LMFDB - Embedded newform 429.2.b.b.298.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(298,429)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("429.298");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 23x^{12} + 201x^{10} + 835x^{8} + 1695x^{6} + 1565x^{4} + 511x^{2} + 49 $ x^14 + 23x^12 + 201x^10 + 835x^8 + 1695x^6 + 1565x^4 + 511x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			298.10
Root			$1.36814i$ of defining polynomial
Character	$\chi$	$=$	429.298
Dual form			429.2.b.b.298.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.36814i q^{2} +1.00000 q^{3} +0.128197 q^{4} -2.18365i q^{5} +1.36814i q^{6} -4.27070i q^{7} +2.91167i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.36814i q^{2} +1.00000 q^{3} +0.128197 q^{4} -2.18365i q^{5} +1.36814i q^{6} -4.27070i q^{7} +2.91167i q^{8} +1.00000 q^{9} +2.98753 q^{10} +1.00000i q^{11} +0.128197 q^{12} +(-0.922450 - 3.48555i) q^{13} +5.84291 q^{14} -2.18365i q^{15} -3.72717 q^{16} +3.79173 q^{17} +1.36814i q^{18} +3.17118i q^{19} -0.279937i q^{20} -4.27070i q^{21} -1.36814 q^{22} +4.94243 q^{23} +2.91167i q^{24} +0.231676 q^{25} +(4.76872 - 1.26204i) q^{26} +1.00000 q^{27} -0.547491i q^{28} -7.35483 q^{29} +2.98753 q^{30} -0.0727448i q^{31} +0.724050i q^{32} +1.00000i q^{33} +5.18761i q^{34} -9.32571 q^{35} +0.128197 q^{36} +3.66658i q^{37} -4.33862 q^{38} +(-0.922450 - 3.48555i) q^{39} +6.35806 q^{40} +4.16722i q^{41} +5.84291 q^{42} -7.11697 q^{43} +0.128197i q^{44} -2.18365i q^{45} +6.76193i q^{46} +11.6337i q^{47} -3.72717 q^{48} -11.2389 q^{49} +0.316965i q^{50} +3.79173 q^{51} +(-0.118255 - 0.446838i) q^{52} +5.11268 q^{53} +1.36814i q^{54} +2.18365 q^{55} +12.4349 q^{56} +3.17118i q^{57} -10.0624i q^{58} +5.62765i q^{59} -0.279937i q^{60} -5.40800 q^{61} +0.0995250 q^{62} -4.27070i q^{63} -8.44494 q^{64} +(-7.61123 + 2.01431i) q^{65} -1.36814 q^{66} -10.1145i q^{67} +0.486088 q^{68} +4.94243 q^{69} -12.7589i q^{70} -9.62239i q^{71} +2.91167i q^{72} +6.44736i q^{73} -5.01639 q^{74} +0.231676 q^{75} +0.406536i q^{76} +4.27070 q^{77} +(4.76872 - 1.26204i) q^{78} +10.1209 q^{79} +8.13884i q^{80} +1.00000 q^{81} -5.70134 q^{82} +7.80918i q^{83} -0.547491i q^{84} -8.27981i q^{85} -9.73700i q^{86} -7.35483 q^{87} -2.91167 q^{88} +2.87912i q^{89} +2.98753 q^{90} +(-14.8858 + 3.93951i) q^{91} +0.633605 q^{92} -0.0727448i q^{93} -15.9166 q^{94} +6.92475 q^{95} +0.724050i q^{96} -3.79281i q^{97} -15.3764i q^{98} +1.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 14 q^{3} - 18 q^{4} + 14 q^{9}+O(q^{10}) $ 14 * q + 14 * q^3 - 18 * q^4 + 14 * q^9	$ 14 q + 14 q^{3} - 18 q^{4} + 14 q^{9} - 18 q^{12} + 16 q^{14} + 34 q^{16} + 4 q^{17} + 6 q^{22} - 8 q^{23} - 26 q^{25} - 6 q^{26} + 14 q^{27} - 24 q^{29} - 8 q^{35} - 18 q^{36} - 32 q^{38} - 20 q^{40} + 16 q^{42} + 32 q^{43} + 34 q^{48} - 46 q^{49} + 4 q^{51} + 4 q^{52} + 20 q^{53} + 12 q^{55} - 32 q^{56} - 20 q^{61} + 72 q^{62} - 58 q^{64} + 12 q^{65} + 6 q^{66} - 20 q^{68} - 8 q^{69} - 26 q^{75} - 12 q^{77} - 6 q^{78} + 12 q^{79} + 14 q^{81} + 20 q^{82} - 24 q^{87} - 30 q^{88} + 16 q^{91} - 24 q^{92} + 64 q^{94} - 36 q^{95}+O(q^{100}) $ 14 * q + 14 * q^3 - 18 * q^4 + 14 * q^9 - 18 * q^12 + 16 * q^14 + 34 * q^16 + 4 * q^17 + 6 * q^22 - 8 * q^23 - 26 * q^25 - 6 * q^26 + 14 * q^27 - 24 * q^29 - 8 * q^35 - 18 * q^36 - 32 * q^38 - 20 * q^40 + 16 * q^42 + 32 * q^43 + 34 * q^48 - 46 * q^49 + 4 * q^51 + 4 * q^52 + 20 * q^53 + 12 * q^55 - 32 * q^56 - 20 * q^61 + 72 * q^62 - 58 * q^64 + 12 * q^65 + 6 * q^66 - 20 * q^68 - 8 * q^69 - 26 * q^75 - 12 * q^77 - 6 * q^78 + 12 * q^79 + 14 * q^81 + 20 * q^82 - 24 * q^87 - 30 * q^88 + 16 * q^91 - 24 * q^92 + 64 * q^94 - 36 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$			1.36814i			0.967420i	0.875228	+	0.483710i	$0.160711\pi$
$2$			1.36814i			0.967420i	−0.875228	+	0.483710i	$0.839289\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	0.128197			0.0640985
$5$		−	2.18365i		−	0.976558i	−0.872688	−	0.488279i	$-0.837625\pi$
$5$		−	2.18365i		−	0.976558i	0.872688	−	0.488279i	$-0.162375\pi$
$6$			1.36814i			0.558540i
$7$		−	4.27070i		−	1.61417i	−0.590433	−	0.807087i	$-0.701043\pi$
$7$		−	4.27070i		−	1.61417i	0.590433	−	0.807087i	$-0.298957\pi$
$8$			2.91167i			1.02943i
$9$	1.00000			0.333333
$10$	2.98753			0.944741
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$	0.128197			0.0370073
$13$	−0.922450	−	3.48555i	−0.255842	−	0.966719i
$13$	−0.922450	−	3.48555i	−0.255842	−	0.966719i
$14$	5.84291			1.56158
$15$		−	2.18365i		−	0.563816i
$16$	−3.72717			−0.931793
$17$	3.79173			0.919629			0.459815	−	0.888015i	$-0.347916\pi$
$17$	3.79173			0.919629			0.459815	+	0.888015i	$0.347916\pi$
$18$			1.36814i			0.322473i
$19$			3.17118i			0.727519i	0.931493	+	0.363760i	$0.118507\pi$
$19$			3.17118i			0.727519i	−0.931493	+	0.363760i	$0.881493\pi$
$20$		−	0.279937i		−	0.0625959i
$21$		−	4.27070i		−	0.931943i
$22$	−1.36814			−0.291688
$23$	4.94243			1.03057			0.515284	−	0.857020i	$-0.327687\pi$
$23$	4.94243			1.03057			0.515284	+	0.857020i	$0.327687\pi$
$24$			2.91167i			0.594342i
$25$	0.231676			0.0463352
$26$	4.76872	−	1.26204i	0.935223	−	0.247506i
$27$	1.00000			0.192450
$28$		−	0.547491i		−	0.103466i
$29$	−7.35483			−1.36576			−0.682879	−	0.730531i	$-0.739272\pi$
$29$	−7.35483			−1.36576			−0.682879	+	0.730531i	$0.739272\pi$
$30$	2.98753			0.545447
$31$		−	0.0727448i		−	0.0130654i	−0.999979	−	0.00653268i	$-0.997921\pi$
$31$		−	0.0727448i		−	0.0130654i	0.999979	−	0.00653268i	$-0.00207943\pi$
$32$			0.724050i			0.127995i
$33$			1.00000i			0.174078i
$34$			5.18761i			0.889668i
$35$	−9.32571			−1.57633
$36$	0.128197			0.0213662
$37$			3.66658i			0.602782i	0.953501	+	0.301391i	$0.0974510\pi$
$37$			3.66658i			0.602782i	−0.953501	+	0.301391i	$0.902549\pi$
$38$	−4.33862			−0.703817
$39$	−0.922450	−	3.48555i	−0.147710	−	0.558135i
$40$	6.35806			1.00530
$41$			4.16722i			0.650811i	0.945575	+	0.325405i	$0.105501\pi$
$41$			4.16722i			0.650811i	−0.945575	+	0.325405i	$0.894499\pi$
$42$	5.84291			0.901581
$43$	−7.11697			−1.08533			−0.542664	−	0.839950i	$-0.682584\pi$
$43$	−7.11697			−1.08533			−0.542664	+	0.839950i	$0.682584\pi$
$44$			0.128197i			0.0193264i
$45$		−	2.18365i		−	0.325519i
$46$			6.76193i			0.996992i
$47$			11.6337i			1.69695i	0.529232	+	0.848477i	$0.322480\pi$
$47$			11.6337i			1.69695i	−0.529232	+	0.848477i	$0.677520\pi$
$48$	−3.72717			−0.537971
$49$	−11.2389			−1.60556
$50$			0.316965i			0.0448256i
$51$	3.79173			0.530948
$52$	−0.118255	−	0.446838i	−0.0163991	−	0.0619652i
$53$	5.11268			0.702281			0.351140	−	0.936323i	$-0.385794\pi$
$53$	5.11268			0.702281			0.351140	+	0.936323i	$0.385794\pi$
$54$			1.36814i			0.186180i
$55$	2.18365			0.294443
$56$	12.4349			1.66168
$57$			3.17118i			0.420034i
$58$		−	10.0624i		−	1.32126i
