	$-0.237194\pi$
$419$	6.82194e19			1.46995			0.734976	+	0.678093i	$0.237194\pi$
$420$		−	1.41027e20i		−	2.98492i
$421$			7.69433e19i			1.59976i	0.600159	+	0.799880i	$0.295104\pi$
$421$			7.69433e19i			1.59976i	−0.600159	+	0.799880i	$0.704896\pi$
$422$	6.16705e19			1.25961
$423$			2.06164e19i			0.413677i
$424$			1.19318e17i			0.00235212i
$425$			1.28162e20i			2.48223i
$426$	9.80181e19			1.86524
$427$		−	7.20963e19i		−	1.34804i
$428$	−8.59339e18			−0.157883
$429$	−5.67579e19			−1.02470
$430$	−4.82337e19			−0.855730
$431$	6.74886e19			1.17666			0.588330	−	0.808621i	$-0.299786\pi$
$431$	6.74886e19			1.17666			0.588330	+	0.808621i	$0.299786\pi$
$432$		−	4.62454e19i		−	0.792393i
$433$		−	6.55702e19i		−	1.10420i	−0.833778	−	0.552099i	$-0.813827\pi$
$433$		−	6.55702e19i		−	1.10420i	0.833778	−	0.552099i	$-0.186173\pi$
$434$	7.31728e19			1.21109
$435$	8.20209e19	−	8.02558e19i	1.33430	−	1.30559i
$436$	5.71813e19			0.914334
$437$		−	2.58516e19i		−	0.406329i
$438$			1.32676e20i			2.04992i
$439$	−7.40022e18			−0.112399			−0.0561993	−	0.998420i	$-0.517898\pi$
$439$	−7.40022e18			−0.112399			−0.0561993	+	0.998420i	$0.517898\pi$
$440$	3.84549e17			0.00574191
$441$	−3.36395e19			−0.493810
$442$	−2.78043e20			−4.01278
$443$		−	8.70735e19i		−	1.23554i	−0.786357	−	0.617772i	$-0.788035\pi$
$443$		−	8.70735e19i		−	1.23554i	0.786357	−	0.617772i	$-0.211965\pi$
$444$	−4.73171e19			−0.660155
$445$		−	2.47421e19i		−	0.339419i
$446$			4.68092e19i			0.631422i
$447$			3.57240e19i			0.473864i
$448$	−1.21925e20			−1.59041
$449$			1.09748e20i			1.40782i	0.710287	+	0.703912i	$0.248565\pi$
$449$			1.09748e20i			1.40782i	−0.710287	+	0.703912i	$0.751435\pi$
$450$			5.78232e19i			0.729472i
$451$	−1.38030e19			−0.171257
$452$		−	8.18767e18i		−	0.0999131i
$453$			6.38719e17i			0.00766607i
$454$		−	1.94036e20i		−	2.29067i
$455$	−4.27848e20			−4.96826
$456$		−	8.95174e17i		−	0.0102252i
$457$	1.00521e20			1.12950			0.564749	−	0.825263i	$-0.308973\pi$
$457$	1.00521e20			1.12950			0.564749	+	0.825263i	$0.308973\pi$
$458$	−1.06214e20			−1.17406
$459$	−1.08609e20			−1.18105
$460$	5.14995e19			0.550959
$461$			9.34524e19i			0.983634i	0.870699	+	0.491817i	$0.163667\pi$
$461$			9.34524e19i			0.983634i	−0.870699	+	0.491817i	$0.836333\pi$
$462$			1.18465e20i			1.22681i
$463$	1.09562e20			1.11636			0.558179	−	0.829721i	$-0.311500\pi$
$463$	1.09562e20			1.11636			0.558179	+	0.829721i	$0.311500\pi$
$464$	−7.01249e19	−	7.16672e19i	−0.703052	−	0.718515i
$465$	−1.00947e20			−0.995855
$466$			1.58403e20i			1.53769i
$467$		−	2.57907e19i		−	0.246369i	−0.992384	−	0.123184i	$-0.960689\pi$
$467$		−	2.57907e19i		−	0.246369i	0.992384	−	0.123184i	$-0.0393107\pi$
$468$	−6.25565e19			−0.588069
$469$	1.16665e20			1.07930
$470$	3.35483e20			3.05448
$471$	2.15710e19			0.193292
$472$			1.49773e18i			0.0132090i
$473$	2.02049e19			0.175387
$474$		−	2.88587e20i		−	2.46570i
$475$		−	2.35539e20i		−	1.98089i
$476$			2.89397e20i			2.39576i
$477$	1.20521e19			0.0982145
$478$			1.17807e20i			0.945067i
$479$		−	1.57319e19i		−	0.124241i	−0.998069	−	0.0621204i	$-0.980214\pi$
$479$		−	1.57319e19i		−	0.124241i	0.998069	−	0.0621204i	$-0.0197863\pi$
$480$	3.39105e20			2.63649
$481$			1.43551e20i			1.09880i
$482$		−	2.09197e20i		−	1.57653i
$483$		−	8.43184e19i		−	0.625632i
$484$	−1.05847e20			−0.773282
$485$		−	2.19934e20i		−	1.58209i
$486$	−1.20200e20			−0.851400
$487$	4.24451e19			0.296047			0.148023	−	0.988984i	$-0.452709\pi$
$487$	4.24451e19			0.296047			0.148023	+	0.988984i	$0.452709\pi$
$488$	9.11658e17			0.00626157
$489$	−1.82929e20			−1.23727
$490$			5.47403e20i			3.64616i
$491$			9.14927e19i			0.600171i	0.953912	+	0.300086i	$0.0970152\pi$
$491$			9.14927e19i			0.600171i	−0.953912	+	0.300086i	$0.902985\pi$
$492$	−6.40094e19			−0.413529
$493$	−1.68313e20	+	1.64690e20i	−1.07094	+	1.04789i
