LMFDB - Embedded newform 29.10.b.a.28.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,10,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, 10, names="a")

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

chi := DirichletCharacter("29.28");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 10 $
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:	$14.9360392488$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			28.2
Character	$\chi$	$=$	29.28
Dual form			29.10.b.a.28.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-39.9552i q^{2} +171.812i q^{3} -1084.42 q^{4} +917.921 q^{5} +6864.79 q^{6} +835.627 q^{7} +22871.2i q^{8} -9836.35 q^{9} +O(q^{10})$	\(q-39.9552i q^{2} +171.812i q^{3} -1084.42 q^{4} +917.921 q^{5} +6864.79 q^{6} +835.627 q^{7} +22871.2i q^{8} -9836.35 q^{9} -36675.8i q^{10} -88341.6i q^{11} -186317. i q^{12} +12711.2 q^{13} -33387.7i q^{14} +157710. i q^{15} +358602. q^{16} -319667. i q^{17} +393014. i q^{18} -170165. i q^{19} -995413. q^{20} +143571. i q^{21} -3.52971e6 q^{22} +1.41437e6 q^{23} -3.92955e6 q^{24} -1.11055e6 q^{25} -507880. i q^{26} +1.69177e6i q^{27} -906171. q^{28} +(2.90225e6 - 2.46660e6i) q^{29} +6.30133e6 q^{30} -6.77977e6i q^{31} -2.61796e6i q^{32} +1.51781e7 q^{33} -1.27724e7 q^{34} +767039. q^{35} +1.06667e7 q^{36} -7.64041e6i q^{37} -6.79898e6 q^{38} +2.18394e6i q^{39} +2.09940e7i q^{40} -2.65188e7i q^{41} +5.73640e6 q^{42} -7.74142e6i q^{43} +9.57995e7i q^{44} -9.02899e6 q^{45} -5.65113e7i q^{46} +3.23182e7i q^{47} +6.16121e7i q^{48} -3.96553e7 q^{49} +4.43721e7i q^{50} +5.49225e7 q^{51} -1.37843e7 q^{52} +7.70109e7 q^{53} +6.75952e7 q^{54} -8.10906e7i q^{55} +1.91118e7i q^{56} +2.92364e7 q^{57} +(-9.85534e7 - 1.15960e8i) q^{58} -1.92652e7 q^{59} -1.71024e8i q^{60} +1.10408e8i q^{61} -2.70888e8 q^{62} -8.21951e6 q^{63} +7.90031e7 q^{64} +1.16679e7 q^{65} -6.06446e8i q^{66} +1.38384e7 q^{67} +3.46653e8i q^{68} +2.43005e8i q^{69} -3.06472e7i q^{70} +2.80598e8 q^{71} -2.24969e8i q^{72} +4.52807e8i q^{73} -3.05274e8 q^{74} -1.90805e8i q^{75} +1.84531e8i q^{76} -7.38206e7i q^{77} +8.72598e7 q^{78} -2.14122e8i q^{79} +3.29168e8 q^{80} -4.84276e8 q^{81} -1.05957e9 q^{82} -5.71761e8 q^{83} -1.55691e8i q^{84} -2.93429e8i q^{85} -3.09310e8 q^{86} +(4.23791e8 + 4.98641e8i) q^{87} +2.02048e9 q^{88} +2.66645e8i q^{89} +3.60755e8i q^{90} +1.06218e7 q^{91} -1.53377e9 q^{92} +1.16485e9 q^{93} +1.29128e9 q^{94} -1.56198e8i q^{95} +4.49796e8 q^{96} +1.26414e9i q^{97} +1.58444e9i q^{98} +8.68959e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 5804 q^{4} - 1374 q^{5} - 8304 q^{6} - 4956 q^{7} - 112244 q^{9}+O(q^{10}) $ 22 * q - 5804 * q^4 - 1374 * q^5 - 8304 * q^6 - 4956 * q^7 - 112244 * q^9	$ 22 q - 5804 q^{4} - 1374 q^{5} - 8304 q^{6} - 4956 q^{7} - 112244 q^{9} - 244222 q^{13} + 1246804 q^{16} - 1658748 q^{20} + 822328 q^{22} - 874956 q^{23} + 8668172 q^{24} + 5307748 q^{25} - 620352 q^{28} - 2425374 q^{29} - 8942448 q^{30} + 10134274 q^{33} - 37785784 q^{34} - 20790348 q^{35} + 34550680 q^{36} - 30663552 q^{38} + 56872008 q^{42} - 43877176 q^{45} - 131743922 q^{49} - 6194732 q^{51} + 342496580 q^{52} + 34886610 q^{53} + 116488784 q^{54} - 308361676 q^{57} + 342193888 q^{58} + 175799052 q^{59} - 484313328 q^{62} - 190643424 q^{63} - 419498924 q^{64} - 149739966 q^{65} - 508277640 q^{67} + 263144256 q^{71} + 435201408 q^{74} + 1065897336 q^{78} + 2990464236 q^{80} - 129895134 q^{81} - 527065064 q^{82} + 1555989756 q^{83} - 3422424120 q^{86} + 2176720604 q^{87} - 387386068 q^{88} - 1493579244 q^{91} - 1262849472 q^{92} + 2042413382 q^{93} + 166226488 q^{94} - 6686432820 q^{96}+O(q^{100}) $ 22 * q - 5804 * q^4 - 1374 * q^5 - 8304 * q^6 - 4956 * q^7 - 112244 * q^9 - 244222 * q^13 + 1246804 * q^16 - 1658748 * q^20 + 822328 * q^22 - 874956 * q^23 + 8668172 * q^24 + 5307748 * q^25 - 620352 * q^28 - 2425374 * q^29 - 8942448 * q^30 + 10134274 * q^33 - 37785784 * q^34 - 20790348 * q^35 + 34550680 * q^36 - 30663552 * q^38 + 56872008 * q^42 - 43877176 * q^45 - 131743922 * q^49 - 6194732 * q^51 + 342496580 * q^52 + 34886610 * q^53 + 116488784 * q^54 - 308361676 * q^57 + 342193888 * q^58 + 175799052 * q^59 - 484313328 * q^62 - 190643424 * q^63 - 419498924 * q^64 - 149739966 * q^65 - 508277640 * q^67 + 263144256 * q^71 + 435201408 * q^74 + 1065897336 * q^78 + 2990464236 * q^80 - 129895134 * q^81 - 527065064 * q^82 + 1555989756 * q^83 - 3422424120 * q^86 + 2176720604 * q^87 - 387386068 * q^88 - 1493579244 * q^91 - 1262849472 * q^92 + 2042413382 * q^93 + 166226488 * q^94 - 6686432820 * 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 $

$2$		−	39.9552i		−	1.76579i	−0.469571	−	0.882894i	$-0.655592\pi$
$2$		−	39.9552i		−	1.76579i	0.469571	−	0.882894i	$-0.344408\pi$
$3$			171.812i			1.22464i	0.790611	+	0.612319i	$0.209763\pi$
$3$			171.812i			1.22464i	−0.790611	+	0.612319i	$0.790237\pi$
$4$	−1084.42			−2.11801
$5$	917.921			0.656811			0.328405	−	0.944537i	$-0.393489\pi$
$5$	917.921			0.656811			0.328405	+	0.944537i	$0.393489\pi$
$6$	6864.79			2.16245
$7$	835.627			0.131544			0.0657720	−	0.997835i	$-0.479049\pi$
$7$	835.627			0.131544			0.0657720	+	0.997835i	$0.479049\pi$
$8$			22871.2i			1.97417i
$9$	−9836.35			−0.499738
$10$		−	36675.8i		−	1.15979i
$11$		−	88341.6i		−	1.81927i	−0.415404	−	0.909637i	$-0.636360\pi$
$11$		−	88341.6i		−	1.81927i	0.415404	−	0.909637i	$-0.363640\pi$
$12$		−	186317.i		−	2.59380i
$13$	12711.2			0.123436			0.0617180	−	0.998094i	$-0.480342\pi$
$13$	12711.2			0.123436			0.0617180	+	0.998094i	$0.480342\pi$
$14$		−	33387.7i		−	0.232279i
$15$			157710.i			0.804355i
$16$	358602.			1.36796
$17$		−	319667.i		−	0.928276i	−0.885763	−	0.464138i	$-0.846364\pi$
$17$		−	319667.i		−	0.928276i	0.885763	−	0.464138i	$-0.153636\pi$
$18$			393014.i			0.882432i
$19$		−	170165.i		−	0.299557i	−0.988720	−	0.149778i	$-0.952144\pi$
$19$		−	170165.i		−	0.299557i	0.988720	−	0.149778i	$-0.0478560\pi$
$20$	−995413.			−1.39113
$21$			143571.i			0.161094i
$22$	−3.52971e6			−3.21245
$23$	1.41437e6			1.05387			0.526934	−	0.849906i	$-0.323341\pi$
$23$	1.41437e6			1.05387			0.526934	+	0.849906i	$0.323341\pi$
$24$	−3.92955e6			−2.41764
$25$	−1.11055e6			−0.568600
$26$		−	507880.i		−	0.217962i
$27$			1.69177e6i			0.612640i
$28$	−906171.			−0.278612
$29$	2.90225e6	−	2.46660e6i	0.761980	−	0.647600i
$29$	2.90225e6	−	2.46660e6i	0.761980	−	0.647600i
$30$	6.30133e6			1.42032
$31$		−	6.77977e6i		−	1.31852i	−0.751914	−	0.659261i	$-0.770869\pi$
$31$		−	6.77977e6i		−	1.31852i	0.751914	−	0.659261i	$-0.229131\pi$
$32$		−	2.61796e6i		−	0.441355i
$33$	1.51781e7			2.22795
$34$	−1.27724e7			−1.63914
$35$	767039.			0.0863995
$36$	1.06667e7			1.05845
$37$		−	7.64041e6i		−	0.670207i	−0.942181	−	0.335103i	$-0.891229\pi$
$37$		−	7.64041e6i		−	0.670207i	0.942181	−	0.335103i	$-0.108771\pi$
$38$	−6.79898e6			−0.528954
$39$			2.18394e6i			0.151164i
$40$			2.09940e7i			1.29666i
$41$		−	2.65188e7i		−	1.46564i	−0.680424	−	0.732819i	$-0.738204\pi$
$41$		−	2.65188e7i		−	1.46564i	0.680424	−	0.732819i	$-0.261796\pi$
$42$	5.73640e6			0.284458
$43$		−	7.74142e6i		−	0.345313i	−0.984982	−	0.172656i	$-0.944765\pi$
$43$		−	7.74142e6i		−	0.345313i	0.984982	−	0.172656i	$-0.0552350\pi$
$44$			9.57995e7i			3.85324i
$45$	−9.02899e6			−0.328233
$46$		−	5.65113e7i		−	1.86091i
