LMFDB - Embedded newform 756.2.be.e.107.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(107,756)]

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, 3, 2]))

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

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

chi := DirichletCharacter("756.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.be (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:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.9
Character	$\chi$	$=$	756.107
Dual form			756.2.be.e.431.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.956512 - 1.04167i) q^{2} +(-0.170171 + 1.99275i) q^{4} +(3.20305 + 1.84928i) q^{5} +(2.45439 + 0.987919i) q^{7} +(2.23856 - 1.72882i) q^{8} +O(q^{10})$	\(q+(-0.956512 - 1.04167i) q^{2} +(-0.170171 + 1.99275i) q^{4} +(3.20305 + 1.84928i) q^{5} +(2.45439 + 0.987919i) q^{7} +(2.23856 - 1.72882i) q^{8} +(-1.13740 - 5.10539i) q^{10} +(-2.49232 - 4.31682i) q^{11} -1.51986 q^{13} +(-1.31856 - 3.50163i) q^{14} +(-3.94208 - 0.678214i) q^{16} +(6.93049 - 4.00132i) q^{17} +(0.597189 + 0.344787i) q^{19} +(-4.23021 + 6.06817i) q^{20} +(-2.11279 + 6.72528i) q^{22} +(2.21805 - 3.84178i) q^{23} +(4.33967 + 7.51653i) q^{25} +(1.45377 + 1.58320i) q^{26} +(-2.38634 + 4.72286i) q^{28} +4.63234i q^{29} +(-1.20328 + 0.694712i) q^{31} +(3.06417 + 4.75509i) q^{32} +(-10.7972 - 3.39201i) q^{34} +(6.03458 + 7.70320i) q^{35} +(-1.32034 + 2.28690i) q^{37} +(-0.212062 - 0.951869i) q^{38} +(10.3673 - 1.39777i) q^{40} +2.30280i q^{41} +7.31875i q^{43} +(9.02646 - 4.23196i) q^{44} +(-6.12347 + 1.36422i) q^{46} +(3.71238 - 6.43004i) q^{47} +(5.04803 + 4.84947i) q^{49} +(3.67883 - 11.7102i) q^{50} +(0.258636 - 3.02870i) q^{52} +(-4.04298 + 2.33422i) q^{53} -18.4360i q^{55} +(7.20224 - 2.03168i) q^{56} +(4.82539 - 4.43089i) q^{58} +(1.39305 + 2.41283i) q^{59} +(2.79023 - 4.83282i) q^{61} +(1.87461 + 0.588922i) q^{62} +(2.02234 - 7.74017i) q^{64} +(-4.86819 - 2.81065i) q^{65} +(5.18080 - 2.99114i) q^{67} +(6.79426 + 14.4916i) q^{68} +(2.25208 - 13.6543i) q^{70} -12.7979 q^{71} +(5.04592 + 8.73979i) q^{73} +(3.64512 - 0.812079i) q^{74} +(-0.788697 + 1.13137i) q^{76} +(-1.85244 - 13.0574i) q^{77} +(-9.17795 - 5.29889i) q^{79} +(-11.3725 - 9.46237i) q^{80} +(2.39877 - 2.20266i) q^{82} -11.9155 q^{83} +29.5983 q^{85} +(7.62375 - 7.00047i) q^{86} +(-13.0422 - 5.35470i) q^{88} +(1.07751 + 0.622098i) q^{89} +(-3.73033 - 1.50150i) q^{91} +(7.27825 + 5.07377i) q^{92} +(-10.2489 + 2.28331i) q^{94} +(1.27521 + 2.20874i) q^{95} -0.524083 q^{97} +(0.223067 - 9.89698i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q - 16 q^{13} + 8 q^{16} - 28 q^{22} + 36 q^{25} + 26 q^{28} - 56 q^{34} - 8 q^{37} + 22 q^{40} - 18 q^{46} + 28 q^{49} - 26 q^{52} - 36 q^{58} + 16 q^{61} - 12 q^{64} - 18 q^{70} + 32 q^{73} - 144 q^{76} + 34 q^{82} + 32 q^{85} - 20 q^{88} - 78 q^{94} + 56 q^{97}+O(q^{100}) $ 64 * q - 16 * q^13 + 8 * q^16 - 28 * q^22 + 36 * q^25 + 26 * q^28 - 56 * q^34 - 8 * q^37 + 22 * q^40 - 18 * q^46 + 28 * q^49 - 26 * q^52 - 36 * q^58 + 16 * q^61 - 12 * q^64 - 18 * q^70 + 32 * q^73 - 144 * q^76 + 34 * q^82 + 32 * q^85 - 20 * q^88 - 78 * q^94 + 56 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.956512	−	1.04167i	−0.676356	−	0.736575i
$2$	−0.956512	−	1.04167i	−0.676356	−	0.736575i
$3$		0			0
$3$		0			0
$4$	−0.170171	+	1.99275i	−0.0850853	+	0.996374i
$5$	3.20305	+	1.84928i	1.43245	+	0.827023i	0.997307	−	0.0733406i	$-0.0233660\pi$
$5$	3.20305	+	1.84928i	1.43245	+	0.827023i	0.435139	+	0.900363i	$0.356699\pi$
$6$		0			0
$7$	2.45439	+	0.987919i	0.927671	+	0.373398i
$7$	2.45439	+	0.987919i	0.927671	+	0.373398i
$8$	2.23856	−	1.72882i	0.791452	−	0.611232i
$9$		0			0
$10$	−1.13740	−	5.10539i	−0.359679	−	1.61447i
$11$	−2.49232	−	4.31682i	−0.751462	−	1.30157i	−0.947114	−	0.320897i	$-0.896016\pi$
$11$	−2.49232	−	4.31682i	−0.751462	−	1.30157i	0.195652	−	0.980673i	$-0.437318\pi$
$12$		0			0
$13$	−1.51986			−0.421534			−0.210767	−	0.977536i	$-0.567596\pi$
$13$	−1.51986			−0.421534			−0.210767	+	0.977536i	$0.567596\pi$
$14$	−1.31856	−	3.50163i	−0.352400	−	0.935849i
$15$		0			0
$16$	−3.94208	−	0.678214i	−0.985521	−	0.169554i
$17$	6.93049	−	4.00132i	1.68089	−	0.970463i	0.719822	−	0.694159i	$-0.244224\pi$
$17$	6.93049	−	4.00132i	1.68089	−	0.970463i	0.961070	−	0.276304i	$-0.0891098\pi$
$18$		0			0
$19$	0.597189	+	0.344787i	0.137004	+	0.0790996i	0.566936	−	0.823762i	$-0.308129\pi$
$19$	0.597189	+	0.344787i	0.137004	+	0.0790996i	−0.429931	+	0.902862i	$0.641462\pi$
$20$	−4.23021	+	6.06817i	−0.945904	+	1.35688i
$21$		0			0
$22$	−2.11279	+	6.72528i	−0.450449	+	1.43383i
$23$	2.21805	−	3.84178i	0.462496	−	0.801066i	−0.536589	−	0.843844i	$-0.680287\pi$
$23$	2.21805	−	3.84178i	0.462496	−	0.801066i	0.999085	+	0.0427777i	$0.0136207\pi$
$24$		0			0
$25$	4.33967	+	7.51653i	0.867934	+	1.50331i
$26$	1.45377	+	1.58320i	0.285107	+	0.310491i
$27$		0			0
$28$	−2.38634	+	4.72286i	−0.450975	+	0.892536i
$29$			4.63234i			0.860204i	0.902780	+	0.430102i	$0.141522\pi$
$29$			4.63234i			0.860204i	−0.902780	+	0.430102i	$0.858478\pi$
$30$		0			0
$31$	−1.20328	+	0.694712i	−0.216115	+	0.124774i	−0.604150	−	0.796871i	$-0.706487\pi$
$31$	−1.20328	+	0.694712i	−0.216115	+	0.124774i	0.388035	+	0.921645i	$0.373154\pi$
$32$	3.06417	+	4.75509i	0.541674	+	0.840589i
$33$		0			0
$34$	−10.7972	−	3.39201i	−1.85170	−	0.581724i
$35$	6.03458	+	7.70320i	1.02003	+	1.30208i
$36$		0			0
$37$	−1.32034	+	2.28690i	−0.217063	+	0.375963i	−0.953909	−	0.300097i	$-0.902981\pi$
$37$	−1.32034	+	2.28690i	−0.217063	+	0.375963i	0.736846	+	0.676061i	$0.236314\pi$
$38$	−0.212062	−	0.951869i	−0.0344010	−	0.154414i
$39$		0			0
$40$	10.3673	−	1.39777i	1.63921	−	0.221007i
$41$			2.30280i			0.359637i	0.983700	+	0.179819i	$0.0575511\pi$
$41$			2.30280i			0.359637i	−0.983700	+	0.179819i	$0.942449\pi$
$42$		0			0
$43$			7.31875i			1.11610i	0.829808	+	0.558049i	$0.188450\pi$
$43$			7.31875i			1.11610i	−0.829808	+	0.558049i	$0.811550\pi$
$44$	9.02646	−	4.23196i	1.36079	−	0.637993i
$45$		0			0
$46$	−6.12347	+	1.36422i	−0.902857	+	0.201143i
$47$	3.71238	−	6.43004i	0.541507	−	0.937917i	−0.457311	−	0.889307i	$-0.651187\pi$
$47$	3.71238	−	6.43004i	0.541507	−	0.937917i	0.998818	−	0.0486103i	$-0.0154793\pi$
$48$		0			0
$49$	5.04803	+	4.84947i	0.721147	+	0.692782i
$50$	3.67883	−	11.7102i	0.520265	−	1.65607i
$51$		0			0
$52$	0.258636	−	3.02870i	0.0358664	−	0.420005i
$53$	−4.04298	+	2.33422i	−0.555347	+	0.320630i	−0.751276	−	0.659989i	$-0.770561\pi$
$53$	−4.04298	+	2.33422i	−0.555347	+	0.320630i	0.195929	+	0.980618i	$0.437228\pi$
$54$		0			0
$55$		−	18.4360i		−	2.48591i
$56$	7.20224	−	2.03168i	0.962440	−	0.271495i
$57$		0			0
$58$	4.82539	−	4.43089i	0.633604	−	0.581804i
$59$	1.39305	+	2.41283i	0.181360	+	0.314124i	0.942344	−	0.334646i	$-0.108617\pi$
$59$	1.39305	+	2.41283i	0.181360	+	0.314124i	−0.760984	+	0.648771i	$0.775283\pi$
$60$		0			0
$61$	2.79023	−	4.83282i	0.357252	−	0.618779i	−0.630249	−	0.776393i	$-0.717047\pi$
$61$	2.79023	−	4.83282i	0.357252	−	0.618779i	0.987501	+	0.157615i	$0.0503804\pi$
$62$	1.87461	+	0.588922i	0.238076	+	0.0747932i
$63$		0			0
$64$	2.02234	−	7.74017i	0.252792	−	0.967521i
$65$	−4.86819	−	2.81065i	−0.603825	−	0.348618i
$66$		0			0
$67$	5.18080	−	2.99114i	0.632936	−	0.365426i	−0.148953	−	0.988844i	$-0.547590\pi$
$67$	5.18080	−	2.99114i	0.632936	−	0.365426i	0.781888	+	0.623419i	$0.214257\pi$
$68$	6.79426	+	14.4916i	0.823925	+	1.75737i
$69$		0			0
$70$	2.25208	−	13.6543i	0.269175	−	1.63200i
