LMFDB - Embedded newform 216.2.f.a.107.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(107,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("216.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.f (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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.23123460096.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 2x^{6} + 6x^{4} + 8x^{2} + 16 $ x^8 + 2x^6 + 6x^4 + 8*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			107.3
Root			$0.563016 - 1.29731i$ of defining polynomial
Character	$\chi$	$=$	216.107
Dual form			216.2.f.a.107.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.563016 - 1.29731i) q^{2} +(-1.36603 + 1.46081i) q^{4} +3.07638 q^{5} +3.99102i q^{7} +(2.66422 + 0.949697i) q^{8} +O(q^{10})$	\(q+(-0.563016 - 1.29731i) q^{2} +(-1.36603 + 1.46081i) q^{4} +3.07638 q^{5} +3.99102i q^{7} +(2.66422 + 0.949697i) q^{8} +(-1.73205 - 3.99102i) q^{10} +1.89939i q^{11} +1.06939i q^{13} +(5.17758 - 2.24701i) q^{14} +(-0.267949 - 3.99102i) q^{16} -7.08863i q^{17} +3.73205 q^{19} +(-4.20241 + 4.49401i) q^{20} +(2.46410 - 1.06939i) q^{22} -0.824313 q^{23} +4.46410 q^{25} +(1.38733 - 0.602084i) q^{26} +(-5.83013 - 5.45183i) q^{28} -4.50413 q^{29} -5.84325i q^{31} +(-5.02672 + 2.59462i) q^{32} +(-9.19615 + 3.99102i) q^{34} +12.2779i q^{35} +6.91264i q^{37} +(-2.10121 - 4.84163i) q^{38} +(8.19615 + 2.92163i) q^{40} -3.79879i q^{41} +2.00000 q^{43} +(-2.77466 - 2.59462i) q^{44} +(0.464102 + 1.06939i) q^{46} -6.97707 q^{47} -8.92820 q^{49} +(-2.51336 - 5.79132i) q^{50} +(-1.56218 - 1.46081i) q^{52} +10.6569 q^{53} +5.84325i q^{55} +(-3.79025 + 10.6329i) q^{56} +(2.53590 + 5.84325i) q^{58} +1.89939i q^{59} -1.06939i q^{61} +(-7.58051 + 3.28985i) q^{62} +(6.19615 + 5.06040i) q^{64} +3.28985i q^{65} -9.19615 q^{67} +(10.3552 + 9.68325i) q^{68} +(15.9282 - 6.91264i) q^{70} -10.6569 q^{71} +5.92820 q^{73} +(8.96784 - 3.89193i) q^{74} +(-5.09808 + 5.45183i) q^{76} -7.58051 q^{77} -6.12979i q^{79} +(-0.824313 - 12.2779i) q^{80} +(-4.92820 + 2.13878i) q^{82} -10.3785i q^{83} -21.8073i q^{85} +(-1.12603 - 2.59462i) q^{86} +(-1.80385 + 5.06040i) q^{88} -13.6683i q^{89} -4.26795 q^{91} +(1.12603 - 1.20417i) q^{92} +(3.92820 + 9.05142i) q^{94} +11.4812 q^{95} -11.3923 q^{97} +(5.02672 + 11.5826i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4}+O(q^{10}) $ 8 * q - 4 * q^4	$ 8 q - 4 q^{4} - 16 q^{16} + 16 q^{19} - 8 q^{22} + 8 q^{25} - 12 q^{28} - 32 q^{34} + 24 q^{40} + 16 q^{43} - 24 q^{46} - 16 q^{49} + 36 q^{52} + 48 q^{58} + 8 q^{64} - 32 q^{67} + 72 q^{70} - 8 q^{73} - 20 q^{76} + 16 q^{82} - 56 q^{88} - 48 q^{91} - 24 q^{94} - 8 q^{97}+O(q^{100}) $ 8 * q - 4 * q^4 - 16 * q^16 + 16 * q^19 - 8 * q^22 + 8 * q^25 - 12 * q^28 - 32 * q^34 + 24 * q^40 + 16 * q^43 - 24 * q^46 - 16 * q^49 + 36 * q^52 + 48 * q^58 + 8 * q^64 - 32 * q^67 + 72 * q^70 - 8 * q^73 - 20 * q^76 + 16 * q^82 - 56 * q^88 - 48 * q^91 - 24 * q^94 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−0.563016	−	1.29731i	−0.398113	−	0.917337i
$2$	−0.563016	−	1.29731i	−0.398113	−	0.917337i
$3$		0			0
$3$		0			0
$4$	−1.36603	+	1.46081i	−0.683013	+	0.730406i
$5$	3.07638			1.37580			0.687899	−	0.725806i	$-0.258533\pi$
$5$	3.07638			1.37580			0.687899	+	0.725806i	$0.258533\pi$
$6$		0			0
$7$			3.99102i			1.50846i	0.656609	+	0.754231i	$0.271990\pi$
$7$			3.99102i			1.50846i	−0.656609	+	0.754231i	$0.728010\pi$
$8$	2.66422	+	0.949697i	0.941945	+	0.335768i
$9$		0			0
$10$	−1.73205	−	3.99102i	−0.547723	−	1.26207i
$11$			1.89939i			0.572689i	0.958127	+	0.286344i	$0.0924401\pi$
$11$			1.89939i			0.572689i	−0.958127	+	0.286344i	$0.907560\pi$
$12$		0			0
$13$			1.06939i			0.296595i	0.988943	+	0.148298i	$0.0473794\pi$
$13$			1.06939i			0.296595i	−0.988943	+	0.148298i	$0.952621\pi$
$14$	5.17758	−	2.24701i	1.38377	−	0.600538i
$15$		0			0
$16$	−0.267949	−	3.99102i	−0.0669873	−	0.997754i
$17$		−	7.08863i		−	1.71925i	−0.510929	−	0.859623i	$-0.670698\pi$
$17$		−	7.08863i		−	1.71925i	0.510929	−	0.859623i	$-0.329302\pi$
$18$		0			0
$19$	3.73205			0.856191			0.428096	−	0.903733i	$-0.359185\pi$
$19$	3.73205			0.856191			0.428096	+	0.903733i	$0.359185\pi$
$20$	−4.20241	+	4.49401i	−0.939688	+	1.00489i
$21$		0			0
$22$	2.46410	−	1.06939i	0.525348	−	0.227995i
$23$	−0.824313			−0.171881			−0.0859406	−	0.996300i	$-0.527390\pi$
$23$	−0.824313			−0.171881			−0.0859406	+	0.996300i	$0.527390\pi$
$24$		0			0
$25$	4.46410			0.892820
$26$	1.38733	−	0.602084i	0.272078	−	0.118078i
$27$		0			0
$28$	−5.83013	−	5.45183i	−1.10179	−	1.03030i
$29$	−4.50413			−0.836396			−0.418198	−	0.908356i	$-0.637338\pi$
$29$	−4.50413			−0.836396			−0.418198	+	0.908356i	$0.637338\pi$
$30$		0			0
$31$		−	5.84325i		−	1.04948i	−0.851263	−	0.524740i	$-0.824163\pi$
$31$		−	5.84325i		−	1.04948i	0.851263	−	0.524740i	$-0.175837\pi$
$32$	−5.02672	+	2.59462i	−0.888608	+	0.458668i
$33$		0			0
$34$	−9.19615	+	3.99102i	−1.57713	+	0.684453i
$35$			12.2779i			2.07534i
$36$		0			0
$37$			6.91264i			1.13643i	0.822880	+	0.568216i	$0.192366\pi$
$37$			6.91264i			1.13643i	−0.822880	+	0.568216i	$0.807634\pi$
$38$	−2.10121	−	4.84163i	−0.340861	−	0.785415i
$39$		0			0
$40$	8.19615	+	2.92163i	1.29593	+	0.461950i
$41$		−	3.79879i		−	0.593271i	−0.954991	−	0.296635i	$-0.904135\pi$
$41$		−	3.79879i		−	0.593271i	0.954991	−	0.296635i	$-0.0958646\pi$
$42$		0			0
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	−2.77466	−	2.59462i	−0.418296	−	0.391154i
$45$		0			0
$46$	0.464102	+	1.06939i	0.0684280	+	0.157673i
$47$	−6.97707			−1.01771			−0.508855	−	0.860852i	$-0.669931\pi$
$47$	−6.97707			−1.01771			−0.508855	+	0.860852i	$0.669931\pi$
$48$		0			0
$49$	−8.92820			−1.27546
$50$	−2.51336	−	5.79132i	−0.355443	−	0.819017i
$51$		0			0
$52$	−1.56218	−	1.46081i	−0.216635	−	0.202578i
$53$	10.6569			1.46384			0.731918	−	0.681393i	$-0.238625\pi$
$53$	10.6569			1.46384			0.731918	+	0.681393i	$0.238625\pi$
$54$		0			0
$55$			5.84325i			0.787904i
$56$	−3.79025	+	10.6329i	−0.506494	+	1.42089i
$57$		0			0
$58$	2.53590	+	5.84325i	0.332980	+	0.767257i
$59$			1.89939i			0.247280i	0.992327	+	0.123640i	$0.0394568\pi$
$59$			1.89939i			0.247280i	−0.992327	+	0.123640i	$0.960543\pi$
$60$		0			0
$61$		−	1.06939i		−	0.136921i	−0.997654	−	0.0684606i	$-0.978191\pi$
$61$		−	1.06939i		−	0.136921i	0.997654	−	0.0684606i	$-0.0218088\pi$
$62$	−7.58051	+	3.28985i	−0.962725	+	0.417811i
$63$		0			0
$64$	6.19615	+	5.06040i	0.774519	+	0.632551i
$65$			3.28985i			0.408055i
$66$		0			0
$67$	−9.19615			−1.12349			−0.561744	−	0.827311i	$-0.689870\pi$
$67$	−9.19615			−1.12349			−0.561744	+	0.827311i	$0.689870\pi$
$68$	10.3552	+	9.68325i	1.25575	+	1.17427i
$69$		0			0
