LMFDB - Embedded newform 1122.2.l.b.727.1

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:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			727.1
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1122.727
Dual form			1122.2.l.b.463.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(0.414214 + 0.414214i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(2.82843 - 2.82843i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(0.414214 + 0.414214i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(2.82843 - 2.82843i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +(0.414214 - 0.414214i) q^{10} +(-0.707107 + 0.707107i) q^{11} +(0.707107 + 0.707107i) q^{12} +6.82843 q^{13} +(-2.82843 - 2.82843i) q^{14} -0.585786i q^{15} +1.00000 q^{16} +(3.00000 + 2.82843i) q^{17} +1.00000 q^{18} +2.00000i q^{19} +(-0.414214 - 0.414214i) q^{20} -4.00000 q^{21} +(0.707107 + 0.707107i) q^{22} +(-4.82843 + 4.82843i) q^{23} +(0.707107 - 0.707107i) q^{24} -4.65685i q^{25} -6.82843i q^{26} +(0.707107 - 0.707107i) q^{27} +(-2.82843 + 2.82843i) q^{28} +(5.00000 + 5.00000i) q^{29} -0.585786 q^{30} +(6.00000 + 6.00000i) q^{31} -1.00000i q^{32} +1.00000 q^{33} +(2.82843 - 3.00000i) q^{34} +2.34315 q^{35} -1.00000i q^{36} +(-6.65685 - 6.65685i) q^{37} +2.00000 q^{38} +(-4.82843 - 4.82843i) q^{39} +(-0.414214 + 0.414214i) q^{40} +(6.65685 - 6.65685i) q^{41} +4.00000i q^{42} -2.00000i q^{43} +(0.707107 - 0.707107i) q^{44} +(-0.414214 + 0.414214i) q^{45} +(4.82843 + 4.82843i) q^{46} +0.343146 q^{47} +(-0.707107 - 0.707107i) q^{48} -9.00000i q^{49} -4.65685 q^{50} +(-0.121320 - 4.12132i) q^{51} -6.82843 q^{52} -12.4853i q^{53} +(-0.707107 - 0.707107i) q^{54} -0.585786 q^{55} +(2.82843 + 2.82843i) q^{56} +(1.41421 - 1.41421i) q^{57} +(5.00000 - 5.00000i) q^{58} +3.65685i q^{59} +0.585786i q^{60} +(3.24264 - 3.24264i) q^{61} +(6.00000 - 6.00000i) q^{62} +(2.82843 + 2.82843i) q^{63} -1.00000 q^{64} +(2.82843 + 2.82843i) q^{65} -1.00000i q^{66} -13.6569 q^{67} +(-3.00000 - 2.82843i) q^{68} +6.82843 q^{69} -2.34315i q^{70} +(-2.82843 - 2.82843i) q^{71} -1.00000 q^{72} +(1.24264 + 1.24264i) q^{73} +(-6.65685 + 6.65685i) q^{74} +(-3.29289 + 3.29289i) q^{75} -2.00000i q^{76} +4.00000i q^{77} +(-4.82843 + 4.82843i) q^{78} +(-4.82843 + 4.82843i) q^{79} +(0.414214 + 0.414214i) q^{80} -1.00000 q^{81} +(-6.65685 - 6.65685i) q^{82} +4.00000i q^{83} +4.00000 q^{84} +(0.0710678 + 2.41421i) q^{85} -2.00000 q^{86} -7.07107i q^{87} +(-0.707107 - 0.707107i) q^{88} +10.8284 q^{89} +(0.414214 + 0.414214i) q^{90} +(19.3137 - 19.3137i) q^{91} +(4.82843 - 4.82843i) q^{92} -8.48528i q^{93} -0.343146i q^{94} +(-0.828427 + 0.828427i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(-6.65685 - 6.65685i) q^{97} -9.00000 q^{98} +(-0.707107 - 0.707107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 4 q^{5}+O(q^{10}) $ 4 * q - 4 * q^4 - 4 * q^5	$ 4 q - 4 q^{4} - 4 q^{5} - 4 q^{10} + 16 q^{13} + 4 q^{16} + 12 q^{17} + 4 q^{18} + 4 q^{20} - 16 q^{21} - 8 q^{23} + 20 q^{29} - 8 q^{30} + 24 q^{31} + 4 q^{33} + 32 q^{35} - 4 q^{37} + 8 q^{38} - 8 q^{39} + 4 q^{40} + 4 q^{41} + 4 q^{45} + 8 q^{46} + 24 q^{47} + 4 q^{50} + 8 q^{51} - 16 q^{52} - 8 q^{55} + 20 q^{58} - 4 q^{61} + 24 q^{62} - 4 q^{64} - 32 q^{67} - 12 q^{68} + 16 q^{69} - 4 q^{72} - 12 q^{73} - 4 q^{74} - 16 q^{75} - 8 q^{78} - 8 q^{79} - 4 q^{80} - 4 q^{81} - 4 q^{82} + 16 q^{84} - 28 q^{85} - 8 q^{86} + 32 q^{89} - 4 q^{90} + 32 q^{91} + 8 q^{92} + 8 q^{95} - 4 q^{97} - 36 q^{98}+O(q^{100}) $ 4 * q - 4 * q^4 - 4 * q^5 - 4 * q^10 + 16 * q^13 + 4 * q^16 + 12 * q^17 + 4 * q^18 + 4 * q^20 - 16 * q^21 - 8 * q^23 + 20 * q^29 - 8 * q^30 + 24 * q^31 + 4 * q^33 + 32 * q^35 - 4 * q^37 + 8 * q^38 - 8 * q^39 + 4 * q^40 + 4 * q^41 + 4 * q^45 + 8 * q^46 + 24 * q^47 + 4 * q^50 + 8 * q^51 - 16 * q^52 - 8 * q^55 + 20 * q^58 - 4 * q^61 + 24 * q^62 - 4 * q^64 - 32 * q^67 - 12 * q^68 + 16 * q^69 - 4 * q^72 - 12 * q^73 - 4 * q^74 - 16 * q^75 - 8 * q^78 - 8 * q^79 - 4 * q^80 - 4 * q^81 - 4 * q^82 + 16 * q^84 - 28 * q^85 - 8 * q^86 + 32 * q^89 - 4 * q^90 + 32 * q^91 + 8 * q^92 + 8 * 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
$5$	0.414214	+	0.414214i	0.185242	+	0.185242i	0.793635	−	0.608394i	$-0.208186\pi$
$5$	0.414214	+	0.414214i	0.185242	+	0.185242i	−0.608394	+	0.793635i	$0.708186\pi$
$6$	−0.707107	+	0.707107i	−0.288675	+	0.288675i
$7$	2.82843	−	2.82843i	1.06904	−	1.06904i	0.0716124	−	0.997433i	$-0.477186\pi$
$7$	2.82843	−	2.82843i	1.06904	−	1.06904i	0.997433	−	0.0716124i	$-0.0228145\pi$
$8$			1.00000i			0.353553i
$9$			1.00000i			0.333333i
$10$	0.414214	−	0.414214i	0.130986	−	0.130986i
$11$	−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
$13$	6.82843			1.89386			0.946932	−	0.321433i	$-0.104164\pi$
$13$	6.82843			1.89386			0.946932	+	0.321433i	$0.104164\pi$
$14$	−2.82843	−	2.82843i	−0.755929	−	0.755929i
$15$		−	0.585786i		−	0.151249i
$16$	1.00000			0.250000
$17$	3.00000	+	2.82843i	0.727607	+	0.685994i
$17$	3.00000	+	2.82843i	0.727607	+	0.685994i
$18$	1.00000			0.235702
$19$			2.00000i			0.458831i	0.973329	+	0.229416i	$0.0736815\pi$
$19$			2.00000i			0.458831i	−0.973329	+	0.229416i	$0.926318\pi$
$20$	−0.414214	−	0.414214i	−0.0926210	−	0.0926210i
$21$	−4.00000			−0.872872
$22$	0.707107	+	0.707107i	0.150756	+	0.150756i
$23$	−4.82843	+	4.82843i	−1.00680	+	1.00680i	−0.00681991	+	0.999977i	$0.502171\pi$
$23$	−4.82843	+	4.82843i	−1.00680	+	1.00680i	−0.999977	+	0.00681991i	$0.997829\pi$
$24$	0.707107	−	0.707107i	0.144338	−	0.144338i
$25$		−	4.65685i		−	0.931371i
$26$		−	6.82843i		−	1.33916i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−2.82843	+	2.82843i	−0.534522	+	0.534522i
$29$	5.00000	+	5.00000i	0.928477	+	0.928477i	0.997608	−	0.0691309i	$-0.0220226\pi$
$29$	5.00000	+	5.00000i	0.928477	+	0.928477i	−0.0691309	+	0.997608i	$0.522023\pi$
$30$	−0.585786			−0.106949
$31$	6.00000	+	6.00000i	1.07763	+	1.07763i	0.996721	+	0.0809104i	$0.0257828\pi$
$31$	6.00000	+	6.00000i	1.07763	+	1.07763i	0.0809104	+	0.996721i	$0.474217\pi$
$32$		−	1.00000i		−	0.176777i
$33$	1.00000			0.174078
$34$	2.82843	−	3.00000i	0.485071	−	0.514496i
$35$	2.34315			0.396064
$36$		−	1.00000i		−	0.166667i
$37$	−6.65685	−	6.65685i	−1.09438	−	1.09438i	−0.995055	−	0.0993251i	$-0.968332\pi$
$37$	−6.65685	−	6.65685i	−1.09438	−	1.09438i	−0.0993251	−	0.995055i	$-0.531668\pi$
$38$	2.00000			0.324443
$39$	−4.82843	−	4.82843i	−0.773167	−	0.773167i
$40$	−0.414214	+	0.414214i	−0.0654929	+	0.0654929i
$41$	6.65685	−	6.65685i	1.03963	−	1.03963i	0.0404442	−	0.999182i	$-0.487123\pi$
$41$	6.65685	−	6.65685i	1.03963	−	1.03963i	0.999182	−	0.0404442i	$-0.0128773\pi$
$42$			4.00000i			0.617213i
$43$		−	2.00000i		−	0.304997i	−0.988304	−	0.152499i	$-0.951268\pi$
$43$		−	2.00000i		−	0.304997i	0.988304	−	0.152499i	$-0.0487319\pi$
$44$	0.707107	−	0.707107i	0.106600	−	0.106600i
$45$	−0.414214	+	0.414214i	−0.0617473	+	0.0617473i
$46$	4.82843	+	4.82843i	0.711913	+	0.711913i
$47$	0.343146			0.0500530			0.0250265	−	0.999687i	$-0.492033\pi$
$47$	0.343146			0.0500530			0.0250265	+	0.999687i	$0.492033\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$		−	9.00000i		−	1.28571i
$50$	−4.65685			−0.658579
$51$	−0.121320	−	4.12132i	−0.0169882	−	0.577100i
$52$	−6.82843			−0.946932
$53$		−	12.4853i		−	1.71499i	−0.514496	−	0.857493i	$-0.672021\pi$
$53$		−	12.4853i		−	1.71499i	0.514496	−	0.857493i	$-0.327979\pi$
$54$	−0.707107	−	0.707107i	−0.0962250	−	0.0962250i
$55$	−0.585786			−0.0789874
$56$	2.82843	+	2.82843i	0.377964	+	0.377964i
$57$	1.41421	−	1.41421i	0.187317	−	0.187317i
$58$	5.00000	−	5.00000i	0.656532	−	0.656532i
$59$			3.65685i			0.476082i	0.971255	+	0.238041i	$0.0765052\pi$
$59$			3.65685i			0.476082i	−0.971255	+	0.238041i	$0.923495\pi$
$60$			0.585786i			0.0756247i
$61$	3.24264	−	3.24264i	0.415178	−	0.415178i	−0.468360	−	0.883538i	$-0.655155\pi$
$61$	3.24264	−	3.24264i	0.415178	−	0.415178i	0.883538	+	0.468360i	$0.155155\pi$
$62$	6.00000	−	6.00000i	0.762001	−	0.762001i
$63$	2.82843	+	2.82843i	0.356348	+	0.356348i
$64$	−1.00000			−0.125000
$65$	2.82843	+	2.82843i	0.350823	+	0.350823i
$66$		−	1.00000i		−	0.123091i
$67$	−13.6569			−1.66845			−0.834225	−	0.551424i	$-0.814085\pi$
