LMFDB - Embedded newform 65.2.b.a.14.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,2,Mod(14,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("65.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	65.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:	$0.519027613138$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			14.4
Root			$1.45161 - 1.45161i$ of defining polynomial
Character	$\chi$	$=$	65.14
Dual form			65.2.b.a.14.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.21432i q^{2} +1.31111i q^{3} +0.525428 q^{4} +(-2.21432 - 0.311108i) q^{5} -1.59210 q^{6} -2.90321i q^{7} +3.06668i q^{8} +1.28100 q^{9} +O(q^{10})$	\(q+1.21432i q^{2} +1.31111i q^{3} +0.525428 q^{4} +(-2.21432 - 0.311108i) q^{5} -1.59210 q^{6} -2.90321i q^{7} +3.06668i q^{8} +1.28100 q^{9} +(0.377784 - 2.68889i) q^{10} +0.214320 q^{11} +0.688892i q^{12} -1.00000i q^{13} +3.52543 q^{14} +(0.407896 - 2.90321i) q^{15} -2.67307 q^{16} -6.42864i q^{17} +1.55554i q^{18} -2.21432 q^{19} +(-1.16346 - 0.163465i) q^{20} +3.80642 q^{21} +0.260253i q^{22} +4.68889i q^{23} -4.02074 q^{24} +(4.80642 + 1.37778i) q^{25} +1.21432 q^{26} +5.61285i q^{27} -1.52543i q^{28} -8.70964 q^{29} +(3.52543 + 0.495316i) q^{30} -5.59210 q^{31} +2.88739i q^{32} +0.280996i q^{33} +7.80642 q^{34} +(-0.903212 + 6.42864i) q^{35} +0.673071 q^{36} -2.28100i q^{37} -2.68889i q^{38} +1.31111 q^{39} +(0.954067 - 6.79060i) q^{40} +3.05086 q^{41} +4.62222i q^{42} +6.36196i q^{43} +0.112610 q^{44} +(-2.83654 - 0.398528i) q^{45} -5.69381 q^{46} -1.09679i q^{47} -3.50468i q^{48} -1.42864 q^{49} +(-1.67307 + 5.83654i) q^{50} +8.42864 q^{51} -0.525428i q^{52} -6.23506i q^{53} -6.81579 q^{54} +(-0.474572 - 0.0666765i) q^{55} +8.90321 q^{56} -2.90321i q^{57} -10.5763i q^{58} +9.26517 q^{59} +(0.214320 - 1.52543i) q^{60} -0.280996 q^{61} -6.79060i q^{62} -3.71900i q^{63} -8.85236 q^{64} +(-0.311108 + 2.21432i) q^{65} -0.341219 q^{66} +7.76049i q^{67} -3.37778i q^{68} -6.14764 q^{69} +(-7.80642 - 1.09679i) q^{70} -6.08097 q^{71} +3.92840i q^{72} -10.2810i q^{73} +2.76986 q^{74} +(-1.80642 + 6.30174i) q^{75} -1.16346 q^{76} -0.622216i q^{77} +1.59210i q^{78} +14.2351 q^{79} +(5.91903 + 0.831613i) q^{80} -3.51606 q^{81} +3.70471i q^{82} +9.52543i q^{83} +2.00000 q^{84} +(-2.00000 + 14.2351i) q^{85} -7.72546 q^{86} -11.4193i q^{87} +0.657249i q^{88} +5.61285 q^{89} +(0.483940 - 3.44446i) q^{90} -2.90321 q^{91} +2.46367i q^{92} -7.33185i q^{93} +1.33185 q^{94} +(4.90321 + 0.688892i) q^{95} -3.78568 q^{96} +18.0415i q^{97} -1.73483i q^{98} +0.274543 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 10 q^{4} + 4 q^{6} - 6 q^{9}+O(q^{10}) $ 6 * q - 10 * q^4 + 4 * q^6 - 6 * q^9	$ 6 q - 10 q^{4} + 4 q^{6} - 6 q^{9} + 2 q^{10} - 12 q^{11} + 8 q^{14} + 16 q^{15} + 10 q^{16} - 20 q^{20} - 4 q^{21} + 16 q^{24} + 2 q^{25} - 6 q^{26} - 12 q^{29} + 8 q^{30} - 20 q^{31} + 20 q^{34} + 8 q^{35} - 22 q^{36} + 8 q^{39} - 34 q^{40} - 8 q^{41} + 40 q^{44} - 4 q^{45} + 32 q^{46} + 18 q^{49} + 16 q^{50} + 24 q^{51} - 68 q^{54} - 16 q^{55} + 40 q^{56} + 16 q^{59} - 12 q^{60} + 12 q^{61} - 66 q^{64} - 2 q^{65} - 16 q^{66} - 24 q^{69} - 20 q^{70} - 24 q^{71} + 4 q^{74} + 16 q^{75} - 20 q^{76} + 32 q^{79} + 48 q^{80} + 46 q^{81} + 12 q^{84} - 12 q^{85} - 32 q^{86} - 20 q^{89} + 70 q^{90} - 4 q^{91} - 32 q^{94} + 16 q^{95} - 36 q^{96} + 16 q^{99}+O(q^{100}) $ 6 * q - 10 * q^4 + 4 * q^6 - 6 * q^9 + 2 * q^10 - 12 * q^11 + 8 * q^14 + 16 * q^15 + 10 * q^16 - 20 * q^20 - 4 * q^21 + 16 * q^24 + 2 * q^25 - 6 * q^26 - 12 * q^29 + 8 * q^30 - 20 * q^31 + 20 * q^34 + 8 * q^35 - 22 * q^36 + 8 * q^39 - 34 * q^40 - 8 * q^41 + 40 * q^44 - 4 * q^45 + 32 * q^46 + 18 * q^49 + 16 * q^50 + 24 * q^51 - 68 * q^54 - 16 * q^55 + 40 * q^56 + 16 * q^59 - 12 * q^60 + 12 * q^61 - 66 * q^64 - 2 * q^65 - 16 * q^66 - 24 * q^69 - 20 * q^70 - 24 * q^71 + 4 * q^74 + 16 * q^75 - 20 * q^76 + 32 * q^79 + 48 * q^80 + 46 * q^81 + 12 * q^84 - 12 * q^85 - 32 * q^86 - 20 * q^89 + 70 * q^90 - 4 * q^91 - 32 * q^94 + 16 * q^95 - 36 * q^96 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$1$

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 $

$2$			1.21432i			0.858654i	0.903149	+	0.429327i	$0.141249\pi$
$2$			1.21432i			0.858654i	−0.903149	+	0.429327i	$0.858751\pi$
$3$			1.31111i			0.756968i	0.925608	+	0.378484i	$0.123555\pi$
$3$			1.31111i			0.756968i	−0.925608	+	0.378484i	$0.876445\pi$
$4$	0.525428			0.262714
$5$	−2.21432	−	0.311108i	−0.990274	−	0.139132i
$5$	−2.21432	−	0.311108i	−0.990274	−	0.139132i
$6$	−1.59210			−0.649974
$7$		−	2.90321i		−	1.09731i	−0.836049	−	0.548655i	$-0.815140\pi$
$7$		−	2.90321i		−	1.09731i	0.836049	−	0.548655i	$-0.184860\pi$
$8$			3.06668i			1.08423i
$9$	1.28100			0.426999
$10$	0.377784	−	2.68889i	0.119466	−	0.850302i
$11$	0.214320			0.0646198			0.0323099	−	0.999478i	$-0.489714\pi$
$11$	0.214320			0.0646198			0.0323099	+	0.999478i	$0.489714\pi$
$12$			0.688892i			0.198866i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	3.52543			0.942210
$15$	0.407896	−	2.90321i	0.105318	−	0.749606i
$16$	−2.67307			−0.668268
$17$		−	6.42864i		−	1.55917i	−0.626294	−	0.779587i	$-0.715429\pi$
$17$		−	6.42864i		−	1.55917i	0.626294	−	0.779587i	$-0.284571\pi$
$18$			1.55554i			0.366644i
$19$	−2.21432			−0.508000			−0.254000	−	0.967204i	$-0.581746\pi$
$19$	−2.21432			−0.508000			−0.254000	+	0.967204i	$0.581746\pi$
$20$	−1.16346	−	0.163465i	−0.260159	−	0.0365518i
$21$	3.80642			0.830630
$22$			0.260253i			0.0554861i
$23$			4.68889i			0.977702i	0.872367	+	0.488851i	$0.162584\pi$
$23$			4.68889i			0.977702i	−0.872367	+	0.488851i	$0.837416\pi$
$24$	−4.02074			−0.820731
$25$	4.80642	+	1.37778i	0.961285	+	0.275557i
$26$	1.21432			0.238148
$27$			5.61285i			1.08019i
$28$		−	1.52543i		−	0.288279i
$29$	−8.70964			−1.61734			−0.808669	−	0.588263i	$-0.799812\pi$
$29$	−8.70964			−1.61734			−0.808669	+	0.588263i	$0.799812\pi$
$30$	3.52543	+	0.495316i	0.643652	+	0.0904319i
$31$	−5.59210			−1.00437			−0.502186	−	0.864760i	$-0.667471\pi$
$31$	−5.59210			−1.00437			−0.502186	+	0.864760i	$0.667471\pi$
$32$			2.88739i			0.510423i
$33$			0.280996i			0.0489152i
$34$	7.80642			1.33879
$35$	−0.903212	+	6.42864i	−0.152671	+	1.08664i
$36$	0.673071			0.112178
$37$		−	2.28100i		−	0.374993i	−0.982265	−	0.187497i	$-0.939963\pi$
$37$		−	2.28100i		−	0.374993i	0.982265	−	0.187497i	$-0.0600374\pi$
$38$		−	2.68889i		−	0.436196i
$39$	1.31111			0.209945
$40$	0.954067	−	6.79060i	0.150851	−	1.07369i
$41$	3.05086			0.476464			0.238232	−	0.971208i	$-0.423432\pi$
$41$	3.05086			0.476464			0.238232	+	0.971208i	$0.423432\pi$
$42$			4.62222i			0.713223i
$43$			6.36196i			0.970190i	0.874461	+	0.485095i	$0.161215\pi$
$43$			6.36196i			0.970190i	−0.874461	+	0.485095i	$0.838785\pi$
$44$	0.112610			0.0169765
$45$	−2.83654	−	0.398528i	−0.422846	−	0.0594090i
$46$	−5.69381			−0.839507
$47$		−	1.09679i		−	0.159983i	−0.996796	−	0.0799915i	$-0.974511\pi$
$47$		−	1.09679i		−	0.159983i	0.996796	−	0.0799915i	$-0.0254893\pi$
$48$		−	3.50468i		−	0.505858i
$49$	−1.42864			−0.204091
$50$	−1.67307	+	5.83654i	−0.236608	+	0.825411i
$51$	8.42864			1.18025
$52$		−	0.525428i		−	0.0728637i
$53$		−	6.23506i		−	0.856452i	−0.903672	−	0.428226i	$-0.859139\pi$
$53$		−	6.23506i		−	0.856452i	0.903672	−	0.428226i	$-0.140861\pi$
$54$	−6.81579			−0.927512
$55$	−0.474572	−	0.0666765i	−0.0639913	−	0.00899066i
$56$	8.90321			1.18974
$57$		−	2.90321i		−	0.384540i
$58$		−	10.5763i		−	1.38873i
$59$	9.26517			1.20622			0.603112	−	0.797657i	$-0.293927\pi$
