LMFDB - Embedded newform 1122.2.l.g.727.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1122,2,Mod(463,1122)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1122, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

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

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

chi := DirichletCharacter("1122.463");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1122 = 2 \cdot 3 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1122.l (of order $4$, degree $2$, 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:	$8.95921510679$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 44 x^{18} + 732 x^{16} + 6050 x^{14} + 27262 x^{12} + 69598 x^{10} + 100205 x^{8} + 77682 x^{6} + \cdots + 289 $ x^20 + 44x^18 + 732x^16 + 6050x^14 + 27262x^12 + 69598x^10 + 100205x^8 + 77682x^6 + 29931x^4 + 5170*x^2 + 289
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			727.3
Root			$-4.20168i$ of defining polynomial
Character	$\chi$	$=$	1122.727
Dual form			1122.2.l.g.463.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(0.653251 + 0.653251i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-2.55471 + 2.55471i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(0.653251 + 0.653251i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-2.55471 + 2.55471i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(-0.653251 + 0.653251i) q^{10} +(0.707107 - 0.707107i) q^{11} +(0.707107 + 0.707107i) q^{12} -4.55296 q^{13} +(-2.55471 - 2.55471i) q^{14} -0.923837i q^{15} +1.00000 q^{16} +(1.52654 + 3.83010i) q^{17} -1.00000 q^{18} +0.110930i q^{19} +(-0.653251 - 0.653251i) q^{20} +3.61290 q^{21} +(0.707107 + 0.707107i) q^{22} +(5.38067 - 5.38067i) q^{23} +(-0.707107 + 0.707107i) q^{24} -4.14653i q^{25} -4.55296i q^{26} +(0.707107 - 0.707107i) q^{27} +(2.55471 - 2.55471i) q^{28} +(-6.02136 - 6.02136i) q^{29} +0.923837 q^{30} +(-2.65161 - 2.65161i) q^{31} +1.00000i q^{32} -1.00000 q^{33} +(-3.83010 + 1.52654i) q^{34} -3.33773 q^{35} -1.00000i q^{36} +(-1.69343 - 1.69343i) q^{37} -0.110930 q^{38} +(3.21943 + 3.21943i) q^{39} +(0.653251 - 0.653251i) q^{40} +(-7.16587 + 7.16587i) q^{41} +3.61290i q^{42} -1.35561i q^{43} +(-0.707107 + 0.707107i) q^{44} +(-0.653251 + 0.653251i) q^{45} +(5.38067 + 5.38067i) q^{46} -9.38416 q^{47} +(-0.707107 - 0.707107i) q^{48} -6.05308i q^{49} +4.14653 q^{50} +(1.62887 - 3.78772i) q^{51} +4.55296 q^{52} +1.89084i q^{53} +(0.707107 + 0.707107i) q^{54} +0.923837 q^{55} +(2.55471 + 2.55471i) q^{56} +(0.0784396 - 0.0784396i) q^{57} +(6.02136 - 6.02136i) q^{58} -9.89347i q^{59} +0.923837i q^{60} +(0.729162 - 0.729162i) q^{61} +(2.65161 - 2.65161i) q^{62} +(-2.55471 - 2.55471i) q^{63} -1.00000 q^{64} +(-2.97423 - 2.97423i) q^{65} -1.00000i q^{66} +3.30301 q^{67} +(-1.52654 - 3.83010i) q^{68} -7.60941 q^{69} -3.33773i q^{70} +(-1.30825 - 1.30825i) q^{71} +1.00000 q^{72} +(-5.34428 - 5.34428i) q^{73} +(1.69343 - 1.69343i) q^{74} +(-2.93204 + 2.93204i) q^{75} -0.110930i q^{76} +3.61290i q^{77} +(-3.21943 + 3.21943i) q^{78} +(1.51771 - 1.51771i) q^{79} +(0.653251 + 0.653251i) q^{80} -1.00000 q^{81} +(-7.16587 - 7.16587i) q^{82} -7.29713i q^{83} -3.61290 q^{84} +(-1.50481 + 3.49923i) q^{85} +1.35561 q^{86} +8.51549i q^{87} +(-0.707107 - 0.707107i) q^{88} -15.6166 q^{89} +(-0.653251 - 0.653251i) q^{90} +(11.6315 - 11.6315i) q^{91} +(-5.38067 + 5.38067i) q^{92} +3.74995i q^{93} -9.38416i q^{94} +(-0.0724654 + 0.0724654i) q^{95} +(0.707107 - 0.707107i) q^{96} +(1.28422 + 1.28422i) q^{97} +6.05308 q^{98} +(0.707107 + 0.707107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{4} - 4 q^{5}+O(q^{10}) $ 20 * q - 20 * q^4 - 4 * q^5	$ 20 q - 20 q^{4} - 4 q^{5} + 4 q^{10} + 20 q^{16} - 12 q^{17} - 20 q^{18} + 4 q^{20} + 16 q^{23} + 4 q^{29} - 8 q^{31} - 20 q^{33} + 16 q^{35} - 20 q^{37} + 8 q^{39} - 4 q^{40} + 20 q^{41} + 4 q^{45} + 16 q^{46} - 16 q^{47} - 68 q^{50} + 8 q^{57} - 4 q^{58} - 20 q^{61} + 8 q^{62} - 20 q^{64} + 8 q^{65} - 48 q^{67} + 12 q^{68} - 32 q^{71} + 20 q^{72} + 20 q^{73} + 20 q^{74} - 8 q^{75} - 8 q^{78} - 16 q^{79} - 4 q^{80} - 20 q^{81} + 20 q^{82} - 4 q^{85} - 16 q^{86} + 4 q^{90} + 88 q^{91} - 16 q^{92} - 48 q^{95} + 4 q^{97} + 36 q^{98}+O(q^{100}) $ 20 * q - 20 * q^4 - 4 * q^5 + 4 * q^10 + 20 * q^16 - 12 * q^17 - 20 * q^18 + 4 * q^20 + 16 * q^23 + 4 * q^29 - 8 * q^31 - 20 * q^33 + 16 * q^35 - 20 * q^37 + 8 * q^39 - 4 * q^40 + 20 * q^41 + 4 * q^45 + 16 * q^46 - 16 * q^47 - 68 * q^50 + 8 * q^57 - 4 * q^58 - 20 * q^61 + 8 * q^62 - 20 * q^64 + 8 * q^65 - 48 * q^67 + 12 * q^68 - 32 * q^71 + 20 * q^72 + 20 * q^73 + 20 * q^74 - 8 * q^75 - 8 * q^78 - 16 * q^79 - 4 * q^80 - 20 * q^81 + 20 * q^82 - 4 * q^85 - 16 * q^86 + 4 * q^90 + 88 * q^91 - 16 * q^92 - 48 * q^95 + 4 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1122\mathbb{Z}\right)^\times$.

$n$	$409$	$749$	$1057$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	−1.00000			−0.500000
$5$	0.653251	+	0.653251i	0.292143	+	0.292143i	0.837926	−	0.545783i	$-0.183768\pi$
$5$	0.653251	+	0.653251i	0.292143	+	0.292143i	−0.545783	+	0.837926i	$0.683768\pi$
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$	−2.55471	+	2.55471i	−0.965589	+	0.965589i	−0.999427	−	0.0338381i	$-0.989227\pi$
$7$	−2.55471	+	2.55471i	−0.965589	+	0.965589i	0.0338381	+	0.999427i	$0.489227\pi$
$8$		−	1.00000i		−	0.353553i
$9$			1.00000i			0.333333i
$10$	−0.653251	+	0.653251i	−0.206576	+	0.206576i
$11$	0.707107	−	0.707107i	0.213201	−	0.213201i
$11$	0.707107	−	0.707107i	0.213201	−	0.213201i
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	−4.55296			−1.26276			−0.631382	−	0.775472i	$-0.717512\pi$
$13$	−4.55296			−1.26276			−0.631382	+	0.775472i	$0.717512\pi$
$14$	−2.55471	−	2.55471i	−0.682775	−	0.682775i
$15$		−	0.923837i		−	0.238534i
$16$	1.00000			0.250000
$17$	1.52654	+	3.83010i	0.370240	+	0.928936i
$17$	1.52654	+	3.83010i	0.370240	+	0.928936i
$18$	−1.00000			−0.235702
$19$			0.110930i			0.0254492i	0.999919	+	0.0127246i	$0.00405047\pi$
$19$			0.110930i			0.0254492i	−0.999919	+	0.0127246i	$0.995950\pi$
$20$	−0.653251	−	0.653251i	−0.146071	−	0.146071i
$21$	3.61290			0.788400
$22$	0.707107	+	0.707107i	0.150756	+	0.150756i
$23$	5.38067	−	5.38067i	1.12195	−	1.12195i	0.130498	−	0.991449i	$-0.458342\pi$
$23$	5.38067	−	5.38067i	1.12195	−	1.12195i	0.991449	−	0.130498i	$-0.0416576\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$		−	4.14653i		−	0.829305i
$26$		−	4.55296i		−	0.892909i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	2.55471	−	2.55471i	0.482795	−	0.482795i
$29$	−6.02136	−	6.02136i	−1.11814	−	1.11814i	−0.992014	−	0.126124i	$-0.959746\pi$
$29$	−6.02136	−	6.02136i	−1.11814	−	1.11814i	−0.126124	−	0.992014i	$-0.540254\pi$
$30$	0.923837			0.168669
$31$	−2.65161	−	2.65161i	−0.476244	−	0.476244i	0.427684	−	0.903928i	$-0.359329\pi$
$31$	−2.65161	−	2.65161i	−0.476244	−	0.476244i	−0.903928	+	0.427684i	$0.859329\pi$
$32$			1.00000i			0.176777i
$33$	−1.00000			−0.174078
$34$	−3.83010	+	1.52654i	−0.656857	+	0.261799i
$35$	−3.33773			−0.564180
$36$		−	1.00000i		−	0.166667i
$37$	−1.69343	−	1.69343i	−0.278398	−	0.278398i	0.554071	−	0.832469i	$-0.313074\pi$
$37$	−1.69343	−	1.69343i	−0.278398	−	0.278398i	−0.832469	+	0.554071i	$0.813074\pi$
$38$	−0.110930			−0.0179953
$39$	3.21943	+	3.21943i	0.515521	+	0.515521i
$40$	0.653251	−	0.653251i	0.103288	−	0.103288i
$41$	−7.16587	+	7.16587i	−1.11912	+	1.11912i	−0.127250	+	0.991871i	$0.540615\pi$
$41$	−7.16587	+	7.16587i	−1.11912	+	1.11912i	−0.991871	+	0.127250i	$0.959385\pi$
$42$			3.61290i			0.557483i
$43$		−	1.35561i		−	0.206729i	−0.994644	−	0.103364i	$-0.967039\pi$
$43$		−	1.35561i		−	0.206729i	0.994644	−	0.103364i	$-0.0329608\pi$
$44$	−0.707107	+	0.707107i	−0.106600	+	0.106600i
$45$	−0.653251	+	0.653251i	−0.0973809	+	0.0973809i
$46$	5.38067	+	5.38067i	0.793336	+	0.793336i
$47$	−9.38416			−1.36882			−0.684410	−	0.729097i	$-0.739940\pi$
$47$	−9.38416			−1.36882			−0.684410	+	0.729097i	$0.739940\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$		−	6.05308i		−	0.864725i
$50$	4.14653			0.586407
$51$	1.62887	−	3.78772i	0.228087	−	0.530386i
$52$	4.55296			0.631382
$53$			1.89084i			0.259727i	0.991532	+	0.129863i	$0.0414539\pi$
$53$			1.89084i			0.259727i	−0.991532	+	0.129863i	$0.958546\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	0.923837			0.124570