$59$			5.62765i			0.732658i	0.930485	+	0.366329i	$0.119386\pi$
$59$			5.62765i			0.732658i	−0.930485	+	0.366329i	$0.880614\pi$
$60$		−	0.279937i		−	0.0361398i
$61$	−5.40800			−0.692424			−0.346212	−	0.938156i	$-0.612532\pi$
$61$	−5.40800			−0.692424			−0.346212	+	0.938156i	$0.612532\pi$
$62$	0.0995250			0.0126397
$63$		−	4.27070i		−	0.538058i
$64$	−8.44494			−1.05562
$65$	−7.61123	+	2.01431i	−0.944057	+	0.249844i
$66$	−1.36814			−0.168406
$67$		−	10.1145i		−	1.23569i	−0.786302	−	0.617843i	$-0.788007\pi$
$67$		−	10.1145i		−	1.23569i	0.786302	−	0.617843i	$-0.211993\pi$
$68$	0.486088			0.0589469
$69$	4.94243			0.594998
$70$		−	12.7589i		−	1.52498i
$71$		−	9.62239i		−	1.14197i	−0.820961	−	0.570984i	$-0.806562\pi$
$71$		−	9.62239i		−	1.14197i	0.820961	−	0.570984i	$-0.193438\pi$
$72$			2.91167i			0.343143i
$73$			6.44736i			0.754607i	0.926090	+	0.377303i	$0.123149\pi$
$73$			6.44736i			0.754607i	−0.926090	+	0.377303i	$0.876851\pi$
$74$	−5.01639			−0.583144
$75$	0.231676			0.0267516
$76$			0.406536i			0.0466329i
$77$	4.27070			0.486692
$78$	4.76872	−	1.26204i	0.539951	−	0.142898i
$79$	10.1209			1.13869			0.569347	−	0.822097i	$-0.307196\pi$
$79$	10.1209			1.13869			0.569347	+	0.822097i	$0.307196\pi$
$80$			8.13884i			0.909949i
$81$	1.00000			0.111111
$82$	−5.70134			−0.629607
$83$			7.80918i			0.857169i	0.903502	+	0.428585i	$0.140988\pi$
$83$			7.80918i			0.857169i	−0.903502	+	0.428585i	$0.859012\pi$
$84$		−	0.547491i		−	0.0597362i
$85$		−	8.27981i		−	0.898071i
$86$		−	9.73700i		−	1.04997i
$87$	−7.35483			−0.788521
$88$	−2.91167			−0.310385
$89$			2.87912i			0.305187i	0.988289	+	0.152593i	$0.0487624\pi$
$89$			2.87912i			0.305187i	−0.988289	+	0.152593i	$0.951238\pi$
$90$	2.98753			0.314914
$91$	−14.8858	+	3.93951i	−1.56045	+	0.412973i
$92$	0.633605			0.0660579
$93$		−	0.0727448i		−	0.00754329i
$94$	−15.9166			−1.64167
$95$	6.92475			0.710465
$96$			0.724050i			0.0738980i
$97$		−	3.79281i		−	0.385101i	−0.981287	−	0.192551i	$-0.938324\pi$
$97$		−	3.79281i		−	0.385101i	0.981287	−	0.192551i	$-0.0616760\pi$
$98$		−	15.3764i		−	1.55325i
$99$			1.00000i			0.100504i
$100$	0.0297002			0.00297002
$101$	−12.8641			−1.28003			−0.640014	−	0.768363i	$-0.721072\pi$
$101$	−12.8641			−1.28003			−0.640014	+	0.768363i	$0.721072\pi$
$102$			5.18761i			0.513650i
$103$	16.9975			1.67482			0.837409	−	0.546577i	$-0.184070\pi$
$103$	16.9975			1.67482			0.837409	+	0.546577i	$0.184070\pi$
$104$	10.1488	−	2.68587i	0.995169	−	0.263371i
$105$	−9.32571			−0.910096
$106$			6.99486i			0.679400i
$107$	−12.6819			−1.22600			−0.613001	−	0.790082i	$-0.710038\pi$
$107$	−12.6819			−1.22600			−0.613001	+	0.790082i	$0.710038\pi$
$108$	0.128197			0.0123358
$109$		−	8.89607i		−	0.852089i	−0.904702	−	0.426045i	$-0.859907\pi$
$109$		−	8.89607i		−	0.852089i	0.904702	−	0.426045i	$-0.140093\pi$
$110$			2.98753i			0.284850i
$111$			3.66658i			0.348017i
$112$			15.9176i			1.50408i
$113$	1.36552			0.128457			0.0642287	−	0.997935i	$-0.479541\pi$
$113$	1.36552			0.128457			0.0642287	+	0.997935i	$0.479541\pi$
$114$	−4.33862			−0.406349
$115$		−	10.7925i		−	1.00641i
$116$	−0.942868			−0.0875431
$117$	−0.922450	−	3.48555i	−0.0852805	−	0.322240i
$118$	−7.69941			−0.708788
$119$		−	16.1933i		−	1.48444i
$120$	6.35806			0.580409
$121$	−1.00000			−0.0909091
$122$		−	7.39890i		−	0.669865i
$123$			4.16722i			0.375746i
$124$		−	0.00932567i		−	0.000837470i
$125$		−	11.4241i		−	1.02181i
$126$	5.84291			0.520528
$127$	−10.4027			−0.923093			−0.461546	−	0.887116i	$-0.652705\pi$
$127$	−10.4027			−0.923093			−0.461546	+	0.887116i	$0.652705\pi$
$128$		−	10.1058i		−	0.893231i
$129$	−7.11697			−0.626614
$130$	−2.75585	−	10.4132i	−0.241704	−	0.913299i
$131$	−12.0678			−1.05437			−0.527183	−	0.849752i	$-0.676752\pi$
$131$	−12.0678			−1.05437			−0.527183	+	0.849752i	$0.676752\pi$
$132$			0.128197i			0.0111581i
$133$	13.5432			1.17434
$134$	13.8381			1.19543
$135$		−	2.18365i		−	0.187939i
$136$			11.0403i			0.946694i
$137$			3.96114i			0.338423i	0.985580	+	0.169211i	$0.0541221\pi$
$137$			3.96114i			0.338423i	−0.985580	+	0.169211i	$0.945878\pi$
$138$			6.76193i			0.575613i
$139$	18.2437			1.54741			0.773703	−	0.633548i	$-0.218402\pi$
$139$	18.2437			1.54741			0.773703	+	0.633548i	$0.218402\pi$
$140$	−1.19553			−0.101041
$141$			11.6337i			0.979737i
$142$	13.1648			1.10476
$143$	3.48555	−	0.922450i	0.291477	−	0.0771391i
$144$	−3.72717			−0.310598
$145$			16.0604i			1.33374i
$146$	−8.82089			−0.730022
$147$	−11.2389			−0.926968
$148$			0.470045i			0.0386375i
$149$		−	13.8984i		−	1.13860i	−0.822131	−	0.569299i	$-0.807215\pi$
$149$		−	13.8984i		−	1.13860i	0.822131	−	0.569299i	$-0.192785\pi$
$150$			0.316965i			0.0258801i
$151$		−	2.29739i		−	0.186959i	−0.995621	−	0.0934795i	$-0.970201\pi$
$151$		−	2.29739i		−	0.186959i	0.995621	−	0.0934795i	$-0.0297990\pi$
$152$	−9.23344			−0.748931
$153$	3.79173			0.306543
$154$			5.84291i			0.470835i
$155$	−0.158849			−0.0127591
$156$	−0.118255	−	0.446838i	−0.00946801	−	0.0357756i
$157$	−15.6293			−1.24736			−0.623678	−	0.781682i	$-0.714362\pi$
$157$	−15.6293			−1.24736			−0.623678	+	0.781682i	$0.714362\pi$
$158$			13.8468i			1.10160i
$159$	5.11268			0.405462
$160$	1.58107			0.124995
$161$		−	21.1076i		−	1.66351i
$162$			1.36814i			0.107491i
$163$			1.25583i			0.0983643i	0.998790	+	0.0491822i	$0.0156615\pi$
$163$			1.25583i			0.0983643i	−0.998790	+	0.0491822i	$0.984339\pi$
$164$			0.534226i			0.0417160i
$165$	2.18365			0.169997
$166$	−10.6840			−0.829243
$167$			17.3823i			1.34509i	0.740058	+	0.672543i	$0.234798\pi$
$167$			17.3823i			1.34509i	−0.740058	+	0.672543i	$0.765202\pi$
$168$	12.4349			0.959371
$169$	−11.2982	+	6.43050i	−0.869090	+	0.494654i
$170$	11.3279			0.868812
$171$			3.17118i			0.242506i
$172$	−0.912375			−0.0695679
$173$	12.0899			0.919178			0.459589	−	0.888132i	$-0.347997\pi$
$173$	12.0899			0.919178			0.459589	+	0.888132i	$0.347997\pi$
$174$		−	10.0624i		−	0.762831i
$175$		−	0.989418i		−	0.0747930i
$176$		−	3.72717i		−	0.280946i
$177$			5.62765i			0.423000i
$178$	−3.93904			−0.295244
$179$	5.13094			0.383504			0.191752	−	0.981443i	$-0.438583\pi$
$179$	5.13094			0.383504			0.191752	+	0.981443i	$0.438583\pi$
$180$		−	0.279937i		−	0.0208653i
$181$	23.3170			1.73314			0.866568	−	0.499059i	$-0.166321\pi$
$181$	23.3170			1.73314			0.866568	+	0.499059i	$0.166321\pi$
$182$	−5.38979	−	20.3658i	−0.399518	−	1.50961i
$183$	−5.40800			−0.399771
$184$			14.3907i			1.06090i
$185$	8.00653			0.588652
$186$	0.0995250			0.00729753
$187$			3.79173i			0.277279i
$188$			1.49141i			0.108772i
$189$		−	4.27070i		−	0.310648i
$190$			9.47402i			0.687318i
$191$	11.1231			0.804838			0.402419	−	0.915456i	$-0.368169\pi$
$191$	11.1231			0.804838			0.402419	+	0.915456i	$0.368169\pi$
$192$	−8.44494			−0.609461
$193$			23.1664i			1.66756i	0.552099	+	0.833778i	$0.313827\pi$
