LMFDB - Embedded newform 1638.2.dm.c.415.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1638,2,Mod(415,1638)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1638, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1638.415"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.dm (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,6,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.752609431977984.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 15x^{10} + 90x^{8} - 247x^{6} + 270x^{4} + 21x^{2} + 49 $ x^12 - 15x^10 + 90x^8 - 247x^6 + 270x^4 + 21*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			415.1
Root			$-0.385124 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1638.415
Dual form			1638.2.dm.c.1117.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.25312 - 1.30084i) q^{5} +(-1.49160 - 2.18521i) q^{7} -1.00000i q^{8} +(1.30084 + 2.25312i) q^{10} +(-3.11915 + 1.80084i) q^{11} +(3.60168 - 0.167055i) q^{13} +(0.199160 + 2.63824i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.41647 - 2.45340i) q^{17} +(-1.15537 - 0.667055i) q^{19} -2.60168i q^{20} +3.60168 q^{22} +(1.46789 - 2.54247i) q^{23} +(0.884367 + 1.53177i) q^{25} +(-3.20267 - 1.65617i) q^{26} +(1.14664 - 2.38437i) q^{28} -8.97209 q^{29} +(-3.46410 + 2.00000i) q^{31} +(0.866025 - 0.500000i) q^{32} +2.83294i q^{34} +(0.518152 + 6.86387i) q^{35} +(-0.144674 - 0.0835276i) q^{37} +(0.667055 + 1.15537i) q^{38} +(-1.30084 + 2.25312i) q^{40} +3.03630i q^{41} +2.33411 q^{43} +(-3.11915 - 1.80084i) q^{44} +(-2.54247 + 1.46789i) q^{46} +(8.43580 + 4.87041i) q^{47} +(-2.55026 + 6.51891i) q^{49} -1.76873i q^{50} +(1.94551 + 3.03562i) q^{52} +(1.50000 + 2.59808i) q^{53} +9.37041 q^{55} +(-2.18521 + 1.49160i) q^{56} +(7.77006 + 4.48605i) q^{58} +(10.0232 - 5.78689i) q^{59} +(-2.01815 + 3.49554i) q^{61} +4.00000 q^{62} -1.00000 q^{64} +(-8.33233 - 4.30881i) q^{65} +(10.1679 - 5.87041i) q^{67} +(1.41647 - 2.45340i) q^{68} +(2.98320 - 6.20336i) q^{70} +5.76873i q^{71} +(-9.93411 + 5.73546i) q^{73} +(0.0835276 + 0.144674i) q^{74} -1.33411i q^{76} +(8.58773 + 4.12985i) q^{77} +(-3.37041 + 5.83773i) q^{79} +(2.25312 - 1.30084i) q^{80} +(1.51815 - 2.62952i) q^{82} +8.10051i q^{83} +7.37041i q^{85} +(-2.02140 - 1.16706i) q^{86} +(1.80084 + 3.11915i) q^{88} +(7.07288 + 4.08353i) q^{89} +(-5.73732 - 7.62123i) q^{91} +2.93579 q^{92} +(-4.87041 - 8.43580i) q^{94} +(1.73546 + 3.00591i) q^{95} +0.139148i q^{97} +(5.46804 - 4.37041i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4} + 12 q^{13} + 18 q^{14} - 6 q^{16} - 18 q^{17} + 12 q^{22} - 6 q^{25} - 12 q^{29} - 24 q^{35} + 6 q^{38} + 24 q^{43} - 18 q^{49} + 6 q^{52} + 18 q^{53} + 48 q^{55} + 6 q^{56} + 6 q^{61} + 48 q^{62}+ \cdots - 24 q^{95}+O(q^{100}) $ 12 * q + 6 * q^4 + 12 * q^13 + 18 * q^14 - 6 * q^16 - 18 * q^17 + 12 * q^22 - 6 * q^25 - 12 * q^29 - 24 * q^35 + 6 * q^38 + 24 * q^43 - 18 * q^49 + 6 * q^52 + 18 * q^53 + 48 * q^55 + 6 * q^56 + 6 * q^61 + 48 * q^62 - 12 * q^64 + 12 * q^65 + 18 * q^68 + 24 * q^77 + 24 * q^79 - 12 * q^82 + 6 * q^88 - 24 * q^91 + 6 * q^94 - 24 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−2.25312	−	1.30084i	−1.00763	−	0.581753i	−0.0971303	−	0.995272i	$-0.530966\pi$
$5$	−2.25312	−	1.30084i	−1.00763	−	0.581753i	−0.910496	+	0.413519i	$0.864300\pi$
$6$		0			0
$7$	−1.49160	−	2.18521i	−0.563772	−	0.825931i
$7$	−1.49160	−	2.18521i	−0.563772	−	0.825931i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	1.30084	+	2.25312i	0.411362	+	0.712499i
$11$	−3.11915	+	1.80084i	−0.940458	+	0.542974i	−0.890104	−	0.455758i	$-0.849368\pi$
$11$	−3.11915	+	1.80084i	−0.940458	+	0.542974i	−0.0503540	+	0.998731i	$0.516035\pi$
$12$		0			0
$13$	3.60168	−	0.167055i	0.998926	−	0.0463328i
$13$	3.60168	−	0.167055i	0.998926	−	0.0463328i
$14$	0.199160	+	2.63824i	0.0532279	+	0.705101i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.41647	−	2.45340i	−0.343545	−	0.595037i	0.641543	−	0.767087i	$-0.278294\pi$
$17$	−1.41647	−	2.45340i	−0.343545	−	0.595037i	−0.985088	+	0.172049i	$0.944961\pi$
$18$		0			0
$19$	−1.15537	−	0.667055i	−0.265061	−	0.153033i	0.361580	−	0.932341i	$-0.382237\pi$
$19$	−1.15537	−	0.667055i	−0.265061	−	0.153033i	−0.626641	+	0.779308i	$0.715571\pi$
$20$		−	2.60168i		−	0.581753i
$21$		0			0
$22$	3.60168			0.767881
$23$	1.46789	−	2.54247i	0.306077	−	0.530141i	−0.671423	−	0.741074i	$-0.734317\pi$
$23$	1.46789	−	2.54247i	0.306077	−	0.530141i	0.977501	+	0.210933i	$0.0676501\pi$
$24$		0			0
$25$	0.884367	+	1.53177i	0.176873	+	0.306354i
$26$	−3.20267	−	1.65617i	−0.628096	−	0.324801i
$27$		0			0
$28$	1.14664	−	2.38437i	0.216695	−	0.450603i
$29$	−8.97209			−1.66608			−0.833038	−	0.553216i	$-0.813400\pi$
$29$	−8.97209			−1.66608			−0.833038	+	0.553216i	$0.813400\pi$
$30$		0			0
$31$	−3.46410	+	2.00000i	−0.622171	+	0.359211i	−0.777714	−	0.628619i	$-0.783621\pi$
$31$	−3.46410	+	2.00000i	−0.622171	+	0.359211i	0.155543	+	0.987829i	$0.450287\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$			2.83294i			0.485846i
$35$	0.518152	+	6.86387i	0.0875836	+	1.16021i
$36$		0			0
$37$	−0.144674	−	0.0835276i	−0.0237843	−	0.0137319i	0.488061	−	0.872810i	$-0.337704\pi$
$37$	−0.144674	−	0.0835276i	−0.0237843	−	0.0137319i	−0.511845	+	0.859078i	$0.671038\pi$
$38$	0.667055	+	1.15537i	0.108211	+	0.187426i
$39$		0			0
$40$	−1.30084	+	2.25312i	−0.205681	+	0.356250i
$41$			3.03630i			0.474191i	0.971486	+	0.237095i	$0.0761954\pi$
$41$			3.03630i			0.474191i	−0.971486	+	0.237095i	$0.923805\pi$
$42$		0			0
$43$	2.33411			0.355948			0.177974	−	0.984035i	$-0.443046\pi$
$43$	2.33411			0.355948			0.177974	+	0.984035i	$0.443046\pi$
$44$	−3.11915	−	1.80084i	−0.470229	−	0.271487i
$45$		0			0
$46$	−2.54247	+	1.46789i	−0.374866	+	0.216429i
$47$	8.43580	+	4.87041i	1.23049	+	0.710423i	0.967132	−	0.254276i	$-0.0818371\pi$
$47$	8.43580	+	4.87041i	1.23049	+	0.710423i	0.263357	+	0.964699i	$0.415170\pi$
$48$		0			0
$49$	−2.55026	+	6.51891i	−0.364322	+	0.931273i
$50$		−	1.76873i		−	0.250137i
$51$		0			0
$52$	1.94551	+	3.03562i	0.269794	+	0.420964i
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	0.950464	−	0.310835i	$-0.100609\pi$
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	−0.744423	+	0.667708i	$0.767275\pi$
$54$		0			0
$55$	9.37041			1.26351
$56$	−2.18521	+	1.49160i	−0.292011	+	0.199323i
$57$		0			0
$58$	7.77006	+	4.48605i	1.02026	+	0.589047i
$59$	10.0232	−	5.78689i	1.30491	−	0.753388i	0.323666	−	0.946172i	$-0.395085\pi$
$59$	10.0232	−	5.78689i	1.30491	−	0.753388i	0.981241	+	0.192783i	$0.0617514\pi$
$60$		0			0
$61$	−2.01815	+	3.49554i	−0.258398	+	0.447558i	−0.965813	−	0.259240i	$-0.916528\pi$
$61$	−2.01815	+	3.49554i	−0.258398	+	0.447558i	0.707415	+	0.706798i	$0.249861\pi$
$62$	4.00000			0.508001
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−8.33233	−	4.30881i	−1.03350	−	0.534442i
$66$		0			0
$67$	10.1679	−	5.87041i	1.24220	−	0.717185i	0.272659	−	0.962111i	$-0.412097\pi$
$67$	10.1679	−	5.87041i	1.24220	−	0.717185i	0.969542	+	0.244926i	$0.0787635\pi$
$68$	1.41647	−	2.45340i	0.171773	−	0.297519i
$69$		0			0
$70$	2.98320	−	6.20336i	0.356561	−	0.741443i
$71$			5.76873i			0.684623i	0.939587	+	0.342311i	$0.111210\pi$
$71$			5.76873i			0.684623i	−0.939587	+	0.342311i	$0.888790\pi$
$72$		0			0
$73$	−9.93411	+	5.73546i	−1.16270	+	0.671285i	−0.951950	−	0.306255i	$-0.900924\pi$
