LMFDB - Embedded newform 756.2.bf.a.703.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(271,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("756.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bf (of order $6$, degree $2$, 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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			703.12
Character	$\chi$	$=$	756.703
Dual form			756.2.bf.a.271.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.922848 - 1.07161i) q^{2} +(-0.296703 - 1.97787i) q^{4} +(-3.59250 + 2.07413i) q^{5} +(2.54686 + 0.716577i) q^{7} +(-2.39332 - 1.50732i) q^{8} +O(q^{10})$	\(q+(0.922848 - 1.07161i) q^{2} +(-0.296703 - 1.97787i) q^{4} +(-3.59250 + 2.07413i) q^{5} +(2.54686 + 0.716577i) q^{7} +(-2.39332 - 1.50732i) q^{8} +(-1.09267 + 5.76388i) q^{10} +(1.49910 + 0.865507i) q^{11} +6.01127i q^{13} +(3.11826 - 2.06796i) q^{14} +(-3.82393 + 1.17368i) q^{16} +(-0.154193 - 0.0890232i) q^{17} +(2.46379 + 4.26741i) q^{19} +(5.16827 + 6.49010i) q^{20} +(2.31093 - 0.807724i) q^{22} +(-4.76183 + 2.74924i) q^{23} +(6.10406 - 10.5725i) q^{25} +(6.44175 + 5.54749i) q^{26} +(0.661633 - 5.24998i) q^{28} +6.17658 q^{29} +(0.931308 - 1.61307i) q^{31} +(-2.27118 + 5.18090i) q^{32} +(-0.237695 + 0.0830798i) q^{34} +(-10.6359 + 2.70823i) q^{35} +(0.349105 + 0.604667i) q^{37} +(6.84671 + 1.29794i) q^{38} +(11.7244 + 0.450999i) q^{40} -3.19527i q^{41} +2.07927i q^{43} +(1.26707 - 3.22183i) q^{44} +(-1.44832 + 7.63996i) q^{46} +(5.08258 + 8.80328i) q^{47} +(5.97304 + 3.65005i) q^{49} +(-5.69654 - 16.2980i) q^{50} +(11.8895 - 1.78356i) q^{52} +(-2.31084 + 4.00249i) q^{53} -7.18071 q^{55} +(-5.01535 - 5.55394i) q^{56} +(5.70004 - 6.61889i) q^{58} +(-0.333175 + 0.577077i) q^{59} +(-0.664061 + 0.383396i) q^{61} +(-0.869132 - 2.48662i) q^{62} +(3.45596 + 7.21501i) q^{64} +(-12.4682 - 21.5955i) q^{65} +(-2.88737 - 1.66702i) q^{67} +(-0.130327 + 0.331386i) q^{68} +(-6.91315 + 13.8968i) q^{70} +3.37323i q^{71} +(-10.1866 - 5.88124i) q^{73} +(0.970139 + 0.183911i) q^{74} +(7.70937 - 6.13921i) q^{76} +(3.19781 + 3.27855i) q^{77} +(-8.75675 + 5.05571i) q^{79} +(11.3031 - 12.1478i) q^{80} +(-3.42409 - 2.94875i) q^{82} -14.7627 q^{83} +0.738584 q^{85} +(2.22817 + 1.91885i) q^{86} +(-2.28323 - 4.33107i) q^{88} +(9.19642 - 5.30955i) q^{89} +(-4.30754 + 15.3099i) q^{91} +(6.85049 + 8.60257i) q^{92} +(14.1241 + 2.67754i) q^{94} +(-17.7024 - 10.2205i) q^{95} +8.77209i q^{97} +(9.42364 - 3.03233i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{7}+O(q^{10}) $ 32 * q - 2 * q^7	$ 32 q - 2 q^{7} - 4 q^{10} - 28 q^{16} + 6 q^{19} + 20 q^{22} + 20 q^{25} + 28 q^{28} - 8 q^{34} - 2 q^{37} + 8 q^{40} - 12 q^{46} - 10 q^{49} + 20 q^{52} - 16 q^{55} + 40 q^{58} + 48 q^{64} - 42 q^{67} - 56 q^{70} - 18 q^{73} + 40 q^{76} + 6 q^{79} + 88 q^{82} - 8 q^{85} + 76 q^{88} - 8 q^{91} + 8 q^{94}+O(q^{100}) $ 32 * q - 2 * q^7 - 4 * q^10 - 28 * q^16 + 6 * q^19 + 20 * q^22 + 20 * q^25 + 28 * q^28 - 8 * q^34 - 2 * q^37 + 8 * q^40 - 12 * q^46 - 10 * q^49 + 20 * q^52 - 16 * q^55 + 40 * q^58 + 48 * q^64 - 42 * q^67 - 56 * q^70 - 18 * q^73 + 40 * q^76 + 6 * q^79 + 88 * q^82 - 8 * q^85 + 76 * q^88 - 8 * q^91 + 8 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	0.922848	−	1.07161i	0.652552	−	0.757744i
$2$	0.922848	−	1.07161i	0.652552	−	0.757744i
$3$		0			0
$3$		0			0
$4$	−0.296703	−	1.97787i	−0.148352	−	0.988935i
$5$	−3.59250	+	2.07413i	−1.60662	+	0.927581i	−0.616497	+	0.787357i	$0.711449\pi$
$5$	−3.59250	+	2.07413i	−1.60662	+	0.927581i	−0.990120	+	0.140224i	$0.955218\pi$
$6$		0			0
$7$	2.54686	+	0.716577i	0.962624	+	0.270841i
$7$	2.54686	+	0.716577i	0.962624	+	0.270841i
$8$	−2.39332	−	1.50732i	−0.846166	−	0.532919i
$9$		0			0
$10$	−1.09267	+	5.76388i	−0.345533	+	1.82270i
$11$	1.49910	+	0.865507i	0.451996	+	0.260960i	0.708673	−	0.705537i	$-0.249294\pi$
$11$	1.49910	+	0.865507i	0.451996	+	0.260960i	−0.256677	+	0.966497i	$0.582627\pi$
$12$		0			0
$13$			6.01127i			1.66723i	0.552349	+	0.833613i	$0.313732\pi$
$13$			6.01127i			1.66723i	−0.552349	+	0.833613i	$0.686268\pi$
$14$	3.11826	−	2.06796i	0.833390	−	0.552685i
$15$		0			0
$16$	−3.82393	+	1.17368i	−0.955984	+	0.293420i
$17$	−0.154193	−	0.0890232i	−0.0373972	−	0.0215913i	0.481185	−	0.876619i	$-0.340207\pi$
$17$	−0.154193	−	0.0890232i	−0.0373972	−	0.0215913i	−0.518582	+	0.855028i	$0.673540\pi$
$18$		0			0
$19$	2.46379	+	4.26741i	0.565232	+	0.979011i	0.997028	+	0.0770395i	$0.0245468\pi$
$19$	2.46379	+	4.26741i	0.565232	+	0.979011i	−0.431796	+	0.901971i	$0.642120\pi$
$20$	5.16827	+	6.49010i	1.15566	+	1.45123i
$21$		0			0
$22$	2.31093	−	0.807724i	0.492692	−	0.172207i
$23$	−4.76183	+	2.74924i	−0.992910	+	0.573257i	−0.906143	−	0.422972i	$-0.860987\pi$
$23$	−4.76183	+	2.74924i	−0.992910	+	0.573257i	−0.0867671	+	0.996229i	$0.527654\pi$
$24$		0			0
$25$	6.10406	−	10.5725i	1.22081	−	2.11451i
$26$	6.44175	+	5.54749i	1.26333	+	1.08795i
$27$		0			0
$28$	0.661633	−	5.24998i	0.125037	−	0.992152i
$29$	6.17658			1.14696			0.573481	−	0.819219i	$-0.305593\pi$
$29$	6.17658			1.14696			0.573481	+	0.819219i	$0.305593\pi$
$30$		0			0
$31$	0.931308	−	1.61307i	0.167268	−	0.289716i	−0.770190	−	0.637814i	$-0.779839\pi$
$31$	0.931308	−	1.61307i	0.167268	−	0.289716i	0.937458	+	0.348098i	$0.113172\pi$
$32$	−2.27118	+	5.18090i	−0.401492	+	0.915863i
$33$		0			0
$34$	−0.237695	+	0.0830798i	−0.0407643	+	0.0142481i
$35$	−10.6359	+	2.70823i	−1.79779	+	0.457775i
$36$		0			0
$37$	0.349105	+	0.604667i	0.0573925	+	0.0994067i	0.893294	−	0.449472i	$-0.148388\pi$
$37$	0.349105	+	0.604667i	0.0573925	+	0.0994067i	−0.835902	+	0.548879i	$0.815055\pi$
$38$	6.84671	+	1.29794i	1.11068	+	0.210554i
$39$		0			0
$40$	11.7244	+	0.450999i	1.85379	+	0.0713091i
$41$		−	3.19527i		−	0.499018i	−0.968372	−	0.249509i	$-0.919731\pi$
$41$		−	3.19527i		−	0.499018i	0.968372	−	0.249509i	$-0.0802692\pi$
$42$		0			0
$43$			2.07927i			0.317086i	0.987352	+	0.158543i	$0.0506797\pi$
$43$			2.07927i			0.317086i	−0.987352	+	0.158543i	$0.949320\pi$
$44$	1.26707	−	3.22183i	0.191018	−	0.485709i
$45$		0			0
$46$	−1.44832	+	7.63996i	−0.213544	+	1.12645i
$47$	5.08258	+	8.80328i	0.741370	+	1.28409i	0.951872	+	0.306497i	$0.0991569\pi$
$47$	5.08258	+	8.80328i	0.741370	+	1.28409i	−0.210502	+	0.977593i	$0.567510\pi$
$48$		0			0
$49$	5.97304	+	3.65005i	0.853291	+	0.521435i
$50$	−5.69654	−	16.2980i	−0.805612	−	2.30489i
$51$		0			0
$52$	11.8895	−	1.78356i	1.64878	−	0.247336i
$53$	−2.31084	+	4.00249i	−0.317418	+	0.549785i	−0.979949	−	0.199250i	$-0.936149\pi$
$53$	−2.31084	+	4.00249i	−0.317418	+	0.549785i	0.662530	+	0.749035i	$0.269483\pi$
$54$		0			0
$55$	−7.18071			−0.968247
$56$	−5.01535	−	5.55394i	−0.670204	−	0.742177i
$57$		0			0
$58$	5.70004	−	6.61889i	0.748452	−	0.869103i
$59$	−0.333175	+	0.577077i	−0.0433757	+	0.0751290i	−0.886898	−	0.461965i	$-0.847145\pi$
$59$	−0.333175	+	0.577077i	−0.0433757	+	0.0751290i	0.843522	+	0.537094i	$0.180478\pi$
$60$		0			0
$61$	−0.664061	+	0.383396i	−0.0850243	+	0.0490888i	−0.541909	−	0.840437i	$-0.682298\pi$
$61$	−0.664061	+	0.383396i	−0.0850243	+	0.0490888i	0.456885	+	0.889526i	$0.348965\pi$
$62$	−0.869132	−	2.48662i	−0.110380	−	0.315801i
$63$		0			0
$64$	3.45596	+	7.21501i	0.431995	+	0.901876i
$65$	−12.4682	−	21.5955i	−1.54649	−	2.67859i
$66$		0			0
$67$	−2.88737	−	1.66702i	−0.352748	−	0.203659i	0.313147	−	0.949705i	$-0.398617\pi$
$67$	−2.88737	−	1.66702i	−0.352748	−	0.203659i	−0.665895	+	0.746046i	$0.731950\pi$
$68$	−0.130327	+	0.331386i	−0.0158044	+	0.0401865i
$69$		0			0