$59$	9.26517			1.20622			0.603112	+	0.797657i	$0.293927\pi$
$60$	0.214320	−	1.52543i	0.0276686	−	0.196932i
$61$	−0.280996			−0.0359779			−0.0179889	−	0.999838i	$-0.505726\pi$
$61$	−0.280996			−0.0359779			−0.0179889	+	0.999838i	$0.505726\pi$
$62$		−	6.79060i		−	0.862407i
$63$		−	3.71900i		−	0.468550i
$64$	−8.85236			−1.10654
$65$	−0.311108	+	2.21432i	−0.0385882	+	0.274653i
$66$	−0.341219			−0.0420012
$67$			7.76049i			0.948095i	0.880499	+	0.474047i	$0.157207\pi$
$67$			7.76049i			0.948095i	−0.880499	+	0.474047i	$0.842793\pi$
$68$		−	3.37778i		−	0.409617i
$69$	−6.14764			−0.740089
$70$	−7.80642	−	1.09679i	−0.933046	−	0.131091i
$71$	−6.08097			−0.721678			−0.360839	−	0.932628i	$-0.617510\pi$
$71$	−6.08097			−0.721678			−0.360839	+	0.932628i	$0.617510\pi$
$72$			3.92840i			0.462967i
$73$		−	10.2810i		−	1.20330i	−0.798760	−	0.601650i	$-0.794510\pi$
$73$		−	10.2810i		−	1.20330i	0.798760	−	0.601650i	$-0.205490\pi$
$74$	2.76986			0.321990
$75$	−1.80642	+	6.30174i	−0.208588	+	0.727662i
$76$	−1.16346			−0.133459
$77$		−	0.622216i		−	0.0709081i
$78$			1.59210i			0.180270i
$79$	14.2351			1.60157			0.800785	−	0.598952i	$-0.204416\pi$
$79$	14.2351			1.60157			0.800785	+	0.598952i	$0.204416\pi$
$80$	5.91903	+	0.831613i	0.661768	+	0.0929772i
$81$	−3.51606			−0.390673
$82$			3.70471i			0.409117i
$83$			9.52543i			1.04555i	0.852470	+	0.522776i	$0.175103\pi$
$83$			9.52543i			1.04555i	−0.852470	+	0.522776i	$0.824897\pi$
$84$	2.00000			0.218218
$85$	−2.00000	+	14.2351i	−0.216930	+	1.54401i
$86$	−7.72546			−0.833057
$87$		−	11.4193i		−	1.22427i
$88$			0.657249i			0.0700630i
$89$	5.61285			0.594961			0.297480	−	0.954728i	$-0.403854\pi$
$89$	5.61285			0.594961			0.297480	+	0.954728i	$0.403854\pi$
$90$	0.483940	−	3.44446i	0.0510118	−	0.363078i
$91$	−2.90321			−0.304339
$92$			2.46367i			0.256856i
$93$		−	7.33185i		−	0.760278i
$94$	1.33185			0.137370
$95$	4.90321	+	0.688892i	0.503059	+	0.0706788i
$96$	−3.78568			−0.386374
$97$			18.0415i			1.83184i	0.401366	+	0.915918i	$0.368536\pi$
$97$			18.0415i			1.83184i	−0.401366	+	0.915918i	$0.631464\pi$
$98$		−	1.73483i		−	0.175244i
$99$	0.274543			0.0275926
$100$	2.52543	+	0.723926i	0.252543	+	0.0723926i
$101$	3.93978			0.392022			0.196011	−	0.980602i	$-0.437201\pi$
$101$	3.93978			0.392022			0.196011	+	0.980602i	$0.437201\pi$
$102$			10.2351i			1.01342i
$103$			2.82225i			0.278084i	0.990286	+	0.139042i	$0.0444023\pi$
$103$			2.82225i			0.278084i	−0.990286	+	0.139042i	$0.955598\pi$
$104$	3.06668			0.300712
$105$	−8.42864	−	1.18421i	−0.822551	−	0.115567i
$106$	7.57136			0.735396
$107$		−	17.1175i		−	1.65481i	−0.561603	−	0.827407i	$-0.689815\pi$
$107$		−	17.1175i		−	1.65481i	0.561603	−	0.827407i	$-0.310185\pi$
$108$			2.94914i			0.283782i
$109$	16.7239			1.60186			0.800931	−	0.598757i	$-0.204338\pi$
$109$	16.7239			1.60186			0.800931	+	0.598757i	$0.204338\pi$
$110$	0.0809666	−	0.576283i	0.00771987	−	0.0549464i
$111$	2.99063			0.283858
$112$			7.76049i			0.733297i
$113$			1.18421i			0.111401i	0.998448	+	0.0557005i	$0.0177392\pi$
$113$			1.18421i			0.111401i	−0.998448	+	0.0557005i	$0.982261\pi$
$114$	3.52543			0.330187
$115$	1.45875	−	10.3827i	0.136029	−	0.968192i
$116$	−4.57628			−0.424897
$117$		−	1.28100i		−	0.118428i
$118$			11.2509i			1.03573i
$119$	−18.6637			−1.71090
$120$	8.90321	+	1.25088i	0.812748	+	0.114190i
$121$	−10.9541			−0.995824
$122$		−	0.341219i		−	0.0308925i
$123$			4.00000i			0.360668i
$124$	−2.93825			−0.263862
$125$	−10.2143	−	4.54617i	−0.913597	−	0.406622i
$126$	4.51606			0.402323
$127$		−	2.30174i		−	0.204246i	−0.994772	−	0.102123i	$-0.967436\pi$
$127$		−	2.30174i		−	0.204246i	0.994772	−	0.102123i	$-0.0325636\pi$
$128$		−	4.97481i		−	0.439715i
$129$	−8.34122			−0.734403
$130$	−2.68889	−	0.377784i	−0.235831	−	0.0331339i
$131$	−13.4193			−1.17245			−0.586224	−	0.810149i	$-0.699386\pi$
$131$	−13.4193			−1.17245			−0.586224	+	0.810149i	$0.699386\pi$
$132$			0.147643i			0.0128507i
$133$			6.42864i			0.557434i
$134$	−9.42372			−0.814085
$135$	1.74620	−	12.4286i	0.150289	−	1.06969i
$136$	19.7146			1.69051
$137$		−	19.1526i		−	1.63631i	−0.574995	−	0.818157i	$-0.694996\pi$
$137$		−	19.1526i		−	1.63631i	0.574995	−	0.818157i	$-0.305004\pi$
$138$		−	7.46520i		−	0.635480i
$139$	−19.0923			−1.61939			−0.809696	−	0.586850i	$-0.800368\pi$
$139$	−19.0923			−1.61939			−0.809696	+	0.586850i	$0.800368\pi$
$140$	−0.474572	+	3.37778i	−0.0401087	+	0.285475i
$141$	1.43801			0.121102
$142$		−	7.38424i		−	0.619671i
$143$		−	0.214320i		−	0.0179223i
$144$	−3.42419			−0.285349
$145$	19.2859	+	2.70964i	1.60161	+	0.225023i
$146$	12.4844			1.03322
$147$		−	1.87310i		−	0.154491i
$148$		−	1.19850i		−	0.0985160i
$149$	3.57136			0.292577			0.146289	−	0.989242i	$-0.453267\pi$
$149$	3.57136			0.292577			0.146289	+	0.989242i	$0.453267\pi$
$150$	−7.65233	−	2.19358i	−0.624810	−	0.179105i
$151$	−1.26517			−0.102958			−0.0514792	−	0.998674i	$-0.516394\pi$
$151$	−1.26517			−0.102958			−0.0514792	+	0.998674i	$0.516394\pi$
$152$		−	6.79060i		−	0.550791i
$153$		−	8.23506i		−	0.665765i
$154$	0.755569			0.0608855
$155$	12.3827	+	1.73975i	0.994603	+	0.139740i
$156$	0.688892			0.0551555
$157$			5.61285i			0.447954i	0.974594	+	0.223977i	$0.0719041\pi$
$157$			5.61285i			0.447954i	−0.974594	+	0.223977i	$0.928096\pi$
$158$			17.2859i			1.37519i
$159$	8.17484			0.648307
$160$	0.898290	−	6.39361i	0.0710160	−	0.505459i
$161$	13.6128			1.07284
$162$		−	4.26962i		−	0.335453i
$163$			3.71900i			0.291295i	0.989337	+	0.145647i	$0.0465265\pi$
$163$			3.71900i			0.291295i	−0.989337	+	0.145647i	$0.953473\pi$
$164$	1.60300			0.125174
$165$	0.0874201	−	0.622216i	0.00680565	−	0.0484394i
$166$	−11.5669			−0.897767
$167$			7.03657i			0.544506i	0.962226	+	0.272253i	$0.0877687\pi$
$167$			7.03657i			0.544506i	−0.962226	+	0.272253i	$0.912231\pi$
$168$			11.6731i			0.900597i
$169$	−1.00000			−0.0769231
$170$	−17.2859	−	2.42864i	−1.32577	−	0.186268i
$171$	−2.83654			−0.216915
$172$			3.34275i			0.254882i
$173$			0.723926i			0.0550391i	0.999621	+	0.0275195i	$0.00876085\pi$
$173$			0.723926i			0.0550391i	−0.999621	+	0.0275195i	$0.991239\pi$
$174$	13.8666			1.05123
$175$	4.00000	−	13.9541i	0.302372	−	1.05483i
$176$	−0.572892			−0.0431833
$177$			12.1476i			0.913073i
$178$			6.81579i			0.510865i
$179$	4.04149			0.302075			0.151037	−	0.988528i	$-0.451739\pi$
$179$	4.04149			0.302075			0.151037	+	0.988528i	$0.451739\pi$
$180$	−1.49039	−	0.209398i	−0.111087	−	0.0156076i
$181$	2.34122			0.174021			0.0870107	−	0.996207i	$-0.472269\pi$
$181$	2.34122			0.174021			0.0870107	+	0.996207i	$0.472269\pi$
$182$		−	3.52543i		−	0.261322i
$183$		−	0.368416i		−	0.0272341i
$184$	−14.3793			−1.06006
$185$	−0.709636	+	5.05086i	−0.0521735	+	0.371346i
$186$	8.90321			0.652815
$187$		−	1.37778i		−	0.100754i
$188$		−	0.576283i		−	0.0420297i
$189$	16.2953			1.18531
$190$	−0.836535	+	5.95407i	−0.0606887	+	0.431953i
$191$	−2.10171			−0.152074			−0.0760372	−	0.997105i	$-0.524227\pi$
$191$	−2.10171			−0.152074			−0.0760372	+	0.997105i	$0.524227\pi$
$192$		−	11.6064i		−	0.837619i
$193$			13.5210i			0.973262i	0.873608	+	0.486631i	$0.161774\pi$
$193$			13.5210i			0.973262i	−0.873608	+	0.486631i	$0.838226\pi$
$194$	−21.9081			−1.57291
$195$	−2.90321	−	0.407896i	−0.207903	−	0.0292100i
$196$	−0.750647			−0.0536176
$197$		−	2.00000i		−	0.142494i	−0.997459	−	0.0712470i	$-0.977302\pi$
$197$		−	2.00000i		−	0.142494i	0.997459	−	0.0712470i	$-0.0226979\pi$
$198$			0.333383i			0.0236925i