$71$	−12.7979			−1.51883			−0.759416	−	0.650605i	$-0.774515\pi$
$71$	−12.7979			−1.51883			−0.759416	+	0.650605i	$0.774515\pi$
$72$		0			0
$73$	5.04592	+	8.73979i	0.590581	+	1.02292i	0.994154	+	0.107968i	$0.0344345\pi$
$73$	5.04592	+	8.73979i	0.590581	+	1.02292i	−0.403574	+	0.914947i	$0.632232\pi$
$74$	3.64512	−	0.812079i	0.423737	−	0.0944022i
$75$		0			0
$76$	−0.788697	+	1.13137i	−0.0904698	+	0.129777i
$77$	−1.85244	−	13.0574i	−0.211106	−	1.48802i
$78$		0			0
$79$	−9.17795	−	5.29889i	−1.03260	−	0.596172i	−0.114872	−	0.993380i	$-0.536646\pi$
$79$	−9.17795	−	5.29889i	−1.03260	−	0.596172i	−0.917728	+	0.397208i	$0.869979\pi$
$80$	−11.3725	−	9.46237i	−1.27148	−	1.05792i
$81$		0			0
$82$	2.39877	−	2.20266i	0.264900	−	0.243243i
$83$	−11.9155			−1.30790			−0.653950	−	0.756538i	$-0.726889\pi$
$83$	−11.9155			−1.30790			−0.653950	+	0.756538i	$0.726889\pi$
$84$		0			0
$85$	29.5983			3.21038
$86$	7.62375	−	7.00047i	0.822091	−	0.754880i
$87$		0			0
$88$	−13.0422	−	5.35470i	−1.39031	−	0.570813i
$89$	1.07751	+	0.622098i	0.114215	+	0.0659423i	0.556019	−	0.831169i	$-0.312328\pi$
$89$	1.07751	+	0.622098i	0.114215	+	0.0659423i	−0.441804	+	0.897112i	$0.645661\pi$
$90$		0			0
$91$	−3.73033	−	1.50150i	−0.391045	−	0.157400i
$92$	7.27825	+	5.07377i	0.758810	+	0.528978i
$93$		0			0
$94$	−10.2489	+	2.28331i	−1.05710	+	0.235506i
$95$	1.27521	+	2.20874i	0.130834	+	0.226612i
$96$		0			0
$97$	−0.524083			−0.0532126			−0.0266063	−	0.999646i	$-0.508470\pi$
$97$	−0.524083			−0.0532126			−0.0266063	+	0.999646i	$0.508470\pi$
$98$	0.223067	−	9.89698i	0.0225332	−	0.999746i
$99$		0			0
$100$	−15.7170	+	7.36877i	−1.57170	+	0.736877i
$101$	−8.72864	+	5.03948i	−0.868532	+	0.501447i	−0.866860	−	0.498552i	$-0.833865\pi$
$101$	−8.72864	+	5.03948i	−0.868532	+	0.501447i	−0.00167165	+	0.999999i	$0.500532\pi$
$102$		0			0
$103$	4.81641	+	2.78076i	0.474575	+	0.273996i	0.718153	−	0.695885i	$-0.244988\pi$
$103$	4.81641	+	2.78076i	0.474575	+	0.273996i	−0.243578	+	0.969881i	$0.578321\pi$
$104$	−3.40231	+	2.62757i	−0.333624	+	0.257655i
$105$		0			0
$106$	6.29866	+	1.97877i	0.611780	+	0.192195i
$107$	−4.97561	+	8.61801i	−0.481010	+	0.833135i	−0.999763	−	0.0217901i	$-0.993063\pi$
$107$	−4.97561	+	8.61801i	−0.481010	+	0.833135i	0.518752	+	0.854925i	$0.326397\pi$
$108$		0			0
$109$	−4.74966	−	8.22666i	−0.454935	−	0.787971i	0.543749	−	0.839248i	$-0.317004\pi$
$109$	−4.74966	−	8.22666i	−0.454935	−	0.787971i	−0.998684	+	0.0512766i	$0.983671\pi$
$110$	−19.2043	+	17.6342i	−1.83106	+	1.68136i
$111$		0			0
$112$	−9.00538	−	5.55906i	−0.850928	−	0.525282i
$113$			0.626603i			0.0589458i	0.999566	+	0.0294729i	$0.00938288\pi$
$113$			0.626603i			0.0589458i	−0.999566	+	0.0294729i	$0.990617\pi$
$114$		0			0
$115$	14.2090	−	8.20359i	1.32500	−	0.764989i
$116$	−9.23108	−	0.788288i	−0.857084	−	0.0731907i
$117$		0			0
$118$	1.18092	−	3.75901i	0.108712	−	0.346045i
$119$	20.9631	−	2.97403i	1.92168	−	0.272629i
$120$		0			0
$121$	−6.92330	+	11.9915i	−0.629391	+	1.09014i
$122$	−7.70311	+	1.71614i	−0.697406	+	0.155372i
$123$		0			0
$124$	−1.17962	−	2.51605i	−0.105933	−	0.225948i
$125$			13.6082i			1.21716i
$126$		0			0
$127$			11.6552i			1.03423i	0.855916	+	0.517115i	$0.172994\pi$
$127$			11.6552i			1.03423i	−0.855916	+	0.517115i	$0.827006\pi$
$128$	−9.99712	+	5.29694i	−0.883629	+	0.468188i
$129$		0			0
$130$	1.72870	+	7.75949i	0.151617	+	0.680552i
$131$	7.55755	−	13.0901i	0.660306	−	1.14368i	−0.320229	−	0.947340i	$-0.603760\pi$
$131$	7.55755	−	13.0901i	0.660306	−	1.14368i	0.980535	−	0.196344i	$-0.0629068\pi$
$132$		0			0
$133$	1.12511	+	1.43621i	0.0975594	+	0.124536i
$134$	−8.07129	−	2.53565i	−0.697253	−	0.219047i
$135$		0			0
$136$	8.59677	−	20.9388i	0.737167	−	1.79549i
$137$	11.8335	−	6.83209i	1.01101	−	0.583705i	0.0995203	−	0.995036i	$-0.468269\pi$
$137$	11.8335	−	6.83209i	1.01101	−	0.583705i	0.911486	+	0.411331i	$0.134936\pi$
$138$		0			0
$139$			12.4537i			1.05631i	0.849148	+	0.528154i	$0.177116\pi$
$139$			12.4537i			1.05631i	−0.849148	+	0.528154i	$0.822884\pi$
$140$	−16.3774	+	10.7145i	−1.38415	+	0.905543i
$141$		0			0
$142$	12.2413	+	13.3312i	1.02727	+	1.11873i
$143$	3.78798	+	6.56098i	0.316767	+	0.548657i
$144$		0			0
$145$	−8.56649	+	14.8376i	−0.711408	+	1.23219i
$146$	4.27753	−	13.6159i	0.354011	−	1.12686i
$147$		0			0
$148$	−4.33252	−	3.02027i	−0.356131	−	0.248264i
$149$	−1.11294	−	0.642558i	−0.0911758	−	0.0526404i	0.453719	−	0.891145i	$-0.350097\pi$
$149$	−1.11294	−	0.642558i	−0.0911758	−	0.0526404i	−0.544895	+	0.838505i	$0.683430\pi$
$150$		0			0
$151$	13.7684	−	7.94918i	1.12045	−	0.646895i	0.178938	−	0.983860i	$-0.442734\pi$
$151$	13.7684	−	7.94918i	1.12045	−	0.646895i	0.941517	+	0.336965i	$0.109401\pi$
$152$	1.93292	−	0.260606i	0.156781	−	0.0211379i
$153$		0			0
$154$	−11.8296	+	14.4192i	−0.953259	+	1.16193i
$155$	−5.13887			−0.412764
$156$		0			0
$157$	−10.2490	−	17.7518i	−0.817958	−	1.41674i	−0.907184	−	0.420734i	$-0.861773\pi$
$157$	−10.2490	−	17.7518i	−0.817958	−	1.41674i	0.0892262	−	0.996011i	$-0.471561\pi$
$158$	3.25910	+	14.6289i	0.259280	+	1.16381i
$159$		0			0
$160$	1.02120	+	20.8973i	0.0807326	+	1.65207i
$161$	9.23932	−	7.23796i	0.728161	−	0.570431i
$162$		0			0
$163$	0.381895	+	0.220487i	0.0299123	+	0.0172699i	0.514882	−	0.857261i	$-0.327836\pi$
$163$	0.381895	+	0.220487i	0.0299123	+	0.0172699i	−0.484969	+	0.874531i	$0.661169\pi$
$164$	−4.58890	−	0.391869i	−0.358333	−	0.0305999i
$165$		0			0
$166$	11.3973	+	12.4121i	0.884605	+	0.963366i
$167$	−17.6888			−1.36880			−0.684399	−	0.729108i	$-0.739935\pi$
$167$	−17.6888			−1.36880			−0.684399	+	0.729108i	$0.739935\pi$
$168$		0			0
$169$	−10.6900			−0.822309
$170$	−28.3111	−	30.8317i	−2.17136	−	2.36469i
$171$		0			0
$172$	−14.5844	−	1.24544i	−1.11205	−	0.0949636i
$173$	−10.4426	−	6.02905i	−0.793938	−	0.458380i	0.0474092	−	0.998876i	$-0.484904\pi$
$173$	−10.4426	−	6.02905i	−0.793938	−	0.458380i	−0.841347	+	0.540495i	$0.818237\pi$
$174$		0			0
$175$	3.22551	+	22.7357i	0.243825	+	1.71866i
$176$	6.89720	+	18.7076i	0.519896	+	1.41014i
$177$		0			0
$178$	−0.382623	−	1.71745i	−0.0286788	−	0.128729i
$179$	11.9500	+	20.6980i	0.893183	+	1.54704i	0.836038	+	0.548672i	$0.184866\pi$
$179$	11.9500	+	20.6980i	0.893183	+	1.54704i	0.0571452	+	0.998366i	$0.481800\pi$
$180$		0			0
$181$	11.7087			0.870304			0.435152	−	0.900357i	$-0.356695\pi$
$181$	11.7087			0.870304			0.435152	+	0.900357i	$0.356695\pi$
$182$	2.00403	+	5.32199i	0.148549	+	0.394492i
$183$		0			0
$184$	−1.67651	−	12.4347i	−0.123594	−	0.916697i
$185$	−8.45822	+	4.88336i	−0.621861	+	0.359031i
$186$		0			0
$187$	−34.5460	−	19.9451i	−2.52625	−	1.45853i
$188$	12.1817	+	8.49204i	0.888442	+	0.619346i
$189$		0			0
$190$	1.08103	−	3.44104i	0.0784259	−	0.249639i
$191$	7.17341	−	12.4247i	0.519050	−	0.899021i	−0.480705	−	0.876882i	$-0.659619\pi$
$191$	7.17341	−	12.4247i	0.519050	−	0.899021i	0.999755	−	0.0221385i	$-0.00704747\pi$
$192$		0			0
$193$	−4.75482	−	8.23559i	−0.342260	−	0.592811i	0.642592	−	0.766208i	$-0.277859\pi$
$193$	−4.75482	−	8.23559i	−0.342260	−	0.592811i	−0.984852	+	0.173397i	$0.944526\pi$
$194$	0.501291	+	0.545924i	0.0359906	+	0.0391950i
$195$		0			0
$196$	−10.5228	+	9.23422i	−0.751628	+	0.659587i
$197$		−	0.668076i		−	0.0475985i	−0.999717	−	0.0237992i	$-0.992424\pi$
$197$		−	0.668076i		−	0.0475985i	0.999717	−	0.0237992i	$-0.00757624\pi$
$198$		0			0
$199$	−16.1865	+	9.34529i	−1.14743	+	0.662470i	−0.948260	−	0.317494i	$-0.897159\pi$
$199$	−16.1865	+	9.34529i	−1.14743	+	0.662470i	−0.199172	+	0.979965i	$0.563825\pi$
