LMFDB - Embedded newform 297.2.e.e.100.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(100,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("297.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.e (of order $3$, degree $2$, not 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:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.508277025.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 15x^{5} + 21x^{4} + 3x^{3} - 22x^{2} + 3x + 19 $ x^8 - 3x^7 + 5x^6 - 15x^5 + 21x^4 + 3x^3 - 22x^2 + 3*x + 19
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.1
Root			$1.86526 + 0.199842i$ of defining polynomial
Character	$\chi$	$=$	297.100
Dual form			297.2.e.e.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36526 + 2.36469i) q^{2} +(-2.72785 - 4.72478i) q^{4} +(-0.468293 - 0.811107i) q^{5} +(0.259560 - 0.449571i) q^{7} +9.43585 q^{8} +2.55736 q^{10} +(0.500000 - 0.866025i) q^{11} +(2.35267 + 4.07494i) q^{13} +(0.708733 + 1.22756i) q^{14} +(-7.42666 + 12.8634i) q^{16} +2.69227 q^{17} +3.41747 q^{19} +(-2.55487 + 4.42516i) q^{20} +(1.36526 + 2.36469i) q^{22} +(3.48741 + 6.04038i) q^{23} +(2.06140 - 3.57046i) q^{25} -12.8480 q^{26} -2.83217 q^{28} +(2.09311 - 3.62537i) q^{29} +(-2.59311 - 4.49140i) q^{31} +(-10.8427 - 18.7802i) q^{32} +(-3.67564 + 6.36640i) q^{34} -0.486201 q^{35} +2.06874 q^{37} +(-4.66572 + 8.08126i) q^{38} +(-4.41875 - 7.65349i) q^{40} +(0.0865763 + 0.149955i) q^{41} +(1.13474 - 1.96543i) q^{43} -5.45571 q^{44} -19.0449 q^{46} +(-0.153863 + 0.266499i) q^{47} +(3.36526 + 5.82880i) q^{49} +(5.62869 + 9.74918i) q^{50} +(12.8355 - 22.2317i) q^{52} +1.89835 q^{53} -0.936586 q^{55} +(2.44917 - 4.24209i) q^{56} +(5.71527 + 9.89913i) q^{58} +(1.98741 + 3.44230i) q^{59} +(-2.25956 + 3.91367i) q^{61} +14.1610 q^{62} +29.5059 q^{64} +(2.20348 - 3.81654i) q^{65} +(-1.68823 - 2.92410i) q^{67} +(-7.34413 - 12.7204i) q^{68} +(0.663789 - 1.14972i) q^{70} -2.90367 q^{71} +9.52444 q^{73} +(-2.82436 + 4.89193i) q^{74} +(-9.32234 - 16.1468i) q^{76} +(-0.259560 - 0.449571i) q^{77} +(1.02178 - 1.76978i) q^{79} +13.9114 q^{80} -0.472796 q^{82} +(7.02970 - 12.1758i) q^{83} +(-1.26077 - 2.18372i) q^{85} +(3.09843 + 5.36664i) q^{86} +(4.71793 - 8.17169i) q^{88} -7.53751 q^{89} +2.44264 q^{91} +(19.0263 - 32.9545i) q^{92} +(-0.420126 - 0.727680i) q^{94} +(-1.60038 - 2.77193i) q^{95} +(-8.16710 + 14.1458i) q^{97} -18.3778 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 11 q^{4} + 4 q^{5} - q^{7} + 2 q^{10} + 4 q^{11} - 7 q^{13} + q^{14} - 17 q^{16} + 10 q^{17} + 18 q^{19} - 10 q^{20} - q^{22} + 14 q^{23} - 14 q^{25} - 44 q^{26} - 2 q^{28} - 6 q^{29}+ \cdots - 30 q^{98}+O(q^{100}) $ 8 * q + q^2 - 11 * q^4 + 4 * q^5 - q^7 + 2 * q^10 + 4 * q^11 - 7 * q^13 + q^14 - 17 * q^16 + 10 * q^17 + 18 * q^19 - 10 * q^20 - q^22 + 14 * q^23 - 14 * q^25 - 44 * q^26 - 2 * q^28 - 6 * q^29 + 2 * q^31 - 34 * q^32 - 16 * q^34 + 16 * q^35 + 6 * q^37 + 3 * q^38 - 12 * q^40 - 2 * q^41 + 21 * q^43 - 22 * q^44 + 4 * q^46 - 7 * q^47 + 15 * q^49 + 23 * q^50 + 10 * q^52 + 12 * q^53 + 8 * q^55 + 18 * q^56 + 21 * q^58 + 2 * q^59 - 15 * q^61 + 40 * q^62 + 32 * q^64 + 19 * q^65 - 14 * q^67 - 7 * q^68 + 38 * q^70 + 6 * q^71 + 44 * q^73 - 36 * q^74 - 42 * q^76 + q^77 - 11 * q^79 + 68 * q^80 - 34 * q^82 + 18 * q^83 - 13 * q^85 - 24 * q^86 + 12 * q^89 + 38 * q^91 + 67 * q^92 + 19 * q^94 - 30 * q^95 - 26 * q^97 - 30 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−1.36526	+	2.36469i	−0.965382	+	1.67209i	−0.256799	+	0.966465i	$0.582668\pi$
$2$	−1.36526	+	2.36469i	−0.965382	+	1.67209i	−0.708584	+	0.705627i	$0.750666\pi$
$3$		0			0
$3$		0			0
$4$	−2.72785	−	4.72478i	−1.36393	−	2.36239i
$5$	−0.468293	−	0.811107i	−0.209427	−	0.362738i	0.742107	−	0.670281i	$-0.233827\pi$
$5$	−0.468293	−	0.811107i	−0.209427	−	0.362738i	−0.951534	+	0.307543i	$0.900493\pi$
$6$		0			0
$7$	0.259560	−	0.449571i	0.0981045	−	0.169922i	−0.812796	−	0.582549i	$-0.802055\pi$
$7$	0.259560	−	0.449571i	0.0981045	−	0.169922i	0.910900	+	0.412627i	$0.135389\pi$
$8$	9.43585			3.33608
$9$		0			0
$10$	2.55736			0.808709
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$		0			0
$13$	2.35267	+	4.07494i	0.652513	+	1.13019i	0.982511	+	0.186205i	$0.0596187\pi$
$13$	2.35267	+	4.07494i	0.652513	+	1.13019i	−0.329998	+	0.943982i	$0.607048\pi$
$14$	0.708733	+	1.22756i	0.189417	+	0.328080i
$15$		0			0
$16$	−7.42666	+	12.8634i	−1.85667	+	3.21584i
$17$	2.69227			0.652972			0.326486	−	0.945202i	$-0.394135\pi$
$17$	2.69227			0.652972			0.326486	+	0.945202i	$0.394135\pi$
$18$		0			0
$19$	3.41747			0.784020			0.392010	−	0.919961i	$-0.371780\pi$
$19$	3.41747			0.784020			0.392010	+	0.919961i	$0.371780\pi$
$20$	−2.55487	+	4.42516i	−0.571286	+	0.989497i
$21$		0			0
$22$	1.36526	+	2.36469i	0.291074	+	0.504155i
$23$	3.48741	+	6.04038i	0.727176	+	1.25951i	0.958072	+	0.286527i	$0.0925009\pi$
$23$	3.48741	+	6.04038i	0.727176	+	1.25951i	−0.230896	+	0.972978i	$0.574166\pi$
$24$		0			0
$25$	2.06140	−	3.57046i	0.412281	−	0.714091i
$26$	−12.8480			−2.51970
$27$		0			0
$28$	−2.83217			−0.535230
$29$	2.09311	−	3.62537i	0.388681	−	0.673215i	−0.603592	−	0.797294i	$-0.706264\pi$
$29$	2.09311	−	3.62537i	0.388681	−	0.673215i	0.992272	+	0.124079i	$0.0395976\pi$
$30$		0			0
$31$	−2.59311	−	4.49140i	−0.465736	−	0.806679i	0.533498	−	0.845801i	$-0.320877\pi$
$31$	−2.59311	−	4.49140i	−0.465736	−	0.806679i	−0.999234	+	0.0391223i	$0.987544\pi$
$32$	−10.8427	−	18.7802i	−1.91674	−	3.31990i
$33$		0			0
$34$	−3.67564	+	6.36640i	−0.630368	+	1.09183i
$35$	−0.486201			−0.0821830
$36$		0			0
$37$	2.06874			0.340098			0.170049	−	0.985436i	$-0.445607\pi$
$37$	2.06874			0.340098			0.170049	+	0.985436i	$0.445607\pi$
$38$	−4.66572	+	8.08126i	−0.756880	+	1.31095i
$39$		0			0
$40$	−4.41875	−	7.65349i	−0.698665	−	1.21012i
$41$	0.0865763	+	0.149955i	0.0135209	+	0.0234190i	0.872707	−	0.488245i	$-0.162363\pi$
$41$	0.0865763	+	0.149955i	0.0135209	+	0.0234190i	−0.859186	+	0.511664i	$0.829029\pi$
$42$		0			0
$43$	1.13474	−	1.96543i	0.173047	−	0.299726i	−0.766437	−	0.642320i	$-0.777972\pi$
$43$	1.13474	−	1.96543i	0.173047	−	0.299726i	0.939484	+	0.342594i	$0.111306\pi$
$44$	−5.45571			−0.822479
$45$		0			0
$46$	−19.0449			−2.80801
$47$	−0.153863	+	0.266499i	−0.0224433	+	0.0388729i	−0.877029	−	0.480438i	$-0.840478\pi$
$47$	−0.153863	+	0.266499i	−0.0224433	+	0.0388729i	0.854586	+	0.519311i	$0.173811\pi$
$48$		0			0
$49$	3.36526	+	5.82880i	0.480751	+	0.832685i
$50$	5.62869	+	9.74918i	0.796017	+	1.37874i
$51$		0			0
$52$	12.8355	−	22.2317i	1.77996	−	3.08298i
$53$	1.89835			0.260758			0.130379	−	0.991464i	$-0.458381\pi$
$53$	1.89835			0.260758			0.130379	+	0.991464i	$0.458381\pi$
$54$		0			0
$55$	−0.936586			−0.126289
$56$	2.44917	−	4.24209i	0.327284	−	0.566873i
$57$		0			0
$58$	5.71527	+	9.89913i	0.750451	+	1.29982i
$59$	1.98741	+	3.44230i	0.258739	+	0.448149i	0.965904	−	0.258899i	$-0.0833596\pi$
$59$	1.98741	+	3.44230i	0.258739	+	0.448149i	−0.707165	+	0.707048i	$0.750026\pi$
$60$		0			0
$61$	−2.25956	+	3.91367i	−0.289307	+	0.501094i	−0.973645	−	0.228071i	$-0.926758\pi$
$61$	−2.25956	+	3.91367i	−0.289307	+	0.501094i	0.684337	+	0.729165i	$0.260092\pi$