$494$	5.10993e20			3.20231
$495$		−	3.88428e19i		−	0.239757i
$496$			8.82042e19i			0.536261i
$497$	−3.09511e20			−1.85354
$498$	−2.04871e20			−1.20854
$499$	1.74223e20			1.01240			0.506200	−	0.862416i	$-0.331050\pi$
$499$	1.74223e20			1.01240			0.506200	+	0.862416i	$0.331050\pi$
$500$	1.85989e20			1.06466
$501$			1.31477e20i			0.741422i
$502$	2.76466e20			1.53591
$503$			3.30501e20i			1.80889i	0.426585	+	0.904447i	$0.359716\pi$
$503$			3.30501e20i			1.80889i	−0.426585	+	0.904447i	$0.640284\pi$
$504$		−	6.93932e17i		−	0.00374186i
$505$			4.49582e20i			2.38849i
$506$	−4.32605e19			−0.226445
$507$			5.76448e20i			2.97304i
$508$		−	4.00885e19i		−	0.203724i
$509$	−2.29927e20			−1.15135			−0.575673	−	0.817680i	$-0.695260\pi$
$509$	−2.29927e20			−1.15135			−0.575673	+	0.817680i	$0.695260\pi$
$510$		−	8.00610e20i		−	3.95043i
$511$		−	4.18951e20i		−	2.03707i
$512$		−	2.94733e20i		−	1.41222i
$513$	1.99604e20			0.942514
$514$			2.05967e20i			0.958463i
$515$	−2.01576e20			−0.924452
$516$	9.36974e19			0.423501
$517$	−1.40533e20			−0.626035
$518$	2.99620e20			1.31552
$519$		−	3.74476e20i		−	1.62058i
$520$		−	5.41015e18i		−	0.0230772i
$521$	1.68927e20			0.710256			0.355128	−	0.934818i	$-0.384437\pi$
$521$	1.68927e20			0.710256			0.355128	+	0.934818i	$0.384437\pi$
$522$	−7.59380e19	+	7.43038e19i	−0.314725	+	0.307952i
$523$	−2.34252e20			−0.957020			−0.478510	−	0.878082i	$-0.658823\pi$
$523$	−2.34252e20			−0.957020			−0.478510	+	0.878082i	$0.658823\pi$
$524$		−	3.52293e19i		−	0.141879i
$525$		−	7.68240e20i		−	3.05001i
$526$	−2.65084e20			−1.03750
$527$	2.07150e20			0.799292
$528$	−1.42801e20			−0.543221
$529$	−2.35844e20			−0.884521
$530$		−	1.96120e20i		−	0.725190i
$531$	1.51284e20			0.551550
$532$		−	5.31861e20i		−	1.91188i
$533$			1.94192e20i			0.688299i
$534$			9.63819e19i			0.336850i
$535$	−7.50690e19			−0.258706
$536$			1.47523e18i			0.00501329i
$537$		−	5.10839e19i		−	0.171189i
$538$	4.12209e20			1.36223
$539$		−	2.29305e20i		−	0.747305i
$540$			3.97633e20i			1.27800i
$541$		−	2.32111e20i		−	0.735725i	−0.929880	−	0.367862i	$-0.880090\pi$
$541$		−	2.32111e20i		−	0.735725i	0.929880	−	0.367862i	$-0.119910\pi$
$542$	−3.36655e20			−1.05242
$543$		−	1.28556e20i		−	0.396365i
$544$	−6.95868e20			−2.11609
$545$	4.99516e20			1.49822
$546$	1.66667e21			4.93065
$547$	−2.22198e20			−0.648389			−0.324194	−	0.945990i	$-0.605093\pi$
$547$	−2.22198e20			−0.648389			−0.324194	+	0.945990i	$0.605093\pi$
$548$			4.68131e19i			0.134745i
$549$		−	9.20855e19i		−	0.261456i
$550$	−3.94154e20			−1.10394
$551$	3.09328e20	−	3.02671e20i	0.854639	−	0.836247i
$552$	1.06621e18			0.00290602
$553$			9.11269e20i			2.45024i
$554$		−	3.69128e20i		−	0.979160i
$555$	−4.13346e20			−1.08172
$556$	2.15815e20			0.557212
$557$	1.35931e19			0.0346261			0.0173130	−	0.999850i	$-0.494489\pi$
$557$	1.35931e19			0.0346261			0.0173130	+	0.999850i	$0.494489\pi$
$558$	9.34605e19			0.234894
$559$		−	2.84259e20i		−	0.704897i
$560$	−1.07645e21			−2.63381
$561$			3.35372e20i			0.809666i
$562$			7.62737e19i			0.181699i
$563$		−	5.79512e20i		−	1.36223i	−0.732178	−	0.681113i	$-0.761496\pi$
$563$		−	5.79512e20i		−	1.36223i	0.732178	−	0.681113i	$-0.238504\pi$
$564$	−6.51701e20			−1.51166
$565$		−	7.15247e19i		−	0.163717i
$566$		−	7.50514e20i		−	1.69526i
$567$	8.75856e20			1.95236
$568$		−	3.91377e18i		−	0.00860959i
$569$			4.69107e20i			1.01843i	0.860640	+	0.509213i	$0.170064\pi$
$569$			4.69107e20i			1.01843i	−0.860640	+	0.509213i	$0.829936\pi$
$570$			1.47138e21i			3.15255i
$571$	−1.84478e20			−0.390098			−0.195049	−	0.980794i	$-0.562487\pi$
$571$	−1.84478e20			−0.390098			−0.195049	+	0.980794i	$0.562487\pi$
$572$		−	4.26419e20i		−	0.889951i
$573$	5.03791e20			1.03774
$574$	4.05318e20			0.824057
$575$	2.80541e20			0.562973
$576$	−1.55730e20			−0.308464
