LMFDB - Embedded newform 756.2.bp.a.193.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(193,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2, 12]))

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

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

chi := DirichletCharacter("756.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bp (of order $9$, degree $6$, 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:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			193.2
Character	$\chi$	$=$	756.193
Dual form			756.2.bp.a.709.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72611 - 0.143355i) q^{3} +(1.14483 - 0.416685i) q^{5} +(-1.12940 + 2.39259i) q^{7} +(2.95890 + 0.494894i) q^{9} +O(q^{10})$	\(q+(-1.72611 - 0.143355i) q^{3} +(1.14483 - 0.416685i) q^{5} +(-1.12940 + 2.39259i) q^{7} +(2.95890 + 0.494894i) q^{9} +(-5.16885 - 1.88131i) q^{11} +(-0.220139 + 0.0801240i) q^{13} +(-2.03584 + 0.555126i) q^{15} +(0.198933 + 0.344562i) q^{17} +(2.35358 - 4.07652i) q^{19} +(2.29245 - 3.96796i) q^{21} +(0.709167 - 4.02188i) q^{23} +(-2.69321 + 2.25987i) q^{25} +(-5.03643 - 1.27841i) q^{27} +(-1.61354 - 0.587281i) q^{29} +(-8.70131 + 3.16702i) q^{31} +(8.65229 + 3.98832i) q^{33} +(-0.296015 + 3.20971i) q^{35} +2.66416 q^{37} +(0.391470 - 0.106745i) q^{39} +(-6.69778 + 2.43779i) q^{41} +(-0.664453 - 3.76830i) q^{43} +(3.59366 - 0.666358i) q^{45} +(-10.1867 - 3.70767i) q^{47} +(-4.44893 - 5.40435i) q^{49} +(-0.293985 - 0.623270i) q^{51} +(3.57130 - 6.18567i) q^{53} -6.70138 q^{55} +(-4.64692 + 6.69911i) q^{57} +(-2.88779 - 2.42315i) q^{59} +(-11.7217 - 4.26634i) q^{61} +(-4.52584 + 6.52049i) q^{63} +(-0.218636 + 0.183457i) q^{65} +(-1.15447 + 6.54730i) q^{67} +(-1.80066 + 6.84054i) q^{69} +(5.75904 - 9.97495i) q^{71} -12.8873 q^{73} +(4.97273 - 3.51469i) q^{75} +(10.3389 - 10.2422i) q^{77} +(2.44702 + 13.8778i) q^{79} +(8.51016 + 2.92868i) q^{81} +(7.01325 + 2.55262i) q^{83} +(0.371319 + 0.311574i) q^{85} +(2.70095 + 1.24502i) q^{87} +(-0.807133 + 1.39800i) q^{89} +(0.0569205 - 0.617193i) q^{91} +(15.4734 - 4.21923i) q^{93} +(0.995830 - 5.64763i) q^{95} +(1.60207 + 9.08578i) q^{97} +(-14.3630 - 8.12462i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9}+O(q^{10}) $ 144 * q - 12 * q^9	$ 144 q - 12 q^{9} - 12 q^{11} - 12 q^{15} - 24 q^{17} - 3 q^{21} + 15 q^{23} + 6 q^{29} + 18 q^{33} + 18 q^{35} + 18 q^{39} - 12 q^{41} + 6 q^{45} + 18 q^{47} + 36 q^{49} + 18 q^{51} + 15 q^{53} + 3 q^{57} + 30 q^{59} + 18 q^{61} + 3 q^{63} + 9 q^{65} + 30 q^{69} - 12 q^{71} - 36 q^{73} + 102 q^{75} + 69 q^{77} + 18 q^{79} + 12 q^{81} - 36 q^{85} + 78 q^{87} - 72 q^{89} - 18 q^{91} - 60 q^{93} + 42 q^{95} - 72 q^{99}+O(q^{100}) $ 144 * q - 12 * q^9 - 12 * q^11 - 12 * q^15 - 24 * q^17 - 3 * q^21 + 15 * q^23 + 6 * q^29 + 18 * q^33 + 18 * q^35 + 18 * q^39 - 12 * q^41 + 6 * q^45 + 18 * q^47 + 36 * q^49 + 18 * q^51 + 15 * q^53 + 3 * q^57 + 30 * q^59 + 18 * q^61 + 3 * q^63 + 9 * q^65 + 30 * q^69 - 12 * q^71 - 36 * q^73 + 102 * q^75 + 69 * q^77 + 18 * q^79 + 12 * q^81 - 36 * q^85 + 78 * q^87 - 72 * q^89 - 18 * q^91 - 60 * q^93 + 42 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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			0
$2$		0			0
$3$	−1.72611	−	0.143355i	−0.996569	−	0.0827663i
$3$	−1.72611	−	0.143355i	−0.996569	−	0.0827663i
$4$		0			0
$5$	1.14483	−	0.416685i	0.511985	−	0.186347i	−0.0730918	−	0.997325i	$-0.523287\pi$
$5$	1.14483	−	0.416685i	0.511985	−	0.186347i	0.585077	+	0.810978i	$0.301064\pi$
$6$		0			0
$7$	−1.12940	+	2.39259i	−0.426872	+	0.904312i
$7$	−1.12940	+	2.39259i	−0.426872	+	0.904312i
$8$		0			0
$9$	2.95890	+	0.494894i	0.986299	+	0.164965i
$10$		0			0
$11$	−5.16885	−	1.88131i	−1.55847	−	0.567235i	−0.588081	−	0.808802i	$-0.700116\pi$
$11$	−5.16885	−	1.88131i	−1.55847	−	0.567235i	−0.970384	+	0.241567i	$0.922339\pi$
$12$		0			0
$13$	−0.220139	+	0.0801240i	−0.0610555	+	0.0222224i	−0.372367	−	0.928085i	$-0.621454\pi$
$13$	−0.220139	+	0.0801240i	−0.0610555	+	0.0222224i	0.311312	+	0.950308i	$0.399232\pi$
$14$		0			0
$15$	−2.03584	+	0.555126i	−0.525652	+	0.143333i
$16$		0			0
$17$	0.198933	+	0.344562i	0.0482483	+	0.0835686i	0.889141	−	0.457633i	$-0.151303\pi$
$17$	0.198933	+	0.344562i	0.0482483	+	0.0835686i	−0.840893	+	0.541202i	$0.817969\pi$
$18$		0			0
$19$	2.35358	−	4.07652i	0.539948	−	0.935217i	−0.458958	−	0.888458i	$-0.651777\pi$
$19$	2.35358	−	4.07652i	0.539948	−	0.935217i	0.998906	−	0.0467594i	$-0.0148894\pi$
$20$		0			0
$21$	2.29245	−	3.96796i	0.500254	−	0.865879i
$22$		0			0
$23$	0.709167	−	4.02188i	0.147871	−	0.838621i	−0.817145	−	0.576432i	$-0.804445\pi$
$23$	0.709167	−	4.02188i	0.147871	−	0.838621i	0.965017	−	0.262189i	$-0.0844443\pi$
$24$		0			0
$25$	−2.69321	+	2.25987i	−0.538641	+	0.451974i
$26$		0			0
$27$	−5.03643	−	1.27841i	−0.969262	−	0.246031i
$28$		0			0
$29$	−1.61354	−	0.587281i	−0.299627	−	0.109055i	0.187832	−	0.982201i	$-0.439854\pi$
$29$	−1.61354	−	0.587281i	−0.299627	−	0.109055i	−0.487459	+	0.873146i	$0.662076\pi$
$30$		0			0
$31$	−8.70131	+	3.16702i	−1.56280	+	0.568813i	−0.971376	−	0.237547i	$-0.923657\pi$
$31$	−8.70131	+	3.16702i	−1.56280	+	0.568813i	−0.591425	+	0.806360i	$0.701434\pi$
$32$		0			0
$33$	8.65229	+	3.98832i	1.50617	+	0.694277i
$34$		0			0
$35$	−0.296015	+	3.20971i	−0.0500357	+	0.542541i
$36$		0			0
$37$	2.66416			0.437986			0.218993	−	0.975726i	$-0.429723\pi$
$37$	2.66416			0.437986			0.218993	+	0.975726i	$0.429723\pi$
$38$		0			0
$39$	0.391470	−	0.106745i	0.0626853	−	0.0170928i
$40$		0			0
$41$	−6.69778	+	2.43779i	−1.04602	+	0.380719i	−0.807158	−	0.590335i	$-0.798996\pi$
$41$	−6.69778	+	2.43779i	−1.04602	+	0.380719i	−0.238859	+	0.971054i	$0.576773\pi$
$42$		0			0
$43$	−0.664453	−	3.76830i	−0.101328	−	0.574660i	−0.992624	−	0.121237i	$-0.961314\pi$
$43$	−0.664453	−	3.76830i	−0.101328	−	0.574660i	0.891295	−	0.453423i	$-0.149797\pi$
$44$		0			0
$45$	3.59366	−	0.666358i	0.535711	−	0.0993349i
$46$		0			0
$47$	−10.1867	−	3.70767i	−1.48589	−	0.540819i	−0.533525	−	0.845784i	$-0.679133\pi$
$47$	−10.1867	−	3.70767i	−1.48589	−	0.540819i	−0.952364	+	0.304965i	$0.901355\pi$
$48$		0			0
$49$	−4.44893	−	5.40435i	−0.635561	−	0.772050i
$50$		0			0
$51$	−0.293985	−	0.623270i	−0.0411661	−	0.0872752i
$52$		0			0
$53$	3.57130	−	6.18567i	0.490556	−	0.849668i	−0.509385	−	0.860539i	$-0.670127\pi$
$53$	3.57130	−	6.18567i	0.490556	−	0.849668i	0.999941	+	0.0108711i	$0.00346044\pi$
$54$		0			0
$55$	−6.70138			−0.903614
$56$		0			0
$57$	−4.64692	+	6.69911i	−0.615500	+	0.887319i
$58$		0			0
$59$	−2.88779	−	2.42315i	−0.375959	−	0.315467i	0.435155	−	0.900356i	$-0.356694\pi$
$59$	−2.88779	−	2.42315i	−0.375959	−	0.315467i	−0.811113	+	0.584889i	$0.801138\pi$
$60$		0			0
$61$	−11.7217	−	4.26634i	−1.50081	−	0.546249i	−0.544538	−	0.838736i	$-0.683295\pi$
$61$	−11.7217	−	4.26634i	−1.50081	−	0.546249i	−0.956270	+	0.292486i	$0.905517\pi$
$62$		0			0
$63$	−4.52584	+	6.52049i	−0.570203	+	0.821504i
$64$		0			0
$65$	−0.218636	+	0.183457i	−0.0271184	+	0.0227551i
