LMFDB - Embedded newform 756.2.bf.d.271.15

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			271.15
Character	$\chi$	$=$	756.271
Dual form			756.2.bf.d.703.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38947 + 0.263404i) q^{2} +(1.86124 + 0.731982i) q^{4} +(3.59250 + 2.07413i) q^{5} +(-2.54686 + 0.716577i) q^{7} +(2.39332 + 1.50732i) q^{8} +O(q^{10})$	\(q+(1.38947 + 0.263404i) q^{2} +(1.86124 + 0.731982i) q^{4} +(3.59250 + 2.07413i) q^{5} +(-2.54686 + 0.716577i) q^{7} +(2.39332 + 1.50732i) q^{8} +(4.44533 + 3.82822i) q^{10} +(1.49910 - 0.865507i) q^{11} -6.01127i q^{13} +(-3.72753 + 0.324806i) q^{14} +(2.92840 + 2.72478i) q^{16} +(0.154193 - 0.0890232i) q^{17} +(-2.46379 + 4.26741i) q^{19} +(5.16827 + 6.49010i) q^{20} +(2.31093 - 0.807724i) q^{22} +(-4.76183 - 2.74924i) q^{23} +(6.10406 + 10.5725i) q^{25} +(1.58339 - 8.35246i) q^{26} +(-5.26484 - 0.530541i) q^{28} -6.17658 q^{29} +(-0.931308 - 1.61307i) q^{31} +(3.35120 + 4.55735i) q^{32} +(0.237695 - 0.0830798i) q^{34} +(-10.6359 - 2.70823i) q^{35} +(0.349105 - 0.604667i) q^{37} +(-4.54741 + 5.28045i) q^{38} +(5.47162 + 10.3791i) q^{40} -3.19527i q^{41} +2.07927i q^{43} +(3.42372 - 0.513597i) q^{44} +(-5.89224 - 5.07427i) q^{46} +(5.08258 - 8.80328i) q^{47} +(5.97304 - 3.65005i) q^{49} +(5.69654 + 16.2980i) q^{50} +(4.40014 - 11.1884i) q^{52} +(2.31084 + 4.00249i) q^{53} +7.18071 q^{55} +(-7.17557 - 2.12395i) q^{56} +(-8.58215 - 1.62694i) q^{58} +(-0.333175 - 0.577077i) q^{59} +(-0.664061 - 0.383396i) q^{61} +(-0.869132 - 2.48662i) q^{62} +(3.45596 + 7.21501i) q^{64} +(12.4682 - 21.5955i) q^{65} +(2.88737 - 1.66702i) q^{67} +(0.352153 - 0.0528269i) q^{68} +(-14.0649 - 6.56454i) q^{70} -3.37323i q^{71} +(-10.1866 + 5.88124i) q^{73} +(0.644342 - 0.748210i) q^{74} +(-7.70937 + 6.13921i) q^{76} +(-3.19781 + 3.27855i) q^{77} +(8.75675 + 5.05571i) q^{79} +(4.86874 + 15.8627i) q^{80} +(0.841648 - 4.43973i) q^{82} -14.7627 q^{83} +0.738584 q^{85} +(-0.547689 + 2.88908i) q^{86} +(4.89243 + 0.188195i) q^{88} +(-9.19642 - 5.30955i) q^{89} +(4.30754 + 15.3099i) q^{91} +(-6.85049 - 8.60257i) q^{92} +(9.38089 - 10.8931i) q^{94} +(-17.7024 + 10.2205i) q^{95} -8.77209i q^{97} +(9.26077 - 3.49830i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{7}+O(q^{10}) $ 32 * q + 2 * q^7	$ 32 q + 2 q^{7} + 4 q^{10} + 20 q^{16} - 6 q^{19} + 20 q^{22} + 20 q^{25} - 24 q^{28} + 8 q^{34} - 2 q^{37} + 52 q^{40} + 24 q^{46} - 10 q^{49} + 16 q^{52} + 16 q^{55} - 80 q^{58} + 48 q^{64} + 42 q^{67} + 32 q^{70} - 18 q^{73} - 40 q^{76} - 6 q^{79} + 8 q^{82} - 8 q^{85} - 80 q^{88} + 8 q^{91} - 8 q^{94}+O(q^{100}) $ 32 * q + 2 * q^7 + 4 * q^10 + 20 * q^16 - 6 * q^19 + 20 * q^22 + 20 * q^25 - 24 * q^28 + 8 * q^34 - 2 * q^37 + 52 * q^40 + 24 * q^46 - 10 * q^49 + 16 * q^52 + 16 * q^55 - 80 * q^58 + 48 * q^64 + 42 * q^67 + 32 * q^70 - 18 * q^73 - 40 * q^76 - 6 * q^79 + 8 * q^82 - 8 * q^85 - 80 * q^88 + 8 * q^91 - 8 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	1.38947	+	0.263404i	0.982501	+	0.186255i
$2$	1.38947	+	0.263404i	0.982501	+	0.186255i
$3$		0			0
$3$		0			0
$4$	1.86124	+	0.731982i	0.930618	+	0.365991i
$5$	3.59250	+	2.07413i	1.60662	+	0.927581i	0.990120	+	0.140224i	$0.0447821\pi$
$5$	3.59250	+	2.07413i	1.60662	+	0.927581i	0.616497	+	0.787357i	$0.288551\pi$
$6$		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
$10$	4.44533	+	3.82822i	1.40574	+	1.21059i
$11$	1.49910	−	0.865507i	0.451996	−	0.260960i	−0.256677	−	0.966497i	$-0.582627\pi$
$11$	1.49910	−	0.865507i	0.451996	−	0.260960i	0.708673	+	0.705537i	$0.249294\pi$
$12$		0			0
$13$		−	6.01127i		−	1.66723i	−0.552349	−	0.833613i	$-0.686268\pi$
$13$		−	6.01127i		−	1.66723i	0.552349	−	0.833613i	$-0.313732\pi$
$14$	−3.72753	+	0.324806i	−0.996225	+	0.0868079i
$15$		0			0
$16$	2.92840	+	2.72478i	0.732101	+	0.681196i
$17$	0.154193	−	0.0890232i	0.0373972	−	0.0215913i	−0.481185	−	0.876619i	$-0.659793\pi$
$17$	0.154193	−	0.0890232i	0.0373972	−	0.0215913i	0.518582	+	0.855028i	$0.326460\pi$
$18$		0			0
$19$	−2.46379	+	4.26741i	−0.565232	+	0.979011i	0.431796	+	0.901971i	$0.357880\pi$
$19$	−2.46379	+	4.26741i	−0.565232	+	0.979011i	−0.997028	+	0.0770395i	$0.975453\pi$
$20$	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	−0.0867671	−	0.996229i	$-0.527654\pi$
$23$	−4.76183	−	2.74924i	−0.992910	−	0.573257i	−0.906143	+	0.422972i	$0.860987\pi$
$24$		0			0
$25$	6.10406	+	10.5725i	1.22081	+	2.11451i
$26$	1.58339	−	8.35246i	0.310529	−	1.63805i
$27$		0			0
$28$	−5.26484	−	0.530541i	−0.994961	−	0.100263i
$29$	−6.17658			−1.14696			−0.573481	−	0.819219i	$-0.694407\pi$
$29$	−6.17658			−1.14696			−0.573481	+	0.819219i	$0.694407\pi$
$30$		0			0
$31$	−0.931308	−	1.61307i	−0.167268	−	0.289716i	0.770190	−	0.637814i	$-0.220161\pi$
$31$	−0.931308	−	1.61307i	−0.167268	−	0.289716i	−0.937458	+	0.348098i	$0.886828\pi$
$32$	3.35120	+	4.55735i	0.592414	+	0.805634i
$33$		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	−0.835902	−	0.548879i	$-0.815055\pi$
$37$	0.349105	−	0.604667i	0.0573925	−	0.0994067i	0.893294	+	0.449472i	$0.148388\pi$
$38$	−4.54741	+	5.28045i	−0.737687	+	0.856602i
$39$		0			0
$40$	5.47162	+	10.3791i	0.865140	+	1.64108i
$41$		−	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	$0.949320\pi$
$44$	3.42372	−	0.513597i	0.516145	−	0.0774277i
$45$		0			0
$46$	−5.89224	−	5.07427i	−0.868764	−	0.748160i
$47$	5.08258	−	8.80328i	0.741370	−	1.28409i	−0.210502	−	0.977593i	$-0.567510\pi$
$47$	5.08258	−	8.80328i	0.741370	−	1.28409i	0.951872	−	0.306497i	$-0.0991569\pi$
$48$		0			0
$49$	5.97304	−	3.65005i	0.853291	−	0.521435i
$50$	5.69654	+	16.2980i	0.805612	+	2.30489i
$51$		0			0
$52$	4.40014	−	11.1884i	0.610190	−	1.55155i
$53$	2.31084	+	4.00249i	0.317418	+	0.549785i	0.979949	−	0.199250i	$-0.0638507\pi$
$53$	2.31084	+	4.00249i	0.317418	+	0.549785i	−0.662530	+	0.749035i	$0.730517\pi$
$54$		0			0
$55$	7.18071			0.968247
$56$	−7.17557	−	2.12395i	−0.958876	−	0.283825i
$57$		0			0
$58$	−8.58215	−	1.62694i	−1.12689	−	0.213627i
$59$	−0.333175	−	0.577077i	−0.0433757	−	0.0751290i	0.843522	−	0.537094i	$-0.180478\pi$
$59$	−0.333175	−	0.577077i	−0.0433757	−	0.0751290i	−0.886898	+	0.461965i	$0.847145\pi$
$60$		0			0