$47$			3.23182e7i			0.966065i	0.875602	+	0.483032i	$0.160465\pi$
$47$			3.23182e7i			0.966065i	−0.875602	+	0.483032i	$0.839535\pi$
$48$			6.16121e7i			1.67525i
$49$	−3.96553e7			−0.982696
$50$			4.43721e7i			1.00403i
$51$	5.49225e7			1.13680
$52$	−1.37843e7			−0.261439
$53$	7.70109e7			1.34063			0.670317	−	0.742074i	$-0.266158\pi$
$53$	7.70109e7			1.34063			0.670317	+	0.742074i	$0.266158\pi$
$54$	6.75952e7			1.08179
$55$		−	8.10906e7i		−	1.19492i
$56$			1.91118e7i			0.259690i
$57$	2.92364e7			0.366848
$58$	−9.85534e7	−	1.15960e8i	−1.14353	−	1.34550i
$59$	−1.92652e7			−0.206986			−0.103493	−	0.994630i	$-0.533002\pi$
$59$	−1.92652e7			−0.206986			−0.103493	+	0.994630i	$0.533002\pi$
$60$		−	1.71024e8i		−	1.70363i
$61$			1.10408e8i			1.02098i	0.859883	+	0.510490i	$0.170536\pi$
$61$			1.10408e8i			1.02098i	−0.859883	+	0.510490i	$0.829464\pi$
$62$	−2.70888e8			−2.32823
$63$	−8.21951e6			−0.0657376
$64$	7.90031e7			0.588619
$65$	1.16679e7			0.0810741
$66$		−	6.06446e8i		−	3.93409i
$67$	1.38384e7			0.0838977			0.0419489	−	0.999120i	$-0.486643\pi$
$67$	1.38384e7			0.0838977			0.0419489	+	0.999120i	$0.486643\pi$
$68$			3.46653e8i			1.96610i
$69$			2.43005e8i			1.29061i
$70$		−	3.06472e7i		−	0.152563i
$71$	2.80598e8			1.31045			0.655227	−	0.755432i	$-0.272573\pi$
$71$	2.80598e8			1.31045			0.655227	+	0.755432i	$0.272573\pi$
$72$		−	2.24969e8i		−	0.986568i
$73$			4.52807e8i			1.86621i	0.359606	+	0.933104i	$0.382911\pi$
$73$			4.52807e8i			1.86621i	−0.359606	+	0.933104i	$0.617089\pi$
$74$	−3.05274e8			−1.18344
$75$		−	1.90805e8i		−	0.696329i
$76$			1.84531e8i			0.634464i
$77$		−	7.38206e7i		−	0.239315i
$78$	8.72598e7			0.266925
$79$		−	2.14122e8i		−	0.618498i	−0.950981	−	0.309249i	$-0.899922\pi$
$79$		−	2.14122e8i		−	0.618498i	0.950981	−	0.309249i	$-0.100078\pi$
$80$	3.29168e8			0.898489
$81$	−4.84276e8			−1.25000
$82$	−1.05957e9			−2.58801
$83$	−5.71761e8			−1.32240			−0.661200	−	0.750209i	$-0.729953\pi$
$83$	−5.71761e8			−1.32240			−0.661200	+	0.750209i	$0.729953\pi$
$84$		−	1.55691e8i		−	0.341198i
$85$		−	2.93429e8i		−	0.609702i
$86$	−3.09310e8			−0.609749
$87$	4.23791e8	+	4.98641e8i	0.793076	+	0.933150i
$88$	2.02048e9			3.59156
$89$			2.66645e8i			0.450483i	0.974303	+	0.225242i	$0.0723172\pi$
$89$			2.66645e8i			0.450483i	−0.974303	+	0.225242i	$0.927683\pi$
$90$			3.60755e8i			0.579591i
$91$	1.06218e7			0.0162373
$92$	−1.53377e9			−2.23210
$93$	1.16485e9			1.61471
$94$	1.29128e9			1.70587
$95$		−	1.56198e8i		−	0.196752i
$96$	4.49796e8			0.540500
$97$			1.26414e9i			1.44985i	0.688827	+	0.724926i	$0.258126\pi$
$97$			1.26414e9i			1.44985i	−0.688827	+	0.724926i	$0.741874\pi$
$98$			1.58444e9i			1.73523i
$99$			8.68959e8i			0.909161i
$100$	1.20430e9			1.20430
$101$		−	1.00374e9i		−	0.959791i	−0.877326	−	0.479895i	$-0.840675\pi$
$101$		−	1.00374e9i		−	0.959791i	0.877326	−	0.479895i	$-0.159325\pi$
$102$		−	2.19444e9i		−	2.00735i
$103$	−1.38708e8			−0.121432			−0.0607160	−	0.998155i	$-0.519338\pi$
$103$	−1.38708e8			−0.121432			−0.0607160	+	0.998155i	$0.519338\pi$
$104$			2.90721e8i			0.243684i
$105$			1.31787e8i			0.105808i
$106$		−	3.07699e9i		−	2.36728i
$107$	−9.60634e8			−0.708485			−0.354243	−	0.935154i	$-0.615261\pi$
$107$	−9.60634e8			−0.708485			−0.354243	+	0.935154i	$0.615261\pi$
$108$		−	1.83459e9i		−	1.29758i
$109$	1.96159e9			1.33103			0.665515	−	0.746384i	$-0.268212\pi$
$109$	1.96159e9			1.33103			0.665515	+	0.746384i	$0.268212\pi$
$110$	−3.23999e9			−2.10997
$111$	1.31271e9			0.820760
$112$	2.99657e8			0.179947
$113$			3.05071e9i			1.76015i	0.474839	+	0.880073i	$0.342506\pi$
$113$			3.05071e9i			1.76015i	−0.474839	+	0.880073i	$0.657494\pi$
$114$		−	1.16815e9i		−	0.647777i
$115$	1.29828e9			0.692192
$116$	−3.14726e9	+	2.67483e9i	−1.61388	+	1.37162i
$117$	−1.25032e8			−0.0616857
$118$			7.69747e8i			0.365493i
$119$		−	2.67122e8i		−	0.122109i
$120$	−3.60702e9			−1.58793
$121$	−5.44629e9			−2.30976
$122$	4.41139e9			1.80284
$123$	4.55625e9			1.79488
$124$			7.35213e9i			2.79265i
$125$	−2.81221e9			−1.03027
$126$			3.28413e8i			0.116079i
$127$		−	4.91848e9i		−	1.67770i	−0.544364	−	0.838849i	$-0.683229\pi$
$127$		−	4.91848e9i		−	1.67770i	0.544364	−	0.838849i	$-0.316771\pi$
$128$		−	4.49698e9i		−	1.48073i
$129$	1.33007e9			0.422883
$130$		−	4.66193e8i		−	0.143160i
$131$		−	9.86788e8i		−	0.292754i	−0.989229	−	0.146377i	$-0.953239\pi$
$131$		−	9.86788e8i		−	0.292754i	0.989229	−	0.146377i	$-0.0467613\pi$
$132$	−1.64595e10			−4.71883
$133$		−	1.42194e8i		−	0.0394049i
$134$		−	5.52918e8i		−	0.148146i
$135$			1.55291e9i			0.402388i
$136$	7.31117e9			1.83258
$137$			7.41423e8i			0.179814i	0.995950	+	0.0899070i	$0.0286570\pi$
$137$			7.41423e8i			0.179814i	−0.995950	+	0.0899070i	$0.971343\pi$
$138$	9.70932e9			2.27894
$139$	−5.60606e7			−0.0127377			−0.00636885	−	0.999980i	$-0.502027\pi$
$139$	−5.60606e7			−0.0127377			−0.00636885	+	0.999980i	$0.502027\pi$
$140$	−8.31794e8			−0.182995
$141$	−5.55265e9			−1.18308
$142$		−	1.12114e10i		−	2.31399i
$143$		−	1.12293e9i		−	0.224564i
$144$	−3.52733e9			−0.683621
$145$	2.66404e9	−	2.26414e9i	0.500477	−	0.425351i
$146$	1.80920e10			3.29533
$147$		−	6.81326e9i		−	1.20345i
$148$			8.28542e9i			1.41950i
$149$	2.68016e9			0.445474			0.222737	−	0.974879i	$-0.428501\pi$
$149$	2.68016e9			0.445474			0.222737	+	0.974879i	$0.428501\pi$
$150$	−7.62366e9			−1.22957
$151$	7.16042e9			1.12084			0.560418	−	0.828210i	$-0.310640\pi$
$151$	7.16042e9			1.12084			0.560418	+	0.828210i	$0.310640\pi$
$152$	3.89188e9			0.591376
$153$			3.14435e9i			0.463895i
$154$	−2.94952e9			−0.422579
$155$		−	6.22330e9i		−	0.866020i
$156$		−	2.36831e9i		−	0.320168i
$157$		−	1.17697e9i		−	0.154603i	−0.997008	−	0.0773014i	$-0.975370\pi$
$157$		−	1.17697e9i		−	0.154603i	0.997008	−	0.0773014i	$-0.0246304\pi$
$158$	−8.55528e9			−1.09214
$159$			1.32314e10i			1.64179i
$160$		−	2.40308e9i		−	0.289886i
$161$	1.18188e9			0.138630
$162$			1.93493e10i			2.20724i
$163$		−	9.47972e9i		−	1.05184i	−0.850533	−	0.525922i	$-0.823720\pi$
$163$		−	9.47972e9i		−	1.05184i	0.850533	−	0.525922i	$-0.176280\pi$
$164$			2.87576e10i			3.10424i
$165$	1.39323e10			1.46334
$166$			2.28449e10i			2.33508i
$167$	9.53728e8			0.0948856			0.0474428	−	0.998874i	$-0.484893\pi$
$167$	9.53728e8			0.0948856			0.0474428	+	0.998874i	$0.484893\pi$
$168$	−3.28364e9			−0.318027
$169$	−1.04429e10			−0.984764
$170$	−1.17240e10			−1.07660
$171$			1.67380e9i			0.149700i
$172$			8.39496e9i			0.731376i
$173$	−1.65134e10			−1.40162			−0.700808	−	0.713350i	$-0.747177\pi$
$173$	−1.65134e10			−1.40162			−0.700808	+	0.713350i	$0.747177\pi$
$174$	1.99233e10	−	1.69327e10i	1.64775	−	1.40040i
$175$	−9.28002e8			−0.0747959
$176$		−	3.16795e10i		−	2.48869i
$177$		−	3.31000e9i		−	0.253482i
$178$	1.06539e10			0.795459
$179$	−1.35712e10			−0.988048			−0.494024	−	0.869448i	$-0.664475\pi$
$179$	−1.35712e10			−0.988048			−0.494024	+	0.869448i	$0.664475\pi$
$180$	9.79123e9			0.695202
$181$	9.65788e9			0.668849			0.334425	−	0.942423i	$-0.391458\pi$
$181$	9.65788e9			0.668849			0.334425	+	0.942423i	$0.391458\pi$
$182$		−	4.24398e8i		−	0.0286716i
$183$	−1.89695e10			−1.25033
$184$			3.23483e10i			2.08052i
$185$		−	7.01329e9i		−	0.440199i
$186$		−	4.65417e10i		−	2.85124i
$187$	−2.82399e10			−1.68879
$188$		−	3.50465e10i		−	2.04614i
