LMFDB - Embedded newform 1122.2.l.g.727.8

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			727.8
Root			$-0.590127i$ of defining polynomial
Character	$\chi$	$=$	1122.727
Dual form			1122.2.l.g.463.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-0.105899 - 0.105899i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(2.56507 - 2.56507i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-0.105899 - 0.105899i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(2.56507 - 2.56507i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(0.105899 - 0.105899i) q^{10} +(-0.707107 + 0.707107i) q^{11} +(-0.707107 - 0.707107i) q^{12} +2.98747 q^{13} +(2.56507 + 2.56507i) q^{14} -0.149764i q^{15} +1.00000 q^{16} +(1.57958 - 3.80853i) q^{17} -1.00000 q^{18} -5.82626i q^{19} +(0.105899 + 0.105899i) q^{20} +3.62756 q^{21} +(-0.707107 - 0.707107i) q^{22} +(-1.96771 + 1.96771i) q^{23} +(0.707107 - 0.707107i) q^{24} -4.97757i q^{25} +2.98747i q^{26} +(-0.707107 + 0.707107i) q^{27} +(-2.56507 + 2.56507i) q^{28} +(-2.44858 - 2.44858i) q^{29} +0.149764 q^{30} +(5.64415 + 5.64415i) q^{31} +1.00000i q^{32} -1.00000 q^{33} +(3.80853 + 1.57958i) q^{34} -0.543276 q^{35} -1.00000i q^{36} +(5.60260 + 5.60260i) q^{37} +5.82626 q^{38} +(2.11246 + 2.11246i) q^{39} +(-0.105899 + 0.105899i) q^{40} +(0.359909 - 0.359909i) q^{41} +3.62756i q^{42} -7.17235i q^{43} +(0.707107 - 0.707107i) q^{44} +(0.105899 - 0.105899i) q^{45} +(-1.96771 - 1.96771i) q^{46} +9.58204 q^{47} +(0.707107 + 0.707107i) q^{48} -6.15917i q^{49} +4.97757 q^{50} +(3.80997 - 1.57610i) q^{51} -2.98747 q^{52} +0.360811i q^{53} +(-0.707107 - 0.707107i) q^{54} +0.149764 q^{55} +(-2.56507 - 2.56507i) q^{56} +(4.11979 - 4.11979i) q^{57} +(2.44858 - 2.44858i) q^{58} +7.74214i q^{59} +0.149764i q^{60} +(-3.43942 + 3.43942i) q^{61} +(-5.64415 + 5.64415i) q^{62} +(2.56507 + 2.56507i) q^{63} -1.00000 q^{64} +(-0.316369 - 0.316369i) q^{65} -1.00000i q^{66} -3.05659 q^{67} +(-1.57958 + 3.80853i) q^{68} -2.78276 q^{69} -0.543276i q^{70} +(-2.21060 - 2.21060i) q^{71} +1.00000 q^{72} +(6.92743 + 6.92743i) q^{73} +(-5.60260 + 5.60260i) q^{74} +(3.51967 - 3.51967i) q^{75} +5.82626i q^{76} +3.62756i q^{77} +(-2.11246 + 2.11246i) q^{78} +(-1.61324 + 1.61324i) q^{79} +(-0.105899 - 0.105899i) q^{80} -1.00000 q^{81} +(0.359909 + 0.359909i) q^{82} +11.4092i q^{83} -3.62756 q^{84} +(-0.570596 + 0.236043i) q^{85} +7.17235 q^{86} -3.46282i q^{87} +(0.707107 + 0.707107i) q^{88} -12.9576 q^{89} +(0.105899 + 0.105899i) q^{90} +(7.66306 - 7.66306i) q^{91} +(1.96771 - 1.96771i) q^{92} +7.98203i q^{93} +9.58204i q^{94} +(-0.616995 + 0.616995i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(1.94936 + 1.94936i) q^{97} +6.15917 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
$5$	−0.105899	−	0.105899i	−0.0473594	−	0.0473594i	0.683030	−	0.730390i	$-0.260662\pi$
$5$	−0.105899	−	0.105899i	−0.0473594	−	0.0473594i	−0.730390	+	0.683030i	$0.760662\pi$
$6$	−0.707107	+	0.707107i	−0.288675	+	0.288675i
$7$	2.56507	−	2.56507i	0.969505	−	0.969505i	−0.0300432	−	0.999549i	$-0.509564\pi$
$7$	2.56507	−	2.56507i	0.969505	−	0.969505i	0.999549	+	0.0300432i	$0.00956449\pi$
$8$		−	1.00000i		−	0.353553i
$9$			1.00000i			0.333333i
$10$	0.105899	−	0.105899i	0.0334882	−	0.0334882i
$11$	−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
$13$	2.98747			0.828574			0.414287	−	0.910146i	$-0.364031\pi$
$13$	2.98747			0.828574			0.414287	+	0.910146i	$0.364031\pi$
$14$	2.56507	+	2.56507i	0.685544	+	0.685544i
$15$		−	0.149764i		−	0.0386688i
$16$	1.00000			0.250000
$17$	1.57958	−	3.80853i	0.383106	−	0.923705i
$17$	1.57958	−	3.80853i	0.383106	−	0.923705i
$18$	−1.00000			−0.235702
$19$		−	5.82626i		−	1.33664i	−0.743876	−	0.668318i	$-0.767015\pi$
$19$		−	5.82626i		−	1.33664i	0.743876	−	0.668318i	$-0.232985\pi$
$20$	0.105899	+	0.105899i	0.0236797	+	0.0236797i
$21$	3.62756			0.791598
$22$	−0.707107	−	0.707107i	−0.150756	−	0.150756i
$23$	−1.96771	+	1.96771i	−0.410296	+	0.410296i	−0.881842	−	0.471545i	$-0.843696\pi$
$23$	−1.96771	+	1.96771i	−0.410296	+	0.410296i	0.471545	+	0.881842i	$0.343696\pi$
$24$	0.707107	−	0.707107i	0.144338	−	0.144338i
$25$		−	4.97757i		−	0.995514i
$26$			2.98747i			0.585890i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−2.56507	+	2.56507i	−0.484753	+	0.484753i
$29$	−2.44858	−	2.44858i	−0.454690	−	0.454690i	0.442218	−	0.896908i	$-0.354192\pi$
$29$	−2.44858	−	2.44858i	−0.454690	−	0.454690i	−0.896908	+	0.442218i	$0.854192\pi$
$30$	0.149764			0.0273430
$31$	5.64415	+	5.64415i	1.01372	+	1.01372i	0.999905	+	0.0138141i	$0.00439731\pi$
$31$	5.64415	+	5.64415i	1.01372	+	1.01372i	0.0138141	+	0.999905i	$0.495603\pi$
$32$			1.00000i			0.176777i
$33$	−1.00000			−0.174078
$34$	3.80853	+	1.57958i	0.653158	+	0.270897i
$35$	−0.543276			−0.0918305
$36$		−	1.00000i		−	0.166667i
$37$	5.60260	+	5.60260i	0.921061	+	0.921061i	0.997105	−	0.0760435i	$-0.0242288\pi$
$37$	5.60260	+	5.60260i	0.921061	+	0.921061i	−0.0760435	+	0.997105i	$0.524229\pi$
$38$	5.82626			0.945144
$39$	2.11246	+	2.11246i	0.338264	+	0.338264i
$40$	−0.105899	+	0.105899i	−0.0167441	+	0.0167441i
$41$	0.359909	−	0.359909i	0.0562084	−	0.0562084i	−0.678444	−	0.734652i	$-0.737345\pi$
$41$	0.359909	−	0.359909i	0.0562084	−	0.0562084i	0.734652	+	0.678444i	$0.237345\pi$
$42$			3.62756i			0.559744i
$43$		−	7.17235i		−	1.09377i	−0.837207	−	0.546887i	$-0.815813\pi$
$43$		−	7.17235i		−	1.09377i	0.837207	−	0.546887i	$-0.184187\pi$
$44$	0.707107	−	0.707107i	0.106600	−	0.106600i
$45$	0.105899	−	0.105899i	0.0157865	−	0.0157865i
$46$	−1.96771	−	1.96771i	−0.290123	−	0.290123i
$47$	9.58204			1.39768			0.698842	−	0.715276i	$-0.253699\pi$
$47$	9.58204			1.39768			0.698842	+	0.715276i	$0.253699\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$		−	6.15917i		−	0.879881i
$50$	4.97757			0.703935
$51$	3.80997	−	1.57610i	0.533503	−	0.220699i
$52$	−2.98747			−0.414287
$53$			0.360811i			0.0495612i	0.999693	+	0.0247806i	$0.00788871\pi$
$53$			0.360811i			0.0495612i	−0.999693	+	0.0247806i	$0.992111\pi$
$54$	−0.707107	−	0.707107i	−0.0962250	−	0.0962250i
$55$	0.149764			0.0201941
$56$	−2.56507	−	2.56507i	−0.342772	−	0.342772i
$57$	4.11979	−	4.11979i	0.545679	−	0.545679i
$58$	2.44858	−	2.44858i	0.321514	−	0.321514i
$59$			7.74214i			1.00794i	0.863721	+	0.503970i	$0.168128\pi$
$59$			7.74214i			1.00794i	−0.863721	+	0.503970i	$0.831872\pi$
$60$			0.149764i			0.0193344i
$61$	−3.43942	+	3.43942i	−0.440372	+	0.440372i	−0.892137	−	0.451765i	$-0.850795\pi$
$61$	−3.43942	+	3.43942i	−0.440372	+	0.440372i	0.451765	+	0.892137i	$0.350795\pi$
$62$	−5.64415	+	5.64415i	−0.716807	+	0.716807i
$63$	2.56507	+	2.56507i	0.323168	+	0.323168i
$64$	−1.00000			−0.125000
$65$	−0.316369	−	0.316369i	−0.0392408	−	0.0392408i
$66$		−	1.00000i		−	0.123091i
$67$	−3.05659			−0.373422			−0.186711	−	0.982415i	$-0.559783\pi$
$67$	−3.05659			−0.373422			−0.186711	+	0.982415i	$0.559783\pi$
$68$	−1.57958	+	3.80853i	−0.191553	+	0.461852i
$69$	−2.78276			−0.335006
$70$		−	0.543276i		−	0.0649339i
$71$	−2.21060	−	2.21060i	−0.262350	−	0.262350i	0.563658	−	0.826008i	$-0.309393\pi$
$71$	−2.21060	−	2.21060i	−0.262350	−	0.262350i	−0.826008	+	0.563658i	$0.809393\pi$
$72$	1.00000			0.117851
$73$	6.92743	+	6.92743i	0.810795	+	0.810795i	0.984753	−	0.173958i	$-0.0556558\pi$
$73$	6.92743	+	6.92743i	0.810795	+	0.810795i	−0.173958	+	0.984753i	$0.555656\pi$
$74$	−5.60260	+	5.60260i	−0.651288	+	0.651288i
$75$	3.51967	−	3.51967i	0.406417	−	0.406417i
$76$			5.82626i			0.668318i
$77$			3.62756i			0.413398i
$78$	−2.11246	+	2.11246i	−0.239189	+	0.239189i
$79$	−1.61324	+	1.61324i	−0.181504	+	0.181504i	−0.792011	−	0.610507i	$-0.790966\pi$
$79$	−1.61324	+	1.61324i	−0.181504	+	0.181504i	0.610507	+	0.792011i	$0.290966\pi$
$80$	−0.105899	−	0.105899i	−0.0118399	−	0.0118399i
$81$	−1.00000			−0.111111
$82$	0.359909	+	0.359909i	0.0397453	+	0.0397453i
$83$			11.4092i			1.25233i	0.779692	+	0.626163i	$0.215375\pi$
