LMFDB - Embedded newform 1638.2.dm.c.415.6

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			415.6
Root			$0.385124 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1638.415
Dual form			1638.2.dm.c.1117.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(2.25312 + 1.30084i) q^{5} +(1.49160 + 2.18521i) q^{7} +1.00000i q^{8} +(1.30084 + 2.25312i) q^{10} +(3.11915 - 1.80084i) q^{11} +(3.60168 + 0.167055i) q^{13} +(0.199160 + 2.63824i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.41647 - 2.45340i) q^{17} +(1.15537 + 0.667055i) q^{19} +2.60168i q^{20} +3.60168 q^{22} +(1.46789 - 2.54247i) q^{23} +(0.884367 + 1.53177i) q^{25} +(3.03562 + 1.94551i) q^{26} +(-1.14664 + 2.38437i) q^{28} -8.97209 q^{29} +(3.46410 - 2.00000i) q^{31} +(-0.866025 + 0.500000i) q^{32} -2.83294i q^{34} +(0.518152 + 6.86387i) q^{35} +(0.144674 + 0.0835276i) q^{37} +(0.667055 + 1.15537i) q^{38} +(-1.30084 + 2.25312i) q^{40} -3.03630i q^{41} +2.33411 q^{43} +(3.11915 + 1.80084i) q^{44} +(2.54247 - 1.46789i) q^{46} +(-8.43580 - 4.87041i) q^{47} +(-2.55026 + 6.51891i) q^{49} +1.76873i q^{50} +(1.65617 + 3.20267i) q^{52} +(1.50000 + 2.59808i) q^{53} +9.37041 q^{55} +(-2.18521 + 1.49160i) q^{56} +(-7.77006 - 4.48605i) q^{58} +(-10.0232 + 5.78689i) q^{59} +(-2.01815 + 3.49554i) q^{61} +4.00000 q^{62} -1.00000 q^{64} +(7.89770 + 5.06160i) q^{65} +(-10.1679 + 5.87041i) q^{67} +(1.41647 - 2.45340i) q^{68} +(-2.98320 + 6.20336i) q^{70} -5.76873i q^{71} +(9.93411 - 5.73546i) q^{73} +(0.0835276 + 0.144674i) q^{74} +1.33411i q^{76} +(8.58773 + 4.12985i) q^{77} +(-3.37041 + 5.83773i) q^{79} +(-2.25312 + 1.30084i) q^{80} +(1.51815 - 2.62952i) q^{82} -8.10051i q^{83} -7.37041i q^{85} +(2.02140 + 1.16706i) q^{86} +(1.80084 + 3.11915i) q^{88} +(-7.07288 - 4.08353i) q^{89} +(5.00722 + 8.11959i) q^{91} +2.93579 q^{92} +(-4.87041 - 8.43580i) q^{94} +(1.73546 + 3.00591i) q^{95} -0.139148i q^{97} +(-5.46804 + 4.37041i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	0.910496	−	0.413519i	$-0.135700\pi$
$5$	2.25312	+	1.30084i	1.00763	+	0.581753i	0.0971303	+	0.995272i	$0.469034\pi$
$6$		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	0.0503540	−	0.998731i	$-0.483965\pi$
$11$	3.11915	−	1.80084i	0.940458	−	0.542974i	0.890104	+	0.455758i	$0.150632\pi$
$12$		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	0.626641	−	0.779308i	$-0.284429\pi$
$19$	1.15537	+	0.667055i	0.265061	+	0.153033i	−0.361580	+	0.932341i	$0.617763\pi$
$20$			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
$26$	3.03562	+	1.94551i	0.595334	+	0.381547i
$27$		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	−0.155543	−	0.987829i	$-0.549713\pi$
$31$	3.46410	−	2.00000i	0.622171	−	0.359211i	0.777714	+	0.628619i	$0.216379\pi$
$32$	−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	0.511845	−	0.859078i	$-0.328962\pi$
$37$	0.144674	+	0.0835276i	0.0237843	+	0.0137319i	−0.488061	+	0.872810i	$0.662296\pi$
$38$	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	$-0.923805\pi$
$41$		−	3.03630i		−	0.474191i	0.971486	−	0.237095i	$-0.0761954\pi$
$42$		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	−0.263357	−	0.964699i	$-0.584830\pi$
$47$	−8.43580	−	4.87041i	−1.23049	−	0.710423i	−0.967132	+	0.254276i	$0.918163\pi$
$48$		0			0