$67$	−13.6569			−1.66845			−0.834225	+	0.551424i	$0.814085\pi$
$68$	−3.00000	−	2.82843i	−0.363803	−	0.342997i
$69$	6.82843			0.822046
$70$		−	2.34315i		−	0.280059i
$71$	−2.82843	−	2.82843i	−0.335673	−	0.335673i	0.519063	−	0.854736i	$-0.326281\pi$
$71$	−2.82843	−	2.82843i	−0.335673	−	0.335673i	−0.854736	+	0.519063i	$0.826281\pi$
$72$	−1.00000			−0.117851
$73$	1.24264	+	1.24264i	0.145440	+	0.145440i	0.776078	−	0.630637i	$-0.217206\pi$
$73$	1.24264	+	1.24264i	0.145440	+	0.145440i	−0.630637	+	0.776078i	$0.717206\pi$
$74$	−6.65685	+	6.65685i	−0.773844	+	0.773844i
$75$	−3.29289	+	3.29289i	−0.380231	+	0.380231i
$76$		−	2.00000i		−	0.229416i
$77$			4.00000i			0.455842i
$78$	−4.82843	+	4.82843i	−0.546712	+	0.546712i
$79$	−4.82843	+	4.82843i	−0.543240	+	0.543240i	−0.924477	−	0.381237i	$-0.875498\pi$
$79$	−4.82843	+	4.82843i	−0.543240	+	0.543240i	0.381237	+	0.924477i	$0.375498\pi$
$80$	0.414214	+	0.414214i	0.0463105	+	0.0463105i
$81$	−1.00000			−0.111111
$82$	−6.65685	−	6.65685i	−0.735127	−	0.735127i
$83$			4.00000i			0.439057i	0.975606	+	0.219529i	$0.0704519\pi$
$83$			4.00000i			0.439057i	−0.975606	+	0.219529i	$0.929548\pi$
$84$	4.00000			0.436436
$85$	0.0710678	+	2.41421i	0.00770839	+	0.261858i
$86$	−2.00000			−0.215666
$87$		−	7.07107i		−	0.758098i
$88$	−0.707107	−	0.707107i	−0.0753778	−	0.0753778i
$89$	10.8284			1.14781			0.573905	−	0.818922i	$-0.305428\pi$
$89$	10.8284			1.14781			0.573905	+	0.818922i	$0.305428\pi$
$90$	0.414214	+	0.414214i	0.0436619	+	0.0436619i
$91$	19.3137	−	19.3137i	2.02463	−	2.02463i
$92$	4.82843	−	4.82843i	0.503398	−	0.503398i
$93$		−	8.48528i		−	0.879883i
$94$		−	0.343146i		−	0.0353928i
$95$	−0.828427	+	0.828427i	−0.0849948	+	0.0849948i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$	−6.65685	−	6.65685i	−0.675901	−	0.675901i	0.283169	−	0.959070i	$-0.408614\pi$
$97$	−6.65685	−	6.65685i	−0.675901	−	0.675901i	−0.959070	+	0.283169i	$0.908614\pi$
$98$	−9.00000			−0.909137
$99$	−0.707107	−	0.707107i	−0.0710669	−	0.0710669i
$100$			4.65685i			0.465685i
$101$	−12.0000			−1.19404			−0.597022	−	0.802225i	$-0.703650\pi$
$101$	−12.0000			−1.19404			−0.597022	+	0.802225i	$0.703650\pi$
$102$	−4.12132	+	0.121320i	−0.408072	+	0.0120125i
$103$	2.34315			0.230877			0.115439	−	0.993315i	$-0.463173\pi$
$103$	2.34315			0.230877			0.115439	+	0.993315i	$0.463173\pi$
$104$			6.82843i			0.669582i
$105$	−1.65685	−	1.65685i	−0.161692	−	0.161692i
$106$	−12.4853			−1.21268
$107$	0.343146	+	0.343146i	0.0331732	+	0.0331732i	0.723499	−	0.690326i	$-0.242533\pi$
$107$	0.343146	+	0.343146i	0.0331732	+	0.0331732i	−0.690326	+	0.723499i	$0.742533\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$	11.2426	−	11.2426i	1.07685	−	1.07685i	0.0800596	−	0.996790i	$-0.474489\pi$
$109$	11.2426	−	11.2426i	1.07685	−	1.07685i	0.996790	−	0.0800596i	$-0.0255111\pi$
$110$			0.585786i			0.0558525i
$111$			9.41421i			0.893558i
$112$	2.82843	−	2.82843i	0.267261	−	0.267261i
$113$	−9.24264	+	9.24264i	−0.869474	+	0.869474i	−0.992414	−	0.122940i	$-0.960768\pi$
$113$	−9.24264	+	9.24264i	−0.869474	+	0.869474i	0.122940	+	0.992414i	$0.460768\pi$
$114$	−1.41421	−	1.41421i	−0.132453	−	0.132453i
$115$	−4.00000			−0.373002
$116$	−5.00000	−	5.00000i	−0.464238	−	0.464238i
$117$			6.82843i			0.631288i
$118$	3.65685			0.336641
$119$	16.4853	−	0.485281i	1.51120	−	0.0444857i
$120$	0.585786			0.0534747
$121$		−	1.00000i		−	0.0909091i
$122$	−3.24264	−	3.24264i	−0.293575	−	0.293575i
$123$	−9.41421			−0.848851
$124$	−6.00000	−	6.00000i	−0.538816	−	0.538816i
$125$	4.00000	−	4.00000i	0.357771	−	0.357771i
$126$	2.82843	−	2.82843i	0.251976	−	0.251976i
$127$		−	11.6569i		−	1.03438i	−0.855871	−	0.517189i	$-0.826978\pi$
$127$		−	11.6569i		−	1.03438i	0.855871	−	0.517189i	$-0.173022\pi$
$128$			1.00000i			0.0883883i
$129$	−1.41421	+	1.41421i	−0.124515	+	0.124515i
$130$	2.82843	−	2.82843i	0.248069	−	0.248069i
$131$	9.31371	+	9.31371i	0.813742	+	0.813742i	0.985193	−	0.171450i	$-0.0548453\pi$
$131$	9.31371	+	9.31371i	0.813742	+	0.813742i	−0.171450	+	0.985193i	$0.554845\pi$
$132$	−1.00000			−0.0870388
$133$	5.65685	+	5.65685i	0.490511	+	0.490511i
$134$			13.6569i			1.17977i
$135$	0.585786			0.0504165
$136$	−2.82843	+	3.00000i	−0.242536	+	0.257248i
$137$	0.485281			0.0414604			0.0207302	−	0.999785i	$-0.493401\pi$
$137$	0.485281			0.0414604			0.0207302	+	0.999785i	$0.493401\pi$
$138$		−	6.82843i		−	0.581274i
$139$	8.82843	+	8.82843i	0.748817	+	0.748817i	0.974257	−	0.225440i	$-0.0723819\pi$
$139$	8.82843	+	8.82843i	0.748817	+	0.748817i	−0.225440	+	0.974257i	$0.572382\pi$
$140$	−2.34315			−0.198032
$141$	−0.242641	−	0.242641i	−0.0204340	−	0.0204340i
$142$	−2.82843	+	2.82843i	−0.237356	+	0.237356i
$143$	−4.82843	+	4.82843i	−0.403773	+	0.403773i
$144$			1.00000i			0.0833333i
$145$			4.14214i			0.343986i
$146$	1.24264	−	1.24264i	0.102842	−	0.102842i
$147$	−6.36396	+	6.36396i	−0.524891	+	0.524891i
$148$	6.65685	+	6.65685i	0.547190	+	0.547190i
$149$	−21.3137			−1.74609			−0.873044	−	0.487642i	$-0.837857\pi$
$149$	−21.3137			−1.74609			−0.873044	+	0.487642i	$0.837857\pi$
$150$	3.29289	+	3.29289i	0.268864	+	0.268864i
$151$			0.343146i			0.0279248i	0.999903	+	0.0139624i	$0.00444452\pi$
$151$			0.343146i			0.0279248i	−0.999903	+	0.0139624i	$0.995555\pi$
$152$	−2.00000			−0.162221
$153$	−2.82843	+	3.00000i	−0.228665	+	0.242536i
$154$	4.00000			0.322329
$155$			4.97056i			0.399245i
$156$	4.82843	+	4.82843i	0.386584	+	0.386584i
$157$	−14.0000			−1.11732			−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000			−1.11732			−0.558661	+	0.829396i	$0.688685\pi$
$158$	4.82843	+	4.82843i	0.384129	+	0.384129i
$159$	−8.82843	+	8.82843i	−0.700140	+	0.700140i
$160$	0.414214	−	0.414214i	0.0327465	−	0.0327465i
$161$			27.3137i			2.15262i
$162$			1.00000i			0.0785674i
$163$	−6.00000	+	6.00000i	−0.469956	+	0.469956i	−0.901900	−	0.431944i	$-0.857828\pi$
$163$	−6.00000	+	6.00000i	−0.469956	+	0.469956i	0.431944	+	0.901900i	$0.357828\pi$
$164$	−6.65685	+	6.65685i	−0.519813	+	0.519813i
$165$	0.414214	+	0.414214i	0.0322465	+	0.0322465i
$166$	4.00000			0.310460
$167$	−5.31371	−	5.31371i	−0.411187	−	0.411187i	0.470965	−	0.882152i	$-0.343906\pi$
$167$	−5.31371	−	5.31371i	−0.411187	−	0.411187i	−0.882152	+	0.470965i	$0.843906\pi$
$168$		−	4.00000i		−	0.308607i
$169$	33.6274			2.58672
$170$	2.41421	−	0.0710678i	0.185162	−	0.00545065i
$171$	−2.00000			−0.152944
$172$			2.00000i			0.152499i
$173$	−0.656854	−	0.656854i	−0.0499397	−	0.0499397i	0.681696	−	0.731636i	$-0.261243\pi$
$173$	−0.656854	−	0.656854i	−0.0499397	−	0.0499397i	−0.731636	+	0.681696i	$0.761243\pi$
$174$	−7.07107			−0.536056
$175$	−13.1716	−	13.1716i	−0.995677	−	0.995677i
$176$	−0.707107	+	0.707107i	−0.0533002	+	0.0533002i
$177$	2.58579	−	2.58579i	0.194360	−	0.194360i
$178$		−	10.8284i		−	0.811625i
$179$			10.9706i			0.819978i	0.912090	+	0.409989i	$0.134468\pi$
$179$			10.9706i			0.819978i	−0.912090	+	0.409989i	$0.865532\pi$
$180$	0.414214	−	0.414214i	0.0308737	−	0.0308737i
$181$	4.17157	−	4.17157i	0.310071	−	0.310071i	−0.534866	−	0.844937i	$-0.679638\pi$
$181$	4.17157	−	4.17157i	0.310071	−	0.310071i	0.844937	+	0.534866i	$0.179638\pi$
$182$	−19.3137	−	19.3137i	−1.43163	−	1.43163i
$183$	−4.58579			−0.338991
$184$	−4.82843	−	4.82843i	−0.355956	−	0.355956i
$185$		−	5.51472i		−	0.405450i
$186$	−8.48528			−0.622171
$187$	−4.12132	+	0.121320i	−0.301381	+	0.00887182i
$188$	−0.343146			−0.0250265
$189$		−	4.00000i		−	0.290957i
$190$	0.828427	+	0.828427i	0.0601004	+	0.0601004i
$191$	−18.9706			−1.37266			−0.686331	−	0.727289i	$-0.740780\pi$
$191$	−18.9706			−1.37266			−0.686331	+	0.727289i	$0.740780\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$	−8.41421	+	8.41421i	−0.605668	+	0.605668i	−0.941811	−	0.336143i	$-0.890878\pi$
$193$	−8.41421	+	8.41421i	−0.605668	+	0.605668i	0.336143	+	0.941811i	$0.390878\pi$
$194$	−6.65685	+	6.65685i	−0.477934	+	0.477934i
$195$		−	4.00000i		−	0.286446i
$196$			9.00000i			0.642857i
$197$	−1.34315	+	1.34315i	−0.0956952	+	0.0956952i	−0.753334	−	0.657638i	$-0.771555\pi$
$197$	−1.34315	+	1.34315i	−0.0956952	+	0.0956952i	0.657638	+	0.753334i	$0.271555\pi$
$198$	−0.707107	+	0.707107i	−0.0502519	+	0.0502519i
$199$	10.8284	+	10.8284i	0.767607	+	0.767607i	0.977685	−	0.210078i	$-0.0673717\pi$