$62$	14.1610			1.79845
$63$		0			0
$64$	29.5059			3.68824
$65$	2.20348	−	3.81654i	0.273308	−	0.473383i
$66$		0			0
$67$	−1.68823	−	2.92410i	−0.206250	−	0.357236i	0.744280	−	0.667868i	$-0.232793\pi$
$67$	−1.68823	−	2.92410i	−0.206250	−	0.357236i	−0.950530	+	0.310632i	$0.899459\pi$
$68$	−7.34413	−	12.7204i	−0.890606	−	1.54257i
$69$		0			0
$70$	0.663789	−	1.14972i	0.0793380	−	0.137417i
$71$	−2.90367			−0.344602			−0.172301	−	0.985044i	$-0.555120\pi$
$71$	−2.90367			−0.344602			−0.172301	+	0.985044i	$0.555120\pi$
$72$		0			0
$73$	9.52444			1.11475			0.557376	−	0.830260i	$-0.311808\pi$
$73$	9.52444			1.11475			0.557376	+	0.830260i	$0.311808\pi$
$74$	−2.82436	+	4.89193i	−0.328325	+	0.568675i
$75$		0			0
$76$	−9.32234	−	16.1468i	−1.06935	−	1.85216i
$77$	−0.259560	−	0.449571i	−0.0295796	−	0.0512334i
$78$		0			0
$79$	1.02178	−	1.76978i	0.114959	−	0.199115i	−0.802804	−	0.596243i	$-0.796660\pi$
$79$	1.02178	−	1.76978i	0.114959	−	0.199115i	0.917764	+	0.397127i	$0.129993\pi$
$80$	13.9114			1.55534
$81$		0			0
$82$	−0.472796			−0.0522115
$83$	7.02970	−	12.1758i	0.771609	−	1.33647i	−0.165071	−	0.986282i	$-0.552785\pi$
$83$	7.02970	−	12.1758i	0.771609	−	1.33647i	0.936681	−	0.350185i	$-0.113881\pi$
$84$		0			0
$85$	−1.26077	−	2.18372i	−0.136750	−	0.236858i
$86$	3.09843	+	5.36664i	0.334112	+	0.578700i
$87$		0			0
$88$	4.71793	−	8.17169i	0.502933	−	0.871105i
$89$	−7.53751			−0.798974			−0.399487	−	0.916739i	$-0.630812\pi$
$89$	−7.53751			−0.798974			−0.399487	+	0.916739i	$0.630812\pi$
$90$		0			0
$91$	2.44264			0.256058
$92$	19.0263	−	32.9545i	1.98363	−	3.43575i
$93$		0			0
$94$	−0.420126	−	0.727680i	−0.0433327	−	0.0750545i
$95$	−1.60038	−	2.77193i	−0.164195	−	0.284394i
$96$		0			0
$97$	−8.16710	+	14.1458i	−0.829243	+	1.43629i	0.0693892	+	0.997590i	$0.477895\pi$
$97$	−8.16710	+	14.1458i	−0.829243	+	1.43629i	−0.898633	+	0.438702i	$0.855438\pi$
$98$	−18.3778			−1.85643
$99$		0			0
$100$	−22.4928			−2.24928
$101$	−4.99129	+	8.64516i	−0.496652	+	0.860226i	−0.999993	−	0.00386211i	$-0.998771\pi$
$101$	−4.99129	+	8.64516i	−0.496652	+	0.860226i	0.503341	+	0.864088i	$0.332104\pi$
$102$		0			0
$103$	−3.27747	−	5.67674i	−0.322939	−	0.559346i	0.658154	−	0.752883i	$-0.271337\pi$
$103$	−3.27747	−	5.67674i	−0.322939	−	0.559346i	−0.981093	+	0.193537i	$0.938004\pi$
$104$	22.1995	+	38.4506i	2.17684	+	3.77039i
$105$		0			0
$106$	−2.59173	+	4.48901i	−0.251731	+	0.436011i
$107$	−14.5151			−1.40323			−0.701614	−	0.712557i	$-0.747537\pi$
$107$	−14.5151			−1.40323			−0.701614	+	0.712557i	$0.747537\pi$
$108$		0			0
$109$	11.6802			1.11876			0.559379	−	0.828912i	$-0.311040\pi$
$109$	11.6802			1.11876			0.559379	+	0.828912i	$0.311040\pi$
$110$	1.27868	−	2.21474i	0.121917	−	0.211167i
$111$		0			0
$112$	3.85533	+	6.67763i	0.364295	+	0.630977i
$113$	−0.603036	−	1.04449i	−0.0567289	−	0.0982573i	0.836266	−	0.548323i	$-0.184734\pi$
$113$	−0.603036	−	1.04449i	−0.0567289	−	0.0982573i	−0.892995	+	0.450066i	$0.851400\pi$
$114$		0			0
$115$	3.26626	−	5.65733i	0.304581	−	0.527549i
$116$	−22.8388			−2.12053
$117$		0			0
$118$	−10.8533			−0.999129
$119$	0.698807	−	1.21037i	0.0640595	−	0.110954i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−6.16976	−	10.6863i	−0.558584	−	0.967496i
$123$		0			0
$124$	−14.1472	+	24.5038i	−1.27046	+	2.20050i
$125$	−8.54429			−0.764225
$126$		0			0
$127$	−10.4533			−0.927579			−0.463789	−	0.885945i	$-0.653511\pi$
$127$	−10.4533			−0.927579			−0.463789	+	0.885945i	$0.653511\pi$
$128$	−18.5976	+	32.2120i	−1.64381	+	2.84717i
$129$		0			0
$130$	6.01663	+	10.4211i	0.527693	+	0.913991i
$131$	−6.73051	−	11.6576i	−0.588048	−	1.01853i	−0.994488	−	0.104851i	$-0.966563\pi$
$131$	−6.73051	−	11.6576i	−0.588048	−	1.01853i	0.406440	−	0.913677i	$-0.366770\pi$
$132$		0			0
$133$	0.887038	−	1.53640i	0.0769160	−	0.133222i
$134$	9.21948			0.796442
$135$		0			0
$136$	25.4039			2.17837
$137$	10.4318	−	18.0684i	0.891250	−	1.54369i	0.0528716	−	0.998601i	$-0.483163\pi$
$137$	10.4318	−	18.0684i	0.891250	−	1.54369i	0.838378	−	0.545089i	$-0.183504\pi$
$138$		0			0
$139$	−0.433925	−	0.751581i	−0.0368051	−	0.0637482i	0.847036	−	0.531535i	$-0.178385\pi$
$139$	−0.433925	−	0.751581i	−0.0368051	−	0.0637482i	−0.883841	+	0.467787i	$0.845051\pi$
$140$	1.32628	+	2.29719i	0.112092	+	0.194148i
$141$		0			0
$142$	3.96425	−	6.86628i	0.332673	−	0.576206i
$143$	4.70534			0.393480
$144$		0			0
$145$	−3.92076			−0.325601
$146$	−13.0033	+	22.5224i	−1.07616	+	1.86397i
$147$		0			0
$148$	−5.64321	−	9.77432i	−0.463869	−	0.803444i
$149$	3.28272	+	5.68584i	0.268931	+	0.465802i	0.968586	−	0.248679i	$-0.0799963\pi$
$149$	3.28272	+	5.68584i	0.268931	+	0.465802i	−0.699655	+	0.714481i	$0.746663\pi$
$150$		0			0
$151$	−6.32096	+	10.9482i	−0.514393	+	0.890954i	0.485468	+	0.874255i	$0.338649\pi$
$151$	−6.32096	+	10.9482i	−0.514393	+	0.890954i	−0.999861	+	0.0166998i	$0.994684\pi$
$152$	32.2467			2.61555
$153$		0			0
$154$	1.41747			0.114223
$155$	−2.42867	+	4.20658i	−0.195076	+	0.337881i
$156$		0			0
$157$	−7.00919	−	12.1403i	−0.559395	−	0.968900i	−0.997547	−	0.0699992i	$-0.977700\pi$
$157$	−7.00919	−	12.1403i	−0.559395	−	0.968900i	0.438152	−	0.898901i	$-0.355633\pi$
$158$	2.78999	+	4.83240i	0.221960	+	0.384445i
$159$		0			0
$160$	−10.1552	+	17.5893i	−0.802836	+	1.39055i
$161$	3.62078			0.285357
$162$		0			0
$163$	−21.6245			−1.69376			−0.846881	−	0.531783i	$-0.821522\pi$
$163$	−21.6245			−1.69376			−0.846881	+	0.531783i	$0.821522\pi$
$164$	0.472335	−	0.818108i	0.0368832	−	0.0638835i
$165$		0			0
$166$	19.1947	+	33.2462i	1.48980	+	2.58040i
$167$	2.51058	+	4.34844i	0.194274	+	0.336493i	0.946662	−	0.322227i	$-0.104432\pi$
$167$	2.51058	+	4.34844i	0.194274	+	0.336493i	−0.752388	+	0.658720i	$0.771098\pi$
$168$		0			0
$169$	−4.57012	+	7.91567i	−0.351547	+	0.608898i
$170$	6.88512			0.528064
$171$		0			0
$172$	−12.3816			−0.944092
$173$	0.229066	−	0.396754i	0.0174155	−	0.0301646i	−0.857186	−	0.515006i	$-0.827790\pi$
$173$	0.229066	−	0.396754i	0.0174155	−	0.0301646i	0.874602	+	0.484842i	$0.161123\pi$
$174$		0			0
$175$	−1.07012	−	1.85350i	−0.0808932	−	0.140111i
$176$	7.42666	+	12.8634i	0.559806	+	0.969612i
$177$		0			0
$178$	10.2906	−	17.8239i	0.771316	−	1.33596i
$179$	−9.19929			−0.687587			−0.343794	−	0.939045i	$-0.611712\pi$
$179$	−9.19929			−0.687587			−0.343794	+	0.939045i	$0.611712\pi$
$180$		0			0
$181$	15.1557			1.12652			0.563258	−	0.826281i	$-0.309548\pi$
$181$	15.1557			1.12652			0.563258	+	0.826281i	$0.309548\pi$
$182$	−3.33483	+	5.77609i	−0.247194	+	0.428153i
$183$		0			0
$184$	32.9067	+	56.9961i	2.42592	+	4.20181i
$185$	−0.968774	−	1.67797i	−0.0712257	−	0.123367i
$186$		0			0
$187$	1.34614	−	2.33158i	0.0984393	−	0.170502i
$188$	1.67887			0.122444
$189$		0			0
$190$	8.73969			0.634044
$191$	−10.4716	+	18.1373i	−0.757699	+	1.31237i	0.186323	+	0.982489i	$0.440343\pi$
$191$	−10.4716	+	18.1373i	−0.757699	+	1.31237i	−0.944021	+	0.329884i	$0.892990\pi$
$192$		0			0
$193$	5.22446	+	9.04903i	0.376065	+	0.651364i	0.990486	−	0.137615i	$-0.0439436\pi$
$193$	5.22446	+	9.04903i	0.376065	+	0.651364i	−0.614421	+	0.788978i	$0.710610\pi$
$194$	−22.3004	−	38.6254i	−1.60107	−	2.77314i
$195$		0			0
$196$	18.3599	−	31.8002i	1.31142	−	2.27144i