$70$	−6.91315	+	13.8968i	−0.826279	+	1.66099i
$71$			3.37323i			0.400329i	0.979762	+	0.200165i	$0.0641477\pi$
$71$			3.37323i			0.400329i	−0.979762	+	0.200165i	$0.935852\pi$
$72$		0			0
$73$	−10.1866	−	5.88124i	−1.19225	−	0.688347i	−0.233436	−	0.972372i	$-0.574997\pi$
$73$	−10.1866	−	5.88124i	−1.19225	−	0.688347i	−0.958817	+	0.284025i	$0.908330\pi$
$74$	0.970139	+	0.183911i	0.112776	+	0.0213793i
$75$		0			0
$76$	7.70937	−	6.13921i	0.884325	−	0.704215i
$77$	3.19781	+	3.27855i	0.364424	+	0.373626i
$78$		0			0
$79$	−8.75675	+	5.05571i	−0.985211	+	0.568812i	−0.903839	−	0.427872i	$-0.859263\pi$
$79$	−8.75675	+	5.05571i	−0.985211	+	0.568812i	−0.0813719	+	0.996684i	$0.525930\pi$
$80$	11.3031	−	12.1478i	1.26373	−	1.35817i
$81$		0			0
$82$	−3.42409	−	2.94875i	−0.378128	−	0.325635i
$83$	−14.7627			−1.62041			−0.810207	−	0.586143i	$-0.800646\pi$
$83$	−14.7627			−1.62041			−0.810207	+	0.586143i	$0.800646\pi$
$84$		0			0
$85$	0.738584			0.0801107
$86$	2.22817	+	1.91885i	0.240270	+	0.206915i
$87$		0			0
$88$	−2.28323	−	4.33107i	−0.243393	−	0.461693i
$89$	9.19642	−	5.30955i	0.974818	−	0.562812i	0.0741166	−	0.997250i	$-0.476386\pi$
$89$	9.19642	−	5.30955i	0.974818	−	0.562812i	0.900702	+	0.434438i	$0.143053\pi$
$90$		0			0
$91$	−4.30754	+	15.3099i	−0.451553	+	1.60491i
$92$	6.85049	+	8.60257i	0.714213	+	0.896880i
$93$		0			0
$94$	14.1241	+	2.67754i	1.45679	+	0.276167i
$95$	−17.7024	−	10.2205i	−1.81622	−	1.04860i
$96$		0			0
$97$			8.77209i			0.890671i	0.895364	+	0.445336i	$0.146916\pi$
$97$			8.77209i			0.890671i	−0.895364	+	0.445336i	$0.853084\pi$
$98$	9.42364	−	3.03233i	0.951931	−	0.306312i
$99$		0			0
$100$	−22.7222	−	8.93613i	−2.27222	−	0.893613i
$101$	−7.35922	−	4.24885i	−0.732270	−	0.422776i	0.0869822	−	0.996210i	$-0.472278\pi$
$101$	−7.35922	−	4.24885i	−0.732270	−	0.422776i	−0.819252	+	0.573434i	$0.805611\pi$
$102$		0			0
$103$	−5.87009	−	10.1673i	−0.578397	−	1.00181i	−0.995663	−	0.0930291i	$-0.970345\pi$
$103$	−5.87009	−	10.1673i	−0.578397	−	1.00181i	0.417266	−	0.908784i	$-0.362988\pi$
$104$	9.06092	−	14.3869i	0.888496	−	1.41075i
$105$		0			0
$106$	2.15656	+	6.17002i	0.209464	+	0.599285i
$107$	3.62222	−	2.09129i	0.350173	−	0.202172i	−0.314589	−	0.949228i	$-0.601867\pi$
$107$	3.62222	−	2.09129i	0.350173	−	0.202172i	0.664761	+	0.747056i	$0.268533\pi$
$108$		0			0
$109$	6.67117	−	11.5548i	0.638983	−	1.10675i	−0.346674	−	0.937986i	$-0.612689\pi$
$109$	6.67117	−	11.5548i	0.638983	−	1.10675i	0.985656	−	0.168765i	$-0.0539777\pi$
$110$	−6.62671	+	7.69493i	−0.631832	+	0.733683i
$111$		0			0
$112$	−10.5801	+	0.249059i	−0.999723	+	0.0235339i
$113$	−2.44926			−0.230407			−0.115203	−	0.993342i	$-0.536752\pi$
$113$	−2.44926			−0.230407			−0.115203	+	0.993342i	$0.536752\pi$
$114$		0			0
$115$	11.4046	−	19.7533i	1.06348	−	1.84201i
$116$	−1.83261	−	12.2165i	−0.170153	−	1.13427i
$117$		0			0
$118$	0.310932	+	0.889589i	0.0286236	+	0.0818933i
$119$	−0.328916	−	0.337221i	−0.0301517	−	0.0309130i
$120$		0			0
$121$	−4.00179	−	6.93131i	−0.363799	−	0.630119i
$122$	−0.201976	+	1.06543i	−0.0182861	+	0.0964597i
$123$		0			0
$124$	−3.46677	−	1.36340i	−0.311325	−	0.122437i
$125$			29.9012i			2.67445i
$126$		0			0
$127$			3.04776i			0.270445i	0.990815	+	0.135223i	$0.0431749\pi$
$127$			3.04776i			0.270445i	−0.990815	+	0.135223i	$0.956825\pi$
$128$	10.9210	+	2.95491i	0.965290	+	0.261180i
$129$		0			0
$130$	−34.6482	−	6.56834i	−3.03885	−	0.576081i
$131$	6.20725	+	10.7513i	0.542330	+	0.939342i	0.998770	+	0.0495882i	$0.0157909\pi$
$131$	6.20725	+	10.7513i	0.542330	+	0.939342i	−0.456440	+	0.889754i	$0.650876\pi$
$132$		0			0
$133$	3.21701	+	12.6340i	0.278950	+	1.09551i
$134$	−4.45100	+	1.55573i	−0.384508	+	0.134394i
$135$		0			0
$136$	0.234846	+	0.445479i	0.0201379	+	0.0381995i
$137$	6.62094	−	11.4678i	0.565665	−	0.979761i	−0.431322	−	0.902198i	$-0.641953\pi$
$137$	6.62094	−	11.4678i	0.565665	−	0.979761i	0.996987	−	0.0775631i	$-0.0247139\pi$
$138$		0			0
$139$	11.5492			0.979591			0.489796	−	0.871837i	$-0.337071\pi$
$139$	11.5492			0.979591			0.489796	+	0.871837i	$0.337071\pi$
$140$	8.51223	+	20.2329i	0.719415	+	1.70999i
$141$		0			0
$142$	3.61480	+	3.11298i	0.303347	+	0.261236i
$143$	−5.20280	+	9.01151i	−0.435080	+	0.753580i
$144$		0			0
$145$	−22.1894	+	12.8110i	−1.84273	+	1.06390i
$146$	−15.7031	+	5.48860i	−1.29960	+	0.454240i
$147$		0			0
$148$	1.09237	−	0.869891i	0.0897925	−	0.0715046i
$149$	2.35210	+	4.07396i	0.192692	+	0.333751i	0.946141	−	0.323754i	$-0.104945\pi$
$149$	2.35210	+	4.07396i	0.192692	+	0.333751i	−0.753450	+	0.657505i	$0.771612\pi$
$150$		0			0
$151$	4.37574	+	2.52633i	0.356092	+	0.205590i	0.667365	−	0.744731i	$-0.267422\pi$
$151$	4.37574	+	2.52633i	0.356092	+	0.205590i	−0.311273	+	0.950321i	$0.600755\pi$
$152$	0.535725	−	13.9270i	0.0434531	−	1.12963i
$153$		0			0
$154$	6.46443	−	0.401203i	0.520918	−	0.0323299i
$155$			7.72663i			0.620618i
$156$		0			0
$157$	3.64369	+	2.10369i	0.290798	+	0.167892i	0.638302	−	0.769786i	$-0.279637\pi$
$157$	3.64369	+	2.10369i	0.290798	+	0.167892i	−0.347504	+	0.937679i	$0.612971\pi$
$158$	−2.66339	+	14.0495i	−0.211888	+	1.11772i
$159$		0			0
$160$	−2.58665	−	23.3231i	−0.204493	−	1.84386i
$161$	−14.0978	+	3.58973i	−1.11106	+	0.282911i
$162$		0			0
$163$	13.5416	−	7.81822i	1.06066	−	0.612371i	0.135043	−	0.990840i	$-0.456883\pi$
$163$	13.5416	−	7.81822i	1.06066	−	0.612371i	0.925614	+	0.378469i	$0.123549\pi$
$164$	−6.31984	+	0.948048i	−0.493496	+	0.0740301i
$165$		0			0
$166$	−13.6237	+	15.8199i	−1.05741	+	1.22786i
$167$	2.38478			0.184539			0.0922697	−	0.995734i	$-0.470588\pi$
$167$	2.38478			0.184539			0.0922697	+	0.995734i	$0.470588\pi$
$168$		0			0
$169$	−23.1354			−1.77964
$170$	0.681601	−	0.791475i	0.0522764	−	0.0607034i
$171$		0			0
$172$	4.11253	−	0.616927i	0.313578	−	0.0470402i
$173$	12.6049	−	7.27743i	0.958332	−	0.553293i	0.0626725	−	0.998034i	$-0.480038\pi$
$173$	12.6049	−	7.27743i	0.958332	−	0.553293i	0.895659	+	0.444741i	$0.146704\pi$
$174$		0			0
$175$	23.1223	−	22.5528i	1.74788	−	1.70483i
$176$	−6.74830	−	1.55018i	−0.508672	−	0.116849i
$177$		0			0
$178$	2.79712	−	14.7549i	0.209653	−	1.10593i
$179$	5.41293	+	3.12516i	0.404582	+	0.233585i	0.688459	−	0.725275i	$-0.258288\pi$
$179$	5.41293	+	3.12516i	0.404582	+	0.233585i	−0.283877	+	0.958861i	$0.591621\pi$
$180$		0			0
$181$			5.07289i			0.377065i	0.982067	+	0.188533i	$0.0603731\pi$
$181$			5.07289i			0.377065i	−0.982067	+	0.188533i	$0.939627\pi$
$182$	12.4311	+	18.7447i	0.921451	+	1.38945i
$183$		0			0
$184$	15.5406	+	0.597794i	1.14567	+	0.0440700i
$185$	−2.50832	−	1.44818i	−0.184416	−	0.106472i
$186$		0			0
$187$	−0.154100	−	0.266910i	−0.0112689	−	0.0195184i
$188$	15.9037	−	12.6646i	1.15990	−	0.923663i
$189$		0			0
$190$	−27.2889	+	9.53812i	−1.97975	+	0.691968i
$191$	21.7201	−	12.5401i	1.57161	−	0.907371i	0.575642	−	0.817702i	$-0.304752\pi$
$191$	21.7201	−	12.5401i	1.57161	−	0.907371i	0.995972	−	0.0896693i	$-0.0285810\pi$
$192$		0			0
$193$	6.75702	−	11.7035i	0.486381	−	0.842437i	−0.513496	−	0.858092i	$-0.671650\pi$
$193$	6.75702	−	11.7035i	0.486381	−	0.842437i	0.999877	+	0.0156550i	$0.00498335\pi$
$194$	9.40028	+	8.09531i	0.674901	+	0.581209i
$195$		0			0
$196$	5.44710	−	12.8969i	0.389079	−	0.921205i
$197$	3.34054			0.238003			0.119002	−	0.992894i	$-0.462031\pi$
$197$	3.34054			0.238003			0.119002	+	0.992894i	$0.462031\pi$
$198$		0			0
$199$	4.42967	−	7.67241i	0.314011	−	0.543883i	−0.665216	−	0.746651i	$-0.731661\pi$
$199$	4.42967	−	7.67241i	0.314011	−	0.543883i	0.979227	+	0.202768i	$0.0649939\pi$
$200$	−30.5452	+	16.1027i	−2.15987	+	1.13863i