$189$			1.41369e9i			0.0805891i
$190$	−6.24093e9			−0.347423
$191$			4.86952e8i			0.0264750i	0.999912	+	0.0132375i	$0.00421375\pi$
$191$			4.86952e8i			0.0264750i	−0.999912	+	0.0132375i	$0.995786\pi$
$192$			1.35737e10i			0.720845i
$193$			2.47013e9i			0.128148i	0.997945	+	0.0640740i	$0.0204094\pi$
$193$			2.47013e9i			0.128148i	−0.997945	+	0.0640740i	$0.979591\pi$
$194$	5.05092e10			2.56013
$195$			2.00468e9i			0.0992864i
$196$	4.30031e10			2.08136
$197$	4.74490e9			0.224455			0.112228	−	0.993683i	$-0.464201\pi$
$197$	4.74490e9			0.224455			0.112228	+	0.993683i	$0.464201\pi$
$198$	3.47195e10			1.60539
$199$	1.91200e10			0.864269			0.432135	−	0.901809i	$-0.357761\pi$
$199$	1.91200e10			0.864269			0.432135	+	0.901809i	$0.357761\pi$
$200$		−	2.53996e10i		−	1.12251i
$201$			2.37761e9i			0.102744i
$202$	−4.01048e10			−1.69479
$203$	2.42520e9	−	2.06115e9i	0.100234	−	0.0851879i
$204$	−5.95592e10			−2.40776
$205$		−	2.43422e10i		−	0.962646i
$206$			5.54210e9i			0.214423i
$207$	−1.39122e10			−0.526658
$208$	4.55827e9			0.168855
$209$	−1.50326e10			−0.544976
$210$	5.26556e9			0.186835
$211$			1.83544e10i			0.637484i	0.947841	+	0.318742i	$0.103260\pi$
$211$			1.83544e10i			0.637484i	−0.947841	+	0.318742i	$0.896740\pi$
$212$	−8.35122e10			−2.83948
$213$			4.82101e10i			1.60483i
$214$			3.83824e10i			1.25104i
$215$		−	7.10601e9i		−	0.226805i
$216$	−3.86929e10			−1.20946
$217$		−	5.66536e9i		−	0.173444i
$218$		−	7.83756e10i		−	2.35032i
$219$	−7.77976e10			−2.28543
$220$			8.79364e10i			2.53085i
$221$		−	4.06335e9i		−	0.114583i
$222$		−	5.24498e10i		−	1.44929i
$223$	−1.05192e10			−0.284847			−0.142424	−	0.989806i	$-0.545490\pi$
$223$	−1.05192e10			−0.284847			−0.142424	+	0.989806i	$0.545490\pi$
$224$		−	2.18763e9i		−	0.0580576i
$225$	1.09237e10			0.284151
$226$	1.21892e11			3.10805
$227$	7.17551e10			1.79365			0.896823	−	0.442390i	$-0.145869\pi$
$227$	7.17551e10			1.79365			0.896823	+	0.442390i	$0.145869\pi$
$228$	−3.17046e10			−0.776989
$229$			7.77788e10i			1.86897i	0.356006	+	0.934484i	$0.384138\pi$
$229$			7.77788e10i			1.86897i	−0.356006	+	0.934484i	$0.615862\pi$
$230$		−	5.18729e10i		−	1.22226i
$231$	1.26833e10			0.293074
$232$	5.64141e10	+	6.63780e10i	1.27847	+	1.50428i
$233$	6.52044e10			1.44936			0.724679	−	0.689087i	$-0.241988\pi$
$233$	6.52044e10			1.44936			0.724679	+	0.689087i	$0.241988\pi$
$234$			4.99568e9i			0.108924i
$235$			2.96655e10i			0.634522i
$236$	2.08916e10			0.438398
$237$	3.67886e10			0.757436
$238$	−1.06729e10			−0.215619
$239$	−6.47822e10			−1.28430			−0.642148	−	0.766581i	$-0.721956\pi$
$239$	−6.47822e10			−1.28430			−0.642148	+	0.766581i	$0.721956\pi$
$240$			5.65550e10i			1.10032i
$241$	4.71029e10			0.899437			0.449718	−	0.893170i	$-0.351524\pi$
$241$	4.71029e10			0.899437			0.449718	+	0.893170i	$0.351524\pi$
$242$			2.17608e11i			4.07855i
$243$		−	4.99052e10i		−	0.918158i
$244$		−	1.19729e11i		−	2.16245i
$245$	−3.64005e10			−0.645445
$246$		−	1.82046e11i		−	3.16937i
$247$		−	2.16300e9i		−	0.0369761i
$248$	1.55062e11			2.60299
$249$		−	9.82354e10i		−	1.61946i
$250$			1.12362e11i			1.81924i
$251$		−	6.37152e10i		−	1.01324i	−0.862170	−	0.506619i	$-0.830895\pi$
$251$		−	6.37152e10i		−	1.01324i	0.862170	−	0.506619i	$-0.169105\pi$
$252$	8.91342e9			0.139233
$253$		−	1.24947e11i		−	1.91728i
$254$	−1.96519e11			−2.96246
$255$	5.04145e10			0.746664
$256$	−1.39228e11			−2.02604
$257$	1.04092e11			1.48839			0.744196	−	0.667961i	$-0.232833\pi$
$257$	1.04092e11			1.48839			0.744196	+	0.667961i	$0.232833\pi$
$258$		−	5.31432e10i		−	0.746722i
$259$		−	6.38453e9i		−	0.0881617i
$260$	−1.26529e10			−0.171716
$261$	−2.85475e10	+	2.42623e10i	−0.380791	+	0.323631i
$262$	−3.94273e10			−0.516942
$263$		−	4.15248e10i		−	0.535188i	−0.963532	−	0.267594i	$-0.913771\pi$
$263$		−	4.15248e10i		−	0.535188i	0.963532	−	0.267594i	$-0.0862286\pi$
$264$			3.47143e11i			4.39836i
$265$	7.06899e10			0.880543
$266$	−5.68141e9			−0.0695807
$267$	−4.58128e10			−0.551679
$268$	−1.50067e10			−0.177696
$269$			7.30390e10i			0.850490i	0.905078	+	0.425245i	$0.139812\pi$
$269$			7.30390e10i			0.850490i	−0.905078	+	0.425245i	$0.860188\pi$
$270$	6.20470e10			0.710533
$271$			3.44898e9i			0.0388444i	0.999811	+	0.0194222i	$0.00618267\pi$
$271$			3.44898e9i			0.0388444i	−0.999811	+	0.0194222i	$0.993817\pi$
$272$		−	1.14633e11i		−	1.26984i
$273$			1.82496e9i			0.0198848i
$274$	2.96237e10			0.317513
$275$			9.81074e10i			1.03444i
$276$		−	2.63520e11i		−	2.73352i
$277$	9.03735e10			0.922321			0.461161	−	0.887317i	$-0.347433\pi$
$277$	9.03735e10			0.922321			0.461161	+	0.887317i	$0.347433\pi$
$278$			2.23991e9i			0.0224921i
$279$			6.66882e10i			0.658916i
$280$			1.75431e10i			0.170567i
$281$	−4.64916e10			−0.444832			−0.222416	−	0.974952i	$-0.571394\pi$
$281$	−4.64916e10			−0.444832			−0.222416	+	0.974952i	$0.571394\pi$
$282$			2.21857e11i			2.08907i
$283$	4.19254e10			0.388542			0.194271	−	0.980948i	$-0.437766\pi$
$283$	4.19254e10			0.388542			0.194271	+	0.980948i	$0.437766\pi$
$284$	−3.04287e11			−2.77556
$285$	2.68367e10			0.240950
$286$	−4.48669e10			−0.396533
$287$		−	2.21598e10i		−	0.192796i
$288$			2.57511e10i			0.220562i
$289$	1.64011e10			0.138304
$290$	−9.04643e10	−	1.06442e11i	−0.751080	−	0.883736i
$291$	−2.17195e11			−1.77554
$292$		−	4.91033e11i		−	3.95265i
$293$			1.71310e11i			1.35793i	0.734171	+	0.678965i	$0.237571\pi$
$293$			1.71310e11i			1.35793i	−0.734171	+	0.678965i	$0.762429\pi$
$294$	−2.72225e11			−2.12503
$295$	−1.76840e10			−0.135950
$296$	1.74746e11			1.32310
$297$	1.49454e11			1.11456
$298$		−	1.07087e11i		−	0.786614i
$299$	1.79783e10			0.130085
$300$			2.06913e11i			1.47483i
$301$		−	6.46893e9i		−	0.0454238i
$302$		−	2.86096e11i		−	1.97916i
$303$	1.72455e11			1.17540
$304$		−	6.10215e10i		−	0.409781i
$305$			1.01346e11i			0.670591i
$306$	1.25633e11			0.819141
$307$			6.80817e9i			0.0437429i	0.999761	+	0.0218714i	$0.00696245\pi$
$307$			6.80817e9i			0.0437429i	−0.999761	+	0.0218714i	$0.993038\pi$
$308$			8.00526e10i			0.506871i
$309$		−	2.38316e10i		−	0.148710i
$310$	−2.48653e11			−1.52921
$311$			1.22554e11i			0.742858i	0.928461	+	0.371429i	$0.121132\pi$
$311$			1.22554e11i			0.742858i	−0.928461	+	0.371429i	$0.878868\pi$
$312$	−4.99494e10			−0.298424
$313$	3.85007e9			0.0226735			0.0113368	−	0.999936i	$-0.496391\pi$
$313$	3.85007e9			0.0226735			0.0113368	+	0.999936i	$0.496391\pi$
$314$	−4.70262e10			−0.272996
$315$	−7.54486e9			−0.0431771
$316$			2.32198e11i			1.30999i
$317$			2.87336e11i			1.59817i	0.601217	+	0.799085i	$0.294683\pi$
$317$			2.87336e11i			1.59817i	−0.601217	+	0.799085i	$0.705317\pi$
$318$	5.28663e11			2.89906
$319$	−2.17903e11	−	2.56389e11i	−1.17816	−	1.38625i
$320$	7.25186e10			0.386611
$321$		−	1.65048e11i		−	0.867638i
$322$		−	4.72224e10i		−	0.244791i
$323$	−5.43961e10			−0.278071
$324$	5.25159e11			2.64751
$325$	−1.41164e10			−0.0701857
$326$	−3.78765e11			−1.85734
$327$			3.37024e11i			1.63003i
$328$	6.06518e11			2.89342
$329$			2.70059e10i			0.127080i
$330$		−	5.56670e11i		−	2.58395i
$331$		−	2.81164e11i		−	1.28746i	−0.765252	−	0.643731i	$-0.777386\pi$
$331$		−	2.81164e11i		−	1.28746i	0.765252	−	0.643731i	$-0.222614\pi$
$332$	6.20030e11			2.80086
$333$			7.51537e10i			0.334928i
$334$		−	3.81064e10i		−	0.167548i