$197$	20.9855			1.49515			0.747576	−	0.664176i	$-0.231217\pi$
$197$	20.9855			1.49515			0.747576	+	0.664176i	$0.231217\pi$
$198$		0			0
$199$	−19.0502			−1.35043			−0.675216	−	0.737620i	$-0.735950\pi$
$199$	−19.0502			−1.35043			−0.675216	+	0.737620i	$0.735950\pi$
$200$	19.4511	−	33.6903i	1.37540	−	2.38226i
$201$		0			0
$202$	−13.6288	−	23.6057i	−0.958917	−	1.66089i
$203$	−1.08658	−	1.88201i	−0.0762627	−	0.132091i
$204$		0			0
$205$	0.0810862	−	0.140445i	0.00566330	−	0.00980913i
$206$	17.8983			1.24704
$207$		0			0
$208$	−69.8899			−4.84600
$209$	1.70873	−	2.95961i	0.118196	−	0.204721i
$210$		0			0
$211$	−8.14459	−	14.1068i	−0.560697	−	0.971155i	−0.997436	−	0.0715668i	$-0.977200\pi$
$211$	−8.14459	−	14.1068i	−0.560697	−	0.971155i	0.436739	−	0.899588i	$-0.356133\pi$
$212$	−5.17841	−	8.96926i	−0.355654	−	0.616012i
$213$		0			0
$214$	19.8168	−	34.3238i	1.35465	−	2.34632i
$215$	−2.12557			−0.144963
$216$		0			0
$217$	−2.69227			−0.182763
$218$	−15.9464	+	27.6200i	−1.08003	+	1.87066i
$219$		0			0
$220$	2.55487	+	4.42516i	0.172249	+	0.298344i
$221$	6.33403	+	10.9709i	0.426073	+	0.737980i
$222$		0			0
$223$	4.52251	−	7.83322i	0.302850	−	0.524551i	−0.673930	−	0.738795i	$-0.735395\pi$
$223$	4.52251	−	7.83322i	0.302850	−	0.524551i	0.976780	+	0.214244i	$0.0687286\pi$
$224$	−11.2574			−0.752165
$225$		0			0
$226$	3.29320			0.219060
$227$	−2.58585	+	4.47882i	−0.171629	+	0.297269i	−0.938989	−	0.343946i	$-0.888236\pi$
$227$	−2.58585	+	4.47882i	−0.171629	+	0.297269i	0.767361	+	0.641216i	$0.221570\pi$
$228$		0			0
$229$	−8.01186	−	13.8769i	−0.529438	−	0.917014i	−0.999410	−	0.0343328i	$-0.989069\pi$
$229$	−8.01186	−	13.8769i	−0.529438	−	0.917014i	0.469972	−	0.882681i	$-0.344264\pi$
$230$	8.91858	+	15.4474i	0.588074	+	1.01857i
$231$		0			0
$232$	19.7503	−	34.2085i	1.29667	−	2.24590i
$233$	16.9177			1.10832			0.554158	−	0.832412i	$-0.313040\pi$
$233$	16.9177			1.10832			0.554158	+	0.832412i	$0.313040\pi$
$234$		0			0
$235$	0.288213			0.0188009
$236$	10.8427	−	18.7802i	0.705803	−	1.22249i
$237$		0			0
$238$	1.90810	+	3.30493i	0.123684	+	0.214227i
$239$	0.361215	+	0.625643i	0.0233651	+	0.0404695i	0.877472	−	0.479629i	$-0.159229\pi$
$239$	0.361215	+	0.625643i	0.0233651	+	0.0404695i	−0.854106	+	0.520098i	$0.825895\pi$
$240$		0			0
$241$	−6.82346	+	11.8186i	−0.439537	+	0.761301i	−0.997654	−	0.0684616i	$-0.978191\pi$
$241$	−6.82346	+	11.8186i	−0.439537	+	0.761301i	0.558116	+	0.829763i	$0.311524\pi$
$242$	2.73051			0.175524
$243$		0			0
$244$	24.6550			1.57837
$245$	3.15185	−	5.45917i	0.201364	−	0.348774i
$246$		0			0
$247$	8.04017	+	13.9260i	0.511584	+	0.886089i
$248$	−24.4682	−	42.3802i	−1.55373	−	2.69114i
$249$		0			0
$250$	11.6652	−	20.2046i	0.737769	−	1.27785i
$251$	−20.5733			−1.29858			−0.649288	−	0.760542i	$-0.724933\pi$
$251$	−20.5733			−1.29858			−0.649288	+	0.760542i	$0.724933\pi$
$252$		0			0
$253$	6.97483			0.438504
$254$	14.2714	−	24.7188i	0.895468	−	1.55100i
$255$		0			0
$256$	−21.2752	−	36.8497i	−1.32970	−	2.30311i
$257$	2.63208	+	4.55890i	0.164185	+	0.284376i	0.936365	−	0.351027i	$-0.114167\pi$
$257$	2.63208	+	4.55890i	0.164185	+	0.284376i	−0.772181	+	0.635403i	$0.780834\pi$
$258$		0			0
$259$	0.536961	−	0.930044i	0.0333652	−	0.0577901i
$260$	−24.0431			−1.49109
$261$		0			0
$262$	36.7555			2.27076
$263$	1.29918	−	2.25025i	0.0801110	−	0.138756i	−0.823186	−	0.567771i	$-0.807806\pi$
$263$	1.29918	−	2.25025i	0.0801110	−	0.138756i	0.903297	+	0.429015i	$0.141139\pi$
$264$		0			0
$265$	−0.888982	−	1.53976i	−0.0546097	−	0.0945868i
$266$	2.42207	+	4.19515i	0.148507	+	0.257221i
$267$		0			0
$268$	−9.21049	+	15.9530i	−0.562620	+	0.974487i
$269$	10.0952			0.615516			0.307758	−	0.951465i	$-0.400421\pi$
$269$	10.0952			0.615516			0.307758	+	0.951465i	$0.400421\pi$
$270$		0			0
$271$	32.3022			1.96222			0.981111	−	0.193447i	$-0.0619667\pi$
$271$	32.3022			1.96222			0.981111	+	0.193447i	$0.0619667\pi$
$272$	−19.9946	+	34.6317i	−1.21235	+	2.09985i
$273$		0			0
$274$	28.4842	+	49.3361i	1.72079	+	2.98050i
$275$	−2.06140	−	3.57046i	−0.124307	−	0.215307i
$276$		0			0
$277$	−16.1690	+	28.0055i	−0.971499	+	1.68269i	−0.280463	+	0.959865i	$0.590488\pi$
$277$	−16.1690	+	28.0055i	−0.971499	+	1.68269i	−0.691036	+	0.722820i	$0.742845\pi$
$278$	2.36968			0.142124
$279$		0			0
$280$	−4.58772			−0.274169
$281$	−4.77135	+	8.26422i	−0.284635	+	0.493002i	−0.972521	−	0.232817i	$-0.925206\pi$
$281$	−4.77135	+	8.26422i	−0.284635	+	0.493002i	0.687886	+	0.725819i	$0.258539\pi$
$282$		0			0
$283$	2.96038	+	5.12752i	0.175976	+	0.304800i	0.940499	−	0.339797i	$-0.110358\pi$
$283$	2.96038	+	5.12752i	0.175976	+	0.304800i	−0.764522	+	0.644597i	$0.777025\pi$
$284$	7.92078	+	13.7192i	0.470012	+	0.814084i
$285$		0			0
$286$	−6.42400	+	11.1267i	−0.379859	+	0.657935i
$287$	0.0898871			0.00530587
$288$		0			0
$289$	−9.75167			−0.573627
$290$	5.35284	−	9.27139i	0.314330	−	0.544435i
$291$		0			0
$292$	−25.9813	−	45.0009i	−1.52044	−	2.63348i
$293$	7.21454	+	12.4959i	0.421478	+	0.730021i	0.996084	−	0.0884090i	$-0.0281783\pi$
$293$	7.21454	+	12.4959i	0.421478	+	0.730021i	−0.574607	+	0.818430i	$0.694845\pi$
$294$		0			0
$295$	1.86138	−	3.22401i	0.108374	−	0.187709i
$296$	19.5203			1.13459
$297$		0			0
$298$	−17.9270			−1.03849
$299$	−16.4095	+	28.4220i	−0.948984	+	1.64369i
$300$		0			0
$301$	−0.589068	−	1.02030i	−0.0339533	−	0.0588089i
$302$	−17.2595	−	29.8943i	−0.993171	−	1.72022i
$303$		0			0
$304$	−25.3804	+	43.9601i	−1.45566	+	2.52128i
$305$	4.23255			0.242355
$306$		0			0
$307$	9.60611			0.548250			0.274125	−	0.961694i	$-0.411612\pi$
$307$	9.60611			0.548250			0.274125	+	0.961694i	$0.411612\pi$
$308$	−1.41608	+	2.45273i	−0.0806889	+	0.139757i
$309$		0			0
$310$	−6.63152	−	11.4861i	−0.376645	−	0.652368i
$311$	0.171704	+	0.297401i	0.00973646	+	0.0168641i	0.870853	−	0.491544i	$-0.163567\pi$
$311$	0.171704	+	0.297401i	0.00973646	+	0.0168641i	−0.861116	+	0.508408i	$0.830234\pi$
$312$		0			0
$313$	4.17952	−	7.23914i	0.236240	−	0.409180i	−0.723392	−	0.690437i	$-0.757418\pi$
$313$	4.17952	−	7.23914i	0.236240	−	0.409180i	0.959632	+	0.281257i	$0.0907514\pi$
$314$	38.2774			2.16012
$315$		0			0
$316$	−11.1491			−0.627185
$317$	−6.70413	+	11.6119i	−0.376541	+	0.652189i	−0.990556	−	0.137106i	$-0.956220\pi$
$317$	−6.70413	+	11.6119i	−0.376541	+	0.652189i	0.614015	+	0.789294i	$0.289553\pi$
$318$		0			0
$319$	−2.09311	−	3.62537i	−0.117192	−	0.202982i
$320$	−13.8174	−	23.9324i	−0.772416	−	1.33786i
$321$		0			0
$322$	−4.94329	+	8.56203i	−0.275479	+	0.477143i
$323$	9.20075			0.511943
$324$		0			0
$325$	19.3992			1.07607
$326$	29.5230	−	51.1353i	1.63513	−	2.83212i
$327$		0			0
$328$	0.816922	+	1.41495i	0.0451069	+	0.0781275i
$329$	0.0798737	+	0.138345i	0.00440358	+	0.00762722i
$330$		0			0
$331$	14.9247	−	25.8504i	0.820337	−	1.42086i	−0.0850951	−	0.996373i	$-0.527119\pi$
$331$	14.9247	−	25.8504i	0.820337	−	1.42086i	0.905432	−	0.424492i	$-0.139547\pi$
$332$	−76.7039			−4.20967
$333$		0			0
$334$	−13.7103			−0.750196
$335$	−1.58117	+	2.73867i	−0.0863888	+	0.149630i
$336$		0			0
$337$	10.8619	+	18.8133i	0.591683	+	1.02483i	0.994006	+	0.109328i	$0.0348698\pi$
$337$	10.8619	+	18.8133i	0.591683	+	1.02483i	−0.402322	+	0.915498i	$0.631797\pi$
