LMFDB - Embedded newform 539.2.e.l.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(67,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("539.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.30393666895$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1783323.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 $ x^6 - x^5 + 5x^4 - 2x^3 + 19x^2 - 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$1.09935 - 1.90412i$ of defining polynomial
Character	$\chi$	$=$	539.67
Dual form			539.2.e.l.177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.917122 - 1.58850i) q^{2} +(-1.09935 + 1.90412i) q^{3} +(-0.682224 + 1.18165i) q^{4} +(-0.317776 - 0.550404i) q^{5} +4.03293 q^{6} -1.16576 q^{8} +(-0.917122 - 1.58850i) q^{9} +O(q^{10})$	\(q+(-0.917122 - 1.58850i) q^{2} +(-1.09935 + 1.90412i) q^{3} +(-0.682224 + 1.18165i) q^{4} +(-0.317776 - 0.550404i) q^{5} +4.03293 q^{6} -1.16576 q^{8} +(-0.917122 - 1.58850i) q^{9} +(-0.582878 + 1.00958i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-1.50000 - 2.59808i) q^{12} +1.80131 q^{13} +1.39738 q^{15} +(2.43359 + 4.21510i) q^{16} +(-1.41712 + 2.45453i) q^{17} +(-1.68222 + 2.91370i) q^{18} +(-2.78157 - 4.81782i) q^{19} +0.867178 q^{20} -1.83424 q^{22} +(-1.08288 - 1.87560i) q^{23} +(1.28157 - 2.21974i) q^{24} +(2.29804 - 3.98032i) q^{25} +(-1.65202 - 2.86138i) q^{26} -2.56314 q^{27} -10.4303 q^{29} +(-1.28157 - 2.21974i) q^{30} +(3.21516 - 5.56882i) q^{31} +(3.29804 - 5.71237i) q^{32} +(1.09935 + 1.90412i) q^{33} +5.19869 q^{34} +2.50273 q^{36} +(-3.03293 - 5.25320i) q^{37} +(-5.10208 + 8.83705i) q^{38} +(-1.98026 + 3.42991i) q^{39} +(0.370450 + 0.641637i) q^{40} -7.53566 q^{41} -4.86718 q^{43} +(0.682224 + 1.18165i) q^{44} +(-0.582878 + 1.00958i) q^{45} +(-1.98626 + 3.44031i) q^{46} +(-1.41712 - 2.45453i) q^{47} -10.7014 q^{48} -8.43032 q^{50} +(-3.11581 - 5.39675i) q^{51} +(-1.22890 + 2.12851i) q^{52} +(-3.73490 + 6.46903i) q^{53} +(2.35071 + 4.07155i) q^{54} -0.635552 q^{55} +12.2316 q^{57} +(9.56587 + 16.5686i) q^{58} +(5.90338 - 10.2250i) q^{59} +(-0.953328 + 1.65121i) q^{60} +(-2.16576 - 3.75120i) q^{61} -11.7948 q^{62} -2.36445 q^{64} +(-0.572413 - 0.991448i) q^{65} +(2.01647 - 3.49262i) q^{66} +(0.801309 - 1.38791i) q^{67} +(-1.93359 - 3.34907i) q^{68} +4.76183 q^{69} +4.29204 q^{71} +(1.06914 + 1.85181i) q^{72} +(-7.99673 + 13.8507i) q^{73} +(-5.56314 + 9.63564i) q^{74} +(5.05267 + 8.75149i) q^{75} +7.59061 q^{76} +7.26456 q^{78} +(-2.38092 - 4.12387i) q^{79} +(1.54667 - 2.67891i) q^{80} +(5.56914 - 9.64603i) q^{81} +(6.91112 + 11.9704i) q^{82} +9.23163 q^{83} +1.80131 q^{85} +(4.46379 + 7.73152i) q^{86} +(11.4665 - 19.8606i) q^{87} +(-0.582878 + 1.00958i) q^{88} +(0.182224 + 0.315621i) q^{89} +2.13828 q^{90} +2.95506 q^{92} +(7.06914 + 12.2441i) q^{93} +(-2.59935 + 4.50220i) q^{94} +(-1.76783 + 3.06197i) q^{95} +(7.25136 + 12.5597i) q^{96} +2.59607 q^{97} -1.83424 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{3} - 4 q^{4} - 2 q^{5} + 2 q^{6} - 18 q^{8}+O(q^{10}) $ 6 * q - q^3 - 4 * q^4 - 2 * q^5 + 2 * q^6 - 18 * q^8	$ 6 q - q^{3} - 4 q^{4} - 2 q^{5} + 2 q^{6} - 18 q^{8} - 9 q^{10} + 3 q^{11} - 9 q^{12} + 22 q^{13} - 14 q^{15} - 2 q^{16} - 3 q^{17} - 10 q^{18} - 11 q^{19} - 28 q^{20} - 12 q^{23} + 2 q^{24} - 3 q^{25} + q^{26} - 4 q^{27} - 18 q^{29} - 2 q^{30} - 3 q^{31} + 3 q^{32} + q^{33} + 20 q^{34} - 18 q^{36} + 4 q^{37} + 8 q^{38} + 5 q^{39} - 3 q^{40} + 10 q^{41} + 4 q^{43} + 4 q^{44} - 9 q^{45} + 10 q^{46} - 3 q^{47} - 20 q^{48} - 6 q^{50} - 2 q^{51} - 7 q^{52} - 17 q^{53} - 8 q^{54} - 4 q^{55} + 40 q^{57} + 13 q^{58} + 8 q^{59} - 6 q^{60} - 24 q^{61} - 26 q^{62} - 14 q^{64} - 15 q^{65} + q^{66} + 16 q^{67} + 5 q^{68} + 6 q^{69} + 14 q^{71} - 10 q^{72} - 20 q^{73} - 22 q^{74} + 25 q^{75} + 78 q^{76} - 12 q^{78} - 3 q^{79} + 9 q^{80} + 17 q^{81} + 41 q^{82} + 22 q^{83} + 22 q^{85} + 21 q^{86} + 30 q^{87} - 9 q^{88} + q^{89} - 20 q^{90} + 50 q^{92} + 26 q^{93} - 10 q^{94} + 17 q^{95} + 27 q^{96} - 18 q^{97}+O(q^{100}) $ 6 * q - q^3 - 4 * q^4 - 2 * q^5 + 2 * q^6 - 18 * q^8 - 9 * q^10 + 3 * q^11 - 9 * q^12 + 22 * q^13 - 14 * q^15 - 2 * q^16 - 3 * q^17 - 10 * q^18 - 11 * q^19 - 28 * q^20 - 12 * q^23 + 2 * q^24 - 3 * q^25 + q^26 - 4 * q^27 - 18 * q^29 - 2 * q^30 - 3 * q^31 + 3 * q^32 + q^33 + 20 * q^34 - 18 * q^36 + 4 * q^37 + 8 * q^38 + 5 * q^39 - 3 * q^40 + 10 * q^41 + 4 * q^43 + 4 * q^44 - 9 * q^45 + 10 * q^46 - 3 * q^47 - 20 * q^48 - 6 * q^50 - 2 * q^51 - 7 * q^52 - 17 * q^53 - 8 * q^54 - 4 * q^55 + 40 * q^57 + 13 * q^58 + 8 * q^59 - 6 * q^60 - 24 * q^61 - 26 * q^62 - 14 * q^64 - 15 * q^65 + q^66 + 16 * q^67 + 5 * q^68 + 6 * q^69 + 14 * q^71 - 10 * q^72 - 20 * q^73 - 22 * q^74 + 25 * q^75 + 78 * q^76 - 12 * q^78 - 3 * q^79 + 9 * q^80 + 17 * q^81 + 41 * q^82 + 22 * q^83 + 22 * q^85 + 21 * q^86 + 30 * q^87 - 9 * q^88 + q^89 - 20 * q^90 + 50 * q^92 + 26 * q^93 - 10 * q^94 + 17 * q^95 + 27 * q^96 - 18 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.917122	−	1.58850i	−0.648503	−	1.12324i	−0.983481	−	0.181014i	$-0.942062\pi$
$2$	−0.917122	−	1.58850i	−0.648503	−	1.12324i	0.334978	−	0.942226i	$-0.391271\pi$
$3$	−1.09935	+	1.90412i	−0.634707	+	1.09935i	0.351870	+	0.936049i	$0.385546\pi$
$3$	−1.09935	+	1.90412i	−0.634707	+	1.09935i	−0.986577	+	0.163297i	$0.947787\pi$
$4$	−0.682224	+	1.18165i	−0.341112	+	0.590823i
$5$	−0.317776	−	0.550404i	−0.142114	−	0.246148i	0.786179	−	0.617999i	$-0.212057\pi$
$5$	−0.317776	−	0.550404i	−0.142114	−	0.246148i	−0.928292	+	0.371851i	$0.878723\pi$
$6$	4.03293			1.64644
$7$		0			0
$7$		0			0
$8$	−1.16576			−0.412157
$9$	−0.917122	−	1.58850i	−0.305707	−	0.529500i
$10$	−0.582878	+	1.00958i	−0.184322	+	0.319256i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	−1.50000	−	2.59808i	−0.433013	−	0.750000i
$13$	1.80131			0.499593			0.249797	−	0.968298i	$-0.419636\pi$
$13$	1.80131			0.499593			0.249797	+	0.968298i	$0.419636\pi$
$14$		0			0
$15$	1.39738			0.360803
$16$	2.43359	+	4.21510i	0.608397	+	1.05377i
$17$	−1.41712	+	2.45453i	−0.343702	+	0.595310i	−0.985117	−	0.171884i	$-0.945014\pi$
$17$	−1.41712	+	2.45453i	−0.343702	+	0.595310i	0.641415	+	0.767194i	$0.278348\pi$
$18$	−1.68222	+	2.91370i	−0.396504	+	0.686765i
$19$	−2.78157	−	4.81782i	−0.638136	−	1.10528i	−0.985841	−	0.167680i	$-0.946372\pi$
$19$	−2.78157	−	4.81782i	−0.638136	−	1.10528i	0.347706	−	0.937604i	$-0.386961\pi$
$20$	0.867178			0.193907
$21$		0			0
$22$	−1.83424			−0.391062
$23$	−1.08288	−	1.87560i	−0.225796	−	0.391090i	0.730762	−	0.682632i	$-0.239165\pi$
$23$	−1.08288	−	1.87560i	−0.225796	−	0.391090i	−0.956558	+	0.291542i	$0.905832\pi$
$24$	1.28157	−	2.21974i	0.261599	−	0.453103i
$25$	2.29804	−	3.98032i	0.459607	−	0.796063i
$26$	−1.65202	−	2.86138i	−0.323988	−	0.561163i
$27$	−2.56314			−0.493276
$28$		0			0
$29$	−10.4303			−1.93686			−0.968431	−	0.249283i	$-0.919805\pi$
$29$	−10.4303			−1.93686			−0.968431	+	0.249283i	$0.919805\pi$
$30$	−1.28157	−	2.21974i	−0.233982	−	0.405268i
$31$	3.21516	−	5.56882i	0.577460	−	1.00019i	−0.418310	−	0.908304i	$-0.637377\pi$
$31$	3.21516	−	5.56882i	0.577460	−	1.00019i	0.995770	−	0.0918849i	$-0.0292892\pi$
$32$	3.29804	−	5.71237i	0.583016	−	1.00981i
$33$	1.09935	+	1.90412i	0.191372	+	0.331465i
$34$	5.19869			0.891568
$35$		0			0
$36$	2.50273			0.417122
$37$	−3.03293	−	5.25320i	−0.498611	−	0.863620i	0.501387	−	0.865223i	$-0.332823\pi$
$37$	−3.03293	−	5.25320i	−0.498611	−	0.863620i	−0.999999	+	0.00160274i	$0.999490\pi$
$38$	−5.10208	+	8.83705i	−0.827666	+	1.43356i
$39$	−1.98026	+	3.42991i	−0.317096	+	0.549226i
$40$	0.370450	+	0.641637i	0.0585732	+	0.101452i
$41$	−7.53566			−1.17687			−0.588436	−	0.808543i	$-0.700256\pi$
$41$	−7.53566			−1.17687			−0.588436	+	0.808543i	$0.700256\pi$
$42$		0			0
$43$	−4.86718			−0.742238			−0.371119	−	0.928585i	$-0.621026\pi$
$43$	−4.86718			−0.742238			−0.371119	+	0.928585i	$0.621026\pi$
$44$	0.682224	+	1.18165i	0.102849	+	0.178140i
$45$	−0.582878	+	1.00958i	−0.0868904	+	0.150499i
$46$	−1.98626	+	3.44031i	−0.292858	+	0.507246i
$47$	−1.41712	−	2.45453i	−0.206708	−	0.358030i	0.743967	−	0.668216i	$-0.232942\pi$
$47$	−1.41712	−	2.45453i	−0.206708	−	0.358030i	−0.950676	+	0.310187i	$0.899608\pi$
$48$	−10.7014			−1.54462
$49$		0			0
$50$	−8.43032			−1.19223
$51$	−3.11581	−	5.39675i	−0.436301	−	0.755696i
$52$	−1.22890	+	2.12851i	−0.170417	+	0.295171i
$53$	−3.73490	+	6.46903i	−0.513028	+	0.888590i	0.486858	+	0.873481i	$0.338143\pi$