$49$	−2.55026	+	6.51891i	−0.364322	+	0.931273i
$50$			1.76873i			0.250137i
$51$		0			0
$52$	1.65617	+	3.20267i	0.229669	+	0.444131i
$53$	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	−0.981241	−	0.192783i	$-0.938249\pi$
$59$	−10.0232	+	5.78689i	−1.30491	+	0.753388i	−0.323666	+	0.946172i	$0.604915\pi$
$60$		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
$65$	7.89770	+	5.06160i	0.979590	+	0.627814i
$66$		0			0
$67$	−10.1679	+	5.87041i	−1.24220	+	0.717185i	−0.969542	−	0.244926i	$-0.921236\pi$
$67$	−10.1679	+	5.87041i	−1.24220	+	0.717185i	−0.272659	+	0.962111i	$0.587903\pi$
$68$	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	$-0.888790\pi$
$71$		−	5.76873i		−	0.684623i	0.939587	−	0.342311i	$-0.111210\pi$
$72$		0			0
$73$	9.93411	−	5.73546i	1.16270	−	0.671285i	0.210751	−	0.977540i	$-0.432409\pi$
$73$	9.93411	−	5.73546i	1.16270	−	0.671285i	0.951950	+	0.306255i	$0.0990759\pi$
$74$	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	$-0.853355\pi$
$83$		−	8.10051i		−	0.889147i	0.895742	−	0.444573i	$-0.146645\pi$
$84$		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	0.0758705	−	0.997118i	$-0.475826\pi$
$89$	−7.07288	−	4.08353i	−0.749723	−	0.432853i	−0.825594	+	0.564265i	$0.809160\pi$
$90$		0			0
$91$	5.00722	+	8.11959i	0.524899	+	0.851165i
$92$	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	$-0.997751\pi$
$97$		−	0.139148i		−	0.0141283i	0.999975	−	0.00706416i	$-0.00224861\pi$
$98$	−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	0.140007	−	0.990150i	$-0.455287\pi$
$109$	11.1451	−	6.43462i	1.06751	−	0.616325i	0.927499	+	0.373825i	$0.121954\pi$
$110$	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
$130$	4.30881	+	8.33233i	0.377908	+	0.730794i
$131$	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	−0.318854	−	0.947804i	$-0.603298\pi$
$137$	4.00934	−	2.31479i	0.342541	−	0.197766i	0.661395	+	0.750038i	$0.269965\pi$
$138$		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
$143$	11.5350	−	5.96498i	0.964605	−	0.498816i
$144$		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	0.760120	−	0.649782i	$-0.225140\pi$
$149$	7.04871	+	4.06957i	0.577453	+	0.333392i	−0.182668	+	0.983175i	$0.558473\pi$
$150$		0			0
$151$	−17.3278	+	10.0042i	−1.41011	+	0.814130i	−0.995399	−	0.0958208i	$-0.969452\pi$
$151$	−17.3278	+	10.0042i	−1.41011	+	0.814130i	−0.414716	+	0.909951i	$0.636119\pi$
$152$	−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	0.534457	−	0.845195i	$-0.320516\pi$
$163$	0.890194	+	0.513954i	0.0697254	+	0.0402560i	−0.464732	+	0.885451i	$0.653849\pi$
$164$	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	$-0.925808\pi$
$167$		−	5.96976i		−	0.461954i	0.972959	−	0.230977i	$-0.0741922\pi$
$168$		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	$0.505042\pi$
$182$	0.276580	+	9.53538i	0.0205014	+	0.706810i
$183$		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	−0.265388	−	0.964142i	$-0.585500\pi$
$193$	6.06945	−	3.50420i	0.436888	−	0.252238i	0.702277	+	0.711904i	$0.252167\pi$
$194$	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	$0.218703\pi$
$197$			17.8050i			1.26856i	−0.773105	+	0.634278i	$0.781297\pi$
$198$		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
$208$	−1.94551	+	3.03562i	−0.134897	+	0.210482i