$338$	−12.4788	−	21.6139i	−0.678755	−	1.17564i
$339$		0			0
$340$	−6.87841	+	11.9137i	−0.373034	+	0.646114i
$341$	−5.18622			−0.280850
$342$		0			0
$343$	7.12779			0.384865
$344$	10.7073	−	18.5455i	0.577297	−	0.999908i
$345$		0			0
$346$	0.625467	+	1.08334i	0.0336253	+	0.0582408i
$347$	−14.1149	−	24.4477i	−0.757727	−	1.31242i	−0.944007	−	0.329925i	$-0.892977\pi$
$347$	−14.1149	−	24.4477i	−0.757727	−	1.31242i	0.186280	−	0.982497i	$-0.440357\pi$
$348$		0			0
$349$	3.57851	−	6.19817i	0.191553	−	0.331780i	−0.754212	−	0.656631i	$-0.771981\pi$
$349$	3.57851	−	6.19817i	0.191553	−	0.331780i	0.945765	+	0.324851i	$0.105314\pi$
$350$	5.84394			0.312372
$351$		0			0
$352$	−21.6855			−1.15584
$353$	−14.8149	+	25.6602i	−0.788518	+	1.36575i	0.138357	+	0.990382i	$0.455818\pi$
$353$	−14.8149	+	25.6602i	−0.788518	+	1.36575i	−0.926875	+	0.375371i	$0.877515\pi$
$354$		0			0
$355$	1.35977	+	2.35519i	0.0721689	+	0.125000i
$356$	20.5612	+	35.6131i	1.08974	+	1.88749i
$357$		0			0
$358$	12.5594	−	21.7535i	0.663785	−	1.14971i
$359$	13.0116			0.686726			0.343363	−	0.939203i	$-0.388434\pi$
$359$	13.0116			0.686726			0.343363	+	0.939203i	$0.388434\pi$
$360$		0			0
$361$	−7.32093			−0.385312
$362$	−20.6915	+	35.8387i	−1.08752	+	1.88364i
$363$		0			0
$364$	−6.66316	−	11.5409i	−0.349244	−	0.604909i
$365$	−4.46023	−	7.72534i	−0.233459	−	0.404363i
$366$		0			0
$367$	−16.0581	+	27.8134i	−0.838225	+	1.45185i	0.0531526	+	0.998586i	$0.483073\pi$
$367$	−16.0581	+	27.8134i	−0.838225	+	1.45185i	−0.891378	+	0.453262i	$0.850260\pi$
$368$	−103.599			−5.40049
$369$		0			0
$370$	5.29050			0.275040
$371$	0.492735	−	0.853442i	0.0255815	−	0.0443085i
$372$		0			0
$373$	−17.4578	−	30.2378i	−0.903931	−	1.56565i	−0.822346	−	0.568988i	$-0.807335\pi$
$373$	−17.4578	−	30.2378i	−0.903931	−	1.56565i	−0.0815849	−	0.996666i	$-0.525998\pi$
$374$	3.67564	+	6.36640i	0.190063	+	0.329199i
$375$		0			0
$376$	−1.45183	+	2.51465i	−0.0748726	+	0.129683i
$377$	19.6976			1.01448
$378$		0			0
$379$	−11.4728			−0.589320			−0.294660	−	0.955602i	$-0.595206\pi$
$379$	−11.4728			−0.589320			−0.294660	+	0.955602i	$0.595206\pi$
$380$	−8.73118	+	15.1228i	−0.447900	+	0.775786i
$381$		0			0
$382$	−28.5929	−	49.5243i	−1.46294	−	2.53388i
$383$	15.1180	+	26.1851i	0.772492	+	1.33800i	0.936193	+	0.351485i	$0.114323\pi$
$383$	15.1180	+	26.1851i	0.772492	+	1.33800i	−0.163701	+	0.986510i	$0.552343\pi$
$384$		0			0
$385$	−0.243100	+	0.421062i	−0.0123895	+	0.0214593i
$386$	−28.5309			−1.45219
$387$		0			0
$388$	89.1146			4.52411
$389$	−13.0540	+	22.6101i	−0.661863	+	1.14638i	0.318263	+	0.948002i	$0.396900\pi$
$389$	−13.0540	+	22.6101i	−0.661863	+	1.14638i	−0.980126	+	0.198377i	$0.936433\pi$
$390$		0			0
$391$	9.38907	+	16.2623i	0.474826	+	0.822422i
$392$	31.7541	+	54.9997i	1.60382	+	2.77790i
$393$		0			0
$394$	−28.6506	+	49.6242i	−1.44339	+	2.50003i
$395$	−1.91397			−0.0963024
$396$		0			0
$397$	−9.94467			−0.499109			−0.249554	−	0.968361i	$-0.580284\pi$
$397$	−9.94467			−0.499109			−0.249554	+	0.968361i	$0.580284\pi$
$398$	26.0084	−	45.0479i	1.30368	−	2.25805i
$399$		0			0
$400$	30.6187	+	53.0331i	1.53093	+	2.65166i
$401$	−11.7984	−	20.4354i	−0.589183	−	1.02050i	−0.994340	−	0.106248i	$-0.966116\pi$
$401$	−11.7984	−	20.4354i	−0.589183	−	1.02050i	0.405156	−	0.914247i	$-0.367217\pi$
$402$		0			0
$403$	12.2015	−	21.1336i	0.607798	−	1.05274i
$404$	54.4620			2.70959
$405$		0			0
$406$	5.93382			0.294491
$407$	1.03437	−	1.79158i	0.0512717	−	0.0888052i
$408$		0			0
$409$	1.30329	+	2.25737i	0.0644436	+	0.111620i	0.896447	−	0.443151i	$-0.146139\pi$
$409$	1.30329	+	2.25737i	0.0644436	+	0.111620i	−0.832003	+	0.554770i	$0.812806\pi$
$410$	0.221407	+	0.383488i	0.0109345	+	0.0189391i
$411$		0			0
$412$	−17.8809	+	30.9706i	−0.880929	+	1.52581i
$413$	2.06341			0.101534
$414$		0			0
$415$	−13.1678			−0.646383
$416$	51.0188	−	88.3672i	2.50140	−	4.33256i
$417$		0			0
$418$	4.66572	+	8.08126i	0.228208	+	0.395267i
$419$	−8.80232	−	15.2461i	−0.430022	−	0.744819i	0.566853	−	0.823819i	$-0.308161\pi$
$419$	−8.80232	−	15.2461i	−0.430022	−	0.744819i	−0.996875	+	0.0789996i	$0.974827\pi$
$420$		0			0
$421$	−3.17824	+	5.50487i	−0.154898	+	0.268291i	−0.933022	−	0.359820i	$-0.882838\pi$
$421$	−3.17824	+	5.50487i	−0.154898	+	0.268291i	0.778124	+	0.628111i	$0.216172\pi$
$422$	44.4778			2.16515
$423$		0			0
$424$	17.9125			0.869908
$425$	5.54986	−	9.61264i	0.269208	−	0.466282i
$426$		0			0
$427$	1.17298	+	2.03167i	0.0567647	+	0.0983193i
$428$	39.5951	+	68.5807i	1.91390	+	3.31497i
$429$		0			0
$430$	2.90195	−	5.02632i	0.139944	−	0.242391i
$431$	−29.1820			−1.40565			−0.702824	−	0.711364i	$-0.748078\pi$
$431$	−29.1820			−1.40565			−0.702824	+	0.711364i	$0.748078\pi$
$432$		0			0
$433$	13.7210			0.659388			0.329694	−	0.944088i	$-0.393054\pi$
$433$	13.7210			0.659388			0.329694	+	0.944088i	$0.393054\pi$
$434$	3.67564	−	6.36640i	0.176437	−	0.305597i
$435$		0			0
$436$	−31.8618	−	55.1862i	−1.52590	−	2.64294i
$437$	11.9181	+	20.6428i	0.570121	+	0.987478i
$438$		0			0
$439$	1.00243	−	1.73625i	0.0478431	−	0.0828667i	−0.841112	−	0.540861i	$-0.818099\pi$
$439$	1.00243	−	1.73625i	0.0478431	−	0.0828667i	0.888955	+	0.457994i	$0.151432\pi$
$440$	−8.83749			−0.421311
$441$		0			0
$442$	−34.5903			−1.64529
$443$	17.2972	−	29.9597i	0.821817	−	1.42343i	−0.0825115	−	0.996590i	$-0.526294\pi$
$443$	17.2972	−	29.9597i	0.821817	−	1.42343i	0.904328	−	0.426838i	$-0.140373\pi$
$444$		0			0
$445$	3.52976	+	6.11373i	0.167327	+	0.289819i
$446$	12.3488	+	21.3887i	0.584732	+	1.01279i
$447$		0			0
$448$	7.65856	−	13.2650i	0.361833	−	0.626713i
$449$	2.43875			0.115092			0.0575459	−	0.998343i	$-0.481672\pi$
$449$	2.43875			0.115092			0.0575459	+	0.998343i	$0.481672\pi$
$450$		0			0
$451$	0.173153			0.00815344
$452$	−3.28999	+	5.69843i	−0.154748	+	0.268031i
$453$		0			0
$454$	−7.06069	−	12.2295i	−0.331374	−	0.573957i
$455$	−1.14387	−	1.98124i	−0.0536255	−	0.0928821i
$456$		0			0
$457$	20.9497	−	36.2860i	0.979988	−	1.69739i	0.317604	−	0.948223i	$-0.397122\pi$
$457$	20.9497	−	36.2860i	0.979988	−	1.69739i	0.662384	−	0.749165i	$-0.269545\pi$
$458$	43.7530			2.04444
$459$		0			0
$460$	−35.6395			−1.66170
$461$	19.1941	−	33.2451i	0.893956	−	1.54838i	0.0588651	−	0.998266i	$-0.481252\pi$
$461$	19.1941	−	33.2451i	0.893956	−	1.54838i	0.835091	−	0.550112i	$-0.185415\pi$
$462$		0			0
$463$	0.121675	+	0.210748i	0.00565472	+	0.00979427i	0.868839	−	0.495095i	$-0.164867\pi$
$463$	0.121675	+	0.210748i	0.00565472	+	0.00979427i	−0.863184	+	0.504889i	$0.831533\pi$
$464$	31.0896	+	53.8488i	1.44330	+	2.49987i
$465$		0			0
$466$	−23.0970	+	40.0052i	−1.06995	+	1.85320i
$467$	15.6918			0.726129			0.363064	−	0.931764i	$-0.381731\pi$
$467$	15.6918			0.726129			0.363064	+	0.931764i	$0.381731\pi$
$468$		0			0
$469$	−1.75279			−0.0809363
$470$	−0.393484	+	0.681535i	−0.0181501	+	0.0314369i
$471$		0			0
$472$	18.7529	+	32.4811i	0.863174	+	1.49506i
$473$	−1.13474	−	1.96543i	−0.0521755	−	0.0903707i
$474$		0			0
$475$	7.04477	−	12.2019i	0.323236	−	0.559862i
$476$	−7.62497			−0.349490
$477$		0			0
$478$	−1.97261			−0.0902249
$479$	−8.14023	+	14.0993i	−0.371937	+	0.644213i	−0.989863	−	0.142022i	$-0.954640\pi$