$56$	2.55471	+	2.55471i	0.341387	+	0.341387i
$57$	0.0784396	−	0.0784396i	0.0103896	−	0.0103896i
$58$	6.02136	−	6.02136i	0.790644	−	0.790644i
$59$		−	9.89347i		−	1.28802i	−0.765017	−	0.644010i	$-0.777269\pi$
$59$		−	9.89347i		−	1.28802i	0.765017	−	0.644010i	$-0.222731\pi$
$60$			0.923837i			0.119267i
$61$	0.729162	−	0.729162i	0.0933596	−	0.0933596i	−0.658885	−	0.752244i	$-0.728971\pi$
$61$	0.729162	−	0.729162i	0.0933596	−	0.0933596i	0.752244	+	0.658885i	$0.228971\pi$
$62$	2.65161	−	2.65161i	0.336755	−	0.336755i
$63$	−2.55471	−	2.55471i	−0.321863	−	0.321863i
$64$	−1.00000			−0.125000
$65$	−2.97423	−	2.97423i	−0.368908	−	0.368908i
$66$		−	1.00000i		−	0.123091i
$67$	3.30301			0.403527			0.201763	−	0.979434i	$-0.435333\pi$
$67$	3.30301			0.403527			0.201763	+	0.979434i	$0.435333\pi$
$68$	−1.52654	−	3.83010i	−0.185120	−	0.464468i
$69$	−7.60941			−0.916065
$70$		−	3.33773i		−	0.398935i
$71$	−1.30825	−	1.30825i	−0.155261	−	0.155261i	0.625202	−	0.780463i	$-0.285016\pi$
$71$	−1.30825	−	1.30825i	−0.155261	−	0.155261i	−0.780463	+	0.625202i	$0.785016\pi$
$72$	1.00000			0.117851
$73$	−5.34428	−	5.34428i	−0.625501	−	0.625501i	0.321432	−	0.946933i	$-0.395836\pi$
$73$	−5.34428	−	5.34428i	−0.625501	−	0.625501i	−0.946933	+	0.321432i	$0.895836\pi$
$74$	1.69343	−	1.69343i	0.196857	−	0.196857i
$75$	−2.93204	+	2.93204i	−0.338562	+	0.338562i
$76$		−	0.110930i		−	0.0127246i
$77$			3.61290i			0.411729i
$78$	−3.21943	+	3.21943i	−0.364529	+	0.364529i
$79$	1.51771	−	1.51771i	0.170756	−	0.170756i	−0.616556	−	0.787311i	$-0.711473\pi$
$79$	1.51771	−	1.51771i	0.170756	−	0.170756i	0.787311	+	0.616556i	$0.211473\pi$
$80$	0.653251	+	0.653251i	0.0730357	+	0.0730357i
$81$	−1.00000			−0.111111
$82$	−7.16587	−	7.16587i	−0.791338	−	0.791338i
$83$		−	7.29713i		−	0.800964i	−0.916305	−	0.400482i	$-0.868843\pi$
$83$		−	7.29713i		−	0.800964i	0.916305	−	0.400482i	$-0.131157\pi$
$84$	−3.61290			−0.394200
$85$	−1.50481	+	3.49923i	−0.163219	+	0.379545i
$86$	1.35561			0.146179
$87$			8.51549i			0.912957i
$88$	−0.707107	−	0.707107i	−0.0753778	−	0.0753778i
$89$	−15.6166			−1.65536			−0.827679	−	0.561202i	$-0.810339\pi$
$89$	−15.6166			−1.65536			−0.827679	+	0.561202i	$0.810339\pi$
$90$	−0.653251	−	0.653251i	−0.0688587	−	0.0688587i
$91$	11.6315	−	11.6315i	1.21931	−	1.21931i
$92$	−5.38067	+	5.38067i	−0.560973	+	0.560973i
$93$			3.74995i			0.388851i
$94$		−	9.38416i		−	0.967902i
$95$	−0.0724654	+	0.0724654i	−0.00743479	+	0.00743479i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$	1.28422	+	1.28422i	0.130393	+	0.130393i	0.769291	−	0.638898i	$-0.220610\pi$
$97$	1.28422	+	1.28422i	0.130393	+	0.130393i	−0.638898	+	0.769291i	$0.720610\pi$
$98$	6.05308			0.611453
$99$	0.707107	+	0.707107i	0.0710669	+	0.0710669i
$100$			4.14653i			0.414653i
$101$	−18.1254			−1.80354			−0.901770	−	0.432216i	$-0.857732\pi$
$101$	−18.1254			−1.80354			−0.901770	+	0.432216i	$0.857732\pi$
$102$	3.78772	+	1.62887i	0.375040	+	0.161282i
$103$	15.5369			1.53090			0.765450	−	0.643495i	$-0.222516\pi$
$103$	15.5369			1.53090			0.765450	+	0.643495i	$0.222516\pi$
$104$			4.55296i			0.446455i
$105$	2.36013	+	2.36013i	0.230325	+	0.230325i
$106$	−1.89084			−0.183655
$107$	2.09773	+	2.09773i	0.202795	+	0.202795i	0.801196	−	0.598401i	$-0.204197\pi$
$107$	2.09773	+	2.09773i	0.202795	+	0.202795i	−0.598401	+	0.801196i	$0.704197\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$	7.39851	−	7.39851i	0.708649	−	0.708649i	−0.257602	−	0.966251i	$-0.582932\pi$
$109$	7.39851	−	7.39851i	0.708649	−	0.708649i	0.966251	+	0.257602i	$0.0829323\pi$
$110$			0.923837i			0.0880844i
$111$			2.39487i			0.227311i
$112$	−2.55471	+	2.55471i	−0.241397	+	0.241397i
$113$	−1.82308	+	1.82308i	−0.171501	+	0.171501i	−0.787638	−	0.616138i	$-0.788696\pi$
$113$	−1.82308	+	1.82308i	−0.171501	+	0.171501i	0.616138	+	0.787638i	$0.288696\pi$
$114$	0.0784396	+	0.0784396i	0.00734654	+	0.00734654i
$115$	7.02985			0.655537
$116$	6.02136	+	6.02136i	0.559069	+	0.559069i
$117$		−	4.55296i		−	0.420922i
$118$	9.89347			0.910768
$119$	−13.6847	−	5.88493i	−1.25447	−	0.539471i
$120$	−0.923837			−0.0843344
$121$		−	1.00000i		−	0.0909091i
$122$	0.729162	+	0.729162i	0.0660152	+	0.0660152i
$123$	10.1341			0.913758
$124$	2.65161	+	2.65161i	0.238122	+	0.238122i
$125$	5.97498	−	5.97498i	0.534418	−	0.534418i
$126$	2.55471	−	2.55471i	0.227592	−	0.227592i
$127$			15.4175i			1.36808i	0.729443	+	0.684041i	$0.239779\pi$
$127$			15.4175i			1.36808i	−0.729443	+	0.684041i	$0.760221\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−0.958561	+	0.958561i	−0.0843966	+	0.0843966i
$130$	2.97423	−	2.97423i	0.260857	−	0.260857i
$131$	8.18548	+	8.18548i	0.715169	+	0.715169i	0.967612	−	0.252443i	$-0.0812340\pi$
$131$	8.18548	+	8.18548i	0.715169	+	0.715169i	−0.252443	+	0.967612i	$0.581234\pi$
$132$	1.00000			0.0870388
$133$	−0.283395	−	0.283395i	−0.0245734	−	0.0245734i
$134$			3.30301i			0.285337i
$135$	0.923837			0.0795112
$136$	3.83010	−	1.52654i	0.328429	−	0.130900i
$137$	7.89615			0.674614			0.337307	−	0.941395i	$-0.390484\pi$
$137$	7.89615			0.674614			0.337307	+	0.941395i	$0.390484\pi$
$138$		−	7.60941i		−	0.647756i
$139$	−7.35344	−	7.35344i	−0.623711	−	0.623711i	0.322767	−	0.946478i	$-0.395387\pi$
$139$	−7.35344	−	7.35344i	−0.623711	−	0.623711i	−0.946478	+	0.322767i	$0.895387\pi$
$140$	3.33773			0.282090
$141$	6.63560	+	6.63560i	0.558819	+	0.558819i
$142$	1.30825	−	1.30825i	0.109786	−	0.109786i
$143$	−3.21943	+	3.21943i	−0.269222	+	0.269222i
$144$			1.00000i			0.0833333i
$145$		−	7.86692i		−	0.653312i
$146$	5.34428	−	5.34428i	0.442296	−	0.442296i
$147$	−4.28017	+	4.28017i	−0.353023	+	0.353023i
$148$	1.69343	+	1.69343i	0.139199	+	0.139199i
$149$	−13.3647			−1.09488			−0.547441	−	0.836844i	$-0.684398\pi$
$149$	−13.3647			−1.09488			−0.547441	+	0.836844i	$0.684398\pi$
$150$	−2.93204	−	2.93204i	−0.239400	−	0.239400i
$151$		−	13.6519i		−	1.11097i	−0.831525	−	0.555487i	$-0.812532\pi$
$151$		−	13.6519i		−	1.11097i	0.831525	−	0.555487i	$-0.187468\pi$
$152$	0.110930			0.00899764
$153$	−3.83010	+	1.52654i	−0.309645	+	0.123413i
$154$	−3.61290			−0.291136
$155$		−	3.46434i		−	0.278262i
$156$	−3.21943	−	3.21943i	−0.257761	−	0.257761i
$157$	4.69564			0.374753			0.187376	−	0.982288i	$-0.440002\pi$
$157$	4.69564			0.374753			0.187376	+	0.982288i	$0.440002\pi$
$158$	1.51771	+	1.51771i	0.120742	+	0.120742i
$159$	1.33703	−	1.33703i	0.106033	−	0.106033i
$160$	−0.653251	+	0.653251i	−0.0516440	+	0.0516440i
$161$			27.4921i			2.16668i
$162$		−	1.00000i		−	0.0785674i
$163$	−6.62628	+	6.62628i	−0.519010	+	0.519010i	−0.917272	−	0.398262i	$-0.869614\pi$
$163$	−6.62628	+	6.62628i	−0.519010	+	0.519010i	0.398262	+	0.917272i	$0.369614\pi$
$164$	7.16587	−	7.16587i	0.559560	−	0.559560i
$165$	−0.653251	−	0.653251i	−0.0508555	−	0.0508555i
$166$	7.29713			0.566367
$167$	7.17103	+	7.17103i	0.554911	+	0.554911i	0.927854	−	0.372943i	$-0.121651\pi$
$167$	7.17103	+	7.17103i	0.554911	+	0.554911i	−0.372943	+	0.927854i	$0.621651\pi$
$168$		−	3.61290i		−	0.278742i
$169$	7.72947			0.594574
$170$	−3.49923	−	1.50481i	−0.268379	−	0.115413i
$171$	−0.110930			−0.00848305
$172$			1.35561i			0.103364i
$173$	4.53335	+	4.53335i	0.344664	+	0.344664i	0.858117	−	0.513453i	$-0.171634\pi$
$173$	4.53335	+	4.53335i	0.344664	+	0.344664i	−0.513453	+	0.858117i	$0.671634\pi$
$174$	−8.51549			−0.645558
$175$	10.5932	+	10.5932i	0.800768	+	0.800768i
$176$	0.707107	−	0.707107i	0.0533002	−	0.0533002i
$177$	−6.99574	+	6.99574i	−0.525832	+	0.525832i
$178$		−	15.6166i		−	1.17052i
$179$			6.38071i			0.476916i	0.971153	+	0.238458i	$0.0766420\pi$
$179$			6.38071i			0.476916i	−0.971153	+	0.238458i	$0.923358\pi$
$180$	0.653251	−	0.653251i	0.0486905	−	0.0486905i
$181$	−12.7190	+	12.7190i	−0.945396	+	0.945396i	−0.998584	−	0.0531889i	$-0.983061\pi$
$181$	−12.7190	+	12.7190i	−0.945396	+	0.945396i	0.0531889	+	0.998584i	$0.483061\pi$
$182$	11.6315	+	11.6315i	0.862184	+	0.862184i
$183$	−1.03119			−0.0762278
$184$	−5.38067	−	5.38067i	−0.396668	−	0.396668i
$185$		−	2.21247i		−	0.162664i
$186$	−3.74995			−0.274959
$187$	3.78772	+	1.62887i	0.276985	+	0.119114i
$188$	9.38416			0.684410
$189$			3.61290i			0.262800i
$190$	−0.0724654	−	0.0724654i	−0.00525719	−	0.00525719i
$191$	−10.8186			−0.782807			−0.391403	−	0.920219i	$-0.628010\pi$