$201$		0			0
$202$	−11.3446	+	3.96518i	−0.798200	+	0.278989i
$203$	15.7309	+	4.42599i	1.10409	+	0.310644i
$204$		0			0
$205$	6.62743	+	11.4790i	0.462880	+	0.801731i
$206$	−16.3126	−	3.09241i	−1.13655	−	0.215459i
$207$		0			0
$208$	−7.05530	−	22.9867i	−0.489197	−	1.59384i
$209$			8.52971i			0.590013i
$210$		0			0
$211$			17.3186i			1.19226i	0.802888	+	0.596130i	$0.203296\pi$
$211$			17.3186i			1.19226i	−0.802888	+	0.596130i	$0.796704\pi$
$212$	8.60205	+	3.38299i	0.590791	+	0.232345i
$213$		0			0
$214$	1.10171	−	5.81155i	0.0753111	−	0.397269i
$215$	−4.31269	−	7.46980i	−0.294123	−	0.509436i
$216$		0			0
$217$	3.52781	−	3.44092i	0.239483	−	0.233585i
$218$	−6.22579	−	17.8122i	−0.421664	−	1.20640i
$219$		0			0
$220$	2.13054	+	14.2025i	0.143641	+	0.957533i
$221$	0.535142	−	0.926894i	0.0359976	−	0.0623496i
$222$		0			0
$223$	−18.1129			−1.21293			−0.606463	−	0.795112i	$-0.707412\pi$
$223$	−18.1129			−1.21293			−0.606463	+	0.795112i	$0.707412\pi$
$224$	−9.49691	+	11.5676i	−0.634539	+	0.772891i
$225$		0			0
$226$	−2.26029	+	2.62465i	−0.150352	+	0.174589i
$227$	13.7345	−	23.7888i	0.911588	−	1.57892i	0.0997672	−	0.995011i	$-0.468190\pi$
$227$	13.7345	−	23.7888i	0.911588	−	1.57892i	0.811821	−	0.583906i	$-0.198476\pi$
$228$		0			0
$229$	4.77076	−	2.75440i	0.315261	−	0.182016i	−0.334018	−	0.942567i	$-0.608404\pi$
$229$	4.77076	−	2.75440i	0.315261	−	0.182016i	0.649278	+	0.760551i	$0.275071\pi$
$230$	−10.6432	−	30.4506i	−0.701792	−	2.00785i
$231$		0			0
$232$	−14.7825	−	9.31009i	−0.970520	−	0.611238i
$233$	5.42805	+	9.40167i	0.355604	+	0.615924i	0.987221	−	0.159357i	$-0.0509420\pi$
$233$	5.42805	+	9.40167i	0.355604	+	0.615924i	−0.631617	+	0.775280i	$0.717609\pi$
$234$		0			0
$235$	−36.5184	−	21.0839i	−2.38219	−	1.37536i
$236$	1.24024	+	0.487757i	0.0807325	+	0.0317503i
$237$		0			0
$238$	−0.664909	+	0.0412664i	−0.0430997	+	0.00267491i
$239$		−	9.38509i		−	0.607071i	−0.952820	−	0.303536i	$-0.901833\pi$
$239$		−	9.38509i		−	0.607071i	0.952820	−	0.303536i	$-0.0981671\pi$
$240$		0			0
$241$	−7.83648	−	4.52439i	−0.504792	−	0.291442i	0.225898	−	0.974151i	$-0.427468\pi$
$241$	−7.83648	−	4.52439i	−0.504792	−	0.291442i	−0.730690	+	0.682709i	$0.760802\pi$
$242$	−11.1207	−	2.10818i	−0.714867	−	0.135519i
$243$		0			0
$244$	0.955336	+	1.19967i	0.0611591	+	0.0768011i
$245$	−29.0288	−	0.723943i	−1.85458	−	0.0462510i
$246$		0			0
$247$	−25.6526	+	14.8105i	−1.63223	+	0.942370i
$248$	−4.66034	+	2.45682i	−0.295932	+	0.156008i
$249$		0			0
$250$	32.0425	+	27.5943i	2.02654	+	1.74522i
$251$	−15.8131			−0.998117			−0.499058	−	0.866568i	$-0.666321\pi$
$251$	−15.8131			−0.998117			−0.499058	+	0.866568i	$0.666321\pi$
$252$		0			0
$253$	−9.51796			−0.598389
$254$	3.26602	+	2.81262i	0.204928	+	0.176480i
$255$		0			0
$256$	13.2450	−	8.97615i	0.827810	−	0.561009i
$257$	3.63962	−	2.10133i	0.227033	−	0.131078i	−0.382169	−	0.924092i	$-0.624823\pi$
$257$	3.63962	−	2.10133i	0.227033	−	0.131078i	0.609203	+	0.793015i	$0.291490\pi$
$258$		0			0
$259$	0.455832	+	1.79017i	0.0283240	+	0.111236i
$260$	−39.0138	+	31.0679i	−2.41953	+	1.92675i
$261$		0			0
$262$	17.2495	+	3.27003i	1.06568	+	0.202023i
$263$	13.5793	+	7.84001i	0.837335	+	0.483436i	0.856358	−	0.516383i	$-0.172722\pi$
$263$	13.5793	+	7.84001i	0.837335	+	0.483436i	−0.0190222	+	0.999819i	$0.506055\pi$
$264$		0			0
$265$		−	19.1720i		−	1.17773i
$266$	16.5076	+	8.21188i	1.01214	+	0.503503i
$267$		0			0
$268$	−2.44046	+	6.20544i	−0.149075	+	0.379058i
$269$	6.29125	+	3.63225i	0.383584	+	0.221462i	0.679377	−	0.733790i	$-0.262250\pi$
$269$	6.29125	+	3.63225i	0.383584	+	0.221462i	−0.295792	+	0.955252i	$0.595584\pi$
$270$		0			0
$271$	13.5502	+	23.4696i	0.823116	+	1.42568i	0.903351	+	0.428903i	$0.141100\pi$
$271$	13.5502	+	23.4696i	0.823116	+	1.42568i	−0.0802344	+	0.996776i	$0.525567\pi$
$272$	0.694108	+	0.159446i	0.0420865	+	0.00966784i
$273$		0			0
$274$	−6.17891	−	17.6781i	−0.373282	−	1.06797i
$275$	18.3012	−	10.5662i	1.10361	−	0.637167i
$276$		0			0
$277$	−7.17183	+	12.4220i	−0.430914	+	0.746365i	−0.996952	−	0.0780143i	$-0.975142\pi$
$277$	−7.17183	+	12.4220i	−0.430914	+	0.746365i	0.566038	+	0.824379i	$0.308475\pi$
$278$	10.6582	−	12.3763i	0.639234	−	0.742279i
$279$		0			0
$280$	29.5373	+	9.55007i	1.76519	+	0.570726i
$281$	19.7640			1.17902			0.589512	−	0.807760i	$-0.299320\pi$
$281$	19.7640			1.17902			0.589512	+	0.807760i	$0.299320\pi$
$282$		0			0
$283$	−3.51739	+	6.09230i	−0.209087	+	0.362150i	−0.951427	−	0.307874i	$-0.900383\pi$
$283$	−3.51739	+	6.09230i	−0.209087	+	0.362150i	0.742340	+	0.670023i	$0.233716\pi$
$284$	6.67182	−	1.00085i	0.395900	−	0.0593895i
$285$		0			0
$286$	4.85545	+	13.8916i	0.287109	+	0.821430i
$287$	2.28966	−	8.13793i	0.135154	−	0.480367i
$288$		0			0
$289$	−8.48415	−	14.6950i	−0.499068	−	0.864410i
$290$	−6.74896	+	35.6010i	−0.396313	+	2.09057i
$291$		0			0
$292$	−8.60993	+	21.8928i	−0.503858	+	1.28118i
$293$			1.73824i			0.101549i	0.998710	+	0.0507747i	$0.0161690\pi$
$293$			1.73824i			0.101549i	−0.998710	+	0.0507747i	$0.983831\pi$
$294$		0			0
$295$		−	2.76420i		−	0.160938i
$296$	0.0759092	−	1.97338i	0.00441213	−	0.114700i
$297$		0			0
$298$	6.53633	+	1.23911i	0.378639	+	0.0717794i
$299$	−16.5264	−	28.6246i	−0.955749	−	1.65541i
$300$		0			0
$301$	−1.48996	+	5.29563i	−0.0858798	+	0.305235i
$302$	6.74539	−	2.35767i	0.388153	−	0.135669i
$303$		0			0
$304$	−14.4299	−	13.4266i	−0.827614	−	0.770068i
$305$	1.59043	−	2.75470i	0.0910677	−	0.157734i
$306$		0			0
$307$	−10.3978			−0.593431			−0.296716	−	0.954966i	$-0.595891\pi$
$307$	−10.3978			−0.593431			−0.296716	+	0.954966i	$0.595891\pi$
$308$	5.53575	−	7.29760i	0.315429	−	0.415820i
$309$		0			0
$310$	8.27994	+	7.13050i	0.470269	+	0.404985i
$311$	−12.6628	+	21.9326i	−0.718040	+	1.24368i	0.243735	+	0.969842i	$0.421627\pi$
$311$	−12.6628	+	21.9326i	−0.718040	+	1.24368i	−0.961775	+	0.273841i	$0.911706\pi$
$312$		0			0
$313$	27.4010	−	15.8200i	1.54880	−	0.894199i	0.550565	−	0.834792i	$-0.314412\pi$
$313$	27.4010	−	15.8200i	1.54880	−	0.894199i	0.998234	−	0.0594068i	$-0.0189209\pi$
$314$	5.61691	−	1.96324i	0.316980	−	0.110792i
$315$		0			0
$316$	12.5977	+	15.8197i	0.708675	+	0.889926i
$317$	−5.82693	−	10.0925i	−0.327273	−	0.566854i	0.654697	−	0.755892i	$-0.272796\pi$
$317$	−5.82693	−	10.0925i	−0.327273	−	0.566854i	−0.981970	+	0.189038i	$0.939463\pi$
$318$		0			0
$319$	9.25932	+	5.34587i	0.518423	+	0.299311i
$320$	−27.3804	−	18.7518i	−1.53061	−	1.04826i
$321$		0			0
$322$	−9.16330	+	18.4201i	−0.510651	+	1.02651i
$323$		−	0.877338i		−	0.0488164i
$324$		0			0
$325$	63.5544	+	36.6932i	3.52536	+	2.03537i
$326$	4.11870	−	21.7263i	0.228114	−	1.20331i
$327$		0			0
$328$	−4.81631	+	7.64731i	−0.265936	+	0.422252i
$329$	6.63640	+	26.0628i	0.365877	+	1.43689i
$330$		0			0
$331$	−17.7580	+	10.2526i	−0.976066	+	0.563532i	−0.901080	−	0.433652i	$-0.857225\pi$
$331$	−17.7580	+	10.2526i	−0.976066	+	0.563532i	−0.0749861	+	0.997185i	$0.523891\pi$
$332$	4.38013	+	29.1987i	0.240391	+	1.60248i
$333$		0			0
$334$	2.20079	−	2.55555i	0.120422	−	0.139834i
$335$	13.8305			0.755641
$336$		0			0
$337$	−21.1249			−1.15075			−0.575373	−	0.817891i	$-0.695143\pi$
$337$	−21.1249			−1.15075			−0.575373	+	0.817891i	$0.695143\pi$
$338$	−21.3504	+	24.7921i	−1.16131	+	1.34851i
$339$		0			0
$340$	−0.219140	−	1.46082i	−0.0118845	−	0.0792242i
$341$	2.79225	−	1.61211i	0.151209	−	0.0873005i
$342$		0			0
$343$	12.5970	+	13.5763i	0.680172	+	0.733052i
$344$	3.13414	−	4.97637i	0.168981	−	0.268308i
$345$		0			0
$346$	3.83381	−	20.2235i	0.206107	−	1.08722i