$193$			23.1664i			1.66756i	−0.552099	+	0.833778i	$0.686173\pi$
$194$	5.18909			0.372555
$195$	−7.61123	+	2.01431i	−0.545051	+	0.144248i
$196$	−1.44079			−0.102914
$197$		−	9.18435i		−	0.654358i	−0.944962	−	0.327179i	$-0.893902\pi$
$197$		−	9.18435i		−	0.654358i	0.944962	−	0.327179i	$-0.106098\pi$
$198$	−1.36814			−0.0972294
$199$	−6.38937			−0.452930			−0.226465	−	0.974019i	$-0.572717\pi$
$199$	−6.38937			−0.452930			−0.226465	+	0.974019i	$0.572717\pi$
$200$			0.674563i			0.0476988i
$201$		−	10.1145i		−	0.713423i
$202$		−	17.5999i		−	1.23833i
$203$			31.4103i			2.20457i
$204$	0.486088			0.0340330
$205$	9.09975			0.635554
$206$			23.2550i			1.62025i
$207$	4.94243			0.343522
$208$	3.43813	+	12.9913i	0.238391	+	0.900782i
$209$	−3.17118			−0.219355
$210$		−	12.7589i		−	0.880446i
$211$	22.4436			1.54508			0.772541	−	0.634965i	$-0.218985\pi$
$211$	22.4436			1.54508			0.772541	+	0.634965i	$0.218985\pi$
$212$	0.655431			0.0450152
$213$		−	9.62239i		−	0.659315i
$214$		−	17.3505i		−	1.18606i
$215$			15.5410i			1.05989i
$216$			2.91167i			0.198114i
$217$	−0.310671			−0.0210897
$218$	12.1711			0.824328
$219$			6.44736i			0.435673i
$220$	0.279937			0.0188734
$221$	−3.49768	−	13.2163i	−0.235279	−	0.889023i
$222$	−5.01639			−0.336678
$223$			16.5344i			1.10722i	0.832775	+	0.553611i	$0.186751\pi$
$223$			16.5344i			1.10722i	−0.832775	+	0.553611i	$0.813249\pi$
$224$	3.09220			0.206606
$225$	0.231676			0.0154451
$226$			1.86822i			0.124272i
$227$			19.9826i			1.32630i	0.748489	+	0.663148i	$0.230780\pi$
$227$			19.9826i			1.32630i	−0.748489	+	0.663148i	$0.769220\pi$
$228$			0.406536i			0.0269235i
$229$			15.8459i			1.04713i	0.851986	+	0.523564i	$0.175398\pi$
$229$			15.8459i			1.04713i	−0.851986	+	0.523564i	$0.824602\pi$
$230$	14.7657			0.973620
$231$	4.27070			0.280992
$232$		−	21.4148i		−	1.40595i
$233$	−15.9195			−1.04292			−0.521460	−	0.853276i	$-0.674612\pi$
$233$	−15.9195			−1.04292			−0.521460	+	0.853276i	$0.674612\pi$
$234$	4.76872	−	1.26204i	0.311741	−	0.0825021i
$235$	25.4040			1.65717
$236$			0.721449i			0.0469623i
$237$	10.1209			0.657425
$238$	22.1547			1.43608
$239$		−	16.9898i		−	1.09898i	−0.835500	−	0.549491i	$-0.814822\pi$
$239$		−	16.9898i		−	1.09898i	0.835500	−	0.549491i	$-0.185178\pi$
$240$			8.13884i			0.525360i
$241$		−	21.9883i		−	1.41639i	−0.706015	−	0.708197i	$-0.749509\pi$
$241$		−	21.9883i		−	1.41639i	0.706015	−	0.708197i	$-0.250491\pi$
$242$		−	1.36814i		−	0.0879473i
$243$	1.00000			0.0641500
$244$	−0.693290			−0.0443834
$245$			24.5418i			1.56792i
$246$	−5.70134			−0.363504
$247$	11.0533	−	2.92526i	0.703307	−	0.186130i
$248$	0.211809			0.0134499
$249$			7.80918i			0.494887i
$250$	15.6298			0.988516
$251$	−11.9461			−0.754029			−0.377015	−	0.926207i	$-0.623049\pi$
$251$	−11.9461			−0.754029			−0.377015	+	0.926207i	$0.623049\pi$
$252$		−	0.547491i		−	0.0344887i
$253$			4.94243i			0.310728i
$254$		−	14.2324i		−	0.893019i
$255$		−	8.27981i		−	0.518502i
$256$	−3.06382			−0.191489
$257$	−28.3671			−1.76949			−0.884746	−	0.466074i	$-0.845668\pi$
$257$	−28.3671			−1.76949			−0.884746	+	0.466074i	$0.845668\pi$
$258$		−	9.73700i		−	0.606199i
$259$	15.6589			0.972995
$260$	−0.975737	+	0.258228i	−0.0605126	+	0.0160146i
$261$	−7.35483			−0.455253
$262$		−	16.5104i		−	1.02001i
$263$	−1.37798			−0.0849699			−0.0424849	−	0.999097i	$-0.513527\pi$
$263$	−1.37798			−0.0849699			−0.0424849	+	0.999097i	$0.513527\pi$
$264$	−2.91167			−0.179201
$265$		−	11.1643i		−	0.685818i
$266$			18.5289i			1.13608i
$267$			2.87912i			0.176200i
$268$		−	1.29665i		−	0.0792056i
$269$	−14.6274			−0.891847			−0.445923	−	0.895071i	$-0.647125\pi$
$269$	−14.6274			−0.891847			−0.445923	+	0.895071i	$0.647125\pi$
$270$	2.98753			0.181816
$271$			13.3040i			0.808158i	0.914724	+	0.404079i	$0.132408\pi$
$271$			13.3040i			0.808158i	−0.914724	+	0.404079i	$0.867592\pi$
$272$	−14.1324			−0.856904
$273$	−14.8858	+	3.93951i	−0.900927	+	0.238430i
$274$	−5.41938			−0.327397
$275$			0.231676i			0.0139706i
$276$	0.633605			0.0381385
$277$	−22.1581			−1.33135			−0.665676	−	0.746241i	$-0.731857\pi$
$277$	−22.1581			−1.33135			−0.665676	+	0.746241i	$0.731857\pi$
$278$			24.9598i			1.49699i
$279$		−	0.0727448i		−	0.00435512i
$280$		−	27.1534i		−	1.62273i
$281$		−	2.12589i		−	0.126820i	−0.997988	−	0.0634100i	$-0.979802\pi$
$281$		−	2.12589i		−	0.126820i	0.997988	−	0.0634100i	$-0.0201976\pi$
$282$	−15.9166			−0.947817
$283$	31.1036			1.84892			0.924458	−	0.381283i	$-0.124518\pi$
$283$	31.1036			1.84892			0.924458	+	0.381283i	$0.124518\pi$
$284$		−	1.23356i		−	0.0731984i
$285$	6.92475			0.410187
$286$	1.26204	+	4.76872i	0.0746259	+	0.281980i
$287$	17.7970			1.05052
$288$			0.724050i			0.0426650i
$289$	−2.62279			−0.154282
$290$	−21.9728			−1.29029
$291$		−	3.79281i		−	0.222338i
$292$			0.826533i			0.0483692i
$293$			16.9009i			0.987363i	0.869643	+	0.493682i	$0.164349\pi$
$293$			16.9009i			0.987363i	−0.869643	+	0.493682i	$0.835651\pi$
$294$		−	15.3764i		−	0.896767i
$295$	12.2888			0.715483
$296$	−10.6759			−0.620523
$297$			1.00000i			0.0580259i
$298$	19.0149			1.10150
$299$	−4.55914	−	17.2271i	−0.263662	−	0.996269i
$300$	0.0297002			0.00171474
$301$			30.3945i			1.75191i
$302$	3.14315			0.180868
$303$	−12.8641			−0.739025
$304$		−	11.8195i		−	0.677897i
$305$			11.8092i			0.676192i
$306$			5.18761i			0.296556i
$307$		−	24.6110i		−	1.40462i	−0.711869	−	0.702312i	$-0.752151\pi$
$307$		−	24.6110i		−	1.40462i	0.711869	−	0.702312i	$-0.247849\pi$
$308$	0.547491			0.0311962
$309$	16.9975			0.966956
$310$		−	0.217328i		−	0.0123434i
$311$	1.00504			0.0569904			0.0284952	−	0.999594i	$-0.490928\pi$
$311$	1.00504			0.0569904			0.0284952	+	0.999594i	$0.490928\pi$
$312$	10.1488	−	2.68587i	0.574561	−	0.152057i
$313$	−13.8744			−0.784227			−0.392114	−	0.919917i	$-0.628256\pi$
$313$	−13.8744			−0.784227			−0.392114	+	0.919917i	$0.628256\pi$
$314$		−	21.3831i		−	1.20672i
$315$	−9.32571			−0.525444
$316$	1.29747			0.0729886
$317$		−	15.6405i		−	0.878460i	−0.898375	−	0.439230i	$-0.855251\pi$
$317$		−	15.6405i		−	0.878460i	0.898375	−	0.439230i	$-0.144749\pi$
$318$			6.99486i			0.392252i
$319$		−	7.35483i		−	0.411792i
$320$			18.4408i			1.03087i
$321$	−12.6819			−0.707832
$322$	28.8782			1.60932
$323$			12.0243i			0.669048i
$324$	0.128197			0.00712206
$325$	−0.213709	−	0.807519i	−0.0118545	−	0.0447931i
$326$	−1.71815			−0.0951596
$327$		−	8.89607i		−	0.491954i
$328$	−12.1336			−0.669964
$329$	49.6842			2.73918
$330$			2.98753i			0.164458i
$331$		−	23.1426i		−	1.27203i	−0.771675	−	0.636017i	$-0.780581\pi$
$331$		−	23.1426i		−	1.27203i	0.771675	−	0.636017i	$-0.219419\pi$
$332$			1.00111i			0.0549433i
$333$			3.66658i			0.200927i
$334$	−23.7814			−1.30126
$335$	−22.0866			−1.20672
$336$			15.9176i			0.868378i
$337$	−15.1946			−0.827705			−0.413853	−	0.910344i	$-0.635817\pi$
