LMFDB - Embedded newform 756.2.b.c.55.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(55,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("756.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.60771337450861625344.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{10} + 11x^{8} - 26x^{6} + 44x^{4} - 64x^{2} + 64 $ x^12 - 4x^10 + 11x^8 - 26x^6 + 44x^4 - 64*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			55.10
Root			$-1.15343 + 0.818285i$ of defining polynomial
Character	$\chi$	$=$	756.55
Dual form			756.2.b.c.55.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15343 + 0.818285i) q^{2} +(0.660819 + 1.88768i) q^{4} -2.16295i q^{5} +(1.94827 + 1.79004i) q^{7} +(-0.782447 + 2.71805i) q^{8} +O(q^{10})$	\(q+(1.15343 + 0.818285i) q^{2} +(0.660819 + 1.88768i) q^{4} -2.16295i q^{5} +(1.94827 + 1.79004i) q^{7} +(-0.782447 + 2.71805i) q^{8} +(1.76991 - 2.49482i) q^{10} +0.414503i q^{11} +2.36578i q^{13} +(0.782447 + 3.65893i) q^{14} +(-3.12664 + 2.49482i) q^{16} +0.695686i q^{17} +5.21819 q^{19} +(4.08295 - 1.42932i) q^{20} +(-0.339181 + 0.478101i) q^{22} -0.414503i q^{23} +0.321637 q^{25} +(-1.93588 + 2.72877i) q^{26} +(-2.09155 + 4.86060i) q^{28} +9.73080 q^{29} -2.03509 q^{31} +(-5.64785 + 0.319131i) q^{32} +(-0.569269 + 0.802428i) q^{34} +(3.87176 - 4.21403i) q^{35} -7.43637 q^{37} +(6.01883 + 4.26997i) q^{38} +(5.87901 + 1.69239i) q^{40} -10.5910i q^{41} +8.76500i q^{43} +(-0.782447 + 0.273911i) q^{44} +(0.339181 - 0.478101i) q^{46} -5.11706 q^{47} +(0.591549 + 6.97496i) q^{49} +(0.370987 + 0.263191i) q^{50} +(-4.46582 + 1.56335i) q^{52} +3.12979 q^{53} +0.896550 q^{55} +(-6.38982 + 3.89489i) q^{56} +(11.2238 + 7.96257i) q^{58} -11.2147 q^{59} -3.97063i q^{61} +(-2.34734 - 1.66528i) q^{62} +(-6.77555 - 4.25345i) q^{64} +5.11706 q^{65} +2.36578i q^{67} +(-1.31323 + 0.459722i) q^{68} +(7.91409 - 1.69239i) q^{70} -4.04472i q^{71} -12.3451i q^{73} +(-8.57736 - 6.08507i) q^{74} +(3.44827 + 9.85024i) q^{76} +(-0.741974 + 0.807565i) q^{77} -7.61351i q^{79} +(5.39618 + 6.76277i) q^{80} +(8.66646 - 12.2160i) q^{82} -12.8606 q^{83} +1.50474 q^{85} +(-7.17227 + 10.1098i) q^{86} +(-1.12664 - 0.324326i) q^{88} -14.6931i q^{89} +(-4.23482 + 4.60918i) q^{91} +(0.782447 - 0.273911i) q^{92} +(-5.90219 - 4.18722i) q^{94} -11.2867i q^{95} +3.97063i q^{97} +(-5.02519 + 8.52921i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{4} - 2 q^{7}+O(q^{10}) $ 12 * q + 8 * q^4 - 2 * q^7	$ 12 q + 8 q^{4} - 2 q^{7} - 4 q^{10} - 12 q^{16} + 12 q^{19} - 4 q^{22} + 4 q^{25} - 24 q^{31} - 32 q^{34} + 12 q^{37} + 20 q^{40} + 4 q^{46} - 18 q^{49} - 28 q^{52} - 40 q^{55} + 8 q^{58} + 20 q^{64} + 44 q^{70} + 16 q^{76} + 28 q^{82} - 32 q^{85} + 12 q^{88} - 26 q^{91} + 56 q^{94}+O(q^{100}) $ 12 * q + 8 * q^4 - 2 * q^7 - 4 * q^10 - 12 * q^16 + 12 * q^19 - 4 * q^22 + 4 * q^25 - 24 * q^31 - 32 * q^34 + 12 * q^37 + 20 * q^40 + 4 * q^46 - 18 * q^49 - 28 * q^52 - 40 * q^55 + 8 * q^58 + 20 * q^64 + 44 * q^70 + 16 * q^76 + 28 * q^82 - 32 * q^85 + 12 * q^88 - 26 * q^91 + 56 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.15343	+	0.818285i	0.815601	+	0.578615i
$2$	1.15343	+	0.818285i	0.815601	+	0.578615i
$3$		0			0
$3$		0			0
$4$	0.660819	+	1.88768i	0.330409	+	0.943838i
$5$		−	2.16295i		−	0.967302i	−0.875261	−	0.483651i	$-0.839310\pi$
$5$		−	2.16295i		−	0.967302i	0.875261	−	0.483651i	$-0.160690\pi$
$6$		0			0
$7$	1.94827	+	1.79004i	0.736379	+	0.676570i
$7$	1.94827	+	1.79004i	0.736379	+	0.676570i
$8$	−0.782447	+	2.71805i	−0.276637	+	0.960975i
$9$		0			0
$10$	1.76991	−	2.49482i	0.559695	−	0.788932i
$11$			0.414503i			0.124977i	0.998046	+	0.0624886i	$0.0199037\pi$
$11$			0.414503i			0.124977i	−0.998046	+	0.0624886i	$0.980096\pi$
$12$		0			0
$13$			2.36578i			0.656148i	0.944652	+	0.328074i	$0.106400\pi$
$13$			2.36578i			0.656148i	−0.944652	+	0.328074i	$0.893600\pi$
$14$	0.782447	+	3.65893i	0.209118	+	0.977890i
$15$		0			0
$16$	−3.12664	+	2.49482i	−0.781659	+	0.623706i
$17$			0.695686i			0.168729i	0.996435	+	0.0843643i	$0.0268859\pi$
$17$			0.695686i			0.168729i	−0.996435	+	0.0843643i	$0.973114\pi$
$18$		0			0
$19$	5.21819			1.19713			0.598567	−	0.801073i	$-0.295737\pi$
$19$	5.21819			1.19713			0.598567	+	0.801073i	$0.295737\pi$
$20$	4.08295	−	1.42932i	0.912976	−	0.319605i
$21$		0			0
$22$	−0.339181	+	0.478101i	−0.0723137	+	0.101932i
$23$		−	0.414503i		−	0.0864298i	−0.999066	−	0.0432149i	$-0.986240\pi$
$23$		−	0.414503i		−	0.0864298i	0.999066	−	0.0432149i	$-0.0137600\pi$
$24$		0			0
$25$	0.321637			0.0643274
$26$	−1.93588	+	2.72877i	−0.379657	+	0.535155i
$27$		0			0
$28$	−2.09155	+	4.86060i	−0.395266	+	0.918567i
$29$	9.73080			1.80696			0.903482	−	0.428626i	$-0.141002\pi$
$29$	9.73080			1.80696			0.903482	+	0.428626i	$0.141002\pi$
$30$		0			0
$31$	−2.03509			−0.365513			−0.182756	−	0.983158i	$-0.558502\pi$
$31$	−2.03509			−0.365513			−0.182756	+	0.983158i	$0.558502\pi$
$32$	−5.64785	+	0.319131i	−0.998407	+	0.0564148i
$33$		0			0
$34$	−0.569269	+	0.802428i	−0.0976289	+	0.137615i
$35$	3.87176	−	4.21403i	0.654447	−	0.712300i
$36$		0			0
$37$	−7.43637			−1.22253			−0.611266	−	0.791425i	$-0.709339\pi$
$37$	−7.43637			−1.22253			−0.611266	+	0.791425i	$0.709339\pi$
$38$	6.01883	+	4.26997i	0.976384	+	0.692680i
$39$		0			0
$40$	5.87901	+	1.69239i	0.929552	+	0.267591i
$41$		−	10.5910i		−	1.65404i	−0.562175	−	0.827018i	$-0.690035\pi$
$41$		−	10.5910i		−	1.65404i	0.562175	−	0.827018i	$-0.309965\pi$
$42$		0			0
$43$			8.76500i			1.33665i	0.743870	+	0.668325i	$0.232988\pi$
$43$			8.76500i			1.33665i	−0.743870	+	0.668325i	$0.767012\pi$
$44$	−0.782447	+	0.273911i	−0.117958	+	0.0412936i
$45$		0			0
$46$	0.339181	−	0.478101i	0.0500096	−	0.0704922i
$47$	−5.11706			−0.746400			−0.373200	−	0.927751i	$-0.621740\pi$
$47$	−5.11706			−0.746400			−0.373200	+	0.927751i	$0.621740\pi$
$48$		0			0
$49$	0.591549	+	6.97496i	0.0845070	+	0.996423i
$50$	0.370987	+	0.263191i	0.0524655	+	0.0372208i
$51$		0			0
$52$	−4.46582	+	1.56335i	−0.619298	+	0.216798i
$53$	3.12979			0.429909			0.214955	−	0.976624i	$-0.431040\pi$
$53$	3.12979			0.429909			0.214955	+	0.976624i	$0.431040\pi$
$54$		0			0
$55$	0.896550			0.120891
$56$	−6.38982	+	3.89489i	−0.853876	+	0.520477i
$57$		0			0
$58$	11.2238	+	7.96257i	1.47376	+	1.04554i
$59$	−11.2147			−1.46004			−0.730018	−	0.683428i	$-0.760488\pi$
$59$	−11.2147			−1.46004			−0.730018	+	0.683428i	$0.760488\pi$
$60$		0			0
$61$		−	3.97063i		−	0.508387i	−0.967153	−	0.254194i	$-0.918190\pi$
$61$		−	3.97063i		−	0.508387i	0.967153	−	0.254194i	$-0.0818101\pi$
$62$	−2.34734	−	1.66528i	−0.298112	−	0.211491i
$63$		0			0
$64$	−6.77555	−	4.25345i	−0.846944	−	0.531682i
$65$	5.11706			0.634693
$66$		0			0
$67$			2.36578i			0.289026i	0.989503	+	0.144513i	$0.0461615\pi$
$67$			2.36578i			0.289026i	−0.989503	+	0.144513i	$0.953839\pi$