$61$	−0.664061	−	0.383396i	−0.0850243	−	0.0490888i	0.456885	−	0.889526i	$-0.348965\pi$
$61$	−0.664061	−	0.383396i	−0.0850243	−	0.0490888i	−0.541909	+	0.840437i	$0.682298\pi$
$62$	−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	$-0.601383\pi$
$67$	2.88737	−	1.66702i	0.352748	−	0.203659i	0.665895	+	0.746046i	$0.268050\pi$
$68$	0.352153	−	0.0528269i	0.0427048	−	0.00640620i
$69$		0			0
$70$	−14.0649	−	6.56454i	−1.68107	−	0.784612i
$71$		−	3.37323i		−	0.400329i	−0.979762	−	0.200165i	$-0.935852\pi$
$71$		−	3.37323i		−	0.400329i	0.979762	−	0.200165i	$-0.0641477\pi$
$72$		0			0
$73$	−10.1866	+	5.88124i	−1.19225	+	0.688347i	−0.958817	−	0.284025i	$-0.908330\pi$
$73$	−10.1866	+	5.88124i	−1.19225	+	0.688347i	−0.233436	+	0.972372i	$0.574997\pi$
$74$	0.644342	−	0.748210i	0.0749032	−	0.0869776i
$75$		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	$-0.140737\pi$
$79$	8.75675	+	5.05571i	0.985211	+	0.568812i	0.0813719	+	0.996684i	$0.474070\pi$
$80$	4.86874	+	15.8627i	0.544341	+	1.77350i
$81$		0			0
$82$	0.841648	−	4.43973i	0.0929445	−	0.490286i
$83$	−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
$86$	−0.547689	+	2.88908i	−0.0590588	+	0.311538i
$87$		0			0
$88$	4.89243	+	0.188195i	0.521535	+	0.0200617i
$89$	−9.19642	−	5.30955i	−0.974818	−	0.562812i	−0.0741166	−	0.997250i	$-0.523614\pi$
$89$	−9.19642	−	5.30955i	−0.974818	−	0.562812i	−0.900702	+	0.434438i	$0.856947\pi$
$90$		0			0
$91$	4.30754	+	15.3099i	0.451553	+	1.60491i
$92$	−6.85049	−	8.60257i	−0.714213	−	0.896880i
$93$		0			0
$94$	9.38089	−	10.8931i	0.967565	−	1.12354i
$95$	−17.7024	+	10.2205i	−1.81622	+	1.04860i
$96$		0			0
$97$		−	8.77209i		−	0.890671i	−0.895364	−	0.445336i	$-0.853084\pi$
$97$		−	8.77209i		−	0.890671i	0.895364	−	0.445336i	$-0.146916\pi$
$98$	9.26077	−	3.49830i	0.935479	−	0.353382i
$99$		0			0
$100$	3.62219	+	24.1461i	0.362219	+	2.41461i
$101$	7.35922	−	4.24885i	0.732270	−	0.422776i	−0.0869822	−	0.996210i	$-0.527722\pi$
$101$	7.35922	−	4.24885i	0.732270	−	0.422776i	0.819252	+	0.573434i	$0.194389\pi$
$102$		0			0
$103$	5.87009	−	10.1673i	0.578397	−	1.00181i	−0.417266	−	0.908784i	$-0.637012\pi$
$103$	5.87009	−	10.1673i	0.578397	−	1.00181i	0.995663	−	0.0930291i	$-0.0296550\pi$
$104$	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	0.664761	−	0.747056i	$-0.268533\pi$
$107$	3.62222	+	2.09129i	0.350173	+	0.202172i	−0.314589	+	0.949228i	$0.601867\pi$
$108$		0			0
$109$	6.67117	+	11.5548i	0.638983	+	1.10675i	0.985656	+	0.168765i	$0.0539777\pi$
$109$	6.67117	+	11.5548i	0.638983	+	1.10675i	−0.346674	+	0.937986i	$0.612689\pi$
$110$	9.97736	+	1.89143i	0.951304	+	0.180341i
$111$		0			0
$112$	−9.41076	−	4.84123i	−0.889234	−	0.457453i
$113$	2.44926			0.230407			0.115203	−	0.993342i	$-0.463248\pi$
$113$	2.44926			0.230407			0.115203	+	0.993342i	$0.463248\pi$
$114$		0			0
$115$	−11.4046	−	19.7533i	−1.06348	−	1.84201i
$116$	−11.4961	−	4.52115i	−1.06738	−	0.419778i
$117$		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
$122$	−0.821703	−	0.707632i	−0.0743935	−	0.0640660i
$123$		0			0
$124$	−0.552644	−	3.68401i	−0.0496289	−	0.330834i
$125$			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	$0.956825\pi$
$128$	2.90148	+	10.9353i	0.256457	+	0.966556i
$129$		0			0
$130$	23.0125	−	26.7221i	2.01833	−	2.34368i
$131$	6.20725	−	10.7513i	0.542330	−	0.939342i	−0.456440	−	0.889754i	$-0.650876\pi$
$131$	6.20725	−	10.7513i	0.542330	−	0.939342i	0.998770	−	0.0495882i	$-0.0157909\pi$
$132$		0			0
$133$	3.21701	−	12.6340i	0.278950	−	1.09551i
$134$	4.45100	−	1.55573i	0.384508	−	0.134394i
$135$		0			0
$136$	0.503219	+	0.0193572i	0.0431507	+	0.00165986i
$137$	−6.62094	−	11.4678i	−0.565665	−	0.979761i	−0.996987	−	0.0775631i	$-0.975286\pi$
$137$	−6.62094	−	11.4678i	−0.565665	−	0.979761i	0.431322	−	0.902198i	$-0.358047\pi$
$138$		0			0
$139$	−11.5492			−0.979591			−0.489796	−	0.871837i	$-0.662929\pi$
$139$	−11.5492			−0.979591			−0.489796	+	0.871837i	$0.662929\pi$
$140$	−17.8135	−	12.8259i	−1.50552	−	1.08399i
$141$		0			0
$142$	0.888524	−	4.68700i	0.0745632	−	0.393324i
$143$	−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	$-0.895055\pi$
$149$	−2.35210	+	4.07396i	−0.192692	+	0.333751i	0.753450	+	0.657505i	$0.228388\pi$
$150$		0			0
$151$	−4.37574	+	2.52633i	−0.356092	+	0.205590i	−0.667365	−	0.744731i	$-0.732578\pi$
$151$	−4.37574	+	2.52633i	−0.356092	+	0.205590i	0.311273	+	0.950321i	$0.399245\pi$
$152$	−12.3290	+	6.49955i	−1.00001	+	0.527183i
$153$		0			0
$154$	−5.30683	+	3.71312i	−0.427637	+	0.299212i
$155$		−	7.72663i		−	0.620618i
$156$		0			0
$157$	3.64369	−	2.10369i	0.290798	−	0.167892i	−0.347504	−	0.937679i	$-0.612971\pi$
$157$	3.64369	−	2.10369i	0.290798	−	0.167892i	0.638302	+	0.769786i	$0.279637\pi$
$158$	10.8355	+	9.33131i	0.862028	+	0.742359i
$159$		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	$-0.543117\pi$
$163$	−13.5416	−	7.81822i	−1.06066	−	0.612371i	−0.925614	+	0.378469i	$0.876451\pi$
$164$	2.33888	−	5.94716i	0.182636	−	0.464395i
$165$		0			0
$166$	−20.5123	−	3.88855i	−1.59206	−	0.301810i
$167$	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
$170$	1.02624	+	0.194546i	0.0787089	+	0.0149210i
$171$		0			0
$172$	−1.52199	+	3.87002i	−0.116051	+	0.295086i
$173$	−12.6049	−	7.27743i	−0.958332	−	0.553293i	−0.0626725	−	0.998034i	$-0.519962\pi$
$173$	−12.6049	−	7.27743i	−0.958332	−	0.553293i	−0.895659	+	0.444741i	$0.853296\pi$
$174$		0			0
$175$	−23.1223	−	22.5528i	−1.74788	−	1.70483i
$176$	6.74830	+	1.55018i	0.508672	+	0.116849i
$177$		0			0
$178$	−11.3796	−	9.79982i	−0.852934	−	0.734528i
$179$	5.41293	−	3.12516i	0.404582	−	0.233585i	−0.283877	−	0.958861i	$-0.591621\pi$
$179$	5.41293	−	3.12516i	0.404582	−	0.233585i	0.688459	+	0.725275i	$0.258288\pi$
$180$		0			0
$181$		−	5.07289i		−	0.377065i	−0.982067	−	0.188533i	$-0.939627\pi$
$181$		−	5.07289i		−	0.377065i	0.982067	−	0.188533i	$-0.0603731\pi$
$182$	1.95249	+	22.4072i	0.144728	+	1.66093i
$183$		0			0
$184$	−7.25258	−	13.7574i	−0.534667	−	1.01421i
$185$	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	0.995972	+	0.0896693i	$0.0285810\pi$
$191$	21.7201	+	12.5401i	1.57161	+	0.907371i	0.575642	+	0.817702i	$0.304752\pi$
$192$		0			0