$199$	−22.1432			−1.56969			−0.784845	−	0.619692i	$-0.787257\pi$
$199$	−22.1432			−1.56969			−0.784845	+	0.619692i	$0.787257\pi$
$200$	−4.22522	+	14.7397i	−0.298768	+	1.04226i
$201$	−10.1748			−0.717678
$202$			4.78415i			0.336612i
$203$			25.2859i			1.77472i
$204$	4.42864			0.310067
$205$	−6.75557	−	0.949145i	−0.471829	−	0.0662912i
$206$	−3.42711			−0.238778
$207$			6.00645i			0.417477i
$208$			2.67307i			0.185344i
$209$	−0.474572			−0.0328269
$210$	1.43801	−	10.2351i	0.0992319	−	0.706286i
$211$	19.6543			1.35306			0.676530	−	0.736415i	$-0.263483\pi$
$211$	19.6543			1.35306			0.676530	+	0.736415i	$0.263483\pi$
$212$		−	3.27607i		−	0.225002i
$213$		−	7.97280i		−	0.546287i
$214$	20.7862			1.42091
$215$	1.97926	−	14.0874i	0.134984	−	0.960754i
$216$	−17.2128			−1.17118
$217$			16.2351i			1.10211i
$218$			20.3082i			1.37544i
$219$	13.4795			0.910860
$220$	−0.249353	−	0.0350337i	−0.0168114	−	0.00236197i
$221$	−6.42864			−0.432437
$222$			3.63158i			0.243736i
$223$		−	19.6686i		−	1.31711i	−0.752533	−	0.658554i	$-0.771168\pi$
$223$		−	19.6686i		−	1.31711i	0.752533	−	0.658554i	$-0.228832\pi$
$224$	8.38271			0.560093
$225$	6.15701	+	1.76494i	0.410467	+	0.117662i
$226$	−1.43801			−0.0956548
$227$		−	13.2716i		−	0.880869i	−0.897785	−	0.440434i	$-0.854824\pi$
$227$		−	13.2716i		−	0.880869i	0.897785	−	0.440434i	$-0.145176\pi$
$228$		−	1.52543i		−	0.101024i
$229$	2.42864			0.160489			0.0802445	−	0.996775i	$-0.474430\pi$
$229$	2.42864			0.160489			0.0802445	+	0.996775i	$0.474430\pi$
$230$	12.6079	+	1.77139i	0.831342	+	0.116802i
$231$	0.815792			0.0536752
$232$		−	26.7096i		−	1.75357i
$233$		−	16.1748i		−	1.05965i	−0.848107	−	0.529825i	$-0.822258\pi$
$233$		−	16.1748i		−	1.05965i	0.848107	−	0.529825i	$-0.177742\pi$
$234$	1.55554			0.101689
$235$	−0.341219	+	2.42864i	−0.0222587	+	0.158427i
$236$	4.86818			0.316891
$237$			18.6637i			1.21234i
$238$		−	22.6637i		−	1.46907i
$239$	12.7763			0.826431			0.413215	−	0.910633i	$-0.364406\pi$
$239$	12.7763			0.826431			0.413215	+	0.910633i	$0.364406\pi$
$240$	−1.09033	+	7.76049i	−0.0703808	+	0.500938i
$241$	−5.89829			−0.379942			−0.189971	−	0.981790i	$-0.560839\pi$
$241$	−5.89829			−0.379942			−0.189971	+	0.981790i	$0.560839\pi$
$242$		−	13.3017i		−	0.855068i
$243$			12.2286i			0.784466i
$244$	−0.147643			−0.00945189
$245$	3.16346	+	0.444461i	0.202106	+	0.0283956i
$246$	−4.85728			−0.309689
$247$			2.21432i			0.140894i
$248$		−	17.1492i		−	1.08897i
$249$	−12.4889			−0.791450
$250$	5.52051	−	12.4035i	0.349147	−	0.784463i
$251$	−2.07313			−0.130855			−0.0654274	−	0.997857i	$-0.520841\pi$
$251$	−2.07313			−0.130855			−0.0654274	+	0.997857i	$0.520841\pi$
$252$		−	1.95407i		−	0.123095i
$253$			1.00492i			0.0631789i
$254$	2.79505			0.175377
$255$	−18.6637	−	2.62222i	−1.16877	−	0.164210i
$256$	−11.6637			−0.728981
$257$			18.3970i			1.14757i	0.819005	+	0.573787i	$0.194526\pi$
$257$			18.3970i			1.14757i	−0.819005	+	0.573787i	$0.805474\pi$
$258$		−	10.1289i		−	0.630598i
$259$	−6.62222			−0.411484
$260$	−0.163465	+	1.16346i	−0.0101376	+	0.0721550i
$261$	−11.1570			−0.690602
$262$		−	16.2953i		−	1.00673i
$263$		−	11.0257i		−	0.679872i	−0.940449	−	0.339936i	$-0.889595\pi$
$263$		−	11.0257i		−	0.679872i	0.940449	−	0.339936i	$-0.110405\pi$
$264$	−0.861725			−0.0530355
$265$	−1.93978	+	13.8064i	−0.119160	+	0.848122i
$266$	−7.80642			−0.478643
$267$			7.35905i			0.450366i
$268$			4.07758i			0.249078i
$269$	16.1432			0.984268			0.492134	−	0.870519i	$-0.336217\pi$
$269$	16.1432			0.984268			0.492134	+	0.870519i	$0.336217\pi$
$270$	15.0923	+	2.12045i	0.918491	+	0.129046i
$271$	13.0114			0.790385			0.395192	−	0.918598i	$-0.370678\pi$
$271$	13.0114			0.790385			0.395192	+	0.918598i	$0.370678\pi$
$272$			17.1842i			1.04195i
$273$		−	3.80642i		−	0.230375i
$274$	23.2573			1.40503
$275$	1.03011	+	0.295286i	0.0621181	+	0.0178064i
$276$	−3.23014			−0.194432
$277$			7.57136i			0.454919i	0.973788	+	0.227459i	$0.0730419\pi$
$277$			7.57136i			0.454919i	−0.973788	+	0.227459i	$0.926958\pi$
$278$		−	23.1842i		−	1.39050i
$279$	−7.16346			−0.428865
$280$	−19.7146	−	2.76986i	−1.17817	−	0.165531i
$281$	6.75557			0.403003			0.201502	−	0.979488i	$-0.435418\pi$
$281$	6.75557			0.403003			0.201502	+	0.979488i	$0.435418\pi$
$282$			1.74620i			0.103985i
$283$		−	19.0859i		−	1.13454i	−0.823532	−	0.567269i	$-0.808000\pi$
$283$		−	19.0859i		−	1.13454i	0.823532	−	0.567269i	$-0.192000\pi$
$284$	−3.19511			−0.189595
$285$	−0.903212	+	6.42864i	−0.0535017	+	0.380800i
$286$	0.260253			0.0153891
$287$		−	8.85728i		−	0.522829i
$288$			3.69874i			0.217950i
$289$	−24.3274			−1.43102
$290$	−3.29036	+	23.4193i	−0.193217	+	1.37523i
$291$	−23.6543			−1.38664
$292$		−	5.40192i		−	0.316123i
$293$			8.08742i			0.472472i	0.971696	+	0.236236i	$0.0759139\pi$
$293$			8.08742i			0.472472i	−0.971696	+	0.236236i	$0.924086\pi$
$294$	2.27454			0.132654
$295$	−20.5161	−	2.88247i	−1.19449	−	0.167824i
$296$	6.99508			0.406581
$297$			1.20294i			0.0698019i
$298$			4.33677i			0.251223i
$299$	4.68889			0.271166
$300$	−0.949145	+	3.31111i	−0.0547989	+	0.191167i
$301$	18.4701			1.06460
$302$		−	1.53633i		−	0.0884057i
$303$			5.16547i			0.296749i
$304$	5.91903			0.339480
$305$	0.622216	+	0.0874201i	0.0356280	+	0.00500566i
$306$	10.0000			0.571662
$307$		−	13.4336i		−	0.766694i	−0.923604	−	0.383347i	$-0.874771\pi$
$307$		−	13.4336i		−	0.766694i	0.923604	−	0.383347i	$-0.125229\pi$
$308$		−	0.326929i		−	0.0186285i
$309$	−3.70027			−0.210501
$310$	−2.11261	+	15.0366i	−0.119988	+	0.854020i
$311$	20.2034			1.14563			0.572815	−	0.819684i	$-0.305851\pi$
$311$	20.2034			1.14563			0.572815	+	0.819684i	$0.305851\pi$
$312$			4.02074i			0.227630i
$313$		−	15.1111i		−	0.854129i	−0.904221	−	0.427064i	$-0.859548\pi$
$313$		−	15.1111i		−	0.854129i	0.904221	−	0.427064i	$-0.140452\pi$
$314$	−6.81579			−0.384637
$315$	−1.15701	+	8.23506i	−0.0651902	+	0.463993i
$316$	7.47949			0.420754
$317$			22.2810i			1.25143i	0.780054	+	0.625713i	$0.215192\pi$
$317$			22.2810i			1.25143i	−0.780054	+	0.625713i	$0.784808\pi$
$318$			9.92687i			0.556671i
$319$	−1.86665			−0.104512
$320$	19.6019	+	2.75404i	1.09578	+	0.153955i
$321$	22.4429			1.25264
$322$			16.5303i			0.921200i
$323$			14.2351i			0.792060i
$324$	−1.84743			−0.102635
$325$	1.37778	−	4.80642i	0.0764257	−	0.266612i
$326$	−4.51606			−0.250121
$327$			21.9269i			1.21256i
$328$			9.35599i			0.516598i
$329$	−3.18421			−0.175551
$330$	0.755569	+	0.106156i	0.0415927	+	0.00584370i
$331$	8.25581			0.453780			0.226890	−	0.973920i	$-0.427144\pi$
$331$	8.25581			0.453780			0.226890	+	0.973920i	$0.427144\pi$
$332$			5.00492i			0.274681i
$333$		−	2.92195i		−	0.160122i
$334$	−8.54464			−0.467542
$335$	2.41435	−	17.1842i	0.131910	−	0.938874i
$336$	−10.1748			−0.555083
$337$		−	13.7462i		−	0.748803i	−0.927267	−	0.374402i	$-0.877848\pi$
$337$		−	13.7462i		−	0.748803i	0.927267	−	0.374402i	$-0.122152\pi$
$338$		−	1.21432i		−	0.0660503i
$339$	−1.55262			−0.0843270
$340$	−1.05086	+	7.47949i	−0.0569906	+	0.405633i
$341$	−1.19850			−0.0649023
$342$		−	3.44446i		−	0.186255i
$343$		−	16.1748i		−	0.873359i
$344$	−19.5101			−1.05191
$345$	13.6128	+	1.91258i	0.732891	+	0.102970i
$346$	−0.879077			−0.0472595
$347$			1.21924i			0.0654523i	0.999464	+	0.0327262i	$0.0104189\pi$
$347$			1.21924i			0.0654523i	−0.999464	+	0.0327262i	$0.989581\pi$
$348$		−	6.00000i		−	0.321634i
$349$	−22.5116			−1.20502			−0.602510	−	0.798112i	$-0.705832\pi$
$349$	−22.5116			−1.20502			−0.602510	+	0.798112i	$0.705832\pi$