$200$	22.7094	+	9.32370i	1.60580	+	0.659285i
$201$		0			0
$202$	13.5985	+	4.27207i	0.956790	+	0.300582i
$203$	−4.57637	+	11.3696i	−0.321199	+	0.797986i
$204$		0			0
$205$	−4.25852	+	7.37598i	−0.297428	+	0.515161i
$206$	−1.71031	−	7.67696i	−0.119163	−	0.534879i
$207$		0			0
$208$	5.99143	+	1.03079i	0.415431	+	0.0714726i
$209$		−	3.43728i		−	0.237761i
$210$		0			0
$211$			4.14073i			0.285060i	0.989790	+	0.142530i	$0.0455237\pi$
$211$			4.14073i			0.285060i	−0.989790	+	0.142530i	$0.954476\pi$
$212$	−3.96351	−	8.45386i	−0.272215	−	0.580614i
$213$		0			0
$214$	13.7364	−	3.06026i	0.939000	−	0.209195i
$215$	−13.5344	+	23.4423i	−0.923039	+	1.59875i
$216$		0			0
$217$	−3.63963	+	0.516353i	−0.247074	+	0.0350523i
$218$	−4.02639	+	12.8165i	−0.272702	+	0.868043i
$219$		0			0
$220$	36.7382	+	3.13726i	2.47689	+	0.211514i
$221$	−10.5334	+	6.08146i	−0.708553	+	0.409083i
$222$		0			0
$223$			3.06563i			0.205290i	0.994718	+	0.102645i	$0.0327306\pi$
$223$			3.06563i			0.205290i	−0.994718	+	0.102645i	$0.967269\pi$
$224$	2.82302	+	14.6980i	0.188621	+	0.982050i
$225$		0			0
$226$	0.652716	−	0.599353i	0.0434180	−	0.0398683i
$227$	−4.48068	−	7.76076i	−0.297393	−	0.515100i	0.678146	−	0.734927i	$-0.262784\pi$
$227$	−4.48068	−	7.76076i	−0.297393	−	0.515100i	−0.975539	+	0.219828i	$0.929450\pi$
$228$		0			0
$229$	8.09515	−	14.0212i	0.534943	−	0.926548i	−0.464223	−	0.885718i	$-0.653666\pi$
$229$	8.09515	−	14.0212i	0.534943	−	0.926548i	0.999166	−	0.0408299i	$-0.0130002\pi$
$230$	−22.1366	−	6.95436i	−1.45964	−	0.458557i
$231$		0			0
$232$	8.00850	+	10.3698i	0.525784	+	0.680810i
$233$	−4.31889	−	2.49351i	−0.282940	−	0.163356i	0.351814	−	0.936070i	$-0.385565\pi$
$233$	−4.31889	−	2.49351i	−0.282940	−	0.163356i	−0.634754	+	0.772715i	$0.718898\pi$
$234$		0			0
$235$	23.7819	−	13.7305i	1.55136	−	0.895677i
$236$	−5.04523	+	2.36540i	−0.328416	+	0.153975i
$237$		0			0
$238$	−23.1494	−	18.9920i	−1.50055	−	1.23107i
$239$	−4.55503			−0.294640			−0.147320	−	0.989089i	$-0.547065\pi$
$239$	−4.55503			−0.294640			−0.147320	+	0.989089i	$0.547065\pi$
$240$		0			0
$241$	2.73568	+	4.73833i	0.176221	+	0.305223i	0.940583	−	0.339564i	$-0.110279\pi$
$241$	2.73568	+	4.73833i	0.176221	+	0.305223i	−0.764362	+	0.644787i	$0.776946\pi$
$242$	19.1135	−	4.25820i	1.22866	−	0.273727i
$243$		0			0
$244$	9.15577	+	6.38262i	0.586138	+	0.408606i
$245$	7.20105	+	24.8683i	0.460058	+	1.58878i
$246$		0			0
$247$	−0.907645	−	0.524029i	−0.0577520	−	0.0333432i
$248$	−1.49258	+	3.63541i	−0.0947787	+	0.230849i
$249$		0			0
$250$	14.1754	−	13.0164i	0.896528	−	0.823232i
$251$	−3.64701			−0.230197			−0.115099	−	0.993354i	$-0.536718\pi$
$251$	−3.64701			−0.230197			−0.115099	+	0.993354i	$0.536718\pi$
$252$		0			0
$253$	−22.1124			−1.39019
$254$	12.1409	−	11.1483i	0.761787	−	0.699507i
$255$		0			0
$256$	15.0801	+	5.34716i	0.942503	+	0.334197i
$257$	−12.7250	−	7.34677i	−0.793763	−	0.458279i	0.0475229	−	0.998870i	$-0.484867\pi$
$257$	−12.7250	−	7.34677i	−0.793763	−	0.458279i	−0.841285	+	0.540591i	$0.818201\pi$
$258$		0			0
$259$	−5.49989	+	4.30854i	−0.341747	+	0.267720i
$260$	6.42934	−	9.22278i	0.398731	−	0.571973i
$261$		0			0
$262$	−20.8645	+	4.64829i	−1.28901	+	0.287172i
$263$	−2.24118	−	3.88183i	−0.138197	−	0.239364i	0.788617	−	0.614884i	$-0.210797\pi$
$263$	−2.24118	−	3.88183i	−0.138197	−	0.239364i	−0.926814	+	0.375520i	$0.877464\pi$
$264$		0			0
$265$	−17.2665			−1.06067
$266$	0.419887	−	2.54575i	0.0257449	−	0.156090i
$267$		0			0
$268$	5.07896	+	10.8330i	0.310247	+	0.661733i
$269$	−9.40005	+	5.42712i	−0.573131	+	0.330897i	−0.758399	−	0.651791i	$-0.774018\pi$
$269$	−9.40005	+	5.42712i	−0.573131	+	0.330897i	0.185268	+	0.982688i	$0.440685\pi$
$270$		0			0
$271$	2.52843	+	1.45979i	0.153591	+	0.0886759i	0.574826	−	0.818276i	$-0.305070\pi$
$271$	2.52843	+	1.45979i	0.153591	+	0.0886759i	−0.421235	+	0.906952i	$0.638403\pi$
$272$	−30.0343	+	11.0732i	−1.82110	+	0.671411i
$273$		0			0
$274$	−18.4357	−	5.79171i	−1.11374	−	0.349890i
$275$	21.6317	−	37.4671i	1.30444	−	2.25935i
$276$		0			0
$277$	−10.6321	−	18.4153i	−0.638818	−	1.10647i	−0.985692	−	0.168554i	$-0.946090\pi$
$277$	−10.6321	−	18.4153i	−0.638818	−	1.10647i	0.346874	−	0.937912i	$-0.387243\pi$
$278$	12.9727	−	11.9121i	0.778051	−	0.714441i
$279$		0			0
$280$	26.8263	+	6.81138i	1.60318	+	0.407058i
$281$		−	27.4407i		−	1.63697i	−0.574526	−	0.818486i	$-0.694814\pi$
$281$		−	27.4407i		−	1.63697i	0.574526	−	0.818486i	$-0.305186\pi$
$282$		0			0
$283$	−10.1979	+	5.88775i	−0.606201	+	0.349990i	−0.771477	−	0.636257i	$-0.780482\pi$
$283$	−10.1979	+	5.88775i	−0.606201	+	0.349990i	0.165276	+	0.986247i	$0.447148\pi$
$284$	2.17783	−	25.5030i	0.129230	−	1.51332i
$285$		0			0
$286$	3.21115	−	10.2215i	0.189879	−	0.604410i
$287$	−2.27498	+	5.65197i	−0.134288	+	0.333625i
$288$		0			0
$289$	23.5212	−	40.7399i	1.38360	−	2.39646i
$290$	23.6499	−	5.26884i	1.38877	−	0.309397i
$291$		0			0
$292$	−18.2749	+	8.56799i	−1.06946	+	0.501404i
$293$			9.82250i			0.573836i	0.957955	+	0.286918i	$0.0926308\pi$
$293$			9.82250i			0.573836i	−0.957955	+	0.286918i	$0.907369\pi$
$294$		0			0
$295$			10.3046i			0.599955i
$296$	0.997975	+	7.40200i	0.0580061	+	0.430232i
$297$		0			0
$298$	0.395207	+	1.77394i	0.0228937	+	0.102761i
$299$	−3.37113	+	5.83898i	−0.194958	+	0.337677i
$300$		0			0
$301$	−7.23033	+	17.9630i	−0.416749	+	1.03537i
$302$	−21.4501	−	6.73869i	−1.23431	−	0.387768i
$303$		0			0
$304$	−2.12033	−	1.76420i	−0.121609	−	0.101184i
$305$	17.8745	−	10.3198i	1.02349	−	0.590911i
$306$		0			0
$307$		−	2.16494i		−	0.123560i	−0.998090	−	0.0617798i	$-0.980322\pi$
$307$		−	2.16494i		−	0.123560i	0.998090	−	0.0617798i	$-0.0196777\pi$
$308$	26.3353	−	1.46947i	1.50059	−	0.0837310i
$309$		0			0
$310$	4.91539	+	5.35303i	0.279175	+	0.304031i
$311$	−1.71830	−	2.97618i	−0.0974356	−	0.168763i	0.813187	−	0.582003i	$-0.197731\pi$
$311$	−1.71830	−	2.97618i	−0.0974356	−	0.168763i	−0.910623	+	0.413239i	$0.864397\pi$
$312$		0			0
$313$	−4.17455	+	7.23053i	−0.235960	+	0.408694i	−0.959551	−	0.281534i	$-0.909157\pi$
$313$	−4.17455	+	7.23053i	−0.235960	+	0.408694i	0.723592	+	0.690228i	$0.242490\pi$
$314$	−8.68828	+	27.6559i	−0.490308	+	1.56071i
$315$		0			0
$316$	12.1212	−	17.3876i	0.681869	−	0.978130i
$317$	−27.0304	−	15.6060i	−1.51818	−	0.876521i	−0.999771	−	0.0213871i	$-0.993192\pi$
$317$	−27.0304	−	15.6060i	−1.51818	−	0.876521i	−0.518407	−	0.855134i	$-0.673475\pi$
$318$		0			0
$319$	19.9970	−	11.5453i	1.11962	−	0.646411i
$320$	20.7914	−	21.0522i	1.16227	−	1.17686i
$321$		0			0
$322$	−16.3771	−	2.70118i	−0.912661	−	0.150531i
$323$	5.51842			0.307053
$324$		0			0
$325$	−6.59570	−	11.4241i	−0.365864	−	0.633694i
$326$	−0.135611	−	0.608709i	−0.00751081	−	0.0337133i
$327$		0			0
$328$	3.98114	+	5.15497i	0.219822	+	0.284636i
$329$	15.4640	−	12.1143i	0.852557	−	0.667881i
$330$		0			0
$331$	17.3902	+	10.0402i	0.955853	+	0.551862i	0.894894	−	0.446278i	$-0.147251\pi$
$331$	17.3902	+	10.0402i	0.955853	+	0.551862i	0.0609587	+	0.998140i	$0.480584\pi$
$332$	2.02767	−	23.7446i	0.111283	−	1.30316i
$333$		0			0
$334$	16.9195	+	18.4259i	0.925795	+	1.00822i
$335$	22.1258			1.20886
$336$		0			0
$337$	2.98305			0.162497			0.0812484	−	0.996694i	$-0.474109\pi$
$337$	2.98305			0.162497			0.0812484	+	0.996694i	$0.474109\pi$
$338$	10.2251	+	11.1355i	0.556174	+	0.605692i
$339$		0			0
$340$	−5.03675	+	58.9818i	−0.273156	+	3.19874i
$341$	5.99790	+	3.46289i	0.324804	+	0.187526i
$342$		0			0
$343$	7.59894	+	16.8895i	0.410304	+	0.911949i
$344$	12.6528	+	16.3835i	0.682195	+	0.883339i
