LMFDB - Embedded newform 756.2.be.e.107.20

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			107.20
Character	$\chi$	$=$	756.107
Dual form			756.2.be.e.431.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.393322 + 1.35842i) q^{2} +(-1.69060 + 1.06859i) q^{4} +(3.53194 + 2.03916i) q^{5} +(-1.92589 + 1.81410i) q^{7} +(-2.11654 - 1.87623i) q^{8} +O(q^{10})$	\(q+(0.393322 + 1.35842i) q^{2} +(-1.69060 + 1.06859i) q^{4} +(3.53194 + 2.03916i) q^{5} +(-1.92589 + 1.81410i) q^{7} +(-2.11654 - 1.87623i) q^{8} +(-1.38085 + 5.59989i) q^{10} +(0.258599 + 0.447907i) q^{11} -4.00857 q^{13} +(-3.22180 - 1.90264i) q^{14} +(1.71623 - 3.61311i) q^{16} +(-5.05144 + 2.91645i) q^{17} +(4.10015 + 2.36722i) q^{19} +(-8.15011 + 0.326792i) q^{20} +(-0.506732 + 0.527458i) q^{22} +(0.974850 - 1.68849i) q^{23} +(5.81638 + 10.0743i) q^{25} +(-1.57666 - 5.44532i) q^{26} +(1.31737 - 5.12489i) q^{28} -2.05067i q^{29} +(7.53503 - 4.35035i) q^{31} +(5.58314 + 0.910238i) q^{32} +(-5.94860 - 5.71486i) q^{34} +(-10.5014 + 2.48008i) q^{35} +(-3.53252 + 6.11850i) q^{37} +(-1.60300 + 6.50079i) q^{38} +(-3.64954 - 10.9427i) q^{40} -2.50300i q^{41} +2.99519i q^{43} +(-0.915817 - 0.480893i) q^{44} +(2.67710 + 0.660133i) q^{46} +(-4.97255 + 8.61270i) q^{47} +(0.418094 - 6.98750i) q^{49} +(-11.3973 + 11.8635i) q^{50} +(6.77688 - 4.28353i) q^{52} +(7.05724 - 4.07450i) q^{53} +2.10931i q^{55} +(7.47990 - 0.226195i) q^{56} +(2.78566 - 0.806573i) q^{58} +(-6.07396 - 10.5204i) q^{59} +(-1.71003 + 2.96186i) q^{61} +(8.87329 + 8.52463i) q^{62} +(0.959489 + 7.94225i) q^{64} +(-14.1580 - 8.17414i) q^{65} +(-1.72609 + 0.996560i) q^{67} +(5.42345 - 10.3285i) q^{68} +(-7.49939 - 13.2898i) q^{70} -2.86671 q^{71} +(4.04598 + 7.00785i) q^{73} +(-9.70090 - 2.39209i) q^{74} +(-9.46129 + 0.379366i) q^{76} +(-1.31058 - 0.393495i) q^{77} +(4.28947 + 2.47652i) q^{79} +(13.4293 - 9.26160i) q^{80} +(3.40012 - 0.984485i) q^{82} +1.91175 q^{83} -23.7885 q^{85} +(-4.06872 + 1.17808i) q^{86} +(0.293043 - 1.43321i) q^{88} +(11.7420 + 6.77926i) q^{89} +(7.72007 - 7.27195i) q^{91} +(0.156227 + 3.89627i) q^{92} +(-13.6555 - 3.36723i) q^{94} +(9.65431 + 16.7218i) q^{95} +4.24721 q^{97} +(9.65639 - 2.18039i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.393322	+	1.35842i	0.278121	+	0.960546i
$2$	0.393322	+	1.35842i	0.278121	+	0.960546i
$3$		0			0
$3$		0			0
$4$	−1.69060	+	1.06859i	−0.845298	+	0.534295i
$5$	3.53194	+	2.03916i	1.57953	+	0.911942i	0.994925	+	0.100624i	$0.0320839\pi$
$5$	3.53194	+	2.03916i	1.57953	+	0.911942i	0.584605	+	0.811318i	$0.301249\pi$
$6$		0			0
$7$	−1.92589	+	1.81410i	−0.727917	+	0.685665i
$7$	−1.92589	+	1.81410i	−0.727917	+	0.685665i
$8$	−2.11654	−	1.87623i	−0.748310	−	0.663349i
$9$		0			0
$10$	−1.38085	+	5.59989i	−0.436662	+	1.77084i
$11$	0.258599	+	0.447907i	0.0779707	+	0.135049i	0.902374	−	0.430953i	$-0.141823\pi$
$11$	0.258599	+	0.447907i	0.0779707	+	0.135049i	−0.824404	+	0.566002i	$0.808489\pi$
$12$		0			0
$13$	−4.00857			−1.11178			−0.555889	−	0.831256i	$-0.687622\pi$
$13$	−4.00857			−1.11178			−0.555889	+	0.831256i	$0.687622\pi$
$14$	−3.22180	−	1.90264i	−0.861062	−	0.508501i
$15$		0			0
$16$	1.71623	−	3.61311i	0.429057	−	0.903277i
$17$	−5.05144	+	2.91645i	−1.22515	+	0.707343i	−0.966012	−	0.258496i	$-0.916773\pi$
$17$	−5.05144	+	2.91645i	−1.22515	+	0.707343i	−0.259142	+	0.965839i	$0.583440\pi$
$18$		0			0
$19$	4.10015	+	2.36722i	0.940639	+	0.543078i	0.890160	−	0.455647i	$-0.150592\pi$
$19$	4.10015	+	2.36722i	0.940639	+	0.543078i	0.0504782	+	0.998725i	$0.483925\pi$
$20$	−8.15011	+	0.326792i	−1.82242	+	0.0730729i
$21$		0			0
$22$	−0.506732	+	0.527458i	−0.108036	+	0.112454i
$23$	0.974850	−	1.68849i	0.203270	−	0.352074i	−0.746310	−	0.665599i	$-0.768176\pi$
$23$	0.974850	−	1.68849i	0.203270	−	0.352074i	0.949580	+	0.313524i	$0.101510\pi$
$24$		0			0
$25$	5.81638	+	10.0743i	1.16328	+	2.01485i
$26$	−1.57666	−	5.44532i	−0.309209	−	1.06791i
$27$		0			0
$28$	1.31737	−	5.12489i	0.248960	−	0.968514i
$29$		−	2.05067i		−	0.380799i	−0.981707	−	0.190400i	$-0.939022\pi$
$29$		−	2.05067i		−	0.380799i	0.981707	−	0.190400i	$-0.0609784\pi$
$30$		0			0
$31$	7.53503	−	4.35035i	1.35333	−	0.781346i	0.364617	−	0.931158i	$-0.381200\pi$
$31$	7.53503	−	4.35035i	1.35333	−	0.781346i	0.988715	+	0.149811i	$0.0478666\pi$
$32$	5.58314	+	0.910238i	0.986969	+	0.160909i
$33$		0			0
$34$	−5.94860	−	5.71486i	−1.02018	−	0.980091i
$35$	−10.5014	+	2.48008i	−1.77505	+	0.419209i
$36$		0			0
$37$	−3.53252	+	6.11850i	−0.580743	+	1.00588i	0.414649	+	0.909981i	$0.363904\pi$
$37$	−3.53252	+	6.11850i	−0.580743	+	1.00588i	−0.995392	+	0.0958942i	$0.969429\pi$
$38$	−1.60300	+	6.50079i	−0.260040	+	1.05457i
$39$		0			0
$40$	−3.64954	−	10.9427i	−0.577042	−	1.73019i
$41$		−	2.50300i		−	0.390903i	−0.980713	−	0.195452i	$-0.937383\pi$
$41$		−	2.50300i		−	0.390903i	0.980713	−	0.195452i	$-0.0626172\pi$
$42$		0			0
$43$			2.99519i			0.456763i	0.973572	+	0.228381i	$0.0733433\pi$
$43$			2.99519i			0.456763i	−0.973572	+	0.228381i	$0.926657\pi$
$44$	−0.915817	−	0.480893i	−0.138065	−	0.0724974i
$45$		0			0
$46$	2.67710	+	0.660133i	0.394717	+	0.0973313i
$47$	−4.97255	+	8.61270i	−0.725321	+	1.25629i	0.233521	+	0.972352i	$0.424975\pi$
$47$	−4.97255	+	8.61270i	−0.725321	+	1.25629i	−0.958842	+	0.283940i	$0.908358\pi$
$48$		0			0
$49$	0.418094	−	6.98750i	0.0597277	−	0.998215i
$50$	−11.3973	+	11.8635i	−1.61183	+	1.67775i
$51$		0			0
$52$	6.77688	−	4.28353i	0.939784	−	0.594018i
$53$	7.05724	−	4.07450i	0.969386	−	0.559675i	0.0703372	−	0.997523i	$-0.477592\pi$
$53$	7.05724	−	4.07450i	0.969386	−	0.559675i	0.899049	+	0.437848i	$0.144259\pi$
$54$		0			0
$55$			2.10931i			0.284419i
$56$	7.47990	−	0.226195i	0.999543	−	0.0302265i
$57$		0			0
$58$	2.78566	−	0.806573i	0.365775	−	0.105908i
$59$	−6.07396	−	10.5204i	−0.790762	−	1.36964i	−0.925496	−	0.378758i	$-0.876351\pi$
$59$	−6.07396	−	10.5204i	−0.790762	−	1.36964i	0.134734	−	0.990882i	$-0.456982\pi$
$60$		0			0
$61$	−1.71003	+	2.96186i	−0.218947	+	0.379227i	−0.954486	−	0.298255i	$-0.903596\pi$
$61$	−1.71003	+	2.96186i	−0.218947	+	0.379227i	0.735539	+	0.677482i	$0.236929\pi$
$62$	8.87329	+	8.52463i	1.12691	+	1.08263i
$63$		0			0
$64$	0.959489	+	7.94225i	0.119936	+	0.992782i
$65$	−14.1580	−	8.17414i	−1.75609	−	1.01388i
$66$		0			0
$67$	−1.72609	+	0.996560i	−0.210876	+	0.121749i	−0.601718	−	0.798708i	$-0.705517\pi$
$67$	−1.72609	+	0.996560i	−0.210876	+	0.121749i	0.390843	+	0.920458i	$0.372184\pi$
$68$	5.42345	−	10.3285i	0.657690	−	1.25251i
$69$		0			0
$70$	−7.49939	−	13.2898i	−0.896349	−	1.58843i
$71$	−2.86671			−0.340216			−0.170108	−	0.985425i	$-0.554412\pi$
$71$	−2.86671			−0.340216			−0.170108	+	0.985425i	$0.554412\pi$
$72$		0			0
$73$	4.04598	+	7.00785i	0.473547	+	0.820207i	0.999541	−	0.0302810i	$-0.00964022\pi$
$73$	4.04598	+	7.00785i	0.473547	+	0.820207i	−0.525995	+	0.850488i	$0.676307\pi$
$74$	−9.70090	−	2.39209i	−1.12771	−	0.278075i
$75$		0			0
$76$	−9.46129	+	0.379366i	−1.08528	+	0.0435162i
$77$	−1.31058	−	0.393495i	−0.149355	−	0.0448429i
$78$		0			0
$79$	4.28947	+	2.47652i	0.482603	+	0.278631i	0.721500	−	0.692414i	$-0.243453\pi$
$79$	4.28947	+	2.47652i	0.482603	+	0.278631i	−0.238898	+	0.971045i	$0.576786\pi$
$80$	13.4293	−	9.26160i	1.50144	−	1.03548i
$81$		0			0
$82$	3.40012	−	0.984485i	0.375480	−	0.108718i