$73$	−9.93411	+	5.73546i	−1.16270	+	0.671285i	−0.210751	+	0.977540i	$0.567591\pi$
$74$	0.0835276	+	0.144674i	0.00970988	+	0.0168180i
$75$		0			0
$76$		−	1.33411i		−	0.153033i
$77$	8.58773	+	4.12985i	0.978662	+	0.470640i
$78$		0			0
$79$	−3.37041	+	5.83773i	−0.379201	+	0.656796i	−0.990946	−	0.134259i	$-0.957134\pi$
$79$	−3.37041	+	5.83773i	−0.379201	+	0.656796i	0.611745	+	0.791055i	$0.290468\pi$
$80$	2.25312	−	1.30084i	0.251906	−	0.145438i
$81$		0			0
$82$	1.51815	−	2.62952i	0.167652	−	0.290381i
$83$			8.10051i			0.889147i	0.895742	+	0.444573i	$0.146645\pi$
$83$			8.10051i			0.889147i	−0.895742	+	0.444573i	$0.853355\pi$
$84$		0			0
$85$			7.37041i			0.799434i
$86$	−2.02140	−	1.16706i	−0.217973	−	0.125847i
$87$		0			0
$88$	1.80084	+	3.11915i	0.191970	+	0.332502i
$89$	7.07288	+	4.08353i	0.749723	+	0.432853i	0.825594	−	0.564265i	$-0.190840\pi$
$89$	7.07288	+	4.08353i	0.749723	+	0.432853i	−0.0758705	+	0.997118i	$0.524174\pi$
$90$		0			0
$91$	−5.73732	−	7.62123i	−0.601434	−	0.798922i
$92$	2.93579			0.306077
$93$		0			0
$94$	−4.87041	−	8.43580i	−0.502345	−	0.870087i
$95$	1.73546	+	3.00591i	0.178055	+	0.308400i
$96$		0			0
$97$			0.139148i			0.0141283i	0.999975	+	0.00706416i	$0.00224861\pi$
$97$			0.139148i			0.0141283i	−0.999975	+	0.00706416i	$0.997751\pi$
$98$	5.46804	−	4.37041i	0.552356	−	0.441478i
$99$		0			0
$100$	−0.884367	+	1.53177i	−0.0884367	+	0.153177i
$101$	1.78269	+	3.08771i	0.177384	+	0.307238i	0.940984	−	0.338452i	$-0.109903\pi$
$101$	1.78269	+	3.08771i	0.177384	+	0.307238i	−0.763600	+	0.645690i	$0.776570\pi$
$102$		0			0
$103$	−9.53747	+	16.5194i	−0.939755	+	1.62770i	−0.173827	+	0.984776i	$0.555613\pi$
$103$	−9.53747	+	16.5194i	−0.939755	+	1.62770i	−0.765928	+	0.642927i	$0.777720\pi$
$104$	−0.167055	−	3.60168i	−0.0163811	−	0.353174i
$105$		0			0
$106$		−	3.00000i		−	0.291386i
$107$	−4.03630	+	6.99108i	−0.390204	+	0.675853i	−0.992476	−	0.122437i	$-0.960929\pi$
$107$	−4.03630	+	6.99108i	−0.390204	+	0.675853i	0.602272	+	0.798291i	$0.294262\pi$
$108$		0			0
$109$	−11.1451	+	6.43462i	−1.06751	+	0.616325i	−0.927499	−	0.373825i	$-0.878046\pi$
$109$	−11.1451	+	6.43462i	−1.06751	+	0.616325i	−0.140007	+	0.990150i	$0.544713\pi$
$110$	−8.11502	−	4.68521i	−0.773736	−	0.446717i
$111$		0			0
$112$	2.63824	−	0.199160i	0.249291	−	0.0188189i
$113$	19.8800			1.87015			0.935075	−	0.354449i	$-0.115332\pi$
$113$	19.8800			1.87015			0.935075	+	0.354449i	$0.115332\pi$
$114$		0			0
$115$	−6.61469	+	3.81899i	−0.616823	+	0.356123i
$116$	−4.48605	−	7.77006i	−0.416519	−	0.721432i
$117$		0			0
$118$	−11.5738			−1.06545
$119$	−3.24838	+	6.75478i	−0.297779	+	0.619210i
$120$		0			0
$121$	0.986046	−	1.70788i	0.0896406	−	0.155262i
$122$	3.49554	−	2.01815i	0.316471	−	0.182715i
$123$		0			0
$124$	−3.46410	−	2.00000i	−0.311086	−	0.179605i
$125$			8.40672i			0.751920i
$126$		0			0
$127$	−10.0386			−0.890785			−0.445392	−	0.895335i	$-0.646936\pi$
$127$	−10.0386			−0.890785			−0.445392	+	0.895335i	$0.646936\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	5.06160	+	7.89770i	0.443932	+	0.692674i
$131$	4.05562	−	7.02454i	0.354341	−	0.613737i	−0.632664	−	0.774427i	$-0.718038\pi$
$131$	4.05562	−	7.02454i	0.354341	−	0.613737i	0.987005	+	0.160690i	$0.0513718\pi$
$132$		0			0
$133$	0.265702	+	3.51971i	0.0230393	+	0.305198i
$134$	−11.7408			−1.01425
$135$		0			0
$136$	−2.45340	+	1.41647i	−0.210378	+	0.121462i
$137$	−4.00934	+	2.31479i	−0.342541	+	0.197766i	−0.661395	−	0.750038i	$-0.730035\pi$
$137$	−4.00934	+	2.31479i	−0.342541	+	0.197766i	0.318854	+	0.947804i	$0.396702\pi$
$138$		0			0
$139$	−0.935789			−0.0793726			−0.0396863	−	0.999212i	$-0.512636\pi$
$139$	−0.935789			−0.0793726			−0.0396863	+	0.999212i	$0.512636\pi$
$140$	−5.68521	+	3.88067i	−0.480488	+	0.327976i
$141$		0			0
$142$	2.88437	−	4.99587i	0.242051	−	0.419244i
$143$	−10.9333	+	7.00712i	−0.914290	+	0.585964i
$144$		0			0
$145$	20.2152	+	11.6713i	1.67878	+	0.969245i
$146$	11.4709			0.949341
$147$		0			0
$148$		−	0.167055i		−	0.0137319i
$149$	−7.04871	−	4.06957i	−0.577453	−	0.333392i	0.182668	−	0.983175i	$-0.441527\pi$
$149$	−7.04871	−	4.06957i	−0.577453	−	0.333392i	−0.760120	+	0.649782i	$0.774860\pi$
$150$		0			0
$151$	17.3278	−	10.0042i	1.41011	−	0.814130i	0.414716	−	0.909951i	$-0.363881\pi$
$151$	17.3278	−	10.0042i	1.41011	−	0.814130i	0.995399	+	0.0958208i	$0.0305476\pi$
$152$	−0.667055	+	1.15537i	−0.0541053	+	0.0937132i
$153$		0			0
$154$	−5.37227	−	7.87041i	−0.432910	−	0.634216i
$155$	10.4067			0.835888
$156$		0			0
$157$	−10.6724	−	18.4852i	−0.851752	−	1.47528i	−0.879626	−	0.475666i	$-0.842207\pi$
$157$	−10.6724	−	18.4852i	−0.851752	−	1.47528i	0.0278743	−	0.999611i	$-0.491126\pi$
$158$	5.83773	−	3.37041i	0.464425	−	0.268136i
$159$		0			0
$160$	−2.60168			−0.205681
$161$	−7.74533	+	0.584693i	−0.610418	+	0.0460803i
$162$		0			0
$163$	−0.890194	−	0.513954i	−0.0697254	−	0.0402560i	0.464732	−	0.885451i	$-0.346151\pi$
$163$	−0.890194	−	0.513954i	−0.0697254	−	0.0402560i	−0.534457	+	0.845195i	$0.679484\pi$
$164$	−2.62952	+	1.51815i	−0.205331	+	0.118548i
$165$		0			0
$166$	4.05026	−	7.01525i	0.314361	−	0.544489i
$167$			5.96976i			0.461954i	0.972959	+	0.230977i	$0.0741922\pi$
$167$			5.96976i			0.461954i	−0.972959	+	0.230977i	$0.925808\pi$
$168$		0			0
$169$	12.9442	−	1.20336i	0.995707	−	0.0925660i
$170$	3.68521	−	6.38297i	0.282642	−	0.489551i
$171$		0			0
$172$	1.16706	+	2.02140i	0.0889871	+	0.154130i
$173$	−8.29108	+	14.3606i	−0.630359	+	1.09181i	0.357119	+	0.934059i	$0.383759\pi$
$173$	−8.29108	+	14.3606i	−0.630359	+	1.09181i	−0.987478	+	0.157756i	$0.949574\pi$
$174$		0			0
$175$	2.02811	−	4.21731i	0.153311	−	0.318799i
$176$		−	3.60168i		−	0.271487i
$177$		0			0
$178$	−4.08353	−	7.07288i	−0.306073	−	0.530135i
$179$	−9.37041	−	16.2300i	−0.700378	−	1.21309i	−0.968334	−	0.249659i	$-0.919682\pi$
$179$	−9.37041	−	16.2300i	−0.700378	−	1.21309i	0.267956	−	0.963431i	$-0.413652\pi$
$180$		0			0
$181$	−0.426228			−0.0316813			−0.0158406	−	0.999875i	$-0.505042\pi$
$181$	−0.426228			−0.0316813			−0.0158406	+	0.999875i	$0.505042\pi$
$182$	1.15804	+	9.46884i	0.0858400	+	0.701877i
$183$		0			0
$184$	−2.54247	−	1.46789i	−0.187433	−	0.108215i
$185$	0.217312	+	0.376395i	0.0159771	+	0.0276731i
$186$		0			0
$187$	8.83637	+	5.10168i	0.646179	+	0.373072i
$188$			9.74083i			0.710423i
$189$		0			0
$190$		−	3.47093i		−	0.251808i
$191$	−4.43462	+	7.68099i	−0.320878	+	0.555777i	−0.980669	−	0.195672i	$-0.937311\pi$
$191$	−4.43462	+	7.68099i	−0.320878	+	0.555777i	0.659791	+	0.751449i	$0.270645\pi$
$192$		0			0
$193$	−6.06945	+	3.50420i	−0.436888	+	0.252238i	−0.702277	−	0.711904i	$-0.747833\pi$
$193$	−6.06945	+	3.50420i	−0.436888	+	0.252238i	0.265388	+	0.964142i	$0.414500\pi$
$194$	0.0695739	−	0.120505i	0.00499511	−	0.00865179i
$195$		0			0
$196$	−6.92067	+	1.05087i	−0.494334	+	0.0750620i
$197$		−	17.8050i		−	1.26856i	−0.773105	−	0.634278i	$-0.781297\pi$
$197$		−	17.8050i		−	1.26856i	0.773105	−	0.634278i	$-0.218703\pi$
$198$		0			0
$199$	13.5545	+	23.4770i	0.960850	+	1.66424i	0.720374	+	0.693585i	$0.243970\pi$
$199$	13.5545	+	23.4770i	0.960850	+	1.66424i	0.240475	+	0.970655i	$0.422697\pi$
$200$	1.53177	−	0.884367i	0.108312	−	0.0625342i
$201$		0			0
$202$		−	3.56538i		−	0.250859i
$203$	13.3828	+	19.6059i	0.939287	+	1.37606i