$70$	15.9282	−	6.91264i	1.90378	−	0.826219i
$71$	−10.6569			−1.26474			−0.632370	−	0.774667i	$-0.717918\pi$
$71$	−10.6569			−1.26474			−0.632370	+	0.774667i	$0.717918\pi$
$72$		0			0
$73$	5.92820			0.693844			0.346922	−	0.937894i	$-0.387227\pi$
$73$	5.92820			0.693844			0.346922	+	0.937894i	$0.387227\pi$
$74$	8.96784	−	3.89193i	1.04249	−	0.452428i
$75$		0			0
$76$	−5.09808	+	5.45183i	−0.584789	+	0.625368i
$77$	−7.58051			−0.863879
$78$		0			0
$79$		−	6.12979i		−	0.689656i	−0.938666	−	0.344828i	$-0.887937\pi$
$79$		−	6.12979i		−	0.689656i	0.938666	−	0.344828i	$-0.112063\pi$
$80$	−0.824313	−	12.2779i	−0.0921610	−	1.37271i
$81$		0			0
$82$	−4.92820	+	2.13878i	−0.544229	+	0.236189i
$83$		−	10.3785i		−	1.13919i	−0.821927	−	0.569593i	$-0.807101\pi$
$83$		−	10.3785i		−	1.13919i	0.821927	−	0.569593i	$-0.192899\pi$
$84$		0			0
$85$		−	21.8073i		−	2.36534i
$86$	−1.12603	−	2.59462i	−0.121423	−	0.279785i
$87$		0			0
$88$	−1.80385	+	5.06040i	−0.192291	+	0.539441i
$89$		−	13.6683i		−	1.44884i	−0.689359	−	0.724420i	$-0.742108\pi$
$89$		−	13.6683i		−	1.44884i	0.689359	−	0.724420i	$-0.257892\pi$
$90$		0			0
$91$	−4.26795			−0.447403
$92$	1.12603	−	1.20417i	0.117397	−	0.125543i
$93$		0			0
$94$	3.92820	+	9.05142i	0.405163	+	0.933583i
$95$	11.4812			1.17795
$96$		0			0
$97$	−11.3923			−1.15671			−0.578357	−	0.815784i	$-0.696306\pi$
$97$	−11.3923			−1.15671			−0.578357	+	0.815784i	$0.696306\pi$
$98$	5.02672	+	11.5826i	0.507776	+	1.17002i
$99$		0			0
$100$	−6.09808	+	6.52122i	−0.609808	+	0.652122i
$101$	6.15276			0.612222			0.306111	−	0.951996i	$-0.400972\pi$
$101$	6.15276			0.612222			0.306111	+	0.951996i	$0.400972\pi$
$102$		0			0
$103$		−	3.99102i		−	0.393246i	−0.980479	−	0.196623i	$-0.937002\pi$
$103$		−	3.99102i		−	0.393246i	0.980479	−	0.196623i	$-0.0629976\pi$
$104$	−1.01560	+	2.84909i	−0.0995873	+	0.279376i
$105$		0			0
$106$	−6.00000	−	13.8253i	−0.582772	−	1.34283i
$107$			8.47908i			0.819704i	0.912152	+	0.409852i	$0.134420\pi$
$107$			8.47908i			0.819704i	−0.912152	+	0.409852i	$0.865580\pi$
$108$		0			0
$109$		−	10.1208i		−	0.969398i	−0.874681	−	0.484699i	$-0.838929\pi$
$109$		−	10.1208i		−	0.969398i	0.874681	−	0.484699i	$-0.161071\pi$
$110$	7.58051	−	3.28985i	0.722773	−	0.313674i
$111$		0			0
$112$	15.9282	−	1.06939i	1.50507	−	0.101048i
$113$			10.8874i			1.02420i	0.858925	+	0.512101i	$0.171133\pi$
$113$			10.8874i			1.02420i	−0.858925	+	0.512101i	$0.828867\pi$
$114$		0			0
$115$	−2.53590			−0.236474
$116$	6.15276	−	6.57969i	0.571269	−	0.610909i
$117$		0			0
$118$	2.46410	−	1.06939i	0.226839	−	0.0984453i
$119$	28.2908			2.59342
$120$		0			0
$121$	7.39230			0.672028
$122$	−1.38733	+	0.602084i	−0.125603	+	0.0545101i
$123$		0			0
$124$	8.53590	+	7.98203i	0.766546	+	0.716808i
$125$	−1.64863			−0.147458
$126$		0			0
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$	3.07638	−	10.8874i	0.271916	−	0.962321i
$129$		0			0
$130$	4.26795	−	1.85224i	0.374324	−	0.162452i
$131$		−	10.3785i		−	0.906772i	−0.891314	−	0.453386i	$-0.850216\pi$
$131$		−	10.3785i		−	0.906772i	0.891314	−	0.453386i	$-0.149784\pi$
$132$		0			0
$133$			14.8947i			1.29153i
$134$	5.17758	+	11.9303i	0.447275	+	1.03062i
$135$		0			0
$136$	6.73205	−	18.8857i	0.577269	−	1.61943i
$137$			17.4671i			1.49232i	0.665769	+	0.746158i	$0.268104\pi$
$137$			17.4671i			1.49232i	−0.665769	+	0.746158i	$0.731896\pi$
$138$		0			0
$139$	−3.19615			−0.271094			−0.135547	−	0.990771i	$-0.543279\pi$
$139$	−3.19615			−0.271094			−0.135547	+	0.990771i	$0.543279\pi$
$140$	−17.9357	−	16.7719i	−1.51584	−	1.41748i
$141$		0			0
$142$	6.00000	+	13.8253i	0.503509	+	1.16019i
$143$	−2.03119			−0.169857
$144$		0			0
$145$	−13.8564			−1.15071
$146$	−3.33767	−	7.69072i	−0.276228	−	0.636488i
$147$		0			0
$148$	−10.0981	−	9.44284i	−0.830057	−	0.776197i
$149$	−6.15276			−0.504053			−0.252027	−	0.967720i	$-0.581097\pi$
$149$	−6.15276			−0.504053			−0.252027	+	0.967720i	$0.581097\pi$
$150$		0			0
$151$		−	9.83427i		−	0.800301i	−0.916449	−	0.400151i	$-0.868958\pi$
$151$		−	9.83427i		−	0.800301i	0.916449	−	0.400151i	$-0.131042\pi$
$152$	9.94301	+	3.54432i	0.806485	+	0.287482i
$153$		0			0
$154$	4.26795	+	9.83427i	0.343921	+	0.792468i
$155$		−	17.9761i		−	1.44387i
$156$		0			0
$157$			21.8073i			1.74041i	0.492687	+	0.870207i	$0.336015\pi$
$157$			21.8073i			1.74041i	−0.492687	+	0.870207i	$0.663985\pi$
$158$	−7.95224	+	3.45117i	−0.632646	+	0.274561i
$159$		0			0
$160$	−15.4641	+	7.98203i	−1.22254	+	0.631035i
$161$		−	3.28985i		−	0.259276i
$162$		0			0
$163$	8.80385			0.689571			0.344785	−	0.938682i	$-0.387952\pi$
$163$	8.80385			0.689571			0.344785	+	0.938682i	$0.387952\pi$
$164$	5.54932	+	5.18924i	0.433329	+	0.405212i
$165$		0			0
$166$	−13.4641	+	5.84325i	−1.04502	+	0.453524i
$167$	−22.1381			−1.71310			−0.856548	−	0.516067i	$-0.827396\pi$
$167$	−22.1381			−1.71310			−0.856548	+	0.516067i	$0.827396\pi$
$168$		0			0
$169$	11.8564			0.912031
$170$	−28.2908	+	12.2779i	−2.16981	+	0.941670i
$171$		0			0
$172$	−2.73205	+	2.92163i	−0.208317	+	0.222772i
$173$	−1.64863			−0.125343			−0.0626714	−	0.998034i	$-0.519962\pi$
$173$	−1.64863			−0.125343			−0.0626714	+	0.998034i	$0.519962\pi$
$174$		0			0
$175$			17.8163i			1.34679i
$176$	7.58051	−	0.508941i	0.571402	−	0.0383629i
$177$		0			0
$178$	−17.7321	+	7.69549i	−1.32907	+	0.576801i
$179$		−	3.79879i		−	0.283935i	−0.989871	−	0.141967i	$-0.954657\pi$
$179$		−	3.79879i		−	0.283935i	0.989871	−	0.141967i	$-0.0453428\pi$
$180$		0			0
$181$			3.20817i			0.238461i	0.992867	+	0.119231i	$0.0380428\pi$
$181$			3.20817i			0.238461i	−0.992867	+	0.119231i	$0.961957\pi$
$182$	2.40292	+	5.53685i	0.178117	+	0.410419i
$183$		0			0
$184$	−2.19615	−	0.782847i	−0.161903	−	0.0577123i
$185$			21.2659i			1.56350i
$186$		0			0
$187$	13.4641			0.984593
$188$	9.53085	−	10.1922i	0.695109	−	0.743342i
$189$		0			0
$190$	−6.46410	−	14.8947i	−0.468955	−	1.08057i
$191$	−6.97707			−0.504843			−0.252421	−	0.967617i	$-0.581227\pi$
$191$	−6.97707			−0.504843			−0.252421	+	0.967617i	$0.581227\pi$
$192$		0			0
$193$	−5.39230			−0.388147			−0.194073	−	0.980987i	$-0.562170\pi$
$193$	−5.39230			−0.388147			−0.194073	+	0.980987i	$0.562170\pi$
$194$	6.41405	+	14.7793i	0.460502	+	1.06110i
$195$		0			0
$196$	12.1962	−	13.0424i	0.871154	−	0.931603i
$197$	−17.0305			−1.21337			−0.606687	−	0.794941i	$-0.707502\pi$
$197$	−17.0305			−1.21337			−0.606687	+	0.794941i	$0.707502\pi$
$198$		0			0
$199$		−	15.6775i		−	1.11135i	−0.831400	−	0.555675i	$-0.812460\pi$
$199$		−	15.6775i		−	1.11135i	0.831400	−	0.555675i	$-0.187540\pi$
$200$	11.8934	+	4.23954i	0.840987	+	0.299781i
$201$		0			0
$202$	−3.46410	−	7.98203i	−0.243733	−	0.561614i
$203$		−	17.9761i		−	1.26167i
$204$		0			0
$205$		−	11.6865i		−	0.816221i