$350$	16.9447	+	4.85728i	0.905732	+	0.259632i
$351$	5.61285			0.299592
$352$			0.618825i			0.0329835i
$353$			14.2810i			0.760101i	0.924966	+	0.380050i	$0.124093\pi$
$353$			14.2810i			0.760101i	−0.924966	+	0.380050i	$0.875907\pi$
$354$	−14.7511			−0.784013
$355$	13.4652	+	1.89184i	0.714659	+	0.100408i
$356$	2.94914			0.156304
$357$		−	24.4701i		−	1.29510i
$358$			4.90766i			0.259378i
$359$	12.1541			0.641469			0.320734	−	0.947169i	$-0.396070\pi$
$359$	12.1541			0.641469			0.320734	+	0.947169i	$0.396070\pi$
$360$	1.22216	−	8.69874i	0.0644133	−	0.458464i
$361$	−14.0968			−0.741936
$362$			2.84299i			0.149424i
$363$		−	14.3620i		−	0.753808i
$364$	−1.52543			−0.0799541
$365$	−3.19850	+	22.7654i	−0.167417	+	1.19160i
$366$	0.447375			0.0233847
$367$		−	4.65725i		−	0.243106i	−0.992585	−	0.121553i	$-0.961212\pi$
$367$		−	4.65725i		−	0.243106i	0.992585	−	0.121553i	$-0.0387875\pi$
$368$		−	12.5337i		−	0.653366i
$369$	3.90813			0.203449
$370$	−6.13335	−	0.861725i	−0.318858	−	0.0447989i
$371$	−18.1017			−0.939794
$372$		−	3.85236i		−	0.199735i
$373$		−	34.9403i		−	1.80914i	−0.426328	−	0.904569i	$-0.640193\pi$
$373$		−	34.9403i		−	1.80914i	0.426328	−	0.904569i	$-0.359807\pi$
$374$	1.67307			0.0865124
$375$	5.96052	−	13.3921i	0.307800	−	0.691564i
$376$	3.36349			0.173459
$377$			8.70964i			0.448569i
$378$			19.7877i			1.01777i
$379$	17.4717			0.897459			0.448729	−	0.893668i	$-0.351877\pi$
$379$	17.4717			0.897459			0.448729	+	0.893668i	$0.351877\pi$
$380$	2.57628	+	0.361963i	0.132161	+	0.0185683i
$381$	3.01783			0.154608
$382$		−	2.55215i		−	0.130579i
$383$			18.6780i			0.954401i	0.878794	+	0.477200i	$0.158348\pi$
$383$			18.6780i			0.954401i	−0.878794	+	0.477200i	$0.841652\pi$
$384$	6.52251			0.332851
$385$	−0.193576	+	1.37778i	−0.00986555	+	0.0702184i
$386$	−16.4188			−0.835695
$387$			8.14965i			0.414270i
$388$			9.47949i			0.481248i
$389$	−1.61285			−0.0817746			−0.0408873	−	0.999164i	$-0.513018\pi$
$389$	−1.61285			−0.0817746			−0.0408873	+	0.999164i	$0.513018\pi$
$390$	0.495316	−	3.52543i	0.0250813	−	0.178517i
$391$	30.1432			1.52441
$392$		−	4.38118i		−	0.221283i
$393$		−	17.5941i		−	0.887506i
$394$	2.42864			0.122353
$395$	−31.5210	−	4.42864i	−1.58599	−	0.222829i
$396$	0.144252			0.00724895
$397$			6.57628i			0.330054i	0.986289	+	0.165027i	$0.0527712\pi$
$397$			6.57628i			0.330054i	−0.986289	+	0.165027i	$0.947229\pi$
$398$		−	26.8889i		−	1.34782i
$399$	−8.42864			−0.421960
$400$	−12.8479	−	3.68292i	−0.642396	−	0.184146i
$401$	−21.9081			−1.09404			−0.547020	−	0.837120i	$-0.684238\pi$
$401$	−21.9081			−1.09404			−0.547020	+	0.837120i	$0.684238\pi$
$402$		−	12.3555i		−	0.616237i
$403$			5.59210i			0.278563i
$404$	2.07007			0.102990
$405$	7.78568	+	1.09387i	0.386874	+	0.0543550i
$406$	−30.7052			−1.52387
$407$		−	0.488863i		−	0.0242320i
$408$			25.8479i			1.27966i
$409$	10.1936			0.504040			0.252020	−	0.967722i	$-0.418905\pi$
$409$	10.1936			0.504040			0.252020	+	0.967722i	$0.418905\pi$
$410$	1.15257	−	8.20342i	0.0569211	−	0.405138i
$411$	25.1111			1.23864
$412$			1.48289i			0.0730565i
$413$		−	26.8988i		−	1.32360i
$414$	−7.29376			−0.358469
$415$	2.96343	−	21.0923i	0.145469	−	1.03538i
$416$	2.88739			0.141566
$417$		−	25.0321i		−	1.22583i
$418$		−	0.576283i		−	0.0281869i
$419$	−7.31756			−0.357486			−0.178743	−	0.983896i	$-0.557203\pi$
$419$	−7.31756			−0.357486			−0.178743	+	0.983896i	$0.557203\pi$
$420$	−4.42864	−	0.622216i	−0.216095	−	0.0303610i
$421$	−7.86665			−0.383397			−0.191698	−	0.981454i	$-0.561400\pi$
$421$	−7.86665			−0.383397			−0.191698	+	0.981454i	$0.561400\pi$
$422$			23.8666i			1.16181i
$423$		−	1.40498i		−	0.0683125i
$424$	19.1209			0.928594
$425$	8.85728	−	30.8988i	0.429641	−	1.49881i
$426$	9.68153			0.469072
$427$			0.815792i			0.0394789i
$428$		−	8.99402i		−	0.434743i
$429$	0.280996			0.0135666
$430$	17.1066	+	2.40345i	0.824955	+	0.115905i
$431$	−38.9195			−1.87469			−0.937343	−	0.348407i	$-0.886723\pi$
$431$	−38.9195			−1.87469			−0.937343	+	0.348407i	$0.886723\pi$
$432$		−	15.0035i		−	0.721858i
$433$			20.2034i			0.970914i	0.874260	+	0.485457i	$0.161347\pi$
$433$			20.2034i			0.970914i	−0.874260	+	0.485457i	$0.838653\pi$
$434$	−19.7146			−0.946329
$435$	−3.55262	+	25.2859i	−0.170335	+	1.21237i
$436$	8.78721			0.420831
$437$		−	10.3827i		−	0.496672i
$438$			16.3684i			0.782113i
$439$	−10.8889			−0.519700			−0.259850	−	0.965649i	$-0.583673\pi$
$439$	−10.8889			−0.519700			−0.259850	+	0.965649i	$0.583673\pi$
$440$	0.204475	−	1.45536i	0.00974798	−	0.0693816i
$441$	−1.83008			−0.0871468
$442$		−	7.80642i		−	0.371314i
$443$			28.6287i			1.36019i	0.733124	+	0.680095i	$0.238061\pi$
$443$			28.6287i			1.36019i	−0.733124	+	0.680095i	$0.761939\pi$
$444$	1.57136			0.0745735
$445$	−12.4286	−	1.74620i	−0.589174	−	0.0827779i
$446$	23.8840			1.13094
$447$			4.68244i			0.221472i
$448$			25.7003i			1.21422i
$449$	10.9304			0.515838			0.257919	−	0.966167i	$-0.416963\pi$
$449$	10.9304			0.515838			0.257919	+	0.966167i	$0.416963\pi$
$450$	−2.14320	+	7.47658i	−0.101031	+	0.352449i
$451$	0.653858			0.0307890
$452$			0.622216i			0.0292666i
$453$		−	1.65878i		−	0.0779363i
$454$	16.1160			0.756361
$455$	6.42864	+	0.903212i	0.301379	+	0.0423432i
$456$	8.90321			0.416931
$457$		−	11.4064i		−	0.533567i	−0.963756	−	0.266784i	$-0.914039\pi$
$457$		−	11.4064i		−	0.533567i	0.963756	−	0.266784i	$-0.0859609\pi$
$458$			2.94914i			0.137804i
$459$	36.0830			1.68421
$460$	0.766468	−	5.45536i	0.0357368	−	0.254357i
$461$	−26.1334			−1.21715			−0.608576	−	0.793496i	$-0.708259\pi$
$461$	−26.1334			−1.21715			−0.608576	+	0.793496i	$0.708259\pi$
$462$			0.990632i			0.0460884i
$463$			7.92242i			0.368186i	0.982909	+	0.184093i	$0.0589348\pi$
$463$			7.92242i			0.368186i	−0.982909	+	0.184093i	$0.941065\pi$
$464$	23.2815			1.08082
$465$	−2.28100	+	16.2351i	−0.105779	+	0.752883i
$466$	19.6414			0.909872
$467$			10.8923i			0.504036i	0.967723	+	0.252018i	$0.0810942\pi$
$467$			10.8923i			0.504036i	−0.967723	+	0.252018i	$0.918906\pi$
$468$		−	0.673071i		−	0.0311127i
$469$	22.5303			1.04035
$470$	−2.94914	−	0.414349i	−0.136034	−	0.0191125i
$471$	−7.35905			−0.339087
$472$			28.4133i			1.30783i
$473$			1.36349i			0.0626935i
$474$	−22.6637			−1.04098
$475$	−10.6430	−	3.05086i	−0.488332	−	0.139983i
$476$	−9.80642			−0.449477
$477$		−	7.98709i		−	0.365704i
$478$			15.5145i			0.709618i
$479$	9.13182			0.417244			0.208622	−	0.977996i	$-0.433102\pi$
$479$	9.13182			0.417244			0.208622	+	0.977996i	$0.433102\pi$
$480$	8.38271	+	1.17775i	0.382616	+	0.0537569i
$481$	−2.28100			−0.104004
$482$		−	7.16241i		−	0.326239i
$483$			17.8479i			0.812108i
$484$	−5.75557			−0.261617
$485$	5.61285	−	39.9496i	0.254866	−	1.81402i
$486$	−14.8494			−0.673584
$487$		−	16.1891i		−	0.733600i	−0.930300	−	0.366800i	$-0.880453\pi$
$487$		−	16.1891i		−	0.733600i	0.930300	−	0.366800i	$-0.119547\pi$
$488$		−	0.861725i		−	0.0390084i
$489$	−4.87601			−0.220501
$490$	−0.539718	+	3.84146i	−0.0243820	+	0.173539i
$491$	26.2636			1.18526			0.592631	−	0.805474i	$-0.298089\pi$
$491$	26.2636			1.18526			0.592631	+	0.805474i	$0.298089\pi$
$492$			2.10171i			0.0947524i
$493$			55.9911i			2.52171i
$494$	−2.68889			−0.120979
$495$	−0.607926	−	0.0854124i	−0.0273242	−	0.00383900i
$496$	14.9481			0.671189
$497$			17.6543i			0.791905i
$498$		−	15.1655i		−	0.679581i
$499$	−30.0306			−1.34435			−0.672177	−	0.740391i	$-0.734641\pi$
$499$	−30.0306			−1.34435			−0.672177	+	0.740391i	$0.734641\pi$
$500$	−5.36689	−	2.38868i	−0.240014	−	0.106825i
