LMFDB - Embedded newform 756.2.bf.d.703.4

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			703.4
Character	$\chi$	$=$	756.703
Dual form			756.2.bf.d.271.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15218 - 0.820056i) q^{2} +(0.655017 + 1.88970i) q^{4} +(-2.47070 + 1.42646i) q^{5} +(2.58673 + 0.555723i) q^{7} +(0.794961 - 2.71441i) q^{8} +O(q^{10})$	\(q+(-1.15218 - 0.820056i) q^{2} +(0.655017 + 1.88970i) q^{4} +(-2.47070 + 1.42646i) q^{5} +(2.58673 + 0.555723i) q^{7} +(0.794961 - 2.71441i) q^{8} +(4.01646 + 0.382580i) q^{10} +(-1.53279 - 0.884955i) q^{11} -4.22305i q^{13} +(-2.52464 - 2.76155i) q^{14} +(-3.14190 + 2.47557i) q^{16} +(5.64493 + 3.25910i) q^{17} +(0.271768 + 0.470716i) q^{19} +(-4.31393 - 3.73452i) q^{20} +(1.04033 + 2.27659i) q^{22} +(-2.52145 + 1.45576i) q^{23} +(1.56957 - 2.71857i) q^{25} +(-3.46313 + 4.86569i) q^{26} +(0.644206 + 5.25214i) q^{28} +3.89613 q^{29} +(-3.59524 + 6.22714i) q^{31} +(5.65013 - 0.275753i) q^{32} +(-3.83130 - 8.38421i) q^{34} +(-7.18375 + 2.31684i) q^{35} +(3.62654 + 6.28136i) q^{37} +(0.0728888 - 0.765212i) q^{38} +(1.90789 + 7.84048i) q^{40} +10.1889i q^{41} +8.47781i q^{43} +(0.668294 - 3.47616i) q^{44} +(4.09896 + 0.390439i) q^{46} +(0.518260 + 0.897653i) q^{47} +(6.38234 + 2.87501i) q^{49} +(-4.03780 + 1.84514i) q^{50} +(7.98028 - 2.76617i) q^{52} +(2.96863 - 5.14181i) q^{53} +5.04941 q^{55} +(3.56481 - 6.57968i) q^{56} +(-4.48903 - 3.19505i) q^{58} +(-0.373043 + 0.646129i) q^{59} +(-3.14727 + 1.81708i) q^{61} +(9.24895 - 4.22646i) q^{62} +(-6.73607 - 4.31570i) q^{64} +(6.02400 + 10.4339i) q^{65} +(-13.4826 - 7.78415i) q^{67} +(-2.46118 + 12.8020i) q^{68} +(10.1769 + 3.22167i) q^{70} -1.60291i q^{71} +(7.52594 + 4.34510i) q^{73} +(0.972647 - 10.2112i) q^{74} +(-0.711497 + 0.821885i) q^{76} +(-3.47312 - 3.14094i) q^{77} +(0.876737 - 0.506185i) q^{79} +(4.23140 - 10.5982i) q^{80} +(8.35544 - 11.7394i) q^{82} +15.3161 q^{83} -18.5959 q^{85} +(6.95228 - 9.76793i) q^{86} +(-3.62064 + 3.45711i) q^{88} +(-6.49151 + 3.74787i) q^{89} +(2.34684 - 10.9239i) q^{91} +(-4.40254 - 3.81123i) q^{92} +(0.138999 - 1.45926i) q^{94} +(-1.34291 - 0.775331i) q^{95} +7.23796i q^{97} +(-4.99592 - 8.54639i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.15218	−	0.820056i	−0.814711	−	0.579867i
$2$	−1.15218	−	0.820056i	−0.814711	−	0.579867i
$3$		0			0
$3$		0			0
$4$	0.655017	+	1.88970i	0.327509	+	0.944848i
$5$	−2.47070	+	1.42646i	−1.10493	+	0.637932i	−0.937512	−	0.347954i	$-0.886877\pi$
$5$	−2.47070	+	1.42646i	−1.10493	+	0.637932i	−0.167419	+	0.985886i	$0.553543\pi$
$6$		0			0
$7$	2.58673	+	0.555723i	0.977692	+	0.210043i
$7$	2.58673	+	0.555723i	0.977692	+	0.210043i
$8$	0.794961	−	2.71441i	0.281061	−	0.959690i
$9$		0			0
$10$	4.01646	+	0.382580i	1.27011	+	0.120982i
$11$	−1.53279	−	0.884955i	−0.462153	−	0.266824i	0.250796	−	0.968040i	$-0.419308\pi$
$11$	−1.53279	−	0.884955i	−0.462153	−	0.266824i	−0.712949	+	0.701216i	$0.752641\pi$
$12$		0			0
$13$		−	4.22305i		−	1.17126i	−0.810578	−	0.585631i	$-0.800847\pi$
$13$		−	4.22305i		−	1.17126i	0.810578	−	0.585631i	$-0.199153\pi$
$14$	−2.52464	−	2.76155i	−0.674739	−	0.738056i
$15$		0			0
$16$	−3.14190	+	2.47557i	−0.785476	+	0.618892i
$17$	5.64493	+	3.25910i	1.36910	+	0.790448i	0.990813	−	0.135242i	$-0.0431813\pi$
$17$	5.64493	+	3.25910i	1.36910	+	0.790448i	0.378283	+	0.925690i	$0.376515\pi$
$18$		0			0
$19$	0.271768	+	0.470716i	0.0623478	+	0.107990i	0.895514	−	0.445032i	$-0.146808\pi$
$19$	0.271768	+	0.470716i	0.0623478	+	0.107990i	−0.833167	+	0.553022i	$0.813475\pi$
$20$	−4.31393	−	3.73452i	−0.964623	−	0.835063i
$21$		0			0
$22$	1.04033	+	2.27659i	0.221799	+	0.485371i
$23$	−2.52145	+	1.45576i	−0.525759	+	0.303547i	−0.739288	−	0.673390i	$-0.764838\pi$
$23$	−2.52145	+	1.45576i	−0.525759	+	0.303547i	0.213528	+	0.976937i	$0.431504\pi$
$24$		0			0
$25$	1.56957	−	2.71857i	0.313914	−	0.543715i
$26$	−3.46313	+	4.86569i	−0.679176	+	0.954241i
$27$		0			0
$28$	0.644206	+	5.25214i	0.121744	+	0.992562i
$29$	3.89613			0.723494			0.361747	−	0.932276i	$-0.382180\pi$
$29$	3.89613			0.723494			0.361747	+	0.932276i	$0.382180\pi$
$30$		0			0
$31$	−3.59524	+	6.22714i	−0.645724	+	1.11843i	0.338410	+	0.940999i	$0.390111\pi$
$31$	−3.59524	+	6.22714i	−0.645724	+	1.11843i	−0.984134	+	0.177428i	$0.943222\pi$
$32$	5.65013	−	0.275753i	0.998811	−	0.0487467i
$33$		0			0
$34$	−3.83130	−	8.38421i	−0.657063	−	1.43788i
$35$	−7.18375	+	2.31684i	−1.21427	+	0.391618i
$36$		0			0
$37$	3.62654	+	6.28136i	0.596200	+	1.03265i	0.993376	+	0.114906i	$0.0366567\pi$
$37$	3.62654	+	6.28136i	0.596200	+	1.03265i	−0.397177	+	0.917742i	$0.630010\pi$
$38$	0.0728888	−	0.765212i	0.0118241	−	0.124134i
$39$		0			0
$40$	1.90789	+	7.84048i	0.301664	+	1.23969i
$41$			10.1889i			1.59123i	0.605800	+	0.795617i	$0.292853\pi$
$41$			10.1889i			1.59123i	−0.605800	+	0.795617i	$0.707147\pi$
$42$		0			0
$43$			8.47781i			1.29285i	0.762976	+	0.646427i	$0.223738\pi$
$43$			8.47781i			1.29285i	−0.762976	+	0.646427i	$0.776262\pi$
$44$	0.668294	−	3.47616i	0.100749	−	0.524051i
$45$		0			0
$46$	4.09896	+	0.390439i	0.604359	+	0.0575671i
$47$	0.518260	+	0.897653i	0.0755961	+	0.130936i	0.901345	−	0.433101i	$-0.142581\pi$
$47$	0.518260	+	0.897653i	0.0755961	+	0.130936i	−0.825749	+	0.564037i	$0.809247\pi$
$48$		0			0
$49$	6.38234	+	2.87501i	0.911764	+	0.410716i
$50$	−4.03780	+	1.84514i	−0.571031	+	0.260942i
$51$		0			0
$52$	7.98028	−	2.76617i	1.10667	−	0.383599i
$53$	2.96863	−	5.14181i	0.407772	−	0.706282i	−0.586867	−	0.809683i	$-0.699639\pi$
$53$	2.96863	−	5.14181i	0.407772	−	0.706282i	0.994640	+	0.103401i	$0.0329724\pi$
$54$		0			0
$55$	5.04941			0.680862
$56$	3.56481	−	6.57968i	0.476368	−	0.879246i
$57$		0			0
$58$	−4.48903	−	3.19505i	−0.589438	−	0.419530i
$59$	−0.373043	+	0.646129i	−0.0485660	+	0.0841188i	−0.889286	−	0.457351i	$-0.848798\pi$
$59$	−0.373043	+	0.646129i	−0.0485660	+	0.0841188i	0.840720	+	0.541469i	$0.182132\pi$
$60$		0			0
$61$	−3.14727	+	1.81708i	−0.402967	+	0.232653i	−0.687763	−	0.725935i	$-0.741407\pi$
$61$	−3.14727	+	1.81708i	−0.402967	+	0.232653i	0.284796	+	0.958588i	$0.408074\pi$
$62$	9.24895	−	4.22646i	1.17462	−	0.536761i
$63$		0			0
$64$	−6.73607	−	4.31570i	−0.842009	−	0.539463i
$65$	6.02400	+	10.4339i	0.747186	+	1.29416i
$66$		0			0
$67$	−13.4826	−	7.78415i	−1.64716	−	0.950986i	−0.978195	−	0.207688i	$-0.933406\pi$
$67$	−13.4826	−	7.78415i	−1.64716	−	0.950986i	−0.668960	−	0.743298i	$-0.733260\pi$
$68$	−2.46118	+	12.8020i	−0.298462	+	1.55247i
$69$		0			0
$70$	10.1769	+	3.22167i	1.21637	+	0.385063i
$71$		−	1.60291i		−	0.190230i	−0.995466	−	0.0951150i	$-0.969678\pi$
$71$		−	1.60291i		−	0.190230i	0.995466	−	0.0951150i	$-0.0303219\pi$
$72$		0			0
$73$	7.52594	+	4.34510i	0.880844	+	0.508556i	0.870937	−	0.491395i	$-0.163513\pi$
$73$	7.52594	+	4.34510i	0.880844	+	0.508556i	0.00990761	+	0.999951i	$0.496846\pi$
$74$	0.972647	−	10.2112i	0.113068	−	1.18703i
$75$		0			0
$76$	−0.711497	+	0.821885i	−0.0816143	+	0.0942767i
$77$	−3.47312	−	3.14094i	−0.395798	−	0.357944i
$78$		0			0
$79$	0.876737	−	0.506185i	0.0986407	−	0.0569502i	−0.449868	−	0.893095i	$-0.648529\pi$
$79$	0.876737	−	0.506185i	0.0986407	−	0.0569502i	0.548509	+	0.836145i	$0.315196\pi$
$80$	4.23140	−	10.5982i	0.473085	−	1.18491i
$81$		0			0
$82$	8.35544	−	11.7394i	0.922704	−	1.29640i