$191$	−10.8186			−0.782807			−0.391403	+	0.920219i	$0.628010\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$	−3.72122	+	3.72122i	−0.267859	+	0.267859i	−0.828237	−	0.560378i	$-0.810656\pi$
$193$	−3.72122	+	3.72122i	−0.267859	+	0.267859i	0.560378	+	0.828237i	$0.310656\pi$
$194$	−1.28422	+	1.28422i	−0.0922018	+	0.0922018i
$195$			4.20619i			0.301212i
$196$			6.05308i			0.432363i
$197$	−8.23069	+	8.23069i	−0.586413	+	0.586413i	−0.936658	−	0.350245i	$-0.886098\pi$
$197$	−8.23069	+	8.23069i	−0.586413	+	0.586413i	0.350245	+	0.936658i	$0.386098\pi$
$198$	−0.707107	+	0.707107i	−0.0502519	+	0.0502519i
$199$	2.50001	+	2.50001i	0.177221	+	0.177221i	0.790143	−	0.612922i	$-0.210006\pi$
$199$	2.50001	+	2.50001i	0.177221	+	0.177221i	−0.612922	+	0.790143i	$0.710006\pi$
$200$	−4.14653			−0.293204
$201$	−2.33558	−	2.33558i	−0.164739	−	0.164739i
$202$		−	18.1254i		−	1.27530i
$203$	30.7657			2.15933
$204$	−1.62887	+	3.78772i	−0.114043	+	0.265193i
$205$	−9.36222			−0.653886
$206$			15.5369i			1.08251i
$207$	5.38067	+	5.38067i	0.373982	+	0.373982i
$208$	−4.55296			−0.315691
$209$	0.0784396	+	0.0784396i	0.00542578	+	0.00542578i
$210$	−2.36013	+	2.36013i	−0.162865	+	0.162865i
$211$	6.97436	−	6.97436i	0.480134	−	0.480134i	−0.425040	−	0.905175i	$-0.639740\pi$
$211$	6.97436	−	6.97436i	0.480134	−	0.480134i	0.905175	+	0.425040i	$0.139740\pi$
$212$		−	1.89084i		−	0.129863i
$213$			1.85014i			0.126770i
$214$	−2.09773	+	2.09773i	−0.143398	+	0.143398i
$215$	0.885554	−	0.885554i	0.0603943	−	0.0603943i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	13.5482			0.919712
$218$	7.39851	+	7.39851i	0.501091	+	0.501091i
$219$			7.55795i			0.510719i
$220$	−0.923837			−0.0622850
$221$	−6.95027	−	17.4383i	−0.467526	−	1.17303i
$222$	−2.39487			−0.160733
$223$			6.66357i			0.446226i	0.974793	+	0.223113i	$0.0716218\pi$
$223$			6.66357i			0.446226i	−0.974793	+	0.223113i	$0.928378\pi$
$224$	−2.55471	−	2.55471i	−0.170694	−	0.170694i
$225$	4.14653			0.276435
$226$	−1.82308	−	1.82308i	−0.121269	−	0.121269i
$227$	−1.45046	+	1.45046i	−0.0962703	+	0.0962703i	−0.753602	−	0.657331i	$-0.771685\pi$
$227$	−1.45046	+	1.45046i	−0.0962703	+	0.0962703i	0.657331	+	0.753602i	$0.271685\pi$
$228$	−0.0784396	+	0.0784396i	−0.00519479	+	0.00519479i
$229$			15.6073i			1.03136i	0.856781	+	0.515681i	$0.172461\pi$
$229$			15.6073i			1.03136i	−0.856781	+	0.515681i	$0.827539\pi$
$230$			7.02985i			0.463535i
$231$	2.55471	−	2.55471i	0.168088	−	0.168088i
$232$	−6.02136	+	6.02136i	−0.395322	+	0.395322i
$233$	16.5888	+	16.5888i	1.08677	+	1.08677i	0.995859	+	0.0909063i	$0.0289764\pi$
$233$	16.5888	+	16.5888i	1.08677	+	1.08677i	0.0909063	+	0.995859i	$0.471024\pi$
$234$	4.55296			0.297636
$235$	−6.13021	−	6.13021i	−0.399891	−	0.399891i
$236$			9.89347i			0.644010i
$237$	−2.14636			−0.139421
$238$	5.88493	−	13.6847i	0.381464	−	0.887045i
$239$	−1.40481			−0.0908698			−0.0454349	−	0.998967i	$-0.514467\pi$
$239$	−1.40481			−0.0908698			−0.0454349	+	0.998967i	$0.514467\pi$
$240$		−	0.923837i		−	0.0596334i
$241$	10.1828	+	10.1828i	0.655929	+	0.655929i	0.954414	−	0.298486i	$-0.0964815\pi$
$241$	10.1828	+	10.1828i	0.655929	+	0.655929i	−0.298486	+	0.954414i	$0.596481\pi$
$242$	1.00000			0.0642824
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−0.729162	+	0.729162i	−0.0466798	+	0.0466798i
$245$	3.95418	−	3.95418i	0.252623	−	0.252623i
$246$			10.1341i			0.646124i
$247$		−	0.505062i		−	0.0321363i
$248$	−2.65161	+	2.65161i	−0.168378	+	0.168378i
$249$	−5.15985	+	5.15985i	−0.326992	+	0.326992i
$250$	5.97498	+	5.97498i	0.377891	+	0.377891i
$251$	−6.40037			−0.403988			−0.201994	−	0.979387i	$-0.564742\pi$
$251$	−6.40037			−0.403988			−0.201994	+	0.979387i	$0.564742\pi$
$252$	2.55471	+	2.55471i	0.160932	+	0.160932i
$253$		−	7.60941i		−	0.478400i
$254$	−15.4175			−0.967381
$255$	3.53839	−	1.41027i	0.221582	−	0.0883147i
$256$	1.00000			0.0625000
$257$			20.8836i			1.30268i	0.758785	+	0.651341i	$0.225793\pi$
$257$			20.8836i			1.30268i	−0.758785	+	0.651341i	$0.774207\pi$
$258$	−0.958561	−	0.958561i	−0.0596774	−	0.0596774i
$259$	8.65245			0.537637
$260$	2.97423	+	2.97423i	0.184454	+	0.184454i
$261$	6.02136	−	6.02136i	0.372713	−	0.372713i
$262$	−8.18548	+	8.18548i	−0.505701	+	0.505701i
$263$		−	22.0473i		−	1.35950i	−0.733445	−	0.679749i	$-0.762089\pi$
$263$		−	22.0473i		−	1.35950i	0.733445	−	0.679749i	$-0.237911\pi$
$264$			1.00000i			0.0615457i
$265$	−1.23519	+	1.23519i	−0.0758773	+	0.0758773i
$266$	0.283395	−	0.283395i	0.0173760	−	0.0173760i
$267$	11.0426	+	11.0426i	0.675797	+	0.675797i
$268$	−3.30301			−0.201763
$269$	0.790567	+	0.790567i	0.0482017	+	0.0482017i	0.730797	−	0.682595i	$-0.239149\pi$
$269$	0.790567	+	0.790567i	0.0482017	+	0.0482017i	−0.682595	+	0.730797i	$0.739149\pi$
$270$			0.923837i			0.0562229i
$271$	−31.3428			−1.90394			−0.951970	−	0.306191i	$-0.900945\pi$
$271$	−31.3428			−1.90394			−0.951970	+	0.306191i	$0.900945\pi$
$272$	1.52654	+	3.83010i	0.0925600	+	0.232234i
$273$	−16.4494			−0.995564
$274$			7.89615i			0.477024i
$275$	−2.93204	−	2.93204i	−0.176808	−	0.176808i
$276$	7.60941			0.458033
$277$	−7.69746	−	7.69746i	−0.462496	−	0.462496i	0.436977	−	0.899473i	$-0.356049\pi$
$277$	−7.69746	−	7.69746i	−0.462496	−	0.462496i	−0.899473	+	0.436977i	$0.856049\pi$
$278$	7.35344	−	7.35344i	0.441030	−	0.441030i
$279$	2.65161	−	2.65161i	0.158748	−	0.158748i
$280$			3.33773i			0.199468i
$281$			31.0347i			1.85138i	0.378288	+	0.925688i	$0.376513\pi$
$281$			31.0347i			1.85138i	−0.378288	+	0.925688i	$0.623487\pi$
$282$	−6.63560	+	6.63560i	−0.395144	+	0.395144i
$283$	−0.437401	+	0.437401i	−0.0260008	+	0.0260008i	−0.719988	−	0.693987i	$-0.755853\pi$
$283$	−0.437401	+	0.437401i	−0.0260008	+	0.0260008i	0.693987	+	0.719988i	$0.255853\pi$
$284$	1.30825	+	1.30825i	0.0776303	+	0.0776303i
$285$	0.102481			0.00607048
$286$	−3.21943	−	3.21943i	−0.190369	−	0.190369i
$287$		−	36.6134i		−	2.16122i
$288$	−1.00000			−0.0589256
$289$	−12.3394	+	11.6936i	−0.725845	+	0.687859i
$290$	7.86692			0.461962
$291$		−	1.81617i		−	0.106466i
$292$	5.34428	+	5.34428i	0.312750	+	0.312750i
$293$	−25.1424			−1.46884			−0.734419	−	0.678697i	$-0.762545\pi$
$293$	−25.1424			−1.46884			−0.734419	+	0.678697i	$0.762545\pi$
$294$	−4.28017	−	4.28017i	−0.249625	−	0.249625i
$295$	6.46292	−	6.46292i	0.376286	−	0.376286i
$296$	−1.69343	+	1.69343i	−0.0984287	+	0.0984287i
$297$		−	1.00000i		−	0.0580259i
$298$		−	13.3647i		−	0.774199i
$299$	−24.4980	+	24.4980i	−1.41675	+	1.41675i
$300$	2.93204	−	2.93204i	0.169281	−	0.169281i
$301$	3.46319	+	3.46319i	0.199615	+	0.199615i
$302$	13.6519			0.785578
$303$	12.8166	+	12.8166i	0.736292	+	0.736292i
$304$			0.110930i			0.00636229i
$305$	0.952651			0.0545487
$306$	−1.52654	−	3.83010i	−0.0872664	−	0.218952i
$307$	4.09661			0.233806			0.116903	−	0.993143i	$-0.462703\pi$
$307$	4.09661			0.233806			0.116903	+	0.993143i	$0.462703\pi$
$308$		−	3.61290i		−	0.205864i
$309$	−10.9863	−	10.9863i	−0.624987	−	0.624987i
$310$	3.46434			0.196761
$311$	−20.4341	−	20.4341i	−1.15871	−	1.15871i	−0.984752	−	0.173962i	$-0.944343\pi$
$311$	−20.4341	−	20.4341i	−1.15871	−	1.15871i	−0.173962	−	0.984752i	$-0.555657\pi$
$312$	3.21943	−	3.21943i	0.182264	−	0.182264i
$313$	13.2555	−	13.2555i	0.749247	−	0.749247i	−0.225091	−	0.974338i	$-0.572268\pi$
$313$	13.2555	−	13.2555i	0.749247	−	0.749247i	0.974338	+	0.225091i	$0.0722678\pi$
$314$			4.69564i			0.264990i
$315$		−	3.33773i		−	0.188060i
$316$	−1.51771	+	1.51771i	−0.0853778	+	0.0853778i
$317$	7.52516	−	7.52516i	0.422655	−	0.422655i	−0.463462	−	0.886117i	$-0.653393\pi$
$317$	7.52516	−	7.52516i	0.422655	−	0.422655i	0.886117	+	0.463462i	$0.153393\pi$
$318$	1.33703	+	1.33703i	0.0749766	+	0.0749766i
$319$	−8.51549			−0.476776
$320$	−0.653251	−	0.653251i	−0.0365178	−	0.0365178i
$321$		−	2.96663i		−	0.165581i
$322$	−27.4921			−1.53207
$323$	−0.424874	+	0.169339i	−0.0236406	+	0.00942230i
$324$	1.00000			0.0555556
$325$			18.8790i			1.04722i
$326$	−6.62628	−	6.62628i	−0.366996	−	0.366996i
$327$	−10.4631			−0.578610
$328$	7.16587	+	7.16587i	0.395669	+	0.395669i
$329$	23.9738	−	23.9738i	1.32172	−	1.32172i
$330$	0.653251	−	0.653251i	0.0359603	−	0.0359603i
$331$		−	13.0104i		−	0.715117i	−0.933891	−	0.357559i	$-0.883609\pi$
$331$		−	13.0104i		−	0.715117i	0.933891	−	0.357559i	$-0.116391\pi$
$332$			7.29713i			0.400482i
$333$	1.69343	−	1.69343i	0.0927994	−	0.0927994i