$206$	−5.17758	+	2.24701i	−0.360739	+	0.156556i
$207$		0			0
$208$	4.26795	−	0.286542i	0.295929	−	0.0198681i
$209$			7.08863i			0.490331i
$210$		0			0
$211$	21.0526			1.44932			0.724659	−	0.689108i	$-0.241997\pi$
$211$	21.0526			1.44932			0.724659	+	0.689108i	$0.241997\pi$
$212$	−14.5576	+	15.5677i	−0.999818	+	1.06920i
$213$		0			0
$214$	11.0000	−	4.77386i	0.751945	−	0.326335i
$215$	6.15276			0.419614
$216$		0			0
$217$	23.3205			1.58310
$218$	−13.1298	+	5.69818i	−0.889264	+	0.385929i
$219$		0			0
$220$	−8.53590	−	7.98203i	−0.575490	−	0.538148i
$221$	7.58051			0.509920
$222$		0			0
$223$			26.0849i			1.74677i	0.487029	+	0.873386i	$0.338081\pi$
$223$			26.0849i			1.74677i	−0.487029	+	0.873386i	$0.661919\pi$
$224$	−10.3552	−	20.0617i	−0.691884	−	1.34043i
$225$		0			0
$226$	14.1244	−	6.12979i	0.939538	−	0.407748i
$227$		−	3.79879i		−	0.252134i	−0.992022	−	0.126067i	$-0.959765\pi$
$227$		−	3.79879i		−	0.252134i	0.992022	−	0.126067i	$-0.0402355\pi$
$228$		0			0
$229$			11.6865i			0.772266i	0.922443	+	0.386133i	$0.126189\pi$
$229$			11.6865i			0.772266i	−0.922443	+	0.386133i	$0.873811\pi$
$230$	1.42775	+	3.28985i	0.0941432	+	0.216926i
$231$		0			0
$232$	−12.0000	−	4.27756i	−0.787839	−	0.280835i
$233$			14.1773i			0.928784i	0.885630	+	0.464392i	$0.153727\pi$
$233$			14.1773i			0.928784i	−0.885630	+	0.464392i	$0.846273\pi$
$234$		0			0
$235$	−21.4641			−1.40016
$236$	−2.77466	−	2.59462i	−0.180615	−	0.168895i
$237$		0			0
$238$	−15.9282	−	36.7020i	−1.03247	−	2.37904i
$239$	12.3055			0.795977			0.397989	−	0.917390i	$-0.369708\pi$
$239$	12.3055			0.795977			0.397989	+	0.917390i	$0.369708\pi$
$240$		0			0
$241$	−5.39230			−0.347349			−0.173674	−	0.984803i	$-0.555564\pi$
$241$	−5.39230			−0.347349			−0.173674	+	0.984803i	$0.555564\pi$
$242$	−4.16199	−	9.59011i	−0.267543	−	0.616476i
$243$		0			0
$244$	1.56218	+	1.46081i	0.100008	+	0.0935190i
$245$	−27.4665			−1.75477
$246$		0			0
$247$			3.99102i			0.253942i
$248$	5.54932	−	15.5677i	0.352382	−	0.988551i
$249$		0			0
$250$	0.928203	+	2.13878i	0.0587047	+	0.135268i
$251$			14.1773i			0.894861i	0.894319	+	0.447431i	$0.147661\pi$
$251$			14.1773i			0.894861i	−0.894319	+	0.447431i	$0.852339\pi$
$252$		0			0
$253$		−	1.56569i		−	0.0984344i
$254$		0			0
$255$		0			0
$256$	−15.8564	+	2.13878i	−0.991025	+	0.133674i
$257$		−	3.79879i		−	0.236962i	−0.992956	−	0.118481i	$-0.962198\pi$
$257$		−	3.79879i		−	0.236962i	0.992956	−	0.118481i	$-0.0378024\pi$
$258$		0			0
$259$	−27.5885			−1.71426
$260$	−4.80585	−	4.49401i	−0.298046	−	0.278707i
$261$		0			0
$262$	−13.4641	+	5.84325i	−0.831815	+	0.360997i
$263$	3.29725			0.203317			0.101659	−	0.994819i	$-0.467585\pi$
$263$	3.29725			0.203317			0.101659	+	0.994819i	$0.467585\pi$
$264$		0			0
$265$	32.7846			2.01394
$266$	19.3230	−	8.38594i	1.18477	−	0.514175i
$267$		0			0
$268$	12.5622	−	13.4339i	0.767357	−	0.820604i
$269$	19.8860			1.21247			0.606236	−	0.795285i	$-0.292679\pi$
$269$	19.8860			1.21247			0.606236	+	0.795285i	$0.292679\pi$
$270$		0			0
$271$			11.9730i			0.727311i	0.931534	+	0.363655i	$0.118471\pi$
$271$			11.9730i			0.727311i	−0.931534	+	0.363655i	$0.881529\pi$
$272$	−28.2908	+	1.89939i	−1.71538	+	0.115168i
$273$		0			0
$274$	22.6603	−	9.83427i	1.36896	−	0.594110i
$275$			8.47908i			0.511308i
$276$		0			0
$277$		−	21.8073i		−	1.31027i	−0.755510	−	0.655137i	$-0.772611\pi$
$277$		−	21.8073i		−	1.31027i	0.755510	−	0.655137i	$-0.227389\pi$
$278$	1.79949	+	4.14640i	0.107926	+	0.248685i
$279$		0			0
$280$	−11.6603	+	32.7110i	−0.696833	+	1.95485i
$281$		−	10.3785i		−	0.619128i	−0.950879	−	0.309564i	$-0.899817\pi$
$281$		−	10.3785i		−	0.619128i	0.950879	−	0.309564i	$-0.100183\pi$
$282$		0			0
$283$	27.8564			1.65589			0.827946	−	0.560808i	$-0.189509\pi$
$283$	27.8564			1.65589			0.827946	+	0.560808i	$0.189509\pi$
$284$	14.5576	−	15.5677i	0.863833	−	0.923774i
$285$		0			0
$286$	1.14359	+	2.63508i	0.0676221	+	0.155816i
$287$	15.1610			0.894926
$288$		0			0
$289$	−33.2487			−1.95581
$290$	7.80138	+	17.9761i	0.458113	+	1.05559i
$291$		0			0
$292$	−8.09808	+	8.66000i	−0.473904	+	0.506788i
$293$	−7.58051			−0.442858			−0.221429	−	0.975176i	$-0.571072\pi$
$293$	−7.58051			−0.442858			−0.221429	+	0.975176i	$0.571072\pi$
$294$		0			0
$295$			5.84325i			0.340207i
$296$	−6.56491	+	18.4168i	−0.381578	+	1.07046i
$297$		0			0
$298$	3.46410	+	7.98203i	0.200670	+	0.462387i
$299$		−	0.881512i		−	0.0509791i
$300$		0			0
$301$			7.98203i			0.460077i
$302$	−12.7581	+	5.53685i	−0.734146	+	0.318610i
$303$		0			0
$304$	−1.00000	−	14.8947i	−0.0573539	−	0.854268i
$305$		−	3.28985i		−	0.188376i
$306$		0			0
$307$	20.9282			1.19444			0.597218	−	0.802079i	$-0.296273\pi$
$307$	20.9282			1.19444			0.597218	+	0.802079i	$0.296273\pi$
$308$	10.3552	−	11.0737i	0.590040	−	0.630983i
$309$		0			0
$310$	−23.3205	+	10.1208i	−1.32452	+	0.574823i
$311$	20.4895			1.16185			0.580925	−	0.813957i	$-0.302691\pi$
$311$	20.4895			1.16185			0.580925	+	0.813957i	$0.302691\pi$
$312$		0			0
$313$	9.39230			0.530884			0.265442	−	0.964127i	$-0.414482\pi$
$313$	9.39230			0.530884			0.265442	+	0.964127i	$0.414482\pi$
$314$	28.2908	−	12.2779i	1.59654	−	0.692880i
$315$		0			0
$316$	8.95448	+	8.37345i	0.503729	+	0.471044i
$317$	16.8096			0.944124			0.472062	−	0.881565i	$-0.343510\pi$
$317$	16.8096			0.944124			0.472062	+	0.881565i	$0.343510\pi$
$318$		0			0
$319$		−	8.55511i		−	0.478994i
$320$	19.0617	+	15.5677i	1.06558	+	0.870262i
$321$		0			0
$322$	−4.26795	+	1.85224i	−0.237844	+	0.103221i
$323$		−	26.4551i		−	1.47200i
$324$		0			0
$325$			4.77386i			0.264806i
$326$	−4.95671	−	11.4213i	−0.274527	−	0.632568i
$327$		0			0
$328$	3.60770	−	10.1208i	0.199202	−	0.558828i
$329$		−	27.8456i		−	1.53518i
$330$		0			0
$331$	1.87564			0.103095			0.0515474	−	0.998671i	$-0.483585\pi$
$331$	1.87564			0.103095			0.0515474	+	0.998671i	$0.483585\pi$
$332$	15.1610	+	14.1773i	0.832069	+	0.778079i
$333$		0			0
$334$	12.4641	+	28.7200i	0.682005	+	1.57149i
$335$	−28.2908			−1.54569
$336$		0			0
$337$	−11.3923			−0.620578			−0.310289	−	0.950642i	$-0.600426\pi$
$337$	−11.3923			−0.620578			−0.310289	+	0.950642i	$0.600426\pi$
$338$	−6.67535	−	15.3814i	−0.363091	−	0.836640i
$339$		0			0
$340$	31.8564	+	29.7893i	1.72766	+	1.61555i
$341$	11.0986			0.601025
$342$		0			0
$343$		−	7.69549i		−	0.415517i
$344$	5.32844	+	1.89939i	0.287290	+	0.102408i
$345$		0			0
$346$	0.928203	+	2.13878i	0.0499005	+	0.114981i
$347$			7.59757i			0.407859i	0.978986	+	0.203930i	$0.0653714\pi$
$347$			7.59757i			0.407859i	−0.978986	+	0.203930i	$0.934629\pi$
$348$		0			0
$349$			2.63508i			0.141053i	0.997510	+	0.0705264i	$0.0224679\pi$
$349$			2.63508i			0.141053i	−0.997510	+	0.0705264i	$0.977532\pi$