$83$	15.3161			1.68116			0.840579	−	0.541688i	$-0.182215\pi$
$83$	15.3161			1.68116			0.840579	+	0.541688i	$0.182215\pi$
$84$		0			0
$85$	−18.5959			−2.01701
$86$	6.95228	−	9.76793i	0.749683	−	1.05330i
$87$		0			0
$88$	−3.62064	+	3.45711i	−0.385961	+	0.368529i
$89$	−6.49151	+	3.74787i	−0.688099	+	0.397274i	−0.802899	−	0.596115i	$-0.796710\pi$
$89$	−6.49151	+	3.74787i	−0.688099	+	0.397274i	0.114801	+	0.993389i	$0.463377\pi$
$90$		0			0
$91$	2.34684	−	10.9239i	0.246016	−	1.14513i
$92$	−4.40254	−	3.81123i	−0.458997	−	0.397348i
$93$		0			0
$94$	0.138999	−	1.45926i	0.0143366	−	0.150511i
$95$	−1.34291	−	0.775331i	−0.137780	−	0.0795473i
$96$		0			0
$97$			7.23796i			0.734903i	0.930043	+	0.367452i	$0.119770\pi$
$97$			7.23796i			0.734903i	−0.930043	+	0.367452i	$0.880230\pi$
$98$	−4.99592	−	8.54639i	−0.504664	−	0.863316i
$99$		0			0
$100$	6.16538	+	1.18530i	0.616538	+	0.118530i
$101$	7.47225	+	4.31411i	0.743517	+	0.429270i	0.823347	−	0.567539i	$-0.192104\pi$
$101$	7.47225	+	4.31411i	0.743517	+	0.429270i	−0.0798298	+	0.996809i	$0.525438\pi$
$102$		0			0
$103$	7.01107	+	12.1435i	0.690822	+	1.19654i	0.971569	+	0.236756i	$0.0760844\pi$
$103$	7.01107	+	12.1435i	0.690822	+	1.19654i	−0.280747	+	0.959782i	$0.590582\pi$
$104$	−11.4631	−	3.35716i	−1.12405	−	0.329196i
$105$		0			0
$106$	−7.63695	+	3.48983i	−0.741767	+	0.338963i
$107$	−13.2085	+	7.62593i	−1.27691	+	0.737227i	−0.976280	−	0.216513i	$-0.930532\pi$
$107$	−13.2085	+	7.62593i	−1.27691	+	0.737227i	−0.300635	+	0.953739i	$0.597198\pi$
$108$		0			0
$109$	8.60620	−	14.9064i	0.824325	−	1.42777i	−0.0781095	−	0.996945i	$-0.524888\pi$
$109$	8.60620	−	14.9064i	0.824325	−	1.42777i	0.902434	−	0.430828i	$-0.141778\pi$
$110$	−5.81780	−	4.14079i	−0.554706	−	0.394809i
$111$		0			0
$112$	−9.50299	+	4.65760i	−0.897948	+	0.440102i
$113$	15.2599			1.43554			0.717768	−	0.696283i	$-0.245164\pi$
$113$	15.2599			1.43554			0.717768	+	0.696283i	$0.245164\pi$
$114$		0			0
$115$	4.15317	−	7.19350i	0.387285	−	0.670797i
$116$	2.55204	+	7.36251i	0.236951	+	0.683592i
$117$		0			0
$118$	0.959673	−	0.438538i	0.0883450	−	0.0403707i
$119$	12.7907	+	11.5674i	1.17253	+	1.06038i
$120$		0			0
$121$	−3.93371	−	6.81339i	−0.357610	−	0.619399i
$122$	5.11632	+	0.487345i	0.463210	+	0.0441222i
$123$		0			0
$124$	−14.1223	−	2.71503i	−1.26822	−	0.243817i
$125$		−	5.30888i		−	0.474841i
$126$		0			0
$127$		−	6.47523i		−	0.574583i	−0.957843	−	0.287292i	$-0.907245\pi$
$127$		−	6.47523i		−	0.574583i	0.957843	−	0.287292i	$-0.0927549\pi$
$128$	4.22202	+	10.4964i	0.373178	+	0.927760i
$129$		0			0
$130$	1.61565	−	16.9617i	0.141702	−	1.48764i
$131$	5.03534	+	8.72146i	0.439939	+	0.761997i	0.997684	−	0.0680150i	$-0.0216666\pi$
$131$	5.03534	+	8.72146i	0.439939	+	0.761997i	−0.557745	+	0.830012i	$0.688333\pi$
$132$		0			0
$133$	0.441403	+	1.36864i	0.0382745	+	0.118676i
$134$	9.15083	+	20.0252i	0.790511	+	1.72991i
$135$		0			0
$136$	13.3340	−	12.7318i	1.14338	−	1.09174i
$137$	−4.21760	+	7.30510i	−0.360334	+	0.624117i	−0.988016	−	0.154353i	$-0.950671\pi$
$137$	−4.21760	+	7.30510i	−0.360334	+	0.624117i	0.627682	+	0.778470i	$0.284004\pi$
$138$		0			0
$139$	11.5050			0.975842			0.487921	−	0.872888i	$-0.337755\pi$
$139$	11.5050			0.975842			0.487921	+	0.872888i	$0.337755\pi$
$140$	−9.08361	−	12.0575i	−0.767705	−	1.01905i
$141$		0			0
$142$	−1.31447	+	1.84683i	−0.110308	+	0.154982i
$143$	−3.73721	+	6.47303i	−0.312521	+	0.541302i
$144$		0			0
$145$	−9.62617	+	5.55767i	−0.799410	+	0.461540i
$146$	−5.10798	−	11.1780i	−0.422739	−	0.925098i
$147$		0			0
$148$	−9.49441	+	10.9675i	−0.780435	+	0.901520i
$149$	3.45428	+	5.98299i	0.282985	+	0.490145i	0.972119	−	0.234489i	$-0.0753418\pi$
$149$	3.45428	+	5.98299i	0.282985	+	0.490145i	−0.689133	+	0.724635i	$0.742009\pi$
$150$		0			0
$151$	−11.4724	−	6.62359i	−0.933610	−	0.539020i	−0.0456586	−	0.998957i	$-0.514539\pi$
$151$	−11.4724	−	6.62359i	−0.933610	−	0.539020i	−0.887952	+	0.459937i	$0.847872\pi$
$152$	1.49376	−	0.363489i	0.121160	−	0.0294829i
$153$		0			0
$154$	1.42589	+	6.46707i	0.114902	+	0.521131i
$155$		−	20.5138i		−	1.64771i
$156$		0			0
$157$	−4.86499	−	2.80880i	−0.388268	−	0.224167i	0.293141	−	0.956069i	$-0.405299\pi$
$157$	−4.86499	−	2.80880i	−0.388268	−	0.224167i	−0.681409	+	0.731902i	$0.738633\pi$
$158$	−1.42526	−	0.135760i	−0.113387	−	0.0108005i
$159$		0			0
$160$	−13.5664	+	8.74098i	−1.07252	+	0.691035i
$161$	−7.33132	+	2.36443i	−0.577789	+	0.186344i
$162$		0			0
$163$	−8.95891	+	5.17243i	−0.701716	+	0.405136i	−0.807986	−	0.589201i	$-0.799442\pi$
$163$	−8.95891	+	5.17243i	−0.701716	+	0.405136i	0.106270	+	0.994337i	$0.466109\pi$
$164$	−19.2539	+	6.67389i	−1.50347	+	0.521143i
$165$		0			0
$166$	−17.6468	−	12.5600i	−1.36966	−	0.974848i
$167$	−21.0063			−1.62551			−0.812756	−	0.582604i	$-0.802034\pi$
$167$	−21.0063			−1.62551			−0.812756	+	0.582604i	$0.802034\pi$
$168$		0			0
$169$	−4.83413			−0.371856
$170$	21.4257	+	15.2497i	1.64328	+	1.16960i
$171$		0			0
$172$	−16.0205	+	5.55312i	−1.22155	+	0.423421i
$173$	−5.53238	+	3.19412i	−0.420619	+	0.242845i	−0.695342	−	0.718679i	$-0.744747\pi$
$173$	−5.53238	+	3.19412i	−0.420619	+	0.242845i	0.274723	+	0.961523i	$0.411414\pi$
$174$		0			0
$175$	5.57083	−	6.15997i	0.421115	−	0.465650i
$176$	7.00664	−	1.01407i	0.528145	−	0.0764388i
$177$		0			0
$178$	10.5528	+	1.00519i	0.790968	+	0.0753421i
$179$	−21.1867	−	12.2322i	−1.58357	−	0.914274i	−0.994333	−	0.106314i	$-0.966095\pi$
$179$	−21.1867	−	12.2322i	−1.58357	−	0.914274i	−0.589237	−	0.807960i	$-0.700572\pi$
$180$		0			0
$181$		−	7.55083i		−	0.561249i	−0.959818	−	0.280624i	$-0.909459\pi$
$181$		−	7.55083i		−	0.561249i	0.959818	−	0.280624i	$-0.0905415\pi$
$182$	−11.6622	+	10.6617i	−0.864457	+	0.790297i
$183$		0			0
$184$	1.94708	+	8.00154i	0.143541	+	0.589881i
$185$	−17.9202	−	10.3462i	−1.31752	−	0.760670i
$186$		0			0
$187$	−5.76831	−	9.99101i	−0.421821	−	0.730615i
$188$	−1.35682	+	1.56733i	−0.0989565	+	0.114310i
$189$		0			0
$190$	0.911457	+	1.99458i	0.0661240	+	0.144702i
$191$	8.74199	−	5.04719i	0.632548	−	0.365202i	−0.149190	−	0.988809i	$-0.547667\pi$
$191$	8.74199	−	5.04719i	0.632548	−	0.365202i	0.781738	+	0.623607i	$0.214333\pi$
$192$		0			0
$193$	−1.38182	+	2.39339i	−0.0994659	+	0.172280i	−0.911464	−	0.411380i	$-0.865047\pi$
$193$	−1.38182	+	2.39339i	−0.0994659	+	0.172280i	0.811998	+	0.583660i	$0.198380\pi$
$194$	5.93553	−	8.33940i	0.426146	−	0.598734i
$195$		0			0
$196$	−1.25235	+	13.9439i	−0.0894533	+	0.995991i
$197$	9.57163			0.681950			0.340975	−	0.940072i	$-0.389243\pi$
$197$	9.57163			0.681950			0.340975	+	0.940072i	$0.389243\pi$
$198$		0			0
$199$	8.32073	−	14.4119i	0.589841	−	1.02164i	−0.404412	−	0.914577i	$-0.632524\pi$
$199$	8.32073	−	14.4119i	0.589841	−	1.02164i	0.994253	−	0.107058i	$-0.0341430\pi$
$200$	−6.13159	−	6.42162i	−0.433569	−	0.454077i
$201$		0			0
$202$	−5.07154	−	11.0983i	−0.356832	−	0.780872i
$203$	10.0782	+	2.16517i	0.707354	+	0.151965i
$204$		0			0
$205$	−14.5340	−	25.1736i	−1.01510	−	1.75820i
$206$	1.88039	−	19.7410i	0.131013	−	1.37542i
$207$		0			0
$208$	10.4544	+	13.2684i	0.724885	+	0.919999i
$209$		−	0.962009i		−	0.0665435i
$210$		0			0
$211$			12.5015i			0.860640i	0.902676	+	0.430320i	$0.141599\pi$
$211$			12.5015i			0.860640i	−0.902676	+	0.430320i	$0.858401\pi$
$212$	11.6610	+	2.24183i	0.800879	+	0.153969i
$213$		0			0