$347$	20.2502	+	11.6914i	1.08709	+	0.627630i	0.932799	−	0.360396i	$-0.117359\pi$
$347$	20.2502	+	11.6914i	1.08709	+	0.627630i	0.154287	+	0.988026i	$0.450692\pi$
$348$		0			0
$349$		−	30.6174i		−	1.63891i	−0.573141	−	0.819457i	$-0.694275\pi$
$349$		−	30.6174i		−	1.63891i	0.573141	−	0.819457i	$-0.305725\pi$
$350$	−2.82952	−	45.5909i	−0.151244	−	2.43694i
$351$		0			0
$352$	−7.88884	+	5.80098i	−0.420477	+	0.309193i
$353$	−13.6872	−	7.90229i	−0.728495	−	0.420597i	0.0893765	−	0.995998i	$-0.471513\pi$
$353$	−13.6872	−	7.90229i	−0.728495	−	0.420597i	−0.817871	+	0.575401i	$0.804846\pi$
$354$		0			0
$355$	−6.99654	−	12.1184i	−0.371338	−	0.643176i
$356$	−13.2302	−	16.6140i	−0.701200	−	0.880538i
$357$		0			0
$358$	8.34427	−	2.91652i	0.441008	−	0.154143i
$359$	15.9270	−	9.19546i	0.840595	−	0.485318i	−0.0168713	−	0.999858i	$-0.505371\pi$
$359$	15.9270	−	9.19546i	0.840595	−	0.485318i	0.857466	+	0.514540i	$0.172037\pi$
$360$		0			0
$361$	−2.64052	+	4.57352i	−0.138975	+	0.240712i
$362$	5.43617	+	4.68151i	0.285719	+	0.246055i
$363$		0			0
$364$	31.5590	+	3.97726i	1.65414	+	0.208465i
$365$	48.7939			2.55399
$366$		0			0
$367$	0.651832	−	1.12901i	0.0340254	−	0.0589336i	−0.848511	−	0.529177i	$-0.822501\pi$
$367$	0.651832	−	1.12901i	0.0340254	−	0.0589336i	0.882537	+	0.470244i	$0.155834\pi$
$368$	14.9822	−	16.1018i	0.781001	−	0.839364i
$369$		0			0
$370$	−3.86669	+	1.35150i	−0.201019	+	0.0702610i
$371$	−8.75350	+	8.53792i	−0.454459	+	0.443266i
$372$		0			0
$373$	2.25895	+	3.91262i	0.116964	+	0.202588i	0.918563	−	0.395274i	$-0.129350\pi$
$373$	2.25895	+	3.91262i	0.116964	+	0.202588i	−0.801599	+	0.597862i	$0.796017\pi$
$374$	−0.428235	−	0.0811814i	−0.0221435	−	0.00419779i
$375$		0			0
$376$	1.10515	−	28.7301i	0.0569939	−	1.48164i
$377$			37.1291i			1.91224i
$378$		0			0
$379$			1.61231i			0.0828190i	0.999142	+	0.0414095i	$0.0131848\pi$
$379$			1.61231i			0.0828190i	−0.999142	+	0.0414095i	$0.986815\pi$
$380$	−14.9624	+	38.0454i	−0.767555	+	1.95169i
$381$		0			0
$382$	6.60624	−	34.8482i	0.338004	−	1.78299i
$383$	4.81300	+	8.33636i	0.245933	+	0.425968i	0.962393	−	0.271659i	$-0.0875724\pi$
$383$	4.81300	+	8.33636i	0.245933	+	0.425968i	−0.716461	+	0.697627i	$0.754239\pi$
$384$		0			0
$385$	−18.2883	−	5.14553i	−0.932058	−	0.262241i
$386$	−6.30591	−	18.0415i	−0.320962	−	0.918286i
$387$		0			0
$388$	17.3501	−	2.60271i	0.880816	−	0.132132i
$389$	6.47225	−	11.2103i	0.328156	−	0.568383i	−0.653990	−	0.756503i	$-0.726906\pi$
$389$	6.47225	−	11.2103i	0.328156	−	0.568383i	0.982146	+	0.188120i	$0.0602394\pi$
$390$		0			0
$391$	0.978986			0.0495094
$392$	−8.79358	−	17.7390i	−0.444143	−	0.895956i
$393$		0			0
$394$	3.08281	−	3.57976i	0.155310	−	0.180346i
$395$	20.9724	−	36.3253i	1.05524	−	1.82773i
$396$		0			0
$397$	−4.56287	+	2.63438i	−0.229004	+	0.132216i	−0.610112	−	0.792315i	$-0.708876\pi$
$397$	−4.56287	+	2.63438i	−0.229004	+	0.132216i	0.381109	+	0.924530i	$0.375542\pi$
$398$	−4.13393	−	11.8274i	−0.207215	−	0.592851i
$399$		0			0
$400$	−10.9328	+	47.5929i	−0.546638	+	2.37965i
$401$	−16.9244	−	29.3140i	−0.845166	−	1.46387i	−0.885477	−	0.464683i	$-0.846168\pi$
$401$	−16.9244	−	29.3140i	−0.845166	−	1.46387i	0.0403107	−	0.999187i	$-0.487165\pi$
$402$		0			0
$403$	9.69661	+	5.59834i	0.483023	+	0.278873i
$404$	−6.22016	+	15.8162i	−0.309465	+	0.786886i
$405$		0			0
$406$	19.2602	−	12.7729i	0.955867	−	0.633908i
$407$			1.20861i			0.0599086i
$408$		0			0
$409$	19.6739	+	11.3587i	0.972813	+	0.561654i	0.900093	−	0.435699i	$-0.143499\pi$
$409$	19.6739	+	11.3587i	0.972813	+	0.561654i	0.0727202	+	0.997352i	$0.476832\pi$
$410$	18.4172	+	3.49138i	0.909560	+	0.172427i
$411$		0			0
$412$	−18.3679	+	14.6269i	−0.904922	+	0.720618i
$413$	−1.26207	+	1.23099i	−0.0621025	+	0.0605731i
$414$		0			0
$415$	53.0350	−	30.6198i	2.60339	−	1.50307i
$416$	−31.1438	−	13.6527i	−1.52695	−	0.669378i
$417$		0			0
$418$	9.14054	+	7.87163i	0.447078	+	0.385014i
$419$	6.66801			0.325754			0.162877	−	0.986646i	$-0.447923\pi$
$419$	6.66801			0.325754			0.162877	+	0.986646i	$0.447923\pi$
$420$		0			0
$421$	32.9589			1.60632			0.803160	−	0.595763i	$-0.203150\pi$
$421$	32.9589			1.60632			0.803160	+	0.595763i	$0.203150\pi$
$422$	18.5588	+	15.9824i	0.903427	+	0.778012i
$423$		0			0
$424$	11.5636	−	6.09607i	0.561580	−	0.296051i
$425$	−1.88240	+	1.08681i	−0.0913100	+	0.0527178i
$426$		0			0
$427$	−1.96601	+	0.500607i	−0.0951417	+	0.0242260i
$428$	−5.21102	−	6.54378i	−0.251884	−	0.316305i
$429$		0			0
$430$	−11.9847	−	2.27196i	−0.577953	−	0.109564i
$431$	−18.6066	−	10.7425i	−0.896248	−	0.517449i	−0.0202672	−	0.999795i	$-0.506452\pi$
$431$	−18.6066	−	10.7425i	−0.896248	−	0.517449i	−0.875981	+	0.482345i	$0.839785\pi$
$432$		0			0
$433$		−	28.1941i		−	1.35492i	−0.735559	−	0.677461i	$-0.763080\pi$
$433$		−	28.1941i		−	1.35492i	0.735559	−	0.677461i	$-0.236920\pi$
$434$	−0.431705	−	6.95589i	−0.0207225	−	0.333893i
$435$		0			0
$436$	−24.8333	−	9.76636i	−1.18930	−	0.467724i
$437$	−23.4643	−	13.5471i	−1.12245	−	0.648046i
$438$		0			0
$439$	14.2486	+	24.6793i	0.680049	+	1.17788i	0.974965	+	0.222356i	$0.0713748\pi$
$439$	14.2486	+	24.6793i	0.680049	+	1.17788i	−0.294916	+	0.955523i	$0.595292\pi$
$440$	17.1857	+	10.8236i	0.819298	+	0.515997i
$441$		0			0
$442$	−0.499415	−	1.42885i	−0.0237548	−	0.0679633i
$443$	−22.3028	+	12.8765i	−1.05964	+	0.611782i	−0.925332	−	0.379158i	$-0.876214\pi$
$443$	−22.3028	+	12.8765i	−1.05964	+	0.611782i	−0.134305	+	0.990940i	$0.542880\pi$
$444$		0			0
$445$	−22.0255	+	38.1492i	−1.04411	+	1.80845i
$446$	−16.7154	+	19.4099i	−0.791498	+	0.919087i
$447$		0			0
$448$	3.63175	+	20.8521i	0.171584	+	0.985170i
$449$	17.0105			0.802776			0.401388	−	0.915908i	$-0.368528\pi$
$449$	17.0105			0.802776			0.401388	+	0.915908i	$0.368528\pi$
$450$		0			0
$451$	2.76553	−	4.79005i	0.130224	−	0.225554i
$452$	0.726702	+	4.84431i	0.0341812	+	0.227857i
$453$		0			0
$454$	−12.8175	−	36.6714i	−0.601556	−	1.72108i
$455$	−16.2799	−	63.9353i	−0.763214	−	2.99733i
$456$		0			0
$457$	2.15931	+	3.74003i	0.101008	+	0.174951i	0.912100	−	0.409967i	$-0.134460\pi$
$457$	2.15931	+	3.74003i	0.101008	+	0.174951i	−0.811092	+	0.584918i	$0.801127\pi$
$458$	1.45104	−	7.65429i	0.0678026	−	0.357661i
$459$		0			0
$460$	−42.4533	−	16.6959i	−1.97940	−	0.778451i
$461$		−	20.7518i		−	0.966509i	−0.875480	−	0.483254i	$-0.839455\pi$
$461$		−	20.7518i		−	0.966509i	0.875480	−	0.483254i	$-0.160545\pi$
$462$		0			0
$463$			31.0123i			1.44127i	0.693317	+	0.720633i	$0.256149\pi$
$463$			31.0123i			1.44127i	−0.693317	+	0.720633i	$0.743851\pi$
$464$	−23.6188	+	7.24932i	−1.09648	+	0.336541i
$465$		0			0
$466$	15.0842	+	2.85954i	0.698762	+	0.132466i
$467$	1.21961	+	2.11243i	0.0564370	+	0.0977517i	0.892864	−	0.450327i	$-0.148693\pi$
$467$	1.21961	+	2.11243i	0.0564370	+	0.0977517i	−0.836427	+	0.548079i	$0.815359\pi$
$468$		0			0
$469$	−6.15918	−	6.31470i	−0.284405	−	0.291586i
$470$	−56.2946	+	19.6763i	−2.59668	+	0.907599i
$471$		0			0
$472$	1.66724	−	0.878926i	0.0767407	−	0.0404559i
$473$	−1.79963	+	3.11704i	−0.0827469	+	0.143322i
$474$		0			0
$475$	60.1565			2.76017
$476$	−0.569389	+	0.750607i	−0.0260979	+	0.0344040i
$477$		0			0
$478$	−10.0572	−	8.66102i	−0.460004	−	0.396146i
$479$	3.25092	−	5.63076i	0.148538	−	0.257276i	−0.782149	−	0.623091i	$-0.785876\pi$
$479$	3.25092	−	5.63076i	0.148538	−	0.257276i	0.930687	+	0.365815i	$0.119210\pi$
$480$		0			0
$481$	−3.63482	+	2.09856i	−0.165733	+	0.0956863i
$482$	−12.0803	+	4.22234i	−0.550241	+	0.192322i
$483$		0			0
$484$	−12.5219	+	9.97157i	−0.569176	+	0.453253i