$83$			11.4092i			1.25233i	−0.779692	+	0.626163i	$0.784625\pi$
$84$	−3.62756			−0.395799
$85$	−0.570596	+	0.236043i	−0.0618898	+	0.0256025i
$86$	7.17235			0.773415
$87$		−	3.46282i		−	0.371253i
$88$	0.707107	+	0.707107i	0.0753778	+	0.0753778i
$89$	−12.9576			−1.37350			−0.686749	−	0.726894i	$-0.740963\pi$
$89$	−12.9576			−1.37350			−0.686749	+	0.726894i	$0.740963\pi$
$90$	0.105899	+	0.105899i	0.0111627	+	0.0111627i
$91$	7.66306	−	7.66306i	0.803307	−	0.803307i
$92$	1.96771	−	1.96771i	0.205148	−	0.205148i
$93$			7.98203i			0.827698i
$94$			9.58204i			0.988312i
$95$	−0.616995	+	0.616995i	−0.0633023	+	0.0633023i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$	1.94936	+	1.94936i	0.197928	+	0.197928i	0.799111	−	0.601183i	$-0.205304\pi$
$97$	1.94936	+	1.94936i	0.197928	+	0.197928i	−0.601183	+	0.799111i	$0.705304\pi$
$98$	6.15917			0.622170
$99$	−0.707107	−	0.707107i	−0.0710669	−	0.0710669i
$100$			4.97757i			0.497757i
$101$	−6.21450			−0.618366			−0.309183	−	0.951003i	$-0.600055\pi$
$101$	−6.21450			−0.618366			−0.309183	+	0.951003i	$0.600055\pi$
$102$	1.57610	+	3.80997i	0.156057	+	0.377244i
$103$	−1.59372			−0.157034			−0.0785170	−	0.996913i	$-0.525019\pi$
$103$	−1.59372			−0.157034			−0.0785170	+	0.996913i	$0.525019\pi$
$104$		−	2.98747i		−	0.292945i
$105$	−0.384154	−	0.384154i	−0.0374896	−	0.0374896i
$106$	−0.360811			−0.0350450
$107$	−3.68250	−	3.68250i	−0.356001	−	0.356001i	0.506336	−	0.862336i	$-0.331000\pi$
$107$	−3.68250	−	3.68250i	−0.356001	−	0.356001i	−0.862336	+	0.506336i	$0.831000\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$	5.95837	−	5.95837i	0.570708	−	0.570708i	−0.361618	−	0.932326i	$-0.617776\pi$
$109$	5.95837	−	5.95837i	0.570708	−	0.570708i	0.932326	+	0.361618i	$0.117776\pi$
$110$			0.149764i			0.0142794i
$111$			7.92327i			0.752043i
$112$	2.56507	−	2.56507i	0.242376	−	0.242376i
$113$	−4.30013	+	4.30013i	−0.404522	+	0.404522i	−0.879823	−	0.475301i	$-0.842339\pi$
$113$	−4.30013	+	4.30013i	−0.404522	+	0.404522i	0.475301	+	0.879823i	$0.342339\pi$
$114$	4.11979	+	4.11979i	0.385854	+	0.385854i
$115$	0.416757			0.0388628
$116$	2.44858	+	2.44858i	0.227345	+	0.227345i
$117$			2.98747i			0.276191i
$118$	−7.74214			−0.712722
$119$	−5.71740	−	13.8209i	−0.524114	−	1.26696i
$120$	−0.149764			−0.0136715
$121$		−	1.00000i		−	0.0909091i
$122$	−3.43942	−	3.43942i	−0.311390	−	0.311390i
$123$	0.508988			0.0458939
$124$	−5.64415	−	5.64415i	−0.506859	−	0.506859i
$125$	−1.05661	+	1.05661i	−0.0945064	+	0.0945064i
$126$	−2.56507	+	2.56507i	−0.228515	+	0.228515i
$127$			5.03593i			0.446867i	0.974719	+	0.223433i	$0.0717265\pi$
$127$			5.03593i			0.446867i	−0.974719	+	0.223433i	$0.928274\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	5.07162	−	5.07162i	0.446531	−	0.446531i
$130$	0.316369	−	0.316369i	0.0277474	−	0.0277474i
$131$	4.94617	+	4.94617i	0.432149	+	0.432149i	0.889359	−	0.457210i	$-0.151151\pi$
$131$	4.94617	+	4.94617i	0.432149	+	0.432149i	−0.457210	+	0.889359i	$0.651151\pi$
$132$	1.00000			0.0870388
$133$	−14.9448	−	14.9448i	−1.29588	−	1.29588i
$134$		−	3.05659i		−	0.264049i
$135$	0.149764			0.0128896
$136$	−3.80853	−	1.57958i	−0.326579	−	0.135448i
$137$	10.1318			0.865615			0.432807	−	0.901486i	$-0.357523\pi$
$137$	10.1318			0.865615			0.432807	+	0.901486i	$0.357523\pi$
$138$		−	2.78276i		−	0.236885i
$139$	−14.1411	−	14.1411i	−1.19943	−	1.19943i	−0.974337	−	0.225095i	$-0.927731\pi$
$139$	−14.1411	−	14.1411i	−1.19943	−	1.19943i	−0.225095	−	0.974337i	$-0.572269\pi$
$140$	0.543276			0.0459152
$141$	6.77552	+	6.77552i	0.570602	+	0.570602i
$142$	2.21060	−	2.21060i	0.185509	−	0.185509i
$143$	−2.11246	+	2.11246i	−0.176653	+	0.176653i
$144$			1.00000i			0.0833333i
$145$			0.518604i			0.0430677i
$146$	−6.92743	+	6.92743i	−0.573318	+	0.573318i
$147$	4.35519	−	4.35519i	0.359210	−	0.359210i
$148$	−5.60260	−	5.60260i	−0.460531	−	0.460531i
$149$	11.3247			0.927759			0.463880	−	0.885898i	$-0.346457\pi$
$149$	11.3247			0.927759			0.463880	+	0.885898i	$0.346457\pi$
$150$	3.51967	+	3.51967i	0.287380	+	0.287380i
$151$		−	12.2166i		−	0.994176i	−0.867700	−	0.497088i	$-0.834403\pi$
$151$		−	12.2166i		−	0.994176i	0.867700	−	0.497088i	$-0.165597\pi$
$152$	−5.82626			−0.472572
$153$	3.80853	+	1.57958i	0.307902	+	0.127702i
$154$	−3.62756			−0.292317
$155$		−	1.19542i		−	0.0960183i
$156$	−2.11246	−	2.11246i	−0.169132	−	0.169132i
$157$	−3.10626			−0.247907			−0.123953	−	0.992288i	$-0.539557\pi$
$157$	−3.10626			−0.247907			−0.123953	+	0.992288i	$0.539557\pi$
$158$	−1.61324	−	1.61324i	−0.128342	−	0.128342i
$159$	−0.255132	+	0.255132i	−0.0202333	+	0.0202333i
$160$	0.105899	−	0.105899i	0.00837204	−	0.00837204i
$161$			10.0946i			0.795569i
$162$		−	1.00000i		−	0.0785674i
$163$	3.12893	−	3.12893i	0.245077	−	0.245077i	−0.573870	−	0.818947i	$-0.694558\pi$
$163$	3.12893	−	3.12893i	0.245077	−	0.245077i	0.818947	+	0.573870i	$0.194558\pi$
$164$	−0.359909	+	0.359909i	−0.0281042	+	0.0281042i
$165$	0.105899	+	0.105899i	0.00824422	+	0.00824422i
$166$	−11.4092			−0.885528
$167$	12.0127	+	12.0127i	0.929574	+	0.929574i	0.997678	−	0.0681042i	$-0.0216950\pi$
$167$	12.0127	+	12.0127i	0.929574	+	0.929574i	−0.0681042	+	0.997678i	$0.521695\pi$
$168$		−	3.62756i		−	0.279872i
$169$	−4.07505			−0.313465
$170$	−0.236043	−	0.570596i	−0.0181037	−	0.0437627i
$171$	5.82626			0.445545
$172$			7.17235i			0.546887i
$173$	−13.4728	−	13.4728i	−1.02432	−	1.02432i	−0.999697	−	0.0246187i	$-0.992163\pi$
$173$	−13.4728	−	13.4728i	−1.02432	−	1.02432i	−0.0246187	−	0.999697i	$-0.507837\pi$
$174$	3.46282			0.262515
$175$	−12.7678	−	12.7678i	−0.965156	−	0.965156i
$176$	−0.707107	+	0.707107i	−0.0533002	+	0.0533002i
$177$	−5.47452	+	5.47452i	−0.411490	+	0.411490i
$178$		−	12.9576i		−	0.971210i
$179$			13.9538i			1.04295i	0.853265	+	0.521477i	$0.174619\pi$
$179$			13.9538i			1.04295i	−0.853265	+	0.521477i	$0.825381\pi$
$180$	−0.105899	+	0.105899i	−0.00789324	+	0.00789324i
$181$	−3.41587	+	3.41587i	−0.253899	+	0.253899i	−0.822567	−	0.568668i	$-0.807459\pi$
$181$	−3.41587	+	3.41587i	−0.253899	+	0.253899i	0.568668	+	0.822567i	$0.307459\pi$
$182$	7.66306	+	7.66306i	0.568024	+	0.568024i
$183$	−4.86407			−0.359562
$184$	1.96771	+	1.96771i	0.145062	+	0.145062i
$185$		−	1.18662i		−	0.0872419i
$186$	−7.98203			−0.585271
$187$	1.57610	+	3.80997i	0.115256	+	0.278613i
$188$	−9.58204			−0.698842
$189$			3.62756i			0.263866i
$190$	−0.616995	−	0.616995i	−0.0447615	−	0.0447615i
$191$	−24.0371			−1.73926			−0.869631	−	0.493702i	$-0.835643\pi$
$191$	−24.0371			−1.73926			−0.869631	+	0.493702i	$0.835643\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$	18.8585	−	18.8585i	1.35746	−	1.35746i	0.480426	−	0.877035i	$-0.340482\pi$
$193$	18.8585	−	18.8585i	1.35746	−	1.35746i	0.877035	−	0.480426i	$-0.159518\pi$
$194$	−1.94936	+	1.94936i	−0.139956	+	0.139956i
$195$		−	0.447414i		−	0.0320400i
$196$			6.15917i			0.439941i
$197$	17.7197	−	17.7197i	1.26248	−	1.26248i	0.312585	−	0.949890i	$-0.398805\pi$
$197$	17.7197	−	17.7197i	1.26248	−	1.26248i	0.949890	−	0.312585i	$-0.101195\pi$
$198$	0.707107	−	0.707107i	0.0502519	−	0.0502519i
$199$	3.26632	+	3.26632i	0.231543	+	0.231543i	0.813337	−	0.581794i	$-0.197649\pi$
$199$	3.26632	+	3.26632i	0.231543	+	0.231543i	−0.581794	+	0.813337i	$0.697649\pi$
$200$	−4.97757			−0.351967
$201$	−2.16134	−	2.16134i	−0.152449	−	0.152449i
$202$		−	6.21450i		−	0.437251i
$203$	−12.5616			−0.881649
$204$	−3.80997	+	1.57610i	−0.266752	+	0.110349i
$205$	−0.0762280			−0.00532399
$206$		−	1.59372i		−	0.111040i
$207$	−1.96771	−	1.96771i	−0.136765	−	0.136765i
$208$	2.98747			0.207144
$209$	4.11979	+	4.11979i	0.284972	+	0.284972i
$210$	0.384154	−	0.384154i	0.0265092	−	0.0265092i
$211$	−13.7187	+	13.7187i	−0.944434	+	0.944434i	−0.998535	−	0.0541011i	$-0.982771\pi$
$211$	−13.7187	+	13.7187i	−0.944434	+	0.944434i	0.0541011	+	0.998535i	$0.482771\pi$
$212$		−	0.360811i		−	0.0247806i