$337$	−15.1946			−0.827705			−0.413853	+	0.910344i	$0.635817\pi$
$338$	−8.79781	−	15.4575i	−0.478538	−	0.840775i
$339$	1.36552			0.0741650
$340$		−	1.06145i		−	0.0575650i
$341$	0.0727448			0.00393935
$342$	−4.33862			−0.234606
$343$			18.1030i			0.977472i
$344$		−	20.7223i		−	1.11727i
$345$		−	10.7925i		−	0.581050i
$346$			16.5407i			0.889231i
$347$	16.6545			0.894061			0.447030	−	0.894519i	$-0.352482\pi$
$347$	16.6545			0.894061			0.447030	+	0.894519i	$0.352482\pi$
$348$	−0.942868			−0.0505430
$349$		−	29.1080i		−	1.55812i	−0.626952	−	0.779058i	$-0.715698\pi$
$349$		−	29.1080i		−	1.55812i	0.626952	−	0.779058i	$-0.284302\pi$
$350$	1.35366			0.0723562
$351$	−0.922450	−	3.48555i	−0.0492367	−	0.186045i
$352$	−0.724050			−0.0385920
$353$		−	29.1723i		−	1.55268i	−0.630312	−	0.776342i	$-0.717073\pi$
$353$		−	29.1723i		−	1.55268i	0.630312	−	0.776342i	$-0.282927\pi$
$354$	−7.69941			−0.409219
$355$	−21.0119			−1.11520
$356$			0.369095i			0.0195620i
$357$		−	16.1933i		−	0.857043i
$358$			7.01983i			0.371010i
$359$		−	18.0809i		−	0.954271i	−0.878830	−	0.477136i	$-0.841675\pi$
$359$		−	18.0809i		−	0.954271i	0.878830	−	0.477136i	$-0.158325\pi$
$360$	6.35806			0.335099
$361$	8.94359			0.470715
$362$			31.9008i			1.67667i
$363$	−1.00000			−0.0524864
$364$	−1.90831	+	0.505033i	−0.100023	+	0.0264709i
$365$	14.0788			0.736917
$366$		−	7.39890i		−	0.386747i
$367$	18.1338			0.946578			0.473289	−	0.880907i	$-0.343067\pi$
$367$	18.1338			0.946578			0.473289	+	0.880907i	$0.343067\pi$
$368$	−18.4213			−0.960275
$369$			4.16722i			0.216937i
$370$			10.9540i			0.569474i
$371$		−	21.8347i		−	1.13360i
$372$		−	0.00932567i		−	0.000483513i
$373$	−15.8564			−0.821012			−0.410506	−	0.911858i	$-0.634648\pi$
$373$	−15.8564			−0.821012			−0.410506	+	0.911858i	$0.634648\pi$
$374$	−5.18761			−0.268245
$375$		−	11.4241i		−	0.589940i
$376$	−33.8736			−1.74690
$377$	6.78447	+	25.6357i	0.349418	+	1.32030i
$378$	5.84291			0.300527
$379$			18.3431i			0.942224i	0.882073	+	0.471112i	$0.156147\pi$
$379$			18.3431i			0.942224i	−0.882073	+	0.471112i	$0.843853\pi$
$380$	0.887733			0.0455397
$381$	−10.4027			−0.532948
$382$			15.2179i			0.778617i
$383$		−	16.1019i		−	0.822768i	−0.911462	−	0.411384i	$-0.865046\pi$
$383$		−	16.1019i		−	0.822768i	0.911462	−	0.411384i	$-0.134954\pi$
$384$		−	10.1058i		−	0.515707i
$385$		−	9.32571i		−	0.475282i
$386$	−31.6949			−1.61323
$387$	−7.11697			−0.361776
$388$		−	0.486227i		−	0.0246844i
$389$	−32.7166			−1.65880			−0.829400	−	0.558655i	$-0.811317\pi$
$389$	−32.7166			−1.65880			−0.829400	+	0.558655i	$0.811317\pi$
$390$	−2.75585	−	10.4132i	−0.139548	−	0.527294i
$391$	18.7403			0.947740
$392$		−	32.7239i		−	1.65281i
$393$	−12.0678			−0.608738
$394$	12.5655			0.633039
$395$		−	22.1006i		−	1.11200i
$396$			0.128197i			0.00644214i
$397$			3.51685i			0.176506i	0.996098	+	0.0882529i	$0.0281284\pi$
$397$			3.51685i			0.176506i	−0.996098	+	0.0882529i	$0.971872\pi$
$398$		−	8.74154i		−	0.438174i
$399$	13.5432			0.678007
$400$	−0.863496			−0.0431748
$401$		−	18.6231i		−	0.929992i	−0.885313	−	0.464996i	$-0.846056\pi$
$401$		−	18.6231i		−	0.929992i	0.885313	−	0.464996i	$-0.153944\pi$
$402$	13.8381			0.690180
$403$	−0.253556	+	0.0671034i	−0.0126305	+	0.00334266i
$404$	−1.64914			−0.0820480
$405$		−	2.18365i		−	0.108506i
$406$	−42.9736			−2.13275
$407$	−3.66658			−0.181746
$408$			11.0403i			0.546574i
$409$		−	17.6809i		−	0.874262i	−0.899398	−	0.437131i	$-0.855995\pi$
$409$		−	17.6809i		−	0.874262i	0.899398	−	0.437131i	$-0.144005\pi$
$410$			12.4497i			0.614848i
$411$			3.96114i			0.195388i
$412$	2.17903			0.107353
$413$	24.0340			1.18264
$414$			6.76193i			0.332331i
$415$	17.0525			0.837075
$416$	2.52371	−	0.667900i	0.123735	−	0.0327465i
$417$	18.2437			0.893395
$418$		−	4.33862i		−	0.212209i
$419$	−1.93036			−0.0943044			−0.0471522	−	0.998888i	$-0.515015\pi$
$419$	−1.93036			−0.0943044			−0.0471522	+	0.998888i	$0.515015\pi$
$420$	−1.19553			−0.0583358
$421$			7.21742i			0.351756i	0.984412	+	0.175878i	$0.0562764\pi$
$421$			7.21742i			0.351756i	−0.984412	+	0.175878i	$0.943724\pi$
$422$			30.7060i			1.49474i
$423$			11.6337i			0.565651i
$424$			14.8864i			0.722949i
$425$	0.878452			0.0426112
$426$	13.1648			0.637835
$427$			23.0960i			1.11769i
$428$	−1.62578			−0.0785849
$429$	3.48555	−	0.922450i	0.168284	−	0.0445363i
$430$	−21.2622			−1.02535
$431$			29.7876i			1.43482i	0.696653	+	0.717408i	$0.254672\pi$
$431$			29.7876i			1.43482i	−0.696653	+	0.717408i	$0.745328\pi$
$432$	−3.72717			−0.179324
$433$	25.2468			1.21329			0.606643	−	0.794975i	$-0.292516\pi$
$433$	25.2468			1.21329			0.606643	+	0.794975i	$0.292516\pi$
$434$		−	0.425041i		−	0.0204026i
$435$			16.0604i			0.770036i
$436$		−	1.14045i		−	0.0546177i
$437$			15.6733i			0.749758i
$438$	−8.82089			−0.421478
$439$	9.07110			0.432940			0.216470	−	0.976289i	$-0.430546\pi$
$439$	9.07110			0.432940			0.216470	+	0.976289i	$0.430546\pi$
$440$			6.35806i			0.303109i
$441$	−11.2389			−0.535185
$442$	18.0817	−	4.78531i	0.860059	−	0.227614i
$443$	−12.0753			−0.573715			−0.286858	−	0.957973i	$-0.592611\pi$
$443$	−12.0753			−0.573715			−0.286858	+	0.957973i	$0.592611\pi$
$444$			0.470045i			0.0223074i
$445$	6.28700			0.298032
$446$	−22.6213			−1.07115
$447$		−	13.8984i		−	0.657370i
$448$			36.0658i			1.70395i
$449$			8.94438i			0.422111i	0.977474	+	0.211056i	$0.0676901\pi$
$449$			8.94438i			0.422111i	−0.977474	+	0.211056i	$0.932310\pi$
$450$			0.316965i			0.0149419i
$451$	−4.16722			−0.196227
$452$	0.175056			0.00823394
$453$		−	2.29739i		−	0.107941i
$454$	−27.3390			−1.28308
$455$	8.60250	+	32.5053i	0.403292	+	1.52387i
$456$	−9.23344			−0.432395
$457$			28.4975i			1.33305i	0.745481	+	0.666527i	$0.232220\pi$
$457$			28.4975i			1.33305i	−0.745481	+	0.666527i	$0.767780\pi$
$458$	−21.6794			−1.01301
$459$	3.79173			0.176983
$460$		−	1.38357i		−	0.0645093i
$461$			19.2580i			0.896932i	0.893800	+	0.448466i	$0.148030\pi$
$461$			19.2580i			0.896932i	−0.893800	+	0.448466i	$0.851970\pi$
$462$			5.84291i			0.271837i
$463$			36.3639i			1.68997i	0.534787	+	0.844987i	$0.320392\pi$
$463$			36.3639i			1.68997i	−0.534787	+	0.844987i	$0.679608\pi$
$464$	27.4127			1.27260
$465$	−0.158849			−0.00736645
$466$		−	21.7801i		−	1.00894i
$467$	−1.70345			−0.0788264			−0.0394132	−	0.999223i	$-0.512549\pi$
$467$	−1.70345			−0.0788264			−0.0394132	+	0.999223i	$0.512549\pi$
$468$	−0.118255	−	0.446838i	−0.00546636	−	0.0206551i
$469$	−43.1961			−1.99461
$470$			34.7562i			1.60318i
$471$	−15.6293			−0.720161
$472$	−16.3859			−0.754220
$473$		−	7.11697i		−	0.327239i
$474$			13.8468i			0.636006i
$475$			0.734687i			0.0337097i
$476$		−	2.07594i		−	0.0951505i
$477$	5.11268			0.234094
$478$	23.2444			1.06318
$479$		−	24.5812i		−	1.12314i	−0.827429	−	0.561571i	$-0.810197\pi$
$479$		−	24.5812i		−	1.12314i	0.827429	−	0.561571i	$-0.189803\pi$