$334$	−7.17103	+	7.17103i	−0.392381	+	0.392381i
$335$	2.15769	+	2.15769i	0.117887	+	0.117887i
$336$	3.61290			0.197100
$337$	−0.877772	−	0.877772i	−0.0478153	−	0.0478153i	0.682795	−	0.730610i	$-0.260764\pi$
$337$	−0.877772	−	0.877772i	−0.0478153	−	0.0478153i	−0.730610	+	0.682795i	$0.760764\pi$
$338$			7.72947i			0.420428i
$339$	2.57822			0.140030
$340$	1.50481	−	3.49923i	0.0816095	−	0.189772i
$341$	−3.74995			−0.203071
$342$		−	0.110930i		−	0.00599843i
$343$	−2.41911	−	2.41911i	−0.130620	−	0.130620i
$344$	−1.35561			−0.0730896
$345$	−4.97086	−	4.97086i	−0.267622	−	0.267622i
$346$	−4.53335	+	4.53335i	−0.243714	+	0.243714i
$347$	5.27318	−	5.27318i	0.283079	−	0.283079i	−0.551257	−	0.834336i	$-0.685851\pi$
$347$	5.27318	−	5.27318i	0.283079	−	0.283079i	0.834336	+	0.551257i	$0.185851\pi$
$348$		−	8.51549i		−	0.456478i
$349$		−	21.3796i		−	1.14442i	−0.820106	−	0.572212i	$-0.806085\pi$
$349$		−	21.3796i		−	1.14442i	0.820106	−	0.572212i	$-0.193915\pi$
$350$	−10.5932	+	10.5932i	−0.566229	+	0.566229i
$351$	−3.21943	+	3.21943i	−0.171840	+	0.171840i
$352$	0.707107	+	0.707107i	0.0376889	+	0.0376889i
$353$	−30.3340			−1.61452			−0.807258	−	0.590199i	$-0.799049\pi$
$353$	−30.3340			−1.61452			−0.807258	+	0.590199i	$0.799049\pi$
$354$	−6.99574	−	6.99574i	−0.371820	−	0.371820i
$355$		−	1.70923i		−	0.0907165i
$356$	15.6166			0.827679
$357$	5.51524	+	13.8378i	0.291897	+	0.732374i
$358$	−6.38071			−0.337231
$359$			21.2585i			1.12198i	0.827823	+	0.560989i	$0.189579\pi$
$359$			21.2585i			1.12198i	−0.827823	+	0.560989i	$0.810421\pi$
$360$	0.653251	+	0.653251i	0.0344294	+	0.0344294i
$361$	18.9877			0.999352
$362$	−12.7190	−	12.7190i	−0.668496	−	0.668496i
$363$	−0.707107	+	0.707107i	−0.0371135	+	0.0371135i
$364$	−11.6315	+	11.6315i	−0.609656	+	0.609656i
$365$		−	6.98231i		−	0.365471i
$366$		−	1.03119i		−	0.0539012i
$367$	23.2573	−	23.2573i	1.21402	−	1.21402i	0.244328	−	0.969693i	$-0.421432\pi$
$367$	23.2573	−	23.2573i	1.21402	−	1.21402i	0.969693	−	0.244328i	$-0.0785675\pi$
$368$	5.38067	−	5.38067i	0.280487	−	0.280487i
$369$	−7.16587	−	7.16587i	−0.373040	−	0.373040i
$370$	2.21247			0.115021
$371$	−4.83054	−	4.83054i	−0.250789	−	0.250789i
$372$		−	3.74995i		−	0.194426i
$373$	−36.9116			−1.91121			−0.955606	−	0.294648i	$-0.904798\pi$
$373$	−36.9116			−1.91121			−0.955606	+	0.294648i	$0.904798\pi$
$374$	−1.62887	+	3.78772i	−0.0842266	+	0.195858i
$375$	−8.44989			−0.436351
$376$			9.38416i			0.483951i
$377$	27.4150	+	27.4150i	1.41195	+	1.41195i
$378$	−3.61290			−0.185828
$379$	2.60885	+	2.60885i	0.134008	+	0.134008i	0.770929	−	0.636921i	$-0.219792\pi$
$379$	2.60885	+	2.60885i	0.134008	+	0.134008i	−0.636921	+	0.770929i	$0.719792\pi$
$380$	0.0724654	−	0.0724654i	0.00371739	−	0.00371739i
$381$	10.9018	−	10.9018i	0.558518	−	0.558518i
$382$		−	10.8186i		−	0.553528i
$383$			25.6205i			1.30915i	0.755999	+	0.654573i	$0.227152\pi$
$383$			25.6205i			1.30915i	−0.755999	+	0.654573i	$0.772848\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	−2.36013	+	2.36013i	−0.120284	+	0.120284i
$386$	−3.72122	−	3.72122i	−0.189405	−	0.189405i
$387$	1.35561			0.0689095
$388$	−1.28422	−	1.28422i	−0.0651965	−	0.0651965i
$389$		−	10.3295i		−	0.523728i	−0.965105	−	0.261864i	$-0.915663\pi$
$389$		−	10.3295i		−	0.523728i	0.965105	−	0.261864i	$-0.0843371\pi$
$390$	−4.20619			−0.212989
$391$	28.8223	+	12.3947i	1.45761	+	0.626827i
$392$	−6.05308			−0.305727
$393$		−	11.5760i		−	0.583933i
$394$	−8.23069	−	8.23069i	−0.414656	−	0.414656i
$395$	1.98289			0.0997700
$396$	−0.707107	−	0.707107i	−0.0355335	−	0.0355335i
$397$	10.8401	−	10.8401i	0.544051	−	0.544051i	−0.380663	−	0.924714i	$-0.624304\pi$
$397$	10.8401	−	10.8401i	0.544051	−	0.544051i	0.924714	+	0.380663i	$0.124304\pi$
$398$	−2.50001	+	2.50001i	−0.125314	+	0.125314i
$399$			0.400781i			0.0200641i
$400$		−	4.14653i		−	0.207326i
$401$	13.1527	−	13.1527i	0.656813	−	0.656813i	−0.297811	−	0.954625i	$-0.596257\pi$
$401$	13.1527	−	13.1527i	0.656813	−	0.656813i	0.954625	+	0.297811i	$0.0962567\pi$
$402$	2.33558	−	2.33558i	0.116488	−	0.116488i
$403$	12.0727	+	12.0727i	0.601384	+	0.601384i
$404$	18.1254			0.901770
$405$	−0.653251	−	0.653251i	−0.0324603	−	0.0324603i
$406$			30.7657i			1.52687i
$407$	−2.39487			−0.118709
$408$	−3.78772	−	1.62887i	−0.187520	−	0.0806409i
$409$	−25.9081			−1.28107			−0.640537	−	0.767928i	$-0.721288\pi$
$409$	−25.9081			−1.28107			−0.640537	+	0.767928i	$0.721288\pi$
$410$		−	9.36222i		−	0.462367i
$411$	−5.58342	−	5.58342i	−0.275410	−	0.275410i
$412$	−15.5369			−0.765450
$413$	25.2749	+	25.2749i	1.24370	+	1.24370i
$414$	−5.38067	+	5.38067i	−0.264445	+	0.264445i
$415$	4.76686	−	4.76686i	0.233996	−	0.233996i
$416$		−	4.55296i		−	0.223227i
$417$			10.3993i			0.509258i
$418$	−0.0784396	+	0.0784396i	−0.00383661	+	0.00383661i
$419$	13.7667	−	13.7667i	0.672547	−	0.672547i	−0.285756	−	0.958302i	$-0.592245\pi$
$419$	13.7667	−	13.7667i	0.672547	−	0.672547i	0.958302	+	0.285756i	$0.0922447\pi$
$420$	−2.36013	−	2.36013i	−0.115163	−	0.115163i
$421$	19.4284			0.946881			0.473440	−	0.880826i	$-0.343012\pi$
$421$	19.4284			0.946881			0.473440	+	0.880826i	$0.343012\pi$
$422$	6.97436	+	6.97436i	0.339506	+	0.339506i
$423$		−	9.38416i		−	0.456273i
$424$	1.89084			0.0918273
$425$	15.8816	−	6.32983i	0.770372	−	0.307042i
$426$	−1.85014			−0.0896397
$427$			3.72559i			0.180294i
$428$	−2.09773	−	2.09773i	−0.101397	−	0.101397i
$429$	4.55296			0.219819
$430$	0.885554	+	0.885554i	0.0427052	+	0.0427052i
$431$	−3.77731	+	3.77731i	−0.181947	+	0.181947i	−0.792204	−	0.610257i	$-0.791066\pi$
$431$	−3.77731	+	3.77731i	−0.181947	+	0.181947i	0.610257	+	0.792204i	$0.291066\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$			30.9024i			1.48507i	0.669806	+	0.742537i	$0.266377\pi$
$433$			30.9024i			1.48507i	−0.669806	+	0.742537i	$0.733623\pi$
$434$			13.5482i			0.650334i
$435$	−5.56275	+	5.56275i	−0.266714	+	0.266714i
$436$	−7.39851	+	7.39851i	−0.354325	+	0.354325i
$437$	0.596879	+	0.596879i	0.0285526	+	0.0285526i
$438$	−7.55795			−0.361133
$439$	25.6228	+	25.6228i	1.22291	+	1.22291i	0.966593	+	0.256315i	$0.0825083\pi$
$439$	25.6228	+	25.6228i	1.22291	+	1.22291i	0.256315	+	0.966593i	$0.417492\pi$
$440$		−	0.923837i		−	0.0440422i
$441$	6.05308			0.288242
$442$	17.4383	−	6.95027i	0.829456	−	0.330591i
$443$	−24.8379			−1.18008			−0.590041	−	0.807373i	$-0.700889\pi$
$443$	−24.8379			−1.18008			−0.590041	+	0.807373i	$0.700889\pi$
$444$		−	2.39487i		−	0.113656i
$445$	−10.2016	−	10.2016i	−0.483601	−	0.483601i
$446$	−6.66357			−0.315529
$447$	9.45031	+	9.45031i	0.446984	+	0.446984i
$448$	2.55471	−	2.55471i	0.120699	−	0.120699i
$449$	26.5532	−	26.5532i	1.25312	−	1.25312i	0.298809	−	0.954313i	$-0.403411\pi$
$449$	26.5532	−	26.5532i	1.25312	−	1.25312i	0.954313	−	0.298809i	$-0.0965894\pi$
$450$			4.14653i			0.195469i
$451$			10.1341i			0.477195i
$452$	1.82308	−	1.82308i	0.0857503	−	0.0857503i
$453$	−9.65334	+	9.65334i	−0.453554	+	0.453554i
$454$	−1.45046	−	1.45046i	−0.0680734	−	0.0680734i
$455$	15.1966			0.712426
$456$	−0.0784396	−	0.0784396i	−0.00367327	−	0.00367327i
$457$			2.27195i			0.106277i	0.998587	+	0.0531387i	$0.0169226\pi$
$457$			2.27195i			0.106277i	−0.998587	+	0.0531387i	$0.983077\pi$
$458$	−15.6073			−0.729283
$459$	3.78772	+	1.62887i	0.176795	+	0.0760289i
$460$	−7.02985			−0.327769
$461$		−	25.0321i		−	1.16586i	−0.812522	−	0.582930i	$-0.801906\pi$
$461$		−	25.0321i		−	1.16586i	0.812522	−	0.582930i	$-0.198094\pi$
$462$	2.55471	+	2.55471i	0.118856	+	0.118856i
$463$	−34.9062			−1.62223			−0.811115	−	0.584886i	$-0.801139\pi$
$463$	−34.9062			−1.62223			−0.811115	+	0.584886i	$0.801139\pi$
$464$	−6.02136	−	6.02136i	−0.279535	−	0.279535i
$465$	−2.44966	+	2.44966i	−0.113600	+	0.113600i
$466$	−16.5888	+	16.5888i	−0.768459	+	0.768459i
$467$		−	6.18677i		−	0.286289i	−0.989702	−	0.143145i	$-0.954279\pi$
$467$		−	6.18677i		−	0.286289i	0.989702	−	0.143145i	$-0.0457214\pi$
$468$			4.55296i			0.210461i
$469$	−8.43823	+	8.43823i	−0.389641	+	0.389641i
$470$	6.13021	−	6.13021i	0.282766	−	0.282766i
$471$	−3.32032	−	3.32032i	−0.152992	−	0.152992i
$472$	−9.89347			−0.455384
$473$	−0.958561	−	0.958561i	−0.0440747	−	0.0440747i
$474$		−	2.14636i		−	0.0985857i
$475$	0.459976			0.0211051
$476$	13.6847	+	5.88493i	0.627235	+	0.269736i
$477$	−1.89084			−0.0865756
$478$		−	1.40481i		−	0.0642546i