$213$		−	3.12626i		−	0.214208i
$214$	3.68250	−	3.68250i	0.251731	−	0.251731i
$215$	−0.759544	+	0.759544i	−0.0518005	+	0.0518005i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	28.9553			1.96561
$218$	5.95837	+	5.95837i	0.403552	+	0.403552i
$219$			9.79687i			0.662011i
$220$	−0.149764			−0.0100971
$221$	4.71896	−	11.3779i	0.317431	−	0.765358i
$222$	−7.92327			−0.531775
$223$		−	11.0446i		−	0.739604i	−0.929111	−	0.369802i	$-0.879426\pi$
$223$		−	11.0446i		−	0.739604i	0.929111	−	0.369802i	$-0.120574\pi$
$224$	2.56507	+	2.56507i	0.171386	+	0.171386i
$225$	4.97757			0.331838
$226$	−4.30013	−	4.30013i	−0.286041	−	0.286041i
$227$	−7.24271	+	7.24271i	−0.480716	+	0.480716i	−0.905360	−	0.424645i	$-0.860399\pi$
$227$	−7.24271	+	7.24271i	−0.480716	+	0.480716i	0.424645	+	0.905360i	$0.360399\pi$
$228$	−4.11979	+	4.11979i	−0.272840	+	0.272840i
$229$			0.817874i			0.0540466i	0.999635	+	0.0270233i	$0.00860284\pi$
$229$			0.817874i			0.0540466i	−0.999635	+	0.0270233i	$0.991397\pi$
$230$			0.416757i			0.0274802i
$231$	−2.56507	+	2.56507i	−0.168769	+	0.168769i
$232$	−2.44858	+	2.44858i	−0.160757	+	0.160757i
$233$	17.8135	+	17.8135i	1.16700	+	1.16700i	0.982908	+	0.184096i	$0.0589357\pi$
$233$	17.8135	+	17.8135i	1.16700	+	1.16700i	0.184096	+	0.982908i	$0.441064\pi$
$234$	−2.98747			−0.195297
$235$	−1.01473	−	1.01473i	−0.0661935	−	0.0661935i
$236$		−	7.74214i		−	0.503970i
$237$	−2.28147			−0.148197
$238$	13.8209	−	5.71740i	0.895876	−	0.370604i
$239$	11.1377			0.720437			0.360219	−	0.932868i	$-0.382702\pi$
$239$	11.1377			0.720437			0.360219	+	0.932868i	$0.382702\pi$
$240$		−	0.149764i		−	0.00966720i
$241$	−1.21793	−	1.21793i	−0.0784538	−	0.0784538i	0.666791	−	0.745245i	$-0.267667\pi$
$241$	−1.21793	−	1.21793i	−0.0784538	−	0.0784538i	−0.745245	+	0.666791i	$0.767667\pi$
$242$	1.00000			0.0642824
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	3.43942	−	3.43942i	0.220186	−	0.220186i
$245$	−0.652249	+	0.652249i	−0.0416707	+	0.0416707i
$246$			0.508988i			0.0324519i
$247$		−	17.4058i		−	1.10750i
$248$	5.64415	−	5.64415i	0.358404	−	0.358404i
$249$	−8.06754	+	8.06754i	−0.511260	+	0.511260i
$250$	−1.05661	−	1.05661i	−0.0668261	−	0.0668261i
$251$	−8.44414			−0.532989			−0.266495	−	0.963836i	$-0.585865\pi$
$251$	−8.44414			−0.532989			−0.266495	+	0.963836i	$0.585865\pi$
$252$	−2.56507	−	2.56507i	−0.161584	−	0.161584i
$253$		−	2.78276i		−	0.174951i
$254$	−5.03593			−0.315982
$255$	−0.570380	−	0.236564i	−0.0357186	−	0.0148142i
$256$	1.00000			0.0625000
$257$		−	11.4777i		−	0.715958i	−0.933730	−	0.357979i	$-0.883466\pi$
$257$		−	11.4777i		−	0.715958i	0.933730	−	0.357979i	$-0.116534\pi$
$258$	5.07162	+	5.07162i	0.315745	+	0.315745i
$259$	28.7421			1.78595
$260$	0.316369	+	0.316369i	0.0196204	+	0.0196204i
$261$	2.44858	−	2.44858i	0.151563	−	0.151563i
$262$	−4.94617	+	4.94617i	−0.305576	+	0.305576i
$263$			18.9029i			1.16561i	0.812614	+	0.582803i	$0.198044\pi$
$263$			18.9029i			1.16561i	−0.812614	+	0.582803i	$0.801956\pi$
$264$			1.00000i			0.0615457i
$265$	0.0382095	−	0.0382095i	0.00234719	−	0.00234719i
$266$	14.9448	−	14.9448i	0.916323	−	0.916323i
$267$	−9.16238	−	9.16238i	−0.560728	−	0.560728i
$268$	3.05659			0.186711
$269$	−12.7910	−	12.7910i	−0.779878	−	0.779878i	0.199932	−	0.979810i	$-0.435928\pi$
$269$	−12.7910	−	12.7910i	−0.779878	−	0.779878i	−0.979810	+	0.199932i	$0.935928\pi$
$270$			0.149764i			0.00911433i
$271$	−23.6954			−1.43939			−0.719697	−	0.694288i	$-0.755719\pi$
$271$	−23.6954			−1.43939			−0.719697	+	0.694288i	$0.755719\pi$
$272$	1.57958	−	3.80853i	0.0957764	−	0.230926i
$273$	10.8372			0.655897
$274$			10.1318i			0.612082i
$275$	3.51967	+	3.51967i	0.212244	+	0.212244i
$276$	2.78276			0.167503
$277$	−19.5922	−	19.5922i	−1.17718	−	1.17718i	−0.980459	−	0.196722i	$-0.936970\pi$
$277$	−19.5922	−	19.5922i	−1.17718	−	1.17718i	−0.196722	−	0.980459i	$-0.563030\pi$
$278$	14.1411	−	14.1411i	0.848126	−	0.848126i
$279$	−5.64415	+	5.64415i	−0.337906	+	0.337906i
$280$			0.543276i			0.0324670i
$281$			19.8694i			1.18531i	0.805458	+	0.592653i	$0.201920\pi$
$281$			19.8694i			1.18531i	−0.805458	+	0.592653i	$0.798080\pi$
$282$	−6.77552	+	6.77552i	−0.403477	+	0.403477i
$283$	−7.70083	+	7.70083i	−0.457767	+	0.457767i	−0.897922	−	0.440155i	$-0.854924\pi$
$283$	−7.70083	+	7.70083i	−0.457767	+	0.457767i	0.440155	+	0.897922i	$0.354924\pi$
$284$	2.21060	+	2.21060i	0.131175	+	0.131175i
$285$	−0.872562			−0.0516861
$286$	−2.11246	−	2.11246i	−0.124912	−	0.124912i
$287$		−	1.84638i		−	0.108989i
$288$	−1.00000			−0.0589256
$289$	−12.0098	−	12.0318i	−0.706460	−	0.707753i
$290$	−0.518604			−0.0304535
$291$			2.75682i			0.161607i
$292$	−6.92743	−	6.92743i	−0.405397	−	0.405397i
$293$	−19.3233			−1.12888			−0.564438	−	0.825475i	$-0.690907\pi$
$293$	−19.3233			−1.12888			−0.564438	+	0.825475i	$0.690907\pi$
$294$	4.35519	+	4.35519i	0.254000	+	0.254000i
$295$	0.819884	−	0.819884i	0.0477355	−	0.0477355i
$296$	5.60260	−	5.60260i	0.325644	−	0.325644i
$297$		−	1.00000i		−	0.0580259i
$298$			11.3247i			0.656025i
$299$	−5.87847	+	5.87847i	−0.339961	+	0.339961i
$300$	−3.51967	+	3.51967i	−0.203208	+	0.203208i
$301$	−18.3976	−	18.3976i	−1.06042	−	1.06042i
$302$	12.2166			0.702989
$303$	−4.39431	−	4.39431i	−0.252447	−	0.252447i
$304$		−	5.82626i		−	0.334159i
$305$	0.728461			0.0417116
$306$	−1.57958	+	3.80853i	−0.0902989	+	0.217719i
$307$	−14.3384			−0.818337			−0.409168	−	0.912459i	$-0.634181\pi$
$307$	−14.3384			−0.818337			−0.409168	+	0.912459i	$0.634181\pi$
$308$		−	3.62756i		−	0.206699i
$309$	−1.12693	−	1.12693i	−0.0641089	−	0.0641089i
$310$	1.19542			0.0678952
$311$	−0.386942	−	0.386942i	−0.0219415	−	0.0219415i	0.696051	−	0.717992i	$-0.254939\pi$
$311$	−0.386942	−	0.386942i	−0.0219415	−	0.0219415i	−0.717992	+	0.696051i	$0.754939\pi$
$312$	2.11246	−	2.11246i	0.119594	−	0.119594i
$313$	11.3577	−	11.3577i	0.641973	−	0.641973i	−0.309068	−	0.951040i	$-0.600017\pi$
$313$	11.3577	−	11.3577i	0.641973	−	0.641973i	0.951040	+	0.309068i	$0.100017\pi$
$314$		−	3.10626i		−	0.175296i
$315$		−	0.543276i		−	0.0306102i
$316$	1.61324	−	1.61324i	0.0907518	−	0.0907518i
$317$	0.952898	−	0.952898i	0.0535201	−	0.0535201i	−0.679840	−	0.733360i	$-0.737951\pi$
$317$	0.952898	−	0.952898i	0.0535201	−	0.0535201i	0.733360	+	0.679840i	$0.237951\pi$
$318$	−0.255132	−	0.255132i	−0.0143071	−	0.0143071i
$319$	3.46282			0.193881
$320$	0.105899	+	0.105899i	0.00591993	+	0.00591993i
$321$		−	5.20784i		−	0.290673i
$322$	−10.0946			−0.562552
$323$	−22.1895	−	9.20307i	−1.23466	−	0.512073i
$324$	1.00000			0.0555556
$325$		−	14.8703i		−	0.824857i
$326$	3.12893	+	3.12893i	0.173295	+	0.173295i
$327$	8.42641			0.465981
$328$	−0.359909	−	0.359909i	−0.0198727	−	0.0198727i
$329$	24.5786	−	24.5786i	1.35506	−	1.35506i
$330$	−0.105899	+	0.105899i	−0.00582954	+	0.00582954i
$331$			29.0572i			1.59713i	0.601908	+	0.798565i	$0.294407\pi$
$331$			29.0572i			1.59713i	−0.601908	+	0.798565i	$0.705593\pi$
$332$		−	11.4092i		−	0.626163i
$333$	−5.60260	+	5.60260i	−0.307020	+	0.307020i
$334$	−12.0127	+	12.0127i	−0.657308	+	0.657308i
$335$	0.323690	+	0.323690i	0.0176851	+	0.0176851i
$336$	3.62756			0.197899
$337$	−8.34759	−	8.34759i	−0.454722	−	0.454722i	0.442196	−	0.896918i	$-0.354200\pi$
$337$	−8.34759	−	8.34759i	−0.454722	−	0.454722i	−0.896918	+	0.442196i	$0.854200\pi$
$338$		−	4.07505i		−	0.221653i
$339$	−6.08131			−0.330291
$340$	0.570596	−	0.236043i	0.0309449	−	0.0128012i
$341$	−7.98203			−0.432251
$342$			5.82626i			0.315048i
$343$	2.15679	+	2.15679i	0.116456	+	0.116456i
$344$	−7.17235			−0.386707
$345$	0.294692	+	0.294692i	0.0158657	+	0.0158657i
$346$	13.4728	−	13.4728i	0.724301	−	0.724301i
$347$	−21.2168	+	21.2168i	−1.13898	+	1.13898i	−0.150341	+	0.988634i	$0.548037\pi$
$347$	−21.2168	+	21.2168i	−1.13898	+	1.13898i	−0.988634	+	0.150341i	$0.951963\pi$
$348$			3.46282i			0.185626i
$349$			19.4228i			1.03968i	0.854264	+	0.519839i	$0.174008\pi$