$193$	6.75702	+	11.7035i	0.486381	+	0.842437i	0.999877	−	0.0156550i	$-0.00498335\pi$
$193$	6.75702	+	11.7035i	0.486381	+	0.842437i	−0.513496	+	0.858092i	$0.671650\pi$
$194$	2.31061	−	12.1885i	0.165892	−	0.875086i
$195$		0			0
$196$	13.7890	−	2.42145i	0.984929	−	0.172961i
$197$	−3.34054			−0.238003			−0.119002	−	0.992894i	$-0.537969\pi$
$197$	−3.34054			−0.238003			−0.119002	+	0.992894i	$0.537969\pi$
$198$		0			0
$199$	−4.42967	−	7.67241i	−0.314011	−	0.543883i	0.665216	−	0.746651i	$-0.268339\pi$
$199$	−4.42967	−	7.67241i	−0.314011	−	0.543883i	−0.979227	+	0.202768i	$0.935006\pi$
$200$	−1.32726	+	34.5043i	−0.0938517	+	2.43982i
$201$		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
$206$	10.8344	−	12.5809i	0.754869	−	0.876554i
$207$		0			0
$208$	16.3794	−	17.6034i	1.13571	−	1.22058i
$209$			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	$0.796704\pi$
$212$	1.37127	+	9.14109i	0.0941790	+	0.627812i
$213$		0			0
$214$	4.48210	+	3.85988i	0.306390	+	0.263856i
$215$	−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
$220$	13.3650	+	5.25615i	0.901068	+	0.354370i
$221$	−0.535142	−	0.926894i	−0.0359976	−	0.0623496i
$222$		0			0
$223$	18.1129			1.21293			0.606463	−	0.795112i	$-0.292588\pi$
$223$	18.1129			1.21293			0.606463	+	0.795112i	$0.292588\pi$
$224$	−11.8007	−	9.20556i	−0.788471	−	0.615073i
$225$		0			0
$226$	3.40316	+	0.645144i	0.226375	+	0.0429144i
$227$	13.7345	+	23.7888i	0.911588	+	1.57892i	0.811821	+	0.583906i	$0.198476\pi$
$227$	13.7345	+	23.7888i	0.911588	+	1.57892i	0.0997672	+	0.995011i	$0.468190\pi$
$228$		0			0
$229$	4.77076	+	2.75440i	0.315261	+	0.182016i	0.649278	−	0.760551i	$-0.275071\pi$
$229$	4.77076	+	2.75440i	0.315261	+	0.182016i	−0.334018	+	0.942567i	$0.608404\pi$
$230$	−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	$-0.949058\pi$
$233$	−5.42805	+	9.40167i	−0.355604	+	0.615924i	0.631617	+	0.775280i	$0.282391\pi$
$234$		0			0
$235$	36.5184	−	21.0839i	2.38219	−	1.37536i
$236$	−0.197708	−	1.31795i	−0.0128697	−	0.0857915i
$237$		0			0
$238$	−0.545843	+	0.381920i	−0.0353818	+	0.0247562i
$239$			9.38509i			0.607071i	0.952820	+	0.303536i	$0.0981671\pi$
$239$			9.38509i			0.607071i	−0.952820	+	0.303536i	$0.901833\pi$
$240$		0			0
$241$	−7.83648	+	4.52439i	−0.504792	+	0.291442i	−0.730690	−	0.682709i	$-0.760802\pi$
$241$	−7.83648	+	4.52439i	−0.504792	+	0.291442i	0.225898	+	0.974151i	$0.427468\pi$
$242$	−7.38610	+	8.57674i	−0.474796	+	0.551334i
$243$		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
$248$	0.202503	−	5.26438i	0.0128590	−	0.334288i
$249$		0			0
$250$	−7.87610	+	41.5467i	−0.498128	+	2.62765i
$251$	−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
$254$	−0.802793	+	4.23476i	−0.0503717	+	0.265713i
$255$		0			0
$256$	1.15110	+	15.9585i	0.0719435	+	0.997409i
$257$	−3.63962	−	2.10133i	−0.227033	−	0.131078i	0.382169	−	0.924092i	$-0.375177\pi$
$257$	−3.63962	−	2.10133i	−0.227033	−	0.131078i	−0.609203	+	0.793015i	$0.708510\pi$
$258$		0			0
$259$	−0.455832	+	1.79017i	−0.0283240	+	0.111236i
$260$	39.0138	−	31.0679i	2.41953	−	1.92675i
$261$		0			0
$262$	11.4567	−	13.3035i	0.707797	−	0.821894i
$263$	13.5793	−	7.84001i	0.837335	−	0.483436i	−0.0190222	−	0.999819i	$-0.506055\pi$
$263$	13.5793	−	7.84001i	0.837335	−	0.483436i	0.856358	+	0.516383i	$0.172722\pi$
$264$		0			0
$265$			19.1720i			1.17773i
$266$	7.79778	−	16.7072i	0.478113	−	1.02438i
$267$		0			0
$268$	6.59430	−	0.989221i	0.402811	−	0.0604263i
$269$	−6.29125	+	3.63225i	−0.383584	+	0.221462i	−0.679377	−	0.733790i	$-0.737750\pi$
$269$	−6.29125	+	3.63225i	−0.383584	+	0.221462i	0.295792	+	0.955252i	$0.404416\pi$
$270$		0			0
$271$	−13.5502	+	23.4696i	−0.823116	+	1.42568i	0.0802344	+	0.996776i	$0.474433\pi$
$271$	−13.5502	+	23.4696i	−0.823116	+	1.42568i	−0.903351	+	0.428903i	$0.858900\pi$
$272$	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	0.566038	−	0.824379i	$-0.308475\pi$
$277$	−7.17183	−	12.4220i	−0.430914	−	0.746365i	−0.996952	+	0.0780143i	$0.975142\pi$
$278$	−16.0472	−	3.04211i	−0.962450	−	0.182454i
$279$		0			0
$280$	−21.3729	−	22.5134i	−1.27728	−	1.34543i
$281$	−19.7640			−1.17902			−0.589512	−	0.807760i	$-0.700680\pi$
$281$	−19.7640			−1.17902			−0.589512	+	0.807760i	$0.700680\pi$
$282$		0			0
$283$	3.51739	+	6.09230i	0.209087	+	0.362150i	0.951427	−	0.307874i	$-0.0996174\pi$
$283$	3.51739	+	6.09230i	0.209087	+	0.362150i	−0.742340	+	0.670023i	$0.766284\pi$
$284$	2.46915	−	6.27839i	0.146517	−	0.372554i
$285$		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
$290$	−27.4569	−	23.6453i	−1.61233	−	1.38850i
$291$		0			0
$292$	−23.2647	+	3.48997i	−1.36146	+	0.204235i
$293$			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
$296$	1.74695	−	0.920949i	0.101539	−	0.0535291i
$297$		0			0
$298$	−4.34126	+	5.04107i	−0.251482	+	0.292022i
$299$	−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
$304$	−18.8427	+	5.78340i	−1.08071	+	0.331701i
$305$	−1.59043	−	2.75470i	−0.0910677	−	0.157734i
$306$		0			0
$307$	10.3978			0.593431			0.296716	−	0.954966i	$-0.404109\pi$
$307$	10.3978			0.593431			0.296716	+	0.954966i	$0.404109\pi$
$308$	−8.35172	+	3.76142i	−0.475883	+	0.214327i
$309$		0			0
$310$	2.03522	−	10.7359i	0.115593	−	0.609758i
$311$	−12.6628	−	21.9326i	−0.718040	−	1.24368i	−0.961775	−	0.273841i	$-0.911706\pi$
$311$	−12.6628	−	21.9326i	−0.718040	−	1.24368i	0.243735	−	0.969842i	$-0.421627\pi$
$312$		0			0
$313$	27.4010	+	15.8200i	1.54880	+	0.894199i	0.998234	+	0.0594068i	$0.0189209\pi$
$313$	27.4010	+	15.8200i	1.54880	+	0.894199i	0.550565	+	0.834792i	$0.314412\pi$
$314$	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	$-0.727204\pi$
$317$	5.82693	−	10.0925i	0.327273	−	0.566854i	0.981970	+	0.189038i	$0.0605369\pi$
$318$		0			0
$319$	−9.25932	+	5.34587i	−0.518423	+	0.299311i
$320$	−2.54935	+	33.0881i	−0.142513	+	1.84968i
$321$		0			0
$322$	18.6428	+	8.70122i	1.03892	+	0.484900i
$323$			0.877338i			0.0488164i
$324$		0			0
$325$	63.5544	−	36.6932i	3.52536	−	2.03537i
$326$	−16.7562	−	14.4301i	−0.928040	−	0.799207i
$327$		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	$-0.142775\pi$
$331$	17.7580	+	10.2526i	0.976066	+	0.563532i	0.0749861	+	0.997185i	$0.476109\pi$
$332$	−27.4768	−	10.8060i	−1.50799	−	0.593058i