$345$		0			0
$346$	3.70818	+	16.6447i	0.199353	+	0.894823i
$347$	−1.17874	−	2.04163i	−0.0632778	−	0.109600i	0.832651	−	0.553798i	$-0.186822\pi$
$347$	−1.17874	−	2.04163i	−0.0632778	−	0.109600i	−0.895929	+	0.444198i	$0.853489\pi$
$348$		0			0
$349$	−28.5738			−1.52952			−0.764761	−	0.644314i	$-0.777143\pi$
$349$	−28.5738			−1.52952			−0.764761	+	0.644314i	$0.777143\pi$
$350$	20.5980	−	25.1069i	1.10101	−	1.34202i
$351$		0			0
$352$	12.8900	−	25.0787i	0.687038	−	1.33670i
$353$	0.883564	−	0.510126i	0.0470274	−	0.0271513i	−0.476302	−	0.879282i	$-0.658023\pi$
$353$	0.883564	−	0.510126i	0.0470274	−	0.0271513i	0.523329	+	0.852130i	$0.324690\pi$
$354$		0			0
$355$	−40.9923	−	23.6669i	−2.17564	−	1.25611i
$356$	−1.42304	+	2.04133i	−0.0754212	+	0.108190i
$357$		0			0
$358$	10.1302	−	32.2458i	0.535400	−	1.70424i
$359$	0.336562	−	0.582942i	0.0177630	−	0.0307665i	−0.857007	−	0.515304i	$-0.827679\pi$
$359$	0.336562	−	0.582942i	0.0177630	−	0.0307665i	0.874770	+	0.484538i	$0.161012\pi$
$360$		0			0
$361$	−9.26224	−	16.0427i	−0.487487	−	0.844351i
$362$	−11.1996	−	12.1967i	−0.588635	−	0.641044i
$363$		0			0
$364$	3.62691	−	7.17810i	0.190102	−	0.376235i
$365$			37.3253i			1.95369i
$366$		0			0
$367$	−12.9337	+	7.46728i	−0.675134	+	0.389789i	−0.798019	−	0.602632i	$-0.794119\pi$
$367$	−12.9337	+	7.46728i	−0.675134	+	0.389789i	0.122885	+	0.992421i	$0.460785\pi$
$368$	−11.3493	+	13.6403i	−0.591623	+	0.711050i
$369$		0			0
$370$	13.1773	+	4.13972i	0.685053	+	0.215214i
$371$	−12.2291	+	1.73493i	−0.634902	+	0.0900733i
$372$		0			0
$373$	−9.34358	+	16.1836i	−0.483792	+	0.837953i	−0.999827	−	0.0186148i	$-0.994074\pi$
$373$	−9.34358	+	16.1836i	−0.483792	+	0.837953i	0.516034	+	0.856568i	$0.327408\pi$
$374$	12.2673	+	55.0634i	0.634328	+	2.84726i
$375$		0			0
$376$	−2.80599	−	20.8121i	−0.144708	−	1.07330i
$377$		−	7.04052i		−	0.362605i
$378$		0			0
$379$			34.8225i			1.78871i	0.447358	+	0.894355i	$0.352365\pi$
$379$			34.8225i			1.78871i	−0.447358	+	0.894355i	$0.647635\pi$
$380$	−4.61846	+	2.16532i	−0.236922	+	0.111079i
$381$		0			0
$382$	−19.8040	+	4.41203i	−1.01326	+	0.225739i
$383$	−9.21751	+	15.9652i	−0.470993	+	0.815783i	−0.999449	−	0.0331769i	$-0.989438\pi$
$383$	−9.21751	+	15.9652i	−0.470993	+	0.815783i	0.528457	+	0.848960i	$0.322771\pi$
$384$		0			0
$385$	18.2132	−	45.2490i	0.928233	−	2.30610i
$386$	−4.03076	+	12.8304i	−0.205160	+	0.653051i
$387$		0			0
$388$	0.0891835	−	1.04436i	0.00452761	−	0.0530196i
$389$	18.3320	−	10.5840i	0.929468	−	0.536628i	0.0428245	−	0.999083i	$-0.486364\pi$
$389$	18.3320	−	10.5840i	0.929468	−	0.536628i	0.886643	+	0.462454i	$0.153031\pi$
$390$		0			0
$391$		−	35.5006i		−	1.79534i
$392$	19.6842	+	2.12869i	0.994203	+	0.107515i
$393$		0			0
$394$	−0.695918	+	0.639023i	−0.0350598	+	0.0321935i
$395$	−19.5983	−	33.9452i	−0.986096	−	1.70797i
$396$		0			0
$397$	−13.8762	+	24.0342i	−0.696425	+	1.20624i	0.273273	+	0.961937i	$0.411894\pi$
$397$	−13.8762	+	24.0342i	−0.696425	+	1.20624i	−0.969698	+	0.244307i	$0.921439\pi$
$398$	25.2174	+	7.92220i	1.26403	+	0.397104i
$399$		0			0
$400$	−12.0095	−	32.5740i	−0.600476	−	1.62870i
$401$	17.3528	+	10.0187i	0.866559	+	0.500308i	0.866203	−	0.499692i	$-0.166553\pi$
$401$	17.3528	+	10.0187i	0.866559	+	0.500308i	0.000355964		1.00000i	$0.499887\pi$
$402$		0			0
$403$	1.82882	−	1.05587i	0.0910998	−	0.0525965i
$404$	−8.55705	−	18.2515i	−0.425729	−	0.908048i
$405$		0			0
$406$	16.2207	−	6.10802i	0.805021	−	0.303136i
$407$	13.1628			0.652457
$408$		0			0
$409$	−10.5629	−	18.2955i	−0.522302	−	0.904654i	−0.999663	−	0.0259471i	$-0.991740\pi$
$409$	−10.5629	−	18.2955i	−0.522302	−	0.904654i	0.477361	−	0.878707i	$-0.341593\pi$
$410$	11.7567	−	2.61922i	0.580622	−	0.129354i
$411$		0			0
$412$	−6.36096	+	9.12469i	−0.313382	+	0.449541i
$413$	1.03540	+	7.29825i	0.0509487	+	0.359124i
$414$		0			0
$415$	−38.1660	−	22.0351i	−1.87349	−	1.08166i
$416$	−4.65712	−	7.22708i	−0.228334	−	0.354337i
$417$		0			0
$418$	−3.58052	+	3.28779i	−0.175129	+	0.160811i
$419$	8.17434			0.399343			0.199671	−	0.979863i	$-0.436013\pi$
$419$	8.17434			0.399343			0.199671	+	0.979863i	$0.436013\pi$
$420$		0			0
$421$	19.9807			0.973799			0.486899	−	0.873458i	$-0.338128\pi$
$421$	19.9807			0.973799			0.486899	+	0.873458i	$0.338128\pi$
$422$	4.31329	−	3.96066i	0.209968	−	0.192802i
$423$		0			0
$424$	−5.01503	+	12.2149i	−0.243551	+	0.593208i
$425$	60.1521	+	34.7288i	2.91780	+	1.68460i
$426$		0			0
$427$	11.6227	−	9.10508i	0.562463	−	0.440626i
$428$	−16.3268	−	11.3817i	−0.789186	−	0.550154i
$429$		0			0
$430$	37.3651	−	8.32438i	1.80190	−	0.401437i
$431$	9.62668	+	16.6739i	0.463701	+	0.803153i	0.999142	−	0.0414192i	$-0.0131879\pi$
$431$	9.62668	+	16.6739i	0.463701	+	0.803153i	−0.535441	+	0.844573i	$0.679855\pi$
$432$		0			0
$433$	22.9972			1.10517			0.552587	−	0.833455i	$-0.313641\pi$
$433$	22.9972			1.10517			0.552587	+	0.833455i	$0.313641\pi$
$434$	4.01922	+	3.29741i	0.192929	+	0.158281i
$435$		0			0
$436$	17.2019	−	8.06495i	0.823822	−	0.386241i
$437$	2.64919	−	1.52951i	0.126728	−	0.0731664i
$438$		0			0
$439$	19.7612	+	11.4091i	0.943150	+	0.544528i	0.890946	−	0.454109i	$-0.150042\pi$
$439$	19.7612	+	11.4091i	0.943150	+	0.544528i	0.0522036	+	0.998636i	$0.483376\pi$
$440$	−31.8725	−	41.2701i	−1.51946	−	1.96747i
$441$		0			0
$442$	16.4102	+	5.15538i	0.780555	+	0.245217i
$443$	6.80518	−	11.7869i	0.323324	−	0.560014i	−0.657848	−	0.753151i	$-0.728533\pi$
$443$	6.80518	−	11.7869i	0.323324	−	0.560014i	0.981172	+	0.193137i	$0.0618663\pi$
$444$		0			0
$445$	2.30087	+	3.98522i	0.109072	+	0.188917i
$446$	3.19339	−	2.93232i	0.151212	−	0.138849i
$447$		0			0
$448$	12.6103	−	16.9995i	0.595778	−	0.803149i
$449$			19.0355i			0.898340i	0.893446	+	0.449170i	$0.148280\pi$
$449$			19.0355i			0.898340i	−0.893446	+	0.449170i	$0.851720\pi$
$450$		0			0
$451$	9.94079	−	5.73932i	0.468093	−	0.270254i
$452$	−1.24866	−	0.106629i	−0.0587321	−	0.00501542i
$453$		0			0
$454$	−3.79837	+	12.0907i	−0.178266	+	0.567443i
$455$	−9.17173	−	11.7078i	−0.429977	−	0.548870i
$456$		0			0
$457$	3.12795	−	5.41777i	0.146319	−	0.253432i	−0.783545	−	0.621335i	$-0.786591\pi$
$457$	3.12795	−	5.41777i	0.146319	−	0.253432i	0.929864	+	0.367903i	$0.119924\pi$
$458$	−22.3486	+	4.97894i	−1.04428	+	0.232651i
$459$		0			0
$460$	13.9297	+	29.7110i	0.649477	+	1.38528i
$461$			12.0657i			0.561955i	0.959714	+	0.280978i	$0.0906587\pi$
$461$			12.0657i			0.561955i	−0.959714	+	0.280978i	$0.909341\pi$
$462$		0			0
$463$		−	23.2536i		−	1.08069i	−0.841444	−	0.540344i	$-0.818294\pi$
$463$		−	23.2536i		−	1.08069i	0.841444	−	0.540344i	$-0.181706\pi$
$464$	3.14172	−	18.2611i	0.145851	−	0.847749i
$465$		0			0
$466$	1.53364	+	6.88395i	0.0710446	+	0.318893i
$467$	−3.29279	+	5.70328i	−0.152372	+	0.263916i	−0.932099	−	0.362203i	$-0.882025\pi$
$467$	−3.29279	+	5.70328i	−0.152372	+	0.263916i	0.779727	+	0.626120i	$0.215358\pi$
$468$		0			0
$469$	15.6707	−	2.22320i	0.723605	−	0.102658i
$470$	−37.0503	−	11.6396i	−1.70900	−	0.536895i
$471$		0			0
$472$	7.28980	+	2.99295i	0.335540	+	0.137761i
$473$	31.5937	−	18.2407i	1.45268	−	0.838706i
$474$		0			0
$475$			5.98504i			0.274613i
$476$	2.35918	+	42.2803i	0.108133	+	1.93791i
$477$		0			0
$478$	4.35694	+	4.74485i	0.199282	+	0.217025i
$479$	−18.7952	−	32.5542i	−0.858774	−	1.48744i	−0.873099	−	0.487542i	$-0.837893\pi$
$479$	−18.7952	−	32.5542i	−0.858774	−	1.48744i	0.0143257	−	0.999897i	$-0.495440\pi$
$480$		0			0
$481$	2.00674	−	3.47577i	0.0914993	−	0.158481i
$482$	2.31909	−	7.38196i	0.105632	−	0.336239i