$577$			8.44492e20i			1.65111i	0.564319	+	0.825557i	$0.309139\pi$
$577$			8.44492e20i			1.65111i	−0.564319	+	0.825557i	$0.690861\pi$
$578$			9.11095e20i			1.75835i
$579$	−2.64776e20			−0.504417
$580$	6.02957e20	+	6.16218e20i	1.13390	+	1.15884i
$581$	6.46919e20			1.20096
$582$			8.56747e20i			1.57011i
$583$			8.21538e19i			0.148632i
$584$	5.29764e18			0.00946206
$585$	−5.46472e20			−0.963605
$586$	1.06604e20			0.185584
$587$	−1.60919e20			−0.276581			−0.138290	−	0.990392i	$-0.544161\pi$
$587$	−1.60919e20			−0.276581			−0.138290	+	0.990392i	$0.544161\pi$
$588$		−	1.06337e21i		−	1.80449i
$589$	−3.80705e20			−0.637858
$590$		−	2.46179e21i		−	4.07250i
$591$			6.29169e20i			1.02769i
$592$			3.61169e20i			0.582502i
$593$	−8.31862e20			−1.32477			−0.662386	−	0.749163i	$-0.730456\pi$
$593$	−8.31862e20			−1.32477			−0.662386	+	0.749163i	$0.730456\pi$
$594$		−	3.34020e20i		−	0.525259i
$595$			2.52808e21i			3.92567i
$596$	−2.68392e20			−0.411550
$597$		−	2.84078e20i		−	0.430160i
$598$			6.08624e20i			0.910103i
$599$		−	1.00224e21i		−	1.48003i	−0.672591	−	0.740015i	$-0.734818\pi$
$599$		−	1.00224e21i		−	1.48003i	0.672591	−	0.740015i	$-0.265182\pi$
$600$	9.71440e18			0.0141671
$601$			3.40833e20i			0.490889i	0.969411	+	0.245444i	$0.0789339\pi$
$601$			3.40833e20i			0.490889i	−0.969411	+	0.245444i	$0.921066\pi$
$602$	−5.93307e20			−0.843929
$603$	1.49011e20			0.209333
$604$	−4.79865e18			−0.00665798
$605$	−9.24643e20			−1.26709
$606$		−	1.75133e21i		−	2.37041i
$607$		−	5.19063e20i		−	0.693912i	−0.937881	−	0.346956i	$-0.887215\pi$
$607$		−	5.19063e20i		−	0.693912i	0.937881	−	0.346956i	$-0.112785\pi$
$608$	1.27888e21			1.68870
$609$	1.00891e21	−	9.87201e20i	1.31590	−	1.28758i
$610$	−1.49847e21			−1.93052
$611$			1.97713e21i			2.51609i
$612$			3.69635e20i			0.464662i
$613$	7.83100e20			0.972441			0.486221	−	0.873836i	$-0.338375\pi$
$613$	7.83100e20			0.972441			0.486221	+	0.873836i	$0.338375\pi$
$614$	−9.76110e20			−1.19739
$615$	−5.59165e20			−0.677605
$616$	4.73021e18			0.00566272
$617$			7.90013e19i			0.0934320i	0.998908	+	0.0467160i	$0.0148756\pi$
$617$			7.90013e19i			0.0934320i	−0.998908	+	0.0467160i	$0.985124\pi$
$618$	7.85232e20			0.917454
$619$		−	1.23364e21i		−	1.42399i	−0.702182	−	0.711997i	$-0.747791\pi$
$619$		−	1.23364e21i		−	1.42399i	0.702182	−	0.711997i	$-0.252209\pi$
$620$		−	7.58408e20i		−	0.864899i
$621$			2.37740e20i			0.267865i
$622$	−2.70403e20			−0.301012
$623$		−	3.04344e20i		−	0.334738i
$624$			2.00904e21i			2.18325i
$625$	8.18464e19			0.0878819
$626$			9.78421e20i			1.03805i
$627$		−	6.16354e20i		−	0.646136i
$628$			1.62062e20i			0.167874i
$629$	8.48215e20			0.868213
$630$			1.14060e21i			1.15366i
$631$	1.03142e21			1.03090			0.515448	−	0.856921i	$-0.327626\pi$
$631$	1.03142e21			1.03090			0.515448	+	0.856921i	$0.327626\pi$
$632$	−1.15230e19			−0.0113812
$633$	−1.04653e21			−1.02146
$634$	−1.53166e21			−1.47739
$635$		−	3.50199e20i		−	0.333820i
$636$			3.80976e20i			0.358897i
$637$	−3.22605e21			−3.00348
$638$	−5.06495e20	−	5.17635e20i	−0.466037	−	0.476287i
$639$	−3.95325e20			−0.359499
$640$		−	2.70807e19i		−	0.0243394i
$641$		−	1.86556e21i		−	1.65719i	−0.559845	−	0.828597i	$-0.689139\pi$
$641$		−	1.86556e21i		−	1.65719i	0.559845	−	0.828597i	$-0.310861\pi$
$642$	2.92429e20			0.256748
$643$	3.01586e20			0.261715			0.130858	−	0.991401i	$-0.458227\pi$
$643$	3.01586e20			0.261715			0.130858	+	0.991401i	$0.458227\pi$
$644$	6.33479e20			0.543360
$645$	8.18508e20			0.693945
$646$		−	3.01937e21i		−	2.53030i
$647$	9.00833e20			0.746212			0.373106	−	0.927789i	$-0.378293\pi$
$647$	9.00833e20			0.746212			0.373106	+	0.927789i	$0.378293\pi$
$648$			1.10752e19i			0.00906859i
$649$			1.03124e21i			0.834685i
$650$			5.54528e21i			4.43684i
$651$	−1.24172e21			−0.982121