$479$	−14.1647	−	14.1647i	−0.647200	−	0.647200i	0.305116	−	0.952315i	$-0.401305\pi$
$479$	−14.1647	−	14.1647i	−0.647200	−	0.647200i	−0.952315	+	0.305116i	$0.901305\pi$
$480$	0.923837			0.0421672
$481$	7.71013	+	7.71013i	0.351552	+	0.351552i
$482$	−10.1828	+	10.1828i	−0.463812	+	0.463812i
$483$	19.4398	−	19.4398i	0.884543	−	0.884543i
$484$			1.00000i			0.0454545i
$485$			1.67784i			0.0761868i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$	−19.3387	+	19.3387i	−0.876321	+	0.876321i	−0.993152	−	0.116831i	$-0.962726\pi$
$487$	−19.3387	+	19.3387i	−0.876321	+	0.876321i	0.116831	+	0.993152i	$0.462726\pi$
$488$	−0.729162	−	0.729162i	−0.0330076	−	0.0330076i
$489$	9.37098			0.423770
$490$	3.95418	+	3.95418i	0.178632	+	0.178632i
$491$			1.70348i			0.0768770i	0.999261	+	0.0384385i	$0.0122384\pi$
$491$			1.70348i			0.0768770i	−0.999261	+	0.0384385i	$0.987762\pi$
$492$	−10.1341			−0.456879
$493$	13.8706	−	32.2543i	0.624700	−	1.45266i
$494$	0.505062			0.0227238
$495$			0.923837i			0.0415234i
$496$	−2.65161	−	2.65161i	−0.119061	−	0.119061i
$497$	6.68439			0.299836
$498$	−5.15985	−	5.15985i	−0.231218	−	0.231218i
$499$	18.3515	−	18.3515i	0.821526	−	0.821526i	−0.164801	−	0.986327i	$-0.552698\pi$
$499$	18.3515	−	18.3515i	0.821526	−	0.821526i	0.986327	+	0.164801i	$0.0526981\pi$
$500$	−5.97498	+	5.97498i	−0.267209	+	0.267209i
$501$		−	10.1414i		−	0.453083i
$502$		−	6.40037i		−	0.285663i
$503$	21.8356	−	21.8356i	0.973600	−	0.973600i	−0.0260602	−	0.999660i	$-0.508296\pi$
$503$	21.8356	−	21.8356i	0.973600	−	0.973600i	0.999660	+	0.0260602i	$0.00829614\pi$
$504$	−2.55471	+	2.55471i	−0.113796	+	0.113796i
$505$	−11.8404	−	11.8404i	−0.526891	−	0.526891i
$506$	7.60941			0.338280
$507$	−5.46556	−	5.46556i	−0.242734	−	0.242734i
$508$		−	15.4175i		−	0.684041i
$509$	−41.7590			−1.85093			−0.925467	−	0.378827i	$-0.876327\pi$
$509$	−41.7590			−1.85093			−0.925467	+	0.378827i	$0.876327\pi$
$510$	1.41027	+	3.53839i	0.0624479	+	0.156682i
$511$	27.3062			1.20795
$512$			1.00000i			0.0441942i
$513$	0.0784396	+	0.0784396i	0.00346319	+	0.00346319i
$514$	−20.8836			−0.921136
$515$	10.1495	+	10.1495i	0.447241	+	0.447241i
$516$	0.958561	−	0.958561i	0.0421983	−	0.0421983i
$517$	−6.63560	+	6.63560i	−0.291833	+	0.291833i
$518$			8.65245i			0.380167i
$519$		−	6.41112i		−	0.281417i
$520$	−2.97423	+	2.97423i	−0.130429	+	0.130429i
$521$	−16.6825	+	16.6825i	−0.730875	+	0.730875i	−0.970793	−	0.239918i	$-0.922879\pi$
$521$	−16.6825	+	16.6825i	−0.730875	+	0.730875i	0.239918	+	0.970793i	$0.422879\pi$
$522$	6.02136	+	6.02136i	0.263548	+	0.263548i
$523$	41.2128			1.80211			0.901054	−	0.433706i	$-0.142795\pi$
$523$	41.2128			1.80211			0.901054	+	0.433706i	$0.142795\pi$
$524$	−8.18548	−	8.18548i	−0.357584	−	0.357584i
$525$		−	14.9810i		−	0.653825i
$526$	22.0473			0.961310
$527$	6.10816	−	14.2037i	0.266076	−	0.618724i
$528$	−1.00000			−0.0435194
$529$		−	34.9031i		−	1.51753i
$530$	−1.23519	−	1.23519i	−0.0536533	−	0.0536533i
$531$	9.89347			0.429340
$532$	0.283395	+	0.283395i	0.0122867	+	0.0122867i
$533$	32.6259	−	32.6259i	1.41319	−	1.41319i
$534$	−11.0426	+	11.0426i	−0.477861	+	0.477861i
$535$			2.74068i			0.118490i
$536$		−	3.30301i		−	0.142668i
$537$	4.51184	−	4.51184i	0.194700	−	0.194700i
$538$	−0.790567	+	0.790567i	−0.0340837	+	0.0340837i
$539$	−4.28017	−	4.28017i	−0.184360	−	0.184360i
$540$	−0.923837			−0.0397556
$541$	−15.2816	−	15.2816i	−0.657007	−	0.657007i	0.297664	−	0.954671i	$-0.403792\pi$
$541$	−15.2816	−	15.2816i	−0.657007	−	0.657007i	−0.954671	+	0.297664i	$0.903792\pi$
$542$		−	31.3428i		−	1.34629i
$543$	17.9874			0.771912
$544$	−3.83010	+	1.52654i	−0.164214	+	0.0654498i
$545$	9.66617			0.414053
$546$		−	16.4494i		−	0.703970i
$547$	−2.35091	−	2.35091i	−0.100518	−	0.100518i	0.655060	−	0.755577i	$-0.272644\pi$
$547$	−2.35091	−	2.35091i	−0.100518	−	0.100518i	−0.755577	+	0.655060i	$0.772644\pi$
$548$	−7.89615			−0.337307
$549$	0.729162	+	0.729162i	0.0311199	+	0.0311199i
$550$	2.93204	−	2.93204i	0.125022	−	0.125022i
$551$	0.667952	−	0.667952i	0.0284557	−	0.0284557i
$552$			7.60941i			0.323878i
$553$			7.75461i			0.329759i
$554$	7.69746	−	7.69746i	0.327034	−	0.327034i
$555$	−1.56445	+	1.56445i	−0.0664073	+	0.0664073i
$556$	7.35344	+	7.35344i	0.311855	+	0.311855i
$557$	10.2619			0.434811			0.217405	−	0.976081i	$-0.430241\pi$
$557$	10.2619			0.434811			0.217405	+	0.976081i	$0.430241\pi$
$558$	2.65161	+	2.65161i	0.112252	+	0.112252i
$559$			6.17204i			0.261050i
$560$	−3.33773			−0.141045
$561$	−1.52654	−	3.83010i	−0.0644505	−	0.161707i
$562$	−31.0347			−1.30912
$563$			20.0687i			0.845794i	0.906178	+	0.422897i	$0.138987\pi$
$563$			20.0687i			0.845794i	−0.906178	+	0.422897i	$0.861013\pi$
$564$	−6.63560	−	6.63560i	−0.279409	−	0.279409i
$565$	−2.38185			−0.100205
$566$	−0.437401	−	0.437401i	−0.0183854	−	0.0183854i
$567$	2.55471	−	2.55471i	0.107288	−	0.107288i
$568$	−1.30825	+	1.30825i	−0.0548929	+	0.0548929i
$569$			12.9741i			0.543902i	0.962311	+	0.271951i	$0.0876689\pi$
$569$			12.9741i			0.543902i	−0.962311	+	0.271951i	$0.912331\pi$
$570$			0.102481i			0.00429248i
$571$	26.3058	−	26.3058i	1.10086	−	1.10086i	0.106557	−	0.994307i	$-0.466017\pi$
$571$	26.3058	−	26.3058i	1.10086	−	1.10086i	0.994307	−	0.106557i	$-0.0339826\pi$
$572$	3.21943	−	3.21943i	0.134611	−	0.134611i
$573$	7.64991	+	7.64991i	0.319579	+	0.319579i
$574$	36.6134			1.52821
$575$	−22.3111	−	22.3111i	−0.930436	−	0.930436i
$576$		−	1.00000i		−	0.0416667i
$577$	−31.5031			−1.31149			−0.655745	−	0.754983i	$-0.727645\pi$
$577$	−31.5031			−1.31149			−0.655745	+	0.754983i	$0.727645\pi$
$578$	−11.6936	−	12.3394i	−0.486389	−	0.513250i
$579$	5.26260			0.218706
$580$			7.86692i			0.326656i
$581$	18.6420	+	18.6420i	0.773402	+	0.773402i
$582$	1.81617			0.0752825
$583$	1.33703	+	1.33703i	0.0553739	+	0.0553739i
$584$	−5.34428	+	5.34428i	−0.221148	+	0.221148i
$585$	2.97423	−	2.97423i	0.122969	−	0.122969i
$586$		−	25.1424i		−	1.03862i
$587$			28.1426i			1.16157i	0.814057	+	0.580785i	$0.197254\pi$
$587$			28.1426i			1.16157i	−0.814057	+	0.580785i	$0.802746\pi$
$588$	4.28017	−	4.28017i	0.176511	−	0.176511i
$589$	0.294144	−	0.294144i	0.0121200	−	0.0121200i
$590$	6.46292	+	6.46292i	0.266074	+	0.266074i
$591$	11.6400			0.478804
$592$	−1.69343	−	1.69343i	−0.0695996	−	0.0695996i
$593$		−	19.6457i		−	0.806751i	−0.915035	−	0.403375i	$-0.867837\pi$
$593$		−	19.6457i		−	0.806751i	0.915035	−	0.403375i	$-0.132163\pi$
$594$	1.00000			0.0410305
$595$	−5.09518	−	12.7839i	−0.208882	−	0.524087i
$596$	13.3647			0.547441
$597$		−	3.53555i		−	0.144700i
$598$	−24.4980	−	24.4980i	−1.00180	−	1.00180i
$599$	−38.3923			−1.56867			−0.784333	−	0.620339i	$-0.786995\pi$
$599$	−38.3923			−1.56867			−0.784333	+	0.620339i	$0.786995\pi$
$600$	2.93204	+	2.93204i	0.119700	+	0.119700i
$601$	−15.8908	+	15.8908i	−0.648199	+	0.648199i	−0.952557	−	0.304359i	$-0.901558\pi$
$601$	−15.8908	+	15.8908i	−0.648199	+	0.648199i	0.304359	+	0.952557i	$0.401558\pi$
$602$	−3.46319	+	3.46319i	−0.141149	+	0.141149i
$603$			3.30301i			0.134509i
$604$			13.6519i			0.555487i
$605$	0.653251	−	0.653251i	0.0265584	−	0.0265584i
$606$	−12.8166	+	12.8166i	−0.520637	+	0.520637i
$607$	28.3374	+	28.3374i	1.15018	+	1.15018i	0.986516	+	0.163663i	$0.0523311\pi$
$607$	28.3374	+	28.3374i	1.15018	+	1.15018i	0.163663	+	0.986516i	$0.447669\pi$
$608$	−0.110930			−0.00449882
$609$	−21.7546	−	21.7546i	−0.881541	−	0.881541i
$610$			0.952651i			0.0385717i
$611$	42.7257			1.72850
$612$	3.83010	−	1.52654i	0.154823	−	0.0617067i
$613$	39.8197			1.60830			0.804151	−	0.594426i	$-0.202621\pi$
$613$	39.8197			1.60830			0.804151	+	0.594426i	$0.202621\pi$
$614$			4.09661i			0.165326i
$615$	6.62009	+	6.62009i	0.266948	+	0.266948i
$616$	3.61290			0.145568
$617$	−5.73583	−	5.73583i	−0.230916	−	0.230916i	0.582159	−	0.813075i	$-0.302208\pi$
$617$	−5.73583	−	5.73583i	−0.230916	−	0.230916i	−0.813075	+	0.582159i	$0.802208\pi$
$618$	10.9863	−	10.9863i	0.441933	−	0.441933i
$619$	1.06214	−	1.06214i	0.0426910	−	0.0426910i	−0.685439	−	0.728130i	$-0.740390\pi$
$619$	1.06214	−	1.06214i	0.0426910	−	0.0426910i	0.728130	+	0.685439i	$0.240390\pi$
$620$			3.46434i			0.139131i
$621$		−	7.60941i		−	0.305355i
$622$	20.4341	−	20.4341i	0.819335	−	0.819335i
$623$	39.8959	−	39.8959i	1.59840	−	1.59840i
$624$	3.21943	+	3.21943i	0.128880	+	0.128880i
$625$	−12.9263			−0.517052