$83$	1.91175			0.209842			0.104921	−	0.994481i	$-0.466541\pi$
$83$	1.91175			0.209842			0.104921	+	0.994481i	$0.466541\pi$
$84$		0			0
$85$	−23.7885			−2.58022
$86$	−4.06872	+	1.17808i	−0.438742	+	0.127035i
$87$		0			0
$88$	0.293043	−	1.43321i	0.0312385	−	0.152780i
$89$	11.7420	+	6.77926i	1.24465	+	0.718600i	0.970038	−	0.242955i	$-0.0781166\pi$
$89$	11.7420	+	6.77926i	1.24465	+	0.718600i	0.274614	+	0.961555i	$0.411450\pi$
$90$		0			0
$91$	7.72007	−	7.27195i	0.809283	−	0.762307i
$92$	0.156227	+	3.89627i	0.0162878	+	0.406214i
$93$		0			0
$94$	−13.6555	−	3.36723i	−1.40845	−	0.347303i
$95$	9.65431	+	16.7218i	0.990511	+	1.71562i
$96$		0			0
$97$	4.24721			0.431238			0.215619	−	0.976478i	$-0.430823\pi$
$97$	4.24721			0.431238			0.215619	+	0.976478i	$0.430823\pi$
$98$	9.65639	−	2.18039i	0.975443	−	0.220253i
$99$		0			0
$100$	−20.5984	−	10.8162i	−2.05984	−	1.08162i
$101$	0.668392	−	0.385896i	0.0665075	−	0.0383981i	−0.466378	−	0.884586i	$-0.654441\pi$
$101$	0.668392	−	0.385896i	0.0665075	−	0.0383981i	0.532885	+	0.846188i	$0.321108\pi$
$102$		0			0
$103$	13.8054	+	7.97056i	1.36029	+	0.785363i	0.989662	−	0.143420i	$-0.0458099\pi$
$103$	13.8054	+	7.97056i	1.36029	+	0.785363i	0.370626	+	0.928782i	$0.379143\pi$
$104$	8.48431	+	7.52103i	0.831955	+	0.737497i
$105$		0			0
$106$	8.31064	+	7.98409i	0.807200	+	0.775483i
$107$	0.733470	−	1.27041i	0.0709072	−	0.122815i	−0.828392	−	0.560149i	$-0.810744\pi$
$107$	0.733470	−	1.27041i	0.0709072	−	0.122815i	0.899299	+	0.437334i	$0.144077\pi$
$108$		0			0
$109$	3.23374	+	5.60100i	0.309736	+	0.536479i	0.978305	−	0.207172i	$-0.0664259\pi$
$109$	3.23374	+	5.60100i	0.309736	+	0.536479i	−0.668568	+	0.743651i	$0.733093\pi$
$110$	−2.86532	+	0.829637i	−0.273197	+	0.0791027i
$111$		0			0
$112$	3.24927	+	10.0719i	0.307028	+	0.951701i
$113$		−	11.3550i		−	1.06819i	−0.845424	−	0.534095i	$-0.820652\pi$
$113$		−	11.3550i		−	1.06819i	0.845424	−	0.534095i	$-0.179348\pi$
$114$		0			0
$115$	6.88621	−	3.97576i	0.642143	−	0.370741i
$116$	2.19132	+	3.46685i	0.203459	+	0.321889i
$117$		0			0
$118$	11.9021	−	12.3889i	1.09567	−	1.14049i
$119$	4.43778	−	14.7806i	0.406811	−	1.35493i
$120$		0			0
$121$	5.36625	−	9.29462i	0.487841	−	0.844966i
$122$	−4.69603	−	1.15797i	−0.425159	−	0.104838i
$123$		0			0
$124$	−8.08994	+	15.4066i	−0.726498	+	1.38355i
$125$			27.0506i			2.41948i
$126$		0			0
$127$		−	4.46382i		−	0.396100i	−0.980192	−	0.198050i	$-0.936539\pi$
$127$		−	4.46382i		−	0.396100i	0.980192	−	0.198050i	$-0.0634609\pi$
$128$	−10.4115	+	4.42725i	−0.920256	+	0.391317i
$129$		0			0
$130$	5.53523	−	22.4476i	0.485472	−	1.96878i
$131$	3.89148	−	6.74025i	0.340001	−	0.588898i	−0.644432	−	0.764662i	$-0.722906\pi$
$131$	3.89148	−	6.74025i	0.340001	−	0.588898i	0.984432	+	0.175764i	$0.0562394\pi$
$132$		0			0
$133$	−12.1908	+	2.87907i	−1.05708	+	0.249647i
$134$	−2.03265	−	1.95279i	−0.175595	−	0.168695i
$135$		0			0
$136$	16.1635	+	3.30490i	1.38601	+	0.283393i
$137$	7.70211	−	4.44682i	0.658036	−	0.379917i	−0.133492	−	0.991050i	$-0.542619\pi$
$137$	7.70211	−	4.44682i	0.658036	−	0.379917i	0.791528	+	0.611133i	$0.209286\pi$
$138$		0			0
$139$		−	0.116187i		−	0.00985482i	−0.999988	−	0.00492741i	$-0.998432\pi$
$139$		−	0.116187i		−	0.00985482i	0.999988	−	0.00492741i	$-0.00156845\pi$
$140$	15.1034	−	15.4145i	1.27647	−	1.30276i
$141$		0			0
$142$	−1.12754	−	3.89419i	−0.0946211	−	0.326793i
$143$	−1.03662	−	1.79547i	−0.0866861	−	0.150145i
$144$		0			0
$145$	4.18165	−	7.24283i	0.347267	−	0.601484i
$146$	−7.92821	+	8.25248i	−0.656143	+	0.682980i
$147$		0			0
$148$	−0.566114	−	14.1187i	−0.0465343	−	1.16055i
$149$	−3.58054	−	2.06723i	−0.293329	−	0.169354i	0.346113	−	0.938193i	$-0.387501\pi$
$149$	−3.58054	−	2.06723i	−0.293329	−	0.169354i	−0.639442	+	0.768839i	$0.720835\pi$
$150$		0			0
$151$	3.94574	−	2.27807i	0.321100	−	0.185387i	−0.330783	−	0.943707i	$-0.607313\pi$
$151$	3.94574	−	2.27807i	0.321100	−	0.185387i	0.651883	+	0.758320i	$0.273979\pi$
$152$	−4.23667	−	12.7032i	−0.343639	−	1.03036i
$153$		0			0
$154$	0.0190497	−	1.93509i	0.00153507	−	0.155934i
$155$	35.4843			2.85017
$156$		0			0
$157$	8.18445	+	14.1759i	0.653190	+	1.13136i	0.982344	+	0.187082i	$0.0599031\pi$
$157$	8.18445	+	14.1759i	0.653190	+	1.13136i	−0.329154	+	0.944276i	$0.606764\pi$
$158$	−1.67701	+	6.80096i	−0.133416	+	0.541055i
$159$		0			0
$160$	17.8632	+	14.5998i	1.41221	+	1.15422i
$161$	1.18563	+	5.02032i	0.0934410	+	0.395656i
$162$		0			0
$163$	−0.616691	−	0.356047i	−0.0483030	−	0.0278877i	0.475654	−	0.879632i	$-0.342211\pi$
$163$	−0.616691	−	0.356047i	−0.0483030	−	0.0278877i	−0.523957	+	0.851745i	$0.675545\pi$
$164$	2.67468	+	4.23156i	0.208858	+	0.330430i
$165$		0			0
$166$	0.751933	+	2.59695i	0.0583613	+	0.201563i
$167$	14.8541			1.14944			0.574721	−	0.818349i	$-0.305111\pi$
$167$	14.8541			1.14944			0.574721	+	0.818349i	$0.305111\pi$
$168$		0			0
$169$	3.06867			0.236052
$170$	−9.35654	−	32.3147i	−0.717613	−	2.47842i
$171$		0			0
$172$	−3.20064	−	5.06366i	−0.244046	−	0.386101i
$173$	3.66034	+	2.11330i	0.278291	+	0.160671i	0.632649	−	0.774438i	$-0.281967\pi$
$173$	3.66034	+	2.11330i	0.278291	+	0.160671i	−0.354359	+	0.935110i	$0.615301\pi$
$174$		0			0
$175$	−29.4774	−	8.85043i	−2.22828	−	0.669029i
$176$	2.06215	−	0.165637i	0.155441	−	0.0124854i
$177$		0			0
$178$	−4.59067	+	18.6170i	−0.344085	+	1.39540i
$179$	−1.11308	−	1.92790i	−0.0831952	−	0.144098i	0.821426	−	0.570316i	$-0.193179\pi$
$179$	−1.11308	−	1.92790i	−0.0831952	−	0.144098i	−0.904621	+	0.426218i	$0.859846\pi$
$180$		0			0
$181$	11.4376			0.850150			0.425075	−	0.905158i	$-0.360248\pi$
$181$	11.4376			0.850150			0.425075	+	0.905158i	$0.360248\pi$
$182$	12.9148	+	7.62686i	0.957310	+	0.565340i
$183$		0			0
$184$	−5.23131	+	1.74471i	−0.385657	+	0.128622i
$185$	−24.9533	+	14.4068i	−1.83460	+	1.05921i
$186$		0			0
$187$	−2.61260	−	1.50839i	−0.191052	−	0.110304i
$188$	−0.796890	−	19.8742i	−0.0581191	−	1.44948i
$189$		0			0
$190$	−18.9179	+	19.6916i	−1.37245	+	1.42858i
$191$	6.16406	−	10.6765i	0.446016	−	0.772522i	−0.552107	−	0.833774i	$-0.686176\pi$
$191$	6.16406	−	10.6765i	0.446016	−	0.772522i	0.998122	+	0.0612515i	$0.0195092\pi$
$192$		0			0
$193$	−0.872412	−	1.51106i	−0.0627976	−	0.108769i	0.832917	−	0.553397i	$-0.186669\pi$
$193$	−0.872412	−	1.51106i	−0.0627976	−	0.108769i	−0.895715	+	0.444629i	$0.853336\pi$
$194$	1.67052	+	5.76948i	0.119936	+	0.414224i
$195$		0			0
$196$	6.75995	+	12.2598i	0.482854	+	0.875701i
$197$			5.29064i			0.376943i	0.982079	+	0.188471i	$0.0603533\pi$
$197$			5.29064i			0.376943i	−0.982079	+	0.188471i	$0.939647\pi$
$198$		0			0
$199$	−9.73931	+	5.62299i	−0.690401	+	0.398603i	−0.803762	−	0.594950i	$-0.797172\pi$
$199$	−9.73931	+	5.62299i	−0.690401	+	0.398603i	0.113361	+	0.993554i	$0.463838\pi$
$200$	6.59108	−	32.2355i	0.466060	−	2.27939i
$201$		0			0
$202$	0.787102	+	0.756174i	0.0553803	+	0.0532042i
$203$	3.72011	+	3.94936i	0.261101	+	0.277191i
$204$		0			0
$205$	5.10403	−	8.84044i	0.356481	−	0.617443i
$206$	−5.39737	+	21.8885i	−0.376053	+	1.52504i
$207$		0			0
$208$	−6.87963	+	14.4834i	−0.477016	+	1.00424i
$209$			2.44865i			0.169377i
$210$		0			0
$211$			25.0975i			1.72778i	0.503677	+	0.863892i	$0.331980\pi$
$211$			25.0975i			1.72778i	−0.503677	+	0.863892i	$0.668020\pi$
$212$	−7.57697	+	14.4296i	−0.520388	+	0.991031i
$213$		0			0