$53$	−3.73490	+	6.46903i	−0.513028	+	0.888590i	−0.999886	+	0.0151089i	$0.995190\pi$
$54$	2.35071	+	4.07155i	0.319891	+	0.554068i
$55$	−0.635552			−0.0856978
$56$		0			0
$57$	12.2316			1.62012
$58$	9.56587	+	16.5686i	1.25606	+	2.17556i
$59$	5.90338	−	10.2250i	0.768555	−	1.33118i	−0.169791	−	0.985480i	$-0.554309\pi$
$59$	5.90338	−	10.2250i	0.768555	−	1.33118i	0.938346	−	0.345696i	$-0.112357\pi$
$60$	−0.953328	+	1.65121i	−0.123074	+	0.213171i
$61$	−2.16576	−	3.75120i	−0.277297	−	0.480292i	0.693415	−	0.720538i	$-0.256105\pi$
$61$	−2.16576	−	3.75120i	−0.277297	−	0.480292i	−0.970712	+	0.240246i	$0.922772\pi$
$62$	−11.7948			−1.49794
$63$		0			0
$64$	−2.36445			−0.295556
$65$	−0.572413	−	0.991448i	−0.0709990	−	0.122974i
$66$	2.01647	−	3.49262i	0.248210	−	0.429912i
$67$	0.801309	−	1.38791i	0.0978954	−	0.169560i	−0.812918	−	0.582378i	$-0.802122\pi$
$67$	0.801309	−	1.38791i	0.0978954	−	0.169560i	0.910813	+	0.412818i	$0.135456\pi$
$68$	−1.93359	−	3.34907i	−0.234482	−	0.406135i
$69$	4.76183			0.573257
$70$		0			0
$71$	4.29204			0.509371			0.254685	−	0.967024i	$-0.418028\pi$
$71$	4.29204			0.509371			0.254685	+	0.967024i	$0.418028\pi$
$72$	1.06914	+	1.85181i	0.125999	+	0.218237i
$73$	−7.99673	+	13.8507i	−0.935946	+	1.62111i	−0.163008	+	0.986625i	$0.552120\pi$
$73$	−7.99673	+	13.8507i	−0.935946	+	1.62111i	−0.772938	+	0.634482i	$0.781214\pi$
$74$	−5.56314	+	9.63564i	−0.646702	+	1.12012i
$75$	5.05267	+	8.75149i	0.583432	+	1.01053i
$76$	7.59061			0.870703
$77$		0			0
$78$	7.26456			0.822549
$79$	−2.38092	−	4.12387i	−0.267874	−	0.463971i	0.700439	−	0.713713i	$-0.252988\pi$
$79$	−2.38092	−	4.12387i	−0.267874	−	0.463971i	−0.968313	+	0.249741i	$0.919654\pi$
$80$	1.54667	−	2.67891i	0.172923	−	0.299512i
$81$	5.56914	−	9.64603i	0.618793	−	1.07178i
$82$	6.91112	+	11.9704i	0.763206	+	1.32191i
$83$	9.23163			1.01330			0.506651	−	0.862151i	$-0.330883\pi$
$83$	9.23163			1.01330			0.506651	+	0.862151i	$0.330883\pi$
$84$		0			0
$85$	1.80131			0.195379
$86$	4.46379	+	7.73152i	0.481343	+	0.833711i
$87$	11.4665	−	19.8606i	1.22934	−	2.12928i
$88$	−0.582878	+	1.00958i	−0.0621350	+	0.107621i
$89$	0.182224	+	0.315621i	0.0193157	+	0.0334558i	0.875522	−	0.483179i	$-0.160518\pi$
$89$	0.182224	+	0.315621i	0.0193157	+	0.0334558i	−0.856206	+	0.516635i	$0.827185\pi$
$90$	2.13828			0.225395
$91$		0			0
$92$	2.95506			0.308087
$93$	7.06914	+	12.2441i	0.733036	+	1.26966i
$94$	−2.59935	+	4.50220i	−0.268102	+	0.464366i
$95$	−1.76783	+	3.06197i	−0.181376	+	0.314152i
$96$	7.25136	+	12.5597i	0.740089	+	1.28187i
$97$	2.59607			0.263591			0.131796	−	0.991277i	$-0.457926\pi$
$97$	2.59607			0.263591			0.131796	+	0.991277i	$0.457926\pi$
$98$		0			0
$99$	−1.83424			−0.184348
$100$	3.13555	+	5.43094i	0.313555	+	0.543094i
$101$	−4.95006	+	8.57375i	−0.492549	+	0.853120i	−0.999963	−	0.00858243i	$-0.997268\pi$
$101$	−4.95006	+	8.57375i	−0.492549	+	0.853120i	0.507414	+	0.861702i	$0.330601\pi$
$102$	−5.71516	+	9.89894i	−0.565885	+	0.980142i
$103$	3.11581	+	5.39675i	0.307010	+	0.531757i	0.977707	−	0.209975i	$-0.0673381\pi$
$103$	3.11581	+	5.39675i	0.307010	+	0.531757i	−0.670697	+	0.741732i	$0.734005\pi$
$104$	−2.09989			−0.205911
$105$		0			0
$106$	13.7014			1.33080
$107$	−5.54940	−	9.61185i	−0.536481	−	0.929212i	−0.999090	−	0.0426499i	$-0.986420\pi$
$107$	−5.54940	−	9.61185i	−0.536481	−	0.929212i	0.462609	−	0.886562i	$-0.346913\pi$
$108$	1.74864	−	3.02873i	0.168263	−	0.291439i
$109$	7.15202	−	12.3877i	0.685039	−	1.18652i	−0.288385	−	0.957514i	$-0.593118\pi$
$109$	7.15202	−	12.3877i	0.685039	−	1.18652i	0.973424	−	0.229008i	$-0.0735483\pi$
$110$	0.582878	+	1.00958i	0.0555753	+	0.0962592i
$111$	13.3370			1.26589
$112$		0			0
$113$	−8.68942			−0.817432			−0.408716	−	0.912662i	$-0.634023\pi$
$113$	−8.68942			−0.817432			−0.408716	+	0.912662i	$0.634023\pi$
$114$	−11.2179	−	19.4300i	−1.05065	−	1.81978i
$115$	−0.688225	+	1.19204i	−0.0641774	+	0.111158i
$116$	7.11581	−	12.3249i	0.660687	−	1.14434i
$117$	−1.65202	−	2.86138i	−0.152729	−	0.264535i
$118$	−21.6565			−1.99364
$119$		0			0
$120$	−1.62901			−0.148707
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−3.97252	+	6.88061i	−0.359655	+	0.622942i
$123$	8.28430	−	14.3488i	0.746970	−	1.29379i
$124$	4.38692	+	7.59836i	0.393957	+	0.682353i
$125$	−6.09880			−0.545494
$126$		0			0
$127$	20.9989			1.86335			0.931676	−	0.363290i	$-0.118346\pi$
$127$	20.9989			1.86335			0.931676	+	0.363290i	$0.118346\pi$
$128$	−4.42759	−	7.66881i	−0.391347	−	0.677833i
$129$	5.35071	−	9.26770i	0.471104	−	0.815976i
$130$	−1.04994	+	1.81856i	−0.0920862	+	0.159498i
$131$	−6.85071	−	11.8658i	−0.598549	−	1.03672i	−0.993035	−	0.117816i	$-0.962411\pi$
$131$	−6.85071	−	11.8658i	−0.598549	−	1.03672i	0.394486	−	0.918902i	$-0.370923\pi$
$132$	−3.00000			−0.261116
$133$		0			0
$134$	−2.93959			−0.253942
$135$	0.814504	+	1.41076i	0.0701013	+	0.121419i
$136$	1.65202	−	2.86138i	0.141659	−	0.245361i
$137$	−3.63228	+	6.29129i	−0.310327	+	0.537501i	−0.978433	−	0.206564i	$-0.933772\pi$
$137$	−3.63228	+	6.29129i	−0.310327	+	0.537501i	0.668106	+	0.744066i	$0.267105\pi$
$138$	−4.36718	−	7.56417i	−0.371759	−	0.643905i
$139$	2.60262			0.220751			0.110376	−	0.993890i	$-0.464795\pi$
$139$	2.60262			0.220751			0.110376	+	0.993890i	$0.464795\pi$
$140$		0			0
$141$	6.23163			0.524798
$142$	−3.93632	−	6.81790i	−0.330328	−	0.572146i
$143$	0.900654	−	1.55998i	0.0753165	−	0.130452i
$144$	4.46379	−	7.73152i	0.371983	−	0.644293i
$145$	3.31450	+	5.74089i	0.275255	+	0.476755i
$146$	29.3359			2.42786
$147$		0			0
$148$	8.27656			0.680329
$149$	0.500000	+	0.866025i	0.0409616	+	0.0709476i	0.885779	−	0.464107i	$-0.153625\pi$
$149$	0.500000	+	0.866025i	0.0409616	+	0.0709476i	−0.844818	+	0.535054i	$0.820291\pi$
$150$	9.26783	−	16.0524i	0.756715	−	1.31067i
$151$	−0.867720	+	1.50294i	−0.0706140	+	0.122307i	−0.899171	−	0.437598i	$-0.855829\pi$
$151$	−0.867720	+	1.50294i	−0.0706140	+	0.122307i	0.828557	+	0.559905i	$0.189163\pi$
$152$	3.24263	+	5.61641i	0.263012	+	0.455551i
$153$	5.19869			0.420289
$154$		0			0
$155$	−4.08680			−0.328260
$156$	−2.70196	−	4.67994i	−0.216330	−	0.374695i
$157$	−3.96980	+	6.87589i	−0.316824	+	0.548756i	−0.979824	−	0.199864i	$-0.935950\pi$
$157$	−3.96980	+	6.87589i	−0.316824	+	0.548756i	0.662999	+	0.748620i	$0.269283\pi$
$158$	−4.36718	+	7.56417i	−0.347434	+	0.601773i
$159$	−8.21189	−	14.2234i	−0.651245	−	1.12799i
$160$	−4.19215			−0.331418
$161$		0			0
$162$	−20.4303			−1.60516
$163$	8.00273	+	13.8611i	0.626822	+	1.08569i	0.988185	+	0.153263i	$0.0489781\pi$
$163$	8.00273	+	13.8611i	0.626822	+	1.08569i	−0.361363	+	0.932425i	$0.617689\pi$
$164$	5.14101	−	8.90449i	0.401446	−	0.695324i
$165$	0.698691	−	1.21017i	0.0543930	−	0.0942115i
$166$	−8.46652	−	14.6644i	−0.657130	−	1.13818i
$167$	−1.15921			−0.0897026			−0.0448513	−	0.998994i	$-0.514281\pi$
$167$	−1.15921			−0.0897026			−0.0448513	+	0.998994i	$0.514281\pi$
$168$		0			0
$169$	−9.75529			−0.750407
$170$	−1.65202	−	2.86138i	−0.126704	−	0.219458i
$171$	−5.10208	+	8.83705i	−0.390165	+	0.675786i
$172$	3.32051	−	5.75128i	0.253186	−	0.438531i
$173$	−0.496728	−	0.860358i	−0.0377655	−	0.0654118i	0.846525	−	0.532349i	$-0.178691\pi$
$173$	−0.496728	−	0.860358i	−0.0377655	−	0.0654118i	−0.884290	+	0.466937i	$0.845357\pi$
$174$	−42.0648			−3.18892
$175$		0			0
$176$	4.86718			0.366877
$177$	12.9797	+	22.4815i	0.975615	+	1.68982i
$178$	0.334243	−	0.578926i	0.0250526	−	0.0433924i
$179$	9.83097	−	17.0277i	0.734801	−	1.27271i	−0.220009	−	0.975498i	$-0.570609\pi$
$179$	9.83097	−	17.0277i	0.734801	−	1.27271i	0.954810	−	0.297215i	$-0.0960579\pi$
$180$	−0.795307	−	1.37751i	−0.0592787	−	0.102674i
$181$	23.8726			1.77444			0.887220	−	0.461347i	$-0.152634\pi$
$181$	23.8726			1.77444			0.887220	+	0.461347i	$0.152634\pi$
$182$		0			0
$183$	9.52366			0.704009
$184$	1.26237	+	2.18649i	0.0930634	+	0.161190i
$185$	−1.92759	+	3.33868i	−0.141719	+	0.245465i
$186$	12.9665	−	22.4587i	0.950752	−	1.64675i
$187$	1.41712	+	2.45453i	0.103630	+	0.179493i
$188$	3.86718			0.282043
$189$		0			0
$190$	6.48527			0.470491
$191$	5.56587	+	9.64037i	0.402732	+	0.697553i	0.994055	−	0.108883i	$-0.0347273\pi$
$191$	5.56587	+	9.64037i	0.402732	+	0.697553i	−0.591322	+	0.806435i	$0.701394\pi$
$192$	2.59935	−	4.50220i	0.187592	−	0.324918i
$193$	−1.80731	+	3.13035i	−0.130093	+	0.225328i	−0.923712	−	0.383087i	$-0.874861\pi$
$193$	−1.80731	+	3.13035i	−0.130093	+	0.225328i	0.793619	+	0.608415i	$0.208194\pi$
$194$	−2.38092	−	4.12387i	−0.170940	−	0.296076i