$501$	−9.22570			−0.412174
$502$		−	2.51744i		−	0.112359i
$503$			16.7304i			0.745971i	0.927837	+	0.372985i	$0.121666\pi$
$503$			16.7304i			0.745971i	−0.927837	+	0.372985i	$0.878334\pi$
$504$	11.4050			0.508018
$505$	−8.72393	−	1.22570i	−0.388210	−	0.0545427i
$506$	−1.22030			−0.0542488
$507$		−	1.31111i		−	0.0582283i
$508$		−	1.20940i		−	0.0536583i
$509$	11.9684			0.530488			0.265244	−	0.964181i	$-0.414547\pi$
$509$	11.9684			0.530488			0.265244	+	0.964181i	$0.414547\pi$
$510$	3.18421	−	22.6637i	0.140999	−	1.00357i
$511$	−29.8479			−1.32039
$512$		−	24.1131i		−	1.06566i
$513$		−	12.4286i		−	0.548738i
$514$	−22.3398			−0.985368
$515$	0.878023	−	6.24935i	0.0386903	−	0.275379i
$516$	−4.38271			−0.192938
$517$		−	0.235063i		−	0.0103381i
$518$		−	8.04149i		−	0.353323i
$519$	−0.949145			−0.0416628
$520$	−6.79060	−	0.954067i	−0.297788	−	0.0418386i
$521$	5.75065			0.251940			0.125970	−	0.992034i	$-0.459796\pi$
$521$	5.75065			0.251940			0.125970	+	0.992034i	$0.459796\pi$
$522$		−	13.5482i		−	0.592988i
$523$			20.8035i			0.909674i	0.890575	+	0.454837i	$0.150302\pi$
$523$			20.8035i			0.909674i	−0.890575	+	0.454837i	$0.849698\pi$
$524$	−7.05086			−0.308018
$525$	18.2953	+	5.24443i	0.798472	+	0.228886i
$526$	13.3887			0.583774
$527$			35.9496i			1.56599i
$528$		−	0.751123i		−	0.0326884i
$529$	1.01429			0.0440996
$530$	−16.7654	−	2.35551i	−0.728243	−	0.102317i
$531$	11.8687			0.515056
$532$			3.37778i			0.146446i
$533$		−	3.05086i		−	0.132147i
$534$	−8.93624			−0.386709
$535$	−5.32540	+	37.9037i	−0.230237	+	1.63872i
$536$	−23.7989			−1.02796
$537$			5.29883i			0.228661i
$538$			19.6030i			0.845145i
$539$	−0.306186			−0.0131883
$540$	0.917502	−	6.53035i	0.0394830	−	0.281022i
$541$	16.6222			0.714645			0.357322	−	0.933981i	$-0.383690\pi$
$541$	16.6222			0.714645			0.357322	+	0.933981i	$0.383690\pi$
$542$			15.8000i			0.678667i
$543$			3.06959i			0.131729i
$544$	18.5620			0.795839
$545$	−37.0321	−	5.20294i	−1.58628	−	0.222870i
$546$	4.62222			0.197813
$547$		−	29.9748i		−	1.28163i	−0.767695	−	0.640815i	$-0.778596\pi$
$547$		−	29.9748i		−	1.28163i	0.767695	−	0.640815i	$-0.221404\pi$
$548$		−	10.0633i		−	0.429882i
$549$	−0.359955			−0.0153625
$550$	−0.358572	+	1.25088i	−0.0152896	+	0.0533379i
$551$	19.2859			0.821608
$552$		−	18.8528i		−	0.802430i
$553$		−	41.3274i		−	1.75742i
$554$	−9.19405			−0.390618
$555$	−6.62222	−	0.930409i	−0.281097	−	0.0394937i
$556$	−10.0316			−0.425436
$557$		−	5.03657i		−	0.213406i	−0.994291	−	0.106703i	$-0.965971\pi$
$557$		−	5.03657i		−	0.213406i	0.994291	−	0.106703i	$-0.0340294\pi$
$558$		−	8.69874i		−	0.368247i
$559$	6.36196			0.269082
$560$	2.41435	−	17.1842i	0.102025	−	0.726165i
$561$	1.80642			0.0762673
$562$			8.20342i			0.346040i
$563$		−	2.88247i		−	0.121482i	−0.998154	−	0.0607408i	$-0.980654\pi$
$563$		−	2.88247i		−	0.121482i	0.998154	−	0.0607408i	$-0.0193463\pi$
$564$	0.755569			0.0318152
$565$	0.368416	−	2.62222i	0.0154994	−	0.110317i
$566$	23.1764			0.974176
$567$			10.2079i			0.428690i
$568$		−	18.6484i		−	0.782468i
$569$	4.37286			0.183320			0.0916600	−	0.995790i	$-0.470783\pi$
$569$	4.37286			0.183320			0.0916600	+	0.995790i	$0.470783\pi$
$570$	−7.80642	−	1.09679i	−0.326975	−	0.0459394i
$571$	−1.58120			−0.0661714			−0.0330857	−	0.999453i	$-0.510533\pi$
$571$	−1.58120			−0.0661714			−0.0330857	+	0.999453i	$0.510533\pi$
$572$		−	0.112610i		−	0.00470844i
$573$		−	2.75557i		−	0.115116i
$574$	10.7556			0.448929
$575$	−6.46028	+	22.5368i	−0.269412	+	0.939850i
$576$	−11.3398			−0.472493
$577$		−	7.61729i		−	0.317112i	−0.987350	−	0.158556i	$-0.949316\pi$
$577$		−	7.61729i		−	0.317112i	0.987350	−	0.158556i	$-0.0506839\pi$
$578$		−	29.5412i		−	1.22875i
$579$	−17.7275			−0.736728
$580$	10.1334	+	1.42372i	0.420765	+	0.0591166i
$581$	27.6543			1.14730
$582$		−	28.7239i		−	1.19065i
$583$		−	1.33630i		−	0.0553438i
$584$	31.5285			1.30466
$585$	−0.398528	+	2.83654i	−0.0164771	+	0.117276i
$586$	−9.82071			−0.405690
$587$		−	46.8243i		−	1.93264i	−0.257336	−	0.966322i	$-0.582845\pi$
$587$		−	46.8243i		−	1.93264i	0.257336	−	0.966322i	$-0.417155\pi$
$588$		−	0.984179i		−	0.0405868i
$589$	12.3827			0.510221
$590$	3.50024	−	24.9131i	0.144103	−	1.02565i
$591$	2.62222			0.107864
$592$			6.09726i			0.250596i
$593$			15.9398i			0.654568i	0.944926	+	0.327284i	$0.106133\pi$
$593$			15.9398i			0.654568i	−0.944926	+	0.327284i	$0.893867\pi$
$594$	−1.46076			−0.0599357
$595$	41.3274	+	5.80642i	1.69426	+	0.238040i
$596$	1.87649			0.0768641
$597$		−	29.0321i		−	1.18821i
$598$			5.69381i			0.232837i
$599$	−18.4889			−0.755434			−0.377717	−	0.925921i	$-0.623291\pi$
$599$	−18.4889			−0.755434			−0.377717	+	0.925921i	$0.623291\pi$
$600$	−19.3254	−	5.53972i	−0.788956	−	0.226158i
$601$	20.7556			0.846637			0.423319	−	0.905981i	$-0.360865\pi$
$601$	20.7556			0.846637			0.423319	+	0.905981i	$0.360865\pi$
$602$			22.4286i			0.914123i
$603$			9.94116i			0.404835i
$604$	−0.664758			−0.0270486
$605$	24.2558	+	3.40790i	0.986139	+	0.138551i
$606$	−6.27254			−0.254804
$607$			36.0765i			1.46430i	0.681143	+	0.732150i	$0.261483\pi$
$607$			36.0765i			1.46430i	−0.681143	+	0.732150i	$0.738517\pi$
$608$		−	6.39361i		−	0.259295i
$609$	−33.1526			−1.34341
$610$	−0.106156	+	0.755569i	−0.00429813	+	0.0305921i
$611$	−1.09679			−0.0443713
$612$		−	4.32693i		−	0.174906i
$613$		−	9.94962i		−	0.401861i	−0.979605	−	0.200931i	$-0.935603\pi$
$613$		−	9.94962i		−	0.401861i	0.979605	−	0.200931i	$-0.0643966\pi$
$614$	16.3126			0.658325
$615$	1.24443	−	8.85728i	0.0501803	−	0.357160i
$616$	1.90813			0.0768809
$617$			2.09187i			0.0842154i	0.999113	+	0.0421077i	$0.0134073\pi$
$617$			2.09187i			0.0842154i	−0.999113	+	0.0421077i	$0.986593\pi$
$618$		−	4.49331i		−	0.180747i
$619$	−18.4681			−0.742296			−0.371148	−	0.928574i	$-0.621036\pi$
$619$	−18.4681			−0.742296			−0.371148	+	0.928574i	$0.621036\pi$
$620$	6.50622	+	0.914111i	0.261296	+	0.0367116i
$621$	−26.3180			−1.05611
$622$			24.5334i			0.983700i
$623$		−	16.2953i		−	0.652857i
$624$	−3.50468			−0.140300
$625$	21.2034	+	13.2444i	0.848137	+	0.529777i
$626$	18.3497			0.733401
$627$		−	0.622216i		−	0.0248489i
$628$			2.94914i			0.117684i
$629$	−14.6637			−0.584680
$630$	−10.0000	−	1.40498i	−0.398410	−	0.0559758i
$631$	−38.6657			−1.53926			−0.769629	−	0.638492i	$-0.779559\pi$
$631$	−38.6657			−1.53926			−0.769629	+	0.638492i	$0.779559\pi$
$632$			43.6543i			1.73648i
$633$			25.7690i			1.02422i
$634$	−27.0563			−1.07454
$635$	−0.716089	+	5.09679i	−0.0284171	+	0.202260i
$636$	4.29529			0.170319
$637$			1.42864i			0.0566048i
$638$		−	2.26671i		−	0.0897398i
$639$	−7.78970			−0.308156
$640$	−1.54770	+	11.0158i	−0.0611783	+	0.435439i
$641$	24.5718			0.970529			0.485265	−	0.874367i	$-0.338723\pi$
$641$	24.5718			0.970529			0.485265	+	0.874367i	$0.338723\pi$
$642$			27.2529i			1.07559i
$643$		−	27.4938i		−	1.08425i	−0.840298	−	0.542125i	$-0.817620\pi$
$643$		−	27.4938i		−	1.08425i	0.840298	−	0.542125i	$-0.182380\pi$
$644$	7.15257			0.281851
$645$	18.4701	+	2.59502i	0.727261	+	0.102179i
$646$	−17.2859			−0.680105
$647$			13.7812i			0.541796i	0.962608	+	0.270898i	$0.0873207\pi$
$647$			13.7812i			0.541796i	−0.962608	+	0.270898i	$0.912679\pi$
$648$		−	10.7826i		−	0.423581i
$649$	1.98571			0.0779459
$650$	5.83654	+	1.67307i	0.228928	+	0.0656232i
$651$	−21.2859			−0.834261
$652$			1.95407i			0.0765272i
$653$			2.12045i			0.0829795i	0.999139	+	0.0414897i	$0.0132104\pi$
$653$			2.12045i			0.0829795i	−0.999139	+	0.0414897i	$0.986790\pi$
