LMFDB - Embedded newform 1078.2.e.v.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(67,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1078.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.60787333789$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$-1.32288 + 2.29129i$ of defining polynomial
Character	$\chi$	$=$	1078.67
Dual form			1078.2.e.v.177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-1.32288 + 2.29129i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.82288 + 3.15731i) q^{5} -2.64575 q^{6} -1.00000 q^{8} +(-2.00000 - 3.46410i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.32288 + 2.29129i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.82288 + 3.15731i) q^{5} -2.64575 q^{6} -1.00000 q^{8} +(-2.00000 - 3.46410i) q^{9} +(-1.82288 + 3.15731i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-1.32288 - 2.29129i) q^{12} -5.00000 q^{13} -9.64575 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(2.00000 - 3.46410i) q^{18} +(-0.177124 - 0.306788i) q^{19} -3.64575 q^{20} -1.00000 q^{22} +(1.82288 + 3.15731i) q^{23} +(1.32288 - 2.29129i) q^{24} +(-4.14575 + 7.18065i) q^{25} +(-2.50000 - 4.33013i) q^{26} +2.64575 q^{27} -4.29150 q^{29} +(-4.82288 - 8.35347i) q^{30} +(-2.00000 + 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.32288 - 2.29129i) q^{33} +6.00000 q^{34} +4.00000 q^{36} +(0.822876 + 1.42526i) q^{37} +(0.177124 - 0.306788i) q^{38} +(6.61438 - 11.4564i) q^{39} +(-1.82288 - 3.15731i) q^{40} +4.93725 q^{41} -4.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(7.29150 - 12.6293i) q^{45} +(-1.82288 + 3.15731i) q^{46} +(6.64575 + 11.5108i) q^{47} +2.64575 q^{48} -8.29150 q^{50} +(7.93725 + 13.7477i) q^{51} +(2.50000 - 4.33013i) q^{52} +(1.82288 - 3.15731i) q^{53} +(1.32288 + 2.29129i) q^{54} -3.64575 q^{55} +0.937254 q^{57} +(-2.14575 - 3.71655i) q^{58} +(-0.322876 + 0.559237i) q^{59} +(4.82288 - 8.35347i) q^{60} +(1.85425 + 3.21165i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(-9.11438 - 15.7866i) q^{65} +(1.32288 - 2.29129i) q^{66} +(-1.96863 + 3.40976i) q^{67} +(3.00000 + 5.19615i) q^{68} -9.64575 q^{69} +9.64575 q^{71} +(2.00000 + 3.46410i) q^{72} +(2.82288 - 4.88936i) q^{73} +(-0.822876 + 1.42526i) q^{74} +(-10.9686 - 18.9982i) q^{75} +0.354249 q^{76} +13.2288 q^{78} +(-1.32288 - 2.29129i) q^{79} +(1.82288 - 3.15731i) q^{80} +(2.50000 - 4.33013i) q^{81} +(2.46863 + 4.27579i) q^{82} -13.2915 q^{83} +21.8745 q^{85} +(-2.00000 - 3.46410i) q^{86} +(5.67712 - 9.83307i) q^{87} +(0.500000 - 0.866025i) q^{88} +(-7.29150 - 12.6293i) q^{89} +14.5830 q^{90} -3.64575 q^{92} +(-5.29150 - 9.16515i) q^{93} +(-6.64575 + 11.5108i) q^{94} +(0.645751 - 1.11847i) q^{95} +(1.32288 + 2.29129i) q^{96} +5.70850 q^{97} +4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^8 - 8 * q^9	$ 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{8} - 8 q^{9} - 2 q^{10} - 2 q^{11} - 20 q^{13} - 28 q^{15} - 2 q^{16} + 12 q^{17} + 8 q^{18} - 6 q^{19} - 4 q^{20} - 4 q^{22} + 2 q^{23} - 6 q^{25} - 10 q^{26} + 4 q^{29} - 14 q^{30} - 8 q^{31} + 2 q^{32} + 24 q^{34} + 16 q^{36} - 2 q^{37} + 6 q^{38} - 2 q^{40} - 12 q^{41} - 16 q^{43} - 2 q^{44} + 8 q^{45} - 2 q^{46} + 16 q^{47} - 12 q^{50} + 10 q^{52} + 2 q^{53} - 4 q^{55} - 28 q^{57} + 2 q^{58} + 4 q^{59} + 14 q^{60} + 18 q^{61} - 16 q^{62} + 4 q^{64} - 10 q^{65} + 8 q^{67} + 12 q^{68} - 28 q^{69} + 28 q^{71} + 8 q^{72} + 6 q^{73} + 2 q^{74} - 28 q^{75} + 12 q^{76} + 2 q^{80} + 10 q^{81} - 6 q^{82} - 32 q^{83} + 24 q^{85} - 8 q^{86} + 28 q^{87} + 2 q^{88} - 8 q^{89} + 16 q^{90} - 4 q^{92} - 16 q^{94} - 8 q^{95} + 44 q^{97} + 16 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^8 - 8 * q^9 - 2 * q^10 - 2 * q^11 - 20 * q^13 - 28 * q^15 - 2 * q^16 + 12 * q^17 + 8 * q^18 - 6 * q^19 - 4 * q^20 - 4 * q^22 + 2 * q^23 - 6 * q^25 - 10 * q^26 + 4 * q^29 - 14 * q^30 - 8 * q^31 + 2 * q^32 + 24 * q^34 + 16 * q^36 - 2 * q^37 + 6 * q^38 - 2 * q^40 - 12 * q^41 - 16 * q^43 - 2 * q^44 + 8 * q^45 - 2 * q^46 + 16 * q^47 - 12 * q^50 + 10 * q^52 + 2 * q^53 - 4 * q^55 - 28 * q^57 + 2 * q^58 + 4 * q^59 + 14 * q^60 + 18 * q^61 - 16 * q^62 + 4 * q^64 - 10 * q^65 + 8 * q^67 + 12 * q^68 - 28 * q^69 + 28 * q^71 + 8 * q^72 + 6 * q^73 + 2 * q^74 - 28 * q^75 + 12 * q^76 + 2 * q^80 + 10 * q^81 - 6 * q^82 - 32 * q^83 + 24 * q^85 - 8 * q^86 + 28 * q^87 + 2 * q^88 - 8 * q^89 + 16 * q^90 - 4 * q^92 - 16 * q^94 - 8 * q^95 + 44 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.32288	+	2.29129i	−0.763763	+	1.32288i	0.177136	+	0.984186i	$0.443317\pi$
$3$	−1.32288	+	2.29129i	−0.763763	+	1.32288i	−0.940898	+	0.338689i	$0.890016\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.82288	+	3.15731i	0.815215	+	1.41199i	0.909174	+	0.416417i	$0.136714\pi$
$5$	1.82288	+	3.15731i	0.815215	+	1.41199i	−0.0939588	+	0.995576i	$0.529952\pi$
$6$	−2.64575			−1.08012
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−2.00000	−	3.46410i	−0.666667	−	1.15470i
$10$	−1.82288	+	3.15731i	−0.576444	+	0.998430i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	−1.32288	−	2.29129i	−0.381881	−	0.661438i
$13$	−5.00000			−1.38675			−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−5.00000			−1.38675			−0.693375	+	0.720577i	$0.743877\pi$
$14$		0			0
$15$	−9.64575			−2.49052
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	−0.230285	−	0.973123i	$-0.573966\pi$
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	0.957892	−	0.287129i	$-0.0927008\pi$
$18$	2.00000	−	3.46410i	0.471405	−	0.816497i
$19$	−0.177124	−	0.306788i	−0.0406351	−	0.0703821i	0.844993	−	0.534778i	$-0.179605\pi$
$19$	−0.177124	−	0.306788i	−0.0406351	−	0.0703821i	−0.885628	+	0.464396i	$0.846271\pi$
$20$	−3.64575			−0.815215
$21$		0			0
$22$	−1.00000			−0.213201
$23$	1.82288	+	3.15731i	0.380096	+	0.658345i	0.991076	−	0.133301i	$-0.0425577\pi$
$23$	1.82288	+	3.15731i	0.380096	+	0.658345i	−0.610980	+	0.791646i	$0.709224\pi$
$24$	1.32288	−	2.29129i	0.270031	−	0.467707i
$25$	−4.14575	+	7.18065i	−0.829150	+	1.43613i
$26$	−2.50000	−	4.33013i	−0.490290	−	0.849208i
$27$	2.64575			0.509175
$28$		0			0
$29$	−4.29150			−0.796912			−0.398456	−	0.917187i	$-0.630454\pi$
$29$	−4.29150			−0.796912			−0.398456	+	0.917187i	$0.630454\pi$