$350$	23.1133	−	10.0309i	1.23546	−	0.536172i
$351$		0			0
$352$	−4.92820	−	9.54773i	−0.262674	−	0.508895i
$353$			7.59757i			0.404378i	0.979347	+	0.202189i	$0.0648055\pi$
$353$			7.59757i			0.404378i	−0.979347	+	0.202189i	$0.935194\pi$
$354$		0			0
$355$	−32.7846			−1.74003
$356$	19.9669	+	18.6713i	1.05824	+	0.989576i
$357$		0			0
$358$	−4.92820	+	2.13878i	−0.260464	+	0.113038i
$359$	−23.7867			−1.25541			−0.627707	−	0.778449i	$-0.716007\pi$
$359$	−23.7867			−1.25541			−0.627707	+	0.778449i	$0.716007\pi$
$360$		0			0
$361$	−5.07180			−0.266937
$362$	4.16199	−	1.80625i	0.218749	−	0.0949344i
$363$		0			0
$364$	5.83013	−	6.23468i	0.305582	−	0.326786i
$365$	18.2374			0.954589
$366$		0			0
$367$		−	37.4848i		−	1.95669i	−0.206975	−	0.978346i	$-0.566362\pi$
$367$		−	37.4848i		−	1.95669i	0.206975	−	0.978346i	$-0.433638\pi$
$368$	0.220874	+	3.28985i	0.0115139	+	0.171495i
$369$		0			0
$370$	27.5885	−	11.9730i	1.43426	−	0.622449i
$371$			42.5318i			2.20814i
$372$		0			0
$373$			18.5991i			0.963027i	0.876439	+	0.481514i	$0.159913\pi$
$373$			18.5991i			0.963027i	−0.876439	+	0.481514i	$0.840087\pi$
$374$	−7.58051	−	17.4671i	−0.391979	−	0.903203i
$375$		0			0
$376$	−18.5885	−	6.62610i	−0.958626	−	0.341715i
$377$		−	4.81667i		−	0.248071i
$378$		0			0
$379$	−26.2679			−1.34929			−0.674647	−	0.738141i	$-0.735704\pi$
$379$	−26.2679			−1.34929			−0.674647	+	0.738141i	$0.735704\pi$
$380$	−15.6836	+	16.7719i	−0.804552	+	0.860380i
$381$		0			0
$382$	3.92820	+	9.05142i	0.200984	+	0.463111i
$383$	1.64863			0.0842409			0.0421204	−	0.999113i	$-0.486589\pi$
$383$	1.64863			0.0842409			0.0421204	+	0.999113i	$0.486589\pi$
$384$		0			0
$385$	−23.3205			−1.18852
$386$	3.03596	+	6.99549i	0.154526	+	0.356061i
$387$		0			0
$388$	15.5622	−	16.6420i	0.790050	−	0.844871i
$389$	15.3819			0.779893			0.389946	−	0.920838i	$-0.372494\pi$
$389$	15.3819			0.779893			0.389946	+	0.920838i	$0.372494\pi$
$390$		0			0
$391$			5.84325i			0.295506i
$392$	−23.7867	−	8.47908i	−1.20141	−	0.428258i
$393$		0			0
$394$	9.58846	+	22.0939i	0.483059	+	1.11307i
$395$		−	18.8576i		−	0.948827i
$396$		0			0
$397$		−	10.1208i		−	0.507949i	−0.967211	−	0.253974i	$-0.918262\pi$
$397$		−	10.1208i		−	0.507949i	0.967211	−	0.253974i	$-0.0817379\pi$
$398$	−20.3386	+	8.82670i	−1.01948	+	0.442442i
$399$		0			0
$400$	−1.19615	−	17.8163i	−0.0598076	−	0.890815i
$401$		−	15.1951i		−	0.758809i	−0.925231	−	0.379405i	$-0.876129\pi$
$401$		−	15.1951i		−	0.758809i	0.925231	−	0.379405i	$-0.123871\pi$
$402$		0			0
$403$	6.24871			0.311270
$404$	−8.40482	+	8.98803i	−0.418155	+	0.447171i
$405$		0			0
$406$	−23.3205	+	10.1208i	−1.15738	+	0.502287i
$407$	−13.1298			−0.650821
$408$		0			0
$409$	−8.60770			−0.425623			−0.212812	−	0.977093i	$-0.568262\pi$
$409$	−8.60770			−0.425623			−0.212812	+	0.977093i	$0.568262\pi$
$410$	−15.1610	+	6.57969i	−0.748749	+	0.324948i
$411$		0			0
$412$	5.83013	+	5.45183i	0.287230	+	0.268592i
$413$	−7.58051			−0.373012
$414$		0			0
$415$		−	31.9281i		−	1.56729i
$416$	−2.77466	−	5.37552i	−0.136039	−	0.263557i
$417$		0			0
$418$	9.19615	−	3.99102i	0.449799	−	0.195207i
$419$			26.4551i			1.29242i	0.763160	+	0.646209i	$0.223647\pi$
$419$			26.4551i			1.29242i	−0.763160	+	0.646209i	$0.776353\pi$
$420$		0			0
$421$		−	4.77386i		−	0.232664i	−0.993210	−	0.116332i	$-0.962886\pi$
$421$		−	4.77386i		−	0.232664i	0.993210	−	0.116332i	$-0.0371136\pi$
$422$	−11.8529	−	27.3117i	−0.576992	−	1.32951i
$423$		0			0
$424$	28.3923	+	10.1208i	1.37885	+	0.491510i
$425$		−	31.6444i		−	1.53498i
$426$		0			0
$427$	4.26795			0.206541
$428$	−12.3864	−	11.5826i	−0.598717	−	0.559868i
$429$		0			0
$430$	−3.46410	−	7.98203i	−0.167054	−	0.384928i
$431$	0.382565			0.0184275			0.00921375	−	0.999958i	$-0.497067\pi$
$431$	0.382565			0.0184275			0.00921375	+	0.999958i	$0.497067\pi$
$432$		0			0
$433$	4.53590			0.217981			0.108991	−	0.994043i	$-0.465238\pi$
$433$	4.53590			0.217981			0.108991	+	0.994043i	$0.465238\pi$
$434$	−13.1298	−	30.2539i	−0.630252	−	1.45223i
$435$		0			0
$436$	14.7846	+	13.8253i	0.708054	+	0.662111i
$437$	−3.07638			−0.147163
$438$		0			0
$439$		−	14.3984i		−	0.687197i	−0.939117	−	0.343598i	$-0.888354\pi$
$439$		−	14.3984i		−	0.687197i	0.939117	−	0.343598i	$-0.111646\pi$
$440$	−5.54932	+	15.5677i	−0.264553	+	0.742162i
$441$		0			0
$442$	−4.26795	−	9.83427i	−0.203006	−	0.467768i
$443$			27.3366i			1.29880i	0.760446	+	0.649402i	$0.224981\pi$
$443$			27.3366i			1.29880i	−0.760446	+	0.649402i	$0.775019\pi$
$444$		0			0
$445$		−	42.0489i		−	1.99331i
$446$	33.8402	−	14.6862i	1.60238	−	0.695412i
$447$		0			0
$448$	−20.1962	+	24.7289i	−0.954179	+	1.16833i
$449$			24.0468i			1.13484i	0.823429	+	0.567419i	$0.192058\pi$
$449$			24.0468i			1.13484i	−0.823429	+	0.567419i	$0.807942\pi$
$450$		0			0
$451$	7.21539			0.339759
$452$	−15.9045	−	14.8725i	−0.748084	−	0.699543i
$453$		0			0
$454$	−4.92820	+	2.13878i	−0.231292	+	0.100378i
$455$	−13.1298			−0.615536
$456$		0			0
$457$	6.39230			0.299019			0.149510	−	0.988760i	$-0.452230\pi$
$457$	6.39230			0.299019			0.149510	+	0.988760i	$0.452230\pi$
$458$	15.1610	−	6.57969i	0.708428	−	0.307449i
$459$		0			0
$460$	3.46410	−	3.70447i	0.161515	−	0.172722i
$461$	−5.93188			−0.276275			−0.138138	−	0.990413i	$-0.544112\pi$
$461$	−5.93188			−0.276275			−0.138138	+	0.990413i	$0.544112\pi$
$462$		0			0
$463$			2.42532i			0.112714i	0.998411	+	0.0563571i	$0.0179485\pi$
$463$			2.42532i			0.112714i	−0.998411	+	0.0563571i	$0.982051\pi$
$464$	1.20688	+	17.9761i	0.0560279	+	0.834517i
$465$		0			0
$466$	18.3923	−	7.98203i	0.852007	−	0.369760i
$467$			19.8754i			0.919726i	0.887990	+	0.459863i	$0.152101\pi$
$467$			19.8754i			0.919726i	−0.887990	+	0.459863i	$0.847899\pi$
$468$		0			0
$469$		−	36.7020i		−	1.69474i
$470$	12.0846	+	27.8456i	0.557423	+	1.28442i
$471$		0			0
$472$	−1.80385	+	5.06040i	−0.0830288	+	0.232924i
$473$			3.79879i			0.174668i
$474$		0			0
$475$	16.6603			0.764425
$476$	−38.6460	+	41.3276i	−1.77134	+	1.89425i
$477$		0			0
$478$	−6.92820	−	15.9641i	−0.316889	−	0.730179i
$479$	6.15276			0.281127			0.140563	−	0.990072i	$-0.455109\pi$
$479$	6.15276			0.281127			0.140563	+	0.990072i	$0.455109\pi$
$480$		0			0
$481$	−7.39230			−0.337060
$482$	3.03596	+	6.99549i	0.138284	+	0.318636i
$483$		0			0
$484$	−10.0981	+	10.7988i	−0.459003	+	0.490853i
$485$	−35.0470			−1.59140
$486$		0			0
$487$			33.2073i			1.50477i	0.658726	+	0.752383i	$0.271096\pi$
$487$			33.2073i			1.50477i	−0.658726	+	0.752383i	$0.728904\pi$
$488$	1.01560	−	2.84909i	0.0459738	−	0.128972i
$489$		0			0
$490$	15.4641	+	35.6326i	0.698597	+	1.60972i
$491$			33.0348i			1.49084i	0.666595	+	0.745420i	$0.267751\pi$
$491$			33.0348i			1.49084i	−0.666595	+	0.745420i	$0.732249\pi$