$66$		0			0
$67$	−1.15447	+	6.54730i	−0.141040	+	0.799880i	0.829421	+	0.558624i	$0.188670\pi$
$67$	−1.15447	+	6.54730i	−0.141040	+	0.799880i	−0.970462	+	0.241256i	$0.922441\pi$
$68$		0			0
$69$	−1.80066	+	6.84054i	−0.216774	+	0.823505i
$70$		0			0
$71$	5.75904	−	9.97495i	0.683473	−	1.18381i	−0.290442	−	0.956893i	$-0.593802\pi$
$71$	5.75904	−	9.97495i	0.683473	−	1.18381i	0.973914	−	0.226916i	$-0.0728644\pi$
$72$		0			0
$73$	−12.8873			−1.50834			−0.754169	−	0.656680i	$-0.771960\pi$
$73$	−12.8873			−1.50834			−0.754169	+	0.656680i	$0.771960\pi$
$74$		0			0
$75$	4.97273	−	3.51469i	0.574201	−	0.405842i
$76$		0			0
$77$	10.3389	−	10.2422i	1.17822	−	1.16720i
$78$		0			0
$79$	2.44702	+	13.8778i	0.275312	+	1.56137i	0.737970	+	0.674833i	$0.235784\pi$
$79$	2.44702	+	13.8778i	0.275312	+	1.56137i	−0.462659	+	0.886536i	$0.653104\pi$
$80$		0			0
$81$	8.51016	+	2.92868i	0.945573	+	0.325409i
$82$		0			0
$83$	7.01325	+	2.55262i	0.769805	+	0.280186i	0.696915	−	0.717154i	$-0.254556\pi$
$83$	7.01325	+	2.55262i	0.769805	+	0.280186i	0.0728900	+	0.997340i	$0.476778\pi$
$84$		0			0
$85$	0.371319	+	0.311574i	0.0402752	+	0.0337949i
$86$		0			0
$87$	2.70095	+	1.24502i	0.289573	+	0.133480i
$88$		0			0
$89$	−0.807133	+	1.39800i	−0.0855560	+	0.148187i	−0.905628	−	0.424073i	$-0.860600\pi$
$89$	−0.807133	+	1.39800i	−0.0855560	+	0.148187i	0.820072	+	0.572260i	$0.193933\pi$
$90$		0			0
$91$	0.0569205	−	0.617193i	0.00596689	−	0.0646994i
$92$		0			0
$93$	15.4734	−	4.21923i	1.60452	−	0.437514i
$94$		0			0
$95$	0.995830	−	5.64763i	0.102170	−	0.579435i
$96$		0			0
$97$	1.60207	+	9.08578i	0.162665	+	0.922521i	0.951439	+	0.307838i	$0.0996053\pi$
$97$	1.60207	+	9.08578i	0.162665	+	0.922521i	−0.788774	+	0.614684i	$0.789284\pi$
$98$		0			0
$99$	−14.3630	−	8.12462i	−1.44354	−	0.816555i
$100$		0			0
$101$	−1.89861	−	10.7675i	−0.188918	−	1.07141i	−0.920817	−	0.389995i	$-0.872477\pi$
$101$	−1.89861	−	10.7675i	−0.188918	−	1.07141i	0.731898	−	0.681414i	$-0.238635\pi$
$102$		0			0
$103$	5.13168	−	1.86778i	0.505640	−	0.184038i	−0.0765892	−	0.997063i	$-0.524403\pi$
$103$	5.13168	−	1.86778i	0.505640	−	0.184038i	0.582229	+	0.813025i	$0.302181\pi$
$104$		0			0
$105$	0.971084	−	5.49788i	0.0947681	−	0.536538i
$106$		0			0
$107$	8.24375	+	14.2786i	0.796953	+	1.38036i	0.921592	+	0.388161i	$0.126890\pi$
$107$	8.24375	+	14.2786i	0.796953	+	1.38036i	−0.124638	+	0.992202i	$0.539777\pi$
$108$		0			0
$109$	0.315560	−	0.546565i	0.0302251	−	0.0523515i	−0.850517	−	0.525947i	$-0.823711\pi$
$109$	0.315560	−	0.546565i	0.0302251	−	0.0523515i	0.880742	+	0.473596i	$0.157044\pi$
$110$		0			0
$111$	−4.59864	−	0.381922i	−0.436483	−	0.0362505i
$112$		0			0
$113$	3.05004	−	17.2977i	0.286924	−	1.62723i	−0.411407	−	0.911452i	$-0.634962\pi$
$113$	3.05004	−	17.2977i	0.286924	−	1.62723i	0.698331	−	0.715775i	$-0.253926\pi$
$114$		0			0
$115$	−0.863982	−	4.89989i	−0.0805668	−	0.456917i
$116$		0			0
$117$	−0.691021	+	0.128133i	−0.0638849	+	0.0118459i
$118$		0			0
$119$	−1.04907	+	0.0868171i	−0.0961679	+	0.00795851i
$120$		0			0
$121$	14.7512	+	12.3777i	1.34101	+	1.12524i
$122$		0			0
$123$	11.9106	−	3.24773i	1.07394	−	0.292838i
$124$		0			0
$125$	−5.18738	+	8.98481i	−0.463974	+	0.803626i
$126$		0			0
$127$	2.92054	+	5.05852i	0.259156	+	0.448871i	0.966016	−	0.258482i	$-0.0832224\pi$
$127$	2.92054	+	5.05852i	0.259156	+	0.448871i	−0.706860	+	0.707353i	$0.749889\pi$
$128$		0			0
$129$	0.606712	+	6.59974i	0.0534180	+	0.581075i
$130$		0			0
$131$	−1.46750	+	8.32263i	−0.128216	+	0.727151i	0.851129	+	0.524957i	$0.175918\pi$
$131$	−1.46750	+	8.32263i	−0.128216	+	0.727151i	−0.979345	+	0.202195i	$0.935193\pi$
$132$		0			0
$133$	7.09529	+	10.2351i	0.615240	+	0.887499i
$134$		0			0
$135$	−6.29857	+	0.635036i	−0.542095	+	0.0546552i
$136$		0			0
$137$	14.2420	−	11.9504i	1.21677	−	1.02100i	0.217788	−	0.975996i	$-0.430116\pi$
$137$	14.2420	−	11.9504i	1.21677	−	1.02100i	0.998987	−	0.0449992i	$-0.0143285\pi$
$138$		0			0
$139$	3.74199	+	3.13990i	0.317391	+	0.266323i	0.787539	−	0.616265i	$-0.211355\pi$
$139$	3.74199	+	3.13990i	0.317391	+	0.266323i	−0.470148	+	0.882588i	$0.655799\pi$
$140$		0			0
$141$	17.0519	+	7.86016i	1.43603	+	0.661945i
$142$		0			0
$143$	1.28860			0.107758
$144$		0			0
$145$	−2.09195			−0.173727
$146$		0			0
$147$	6.90459	+	9.96628i	0.569481	+	0.822005i
$148$		0			0
$149$	−7.55782	−	6.34177i	−0.619161	−	0.519538i	0.278379	−	0.960471i	$-0.410203\pi$
$149$	−7.55782	−	6.34177i	−0.619161	−	0.519538i	−0.897540	+	0.440934i	$0.854647\pi$
$150$		0			0
$151$	−11.6346	−	4.23466i	−0.946813	−	0.344612i	−0.177960	−	0.984038i	$-0.556950\pi$
$151$	−11.6346	−	4.23466i	−0.946813	−	0.344612i	−0.768853	+	0.639426i	$0.779172\pi$
$152$		0			0
$153$	0.418101	+	1.11797i	0.0338015	+	0.0903829i
$154$		0			0
$155$	−8.64190	+	7.25141i	−0.694134	+	0.582447i
$156$		0			0
$157$	15.9848	+	13.4129i	1.27573	+	1.07046i	0.993818	+	0.111021i	$0.0354121\pi$
$157$	15.9848	+	13.4129i	1.27573	+	1.07046i	0.281909	+	0.959441i	$0.409032\pi$
$158$		0			0
$159$	−7.05120	+	10.1652i	−0.559197	+	0.806151i
$160$		0			0
$161$	8.82177	+	6.23904i	0.695253	+	0.491705i
$162$		0			0
$163$	−0.923839	−	1.60014i	−0.0723606	−	0.125332i	0.827575	−	0.561355i	$-0.189720\pi$
$163$	−0.923839	−	1.60014i	−0.0723606	−	0.125332i	−0.899935	+	0.436023i	$0.856387\pi$
$164$		0			0
$165$	11.5673	+	0.960678i	0.900513	+	0.0747887i
$166$		0			0
$167$	0.0222328	−	0.126089i	0.00172043	−	0.00975704i	−0.983935	−	0.178525i	$-0.942868\pi$
$167$	0.0222328	−	0.126089i	0.00172043	−	0.00975704i	0.985656	+	0.168768i	$0.0539787\pi$
$168$		0			0
$169$	−9.91654	+	8.32096i	−0.762811	+	0.640074i
$170$		0			0
$171$	8.98144	−	10.8972i	0.686828	−	0.833332i
$172$		0			0
$173$	5.90407	−	4.95411i	0.448878	−	0.376654i	−0.390141	−	0.920755i	$-0.627574\pi$
$173$	5.90407	−	4.95411i	0.448878	−	0.376654i	0.839019	+	0.544101i	$0.183129\pi$
$174$		0			0
$175$	−2.36523	−	8.99601i	−0.178795	−	0.680034i
$176$		0			0
$177$	4.63727	+	4.59659i	0.348559	+	0.345501i
$178$		0			0
$179$	−0.558230	−	0.966883i	−0.0417241	−	0.0722683i	0.844409	−	0.535699i	$-0.179952\pi$
$179$	−0.558230	−	0.966883i	−0.0417241	−	0.0722683i	−0.886133	+	0.463430i	$0.846618\pi$
$180$		0			0
$181$	−5.29862	−	9.17747i	−0.393843	−	0.682156i	0.599110	−	0.800667i	$-0.295521\pi$
$181$	−5.29862	−	9.17747i	−0.393843	−	0.682156i	−0.992953	+	0.118511i	$0.962188\pi$
$182$		0			0
$183$	19.6213	+	9.04454i	1.45045	+	0.668592i
$184$		0			0
$185$	3.05002	−	1.11012i	0.224242	−	0.0816175i
$186$		0			0
$187$	−0.380027	−	2.15524i	−0.0277903	−	0.157607i
$188$		0			0
$189$	8.74684	−	10.6063i	0.636239	−	0.771492i
$190$		0			0
$191$	2.53204	+	14.3599i	0.183212	+	1.03905i	0.928231	+	0.372005i	$0.121329\pi$
$191$	2.53204	+	14.3599i	0.183212	+	1.03905i	−0.745019	+	0.667044i	$0.767559\pi$
$192$		0			0
$193$	2.70094	−	0.983060i	0.194418	−	0.0707622i	−0.242976	−	0.970032i	$-0.578124\pi$
$193$	2.70094	−	0.983060i	0.194418	−	0.0707622i	0.437394	+	0.899270i	$0.355902\pi$
$194$		0			0
$195$	0.403689	−	0.285324i	0.0289087	−	0.0204325i