$209$	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
$221$	−4.69183	−	9.07300i	−0.315606	−	0.610316i
$222$		0			0
$223$		−	9.19496i		−	0.615740i	−0.951428	−	0.307870i	$-0.900384\pi$
$223$		−	9.19496i		−	0.615740i	0.951428	−	0.307870i	$-0.0996162\pi$
$224$	−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	−0.835769	−	0.549081i	$-0.814978\pi$
$227$	−11.7238	+	6.76873i	−0.778135	+	0.449257i	0.0576337	+	0.998338i	$0.481644\pi$
$228$		0			0
$229$	−15.9407	−	9.20336i	−1.05339	−	0.608175i	−0.129794	−	0.991541i	$-0.541431\pi$
$229$	−15.9407	−	9.20336i	−1.05339	−	0.608175i	−0.923597	+	0.383366i	$0.874765\pi$
$230$	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	$0.117689\pi$
$239$			11.1731i			0.722729i	−0.932425	+	0.361365i	$0.882311\pi$
$240$		0			0
$241$	12.7659	−	7.37041i	0.822326	−	0.474770i	−0.0288920	−	0.999583i	$-0.509198\pi$
$241$	12.7659	−	7.37041i	0.822326	−	0.474770i	0.851218	+	0.524812i	$0.175865\pi$
$242$	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
$247$	4.04985	+	2.59553i	0.257686	+	0.165150i
$248$	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	0.446241	−	0.894913i	$-0.352763\pi$
$271$	−1.73932	−	1.00420i	−0.105656	−	0.0610007i	−0.551897	+	0.833912i	$0.686096\pi$
$272$	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	$-0.834372\pi$
$281$		−	16.6682i		−	0.994343i	0.867652	−	0.497171i	$-0.165628\pi$
$282$		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	$-0.718609\pi$
$293$		−	26.4733i		−	1.54658i	0.634050	−	0.773292i	$-0.281391\pi$
$294$		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
$299$	5.71162	−	8.91194i	0.330311	−	0.515391i
$300$		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	$-0.768738\pi$
$307$		−	23.2783i		−	1.32856i	0.747483	−	0.664281i	$-0.231262\pi$
$308$	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	0.920216	−	0.391410i	$-0.128012\pi$
$317$	18.5408	+	10.7045i	1.04135	+	0.601226i	0.121137	+	0.992636i	$0.461346\pi$
$318$		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
$325$	2.92932	+	5.66468i	0.162489	+	0.314220i
$326$	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	$0.112460\pi$
$331$	31.0561	+	17.9302i	1.70700	+	0.985535i	0.768761	+	0.639536i	$0.220874\pi$
$332$	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	$0.441246\pi$
$338$	10.6083	+	7.51423i	0.577016	+	0.408720i
$339$		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	$-0.801937\pi$
$349$		−	21.7771i		−	1.16570i	0.812579	−	0.582852i	$-0.198063\pi$
$350$	−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	0.0487029	−	0.998813i	$-0.484491\pi$
$353$	17.6244	−	10.1755i	0.938052	−	0.541585i	0.889349	+	0.457229i	$0.151158\pi$
$354$		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	0.532376	−	0.846508i	$-0.321299\pi$
$359$	1.24040	+	0.716146i	0.0654659	+	0.0377968i	−0.466910	+	0.884305i	$0.654633\pi$
$360$		0			0
$361$	−8.61007	−	14.9131i	−0.453162	−	0.784899i
$362$	−0.369125	−	0.213114i	−0.0194008	−	0.0112010i
$363$		0			0
$364$	−4.52817	+	8.39617i	−0.237340	+	0.440079i
$365$	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	$0.0228829\pi$
$379$			2.79664i			0.143654i	−0.997417	+	0.0718269i	$0.977117\pi$
$380$	−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	0.701730	−	0.712443i	$-0.252411\pi$