$199$	10.8284	+	10.8284i	0.767607	+	0.767607i	−0.210078	+	0.977685i	$0.567372\pi$
$200$	4.65685			0.329289
$201$	9.65685	+	9.65685i	0.681142	+	0.681142i
$202$			12.0000i			0.844317i
$203$	28.2843			1.98517
$204$	0.121320	+	4.12132i	0.00849412	+	0.288550i
$205$	5.51472			0.385165
$206$		−	2.34315i		−	0.163255i
$207$	−4.82843	−	4.82843i	−0.335599	−	0.335599i
$208$	6.82843			0.473466
$209$	−1.41421	−	1.41421i	−0.0978232	−	0.0978232i
$210$	−1.65685	+	1.65685i	−0.114334	+	0.114334i
$211$	14.8284	−	14.8284i	1.02083	−	1.02083i	0.0210527	−	0.999778i	$-0.493298\pi$
$211$	14.8284	−	14.8284i	1.02083	−	1.02083i	0.999778	−	0.0210527i	$-0.00670176\pi$
$212$			12.4853i			0.857493i
$213$			4.00000i			0.274075i
$214$	0.343146	−	0.343146i	0.0234570	−	0.0234570i
$215$	0.828427	−	0.828427i	0.0564983	−	0.0564983i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	33.9411			2.30407
$218$	−11.2426	−	11.2426i	−0.761448	−	0.761448i
$219$		−	1.75736i		−	0.118751i
$220$	0.585786			0.0394937
$221$	20.4853	+	19.3137i	1.37799	+	1.29918i
$222$	9.41421			0.631841
$223$			8.00000i			0.535720i	0.963458	+	0.267860i	$0.0863164\pi$
$223$			8.00000i			0.535720i	−0.963458	+	0.267860i	$0.913684\pi$
$224$	−2.82843	−	2.82843i	−0.188982	−	0.188982i
$225$	4.65685			0.310457
$226$	9.24264	+	9.24264i	0.614811	+	0.614811i
$227$	1.17157	−	1.17157i	0.0777600	−	0.0777600i	−0.667157	−	0.744917i	$-0.732489\pi$
$227$	1.17157	−	1.17157i	0.0777600	−	0.0777600i	0.744917	+	0.667157i	$0.232489\pi$
$228$	−1.41421	+	1.41421i	−0.0936586	+	0.0936586i
$229$			17.3137i			1.14412i	0.820211	+	0.572061i	$0.193856\pi$
$229$			17.3137i			1.14412i	−0.820211	+	0.572061i	$0.806144\pi$
$230$			4.00000i			0.263752i
$231$	2.82843	−	2.82843i	0.186097	−	0.186097i
$232$	−5.00000	+	5.00000i	−0.328266	+	0.328266i
$233$	5.34315	+	5.34315i	0.350041	+	0.350041i	0.860125	−	0.510084i	$-0.170386\pi$
$233$	5.34315	+	5.34315i	0.350041	+	0.350041i	−0.510084	+	0.860125i	$0.670386\pi$
$234$	6.82843			0.446388
$235$	0.142136	+	0.142136i	0.00927191	+	0.00927191i
$236$		−	3.65685i		−	0.238041i
$237$	6.82843			0.443554
$238$	−0.485281	−	16.4853i	−0.0314561	−	1.06858i
$239$	6.34315			0.410304			0.205152	−	0.978730i	$-0.434231\pi$
$239$	6.34315			0.410304			0.205152	+	0.978730i	$0.434231\pi$
$240$		−	0.585786i		−	0.0378124i
$241$	15.5858	+	15.5858i	1.00397	+	1.00397i	0.999992	+	0.00397667i	$0.00126582\pi$
$241$	15.5858	+	15.5858i	1.00397	+	1.00397i	0.00397667	+	0.999992i	$0.498734\pi$
$242$	−1.00000			−0.0642824
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−3.24264	+	3.24264i	−0.207589	+	0.207589i
$245$	3.72792	−	3.72792i	0.238168	−	0.238168i
$246$			9.41421i			0.600228i
$247$			13.6569i			0.868965i
$248$	−6.00000	+	6.00000i	−0.381000	+	0.381000i
$249$	2.82843	−	2.82843i	0.179244	−	0.179244i
$250$	−4.00000	−	4.00000i	−0.252982	−	0.252982i
$251$	−1.31371			−0.0829205			−0.0414603	−	0.999140i	$-0.513201\pi$
$251$	−1.31371			−0.0829205			−0.0414603	+	0.999140i	$0.513201\pi$
$252$	−2.82843	−	2.82843i	−0.178174	−	0.178174i
$253$		−	6.82843i		−	0.429300i
$254$	−11.6569			−0.731416
$255$	1.65685	−	1.75736i	0.103756	−	0.110050i
$256$	1.00000			0.0625000
$257$		−	2.68629i		−	0.167566i	−0.996484	−	0.0837831i	$-0.973300\pi$
$257$		−	2.68629i		−	0.167566i	0.996484	−	0.0837831i	$-0.0267003\pi$
$258$	1.41421	+	1.41421i	0.0880451	+	0.0880451i
$259$	−37.6569			−2.33988
$260$	−2.82843	−	2.82843i	−0.175412	−	0.175412i
$261$	−5.00000	+	5.00000i	−0.309492	+	0.309492i
$262$	9.31371	−	9.31371i	0.575403	−	0.575403i
$263$		−	24.9706i		−	1.53975i	−0.638194	−	0.769875i	$-0.720318\pi$
$263$		−	24.9706i		−	1.53975i	0.638194	−	0.769875i	$-0.279682\pi$
$264$			1.00000i			0.0615457i
$265$	5.17157	−	5.17157i	0.317687	−	0.317687i
$266$	5.65685	−	5.65685i	0.346844	−	0.346844i
$267$	−7.65685	−	7.65685i	−0.468592	−	0.468592i
$268$	13.6569			0.834225
$269$	−15.5858	−	15.5858i	−0.950282	−	0.950282i	0.0485391	−	0.998821i	$-0.484543\pi$
$269$	−15.5858	−	15.5858i	−0.950282	−	0.950282i	−0.998821	+	0.0485391i	$0.984543\pi$
$270$		−	0.585786i		−	0.0356498i
$271$	−6.68629			−0.406163			−0.203082	−	0.979162i	$-0.565096\pi$
$271$	−6.68629			−0.406163			−0.203082	+	0.979162i	$0.565096\pi$
$272$	3.00000	+	2.82843i	0.181902	+	0.171499i
$273$	−27.3137			−1.65310
$274$		−	0.485281i		−	0.0293169i
$275$	3.29289	+	3.29289i	0.198569	+	0.198569i
$276$	−6.82843			−0.411023
$277$	13.2426	+	13.2426i	0.795673	+	0.795673i	0.982410	−	0.186737i	$-0.0597912\pi$
$277$	13.2426	+	13.2426i	0.795673	+	0.795673i	−0.186737	+	0.982410i	$0.559791\pi$
$278$	8.82843	−	8.82843i	0.529494	−	0.529494i
$279$	−6.00000	+	6.00000i	−0.359211	+	0.359211i
$280$			2.34315i			0.140030i
$281$			0.686292i			0.0409407i	0.999790	+	0.0204704i	$0.00651637\pi$
$281$			0.686292i			0.0409407i	−0.999790	+	0.0204704i	$0.993484\pi$
$282$	−0.242641	+	0.242641i	−0.0144490	+	0.0144490i
$283$	12.4853	−	12.4853i	0.742173	−	0.742173i	−0.230823	−	0.972996i	$-0.574142\pi$
$283$	12.4853	−	12.4853i	0.742173	−	0.742173i	0.972996	+	0.230823i	$0.0741418\pi$
$284$	2.82843	+	2.82843i	0.167836	+	0.167836i
$285$	1.17157			0.0693980
$286$	4.82843	+	4.82843i	0.285511	+	0.285511i
$287$		−	37.6569i		−	2.22281i
$288$	1.00000			0.0589256
$289$	1.00000	+	16.9706i	0.0588235	+	0.998268i
$290$	4.14214			0.243235
$291$			9.41421i			0.551871i
$292$	−1.24264	−	1.24264i	−0.0727200	−	0.0727200i
$293$	17.3137			1.01148			0.505739	−	0.862687i	$-0.331220\pi$
$293$	17.3137			1.01148			0.505739	+	0.862687i	$0.331220\pi$
$294$	6.36396	+	6.36396i	0.371154	+	0.371154i
$295$	−1.51472	+	1.51472i	−0.0881903	+	0.0881903i
$296$	6.65685	−	6.65685i	0.386922	−	0.386922i
$297$			1.00000i			0.0580259i
$298$			21.3137i			1.23467i
$299$	−32.9706	+	32.9706i	−1.90674	+	1.90674i
$300$	3.29289	−	3.29289i	0.190115	−	0.190115i
$301$	−5.65685	−	5.65685i	−0.326056	−	0.326056i
$302$	0.343146			0.0197458
$303$	8.48528	+	8.48528i	0.487467	+	0.487467i
$304$			2.00000i			0.114708i
$305$	2.68629			0.153817
$306$	3.00000	+	2.82843i	0.171499	+	0.161690i
$307$	−26.9706			−1.53929			−0.769646	−	0.638471i	$-0.779567\pi$
$307$	−26.9706			−1.53929			−0.769646	+	0.638471i	$0.779567\pi$
$308$		−	4.00000i		−	0.227921i
$309$	−1.65685	−	1.65685i	−0.0942551	−	0.0942551i
$310$	4.97056			0.282309
$311$	12.4853	+	12.4853i	0.707975	+	0.707975i	0.966109	−	0.258134i	$-0.0831075\pi$
$311$	12.4853	+	12.4853i	0.707975	+	0.707975i	−0.258134	+	0.966109i	$0.583108\pi$
$312$	4.82843	−	4.82843i	0.273356	−	0.273356i
$313$	−8.65685	+	8.65685i	−0.489314	+	0.489314i	−0.908090	−	0.418775i	$-0.862459\pi$
$313$	−8.65685	+	8.65685i	−0.489314	+	0.489314i	0.418775	+	0.908090i	$0.362459\pi$
$314$			14.0000i			0.790066i
$315$			2.34315i			0.132021i
$316$	4.82843	−	4.82843i	0.271620	−	0.271620i
$317$	−14.7574	+	14.7574i	−0.828856	+	0.828856i	−0.987359	−	0.158503i	$-0.949333\pi$
$317$	−14.7574	+	14.7574i	−0.828856	+	0.828856i	0.158503	+	0.987359i	$0.449333\pi$
$318$	8.82843	+	8.82843i	0.495074	+	0.495074i
$319$	−7.07107			−0.395904
$320$	−0.414214	−	0.414214i	−0.0231552	−	0.0231552i
$321$		−	0.485281i		−	0.0270858i
$322$	27.3137			1.52213
$323$	−5.65685	+	6.00000i	−0.314756	+	0.333849i
$324$	1.00000			0.0555556
$325$		−	31.7990i		−	1.76389i
$326$	6.00000	+	6.00000i	0.332309	+	0.332309i
$327$	−15.8995			−0.879244
$328$	6.65685	+	6.65685i	0.367563	+	0.367563i
$329$	0.970563	−	0.970563i	0.0535089	−	0.0535089i
$330$	0.414214	−	0.414214i	0.0228017	−	0.0228017i
$331$		−	16.9706i		−	0.932786i	−0.884577	−	0.466393i	$-0.845553\pi$
$331$		−	16.9706i		−	0.932786i	0.884577	−	0.466393i	$-0.154447\pi$
$332$		−	4.00000i		−	0.219529i
$333$	6.65685	−	6.65685i	0.364793	−	0.364793i
$334$	−5.31371	+	5.31371i	−0.290753	+	0.290753i
$335$	−5.65685	−	5.65685i	−0.309067	−	0.309067i
$336$	−4.00000			−0.218218
$337$	−2.75736	−	2.75736i	−0.150203	−	0.150203i	0.628006	−	0.778209i	$-0.283871\pi$
$337$	−2.75736	−	2.75736i	−0.150203	−	0.150203i	−0.778209	+	0.628006i	$0.783871\pi$
$338$		−	33.6274i		−	1.82909i
$339$	13.0711			0.709923
$340$	−0.0710678	−	2.41421i	−0.00385419	−	0.130929i
$341$	−8.48528			−0.459504
$342$			2.00000i			0.108148i
$343$	−5.65685	−	5.65685i	−0.305441	−	0.305441i
$344$	2.00000			0.107833
$345$	2.82843	+	2.82843i	0.152277	+	0.152277i