$195$	2.51712			0.180255
$196$		0			0
$197$	2.41831			0.172298			0.0861489	−	0.996282i	$-0.472544\pi$
$197$	2.41831			0.172298			0.0861489	+	0.996282i	$0.472544\pi$
$198$	1.68222	+	2.91370i	0.119550	+	0.207067i
$199$	−9.24809	+	16.0182i	−0.655580	+	1.13550i	0.326168	+	0.945312i	$0.394242\pi$
$199$	−9.24809	+	16.0182i	−0.655580	+	1.13550i	−0.981748	+	0.190186i	$0.939091\pi$
$200$	−2.67895	+	4.64008i	−0.189431	+	0.328103i
$201$	1.76183	+	3.05158i	0.124270	+	0.215242i
$202$	18.1592			1.27768
$203$		0			0
$204$	8.50273			0.595310
$205$	2.39465	+	4.14766i	0.167250	+	0.289685i
$206$	5.71516	−	9.89894i	0.398194	−	0.689692i
$207$	−1.98626	+	3.44031i	−0.138055	+	0.239118i
$208$	4.38364	+	7.59270i	0.303951	+	0.526459i
$209$	−5.56314			−0.384810
$210$		0			0
$211$	−7.85517			−0.540773			−0.270386	−	0.962752i	$-0.587151\pi$
$211$	−7.85517			−0.540773			−0.270386	+	0.962752i	$0.587151\pi$
$212$	−5.09607	−	8.82666i	−0.350000	−	0.606217i
$213$	−4.71843	+	8.17256i	−0.323302	+	0.559975i
$214$	−10.1790	+	17.6305i	−0.695819	+	1.20519i
$215$	1.54667	+	2.67891i	0.105482	+	0.182700i
$216$	2.98800			0.203307
$217$		0			0
$218$	−26.2371			−1.77700
$219$	−17.5823	−	30.4535i	−1.18810	−	2.05786i
$220$	0.433589	−	0.750998i	0.0292326	−	0.0506323i
$221$	−2.55267	+	4.42136i	−0.171711	+	0.297413i
$222$	−12.2316	−	21.1858i	−0.820933	−	1.42190i
$223$	−20.3370			−1.36186			−0.680932	−	0.732346i	$-0.738425\pi$
$223$	−20.3370			−1.36186			−0.680932	+	0.732346i	$0.738425\pi$
$224$		0			0
$225$	−8.43032			−0.562021
$226$	7.96925	+	13.8032i	0.530107	+	0.918172i
$227$	3.60981	−	6.25238i	0.239592	−	0.414985i	−0.721006	−	0.692929i	$-0.756320\pi$
$227$	3.60981	−	6.25238i	0.239592	−	0.414985i	0.960597	+	0.277944i	$0.0896531\pi$
$228$	−8.34471	+	14.4535i	−0.552642	+	0.957204i
$229$	6.03566	+	10.4541i	0.398848	+	0.690825i	0.993584	−	0.113096i	$-0.0360768\pi$
$229$	6.03566	+	10.4541i	0.398848	+	0.690825i	−0.594736	+	0.803921i	$0.702743\pi$
$230$	2.52475			0.166477
$231$		0			0
$232$	12.1592			0.798291
$233$	3.77110	+	6.53174i	0.247053	+	0.427909i	0.962707	−	0.270547i	$-0.0872044\pi$
$233$	3.77110	+	6.53174i	0.247053	+	0.427909i	−0.715654	+	0.698455i	$0.753871\pi$
$234$	−3.03020	+	5.24847i	−0.198091	+	0.343103i
$235$	−0.900654	+	1.55998i	−0.0587522	+	0.101762i
$236$	8.05486	+	13.9514i	0.524327	+	0.908161i
$237$	10.4698			0.680086
$238$		0			0
$239$	−9.84625			−0.636901			−0.318450	−	0.947940i	$-0.603162\pi$
$239$	−9.84625			−0.636901			−0.318450	+	0.947940i	$0.603162\pi$
$240$	3.40065	+	5.89011i	0.219511	+	0.380205i
$241$	−0.837515	+	1.45062i	−0.0539491	+	0.0934426i	−0.891739	−	0.452551i	$-0.850514\pi$
$241$	−0.837515	+	1.45062i	−0.0539491	+	0.0934426i	0.837790	+	0.545993i	$0.183848\pi$
$242$	−0.917122	+	1.58850i	−0.0589548	+	0.102113i
$243$	8.40011	+	14.5494i	0.538867	+	0.933346i
$244$	5.91013			0.378357
$245$		0			0
$246$	−30.3908			−1.93765
$247$	−5.01047	−	8.67838i	−0.318808	−	0.552192i
$248$	−3.74809	+	6.49189i	−0.238004	+	0.412235i
$249$	−10.1487	+	17.5781i	−0.643151	+	1.11397i
$250$	5.59334	+	9.68796i	0.353754	+	0.612720i
$251$	−19.7738			−1.24811			−0.624057	−	0.781379i	$-0.714517\pi$
$251$	−19.7738			−1.24811			−0.624057	+	0.781379i	$0.714517\pi$
$252$		0			0
$253$	−2.16576			−0.136160
$254$	−19.2586	−	33.3568i	−1.20839	−	2.09299i
$255$	−1.98026	+	3.42991i	−0.124009	+	0.214789i
$256$	−10.4857	+	18.1618i	−0.655358	+	1.13511i
$257$	1.35998	+	2.35556i	0.0848335	+	0.146936i	0.905320	−	0.424730i	$-0.139631\pi$
$257$	1.35998	+	2.35556i	0.0848335	+	0.146936i	−0.820487	+	0.571665i	$0.806298\pi$
$258$	−19.6290			−1.22205
$259$		0			0
$260$	1.56205			0.0968745
$261$	9.56587	+	16.5686i	0.592112	+	1.02557i
$262$	−12.5659	+	21.7647i	−0.776322	+	1.34463i
$263$	−6.34744	+	10.9941i	−0.391400	+	0.677924i	−0.992634	−	0.121148i	$-0.961342\pi$
$263$	−6.34744	+	10.9941i	−0.391400	+	0.677924i	0.601235	+	0.799073i	$0.294676\pi$
$264$	−1.28157	−	2.21974i	−0.0788752	−	0.136616i
$265$	4.74744			0.291633
$266$		0			0
$267$	−0.801309			−0.0490393
$268$	1.09334	+	1.89373i	0.0667866	+	0.115678i
$269$	−3.54667	+	6.14302i	−0.216244	+	0.374546i	−0.953657	−	0.300896i	$-0.902714\pi$
$269$	−3.54667	+	6.14302i	−0.216244	+	0.374546i	0.737412	+	0.675443i	$0.236047\pi$
$270$	1.49400	−	2.58768i	0.0909219	−	0.157481i
$271$	−9.10808	−	15.7757i	−0.553276	−	0.958303i	−0.998035	−	0.0626524i	$-0.980044\pi$
$271$	−9.10808	−	15.7757i	−0.553276	−	0.958303i	0.444759	−	0.895650i	$-0.353289\pi$
$272$	−13.7948			−0.836430
$273$		0			0
$274$	13.3250			0.804991
$275$	−2.29804	−	3.98032i	−0.138577	−	0.240022i
$276$	−3.24864	+	5.62680i	−0.195545	+	0.338694i
$277$	−6.92432	+	11.9933i	−0.416042	+	0.720606i	−0.995537	−	0.0943700i	$-0.969916\pi$
$277$	−6.92432	+	11.9933i	−0.416042	+	0.720606i	0.579495	+	0.814976i	$0.303250\pi$
$278$	−2.38692	−	4.13426i	−0.143158	−	0.247956i
$279$	−11.7948			−0.706134
$280$		0			0
$281$	21.0329			1.25472			0.627360	−	0.778730i	$-0.284136\pi$
$281$	21.0329			1.25472			0.627360	+	0.778730i	$0.284136\pi$
$282$	−5.71516	−	9.89894i	−0.340333	−	0.589474i
$283$	0.176223	−	0.305226i	0.0104753	−	0.0181438i	−0.860740	−	0.509044i	$-0.829999\pi$
$283$	0.176223	−	0.305226i	0.0104753	−	0.0181438i	0.871216	+	0.490901i	$0.163332\pi$
$284$	−2.92813	+	5.07167i	−0.173753	+	0.300948i
$285$	−3.88692	−	6.73234i	−0.230241	−	0.398789i
$286$	−3.30404			−0.195372
$287$		0			0
$288$	−12.0988			−0.712929
$289$	4.48353	+	7.76571i	0.263737	+	0.456806i
$290$	6.07961	−	10.5302i	0.357007	−	0.618354i
$291$	−2.85398	+	4.94324i	−0.167303	+	0.289778i
$292$	−10.9111	−	18.8986i	−0.638525	−	1.10596i
$293$	3.46325			0.202325			0.101163	−	0.994870i	$-0.467744\pi$
$293$	3.46325			0.202325			0.101163	+	0.994870i	$0.467744\pi$
$294$		0			0
$295$	−7.50381			−0.436889
$296$	3.53566	+	6.12395i	0.205506	+	0.355947i
$297$	−1.28157	+	2.21974i	−0.0743642	+	0.128803i
$298$	0.917122	−	1.58850i	0.0531274	−	0.0920194i
$299$	−1.95060	−	3.37854i	−0.112806	−	0.195386i
$300$	−13.7882			−0.796063
$301$		0			0
$302$	3.18322			0.183174
$303$	−10.8836	−	18.8510i	−0.625249	−	1.08296i
$304$	13.5384	−	23.4492i	0.776480	−	1.34490i
$305$	−1.37645	+	2.38408i	−0.0788154	+	0.136512i
$306$	−4.76783	−	8.25813i	−0.272559	−	0.472086i
$307$	6.51473			0.371815			0.185908	−	0.982567i	$-0.440477\pi$
$307$	6.51473			0.371815			0.185908	+	0.982567i	$0.440477\pi$
$308$		0			0
$309$	−13.7014			−0.779447
$310$	3.74809	+	6.49189i	0.212877	+	0.368714i
$311$	5.81505	−	10.0720i	0.329741	−	0.571128i	−0.652719	−	0.757600i	$-0.726372\pi$
$311$	5.81505	−	10.0720i	0.329741	−	0.571128i	0.982460	+	0.186472i	$0.0597052\pi$
$312$	2.30850	−	3.99844i	0.130693	−	0.226367i
$313$	−13.5489	−	23.4673i	−0.765827	−	1.32645i	−0.939808	−	0.341702i	$-0.888997\pi$
$313$	−13.5489	−	23.4673i	−0.765827	−	1.32645i	0.173982	−	0.984749i	$-0.444337\pi$
$314$	14.5631			0.821845
$315$		0			0
$316$	6.49727			0.365500
$317$	−1.93086	−	3.34435i	−0.108448	−	0.187837i	0.806694	−	0.590970i	$-0.201255\pi$
$317$	−1.93086	−	3.34435i	−0.108448	−	0.187837i	−0.915142	+	0.403132i	$0.867921\pi$
$318$	−15.0626	+	26.0892i	−0.844668	+	1.46301i
$319$	−5.21516	+	9.03292i	−0.291993	+	0.505746i
$320$	0.751365	+	1.30140i	0.0420026	+	0.0727506i
$321$	24.4028			1.36203
$322$		0			0
$323$	15.7673			0.877315
$324$	7.59880	+	13.1615i	0.422156	+	0.731195i
$325$	4.13947	−	7.16978i	0.229617	−	0.397708i
$326$	14.6790	−	25.4247i	0.812992	−	1.40814i
$327$	15.7251	+	27.2366i	0.869599	+	1.50619i
$328$	8.78475			0.485057
$329$		0			0
$330$	−2.56314			−0.141096
$331$	−3.07514	−	5.32630i	−0.169025	−	0.292760i	0.769052	−	0.639186i	$-0.220729\pi$
$331$	−3.07514	−	5.32630i	−0.169025	−	0.292760i	−0.938077	+	0.346426i	$0.887395\pi$
$332$	−6.29804	+	10.9085i	−0.345650	+	0.598683i
$333$	−5.56314	+	9.63564i	−0.304858	+	0.528030i
$334$	1.06314	+	1.84141i	0.0581724	+	0.100758i
$335$	−1.01855			−0.0556491
$336$		0			0
$337$	−11.7607			−0.640649			−0.320324	−	0.947308i	$-0.603792\pi$
$337$	−11.7607			−0.640649			−0.320324	+	0.947308i	$0.603792\pi$
$338$	8.94678	+	15.4963i	0.486641	+	0.842887i
$339$	9.55267	−	16.5457i	0.518830	−	0.898640i
$340$	−1.22890	+	2.12851i	−0.0666462	+	0.115435i
$341$	−3.21516	−	5.56882i	−0.174111	−	0.301568i
$342$	18.7169			1.01209
$343$		0			0
$344$	5.67395			0.305919
$345$	−1.51320	−	2.62093i	−0.0814677	−	0.141106i
$346$	−0.911120	+	1.57811i	−0.0489821	+	0.0848395i
$347$	0.420393	−	0.728143i	0.0225679	−	0.0390888i	−0.854521	−	0.519417i	$-0.826149\pi$