$483$		0			0
$484$	−22.7179	−	15.8370i	−1.03263	−	0.719864i
$485$	−1.67866	−	0.969176i	−0.0762241	−	0.0440080i
$486$		0			0
$487$	−15.2301	+	8.79312i	−0.690143	+	0.398454i	−0.803666	−	0.595081i	$-0.797120\pi$
$487$	−15.2301	+	8.79312i	−0.690143	+	0.398454i	0.113522	+	0.993535i	$0.463787\pi$
$488$	−2.10898	−	15.6424i	−0.0954692	−	0.708097i
$489$		0			0
$490$	19.0168	−	31.2880i	0.859090	−	1.41345i
$491$	34.6549			1.56396			0.781978	−	0.623306i	$-0.214211\pi$
$491$	34.6549			1.56396			0.781978	+	0.623306i	$0.214211\pi$
$492$		0			0
$493$	18.5355	+	32.1044i	0.834796	+	1.44591i
$494$	0.322305	+	1.44671i	0.0145012	+	0.0650906i
$495$		0			0
$496$	5.21458	−	1.92253i	0.234142	−	0.0863243i
$497$	−31.4110	−	12.6433i	−1.40898	−	0.567129i
$498$		0			0
$499$	2.07295	+	1.19682i	0.0927982	+	0.0535771i	0.545681	−	0.837993i	$-0.316271\pi$
$499$	2.07295	+	1.19682i	0.0927982	+	0.0535771i	−0.452883	+	0.891570i	$0.649604\pi$
$500$	−27.1178	−	2.31572i	−1.21274	−	0.103562i
$501$		0			0
$502$	3.48841	+	3.79900i	0.155695	+	0.169558i
$503$	−19.9230			−0.888323			−0.444162	−	0.895947i	$-0.646498\pi$
$503$	−19.9230			−0.888323			−0.444162	+	0.895947i	$0.646498\pi$
$504$		0			0
$505$	−37.2776			−1.65883
$506$	21.1507	+	23.0339i	0.940265	+	1.02398i
$507$		0			0
$508$	−23.2258	−	1.98337i	−1.03048	−	0.0879978i
$509$	−4.71119	−	2.72001i	−0.208820	−	0.120562i	0.391943	−	0.919990i	$-0.371803\pi$
$509$	−4.71119	−	2.72001i	−0.208820	−	0.120562i	−0.600763	+	0.799427i	$0.705136\pi$
$510$		0			0
$511$	3.75044	+	26.4358i	0.165910	+	1.16945i
$512$	−8.85425	−	20.8231i	−0.391306	−	0.920260i
$513$		0			0
$514$	4.51865	+	20.2826i	0.199309	+	0.894625i
$515$	10.2848	+	17.8138i	0.453202	+	0.784969i
$516$		0			0
$517$	−37.0098			−1.62769
$518$	9.74881	+	1.60793i	0.428338	+	0.0706484i
$519$		0			0
$520$	−15.7569	+	2.12442i	−0.690985	+	0.0931620i
$521$	39.1736	−	22.6169i	1.71623	−	0.990865i	0.790686	−	0.612222i	$-0.209724\pi$
$521$	39.1736	−	22.6169i	1.71623	−	0.990865i	0.925543	−	0.378643i	$-0.123609\pi$
$522$		0			0
$523$	−10.5505	−	6.09135i	−0.461343	−	0.266356i	0.251266	−	0.967918i	$-0.419153\pi$
$523$	−10.5505	−	6.09135i	−0.461343	−	0.266356i	−0.712609	+	0.701562i	$0.752486\pi$
$524$	24.7991	+	17.2878i	1.08335	+	0.755222i
$525$		0			0
$526$	−1.89989	+	6.04759i	−0.0828392	+	0.263688i
$527$	−5.55954	+	9.62940i	−0.242177	+	0.419463i
$528$		0			0
$529$	1.66050	+	2.87606i	0.0721955	+	0.125046i
$530$	16.5156	+	17.9861i	0.717392	+	0.781264i
$531$		0			0
$532$	−3.05347	+	1.99766i	−0.132385	+	0.0866095i
$533$		−	3.49994i		−	0.151599i
$534$		0			0
$535$	−31.8742	+	18.4026i	−1.37804	+	0.795613i
$536$	6.42641	−	15.6525i	0.277578	−	0.676087i
$537$		0			0
$538$	14.6445	+	4.60068i	0.631371	+	0.198350i
$539$	8.35300	−	33.8779i	0.359789	−	1.45922i
$540$		0			0
$541$	−7.06156	+	12.2310i	−0.303600	+	0.525851i	−0.976949	−	0.213474i	$-0.931522\pi$
$541$	−7.06156	+	12.2310i	−0.303600	+	0.525851i	0.673348	+	0.739325i	$0.264855\pi$
$542$	−0.897847	−	4.03011i	−0.0385658	−	0.173108i
$543$		0			0
$544$	40.2629	+	20.6944i	1.72626	+	0.887264i
$545$		−	35.1338i		−	1.50497i
$546$		0			0
$547$			28.7589i			1.22964i	0.788666	+	0.614822i	$0.210772\pi$
$547$			28.7589i			1.22964i	−0.788666	+	0.614822i	$0.789228\pi$
$548$	11.6009	+	24.7439i	0.495566	+	1.05701i
$549$		0			0
$550$	−59.7195	+	13.3046i	−2.54645	+	0.567311i
$551$	−1.59717	+	2.76638i	−0.0680417	+	0.117852i
$552$		0			0
$553$	−17.2914	−	22.0726i	−0.735304	−	0.938623i
$554$	−9.01302	+	28.6895i	−0.382926	+	1.21890i
$555$		0			0
$556$	−24.8171	−	2.11925i	−1.05248	−	0.0898764i
$557$	−24.2460	+	13.9985i	−1.02734	+	0.593134i	−0.916221	−	0.400674i	$-0.868776\pi$
$557$	−24.2460	+	13.9985i	−1.02734	+	0.593134i	−0.111117	+	0.993807i	$0.535443\pi$
$558$		0			0
$559$		−	11.1235i		−	0.470474i
$560$	−18.5644	−	34.4594i	−0.784489	−	1.45617i
$561$		0			0
$562$	−28.5842	+	26.2473i	−1.20575	+	1.10718i
$563$	7.48247	+	12.9600i	0.315349	+	0.546200i	0.979512	−	0.201388i	$-0.0645452\pi$
$563$	7.48247	+	12.9600i	0.315349	+	0.546200i	−0.664163	+	0.747588i	$0.731212\pi$
$564$		0			0
$565$	−1.15876	+	2.00704i	−0.0487495	+	0.0844367i
$566$	15.8875	+	4.99117i	0.667801	+	0.209794i
$567$		0			0
$568$	−28.6489	+	22.1253i	−1.20208	+	0.928358i
$569$	−6.88079	−	3.97263i	−0.288458	−	0.166541i	0.348788	−	0.937202i	$-0.386593\pi$
$569$	−6.88079	−	3.97263i	−0.288458	−	0.166541i	−0.637246	+	0.770660i	$0.719927\pi$
$570$		0			0
$571$	15.0223	−	8.67314i	0.628665	−	0.362960i	−0.151570	−	0.988447i	$-0.548433\pi$
$571$	15.0223	−	8.67314i	0.628665	−	0.362960i	0.780235	+	0.625487i	$0.215100\pi$
$572$	−13.7190	+	6.43201i	−0.573619	+	0.268936i
$573$		0			0
$574$	8.06356	−	3.03638i	0.336566	−	0.126736i
$575$	38.5024			1.60566
$576$		0			0
$577$	20.5305	+	35.5599i	0.854696	+	1.48038i	0.876926	+	0.480625i	$0.159590\pi$
$577$	20.5305	+	35.5599i	0.854696	+	1.48038i	−0.0222299	+	0.999753i	$0.507077\pi$
$578$	−64.9359	+	14.4668i	−2.70098	+	0.601738i
$579$		0			0
$580$	−28.1098	−	19.5958i	−1.16720	−	0.813670i
$581$	−29.2453	−	11.7716i	−1.21330	−	0.488367i
$582$		0			0
$583$	20.1528	+	11.6352i	0.834644	+	0.481882i
$584$	26.4052	+	10.8411i	1.09265	+	0.448607i
$585$		0			0
$586$	10.2318	−	9.39533i	0.422674	−	0.388118i
$587$	−18.7470			−0.773771			−0.386885	−	0.922128i	$-0.626449\pi$
$587$	−18.7470			−0.773771			−0.386885	+	0.922128i	$0.626449\pi$
$588$		0			0
$589$	−0.958111			−0.0394783
$590$	10.7340	−	9.85643i	0.441912	−	0.405783i
$591$		0			0
$592$	6.75590	−	8.11966i	0.277666	−	0.333716i
$593$	−22.0662	−	12.7399i	−0.906149	−	0.523166i	−0.0269592	−	0.999637i	$-0.508582\pi$
$593$	−22.0662	−	12.7399i	−0.906149	−	0.523166i	−0.879190	+	0.476471i	$0.841916\pi$
$594$		0			0
$595$	72.6456	+	29.2407i	2.97818	+	1.19875i
$596$	1.46985	−	2.10847i	0.0602072	−	0.0863662i
$597$		0			0
$598$	9.30684	−	2.07342i	0.380585	−	0.0847886i
$599$	−2.83662	−	4.91317i	−0.115901	−	0.200747i	0.802239	−	0.597004i	$-0.203642\pi$
$599$	−2.83662	−	4.91317i	−0.115901	−	0.200747i	−0.918140	+	0.396257i	$0.870309\pi$
$600$		0			0
$601$	−0.119466			−0.00487313			−0.00243656	−	0.999997i	$-0.500776\pi$
$601$	−0.119466			−0.00487313			−0.00243656	+	0.999997i	$0.500776\pi$
$602$	25.6275	−	9.65021i	1.04450	−	0.393313i
$603$		0			0
$604$	13.4977	+	28.7896i	0.549215	+	1.17143i
$605$	−44.3513	+	25.6062i	−1.80314	+	1.04104i
$606$		0			0
$607$	−7.51718	−	4.34005i	−0.305113	−	0.176157i	0.339625	−	0.940561i	$-0.389700\pi$
$607$	−7.51718	−	4.34005i	−0.305113	−	0.176157i	−0.644737	+	0.764404i	$0.723033\pi$
$608$	0.190396	+	3.89617i	0.00772157	+	0.158011i
$609$		0			0
$610$	−27.8470	−	8.74833i	−1.12749	−	0.354209i
$611$	−5.64231	+	9.77277i	−0.228264	+	0.395364i
$612$		0			0
$613$	1.54426	+	2.67473i	0.0623719	+	0.108031i	0.895525	−	0.445011i	$-0.146800\pi$
$613$	1.54426	+	2.67473i	0.0623719	+	0.108031i	−0.833153	+	0.553042i	$0.813467\pi$
$614$	−2.25516	+	2.07079i	−0.0910110	+	0.0835703i
$615$		0			0
$616$	−26.7207	−	26.0272i	−1.07661	−	1.04867i
$617$		−	15.5803i		−	0.627237i	−0.949549	−	0.313619i	$-0.898459\pi$
$617$		−	15.5803i		−	0.627237i	0.949549	−	0.313619i	$-0.101541\pi$
$618$		0			0
$619$	−31.1635	+	17.9923i	−1.25257	+	0.723171i	−0.971619	−	0.236552i	$-0.923983\pi$
$619$	−31.1635	+	17.9923i	−1.25257	+	0.723171i	−0.280950	+	0.959722i	$0.590649\pi$
$620$	0.874485	−	10.2405i	0.0351201	−	0.411267i
$621$		0			0
$622$	−1.45664	+	4.63665i	−0.0584058	+	0.185913i
$623$	2.03003	+	2.59136i	0.0813316	+	0.103821i
$624$		0			0
$625$	−3.46709	+	6.00518i	−0.138684	+	0.240207i