$196$		0			0
$197$	0.627545	+	1.08694i	0.0447107	+	0.0774412i	0.887515	−	0.460779i	$-0.152430\pi$
$197$	0.627545	+	1.08694i	0.0447107	+	0.0774412i	−0.842804	+	0.538221i	$0.819097\pi$
$198$		0			0
$199$	2.55118	+	4.41878i	0.180849	+	0.313239i	0.942170	−	0.335136i	$-0.108782\pi$
$199$	2.55118	+	4.41878i	0.180849	+	0.313239i	−0.761321	+	0.648375i	$0.775449\pi$
$200$		0			0
$201$	2.93132	−	11.1358i	0.206760	−	0.785462i
$202$		0			0
$203$	3.22744	−	3.19726i	0.226522	−	0.224404i
$204$		0			0
$205$	−6.65205	+	5.58173i	−0.464599	+	0.389845i
$206$		0			0
$207$	4.08876	−	11.5494i	0.284188	−	0.802738i
$208$		0			0
$209$	−19.8345	+	16.6431i	−1.37198	+	1.15123i
$210$		0			0
$211$	3.22312	−	18.2792i	0.221889	−	1.25839i	−0.646655	−	0.762783i	$-0.723833\pi$
$211$	3.22312	−	18.2792i	0.221889	−	1.25839i	0.868544	−	0.495612i	$-0.165056\pi$
$212$		0			0
$213$	−11.3707	+	16.3923i	−0.779107	+	1.12318i
$214$		0			0
$215$	−2.33088	−	4.03721i	−0.158965	−	0.275335i
$216$		0			0
$217$	2.24987	−	24.3954i	0.152731	−	1.65607i
$218$		0			0
$219$	22.2448	+	1.84746i	1.50316	+	0.124840i
$220$		0			0
$221$	−0.0714006	−	0.0599122i	−0.00480292	−	0.00403013i
$222$		0			0
$223$	10.1084	−	8.48196i	0.676909	−	0.567994i	−0.238193	−	0.971218i	$-0.576555\pi$
$223$	10.1084	−	8.48196i	0.676909	−	0.567994i	0.915101	+	0.403224i	$0.132111\pi$
$224$		0			0
$225$	−9.08732	+	5.35387i	−0.605821	+	0.356925i
$226$		0			0
$227$	−10.0690	−	3.66483i	−0.668305	−	0.243243i	−0.0144871	−	0.999895i	$-0.504612\pi$
$227$	−10.0690	−	3.66483i	−0.668305	−	0.243243i	−0.653818	+	0.756652i	$0.726834\pi$
$228$		0			0
$229$	10.7345	+	9.00735i	0.709359	+	0.595222i	0.924419	−	0.381378i	$-0.124550\pi$
$229$	10.7345	+	9.00735i	0.709359	+	0.595222i	−0.215061	+	0.976601i	$0.568995\pi$
$230$		0			0
$231$	−19.3143	+	16.1970i	−1.27078	+	1.06568i
$232$		0			0
$233$	−11.9704			−0.784204			−0.392102	−	0.919922i	$-0.628252\pi$
$233$	−11.9704			−0.784204			−0.392102	+	0.919922i	$0.628252\pi$
$234$		0			0
$235$	−13.2070			−0.861533
$236$		0			0
$237$	−2.23438	−	24.3053i	−0.145138	−	1.57880i
$238$		0			0
$239$	4.66508	+	3.91447i	0.301759	+	0.253206i	0.781076	−	0.624436i	$-0.214671\pi$
$239$	4.66508	+	3.91447i	0.301759	+	0.253206i	−0.479317	+	0.877642i	$0.659116\pi$
$240$		0			0
$241$	−1.71744	+	1.44110i	−0.110630	+	0.0928296i	−0.696425	−	0.717630i	$-0.745227\pi$
$241$	−1.71744	+	1.44110i	−0.110630	+	0.0928296i	0.585795	+	0.810460i	$0.300783\pi$
$242$		0			0
$243$	−14.2696	−	6.27520i	−0.915396	−	0.402554i
$244$		0			0
$245$	−7.34519	−	4.33328i	−0.469267	−	0.276843i
$246$		0			0
$247$	−0.191487	+	1.08598i	−0.0121840	+	0.0690991i
$248$		0			0
$249$	−11.7397	−	5.41148i	−0.743974	−	0.342939i
$250$		0			0
$251$	3.09507	+	5.36082i	0.195359	+	0.338372i	0.947018	−	0.321180i	$-0.104079\pi$
$251$	3.09507	+	5.36082i	0.195359	+	0.338372i	−0.751659	+	0.659552i	$0.770746\pi$
$252$		0			0
$253$	−11.2320	+	19.4543i	−0.706148	+	1.22308i
$254$		0			0
$255$	−0.596271	−	0.591040i	−0.0373399	−	0.0370124i
$256$		0			0
$257$	−4.82947	−	4.05241i	−0.301254	−	0.252782i	0.479612	−	0.877481i	$-0.340777\pi$
$257$	−4.82947	−	4.05241i	−0.301254	−	0.252782i	−0.780866	+	0.624698i	$0.785222\pi$
$258$		0			0
$259$	−3.00890	+	6.37424i	−0.186964	+	0.396076i
$260$		0			0
$261$	−4.48366	−	2.53623i	−0.277532	−	0.156989i
$262$		0			0
$263$	−3.53124	−	20.0267i	−0.217746	−	1.23490i	−0.876078	−	0.482170i	$-0.839849\pi$
$263$	−3.53124	−	20.0267i	−0.217746	−	1.23490i	0.658332	−	0.752728i	$-0.271262\pi$
$264$		0			0
$265$	1.51106	−	8.56967i	0.0928239	−	0.526431i
$266$		0			0
$267$	1.59361	−	2.29739i	0.0975273	−	0.140598i
$268$		0			0
$269$	1.65112	−	2.85982i	0.100670	−	0.174366i	−0.811291	−	0.584643i	$-0.801235\pi$
$269$	1.65112	−	2.85982i	0.100670	−	0.174366i	0.911961	+	0.410277i	$0.134568\pi$
$270$		0			0
$271$	−12.0851	−	20.9320i	−0.734116	−	1.27153i	−0.955110	−	0.296251i	$-0.904264\pi$
$271$	−12.0851	−	20.9320i	−0.734116	−	1.27153i	0.220994	−	0.975275i	$-0.429070\pi$
$272$		0			0
$273$	−0.186729	+	1.05718i	−0.0113013	+	0.0639835i
$274$		0			0
$275$	18.1723	−	6.61416i	1.09583	−	0.398849i
$276$		0			0
$277$	2.85278	+	16.1789i	0.171407	+	0.972096i	0.942210	+	0.335023i	$0.108744\pi$
$277$	2.85278	+	16.1789i	0.171407	+	0.972096i	−0.770803	+	0.637073i	$0.780145\pi$
$278$		0			0
$279$	−27.3136	+	5.06466i	−1.63522	+	0.303213i
$280$		0			0
$281$	4.39308	+	24.9144i	0.262069	+	1.48627i	0.777253	+	0.629188i	$0.216612\pi$
$281$	4.39308	+	24.9144i	0.262069	+	1.48627i	−0.515184	+	0.857080i	$0.672276\pi$
$282$		0			0
$283$	0.662491	−	3.75717i	0.0393810	−	0.223341i	−0.958765	−	0.284199i	$-0.908272\pi$
$283$	0.662491	−	3.75717i	0.0393810	−	0.223341i	0.998146	+	0.0608578i	$0.0193836\pi$
$284$		0			0
$285$	−2.52853	+	9.60567i	−0.149777	+	0.568991i
$286$		0			0
$287$	1.73182	−	18.7782i	0.102226	−	1.10844i
$288$		0			0
$289$	8.42085	−	14.5853i	0.495344	−	0.857961i
$290$		0			0
$291$	−1.46285	−	15.9127i	−0.0857537	−	0.932820i
$292$		0			0
$293$	−6.55236	−	5.49808i	−0.382793	−	0.321201i	0.431005	−	0.902350i	$-0.358159\pi$
$293$	−6.55236	−	5.49808i	−0.382793	−	0.321201i	−0.813798	+	0.581148i	$0.802604\pi$
$294$		0			0
$295$	−4.31573	−	1.57080i	−0.251272	−	0.0914554i
$296$		0			0
$297$	23.6275	+	16.0830i	1.37100	+	0.933230i
$298$		0			0
$299$	0.166134	+	0.942194i	0.00960779	+	0.0544885i
$300$		0			0
$301$	9.76641	+	2.66614i	0.562926	+	0.153674i
$302$		0			0
$303$	1.73362	+	18.8581i	0.0995936	+	1.08337i
$304$		0			0
$305$	−15.1971			−0.870183
$306$		0			0
$307$	2.15691	−	3.73588i	0.123101	−	0.213218i	−0.797888	−	0.602806i	$-0.794049\pi$
$307$	2.15691	−	3.73588i	0.123101	−	0.213218i	0.920989	+	0.389588i	$0.127383\pi$
$308$		0			0
$309$	−9.12560	+	2.48834i	−0.519137	+	0.141556i
$310$		0			0
$311$	−4.74727	+	26.9231i	−0.269193	+	1.52667i	0.487631	+	0.873050i	$0.337861\pi$
$311$	−4.74727	+	26.9231i	−0.269193	+	1.52667i	−0.756824	+	0.653619i	$0.773250\pi$
$312$		0			0
$313$	−24.3027	+	20.3924i	−1.37367	+	1.15265i	−0.402183	+	0.915560i	$0.631748\pi$
$313$	−24.3027	+	20.3924i	−1.37367	+	1.15265i	−0.971488	+	0.237087i	$0.923807\pi$
$314$		0			0
$315$	−2.46435	+	9.35072i	−0.138850	+	0.526853i
$316$		0			0
$317$	−9.40882	−	3.42453i	−0.528452	−	0.192341i	0.0639950	−	0.997950i	$-0.479616\pi$
$317$	−9.40882	−	3.42453i	−0.528452	−	0.192341i	−0.592447	+	0.805609i	$0.701838\pi$
$318$		0			0
$319$	7.23528	+	6.07112i	0.405098	+	0.339918i
$320$		0			0
$321$	−12.1827	−	25.8282i	−0.679971	−	1.44159i
$322$		0			0
$323$	1.87282			0.104206
$324$		0			0
$325$	0.411810	−	0.713275i	0.0228431	−	0.0395654i
$326$		0			0
$327$	−0.623043	+	0.898194i	−0.0344544	+	0.0496702i
$328$		0			0
$329$	20.3758	−	20.1852i	1.12335	−	1.11285i
$330$		0			0
$331$	19.1189	+	6.95870i	1.05087	+	0.382485i	0.808990	−	0.587822i	$-0.200014\pi$
$331$	19.1189	+	6.95870i	1.05087	+	0.382485i	0.241878	+	0.970307i	$0.422237\pi$
$332$		0			0
$333$	7.88299	+	1.31848i	0.431985	+	0.0722522i
$334$		0			0
$335$	1.40649	+	7.97661i	0.0768449	+	0.435809i
$336$		0			0