$346$	−0.656854	+	0.656854i	−0.0353127	+	0.0353127i
$347$	−19.6569	+	19.6569i	−1.05524	+	1.05524i	−0.0568526	+	0.998383i	$0.518107\pi$
$347$	−19.6569	+	19.6569i	−1.05524	+	1.05524i	−0.998383	+	0.0568526i	$0.981893\pi$
$348$			7.07107i			0.379049i
$349$		−	4.48528i		−	0.240092i	−0.992768	−	0.120046i	$-0.961696\pi$
$349$		−	4.48528i		−	0.240092i	0.992768	−	0.120046i	$-0.0383041\pi$
$350$	−13.1716	+	13.1716i	−0.704050	+	0.704050i
$351$	4.82843	−	4.82843i	0.257722	−	0.257722i
$352$	0.707107	+	0.707107i	0.0376889	+	0.0376889i
$353$	33.3137			1.77311			0.886555	−	0.462623i	$-0.153092\pi$
$353$	33.3137			1.77311			0.886555	+	0.462623i	$0.153092\pi$
$354$	−2.58579	−	2.58579i	−0.137433	−	0.137433i
$355$		−	2.34315i		−	0.124361i
$356$	−10.8284			−0.573905
$357$	−12.0000	−	11.3137i	−0.635107	−	0.598785i
$358$	10.9706			0.579812
$359$			8.97056i			0.473448i	0.971577	+	0.236724i	$0.0760737\pi$
$359$			8.97056i			0.473448i	−0.971577	+	0.236724i	$0.923926\pi$
$360$	−0.414214	−	0.414214i	−0.0218310	−	0.0218310i
$361$	15.0000			0.789474
$362$	−4.17157	−	4.17157i	−0.219253	−	0.219253i
$363$	−0.707107	+	0.707107i	−0.0371135	+	0.0371135i
$364$	−19.3137	+	19.3137i	−1.01231	+	1.01231i
$365$			1.02944i			0.0538832i
$366$			4.58579i			0.239703i
$367$	−14.0000	+	14.0000i	−0.730794	+	0.730794i	−0.970777	−	0.239983i	$-0.922858\pi$
$367$	−14.0000	+	14.0000i	−0.730794	+	0.730794i	0.239983	+	0.970777i	$0.422858\pi$
$368$	−4.82843	+	4.82843i	−0.251699	+	0.251699i
$369$	6.65685	+	6.65685i	0.346542	+	0.346542i
$370$	−5.51472			−0.286697
$371$	−35.3137	−	35.3137i	−1.83340	−	1.83340i
$372$			8.48528i			0.439941i
$373$	−9.17157			−0.474886			−0.237443	−	0.971401i	$-0.576309\pi$
$373$	−9.17157			−0.474886			−0.237443	+	0.971401i	$0.576309\pi$
$374$	0.121320	+	4.12132i	0.00627333	+	0.213108i
$375$	−5.65685			−0.292119
$376$			0.343146i			0.0176964i
$377$	34.1421	+	34.1421i	1.75841	+	1.75841i
$378$	−4.00000			−0.205738
$379$	−26.8284	−	26.8284i	−1.37808	−	1.37808i	−0.847854	−	0.530230i	$-0.822106\pi$
$379$	−26.8284	−	26.8284i	−1.37808	−	1.37808i	−0.530230	−	0.847854i	$-0.677894\pi$
$380$	0.828427	−	0.828427i	0.0424974	−	0.0424974i
$381$	−8.24264	+	8.24264i	−0.422283	+	0.422283i
$382$			18.9706i			0.970618i
$383$		−	2.00000i		−	0.102195i	−0.998694	−	0.0510976i	$-0.983728\pi$
$383$		−	2.00000i		−	0.102195i	0.998694	−	0.0510976i	$-0.0162720\pi$
$384$	0.707107	−	0.707107i	0.0360844	−	0.0360844i
$385$	−1.65685	+	1.65685i	−0.0844411	+	0.0844411i
$386$	8.41421	+	8.41421i	0.428272	+	0.428272i
$387$	2.00000			0.101666
$388$	6.65685	+	6.65685i	0.337951	+	0.337951i
$389$		−	8.34315i		−	0.423014i	−0.977376	−	0.211507i	$-0.932163\pi$
$389$		−	8.34315i		−	0.423014i	0.977376	−	0.211507i	$-0.0678372\pi$
$390$	−4.00000			−0.202548
$391$	−28.1421	+	0.828427i	−1.42321	+	0.0418954i
$392$	9.00000			0.454569
$393$		−	13.1716i		−	0.664418i
$394$	1.34315	+	1.34315i	0.0676667	+	0.0676667i
$395$	−4.00000			−0.201262
$396$	0.707107	+	0.707107i	0.0355335	+	0.0355335i
$397$	13.8284	−	13.8284i	0.694029	−	0.694029i	−0.269087	−	0.963116i	$-0.586722\pi$
$397$	13.8284	−	13.8284i	0.694029	−	0.694029i	0.963116	+	0.269087i	$0.0867219\pi$
$398$	10.8284	−	10.8284i	0.542780	−	0.542780i
$399$		−	8.00000i		−	0.400501i
$400$		−	4.65685i		−	0.232843i
$401$	−16.8995	+	16.8995i	−0.843921	+	0.843921i	−0.989366	−	0.145446i	$-0.953538\pi$
$401$	−16.8995	+	16.8995i	−0.843921	+	0.843921i	0.145446	+	0.989366i	$0.453538\pi$
$402$	9.65685	−	9.65685i	0.481640	−	0.481640i
$403$	40.9706	+	40.9706i	2.04089	+	2.04089i
$404$	12.0000			0.597022
$405$	−0.414214	−	0.414214i	−0.0205824	−	0.0205824i
$406$		−	28.2843i		−	1.40372i
$407$	9.41421			0.466645
$408$	4.12132	−	0.121320i	0.204036	−	0.00600625i
$409$	−8.62742			−0.426598			−0.213299	−	0.976987i	$-0.568421\pi$
$409$	−8.62742			−0.426598			−0.213299	+	0.976987i	$0.568421\pi$
$410$		−	5.51472i		−	0.272353i
$411$	−0.343146	−	0.343146i	−0.0169261	−	0.0169261i
$412$	−2.34315			−0.115439
$413$	10.3431	+	10.3431i	0.508953	+	0.508953i
$414$	−4.82843	+	4.82843i	−0.237304	+	0.237304i
$415$	−1.65685	+	1.65685i	−0.0813318	+	0.0813318i
$416$		−	6.82843i		−	0.334791i
$417$		−	12.4853i		−	0.611407i
$418$	−1.41421	+	1.41421i	−0.0691714	+	0.0691714i
$419$	−12.1421	+	12.1421i	−0.593182	+	0.593182i	−0.938490	−	0.345307i	$-0.887775\pi$
$419$	−12.1421	+	12.1421i	−0.593182	+	0.593182i	0.345307	+	0.938490i	$0.387775\pi$
$420$	1.65685	+	1.65685i	0.0808462	+	0.0808462i
$421$	−19.3137			−0.941293			−0.470646	−	0.882322i	$-0.655979\pi$
$421$	−19.3137			−0.941293			−0.470646	+	0.882322i	$0.655979\pi$
$422$	−14.8284	−	14.8284i	−0.721837	−	0.721837i
$423$			0.343146i			0.0166843i
$424$	12.4853			0.606339
$425$	13.1716	−	13.9706i	0.638915	−	0.677672i
$426$	4.00000			0.193801
$427$		−	18.3431i		−	0.887687i
$428$	−0.343146	−	0.343146i	−0.0165866	−	0.0165866i
$429$	6.82843			0.329680
$430$	−0.828427	−	0.828427i	−0.0399503	−	0.0399503i
$431$	−2.00000	+	2.00000i	−0.0963366	+	0.0963366i	−0.753633	−	0.657296i	$-0.771700\pi$
$431$	−2.00000	+	2.00000i	−0.0963366	+	0.0963366i	0.657296	+	0.753633i	$0.271700\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$			25.3137i			1.21650i	0.793746	+	0.608250i	$0.208128\pi$
$433$			25.3137i			1.21650i	−0.793746	+	0.608250i	$0.791872\pi$
$434$		−	33.9411i		−	1.62923i
$435$	2.92893	−	2.92893i	0.140432	−	0.140432i
$436$	−11.2426	+	11.2426i	−0.538425	+	0.538425i
$437$	−9.65685	−	9.65685i	−0.461950	−	0.461950i
$438$	−1.75736			−0.0839699
$439$	−7.17157	−	7.17157i	−0.342280	−	0.342280i	0.514944	−	0.857224i	$-0.327813\pi$
$439$	−7.17157	−	7.17157i	−0.342280	−	0.342280i	−0.857224	+	0.514944i	$0.827813\pi$
$440$		−	0.585786i		−	0.0279263i
$441$	9.00000			0.428571
$442$	19.3137	−	20.4853i	0.918659	−	0.974385i
$443$	−22.0000			−1.04525			−0.522626	−	0.852562i	$-0.675047\pi$
$443$	−22.0000			−1.04525			−0.522626	+	0.852562i	$0.675047\pi$
$444$		−	9.41421i		−	0.446779i
$445$	4.48528	+	4.48528i	0.212623	+	0.212623i
$446$	8.00000			0.378811
$447$	15.0711	+	15.0711i	0.712837	+	0.712837i
$448$	−2.82843	+	2.82843i	−0.133631	+	0.133631i
$449$	−4.55635	+	4.55635i	−0.215027	+	0.215027i	−0.806399	−	0.591372i	$-0.798587\pi$
$449$	−4.55635	+	4.55635i	−0.215027	+	0.215027i	0.591372	+	0.806399i	$0.298587\pi$
$450$		−	4.65685i		−	0.219526i
$451$			9.41421i			0.443298i
$452$	9.24264	−	9.24264i	0.434737	−	0.434737i
$453$	0.242641	−	0.242641i	0.0114003	−	0.0114003i
$454$	−1.17157	−	1.17157i	−0.0549846	−	0.0549846i
$455$	16.0000			0.750092
$456$	1.41421	+	1.41421i	0.0662266	+	0.0662266i
$457$		−	28.6274i		−	1.33913i	−0.742752	−	0.669567i	$-0.766480\pi$
$457$		−	28.6274i		−	1.33913i	0.742752	−	0.669567i	$-0.233520\pi$
$458$	17.3137			0.809016
$459$	4.12132	−	0.121320i	0.192367	−	0.00566275i
$460$	4.00000			0.186501
$461$			5.65685i			0.263466i	0.991285	+	0.131733i	$0.0420541\pi$
$461$			5.65685i			0.263466i	−0.991285	+	0.131733i	$0.957946\pi$
$462$	−2.82843	−	2.82843i	−0.131590	−	0.131590i
$463$	22.3431			1.03837			0.519187	−	0.854661i	$-0.326235\pi$
$463$	22.3431			1.03837			0.519187	+	0.854661i	$0.326235\pi$
$464$	5.00000	+	5.00000i	0.232119	+	0.232119i
$465$	3.51472	−	3.51472i	0.162991	−	0.162991i
$466$	5.34315	−	5.34315i	0.247516	−	0.247516i
$467$		−	38.9706i		−	1.80334i	−0.432422	−	0.901671i	$-0.642341\pi$
$467$		−	38.9706i		−	1.80334i	0.432422	−	0.901671i	$-0.357659\pi$
$468$		−	6.82843i		−	0.315644i
$469$	−38.6274	+	38.6274i	−1.78365	+	1.78365i
$470$	0.142136	−	0.142136i	0.00655623	−	0.00655623i
$471$	9.89949	+	9.89949i	0.456145	+	0.456145i
$472$	−3.65685			−0.168320
$473$	1.41421	+	1.41421i	0.0650256	+	0.0650256i
$474$		−	6.82843i		−	0.313640i
$475$	9.31371			0.427342
$476$	−16.4853	+	0.485281i	−0.755602	+	0.0222428i
$477$	12.4853			0.571662
$478$		−	6.34315i		−	0.290129i
$479$	−11.5147	−	11.5147i	−0.526121	−	0.526121i	0.393292	−	0.919413i	$-0.371336\pi$
$479$	−11.5147	−	11.5147i	−0.526121	−	0.526121i	−0.919413	+	0.393292i	$0.871336\pi$
$480$	−0.585786			−0.0267374
$481$	−45.4558	−	45.4558i	−2.07261	−	2.07261i
$482$	15.5858	−	15.5858i	0.709913	−	0.709913i
$483$	19.3137	−	19.3137i	0.878804	−	0.878804i
$484$			1.00000i			0.0454545i
$485$		−	5.51472i		−	0.250410i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$	8.48528	−	8.48528i	0.384505	−	0.384505i	−0.488217	−	0.872722i	$-0.662353\pi$