$335$	1.27026e10			0.0551049
$336$			5.14847e10i			0.220370i
$337$			7.74083e10i			0.326928i	0.986549	+	0.163464i	$0.0522668\pi$
$337$			7.74083e10i			0.326928i	−0.986549	+	0.163464i	$0.947733\pi$
$338$			4.17250e11i			1.73888i
$339$	−5.24149e11			−2.15554
$340$			3.18200e11i			1.29135i
$341$	−5.98936e11			−2.39875
$342$	6.68772e10			0.264338
$343$	−6.68576e10			−0.260812
$344$	1.77056e11			0.681706
$345$			2.23059e11i			0.847685i
$346$			6.59797e11i			2.47496i
$347$	3.20811e11			1.18786			0.593931	−	0.804516i	$-0.297575\pi$
$347$	3.20811e11			1.18786			0.593931	+	0.804516i	$0.297575\pi$
$348$	−4.59568e11	−	5.40737e11i	−1.67974	−	1.97642i
$349$	1.32366e11			0.477599			0.238800	−	0.971069i	$-0.423246\pi$
$349$	1.32366e11			0.477599			0.238800	+	0.971069i	$0.423246\pi$
$350$			3.70786e10i			0.132074i
$351$			2.15045e10i			0.0756218i
$352$	−2.31274e11			−0.802945
$353$	−5.18292e11			−1.77660			−0.888298	−	0.459268i	$-0.848112\pi$
$353$	−5.18292e11			−1.77660			−0.888298	+	0.459268i	$0.848112\pi$
$354$	−1.32252e11			−0.447596
$355$	2.57567e11			0.860721
$356$		−	2.89156e11i		−	0.954128i
$357$	4.58947e10			0.149540
$358$			5.42239e11i			1.74468i
$359$		−	2.65270e11i		−	0.842876i	−0.906857	−	0.421438i	$-0.861526\pi$
$359$		−	2.65270e11i		−	0.842876i	0.906857	−	0.421438i	$-0.138474\pi$
$360$		−	2.06504e11i		−	0.647989i
$361$	2.93732e11			0.910266
$362$		−	3.85883e11i		−	1.18105i
$363$		−	9.35738e11i		−	2.82862i
$364$	−1.15185e10			−0.0343907
$365$			4.15641e11i			1.22575i
$366$			7.57930e11i			2.20782i
$367$		−	2.18270e11i		−	0.628054i	−0.949414	−	0.314027i	$-0.898322\pi$
$367$		−	2.18270e11i		−	0.628054i	0.949414	−	0.314027i	$-0.101678\pi$
$368$	5.07194e11			1.44165
$369$			2.60848e11i			0.732435i
$370$	−2.80218e11			−0.777298
$371$	6.43523e10			0.176353
$372$	−1.26318e12			−3.41998
$373$	3.68393e11			0.985422			0.492711	−	0.870193i	$-0.336006\pi$
$373$	3.68393e11			0.985422			0.492711	+	0.870193i	$0.336006\pi$
$374$			1.12833e12i			2.98204i
$375$		−	4.83171e11i		−	1.26171i
$376$	−7.39156e11			−1.90718
$377$	3.68911e10	−	3.13534e10i	0.0940558	−	0.0799372i
$378$	5.64843e10			0.142303
$379$			2.38907e11i			0.594775i	0.954757	+	0.297388i	$0.0961154\pi$
$379$			2.38907e11i			0.594775i	−0.954757	+	0.297388i	$0.903885\pi$
$380$			1.69384e11i			0.416723i
$381$	8.45053e11			2.05457
$382$	1.94563e10			0.0467493
$383$	−1.28943e11			−0.306200			−0.153100	−	0.988211i	$-0.548926\pi$
$383$	−1.28943e11			−0.306200			−0.153100	+	0.988211i	$0.548926\pi$
$384$	7.72635e11			1.81336
$385$		−	6.77615e10i		−	0.157184i
$386$	9.86947e10			0.226282
$387$			7.61473e10i			0.172566i
$388$		−	1.37086e12i		−	3.07080i
$389$		−	2.25144e11i		−	0.498525i	−0.968436	−	0.249262i	$-0.919812\pi$
$389$		−	2.25144e11i		−	0.498525i	0.968436	−	0.249262i	$-0.0801881\pi$
$390$	8.00976e10			0.175319
$391$		−	4.52125e11i		−	0.978281i
$392$		−	9.06966e11i		−	1.94001i
$393$	1.69542e11			0.358518
$394$		−	1.89584e11i		−	0.396340i
$395$		−	1.96547e11i		−	0.406236i
$396$		−	9.42317e11i		−	1.92561i
$397$	−5.37007e11			−1.08498			−0.542492	−	0.840061i	$-0.682519\pi$
$397$	−5.37007e11			−1.08498			−0.542492	+	0.840061i	$0.682519\pi$
$398$		−	7.63944e11i		−	1.52612i
$399$	2.44307e10			0.0482567
$400$	−3.98244e11			−0.777821
$401$	9.36295e11			1.80827			0.904135	−	0.427248i	$-0.140517\pi$
$401$	9.36295e11			1.80827			0.904135	+	0.427248i	$0.140517\pi$
$402$	9.49979e10			0.181425
$403$		−	8.61792e10i		−	0.162753i
$404$			1.08848e12i			2.03285i
$405$	−4.44527e11			−0.821013
$406$	−8.23539e10	−	9.68993e10i	−0.150424	−	0.176992i
$407$	−6.74966e11			−1.21929
$408$			1.25615e12i			2.24424i
$409$		−	6.50067e11i		−	1.14869i	−0.818613	−	0.574346i	$-0.805256\pi$
$409$		−	6.50067e11i		−	1.14869i	0.818613	−	0.574346i	$-0.194744\pi$
$410$	−9.72597e11			−1.69983
$411$	−1.27385e11			−0.220207
$412$	1.50418e11			0.257194
$413$	−1.60985e10			−0.0272277
$414$			5.55865e11i			0.929967i
$415$	−5.24831e11			−0.868567
$416$		−	3.32774e10i		−	0.0544791i
$417$		−	9.63188e9i		−	0.0155991i
$418$			6.00633e11i			0.962312i
$419$	−5.42695e11			−0.860187			−0.430094	−	0.902784i	$-0.641519\pi$
$419$	−5.42695e11			−0.860187			−0.430094	+	0.902784i	$0.641519\pi$
$420$		−	1.42912e11i		−	0.224103i
$421$			3.91478e11i			0.607348i	0.952776	+	0.303674i	$0.0982134\pi$
$421$			3.91478e11i			0.607348i	−0.952776	+	0.303674i	$0.901787\pi$
$422$	7.33355e11			1.12566
$423$		−	3.17893e11i		−	0.482780i
$424$			1.76133e12i			2.64664i
$425$			3.55005e11i			0.527817i
$426$	1.92625e12			2.83380
$427$			9.22601e10i			0.134304i
$428$	1.04173e12			1.50058
$429$	1.92933e11			0.275010
$430$	−2.83922e11			−0.400490
$431$	1.45054e11			0.202480			0.101240	−	0.994862i	$-0.467719\pi$
$431$	1.45054e11			0.202480			0.101240	+	0.994862i	$0.467719\pi$
$432$			6.06673e11i			0.838065i
$433$			5.49445e10i			0.0751154i	0.999294	+	0.0375577i	$0.0119578\pi$
$433$			5.49445e10i			0.0751154i	−0.999294	+	0.0375577i	$0.988042\pi$
$434$	−2.26361e11			−0.306265
$435$	3.89006e11	+	4.57713e11i	0.520901	+	0.612903i
$436$	−2.12718e12			−2.81914
$437$		−	2.40675e11i		−	0.315693i
$438$			3.10842e12i			4.03559i
$439$	2.65188e11			0.340771			0.170386	−	0.985377i	$-0.445499\pi$
$439$	2.65188e11			0.340771			0.170386	+	0.985377i	$0.445499\pi$
$440$	1.85464e12			2.35897
$441$	3.90064e11			0.491091
$442$	−1.62352e11			−0.202329
$443$		−	1.46734e12i		−	1.81014i	−0.425259	−	0.905072i	$-0.639817\pi$
$443$		−	1.46734e12i		−	1.81014i	0.425259	−	0.905072i	$-0.360183\pi$
$444$	−1.42353e12			−1.73838
$445$			2.44759e11i			0.295882i
$446$			4.20299e11i			0.502980i
$447$			4.60484e11i			0.545545i
$448$	6.60171e10			0.0774293
$449$			7.56973e10i			0.0878965i	0.999034	+	0.0439483i	$0.0139937\pi$
$449$			7.56973e10i			0.0878965i	−0.999034	+	0.0439483i	$0.986006\pi$
$450$		−	4.36460e11i		−	0.501751i
$451$	−2.34271e12			−2.66640
$452$		−	3.30826e12i		−	3.72801i
$453$			1.23025e12i			1.37262i
$454$		−	2.86699e12i		−	3.16720i
$455$	9.75000e9			0.0106648
$456$			6.68672e11i			0.724221i
$457$	1.95158e11			0.209297			0.104648	−	0.994509i	$-0.466628\pi$
$457$	1.95158e11			0.209297			0.104648	+	0.994509i	$0.466628\pi$
$458$	3.10767e12			3.30020
$459$	5.40803e11			0.568699
$460$	−1.40788e12			−1.46607
$461$			5.74590e11i			0.592521i	0.955107	+	0.296260i	$0.0957397\pi$
$461$			5.74590e11i			0.592521i	−0.955107	+	0.296260i	$0.904260\pi$
$462$		−	5.06763e11i		−	0.517506i
$463$	−2.51338e11			−0.254182			−0.127091	−	0.991891i	$-0.540564\pi$
$463$	−2.51338e11			−0.254182			−0.127091	+	0.991891i	$0.540564\pi$
$464$	1.04075e12	−	8.84526e11i	1.04236	−	0.885890i
$465$	1.06924e12			1.06056
$466$		−	2.60526e12i		−	2.55926i
$467$			1.09991e12i			1.07012i	0.844814	+	0.535061i	$0.179711\pi$
$467$			1.09991e12i			1.07012i	−0.844814	+	0.535061i	$0.820289\pi$
$468$	1.35587e11			0.130651
$469$	1.15638e10			0.0110362
$470$	1.18529e12			1.12043
$471$	2.02218e11			0.189333
$472$		−	4.40619e11i		−	0.408625i
$473$	−6.83889e11			−0.628218
$474$		−	1.46990e12i		−	1.33747i
$475$			1.88976e11i			0.170328i
$476$			2.89673e11i			0.258628i
$477$	−7.57506e11			−0.669967
$478$			2.58839e12i			2.26780i
$479$			6.85017e11i			0.594554i	0.954791	+	0.297277i	$0.0960786\pi$
$479$			6.85017e11i			0.594554i	−0.954791	+	0.297277i	$0.903921\pi$
$480$	4.12877e11			0.355006
