LMFDB - Embedded newform 637.2.u.g.30.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(30,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("637.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.u (of order $6$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			30.1
Root			$1.32725 - 0.488273i$ of defining polynomial
Character	$\chi$	$=$	637.30
Dual form			637.2.u.g.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.24179 + 1.29430i) q^{2} -0.518466 q^{3} +(2.35043 - 4.07106i) q^{4} +(-1.39608 - 0.806027i) q^{5} +(1.16229 - 0.671051i) q^{6} +6.99143i q^{8} -2.73119 q^{9} +O(q^{10})$	\(q+(-2.24179 + 1.29430i) q^{2} -0.518466 q^{3} +(2.35043 - 4.07106i) q^{4} +(-1.39608 - 0.806027i) q^{5} +(1.16229 - 0.671051i) q^{6} +6.99143i q^{8} -2.73119 q^{9} +4.17296 q^{10} +2.70496i q^{11} +(-1.21862 + 2.11070i) q^{12} +(-2.36840 - 2.71858i) q^{13} +(0.723819 + 0.417897i) q^{15} +(-4.34816 - 7.53123i) q^{16} +(-1.56330 + 2.70772i) q^{17} +(6.12277 - 3.53498i) q^{18} +3.68150i q^{19} +(-6.56276 + 3.78901i) q^{20} +(-3.50103 - 6.06396i) q^{22} +(0.993019 + 1.71996i) q^{23} -3.62482i q^{24} +(-1.20064 - 2.07957i) q^{25} +(8.82813 + 3.02907i) q^{26} +2.97143 q^{27} +(2.68636 - 4.65290i) q^{29} -2.16354 q^{30} +(9.07425 - 5.23902i) q^{31} +(7.38583 + 4.26421i) q^{32} -1.40243i q^{33} -8.09354i q^{34} +(-6.41947 + 11.1188i) q^{36} +(5.15585 - 2.97673i) q^{37} +(-4.76497 - 8.25317i) q^{38} +(1.22794 + 1.40949i) q^{39} +(5.63528 - 9.76059i) q^{40} +(6.66970 + 3.85075i) q^{41} +(-1.67800 - 2.90638i) q^{43} +(11.0120 + 6.35780i) q^{44} +(3.81296 + 2.20141i) q^{45} +(-4.45229 - 2.57053i) q^{46} +(0.913730 + 0.527542i) q^{47} +(2.25437 + 3.90469i) q^{48} +(5.38318 + 3.10798i) q^{50} +(0.810520 - 1.40386i) q^{51} +(-16.6343 + 3.25208i) q^{52} +(-3.63284 - 6.29226i) q^{53} +(-6.66133 + 3.84592i) q^{54} +(2.18027 - 3.77633i) q^{55} -1.90873i q^{57} +13.9078i q^{58} +(9.89352 + 5.71203i) q^{59} +(3.40257 - 1.96447i) q^{60} +2.92507 q^{61} +(-13.5617 + 23.4896i) q^{62} -4.68406 q^{64} +(1.11523 + 5.70435i) q^{65} +(1.81516 + 3.14395i) q^{66} +13.5818i q^{67} +(7.34886 + 12.7286i) q^{68} +(-0.514846 - 0.891740i) q^{69} +(1.17009 - 0.675554i) q^{71} -19.0949i q^{72} +(-7.88374 + 4.55168i) q^{73} +(-7.70557 + 13.3464i) q^{74} +(0.622492 + 1.07819i) q^{75} +(14.9876 + 8.65311i) q^{76} +(-4.57708 - 1.57047i) q^{78} +(3.10289 - 5.37436i) q^{79} +14.0189i q^{80} +6.65300 q^{81} -19.9361 q^{82} -2.69672i q^{83} +(4.36499 - 2.52013i) q^{85} +(7.52346 + 4.34367i) q^{86} +(-1.39278 + 2.41237i) q^{87} -18.9115 q^{88} +(-1.52410 + 0.879938i) q^{89} -11.3972 q^{90} +9.33607 q^{92} +(-4.70469 + 2.71625i) q^{93} -2.73119 q^{94} +(2.96739 - 5.13967i) q^{95} +(-3.82930 - 2.21085i) q^{96} +(13.4078 - 7.74102i) q^{97} -7.38776i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} + 4 q^{4} - 3 q^{5} + 9 q^{6} + 2 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 + 4 * q^4 - 3 * q^5 + 9 * q^6 + 2 * q^9	$ 12 q - 6 q^{3} + 4 q^{4} - 3 q^{5} + 9 q^{6} + 2 q^{9} + 24 q^{10} + q^{12} + 2 q^{13} - 12 q^{15} - 8 q^{16} - 17 q^{17} - 3 q^{18} + 3 q^{20} - 15 q^{22} + 3 q^{23} - 5 q^{25} + 9 q^{26} - 12 q^{27} - q^{29} - 22 q^{30} + 18 q^{31} + 18 q^{32} - 13 q^{36} + 15 q^{37} - 19 q^{38} - q^{39} + q^{40} + 6 q^{41} + 11 q^{43} + 33 q^{44} + 9 q^{45} - 30 q^{46} - 15 q^{47} - 19 q^{48} + 18 q^{50} + 4 q^{51} - 47 q^{52} - 8 q^{53} - 6 q^{54} + 15 q^{55} - 27 q^{59} + 30 q^{60} + 10 q^{61} - 41 q^{62} + 2 q^{64} - 3 q^{65} + 34 q^{66} + 11 q^{68} - 7 q^{69} + 30 q^{71} + 42 q^{73} - 33 q^{74} - q^{75} + 45 q^{76} + 44 q^{78} - 35 q^{79} - 28 q^{81} + 10 q^{82} - 21 q^{85} + 57 q^{86} - 10 q^{87} + 28 q^{88} - 48 q^{89} - 66 q^{92} - 81 q^{93} + 2 q^{94} + 2 q^{95} + 21 q^{96} + 3 q^{97}+O(q^{100}) $ 12 * q - 6 * q^3 + 4 * q^4 - 3 * q^5 + 9 * q^6 + 2 * q^9 + 24 * q^10 + q^12 + 2 * q^13 - 12 * q^15 - 8 * q^16 - 17 * q^17 - 3 * q^18 + 3 * q^20 - 15 * q^22 + 3 * q^23 - 5 * q^25 + 9 * q^26 - 12 * q^27 - q^29 - 22 * q^30 + 18 * q^31 + 18 * q^32 - 13 * q^36 + 15 * q^37 - 19 * q^38 - q^39 + q^40 + 6 * q^41 + 11 * q^43 + 33 * q^44 + 9 * q^45 - 30 * q^46 - 15 * q^47 - 19 * q^48 + 18 * q^50 + 4 * q^51 - 47 * q^52 - 8 * q^53 - 6 * q^54 + 15 * q^55 - 27 * q^59 + 30 * q^60 + 10 * q^61 - 41 * q^62 + 2 * q^64 - 3 * q^65 + 34 * q^66 + 11 * q^68 - 7 * q^69 + 30 * q^71 + 42 * q^73 - 33 * q^74 - q^75 + 45 * q^76 + 44 * q^78 - 35 * q^79 - 28 * q^81 + 10 * q^82 - 21 * q^85 + 57 * q^86 - 10 * q^87 + 28 * q^88 - 48 * q^89 - 66 * q^92 - 81 * q^93 + 2 * q^94 + 2 * q^95 + 21 * q^96 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−2.24179	+	1.29430i	−1.58519	+	0.915209i	−0.591104	+	0.806596i	$0.701308\pi$
$2$	−2.24179	+	1.29430i	−1.58519	+	0.915209i	−0.994084	+	0.108613i	$0.965359\pi$
$3$	−0.518466			−0.299336			−0.149668	−	0.988736i	$-0.547821\pi$
$3$	−0.518466			−0.299336			−0.149668	+	0.988736i	$0.547821\pi$
$4$	2.35043	−	4.07106i	1.17521	−	2.03553i
$5$	−1.39608	−	0.806027i	−0.624346	−	0.360466i	0.154213	−	0.988038i	$-0.450716\pi$
$5$	−1.39608	−	0.806027i	−0.624346	−	0.360466i	−0.778559	+	0.627571i	$0.784049\pi$
$6$	1.16229	−	0.671051i	0.474504	−	0.273955i
$7$		0			0
$7$		0			0
$8$			6.99143i			2.47184i
$9$	−2.73119			−0.910398
$10$	4.17296			1.31961
$11$			2.70496i			0.815575i	0.913077	+	0.407788i	$0.133700\pi$
$11$			2.70496i			0.815575i	−0.913077	+	0.407788i	$0.866300\pi$
$12$	−1.21862	+	2.11070i	−0.351784	+	0.609308i
$13$	−2.36840	−	2.71858i	−0.656876	−	0.753998i
$13$	−2.36840	−	2.71858i	−0.656876	−	0.753998i
$14$		0			0
$15$	0.723819	+	0.417897i	0.186889	+	0.107901i
$16$	−4.34816	−	7.53123i	−1.08704	−	1.88281i
$17$	−1.56330	+	2.70772i	−0.379157	+	0.656719i	−0.990940	−	0.134307i	$-0.957119\pi$
$17$	−1.56330	+	2.70772i	−0.379157	+	0.656719i	0.611783	+	0.791026i	$0.290453\pi$
$18$	6.12277	−	3.53498i	1.44315	−	0.833204i
$19$			3.68150i			0.844595i	0.906457	+	0.422297i	$0.138776\pi$
$19$			3.68150i			0.844595i	−0.906457	+	0.422297i	$0.861224\pi$
$20$	−6.56276	+	3.78901i	−1.46748	+	0.847249i
$21$		0			0
$22$	−3.50103	−	6.06396i	−0.746421	−	1.29284i
$23$	0.993019	+	1.71996i	0.207059	+	0.358636i	0.950787	−	0.309846i	$-0.100278\pi$
$23$	0.993019	+	1.71996i	0.207059	+	0.358636i	−0.743728	+	0.668482i	$0.766944\pi$
$24$		−	3.62482i		−	0.739913i
$25$	−1.20064	−	2.07957i	−0.240128	−	0.415914i
$26$	8.82813	+	3.02907i	1.73134	+	0.594050i
$27$	2.97143			0.571852
$28$		0			0
$29$	2.68636	−	4.65290i	0.498844	−	0.864023i	−0.501155	−	0.865357i	$-0.667092\pi$
$29$	2.68636	−	4.65290i	0.498844	−	0.864023i	0.999999	+	0.00133469i	$0.000424845\pi$
$30$	−2.16354			−0.395006
$31$	9.07425	−	5.23902i	1.62978	−	0.940956i	0.645627	−	0.763653i	$-0.276596\pi$
$31$	9.07425	−	5.23902i	1.62978	−	0.940956i	0.984156	−	0.177303i	$-0.0567372\pi$
$32$	7.38583	+	4.26421i	1.30564	+	0.753813i
$33$		−	1.40243i		−	0.244131i
$34$		−	8.09354i		−	1.38803i
$35$		0			0
$36$	−6.41947	+	11.1188i	−1.06991	+	1.85314i
$37$	5.15585	−	2.97673i	0.847616	−	0.489371i	−0.0122297	−	0.999925i	$-0.503893\pi$
$37$	5.15585	−	2.97673i	0.847616	−	0.489371i	0.859846	+	0.510554i	$0.170560\pi$
$38$	−4.76497	−	8.25317i	−0.772981	−	1.33884i
$39$	1.22794	+	1.40949i	0.196627	+	0.225699i
$40$	5.63528	−	9.76059i	0.891016	−	1.54329i
$41$	6.66970	+	3.85075i	1.04163	+	0.601386i	0.920295	−	0.391225i	$-0.127949\pi$
$41$	6.66970	+	3.85075i	1.04163	+	0.601386i	0.121337	+	0.992611i	$0.461282\pi$
$42$		0			0
$43$	−1.67800	−	2.90638i	−0.255892	−	0.443219i	0.709245	−	0.704962i	$-0.249036\pi$
$43$	−1.67800	−	2.90638i	−0.255892	−	0.443219i	−0.965138	+	0.261743i	$0.915703\pi$
$44$	11.0120	+	6.35780i	1.66013	+	0.958475i
$45$	3.81296	+	2.20141i	0.568403	+	0.328168i
$46$	−4.45229	−	2.57053i	−0.656454	−	0.379004i
$47$	0.913730	+	0.527542i	0.133281	+	0.0769500i	0.565158	−	0.824983i	$-0.308815\pi$
$47$	0.913730	+	0.527542i	0.133281	+	0.0769500i	−0.431877	+	0.901933i	$0.642148\pi$
$48$	2.25437	+	3.90469i	0.325390	+	0.563593i
$49$		0			0
$50$	5.38318	+	3.10798i	0.761297	+	0.439535i
$51$	0.810520	−	1.40386i	0.113495	−	0.196580i
$52$	−16.6343	+	3.25208i	−2.30676	+	0.450982i
$53$	−3.63284	−	6.29226i	−0.499009	−	0.864308i	0.500991	−	0.865453i	$-0.332969\pi$
$53$	−3.63284	−	6.29226i	−0.499009	−	0.864308i	−0.999999	+	0.00114437i	$0.999636\pi$
$54$	−6.66133	+	3.84592i	−0.906492	+	0.523363i
$55$	2.18027	−	3.77633i	0.293987	−	0.509201i
$56$		0			0
$57$		−	1.90873i		−	0.252818i