$30$	−4.82288	−	8.35347i	−0.880533	−	1.52513i
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	0.628619	+	0.777714i	$0.283621\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−1.32288	−	2.29129i	−0.230283	−	0.398862i
$34$	6.00000			1.02899
$35$		0			0
$36$	4.00000			0.666667
$37$	0.822876	+	1.42526i	0.135280	+	0.234312i	0.925704	−	0.378248i	$-0.123473\pi$
$37$	0.822876	+	1.42526i	0.135280	+	0.234312i	−0.790424	+	0.612560i	$0.790140\pi$
$38$	0.177124	−	0.306788i	0.0287334	−	0.0497676i
$39$	6.61438	−	11.4564i	1.05915	−	1.83450i
$40$	−1.82288	−	3.15731i	−0.288222	−	0.499215i
$41$	4.93725			0.771070			0.385535	−	0.922693i	$-0.374017\pi$
$41$	4.93725			0.771070			0.385535	+	0.922693i	$0.374017\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$	−0.500000	−	0.866025i	−0.0753778	−	0.130558i
$45$	7.29150	−	12.6293i	1.08695	−	1.88266i
$46$	−1.82288	+	3.15731i	−0.268768	+	0.465520i
$47$	6.64575	+	11.5108i	0.969382	+	1.67902i	0.697349	+	0.716732i	$0.254363\pi$
$47$	6.64575	+	11.5108i	0.969382	+	1.67902i	0.272034	+	0.962288i	$0.412304\pi$
$48$	2.64575			0.381881
$49$		0			0
$50$	−8.29150			−1.17260
$51$	7.93725	+	13.7477i	1.11144	+	1.92507i
$52$	2.50000	−	4.33013i	0.346688	−	0.600481i
$53$	1.82288	−	3.15731i	0.250391	−	0.433690i	−0.713242	−	0.700918i	$-0.752774\pi$
$53$	1.82288	−	3.15731i	0.250391	−	0.433690i	0.963634	+	0.267227i	$0.0861074\pi$
$54$	1.32288	+	2.29129i	0.180021	+	0.311805i
$55$	−3.64575			−0.491593
$56$		0			0
$57$	0.937254			0.124142
$58$	−2.14575	−	3.71655i	−0.281751	−	0.488007i
$59$	−0.322876	+	0.559237i	−0.0420348	+	0.0728065i	−0.886277	−	0.463155i	$-0.846717\pi$
$59$	−0.322876	+	0.559237i	−0.0420348	+	0.0728065i	0.844243	+	0.535961i	$0.180051\pi$
$60$	4.82288	−	8.35347i	0.622631	−	1.07843i
$61$	1.85425	+	3.21165i	0.237412	+	0.411210i	0.959971	−	0.280099i	$-0.0903675\pi$
$61$	1.85425	+	3.21165i	0.237412	+	0.411210i	−0.722559	+	0.691310i	$0.757034\pi$
$62$	−4.00000			−0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	−9.11438	−	15.7866i	−1.13050	−	1.95808i
$66$	1.32288	−	2.29129i	0.162835	−	0.282038i
$67$	−1.96863	+	3.40976i	−0.240506	+	0.416569i	−0.960859	−	0.277039i	$-0.910647\pi$
$67$	−1.96863	+	3.40976i	−0.240506	+	0.416569i	0.720352	+	0.693608i	$0.243980\pi$
$68$	3.00000	+	5.19615i	0.363803	+	0.630126i
$69$	−9.64575			−1.16121
$70$		0			0
$71$	9.64575			1.14474			0.572370	−	0.819995i	$-0.306024\pi$
$71$	9.64575			1.14474			0.572370	+	0.819995i	$0.306024\pi$
$72$	2.00000	+	3.46410i	0.235702	+	0.408248i
$73$	2.82288	−	4.88936i	0.330393	−	0.572257i	−0.652196	−	0.758050i	$-0.726152\pi$
$73$	2.82288	−	4.88936i	0.330393	−	0.572257i	0.982589	+	0.185793i	$0.0594855\pi$
$74$	−0.822876	+	1.42526i	−0.0956574	+	0.165683i
$75$	−10.9686	−	18.9982i	−1.26655	−	2.19373i
$76$	0.354249			0.0406351
$77$		0			0
$78$	13.2288			1.49786
$79$	−1.32288	−	2.29129i	−0.148835	−	0.257790i	0.781962	−	0.623326i	$-0.214219\pi$
$79$	−1.32288	−	2.29129i	−0.148835	−	0.257790i	−0.930797	+	0.365536i	$0.880886\pi$
$80$	1.82288	−	3.15731i	0.203804	−	0.352998i
$81$	2.50000	−	4.33013i	0.277778	−	0.481125i
$82$	2.46863	+	4.27579i	0.272614	+	0.472182i
$83$	−13.2915			−1.45893			−0.729466	−	0.684017i	$-0.760231\pi$
$83$	−13.2915			−1.45893			−0.729466	+	0.684017i	$0.760231\pi$
$84$		0			0
$85$	21.8745			2.37262
$86$	−2.00000	−	3.46410i	−0.215666	−	0.373544i
$87$	5.67712	−	9.83307i	0.608652	−	1.05422i
$88$	0.500000	−	0.866025i	0.0533002	−	0.0923186i
$89$	−7.29150	−	12.6293i	−0.772898	−	1.33870i	−0.935968	−	0.352084i	$-0.885473\pi$
$89$	−7.29150	−	12.6293i	−0.772898	−	1.33870i	0.163071	−	0.986614i	$-0.447860\pi$
$90$	14.5830			1.53718
$91$		0			0
$92$	−3.64575			−0.380096
$93$	−5.29150	−	9.16515i	−0.548703	−	0.950382i
$94$	−6.64575	+	11.5108i	−0.685457	+	1.18725i
$95$	0.645751	−	1.11847i	0.0662527	−	0.114753i
$96$	1.32288	+	2.29129i	0.135015	+	0.233854i
$97$	5.70850			0.579610			0.289805	−	0.957086i	$-0.406410\pi$
$97$	5.70850			0.579610			0.289805	+	0.957086i	$0.406410\pi$
$98$		0			0
$99$	4.00000			0.402015
$100$	−4.14575	−	7.18065i	−0.414575	−	0.718065i
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	−0.781697	−	0.623658i	$-0.785646\pi$
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	0.930953	+	0.365140i	$0.118979\pi$
$102$	−7.93725	+	13.7477i	−0.785905	+	1.36123i
$103$	6.46863	+	11.2040i	0.637373	+	1.10396i	0.986007	+	0.166703i	$0.0533122\pi$
$103$	6.46863	+	11.2040i	0.637373	+	1.10396i	−0.348634	+	0.937259i	$0.613354\pi$
$104$	5.00000			0.490290
$105$		0			0
$106$	3.64575			0.354107
$107$	−2.46863	−	4.27579i	−0.238651	−	0.413356i	0.721676	−	0.692231i	$-0.243372\pi$
$107$	−2.46863	−	4.27579i	−0.238651	−	0.413356i	−0.960327	+	0.278875i	$0.910039\pi$
$108$	−1.32288	+	2.29129i	−0.127294	+	0.220479i
$109$	−5.29150	+	9.16515i	−0.506834	+	0.877862i	0.493135	+	0.869953i	$0.335851\pi$
$109$	−5.29150	+	9.16515i	−0.506834	+	0.877862i	−0.999969	+	0.00790932i	$0.997482\pi$
$110$	−1.82288	−	3.15731i	−0.173804	−	0.301038i
$111$	−4.35425			−0.413287
$112$		0			0
$113$	−7.70850			−0.725154			−0.362577	−	0.931954i	$-0.618103\pi$
$113$	−7.70850			−0.725154			−0.362577	+	0.931954i	$0.618103\pi$
$114$	0.468627	+	0.811686i	0.0438909	+	0.0760213i
$115$	−6.64575	+	11.5108i	−0.619720	+	1.07339i
$116$	2.14575	−	3.71655i	0.199228	−	0.345073i
$117$	10.0000	+	17.3205i	0.924500	+	1.60128i
$118$	−0.645751			−0.0594462
$119$		0			0
$120$	9.64575			0.880533
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−1.85425	+	3.21165i	−0.167876	+	0.290769i
$123$	−6.53137	+	11.3127i	−0.588914	+	1.02003i
$124$	−2.00000	−	3.46410i	−0.179605	−	0.311086i
$125$	−12.0000			−1.07331
$126$		0			0
$127$	0.0627461			0.00556781			0.00278391	−	0.999996i	$-0.499114\pi$
$127$	0.0627461			0.00556781			0.00278391	+	0.999996i	$0.499114\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	5.29150	−	9.16515i	0.465891	−	0.806947i
$130$	9.11438	−	15.7866i	0.799384	−	1.38457i
$131$	7.82288	+	13.5496i	0.683488	+	1.18384i	0.973909	+	0.226937i	$0.0728711\pi$
$131$	7.82288	+	13.5496i	0.683488	+	1.18384i	−0.290422	+	0.956899i	$0.593796\pi$
$132$	2.64575			0.230283
$133$		0			0
$134$	−3.93725			−0.340127
$135$	4.82288	+	8.35347i	0.415087	+	0.718952i
$136$	−3.00000	+	5.19615i	−0.257248	+	0.445566i