$68$	−1.31323	+	0.459722i	−0.159252	+	0.0557495i
$69$		0			0
$70$	7.91409	−	1.69239i	0.945915	−	0.202280i
$71$		−	4.04472i		−	0.480020i	−0.970770	−	0.240010i	$-0.922849\pi$
$71$		−	4.04472i		−	0.480020i	0.970770	−	0.240010i	$-0.0771507\pi$
$72$		0			0
$73$		−	12.3451i		−	1.44488i	−0.691433	−	0.722440i	$-0.743020\pi$
$73$		−	12.3451i		−	1.44488i	0.691433	−	0.722440i	$-0.256980\pi$
$74$	−8.57736	−	6.08507i	−0.997098	−	0.707376i
$75$		0			0
$76$	3.44827	+	9.85024i	0.395544	+	1.12990i
$77$	−0.741974	+	0.807565i	−0.0845558	+	0.0920306i
$78$		0			0
$79$		−	7.61351i		−	0.856587i	−0.903640	−	0.428293i	$-0.859115\pi$
$79$		−	7.61351i		−	0.856587i	0.903640	−	0.428293i	$-0.140885\pi$
$80$	5.39618	+	6.76277i	0.603311	+	0.756100i
$81$		0			0
$82$	8.66646	−	12.2160i	0.957051	−	1.34903i
$83$	−12.8606			−1.41163			−0.705816	−	0.708395i	$-0.749420\pi$
$83$	−12.8606			−1.41163			−0.705816	+	0.708395i	$0.749420\pi$
$84$		0			0
$85$	1.50474			0.163211
$86$	−7.17227	+	10.1098i	−0.773405	+	1.09017i
$87$		0			0
$88$	−1.12664	−	0.324326i	−0.120100	−	0.0345733i
$89$		−	14.6931i		−	1.55747i	−0.627353	−	0.778735i	$-0.715861\pi$
$89$		−	14.6931i		−	1.55747i	0.627353	−	0.778735i	$-0.284139\pi$
$90$		0			0
$91$	−4.23482	+	4.60918i	−0.443930	+	0.483174i
$92$	0.782447	−	0.273911i	0.0815757	−	0.0285572i
$93$		0			0
$94$	−5.90219	−	4.18722i	−0.608765	−	0.431878i
$95$		−	11.2867i		−	1.15799i
$96$		0			0
$97$			3.97063i			0.403157i	0.979472	+	0.201578i	$0.0646070\pi$
$97$			3.97063i			0.403157i	−0.979472	+	0.201578i	$0.935393\pi$
$98$	−5.02519	+	8.52921i	−0.507621	+	0.861580i
$99$		0			0
$100$	0.212544	+	0.607147i	0.0212544	+	0.0607147i
$101$			14.8410i			1.47674i	0.674398	+	0.738368i	$0.264403\pi$
$101$			14.8410i			1.47674i	−0.674398	+	0.738368i	$0.735597\pi$
$102$		0			0
$103$	3.42509			0.337484			0.168742	−	0.985660i	$-0.446030\pi$
$103$	3.42509			0.337484			0.168742	+	0.985660i	$0.446030\pi$
$104$	−6.43029	−	1.85109i	−0.630542	−	0.181515i
$105$		0			0
$106$	3.61000	+	2.56106i	0.350634	+	0.248752i
$107$		−	14.5024i		−	1.40200i	−0.713161	−	0.701000i	$-0.752737\pi$
$107$		−	14.5024i		−	1.40200i	0.713161	−	0.701000i	$-0.247263\pi$
$108$		0			0
$109$	−8.40128			−0.804697			−0.402349	−	0.915487i	$-0.631806\pi$
$109$	−8.40128			−0.804697			−0.402349	+	0.915487i	$0.631806\pi$
$110$	1.03411	+	0.733633i	0.0985986	+	0.0699492i
$111$		0			0
$112$	−10.5574	−	0.736192i	−0.997578	−	0.0695636i
$113$	−4.61373			−0.434024			−0.217012	−	0.976169i	$-0.569631\pi$
$113$	−4.61373			−0.434024			−0.217012	+	0.976169i	$0.569631\pi$
$114$		0			0
$115$	−0.896550			−0.0836037
$116$	6.43029	+	18.3686i	0.597038	+	1.70548i
$117$		0			0
$118$	−12.9355	−	9.17686i	−1.19081	−	0.844799i
$119$	−1.24530	+	1.35539i	−0.114157	+	0.124248i
$120$		0			0
$121$	10.8282			0.984381
$122$	3.24911	−	4.57986i	0.294161	−	0.414641i
$123$		0			0
$124$	−1.34482	−	3.84159i	−0.120769	−	0.344985i
$125$		−	11.5104i		−	1.02953i
$126$		0			0
$127$		−	6.33641i		−	0.562265i	−0.959669	−	0.281133i	$-0.909290\pi$
$127$		−	6.33641i		−	0.562265i	0.959669	−	0.281133i	$-0.0907101\pi$
$128$	−4.33462	−	10.4504i	−0.383130	−	0.923695i
$129$		0			0
$130$	5.90219	+	4.18722i	0.517657	+	0.367243i
$131$	18.9583			1.65639			0.828196	−	0.560439i	$-0.189368\pi$
$131$	18.9583			1.65639			0.828196	+	0.560439i	$0.189368\pi$
$132$		0			0
$133$	10.1665	+	9.34074i	0.881544	+	0.809945i
$134$	−1.93588	+	2.72877i	−0.167235	+	0.235730i
$135$		0			0
$136$	−1.89091	−	0.544337i	−0.162144	−	0.0466765i
$137$	1.98728			0.169784			0.0848922	−	0.996390i	$-0.472945\pi$
$137$	1.98728			0.169784			0.0848922	+	0.996390i	$0.472945\pi$
$138$		0			0
$139$	−13.6195			−1.15519			−0.577594	−	0.816324i	$-0.696008\pi$
$139$	−13.6195			−1.15519			−0.577594	+	0.816324i	$0.696008\pi$
$140$	10.5132	+	4.52392i	0.888531	+	0.382341i
$141$		0			0
$142$	3.30974	−	4.66532i	0.277747	−	0.391505i
$143$	−0.980621			−0.0820036
$144$		0			0
$145$		−	21.0473i		−	1.74788i
$146$	10.1018	−	14.2392i	0.836030	−	1.17845i
$147$		0			0
$148$	−4.91409	−	14.0375i	−0.403936	−	1.15387i
$149$	12.3573			1.01235			0.506173	−	0.862432i	$-0.331060\pi$
$149$	12.3573			1.01235			0.506173	+	0.862432i	$0.331060\pi$
$150$		0			0
$151$		−	15.8623i		−	1.29086i	−0.763820	−	0.645429i	$-0.776679\pi$
$151$		−	15.8623i		−	1.29086i	0.763820	−	0.645429i	$-0.223321\pi$
$152$	−4.08295	+	14.1833i	−0.331171	+	1.15042i
$153$		0			0
$154$	−1.51664	+	0.324326i	−0.122214	+	0.0261349i
$155$			4.40180i			0.353561i
$156$		0			0
$157$			8.37443i			0.668353i	0.942511	+	0.334176i	$0.108458\pi$
$157$			8.37443i			0.668353i	−0.942511	+	0.334176i	$0.891542\pi$
$158$	6.23002	−	8.78168i	0.495634	−	0.698633i
$159$		0			0
$160$	0.690264	+	12.2160i	0.0545702	+	0.965761i
$161$	0.741974	−	0.807565i	0.0584758	−	0.0636450i
$162$		0			0
$163$		−	17.0766i		−	1.33754i	−0.743468	−	0.668772i	$-0.766820\pi$
$163$		−	17.0766i		−	1.33754i	0.743468	−	0.668772i	$-0.233180\pi$
$164$	19.9924	−	6.99873i	1.56114	−	0.546509i
$165$		0			0
$166$	−14.8338	−	10.5236i	−1.15133	−	0.816792i
$167$	−7.74352			−0.599212			−0.299606	−	0.954063i	$-0.596855\pi$
$167$	−7.74352			−0.599212			−0.299606	+	0.954063i	$0.596855\pi$
$168$		0			0
$169$	7.40310			0.569469
$170$	1.73561	+	1.23130i	0.133115	+	0.0944366i
$171$		0			0
$172$	−16.5455	+	5.79207i	−1.26158	+	0.441641i
$173$		−	4.25001i		−	0.323122i	−0.986863	−	0.161561i	$-0.948347\pi$
$173$		−	4.25001i		−	0.323122i	0.986863	−	0.161561i	$-0.0516529\pi$
$174$		0			0
$175$	0.626638	+	0.575742i	0.0473693	+	0.0435220i
$176$	−1.03411	−	1.29600i	−0.0779490	−	0.0976896i
$177$		0			0
$178$	12.0232	−	16.9476i	0.901176	−	1.27027i
$179$			8.85710i			0.662011i	0.943629	+	0.331005i	$0.107388\pi$
$179$			8.85710i			0.662011i	−0.943629	+	0.331005i	$0.892612\pi$
$180$		0			0
$181$			23.9292i			1.77864i	0.457281	+	0.889322i	$0.348823\pi$
$181$			23.9292i			1.77864i	−0.457281	+	0.889322i	$0.651177\pi$
$182$	−8.65621	+	1.85109i	−0.641641	+	0.137212i
$183$		0			0
$184$	1.12664	+	0.324326i	0.0830568	+	0.0239096i
$185$			16.0845i			1.18256i
$186$		0			0
$187$	−0.288364			−0.0210872
$188$	−3.38145	−	9.65935i	−0.246618	−	0.704481i
$189$		0			0
$190$	9.23573	−	13.0184i	0.670030	−	0.944457i
$191$			25.9224i			1.87568i	0.347068	+	0.937840i	$0.387177\pi$
$191$			25.9224i			1.87568i	−0.347068	+	0.937840i	$0.612823\pi$
$192$		0			0
$193$	11.6896			0.841439			0.420720	−	0.907191i	$-0.361778\pi$
$193$	11.6896			0.841439			0.420720	+	0.907191i	$0.361778\pi$
$194$	−3.24911	+	4.57986i	−0.233272	+	0.328815i
$195$		0			0
$196$	−12.7756	+	5.72584i	−0.912540	+	0.408988i
$197$	−11.7181			−0.834878			−0.417439	−	0.908705i	$-0.637072\pi$
$197$	−11.7181			−0.834878			−0.417439	+	0.908705i	$0.637072\pi$
$198$		0			0
$199$	−6.72292			−0.476575			−0.238288	−	0.971195i	$-0.576586\pi$