$383$	8.52487	+	4.92184i	0.435600	+	0.251494i	−0.266129	+	0.963937i	$0.585745\pi$
$384$		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	0.613603	−	0.789615i	$-0.289719\pi$
$397$	4.71379	+	2.72151i	0.236579	+	0.136589i	−0.377025	+	0.926203i	$0.623053\pi$
$398$			27.1089i			1.35885i
$399$		0			0
$400$	−1.76873			−0.0884367
$401$	15.2214	+	8.78805i	0.760118	+	0.438854i	0.829338	−	0.558747i	$-0.188718\pi$
$401$	15.2214	+	8.78805i	0.760118	+	0.438854i	−0.0692201	+	0.997601i	$0.522051\pi$
$402$		0			0
$403$	12.8107	−	6.62466i	0.638146	−	0.329998i
$404$	−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	−0.0343552	−	0.999410i	$-0.510938\pi$
$409$	16.4618	−	9.50420i	0.813981	−	0.469952i	0.848337	+	0.529457i	$0.177604\pi$
$410$	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
$416$	−3.20267	+	1.65617i	−0.157024	+	0.0812002i
$417$		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	$0.0245723\pi$
$421$			3.16472i			0.154239i	−0.997022	+	0.0771196i	$0.975428\pi$
$422$	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	−0.786135	−	0.618054i	$-0.787921\pi$
$431$	−13.3688	+	7.71848i	−0.643952	+	0.371786i	0.142183	+	0.989840i	$0.454588\pi$
$432$		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	$0.0194728\pi$
$449$			2.59095i			0.122275i	−0.998129	+	0.0611373i	$0.980527\pi$
$450$		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
$455$	0.719571	+	24.8080i	0.0337340	+	1.16302i
$456$		0			0
$457$	9.06607	+	5.23430i	0.424093	+	0.244850i	0.696827	−	0.717239i	$-0.254595\pi$
$457$	9.06607	+	5.23430i	0.424093	+	0.244850i	−0.272734	+	0.962089i	$0.587928\pi$
$458$	−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	$0.246376\pi$
$461$			30.0168i			1.39802i	−0.715111	+	0.699011i	$0.753624\pi$
$462$		0			0
$463$			19.4649i			0.904609i	0.891864	+	0.452304i	$0.149398\pi$
$463$			19.4649i			0.904609i	−0.891864	+	0.452304i	$0.850602\pi$
$464$	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	0.0453996	−	0.998969i	$-0.485544\pi$
$479$	20.4248	−	11.7922i	0.933232	−	0.538802i	0.887832	+	0.460167i	$0.152211\pi$
$480$		0			0
$481$	0.507116	+	0.325008i	0.0231225	+	0.0148191i
$482$	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	−0.987359	−	0.158502i	$-0.949333\pi$
$487$	−29.6544	+	17.1210i	−1.34377	+	0.775826i	−0.356412	+	0.934329i	$0.616000\pi$
$488$	−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
$494$	2.20951	+	4.27272i	0.0994104	+	0.192239i
$495$		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	0.243371	−	0.969933i	$-0.421747\pi$
$499$	−10.6091	−	6.12519i	−0.474931	−	0.274201i	−0.718301	+	0.695732i	$0.755080\pi$
$500$	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	0.979206	−	0.202869i	$-0.0650266\pi$
$509$	29.1741	+	16.8437i	1.29312	+	0.746583i	0.313913	+	0.949452i	$0.398360\pi$
$510$		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
$520$	−5.06160	+	7.89770i	−0.221966	+	0.346337i
$521$	−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	0.846524	−	0.532350i	$-0.178691\pi$
$541$	18.8112	+	10.8607i	0.808757	+	0.466936i	−0.0377670	+	0.999287i	$0.512024\pi$
$542$	−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	0.413999	−	0.910277i	$-0.364132\pi$
$557$	33.2612	−	19.2034i	1.40932	−	0.813672i	0.995323	+	0.0966049i	$0.0307983\pi$