$204$		0			0
$205$	3.94974	−	6.84116i	0.275862	−	0.477807i
$206$	16.5194	−	9.53747i	1.15096	−	0.664507i
$207$		0			0
$208$	−1.65617	+	3.20267i	−0.114834	+	0.222065i
$209$	4.80504			0.332371
$210$		0			0
$211$	22.6743			1.56096			0.780481	−	0.625179i	$-0.214974\pi$
$211$	22.6743			1.56096			0.780481	+	0.625179i	$0.214974\pi$
$212$	−1.50000	+	2.59808i	−0.103020	+	0.178437i
$213$		0			0
$214$	6.99108	−	4.03630i	0.477901	−	0.275916i
$215$	−5.25903	−	3.03630i	−0.358663	−	0.207074i
$216$		0			0
$217$	9.53747	+	4.58658i	0.647446	+	0.311357i
$218$	12.8692			0.871615
$219$		0			0
$220$	4.68521	+	8.11502i	0.315877	+	0.547114i
$221$	−5.51153	−	8.59974i	−0.370746	−	0.578481i
$222$		0			0
$223$			9.19496i			0.615740i	0.951428	+	0.307870i	$0.0996162\pi$
$223$			9.19496i			0.615740i	−0.951428	+	0.307870i	$0.900384\pi$
$224$	−2.38437	−	1.14664i	−0.159312	−	0.0766134i
$225$		0			0
$226$	−17.2166	−	9.93999i	−1.14523	−	0.661198i
$227$	11.7238	−	6.76873i	0.778135	−	0.449257i	−0.0576337	−	0.998338i	$-0.518356\pi$
$227$	11.7238	−	6.76873i	0.778135	−	0.449257i	0.835769	+	0.549081i	$0.185022\pi$
$228$		0			0
$229$	15.9407	+	9.20336i	1.05339	+	0.608175i	0.923597	−	0.383366i	$-0.125235\pi$
$229$	15.9407	+	9.20336i	1.05339	+	0.608175i	0.129794	+	0.991541i	$0.458569\pi$
$230$	7.63798			0.503634
$231$		0			0
$232$			8.97209i			0.589047i
$233$	−5.86505	+	10.1586i	−0.384232	+	0.665510i	−0.991662	−	0.128863i	$-0.958867\pi$
$233$	−5.86505	+	10.1586i	−0.384232	+	0.665510i	0.607430	+	0.794373i	$0.292200\pi$
$234$		0			0
$235$	−12.6713	−	21.9473i	−0.826581	−	1.43168i
$236$	10.0232	+	5.78689i	0.652453	+	0.376694i
$237$		0			0
$238$	6.19057	−	4.22562i	0.401275	−	0.273906i
$239$		−	11.1731i		−	0.722729i	−0.932425	−	0.361365i	$-0.882311\pi$
$239$		−	11.1731i		−	0.722729i	0.932425	−	0.361365i	$-0.117689\pi$
$240$		0			0
$241$	−12.7659	+	7.37041i	−0.822326	+	0.474770i	−0.851218	−	0.524812i	$-0.824135\pi$
$241$	−12.7659	+	7.37041i	−0.822326	+	0.474770i	0.0288920	+	0.999583i	$0.490802\pi$
$242$	−1.70788	+	0.986046i	−0.109787	+	0.0633855i
$243$		0			0
$244$	−4.03630			−0.258398
$245$	14.2261	−	11.3704i	0.908872	−	0.726429i
$246$		0			0
$247$	−4.27272	−	2.20951i	−0.271867	−	0.140588i
$248$	2.00000	+	3.46410i	0.127000	+	0.219971i
$249$		0			0
$250$	4.20336	−	7.28043i	0.265844	−	0.460455i
$251$	−22.9465			−1.44837			−0.724186	−	0.689605i	$-0.757784\pi$
$251$	−22.9465			−1.44837			−0.724186	+	0.689605i	$0.757784\pi$
$252$		0			0
$253$			10.5738i			0.664767i
$254$	8.69371	+	5.01932i	0.545492	+	0.314940i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.370413	+	0.641575i	−0.0231058	+	0.0400203i	−0.877347	−	0.479856i	$-0.840689\pi$
$257$	−0.370413	+	0.641575i	−0.0231058	+	0.0400203i	0.854241	+	0.519877i	$0.174022\pi$
$258$		0			0
$259$	0.0332708	+	0.440732i	0.00206735	+	0.0273858i
$260$	−0.434624	−	9.37041i	−0.0269542	−	0.581128i
$261$		0			0
$262$	−7.02454	+	4.05562i	−0.433978	+	0.250557i
$263$	−10.5042	−	18.1938i	−0.647717	−	1.12188i	−0.983667	−	0.179998i	$-0.942391\pi$
$263$	−10.5042	−	18.1938i	−0.647717	−	1.12188i	0.335950	−	0.941880i	$-0.390943\pi$
$264$		0			0
$265$		−	7.80504i		−	0.479460i
$266$	1.52975	−	3.18101i	0.0937950	−	0.195040i
$267$		0			0
$268$	10.1679	+	5.87041i	0.621101	+	0.358593i
$269$	−15.5587	−	26.9484i	−0.948628	−	1.64307i	−0.748319	−	0.663339i	$-0.769139\pi$
$269$	−15.5587	−	26.9484i	−0.948628	−	1.64307i	−0.200308	−	0.979733i	$-0.564194\pi$
$270$		0			0
$271$	1.73932	+	1.00420i	0.105656	+	0.0610007i	0.551897	−	0.833912i	$-0.313904\pi$
$271$	1.73932	+	1.00420i	0.105656	+	0.0610007i	−0.446241	+	0.894913i	$0.647237\pi$
$272$	2.83294			0.171773
$273$		0			0
$274$	4.62959			0.279684
$275$	−5.51694	−	3.18521i	−0.332684	−	0.192075i
$276$		0			0
$277$	−7.68404	−	13.3091i	−0.461689	−	0.799669i	0.537356	−	0.843356i	$-0.319423\pi$
$277$	−7.68404	−	13.3091i	−0.461689	−	0.799669i	−0.999045	+	0.0436862i	$0.986090\pi$
$278$	0.810417	+	0.467895i	0.0486056	+	0.0280625i
$279$		0			0
$280$	6.86387	−	0.518152i	0.410194	−	0.0309655i
$281$			16.6682i			0.994343i	0.867652	+	0.497171i	$0.165628\pi$
$281$			16.6682i			0.994343i	−0.867652	+	0.497171i	$0.834372\pi$
$282$		0			0
$283$	−8.90252	−	15.4196i	−0.529200	−	0.916601i	−0.999420	−	0.0340519i	$-0.989159\pi$
$283$	−8.90252	−	15.4196i	−0.529200	−	0.916601i	0.470220	−	0.882549i	$-0.344174\pi$
$284$	−4.99587	+	2.88437i	−0.296450	+	0.171156i
$285$		0			0
$286$	12.9721	−	0.601679i	0.767056	−	0.0355780i
$287$	6.63495	−	4.52895i	0.391649	−	0.267336i
$288$		0			0
$289$	4.48721	−	7.77208i	0.263954	−	0.457181i
$290$	−11.6713	−	20.2152i	−0.685360	−	1.18708i
$291$		0			0
$292$	−9.93411	−	5.73546i	−0.581350	−	0.335643i
$293$			26.4733i			1.54658i	0.634050	+	0.773292i	$0.281391\pi$
$293$			26.4733i			1.54658i	−0.634050	+	0.773292i	$0.718609\pi$
$294$		0			0
$295$	−30.1112			−1.75314
$296$	−0.0835276	+	0.144674i	−0.00485494	+	0.00840901i
$297$		0			0
$298$	4.06957	+	7.04871i	0.235744	+	0.408321i
$299$	4.86215	−	9.40237i	0.281186	−	0.543753i
$300$		0			0
$301$	−3.48156	−	5.10051i	−0.200674	−	0.293989i
$302$	−20.0084			−1.15135
$303$		0			0
$304$	1.15537	−	0.667055i	0.0662652	−	0.0382582i
$305$	9.09428	−	5.25058i	0.520737	−	0.300647i
$306$		0			0
$307$			23.2783i			1.32856i	0.747483	+	0.664281i	$0.231262\pi$
$307$			23.2783i			1.32856i	−0.747483	+	0.664281i	$0.768738\pi$
$308$	0.717312	+	9.50211i	0.0408726	+	0.541433i
$309$		0			0
$310$	−9.01248	−	5.20336i	−0.511875	−	0.295531i
$311$	8.27293	+	14.3291i	0.469115	+	0.812531i	0.999377	−	0.0353031i	$-0.0112397\pi$
$311$	8.27293	+	14.3291i	0.469115	+	0.812531i	−0.530262	+	0.847834i	$0.677906\pi$
$312$		0			0
$313$	5.01395	−	8.68442i	0.283405	−	0.490873i	−0.688816	−	0.724936i	$-0.741869\pi$
$313$	5.01395	−	8.68442i	0.283405	−	0.490873i	0.972221	+	0.234064i	$0.0752025\pi$
$314$			21.3448i			1.20456i
$315$		0			0
$316$	−6.74083			−0.379201
$317$	−18.5408	−	10.7045i	−1.04135	−	0.601226i	−0.121137	−	0.992636i	$-0.538654\pi$
$317$	−18.5408	−	10.7045i	−1.04135	−	0.601226i	−0.920216	+	0.391410i	$0.871988\pi$
$318$		0			0
$319$	27.9853	−	16.1573i	1.56687	−	0.904635i
$320$	2.25312	+	1.30084i	0.125953	+	0.0727191i
$321$		0			0
$322$	7.00000	+	3.36631i	0.390095	+	0.187597i
$323$			3.77946i			0.210295i
$324$		0			0
$325$	3.44110	+	5.36920i	0.190878	+	0.297830i
$326$	0.513954	+	0.890194i	0.0284653	+	0.0493033i
$327$		0			0
$328$	3.03630			0.167652
$329$	−1.93999	−	25.6987i	−0.106955	−	1.41681i
$330$		0			0
$331$	−31.0561	−	17.9302i	−1.70700	−	0.985535i	−0.938235	−	0.345998i	$-0.887540\pi$
$331$	−31.0561	−	17.9302i	−1.70700	−	0.985535i	−0.768761	−	0.639536i	$-0.779126\pi$
$332$	−7.01525	+	4.05026i	−0.385012	+	0.222287i
$333$		0			0
$334$	2.98488	−	5.16997i	0.163325	−	0.282888i
$335$	−30.5459			−1.66890
$336$		0			0
$337$	6.73850			0.367069			0.183535	−	0.983013i	$-0.441246\pi$
$337$	6.73850			0.367069			0.183535	+	0.983013i	$0.441246\pi$
$338$	−11.8117	−	5.42995i	−0.642470	−	0.295351i
$339$		0			0
$340$	−6.38297	+	3.68521i	−0.346165	+	0.199858i
$341$	7.20336	−	12.4766i	0.390084	−	0.675645i
$342$		0			0
$343$	18.0491	−	4.15077i	0.974561	−	0.224121i
$344$		−	2.33411i		−	0.125847i
$345$		0			0
$346$	14.3606	−	8.29108i	0.772029	−	0.445731i
$347$	17.2869	+	29.9418i	0.928009	+	1.60736i	0.786650	+	0.617400i	$0.211814\pi$