$485$	−18.1945	−	31.5138i	−0.826170	−	1.43097i
$486$		0			0
$487$	−11.9555	−	6.90251i	−0.541755	−	0.312783i	0.204035	−	0.978964i	$-0.434594\pi$
$487$	−11.9555	−	6.90251i	−0.541755	−	0.312783i	−0.745790	+	0.666181i	$0.767928\pi$
$488$	2.16721	+	0.0833654i	0.0981051	+	0.00377378i
$489$		0			0
$490$	−27.5650	+	30.4396i	−1.24526	+	1.37512i
$491$			6.08856i			0.274773i	0.990518	+	0.137386i	$0.0438702\pi$
$491$			6.08856i			0.274773i	−0.990518	+	0.137386i	$0.956130\pi$
$492$		0			0
$493$	−0.952383	−	0.549859i	−0.0428932	−	0.0247644i
$494$	−7.80229	+	41.1574i	−0.351042	+	1.85176i
$495$		0			0
$496$	−1.66803	+	7.26134i	−0.0748968	+	0.326044i
$497$	−2.41718	+	8.59117i	−0.108425	+	0.385367i
$498$		0			0
$499$	−8.00880	+	4.62388i	−0.358523	+	0.206993i	−0.668433	−	0.743773i	$-0.733035\pi$
$499$	−8.00880	+	4.62388i	−0.358523	+	0.206993i	0.309910	+	0.950766i	$0.399701\pi$
$500$	59.1407	−	8.87178i	2.64485	−	0.396758i
$501$		0			0
$502$	−14.5931	+	16.9455i	−0.651323	+	0.756317i
$503$	32.9505			1.46919			0.734596	−	0.678505i	$-0.237372\pi$
$503$	32.9505			1.46919			0.734596	+	0.678505i	$0.237372\pi$
$504$		0			0
$505$	35.2507			1.56864
$506$	−8.78363	+	10.1996i	−0.390480	+	0.453426i
$507$		0			0
$508$	6.02807	−	0.904280i	0.267453	−	0.0401209i
$509$	−29.0117	+	16.7499i	−1.28592	+	0.742426i	−0.977924	−	0.208962i	$-0.932992\pi$
$509$	−29.0117	+	16.7499i	−1.28592	+	0.742426i	−0.307996	+	0.951388i	$0.599658\pi$
$510$		0			0
$511$	−21.7296	−	22.2782i	−0.961259	−	0.985530i
$512$	2.60413	−	22.4771i	0.115088	−	0.993355i
$513$		0			0
$514$	1.10700	−	5.83947i	0.0488277	−	0.257568i
$515$	42.1767	+	24.3507i	1.85853	+	1.07302i
$516$		0			0
$517$			17.5960i			0.773872i
$518$	2.33903	+	1.16358i	0.102771	+	0.0511246i
$519$		0			0
$520$	−2.71107	+	70.4785i	−0.118888	+	3.09069i
$521$	25.3738	+	14.6496i	1.11165	+	0.641809i	0.939255	−	0.343220i	$-0.111517\pi$
$521$	25.3738	+	14.6496i	1.11165	+	0.641809i	0.172391	+	0.985029i	$0.444851\pi$
$522$		0			0
$523$	−9.05856	−	15.6899i	−0.396103	−	0.686071i	0.597138	−	0.802138i	$-0.296304\pi$
$523$	−9.05856	−	15.6899i	−0.396103	−	0.686071i	−0.993241	+	0.116068i	$0.962971\pi$
$524$	19.4229	−	15.4671i	0.848493	−	0.675681i
$525$		0			0
$526$	20.9331	−	7.31660i	0.912726	−	0.319019i
$527$	−0.287202	+	0.165816i	−0.0125107	+	0.00722306i
$528$		0			0
$529$	3.61667	−	6.26426i	0.157247	−	0.272359i
$530$	−20.5449	−	17.6928i	−0.892414	−	0.768527i
$531$		0			0
$532$	24.0339	−	10.1114i	1.04200	−	0.438384i
$533$	19.2077			0.831976
$534$		0			0
$535$	−8.67522	+	15.0259i	−0.375062	+	0.649627i
$536$	4.39765	+	8.34191i	0.189950	+	0.360315i
$537$		0			0
$538$	9.69823	−	3.38976i	0.418120	−	0.146143i
$539$	5.79505	+	10.6415i	0.249610	+	0.458362i
$540$		0			0
$541$	0.875255	+	1.51599i	0.0376301	+	0.0651773i	0.884227	−	0.467057i	$-0.154686\pi$
$541$	0.875255	+	1.51599i	0.0376301	+	0.0651773i	−0.846597	+	0.532235i	$0.821352\pi$
$542$	37.6551	+	7.13836i	1.61743	+	0.306619i
$543$		0			0
$544$	0.811420	−	0.596669i	0.0347893	−	0.0255820i
$545$			55.3476i			2.37083i
$546$		0			0
$547$			9.83793i			0.420639i	0.977633	+	0.210320i	$0.0674505\pi$
$547$			9.83793i			0.420639i	−0.977633	+	0.210320i	$0.932549\pi$
$548$	−24.6463	−	9.69283i	−1.05284	−	0.414057i
$549$		0			0
$550$	5.56637	−	29.3628i	0.237351	−	1.25203i
$551$	15.2178	+	26.3580i	0.648300	+	1.12289i
$552$		0			0
$553$	−25.9251	+	6.60133i	−1.10245	+	0.280717i
$554$	6.69303	+	19.1490i	0.284359	+	0.813564i
$555$		0			0
$556$	−3.42668	−	22.8428i	−0.145324	−	0.968752i
$557$	14.1857	−	24.5703i	0.601066	−	1.04108i	−0.391594	−	0.920138i	$-0.628076\pi$
$557$	14.1857	−	24.5703i	0.601066	−	1.04108i	0.992660	−	0.120939i	$-0.0385906\pi$
$558$		0			0
$559$	−12.4991			−0.528654
$560$	37.4924	−	22.8392i	1.58434	−	0.965134i
$561$		0			0
$562$	18.2392	−	21.1794i	0.769374	−	0.893398i
$563$	−7.18586	+	12.4463i	−0.302848	+	0.524548i	−0.976780	−	0.214245i	$-0.931271\pi$
$563$	−7.18586	+	12.4463i	−0.302848	+	0.524548i	0.673932	+	0.738794i	$0.264604\pi$
$564$		0			0
$565$	8.79897	−	5.08009i	0.370176	−	0.213721i
$566$	3.28256	+	9.39155i	0.137976	+	0.394756i
$567$		0			0
$568$	5.08455	−	8.07323i	0.213343	−	0.338745i
$569$	15.1308	+	26.2074i	0.634318	+	1.09867i	0.986659	+	0.162799i	$0.0520523\pi$
$569$	15.1308	+	26.2074i	0.634318	+	1.09867i	−0.352341	+	0.935872i	$0.614614\pi$
$570$		0			0
$571$	−16.7991	−	9.69895i	−0.703020	−	0.405889i	0.105451	−	0.994424i	$-0.466371\pi$
$571$	−16.7991	−	9.69895i	−0.703020	−	0.405889i	−0.808471	+	0.588536i	$0.799705\pi$
$572$	19.3673	+	7.61671i	0.809787	+	0.318471i
$573$		0			0
$574$	−6.60769	−	9.96370i	−0.275800	−	0.415877i
$575$			67.1262i			2.79936i
$576$		0			0
$577$	−11.0229	−	6.36408i	−0.458889	−	0.264940i	0.252688	−	0.967548i	$-0.418685\pi$
$577$	−11.0229	−	6.36408i	−0.458889	−	0.264940i	−0.711577	+	0.702608i	$0.752019\pi$
$578$	−23.5769	−	4.46952i	−0.980669	−	0.185907i
$579$		0			0
$580$	31.9222	+	40.0866i	1.32550	+	1.66451i
$581$	−37.5985	−	10.5786i	−1.55985	−	0.438874i
$582$		0			0
$583$	−6.92838	+	4.00010i	−0.286944	+	0.165667i
$584$	15.5149	+	29.4302i	0.642011	+	1.21783i
$585$		0			0
$586$	1.86272	+	1.60414i	0.0769484	+	0.0662662i
$587$	−39.1658			−1.61654			−0.808272	−	0.588809i	$-0.799597\pi$
$587$	−39.1658			−1.61654			−0.808272	+	0.588809i	$0.799597\pi$
$588$		0			0
$589$	9.17819			0.378181
$590$	−2.96215	−	2.55094i	−0.121950	−	0.105020i
$591$		0			0
$592$	−2.04464	−	1.90247i	−0.0840342	−	0.0781911i
$593$	−24.8266	+	14.3336i	−1.01951	+	0.588612i	−0.913961	−	0.405802i	$-0.866992\pi$
$593$	−24.8266	+	14.3336i	−1.01951	+	0.588612i	−0.105545	+	0.994414i	$0.533659\pi$
$594$		0			0
$595$	1.88107	+	0.529252i	0.0771165	+	0.0216972i
$596$	7.35988	−	5.86090i	0.301472	−	0.240072i
$597$		0			0
$598$	−45.9259	−	8.70626i	−1.87805	−	0.356026i
$599$	−34.1681	−	19.7270i	−1.39607	−	0.806023i	−0.402094	−	0.915599i	$-0.631717\pi$
$599$	−34.1681	−	19.7270i	−1.39607	−	0.806023i	−0.993978	+	0.109576i	$0.965051\pi$
$600$		0			0
$601$		−	17.8483i		−	0.728047i	−0.931390	−	0.364023i	$-0.881403\pi$
$601$		−	17.8483i		−	0.728047i	0.931390	−	0.364023i	$-0.118597\pi$
$602$	4.29985	+	6.48372i	0.175249	+	0.264257i
$603$		0			0
$604$	3.69846	−	9.40421i	0.150488	−	0.382652i
$605$	28.7529	+	16.6005i	1.16897	+	0.674907i
$606$		0			0
$607$	2.21465	+	3.83589i	0.0898900	+	0.155694i	0.907464	−	0.420129i	$-0.138015\pi$
$607$	2.21465	+	3.83589i	0.0898900	+	0.155694i	−0.817574	+	0.575823i	$0.804682\pi$
$608$	−27.7047	+	3.07259i	−1.12358	+	0.124610i
$609$		0			0
$610$	−1.48425	−	4.24650i	−0.0600955	−	0.171936i
$611$	−52.9189	+	30.5527i	−2.14087	+	1.23603i
$612$		0			0
$613$	4.37852	−	7.58382i	0.176847	−	0.306307i	−0.763952	−	0.645273i	$-0.776744\pi$
$613$	4.37852	−	7.58382i	0.176847	−	0.306307i	0.940799	+	0.338966i	$0.110077\pi$
$614$	−9.59554	+	11.1424i	−0.387245	+	0.449669i
$615$		0			0
$616$	−2.71154	−	12.6668i	−0.109251	−	0.510358i
$617$	38.2445			1.53966			0.769832	−	0.638247i	$-0.220340\pi$
$617$	38.2445			1.53966			0.769832	+	0.638247i	$0.220340\pi$
$618$		0			0
$619$	−6.47648	+	11.2176i	−0.260312	+	0.450873i	−0.966325	−	0.257326i	$-0.917159\pi$
$619$	−6.47648	+	11.2176i	−0.260312	+	0.450873i	0.706013	+	0.708199i	$0.250492\pi$
$620$	15.2823	−	2.29251i	0.613750	−	0.0920696i
$621$		0			0
$622$	11.8174	+	33.8100i	0.473834	+	1.35566i
$623$	27.2267	−	6.93277i	1.09082	−	0.277756i
$624$		0			0
$625$	−31.4988	−	54.5575i	−1.25995	−	2.18230i
$626$	8.33410	−	43.9627i	0.333098	−	1.75710i
$627$		0			0
$628$	3.07972	−	7.83091i	0.122894	−	0.312487i