$558$		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	$0.516508\pi$
$572$	10.9333	+	7.00712i	0.457145	+	0.292982i
$573$		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	−0.507314	−	0.861761i	$-0.669361\pi$
$577$	−0.352227	+	0.203358i	−0.0146634	+	0.00846592i	0.492650	+	0.870227i	$0.336028\pi$
$578$	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	$0.150106\pi$
$587$			22.0131i			0.908576i	−0.890855	+	0.454288i	$0.849894\pi$
$588$		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	−0.170494	−	0.985359i	$-0.554536\pi$
$593$	−27.0080	−	15.5931i	−1.10909	−	0.640331i	−0.938593	+	0.345027i	$0.887870\pi$
$594$		0			0
$595$	16.1059	−	10.9937i	0.660277	−	0.450698i
$596$			8.13915i			0.333392i
$597$		0			0
$598$	9.40237	−	4.86215i	0.384492	−	0.198828i
$599$	−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
$611$	−29.5694	−	18.9509i	−1.19625	−	0.766672i
$612$		0			0
$613$	7.37710	−	4.25917i	0.297958	−	0.172026i	−0.343567	−	0.939128i	$-0.611635\pi$
$613$	7.37710	−	4.25917i	0.297958	−	0.172026i	0.641525	+	0.767102i	$0.278302\pi$
$614$	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	$0.00902945\pi$
$617$			1.40905i			0.0567261i	−0.999598	+	0.0283631i	$0.990971\pi$
$618$		0			0
$619$	39.3641	−	22.7269i	1.58218	−	0.913470i	0.587635	−	0.809126i	$-0.300059\pi$
$619$	39.3641	−	22.7269i	1.58218	−	0.913470i	0.994541	−	0.104344i	$-0.0332744\pi$
$620$	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	$-0.752618\pi$
$631$		−	35.2313i		−	1.40253i	0.712898	−	0.701267i	$-0.247382\pi$
$632$	−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
$637$	−10.2742	+	23.0530i	−0.407080	+	0.913393i
$638$	−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	$0.0228679\pi$
$643$			3.64031i			0.143560i	−0.997420	+	0.0717800i	$0.977132\pi$
$644$	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	−0.836734	−	0.547609i	$-0.815538\pi$
$661$	−20.0758	+	11.5908i	−0.780857	+	0.450828i	0.0558767	+	0.998438i	$0.482205\pi$
$662$	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
$676$	5.42995	+	11.8117i	0.208844	+	0.454295i
$677$	−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	−0.790079	−	0.613005i	$-0.789960\pi$
$683$	−17.0981	+	9.87158i	−0.654240	+	0.377725i	0.135839	+	0.990731i	$0.456627\pi$
$684$		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
$689$	4.96850	+	9.60802i	0.189285	+	0.366036i
$690$		0			0
$691$	23.4013	+	13.5107i	0.890226	+	0.513972i	0.874016	−	0.485896i	$-0.161507\pi$
$691$	23.4013	+	13.5107i	0.890226	+	0.513972i	0.0162096	+	0.999869i	$0.494840\pi$
$692$	−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	0.987352	−	0.158542i	$-0.0506793\pi$
$709$	35.7795	+	20.6573i	1.34373	+	0.775801i	0.356375	+	0.934343i	$0.384013\pi$
$710$	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	$0.360486\pi$
$728$	−8.11959	+	5.00722i	−0.300932	+	0.185580i
$729$		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	−0.278255	−	0.960507i	$-0.589756\pi$
$733$	−33.8210	−	19.5265i	−1.24921	−	0.721229i	−0.970951	+	0.239278i	$0.923089\pi$
$734$		−	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	$0.696940\pi$
$739$	−42.8282	+	24.7269i	−1.57546	+	0.909593i	−0.995481	+	0.0949620i	$0.969727\pi$
$740$	−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	$0.00118738\pi$