$481$		−	9.71188e10i		−	0.0827276i
$482$		−	1.88201e12i		−	1.58822i
$483$			2.03061e11i			0.169772i
$484$	5.90607e12			4.89209
$485$			1.16038e12i			0.952278i
$486$	−1.99397e12			−1.62127
$487$	1.55986e12			1.25663			0.628313	−	0.777961i	$-0.283746\pi$
$487$	1.55986e12			1.25663			0.628313	+	0.777961i	$0.283746\pi$
$488$	−2.52517e12			−2.01559
$489$	1.62873e12			1.28813
$490$			1.45439e12i			1.13972i
$491$			1.15486e12i			0.896731i	0.893850	+	0.448365i	$0.147994\pi$
$491$			1.15486e12i			0.896731i	−0.893850	+	0.448365i	$0.852006\pi$
$492$	−4.94089e12			−3.80156
$493$	−7.88488e11	−	9.27752e11i	−0.601152	−	0.707328i
$494$	−8.64233e10			−0.0652920
$495$			7.97635e11i			0.597147i
$496$		−	2.43124e12i		−	1.80368i
$497$	2.34475e11			0.172383
$498$	−3.92502e12			−2.85963
$499$	−6.93825e11			−0.500953			−0.250477	−	0.968123i	$-0.580587\pi$
$499$	−6.93825e11			−0.500953			−0.250477	+	0.968123i	$0.580587\pi$
$500$	3.04962e12			2.18213
$501$			1.63862e11i			0.116201i
$502$	−2.54576e12			−1.78916
$503$			1.14048e12i			0.794388i	0.917735	+	0.397194i	$0.130016\pi$
$503$			1.14048e12i			0.794388i	−0.917735	+	0.397194i	$0.869984\pi$
$504$		−	1.87990e11i		−	0.129777i
$505$		−	9.21357e11i		−	0.630401i
$506$	−4.99230e12			−3.38550
$507$		−	1.79422e12i		−	1.20598i
$508$			5.33370e12i			3.55338i
$509$	−2.24724e12			−1.48395			−0.741975	−	0.670428i	$-0.766111\pi$
$509$	−2.24724e12			−1.48395			−0.741975	+	0.670428i	$0.766111\pi$
$510$		−	2.01433e12i		−	1.31845i
$511$			3.78378e11i			0.245489i
$512$			3.26045e12i			2.09683i
$513$	2.87880e11			0.183520
$514$		−	4.15901e12i		−	2.62819i
$515$	−1.27323e11			−0.0797579
$516$	−1.44235e12			−0.895670
$517$	2.85504e12			1.75754
$518$	−2.55095e11			−0.155675
$519$		−	2.83720e12i		−	1.71647i
$520$			2.66859e11i			0.160054i
$521$	1.69688e11			0.100898			0.0504490	−	0.998727i	$-0.483935\pi$
$521$	1.69688e11			0.100898			0.0504490	+	0.998727i	$0.483935\pi$
$522$	9.69406e11	+	1.14062e12i	0.571463	+	0.672396i
$523$	1.89888e12			1.10979			0.554894	−	0.831921i	$-0.312759\pi$
$523$	1.89888e12			1.10979			0.554894	+	0.831921i	$0.312759\pi$
$524$			1.07009e12i			0.620056i
$525$		−	1.59442e11i		−	0.0915979i
$526$	−1.65913e12			−0.945029
$527$	−2.16727e12			−1.22395
$528$	5.44291e12			3.04775
$529$	1.99277e11			0.110638
$530$		−	2.82443e12i		−	1.55485i
$531$	1.89499e11			0.103439
$532$			1.54199e11i			0.0834600i
$533$		−	3.37086e11i		−	0.180912i
$534$			1.83046e12i			0.974149i
$535$	−8.81786e11			−0.465341
$536$			3.16502e11i			0.165628i
$537$		−	2.33169e12i		−	1.21000i
$538$	2.91829e12			1.50179
$539$			3.50322e12i			1.78779i
$540$		−	1.68401e12i		−	0.852263i
$541$			1.72565e12i			0.866092i	0.901372	+	0.433046i	$0.142561\pi$
$541$			1.72565e12i			0.866092i	−0.901372	+	0.433046i	$0.857439\pi$
$542$	1.37805e11			0.0685910
$543$			1.65934e12i			0.819098i
$544$	−8.36873e11			−0.409699
$545$	1.80058e12			0.874235
$546$	7.29166e10			0.0351123
$547$	2.37605e12			1.13478			0.567390	−	0.823449i	$-0.307953\pi$
$547$	2.37605e12			1.13478			0.567390	+	0.823449i	$0.307953\pi$
$548$		−	8.04015e11i		−	0.380848i
$549$		−	1.08601e12i		−	0.510223i
$550$	3.91991e12			1.82660
$551$	−4.19728e11	−	4.93861e11i	−0.193993	−	0.228256i
$552$	−5.55782e12			−2.54788
$553$		−	1.78926e11i		−	0.0813597i
$554$		−	3.61090e12i		−	1.62862i
$555$	1.20497e12			0.539084
$556$	6.07933e10			0.0269786
$557$	1.47719e12			0.650260			0.325130	−	0.945669i	$-0.394592\pi$
$557$	1.47719e12			0.650260			0.325130	+	0.945669i	$0.394592\pi$
$558$	2.66454e12			1.16351
$559$		−	9.84028e10i		−	0.0426240i
$560$	2.75062e11			0.118191
$561$		−	4.85194e12i		−	2.06815i
$562$			1.85758e12i			0.785479i
$563$			2.80566e12i			1.17692i	0.808526	+	0.588460i	$0.200266\pi$
$563$			2.80566e12i			1.17692i	−0.808526	+	0.588460i	$0.799734\pi$
$564$	6.02141e12			2.50578
$565$			2.80031e12i			1.15608i
$566$		−	1.67514e12i		−	0.686084i
$567$	−4.04674e11			−0.164430
$568$			6.41762e12i			2.58706i
$569$		−	3.99239e12i		−	1.59671i	−0.602184	−	0.798357i	$-0.705703\pi$
$569$		−	3.99239e12i		−	1.59671i	0.602184	−	0.798357i	$-0.294297\pi$
$570$		−	1.07227e12i		−	0.425467i
$571$	−2.35227e11			−0.0926029			−0.0463014	−	0.998928i	$-0.514743\pi$
$571$	−2.35227e11			−0.0926029			−0.0463014	+	0.998928i	$0.514743\pi$
$572$			1.21773e12i			0.475629i
$573$	−8.36642e10			−0.0324223
$574$	−8.85401e11			−0.340437
$575$	−1.57072e12			−0.599229
$576$	−7.77102e11			−0.294155
$577$			2.14604e12i			0.806022i	0.915195	+	0.403011i	$0.132036\pi$
$577$			2.14604e12i			0.806022i	−0.915195	+	0.403011i	$0.867964\pi$
$578$		−	6.55312e11i		−	0.244215i
$579$	−4.24398e11			−0.156935
$580$	−2.88894e12	+	2.45528e12i	−1.06002	+	0.900897i
$581$	−4.77779e11			−0.173954
$582$			8.67808e12i			3.13524i
$583$		−	6.80326e12i		−	2.43898i
$584$	−1.03563e13			−3.68421
$585$	−1.14769e11			−0.0405158
$586$	6.84471e12			2.39782
$587$	4.65860e11			0.161951			0.0809756	−	0.996716i	$-0.474196\pi$
$587$	4.65860e11			0.161951			0.0809756	+	0.996716i	$0.474196\pi$
$588$			7.38845e12i			2.54891i
$589$	−1.15368e12			−0.394972
$590$			7.06567e11i			0.240060i
$591$			8.15231e11i			0.274876i
$592$		−	2.73986e12i		−	0.916814i
$593$	3.81774e12			1.26783			0.633913	−	0.773404i	$-0.281448\pi$
$593$	3.81774e12			1.26783			0.633913	+	0.773404i	$0.281448\pi$
$594$		−	5.97147e12i		−	1.96808i
$595$		−	2.45197e11i		−	0.0802026i
$596$	−2.90643e12			−0.943520
$597$			3.28504e12i			1.05842i
$598$		−	7.18327e11i		−	0.229703i
$599$			3.18469e12i			1.01076i	0.862898	+	0.505378i	$0.168647\pi$
$599$			3.18469e12i			1.01076i	−0.862898	+	0.505378i	$0.831353\pi$
$600$	4.36395e12			1.37467
$601$		−	3.24053e12i		−	1.01317i	−0.862191	−	0.506584i	$-0.830908\pi$
$601$		−	3.24053e12i		−	1.01317i	0.862191	−	0.506584i	$-0.169092\pi$
$602$	−2.58468e11			−0.0802088
$603$	−1.36120e11			−0.0419269
$604$	−7.76491e12			−2.37394
$605$	−4.99926e12			−1.51707
$606$		−	6.89049e12i		−	2.07550i
$607$			2.78660e11i			0.0833155i	0.999132	+	0.0416578i	$0.0132639\pi$
$607$			2.78660e11i			0.0833155i	−0.999132	+	0.0416578i	$0.986736\pi$
$608$	−4.45485e11			−0.132211
$609$	3.54131e11	+	4.16678e11i	0.104324	+	0.122750i
$610$	4.04931e12			1.18412
$611$			4.10803e11i			0.119247i
$612$		−	3.40980e12i		−	0.982534i
$613$	−3.04818e12			−0.871904			−0.435952	−	0.899970i	$-0.643588\pi$
$613$	−3.04818e12			−0.871904			−0.435952	+	0.899970i	$0.643588\pi$
$614$	2.72022e11			0.0772407
$615$	4.18227e12			1.17889
$616$	1.68837e12			0.472448
$617$			1.75724e12i			0.488143i	0.969757	+	0.244071i	$0.0784831\pi$
$617$			1.75724e12i			0.488143i	−0.969757	+	0.244071i	$0.921517\pi$
$618$	−9.52199e11			−0.262591
$619$		−	1.82481e12i		−	0.499585i	−0.968299	−	0.249793i	$-0.919638\pi$
$619$		−	1.82481e12i		−	0.499585i	0.968299	−	0.249793i	$-0.0803625\pi$
$620$			6.74868e12i			1.83424i
$621$			2.39278e12i			0.645641i
$622$	4.89668e12			1.31173
$623$			2.22816e11i			0.0592584i
$624$			7.83165e11i			0.206787i
$625$	−4.12349e11			−0.108095
$626$		−	1.53831e11i		−	0.0400367i
$627$		−	2.58279e12i		−	0.667398i
$628$			1.27633e12i			0.327451i
$629$	−2.44238e12			−0.622137
$630$			3.01457e11i			0.0762417i
$631$	−6.42827e12			−1.61422			−0.807108	−	0.590404i	$-0.798969\pi$
$631$	−6.42827e12			−1.61422			−0.807108	+	0.590404i	$0.798969\pi$
$632$	4.89722e12			1.22102