$487$	8.48528	−	8.48528i	0.384505	−	0.384505i	0.872722	+	0.488217i	$0.162353\pi$
$488$	3.24264	+	3.24264i	0.146787	+	0.146787i
$489$	8.48528			0.383718
$490$	−3.72792	−	3.72792i	−0.168410	−	0.168410i
$491$		−	0.686292i		−	0.0309719i	−0.999880	−	0.0154860i	$-0.995070\pi$
$491$		−	0.686292i		−	0.0309719i	0.999880	−	0.0154860i	$-0.00492953\pi$
$492$	9.41421			0.424426
$493$	0.857864	+	29.1421i	0.0386363	+	1.31250i
$494$	13.6569			0.614451
$495$		−	0.585786i		−	0.0263291i
$496$	6.00000	+	6.00000i	0.269408	+	0.269408i
$497$	−16.0000			−0.717698
$498$	−2.82843	−	2.82843i	−0.126745	−	0.126745i
$499$	−0.343146	+	0.343146i	−0.0153613	+	0.0153613i	−0.714746	−	0.699384i	$-0.753458\pi$
$499$	−0.343146	+	0.343146i	−0.0153613	+	0.0153613i	0.699384	+	0.714746i	$0.253458\pi$
$500$	−4.00000	+	4.00000i	−0.178885	+	0.178885i
$501$			7.51472i			0.335733i
$502$			1.31371i			0.0586337i
$503$	9.17157	−	9.17157i	0.408940	−	0.408940i	−0.472429	−	0.881369i	$-0.656623\pi$
$503$	9.17157	−	9.17157i	0.408940	−	0.408940i	0.881369	+	0.472429i	$0.156623\pi$
$504$	−2.82843	+	2.82843i	−0.125988	+	0.125988i
$505$	−4.97056	−	4.97056i	−0.221187	−	0.221187i
$506$	−6.82843			−0.303561
$507$	−23.7782	−	23.7782i	−1.05603	−	1.05603i
$508$			11.6569i			0.517189i
$509$	−30.9706			−1.37275			−0.686373	−	0.727250i	$-0.740798\pi$
$509$	−30.9706			−1.37275			−0.686373	+	0.727250i	$0.740798\pi$
$510$	−1.75736	−	1.65685i	−0.0778172	−	0.0733667i
$511$	7.02944			0.310964
$512$		−	1.00000i		−	0.0441942i
$513$	1.41421	+	1.41421i	0.0624391	+	0.0624391i
$514$	−2.68629			−0.118487
$515$	0.970563	+	0.970563i	0.0427681	+	0.0427681i
$516$	1.41421	−	1.41421i	0.0622573	−	0.0622573i
$517$	−0.242641	+	0.242641i	−0.0106713	+	0.0106713i
$518$			37.6569i			1.65455i
$519$			0.928932i			0.0407756i
$520$	−2.82843	+	2.82843i	−0.124035	+	0.124035i
$521$	5.72792	−	5.72792i	0.250945	−	0.250945i	−0.570413	−	0.821358i	$-0.693217\pi$
$521$	5.72792	−	5.72792i	0.250945	−	0.250945i	0.821358	+	0.570413i	$0.193217\pi$
$522$	5.00000	+	5.00000i	0.218844	+	0.218844i
$523$	−41.5980			−1.81895			−0.909476	−	0.415756i	$-0.863517\pi$
$523$	−41.5980			−1.81895			−0.909476	+	0.415756i	$0.863517\pi$
$524$	−9.31371	−	9.31371i	−0.406871	−	0.406871i
$525$			18.6274i			0.812967i
$526$	−24.9706			−1.08877
$527$	1.02944	+	34.9706i	0.0448430	+	1.52334i
$528$	1.00000			0.0435194
$529$		−	23.6274i		−	1.02728i
$530$	−5.17157	−	5.17157i	−0.224639	−	0.224639i
$531$	−3.65685			−0.158694
$532$	−5.65685	−	5.65685i	−0.245256	−	0.245256i
$533$	45.4558	−	45.4558i	1.96891	−	1.96891i
$534$	−7.65685	+	7.65685i	−0.331344	+	0.331344i
$535$			0.284271i			0.0122901i
$536$		−	13.6569i		−	0.589886i
$537$	7.75736	−	7.75736i	0.334755	−	0.334755i
$538$	−15.5858	+	15.5858i	−0.671951	+	0.671951i
$539$	6.36396	+	6.36396i	0.274115	+	0.274115i
$540$	−0.585786			−0.0252082
$541$	24.4142	+	24.4142i	1.04965	+	1.04965i	0.998701	+	0.0509477i	$0.0162242\pi$
$541$	24.4142	+	24.4142i	1.04965	+	1.04965i	0.0509477	+	0.998701i	$0.483776\pi$
$542$			6.68629i			0.287201i
$543$	−5.89949			−0.253172
$544$	2.82843	−	3.00000i	0.121268	−	0.128624i
$545$	9.31371			0.398955
$546$			27.3137i			1.16892i
$547$	−4.48528	−	4.48528i	−0.191777	−	0.191777i	0.604687	−	0.796463i	$-0.293298\pi$
$547$	−4.48528	−	4.48528i	−0.191777	−	0.191777i	−0.796463	+	0.604687i	$0.793298\pi$
$548$	−0.485281			−0.0207302
$549$	3.24264	+	3.24264i	0.138393	+	0.138393i
$550$	3.29289	−	3.29289i	0.140409	−	0.140409i
$551$	−10.0000	+	10.0000i	−0.426014	+	0.426014i
$552$			6.82843i			0.290637i
$553$			27.3137i			1.16150i
$554$	13.2426	−	13.2426i	0.562626	−	0.562626i
$555$	−3.89949	+	3.89949i	−0.165524	+	0.165524i
$556$	−8.82843	−	8.82843i	−0.374409	−	0.374409i
$557$	−16.2843			−0.689987			−0.344993	−	0.938605i	$-0.612119\pi$
$557$	−16.2843			−0.689987			−0.344993	+	0.938605i	$0.612119\pi$
$558$	6.00000	+	6.00000i	0.254000	+	0.254000i
$559$		−	13.6569i		−	0.577623i
$560$	2.34315			0.0990160
$561$	3.00000	+	2.82843i	0.126660	+	0.119416i
$562$	0.686292			0.0289495
$563$		−	20.6863i		−	0.871823i	−0.899989	−	0.435912i	$-0.856426\pi$
$563$		−	20.6863i		−	0.871823i	0.899989	−	0.435912i	$-0.143574\pi$
$564$	0.242641	+	0.242641i	0.0102170	+	0.0102170i
$565$	−7.65685			−0.322126
$566$	−12.4853	−	12.4853i	−0.524796	−	0.524796i
$567$	−2.82843	+	2.82843i	−0.118783	+	0.118783i
$568$	2.82843	−	2.82843i	0.118678	−	0.118678i
$569$		−	34.3431i		−	1.43974i	−0.694109	−	0.719870i	$-0.744201\pi$
$569$		−	34.3431i		−	1.43974i	0.694109	−	0.719870i	$-0.255799\pi$
$570$		−	1.17157i		−	0.0490718i
$571$	−12.8284	+	12.8284i	−0.536853	+	0.536853i	−0.922603	−	0.385750i	$-0.873943\pi$
$571$	−12.8284	+	12.8284i	−0.536853	+	0.536853i	0.385750	+	0.922603i	$0.373943\pi$
$572$	4.82843	−	4.82843i	0.201887	−	0.201887i
$573$	13.4142	+	13.4142i	0.560387	+	0.560387i
$574$	−37.6569			−1.57177
$575$	22.4853	+	22.4853i	0.937701	+	0.937701i
$576$		−	1.00000i		−	0.0416667i
$577$	−18.3431			−0.763635			−0.381818	−	0.924238i	$-0.624702\pi$
$577$	−18.3431			−0.763635			−0.381818	+	0.924238i	$0.624702\pi$
$578$	16.9706	−	1.00000i	0.705882	−	0.0415945i
$579$	11.8995			0.494526
$580$		−	4.14214i		−	0.171993i
$581$	11.3137	+	11.3137i	0.469372	+	0.469372i
$582$	9.41421			0.390232
$583$	8.82843	+	8.82843i	0.365636	+	0.365636i
$584$	−1.24264	+	1.24264i	−0.0514208	+	0.0514208i
$585$	−2.82843	+	2.82843i	−0.116941	+	0.116941i
$586$		−	17.3137i		−	0.715223i
$587$		−	2.97056i		−	0.122608i	−0.998119	−	0.0613041i	$-0.980474\pi$
$587$		−	2.97056i		−	0.122608i	0.998119	−	0.0613041i	$-0.0195260\pi$
$588$	6.36396	−	6.36396i	0.262445	−	0.262445i
$589$	−12.0000	+	12.0000i	−0.494451	+	0.494451i
$590$	1.51472	+	1.51472i	0.0623600	+	0.0623600i
$591$	1.89949			0.0781348
$592$	−6.65685	−	6.65685i	−0.273595	−	0.273595i
$593$		−	20.0000i		−	0.821302i	−0.911793	−	0.410651i	$-0.865302\pi$
$593$		−	20.0000i		−	0.821302i	0.911793	−	0.410651i	$-0.134698\pi$
$594$	1.00000			0.0410305
$595$	7.02944	+	6.62742i	0.288179	+	0.271698i
$596$	21.3137			0.873044
$597$		−	15.3137i		−	0.626748i
$598$	32.9706	+	32.9706i	1.34827	+	1.34827i
$599$	4.34315			0.177456			0.0887281	−	0.996056i	$-0.471720\pi$
$599$	4.34315			0.177456			0.0887281	+	0.996056i	$0.471720\pi$
$600$	−3.29289	−	3.29289i	−0.134432	−	0.134432i
$601$	−16.4142	+	16.4142i	−0.669550	+	0.669550i	−0.957612	−	0.288062i	$-0.906989\pi$
$601$	−16.4142	+	16.4142i	−0.669550	+	0.669550i	0.288062	+	0.957612i	$0.406989\pi$
$602$	−5.65685	+	5.65685i	−0.230556	+	0.230556i
$603$		−	13.6569i		−	0.556150i
$604$		−	0.343146i		−	0.0139624i
$605$	0.414214	−	0.414214i	0.0168402	−	0.0168402i
$606$	8.48528	−	8.48528i	0.344691	−	0.344691i
$607$	13.5147	+	13.5147i	0.548546	+	0.548546i	0.926020	−	0.377474i	$-0.123207\pi$
$607$	13.5147	+	13.5147i	0.548546	+	0.548546i	−0.377474	+	0.926020i	$0.623207\pi$
$608$	2.00000			0.0811107
$609$	−20.0000	−	20.0000i	−0.810441	−	0.810441i
$610$		−	2.68629i		−	0.108765i
$611$	2.34315			0.0947935
$612$	2.82843	−	3.00000i	0.114332	−	0.121268i
$613$	6.97056			0.281538			0.140769	−	0.990042i	$-0.455042\pi$
$613$	6.97056			0.281538			0.140769	+	0.990042i	$0.455042\pi$
$614$			26.9706i			1.08844i
$615$	−3.89949	−	3.89949i	−0.157243	−	0.157243i
$616$	−4.00000			−0.161165
$617$	23.2426	+	23.2426i	0.935713	+	0.935713i	0.998055	−	0.0623414i	$-0.0198568\pi$
$617$	23.2426	+	23.2426i	0.935713	+	0.935713i	−0.0623414	+	0.998055i	$0.519857\pi$
$618$	−1.65685	+	1.65685i	−0.0666485	+	0.0666485i
$619$	11.5147	−	11.5147i	0.462816	−	0.462816i	−0.436762	−	0.899577i	$-0.643875\pi$
$619$	11.5147	−	11.5147i	0.462816	−	0.462816i	0.899577	+	0.436762i	$0.143875\pi$
$620$		−	4.97056i		−	0.199623i
$621$			6.82843i			0.274015i
$622$	12.4853	−	12.4853i	0.500614	−	0.500614i
$623$	30.6274	−	30.6274i	1.22706	−	1.22706i
$624$	−4.82843	−	4.82843i	−0.193292	−	0.193292i
$625$	−19.9706			−0.798823
$626$	8.65685	+	8.65685i	0.345997	+	0.345997i
$627$			2.00000i			0.0798723i
$628$	14.0000			0.558661
$629$	−1.14214	−	38.7990i	−0.0455399	−	1.54702i
$630$	2.34315			0.0933532
$631$		−	12.6863i		−	0.505033i	−0.967593	−	0.252517i	$-0.918742\pi$
$631$		−	12.6863i		−	0.505033i	0.967593	−	0.252517i	$-0.0812582\pi$
$632$	−4.82843	−	4.82843i	−0.192065	−	0.192065i