$214$	21.4722	+	2.04529i	1.46781	+	0.139813i
$215$	−12.0933	−	20.9461i	−0.824753	−	1.42851i
$216$		0			0
$217$	−12.7605	+	14.1100i	−0.866238	+	0.957847i
$218$	−22.1399	+	10.1172i	−1.49950	+	0.685224i
$219$		0			0
$220$	3.30745	+	9.54184i	0.222988	+	0.643311i
$221$	13.7633	−	23.8388i	0.925822	−	1.60357i
$222$		0			0
$223$	−15.0867			−1.01028			−0.505139	−	0.863038i	$-0.668559\pi$
$223$	−15.0867			−1.01028			−0.505139	+	0.863038i	$0.668559\pi$
$224$	14.7686	+	2.42661i	0.986769	+	0.162134i
$225$		0			0
$226$	−17.5821	−	12.5140i	−1.16955	−	0.832419i
$227$	−4.05477	+	7.02306i	−0.269124	+	0.466137i	−0.968636	−	0.248484i	$-0.920068\pi$
$227$	−4.05477	+	7.02306i	−0.269124	+	0.466137i	0.699512	+	0.714621i	$0.253401\pi$
$228$		0			0
$229$	7.99201	−	4.61419i	0.528127	−	0.304914i	−0.212127	−	0.977242i	$-0.568039\pi$
$229$	7.99201	−	4.61419i	0.528127	−	0.304914i	0.740253	+	0.672328i	$0.234706\pi$
$230$	−10.6842	+	4.88235i	−0.704499	+	0.321932i
$231$		0			0
$232$	3.09727	−	10.5757i	0.203346	−	0.694330i
$233$	−5.62489	−	9.74260i	−0.368499	−	0.638259i	0.620832	−	0.783943i	$-0.286795\pi$
$233$	−5.62489	−	9.74260i	−0.368499	−	0.638259i	−0.989331	+	0.145685i	$0.953461\pi$
$234$		0			0
$235$	−2.56093	−	1.47855i	−0.167057	−	0.0964503i
$236$	−1.46534	−	0.281712i	−0.0953853	−	0.0183379i
$237$		0			0
$238$	−5.25125	−	23.8168i	−0.340388	−	1.54382i
$239$		−	23.6492i		−	1.52974i	−0.644186	−	0.764869i	$-0.722804\pi$
$239$		−	23.6492i		−	1.52974i	0.644186	−	0.764869i	$-0.277196\pi$
$240$		0			0
$241$	19.7110	+	11.3802i	1.26970	+	0.733061i	0.974931	−	0.222508i	$-0.0714242\pi$
$241$	19.7110	+	11.3802i	1.26970	+	0.733061i	0.294768	+	0.955569i	$0.404758\pi$
$242$	−1.05503	+	11.0761i	−0.0678199	+	0.711997i
$243$		0			0
$244$	−5.49525	−	4.75717i	−0.351797	−	0.304547i
$245$	−19.8699	+	2.00087i	−1.26944	+	0.127831i
$246$		0			0
$247$	1.98785	−	1.14769i	0.126484	−	0.0730257i
$248$	14.0449	+	14.7093i	0.891855	+	0.934041i
$249$		0			0
$250$	−4.35358	+	6.11677i	−0.275345	+	0.386858i
$251$	29.9219			1.88866			0.944328	−	0.329007i	$-0.106714\pi$
$251$	29.9219			1.88866			0.944328	+	0.329007i	$0.106714\pi$
$252$		0			0
$253$	5.15313			0.323975
$254$	−5.31005	+	7.46060i	−0.333182	+	0.468120i
$255$		0			0
$256$	3.74312	−	15.5560i	0.233945	−	0.972250i
$257$	9.26721	−	5.35043i	0.578073	−	0.333751i	−0.182294	−	0.983244i	$-0.558352\pi$
$257$	9.26721	−	5.35043i	0.578073	−	0.333751i	0.760367	+	0.649493i	$0.225019\pi$
$258$		0			0
$259$	5.89019	+	18.2635i	0.365999	+	1.13484i
$260$	−15.7710	+	18.2179i	−0.978078	+	1.12983i
$261$		0			0
$262$	1.35049	−	14.1779i	0.0834335	−	0.875914i
$263$	10.5762	+	6.10617i	0.652156	+	0.376522i	0.789282	−	0.614031i	$-0.210453\pi$
$263$	10.5762	+	6.10617i	0.652156	+	0.376522i	−0.137126	+	0.990554i	$0.543786\pi$
$264$		0			0
$265$			16.9385i			1.04052i
$266$	0.613789	−	1.93889i	0.0376338	−	0.118881i
$267$		0			0
$268$	5.87838	−	30.5767i	0.359079	−	1.86777i
$269$	−18.6888	−	10.7900i	−1.13948	−	0.657878i	−0.193177	−	0.981164i	$-0.561879\pi$
$269$	−18.6888	−	10.7900i	−1.13948	−	0.657878i	−0.946301	+	0.323286i	$0.895212\pi$
$270$		0			0
$271$	2.75842	+	4.77772i	0.167562	+	0.290226i	0.937562	−	0.347818i	$-0.113077\pi$
$271$	2.75842	+	4.77772i	0.167562	+	0.290226i	−0.770000	+	0.638044i	$0.779744\pi$
$272$	−25.8039	+	3.73462i	−1.56459	+	0.226445i
$273$		0			0
$274$	10.8500	−	4.95809i	0.655473	−	0.299529i
$275$	−4.81163	+	2.77800i	−0.290152	+	0.167519i
$276$		0			0
$277$	0.733850	−	1.27107i	0.0440928	−	0.0763709i	−0.843137	−	0.537699i	$-0.819294\pi$
$277$	0.733850	−	1.27107i	0.0440928	−	0.0763709i	0.887230	+	0.461328i	$0.152627\pi$
$278$	−13.2558	−	9.43475i	−0.795030	−	0.565859i
$279$		0			0
$280$	0.578063	+	21.3415i	0.0345459	+	1.27540i
$281$	−11.4020			−0.680186			−0.340093	−	0.940392i	$-0.610459\pi$
$281$	−11.4020			−0.680186			−0.340093	+	0.940392i	$0.610459\pi$
$282$		0			0
$283$	5.20093	−	9.00827i	0.309163	−	0.535486i	−0.669016	−	0.743248i	$-0.733284\pi$
$283$	5.20093	−	9.00827i	0.309163	−	0.535486i	0.978180	+	0.207761i	$0.0666178\pi$
$284$	3.02901	−	1.04993i	0.179738	−	0.0623020i
$285$		0			0
$286$	9.61416	−	4.39335i	0.568497	−	0.259784i
$287$	−5.66219	+	26.3559i	−0.334228	+	1.55574i
$288$		0			0
$289$	12.7435	+	22.0723i	0.749615	+	1.29837i
$290$	15.6486	+	1.49058i	0.918920	+	0.0875299i
$291$		0			0
$292$	−3.28130	+	17.0679i	−0.192024	+	0.998821i
$293$			7.17534i			0.419188i	0.977789	+	0.209594i	$0.0672142\pi$
$293$			7.17534i			0.419188i	−0.977789	+	0.209594i	$0.932786\pi$
$294$		0			0
$295$		−	2.12852i		−	0.123927i
$296$	19.9332	−	4.85050i	1.15859	−	0.281930i
$297$		0			0
$298$	0.926446	−	9.72615i	0.0536676	−	0.563421i
$299$	6.14775	+	10.6482i	0.355534	+	0.615802i
$300$		0			0
$301$	−4.71131	+	21.9298i	−0.271556	+	1.26401i
$302$	7.78650	+	17.0395i	0.448063	+	0.980515i
$303$		0			0
$304$	−2.01916	−	0.806164i	−0.115807	−	0.0462367i
$305$	5.18398	−	8.97892i	0.296834	−	0.514131i
$306$		0			0
$307$	−14.0299			−0.800731			−0.400366	−	0.916355i	$-0.631117\pi$
$307$	−14.0299			−0.800731			−0.400366	+	0.916355i	$0.631117\pi$
$308$	3.66048	−	8.62051i	0.208575	−	0.491199i
$309$		0			0
$310$	−16.8225	+	23.6356i	−0.955453	+	1.34241i
$311$	1.27111	−	2.20163i	0.0720783	−	0.124843i	−0.827734	−	0.561121i	$-0.810370\pi$
$311$	1.27111	−	2.20163i	0.0720783	−	0.124843i	0.899812	+	0.436278i	$0.143704\pi$
$312$		0			0
$313$	−0.829959	+	0.479177i	−0.0469121	+	0.0270847i	−0.523273	−	0.852165i	$-0.675289\pi$
$313$	−0.829959	+	0.479177i	−0.0469121	+	0.0270847i	0.476361	+	0.879250i	$0.341956\pi$
$314$	3.30195	+	7.22579i	0.186340	+	0.407775i
$315$		0			0
$316$	1.53081	+	1.32521i	0.0861150	+	0.0745488i
$317$	−8.76308	−	15.1781i	−0.492184	−	0.852487i	0.507776	−	0.861489i	$-0.330468\pi$
$317$	−8.76308	−	15.1781i	−0.492184	−	0.852487i	−0.999959	+	0.00900231i	$0.997134\pi$
$318$		0			0
$319$	−5.97194	−	3.44790i	−0.334364	−	0.193045i
$320$	22.7990	+	1.05407i	1.27450	+	0.0589246i
$321$		0			0
$322$	10.3859	+	3.28785i	0.578786	+	0.183225i
$323$			3.54287i			0.197131i
$324$		0			0
$325$	−11.4807	−	6.62837i	−0.636833	−	0.367676i
$326$	14.5639	+	1.38726i	0.806621	+	0.0768331i
$327$		0			0
$328$	27.6568	+	8.09976i	1.52709	+	0.447234i
$329$	0.841754	+	2.61000i	0.0464074	+	0.143894i
$330$		0			0
$331$	20.7797	−	11.9972i	1.14216	−	0.659425i	0.195193	−	0.980765i	$-0.437467\pi$
$331$	20.7797	−	11.9972i	1.14216	−	0.659425i	0.946964	+	0.321340i	$0.104133\pi$
$332$	10.0323	+	28.9428i	0.550594	+	1.58844i
$333$		0			0
$334$	24.2029	+	17.2263i	1.32432	+	0.942581i
$335$	44.4151			2.42666
$336$		0			0
$337$	20.3650			1.10935			0.554677	−	0.832066i	$-0.312842\pi$
$337$	20.3650			1.10935			0.554677	+	0.832066i	$0.312842\pi$
$338$	5.56977	+	3.96426i	0.302955	+	0.215627i
$339$		0			0
$340$	−12.1806	−	35.1406i	−0.660587	−	1.90577i
$341$	11.0215	−	6.36325i	0.596846	−	0.344589i
$342$		0			0
$343$	14.9117	+	10.9837i	0.805156	+	0.593063i
$344$	23.0123	+	6.73953i	1.24074	+	0.363371i
$345$		0			0
$346$	8.99364	+	0.856671i	0.483501	+	0.0460549i
$347$	8.46776	+	4.88887i	0.454573	+	0.262448i	0.709760	−	0.704444i	$-0.248803\pi$
$347$	8.46776	+	4.88887i	0.454573	+	0.262448i	−0.255186	+	0.966892i	$0.582137\pi$
$348$		0			0
$349$		−	10.8570i		−	0.581161i	−0.956851	−	0.290580i	$-0.906152\pi$
$349$		−	10.8570i		−	0.581161i	0.956851	−	0.290580i	$-0.0938484\pi$
$350$	−11.4701	+	2.52898i	−0.613102	+	0.135180i