$137$	−9.43725	+	16.3458i	−0.806279	+	1.39652i	0.109145	+	0.994026i	$0.465189\pi$
$137$	−9.43725	+	16.3458i	−0.806279	+	1.39652i	−0.915424	+	0.402490i	$0.868145\pi$
$138$	−4.82288	−	8.35347i	−0.410550	−	0.711094i
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$	−35.1660			−2.96151
$142$	4.82288	+	8.35347i	0.404727	+	0.701007i
$143$	2.50000	−	4.33013i	0.209061	−	0.362103i
$144$	−2.00000	+	3.46410i	−0.166667	+	0.288675i
$145$	−7.82288	−	13.5496i	−0.649654	−	1.12523i
$146$	5.64575			0.467246
$147$		0			0
$148$	−1.64575			−0.135280
$149$	2.35425	+	4.07768i	0.192868	+	0.334056i	0.946199	−	0.323584i	$-0.104888\pi$
$149$	2.35425	+	4.07768i	0.192868	+	0.334056i	−0.753332	+	0.657641i	$0.771555\pi$
$150$	10.9686	−	18.9982i	0.895585	−	1.55120i
$151$	1.67712	−	2.90486i	0.136482	−	0.236395i	−0.789680	−	0.613519i	$-0.789754\pi$
$151$	1.67712	−	2.90486i	0.136482	−	0.236395i	0.926163	+	0.377124i	$0.123087\pi$
$152$	0.177124	+	0.306788i	0.0143667	+	0.0248838i
$153$	−24.0000			−1.94029
$154$		0			0
$155$	−14.5830			−1.17134
$156$	6.61438	+	11.4564i	0.529574	+	0.917249i
$157$	−10.5830	+	18.3303i	−0.844616	+	1.46292i	0.0413387	+	0.999145i	$0.486838\pi$
$157$	−10.5830	+	18.3303i	−0.844616	+	1.46292i	−0.885954	+	0.463772i	$0.846496\pi$
$158$	1.32288	−	2.29129i	0.105242	−	0.182285i
$159$	4.82288	+	8.35347i	0.382479	+	0.662473i
$160$	3.64575			0.288222
$161$		0			0
$162$	5.00000			0.392837
$163$	2.32288	+	4.02334i	0.181942	+	0.315132i	0.942542	−	0.334089i	$-0.108428\pi$
$163$	2.32288	+	4.02334i	0.181942	+	0.315132i	−0.760600	+	0.649221i	$0.775095\pi$
$164$	−2.46863	+	4.27579i	−0.192767	+	0.333883i
$165$	4.82288	−	8.35347i	0.375460	−	0.650316i
$166$	−6.64575	−	11.5108i	−0.515810	−	0.893410i
$167$	−15.2288			−1.17844			−0.589218	−	0.807974i	$-0.700564\pi$
$167$	−15.2288			−1.17844			−0.589218	+	0.807974i	$0.700564\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$	10.9373	+	18.9439i	0.838849	+	1.45293i
$171$	−0.708497	+	1.22715i	−0.0541801	+	0.0938428i
$172$	2.00000	−	3.46410i	0.152499	−	0.264135i
$173$	5.14575	+	8.91270i	0.391224	+	0.677620i	0.992611	−	0.121338i	$-0.0387184\pi$
$173$	5.14575	+	8.91270i	0.391224	+	0.677620i	−0.601387	+	0.798958i	$0.705385\pi$
$174$	11.3542			0.860763
$175$		0			0
$176$	1.00000			0.0753778
$177$	−0.854249	−	1.47960i	−0.0642093	−	0.111214i
$178$	7.29150	−	12.6293i	0.546521	−	0.946603i
$179$	2.03137	−	3.51844i	0.151832	−	0.262981i	−0.780069	−	0.625693i	$-0.784816\pi$
$179$	2.03137	−	3.51844i	0.151832	−	0.262981i	0.931901	+	0.362713i	$0.118149\pi$
$180$	7.29150	+	12.6293i	0.543477	+	0.941329i
$181$	10.0000			0.743294			0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000			0.743294			0.371647	+	0.928374i	$0.378793\pi$
$182$		0			0
$183$	−9.81176			−0.725306
$184$	−1.82288	−	3.15731i	−0.134384	−	0.232760i
$185$	−3.00000	+	5.19615i	−0.220564	+	0.382029i
$186$	5.29150	−	9.16515i	0.387992	−	0.672022i
$187$	3.00000	+	5.19615i	0.219382	+	0.379980i
$188$	−13.2915			−0.969382
$189$		0			0
$190$	1.29150			0.0936954
$191$	6.64575	+	11.5108i	0.480870	+	0.832891i	0.999759	−	0.0219507i	$-0.00698768\pi$
$191$	6.64575	+	11.5108i	0.480870	+	0.832891i	−0.518889	+	0.854841i	$0.673654\pi$
$192$	−1.32288	+	2.29129i	−0.0954703	+	0.165359i
$193$	5.76013	−	9.97684i	0.414623	−	0.718148i	−0.580766	−	0.814071i	$-0.697247\pi$
$193$	5.76013	−	9.97684i	0.414623	−	0.718148i	0.995389	+	0.0959224i	$0.0305801\pi$
$194$	2.85425	+	4.94370i	0.204923	+	0.354937i
$195$	48.2288			3.45373
$196$		0			0
$197$	18.8745			1.34475			0.672377	−	0.740209i	$-0.265274\pi$
$197$	18.8745			1.34475			0.672377	+	0.740209i	$0.265274\pi$
$198$	2.00000	+	3.46410i	0.142134	+	0.246183i
$199$	−11.1144	+	19.2507i	−0.787877	+	1.36464i	0.139388	+	0.990238i	$0.455487\pi$
$199$	−11.1144	+	19.2507i	−0.787877	+	1.36464i	−0.927265	+	0.374406i	$0.877847\pi$
$200$	4.14575	−	7.18065i	0.293149	−	0.507749i
$201$	−5.20850	−	9.02138i	−0.367379	−	0.636319i
$202$	3.00000			0.211079
$203$		0			0
$204$	−15.8745			−1.11144
$205$	9.00000	+	15.5885i	0.628587	+	1.08875i
$206$	−6.46863	+	11.2040i	−0.450691	+	0.780619i
$207$	7.29150	−	12.6293i	0.506794	−	0.877794i
$208$	2.50000	+	4.33013i	0.173344	+	0.300240i
$209$	0.354249			0.0245039
$210$		0			0
$211$	−14.9373			−1.02832			−0.514161	−	0.857693i	$-0.671897\pi$
$211$	−14.9373			−1.02832			−0.514161	+	0.857693i	$0.671897\pi$
$212$	1.82288	+	3.15731i	0.125196	+	0.216845i
$213$	−12.7601	+	22.1012i	−0.874310	+	1.51435i
$214$	2.46863	−	4.27579i	0.168752	−	0.292287i
$215$	−7.29150	−	12.6293i	−0.497276	−	0.861308i
$216$	−2.64575			−0.180021
$217$		0			0
$218$	−10.5830			−0.716772
$219$	7.46863	+	12.9360i	0.504683	+	0.874137i
$220$	1.82288	−	3.15731i	0.122898	−	0.212866i
$221$	−15.0000	+	25.9808i	−1.00901	+	1.74766i
$222$	−2.17712	−	3.77089i	−0.146119	−	0.253086i
$223$	12.3542			0.827302			0.413651	−	0.910436i	$-0.364253\pi$
$223$	12.3542			0.827302			0.413651	+	0.910436i	$0.364253\pi$
$224$		0			0
$225$	33.1660			2.21107
$226$	−3.85425	−	6.67575i	−0.256381	−	0.444065i
$227$	−6.64575	+	11.5108i	−0.441094	+	0.763997i	−0.997771	−	0.0667318i	$-0.978743\pi$
$227$	−6.64575	+	11.5108i	−0.441094	+	0.763997i	0.556677	+	0.830729i	$0.312076\pi$
$228$	−0.468627	+	0.811686i	−0.0310356	+	0.0537552i
$229$	−8.00000	−	13.8564i	−0.528655	−	0.915657i	−0.999442	−	0.0334101i	$-0.989363\pi$
$229$	−8.00000	−	13.8564i	−0.528655	−	0.915657i	0.470787	−	0.882247i	$-0.343970\pi$
$230$	−13.2915			−0.876416
$231$		0			0
$232$	4.29150			0.281751
$233$	−8.46863	−	14.6681i	−0.554798	−	0.960939i	−0.997919	−	0.0644769i	$-0.979462\pi$
$233$	−8.46863	−	14.6681i	−0.554798	−	0.960939i	0.443121	−	0.896462i	$-0.353871\pi$
$234$	−10.0000	+	17.3205i	−0.653720	+	1.13228i
$235$	−24.2288	+	41.9654i	−1.58051	+	2.73752i
$236$	−0.322876	−	0.559237i	−0.0210174	−	0.0364032i
$237$	7.00000			0.454699
$238$		0			0
$239$	9.22876			0.596959			0.298479	−	0.954416i	$-0.403521\pi$
$239$	9.22876			0.596959			0.298479	+	0.954416i	$0.403521\pi$
$240$	4.82288	+	8.35347i	0.311315	+	0.539214i
$241$	11.4059	−	19.7556i	0.734717	−	1.27257i	−0.220130	−	0.975471i	$-0.570648\pi$
$241$	11.4059	−	19.7556i	0.734717	−	1.27257i	0.954847	−	0.297097i	$-0.0960186\pi$
$242$	0.500000	−	0.866025i	0.0321412	−	0.0556702i