$214$	2.01423	+	0.496679i	0.137690	+	0.0339523i
$215$	−6.10769	+	10.5788i	−0.416541	+	0.721470i
$216$		0			0
$217$	−6.61966	+	22.0476i	−0.449372	+	1.49669i
$218$	−6.33660	+	6.59577i	−0.429169	+	0.446722i
$219$		0			0
$220$	−2.25399	−	3.56598i	−0.151964	−	0.240419i
$221$	20.2491	−	11.6908i	1.36210	−	0.786409i
$222$		0			0
$223$			17.9029i			1.19887i	0.800423	+	0.599435i	$0.204608\pi$
$223$			17.9029i			1.19887i	−0.800423	+	0.599435i	$0.795392\pi$
$224$	−12.4038	+	8.37535i	−0.828762	+	0.559602i
$225$		0			0
$226$	15.4249	−	4.46618i	1.02605	−	0.297086i
$227$	7.08833	+	12.2774i	0.470469	+	0.814877i	0.999430	−	0.0337699i	$-0.0107513\pi$
$227$	7.08833	+	12.2774i	0.470469	+	0.814877i	−0.528960	+	0.848647i	$0.677418\pi$
$228$		0			0
$229$	1.86807	−	3.23559i	0.123446	−	0.213814i	−0.797679	−	0.603083i	$-0.793939\pi$
$229$	1.86807	−	3.23559i	0.123446	−	0.213814i	0.921124	+	0.389269i	$0.127272\pi$
$230$	8.10924	+	7.79060i	0.534707	+	0.513697i
$231$		0			0
$232$	−3.84753	+	4.34032i	−0.252603	+	0.284956i
$233$	−23.9146	−	13.8071i	−1.56670	−	0.904532i	−0.996551	−	0.0829878i	$-0.973554\pi$
$233$	−23.9146	−	13.8071i	−1.56670	−	0.904532i	−0.570145	−	0.821544i	$-0.693113\pi$
$234$		0			0
$235$	−35.1254	+	20.2797i	−2.29133	+	1.32290i
$236$	21.5106	+	11.2952i	1.40022	+	0.735253i
$237$		0			0
$238$	21.8237	+	0.214840i	1.41462	+	0.0139260i
$239$	−13.8753			−0.897520			−0.448760	−	0.893652i	$-0.648134\pi$
$239$	−13.8753			−0.897520			−0.448760	+	0.893652i	$0.648134\pi$
$240$		0			0
$241$	−12.8683	−	22.2886i	−0.828921	−	1.43573i	−0.898885	−	0.438184i	$-0.855622\pi$
$241$	−12.8683	−	22.2886i	−0.828921	−	1.43573i	0.0699642	−	0.997550i	$-0.477711\pi$
$242$	14.7366	+	3.63383i	0.947307	+	0.233592i
$243$		0			0
$244$	−0.274046	−	6.83463i	−0.0175440	−	0.437542i
$245$	15.7253	−	23.8268i	1.00466	−	1.52224i
$246$		0			0
$247$	−16.4358	−	9.48919i	−1.04578	−	0.603782i
$248$	−24.1105	−	4.92979i	−1.53102	−	0.313042i
$249$		0			0
$250$	−36.7460	+	10.6396i	−2.32402	+	0.672906i
$251$	−21.4777			−1.35566			−0.677829	−	0.735219i	$-0.737079\pi$
$251$	−21.4777			−1.35566			−0.677829	+	0.735219i	$0.737079\pi$
$252$		0			0
$253$	1.00838			0.0633965
$254$	6.06373	−	1.75572i	0.380473	−	0.110164i
$255$		0			0
$256$	−10.1091	−	12.4018i	−0.631820	−	0.775115i
$257$	4.93576	+	2.84966i	0.307884	+	0.177757i	0.645979	−	0.763355i	$-0.276449\pi$
$257$	4.93576	+	2.84966i	0.307884	+	0.177757i	−0.338095	+	0.941112i	$0.609783\pi$
$258$		0			0
$259$	−4.29633	−	18.1919i	−0.266961	−	1.13039i
$260$	32.6703	−	1.30997i	2.02613	−	0.0812409i
$261$		0			0
$262$	10.6867	+	2.63517i	0.660225	+	0.162801i
$263$	−14.8083	−	25.6487i	−0.913117	−	1.58157i	−0.809635	−	0.586934i	$-0.800335\pi$
$263$	−14.8083	−	25.6487i	−0.913117	−	1.58157i	−0.103482	−	0.994631i	$-0.532998\pi$
$264$		0			0
$265$	33.2343			2.04157
$266$	−8.70589	−	15.4278i	−0.533792	−	0.945939i
$267$		0			0
$268$	1.85321	−	3.52927i	0.113203	−	0.215584i
$269$	5.49978	−	3.17530i	0.335328	−	0.193601i	−0.322876	−	0.946441i	$-0.604650\pi$
$269$	5.49978	−	3.17530i	0.335328	−	0.193601i	0.658204	+	0.752840i	$0.271316\pi$
$270$		0			0
$271$	17.5939	+	10.1579i	1.06876	+	0.617046i	0.927841	−	0.372976i	$-0.121663\pi$
$271$	17.5939	+	10.1579i	1.06876	+	0.617046i	0.140914	+	0.990022i	$0.454996\pi$
$272$	1.86804	+	23.2567i	0.113266	+	1.41015i
$273$		0			0
$274$	9.07004	+	8.71365i	0.547941	+	0.526411i
$275$	−3.00823	+	5.21040i	−0.181403	+	0.314199i
$276$		0			0
$277$	−2.95274	−	5.11429i	−0.177413	−	0.307288i	0.763581	−	0.645712i	$-0.223439\pi$
$277$	−2.95274	−	5.11429i	−0.177413	−	0.307288i	−0.940994	+	0.338424i	$0.890106\pi$
$278$	0.157830	−	0.0456988i	0.00946601	−	0.00274083i
$279$		0			0
$280$	26.8798	+	14.4538i	1.60637	+	0.863781i
$281$			7.21240i			0.430256i	0.976586	+	0.215128i	$0.0690169\pi$
$281$			7.21240i			0.430256i	−0.976586	+	0.215128i	$0.930983\pi$
$282$		0			0
$283$	18.9031	−	10.9137i	1.12367	−	0.648751i	0.181335	−	0.983421i	$-0.441958\pi$
$283$	18.9031	−	10.9137i	1.12367	−	0.648751i	0.942335	+	0.334670i	$0.108625\pi$
$284$	4.84645	−	3.06334i	0.287584	−	0.181776i
$285$		0			0
$286$	2.03127	−	2.11435i	0.120112	−	0.125024i
$287$	4.54069	+	4.82050i	0.268028	+	0.284545i
$288$		0			0
$289$	8.51138	−	14.7421i	0.500669	−	0.867184i
$290$	11.4835	+	2.83166i	0.674335	+	0.166281i
$291$		0			0
$292$	−14.3286	−	7.52394i	−0.838521	−	0.440305i
$293$		−	10.6245i		−	0.620690i	−0.950624	−	0.310345i	$-0.899555\pi$
$293$		−	10.6245i		−	0.620690i	0.950624	−	0.310345i	$-0.100445\pi$
$294$		0			0
$295$		−	49.5432i		−	2.88452i
$296$	18.9565	−	6.32223i	1.10182	−	0.367472i
$297$		0			0
$298$	1.39985	−	5.67695i	0.0810911	−	0.328857i
$299$	−3.90776	+	6.76844i	−0.225992	+	0.391429i
$300$		0			0
$301$	−5.43358	−	5.76841i	−0.313186	−	0.332486i
$302$	4.64652	+	4.46394i	0.267377	+	0.256871i
$303$		0			0
$304$	15.5898	−	10.7516i	0.894138	−	0.616646i
$305$	−12.0794	+	6.97407i	−0.691666	+	0.399334i
$306$		0			0
$307$		−	28.9860i		−	1.65432i	−0.561967	−	0.827160i	$-0.689955\pi$
$307$		−	28.9860i		−	1.65432i	0.561967	−	0.827160i	$-0.310045\pi$
$308$	2.63615	−	0.735235i	0.150209	−	0.0418939i
$309$		0			0
$310$	13.9568	+	48.2025i	0.792691	+	2.73772i
$311$	3.60735	+	6.24811i	0.204554	+	0.354298i	0.949990	−	0.312279i	$-0.101092\pi$
$311$	3.60735	+	6.24811i	0.204554	+	0.354298i	−0.745437	+	0.666576i	$0.767759\pi$
$312$		0			0
$313$	3.16439	−	5.48089i	0.178862	−	0.309798i	−0.762629	−	0.646836i	$-0.776092\pi$
$313$	3.16439	−	5.48089i	0.178862	−	0.309798i	0.941491	+	0.337038i	$0.109425\pi$
$314$	−16.0376	+	16.6936i	−0.905056	+	0.942073i
$315$		0			0
$316$	−9.89814	+	0.396882i	−0.556814	+	0.0223264i
$317$	7.29993	+	4.21462i	0.410005	+	0.236717i	0.690792	−	0.723054i	$-0.257262\pi$
$317$	7.29993	+	4.21462i	0.410005	+	0.236717i	−0.280787	+	0.959770i	$0.590595\pi$
$318$		0			0
$319$	0.918509	−	0.530302i	0.0514266	−	0.0296912i
$320$	−12.8067	+	30.0081i	−0.715916	+	1.67750i
$321$		0			0
$322$	−6.35335	+	3.58519i	−0.354058	+	0.199795i
$323$	−27.6156			−1.53657
$324$		0			0
$325$	−23.3154	−	40.3834i	−1.29331	−	2.24007i
$326$	0.241102	−	0.977765i	0.0133534	−	0.0541534i
$327$		0			0
$328$	−4.69622	+	5.29770i	−0.259305	+	0.292517i
$329$	−6.04772	−	25.6078i	−0.333422	−	1.41180i
$330$		0			0
$331$	8.94368	+	5.16363i	0.491589	+	0.283819i	0.725233	−	0.688503i	$-0.241732\pi$
$331$	8.94368	+	5.16363i	0.491589	+	0.283819i	−0.233644	+	0.972322i	$0.575065\pi$
$332$	−3.23200	+	2.04288i	−0.177379	+	0.112117i
$333$		0			0
$334$	5.84243	+	20.1780i	0.319684	+	1.10409i
$335$	−8.12860			−0.444113
$336$		0			0
$337$	−36.2097			−1.97247			−0.986235	−	0.165351i	$-0.947124\pi$
$337$	−36.2097			−1.97247			−0.986235	+	0.165351i	$0.947124\pi$
$338$	1.20698	+	4.16854i	0.0656508	+	0.226738i
$339$		0			0
$340$	40.2167	−	25.4202i	2.18106	−	1.37860i
$341$	3.89711	+	2.25000i	0.211040	+	0.121844i
$342$		0			0
$343$	11.8708	+	14.2156i	0.640964	+	0.767571i
$344$	5.61969	−	6.33945i	0.302993	−	0.341800i
$345$		0			0
$346$	−1.43105	+	5.80348i	−0.0769337	+	0.311997i
$347$	−9.40691	−	16.2933i	−0.504990	−	0.874668i	−0.999983	−	0.00577106i	$-0.998163\pi$
$347$	−9.40691	−	16.2933i	−0.504990	−	0.874668i	0.494994	−	0.868897i	$-0.335170\pi$
$348$		0			0
$349$	11.5487			0.618186			0.309093	−	0.951032i	$-0.399975\pi$
$349$	11.5487			0.618186			0.309093	+	0.951032i	$0.399975\pi$
$350$	0.428462	−	43.5237i	0.0229023	−	2.32644i