$633$	−3.15351e12			−0.780687
$634$	1.14806e13			2.82203
$635$		−	4.51477e12i		−	1.10193i
$636$		−	1.43484e13i		−	3.47733i
$637$	−5.04067e11			−0.121300
$638$	−1.02441e13	+	8.70637e12i	−2.44783	+	2.08039i
$639$	−2.76006e12			−0.654884
$640$		−	4.12787e12i		−	0.972560i
$641$			6.85056e11i			0.160275i	0.996784	+	0.0801373i	$0.0255359\pi$
$641$			6.85056e11i			0.160275i	−0.996784	+	0.0801373i	$0.974464\pi$
$642$	−6.59455e12			−1.53207
$643$	−1.57499e12			−0.363352			−0.181676	−	0.983358i	$-0.558152\pi$
$643$	−1.57499e12			−0.363352			−0.181676	+	0.983358i	$0.558152\pi$
$644$	−1.28166e12			−0.293620
$645$	1.22090e12			0.277754
$646$			2.17341e12i			0.491015i
$647$	7.33855e12			1.64642			0.823210	−	0.567737i	$-0.192181\pi$
$647$	7.33855e12			1.64642			0.823210	+	0.567737i	$0.192181\pi$
$648$		−	1.10760e13i		−	2.46771i
$649$			1.70192e12i			0.376563i
$650$			5.64024e11i			0.123933i
$651$	9.73377e11			0.212406
$652$			1.02800e13i			2.22782i
$653$		−	1.54198e12i		−	0.331871i	−0.986137	−	0.165935i	$-0.946936\pi$
$653$		−	1.54198e12i		−	0.331871i	0.986137	−	0.165935i	$-0.0530643\pi$
$654$	1.34659e13			2.87829
$655$		−	9.05793e11i		−	0.192284i
$656$		−	9.50969e12i		−	2.00493i
$657$		−	4.45397e12i		−	0.932616i
$658$	1.07903e12			0.224397
$659$			5.66005e12i			1.16906i	0.811373	+	0.584529i	$0.198721\pi$
$659$			5.66005e12i			1.16906i	−0.811373	+	0.584529i	$0.801279\pi$
$660$	−1.51085e13			−3.09938
$661$	−8.72198e12			−1.77709			−0.888543	−	0.458792i	$-0.848282\pi$
$661$	−8.72198e12			−1.77709			−0.888543	+	0.458792i	$0.848282\pi$
$662$	−1.12340e13			−2.27339
$663$	6.98132e11			0.140322
$664$		−	1.30769e13i		−	2.61065i
$665$		−	1.30523e11i		−	0.0258816i
$666$	3.00278e12			0.591412
$667$	4.10484e12	−	3.48867e12i	0.803027	−	0.682485i
$668$	−1.03424e12			−0.200969
$669$		−	1.80733e12i		−	0.348835i
$670$		−	5.07535e11i		−	0.0973036i
$671$	9.75365e12			1.85744
$672$	3.75862e11			0.0710995
$673$	−7.06905e12			−1.32829			−0.664145	−	0.747604i	$-0.731204\pi$
$673$	−7.06905e12			−1.32829			−0.664145	+	0.747604i	$0.731204\pi$
$674$	3.09287e12			0.577287
$675$		−	1.87879e12i		−	0.348347i
$676$	1.13245e13			2.08574
$677$		−	4.85886e12i		−	0.888967i	−0.895787	−	0.444483i	$-0.853387\pi$
$677$		−	4.85886e12i		−	0.888967i	0.895787	−	0.444483i	$-0.146613\pi$
$678$			2.09425e13i			3.80623i
$679$			1.05635e12i			0.190719i
$680$	6.71108e12			1.20365
$681$			1.23284e13i			2.19657i
$682$			2.39306e13i			4.23569i
$683$	6.86473e12			1.20706			0.603532	−	0.797339i	$-0.293759\pi$
$683$	6.86473e12			1.20706			0.603532	+	0.797339i	$0.293759\pi$
$684$		−	1.81511e12i		−	0.317066i
$685$			6.80567e11i			0.118104i
$686$			2.67131e12i			0.460539i
$687$	−1.33633e13			−2.28881
$688$		−	2.77609e12i		−	0.472373i
$689$	9.78901e11			0.165483
$690$	8.91239e12			1.49683
$691$	6.24343e12			1.04177			0.520885	−	0.853627i	$-0.325602\pi$
$691$	6.24343e12			1.04177			0.520885	+	0.853627i	$0.325602\pi$
$692$	1.79075e13			2.96864
$693$			7.26125e11i			0.119595i
$694$		−	1.28181e13i		−	2.09752i
$695$	−5.14592e10			−0.00836626
$696$	−1.14045e13	+	9.69262e12i	−1.84220	+	1.56567i
$697$	−8.47717e12			−1.36052
$698$		−	5.28874e12i		−	0.843340i
$699$			1.12029e13i			1.77494i
$700$	1.00635e12			0.158418
$701$	4.14486e12			0.648305			0.324152	−	0.946005i	$-0.394921\pi$
$701$	4.14486e12			0.648305			0.324152	+	0.946005i	$0.394921\pi$
$702$	8.59217e11			0.133532
$703$	−1.30013e12			−0.200765
$704$		−	6.97926e12i		−	1.07086i
$705$	−5.09689e12			−0.777060
$706$			2.07085e13i			3.13709i
$707$		−	8.38755e11i		−	0.126255i
$708$			3.58943e12i			0.536878i
$709$	2.97536e12			0.442213			0.221106	−	0.975250i	$-0.429033\pi$
$709$	2.97536e12			0.442213			0.221106	+	0.975250i	$0.429033\pi$
$710$		−	1.02911e13i		−	1.51985i
$711$			2.10617e12i			0.309087i
$712$	−6.09851e12			−0.889331
$713$		−	9.58908e12i		−	1.38955i
$714$		−	1.83374e12i		−	0.264055i
$715$		−	1.03076e12i		−	0.147496i
$716$	1.47168e13			2.09270
$717$		−	1.11304e13i		−	1.57280i
$718$	−1.05989e13			−1.48834
$719$	−2.47150e12			−0.344890			−0.172445	−	0.985019i	$-0.555167\pi$
$719$	−2.47150e12			−0.344890			−0.172445	+	0.985019i	$0.555167\pi$
$720$	−3.23781e12			−0.449010
$721$	−1.15908e11			−0.0159737
$722$		−	1.17361e13i		−	1.60734i
$723$			8.09283e12i			1.10148i
$724$	−1.04732e13			−1.41663
$725$	−3.22308e12	+	2.73927e12i	−0.433262	+	0.368225i
$726$	−3.73876e13			−4.99474
$727$		−	7.01053e11i		−	0.0930778i	−0.998916	−	0.0465389i	$-0.985181\pi$
$727$		−	7.01053e11i		−	0.0930778i	0.998916	−	0.0465389i	$-0.0148191\pi$
$728$			2.42934e11i			0.0320551i
$729$	−9.57691e11			−0.125589
$730$	1.66070e13			2.16441
$731$	−2.47467e12			−0.320545
$732$	2.05709e13			2.64822
$733$			1.40442e13i			1.79692i	0.439059	+	0.898458i	$0.355312\pi$
$733$			1.40442e13i			1.79692i	−0.439059	+	0.898458i	$0.644688\pi$
$734$	−8.72103e12			−1.10901
$735$		−	6.25403e12i		−	0.790437i
$736$		−	3.70275e12i		−	0.465130i
$737$		−	1.22251e12i		−	0.152633i
$738$	1.04222e13			1.29333
$739$			1.39610e12i			0.172194i	0.996287	+	0.0860969i	$0.0274395\pi$
$739$			1.39610e12i			0.172194i	−0.996287	+	0.0860969i	$0.972561\pi$
$740$			7.60536e12i			0.932346i
$741$	3.71630e11			0.0452823
$742$		−	2.57121e12i		−	0.311401i
$743$		−	1.31903e13i		−	1.58783i	−0.608026	−	0.793917i	$-0.708038\pi$
$743$		−	1.31903e13i		−	1.58783i	0.608026	−	0.793917i	$-0.291962\pi$
$744$			2.66415e13i			3.18772i
$745$	2.46018e12			0.292592
$746$		−	1.47192e13i		−	1.74005i
$747$	5.62404e12			0.660854
$748$	3.06239e13			3.57687
$749$	−8.02731e11			−0.0931970
$750$	−1.93052e13			−2.22792
$751$			4.51876e12i			0.518369i	0.965828	+	0.259185i	$0.0834538\pi$
$751$			4.51876e12i			0.518369i	−0.965828	+	0.259185i	$0.916546\pi$
$752$			1.15894e13i			1.32154i
$753$	1.09470e13			1.24085
$754$	−1.25273e12	−	1.47399e12i	−0.141152	−	0.166083i
$755$	6.57270e12			0.736177
$756$		−	1.53304e12i		−	0.170689i
$757$		−	1.38772e13i		−	1.53592i	−0.640495	−	0.767962i	$-0.721271\pi$
$757$		−	1.38772e13i		−	1.53592i	0.640495	−	0.767962i	$-0.278729\pi$
$758$	9.54560e12			1.05025
$759$	2.14674e13			2.34797
$760$	3.57244e12			0.388422
$761$	−1.19040e13			−1.28665			−0.643325	−	0.765593i	$-0.722446\pi$
$761$	−1.19040e13			−1.28665			−0.643325	+	0.765593i	$0.722446\pi$
$762$		−	3.37643e13i		−	3.62794i
$763$	1.63915e12			0.175089
$764$		−	5.28061e11i		−	0.0560744i
$765$			2.88627e12i			0.304691i
$766$			5.15197e12i			0.540684i
$767$	−2.44884e11			−0.0255495
$768$		−	2.39211e13i		−	2.48117i
$769$			8.44879e11i			0.0871216i	0.999051	+	0.0435608i	$0.0138702\pi$
$769$			8.44879e11i			0.0871216i	−0.999051	+	0.0435608i	$0.986130\pi$
$770$	−2.70743e12			−0.277555
$771$			1.78842e13i			1.82274i
$772$		−	2.67866e12i		−	0.271419i
$773$		−	6.90321e12i		−	0.695414i	−0.937603	−	0.347707i	$-0.886960\pi$
$773$		−	6.90321e12i		−	0.695414i	0.937603	−	0.347707i	$-0.113040\pi$
$774$	3.04248e12			0.304715
$775$			7.52925e12i			0.749712i
$776$	−2.89125e13			−2.86225
$777$	1.09694e12			0.107966
$778$	−8.99567e12			−0.880289
$779$	−4.51257e12			−0.439041
$780$		−	2.17392e12i		−	0.210290i
$781$		−	2.47885e13i		−	2.38408i
$782$	−1.80648e13			−1.72744
$783$	4.17292e12	+	4.90995e12i	0.396746	+	0.466819i
$784$	−1.42205e13			−1.34429
$785$		−	1.08037e12i		−	0.101545i
$786$		−	6.77409e12i		−	0.633067i