$479$	−8.14023	+	14.0993i	−0.371937	+	0.644213i	0.617927	+	0.786236i	$0.287973\pi$
$480$		0			0
$481$	4.86705	+	8.42998i	0.221918	+	0.384374i
$482$	−18.6315	−	32.2708i	−0.848643	−	1.46989i
$483$		0			0
$484$	−2.72785	+	4.72478i	−0.123993	+	0.214763i
$485$	15.2984			0.694664
$486$		0			0
$487$	−32.0421			−1.45197			−0.725983	−	0.687713i	$-0.758615\pi$
$487$	−32.0421			−1.45197			−0.725983	+	0.687713i	$0.758615\pi$
$488$	−21.3209	+	36.9289i	−0.965151	+	1.67169i
$489$		0			0
$490$	8.60618	+	14.9063i	0.388787	+	0.673400i
$491$	−10.4729	−	18.1396i	−0.472635	−	0.818627i	0.526875	−	0.849943i	$-0.323364\pi$
$491$	−10.4729	−	18.1396i	−0.472635	−	0.818627i	−0.999510	+	0.0313157i	$0.990030\pi$
$492$		0			0
$493$	5.63522	−	9.76049i	0.253798	−	0.439591i
$494$	−43.9076			−1.97550
$495$		0			0
$496$	77.0326			3.45887
$497$	−0.753676	+	1.30541i	−0.0338070	+	0.0585554i
$498$		0			0
$499$	−3.61552	−	6.26227i	−0.161853	−	0.280338i	0.773680	−	0.633576i	$-0.218414\pi$
$499$	−3.61552	−	6.26227i	−0.161853	−	0.280338i	−0.935533	+	0.353239i	$0.885080\pi$
$500$	23.3076	+	40.3699i	1.04235	+	1.80540i
$501$		0			0
$502$	28.0879	−	48.6496i	1.25362	−	2.17134i
$503$	5.90333			0.263216			0.131608	−	0.991302i	$-0.457986\pi$
$503$	5.90333			0.263216			0.131608	+	0.991302i	$0.457986\pi$
$504$		0			0
$505$	9.34954			0.416049
$506$	−9.52243	+	16.4933i	−0.423324	+	0.733218i
$507$		0			0
$508$	28.5150	+	49.3895i	1.26515	+	2.19130i
$509$	−5.42002	−	9.38776i	−0.240238	−	0.416105i	0.720544	−	0.693409i	$-0.243892\pi$
$509$	−5.42002	−	9.38776i	−0.240238	−	0.416105i	−0.960782	+	0.277304i	$0.910559\pi$
$510$		0			0
$511$	2.47217	−	4.28192i	0.109362	−	0.189421i
$512$	41.7940			1.84705
$513$		0			0
$514$	−14.3739			−0.634004
$515$	−3.06963	+	5.31676i	−0.135264	+	0.234284i
$516$		0			0
$517$	0.153863	+	0.266499i	0.00676691	+	0.0117206i
$518$	1.46618	+	2.53950i	0.0644203	+	0.111579i
$519$		0			0
$520$	20.7917	−	36.0123i	0.911776	−	1.57924i
$521$	−14.7412			−0.645822			−0.322911	−	0.946429i	$-0.604661\pi$
$521$	−14.7412			−0.645822			−0.322911	+	0.946429i	$0.604661\pi$
$522$		0			0
$523$	−16.8230			−0.735617			−0.367808	−	0.929902i	$-0.619892\pi$
$523$	−16.8230			−0.735617			−0.367808	+	0.929902i	$0.619892\pi$
$524$	−36.7197	+	63.6004i	−1.60411	+	2.77840i
$525$		0			0
$526$	3.54744	+	6.14434i	0.154676	+	0.267906i
$527$	−6.98136	−	12.0921i	−0.304113	−	0.526739i
$528$		0			0
$529$	−12.8241	+	22.2120i	−0.557570	+	0.965739i
$530$	4.85475			0.210877
$531$		0			0
$532$	−9.67884			−0.419631
$533$	−0.407371	+	0.705587i	−0.0176452	+	0.0305624i
$534$		0			0
$535$	6.79732	+	11.7733i	0.293874	+	0.509004i
$536$	−15.9299	−	27.5914i	−0.688067	−	1.19177i
$537$		0			0
$538$	−13.7826	+	23.8721i	−0.594208	+	1.02920i
$539$	6.73051			0.289904
$540$		0			0
$541$	−22.5357			−0.968886			−0.484443	−	0.874823i	$-0.660978\pi$
$541$	−22.5357			−0.968886			−0.484443	+	0.874823i	$0.660978\pi$
$542$	−44.1009	+	76.3849i	−1.89429	+	3.28101i
$543$		0			0
$544$	−29.1916	−	50.5614i	−1.25158	−	2.16780i
$545$	−5.46974	−	9.47387i	−0.234298	−	0.405816i
$546$		0			0
$547$	−14.2139	+	24.6192i	−0.607743	+	1.05264i	0.383869	+	0.923388i	$0.374591\pi$
$547$	−14.2139	+	24.6192i	−0.607743	+	1.05264i	−0.991612	+	0.129254i	$0.958742\pi$
$548$	−113.826			−4.86240
$549$		0			0
$550$	11.2574			0.480016
$551$	7.15313	−	12.3896i	0.304734	−	0.527814i
$552$		0			0
$553$	−0.530427	−	0.918727i	−0.0225561	−	0.0390683i
$554$	−44.1496	−	76.4693i	−1.87574	−	3.24887i
$555$		0			0
$556$	−2.36737	+	4.10040i	−0.100399	+	0.173896i
$557$	−43.1863			−1.82986			−0.914930	−	0.403612i	$-0.867755\pi$
$557$	−43.1863			−1.82986			−0.914930	+	0.403612i	$0.867755\pi$
$558$		0			0
$559$	10.6787			0.451661
$560$	3.61085	−	6.25417i	0.152586	−	0.264287i
$561$		0			0
$562$	−13.0282	−	22.5656i	−0.549563	−	0.951871i
$563$	−0.482261	−	0.835300i	−0.0203249	−	0.0352037i	0.855684	−	0.517499i	$-0.173137\pi$
$563$	−0.482261	−	0.835300i	−0.0203249	−	0.0352037i	−0.876009	+	0.482295i	$0.839803\pi$
$564$		0			0
$565$	−0.564795	+	0.978254i	−0.0237611	+	0.0411555i
$566$	−16.1667			−0.679537
$567$		0			0
$568$	−27.3986			−1.14962
$569$	4.26416	−	7.38575i	0.178763	−	0.309627i	−0.762694	−	0.646759i	$-0.776124\pi$
$569$	4.26416	−	7.38575i	0.178763	−	0.309627i	0.941457	+	0.337133i	$0.109457\pi$
$570$		0			0
$571$	−8.80176	−	15.2451i	−0.368342	−	0.637988i	0.620964	−	0.783839i	$-0.286741\pi$
$571$	−8.80176	−	15.2451i	−0.368342	−	0.637988i	−0.989307	+	0.145851i	$0.953408\pi$
$572$	−12.8355	−	22.2317i	−0.536678	−	0.929554i
$573$		0			0
$574$	−0.122719	+	0.212555i	−0.00512219	+	0.00887189i
$575$	28.7559			1.19920
$576$		0			0
$577$	−11.1810			−0.465472			−0.232736	−	0.972540i	$-0.574768\pi$
$577$	−11.1810			−0.465472			−0.232736	+	0.972540i	$0.574768\pi$
$578$	13.3135	−	23.0597i	0.553770	−	0.959157i
$579$		0			0
$580$	10.6952	+	18.5247i	0.444096	+	0.769197i
$581$	−3.64926	−	6.32070i	−0.151397	−	0.262227i
$582$		0			0
$583$	0.949173	−	1.64402i	0.0393107	−	0.0680882i
$584$	89.8713			3.71890
$585$		0			0
$586$	−39.3988			−1.62755
$587$	10.8373	−	18.7708i	0.447305	−	0.774755i	−0.550905	−	0.834568i	$-0.685717\pi$
$587$	10.8373	−	18.7708i	0.447305	−	0.774755i	0.998210	+	0.0598133i	$0.0190505\pi$
$588$		0			0
$589$	−8.86187	−	15.3492i	−0.365147	−	0.632453i
$590$	5.08253	+	8.80321i	0.209245	+	0.362422i
$591$		0			0
$592$	−15.3638	+	26.6109i	−0.631448	+	1.09370i
$593$	7.82200			0.321211			0.160605	−	0.987019i	$-0.448655\pi$
$593$	7.82200			0.321211			0.160605	+	0.987019i	$0.448655\pi$
$594$		0			0
$595$	−1.30899			−0.0536632
$596$	17.9096	−	31.0203i	0.733605	−	1.27064i
$597$		0			0
$598$	−44.8063	−	77.6068i	−1.83227	−	3.17358i
$599$	−5.25399	−	9.10018i	−0.214672	−	0.371823i	0.738499	−	0.674255i	$-0.235535\pi$
$599$	−5.25399	−	9.10018i	−0.214672	−	0.371823i	−0.953171	+	0.302432i	$0.902202\pi$
$600$		0			0
$601$	−18.5488	+	32.1275i	−0.756622	+	1.31051i	0.187942	+	0.982180i	$0.439818\pi$
$601$	−18.5488	+	32.1275i	−0.756622	+	1.31051i	−0.944564	+	0.328328i	$0.893515\pi$
$602$	3.21692			0.131112
$603$		0			0
$604$	68.9706			2.80638
$605$	−0.468293	+	0.811107i	−0.0190388	+	0.0329762i
$606$		0			0
$607$	20.7558	+	35.9501i	0.842451	+	1.45917i	0.887817	+	0.460197i	$0.152221\pi$
$607$	20.7558	+	35.9501i	0.842451	+	1.45917i	−0.0453658	+	0.998970i	$0.514445\pi$
$608$	−37.0547	−	64.1806i	−1.50277	−	2.60287i
$609$		0			0
$610$	−5.77851	+	10.0087i	−0.233965	+	0.405239i
$611$	−1.44796			−0.0585782
$612$		0			0
$613$	33.7344			1.36252			0.681259	−	0.732042i	$-0.261433\pi$
$613$	33.7344			1.36252			0.681259	+	0.732042i	$0.261433\pi$
$614$	−13.1148	+	22.7155i	−0.529271	+	0.916724i
$615$		0			0
$616$	−2.44917	−	4.24209i	−0.0986800	−	0.170919i
$617$	−14.0298	−	24.3003i	−0.564817	−	0.978292i	−0.997067	−	0.0765378i	$-0.975613\pi$
$617$	−14.0298	−	24.3003i	−0.564817	−	0.978292i	0.432250	−	0.901754i	$-0.357720\pi$
$618$		0			0
$619$	15.9049	−	27.5480i	0.639270	−	1.10725i	−0.346323	−	0.938115i	$-0.612570\pi$
$619$	15.9049	−	27.5480i	0.639270	−	1.10725i	0.985593	−	0.169134i	$-0.0540969\pi$
$620$	26.5002			1.06427
$621$		0			0
$622$	−0.937683			−0.0375976
$623$	−1.95644	+	3.38865i	−0.0783830	+	0.135763i
$624$		0			0