$351$		0			0
$352$	1.03609	+	2.73612i	0.0552240	+	0.145836i
$353$	7.46456	−	4.30967i	0.397298	−	0.229380i	−0.288019	−	0.957625i	$-0.592997\pi$
$353$	7.46456	−	4.30967i	0.397298	−	0.229380i	0.685318	+	0.728244i	$0.259663\pi$
$354$		0			0
$355$	−10.1250	−	5.84570i	−0.537382	−	0.310257i
$356$	−27.0953	+	1.08643i	−1.43605	+	0.0575806i
$357$		0			0
$358$	2.18110	−	2.27031i	0.115275	−	0.119989i
$359$	−10.5681	+	18.3045i	−0.557765	+	0.966077i	0.439918	+	0.898038i	$0.355008\pi$
$359$	−10.5681	+	18.3045i	−0.557765	+	0.966077i	−0.997683	+	0.0680390i	$0.978326\pi$
$360$		0			0
$361$	1.70748	+	2.95745i	0.0898675	+	0.155655i
$362$	4.49866	+	15.5370i	0.236444	+	0.816609i
$363$		0			0
$364$	−5.28078	+	20.5435i	−0.276788	+	1.07677i
$365$			33.0017i			1.72739i
$366$		0			0
$367$	−20.0270	+	11.5626i	−1.04540	+	0.603561i	−0.921358	−	0.388716i	$-0.872919\pi$
$367$	−20.0270	+	11.5626i	−1.04540	+	0.603561i	−0.124041	+	0.992277i	$0.539586\pi$
$368$	−4.42763	−	6.42007i	−0.230806	−	0.334669i
$369$		0			0
$370$	−29.3851	−	28.2304i	−1.52766	−	1.46763i
$371$	−6.19991	+	20.6496i	−0.321883	+	1.07207i
$372$		0			0
$373$	13.1467	−	22.7708i	0.680711	−	1.17903i	−0.294054	−	0.955789i	$-0.595004\pi$
$373$	13.1467	−	22.7708i	0.680711	−	1.17903i	0.974764	−	0.223236i	$-0.0716622\pi$
$374$	1.02142	−	4.14228i	0.0528166	−	0.214192i
$375$		0			0
$376$	26.6840	−	8.89947i	1.37612	−	0.458955i
$377$			8.22026i			0.423365i
$378$		0			0
$379$		−	28.0266i		−	1.43963i	−0.694167	−	0.719814i	$-0.744227\pi$
$379$		−	28.0266i		−	1.43963i	0.694167	−	0.719814i	$-0.255773\pi$
$380$	−34.1902	−	17.9532i	−1.75392	−	0.920981i
$381$		0			0
$382$	16.9276	+	4.17408i	0.866089	+	0.213564i
$383$	4.60294	−	7.97253i	0.235199	−	0.407377i	−0.724131	−	0.689662i	$-0.757759\pi$
$383$	4.60294	−	7.97253i	0.235199	−	0.407377i	0.959331	+	0.282285i	$0.0910923\pi$
$384$		0			0
$385$	−3.82649	−	4.06229i	−0.195016	−	0.207033i
$386$	1.70951	−	1.77943i	0.0870120	−	0.0905708i
$387$		0			0
$388$	−7.18031	+	4.53852i	−0.364525	+	0.230409i
$389$	−7.16218	+	4.13509i	−0.363137	+	0.209657i	−0.670456	−	0.741949i	$-0.733901\pi$
$389$	−7.16218	+	4.13509i	−0.363137	+	0.209657i	0.307319	+	0.951607i	$0.400568\pi$
$390$		0			0
$391$			11.3724i			0.575127i
$392$	−13.9951	+	14.0049i	−0.706860	+	0.707354i
$393$		0			0
$394$	−7.18690	+	2.08093i	−0.362071	+	0.104836i
$395$	10.1001	+	17.4938i	0.508190	+	0.880211i
$396$		0			0
$397$	16.6044	−	28.7597i	0.833353	−	1.44341i	−0.0620122	−	0.998075i	$-0.519752\pi$
$397$	16.6044	−	28.7597i	0.833353	−	1.44341i	0.895365	−	0.445334i	$-0.146915\pi$
$398$	−11.4691	−	11.0184i	−0.574892	−	0.552303i
$399$		0			0
$400$	46.3817	−	3.72549i	2.31908	−	0.186274i
$401$	−11.4810	−	6.62858i	−0.573336	−	0.331015i	0.185145	−	0.982711i	$-0.440725\pi$
$401$	−11.4810	−	6.62858i	−0.573336	−	0.331015i	−0.758480	+	0.651696i	$0.774058\pi$
$402$		0			0
$403$	−30.2047	+	17.4387i	−1.50460	+	0.868684i
$404$	−0.717616	+	1.36663i	−0.0357027	+	0.0679925i
$405$		0			0
$406$	−3.90167	+	6.60684i	−0.193637	+	0.327892i
$407$	−3.65403			−0.181124
$408$		0			0
$409$	3.75064	+	6.49630i	0.185457	+	0.321222i	0.943731	−	0.330715i	$-0.107290\pi$
$409$	3.75064	+	6.49630i	0.185457	+	0.321222i	−0.758273	+	0.651937i	$0.773957\pi$
$410$	14.0165	+	3.45626i	0.692227	+	0.170693i
$411$		0			0
$412$	−31.8566	+	1.27734i	−1.56946	+	0.0629302i
$413$	30.7828	+	9.24237i	1.51472	+	0.454787i
$414$		0			0
$415$	6.75218	+	3.89837i	0.331451	+	0.191363i
$416$	−22.3804	−	3.64876i	−1.09729	−	0.178895i
$417$		0			0
$418$	−3.32629	+	0.963108i	−0.162694	+	0.0471071i
$419$	−1.05849			−0.0517104			−0.0258552	−	0.999666i	$-0.508231\pi$
$419$	−1.05849			−0.0517104			−0.0258552	+	0.999666i	$0.508231\pi$
$420$		0			0
$421$	15.7988			0.769988			0.384994	−	0.922919i	$-0.374203\pi$
$421$	15.7988			0.769988			0.384994	+	0.922919i	$0.374203\pi$
$422$	−34.0929	+	9.87140i	−1.65962	+	0.480532i
$423$		0			0
$424$	−22.5816	−	4.61719i	−1.09666	−	0.224231i
$425$	−58.7622	−	33.9264i	−2.85039	−	1.64567i
$426$		0			0
$427$	−2.07978	−	8.80638i	−0.100647	−	0.426170i
$428$	0.117544	+	2.93152i	0.00568172	+	0.141701i
$429$		0			0
$430$	−16.7728	−	4.13591i	−0.808854	−	0.199451i
$431$	−6.94337	−	12.0263i	−0.334450	−	0.579285i	0.648929	−	0.760849i	$-0.275217\pi$
$431$	−6.94337	−	12.0263i	−0.334450	−	0.579285i	−0.983379	+	0.181564i	$0.941884\pi$
$432$		0			0
$433$	−37.7930			−1.81622			−0.908109	−	0.418734i	$-0.862474\pi$
$433$	−37.7930			−1.81622			−0.908109	+	0.418734i	$0.862474\pi$
$434$	−32.5535	−	0.320468i	−1.56262	−	0.0153829i
$435$		0			0
$436$	−11.4521	−	6.01349i	−0.548457	−	0.287994i
$437$	7.99406	−	4.61537i	0.382408	−	0.220783i
$438$		0			0
$439$	−0.157376	−	0.0908612i	−0.00751116	−	0.00433657i	0.496240	−	0.868186i	$-0.334714\pi$
$439$	−0.157376	−	0.0908612i	−0.00751116	−	0.00433657i	−0.503751	+	0.863849i	$0.668047\pi$
$440$	3.95755	−	4.46443i	0.188669	−	0.212834i
$441$		0			0
$442$	23.8454	+	22.9085i	1.13421	+	1.08964i
$443$	5.02268	−	8.69954i	0.238635	−	0.413327i	−0.721688	−	0.692218i	$-0.756633\pi$
$443$	5.02268	−	8.69954i	0.238635	−	0.413327i	0.960323	+	0.278891i	$0.0899668\pi$
$444$		0			0
$445$	27.6480	+	47.8878i	1.31064	+	2.27010i
$446$	−24.3197	+	7.04162i	−1.15157	+	0.333430i
$447$		0			0
$448$	−16.2559	−	13.5553i	−0.768019	−	0.640427i
$449$			9.54508i			0.450460i	0.974306	+	0.225230i	$0.0723134\pi$
$449$			9.54508i			0.450460i	−0.974306	+	0.225230i	$0.927687\pi$
$450$		0			0
$451$	1.12111	−	0.647275i	0.0527911	−	0.0304790i
$452$	12.1339	+	19.1967i	0.570729	+	0.902939i
$453$		0			0
$454$	−13.8898	+	14.4579i	−0.651879	+	0.678541i
$455$	42.0955	−	9.94157i	1.97347	−	0.466068i
$456$		0			0
$457$	−13.6611	+	23.6617i	−0.639039	+	1.10685i	0.346605	+	0.938011i	$0.387334\pi$
$457$	−13.6611	+	23.6617i	−0.639039	+	1.10685i	−0.985644	+	0.168836i	$0.945999\pi$
$458$	5.13004	+	1.26499i	0.239711	+	0.0591091i
$459$		0			0
$460$	−7.39335	+	14.0799i	−0.344717	+	0.656481i
$461$			32.7076i			1.52335i	0.647961	+	0.761673i	$0.275622\pi$
$461$			32.7076i			1.52335i	−0.647961	+	0.761673i	$0.724378\pi$
$462$		0			0
$463$		−	29.7571i		−	1.38293i	−0.722411	−	0.691464i	$-0.756966\pi$
$463$		−	29.7571i		−	1.38293i	0.722411	−	0.691464i	$-0.243034\pi$
$464$	−7.40929	−	3.51941i	−0.343968	−	0.163385i
$465$		0			0
$466$	9.34966	−	37.9166i	0.433114	−	1.75645i
$467$	17.4458	−	30.2171i	0.807297	−	1.39828i	−0.107432	−	0.994212i	$-0.534263\pi$
$467$	17.4458	−	30.2171i	0.807297	−	1.39828i	0.914729	−	0.404067i	$-0.132404\pi$
$468$		0			0
$469$	1.51640	−	5.05057i	0.0700210	−	0.233213i
$470$	−41.3639	−	39.7386i	−1.90797	−	1.83300i
$471$		0			0
$472$	−6.88296	+	33.6630i	−0.316814	+	1.54947i
$473$	−1.34157	+	0.774556i	−0.0616854	+	0.0356141i
$474$		0			0
$475$			55.0747i			2.52700i
$476$	8.29188	+	29.7301i	0.380058	+	1.36268i
$477$		0			0
$478$	−5.45747	−	18.8485i	−0.249619	−	0.862109i
$479$	−17.1476	−	29.7004i	−0.783492	−	1.35705i	−0.929896	−	0.367823i	$-0.880103\pi$
$479$	−17.1476	−	29.7004i	−0.783492	−	1.35705i	0.146404	−	0.989225i	$-0.453230\pi$
$480$		0			0
$481$	14.1604	−	24.5265i	0.645657	−	1.11831i
$482$	25.2158	−	26.2471i	1.14855	−	1.19552i
$483$		0			0
$484$	0.859984	+	21.4478i	0.0390902	+	0.974899i
$485$	15.0009	+	8.66075i	0.681154	+	0.393264i
$486$		0			0
$487$	−27.0016	+	15.5894i	−1.22356	+	0.706423i	−0.965675	−	0.259753i	$-0.916359\pi$