$349$			19.4228i			1.03968i	−0.854264	+	0.519839i	$0.825992\pi$
$350$	12.7678	−	12.7678i	0.682469	−	0.682469i
$351$	−2.11246	+	2.11246i	−0.112755	+	0.112755i
$352$	−0.707107	−	0.707107i	−0.0376889	−	0.0376889i
$353$	1.13646			0.0604875			0.0302437	−	0.999543i	$-0.490372\pi$
$353$	1.13646			0.0604875			0.0302437	+	0.999543i	$0.490372\pi$
$354$	−5.47452	−	5.47452i	−0.290967	−	0.290967i
$355$			0.468200i			0.0248495i
$356$	12.9576			0.686749
$357$	5.73003	−	13.8157i	0.303266	−	0.731203i
$358$	−13.9538			−0.737480
$359$		−	30.2829i		−	1.59827i	−0.601150	−	0.799136i	$-0.705291\pi$
$359$		−	30.2829i		−	1.59827i	0.601150	−	0.799136i	$-0.294709\pi$
$360$	−0.105899	−	0.105899i	−0.00558136	−	0.00558136i
$361$	−14.9453			−0.786596
$362$	−3.41587	−	3.41587i	−0.179534	−	0.179534i
$363$	0.707107	−	0.707107i	0.0371135	−	0.0371135i
$364$	−7.66306	+	7.66306i	−0.401654	+	0.401654i
$365$		−	1.46722i		−	0.0767976i
$366$		−	4.86407i		−	0.254249i
$367$	−9.28381	+	9.28381i	−0.484611	+	0.484611i	−0.906601	−	0.421990i	$-0.861332\pi$
$367$	−9.28381	+	9.28381i	−0.484611	+	0.484611i	0.421990	+	0.906601i	$0.361332\pi$
$368$	−1.96771	+	1.96771i	−0.102574	+	0.102574i
$369$	0.359909	+	0.359909i	0.0187361	+	0.0187361i
$370$	1.18662			0.0616893
$371$	0.925505	+	0.925505i	0.0480498	+	0.0480498i
$372$		−	7.98203i		−	0.413849i
$373$	23.4581			1.21461			0.607307	−	0.794467i	$-0.292250\pi$
$373$	23.4581			1.21461			0.607307	+	0.794467i	$0.292250\pi$
$374$	−3.80997	+	1.57610i	−0.197009	+	0.0814984i
$375$	−1.49428			−0.0771642
$376$		−	9.58204i		−	0.494156i
$377$	−7.31505	−	7.31505i	−0.376744	−	0.376744i
$378$	−3.62756			−0.186581
$379$	8.31104	+	8.31104i	0.426909	+	0.426909i	0.887574	−	0.460665i	$-0.152389\pi$
$379$	8.31104	+	8.31104i	0.426909	+	0.426909i	−0.460665	+	0.887574i	$0.652389\pi$
$380$	0.616995	−	0.616995i	0.0316512	−	0.0316512i
$381$	−3.56094	+	3.56094i	−0.182433	+	0.182433i
$382$		−	24.0371i		−	1.22984i
$383$		−	5.90450i		−	0.301706i	−0.988556	−	0.150853i	$-0.951798\pi$
$383$		−	5.90450i		−	0.301706i	0.988556	−	0.150853i	$-0.0482020\pi$
$384$	0.707107	−	0.707107i	0.0360844	−	0.0360844i
$385$	0.384154	−	0.384154i	0.0195783	−	0.0195783i
$386$	18.8585	+	18.8585i	0.959870	+	0.959870i
$387$	7.17235			0.364591
$388$	−1.94936	−	1.94936i	−0.0989639	−	0.0989639i
$389$		−	8.73263i		−	0.442762i	−0.975187	−	0.221381i	$-0.928944\pi$
$389$		−	8.73263i		−	0.442762i	0.975187	−	0.221381i	$-0.0710564\pi$
$390$	0.447414			0.0226557
$391$	4.38592	+	10.6023i	0.221806	+	0.536179i
$392$	−6.15917			−0.311085
$393$			6.99494i			0.352848i
$394$	17.7197	+	17.7197i	0.892705	+	0.892705i
$395$	0.341681			0.0171918
$396$	0.707107	+	0.707107i	0.0355335	+	0.0355335i
$397$	−0.914752	+	0.914752i	−0.0459101	+	0.0459101i	−0.729689	−	0.683779i	$-0.760335\pi$
$397$	−0.914752	+	0.914752i	−0.0459101	+	0.0459101i	0.683779	+	0.729689i	$0.260335\pi$
$398$	−3.26632	+	3.26632i	−0.163726	+	0.163726i
$399$		−	21.1351i		−	1.05808i
$400$		−	4.97757i		−	0.248879i
$401$	2.46188	−	2.46188i	0.122940	−	0.122940i	−0.642960	−	0.765900i	$-0.722294\pi$
$401$	2.46188	−	2.46188i	0.122940	−	0.122940i	0.765900	+	0.642960i	$0.222294\pi$
$402$	2.16134	−	2.16134i	0.107798	−	0.107798i
$403$	16.8617	+	16.8617i	0.839941	+	0.839941i
$404$	6.21450			0.309183
$405$	0.105899	+	0.105899i	0.00526216	+	0.00526216i
$406$		−	12.5616i		−	0.623420i
$407$	−7.92327			−0.392742
$408$	−1.57610	−	3.80997i	−0.0780287	−	0.188622i
$409$	27.7960			1.37443			0.687213	−	0.726456i	$-0.258834\pi$
$409$	27.7960			1.37443			0.687213	+	0.726456i	$0.258834\pi$
$410$		−	0.0762280i		−	0.00376463i
$411$	7.16424	+	7.16424i	0.353386	+	0.353386i
$412$	1.59372			0.0785170
$413$	19.8591	+	19.8591i	0.977204	+	0.977204i
$414$	1.96771	−	1.96771i	0.0967078	−	0.0967078i
$415$	1.20822	−	1.20822i	0.0593094	−	0.0593094i
$416$			2.98747i			0.146473i
$417$		−	19.9985i		−	0.979332i
$418$	−4.11979	+	4.11979i	−0.201505	+	0.201505i
$419$	−5.96153	+	5.96153i	−0.291240	+	0.291240i	−0.837570	−	0.546330i	$-0.816024\pi$
$419$	−5.96153	+	5.96153i	−0.291240	+	0.291240i	0.546330	+	0.837570i	$0.316024\pi$
$420$	0.384154	+	0.384154i	0.0187448	+	0.0187448i
$421$	−22.8344			−1.11288			−0.556441	−	0.830887i	$-0.687834\pi$
$421$	−22.8344			−1.11288			−0.556441	+	0.830887i	$0.687834\pi$
$422$	−13.7187	−	13.7187i	−0.667816	−	0.667816i
$423$			9.58204i			0.465895i
$424$	0.360811			0.0175225
$425$	−18.9572	−	7.86250i	−0.919561	−	0.381387i
$426$	3.12626			0.151468
$427$			17.6447i			0.853886i
$428$	3.68250	+	3.68250i	0.178000	+	0.178000i
$429$	−2.98747			−0.144236
$430$	−0.759544	−	0.759544i	−0.0366285	−	0.0366285i
$431$	−12.6106	+	12.6106i	−0.607431	+	0.607431i	−0.942274	−	0.334843i	$-0.891317\pi$
$431$	−12.6106	+	12.6106i	−0.607431	+	0.607431i	0.334843	+	0.942274i	$0.391317\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$			38.1510i			1.83342i	0.399555	+	0.916709i	$0.369165\pi$
$433$			38.1510i			1.83342i	−0.399555	+	0.916709i	$0.630835\pi$
$434$			28.9553i			1.38990i
$435$	−0.366709	+	0.366709i	−0.0175823	+	0.0175823i
$436$	−5.95837	+	5.95837i	−0.285354	+	0.285354i
$437$	11.4644	+	11.4644i	0.548417	+	0.548417i
$438$	−9.79687			−0.468112
$439$	14.2867	+	14.2867i	0.681866	+	0.681866i	0.960421	−	0.278554i	$-0.0898552\pi$
$439$	14.2867	+	14.2867i	0.681866	+	0.681866i	−0.278554	+	0.960421i	$0.589855\pi$
$440$		−	0.149764i		−	0.00713970i
$441$	6.15917			0.293294
$442$	11.3779	+	4.71896i	0.541190	+	0.224458i
$443$	−20.9317			−0.994496			−0.497248	−	0.867608i	$-0.665656\pi$
$443$	−20.9317			−0.994496			−0.497248	+	0.867608i	$0.665656\pi$
$444$		−	7.92327i		−	0.376022i
$445$	1.37219	+	1.37219i	0.0650481	+	0.0650481i
$446$	11.0446			0.522979
$447$	8.00780	+	8.00780i	0.378756	+	0.378756i
$448$	−2.56507	+	2.56507i	−0.121188	+	0.121188i
$449$	8.39529	−	8.39529i	0.396198	−	0.396198i	−0.480692	−	0.876890i	$-0.659614\pi$
$449$	8.39529	−	8.39529i	0.396198	−	0.396198i	0.876890	+	0.480692i	$0.159614\pi$
$450$			4.97757i			0.234645i
$451$			0.508988i			0.0239673i
$452$	4.30013	−	4.30013i	0.202261	−	0.202261i
$453$	8.63847	−	8.63847i	0.405871	−	0.405871i
$454$	−7.24271	−	7.24271i	−0.339917	−	0.339917i
$455$	−1.62302			−0.0760883
$456$	−4.11979	−	4.11979i	−0.192927	−	0.192927i
$457$			9.66984i			0.452336i	0.974088	+	0.226168i	$0.0726198\pi$
$457$			9.66984i			0.452336i	−0.974088	+	0.226168i	$0.927380\pi$
$458$	−0.817874			−0.0382167
$459$	1.57610	+	3.80997i	0.0735662	+	0.177834i
$460$	−0.416757			−0.0194314
$461$			9.61054i			0.447607i	0.974634	+	0.223804i	$0.0718474\pi$
$461$			9.61054i			0.447607i	−0.974634	+	0.223804i	$0.928153\pi$
$462$	−2.56507	−	2.56507i	−0.119338	−	0.119338i
$463$	−21.1925			−0.984899			−0.492449	−	0.870341i	$-0.663898\pi$
$463$	−21.1925			−0.984899			−0.492449	+	0.870341i	$0.663898\pi$
$464$	−2.44858	−	2.44858i	−0.113673	−	0.113673i
$465$	0.845288	−	0.845288i	0.0391993	−	0.0391993i
$466$	−17.8135	+	17.8135i	−0.825197	+	0.825197i
$467$		−	8.67124i		−	0.401257i	−0.979667	−	0.200629i	$-0.935702\pi$
$467$		−	8.67124i		−	0.401257i	0.979667	−	0.200629i	$-0.0642984\pi$
$468$		−	2.98747i		−	0.138096i
$469$	−7.84037	+	7.84037i	−0.362035	+	0.362035i
$470$	1.01473	−	1.01473i	0.0468059	−	0.0468059i
$471$	−2.19646	−	2.19646i	−0.101207	−	0.101207i
$472$	7.74214			0.356361
$473$	5.07162	+	5.07162i	0.233193	+	0.233193i
$474$		−	2.28147i		−	0.104791i
$475$	−29.0006			−1.33064
$476$	5.71740	+	13.8209i	0.262057	+	0.633480i
$477$	−0.360811			−0.0165204
$478$			11.1377i			0.509426i
$479$	6.30005	+	6.30005i	0.287857	+	0.287857i	0.836232	−	0.548375i	$-0.184754\pi$
$479$	6.30005	+	6.30005i	0.287857	+	0.287857i	−0.548375	+	0.836232i	$0.684754\pi$
$480$	0.149764			0.00683575
$481$	16.7376	+	16.7376i	0.763167	+	0.763167i
$482$	1.21793	−	1.21793i	0.0554752	−	0.0554752i
$483$	−7.13799	+	7.13799i	−0.324790	+	0.324790i
$484$			1.00000i			0.0454545i
$485$		−	0.412871i		−	0.0187475i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$	−20.8646	+	20.8646i	−0.945466	+	0.945466i	−0.998588	−	0.0531216i	$-0.983083\pi$