$743$			0.203358i			0.00746049i	−0.999993	+	0.00373025i	$0.998813\pi$
$744$		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
$754$	−27.2358	−	17.4553i	−0.991871	−	0.635686i
$755$	−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	−0.335474	−	0.942049i	$-0.608896\pi$
$761$	−36.3876	−	21.0084i	−1.31905	−	0.761554i	−0.983576	+	0.180496i	$0.942230\pi$
$762$		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
$767$	−37.0670	+	19.1681i	−1.33841	+	0.692119i
$768$		0			0
$769$		−	51.9502i		−	1.87337i	−0.350168	−	0.936687i	$-0.613875\pi$
$769$		−	51.9502i		−	1.87337i	0.350168	−	0.936687i	$-0.386125\pi$
$770$	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	0.327316	−	0.944915i	$-0.393856\pi$
$773$	36.4022	−	21.0168i	1.30929	−	0.755921i	0.981978	+	0.188993i	$0.0605225\pi$
$774$		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	−0.358078	−	0.933692i	$-0.616568\pi$
$787$	7.61610	−	4.39716i	0.271485	−	0.156742i	0.629562	+	0.776950i	$0.283234\pi$
$788$	−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
$793$	−7.85268	+	12.2527i	−0.278857	+	0.435105i
$794$	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	$-0.826636\pi$
$811$		−	29.5096i		−	1.03622i	0.855314	−	0.518110i	$-0.173364\pi$
$812$	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	0.818459	−	0.574565i	$-0.194829\pi$
$821$	20.9197	+	12.0780i	0.730101	+	0.421524i	−0.0883581	+	0.996089i	$0.528162\pi$
$822$		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	$-0.981597\pi$
$827$		−	3.32338i		−	0.115565i	0.998329	−	0.0577827i	$-0.0184031\pi$
$828$		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	$0.0303317\pi$
$839$			5.51189i			0.190292i	−0.995463	+	0.0951458i	$0.969668\pi$
$840$		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
$845$	27.5994	+	19.5496i	0.949449	+	0.672527i
$846$		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	$0.199510\pi$
$853$			34.2611i			1.17308i	−0.809921	+	0.586539i	$0.800490\pi$
$854$	−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	0.285710	−	0.958316i	$-0.407770\pi$
$863$	−11.7907	−	6.80737i	−0.401360	−	0.231726i	−0.687071	+	0.726590i	$0.741104\pi$
$864$		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
$871$	−37.6020	+	19.4448i	−1.27410	+	0.658860i
$872$	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	0.845097	−	0.534614i	$-0.179543\pi$
$877$	23.8292	+	13.7578i	0.804656	+	0.464568i	−0.0404407	+	0.999182i	$0.512876\pi$
$878$	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	$0.450056\pi$
$884$	5.51153	−	8.59974i	0.185373	−	0.289241i
$885$		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
$910$	−11.7808	+	21.8441i	−0.390531	+	0.724126i
$911$	−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	0.595368	−	0.803453i	$-0.297006\pi$
$929$	6.01182	+	3.47093i	0.197241	+	0.113877i	−0.398127	+	0.917330i	$0.630340\pi$
$930$		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	−0.376545	−	0.926398i	$-0.622888\pi$
$941$	7.28447	−	4.20569i	0.237467	−	0.137102i	0.614012	+	0.789297i	$0.289555\pi$
$942$		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	0.810414	−	0.585858i	$-0.199242\pi$
$947$	21.7953	+	12.5835i	0.708252	+	0.408910i	−0.102161	+	0.994768i	$0.532576\pi$
$948$		0			0
$949$	36.7376	−	18.9978i	1.19255	−	0.616693i