$347$	0.420393	−	0.728143i	0.0225679	−	0.0390888i	0.877089	+	0.480328i	$0.159482\pi$
$348$	15.6455	+	27.0988i	0.838686	+	1.45265i
$349$	−9.13174			−0.488811			−0.244405	−	0.969673i	$-0.578593\pi$
$349$	−9.13174			−0.488811			−0.244405	+	0.969673i	$0.578593\pi$
$350$		0			0
$351$	−4.61701			−0.246438
$352$	−3.29804	−	5.71237i	−0.175786	−	0.304470i
$353$	11.3639	−	19.6829i	0.604840	−	1.04761i	−0.387237	−	0.921980i	$-0.626571\pi$
$353$	11.3639	−	19.6829i	0.604840	−	1.04761i	0.992077	−	0.125633i	$-0.0400961\pi$
$354$	23.8080	−	41.2366i	1.26538	−	2.19170i
$355$	−1.36391	−	2.36235i	−0.0723886	−	0.125381i
$356$	−0.497270			−0.0263553
$357$		0			0
$358$	−36.0648			−1.90608
$359$	13.1093	+	22.7059i	0.691881	+	1.19837i	0.971221	+	0.238180i	$0.0765510\pi$
$359$	13.1093	+	22.7059i	0.691881	+	1.19837i	−0.279340	+	0.960192i	$0.590116\pi$
$360$	0.679494	−	1.17692i	0.0358125	−	0.0620291i
$361$	−5.97426	+	10.3477i	−0.314435	+	0.544617i
$362$	−21.8941	−	37.9217i	−1.15073	−	1.99312i
$363$	2.19869			0.115401
$364$		0			0
$365$	10.1647			0.532043
$366$	−8.73436	−	15.1283i	−0.456552	−	0.790771i
$367$	−1.91112	+	3.31016i	−0.0997597	+	0.172789i	−0.911585	−	0.411111i	$-0.865141\pi$
$367$	−1.91112	+	3.31016i	−0.0997597	+	0.172789i	0.811825	+	0.583900i	$0.198474\pi$
$368$	5.27056	−	9.12888i	0.274747	−	0.475876i
$369$	6.91112	+	11.9704i	0.359779	+	0.623155i
$370$	7.07133			0.367621
$371$		0			0
$372$	−19.2910			−1.00019
$373$	−7.55387	−	13.0837i	−0.391124	−	0.677447i	0.601474	−	0.798893i	$-0.294580\pi$
$373$	−7.55387	−	13.0837i	−0.391124	−	0.677447i	−0.992598	+	0.121445i	$0.961247\pi$
$374$	2.59935	−	4.50220i	0.134409	−	0.232803i
$375$	6.70469	−	11.6129i	0.346229	−	0.599686i
$376$	1.65202	+	2.86138i	0.0851964	+	0.147564i
$377$	−18.7882			−0.967643
$378$		0			0
$379$	−11.3765			−0.584369			−0.292185	−	0.956362i	$-0.594382\pi$
$379$	−11.3765			−0.584369			−0.292185	+	0.956362i	$0.594382\pi$
$380$	−2.41211	−	4.17791i	−0.123739	−	0.214322i
$381$	−23.0851	+	39.9845i	−1.18268	+	2.04847i
$382$	10.2092	−	17.6828i	0.522346	−	0.904730i
$383$	4.44286	+	7.69526i	0.227020	+	0.393210i	0.956923	−	0.290340i	$-0.0937685\pi$
$383$	4.44286	+	7.69526i	0.227020	+	0.393210i	−0.729904	+	0.683550i	$0.760435\pi$
$384$	19.4698			0.993564
$385$		0			0
$386$	6.63009			0.337463
$387$	4.46379	+	7.73152i	0.226907	+	0.393015i
$388$	−1.77110	+	3.06764i	−0.0899142	+	0.155736i
$389$	9.94951	−	17.2331i	0.504460	−	0.873751i	−0.495526	−	0.868593i	$-0.665025\pi$
$389$	9.94951	−	17.2331i	0.504460	−	0.873751i	0.999987	−	0.00515807i	$-0.00164187\pi$
$390$	−2.30850	−	3.99844i	−0.116896	−	0.202469i
$391$	6.13828			0.310426
$392$		0			0
$393$	30.1252			1.51962
$394$	−2.21789	−	3.84149i	−0.111736	−	0.193532i
$395$	−1.51320	+	2.62093i	−0.0761371	+	0.131873i
$396$	1.25136	−	2.16743i	0.0628834	−	0.108917i
$397$	−17.4303	−	30.1902i	−0.874803	−	1.51520i	−0.856973	−	0.515361i	$-0.827658\pi$
$397$	−17.4303	−	30.1902i	−0.874803	−	1.51520i	−0.0178296	−	0.999841i	$-0.505676\pi$
$398$	33.9265			1.70058
$399$		0			0
$400$	22.3699			1.11850
$401$	−5.69815	−	9.86948i	−0.284552	−	0.492858i	0.687948	−	0.725760i	$-0.258511\pi$
$401$	−5.69815	−	9.86948i	−0.284552	−	0.492858i	−0.972500	+	0.232901i	$0.925178\pi$
$402$	3.23163	−	5.59734i	0.161179	−	0.279170i
$403$	5.79149	−	10.0312i	0.288495	−	0.499688i
$404$	−6.75409	−	11.6984i	−0.336029	−	0.582019i
$405$	−7.07896			−0.351756
$406$		0			0
$407$	−6.06587			−0.300674
$408$	3.63228	+	6.29129i	0.179825	+	0.311465i
$409$	−2.04394	+	3.54021i	−0.101066	+	0.175052i	−0.912124	−	0.409914i	$-0.865559\pi$
$409$	−2.04394	+	3.54021i	−0.101066	+	0.175052i	0.811058	+	0.584966i	$0.198892\pi$
$410$	4.39238	−	7.60782i	0.216924	−	0.375723i
$411$	−7.98626	−	13.8326i	−0.393933	−	0.682312i
$412$	−8.50273			−0.418899
$413$		0			0
$414$	7.28658			0.358116
$415$	−2.93359	−	5.08112i	−0.144004	−	0.249423i
$416$	5.94078	−	10.2897i	0.291271	−	0.504496i
$417$	−2.86118	+	4.95570i	−0.140112	+	0.242682i
$418$	5.10208	+	8.83705i	0.249551	+	0.432234i
$419$	−32.8002			−1.60240			−0.801198	−	0.598399i	$-0.795804\pi$
$419$	−32.8002			−1.60240			−0.801198	+	0.598399i	$0.795804\pi$
$420$		0			0
$421$	−8.52128			−0.415302			−0.207651	−	0.978203i	$-0.566582\pi$
$421$	−8.52128			−0.415302			−0.207651	+	0.978203i	$0.566582\pi$
$422$	7.20415	+	12.4780i	0.350693	+	0.607417i
$423$	−2.59935	+	4.50220i	−0.126385	+	0.218904i
$424$	4.35398	−	7.54132i	0.211448	−	0.366239i
$425$	6.51320	+	11.2812i	0.315936	+	0.547218i
$426$	17.3095			0.838648
$427$		0			0
$428$	15.1437			0.732000
$429$	1.98026	+	3.42991i	0.0956079	+	0.165598i
$430$	2.83697	−	4.91378i	0.136811	−	0.236964i
$431$	8.36718	−	14.4924i	0.403033	−	0.698073i	−0.591058	−	0.806629i	$-0.701289\pi$
$431$	8.36718	−	14.4924i	0.403033	−	0.698073i	0.994090	+	0.108556i	$0.0346227\pi$
$432$	−6.23763	−	10.8039i	−0.300108	−	0.519802i
$433$	25.8661			1.24305			0.621523	−	0.783396i	$-0.286514\pi$
$433$	25.8661			1.24305			0.621523	+	0.783396i	$0.286514\pi$
$434$		0			0
$435$	−14.5751			−0.698825
$436$	9.75856	+	16.9023i	0.467350	+	0.809474i
$437$	−6.02420	+	10.4342i	−0.288177	+	0.499137i
$438$	−32.2503	+	55.8591i	−1.54098	+	2.66905i
$439$	−4.78430	−	8.28665i	−0.228342	−	0.395500i	0.728975	−	0.684541i	$-0.239997\pi$
$439$	−4.78430	−	8.28665i	−0.228342	−	0.395500i	−0.957317	+	0.289040i	$0.906664\pi$
$440$	0.740899			0.0353210
$441$		0			0
$442$	9.36445			0.445421
$443$	−9.51647	−	16.4830i	−0.452141	−	0.783131i	0.546378	−	0.837539i	$-0.316006\pi$
$443$	−9.51647	−	16.4830i	−0.452141	−	0.783131i	−0.998519	+	0.0544076i	$0.982673\pi$
$444$	−9.09880	+	15.7596i	−0.431810	+	0.747917i
$445$	0.115813	−	0.200594i	0.00549005	−	0.00950905i
$446$	18.6515	+	32.3053i	0.883173	+	1.52970i
$447$	−2.19869			−0.103995
$448$		0			0
$449$	33.3424			1.57353			0.786763	−	0.617255i	$-0.211755\pi$
$449$	33.3424			1.57353			0.786763	+	0.617255i	$0.211755\pi$
$450$	7.73163	+	13.3916i	0.364472	+	0.631285i
$451$	−3.76783	+	6.52608i	−0.177420	+	0.307301i
$452$	5.92813	−	10.2678i	0.278836	−	0.482958i
$453$	−1.90785	−	3.30449i	−0.0896385	−	0.155258i
$454$	−13.2425			−0.621503
$455$		0			0
$456$	−14.2591			−0.667744
$457$	−5.98026	−	10.3581i	−0.279745	−	0.484532i	0.691576	−	0.722303i	$-0.256917\pi$
$457$	−5.98026	−	10.3581i	−0.279745	−	0.484532i	−0.971321	+	0.237771i	$0.923583\pi$
$458$	11.0709	−	19.1753i	0.517308	−	0.896004i
$459$	3.63228	−	6.29129i	0.169540	−	0.293652i
$460$	−0.939048	−	1.62648i	−0.0437833	−	0.0758350i
$461$	−12.4896			−0.581701			−0.290850	−	0.956769i	$-0.593938\pi$
$461$	−12.4896			−0.581701			−0.290850	+	0.956769i	$0.593938\pi$
$462$		0			0
$463$	12.3095			0.572071			0.286035	−	0.958219i	$-0.407662\pi$
$463$	12.3095			0.572071			0.286035	+	0.958219i	$0.407662\pi$
$464$	−25.3831	−	43.9648i	−1.17838	−	2.04102i
$465$	4.49281	−	7.78177i	0.208349	−	0.360871i
$466$	6.91712	−	11.9808i	0.320429	−	0.555000i
$467$	16.3804	+	28.3716i	0.757993	+	1.31288i	0.943872	+	0.330310i	$0.107153\pi$
$467$	16.3804	+	28.3716i	0.757993	+	1.31288i	−0.185879	+	0.982573i	$0.559513\pi$
$468$	4.50819			0.208391
$469$		0			0
$470$	3.30404			0.152404
$471$	−8.72835	−	15.1180i	−0.402181	−	0.696598i
$472$	−6.88191	+	11.9198i	−0.316766	+	0.548654i
$473$	−2.43359	+	4.21510i	−0.111897	+	0.193810i
$474$	−9.60208	−	16.6313i	−0.441038	−	0.763900i
$475$	−25.5686			−1.17317
$476$		0			0
$477$	13.7014			0.627345
$478$	9.03020	+	15.6408i	0.413032	+	0.715392i
$479$	12.9890	−	22.4976i	0.593482	−	1.02794i	−0.400277	−	0.916394i	$-0.631086\pi$
$479$	12.9890	−	22.4976i	0.593482	−	1.02794i	0.993759	−	0.111547i	$-0.0355806\pi$
$480$	4.60862	−	7.98236i	0.210354	−	0.364343i
$481$	−5.46325	−	9.46263i	−0.249103	−	0.431459i
$482$	3.07241			0.139945
$483$		0			0
$484$	1.36445			0.0620204
$485$	−0.824970	−	1.42889i	−0.0374600	−	0.0648825i
$486$	15.4078	−	26.6872i	0.698914	−	1.21055i
$487$	−7.26783	+	12.5883i	−0.329337	+	0.570428i	−0.982380	−	0.186892i	$-0.940159\pi$
$487$	−7.26783	+	12.5883i	−0.329337	+	0.570428i	0.653044	+	0.757320i	$0.273492\pi$
$488$	2.52475	+	4.37299i	0.114290	+	0.197956i
$489$	−35.1911			−1.59139
$490$		0			0
$491$	−39.3952			−1.77788			−0.888941	−	0.458023i	$-0.848558\pi$
$491$	−39.3952			−1.77788			−0.888941	+	0.458023i	$0.848558\pi$
$492$	11.3035	+	19.5782i	0.509601	+	0.882655i
$493$	14.7810	−	25.6015i	0.665704	−	1.15303i
$494$	−9.19041	+	15.9183i	−0.413496	+	0.716196i
$495$	0.582878	+	1.00958i	0.0261984	+	0.0453770i
$496$	31.2975			1.40530
$497$		0			0
$498$	37.2305			1.66834