$626$	13.2555	+	13.2555i	0.529798	+	0.529798i
$627$		−	0.110930i		−	0.00443013i
$628$	−4.69564			−0.187376
$629$	3.90093	−	9.07110i	0.155540	−	0.361688i
$630$	3.33773			0.132978
$631$		−	14.7173i		−	0.585888i	−0.956130	−	0.292944i	$-0.905365\pi$
$631$		−	14.7173i		−	0.585888i	0.956130	−	0.292944i	$-0.0946350\pi$
$632$	−1.51771	−	1.51771i	−0.0603712	−	0.0603712i
$633$	−9.86323			−0.392028
$634$	7.52516	+	7.52516i	0.298862	+	0.298862i
$635$	−10.0715	+	10.0715i	−0.399676	+	0.399676i
$636$	−1.33703	+	1.33703i	−0.0530165	+	0.0530165i
$637$			27.5594i			1.09194i
$638$		−	8.51549i		−	0.337132i
$639$	1.30825	−	1.30825i	0.0517535	−	0.0517535i
$640$	0.653251	−	0.653251i	0.0258220	−	0.0258220i
$641$	−17.2963	−	17.2963i	−0.683164	−	0.683164i	0.277548	−	0.960712i	$-0.410478\pi$
$641$	−17.2963	−	17.2963i	−0.683164	−	0.683164i	−0.960712	+	0.277548i	$0.910478\pi$
$642$	2.96663			0.117084
$643$	1.47479	+	1.47479i	0.0581601	+	0.0581601i	0.735589	−	0.677429i	$-0.236906\pi$
$643$	1.47479	+	1.47479i	0.0581601	+	0.0581601i	−0.677429	+	0.735589i	$0.736906\pi$
$644$		−	27.4921i		−	1.08334i
$645$	−1.25236			−0.0493117
$646$	−0.169339	−	0.424874i	−0.00666257	−	0.0167165i
$647$	−9.32780			−0.366714			−0.183357	−	0.983046i	$-0.558696\pi$
$647$	−9.32780			−0.366714			−0.183357	+	0.983046i	$0.558696\pi$
$648$			1.00000i			0.0392837i
$649$	−6.99574	−	6.99574i	−0.274607	−	0.274607i
$650$	−18.8790			−0.740494
$651$	−9.58002	−	9.58002i	−0.375471	−	0.375471i
$652$	6.62628	−	6.62628i	0.259505	−	0.259505i
$653$	−25.0681	+	25.0681i	−0.980991	+	0.980991i	−0.999823	−	0.0188320i	$-0.994005\pi$
$653$	−25.0681	+	25.0681i	−0.980991	+	0.980991i	0.0188320	+	0.999823i	$0.494005\pi$
$654$		−	10.4631i		−	0.409139i
$655$			10.6943i			0.417863i
$656$	−7.16587	+	7.16587i	−0.279780	+	0.279780i
$657$	5.34428	−	5.34428i	0.208500	−	0.208500i
$658$	23.9738	+	23.9738i	0.934596	+	0.934596i
$659$	−12.2027			−0.475350			−0.237675	−	0.971345i	$-0.576385\pi$
$659$	−12.2027			−0.475350			−0.237675	+	0.971345i	$0.576385\pi$
$660$	0.653251	+	0.653251i	0.0254278	+	0.0254278i
$661$		−	15.1723i		−	0.590135i	−0.955476	−	0.295067i	$-0.904658\pi$
$661$		−	15.1723i		−	0.590135i	0.955476	−	0.295067i	$-0.0953421\pi$
$662$	13.0104			0.505664
$663$	−7.41616	+	17.2453i	−0.288020	+	0.669753i
$664$	−7.29713			−0.283184
$665$		−	0.370256i		−	0.0143579i
$666$	1.69343	+	1.69343i	0.0656191	+	0.0656191i
$667$	−64.7979			−2.50898
$668$	−7.17103	−	7.17103i	−0.277455	−	0.277455i
$669$	4.71186	−	4.71186i	0.182171	−	0.182171i
$670$	−2.15769	+	2.15769i	−0.0833590	+	0.0833590i
$671$		−	1.03119i		−	0.0398087i
$672$			3.61290i			0.139371i
$673$	−10.3344	+	10.3344i	−0.398363	+	0.398363i	−0.877655	−	0.479292i	$-0.840893\pi$
$673$	−10.3344	+	10.3344i	−0.398363	+	0.398363i	0.479292	+	0.877655i	$0.340893\pi$
$674$	0.877772	−	0.877772i	0.0338105	−	0.0338105i
$675$	−2.93204	−	2.93204i	−0.112854	−	0.112854i
$676$	−7.72947			−0.297287
$677$	−19.6841	−	19.6841i	−0.756520	−	0.756520i	0.219167	−	0.975687i	$-0.429666\pi$
$677$	−19.6841	−	19.6841i	−0.756520	−	0.756520i	−0.975687	+	0.219167i	$0.929666\pi$
$678$			2.57822i			0.0990160i
$679$	−6.56163			−0.251812
$680$	3.49923	+	1.50481i	0.134189	+	0.0577066i
$681$	2.05126			0.0786044
$682$		−	3.74995i		−	0.143593i
$683$	−3.94421	−	3.94421i	−0.150921	−	0.150921i	0.627608	−	0.778529i	$-0.284034\pi$
$683$	−3.94421	−	3.94421i	−0.150921	−	0.150921i	−0.778529	+	0.627608i	$0.784034\pi$
$684$	0.110930			0.00424153
$685$	5.15817	+	5.15817i	0.197083	+	0.197083i
$686$	2.41911	−	2.41911i	0.0923622	−	0.0923622i
$687$	11.0360	−	11.0360i	0.421051	−	0.421051i
$688$		−	1.35561i		−	0.0516822i
$689$		−	8.60892i		−	0.327974i
$690$	4.97086	−	4.97086i	0.189237	−	0.189237i
$691$	−7.12384	+	7.12384i	−0.271004	+	0.271004i	−0.829504	−	0.558501i	$-0.811377\pi$
$691$	−7.12384	+	7.12384i	−0.271004	+	0.271004i	0.558501	+	0.829504i	$0.311377\pi$
$692$	−4.53335	−	4.53335i	−0.172332	−	0.172332i
$693$	−3.61290			−0.137243
$694$	5.27318	+	5.27318i	0.200167	+	0.200167i
$695$		−	9.60729i		−	0.364425i
$696$	8.51549			0.322779
$697$	−38.3850	−	16.5070i	−1.45393	−	0.625248i
$698$	21.3796			0.809230
$699$		−	23.4600i		−	0.887341i
$700$	−10.5932	−	10.5932i	−0.400384	−	0.400384i
$701$	35.8715			1.35485			0.677424	−	0.735593i	$-0.263096\pi$
$701$	35.8715			1.35485			0.677424	+	0.735593i	$0.263096\pi$
$702$	−3.21943	−	3.21943i	−0.121510	−	0.121510i
$703$	0.187853	−	0.187853i	0.00708500	−	0.00708500i
$704$	−0.707107	+	0.707107i	−0.0266501	+	0.0266501i
$705$			8.66943i			0.326510i
$706$		−	30.3340i		−	1.14163i
$707$	46.3050	−	46.3050i	1.74148	−	1.74148i
$708$	6.99574	−	6.99574i	0.262916	−	0.262916i
$709$	12.9093	+	12.9093i	0.484820	+	0.484820i	0.906667	−	0.421847i	$-0.138618\pi$
$709$	12.9093	+	12.9093i	0.484820	+	0.484820i	−0.421847	+	0.906667i	$0.638618\pi$
$710$	1.70923			0.0641463
$711$	1.51771	+	1.51771i	0.0569185	+	0.0569185i
$712$			15.6166i			0.585258i
$713$	−28.5349			−1.06864
$714$	−13.8378	+	5.51524i	−0.517866	+	0.206403i
$715$	−4.20619			−0.157303
$716$		−	6.38071i		−	0.238458i
$717$	0.993353	+	0.993353i	0.0370974	+	0.0370974i
$718$	−21.2585			−0.793359
$719$	17.9016	+	17.9016i	0.667615	+	0.667615i	0.957163	−	0.289548i	$-0.0935050\pi$
$719$	17.9016	+	17.9016i	0.667615	+	0.667615i	−0.289548	+	0.957163i	$0.593505\pi$
$720$	−0.653251	+	0.653251i	−0.0243452	+	0.0243452i
$721$	−39.6924	+	39.6924i	−1.47822	+	1.47822i
$722$			18.9877i			0.706649i
$723$		−	14.4006i		−	0.535563i
$724$	12.7190	−	12.7190i	0.472698	−	0.472698i
$725$	−24.9677	+	24.9677i	−0.927278	+	0.927278i
$726$	−0.707107	−	0.707107i	−0.0262432	−	0.0262432i
$727$	−37.1346			−1.37725			−0.688624	−	0.725119i	$-0.741785\pi$
$727$	−37.1346			−1.37725			−0.688624	+	0.725119i	$0.741785\pi$
$728$	−11.6315	−	11.6315i	−0.431092	−	0.431092i
$729$		−	1.00000i		−	0.0370370i
$730$	6.98231			0.258427
$731$	5.19213	−	2.06939i	0.192038	−	0.0765392i
$732$	1.03119			0.0381139
$733$		−	45.9328i		−	1.69657i	−0.529542	−	0.848284i	$-0.677636\pi$
$733$		−	45.9328i		−	1.69657i	0.529542	−	0.848284i	$-0.322364\pi$
$734$	23.2573	+	23.2573i	0.858442	+	0.858442i
$735$	−5.59205			−0.206266
$736$	5.38067	+	5.38067i	0.198334	+	0.198334i
$737$	2.33558	−	2.33558i	0.0860322	−	0.0860322i
$738$	7.16587	−	7.16587i	0.263779	−	0.263779i
$739$			40.3869i			1.48566i	0.669482	+	0.742828i	$0.266516\pi$
$739$			40.3869i			1.48566i	−0.669482	+	0.742828i	$0.733484\pi$
$740$			2.21247i			0.0813321i
$741$	−0.357133	+	0.357133i	−0.0131196	+	0.0131196i
$742$	4.83054	−	4.83054i	0.177335	−	0.177335i
$743$	−20.8605	−	20.8605i	−0.765298	−	0.765298i	0.211977	−	0.977275i	$-0.432010\pi$
$743$	−20.8605	−	20.8605i	−0.765298	−	0.765298i	−0.977275	+	0.211977i	$0.932010\pi$
$744$	3.74995			0.137480
$745$	−8.73054	−	8.73054i	−0.319862	−	0.319862i
$746$		−	36.9116i		−	1.35143i
$747$	7.29713			0.266988
$748$	−3.78772	−	1.62887i	−0.138493	−	0.0595572i
$749$	−10.7182			−0.391633
$750$		−	8.44989i		−	0.308547i
$751$	−15.9321	−	15.9321i	−0.581369	−	0.581369i	0.353910	−	0.935279i	$-0.384852\pi$
$751$	−15.9321	−	15.9321i	−0.581369	−	0.581369i	−0.935279	+	0.353910i	$0.884852\pi$
$752$	−9.38416			−0.342205
$753$	4.52575	+	4.52575i	0.164927	+	0.164927i
$754$	−27.4150	+	27.4150i	−0.998397	+	0.998397i
$755$	8.91811	−	8.91811i	0.324563	−	0.324563i
$756$		−	3.61290i		−	0.131400i
$757$			12.8313i			0.466361i	0.972433	+	0.233180i	$0.0749133\pi$
$757$			12.8313i			0.466361i	−0.972433	+	0.233180i	$0.925087\pi$
$758$	−2.60885	+	2.60885i	−0.0947576	+	0.0947576i
$759$	−5.38067	+	5.38067i	−0.195306	+	0.195306i
$760$	0.0724654	+	0.0724654i	0.00262859	+	0.00262859i
$761$	4.73509			0.171647			0.0858235	−	0.996310i	$-0.472648\pi$
$761$	4.73509			0.171647			0.0858235	+	0.996310i	$0.472648\pi$
$762$	10.9018	+	10.9018i	0.394932	+	0.394932i
$763$			37.8021i			1.36853i
$764$	10.8186			0.391403
$765$	−3.49923	−	1.50481i	−0.126515	−	0.0544064i
$766$	−25.6205			−0.925706
$767$			45.0446i			1.62647i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	−23.4526			−0.845722			−0.422861	−	0.906195i	$-0.638974\pi$
$769$	−23.4526			−0.845722			−0.422861	+	0.906195i	$0.638974\pi$
$770$	−2.36013	−	2.36013i	−0.0850533	−	0.0850533i
$771$	14.7669	−	14.7669i	0.531818	−	0.531818i
$772$	3.72122	−	3.72122i	0.133930	−	0.133930i
$773$		−	17.6310i		−	0.634144i	−0.948401	−	0.317072i	$-0.897300\pi$