$492$		0			0
$493$			31.9281i			1.43797i
$494$	5.17758	−	2.24701i	0.232950	−	0.101098i
$495$		0			0
$496$	−23.3205	+	1.56569i	−1.04712	+	0.0703018i
$497$		−	42.5318i		−	1.90781i
$498$		0			0
$499$	−5.60770			−0.251035			−0.125517	−	0.992091i	$-0.540059\pi$
$499$	−5.60770			−0.251035			−0.125517	+	0.992091i	$0.540059\pi$
$500$	2.25207	−	2.40833i	0.100715	−	0.107704i
$501$		0			0
$502$	18.3923	−	7.98203i	0.820889	−	0.356255i
$503$	29.4977			1.31524			0.657619	−	0.753351i	$-0.271564\pi$
$503$	29.4977			1.31524			0.657619	+	0.753351i	$0.271564\pi$
$504$		0			0
$505$	18.9282			0.842294
$506$	−2.03119	+	0.881512i	−0.0902975	+	0.0391880i
$507$		0			0
$508$		0			0
$509$	0.220874			0.00979007			0.00489503	−	0.999988i	$-0.498442\pi$
$509$	0.220874			0.00979007			0.00489503	+	0.999988i	$0.498442\pi$
$510$		0			0
$511$			23.6595i			1.04664i
$512$	11.7021	+	19.3665i	0.517163	+	0.855887i
$513$		0			0
$514$	−4.92820	+	2.13878i	−0.217374	+	0.0943375i
$515$		−	12.2779i		−	0.541028i
$516$		0			0
$517$		−	13.2522i		−	0.582831i
$518$	15.5327	+	35.7908i	0.682470	+	1.57256i
$519$		0			0
$520$	−3.12436	+	8.76488i	−0.137012	+	0.384365i
$521$		−	7.08863i		−	0.310559i	−0.987871	−	0.155279i	$-0.950372\pi$
$521$		−	7.08863i		−	0.310559i	0.987871	−	0.155279i	$-0.0496278\pi$
$522$		0			0
$523$	−37.5885			−1.64363			−0.821814	−	0.569756i	$-0.807038\pi$
$523$	−37.5885			−1.64363			−0.821814	+	0.569756i	$0.807038\pi$
$524$	15.1610	+	14.1773i	0.662312	+	0.619337i
$525$		0			0
$526$	−1.85641	−	4.27756i	−0.0809432	−	0.186510i
$527$	−41.4207			−1.80431
$528$		0			0
$529$	−22.3205			−0.970457
$530$	−18.4583	−	42.5318i	−0.801776	−	1.84746i
$531$		0			0
$532$	−21.7583	−	20.3465i	−0.943343	−	0.882133i
$533$	4.06238			0.175961
$534$		0			0
$535$			26.0849i			1.12775i
$536$	−24.5006	−	8.73356i	−1.05826	−	0.377232i
$537$		0			0
$538$	−11.1962	−	25.7983i	−0.482700	−	1.11224i
$539$		−	16.9582i		−	0.730440i
$540$		0			0
$541$			34.5632i			1.48599i	0.669298	+	0.742994i	$0.266595\pi$
$541$			34.5632i			1.48599i	−0.669298	+	0.742994i	$0.733405\pi$
$542$	15.5327	−	6.74102i	0.667189	−	0.289552i
$543$		0			0
$544$	18.3923	+	35.6326i	0.788564	+	1.52773i
$545$		−	31.1354i		−	1.33370i
$546$		0			0
$547$	−31.5885			−1.35062			−0.675312	−	0.737532i	$-0.735991\pi$
$547$	−31.5885			−1.35062			−0.675312	+	0.737532i	$0.735991\pi$
$548$	−25.5162	−	23.8605i	−1.09000	−	1.01927i
$549$		0			0
$550$	11.0000	−	4.77386i	0.469042	−	0.203558i
$551$	−16.8096			−0.716115
$552$		0			0
$553$	24.4641			1.04032
$554$	−28.2908	+	12.2779i	−1.20196	+	0.521637i
$555$		0			0
$556$	4.36603	−	4.66898i	0.185161	−	0.198009i
$557$	−14.9401			−0.633034			−0.316517	−	0.948587i	$-0.602513\pi$
$557$	−14.9401			−0.633034			−0.316517	+	0.948587i	$0.602513\pi$
$558$		0			0
$559$			2.13878i			0.0904607i
$560$	49.0012	−	3.28985i	2.07068	−	0.139021i
$561$		0			0
$562$	−13.4641	+	5.84325i	−0.567949	+	0.246483i
$563$		−	34.9342i		−	1.47230i	−0.676817	−	0.736151i	$-0.736641\pi$
$563$		−	34.9342i		−	1.47230i	0.676817	−	0.736151i	$-0.263359\pi$
$564$		0			0
$565$			33.4938i			1.40910i
$566$	−15.6836	−	36.1384i	−0.659231	−	1.51901i
$567$		0			0
$568$	−28.3923	−	10.1208i	−1.19131	−	0.424660i
$569$			6.07075i			0.254499i	0.991871	+	0.127250i	$0.0406149\pi$
$569$			6.07075i			0.254499i	−0.991871	+	0.127250i	$0.959385\pi$
$570$		0			0
$571$	−3.19615			−0.133755			−0.0668774	−	0.997761i	$-0.521304\pi$
$571$	−3.19615			−0.133755			−0.0668774	+	0.997761i	$0.521304\pi$
$572$	2.77466	−	2.96719i	0.116014	−	0.124064i
$573$		0			0
$574$	−8.53590	−	19.6685i	−0.356282	−	0.820949i
$575$	−3.67982			−0.153459
$576$		0			0
$577$	11.9282			0.496578			0.248289	−	0.968686i	$-0.420132\pi$
$577$	11.9282			0.496578			0.248289	+	0.968686i	$0.420132\pi$
$578$	18.7196	+	43.1339i	0.778631	+	1.79413i
$579$		0			0
$580$	18.9282	−	20.2416i	0.785951	−	0.840487i
$581$	41.4207			1.71842
$582$		0			0
$583$			20.2416i			0.838322i
$584$	15.7940	+	5.62999i	0.653562	+	0.232971i
$585$		0			0
$586$	4.26795	+	9.83427i	0.176307	+	0.406250i
$587$			33.0348i			1.36349i	0.731588	+	0.681747i	$0.238779\pi$
$587$			33.0348i			1.36349i	−0.731588	+	0.681747i	$0.761221\pi$
$588$		0			0
$589$		−	21.8073i		−	0.898555i
$590$	7.58051	−	3.28985i	0.312085	−	0.135441i
$591$		0			0
$592$	27.5885	−	1.85224i	1.13388	−	0.0761265i
$593$			38.7330i			1.59057i	0.606233	+	0.795287i	$0.292680\pi$
$593$			38.7330i			1.59057i	−0.606233	+	0.795287i	$0.707320\pi$
$594$		0			0
$595$	87.0333			3.56802
$596$	8.40482	−	8.98803i	0.344275	−	0.368164i
$597$		0			0
$598$	−1.14359	+	0.496305i	−0.0467650	+	0.0202954i
$599$	−22.5207			−0.920169			−0.460084	−	0.887875i	$-0.652181\pi$
$599$	−22.5207			−0.920169			−0.460084	+	0.887875i	$0.652181\pi$
$600$		0			0
$601$	30.3923			1.23973			0.619864	−	0.784709i	$-0.287188\pi$
$601$	30.3923			1.23973			0.619864	+	0.784709i	$0.287188\pi$
$602$	10.3552	−	4.49401i	0.422045	−	0.183162i
$603$		0			0
$604$	14.3660	+	13.4339i	0.584545	+	0.546616i
$605$	22.7415			0.924574
$606$		0			0
$607$		−	35.3461i		−	1.43465i	−0.696738	−	0.717326i	$-0.745366\pi$
$607$		−	35.3461i		−	1.43465i	0.696738	−	0.717326i	$-0.254634\pi$
$608$	−18.7600	+	9.68325i	−0.760818	+	0.392708i
$609$		0			0
$610$	−4.26795	+	1.85224i	−0.172804	+	0.0749949i
$611$		−	7.46120i		−	0.301848i
$612$		0			0
$613$		−	6.91264i		−	0.279199i	−0.990208	−	0.139599i	$-0.955418\pi$
$613$		−	6.91264i		−	0.279199i	0.990208	−	0.139599i	$-0.0445815\pi$
$614$	−11.7829	−	27.1504i	−0.475520	−	1.09570i
$615$		0			0
$616$	−20.1962	−	7.19918i	−0.813726	−	0.290063i
$617$			28.8635i			1.16200i	0.813904	+	0.581000i	$0.197338\pi$
$617$			28.8635i			1.16200i	−0.813904	+	0.581000i	$0.802662\pi$
$618$		0			0
$619$	37.1962			1.49504			0.747520	−	0.664240i	$-0.231245\pi$
$619$	37.1962			1.49504			0.747520	+	0.664240i	$0.231245\pi$
$620$	26.2597	+	24.5557i	1.05461	+	0.986182i
$621$		0			0
$622$	−11.5359	−	26.5812i	−0.462547	−	1.06581i
$623$	54.5505			2.18552
$624$		0			0
$625$	−27.3923			−1.09569
$626$	−5.28802	−	12.1847i	−0.211352	−	0.487000i
$627$		0			0
$628$	−31.8564	−	29.7893i	−1.27121	−	1.18872i
$629$	49.0012			1.95380
$630$		0			0
$631$			22.0939i			0.879542i	0.898110	+	0.439771i	$0.144940\pi$
$631$			22.0939i			0.879542i	−0.898110	+	0.439771i	$0.855060\pi$
$632$	5.82145	−	16.3311i	0.231565	−	0.649617i
$633$		0			0
$634$	−9.46410	−	21.8073i	−0.375867	−	0.866079i
$635$		0			0
$636$		0			0
$637$		−	9.54773i		−	0.378295i
$638$	−11.0986	+	4.81667i	−0.439399	+	0.190694i
$639$		0			0
$640$	9.46410	−	33.4938i	0.374101	−	1.32396i
$641$		−	34.9342i		−	1.37982i	−0.723896	−	0.689909i	$-0.757650\pi$
$641$		−	34.9342i		−	1.37982i	0.723896	−	0.689909i	$-0.242350\pi$
$642$		0			0