$351$		0			0
$352$	−8.90447	−	4.57744i	−0.474610	−	0.243978i
$353$	4.78811	+	2.76442i	0.254845	+	0.147135i	0.621981	−	0.783032i	$-0.286328\pi$
$353$	4.78811	+	2.76442i	0.254845	+	0.147135i	−0.367135	+	0.930167i	$0.619661\pi$
$354$		0			0
$355$	2.28648	+	3.96030i	0.121354	+	0.210191i
$356$	−11.3344	−	9.81206i	−0.600722	−	0.520038i
$357$		0			0
$358$	14.3798	+	31.4679i	0.759995	+	1.66313i
$359$	−3.87215	+	2.23558i	−0.204364	+	0.117990i	−0.598689	−	0.800981i	$-0.704312\pi$
$359$	−3.87215	+	2.23558i	−0.204364	+	0.117990i	0.394325	+	0.918971i	$0.370978\pi$
$360$		0			0
$361$	9.35228	−	16.1986i	0.492226	−	0.852560i
$362$	−6.19210	+	8.69988i	−0.325450	+	0.457256i
$363$		0			0
$364$	22.1800	−	2.72051i	1.16255	−	0.142594i
$365$	−24.7924			−1.29770
$366$		0			0
$367$	−8.01670	+	13.8853i	−0.418468	+	0.724808i	−0.995786	−	0.0917116i	$-0.970766\pi$
$367$	−8.01670	+	13.8853i	−0.418468	+	0.724808i	0.577317	+	0.816520i	$0.304100\pi$
$368$	4.31833	−	10.8159i	0.225108	−	0.563817i
$369$		0			0
$370$	12.1627	+	26.6162i	0.632310	+	1.38371i
$371$	10.5365	−	11.6508i	0.547026	−	0.604877i
$372$		0			0
$373$	−14.5208	−	25.1507i	−0.751856	−	1.30225i	−0.946922	−	0.321463i	$-0.895825\pi$
$373$	−14.5208	−	25.1507i	−0.751856	−	1.30225i	0.195066	−	0.980790i	$-0.437508\pi$
$374$	−1.54707	+	16.2417i	−0.0799973	+	0.839840i
$375$		0			0
$376$	2.84860	−	0.693173i	0.146905	−	0.0357477i
$377$		−	16.4536i		−	0.847401i
$378$		0			0
$379$			35.9866i			1.84851i	0.381779	+	0.924253i	$0.375311\pi$
$379$			35.9866i			1.84851i	−0.381779	+	0.924253i	$0.624689\pi$
$380$	0.585509	−	3.04555i	0.0300360	−	0.156234i
$381$		0			0
$382$	−14.2113	−	1.35367i	−0.727113	−	0.0692597i
$383$	−10.3619	−	17.9473i	−0.529466	−	0.917063i	−0.999409	−	0.0343660i	$-0.989059\pi$
$383$	−10.3619	−	17.9473i	−0.529466	−	0.917063i	0.469943	−	0.882697i	$-0.344275\pi$
$384$		0			0
$385$	13.0615	+	2.80607i	0.665673	+	0.143011i
$386$	3.55482	−	1.62443i	0.180935	−	0.0826815i
$387$		0			0
$388$	−13.6775	+	4.74099i	−0.694372	+	0.240687i
$389$	−6.96776	+	12.0685i	−0.353280	+	0.611898i	−0.986822	−	0.161810i	$-0.948267\pi$
$389$	−6.96776	+	12.0685i	−0.353280	+	0.611898i	0.633542	+	0.773708i	$0.281600\pi$
$390$		0			0
$391$	−18.9779			−0.959753
$392$	12.8777	−	15.0388i	0.650421	−	0.759574i
$393$		0			0
$394$	−11.0282	−	7.84927i	−0.555593	−	0.395440i
$395$	−1.44410	+	2.50126i	−0.0726607	+	0.125852i
$396$		0			0
$397$	1.53132	−	0.884110i	0.0768549	−	0.0443722i	−0.461080	−	0.887359i	$-0.652538\pi$
$397$	1.53132	−	0.884110i	0.0768549	−	0.0443722i	0.537935	+	0.842986i	$0.319205\pi$
$398$	−21.4055	+	9.78162i	−1.07296	+	0.490308i
$399$		0			0
$400$	1.79858	+	12.4271i	0.0899289	+	0.621354i
$401$	−18.5971	−	32.2110i	−0.928693	−	1.60854i	−0.785512	−	0.618846i	$-0.787600\pi$
$401$	−18.5971	−	32.2110i	−0.928693	−	1.60854i	−0.143181	−	0.989697i	$-0.545733\pi$
$402$		0			0
$403$	26.2975	+	15.1829i	1.30997	+	0.756312i
$404$	−3.25790	+	16.9461i	−0.162086	+	0.843100i
$405$		0			0
$406$	−9.83635	−	10.7594i	−0.488170	−	0.533979i
$407$		−	12.8373i		−	0.636322i
$408$		0			0
$409$	24.5693	+	14.1851i	1.21487	+	0.701408i	0.963817	−	0.266565i	$-0.0858886\pi$
$409$	24.5693	+	14.1851i	1.21487	+	0.701408i	0.251057	+	0.967972i	$0.419222\pi$
$410$	−3.89806	+	40.9231i	−0.192511	+	2.02105i
$411$		0			0
$412$	−18.3552	+	21.2030i	−0.904297	+	1.04460i
$413$	−1.32403	+	1.46405i	−0.0651512	+	0.0720413i
$414$		0			0
$415$	−37.8414	+	21.8478i	−1.85756	+	1.07246i
$416$	−1.16452	−	23.8608i	−0.0570952	−	1.16987i
$417$		0			0
$418$	−0.788901	+	1.10840i	−0.0385864	+	0.0542138i
$419$	27.0904			1.32345			0.661727	−	0.749745i	$-0.269824\pi$
$419$	27.0904			1.32345			0.661727	+	0.749745i	$0.269824\pi$
$420$		0			0
$421$	−8.47627			−0.413108			−0.206554	−	0.978435i	$-0.566225\pi$
$421$	−8.47627			−0.413108			−0.206554	+	0.978435i	$0.566225\pi$
$422$	10.2519	−	14.4039i	0.499057	−	0.701173i
$423$		0			0
$424$	−11.5971	−	12.1456i	−0.563203	−	0.589844i
$425$	17.7202	−	10.2308i	0.859556	−	0.496265i
$426$		0			0
$427$	−9.15094	+	2.95128i	−0.442845	+	0.142823i
$428$	−23.0625	−	19.9649i	−1.11477	−	0.965042i
$429$		0			0
$430$	−3.24344	+	34.0508i	−0.156413	+	1.64207i
$431$	−8.14605	−	4.70312i	−0.392381	−	0.226541i	0.290810	−	0.956781i	$-0.406075\pi$
$431$	−8.14605	−	4.70312i	−0.392381	−	0.226541i	−0.683191	+	0.730239i	$0.739409\pi$
$432$		0			0
$433$		−	14.0832i		−	0.676795i	−0.941003	−	0.338397i	$-0.890115\pi$
$433$		−	14.0832i		−	0.676795i	0.941003	−	0.338397i	$-0.109885\pi$
$434$	26.2733	−	5.79286i	1.26116	−	0.278066i
$435$		0			0
$436$	33.8057	+	6.49917i	1.61900	+	0.311254i
$437$	−1.37050	−	0.791258i	−0.0655599	−	0.0378510i
$438$		0			0
$439$	−7.33905	−	12.7116i	−0.350274	−	0.606692i	0.636024	−	0.771670i	$-0.280578\pi$
$439$	−7.33905	−	12.7116i	−0.350274	−	0.606692i	−0.986297	+	0.164978i	$0.947245\pi$
$440$	4.01408	−	13.7062i	0.191364	−	0.653416i
$441$		0			0
$442$	−35.4069	+	16.1798i	−1.68413	+	0.769593i
$443$	−22.9252	+	13.2359i	−1.08921	+	0.628856i	−0.933366	−	0.358926i	$-0.883143\pi$
$443$	−22.9252	+	13.2359i	−1.08921	+	0.628856i	−0.155844	+	0.987782i	$0.549810\pi$
$444$		0			0
$445$	10.6924	−	18.5197i	0.506867	−	0.877920i
$446$	17.3825	+	12.3719i	0.823085	+	0.585827i
$447$		0			0
$448$	−15.0261	−	14.9070i	−0.709915	−	0.704287i
$449$	7.11931			0.335981			0.167990	−	0.985789i	$-0.446272\pi$
$449$	7.11931			0.335981			0.167990	+	0.985789i	$0.446272\pi$
$450$		0			0
$451$	9.01669	−	15.6174i	0.424579	−	0.735393i
$452$	9.99553	+	28.8367i	0.470150	+	1.35636i
$453$		0			0
$454$	10.4311	−	4.76667i	0.489556	−	0.223711i
$455$	9.78413	+	30.3373i	0.458687	+	1.42223i
$456$		0			0
$457$	6.79394	+	11.7675i	0.317807	+	0.550458i	0.980030	−	0.198849i	$-0.0637202\pi$
$457$	6.79394	+	11.7675i	0.317807	+	0.550458i	−0.662223	+	0.749307i	$0.730387\pi$
$458$	−12.9921	−	1.23754i	−0.607080	−	0.0578263i
$459$		0			0
$460$	16.3139	+	3.13636i	0.760641	+	0.146234i
$461$			9.08913i			0.423323i	0.977343	+	0.211661i	$0.0678874\pi$
$461$			9.08913i			0.423323i	−0.977343	+	0.211661i	$0.932113\pi$
$462$		0			0
$463$		−	15.6693i		−	0.728215i	−0.931357	−	0.364108i	$-0.881374\pi$
$463$		−	15.6693i		−	0.728215i	0.931357	−	0.364108i	$-0.118626\pi$
$464$	−12.2413	+	9.64514i	−0.568287	+	0.447764i
$465$		0			0
$466$	−1.50861	+	15.8379i	−0.0698850	+	0.733677i
$467$	−5.95250	−	10.3100i	−0.275449	−	0.477091i	0.694799	−	0.719204i	$-0.255493\pi$
$467$	−5.95250	−	10.3100i	−0.275449	−	0.477091i	−0.970248	+	0.242112i	$0.922160\pi$
$468$		0			0
$469$	−30.5499	−	27.6281i	−1.41066	−	1.27575i
$470$	1.73815	+	3.80366i	0.0801747	+	0.175450i
$471$		0			0
$472$	1.45731	+	1.52624i	0.0670780	+	0.0702509i
$473$	7.50248	−	12.9947i	0.344964	−	0.597496i
$474$		0			0
$475$	1.70623			0.0782874
$476$	−13.4808	+	31.7475i	−0.617889	+	1.45514i
$477$		0			0
$478$	−19.3936	+	27.2480i	−0.887044	+	1.24629i
$479$	8.41649	−	14.5778i	0.384559	−	0.666076i	−0.607149	−	0.794588i	$-0.707687\pi$
$479$	8.41649	−	14.5778i	0.384559	−	0.666076i	0.991708	+	0.128512i	$0.0410201\pi$
$480$		0			0
$481$	26.5265	−	15.3151i	1.20950	−	0.698307i
$482$	−13.3782	−	29.2761i	−0.609360	−	1.33349i
$483$		0			0
$484$	10.2986	−	11.8964i	0.468117	−	0.540746i
$485$	−10.3247	−	17.8828i	−0.468818	−	0.812017i
$486$		0			0
$487$	17.5227	+	10.1167i	0.794030	+	0.458433i	0.841379	−	0.540445i	$-0.181744\pi$