$58$			13.9078i			1.82618i
$59$	9.89352	+	5.71203i	1.28803	+	0.743643i	0.978302	−	0.207183i	$-0.0664297\pi$
$59$	9.89352	+	5.71203i	1.28803	+	0.743643i	0.309725	+	0.950826i	$0.399763\pi$
$60$	3.40257	−	1.96447i	0.439270	−	0.253613i
$61$	2.92507			0.374517			0.187259	−	0.982311i	$-0.440040\pi$
$61$	2.92507			0.374517			0.187259	+	0.982311i	$0.440040\pi$
$62$	−13.5617	+	23.4896i	−1.72234	+	2.98318i
$63$		0			0
$64$	−4.68406			−0.585507
$65$	1.11523	+	5.70435i	0.138327	+	0.707537i
$66$	1.81516	+	3.14395i	0.223431	+	0.386994i
$67$			13.5818i			1.65928i	0.558296	+	0.829642i	$0.311455\pi$
$67$			13.5818i			1.65928i	−0.558296	+	0.829642i	$0.688545\pi$
$68$	7.34886	+	12.7286i	0.891180	+	1.54357i
$69$	−0.514846	−	0.891740i	−0.0619802	−	0.107353i
$70$		0			0
$71$	1.17009	−	0.675554i	0.138865	−	0.0801736i	−0.428958	−	0.903324i	$-0.641119\pi$
$71$	1.17009	−	0.675554i	0.138865	−	0.0801736i	0.567823	+	0.823151i	$0.307786\pi$
$72$		−	19.0949i		−	2.25036i
$73$	−7.88374	+	4.55168i	−0.922721	+	0.532733i	−0.884502	−	0.466536i	$-0.845502\pi$
$73$	−7.88374	+	4.55168i	−0.922721	+	0.532733i	−0.0382192	+	0.999269i	$0.512169\pi$
$74$	−7.70557	+	13.3464i	−0.895754	+	1.55149i
$75$	0.622492	+	1.07819i	0.0718791	+	0.124498i
$76$	14.9876	+	8.65311i	1.71920	+	0.992579i
$77$		0			0
$78$	−4.57708	−	1.57047i	−0.518252	−	0.177821i
$79$	3.10289	−	5.37436i	0.349102	−	0.604663i	−0.636988	−	0.770874i	$-0.719820\pi$
$79$	3.10289	−	5.37436i	0.349102	−	0.604663i	0.986090	+	0.166211i	$0.0531532\pi$
$80$			14.0189i			1.56736i
$81$	6.65300			0.739222
$82$	−19.9361			−2.20158
$83$		−	2.69672i		−	0.296003i	−0.988987	−	0.148002i	$-0.952716\pi$
$83$		−	2.69672i		−	0.296003i	0.988987	−	0.148002i	$-0.0472841\pi$
$84$		0			0
$85$	4.36499	−	2.52013i	0.473450	−	0.273346i
$86$	7.52346	+	4.34367i	0.811275	+	0.468390i
$87$	−1.39278	+	2.41237i	−0.149322	+	0.258633i
$88$	−18.9115			−2.01597
$89$	−1.52410	+	0.879938i	−0.161554	+	0.0932732i	−0.578597	−	0.815613i	$-0.696400\pi$
$89$	−1.52410	+	0.879938i	−0.161554	+	0.0932732i	0.417043	+	0.908887i	$0.363066\pi$
$90$	−11.3972			−1.20137
$91$		0			0
$92$	9.33607			0.973353
$93$	−4.70469	+	2.71625i	−0.487853	+	0.281662i
$94$	−2.73119			−0.281701
$95$	2.96739	−	5.13967i	0.304448	−	0.527319i
$96$	−3.82930	−	2.21085i	−0.390827	−	0.225644i
$97$	13.4078	−	7.74102i	1.36136	−	0.785981i	0.371555	−	0.928411i	$-0.378825\pi$
$97$	13.4078	−	7.74102i	1.36136	−	0.785981i	0.989805	+	0.142430i	$0.0454915\pi$
$98$		0			0
$99$		−	7.38776i		−	0.742498i
$100$	−11.2881			−1.12881
$101$	−1.27930			−0.127295			−0.0636477	−	0.997972i	$-0.520273\pi$
$101$	−1.27930			−0.127295			−0.0636477	+	0.997972i	$0.520273\pi$
$102$			4.19622i			0.415488i
$103$	5.73367	−	9.93101i	0.564956	−	0.978532i	−0.432098	−	0.901827i	$-0.642227\pi$
$103$	5.73367	−	9.93101i	0.564956	−	0.978532i	0.997054	−	0.0767054i	$-0.0244401\pi$
$104$	19.0068	−	16.5585i	1.86377	−	1.62370i
$105$		0			0
$106$	16.2881	+	9.40397i	1.58204	+	0.913394i
$107$	2.56763	+	4.44726i	0.248222	+	0.429933i	0.963033	−	0.269385i	$-0.0868205\pi$
$107$	2.56763	+	4.44726i	0.248222	+	0.429933i	−0.714811	+	0.699318i	$0.753487\pi$
$108$	6.98412	−	12.0969i	0.672048	−	1.16402i
$109$	−1.49635	+	0.863916i	−0.143324	+	0.0827481i	−0.569947	−	0.821681i	$-0.693036\pi$
$109$	−1.49635	+	0.863916i	−0.143324	+	0.0827481i	0.426623	+	0.904429i	$0.359703\pi$
$110$			11.2877i			1.07624i
$111$	−2.67313	+	1.54333i	−0.253722	+	0.146487i
$112$		0			0
$113$	4.29556	+	7.44014i	0.404093	+	0.699909i	0.994215	−	0.107404i	$-0.0342540\pi$
$113$	4.29556	+	7.44014i	0.404093	+	0.699909i	−0.590123	+	0.807314i	$0.700921\pi$
$114$	2.47048	+	4.27899i	0.231381	+	0.400764i
$115$		−	3.20160i		−	0.298551i
$116$	−12.6282	−	21.8726i	−1.17250	−	2.03082i
$117$	6.46856	+	7.42497i	0.598019	+	0.686438i
$118$	−29.5723			−2.72235
$119$		0			0
$120$	−2.92170	+	5.06053i	−0.266714	+	0.461961i
$121$	3.68321			0.334837
$122$	−6.55741	+	3.78592i	−0.593680	+	0.342761i
$123$	−3.45801	−	1.99648i	−0.311798	−	0.180017i
$124$		−	49.2557i		−	4.42330i
$125$			11.9313i			1.06716i
$126$		0			0
$127$	−1.56206	+	2.70556i	−0.138610	+	0.240080i	−0.926971	−	0.375133i	$-0.877597\pi$
$127$	−1.56206	+	2.70556i	−0.138610	+	0.240080i	0.788361	+	0.615214i	$0.210930\pi$
$128$	−4.27097	+	2.46585i	−0.377504	+	0.217952i
$129$	0.869985	+	1.50686i	0.0765979	+	0.132671i
$130$	−9.88325	−	11.3445i	−0.866818	−	0.994981i
$131$	5.10460	−	8.84142i	0.445991	−	0.772479i	−0.552130	−	0.833758i	$-0.686185\pi$
$131$	5.10460	−	8.84142i	0.445991	−	0.772479i	0.998121	+	0.0612793i	$0.0195180\pi$
$132$	−5.70937	−	3.29630i	−0.496936	−	0.286906i
$133$		0			0
$134$	−17.5790	−	30.4476i	−1.51859	−	2.63028i
$135$	−4.14835	−	2.39505i	−0.357033	−	0.206133i
$136$	−18.9308	−	10.9297i	−1.62331	−	0.937216i
$137$	8.65385	+	4.99630i	0.739348	+	0.426863i	0.821832	−	0.569729i	$-0.192952\pi$
$137$	8.65385	+	4.99630i	0.739348	+	0.426863i	−0.0824839	+	0.996592i	$0.526285\pi$
$138$	2.30836	+	1.33273i	0.196501	+	0.113450i
$139$	−0.832100	−	1.44124i	−0.0705778	−	0.122244i	0.828577	−	0.559875i	$-0.189151\pi$
$139$	−0.832100	−	1.44124i	−0.0705778	−	0.122244i	−0.899155	+	0.437631i	$0.855818\pi$
$140$		0			0
$141$	−0.473738	−	0.273513i	−0.0398959	−	0.0230339i
$142$	−1.74874	+	3.02891i	−0.146751	+	0.254180i
$143$	7.35364	−	6.40642i	0.614942	−	0.535732i
$144$	11.8757	+	20.5692i	0.989638	+	1.71410i
$145$	−7.50073	+	4.33055i	−0.622902	+	0.359633i
$146$	11.7825	−	20.4078i	0.975124	−	1.68897i
$147$		0			0
$148$		−	27.9863i		−	2.30046i
$149$		−	19.7980i		−	1.62192i	−0.585103	−	0.810959i	$-0.698946\pi$
$149$		−	19.7980i		−	1.62192i	0.585103	−	0.810959i	$-0.301054\pi$
$150$	−2.79100	−	1.61138i	−0.227884	−	0.131569i
$151$	6.52544	−	3.76746i	0.531033	−	0.306592i	−0.210404	−	0.977614i	$-0.567478\pi$
$151$	6.52544	−	3.76746i	0.531033	−	0.306592i	0.741437	+	0.671023i	$0.234145\pi$
$152$	−25.7390			−2.08771
$153$	4.26968	−	7.39531i	0.345183	−	0.597875i
$154$		0			0
$155$	−16.8912			−1.35673
$156$	8.62429	−	1.68609i	0.690496	−	0.134995i
$157$	7.00223	+	12.1282i	0.558839	+	0.967938i	0.997594	+	0.0693309i	$0.0220864\pi$
$157$	7.00223	+	12.1282i	0.558839	+	0.967938i	−0.438755	+	0.898607i	$0.644580\pi$
$158$			16.0643i			1.27801i
$159$	1.88350	+	3.26232i	0.149371	+	0.258719i
$160$	−6.87414	−	11.9064i	−0.543448	−	0.941280i
$161$		0			0
$162$	−14.9146	+	8.61097i	−1.17181	+	0.676542i
$163$		−	7.16995i		−	0.561594i	−0.959767	−	0.280797i	$-0.909401\pi$
$163$		−	7.16995i		−	0.561594i	0.959767	−	0.280797i	$-0.0905987\pi$
$164$	31.3533	−	18.1018i	2.44828	−	1.41351i
$165$	−1.13039	+	1.95790i	−0.0880011	+	0.152422i
$166$	3.49036	+	6.04548i	0.270904	+	0.469220i
$167$	−15.5716	−	8.99027i	−1.20497	−	0.695688i	−0.243312	−	0.969948i	$-0.578234\pi$
$167$	−15.5716	−	8.99027i	−1.20497	−	0.695688i	−0.961656	+	0.274260i	$0.911567\pi$
$168$		0			0
$169$	−1.78135	+	12.8774i	−0.137027	+	0.990567i
$170$	−6.52361	+	11.2992i	−0.500338	+	0.866611i
$171$		−	10.0549i		−	0.768917i
$172$	−15.7761			−1.20291
$173$	−12.8116			−0.974047			−0.487023	−	0.873389i	$-0.661917\pi$
$173$	−12.8116			−0.974047			−0.487023	+	0.873389i	$0.661917\pi$
$174$		−	7.21072i		−	0.546643i
$175$		0			0
$176$	20.3717	−	11.7616i	1.53557	−	0.886562i
$177$	−5.12945	−	2.96149i	−0.385553	−	0.222599i
$178$	2.27781	−	3.94528i	0.170729	−	0.295711i
$179$	−1.84022			−0.137545			−0.0687723	−	0.997632i	$-0.521908\pi$
$179$	−1.84022			−0.137545			−0.0687723	+	0.997632i	$0.521908\pi$
$180$	17.9242	−	10.3485i	1.33599	−	0.771334i
$181$	3.29928			0.245234			0.122617	−	0.992454i	$-0.460871\pi$
$181$	3.29928			0.245234			0.122617	+	0.992454i	$0.460871\pi$
$182$		0			0
$183$	−1.51655			−0.112107
$184$	−12.0250	+	6.94262i	−0.886493	+	0.511817i
$185$	−9.59730			−0.705607
$186$	7.03129	−	12.1786i	0.515560	−	0.892975i
$187$	−7.32427	−	4.22867i	−0.535604	−	0.309231i
$188$	4.29531	−	2.47990i	0.313268	−	0.180865i
$189$		0			0
$190$			15.3628i			1.11453i
$191$	4.89614			0.354272			0.177136	−	0.984186i	$-0.443317\pi$
$191$	4.89614			0.354272			0.177136	+	0.984186i	$0.443317\pi$
$192$	2.42852			0.175264
$193$			3.01910i			0.217320i	0.994079	+	0.108660i	$0.0346559\pi$
$193$			3.01910i			0.217320i	−0.994079	+	0.108660i	$0.965344\pi$
$194$	−20.0384	+	34.7075i	−1.43867	+	2.49186i
$195$	−0.578207	−	2.95751i	−0.0414063	−	0.211792i
$196$		0			0
$197$	4.02694	+	2.32496i	0.286908	+	0.165646i	0.636546	−	0.771238i	$-0.280362\pi$