$629$		−	0.124314i		−	0.00495671i
$630$		0			0
$631$		−	34.9294i		−	1.39052i	−0.718759	−	0.695259i	$-0.755290\pi$
$631$		−	34.9294i		−	1.39052i	0.718759	−	0.695259i	$-0.244710\pi$
$632$	28.5783	+	1.09931i	1.13678	+	0.0437283i
$633$		0			0
$634$	−16.1927	−	3.06968i	−0.643093	−	0.121912i
$635$	−6.32146	−	10.9491i	−0.250860	−	0.434502i
$636$		0			0
$637$	−21.9414	+	35.9055i	−0.869351	+	1.42263i
$638$	14.2736	−	4.98897i	0.565099	−	0.197515i
$639$		0			0
$640$	−45.3627	+	12.0361i	−1.79312	+	0.475769i
$641$	−12.2786	+	21.2671i	−0.484974	+	0.840000i	−0.999851	−	0.0172641i	$-0.994504\pi$
$641$	−12.2786	+	21.2671i	−0.484974	+	0.840000i	0.514877	+	0.857264i	$0.327838\pi$
$642$		0			0
$643$	−12.7388			−0.502371			−0.251186	−	0.967939i	$-0.580820\pi$
$643$	−12.7388			−0.502371			−0.251186	+	0.967939i	$0.580820\pi$
$644$	11.2829	+	26.8185i	0.444608	+	1.05680i
$645$		0			0
$646$	−0.940166	−	0.809650i	−0.0369903	−	0.0318552i
$647$	1.84146	−	3.18950i	0.0723952	−	0.125392i	−0.827555	−	0.561384i	$-0.810269\pi$
$647$	1.84146	−	3.18950i	0.0723952	−	0.125392i	0.899951	+	0.435992i	$0.143602\pi$
$648$		0			0
$649$	−0.998928	+	0.576731i	−0.0392114	+	0.0226387i
$650$	97.9719	−	34.2434i	3.84277	−	1.34314i
$651$		0			0
$652$	−19.4812	−	24.4638i	−0.762945	−	0.958074i
$653$	−2.81401	−	4.87402i	−0.110121	−	0.190735i	0.805698	−	0.592327i	$-0.201790\pi$
$653$	−2.81401	−	4.87402i	−0.110121	−	0.190735i	−0.915819	+	0.401592i	$0.868457\pi$
$654$		0			0
$655$	−44.5991	−	25.7493i	−1.74263	−	1.00611i
$656$	3.75023	+	12.2185i	0.146422	+	0.477053i
$657$		0			0
$658$	34.0536	+	16.9404i	1.32755	+	0.660404i
$659$		−	37.2731i		−	1.45196i	−0.687718	−	0.725978i	$-0.741388\pi$
$659$		−	37.2731i		−	1.45196i	0.687718	−	0.725978i	$-0.258612\pi$
$660$		0			0
$661$	−11.8737	−	6.85527i	−0.461833	−	0.266639i	0.250982	−	0.967992i	$-0.419247\pi$
$661$	−11.8737	−	6.85527i	−0.461833	−	0.266639i	−0.712815	+	0.701353i	$0.752580\pi$
$662$	−5.40114	+	28.4912i	−0.209921	+	1.10734i
$663$		0			0
$664$	35.3318	+	22.2521i	1.37114	+	0.863550i
$665$	−37.7618	−	38.7152i	−1.46434	−	1.50131i
$666$		0			0
$667$	−29.4118	+	16.9809i	−1.13883	+	0.657503i
$668$	−0.707570	−	4.71677i	−0.0273767	−	0.182497i
$669$		0			0
$670$	12.7635	−	14.8209i	0.493095	−	0.572582i
$671$	−1.32733			−0.0512409
$672$		0			0
$673$	−34.8824			−1.34462			−0.672310	−	0.740270i	$-0.734698\pi$
$673$	−34.8824			−1.34462			−0.672310	+	0.740270i	$0.734698\pi$
$674$	−19.4951	+	22.6377i	−0.750922	+	0.871971i
$675$		0			0
$676$	6.86433	+	45.7587i	0.264013	+	1.75995i
$677$	−21.5264	+	12.4283i	−0.827327	+	0.477657i	−0.852936	−	0.522015i	$-0.825181\pi$
$677$	−21.5264	+	12.4283i	−0.827327	+	0.477657i	0.0256098	+	0.999672i	$0.491847\pi$
$678$		0			0
$679$	−6.28588	+	22.3413i	−0.241230	+	0.857382i
$680$	−1.76767	−	1.11328i	−0.0677870	−	0.0426925i
$681$		0			0
$682$	0.849271	−	4.47994i	0.0325203	−	0.171546i
$683$	23.5666	+	13.6062i	0.901750	+	0.520626i	0.877768	−	0.479087i	$-0.159032\pi$
$683$	23.5666	+	13.6062i	0.901750	+	0.520626i	0.0239824	+	0.999712i	$0.492365\pi$
$684$		0			0
$685$			54.9309i			2.09880i
$686$	26.1736	−	0.970182i	0.999314	−	0.0370417i
$687$		0			0
$688$	−2.44040	−	7.95100i	−0.0930394	−	0.303129i
$689$	−24.0601	−	13.8911i	−0.916616	−	0.529208i
$690$		0			0
$691$	−0.920566	−	1.59447i	−0.0350200	−	0.0606564i	0.847984	−	0.530022i	$-0.177816\pi$
$691$	−0.920566	−	1.59447i	−0.0350200	−	0.0606564i	−0.883004	+	0.469365i	$0.844483\pi$
$692$	−18.1337	−	22.7716i	−0.689341	−	0.865646i
$693$		0			0
$694$	31.2165	−	10.9109i	1.18496	−	0.414172i
$695$	−41.4906	+	23.9546i	−1.57383	+	0.908650i
$696$		0			0
$697$	−0.284454	+	0.492688i	−0.0107744	+	0.0186619i
$698$	−32.8100	−	28.2552i	−1.24188	−	1.06948i
$699$		0			0
$700$	−51.4669	−	39.0413i	−1.94527	−	1.47562i
$701$	−34.4094			−1.29963			−0.649813	−	0.760094i	$-0.725153\pi$
$701$	−34.4094			−1.29963			−0.649813	+	0.760094i	$0.725153\pi$
$702$		0			0
$703$	−1.72024	+	2.97955i	−0.0648802	+	0.112376i
$704$	−1.06381	+	13.8072i	−0.0400938	+	0.520378i
$705$		0			0
$706$	−21.0994	+	7.37472i	−0.794085	+	0.277551i
$707$	−15.6983	−	16.0947i	−0.590396	−	0.605303i
$708$		0			0
$709$	9.68753	+	16.7793i	0.363823	+	0.630160i	0.988587	−	0.150654i	$-0.0481380\pi$
$709$	9.68753	+	16.7793i	0.363823	+	0.630160i	−0.624764	+	0.780814i	$0.714805\pi$
$710$	−19.4429	−	3.68583i	−0.729680	−	0.138327i
$711$		0			0
$712$	−30.0132	−	1.15451i	−1.12479	−	0.0432670i
$713$			10.2416i			0.383550i
$714$		0			0
$715$		−	43.1652i		−	1.61429i
$716$	4.57512	−	11.6333i	0.170980	−	0.434758i
$717$		0			0
$718$	4.84424	−	25.5536i	0.180786	−	0.953651i
$719$	−13.2505	−	22.9505i	−0.494160	−	0.855910i	0.505817	−	0.862641i	$-0.331191\pi$
$719$	−13.2505	−	22.9505i	−0.494160	−	0.855910i	−0.999977	+	0.00673050i	$0.997858\pi$
$720$		0			0
$721$	−7.66468	−	30.1011i	−0.285447	−	1.12102i
$722$	2.46424	+	7.05028i	0.0917094	+	0.262384i
$723$		0			0
$724$	10.0335	−	1.50514i	0.372893	−	0.0559382i
$725$	37.7022	−	65.3021i	1.40022	−	2.42526i
$726$		0			0
$727$	−29.5400			−1.09558			−0.547788	−	0.836617i	$-0.684530\pi$
$727$	−29.5400			−1.09558			−0.547788	+	0.836617i	$0.684530\pi$
$728$	33.3863	−	30.1486i	1.23738	−	1.11738i
$729$		0			0
$730$	45.0294	−	52.2882i	1.66661	−	1.93527i
$731$	0.185104	−	0.320609i	0.00684630	−	0.0118581i
$732$		0			0
$733$	3.29938	−	1.90490i	0.121865	−	0.0703589i	−0.437828	−	0.899059i	$-0.644252\pi$
$733$	3.29938	−	1.90490i	0.121865	−	0.0703589i	0.559694	+	0.828700i	$0.310919\pi$
$734$	−0.608314	−	1.74041i	−0.0224533	−	0.0642398i
$735$		0			0
$736$	−3.42858	−	30.9146i	−0.126379	−	1.13953i
$737$	−2.88564	−	4.99807i	−0.106294	−	0.184106i
$738$		0			0
$739$	30.2459	+	17.4625i	1.11261	+	0.642367i	0.939505	−	0.342536i	$-0.111286\pi$
$739$	30.2459	+	17.4625i	1.11261	+	0.642367i	0.173107	+	0.984903i	$0.444619\pi$
$740$	−2.12008	+	5.39081i	−0.0779359	+	0.198170i
$741$		0			0
$742$	1.07118	+	17.2595i	0.0393244	+	0.633618i
$743$			33.8918i			1.24337i	0.783267	+	0.621685i	$0.213552\pi$
$743$			33.8918i			1.24337i	−0.783267	+	0.621685i	$0.786448\pi$
$744$		0			0
$745$	−16.8999	−	9.75714i	−0.619163	−	0.357474i
$746$	6.27748	+	1.19004i	0.229835	+	0.0435703i
$747$		0			0
$748$	−0.482191	+	0.383984i	−0.0176306	+	0.0140398i
$749$	10.7239	−	2.73063i	0.391841	−	0.0997750i
$750$		0			0
$751$	32.2321	−	18.6092i	1.17617	−	0.679059i	0.221041	−	0.975265i	$-0.429055\pi$
$751$	32.2321	−	18.6092i	1.17617	−	0.679059i	0.955124	+	0.296205i	$0.0957212\pi$
$752$	−29.7677	−	27.6978i	−1.08552	−	1.01004i
$753$		0			0
$754$	39.7879	+	34.2645i	1.44899	+	1.24784i
$755$	−20.9598			−0.762806
$756$		0			0
$757$	−10.2595			−0.372888			−0.186444	−	0.982466i	$-0.559696\pi$
$757$	−10.2595			−0.372888			−0.186444	+	0.982466i	$0.559696\pi$
$758$	1.72777	+	1.48792i	0.0627556	+	0.0540437i
$759$		0			0
$760$	26.9619	+	51.1440i	0.978010	+	1.85519i
$761$	21.1777	−	12.2270i	0.767693	−	0.443227i	−0.0643583	−	0.997927i	$-0.520500\pi$
$761$	21.1777	−	12.2270i	0.767693	−	0.443227i	0.832051	+	0.554699i	$0.187167\pi$
$762$		0			0
$763$	25.2705	−	24.6481i	0.914853	−	0.892322i
$764$	−31.2471	−	39.2389i	−1.13048	−	1.41961i
$765$		0			0
$766$	13.3750	+	2.53553i	0.483259	+	0.0916123i
$767$	−3.46896	−	2.00281i	−0.125257	−	0.0723172i
$768$		0			0
$769$		−	2.46179i		−	0.0887745i	−0.999014	−	0.0443873i	$-0.985866\pi$
$769$		−	2.46179i		−	0.0887745i	0.999014	−	0.0443873i	$-0.0141335\pi$
$770$	−22.3913	+	14.8494i	−0.806928	+	0.535136i
$771$		0			0
$772$	−25.1528	−	9.89204i	−0.905270	−	0.356022i
$773$	−29.2019	−	16.8597i	−1.05032	−	0.606403i	−0.127582	−	0.991828i	$-0.540721\pi$