$487$	−27.0016	+	15.5894i	−1.22356	+	0.706423i	−0.257885	+	0.966176i	$0.583026\pi$
$488$	9.17649	−	3.06048i	0.415400	−	0.138541i
$489$		0			0
$490$	38.5519	+	11.9900i	1.74160	+	0.541651i
$491$	−29.3983			−1.32673			−0.663363	−	0.748297i	$-0.730872\pi$
$491$	−29.3983			−1.32673			−0.663363	+	0.748297i	$0.730872\pi$
$492$		0			0
$493$	5.98067	+	10.3588i	0.269356	+	0.466538i
$494$	6.42573	−	26.0589i	0.289107	−	1.17245i
$495$		0			0
$496$	−2.78647	−	34.6911i	−0.125116	−	1.55768i
$497$	5.52097	−	5.20050i	0.247649	−	0.233274i
$498$		0			0
$499$	4.13651	+	2.38822i	0.185176	+	0.106911i	0.589722	−	0.807606i	$-0.299237\pi$
$499$	4.13651	+	2.38822i	0.185176	+	0.106911i	−0.404546	+	0.914517i	$0.632571\pi$
$500$	−28.9060	−	45.7316i	−1.29271	−	2.04518i
$501$		0			0
$502$	−8.44764	−	29.1756i	−0.377037	−	1.30217i
$503$	−18.2902			−0.815519			−0.407760	−	0.913089i	$-0.633690\pi$
$503$	−18.2902			−0.815519			−0.407760	+	0.913089i	$0.633690\pi$
$504$		0			0
$505$	3.14762			0.140067
$506$	0.396619	+	1.36980i	0.0176319	+	0.0608952i
$507$		0			0
$508$	4.77000	+	7.54652i	0.211635	+	0.334823i
$509$	22.1503	+	12.7885i	0.981795	+	0.566840i	0.902812	−	0.430036i	$-0.141499\pi$
$509$	22.1503	+	12.7885i	0.981795	+	0.566840i	0.0789836	+	0.996876i	$0.474833\pi$
$510$		0			0
$511$	−20.5050	−	6.15652i	−0.907090	−	0.272349i
$512$	12.8707	−	18.6103i	0.568811	−	0.822468i
$513$		0			0
$514$	−1.92969	+	7.82566i	−0.0851149	+	0.345175i
$515$	32.5066	+	56.3030i	1.43241	+	2.48101i
$516$		0			0
$517$	−5.14359			−0.226215
$518$	23.0223	−	12.9915i	1.01154	−	0.570813i
$519$		0			0
$520$	14.6294	+	43.8647i	0.641543	+	1.92359i
$521$	10.2479	−	5.91663i	0.448969	−	0.259212i	−0.258426	−	0.966031i	$-0.583204\pi$
$521$	10.2479	−	5.91663i	0.448969	−	0.259212i	0.707395	+	0.706819i	$0.249870\pi$
$522$		0			0
$523$	−11.6681	−	6.73657i	−0.510210	−	0.294570i	0.222710	−	0.974885i	$-0.428510\pi$
$523$	−11.6681	−	6.73657i	−0.510210	−	0.294570i	−0.732920	+	0.680315i	$0.761843\pi$
$524$	0.623641	+	15.5534i	0.0272439	+	0.679455i
$525$		0			0
$526$	29.0172	−	30.2040i	1.26521	−	1.31696i
$527$	−25.3752	+	43.9511i	−1.10536	+	1.91454i
$528$		0			0
$529$	9.59934	+	16.6265i	0.417362	+	0.722893i
$530$	13.0718	+	45.1460i	0.567802	+	1.96102i
$531$		0			0
$532$	17.5332	−	17.8943i	0.760160	−	0.775817i
$533$			10.0335i			0.434598i
$534$		0			0
$535$	5.18114	−	2.99133i	0.224000	−	0.129327i
$536$	5.52313	+	1.12929i	0.238563	+	0.0487781i
$537$		0			0
$538$	6.47657	+	6.22208i	0.279225	+	0.268253i
$539$	3.23787	−	1.61970i	0.139465	−	0.0697653i
$540$		0			0
$541$	−15.8103	+	27.3843i	−0.679740	+	1.17734i	0.295320	+	0.955398i	$0.404574\pi$
$541$	−15.8103	+	27.3843i	−0.679740	+	1.17734i	−0.975059	+	0.221945i	$0.928759\pi$
$542$	−6.87854	+	27.8952i	−0.295458	+	1.19820i
$543$		0			0
$544$	−30.8576	+	11.6849i	−1.32301	+	0.500988i
$545$			26.3765i			1.12985i
$546$		0			0
$547$			23.9671i			1.02476i	0.858759	+	0.512381i	$0.171236\pi$
$547$			23.9671i			1.02476i	−0.858759	+	0.512381i	$0.828764\pi$
$548$	−8.26933	+	15.7482i	−0.353248	+	0.672729i
$549$		0			0
$550$	−8.26110	−	2.03706i	−0.352254	−	0.0868606i
$551$	4.85439	−	8.40804i	0.206804	−	0.358195i
$552$		0			0
$553$	−12.7537	+	3.01200i	−0.542342	+	0.128083i
$554$	5.78596	−	6.02261i	0.245822	−	0.255876i
$555$		0			0
$556$	0.124156	+	0.196425i	0.00526539	+	0.00833026i
$557$	2.55943	−	1.47769i	0.108446	−	0.0626116i	−0.444796	−	0.895632i	$-0.646724\pi$
$557$	2.55943	−	1.47769i	0.108446	−	0.0626116i	0.553242	+	0.833020i	$0.313390\pi$
$558$		0			0
$559$		−	12.0065i		−	0.507819i
$560$	−9.06193	+	42.1989i	−0.382937	+	1.78323i
$561$		0			0
$562$	−9.79746	+	2.83680i	−0.413281	+	0.119663i
$563$	5.73102	+	9.92642i	0.241534	+	0.418349i	0.961151	−	0.276022i	$-0.0890162\pi$
$563$	5.73102	+	9.92642i	0.241534	+	0.418349i	−0.719618	+	0.694371i	$0.755683\pi$
$564$		0			0
$565$	23.1547	−	40.1052i	0.974127	−	1.68724i
$566$	22.2603	+	21.3856i	0.935671	+	0.898906i
$567$		0			0
$568$	6.06751	+	5.37862i	0.254587	+	0.225682i
$569$	−1.53807	−	0.888004i	−0.0644792	−	0.0372271i	0.467414	−	0.884039i	$-0.345186\pi$
$569$	−1.53807	−	0.888004i	−0.0644792	−	0.0372271i	−0.531893	+	0.846812i	$0.678519\pi$
$570$		0			0
$571$	−2.13249	+	1.23120i	−0.0892421	+	0.0515239i	−0.543957	−	0.839113i	$-0.683075\pi$
$571$	−2.13249	+	1.23120i	−0.0892421	+	0.0515239i	0.454715	+	0.890637i	$0.349741\pi$
$572$	3.67112	+	1.92770i	0.153497	+	0.0806010i
$573$		0			0
$574$	−4.76230	+	8.06416i	−0.198775	+	0.336592i
$575$	22.6804			0.945838
$576$		0			0
$577$	−6.51529	−	11.2848i	−0.271235	−	0.469793i	0.697943	−	0.716153i	$-0.254099\pi$
$577$	−6.51529	−	11.2848i	−0.271235	−	0.469793i	−0.969178	+	0.246360i	$0.920765\pi$
$578$	23.3737	+	5.76360i	0.972217	+	0.239734i
$579$		0			0
$580$	0.670142	+	16.7132i	0.0278261	+	0.693976i
$581$	−3.68182	+	3.46810i	−0.152747	+	0.143881i
$582$		0			0
$583$	3.65000	+	2.10733i	0.151167	+	0.0872765i
$584$	4.58488	−	22.4236i	0.189724	−	0.927896i
$585$		0			0
$586$	14.4325	−	4.17885i	0.596202	−	0.172627i
$587$	27.5904			1.13878			0.569389	−	0.822068i	$-0.307180\pi$
$587$	27.5904			1.13878			0.569389	+	0.822068i	$0.307180\pi$
$588$		0			0
$589$	41.1930			1.69733
$590$	67.3003	−	19.4864i	2.77071	−	0.802243i
$591$		0			0
$592$	16.0442	+	23.2641i	0.659413	+	0.956150i
$593$	−12.6506	−	7.30385i	−0.519500	−	0.299933i	0.217230	−	0.976120i	$-0.430298\pi$
$593$	−12.6506	−	7.30385i	−0.519500	−	0.299933i	−0.736730	+	0.676187i	$0.763631\pi$
$594$		0			0
$595$	45.8140	−	43.1547i	1.87819	−	1.76917i
$596$	8.26226	−	0.331289i	0.338435	−	0.0135701i
$597$		0			0
$598$	−10.7314	−	2.64619i	−0.438838	−	0.108211i
$599$	−19.2913	−	33.4136i	−0.788222	−	1.36524i	−0.927055	−	0.374925i	$-0.877668\pi$
$599$	−19.2913	−	33.4136i	−0.788222	−	1.36524i	0.138833	−	0.990316i	$-0.455665\pi$
$600$		0			0
$601$	−29.5034			−1.20347			−0.601735	−	0.798696i	$-0.705524\pi$
$601$	−29.5034			−1.20347			−0.601735	+	0.798696i	$0.705524\pi$
$602$	5.69876	−	9.64991i	0.232264	−	0.393301i
$603$		0			0
$604$	−4.23632	+	8.06768i	−0.172373	+	0.328269i
$605$	37.9065	−	21.8853i	1.54112	−	0.889766i
$606$		0			0
$607$	33.9174	+	19.5822i	1.37666	+	0.794817i	0.991756	−	0.128138i	$-0.0409000\pi$
$607$	33.9174	+	19.5822i	1.37666	+	0.794817i	0.384907	+	0.922955i	$0.374233\pi$
$608$	20.7370	+	16.9486i	0.840995	+	0.687358i
$609$		0			0
$610$	−14.2248	−	13.6659i	−0.575945	−	0.553315i
$611$	19.9328	−	34.5247i	0.806396	−	1.39672i
$612$		0			0
$613$	3.93298	+	6.81212i	0.158851	+	0.275139i	0.934455	−	0.356082i	$-0.115888\pi$
$613$	3.93298	+	6.81212i	0.158851	+	0.275139i	−0.775603	+	0.631221i	$0.782554\pi$
$614$	39.3751	−	11.4008i	1.58905	−	0.460100i
$615$		0			0
$616$	2.03561	+	3.29181i	0.0820171	+	0.132631i
$617$		−	42.0669i		−	1.69355i	−0.531950	−	0.846776i	$-0.678541\pi$
$617$		−	42.0669i		−	1.69355i	0.531950	−	0.846776i	$-0.321459\pi$
$618$		0			0
$619$	30.0148	−	17.3290i	1.20639	−	0.696512i	0.244425	−	0.969668i	$-0.421401\pi$
$619$	30.0148	−	17.3290i	1.20639	−	0.696512i	0.961970	+	0.273156i	$0.0880675\pi$
$620$	−59.9896	+	37.9182i	−2.40924	+	1.52283i
$621$		0			0
$622$	−7.06869	+	7.35780i	−0.283429	+	0.295021i
$623$	−34.9121	+	8.24508i	−1.39872	+	0.330332i
$624$		0			0
$625$	−26.0786	+	45.1695i	−1.04315	+	1.80678i
$626$	8.68996	+	2.14281i	0.347321	+	0.0856440i
$627$		0			0