$499$	13.1153	+	22.7163i	0.587120	+	1.01692i	0.994607	+	0.103711i	$0.0330717\pi$
$499$	13.1153	+	22.7163i	0.587120	+	1.01692i	−0.407487	+	0.913211i	$0.633595\pi$
$500$	4.16075	−	7.20663i	0.186074	−	0.322290i
$501$	1.27438	−	2.20728i	0.0569349	−	0.0986142i
$502$	18.1350	+	31.4108i	0.809405	+	1.40193i
$503$	−3.94613			−0.175949			−0.0879747	−	0.996123i	$-0.528039\pi$
$503$	−3.94613			−0.175949			−0.0879747	+	0.996123i	$0.528039\pi$
$504$		0			0
$505$	6.29204			0.279992
$506$	1.98626	+	3.44031i	0.0883001	+	0.152940i
$507$	10.7244	−	18.5753i	0.476289	−	0.824956i
$508$	−14.3260	+	24.8133i	−0.635612	+	1.10091i
$509$	8.45279	+	14.6407i	0.374663	+	0.648936i	0.990277	−	0.139113i	$-0.0444250\pi$
$509$	8.45279	+	14.6407i	0.374663	+	0.648936i	−0.615613	+	0.788048i	$0.711092\pi$
$510$	7.26456			0.321680
$511$		0			0
$512$	20.7564			0.917311
$513$	7.12955	+	12.3487i	0.314777	+	0.545210i
$514$	2.49454	−	4.32067i	0.110029	−	0.190577i
$515$	1.98026	−	3.42991i	0.0872607	−	0.151140i
$516$	7.30077	+	12.6453i	0.321398	+	0.556678i
$517$	−2.83424			−0.124650
$518$		0			0
$519$	2.18430			0.0958803
$520$	0.667294	+	1.15579i	0.0292628	+	0.0506846i
$521$	0.778840	−	1.34899i	0.0341216	−	0.0591004i	−0.848460	−	0.529259i	$-0.822470\pi$
$521$	0.778840	−	1.34899i	0.0341216	−	0.0591004i	0.882582	+	0.470159i	$0.155803\pi$
$522$	17.5461	−	30.3908i	0.767973	−	1.33017i
$523$	−6.25136	−	10.8277i	−0.273353	−	0.473461i	0.696365	−	0.717688i	$-0.254799\pi$
$523$	−6.25136	−	10.8277i	−0.273353	−	0.473461i	−0.969718	+	0.244226i	$0.921466\pi$
$524$	18.6949			0.816689
$525$		0			0
$526$	23.2855			1.01530
$527$	9.11254	+	15.7834i	0.396949	+	0.687535i
$528$	−5.35071	+	9.26770i	−0.232860	+	0.403325i
$529$	9.15475	−	15.8565i	0.398033	−	0.689413i
$530$	−4.35398	−	7.54132i	−0.189125	−	0.327574i
$531$	−21.6565			−0.939811
$532$		0			0
$533$	−13.5741			−0.587958
$534$	0.734898	+	1.27288i	0.0318021	+	0.0550829i
$535$	−3.52693	+	6.10883i	−0.152483	+	0.264108i
$536$	−0.934131	+	1.61796i	−0.0403483	+	0.0698853i
$537$	21.6153	+	37.4387i	0.932768	+	1.61560i
$538$	13.0109			0.560941
$539$		0			0
$540$	−2.22270			−0.0956497
$541$	8.28103	+	14.3432i	0.356029	+	0.616661i	0.987294	−	0.158907i	$-0.0507970\pi$
$541$	8.28103	+	14.3432i	0.356029	+	0.616661i	−0.631264	+	0.775568i	$0.717464\pi$
$542$	−16.7064	+	28.9364i	−0.717603	+	1.24292i
$543$	−26.2443	+	45.4564i	−1.12625	+	1.95072i
$544$	9.34744	+	16.1902i	0.400768	+	0.694151i
$545$	−9.09096			−0.389414
$546$		0			0
$547$	−6.64448			−0.284097			−0.142049	−	0.989860i	$-0.545369\pi$
$547$	−6.64448			−0.284097			−0.142049	+	0.989860i	$0.545369\pi$
$548$	−4.95606	−	8.58414i	−0.211712	−	0.366696i
$549$	−3.97252	+	6.88061i	−0.169543	+	0.293657i
$550$	−4.21516	+	7.30087i	−0.179735	+	0.311310i
$551$	29.0127	+	50.2514i	1.23598	+	2.14078i
$552$	−5.55114			−0.236272
$553$		0			0
$554$	25.4018			1.07922
$555$	−4.23817	−	7.34072i	−0.179900	−	0.311596i
$556$	−1.77557	+	3.07537i	−0.0753009	+	0.130425i
$557$	−6.55595	+	11.3552i	−0.277784	+	0.481137i	−0.970834	−	0.239753i	$-0.922933\pi$
$557$	−6.55595	+	11.3552i	−0.277784	+	0.481137i	0.693049	+	0.720890i	$0.256267\pi$
$558$	10.8172	+	18.7360i	0.457930	+	0.793158i
$559$	−8.76729			−0.370817
$560$		0			0
$561$	−6.23163			−0.263099
$562$	−19.2898	−	33.4108i	−0.813689	−	1.40935i
$563$	15.2443	−	26.4039i	0.642470	−	1.11279i	−0.342410	−	0.939551i	$-0.611243\pi$
$563$	15.2443	−	26.4039i	0.642470	−	1.11279i	0.984880	−	0.173240i	$-0.0554235\pi$
$564$	−4.25136	+	7.36358i	−0.179015	+	0.310063i
$565$	2.76129	+	4.78269i	0.116168	+	0.201209i
$566$	−0.646470			−0.0271732
$567$		0			0
$568$	−5.00347			−0.209941
$569$	17.6790	+	30.6208i	0.741140	+	1.28369i	0.951976	+	0.306171i	$0.0990480\pi$
$569$	17.6790	+	30.6208i	0.741140	+	1.28369i	−0.210836	+	0.977521i	$0.567619\pi$
$570$	−7.12955	+	12.3487i	−0.298624	+	0.517232i
$571$	20.6422	−	35.7533i	0.863849	−	1.49623i	−0.00433587	−	0.999991i	$-0.501380\pi$
$571$	20.6422	−	35.7533i	0.863849	−	1.49623i	0.868185	−	0.496240i	$-0.165287\pi$
$572$	1.22890	+	2.12851i	0.0513827	+	0.0889975i
$573$	−24.4753			−1.02247
$574$		0			0
$575$	−9.95398			−0.415110
$576$	2.16849	+	3.75593i	0.0903536	+	0.156497i
$577$	4.35125	−	7.53659i	0.181145	−	0.313752i	−0.761126	−	0.648604i	$-0.775353\pi$
$577$	4.35125	−	7.53659i	0.181145	−	0.313752i	0.942271	+	0.334852i	$0.108686\pi$
$578$	8.22389	−	14.2442i	0.342069	−	0.592480i
$579$	−3.97372	−	6.88268i	−0.165142	−	0.286034i
$580$	−9.04494			−0.375571
$581$		0			0
$582$	10.4698			0.433987
$583$	3.73490	+	6.46903i	0.154684	+	0.267920i
$584$	9.32224	−	16.1466i	0.385757	−	0.668151i
$585$	−1.04994	+	1.81856i	−0.0434098	+	0.0751881i
$586$	−3.17622	−	5.50138i	−0.131209	−	0.227260i
$587$	23.0539			0.951535			0.475767	−	0.879571i	$-0.342170\pi$
$587$	23.0539			0.951535			0.475767	+	0.879571i	$0.342170\pi$
$588$		0			0
$589$	−35.7727			−1.47399
$590$	6.88191	+	11.9198i	0.283324	+	0.490731i
$591$	−2.65856	+	4.60477i	−0.109359	+	0.189415i
$592$	14.7618	−	25.5682i	0.606707	−	1.05085i
$593$	15.0494	+	26.0663i	0.618005	+	1.07042i	0.989849	+	0.142121i	$0.0453921\pi$
$593$	15.0494	+	26.0663i	0.618005	+	1.07042i	−0.371844	+	0.928295i	$0.621275\pi$
$594$	4.70142			0.192902
$595$		0			0
$596$	−1.36445			−0.0558900
$597$	−20.3337	−	35.2190i	−0.832203	−	1.44142i
$598$	−3.57787	+	6.19706i	−0.146310	+	0.253416i
$599$	−14.6257	+	25.3325i	−0.597591	+	1.03506i	0.395584	+	0.918430i	$0.370542\pi$
$599$	−14.6257	+	25.3325i	−0.597591	+	1.03506i	−0.993176	+	0.116629i	$0.962791\pi$
$600$	−5.89019	−	10.2021i	−0.240466	−	0.416499i
$601$	26.8222			1.09410			0.547051	−	0.837099i	$-0.315750\pi$
$601$	26.8222			1.09410			0.547051	+	0.837099i	$0.315750\pi$
$602$		0			0
$603$	−2.93959			−0.119709
$604$	−1.18396	−	2.05068i	−0.0481746	−	0.0834409i
$605$	−0.317776	+	0.550404i	−0.0129194	+	0.0223771i
$606$	−19.9633	+	34.5774i	−0.810952	+	1.40461i
$607$	16.1048	+	27.8943i	0.653674	+	1.13220i	0.982224	+	0.187710i	$0.0601065\pi$
$607$	16.1048	+	27.8943i	0.653674	+	1.13220i	−0.328551	+	0.944486i	$0.606560\pi$
$608$	−36.6949			−1.48817
$609$		0			0
$610$	5.04949			0.204448
$611$	−2.55267	−	4.42136i	−0.103270	−	0.178869i
$612$	−3.54667	+	6.14302i	−0.143366	+	0.248317i
$613$	−22.2975	+	38.6204i	−0.900587	+	1.55986i	−0.0738539	+	0.997269i	$0.523530\pi$
$613$	−22.2975	+	38.6204i	−0.900587	+	1.55986i	−0.826733	+	0.562594i	$0.809803\pi$
$614$	−5.97480	−	10.3487i	−0.241123	−	0.417638i
$615$	−10.5302			−0.424619
$616$		0			0
$617$	−0.531290			−0.0213889			−0.0106945	−	0.999943i	$-0.503404\pi$
$617$	−0.531290			−0.0213889			−0.0106945	+	0.999943i	$0.503404\pi$
$618$	12.5659	+	21.7647i	0.505473	+	0.875506i
$619$	20.8726	−	36.1525i	0.838942	−	1.45309i	−0.0518379	−	0.998656i	$-0.516508\pi$
$619$	20.8726	−	36.1525i	0.838942	−	1.45309i	0.890780	−	0.454435i	$-0.150159\pi$
$620$	2.78811	−	4.82915i	0.111973	−	0.193943i
$621$	2.77557	+	4.80743i	0.111380	+	0.192915i
$622$	−21.3324			−0.855352
$623$		0			0
$624$	−19.2766			−0.771680
$625$	−9.55213	−	16.5448i	−0.382085	−	0.661791i
$626$	−24.8519	+	43.0448i	−0.993282	+	1.72041i
$627$	6.11581	−	10.5929i	0.244242	−	0.423040i
$628$	−5.41658	−	9.38179i	−0.216145	−	0.374374i
$629$	17.1921			0.685496
$630$		0			0
$631$	−0.217238			−0.00864810			−0.00432405	−	0.999991i	$-0.501376\pi$
$631$	−0.217238			−0.00864810			−0.00432405	+	0.999991i	$0.501376\pi$
$632$	2.77557	+	4.80743i	0.110406	+	0.191229i
$633$	8.63555	−	14.9572i	0.343232	−	0.594496i
$634$	−3.54167	+	6.13434i	−0.140658	+	0.243626i
$635$	−6.67295	−	11.5579i	−0.264808	−	0.458661i
$636$	22.4094			0.888590
$637$		0			0
$638$	19.1317			0.757433
$639$	−3.93632	−	6.81790i	−0.155718	−	0.269712i
$640$	−2.81396	+	4.87392i	−0.111232	+	0.192659i
$641$	4.84525	−	8.39222i	0.191376	−	0.331473i	−0.754331	−	0.656495i	$-0.772038\pi$
$641$	4.84525	−	8.39222i	0.191376	−	0.331473i	0.945706	+	0.325022i	$0.105372\pi$
$642$	−22.3804	−	38.7639i	−0.883283	−	1.52989i
$643$	−16.4633			−0.649247			−0.324624	−	0.945843i	$-0.605238\pi$
$643$	−16.4633			−0.649247			−0.324624	+	0.945843i	$0.605238\pi$
$644$		0			0
$645$	−6.80131			−0.267801
$646$	−14.4605	−	25.0464i	−0.568942	−	0.985436i
$647$	0.436861	−	0.756665i	0.0171748	−	0.0297476i	−0.857310	−	0.514800i	$-0.827866\pi$
$647$	0.436861	−	0.756665i	0.0171748	−	0.0297476i	0.874485	+	0.485052i	$0.161199\pi$
$648$	−6.49226	+	11.2449i	−0.255040	+	0.441743i
$649$	−5.90338	−	10.2250i	−0.231728	−	0.401365i
$650$	−15.1856			−0.595628
$651$		0			0
$652$	−21.8386			−0.855266