$337$	17.2276	−	6.27032i	0.938444	−	0.341566i	0.172893	−	0.984941i	$-0.444688\pi$
$337$	17.2276	−	6.27032i	0.938444	−	0.341566i	0.765551	+	0.643375i	$0.222466\pi$
$338$		0			0
$339$	−7.74442	+	29.4204i	−0.420619	+	1.59790i
$340$		0			0
$341$	50.9338			2.75822
$342$		0			0
$343$	17.9550	−	4.54079i	0.969478	−	0.245179i
$344$		0			0
$345$	0.788902	+	8.58159i	0.0424730	+	0.462017i
$346$		0			0
$347$	25.5636	−	9.30439i	1.37233	−	0.499486i	0.452483	−	0.891773i	$-0.350538\pi$
$347$	25.5636	−	9.30439i	1.37233	−	0.499486i	0.919843	+	0.392287i	$0.128316\pi$
$348$		0			0
$349$	−10.2176	−	3.71889i	−0.546934	−	0.199068i	0.0537500	−	0.998554i	$-0.482883\pi$
$349$	−10.2176	−	3.71889i	−0.546934	−	0.199068i	−0.600684	+	0.799487i	$0.705105\pi$
$350$		0			0
$351$	1.21115	−	0.122111i	0.0646462	−	0.00651778i
$352$		0			0
$353$	−9.41217	+	7.89775i	−0.500959	+	0.420355i	−0.857934	−	0.513759i	$-0.828252\pi$
$353$	−9.41217	+	7.89775i	−0.500959	+	0.420355i	0.356975	+	0.934114i	$0.383808\pi$
$354$		0			0
$355$	2.43673	−	13.8194i	0.129328	−	0.733456i
$356$		0			0
$357$	1.82325		0.000533867i	0.0964967		2.82553e-5i
$358$		0			0
$359$	−9.63957	+	16.6962i	−0.508757	+	0.881193i	0.491191	+	0.871052i	$0.336562\pi$
$359$	−9.63957	+	16.6962i	−0.508757	+	0.881193i	−0.999949	+	0.0101418i	$0.996772\pi$
$360$		0			0
$361$	−1.57866	−	2.73432i	−0.0830875	−	0.143912i
$362$		0			0
$363$	−23.6877	−	23.4799i	−1.24328	−	1.23237i
$364$		0			0
$365$	−14.7538	+	5.36993i	−0.772247	+	0.281075i
$366$		0			0
$367$	9.84368	+	3.58281i	0.513836	+	0.187021i	0.585907	−	0.810379i	$-0.300739\pi$
$367$	9.84368	+	3.58281i	0.513836	+	0.187021i	−0.0720707	+	0.997400i	$0.522961\pi$
$368$		0			0
$369$	−21.0245	+	3.89849i	−1.09449	+	0.202947i
$370$		0			0
$371$	10.7663	+	15.5307i	0.558960	+	0.806315i
$372$		0			0
$373$	−19.4632	+	7.08403i	−1.00777	+	0.366797i	−0.792575	−	0.609775i	$-0.791260\pi$
$373$	−19.4632	+	7.08403i	−1.00777	+	0.366797i	−0.215192	+	0.976572i	$0.569038\pi$
$374$		0			0
$375$	10.2420	−	14.7651i	0.528895	−	0.762467i
$376$		0			0
$377$	0.402258			0.0207173
$378$		0			0
$379$	−30.0462			−1.54337			−0.771684	−	0.636007i	$-0.780585\pi$
$379$	−30.0462			−1.54337			−0.771684	+	0.636007i	$0.780585\pi$
$380$		0			0
$381$	−4.31600	−	9.15022i	−0.221115	−	0.468780i
$382$		0			0
$383$	18.5367	−	6.74681i	0.947181	−	0.344746i	0.178184	−	0.983997i	$-0.442978\pi$
$383$	18.5367	−	6.74681i	0.947181	−	0.344746i	0.768998	+	0.639251i	$0.220756\pi$
$384$		0			0
$385$	7.56851	−	16.0336i	0.385727	−	0.817149i
$386$		0			0
$387$	−0.101141	−	11.4788i	−0.00514128	−	0.583503i
$388$		0			0
$389$	−29.0212	−	10.5629i	−1.47143	−	0.535558i	−0.522944	−	0.852367i	$-0.675167\pi$
$389$	−29.0212	−	10.5629i	−1.47143	−	0.535558i	−0.948490	+	0.316809i	$0.897389\pi$
$390$		0			0
$391$	1.52687	−	0.555734i	0.0772169	−	0.0281047i
$392$		0			0
$393$	3.72616	−	14.1554i	0.187960	−	0.714044i
$394$		0			0
$395$	8.58409	+	14.8681i	0.431912	+	0.748094i
$396$		0			0
$397$	4.36043	−	7.55248i	0.218844	−	0.379048i	−0.735611	−	0.677404i	$-0.763105\pi$
$397$	4.36043	−	7.55248i	0.218844	−	0.379048i	0.954455	+	0.298356i	$0.0964382\pi$
$398$		0			0
$399$	−10.7800	−	18.6841i	−0.539674	−	0.935375i
$400$		0			0
$401$	−0.636927	+	3.61219i	−0.0318066	+	0.180384i	−0.996572	−	0.0827263i	$-0.973637\pi$
$401$	−0.636927	+	3.61219i	−0.0318066	+	0.180384i	0.964766	+	0.263110i	$0.0847484\pi$
$402$		0			0
$403$	1.66174	−	1.39437i	0.0827773	−	0.0694584i
$404$		0			0
$405$	10.9631	−	0.193207i	0.544758	−	0.00960055i
$406$		0			0
$407$	−13.7707	−	5.01211i	−0.682586	−	0.248441i
$408$		0			0
$409$	−25.4509	+	9.26338i	−1.25847	+	0.458045i	−0.883255	−	0.468894i	$-0.844653\pi$
$409$	−25.4509	+	9.26338i	−1.25847	+	0.458045i	−0.375213	+	0.926939i	$0.622430\pi$
$410$		0			0
$411$	−26.2964	+	18.5861i	−1.29710	+	0.916784i
$412$		0			0
$413$	9.05905	−	4.17260i	0.445767	−	0.205320i
$414$		0			0
$415$	9.09264			0.446340
$416$		0			0
$417$	−6.00896	−	5.95624i	−0.294260	−	0.291679i
$418$		0			0
$419$	−29.7295	+	10.8206i	−1.45238	+	0.528623i	−0.943255	−	0.332070i	$-0.892253\pi$
$419$	−29.7295	+	10.8206i	−1.45238	+	0.528623i	−0.509125	+	0.860693i	$0.670031\pi$
$420$		0			0
$421$	0.0273837	+	0.155301i	0.00133460	+	0.00756890i	0.985468	−	0.169862i	$-0.0543323\pi$
$421$	0.0273837	+	0.155301i	0.00133460	+	0.00756890i	−0.984133	+	0.177431i	$0.943221\pi$
$422$		0			0
$423$	−28.3066	−	16.0120i	−1.37632	−	0.778529i
$424$		0			0
$425$	−1.31443	−	0.478414i	−0.0637593	−	0.0232065i
$426$		0			0
$427$	23.4460	−	23.2267i	1.13463	−	1.12402i
$428$		0			0
$429$	−2.22427	−	0.184728i	−0.107389	−	0.00891875i
$430$		0			0
$431$	−20.0014	+	34.6435i	−0.963434	+	1.66872i	−0.249669	+	0.968331i	$0.580322\pi$
$431$	−20.0014	+	34.6435i	−0.963434	+	1.66872i	−0.713765	+	0.700385i	$0.753012\pi$
$432$		0			0
$433$	20.3234			0.976681			0.488340	−	0.872653i	$-0.337603\pi$
$433$	20.3234			0.976681			0.488340	+	0.872653i	$0.337603\pi$
$434$		0			0
$435$	3.61092	+	0.299892i	0.173131	+	0.0143787i
$436$		0			0
$437$	−14.7262	−	12.3568i	−0.704450	−	0.591104i
$438$		0			0
$439$	−34.8805	−	12.6955i	−1.66475	−	0.605921i	−0.673655	−	0.739046i	$-0.735277\pi$
$439$	−34.8805	−	12.6955i	−1.66475	−	0.605921i	−0.991099	+	0.133124i	$0.957499\pi$
$440$		0			0
$441$	−10.4893	−	18.1927i	−0.499493	−	0.866318i
$442$		0			0
$443$	−15.9101	+	13.3502i	−0.755911	+	0.634285i	−0.937059	−	0.349171i	$-0.886463\pi$
$443$	−15.9101	+	13.3502i	−0.755911	+	0.634285i	0.181148	+	0.983456i	$0.442019\pi$
$444$		0			0
$445$	−0.341509	+	1.93679i	−0.0161891	+	0.0918128i
$446$		0			0
$447$	12.1365	+	12.0300i	0.574036	+	0.569001i
$448$		0			0
$449$	0.851865	−	1.47547i	0.0402020	−	0.0696319i	−0.845224	−	0.534412i	$-0.820533\pi$
$449$	0.851865	−	1.47547i	0.0402020	−	0.0696319i	0.885426	+	0.464780i	$0.153867\pi$
$450$		0			0
$451$	39.2060			1.84614
$452$		0			0
$453$	19.4756	+	8.97737i	0.915043	+	0.421794i
$454$		0			0
$455$	−0.192011	−	0.730301i	−0.00900159	−	0.0342370i
$456$		0			0
$457$	−2.48955	−	14.1189i	−0.116456	−	0.660455i	−0.986019	−	0.166633i	$-0.946711\pi$
$457$	−2.48955	−	14.1189i	−0.116456	−	0.660455i	0.869563	−	0.493822i	$-0.164401\pi$
$458$		0			0
$459$	−0.561420	−	1.98968i	−0.0262048	−	0.0928704i
$460$		0			0
$461$	−23.0106	−	8.37518i	−1.07171	−	0.390071i	−0.254895	−	0.966969i	$-0.582041\pi$
$461$	−23.0106	−	8.37518i	−1.07171	−	0.390071i	−0.816816	+	0.576898i	$0.804263\pi$
$462$		0			0
$463$	−19.3702	−	16.2535i	−0.900208	−	0.755364i	0.0700233	−	0.997545i	$-0.477693\pi$
$463$	−19.3702	−	16.2535i	−0.900208	−	0.755364i	−0.970231	+	0.242181i	$0.922137\pi$
$464$		0			0
$465$	15.9564	−	11.2779i	0.739959	−	0.522998i
$466$		0			0
$467$	5.31043	−	9.19794i	0.245738	−	0.425630i	−0.716601	−	0.697483i	$-0.754303\pi$
$467$	5.31043	−	9.19794i	0.245738	−	0.425630i	0.962339	+	0.271853i	$0.0876365\pi$
$468$		0			0
$469$	−14.3611	−	10.1567i	−0.663135	−	0.468991i
$470$		0			0
$471$	−25.6687	−	25.4435i	−1.18275	−	1.17238i
$472$		0			0
$473$	−3.65487	+	20.7278i	−0.168051	+	0.953065i
$474$		0			0
$475$	2.87372	+	16.2977i	0.131855	+	0.747789i