$643$	−18.7846			−0.740793			−0.370396	−	0.928874i	$-0.620778\pi$
$643$	−18.7846			−0.740793			−0.370396	+	0.928874i	$0.620778\pi$
$644$	4.80585	+	4.49401i	0.189377	+	0.177089i
$645$		0			0
$646$	−34.3205	+	14.8947i	−1.35032	+	0.586023i
$647$	39.7720			1.56360			0.781800	−	0.623529i	$-0.214302\pi$
$647$	39.7720			1.56360			0.781800	+	0.623529i	$0.214302\pi$
$648$		0			0
$649$	−3.60770			−0.141614
$650$	6.19318	−	2.68776i	0.242916	−	0.105423i
$651$		0			0
$652$	−12.0263	+	12.8608i	−0.470985	+	0.503667i
$653$	−32.4124			−1.26840			−0.634198	−	0.773171i	$-0.718669\pi$
$653$	−32.4124			−1.26840			−0.634198	+	0.773171i	$0.718669\pi$
$654$		0			0
$655$		−	31.9281i		−	1.24753i
$656$	−15.1610	+	1.01788i	−0.591938	+	0.0397416i
$657$		0			0
$658$	−36.1244	+	15.6775i	−1.40827	+	0.611173i
$659$		−	21.7748i		−	0.848227i	−0.905609	−	0.424114i	$-0.860586\pi$
$659$		−	21.7748i		−	0.848227i	0.905609	−	0.424114i	$-0.139414\pi$
$660$		0			0
$661$			45.2571i			1.76030i	0.474698	+	0.880149i	$0.342557\pi$
$661$			45.2571i			1.76030i	−0.474698	+	0.880149i	$0.657443\pi$
$662$	−1.05602	−	2.43329i	−0.0410433	−	0.0945726i
$663$		0			0
$664$	9.85641	−	27.6506i	0.382503	−	1.07305i
$665$			45.8216i			1.77689i
$666$		0			0
$667$	3.71281			0.143761
$668$	30.2412	−	32.3396i	1.17007	−	1.25126i
$669$		0			0
$670$	15.9282	+	36.7020i	0.615360	+	1.41792i
$671$	2.03119			0.0784133
$672$		0			0
$673$	35.2487			1.35874			0.679369	−	0.733797i	$-0.262254\pi$
$673$	35.2487			1.35874			0.679369	+	0.733797i	$0.262254\pi$
$674$	6.41405	+	14.7793i	0.247060	+	0.569279i
$675$		0			0
$676$	−16.1962	+	17.3200i	−0.622929	+	0.666154i
$677$	44.4970			1.71016			0.855080	−	0.518496i	$-0.173508\pi$
$677$	44.4970			1.71016			0.855080	+	0.518496i	$0.173508\pi$
$678$		0			0
$679$		−	45.4669i		−	1.74486i
$680$	20.7103	−	58.0995i	0.794205	−	2.22801i
$681$		0			0
$682$	−6.24871	−	14.3984i	−0.239276	−	0.551342i
$683$		−	39.7509i		−	1.52103i	−0.649323	−	0.760513i	$-0.724948\pi$
$683$		−	39.7509i		−	1.52103i	0.649323	−	0.760513i	$-0.275052\pi$
$684$		0			0
$685$			53.7354i			2.05313i
$686$	−9.98343	+	4.33269i	−0.381169	+	0.165423i
$687$		0			0
$688$	−0.535898	−	7.98203i	−0.0204309	−	0.304312i
$689$			11.3964i			0.434167i
$690$		0			0
$691$	3.85641			0.146705			0.0733523	−	0.997306i	$-0.476630\pi$
$691$	3.85641			0.146705			0.0733523	+	0.997306i	$0.476630\pi$
$692$	2.25207	−	2.40833i	0.0856107	−	0.0915511i
$693$		0			0
$694$	9.85641	−	4.27756i	0.374144	−	0.162374i
$695$	−9.83257			−0.372971
$696$		0			0
$697$	−26.9282			−1.01998
$698$	3.41852	−	1.48360i	0.129393	−	0.0561549i
$699$		0			0
$700$	−26.0263	−	24.3375i	−0.983701	−	0.919872i
$701$	−51.8567			−1.95860			−0.979300	−	0.202415i	$-0.935121\pi$
$701$	−51.8567			−1.95860			−0.979300	+	0.202415i	$0.935121\pi$
$702$		0			0
$703$			25.7983i			0.973002i
$704$	−9.61170	+	11.7689i	−0.362255	+	0.443558i
$705$		0			0
$706$	9.85641	−	4.27756i	0.370951	−	0.160988i
$707$			24.5557i			0.923514i
$708$		0			0
$709$		−	35.1363i		−	1.31957i	−0.751454	−	0.659786i	$-0.770647\pi$
$709$		−	35.1363i		−	1.31957i	0.751454	−	0.659786i	$-0.229353\pi$
$710$	18.4583	+	42.5318i	0.692726	+	1.59619i
$711$		0			0
$712$	12.9808	−	36.4154i	0.486475	−	1.36473i
$713$			4.81667i			0.180386i
$714$		0			0
$715$	−6.24871			−0.233689
$716$	5.54932	+	5.18924i	0.207388	+	0.193931i
$717$		0			0
$718$	13.3923	+	30.8587i	0.499796	+	1.15164i
$719$	−7.80138			−0.290942			−0.145471	−	0.989362i	$-0.546470\pi$
$719$	−7.80138			−0.290942			−0.145471	+	0.989362i	$0.546470\pi$
$720$		0			0
$721$	15.9282			0.593197
$722$	2.85550	+	6.57969i	0.106271	+	0.244871i
$723$		0			0
$724$	−4.68653	−	4.38244i	−0.174174	−	0.162872i
$725$	−20.1069			−0.746751
$726$		0			0
$727$			26.0849i			0.967434i	0.875224	+	0.483717i	$0.160714\pi$
$727$			26.0849i			0.967434i	−0.875224	+	0.483717i	$0.839286\pi$
$728$	−11.3708	−	4.05326i	−0.421428	−	0.150224i
$729$		0			0
$730$	−10.2679	−	23.6595i	−0.380034	−	0.875679i
$731$		−	14.1773i		−	0.524365i
$732$		0			0
$733$		−	13.2522i		−	0.489481i	−0.969589	−	0.244741i	$-0.921297\pi$
$733$		−	13.2522i		−	0.489481i	0.969589	−	0.244741i	$-0.0787028\pi$
$734$	−48.6294	+	21.1046i	−1.79495	+	0.778984i
$735$		0			0
$736$	4.14359	−	2.13878i	0.152735	−	0.0788364i
$737$		−	17.4671i		−	0.643409i
$738$		0			0
$739$	−20.6410			−0.759292			−0.379646	−	0.925132i	$-0.623954\pi$
$739$	−20.6410			−0.759292			−0.379646	+	0.925132i	$0.623954\pi$
$740$	−31.0655	−	29.0498i	−1.14199	−	1.06789i
$741$		0			0
$742$	55.1769	−	23.9461i	2.02561	−	0.879089i
$743$	51.6950			1.89651			0.948253	−	0.317517i	$-0.102849\pi$
$743$	51.6950			1.89651			0.948253	+	0.317517i	$0.102849\pi$
$744$		0			0
$745$	−18.9282			−0.693476
$746$	24.1289	−	10.4716i	0.883420	−	0.383393i
$747$		0			0
$748$	−18.3923	+	19.6685i	−0.672489	+	0.719153i
$749$	−33.8402			−1.23649
$750$		0			0
$751$			19.9551i			0.728171i	0.931366	+	0.364086i	$0.118618\pi$
$751$			19.9551i			0.728171i	−0.931366	+	0.364086i	$0.881382\pi$
$752$	1.86950	+	27.8456i	0.0681737	+	1.01542i
$753$		0			0
$754$	−6.24871	+	2.71186i	−0.227565	+	0.0987602i
$755$		−	30.2539i		−	1.10105i
$756$		0			0
$757$			52.0930i			1.89335i	0.322189	+	0.946675i	$0.395581\pi$
$757$			52.0930i			1.89335i	−0.322189	+	0.946675i	$0.604419\pi$
$758$	14.7893	+	34.0777i	0.537171	+	1.23776i
$759$		0			0
$760$	30.5885	+	10.9037i	1.10956	+	0.395517i
$761$		−	43.0407i		−	1.56023i	−0.625639	−	0.780113i	$-0.715162\pi$
$761$		−	43.0407i		−	1.56023i	0.625639	−	0.780113i	$-0.284838\pi$
$762$		0			0
$763$	40.3923			1.46230
$764$	9.53085	−	10.1922i	0.344814	−	0.368741i
$765$		0			0
$766$	−0.928203	−	2.13878i	−0.0335373	−	0.0772772i
$767$	−2.03119			−0.0733421
$768$		0			0
$769$	4.07180			0.146833			0.0734164	−	0.997301i	$-0.476610\pi$
$769$	4.07180			0.146833			0.0734164	+	0.997301i	$0.476610\pi$
$770$	13.1298	+	30.2539i	0.473166	+	1.09028i
$771$		0			0
$772$	7.36603	−	7.87715i	0.265109	−	0.283505i
$773$	−44.7179			−1.60839			−0.804196	−	0.594364i	$-0.797404\pi$
$773$	−44.7179			−1.60839			−0.804196	+	0.594364i	$0.797404\pi$
$774$		0			0
$775$		−	26.0849i		−	0.936996i
$776$	−30.3516	−	10.8192i	−1.08956	−	0.388388i
$777$		0			0
$778$	−8.66025	−	19.9551i	−0.310485	−	0.715424i
$779$		−	14.1773i		−	0.507953i
$780$		0			0
$781$		−	20.2416i		−	0.724302i
$782$	7.58051	−	3.28985i	0.271078	−	0.117645i
$783$		0			0
$784$	2.39230	+	35.6326i	0.0854395	+	1.27259i
$785$			67.0875i			2.39446i
$786$		0			0
$787$	7.44486			0.265381			0.132690	−	0.991158i	$-0.457638\pi$
$787$	7.44486			0.265381			0.132690	+	0.991158i	$0.457638\pi$
$788$	23.2641	−	24.8784i	0.828750	−	0.886256i
$789$		0			0
$790$	−24.4641	+	10.6171i	−0.870394	+	0.377740i
$791$	−43.4519			−1.54497
$792$		0			0