$628$	−28.9848	−	15.2199i	−1.15662	−	0.607338i
$629$		−	41.2097i		−	1.64314i
$630$		0			0
$631$			13.1561i			0.523737i	0.965104	+	0.261868i	$0.0843387\pi$
$631$			13.1561i			0.523737i	−0.965104	+	0.261868i	$0.915661\pi$
$632$	−4.43229	−	13.2897i	−0.176307	−	0.528636i
$633$		0			0
$634$	−2.85399	+	11.5741i	−0.113346	+	0.459665i
$635$	9.10247	−	15.7659i	0.361220	−	0.625652i
$636$		0			0
$637$	−1.67596	+	28.0099i	−0.0664039	+	1.10979i
$638$	1.08164	+	1.03914i	0.0428226	+	0.0411399i
$639$		0			0
$640$	−45.8007	−	5.59401i	−1.81043	−	0.221123i
$641$	−21.0414	+	12.1482i	−0.831084	+	0.479827i	−0.854224	−	0.519906i	$-0.825967\pi$
$641$	−21.0414	+	12.1482i	−0.831084	+	0.479827i	0.0231396	+	0.999732i	$0.492634\pi$
$642$		0			0
$643$			25.3313i			0.998968i	0.866323	+	0.499484i	$0.166477\pi$
$643$			25.3313i			0.998968i	−0.866323	+	0.499484i	$0.833523\pi$
$644$	−7.36909	−	7.22037i	−0.290383	−	0.284522i
$645$		0			0
$646$	−10.8618	−	37.5134i	−0.427352	−	1.47595i
$647$	18.5185	+	32.0749i	0.728036	+	1.26100i	0.957712	+	0.287728i	$0.0928999\pi$
$647$	18.5185	+	32.0749i	0.728036	+	1.26100i	−0.229676	+	0.973267i	$0.573767\pi$
$648$		0			0
$649$	3.14144	−	5.44114i	0.123312	−	0.213583i
$650$	45.6871	−	47.5557i	1.79200	−	1.86529i
$651$		0			0
$652$	1.42304	−	0.0570593i	0.0557307	−	0.00223461i
$653$	7.04637	+	4.06822i	0.275746	+	0.159202i	0.631496	−	0.775379i	$-0.282441\pi$
$653$	7.04637	+	4.06822i	0.275746	+	0.159202i	−0.355750	+	0.934581i	$0.615775\pi$
$654$		0			0
$655$	27.4889	−	15.8707i	1.07408	−	0.620121i
$656$	−9.04362	−	4.29572i	−0.353094	−	0.167720i
$657$		0			0
$658$	32.4074	−	18.2874i	1.26337	−	0.712919i
$659$	−46.2323			−1.80095			−0.900477	−	0.434904i	$-0.856782\pi$
$659$	−46.2323			−1.80095			−0.900477	+	0.434904i	$0.856782\pi$
$660$		0			0
$661$	−4.95426	−	8.58103i	−0.192698	−	0.333764i	0.753445	−	0.657511i	$-0.228391\pi$
$661$	−4.95426	−	8.58103i	−0.192698	−	0.333764i	−0.946144	+	0.323747i	$0.895057\pi$
$662$	−3.49663	+	14.1802i	−0.135900	+	0.551130i
$663$		0			0
$664$	−4.04630	−	3.58689i	−0.157027	−	0.139198i
$665$	−48.9280	−	14.6904i	−1.89735	−	0.569668i
$666$		0			0
$667$	−3.46253	−	1.99909i	−0.134070	−	0.0774052i
$668$	−25.1122	+	15.8729i	−0.971621	+	0.614142i
$669$		0			0
$670$	−3.19716	−	11.0420i	−0.123517	−	0.426591i
$671$	−1.76885			−0.0682858
$672$		0			0
$673$	−14.7303			−0.567811			−0.283906	−	0.958852i	$-0.591630\pi$
$673$	−14.7303			−0.567811			−0.283906	+	0.958852i	$0.591630\pi$
$674$	−14.2421	−	49.1879i	−0.548584	−	1.89465i
$675$		0			0
$676$	−5.18788	+	3.27915i	−0.199534	+	0.126121i
$677$	4.80739	+	2.77555i	0.184763	+	0.106673i	0.589529	−	0.807748i	$-0.299314\pi$
$677$	4.80739	+	2.77555i	0.184763	+	0.106673i	−0.404766	+	0.914420i	$0.632647\pi$
$678$		0			0
$679$	−8.17964	+	7.70485i	−0.313906	+	0.295685i
$680$	50.3493	+	44.6328i	1.93081	+	1.71159i
$681$		0			0
$682$	−1.52362	+	6.17888i	−0.0583423	+	0.236601i
$683$	0.804069	+	1.39269i	0.0307669	+	0.0532898i	0.880999	−	0.473118i	$-0.156872\pi$
$683$	0.804069	+	1.39269i	0.0307669	+	0.0532898i	−0.850232	+	0.526408i	$0.823538\pi$
$684$		0			0
$685$	36.2711			1.38585
$686$	−14.6417	+	21.7168i	−0.559022	+	0.829153i
$687$		0			0
$688$	10.8220	+	5.14043i	0.412584	+	0.195977i
$689$	−28.2895	+	16.3329i	−1.07774	+	0.622235i
$690$		0			0
$691$	5.92991	+	3.42364i	0.225584	+	0.130241i	0.608533	−	0.793528i	$-0.291758\pi$
$691$	5.92991	+	3.42364i	0.225584	+	0.130241i	−0.382949	+	0.923770i	$0.625091\pi$
$692$	−8.44641	+	0.338673i	−0.321084	+	0.0128744i
$693$		0			0
$694$	18.4331	−	19.1870i	0.699711	−	0.728329i
$695$	0.236924	−	0.410364i	0.00898703	−	0.0155660i
$696$		0			0
$697$	7.29988	+	12.6438i	0.276503	+	0.478917i
$698$	4.54235	+	15.6879i	0.171930	+	0.593796i
$699$		0			0
$700$	59.2919	−	16.5368i	2.24102	−	0.625032i
$701$		−	22.3346i		−	0.843567i	−0.906697	−	0.421784i	$-0.861404\pi$
$701$		−	22.3346i		−	0.843567i	0.906697	−	0.421784i	$-0.138596\pi$
$702$		0			0
$703$	−28.9677	+	16.7245i	−1.09254	+	0.630777i
$704$	−3.30927	+	2.48362i	−0.124723	+	0.0936051i
$705$		0			0
$706$	8.79030	+	8.44490i	0.330827	+	0.317828i
$707$	−0.587195	+	1.95572i	−0.0220837	+	0.0735525i
$708$		0			0
$709$	0.883842	−	1.53086i	0.0331934	−	0.0574926i	−0.848951	−	0.528471i	$-0.822766\pi$
$709$	0.883842	−	1.53086i	0.0331934	−	0.0574926i	0.882145	+	0.470978i	$0.156099\pi$
$710$	3.95849	−	16.0533i	0.148560	−	0.602469i
$711$		0			0
$712$	−12.1330	−	36.3794i	−0.454703	−	1.36337i
$713$		−	16.9638i		−	0.635298i
$714$		0			0
$715$		−	8.45531i		−	0.316211i
$716$	3.94190	+	2.06988i	0.147316	+	0.0773551i
$717$		0			0
$718$	−29.0219	−	7.15636i	−1.08309	−	0.267073i
$719$	15.3487	−	26.5848i	0.572411	−	0.991446i	−0.423906	−	0.905706i	$-0.639341\pi$
$719$	15.3487	−	26.5848i	0.572411	−	0.991446i	0.996318	−	0.0857396i	$-0.0273253\pi$
$720$		0			0
$721$	−41.0471	+	9.69397i	−1.52867	+	0.361022i
$722$	−3.34586	+	3.48270i	−0.124520	+	0.129613i
$723$		0			0
$724$	−19.3364	+	12.2221i	−0.718630	+	0.454231i
$725$	20.6590	−	11.9275i	0.767255	−	0.442975i
$726$		0			0
$727$		−	25.2505i		−	0.936488i	−0.883599	−	0.468244i	$-0.844887\pi$
$727$		−	25.2505i		−	0.936488i	0.883599	−	0.468244i	$-0.155113\pi$
$728$	−29.9837	+	0.906719i	−1.11127	+	0.0336052i
$729$		0			0
$730$	−44.8301	+	12.9803i	−1.65924	+	0.480422i
$731$	−8.73534	−	15.1300i	−0.323088	−	0.559605i
$732$		0			0
$733$	−17.1670	+	29.7341i	−0.634077	+	1.09825i	0.352632	+	0.935762i	$0.385287\pi$
$733$	−17.1670	+	29.7341i	−0.634077	+	1.09825i	−0.986710	+	0.162492i	$0.948047\pi$
$734$	−23.5838	−	22.6572i	−0.870496	−	0.836291i
$735$		0			0
$736$	6.97965	−	8.53973i	0.257273	−	0.314779i
$737$	−0.892733	−	0.515420i	−0.0328842	−	0.0189857i
$738$		0			0
$739$	−17.6194	+	10.1725i	−0.648139	+	0.374203i	−0.787743	−	0.616004i	$-0.788750\pi$
$739$	−17.6194	+	10.1725i	−0.648139	+	0.374203i	0.139604	+	0.990207i	$0.455417\pi$
$740$	26.7909	−	51.0208i	0.984854	−	1.87556i
$741$		0			0
$742$	−30.4893	−	0.300147i	−1.11930	−	0.0110187i
$743$	34.6692			1.27189			0.635945	−	0.771734i	$-0.280610\pi$
$743$	34.6692			1.27189			0.635945	+	0.771734i	$0.280610\pi$
$744$		0			0
$745$	−8.43082	−	14.6026i	−0.308881	−	0.534998i
$746$	36.1031	+	8.90247i	1.32183	+	0.325943i
$747$		0			0
$748$	6.02870	−	0.241731i	0.220431	−	0.00883854i
$749$	0.892062	+	3.77725i	0.0325953	+	0.138018i
$750$		0			0
$751$	27.9988	+	16.1651i	1.02169	+	0.589872i	0.914593	−	0.404376i	$-0.132511\pi$
$751$	27.9988	+	16.1651i	1.02169	+	0.589872i	0.107096	+	0.994249i	$0.465845\pi$
$752$	22.5846	+	32.7477i	0.823577	+	1.19419i
$753$		0			0
$754$	−11.1665	+	3.23321i	−0.406661	+	0.117746i
$755$	18.5815			0.676248
$756$		0			0
$757$	−17.0256			−0.618806			−0.309403	−	0.950931i	$-0.600129\pi$
$757$	−17.0256			−0.618806			−0.309403	+	0.950931i	$0.600129\pi$
$758$	38.0718	−	11.0235i	1.38283	−	0.400390i
$759$		0			0
$760$	10.9402	−	53.5060i	0.396842	−	1.94087i
$761$	−10.5633	−	6.09870i	−0.382918	−	0.221078i	0.296169	−	0.955135i	$-0.404291\pi$
$761$	−10.5633	−	6.09870i	−0.382918	−	0.221078i	−0.679087	+	0.734058i	$0.737624\pi$
$762$		0			0
$763$	−16.3886	−	4.92058i	−0.593307	−	0.178137i
$764$	0.987839	+	24.6365i	0.0357388	+	0.891315i
$765$		0			0
$766$	12.6405	+	3.11695i	0.456719	+	0.112620i
$767$	24.3479	+	42.1718i	0.879152	+	1.52274i
$768$		0			0
$769$	−5.45133			−0.196580			−0.0982899	−	0.995158i	$-0.531337\pi$