$199$	−6.72292			−0.476575			−0.238288	+	0.971195i	$0.576586\pi$
$200$	−0.251664	+	0.874225i	−0.0177953	+	0.0618170i
$201$		0			0
$202$	−12.1442	+	17.1181i	−0.854462	+	1.20443i
$203$	18.9583	+	17.4185i	1.33061	+	1.22254i
$204$		0			0
$205$	−22.9078			−1.59995
$206$	3.95061	+	2.80270i	0.275252	+	0.195273i
$207$		0			0
$208$	−5.90219	−	7.39693i	−0.409243	−	0.512885i
$209$			2.16295i			0.149615i
$210$		0			0
$211$		−	6.39922i		−	0.440540i	−0.975439	−	0.220270i	$-0.929306\pi$
$211$		−	6.39922i		−	0.440540i	0.975439	−	0.220270i	$-0.0706939\pi$
$212$	2.06822	+	5.90802i	0.142046	+	0.405765i
$213$		0			0
$214$	11.8671	−	16.7276i	0.811219	−	1.14347i
$215$	18.9583			1.29294
$216$		0			0
$217$	−3.96491	−	3.64288i	−0.269156	−	0.247295i
$218$	−9.69033	−	6.87465i	−0.656312	−	0.465610i
$219$		0			0
$220$	0.592457	+	1.69239i	0.0399434	+	0.114101i
$221$	−1.64584			−0.110711
$222$		0			0
$223$	−8.82637			−0.591058			−0.295529	−	0.955334i	$-0.595496\pi$
$223$	−8.82637			−0.591058			−0.295529	+	0.955334i	$0.595496\pi$
$224$	−11.5748	−	9.48809i	−0.773374	−	0.633949i
$225$		0			0
$226$	−5.32164	−	3.77535i	−0.353990	−	0.251133i
$227$	−21.5847			−1.43263			−0.716314	−	0.697778i	$-0.754172\pi$
$227$	−21.5847			−1.43263			−0.716314	+	0.697778i	$0.754172\pi$
$228$		0			0
$229$		−	22.6521i		−	1.49689i	−0.663195	−	0.748447i	$-0.730800\pi$
$229$		−	22.6521i		−	1.49689i	0.663195	−	0.748447i	$-0.269200\pi$
$230$	−1.03411	−	0.733633i	−0.0681872	−	0.0483743i
$231$		0			0
$232$	−7.61383	+	26.4488i	−0.499872	+	1.73645i
$233$	−22.5914			−1.48001			−0.740005	−	0.672601i	$-0.765177\pi$
$233$	−22.5914			−1.48001			−0.740005	+	0.672601i	$0.765177\pi$
$234$		0			0
$235$			11.0680i			0.721994i
$236$	−7.41091	−	21.1698i	−0.482409	−	1.37804i
$237$		0			0
$238$	−2.54547	+	0.544337i	−0.164998	+	0.0352841i
$239$		−	4.68298i		−	0.302917i	−0.988464	−	0.151458i	$-0.951603\pi$
$239$		−	4.68298i		−	0.302917i	0.988464	−	0.151458i	$-0.0483970\pi$
$240$		0			0
$241$		−	2.36578i		−	0.152393i	−0.997093	−	0.0761965i	$-0.975722\pi$
$241$		−	2.36578i		−	0.152393i	0.997093	−	0.0761965i	$-0.0242776\pi$
$242$	12.4896	+	8.86055i	0.802862	+	0.569577i
$243$		0			0
$244$	7.49526	−	2.62387i	0.479835	−	0.167976i
$245$	15.0865	−	1.27949i	0.963842	−	0.0817438i
$246$		0			0
$247$			12.3451i			0.785498i
$248$	1.59235	−	5.53147i	0.101114	−	0.351248i
$249$		0			0
$250$	9.41883	−	13.2765i	0.595699	−	0.839682i
$251$	10.2341			0.645972			0.322986	−	0.946404i	$-0.395313\pi$
$251$	10.2341			0.645972			0.322986	+	0.946404i	$0.395313\pi$
$252$		0			0
$253$	0.171812			0.0108018
$254$	5.18499	−	7.30863i	0.325335	−	0.458584i
$255$		0			0
$256$	3.55173	−	15.6008i	0.221983	−	0.975051i
$257$			0.0758947i			0.00473418i	0.999997	+	0.00236709i	$0.000753469\pi$
$257$			0.0758947i			0.00473418i	−0.999997	+	0.00236709i	$0.999247\pi$
$258$		0			0
$259$	−14.4881	−	13.3114i	−0.900247	−	0.827128i
$260$	3.38145	+	9.65935i	0.209709	+	0.599048i
$261$		0			0
$262$	21.8671	+	15.5133i	1.35095	+	0.958413i
$263$			15.2740i			0.941834i	0.882177	+	0.470917i	$0.156077\pi$
$263$			15.2740i			0.941834i	−0.882177	+	0.470917i	$0.843923\pi$
$264$		0			0
$265$		−	6.76958i		−	0.415852i
$266$	4.08295	+	19.0930i	0.250342	+	1.17067i
$267$		0			0
$268$	−4.46582	+	1.56335i	−0.272793	+	0.0954968i
$269$			17.0040i			1.03675i	0.855153	+	0.518375i	$0.173463\pi$
$269$			17.0040i			1.03675i	−0.855153	+	0.518375i	$0.826537\pi$
$270$		0			0
$271$	0.676548			0.0410974			0.0205487	−	0.999789i	$-0.493459\pi$
$271$	0.676548			0.0410974			0.0205487	+	0.999789i	$0.493459\pi$
$272$	−1.73561	−	2.17516i	−0.105237	−	0.131888i
$273$		0			0
$274$	2.29219	+	1.62616i	0.138476	+	0.0982399i
$275$			0.133319i			0.00803947i
$276$		0			0
$277$	−0.323452			−0.0194344			−0.00971718	−	0.999953i	$-0.503093\pi$
$277$	−0.323452			−0.0194344			−0.00971718	+	0.999953i	$0.503093\pi$
$278$	−15.7092	−	11.1446i	−0.942173	−	0.668409i
$279$		0			0
$280$	8.42447	+	13.8209i	0.503459	+	0.825955i
$281$	−3.63311			−0.216733			−0.108367	−	0.994111i	$-0.534562\pi$
$281$	−3.63311			−0.216733			−0.108367	+	0.994111i	$0.534562\pi$
$282$		0			0
$283$	27.5862			1.63983			0.819915	−	0.572486i	$-0.194021\pi$
$283$	27.5862			1.63983			0.819915	+	0.572486i	$0.194021\pi$
$284$	7.63512	−	2.67283i	0.453061	−	0.158603i
$285$		0			0
$286$	−1.13108	−	0.802428i	−0.0668822	−	0.0474485i
$287$	18.9583	−	20.6342i	1.11907	−	1.21800i
$288$		0			0
$289$	16.5160			0.971531
$290$	17.2227	−	24.2766i	1.01135	−	1.42557i
$291$		0			0
$292$	23.3035	−	8.15785i	1.36373	−	0.477402i
$293$			20.4863i			1.19682i	0.801189	+	0.598412i	$0.204201\pi$
$293$			20.4863i			1.19682i	−0.801189	+	0.598412i	$0.795799\pi$
$294$		0			0
$295$			24.2570i			1.41229i
$296$	5.81856	−	20.2124i	0.338197	−	1.17482i
$297$		0			0
$298$	14.2533	+	10.1118i	0.825670	+	0.585759i
$299$	0.980621			0.0567108
$300$		0			0
$301$	−15.6896	+	17.0766i	−0.904336	+	0.984280i
$302$	12.9799	−	18.2961i	0.746910	−	1.05282i
$303$		0			0
$304$	−16.3154	+	13.0184i	−0.935751	+	0.746659i
$305$	−8.58829			−0.491764
$306$		0			0
$307$	20.6308			1.17746			0.588730	−	0.808330i	$-0.299628\pi$
$307$	20.6308			1.17746			0.588730	+	0.808330i	$0.299628\pi$
$308$	−2.01473	−	0.866953i	−0.114800	−	0.0493992i
$309$		0			0
$310$	−3.60193	+	5.07718i	−0.204576	+	0.288365i
$311$	−16.4677			−0.933795			−0.466898	−	0.884311i	$-0.654628\pi$
$311$	−16.4677			−0.933795			−0.466898	+	0.884311i	$0.654628\pi$
$312$		0			0
$313$		−	27.0559i		−	1.52929i	−0.644452	−	0.764645i	$-0.722914\pi$
$313$		−	27.0559i		−	1.52929i	0.644452	−	0.764645i	$-0.277086\pi$
$314$	−6.85268	+	9.65935i	−0.386719	+	0.545109i
$315$		0			0
$316$	14.3718	−	5.03115i	0.808479	−	0.283024i
$317$	−31.3155			−1.75885			−0.879427	−	0.476033i	$-0.842074\pi$
$317$	−31.3155			−1.75885			−0.879427	+	0.476033i	$0.842074\pi$
$318$		0			0
$319$			4.03344i			0.225829i
$320$	−9.20001	+	14.6552i	−0.514296	+	0.819251i
$321$		0			0
$322$	1.51664	−	0.324326i	0.0845189	−	0.0180740i
$323$			3.63022i			0.201991i
$324$		0			0
$325$			0.760922i			0.0422083i
$326$	13.9735	−	19.6967i	0.773923	−	1.09090i
$327$		0			0
$328$	28.7868	+	8.28689i	1.58949	+	0.457567i
$329$	−9.96944	−	9.15972i	−0.549633	−	0.504992i
$330$		0			0
$331$			21.1101i			1.16031i	0.814505	+	0.580157i	$0.197009\pi$
$331$			21.1101i			1.16031i	−0.814505	+	0.580157i	$0.802991\pi$
$332$	−8.49851	−	24.2766i	−0.466416	−	1.33235i
$333$		0			0
$334$	−8.93164	−	6.33641i	−0.488717	−	0.346713i
$335$	5.11706			0.279575
$336$		0			0
$337$	−11.8727			−0.646750			−0.323375	−	0.946271i	$-0.604817\pi$
$337$	−11.8727			−0.646750			−0.323375	+	0.946271i	$0.604817\pi$
$338$	8.53898	+	6.05785i	0.464460	+	0.329503i
$339$		0			0
$340$	0.994357	+	2.84045i	0.0539266	+	0.154045i
$341$		−	0.843550i		−	0.0456808i
$342$		0			0