$773$		−	17.6310i		−	0.634144i	0.948401	−	0.317072i	$-0.102700\pi$
$774$			1.35561i			0.0487264i
$775$	−10.9950	+	10.9950i	−0.394951	+	0.394951i
$776$	1.28422	−	1.28422i	0.0461009	−	0.0461009i
$777$	−6.11820	−	6.11820i	−0.219489	−	0.219489i
$778$	10.3295			0.370331
$779$	−0.794912	−	0.794912i	−0.0284807	−	0.0284807i
$780$		−	4.20619i		−	0.150606i
$781$	−1.85014			−0.0662033
$782$	−12.3947	+	28.8223i	−0.443234	+	1.03068i
$783$	−8.51549			−0.304319
$784$		−	6.05308i		−	0.216181i
$785$	3.06743	+	3.06743i	0.109481	+	0.109481i
$786$	11.5760			0.412903
$787$	15.7480	+	15.7480i	0.561356	+	0.561356i	0.929693	−	0.368336i	$-0.120072\pi$
$787$	15.7480	+	15.7480i	0.561356	+	0.561356i	−0.368336	+	0.929693i	$0.620072\pi$
$788$	8.23069	−	8.23069i	0.293206	−	0.293206i
$789$	−15.5898	+	15.5898i	−0.555013	+	0.555013i
$790$			1.98289i			0.0705480i
$791$		−	9.31486i		−	0.331198i
$792$	0.707107	−	0.707107i	0.0251259	−	0.0251259i
$793$	−3.31985	+	3.31985i	−0.117891	+	0.117891i
$794$	10.8401	+	10.8401i	0.384702	+	0.384702i
$795$	1.74683			0.0619535
$796$	−2.50001	−	2.50001i	−0.0886105	−	0.0886105i
$797$			55.6550i			1.97140i	0.168505	+	0.985701i	$0.446106\pi$
$797$			55.6550i			1.97140i	−0.168505	+	0.985701i	$0.553894\pi$
$798$	−0.400781			−0.0141875
$799$	−14.3253	−	35.9423i	−0.506792	−	1.27155i
$800$	4.14653			0.146602
$801$		−	15.6166i		−	0.551786i
$802$	13.1527	+	13.1527i	0.464437	+	0.464437i
$803$	−7.55795			−0.266714
$804$	2.33558	+	2.33558i	0.0823696	+	0.0823696i
$805$	−17.9592	+	17.9592i	−0.632980	+	0.632980i
$806$	−12.0727	+	12.0727i	−0.425242	+	0.425242i
$807$		−	1.11803i		−	0.0393565i
$808$			18.1254i			0.637648i
$809$	−8.71954	+	8.71954i	−0.306563	+	0.306563i	−0.843575	−	0.537012i	$-0.819553\pi$
$809$	−8.71954	+	8.71954i	−0.306563	+	0.306563i	0.537012	+	0.843575i	$0.319553\pi$
$810$	0.653251	−	0.653251i	0.0229529	−	0.0229529i
$811$	31.4040	+	31.4040i	1.10274	+	1.10274i	0.994079	+	0.108664i	$0.0346573\pi$
$811$	31.4040	+	31.4040i	1.10274	+	1.10274i	0.108664	+	0.994079i	$0.465343\pi$
$812$	−30.7657			−1.07966
$813$	22.1627	+	22.1627i	0.777280	+	0.777280i
$814$		−	2.39487i		−	0.0839403i
$815$	−8.65725			−0.303250
$816$	1.62887	−	3.78772i	0.0570217	−	0.132597i
$817$	0.150378			0.00526107
$818$		−	25.9081i		−	0.905856i
$819$	11.6315	+	11.6315i	0.406437	+	0.406437i
$820$	9.36222			0.326943
$821$	−28.3079	−	28.3079i	−0.987954	−	0.987954i	0.0119746	−	0.999928i	$-0.496188\pi$
$821$	−28.3079	−	28.3079i	−0.987954	−	0.987954i	−0.999928	+	0.0119746i	$0.996188\pi$
$822$	5.58342	−	5.58342i	0.194744	−	0.194744i
$823$	35.8500	−	35.8500i	1.24965	−	1.24965i	0.293780	−	0.955873i	$-0.405087\pi$
$823$	35.8500	−	35.8500i	1.24965	−	1.24965i	0.955873	−	0.293780i	$-0.0949134\pi$
$824$		−	15.5369i		−	0.541255i
$825$			4.14653i			0.144364i
$826$	−25.2749	+	25.2749i	−0.879428	+	0.879428i
$827$	3.67953	−	3.67953i	0.127950	−	0.127950i	−0.640232	−	0.768182i	$-0.721162\pi$
$827$	3.67953	−	3.67953i	0.127950	−	0.127950i	0.768182	+	0.640232i	$0.221162\pi$
$828$	−5.38067	−	5.38067i	−0.186991	−	0.186991i
$829$	20.7954			0.722255			0.361128	−	0.932516i	$-0.382392\pi$
$829$	20.7954			0.722255			0.361128	+	0.932516i	$0.382392\pi$
$830$	4.76686	+	4.76686i	0.165460	+	0.165460i
$831$			10.8859i			0.377626i
$832$	4.55296			0.157846
$833$	23.1839	−	9.24025i	0.803275	−	0.320156i
$834$	−10.3993			−0.360100
$835$			9.36896i			0.324226i
$836$	−0.0784396	−	0.0784396i	−0.00271289	−	0.00271289i
$837$	−3.74995			−0.129617
$838$	13.7667	+	13.7667i	0.475562	+	0.475562i
$839$	1.41618	−	1.41618i	0.0488920	−	0.0488920i	−0.682238	−	0.731130i	$-0.738993\pi$
$839$	1.41618	−	1.41618i	0.0488920	−	0.0488920i	0.731130	+	0.682238i	$0.238993\pi$
$840$	2.36013	−	2.36013i	0.0814323	−	0.0814323i
$841$			43.5136i			1.50047i
$842$			19.4284i			0.669546i
$843$	21.9449	−	21.9449i	0.755821	−	0.755821i
$844$	−6.97436	+	6.97436i	−0.240067	+	0.240067i
$845$	5.04928	+	5.04928i	0.173701	+	0.173701i
$846$	9.38416			0.322634
$847$	2.55471	+	2.55471i	0.0877808	+	0.0877808i
$848$			1.89084i			0.0649317i
$849$	0.618579			0.0212296
$850$	6.32983	+	15.8816i	0.217111	+	0.544735i
$851$	−18.2236			−0.624696
$852$		−	1.85014i		−	0.0633849i
$853$	26.9966	+	26.9966i	0.924346	+	0.924346i	0.997333	−	0.0729870i	$-0.0232531\pi$
$853$	26.9966	+	26.9966i	0.924346	+	0.924346i	−0.0729870	+	0.997333i	$0.523253\pi$
$854$	−3.72559			−0.127487
$855$	−0.0724654	−	0.0724654i	−0.00247826	−	0.00247826i
$856$	2.09773	−	2.09773i	0.0716988	−	0.0716988i
$857$	14.9267	−	14.9267i	0.509885	−	0.509885i	−0.404606	−	0.914491i	$-0.632591\pi$
$857$	14.9267	−	14.9267i	0.509885	−	0.509885i	0.914491	+	0.404606i	$0.132591\pi$
$858$			4.55296i			0.155436i
$859$			17.0212i			0.580755i	0.956912	+	0.290377i	$0.0937808\pi$
$859$			17.0212i			0.580755i	−0.956912	+	0.290377i	$0.906219\pi$
$860$	−0.885554	+	0.885554i	−0.0301971	+	0.0301971i
$861$	−25.8896	+	25.8896i	−0.882315	+	0.882315i
$862$	−3.77731	−	3.77731i	−0.128656	−	0.128656i
$863$	−11.0537			−0.376271			−0.188135	−	0.982143i	$-0.560244\pi$
$863$	−11.0537			−0.376271			−0.188135	+	0.982143i	$0.560244\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$			5.92283i			0.201382i
$866$	−30.9024			−1.05011
$867$	16.9939	+	0.456625i	0.577142	+	0.0155078i
$868$	−13.5482			−0.459856
$869$		−	2.14636i		−	0.0728104i
$870$	−5.56275	−	5.56275i	−0.188595	−	0.188595i
$871$	−15.0385			−0.509559
$872$	−7.39851	−	7.39851i	−0.250545	−	0.250545i
$873$	−1.28422	+	1.28422i	−0.0434644	+	0.0434644i
$874$	−0.596879	+	0.596879i	−0.0201897	+	0.0201897i
$875$			30.5287i			1.03206i
$876$		−	7.55795i		−	0.255360i
$877$	7.27783	−	7.27783i	0.245755	−	0.245755i	−0.573471	−	0.819226i	$-0.694404\pi$
$877$	7.27783	−	7.27783i	0.245755	−	0.245755i	0.819226	+	0.573471i	$0.194404\pi$
$878$	−25.6228	+	25.6228i	−0.864727	+	0.864727i
$879$	17.7784	+	17.7784i	0.599650	+	0.599650i
$880$	0.923837			0.0311425
$881$	−3.10019	−	3.10019i	−0.104448	−	0.104448i	0.652952	−	0.757400i	$-0.273530\pi$
$881$	−3.10019	−	3.10019i	−0.104448	−	0.104448i	−0.757400	+	0.652952i	$0.773530\pi$
$882$			6.05308i			0.203818i
$883$	21.5270			0.724442			0.362221	−	0.932092i	$-0.382019\pi$
$883$	21.5270			0.724442			0.362221	+	0.932092i	$0.382019\pi$
$884$	6.95027	+	17.4383i	0.233763	+	0.586514i
$885$	−9.13995			−0.307236
$886$		−	24.8379i		−	0.834444i
$887$	25.1473	+	25.1473i	0.844364	+	0.844364i	0.989423	−	0.145059i	$-0.0463371\pi$
$887$	25.1473	+	25.1473i	0.844364	+	0.844364i	−0.145059	+	0.989423i	$0.546337\pi$
$888$	2.39487			0.0803667
$889$	−39.3873	−	39.3873i	−1.32101	−	1.32101i
$890$	10.2016	−	10.2016i	0.341957	−	0.341957i
$891$	−0.707107	+	0.707107i	−0.0236890	+	0.0236890i
$892$		−	6.66357i		−	0.223113i
$893$		−	1.04099i		−	0.0348353i
$894$	−9.45031	+	9.45031i	−0.316065	+	0.316065i
$895$	−4.16820	+	4.16820i	−0.139328	+	0.139328i
$896$	2.55471	+	2.55471i	0.0853468	+	0.0853468i
$897$	34.6454			1.15677
$898$	26.5532	+	26.5532i	0.886091	+	0.886091i
$899$			31.9326i			1.06501i
$900$	−4.14653			−0.138218
$901$	−7.24211	+	2.88644i	−0.241270	+	0.0961612i
$902$	−10.1341			−0.337427
$903$		−	4.89769i		−	0.162985i
$904$	1.82308	+	1.82308i	0.0606346	+	0.0606346i
$905$	−16.6174			−0.552381
$906$	−9.65334	−	9.65334i	−0.320711	−	0.320711i
$907$	2.76608	−	2.76608i	0.0918461	−	0.0918461i	−0.659691	−	0.751537i	$-0.729313\pi$
$907$	2.76608	−	2.76608i	0.0918461	−	0.0918461i	0.751537	+	0.659691i	$0.229313\pi$
$908$	1.45046	−	1.45046i	0.0481351	−	0.0481351i
$909$		−	18.1254i		−	0.601180i
$910$			15.1966i			0.503761i
$911$	−8.92571	+	8.92571i	−0.295722	+	0.295722i	−0.839336	−	0.543614i	$-0.817056\pi$
$911$	−8.92571	+	8.92571i	−0.295722	+	0.295722i	0.543614	+	0.839336i	$0.317056\pi$
$912$	0.0784396	−	0.0784396i	0.00259739	−	0.00259739i
$913$	−5.15985	−	5.15985i	−0.170766	−	0.170766i
$914$	−2.27195			−0.0751495
$915$	−0.673626	−	0.673626i	−0.0222694	−	0.0222694i
$916$		−	15.6073i		−	0.515681i
$917$	−41.8230			−1.38112
$918$	−1.62887	+	3.78772i	−0.0537606	+	0.125013i
$919$	−42.3850			−1.39815			−0.699076	−	0.715047i	$-0.746405\pi$
$919$	−42.3850			−1.39815			−0.699076	+	0.715047i	$0.746405\pi$
$920$		−	7.02985i		−	0.231767i
$921$	−2.89674	−	2.89674i	−0.0954508	−	0.0954508i
$922$	25.0321			0.824388
$923$	5.95641	+	5.95641i	0.196058	+	0.196058i
$924$	−2.55471	+	2.55471i	−0.0840438	+	0.0840438i
$925$	−7.02186	+	7.02186i	−0.230877	+	0.230877i