$347$	17.2869	+	29.9418i	0.928009	+	1.60736i	0.141359	+	0.989958i	$0.454853\pi$
$348$		0			0
$349$			21.7771i			1.16570i	0.812579	+	0.582852i	$0.198063\pi$
$349$			21.7771i			1.16570i	−0.812579	+	0.582852i	$0.801937\pi$
$350$	−3.86505	+	2.63824i	−0.206596	+	0.141020i
$351$		0			0
$352$	−1.80084	+	3.11915i	−0.0959851	+	0.166251i
$353$	−17.6244	+	10.1755i	−0.938052	+	0.541585i	−0.889349	−	0.457229i	$-0.848842\pi$
$353$	−17.6244	+	10.1755i	−0.938052	+	0.541585i	−0.0487029	+	0.998813i	$0.515509\pi$
$354$		0			0
$355$	7.50420	−	12.9977i	0.398281	−	0.689844i
$356$			8.16706i			0.432853i
$357$		0			0
$358$			18.7408i			0.990483i
$359$	−1.24040	−	0.716146i	−0.0654659	−	0.0377968i	0.466910	−	0.884305i	$-0.345367\pi$
$359$	−1.24040	−	0.716146i	−0.0654659	−	0.0377968i	−0.532376	+	0.846508i	$0.678701\pi$
$360$		0			0
$361$	−8.61007	−	14.9131i	−0.453162	−	0.784899i
$362$	0.369125	+	0.213114i	0.0194008	+	0.0112010i
$363$		0			0
$364$	3.73152	−	8.77928i	0.195585	−	0.460159i
$365$	29.8437			1.56209
$366$		0			0
$367$	−12.1755	−	21.0885i	−0.635553	−	1.10081i	−0.986398	−	0.164377i	$-0.947439\pi$
$367$	−12.1755	−	21.0885i	−0.635553	−	1.10081i	0.350844	−	0.936434i	$-0.385895\pi$
$368$	1.46789	+	2.54247i	0.0765193	+	0.132535i
$369$		0			0
$370$		−	0.434624i		−	0.0225950i
$371$	3.43993	−	7.15310i	0.178592	−	0.371371i
$372$		0			0
$373$	−15.9763	+	27.6717i	−0.827221	+	1.43279i	0.0729891	+	0.997333i	$0.476746\pi$
$373$	−15.9763	+	27.6717i	−0.827221	+	1.43279i	−0.900210	+	0.435456i	$0.856587\pi$
$374$	−5.10168	−	8.83637i	−0.263802	−	0.456918i
$375$		0			0
$376$	4.87041	−	8.43580i	0.251172	−	0.435043i
$377$	−32.3146	+	1.49883i	−1.66429	+	0.0771939i
$378$		0			0
$379$		−	2.79664i		−	0.143654i	−0.997417	−	0.0718269i	$-0.977117\pi$
$379$		−	2.79664i		−	0.143654i	0.997417	−	0.0718269i	$-0.0228829\pi$
$380$	−1.73546	+	3.00591i	−0.0890274	+	0.154200i
$381$		0			0
$382$	7.68099	−	4.43462i	0.392994	−	0.226895i
$383$	−8.52487	−	4.92184i	−0.435600	−	0.251494i	0.266129	−	0.963937i	$-0.414255\pi$
$383$	−8.52487	−	4.92184i	−0.435600	−	0.251494i	−0.701730	+	0.712443i	$0.747589\pi$
$384$		0			0
$385$	−13.9769	−	20.4763i	−0.712329	−	1.04357i
$386$	7.00840			0.356718
$387$		0			0
$388$	−0.120505	+	0.0695739i	−0.00611774	+	0.00353208i
$389$	8.19057	+	14.1865i	0.415278	+	0.719283i	0.995458	−	0.0952056i	$-0.0303508\pi$
$389$	8.19057	+	14.1865i	0.415278	+	0.719283i	−0.580179	+	0.814489i	$0.697018\pi$
$390$		0			0
$391$	−8.31693			−0.420605
$392$	6.51891	+	2.55026i	0.329255	+	0.128807i
$393$		0			0
$394$	−8.90252	+	15.4196i	−0.448502	+	0.776829i
$395$	15.1879	−	8.76873i	0.764186	−	0.441203i
$396$		0			0
$397$	−4.71379	−	2.72151i	−0.236579	−	0.136589i	0.377025	−	0.926203i	$-0.376947\pi$
$397$	−4.71379	−	2.72151i	−0.236579	−	0.136589i	−0.613603	+	0.789615i	$0.710281\pi$
$398$		−	27.1089i		−	1.35885i
$399$		0			0
$400$	−1.76873			−0.0884367
$401$	−15.2214	−	8.78805i	−0.760118	−	0.438854i	0.0692201	−	0.997601i	$-0.477949\pi$
$401$	−15.2214	−	8.78805i	−0.760118	−	0.438854i	−0.829338	+	0.558747i	$0.811282\pi$
$402$		0			0
$403$	−12.1425	+	7.78205i	−0.604860	+	0.387652i
$404$	−1.78269	+	3.08771i	−0.0886920	+	0.153619i
$405$		0			0
$406$	−1.78689	−	23.6706i	−0.0886817	−	1.17475i
$407$	0.601679			0.0298241
$408$		0			0
$409$	−16.4618	+	9.50420i	−0.813981	+	0.469952i	−0.848337	−	0.529457i	$-0.822396\pi$
$409$	−16.4618	+	9.50420i	−0.813981	+	0.469952i	0.0343552	+	0.999410i	$0.489062\pi$
$410$	−6.84116	+	3.94974i	−0.337861	+	0.195064i
$411$		0			0
$412$	−19.0749			−0.939755
$413$	−27.5961	−	13.2710i	−1.35792	−	0.653023i
$414$		0			0
$415$	10.5375	−	18.2514i	0.517264	−	0.895928i
$416$	3.03562	−	1.94551i	0.148833	−	0.0953867i
$417$		0			0
$418$	−4.16128	−	2.40252i	−0.203535	−	0.117511i
$419$	−5.48165			−0.267796			−0.133898	−	0.990995i	$-0.542750\pi$
$419$	−5.48165			−0.267796			−0.133898	+	0.990995i	$0.542750\pi$
$420$		0			0
$421$		−	3.16472i		−	0.154239i	−0.997022	−	0.0771196i	$-0.975428\pi$
$421$		−	3.16472i		−	0.154239i	0.997022	−	0.0771196i	$-0.0245723\pi$
$422$	−19.6365	−	11.3371i	−0.955890	−	0.551883i
$423$		0			0
$424$	2.59808	−	1.50000i	0.126174	−	0.0728464i
$425$	2.50536	−	4.33942i	0.121528	−	0.210493i
$426$		0			0
$427$	10.6488	−	0.803872i	0.515329	−	0.0389021i
$428$	−8.07261			−0.390204
$429$		0			0
$430$	3.03630	+	5.25903i	0.146424	+	0.253613i
$431$	13.3688	−	7.71848i	0.643952	−	0.371786i	−0.142183	−	0.989840i	$-0.545412\pi$
$431$	13.3688	−	7.71848i	0.643952	−	0.371786i	0.786135	+	0.618054i	$0.212079\pi$
$432$		0			0
$433$	13.9419			0.670003			0.335001	−	0.942218i	$-0.391263\pi$
$433$	13.9419			0.670003			0.335001	+	0.942218i	$0.391263\pi$
$434$	−5.96640	−	8.74083i	−0.286396	−	0.419573i
$435$		0			0
$436$	−11.1451	−	6.43462i	−0.533753	−	0.308163i
$437$	−3.39193	+	1.95833i	−0.162258	+	0.0936798i
$438$		0			0
$439$	13.6936	−	23.7180i	0.653560	−	1.13200i	−0.328693	−	0.944437i	$-0.606608\pi$
$439$	13.6936	−	23.7180i	0.653560	−	1.13200i	0.982253	−	0.187562i	$-0.0600586\pi$
$440$		−	9.37041i		−	0.446717i
$441$		0			0
$442$	0.473258	+	10.2034i	0.0225106	+	0.485324i
$443$	12.0556	−	20.8809i	0.572780	−	0.992084i	−0.423499	−	0.905896i	$-0.639198\pi$
$443$	12.0556	−	20.8809i	0.572780	−	0.992084i	0.996279	−	0.0861872i	$-0.0274683\pi$
$444$		0			0
$445$	−10.6240	−	18.4014i	−0.503627	−	0.872308i
$446$	4.59748	−	7.96307i	0.217697	−	0.377062i
$447$		0			0
$448$	1.49160	+	2.18521i	0.0704715	+	0.103241i
$449$		−	2.59095i		−	0.122275i	−0.998129	−	0.0611373i	$-0.980527\pi$
$449$		−	2.59095i		−	0.122275i	0.998129	−	0.0611373i	$-0.0194728\pi$
$450$		0			0
$451$	−5.46789	−	9.47067i	−0.257473	−	0.445957i
$452$	9.93999	+	17.2166i	0.467538	+	0.809799i
$453$		0			0
$454$	−13.5375			−0.635345
$455$	3.01286	+	24.6349i	0.141245	+	1.15490i
$456$		0			0
$457$	−9.06607	−	5.23430i	−0.424093	−	0.244850i	0.272734	−	0.962089i	$-0.412072\pi$
$457$	−9.06607	−	5.23430i	−0.424093	−	0.244850i	−0.696827	+	0.717239i	$0.745405\pi$
$458$	−9.20336	−	15.9407i	−0.430045	−	0.744859i
$459$		0			0
$460$	−6.61469	−	3.81899i	−0.308411	−	0.178061i
$461$		−	30.0168i		−	1.39802i	−0.715111	−	0.699011i	$-0.753624\pi$
$461$		−	30.0168i		−	1.39802i	0.715111	−	0.699011i	$-0.246376\pi$
$462$		0			0
$463$		−	19.4649i		−	0.904609i	−0.891864	−	0.452304i	$-0.850602\pi$
$463$		−	19.4649i		−	0.904609i	0.891864	−	0.452304i	$-0.149398\pi$
$464$	4.48605	−	7.77006i	0.208259	−	0.360716i
$465$		0			0
$466$	10.1586	−	5.86505i	0.470586	−	0.271693i
$467$	−0.150069	+	0.259927i	−0.00694437	+	0.0120280i	−0.869477	−	0.493974i	$-0.835544\pi$
$467$	−0.150069	+	0.259927i	−0.00694437	+	0.0120280i	0.862532	+	0.506002i	$0.168877\pi$
$468$		0			0
$469$	−27.9944	−	13.4626i	−1.29266	−	0.621643i
$470$			25.3425i			1.16896i
$471$		0			0
$472$	−5.78689	−	10.0232i	−0.266363	−	0.461354i
$473$	−7.28043	+	4.20336i	−0.334755	+	0.193271i
$474$		0			0
$475$		−	2.35969i		−	0.108270i
$476$	−7.47400	+	0.564211i	−0.342570	+	0.0258605i
$477$		0			0
$478$	−5.58656	+	9.67621i	−0.255523	+	0.442579i
$479$	−20.4248	+	11.7922i	−0.933232	+	0.538802i	−0.887832	−	0.460167i	$-0.847789\pi$
$479$	−20.4248	+	11.7922i	−0.933232	+	0.538802i	−0.0453996	+	0.998969i	$0.514456\pi$
$480$		0			0
$481$	−0.535023	−	0.276671i	−0.0243950	−	0.0126151i
$482$	14.7408			0.671426
$483$		0			0
$484$	1.97209			0.0896406
$485$	0.181009	−	0.313517i	0.00821919	−	0.0142361i