$487$	17.5227	+	10.1167i	0.794030	+	0.458433i	−0.0473495	+	0.998878i	$0.515077\pi$
$488$	2.43034	+	9.98751i	0.110017	+	0.452113i
$489$		0			0
$490$	24.5345	+	13.9891i	1.10835	+	0.631963i
$491$		−	41.3354i		−	1.86544i	−0.360598	−	0.932721i	$-0.617427\pi$
$491$		−	41.3354i		−	1.86544i	0.360598	−	0.932721i	$-0.382573\pi$
$492$		0			0
$493$	21.9934	+	12.6979i	0.990532	+	0.571884i
$494$	−3.23153	−	0.307813i	−0.145393	−	0.0138491i
$495$		0			0
$496$	−4.11981	−	28.4653i	−0.184985	−	1.27813i
$497$	0.890771	−	4.14629i	0.0399565	−	0.185986i
$498$		0			0
$499$	0.390579	−	0.225501i	0.0174847	−	0.0100948i	−0.491232	−	0.871029i	$-0.663453\pi$
$499$	0.390579	−	0.225501i	0.0174847	−	0.0100948i	0.508717	+	0.860934i	$0.330120\pi$
$500$	10.0322	−	3.47741i	0.448653	−	0.155515i
$501$		0			0
$502$	−34.4753	−	24.5376i	−1.53871	−	1.09517i
$503$	13.4711			0.600648			0.300324	−	0.953837i	$-0.402905\pi$
$503$	13.4711			0.600648			0.300324	+	0.953837i	$0.402905\pi$
$504$		0			0
$505$	−24.6156			−1.09538
$506$	−5.93732	−	4.22586i	−0.263946	−	0.187862i
$507$		0			0
$508$	12.2362	−	4.24139i	0.542894	−	0.188181i
$509$	−24.4715	+	14.1286i	−1.08468	+	0.626241i	−0.932156	−	0.362058i	$-0.882074\pi$
$509$	−24.4715	+	14.1286i	−1.08468	+	0.626241i	−0.152526	+	0.988299i	$0.548741\pi$
$510$		0			0
$511$	17.0529	+	15.4219i	0.754376	+	0.682226i
$512$	−17.0695	+	14.8537i	−0.754373	+	0.656446i
$513$		0			0
$514$	−15.0651	−	1.43500i	−0.664493	−	0.0632950i
$515$	−34.6445	−	20.0020i	−1.52662	−	0.881394i
$516$		0			0
$517$		−	1.83455i		−	0.0806834i
$518$	8.19057	−	25.8731i	0.359873	−	1.13680i
$519$		0			0
$520$	33.1107	−	8.05711i	1.45200	−	0.353327i
$521$	−2.78447	−	1.60761i	−0.121990	−	0.0704308i	0.437763	−	0.899090i	$-0.355771\pi$
$521$	−2.78447	−	1.60761i	−0.121990	−	0.0704308i	−0.559753	+	0.828659i	$0.689104\pi$
$522$		0			0
$523$	4.55871	+	7.89592i	0.199339	+	0.345265i	0.948314	−	0.317333i	$-0.102787\pi$
$523$	4.55871	+	7.89592i	0.199339	+	0.345265i	−0.748976	+	0.662598i	$0.769454\pi$
$524$	−13.1827	+	15.2280i	−0.575888	+	0.665237i
$525$		0			0
$526$	−7.17823	−	15.7084i	−0.312986	−	0.684921i
$527$	−40.5897	+	23.4345i	−1.76812	+	1.02082i
$528$		0			0
$529$	−7.26151	+	12.5773i	−0.315718	+	0.546840i
$530$	13.8905	−	19.5161i	0.603365	−	0.847726i
$531$		0			0
$532$	−2.29719	+	1.73060i	−0.0995958	+	0.0750311i
$533$	43.0281			1.86375
$534$		0			0
$535$	21.7562	−	37.6828i	0.940601	−	1.62917i
$536$	−31.8475	+	30.4091i	−1.37560	+	1.31347i
$537$		0			0
$538$	12.6844	+	27.7579i	0.546864	+	1.19673i
$539$	−7.23852	−	10.0549i	−0.311785	−	0.433094i
$540$		0			0
$541$	0.174562	+	0.302350i	0.00750501	+	0.0129991i	0.869754	−	0.493486i	$-0.164278\pi$
$541$	0.174562	+	0.302350i	0.00750501	+	0.0129991i	−0.862249	+	0.506485i	$0.830944\pi$
$542$	0.739814	−	7.76683i	0.0317777	−	0.333614i
$543$		0			0
$544$	32.7933	+	16.8577i	1.40600	+	0.722769i
$545$			49.1056i			2.10345i
$546$		0			0
$547$		−	4.43293i		−	0.189538i	−0.995499	−	0.0947691i	$-0.969789\pi$
$547$		−	4.43293i		−	0.189538i	0.995499	−	0.0947691i	$-0.0302113\pi$
$548$	−16.5670	−	3.18502i	−0.707708	−	0.136057i
$549$		0			0
$550$	7.82196	+	0.745065i	0.333529	+	0.0317697i
$551$	1.05884	+	1.83397i	0.0451082	+	0.0781298i
$552$		0			0
$553$	2.54918	−	0.822140i	0.108402	−	0.0349610i
$554$	−1.88787	+	0.862693i	−0.0802079	+	0.0366523i
$555$		0			0
$556$	7.53598	+	21.7410i	0.319597	+	0.922023i
$557$	−22.3160	+	38.6524i	−0.945559	+	1.63776i	−0.190931	+	0.981603i	$0.561151\pi$
$557$	−22.3160	+	38.6524i	−0.945559	+	1.63776i	−0.754628	+	0.656153i	$0.772183\pi$
$558$		0			0
$559$	35.8022			1.51427
$560$	16.8351	−	25.0631i	0.711415	−	1.05911i
$561$		0			0
$562$	13.1371	+	9.35027i	0.554155	+	0.394417i
$563$	−13.0308	+	22.5701i	−0.549184	+	0.951215i	0.449147	+	0.893458i	$0.351728\pi$
$563$	−13.0308	+	22.5701i	−0.549184	+	0.951215i	−0.998331	+	0.0577567i	$0.981605\pi$
$564$		0			0
$565$	−37.7027	+	21.7677i	−1.58617	+	0.915774i
$566$	−13.3797	+	6.11406i	−0.562389	+	0.256993i
$567$		0			0
$568$	−4.35095	−	1.27425i	−0.182562	−	0.0534662i
$569$	−23.2605	−	40.2883i	−0.975129	−	1.68897i	−0.679509	−	0.733667i	$-0.737807\pi$
$569$	−23.2605	−	40.2883i	−0.975129	−	1.68897i	−0.295619	−	0.955306i	$-0.595526\pi$
$570$		0			0
$571$	14.5851	+	8.42069i	0.610366	+	0.352395i	0.773109	−	0.634274i	$-0.218701\pi$
$571$	14.5851	+	8.42069i	0.610366	+	0.352395i	−0.162743	+	0.986669i	$0.552034\pi$
$572$	−14.6800	−	2.82224i	−0.613802	−	0.118004i
$573$		0			0
$574$	28.1371	−	25.7233i	1.17442	−	1.07367i
$575$			9.13968i			0.381151i
$576$		0			0
$577$	4.72176	+	2.72611i	0.196569	+	0.113489i	0.595054	−	0.803686i	$-0.297131\pi$
$577$	4.72176	+	2.72611i	0.196569	+	0.113489i	−0.398485	+	0.917175i	$0.630464\pi$
$578$	3.41783	−	35.8815i	0.142163	−	1.49247i
$579$		0			0
$580$	−16.8076	−	14.5502i	−0.697899	−	0.604163i
$581$	39.6186	+	8.51150i	1.64366	+	0.353116i
$582$		0			0
$583$	−9.10055	+	5.25420i	−0.376906	+	0.217607i
$584$	17.7772	−	16.9743i	0.735627	−	0.702402i
$585$		0			0
$586$	5.88418	−	8.26725i	0.243073	−	0.341517i
$587$	−10.5171			−0.434086			−0.217043	−	0.976162i	$-0.569641\pi$
$587$	−10.5171			−0.434086			−0.217043	+	0.976162i	$0.569641\pi$
$588$		0			0
$589$	−3.90828			−0.161038
$590$	−1.74551	+	2.45243i	−0.0718613	+	0.100965i
$591$		0			0
$592$	−26.9442	−	10.7577i	−1.10740	−	0.442137i
$593$	8.88810	−	5.13154i	0.364990	−	0.210727i	−0.306277	−	0.951942i	$-0.599083\pi$
$593$	8.88810	−	5.13154i	0.364990	−	0.210727i	0.671268	+	0.741215i	$0.265750\pi$
$594$		0			0
$595$	−48.1025	−	10.3342i	−1.97201	−	0.423659i
$596$	−9.04341	+	10.4465i	−0.370433	+	0.427905i
$597$		0			0
$598$	1.64884	−	17.3101i	0.0674261	−	0.707863i
$599$	12.6954	+	7.32969i	0.518720	+	0.299483i	0.736411	−	0.676535i	$-0.236519\pi$
$599$	12.6954	+	7.32969i	0.518720	+	0.299483i	−0.217691	+	0.976018i	$0.569852\pi$
$600$		0			0
$601$			14.0269i			0.572171i	0.958204	+	0.286085i	$0.0923541\pi$
$601$			14.0269i			0.572171i	−0.958204	+	0.286085i	$0.907646\pi$
$602$	23.4119	−	21.4035i	0.954199	−	0.872340i
$603$		0			0
$604$	5.00195	−	26.0179i	0.203527	−	1.05865i
$605$	19.4380	+	11.2226i	0.790268	+	0.456262i
$606$		0			0
$607$	−7.69932	−	13.3356i	−0.312506	−	0.541276i	0.666398	−	0.745596i	$-0.267835\pi$
$607$	−7.69932	−	13.3356i	−0.312506	−	0.541276i	−0.978904	+	0.204320i	$0.934502\pi$
$608$	1.66532	+	2.58466i	0.0675378	+	0.104822i
$609$		0			0
$610$	−13.3361	+	6.09414i	−0.539962	+	0.246744i
$611$	3.79083	−	2.18864i	0.153361	−	0.0885428i
$612$		0			0
$613$	−12.0789	+	20.9213i	−0.487862	+	0.845001i	−0.999903	−	0.0139598i	$-0.995556\pi$
$613$	−12.0789	+	20.9213i	−0.487862	+	0.845001i	0.512041	+	0.858961i	$0.328890\pi$
$614$	16.1650	+	11.5053i	0.652365	+	0.464318i
$615$		0			0
$616$	−11.2868	+	6.93054i	−0.454758	+	0.279240i
$617$	−12.8036			−0.515452			−0.257726	−	0.966218i	$-0.582973\pi$
$617$	−12.8036			−0.515452			−0.257726	+	0.966218i	$0.582973\pi$
$618$		0			0
$619$	1.93550	−	3.35239i	0.0777943	−	0.134744i	−0.824504	−	0.565857i	$-0.808546\pi$
$619$	1.93550	−	3.35239i	0.0777943	−	0.134744i	0.902298	+	0.431113i	$0.141879\pi$
$620$	38.7649	−	13.4369i	1.55684	−	0.539640i
$621$		0			0
$622$	−3.27001	+	1.49429i	−0.131115	+	0.0599154i
$623$	−18.8746	+	6.08726i	−0.756193	+	0.243881i
$624$		0			0
$625$	15.4208	+	26.7095i	0.616830	+	1.06838i
$626$	1.34921	+	0.128516i	0.0539253	+	0.00513655i