$343$	−11.3329	+	14.6480i	−0.611920	+	0.790919i
$344$	−23.8237	−	6.85814i	−1.28449	−	0.369766i
$345$		0			0
$346$	3.47772	−	4.90210i	0.186963	−	0.263539i
$347$		−	19.8052i		−	1.06320i	−0.846996	−	0.531599i	$-0.821591\pi$
$347$		−	19.8052i		−	1.06320i	0.846996	−	0.531599i	$-0.178409\pi$
$348$		0			0
$349$			15.4718i			0.828185i	0.910235	+	0.414092i	$0.135901\pi$
$349$			15.4718i			0.828185i	−0.910235	+	0.414092i	$0.864099\pi$
$350$	0.251664	+	1.17685i	0.0134520	+	0.0629052i
$351$		0			0
$352$	−0.132280	−	2.34105i	−0.00705057	−	0.124778i
$353$			27.4471i			1.46086i	0.682986	+	0.730431i	$0.260681\pi$
$353$			27.4471i			1.46086i	−0.682986	+	0.730431i	$0.739319\pi$
$354$		0			0
$355$	−8.74854			−0.464324
$356$	27.7359	−	9.70951i	1.47000	−	0.514603i
$357$		0			0
$358$	−7.24763	+	10.2161i	−0.383049	+	0.539936i
$359$		−	8.33761i		−	0.440042i	−0.975495	−	0.220021i	$-0.929387\pi$
$359$		−	8.33761i		−	0.440042i	0.975495	−	0.220021i	$-0.0706126\pi$
$360$		0			0
$361$	8.22947			0.433130
$362$	−19.5809	+	27.6008i	−1.02915	+	1.45066i
$363$		0			0
$364$	−11.4991	−	4.94814i	−0.602716	−	0.259353i
$365$	−26.7018			−1.39764
$366$		0			0
$367$	16.3091			0.851329			0.425665	−	0.904881i	$-0.360040\pi$
$367$	16.3091			0.851329			0.425665	+	0.904881i	$0.360040\pi$
$368$	1.03411	+	1.29600i	0.0539067	+	0.0675587i
$369$		0			0
$370$	−13.1617	+	18.5524i	−0.684246	+	0.964495i
$371$	6.09768	+	5.60243i	0.316576	+	0.290864i
$372$		0			0
$373$	1.42509			0.0737882			0.0368941	−	0.999319i	$-0.488254\pi$
$373$	1.42509			0.0737882			0.0368941	+	0.999319i	$0.488254\pi$
$374$	−0.332608	−	0.235964i	−0.0171988	−	0.0122014i
$375$		0			0
$376$	4.00383	−	13.9084i	0.206482	−	0.717272i
$377$			23.0209i			1.18564i
$378$		0			0
$379$		−	27.4465i		−	1.40983i	−0.709292	−	0.704915i	$-0.750985\pi$
$379$		−	27.4465i		−	1.40983i	0.709292	−	0.704915i	$-0.249015\pi$
$380$	21.3056	−	7.45845i	1.09295	−	0.382611i
$381$		0			0
$382$	−21.2119	+	29.8998i	−1.08530	+	1.52981i
$383$	6.09768			0.311577			0.155789	−	0.987790i	$-0.450208\pi$
$383$	6.09768			0.311577			0.155789	+	0.987790i	$0.450208\pi$
$384$		0			0
$385$	1.74672	+	1.60486i	0.0890213	+	0.0817910i
$386$	13.4832	+	9.56547i	0.686279	+	0.486869i
$387$		0			0
$388$	−7.49526	+	2.62387i	−0.380514	+	0.133207i
$389$	−4.61373			−0.233926			−0.116963	−	0.993136i	$-0.537316\pi$
$389$	−4.61373			−0.233926			−0.116963	+	0.993136i	$0.537316\pi$
$390$		0			0
$391$	0.288364			0.0145832
$392$	−19.4211	−	3.84968i	−0.980915	−	0.194438i
$393$		0			0
$394$	−13.5160	−	9.58873i	−0.680927	−	0.483073i
$395$	−16.4677			−0.828578
$396$		0			0
$397$			26.2120i			1.31554i	0.753218	+	0.657771i	$0.228500\pi$
$397$			26.2120i			1.31554i	−0.753218	+	0.657771i	$0.771500\pi$
$398$	−7.75444	−	5.50127i	−0.388695	−	0.275754i
$399$		0			0
$400$	−1.00564	+	0.802428i	−0.0502821	+	0.0401214i
$401$	21.0814			1.05275			0.526377	−	0.850251i	$-0.323550\pi$
$401$	21.0814			1.05275			0.526377	+	0.850251i	$0.323550\pi$
$402$		0			0
$403$		−	4.81457i		−	0.239831i
$404$	−28.0150	+	9.80722i	−1.39380	+	0.487927i
$405$		0			0
$406$	7.61383	+	35.6043i	0.377868	+	1.76701i
$407$		−	3.08240i		−	0.152789i
$408$		0			0
$409$			0.843933i			0.0417298i	0.999782	+	0.0208649i	$0.00664199\pi$
$409$			0.843933i			0.0417298i	−0.999782	+	0.0208649i	$0.993358\pi$
$410$	−26.4227	−	18.7451i	−1.30492	−	0.925757i
$411$		0			0
$412$	2.26336	+	6.46545i	0.111508	+	0.318530i
$413$	−21.8494	−	20.0748i	−1.07514	−	0.987816i
$414$		0			0
$415$			27.8168i			1.36547i
$416$	−0.754992	−	13.3615i	−0.0370165	−	0.655103i
$417$		0			0
$418$	−1.76991	+	2.49482i	−0.0865692	+	0.122026i
$419$	1.64584			0.0804044			0.0402022	−	0.999192i	$-0.487200\pi$
$419$	1.64584			0.0804044			0.0402022	+	0.999192i	$0.487200\pi$
$420$		0			0
$421$	−28.8822			−1.40763			−0.703817	−	0.710382i	$-0.748522\pi$
$421$	−28.8822			−1.40763			−0.703817	+	0.710382i	$0.748522\pi$
$422$	5.23639	−	7.38107i	0.254903	−	0.359305i
$423$		0			0
$424$	−2.44889	+	8.50690i	−0.118929	+	0.413132i
$425$			0.223758i			0.0108539i
$426$		0			0
$427$	7.10757	−	7.73588i	0.343959	−	0.374366i
$428$	27.3758	−	9.58346i	1.32326	−	0.463234i
$429$		0			0
$430$	21.8671	+	15.5133i	1.05453	+	0.748116i
$431$			35.5181i			1.71085i	0.517930	+	0.855423i	$0.326703\pi$
$431$			35.5181i			1.71085i	−0.517930	+	0.855423i	$0.673297\pi$
$432$		0			0
$433$			21.0473i			1.01147i	0.862690	+	0.505733i	$0.168778\pi$
$433$			21.0473i			1.01147i	−0.862690	+	0.505733i	$0.831222\pi$
$434$	−1.59235	−	7.44625i	−0.0764351	−	0.357431i
$435$		0			0
$436$	−5.55173	−	15.8589i	−0.265879	−	0.759504i
$437$		−	2.16295i		−	0.103468i
$438$		0			0
$439$	30.2295			1.44277			0.721387	−	0.692532i	$-0.243505\pi$
$439$	30.2295			1.44277			0.721387	+	0.692532i	$0.243505\pi$
$440$	−0.701502	+	2.43686i	−0.0334428	+	0.116173i
$441$		0			0
$442$	−1.89836	−	1.34676i	−0.0902960	−	0.0640591i
$443$			2.14448i			0.101887i	0.998702	+	0.0509437i	$0.0162229\pi$
$443$			2.14448i			0.101887i	−0.998702	+	0.0509437i	$0.983777\pi$
$444$		0			0
$445$	−31.7806			−1.50654
$446$	−10.1806	−	7.22249i	−0.482067	−	0.341995i
$447$		0			0
$448$	−5.58681	−	20.4154i	−0.263952	−	0.964536i
$449$	27.2051			1.28389			0.641944	−	0.766751i	$-0.278128\pi$
$449$	27.2051			1.28389			0.641944	+	0.766751i	$0.278128\pi$
$450$		0			0
$451$	4.39000			0.206717
$452$	−3.04884	−	8.70923i	−0.143405	−	0.409648i
$453$		0			0
$454$	−24.8965	−	17.6625i	−1.16845	−	0.828940i
$455$	9.96944	+	9.15972i	0.467375	+	0.429414i
$456$		0			0
$457$	32.2057			1.50652			0.753259	−	0.657724i	$-0.228481\pi$
$457$	32.2057			1.50652			0.753259	+	0.657724i	$0.228481\pi$
$458$	18.5359	−	26.1277i	0.866125	−	1.22087i
$459$		0			0
$460$	−0.592457	−	1.69239i	−0.0276234	−	0.0789083i
$461$			23.8169i			1.10926i	0.832096	+	0.554631i	$0.187141\pi$
$461$			23.8169i			1.10926i	−0.832096	+	0.554631i	$0.812859\pi$
$462$		0			0
$463$		−	18.6815i		−	0.868202i	−0.900864	−	0.434101i	$-0.857066\pi$
$463$		−	18.6815i		−	0.868202i	0.900864	−	0.434101i	$-0.142934\pi$
$464$	−30.4247	+	24.2766i	−1.41243	+	1.12701i
$465$		0			0
$466$	−26.0577	−	18.4862i	−1.20710	−	0.856356i
$467$	26.7018			1.23561			0.617806	−	0.786331i	$-0.288022\pi$
$467$	26.7018			1.23561			0.617806	+	0.786331i	$0.288022\pi$
$468$		0			0
$469$	−4.23482	+	4.60918i	−0.195546	+	0.212832i
$470$	−9.05675	+	12.7662i	−0.417757	+	0.588859i
$471$		0			0
$472$	8.77494	−	30.4822i	0.403899	−	1.40306i
$473$	−3.63311			−0.167051
$474$		0			0
$475$	1.67836			0.0770086
$476$	−3.38145	−	1.45506i	−0.154989	−	0.0666926i
$477$		0			0
$478$	3.83202	−	5.40151i	0.175272	−	0.247059i
$479$	−37.9165			−1.73245			−0.866225	−	0.499654i	$-0.833461\pi$
$479$	−37.9165			−1.73245			−0.866225	+	0.499654i	$0.833461\pi$
$480$		0			0
$481$		−	17.5928i		−	0.802163i
$482$	1.93588	−	2.72877i	0.0881769	−	0.124292i