$243$	10.5830	+	18.3303i	0.678900	+	1.17589i
$244$	−3.70850			−0.237412
$245$		0			0
$246$	−13.0627			−0.832850
$247$	0.885622	+	1.53394i	0.0563508	+	0.0976024i
$248$	2.00000	−	3.46410i	0.127000	−	0.219971i
$249$	17.5830	−	30.4547i	1.11428	−	1.92999i
$250$	−6.00000	−	10.3923i	−0.379473	−	0.657267i
$251$	−7.29150			−0.460236			−0.230118	−	0.973163i	$-0.573911\pi$
$251$	−7.29150			−0.460236			−0.230118	+	0.973163i	$0.573911\pi$
$252$		0			0
$253$	−3.64575			−0.229206
$254$	0.0313730	+	0.0543397i	0.00196852	+	0.00340958i
$255$	−28.9373	+	50.1208i	−1.81212	+	3.13869i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.208497	−	0.361128i	−0.0130057	−	0.0225265i	0.859449	−	0.511221i	$-0.170807\pi$
$257$	−0.208497	−	0.361128i	−0.0130057	−	0.0225265i	−0.872455	+	0.488694i	$0.837473\pi$
$258$	10.5830			0.658869
$259$		0			0
$260$	18.2288			1.13050
$261$	8.58301	+	14.8662i	0.531275	+	0.920195i
$262$	−7.82288	+	13.5496i	−0.483299	+	0.837098i
$263$	−2.03137	+	3.51844i	−0.125260	+	0.216956i	−0.921834	−	0.387584i	$-0.873310\pi$
$263$	−2.03137	+	3.51844i	−0.125260	+	0.216956i	0.796575	+	0.604540i	$0.206643\pi$
$264$	1.32288	+	2.29129i	0.0814174	+	0.141019i
$265$	13.2915			0.816491
$266$		0			0
$267$	38.5830			2.36124
$268$	−1.96863	−	3.40976i	−0.120253	−	0.208284i
$269$	13.2915	−	23.0216i	0.810397	−	1.40365i	−0.102189	−	0.994765i	$-0.532585\pi$
$269$	13.2915	−	23.0216i	0.810397	−	1.40365i	0.912586	−	0.408884i	$-0.134082\pi$
$270$	−4.82288	+	8.35347i	−0.293511	+	0.508376i
$271$	−8.96863	−	15.5341i	−0.544805	−	0.943630i	−0.998619	−	0.0525339i	$-0.983270\pi$
$271$	−8.96863	−	15.5341i	−0.544805	−	0.943630i	0.453814	−	0.891097i	$-0.350063\pi$
$272$	−6.00000			−0.363803
$273$		0			0
$274$	−18.8745			−1.14025
$275$	−4.14575	−	7.18065i	−0.249998	−	0.433010i
$276$	4.82288	−	8.35347i	0.290303	−	0.502820i
$277$	5.85425	−	10.1399i	0.351748	−	0.609245i	−0.634808	−	0.772670i	$-0.718921\pi$
$277$	5.85425	−	10.1399i	0.351748	−	0.609245i	0.986556	+	0.163425i	$0.0522542\pi$
$278$	2.00000	+	3.46410i	0.119952	+	0.207763i
$279$	16.0000			0.957895
$280$		0			0
$281$	−7.06275			−0.421328			−0.210664	−	0.977559i	$-0.567563\pi$
$281$	−7.06275			−0.421328			−0.210664	+	0.977559i	$0.567563\pi$
$282$	−17.5830	−	30.4547i	−1.04705	−	1.81355i
$283$	−3.82288	+	6.62141i	−0.227246	+	0.393602i	−0.956991	−	0.290118i	$-0.906306\pi$
$283$	−3.82288	+	6.62141i	−0.227246	+	0.393602i	0.729745	+	0.683720i	$0.239639\pi$
$284$	−4.82288	+	8.35347i	−0.286185	+	0.495687i
$285$	1.70850	+	2.95920i	0.101203	+	0.175288i
$286$	5.00000			0.295656
$287$		0			0
$288$	−4.00000			−0.235702
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$	7.82288	−	13.5496i	0.459375	−	0.795661i
$291$	−7.55163	+	13.0798i	−0.442685	+	0.766752i
$292$	2.82288	+	4.88936i	0.165196	+	0.286128i
$293$	−12.0000			−0.701047			−0.350524	−	0.936554i	$-0.613996\pi$
$293$	−12.0000			−0.701047			−0.350524	+	0.936554i	$0.613996\pi$
$294$		0			0
$295$	−2.35425			−0.137070
$296$	−0.822876	−	1.42526i	−0.0478287	−	0.0828417i
$297$	−1.32288	+	2.29129i	−0.0767610	+	0.132954i
$298$	−2.35425	+	4.07768i	−0.136378	+	0.236214i
$299$	−9.11438	−	15.7866i	−0.527098	−	0.912961i
$300$	21.9373			1.26655
$301$		0			0
$302$	3.35425			0.193015
$303$	3.96863	+	6.87386i	0.227992	+	0.394893i
$304$	−0.177124	+	0.306788i	−0.0101588	+	0.0175955i
$305$	−6.76013	+	11.7089i	−0.387084	+	0.670449i
$306$	−12.0000	−	20.7846i	−0.685994	−	1.18818i
$307$	4.22876			0.241348			0.120674	−	0.992692i	$-0.461494\pi$
$307$	4.22876			0.241348			0.120674	+	0.992692i	$0.461494\pi$
$308$		0			0
$309$	−34.2288			−1.94721
$310$	−7.29150	−	12.6293i	−0.414130	−	0.717293i
$311$	8.46863	−	14.6681i	0.480212	−	0.831751i	−0.519531	−	0.854452i	$-0.673893\pi$
$311$	8.46863	−	14.6681i	0.480212	−	0.831751i	0.999742	+	0.0227007i	$0.00722647\pi$
$312$	−6.61438	+	11.4564i	−0.374465	+	0.648593i
$313$	1.20850	+	2.09318i	0.0683083	+	0.118313i	0.898157	−	0.439675i	$-0.144907\pi$
$313$	1.20850	+	2.09318i	0.0683083	+	0.118313i	−0.829848	+	0.557989i	$0.811573\pi$
$314$	−21.1660			−1.19447
$315$		0			0
$316$	2.64575			0.148835
$317$	−6.00000	−	10.3923i	−0.336994	−	0.583690i	0.646872	−	0.762598i	$-0.276077\pi$
$317$	−6.00000	−	10.3923i	−0.336994	−	0.583690i	−0.983866	+	0.178908i	$0.942743\pi$
$318$	−4.82288	+	8.35347i	−0.270453	+	0.468439i
$319$	2.14575	−	3.71655i	0.120139	−	0.208087i
$320$	1.82288	+	3.15731i	0.101902	+	0.176499i
$321$	13.0627			0.729091
$322$		0			0
$323$	−2.12549			−0.118266
$324$	2.50000	+	4.33013i	0.138889	+	0.240563i
$325$	20.7288	−	35.9033i	1.14982	−	1.99155i
$326$	−2.32288	+	4.02334i	−0.128652	+	0.222832i
$327$	−14.0000	−	24.2487i	−0.774202	−	1.34096i
$328$	−4.93725			−0.272614
$329$		0			0
$330$	9.64575			0.530981
$331$	7.67712	+	13.2972i	0.421973	+	0.730879i	0.996132	−	0.0878650i	$-0.0280044\pi$
$331$	7.67712	+	13.2972i	0.421973	+	0.730879i	−0.574159	+	0.818743i	$0.694671\pi$
$332$	6.64575	−	11.5108i	0.364733	−	0.631736i
$333$	3.29150	−	5.70105i	0.180373	−	0.312416i
$334$	−7.61438	−	13.1885i	−0.416640	−	0.721642i
$335$	−14.3542			−0.784256
$336$		0			0
$337$	24.9373			1.35842			0.679209	−	0.733945i	$-0.262323\pi$
$337$	24.9373			1.35842			0.679209	+	0.733945i	$0.262323\pi$
$338$	6.00000	+	10.3923i	0.326357	+	0.565267i
$339$	10.1974	−	17.6624i	0.553846	−	0.959289i
$340$	−10.9373	+	18.9439i	−0.593156	+	1.02738i
$341$	−2.00000	−	3.46410i	−0.108306	−	0.187592i
$342$	−1.41699			−0.0766223
$343$		0			0
$344$	4.00000			0.215666
$345$	−17.5830	−	30.4547i	−0.946637	−	1.63962i
$346$	−5.14575	+	8.91270i	−0.276637	+	0.479150i
$347$	−13.4059	+	23.2197i	−0.719665	+	1.24650i	0.241467	+	0.970409i	$0.422371\pi$
$347$	−13.4059	+	23.2197i	−0.719665	+	1.24650i	−0.961132	+	0.276088i	$0.910962\pi$
$348$	5.67712	+	9.83307i	0.304326	+	0.527108i
$349$	−29.8745			−1.59915			−0.799573	−	0.600569i	$-0.794941\pi$
$349$	−29.8745			−1.59915			−0.799573	+	0.600569i	$0.794941\pi$
$350$		0			0
$351$	−13.2288			−0.706099
$352$	0.500000	+	0.866025i	0.0266501	+	0.0461593i
$353$	−17.5830	+	30.4547i	−0.935849	+	1.62094i	−0.162736	+	0.986670i	$0.552032\pi$
$353$	−17.5830	+	30.4547i	−0.935849	+	1.62094i	−0.773113	+	0.634268i	$0.781301\pi$
$354$	0.854249	−	1.47960i	0.0454028	−	0.0786400i