$633$	−20.9706			−0.833505
$634$	14.7574	+	14.7574i	0.586090	+	0.586090i
$635$	4.82843	−	4.82843i	0.191610	−	0.191610i
$636$	8.82843	−	8.82843i	0.350070	−	0.350070i
$637$		−	61.4558i		−	2.43497i
$638$			7.07107i			0.279946i
$639$	2.82843	−	2.82843i	0.111891	−	0.111891i
$640$	−0.414214	+	0.414214i	−0.0163732	+	0.0163732i
$641$	−14.4142	−	14.4142i	−0.569327	−	0.569327i	0.362613	−	0.931940i	$-0.381885\pi$
$641$	−14.4142	−	14.4142i	−0.569327	−	0.569327i	−0.931940	+	0.362613i	$0.881885\pi$
$642$	−0.485281			−0.0191525
$643$	−28.6274	−	28.6274i	−1.12896	−	1.12896i	−0.990347	−	0.138608i	$-0.955737\pi$
$643$	−28.6274	−	28.6274i	−1.12896	−	1.12896i	−0.138608	−	0.990347i	$-0.544263\pi$
$644$		−	27.3137i		−	1.07631i
$645$	−1.17157			−0.0461306
$646$	6.00000	+	5.65685i	0.236067	+	0.222566i
$647$	6.97056			0.274041			0.137021	−	0.990568i	$-0.456247\pi$
$647$	6.97056			0.274041			0.137021	+	0.990568i	$0.456247\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−2.58579	−	2.58579i	−0.101501	−	0.101501i
$650$	−31.7990			−1.24726
$651$	−24.0000	−	24.0000i	−0.940634	−	0.940634i
$652$	6.00000	−	6.00000i	0.234978	−	0.234978i
$653$	−32.8995	+	32.8995i	−1.28746	+	1.28746i	−0.351130	+	0.936327i	$0.614202\pi$
$653$	−32.8995	+	32.8995i	−1.28746	+	1.28746i	−0.936327	+	0.351130i	$0.885798\pi$
$654$			15.8995i			0.621719i
$655$			7.71573i			0.301478i
$656$	6.65685	−	6.65685i	0.259906	−	0.259906i
$657$	−1.24264	+	1.24264i	−0.0484800	+	0.0484800i
$658$	−0.970563	−	0.970563i	−0.0378365	−	0.0378365i
$659$	−22.3431			−0.870365			−0.435183	−	0.900342i	$-0.643316\pi$
$659$	−22.3431			−0.870365			−0.435183	+	0.900342i	$0.643316\pi$
$660$	−0.414214	−	0.414214i	−0.0161232	−	0.0161232i
$661$			40.2843i			1.56688i	0.621470	+	0.783438i	$0.286536\pi$
$661$			40.2843i			1.56688i	−0.621470	+	0.783438i	$0.713464\pi$
$662$	−16.9706			−0.659580
$663$	−0.828427	−	28.1421i	−0.0321734	−	1.09295i
$664$	−4.00000			−0.155230
$665$			4.68629i			0.181727i
$666$	−6.65685	−	6.65685i	−0.257948	−	0.257948i
$667$	−48.2843			−1.86957
$668$	5.31371	+	5.31371i	0.205594	+	0.205594i
$669$	5.65685	−	5.65685i	0.218707	−	0.218707i
$670$	−5.65685	+	5.65685i	−0.218543	+	0.218543i
$671$			4.58579i			0.177032i
$672$			4.00000i			0.154303i
$673$	−0.272078	+	0.272078i	−0.0104878	+	0.0104878i	−0.712331	−	0.701843i	$-0.752361\pi$
$673$	−0.272078	+	0.272078i	−0.0104878	+	0.0104878i	0.701843	+	0.712331i	$0.252361\pi$
$674$	−2.75736	+	2.75736i	−0.106210	+	0.106210i
$675$	−3.29289	−	3.29289i	−0.126744	−	0.126744i
$676$	−33.6274			−1.29336
$677$	−12.6569	−	12.6569i	−0.486442	−	0.486442i	0.420739	−	0.907182i	$-0.361771\pi$
$677$	−12.6569	−	12.6569i	−0.486442	−	0.486442i	−0.907182	+	0.420739i	$0.861771\pi$
$678$		−	13.0711i		−	0.501991i
$679$	−37.6569			−1.44514
$680$	−2.41421	+	0.0710678i	−0.0925809	+	0.00272533i
$681$	−1.65685			−0.0634908
$682$			8.48528i			0.324918i
$683$	31.4558	+	31.4558i	1.20362	+	1.20362i	0.973056	+	0.230568i	$0.0740585\pi$
$683$	31.4558	+	31.4558i	1.20362	+	1.20362i	0.230568	+	0.973056i	$0.425941\pi$
$684$	2.00000			0.0764719
$685$	0.201010	+	0.201010i	0.00768020	+	0.00768020i
$686$	−5.65685	+	5.65685i	−0.215980	+	0.215980i
$687$	12.2426	−	12.2426i	0.467086	−	0.467086i
$688$		−	2.00000i		−	0.0762493i
$689$		−	85.2548i		−	3.24795i
$690$	2.82843	−	2.82843i	0.107676	−	0.107676i
$691$	22.9706	−	22.9706i	0.873841	−	0.873841i	−0.119047	−	0.992889i	$-0.537984\pi$
$691$	22.9706	−	22.9706i	0.873841	−	0.873841i	0.992889	+	0.119047i	$0.0379840\pi$
$692$	0.656854	+	0.656854i	0.0249699	+	0.0249699i
$693$	−4.00000			−0.151947
$694$	19.6569	+	19.6569i	0.746164	+	0.746164i
$695$			7.31371i			0.277425i
$696$	7.07107			0.268028
$697$	38.7990	−	1.14214i	1.46962	−	0.0432615i
$698$	−4.48528			−0.169770
$699$		−	7.55635i		−	0.285807i
$700$	13.1716	+	13.1716i	0.497839	+	0.497839i
$701$	−32.9706			−1.24528			−0.622640	−	0.782508i	$-0.713940\pi$
$701$	−32.9706			−1.24528			−0.622640	+	0.782508i	$0.713940\pi$
$702$	−4.82843	−	4.82843i	−0.182237	−	0.182237i
$703$	13.3137	−	13.3137i	0.502136	−	0.502136i
$704$	0.707107	−	0.707107i	0.0266501	−	0.0266501i
$705$		−	0.201010i		−	0.00757048i
$706$		−	33.3137i		−	1.25378i
$707$	−33.9411	+	33.9411i	−1.27649	+	1.27649i
$708$	−2.58579	+	2.58579i	−0.0971798	+	0.0971798i
$709$	13.4853	+	13.4853i	0.506450	+	0.506450i	0.913435	−	0.406985i	$-0.133420\pi$
$709$	13.4853	+	13.4853i	0.506450	+	0.506450i	−0.406985	+	0.913435i	$0.633420\pi$
$710$	−2.34315			−0.0879367
$711$	−4.82843	−	4.82843i	−0.181080	−	0.181080i
$712$			10.8284i			0.405812i
$713$	−57.9411			−2.16991
$714$	−11.3137	+	12.0000i	−0.423405	+	0.449089i
$715$	−4.00000			−0.149592
$716$		−	10.9706i		−	0.409989i
$717$	−4.48528	−	4.48528i	−0.167506	−	0.167506i
$718$	8.97056			0.334778
$719$	22.4853	+	22.4853i	0.838559	+	0.838559i	0.988669	−	0.150110i	$-0.0479627\pi$
$719$	22.4853	+	22.4853i	0.838559	+	0.838559i	−0.150110	+	0.988669i	$0.547963\pi$
$720$	−0.414214	+	0.414214i	−0.0154368	+	0.0154368i
$721$	6.62742	−	6.62742i	0.246818	−	0.246818i
$722$		−	15.0000i		−	0.558242i
$723$		−	22.0416i		−	0.819737i
$724$	−4.17157	+	4.17157i	−0.155035	+	0.155035i
$725$	23.2843	−	23.2843i	0.864756	−	0.864756i
$726$	0.707107	+	0.707107i	0.0262432	+	0.0262432i
$727$	31.3137			1.16136			0.580681	−	0.814131i	$-0.302787\pi$
$727$	31.3137			1.16136			0.580681	+	0.814131i	$0.302787\pi$
$728$	19.3137	+	19.3137i	0.715814	+	0.715814i
$729$		−	1.00000i		−	0.0370370i
$730$	1.02944			0.0381012
$731$	5.65685	−	6.00000i	0.209226	−	0.221918i
$732$	4.58579			0.169496
$733$		−	20.4853i		−	0.756641i	−0.925675	−	0.378321i	$-0.876502\pi$
$733$		−	20.4853i		−	0.756641i	0.925675	−	0.378321i	$-0.123498\pi$
$734$	14.0000	+	14.0000i	0.516749	+	0.516749i
$735$	−5.27208			−0.194464
$736$	4.82843	+	4.82843i	0.177978	+	0.177978i
$737$	9.65685	−	9.65685i	0.355715	−	0.355715i
$738$	6.65685	−	6.65685i	0.245042	−	0.245042i
$739$			18.0000i			0.662141i	0.943606	+	0.331070i	$0.107410\pi$
$739$			18.0000i			0.662141i	−0.943606	+	0.331070i	$0.892590\pi$
$740$			5.51472i			0.202725i
$741$	9.65685	−	9.65685i	0.354753	−	0.354753i
$742$	−35.3137	+	35.3137i	−1.29641	+	1.29641i
$743$	14.1421	+	14.1421i	0.518825	+	0.518825i	0.917216	−	0.398391i	$-0.130431\pi$
$743$	14.1421	+	14.1421i	0.518825	+	0.518825i	−0.398391	+	0.917216i	$0.630431\pi$
$744$	8.48528			0.311086
$745$	−8.82843	−	8.82843i	−0.323449	−	0.323449i
$746$			9.17157i			0.335795i
$747$	−4.00000			−0.146352
$748$	4.12132	−	0.121320i	0.150690	−	0.00443591i
$749$	1.94113			0.0709272
$750$			5.65685i			0.206559i
$751$	38.1421	+	38.1421i	1.39183	+	1.39183i	0.821232	+	0.570594i	$0.193287\pi$
$751$	38.1421	+	38.1421i	1.39183	+	1.39183i	0.570594	+	0.821232i	$0.306713\pi$
$752$	0.343146			0.0125132
$753$	0.928932	+	0.928932i	0.0338522	+	0.0338522i
$754$	34.1421	−	34.1421i	1.24338	−	1.24338i
$755$	−0.142136	+	0.142136i	−0.00517284	+	0.00517284i
$756$			4.00000i			0.145479i
$757$		−	7.37258i		−	0.267961i	−0.990984	−	0.133981i	$-0.957224\pi$
$757$		−	7.37258i		−	0.267961i	0.990984	−	0.133981i	$-0.0427760\pi$
$758$	−26.8284	+	26.8284i	−0.974452	+	0.974452i
$759$	−4.82843	+	4.82843i	−0.175261	+	0.175261i
$760$	−0.828427	−	0.828427i	−0.0300502	−	0.0300502i
$761$	−3.02944			−0.109817			−0.0549085	−	0.998491i	$-0.517487\pi$
$761$	−3.02944			−0.109817			−0.0549085	+	0.998491i	$0.517487\pi$
$762$	8.24264	+	8.24264i	0.298599	+	0.298599i
$763$		−	63.5980i		−	2.30240i
$764$	18.9706			0.686331
$765$	−2.41421	+	0.0710678i	−0.0872861	+	0.00256946i
$766$	−2.00000			−0.0722629
$767$			24.9706i			0.901635i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	25.4558			0.917961			0.458981	−	0.888446i	$-0.348215\pi$
$769$	25.4558			0.917961			0.458981	+	0.888446i	$0.348215\pi$
$770$	1.65685	+	1.65685i	0.0597089	+	0.0597089i
$771$	−1.89949	+	1.89949i	−0.0684086	+	0.0684086i
$772$	8.41421	−	8.41421i	0.302834	−	0.302834i
$773$			18.2843i			0.657640i	0.944393	+	0.328820i	$0.106651\pi$
$773$			18.2843i			0.657640i	−0.944393	+	0.328820i	$0.893349\pi$
$774$		−	2.00000i		−	0.0718885i
$775$	27.9411	−	27.9411i	1.00367	−	1.00367i
$776$	6.65685	−	6.65685i	0.238967	−	0.238967i
$777$	26.6274	+	26.6274i	0.955253	+	0.955253i
$778$	−8.34315			−0.299116