$483$		0			0
$484$	7.15547	+	20.4401i	0.325249	+	0.929096i
$485$	8.58829			0.389974
$486$		0			0
$487$			32.6942i			1.48152i	0.671772	+	0.740758i	$0.265533\pi$
$487$			32.6942i			1.48152i	−0.671772	+	0.740758i	$0.734467\pi$
$488$	10.7924	+	3.10681i	0.488547	+	0.140639i
$489$		0			0
$490$	18.4483	+	10.8693i	0.833408	+	0.491023i
$491$			36.8850i			1.66460i	0.554327	+	0.832299i	$0.312976\pi$
$491$			36.8850i			1.66460i	−0.554327	+	0.832299i	$0.687024\pi$
$492$		0			0
$493$			6.76958i			0.304886i
$494$	−10.1018	+	14.2392i	−0.454501	+	0.640653i
$495$		0			0
$496$	6.36298	−	5.07718i	0.285706	−	0.227972i
$497$	7.24019	−	7.88023i	0.324767	−	0.353477i
$498$		0			0
$499$		−	8.24881i		−	0.369268i	−0.982807	−	0.184634i	$-0.940890\pi$
$499$		−	8.24881i		−	0.369268i	0.982807	−	0.184634i	$-0.0591099\pi$
$500$	21.7280	−	7.60632i	0.971705	−	0.340165i
$501$		0			0
$502$	11.8044	+	8.37443i	0.526855	+	0.373769i
$503$	−11.2147			−0.500041			−0.250020	−	0.968241i	$-0.580437\pi$
$503$	−11.2147			−0.500041			−0.250020	+	0.968241i	$0.580437\pi$
$504$		0			0
$505$	32.1004			1.42845
$506$	0.198174	+	0.140592i	0.00880992	+	0.00625006i
$507$		0			0
$508$	11.9611	−	4.18722i	0.530687	−	0.185778i
$509$		−	24.3647i		−	1.07995i	−0.841682	−	0.539973i	$-0.818434\pi$
$509$		−	24.3647i		−	1.07995i	0.841682	−	0.539973i	$-0.181566\pi$
$510$		0			0
$511$	22.0981	−	24.0516i	0.977562	−	1.06398i
$512$	16.8626	−	15.0882i	0.745228	−	0.666809i
$513$		0			0
$514$	−0.0621035	+	0.0875395i	−0.00273927	+	0.00386120i
$515$		−	7.40830i		−	0.326449i
$516$		0			0
$517$		−	2.12104i		−	0.0932831i
$518$	−5.81856	−	27.2092i	−0.255653	−	1.19550i
$519$		0			0
$520$	−4.00383	+	13.9084i	−0.175579	+	0.609924i
$521$		−	3.52991i		−	0.154648i	−0.997006	−	0.0773242i	$-0.975362\pi$
$521$		−	3.52991i		−	0.154648i	0.997006	−	0.0773242i	$-0.0246376\pi$
$522$		0			0
$523$	−2.28655			−0.0999838			−0.0499919	−	0.998750i	$-0.515920\pi$
$523$	−2.28655			−0.0999838			−0.0499919	+	0.998750i	$0.515920\pi$
$524$	12.5280	+	35.7871i	0.547287	+	1.56336i
$525$		0			0
$526$	−12.4985	+	17.6175i	−0.544959	+	0.768161i
$527$		−	1.41578i		−	0.0616724i
$528$		0			0
$529$	22.8282			0.992530
$530$	5.53945	−	7.80826i	0.240618	−	0.339169i
$531$		0			0
$532$	−10.9141	+	25.3635i	−0.473186	+	1.09965i
$533$	25.0560			1.08529
$534$		0			0
$535$	−31.3680			−1.35616
$536$	−6.43029	−	1.85109i	−0.277746	−	0.0799551i
$537$		0			0
$538$	−13.9141	+	19.6129i	−0.599879	+	0.845574i
$539$	−2.89114	+	0.245199i	−0.124530	+	0.0105615i
$540$		0			0
$541$	0.216372			0.00930255			0.00465127	−	0.999989i	$-0.498519\pi$
$541$	0.216372			0.00930255			0.00465127	+	0.999989i	$0.498519\pi$
$542$	0.780353	+	0.553609i	0.0335190	+	0.0237795i
$543$		0			0
$544$	−0.222015	−	3.92913i	−0.00951880	−	0.168460i
$545$			18.1716i			0.778385i
$546$		0			0
$547$			32.8761i			1.40568i	0.711347	+	0.702841i	$0.248085\pi$
$547$			32.8761i			1.40568i	−0.711347	+	0.702841i	$0.751915\pi$
$548$	1.31323	+	3.75133i	0.0560984	+	0.160249i
$549$		0			0
$550$	−0.109093	+	0.153775i	−0.00465176	+	0.00655700i
$551$	50.7771			2.16318
$552$		0			0
$553$	13.6285	−	14.8332i	0.579541	−	0.630772i
$554$	−0.373081	−	0.264676i	−0.0158507	−	0.0112450i
$555$		0			0
$556$	−9.00000	−	25.7091i	−0.381685	−	1.09031i
$557$	−1.48395			−0.0628769			−0.0314385	−	0.999506i	$-0.510009\pi$
$557$	−1.48395			−0.0628769			−0.0314385	+	0.999506i	$0.510009\pi$
$558$		0			0
$559$	−20.7360			−0.877040
$560$	−1.59235	+	22.8351i	−0.0672890	+	0.964958i
$561$		0			0
$562$	−4.19056	−	2.97292i	−0.176768	−	0.125405i
$563$	7.60767			0.320625			0.160312	−	0.987066i	$-0.448750\pi$
$563$	7.60767			0.320625			0.160312	+	0.987066i	$0.448750\pi$
$564$		0			0
$565$			9.97929i			0.419832i
$566$	31.8189	+	22.5734i	1.33745	+	0.948830i
$567$		0			0
$568$	10.9937	+	3.16478i	0.461287	+	0.132791i
$569$	−0.477293			−0.0200092			−0.0100046	−	0.999950i	$-0.503185\pi$
$569$	−0.477293			−0.0200092			−0.0100046	+	0.999950i	$0.503185\pi$
$570$		0			0
$571$			3.97063i			0.166166i	0.996543	+	0.0830829i	$0.0264766\pi$
$571$			3.97063i			0.166166i	−0.996543	+	0.0830829i	$0.973523\pi$
$572$	−0.648012	−	1.85109i	−0.0270948	−	0.0773981i
$573$		0			0
$574$	38.7518	−	8.28689i	1.61747	−	0.345888i
$575$		−	0.133319i		−	0.00555981i
$576$		0			0
$577$		−	10.7402i		−	0.447121i	−0.974690	−	0.223560i	$-0.928232\pi$
$577$		−	10.7402i		−	0.447121i	0.974690	−	0.223560i	$-0.0717680\pi$
$578$	19.0501	+	13.5148i	0.792381	+	0.562142i
$579$		0			0
$580$	39.7304	−	13.9084i	1.64971	−	0.577515i
$581$	−25.0560	−	23.0209i	−1.03950	−	0.955068i
$582$		0			0
$583$			1.29730i			0.0537289i
$584$	33.5545	+	9.65935i	1.38849	+	0.399707i
$585$		0			0
$586$	−16.7637	+	23.6296i	−0.692500	+	0.976130i
$587$	1.64584			0.0679310			0.0339655	−	0.999423i	$-0.489186\pi$
$587$	1.64584			0.0679310			0.0339655	+	0.999423i	$0.489186\pi$
$588$		0			0
$589$	−10.6195			−0.437568
$590$	−19.8491	+	27.9788i	−0.817175	+	1.15187i
$591$		0			0
$592$	23.2508	−	18.5524i	0.955604	−	0.762500i
$593$			8.28019i			0.340027i	0.985442	+	0.170013i	$0.0543811\pi$
$593$			8.28019i			0.340027i	−0.985442	+	0.170013i	$0.945619\pi$
$594$		0			0
$595$	2.93164	+	2.69353i	0.120185	+	0.110424i
$596$	8.16590	+	23.3265i	0.334488	+	0.955490i
$597$		0			0
$598$	1.13108	+	0.802428i	0.0462533	+	0.0328137i
$599$		−	19.0006i		−	0.776343i	−0.921587	−	0.388171i	$-0.873107\pi$
$599$		−	19.0006i		−	0.776343i	0.921587	−	0.388171i	$-0.126893\pi$
$600$		0			0
$601$		−	27.8168i		−	1.13467i	−0.823486	−	0.567336i	$-0.807974\pi$
$601$		−	27.8168i		−	1.13467i	0.823486	−	0.567336i	$-0.192026\pi$
$602$	−32.0705	+	6.85814i	−1.30710	+	0.279517i
$603$		0			0
$604$	29.9429	−	10.4821i	1.21836	−	0.426511i
$605$		−	23.4209i		−	0.952193i
$606$		0			0
$607$	19.1166			0.775917			0.387958	−	0.921677i	$-0.373180\pi$
$607$	19.1166			0.775917			0.387958	+	0.921677i	$0.373180\pi$
$608$	−29.4715	+	1.66528i	−1.19523	+	0.0675361i
$609$		0			0
$610$	−9.90602	−	7.02767i	−0.401083	−	0.284542i
$611$		−	12.1058i		−	0.489749i
$612$		0			0
$613$	−0.345440			−0.0139522			−0.00697609	−	0.999976i	$-0.502221\pi$
$613$	−0.345440			−0.0139522			−0.00697609	+	0.999976i	$0.502221\pi$
$614$	23.7962	+	16.8818i	0.960337	+	0.681296i
$615$		0			0
$616$	−1.61444	−	2.64860i	−0.0650478	−	0.106715i
$617$	−13.3379			−0.536963			−0.268481	−	0.963285i	$-0.586522\pi$
$617$	−13.3379			−0.536963			−0.268481	+	0.963285i	$0.586522\pi$
$618$		0			0
$619$	−21.4589			−0.862508			−0.431254	−	0.902231i	$-0.641929\pi$
$619$	−21.4589			−0.862508			−0.431254	+	0.902231i	$0.641929\pi$
$620$	−8.30917	+	2.90879i	−0.333704	+	0.116820i
$621$		0			0
$622$	−18.9944	−	13.4752i	−0.761604	−	0.540308i
$623$	26.3013	−	28.6263i	1.05374	−	1.14689i
$624$		0			0
$625$	−23.2884			−0.931535
$626$	22.1394	−	31.2072i	0.884870	−	1.24729i