$625$	−6.30578	−	10.9219i	−0.252231	−	0.436877i
$626$	11.4122	+	19.7666i	0.456125	+	0.790031i
$627$		0			0
$628$	−38.2401	+	66.2338i	−1.52595	+	2.64302i
$629$	5.56960			0.222075
$630$		0			0
$631$	−23.4280			−0.932653			−0.466326	−	0.884613i	$-0.654423\pi$
$631$	−23.4280			−0.932653			−0.466326	+	0.884613i	$0.654423\pi$
$632$	9.64138	−	16.6994i	0.383513	−	0.664265i
$633$		0			0
$634$	−18.3057	−	31.7064i	−0.727013	−	1.25922i
$635$	4.89520	+	8.47873i	0.194260	+	0.336468i
$636$		0			0
$637$	−15.8347	+	27.4265i	−0.627393	+	1.08668i
$638$	11.4305			0.452539
$639$		0			0
$640$	34.8366			1.37704
$641$	7.75779	−	13.4369i	0.306414	−	0.530725i	−0.671161	−	0.741312i	$-0.734204\pi$
$641$	7.75779	−	13.4369i	0.306414	−	0.530725i	0.977575	+	0.210587i	$0.0675374\pi$
$642$		0			0
$643$	5.47372	+	9.48075i	0.215862	+	0.373884i	0.953539	−	0.301270i	$-0.0974104\pi$
$643$	5.47372	+	9.48075i	0.215862	+	0.373884i	−0.737677	+	0.675154i	$0.764077\pi$
$644$	−9.87694	−	17.1074i	−0.389206	−	0.674125i
$645$		0			0
$646$	−12.5614	+	21.7570i	−0.494221	+	0.856016i
$647$	−16.9732			−0.667287			−0.333643	−	0.942699i	$-0.608278\pi$
$647$	−16.9732			−0.667287			−0.333643	+	0.942699i	$0.608278\pi$
$648$		0			0
$649$	3.97483			0.156026
$650$	−26.4849	+	45.8732i	−1.03882	+	1.79930i
$651$		0			0
$652$	58.9885	+	102.171i	2.31017	+	4.00133i
$653$	0.227291	+	0.393679i	0.00889458	+	0.0154059i	0.870438	−	0.492277i	$-0.163835\pi$
$653$	0.227291	+	0.393679i	0.00889458	+	0.0154059i	−0.861544	+	0.507683i	$0.830502\pi$
$654$		0			0
$655$	−6.30371	+	10.9183i	−0.246306	+	0.426615i
$656$	−2.57189			−0.100415
$657$		0			0
$658$	−0.436192			−0.0170045
$659$	−1.57851	+	2.73406i	−0.0614901	+	0.106504i	−0.895132	−	0.445802i	$-0.852919\pi$
$659$	−1.57851	+	2.73406i	−0.0614901	+	0.106504i	0.833642	+	0.552306i	$0.186252\pi$
$660$		0			0
$661$	13.2786	+	22.9992i	0.516478	+	0.894566i	0.999817	+	0.0191324i	$0.00609042\pi$
$661$	13.2786	+	22.9992i	0.516478	+	0.894566i	−0.483339	+	0.875433i	$0.660576\pi$
$662$	40.7521	+	70.5848i	1.58388	+	2.74336i
$663$		0			0
$664$	66.3312	−	114.889i	2.57415	−	4.45856i
$665$	−1.66158			−0.0644331
$666$		0			0
$667$	29.1982			1.13056
$668$	13.6970	−	23.7238i	0.529951	−	0.917903i
$669$		0			0
$670$	−4.31742	−	7.47799i	−0.166796	−	0.288900i
$671$	2.25956	+	3.91367i	0.0872294	+	0.151086i
$672$		0			0
$673$	13.6485	−	23.6398i	0.526110	−	0.911248i	−0.473428	−	0.880833i	$-0.656984\pi$
$673$	13.6485	−	23.6398i	0.526110	−	0.911248i	0.999537	−	0.0304158i	$-0.00968314\pi$
$674$	−59.3169			−2.28480
$675$		0			0
$676$	49.8664			1.91794
$677$	−0.200168	+	0.346700i	−0.00769307	+	0.0133248i	−0.869846	−	0.493323i	$-0.835782\pi$
$677$	−0.200168	+	0.346700i	−0.00769307	+	0.0133248i	0.862153	+	0.506648i	$0.169115\pi$
$678$		0			0
$679$	4.23971	+	7.34339i	0.162705	+	0.281813i
$680$	−11.8965	−	20.6053i	−0.456209	−	0.790177i
$681$		0			0
$682$	7.08052	−	12.2638i	0.271127	−	0.469606i
$683$	26.2154			1.00310			0.501552	−	0.865127i	$-0.332762\pi$
$683$	26.2154			1.00310			0.501552	+	0.865127i	$0.332762\pi$
$684$		0			0
$685$	−19.5406			−0.746607
$686$	−9.73127	+	16.8550i	−0.371541	+	0.643529i
$687$		0			0
$688$	16.8547	+	29.1932i	0.642579	+	1.11298i
$689$	4.46618	+	7.73565i	0.170148	+	0.294705i
$690$		0			0
$691$	7.79814	−	13.5068i	0.296655	−	0.513822i	−0.678713	−	0.734403i	$-0.737462\pi$
$691$	7.79814	−	13.5068i	0.296655	−	0.513822i	0.975369	+	0.220581i	$0.0707955\pi$
$692$	−2.49943			−0.0950141
$693$		0			0
$694$	77.0818			2.92599
$695$	−0.406408	+	0.703920i	−0.0154160	+	0.0267012i
$696$		0			0
$697$	0.233087	+	0.403719i	0.00882880	+	0.0152919i
$698$	9.77118	+	16.9242i	0.369845	+	0.640590i
$699$		0			0
$700$	−5.83824	+	10.1121i	−0.220665	+	0.382203i
$701$	−27.4965			−1.03853			−0.519265	−	0.854613i	$-0.673794\pi$
$701$	−27.4965			−1.03853			−0.519265	+	0.854613i	$0.673794\pi$
$702$		0			0
$703$	7.06983			0.266644
$704$	14.7529	−	25.5529i	0.556023	−	0.963059i
$705$		0			0
$706$	−40.4523	−	70.0655i	−1.52244	−	2.63695i
$707$	2.59108	+	4.48788i	0.0974476	+	0.168784i
$708$		0			0
$709$	15.3257	−	26.5449i	0.575570	−	0.996916i	−0.420410	−	0.907334i	$-0.638114\pi$
$709$	15.3257	−	26.5449i	0.575570	−	0.996916i	0.995979	−	0.0895815i	$-0.0285529\pi$
$710$	−7.42572			−0.278682
$711$		0			0
$712$	−71.1228			−2.66544
$713$	18.0865	−	31.3267i	0.677345	−	1.17320i
$714$		0			0
$715$	−2.20348	−	3.81654i	−0.0824054	−	0.142730i
$716$	25.0943	+	43.4646i	0.937818	+	1.62435i
$717$		0			0
$718$	−17.7642	+	30.7685i	−0.662954	+	1.14827i
$719$	19.7250			0.735620			0.367810	−	0.929901i	$-0.380108\pi$
$719$	19.7250			0.735620			0.367810	+	0.929901i	$0.380108\pi$
$720$		0			0
$721$	−3.40280			−0.126727
$722$	9.99495	−	17.3118i	0.371973	−	0.644277i
$723$		0			0
$724$	−41.3426	−	71.6075i	−1.53649	−	2.66127i
$725$	−8.62949	−	14.9467i	−0.320491	−	0.555107i
$726$		0			0
$727$	2.70607	−	4.68705i	0.100363	−	0.173833i	−0.811471	−	0.584392i	$-0.801333\pi$
$727$	2.70607	−	4.68705i	0.100363	−	0.173833i	0.911834	+	0.410559i	$0.134666\pi$
$728$	23.0484			0.854230
$729$		0			0
$730$	24.3574			0.901509
$731$	3.05504	−	5.29148i	0.112995	−	0.195713i
$732$		0			0
$733$	0.819020	+	1.41858i	0.0302512	+	0.0523966i	0.880755	−	0.473573i	$-0.157036\pi$
$733$	0.819020	+	1.41858i	0.0302512	+	0.0523966i	−0.850503	+	0.525969i	$0.823703\pi$
$734$	−43.8468	−	75.9449i	−1.61842	−	2.80318i
$735$		0			0
$736$	75.6263	−	130.989i	2.78762	−	4.82830i
$737$	−3.37646			−0.124374
$738$		0			0
$739$	−12.8306			−0.471980			−0.235990	−	0.971755i	$-0.575833\pi$
$739$	−12.8306			−0.471980			−0.235990	+	0.971755i	$0.575833\pi$
$740$	−5.28535	+	9.15449i	−0.194293	+	0.336526i
$741$		0			0
$742$	1.34542	+	2.33033i	0.0493919	+	0.0855493i
$743$	18.1559	+	31.4469i	0.666074	+	1.15367i	0.978993	+	0.203894i	$0.0653598\pi$
$743$	18.1559	+	31.4469i	0.666074	+	1.15367i	−0.312919	+	0.949780i	$0.601307\pi$
$744$		0			0
$745$	3.07455	−	5.32528i	0.112643	−	0.195103i
$746$	95.3376			3.49056
$747$		0			0
$748$	−14.6883			−0.537056
$749$	−3.76754	+	6.52557i	−0.137663	+	0.238439i
$750$		0			0
$751$	−10.3163	−	17.8683i	−0.376447	−	0.652025i	0.614096	−	0.789232i	$-0.289521\pi$
$751$	−10.3163	−	17.8683i	−0.376447	−	0.652025i	−0.990542	+	0.137207i	$0.956188\pi$
$752$	−2.28538	−	3.95840i	−0.0833394	−	0.144348i
$753$		0			0
$754$	−26.8923	+	46.5788i	−0.979359	+	1.69630i
$755$	11.8403			0.430911
$756$		0			0
$757$	13.5638			0.492986			0.246493	−	0.969145i	$-0.420722\pi$
$757$	13.5638			0.492986			0.246493	+	0.969145i	$0.420722\pi$
$758$	15.6634	−	27.1298i	0.568919	−	0.985397i
$759$		0			0
$760$	−15.1009	−	26.1555i	−0.547768	−	0.948761i
$761$	7.99799	+	13.8529i	0.289927	+	0.502168i	0.973792	−	0.227440i	$-0.0730357\pi$
$761$	7.99799	+	13.8529i	0.289927	+	0.502168i	−0.683865	+	0.729608i	$0.739702\pi$
$762$		0			0
$763$	3.03171	−	5.25107i	0.109755	−	0.190102i
$764$	114.260			4.13378
$765$		0			0
$766$	−82.5596			−2.98300
$767$	−9.35146	+	16.1972i	−0.337662	+	0.584847i
$768$		0			0
$769$	−13.2839	−	23.0083i	−0.479028	−	0.829701i	0.520683	−	0.853750i	$-0.325677\pi$
$769$	−13.2839	−	23.0083i	−0.479028	−	0.829701i	−0.999711	+	0.0240494i	$0.992344\pi$
$770$	−0.663789	−	1.14972i	−0.0239213	−	0.0414329i