$197$	4.02694	+	2.32496i	0.286908	+	0.165646i	−0.349639	+	0.936885i	$0.613696\pi$
$198$	9.56198	+	16.5618i	0.679540	+	1.17700i
$199$	−0.205360	+	0.355694i	−0.0145576	+	0.0252145i	−0.873212	−	0.487340i	$-0.837967\pi$
$199$	−0.205360	+	0.355694i	−0.0145576	+	0.0252145i	0.858655	+	0.512554i	$0.171301\pi$
$200$	14.5392	−	8.39420i	1.02808	−	0.593560i
$201$		−	7.04171i		−	0.496684i
$202$	2.86793	−	1.65580i	0.201787	−	0.116502i
$203$		0			0
$204$	−3.81013	−	6.59934i	−0.266763	−	0.462047i
$205$	−6.20762	−	10.7519i	−0.433559	−	0.750946i
$206$			29.6844i			2.06821i
$207$	−2.71213	−	4.69754i	−0.188506	−	0.326502i
$208$	−10.1761	+	29.6578i	−0.705583	+	2.05640i
$209$	−9.95831			−0.688831
$210$		0			0
$211$	3.75800	−	6.50905i	0.258711	−	0.448101i	−0.707186	−	0.707028i	$-0.750035\pi$
$211$	3.75800	−	6.50905i	0.258711	−	0.448101i	0.965897	+	0.258927i	$0.0833688\pi$
$212$	−34.1549			−2.34577
$213$	−0.606654	+	0.350252i	−0.0415672	+	0.0239989i
$214$	−11.5122	−	6.64656i	−0.786956	−	0.454349i
$215$			5.41005i			0.368962i
$216$			20.7745i			1.41353i
$217$		0			0
$218$	2.23633	−	3.87344i	0.151464	−	0.262343i
$219$	4.08745	−	2.35989i	0.276204	−	0.159467i
$220$	−10.2491	−	17.7520i	−0.690996	−	1.19684i
$221$	11.0637	−	2.16300i	0.744224	−	0.145499i
$222$	3.99507	−	6.91967i	0.268132	−	0.464418i
$223$	19.5544	+	11.2897i	1.30946	+	0.756016i	0.982006	−	0.188852i	$-0.0604766\pi$
$223$	19.5544	+	11.2897i	1.30946	+	0.756016i	0.327452	+	0.944868i	$0.393810\pi$
$224$		0			0
$225$	3.27918	+	5.67971i	0.218612	+	0.378648i
$226$	−19.2595	−	11.1195i	−1.28113	−	0.739658i
$227$	−11.8401	−	6.83586i	−0.785853	−	0.453712i	0.0526478	−	0.998613i	$-0.483234\pi$
$227$	−11.8401	−	6.83586i	−0.785853	−	0.453712i	−0.838500	+	0.544901i	$0.816567\pi$
$228$	−7.77057	−	4.48634i	−0.514618	−	0.297115i
$229$	6.86832	+	3.96543i	0.453872	+	0.262043i	0.709464	−	0.704742i	$-0.248937\pi$
$229$	6.86832	+	3.96543i	0.453872	+	0.262043i	−0.255592	+	0.966785i	$0.582270\pi$
$230$	4.14383	+	7.17733i	0.273236	+	0.473259i
$231$		0			0
$232$	32.5305	+	18.7815i	2.13573	+	1.23306i
$233$	−3.28585	+	5.69127i	−0.215263	+	0.372847i	−0.953354	−	0.301854i	$-0.902394\pi$
$233$	−3.28585	+	5.69127i	−0.215263	+	0.372847i	0.738091	+	0.674702i	$0.235728\pi$
$234$	−24.1113	−	8.27298i	−1.57621	−	0.540822i
$235$	−0.850427	−	1.47298i	−0.0554757	−	0.0960868i
$236$	46.5080	−	26.8514i	3.02741	−	1.74788i
$237$	−1.60874	+	2.78642i	−0.104499	+	0.180998i
$238$		0			0
$239$			9.39284i			0.607572i	0.952740	+	0.303786i	$0.0982508\pi$
$239$			9.39284i			0.607572i	−0.952740	+	0.303786i	$0.901749\pi$
$240$		−	7.26833i		−	0.469169i
$241$	−8.73460	−	5.04292i	−0.562645	−	0.324843i	0.191562	−	0.981481i	$-0.438645\pi$
$241$	−8.73460	−	5.04292i	−0.562645	−	0.324843i	−0.754206	+	0.656637i	$0.771978\pi$
$242$	−8.25699	+	4.76718i	−0.530780	+	0.306446i
$243$	−12.3636			−0.793128
$244$	6.87517	−	11.9081i	0.440137	−	0.762340i
$245$		0			0
$246$	10.3362			0.659012
$247$	10.0085	−	8.71928i	0.636823	−	0.554794i
$248$	36.6282	+	63.4420i	2.32590	+	4.02857i
$249$			1.39816i			0.0886045i
$250$	−15.4426	−	26.7474i	−0.976678	−	1.69166i
$251$	5.17427	+	8.96209i	0.326597	+	0.565682i	0.981834	−	0.189741i	$-0.0607648\pi$
$251$	5.17427	+	8.96209i	0.326597	+	0.565682i	−0.655237	+	0.755423i	$0.727431\pi$
$252$		0			0
$253$	−4.65242	+	2.68607i	−0.292495	+	0.168872i
$254$		−	8.08709i		−	0.507429i
$255$	−2.26310	+	1.30660i	−0.141721	+	0.0818225i
$256$	11.0672	−	19.1689i	0.691697	−	1.19805i
$257$	−3.99329	−	6.91658i	−0.249095	−	0.431445i	0.714180	−	0.699962i	$-0.246800\pi$
$257$	−3.99329	−	6.91658i	−0.249095	−	0.431445i	−0.963275	+	0.268517i	$0.913466\pi$
$258$	−3.90065	−	2.25204i	−0.242844	−	0.140206i
$259$		0			0
$260$	25.8440	+	8.86749i	1.60278	+	0.549939i
$261$	−7.33696	+	12.7080i	−0.454146	+	0.786604i
$262$			26.4275i			1.63270i
$263$	5.05934			0.311972			0.155986	−	0.987759i	$-0.450144\pi$
$263$	5.05934			0.311972			0.155986	+	0.987759i	$0.450144\pi$
$264$	9.80498			0.603455
$265$			11.7127i			0.719503i
$266$		0			0
$267$	0.790192	−	0.456218i	0.0483590	−	0.0279201i
$268$	55.2924	+	31.9231i	3.37752	+	1.95001i
$269$	6.94512	−	12.0293i	0.423451	−	0.733439i	−0.572823	−	0.819679i	$-0.694152\pi$
$269$	6.94512	−	12.0293i	0.423451	−	0.733439i	0.996274	+	0.0862400i	$0.0274852\pi$
$270$	12.3997			0.754619
$271$	7.21158	−	4.16361i	0.438072	−	0.252921i	−0.264707	−	0.964329i	$-0.585275\pi$
$271$	7.21158	−	4.16361i	0.438072	−	0.252921i	0.702780	+	0.711408i	$0.251942\pi$
$272$	27.1900			1.64863
$273$		0			0
$274$	−25.8669			−1.56267
$275$	5.62515	−	3.24768i	0.339210	−	0.195843i
$276$	−4.84043			−0.291360
$277$	−11.6058	+	20.1018i	−0.697325	+	1.20780i	0.272066	+	0.962279i	$0.412293\pi$
$277$	−11.6058	+	20.1018i	−0.697325	+	1.20780i	−0.969391	+	0.245523i	$0.921040\pi$
$278$	3.73080	+	2.15398i	0.223758	+	0.129187i
$279$	−24.7835	+	14.3088i	−1.48375	+	0.856644i
$280$		0			0
$281$			27.1595i			1.62020i	0.586292	+	0.810100i	$0.300587\pi$
$281$			27.1595i			1.62020i	−0.586292	+	0.810100i	$0.699413\pi$
$282$	1.41603			0.0843234
$283$	−16.1513			−0.960092			−0.480046	−	0.877243i	$-0.659380\pi$
$283$	−16.1513			−0.960092			−0.480046	+	0.877243i	$0.659380\pi$
$284$		−	6.35136i		−	0.376884i
$285$	−1.53849	+	2.66474i	−0.0911323	+	0.157846i
$286$	−8.19351	+	23.8797i	−0.484493	+	1.41204i
$287$		0			0
$288$	−20.1721	−	11.6464i	−1.18865	−	0.686270i
$289$	3.61216	+	6.25645i	0.212480	+	0.368027i
$290$	11.2101	−	19.4164i	0.658278	−	1.14017i
$291$	−6.95151	+	4.01345i	−0.407504	+	0.235273i
$292$			42.7935i			2.50430i
$293$	12.6831	−	7.32260i	0.740956	−	0.427791i	−0.0814609	−	0.996677i	$-0.525959\pi$
$293$	12.6831	−	7.32260i	0.740956	−	0.427791i	0.822417	+	0.568885i	$0.192625\pi$
$294$		0			0
$295$	−9.20810	−	15.9489i	−0.536116	−	0.928580i
$296$	20.8116	+	36.0468i	1.20965	+	2.09517i
$297$			8.03758i			0.466388i
$298$	25.6246	+	44.3831i	1.48439	+	2.57104i
$299$	2.32398	−	6.77315i	0.134399	−	0.391702i
$300$	5.85248			0.337893
$301$		0			0
$302$	−9.75246	+	16.8918i	−0.561191	+	0.972011i
$303$	0.663274			0.0381041
$304$	27.7263	−	16.0078i	1.59021	−	0.918108i
$305$	−4.08363	−	2.35769i	−0.233828	−	0.135001i
$306$			22.1050i			1.26366i
$307$			8.97844i			0.512427i	0.966620	+	0.256213i	$0.0824750\pi$
$307$			8.97844i			0.512427i	−0.966620	+	0.256213i	$0.917525\pi$
$308$		0			0
$309$	−2.97271	+	5.14889i	−0.169112	+	0.292910i
$310$	37.8665	−	21.8622i	2.15067	−	1.24169i
$311$	−6.09080	−	10.5496i	−0.345378	−	0.598212i	0.640045	−	0.768338i	$-0.278916\pi$
$311$	−6.09080	−	10.5496i	−0.345378	−	0.598212i	−0.985422	+	0.170126i	$0.945583\pi$
$312$	−9.85436	+	8.58502i	−0.557893	+	0.486031i
$313$	6.56198	−	11.3657i	0.370905	−	0.642427i	−0.618800	−	0.785549i	$-0.712381\pi$
$313$	6.56198	−	11.3657i	0.370905	−	0.642427i	0.989705	+	0.143122i	$0.0457141\pi$
$314$	−31.3951	−	18.1260i	−1.77173	−	1.02291i
$315$		0			0
$316$	−14.5862	−	25.2641i	−0.820540	−	1.42122i
$317$	−14.4761	−	8.35775i	−0.813056	−	0.469418i	0.0349599	−	0.999389i	$-0.488870\pi$
$317$	−14.4761	−	8.35775i	−0.813056	−	0.469418i	−0.848016	+	0.529971i	$0.822203\pi$
$318$	−8.44485	−	4.87563i	−0.473564	−	0.273412i
$319$	12.5859	+	7.26648i	0.704675	+	0.406845i
$320$	6.53932	+	3.77548i	0.365559	+	0.211056i
$321$	−1.33123	−	2.30575i	−0.0743018	−	0.128695i
$322$		0			0
$323$	−9.96849	−	5.75531i	−0.554661	−	0.320234i
$324$	15.6374	−	27.0847i	0.868743	−	1.50471i
$325$	−2.80988	+	8.18930i	−0.155864	+	0.454261i
$326$	9.28007	+	16.0736i	0.513976	+	0.890232i
$327$	0.775804	−	0.447911i	0.0429021	−	0.0247695i
$328$	−26.9223	+	46.6307i	−1.48653	+	2.57475i
$329$		0			0
$330$		−	5.85228i		−	0.322157i
$331$			3.96665i			0.218027i	0.994040	+	0.109013i	$0.0347691\pi$
$331$			3.96665i			0.218027i	−0.994040	+	0.109013i	$0.965231\pi$
$332$	−10.9785	−	6.33843i	−0.602523	−	0.347867i
$333$	−14.0816	+	8.13002i	−0.771668	+	0.445523i
$334$	46.5445			2.54680
$335$	10.9473	−	18.9613i	0.598116	−	1.03597i
$336$		0			0
$337$	−13.7032			−0.746461			−0.373230	−	0.927739i	$-0.621750\pi$
$337$	−13.7032			−0.746461			−0.373230	+	0.927739i	$0.621750\pi$
$338$	−12.6738	−	31.1740i	−0.689362	−	1.69564i
$339$	−2.22710	−	3.85746i	−0.120960	−	0.209508i
$340$		−	23.6935i		−	1.28496i
$341$	14.1713	+	24.5455i	0.767420	+	1.32921i
$342$	13.0141	+	22.5410i	0.703720	+	1.21888i
$343$		0			0
$344$	20.3197	−	11.7316i	1.09557	−	0.632526i
$345$			1.65992i			0.0893671i
$346$	28.7209	−	16.5820i	1.54405	−	0.891456i