$626$	11.5249	−	2.56757i	0.460626	−	0.102621i
$627$		0			0
$628$	37.1189	−	17.4028i	1.48120	−	0.694448i
$629$			21.1324i			0.842605i
$630$		0			0
$631$		−	21.3737i		−	0.850874i	−0.904988	−	0.425437i	$-0.860120\pi$
$631$		−	21.3737i		−	0.850874i	0.904988	−	0.425437i	$-0.139880\pi$
$632$	−29.7063	+	4.00515i	−1.18165	+	0.159316i
$633$		0			0
$634$	9.59852	+	43.0842i	0.381206	+	1.71109i
$635$	−21.5537	+	37.3321i	−0.855331	+	1.48148i
$636$		0			0
$637$	−7.67232	−	7.37053i	−0.303988	−	0.292031i
$638$	−31.1538	−	9.78716i	−1.23339	−	0.387477i
$639$		0			0
$640$	−41.8168	−	1.52112i	−1.65295	−	0.0601275i
$641$	−38.9817	+	22.5061i	−1.53969	+	0.888938i	−0.540829	+	0.841133i	$0.681889\pi$
$641$	−38.9817	+	22.5061i	−1.53969	+	0.888938i	−0.998857	+	0.0478053i	$0.984777\pi$
$642$		0			0
$643$		−	17.3524i		−	0.684310i	−0.939643	−	0.342155i	$-0.888843\pi$
$643$		−	17.3524i		−	0.684310i	0.939643	−	0.342155i	$-0.111157\pi$
$644$	12.8512	+	19.6433i	0.506406	+	0.774055i
$645$		0			0
$646$	−5.27843	−	5.74839i	−0.207677	−	0.226167i
$647$	4.89690	+	8.48168i	0.192517	+	0.333449i	0.946084	−	0.323922i	$-0.105002\pi$
$647$	4.89690	+	8.48168i	0.192517	+	0.333449i	−0.753567	+	0.657371i	$0.771668\pi$
$648$		0			0
$649$	6.94385	−	12.0271i	0.272570	−	0.472105i
$650$	−5.59131	+	17.7978i	−0.219309	+	0.698089i
$651$		0			0
$652$	−0.504363	+	0.723500i	−0.0197524	+	0.0283344i
$653$	−1.61172	−	0.930530i	−0.0630717	−	0.0364144i	0.468133	−	0.883658i	$-0.344927\pi$
$653$	−1.61172	−	0.930530i	−0.0630717	−	0.0364144i	−0.531204	+	0.847244i	$0.678260\pi$
$654$		0			0
$655$	48.4144	−	27.9520i	1.89171	−	1.09218i
$656$	1.56179	−	9.07784i	0.0609778	−	0.354430i
$657$		0			0
$658$	−27.4106	−	4.52099i	−1.06858	−	0.176247i
$659$	−46.9354			−1.82834			−0.914171	−	0.405329i	$-0.867157\pi$
$659$	−46.9354			−1.82834			−0.914171	+	0.405329i	$0.867157\pi$
$660$		0			0
$661$	17.8768	+	30.9634i	0.695325	+	1.20434i	0.970071	+	0.242822i	$0.0780730\pi$
$661$	17.8768	+	30.9634i	0.695325	+	1.20434i	−0.274746	+	0.961517i	$0.588594\pi$
$662$	−6.17528	−	27.7186i	−0.240009	−	1.07731i
$663$		0			0
$664$	−26.6737	+	20.5999i	−1.03514	+	0.799429i
$665$	0.947818	+	6.68090i	0.0367548	+	0.259074i
$666$		0			0
$667$	17.7964	+	10.2748i	0.689080	+	0.397840i
$668$	3.01011	−	35.2493i	0.116465	−	1.36383i
$669$		0			0
$670$	−21.1636	−	23.0479i	−0.817620	−	0.890417i
$671$	−27.8165			−1.07385
$672$		0			0
$673$	11.4781			0.442449			0.221224	−	0.975223i	$-0.428995\pi$
$673$	11.4781			0.442449			0.221224	+	0.975223i	$0.428995\pi$
$674$	−2.85332	−	3.10736i	−0.109906	−	0.119691i
$675$		0			0
$676$	1.81913	−	21.3025i	0.0699664	−	0.819327i
$677$	20.6080	+	11.8980i	0.792029	+	0.457278i	0.840676	−	0.541538i	$-0.182158\pi$
$677$	20.6080	+	11.8980i	0.792029	+	0.457278i	−0.0486474	+	0.998816i	$0.515491\pi$
$678$		0			0
$679$	−1.28630	−	0.517751i	−0.0493638	−	0.0198695i
$680$	66.2576	−	51.1702i	2.54086	−	1.96229i
$681$		0			0
$682$	−2.12986	−	9.56015i	−0.0815565	−	0.366077i
$683$	0.389408	+	0.674474i	0.0149003	+	0.0258080i	0.873379	−	0.487040i	$-0.161924\pi$
$683$	0.389408	+	0.674474i	0.0149003	+	0.0258080i	−0.858479	+	0.512849i	$0.828590\pi$
$684$		0			0
$685$	50.5378			1.93095
$686$	10.3249	−	24.0707i	0.394207	−	0.919022i
$687$		0			0
$688$	4.96368	−	28.8511i	0.189239	−	1.09994i
$689$	6.14478	−	3.54769i	0.234098	−	0.135156i
$690$		0			0
$691$	−24.8551	−	14.3501i	−0.945531	−	0.545903i	−0.0538411	−	0.998550i	$-0.517146\pi$
$691$	−24.8551	−	14.3501i	−0.945531	−	0.545903i	−0.891690	+	0.452647i	$0.850480\pi$
$692$	13.7914	−	19.7835i	0.524270	−	0.752057i
$693$		0			0
$694$	−0.999239	+	3.18070i	−0.0379306	+	0.120738i
$695$	−23.0304	+	39.8898i	−0.873592	+	1.51311i
$696$		0			0
$697$	9.21425	+	15.9596i	0.349015	+	0.604511i
$698$	27.3312	+	29.7646i	1.03450	+	1.12661i
$699$		0			0
$700$	−45.8554	+	2.55867i	−1.73317	+	0.0967087i
$701$		−	28.1427i		−	1.06294i	−0.847079	−	0.531468i	$-0.821641\pi$
$701$		−	28.1427i		−	1.06294i	0.847079	−	0.531468i	$-0.178359\pi$
$702$		0			0
$703$	−1.57698	+	0.910472i	−0.0594771	+	0.0343391i
$704$	−38.4532	+	10.5609i	−1.44926	+	0.398028i
$705$		0			0
$706$	−1.37652	−	0.432445i	−0.0518062	−	0.0162753i
$707$	−26.4020	+	3.74565i	−0.992951	+	0.140870i
$708$		0			0
$709$	6.93710	−	12.0154i	0.260528	−	0.451248i	−0.705854	−	0.708357i	$-0.749437\pi$
$709$	6.93710	−	12.0154i	0.260528	−	0.451248i	0.966382	+	0.257109i	$0.0827699\pi$
$710$	14.5564	+	65.3383i	0.546292	+	2.45210i
$711$		0			0
$712$	3.48756	−	0.470211i	0.130702	−	0.0176219i
$713$			6.16363i			0.230830i
$714$		0			0
$715$			28.0201i			1.04789i
$716$	−43.2793	+	20.2911i	−1.61742	+	0.758314i
$717$		0			0
$718$	−0.929161	+	0.207003i	−0.0346760	+	0.00772529i
$719$	4.85706	−	8.41268i	0.181138	−	0.313740i	−0.761130	−	0.648599i	$-0.775355\pi$
$719$	4.85706	−	8.41268i	0.181138	−	0.313740i	0.942268	+	0.334859i	$0.108689\pi$
$720$		0			0
$721$	9.07417	+	11.5833i	0.337940	+	0.431384i
$722$	−7.85180	+	24.9932i	−0.292214	+	0.930152i
$723$		0			0
$724$	−1.99249	+	23.3326i	−0.0740501	+	0.867148i
$725$	−34.8191	+	20.1028i	−1.29315	+	0.746600i
$726$		0			0
$727$		−	18.5076i		−	0.686410i	−0.939260	−	0.343205i	$-0.888487\pi$
$727$		−	18.5076i		−	0.686410i	0.939260	−	0.343205i	$-0.111513\pi$
$728$	−10.9464	+	3.08788i	−0.405701	+	0.114444i
$729$		0			0
$730$	38.8808	−	35.7021i	1.43904	−	1.32139i
$731$	29.2847	+	50.7226i	1.08313	+	1.87604i
$732$		0			0
$733$	−10.5257	+	18.2311i	−0.388776	+	0.673379i	−0.992285	−	0.123977i	$-0.960435\pi$
$733$	−10.5257	+	18.2311i	−0.388776	+	0.673379i	0.603509	+	0.797356i	$0.293769\pi$
$734$	20.1497	+	6.33017i	0.743740	+	0.233651i
$735$		0			0
$736$	25.0645	−	1.22484i	0.923889	−	0.0451481i
$737$	−25.8244	−	14.9097i	−0.951254	−	0.549207i
$738$		0			0
$739$	−29.7275	+	17.1632i	−1.09354	+	0.631358i	−0.934518	−	0.355917i	$-0.884169\pi$
$739$	−29.7275	+	17.1632i	−1.09354	+	0.631358i	−0.159026	+	0.987274i	$0.550835\pi$
$740$	−8.29195	−	17.6861i	−0.304818	−	0.650154i
$741$		0			0
$742$	13.5045	+	11.0792i	0.495765	+	0.406731i
$743$	45.7213			1.67735			0.838676	−	0.544631i	$-0.183330\pi$
$743$	45.7213			1.67735			0.838676	+	0.544631i	$0.183330\pi$
$744$		0			0
$745$	−2.37654	−	4.11628i	−0.0870696	−	0.150809i
$746$	25.7952	−	5.74680i	0.944431	−	0.210405i
$747$		0			0
$748$	45.6243	−	65.4474i	1.66819	−	2.39299i
$749$	−20.7260	+	16.2364i	−0.757311	+	0.593266i
$750$		0			0
$751$	5.37869	+	3.10539i	0.196271	+	0.113317i	0.594915	−	0.803789i	$-0.297186\pi$
$751$	5.37869	+	3.10539i	0.196271	+	0.113317i	−0.398644	+	0.917106i	$0.630519\pi$
$752$	−18.9955	+	22.8299i	−0.692693	+	0.832523i
$753$		0			0
$754$	−7.33393	+	6.73434i	−0.267086	+	0.245250i
$755$	58.8010			2.13999
$756$		0			0
$757$	34.6075			1.25783			0.628915	−	0.777474i	$-0.283499\pi$
$757$	34.6075			1.25783			0.628915	+	0.777474i	$0.283499\pi$
$758$	36.2737	−	33.3081i	1.31752	−	1.20980i
$759$		0			0
$760$	6.67317	+	2.73978i	0.242061	+	0.0993822i
$761$	−39.0205	−	22.5285i	−1.41449	−	0.816658i	−0.418685	−	0.908131i	$-0.637509\pi$
$761$	−39.0205	−	22.5285i	−1.41449	−	0.816658i	−0.995807	+	0.0914738i	$0.970842\pi$
$762$		0			0
$763$	−3.53024	−	24.8837i	−0.127803	−	0.900850i
$764$	23.5386	+	16.4091i	0.851597	+	0.593661i
$765$		0			0
$766$	25.4472	−	5.66925i	0.919444	−	0.204838i
$767$	−2.11725	−	3.66718i	−0.0764493	−	0.132414i
$768$		0			0
$769$	37.1518			1.33973			0.669863	−	0.742484i	$-0.266353\pi$
$769$	37.1518			1.33973			0.669863	+	0.742484i	$0.266353\pi$
$770$	−64.5559	+	24.3089i	−2.32643	+	0.876033i
$771$		0			0
$772$	17.2206	−	8.07370i	0.619783	−	0.290579i