$486$		0			0
$487$	29.6544	−	17.1210i	1.34377	−	0.775826i	0.356412	−	0.934329i	$-0.384000\pi$
$487$	29.6544	−	17.1210i	1.34377	−	0.775826i	0.987359	+	0.158502i	$0.0506666\pi$
$488$	3.49554	+	2.01815i	0.158236	+	0.0913574i
$489$		0			0
$490$	−18.0054	+	2.73402i	−0.813399	+	0.123510i
$491$	39.7553			1.79413			0.897065	−	0.441898i	$-0.145695\pi$
$491$	39.7553			1.79413			0.897065	+	0.441898i	$0.145695\pi$
$492$		0			0
$493$	12.7087	+	22.0122i	0.572372	+	0.991377i
$494$	2.59553	+	4.04985i	0.116778	+	0.182211i
$495$		0			0
$496$		−	4.00000i		−	0.179605i
$497$	12.6059	−	8.60465i	0.565451	−	0.385971i
$498$		0			0
$499$	10.6091	+	6.12519i	0.474931	+	0.274201i	0.718301	−	0.695732i	$-0.244920\pi$
$499$	10.6091	+	6.12519i	0.474931	+	0.274201i	−0.243371	+	0.969933i	$0.578253\pi$
$500$	−7.28043	+	4.20336i	−0.325591	+	0.187980i
$501$		0			0
$502$	19.8723	+	11.4733i	0.886943	+	0.512077i
$503$	−2.12842			−0.0949016			−0.0474508	−	0.998874i	$-0.515110\pi$
$503$	−2.12842			−0.0949016			−0.0474508	+	0.998874i	$0.515110\pi$
$504$		0			0
$505$		−	9.27596i		−	0.412775i
$506$	5.28689	−	9.15715i	0.235031	−	0.407085i
$507$		0			0
$508$	−5.01932	−	8.69371i	−0.222696	−	0.385721i
$509$	−29.1741	−	16.8437i	−1.29312	−	0.746583i	−0.313913	−	0.949452i	$-0.601640\pi$
$509$	−29.1741	−	16.8437i	−1.29312	−	0.746583i	−0.979206	+	0.202869i	$0.934973\pi$
$510$		0			0
$511$	27.3509	+	13.1531i	1.20993	+	0.581858i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	0.641575	−	0.370413i	0.0282987	−	0.0163382i
$515$	42.9781	−	24.8134i	1.89384	−	1.09341i
$516$		0			0
$517$	−35.0833			−1.54296
$518$	0.191553	−	0.398321i	0.00841635	−	0.0175012i
$519$		0			0
$520$	−4.30881	+	8.33233i	−0.188954	+	0.365397i
$521$	−0.130752	−	0.226469i	−0.00572835	−	0.00992180i	0.863147	−	0.504953i	$-0.168490\pi$
$521$	−0.130752	−	0.226469i	−0.00572835	−	0.00992180i	−0.868875	+	0.495031i	$0.835157\pi$
$522$		0			0
$523$	−5.23966	+	9.07536i	−0.229114	+	0.396838i	−0.957546	−	0.288281i	$-0.906916\pi$
$523$	−5.23966	+	9.07536i	−0.229114	+	0.396838i	0.728432	+	0.685119i	$0.240250\pi$
$524$	8.11124			0.354341
$525$		0			0
$526$			21.0084i			0.916010i
$527$	9.81361	+	5.66589i	0.427488	+	0.246810i
$528$		0			0
$529$	7.19057	+	12.4544i	0.312633	+	0.541497i
$530$	−3.90252	+	6.75936i	−0.169515	+	0.293608i
$531$		0			0
$532$	−2.91531	+	1.98996i	−0.126395	+	0.0862757i
$533$	0.507230	+	10.9358i	0.0219706	+	0.473682i
$534$		0			0
$535$	18.1886	−	10.5012i	0.786360	−	0.454005i
$536$	−5.87041	−	10.1679i	−0.253563	−	0.439184i
$537$		0			0
$538$			31.1173i			1.34156i
$539$	−3.78489	−	24.9260i	−0.163027	−	1.07364i
$540$		0			0
$541$	−18.8112	−	10.8607i	−0.808757	−	0.466936i	0.0377670	−	0.999287i	$-0.487976\pi$
$541$	−18.8112	−	10.8607i	−0.808757	−	0.466936i	−0.846524	+	0.532350i	$0.821309\pi$
$542$	−1.00420	−	1.73932i	−0.0431340	−	0.0747103i
$543$		0			0
$544$	−2.45340	−	1.41647i	−0.105189	−	0.0607308i
$545$	33.4817			1.43420
$546$		0			0
$547$	−33.3593			−1.42634			−0.713170	−	0.700991i	$-0.752741\pi$
$547$	−33.3593			−1.42634			−0.713170	+	0.700991i	$0.752741\pi$
$548$	−4.00934	−	2.31479i	−0.171270	−	0.0988831i
$549$		0			0
$550$	3.18521	+	5.51694i	0.135818	+	0.235243i
$551$	10.3661	+	5.98488i	0.441611	+	0.254964i
$552$		0			0
$553$	17.7840	−	1.34251i	0.756251	−	0.0570892i
$554$			15.3681i			0.652927i
$555$		0			0
$556$	−0.467895	−	0.810417i	−0.0198432	−	0.0343694i
$557$	−33.2612	+	19.2034i	−1.40932	+	0.813672i	−0.995323	−	0.0966049i	$-0.969202\pi$
$557$	−33.2612	+	19.2034i	−1.40932	+	0.813672i	−0.413999	+	0.910277i	$0.635868\pi$
$558$		0			0
$559$	8.40672	−	0.389925i	0.355566	−	0.0164921i
$560$	−6.20336	−	2.98320i	−0.262140	−	0.126063i
$561$		0			0
$562$	8.33411	−	14.4351i	0.351553	−	0.608908i
$563$	1.93346	+	3.34885i	0.0814856	+	0.141137i	0.903888	−	0.427769i	$-0.140700\pi$
$563$	1.93346	+	3.34885i	0.0814856	+	0.141137i	−0.822403	+	0.568906i	$0.807367\pi$
$564$		0			0
$565$	−44.7920	−	25.8607i	−1.88441	−	1.08797i
$566$			17.8050i			0.748402i
$567$		0			0
$568$	5.76873			0.242051
$569$	−13.8371	+	23.9666i	−0.580083	+	1.00473i	0.415386	+	0.909645i	$0.363647\pi$
$569$	−13.8371	+	23.9666i	−0.580083	+	1.00473i	−0.995469	+	0.0950882i	$0.969687\pi$
$570$		0			0
$571$	20.0470	+	34.7225i	0.838942	+	1.45309i	0.890780	+	0.454435i	$0.150159\pi$
$571$	20.0470	+	34.7225i	0.838942	+	1.45309i	−0.0518379	+	0.998656i	$0.516508\pi$
$572$	−11.5350	−	5.96498i	−0.482303	−	0.249408i
$573$		0			0
$574$	−8.01051	+	0.604711i	−0.334352	+	0.0252402i
$575$	5.19263			0.216548
$576$		0			0
$577$	0.352227	−	0.203358i	0.0146634	−	0.00846592i	−0.492650	−	0.870227i	$-0.663972\pi$
$577$	0.352227	−	0.203358i	0.0146634	−	0.00846592i	0.507314	+	0.861761i	$0.330639\pi$
$578$	−7.77208	+	4.48721i	−0.323276	+	0.186643i
$579$		0			0
$580$			23.3425i			0.969245i
$581$	17.7013	−	12.0827i	0.734374	−	0.501276i
$582$		0			0
$583$	−9.35744	−	5.40252i	−0.387545	−	0.223749i
$584$	5.73546	+	9.93411i	0.237335	+	0.411077i
$585$		0			0
$586$	13.2366	−	22.9265i	0.546800	−	0.947086i
$587$		−	22.0131i		−	0.908576i	−0.890855	−	0.454288i	$-0.849894\pi$
$587$		−	22.0131i		−	0.908576i	0.890855	−	0.454288i	$-0.150106\pi$
$588$		0			0
$589$	5.33644			0.219884
$590$	26.0771	+	15.0556i	1.07358	+	0.619830i
$591$		0			0
$592$	0.144674	−	0.0835276i	0.00594607	−	0.00343296i
$593$	27.0080	+	15.5931i	1.10909	+	0.640331i	0.938593	−	0.345027i	$-0.112130\pi$
$593$	27.0080	+	15.5931i	1.10909	+	0.640331i	0.170494	+	0.985359i	$0.445464\pi$
$594$		0			0
$595$	16.1059	−	10.9937i	0.660277	−	0.450698i
$596$		−	8.13915i		−	0.333392i
$597$		0			0
$598$	−8.91194	+	5.71162i	−0.364436	+	0.233565i
$599$	−3.17009	−	5.49075i	−0.129526	−	0.224346i	0.793967	−	0.607961i	$-0.208012\pi$
$599$	−3.17009	−	5.49075i	−0.129526	−	0.224346i	−0.923493	+	0.383615i	$0.874679\pi$
$600$		0			0
$601$	−23.5566			−0.960893			−0.480447	−	0.877024i	$-0.659525\pi$
$601$	−23.5566			−0.960893			−0.480447	+	0.877024i	$0.659525\pi$
$602$	0.464862	+	6.15795i	0.0189464	+	0.250979i
$603$		0			0
$604$	17.3278	+	10.0042i	0.705057	+	0.407065i
$605$	−4.44336	+	2.56538i	−0.180648	+	0.104297i
$606$		0			0
$607$	−8.01932	+	13.8899i	−0.325494	+	0.563772i	−0.981612	−	0.190886i	$-0.938864\pi$
$607$	−8.01932	+	13.8899i	−0.325494	+	0.563772i	0.656118	+	0.754658i	$0.272197\pi$
$608$	−1.33411			−0.0541053
$609$		0			0
$610$	−10.5012			−0.425180
$611$	31.1967	+	16.1324i	1.26208	+	0.652648i
$612$		0			0
$613$	−7.37710	+	4.25917i	−0.297958	+	0.172026i	−0.641525	−	0.767102i	$-0.721698\pi$
$613$	−7.37710	+	4.25917i	−0.297958	+	0.172026i	0.343567	+	0.939128i	$0.388365\pi$
$614$	11.6391	−	20.1596i	0.469718	−	0.813575i
$615$		0			0
$616$	4.12985	−	8.58773i	0.166396	−	0.346009i
$617$		−	1.40905i		−	0.0567261i	−0.999598	−	0.0283631i	$-0.990971\pi$
$617$		−	1.40905i		−	0.0567261i	0.999598	−	0.0283631i	$-0.00902945\pi$
$618$		0			0
$619$	−39.3641	+	22.7269i	−1.58218	+	0.913470i	−0.587635	+	0.809126i	$0.699941\pi$
$619$	−39.3641	+	22.7269i	−1.58218	+	0.913470i	−0.994541	+	0.104344i	$0.966726\pi$
$620$	5.20336	+	9.01248i	0.208972	+	0.361950i
$621$		0			0
$622$		−	16.5459i		−	0.663429i
$623$	−1.62655	−	21.5467i	−0.0651665	−	0.863250i
$624$		0			0
$625$	15.3576	−	26.6002i	0.614305	−	1.06401i
$626$	−8.68442	+	5.01395i	−0.347099	+	0.200398i
$627$		0			0