$787$	−1.81394e13			−1.68553			−0.842764	−	0.538283i	$-0.819073\pi$
$787$	−1.81394e13			−1.68553			−0.842764	+	0.538283i	$0.819073\pi$
$788$	−5.14548e12			−0.475398
$789$	7.13445e12			0.655411
$790$	−7.85307e12			−0.717327
$791$			2.54926e12i			0.231537i
$792$	−1.98742e13			−1.79484
$793$			1.40342e12i			0.126026i
$794$			2.14563e13i			1.91585i
$795$			1.21454e13i			1.07835i
$796$	−2.07341e13			−1.83053
$797$			8.81321e12i			0.773698i	0.922143	+	0.386849i	$0.126437\pi$
$797$			8.81321e12i			0.773698i	−0.922143	+	0.386849i	$0.873563\pi$
$798$		−	9.76134e11i		−	0.0852112i
$799$	1.03310e13			0.896775
$800$			2.90736e12i			0.250954i
$801$		−	2.62281e12i		−	0.225124i
$802$		−	3.74099e13i		−	3.19302i
$803$	4.00017e13			3.39514
$804$		−	2.57833e12i		−	0.217614i
$805$	1.08487e12			0.0910537
$806$	−3.44331e12			−0.287388
$807$	−1.25490e13			−1.04154
$808$	2.29569e13			1.89479
$809$			1.45964e13i			1.19806i	0.800727	+	0.599029i	$0.204447\pi$
$809$			1.45964e13i			1.19806i	−0.800727	+	0.599029i	$0.795553\pi$
$810$			1.77612e13i			1.44974i
$811$	−1.29105e13			−1.04797			−0.523987	−	0.851726i	$-0.675556\pi$
$811$	−1.29105e13			−1.04797			−0.523987	+	0.851726i	$0.675556\pi$
$812$	−2.62994e12	+	2.23516e12i	−0.212297	+	0.180429i
$813$	−5.92576e11			−0.0475704
$814$			2.69684e13i			2.15301i
$815$		−	8.70164e12i		−	0.690863i
$816$	1.96953e13			1.55510
$817$	−1.31732e12			−0.103441
$818$	−2.59736e13			−2.02835
$819$	−1.04480e11			−0.00811439
$820$			2.63972e13i			2.03889i
$821$	2.13719e13			1.64172			0.820858	−	0.571132i	$-0.193496\pi$
$821$	2.13719e13			1.64172			0.820858	+	0.571132i	$0.193496\pi$
$822$			5.08971e12i			0.388839i
$823$		−	4.10707e12i		−	0.312056i	−0.987753	−	0.156028i	$-0.950131\pi$
$823$		−	4.10707e12i		−	0.312056i	0.987753	−	0.156028i	$-0.0498690\pi$
$824$		−	3.17242e12i		−	0.239728i
$825$	−1.68560e13			−1.26681
$826$			6.43221e11i			0.0480784i
$827$		−	2.55744e13i		−	1.90121i	−0.310398	−	0.950607i	$-0.600462\pi$
$827$		−	2.55744e13i		−	1.90121i	0.310398	−	0.950607i	$-0.399538\pi$
$828$	1.50867e13			1.11547
$829$			9.90704e12i			0.728531i	0.931295	+	0.364266i	$0.118680\pi$
$829$			9.90704e12i			0.728531i	−0.931295	+	0.364266i	$0.881320\pi$
$830$			2.09698e13i			1.53371i
$831$			1.55272e13i			1.12951i
$832$	1.00423e12			0.0726568
$833$			1.26765e13i			0.912213i
$834$	−3.84844e11			−0.0275447
$835$	8.75447e11			0.0623219
$836$	1.63017e13			1.15426
$837$	1.14698e13			0.807779
$838$			2.16835e13i			1.51891i
$839$			6.28706e12i			0.438045i	0.975720	+	0.219023i	$0.0702869\pi$
$839$			6.28706e12i			0.438045i	−0.975720	+	0.219023i	$0.929713\pi$
$840$	−3.01412e12			−0.208883
$841$	2.33896e12	−	1.43174e13i	0.161228	−	0.986917i
$842$	1.56416e13			1.07245
$843$		−	7.98781e12i		−	0.544758i
$844$		−	1.99039e13i		−	1.35020i
$845$	−9.58578e12			−0.646803
$846$	−1.27015e13			−0.852487
$847$	−4.55106e12			−0.303835
$848$	2.76162e13			1.83393
$849$			7.20329e12i			0.475824i
$850$	1.41843e13			0.932014
$851$		−	1.08063e13i		−	0.706309i
$852$		−	5.22801e13i		−	3.39905i
$853$		−	1.76361e13i		−	1.14060i	−0.821437	−	0.570300i	$-0.806827\pi$
$853$		−	1.76361e13i		−	1.14060i	0.821437	−	0.570300i	$-0.193173\pi$
$854$	3.68628e12			0.237152
$855$			1.53642e12i			0.0983245i
$856$		−	2.19709e13i		−	1.39867i
$857$	3.82473e12			0.242207			0.121104	−	0.992640i	$-0.461357\pi$
$857$	3.82473e12			0.242207			0.121104	+	0.992640i	$0.461357\pi$
$858$		−	7.70867e12i		−	0.485609i
$859$			7.25768e12i			0.454809i	0.973800	+	0.227404i	$0.0730239\pi$
$859$			7.25768e12i			0.454809i	−0.973800	+	0.227404i	$0.926976\pi$
$860$			7.70591e12i			0.480375i
$861$	3.80732e12			0.236105
$862$		−	5.79567e12i		−	0.357537i
$863$	2.00514e13			1.23054			0.615271	−	0.788316i	$-0.289047\pi$
$863$	2.00514e13			1.23054			0.615271	+	0.788316i	$0.289047\pi$
$864$	4.42899e12			0.270391
$865$	−1.51580e13			−0.920596
$866$	2.19532e12			0.132638
$867$			2.81791e12i			0.169372i
$868$			6.14364e12i			0.367356i
$869$	−1.89158e13			−1.12522
$870$	1.82880e13	−	1.55428e13i	1.08226	−	0.919801i
$871$	1.75903e11			0.0103560
$872$			4.48639e13i			2.62768i
$873$		−	1.24346e13i		−	0.724546i
$874$	−9.61625e12			−0.557448
$875$	−2.34996e12			−0.135526
$876$	8.43654e13			4.84056
$877$	4.95193e12			0.282668			0.141334	−	0.989962i	$-0.454861\pi$
$877$	4.95193e12			0.282668			0.141334	+	0.989962i	$0.454861\pi$
$878$		−	1.05956e13i		−	0.601730i
$879$	−2.94330e13			−1.66297
$880$		−	2.90792e13i		−	1.63460i
$881$		−	1.76705e13i		−	0.988226i	−0.869398	−	0.494113i	$-0.835493\pi$
$881$		−	1.76705e13i		−	0.988226i	0.869398	−	0.494113i	$-0.164507\pi$
$882$		−	1.55851e13i		−	0.867163i
$883$	−5.50852e12			−0.304938			−0.152469	−	0.988308i	$-0.548722\pi$
$883$	−5.50852e12			−0.304938			−0.152469	+	0.988308i	$0.548722\pi$
$884$			4.40638e12i			0.242687i
$885$		−	3.03831e12i		−	0.166490i
$886$	−5.86278e13			−3.19633
$887$			3.05104e13i			1.65498i	0.561483	+	0.827488i	$0.310231\pi$
$887$			3.05104e13i			1.65498i	−0.561483	+	0.827488i	$0.689769\pi$
$888$			3.00234e13i			1.62032i
$889$		−	4.11001e12i		−	0.220691i
$890$	9.77941e12			0.522466
$891$			4.27817e13i			2.27409i
$892$	1.14073e13			0.603310
$893$	5.49942e12			0.289391
$894$	1.83987e13			0.963317
$895$	−1.24572e13			−0.648961
$896$		−	3.75780e12i		−	0.194781i
$897$			3.08889e12i			0.159307i
$898$	3.02450e12			0.155207
$899$	−1.67230e13	−	1.96766e13i	−0.853876	−	1.00469i
$900$	−1.18459e13			−0.601835
$901$		−	2.46178e13i		−	1.24448i
$902$			9.36037e13i			4.70829i
$903$	1.11144e12			0.0556277
$904$	−6.97736e13			−3.47483
$905$	8.86517e12			0.439307
$906$	4.91548e13			2.42375
$907$			2.64970e12i			0.130006i	0.997885	+	0.0650032i	$0.0207058\pi$
$907$			2.64970e12i			0.130006i	−0.997885	+	0.0650032i	$0.979294\pi$
$908$	−7.78128e13			−3.79896
$909$			9.87317e12i			0.479644i
$910$		−	3.89564e11i		−	0.0188318i
$911$			2.55243e13i			1.22778i	0.789391	+	0.613891i	$0.210396\pi$
$911$			2.55243e13i			1.22778i	−0.789391	+	0.613891i	$0.789604\pi$
$912$	1.04842e13			0.501833
$913$			5.05103e13i			2.40581i
$914$		−	7.79757e12i		−	0.369574i
$915$	−1.74125e13			−0.821231
$916$		−	8.43450e13i		−	3.95849i
$917$		−	8.24586e11i		−	0.0385101i
$918$		−	2.16079e13i		−	1.00420i
$919$	8.92051e12			0.412543			0.206272	−	0.978495i	$-0.433867\pi$
$919$	8.92051e12			0.412543			0.206272	+	0.978495i	$0.433867\pi$
$920$			2.96932e13i			1.36651i
$921$	−1.16972e12			−0.0535692
$922$	2.29579e13			1.04627
$923$	3.56674e12			0.161757
$924$	−1.37540e13			−0.620733
$925$			8.48502e12i			0.381079i
$926$			1.00423e13i			0.448831i
$927$	1.36438e12			0.0606842
$928$	−6.45744e12	−	7.59796e12i	−0.285821	−	0.336303i
$929$	3.67778e13			1.62000			0.809999	−	0.586431i	$-0.199467\pi$
$929$	3.67778e13			1.62000			0.809999	+	0.586431i	$0.199467\pi$
$930$		−	4.27216e13i		−	1.87273i
$931$			6.74795e12i			0.294373i
$932$	−7.07091e13			−3.06975
$933$	−2.10562e13			−0.909732
$934$	4.39474e13			1.88961
$935$	−2.59220e13			−1.10921
$936$		−	2.85963e12i		−	0.121778i
$937$	1.93471e13			0.819951			0.409976	−	0.912096i	$-0.365537\pi$
$937$	1.93471e13			0.819951			0.409976	+	0.912096i	$0.365537\pi$
$938$		−	4.62033e11i		−	0.0194877i
$939$			6.61489e11i			0.0277669i
$940$		−	3.21699e13i		−	1.34392i
$941$	−2.29169e12			−0.0952803			−0.0476401	−	0.998865i	$-0.515170\pi$