$333$		0			0
$334$	3.31357	+	0.628159i	0.181310	+	0.0343714i
$335$	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	$0.695143\pi$
$338$	−32.1458	−	6.09395i	−1.74850	−	0.331467i
$339$		0			0
$340$	1.37468	+	0.540630i	0.0745525	+	0.0293198i
$341$	−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
$346$	−15.5972	−	13.4319i	−0.838509	−	0.722105i
$347$	20.2502	−	11.6914i	1.08709	−	0.627630i	0.154287	−	0.988026i	$-0.450692\pi$
$347$	20.2502	−	11.6914i	1.08709	−	0.627630i	0.932799	+	0.360396i	$0.117359\pi$
$348$		0			0
$349$			30.6174i			1.63891i	0.573141	+	0.819457i	$0.305725\pi$
$349$			30.6174i			1.63891i	−0.573141	+	0.819457i	$0.694275\pi$
$350$	−26.1871	−	37.4269i	−1.39976	−	2.00055i
$351$		0			0
$352$	8.96822	+	3.93145i	0.478008	+	0.209547i
$353$	13.6872	−	7.90229i	0.728495	−	0.420597i	−0.0893765	−	0.995998i	$-0.528487\pi$
$353$	13.6872	−	7.90229i	0.728495	−	0.420597i	0.817871	+	0.575401i	$0.195154\pi$
$354$		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	0.857466	−	0.514540i	$-0.172037\pi$
$359$	15.9270	+	9.19546i	0.840595	+	0.485318i	−0.0168713	+	0.999858i	$0.505371\pi$
$360$		0			0
$361$	−2.64052	−	4.57352i	−0.138975	−	0.240712i
$362$	1.33622	−	7.04862i	0.0702302	−	0.370467i
$363$		0			0
$364$	−3.18922	+	31.6484i	−0.167161	+	1.65883i
$365$	−48.7939			−2.55399
$366$		0			0
$367$	−0.651832	−	1.12901i	−0.0340254	−	0.0589336i	0.848511	−	0.529177i	$-0.177499\pi$
$367$	−0.651832	−	1.12901i	−0.0340254	−	0.0589336i	−0.882537	+	0.470244i	$0.844166\pi$
$368$	−6.45346	−	21.0259i	−0.336410	−	1.09605i
$369$		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	−0.801599	−	0.597862i	$-0.796017\pi$
$373$	2.25895	−	3.91262i	0.116964	−	0.202588i	0.918563	+	0.395274i	$0.129350\pi$
$374$	0.284423	−	0.330272i	0.0147071	−	0.0170779i
$375$		0			0
$376$	25.4336	−	13.4080i	1.31164	−	0.691464i
$377$			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	$0.986815\pi$
$380$	−40.4295	+	6.06488i	−2.07399	+	0.311122i
$381$		0			0
$382$	26.8763	+	23.1453i	1.37511	+	1.18421i
$383$	4.81300	−	8.33636i	0.245933	−	0.425968i	−0.716461	−	0.697627i	$-0.754239\pi$
$383$	4.81300	−	8.33636i	0.245933	−	0.425968i	0.962393	+	0.271659i	$0.0875724\pi$
$384$		0			0
$385$	−18.2883	+	5.14553i	−0.932058	+	0.262241i
$386$	6.30591	+	18.0415i	0.320962	+	0.918286i
$387$		0			0
$388$	6.42102	−	16.3269i	0.325978	−	0.828875i
$389$	−6.47225	−	11.2103i	−0.328156	−	0.568383i	0.653990	−	0.756503i	$-0.273094\pi$
$389$	−6.47225	−	11.2103i	−0.328156	−	0.568383i	−0.982146	+	0.188120i	$0.939761\pi$
$390$		0			0
$391$	−0.978986			−0.0495094
$392$	19.7972	+	0.267558i	0.999909	+	0.0135137i
$393$		0			0
$394$	−4.64157	−	0.879911i	−0.233839	−	0.0443293i
$395$	20.9724	+	36.3253i	1.05524	+	1.82773i
$396$		0			0
$397$	−4.56287	−	2.63438i	−0.229004	−	0.132216i	0.381109	−	0.924530i	$-0.375542\pi$
$397$	−4.56287	−	2.63438i	−0.229004	−	0.132216i	−0.610112	+	0.792315i	$0.708876\pi$
$398$	−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	−0.0403107	−	0.999187i	$-0.512835\pi$
$401$	16.9244	−	29.3140i	0.845166	−	1.46387i	0.885477	−	0.464683i	$-0.153832\pi$
$402$		0			0
$403$	−9.69661	+	5.59834i	−0.483023	+	0.278873i
$404$	16.8073	−	2.52129i	0.836196	−	0.125439i
$405$		0			0
$406$	23.0234	−	2.00619i	1.14263	−	0.0995654i
$407$		−	1.20861i		−	0.0599086i
$408$		0			0
$409$	19.6739	−	11.3587i	0.972813	−	0.561654i	0.0727202	−	0.997352i	$-0.476832\pi$
$409$	19.6739	−	11.3587i	0.972813	−	0.561654i	0.900093	+	0.435699i	$0.143499\pi$
$410$	12.2322	−	14.2041i	0.604106	−	0.701488i
$411$		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
$416$	27.3955	−	20.1450i	1.34317	−	0.987688i
$417$		0			0
$418$	−2.24676	+	11.8518i	−0.109893	+	0.579688i
$419$	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	$0.203150\pi$
$422$	−4.56178	+	24.0636i	−0.222064	+	1.17140i
$423$		0			0
$424$	−0.502468	+	13.0624i	−0.0244020	+	0.634368i
$425$	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
$430$	−7.95992	+	9.24306i	−0.383861	+	0.445740i
$431$	−18.6066	+	10.7425i	−0.896248	+	0.517449i	−0.875981	−	0.482345i	$-0.839785\pi$
$431$	−18.6066	+	10.7425i	−0.896248	+	0.517449i	−0.0202672	+	0.999795i	$0.506452\pi$
$432$		0			0
$433$			28.1941i			1.35492i	0.735559	+	0.677461i	$0.236920\pi$
$433$			28.1941i			1.35492i	−0.735559	+	0.677461i	$0.763080\pi$
$434$	3.99542	+	5.71029i	0.191786	+	0.274103i
$435$		0			0
$436$	3.95871	+	26.3894i	0.189588	+	1.26382i
$437$	23.4643	−	13.5471i	1.12245	−	0.648046i
$438$		0			0
$439$	−14.2486	+	24.6793i	−0.680049	+	1.17788i	0.294916	+	0.955523i	$0.404708\pi$
$439$	−14.2486	+	24.6793i	−0.680049	+	1.17788i	−0.974965	+	0.222356i	$0.928625\pi$
$440$	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	−0.134305	−	0.990940i	$-0.542880\pi$
$443$	−22.3028	−	12.8765i	−1.05964	−	0.611782i	−0.925332	+	0.379158i	$0.876214\pi$
$444$		0			0
$445$	−22.0255	−	38.1492i	−1.04411	−	1.80845i
$446$	25.1672	+	4.77100i	1.19170	+	0.225913i
$447$		0			0
$448$	−13.9720	−	15.8992i	−0.660113	−	0.751166i
$449$	−17.0105			−0.802776			−0.401388	−	0.915908i	$-0.631472\pi$
$449$	−17.0105			−0.802776			−0.401388	+	0.915908i	$0.631472\pi$
$450$		0			0
$451$	−2.76553	−	4.79005i	−0.130224	−	0.225554i
$452$	4.55865	+	1.79281i	0.214421	+	0.0843269i
$453$		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	−0.811092	−	0.584918i	$-0.801127\pi$
$457$	2.15931	−	3.74003i	0.101008	−	0.174951i	0.912100	+	0.409967i	$0.134460\pi$
$458$	5.90329	+	5.08378i	0.275843	+	0.237550i
$459$		0			0
$460$	−6.76755	−	45.1136i	−0.315539	−	2.10343i
$461$		−	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	$0.743851\pi$
$464$	−18.0875	−	16.8298i	−0.839692	−	0.781306i
$465$		0			0
$466$	−10.0185	+	11.6335i	−0.464100	+	0.538913i
$467$	1.21961	−	2.11243i	0.0564370	−	0.0977517i	−0.836427	−	0.548079i	$-0.815359\pi$
$467$	1.21961	−	2.11243i	0.0564370	−	0.0977517i	0.892864	+	0.450327i	$0.148693\pi$
$468$		0			0
$469$	−6.15918	+	6.31470i	−0.284405	+	0.291586i
$470$	56.2946	−	19.6763i	2.59668	−	0.907599i
$471$		0			0
$472$	0.0724455	−	1.88333i	0.00333457	−	0.0866874i
$473$	1.79963	+	3.11704i	0.0827469	+	0.143322i
$474$		0			0
$475$	−60.1565			−2.76017
$476$	−0.859030	+	0.386887i	−0.0393736	+	0.0177330i