$487$	−20.8646	+	20.8646i	−0.945466	+	0.945466i	0.0531216	+	0.998588i	$0.483083\pi$
$488$	3.43942	+	3.43942i	0.155695	+	0.155695i
$489$	4.42497			0.200104
$490$	−0.652249	−	0.652249i	−0.0294656	−	0.0294656i
$491$			5.52514i			0.249346i	0.992198	+	0.124673i	$0.0397882\pi$
$491$			5.52514i			0.249346i	−0.992198	+	0.124673i	$0.960212\pi$
$492$	−0.508988			−0.0229470
$493$	−13.1932	+	5.45776i	−0.594194	+	0.245805i
$494$	17.4058			0.783122
$495$			0.149764i			0.00673138i
$496$	5.64415	+	5.64415i	0.253430	+	0.253430i
$497$	−11.3407			−0.508699
$498$	−8.06754	−	8.06754i	−0.361515	−	0.361515i
$499$	21.7762	−	21.7762i	0.974835	−	0.974835i	−0.0248559	−	0.999691i	$-0.507913\pi$
$499$	21.7762	−	21.7762i	0.974835	−	0.974835i	0.999691	+	0.0248559i	$0.00791271\pi$
$500$	1.05661	−	1.05661i	0.0472532	−	0.0472532i
$501$			16.9886i			0.758994i
$502$		−	8.44414i		−	0.376880i
$503$	8.51331	−	8.51331i	0.379590	−	0.379590i	−0.491364	−	0.870954i	$-0.663502\pi$
$503$	8.51331	−	8.51331i	0.379590	−	0.379590i	0.870954	+	0.491364i	$0.163502\pi$
$504$	2.56507	−	2.56507i	0.114257	−	0.114257i
$505$	0.658109	+	0.658109i	0.0292854	+	0.0292854i
$506$	2.78276			0.123709
$507$	−2.88149	−	2.88149i	−0.127972	−	0.127972i
$508$		−	5.03593i		−	0.223433i
$509$	20.1290			0.892204			0.446102	−	0.894982i	$-0.352812\pi$
$509$	20.1290			0.892204			0.446102	+	0.894982i	$0.352812\pi$
$510$	0.236564	−	0.570380i	0.0104753	−	0.0252568i
$511$	35.5387			1.57214
$512$			1.00000i			0.0441942i
$513$	4.11979	+	4.11979i	0.181893	+	0.181893i
$514$	11.4777			0.506259
$515$	0.168773	+	0.168773i	0.00743705	+	0.00743705i
$516$	−5.07162	+	5.07162i	−0.223266	+	0.223266i
$517$	−6.77552	+	6.77552i	−0.297987	+	0.297987i
$518$			28.7421i			1.26286i
$519$		−	19.0534i		−	0.836350i
$520$	−0.316369	+	0.316369i	−0.0138737	+	0.0138737i
$521$	25.0173	−	25.0173i	1.09603	−	1.09603i	0.101157	−	0.994870i	$-0.467745\pi$
$521$	25.0173	−	25.0173i	1.09603	−	1.09603i	0.994870	−	0.101157i	$-0.0322546\pi$
$522$	2.44858	+	2.44858i	0.107171	+	0.107171i
$523$	12.1751			0.532378			0.266189	−	0.963921i	$-0.414235\pi$
$523$	12.1751			0.532378			0.266189	+	0.963921i	$0.414235\pi$
$524$	−4.94617	−	4.94617i	−0.216075	−	0.216075i
$525$		−	18.0564i		−	0.788047i
$526$	−18.9029			−0.824207
$527$	30.4113	−	12.5805i	1.32474	−	0.548015i
$528$	−1.00000			−0.0435194
$529$			15.2562i			0.663314i
$530$	0.0382095	+	0.0382095i	0.00165971	+	0.00165971i
$531$	−7.74214			−0.335980
$532$	14.9448	+	14.9448i	0.647938	+	0.647938i
$533$	1.07522	−	1.07522i	0.0465728	−	0.0465728i
$534$	9.16238	−	9.16238i	0.396495	−	0.396495i
$535$			0.779946i			0.0337200i
$536$			3.05659i			0.132025i
$537$	−9.86681	+	9.86681i	−0.425784	+	0.425784i
$538$	12.7910	−	12.7910i	0.551457	−	0.551457i
$539$	4.35519	+	4.35519i	0.187591	+	0.187591i
$540$	−0.149764			−0.00644480
$541$	20.5056	+	20.5056i	0.881606	+	0.881606i	0.993698	−	0.112092i	$-0.0357552\pi$
$541$	20.5056	+	20.5056i	0.881606	+	0.881606i	−0.112092	+	0.993698i	$0.535755\pi$
$542$		−	23.6954i		−	1.01781i
$543$	−4.83076			−0.207308
$544$	3.80853	+	1.57958i	0.163289	+	0.0677241i
$545$	−1.26197			−0.0540569
$546$			10.8372i			0.463790i
$547$	29.0454	+	29.0454i	1.24189	+	1.24189i	0.959216	+	0.282675i	$0.0912219\pi$
$547$	29.0454	+	29.0454i	1.24189	+	1.24189i	0.282675	+	0.959216i	$0.408778\pi$
$548$	−10.1318			−0.432807
$549$	−3.43942	−	3.43942i	−0.146791	−	0.146791i
$550$	−3.51967	+	3.51967i	−0.150079	+	0.150079i
$551$	−14.2661	+	14.2661i	−0.607755	+	0.607755i
$552$			2.78276i			0.118442i
$553$			8.27615i			0.351938i
$554$	19.5922	−	19.5922i	0.832393	−	0.832393i
$555$	0.839065	−	0.839065i	0.0356163	−	0.0356163i
$556$	14.1411	+	14.1411i	0.599716	+	0.599716i
$557$	−35.8745			−1.52005			−0.760025	−	0.649893i	$-0.774813\pi$
$557$	−35.8745			−1.52005			−0.760025	+	0.649893i	$0.774813\pi$
$558$	−5.64415	−	5.64415i	−0.238936	−	0.238936i
$559$		−	21.4272i		−	0.906272i
$560$	−0.543276			−0.0229576
$561$	−1.57958	+	3.80853i	−0.0666901	+	0.160796i
$562$	−19.8694			−0.838138
$563$		−	9.65311i		−	0.406830i	−0.979093	−	0.203415i	$-0.934796\pi$
$563$		−	9.65311i		−	0.406830i	0.979093	−	0.203415i	$-0.0652040\pi$
$564$	−6.77552	−	6.77552i	−0.285301	−	0.285301i
$565$	0.910759			0.0383159
$566$	−7.70083	−	7.70083i	−0.323690	−	0.323690i
$567$	−2.56507	+	2.56507i	−0.107723	+	0.107723i
$568$	−2.21060	+	2.21060i	−0.0927546	+	0.0927546i
$569$		−	23.0062i		−	0.964468i	−0.876042	−	0.482234i	$-0.839825\pi$
$569$		−	23.0062i		−	0.964468i	0.876042	−	0.482234i	$-0.160175\pi$
$570$		−	0.872562i		−	0.0365476i
$571$	−17.2083	+	17.2083i	−0.720146	+	0.720146i	−0.968635	−	0.248488i	$-0.920066\pi$
$571$	−17.2083	+	17.2083i	−0.720146	+	0.720146i	0.248488	+	0.968635i	$0.420066\pi$
$572$	2.11246	−	2.11246i	0.0883263	−	0.0883263i
$573$	−16.9968	−	16.9968i	−0.710051	−	0.710051i
$574$	1.84638			0.0770666
$575$	9.79443	+	9.79443i	0.408456	+	0.408456i
$576$		−	1.00000i		−	0.0416667i
$577$	1.20577			0.0501967			0.0250983	−	0.999685i	$-0.492010\pi$
$577$	1.20577			0.0501967			0.0250983	+	0.999685i	$0.492010\pi$
$578$	12.0318	−	12.0098i	0.500457	−	0.499543i
$579$	26.6699			1.10836
$580$		−	0.518604i		−	0.0215339i
$581$	29.2655	+	29.2655i	1.21414	+	1.21414i
$582$	−2.75682			−0.114274
$583$	−0.255132	−	0.255132i	−0.0105665	−	0.0105665i
$584$	6.92743	−	6.92743i	0.286659	−	0.286659i
$585$	0.316369	−	0.316369i	0.0130803	−	0.0130803i
$586$		−	19.3233i		−	0.798236i
$587$			3.35433i			0.138448i	0.997601	+	0.0692239i	$0.0220523\pi$
$587$			3.35433i			0.138448i	−0.997601	+	0.0692239i	$0.977948\pi$
$588$	−4.35519	+	4.35519i	−0.179605	+	0.179605i
$589$	32.8843	−	32.8843i	1.35497	−	1.35497i
$590$	0.819884	+	0.819884i	0.0337541	+	0.0337541i
$591$	25.0594			1.03081
$592$	5.60260	+	5.60260i	0.230265	+	0.230265i
$593$			20.4586i			0.840133i	0.907493	+	0.420067i	$0.137993\pi$
$593$			20.4586i			0.840133i	−0.907493	+	0.420067i	$0.862007\pi$
$594$	1.00000			0.0410305
$595$	−0.858151	+	2.06908i	−0.0351808	+	0.0848242i
$596$	−11.3247			−0.463880
$597$			4.61927i			0.189054i
$598$	−5.87847	−	5.87847i	−0.240389	−	0.240389i
$599$	6.00344			0.245294			0.122647	−	0.992450i	$-0.460862\pi$
$599$	6.00344			0.245294			0.122647	+	0.992450i	$0.460862\pi$
$600$	−3.51967	−	3.51967i	−0.143690	−	0.143690i
$601$	9.29644	−	9.29644i	0.379210	−	0.379210i	−0.491607	−	0.870817i	$-0.663590\pi$
$601$	9.29644	−	9.29644i	0.379210	−	0.379210i	0.870817	+	0.491607i	$0.163590\pi$
$602$	18.3976	−	18.3976i	0.749830	−	0.749830i
$603$		−	3.05659i		−	0.124474i
$604$			12.2166i			0.497088i
$605$	−0.105899	+	0.105899i	−0.00430540	+	0.00430540i
$606$	4.39431	−	4.39431i	0.178507	−	0.178507i
$607$	25.5848	+	25.5848i	1.03846	+	1.03846i	0.999230	+	0.0392262i	$0.0124893\pi$
$607$	25.5848	+	25.5848i	1.03846	+	1.03846i	0.0392262	+	0.999230i	$0.487511\pi$
$608$	5.82626			0.236286
$609$	−8.88237	−	8.88237i	−0.359932	−	0.359932i
$610$			0.728461i			0.0294945i
$611$	28.6260			1.15808
$612$	−3.80853	−	1.57958i	−0.153951	−	0.0638509i
$613$	5.75386			0.232396			0.116198	−	0.993226i	$-0.462929\pi$
$613$	5.75386			0.232396			0.116198	+	0.993226i	$0.462929\pi$
$614$		−	14.3384i		−	0.578651i
$615$	−0.0539013	−	0.0539013i	−0.00217351	−	0.00217351i
$616$	3.62756			0.146158
$617$	−32.9703	−	32.9703i	−1.32733	−	1.32733i	−0.907688	−	0.419646i	$-0.862154\pi$
$617$	−32.9703	−	32.9703i	−1.32733	−	1.32733i	−0.419646	−	0.907688i	$-0.637846\pi$
$618$	1.12693	−	1.12693i	0.0453318	−	0.0453318i
$619$	−26.3832	+	26.3832i	−1.06043	+	1.06043i	−0.0623781	+	0.998053i	$0.519868\pi$
$619$	−26.3832	+	26.3832i	−1.06043	+	1.06043i	−0.998053	+	0.0623781i	$0.980132\pi$
$620$			1.19542i			0.0480091i
$621$		−	2.78276i		−	0.111669i
$622$	0.386942	−	0.386942i	0.0155150	−	0.0155150i
$623$	−33.2371	+	33.2371i	−1.33161	+	1.33161i
$624$	2.11246	+	2.11246i	0.0845660	+	0.0845660i
$625$	−24.6641			−0.986563