$627$		0			0
$628$	−15.8082	+	5.53398i	−0.630816	+	0.220830i
$629$		−	5.17338i		−	0.206276i
$630$		0			0
$631$		−	33.4753i		−	1.33263i	−0.745670	−	0.666316i	$-0.767870\pi$
$631$		−	33.4753i		−	1.33263i	0.745670	−	0.666316i	$-0.232130\pi$
$632$	20.6939	+	5.95717i	0.823158	+	0.236963i
$633$		0			0
$634$	−36.1204	−	25.6250i	−1.43452	−	1.01770i
$635$	−13.7054			−0.543880
$636$		0			0
$637$	−16.5012	+	1.39947i	−0.653801	+	0.0554491i
$638$	−3.30051	+	4.65231i	−0.130668	+	0.184187i
$639$		0			0
$640$	−22.6037	+	9.37557i	−0.893491	+	0.370602i
$641$	3.12979			0.123619			0.0618096	−	0.998088i	$-0.480313\pi$
$641$	3.12979			0.123619			0.0618096	+	0.998088i	$0.480313\pi$
$642$		0			0
$643$	−2.40128			−0.0946974			−0.0473487	−	0.998878i	$-0.515077\pi$
$643$	−2.40128			−0.0946974			−0.0473487	+	0.998878i	$0.515077\pi$
$644$	2.01473	+	0.866953i	0.0793915	+	0.0341627i
$645$		0			0
$646$	−2.97055	+	4.18722i	−0.116875	+	0.164744i
$647$	−44.6794			−1.75653			−0.878265	−	0.478174i	$-0.841299\pi$
$647$	−44.6794			−1.75653			−0.878265	+	0.478174i	$0.841299\pi$
$648$		0			0
$649$		−	4.64854i		−	0.182471i
$650$	−0.622651	+	0.877673i	−0.0244224	+	0.0344252i
$651$		0			0
$652$	32.2351	−	11.2845i	1.26242	−	0.441937i
$653$	37.4132			1.46409			0.732046	−	0.681255i	$-0.238566\pi$
$653$	37.4132			1.46409			0.732046	+	0.681255i	$0.238566\pi$
$654$		0			0
$655$		−	41.0058i		−	1.60223i
$656$	26.4227	+	33.1142i	1.03163	+	1.29289i
$657$		0			0
$658$	−4.00383	−	18.7230i	−0.156085	−	0.729898i
$659$		−	34.3505i		−	1.33810i	−0.743216	−	0.669052i	$-0.766700\pi$
$659$		−	34.3505i		−	1.33810i	0.743216	−	0.669052i	$-0.233300\pi$
$660$		0			0
$661$		−	17.0766i		−	0.664203i	−0.943244	−	0.332102i	$-0.892242\pi$
$661$		−	17.0766i		−	0.664203i	0.943244	−	0.332102i	$-0.107758\pi$
$662$	−17.2741	+	24.3491i	−0.671375	+	0.946353i
$663$		0			0
$664$	10.0627	−	34.9557i	0.390509	−	1.35654i
$665$	20.2036	−	21.9896i	0.783461	−	0.852719i
$666$		0			0
$667$		−	4.03344i		−	0.156175i
$668$	−5.11706	−	14.6173i	−0.197985	−	0.565559i
$669$		0			0
$670$	5.90219	+	4.18722i	0.228022	+	0.161766i
$671$	1.64584			0.0635369
$672$		0			0
$673$	−22.0333			−0.849320			−0.424660	−	0.905353i	$-0.639606\pi$
$673$	−22.0333			−0.849320			−0.424660	+	0.905353i	$0.639606\pi$
$674$	−13.6944	−	9.71529i	−0.527490	−	0.374219i
$675$		0			0
$676$	4.89211	+	13.9747i	0.188158	+	0.537487i
$677$		−	10.3672i		−	0.398446i	−0.979954	−	0.199223i	$-0.936158\pi$
$677$		−	10.3672i		−	0.398446i	0.979954	−	0.199223i	$-0.0638417\pi$
$678$		0			0
$679$	−7.10757	+	7.73588i	−0.272764	+	0.296876i
$680$	−1.17738	+	4.08994i	−0.0451503	+	0.156842i
$681$		0			0
$682$	0.690264	−	0.972979i	0.0264316	−	0.0372573i
$683$		−	11.8919i		−	0.455032i	−0.973774	−	0.227516i	$-0.926940\pi$
$683$		−	11.8919i		−	0.455032i	0.973774	−	0.227516i	$-0.0730604\pi$
$684$		0			0
$685$		−	4.29838i		−	0.164233i
$686$	−25.0580	+	7.62197i	−0.956721	+	0.291008i
$687$		0			0
$688$	−21.8671	−	27.4050i	−0.833676	−	1.04480i
$689$			7.40438i			0.282084i
$690$		0			0
$691$	−45.2389			−1.72097			−0.860485	−	0.509475i	$-0.829840\pi$
$691$	−45.2389			−1.72097			−0.860485	+	0.509475i	$0.829840\pi$
$692$	8.02264	−	2.80849i	0.304975	−	0.106763i
$693$		0			0
$694$	16.2063	−	22.8440i	0.615182	−	0.867145i
$695$			29.4583i			1.11742i
$696$		0			0
$697$	7.36801			0.279083
$698$	−12.6603	+	17.8457i	−0.479200	+	0.675468i
$699$		0			0
$700$	−0.672720	+	1.56335i	−0.0254264	+	0.0590891i
$701$	18.3191			0.691902			0.345951	−	0.938253i	$-0.387556\pi$
$701$	18.3191			0.691902			0.345951	+	0.938253i	$0.387556\pi$
$702$		0			0
$703$	−38.8044			−1.46354
$704$	1.76307	−	2.80849i	0.0664481	−	0.105849i
$705$		0			0
$706$	−22.4596	+	31.6584i	−0.845277	+	1.19148i
$707$	−26.5659	+	28.9144i	−0.999115	+	1.08744i
$708$		0			0
$709$	5.79491			0.217633			0.108816	−	0.994062i	$-0.465294\pi$
$709$	5.79491			0.217633			0.108816	+	0.994062i	$0.465294\pi$
$710$	−10.0909	−	7.15880i	−0.378703	−	0.268665i
$711$		0			0
$712$	39.9367	+	11.4966i	1.49669	+	0.430853i
$713$			0.843550i			0.0315912i
$714$		0			0
$715$			2.12104i			0.0793223i
$716$	−16.7193	+	5.85293i	−0.624831	+	0.218734i
$717$		0			0
$718$	6.82254	−	9.61688i	0.254615	−	0.358899i
$719$	−7.60767			−0.283718			−0.141859	−	0.989887i	$-0.545308\pi$
$719$	−7.60767			−0.283718			−0.141859	+	0.989887i	$0.545308\pi$
$720$		0			0
$721$	6.67301	+	6.13103i	0.248516	+	0.228331i
$722$	9.49215	+	6.73406i	0.353261	+	0.250616i
$723$		0			0
$724$	−45.1706	+	15.8129i	−1.67875	+	0.587681i
$725$	3.12979			0.116237
$726$		0			0
$727$	0.366196			0.0135815			0.00679074	−	0.999977i	$-0.497838\pi$
$727$	0.366196			0.0135815			0.00679074	+	0.999977i	$0.497838\pi$
$728$	−9.21445	−	15.1169i	−0.341510	−	0.560269i
$729$		0			0
$730$	−30.7987	−	21.8497i	−1.13991	−	0.808693i
$731$	−6.09768			−0.225531
$732$		0			0
$733$			41.5220i			1.53365i	0.641856	+	0.766825i	$0.278165\pi$
$733$			41.5220i			1.53365i	−0.641856	+	0.766825i	$0.721835\pi$
$734$	18.8115	+	13.3455i	0.694345	+	0.492592i
$735$		0			0
$736$	0.132280	+	2.34105i	0.00487592	+	0.0862921i
$737$	−0.980621			−0.0361216
$738$		0			0
$739$		−	8.29142i		−	0.305005i	−0.988303	−	0.152502i	$-0.951267\pi$
$739$		−	8.29142i		−	0.305005i	0.988303	−	0.152502i	$-0.0487332\pi$
$740$	−30.3624	+	10.6290i	−1.11614	+	0.390728i
$741$		0			0
$742$	2.44889	+	11.4517i	0.0899016	+	0.420404i
$743$		−	16.4172i		−	0.602288i	−0.953579	−	0.301144i	$-0.902631\pi$
$743$		−	16.4172i		−	0.602288i	0.953579	−	0.301144i	$-0.0973685\pi$
$744$		0			0
$745$		−	26.7282i		−	0.979244i
$746$	1.64374	+	1.16613i	0.0601817	+	0.0426950i
$747$		0			0
$748$	−0.190556	−	0.544337i	−0.00696742	−	0.0199029i
$749$	25.9598	−	28.2547i	0.948551	−	1.03240i
$750$		0			0
$751$		−	20.4119i		−	0.744843i	−0.928064	−	0.372421i	$-0.878528\pi$
$751$		−	20.4119i		−	0.744843i	0.928064	−	0.372421i	$-0.121472\pi$
$752$	15.9992	−	12.7662i	0.583431	−	0.465534i
$753$		0			0
$754$	−18.8377	+	26.5531i	−0.686027	+	0.967006i
$755$	−34.3095			−1.24865
$756$		0			0
$757$	−3.04637			−0.110722			−0.0553612	−	0.998466i	$-0.517631\pi$
$757$	−3.04637			−0.110722			−0.0553612	+	0.998466i	$0.517631\pi$
$758$	22.4590	−	31.6577i	0.815749	−	1.14986i
$759$		0			0
$760$	30.6777	+	8.83123i	1.11280	+	0.320342i
$761$		−	23.2691i		−	0.843503i	−0.906711	−	0.421751i	$-0.861415\pi$
$761$		−	23.2691i		−	0.843503i	0.906711	−	0.421751i	$-0.138585\pi$
$762$		0			0
$763$	−16.3680	−	15.0386i	−0.592562	−	0.544434i
$764$	−48.9331	+	17.1300i	−1.77034	+	0.619742i
$765$		0			0
$766$	7.03327	+	4.98964i	0.254123	+	0.180283i
$767$		−	26.5316i		−	0.958000i
$768$		0			0
$769$		−	34.4810i		−	1.24342i	−0.783249	−	0.621708i	$-0.786439\pi$
$769$		−	34.4810i		−	1.24342i	0.783249	−	0.621708i	$-0.213561\pi$
$770$	0.701502	+	3.28041i	0.0252804	+	0.118218i
$771$		0			0