$355$	17.5830	+	30.4547i	0.933209	+	1.61637i
$356$	14.5830			0.772898
$357$		0			0
$358$	4.06275			0.214723
$359$	5.03137	+	8.71459i	0.265546	+	0.459939i	0.967706	−	0.252080i	$-0.0811145\pi$
$359$	5.03137	+	8.71459i	0.265546	+	0.459939i	−0.702161	+	0.712018i	$0.747781\pi$
$360$	−7.29150	+	12.6293i	−0.384296	+	0.665620i
$361$	9.43725	−	16.3458i	0.496698	−	0.860305i
$362$	5.00000	+	8.66025i	0.262794	+	0.455173i
$363$	2.64575			0.138866
$364$		0			0
$365$	20.5830			1.07736
$366$	−4.90588	−	8.49723i	−0.256435	−	0.444158i
$367$	−4.88562	+	8.46215i	−0.255027	+	0.441720i	−0.964903	−	0.262607i	$-0.915418\pi$
$367$	−4.88562	+	8.46215i	−0.255027	+	0.441720i	0.709876	+	0.704327i	$0.248751\pi$
$368$	1.82288	−	3.15731i	0.0950240	−	0.164586i
$369$	−9.87451	−	17.1031i	−0.514046	−	0.890354i
$370$	−6.00000			−0.311925
$371$		0			0
$372$	10.5830			0.548703
$373$	5.43725	+	9.41760i	0.281530	+	0.487625i	0.971762	−	0.235964i	$-0.0758247\pi$
$373$	5.43725	+	9.41760i	0.281530	+	0.487625i	−0.690232	+	0.723589i	$0.742491\pi$
$374$	−3.00000	+	5.19615i	−0.155126	+	0.268687i
$375$	15.8745	−	27.4955i	0.819756	−	1.41986i
$376$	−6.64575	−	11.5108i	−0.342728	−	0.593623i
$377$	21.4575			1.10512
$378$		0			0
$379$	21.9373			1.12684			0.563421	−	0.826170i	$-0.309485\pi$
$379$	21.9373			1.12684			0.563421	+	0.826170i	$0.309485\pi$
$380$	0.645751	+	1.11847i	0.0331263	+	0.0573765i
$381$	−0.0830052	+	0.143769i	−0.00425249	+	0.00736552i
$382$	−6.64575	+	11.5108i	−0.340026	+	0.588943i
$383$	−17.0516	−	29.5343i	−0.871298	−	1.50913i	−0.860655	−	0.509189i	$-0.829946\pi$
$383$	−17.0516	−	29.5343i	−0.871298	−	1.50913i	−0.0106427	−	0.999943i	$-0.503388\pi$
$384$	−2.64575			−0.135015
$385$		0			0
$386$	11.5203			0.586366
$387$	8.00000	+	13.8564i	0.406663	+	0.704361i
$388$	−2.85425	+	4.94370i	−0.144903	+	0.250979i
$389$	10.4059	−	18.0235i	0.527599	−	0.913828i	−0.471883	−	0.881661i	$-0.656426\pi$
$389$	10.4059	−	18.0235i	0.527599	−	0.913828i	0.999482	−	0.0321675i	$-0.0102410\pi$
$390$	24.1144	+	41.7673i	1.22108	+	2.11497i
$391$	21.8745			1.10624
$392$		0			0
$393$	−41.3948			−2.08809
$394$	9.43725	+	16.3458i	0.475442	+	0.823490i
$395$	4.82288	−	8.35347i	0.242665	−	0.420308i
$396$	−2.00000	+	3.46410i	−0.100504	+	0.174078i
$397$	15.5830	+	26.9906i	0.782089	+	1.35462i	0.930723	+	0.365725i	$0.119179\pi$
$397$	15.5830	+	26.9906i	0.782089	+	1.35462i	−0.148634	+	0.988892i	$0.547488\pi$
$398$	−22.2288			−1.11423
$399$		0			0
$400$	8.29150			0.414575
$401$	−0.208497	−	0.361128i	−0.0104119	−	0.0180339i	0.860773	−	0.508990i	$-0.169981\pi$
$401$	−0.208497	−	0.361128i	−0.0104119	−	0.0180339i	−0.871184	+	0.490956i	$0.836648\pi$
$402$	5.20850	−	9.02138i	0.259776	−	0.449946i
$403$	10.0000	−	17.3205i	0.498135	−	0.862796i
$404$	1.50000	+	2.59808i	0.0746278	+	0.129259i
$405$	18.2288			0.905794
$406$		0			0
$407$	−1.64575			−0.0815769
$408$	−7.93725	−	13.7477i	−0.392953	−	0.680614i
$409$	9.46863	−	16.4001i	0.468193	−	0.810935i	−0.531146	−	0.847280i	$-0.678238\pi$
$409$	9.46863	−	16.4001i	0.468193	−	0.810935i	0.999339	+	0.0363456i	$0.0115717\pi$
$410$	−9.00000	+	15.5885i	−0.444478	+	0.769859i
$411$	−24.9686	−	43.2469i	−1.23161	−	2.13321i
$412$	−12.9373			−0.637373
$413$		0			0
$414$	14.5830			0.716716
$415$	−24.2288	−	41.9654i	−1.18934	−	2.06000i
$416$	−2.50000	+	4.33013i	−0.122573	+	0.212302i
$417$	−5.29150	+	9.16515i	−0.259126	+	0.448819i
$418$	0.177124	+	0.306788i	0.00866343	+	0.0150055i
$419$	−21.8745			−1.06864			−0.534320	−	0.845282i	$-0.679432\pi$
$419$	−21.8745			−1.06864			−0.534320	+	0.845282i	$0.679432\pi$
$420$		0			0
$421$	−33.1660			−1.61641			−0.808206	−	0.588900i	$-0.799561\pi$
$421$	−33.1660			−1.61641			−0.808206	+	0.588900i	$0.799561\pi$
$422$	−7.46863	−	12.9360i	−0.363567	−	0.629717i
$423$	26.5830	−	46.0431i	1.29251	−	2.23869i
$424$	−1.82288	+	3.15731i	−0.0885267	+	0.153333i
$425$	24.8745	+	43.0839i	1.20659	+	2.08988i
$426$	−25.5203			−1.23646
$427$		0			0
$428$	4.93725			0.238651
$429$	6.61438	+	11.4564i	0.319345	+	0.553122i
$430$	7.29150	−	12.6293i	0.351627	−	0.609037i
$431$	−1.38562	+	2.39997i	−0.0667430	+	0.115602i	−0.897466	−	0.441084i	$-0.854594\pi$
$431$	−1.38562	+	2.39997i	−0.0667430	+	0.115602i	0.830723	+	0.556686i	$0.187927\pi$
$432$	−1.32288	−	2.29129i	−0.0636469	−	0.110240i
$433$	16.0000			0.768911			0.384455	−	0.923144i	$-0.374389\pi$
$433$	16.0000			0.768911			0.384455	+	0.923144i	$0.374389\pi$
$434$		0			0
$435$	41.3948			1.98473
$436$	−5.29150	−	9.16515i	−0.253417	−	0.438931i
$437$	0.645751	−	1.11847i	0.0308905	−	0.0535039i
$438$	−7.46863	+	12.9360i	−0.356865	+	0.618108i
$439$	−5.96863	−	10.3380i	−0.284867	−	0.493404i	0.687710	−	0.725986i	$-0.258616\pi$
$439$	−5.96863	−	10.3380i	−0.284867	−	0.493404i	−0.972577	+	0.232581i	$0.925283\pi$
$440$	3.64575			0.173804
$441$		0			0
$442$	−30.0000			−1.42695
$443$	9.22876	+	15.9847i	0.438471	+	0.759455i	0.997572	−	0.0696451i	$-0.0221867\pi$
$443$	9.22876	+	15.9847i	0.438471	+	0.759455i	−0.559100	+	0.829100i	$0.688853\pi$
$444$	2.17712	−	3.77089i	0.103322	−	0.178959i
$445$	26.5830	−	46.0431i	1.26016	−	2.18265i
$446$	6.17712	+	10.6991i	0.292495	+	0.506617i
$447$	−12.4575			−0.589220
$448$		0			0
$449$	9.87451			0.466007			0.233003	−	0.972476i	$-0.425145\pi$
$449$	9.87451			0.466007			0.233003	+	0.972476i	$0.425145\pi$
$450$	16.5830	+	28.7226i	0.781730	+	1.35400i
$451$	−2.46863	+	4.27579i	−0.116243	+	0.201339i
$452$	3.85425	−	6.67575i	0.181289	−	0.314001i
$453$	4.43725	+	7.68555i	0.208480	+	0.361099i
$454$	−13.2915			−0.623801
$455$		0			0
$456$	−0.937254			−0.0438909
$457$	19.5830	+	33.9188i	0.916054	+	1.58665i	0.805350	+	0.592799i	$0.201977\pi$
$457$	19.5830	+	33.9188i	0.916054	+	1.58665i	0.110704	+	0.993853i	$0.464689\pi$
$458$	8.00000	−	13.8564i	0.373815	−	0.647467i
$459$	7.93725	−	13.7477i	0.370479	−	0.641689i
$460$	−6.64575	−	11.5108i	−0.309860	−	0.536693i
$461$	32.1660			1.49812			0.749060	−	0.662502i	$-0.230505\pi$
$461$	32.1660			1.49812			0.749060	+	0.662502i	$0.230505\pi$
$462$		0			0
$463$	−22.4575			−1.04369			−0.521845	−	0.853041i	$-0.674756\pi$
$463$	−22.4575			−1.04369			−0.521845	+	0.853041i	$0.674756\pi$
$464$	2.14575	+	3.71655i	0.0996140	+	0.172537i
$465$	19.2915	−	33.4139i	0.894622	−	1.54953i