$347$	13.1989	−	22.8612i	0.708556	−	1.22725i	−0.256837	−	0.966455i	$-0.582680\pi$
$347$	13.1989	−	22.8612i	0.708556	−	1.22725i	0.965393	−	0.260800i	$-0.0839863\pi$
$348$	6.54727	+	11.3402i	0.350971	+	0.607899i
$349$	4.23507	+	2.44512i	0.226698	+	0.130884i	0.609048	−	0.793133i	$-0.291552\pi$
$349$	4.23507	+	2.44512i	0.226698	+	0.130884i	−0.382350	+	0.924018i	$0.624885\pi$
$350$		0			0
$351$	−7.03753	−	8.07806i	−0.375636	−	0.431175i
$352$	−11.5345	+	19.9784i	−0.614792	+	1.06485i
$353$			13.5577i			0.721605i	0.932642	+	0.360802i	$0.117497\pi$
$353$			13.5577i			0.721605i	−0.932642	+	0.360802i	$0.882503\pi$
$354$	15.3322			0.814899
$355$	−2.17806			−0.115599
$356$			8.27291i			0.438464i
$357$		0			0
$358$	4.12540	−	2.38180i	0.218034	−	0.125882i
$359$	−7.43541	−	4.29284i	−0.392426	−	0.226567i	0.290785	−	0.956789i	$-0.406084\pi$
$359$	−7.43541	−	4.29284i	−0.392426	−	0.226567i	−0.683211	+	0.730221i	$0.739417\pi$
$360$	−15.3910	+	26.6581i	−0.811179	+	1.40500i
$361$	5.44653			0.286659
$362$	−7.39632	+	4.27026i	−0.388742	+	0.224440i
$363$	−1.90962			−0.100229
$364$		0			0
$365$	14.6751			0.768130
$366$	3.39979	−	1.96287i	0.177710	−	0.102601i
$367$	1.66322			0.0868196			0.0434098	−	0.999057i	$-0.486178\pi$
$367$	1.66322			0.0868196			0.0434098	+	0.999057i	$0.486178\pi$
$368$	8.63560	−	14.9573i	0.450162	−	0.779703i
$369$	−18.2162	−	10.5171i	−0.948299	−	0.547501i
$370$	21.5152	−	12.4218i	1.11852	−	0.645778i
$371$		0			0
$372$			25.5374i			1.32405i
$373$	13.9635			0.723002			0.361501	−	0.932372i	$-0.382264\pi$
$373$	13.9635			0.723002			0.361501	+	0.932372i	$0.382264\pi$
$374$	21.8927			1.13204
$375$		−	6.18595i		−	0.319441i
$376$	−3.68828	+	6.38828i	−0.190208	+	0.329450i
$377$	−19.0117	+	3.71687i	−0.979150	+	0.191429i
$378$		0			0
$379$	−27.3454	−	15.7879i	−1.40464	−	0.810969i	−0.409775	−	0.912187i	$-0.634393\pi$
$379$	−27.3454	−	15.7879i	−1.40464	−	0.810969i	−0.994864	+	0.101218i	$0.967726\pi$
$380$	−13.9493	−	24.1608i	−0.715582	−	1.23943i
$381$	0.809874	−	1.40274i	0.0414911	−	0.0718647i
$382$	−10.9761	+	6.33707i	−0.561588	+	0.324233i
$383$		−	31.9082i		−	1.63043i	−0.579156	−	0.815217i	$-0.696618\pi$
$383$		−	31.9082i		−	1.63043i	0.579156	−	0.815217i	$-0.303382\pi$
$384$	2.21435	−	1.27846i	0.113001	−	0.0652410i
$385$		0			0
$386$	−3.90762	−	6.76820i	−0.198893	−	0.344492i
$387$	4.58294	+	7.93788i	0.232964	+	0.403505i
$388$		−	72.7788i		−	3.69478i
$389$	−12.7075	−	22.0100i	−0.644296	−	1.11595i	−0.984464	−	0.175589i	$-0.943817\pi$
$389$	−12.7075	−	22.0100i	−0.644296	−	1.11595i	0.340168	−	0.940365i	$-0.389516\pi$
$390$	5.12413	+	5.88175i	0.259470	+	0.297834i
$391$	−6.20956			−0.314031
$392$		0			0
$393$	−2.64656	+	4.58398i	−0.133501	+	0.231231i
$394$	−12.0368			−0.606403
$395$	−8.66376	+	5.00203i	−0.435921	+	0.251679i
$396$	−30.0760	−	17.3644i	−1.51138	−	0.872593i
$397$		−	4.15897i		−	0.208733i	−0.994539	−	0.104366i	$-0.966719\pi$
$397$		−	4.15897i		−	0.208733i	0.994539	−	0.104366i	$-0.0332815\pi$
$398$		−	1.06319i		−	0.0532930i
$399$		0			0
$400$	−10.4412	+	18.0846i	−0.522058	+	0.904231i
$401$	−16.9753	+	9.80067i	−0.847704	+	0.489422i	−0.859875	−	0.510504i	$-0.829459\pi$
$401$	−16.9753	+	9.80067i	−0.847704	+	0.489422i	0.0121716	+	0.999926i	$0.496126\pi$
$402$	9.11409	+	15.7861i	0.454569	+	0.787337i
$403$	−35.7342	−	12.2610i	−1.78005	−	0.610762i
$404$	−3.00691	+	5.20811i	−0.149599	+	0.259113i
$405$	−9.28811	−	5.36249i	−0.461530	−	0.266464i
$406$		0			0
$407$	8.05193	+	13.9463i	0.399119	+	0.691295i
$408$	9.81500	+	5.66669i	0.485915	+	0.280543i
$409$	15.2712	+	8.81685i	0.755114	+	0.435965i	0.827539	−	0.561409i	$-0.189740\pi$
$409$	15.2712	+	8.81685i	0.755114	+	0.435965i	−0.0724249	+	0.997374i	$0.523074\pi$
$410$	27.8324	+	16.0690i	1.37454	+	0.793594i
$411$	−4.48673	−	2.59041i	−0.221314	−	0.127776i
$412$	−26.9532	−	46.6842i	−1.32789	−	2.29997i
$413$		0			0
$414$	12.1601	+	7.02061i	0.597634	+	0.345044i
$415$	−2.17363	+	3.76483i	−0.106699	+	0.184808i
$416$	−5.90001	−	30.1783i	−0.289272	−	1.47962i
$417$	0.431416	+	0.747234i	0.0211265	+	0.0365922i
$418$	22.3245	−	12.8890i	1.09193	−	0.630424i
$419$	14.9455	−	25.8864i	0.730137	−	1.26463i	−0.226688	−	0.973968i	$-0.572790\pi$
$419$	14.9455	−	25.8864i	0.730137	−	1.26463i	0.956824	−	0.290666i	$-0.0938770\pi$
$420$		0			0
$421$			12.8528i			0.626407i	0.949686	+	0.313203i	$0.101402\pi$
$421$			12.8528i			0.626407i	−0.949686	+	0.313203i	$0.898598\pi$
$422$			19.4559i			0.947100i
$423$	−2.49557	−	1.44082i	−0.121339	−	0.0700551i
$424$	43.9919	−	25.3987i	2.13644	−	1.23347i
$425$	7.50787			0.364185
$426$	0.906662	−	1.57038i	0.0439279	−	0.0760854i
$427$		0			0
$428$	24.1401			1.16685
$429$	−3.81261	+	3.32151i	−0.184075	+	0.160364i
$430$	−7.00223	−	12.1282i	−0.337677	−	0.584874i
$431$			8.97060i			0.432098i	0.976382	+	0.216049i	$0.0693172\pi$
$431$			8.97060i			0.432098i	−0.976382	+	0.216049i	$0.930683\pi$
$432$	−12.9202	−	22.3785i	−0.621625	−	1.07669i
$433$	1.72531	+	2.98833i	0.0829132	+	0.143610i	0.904500	−	0.426473i	$-0.140244\pi$
$433$	1.72531	+	2.98833i	0.0829132	+	0.143610i	−0.821587	+	0.570083i	$0.806911\pi$
$434$		0			0
$435$	3.88887	−	2.24524i	0.186457	−	0.107651i
$436$			8.12228i			0.388987i
$437$	−6.33204	+	3.65580i	−0.302902	+	0.174881i
$438$	−6.10881	+	10.5808i	−0.291890	+	0.505569i
$439$	19.2572	+	33.3544i	0.919096	+	1.59192i	0.800792	+	0.598943i	$0.204412\pi$
$439$	19.2572	+	33.3544i	0.919096	+	1.59192i	0.118304	+	0.992977i	$0.462254\pi$
$440$	26.4020	+	15.2432i	1.25867	+	0.726691i
$441$		0			0
$442$	−22.0029	+	19.1687i	−1.04657	+	0.911764i
$443$	7.51997	−	13.0250i	0.357284	−	0.618835i	−0.630222	−	0.776415i	$-0.717036\pi$
$443$	7.51997	−	13.0250i	0.357284	−	0.618835i	0.987506	+	0.157580i	$0.0503693\pi$
$444$			14.5100i			0.688612i
$445$	2.83701			0.134487
$446$	−58.4492			−2.76765
$447$			10.2646i			0.485499i
$448$		0			0
$449$	33.7087	−	19.4617i	1.59081	−	0.918456i	0.597646	−	0.801760i	$-0.296103\pi$
$449$	33.7087	−	19.4617i	1.59081	−	0.918456i	0.993168	−	0.116696i	$-0.0372304\pi$
$450$	−14.7025	−	8.48850i	−0.693083	−	0.400152i
$451$	−10.4161	+	18.0412i	−0.490476	+	0.849529i
$452$	40.3856			1.89958
$453$	−3.38322	+	1.95330i	−0.158957	+	0.0917741i
$454$	35.3906			1.66097
$455$		0			0
$456$	13.3448			0.624927
$457$	−12.0721	+	6.96982i	−0.564708	+	0.326034i	−0.755033	−	0.655687i	$-0.772379\pi$
$457$	−12.0721	+	6.96982i	−0.564708	+	0.326034i	0.190325	+	0.981721i	$0.439046\pi$
$458$	−20.5298			−0.959295
$459$	−4.64524	+	8.04580i	−0.216821	+	0.375546i
$460$	−13.0339	−	7.52512i	−0.607709	−	0.350861i
$461$	−32.4443	+	18.7317i	−1.51108	+	0.872424i	−0.511167	+	0.859481i	$0.670787\pi$
$461$	−32.4443	+	18.7317i	−1.51108	+	0.872424i	−0.999916	+	0.0129430i	$0.995880\pi$
$462$		0			0
$463$		−	6.75275i		−	0.313827i	−0.987612	−	0.156913i	$-0.949846\pi$
$463$		−	6.75275i		−	0.313827i	0.987612	−	0.156913i	$-0.0501544\pi$
$464$	−46.7228			−2.16905
$465$	8.75749			0.406119
$466$		−	17.0115i		−	0.788044i
$467$	−2.52516	+	4.37371i	−0.116851	+	0.202391i	−0.918518	−	0.395379i	$-0.870613\pi$
$467$	−2.52516	+	4.37371i	−0.116851	+	0.202391i	0.801667	+	0.597770i	$0.203947\pi$
$468$	45.4314	−	8.88205i	2.10006	−	0.410573i
$469$		0			0
$470$	3.81296	+	2.20141i	0.175879	+	0.101544i
$471$	−3.63042	−	6.28807i	−0.167281	−	0.289739i
$472$	−39.9353	+	69.1699i	−1.83817	+	3.18380i
$473$	7.86163	−	4.53892i	0.361478	−	0.208700i
$474$		−	8.32878i		−	0.382554i
$475$	7.65595	−	4.42017i	0.351279	−	0.202811i
$476$		0			0
$477$	9.92198	+	17.1854i	0.454296	+	0.786864i
$478$	−12.1572	−	21.0568i	−0.556055	−	0.963116i
$479$		−	9.45319i		−	0.431927i	−0.976401	−	0.215964i	$-0.930711\pi$
$479$		−	9.45319i		−	0.431927i	0.976401	−	0.215964i	$-0.0692892\pi$
$480$	3.56401	+	6.17304i	0.162674	+	0.281759i
$481$	−20.3036	−	6.96649i	−0.925764	−	0.317645i
$482$	26.1082			1.18920
$483$		0			0
$484$	8.65711	−	14.9946i	0.393505	−	0.681571i
$485$	−24.9579			−1.13328
$486$	27.7167	−	16.0023i	1.25726	−	0.725877i
$487$	34.6407	+	19.9998i	1.56972	+	0.906277i	0.996201	+	0.0870831i	$0.0277546\pi$
$487$	34.6407	+	19.9998i	1.56972	+	0.906277i	0.573517	+	0.819194i	$0.305579\pi$
$488$			20.4504i			0.925748i
$489$			3.71737i			0.168105i
$490$		0			0
$491$	−3.38049	+	5.85517i	−0.152559	+	0.264240i	−0.932168	−	0.362027i	$-0.882085\pi$
$491$	−3.38049	+	5.85517i	−0.152559	+	0.264240i	0.779608	+	0.626267i	$0.215418\pi$
$492$	−16.2556	+	9.38518i	−0.732859	+	0.423116i