$950$	−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
$962$	0.276671	+	0.535023i	0.00892023	+	0.0172498i
$963$		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	$-0.910208\pi$
$967$		−	17.3123i		−	0.556725i	0.960476	−	0.278362i	$-0.0897917\pi$
$968$	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	−0.880655	−	0.473758i	$-0.842897\pi$
$977$	−28.4656	+	16.4346i	−0.910695	+	0.525790i	−0.0300405	+	0.999549i	$0.509564\pi$
$978$		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	−0.359653	−	0.933086i	$-0.617105\pi$
$983$	8.42126	−	4.86202i	0.268597	−	0.155074i	0.628250	+	0.778012i	$0.283772\pi$
$984$		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.415.6		12
3.2	odd	2		546.2.bk.b.415.1	yes	12
7.4	even	3	inner	1638.2.dm.c.1117.1		12
13.12	even	2	inner	1638.2.dm.c.415.1		12
21.2	odd	6		3822.2.c.k.883.6		6
21.5	even	6		3822.2.c.j.883.4		6
21.11	odd	6		546.2.bk.b.25.6	yes	12
39.38	odd	2		546.2.bk.b.415.6	yes	12
91.25	even	6	inner	1638.2.dm.c.1117.6		12
273.116	odd	6		546.2.bk.b.25.1	✓	12
273.194	even	6		3822.2.c.j.883.3		6
273.233	odd	6		3822.2.c.k.883.1		6

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

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(2.25312 + 1.30084i) q^{5} +(1.49160 + 2.18521i) q^{7} +1.00000i q^{8} +(1.30084 + 2.25312i) q^{10} +(3.11915 - 1.80084i) q^{11} +(3.60168 + 0.167055i) q^{13} +(0.199160 + 2.63824i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.41647 - 2.45340i) q^{17} +(1.15537 + 0.667055i) q^{19} +2.60168i q^{20} +3.60168 q^{22} +(1.46789 - 2.54247i) q^{23} +(0.884367 + 1.53177i) q^{25} +(3.03562 + 1.94551i) q^{26} +(-1.14664 + 2.38437i) q^{28} -8.97209 q^{29} +(3.46410 - 2.00000i) q^{31} +(-0.866025 + 0.500000i) q^{32} -2.83294i q^{34} +(0.518152 + 6.86387i) q^{35} +(0.144674 + 0.0835276i) q^{37} +(0.667055 + 1.15537i) q^{38} +(-1.30084 + 2.25312i) q^{40} -3.03630i q^{41} +2.33411 q^{43} +(3.11915 + 1.80084i) q^{44} +(2.54247 - 1.46789i) q^{46} +(-8.43580 - 4.87041i) q^{47} +(-2.55026 + 6.51891i) q^{49} +1.76873i q^{50} +(1.65617 + 3.20267i) q^{52} +(1.50000 + 2.59808i) q^{53} +9.37041 q^{55} +(-2.18521 + 1.49160i) q^{56} +(-7.77006 - 4.48605i) q^{58} +(-10.0232 + 5.78689i) q^{59} +(-2.01815 + 3.49554i) q^{61} +4.00000 q^{62} -1.00000 q^{64} +(7.89770 + 5.06160i) q^{65} +(-10.1679 + 5.87041i) q^{67} +(1.41647 - 2.45340i) q^{68} +(-2.98320 + 6.20336i) q^{70} -5.76873i q^{71} +(9.93411 - 5.73546i) q^{73} +(0.0835276 + 0.144674i) q^{74} +1.33411i q^{76} +(8.58773 + 4.12985i) q^{77} +(-3.37041 + 5.83773i) q^{79} +(-2.25312 + 1.30084i) q^{80} +(1.51815 - 2.62952i) q^{82} -8.10051i q^{83} -7.37041i q^{85} +(2.02140 + 1.16706i) q^{86} +(1.80084 + 3.11915i) q^{88} +(-7.07288 - 4.08353i) q^{89} +(5.00722 + 8.11959i) q^{91} +2.93579 q^{92} +(-4.87041 - 8.43580i) q^{94} +(1.73546 + 3.00591i) q^{95} -0.139148i q^{97} +(-5.46804 + 4.37041i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} + 12 q^{13} + 18 q^{14} - 6 q^{16} - 18 q^{17} + 12 q^{22} - 6 q^{25} - 12 q^{29} - 24 q^{35} + 6 q^{38} + 24 q^{43} - 18 q^{49} + 6 q^{52} + 18 q^{53} + 48 q^{55} + 6 q^{56} + 6 q^{61} + 48 q^{62}+ \cdots - 24 q^{95}+O(q^{100}) \) 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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