$476$		0			0
$477$	13.6284	−	16.5354i	0.624000	−	0.757102i
$478$		0			0
$479$	4.08501	+	23.1672i	0.186649	+	1.05854i	0.923819	+	0.382830i	$0.125051\pi$
$479$	4.08501	+	23.1672i	0.186649	+	1.05854i	−0.737170	+	0.675707i	$0.763838\pi$
$480$		0			0
$481$	−0.586486	+	0.213463i	−0.0267415	+	0.00973310i
$482$		0			0
$483$	−14.3329	−	12.0339i	−0.652171	−	0.547562i
$484$		0			0
$485$	5.62001	+	9.73415i	0.255192	+	0.442005i
$486$		0			0
$487$	−3.87498	+	6.71167i	−0.175592	+	0.304135i	−0.940366	−	0.340164i	$-0.889517\pi$
$487$	−3.87498	+	6.71167i	−0.175592	+	0.304135i	0.764774	+	0.644299i	$0.222851\pi$
$488$		0			0
$489$	1.36526	+	2.89444i	0.0617391	+	0.130891i
$490$		0			0
$491$	4.38428	−	24.8645i	0.197860	−	1.12212i	−0.710427	−	0.703771i	$-0.751498\pi$
$491$	4.38428	−	24.8645i	0.197860	−	1.12212i	0.908287	−	0.418348i	$-0.137391\pi$
$492$		0			0
$493$	−0.118632	−	0.672794i	−0.00534291	−	0.0303011i
$494$		0			0
$495$	−19.8287	−	3.31647i	−0.891234	−	0.149064i
$496$		0			0
$497$	17.3617	+	25.0447i	0.778778	+	1.12341i
$498$		0			0
$499$	29.9987	+	25.1719i	1.34293	+	1.12685i	0.980864	+	0.194694i	$0.0623713\pi$
$499$	29.9987	+	25.1719i	1.34293	+	1.12685i	0.362061	+	0.932154i	$0.382073\pi$
$500$		0			0
$501$	−0.0564518	+	0.214456i	−0.00252208	+	0.00958117i
$502$		0			0
$503$	−15.1046	+	26.1619i	−0.673479	+	1.16650i	0.303432	+	0.952853i	$0.401867\pi$
$503$	−15.1046	+	26.1619i	−0.673479	+	1.16650i	−0.976911	+	0.213647i	$0.931466\pi$
$504$		0			0
$505$	−6.66026	−	11.5359i	−0.296378	−	0.513341i
$506$		0			0
$507$	18.3099	−	12.9413i	0.813170	−	0.574743i
$508$		0			0
$509$	1.87184	−	10.6157i	0.0829679	−	0.470534i	−0.914809	−	0.403887i	$-0.867659\pi$
$509$	1.87184	−	10.6157i	0.0829679	−	0.470534i	0.997777	−	0.0666469i	$-0.0212301\pi$
$510$		0			0
$511$	14.5548	−	30.8339i	0.643867	−	1.36401i
$512$		0			0
$513$	−17.0651	+	17.5223i	−0.753443	+	0.773627i
$514$		0			0
$515$	5.09664	−	4.27659i	0.224585	−	0.188449i
$516$		0			0
$517$	45.6784	+	38.3287i	2.00893	+	1.68570i
$518$		0			0
$519$	−10.9013	+	7.70494i	−0.478513	+	0.338209i
$520$		0			0
$521$	−12.6585			−0.554577			−0.277288	−	0.960787i	$-0.589436\pi$
$521$	−12.6585			−0.554577			−0.277288	+	0.960787i	$0.589436\pi$
$522$		0			0
$523$	18.7583			0.820243			0.410122	−	0.912031i	$-0.365486\pi$
$523$	18.7583			0.820243			0.410122	+	0.912031i	$0.365486\pi$
$524$		0			0
$525$	2.79302	+	15.8672i	0.121897	+	0.692499i
$526$		0			0
$527$	−2.82221	−	2.36812i	−0.122937	−	0.103157i
$528$		0			0
$529$	5.94029	+	2.16209i	0.258274	+	0.0940039i
$530$		0			0
$531$	−7.34549	−	8.59900i	−0.318767	−	0.373165i
$532$		0			0
$533$	1.27912	−	1.07331i	0.0554047	−	0.0464900i
$534$		0			0
$535$	15.3874	+	12.9116i	0.665255	+	0.558215i
$536$		0			0
$537$	0.824958	+	1.74897i	0.0355996	+	0.0754736i
$538$		0			0
$539$	12.8286	+	36.3041i	0.552566	+	1.56373i
$540$		0			0
$541$	−6.39915	−	11.0837i	−0.275121	−	0.476524i	0.695045	−	0.718967i	$-0.255385\pi$
$541$	−6.39915	−	11.0837i	−0.275121	−	0.476524i	−0.970166	+	0.242443i	$0.922051\pi$
$542$		0			0
$543$	7.83035	+	16.6009i	0.336032	+	0.712413i
$544$		0			0
$545$	0.133517	−	0.757215i	0.00571926	−	0.0324355i
$546$		0			0
$547$	10.1636	−	8.52828i	0.434564	−	0.364643i	−0.399106	−	0.916905i	$-0.630680\pi$
$547$	10.1636	−	8.52828i	0.434564	−	0.364643i	0.833671	+	0.552262i	$0.186235\pi$
$548$		0			0
$549$	−32.5719	−	18.4247i	−1.39013	−	0.786346i
$550$		0			0
$551$	−6.19165	+	5.19541i	−0.263773	+	0.221332i
$552$		0			0
$553$	−35.9674	−	9.81877i	−1.52949	−	0.417537i
$554$		0			0
$555$	−5.42381	+	1.47895i	−0.230228	+	0.0627778i
$556$		0			0
$557$	1.06890	+	1.85139i	0.0452907	+	0.0784458i	0.887782	−	0.460264i	$-0.152245\pi$
$557$	1.06890	+	1.85139i	0.0452907	+	0.0784458i	−0.842491	+	0.538710i	$0.818912\pi$
$558$		0			0
$559$	0.448203	+	0.776310i	0.0189570	+	0.0328344i
$560$		0			0
$561$	0.347003	+	3.77466i	0.0146505	+	0.159366i
$562$		0			0
$563$	33.9643	−	12.3620i	1.43143	−	0.520997i	0.494086	−	0.869413i	$-0.335503\pi$
$563$	33.9643	−	12.3620i	1.43143	−	0.520997i	0.937340	+	0.348416i	$0.113280\pi$
$564$		0			0
$565$	−3.71589	−	21.0738i	−0.156329	−	0.886583i
$566$		0			0
$567$	−16.6185	+	17.0536i	−0.697910	+	0.716186i
$568$		0			0
$569$	−0.899669	−	5.10228i	−0.0377161	−	0.213899i	0.960125	−	0.279570i	$-0.0901920\pi$
$569$	−0.899669	−	5.10228i	−0.0377161	−	0.213899i	−0.997841	+	0.0656719i	$0.979081\pi$
$570$		0			0
$571$	42.6156	−	15.5108i	1.78341	−	0.649108i	0.783803	−	0.621009i	$-0.213277\pi$
$571$	42.6156	−	15.5108i	1.78341	−	0.649108i	0.999605	−	0.0280986i	$-0.00894523\pi$
$572$		0			0
$573$	−2.31201	−	25.1498i	−0.0965855	−	1.05065i
$574$		0			0
$575$	7.17900	+	12.4344i	0.299385	+	0.518550i
$576$		0			0
$577$	−5.98132	−	10.3600i	−0.249006	−	0.431291i	0.714244	−	0.699896i	$-0.246770\pi$
$577$	−5.98132	−	10.3600i	−0.249006	−	0.431291i	−0.963250	+	0.268606i	$0.913437\pi$
$578$		0			0
$579$	−4.80303	+	1.30967i	−0.199607	+	0.0544282i
$580$		0			0
$581$	−14.0281	+	13.8969i	−0.581983	+	0.576540i
$582$		0			0
$583$	−30.0966	+	25.2541i	−1.24648	+	1.04592i
$584$		0			0
$585$	−0.737713	+	0.434630i	−0.0305007	+	0.0179697i
$586$		0			0
$587$	18.5088	−	15.5307i	0.763940	−	0.641022i	−0.175209	−	0.984531i	$-0.556060\pi$
$587$	18.5088	−	15.5307i	0.763940	−	0.641022i	0.939149	+	0.343509i	$0.111616\pi$
$588$		0			0
$589$	−7.56881	+	42.9249i	−0.311867	+	1.76869i
$590$		0			0
$591$	−0.927391	−	1.96614i	−0.0381478	−	0.0808761i
$592$		0			0
$593$	4.25743	+	7.37408i	0.174832	+	0.302817i	0.940103	−	0.340891i	$-0.110729\pi$
$593$	4.25743	+	7.37408i	0.174832	+	0.302817i	−0.765271	+	0.643708i	$0.777395\pi$
$594$		0			0
$595$	−1.16483	+	0.536522i	−0.0477535	+	0.0219953i
$596$		0			0
$597$	−3.77016	−	7.99301i	−0.154302	−	0.327132i
$598$		0			0
$599$	−31.1483	−	26.1365i	−1.27268	−	1.06791i	−0.994209	−	0.107464i	$-0.965727\pi$
$599$	−31.1483	−	26.1365i	−1.27268	−	1.06791i	−0.278474	−	0.960444i	$-0.589829\pi$
$600$		0			0
$601$	−4.99033	+	4.18739i	−0.203560	+	0.170807i	−0.738869	−	0.673849i	$-0.764640\pi$
$601$	−4.99033	+	4.18739i	−0.203560	+	0.170807i	0.535309	+	0.844656i	$0.320195\pi$
$602$		0			0
$603$	−6.65616	+	18.8015i	−0.271060	+	0.765654i
$604$		0			0
$605$	22.0452	+	8.02380i	0.896266	+	0.326214i
$606$		0			0
$607$	−13.2123	−	11.0864i	−0.536269	−	0.449983i	0.333991	−	0.942576i	$-0.391605\pi$
$607$	−13.2123	−	11.0864i	−0.536269	−	0.449983i	−0.870260	+	0.492593i	$0.836049\pi$
$608$		0			0
$609$	−6.02926	+	5.05614i	−0.244318	+	0.204885i
$610$		0			0
$611$	2.53957			0.102740
$612$		0			0
$613$	−9.64274			−0.389467			−0.194733	−	0.980856i	$-0.562384\pi$
$613$	−9.64274			−0.389467			−0.194733	+	0.980856i	$0.562384\pi$
$614$		0			0
$615$	12.2823	−	8.68107i	0.495271	−	0.350054i
$616$		0			0
$617$	−7.73499	−	6.49043i	−0.311399	−	0.261295i	0.473671	−	0.880702i	$-0.342929\pi$
$617$	−7.73499	−	6.49043i	−0.311399	−	0.261295i	−0.785070	+	0.619407i	$0.787373\pi$
$618$		0			0
$619$	5.16741	−	4.33597i	0.207696	−	0.174278i	−0.533006	−	0.846112i	$-0.678938\pi$