$477$		0			0
$478$	−2.47207	+	13.0403i	−0.113070	+	0.596448i
$479$	3.25092	+	5.63076i	0.148538	+	0.257276i	0.930687	−	0.365815i	$-0.119210\pi$
$479$	3.25092	+	5.63076i	0.148538	+	0.257276i	−0.782149	+	0.623091i	$0.785876\pi$
$480$		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	$-0.565406\pi$
$487$	11.9555	−	6.90251i	0.541755	−	0.312783i	0.745790	+	0.666181i	$0.232072\pi$
$488$	−1.01141	−	1.91854i	−0.0457844	−	0.0868484i
$489$		0			0
$490$	40.5253	+	6.64042i	1.83075	+	0.299984i
$491$		−	6.08856i		−	0.274773i	−0.990518	−	0.137386i	$-0.956130\pi$
$491$		−	6.08856i		−	0.274773i	0.990518	−	0.137386i	$-0.0438702\pi$
$492$		0			0
$493$	−0.952383	+	0.549859i	−0.0428932	+	0.0247644i
$494$	31.7422	+	27.3357i	1.42815	+	1.22989i
$495$		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	$-0.266965\pi$
$499$	8.00880	+	4.62388i	0.358523	+	0.206993i	−0.309910	+	0.950766i	$0.600299\pi$
$500$	−21.8872	+	55.6532i	−0.978824	+	2.48889i
$501$		0			0
$502$	−21.9718	−	4.16525i	−0.980651	−	0.185904i
$503$	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
$506$	−13.2249	−	2.50707i	−0.587918	−	0.111453i
$507$		0			0
$508$	−2.23091	+	5.67261i	−0.0989805	+	0.251681i
$509$	29.0117	+	16.7499i	1.28592	+	0.742426i	0.977924	−	0.208962i	$-0.0670084\pi$
$509$	29.0117	+	16.7499i	1.28592	+	0.742426i	0.307996	+	0.951388i	$0.400342\pi$
$510$		0			0
$511$	21.7296	−	22.2782i	0.961259	−	0.985530i
$512$	−2.60413	+	22.4771i	−0.115088	+	0.993355i
$513$		0			0
$514$	−4.50363	−	3.87842i	−0.198647	−	0.171070i
$515$	42.1767	−	24.3507i	1.85853	−	1.07302i
$516$		0			0
$517$		−	17.5960i		−	0.773872i
$518$	−1.10490	+	2.36731i	−0.0485465	+	0.104014i
$519$		0			0
$520$	62.3917	−	32.8914i	2.73606	−	1.44238i
$521$	−25.3738	+	14.6496i	−1.11165	+	0.641809i	−0.939255	−	0.343220i	$-0.888483\pi$
$521$	−25.3738	+	14.6496i	−1.11165	+	0.641809i	−0.172391	+	0.985029i	$0.555149\pi$
$522$		0			0
$523$	9.05856	−	15.6899i	0.396103	−	0.686071i	−0.597138	−	0.802138i	$-0.703696\pi$
$523$	9.05856	−	15.6899i	0.396103	−	0.686071i	0.993241	+	0.116068i	$0.0370289\pi$
$524$	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
$530$	−5.04998	+	26.6388i	−0.219357	+	1.15712i
$531$		0			0
$532$	15.2355	−	21.1601i	0.660542	−	0.917406i
$533$	−19.2077			−0.831976
$534$		0			0
$535$	8.67522	+	15.0259i	0.375062	+	0.649627i
$536$	9.42313	+	0.362476i	0.407017	+	0.0156566i
$537$		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	−0.846597	−	0.532235i	$-0.821352\pi$
$541$	0.875255	−	1.51599i	0.0376301	−	0.0651773i	0.884227	+	0.467057i	$0.154686\pi$
$542$	−25.0096	+	29.0411i	−1.07425	+	1.24742i
$543$		0			0
$544$	0.922441	+	0.404376i	0.0395493	+	0.0173375i
$545$			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	$0.932549\pi$
$548$	−3.92891	−	26.1907i	−0.167835	−	1.11881i
$549$		0			0
$550$	22.6458	+	19.5020i	0.965619	+	0.831569i
$551$	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
$556$	−21.4958	−	8.45382i	−0.911625	−	0.358522i
$557$	−14.1857	−	24.5703i	−0.601066	−	1.04108i	−0.992660	−	0.120939i	$-0.961409\pi$
$557$	−14.1857	−	24.5703i	−0.601066	−	1.04108i	0.391594	−	0.920138i	$-0.371924\pi$
$558$		0			0
$559$	12.4991			0.528654
$560$	−23.7669	−	36.9113i	−1.00433	−	1.55979i
$561$		0			0
$562$	−27.4615	−	5.20593i	−1.15839	−	0.219599i
$563$	−7.18586	−	12.4463i	−0.302848	−	0.524548i	0.673932	−	0.738794i	$-0.264604\pi$
$563$	−7.18586	−	12.4463i	−0.302848	−	0.524548i	−0.976780	+	0.214245i	$0.931271\pi$
$564$		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	0.352341	+	0.935872i	$0.385386\pi$
$569$	−15.1308	+	26.2074i	−0.634318	+	1.09867i	−0.986659	+	0.162799i	$0.947948\pi$
$570$		0			0
$571$	16.7991	−	9.69895i	0.703020	−	0.405889i	−0.105451	−	0.994424i	$-0.533629\pi$
$571$	16.7991	−	9.69895i	0.703020	−	0.405889i	0.808471	+	0.588536i	$0.200295\pi$
$572$	−3.08737	−	20.5809i	−0.129089	−	0.860531i
$573$		0			0
$574$	1.03784	+	11.9105i	0.0433187	+	0.497134i
$575$		−	67.1262i		−	2.79936i
$576$		0			0
$577$	−11.0229	+	6.36408i	−0.458889	+	0.264940i	−0.711577	−	0.702608i	$-0.752019\pi$
$577$	−11.0229	+	6.36408i	−0.458889	+	0.264940i	0.252688	+	0.967548i	$0.418685\pi$
$578$	−15.6592	+	18.1834i	−0.651335	+	0.756331i
$579$		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
$584$	−33.2447	−	1.27881i	−1.37568	−	0.0529177i
$585$		0			0
$586$	−0.457860	+	2.41523i	−0.0189140	+	0.0997723i
$587$	−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
$590$	0.728102	−	3.84077i	0.0299755	−	0.158122i
$591$		0			0
$592$	2.66991	−	0.819475i	0.109733	−	0.0336802i
$593$	24.8266	+	14.3336i	1.01951	+	0.588612i	0.913961	−	0.405802i	$-0.133008\pi$
$593$	24.8266	+	14.3336i	1.01951	+	0.588612i	0.105545	+	0.994414i	$0.466341\pi$
$594$		0			0
$595$	−1.88107	+	0.529252i	−0.0771165	+	0.0216972i
$596$	−7.35988	+	5.86090i	−0.301472	+	0.240072i
$597$		0			0
$598$	−30.5028	+	35.4199i	−1.24735	+	1.44843i
$599$	−34.1681	+	19.7270i	−1.39607	+	0.806023i	−0.993978	−	0.109576i	$-0.965051\pi$
$599$	−34.1681	+	19.7270i	−1.39607	+	0.806023i	−0.402094	+	0.915599i	$0.631717\pi$
$600$		0			0
$601$			17.8483i			0.728047i	0.931390	+	0.364023i	$0.118597\pi$
$601$			17.8483i			0.728047i	−0.931390	+	0.364023i	$0.881403\pi$
$602$	−0.675360	−	7.75056i	−0.0275256	−	0.315889i
$603$		0			0
$604$	−9.99351	+	1.49914i	−0.406630	+	0.0609992i
$605$	−28.7529	+	16.6005i	−1.16897	+	0.674907i
$606$		0			0
$607$	−2.21465	+	3.83589i	−0.0898900	+	0.155694i	−0.907464	−	0.420129i	$-0.861985\pi$
$607$	−2.21465	+	3.83589i	−0.0898900	+	0.155694i	0.817574	+	0.575823i	$0.195318\pi$
$608$	−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	0.940799	−	0.338966i	$-0.110077\pi$
$613$	4.37852	+	7.58382i	0.176847	+	0.306307i	−0.763952	+	0.645273i	$0.776744\pi$
$614$	14.4473	+	2.73881i	0.583047	+	0.110529i
$615$		0			0
$616$	−12.5952	+	3.02649i	−0.507476	+	0.121941i
$617$	−38.2445			−1.53966			−0.769832	−	0.638247i	$-0.779660\pi$
$617$	−38.2445			−1.53966			−0.769832	+	0.638247i	$0.779660\pi$
$618$		0			0
$619$	6.47648	+	11.2176i	0.260312	+	0.450873i	0.966325	−	0.257326i	$-0.0828413\pi$
$619$	6.47648	+	11.2176i	0.260312	+	0.450873i	−0.706013	+	0.708199i	$0.749508\pi$
$620$	5.65576	−	14.3811i	0.227141	−	0.577558i