$493$	8.39918	+	14.5478i	0.378280	+	0.655200i
$494$	−11.1515	+	32.5008i	−0.501732	+	1.46228i
$495$	−5.95473	+	10.3139i	−0.267645	+	0.463575i
$496$	−78.9125	−	45.5602i	−3.54328	−	2.04571i
$497$		0			0
$498$	−1.80963	−	3.13438i	−0.0810916	−	0.140455i
$499$	9.83591	+	5.67877i	0.440316	+	0.254217i	0.703732	−	0.710466i	$-0.251516\pi$
$499$	9.83591	+	5.67877i	0.440316	+	0.254217i	−0.263416	+	0.964682i	$0.584849\pi$
$500$	48.5729	+	28.0436i	2.17225	+	1.25415i
$501$	8.07335	+	4.66115i	0.360691	+	0.208245i
$502$	−23.1993	−	13.3941i	−1.03543	−	0.597808i
$503$	−6.96423	−	12.0624i	−0.310520	−	0.537836i	0.667955	−	0.744202i	$-0.267170\pi$
$503$	−6.96423	−	12.0624i	−0.310520	−	0.537836i	−0.978475	+	0.206365i	$0.933836\pi$
$504$		0			0
$505$	1.78601	+	1.03115i	0.0794763	+	0.0458857i
$506$	6.95317	−	12.0432i	0.309106	−	0.535388i
$507$	0.923570	−	6.67648i	0.0410172	−	0.296513i
$508$	7.34301	+	12.7185i	0.325793	+	0.564290i
$509$	−17.1602	+	9.90746i	−0.760614	+	0.439141i	−0.829516	−	0.558483i	$-0.811384\pi$
$509$	−17.1602	+	9.90746i	−0.760614	+	0.439141i	0.0689022	+	0.997623i	$0.478050\pi$
$510$	3.38227	−	5.85826i	0.149769	−	0.259408i
$511$		0			0
$512$			47.4335i			2.09628i
$513$			10.9393i			0.482983i
$514$	17.9043	+	10.3370i	0.789724	+	0.455947i
$515$	−16.0093	+	9.24299i	−0.705455	+	0.407295i
$516$	8.17934			0.360076
$517$	−1.42698	+	2.47160i	−0.0627585	+	0.108701i
$518$		0			0
$519$	6.64237			0.291568
$520$	−39.8816	+	7.79704i	−1.74892	+	0.341923i
$521$	−15.5476	−	26.9292i	−0.681151	−	1.17979i	−0.974630	−	0.223823i	$-0.928146\pi$
$521$	−15.5476	−	26.9292i	−0.681151	−	1.17979i	0.293479	−	0.955966i	$-0.405187\pi$
$522$		−	37.9849i		−	1.66255i
$523$	11.3601	+	19.6763i	0.496742	+	0.860383i	0.999993	−	0.00375758i	$-0.00119608\pi$
$523$	11.3601	+	19.6763i	0.496742	+	0.860383i	−0.503251	+	0.864140i	$0.667863\pi$
$524$	−23.9960	−	41.5622i	−1.04827	−	1.81565i
$525$		0			0
$526$	−11.3420	+	6.54831i	−0.494535	+	0.285520i
$527$			32.7607i			1.42708i
$528$	−10.5620	+	6.09798i	−0.459652	+	0.265380i
$529$	9.52783	−	16.5027i	0.414253	−	0.717508i
$530$	−15.1597	−	26.2574i	−0.658495	−	1.14055i
$531$	−27.0211	−	15.6007i	−1.17262	−	0.677011i
$532$		0			0
$533$	−5.32794	−	27.2522i	−0.230779	−	1.18043i
$534$	−1.18097	+	2.04549i	−0.0511054	+	0.0885171i
$535$		−	8.27830i		−	0.357902i
$536$	−94.9564			−4.10149
$537$	0.954091			0.0411721
$538$			35.9563i			1.55018i
$539$		0			0
$540$	−19.5008	+	11.2588i	−0.839180	+	0.484501i
$541$	−1.81754	−	1.04936i	−0.0781423	−	0.0451155i	0.460420	−	0.887701i	$-0.347699\pi$
$541$	−1.81754	−	1.04936i	−0.0781423	−	0.0451155i	−0.538562	+	0.842586i	$0.681032\pi$
$542$	−10.7779	+	18.6679i	−0.462951	+	0.801855i
$543$	−1.71057			−0.0734074
$544$	−23.0926	+	13.3325i	−0.990087	+	0.571627i
$545$	2.78536			0.119312
$546$		0			0
$547$	25.3770			1.08504			0.542521	−	0.840042i	$-0.317470\pi$
$547$	25.3770			1.08504			0.542521	+	0.840042i	$0.317470\pi$
$548$	40.6805	−	23.4869i	1.73778	−	1.00331i
$549$	−7.98894			−0.340959
$550$	−8.40696	+	14.5613i	−0.358474	+	0.620895i
$551$	17.1297	+	9.88983i	0.729749	+	0.421321i
$552$	6.23454	−	3.59951i	0.265360	−	0.153205i
$553$		0			0
$554$		−	60.0855i		−	2.55279i
$555$	4.97587			0.211214
$556$	−7.82316			−0.331776
$557$		−	44.2503i		−	1.87495i	−0.348058	−	0.937473i	$-0.613159\pi$
$557$		−	44.2503i		−	1.87495i	0.348058	−	0.937473i	$-0.386841\pi$
$558$	37.0397	−	64.1547i	1.56802	−	2.71588i
$559$	−3.92705	+	11.4452i	−0.166097	+	0.484082i
$560$		0			0
$561$	3.79738	+	2.19242i	0.160326	+	0.0925641i
$562$	−35.1526	−	60.8860i	−1.48282	−	2.56832i
$563$	19.4453	−	33.6803i	0.819523	−	1.41946i	−0.0865108	−	0.996251i	$-0.527572\pi$
$563$	19.4453	−	33.6803i	0.819523	−	1.41946i	0.906034	−	0.423205i	$-0.139095\pi$
$564$	−2.22697	+	1.28574i	−0.0937725	+	0.0541396i
$565$		−	13.8494i		−	0.582647i
$566$	36.2078	−	20.9046i	1.52193	−	0.878685i
$567$		0			0
$568$	4.72309	+	8.18063i	0.198177	+	0.343252i
$569$	23.0789	+	39.9739i	0.967520	+	1.67579i	0.702687	+	0.711499i	$0.251983\pi$
$569$	23.0789	+	39.9739i	0.967520	+	1.67579i	0.264832	+	0.964294i	$0.414683\pi$
$570$		−	7.96508i		−	0.333620i
$571$	10.5684	+	18.3050i	0.442274	+	0.766041i	0.997858	−	0.0654194i	$-0.0208385\pi$
$571$	10.5684	+	18.3050i	0.442274	+	0.766041i	−0.555584	+	0.831461i	$0.687505\pi$
$572$	−8.79673	−	44.9949i	−0.367810	−	1.88133i
$573$	−2.53848			−0.106047
$574$		0			0
$575$	2.38452	−	4.13011i	0.0994413	−	0.172237i
$576$	12.7931			0.533045
$577$	21.9368	−	12.6652i	0.913239	−	0.527259i	0.0317671	−	0.999495i	$-0.489887\pi$
$577$	21.9368	−	12.6652i	0.913239	−	0.527259i	0.881472	+	0.472237i	$0.156553\pi$
$578$	−16.1955	−	9.35045i	−0.673642	−	0.388927i
$579$		−	1.56530i		−	0.0650517i
$580$			40.7146i			1.69058i
$581$		0			0
$582$	10.3892	−	17.9947i	0.430647	−	0.745903i
$583$	17.0203	−	9.82667i	0.704908	−	0.406979i
$584$	−31.8227	−	55.1186i	−1.31683	−	2.28082i
$585$	−3.04590	−	15.5797i	−0.125933	−	0.644140i
$586$	−18.9553	+	32.8315i	−0.783036	+	1.35626i
$587$	−3.08554	−	1.78144i	−0.127354	−	0.0735278i	0.434970	−	0.900445i	$-0.356759\pi$
$587$	−3.08554	−	1.78144i	−0.127354	−	0.0735278i	−0.562324	+	0.826917i	$0.690092\pi$
$588$		0			0
$589$	19.2875	+	33.4069i	0.794727	+	1.37651i
$590$	41.2853	+	23.8361i	1.69969	+	0.981316i
$591$	−2.08783	−	1.20541i	−0.0858819	−	0.0495839i
$592$	−44.8369	−	25.8866i	−1.84278	−	1.06393i
$593$	21.9568	+	12.6768i	0.901659	+	0.520573i	0.877738	−	0.479141i	$-0.159052\pi$
$593$	21.9568	+	12.6768i	0.901659	+	0.520573i	0.0239212	+	0.999714i	$0.492385\pi$
$594$	−10.4030	−	18.0186i	−0.426842	−	0.739312i
$595$		0			0
$596$	−80.5990	−	46.5338i	−3.30146	−	1.90610i
$597$	0.106472	−	0.184415i	0.00435762	−	0.00754762i
$598$	3.55661	+	18.1919i	0.145441	+	0.743924i
$599$	−5.46078	−	9.45835i	−0.223122	−	0.386458i	0.732633	−	0.680624i	$-0.238291\pi$
$599$	−5.46078	−	9.45835i	−0.223122	−	0.386458i	−0.955754	+	0.294166i	$0.904958\pi$
$600$	−7.53807	+	4.35211i	−0.307740	+	0.177674i
$601$	12.1282	−	21.0067i	0.494720	−	0.856880i	−0.505262	−	0.862966i	$-0.668604\pi$
$601$	12.1282	−	21.0067i	0.494720	−	0.856880i	0.999981	+	0.00608649i	$0.00193740\pi$
$602$		0			0
$603$		−	37.0946i		−	1.51061i
$604$		−	35.4206i		−	1.44124i
$605$	−5.14205	−	2.96876i	−0.209054	−	0.120697i
$606$	−1.48692	+	0.858476i	−0.0604022	+	0.0348732i
$607$	9.85447			0.399981			0.199990	−	0.979798i	$-0.435909\pi$
$607$	9.85447			0.399981			0.199990	+	0.979798i	$0.435909\pi$
$608$	−15.6987	+	27.1910i	−0.636667	+	1.10274i
$609$		0			0
$610$	12.2062			0.494215
$611$	−0.729914	−	3.73348i	−0.0295291	−	0.151040i
$612$	−20.0712	−	34.7643i	−0.811328	−	1.40526i
$613$		−	3.67688i		−	0.148508i	−0.997239	−	0.0742540i	$-0.976342\pi$
$613$		−	3.67688i		−	0.148508i	0.997239	−	0.0742540i	$-0.0236575\pi$
$614$	−11.6208	−	20.1278i	−0.468977	−	0.812293i
$615$	3.21844	+	5.57450i	0.129780	+	0.224785i
$616$		0			0
$617$	16.2352	−	9.37341i	0.653605	−	0.377359i	−0.136231	−	0.990677i	$-0.543499\pi$
$617$	16.2352	−	9.37341i	0.653605	−	0.377359i	0.789836	+	0.613318i	$0.210166\pi$
$618$		−	15.3903i		−	0.619090i
$619$	13.7650	−	7.94725i	0.553264	−	0.319427i	−0.197174	−	0.980369i	$-0.563176\pi$
$619$	13.7650	−	7.94725i	0.553264	−	0.319427i	0.750437	+	0.660942i	$0.229843\pi$
$620$	−39.7014	+	68.7649i	−1.59445	+	2.76167i
$621$	2.95068	+	5.11073i	0.118407	+	0.205087i
$622$	27.3086	+	15.7667i	1.09498	+	0.632185i
$623$		0			0
$624$	5.27594	−	15.3765i	0.211207	−	0.615555i
$625$	3.61371	−	6.25913i	0.144549	−	0.250365i
$626$			33.9727i			1.35782i
$627$	5.16304			0.206192
$628$	65.8330			2.62702
$629$			18.6141i			0.742194i
$630$		0			0
$631$	−17.0998	+	9.87255i	−0.680731	+	0.393020i	−0.800130	−	0.599826i	$-0.795236\pi$
$631$	−17.0998	+	9.87255i	−0.680731	+	0.393020i	0.119400	+	0.992846i	$0.461903\pi$
$632$	37.5745	+	21.6936i	1.49463	+	0.862927i
$633$	−1.94839	+	3.37472i	−0.0774417	+	0.134133i
$634$	43.2698			1.71846
$635$	4.36151	−	2.51812i	0.173081	−	0.0999286i
$636$	17.7081			0.702173
$637$		0			0
$638$	−37.6200			−1.48939
$639$	−3.19575	+	1.84507i	−0.126422	+	0.0729898i
$640$	7.95016			0.314258
$641$	−14.8893	+	25.7890i	−0.588092	+	1.01860i	0.406390	+	0.913699i	$0.366787\pi$
$641$	−14.8893	+	25.7890i	−0.588092	+	1.01860i	−0.994482	+	0.104905i	$0.966546\pi$
$642$	5.96867	+	3.44601i	0.235565	+	0.136003i
$643$	−10.0220	+	5.78623i	−0.395231	+	0.228187i	−0.684424	−	0.729084i	$-0.739946\pi$
$643$	−10.0220	+	5.78623i	−0.395231	+	0.228187i	0.289193	+	0.957271i	$0.406613\pi$