$652$		−	1.37433e21i		−	1.07457i
$653$		−	3.62789e20i		−	0.280417i	−0.990122	−	0.140209i	$-0.955223\pi$
$653$		−	3.62789e20i		−	0.280417i	0.990122	−	0.140209i	$-0.0447773\pi$
$654$	−1.94585e21			−1.48688
$655$		−	3.07751e20i		−	0.232482i
$656$			4.88580e20i			0.364886i
$657$		−	5.35108e20i		−	0.395095i
$658$	4.12668e21			3.01236
$659$		−	5.29577e20i		−	0.382198i	−0.981571	−	0.191099i	$-0.938795\pi$
$659$		−	5.29577e20i		−	0.382198i	0.981571	−	0.191099i	$-0.0612052\pi$
$660$	1.22785e21			0.876124
$661$	1.56762e21			1.10594			0.552968	−	0.833202i	$-0.313495\pi$
$661$	1.56762e21			1.10594			0.552968	+	0.833202i	$0.313495\pi$
$662$	−1.62082e21			−1.13057
$663$	4.71829e21			3.25412
$664$			8.18030e18i			0.00557839i
$665$		−	4.64616e21i		−	3.13279i
$666$	3.82692e20			0.255148
$667$	3.60500e20	+	3.68429e20i	0.237663	+	0.242890i
$668$	−9.87776e20			−0.643924
$669$		−	7.94336e20i		−	0.512045i
$670$		−	2.42480e21i		−	1.54566i
$671$	6.27705e20			0.395673
$672$	4.17123e21			2.60013
$673$	2.01562e21			1.24250			0.621249	−	0.783614i	$-0.286626\pi$
$673$	2.01562e21			1.24250			0.621249	+	0.783614i	$0.286626\pi$
$674$	−3.37524e21			−2.05757
$675$			2.16609e21i			1.30587i
$676$	−4.33081e21			−2.58208
$677$		−	5.30574e20i		−	0.312846i	−0.987690	−	0.156423i	$-0.950004\pi$
$677$		−	5.30574e20i		−	0.312846i	0.987690	−	0.156423i	$-0.0499963\pi$
$678$			2.78622e20i			0.162477i
$679$		−	2.70534e21i		−	1.56027i
$680$	−3.19676e19			−0.0182345
$681$			3.29272e21i			1.85760i
$682$			6.37077e20i			0.355475i
$683$	−2.36144e21			−1.30323			−0.651616	−	0.758549i	$-0.725909\pi$
$683$	−2.36144e21			−1.30323			−0.651616	+	0.758549i	$0.725909\pi$
$684$		−	6.79323e20i		−	0.370814i
$685$			4.08943e20i			0.220792i
$686$			2.48225e21i			1.32561i
$687$	1.80242e21			0.952095
$688$		−	7.15186e20i		−	0.373685i
$689$	1.15581e21			0.597366
$690$	−1.75250e21			−0.895963
$691$	1.18535e21			0.599463			0.299732	−	0.954024i	$-0.403103\pi$
$691$	1.18535e21			0.599463			0.299732	+	0.954024i	$0.403103\pi$
$692$	2.81342e21			1.40747
$693$		−	4.77793e20i		−	0.236451i
$694$		−	4.09136e20i		−	0.200296i
$695$	1.88529e21			0.913043
$696$	1.24832e19	+	1.27577e19i	0.00598075	+	0.00611229i
$697$	1.14744e21			0.543859
$698$		−	2.87673e20i		−	0.134891i
$699$		−	2.68804e21i		−	1.24697i
$700$	5.77174e21			2.64893
$701$	−1.39417e21			−0.633037			−0.316519	−	0.948586i	$-0.602514\pi$
$701$	−1.39417e21			−0.633037			−0.316519	+	0.948586i	$0.602514\pi$
$702$	−4.69926e21			−2.11106
$703$	−1.55887e21			−0.692858
$704$		−	1.06154e21i		−	0.466812i
$705$	−5.69304e21			−2.47700
$706$			5.16086e20i			0.222171i
$707$			5.53017e21i			2.35555i
$708$			4.78221e21i			2.01548i
$709$	7.43617e19			0.0310101			0.0155050	−	0.999880i	$-0.495064\pi$
$709$	7.43617e19			0.0310101			0.0155050	+	0.999880i	$0.495064\pi$
$710$			6.43297e21i			2.65445i
$711$			1.16393e21i			0.475229i
$712$	3.84844e18			0.00155484
$713$		−	4.53443e20i		−	0.181280i
$714$		−	9.84805e21i		−	3.89595i
$715$		−	3.72505e21i		−	1.45827i
$716$	3.83790e20			0.148678
$717$		−	1.99915e21i		−	0.766392i
$718$	4.65359e21			1.76545
$719$	−2.32335e21			−0.872264			−0.436132	−	0.899883i	$-0.643652\pi$
$719$	−2.32335e21			−0.872264			−0.436132	+	0.899883i	$0.643652\pi$
$720$	−1.37491e21			−0.510833
$721$	−2.47952e21			−0.911703
$722$			1.66783e21i			0.606907i
$723$			3.54999e21i			1.27847i
$724$	9.65836e20			0.344242
$725$	3.28458e21	+	3.35682e21i	1.15863	+	1.18411i
$726$	3.60192e21			1.25750
$727$			7.76544e20i			0.268323i	0.990959	+	0.134161i	$0.0428341\pi$
$727$			7.76544e20i			0.268323i	−0.990959	+	0.134161i	$0.957166\pi$
$728$		−	6.65485e19i		−	0.0227590i
$729$	−1.54846e21			−0.524136
$730$	−8.70761e21			−2.91728
$731$	−1.67964e21			−0.556974
$732$	2.91089e21			0.955417
$733$			4.18678e21i			1.36019i	0.733122	+	0.680097i	$0.238062\pi$