$480$	1.58107			0.0721657
$481$	12.7801	−	3.38224i	0.582721	−	0.154217i
$482$	30.0831			1.37025
$483$		−	21.1076i		−	0.960431i
$484$	−0.128197			−0.00582714
$485$	−8.28216			−0.376074
$486$			1.36814i			0.0620600i
$487$		−	40.5270i		−	1.83646i	−0.396053	−	0.918228i	$-0.629620\pi$
$487$		−	40.5270i		−	1.83646i	0.396053	−	0.918228i	$-0.370380\pi$
$488$		−	15.7463i		−	0.712802i
$489$			1.25583i			0.0567907i
$490$	−33.5766			−1.51683
$491$	−16.8245			−0.759277			−0.379639	−	0.925135i	$-0.623952\pi$
$491$	−16.8245			−0.759277			−0.379639	+	0.925135i	$0.623952\pi$
$492$			0.534226i			0.0240848i
$493$	−27.8875			−1.25599
$494$	4.00216	+	15.1225i	0.180066	+	0.680393i
$495$	2.18365			0.0981477
$496$			0.271132i			0.0121742i
$497$	−41.0943			−1.84333
$498$	−10.6840			−0.478764
$499$		−	28.5150i		−	1.27651i	−0.769826	−	0.638254i	$-0.779657\pi$
$499$		−	28.5150i		−	1.27651i	0.769826	−	0.638254i	$-0.220343\pi$
$500$		−	1.46454i		−	0.0654963i
$501$			17.3823i			0.776586i
$502$		−	16.3439i		−	0.729463i
$503$	27.4200			1.22260			0.611299	−	0.791400i	$-0.290647\pi$
$503$	27.4200			1.22260			0.611299	+	0.791400i	$0.290647\pi$
$504$	12.4349			0.553893
$505$			28.0908i			1.25002i
$506$	−6.76193			−0.300604
$507$	−11.2982	+	6.43050i	−0.501769	+	0.285588i
$508$	−1.33360			−0.0591689
$509$			25.4659i			1.12876i	0.825516	+	0.564378i	$0.190884\pi$
$509$			25.4659i			1.12876i	−0.825516	+	0.564378i	$0.809116\pi$
$510$	11.3279			0.501609
$511$	27.5348			1.21807
$512$		−	24.4032i		−	1.07848i
$513$			3.17118i			0.140011i
$514$		−	38.8101i		−	1.71184i
$515$		−	37.1167i		−	1.63556i
$516$	−0.912375			−0.0401651
$517$	−11.6337			−0.511651
$518$			21.4235i			0.941295i
$519$	12.0899			0.530688
$520$	−5.86499	−	22.1614i	−0.257197	−	0.971840i
$521$	2.38806			0.104623			0.0523113	−	0.998631i	$-0.483341\pi$
$521$	2.38806			0.104623			0.0523113	+	0.998631i	$0.483341\pi$
$522$		−	10.0624i		−	0.440421i
$523$	45.6041			1.99413			0.997064	−	0.0765769i	$-0.0243991\pi$
$523$	45.6041			1.99413			0.997064	+	0.0765769i	$0.0243991\pi$
$524$	−1.54705			−0.0675833
$525$		−	0.989418i		−	0.0431818i
$526$		−	1.88527i		−	0.0822015i
$527$		−	0.275829i		−	0.0120153i
$528$		−	3.72717i		−	0.162204i
$529$	1.42760			0.0620694
$530$	15.2743			0.663474
$531$			5.62765i			0.244219i
$532$	1.73620			0.0752736
$533$	14.5251	−	3.84405i	0.629151	−	0.166504i
$534$	−3.93904			−0.170459
$535$			27.6927i			1.19726i
$536$	29.4501			1.27205
$537$	5.13094			0.221416
$538$		−	20.0123i		−	0.862791i
$539$		−	11.2389i		−	0.484093i
$540$		−	0.279937i		−	0.0120466i
$541$		−	29.4997i		−	1.26829i	−0.773214	−	0.634145i	$-0.781352\pi$
$541$		−	29.4997i		−	1.26829i	0.773214	−	0.634145i	$-0.218648\pi$
$542$	−18.2017			−0.781828
$543$	23.3170			1.00063
$544$			2.74540i			0.117708i
$545$	−19.4259			−0.832114
$546$	−5.38979	−	20.3658i	−0.230662	−	0.871575i
$547$	7.75142			0.331427			0.165713	−	0.986174i	$-0.447007\pi$
$547$	7.75142			0.331427			0.165713	+	0.986174i	$0.447007\pi$
$548$			0.507806i			0.0216924i
$549$	−5.40800			−0.230808
$550$	−0.316965			−0.0135154
$551$		−	23.3235i		−	0.993616i
$552$			14.3907i			0.612509i
$553$		−	43.2235i		−	1.83805i
$554$		−	30.3153i		−	1.28798i
$555$	8.00653			0.339858
$556$	2.33878			0.0991865
$557$		−	20.2857i		−	0.859534i	−0.902940	−	0.429767i	$-0.858596\pi$
$557$		−	20.2857i		−	0.859534i	0.902940	−	0.429767i	$-0.141404\pi$
$558$	0.0995250			0.00421323
$559$	6.56505	+	24.8066i	0.277672	+	1.04921i
$560$	34.7585			1.46882
$561$			3.79173i			0.160087i
$562$	2.90851			0.122688
$563$	32.7633			1.38081			0.690403	−	0.723425i	$-0.257433\pi$
$563$	32.7633			1.38081			0.690403	+	0.723425i	$0.257433\pi$
$564$			1.49141i			0.0627997i
$565$		−	2.98182i		−	0.125446i
$566$			42.5540i			1.78868i
$567$		−	4.27070i		−	0.179353i
$568$	28.0172			1.17558
$569$	−27.8002			−1.16545			−0.582723	−	0.812671i	$-0.698013\pi$
$569$	−27.8002			−1.16545			−0.582723	+	0.812671i	$0.698013\pi$
$570$			9.47402i			0.396823i
$571$	−43.4425			−1.81801			−0.909007	−	0.416782i	$-0.863158\pi$
$571$	−43.4425			−1.81801			−0.909007	+	0.416782i	$0.863158\pi$
$572$	0.446838	−	0.118255i	0.0186832	−	0.00494450i
$573$	11.1231			0.464674
$574$			24.3487i			1.01630i
$575$	1.14504			0.0477515
$576$	−8.44494			−0.351873
$577$		−	25.7084i		−	1.07025i	−0.844772	−	0.535127i	$-0.820264\pi$
$577$		−	25.7084i		−	1.07025i	0.844772	−	0.535127i	$-0.179736\pi$
$578$		−	3.58834i		−	0.149255i
$579$			23.1664i			0.962764i
$580$			2.05889i			0.0854909i
$581$	33.3507			1.38362
$582$	5.18909			0.215095
$583$			5.11268i			0.211746i
$584$	−18.7726			−0.776815
$585$	−7.61123	+	2.01431i	−0.314686	+	0.0832814i
$586$	−23.1228			−0.955195
$587$		−	1.44805i		−	0.0597673i	−0.999553	−	0.0298837i	$-0.990486\pi$
$587$		−	1.44805i		−	0.0597673i	0.999553	−	0.0298837i	$-0.00951368\pi$
$588$	−1.44079			−0.0594173
$589$	0.230687			0.00950530
$590$			16.8128i			0.692173i
$591$		−	9.18435i		−	0.377794i
$592$		−	13.6660i		−	0.561668i
$593$			4.27539i			0.175569i	0.996139	+	0.0877845i	$0.0279787\pi$
$593$			4.27539i			0.175569i	−0.996139	+	0.0877845i	$0.972021\pi$
$594$	−1.36814			−0.0561354
$595$	−35.3606			−1.44964
$596$		−	1.78173i		−	0.0729824i
$597$	−6.38937			−0.261499
$598$	23.5691	−	6.23754i	0.963810	−	0.255072i
$599$	15.9807			0.652953			0.326476	−	0.945205i	$-0.394139\pi$
$599$	15.9807			0.652953			0.326476	+	0.945205i	$0.394139\pi$
$600$			0.674563i			0.0275389i
$601$	−25.2647			−1.03057			−0.515283	−	0.857020i	$-0.672313\pi$
$601$	−25.2647			−1.03057			−0.515283	+	0.857020i	$0.672313\pi$
$602$	−41.5838			−1.69483
$603$		−	10.1145i		−	0.411895i
$604$		−	0.294519i		−	0.0119838i
$605$			2.18365i			0.0887780i
$606$		−	17.5999i		−	0.714948i
$607$	41.6506			1.69055			0.845273	−	0.534334i	$-0.179437\pi$
$607$	41.6506			1.69055			0.845273	+	0.534334i	$0.179437\pi$
$608$	−2.29610			−0.0931190
$609$			31.4103i			1.27281i
$610$	−16.1566			−0.654162
$611$	40.5500	−	10.7315i	1.64048	−	0.434151i
$612$	0.486088			0.0196490
$613$		−	16.1620i		−	0.652777i	−0.945236	−	0.326388i	$-0.894168\pi$
$613$		−	16.1620i		−	0.652777i	0.945236	−	0.326388i	$-0.105832\pi$
$614$	33.6713			1.35886
$615$	9.09975			0.366937
$616$			12.4349i			0.501015i
$617$		−	8.12561i		−	0.327125i	−0.986533	−	0.163562i	$-0.947701\pi$
$617$		−	8.12561i		−	0.327125i	0.986533	−	0.163562i	$-0.0522985\pi$
$618$			23.2550i			0.935453i
$619$			7.09593i			0.285209i	0.989780	+	0.142605i	$0.0455478\pi$
$619$			7.09593i			0.285209i	−0.989780	+	0.142605i	$0.954452\pi$
$620$	−0.0203640			−0.000817838
$621$	4.94243			0.198333
$622$			1.37503i			0.0551337i
$623$	12.2959			0.492624
$624$	3.43813	+	12.9913i	0.137635	+	0.520066i
$625$	−23.7879			−0.951518
$626$		−	18.9821i		−	0.758677i
$627$	−3.17118			−0.126645
$628$	−2.00363			−0.0799536
$629$			13.9027i			0.554337i