$653$	19.9665	+	34.5830i	0.781350	+	1.35334i	0.931155	+	0.364623i	$0.118802\pi$
$653$	19.9665	+	34.5830i	0.781350	+	1.35334i	−0.149805	+	0.988716i	$0.547865\pi$
$654$	28.8436	−	49.9586i	1.12787	−	1.95354i
$655$	−4.35398	+	7.54132i	−0.170124	+	0.294664i
$656$	−18.3387	−	31.7636i	−0.716006	−	1.24016i
$657$	29.3359			1.14450
$658$		0			0
$659$	−6.89465			−0.268578			−0.134289	−	0.990942i	$-0.542875\pi$
$659$	−6.89465			−0.268578			−0.134289	+	0.990942i	$0.542875\pi$
$660$	0.953328	+	1.65121i	0.0371082	+	0.0642734i
$661$	−20.0072	+	34.6535i	−0.778190	+	1.34786i	0.154795	+	0.987947i	$0.450528\pi$
$661$	−20.0072	+	34.6535i	−0.778190	+	1.34786i	−0.932984	+	0.359917i	$0.882805\pi$
$662$	−5.64056	+	9.76973i	−0.219227	+	0.379711i
$663$	−5.61254	−	9.72121i	−0.217973	−	0.377540i
$664$	−10.7618			−0.417640
$665$		0			0
$666$	20.4083			0.790806
$667$	11.2948	+	19.5631i	0.437335	+	0.757487i
$668$	0.790843	−	1.36978i	0.0305986	−	0.0529984i
$669$	22.3574	−	38.7241i	0.864386	−	1.49716i
$670$	0.934131	+	1.61796i	0.0360886	+	0.0625073i
$671$	−4.33151			−0.167216
$672$		0			0
$673$	31.3788			1.20957			0.604783	−	0.796391i	$-0.293260\pi$
$673$	31.3788			1.20957			0.604783	+	0.796391i	$0.293260\pi$
$674$	10.7860	+	18.6820i	0.415463	+	0.719602i
$675$	−5.89019	+	10.2021i	−0.226713	+	0.392679i
$676$	6.65529	−	11.5273i	0.255973	−	0.443358i
$677$	−18.2658	−	31.6372i	−0.702010	−	1.21592i	−0.967760	−	0.251875i	$-0.918953\pi$
$677$	−18.2658	−	31.6372i	−0.702010	−	1.21592i	0.265750	−	0.964042i	$-0.414380\pi$
$678$	−35.0439			−1.34585
$679$		0			0
$680$	−2.09989			−0.0805270
$681$	7.93686	+	13.7470i	0.304141	+	0.526788i
$682$	−5.89738	+	10.2146i	−0.225822	+	0.391136i
$683$	7.63501	−	13.2242i	0.292146	−	0.506011i	−0.682171	−	0.731192i	$-0.738964\pi$
$683$	7.63501	−	13.2242i	0.292146	−	0.506011i	0.974317	+	0.225181i	$0.0722975\pi$
$684$	−6.96152	−	12.0577i	−0.266180	−	0.461038i
$685$	4.61701			0.176407
$686$		0			0
$687$	−26.5411			−1.01261
$688$	−11.8447	−	20.5156i	−0.451575	−	0.782151i
$689$	−6.72770	+	11.6527i	−0.256305	+	0.443933i
$690$	−2.77557	+	4.80743i	−0.105664	+	0.183016i
$691$	−19.1921	−	33.2418i	−0.730104	−	1.26458i	−0.956839	−	0.290620i	$-0.906138\pi$
$691$	−19.1921	−	33.2418i	−0.730104	−	1.26458i	0.226735	−	0.973957i	$-0.427195\pi$
$692$	1.35552			0.0515291
$693$		0			0
$694$	−1.54221			−0.0585414
$695$	−0.827049	−	1.43249i	−0.0313718	−	0.0543375i
$696$	−13.3672	+	23.1526i	−0.506682	+	0.877598i
$697$	10.6790	−	18.4965i	0.404494	−	0.700604i
$698$	8.37491	+	14.5058i	0.316995	+	0.549052i
$699$	−16.5830			−0.627226
$700$		0			0
$701$	17.9056			0.676284			0.338142	−	0.941095i	$-0.390202\pi$
$701$	17.9056			0.676284			0.338142	+	0.941095i	$0.390202\pi$
$702$	4.23436	+	7.33412i	0.159815	+	0.276808i
$703$	−16.8726	+	29.2243i	−0.636364	+	1.10221i
$704$	−1.18222	+	2.04767i	−0.0445567	+	0.0771745i
$705$	−1.98026	−	3.42991i	−0.0745809	−	0.129178i
$706$	−41.6883			−1.56896
$707$		0			0
$708$	−35.4203			−1.33118
$709$	−17.1997	−	29.7907i	−0.645948	−	1.11881i	−0.984082	−	0.177716i	$-0.943129\pi$
$709$	−17.1997	−	29.7907i	−0.645948	−	1.11881i	0.338134	−	0.941098i	$-0.390204\pi$
$710$	−2.50173	+	4.33313i	−0.0938884	+	0.162620i
$711$	−4.36718	+	7.56417i	−0.163782	+	0.283679i
$712$	−0.212429	−	0.367938i	−0.00796111	−	0.0137890i
$713$	−13.9265			−0.521552
$714$		0			0
$715$	−1.14483			−0.0428140
$716$	13.4138	+	23.2335i	0.501299	+	0.868276i
$717$	10.8244	−	18.7485i	0.404246	−	0.700174i
$718$	24.0456	−	41.6482i	0.897373	−	1.55430i
$719$	24.7086	+	42.7966i	0.921476	+	1.59604i	0.797133	+	0.603804i	$0.206349\pi$
$719$	24.7086	+	42.7966i	0.921476	+	1.59604i	0.124343	+	0.992239i	$0.460318\pi$
$720$	−5.67395			−0.211455
$721$		0			0
$722$	21.9165			0.815647
$723$	−1.84144	−	3.18946i	−0.0684838	−	0.118617i
$724$	−16.2865	+	28.2090i	−0.605283	+	1.04838i
$725$	−23.9693	+	41.5160i	−0.890196	+	1.54186i
$726$	−2.01647	−	3.49262i	−0.0748381	−	0.129623i
$727$	19.8201			0.735086			0.367543	−	0.930007i	$-0.380199\pi$
$727$	19.8201			0.735086			0.367543	+	0.930007i	$0.380199\pi$
$728$		0			0
$729$	−3.52366			−0.130506
$730$	−9.32224	−	16.1466i	−0.345032	−	0.597612i
$731$	6.89738	−	11.9466i	0.255109	−	0.441862i
$732$	−6.49727	+	11.2536i	−0.240146	+	0.415945i
$733$	−15.3238	−	26.5416i	−0.565997	−	0.980335i	−0.996956	−	0.0779637i	$-0.975158\pi$
$733$	−15.3238	−	26.5416i	−0.565997	−	0.980335i	0.430960	−	0.902371i	$-0.358175\pi$
$734$	7.01092			0.258778
$735$		0			0
$736$	−14.2855			−0.526570
$737$	−0.801309	−	1.38791i	−0.0295166	−	0.0511242i
$738$	12.6767	−	21.9566i	0.466635	−	0.808235i
$739$	−8.55094	+	14.8107i	−0.314551	+	0.544819i	−0.979342	−	0.202211i	$-0.935187\pi$
$739$	−8.55094	+	14.8107i	−0.314551	+	0.544819i	0.664791	+	0.747030i	$0.268521\pi$
$740$	−2.63009	−	4.55545i	−0.0966841	−	0.167462i
$741$	22.0329			0.809400
$742$		0			0
$743$	−6.97252			−0.255797			−0.127899	−	0.991787i	$-0.540823\pi$
$743$	−6.97252			−0.255797			−0.127899	+	0.991787i	$0.540823\pi$
$744$	−8.24090	−	14.2737i	−0.302126	−	0.523298i
$745$	0.317776	−	0.550404i	0.0116424	−	0.0201652i
$746$	−13.8556	+	23.9987i	−0.507291	+	0.878653i
$747$	−8.46652	−	14.6644i	−0.309774	−	0.536544i
$748$	−3.86718			−0.141398
$749$		0			0
$750$	−24.5961			−0.898122
$751$	−7.61636	−	13.1919i	−0.277925	−	0.481380i	0.692944	−	0.720991i	$-0.256313\pi$
$751$	−7.61636	−	13.1919i	−0.277925	−	0.481380i	−0.970869	+	0.239612i	$0.922980\pi$
$752$	6.89738	−	11.9466i	0.251522	−	0.435648i
$753$	21.7383	−	37.6518i	0.792187	−	1.37211i
$754$	17.2311	+	29.8451i	0.627519	+	1.08689i
$755$	1.10296			0.0401409
$756$		0			0
$757$	−14.5326			−0.528196			−0.264098	−	0.964496i	$-0.585074\pi$
$757$	−14.5326			−0.528196			−0.264098	+	0.964496i	$0.585074\pi$
$758$	10.4336	+	18.0715i	0.378965	+	0.656387i
$759$	2.38092	−	4.12387i	0.0864217	−	0.149687i
$760$	2.06086	−	3.56952i	0.0747553	−	0.129480i
$761$	−0.856712	−	1.48387i	−0.0310558	−	0.0537902i	0.850080	−	0.526654i	$-0.176554\pi$
$761$	−0.856712	−	1.48387i	−0.0310558	−	0.0537902i	−0.881136	+	0.472864i	$0.843220\pi$
$762$	84.6872			3.06790
$763$		0			0
$764$	−15.1887			−0.549507
$765$	−1.65202	−	2.86138i	−0.0597289	−	0.103453i
$766$	8.14929	−	14.1150i	0.294446	−	0.509995i
$767$	10.6338	−	18.4183i	0.383965	−	0.665047i
$768$	−23.0549	−	39.9322i	−0.831921	−	1.44093i
$769$	36.5874			1.31937			0.659687	−	0.751540i	$-0.270689\pi$
$769$	36.5874			1.31937			0.659687	+	0.751540i	$0.270689\pi$
$770$		0			0
$771$	−5.98037			−0.215378
$772$	−2.46598	−	4.27120i	−0.0887526	−	0.153724i
$773$	13.4106	−	23.2278i	0.482345	−	0.835446i	−0.517450	−	0.855714i	$-0.673119\pi$
$773$	13.4106	−	23.2278i	0.482345	−	0.835446i	0.999795	+	0.0202677i	$0.00645185\pi$
$774$	8.18768	−	14.1815i	0.294300	−	0.509743i
$775$	−14.7771	−	25.5947i	−0.530809	−	0.919389i
$776$	−3.02639			−0.108641
$777$		0			0
$778$	−36.4997			−1.30858
$779$	20.9610	+	36.3055i	0.751005	+	1.30078i
$780$	−1.71724	+	2.97434i	−0.0614870	+	0.106499i
$781$	2.14602	−	3.71701i	0.0767906	−	0.133005i
$782$	−5.62955	−	9.75067i	−0.201312	−	0.348683i
$783$	26.7344			0.955408
$784$		0			0
$785$	5.04602			0.180100
$786$	−27.6285	−	47.8539i	−0.985475	−	1.70689i
$787$	2.47580	−	4.28821i	0.0882526	−	0.152858i	−0.818520	−	0.574478i	$-0.805205\pi$
$787$	2.47580	−	4.28821i	0.0882526	−	0.152858i	0.906773	+	0.421620i	$0.138538\pi$
$788$	−1.64983	+	2.85759i	−0.0587728	+	0.101798i
$789$	−13.9561	−	24.1726i	−0.496849	−	0.860567i
$790$	5.55114			0.197501
$791$		0			0
$792$	2.13828			0.0759805
$793$	−3.90120	−	6.75707i	−0.138536	−	0.239951i
$794$	−31.9714	+	55.3762i	−1.13462	+	1.96523i
$795$	−5.21908	+	9.03971i	−0.185102	+	0.320606i
$796$	−12.6185	−	21.8560i	−0.447252	−	0.774664i
$797$	26.6818			0.945117			0.472559	−	0.881299i	$-0.343330\pi$
$797$	26.6818			0.945117			0.472559	+	0.881299i	$0.343330\pi$
$798$		0			0
$799$	8.03293			0.284185
$800$	−15.1580	−	26.2545i	−0.535917	−	0.928235i
$801$	0.334243	−	0.578926i	0.0118099	−	0.0204554i
$802$	−10.4518	+	18.1030i	−0.369066	+	0.639240i
$803$	7.99673	+	13.8507i	0.282198	+	0.488782i
$804$	−4.80785			−0.169560
$805$		0			0
$806$	−21.2460			−0.748359
$807$	−7.79804	−	13.5066i	−0.274504	−	0.475455i
$808$	5.77056	−	9.99491i	0.203008	−	0.351620i
$809$	19.7700	−	34.2427i	0.695077	−	1.20391i	−0.275078	−	0.961422i	$-0.588704\pi$
$809$	19.7700	−	34.2427i	0.695077	−	1.20391i	0.970155	−	0.242487i	$-0.0779630\pi$
$810$	6.49226	+	11.2449i	0.228115	+	0.395107i
$811$	33.4543			1.17474			0.587370	−	0.809318i	$-0.300163\pi$