$644$		0			0
$645$		−	2.80493i		−	0.110444i
$646$	29.7964			1.17232
$647$	25.5065			1.00276			0.501382	−	0.865226i	$-0.332825\pi$
$647$	25.5065			1.00276			0.501382	+	0.865226i	$0.332825\pi$
$648$			46.5140i			1.82724i
$649$	−15.4508	+	26.7616i	−0.606497	+	1.05048i
$650$	−4.30024	−	21.9956i	−0.168669	−	0.862737i
$651$		0			0
$652$	−29.1893	−	16.8524i	−1.14314	−	0.659993i
$653$	22.4146	+	38.8233i	0.877152	+	1.51927i	0.854452	+	0.519530i	$0.173893\pi$
$653$	22.4146	+	38.8233i	0.877152	+	1.51927i	0.0227004	+	0.999742i	$0.492774\pi$
$654$	−1.15946	+	2.00825i	−0.0453386	+	0.0785287i
$655$	−14.2529	+	8.22889i	−0.556905	+	0.321529i
$656$		−	66.9747i		−	2.61492i
$657$	21.5320	−	12.4315i	0.840043	−	0.484999i
$658$		0			0
$659$	−20.5867	−	35.6572i	−0.801944	−	1.38901i	−0.918335	−	0.395805i	$-0.870466\pi$
$659$	−20.5867	−	35.6572i	−0.801944	−	1.38901i	0.116390	−	0.993204i	$-0.462868\pi$
$660$	5.31382	+	9.20380i	0.206840	+	0.358258i
$661$			21.8938i			0.851569i	0.904825	+	0.425785i	$0.140002\pi$
$661$			21.8938i			0.851569i	−0.904825	+	0.425785i	$0.859998\pi$
$662$	−5.13404	−	8.89241i	−0.199540	−	0.345613i
$663$	−5.73614	+	1.12144i	−0.222773	+	0.0435533i
$664$	18.8539			0.731673
$665$		0			0
$666$	21.0454	−	36.4517i	0.815492	−	1.41247i
$667$	10.6704			0.413160
$668$	−73.1999	+	42.2620i	−2.83219	+	1.63516i
$669$	−10.1383	−	5.85334i	−0.391968	−	0.226303i
$670$			56.6764i			2.18960i
$671$			7.91219i			0.305447i
$672$		0			0
$673$	17.8344	−	30.8901i	0.687466	−	1.19073i	−0.285189	−	0.958471i	$-0.592056\pi$
$673$	17.8344	−	30.8901i	0.687466	−	1.19073i	0.972655	−	0.232254i	$-0.0746102\pi$
$674$	30.7197	−	17.7361i	1.18328	−	0.683167i
$675$	−3.56762	−	6.17930i	−0.137318	−	0.237841i
$676$	48.2376	+	37.5193i	1.85529	+	1.44305i
$677$	1.27766	−	2.21297i	0.0491044	−	0.0850514i	−0.840428	−	0.541923i	$-0.817697\pi$
$677$	1.27766	−	2.21297i	0.0491044	−	0.0850514i	0.889533	+	0.456871i	$0.151030\pi$
$678$	9.98541	+	5.76508i	0.383488	+	0.221407i
$679$		0			0
$680$	17.6193	+	30.5175i	0.675670	+	1.17029i
$681$	6.13867	+	3.54416i	0.235234	+	0.135813i
$682$	−63.5384	−	36.6839i	−2.43301	−	1.40470i
$683$	−30.9517	−	17.8700i	−1.18433	−	0.683775i	−0.227320	−	0.973820i	$-0.572996\pi$
$683$	−30.9517	−	17.8700i	−1.18433	−	0.683775i	−0.957013	+	0.290045i	$0.906330\pi$
$684$	−40.9341	−	23.6333i	−1.56515	−	0.903642i
$685$	−8.05431	−	13.9505i	−0.307739	−	0.533020i
$686$		0			0
$687$	−3.56099	−	2.05594i	−0.135860	−	0.0784390i
$688$	−14.5924	+	25.2748i	−0.556330	+	0.963592i
$689$	−8.50199	+	24.7788i	−0.323900	+	0.943995i
$690$	−2.14843	−	3.72120i	−0.0817895	−	0.141664i
$691$	−22.5419	+	13.0146i	−0.857536	+	0.495099i	−0.863186	−	0.504885i	$-0.831535\pi$
$691$	−22.5419	+	13.0146i	−0.857536	+	0.495099i	0.00565028	+	0.999984i	$0.498201\pi$
$692$	−30.1127	+	52.1567i	−1.14471	+	1.98270i
$693$		0			0
$694$			68.3335i			2.59391i
$695$			2.68278i			0.101764i
$696$	−16.8659	−	9.73755i	−0.639301	−	0.369101i
$697$	−20.8535	+	12.0398i	−0.789884	+	0.456040i
$698$	−12.6589			−0.479146
$699$	1.70360	−	2.95073i	0.0644362	−	0.111607i
$700$		0			0
$701$	−1.12731			−0.0425779			−0.0212890	−	0.999773i	$-0.506777\pi$
$701$	−1.12731			−0.0425779			−0.0212890	+	0.999773i	$0.506777\pi$
$702$	26.2321	+	9.00067i	0.990068	+	0.339709i
$703$	10.9588	+	18.9813i	0.413321	+	0.715892i
$704$		−	12.6702i		−	0.477525i
$705$	0.440917	+	0.763691i	0.0166059	+	0.0287623i
$706$	−17.5478	−	30.3936i	−0.660419	−	1.14388i
$707$		0			0
$708$	−24.1128	+	13.9215i	−0.906215	+	0.523203i
$709$			6.05031i			0.227224i	0.993525	+	0.113612i	$0.0362421\pi$
$709$			6.05031i			0.227224i	−0.993525	+	0.113612i	$0.963758\pi$
$710$	4.88276	−	2.81906i	0.183247	−	0.105798i
$711$	−8.47459	+	14.6784i	−0.317822	+	0.550484i
$712$	−6.15202	−	10.6556i	−0.230557	−	0.399336i
$713$	18.0218	+	10.4049i	0.674922	+	0.389666i
$714$		0			0
$715$	−15.4300	+	3.01664i	−0.577050	+	0.112816i
$716$	−4.32530	+	7.49164i	−0.161644	+	0.279976i
$717$		−	4.86986i		−	0.181868i
$718$	22.2249			0.829425
$719$	47.1177			1.75719			0.878597	−	0.477563i	$-0.158480\pi$
$719$	47.1177			1.75719			0.878597	+	0.477563i	$0.158480\pi$
$720$		−	38.2884i		−	1.42692i
$721$		0			0
$722$	−12.2100	+	7.04944i	−0.454409	+	0.262353i
$723$	4.52859	+	2.61458i	0.168420	+	0.0972374i
$724$	7.75473	−	13.4316i	0.288202	−	0.499181i
$725$	−12.9014			−0.479146
$726$	4.28097	−	2.47162i	0.158882	−	0.0917303i
$727$	−17.9215			−0.664671			−0.332335	−	0.943161i	$-0.607837\pi$
$727$	−17.9215			−0.664671			−0.332335	+	0.943161i	$0.607837\pi$
$728$		0			0
$729$	−13.5489			−0.501810
$730$	−32.8985	+	18.9940i	−1.21763	+	0.702999i
$731$	10.4929			0.388093
$732$	−3.56454	+	6.17396i	−0.131749	+	0.228196i
$733$	−39.2037	−	22.6343i	−1.44802	−	0.836016i	−0.449658	−	0.893201i	$-0.648454\pi$
$733$	−39.2037	−	22.6343i	−1.44802	−	0.836016i	−0.998364	+	0.0571848i	$0.981788\pi$
$734$	−3.72861	+	2.15271i	−0.137625	+	0.0794581i
$735$		0			0
$736$			16.9378i			0.624335i
$737$	−36.7382			−1.35327
$738$	54.4494			2.00431
$739$			19.2613i			0.708539i	0.935143	+	0.354270i	$0.115270\pi$
$739$			19.2613i			0.708539i	−0.935143	+	0.354270i	$0.884730\pi$
$740$	−22.5577	+	39.0712i	−0.829239	+	1.43628i
$741$	−5.18905	+	4.52065i	−0.190624	+	0.166070i
$742$		0			0
$743$	30.2115	+	17.4426i	1.10835	+	0.639908i	0.938402	−	0.345545i	$-0.112306\pi$
$743$	30.2115	+	17.4426i	1.10835	+	0.639908i	0.169951	+	0.985453i	$0.445639\pi$
$744$	−18.9905	−	32.8925i	−0.696225	−	1.20590i
$745$	−15.9577	+	27.6396i	−0.584647	+	1.01264i
$746$	−31.3032	+	18.0729i	−1.14609	+	0.661697i
$747$			7.36525i			0.269480i
$748$	−34.4303	+	19.8784i	−1.25890	+	0.726825i
$749$		0			0
$750$	8.00648	+	13.8676i	0.292355	+	0.506374i
$751$	−12.4834	−	21.6219i	−0.455526	−	0.788993i	0.543193	−	0.839608i	$-0.317215\pi$
$751$	−12.4834	−	21.6219i	−0.455526	−	0.788993i	−0.998718	+	0.0506146i	$0.983882\pi$
$752$		−	9.17535i		−	0.334591i
$753$	−2.68268	−	4.64654i	−0.0977623	−	0.169329i
$754$	37.8095	−	32.9393i	1.37694	−	1.19958i
$755$	−12.1467			−0.442064
$756$		0			0
$757$	5.30243	−	9.18408i	0.192720	−	0.333801i	−0.753431	−	0.657527i	$-0.771602\pi$
$757$	5.30243	−	9.18408i	0.192720	−	0.333801i	0.946151	+	0.323726i	$0.104936\pi$
$758$	81.7370			2.96882
$759$	2.41212	−	1.39264i	0.0875543	−	0.0505495i
$760$	35.9337	+	20.7463i	1.30345	+	0.752548i
$761$			32.6388i			1.18316i	0.806248	+	0.591578i	$0.201495\pi$
$761$			32.6388i			1.18316i	−0.806248	+	0.591578i	$0.798505\pi$
$762$			4.19288i			0.151892i
$763$		0			0
$764$	11.5080	−	19.9325i	0.416345	−	0.721131i
$765$	−11.9216	+	6.88296i	−0.431028	+	0.248854i
$766$	41.2988	+	71.5316i	1.49219	+	2.58454i
$767$	−7.90323	−	40.4247i	−0.285369	−	1.45965i
$768$	−5.73794	+	9.93841i	−0.207050	+	0.358621i
$769$	45.1851	+	26.0876i	1.62942	+	0.940744i	0.984267	+	0.176686i	$0.0565378\pi$
$769$	45.1851	+	26.0876i	1.62942	+	0.940744i	0.645148	+	0.764057i	$0.276796\pi$
$770$		0			0
$771$	2.07039	+	3.58601i	0.0745631	+	0.129147i
$772$	12.2909	+	7.09618i	0.442360	+	0.255397i
$773$	30.9221	+	17.8529i	1.11219	+	0.642123i	0.939396	−	0.342835i	$-0.111387\pi$
$773$	30.9221	+	17.8529i	1.11219	+	0.642123i	0.172794	+	0.984958i	$0.444721\pi$
$774$	−20.5480	−	11.8634i	−0.738583	−	0.426421i
$775$	−21.7898	−	12.5804i	−0.782714	−	0.451900i
$776$	54.1208	+	93.7400i	1.94282	+	3.36507i
$777$		0			0
$778$	56.9752	+	32.8947i	2.04266	+	1.17933i
$779$	−14.1766	+	24.5545i	−0.507928	+	0.879757i
$780$	−13.3992	−	4.59749i	−0.479769	−	0.164617i
$781$	1.82735	+	3.16506i	0.0653876	+	0.113255i
$782$	13.9206	−	8.03703i	0.497798	−	0.287404i
$783$	7.98231	−	13.8258i	0.285265	−	0.494093i
$784$		0			0
$785$		−	22.5760i		−	0.805770i
$786$		−	13.7018i		−	0.488726i
$787$	−5.28813	−	3.05310i	−0.188501	−	0.108831i	0.402779	−	0.915297i	$-0.368044\pi$
$787$	−5.28813	−	3.05310i	−0.188501	−	0.108831i	−0.591281	+	0.806466i	$0.701378\pi$
$788$	18.9301	−	10.9293i	0.674356	−	0.389339i
$789$	−2.62310			−0.0933847
$790$	12.9482	−	22.4270i	0.460678	−	0.797918i
$791$		0			0
$792$	51.6510			1.83534
$793$	−6.92774	−	7.95204i	−0.246011	−	0.282385i
$794$	5.38296	+	9.32356i	0.191034	+	0.330881i
$795$		−	6.07261i		−	0.215373i
$796$	0.965369	+	1.67207i	0.0342166	+	0.0592649i
$797$	23.1149	+	40.0363i	0.818773	+	1.41816i	0.906586	+	0.422020i	$0.138679\pi$
$797$	23.1149	+	40.0363i	0.818773	+	1.41816i	−0.0878129	+	0.996137i	$0.527988\pi$
$798$		0			0
$799$	−2.85688	+	1.64942i	−0.101069	+	0.0583522i