$769$	−5.45133			−0.196580			−0.0982899	+	0.995158i	$0.531337\pi$
$770$	4.01324	−	6.79576i	0.144627	−	0.244902i
$771$		0			0
$772$	3.08960	+	1.62234i	0.111197	+	0.0583894i
$773$	−23.9152	+	13.8075i	−0.860171	+	0.496620i	−0.864070	−	0.503372i	$-0.832092\pi$
$773$	−23.9152	+	13.8075i	−0.860171	+	0.496620i	0.00389822	+	0.999992i	$0.498759\pi$
$774$		0			0
$775$	87.6532	+	50.6066i	3.14860	+	1.81784i
$776$	−8.98938	−	7.96875i	−0.322700	−	0.286062i
$777$		0			0
$778$	−8.43421	−	8.10281i	−0.302381	−	0.290500i
$779$	5.92516	−	10.2627i	0.212291	−	0.367699i
$780$		0			0
$781$	−0.741330	−	1.28402i	−0.0265269	−	0.0459459i
$782$	−15.4485	+	4.47302i	−0.552436	+	0.159955i
$783$		0			0
$784$	−24.5291	−	13.5028i	−0.876038	−	0.482242i
$785$			66.7577i			2.38269i
$786$		0			0
$787$	−16.6863	+	9.63386i	−0.594804	+	0.343410i	−0.766995	−	0.641654i	$-0.778249\pi$
$787$	−16.6863	+	9.63386i	−0.594804	+	0.343410i	0.172191	+	0.985064i	$0.444915\pi$
$788$	−5.65353	−	8.94434i	−0.201399	−	0.318629i
$789$		0			0
$790$	−19.7914	+	20.6008i	−0.704145	+	0.732945i
$791$	20.5991	+	21.8685i	0.732420	+	0.777554i
$792$		0			0
$793$	6.85478	−	11.8728i	0.243421	−	0.421617i
$794$	45.5986	+	11.2439i	1.61823	+	0.399032i
$795$		0			0
$796$	10.4566	−	19.9135i	0.370623	−	0.705817i
$797$		−	16.1419i		−	0.571776i	−0.958263	−	0.285888i	$-0.907711\pi$
$797$		−	16.1419i		−	0.571776i	0.958263	−	0.285888i	$-0.0922886\pi$
$798$		0			0
$799$		−	58.0088i		−	2.05220i
$800$	23.3037	+	61.5403i	0.823910	+	2.17578i
$801$		0			0
$802$	4.48863	−	18.2032i	0.158499	−	0.642778i
$803$	−2.09258	+	3.62445i	−0.0738455	+	0.127904i
$804$		0			0
$805$	−6.04967	+	20.1491i	−0.213223	+	0.710164i
$806$	−35.5692	−	34.1716i	−1.25287	−	1.20364i
$807$		0			0
$808$	−2.13871	−	0.437295i	−0.0752396	−	0.0153840i
$809$	13.5671	−	7.83297i	0.476994	−	0.275392i	−0.242169	−	0.970234i	$-0.577859\pi$
$809$	13.5671	−	7.83297i	0.476994	−	0.275392i	0.719163	+	0.694842i	$0.244526\pi$
$810$		0			0
$811$			7.64906i			0.268595i	0.990941	+	0.134297i	$0.0428778\pi$
$811$			7.64906i			0.268595i	−0.990941	+	0.134297i	$0.957122\pi$
$812$	−10.5095	−	2.70149i	−0.368810	−	0.0948037i
$813$		0			0
$814$	−1.43721	−	4.96370i	−0.0503742	−	0.173978i
$815$	−1.45208	−	2.51507i	−0.0508640	−	0.0880990i
$816$		0			0
$817$	−7.09029	+	12.2807i	−0.248058	+	0.429649i
$818$	−7.34948	+	7.65008i	−0.256969	+	0.267479i
$819$		0			0
$820$	0.817961	+	20.3997i	0.0285644	+	0.712389i
$821$	31.7178	+	18.3123i	1.10696	+	0.639104i	0.938040	−	0.346526i	$-0.112639\pi$
$821$	31.7178	+	18.3123i	1.10696	+	0.639104i	0.168920	+	0.985630i	$0.445972\pi$
$822$		0			0
$823$	−8.04562	+	4.64514i	−0.280453	+	0.161919i	−0.633628	−	0.773638i	$-0.718435\pi$
$823$	−8.04562	+	4.64514i	−0.280453	+	0.161919i	0.353176	+	0.935557i	$0.385102\pi$
$824$	−14.2651	−	42.7722i	−0.496948	−	1.49004i
$825$		0			0
$826$	−0.447437	+	45.4511i	−0.0155683	+	1.58145i
$827$	30.5486			1.06228			0.531139	−	0.847285i	$-0.321764\pi$
$827$	30.5486			1.06228			0.531139	+	0.847285i	$0.321764\pi$
$828$		0			0
$829$	17.9375	+	31.0687i	0.622997	+	1.07906i	0.988925	+	0.148419i	$0.0474183\pi$
$829$	17.9375	+	31.0687i	0.622997	+	1.07906i	−0.365928	+	0.930643i	$0.619248\pi$
$830$	−2.63984	+	10.7056i	−0.0916300	+	0.371596i
$831$		0			0
$832$	−3.84618	−	31.8371i	−0.133342	−	1.10375i
$833$	18.2667	+	36.5163i	0.632905	+	1.26522i
$834$		0			0
$835$	52.4636	+	30.2899i	1.81558	+	1.04822i
$836$	−2.61660	−	4.13968i	−0.0904971	−	0.143174i
$837$		0			0
$838$	−0.416325	−	1.43786i	−0.0143817	−	0.0496702i
$839$	3.56665			0.123134			0.0615672	−	0.998103i	$-0.480390\pi$
$839$	3.56665			0.123134			0.0615672	+	0.998103i	$0.480390\pi$
$840$		0			0
$841$	24.7948			0.854992
$842$	6.21403	+	21.4614i	0.214150	+	0.739609i
$843$		0			0
$844$	−26.8190	−	42.4298i	−0.923147	−	1.46049i
$845$	10.8383	+	6.25752i	0.372850	+	0.215265i
$846$		0			0
$847$	6.52656	+	27.6353i	0.224255	+	0.949561i
$848$	−2.60978	−	32.4913i	−0.0896204	−	1.11576i
$849$		0			0
$850$	22.9737	−	93.1676i	0.787992	−	3.19562i
$851$	6.88735	+	11.9292i	0.236095	+	0.408929i
$852$		0			0
$853$	−17.6192			−0.603270			−0.301635	−	0.953423i	$-0.597532\pi$
$853$	−17.6192			−0.603270			−0.301635	+	0.953423i	$0.597532\pi$
$854$	11.1447	−	6.28895i	0.381364	−	0.215203i
$855$		0			0
$856$	−3.93600	+	1.31271i	−0.134530	+	0.0448674i
$857$	5.09277	−	2.94031i	0.173966	−	0.100439i	−0.410489	−	0.911866i	$-0.634642\pi$
$857$	5.09277	−	2.94031i	0.173966	−	0.100439i	0.584455	+	0.811426i	$0.301309\pi$
$858$		0			0
$859$	−39.4828	−	22.7954i	−1.34714	−	0.777769i	−0.359293	−	0.933225i	$-0.616982\pi$
$859$	−39.4828	−	22.7954i	−1.34714	−	0.777769i	−0.987843	+	0.155455i	$0.950316\pi$
$860$	−0.978805	−	24.4112i	−0.0333770	−	0.832413i
$861$		0			0
$862$	13.6057	−	14.1622i	0.463412	−	0.482366i
$863$	17.8840	−	30.9760i	0.608778	−	1.05443i	−0.382664	−	0.923887i	$-0.624993\pi$
$863$	17.8840	−	30.9760i	0.608778	−	1.05443i	0.991442	−	0.130547i	$-0.0416733\pi$
$864$		0			0
$865$	8.61873	+	14.9281i	0.293046	+	0.507570i
$866$	−14.8648	−	51.3387i	−0.505128	−	1.74456i
$867$		0			0
$868$	−12.3687	−	44.3473i	−0.419820	−	1.50524i
$869$			2.56171i			0.0869001i
$870$		0			0
$871$	6.91917	−	3.99479i	0.234447	−	0.135358i
$872$	3.66445	−	17.9220i	0.124094	−	0.606916i
$873$		0			0
$874$	9.41384	+	9.04394i	0.318428	+	0.305916i
$875$	−49.0724	−	52.0964i	−1.65895	−	1.76118i
$876$		0			0
$877$	20.8302	−	36.0790i	0.703387	−	1.21830i	−0.263884	−	0.964554i	$-0.585004\pi$
$877$	20.8302	−	36.0790i	0.703387	−	1.21830i	0.967271	−	0.253747i	$-0.0816631\pi$
$878$	0.0615279	−	0.249520i	0.00207647	−	0.00842090i
$879$		0			0
$880$	7.62116	+	3.62005i	0.256909	+	0.122032i
$881$		−	29.0197i		−	0.977700i	−0.872368	−	0.488850i	$-0.837417\pi$
$881$		−	29.0197i		−	0.977700i	0.872368	−	0.488850i	$-0.162583\pi$
$882$		0			0
$883$			6.30954i			0.212333i	0.994348	+	0.106166i	$0.0338576\pi$
$883$			6.30954i			0.212333i	−0.994348	+	0.106166i	$0.966142\pi$
$884$	−21.7403	+	41.4024i	−0.731206	+	1.39251i
$885$		0			0
$886$	13.7931	+	3.40118i	0.463389	+	0.114265i
$887$	−9.23650	+	15.9981i	−0.310131	+	0.537163i	−0.978391	−	0.206765i	$-0.933706\pi$
$887$	−9.23650	+	15.9981i	−0.310131	+	0.537163i	0.668259	+	0.743929i	$0.267040\pi$
$888$		0			0
$889$	8.09781	+	8.59683i	0.271592	+	0.288328i
$890$	−54.1770	+	56.3929i	−1.81602	+	1.89029i
$891$		0			0
$892$	−19.1309	−	30.2666i	−0.640551	−	1.01340i
$893$	−40.7764	+	23.5422i	−1.36453	+	0.787811i
$894$		0			0
$895$		−	9.07897i		−	0.303477i
$896$	12.0199	−	27.4139i	0.401558	−	0.915834i
$897$		0			0
$898$	−12.9662	+	3.75429i	−0.432688	+	0.125282i
$899$	−8.92113	−	15.4518i	−0.297536	−	0.515348i
$900$		0			0
$901$	−23.7662	+	41.1642i	−0.791765	+	1.37138i
$902$	1.32023	+	1.26835i	0.0439588	+	0.0422315i
$903$		0			0
$904$	−21.3047	+	24.0334i	−0.708583	+	0.799338i
$905$	40.3969	+	23.3231i	1.34284	+	0.775288i
$906$		0			0
$907$	37.2566	−	21.5101i	1.23709	−	0.714232i	0.268588	−	0.963255i	$-0.413443\pi$
$907$	37.2566	−	21.5101i	1.23709	−	0.714232i	0.968497	+	0.249023i	$0.0801096\pi$
$908$	−25.1030	−	13.1815i	−0.833071	−	0.437444i
$909$		0			0
$910$	30.0619	+	53.2730i	0.996542	+	1.76598i
$911$	50.4366			1.67104			0.835519	−	0.549461i	$-0.185167\pi$
$911$	50.4366			1.67104			0.835519	+	0.549461i	$0.185167\pi$
$912$		0			0
$913$	0.494377	+	0.856287i	0.0163615	+	0.0283390i