$621$		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
$626$	33.9058	+	29.1989i	1.35515	+	1.16702i
$627$		0			0
$628$	8.32163	−	1.24834i	0.332069	−	0.0498142i
$629$		−	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	$-0.244710\pi$
$632$	13.3371	+	25.2992i	0.530522	+	1.00635i
$633$		0			0
$634$	10.7547	−	12.4884i	0.427126	−	0.495978i
$635$	−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
$640$	−12.2578	+	45.3033i	−0.484531	+	1.79077i
$641$	12.2786	+	21.2671i	0.484974	+	0.840000i	0.999851	−	0.0172641i	$-0.00549559\pi$
$641$	12.2786	+	21.2671i	0.484974	+	0.840000i	−0.514877	+	0.857264i	$0.672162\pi$
$642$		0			0
$643$	12.7388			0.502371			0.251186	−	0.967939i	$-0.419180\pi$
$643$	12.7388			0.502371			0.251186	+	0.967939i	$0.419180\pi$
$644$	23.6117	+	17.0007i	0.930430	+	0.669920i
$645$		0			0
$646$	−0.231094	+	1.21903i	−0.00909229	+	0.0479622i
$647$	1.84146	+	3.18950i	0.0723952	+	0.125392i	0.899951	−	0.435992i	$-0.143602\pi$
$647$	1.84146	+	3.18950i	0.0723952	+	0.125392i	−0.827555	+	0.561384i	$0.810269\pi$
$648$		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	$-0.798210\pi$
$653$	2.81401	−	4.87402i	0.110121	−	0.190735i	0.915819	+	0.401592i	$0.131543\pi$
$654$		0			0
$655$	44.5991	−	25.7493i	1.74263	−	1.00611i
$656$	8.70644	−	9.35705i	0.339929	−	0.365332i
$657$		0			0
$658$	−16.0861	+	34.4654i	−0.627102	+	1.34360i
$659$			37.2731i			1.45196i	0.687718	+	0.725978i	$0.258612\pi$
$659$			37.2731i			1.45196i	−0.687718	+	0.725978i	$0.741388\pi$
$660$		0			0
$661$	−11.8737	+	6.85527i	−0.461833	+	0.266639i	−0.712815	−	0.701353i	$-0.752580\pi$
$661$	−11.8737	+	6.85527i	−0.461833	+	0.266639i	0.250982	+	0.967992i	$0.419247\pi$
$662$	21.9735	+	18.9231i	0.854026	+	0.735468i
$663$		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
$668$	4.43863	+	1.74561i	0.171736	+	0.0675398i
$669$		0			0
$670$	19.2170	+	3.64301i	0.742418	+	0.140742i
$671$	−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	$0.734698\pi$
$674$	−29.3523	−	5.56438i	−1.13061	−	0.214332i
$675$		0			0
$676$	−43.0604	−	16.9347i	−1.65617	−	0.651334i
$677$	21.5264	+	12.4283i	0.827327	+	0.477657i	0.852936	−	0.522015i	$-0.174819\pi$
$677$	21.5264	+	12.4283i	0.827327	+	0.477657i	−0.0256098	+	0.999672i	$0.508153\pi$
$678$		0			0
$679$	6.28588	+	22.3413i	0.241230	+	0.857382i
$680$	1.76767	+	1.11328i	0.0677870	+	0.0426925i
$681$		0			0
$682$	−3.45511	−	2.97546i	−0.132303	−	0.113936i
$683$	23.5666	−	13.6062i	0.901750	−	0.520626i	0.0239824	−	0.999712i	$-0.492365\pi$
$683$	23.5666	−	13.6062i	0.901750	−	0.520626i	0.877768	+	0.479087i	$0.159032\pi$
$684$		0			0
$685$		−	54.9309i		−	2.09880i
$686$	−21.0791	+	15.5457i	−0.804805	+	0.593539i
$687$		0			0
$688$	−5.66557	+	6.08895i	−0.215998	+	0.232139i
$689$	24.0601	−	13.8911i	0.916616	−	0.529208i
$690$		0			0
$691$	0.920566	−	1.59447i	0.0350200	−	0.0606564i	−0.847984	−	0.530022i	$-0.822184\pi$
$691$	0.920566	−	1.59447i	0.0350200	−	0.0606564i	0.883004	+	0.469365i	$0.155517\pi$
$692$	−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
$698$	−8.06476	+	42.5419i	−0.305256	+	1.61024i
$699$		0			0
$700$	−26.5277	−	58.9012i	−1.00265	−	2.22626i
$701$	34.4094			1.29963			0.649813	−	0.760094i	$-0.274847\pi$
$701$	34.4094			1.29963			0.649813	+	0.760094i	$0.274847\pi$
$702$		0			0
$703$	1.72024	+	2.97955i	0.0648802	+	0.112376i
$704$	11.4255	+	7.82488i	0.430614	+	0.294911i
$705$		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	−0.624764	−	0.780814i	$-0.714805\pi$
$709$	9.68753	−	16.7793i	0.363823	−	0.630160i	0.988587	+	0.150654i	$0.0481380\pi$
$710$	12.9135	−	14.9951i	0.484634	−	0.562758i
$711$		0			0
$712$	−14.0068	−	26.5694i	−0.524925	−	0.995732i
$713$			10.2416i			0.383550i
$714$		0			0
$715$		−	43.1652i		−	1.61429i
$716$	12.3623	−	1.85449i	0.462001	−	0.0693055i
$717$		0			0
$718$	19.7079	+	16.9720i	0.735493	+	0.633390i
$719$	−13.2505	+	22.9505i	−0.494160	+	0.855910i	−0.999977	−	0.00673050i	$-0.997858\pi$
$719$	−13.2505	+	22.9505i	−0.494160	+	0.855910i	0.505817	+	0.862641i	$0.331191\pi$
$720$		0			0
$721$	−7.66468	+	30.1011i	−0.285447	+	1.12102i
$722$	−2.46424	−	7.05028i	−0.0917094	−	0.262384i
$723$		0			0
$724$	3.71327	−	9.44186i	0.138003	−	0.350904i
$725$	−37.7022	−	65.3021i	−1.40022	−	2.42526i
$726$		0			0
$727$	29.5400			1.09558			0.547788	−	0.836617i	$-0.315470\pi$
$727$	29.5400			1.09558			0.547788	+	0.836617i	$0.315470\pi$
$728$	−12.7676	+	43.1343i	−0.473200	+	1.59866i
$729$		0			0
$730$	−67.7976	−	12.8525i	−2.50930	−	0.475693i
$731$	0.185104	+	0.320609i	0.00684630	+	0.0118581i
$732$		0			0
$733$	3.29938	+	1.90490i	0.121865	+	0.0703589i	0.559694	−	0.828700i	$-0.310919\pi$
$733$	3.29938	+	1.90490i	0.121865	+	0.0703589i	−0.437828	+	0.899059i	$0.644252\pi$
$734$	−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	$-0.888714\pi$
$739$	−30.2459	+	17.4625i	−1.11261	+	0.642367i	−0.173107	+	0.984903i	$0.555381\pi$
$740$	5.72862	−	0.859359i	0.210588	−	0.0315907i
$741$		0			0
$742$	−9.91377	−	14.1689i	−0.363946	−	0.520155i
$743$		−	33.8918i		−	1.24337i	−0.783267	−	0.621685i	$-0.786448\pi$
$743$		−	33.8918i		−	1.24337i	0.783267	−	0.621685i	$-0.213552\pi$
$744$		0			0
$745$	−16.8999	+	9.75714i	−0.619163	+	0.357474i
$746$	4.16934	−	4.84144i	0.152650	−	0.177258i
$747$		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	$-0.570945\pi$
$751$	−32.2321	−	18.6092i	−1.17617	−	0.679059i	−0.955124	+	0.296205i	$0.904279\pi$
$752$	38.8709	−	11.9306i	1.41747	−	0.435065i
$753$		0			0
$754$	−9.77995	+	51.5896i	−0.356165	+	1.87878i
$755$	−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	$0.559696\pi$
$758$	−0.424690	+	2.24026i	−0.0154254	+	0.0813698i
$759$		0			0
$760$	−57.7729	−	2.22233i	−2.09564	−	0.0806124i
$761$	−21.1777	−	12.2270i	−0.767693	−	0.443227i	0.0643583	−	0.997927i	$-0.479500\pi$
$761$	−21.1777	−	12.2270i	−0.767693	−	0.443227i	−0.832051	+	0.554699i	$0.812833\pi$
$762$		0			0
$763$	−25.2705	−	24.6481i	−0.914853	−	0.892322i
$764$	31.2471	+	39.2389i	1.13048	+	1.41961i
$765$		0			0
$766$	8.88333	−	10.3153i	0.320968	−	0.372708i
$767$	−3.46896	+	2.00281i	−0.125257	+	0.0723172i
$768$		0			0
$769$			2.46179i			0.0887745i	0.999014	+	0.0443873i	$0.0141335\pi$