$654$	−26.6262			−1.04117
$655$	29.7146	+	4.17484i	1.16104	+	0.163125i
$656$	−8.15515			−0.318405
$657$		−	13.1699i		−	0.513807i
$658$		−	3.86665i		−	0.150738i
$659$	−33.8894			−1.32014			−0.660072	−	0.751203i	$-0.729474\pi$
$659$	−33.8894			−1.32014			−0.660072	+	0.751203i	$0.729474\pi$
$660$	0.0459330	−	0.326929i	0.00178794	−	0.0127257i
$661$	−37.3689			−1.45348			−0.726741	−	0.686912i	$-0.758966\pi$
$661$	−37.3689			−1.45348			−0.726741	+	0.686912i	$0.758966\pi$
$662$			10.0252i			0.389640i
$663$		−	8.42864i		−	0.327341i
$664$	−29.2114			−1.13362
$665$	2.00000	−	14.2351i	0.0775567	−	0.552012i
$666$	3.54818			0.137489
$667$		−	40.8385i		−	1.58127i
$668$			3.69721i			0.143049i
$669$	25.7877			0.997010
$670$	20.8671	+	2.93179i	0.806167	+	0.113265i
$671$	−0.0602231			−0.00232489
$672$			10.9906i			0.423973i
$673$			35.4608i			1.36691i	0.729992	+	0.683456i	$0.239524\pi$
$673$			35.4608i			1.36691i	−0.729992	+	0.683456i	$0.760476\pi$
$674$	16.6923			0.642963
$675$	−7.73329	+	26.9777i	−0.297655	+	1.03837i
$676$	−0.525428			−0.0202088
$677$			15.3047i			0.588206i	0.955774	+	0.294103i	$0.0950208\pi$
$677$			15.3047i			0.588206i	−0.955774	+	0.294103i	$0.904979\pi$
$678$		−	1.88538i		−	0.0724077i
$679$	52.3783			2.01009
$680$	−43.6543	−	6.13335i	−1.67407	−	0.235203i
$681$	17.4005			0.666790
$682$		−	1.45536i		−	0.0557286i
$683$			13.0968i			0.501135i	0.968099	+	0.250567i	$0.0806171\pi$
$683$			13.0968i			0.501135i	−0.968099	+	0.250567i	$0.919383\pi$
$684$	−1.49039			−0.0569866
$685$	−5.95851	+	42.4099i	−0.227663	+	1.62040i
$686$	19.6414			0.749913
$687$			3.18421i			0.121485i
$688$		−	17.0060i		−	0.648347i
$689$	−6.23506			−0.237537
$690$	−2.32248	+	16.5303i	−0.0884154	+	0.629300i
$691$	−18.4079			−0.700269			−0.350135	−	0.936699i	$-0.613864\pi$
$691$	−18.4079			−0.700269			−0.350135	+	0.936699i	$0.613864\pi$
$692$			0.380371i			0.0144595i
$693$		−	0.797056i		−	0.0302777i
$694$	−1.48055			−0.0562009
$695$	42.2766	+	5.93978i	1.60364	+	0.225309i
$696$	35.0192			1.32740
$697$		−	19.6128i		−	0.742890i
$698$		−	27.3363i		−	1.03469i
$699$	21.2070			0.802121
$700$	2.10171	−	7.33185i	0.0794372	−	0.277118i
$701$	−31.3689			−1.18479			−0.592393	−	0.805649i	$-0.701817\pi$
$701$	−31.3689			−1.18479			−0.592393	+	0.805649i	$0.701817\pi$
$702$			6.81579i			0.257245i
$703$			5.05086i			0.190497i
$704$	−1.89723			−0.0715047
$705$	−3.18421	−	0.447375i	−0.119924	−	0.0168491i
$706$	−17.3417			−0.652663
$707$		−	11.4380i		−	0.430171i
$708$			6.38271i			0.239877i
$709$	−9.47949			−0.356010			−0.178005	−	0.984030i	$-0.556964\pi$
$709$	−9.47949			−0.356010			−0.178005	+	0.984030i	$0.556964\pi$
$710$	−2.29729	+	16.3511i	−0.0862159	+	0.613644i
$711$	18.2351			0.683868
$712$			17.2128i			0.645077i
$713$		−	26.2208i		−	0.981976i
$714$	29.7146			1.11204
$715$	−0.0666765	+	0.474572i	−0.00249356	+	0.0177480i
$716$	2.12351			0.0793592
$717$			16.7511i			0.625582i
$718$			14.7590i			0.550799i
$719$	29.6227			1.10474			0.552370	−	0.833599i	$-0.313724\pi$
$719$	29.6227			1.10474			0.552370	+	0.833599i	$0.313724\pi$
$720$	7.58226	+	1.06529i	0.282574	+	0.0397011i
$721$	8.19358			0.305145
$722$		−	17.1180i		−	0.637066i
$723$		−	7.73329i		−	0.287604i
$724$	1.23014			0.0457178
$725$	−41.8622	−	12.0000i	−1.55472	−	0.445669i
$726$	17.4400			0.647260
$727$			42.6702i			1.58255i	0.611461	+	0.791274i	$0.290582\pi$
$727$			42.6702i			1.58255i	−0.611461	+	0.791274i	$0.709418\pi$
$728$		−	8.90321i		−	0.329975i
$729$	−26.5812			−0.984489
$730$	−27.6445	−	3.88400i	−1.02317	−	0.143753i
$731$	40.8988			1.51270
$732$		−	0.193576i		−	0.00715478i
$733$		−	26.0830i		−	0.963397i	−0.876337	−	0.481698i	$-0.840020\pi$
$733$		−	26.0830i		−	0.963397i	0.876337	−	0.481698i	$-0.159980\pi$
$734$	5.65539			0.208744
$735$	−0.582736	+	4.14764i	−0.0214945	+	0.152988i
$736$	−13.5387			−0.499042
$737$			1.66323i			0.0612657i
$738$			4.74572i			0.174693i
$739$	28.2687			1.03988			0.519941	−	0.854202i	$-0.325954\pi$
$739$	28.2687			1.03988			0.519941	+	0.854202i	$0.325954\pi$
$740$	−0.372862	+	2.65386i	−0.0137067	+	0.0975578i
$741$	−2.90321			−0.106652
$742$		−	21.9813i		−	0.806958i
$743$		−	20.6681i		−	0.758241i	−0.925347	−	0.379120i	$-0.876227\pi$
$743$		−	20.6681i		−	0.758241i	0.925347	−	0.379120i	$-0.123773\pi$
$744$	22.4844			0.824319
$745$	−7.90813	−	1.11108i	−0.289732	−	0.0407068i
$746$	42.4286			1.55342
$747$			12.2020i			0.446449i
$748$		−	0.723926i		−	0.0264694i
$749$	−49.6958			−1.81585
$750$	16.2623	+	7.23798i	0.593814	+	0.264294i
$751$	2.46028			0.0897770			0.0448885	−	0.998992i	$-0.485707\pi$
$751$	2.46028			0.0897770			0.0448885	+	0.998992i	$0.485707\pi$
$752$			2.93179i			0.106911i
$753$		−	2.71810i		−	0.0990530i
$754$	−10.5763			−0.385165
$755$	2.80150	+	0.393606i	0.101957	+	0.0143248i
$756$	8.56199			0.311397
$757$		−	48.6035i		−	1.76652i	−0.468880	−	0.883262i	$-0.655342\pi$
$757$		−	48.6035i		−	1.76652i	0.468880	−	0.883262i	$-0.344658\pi$
$758$			21.2162i			0.770606i
$759$	−1.31756			−0.0478244
$760$	−2.11261	+	15.0366i	−0.0766324	+	0.545434i
$761$	−13.8252			−0.501162			−0.250581	−	0.968096i	$-0.580622\pi$
$761$	−13.8252			−0.501162			−0.250581	+	0.968096i	$0.580622\pi$
$762$			3.66461i			0.132755i
$763$		−	48.5531i		−	1.75774i
$764$	−1.10430			−0.0399520
$765$	−2.56199	+	18.2351i	−0.0926290	+	0.659290i
$766$	−22.6811			−0.819500
$767$		−	9.26517i		−	0.334546i
$768$		−	15.2924i		−	0.551816i
$769$	38.9688			1.40525			0.702626	−	0.711559i	$-0.252011\pi$
$769$	38.9688			1.40525			0.702626	+	0.711559i	$0.252011\pi$
$770$	−1.67307	−	0.235063i	−0.0602933	−	0.00847109i
$771$	−24.1204			−0.868677
$772$			7.10430i			0.255689i
$773$			0.445992i			0.0160412i	0.999968	+	0.00802061i	$0.00255307\pi$
$773$			0.445992i			0.0160412i	−0.999968	+	0.00802061i	$0.997447\pi$
$774$	−9.89628			−0.355715
$775$	−26.8780	−	7.70471i	−0.965487	−	0.276761i
$776$	−55.3274			−1.98614
$777$		−	8.68244i		−	0.311481i
$778$		−	1.95851i		−	0.0702161i
$779$	−6.75557			−0.242043
$780$	−1.52543	−	0.214320i	−0.0546191	−	0.00767388i
$781$	−1.30327			−0.0466347
$782$			36.6035i			1.30894i
$783$		−	48.8859i		−	1.74704i
$784$	3.81885			0.136388
$785$	1.74620	−	12.4286i	0.0623246	−	0.443597i
$786$	21.3649			0.762060
$787$		−	33.9037i		−	1.20854i	−0.796781	−	0.604268i	$-0.793466\pi$
$787$		−	33.9037i		−	1.20854i	0.796781	−	0.604268i	$-0.206534\pi$
$788$		−	1.05086i		−	0.0374352i
$789$	14.4558			0.514641
$790$	5.37778	−	38.2766i	0.191333	−	1.36182i
$791$	3.43801			0.122241
$792$			0.841934i			0.0299168i
$793$			0.280996i			0.00997847i
$794$	−7.98571			−0.283402
$795$	−18.1017	−	2.54326i	−0.642002	−	0.0902000i
$796$	−11.6346			−0.412379
$797$			10.2953i			0.364678i	0.983236	+	0.182339i	$0.0583668\pi$
$797$			10.2953i			0.364678i	−0.983236	+	0.182339i	$0.941633\pi$
$798$		−	10.2351i		−	0.362317i
$799$	−7.05086			−0.249441
$800$	−3.97820	+	13.8780i	−0.140651	+	0.490662i
$801$	7.19004			0.254047
$802$		−	26.6035i		−	0.939402i
$803$		−	2.20342i		−	0.0777570i
$804$	−5.34614			−0.188544
$805$	−30.1432	−	4.23506i	−1.06241	−	0.149266i
$806$	−6.79060			−0.239189
$807$			21.1655i			0.745060i
$808$			12.0820i			0.425044i
$809$	−7.94422			−0.279304			−0.139652	−	0.990201i	$-0.544598\pi$
$809$	−7.94422			−0.279304			−0.139652	+	0.990201i	$0.544598\pi$
$810$	−1.32831	+	9.45431i	−0.0466721	+	0.332190i
$811$	−8.12245			−0.285218			−0.142609	−	0.989779i	$-0.545549\pi$
$811$	−8.12245			−0.285218			−0.142609	+	0.989779i	$0.545549\pi$
$812$			13.2859i			0.466244i