$772$	7.72474	+	22.0663i	0.278019	+	0.794182i
$773$			18.1472i			0.652708i	0.945248	+	0.326354i	$0.105820\pi$
$773$			18.1472i			0.652708i	−0.945248	+	0.326354i	$0.894180\pi$
$774$		0			0
$775$	−0.654560			−0.0235125
$776$	−10.7924	−	3.10681i	−0.387423	−	0.111528i
$777$		0			0
$778$	−5.32164	−	3.77535i	−0.190790	−	0.135353i
$779$		−	55.2658i		−	1.98010i
$780$		0			0
$781$	1.67655			0.0599916
$782$	0.332608	+	0.235964i	0.0118941	+	0.00843805i
$783$		0			0
$784$	−19.2508	−	20.3324i	−0.687530	−	0.726156i
$785$	18.1135			0.646499
$786$		0			0
$787$	21.1831			0.755096			0.377548	−	0.925990i	$-0.376767\pi$
$787$	21.1831			0.755096			0.377548	+	0.925990i	$0.376767\pi$
$788$	−7.74352	−	22.1199i	−0.275852	−	0.787990i
$789$		0			0
$790$	−18.9944	−	13.4752i	−0.675789	−	0.479428i
$791$	−8.98882	−	8.25875i	−0.319606	−	0.293647i
$792$		0			0
$793$	9.39363			0.333578
$794$	−21.4489	+	30.2338i	−0.761192	+	1.07296i
$795$		0			0
$796$	−4.44263	−	12.6907i	−0.157465	−	0.449810i
$797$		−	1.93919i		−	0.0686898i	−0.999410	−	0.0343449i	$-0.989066\pi$
$797$		−	1.93919i		−	0.0686898i	0.999410	−	0.0343449i	$-0.0109345\pi$
$798$		0			0
$799$		−	3.55987i		−	0.125939i
$800$	−1.81656	+	0.102644i	−0.0642250	+	0.00362902i
$801$		0			0
$802$	24.3160	+	17.2506i	0.858628	+	0.609140i
$803$	5.11706			0.180577
$804$		0			0
$805$	−1.74672	−	1.60486i	−0.0615640	−	0.0565637i
$806$	3.93969	−	5.55328i	0.138770	−	0.195606i
$807$		0			0
$808$	−40.3386	−	11.6123i	−1.41911	−	0.408519i
$809$	30.1990			1.06174			0.530871	−	0.847453i	$-0.321865\pi$
$809$	30.1990			1.06174			0.530871	+	0.847453i	$0.321865\pi$
$810$		0			0
$811$	3.17363			0.111441			0.0557206	−	0.998446i	$-0.482254\pi$
$811$	3.17363			0.111441			0.0557206	+	0.998446i	$0.482254\pi$
$812$	−20.3524	+	47.2975i	−0.714231	+	1.65982i
$813$		0			0
$814$	2.52228	−	3.55534i	0.0884059	−	0.124615i
$815$	−36.9359			−1.29381
$816$		0			0
$817$			45.7374i			1.60015i
$818$	−0.690578	+	0.973421i	−0.0241455	+	0.0340349i
$819$		0			0
$820$	−15.1379	−	43.2426i	−0.528639	−	1.51010i
$821$	−42.8717			−1.49623			−0.748116	−	0.663567i	$-0.769042\pi$
$821$	−42.8717			−1.49623			−0.748116	+	0.663567i	$0.769042\pi$
$822$		0			0
$823$		−	9.21837i		−	0.321332i	−0.987009	−	0.160666i	$-0.948636\pi$
$823$		−	9.21837i		−	0.321332i	0.987009	−	0.160666i	$-0.0513642\pi$
$824$	−2.67995	+	9.30955i	−0.0933604	+	0.324313i
$825$		0			0
$826$	−8.77494	−	41.0340i	−0.305319	−	1.42775i
$827$			20.2956i			0.705746i	0.935671	+	0.352873i	$0.114795\pi$
$827$			20.2956i			0.705746i	−0.935671	+	0.352873i	$0.885205\pi$
$828$		0			0
$829$			31.7875i			1.10402i	0.833836	+	0.552012i	$0.186140\pi$
$829$			31.7875i			1.10402i	−0.833836	+	0.552012i	$0.813860\pi$
$830$	−22.7621	+	32.0849i	−0.790084	+	1.11368i
$831$		0			0
$832$	10.0627	−	16.0295i	0.348862	−	0.555721i
$833$	−4.85238	+	0.411532i	−0.168125	+	0.0142588i
$834$		0			0
$835$			16.7489i			0.579618i
$836$	−4.08295	+	1.42932i	−0.141212	+	0.0494340i
$837$		0			0
$838$	1.89836	+	1.34676i	0.0655779	+	0.0465232i
$839$	−19.8030			−0.683677			−0.341838	−	0.939759i	$-0.611050\pi$
$839$	−19.8030			−0.683677			−0.341838	+	0.939759i	$0.611050\pi$
$840$		0			0
$841$	65.6884			2.26512
$842$	−33.3137	−	23.6339i	−1.14807	−	0.814478i
$843$		0			0
$844$	12.0796	−	4.22872i	0.415799	−	0.145559i
$845$		−	16.0126i		−	0.550849i
$846$		0			0
$847$	21.0963	+	19.3828i	0.724877	+	0.666002i
$848$	−9.78571	+	7.80826i	−0.336043	+	0.268137i
$849$		0			0
$850$	−0.183098	+	0.258091i	−0.00628022	+	0.00885243i
$851$			3.08240i			0.105663i
$852$		0			0
$853$		−	5.49248i		−	0.188059i	−0.995569	−	0.0940294i	$-0.970025\pi$
$853$		−	5.49248i		−	0.188059i	0.995569	−	0.0940294i	$-0.0299748\pi$
$854$	14.5283	−	3.10681i	0.497147	−	0.106313i
$855$		0			0
$856$	39.4182	+	11.3474i	1.34729	+	0.387845i
$857$		−	30.6774i		−	1.04792i	−0.851743	−	0.523959i	$-0.824454\pi$
$857$		−	30.6774i		−	1.04792i	0.851743	−	0.523959i	$-0.175546\pi$
$858$		0			0
$859$	−9.07783			−0.309732			−0.154866	−	0.987936i	$-0.549495\pi$
$859$	−9.07783			−0.309732			−0.154866	+	0.987936i	$0.549495\pi$
$860$	12.5280	+	35.7871i	0.427200	+	1.22033i
$861$		0			0
$862$	−29.0639	+	40.9677i	−0.989921	+	1.39537i
$863$			41.5535i			1.41450i	0.706965	+	0.707248i	$0.250064\pi$
$863$			41.5535i			1.41450i	−0.706965	+	0.707248i	$0.749936\pi$
$864$		0			0
$865$	−9.19257			−0.312557
$866$	−17.2227	+	24.2766i	−0.585250	+	0.824953i
$867$		0			0
$868$	4.25649	−	9.89175i	0.144475	−	0.335748i
$869$	3.15582			0.107054
$870$		0			0
$871$	−5.59690			−0.189644
$872$	6.57356	−	22.8351i	0.222609	−	0.773294i
$873$		0			0
$874$	1.76991	−	2.49482i	0.0598682	−	0.0843886i
$875$	20.6041	−	22.4255i	0.696546	−	0.758121i
$876$		0			0
$877$	−8.63257			−0.291501			−0.145751	−	0.989321i	$-0.546560\pi$
$877$	−8.63257			−0.291501			−0.145751	+	0.989321i	$0.546560\pi$
$878$	34.8677	+	24.7363i	1.17673	+	0.834811i
$879$		0			0
$880$	−2.80319	+	2.23673i	−0.0944954	+	0.0754002i
$881$			19.4666i			0.655845i	0.944705	+	0.327923i	$0.106349\pi$
$881$			19.4666i			0.655845i	−0.944705	+	0.327923i	$0.893651\pi$
$882$		0			0
$883$		−	27.7540i		−	0.933997i	−0.884258	−	0.466999i	$-0.845335\pi$
$883$		−	27.7540i		−	0.933997i	0.884258	−	0.466999i	$-0.154665\pi$
$884$	−1.08760	−	3.10681i	−0.0365799	−	0.104493i
$885$		0			0
$886$	−1.75480	+	2.47352i	−0.0589536	+	0.0830995i
$887$	2.62646			0.0881878			0.0440939	−	0.999027i	$-0.485960\pi$
$887$	2.62646			0.0881878			0.0440939	+	0.999027i	$0.485960\pi$
$888$		0			0
$889$	11.3424	−	12.3451i	0.380412	−	0.414040i
$890$	−36.6568	−	26.0056i	−1.22874	−	0.871709i
$891$		0			0
$892$	−5.83263	−	16.6613i	−0.195291	−	0.557862i
$893$	−26.7018			−0.893541
$894$		0			0
$895$	19.1575			0.640364
$896$	10.2616	−	28.1194i	0.342815	−	0.939403i
$897$		0			0
$898$	31.3793	+	22.2615i	1.04714	+	0.742877i
$899$	−19.8030			−0.660468
$900$		0			0
$901$			2.17735i			0.0725380i
$902$	5.06357	+	3.59227i	0.168599	+	0.119610i
$903$		0			0
$904$	3.61000	−	12.5403i	0.120067	−	0.417086i
$905$	51.7577			1.72049
$906$		0			0
$907$			5.22753i			0.173577i	0.996227	+	0.0867887i	$0.0276605\pi$
$907$			5.22753i			0.173577i	−0.996227	+	0.0867887i	$0.972340\pi$
$908$	−14.2636	−	40.7450i	−0.473354	−	1.35217i
$909$		0			0
$910$	4.00383	+	18.7230i	0.132726	+	0.620661i
$911$		−	52.9940i		−	1.75577i	−0.478873	−	0.877884i	$-0.658954\pi$
$911$		−	52.9940i		−	1.75577i	0.478873	−	0.877884i	$-0.341046\pi$
$912$		0			0
$913$		−	5.33075i		−	0.176422i
$914$	37.1471	+	26.3534i	1.22872	+	0.871694i
$915$		0			0
$916$	42.7598	−	14.9689i	1.41282	−	0.494587i
$917$	36.9359	+	33.9360i	1.21973	+	1.12066i
$918$		0			0
$919$		−	44.9137i		−	1.48156i	−0.671745	−	0.740782i	$-0.734455\pi$
$919$		−	44.9137i		−	1.48156i	0.671745	−	0.740782i	$-0.265545\pi$
$920$	0.701502	−	2.43686i	0.0231278	−	0.0803410i