$941$	−2.29169e12			−0.0952803			−0.0476401	+	0.998865i	$0.515170\pi$
$942$		−	8.07966e12i		−	0.334321i
$943$		−	3.75073e13i		−	1.54459i
$944$	−6.90855e12			−0.283148
$945$			1.29766e12i			0.0529318i
$946$			2.73249e13i			1.10930i
$947$		−	6.15036e12i		−	0.248500i	−0.992251	−	0.124250i	$-0.960348\pi$
$947$		−	6.15036e12i		−	0.248500i	0.992251	−	0.124250i	$-0.0396524\pi$
$948$	−3.98944e13			−1.60426
$949$			5.75573e12i			0.230357i
$950$	7.55058e12			0.300763
$951$	−4.93677e13			−1.95718
$952$	6.10941e12			0.241064
$953$	−3.44531e13			−1.35304			−0.676519	−	0.736425i	$-0.736512\pi$
$953$	−3.44531e13			−1.35304			−0.676519	+	0.736425i	$0.736512\pi$
$954$			3.02663e13i			1.18302i
$955$			4.46984e11i			0.0173891i
$956$	7.02512e13			2.72015
$957$	4.40508e13	−	3.74383e13i	1.69766	−	1.44282i
$958$	2.73700e13			1.04986
$959$			6.19553e11i			0.0236534i
$960$			1.24596e13i			0.473459i
$961$	−1.95257e13			−0.738502
$962$	−3.88041e12			−0.146080
$963$	9.44913e12			0.354057
$964$	−5.10793e13			−1.90502
$965$			2.26738e12i			0.0841690i
$966$	8.11337e12			0.299781
$967$		−	3.13984e13i		−	1.15475i	−0.816478	−	0.577376i	$-0.804077\pi$
$967$		−	3.13984e13i		−	1.15475i	0.816478	−	0.577376i	$-0.195923\pi$
$968$		−	1.24563e14i		−	4.55986i
$969$		−	9.34589e12i		−	0.340537i
$970$	4.63634e13			1.68152
$971$		−	2.65038e13i		−	0.956801i	−0.878142	−	0.478401i	$-0.841217\pi$
$971$		−	2.65038e13i		−	0.956801i	0.878142	−	0.478401i	$-0.158783\pi$
$972$			5.41182e13i			1.94467i
$973$	−4.68457e10			−0.00167557
$974$		−	6.23247e13i		−	2.21894i
$975$		−	2.42536e12i		−	0.0859521i
$976$			3.95926e13i			1.39666i
$977$	7.04042e12			0.247214			0.123607	−	0.992331i	$-0.460554\pi$
$977$	7.04042e12			0.247214			0.123607	+	0.992331i	$0.460554\pi$
$978$		−	6.50763e13i		−	2.27456i
$979$	2.35559e13			0.819553
$980$	3.94734e13			1.36706
$981$	−1.92948e13			−0.665167
$982$	4.61426e13			1.58344
$983$		−	4.01813e13i		−	1.37257i	−0.727334	−	0.686283i	$-0.759241\pi$
$983$		−	4.01813e13i		−	1.37257i	0.727334	−	0.686283i	$-0.240759\pi$
$984$			1.04207e14i			3.54339i
$985$	4.35545e12			0.147425
$986$	−3.70686e13	+	3.15042e13i	−1.24899	+	1.06151i
$987$	−4.63994e12			−0.155627
$988$			2.34561e12i			0.0783157i
$989$		−	1.09492e13i		−	0.363914i
$990$	3.18697e13			1.05443
$991$	−5.84212e12			−0.192415			−0.0962076	−	0.995361i	$-0.530671\pi$
$991$	−5.84212e12			−0.192415			−0.0962076	+	0.995361i	$0.530671\pi$
$992$	−1.77492e13			−0.581936
$993$	4.83074e13			1.57667
$994$		−	9.36851e12i		−	0.304391i
$995$	1.75506e13			0.567661
$996$			1.06529e14i			3.43004i
$997$			3.75846e13i			1.20471i	0.798229	+	0.602354i	$0.205771\pi$
$997$			3.75846e13i			1.20471i	−0.798229	+	0.602354i	$0.794229\pi$
$998$			2.77219e13i			0.884578i
$999$	1.29258e13			0.410595

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.10.b.a.28.2	✓	22
29.28	even	2	inner	29.10.b.a.28.21	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.10.b.a.28.2	✓	22	1.1	even	1	trivial
29.10.b.a.28.21	yes	22	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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	29.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-39.9552i q^{2} +171.812i q^{3} -1084.42 q^{4} +917.921 q^{5} +6864.79 q^{6} +835.627 q^{7} +22871.2i q^{8} -9836.35 q^{9} +O(q^{10})\)	\(q-39.9552i q^{2} +171.812i q^{3} -1084.42 q^{4} +917.921 q^{5} +6864.79 q^{6} +835.627 q^{7} +22871.2i q^{8} -9836.35 q^{9} -36675.8i q^{10} -88341.6i q^{11} -186317. i q^{12} +12711.2 q^{13} -33387.7i q^{14} +157710. i q^{15} +358602. q^{16} -319667. i q^{17} +393014. i q^{18} -170165. i q^{19} -995413. q^{20} +143571. i q^{21} -3.52971e6 q^{22} +1.41437e6 q^{23} -3.92955e6 q^{24} -1.11055e6 q^{25} -507880. i q^{26} +1.69177e6i q^{27} -906171. q^{28} +(2.90225e6 - 2.46660e6i) q^{29} +6.30133e6 q^{30} -6.77977e6i q^{31} -2.61796e6i q^{32} +1.51781e7 q^{33} -1.27724e7 q^{34} +767039. q^{35} +1.06667e7 q^{36} -7.64041e6i q^{37} -6.79898e6 q^{38} +2.18394e6i q^{39} +2.09940e7i q^{40} -2.65188e7i q^{41} +5.73640e6 q^{42} -7.74142e6i q^{43} +9.57995e7i q^{44} -9.02899e6 q^{45} -5.65113e7i q^{46} +3.23182e7i q^{47} +6.16121e7i q^{48} -3.96553e7 q^{49} +4.43721e7i q^{50} +5.49225e7 q^{51} -1.37843e7 q^{52} +7.70109e7 q^{53} +6.75952e7 q^{54} -8.10906e7i q^{55} +1.91118e7i q^{56} +2.92364e7 q^{57} +(-9.85534e7 - 1.15960e8i) q^{58} -1.92652e7 q^{59} -1.71024e8i q^{60} +1.10408e8i q^{61} -2.70888e8 q^{62} -8.21951e6 q^{63} +7.90031e7 q^{64} +1.16679e7 q^{65} -6.06446e8i q^{66} +1.38384e7 q^{67} +3.46653e8i q^{68} +2.43005e8i q^{69} -3.06472e7i q^{70} +2.80598e8 q^{71} -2.24969e8i q^{72} +4.52807e8i q^{73} -3.05274e8 q^{74} -1.90805e8i q^{75} +1.84531e8i q^{76} -7.38206e7i q^{77} +8.72598e7 q^{78} -2.14122e8i q^{79} +3.29168e8 q^{80} -4.84276e8 q^{81} -1.05957e9 q^{82} -5.71761e8 q^{83} -1.55691e8i q^{84} -2.93429e8i q^{85} -3.09310e8 q^{86} +(4.23791e8 + 4.98641e8i) q^{87} +2.02048e9 q^{88} +2.66645e8i q^{89} +3.60755e8i q^{90} +1.06218e7 q^{91} -1.53377e9 q^{92} +1.16485e9 q^{93} +1.29128e9 q^{94} -1.56198e8i q^{95} +4.49796e8 q^{96} +1.26414e9i q^{97} +1.58444e9i q^{98} +8.68959e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 5804 q^{4} - 1374 q^{5} - 8304 q^{6} - 4956 q^{7} - 112244 q^{9}+O(q^{10}) \) 22 * q - 5804 * q^4 - 1374 * q^5 - 8304 * q^6 - 4956 * q^7 - 112244 * q^9	\( 22 q - 5804 q^{4} - 1374 q^{5} - 8304 q^{6} - 4956 q^{7} - 112244 q^{9} - 244222 q^{13} + 1246804 q^{16} - 1658748 q^{20} + 822328 q^{22} - 874956 q^{23} + 8668172 q^{24} + 5307748 q^{25} - 620352 q^{28} - 2425374 q^{29} - 8942448 q^{30} + 10134274 q^{33} - 37785784 q^{34} - 20790348 q^{35} + 34550680 q^{36} - 30663552 q^{38} + 56872008 q^{42} - 43877176 q^{45} - 131743922 q^{49} - 6194732 q^{51} + 342496580 q^{52} + 34886610 q^{53} + 116488784 q^{54} - 308361676 q^{57} + 342193888 q^{58} + 175799052 q^{59} - 484313328 q^{62} - 190643424 q^{63} - 419498924 q^{64} - 149739966 q^{65} - 508277640 q^{67} + 263144256 q^{71} + 435201408 q^{74} + 1065897336 q^{78} + 2990464236 q^{80} - 129895134 q^{81} - 527065064 q^{82} + 1555989756 q^{83} - 3422424120 q^{86} + 2176720604 q^{87} - 387386068 q^{88} - 1493579244 q^{91} - 1262849472 q^{92} + 2042413382 q^{93} + 166226488 q^{94} - 6686432820 q^{96}+O(q^{100}) \) 22 * q - 5804 * q^4 - 1374 * q^5 - 8304 * q^6 - 4956 * q^7 - 112244 * q^9 - 244222 * q^13 + 1246804 * q^16 - 1658748 * q^20 + 822328 * q^22 - 874956 * q^23 + 8668172 * q^24 + 5307748 * q^25 - 620352 * q^28 - 2425374 * q^29 - 8942448 * q^30 + 10134274 * q^33 - 37785784 * q^34 - 20790348 * q^35 + 34550680 * q^36 - 30663552 * q^38 + 56872008 * q^42 - 43877176 * q^45 - 131743922 * q^49 - 6194732 * q^51 + 342496580 * q^52 + 34886610 * q^53 + 116488784 * q^54 - 308361676 * q^57 + 342193888 * q^58 + 175799052 * q^59 - 484313328 * q^62 - 190643424 * q^63 - 419498924 * q^64 - 149739966 * q^65 - 508277640 * q^67 + 263144256 * q^71 + 435201408 * q^74 + 1065897336 * q^78 + 2990464236 * q^80 - 129895134 * q^81 - 527065064 * q^82 + 1555989756 * q^83 - 3422424120 * q^86 + 2176720604 * q^87 - 387386068 * q^88 - 1493579244 * q^91 - 1262849472 * q^92 + 2042413382 * q^93 + 166226488 * q^94 - 6686432820 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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