$811$	33.4543			1.17474			0.587370	+	0.809318i	$0.300163\pi$
$812$		0			0
$813$	40.0517			1.40467
$814$	5.56314	+	9.63564i	0.194988	+	0.337729i
$815$	5.08615	−	8.80947i	0.178160	−	0.308582i
$816$	15.1652	−	26.2669i	0.530889	−	0.919526i
$817$	13.5384	+	23.4492i	0.473648	+	0.820383i
$818$	7.49818			0.262168
$819$		0			0
$820$	−6.53476			−0.228204
$821$	−28.4310	−	49.2439i	−0.992248	−	1.71862i	−0.603751	−	0.797173i	$-0.706328\pi$
$821$	−28.4310	−	49.2439i	−0.992248	−	1.71862i	−0.388497	−	0.921450i	$-0.627006\pi$
$822$	−14.6487	+	25.3724i	−0.510934	+	0.884963i
$823$	20.0878	−	34.7931i	0.700217	−	1.21281i	−0.268174	−	0.963371i	$-0.586420\pi$
$823$	20.0878	−	34.7931i	0.700217	−	1.21281i	0.968390	−	0.249440i	$-0.0802465\pi$
$824$	−3.63228	−	6.29129i	−0.126536	−	0.219168i
$825$	10.1053			0.351823
$826$		0			0
$827$	−5.73544			−0.199441			−0.0997204	−	0.995015i	$-0.531795\pi$
$827$	−5.73544			−0.199441			−0.0997204	+	0.995015i	$0.531795\pi$
$828$	−2.71015	−	4.69412i	−0.0941843	−	0.163132i
$829$	−17.7980	+	30.8271i	−0.618151	+	1.07067i	0.371671	+	0.928364i	$0.378785\pi$
$829$	−17.7980	+	30.8271i	−0.618151	+	1.07067i	−0.989823	+	0.142305i	$0.954549\pi$
$830$	−5.38092	+	9.32002i	−0.186774	+	0.323503i
$831$	−15.2244	−	26.3695i	−0.528130	−	0.914747i
$832$	−4.25910			−0.147658
$833$		0			0
$834$	10.4962			0.363453
$835$	0.368370	+	0.638036i	0.0127480	+	0.0220801i
$836$	3.79531	−	6.57367i	0.131263	−	0.227355i
$837$	−8.24090	+	14.2737i	−0.284847	+	0.493370i
$838$	30.0818	+	52.1032i	1.03916	+	1.79988i
$839$	41.7727			1.44216			0.721078	−	0.692854i	$-0.243647\pi$
$839$	41.7727			1.44216			0.721078	+	0.692854i	$0.243647\pi$
$840$		0			0
$841$	79.7915			2.75143
$842$	7.81505	+	13.5361i	0.269324	+	0.466483i
$843$	−23.1225	+	40.0493i	−0.796380	+	1.37937i
$844$	5.35899	−	9.28204i	0.184464	−	0.319501i
$845$	3.10000	+	5.36935i	0.106643	+	0.184711i
$846$	9.53566			0.327843
$847$		0			0
$848$	−36.3568			−1.24850
$849$	0.387459	+	0.671099i	0.0132976	+	0.0230321i
$850$	11.9468	−	20.6924i	0.409771	−	0.709745i
$851$	−6.56860	+	11.3771i	−0.225169	+	0.390004i
$852$	−6.43805	−	11.1510i	−0.220564	−	0.382028i
$853$	−49.7871			−1.70468			−0.852340	−	0.522989i	$-0.824817\pi$
$853$	−49.7871			−1.70468			−0.852340	+	0.522989i	$0.824817\pi$
$854$		0			0
$855$	6.48527			0.221791
$856$	6.46925	+	11.2051i	0.221115	+	0.382982i
$857$	12.7394	−	22.0652i	0.435168	−	0.753734i	−0.562141	−	0.827041i	$-0.690022\pi$
$857$	12.7394	−	22.0652i	0.435168	−	0.753734i	0.997309	+	0.0733077i	$0.0233555\pi$
$858$	3.63228	−	6.29129i	0.124004	−	0.214781i
$859$	8.08080	+	13.9964i	0.275713	+	0.477549i	0.970315	−	0.241845i	$-0.0777526\pi$
$859$	8.08080	+	13.9964i	0.275713	+	0.477549i	−0.694602	+	0.719395i	$0.744419\pi$
$860$	−4.22071			−0.143925
$861$		0			0
$862$	−30.6949			−1.04547
$863$	−1.44951	−	2.51063i	−0.0493420	−	0.0854629i	0.840300	−	0.542122i	$-0.182379\pi$
$863$	−1.44951	−	2.51063i	−0.0493420	−	0.0854629i	−0.889642	+	0.456660i	$0.849046\pi$
$864$	−8.45333	+	14.6416i	−0.287588	+	0.498117i
$865$	−0.315697	+	0.546802i	−0.0107340	+	0.0185918i
$866$	−23.7224	−	41.0883i	−0.806118	−	1.39624i
$867$	−19.7158			−0.669584
$868$		0			0
$869$	−4.76183			−0.161534
$870$	13.3672	+	23.1526i	0.453190	+	0.784948i
$871$	1.44340	−	2.50005i	0.0489079	−	0.0847110i
$872$	−8.33752	+	14.4410i	−0.282344	+	0.489034i
$873$	−2.38092	−	4.12387i	−0.0805818	−	0.139572i
$874$	22.0997			0.747534
$875$		0			0
$876$	47.9804			1.62111
$877$	4.20742	+	7.28747i	0.142075	+	0.246080i	0.928278	−	0.371888i	$-0.121289\pi$
$877$	4.20742	+	7.28747i	0.142075	+	0.246080i	−0.786203	+	0.617968i	$0.787956\pi$
$878$	−8.77557	+	15.1997i	−0.296161	+	0.512966i
$879$	−3.80731	+	6.59445i	−0.128417	+	0.222425i
$880$	−1.54667	−	2.67891i	−0.0521383	−	0.0903062i
$881$	−41.5335			−1.39930			−0.699649	−	0.714486i	$-0.746660\pi$
$881$	−41.5335			−1.39930			−0.699649	+	0.714486i	$0.746660\pi$
$882$		0			0
$883$	−56.4753			−1.90054			−0.950272	−	0.311422i	$-0.899195\pi$
$883$	−56.4753			−1.90054			−0.950272	+	0.311422i	$0.899195\pi$
$884$	−3.48299	−	6.03272i	−0.117146	−	0.202902i
$885$	8.24929	−	14.2882i	0.277297	−	0.480292i
$886$	−17.4555	+	30.2338i	−0.586429	+	1.01573i
$887$	−17.2898	−	29.9467i	−0.580533	−	1.00551i	−0.995416	−	0.0956383i	$-0.969511\pi$
$887$	−17.2898	−	29.9467i	−0.580533	−	1.00551i	0.414883	−	0.909875i	$-0.363823\pi$
$888$	−15.5477			−0.521746
$889$		0			0
$890$	−0.424858			−0.0142413
$891$	−5.56914	−	9.64603i	−0.186573	−	0.323154i
$892$	13.8744	−	24.0311i	0.464548	−	0.804621i
$893$	−7.88364	+	13.6549i	−0.263816	+	0.456943i
$894$	2.01647	+	3.49262i	0.0674408	+	0.116811i
$895$	−12.4962			−0.417701
$896$		0			0
$897$	8.57753			0.286395
$898$	−30.5791	−	52.9645i	−1.02044	−	1.76745i
$899$	−33.5351	+	58.0845i	−1.11846	+	1.93723i
$900$	5.75136	−	9.96166i	0.191712	−	0.332055i
$901$	−10.5856	−	18.3348i	−0.352658	−	0.610821i
$902$	13.8222			0.460230
$903$		0			0
$904$	10.1297			0.336910
$905$	−7.58615	−	13.1396i	−0.252172	−	0.436775i
$906$	−3.49946	+	6.06124i	−0.116262	+	0.201371i
$907$	−4.20142	+	7.27707i	−0.139506	+	0.241631i	−0.927310	−	0.374295i	$-0.877885\pi$
$907$	−4.20142	+	7.27707i	−0.139506	+	0.241631i	0.787804	+	0.615926i	$0.211218\pi$
$908$	4.92540	+	8.53104i	0.163455	+	0.283113i
$909$	18.1592			0.602303
$910$		0			0
$911$	−0.593689			−0.0196698			−0.00983489	−	0.999952i	$-0.503131\pi$
$911$	−0.593689			−0.0196698			−0.00983489	+	0.999952i	$0.503131\pi$
$912$	29.7667	+	51.5575i	0.985675	+	1.70724i
$913$	4.61581	−	7.99482i	0.152761	−	0.264590i
$914$	−10.9693	+	18.9993i	−0.362831	+	0.628441i
$915$	−3.02639	−	5.24186i	−0.100049	−	0.173291i
$916$	−16.4707			−0.544207
$917$		0			0
$918$	−13.3250			−0.439790
$919$	8.16849	+	14.1482i	0.269454	+	0.466707i	0.968721	−	0.248153i	$-0.0798236\pi$
$919$	8.16849	+	14.1482i	0.269454	+	0.466707i	−0.699267	+	0.714860i	$0.746490\pi$
$920$	0.802304	−	1.38963i	0.0264512	−	0.0458148i
$921$	−7.16194	+	12.4048i	−0.235994	+	0.408754i
$922$	11.4545	+	19.8398i	0.377235	+	0.653389i
$923$	7.73128			0.254478
$924$		0			0
$925$	−27.8792			−0.916662
$926$	−11.2893	−	19.5537i	−0.370990	−	0.642573i
$927$	5.71516	−	9.89894i	0.187710	−	0.325124i
$928$	−34.3996	+	59.5818i	−1.12922	+	1.95587i
$929$	4.45060	+	7.70866i	0.146019	+	0.252913i	0.929753	−	0.368184i	$-0.120020\pi$
$929$	4.45060	+	7.70866i	0.146019	+	0.252913i	−0.783733	+	0.621097i	$0.786687\pi$
$930$	−16.4818			−0.540459
$931$		0			0
$932$	−10.2910			−0.337091
$933$	12.7855	+	22.1451i	0.418578	+	0.724999i
$934$	30.0456	−	52.0405i	0.983122	−	1.70282i
$935$	0.900654	−	1.55998i	0.0294545	−	0.0510168i
$936$	1.92585	+	3.33567i	0.0629485	+	0.109030i
$937$	−45.2360			−1.47780			−0.738898	−	0.673817i	$-0.764653\pi$
$937$	−45.2360			−1.47780			−0.738898	+	0.673817i	$0.764653\pi$
$938$		0			0
$939$	59.5795			1.94430
$940$	−1.22890	−	2.12851i	−0.0400822	−	0.0694244i
$941$	−3.46652	+	6.00419i	−0.113005	+	0.195731i	−0.916981	−	0.398932i	$-0.869381\pi$
$941$	−3.46652	+	6.00419i	−0.113005	+	0.195731i	0.803975	+	0.594663i	$0.202714\pi$
$942$	−16.0099	+	27.7300i	−0.521631	+	0.903492i
$943$	8.16021	+	14.1339i	0.265733	+	0.460263i
$944$	57.4656			1.87035
$945$		0			0
$946$	8.92759			0.290261
$947$	−10.3716	−	17.9642i	−0.337033	−	0.583758i	0.646840	−	0.762626i	$-0.276090\pi$
$947$	−10.3716	−	17.9642i	−0.337033	−	0.583758i	−0.983873	+	0.178867i	$0.942757\pi$
$948$	−7.14275	+	12.3716i	−0.231986	+	0.401811i
$949$	−14.4046	+	24.9495i	−0.467592	+	0.809894i
$950$	23.4495	+	40.6157i	0.760803	+	1.31775i
$951$	8.49073			0.275331
$952$		0			0
$953$	20.2076			0.654589			0.327295	−	0.944922i	$-0.393863\pi$
$953$	20.2076			0.654589			0.327295	+	0.944922i	$0.393863\pi$
$954$	−12.5659	−	21.7647i	−0.406835	−	0.704659i
$955$	3.53740	−	6.12695i	0.114468	−	0.198264i
$956$	6.71735	−	11.6348i	0.217254	−	0.376296i
$957$	−11.4665	−	19.8606i	−0.370660	−	0.642002i
$958$	−47.6499			−1.53950
$959$		0			0
$960$	−3.30404			−0.106637
$961$	−5.17449	−	8.96248i	−0.166919	−	0.289112i
$962$	−10.0209	+	17.3568i	−0.323088	+	0.559604i
$963$	−10.1790	+	17.6305i	−0.328012	+	0.568134i
$964$	−1.14275	−	1.97929i	−0.0368054	−	0.0637488i
$965$	2.29728			0.0739520
$966$		0			0
$967$	−7.98254			−0.256701			−0.128351	−	0.991729i	$-0.540968\pi$
$967$	−7.98254			−0.256701			−0.128351	+	0.991729i	$0.540968\pi$
$968$	0.582878	+	1.00958i	0.0187344	+	0.0324490i
$969$	−17.3337	+	30.0229i	−0.556839	+	0.964473i
$970$	−1.51320	+	2.62093i	−0.0485858	+	0.0841530i