$626$	11.3577	+	11.3577i	0.453943	+	0.453943i
$627$			5.82626i			0.232678i
$628$	3.10626			0.123953
$629$	30.1874	−	12.4879i	1.20365	−	0.497925i
$630$	0.543276			0.0216446
$631$			28.7932i			1.14624i	0.819472	+	0.573119i	$0.194267\pi$
$631$			28.7932i			1.14624i	−0.819472	+	0.573119i	$0.805733\pi$
$632$	1.61324	+	1.61324i	0.0641712	+	0.0641712i
$633$	−19.4012			−0.771127
$634$	0.952898	+	0.952898i	0.0378444	+	0.0378444i
$635$	0.533300	−	0.533300i	0.0211633	−	0.0211633i
$636$	0.255132	−	0.255132i	0.0101166	−	0.0101166i
$637$		−	18.4003i		−	0.729047i
$638$			3.46282i			0.137094i
$639$	2.21060	−	2.21060i	0.0874499	−	0.0874499i
$640$	−0.105899	+	0.105899i	−0.00418602	+	0.00418602i
$641$	33.6192	+	33.6192i	1.32788	+	1.32788i	0.907217	+	0.420662i	$0.138202\pi$
$641$	33.6192	+	33.6192i	1.32788	+	1.32788i	0.420662	+	0.907217i	$0.361798\pi$
$642$	5.20784			0.205537
$643$	27.3106	+	27.3106i	1.07703	+	1.07703i	0.996775	+	0.0802518i	$0.0255725\pi$
$643$	27.3106	+	27.3106i	1.07703	+	1.07703i	0.0802518	+	0.996775i	$0.474428\pi$
$644$		−	10.0946i		−	0.397784i
$645$	−1.07416			−0.0422949
$646$	9.20307	−	22.1895i	0.362090	−	0.873034i
$647$	10.3319			0.406188			0.203094	−	0.979159i	$-0.434900\pi$
$647$	10.3319			0.406188			0.203094	+	0.979159i	$0.434900\pi$
$648$			1.00000i			0.0392837i
$649$	−5.47452	−	5.47452i	−0.214894	−	0.214894i
$650$	14.8703			0.583262
$651$	20.4745	+	20.4745i	0.802458	+	0.802458i
$652$	−3.12893	+	3.12893i	−0.122538	+	0.122538i
$653$	−8.01556	+	8.01556i	−0.313673	+	0.313673i	−0.846331	−	0.532658i	$-0.821193\pi$
$653$	−8.01556	+	8.01556i	−0.313673	+	0.313673i	0.532658	+	0.846331i	$0.321193\pi$
$654$			8.42641i			0.329499i
$655$		−	1.04759i		−	0.0409327i
$656$	0.359909	−	0.359909i	0.0140521	−	0.0140521i
$657$	−6.92743	+	6.92743i	−0.270265	+	0.270265i
$658$	24.5786	+	24.5786i	0.958173	+	0.958173i
$659$	−31.3316			−1.22051			−0.610253	−	0.792207i	$-0.708932\pi$
$659$	−31.3316			−1.22051			−0.610253	+	0.792207i	$0.708932\pi$
$660$	−0.105899	−	0.105899i	−0.00412211	−	0.00412211i
$661$		−	34.6404i		−	1.34735i	−0.739026	−	0.673677i	$-0.764714\pi$
$661$		−	34.6404i		−	1.34735i	0.739026	−	0.673677i	$-0.235286\pi$
$662$	−29.0572			−1.12934
$663$	11.3822	−	4.70855i	0.442047	−	0.182865i
$664$	11.4092			0.442764
$665$			3.16527i			0.122744i
$666$	−5.60260	−	5.60260i	−0.217096	−	0.217096i
$667$	9.63621			0.373115
$668$	−12.0127	−	12.0127i	−0.464787	−	0.464787i
$669$	7.80974	−	7.80974i	0.301942	−	0.301942i
$670$	−0.323690	+	0.323690i	−0.0125052	+	0.0125052i
$671$		−	4.86407i		−	0.187775i
$672$			3.62756i			0.139936i
$673$	−30.1884	+	30.1884i	−1.16368	+	1.16368i	−0.180015	+	0.983664i	$0.557615\pi$
$673$	−30.1884	+	30.1884i	−1.16368	+	1.16368i	−0.983664	+	0.180015i	$0.942385\pi$
$674$	8.34759	−	8.34759i	0.321537	−	0.321537i
$675$	3.51967	+	3.51967i	0.135472	+	0.135472i
$676$	4.07505			0.156733
$677$	−15.0370	−	15.0370i	−0.577920	−	0.577920i	0.356410	−	0.934330i	$-0.384001\pi$
$677$	−15.0370	−	15.0370i	−0.577920	−	0.577920i	−0.934330	+	0.356410i	$0.884001\pi$
$678$		−	6.08131i		−	0.233551i
$679$	10.0005			0.383784
$680$	0.236043	+	0.570596i	0.00905184	+	0.0218813i
$681$	−10.2427			−0.392503
$682$		−	7.98203i		−	0.305648i
$683$	10.9624	+	10.9624i	0.419463	+	0.419463i	0.885019	−	0.465556i	$-0.154145\pi$
$683$	10.9624	+	10.9624i	0.419463	+	0.419463i	−0.465556	+	0.885019i	$0.654145\pi$
$684$	−5.82626			−0.222773
$685$	−1.07294	−	1.07294i	−0.0409950	−	0.0409950i
$686$	−2.15679	+	2.15679i	−0.0823466	+	0.0823466i
$687$	−0.578324	+	0.578324i	−0.0220644	+	0.0220644i
$688$		−	7.17235i		−	0.273443i
$689$			1.07791i			0.0410651i
$690$	−0.294692	+	0.294692i	−0.0112187	+	0.0112187i
$691$	4.11353	−	4.11353i	0.156486	−	0.156486i	−0.624521	−	0.781008i	$-0.714706\pi$
$691$	4.11353	−	4.11353i	0.156486	−	0.156486i	0.781008	+	0.624521i	$0.214706\pi$
$692$	13.4728	+	13.4728i	0.512158	+	0.512158i
$693$	−3.62756			−0.137799
$694$	−21.2168	−	21.2168i	−0.805377	−	0.805377i
$695$			2.99505i			0.113609i
$696$	−3.46282			−0.131258
$697$	−0.802218	−	1.93923i	−0.0303862	−	0.0734537i
$698$	−19.4228			−0.735163
$699$			25.1922i			0.952855i
$700$	12.7678	+	12.7678i	0.482578	+	0.482578i
$701$	−17.2371			−0.651035			−0.325518	−	0.945536i	$-0.605539\pi$
$701$	−17.2371			−0.651035			−0.325518	+	0.945536i	$0.605539\pi$
$702$	−2.11246	−	2.11246i	−0.0797296	−	0.0797296i
$703$	32.6422	−	32.6422i	1.23112	−	1.23112i
$704$	0.707107	−	0.707107i	0.0266501	−	0.0266501i
$705$		−	1.43504i		−	0.0540468i
$706$			1.13646i			0.0427711i
$707$	−15.9406	+	15.9406i	−0.599509	+	0.599509i
$708$	5.47452	−	5.47452i	0.205745	−	0.205745i
$709$	−0.899122	−	0.899122i	−0.0337672	−	0.0337672i	0.690022	−	0.723789i	$-0.257601\pi$
$709$	−0.899122	−	0.899122i	−0.0337672	−	0.0337672i	−0.723789	+	0.690022i	$0.757601\pi$
$710$	−0.468200			−0.0175712
$711$	−1.61324	−	1.61324i	−0.0605012	−	0.0605012i
$712$			12.9576i			0.485605i
$713$	−22.2121			−0.831850
$714$	13.8157	+	5.73003i	0.517038	+	0.214441i
$715$	0.447414			0.0167323
$716$		−	13.9538i		−	0.521477i
$717$	7.87554	+	7.87554i	0.294117	+	0.294117i
$718$	30.2829			1.13015
$719$	−4.10319	−	4.10319i	−0.153023	−	0.153023i	0.626444	−	0.779467i	$-0.284510\pi$
$719$	−4.10319	−	4.10319i	−0.153023	−	0.153023i	−0.779467	+	0.626444i	$0.784510\pi$
$720$	0.105899	−	0.105899i	0.00394662	−	0.00394662i
$721$	−4.08801	+	4.08801i	−0.152245	+	0.152245i
$722$		−	14.9453i		−	0.556207i
$723$		−	1.72241i		−	0.0640573i
$724$	3.41587	−	3.41587i	0.126950	−	0.126950i
$725$	−12.1880	+	12.1880i	−0.452650	+	0.452650i
$726$	0.707107	+	0.707107i	0.0262432	+	0.0262432i
$727$	−48.1800			−1.78690			−0.893449	−	0.449166i	$-0.851721\pi$
$727$	−48.1800			−1.78690			−0.893449	+	0.449166i	$0.851721\pi$
$728$	−7.66306	−	7.66306i	−0.284012	−	0.284012i
$729$		−	1.00000i		−	0.0370370i
$730$	1.46722			0.0543041
$731$	−27.3161	−	11.3293i	−1.01032	−	0.419031i
$732$	4.86407			0.179781
$733$			19.9496i			0.736857i	0.929656	+	0.368428i	$0.120104\pi$
$733$			19.9496i			0.736857i	−0.929656	+	0.368428i	$0.879896\pi$
$734$	−9.28381	−	9.28381i	−0.342672	−	0.342672i
$735$	−0.922420			−0.0340240
$736$	−1.96771	−	1.96771i	−0.0725308	−	0.0725308i
$737$	2.16134	−	2.16134i	0.0796138	−	0.0796138i
$738$	−0.359909	+	0.359909i	−0.0132484	+	0.0132484i
$739$			15.4546i			0.568508i	0.958749	+	0.284254i	$0.0917459\pi$
$739$			15.4546i			0.568508i	−0.958749	+	0.284254i	$0.908254\pi$
$740$			1.18662i			0.0436209i
$741$	12.3077	−	12.3077i	0.452136	−	0.452136i
$742$	−0.925505	+	0.925505i	−0.0339764	+	0.0339764i
$743$	−17.5044	−	17.5044i	−0.642174	−	0.642174i	0.308916	−	0.951089i	$-0.400034\pi$
$743$	−17.5044	−	17.5044i	−0.642174	−	0.642174i	−0.951089	+	0.308916i	$0.900034\pi$
$744$	7.98203			0.292635
$745$	−1.19928	−	1.19928i	−0.0439382	−	0.0439382i
$746$			23.4581i			0.858862i
$747$	−11.4092			−0.417442
$748$	−1.57610	−	3.80997i	−0.0576280	−	0.139306i
$749$	−18.8917			−0.690290
$750$		−	1.49428i		−	0.0545633i
$751$	21.6619	+	21.6619i	0.790452	+	0.790452i	0.981568	−	0.191115i	$-0.0612104\pi$
$751$	21.6619	+	21.6619i	0.790452	+	0.790452i	−0.191115	+	0.981568i	$0.561210\pi$
$752$	9.58204			0.349421
$753$	−5.97091	−	5.97091i	−0.217592	−	0.217592i
$754$	7.31505	−	7.31505i	0.266399	−	0.266399i
$755$	−1.29373	+	1.29373i	−0.0470836	+	0.0470836i
$756$		−	3.62756i		−	0.131933i
$757$			4.56661i			0.165976i	0.996551	+	0.0829881i	$0.0264463\pi$
$757$			4.56661i			0.165976i	−0.996551	+	0.0829881i	$0.973554\pi$
$758$	−8.31104	+	8.31104i	−0.301870	+	0.301870i
$759$	1.96771	−	1.96771i	0.0714234	−	0.0714234i
$760$	0.616995	+	0.616995i	0.0223808	+	0.0223808i
$761$	29.9472			1.08559			0.542793	−	0.839867i	$-0.317367\pi$
$761$	29.9472			1.08559			0.542793	+	0.839867i	$0.317367\pi$
$762$	−3.56094	−	3.56094i	−0.128999	−	0.128999i
$763$		−	30.5673i		−	1.10661i
$764$	24.0371			0.869631
$765$	−0.236043	−	0.570596i	−0.00853415	−	0.0206299i
$766$	5.90450			0.213338