$793$	1.14359			0.0406102
$794$	−13.1298	+	5.69818i	−0.465960	+	0.202221i
$795$		0			0
$796$	22.9019	+	21.4159i	0.811737	+	0.759066i
$797$	−27.4665			−0.972914			−0.486457	−	0.873704i	$-0.661711\pi$
$797$	−27.4665			−0.972914			−0.486457	+	0.873704i	$0.661711\pi$
$798$		0			0
$799$			49.4579i			1.74969i
$800$	−22.4398	+	11.5826i	−0.793367	+	0.409508i
$801$		0			0
$802$	−19.7128	+	8.55511i	−0.696084	+	0.302092i
$803$			11.2600i			0.397356i
$804$		0			0
$805$		−	10.1208i		−	0.356712i
$806$	−3.51813	−	8.10651i	−0.123921	−	0.285540i
$807$		0			0
$808$	16.3923	+	5.84325i	0.576679	+	0.205565i
$809$			14.1773i			0.498446i	0.968446	+	0.249223i	$0.0801752\pi$
$809$			14.1773i			0.498446i	−0.968446	+	0.249223i	$0.919825\pi$
$810$		0			0
$811$	−27.0718			−0.950619			−0.475310	−	0.879819i	$-0.657664\pi$
$811$	−27.0718			−0.950619			−0.475310	+	0.879819i	$0.657664\pi$
$812$	26.2597	+	24.5557i	0.921533	+	0.861738i
$813$		0			0
$814$	7.39230	+	17.0335i	0.259100	+	0.597022i
$815$	27.0840			0.948710
$816$		0			0
$817$	7.46410			0.261136
$818$	4.84627	+	11.1668i	0.169446	+	0.390440i
$819$		0			0
$820$	17.0718	+	15.9641i	0.596173	+	0.557489i
$821$	−10.8778			−0.379636			−0.189818	−	0.981819i	$-0.560790\pi$
$821$	−10.8778			−0.379636			−0.189818	+	0.981819i	$0.560790\pi$
$822$		0			0
$823$		−	24.2326i		−	0.844697i	−0.906434	−	0.422348i	$-0.861206\pi$
$823$		−	24.2326i		−	0.844697i	0.906434	−	0.422348i	$-0.138794\pi$
$824$	3.79025	−	10.6329i	0.132040	−	0.370416i
$825$		0			0
$826$	4.26795	+	9.83427i	0.148501	+	0.342178i
$827$		−	40.6324i		−	1.41293i	−0.707749	−	0.706464i	$-0.750289\pi$
$827$		−	40.6324i		−	1.41293i	0.707749	−	0.706464i	$-0.249711\pi$
$828$		0			0
$829$		−	34.5632i		−	1.20043i	−0.799839	−	0.600215i	$-0.795082\pi$
$829$		−	34.5632i		−	1.20043i	0.799839	−	0.600215i	$-0.204918\pi$
$830$	−41.4207	+	17.9761i	−1.43773	+	0.623958i
$831$		0			0
$832$	−5.41154	+	6.62610i	−0.187611	+	0.229719i
$833$			63.2888i			2.19283i
$834$		0			0
$835$	−68.1051			−2.35687
$836$	−10.3552	−	9.68325i	−0.358141	−	0.334902i
$837$		0			0
$838$	34.3205	−	14.8947i	1.18558	−	0.514528i
$839$	−25.0528			−0.864918			−0.432459	−	0.901654i	$-0.642354\pi$
$839$	−25.0528			−0.864918			−0.432459	+	0.901654i	$0.642354\pi$
$840$		0			0
$841$	−8.71281			−0.300442
$842$	−6.19318	+	2.68776i	−0.213431	+	0.0926264i
$843$		0			0
$844$	−28.7583	+	30.7539i	−0.989903	+	1.05859i
$845$	36.4748			1.25477
$846$		0			0
$847$			29.5028i			1.01373i
$848$	−2.85550	−	42.5318i	−0.0980584	−	1.46055i
$849$		0			0
$850$	−41.0526	+	17.8163i	−1.40809	+	0.611094i
$851$		−	5.69818i		−	0.195331i
$852$		0			0
$853$		−	14.8947i		−	0.509984i	−0.966943	−	0.254992i	$-0.917927\pi$
$853$		−	14.8947i		−	0.509984i	0.966943	−	0.254992i	$-0.0820728\pi$
$854$	−2.40292	−	5.53685i	−0.0822264	−	0.189467i
$855$		0			0
$856$	−8.05256	+	22.5902i	−0.275231	+	0.772116i
$857$			1.01788i			0.0347702i	0.999849	+	0.0173851i	$0.00553413\pi$
$857$			1.01788i			0.0347702i	−0.999849	+	0.0173851i	$0.994466\pi$
$858$		0			0
$859$	11.5885			0.395393			0.197697	−	0.980263i	$-0.436654\pi$
$859$	11.5885			0.395393			0.197697	+	0.980263i	$0.436654\pi$
$860$	−8.40482	+	8.98803i	−0.286602	+	0.306489i
$861$		0			0
$862$	−0.215390	−	0.496305i	−0.00733622	−	0.0169042i
$863$	−15.9853			−0.544147			−0.272073	−	0.962276i	$-0.587709\pi$
$863$	−15.9853			−0.544147			−0.272073	+	0.962276i	$0.587709\pi$
$864$		0			0
$865$	−5.07180			−0.172446
$866$	−2.55378	−	5.88447i	−0.0867811	−	0.199962i
$867$		0			0
$868$	−31.8564	+	34.0669i	−1.08128	+	1.15631i
$869$	11.6429			0.394958
$870$		0			0
$871$		−	9.83427i		−	0.333221i
$872$	9.61170	−	26.9641i	0.325493	−	0.913119i
$873$		0			0
$874$	1.73205	+	3.99102i	0.0585875	+	0.134998i
$875$		−	6.57969i		−	0.222434i
$876$		0			0
$877$		−	19.1722i		−	0.647400i	−0.946160	−	0.323700i	$-0.895073\pi$
$877$		−	19.1722i		−	0.647400i	0.946160	−	0.323700i	$-0.104927\pi$
$878$	−18.6791	+	8.10651i	−0.630391	+	0.273582i
$879$		0			0
$880$	23.3205	−	1.56569i	0.786134	−	0.0527796i
$881$			6.07075i			0.204529i	0.994757	+	0.102264i	$0.0326088\pi$
$881$			6.07075i			0.204529i	−0.994757	+	0.102264i	$0.967391\pi$
$882$		0			0
$883$	44.1244			1.48490			0.742451	−	0.669900i	$-0.233663\pi$
$883$	44.1244			1.48490			0.742451	+	0.669900i	$0.233663\pi$
$884$	−10.3552	+	11.0737i	−0.348282	+	0.372449i
$885$		0			0
$886$	35.4641	−	15.3910i	1.19144	−	0.517070i
$887$	25.8179			0.866880			0.433440	−	0.901182i	$-0.357300\pi$
$887$	25.8179			0.866880			0.433440	+	0.901182i	$0.357300\pi$
$888$		0			0
$889$		0			0
$890$	−54.5505	+	23.6742i	−1.82854	+	0.793562i
$891$		0			0
$892$	−38.1051	−	35.6326i	−1.27585	−	1.19307i
$893$	−26.0388			−0.871354
$894$		0			0
$895$		−	11.6865i		−	0.390637i
$896$	43.4519	+	12.2779i	1.45162	+	0.410175i
$897$		0			0
$898$	31.1962	−	13.5387i	1.04103	−	0.451794i
$899$			26.3188i			0.877780i
$900$		0			0
$901$		−	75.5427i		−	2.51669i
$902$	−4.06238	−	9.36060i	−0.135263	−	0.311674i
$903$		0			0
$904$	−10.3397	+	29.0065i	−0.343895	+	0.964742i
$905$			9.86954i			0.328075i
$906$		0			0
$907$	−46.3731			−1.53979			−0.769896	−	0.638169i	$-0.779692\pi$
$907$	−46.3731			−1.53979			−0.769896	+	0.638169i	$0.779692\pi$
$908$	5.54932	+	5.18924i	0.184161	+	0.172211i
$909$		0			0
$910$	7.39230	+	17.0335i	0.245053	+	0.564653i
$911$	0.441748			0.0146358			0.00731788	−	0.999973i	$-0.497671\pi$
$911$	0.441748			0.0146358			0.00731788	+	0.999973i	$0.497671\pi$
$912$		0			0
$913$	19.7128			0.652399
$914$	−3.59897	−	8.29280i	−0.119043	−	0.274301i
$915$		0			0
$916$	−17.0718	−	15.9641i	−0.564068	−	0.527467i
$917$	41.4207			1.36783
$918$		0			0
$919$		−	58.0130i		−	1.91367i	−0.290628	−	0.956836i	$-0.593864\pi$
$919$		−	58.0130i		−	1.91367i	0.290628	−	0.956836i	$-0.406136\pi$
$920$	−6.75620	−	2.40833i	−0.222745	−	0.0794004i
$921$		0			0
$922$	3.33975	+	7.69549i	0.109989	+	0.253437i
$923$		−	11.3964i		−	0.375116i
$924$		0			0
$925$			30.8587i			1.01463i
$926$	3.14639	−	1.36549i	0.103397	−	0.0448729i
$927$		0			0
$928$	22.6410	−	11.6865i	0.743228	−	0.383628i
$929$			20.7570i			0.681014i	0.940242	+	0.340507i	$0.110599\pi$
$929$			20.7570i			0.681014i	−0.940242	+	0.340507i	$0.889401\pi$
$930$		0			0
$931$	−33.3205			−1.09204
$932$	−20.7103	−	19.3665i	−0.678390	−	0.634371i
$933$		0			0
$934$	25.7846	−	11.1902i	0.843698	−	0.366154i
$935$	41.4207			1.35460
$936$		0			0
$937$	−23.3923			−0.764193			−0.382097	−	0.924122i	$-0.624798\pi$
$937$	−23.3923			−0.764193			−0.382097	+	0.924122i	$0.624798\pi$
$938$	−47.6138	+	20.6638i	−1.55465	+	0.674697i
$939$		0			0
$940$	29.3205	−	31.3550i	0.956330	−	1.02269i
$941$	18.6791			0.608923			0.304461	−	0.952525i	$-0.401524\pi$
$941$	18.6791			0.608923			0.304461	+	0.952525i	$0.401524\pi$