$773$	−8.14384	+	4.70185i	−0.292914	+	0.169114i	−0.639255	−	0.768995i	$-0.720757\pi$
$773$	−8.14384	+	4.70185i	−0.292914	+	0.169114i	0.346341	+	0.938109i	$0.387424\pi$
$774$		0			0
$775$	−10.4436	−	6.02964i	−0.375147	−	0.216591i
$776$	−1.17319	+	0.906047i	−0.0421152	+	0.0325252i
$777$		0			0
$778$	−28.5598	−	8.97225i	−1.02392	−	0.321671i
$779$	−0.793976	+	1.37521i	−0.0284471	+	0.0492719i
$780$		0			0
$781$	31.8965	+	55.2463i	1.14135	+	1.97687i
$782$	−36.9800	+	33.9567i	−1.32240	+	1.21429i
$783$		0			0
$784$	−16.6108	−	22.5407i	−0.593242	−	0.805024i
$785$		−	75.8129i		−	2.70588i
$786$		0			0
$787$	31.0131	−	17.9054i	1.10550	−	0.638259i	0.167837	−	0.985815i	$-0.446322\pi$
$787$	31.0131	−	17.9054i	1.10550	−	0.638259i	0.937659	+	0.347556i	$0.112988\pi$
$788$	1.33131	+	0.113687i	0.0474258	+	0.00404993i
$789$		0			0
$790$	−16.6139	+	52.8840i	−0.591095	+	1.88153i
$791$	−0.619033	+	1.53793i	−0.0220103	+	0.0546823i
$792$		0			0
$793$	−4.24076	+	7.34522i	−0.150594	+	0.260836i
$794$	38.3086	−	8.53458i	1.35952	−	0.302881i
$795$		0			0
$796$	−15.8683	−	33.8459i	−0.562438	−	1.19964i
$797$			3.06554i			0.108587i	0.998525	+	0.0542935i	$0.0172907\pi$
$797$			3.06554i			0.108587i	−0.998525	+	0.0542935i	$0.982709\pi$
$798$		0			0
$799$		−	59.4178i		−	2.10205i
$800$	−22.4442	+	43.6674i	−0.793524	+	1.54388i
$801$		0			0
$802$	−6.16201	−	27.6590i	−0.217588	−	0.976672i
$803$	25.1521	−	43.5647i	0.887598	−	1.53736i
$804$		0			0
$805$	42.9790	−	6.09741i	1.51481	−	0.214906i
$806$	−2.84915	−	0.895081i	−0.100357	−	0.0315279i
$807$		0			0
$808$	−10.8272	+	26.3715i	−0.380901	+	0.927745i
$809$	−3.81118	+	2.20039i	−0.133994	+	0.0773615i	−0.565499	−	0.824749i	$-0.691316\pi$
$809$	−3.81118	+	2.20039i	−0.133994	+	0.0773615i	0.431505	+	0.902111i	$0.357983\pi$
$810$		0			0
$811$		−	34.0869i		−	1.19695i	−0.801140	−	0.598477i	$-0.795773\pi$
$811$		−	34.0869i		−	1.19695i	0.801140	−	0.598477i	$-0.204227\pi$
$812$	−21.8779	−	11.0543i	−0.767763	−	0.387931i
$813$		0			0
$814$	−12.5904	−	13.7114i	−0.441293	−	0.480584i
$815$	0.815485	+	1.41246i	0.0285652	+	0.0494764i
$816$		0			0
$817$	−2.52341	+	4.37067i	−0.0882829	+	0.152911i
$818$	−8.95440	+	28.5030i	−0.313083	+	0.996583i
$819$		0			0
$820$	−13.9738	−	9.74134i	−0.487986	−	0.340182i
$821$	42.3387	+	24.4443i	1.47763	+	0.853111i	0.999681	−	0.0252756i	$-0.00804632\pi$
$821$	42.3387	+	24.4443i	1.47763	+	0.853111i	0.477951	+	0.878387i	$0.341380\pi$
$822$		0			0
$823$	35.8518	−	20.6990i	1.24971	−	0.721523i	0.278661	−	0.960389i	$-0.410109\pi$
$823$	35.8518	−	20.6990i	1.24971	−	0.721523i	0.971052	+	0.238867i	$0.0767760\pi$
$824$	15.5893	−	2.10182i	0.543078	−	0.0732205i
$825$		0			0
$826$	6.61203	−	8.05941i	0.230062	−	0.280423i
$827$	−50.5830			−1.75894			−0.879471	−	0.475952i	$-0.842103\pi$
$827$	−50.5830			−1.75894			−0.879471	+	0.475952i	$0.842103\pi$
$828$		0			0
$829$	−13.6512	−	23.6445i	−0.474125	−	0.821209i	0.525436	−	0.850833i	$-0.323902\pi$
$829$	−13.6512	−	23.6445i	−0.474125	−	0.821209i	−0.999561	+	0.0296244i	$0.990569\pi$
$830$	13.5528	+	60.8334i	0.470424	+	2.11156i
$831$		0			0
$832$	−3.07367	+	11.7640i	−0.106560	+	0.407843i
$833$	54.3897	+	13.4104i	1.88449	+	0.464644i
$834$		0			0
$835$	−56.6579	−	32.7115i	−1.96073	−	1.13203i
$836$	6.84962	+	0.584924i	0.236899	+	0.0202300i
$837$		0			0
$838$	−7.81885	−	8.51500i	−0.270098	−	0.294146i
$839$	21.0286			0.725986			0.362993	−	0.931792i	$-0.381755\pi$
$839$	21.0286			0.725986			0.362993	+	0.931792i	$0.381755\pi$
$840$		0			0
$841$	7.54144			0.260050
$842$	−19.1117	−	20.8134i	−0.658634	−	0.717276i
$843$		0			0
$844$	−8.25143	−	0.704631i	−0.284026	−	0.0242544i
$845$	−34.2406	−	19.7688i	−1.17791	−	0.680068i
$846$		0			0
$847$	−28.8391	+	22.5922i	−0.990924	+	0.776276i
$848$	17.5209	−	6.45967i	0.601670	−	0.221826i
$849$		0			0
$850$	−21.3601	−	95.8774i	−0.732644	−	3.28857i
$851$	5.85717	+	10.1449i	0.200781	+	0.347763i
$852$		0			0
$853$	−0.260365			−0.00891473			−0.00445736	−	0.999990i	$-0.501419\pi$
$853$	−0.260365			−0.00891473			−0.00445736	+	0.999990i	$0.501419\pi$
$854$	−20.6018	−	3.39798i	−0.704979	−	0.116276i
$855$		0			0
$856$	3.76080	+	27.8939i	0.128541	+	0.953395i
$857$	30.0731	−	17.3627i	1.02728	−	0.593098i	0.111073	−	0.993812i	$-0.464571\pi$
$857$	30.0731	−	17.3627i	1.02728	−	0.593098i	0.916203	+	0.400714i	$0.131238\pi$
$858$		0			0
$859$	−33.7911	−	19.5093i	−1.15294	−	0.665649i	−0.203336	−	0.979109i	$-0.565179\pi$
$859$	−33.7911	−	19.5093i	−1.15294	−	0.665649i	−0.949601	+	0.313460i	$0.898512\pi$
$860$	−44.4114	−	30.9599i	−1.51442	−	1.05572i
$861$		0			0
$862$	8.16074	−	25.9766i	0.277956	−	0.884768i
$863$	19.2268	−	33.3018i	0.654487	−	1.13361i	−0.327535	−	0.944839i	$-0.606218\pi$
$863$	19.2268	−	33.3018i	0.654487	−	1.13361i	0.982022	−	0.188766i	$-0.0604488\pi$
$864$		0			0
$865$	−22.2988	−	38.6226i	−0.758182	−	1.31321i
$866$	−21.9971	−	23.9556i	−0.747491	−	0.814043i
$867$		0			0
$868$	−0.409603	−	7.34072i	−0.0139028	−	0.249160i
$869$			52.8261i			1.79200i
$870$		0			0
$871$	−7.87411	+	4.54612i	−0.266804	+	0.154039i
$872$	−24.8549	−	10.2046i	−0.841692	−	0.345570i
$873$		0			0
$874$	−4.12723	−	1.29660i	−0.139606	−	0.0438581i
$875$	−13.4438	+	33.3999i	−0.454485	+	1.12912i
$876$		0			0
$877$	14.6023	−	25.2919i	0.493085	−	0.854048i	−0.506883	−	0.862015i	$-0.669202\pi$
$877$	14.6023	−	25.2919i	0.493085	−	0.854048i	0.999968	+	0.00796634i	$0.00253579\pi$
$878$	−7.01721	−	31.4977i	−0.236819	−	1.06300i
$879$		0			0
$880$	−12.5035	+	72.6762i	−0.421494	+	2.44991i
$881$		−	3.25733i		−	0.109742i	−0.998493	−	0.0548710i	$-0.982525\pi$
$881$		−	3.25733i		−	0.109742i	0.998493	−	0.0548710i	$-0.0174748\pi$
$882$		0			0
$883$			29.5747i			0.995269i	0.867387	+	0.497634i	$0.165798\pi$
$883$			29.5747i			0.995269i	−0.867387	+	0.497634i	$0.834202\pi$
$884$	−10.3263	−	22.0253i	−0.347312	−	0.740791i
$885$		0			0
$886$	−18.7874	+	4.18554i	−0.631174	+	0.140616i
$887$	−0.877187	+	1.51933i	−0.0294531	+	0.0510142i	−0.880376	−	0.474276i	$-0.842710\pi$
$887$	−0.877187	+	1.51933i	−0.0294531	+	0.0510142i	0.850923	+	0.525290i	$0.176043\pi$
$888$		0			0
$889$	−11.5144	+	28.6063i	−0.386179	+	0.959425i
$890$	1.95049	−	6.20866i	0.0653807	−	0.208115i
$891$		0			0
$892$	−6.10904	−	0.521681i	−0.204546	−	0.0174672i
$893$	4.43399	−	2.55996i	0.148378	−	0.0856659i
$894$		0			0
$895$			88.3953i			2.95473i
$896$	−29.7698	+	3.12440i	−0.994538	+	0.104379i
$897$		0			0
$898$	19.8288	−	18.2077i	0.661695	−	0.607598i
$899$	−3.21814	−	5.57399i	−0.107331	−	0.185903i
$900$		0			0
$901$	−18.6799	+	32.3546i	−0.622318	+	1.07789i
$902$	−15.4870	−	4.86534i	−0.515660	−	0.161998i
$903$		0			0
$904$	1.08329	+	1.40269i	0.0360295	+	0.0466528i
$905$	37.5037	+	21.6527i	1.24666	+	0.719762i
$906$		0			0
$907$	36.7789	−	21.2343i	1.22122	−	0.705074i	0.256046	−	0.966665i	$-0.417580\pi$
$907$	36.7789	−	21.2343i	1.22122	−	0.705074i	0.965179	+	0.261590i	$0.0842470\pi$
$908$	16.2277	−	7.60820i	0.538536	−	0.252487i
$909$		0			0
$910$	−3.42285	+	20.7526i	−0.113466	+	0.687942i
$911$	−19.5384			−0.647336			−0.323668	−	0.946171i	$-0.604916\pi$
$911$	−19.5384			−0.647336			−0.323668	+	0.946171i	$0.604916\pi$
$912$		0			0
$913$	29.6973	+	51.4372i	0.982837	+	1.70232i
$914$	−8.63547	+	1.92385i	−0.285636	+	0.0636354i
$915$		0			0
$916$	26.5632	+	18.5176i	0.877672	+	0.611839i
$917$	31.4811	−	24.6618i	1.03960	−	0.814405i
$918$		0			0
$919$	−12.1718	−	7.02738i	−0.401510	−	0.231812i	0.285625	−	0.958341i	$-0.407799\pi$
$919$	−12.1718	−	7.02738i	−0.401510	−	0.231812i	−0.687135	+	0.726529i	$0.741132\pi$