$779$	13.3137	+	13.3137i	0.477013	+	0.477013i
$780$			4.00000i			0.143223i
$781$	4.00000			0.143131
$782$	0.828427	+	28.1421i	0.0296245	+	1.00636i
$783$	7.07107			0.252699
$784$		−	9.00000i		−	0.321429i
$785$	−5.79899	−	5.79899i	−0.206975	−	0.206975i
$786$	−13.1716			−0.469814
$787$	12.1421	+	12.1421i	0.432820	+	0.432820i	0.889587	−	0.456766i	$-0.150992\pi$
$787$	12.1421	+	12.1421i	0.432820	+	0.432820i	−0.456766	+	0.889587i	$0.650992\pi$
$788$	1.34315	−	1.34315i	0.0478476	−	0.0478476i
$789$	−17.6569	+	17.6569i	−0.628601	+	0.628601i
$790$			4.00000i			0.142314i
$791$			52.2843i			1.85901i
$792$	0.707107	−	0.707107i	0.0251259	−	0.0251259i
$793$	22.1421	−	22.1421i	0.786290	−	0.786290i
$794$	−13.8284	−	13.8284i	−0.490753	−	0.490753i
$795$	−7.31371			−0.259391
$796$	−10.8284	−	10.8284i	−0.383803	−	0.383803i
$797$			7.79899i			0.276254i	0.990414	+	0.138127i	$0.0441083\pi$
$797$			7.79899i			0.276254i	−0.990414	+	0.138127i	$0.955892\pi$
$798$	−8.00000			−0.283197
$799$	1.02944	+	0.970563i	0.0364189	+	0.0343360i
$800$	−4.65685			−0.164645
$801$			10.8284i			0.382604i
$802$	16.8995	+	16.8995i	0.596742	+	0.596742i
$803$	−1.75736			−0.0620159
$804$	−9.65685	−	9.65685i	−0.340571	−	0.340571i
$805$	−11.3137	+	11.3137i	−0.398756	+	0.398756i
$806$	40.9706	−	40.9706i	1.44313	−	1.44313i
$807$			22.0416i			0.775902i
$808$		−	12.0000i		−	0.422159i
$809$	3.48528	−	3.48528i	0.122536	−	0.122536i	−0.643179	−	0.765715i	$-0.722385\pi$
$809$	3.48528	−	3.48528i	0.122536	−	0.122536i	0.765715	+	0.643179i	$0.222385\pi$
$810$	−0.414214	+	0.414214i	−0.0145540	+	0.0145540i
$811$	24.8284	+	24.8284i	0.871844	+	0.871844i	0.992673	−	0.120829i	$-0.0385554\pi$
$811$	24.8284	+	24.8284i	0.871844	+	0.871844i	−0.120829	+	0.992673i	$0.538555\pi$
$812$	−28.2843			−0.992583
$813$	4.72792	+	4.72792i	0.165815	+	0.165815i
$814$		−	9.41421i		−	0.329968i
$815$	−4.97056			−0.174111
$816$	−0.121320	−	4.12132i	−0.00424706	−	0.144275i
$817$	4.00000			0.139942
$818$			8.62742i			0.301651i
$819$	19.3137	+	19.3137i	0.674876	+	0.674876i
$820$	−5.51472			−0.192582
$821$	1.68629	+	1.68629i	0.0588520	+	0.0588520i	0.735920	−	0.677068i	$-0.236750\pi$
$821$	1.68629	+	1.68629i	0.0588520	+	0.0588520i	−0.677068	+	0.735920i	$0.736750\pi$
$822$	−0.343146	+	0.343146i	−0.0119686	+	0.0119686i
$823$	29.4558	−	29.4558i	1.02677	−	1.02677i	0.0271344	−	0.999632i	$-0.491362\pi$
$823$	29.4558	−	29.4558i	1.02677	−	1.02677i	0.999632	−	0.0271344i	$-0.00863820\pi$
$824$			2.34315i			0.0816274i
$825$		−	4.65685i		−	0.162131i
$826$	10.3431	−	10.3431i	0.359884	−	0.359884i
$827$	10.1421	−	10.1421i	0.352677	−	0.352677i	−0.508428	−	0.861105i	$-0.669773\pi$
$827$	10.1421	−	10.1421i	0.352677	−	0.352677i	0.861105	+	0.508428i	$0.169773\pi$
$828$	4.82843	+	4.82843i	0.167799	+	0.167799i
$829$	5.31371			0.184553			0.0922764	−	0.995733i	$-0.470586\pi$
$829$	5.31371			0.184553			0.0922764	+	0.995733i	$0.470586\pi$
$830$	1.65685	+	1.65685i	0.0575103	+	0.0575103i
$831$		−	18.7279i		−	0.649664i
$832$	−6.82843			−0.236733
$833$	25.4558	−	27.0000i	0.881993	−	0.935495i
$834$	−12.4853			−0.432330
$835$		−	4.40202i		−	0.152338i
$836$	1.41421	+	1.41421i	0.0489116	+	0.0489116i
$837$	8.48528			0.293294
$838$	12.1421	+	12.1421i	0.419443	+	0.419443i
$839$	−0.142136	+	0.142136i	−0.00490707	+	0.00490707i	−0.709556	−	0.704649i	$-0.751104\pi$
$839$	−0.142136	+	0.142136i	−0.00490707	+	0.00490707i	0.704649	+	0.709556i	$0.251104\pi$
$840$	1.65685	−	1.65685i	0.0571669	−	0.0571669i
$841$			21.0000i			0.724138i
$842$			19.3137i			0.665594i
$843$	0.485281	−	0.485281i	0.0167140	−	0.0167140i
$844$	−14.8284	+	14.8284i	−0.510416	+	0.510416i
$845$	13.9289	+	13.9289i	0.479170	+	0.479170i
$846$	0.343146			0.0117976
$847$	−2.82843	−	2.82843i	−0.0971859	−	0.0971859i
$848$		−	12.4853i		−	0.428746i
$849$	−17.6569			−0.605982
$850$	−13.9706	−	13.1716i	−0.479186	−	0.451781i
$851$	64.2843			2.20364
$852$		−	4.00000i		−	0.137038i
$853$	8.41421	+	8.41421i	0.288097	+	0.288097i	0.836327	−	0.548230i	$-0.184698\pi$
$853$	8.41421	+	8.41421i	0.288097	+	0.288097i	−0.548230	+	0.836327i	$0.684698\pi$
$854$	−18.3431			−0.627690
$855$	−0.828427	−	0.828427i	−0.0283316	−	0.0283316i
$856$	−0.343146	+	0.343146i	−0.0117285	+	0.0117285i
$857$	−30.7990	+	30.7990i	−1.05207	+	1.05207i	−0.0535059	+	0.998568i	$0.517040\pi$
$857$	−30.7990	+	30.7990i	−1.05207	+	1.05207i	−0.998568	+	0.0535059i	$0.982960\pi$
$858$		−	6.82843i		−	0.233119i
$859$			26.3431i			0.898817i	0.893326	+	0.449408i	$0.148365\pi$
$859$			26.3431i			0.898817i	−0.893326	+	0.449408i	$0.851635\pi$
$860$	−0.828427	+	0.828427i	−0.0282491	+	0.0282491i
$861$	−26.6274	+	26.6274i	−0.907460	+	0.907460i
$862$	2.00000	+	2.00000i	0.0681203	+	0.0681203i
$863$	44.3431			1.50946			0.754729	−	0.656037i	$-0.227768\pi$
$863$	44.3431			1.50946			0.754729	+	0.656037i	$0.227768\pi$
$864$	−0.707107	−	0.707107i	−0.0240563	−	0.0240563i
$865$		−	0.544156i		−	0.0185019i
$866$	25.3137			0.860195
$867$	11.2929	−	12.7071i	0.383527	−	0.431556i
$868$	−33.9411			−1.15204
$869$		−	6.82843i		−	0.231639i
$870$	−2.92893	−	2.92893i	−0.0993001	−	0.0993001i
$871$	−93.2548			−3.15982
$872$	11.2426	+	11.2426i	0.380724	+	0.380724i
$873$	6.65685	−	6.65685i	0.225300	−	0.225300i
$874$	−9.65685	+	9.65685i	−0.326648	+	0.326648i
$875$		−	22.6274i		−	0.764946i
$876$			1.75736i			0.0593757i
$877$	−30.4142	+	30.4142i	−1.02702	+	1.02702i	−0.0273902	+	0.999625i	$0.508720\pi$
$877$	−30.4142	+	30.4142i	−1.02702	+	1.02702i	−0.999625	+	0.0273902i	$0.991280\pi$
$878$	−7.17157	+	7.17157i	−0.242029	+	0.242029i
$879$	−12.2426	−	12.2426i	−0.412934	−	0.412934i
$880$	−0.585786			−0.0197469
$881$	7.38478	+	7.38478i	0.248799	+	0.248799i	0.820478	−	0.571678i	$-0.193707\pi$
$881$	7.38478	+	7.38478i	0.248799	+	0.248799i	−0.571678	+	0.820478i	$0.693707\pi$
$882$		−	9.00000i		−	0.303046i
$883$	−45.2548			−1.52295			−0.761473	−	0.648196i	$-0.775524\pi$
$883$	−45.2548			−1.52295			−0.761473	+	0.648196i	$0.775524\pi$
$884$	−20.4853	−	19.3137i	−0.688995	−	0.649590i
$885$	2.14214			0.0720071
$886$			22.0000i			0.739104i
$887$	−10.9706	−	10.9706i	−0.368355	−	0.368355i	0.498522	−	0.866877i	$-0.333876\pi$
$887$	−10.9706	−	10.9706i	−0.368355	−	0.368355i	−0.866877	+	0.498522i	$0.833876\pi$
$888$	−9.41421			−0.315920
$889$	−32.9706	−	32.9706i	−1.10580	−	1.10580i
$890$	4.48528	−	4.48528i	0.150347	−	0.150347i
$891$	0.707107	−	0.707107i	0.0236890	−	0.0236890i
$892$		−	8.00000i		−	0.267860i
$893$			0.686292i			0.0229659i
$894$	15.0711	−	15.0711i	0.504052	−	0.504052i
$895$	−4.54416	+	4.54416i	−0.151894	+	0.151894i
$896$	2.82843	+	2.82843i	0.0944911	+	0.0944911i
$897$	46.6274			1.55684
$898$	4.55635	+	4.55635i	0.152047	+	0.152047i
$899$			60.0000i			2.00111i
$900$	−4.65685			−0.155228
$901$	35.3137	−	37.4558i	1.17647	−	1.24784i
$902$	9.41421			0.313459
$903$			8.00000i			0.266223i
$904$	−9.24264	−	9.24264i	−0.307406	−	0.307406i
$905$	3.45584			0.114876
$906$	−0.242641	−	0.242641i	−0.00806120	−	0.00806120i
$907$	−22.2843	+	22.2843i	−0.739937	+	0.739937i	−0.972566	−	0.232629i	$-0.925267\pi$
$907$	−22.2843	+	22.2843i	−0.739937	+	0.739937i	0.232629	+	0.972566i	$0.425267\pi$
$908$	−1.17157	+	1.17157i	−0.0388800	+	0.0388800i
$909$		−	12.0000i		−	0.398015i
$910$		−	16.0000i		−	0.530395i
$911$	31.7990	−	31.7990i	1.05355	−	1.05355i	0.0550648	−	0.998483i	$-0.482463\pi$
$911$	31.7990	−	31.7990i	1.05355	−	1.05355i	0.998483	−	0.0550648i	$-0.0175365\pi$
$912$	1.41421	−	1.41421i	0.0468293	−	0.0468293i
$913$	−2.82843	−	2.82843i	−0.0936073	−	0.0936073i
$914$	−28.6274			−0.946911
$915$	−1.89949	−	1.89949i	−0.0627954	−	0.0627954i
$916$		−	17.3137i		−	0.572061i
$917$	52.6863			1.73985
$918$	−0.121320	−	4.12132i	−0.00400417	−	0.136024i
$919$	−53.3137			−1.75866			−0.879328	−	0.476216i	$-0.842008\pi$
$919$	−53.3137			−1.75866			−0.879328	+	0.476216i	$0.842008\pi$
$920$		−	4.00000i		−	0.131876i
$921$	19.0711	+	19.0711i	0.628413	+	0.628413i
$922$	5.65685			0.186299
$923$	−19.3137	−	19.3137i	−0.635718	−	0.635718i
$924$	−2.82843	+	2.82843i	−0.0930484	+	0.0930484i
$925$	−31.0000	+	31.0000i	−1.01927	+	1.01927i
$926$		−	22.3431i		−	0.734241i
$927$			2.34315i			0.0769590i
$928$	5.00000	−	5.00000i	0.164133	−	0.164133i
$929$	−1.10051	+	1.10051i	−0.0361064	+	0.0361064i	−0.724929	−	0.688823i	$-0.758128\pi$