$466$	8.46863	−	14.6681i	0.392302	−	0.679486i
$467$	5.35425	+	9.27383i	0.247765	+	0.429142i	0.962905	−	0.269839i	$-0.0869706\pi$
$467$	5.35425	+	9.27383i	0.247765	+	0.429142i	−0.715140	+	0.698981i	$0.753637\pi$
$468$	−20.0000			−0.924500
$469$		0			0
$470$	−48.4575			−2.23518
$471$	−28.0000	−	48.4974i	−1.29017	−	2.23464i
$472$	0.322876	−	0.559237i	0.0148616	−	0.0257410i
$473$	2.00000	−	3.46410i	0.0919601	−	0.159280i
$474$	3.50000	+	6.06218i	0.160760	+	0.278445i
$475$	2.93725			0.134770
$476$		0			0
$477$	−14.5830			−0.667710
$478$	4.61438	+	7.99234i	0.211057	+	0.365561i
$479$	−12.9686	+	22.4623i	−0.592552	+	1.02633i	0.401336	+	0.915931i	$0.368546\pi$
$479$	−12.9686	+	22.4623i	−0.592552	+	1.02633i	−0.993887	+	0.110399i	$0.964787\pi$
$480$	−4.82288	+	8.35347i	−0.220133	+	0.381282i
$481$	−4.11438	−	7.12631i	−0.187600	−	0.324932i
$482$	22.8118			1.03905
$483$		0			0
$484$	1.00000			0.0454545
$485$	10.4059	+	18.0235i	0.472507	+	0.818406i
$486$	−10.5830	+	18.3303i	−0.480055	+	0.831479i
$487$	15.2915	−	26.4857i	0.692924	−	1.20018i	−0.277951	−	0.960595i	$-0.589655\pi$
$487$	15.2915	−	26.4857i	0.692924	−	1.20018i	0.970875	−	0.239585i	$-0.0770113\pi$
$488$	−1.85425	−	3.21165i	−0.0839379	−	0.145385i
$489$	−12.2915			−0.555841
$490$		0			0
$491$	10.7085			0.483268			0.241634	−	0.970367i	$-0.422317\pi$
$491$	10.7085			0.483268			0.241634	+	0.970367i	$0.422317\pi$
$492$	−6.53137	−	11.3127i	−0.294457	−	0.510015i
$493$	−12.8745	+	22.2993i	−0.579839	+	1.00431i
$494$	−0.885622	+	1.53394i	−0.0398460	+	0.0690153i
$495$	7.29150	+	12.6293i	0.327729	+	0.567643i
$496$	4.00000			0.179605
$497$		0			0
$498$	35.1660			1.57583
$499$	−8.93725	−	15.4798i	−0.400086	−	0.692970i	0.593650	−	0.804724i	$-0.297687\pi$
$499$	−8.93725	−	15.4798i	−0.400086	−	0.692970i	−0.993736	+	0.111754i	$0.964353\pi$
$500$	6.00000	−	10.3923i	0.268328	−	0.464758i
$501$	20.1458	−	34.8935i	0.900046	−	1.55893i
$502$	−3.64575	−	6.31463i	−0.162718	−	0.281836i
$503$	19.9373			0.888958			0.444479	−	0.895789i	$-0.353389\pi$
$503$	19.9373			0.888958			0.444479	+	0.895789i	$0.353389\pi$
$504$		0			0
$505$	10.9373			0.486701
$506$	−1.82288	−	3.15731i	−0.0810367	−	0.140360i
$507$	−15.8745	+	27.4955i	−0.705012	+	1.22112i
$508$	−0.0313730	+	0.0543397i	−0.00139195	+	0.00241093i
$509$	10.2915	+	17.8254i	0.456163	+	0.790097i	0.998754	−	0.0498996i	$-0.0158901\pi$
$509$	10.2915	+	17.8254i	0.456163	+	0.790097i	−0.542591	+	0.839997i	$0.682557\pi$
$510$	−57.8745			−2.56273
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−0.468627	−	0.811686i	−0.0206904	−	0.0358368i
$514$	0.208497	−	0.361128i	0.00919643	−	0.0159287i
$515$	−23.5830	+	40.8470i	−1.03919	+	1.79993i
$516$	5.29150	+	9.16515i	0.232945	+	0.403473i
$517$	−13.2915			−0.584560
$518$		0			0
$519$	−27.2288			−1.19521
$520$	9.11438	+	15.7866i	0.399692	+	0.692287i
$521$	−1.06275	+	1.84073i	−0.0465598	+	0.0806439i	−0.888366	−	0.459136i	$-0.848159\pi$
$521$	−1.06275	+	1.84073i	−0.0465598	+	0.0806439i	0.841806	+	0.539780i	$0.181492\pi$
$522$	−8.58301	+	14.8662i	−0.375668	+	0.650676i
$523$	7.76013	+	13.4409i	0.339327	+	0.587731i	0.984306	−	0.176469i	$-0.0564674\pi$
$523$	7.76013	+	13.4409i	0.339327	+	0.587731i	−0.644979	+	0.764200i	$0.723134\pi$
$524$	−15.6458			−0.683488
$525$		0			0
$526$	−4.06275			−0.177144
$527$	12.0000	+	20.7846i	0.522728	+	0.905392i
$528$	−1.32288	+	2.29129i	−0.0575708	+	0.0997155i
$529$	4.85425	−	8.40781i	0.211054	−	0.365557i
$530$	6.64575	+	11.5108i	0.288673	+	0.499996i
$531$	2.58301			0.112093
$532$		0			0
$533$	−24.6863			−1.06928
$534$	19.2915	+	33.4139i	0.834825	+	1.44596i
$535$	9.00000	−	15.5885i	0.389104	−	0.673948i
$536$	1.96863	−	3.40976i	0.0850317	−	0.147279i
$537$	5.37451	+	9.30892i	0.231927	+	0.401710i
$538$	26.5830			1.14607
$539$		0			0
$540$	−9.64575			−0.415087
$541$	4.14575	+	7.18065i	0.178240	+	0.308720i	0.941278	−	0.337633i	$-0.109626\pi$
$541$	4.14575	+	7.18065i	0.178240	+	0.308720i	−0.763038	+	0.646354i	$0.776293\pi$
$542$	8.96863	−	15.5341i	0.385236	−	0.667247i
$543$	−13.2288	+	22.9129i	−0.567700	+	0.983286i
$544$	−3.00000	−	5.19615i	−0.128624	−	0.222783i
$545$	−38.5830			−1.65271
$546$		0			0
$547$	27.5203			1.17668			0.588341	−	0.808613i	$-0.299781\pi$
$547$	27.5203			1.17668			0.588341	+	0.808613i	$0.299781\pi$
$548$	−9.43725	−	16.3458i	−0.403140	−	0.698258i
$549$	7.41699	−	12.8466i	0.316550	−	0.548280i
$550$	4.14575	−	7.18065i	0.176775	−	0.306184i
$551$	0.760130	+	1.31658i	0.0323826	+	0.0560883i
$552$	9.64575			0.410550
$553$		0			0
$554$	11.7085			0.497446
$555$	−7.93725	−	13.7477i	−0.336918	−	0.583559i
$556$	−2.00000	+	3.46410i	−0.0848189	+	0.146911i
$557$	−15.8745	+	27.4955i	−0.672624	+	1.16502i	0.304533	+	0.952502i	$0.401500\pi$
$557$	−15.8745	+	27.4955i	−0.672624	+	1.16502i	−0.977157	+	0.212518i	$0.931834\pi$
$558$	8.00000	+	13.8564i	0.338667	+	0.586588i
$559$	20.0000			0.845910
$560$		0			0
$561$	−15.8745			−0.670222
$562$	−3.53137	−	6.11652i	−0.148962	−	0.258010i
$563$	6.53137	−	11.3127i	0.275265	−	0.476772i	−0.694937	−	0.719070i	$-0.744568\pi$
$563$	6.53137	−	11.3127i	0.275265	−	0.476772i	0.970202	+	0.242298i	$0.0779012\pi$
$564$	17.5830	−	30.4547i	0.740378	−	1.28237i
$565$	−14.0516	−	24.3381i	−0.591157	−	1.02391i
$566$	−7.64575			−0.321375
$567$		0			0
$568$	−9.64575			−0.404727
$569$	20.5830	+	35.6508i	0.862884	+	1.49456i	0.869133	+	0.494579i	$0.164678\pi$
$569$	20.5830	+	35.6508i	0.862884	+	1.49456i	−0.00624806	+	0.999980i	$0.501989\pi$
$570$	−1.70850	+	2.95920i	−0.0715611	+	0.123947i
$571$	22.4686	−	38.9168i	0.940283	−	1.62862i	0.175351	−	0.984506i	$-0.443894\pi$
$571$	22.4686	−	38.9168i	0.940283	−	1.62862i	0.764932	−	0.644112i	$-0.222773\pi$
$572$	2.50000	+	4.33013i	0.104530	+	0.181052i
$573$	−35.1660			−1.46908
$574$		0			0
$575$	−30.2288			−1.26063
$576$	−2.00000	−	3.46410i	−0.0833333	−	0.144338i
$577$	−12.7288	+	22.0469i	−0.529905	+	0.917823i	0.469486	+	0.882940i	$0.344439\pi$
$577$	−12.7288	+	22.0469i	−0.529905	+	0.917823i	−0.999391	+	0.0348828i	$0.988894\pi$
$578$	9.50000	−	16.4545i	0.395148	−	0.684416i
$579$	15.2399	+	26.3962i	0.633347	+	1.09699i
$580$	15.6458			0.649654
$581$		0			0
$582$	−15.1033			−0.626050
$583$	1.82288	+	3.15731i	0.0754958	+	0.130763i
$584$	−2.82288	+	4.88936i	−0.116811	+	0.202323i