$630$		−	12.7589i		−	0.508325i
$631$			3.62153i			0.144171i	0.997398	+	0.0720854i	$0.0229654\pi$
$631$			3.62153i			0.144171i	−0.997398	+	0.0720854i	$0.977035\pi$
$632$			29.4688i			1.17221i
$633$	22.4436			0.892053
$634$	21.3984			0.849840
$635$			22.7159i			0.901453i
$636$	0.655431			0.0259895
$637$	10.3673	+	39.1738i	0.410768	+	1.55212i
$638$	10.0624			0.398375
$639$		−	9.62239i		−	0.380656i
$640$	−22.0674			−0.872291
$641$	8.81244			0.348070			0.174035	−	0.984739i	$-0.444319\pi$
$641$	8.81244			0.348070			0.174035	+	0.984739i	$0.444319\pi$
$642$		−	17.3505i		−	0.684771i
$643$			47.2262i			1.86242i	0.364484	+	0.931210i	$0.381245\pi$
$643$			47.2262i			1.86242i	−0.364484	+	0.931210i	$0.618755\pi$
$644$		−	2.70594i		−	0.106629i
$645$			15.5410i			0.611925i
$646$	−16.4509			−0.647251
$647$	−41.0552			−1.61405			−0.807023	−	0.590520i	$-0.798923\pi$
$647$	−41.0552			−1.61405			−0.807023	+	0.590520i	$0.798923\pi$
$648$			2.91167i			0.114381i
$649$	−5.62765			−0.220905
$650$	1.10480	−	0.292384i	0.0433337	−	0.0114682i
$651$	−0.310671			−0.0121762
$652$			0.160994i			0.00630501i
$653$	36.9362			1.44542			0.722712	−	0.691149i	$-0.242895\pi$
$653$	36.9362			1.44542			0.722712	+	0.691149i	$0.242895\pi$
$654$	12.1711			0.475926
$655$			26.3518i			1.02965i
$656$		−	15.5320i		−	0.606421i
$657$			6.44736i			0.251536i
$658$			67.9748i			2.64994i
$659$	39.7980			1.55031			0.775154	−	0.631772i	$-0.217672\pi$
$659$	39.7980			1.55031			0.775154	+	0.631772i	$0.217672\pi$
$660$	0.279937			0.0108965
$661$		−	21.8622i		−	0.850342i	−0.905113	−	0.425171i	$-0.860214\pi$
$661$		−	21.8622i		−	0.850342i	0.905113	−	0.425171i	$-0.139786\pi$
$662$	31.6623			1.23059
$663$	−3.49768	−	13.2163i	−0.135839	−	0.513278i
$664$	−22.7378			−0.882396
$665$		−	29.5736i		−	1.14681i
$666$	−5.01639			−0.194381
$667$	−36.3507			−1.40751
$668$			2.22836i			0.0862180i
$669$			16.5344i			0.639255i
$670$		−	30.2175i		−	1.16740i
$671$		−	5.40800i		−	0.208774i
$672$	3.09220			0.119284
$673$	32.3152			1.24566			0.622830	−	0.782357i	$-0.285983\pi$
$673$	32.3152			1.24566			0.622830	+	0.782357i	$0.285983\pi$
$674$		−	20.7884i		−	0.800739i
$675$	0.231676			0.00891721
$676$	−1.44839	+	0.824371i	−0.0557074	+	0.0317066i
$677$	−21.1472			−0.812753			−0.406376	−	0.913706i	$-0.633208\pi$
$677$	−21.1472			−0.812753			−0.406376	+	0.913706i	$0.633208\pi$
$678$			1.86822i			0.0717487i
$679$	−16.1979			−0.621620
$680$	24.1081			0.924502
$681$			19.9826i			0.765737i
$682$			0.0995250i			0.00381101i
$683$		−	24.7401i		−	0.946654i	−0.880887	−	0.473327i	$-0.843053\pi$
$683$		−	24.7401i		−	0.946654i	0.880887	−	0.473327i	$-0.156947\pi$
$684$			0.406536i			0.0155443i
$685$	8.64973			0.330489
$686$	−24.7675			−0.945626
$687$			15.8459i			0.604560i
$688$	26.5262			1.01130
$689$	−4.71619	−	17.8205i	−0.179673	−	0.678908i
$690$	14.7657			0.562120
$691$		−	22.7394i		−	0.865047i	−0.901623	−	0.432523i	$-0.857623\pi$
$691$		−	22.7394i		−	0.865047i	0.901623	−	0.432523i	$-0.142377\pi$
$692$	1.54989			0.0589180
$693$	4.27070			0.162231
$694$			22.7857i			0.864932i
$695$		−	39.8377i		−	1.51113i
$696$		−	21.4148i		−	0.811727i
$697$			15.8010i			0.598505i
$698$	39.8238			1.50735
$699$	−15.9195			−0.602130
$700$		−	0.126840i		−	0.00479412i
$701$	23.8173			0.899567			0.449783	−	0.893138i	$-0.351501\pi$
$701$	23.8173			0.899567			0.449783	+	0.893138i	$0.351501\pi$
$702$	4.76872	−	1.26204i	0.179984	−	0.0476326i
$703$	−11.6274			−0.438536
$704$		−	8.44494i		−	0.318281i
$705$	25.4040			0.956769
$706$	39.9117			1.50210
$707$			54.9389i			2.06619i
$708$			0.721449i			0.0271137i
$709$			15.8902i			0.596770i	0.954446	+	0.298385i	$0.0964480\pi$
$709$			15.8902i			0.596770i	−0.954446	+	0.298385i	$0.903552\pi$
$710$		−	28.7472i		−	1.07886i
$711$	10.1209			0.379565
$712$	−8.38305			−0.314168
$713$		−	0.359536i		−	0.0134647i
$714$	22.1547			0.829120
$715$	−2.01431	−	7.61123i	−0.0753308	−	0.284644i
$716$	0.657771			0.0245821
$717$		−	16.9898i		−	0.634497i
$718$	24.7371			0.923181
$719$	−4.64051			−0.173062			−0.0865309	−	0.996249i	$-0.527578\pi$
$719$	−4.64051			−0.173062			−0.0865309	+	0.996249i	$0.527578\pi$
$720$			8.13884i			0.303316i
$721$		−	72.5914i		−	2.70345i
$722$			12.2361i			0.455379i
$723$		−	21.9883i		−	0.817755i
$724$	2.98917			0.111091
$725$	−1.70394			−0.0632826
$726$		−	1.36814i		−	0.0507764i
$727$	14.5583			0.539938			0.269969	−	0.962869i	$-0.412987\pi$
$727$	14.5583			0.539938			0.269969	+	0.962869i	$0.412987\pi$
$728$	−11.4705	−	43.3424i	−0.425127	−	1.60638i
$729$	1.00000			0.0370370
$730$			19.2617i			0.712908i
$731$	−26.9856			−0.998100
$732$	−0.693290			−0.0256247
$733$		−	34.2475i		−	1.26496i	−0.774576	−	0.632480i	$-0.782037\pi$
$733$		−	34.2475i		−	1.26496i	0.774576	−	0.632480i	$-0.217963\pi$
$734$			24.8096i			0.915738i
$735$			24.5418i			0.905238i
$736$			3.57856i			0.131908i
$737$	10.1145			0.372573
$738$	−5.70134			−0.209869
$739$		−	30.5325i		−	1.12316i	−0.827424	−	0.561578i	$-0.810194\pi$
$739$		−	30.5325i		−	1.12316i	0.827424	−	0.561578i	$-0.189806\pi$
$740$	1.02641			0.0377317
$741$	11.0533	−	2.92526i	0.406054	−	0.107462i
$742$	29.8729			1.09667
$743$		−	2.86476i		−	0.105098i	−0.998618	−	0.0525490i	$-0.983265\pi$
$743$		−	2.86476i		−	0.105098i	0.998618	−	0.0525490i	$-0.0167346\pi$
$744$	0.211809			0.00776529
$745$	−30.3491			−1.11191
$746$		−	21.6937i		−	0.794263i
$747$			7.80918i			0.285723i
$748$			0.486088i			0.0177732i
$749$			54.1604i			1.97898i
$750$	15.6298			0.570720
$751$	−38.1810			−1.39324			−0.696621	−	0.717439i	$-0.745314\pi$
$751$	−38.1810			−1.39324			−0.696621	+	0.717439i	$0.745314\pi$
$752$		−	43.3609i		−	1.58121i
$753$	−11.9461			−0.435339
$754$	−35.0731	+	9.28209i	−1.27729	+	0.338034i
$755$	−5.01670			−0.182576
$756$		−	0.547491i		−	0.0199121i
$757$	−38.9456			−1.41550			−0.707750	−	0.706463i	$-0.750290\pi$
$757$	−38.9456			−1.41550			−0.707750	+	0.706463i	$0.750290\pi$
$758$	−25.0960			−0.911526
$759$			4.94243i			0.179399i
$760$			20.1626i			0.731374i
$761$		−	26.9359i		−	0.976427i	−0.872724	−	0.488214i	$-0.837649\pi$
$761$		−	26.9359i		−	0.976427i	0.872724	−	0.488214i	$-0.162351\pi$
$762$		−	14.2324i		−	0.515585i
$763$	−37.9925			−1.37542
$764$	1.42595			0.0515889
$765$		−	8.27981i		−	0.299357i
$766$	22.0296			0.795962
$767$	19.6155	−	5.19123i	0.708274	−	0.187444i
$768$	−3.06382			−0.110556
$769$		−	3.83575i		−	0.138321i	−0.997606	−	0.0691603i	$-0.977968\pi$
$769$		−	3.83575i		−	0.138321i	0.997606	−	0.0691603i	$-0.0220320\pi$
$770$	12.7589			0.459798
$771$	−28.3671			−1.02162
$772$			2.96987i			0.106888i
$773$		−	21.7215i		−	0.781267i	−0.920546	−	0.390633i	$-0.872256\pi$
$773$		−	21.7215i		−	0.781267i	0.920546	−	0.390633i	$-0.127744\pi$
$774$		−	9.73700i		−	0.349989i
$775$		−	0.0168532i		−	0.000605385i
$776$	11.0434			0.396435
$777$	15.6589			0.561759