$929$	−1.10051	+	1.10051i	−0.0361064	+	0.0361064i	0.688823	+	0.724929i	$0.258128\pi$
$930$	−3.51472	−	3.51472i	−0.115252	−	0.115252i
$931$	18.0000			0.589926
$932$	−5.34315	−	5.34315i	−0.175021	−	0.175021i
$933$		−	17.6569i		−	0.578059i
$934$	−38.9706			−1.27516
$935$	−1.75736	−	1.65685i	−0.0574718	−	0.0541849i
$936$	−6.82843			−0.223194
$937$			53.1716i			1.73704i	0.495654	+	0.868520i	$0.334928\pi$
$937$			53.1716i			1.73704i	−0.495654	+	0.868520i	$0.665072\pi$
$938$	38.6274	+	38.6274i	1.26123	+	1.26123i
$939$	12.2426			0.399523
$940$	−0.142136	−	0.142136i	−0.00463595	−	0.00463595i
$941$	27.3431	−	27.3431i	0.891361	−	0.891361i	−0.103290	−	0.994651i	$-0.532937\pi$
$941$	27.3431	−	27.3431i	0.891361	−	0.891361i	0.994651	+	0.103290i	$0.0329370\pi$
$942$	9.89949	−	9.89949i	0.322543	−	0.322543i
$943$			64.2843i			2.09338i
$944$			3.65685i			0.119020i
$945$	1.65685	−	1.65685i	0.0538975	−	0.0538975i
$946$	1.41421	−	1.41421i	0.0459800	−	0.0459800i
$947$	−13.7990	−	13.7990i	−0.448407	−	0.448407i	0.446418	−	0.894825i	$-0.352700\pi$
$947$	−13.7990	−	13.7990i	−0.448407	−	0.448407i	−0.894825	+	0.446418i	$0.852700\pi$
$948$	−6.82843			−0.221777
$949$	8.48528	+	8.48528i	0.275444	+	0.275444i
$950$		−	9.31371i		−	0.302177i
$951$	20.8701			0.676758
$952$	0.485281	+	16.4853i	0.0157281	+	0.534291i
$953$	32.9706			1.06802			0.534011	−	0.845478i	$-0.320684\pi$
$953$	32.9706			1.06802			0.534011	+	0.845478i	$0.320684\pi$
$954$		−	12.4853i		−	0.404226i
$955$	−7.85786	−	7.85786i	−0.254275	−	0.254275i
$956$	−6.34315			−0.205152
$957$	5.00000	+	5.00000i	0.161627	+	0.161627i
$958$	−11.5147	+	11.5147i	−0.372024	+	0.372024i
$959$	1.37258	−	1.37258i	0.0443230	−	0.0443230i
$960$			0.585786i			0.0189062i
$961$			41.0000i			1.32258i
$962$	−45.4558	+	45.4558i	−1.46556	+	1.46556i
$963$	−0.343146	+	0.343146i	−0.0110577	+	0.0110577i
$964$	−15.5858	−	15.5858i	−0.501984	−	0.501984i
$965$	−6.97056			−0.224390
$966$	−19.3137	−	19.3137i	−0.621408	−	0.621408i
$967$			1.02944i			0.0331045i	0.999863	+	0.0165522i	$0.00526898\pi$
$967$			1.02944i			0.0331045i	−0.999863	+	0.0165522i	$0.994731\pi$
$968$	1.00000			0.0321412
$969$	8.24264	−	0.242641i	0.264792	−	0.00779474i
$970$	−5.51472			−0.177067
$971$			53.5980i			1.72004i	0.510259	+	0.860021i	$0.329549\pi$
$971$			53.5980i			1.72004i	−0.510259	+	0.860021i	$0.670451\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$	49.9411			1.60104
$974$	−8.48528	−	8.48528i	−0.271886	−	0.271886i
$975$	−22.4853	+	22.4853i	−0.720105	+	0.720105i
$976$	3.24264	−	3.24264i	0.103794	−	0.103794i
$977$		−	48.4853i		−	1.55118i	−0.631236	−	0.775591i	$-0.717452\pi$
$977$		−	48.4853i		−	1.55118i	0.631236	−	0.775591i	$-0.282548\pi$
$978$		−	8.48528i		−	0.271329i
$979$	−7.65685	+	7.65685i	−0.244714	+	0.244714i
$980$	−3.72792	+	3.72792i	−0.119084	+	0.119084i
$981$	11.2426	+	11.2426i	0.358950	+	0.358950i
$982$	−0.686292			−0.0219004
$983$	−39.4558	−	39.4558i	−1.25845	−	1.25845i	−0.951835	−	0.306611i	$-0.900805\pi$
$983$	−39.4558	−	39.4558i	−1.25845	−	1.25845i	−0.306611	−	0.951835i	$-0.599195\pi$
$984$		−	9.41421i		−	0.300114i
$985$	−1.11270			−0.0354535
$986$	29.1421	−	0.857864i	0.928075	−	0.0273200i
$987$	−1.37258			−0.0436898
$988$		−	13.6569i		−	0.434482i
$989$	9.65685	+	9.65685i	0.307070	+	0.307070i
$990$	−0.585786			−0.0186175
$991$	41.4558	+	41.4558i	1.31689	+	1.31689i	0.916226	+	0.400663i	$0.131220\pi$
$991$	41.4558	+	41.4558i	1.31689	+	1.31689i	0.400663	+	0.916226i	$0.368780\pi$
$992$	6.00000	−	6.00000i	0.190500	−	0.190500i
$993$	−12.0000	+	12.0000i	−0.380808	+	0.380808i
$994$			16.0000i			0.507489i
$995$			8.97056i			0.284386i
$996$	−2.82843	+	2.82843i	−0.0896221	+	0.0896221i
$997$	−42.3553	+	42.3553i	−1.34141	+	1.34141i	−0.446746	+	0.894661i	$0.647417\pi$
$997$	−42.3553	+	42.3553i	−1.34141	+	1.34141i	−0.894661	+	0.446746i	$0.852583\pi$
$998$	0.343146	+	0.343146i	0.0108621	+	0.0108621i
$999$	−9.41421			−0.297853

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1122.2.l.b.727.1	yes	4
17.4	even	4	inner	1122.2.l.b.463.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1122.2.l.b.463.1	✓	4	17.4	even	4	inner
1122.2.l.b.727.1	yes	4	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)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(0.414214 + 0.414214i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(2.82843 - 2.82843i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(0.414214 + 0.414214i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(2.82843 - 2.82843i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +(0.414214 - 0.414214i) q^{10} +(-0.707107 + 0.707107i) q^{11} +(0.707107 + 0.707107i) q^{12} +6.82843 q^{13} +(-2.82843 - 2.82843i) q^{14} -0.585786i q^{15} +1.00000 q^{16} +(3.00000 + 2.82843i) q^{17} +1.00000 q^{18} +2.00000i q^{19} +(-0.414214 - 0.414214i) q^{20} -4.00000 q^{21} +(0.707107 + 0.707107i) q^{22} +(-4.82843 + 4.82843i) q^{23} +(0.707107 - 0.707107i) q^{24} -4.65685i q^{25} -6.82843i q^{26} +(0.707107 - 0.707107i) q^{27} +(-2.82843 + 2.82843i) q^{28} +(5.00000 + 5.00000i) q^{29} -0.585786 q^{30} +(6.00000 + 6.00000i) q^{31} -1.00000i q^{32} +1.00000 q^{33} +(2.82843 - 3.00000i) q^{34} +2.34315 q^{35} -1.00000i q^{36} +(-6.65685 - 6.65685i) q^{37} +2.00000 q^{38} +(-4.82843 - 4.82843i) q^{39} +(-0.414214 + 0.414214i) q^{40} +(6.65685 - 6.65685i) q^{41} +4.00000i q^{42} -2.00000i q^{43} +(0.707107 - 0.707107i) q^{44} +(-0.414214 + 0.414214i) q^{45} +(4.82843 + 4.82843i) q^{46} +0.343146 q^{47} +(-0.707107 - 0.707107i) q^{48} -9.00000i q^{49} -4.65685 q^{50} +(-0.121320 - 4.12132i) q^{51} -6.82843 q^{52} -12.4853i q^{53} +(-0.707107 - 0.707107i) q^{54} -0.585786 q^{55} +(2.82843 + 2.82843i) q^{56} +(1.41421 - 1.41421i) q^{57} +(5.00000 - 5.00000i) q^{58} +3.65685i q^{59} +0.585786i q^{60} +(3.24264 - 3.24264i) q^{61} +(6.00000 - 6.00000i) q^{62} +(2.82843 + 2.82843i) q^{63} -1.00000 q^{64} +(2.82843 + 2.82843i) q^{65} -1.00000i q^{66} -13.6569 q^{67} +(-3.00000 - 2.82843i) q^{68} +6.82843 q^{69} -2.34315i q^{70} +(-2.82843 - 2.82843i) q^{71} -1.00000 q^{72} +(1.24264 + 1.24264i) q^{73} +(-6.65685 + 6.65685i) q^{74} +(-3.29289 + 3.29289i) q^{75} -2.00000i q^{76} +4.00000i q^{77} +(-4.82843 + 4.82843i) q^{78} +(-4.82843 + 4.82843i) q^{79} +(0.414214 + 0.414214i) q^{80} -1.00000 q^{81} +(-6.65685 - 6.65685i) q^{82} +4.00000i q^{83} +4.00000 q^{84} +(0.0710678 + 2.41421i) q^{85} -2.00000 q^{86} -7.07107i q^{87} +(-0.707107 - 0.707107i) q^{88} +10.8284 q^{89} +(0.414214 + 0.414214i) q^{90} +(19.3137 - 19.3137i) q^{91} +(4.82843 - 4.82843i) q^{92} -8.48528i q^{93} -0.343146i q^{94} +(-0.828427 + 0.828427i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(-6.65685 - 6.65685i) q^{97} -9.00000 q^{98} +(-0.707107 - 0.707107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 4 q^{5}+O(q^{10}) \) 4 * q - 4 * q^4 - 4 * q^5	\( 4 q - 4 q^{4} - 4 q^{5} - 4 q^{10} + 16 q^{13} + 4 q^{16} + 12 q^{17} + 4 q^{18} + 4 q^{20} - 16 q^{21} - 8 q^{23} + 20 q^{29} - 8 q^{30} + 24 q^{31} + 4 q^{33} + 32 q^{35} - 4 q^{37} + 8 q^{38} - 8 q^{39} + 4 q^{40} + 4 q^{41} + 4 q^{45} + 8 q^{46} + 24 q^{47} + 4 q^{50} + 8 q^{51} - 16 q^{52} - 8 q^{55} + 20 q^{58} - 4 q^{61} + 24 q^{62} - 4 q^{64} - 32 q^{67} - 12 q^{68} + 16 q^{69} - 4 q^{72} - 12 q^{73} - 4 q^{74} - 16 q^{75} - 8 q^{78} - 8 q^{79} - 4 q^{80} - 4 q^{81} - 4 q^{82} + 16 q^{84} - 28 q^{85} - 8 q^{86} + 32 q^{89} - 4 q^{90} + 32 q^{91} + 8 q^{92} + 8 q^{95} - 4 q^{97} - 36 q^{98}+O(q^{100}) \) 4 * q - 4 * q^4 - 4 * q^5 - 4 * q^10 + 16 * q^13 + 4 * q^16 + 12 * q^17 + 4 * q^18 + 4 * q^20 - 16 * q^21 - 8 * q^23 + 20 * q^29 - 8 * q^30 + 24 * q^31 + 4 * q^33 + 32 * q^35 - 4 * q^37 + 8 * q^38 - 8 * q^39 + 4 * q^40 + 4 * q^41 + 4 * q^45 + 8 * q^46 + 24 * q^47 + 4 * q^50 + 8 * q^51 - 16 * q^52 - 8 * q^55 + 20 * q^58 - 4 * q^61 + 24 * q^62 - 4 * q^64 - 32 * q^67 - 12 * q^68 + 16 * q^69 - 4 * q^72 - 12 * q^73 - 4 * q^74 - 16 * q^75 - 8 * q^78 - 8 * q^79 - 4 * q^80 - 4 * q^81 - 4 * q^82 + 16 * q^84 - 28 * q^85 - 8 * q^86 + 32 * q^89 - 4 * q^90 + 32 * q^91 + 8 * q^92 + 8 * q^95 - 4 * q^97 - 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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