$914$	−37.5157	−	9.25079i	−1.24091	−	0.305989i
$915$		0			0
$916$	0.299373	+	7.46628i	0.00989156	+	0.246693i
$917$	4.73291	+	20.0405i	0.156294	+	0.661796i
$918$		0			0
$919$	−36.7035	−	21.1908i	−1.21074	−	0.699019i	−0.247817	−	0.968807i	$-0.579713\pi$
$919$	−36.7035	−	21.1908i	−1.21074	−	0.699019i	−0.962920	+	0.269787i	$0.913047\pi$
$920$	−22.0344	−	4.50530i	−0.726453	−	0.148535i
$921$		0			0
$922$	−44.4306	+	12.8646i	−1.46324	+	0.423674i
$923$	11.4914			0.378245
$924$		0			0
$925$	−82.1859			−2.70226
$926$	40.4225	−	11.7041i	1.32837	−	0.384621i
$927$		0			0
$928$	1.86660	−	11.4492i	0.0612740	−	0.375837i
$929$	5.26910	+	3.04211i	0.172873	+	0.0998085i	0.583940	−	0.811797i	$-0.301510\pi$
$929$	5.26910	+	3.04211i	0.172873	+	0.0998085i	−0.411067	+	0.911605i	$0.634844\pi$
$930$		0			0
$931$	18.2552	−	27.6601i	0.598291	−	0.906523i
$932$	55.1840	−	2.21269i	1.80761	−	0.0724792i
$933$		0			0
$934$	47.9092	+	11.8137i	1.56764	+	0.386556i
$935$	−6.15169	−	10.6550i	−0.201182	−	0.348457i
$936$		0			0
$937$	36.0029			1.17616			0.588081	−	0.808802i	$-0.299884\pi$
$937$	36.0029			1.17616			0.588081	+	0.808802i	$0.299884\pi$
$938$	7.45721	+	0.0734114i	0.243487	+	0.00239697i
$939$		0			0
$940$	37.7122	−	71.8194i	1.23004	−	2.34249i
$941$	−8.57725	+	4.95208i	−0.279610	+	0.161433i	−0.633247	−	0.773950i	$-0.718278\pi$
$941$	−8.57725	+	4.95208i	−0.279610	+	0.161433i	0.353637	+	0.935383i	$0.384945\pi$
$942$		0			0
$943$	−4.22629	−	2.44005i	−0.137627	−	0.0794590i
$944$	−48.4357	+	3.89047i	−1.57645	+	0.126624i
$945$		0			0
$946$	−1.57984	−	1.51776i	−0.0513650	−	0.0493467i
$947$	6.84359	−	11.8534i	0.222387	−	0.385185i	−0.733145	−	0.680072i	$-0.761949\pi$
$947$	6.84359	−	11.8534i	0.222387	−	0.385185i	0.955532	+	0.294887i	$0.0952819\pi$
$948$		0			0
$949$	−16.2186	−	28.0915i	−0.526479	−	0.911888i
$950$	−74.8144	+	21.6621i	−2.42730	+	0.702810i
$951$		0			0
$952$	−37.1246	+	22.9574i	−1.20321	+	0.744052i
$953$		−	50.1927i		−	1.62590i	−0.582333	−	0.812950i	$-0.697860\pi$
$953$		−	50.1927i		−	1.62590i	0.582333	−	0.812950i	$-0.302140\pi$
$954$		0			0
$955$	43.5421	−	25.1391i	1.40899	−	0.813481i
$956$	23.4576	−	14.8270i	0.758672	−	0.479541i
$957$		0			0
$958$	33.6011	−	34.9754i	1.08560	−	1.13000i
$959$	−6.76645	+	22.5365i	−0.218500	+	0.727740i
$960$		0			0
$961$	22.3511	−	38.7133i	0.721004	−	1.24882i
$962$	38.8868	+	9.58889i	1.25376	+	0.309158i
$963$		0			0
$964$	45.5725	+	23.9300i	1.46779	+	0.770734i
$965$		−	7.11596i		−	0.229071i
$966$		0			0
$967$		−	24.0131i		−	0.772209i	−0.922455	−	0.386104i	$-0.873820\pi$
$967$		−	24.0131i		−	0.772209i	0.922455	−	0.386104i	$-0.126180\pi$
$968$	−28.7968	+	9.60410i	−0.925564	+	0.308687i
$969$		0			0
$970$	−5.86475	+	23.7839i	−0.188306	+	0.763655i
$971$	−24.0246	+	41.6118i	−0.770986	+	1.33539i	0.166037	+	0.986119i	$0.446903\pi$
$971$	−24.0246	+	41.6118i	−0.770986	+	1.33539i	−0.937023	+	0.349267i	$0.886431\pi$
$972$		0			0
$973$	0.210774	+	0.223763i	0.00675711	+	0.00717350i
$974$	−31.7972	−	30.5478i	−1.01885	−	0.978815i
$975$		0			0
$976$	7.76672	+	11.2618i	0.248607	+	0.360480i
$977$	−44.5417	+	25.7162i	−1.42502	+	0.822734i	−0.996722	−	0.0809051i	$-0.974219\pi$
$977$	−44.5417	+	25.7162i	−1.42502	+	0.822734i	−0.428295	+	0.903639i	$0.640886\pi$
$978$		0			0
$979$			7.01245i			0.224119i
$980$	−1.12405	+	57.0855i	−0.0359064	+	1.82353i
$981$		0			0
$982$	−11.5630	−	39.9352i	−0.368990	−	1.27438i
$983$	−5.28876	−	9.16039i	−0.168685	−	0.292171i	0.769273	−	0.638921i	$-0.220619\pi$
$983$	−5.28876	−	9.16039i	−0.168685	−	0.292171i	−0.937958	+	0.346749i	$0.887285\pi$
$984$		0			0
$985$	−10.7885	+	18.6862i	−0.343750	+	0.595392i
$986$	−11.7193	+	12.1986i	−0.373218	+	0.388483i
$987$		0			0
$988$	37.9263	−	1.52072i	1.20660	−	0.0483804i
$989$	5.05735	+	2.91986i	0.160814	+	0.0928463i
$990$		0			0
$991$	−9.82987	+	5.67528i	−0.312256	+	0.180281i	−0.647936	−	0.761695i	$-0.724367\pi$
$991$	−9.82987	+	5.67528i	−0.312256	+	0.180281i	0.335680	+	0.941976i	$0.391034\pi$
$992$	46.0290	−	17.4300i	1.46142	−	0.553402i
$993$		0			0
$994$	9.23597	+	5.45431i	0.292947	+	0.173000i
$995$	−45.8648			−1.45401
$996$		0			0
$997$	15.0483	+	26.0644i	0.476585	+	0.825469i	0.999640	−	0.0268300i	$-0.00854128\pi$
$997$	15.0483	+	26.0644i	0.476585	+	0.825469i	−0.523055	+	0.852299i	$0.675208\pi$
$998$	−1.61721	+	6.55845i	−0.0511920	+	0.207604i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.be.e.107.20	yes	64
3.2	odd	2	inner	756.2.be.e.107.13	yes	64
4.3	odd	2	inner	756.2.be.e.107.30	yes	64
7.4	even	3	inner	756.2.be.e.431.3	yes	64
12.11	even	2	inner	756.2.be.e.107.3	✓	64
21.11	odd	6	inner	756.2.be.e.431.30	yes	64
28.11	odd	6	inner	756.2.be.e.431.13	yes	64
84.11	even	6	inner	756.2.be.e.431.20	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.be.e.107.3	✓	64	12.11	even	2	inner
756.2.be.e.107.13	yes	64	3.2	odd	2	inner
756.2.be.e.107.20	yes	64	1.1	even	1	trivial
756.2.be.e.107.30	yes	64	4.3	odd	2	inner
756.2.be.e.431.3	yes	64	7.4	even	3	inner
756.2.be.e.431.13	yes	64	28.11	odd	6	inner
756.2.be.e.431.20	yes	64	84.11	even	6	inner
756.2.be.e.431.30	yes	64	21.11	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.393322 + 1.35842i) q^{2} +(-1.69060 + 1.06859i) q^{4} +(3.53194 + 2.03916i) q^{5} +(-1.92589 + 1.81410i) q^{7} +(-2.11654 - 1.87623i) q^{8} +O(q^{10})\)	\(q+(0.393322 + 1.35842i) q^{2} +(-1.69060 + 1.06859i) q^{4} +(3.53194 + 2.03916i) q^{5} +(-1.92589 + 1.81410i) q^{7} +(-2.11654 - 1.87623i) q^{8} +(-1.38085 + 5.59989i) q^{10} +(0.258599 + 0.447907i) q^{11} -4.00857 q^{13} +(-3.22180 - 1.90264i) q^{14} +(1.71623 - 3.61311i) q^{16} +(-5.05144 + 2.91645i) q^{17} +(4.10015 + 2.36722i) q^{19} +(-8.15011 + 0.326792i) q^{20} +(-0.506732 + 0.527458i) q^{22} +(0.974850 - 1.68849i) q^{23} +(5.81638 + 10.0743i) q^{25} +(-1.57666 - 5.44532i) q^{26} +(1.31737 - 5.12489i) q^{28} -2.05067i q^{29} +(7.53503 - 4.35035i) q^{31} +(5.58314 + 0.910238i) q^{32} +(-5.94860 - 5.71486i) q^{34} +(-10.5014 + 2.48008i) q^{35} +(-3.53252 + 6.11850i) q^{37} +(-1.60300 + 6.50079i) q^{38} +(-3.64954 - 10.9427i) q^{40} -2.50300i q^{41} +2.99519i q^{43} +(-0.915817 - 0.480893i) q^{44} +(2.67710 + 0.660133i) q^{46} +(-4.97255 + 8.61270i) q^{47} +(0.418094 - 6.98750i) q^{49} +(-11.3973 + 11.8635i) q^{50} +(6.77688 - 4.28353i) q^{52} +(7.05724 - 4.07450i) q^{53} +2.10931i q^{55} +(7.47990 - 0.226195i) q^{56} +(2.78566 - 0.806573i) q^{58} +(-6.07396 - 10.5204i) q^{59} +(-1.71003 + 2.96186i) q^{61} +(8.87329 + 8.52463i) q^{62} +(0.959489 + 7.94225i) q^{64} +(-14.1580 - 8.17414i) q^{65} +(-1.72609 + 0.996560i) q^{67} +(5.42345 - 10.3285i) q^{68} +(-7.49939 - 13.2898i) q^{70} -2.86671 q^{71} +(4.04598 + 7.00785i) q^{73} +(-9.70090 - 2.39209i) q^{74} +(-9.46129 + 0.379366i) q^{76} +(-1.31058 - 0.393495i) q^{77} +(4.28947 + 2.47652i) q^{79} +(13.4293 - 9.26160i) q^{80} +(3.40012 - 0.984485i) q^{82} +1.91175 q^{83} -23.7885 q^{85} +(-4.06872 + 1.17808i) q^{86} +(0.293043 - 1.43321i) q^{88} +(11.7420 + 6.77926i) q^{89} +(7.72007 - 7.27195i) q^{91} +(0.156227 + 3.89627i) q^{92} +(-13.6555 - 3.36723i) q^{94} +(9.65431 + 16.7218i) q^{95} +4.24721 q^{97} +(9.65639 - 2.18039i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 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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