$813$			17.0593i			0.598296i
$814$	0.593635			0.0208069
$815$	1.15701	−	8.23506i	0.0405283	−	0.288462i
$816$	−22.5303			−0.788720
$817$		−	14.0874i		−	0.492856i
$818$			12.3783i			0.432796i
$819$	−3.71900			−0.129953
$820$	−3.54956	−	0.498707i	−0.123956	−	0.0174156i
$821$	−22.2065			−0.775012			−0.387506	−	0.921867i	$-0.626663\pi$
$821$	−22.2065			−0.775012			−0.387506	+	0.921867i	$0.626663\pi$
$822$			30.4929i			1.06356i
$823$			11.1175i			0.387533i	0.981048	+	0.193766i	$0.0620704\pi$
$823$			11.1175i			0.387533i	−0.981048	+	0.193766i	$0.937930\pi$
$824$	−8.65491			−0.301508
$825$	−0.387152	+	1.35059i	−0.0134789	+	0.0470214i
$826$	32.6637			1.13652
$827$		−	23.1570i		−	0.805248i	−0.915365	−	0.402624i	$-0.868098\pi$
$827$		−	23.1570i		−	0.805248i	0.915365	−	0.402624i	$-0.131902\pi$
$828$			3.15596i			0.109677i
$829$	27.1195			0.941901			0.470950	−	0.882160i	$-0.343911\pi$
$829$	27.1195			0.941901			0.470950	+	0.882160i	$0.343911\pi$
$830$	25.6128	+	3.59856i	0.889035	+	0.124908i
$831$	−9.92687			−0.344359
$832$			8.85236i			0.306900i
$833$			9.18421i			0.318214i
$834$	30.3970			1.05256
$835$	2.18913	−	15.5812i	0.0757580	−	0.539210i
$836$	−0.249353			−0.00862407
$837$		−	31.3876i		−	1.08492i
$838$		−	8.88586i		−	0.306957i
$839$	−25.3955			−0.876749			−0.438374	−	0.898792i	$-0.644446\pi$
$839$	−25.3955			−0.876749			−0.438374	+	0.898792i	$0.644446\pi$
$840$	3.63158	−	25.8479i	0.125302	−	0.891838i
$841$	46.8578			1.61578
$842$		−	9.55262i		−	0.329205i
$843$			8.85728i			0.305061i
$844$	10.3269			0.355468
$845$	2.21432	+	0.311108i	0.0761749	+	0.0107024i
$846$	1.70610			0.0586568
$847$			31.8020i			1.09273i
$848$			16.6668i			0.572339i
$849$	25.0237			0.858810
$850$	37.5210	+	10.7556i	1.28696	+	0.368913i
$851$	10.6953			0.366632
$852$		−	4.18913i		−	0.143517i
$853$			25.0651i			0.858214i	0.903254	+	0.429107i	$0.141172\pi$
$853$			25.0651i			0.858214i	−0.903254	+	0.429107i	$0.858828\pi$
$854$	−0.990632			−0.0338987
$855$	6.28100	+	0.882468i	0.214806	+	0.0301798i
$856$	52.4939			1.79421
$857$		−	7.61285i		−	0.260050i	−0.991511	−	0.130025i	$-0.958494\pi$
$857$		−	7.61285i		−	0.260050i	0.991511	−	0.130025i	$-0.0415057\pi$
$858$			0.341219i			0.0116490i
$859$	−42.1432			−1.43791			−0.718954	−	0.695058i	$-0.755379\pi$
$859$	−42.1432			−1.43791			−0.718954	+	0.695058i	$0.755379\pi$
$860$	1.03996	−	7.40192i	0.0354622	−	0.252403i
$861$	11.6128			0.395765
$862$		−	47.2607i		−	1.60971i
$863$			51.5768i			1.75569i	0.478942	+	0.877847i	$0.341020\pi$
$863$			51.5768i			1.75569i	−0.478942	+	0.877847i	$0.658980\pi$
$864$	−16.2065			−0.551356
$865$	0.225219	−	1.60300i	0.00765768	−	0.0545037i
$866$	−24.5334			−0.833679
$867$		−	31.8959i		−	1.08324i
$868$			8.53035i			0.289539i
$869$	3.05086			0.103493
$870$	−30.7052	−	4.31402i	−1.04100	−	0.146259i
$871$	7.76049			0.262954
$872$			51.2869i			1.73679i
$873$			23.1111i			0.782191i
$874$	12.6079			0.426469
$875$	−13.1985	+	29.6543i	−0.446191	+	1.00250i
$876$	7.08250			0.239295
$877$			34.0701i			1.15046i	0.817990	+	0.575232i	$0.195088\pi$
$877$			34.0701i			1.15046i	−0.817990	+	0.575232i	$0.804912\pi$
$878$		−	13.2226i		−	0.446242i
$879$	−10.6035			−0.357646
$880$	1.26857	+	0.178231i	0.0427633	+	0.00600817i
$881$	3.71900			0.125296			0.0626482	−	0.998036i	$-0.480045\pi$
$881$	3.71900			0.125296			0.0626482	+	0.998036i	$0.480045\pi$
$882$		−	2.22230i		−	0.0748289i
$883$		−	42.0163i		−	1.41396i	−0.707233	−	0.706981i	$-0.750057\pi$
$883$		−	42.0163i		−	1.41396i	0.707233	−	0.706981i	$-0.249943\pi$
$884$	−3.37778			−0.113607
$885$	3.77923	−	26.8988i	0.127037	−	0.904192i
$886$	−34.7644			−1.16793
$887$			40.3116i			1.35353i	0.736199	+	0.676765i	$0.236619\pi$
$887$			40.3116i			1.35353i	−0.736199	+	0.676765i	$0.763381\pi$
$888$			9.17130i			0.307769i
$889$	−6.68244			−0.224122
$890$	2.12045	−	15.0923i	0.0710775	−	0.505896i
$891$	−0.753561			−0.0252452
$892$		−	10.3344i		−	0.346023i
$893$			2.42864i			0.0812713i
$894$	−5.68598			−0.190168
$895$	−8.94914	−	1.25734i	−0.299137	−	0.0420282i
$896$	−14.4429			−0.482504
$897$			6.14764i			0.205264i
$898$			13.2730i			0.442926i
$899$	48.7052			1.62441
$900$	3.23506	+	0.927346i	0.107835	+	0.0309115i
$901$	−40.0830			−1.33536
$902$			0.793993i			0.0264371i
$903$			24.2163i			0.805869i
$904$	−3.63158			−0.120785
$905$	−5.18421	−	0.728372i	−0.172329	−	0.0242119i
$906$	2.01429			0.0669203
$907$		−	34.8419i		−	1.15691i	−0.815715	−	0.578454i	$-0.803656\pi$
$907$		−	34.8419i		−	1.15691i	0.815715	−	0.578454i	$-0.196344\pi$
$908$		−	6.97328i		−	0.231416i
$909$	5.04684			0.167393
$910$	−1.09679	+	7.80642i	−0.0363582	+	0.258780i
$911$	23.2672			0.770876			0.385438	−	0.922734i	$-0.374050\pi$
$911$	23.2672			0.770876			0.385438	+	0.922734i	$0.374050\pi$
$912$			7.76049i			0.256976i
$913$			2.04149i			0.0675634i
$914$	13.8510			0.458149
$915$	−0.114617	+	0.815792i	−0.00378913	+	0.0269692i
$916$	1.27607			0.0421627
$917$			38.9590i			1.28654i
$918$			43.8163i			1.44615i
$919$	3.22570			0.106406			0.0532029	−	0.998584i	$-0.483057\pi$
$919$	3.22570			0.106406			0.0532029	+	0.998584i	$0.483057\pi$
$920$	31.8404	+	4.47352i	1.04975	+	0.147488i
$921$	17.6128			0.580363
$922$		−	31.7342i		−	1.04511i
$923$			6.08097i			0.200157i
$924$	0.428639			0.0141012
$925$	3.14272	−	10.9634i	0.103332	−	0.360476i
$926$	−9.62036			−0.316145
$927$			3.61529i			0.118742i
$928$		−	25.1481i		−	0.825527i
$929$	39.3461			1.29091			0.645453	−	0.763800i	$-0.276669\pi$
$929$	39.3461			1.29091			0.645453	+	0.763800i	$0.276669\pi$
$930$	−19.7146	−	2.76986i	−0.646466	−	0.0908272i
$931$	3.16346			0.103678
$932$		−	8.49871i		−	0.278384i
$933$			26.4889i			0.867206i
$934$	−13.2268			−0.432792
$935$	−0.428639	+	3.05086i	−0.0140180	+	0.0997736i
$936$	3.92840			0.128404
$937$			51.6040i			1.68583i	0.538048	+	0.842914i	$0.319162\pi$
$937$			51.6040i			1.68583i	−0.538048	+	0.842914i	$0.680838\pi$
$938$			27.3590i			0.893305i
$939$	19.8123			0.646548
$940$	−0.179286	+	1.27607i	−0.00584767	+	0.0416209i
$941$	37.5081			1.22273			0.611364	−	0.791349i	$-0.290621\pi$
$941$	37.5081			1.22273			0.611364	+	0.791349i	$0.290621\pi$
$942$		−	8.93624i		−	0.291158i
$943$			14.3051i			0.465839i
$944$	−24.7665			−0.806080
$945$	−36.0830	−	5.06959i	−1.17378	−	0.164914i
$946$	−1.65572			−0.0538320
$947$		−	38.1160i		−	1.23860i	−0.785153	−	0.619302i	$-0.787416\pi$
$947$		−	38.1160i		−	1.23860i	0.785153	−	0.619302i	$-0.212584\pi$
$948$			9.80642i			0.318498i
$949$	−10.2810			−0.333735
$950$	3.70471	−	12.9240i	0.120197	−	0.419308i
$951$	−29.2128			−0.947290
$952$		−	57.2355i		−	1.85501i
$953$			28.7368i			0.930877i	0.885080	+	0.465439i	$0.154103\pi$
$953$			28.7368i			0.930877i	−0.885080	+	0.465439i	$0.845897\pi$
$954$	9.69888			0.314013
$955$	4.65386	+	0.653858i	0.150595	+	0.0211584i
$956$	6.71303			0.217115
$957$		−	2.44738i		−	0.0791124i
$958$			11.0890i			0.358268i
$959$	−55.6040			−1.79555
$960$	−3.61084	+	25.7003i	−0.116539	+	0.829473i
$961$	0.271628			0.00876221
$962$		−	2.76986i		−	0.0893038i
$963$		−	21.9275i		−	0.706604i
$964$	−3.09912			−0.0998161
$965$	4.20648	−	29.9398i	0.135411	−	0.963796i
$966$	−21.6731			−0.697320
$967$			29.0593i			0.934485i	0.884129	+	0.467242i	$0.154752\pi$
$967$			29.0593i			0.934485i	−0.884129	+	0.467242i	$0.845248\pi$
$968$		−	33.5926i		−	1.07971i
$969$	−18.6637			−0.599565
$970$	48.5116	+	6.81579i	1.55761	+	0.218842i
$971$	−39.8578			−1.27910			−0.639548	−	0.768751i	$-0.720879\pi$
$971$	−39.8578			−1.27910			−0.639548	+	0.768751i	$0.720879\pi$