$733$			4.18678e21i			1.36019i	−0.733122	+	0.680097i	$0.761938\pi$
$734$	7.81099e21			2.51180
$735$		−	9.28923e21i		−	2.95682i
$736$			1.52322e21i			0.479933i
$737$			1.01574e21i			0.316793i
$738$	5.17696e20			0.159828
$739$			4.94233e20i			0.151042i	0.997144	+	0.0755211i	$0.0240620\pi$
$739$			4.94233e20i			0.151042i	−0.997144	+	0.0755211i	$0.975938\pi$
$740$		−	3.10545e21i		−	0.939477i
$741$	−8.67138e21			−2.59688
$742$		−	2.41241e21i		−	0.715189i
$743$		−	6.32415e21i		−	1.85603i	−0.372537	−	0.928017i	$-0.621512\pi$
$743$		−	6.32415e21i		−	1.85603i	0.372537	−	0.928017i	$-0.378488\pi$
$744$		−	1.57015e19i		−	0.00456189i
$745$	−2.34458e21			−0.674363
$746$		−	8.99773e21i		−	2.56207i
$747$	8.26282e20			0.232929
$748$	−2.51963e21			−0.703194
$749$	−9.23400e20			−0.255139
$750$	−6.32912e21			−1.73135
$751$			4.65232e21i			1.26000i	0.776596	+	0.629999i	$0.216945\pi$
$751$			4.65232e21i			1.26000i	−0.776596	+	0.629999i	$0.783055\pi$
$752$			4.97439e21i			1.33385i
$753$	−4.69154e21			−1.24553
$754$	−7.28251e21	+	7.12578e21i	−1.91424	+	1.87304i
$755$	−4.19194e19			−0.0109097
$756$			4.89116e21i			1.26037i
$757$		−	4.30481e20i		−	0.109834i	−0.998491	−	0.0549168i	$-0.982511\pi$
$757$		−	4.30481e20i		−	0.109834i	0.998491	−	0.0549168i	$-0.0174893\pi$
$758$	6.95439e20			0.175687
$759$	7.34116e20			0.183633
$760$	5.87507e19			0.0145516
$761$	4.45234e21			1.09195			0.545976	−	0.837801i	$-0.316159\pi$
$761$	4.45234e21			1.09195			0.545976	+	0.837801i	$0.316159\pi$
$762$			1.36419e21i			0.331293i
$763$	6.14439e21			1.47756
$764$			3.78495e21i			0.901280i
$765$			3.22901e21i			0.761392i
$766$		−	1.20197e21i		−	0.280657i
$767$	1.45083e22			3.35467
$768$			5.05440e21i			1.15734i
$769$			1.94904e21i			0.441950i	0.975279	+	0.220975i	$0.0709239\pi$
$769$			1.94904e21i			0.441950i	−0.975279	+	0.220975i	$0.929076\pi$
$770$	−7.77495e21			−1.74589
$771$		−	3.49519e21i		−	0.777255i
$772$		−	1.98925e21i		−	0.438086i
$773$			6.12101e21i			1.33499i	0.744616	+	0.667494i	$0.232633\pi$
$773$			6.12101e21i			1.33499i	−0.744616	+	0.667494i	$0.767367\pi$
$774$	−7.57806e20			−0.163682
$775$		−	4.13140e21i		−	0.883760i
$776$	3.42091e19			0.00724734
$777$	−5.08444e21			−1.06681
$778$	−3.25713e21			−0.676844
$779$	−2.10880e21			−0.434014
$780$		−	1.72744e22i		−	3.52122i
$781$		−	2.69475e21i		−	0.544046i
$782$	3.59625e21			0.719117
$783$	−2.84468e21	+	2.78346e21i	−0.563405	+	0.551280i
$784$	−8.11663e21			−1.59223
$785$			1.41572e21i			0.275077i
$786$			1.19883e21i			0.230723i
$787$	1.09371e20			0.0208494			0.0104247	−	0.999946i	$-0.496682\pi$
$787$	1.09371e20			0.0208494			0.0104247	+	0.999946i	$0.496682\pi$
$788$	−4.72691e21			−0.892546
$789$	4.49838e21			0.841353
$790$	1.89401e22			3.50897
$791$		−	8.79803e20i		−	0.161459i
$792$	6.04170e18			0.00109830
$793$		−	8.83106e21i		−	1.59024i
$794$		−	1.02268e21i		−	0.182426i
$795$			3.32808e21i			0.588085i
$796$	2.13426e21			0.373594
$797$			4.61884e21i			0.800931i	0.916312	+	0.400466i	$0.131152\pi$
$797$			4.61884e21i			0.800931i	−0.916312	+	0.400466i	$0.868848\pi$
$798$			1.80989e22i			3.10908i
$799$	1.16825e22			1.98809
$800$			1.38784e22i			2.33972i
$801$		−	3.88726e20i		−	0.0649232i
$802$			1.95686e21i			0.323781i
$803$	3.64758e21			0.597914
$804$			4.71034e21i			0.764948i
$805$	5.53386e21			0.890346
$806$	8.96292e21			1.42869
$807$	−6.99504e21			−1.10468
$808$	−6.99291e19			−0.0109414
$809$		−	6.76902e21i		−	1.04933i	−0.851309	−	0.524665i	$-0.824191\pi$
$809$		−	6.76902e21i		−	1.04933i	0.851309	−	0.524665i	$-0.175809\pi$
$810$		−	1.82041e22i		−	2.79596i
$811$	−5.75713e21			−0.876091			−0.438046	−	0.898953i	$-0.644329\pi$
$811$	−5.75713e21			−0.876091			−0.438046	+	0.898953i	$0.644329\pi$
$812$	7.41678e21	+	7.57990e21i	1.11827	+	1.14286i
$813$	5.71292e21			0.853452