$921$		0			0
$922$	−19.4890	+	27.4712i	−0.641836	+	0.904716i
$923$	9.56891			0.314964
$924$		0			0
$925$	−2.39181			−0.0786424
$926$	15.2868	−	21.5478i	0.502355	−	0.708106i
$927$		0			0
$928$	−54.9580	+	3.10539i	−1.80409	+	0.101940i
$929$		−	32.2964i		−	1.05961i	−0.848119	−	0.529806i	$-0.822265\pi$
$929$		−	32.2964i		−	1.05961i	0.848119	−	0.529806i	$-0.177735\pi$
$930$		0			0
$931$	3.08681	+	36.3966i	0.101166	+	1.19285i
$932$	−14.9288	−	42.6452i	−0.489009	−	1.39689i
$933$		0			0
$934$	30.7987	+	21.8497i	1.00777	+	0.714943i
$935$			0.623717i			0.0203977i
$936$		0			0
$937$		−	40.6781i		−	1.32889i	−0.747335	−	0.664447i	$-0.768667\pi$
$937$		−	40.6781i		−	1.32889i	0.747335	−	0.664447i	$-0.231333\pi$
$938$	−8.65621	+	1.85109i	−0.282635	+	0.0604404i
$939$		0			0
$940$	−20.8927	+	7.31392i	−0.681445	+	0.238554i
$941$			8.52836i			0.278016i	0.990291	+	0.139008i	$0.0443915\pi$
$941$			8.52836i			0.278016i	−0.990291	+	0.139008i	$0.955609\pi$
$942$		0			0
$943$	−4.39000			−0.142958
$944$	35.0644	−	27.9788i	1.14125	−	0.910632i
$945$		0			0
$946$	−4.19056	−	2.97292i	−0.136247	−	0.0966581i
$947$		−	19.9998i		−	0.649908i	−0.945730	−	0.324954i	$-0.894651\pi$
$947$		−	19.9998i		−	0.649908i	0.945730	−	0.324954i	$-0.105349\pi$
$948$		0			0
$949$	29.2057			0.948056
$950$	1.93588	+	1.37338i	0.0628082	+	0.0445583i
$951$		0			0
$952$	−2.70962	−	4.44531i	−0.0878194	−	0.144073i
$953$	−24.5787			−0.796181			−0.398090	−	0.917346i	$-0.630327\pi$
$953$	−24.5787			−0.796181			−0.398090	+	0.917346i	$0.630327\pi$
$954$		0			0
$955$	56.0689			1.81435
$956$	8.83995	−	3.09460i	0.285904	−	0.100087i
$957$		0			0
$958$	−43.7342	−	31.0265i	−1.41299	−	1.00242i
$959$	3.87176	+	3.55729i	0.125026	+	0.114871i
$960$		0			0
$961$	−26.8584			−0.866400
$962$	14.3959	−	20.2921i	0.464143	−	0.654244i
$963$		0			0
$964$	4.46582	−	1.56335i	0.143834	−	0.0503521i
$965$		−	25.2842i		−	0.813926i
$966$		0			0
$967$			40.1619i			1.29152i	0.763541	+	0.645760i	$0.223459\pi$
$967$			40.1619i			1.29152i	−0.763541	+	0.645760i	$0.776541\pi$
$968$	−8.47248	+	29.4315i	−0.272316	+	0.945965i
$969$		0			0
$970$	9.90602	+	7.02767i	0.318063	+	0.225645i
$971$	−24.7405			−0.793962			−0.396981	−	0.917827i	$-0.629942\pi$
$971$	−24.7405			−0.793962			−0.396981	+	0.917827i	$0.629942\pi$
$972$		0			0
$973$	−26.5345	−	24.3793i	−0.850656	−	0.781565i
$974$	−26.7532	+	37.7106i	−0.857227	+	1.20833i
$975$		0			0
$976$	9.90602	+	12.4147i	0.317084	+	0.397386i
$977$	41.8911			1.34021			0.670107	−	0.742264i	$-0.266248\pi$
$977$	41.8911			1.34021			0.670107	+	0.742264i	$0.266248\pi$
$978$		0			0
$979$	6.09035			0.194648
$980$	12.3847	+	27.6329i	0.395615	+	0.882701i
$981$		0			0
$982$	−30.1825	+	42.5444i	−0.963162	+	1.35765i
$983$	24.7405			0.789101			0.394550	−	0.918874i	$-0.370900\pi$
$983$	24.7405			0.789101			0.394550	+	0.918874i	$0.370900\pi$
$984$		0			0
$985$			25.3456i			0.807579i
$986$	−5.53945	+	7.80826i	−0.176412	+	0.248666i
$987$		0			0
$988$	−23.3035	+	8.15785i	−0.741382	+	0.259536i
$989$	3.63311			0.115526
$990$		0			0
$991$			30.8807i			0.980958i	0.871453	+	0.490479i	$0.163178\pi$
$991$			30.8807i			0.980958i	−0.871453	+	0.490479i	$0.836822\pi$
$992$	11.4939	−	0.649459i	0.364931	−	0.0206203i
$993$		0			0
$994$	14.7994	−	3.16478i	0.469407	−	0.100381i
$995$			14.5414i			0.460992i
$996$		0			0
$997$			32.6314i			1.03345i	0.856152	+	0.516723i	$0.172848\pi$
$997$			32.6314i			1.03345i	−0.856152	+	0.516723i	$0.827152\pi$
$998$	6.74988	−	9.51446i	0.213664	−	0.301175i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.b.c.55.10	yes	12
3.2	odd	2	inner	756.2.b.c.55.3	✓	12
4.3	odd	2		756.2.b.d.55.9	yes	12
7.6	odd	2		756.2.b.d.55.10	yes	12
12.11	even	2		756.2.b.d.55.4	yes	12
21.20	even	2		756.2.b.d.55.3	yes	12
28.27	even	2	inner	756.2.b.c.55.9	yes	12
84.83	odd	2	inner	756.2.b.c.55.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.b.c.55.3	✓	12	3.2	odd	2	inner
756.2.b.c.55.4	yes	12	84.83	odd	2	inner
756.2.b.c.55.9	yes	12	28.27	even	2	inner
756.2.b.c.55.10	yes	12	1.1	even	1	trivial
756.2.b.d.55.3	yes	12	21.20	even	2
756.2.b.d.55.4	yes	12	12.11	even	2
756.2.b.d.55.9	yes	12	4.3	odd	2
756.2.b.d.55.10	yes	12	7.6	odd	2

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.15343 + 0.818285i) q^{2} +(0.660819 + 1.88768i) q^{4} -2.16295i q^{5} +(1.94827 + 1.79004i) q^{7} +(-0.782447 + 2.71805i) q^{8} +O(q^{10})\)	\(q+(1.15343 + 0.818285i) q^{2} +(0.660819 + 1.88768i) q^{4} -2.16295i q^{5} +(1.94827 + 1.79004i) q^{7} +(-0.782447 + 2.71805i) q^{8} +(1.76991 - 2.49482i) q^{10} +0.414503i q^{11} +2.36578i q^{13} +(0.782447 + 3.65893i) q^{14} +(-3.12664 + 2.49482i) q^{16} +0.695686i q^{17} +5.21819 q^{19} +(4.08295 - 1.42932i) q^{20} +(-0.339181 + 0.478101i) q^{22} -0.414503i q^{23} +0.321637 q^{25} +(-1.93588 + 2.72877i) q^{26} +(-2.09155 + 4.86060i) q^{28} +9.73080 q^{29} -2.03509 q^{31} +(-5.64785 + 0.319131i) q^{32} +(-0.569269 + 0.802428i) q^{34} +(3.87176 - 4.21403i) q^{35} -7.43637 q^{37} +(6.01883 + 4.26997i) q^{38} +(5.87901 + 1.69239i) q^{40} -10.5910i q^{41} +8.76500i q^{43} +(-0.782447 + 0.273911i) q^{44} +(0.339181 - 0.478101i) q^{46} -5.11706 q^{47} +(0.591549 + 6.97496i) q^{49} +(0.370987 + 0.263191i) q^{50} +(-4.46582 + 1.56335i) q^{52} +3.12979 q^{53} +0.896550 q^{55} +(-6.38982 + 3.89489i) q^{56} +(11.2238 + 7.96257i) q^{58} -11.2147 q^{59} -3.97063i q^{61} +(-2.34734 - 1.66528i) q^{62} +(-6.77555 - 4.25345i) q^{64} +5.11706 q^{65} +2.36578i q^{67} +(-1.31323 + 0.459722i) q^{68} +(7.91409 - 1.69239i) q^{70} -4.04472i q^{71} -12.3451i q^{73} +(-8.57736 - 6.08507i) q^{74} +(3.44827 + 9.85024i) q^{76} +(-0.741974 + 0.807565i) q^{77} -7.61351i q^{79} +(5.39618 + 6.76277i) q^{80} +(8.66646 - 12.2160i) q^{82} -12.8606 q^{83} +1.50474 q^{85} +(-7.17227 + 10.1098i) q^{86} +(-1.12664 - 0.324326i) q^{88} -14.6931i q^{89} +(-4.23482 + 4.60918i) q^{91} +(0.782447 - 0.273911i) q^{92} +(-5.90219 - 4.18722i) q^{94} -11.2867i q^{95} +3.97063i q^{97} +(-5.02519 + 8.52921i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{4} - 2 q^{7}+O(q^{10}) \) 12 * q + 8 * q^4 - 2 * q^7	\( 12 q + 8 q^{4} - 2 q^{7} - 4 q^{10} - 12 q^{16} + 12 q^{19} - 4 q^{22} + 4 q^{25} - 24 q^{31} - 32 q^{34} + 12 q^{37} + 20 q^{40} + 4 q^{46} - 18 q^{49} - 28 q^{52} - 40 q^{55} + 8 q^{58} + 20 q^{64} + 44 q^{70} + 16 q^{76} + 28 q^{82} - 32 q^{85} + 12 q^{88} - 26 q^{91} + 56 q^{94}+O(q^{100}) \) 12 * q + 8 * q^4 - 2 * q^7 - 4 * q^10 - 12 * q^16 + 12 * q^19 - 4 * q^22 + 4 * q^25 - 24 * q^31 - 32 * q^34 + 12 * q^37 + 20 * q^40 + 4 * q^46 - 18 * q^49 - 28 * q^52 - 40 * q^55 + 8 * q^58 + 20 * q^64 + 44 * q^70 + 16 * q^76 + 28 * q^82 - 32 * q^85 + 12 * q^88 - 26 * q^91 + 56 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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