$771$		0			0
$772$	28.5031	−	49.3689i	1.02585	−	1.77682i
$773$	−24.2035			−0.870539			−0.435269	−	0.900300i	$-0.643347\pi$
$773$	−24.2035			−0.870539			−0.435269	+	0.900300i	$0.643347\pi$
$774$		0			0
$775$	−21.3818			−0.768056
$776$	−77.0636	+	133.478i	−2.76642	+	4.79158i
$777$		0			0
$778$	−35.6440	−	61.7373i	−1.27790	−	2.21339i
$779$	0.295872	+	0.512465i	0.0106007	+	0.0183610i
$780$		0			0
$781$	−1.45183	+	2.51465i	−0.0519507	+	0.0899812i
$782$	−51.2740			−1.83355
$783$		0			0
$784$	−99.9705			−3.57037
$785$	−6.56471	+	11.3704i	−0.234305	+	0.405828i
$786$		0			0
$787$	13.6162	+	23.5839i	0.485364	+	0.840675i	0.999859	−	0.0168185i	$-0.00535373\pi$
$787$	13.6162	+	23.5839i	0.485364	+	0.840675i	−0.514494	+	0.857494i	$0.672020\pi$
$788$	−57.2453	−	99.1517i	−2.03928	−	3.53213i
$789$		0			0
$790$	2.61306	−	4.52596i	0.0929686	−	0.161026i
$791$	−0.626097			−0.0222614
$792$		0			0
$793$	−21.2640			−0.755107
$794$	13.5770	−	23.5161i	0.481831	−	0.834555i
$795$		0			0
$796$	51.9661	+	90.0079i	1.84189	+	3.19025i
$797$	19.2846	+	33.4019i	0.683095	+	1.18316i	0.974031	+	0.226413i	$0.0726999\pi$
$797$	19.2846	+	33.4019i	0.683095	+	1.18316i	−0.290936	+	0.956742i	$0.593967\pi$
$798$		0			0
$799$	−0.414242	+	0.717489i	−0.0146548	+	0.0253829i
$800$	−89.4051			−3.16095
$801$		0			0
$802$	64.4313			2.27515
$803$	4.76222	−	8.24841i	0.168055	−	0.291080i
$804$		0			0
$805$	−1.69558	−	2.93684i	−0.0597615	−	0.103510i
$806$	33.3163	+	57.7055i	1.17352	+	2.03259i
$807$		0			0
$808$	−47.0971	+	81.5745i	−1.65687	+	2.86978i
$809$	12.0951			0.425240			0.212620	−	0.977135i	$-0.431800\pi$
$809$	12.0951			0.425240			0.212620	+	0.977135i	$0.431800\pi$
$810$		0			0
$811$	35.0487			1.23073			0.615364	−	0.788243i	$-0.289009\pi$
$811$	35.0487			1.23073			0.615364	+	0.788243i	$0.289009\pi$
$812$	−5.92804	+	10.2677i	−0.208033	+	0.360325i
$813$		0			0
$814$	2.82436	+	4.89193i	0.0989936	+	0.171462i
$815$	10.1266	+	17.5398i	0.354719	+	0.614392i
$816$		0			0
$817$	3.87795	−	6.71680i	0.135672	−	0.234991i
$818$	−7.11731			−0.248851
$819$		0			0
$820$	−0.884765			−0.0308973
$821$	10.0398	−	17.3894i	0.350391	−	0.606895i	−0.635927	−	0.771749i	$-0.719382\pi$
$821$	10.0398	−	17.3894i	0.350391	−	0.606895i	0.986318	+	0.164854i	$0.0527153\pi$
$822$		0			0
$823$	12.8058	+	22.1803i	0.446382	+	0.773156i	0.998147	−	0.0608436i	$-0.0193791\pi$
$823$	12.8058	+	22.1803i	0.446382	+	0.773156i	−0.551766	+	0.833999i	$0.686046\pi$
$824$	−30.9257	−	53.5649i	−1.07735	−	1.86602i
$825$		0			0
$826$	−2.81709	+	4.87934i	−0.0980191	+	0.169774i
$827$	0.864167			0.0300500			0.0150250	−	0.999887i	$-0.495217\pi$
$827$	0.864167			0.0300500			0.0150250	+	0.999887i	$0.495217\pi$
$828$		0			0
$829$	38.1823			1.32613			0.663064	−	0.748563i	$-0.269256\pi$
$829$	38.1823			1.32613			0.663064	+	0.748563i	$0.269256\pi$
$830$	17.9775	−	31.1379i	0.624007	−	1.08081i
$831$		0			0
$832$	69.4176	+	120.235i	2.40662	+	4.16839i
$833$	9.06019	+	15.6927i	0.313917	+	0.543720i
$834$		0			0
$835$	2.35137	−	4.07269i	0.0813725	−	0.140941i
$836$	−18.6447			−0.644840
$837$		0			0
$838$	48.0697			1.66054
$839$	5.85122	−	10.1346i	0.202007	−	0.349886i	−0.747168	−	0.664635i	$-0.768587\pi$
$839$	5.85122	−	10.1346i	0.202007	−	0.349886i	0.949175	+	0.314749i	$0.101920\pi$
$840$		0			0
$841$	5.73778	+	9.93812i	0.197854	+	0.342694i
$842$	−8.67822	−	15.0311i	−0.299071	−	0.518007i
$843$		0			0
$844$	−44.4345	+	76.9628i	−1.52950	+	2.64917i
$845$	8.56062			0.294494
$846$		0			0
$847$	−0.519120			−0.0178372
$848$	−14.0984	+	24.4191i	−0.484140	+	0.838555i
$849$		0			0
$850$	15.1540	+	26.2474i	0.519777	+	0.900280i
$851$	7.21454	+	12.4959i	0.247311	+	0.428355i
$852$		0			0
$853$	8.73776	−	15.1343i	0.299175	−	0.518187i	−0.676772	−	0.736193i	$-0.736622\pi$
$853$	8.73776	−	15.1343i	0.299175	−	0.518187i	0.975948	+	0.218006i	$0.0699551\pi$
$854$	−6.40570			−0.219198
$855$		0			0
$856$	−136.962			−4.68128
$857$	−17.8130	+	30.8530i	−0.608480	+	1.05392i	0.383011	+	0.923744i	$0.374887\pi$
$857$	−17.8130	+	30.8530i	−0.608480	+	1.05392i	−0.991491	+	0.130174i	$0.958446\pi$
$858$		0			0
$859$	5.95893	+	10.3212i	0.203316	+	0.352154i	0.949595	−	0.313480i	$-0.101495\pi$
$859$	5.95893	+	10.3212i	0.203316	+	0.352154i	−0.746279	+	0.665633i	$0.768161\pi$
$860$	5.79824	+	10.0428i	0.197718	+	0.342458i
$861$		0			0
$862$	39.8409	−	69.0065i	1.35699	−	2.35037i
$863$	1.22689			0.0417637			0.0208818	−	0.999782i	$-0.493353\pi$
$863$	1.22689			0.0417637			0.0208818	+	0.999782i	$0.493353\pi$
$864$		0			0
$865$	−0.429080			−0.0145891
$866$	−18.7326	+	32.4459i	−0.636561	+	1.10256i
$867$		0			0
$868$	7.34413	+	12.7204i	0.249276	+	0.431758i
$869$	−1.02178	−	1.76978i	−0.0346616	−	0.0600356i
$870$		0			0
$871$	7.94370	−	13.7589i	0.269162	−	0.466202i
$872$	110.212			3.73226
$873$		0			0
$874$	−65.0852			−2.20154
$875$	−2.21776	+	3.84127i	−0.0749739	+	0.129859i
$876$		0			0
$877$	−12.9867	−	22.4936i	−0.438529	−	0.759555i	0.559047	−	0.829136i	$-0.311167\pi$
$877$	−12.9867	−	22.4936i	−0.438529	−	0.759555i	−0.997576	+	0.0695812i	$0.977834\pi$
$878$	2.73714	+	4.74086i	0.0923738	+	0.159996i
$879$		0			0
$880$	6.95571	−	12.0476i	0.234477	−	0.406126i
$881$	−53.5351			−1.80364			−0.901822	−	0.432107i	$-0.857770\pi$
$881$	−53.5351			−1.80364			−0.901822	+	0.432107i	$0.857770\pi$
$882$		0			0
$883$	17.3818			0.584945			0.292472	−	0.956274i	$-0.405522\pi$
$883$	17.3818			0.584945			0.292472	+	0.956274i	$0.405522\pi$
$884$	34.5566	−	59.8538i	1.16226	−	2.01310i
$885$		0			0
$886$	47.2304	+	81.8054i	1.58673	+	2.74831i
$887$	20.0080	+	34.6549i	0.671803	+	1.16360i	0.977392	+	0.211434i	$0.0678132\pi$
$887$	20.0080	+	34.6549i	0.671803	+	1.16360i	−0.305589	+	0.952163i	$0.598853\pi$
$888$		0			0
$889$	−2.71326	+	4.69950i	−0.0909997	+	0.157616i
$890$	−19.2761			−0.646138
$891$		0			0
$892$	−49.3470			−1.65226
$893$	−0.525823	+	0.910752i	−0.0175960	+	0.0304772i
$894$		0			0
$895$	4.30796	+	7.46161i	0.143999	+	0.249414i
$896$	9.65441	+	16.7219i	0.322531	+	0.558641i
$897$		0			0
$898$	−3.32952	+	5.76690i	−0.111108	+	0.192444i
$899$	−21.7107			−0.724091
$900$		0			0
$901$	5.11086			0.170268
$902$	−0.236398	+	0.409453i	−0.00787119	+	0.0136333i
$903$		0			0
$904$	−5.69016	−	9.85565i	−0.189252	−	0.327794i
$905$	−7.09732	−	12.2929i	−0.235923	−	0.408631i
$906$		0			0
$907$	14.9046	−	25.8156i	0.494900	−	0.857192i	−0.505083	−	0.863071i	$-0.668538\pi$
$907$	14.9046	−	25.8156i	0.494900	−	0.857192i	0.999983	+	0.00587889i	$0.00187132\pi$
$908$	28.2152			0.936355
$909$		0			0
$910$	6.24671			0.207076
$911$	3.75956	−	6.51175i	0.124560	−	0.215744i	−0.797001	−	0.603978i	$-0.793581\pi$
$911$	3.75956	−	6.51175i	0.124560	−	0.215744i	0.921561	+	0.388234i	$0.126915\pi$
$912$		0			0
$913$	−7.02970	−	12.1758i	−0.232649	−	0.402960i
$914$	57.2036	+	99.0795i	1.89213	+	3.27726i
$915$		0			0
$916$	−43.7103	+	75.7085i	−1.44423	+	2.50148i
$917$	−6.98789			−0.230761
$918$		0			0
$919$	−48.1441			−1.58813			−0.794064	−	0.607835i	$-0.792038\pi$
$919$	−48.1441			−1.58813			−0.794064	+	0.607835i	$0.792038\pi$
$920$	30.8200	−	53.3818i	1.01610	−	1.75995i
$921$		0			0
$922$	52.4096	+	90.7761i	1.72602	+	2.98955i
$923$	−6.83137	−	11.8323i	−0.224857	−	0.389464i