$800$		−	20.4792i		−	0.724048i
$801$	4.16260	−	2.40328i	0.147078	−	0.0849157i
$802$	25.3700	−	43.9422i	0.895847	−	1.55165i
$803$	−12.3121	−	21.3252i	−0.434484	−	0.752549i
$804$	−28.6672	−	16.5510i	−1.01101	−	0.583710i
$805$		0			0
$806$	95.9780	−	18.7642i	3.38068	−	0.660939i
$807$	−3.60080	+	6.23678i	−0.126754	+	0.219545i
$808$		−	8.94415i		−	0.314654i
$809$	39.2879			1.38129			0.690644	−	0.723195i	$-0.257327\pi$
$809$	39.2879			1.38129			0.690644	+	0.723195i	$0.257327\pi$
$810$	27.7627			0.975482
$811$		−	6.90664i		−	0.242525i	−0.992620	−	0.121262i	$-0.961306\pi$
$811$		−	6.90664i		−	0.242525i	0.992620	−	0.121262i	$-0.0386943\pi$
$812$		0			0
$813$	−3.73896	+	2.15869i	−0.131131	+	0.0757085i
$814$	−36.1015	−	20.8432i	−1.26536	−	0.730555i
$815$	−5.77917	+	10.0098i	−0.202436	+	0.350629i
$816$	−14.0971			−0.493496
$817$	10.6998	−	6.17756i	0.374340	−	0.216125i
$818$	−45.6466			−1.59600
$819$		0			0
$820$	−58.3622			−2.03810
$821$	−1.65453	+	0.955244i	−0.0577435	+	0.0333382i	−0.528594	−	0.848875i	$-0.677281\pi$
$821$	−1.65453	+	0.955244i	−0.0577435	+	0.0333382i	0.470850	+	0.882213i	$0.343947\pi$
$822$	13.4111			0.467765
$823$	0.789844	−	1.36805i	0.0275322	−	0.0476872i	−0.851931	−	0.523654i	$-0.824568\pi$
$823$	0.789844	−	1.36805i	0.0275322	−	0.0476872i	0.879463	+	0.475967i	$0.157902\pi$
$824$	69.4320	+	40.0866i	2.41878	+	1.39648i
$825$	−2.91645	+	1.68381i	−0.101538	+	0.0586228i
$826$		0			0
$827$			32.5050i			1.13031i	0.824985	+	0.565155i	$0.191184\pi$
$827$			32.5050i			1.13031i	−0.824985	+	0.565155i	$0.808816\pi$
$828$	−25.4986			−0.886138
$829$	−35.0538			−1.21747			−0.608735	−	0.793373i	$-0.708323\pi$
$829$	−35.0538			−1.21747			−0.608735	+	0.793373i	$0.708323\pi$
$830$		−	11.2533i		−	0.390608i
$831$	6.01721	−	10.4221i	0.208735	−	0.361539i
$832$	11.0937	+	12.7340i	0.384606	+	0.441472i
$833$		0			0
$834$	−1.93429	−	1.11676i	−0.0669790	−	0.0386703i
$835$	14.4928	+	25.1023i	0.501544	+	0.868700i
$836$	−23.4063	+	40.5409i	−0.809523	+	1.40214i
$837$	26.9635	−	15.5674i	0.931994	−	0.538087i
$838$			77.3760i			2.67291i
$839$	−4.63746	+	2.67744i	−0.160103	+	0.0924354i	−0.577911	−	0.816100i	$-0.696132\pi$
$839$	−4.63746	+	2.67744i	−0.160103	+	0.0924354i	0.417808	+	0.908535i	$0.362798\pi$
$840$		0			0
$841$	0.0669890	+	0.116028i	0.00230997	+	0.00400098i
$842$	−16.6354	−	28.8133i	−0.573293	−	0.992973i
$843$		−	14.0813i		−	0.484985i
$844$	−17.6658	−	30.5981i	−0.608082	−	1.05323i
$845$	12.8664	−	16.5420i	0.442618	−	0.569063i
$846$	7.45942			0.256460
$847$		0			0
$848$	−31.5923	+	54.7195i	−1.08488	+	1.87907i
$849$	8.37387			0.287391
$850$	−16.8311	+	9.71744i	−0.577302	+	0.333305i
$851$	10.2397	+	5.91190i	0.351013	+	0.202657i
$852$			3.29297i			0.112815i
$853$		−	49.6270i		−	1.69920i	−0.527431	−	0.849598i	$-0.676845\pi$
$853$		−	49.6270i		−	1.69920i	0.527431	−	0.849598i	$-0.323155\pi$
$854$		0			0
$855$	−8.10452	+	14.0374i	−0.277169	+	0.480070i
$856$	−31.0927	+	17.9514i	−1.06273	+	0.613566i
$857$	−2.94196	−	5.09563i	−0.100496	−	0.174063i	0.811393	−	0.584500i	$-0.198709\pi$
$857$	−2.94196	−	5.09563i	−0.100496	−	0.174063i	−0.911889	+	0.410437i	$0.865376\pi$
$858$	4.24806	−	12.3808i	0.145026	−	0.422674i
$859$	21.6931	−	37.5735i	0.740159	−	1.28199i	−0.212264	−	0.977212i	$-0.568084\pi$
$859$	21.6931	−	37.5735i	0.740159	−	1.28199i	0.952423	−	0.304780i	$-0.0985830\pi$
$860$	22.0246	+	12.7159i	0.751033	+	0.433609i
$861$		0			0
$862$	−11.6106	−	20.1102i	−0.395460	−	0.684957i
$863$	−26.9570	−	15.5636i	−0.917626	−	0.529792i	−0.0347490	−	0.999396i	$-0.511063\pi$
$863$	−26.9570	−	15.5636i	−0.917626	−	0.529792i	−0.882877	+	0.469604i	$0.844397\pi$
$864$	21.9465	+	12.6708i	0.746634	+	0.431069i
$865$	17.8860	+	10.3265i	0.608142	+	0.351111i
$866$	−7.73558	−	4.46614i	−0.262866	−	0.151766i
$867$	−1.87278	−	3.24376i	−0.0636031	−	0.110164i
$868$		0			0
$869$	14.5374	+	8.39318i	0.493148	+	0.284719i
$870$	−5.81203	+	10.0667i	−0.197046	+	0.341294i
$871$	36.9233	−	32.1672i	1.25110	−	1.08994i
$872$	−6.04001	−	10.4616i	−0.204540	−	0.354274i
$873$	−36.6194	+	21.1422i	−1.23938	+	0.715556i
$874$	9.46341	−	16.3911i	0.320105	−	0.554438i
$875$		0			0
$876$		−	22.1870i		−	0.749629i
$877$		−	29.9106i		−	1.01001i	−0.863117	−	0.505004i	$-0.831491\pi$
$877$		−	29.9106i		−	1.01001i	0.863117	−	0.505004i	$-0.168509\pi$
$878$	−86.3413	−	49.8492i	−2.91388	−	1.68233i
$879$	−6.57576	+	3.79652i	−0.221795	+	0.128053i
$880$	−37.9206			−1.27830
$881$	−7.28477	+	12.6176i	−0.245430	+	0.425097i	−0.962252	−	0.272159i	$-0.912262\pi$
$881$	−7.28477	+	12.6176i	−0.245430	+	0.425097i	0.716822	+	0.697256i	$0.245596\pi$
$882$		0			0
$883$	48.9296			1.64661			0.823307	−	0.567597i	$-0.192127\pi$
$883$	48.9296			1.64661			0.823307	+	0.567597i	$0.192127\pi$
$884$	17.1987	−	50.1249i	0.578454	−	1.68588i
$885$	4.77408	+	8.26896i	0.160479	+	0.277958i
$886$			38.9324i			1.30796i
$887$	27.2951	+	47.2765i	0.916480	+	1.58739i	0.804719	+	0.593655i	$0.202316\pi$
$887$	27.2951	+	47.2765i	0.916480	+	1.58739i	0.111761	+	0.993735i	$0.464351\pi$
$888$	−10.7901	−	18.6890i	−0.362092	−	0.627162i
$889$		0			0
$890$	−6.36000	+	3.67195i	−0.213188	+	0.123084i
$891$			17.9961i			0.602891i
$892$	91.9222	−	53.0713i	3.07778	−	1.77696i
$893$	−1.94215	+	3.36390i	−0.0649916	+	0.112569i
$894$	−13.2855	−	23.0111i	−0.444333	−	0.769607i
$895$	2.56909	+	1.48327i	0.0858753	+	0.0495801i
$896$		0			0
$897$	−1.20490	+	3.51165i	−0.0402306	+	0.117251i
$898$	−50.3787	+	87.2584i	−1.68116	+	2.91185i
$899$		−	56.2955i		−	1.87756i
$900$	30.8299			1.02766
$901$	22.7169			0.756810
$902$		−	53.9263i		−	1.79555i
$903$		0			0
$904$	−52.0172	+	30.0321i	−1.73007	+	0.998854i
$905$	−4.60606	−	2.65931i	−0.153111	−	0.0883985i
$906$	5.05632	−	8.75780i	0.167985	−	0.290958i
$907$	−22.7255			−0.754589			−0.377295	−	0.926093i	$-0.623146\pi$
$907$	−22.7255			−0.754589			−0.377295	+	0.926093i	$0.623146\pi$
$908$	−55.6584	+	32.1344i	−1.84709	+	1.06642i
$909$	3.49402			0.115889
$910$		0			0
$911$	−42.2359			−1.39934			−0.699669	−	0.714467i	$-0.746669\pi$
$911$	−42.2359			−1.39934			−0.699669	+	0.714467i	$0.746669\pi$
$912$	−14.3751	+	8.29948i	−0.476008	+	0.274823i
$913$	7.29450			0.241413
$914$	18.0421	−	31.2498i	0.596779	−	1.03365i
$915$	2.11722	+	1.22238i	0.0699933	+	0.0404106i
$916$	32.2870	−	18.6409i	1.06679	−	0.615912i
$917$		0			0
$918$		−	24.0494i		−	0.793747i
$919$	30.6940			1.01250			0.506251	−	0.862386i	$-0.331031\pi$
$919$	30.6940			1.01250			0.506251	+	0.862386i	$0.331031\pi$
$920$	22.3838			0.737971
$921$		−	4.65502i		−	0.153388i
$922$	48.4890	−	83.9854i	1.59690	−	2.76591i
$923$	−4.60780	−	1.58101i	−0.151668	−	0.0520396i
$924$		0			0
$925$	−12.3806	−	7.14797i	−0.407073	−	0.235024i
$926$	8.74009	+	15.1383i	0.287217	+	0.497474i
$927$	−15.6598	+	27.1235i	−0.514334	+	0.890853i
$928$	39.6819	−	22.9104i	1.30262	−	0.752070i
$929$		−	37.4250i		−	1.22787i	−0.789355	−	0.613936i	$-0.789585\pi$
$929$		−	37.4250i		−	1.22787i	0.789355	−	0.613936i	$-0.210415\pi$
$930$	−19.6325	+	11.3348i	−0.643775	+	0.371684i
$931$		0			0
$932$	15.4463	+	26.7538i	0.505961	+	0.876350i
$933$	3.15787	+	5.46960i	0.103384	+	0.179067i
$934$		−	13.0733i		−	0.427770i
$935$	6.81684	+	11.8071i	0.222935	+	0.386134i
$936$	−51.9111	+	45.2245i	−1.69677	+	1.47821i
$937$	−44.3386			−1.44848			−0.724239	−	0.689549i	$-0.757809\pi$
$937$	−44.3386			−1.44848			−0.724239	+	0.689549i	$0.757809\pi$
$938$		0			0
$939$	−3.40216	+	5.89272i	−0.111025	+	0.192302i
$940$	−7.99546			−0.260783
$941$	−23.8202	+	13.7526i	−0.776518	+	0.448323i	−0.835195	−	0.549954i	$-0.814645\pi$
$941$	−23.8202	+	13.7526i	−0.776518	+	0.448323i	0.0586770	+	0.998277i	$0.481312\pi$
$942$	16.2773	+	9.39771i	0.530343	+	0.306194i
$943$			15.2955i			0.498089i
$944$		−	99.3472i		−	3.23348i
$945$		0			0
$946$	−11.7494	+	20.3506i	−0.382007	+	0.661656i
$947$	4.40226	−	2.54165i	0.143054	−	0.0825925i	−0.426765	−	0.904363i	$-0.640347\pi$
$947$	4.40226	−	2.54165i	0.143054	−	0.0825925i	0.569819	+	0.821770i	$0.307013\pi$
$948$	7.56246	+	13.0986i	0.245617	+	0.425422i
$949$	31.0459	+	10.6524i	1.00779	+	0.345790i
$950$	−11.4420	+	19.8182i	−0.371229	+	0.642987i
$951$	7.50534	+	4.33321i	0.243377	+	0.140514i
$952$		0			0
$953$	4.90718	+	8.49949i	0.158959	+	0.275326i	0.934494	−	0.355980i	$-0.115853\pi$
$953$	4.90718	+	8.49949i	0.158959	+	0.275326i	−0.775534	+	0.631305i	$0.782519\pi$
$954$	−44.4861	−	25.6840i	−1.44029	−	0.831552i