$767$			23.1294i			0.835153i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	−18.6661			−0.673116			−0.336558	−	0.941663i	$-0.609263\pi$
$769$	−18.6661			−0.673116			−0.336558	+	0.941663i	$0.609263\pi$
$770$	0.384154	+	0.384154i	0.0138440	+	0.0138440i
$771$	8.11594	−	8.11594i	0.292289	−	0.292289i
$772$	−18.8585	+	18.8585i	−0.678731	+	0.678731i
$773$			26.0221i			0.935950i	0.883742	+	0.467975i	$0.155016\pi$
$773$			26.0221i			0.935950i	−0.883742	+	0.467975i	$0.844984\pi$
$774$			7.17235i			0.257805i
$775$	28.0941	−	28.0941i	1.00917	−	1.00917i
$776$	1.94936	−	1.94936i	0.0699781	−	0.0699781i
$777$	20.3237	+	20.3237i	0.729110	+	0.729110i
$778$	8.73263			0.313080
$779$	−2.09693	−	2.09693i	−0.0751301	−	0.0751301i
$780$			0.447414i			0.0160200i
$781$	3.12626			0.111866
$782$	−10.6023	+	4.38592i	−0.379136	+	0.156840i
$783$	3.46282			0.123751
$784$		−	6.15917i		−	0.219970i
$785$	0.328950	+	0.328950i	0.0117407	+	0.0117407i
$786$	−6.99494			−0.249501
$787$	19.4083	+	19.4083i	0.691831	+	0.691831i	0.962635	−	0.270803i	$-0.0872894\pi$
$787$	19.4083	+	19.4083i	0.691831	+	0.691831i	−0.270803	+	0.962635i	$0.587289\pi$
$788$	−17.7197	+	17.7197i	−0.631238	+	0.631238i
$789$	−13.3664	+	13.3664i	−0.475856	+	0.475856i
$790$			0.341681i			0.0121565i
$791$			22.0603i			0.784373i
$792$	−0.707107	+	0.707107i	−0.0251259	+	0.0251259i
$793$	−10.2751	+	10.2751i	−0.364881	+	0.364881i
$794$	−0.914752	−	0.914752i	−0.0324633	−	0.0324633i
$795$	0.0540364			0.00191647
$796$	−3.26632	−	3.26632i	−0.115771	−	0.115771i
$797$		−	34.5654i		−	1.22437i	−0.790715	−	0.612185i	$-0.790291\pi$
$797$		−	34.5654i		−	1.22437i	0.790715	−	0.612185i	$-0.209709\pi$
$798$	21.1351			0.748174
$799$	15.1356	−	36.4935i	0.535460	−	1.29105i
$800$	4.97757			0.175984
$801$		−	12.9576i		−	0.457833i
$802$	2.46188	+	2.46188i	0.0869320	+	0.0869320i
$803$	−9.79687			−0.345724
$804$	2.16134	+	2.16134i	0.0762244	+	0.0762244i
$805$	1.06901	−	1.06901i	0.0376777	−	0.0376777i
$806$	−16.8617	+	16.8617i	−0.593928	+	0.593928i
$807$		−	18.0891i		−	0.636768i
$808$			6.21450i			0.218625i
$809$	37.4310	−	37.4310i	1.31600	−	1.31600i	0.399091	−	0.916911i	$-0.369326\pi$
$809$	37.4310	−	37.4310i	1.31600	−	1.31600i	0.916911	−	0.399091i	$-0.130674\pi$
$810$	−0.105899	+	0.105899i	−0.00372091	+	0.00372091i
$811$	−18.7367	−	18.7367i	−0.657935	−	0.657935i	0.296956	−	0.954891i	$-0.404029\pi$
$811$	−18.7367	−	18.7367i	−0.657935	−	0.657935i	−0.954891	+	0.296956i	$0.904029\pi$
$812$	12.5616			0.440825
$813$	−16.7552	−	16.7552i	−0.587631	−	0.587631i
$814$		−	7.92327i		−	0.277710i
$815$	−0.662701			−0.0232134
$816$	3.80997	−	1.57610i	0.133376	−	0.0551746i
$817$	−41.7880			−1.46198
$818$			27.7960i			0.971865i
$819$	7.66306	+	7.66306i	0.267769	+	0.267769i
$820$	0.0762280			0.00266200
$821$	3.27018	+	3.27018i	0.114130	+	0.114130i	0.761865	−	0.647735i	$-0.224284\pi$
$821$	3.27018	+	3.27018i	0.114130	+	0.114130i	−0.647735	+	0.761865i	$0.724284\pi$
$822$	−7.16424	+	7.16424i	−0.249881	+	0.249881i
$823$	23.1253	−	23.1253i	0.806098	−	0.806098i	−0.177942	−	0.984041i	$-0.556944\pi$
$823$	23.1253	−	23.1253i	0.806098	−	0.806098i	0.984041	+	0.177942i	$0.0569441\pi$
$824$			1.59372i			0.0555199i
$825$			4.97757i			0.173297i
$826$	−19.8591	+	19.8591i	−0.690987	+	0.690987i
$827$	−34.9532	+	34.9532i	−1.21544	+	1.21544i	−0.246228	+	0.969212i	$0.579191\pi$
$827$	−34.9532	+	34.9532i	−1.21544	+	1.21544i	−0.969212	+	0.246228i	$0.920809\pi$
$828$	1.96771	+	1.96771i	0.0683827	+	0.0683827i
$829$	53.3148			1.85170			0.925850	−	0.377891i	$-0.123351\pi$
$829$	53.3148			1.85170			0.925850	+	0.377891i	$0.123351\pi$
$830$	1.20822	+	1.20822i	0.0419381	+	0.0419381i
$831$		−	27.7075i		−	0.961164i
$832$	−2.98747			−0.103572
$833$	−23.4574	−	9.72893i	−0.812750	−	0.337088i
$834$	19.9985			0.692492
$835$		−	2.54427i		−	0.0880482i
$836$	−4.11979	−	4.11979i	−0.142486	−	0.142486i
$837$	−7.98203			−0.275899
$838$	−5.96153	−	5.96153i	−0.205938	−	0.205938i
$839$	5.19776	−	5.19776i	0.179447	−	0.179447i	−0.611668	−	0.791115i	$-0.709501\pi$
$839$	5.19776	−	5.19776i	0.179447	−	0.179447i	0.791115	+	0.611668i	$0.209501\pi$
$840$	−0.384154	+	0.384154i	−0.0132546	+	0.0132546i
$841$		−	17.0089i		−	0.586514i
$842$		−	22.8344i		−	0.786927i
$843$	−14.0498	+	14.0498i	−0.483899	+	0.483899i
$844$	13.7187	−	13.7187i	0.472217	−	0.472217i
$845$	0.431543	+	0.431543i	0.0148455	+	0.0148455i
$846$	−9.58204			−0.329437
$847$	−2.56507	−	2.56507i	−0.0881369	−	0.0881369i
$848$			0.360811i			0.0123903i
$849$	−10.8906			−0.373765
$850$	7.86250	−	18.9572i	0.269681	−	0.650228i
$851$	−22.0486			−0.755816
$852$			3.12626i			0.107104i
$853$	11.0055	+	11.0055i	0.376823	+	0.376823i	0.869955	−	0.493132i	$-0.164148\pi$
$853$	11.0055	+	11.0055i	0.376823	+	0.376823i	−0.493132	+	0.869955i	$0.664148\pi$
$854$	−17.6447			−0.603789
$855$	−0.616995	−	0.616995i	−0.0211008	−	0.0211008i
$856$	−3.68250	+	3.68250i	−0.125865	+	0.125865i
$857$	20.7734	−	20.7734i	0.709607	−	0.709607i	−0.256845	−	0.966453i	$-0.582683\pi$
$857$	20.7734	−	20.7734i	0.709607	−	0.709607i	0.966453	+	0.256845i	$0.0826831\pi$
$858$		−	2.98747i		−	0.101990i
$859$			38.1365i			1.30120i	0.759420	+	0.650601i	$0.225483\pi$
$859$			38.1365i			1.30120i	−0.759420	+	0.650601i	$0.774517\pi$
$860$	0.759544	−	0.759544i	0.0259002	−	0.0259002i
$861$	1.30559	−	1.30559i	0.0444944	−	0.0444944i
$862$	−12.6106	−	12.6106i	−0.429519	−	0.429519i
$863$	45.8768			1.56167			0.780833	−	0.624740i	$-0.214795\pi$
$863$	45.8768			1.56167			0.780833	+	0.624740i	$0.214795\pi$
$864$	−0.707107	−	0.707107i	−0.0240563	−	0.0240563i
$865$			2.85350i			0.0970220i
$866$	−38.1510			−1.29642
$867$	0.0155386	−	17.0000i	0.000527717	−	0.577350i
$868$	−28.9553			−0.982806
$869$		−	2.28147i		−	0.0773934i
$870$	−0.366709	−	0.366709i	−0.0124326	−	0.0124326i
$871$	−9.13146			−0.309408
$872$	−5.95837	−	5.95837i	−0.201776	−	0.201776i
$873$	−1.94936	+	1.94936i	−0.0659760	+	0.0659760i
$874$	−11.4644	+	11.4644i	−0.387789	+	0.387789i
$875$			5.42058i			0.183249i
$876$		−	9.79687i		−	0.331006i
$877$	−22.5908	+	22.5908i	−0.762837	+	0.762837i	−0.976834	−	0.213997i	$-0.931352\pi$
$877$	−22.5908	+	22.5908i	−0.762837	+	0.762837i	0.213997	+	0.976834i	$0.431352\pi$
$878$	−14.2867	+	14.2867i	−0.482152	+	0.482152i
$879$	−13.6636	−	13.6636i	−0.460862	−	0.460862i
$880$	0.149764			0.00504853
$881$	31.8538	+	31.8538i	1.07318	+	1.07318i	0.997102	+	0.0760794i	$0.0242403\pi$
$881$	31.8538	+	31.8538i	1.07318	+	1.07318i	0.0760794	+	0.997102i	$0.475760\pi$
$882$			6.15917i			0.207390i
$883$	−29.1597			−0.981303			−0.490652	−	0.871356i	$-0.663241\pi$
$883$	−29.1597			−0.981303			−0.490652	+	0.871356i	$0.663241\pi$
$884$	−4.71896	+	11.3779i	−0.158716	+	0.382679i
$885$	1.15949			0.0389759
$886$		−	20.9317i		−	0.703215i
$887$	−15.9622	−	15.9622i	−0.535959	−	0.535959i	0.386381	−	0.922339i	$-0.373725\pi$
$887$	−15.9622	−	15.9622i	−0.535959	−	0.535959i	−0.922339	+	0.386381i	$0.873725\pi$
$888$	7.92327			0.265887
$889$	12.9175	+	12.9175i	0.433240	+	0.433240i
$890$	−1.37219	+	1.37219i	−0.0459960	+	0.0459960i
$891$	0.707107	−	0.707107i	0.0236890	−	0.0236890i
$892$			11.0446i			0.369802i
$893$		−	55.8275i		−	1.86819i
$894$	−8.00780	+	8.00780i	−0.267821	+	0.267821i
$895$	1.47769	−	1.47769i	0.0493937	−	0.0493937i
$896$	−2.56507	−	2.56507i	−0.0856930	−	0.0856930i
$897$	−8.31342			−0.277577
$898$	8.39529	+	8.39529i	0.280154	+	0.280154i
$899$		−	27.6403i		−	0.921856i
$900$	−4.97757			−0.165919
$901$	1.37416	+	0.569931i	0.0457799	+	0.0189872i
$902$	−0.508988			−0.0169475
$903$		−	26.0181i		−	0.865829i
$904$	4.30013	+	4.30013i	0.143020	+	0.143020i
$905$	0.723473			0.0240491
$906$	8.63847	+	8.63847i	0.286994	+	0.286994i
$907$	28.3707	−	28.3707i	0.942034	−	0.942034i	−0.0563754	−	0.998410i	$-0.517954\pi$
$907$	28.3707	−	28.3707i	0.942034	−	0.942034i	0.998410	+	0.0563754i	$0.0179544\pi$
$908$	7.24271	−	7.24271i	0.240358	−	0.240358i
$909$		−	6.21450i		−	0.206122i