$924$		0			0
$925$	4.26450	−	7.38633i	0.140216	−	0.242861i
$926$	−0.664472			−0.0218359
$927$		0			0
$928$	−90.7802			−2.98001
$929$	−19.5885	+	33.9283i	−0.642678	+	1.11315i	0.342155	+	0.939644i	$0.388843\pi$
$929$	−19.5885	+	33.9283i	−0.642678	+	1.11315i	−0.984833	+	0.173507i	$0.944490\pi$
$930$		0			0
$931$	11.5007	+	19.9197i	0.376919	+	0.652842i
$932$	−46.1490	−	79.9324i	−1.51166	−	2.61827i
$933$		0			0
$934$	−21.4233	+	37.1062i	−0.700992	+	1.21415i
$935$	−2.52155			−0.0824634
$936$		0			0
$937$	36.6480			1.19724			0.598620	−	0.801033i	$-0.295716\pi$
$937$	36.6480			1.19724			0.598620	+	0.801033i	$0.295716\pi$
$938$	2.39301	−	4.14481i	0.0781345	−	0.135333i
$939$		0			0
$940$	−0.786202	−	1.36174i	−0.0256431	−	0.0444151i
$941$	1.94861	+	3.37509i	0.0635229	+	0.110025i	0.896038	−	0.443978i	$-0.146433\pi$
$941$	1.94861	+	3.37509i	0.0635229	+	0.110025i	−0.832515	+	0.554003i	$0.813100\pi$
$942$		0			0
$943$	−0.603855	+	1.04591i	−0.0196642	+	0.0340594i
$944$	−59.0394			−1.92157
$945$		0			0
$946$	6.19686			0.201477
$947$	22.2020	−	38.4551i	0.721469	−	1.24962i	−0.238942	−	0.971034i	$-0.576800\pi$
$947$	22.2020	−	38.4551i	0.721469	−	1.24962i	0.960411	−	0.278587i	$-0.0898662\pi$
$948$		0			0
$949$	22.4079	+	38.8116i	0.727390	+	1.25988i
$950$	19.2359	+	33.3175i	0.624094	+	1.08096i
$951$		0			0
$952$	6.59384	−	11.4209i	0.213708	−	0.370152i
$953$	−20.1218			−0.651810			−0.325905	−	0.945403i	$-0.605669\pi$
$953$	−20.1218			−0.651810			−0.325905	+	0.945403i	$0.605669\pi$
$954$		0			0
$955$	19.6151			0.634730
$956$	1.97068	−	3.41332i	0.0637365	−	0.110395i
$957$		0			0
$958$	−22.2270	−	38.4983i	−0.718122	−	1.24382i
$959$	−5.41537	−	9.37969i	−0.174871	−	0.302886i
$960$		0			0
$961$	2.05156	−	3.55340i	0.0661793	−	0.114626i
$962$	−26.5791			−0.856945
$963$		0			0
$964$	74.4535			2.39799
$965$	4.89316	−	8.47520i	0.157516	−	0.272826i
$966$		0			0
$967$	−11.5692	−	20.0385i	−0.372041	−	0.644394i	0.617838	−	0.786305i	$-0.288009\pi$
$967$	−11.5692	−	20.0385i	−0.372041	−	0.644394i	−0.989879	+	0.141911i	$0.954675\pi$
$968$	−4.71793	−	8.17169i	−0.151640	−	0.262648i
$969$		0			0
$970$	−20.8862	+	36.1760i	−0.670616	+	1.16154i
$971$	−28.3629			−0.910209			−0.455104	−	0.890438i	$-0.650398\pi$
$971$	−28.3629			−0.910209			−0.455104	+	0.890438i	$0.650398\pi$
$972$		0			0
$973$	−0.450519			−0.0144430
$974$	43.7457	−	75.7698i	1.40170	−	2.42782i
$975$		0			0
$976$	−33.5620	−	58.1310i	−1.07429	−	1.86073i
$977$	7.84482	+	13.5876i	0.250978	+	0.434707i	0.963795	−	0.266643i	$-0.0859145\pi$
$977$	7.84482	+	13.5876i	0.250978	+	0.434707i	−0.712817	+	0.701350i	$0.752581\pi$
$978$		0			0
$979$	−3.76875	+	6.52767i	−0.120450	+	0.208625i
$980$	−34.3912			−1.09859
$981$		0			0
$982$	57.1927			1.82509
$983$	18.0658	−	31.2909i	0.576210	−	0.998026i	−0.419699	−	0.907664i	$-0.637864\pi$
$983$	18.0658	−	31.2909i	0.576210	−	0.998026i	0.995909	−	0.0903621i	$-0.0288024\pi$
$984$		0			0
$985$	−9.82735	−	17.0215i	−0.313125	−	0.542349i
$986$	15.3871	+	26.6512i	0.490024	+	0.848746i
$987$		0			0
$988$	43.8648	−	75.9761i	1.39553	−	2.41712i
$989$	15.8293			0.503342
$990$		0			0
$991$	−8.69420			−0.276180			−0.138090	−	0.990420i	$-0.544096\pi$
$991$	−8.69420			−0.276180			−0.138090	+	0.990420i	$0.544096\pi$
$992$	−56.2329	+	97.3982i	−1.78540	+	3.09240i
$993$		0			0
$994$	−2.05792	−	3.56443i	−0.0652734	−	0.113057i
$995$	8.92107	+	15.4517i	0.282817	+	0.489853i
$996$		0			0
$997$	−17.7648	+	30.7695i	−0.562616	+	0.974480i	0.434651	+	0.900599i	$0.356872\pi$
$997$	−17.7648	+	30.7695i	−0.562616	+	0.974480i	−0.997267	+	0.0738808i	$0.976462\pi$
$998$	19.7445			0.625000
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.e.e.100.1		8
3.2	odd	2		99.2.e.e.34.4	✓	8
9.2	odd	6		891.2.a.q.1.1		4
9.4	even	3	inner	297.2.e.e.199.1		8
9.5	odd	6		99.2.e.e.67.4	yes	8
9.7	even	3		891.2.a.p.1.4		4
33.32	even	2		1089.2.e.i.727.1		8
99.32	even	6		1089.2.e.i.364.1		8
99.43	odd	6		9801.2.a.bl.1.1		4
99.65	even	6		9801.2.a.bi.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.e.e.34.4	✓	8	3.2	odd	2
99.2.e.e.67.4	yes	8	9.5	odd	6
297.2.e.e.100.1		8	1.1	even	1	trivial
297.2.e.e.199.1		8	9.4	even	3	inner
891.2.a.p.1.4		4	9.7	even	3
891.2.a.q.1.1		4	9.2	odd	6
1089.2.e.i.364.1		8	99.32	even	6
1089.2.e.i.727.1		8	33.32	even	2
9801.2.a.bi.1.4		4	99.65	even	6
9801.2.a.bl.1.1		4	99.43	odd	6

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.36526 + 2.36469i) q^{2} +(-2.72785 - 4.72478i) q^{4} +(-0.468293 - 0.811107i) q^{5} +(0.259560 - 0.449571i) q^{7} +9.43585 q^{8} +2.55736 q^{10} +(0.500000 - 0.866025i) q^{11} +(2.35267 + 4.07494i) q^{13} +(0.708733 + 1.22756i) q^{14} +(-7.42666 + 12.8634i) q^{16} +2.69227 q^{17} +3.41747 q^{19} +(-2.55487 + 4.42516i) q^{20} +(1.36526 + 2.36469i) q^{22} +(3.48741 + 6.04038i) q^{23} +(2.06140 - 3.57046i) q^{25} -12.8480 q^{26} -2.83217 q^{28} +(2.09311 - 3.62537i) q^{29} +(-2.59311 - 4.49140i) q^{31} +(-10.8427 - 18.7802i) q^{32} +(-3.67564 + 6.36640i) q^{34} -0.486201 q^{35} +2.06874 q^{37} +(-4.66572 + 8.08126i) q^{38} +(-4.41875 - 7.65349i) q^{40} +(0.0865763 + 0.149955i) q^{41} +(1.13474 - 1.96543i) q^{43} -5.45571 q^{44} -19.0449 q^{46} +(-0.153863 + 0.266499i) q^{47} +(3.36526 + 5.82880i) q^{49} +(5.62869 + 9.74918i) q^{50} +(12.8355 - 22.2317i) q^{52} +1.89835 q^{53} -0.936586 q^{55} +(2.44917 - 4.24209i) q^{56} +(5.71527 + 9.89913i) q^{58} +(1.98741 + 3.44230i) q^{59} +(-2.25956 + 3.91367i) q^{61} +14.1610 q^{62} +29.5059 q^{64} +(2.20348 - 3.81654i) q^{65} +(-1.68823 - 2.92410i) q^{67} +(-7.34413 - 12.7204i) q^{68} +(0.663789 - 1.14972i) q^{70} -2.90367 q^{71} +9.52444 q^{73} +(-2.82436 + 4.89193i) q^{74} +(-9.32234 - 16.1468i) q^{76} +(-0.259560 - 0.449571i) q^{77} +(1.02178 - 1.76978i) q^{79} +13.9114 q^{80} -0.472796 q^{82} +(7.02970 - 12.1758i) q^{83} +(-1.26077 - 2.18372i) q^{85} +(3.09843 + 5.36664i) q^{86} +(4.71793 - 8.17169i) q^{88} -7.53751 q^{89} +2.44264 q^{91} +(19.0263 - 32.9545i) q^{92} +(-0.420126 - 0.727680i) q^{94} +(-1.60038 - 2.77193i) q^{95} +(-8.16710 + 14.1458i) q^{97} -18.3778 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 11 q^{4} + 4 q^{5} - q^{7} + 2 q^{10} + 4 q^{11} - 7 q^{13} + q^{14} - 17 q^{16} + 10 q^{17} + 18 q^{19} - 10 q^{20} - q^{22} + 14 q^{23} - 14 q^{25} - 44 q^{26} - 2 q^{28} - 6 q^{29}+ \cdots - 30 q^{98}+O(q^{100}) \) 8 * q + q^2 - 11 * q^4 + 4 * q^5 - q^7 + 2 * q^10 + 4 * q^11 - 7 * q^13 + q^14 - 17 * q^16 + 10 * q^17 + 18 * q^19 - 10 * q^20 - q^22 + 14 * q^23 - 14 * q^25 - 44 * q^26 - 2 * q^28 - 6 * q^29 + 2 * q^31 - 34 * q^32 - 16 * q^34 + 16 * q^35 + 6 * q^37 + 3 * q^38 - 12 * q^40 - 2 * q^41 + 21 * q^43 - 22 * q^44 + 4 * q^46 - 7 * q^47 + 15 * q^49 + 23 * q^50 + 10 * q^52 + 12 * q^53 + 8 * q^55 + 18 * q^56 + 21 * q^58 + 2 * q^59 - 15 * q^61 + 40 * q^62 + 32 * q^64 + 19 * q^65 - 14 * q^67 - 7 * q^68 + 38 * q^70 + 6 * q^71 + 44 * q^73 - 36 * q^74 - 42 * q^76 + q^77 - 11 * q^79 + 68 * q^80 - 34 * q^82 + 18 * q^83 - 13 * q^85 - 24 * q^86 + 12 * q^89 + 38 * q^91 + 67 * q^92 + 19 * q^94 - 30 * q^95 - 26 * q^97 - 30 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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