$627$		0			0
$628$	2.12113	−	11.0332i	0.0846423	−	0.440271i
$629$			47.2770i			1.88506i
$630$		0			0
$631$		−	27.3742i		−	1.08975i	−0.838517	−	0.544875i	$-0.816577\pi$
$631$		−	27.3742i		−	1.08975i	0.838517	−	0.544875i	$-0.183423\pi$
$632$	−0.677022	−	2.78222i	−0.0269305	−	0.110671i
$633$		0			0
$634$	−2.35028	+	24.6740i	−0.0933415	+	0.979932i
$635$	9.23664	+	15.9983i	0.366545	+	0.634875i
$636$		0			0
$637$	12.1413	−	26.9529i	0.481056	−	1.06791i
$638$	4.05325	+	8.86991i	0.160470	+	0.351163i
$639$		0			0
$640$	−25.4040	−	19.9109i	−1.00418	−	0.787048i
$641$	−10.7778	+	18.6676i	−0.425696	+	0.737327i	−0.996485	−	0.0837699i	$-0.973304\pi$
$641$	−10.7778	+	18.6676i	−0.425696	+	0.737327i	0.570789	+	0.821096i	$0.306637\pi$
$642$		0			0
$643$	−23.6557			−0.932890			−0.466445	−	0.884550i	$-0.654466\pi$
$643$	−23.6557			−0.932890			−0.466445	+	0.884550i	$0.654466\pi$
$644$	−9.27021	−	12.3052i	−0.365297	−	0.484894i
$645$		0			0
$646$	2.90535	−	4.08201i	0.114310	−	0.160605i
$647$	12.1830	−	21.1017i	0.478965	−	0.829592i	−0.520744	−	0.853713i	$-0.674345\pi$
$647$	12.1830	−	21.1017i	0.478965	−	0.829592i	0.999709	+	0.0241213i	$0.00767878\pi$
$648$		0			0
$649$	1.14359	−	0.660252i	0.0448898	−	0.0259172i
$650$	7.79212	+	17.0518i	0.305632	+	0.668828i
$651$		0			0
$652$	−15.6426	−	13.5416i	−0.612610	−	0.530329i
$653$	20.7142	+	35.8781i	0.810611	+	1.40402i	0.912437	+	0.409217i	$0.134198\pi$
$653$	20.7142	+	35.8781i	0.810611	+	1.40402i	−0.101826	+	0.994802i	$0.532468\pi$
$654$		0			0
$655$	−24.8816	−	14.3654i	−0.972205	−	0.561303i
$656$	−25.2232	−	32.0125i	−0.984802	−	1.24988i
$657$		0			0
$658$	1.17049	−	3.69746i	0.0456306	−	0.144142i
$659$			6.41436i			0.249868i	0.992165	+	0.124934i	$0.0398719\pi$
$659$			6.41436i			0.249868i	−0.992165	+	0.124934i	$0.960128\pi$
$660$		0			0
$661$	−19.0811	−	11.0165i	−0.742168	−	0.428491i	0.0806893	−	0.996739i	$-0.474288\pi$
$661$	−19.0811	−	11.0165i	−0.742168	−	0.428491i	−0.822857	+	0.568249i	$0.807621\pi$
$662$	−33.7803	−	3.21767i	−1.31291	−	0.125058i
$663$		0			0
$664$	12.1757	−	41.5742i	0.472508	−	1.61339i
$665$	−3.04288	−	2.75186i	−0.117998	−	0.106713i
$666$		0			0
$667$	−9.82392	+	5.67184i	−0.380384	+	0.219615i
$668$	−13.7595	−	39.6954i	−0.532370	−	1.53586i
$669$		0			0
$670$	−51.1740	−	36.4229i	−1.97702	−	1.40714i
$671$	6.43213			0.248310
$672$		0			0
$673$	22.7070			0.875291			0.437646	−	0.899148i	$-0.355812\pi$
$673$	22.7070			0.875291			0.437646	+	0.899148i	$0.355812\pi$
$674$	−23.4641	−	16.7005i	−0.903803	−	0.643277i
$675$		0			0
$676$	−3.16644	−	9.13504i	−0.121786	−	0.351348i
$677$	27.7601	−	16.0273i	1.06691	−	0.615979i	0.139572	−	0.990212i	$-0.455427\pi$
$677$	27.7601	−	16.0273i	1.06691	−	0.615979i	0.927335	+	0.374233i	$0.122094\pi$
$678$		0			0
$679$	−4.02230	+	18.7226i	−0.154362	+	0.718509i
$680$	−14.7830	+	50.4769i	−0.566902	+	1.93570i
$681$		0			0
$682$	−17.9169	−	1.70664i	−0.686073	−	0.0653506i
$683$	0.190021	+	0.109709i	0.00727095	+	0.00419789i	0.503631	−	0.863919i	$-0.331997\pi$
$683$	0.190021	+	0.109709i	0.00727095	+	0.00419789i	−0.496360	+	0.868117i	$0.665330\pi$
$684$		0			0
$685$		−	24.0649i		−	0.919474i
$686$	−8.17366	−	24.8836i	−0.312072	−	0.950059i
$687$		0			0
$688$	−20.9874	−	26.6365i	−0.800137	−	1.01551i
$689$	−21.7141	−	12.5367i	−0.827242	−	0.477609i
$690$		0			0
$691$	−6.41646	−	11.1136i	−0.244094	−	0.422782i	0.717783	−	0.696267i	$-0.245157\pi$
$691$	−6.41646	−	11.1136i	−0.244094	−	0.422782i	−0.961876	+	0.273485i	$0.911824\pi$
$692$	−9.65973	−	8.36232i	−0.367208	−	0.317888i
$693$		0			0
$694$	−5.74721	−	12.5769i	−0.218161	−	0.477412i
$695$	−28.4254	+	16.4114i	−1.07824	+	0.622521i
$696$		0			0
$697$	−33.2065	+	57.5154i	−1.25779	+	2.17855i
$698$	−8.90333	+	12.5092i	−0.336996	+	0.473478i
$699$		0			0
$700$	15.2895	+	6.49228i	0.577888	+	0.245385i
$701$	20.7329			0.783069			0.391535	−	0.920163i	$-0.371944\pi$
$701$	20.7329			0.783069			0.391535	+	0.920163i	$0.371944\pi$
$702$		0			0
$703$	−1.97115	+	3.41414i	−0.0743435	+	0.128767i
$704$	6.50576	+	12.5762i	0.245195	+	0.473982i
$705$		0			0
$706$	−3.24977	−	7.11161i	−0.122307	−	0.267649i
$707$	16.9313	+	15.3119i	0.636765	+	0.575864i
$708$		0			0
$709$	−14.0235	−	24.2895i	−0.526665	−	0.912211i	−0.999517	−	0.0310690i	$-0.990109\pi$
$709$	−14.0235	−	24.2895i	−0.526665	−	0.912211i	0.472852	−	0.881142i	$-0.343225\pi$
$710$	0.613239	−	6.43800i	0.0230145	−	0.241614i
$711$		0			0
$712$	5.01278	+	20.6001i	0.187862	+	0.772020i
$713$		−	20.9353i		−	0.784031i
$714$		0			0
$715$		−	21.3239i		−	0.797468i
$716$	9.23739	−	48.0487i	0.345218	−	1.79567i
$717$		0			0
$718$	6.29470	+	0.599589i	0.234916	+	0.0223765i
$719$	3.17475	+	5.49883i	0.118398	+	0.205072i	0.919133	−	0.393947i	$-0.128891\pi$
$719$	3.17475	+	5.49883i	0.118398	+	0.205072i	−0.800735	+	0.599019i	$0.795557\pi$
$720$		0			0
$721$	11.3873	+	35.3083i	0.424086	+	1.31495i
$722$	−24.0593	+	10.9943i	−0.895393	+	0.409165i
$723$		0			0
$724$	14.2688	−	4.94592i	0.530295	−	0.183814i
$725$	6.11525	−	10.5919i	0.227115	−	0.393374i
$726$		0			0
$727$	−23.0852			−0.856184			−0.428092	−	0.903735i	$-0.640814\pi$
$727$	−23.0852			−0.856184			−0.428092	+	0.903735i	$0.640814\pi$
$728$	−27.7863	−	15.0544i	−1.02983	−	0.557952i
$729$		0			0
$730$	28.5652	+	20.3312i	1.05725	+	0.752491i
$731$	−27.6300	+	47.8566i	−1.02193	+	1.77004i
$732$		0			0
$733$	−8.36040	+	4.82688i	−0.308798	+	0.178285i	−0.646389	−	0.763008i	$-0.723722\pi$
$733$	−8.36040	+	4.82688i	−0.308798	+	0.178285i	0.337590	+	0.941293i	$0.390388\pi$
$734$	20.6234	−	9.42420i	0.761223	−	0.347854i
$735$		0			0
$736$	−13.8451	+	8.92054i	−0.510337	+	0.328816i
$737$	13.7772	+	23.8629i	0.507491	+	0.879001i
$738$		0			0
$739$	−2.91317	−	1.68192i	−0.107163	−	0.0618705i	0.445461	−	0.895301i	$-0.353040\pi$
$739$	−2.91317	−	1.68192i	−0.107163	−	0.0618705i	−0.552623	+	0.833431i	$0.686373\pi$
$740$	7.81319	−	40.6407i	0.287219	−	1.49398i
$741$		0			0
$742$	−21.6941	+	4.78323i	−0.796416	+	0.175598i
$743$		−	40.5983i		−	1.48941i	−0.667395	−	0.744704i	$-0.732591\pi$
$743$		−	40.5983i		−	1.48941i	0.667395	−	0.744704i	$-0.267409\pi$
$744$		0			0
$745$	−17.0690	−	9.85477i	−0.625358	−	0.361051i
$746$	−3.89450	+	40.8858i	−0.142588	+	1.49694i
$747$		0			0
$748$	15.1016	−	17.4446i	0.552170	−	0.637839i
$749$	−38.4047	+	12.3860i	−1.40328	+	0.452573i
$750$		0			0
$751$	4.08817	−	2.36031i	0.149179	−	0.0861288i	−0.423552	−	0.905872i	$-0.639217\pi$
$751$	4.08817	−	2.36031i	0.149179	−	0.0861288i	0.572732	+	0.819743i	$0.305884\pi$
$752$	−3.85053	−	1.53735i	−0.140414	−	0.0560615i
$753$		0			0
$754$	−13.4928	+	18.9574i	−0.491380	+	0.690387i
$755$	37.7931			1.37543
$756$		0			0
$757$	−22.2141			−0.807385			−0.403693	−	0.914895i	$-0.632273\pi$
$757$	−22.2141			−0.807385			−0.403693	+	0.914895i	$0.632273\pi$
$758$	29.5110	−	41.4629i	1.07189	−	1.50600i
$759$		0			0
$760$	−3.17213	+	3.02886i	−0.115065	+	0.109868i
$761$	10.5025	−	6.06362i	0.380715	−	0.219806i	−0.297414	−	0.954749i	$-0.596124\pi$
$761$	10.5025	−	6.06362i	0.380715	−	0.219806i	0.678129	+	0.734942i	$0.262791\pi$
$762$		0			0
$763$	30.5457	−	33.7761i	1.10583	−	1.22278i
$764$	15.2638	+	13.2137i	0.552225	+	0.478055i
$765$		0			0
$766$	−2.77908	+	29.1757i	−0.100412	+	1.05416i
$767$	2.72863	+	1.57538i	0.0985253	+	0.0568836i
$768$		0			0