$619$	5.16741	−	4.33597i	0.207696	−	0.174278i	0.740702	+	0.671834i	$0.234493\pi$
$620$		0			0
$621$	−8.71330	+	19.3493i	−0.349653	+	0.776462i
$622$		0			0
$623$	−2.43325	−	3.51003i	−0.0974862	−	0.140626i
$624$		0			0
$625$	0.857651	−	4.86398i	0.0343060	−	0.194559i
$626$		0			0
$627$	36.6223	−	25.8844i	1.46255	−	1.03372i
$628$		0			0
$629$	0.529990	+	0.917970i	0.0211321	+	0.0366019i
$630$		0			0
$631$	−5.46454	+	9.46486i	−0.217540	+	0.376790i	−0.954055	−	0.299631i	$-0.903137\pi$
$631$	−5.46454	+	9.46486i	−0.217540	+	0.376790i	0.736515	+	0.676421i	$0.236470\pi$
$632$		0			0
$633$	−8.18389	+	31.0899i	−0.325280	+	1.23571i
$634$		0			0
$635$	5.45134	+	4.57421i	0.216330	+	0.181522i
$636$		0			0
$637$	1.41240	+	0.833242i	0.0559613	+	0.0330143i
$638$		0			0
$639$	21.9770	−	26.6648i	0.869395	−	1.05484i
$640$		0			0
$641$	−5.85961	−	33.2315i	−0.231441	−	1.31257i	−0.849981	−	0.526813i	$-0.823387\pi$
$641$	−5.85961	−	33.2315i	−0.231441	−	1.31257i	0.618540	−	0.785753i	$-0.287724\pi$
$642$		0			0
$643$	7.17274	−	40.6786i	0.282865	−	1.60421i	−0.429948	−	0.902854i	$-0.641468\pi$
$643$	7.17274	−	40.6786i	0.282865	−	1.60421i	0.712813	−	0.701354i	$-0.247421\pi$
$644$		0			0
$645$	3.44460	+	7.30280i	0.135631	+	0.287547i
$646$		0			0
$647$	0.154596	−	0.267767i	0.00607778	−	0.0105270i	−0.862971	−	0.505254i	$-0.831399\pi$
$647$	0.154596	−	0.267767i	0.00607778	−	0.0105270i	0.869048	+	0.494727i	$0.164732\pi$
$648$		0			0
$649$	10.3679	+	17.9577i	0.406975	+	0.704901i
$650$		0			0
$651$	−7.38073	+	41.7866i	−0.289274	+	1.63775i
$652$		0			0
$653$	3.89986	−	1.41943i	0.152613	−	0.0555467i	−0.264584	−	0.964363i	$-0.585235\pi$
$653$	3.89986	−	1.41943i	0.152613	−	0.0555467i	0.417197	+	0.908816i	$0.363012\pi$
$654$		0			0
$655$	1.78787	+	10.1395i	0.0698578	+	0.396183i
$656$		0			0
$657$	−38.1321	−	6.37782i	−1.48767	−	0.248822i
$658$		0			0
$659$	−5.19621	−	29.4692i	−0.202416	−	1.14796i	−0.901455	−	0.432873i	$-0.857500\pi$
$659$	−5.19621	−	29.4692i	−0.202416	−	1.14796i	0.699039	−	0.715083i	$-0.253611\pi$
$660$		0			0
$661$	−0.513213	+	2.91058i	−0.0199617	+	0.113208i	−0.993161	−	0.116757i	$-0.962750\pi$
$661$	−0.513213	+	2.91058i	−0.0199617	+	0.113208i	0.973199	+	0.229965i	$0.0738613\pi$
$662$		0			0
$663$	0.114656	+	0.113651i	0.00445288	+	0.00441382i
$664$		0			0
$665$	12.3878	+	8.76102i	0.480377	+	0.339738i
$666$		0			0
$667$	−3.50624	+	6.07299i	−0.135762	+	0.235147i
$668$		0			0
$669$	−18.6641	+	13.1917i	−0.721597	+	0.510020i
$670$		0			0
$671$	52.5613	+	44.1041i	2.02911	+	1.70262i
$672$		0			0
$673$	44.2385	+	16.1015i	1.70527	+	0.620667i	0.996408	−	0.0846816i	$-0.0269873\pi$
$673$	44.2385	+	16.1015i	1.70527	+	0.620667i	0.708861	+	0.705349i	$0.249210\pi$
$674$		0			0
$675$	16.4532	−	7.93864i	0.633284	−	0.305558i
$676$		0			0
$677$	0.297263	+	1.68586i	0.0114247	+	0.0647930i	0.989987	−	0.141158i	$-0.0450825\pi$
$677$	0.297263	+	1.68586i	0.0114247	+	0.0647930i	−0.978562	+	0.205951i	$0.933971\pi$
$678$		0			0
$679$	−23.5479	−	6.42836i	−0.903685	−	0.246698i
$680$		0			0
$681$	16.8549	+	7.76934i	0.645880	+	0.297722i
$682$		0			0
$683$	−23.5227			−0.900070			−0.450035	−	0.893011i	$-0.648589\pi$
$683$	−23.5227			−0.900070			−0.450035	+	0.893011i	$0.648589\pi$
$684$		0			0
$685$	11.3251	−	19.6157i	0.432711	−	0.749477i
$686$		0			0
$687$	−17.2377	−	17.0865i	−0.657660	−	0.651891i
$688$		0			0
$689$	−0.290561	+	1.64785i	−0.0110695	+	0.0627782i
$690$		0			0
$691$	40.2311	−	33.7579i	1.53046	−	1.28421i	0.735623	−	0.677391i	$-0.236890\pi$
$691$	40.2311	−	33.7579i	1.53046	−	1.28421i	0.794840	−	0.606819i	$-0.207555\pi$
$692$		0			0
$693$	35.6604	−	25.1889i	1.35463	−	0.956847i
$694$		0			0
$695$	5.59230	+	2.03543i	0.212128	+	0.0772083i
$696$		0			0
$697$	−2.17238	−	1.82284i	−0.0822848	−	0.0690451i
$698$		0			0
$699$	20.6621	+	1.71601i	0.781514	+	0.0649056i
$700$		0			0
$701$	41.2696			1.55873			0.779365	−	0.626570i	$-0.215542\pi$
$701$	41.2696			1.55873			0.779365	+	0.626570i	$0.215542\pi$
$702$		0			0
$703$	6.27032	−	10.8605i	0.236490	−	0.409612i
$704$		0			0
$705$	22.7968	+	1.89330i	0.858577	+	0.0713059i
$706$		0			0
$707$	27.9065	+	7.61823i	1.04953	+	0.286513i
$708$		0			0
$709$	−3.18177	−	1.15807i	−0.119494	−	0.0434922i	0.281581	−	0.959537i	$-0.409141\pi$
$709$	−3.18177	−	1.15807i	−0.119494	−	0.0434922i	−0.401075	+	0.916045i	$0.631363\pi$
$710$		0			0
$711$	0.372478	+	42.2739i	0.0139690	+	1.58539i
$712$		0			0
$713$	6.56670	+	37.2416i	0.245925	+	1.39471i
$714$		0			0
$715$	1.47523	−	0.536941i	0.0551706	−	0.0200805i
$716$		0			0
$717$	−7.49127	−	7.42555i	−0.279767	−	0.277312i
$718$		0			0
$719$	−1.68727			−0.0629247			−0.0314623	−	0.999505i	$-0.510016\pi$
$719$	−1.68727			−0.0629247			−0.0314623	+	0.999505i	$0.510016\pi$
$720$		0			0
$721$	−1.32688	+	14.3875i	−0.0494156	+	0.535817i
$722$		0			0
$723$	3.17108	−	2.24130i	0.117934	−	0.0833547i
$724$		0			0
$725$	5.67277	−	2.06472i	0.210681	−	0.0766818i
$726$		0			0
$727$	41.1434	+	14.9750i	1.52592	+	0.555391i	0.962619	−	0.270858i	$-0.0873073\pi$
$727$	41.1434	+	14.9750i	1.52592	+	0.555391i	0.563305	+	0.826249i	$0.309529\pi$
$728$		0			0
$729$	23.7313	+	12.8773i	0.878938	+	0.476937i
$730$		0			0
$731$	1.16623	−	0.978584i	0.0431346	−	0.0361943i
$732$		0			0
$733$	1.02806	−	5.83045i	0.0379724	−	0.215352i	−0.959917	−	0.280283i	$-0.909572\pi$
$733$	1.02806	−	5.83045i	0.0379724	−	0.215352i	0.997890	+	0.0649309i	$0.0206827\pi$
$734$		0			0
$735$	12.0574	+	8.53268i	0.444744	+	0.314733i
$736$		0			0
$737$	18.2847	−	31.6701i	0.673526	−	1.16658i
$738$		0			0
$739$	−2.30545	−	3.99316i	−0.0848075	−	0.146891i	0.820502	−	0.571644i	$-0.193694\pi$
$739$	−2.30545	−	3.99316i	−0.0848075	−	0.146891i	−0.905309	+	0.424753i	$0.860361\pi$
$740$		0			0
$741$	0.486208	−	1.84706i	0.0178613	−	0.0678536i
$742$		0			0
$743$	−18.9230	+	6.88742i	−0.694219	+	0.252675i	−0.664940	−	0.746896i	$-0.731543\pi$
$743$	−18.9230	+	6.88742i	−0.694219	+	0.252675i	−0.0292782	+	0.999571i	$0.509321\pi$
$744$		0			0
$745$	−11.2950	−	4.11103i	−0.413815	−	0.150617i
$746$		0			0
$747$	19.4882	+	11.0237i	0.713037	+	0.403338i
$748$		0			0
$749$	−43.4732	+	3.59768i	−1.58848	+	0.131457i
$750$		0			0
$751$	19.6422	−	7.14916i	0.716753	−	0.260877i	0.0422060	−	0.999109i	$-0.486561\pi$
$751$	19.6422	−	7.14916i	0.716753	−	0.260877i	0.674547	+	0.738232i	$0.264339\pi$
$752$		0			0
$753$	−4.57392	−	9.69705i	−0.166683	−	0.353380i
$754$		0			0
$755$	−15.0842			−0.548972
$756$		0			0
$757$	3.18175			0.115643			0.0578213	−	0.998327i	$-0.481585\pi$
$757$	3.18175			0.115643			0.0578213	+	0.998327i	$0.481585\pi$
$758$		0			0
$759$	22.1765	−	31.9701i	0.804955	−	1.16044i
$760$		0			0
$761$	−22.0630	+	8.03027i	−0.799783	+	0.291097i	−0.709397	−	0.704810i	$-0.751032\pi$
$761$	−22.0630	+	8.03027i	−0.799783	+	0.291097i	−0.0903865	+	0.995907i	$0.528810\pi$
$762$		0			0
$763$	0.951312	+	1.37229i	0.0344398	+	0.0496803i
$764$		0			0
$765$	0.944499	+	1.10568i	0.0341484	+	0.0399759i
$766$		0			0
$767$	0.829868	+	0.302047i	0.0299648	+	0.0109063i
$768$		0			0