$773$	−29.2019	−	16.8597i	−1.05032	−	0.606403i	−0.922739	+	0.385425i	$0.874055\pi$
$774$		0			0
$775$	−11.3695	−	19.6926i	−0.408405	−	0.707379i
$776$	13.2224	−	20.9944i	0.474656	−	0.753656i
$777$		0			0
$778$	−6.04015	−	17.2811i	−0.216550	−	0.619558i
$779$	13.6355	−	7.87249i	0.488544	−	0.282061i
$780$		0			0
$781$	−2.91956	+	5.05683i	−0.104470	+	0.180947i
$782$	0.903455	−	1.04909i	0.0323075	−	0.0375155i
$783$		0			0
$784$	−27.1245	−	6.94712i	−0.968732	−	0.248111i
$785$	−17.4533			−0.622935
$786$		0			0
$787$	11.3105	−	19.5903i	0.403175	−	0.698320i	−0.590932	−	0.806721i	$-0.701240\pi$
$787$	11.3105	−	19.5903i	0.403175	−	0.698320i	0.994107	+	0.108402i	$0.0345732\pi$
$788$	−0.991147	−	6.60715i	−0.0353082	−	0.235370i
$789$		0			0
$790$	−19.5723	−	55.9971i	−0.696350	−	1.99229i
$791$	−6.23793	−	1.75508i	−0.221795	−	0.0624035i
$792$		0			0
$793$	−2.30470	−	3.99185i	−0.0818422	−	0.141755i
$794$	−1.38781	+	7.32075i	−0.0492515	+	0.259804i
$795$		0			0
$796$	−16.4893	−	6.48488i	−0.584448	−	0.229850i
$797$			26.6015i			0.942274i	0.882060	+	0.471137i	$0.156156\pi$
$797$			26.6015i			0.942274i	−0.882060	+	0.471137i	$0.843844\pi$
$798$		0			0
$799$		−	1.80987i		−	0.0640285i
$800$	40.9119	+	55.6367i	1.44645	+	1.96705i
$801$		0			0
$802$	−47.0319	−	8.91593i	−1.66075	−	0.314832i
$803$	−10.1805	−	17.6332i	−0.359263	−	0.622261i
$804$		0			0
$805$	43.2007	−	42.1368i	1.52263	−	1.48513i
$806$	14.9478	−	5.22459i	0.526512	−	0.184028i
$807$		0			0
$808$	11.2086	+	21.2616i	0.394317	+	0.747979i
$809$	12.3077	−	21.3176i	0.432716	−	0.749486i	−0.564390	−	0.825508i	$-0.690889\pi$
$809$	12.3077	−	21.3176i	0.432716	−	0.749486i	0.997106	+	0.0760220i	$0.0242219\pi$
$810$		0			0
$811$	24.8680			0.873233			0.436616	−	0.899648i	$-0.356177\pi$
$811$	24.8680			0.873233			0.436616	+	0.899648i	$0.356177\pi$
$812$	4.08663	−	32.4269i	0.143413	−	1.13796i
$813$		0			0
$814$	1.29516	+	1.11536i	0.0453954	+	0.0390935i
$815$	−32.4321	+	56.1740i	−1.13605	+	1.96769i
$816$		0			0
$817$	−8.87311	+	5.12289i	−0.310431	+	0.179227i
$818$	30.3282	−	10.6004i	1.06040	−	0.370635i
$819$		0			0
$820$	20.7377	−	16.5140i	0.724191	−	0.576696i
$821$	−8.06054	−	13.9613i	−0.281315	−	0.487251i	0.690394	−	0.723433i	$-0.257437\pi$
$821$	−8.06054	−	13.9613i	−0.281315	−	0.487251i	−0.971709	+	0.236182i	$0.924104\pi$
$822$		0			0
$823$	46.5647	+	26.8842i	1.62315	+	0.937123i	0.986072	+	0.166320i	$0.0531884\pi$
$823$	46.5647	+	26.8842i	1.62315	+	0.937123i	0.637073	+	0.770803i	$0.280145\pi$
$824$	−1.27639	+	33.1817i	−0.0444651	+	1.15594i
$825$		0			0
$826$	0.154442	+	2.48847i	0.00537374	+	0.0865849i
$827$		−	6.06391i		−	0.210863i	−0.994427	−	0.105431i	$-0.966378\pi$
$827$		−	6.06391i		−	0.210863i	0.994427	−	0.105431i	$-0.0336224\pi$
$828$		0			0
$829$	−14.6273	−	8.44507i	−0.508027	−	0.293309i	0.223995	−	0.974590i	$-0.428090\pi$
$829$	−14.6273	−	8.44507i	−0.508027	−	0.293309i	−0.732022	+	0.681281i	$0.761423\pi$
$830$	16.1307	−	85.0903i	0.559906	−	2.95353i
$831$		0			0
$832$	−43.3714	+	20.7747i	−1.50363	+	0.720233i
$833$	−0.596059	−	1.09455i	−0.0206522	−	0.0379239i
$834$		0			0
$835$	−8.56732	+	4.94634i	−0.296484	+	0.171175i
$836$	16.8707	−	2.53079i	0.583484	−	0.0875293i
$837$		0			0
$838$	6.15356	−	7.14552i	0.212571	−	0.246838i
$839$	−48.4902			−1.67407			−0.837034	−	0.547151i	$-0.815712\pi$
$839$	−48.4902			−1.67407			−0.837034	+	0.547151i	$0.815712\pi$
$840$		0			0
$841$	9.15010			0.315521
$842$	30.4161	−	35.3192i	1.04821	−	1.21718i
$843$		0			0
$844$	34.2539	−	5.13847i	1.17907	−	0.176874i
$845$	83.1139	−	47.9858i	2.85921	−	1.65076i
$846$		0			0
$847$	−5.22521	−	20.5207i	−0.179540	−	0.705100i
$848$	4.13886	−	18.0175i	0.142129	−	0.618722i
$849$		0			0
$850$	−0.572538	+	3.02016i	−0.0196379	+	0.103591i
$851$	−3.32476	−	1.91955i	−0.113971	−	0.0658013i
$852$		0			0
$853$			18.9879i			0.650134i	0.945691	+	0.325067i	$0.105387\pi$
$853$			18.9879i			0.650134i	−0.945691	+	0.325067i	$0.894613\pi$
$854$	−1.27787	+	2.56878i	−0.0437278	+	0.0879018i
$855$		0			0
$856$	−11.8214	−	0.454728i	−0.404046	−	0.0155423i
$857$	6.59722	+	3.80890i	0.225357	+	0.130110i	0.608428	−	0.793609i	$-0.291800\pi$
$857$	6.59722	+	3.80890i	0.225357	+	0.130110i	−0.383071	+	0.923719i	$0.625134\pi$
$858$		0			0
$859$	−0.495599	−	0.858403i	−0.0169096	−	0.0292883i	0.857447	−	0.514573i	$-0.172049\pi$
$859$	−0.495599	−	0.858403i	−0.0169096	−	0.0292883i	−0.874356	+	0.485284i	$0.838716\pi$
$860$	−13.4947	+	10.7462i	−0.460165	+	0.366444i
$861$		0			0
$862$	−28.6829	+	10.0253i	−0.976943	+	0.341464i
$863$	17.0912	−	9.86760i	0.581791	−	0.335897i	−0.180054	−	0.983657i	$-0.557627\pi$
$863$	17.0912	−	9.86760i	0.581791	−	0.335897i	0.761845	+	0.647760i	$0.224294\pi$
$864$		0			0
$865$	−30.1887	+	52.2884i	−1.02645	+	1.77786i
$866$	−30.2131	−	26.0189i	−1.02668	−	0.884157i
$867$		0			0
$868$	−7.85241	−	5.95661i	−0.266528	−	0.202180i
$869$	−17.5030			−0.593749
$870$		0			0
$871$	10.0209	−	17.3567i	0.339546	−	0.588111i
$872$	−33.3831	+	17.5987i	−1.13049	+	0.595969i
$873$		0			0
$874$	−36.1712	+	12.6427i	−1.22351	+	0.427645i
$875$	−21.4265	+	76.1543i	−0.724348	+	2.57449i
$876$		0			0
$877$	20.8444	+	36.1036i	0.703867	+	1.21913i	0.967099	+	0.254401i	$0.0818782\pi$
$877$	20.8444	+	36.1036i	0.703867	+	1.21913i	−0.263232	+	0.964733i	$0.584788\pi$
$878$	39.5959	+	7.50628i	1.33630	+	0.253325i
$879$		0			0
$880$	27.4586	−	8.42785i	0.925628	−	0.284103i
$881$		−	47.6235i		−	1.60447i	−0.597005	−	0.802237i	$-0.703643\pi$
$881$		−	47.6235i		−	1.60447i	0.597005	−	0.802237i	$-0.296357\pi$
$882$		0			0
$883$			1.25827i			0.0423441i	0.999776	+	0.0211721i	$0.00673978\pi$
$883$			1.25827i			0.0423441i	−0.999776	+	0.0211721i	$0.993260\pi$
$884$	−1.99205	−	0.783430i	−0.0670000	−	0.0263496i
$885$		0			0
$886$	−6.78345	+	35.7830i	−0.227895	+	1.20215i
$887$	24.0985	+	41.7398i	0.809148	+	1.40148i	0.913455	+	0.406940i	$0.133404\pi$
$887$	24.0985	+	41.7398i	0.809148	+	1.40148i	−0.104307	+	0.994545i	$0.533263\pi$
$888$		0			0
$889$	−2.18396	+	7.76223i	−0.0732475	+	0.260337i
$890$	20.5550	+	58.8086i	0.689005	+	1.97127i
$891$		0			0
$892$	5.37414	+	35.8249i	0.179939	+	1.19950i
$893$	−25.0448	+	43.3789i	−0.838092	+	1.45162i
$894$		0			0
$895$	−25.9280			−0.866677
$896$	25.6969	+	15.3515i	0.858474	+	0.512858i
$897$		0			0
$898$	15.6981	−	18.2287i	0.523853	−	0.608298i
$899$	5.75229	−	9.96327i	0.191850	−	0.332294i
$900$		0			0
$901$	0.712630	−	0.411437i	0.0237411	−	0.0137070i
$902$	−2.58090	−	7.38406i	−0.0859346	−	0.245862i
$903$		0			0
$904$	5.86186	+	3.69182i	0.194962	+	0.122788i
$905$	−10.5219	−	18.2244i	−0.349758	−	0.605799i
$906$		0			0
$907$	44.9075	+	25.9274i	1.49113	+	0.860904i	0.999948	−	0.0101533i	$-0.00323196\pi$
$907$	44.9075	+	25.9274i	1.49113	+	0.860904i	0.491181	+	0.871057i	$0.336565\pi$
$908$	−51.1262	−	20.1068i	−1.69668	−	0.667267i
$909$		0			0
$910$	−83.5376	−	41.5568i	−2.76925	−	1.37759i
$911$			0.471351i			0.0156166i	0.999970	+	0.00780828i	$0.00248548\pi$
$911$			0.471351i			0.0156166i	−0.999970	+	0.00780828i	$0.997515\pi$
$912$		0			0
$913$	−22.1308	−	12.7772i	−0.732422	−	0.422864i
$914$	6.00058	+	1.13754i	0.198481	+	0.0376265i
$915$		0			0
$916$	−6.86334	−	8.61870i	−0.226771	−	0.284770i
$917$	8.10490	+	31.8300i	0.267647	+	1.05112i
$918$		0			0
$919$	22.0115	−	12.7083i	0.726092	−	0.419210i	−0.0908987	−	0.995860i	$-0.528974\pi$
$919$	22.0115	−	12.7083i	0.726092	−	0.419210i	0.816991	+	0.576651i	$0.195641\pi$
$920$	−57.0695	+	30.0856i	−1.88153	+	0.991894i
$921$		0			0