$814$			2.60863e21i			0.386127i
$815$		−	1.20057e22i		−	1.76078i
$816$	1.18711e22			1.72510
$817$	3.08687e21			0.444481
$818$	−4.09441e21			−0.584173
$819$	−6.72198e21			−0.950316
$820$		−	4.20097e21i		−	0.588499i
$821$	−1.28543e22			−1.78433			−0.892166	−	0.451707i	$-0.850815\pi$
$821$	−1.28543e22			−1.78433			−0.892166	+	0.451707i	$0.850815\pi$
$822$		−	1.59303e21i		−	0.219121i
$823$			1.29356e22i			1.76314i	0.472050	+	0.881572i	$0.343514\pi$
$823$			1.29356e22i			1.76314i	−0.472050	+	0.881572i	$0.656486\pi$
$824$		−	3.13536e19i		−	0.00423480i
$825$	6.68866e21			0.895230
$826$		−	3.02817e22i		−	4.01634i
$827$			2.33407e21i			0.306777i	0.988166	+	0.153388i	$0.0490186\pi$
$827$			2.33407e21i			0.306777i	−0.988166	+	0.153388i	$0.950981\pi$
$828$	8.09115e20			0.105386
$829$		−	4.46029e21i		−	0.575711i	−0.957674	−	0.287856i	$-0.907058\pi$
$829$		−	4.46029e21i		−	0.575711i	0.957674	−	0.287856i	$-0.0929423\pi$
$830$		−	1.34458e22i		−	1.71989i
$831$			6.26397e21i			0.794040i
$832$	−1.49346e22			−1.87616
$833$			1.90621e22i			2.37320i
$834$	−7.34407e21			−0.906132
$835$	−8.62887e21			−1.05513
$836$	4.63063e21			0.561168
$837$	3.50109e21			0.420496
$838$		−	1.74411e22i		−	2.07608i
$839$		−	1.42692e22i		−	1.68340i	−0.539949	−	0.841698i	$-0.681557\pi$
$839$		−	1.42692e22i		−	1.68340i	0.539949	−	0.841698i	$-0.318443\pi$
$840$	1.91623e20			0.0224054
$841$	−1.87703e20	+	8.62715e21i	−0.0217521	+	0.999763i
$842$	1.96714e22			2.25941
$843$		−	1.29434e21i		−	0.147347i
$844$		−	7.86250e21i		−	0.887140i
$845$	−3.78325e22			−4.23097
$846$	5.27083e21			0.584253
$847$	−1.13737e22			−1.24962
$848$	2.90797e21			0.316680
$849$			1.27360e22i			1.37475i
$850$	3.27661e22			3.50576
$851$		−	1.85671e21i		−	0.196912i
$852$		−	1.24965e22i		−	1.31369i
$853$			1.10174e22i			1.14805i	0.818839	+	0.574023i	$0.194618\pi$
$853$			1.10174e22i			1.14805i	−0.818839	+	0.574023i	$0.805382\pi$
$854$	−1.84322e22			−1.90390
$855$		−	5.93434e21i		−	0.607612i
$856$		−	1.16764e19i		−	0.00118510i
$857$	1.51173e22			1.52096			0.760481	−	0.649360i	$-0.224963\pi$
$857$	1.51173e22			1.52096			0.760481	+	0.649360i	$0.224963\pi$
$858$			1.45108e22i			1.44723i
$859$			8.01931e21i			0.792845i	0.918068	+	0.396423i	$0.129749\pi$
$859$			8.01931e21i			0.792845i	−0.918068	+	0.396423i	$0.870251\pi$
$860$			6.14940e21i			0.602691i
$861$	−6.87811e21			−0.668260
$862$		−	1.72542e22i		−	1.66185i
$863$	−6.73292e21			−0.642869			−0.321434	−	0.946932i	$-0.604165\pi$
$863$	−6.73292e21			−0.642869			−0.321434	+	0.946932i	$0.604165\pi$
$864$	−1.17610e22			−1.11325
$865$	2.45771e22			2.30627
$866$	−1.67638e22			−1.55951
$867$		−	1.54610e22i		−	1.42591i
$868$		−	9.32894e21i		−	0.852971i
$869$	−7.93394e21			−0.719185
$870$	−2.05183e22	−	2.09696e22i	−1.84394	−	1.88450i
$871$	1.42902e22			1.27322
$872$			7.76959e19i			0.00686316i
$873$		−	3.45542e21i		−	0.302617i
$874$	−6.60927e21			−0.573875
$875$	1.99854e22			1.72049
$876$	1.69152e22			1.44376
$877$	−1.83999e22			−1.55711			−0.778553	−	0.627578i	$-0.784046\pi$
$877$	−1.83999e22			−1.55711			−0.778553	+	0.627578i	$0.784046\pi$
$878$			1.89195e21i			0.158745i
$879$	−1.80903e21			−0.150498
$880$		−	9.37210e21i		−	0.773066i
$881$			2.00653e22i			1.64107i	0.571599	+	0.820533i	$0.306323\pi$
$881$			2.00653e22i			1.64107i	−0.571599	+	0.820533i	$0.693677\pi$
$882$			8.60032e21i			0.697429i
$883$	2.38215e22			1.91542			0.957711	−	0.287733i	$-0.0929017\pi$
$883$	2.38215e22			1.91542			0.957711	+	0.287733i	$0.0929017\pi$
$884$			3.54482e22i			2.82620i
$885$			4.17758e22i			3.30255i
$886$	−2.22613e22			−1.74501
$887$			7.38754e21i			0.574213i	0.957899	+	0.287106i	$0.0926933\pi$
$887$			7.38754e21i			0.574213i	−0.957899	+	0.287106i	$0.907307\pi$
$888$		−	6.42928e19i		−	0.00495525i
$889$		−	4.30769e21i		−	0.329216i
$890$	−6.32559e21			−0.479376