$769$	36.7351	−	13.3705i	1.32470	−	0.482152i	0.419739	−	0.907645i	$-0.362121\pi$
$769$	36.7351	−	13.3705i	1.32470	−	0.482152i	0.904962	+	0.425493i	$0.139899\pi$
$770$		0			0
$771$	7.75526	+	7.68723i	0.279299	+	0.276849i
$772$		0			0
$773$	−24.7786	−	42.9178i	−0.891225	−	1.54365i	−0.838409	−	0.545042i	$-0.816514\pi$
$773$	−24.7786	−	42.9178i	−0.891225	−	1.54365i	−0.0528159	−	0.998604i	$-0.516820\pi$
$774$		0			0
$775$	16.2774	−	28.1932i	0.584700	−	1.01273i
$776$		0			0
$777$	6.10746	−	10.5713i	0.219104	−	0.379243i
$778$		0			0
$779$	−5.82605	+	33.0412i	−0.208740	+	1.18382i
$780$		0			0
$781$	−48.5335	+	40.7245i	−1.73667	+	1.45724i
$782$		0			0
$783$	7.37570	+	5.02057i	0.263586	+	0.179421i
$784$		0			0
$785$	23.8889	+	8.69484i	0.852631	+	0.310332i
$786$		0			0
$787$	−25.6804	+	9.34689i	−0.915406	+	0.333181i	−0.756409	−	0.654099i	$-0.773048\pi$
$787$	−25.6804	+	9.34689i	−0.915406	+	0.333181i	−0.158997	+	0.987279i	$0.550826\pi$
$788$		0			0
$789$	3.22438	+	35.0744i	0.114791	+	1.24868i
$790$		0			0
$791$	37.9414	+	26.8334i	1.34904	+	0.954086i
$792$		0			0
$793$	2.92223			0.103772
$794$		0			0
$795$	−3.83677	+	14.5756i	−0.136076	+	0.516942i
$796$		0			0
$797$	−51.6557	+	18.8011i	−1.82974	+	0.665970i	−0.836775	+	0.547547i	$0.815562\pi$
$797$	−51.6557	+	18.8011i	−1.82974	+	0.665970i	−0.992963	+	0.118423i	$0.962216\pi$
$798$		0			0
$799$	−0.748956	−	4.24754i	−0.0264962	−	0.150267i
$800$		0			0
$801$	−3.08009	+	3.73708i	−0.108829	+	0.132043i
$802$		0			0
$803$	66.6122	+	24.2449i	2.35069	+	0.855583i
$804$		0			0
$805$	12.6992	+	3.46676i	0.447587	+	0.122187i
$806$		0			0
$807$	−3.25997	+	4.69966i	−0.114757	+	0.165436i
$808$		0			0
$809$	16.6954	−	28.9172i	0.586978	−	1.01668i	−0.407648	−	0.913139i	$-0.633651\pi$
$809$	16.6954	−	28.9172i	0.586978	−	1.01668i	0.994626	−	0.103537i	$-0.0330159\pi$
$810$		0			0
$811$	17.4469			0.612644			0.306322	−	0.951928i	$-0.400901\pi$
$811$	17.4469			0.612644			0.306322	+	0.951928i	$0.400901\pi$
$812$		0			0
$813$	17.8594	+	37.8633i	0.626358	+	1.32792i
$814$		0			0
$815$	−1.72439	−	1.44694i	−0.0604029	−	0.0506840i
$816$		0			0
$817$	−16.9254	−	6.16033i	−0.592144	−	0.215523i
$818$		0			0
$819$	0.473867	−	1.79804i	0.0165582	−	0.0628286i
$820$		0			0
$821$	5.89983	−	4.95055i	0.205906	−	0.172775i	−0.534003	−	0.845482i	$-0.679313\pi$
$821$	5.89983	−	4.95055i	0.205906	−	0.172775i	0.739909	+	0.672707i	$0.234869\pi$
$822$		0			0
$823$	−2.15886	+	12.2435i	−0.0752532	+	0.426782i	0.923784	+	0.382914i	$0.125079\pi$
$823$	−2.15886	+	12.2435i	−0.0752532	+	0.426782i	−0.999037	+	0.0438684i	$0.986032\pi$
$824$		0			0
$825$	−32.3155	+	8.81167i	−1.12508	+	0.306783i
$826$		0			0
$827$	−18.3204	+	31.7318i	−0.637062	+	1.10342i	0.349012	+	0.937118i	$0.386517\pi$
$827$	−18.3204	+	31.7318i	−0.637062	+	1.10342i	−0.986074	+	0.166306i	$0.946816\pi$
$828$		0			0
$829$	−6.23030			−0.216387			−0.108194	−	0.994130i	$-0.534507\pi$
$829$	−6.23030			−0.216387			−0.108194	+	0.994130i	$0.534507\pi$
$830$		0			0
$831$	−2.60487	−	28.3355i	−0.0903619	−	0.982947i
$832$		0			0
$833$	0.977096	−	2.60804i	0.0338544	−	0.0903631i
$834$		0			0
$835$	−0.0270864	−	0.153615i	−0.000937364	−	0.00531605i
$836$		0			0
$837$	47.8723	−	4.82660i	1.65471	−	0.166832i
$838$		0			0
$839$	13.1462	+	4.78483i	0.453858	+	0.165191i	0.558826	−	0.829285i	$-0.311252\pi$
$839$	13.1462	+	4.78483i	0.453858	+	0.165191i	−0.104968	+	0.994476i	$0.533474\pi$
$840$		0			0
$841$	−19.9567	−	16.7456i	−0.688161	−	0.577436i
$842$		0			0
$843$	−4.01132	−	43.6347i	−0.138157	−	1.50286i
$844$		0			0
$845$	−7.88556	+	13.6582i	−0.271271	+	0.469856i
$846$		0			0
$847$	−46.2746	+	21.3141i	−1.59001	+	0.732361i
$848$		0			0
$849$	−1.68214	+	6.39032i	−0.0577310	+	0.219315i
$850$		0			0
$851$	1.88934	−	10.7150i	0.0647656	−	0.367304i
$852$		0			0
$853$	−0.778234	−	4.41359i	−0.0266462	−	0.151118i	0.968582	−	0.248695i	$-0.0800018\pi$
$853$	−0.778234	−	4.41359i	−0.0266462	−	0.151118i	−0.995228	+	0.0975771i	$0.968891\pi$
$854$		0			0
$855$	5.74154	−	16.2179i	0.196356	−	0.554642i
$856$		0			0
$857$	1.87996	+	10.6618i	0.0642181	+	0.364199i	0.999934	+	0.0114459i	$0.00364341\pi$
$857$	1.87996	+	10.6618i	0.0642181	+	0.364199i	−0.935716	+	0.352753i	$0.885245\pi$
$858$		0			0
$859$	−44.4845	+	16.1910i	−1.51779	+	0.552431i	−0.960596	−	0.277949i	$-0.910345\pi$
$859$	−44.4845	+	16.1910i	−1.51779	+	0.552431i	−0.557197	+	0.830380i	$0.688123\pi$
$860$		0			0
$861$	−5.68127	+	32.1650i	−0.193617	+	1.09618i
$862$		0			0
$863$	−24.9127	−	43.1501i	−0.848039	−	1.46885i	−0.882956	−	0.469456i	$-0.844450\pi$
$863$	−24.9127	−	43.1501i	−0.848039	−	1.46885i	0.0349168	−	0.999390i	$-0.488883\pi$
$864$		0			0
$865$	4.69488	−	8.13177i	0.159631	−	0.276488i
$866$		0			0
$867$	−16.6262	+	23.9687i	−0.564655	+	0.814020i
$868$		0			0
$869$	13.4600	−	76.3356i	0.456600	−	2.58951i
$870$		0			0
$871$	−0.270453	−	1.53382i	−0.00916395	−	0.0519713i
$872$		0			0
$873$	0.243862	+	27.6768i	0.00825347	+	0.936717i
$874$		0			0
$875$	−15.6383	−	22.5587i	−0.528672	−	0.762622i
$876$		0			0
$877$	−7.74993	−	6.50297i	−0.261697	−	0.219590i	0.502493	−	0.864581i	$-0.332416\pi$
$877$	−7.74993	−	6.50297i	−0.261697	−	0.219590i	−0.764189	+	0.644992i	$0.776861\pi$
$878$		0			0
$879$	10.5219	+	10.4296i	0.354895	+	0.351782i
$880$		0			0
$881$	9.75313	−	16.8929i	0.328591	−	0.569137i	−0.653641	−	0.756805i	$-0.726759\pi$
$881$	9.75313	−	16.8929i	0.328591	−	0.569137i	0.982233	+	0.187668i	$0.0600928\pi$
$882$		0			0
$883$	8.36664	+	14.4914i	0.281560	+	0.487676i	0.971769	−	0.235934i	$-0.0758149\pi$
$883$	8.36664	+	14.4914i	0.281560	+	0.487676i	−0.690209	+	0.723610i	$0.742482\pi$
$884$		0			0
$885$	7.22424	+	3.33005i	0.242840	+	0.111938i
$886$		0			0
$887$	−6.84758	+	38.8346i	−0.229919	+	1.30394i	0.623134	+	0.782115i	$0.285859\pi$
$887$	−6.84758	+	38.8346i	−0.229919	+	1.30394i	−0.853054	+	0.521823i	$0.825252\pi$
$888$		0			0
$889$	−15.4014	+	1.27456i	−0.516546	+	0.0427474i
$890$		0			0
$891$	−38.4780	−	31.1481i	−1.28906	−	1.04350i
$892$		0			0
$893$	−39.0897	+	32.8001i	−1.30809	+	1.09761i
$894$		0			0
$895$	−1.04197	−	0.874314i	−0.0348291	−	0.0292251i
$896$		0			0
$897$	−0.151697	−	1.65015i	−0.00506502	−	0.0550968i
$898$		0			0
$899$	15.8998			0.530289
$900$		0			0
$901$	2.84180			0.0946740
$902$		0			0
$903$	−16.4757	−	6.00212i	−0.548276	−	0.199738i
$904$		0			0
$905$	−9.89015	−	8.29882i	−0.328760	−	0.275862i
$906$		0			0
$907$	28.5429	+	10.3888i	0.947752	+	0.344954i	0.769223	−	0.638981i	$-0.220644\pi$
$907$	28.5429	+	10.3888i	0.947752	+	0.344954i	0.178530	+	0.983935i	$0.442866\pi$
$908$		0			0
$909$	−0.289000	−	32.7996i	−0.00958552	−	1.08790i
$910$		0			0
$911$	23.1899	−	19.4586i	0.768314	−	0.644692i	−0.171962	−	0.985104i	$-0.555011\pi$
$911$	23.1899	−	19.4586i	0.768314	−	0.644692i	0.940277	+	0.340411i	$0.110566\pi$
$912$		0			0
$913$	−31.4482	−	26.3882i	−1.04078	−	0.873320i
$914$		0			0
$915$	26.2318	+	2.17859i	0.867198	+	0.0720218i
$916$		0			0
$917$	−18.2552	−	12.9107i	−0.602840	−	0.426348i
$918$		0			0