$972$			6.42525i			0.206090i
$973$			55.4291i			1.77698i
$974$	19.6588			0.629908
$975$	6.30174	+	1.80642i	0.201817	+	0.0578519i
$976$	0.751123			0.0240429
$977$		−	12.8617i		−	0.411483i	−0.978606	−	0.205742i	$-0.934039\pi$
$977$		−	12.8617i		−	0.411483i	0.978606	−	0.205742i	$-0.0659606\pi$
$978$		−	5.92104i		−	0.189334i
$979$	1.20294			0.0384463
$980$	1.66217	+	0.233532i	0.0530961	+	0.00745991i
$981$	21.4233			0.683993
$982$			31.8925i			1.01773i
$983$		−	45.4880i		−	1.45084i	−0.688306	−	0.725420i	$-0.741645\pi$
$983$		−	45.4880i		−	1.45084i	0.688306	−	0.725420i	$-0.258355\pi$
$984$	−12.2667			−0.391048
$985$	−0.622216	+	4.42864i	−0.0198254	+	0.141108i
$986$	−67.9911			−2.16528
$987$		−	4.17484i		−	0.132887i
$988$			1.16346i			0.0370147i
$989$	−29.8306			−0.948557
$990$	0.103718	−	0.738216i	0.00329637	−	0.0234620i
$991$	8.07007			0.256354			0.128177	−	0.991751i	$-0.459087\pi$
$991$	8.07007			0.256354			0.128177	+	0.991751i	$0.459087\pi$
$992$		−	16.1466i		−	0.512655i
$993$			10.8243i			0.343497i
$994$	−21.4380			−0.679972
$995$	49.0321	+	6.88892i	1.55442	+	0.218394i
$996$	−6.56199			−0.207925
$997$		−	32.8158i		−	1.03929i	−0.854383	−	0.519643i	$-0.826065\pi$
$997$		−	32.8158i		−	1.03929i	0.854383	−	0.519643i	$-0.173935\pi$
$998$		−	36.4667i		−	1.15433i
$999$	12.8029			0.405065

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.2.b.a.14.4	yes	6
3.2	odd	2		585.2.c.b.469.3		6
4.3	odd	2		1040.2.d.c.209.2		6
5.2	odd	4		325.2.a.k.1.1		3
5.3	odd	4		325.2.a.j.1.3		3
5.4	even	2	inner	65.2.b.a.14.3	✓	6
13.2	odd	12		845.2.l.e.654.1		12
13.3	even	3		845.2.n.f.529.3		12
13.4	even	6		845.2.n.g.484.3		12
13.5	odd	4		845.2.d.a.844.6		6
13.6	odd	12		845.2.l.e.699.2		12
13.7	odd	12		845.2.l.d.699.6		12
13.8	odd	4		845.2.d.b.844.2		6
13.9	even	3		845.2.n.f.484.4		12
13.10	even	6		845.2.n.g.529.4		12
13.11	odd	12		845.2.l.d.654.5		12
13.12	even	2		845.2.b.c.339.3		6
15.2	even	4		2925.2.a.bf.1.3		3
15.8	even	4		2925.2.a.bj.1.1		3
15.14	odd	2		585.2.c.b.469.4		6
20.3	even	4		5200.2.a.cj.1.2		3
20.7	even	4		5200.2.a.cb.1.2		3
20.19	odd	2		1040.2.d.c.209.5		6
65.4	even	6		845.2.n.g.484.4		12
65.9	even	6		845.2.n.f.484.3		12
65.12	odd	4		4225.2.a.ba.1.3		3
65.19	odd	12		845.2.l.d.699.5		12
65.24	odd	12		845.2.l.e.654.2		12
65.29	even	6		845.2.n.f.529.4		12
65.34	odd	4		845.2.d.a.844.5		6
65.38	odd	4		4225.2.a.bh.1.1		3
65.44	odd	4		845.2.d.b.844.1		6
65.49	even	6		845.2.n.g.529.3		12
65.54	odd	12		845.2.l.d.654.6		12
65.59	odd	12		845.2.l.e.699.1		12
65.64	even	2		845.2.b.c.339.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.b.a.14.3	✓	6	5.4	even	2	inner
65.2.b.a.14.4	yes	6	1.1	even	1	trivial
325.2.a.j.1.3		3	5.3	odd	4
325.2.a.k.1.1		3	5.2	odd	4
585.2.c.b.469.3		6	3.2	odd	2
585.2.c.b.469.4		6	15.14	odd	2
845.2.b.c.339.3		6	13.12	even	2
845.2.b.c.339.4		6	65.64	even	2
845.2.d.a.844.5		6	65.34	odd	4
845.2.d.a.844.6		6	13.5	odd	4
845.2.d.b.844.1		6	65.44	odd	4
845.2.d.b.844.2		6	13.8	odd	4
845.2.l.d.654.5		12	13.11	odd	12
845.2.l.d.654.6		12	65.54	odd	12
845.2.l.d.699.5		12	65.19	odd	12
845.2.l.d.699.6		12	13.7	odd	12
845.2.l.e.654.1		12	13.2	odd	12
845.2.l.e.654.2		12	65.24	odd	12
845.2.l.e.699.1		12	65.59	odd	12
845.2.l.e.699.2		12	13.6	odd	12
845.2.n.f.484.3		12	65.9	even	6
845.2.n.f.484.4		12	13.9	even	3
845.2.n.f.529.3		12	13.3	even	3
845.2.n.f.529.4		12	65.29	even	6
845.2.n.g.484.3		12	13.4	even	6
845.2.n.g.484.4		12	65.4	even	6
845.2.n.g.529.3		12	65.49	even	6
845.2.n.g.529.4		12	13.10	even	6
1040.2.d.c.209.2		6	4.3	odd	2
1040.2.d.c.209.5		6	20.19	odd	2
2925.2.a.bf.1.3		3	15.2	even	4
2925.2.a.bj.1.1		3	15.8	even	4
4225.2.a.ba.1.3		3	65.12	odd	4
4225.2.a.bh.1.1		3	65.38	odd	4
5200.2.a.cb.1.2		3	20.7	even	4
5200.2.a.cj.1.2		3	20.3	even	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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.21432i q^{2} +1.31111i q^{3} +0.525428 q^{4} +(-2.21432 - 0.311108i) q^{5} -1.59210 q^{6} -2.90321i q^{7} +3.06668i q^{8} +1.28100 q^{9} +O(q^{10})\)	\(q+1.21432i q^{2} +1.31111i q^{3} +0.525428 q^{4} +(-2.21432 - 0.311108i) q^{5} -1.59210 q^{6} -2.90321i q^{7} +3.06668i q^{8} +1.28100 q^{9} +(0.377784 - 2.68889i) q^{10} +0.214320 q^{11} +0.688892i q^{12} -1.00000i q^{13} +3.52543 q^{14} +(0.407896 - 2.90321i) q^{15} -2.67307 q^{16} -6.42864i q^{17} +1.55554i q^{18} -2.21432 q^{19} +(-1.16346 - 0.163465i) q^{20} +3.80642 q^{21} +0.260253i q^{22} +4.68889i q^{23} -4.02074 q^{24} +(4.80642 + 1.37778i) q^{25} +1.21432 q^{26} +5.61285i q^{27} -1.52543i q^{28} -8.70964 q^{29} +(3.52543 + 0.495316i) q^{30} -5.59210 q^{31} +2.88739i q^{32} +0.280996i q^{33} +7.80642 q^{34} +(-0.903212 + 6.42864i) q^{35} +0.673071 q^{36} -2.28100i q^{37} -2.68889i q^{38} +1.31111 q^{39} +(0.954067 - 6.79060i) q^{40} +3.05086 q^{41} +4.62222i q^{42} +6.36196i q^{43} +0.112610 q^{44} +(-2.83654 - 0.398528i) q^{45} -5.69381 q^{46} -1.09679i q^{47} -3.50468i q^{48} -1.42864 q^{49} +(-1.67307 + 5.83654i) q^{50} +8.42864 q^{51} -0.525428i q^{52} -6.23506i q^{53} -6.81579 q^{54} +(-0.474572 - 0.0666765i) q^{55} +8.90321 q^{56} -2.90321i q^{57} -10.5763i q^{58} +9.26517 q^{59} +(0.214320 - 1.52543i) q^{60} -0.280996 q^{61} -6.79060i q^{62} -3.71900i q^{63} -8.85236 q^{64} +(-0.311108 + 2.21432i) q^{65} -0.341219 q^{66} +7.76049i q^{67} -3.37778i q^{68} -6.14764 q^{69} +(-7.80642 - 1.09679i) q^{70} -6.08097 q^{71} +3.92840i q^{72} -10.2810i q^{73} +2.76986 q^{74} +(-1.80642 + 6.30174i) q^{75} -1.16346 q^{76} -0.622216i q^{77} +1.59210i q^{78} +14.2351 q^{79} +(5.91903 + 0.831613i) q^{80} -3.51606 q^{81} +3.70471i q^{82} +9.52543i q^{83} +2.00000 q^{84} +(-2.00000 + 14.2351i) q^{85} -7.72546 q^{86} -11.4193i q^{87} +0.657249i q^{88} +5.61285 q^{89} +(0.483940 - 3.44446i) q^{90} -2.90321 q^{91} +2.46367i q^{92} -7.33185i q^{93} +1.33185 q^{94} +(4.90321 + 0.688892i) q^{95} -3.78568 q^{96} +18.0415i q^{97} -1.73483i q^{98} +0.274543 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 10 q^{4} + 4 q^{6} - 6 q^{9}+O(q^{10}) \) 6 * q - 10 * q^4 + 4 * q^6 - 6 * q^9	\( 6 q - 10 q^{4} + 4 q^{6} - 6 q^{9} + 2 q^{10} - 12 q^{11} + 8 q^{14} + 16 q^{15} + 10 q^{16} - 20 q^{20} - 4 q^{21} + 16 q^{24} + 2 q^{25} - 6 q^{26} - 12 q^{29} + 8 q^{30} - 20 q^{31} + 20 q^{34} + 8 q^{35} - 22 q^{36} + 8 q^{39} - 34 q^{40} - 8 q^{41} + 40 q^{44} - 4 q^{45} + 32 q^{46} + 18 q^{49} + 16 q^{50} + 24 q^{51} - 68 q^{54} - 16 q^{55} + 40 q^{56} + 16 q^{59} - 12 q^{60} + 12 q^{61} - 66 q^{64} - 2 q^{65} - 16 q^{66} - 24 q^{69} - 20 q^{70} - 24 q^{71} + 4 q^{74} + 16 q^{75} - 20 q^{76} + 32 q^{79} + 48 q^{80} + 46 q^{81} + 12 q^{84} - 12 q^{85} - 32 q^{86} - 20 q^{89} + 70 q^{90} - 4 q^{91} - 32 q^{94} + 16 q^{95} - 36 q^{96} + 16 q^{99}+O(q^{100}) \) 6 * q - 10 * q^4 + 4 * q^6 - 6 * q^9 + 2 * q^10 - 12 * q^11 + 8 * q^14 + 16 * q^15 + 10 * q^16 - 20 * q^20 - 4 * q^21 + 16 * q^24 + 2 * q^25 - 6 * q^26 - 12 * q^29 + 8 * q^30 - 20 * q^31 + 20 * q^34 + 8 * q^35 - 22 * q^36 + 8 * q^39 - 34 * q^40 - 8 * q^41 + 40 * q^44 - 4 * q^45 + 32 * q^46 + 18 * q^49 + 16 * q^50 + 24 * q^51 - 68 * q^54 - 16 * q^55 + 40 * q^56 + 16 * q^59 - 12 * q^60 + 12 * q^61 - 66 * q^64 - 2 * q^65 - 16 * q^66 - 24 * q^69 - 20 * q^70 - 24 * q^71 + 4 * q^74 + 16 * q^75 - 20 * q^76 + 32 * q^79 + 48 * q^80 + 46 * q^81 + 12 * q^84 - 12 * q^85 - 32 * q^86 - 20 * q^89 + 70 * q^90 - 4 * q^91 - 32 * q^94 + 16 * q^95 - 36 * q^96 + 16 * q^99

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