$778$		−	44.7609i		−	1.60476i
$779$	−13.2150			−0.473478
$780$	−0.975737	+	0.258228i	−0.0349370	+	0.00924605i
$781$	9.62239			0.344316
$782$			25.6394i			0.916863i
$783$	−7.35483			−0.262840
$784$	41.8893			1.49605
$785$			34.1290i			1.21811i
$786$		−	16.5104i		−	0.588905i
$787$			32.8705i			1.17171i	0.810417	+	0.585853i	$0.199240\pi$
$787$			32.8705i			1.17171i	−0.810417	+	0.585853i	$0.800760\pi$
$788$		−	1.17741i		−	0.0419434i
$789$	−1.37798			−0.0490574
$790$	30.2366			1.07577
$791$		−	5.83174i		−	0.207353i
$792$	−2.91167			−0.103462
$793$	4.98861	+	18.8499i	0.177151	+	0.669379i
$794$	−4.81154			−0.170755
$795$		−	11.1643i		−	0.395957i
$796$	−0.819098			−0.0290322
$797$	2.27867			0.0807147			0.0403573	−	0.999185i	$-0.487150\pi$
$797$	2.27867			0.0807147			0.0403573	+	0.999185i	$0.487150\pi$
$798$			18.5289i			0.655918i
$799$			44.1120i			1.56057i
$800$			0.167745i			0.00593068i
$801$			2.87912i			0.101729i
$802$	25.4789			0.899693
$803$	−6.44736			−0.227523
$804$		−	1.29665i		−	0.0457294i
$805$	−46.0917			−1.62452
$806$	−0.0918068	−	0.346900i	−0.00323376	−	0.0122190i
$807$	−14.6274			−0.514908
$808$		−	37.4561i		−	1.31770i
$809$	25.3935			0.892786			0.446393	−	0.894837i	$-0.352708\pi$
$809$	25.3935			0.892786			0.446393	+	0.894837i	$0.352708\pi$
$810$	2.98753			0.104971
$811$			32.7178i			1.14888i	0.818548	+	0.574439i	$0.194780\pi$
$811$			32.7178i			1.14888i	−0.818548	+	0.574439i	$0.805220\pi$
$812$			4.02671i			0.141310i
$813$			13.3040i			0.466590i
$814$		−	5.01639i		−	0.175824i
$815$	2.74230			0.0960584
$816$	−14.1324			−0.494734
$817$		−	22.5692i		−	0.789597i
$818$	24.1899			0.845779
$819$	−14.8858	+	3.93951i	−0.520151	+	0.137658i
$820$	1.16656			0.0407381
$821$			31.2361i			1.09015i	0.838388	+	0.545073i	$0.183498\pi$
$821$			31.2361i			1.09015i	−0.838388	+	0.545073i	$0.816502\pi$
$822$	−5.41938			−0.189023
$823$	−8.94424			−0.311777			−0.155888	−	0.987775i	$-0.549824\pi$
$823$	−8.94424			−0.311777			−0.155888	+	0.987775i	$0.549824\pi$
$824$			49.4912i			1.72411i
$825$			0.231676i			0.00806592i
$826$			32.8819i			1.14411i
$827$		−	28.6667i		−	0.996838i	−0.866936	−	0.498419i	$-0.833914\pi$
$827$		−	28.6667i		−	0.996838i	0.866936	−	0.498419i	$-0.166086\pi$
$828$	0.633605			0.0220193
$829$	−39.5515			−1.37368			−0.686839	−	0.726809i	$-0.741002\pi$
$829$	−39.5515			−1.37368			−0.686839	+	0.726809i	$0.741002\pi$
$830$			23.3302i			0.809803i
$831$	−22.1581			−0.768656
$832$	7.79004	+	29.4353i	0.270071	+	1.02049i
$833$	−42.6148			−1.47652
$834$			24.9598i			0.864289i
$835$	37.9569			1.31355
$836$	−0.406536			−0.0140604
$837$		−	0.0727448i		−	0.00251443i
$838$		−	2.64100i		−	0.0912320i
$839$			45.1833i			1.55990i	0.625840	+	0.779951i	$0.284756\pi$
$839$			45.1833i			1.55990i	−0.625840	+	0.779951i	$0.715244\pi$
$840$		−	27.1534i		−	0.936881i
$841$	25.0936			0.865296
$842$	−9.87443			−0.340295
$843$		−	2.12589i		−	0.0732195i
$844$	2.87720			0.0990375
$845$	14.0420	+	24.6712i	0.483058	+	0.848717i
$846$	−15.9166			−0.547222
$847$			4.27070i			0.146743i
$848$	−19.0558			−0.654380
$849$	31.1036			1.06747
$850$			1.20184i			0.0412229i
$851$			18.1218i			0.621208i
$852$		−	1.23356i		−	0.0422611i
$853$		−	13.2579i		−	0.453943i	−0.973901	−	0.226972i	$-0.927118\pi$
$853$		−	13.2579i		−	0.453943i	0.973901	−	0.226972i	$-0.0728825\pi$
$854$	−31.5985			−1.08128
$855$	6.92475			0.236822
$856$		−	36.9254i		−	1.26208i
$857$	−38.9268			−1.32971			−0.664857	−	0.746971i	$-0.731507\pi$
$857$	−38.9268			−1.32971			−0.664857	+	0.746971i	$0.731507\pi$
$858$	1.26204	+	4.76872i	0.0430853	+	0.162801i
$859$	−21.2750			−0.725893			−0.362947	−	0.931810i	$-0.618229\pi$
$859$	−21.2750			−0.725893			−0.362947	+	0.931810i	$0.618229\pi$
$860$			1.99231i			0.0679371i
$861$	17.7970			0.606519
$862$	−40.7535			−1.38807
$863$			8.94497i			0.304490i	0.988343	+	0.152245i	$0.0486504\pi$
$863$			8.94497i			0.304490i	−0.988343	+	0.152245i	$0.951350\pi$
$864$			0.724050i			0.0246327i
$865$		−	26.4001i		−	0.897630i
$866$			34.5412i			1.17376i
$867$	−2.62279			−0.0890746
$868$	−0.0398271			−0.00135182
$869$			10.1209i			0.343329i
$870$	−21.9728			−0.744948
$871$	−35.2547	+	9.33014i	−1.19456	+	0.316140i
$872$	25.9024			0.877166
$873$		−	3.79281i		−	0.128367i
$874$	−21.4433			−0.725331
$875$	−48.7891			−1.64937
$876$			0.826533i			0.0279260i
$877$		−	11.5696i		−	0.390679i	−0.980736	−	0.195340i	$-0.937419\pi$
$877$		−	11.5696i		−	0.390679i	0.980736	−	0.195340i	$-0.0625809\pi$
$878$			12.4105i			0.418835i
$879$			16.9009i			0.570055i
$880$	−8.13884			−0.274360
$881$	13.2958			0.447947			0.223974	−	0.974595i	$-0.428097\pi$
$881$	13.2958			0.447947			0.223974	+	0.974595i	$0.428097\pi$
$882$		−	15.3764i		−	0.517749i
$883$	18.7422			0.630726			0.315363	−	0.948971i	$-0.397874\pi$
$883$	18.7422			0.630726			0.315363	+	0.948971i	$0.397874\pi$
$884$	−0.448392	−	1.69429i	−0.0150811	−	0.0569851i
$885$	12.2888			0.413084
$886$		−	16.5207i		−	0.555024i
$887$	41.6306			1.39782			0.698910	−	0.715210i	$-0.253669\pi$
$887$	41.6306			1.39782			0.698910	+	0.715210i	$0.253669\pi$
$888$	−10.6759			−0.358259
$889$			44.4269i			1.49003i
$890$			8.60148i			0.288322i
$891$			1.00000i			0.0335013i
$892$			2.11966i			0.0709713i
$893$	−36.8927			−1.23457
$894$	19.0149			0.635953
$895$		−	11.2042i		−	0.374514i
$896$	−43.1586			−1.44183
$897$	−4.55914	−	17.2271i	−0.152225	−	0.575196i
$898$	−12.2372			−0.408359
$899$			0.535026i			0.0178441i
$900$	0.0297002			0.000990005
$901$	19.3859			0.645838
$902$		−	5.70134i		−	0.189834i
$903$			30.3945i			1.01146i
$904$			3.97595i			0.132238i
$905$		−	50.9161i		−	1.69251i
$906$	3.14315			0.104424
$907$	−37.0540			−1.23036			−0.615179	−	0.788387i	$-0.710916\pi$
$907$	−37.0540			−1.23036			−0.615179	+	0.788387i	$0.710916\pi$
$908$			2.56172i			0.0850136i
$909$	−12.8641			−0.426676
$910$	−44.4717	+	11.7694i	−1.47422	+	0.390152i
$911$	−43.8739			−1.45361			−0.726804	−	0.686845i	$-0.758995\pi$
$911$	−43.8739			−1.45361			−0.726804	+	0.686845i	$0.758995\pi$
$912$		−	11.8195i		−	0.391384i
$913$	−7.80918			−0.258446
$914$	−38.9885			−1.28962
$915$			11.8092i			0.390400i
$916$			2.03140i			0.0671194i
$917$			51.5378i			1.70193i
$918$			5.18761i			0.171217i
$919$	−30.1561			−0.994759			−0.497380	−	0.867533i	$-0.665704\pi$
$919$	−30.1561			−0.994759			−0.497380	+	0.867533i	$0.665704\pi$
$920$	31.4243			1.03603
$921$		−	24.6110i		−	0.810961i
$922$	−26.3475			−0.867710
$923$	−33.5393	+	8.87617i	−1.10396	+	0.292163i
$924$	0.547491			0.0180111
$925$			0.849459i			0.0279300i
$926$	−49.7508			−1.63491
$927$	16.9975			0.558272
$928$		−	5.32527i		−	0.174810i
$929$			29.2684i			0.960264i	0.877196	+	0.480132i	$0.159411\pi$
$929$			29.2684i			0.960264i	−0.877196	+	0.480132i	$0.840589\pi$
$930$		−	0.217328i		−	0.00712645i
$931$		−	35.6406i		−	1.16807i