$910$		−	1.62302i		−	0.0538026i
$911$	−4.91420	+	4.91420i	−0.162815	+	0.162815i	−0.783812	−	0.620998i	$-0.786728\pi$
$911$	−4.91420	+	4.91420i	−0.162815	+	0.162815i	0.620998	+	0.783812i	$0.286728\pi$
$912$	4.11979	−	4.11979i	0.136420	−	0.136420i
$913$	−8.06754	−	8.06754i	−0.266997	−	0.266997i
$914$	−9.66984			−0.319850
$915$	0.515100	+	0.515100i	0.0170287	+	0.0170287i
$916$		−	0.817874i		−	0.0270233i
$917$	25.3746			0.837942
$918$	−3.80997	+	1.57610i	−0.125748	+	0.0520192i
$919$	23.6849			0.781294			0.390647	−	0.920541i	$-0.372251\pi$
$919$	23.6849			0.781294			0.390647	+	0.920541i	$0.372251\pi$
$920$		−	0.416757i		−	0.0137401i
$921$	−10.1388	−	10.1388i	−0.334085	−	0.334085i
$922$	−9.61054			−0.316506
$923$	−6.60409	−	6.60409i	−0.217376	−	0.217376i
$924$	2.56507	−	2.56507i	0.0843846	−	0.0843846i
$925$	27.8873	−	27.8873i	0.916929	−	0.916929i
$926$		−	21.1925i		−	0.696429i
$927$		−	1.59372i		−	0.0523447i
$928$	2.44858	−	2.44858i	0.0803786	−	0.0803786i
$929$	−11.4935	+	11.4935i	−0.377090	+	0.377090i	−0.870051	−	0.492961i	$-0.835914\pi$
$929$	−11.4935	+	11.4935i	−0.377090	+	0.377090i	0.492961	+	0.870051i	$0.335914\pi$
$930$	0.845288	+	0.845288i	0.0277181	+	0.0277181i
$931$	−35.8849			−1.17608
$932$	−17.8135	−	17.8135i	−0.583502	−	0.583502i
$933$		−	0.547219i		−	0.0179151i
$934$	8.67124			0.283732
$935$	0.236564	−	0.570380i	0.00773649	−	0.0186534i
$936$	2.98747			0.0976484
$937$			34.3158i			1.12105i	0.828138	+	0.560525i	$0.189401\pi$
$937$			34.3158i			1.12105i	−0.828138	+	0.560525i	$0.810599\pi$
$938$	−7.84037	−	7.84037i	−0.255997	−	0.255997i
$939$	16.0621			0.524168
$940$	1.01473	+	1.01473i	0.0330968	+	0.0330968i
$941$	37.1676	−	37.1676i	1.21163	−	1.21163i	0.241140	−	0.970490i	$-0.422479\pi$
$941$	37.1676	−	37.1676i	1.21163	−	1.21163i	0.970490	−	0.241140i	$-0.0775212\pi$
$942$	2.19646	−	2.19646i	0.0715645	−	0.0715645i
$943$			1.41640i			0.0461242i
$944$			7.74214i			0.251985i
$945$	0.384154	−	0.384154i	0.0124965	−	0.0124965i
$946$	−5.07162	+	5.07162i	−0.164893	+	0.164893i
$947$	−37.0153	−	37.0153i	−1.20284	−	1.20284i	−0.973300	−	0.229535i	$-0.926279\pi$
$947$	−37.0153	−	37.0153i	−1.20284	−	1.20284i	−0.229535	−	0.973300i	$-0.573721\pi$
$948$	2.28147			0.0740986
$949$	20.6955	+	20.6955i	0.671803	+	0.671803i
$950$		−	29.0006i		−	0.940905i
$951$	1.34760			0.0436990
$952$	−13.8209	+	5.71740i	−0.447938	+	0.185302i
$953$	−6.77556			−0.219482			−0.109741	−	0.993960i	$-0.535002\pi$
$953$	−6.77556			−0.219482			−0.109741	+	0.993960i	$0.535002\pi$
$954$		−	0.360811i		−	0.0116817i
$955$	2.54550	+	2.54550i	0.0823705	+	0.0823705i
$956$	−11.1377			−0.360219
$957$	2.44858	+	2.44858i	0.0791514	+	0.0791514i
$958$	−6.30005	+	6.30005i	−0.203546	+	0.203546i
$959$	25.9887	−	25.9887i	0.839218	−	0.839218i
$960$			0.149764i			0.00483360i
$961$			32.7128i			1.05525i
$962$	−16.7376	+	16.7376i	−0.539641	+	0.539641i
$963$	3.68250	−	3.68250i	0.118667	−	0.118667i
$964$	1.21793	+	1.21793i	0.0392269	+	0.0392269i
$965$	−3.99418			−0.128577
$966$	−7.13799	−	7.13799i	−0.229661	−	0.229661i
$967$		−	28.8393i		−	0.927410i	−0.885990	−	0.463705i	$-0.846520\pi$
$967$		−	28.8393i		−	0.927410i	0.885990	−	0.463705i	$-0.153480\pi$
$968$	−1.00000			−0.0321412
$969$	−9.18279	−	22.1979i	−0.294994	−	0.713099i
$970$	0.412871			0.0132565
$971$			7.81967i			0.250945i	0.992097	+	0.125473i	$0.0400447\pi$
$971$			7.81967i			0.250945i	−0.992097	+	0.125473i	$0.959955\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	−72.5458			−2.32571
$974$	−20.8646	−	20.8646i	−0.668546	−	0.668546i
$975$	10.5149	−	10.5149i	0.336747	−	0.336747i
$976$	−3.43942	+	3.43942i	−0.110093	+	0.110093i
$977$			22.3311i			0.714436i	0.934021	+	0.357218i	$0.116275\pi$
$977$			22.3311i			0.714436i	−0.934021	+	0.357218i	$0.883725\pi$
$978$			4.42497i			0.141495i
$979$	9.16238	−	9.16238i	0.292831	−	0.292831i
$980$	0.652249	−	0.652249i	0.0208353	−	0.0208353i
$981$	5.95837	+	5.95837i	0.190236	+	0.190236i
$982$	−5.52514			−0.176314
$983$	−23.7811	−	23.7811i	−0.758498	−	0.758498i	0.217551	−	0.976049i	$-0.430193\pi$
$983$	−23.7811	−	23.7811i	−0.758498	−	0.758498i	−0.976049	+	0.217551i	$0.930193\pi$
$984$		−	0.508988i		−	0.0162260i
$985$	−3.75299			−0.119580
$986$	−5.45776	−	13.1932i	−0.173810	−	0.420158i
$987$	34.7594			1.10640
$988$			17.4058i			0.553751i
$989$	14.1131	+	14.1131i	0.448771	+	0.448771i
$990$	−0.149764			−0.00475980
$991$	7.86542	+	7.86542i	0.249853	+	0.249853i	0.820910	−	0.571057i	$-0.193467\pi$
$991$	7.86542	+	7.86542i	0.249853	+	0.249853i	−0.571057	+	0.820910i	$0.693467\pi$
$992$	−5.64415	+	5.64415i	−0.179202	+	0.179202i
$993$	−20.5466	+	20.5466i	−0.652026	+	0.652026i
$994$		−	11.3407i		−	0.359704i
$995$		−	0.691799i		−	0.0219315i
$996$	8.06754	−	8.06754i	0.255630	−	0.255630i
$997$	43.0908	−	43.0908i	1.36470	−	1.36470i	0.496880	−	0.867820i	$-0.334479\pi$
$997$	43.0908	−	43.0908i	1.36470	−	1.36470i	0.867820	−	0.496880i	$-0.165521\pi$
$998$	21.7762	+	21.7762i	0.689313	+	0.689313i
$999$	−7.92327			−0.250681

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1122.2.l.g.727.8	yes	20
17.4	even	4	inner	1122.2.l.g.463.8	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1122.2.l.g.463.8	✓	20	17.4	even	4	inner
1122.2.l.g.727.8	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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-0.105899 - 0.105899i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(2.56507 - 2.56507i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-0.105899 - 0.105899i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(2.56507 - 2.56507i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(0.105899 - 0.105899i) q^{10} +(-0.707107 + 0.707107i) q^{11} +(-0.707107 - 0.707107i) q^{12} +2.98747 q^{13} +(2.56507 + 2.56507i) q^{14} -0.149764i q^{15} +1.00000 q^{16} +(1.57958 - 3.80853i) q^{17} -1.00000 q^{18} -5.82626i q^{19} +(0.105899 + 0.105899i) q^{20} +3.62756 q^{21} +(-0.707107 - 0.707107i) q^{22} +(-1.96771 + 1.96771i) q^{23} +(0.707107 - 0.707107i) q^{24} -4.97757i q^{25} +2.98747i q^{26} +(-0.707107 + 0.707107i) q^{27} +(-2.56507 + 2.56507i) q^{28} +(-2.44858 - 2.44858i) q^{29} +0.149764 q^{30} +(5.64415 + 5.64415i) q^{31} +1.00000i q^{32} -1.00000 q^{33} +(3.80853 + 1.57958i) q^{34} -0.543276 q^{35} -1.00000i q^{36} +(5.60260 + 5.60260i) q^{37} +5.82626 q^{38} +(2.11246 + 2.11246i) q^{39} +(-0.105899 + 0.105899i) q^{40} +(0.359909 - 0.359909i) q^{41} +3.62756i q^{42} -7.17235i q^{43} +(0.707107 - 0.707107i) q^{44} +(0.105899 - 0.105899i) q^{45} +(-1.96771 - 1.96771i) q^{46} +9.58204 q^{47} +(0.707107 + 0.707107i) q^{48} -6.15917i q^{49} +4.97757 q^{50} +(3.80997 - 1.57610i) q^{51} -2.98747 q^{52} +0.360811i q^{53} +(-0.707107 - 0.707107i) q^{54} +0.149764 q^{55} +(-2.56507 - 2.56507i) q^{56} +(4.11979 - 4.11979i) q^{57} +(2.44858 - 2.44858i) q^{58} +7.74214i q^{59} +0.149764i q^{60} +(-3.43942 + 3.43942i) q^{61} +(-5.64415 + 5.64415i) q^{62} +(2.56507 + 2.56507i) q^{63} -1.00000 q^{64} +(-0.316369 - 0.316369i) q^{65} -1.00000i q^{66} -3.05659 q^{67} +(-1.57958 + 3.80853i) q^{68} -2.78276 q^{69} -0.543276i q^{70} +(-2.21060 - 2.21060i) q^{71} +1.00000 q^{72} +(6.92743 + 6.92743i) q^{73} +(-5.60260 + 5.60260i) q^{74} +(3.51967 - 3.51967i) q^{75} +5.82626i q^{76} +3.62756i q^{77} +(-2.11246 + 2.11246i) q^{78} +(-1.61324 + 1.61324i) q^{79} +(-0.105899 - 0.105899i) q^{80} -1.00000 q^{81} +(0.359909 + 0.359909i) q^{82} +11.4092i q^{83} -3.62756 q^{84} +(-0.570596 + 0.236043i) q^{85} +7.17235 q^{86} -3.46282i q^{87} +(0.707107 + 0.707107i) q^{88} -12.9576 q^{89} +(0.105899 + 0.105899i) q^{90} +(7.66306 - 7.66306i) q^{91} +(1.96771 - 1.96771i) q^{92} +7.98203i q^{93} +9.58204i q^{94} +(-0.616995 + 0.616995i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(1.94936 + 1.94936i) q^{97} +6.15917 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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