$891$			7.62562e21i			0.573050i
$892$	5.96780e21			0.444711
$893$	−2.14704e22			−1.58655
$894$	9.13325e21			0.669258
$895$	3.35266e21			0.243622
$896$		−	3.33111e20i		−	0.0240037i
$897$		−	1.03281e22i		−	0.738038i
$898$	2.80583e22			1.98833
$899$	5.42568e21	−	5.30892e21i	0.381291	−	0.373085i
$900$	7.37199e21			0.513767
$901$		−	6.82945e21i		−	0.472009i
$902$			3.52889e21i			0.241874i
$903$	1.00682e22			0.684375
$904$	1.11251e19			0.000749966
$905$	8.43722e21			0.564073
$906$	1.63296e20			0.0108271
$907$		−	2.28619e22i		−	1.50334i	−0.659537	−	0.751672i	$-0.729248\pi$
$907$		−	2.28619e22i		−	1.50334i	0.659537	−	0.751672i	$-0.270752\pi$
$908$	−2.47380e22			−1.61332
$909$			7.06345e21i			0.456865i
$910$			1.09384e23i			7.01689i
$911$		−	1.71183e22i		−	1.08911i	−0.838724	−	0.544557i	$-0.816698\pi$
$911$		−	1.71183e22i		−	1.08911i	0.838724	−	0.544557i	$-0.183302\pi$
$912$	−2.18169e22			−1.37668
$913$			5.63238e21i			0.352502i
$914$		−	2.56993e22i		−	1.59524i
$915$	2.54286e22			1.56554
$916$			1.35415e22i			0.826893i
$917$		−	3.78555e21i		−	0.229276i
$918$			2.77671e22i			1.66805i
$919$	−1.71070e22			−1.01931			−0.509657	−	0.860378i	$-0.670228\pi$
$919$	−1.71070e22			−1.01931			−0.509657	+	0.860378i	$0.670228\pi$
$920$			6.99757e19i			0.00413560i
$921$	1.65642e22			0.971012
$922$	2.38922e22			1.38923
$923$	−3.79119e22			−2.18657
$924$	1.51034e22			0.864041
$925$		−	1.69168e22i		−	0.959964i
$926$		−	2.80108e22i		−	1.57668i
$927$	−3.16699e21			−0.176827
$928$	−1.82262e22	+	1.78339e22i	−1.00945	+	0.987729i
$929$	−2.46537e22			−1.35445			−0.677226	−	0.735775i	$-0.736818\pi$
$929$	−2.46537e22			−1.35445			−0.677226	+	0.735775i	$0.736818\pi$
$930$			2.58082e22i			1.40649i
$931$		−	3.50328e22i		−	1.89388i
$932$	2.01951e22			1.08300
$933$	4.58864e21			0.244102
$934$	−6.59368e21			−0.347957
$935$	−2.20107e22			−1.15225
$936$		−	8.49996e19i		−	0.00441416i
$937$	1.76985e22			0.911776			0.455888	−	0.890037i	$-0.349322\pi$
$937$	1.76985e22			0.911776			0.455888	+	0.890037i	$0.349322\pi$
$938$		−	2.98267e22i		−	1.52435i
$939$		−	1.66035e22i		−	0.841795i
$940$		−	4.27714e22i		−	2.15127i
$941$	−2.59743e22			−1.29605			−0.648025	−	0.761619i	$-0.724405\pi$
$941$	−2.59743e22			−1.29605			−0.648025	+	0.761619i	$0.724405\pi$
$942$		−	5.51488e21i		−	0.272995i
$943$		−	2.51171e21i		−	0.123348i
$944$	3.65023e22			1.77840
$945$			4.27275e22i			2.06523i
$946$		−	5.16562e21i		−	0.247707i
$947$		−	1.30397e22i		−	0.620358i	−0.950678	−	0.310179i	$-0.899611\pi$
$947$		−	1.30397e22i		−	0.620358i	0.950678	−	0.310179i	$-0.100389\pi$
$948$	−3.67925e22			−1.73659
$949$		−	5.13172e22i		−	2.40307i
$950$	−6.02182e22			−2.79770
$951$	2.59918e22			1.19807
$952$	−3.93223e20			−0.0179830
$953$	−3.63914e21			−0.165121			−0.0825605	−	0.996586i	$-0.526310\pi$
$953$	−3.63914e21			−0.165121			−0.0825605	+	0.996586i	$0.526310\pi$
$954$		−	3.08126e21i		−	0.138713i
$955$			3.30640e22i			1.47683i
$956$	1.50195e22			0.665611
$957$	8.59504e21	+	8.78408e21i	0.377927	+	0.386239i
$958$	−4.02203e21			−0.175471
$959$			5.03028e21i			0.217747i
$960$		−	4.30034e22i		−	1.84701i
$961$	1.67876e22			0.715424
$962$	3.67004e22			1.55188
$963$	−1.17942e21			−0.0494847
$964$	−2.66709e22			−1.11035
$965$		−	1.73774e22i		−	0.717844i
$966$	−2.15570e22			−0.883607
$967$			4.34518e22i			1.76729i	0.468153	+	0.883647i	$0.344919\pi$
$967$			4.34518e22i			1.76729i	−0.468153	+	0.883647i	$0.655081\pi$
$968$		−	1.43821e20i		−	0.00580440i
$969$			5.12376e22i			2.05192i
$970$	−5.62287e22			−2.23445
$971$			1.96744e22i			0.775814i	0.921698	+	0.387907i	$0.126802\pi$
$971$			1.96744e22i			0.775814i	−0.921698	+	0.387907i	$0.873198\pi$
$972$			1.53246e22i			0.599641i
$973$	2.31903e22			0.900451
$974$		−	1.08516e22i		−	0.418119i
$975$		−	9.41015e22i		−	3.59801i