$932$	−2.04083			−0.0668496
$933$	1.00504			0.0329034
$934$		−	2.33056i		−	0.0762583i
$935$	8.27981			0.270779
$936$	10.1488	−	2.68587i	0.331723	−	0.0877904i
$937$	−14.7979			−0.483427			−0.241713	−	0.970348i	$-0.577709\pi$
$937$	−14.7979			−0.483427			−0.241713	+	0.970348i	$0.577709\pi$
$938$		−	59.0983i		−	1.92963i
$939$	−13.8744			−0.452774
$940$	3.25672			0.106222
$941$		−	17.5021i		−	0.570553i	−0.958445	−	0.285276i	$-0.907915\pi$
$941$		−	17.5021i		−	0.570553i	0.958445	−	0.285276i	$-0.0920854\pi$
$942$		−	21.3831i		−	0.696698i
$943$			20.5962i			0.670704i
$944$		−	20.9752i		−	0.682686i
$945$	−9.32571			−0.303365
$946$	9.73700			0.316577
$947$			32.5998i			1.05935i	0.848201	+	0.529675i	$0.177686\pi$
$947$			32.5998i			1.05935i	−0.848201	+	0.529675i	$0.822314\pi$
$948$	1.29747			0.0421400
$949$	22.4726	−	5.94737i	0.729493	−	0.193060i
$950$	−1.00515			−0.0326115
$951$		−	15.6405i		−	0.507179i
$952$	47.1496			1.52813
$953$	44.8368			1.45241			0.726204	−	0.687479i	$-0.241283\pi$
$953$	44.8368			1.45241			0.726204	+	0.687479i	$0.241283\pi$
$954$			6.99486i			0.226467i
$955$		−	24.2889i		−	0.785971i
$956$		−	2.17805i		−	0.0704431i
$957$		−	7.35483i		−	0.237748i
$958$	33.6304			1.08655
$959$	16.9168			0.546273
$960$			18.4408i			0.595174i
$961$	30.9947			0.999829
$962$	4.62737	+	17.4849i	0.149192	+	0.563736i
$963$	−12.6819			−0.408667
$964$		−	2.81884i		−	0.0907887i
$965$	50.5874			1.62847
$966$	28.8782			0.929140
$967$		−	21.7225i		−	0.698550i	−0.937020	−	0.349275i	$-0.886428\pi$
$967$		−	21.7225i		−	0.698550i	0.937020	−	0.349275i	$-0.113572\pi$
$968$		−	2.91167i		−	0.0935846i
$969$			12.0243i			0.386275i
$970$		−	11.3311i		−	0.363821i
$971$	−28.7521			−0.922699			−0.461349	−	0.887219i	$-0.652635\pi$
$971$	−28.7521			−0.922699			−0.461349	+	0.887219i	$0.652635\pi$
$972$	0.128197			0.00411192
$973$		−	77.9132i		−	2.49778i
$974$	55.4466			1.77662
$975$	−0.213709	−	0.807519i	−0.00684418	−	0.0258613i
$976$	20.1566			0.645196
$977$		−	13.7868i		−	0.441077i	−0.975378	−	0.220539i	$-0.929218\pi$
$977$		−	13.7868i		−	0.441077i	0.975378	−	0.220539i	$-0.0707815\pi$
$978$	−1.71815			−0.0549404
$979$	−2.87912			−0.0920172
$980$			3.14619i			0.100501i
$981$		−	8.89607i		−	0.284030i
$982$		−	23.0182i		−	0.734540i
$983$		−	32.5478i		−	1.03811i	−0.854740	−	0.519056i	$-0.826284\pi$
$983$		−	32.5478i		−	1.03811i	0.854740	−	0.519056i	$-0.173716\pi$
$984$	−12.1336			−0.386804
$985$	−20.0554			−0.639018
$986$		−	38.1540i		−	1.21507i
$987$	49.6842			1.58146
$988$	1.41700	−	0.375009i	0.0450809	−	0.0119306i
$989$	−35.1751			−1.11850
$990$			2.98753i			0.0949501i
$991$	−3.97937			−0.126409			−0.0632044	−	0.998001i	$-0.520132\pi$
$991$	−3.97937			−0.126409			−0.0632044	+	0.998001i	$0.520132\pi$
$992$	0.0526709			0.00167230
$993$		−	23.1426i		−	0.734409i
$994$		−	56.2227i		−	1.78328i
$995$			13.9521i			0.442312i
$996$			1.00111i			0.0317215i
$997$	−24.9767			−0.791021			−0.395511	−	0.918461i	$-0.629432\pi$
$997$	−24.9767			−0.791021			−0.395511	+	0.918461i	$0.629432\pi$
$998$	39.0125			1.23492
$999$			3.66658i			0.116006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.b.b.298.10	yes	14
3.2	odd	2		1287.2.b.c.298.5		14
13.5	odd	4		5577.2.a.x.1.6		7
13.8	odd	4		5577.2.a.y.1.2		7
13.12	even	2	inner	429.2.b.b.298.5	✓	14
39.38	odd	2		1287.2.b.c.298.10		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.b.b.298.5	✓	14	13.12	even	2	inner
429.2.b.b.298.10	yes	14	1.1	even	1	trivial
1287.2.b.c.298.5		14	3.2	odd	2
1287.2.b.c.298.10		14	39.38	odd	2
5577.2.a.x.1.6		7	13.5	odd	4
5577.2.a.y.1.2		7	13.8	odd	4

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.36814i q^{2} +1.00000 q^{3} +0.128197 q^{4} -2.18365i q^{5} +1.36814i q^{6} -4.27070i q^{7} +2.91167i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.36814i q^{2} +1.00000 q^{3} +0.128197 q^{4} -2.18365i q^{5} +1.36814i q^{6} -4.27070i q^{7} +2.91167i q^{8} +1.00000 q^{9} +2.98753 q^{10} +1.00000i q^{11} +0.128197 q^{12} +(-0.922450 - 3.48555i) q^{13} +5.84291 q^{14} -2.18365i q^{15} -3.72717 q^{16} +3.79173 q^{17} +1.36814i q^{18} +3.17118i q^{19} -0.279937i q^{20} -4.27070i q^{21} -1.36814 q^{22} +4.94243 q^{23} +2.91167i q^{24} +0.231676 q^{25} +(4.76872 - 1.26204i) q^{26} +1.00000 q^{27} -0.547491i q^{28} -7.35483 q^{29} +2.98753 q^{30} -0.0727448i q^{31} +0.724050i q^{32} +1.00000i q^{33} +5.18761i q^{34} -9.32571 q^{35} +0.128197 q^{36} +3.66658i q^{37} -4.33862 q^{38} +(-0.922450 - 3.48555i) q^{39} +6.35806 q^{40} +4.16722i q^{41} +5.84291 q^{42} -7.11697 q^{43} +0.128197i q^{44} -2.18365i q^{45} +6.76193i q^{46} +11.6337i q^{47} -3.72717 q^{48} -11.2389 q^{49} +0.316965i q^{50} +3.79173 q^{51} +(-0.118255 - 0.446838i) q^{52} +5.11268 q^{53} +1.36814i q^{54} +2.18365 q^{55} +12.4349 q^{56} +3.17118i q^{57} -10.0624i q^{58} +5.62765i q^{59} -0.279937i q^{60} -5.40800 q^{61} +0.0995250 q^{62} -4.27070i q^{63} -8.44494 q^{64} +(-7.61123 + 2.01431i) q^{65} -1.36814 q^{66} -10.1145i q^{67} +0.486088 q^{68} +4.94243 q^{69} -12.7589i q^{70} -9.62239i q^{71} +2.91167i q^{72} +6.44736i q^{73} -5.01639 q^{74} +0.231676 q^{75} +0.406536i q^{76} +4.27070 q^{77} +(4.76872 - 1.26204i) q^{78} +10.1209 q^{79} +8.13884i q^{80} +1.00000 q^{81} -5.70134 q^{82} +7.80918i q^{83} -0.547491i q^{84} -8.27981i q^{85} -9.73700i q^{86} -7.35483 q^{87} -2.91167 q^{88} +2.87912i q^{89} +2.98753 q^{90} +(-14.8858 + 3.93951i) q^{91} +0.633605 q^{92} -0.0727448i q^{93} -15.9166 q^{94} +6.92475 q^{95} +0.724050i q^{96} -3.79281i q^{97} -15.3764i q^{98} +1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 14 q^{3} - 18 q^{4} + 14 q^{9}+O(q^{10}) \) 14 * q + 14 * q^3 - 18 * q^4 + 14 * q^9	\( 14 q + 14 q^{3} - 18 q^{4} + 14 q^{9} - 18 q^{12} + 16 q^{14} + 34 q^{16} + 4 q^{17} + 6 q^{22} - 8 q^{23} - 26 q^{25} - 6 q^{26} + 14 q^{27} - 24 q^{29} - 8 q^{35} - 18 q^{36} - 32 q^{38} - 20 q^{40} + 16 q^{42} + 32 q^{43} + 34 q^{48} - 46 q^{49} + 4 q^{51} + 4 q^{52} + 20 q^{53} + 12 q^{55} - 32 q^{56} - 20 q^{61} + 72 q^{62} - 58 q^{64} + 12 q^{65} + 6 q^{66} - 20 q^{68} - 8 q^{69} - 26 q^{75} - 12 q^{77} - 6 q^{78} + 12 q^{79} + 14 q^{81} + 20 q^{82} - 24 q^{87} - 30 q^{88} + 16 q^{91} - 24 q^{92} + 64 q^{94} - 36 q^{95}+O(q^{100}) \) 14 * q + 14 * q^3 - 18 * q^4 + 14 * q^9 - 18 * q^12 + 16 * q^14 + 34 * q^16 + 4 * q^17 + 6 * q^22 - 8 * q^23 - 26 * q^25 - 6 * q^26 + 14 * q^27 - 24 * q^29 - 8 * q^35 - 18 * q^36 - 32 * q^38 - 20 * q^40 + 16 * q^42 + 32 * q^43 + 34 * q^48 - 46 * q^49 + 4 * q^51 + 4 * q^52 + 20 * q^53 + 12 * q^55 - 32 * q^56 - 20 * q^61 + 72 * q^62 - 58 * q^64 + 12 * q^65 + 6 * q^66 - 20 * q^68 - 8 * q^69 - 26 * q^75 - 12 * q^77 - 6 * q^78 + 12 * q^79 + 14 * q^81 + 20 * q^82 - 24 * q^87 - 30 * q^88 + 16 * q^91 - 24 * q^92 + 64 * q^94 - 36 * q^95

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