$769$			2.46179i			0.0887745i	−0.999014	+	0.0443873i	$0.985866\pi$
$770$	−26.7663	+	2.33234i	−0.964592	+	0.0840515i
$771$		0			0
$772$	4.00966	+	26.7290i	0.144311	+	0.961998i
$773$	29.2019	−	16.8597i	1.05032	−	0.606403i	0.127582	−	0.991828i	$-0.459279\pi$
$773$	29.2019	−	16.8597i	1.05032	−	0.606403i	0.922739	+	0.385425i	$0.125945\pi$
$774$		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
$782$	−1.36027	−	0.257869i	−0.0486431	−	0.00922137i
$783$		0			0
$784$	27.4371	+	5.58642i	0.979895	+	0.199515i
$785$	17.4533			0.622935
$786$		0			0
$787$	−11.3105	−	19.5903i	−0.403175	−	0.698320i	0.590932	−	0.806721i	$-0.298760\pi$
$787$	−11.3105	−	19.5903i	−0.403175	−	0.698320i	−0.994107	+	0.108402i	$0.965427\pi$
$788$	−6.21753	−	2.44521i	−0.221490	−	0.0871072i
$789$		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
$794$	−5.64605	−	4.86226i	−0.200371	−	0.172555i
$795$		0			0
$796$	−2.62859	−	17.5226i	−0.0931679	−	0.621072i
$797$			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
$800$	−27.7269	+	63.2491i	−0.980293	+	2.23619i
$801$		0			0
$802$	31.2374	−	36.2729i	1.10303	−	1.28084i
$803$	−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
$808$	24.0173	+	0.923867i	0.844927	+	0.0325015i
$809$	−12.3077	−	21.3176i	−0.432716	−	0.749486i	0.564390	−	0.825508i	$-0.309111\pi$
$809$	−12.3077	−	21.3176i	−0.432716	−	0.749486i	−0.997106	+	0.0760220i	$0.975778\pi$
$810$		0			0
$811$	−24.8680			−0.873233			−0.436616	−	0.899648i	$-0.643823\pi$
$811$	−24.8680			−0.873233			−0.436616	+	0.899648i	$0.643823\pi$
$812$	32.5187	+	3.27692i	1.14118	+	0.114997i
$813$		0			0
$814$	0.318353	−	1.67933i	0.0111583	−	0.0588603i
$815$	−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	$-0.742563\pi$
$821$	8.06054	−	13.9613i	0.281315	−	0.487251i	0.971709	+	0.236182i	$0.0758962\pi$
$822$		0			0
$823$	−46.5647	+	26.8842i	−1.62315	+	0.937123i	−0.637073	+	0.770803i	$0.719855\pi$
$823$	−46.5647	+	26.8842i	−1.62315	+	0.937123i	−0.986072	+	0.166320i	$0.946812\pi$
$824$	29.3744	−	15.4855i	1.02331	−	0.539462i
$825$		0			0
$826$	1.42936	+	2.04285i	0.0497338	+	0.0710800i
$827$			6.06391i			0.210863i	0.994427	+	0.105431i	$0.0336224\pi$
$827$			6.06391i			0.210863i	−0.994427	+	0.105431i	$0.966378\pi$
$828$		0			0
$829$	−14.6273	+	8.44507i	−0.508027	+	0.293309i	−0.732022	−	0.681281i	$-0.761423\pi$
$829$	−14.6273	+	8.44507i	−0.508027	+	0.293309i	0.223995	+	0.974590i	$0.428090\pi$
$830$	−65.6250	−	56.5148i	−2.27788	−	1.96166i
$831$		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
$836$	−6.24360	+	15.8758i	−0.215939	+	0.549077i
$837$		0			0
$838$	9.26498	+	1.75638i	0.320054	+	0.0606732i
$839$	−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
$842$	45.7954	+	8.68152i	1.57821	+	0.299185i
$843$		0			0
$844$	−12.6769	+	32.2340i	−0.436357	+	1.10954i
$845$	−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
$850$	2.32927	+	2.00591i	0.0798932	+	0.0688023i
$851$	−3.32476	+	1.91955i	−0.113971	+	0.0658013i
$852$		0			0
$853$		−	18.9879i		−	0.650134i	−0.945691	−	0.325067i	$-0.894613\pi$
$853$		−	18.9879i		−	0.650134i	0.945691	−	0.325067i	$-0.105387\pi$
$854$	2.59984	+	1.21343i	0.0889647	+	0.0415227i
$855$		0			0
$856$	5.51688	+	10.4650i	0.188563	+	0.357685i
$857$	−6.59722	+	3.80890i	−0.225357	+	0.130110i	−0.608428	−	0.793609i	$-0.708200\pi$
$857$	−6.59722	+	3.80890i	−0.225357	+	0.130110i	0.383071	+	0.923719i	$0.374866\pi$
$858$		0			0
$859$	0.495599	−	0.858403i	0.0169096	−	0.0292883i	−0.857447	−	0.514573i	$-0.827951\pi$
$859$	0.495599	−	0.858403i	0.0169096	−	0.0292883i	0.874356	+	0.485284i	$0.161284\pi$
$860$	−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	0.761845	−	0.647760i	$-0.224294\pi$
$863$	17.0912	+	9.86760i	0.581791	+	0.335897i	−0.180054	+	0.983657i	$0.557627\pi$
$864$		0			0
$865$	−30.1887	−	52.2884i	−1.02645	−	1.77786i
$866$	−7.42644	+	39.1748i	−0.252361	+	1.33121i
$867$		0			0
$868$	4.04739	+	8.98666i	0.137377	+	0.305027i
$869$	17.5030			0.593749
$870$		0			0
$871$	−10.0209	−	17.3567i	−0.339546	−	0.588111i
$872$	−1.45058	+	37.7100i	−0.0491227	+	1.27702i
$873$		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	−0.263232	−	0.964733i	$-0.584788\pi$
$877$	20.8444	−	36.1036i	0.703867	−	1.21913i	0.967099	−	0.254401i	$-0.0818782\pi$
$878$	−26.2986	+	30.5380i	−0.887535	+	1.03061i
$879$		0			0
$880$	21.0280	+	19.5659i	0.708854	+	0.659566i
$881$		−	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	$0.993260\pi$
$884$	−0.317557	−	2.11688i	−0.0106806	−	0.0711985i
$885$		0			0
$886$	−27.5972	−	23.7661i	−0.927148	−	0.798439i
$887$	24.0985	−	41.7398i	0.809148	−	1.40148i	−0.104307	−	0.994545i	$-0.533263\pi$
$887$	24.0985	−	41.7398i	0.809148	−	1.40148i	0.913455	−	0.406940i	$-0.133404\pi$
$888$		0			0
$889$	−2.18396	−	7.76223i	−0.0732475	−	0.260337i
$890$	−20.5550	−	58.8086i	−0.689005	−	1.97127i
$891$		0			0
$892$	33.7123	+	13.2583i	1.12877	+	0.443920i
$893$	25.0448	+	43.3789i	0.838092	+	1.45162i
$894$		0			0
$895$	25.9280			0.866677
$896$	−15.2257	−	25.7717i	−0.508654	−	0.860971i
$897$		0			0
$898$	−23.6355	−	4.48064i	−0.788728	−	0.149521i
$899$	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	$-0.996768\pi$
$907$	−44.9075	+	25.9274i	−1.49113	+	0.860904i	−0.491181	+	0.871057i	$0.663435\pi$
$908$	8.15011	+	54.3299i	0.270471	+	1.80300i
$909$		0			0
$910$	−39.4612	+	84.5477i	−1.30813	+	2.80273i
$911$		−	0.471351i		−	0.0156166i	−0.999970	−	0.00780828i	$-0.997515\pi$
$911$		−	0.471351i		−	0.0156166i	0.999970	−	0.00780828i	$-0.00248548\pi$
$912$		0			0
$913$	−22.1308	+	12.7772i	−0.732422	+	0.422864i
$914$	3.98543	−	4.62788i	0.131826	−	0.153077i
$915$		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	$-0.471026\pi$
$919$	−22.0115	−	12.7083i	−0.726092	−	0.419210i	−0.816991	+	0.576651i	$0.804359\pi$
$920$	2.47981	−	64.4665i	0.0817569	−	2.12540i
$921$		0			0
$922$	5.46611	−	28.8340i	0.180017	−	0.949596i
$923$	−20.2774			−0.667440
$924$		0			0
$925$	8.52383			0.280262
$926$	−8.16877	+	43.0906i	−0.268443	+	1.41605i
$927$		0			0
$928$	−20.6989	−	28.1488i	−0.679476	−	0.924031i
$929$	−36.9737	−	21.3468i	−1.21307	−	0.700365i	−0.249641	−	0.968338i	$-0.580313\pi$
$929$	−36.9737	−	21.3468i	−1.21307	−	0.700365i	−0.963426	+	0.267974i	$0.913646\pi$