$585$	−36.4575	+	63.1463i	−1.50733	+	2.61078i
$586$	−6.00000	−	10.3923i	−0.247858	−	0.429302i
$587$	7.93725			0.327606			0.163803	−	0.986493i	$-0.447624\pi$
$587$	7.93725			0.327606			0.163803	+	0.986493i	$0.447624\pi$
$588$		0			0
$589$	1.41699			0.0583863
$590$	−1.17712	−	2.03884i	−0.0484614	−	0.0839377i
$591$	−24.9686	+	43.2469i	−1.02707	+	1.77894i
$592$	0.822876	−	1.42526i	0.0338200	−	0.0585779i
$593$	11.4686	+	19.8642i	0.470960	+	0.815727i	0.999448	−	0.0332139i	$-0.0105743\pi$
$593$	11.4686	+	19.8642i	0.470960	+	0.815727i	−0.528488	+	0.848941i	$0.677241\pi$
$594$	−2.64575			−0.108556
$595$		0			0
$596$	−4.70850			−0.192868
$597$	−29.4059	−	50.9325i	−1.20350	−	2.08453i
$598$	9.11438	−	15.7866i	0.372715	−	0.645561i
$599$	9.87451	−	17.1031i	0.403461	−	0.698816i	−0.590680	−	0.806906i	$-0.701140\pi$
$599$	9.87451	−	17.1031i	0.403461	−	0.698816i	0.994141	+	0.108090i	$0.0344736\pi$
$600$	10.9686	+	18.9982i	0.447792	+	0.775599i
$601$	24.5830			1.00276			0.501381	−	0.865227i	$-0.332826\pi$
$601$	24.5830			1.00276			0.501381	+	0.865227i	$0.332826\pi$
$602$		0			0
$603$	15.7490			0.641350
$604$	1.67712	+	2.90486i	0.0682412	+	0.118197i
$605$	1.82288	−	3.15731i	0.0741104	−	0.128363i
$606$	−3.96863	+	6.87386i	−0.161214	+	0.279232i
$607$	10.6458	+	18.4390i	0.432098	+	0.748415i	0.997054	−	0.0767058i	$-0.0244402\pi$
$607$	10.6458	+	18.4390i	0.432098	+	0.748415i	−0.564956	+	0.825121i	$0.691107\pi$
$608$	−0.354249			−0.0143667
$609$		0			0
$610$	−13.5203			−0.547419
$611$	−33.2288	−	57.5539i	−1.34429	−	2.32838i
$612$	12.0000	−	20.7846i	0.485071	−	0.840168i
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	−0.885514	−	0.464614i	$-0.846193\pi$
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	0.845124	+	0.534570i	$0.179527\pi$
$614$	2.11438	+	3.66221i	0.0853294	+	0.147795i
$615$	−47.6235			−1.92037
$616$		0			0
$617$	−16.2915			−0.655871			−0.327936	−	0.944700i	$-0.606353\pi$
$617$	−16.2915			−0.655871			−0.327936	+	0.944700i	$0.606353\pi$
$618$	−17.1144	−	29.6430i	−0.688441	−	1.19242i
$619$	17.2915	−	29.9498i	0.695004	−	1.20378i	−0.275175	−	0.961394i	$-0.588736\pi$
$619$	17.2915	−	29.9498i	0.695004	−	1.20378i	0.970179	−	0.242388i	$-0.0779308\pi$
$620$	7.29150	−	12.6293i	0.292834	−	0.507203i
$621$	4.82288	+	8.35347i	0.193535	+	0.335213i
$622$	16.9373			0.679122
$623$		0			0
$624$	−13.2288			−0.529574
$625$	−1.14575	−	1.98450i	−0.0458301	−	0.0793800i
$626$	−1.20850	+	2.09318i	−0.0483013	+	0.0836603i
$627$	−0.468627	+	0.811686i	−0.0187152	+	0.0324156i
$628$	−10.5830	−	18.3303i	−0.422308	−	0.731459i
$629$	9.87451			0.393722
$630$		0			0
$631$	34.8118			1.38583			0.692917	−	0.721017i	$-0.256325\pi$
$631$	34.8118			1.38583			0.692917	+	0.721017i	$0.256325\pi$
$632$	1.32288	+	2.29129i	0.0526212	+	0.0911425i
$633$	19.7601	−	34.2255i	0.785395	−	1.36034i
$634$	6.00000	−	10.3923i	0.238290	−	0.412731i
$635$	0.114378	+	0.198109i	0.00453896	+	0.00786172i
$636$	−9.64575			−0.382479
$637$		0			0
$638$	4.29150			0.169902
$639$	−19.2915	−	33.4139i	−0.763160	−	1.32183i
$640$	−1.82288	+	3.15731i	−0.0720555	+	0.124804i
$641$	9.43725	−	16.3458i	0.372749	−	0.645620i	−0.617238	−	0.786776i	$-0.711749\pi$
$641$	9.43725	−	16.3458i	0.372749	−	0.645620i	0.989987	+	0.141156i	$0.0450819\pi$
$642$	6.53137	+	11.3127i	0.257773	+	0.446475i
$643$	−6.52026			−0.257134			−0.128567	−	0.991701i	$-0.541038\pi$
$643$	−6.52026			−0.257134			−0.128567	+	0.991701i	$0.541038\pi$
$644$		0			0
$645$	38.5830			1.51920
$646$	−1.06275	−	1.84073i	−0.0418132	−	0.0724226i
$647$	19.4059	−	33.6120i	0.762924	−	1.32142i	−0.178413	−	0.983956i	$-0.557096\pi$
$647$	19.4059	−	33.6120i	0.762924	−	1.32142i	0.941337	−	0.337467i	$-0.109570\pi$
$648$	−2.50000	+	4.33013i	−0.0982093	+	0.170103i
$649$	−0.322876	−	0.559237i	−0.0126740	−	0.0219520i
$650$	41.4575			1.62610
$651$		0			0
$652$	−4.64575			−0.181942
$653$	−1.17712	−	2.03884i	−0.0460644	−	0.0797859i	0.842074	−	0.539362i	$-0.181335\pi$
$653$	−1.17712	−	2.03884i	−0.0460644	−	0.0797859i	−0.888138	+	0.459576i	$0.848001\pi$
$654$	14.0000	−	24.2487i	0.547443	−	0.948200i
$655$	−28.5203	+	49.3985i	−1.11438	+	1.93016i
$656$	−2.46863	−	4.27579i	−0.0963837	−	0.166941i
$657$	−22.5830			−0.881047
$658$		0			0
$659$	14.5830			0.568073			0.284037	−	0.958813i	$-0.408326\pi$
$659$	14.5830			0.568073			0.284037	+	0.958813i	$0.408326\pi$
$660$	4.82288	+	8.35347i	0.187730	+	0.325158i
$661$	14.2915	−	24.7536i	0.555875	−	0.962804i	−0.441960	−	0.897035i	$-0.645717\pi$
$661$	14.2915	−	24.7536i	0.555875	−	0.962804i	0.997835	−	0.0657690i	$-0.0209500\pi$
$662$	−7.67712	+	13.2972i	−0.298380	+	0.516809i
$663$	−39.6863	−	68.7386i	−1.54129	−	2.66959i
$664$	13.2915			0.515810
$665$		0			0
$666$	6.58301			0.255086
$667$	−7.82288	−	13.5496i	−0.302903	−	0.524643i
$668$	7.61438	−	13.1885i	0.294609	−	0.510278i
$669$	−16.3431	+	28.3071i	−0.631862	+	1.09442i
$670$	−7.17712	−	12.4311i	−0.277277	−	0.480257i
$671$	−3.70850			−0.143165
$672$		0			0
$673$	−14.9373			−0.575789			−0.287894	−	0.957662i	$-0.592955\pi$
$673$	−14.9373			−0.575789			−0.287894	+	0.957662i	$0.592955\pi$
$674$	12.4686	+	21.5963i	0.480274	+	0.831858i
$675$	−10.9686	+	18.9982i	−0.422183	+	0.731242i
$676$	−6.00000	+	10.3923i	−0.230769	+	0.399704i
$677$	−1.06275	−	1.84073i	−0.0408446	−	0.0707450i	0.844880	−	0.534955i	$-0.179672\pi$
$677$	−1.06275	−	1.84073i	−0.0408446	−	0.0707450i	−0.885725	+	0.464210i	$0.846338\pi$
$678$	20.3948			0.783256
$679$		0			0
$680$	−21.8745			−0.838849
$681$	−17.5830	−	30.4547i	−0.673782	−	1.16703i
$682$	2.00000	−	3.46410i	0.0765840	−	0.132647i
$683$	6.96863	−	12.0700i	0.266647	−	0.461846i	−0.701347	−	0.712820i	$-0.747418\pi$
$683$	6.96863	−	12.0700i	0.266647	−	0.461846i	0.967994	+	0.250974i	$0.0807509\pi$
$684$	−0.708497	−	1.22715i	−0.0270901	−	0.0469214i
$685$	−68.8118			−2.62916
$686$		0			0
$687$	42.3320			1.61507
$688$	2.00000	+	3.46410i	0.0762493	+	0.132068i
$689$	−9.11438	+	15.7866i	−0.347230	+	0.601420i
$690$	17.5830	−	30.4547i	0.669374	−	1.15939i
$691$	−9.38562	−	16.2564i	−0.357046	−	0.618422i	0.630420	−	0.776254i	$-0.282883\pi$
$691$	−9.38562	−	16.2564i	−0.357046	−	0.618422i	−0.987466	+	0.157833i	$0.949549\pi$
$692$	−10.2915			−0.391224
$693$		0			0
$694$	−26.8118			−1.01776