$919$	11.5954	+	20.0838i	0.382496	+	0.662502i	0.991418	−	0.130727i	$-0.0417313\pi$
$919$	11.5954	+	20.0838i	0.382496	+	0.662502i	−0.608922	+	0.793230i	$0.708398\pi$
$920$		0			0
$921$	−4.25862	+	6.13932i	−0.140326	+	0.202298i
$922$		0			0
$923$	−0.468556	+	2.65731i	−0.0154227	+	0.0874665i
$924$		0			0
$925$	−7.17514	+	6.02066i	−0.235917	+	0.197958i
$926$		0			0
$927$	16.1085	−	2.98693i	0.529072	−	0.0981038i
$928$		0			0
$929$	23.4689	−	19.6927i	0.769988	−	0.646097i	−0.170718	−	0.985320i	$-0.554609\pi$
$929$	23.4689	−	19.6927i	0.769988	−	0.646097i	0.940706	+	0.339223i	$0.110164\pi$
$930$		0			0
$931$	−32.5018	+	5.41657i	−1.06520	+	0.177521i
$932$		0			0
$933$	12.0539	−	45.7916i	0.394626	−	1.49915i
$934$		0			0
$935$	−1.33313	−	2.30904i	−0.0435979	−	0.0755137i
$936$		0			0
$937$	14.7199	+	25.4955i	0.480877	+	0.832903i	0.999759	−	0.0219427i	$-0.00698514\pi$
$937$	14.7199	+	25.4955i	0.480877	+	0.832903i	−0.518883	+	0.854846i	$0.673652\pi$
$938$		0			0
$939$	44.8725	−	31.7156i	1.46436	−	1.03500i
$940$		0			0
$941$	−20.8140	+	7.57567i	−0.678516	+	0.246960i	−0.658210	−	0.752834i	$-0.728686\pi$
$941$	−20.8140	+	7.57567i	−0.678516	+	0.246960i	−0.0203060	+	0.999794i	$0.506464\pi$
$942$		0			0
$943$	5.05468	+	28.6665i	0.164603	+	0.933510i
$944$		0			0
$945$	5.59420	−	15.7871i	0.181979	−	0.513554i
$946$		0			0
$947$	−7.10853	−	40.3145i	−0.230996	−	1.31005i	−0.850884	−	0.525354i	$-0.823933\pi$
$947$	−7.10853	−	40.3145i	−0.230996	−	1.31005i	0.619887	−	0.784691i	$-0.287178\pi$
$948$		0			0
$949$	2.83698	−	1.03258i	0.0920924	−	0.0335189i
$950$		0			0
$951$	15.7497	+	7.25991i	0.510719	+	0.235419i
$952$		0			0
$953$	8.10886	+	14.0450i	0.262672	+	0.454961i	0.966951	−	0.254962i	$-0.0820631\pi$
$953$	8.10886	+	14.0450i	0.262672	+	0.454961i	−0.704279	+	0.709923i	$0.748730\pi$
$954$		0			0
$955$	8.88234	+	15.3847i	0.287426	+	0.497836i
$956$		0			0
$957$	−11.6186	−	11.5166i	−0.375575	−	0.372280i
$958$		0			0
$959$	12.5076	+	47.5719i	0.403892	+	1.53618i
$960$		0			0
$961$	41.9354	−	35.1880i	1.35275	−	1.13510i
$962$		0			0
$963$	17.3260	+	46.3287i	0.558323	+	1.49292i
$964$		0			0
$965$	2.68249	−	2.25088i	0.0863525	−	0.0724584i
$966$		0			0
$967$	−2.39043	+	13.5568i	−0.0768711	+	0.435958i	0.921945	+	0.387320i	$0.126599\pi$
$967$	−2.39043	+	13.5568i	−0.0768711	+	0.435958i	−0.998816	+	0.0486377i	$0.984512\pi$
$968$		0			0
$969$	−3.23269	−	0.268478i	−0.103849	−	0.00862477i
$970$		0			0
$971$	−27.7717	−	48.1020i	−0.891236	−	1.54367i	−0.838395	−	0.545063i	$-0.816506\pi$
$971$	−27.7717	−	48.1020i	−0.891236	−	1.54367i	−0.0528405	−	0.998603i	$-0.516827\pi$
$972$		0			0
$973$	−11.7387	+	5.40684i	−0.376325	+	0.173335i
$974$		0			0
$975$	−0.813080	+	1.17215i	−0.0260394	+	0.0375390i
$976$		0			0
$977$	35.4116	+	29.7138i	1.13292	+	0.950630i	0.999184	−	0.0403872i	$-0.0128591\pi$
$977$	35.4116	+	29.7138i	1.13292	+	0.950630i	0.133733	+	0.991017i	$0.457304\pi$
$978$		0			0
$979$	6.80201	−	5.70756i	0.217393	−	0.182414i
$980$		0			0
$981$	1.20420	−	1.46106i	0.0384472	−	0.0466481i
$982$		0			0
$983$	−16.4667	−	5.99337i	−0.525205	−	0.191159i	0.0657911	−	0.997833i	$-0.479043\pi$
$983$	−16.4667	−	5.99337i	−0.525205	−	0.191159i	−0.590996	+	0.806674i	$0.701265\pi$
$984$		0			0
$985$	1.17135	+	0.982876i	0.0373222	+	0.0313170i
$986$		0			0
$987$	−38.0645	+	31.9209i	−1.21161	+	1.01605i
$988$		0			0
$989$	−15.6269			−0.496906
$990$		0			0
$991$	−10.8666			−0.345189			−0.172594	−	0.984993i	$-0.555215\pi$
$991$	−10.8666			−0.345189			−0.172594	+	0.984993i	$0.555215\pi$
$992$		0			0
$993$	−32.0037	−	14.7523i	−1.01561	−	0.468149i
$994$		0			0
$995$	4.76192	+	3.99572i	0.150963	+	0.126673i
$996$		0			0
$997$	−44.4530	+	37.3005i	−1.40784	+	1.18132i	−0.450351	+	0.892851i	$0.648701\pi$
$997$	−44.4530	+	37.3005i	−1.40784	+	1.18132i	−0.957490	+	0.288467i	$0.906854\pi$
$998$		0			0
$999$	−13.4179	−	3.40591i	−0.424523	−	0.107758i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bp.a.193.2	✓	144
7.2	even	3		756.2.bq.a.625.17	yes	144
27.7	even	9		756.2.bq.a.277.17	yes	144
189.142	even	9	inner	756.2.bp.a.709.2	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bp.a.193.2	✓	144	1.1	even	1	trivial
756.2.bp.a.709.2	yes	144	189.142	even	9	inner
756.2.bq.a.277.17	yes	144	27.7	even	9
756.2.bq.a.625.17	yes	144	7.2	even	3

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.bp (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.72611 - 0.143355i) q^{3} +(1.14483 - 0.416685i) q^{5} +(-1.12940 + 2.39259i) q^{7} +(2.95890 + 0.494894i) q^{9} +O(q^{10})\)	\(q+(-1.72611 - 0.143355i) q^{3} +(1.14483 - 0.416685i) q^{5} +(-1.12940 + 2.39259i) q^{7} +(2.95890 + 0.494894i) q^{9} +(-5.16885 - 1.88131i) q^{11} +(-0.220139 + 0.0801240i) q^{13} +(-2.03584 + 0.555126i) q^{15} +(0.198933 + 0.344562i) q^{17} +(2.35358 - 4.07652i) q^{19} +(2.29245 - 3.96796i) q^{21} +(0.709167 - 4.02188i) q^{23} +(-2.69321 + 2.25987i) q^{25} +(-5.03643 - 1.27841i) q^{27} +(-1.61354 - 0.587281i) q^{29} +(-8.70131 + 3.16702i) q^{31} +(8.65229 + 3.98832i) q^{33} +(-0.296015 + 3.20971i) q^{35} +2.66416 q^{37} +(0.391470 - 0.106745i) q^{39} +(-6.69778 + 2.43779i) q^{41} +(-0.664453 - 3.76830i) q^{43} +(3.59366 - 0.666358i) q^{45} +(-10.1867 - 3.70767i) q^{47} +(-4.44893 - 5.40435i) q^{49} +(-0.293985 - 0.623270i) q^{51} +(3.57130 - 6.18567i) q^{53} -6.70138 q^{55} +(-4.64692 + 6.69911i) q^{57} +(-2.88779 - 2.42315i) q^{59} +(-11.7217 - 4.26634i) q^{61} +(-4.52584 + 6.52049i) q^{63} +(-0.218636 + 0.183457i) q^{65} +(-1.15447 + 6.54730i) q^{67} +(-1.80066 + 6.84054i) q^{69} +(5.75904 - 9.97495i) q^{71} -12.8873 q^{73} +(4.97273 - 3.51469i) q^{75} +(10.3389 - 10.2422i) q^{77} +(2.44702 + 13.8778i) q^{79} +(8.51016 + 2.92868i) q^{81} +(7.01325 + 2.55262i) q^{83} +(0.371319 + 0.311574i) q^{85} +(2.70095 + 1.24502i) q^{87} +(-0.807133 + 1.39800i) q^{89} +(0.0569205 - 0.617193i) q^{91} +(15.4734 - 4.21923i) q^{93} +(0.995830 - 5.64763i) q^{95} +(1.60207 + 9.08578i) q^{97} +(-14.3630 - 8.12462i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9}+O(q^{10}) \) 144 * q - 12 * q^9	\( 144 q - 12 q^{9} - 12 q^{11} - 12 q^{15} - 24 q^{17} - 3 q^{21} + 15 q^{23} + 6 q^{29} + 18 q^{33} + 18 q^{35} + 18 q^{39} - 12 q^{41} + 6 q^{45} + 18 q^{47} + 36 q^{49} + 18 q^{51} + 15 q^{53} + 3 q^{57} + 30 q^{59} + 18 q^{61} + 3 q^{63} + 9 q^{65} + 30 q^{69} - 12 q^{71} - 36 q^{73} + 102 q^{75} + 69 q^{77} + 18 q^{79} + 12 q^{81} - 36 q^{85} + 78 q^{87} - 72 q^{89} - 18 q^{91} - 60 q^{93} + 42 q^{95} - 72 q^{99}+O(q^{100}) \) 144 * q - 12 * q^9 - 12 * q^11 - 12 * q^15 - 24 * q^17 - 3 * q^21 + 15 * q^23 + 6 * q^29 + 18 * q^33 + 18 * q^35 + 18 * q^39 - 12 * q^41 + 6 * q^45 + 18 * q^47 + 36 * q^49 + 18 * q^51 + 15 * q^53 + 3 * q^57 + 30 * q^59 + 18 * q^61 + 3 * q^63 + 9 * q^65 + 30 * q^69 - 12 * q^71 - 36 * q^73 + 102 * q^75 + 69 * q^77 + 18 * q^79 + 12 * q^81 - 36 * q^85 + 78 * q^87 - 72 * q^89 - 18 * q^91 - 60 * q^93 + 42 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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