$769$		−	21.9487i		−	0.791490i	−0.918360	−	0.395745i	$-0.870486\pi$
$769$		−	21.9487i		−	0.791490i	0.918360	−	0.395745i	$-0.129514\pi$
$770$	−12.7480	−	13.9442i	−0.459404	−	0.502514i
$771$		0			0
$772$	−5.42790	−	1.04352i	−0.195354	−	0.0375570i
$773$	16.4032	+	9.47040i	0.589983	+	0.340627i	0.765091	−	0.643923i	$-0.222694\pi$
$773$	16.4032	+	9.47040i	0.589983	+	0.340627i	−0.175108	+	0.984549i	$0.556027\pi$
$774$		0			0
$775$	11.2860	+	19.5479i	0.405404	+	0.702180i
$776$	19.6468	+	5.75390i	0.705279	+	0.206553i
$777$		0			0
$778$	17.9249	−	8.19110i	0.642640	−	0.293665i
$779$	−4.79606	+	2.76901i	−0.171837	+	0.0992100i
$780$		0			0
$781$	−1.41850	+	2.45691i	−0.0507579	+	0.0879153i
$782$	21.8659	+	15.5629i	0.781922	+	0.556529i
$783$		0			0
$784$	−27.1700	+	6.76693i	−0.970357	+	0.241676i
$785$	16.0266			0.572012
$786$		0			0
$787$	−6.74746	+	11.6869i	−0.240521	+	0.416594i	−0.960863	−	0.277025i	$-0.910652\pi$
$787$	−6.74746	+	11.6869i	−0.240521	+	0.416594i	0.720342	+	0.693619i	$0.243985\pi$
$788$	6.26958	+	18.0875i	0.223345	+	0.644340i
$789$		0			0
$790$	3.71503	−	1.69765i	0.132175	−	0.0603995i
$791$	39.4734	+	8.48030i	1.40351	+	0.301525i
$792$		0			0
$793$	7.67361	+	13.2911i	0.272498	+	0.471980i
$794$	−2.48937	−	0.237120i	−0.0883446	−	0.00841509i
$795$		0			0
$796$	32.6844	+	6.28359i	1.15847	+	0.222716i
$797$		−	0.0728981i		−	0.00258218i	−0.999999	−	0.00129109i	$-0.999589\pi$
$797$		−	0.0728981i		−	0.00258218i	0.999999	−	0.00129109i	$-0.000410967\pi$
$798$		0			0
$799$			6.75625i			0.239019i
$800$	8.11862	−	15.7931i	0.287036	−	0.558371i
$801$		0			0
$802$	−4.98777	+	52.3634i	−0.176124	+	1.84902i
$803$	−7.69044	−	13.3202i	−0.271390	−	0.470061i
$804$		0			0
$805$	14.7407	−	16.2996i	0.519542	−	0.574487i
$806$	−17.8485	−	39.0587i	−0.628688	−	1.37579i
$807$		0			0
$808$	17.6504	−	16.8532i	0.620939	−	0.592895i
$809$	−7.07479	+	12.2539i	−0.248737	+	0.430824i	−0.963176	−	0.268873i	$-0.913349\pi$
$809$	−7.07479	+	12.2539i	−0.248737	+	0.430824i	0.714439	+	0.699698i	$0.246682\pi$
$810$		0			0
$811$	−18.1412			−0.637024			−0.318512	−	0.947919i	$-0.603183\pi$
$811$	−18.1412			−0.637024			−0.318512	+	0.947919i	$0.603183\pi$
$812$	2.50991	+	20.4630i	0.0880807	+	0.718112i
$813$		0			0
$814$	−10.5273	+	14.7908i	−0.368982	+	0.518418i
$815$	14.7565	−	25.5590i	0.516898	−	0.895294i
$816$		0			0
$817$	−3.99064	+	2.30400i	−0.139615	+	0.0806066i
$818$	−16.6756	−	36.4919i	−0.583048	−	1.27591i
$819$		0			0
$820$	38.0505	−	43.9540i	1.32878	−	1.53494i
$821$	−2.90469	−	5.03108i	−0.101375	−	0.175586i	0.810877	−	0.585217i	$-0.198991\pi$
$821$	−2.90469	−	5.03108i	−0.101375	−	0.175586i	−0.912251	+	0.409631i	$0.865657\pi$
$822$		0			0
$823$	22.1016	+	12.7604i	0.770414	+	0.444799i	0.833022	−	0.553239i	$-0.186609\pi$
$823$	22.1016	+	12.7604i	0.770414	+	0.444799i	−0.0626083	+	0.998038i	$0.519942\pi$
$824$	38.5361	−	9.37731i	1.34247	−	0.326674i
$825$		0			0
$826$	2.72612	−	0.601069i	0.0948538	−	0.0209138i
$827$		−	6.80233i		−	0.236540i	−0.992981	−	0.118270i	$-0.962265\pi$
$827$		−	6.80233i		−	0.236540i	0.992981	−	0.118270i	$-0.0377349\pi$
$828$		0			0
$829$	−35.3356	−	20.4010i	−1.22726	−	0.708557i	−0.260801	−	0.965393i	$-0.583987\pi$
$829$	−35.3356	−	20.4010i	−1.22726	−	0.708557i	−0.966455	+	0.256836i	$0.917320\pi$
$830$	61.5164	+	5.85962i	2.13526	+	0.203390i
$831$		0			0
$832$	−18.2254	+	28.4468i	−0.631853	+	0.986214i
$833$	26.6579	+	37.0299i	0.923642	+	1.28301i
$834$		0			0
$835$	51.9001	−	29.9646i	1.79608	−	1.03697i
$836$	1.81790	−	0.630133i	0.0628735	−	0.0217936i
$837$		0			0
$838$	−31.2129	−	22.2157i	−1.07823	−	0.767427i
$839$	−52.5454			−1.81407			−0.907035	−	0.421055i	$-0.861660\pi$
$839$	−52.5454			−1.81407			−0.907035	+	0.421055i	$0.861660\pi$
$840$		0			0
$841$	−13.8201			−0.476557
$842$	9.76615	+	6.95101i	0.336564	+	0.239548i
$843$		0			0
$844$	−23.6241	+	8.18871i	−0.813174	+	0.281867i
$845$	11.9437	−	6.89569i	0.410875	−	0.237219i
$846$		0			0
$847$	−6.38909	−	19.8104i	−0.219532	−	0.680695i
$848$	3.40177	+	23.5041i	0.116817	+	0.807135i
$849$		0			0
$850$	−28.8066	−	2.74392i	−0.988058	−	0.0941155i
$851$	−18.2883	−	10.5588i	−0.626915	−	0.361950i
$852$		0			0
$853$		−	12.4666i		−	0.426850i	−0.976959	−	0.213425i	$-0.931538\pi$
$853$		−	12.4666i		−	0.426850i	0.976959	−	0.213425i	$-0.0684619\pi$
$854$	12.9637	+	4.10389i	0.443609	+	0.140432i
$855$		0			0
$856$	10.1997	+	41.9157i	0.348618	+	1.43265i
$857$	32.3050	+	18.6513i	1.10352	+	0.637116i	0.937143	−	0.348947i	$-0.113461\pi$
$857$	32.3050	+	18.6513i	1.10352	+	0.637116i	0.166375	+	0.986063i	$0.446794\pi$
$858$		0			0
$859$	1.68296	+	2.91497i	0.0574219	+	0.0994577i	0.893307	−	0.449446i	$-0.148379\pi$
$859$	1.68296	+	2.91497i	0.0574219	+	0.0994577i	−0.835886	+	0.548904i	$0.815045\pi$
$860$	31.6605	−	36.5727i	1.07961	−	1.24712i
$861$		0			0
$862$	5.52885	+	12.0990i	0.188314	+	0.412095i
$863$	−24.2007	+	13.9723i	−0.823802	+	0.475622i	−0.851726	−	0.523988i	$-0.824444\pi$
$863$	−24.2007	+	13.9723i	−0.823802	+	0.475622i	0.0279238	+	0.999610i	$0.491110\pi$
$864$		0			0
$865$	9.11257	−	15.7834i	0.309837	−	0.536653i
$866$	−11.5490	+	16.2263i	−0.392451	+	0.551392i
$867$		0			0
$868$	−35.0219	−	14.8711i	−1.18872	−	0.504760i
$869$	−1.79180			−0.0607827
$870$		0			0
$871$	−32.8729	+	56.9374i	−1.11385	+	1.92925i
$872$	−33.6205	−	35.2108i	−1.13853	−	1.19239i
$873$		0			0
$874$	0.930180	+	2.03555i	0.0314638	+	0.0688537i
$875$	2.95027	−	13.7326i	0.0997372	−	0.464248i
$876$		0			0
$877$	14.0384	+	24.3153i	0.474044	+	0.821068i	0.999558	−	0.0297165i	$-0.00946046\pi$
$877$	14.0384	+	24.3153i	0.474044	+	0.821068i	−0.525514	+	0.850785i	$0.676127\pi$
$878$	−1.96835	+	20.6644i	−0.0664286	+	0.697391i
$879$		0			0
$880$	−15.8648	+	12.5002i	−0.534801	+	0.421380i
$881$			3.29547i			0.111027i	0.998458	+	0.0555137i	$0.0176796\pi$
$881$			3.29547i			0.111027i	−0.998458	+	0.0555137i	$0.982320\pi$
$882$		0			0
$883$		−	25.4860i		−	0.857671i	−0.903383	−	0.428836i	$-0.858924\pi$
$883$		−	25.4860i		−	0.857671i	0.903383	−	0.428836i	$-0.141076\pi$
$884$	54.0633	+	10.3937i	1.81835	+	0.349578i
$885$		0			0
$886$	37.2681	+	3.54990i	1.25204	+	0.119261i
$887$	2.85042	+	4.93708i	0.0957079	+	0.165771i	0.909904	−	0.414819i	$-0.136155\pi$
$887$	2.85042	+	4.93708i	0.0957079	+	0.165771i	−0.814196	+	0.580590i	$0.802822\pi$
$888$		0			0
$889$	3.59843	−	16.7497i	0.120687	−	0.561766i
$890$	−27.5067	+	12.5697i	−0.922027	+	0.421336i
$891$		0			0
$892$	−9.88203	−	28.5092i	−0.330875	−	0.954559i
$893$	−0.281693	+	0.487907i	−0.00942650	+	0.0163272i
$894$		0			0
$895$	69.7947			2.33298
$896$	5.08814	+	29.4976i	0.169983	+	0.985447i
$897$		0			0
$898$	−8.20269	−	5.83823i	−0.273727	−	0.194824i
$899$	−14.0075	+	24.2618i	−0.467177	+	0.809175i
$900$		0			0
$901$	33.5154	−	19.3501i	1.11656	−	0.644645i
$902$	−23.1959	+	10.5998i	−0.772340	+	0.352933i
$903$		0			0
$904$	12.1311	−	41.4218i	0.403473	−	1.37767i
$905$	10.7709	+	18.6558i	0.358038	+	0.620141i
$906$		0			0
$907$	−37.6912	−	21.7610i	−1.25152	−	0.722563i	−0.280105	−	0.959969i	$-0.590369\pi$
$907$	−37.6912	−	21.7610i	−1.25152	−	0.722563i	−0.971410	+	0.237407i	$0.923703\pi$
$908$	−15.9274	−	3.06205i	−0.528569	−	0.101618i
$909$		0			0
$910$	13.6052	−	42.9774i	0.451009	−	1.42469i
$911$			4.43779i			0.147030i	0.997294	+	0.0735152i	$0.0234218\pi$
$911$			4.43779i			0.147030i	−0.997294	+	0.0735152i	$0.976578\pi$