$955$	−6.83540	−	3.94642i	−0.221188	−	0.127703i
$956$	38.2388	+	22.0772i	1.23673	+	0.714027i
$957$	−6.52536	−	3.76742i	−0.210935	−	0.121783i
$958$	12.2353	+	21.1921i	0.395303	+	0.684685i
$959$		0			0
$960$	−3.39041	−	1.95746i	−0.109425	−	0.0631766i
$961$	39.3947	−	68.2336i	1.27080	−	2.20108i
$962$	54.5332	−	10.6615i	1.75822	−	0.343741i
$963$	−7.01268	−	12.1463i	−0.225981	−	0.391410i
$964$	−41.0601	+	23.7060i	−1.32246	+	0.763520i
$965$	2.43348	−	4.21490i	0.0783364	−	0.135683i
$966$		0			0
$967$			2.69619i			0.0867036i	0.999060	+	0.0433518i	$0.0138036\pi$
$967$			2.69619i			0.0867036i	−0.999060	+	0.0433518i	$0.986196\pi$
$968$			25.7509i			0.827665i
$969$	5.16832	+	2.98393i	0.166030	+	0.0958577i
$970$	55.9504	−	32.3030i	1.79646	−	1.03719i
$971$	−24.9240			−0.799850			−0.399925	−	0.916548i	$-0.630964\pi$
$971$	−24.9240			−0.799850			−0.399925	+	0.916548i	$0.630964\pi$
$972$	−29.0598	+	50.3331i	−0.932094	+	1.61443i
$973$		0			0
$974$	−103.543			−3.31773
$975$	1.45683	−	4.24587i	0.0466558	−	0.135977i
$976$	−12.7187	−	22.0294i	−0.407115	−	0.705144i
$977$			28.3129i			0.905811i	0.891558	+	0.452906i	$0.149613\pi$
$977$			28.3129i			0.905811i	−0.891558	+	0.452906i	$0.850387\pi$
$978$	−4.81140	−	8.33359i	−0.153852	−	0.266479i
$979$	−2.38019	−	4.12262i	−0.0760713	−	0.131759i
$980$		0			0
$981$	4.08681	−	2.35952i	0.130482	−	0.0753337i
$982$		−	17.5015i		−	0.558494i
$983$	−32.7805	+	18.9258i	−1.04554	+	0.603641i	−0.921396	−	0.388624i	$-0.872951\pi$
$983$	−32.7805	+	18.9258i	−1.04554	+	0.603641i	−0.124140	+	0.992265i	$0.539617\pi$
$984$	13.9583	−	24.1764i	0.444974	−	0.770717i
$985$	−3.74795	−	6.49165i	−0.119420	−	0.206841i
$986$	−37.6585	−	21.7421i	−1.19929	−	0.692410i
$987$		0			0
$988$	−11.9725	−	61.2391i	−0.380897	−	1.94827i
$989$	3.33257	−	5.77218i	0.105970	−	0.183545i
$990$		−	30.8289i		−	0.979805i
$991$	58.4158			1.85564			0.927820	−	0.373028i	$-0.121681\pi$
$991$	58.4158			1.85564			0.927820	+	0.373028i	$0.121681\pi$
$992$	89.3612			2.83722
$993$		−	2.05657i		−	0.0652633i
$994$		0			0
$995$	0.573399	−	0.331052i	0.0181780	−	0.0104950i
$996$	5.69197	+	3.28626i	0.180357	+	0.104129i
$997$	14.0294	−	24.2997i	0.444316	−	0.769578i	−0.553688	−	0.832724i	$-0.686780\pi$
$997$	14.0294	−	24.2997i	0.444316	−	0.769578i	0.998004	+	0.0631462i	$0.0201134\pi$
$998$	−29.4001			−0.930645
$999$	15.3202	−	8.84514i	0.484711	−	0.279848i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.u.g.30.1		12
7.2	even	3		637.2.q.i.589.6		12
7.3	odd	6		91.2.k.b.4.1	✓	12
7.4	even	3		637.2.k.i.459.1		12
7.5	odd	6		637.2.q.g.589.6		12
7.6	odd	2		91.2.u.b.30.1	yes	12
13.10	even	6		637.2.k.i.569.6		12
21.17	even	6		819.2.bm.f.550.6		12
21.20	even	2		819.2.do.e.667.6		12
91.6	even	12		1183.2.e.j.170.12		24
91.10	odd	6		91.2.u.b.88.1	yes	12
91.19	even	12		8281.2.a.cp.1.1		12
91.20	even	12		1183.2.e.j.170.1		24
91.23	even	6		637.2.q.i.491.6		12
91.33	even	12		8281.2.a.cp.1.12		12
91.45	even	12		1183.2.e.j.508.12		24
91.58	odd	12		8281.2.a.co.1.1		12
91.59	even	12		1183.2.e.j.508.1		24
91.62	odd	6		91.2.k.b.23.6	yes	12
91.72	odd	12		8281.2.a.co.1.12		12
91.75	odd	6		637.2.q.g.491.6		12
91.88	even	6	inner	637.2.u.g.361.1		12
273.62	even	6		819.2.bm.f.478.1		12
273.101	even	6		819.2.do.e.361.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.1	✓	12	7.3	odd	6
91.2.k.b.23.6	yes	12	91.62	odd	6
91.2.u.b.30.1	yes	12	7.6	odd	2
91.2.u.b.88.1	yes	12	91.10	odd	6
637.2.k.i.459.1		12	7.4	even	3
637.2.k.i.569.6		12	13.10	even	6
637.2.q.g.491.6		12	91.75	odd	6
637.2.q.g.589.6		12	7.5	odd	6
637.2.q.i.491.6		12	91.23	even	6
637.2.q.i.589.6		12	7.2	even	3
637.2.u.g.30.1		12	1.1	even	1	trivial
637.2.u.g.361.1		12	91.88	even	6	inner
819.2.bm.f.478.1		12	273.62	even	6
819.2.bm.f.550.6		12	21.17	even	6
819.2.do.e.361.6		12	273.101	even	6
819.2.do.e.667.6		12	21.20	even	2
1183.2.e.j.170.1		24	91.20	even	12
1183.2.e.j.170.12		24	91.6	even	12
1183.2.e.j.508.1		24	91.59	even	12
1183.2.e.j.508.12		24	91.45	even	12
8281.2.a.co.1.1		12	91.58	odd	12
8281.2.a.co.1.12		12	91.72	odd	12
8281.2.a.cp.1.1		12	91.19	even	12
8281.2.a.cp.1.12		12	91.33	even	12

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.24179 + 1.29430i) q^{2} -0.518466 q^{3} +(2.35043 - 4.07106i) q^{4} +(-1.39608 - 0.806027i) q^{5} +(1.16229 - 0.671051i) q^{6} +6.99143i q^{8} -2.73119 q^{9} +O(q^{10})\)	\(q+(-2.24179 + 1.29430i) q^{2} -0.518466 q^{3} +(2.35043 - 4.07106i) q^{4} +(-1.39608 - 0.806027i) q^{5} +(1.16229 - 0.671051i) q^{6} +6.99143i q^{8} -2.73119 q^{9} +4.17296 q^{10} +2.70496i q^{11} +(-1.21862 + 2.11070i) q^{12} +(-2.36840 - 2.71858i) q^{13} +(0.723819 + 0.417897i) q^{15} +(-4.34816 - 7.53123i) q^{16} +(-1.56330 + 2.70772i) q^{17} +(6.12277 - 3.53498i) q^{18} +3.68150i q^{19} +(-6.56276 + 3.78901i) q^{20} +(-3.50103 - 6.06396i) q^{22} +(0.993019 + 1.71996i) q^{23} -3.62482i q^{24} +(-1.20064 - 2.07957i) q^{25} +(8.82813 + 3.02907i) q^{26} +2.97143 q^{27} +(2.68636 - 4.65290i) q^{29} -2.16354 q^{30} +(9.07425 - 5.23902i) q^{31} +(7.38583 + 4.26421i) q^{32} -1.40243i q^{33} -8.09354i q^{34} +(-6.41947 + 11.1188i) q^{36} +(5.15585 - 2.97673i) q^{37} +(-4.76497 - 8.25317i) q^{38} +(1.22794 + 1.40949i) q^{39} +(5.63528 - 9.76059i) q^{40} +(6.66970 + 3.85075i) q^{41} +(-1.67800 - 2.90638i) q^{43} +(11.0120 + 6.35780i) q^{44} +(3.81296 + 2.20141i) q^{45} +(-4.45229 - 2.57053i) q^{46} +(0.913730 + 0.527542i) q^{47} +(2.25437 + 3.90469i) q^{48} +(5.38318 + 3.10798i) q^{50} +(0.810520 - 1.40386i) q^{51} +(-16.6343 + 3.25208i) q^{52} +(-3.63284 - 6.29226i) q^{53} +(-6.66133 + 3.84592i) q^{54} +(2.18027 - 3.77633i) q^{55} -1.90873i q^{57} +13.9078i q^{58} +(9.89352 + 5.71203i) q^{59} +(3.40257 - 1.96447i) q^{60} +2.92507 q^{61} +(-13.5617 + 23.4896i) q^{62} -4.68406 q^{64} +(1.11523 + 5.70435i) q^{65} +(1.81516 + 3.14395i) q^{66} +13.5818i q^{67} +(7.34886 + 12.7286i) q^{68} +(-0.514846 - 0.891740i) q^{69} +(1.17009 - 0.675554i) q^{71} -19.0949i q^{72} +(-7.88374 + 4.55168i) q^{73} +(-7.70557 + 13.3464i) q^{74} +(0.622492 + 1.07819i) q^{75} +(14.9876 + 8.65311i) q^{76} +(-4.57708 - 1.57047i) q^{78} +(3.10289 - 5.37436i) q^{79} +14.0189i q^{80} +6.65300 q^{81} -19.9361 q^{82} -2.69672i q^{83} +(4.36499 - 2.52013i) q^{85} +(7.52346 + 4.34367i) q^{86} +(-1.39278 + 2.41237i) q^{87} -18.9115 q^{88} +(-1.52410 + 0.879938i) q^{89} -11.3972 q^{90} +9.33607 q^{92} +(-4.70469 + 2.71625i) q^{93} -2.73119 q^{94} +(2.96739 - 5.13967i) q^{95} +(-3.82930 - 2.21085i) q^{96} +(13.4078 - 7.74102i) q^{97} -7.38776i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} + 4 q^{4} - 3 q^{5} + 9 q^{6} + 2 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 + 4 * q^4 - 3 * q^5 + 9 * q^6 + 2 * q^9	\( 12 q - 6 q^{3} + 4 q^{4} - 3 q^{5} + 9 q^{6} + 2 q^{9} + 24 q^{10} + q^{12} + 2 q^{13} - 12 q^{15} - 8 q^{16} - 17 q^{17} - 3 q^{18} + 3 q^{20} - 15 q^{22} + 3 q^{23} - 5 q^{25} + 9 q^{26} - 12 q^{27} - q^{29} - 22 q^{30} + 18 q^{31} + 18 q^{32} - 13 q^{36} + 15 q^{37} - 19 q^{38} - q^{39} + q^{40} + 6 q^{41} + 11 q^{43} + 33 q^{44} + 9 q^{45} - 30 q^{46} - 15 q^{47} - 19 q^{48} + 18 q^{50} + 4 q^{51} - 47 q^{52} - 8 q^{53} - 6 q^{54} + 15 q^{55} - 27 q^{59} + 30 q^{60} + 10 q^{61} - 41 q^{62} + 2 q^{64} - 3 q^{65} + 34 q^{66} + 11 q^{68} - 7 q^{69} + 30 q^{71} + 42 q^{73} - 33 q^{74} - q^{75} + 45 q^{76} + 44 q^{78} - 35 q^{79} - 28 q^{81} + 10 q^{82} - 21 q^{85} + 57 q^{86} - 10 q^{87} + 28 q^{88} - 48 q^{89} - 66 q^{92} - 81 q^{93} + 2 q^{94} + 2 q^{95} + 21 q^{96} + 3 q^{97}+O(q^{100}) \) 12 * q - 6 * q^3 + 4 * q^4 - 3 * q^5 + 9 * q^6 + 2 * q^9 + 24 * q^10 + q^12 + 2 * q^13 - 12 * q^15 - 8 * q^16 - 17 * q^17 - 3 * q^18 + 3 * q^20 - 15 * q^22 + 3 * q^23 - 5 * q^25 + 9 * q^26 - 12 * q^27 - q^29 - 22 * q^30 + 18 * q^31 + 18 * q^32 - 13 * q^36 + 15 * q^37 - 19 * q^38 - q^39 + q^40 + 6 * q^41 + 11 * q^43 + 33 * q^44 + 9 * q^45 - 30 * q^46 - 15 * q^47 - 19 * q^48 + 18 * q^50 + 4 * q^51 - 47 * q^52 - 8 * q^53 - 6 * q^54 + 15 * q^55 - 27 * q^59 + 30 * q^60 + 10 * q^61 - 41 * q^62 + 2 * q^64 - 3 * q^65 + 34 * q^66 + 11 * q^68 - 7 * q^69 + 30 * q^71 + 42 * q^73 - 33 * q^74 - q^75 + 45 * q^76 + 44 * q^78 - 35 * q^79 - 28 * q^81 + 10 * q^82 - 21 * q^85 + 57 * q^86 - 10 * q^87 + 28 * q^88 - 48 * q^89 - 66 * q^92 - 81 * q^93 + 2 * q^94 + 2 * q^95 + 21 * q^96 + 3 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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