$926$		−	34.9062i		−	1.14709i
$927$			15.5369i			0.510300i
$928$	6.02136	−	6.02136i	0.197661	−	0.197661i
$929$	−6.56937	+	6.56937i	−0.215534	+	0.215534i	−0.806613	−	0.591079i	$-0.798702\pi$
$929$	−6.56937	+	6.56937i	−0.215534	+	0.215534i	0.591079	+	0.806613i	$0.298702\pi$
$930$	−2.44966	−	2.44966i	−0.0803274	−	0.0803274i
$931$	0.671470			0.0220065
$932$	−16.5888	−	16.5888i	−0.543383	−	0.543383i
$933$			28.8982i			0.946086i
$934$	6.18677			0.202437
$935$	1.41027	+	3.53839i	0.0461208	+	0.115718i
$936$	−4.55296			−0.148818
$937$		−	6.56644i		−	0.214516i	−0.994231	−	0.107258i	$-0.965793\pi$
$937$		−	6.56644i		−	0.214516i	0.994231	−	0.107258i	$-0.0342071\pi$
$938$	−8.43823	−	8.43823i	−0.275518	−	0.275518i
$939$	−18.7462			−0.611758
$940$	6.13021	+	6.13021i	0.199945	+	0.199945i
$941$	37.9785	−	37.9785i	1.23807	−	1.23807i	0.277274	−	0.960791i	$-0.410569\pi$
$941$	37.9785	−	37.9785i	1.23807	−	1.23807i	0.960791	−	0.277274i	$-0.0894310\pi$
$942$	3.32032	−	3.32032i	0.108182	−	0.108182i
$943$			77.1143i			2.51119i
$944$		−	9.89347i		−	0.322005i
$945$	−2.36013	+	2.36013i	−0.0767751	+	0.0767751i
$946$	0.958561	−	0.958561i	0.0311655	−	0.0311655i
$947$	−22.4129	−	22.4129i	−0.728322	−	0.728322i	0.241964	−	0.970285i	$-0.422209\pi$
$947$	−22.4129	−	22.4129i	−0.728322	−	0.728322i	−0.970285	+	0.241964i	$0.922209\pi$
$948$	2.14636			0.0697106
$949$	24.3323	+	24.3323i	0.789860	+	0.789860i
$950$			0.459976i			0.0149236i
$951$	−10.6422			−0.345096
$952$	−5.88493	+	13.6847i	−0.190732	+	0.443522i
$953$	17.5903			0.569806			0.284903	−	0.958556i	$-0.408039\pi$
$953$	17.5903			0.569806			0.284903	+	0.958556i	$0.408039\pi$
$954$		−	1.89084i		−	0.0612182i
$955$	−7.06726	−	7.06726i	−0.228691	−	0.228691i
$956$	1.40481			0.0454349
$957$	6.02136	+	6.02136i	0.194643	+	0.194643i
$958$	14.1647	−	14.1647i	0.457639	−	0.457639i
$959$	−20.1724	+	20.1724i	−0.651400	+	0.651400i
$960$			0.923837i			0.0298167i
$961$		−	16.9379i		−	0.546384i
$962$	−7.71013	+	7.71013i	−0.248584	+	0.248584i
$963$	−2.09773	+	2.09773i	−0.0675983	+	0.0675983i
$964$	−10.1828	−	10.1828i	−0.327964	−	0.327964i
$965$	−4.86178			−0.156506
$966$	19.4398	+	19.4398i	0.625466	+	0.625466i
$967$		−	44.6949i		−	1.43729i	−0.695376	−	0.718646i	$-0.744762\pi$
$967$		−	44.6949i		−	1.43729i	0.695376	−	0.718646i	$-0.255238\pi$
$968$	−1.00000			−0.0321412
$969$	0.420173	+	0.180691i	0.0134979	+	0.00580462i
$970$	−1.67784			−0.0538722
$971$		−	27.8166i		−	0.892678i	−0.894864	−	0.446339i	$-0.852727\pi$
$971$		−	27.8166i		−	0.892678i	0.894864	−	0.446339i	$-0.147273\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$	37.5718			1.20450
$974$	−19.3387	−	19.3387i	−0.619652	−	0.619652i
$975$	13.3495	−	13.3495i	0.427525	−	0.427525i
$976$	0.729162	−	0.729162i	0.0233399	−	0.0233399i
$977$		−	40.5109i		−	1.29606i	−0.761616	−	0.648028i	$-0.775594\pi$
$977$		−	40.5109i		−	1.29606i	0.761616	−	0.648028i	$-0.224406\pi$
$978$			9.37098i			0.299651i
$979$	−11.0426	+	11.0426i	−0.352924	+	0.352924i
$980$	−3.95418	+	3.95418i	−0.126312	+	0.126312i
$981$	7.39851	+	7.39851i	0.236216	+	0.236216i
$982$	−1.70348			−0.0543602
$983$	−38.8736	−	38.8736i	−1.23988	−	1.23988i	−0.960051	−	0.279824i	$-0.909724\pi$
$983$	−38.8736	−	38.8736i	−1.23988	−	1.23988i	−0.279824	−	0.960051i	$-0.590276\pi$
$984$		−	10.1341i		−	0.323062i
$985$	−10.7534			−0.342632
$986$	32.2543	+	13.8706i	1.02719	+	0.441730i
$987$	−33.9041			−1.07918
$988$			0.505062i			0.0160682i
$989$	−7.29409	−	7.29409i	−0.231938	−	0.231938i
$990$	−0.923837			−0.0293615
$991$	11.2737	+	11.2737i	0.358121	+	0.358121i	0.863120	−	0.504999i	$-0.168507\pi$
$991$	11.2737	+	11.2737i	0.358121	+	0.358121i	−0.504999	+	0.863120i	$0.668507\pi$
$992$	2.65161	−	2.65161i	0.0841888	−	0.0841888i
$993$	−9.19975	+	9.19975i	−0.291945	+	0.291945i
$994$			6.68439i			0.212016i
$995$			3.26627i			0.103548i
$996$	5.15985	−	5.15985i	0.163496	−	0.163496i
$997$	8.89391	−	8.89391i	0.281673	−	0.281673i	−0.552103	−	0.833776i	$-0.686174\pi$
$997$	8.89391	−	8.89391i	0.281673	−	0.281673i	0.833776	+	0.552103i	$0.186174\pi$
$998$	18.3515	+	18.3515i	0.580907	+	0.580907i
$999$	−2.39487			−0.0757704

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1122.2.l.g.727.3	yes	20
17.4	even	4	inner	1122.2.l.g.463.3	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1122.2.l.g.463.3	✓	20	17.4	even	4	inner
1122.2.l.g.727.3	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1122 = 2 \cdot 3 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1122.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(0.653251 + 0.653251i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-2.55471 + 2.55471i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(0.653251 + 0.653251i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-2.55471 + 2.55471i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(-0.653251 + 0.653251i) q^{10} +(0.707107 - 0.707107i) q^{11} +(0.707107 + 0.707107i) q^{12} -4.55296 q^{13} +(-2.55471 - 2.55471i) q^{14} -0.923837i q^{15} +1.00000 q^{16} +(1.52654 + 3.83010i) q^{17} -1.00000 q^{18} +0.110930i q^{19} +(-0.653251 - 0.653251i) q^{20} +3.61290 q^{21} +(0.707107 + 0.707107i) q^{22} +(5.38067 - 5.38067i) q^{23} +(-0.707107 + 0.707107i) q^{24} -4.14653i q^{25} -4.55296i q^{26} +(0.707107 - 0.707107i) q^{27} +(2.55471 - 2.55471i) q^{28} +(-6.02136 - 6.02136i) q^{29} +0.923837 q^{30} +(-2.65161 - 2.65161i) q^{31} +1.00000i q^{32} -1.00000 q^{33} +(-3.83010 + 1.52654i) q^{34} -3.33773 q^{35} -1.00000i q^{36} +(-1.69343 - 1.69343i) q^{37} -0.110930 q^{38} +(3.21943 + 3.21943i) q^{39} +(0.653251 - 0.653251i) q^{40} +(-7.16587 + 7.16587i) q^{41} +3.61290i q^{42} -1.35561i q^{43} +(-0.707107 + 0.707107i) q^{44} +(-0.653251 + 0.653251i) q^{45} +(5.38067 + 5.38067i) q^{46} -9.38416 q^{47} +(-0.707107 - 0.707107i) q^{48} -6.05308i q^{49} +4.14653 q^{50} +(1.62887 - 3.78772i) q^{51} +4.55296 q^{52} +1.89084i q^{53} +(0.707107 + 0.707107i) q^{54} +0.923837 q^{55} +(2.55471 + 2.55471i) q^{56} +(0.0784396 - 0.0784396i) q^{57} +(6.02136 - 6.02136i) q^{58} -9.89347i q^{59} +0.923837i q^{60} +(0.729162 - 0.729162i) q^{61} +(2.65161 - 2.65161i) q^{62} +(-2.55471 - 2.55471i) q^{63} -1.00000 q^{64} +(-2.97423 - 2.97423i) q^{65} -1.00000i q^{66} +3.30301 q^{67} +(-1.52654 - 3.83010i) q^{68} -7.60941 q^{69} -3.33773i q^{70} +(-1.30825 - 1.30825i) q^{71} +1.00000 q^{72} +(-5.34428 - 5.34428i) q^{73} +(1.69343 - 1.69343i) q^{74} +(-2.93204 + 2.93204i) q^{75} -0.110930i q^{76} +3.61290i q^{77} +(-3.21943 + 3.21943i) q^{78} +(1.51771 - 1.51771i) q^{79} +(0.653251 + 0.653251i) q^{80} -1.00000 q^{81} +(-7.16587 - 7.16587i) q^{82} -7.29713i q^{83} -3.61290 q^{84} +(-1.50481 + 3.49923i) q^{85} +1.35561 q^{86} +8.51549i q^{87} +(-0.707107 - 0.707107i) q^{88} -15.6166 q^{89} +(-0.653251 - 0.653251i) q^{90} +(11.6315 - 11.6315i) q^{91} +(-5.38067 + 5.38067i) q^{92} +3.74995i q^{93} -9.38416i q^{94} +(-0.0724654 + 0.0724654i) q^{95} +(0.707107 - 0.707107i) q^{96} +(1.28422 + 1.28422i) q^{97} +6.05308 q^{98} +(0.707107 + 0.707107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{4} - 4 q^{5}+O(q^{10}) \) 20 * q - 20 * q^4 - 4 * q^5	\( 20 q - 20 q^{4} - 4 q^{5} + 4 q^{10} + 20 q^{16} - 12 q^{17} - 20 q^{18} + 4 q^{20} + 16 q^{23} + 4 q^{29} - 8 q^{31} - 20 q^{33} + 16 q^{35} - 20 q^{37} + 8 q^{39} - 4 q^{40} + 20 q^{41} + 4 q^{45} + 16 q^{46} - 16 q^{47} - 68 q^{50} + 8 q^{57} - 4 q^{58} - 20 q^{61} + 8 q^{62} - 20 q^{64} + 8 q^{65} - 48 q^{67} + 12 q^{68} - 32 q^{71} + 20 q^{72} + 20 q^{73} + 20 q^{74} - 8 q^{75} - 8 q^{78} - 16 q^{79} - 4 q^{80} - 20 q^{81} + 20 q^{82} - 4 q^{85} - 16 q^{86} + 4 q^{90} + 88 q^{91} - 16 q^{92} - 48 q^{95} + 4 q^{97} + 36 q^{98}+O(q^{100}) \) 20 * q - 20 * q^4 - 4 * q^5 + 4 * q^10 + 20 * q^16 - 12 * q^17 - 20 * q^18 + 4 * q^20 + 16 * q^23 + 4 * q^29 - 8 * q^31 - 20 * q^33 + 16 * q^35 - 20 * q^37 + 8 * q^39 - 4 * q^40 + 20 * q^41 + 4 * q^45 + 16 * q^46 - 16 * q^47 - 68 * q^50 + 8 * q^57 - 4 * q^58 - 20 * q^61 + 8 * q^62 - 20 * q^64 + 8 * q^65 - 48 * q^67 + 12 * q^68 - 32 * q^71 + 20 * q^72 + 20 * q^73 + 20 * q^74 - 8 * q^75 - 8 * q^78 - 16 * q^79 - 4 * q^80 - 20 * q^81 + 20 * q^82 - 4 * q^85 - 16 * q^86 + 4 * q^90 + 88 * q^91 - 16 * q^92 - 48 * q^95 + 4 * q^97 + 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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