$920$	17.6253	−	42.9292i	0.581088	−	1.41533i
$921$		0			0
$922$	12.5685	−	11.5410i	0.413922	−	0.380082i
$923$	19.4511			0.640239
$924$		0			0
$925$	−22.9194			−0.753584
$926$	−24.2227	+	22.2424i	−0.796008	+	0.730930i
$927$		0			0
$928$	−22.0272	+	14.1943i	−0.723077	+	0.465950i
$929$	42.4219	+	24.4923i	1.39182	+	0.803567i	0.993517	−	0.113687i	$-0.0362662\pi$
$929$	42.4219	+	24.4923i	1.39182	+	0.803567i	0.398302	+	0.917254i	$0.369600\pi$
$930$		0			0
$931$	1.34259	+	4.63654i	0.0440017	+	0.151957i
$932$	5.70389	−	8.18214i	0.186837	−	0.268015i
$933$		0			0
$934$	9.09055	−	2.02524i	0.297452	−	0.0662678i
$935$	−73.7683	−	127.770i	−2.41248	−	4.17854i
$936$		0			0
$937$	4.55352			0.148757			0.0743784	−	0.997230i	$-0.476303\pi$
$937$	4.55352			0.148757			0.0743784	+	0.997230i	$0.476303\pi$
$938$	−17.3050	−	14.1972i	−0.565030	−	0.463556i
$939$		0			0
$940$	23.3144	+	49.7278i	0.760431	+	1.62194i
$941$	19.3187	−	11.1537i	0.629773	−	0.363599i	−0.150891	−	0.988550i	$-0.548214\pi$
$941$	19.3187	−	11.1537i	0.629773	−	0.363599i	0.780664	+	0.624951i	$0.214881\pi$
$942$		0			0
$943$	8.84685	+	5.10773i	0.288093	+	0.166331i
$944$	−3.85510	−	10.4564i	−0.125473	−	0.340326i
$945$		0			0
$946$	−49.2206	−	15.4630i	−1.60030	−	0.502745i
$947$	−13.5722	+	23.5077i	−0.441036	+	0.763897i	−0.997767	−	0.0667962i	$-0.978722\pi$
$947$	−13.5722	+	23.5077i	−0.441036	+	0.763897i	0.556731	+	0.830693i	$0.312056\pi$
$948$		0			0
$949$	−7.66911	−	13.2833i	−0.248950	−	0.431194i
$950$	6.23447	−	5.72476i	0.202273	−	0.185736i
$951$		0			0
$952$	41.7857	−	42.8991i	1.35428	−	1.39037i
$953$			47.7500i			1.54677i	0.633935	+	0.773386i	$0.281439\pi$
$953$			47.7500i			1.54677i	−0.633935	+	0.773386i	$0.718561\pi$
$954$		0			0
$955$	45.9535	−	26.5313i	1.48702	−	0.858532i
$956$	0.775132	−	9.07702i	0.0250696	−	0.293572i
$957$		0			0
$958$	−15.9331	+	50.7169i	−0.514774	+	1.63859i
$959$	35.7936	−	5.07803i	1.15584	−	0.163978i
$960$		0			0
$961$	−14.5347	+	25.1749i	−0.468863	+	0.812094i
$962$	−5.54009	+	1.23425i	−0.178620	+	0.0397938i
$963$		0			0
$964$	−9.90783	+	4.64519i	−0.319110	+	0.149612i
$965$		−	35.1720i		−	1.13223i
$966$		0			0
$967$			33.7485i			1.08528i	0.839966	+	0.542639i	$0.182575\pi$
$967$			33.7485i			1.08528i	−0.839966	+	0.542639i	$0.817425\pi$
$968$	5.23296	+	38.8129i	0.168194	+	1.24750i
$969$		0			0
$970$	0.596094	+	2.67565i	0.0191394	+	0.0859098i
$971$	24.9699	−	43.2491i	0.801322	−	1.38793i	−0.117424	−	0.993082i	$-0.537464\pi$
$971$	24.9699	−	43.2491i	0.801322	−	1.38793i	0.918746	−	0.394849i	$-0.129203\pi$
$972$		0			0
$973$	−12.3032	+	30.5662i	−0.394424	+	0.979907i
$974$	23.7274	+	7.45411i	0.760274	+	0.238845i
$975$		0			0
$976$	−14.2770	+	17.1590i	−0.456996	+	0.549246i
$977$	2.82504	−	1.63104i	0.0903810	−	0.0521815i	−0.454128	−	0.890936i	$-0.650049\pi$
$977$	2.82504	−	1.63104i	0.0903810	−	0.0521815i	0.544509	+	0.838755i	$0.316716\pi$
$978$		0			0
$979$		−	6.20187i		−	0.198213i
$980$	−50.7816	+	10.1180i	−1.62216	+	0.323208i
$981$		0			0
$982$	−33.1479	−	36.0992i	−1.05779	−	1.15197i
$983$	26.0565	+	45.1311i	0.831073	+	1.43946i	0.897188	+	0.441648i	$0.145606\pi$
$983$	26.0565	+	45.1311i	0.831073	+	1.43946i	−0.0661157	+	0.997812i	$0.521061\pi$
$984$		0			0
$985$	1.23546	−	2.13988i	0.0393650	−	0.0681822i
$986$	15.7129	−	50.0162i	0.500401	−	1.59284i
$987$		0			0
$988$	1.19871	−	1.71953i	0.0381361	−	0.0547056i
$989$	28.1170	+	16.2334i	0.894069	+	0.516191i
$990$		0			0
$991$	20.2384	−	11.6846i	0.642894	−	0.371175i	−0.142835	−	0.989747i	$-0.545622\pi$
$991$	20.2384	−	11.6846i	0.642894	−	0.371175i	0.785728	+	0.618572i	$0.212288\pi$
$992$	−6.99046	−	3.59297i	−0.221947	−	0.114077i
$993$		0			0
$994$	16.8748	+	44.8135i	0.535236	+	1.42140i
$995$	−69.1282			−2.19151
$996$		0			0
$997$	−12.9285	−	22.3927i	−0.409448	−	0.709185i	0.585380	−	0.810759i	$-0.300945\pi$
$997$	−12.9285	−	22.3927i	−0.409448	−	0.709185i	−0.994828	+	0.101574i	$0.967612\pi$
$998$	−0.736108	−	3.30412i	−0.0233011	−	0.104590i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.be.e.107.9	yes	64
3.2	odd	2	inner	756.2.be.e.107.24	yes	64
4.3	odd	2	inner	756.2.be.e.107.2	✓	64
7.4	even	3	inner	756.2.be.e.431.31	yes	64
12.11	even	2	inner	756.2.be.e.107.31	yes	64
21.11	odd	6	inner	756.2.be.e.431.2	yes	64
28.11	odd	6	inner	756.2.be.e.431.24	yes	64
84.11	even	6	inner	756.2.be.e.431.9	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.be.e.107.2	✓	64	4.3	odd	2	inner
756.2.be.e.107.9	yes	64	1.1	even	1	trivial
756.2.be.e.107.24	yes	64	3.2	odd	2	inner
756.2.be.e.107.31	yes	64	12.11	even	2	inner
756.2.be.e.431.2	yes	64	21.11	odd	6	inner
756.2.be.e.431.9	yes	64	84.11	even	6	inner
756.2.be.e.431.24	yes	64	28.11	odd	6	inner
756.2.be.e.431.31	yes	64	7.4	even	3	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.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.956512 - 1.04167i) q^{2} +(-0.170171 + 1.99275i) q^{4} +(3.20305 + 1.84928i) q^{5} +(2.45439 + 0.987919i) q^{7} +(2.23856 - 1.72882i) q^{8} +O(q^{10})\)	\(q+(-0.956512 - 1.04167i) q^{2} +(-0.170171 + 1.99275i) q^{4} +(3.20305 + 1.84928i) q^{5} +(2.45439 + 0.987919i) q^{7} +(2.23856 - 1.72882i) q^{8} +(-1.13740 - 5.10539i) q^{10} +(-2.49232 - 4.31682i) q^{11} -1.51986 q^{13} +(-1.31856 - 3.50163i) q^{14} +(-3.94208 - 0.678214i) q^{16} +(6.93049 - 4.00132i) q^{17} +(0.597189 + 0.344787i) q^{19} +(-4.23021 + 6.06817i) q^{20} +(-2.11279 + 6.72528i) q^{22} +(2.21805 - 3.84178i) q^{23} +(4.33967 + 7.51653i) q^{25} +(1.45377 + 1.58320i) q^{26} +(-2.38634 + 4.72286i) q^{28} +4.63234i q^{29} +(-1.20328 + 0.694712i) q^{31} +(3.06417 + 4.75509i) q^{32} +(-10.7972 - 3.39201i) q^{34} +(6.03458 + 7.70320i) q^{35} +(-1.32034 + 2.28690i) q^{37} +(-0.212062 - 0.951869i) q^{38} +(10.3673 - 1.39777i) q^{40} +2.30280i q^{41} +7.31875i q^{43} +(9.02646 - 4.23196i) q^{44} +(-6.12347 + 1.36422i) q^{46} +(3.71238 - 6.43004i) q^{47} +(5.04803 + 4.84947i) q^{49} +(3.67883 - 11.7102i) q^{50} +(0.258636 - 3.02870i) q^{52} +(-4.04298 + 2.33422i) q^{53} -18.4360i q^{55} +(7.20224 - 2.03168i) q^{56} +(4.82539 - 4.43089i) q^{58} +(1.39305 + 2.41283i) q^{59} +(2.79023 - 4.83282i) q^{61} +(1.87461 + 0.588922i) q^{62} +(2.02234 - 7.74017i) q^{64} +(-4.86819 - 2.81065i) q^{65} +(5.18080 - 2.99114i) q^{67} +(6.79426 + 14.4916i) q^{68} +(2.25208 - 13.6543i) q^{70} -12.7979 q^{71} +(5.04592 + 8.73979i) q^{73} +(3.64512 - 0.812079i) q^{74} +(-0.788697 + 1.13137i) q^{76} +(-1.85244 - 13.0574i) q^{77} +(-9.17795 - 5.29889i) q^{79} +(-11.3725 - 9.46237i) q^{80} +(2.39877 - 2.20266i) q^{82} -11.9155 q^{83} +29.5983 q^{85} +(7.62375 - 7.00047i) q^{86} +(-13.0422 - 5.35470i) q^{88} +(1.07751 + 0.622098i) q^{89} +(-3.73033 - 1.50150i) q^{91} +(7.27825 + 5.07377i) q^{92} +(-10.2489 + 2.28331i) q^{94} +(1.27521 + 2.20874i) q^{95} -0.524083 q^{97} +(0.223067 - 9.89698i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q - 16 q^{13} + 8 q^{16} - 28 q^{22} + 36 q^{25} + 26 q^{28} - 56 q^{34} - 8 q^{37} + 22 q^{40} - 18 q^{46} + 28 q^{49} - 26 q^{52} - 36 q^{58} + 16 q^{61} - 12 q^{64} - 18 q^{70} + 32 q^{73} - 144 q^{76} + 34 q^{82} + 32 q^{85} - 20 q^{88} - 78 q^{94} + 56 q^{97}+O(q^{100}) \) 64 * q - 16 * q^13 + 8 * q^16 - 28 * q^22 + 36 * q^25 + 26 * q^28 - 56 * q^34 - 8 * q^37 + 22 * q^40 - 18 * q^46 + 28 * q^49 - 26 * q^52 - 36 * q^58 + 16 * q^61 - 12 * q^64 - 18 * q^70 + 32 * q^73 - 144 * q^76 + 34 * q^82 + 32 * q^85 - 20 * q^88 - 78 * q^94 + 56 * q^97

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