$628$	10.6724	−	18.4852i	0.425876	−	0.737639i
$629$			0.473258i			0.0188700i
$630$		0			0
$631$			35.2313i			1.40253i	0.712898	+	0.701267i	$0.247382\pi$
$631$			35.2313i			1.40253i	−0.712898	+	0.701267i	$0.752618\pi$
$632$	5.83773	+	3.37041i	0.232212	+	0.134068i
$633$		0			0
$634$	10.7045	+	18.5408i	0.425131	+	0.736348i
$635$	22.6182	+	13.0587i	0.897578	+	0.518217i
$636$		0			0
$637$	−8.09619	+	23.9051i	−0.320783	+	0.947153i
$638$	−32.3146			−1.27935
$639$		0			0
$640$	−1.30084	−	2.25312i	−0.0514202	−	0.0890624i
$641$	11.1168	+	19.2549i	0.439087	+	0.760521i	0.997619	−	0.0689616i	$-0.0219686\pi$
$641$	11.1168	+	19.2549i	0.439087	+	0.760521i	−0.558532	+	0.829483i	$0.688635\pi$
$642$		0			0
$643$		−	3.64031i		−	0.143560i	−0.997420	−	0.0717800i	$-0.977132\pi$
$643$		−	3.64031i		−	0.143560i	0.997420	−	0.0717800i	$-0.0228679\pi$
$644$	−4.37902	−	6.41531i	−0.172558	−	0.252799i
$645$		0			0
$646$	1.88973	−	3.27311i	0.0743505	−	0.128779i
$647$	7.02791	+	12.1727i	0.276296	+	0.478558i	0.970461	−	0.241257i	$-0.0775598\pi$
$647$	7.02791	+	12.1727i	0.276296	+	0.478558i	−0.694166	+	0.719815i	$0.744226\pi$
$648$		0			0
$649$	−20.8425	+	36.1003i	−0.818140	+	1.41706i
$650$	−0.295476	−	6.37041i	−0.0115895	−	0.249868i
$651$		0			0
$652$		−	1.02791i		−	0.0402560i
$653$	−8.62403	+	14.9373i	−0.337484	+	0.584540i	−0.983959	−	0.178396i	$-0.942909\pi$
$653$	−8.62403	+	14.9373i	−0.337484	+	0.584540i	0.646475	+	0.762936i	$0.276243\pi$
$654$		0			0
$655$	−18.2756	+	10.5514i	−0.714087	+	0.412278i
$656$	−2.62952	−	1.51815i	−0.102665	−	0.0592739i
$657$		0			0
$658$	−11.1693	+	23.2257i	−0.435423	+	0.905432i
$659$	21.6999			0.845307			0.422653	−	0.906291i	$-0.361099\pi$
$659$	21.6999			0.845307			0.422653	+	0.906291i	$0.361099\pi$
$660$		0			0
$661$	20.0758	−	11.5908i	0.780857	−	0.450828i	−0.0558767	−	0.998438i	$-0.517795\pi$
$661$	20.0758	−	11.5908i	0.780857	−	0.450828i	0.836734	+	0.547609i	$0.184462\pi$
$662$	17.9302	+	31.0561i	0.696878	+	1.20703i
$663$		0			0
$664$	8.10051			0.314361
$665$	3.97992	−	8.27596i	0.154335	−	0.320928i
$666$		0			0
$667$	−13.1701	+	22.8113i	−0.509948	+	0.883256i
$668$	−5.16997	+	2.98488i	−0.200032	+	0.115489i
$669$		0			0
$670$	26.4535	+	15.2729i	1.02199	+	0.590045i
$671$		−	14.5375i		−	0.561213i
$672$		0			0
$673$	7.56538			0.291624			0.145812	−	0.989312i	$-0.453421\pi$
$673$	7.56538			0.291624			0.145812	+	0.989312i	$0.453421\pi$
$674$	−5.83571	−	3.36925i	−0.224783	−	0.129779i
$675$		0			0
$676$	7.51423	+	10.6083i	0.289009	+	0.408012i
$677$	−10.4581	+	18.1140i	−0.401939	+	0.696179i	−0.993960	−	0.109744i	$-0.964997\pi$
$677$	−10.4581	+	18.1140i	−0.401939	+	0.696179i	0.592021	+	0.805923i	$0.298330\pi$
$678$		0			0
$679$	0.304067	−	0.207553i	0.0116690	−	0.00796515i
$680$	7.37041			0.282642
$681$		0			0
$682$	−12.4766	+	7.20336i	−0.477753	+	0.275831i
$683$	17.0981	−	9.87158i	0.654240	−	0.377725i	−0.135839	−	0.990731i	$-0.543373\pi$
$683$	17.0981	−	9.87158i	0.654240	−	0.377725i	0.790079	+	0.613005i	$0.210040\pi$
$684$		0			0
$685$	12.0447			0.460204
$686$	−17.7064	−	5.42989i	−0.676033	−	0.207314i
$687$		0			0
$688$	−1.16706	+	2.02140i	−0.0444936	+	0.0770651i
$689$	5.83654	+	9.10685i	0.222354	+	0.346944i
$690$		0			0
$691$	−23.4013	−	13.5107i	−0.890226	−	0.513972i	−0.0162096	−	0.999869i	$-0.505160\pi$
$691$	−23.4013	−	13.5107i	−0.890226	−	0.513972i	−0.874016	+	0.485896i	$0.838493\pi$
$692$	−16.5822			−0.630359
$693$		0			0
$694$		−	34.5738i		−	1.31240i
$695$	2.10845	+	1.21731i	0.0799779	+	0.0461753i
$696$		0			0
$697$	7.44927	−	4.30084i	0.282161	−	0.162906i
$698$	10.8886	−	18.8595i	0.412138	−	0.713844i
$699$		0			0
$700$	4.66635	−	0.352262i	0.176372	−	0.0133142i
$701$	−46.3956			−1.75234			−0.876169	−	0.482004i	$-0.839909\pi$
$701$	−46.3956			−1.75234			−0.876169	+	0.482004i	$0.839909\pi$
$702$		0			0
$703$	0.111435	+	0.193011i	0.00420285	+	0.00727955i
$704$	3.11915	−	1.80084i	0.117557	−	0.0678717i
$705$		0			0
$706$	20.3509			0.765916
$707$	4.08822	−	8.50117i	0.153753	−	0.319719i
$708$		0			0
$709$	−35.7795	−	20.6573i	−1.34373	−	0.775801i	−0.356375	−	0.934343i	$-0.615987\pi$
$709$	−35.7795	−	20.6573i	−1.34373	−	0.775801i	−0.987352	+	0.158542i	$0.949321\pi$
$710$	−12.9977	+	7.50420i	−0.487793	+	0.281628i
$711$		0			0
$712$	4.08353	−	7.07288i	0.153037	−	0.265067i
$713$			11.7432i			0.439785i
$714$		0			0
$715$	33.7492	−	1.56538i	1.26215	−	0.0585417i
$716$	9.37041	−	16.2300i	0.350189	−	0.606545i
$717$		0			0
$718$	0.716146	+	1.24040i	0.0267263	+	0.0462914i
$719$	−14.9721	+	25.9324i	−0.558365	+	0.967116i	0.439268	+	0.898356i	$0.355238\pi$
$719$	−14.9721	+	25.9324i	−0.558365	+	0.967116i	−0.997633	+	0.0687604i	$0.978096\pi$
$720$		0			0
$721$	50.3244	−	3.79897i	1.87418	−	0.141481i
$722$			17.2201i			0.640868i
$723$		0			0
$724$	−0.213114	−	0.369125i	−0.00792032	−	0.0137184i
$725$	−7.93462	−	13.7432i	−0.294685	−	0.510409i
$726$		0			0
$727$	22.8860			0.848796			0.424398	−	0.905476i	$-0.360486\pi$
$727$	22.8860			0.848796			0.424398	+	0.905476i	$0.360486\pi$
$728$	−7.62123	+	5.73732i	−0.282462	+	0.212639i
$729$		0			0
$730$	−25.8454	−	14.9218i	−0.956580	−	0.552282i
$731$	−3.30620	−	5.72651i	−0.122284	−	0.211803i
$732$		0			0
$733$	33.8210	+	19.5265i	1.24921	+	0.721229i	0.970951	−	0.239278i	$-0.0769107\pi$
$733$	33.8210	+	19.5265i	1.24921	+	0.721229i	0.278255	+	0.960507i	$0.410244\pi$
$734$			24.3509i			0.898808i
$735$		0			0
$736$		−	2.93579i		−	0.108215i
$737$	−21.1433	+	36.6213i	−0.778825	+	1.34896i
$738$		0			0
$739$	42.8282	−	24.7269i	1.57546	−	0.909593i	0.579980	−	0.814631i	$-0.303060\pi$
$739$	42.8282	−	24.7269i	1.57546	−	0.909593i	0.995481	−	0.0949620i	$-0.0302729\pi$
$740$	−0.217312	+	0.376395i	−0.00798855	+	0.0138366i
$741$		0			0
$742$	−6.55562	+	4.47480i	−0.240664	+	0.164275i
$743$		−	0.203358i		−	0.00746049i	−0.999993	−	0.00373025i	$-0.998813\pi$
$743$		−	0.203358i		−	0.00746049i	0.999993	−	0.00373025i	$-0.00118738\pi$
$744$		0			0
$745$	10.5877	+	18.3385i	0.387904	+	0.671870i
$746$	27.6717	−	15.9763i	1.01313	−	0.584934i
$747$		0			0
$748$			10.2034i			0.373072i
$749$	21.2975	−	1.60774i	0.778194	−	0.0587457i
$750$		0			0
$751$	21.4733	−	37.1928i	0.783570	−	1.35718i	−0.146279	−	0.989243i	$-0.546730\pi$
$751$	21.4733	−	37.1928i	0.783570	−	1.35718i	0.929849	−	0.367940i	$-0.119937\pi$
$752$	−8.43580	+	4.87041i	−0.307622	+	0.177606i
$753$		0			0
$754$	28.7347	+	14.8593i	1.04646	+	0.541143i
$755$	−52.0554			−1.89449
$756$		0			0
$757$	−19.5180			−0.709392			−0.354696	−	0.934982i	$-0.615416\pi$
$757$	−19.5180			−0.709392			−0.354696	+	0.934982i	$0.615416\pi$
$758$	−1.39832	+	2.42196i	−0.0507893	+	0.0879696i
$759$		0			0
$760$	3.00591	−	1.73546i	0.109036	−	0.0629519i
$761$	36.3876	+	21.0084i	1.31905	+	0.761554i	0.983576	−	0.180496i	$-0.0577702\pi$
$761$	36.3876	+	21.0084i	1.31905	+	0.761554i	0.335474	+	0.942049i	$0.391104\pi$
$762$		0			0
$763$	30.6850	+	14.7565i	1.11087	+	0.534219i
$764$	−8.86925			−0.320878
$765$		0			0
$766$	4.92184	+	8.52487i	0.177833	+	0.308016i
$767$	35.1336	−	22.5169i	1.26860	−	0.813039i
$768$		0			0
$769$			51.9502i			1.87337i	0.350168	+	0.936687i	$0.386125\pi$
$769$			51.9502i			1.87337i	−0.350168	+	0.936687i	$0.613875\pi$
$770$	1.86622	+	24.7214i	0.0672537	+	0.890899i
$771$		0			0
$772$	−6.06945	−	3.50420i	−0.218444	−	0.126119i