$922$	−22.2379	−	19.1508i	−0.732366	−	0.630697i
$923$	−20.2774			−0.667440
$924$		0			0
$925$	8.52383			0.280262
$926$	33.2332	+	28.6197i	1.09211	+	0.940501i
$927$		0			0
$928$	−14.0281	+	32.0002i	−0.460496	+	1.05046i
$929$	36.9737	−	21.3468i	1.21307	−	0.700365i	0.249641	−	0.968338i	$-0.419687\pi$
$929$	36.9737	−	21.3468i	1.21307	−	0.700365i	0.963426	+	0.267974i	$0.0863540\pi$
$930$		0			0
$931$	−0.859946	+	34.4823i	−0.0281836	+	1.13011i
$932$	16.9847	−	13.5255i	0.556354	−	0.443042i
$933$		0			0
$934$	3.38923	+	0.642502i	0.110899	+	0.0210233i
$935$	1.10721	+	0.639250i	0.0362097	+	0.0209057i
$936$		0			0
$937$			16.2104i			0.529570i	0.964307	+	0.264785i	$0.0853010\pi$
$937$			16.2104i			0.529570i	−0.964307	+	0.264785i	$0.914699\pi$
$938$	−12.4509	+	0.772743i	−0.406536	+	0.0252310i
$939$		0			0
$940$	−30.8661	+	78.4842i	−1.00674	+	2.55987i
$941$	0.907906	+	0.524180i	0.0295969	+	0.0170878i	0.514725	−	0.857355i	$-0.327894\pi$
$941$	0.907906	+	0.524180i	0.0295969	+	0.0170878i	−0.485129	+	0.874443i	$0.661227\pi$
$942$		0			0
$943$	8.78459	+	15.2153i	0.286065	+	0.495480i
$944$	0.596738	−	2.59774i	0.0194222	−	0.0845494i
$945$		0			0
$946$	1.67948	+	4.80506i	0.0546046	+	0.156226i
$947$	1.37253	−	0.792428i	0.0446011	−	0.0257505i	−0.477534	−	0.878613i	$-0.658469\pi$
$947$	1.37253	−	0.792428i	0.0446011	−	0.0257505i	0.522135	+	0.852863i	$0.325136\pi$
$948$		0			0
$949$	35.3537	−	61.2345i	1.14763	−	1.98776i
$950$	55.5153	−	64.4644i	1.80115	−	2.09150i
$951$		0			0
$952$	0.278900	+	1.30286i	0.00903921	+	0.0422259i
$953$	21.8228			0.706910			0.353455	−	0.935451i	$-0.385007\pi$
$953$	21.8228			0.706910			0.353455	+	0.935451i	$0.385007\pi$
$954$		0			0
$955$	−52.0198	+	90.1009i	−1.68332	+	2.91560i
$956$	−18.5625	+	2.78459i	−0.600354	+	0.0900599i
$957$		0			0
$958$	−3.03388	−	8.68007i	−0.0980203	−	0.280440i
$959$	25.0802	−	24.4625i	0.809882	−	0.789937i
$960$		0			0
$961$	13.7653	+	23.8423i	0.444043	+	0.769105i
$962$	−1.10554	+	5.83177i	−0.0356440	+	0.188024i
$963$		0			0
$964$	−6.62355	+	16.8419i	−0.213330	+	0.542442i
$965$			56.0599i			1.80463i
$966$		0			0
$967$		−	25.8912i		−	0.832606i	−0.909226	−	0.416303i	$-0.863326\pi$
$967$		−	25.8912i		−	0.832606i	0.909226	−	0.416303i	$-0.136674\pi$
$968$	−0.870148	+	22.6208i	−0.0279676	+	0.727061i
$969$		0			0
$970$	−50.5613	−	9.58501i	−1.62343	−	0.307756i
$971$	−3.17896	−	5.50612i	−0.102018	−	0.176700i	0.810498	−	0.585741i	$-0.199197\pi$
$971$	−3.17896	−	5.50612i	−0.102018	−	0.176700i	−0.912516	+	0.409041i	$0.865863\pi$
$972$		0			0
$973$	29.4143	+	8.27590i	0.942978	+	0.265313i
$974$	−18.4299	+	6.44168i	−0.590533	+	0.206405i
$975$		0			0
$976$	2.08934	−	2.24548i	0.0668782	−	0.0718759i
$977$	−2.59617	+	4.49670i	−0.0830588	+	0.143862i	−0.904562	−	0.426341i	$-0.859802\pi$
$977$	−2.59617	+	4.49670i	−0.0830588	+	0.143862i	0.821504	+	0.570203i	$0.193136\pi$
$978$		0			0
$979$	18.3818			0.587486
$980$	7.18108	+	57.6301i	0.229391	+	1.84092i
$981$		0			0
$982$	6.52457	+	5.61882i	0.208207	+	0.179304i
$983$	−8.44158	+	14.6212i	−0.269245	+	0.466345i	−0.968667	−	0.248363i	$-0.920107\pi$
$983$	−8.44158	+	14.6212i	−0.269245	+	0.466345i	0.699422	+	0.714709i	$0.253441\pi$
$984$		0			0
$985$	−12.0009	+	6.92872i	−0.382380	+	0.220767i
$986$	−1.46814	+	0.513149i	−0.0467551	+	0.0163420i
$987$		0			0
$988$	36.9044	+	46.3431i	1.17409	+	1.47437i
$989$	−5.71643	−	9.90114i	−0.181772	−	0.314838i
$990$		0			0
$991$	35.9653	+	20.7646i	1.14247	+	0.659608i	0.947042	−	0.321109i	$-0.104056\pi$
$991$	35.9653	+	20.7646i	1.14247	+	0.659608i	0.195432	+	0.980717i	$0.437389\pi$
$992$	6.24200	+	8.48860i	0.198184	+	0.269513i
$993$		0			0
$994$	6.97571	+	10.5186i	0.221256	+	0.333631i
$995$			36.7509i			1.16508i
$996$		0			0
$997$	−16.3573	−	9.44391i	−0.518042	−	0.299092i	0.218091	−	0.975928i	$-0.430017\pi$
$997$	−16.3573	−	9.44391i	−0.518042	−	0.299092i	−0.736133	+	0.676837i	$0.763350\pi$
$998$	−2.43590	+	12.8495i	−0.0771071	+	0.406743i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bf.a.703.12	yes	32
3.2	odd	2	inner	756.2.bf.a.703.5	yes	32
4.3	odd	2		756.2.bf.d.703.2	yes	32
7.5	odd	6		756.2.bf.d.271.2	yes	32
12.11	even	2		756.2.bf.d.703.15	yes	32
21.5	even	6		756.2.bf.d.271.15	yes	32
28.19	even	6	inner	756.2.bf.a.271.12	yes	32
84.47	odd	6	inner	756.2.bf.a.271.5	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bf.a.271.5	✓	32	84.47	odd	6	inner
756.2.bf.a.271.12	yes	32	28.19	even	6	inner
756.2.bf.a.703.5	yes	32	3.2	odd	2	inner
756.2.bf.a.703.12	yes	32	1.1	even	1	trivial
756.2.bf.d.271.2	yes	32	7.5	odd	6
756.2.bf.d.271.15	yes	32	21.5	even	6
756.2.bf.d.703.2	yes	32	4.3	odd	2
756.2.bf.d.703.15	yes	32	12.11	even	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.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.922848 - 1.07161i) q^{2} +(-0.296703 - 1.97787i) q^{4} +(-3.59250 + 2.07413i) q^{5} +(2.54686 + 0.716577i) q^{7} +(-2.39332 - 1.50732i) q^{8} +O(q^{10})\)	\(q+(0.922848 - 1.07161i) q^{2} +(-0.296703 - 1.97787i) q^{4} +(-3.59250 + 2.07413i) q^{5} +(2.54686 + 0.716577i) q^{7} +(-2.39332 - 1.50732i) q^{8} +(-1.09267 + 5.76388i) q^{10} +(1.49910 + 0.865507i) q^{11} +6.01127i q^{13} +(3.11826 - 2.06796i) q^{14} +(-3.82393 + 1.17368i) q^{16} +(-0.154193 - 0.0890232i) q^{17} +(2.46379 + 4.26741i) q^{19} +(5.16827 + 6.49010i) q^{20} +(2.31093 - 0.807724i) q^{22} +(-4.76183 + 2.74924i) q^{23} +(6.10406 - 10.5725i) q^{25} +(6.44175 + 5.54749i) q^{26} +(0.661633 - 5.24998i) q^{28} +6.17658 q^{29} +(0.931308 - 1.61307i) q^{31} +(-2.27118 + 5.18090i) q^{32} +(-0.237695 + 0.0830798i) q^{34} +(-10.6359 + 2.70823i) q^{35} +(0.349105 + 0.604667i) q^{37} +(6.84671 + 1.29794i) q^{38} +(11.7244 + 0.450999i) q^{40} -3.19527i q^{41} +2.07927i q^{43} +(1.26707 - 3.22183i) q^{44} +(-1.44832 + 7.63996i) q^{46} +(5.08258 + 8.80328i) q^{47} +(5.97304 + 3.65005i) q^{49} +(-5.69654 - 16.2980i) q^{50} +(11.8895 - 1.78356i) q^{52} +(-2.31084 + 4.00249i) q^{53} -7.18071 q^{55} +(-5.01535 - 5.55394i) q^{56} +(5.70004 - 6.61889i) q^{58} +(-0.333175 + 0.577077i) q^{59} +(-0.664061 + 0.383396i) q^{61} +(-0.869132 - 2.48662i) q^{62} +(3.45596 + 7.21501i) q^{64} +(-12.4682 - 21.5955i) q^{65} +(-2.88737 - 1.66702i) q^{67} +(-0.130327 + 0.331386i) q^{68} +(-6.91315 + 13.8968i) q^{70} +3.37323i q^{71} +(-10.1866 - 5.88124i) q^{73} +(0.970139 + 0.183911i) q^{74} +(7.70937 - 6.13921i) q^{76} +(3.19781 + 3.27855i) q^{77} +(-8.75675 + 5.05571i) q^{79} +(11.3031 - 12.1478i) q^{80} +(-3.42409 - 2.94875i) q^{82} -14.7627 q^{83} +0.738584 q^{85} +(2.22817 + 1.91885i) q^{86} +(-2.28323 - 4.33107i) q^{88} +(9.19642 - 5.30955i) q^{89} +(-4.30754 + 15.3099i) q^{91} +(6.85049 + 8.60257i) q^{92} +(14.1241 + 2.67754i) q^{94} +(-17.7024 - 10.2205i) q^{95} +8.77209i q^{97} +(9.42364 - 3.03233i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{7}+O(q^{10}) \) 32 * q - 2 * q^7	\( 32 q - 2 q^{7} - 4 q^{10} - 28 q^{16} + 6 q^{19} + 20 q^{22} + 20 q^{25} + 28 q^{28} - 8 q^{34} - 2 q^{37} + 8 q^{40} - 12 q^{46} - 10 q^{49} + 20 q^{52} - 16 q^{55} + 40 q^{58} + 48 q^{64} - 42 q^{67} - 56 q^{70} - 18 q^{73} + 40 q^{76} + 6 q^{79} + 88 q^{82} - 8 q^{85} + 76 q^{88} - 8 q^{91} + 8 q^{94}+O(q^{100}) \) 32 * q - 2 * q^7 - 4 * q^10 - 28 * q^16 + 6 * q^19 + 20 * q^22 + 20 * q^25 + 28 * q^28 - 8 * q^34 - 2 * q^37 + 8 * q^40 - 12 * q^46 - 10 * q^49 + 20 * q^52 - 16 * q^55 + 40 * q^58 + 48 * q^64 - 42 * q^67 - 56 * q^70 - 18 * q^73 + 40 * q^76 + 6 * q^79 + 88 * q^82 - 8 * q^85 + 76 * q^88 - 8 * q^91 + 8 * q^94

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