$942$		0			0
$943$			3.13139i			0.101972i
$944$	7.58051	−	0.508941i	0.246725	−	0.0165646i
$945$		0			0
$946$	4.92820	−	2.13878i	0.160230	−	0.0695377i
$947$		−	29.2360i		−	0.950044i	−0.879974	−	0.475022i	$-0.842440\pi$
$947$		−	29.2360i		−	0.950044i	0.879974	−	0.475022i	$-0.157560\pi$
$948$		0			0
$949$			6.33956i			0.205791i
$950$	−9.37999	−	21.6135i	−0.304327	−	0.701235i
$951$		0			0
$952$	75.3731	+	26.8677i	2.44286	+	0.870788i
$953$			15.7041i			0.508705i	0.967112	+	0.254353i	$0.0818624\pi$
$953$			15.7041i			0.508705i	−0.967112	+	0.254353i	$0.918138\pi$
$954$		0			0
$955$	−21.4641			−0.694562
$956$	−16.8096	+	17.9761i	−0.543663	+	0.581387i
$957$		0			0
$958$	−3.46410	−	7.98203i	−0.111920	−	0.257888i
$959$	−69.7115			−2.25110
$960$		0			0
$961$	−3.14359			−0.101406
$962$	4.16199	+	9.59011i	0.134188	+	0.309198i
$963$		0			0
$964$	7.36603	−	7.87715i	0.237244	−	0.253706i
$965$	−16.5888			−0.534011
$966$		0			0
$967$			9.83427i			0.316249i	0.987419	+	0.158124i	$0.0505447\pi$
$967$			9.83427i			0.316249i	−0.987419	+	0.158124i	$0.949455\pi$
$968$	19.6947	+	7.02045i	0.633013	+	0.225646i
$969$		0			0
$970$	19.7321	+	45.4669i	0.633558	+	1.45985i
$971$			55.8275i			1.79159i	0.444466	+	0.895796i	$0.353393\pi$
$971$			55.8275i			1.79159i	−0.444466	+	0.895796i	$0.646607\pi$
$972$		0			0
$973$		−	12.7559i		−	0.408935i
$974$	43.0801	−	18.6962i	1.38038	−	0.599066i
$975$		0			0
$976$	−4.26795	+	0.286542i	−0.136614	+	0.00917199i
$977$		−	23.5379i		−	0.753043i	−0.926408	−	0.376521i	$-0.877120\pi$
$977$		−	23.5379i		−	0.753043i	0.926408	−	0.376521i	$-0.122880\pi$
$978$		0			0
$979$	25.9615			0.829734
$980$	37.5200	−	40.1235i	1.19853	−	1.28170i
$981$		0			0
$982$	42.8564	−	18.5991i	1.36760	−	0.593523i
$983$	−55.3156			−1.76429			−0.882147	−	0.470974i	$-0.843903\pi$
$983$	−55.3156			−1.76429			−0.882147	+	0.470974i	$0.843903\pi$
$984$		0			0
$985$	−52.3923			−1.66936
$986$	41.4207	−	17.9761i	1.31910	−	0.572474i
$987$		0			0
$988$	−5.83013	−	5.45183i	−0.185481	−	0.173446i
$989$	−1.64863			−0.0524233
$990$		0			0
$991$		−	25.7983i		−	0.819511i	−0.912195	−	0.409755i	$-0.865614\pi$
$991$		−	25.7983i		−	0.819511i	0.912195	−	0.409755i	$-0.134386\pi$
$992$	15.1610	+	29.3724i	0.481363	+	0.932575i
$993$		0			0
$994$	−55.1769	+	23.9461i	−1.75011	+	0.759524i
$995$		−	48.2300i		−	1.52899i
$996$		0			0
$997$		−	1.56569i		−	0.0495860i	−0.999693	−	0.0247930i	$-0.992107\pi$
$997$		−	1.56569i		−	0.0495860i	0.999693	−	0.0247930i	$-0.00789267\pi$
$998$	3.15722	+	7.27492i	0.0999402	+	0.230284i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.f.a.107.3	✓	8
3.2	odd	2	inner	216.2.f.a.107.6	yes	8
4.3	odd	2		864.2.f.a.431.7		8
8.3	odd	2	inner	216.2.f.a.107.5	yes	8
8.5	even	2		864.2.f.a.431.2		8
9.2	odd	6		648.2.l.f.539.6		16
9.4	even	3		648.2.l.f.107.8		16
9.5	odd	6		648.2.l.f.107.1		16
9.7	even	3		648.2.l.f.539.3		16
12.11	even	2		864.2.f.a.431.1		8
24.5	odd	2		864.2.f.a.431.8		8
24.11	even	2	inner	216.2.f.a.107.4	yes	8
36.7	odd	6		2592.2.p.f.2159.1		16
36.11	even	6		2592.2.p.f.2159.7		16
36.23	even	6		2592.2.p.f.431.8		16
36.31	odd	6		2592.2.p.f.431.2		16
72.5	odd	6		2592.2.p.f.431.1		16
72.11	even	6		648.2.l.f.539.8		16
72.13	even	6		2592.2.p.f.431.7		16
72.29	odd	6		2592.2.p.f.2159.2		16
72.43	odd	6		648.2.l.f.539.1		16
72.59	even	6		648.2.l.f.107.3		16
72.61	even	6		2592.2.p.f.2159.8		16
72.67	odd	6		648.2.l.f.107.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.f.a.107.3	✓	8	1.1	even	1	trivial
216.2.f.a.107.4	yes	8	24.11	even	2	inner
216.2.f.a.107.5	yes	8	8.3	odd	2	inner
216.2.f.a.107.6	yes	8	3.2	odd	2	inner
648.2.l.f.107.1		16	9.5	odd	6
648.2.l.f.107.3		16	72.59	even	6
648.2.l.f.107.6		16	72.67	odd	6
648.2.l.f.107.8		16	9.4	even	3
648.2.l.f.539.1		16	72.43	odd	6
648.2.l.f.539.3		16	9.7	even	3
648.2.l.f.539.6		16	9.2	odd	6
648.2.l.f.539.8		16	72.11	even	6
864.2.f.a.431.1		8	12.11	even	2
864.2.f.a.431.2		8	8.5	even	2
864.2.f.a.431.7		8	4.3	odd	2
864.2.f.a.431.8		8	24.5	odd	2
2592.2.p.f.431.1		16	72.5	odd	6
2592.2.p.f.431.2		16	36.31	odd	6
2592.2.p.f.431.7		16	72.13	even	6
2592.2.p.f.431.8		16	36.23	even	6
2592.2.p.f.2159.1		16	36.7	odd	6
2592.2.p.f.2159.2		16	72.29	odd	6
2592.2.p.f.2159.7		16	36.11	even	6
2592.2.p.f.2159.8		16	72.61	even	6

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.563016 - 1.29731i) q^{2} +(-1.36603 + 1.46081i) q^{4} +3.07638 q^{5} +3.99102i q^{7} +(2.66422 + 0.949697i) q^{8} +O(q^{10})\)	\(q+(-0.563016 - 1.29731i) q^{2} +(-1.36603 + 1.46081i) q^{4} +3.07638 q^{5} +3.99102i q^{7} +(2.66422 + 0.949697i) q^{8} +(-1.73205 - 3.99102i) q^{10} +1.89939i q^{11} +1.06939i q^{13} +(5.17758 - 2.24701i) q^{14} +(-0.267949 - 3.99102i) q^{16} -7.08863i q^{17} +3.73205 q^{19} +(-4.20241 + 4.49401i) q^{20} +(2.46410 - 1.06939i) q^{22} -0.824313 q^{23} +4.46410 q^{25} +(1.38733 - 0.602084i) q^{26} +(-5.83013 - 5.45183i) q^{28} -4.50413 q^{29} -5.84325i q^{31} +(-5.02672 + 2.59462i) q^{32} +(-9.19615 + 3.99102i) q^{34} +12.2779i q^{35} +6.91264i q^{37} +(-2.10121 - 4.84163i) q^{38} +(8.19615 + 2.92163i) q^{40} -3.79879i q^{41} +2.00000 q^{43} +(-2.77466 - 2.59462i) q^{44} +(0.464102 + 1.06939i) q^{46} -6.97707 q^{47} -8.92820 q^{49} +(-2.51336 - 5.79132i) q^{50} +(-1.56218 - 1.46081i) q^{52} +10.6569 q^{53} +5.84325i q^{55} +(-3.79025 + 10.6329i) q^{56} +(2.53590 + 5.84325i) q^{58} +1.89939i q^{59} -1.06939i q^{61} +(-7.58051 + 3.28985i) q^{62} +(6.19615 + 5.06040i) q^{64} +3.28985i q^{65} -9.19615 q^{67} +(10.3552 + 9.68325i) q^{68} +(15.9282 - 6.91264i) q^{70} -10.6569 q^{71} +5.92820 q^{73} +(8.96784 - 3.89193i) q^{74} +(-5.09808 + 5.45183i) q^{76} -7.58051 q^{77} -6.12979i q^{79} +(-0.824313 - 12.2779i) q^{80} +(-4.92820 + 2.13878i) q^{82} -10.3785i q^{83} -21.8073i q^{85} +(-1.12603 - 2.59462i) q^{86} +(-1.80385 + 5.06040i) q^{88} -13.6683i q^{89} -4.26795 q^{91} +(1.12603 - 1.20417i) q^{92} +(3.92820 + 9.05142i) q^{94} +11.4812 q^{95} -11.3923 q^{97} +(5.02672 + 11.5826i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4}+O(q^{10}) \) 8 * q - 4 * q^4	\( 8 q - 4 q^{4} - 16 q^{16} + 16 q^{19} - 8 q^{22} + 8 q^{25} - 12 q^{28} - 32 q^{34} + 24 q^{40} + 16 q^{43} - 24 q^{46} - 16 q^{49} + 36 q^{52} + 48 q^{58} + 8 q^{64} - 32 q^{67} + 72 q^{70} - 8 q^{73} - 20 q^{76} + 16 q^{82} - 56 q^{88} - 48 q^{91} - 24 q^{94} - 8 q^{97}+O(q^{100}) \) 8 * q - 4 * q^4 - 16 * q^16 + 16 * q^19 - 8 * q^22 + 8 * q^25 - 12 * q^28 - 32 * q^34 + 24 * q^40 + 16 * q^43 - 24 * q^46 - 16 * q^49 + 36 * q^52 + 48 * q^58 + 8 * q^64 - 32 * q^67 + 72 * q^70 - 8 * q^73 - 20 * q^76 + 16 * q^82 - 56 * q^88 - 48 * q^91 - 24 * q^94 - 8 * q^97

Introduction

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