$930$		0			0
$931$	0.859946	+	34.4823i	0.0281836	+	1.13011i
$932$	−16.9847	+	13.5255i	−0.556354	+	0.443042i
$933$		0			0
$934$	2.25104	−	2.61390i	0.0736561	−	0.0855296i
$935$	1.10721	−	0.639250i	0.0362097	−	0.0209057i
$936$		0			0
$937$		−	16.2104i		−	0.529570i	−0.964307	−	0.264785i	$-0.914699\pi$
$937$		−	16.2104i		−	0.529570i	0.964307	−	0.264785i	$-0.0853010\pi$
$938$	−10.2213	+	7.15171i	−0.333737	+	0.233512i
$939$		0			0
$940$	83.4023	−	12.5113i	2.72028	−	0.408074i
$941$	−0.907906	+	0.524180i	−0.0295969	+	0.0170878i	−0.514725	−	0.857355i	$-0.672106\pi$
$941$	−0.907906	+	0.524180i	−0.0295969	+	0.0170878i	0.485129	+	0.874443i	$0.338773\pi$
$942$		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	0.522135	−	0.852863i	$-0.325136\pi$
$947$	1.37253	+	0.792428i	0.0446011	+	0.0257505i	−0.477534	+	0.878613i	$0.658469\pi$
$948$		0			0
$949$	35.3537	+	61.2345i	1.14763	+	1.98776i
$950$	−83.5855	−	15.8455i	−2.71187	−	0.514095i
$951$		0			0
$952$	−1.29550	+	0.311295i	−0.0419874	+	0.0100891i
$953$	−21.8228			−0.706910			−0.353455	−	0.935451i	$-0.614993\pi$
$953$	−21.8228			−0.706910			−0.353455	+	0.935451i	$0.614993\pi$
$954$		0			0
$955$	52.0198	+	90.1009i	1.68332	+	2.91560i
$956$	−6.86972	+	17.4679i	−0.222183	+	0.564952i
$957$		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
$962$	−4.49769	−	3.87331i	−0.145011	−	0.124881i
$963$		0			0
$964$	−17.8973	+	2.68480i	−0.576434	+	0.0864717i
$965$			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	$-0.136674\pi$
$968$	−20.0253	+	10.5568i	−0.643637	+	0.339310i
$969$		0			0
$970$	33.5815	−	38.9949i	1.07824	−	1.25205i
$971$	−3.17896	+	5.50612i	−0.102018	+	0.176700i	−0.912516	−	0.409041i	$-0.865863\pi$
$971$	−3.17896	+	5.50612i	−0.102018	+	0.176700i	0.810498	+	0.585741i	$0.199197\pi$
$972$		0			0
$973$	29.4143	−	8.27590i	0.942978	−	0.265313i
$974$	18.4299	−	6.44168i	0.590533	−	0.206405i
$975$		0			0
$976$	−0.899968	−	2.93216i	−0.0288073	−	0.0938562i
$977$	2.59617	+	4.49670i	0.0830588	+	0.143862i	0.904562	−	0.426341i	$-0.140198\pi$
$977$	2.59617	+	4.49670i	0.0830588	+	0.143862i	−0.821504	+	0.570203i	$0.806864\pi$
$978$		0			0
$979$	−18.3818			−0.587486
$980$	54.5595	+	19.9012i	1.74284	+	0.635720i
$981$		0			0
$982$	1.60375	−	8.45985i	0.0511778	−	0.269965i
$983$	−8.44158	−	14.6212i	−0.269245	−	0.466345i	0.699422	−	0.714709i	$-0.253441\pi$
$983$	−8.44158	−	14.6212i	−0.269245	−	0.466345i	−0.968667	+	0.248363i	$0.920107\pi$
$984$		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	$-0.895944\pi$
$991$	−35.9653	+	20.7646i	−1.14247	+	0.659608i	−0.195432	+	0.980717i	$0.562611\pi$
$992$	4.23034	−	9.65003i	0.134313	−	0.306389i
$993$		0			0
$994$	1.09565	+	12.5738i	0.0347518	+	0.398818i
$995$		−	36.7509i		−	1.16508i
$996$		0			0
$997$	−16.3573	+	9.44391i	−0.518042	+	0.299092i	−0.736133	−	0.676837i	$-0.763350\pi$
$997$	−16.3573	+	9.44391i	−0.518042	+	0.299092i	0.218091	+	0.975928i	$0.430017\pi$
$998$	9.91002	+	8.53429i	0.313696	+	0.270148i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bf.a.271.5	✓	32	4.3	odd	2
756.2.bf.a.271.12	yes	32	12.11	even	2
756.2.bf.a.703.5	yes	32	7.3	odd	6
756.2.bf.a.703.12	yes	32	21.17	even	6
756.2.bf.d.271.2	yes	32	3.2	odd	2	inner
756.2.bf.d.271.15	yes	32	1.1	even	1	trivial
756.2.bf.d.703.2	yes	32	84.59	odd	6	inner
756.2.bf.d.703.15	yes	32	28.3	even	6	inner

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)

\(f(q)\)	\(=\)	\(q+(1.38947 + 0.263404i) q^{2} +(1.86124 + 0.731982i) q^{4} +(3.59250 + 2.07413i) q^{5} +(-2.54686 + 0.716577i) q^{7} +(2.39332 + 1.50732i) q^{8} +O(q^{10})\)	\(q+(1.38947 + 0.263404i) q^{2} +(1.86124 + 0.731982i) q^{4} +(3.59250 + 2.07413i) q^{5} +(-2.54686 + 0.716577i) q^{7} +(2.39332 + 1.50732i) q^{8} +(4.44533 + 3.82822i) q^{10} +(1.49910 - 0.865507i) q^{11} -6.01127i q^{13} +(-3.72753 + 0.324806i) q^{14} +(2.92840 + 2.72478i) q^{16} +(0.154193 - 0.0890232i) q^{17} +(-2.46379 + 4.26741i) q^{19} +(5.16827 + 6.49010i) q^{20} +(2.31093 - 0.807724i) q^{22} +(-4.76183 - 2.74924i) q^{23} +(6.10406 + 10.5725i) q^{25} +(1.58339 - 8.35246i) q^{26} +(-5.26484 - 0.530541i) q^{28} -6.17658 q^{29} +(-0.931308 - 1.61307i) q^{31} +(3.35120 + 4.55735i) q^{32} +(0.237695 - 0.0830798i) q^{34} +(-10.6359 - 2.70823i) q^{35} +(0.349105 - 0.604667i) q^{37} +(-4.54741 + 5.28045i) q^{38} +(5.47162 + 10.3791i) q^{40} -3.19527i q^{41} +2.07927i q^{43} +(3.42372 - 0.513597i) q^{44} +(-5.89224 - 5.07427i) q^{46} +(5.08258 - 8.80328i) q^{47} +(5.97304 - 3.65005i) q^{49} +(5.69654 + 16.2980i) q^{50} +(4.40014 - 11.1884i) q^{52} +(2.31084 + 4.00249i) q^{53} +7.18071 q^{55} +(-7.17557 - 2.12395i) q^{56} +(-8.58215 - 1.62694i) q^{58} +(-0.333175 - 0.577077i) q^{59} +(-0.664061 - 0.383396i) q^{61} +(-0.869132 - 2.48662i) q^{62} +(3.45596 + 7.21501i) q^{64} +(12.4682 - 21.5955i) q^{65} +(2.88737 - 1.66702i) q^{67} +(0.352153 - 0.0528269i) q^{68} +(-14.0649 - 6.56454i) q^{70} -3.37323i q^{71} +(-10.1866 + 5.88124i) q^{73} +(0.644342 - 0.748210i) q^{74} +(-7.70937 + 6.13921i) q^{76} +(-3.19781 + 3.27855i) q^{77} +(8.75675 + 5.05571i) q^{79} +(4.86874 + 15.8627i) q^{80} +(0.841648 - 4.43973i) q^{82} -14.7627 q^{83} +0.738584 q^{85} +(-0.547689 + 2.88908i) q^{86} +(4.89243 + 0.188195i) q^{88} +(-9.19642 - 5.30955i) q^{89} +(4.30754 + 15.3099i) q^{91} +(-6.85049 - 8.60257i) q^{92} +(9.38089 - 10.8931i) q^{94} +(-17.7024 + 10.2205i) q^{95} -8.77209i q^{97} +(9.26077 - 3.49830i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{7}+O(q^{10}) \) 32 * q + 2 * q^7	\( 32 q + 2 q^{7} + 4 q^{10} + 20 q^{16} - 6 q^{19} + 20 q^{22} + 20 q^{25} - 24 q^{28} + 8 q^{34} - 2 q^{37} + 52 q^{40} + 24 q^{46} - 10 q^{49} + 16 q^{52} + 16 q^{55} - 80 q^{58} + 48 q^{64} + 42 q^{67} + 32 q^{70} - 18 q^{73} - 40 q^{76} - 6 q^{79} + 8 q^{82} - 8 q^{85} - 80 q^{88} + 8 q^{91} - 8 q^{94}+O(q^{100}) \) 32 * q + 2 * q^7 + 4 * q^10 + 20 * q^16 - 6 * q^19 + 20 * q^22 + 20 * q^25 - 24 * q^28 + 8 * q^34 - 2 * q^37 + 52 * q^40 + 24 * q^46 - 10 * q^49 + 16 * q^52 + 16 * q^55 - 80 * q^58 + 48 * q^64 + 42 * q^67 + 32 * q^70 - 18 * q^73 - 40 * q^76 - 6 * q^79 + 8 * q^82 - 8 * q^85 - 80 * q^88 + 8 * q^91 - 8 * q^94

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