$773$	−36.4022	+	21.0168i	−1.30929	+	0.755921i	−0.981978	−	0.188993i	$-0.939477\pi$
$773$	−36.4022	+	21.0168i	−1.30929	+	0.755921i	−0.327316	+	0.944915i	$0.606144\pi$
$774$		0			0
$775$	−6.12708	−	3.53747i	−0.220091	−	0.127070i
$776$	0.139148			0.00499511
$777$		0			0
$778$		−	16.3811i		−	0.587292i
$779$	2.02538	−	3.50806i	0.0725668	−	0.125689i
$780$		0			0
$781$	−10.3886	−	17.9935i	−0.371732	−	0.643859i
$782$	7.20267	+	4.15846i	0.257567	+	0.148706i
$783$		0			0
$784$	−4.37041	−	5.46804i	−0.156086	−	0.195287i
$785$			55.5324i			1.98204i
$786$		0			0
$787$	−7.61610	+	4.39716i	−0.271485	+	0.156742i	−0.629562	−	0.776950i	$-0.716766\pi$
$787$	−7.61610	+	4.39716i	−0.271485	+	0.156742i	0.358078	+	0.933692i	$0.383432\pi$
$788$	15.4196	−	8.90252i	0.549301	−	0.317139i
$789$		0			0
$790$	−17.5375			−0.623955
$791$	−29.6530	−	43.4419i	−1.05434	−	1.54461i
$792$		0			0
$793$	−6.68479	+	12.9270i	−0.237384	+	0.459050i
$794$	2.72151	+	4.71379i	0.0965828	+	0.167286i
$795$		0			0
$796$	−13.5545	+	23.4770i	−0.480425	+	0.832120i
$797$	6.25039			0.221400			0.110700	−	0.993854i	$-0.464691\pi$
$797$	6.25039			0.221400			0.110700	+	0.993854i	$0.464691\pi$
$798$		0			0
$799$		−	27.5952i		−	0.976249i
$800$	1.53177	+	0.884367i	0.0541562	+	0.0312671i
$801$		0			0
$802$	8.78805	+	15.2214i	0.310317	+	0.537485i
$803$	20.6573	−	35.7795i	0.728980	−	1.26263i
$804$		0			0
$805$	18.2118	+	8.75805i	0.641880	+	0.308681i
$806$	14.4067	−	0.668221i	0.507455	−	0.0235371i
$807$		0			0
$808$	3.08771	−	1.78269i	0.108625	−	0.0627147i
$809$	−22.9260	−	39.7091i	−0.806036	−	1.39610i	−0.915589	−	0.402115i	$-0.868275\pi$
$809$	−22.9260	−	39.7091i	−0.806036	−	1.39610i	0.109553	−	0.993981i	$-0.465058\pi$
$810$		0			0
$811$			29.5096i			1.03622i	0.855314	+	0.518110i	$0.173364\pi$
$811$			29.5096i			1.03622i	−0.855314	+	0.518110i	$0.826636\pi$
$812$	−10.2878	+	21.3928i	−0.361031	+	0.750739i
$813$		0			0
$814$	−0.521069	−	0.300840i	−0.0182635	−	0.0105444i
$815$	1.33714	+	2.31600i	0.0468381	+	0.0811259i
$816$		0			0
$817$	−2.69677	−	1.55698i	−0.0943480	−	0.0544718i
$818$	19.0084			0.664613
$819$		0			0
$820$	7.89949			0.275862
$821$	−20.9197	−	12.0780i	−0.730101	−	0.421524i	0.0883581	−	0.996089i	$-0.471838\pi$
$821$	−20.9197	−	12.0780i	−0.730101	−	0.421524i	−0.818459	+	0.574565i	$0.805171\pi$
$822$		0			0
$823$	15.3511	+	26.5889i	0.535106	+	0.926830i	0.999158	+	0.0410224i	$0.0130615\pi$
$823$	15.3511	+	26.5889i	0.535106	+	0.926830i	−0.464053	+	0.885808i	$0.653605\pi$
$824$	16.5194	+	9.53747i	0.575480	+	0.332253i
$825$		0			0
$826$	17.2634	+	25.2911i	0.600672	+	0.879989i
$827$			3.32338i			0.115565i	0.998329	+	0.0577827i	$0.0184031\pi$
$827$			3.32338i			0.115565i	−0.998329	+	0.0577827i	$0.981597\pi$
$828$		0			0
$829$	14.8232	+	25.6745i	0.514831	+	0.891713i	0.999852	+	0.0172105i	$0.00547853\pi$
$829$	14.8232	+	25.6745i	0.514831	+	0.891713i	−0.485021	+	0.874502i	$0.661188\pi$
$830$	−18.2514	+	10.5375i	−0.633516	+	0.365761i
$831$		0			0
$832$	−3.60168	+	0.167055i	−0.124866	+	0.00579160i
$833$	19.6059	−	2.97705i	0.679303	−	0.103149i
$834$		0			0
$835$	7.76570	−	13.4506i	0.268743	−	0.465477i
$836$	2.40252	+	4.16128i	0.0830928	+	0.143921i
$837$		0			0
$838$	4.74725	+	2.74083i	0.163991	+	0.0946803i
$839$		−	5.51189i		−	0.190292i	−0.995463	−	0.0951458i	$-0.969668\pi$
$839$		−	5.51189i		−	0.190292i	0.995463	−	0.0951458i	$-0.0303317\pi$
$840$		0			0
$841$	51.4984			1.77581
$842$	−1.58236	+	2.74073i	−0.0545318	+	0.0944518i
$843$		0			0
$844$	11.3371	+	19.6365i	0.390241	+	0.675916i
$845$	−30.7302	−	14.1270i	−1.05715	−	0.485983i
$846$		0			0
$847$	−5.20286	+	0.392763i	−0.178772	+	0.0134955i
$848$	−3.00000			−0.103020
$849$		0			0
$850$	−4.33942	+	2.50536i	−0.148841	+	0.0859333i
$851$	−0.424732	+	0.245219i	−0.0145596	+	0.00840601i
$852$		0			0
$853$		−	34.2611i		−	1.17308i	−0.809921	−	0.586539i	$-0.800490\pi$
$853$		−	34.2611i		−	1.17308i	0.809921	−	0.586539i	$-0.199510\pi$
$854$	−9.62403	−	4.62820i	−0.329327	−	0.158374i
$855$		0			0
$856$	6.99108	+	4.03630i	0.238950	+	0.137958i
$857$	18.2299	+	31.5751i	0.622722	+	1.07859i	0.988977	+	0.148071i	$0.0473065\pi$
$857$	18.2299	+	31.5751i	0.622722	+	1.07859i	−0.366255	+	0.930515i	$0.619360\pi$
$858$		0			0
$859$	−21.6743	+	37.5410i	−0.739517	+	1.28088i	0.213196	+	0.977009i	$0.431613\pi$
$859$	−21.6743	+	37.5410i	−0.739517	+	1.28088i	−0.952713	+	0.303872i	$0.901721\pi$
$860$		−	6.07261i		−	0.207074i
$861$		0			0
$862$	−15.4370			−0.525785
$863$	11.7907	+	6.80737i	0.401360	+	0.231726i	0.687071	−	0.726590i	$-0.258896\pi$
$863$	11.7907	+	6.80737i	0.401360	+	0.231726i	−0.285710	+	0.958316i	$0.592230\pi$
$864$		0			0
$865$	37.3616	−	21.5707i	1.27033	−	0.733427i
$866$	−12.0740	−	6.97093i	−0.410291	−	0.236882i
$867$		0			0
$868$	0.796642	+	10.5530i	0.0270398	+	0.358191i
$869$		−	24.2783i		−	0.823585i
$870$		0			0
$871$	35.6407	−	22.8419i	1.20764	−	0.773970i
$872$	6.43462	+	11.1451i	0.217904	+	0.377421i
$873$		0			0
$874$	3.91667			0.132483
$875$	18.3704	−	12.5395i	0.621033	−	0.423911i
$876$		0			0
$877$	−23.8292	−	13.7578i	−0.804656	−	0.464568i	0.0404407	−	0.999182i	$-0.487124\pi$
$877$	−23.8292	−	13.7578i	−0.804656	−	0.464568i	−0.845097	+	0.534614i	$0.820457\pi$
$878$	−23.7180	+	13.6936i	−0.800444	+	0.462137i
$879$		0			0
$880$	−4.68521	+	8.11502i	−0.157938	+	0.273557i
$881$	22.3341			0.752455			0.376228	−	0.926527i	$-0.377221\pi$
$881$	22.3341			0.752455			0.376228	+	0.926527i	$0.377221\pi$
$882$		0			0
$883$	9.28669			0.312522			0.156261	−	0.987716i	$-0.450056\pi$
$883$	9.28669			0.312522			0.156261	+	0.987716i	$0.450056\pi$
$884$	4.69183	−	9.07300i	0.157803	−	0.305158i
$885$		0			0
$886$	−20.8809	+	12.0556i	−0.701509	+	0.405016i
$887$	−6.97209	+	12.0760i	−0.234100	+	0.405473i	−0.959011	−	0.283370i	$-0.908548\pi$
$887$	−6.97209	+	12.0760i	−0.234100	+	0.405473i	0.724911	+	0.688843i	$0.241881\pi$
$888$		0			0
$889$	14.9736	+	21.9365i	0.502199	+	0.735726i
$890$			21.2481i			0.712236i
$891$		0			0
$892$	−7.96307	+	4.59748i	−0.266623	+	0.153935i
$893$	−6.49767	−	11.2543i	−0.217436	−	0.376611i
$894$		0			0
$895$			48.7576i			1.62979i
$896$	−0.199160	−	2.63824i	−0.00665348	−	0.0881376i
$897$		0			0
$898$	−1.29548	+	2.24383i	−0.0432306	+	0.0748776i
$899$	31.0802	−	17.9442i	1.03658	−	0.598472i
$900$		0			0
$901$	4.24942	−	7.36021i	0.141569	−	0.245204i
$902$			10.9358i			0.364122i
$903$		0			0
$904$		−	19.8800i		−	0.661198i
$905$	0.960344	+	0.554455i	0.0319229	+	0.0184307i
$906$		0			0
$907$	−2.06957	−	3.58461i	−0.0687191	−	0.119025i	0.829619	−	0.558330i	$-0.188558\pi$
$907$	−2.06957	−	3.58461i	−0.0687191	−	0.119025i	−0.898338	+	0.439306i	$0.855225\pi$
$908$	11.7238	+	6.76873i	0.389068	+	0.224628i
$909$		0			0
$910$	9.70823	−	22.8409i	0.321825	−	0.757167i
$911$	−18.5566			−0.614807			−0.307404	−	0.951579i	$-0.599460\pi$
$911$	−18.5566			−0.614807			−0.307404	+	0.951579i	$0.599460\pi$
$912$		0			0
$913$	−14.5877	−	25.2667i	−0.482783	−	0.836205i
$914$	5.23430	+	9.06607i	0.173135	+	0.299879i
$915$		0			0
$916$			18.4067i			0.608175i
$917$	−21.3994	+	1.61544i	−0.706672	+	0.0533465i
$918$		0			0
$919$	−25.6743	+	44.4692i	−0.846917	+	1.46690i	0.0370298	+	0.999314i	$0.488210\pi$
$919$	−25.6743	+	44.4692i	−0.846917	+	1.46690i	−0.883946	+	0.467588i	$0.845123\pi$
$920$	3.81899	+	6.61469i	0.125908	+	0.218080i
$921$		0			0