$971$	−6.88965	−	11.9332i	−0.221099	−	0.382955i	0.734043	−	0.679103i	$-0.237631\pi$
$971$	−6.88965	−	11.9332i	−0.221099	−	0.382955i	−0.955142	+	0.296148i	$0.904298\pi$
$972$	−22.9230			−0.735257
$973$		0			0
$974$	26.6619			0.854304
$975$	9.10143	+	15.7641i	0.291479	+	0.504856i
$976$	10.5411	−	18.2578i	0.337413	−	0.584417i
$977$	−6.01047	+	10.4104i	−0.192292	+	0.333059i	−0.946009	−	0.324139i	$-0.894925\pi$
$977$	−6.01047	+	10.4104i	−0.192292	+	0.333059i	0.753718	+	0.657199i	$0.228259\pi$
$978$	32.2745	+	55.9010i	1.03202	+	1.78752i
$979$	0.364448			0.0116478
$980$		0			0
$981$	−26.2371			−0.837686
$982$	36.1302	+	62.5793i	1.15296	+	1.99699i
$983$	−22.3272	+	38.6718i	−0.712126	+	1.23344i	0.251932	+	0.967745i	$0.418934\pi$
$983$	−22.3272	+	38.6718i	−0.712126	+	1.23344i	−0.964058	+	0.265693i	$0.914399\pi$
$984$	−9.65748	+	16.7272i	−0.307869	+	0.533245i
$985$	−0.768482	−	1.33105i	−0.0244859	−	0.0424108i
$986$	−54.2240			−1.72684
$987$		0			0
$988$	13.6730			0.434997
$989$	5.27056	+	9.12888i	0.167594	+	0.290282i
$990$	1.06914	−	1.85181i	0.0339795	−	0.0588543i
$991$	11.4830	−	19.8891i	0.364769	−	0.631799i	−0.623970	−	0.781448i	$-0.714481\pi$
$991$	11.4830	−	19.8891i	0.364769	−	0.631799i	0.988739	+	0.149650i	$0.0478146\pi$
$992$	−21.2074	−	36.7323i	−0.673336	−	1.16625i
$993$	13.5226			0.429126
$994$		0			0
$995$	11.7553			0.372668
$996$	−13.8474	−	23.9845i	−0.438773	−	0.759977i
$997$	0.674488	−	1.16825i	0.0213612	−	0.0369988i	−0.855147	−	0.518385i	$-0.826533\pi$
$997$	0.674488	−	1.16825i	0.0213612	−	0.0369988i	0.876508	+	0.481387i	$0.159867\pi$
$998$	24.0566	−	41.6672i	0.761498	−	1.31895i
$999$	7.77383	+	13.4647i	0.245953	+	0.426003i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.e.l.67.1		6
7.2	even	3	inner	539.2.e.l.177.1		6
7.3	odd	6		539.2.a.h.1.3		3
7.4	even	3		539.2.a.i.1.3		3
7.5	odd	6		77.2.e.b.23.1	✓	6
7.6	odd	2		77.2.e.b.67.1	yes	6
21.5	even	6		693.2.i.g.100.3		6
21.11	odd	6		4851.2.a.bn.1.1		3
21.17	even	6		4851.2.a.bo.1.1		3
21.20	even	2		693.2.i.g.298.3		6
28.3	even	6		8624.2.a.cl.1.3		3
28.11	odd	6		8624.2.a.ck.1.1		3
28.19	even	6		1232.2.q.k.177.1		6
28.27	even	2		1232.2.q.k.529.1		6
77.5	odd	30		847.2.n.e.366.1		24
77.6	even	10		847.2.n.d.487.1		24
77.10	even	6		5929.2.a.v.1.1		3
77.13	even	10		847.2.n.d.81.3		24
77.19	even	30		847.2.n.d.9.1		24
77.20	odd	10		847.2.n.e.81.1		24
77.26	odd	30		847.2.n.e.632.1		24
77.27	odd	10		847.2.n.e.487.3		24
77.32	odd	6		5929.2.a.w.1.1		3
77.40	even	30		847.2.n.d.632.3		24
77.41	even	10		847.2.n.d.130.3		24
77.47	odd	30		847.2.n.e.9.3		24
77.48	odd	10		847.2.n.e.753.3		24
77.54	even	6		847.2.e.d.485.3		6
77.61	even	30		847.2.n.d.366.3		24
77.62	even	10		847.2.n.d.753.1		24
77.68	even	30		847.2.n.d.807.1		24
77.69	odd	10		847.2.n.e.130.1		24
77.75	odd	30		847.2.n.e.807.3		24
77.76	even	2		847.2.e.d.606.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.b.23.1	✓	6	7.5	odd	6
77.2.e.b.67.1	yes	6	7.6	odd	2
539.2.a.h.1.3		3	7.3	odd	6
539.2.a.i.1.3		3	7.4	even	3
539.2.e.l.67.1		6	1.1	even	1	trivial
539.2.e.l.177.1		6	7.2	even	3	inner
693.2.i.g.100.3		6	21.5	even	6
693.2.i.g.298.3		6	21.20	even	2
847.2.e.d.485.3		6	77.54	even	6
847.2.e.d.606.3		6	77.76	even	2
847.2.n.d.9.1		24	77.19	even	30
847.2.n.d.81.3		24	77.13	even	10
847.2.n.d.130.3		24	77.41	even	10
847.2.n.d.366.3		24	77.61	even	30
847.2.n.d.487.1		24	77.6	even	10
847.2.n.d.632.3		24	77.40	even	30
847.2.n.d.753.1		24	77.62	even	10
847.2.n.d.807.1		24	77.68	even	30
847.2.n.e.9.3		24	77.47	odd	30
847.2.n.e.81.1		24	77.20	odd	10
847.2.n.e.130.1		24	77.69	odd	10
847.2.n.e.366.1		24	77.5	odd	30
847.2.n.e.487.3		24	77.27	odd	10
847.2.n.e.632.1		24	77.26	odd	30
847.2.n.e.753.3		24	77.48	odd	10
847.2.n.e.807.3		24	77.75	odd	30
1232.2.q.k.177.1		6	28.19	even	6
1232.2.q.k.529.1		6	28.27	even	2
4851.2.a.bn.1.1		3	21.11	odd	6
4851.2.a.bo.1.1		3	21.17	even	6
5929.2.a.v.1.1		3	77.10	even	6
5929.2.a.w.1.1		3	77.32	odd	6
8624.2.a.ck.1.1		3	28.11	odd	6
8624.2.a.cl.1.3		3	28.3	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.917122 - 1.58850i) q^{2} +(-1.09935 + 1.90412i) q^{3} +(-0.682224 + 1.18165i) q^{4} +(-0.317776 - 0.550404i) q^{5} +4.03293 q^{6} -1.16576 q^{8} +(-0.917122 - 1.58850i) q^{9} +O(q^{10})\)	\(q+(-0.917122 - 1.58850i) q^{2} +(-1.09935 + 1.90412i) q^{3} +(-0.682224 + 1.18165i) q^{4} +(-0.317776 - 0.550404i) q^{5} +4.03293 q^{6} -1.16576 q^{8} +(-0.917122 - 1.58850i) q^{9} +(-0.582878 + 1.00958i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-1.50000 - 2.59808i) q^{12} +1.80131 q^{13} +1.39738 q^{15} +(2.43359 + 4.21510i) q^{16} +(-1.41712 + 2.45453i) q^{17} +(-1.68222 + 2.91370i) q^{18} +(-2.78157 - 4.81782i) q^{19} +0.867178 q^{20} -1.83424 q^{22} +(-1.08288 - 1.87560i) q^{23} +(1.28157 - 2.21974i) q^{24} +(2.29804 - 3.98032i) q^{25} +(-1.65202 - 2.86138i) q^{26} -2.56314 q^{27} -10.4303 q^{29} +(-1.28157 - 2.21974i) q^{30} +(3.21516 - 5.56882i) q^{31} +(3.29804 - 5.71237i) q^{32} +(1.09935 + 1.90412i) q^{33} +5.19869 q^{34} +2.50273 q^{36} +(-3.03293 - 5.25320i) q^{37} +(-5.10208 + 8.83705i) q^{38} +(-1.98026 + 3.42991i) q^{39} +(0.370450 + 0.641637i) q^{40} -7.53566 q^{41} -4.86718 q^{43} +(0.682224 + 1.18165i) q^{44} +(-0.582878 + 1.00958i) q^{45} +(-1.98626 + 3.44031i) q^{46} +(-1.41712 - 2.45453i) q^{47} -10.7014 q^{48} -8.43032 q^{50} +(-3.11581 - 5.39675i) q^{51} +(-1.22890 + 2.12851i) q^{52} +(-3.73490 + 6.46903i) q^{53} +(2.35071 + 4.07155i) q^{54} -0.635552 q^{55} +12.2316 q^{57} +(9.56587 + 16.5686i) q^{58} +(5.90338 - 10.2250i) q^{59} +(-0.953328 + 1.65121i) q^{60} +(-2.16576 - 3.75120i) q^{61} -11.7948 q^{62} -2.36445 q^{64} +(-0.572413 - 0.991448i) q^{65} +(2.01647 - 3.49262i) q^{66} +(0.801309 - 1.38791i) q^{67} +(-1.93359 - 3.34907i) q^{68} +4.76183 q^{69} +4.29204 q^{71} +(1.06914 + 1.85181i) q^{72} +(-7.99673 + 13.8507i) q^{73} +(-5.56314 + 9.63564i) q^{74} +(5.05267 + 8.75149i) q^{75} +7.59061 q^{76} +7.26456 q^{78} +(-2.38092 - 4.12387i) q^{79} +(1.54667 - 2.67891i) q^{80} +(5.56914 - 9.64603i) q^{81} +(6.91112 + 11.9704i) q^{82} +9.23163 q^{83} +1.80131 q^{85} +(4.46379 + 7.73152i) q^{86} +(11.4665 - 19.8606i) q^{87} +(-0.582878 + 1.00958i) q^{88} +(0.182224 + 0.315621i) q^{89} +2.13828 q^{90} +2.95506 q^{92} +(7.06914 + 12.2441i) q^{93} +(-2.59935 + 4.50220i) q^{94} +(-1.76783 + 3.06197i) q^{95} +(7.25136 + 12.5597i) q^{96} +2.59607 q^{97} -1.83424 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{3} - 4 q^{4} - 2 q^{5} + 2 q^{6} - 18 q^{8}+O(q^{10}) \) 6 * q - q^3 - 4 * q^4 - 2 * q^5 + 2 * q^6 - 18 * q^8	\( 6 q - q^{3} - 4 q^{4} - 2 q^{5} + 2 q^{6} - 18 q^{8} - 9 q^{10} + 3 q^{11} - 9 q^{12} + 22 q^{13} - 14 q^{15} - 2 q^{16} - 3 q^{17} - 10 q^{18} - 11 q^{19} - 28 q^{20} - 12 q^{23} + 2 q^{24} - 3 q^{25} + q^{26} - 4 q^{27} - 18 q^{29} - 2 q^{30} - 3 q^{31} + 3 q^{32} + q^{33} + 20 q^{34} - 18 q^{36} + 4 q^{37} + 8 q^{38} + 5 q^{39} - 3 q^{40} + 10 q^{41} + 4 q^{43} + 4 q^{44} - 9 q^{45} + 10 q^{46} - 3 q^{47} - 20 q^{48} - 6 q^{50} - 2 q^{51} - 7 q^{52} - 17 q^{53} - 8 q^{54} - 4 q^{55} + 40 q^{57} + 13 q^{58} + 8 q^{59} - 6 q^{60} - 24 q^{61} - 26 q^{62} - 14 q^{64} - 15 q^{65} + q^{66} + 16 q^{67} + 5 q^{68} + 6 q^{69} + 14 q^{71} - 10 q^{72} - 20 q^{73} - 22 q^{74} + 25 q^{75} + 78 q^{76} - 12 q^{78} - 3 q^{79} + 9 q^{80} + 17 q^{81} + 41 q^{82} + 22 q^{83} + 22 q^{85} + 21 q^{86} + 30 q^{87} - 9 q^{88} + q^{89} - 20 q^{90} + 50 q^{92} + 26 q^{93} - 10 q^{94} + 17 q^{95} + 27 q^{96} - 18 q^{97}+O(q^{100}) \) 6 * q - q^3 - 4 * q^4 - 2 * q^5 + 2 * q^6 - 18 * q^8 - 9 * q^10 + 3 * q^11 - 9 * q^12 + 22 * q^13 - 14 * q^15 - 2 * q^16 - 3 * q^17 - 10 * q^18 - 11 * q^19 - 28 * q^20 - 12 * q^23 + 2 * q^24 - 3 * q^25 + q^26 - 4 * q^27 - 18 * q^29 - 2 * q^30 - 3 * q^31 + 3 * q^32 + q^33 + 20 * q^34 - 18 * q^36 + 4 * q^37 + 8 * q^38 + 5 * q^39 - 3 * q^40 + 10 * q^41 + 4 * q^43 + 4 * q^44 - 9 * q^45 + 10 * q^46 - 3 * q^47 - 20 * q^48 - 6 * q^50 - 2 * q^51 - 7 * q^52 - 17 * q^53 - 8 * q^54 - 4 * q^55 + 40 * q^57 + 13 * q^58 + 8 * q^59 - 6 * q^60 - 24 * q^61 - 26 * q^62 - 14 * q^64 - 15 * q^65 + q^66 + 16 * q^67 + 5 * q^68 + 6 * q^69 + 14 * q^71 - 10 * q^72 - 20 * q^73 - 22 * q^74 + 25 * q^75 + 78 * q^76 - 12 * q^78 - 3 * q^79 + 9 * q^80 + 17 * q^81 + 41 * q^82 + 22 * q^83 + 22 * q^85 + 21 * q^86 + 30 * q^87 - 9 * q^88 + q^89 - 20 * q^90 + 50 * q^92 + 26 * q^93 - 10 * q^94 + 17 * q^95 + 27 * q^96 - 18 * q^97

Introduction

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