$976$		−	2.22186e22i		−	0.843032i
$977$	−3.50395e22			−1.31931			−0.659657	−	0.751567i	$-0.729298\pi$
$977$	−3.50395e22			−1.31931			−0.659657	+	0.751567i	$0.729298\pi$
$978$			4.67678e22i			1.74745i
$979$	2.64977e21			0.0982511
$980$	6.97894e22			2.56799
$981$	7.84797e21			0.286576
$982$	2.33911e22			0.847648
$983$		−	3.40553e22i		−	1.22471i	−0.790583	−	0.612355i	$-0.790222\pi$
$983$		−	3.40553e22i		−	1.22471i	0.790583	−	0.612355i	$-0.209778\pi$
$984$		−	8.69738e19i		−	0.00310402i
$985$	−4.12927e22			−1.46252
$986$	4.21050e22	+	4.30310e22i	1.47998	+	1.51253i
$987$	−7.00283e22			−2.44284
$988$		−	6.51475e22i		−	2.25539i
$989$			3.67665e21i			0.126322i
$990$	−9.93061e21			−0.338619
$991$	−5.52381e21			−0.186933			−0.0934666	−	0.995622i	$-0.529795\pi$
$991$	−5.52381e21			−0.186933			−0.0934666	+	0.995622i	$0.529795\pi$
$992$	2.24318e22			0.753402
$993$	2.75047e22			0.916827
$994$			7.91300e22i			2.61784i
$995$	1.86442e22			0.612168
$996$			2.61194e22i			0.851173i
$997$		−	2.57184e22i		−	0.831821i	−0.909406	−	0.415910i	$-0.863463\pi$
$997$		−	2.57184e22i		−	0.831821i	0.909406	−	0.415910i	$-0.136537\pi$
$998$		−	4.45422e22i		−	1.42986i
$999$	1.43359e22			0.456754

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.16.b.a.28.6	✓	36
29.28	even	2	inner	29.16.b.a.28.31	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.16.b.a.28.6	✓	36	1.1	even	1	trivial
29.16.b.a.28.31	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)

\(f(q)\)	\(=\)	\(q-255.661i q^{2} +4338.48i q^{3} -32594.8 q^{4} -284737. q^{5} +1.10918e6 q^{6} -3.50246e6 q^{7} -44288.6i q^{8} -4.47354e6 q^{9} +O(q^{10})\)	\(q-255.661i q^{2} +4338.48i q^{3} -32594.8 q^{4} -284737. q^{5} +1.10918e6 q^{6} -3.50246e6 q^{7} -44288.6i q^{8} -4.47354e6 q^{9} +7.27962e7i q^{10} -3.04941e7i q^{11} -1.41412e8i q^{12} -4.29015e8 q^{13} +8.95444e8i q^{14} -1.23533e9i q^{15} -1.07939e9 q^{16} +2.53498e9i q^{17} +1.14371e9i q^{18} -4.65883e9i q^{19} +9.28093e9 q^{20} -1.51954e10i q^{21} -7.79616e9 q^{22} +5.54895e9 q^{23} +1.92146e8 q^{24} +5.05575e10 q^{25} +1.09683e11i q^{26} +4.28441e10i q^{27} +1.14162e11 q^{28} +(6.49672e10 + 6.63961e10i) q^{29} -3.15825e11 q^{30} -8.17168e10i q^{31} +2.74507e11i q^{32} +1.32298e11 q^{33} +6.48096e11 q^{34} +9.97279e11 q^{35} +1.45814e11 q^{36} -3.34605e11i q^{37} -1.19108e12 q^{38} -1.86128e12i q^{39} +1.26106e10i q^{40} -4.52645e11i q^{41} -3.88487e12 q^{42} +6.62585e11i q^{43} +9.93947e11i q^{44} +1.27378e12 q^{45} -1.41865e12i q^{46} -4.60853e12i q^{47} -4.68291e12i q^{48} +7.51966e12 q^{49} -1.29256e13i q^{50} -1.09980e13 q^{51} +1.39837e13 q^{52} -2.69409e12 q^{53} +1.09536e13 q^{54} +8.68279e12i q^{55} +1.55119e11i q^{56} +2.02123e13 q^{57} +(1.69749e13 - 1.66096e13i) q^{58} -3.38176e13 q^{59} +4.02652e13i q^{60} +2.05845e13i q^{61} -2.08918e13 q^{62} +1.56684e13 q^{63} +3.48114e13 q^{64} +1.22157e14 q^{65} -3.38235e13i q^{66} -3.33094e13 q^{67} -8.26270e13i q^{68} +2.40740e13i q^{69} -2.54966e14i q^{70} +8.83696e13 q^{71} +1.98127e11i q^{72} +1.19616e14i q^{73} -8.55456e13 q^{74} +2.19343e14i q^{75} +1.51854e14i q^{76} +1.06804e14i q^{77} -4.75857e14 q^{78} -2.60180e14i q^{79} +3.07342e14 q^{80} -2.50069e14 q^{81} -1.15724e14 q^{82} -1.84704e14 q^{83} +4.95289e14i q^{84} -7.21801e14i q^{85} +1.69397e14 q^{86} +(-2.88059e14 + 2.81859e14i) q^{87} -1.35054e12 q^{88} +8.68945e13i q^{89} -3.25657e14i q^{90} +1.50261e15 q^{91} -1.80867e14 q^{92} +3.54527e14 q^{93} -1.17822e15 q^{94} +1.32654e15i q^{95} -1.19094e15 q^{96} +7.72413e14i q^{97} -1.92249e15i q^{98} +1.36416e14i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 508108 q^{4} + 470082 q^{5} + 1112016 q^{6} - 4820620 q^{7} - 167460710 q^{9}+O(q^{10}) \) 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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