$912$		0			0
$913$	−23.4763	−	13.5540i	−0.776952	−	0.448573i
$914$	1.82215	−	19.1296i	0.0602714	−	0.632750i
$915$		0			0
$916$	13.9543	+	12.0801i	0.461064	+	0.399137i
$917$	8.17834	+	25.3583i	0.270073	+	0.837405i
$918$		0			0
$919$	34.7761	−	20.0780i	1.14716	−	0.662313i	0.198966	−	0.980006i	$-0.436242\pi$
$919$	34.7761	−	20.0780i	1.14716	−	0.662313i	0.948193	+	0.317694i	$0.102908\pi$
$920$	−16.2245	−	16.9920i	−0.534907	−	0.560209i
$921$		0			0
$922$	7.45359	−	10.4723i	0.245471	−	0.344886i
$923$	−6.76915			−0.222809
$924$		0			0
$925$	22.7684			0.748622
$926$	−12.8497	+	18.0538i	−0.422268	+	0.593285i
$927$		0			0
$928$	22.0137	−	1.07437i	0.722634	−	0.0352679i
$929$	−10.1745	+	5.87425i	−0.333814	+	0.192728i	−0.657533	−	0.753425i	$-0.728400\pi$
$929$	−10.1745	+	5.87425i	−0.333814	+	0.192728i	0.323719	+	0.946153i	$0.395067\pi$
$930$		0			0
$931$	0.381204	+	3.78560i	0.0124935	+	0.124068i
$932$	14.7261	−	17.0109i	0.482371	−	0.557211i
$933$		0			0
$934$	−1.59647	+	16.7603i	−0.0522382	+	0.548415i
$935$	28.5035	+	16.4565i	0.932165	+	0.538186i
$936$		0			0
$937$			38.1940i			1.24774i	0.781527	+	0.623872i	$0.214441\pi$
$937$			38.1940i			1.24774i	−0.781527	+	0.623872i	$0.785559\pi$
$938$	12.5423	+	56.8850i	0.409520	+	1.85736i
$939$		0			0
$940$	1.11656	−	5.80786i	0.0364183	−	0.189432i
$941$	−30.3283	−	17.5101i	−0.988675	−	0.570812i	−0.0837973	−	0.996483i	$-0.526705\pi$
$941$	−30.3283	−	17.5101i	−0.988675	−	0.570812i	−0.904878	+	0.425671i	$0.860038\pi$
$942$		0			0
$943$	−14.8326	−	25.6908i	−0.483015	−	0.836607i
$944$	−0.427472	−	2.95357i	−0.0139130	−	0.0961305i
$945$		0			0
$946$	−19.3005	+	8.81970i	−0.627515	+	0.286753i
$947$	40.7544	−	23.5296i	1.32434	−	0.764608i	0.339923	−	0.940453i	$-0.389599\pi$
$947$	40.7544	−	23.5296i	1.32434	−	0.764608i	0.984418	+	0.175845i	$0.0562657\pi$
$948$		0			0
$949$	18.3496	−	31.7824i	0.595652	−	1.03170i
$950$	−1.96588	−	1.39921i	−0.0637816	−	0.0453963i
$951$		0			0
$952$	41.5669	−	25.5237i	1.34719	−	0.827228i
$953$	24.6733			0.799247			0.399623	−	0.916679i	$-0.369141\pi$
$953$	24.6733			0.799247			0.399623	+	0.916679i	$0.369141\pi$
$954$		0			0
$955$	−14.3992	+	24.9402i	−0.465948	+	0.807045i
$956$	44.6897	−	15.4906i	1.44537	−	0.501002i
$957$		0			0
$958$	−21.6519	+	9.89418i	−0.699540	+	0.319667i
$959$	−14.9694	+	16.5525i	−0.483387	+	0.534508i
$960$		0			0
$961$	−10.3515	−	17.9293i	−0.333919	−	0.578365i
$962$	−43.1223	−	4.10754i	−1.39032	−	0.132432i
$963$		0			0
$964$	−8.59399	+	44.7021i	−0.276794	+	1.43976i
$965$		−	7.88446i		−	0.253810i
$966$		0			0
$967$			16.0848i			0.517253i	0.965977	+	0.258626i	$0.0832699\pi$
$967$			16.0848i			0.517253i	−0.965977	+	0.258626i	$0.916730\pi$
$968$	−21.6215	+	5.26134i	−0.694941	+	0.169106i
$969$		0			0
$970$	−2.76910	+	29.0709i	−0.0889103	+	0.933412i
$971$	10.0719	+	17.4451i	0.323224	+	0.559840i	0.981151	−	0.193241i	$-0.0619000\pi$
$971$	10.0719	+	17.4451i	0.323224	+	0.559840i	−0.657927	+	0.753081i	$0.728567\pi$
$972$		0			0
$973$	29.7604	+	6.39360i	0.954073	+	0.204969i
$974$	−11.8929	−	26.0259i	−0.381075	−	0.833922i
$975$		0			0
$976$	5.39013	−	13.5004i	0.172534	−	0.432137i
$977$	21.1153	−	36.5728i	0.675540	−	1.17007i	−0.300771	−	0.953696i	$-0.597244\pi$
$977$	21.1153	−	36.5728i	0.675540	−	1.17007i	0.976311	−	0.216373i	$-0.0694226\pi$
$978$		0			0
$979$	13.2668			0.424009
$980$	−16.7962	−	36.2375i	−0.536535	−	1.15757i
$981$		0			0
$982$	−33.8974	+	47.6257i	−1.08171	+	1.51980i
$983$	−25.2254	+	43.6917i	−0.804565	+	1.39355i	0.112019	+	0.993706i	$0.464268\pi$
$983$	−25.2254	+	43.6917i	−0.804565	+	1.39355i	−0.916584	+	0.399842i	$0.869065\pi$
$984$		0			0
$985$	−23.6486	+	13.6535i	−0.753508	+	0.435038i
$986$	−14.9273	−	32.6660i	−0.475381	−	1.04030i
$987$		0			0
$988$	3.47086	+	3.00469i	0.110423	+	0.0955918i
$989$	−12.3417	−	21.3764i	−0.392442	−	0.679730i
$990$		0			0
$991$	9.38001	+	5.41555i	0.297966	+	0.172031i	0.641529	−	0.767099i	$-0.278301\pi$
$991$	9.38001	+	5.41555i	0.297966	+	0.172031i	−0.343563	+	0.939130i	$0.611634\pi$
$992$	−18.5964	+	36.1755i	−0.590437	+	1.14857i
$993$		0			0
$994$	−4.42651	+	4.04677i	−0.140400	+	0.128356i
$995$			47.4767i			1.50511i
$996$		0			0
$997$	−23.7636	−	13.7199i	−0.752601	−	0.434515i	0.0740316	−	0.997256i	$-0.476413\pi$
$997$	−23.7636	−	13.7199i	−0.752601	−	0.434515i	−0.826633	+	0.562741i	$0.809747\pi$
$998$	−0.634940	−	0.0604799i	−0.0200987	−	0.00191446i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bf.d.703.4	yes	32
3.2	odd	2	inner	756.2.bf.d.703.13	yes	32
4.3	odd	2		756.2.bf.a.703.8	yes	32
7.5	odd	6		756.2.bf.a.271.8	✓	32
12.11	even	2		756.2.bf.a.703.9	yes	32
21.5	even	6		756.2.bf.a.271.9	yes	32
28.19	even	6	inner	756.2.bf.d.271.4	yes	32
84.47	odd	6	inner	756.2.bf.d.271.13	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bf.a.271.8	✓	32	7.5	odd	6
756.2.bf.a.271.9	yes	32	21.5	even	6
756.2.bf.a.703.8	yes	32	4.3	odd	2
756.2.bf.a.703.9	yes	32	12.11	even	2
756.2.bf.d.271.4	yes	32	28.19	even	6	inner
756.2.bf.d.271.13	yes	32	84.47	odd	6	inner
756.2.bf.d.703.4	yes	32	1.1	even	1	trivial
756.2.bf.d.703.13	yes	32	3.2	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-1.15218 - 0.820056i) q^{2} +(0.655017 + 1.88970i) q^{4} +(-2.47070 + 1.42646i) q^{5} +(2.58673 + 0.555723i) q^{7} +(0.794961 - 2.71441i) q^{8} +O(q^{10})\)	\(q+(-1.15218 - 0.820056i) q^{2} +(0.655017 + 1.88970i) q^{4} +(-2.47070 + 1.42646i) q^{5} +(2.58673 + 0.555723i) q^{7} +(0.794961 - 2.71441i) q^{8} +(4.01646 + 0.382580i) q^{10} +(-1.53279 - 0.884955i) q^{11} -4.22305i q^{13} +(-2.52464 - 2.76155i) q^{14} +(-3.14190 + 2.47557i) q^{16} +(5.64493 + 3.25910i) q^{17} +(0.271768 + 0.470716i) q^{19} +(-4.31393 - 3.73452i) q^{20} +(1.04033 + 2.27659i) q^{22} +(-2.52145 + 1.45576i) q^{23} +(1.56957 - 2.71857i) q^{25} +(-3.46313 + 4.86569i) q^{26} +(0.644206 + 5.25214i) q^{28} +3.89613 q^{29} +(-3.59524 + 6.22714i) q^{31} +(5.65013 - 0.275753i) q^{32} +(-3.83130 - 8.38421i) q^{34} +(-7.18375 + 2.31684i) q^{35} +(3.62654 + 6.28136i) q^{37} +(0.0728888 - 0.765212i) q^{38} +(1.90789 + 7.84048i) q^{40} +10.1889i q^{41} +8.47781i q^{43} +(0.668294 - 3.47616i) q^{44} +(4.09896 + 0.390439i) q^{46} +(0.518260 + 0.897653i) q^{47} +(6.38234 + 2.87501i) q^{49} +(-4.03780 + 1.84514i) q^{50} +(7.98028 - 2.76617i) q^{52} +(2.96863 - 5.14181i) q^{53} +5.04941 q^{55} +(3.56481 - 6.57968i) q^{56} +(-4.48903 - 3.19505i) q^{58} +(-0.373043 + 0.646129i) q^{59} +(-3.14727 + 1.81708i) q^{61} +(9.24895 - 4.22646i) q^{62} +(-6.73607 - 4.31570i) q^{64} +(6.02400 + 10.4339i) q^{65} +(-13.4826 - 7.78415i) q^{67} +(-2.46118 + 12.8020i) q^{68} +(10.1769 + 3.22167i) q^{70} -1.60291i q^{71} +(7.52594 + 4.34510i) q^{73} +(0.972647 - 10.2112i) q^{74} +(-0.711497 + 0.821885i) q^{76} +(-3.47312 - 3.14094i) q^{77} +(0.876737 - 0.506185i) q^{79} +(4.23140 - 10.5982i) q^{80} +(8.35544 - 11.7394i) q^{82} +15.3161 q^{83} -18.5959 q^{85} +(6.95228 - 9.76793i) q^{86} +(-3.62064 + 3.45711i) q^{88} +(-6.49151 + 3.74787i) q^{89} +(2.34684 - 10.9239i) q^{91} +(-4.40254 - 3.81123i) q^{92} +(0.138999 - 1.45926i) q^{94} +(-1.34291 - 0.775331i) q^{95} +7.23796i q^{97} +(-4.99592 - 8.54639i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{7}+O(q^{10}) \) 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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