$922$	−15.0084	+	25.9953i	−0.494275	+	0.856110i
$923$	0.963697	+	20.7771i	0.0317205	+	0.683888i
$924$		0			0
$925$		−	0.295476i		−	0.00971520i
$926$	−9.73243	+	16.8571i	−0.319828	+	0.553958i
$927$		0			0
$928$	−7.77006	+	4.48605i	−0.255065	+	0.147262i
$929$	−6.01182	−	3.47093i	−0.197241	−	0.113877i	0.398127	−	0.917330i	$-0.369660\pi$
$929$	−6.01182	−	3.47093i	−0.197241	−	0.113877i	−0.595368	+	0.803453i	$0.702994\pi$
$930$		0			0
$931$	7.29497	−	5.83061i	0.239083	−	0.191091i
$932$	−11.7301			−0.384232
$933$		0			0
$934$	0.259927	−	0.150069i	0.00850508	−	0.00491041i
$935$	−13.2729	−	22.9894i	−0.434071	−	0.751834i
$936$		0			0
$937$	37.1005			1.21202			0.606010	−	0.795457i	$-0.292769\pi$
$937$	37.1005			1.21202			0.606010	+	0.795457i	$0.292769\pi$
$938$	17.5126	+	25.6561i	0.571807	+	0.837702i
$939$		0			0
$940$	12.6713	−	21.9473i	0.413291	−	0.715840i
$941$	−7.28447	+	4.20569i	−0.237467	+	0.137102i	−0.614012	−	0.789297i	$-0.710445\pi$
$941$	−7.28447	+	4.20569i	−0.237467	+	0.137102i	0.376545	+	0.926398i	$0.377112\pi$
$942$		0			0
$943$	7.71970	+	4.45697i	0.251388	+	0.145139i
$944$			11.5738i			0.376694i
$945$		0			0
$946$	8.40672			0.273326
$947$	−21.7953	−	12.5835i	−0.708252	−	0.408910i	0.102161	−	0.994768i	$-0.467424\pi$
$947$	−21.7953	−	12.5835i	−0.708252	−	0.408910i	−0.810414	+	0.585858i	$0.800758\pi$
$948$		0			0
$949$	−34.8214	+	22.3168i	−1.13035	+	0.724435i
$950$	−1.17984	+	2.04355i	−0.0382792	+	0.0663015i
$951$		0			0
$952$	6.75478	+	3.24838i	0.218924	+	0.105281i
$953$	−35.3681			−1.14568			−0.572842	−	0.819666i	$-0.694159\pi$
$953$	−35.3681			−1.14568			−0.572842	+	0.819666i	$0.694159\pi$
$954$		0			0
$955$	19.9835	−	11.5375i	0.646650	−	0.373344i
$956$	9.67621	−	5.58656i	0.312951	−	0.180682i
$957$		0			0
$958$	23.5845			0.761981
$959$	11.0386	+	5.30849i	0.356456	+	0.171420i
$960$		0			0
$961$	−7.50000	+	12.9904i	−0.241935	+	0.419045i
$962$	0.325008	+	0.507116i	0.0104787	+	0.0163501i
$963$		0			0
$964$	−12.7659	−	7.37041i	−0.411163	−	0.237385i
$965$	18.2336			0.586960
$966$		0			0
$967$			17.3123i			0.556725i	0.960476	+	0.278362i	$0.0897917\pi$
$967$			17.3123i			0.556725i	−0.960476	+	0.278362i	$0.910208\pi$
$968$	−1.70788	−	0.986046i	−0.0548934	−	0.0316927i
$969$		0			0
$970$	−0.313517	+	0.181009i	−0.0100664	+	0.00581185i
$971$	−26.6959	+	46.2387i	−0.856713	+	1.48387i	0.0183332	+	0.999832i	$0.494164\pi$
$971$	−26.6959	+	46.2387i	−0.856713	+	1.48387i	−0.875046	+	0.484039i	$0.839169\pi$
$972$		0			0
$973$	1.39582	+	2.04489i	0.0447481	+	0.0655563i
$974$	−34.2420			−1.09718
$975$		0			0
$976$	−2.01815	−	3.49554i	−0.0645995	−	0.111890i
$977$	28.4656	−	16.4346i	0.910695	−	0.525790i	0.0300405	−	0.999549i	$-0.490436\pi$
$977$	28.4656	−	16.4346i	0.910695	−	0.525790i	0.880655	+	0.473758i	$0.157103\pi$
$978$		0			0
$979$	−29.4151			−0.940111
$980$	16.9601	+	6.63495i	0.541771	+	0.211946i
$981$		0			0
$982$	−34.4291	−	19.8776i	−1.09868	−	0.634321i
$983$	−8.42126	+	4.86202i	−0.268597	+	0.155074i	−0.628250	−	0.778012i	$-0.716228\pi$
$983$	−8.42126	+	4.86202i	−0.268597	+	0.155074i	0.359653	+	0.933086i	$0.382895\pi$
$984$		0			0
$985$	−23.1615	+	40.1169i	−0.737987	+	1.27823i
$986$		−	25.4174i		−	0.809456i
$987$		0			0
$988$	−0.222870	−	4.80504i	−0.00709044	−	0.152869i
$989$	3.42623	−	5.93440i	0.108948	−	0.188703i
$990$		0			0
$991$	−16.2057	−	28.0691i	−0.514791	−	0.891644i	−0.999853	−	0.0171639i	$-0.994536\pi$
$991$	−16.2057	−	28.0691i	−0.514791	−	0.891644i	0.485062	−	0.874480i	$-0.338797\pi$
$992$	−2.00000	+	3.46410i	−0.0635001	+	0.109985i
$993$		0			0
$994$	−15.2193	+	1.14890i	−0.482728	+	0.0364410i
$995$		−	70.5287i		−	2.23591i
$996$		0			0
$997$	22.8395	+	39.5591i	0.723333	+	1.25285i	0.959656	+	0.281176i	$0.0907243\pi$
$997$	22.8395	+	39.5591i	0.723333	+	1.25285i	−0.236323	+	0.971675i	$0.575942\pi$
$998$	−6.12519	−	10.6091i	−0.193890	−	0.335827i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.dm.c.415.1		12
3.2	odd	2		546.2.bk.b.415.6	yes	12
7.4	even	3	inner	1638.2.dm.c.1117.6		12
13.12	even	2	inner	1638.2.dm.c.415.6		12
21.2	odd	6		3822.2.c.k.883.1		6
21.5	even	6		3822.2.c.j.883.3		6
21.11	odd	6		546.2.bk.b.25.1	✓	12
39.38	odd	2		546.2.bk.b.415.1	yes	12
91.25	even	6	inner	1638.2.dm.c.1117.1		12
273.116	odd	6		546.2.bk.b.25.6	yes	12
273.194	even	6		3822.2.c.j.883.4		6
273.233	odd	6		3822.2.c.k.883.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bk.b.25.1	✓	12	21.11	odd	6
546.2.bk.b.25.6	yes	12	273.116	odd	6
546.2.bk.b.415.1	yes	12	39.38	odd	2
546.2.bk.b.415.6	yes	12	3.2	odd	2
1638.2.dm.c.415.1		12	1.1	even	1	trivial
1638.2.dm.c.415.6		12	13.12	even	2	inner
1638.2.dm.c.1117.1		12	91.25	even	6	inner
1638.2.dm.c.1117.6		12	7.4	even	3	inner
3822.2.c.j.883.3		6	21.5	even	6
3822.2.c.j.883.4		6	273.194	even	6
3822.2.c.k.883.1		6	21.2	odd	6
3822.2.c.k.883.6		6	273.233	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.dm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.25312 - 1.30084i) q^{5} +(-1.49160 - 2.18521i) q^{7} -1.00000i q^{8} +(1.30084 + 2.25312i) q^{10} +(-3.11915 + 1.80084i) q^{11} +(3.60168 - 0.167055i) q^{13} +(0.199160 + 2.63824i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.41647 - 2.45340i) q^{17} +(-1.15537 - 0.667055i) q^{19} -2.60168i q^{20} +3.60168 q^{22} +(1.46789 - 2.54247i) q^{23} +(0.884367 + 1.53177i) q^{25} +(-3.20267 - 1.65617i) q^{26} +(1.14664 - 2.38437i) q^{28} -8.97209 q^{29} +(-3.46410 + 2.00000i) q^{31} +(0.866025 - 0.500000i) q^{32} +2.83294i q^{34} +(0.518152 + 6.86387i) q^{35} +(-0.144674 - 0.0835276i) q^{37} +(0.667055 + 1.15537i) q^{38} +(-1.30084 + 2.25312i) q^{40} +3.03630i q^{41} +2.33411 q^{43} +(-3.11915 - 1.80084i) q^{44} +(-2.54247 + 1.46789i) q^{46} +(8.43580 + 4.87041i) q^{47} +(-2.55026 + 6.51891i) q^{49} -1.76873i q^{50} +(1.94551 + 3.03562i) q^{52} +(1.50000 + 2.59808i) q^{53} +9.37041 q^{55} +(-2.18521 + 1.49160i) q^{56} +(7.77006 + 4.48605i) q^{58} +(10.0232 - 5.78689i) q^{59} +(-2.01815 + 3.49554i) q^{61} +4.00000 q^{62} -1.00000 q^{64} +(-8.33233 - 4.30881i) q^{65} +(10.1679 - 5.87041i) q^{67} +(1.41647 - 2.45340i) q^{68} +(2.98320 - 6.20336i) q^{70} +5.76873i q^{71} +(-9.93411 + 5.73546i) q^{73} +(0.0835276 + 0.144674i) q^{74} -1.33411i q^{76} +(8.58773 + 4.12985i) q^{77} +(-3.37041 + 5.83773i) q^{79} +(2.25312 - 1.30084i) q^{80} +(1.51815 - 2.62952i) q^{82} +8.10051i q^{83} +7.37041i q^{85} +(-2.02140 - 1.16706i) q^{86} +(1.80084 + 3.11915i) q^{88} +(7.07288 + 4.08353i) q^{89} +(-5.73732 - 7.62123i) q^{91} +2.93579 q^{92} +(-4.87041 - 8.43580i) q^{94} +(1.73546 + 3.00591i) q^{95} +0.139148i q^{97} +(5.46804 - 4.37041i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} + 12 q^{13} + 18 q^{14} - 6 q^{16} - 18 q^{17} + 12 q^{22} - 6 q^{25} - 12 q^{29} - 24 q^{35} + 6 q^{38} + 24 q^{43} - 18 q^{49} + 6 q^{52} + 18 q^{53} + 48 q^{55} + 6 q^{56} + 6 q^{61} + 48 q^{62}+ \cdots - 24 q^{95}+O(q^{100}) \) 12 * q + 6 * q^4 + 12 * q^13 + 18 * q^14 - 6 * q^16 - 18 * q^17 + 12 * q^22 - 6 * q^25 - 12 * q^29 - 24 * q^35 + 6 * q^38 + 24 * q^43 - 18 * q^49 + 6 * q^52 + 18 * q^53 + 48 * q^55 + 6 * q^56 + 6 * q^61 + 48 * q^62 - 12 * q^64 + 12 * q^65 + 18 * q^68 + 24 * q^77 + 24 * q^79 - 12 * q^82 + 6 * q^88 - 24 * q^91 + 6 * q^94 - 24 * q^95

Introduction

L-functions

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