$695$	7.29150	+	12.6293i	0.276582	+	0.479055i
$696$	−5.67712	+	9.83307i	−0.215191	+	0.372721i
$697$	14.8118	−	25.6547i	0.561035	−	0.971742i
$698$	−14.9373	−	25.8721i	−0.565383	−	0.979273i
$699$	44.8118			1.69494
$700$		0			0
$701$	−6.87451			−0.259647			−0.129823	−	0.991537i	$-0.541441\pi$
$701$	−6.87451			−0.259647			−0.129823	+	0.991537i	$0.541441\pi$
$702$	−6.61438	−	11.4564i	−0.249644	−	0.432395i
$703$	0.291503	−	0.504897i	0.0109942	−	0.0190426i
$704$	−0.500000	+	0.866025i	−0.0188445	+	0.0326396i
$705$	−64.1033	−	111.030i	−2.41427	−	4.18164i
$706$	−35.1660			−1.32349
$707$		0			0
$708$	1.70850			0.0642093
$709$	3.40588	+	5.89916i	0.127911	+	0.221548i	0.922867	−	0.385119i	$-0.125840\pi$
$709$	3.40588	+	5.89916i	0.127911	+	0.221548i	−0.794956	+	0.606667i	$0.792506\pi$
$710$	−17.5830	+	30.4547i	−0.659878	+	1.14294i
$711$	−5.29150	+	9.16515i	−0.198447	+	0.343720i
$712$	7.29150	+	12.6293i	0.273261	+	0.473301i
$713$	−14.5830			−0.546138
$714$		0			0
$715$	18.2288			0.681717
$716$	2.03137	+	3.51844i	0.0759160	+	0.131490i
$717$	−12.2085	+	21.1457i	−0.455935	+	0.789702i
$718$	−5.03137	+	8.71459i	−0.187769	+	0.325226i
$719$	−1.93725	−	3.35542i	−0.0722474	−	0.125136i	0.827639	−	0.561261i	$-0.189684\pi$
$719$	−1.93725	−	3.35542i	−0.0722474	−	0.125136i	−0.899886	+	0.436125i	$0.856350\pi$
$720$	−14.5830			−0.543477
$721$		0			0
$722$	18.8745			0.702436
$723$	30.1771	+	52.2683i	1.12230	+	1.94388i
$724$	−5.00000	+	8.66025i	−0.185824	+	0.321856i
$725$	17.7915	−	30.8158i	0.660760	−	1.14447i
$726$	1.32288	+	2.29129i	0.0490965	+	0.0850377i
$727$	17.2915			0.641306			0.320653	−	0.947197i	$-0.396098\pi$
$727$	17.2915			0.641306			0.320653	+	0.947197i	$0.396098\pi$
$728$		0			0
$729$	−41.0000			−1.51852
$730$	10.2915	+	17.8254i	0.380906	+	0.659748i
$731$	−12.0000	+	20.7846i	−0.443836	+	0.768747i
$732$	4.90588	−	8.49723i	0.181327	−	0.314067i
$733$	20.7288	+	35.9033i	0.765634	+	1.32612i	0.939911	+	0.341420i	$0.110908\pi$
$733$	20.7288	+	35.9033i	0.765634	+	1.32612i	−0.174277	+	0.984697i	$0.555759\pi$
$734$	−9.77124			−0.360663
$735$		0			0
$736$	3.64575			0.134384
$737$	−1.96863	−	3.40976i	−0.0725153	−	0.125600i
$738$	9.87451	−	17.1031i	0.363486	−	0.629576i
$739$	3.93725	−	6.81952i	0.144834	−	0.250860i	−0.784477	−	0.620158i	$-0.787068\pi$
$739$	3.93725	−	6.81952i	0.144834	−	0.250860i	0.929311	+	0.369298i	$0.120402\pi$
$740$	−3.00000	−	5.19615i	−0.110282	−	0.191014i
$741$	−4.68627			−0.172154
$742$		0			0
$743$	−34.7085			−1.27333			−0.636666	−	0.771140i	$-0.719687\pi$
$743$	−34.7085			−1.27333			−0.636666	+	0.771140i	$0.719687\pi$
$744$	5.29150	+	9.16515i	0.193996	+	0.336011i
$745$	−8.58301	+	14.8662i	−0.314457	+	0.544655i
$746$	−5.43725	+	9.41760i	−0.199072	+	0.344803i
$747$	26.5830	+	46.0431i	0.972621	+	1.68463i
$748$	−6.00000			−0.219382
$749$		0			0
$750$	31.7490			1.15931
$751$	8.00000	+	13.8564i	0.291924	+	0.505627i	0.974265	−	0.225407i	$-0.0723712\pi$
$751$	8.00000	+	13.8564i	0.291924	+	0.505627i	−0.682341	+	0.731034i	$0.739038\pi$
$752$	6.64575	−	11.5108i	0.242346	−	0.419755i
$753$	9.64575	−	16.7069i	0.351511	−	0.608834i
$754$	10.7288	+	18.5828i	0.390718	+	0.676744i
$755$	12.2288			0.445050
$756$		0			0
$757$	19.1660			0.696600			0.348300	−	0.937383i	$-0.386759\pi$
$757$	19.1660			0.696600			0.348300	+	0.937383i	$0.386759\pi$
$758$	10.9686	+	18.9982i	0.398398	+	0.690046i
$759$	4.82288	−	8.35347i	0.175059	−	0.303212i
$760$	−0.645751	+	1.11847i	−0.0234239	+	0.0405713i
$761$	−3.00000	−	5.19615i	−0.108750	−	0.188360i	0.806514	−	0.591215i	$-0.201351\pi$
$761$	−3.00000	−	5.19615i	−0.108750	−	0.188360i	−0.915264	+	0.402854i	$0.868018\pi$
$762$	−0.166010			−0.00601393
$763$		0			0
$764$	−13.2915			−0.480870
$765$	−43.7490	−	75.7755i	−1.58175	−	2.73967i
$766$	17.0516	−	29.5343i	0.616101	−	1.06712i
$767$	1.61438	−	2.79619i	0.0582918	−	0.100964i
$768$	−1.32288	−	2.29129i	−0.0477352	−	0.0826797i
$769$	15.1660			0.546900			0.273450	−	0.961886i	$-0.411835\pi$
$769$	15.1660			0.546900			0.273450	+	0.961886i	$0.411835\pi$
$770$		0			0
$771$	1.10326			0.0397331
$772$	5.76013	+	9.97684i	0.207312	+	0.359074i
$773$	1.29150	−	2.23695i	0.0464521	−	0.0804574i	−0.841864	−	0.539689i	$-0.818542\pi$
$773$	1.29150	−	2.23695i	0.0464521	−	0.0804574i	0.888317	+	0.459232i	$0.151875\pi$
$774$	−8.00000	+	13.8564i	−0.287554	+	0.498058i
$775$	−16.5830	−	28.7226i	−0.595679	−	1.03175i
$776$	−5.70850			−0.204923
$777$		0			0
$778$	20.8118			0.746138
$779$	−0.874508	−	1.51469i	−0.0313325	−	0.0542695i
$780$	−24.1144	+	41.7673i	−0.863433	+	1.49551i
$781$	−4.82288	+	8.35347i	−0.172576	+	0.298911i
$782$	10.9373	+	18.9439i	0.391115	+	0.677432i
$783$	−11.3542			−0.405768
$784$		0			0
$785$	−77.1660			−2.75417
$786$	−20.6974	−	35.8489i	−0.738251	−	1.27869i
$787$	−0.405881	+	0.703006i	−0.0144681	+	0.0250595i	−0.873169	−	0.487418i	$-0.837939\pi$
$787$	−0.405881	+	0.703006i	−0.0144681	+	0.0250595i	0.858701	+	0.512477i	$0.171272\pi$
$788$	−9.43725	+	16.3458i	−0.336188	+	0.582295i
$789$	−5.37451	−	9.30892i	−0.191338	−	0.331406i
$790$	9.64575			0.343180
$791$		0			0
$792$	−4.00000			−0.142134
$793$	−9.27124	−	16.0583i	−0.329232	−	0.570246i
$794$	−15.5830	+	26.9906i	−0.553020	+	0.957859i
$795$	−17.5830	+	30.4547i	−0.623605	+	1.08012i
$796$	−11.1144	−	19.2507i	−0.393939	−	0.682322i
$797$	35.1660			1.24564			0.622822	−	0.782364i	$-0.285986\pi$
$797$	35.1660			1.24564			0.622822	+	0.782364i	$0.285986\pi$
$798$		0			0
$799$	79.7490			2.82132
$800$	4.14575	+	7.18065i	0.146574	+	0.253874i
$801$	−29.1660	+	50.5170i	−1.03053	+	1.78493i
$802$	0.208497	−	0.361128i	0.00736230	−	0.0127519i
$803$	2.82288	+	4.88936i	0.0996171	+	0.172542i
$804$	10.4170			0.367379
$805$		0			0
$806$	20.0000			0.704470
$807$	35.1660	+	60.9093i	1.23790	+	2.14411i
$808$	−1.50000	+	2.59808i	−0.0527698	+	0.0914000i
$809$	−25.2915	+	43.8062i	−0.889202	+	1.54014i	−0.0483813	+	0.998829i	$0.515406\pi$
$809$	−25.2915	+	43.8062i	−0.889202	+	1.54014i	−0.840821	+	0.541314i	$0.817927\pi$
$810$	9.11438	+	15.7866i	0.320247	+	0.554683i
$811$	−27.7490			−0.974400			−0.487200	−	0.873290i	$-0.661982\pi$
$811$	−27.7490			−0.974400			−0.487200	+	0.873290i	$0.661982\pi$
$812$		0			0
$813$	47.4575			1.66441
$814$	−0.822876	−	1.42526i	−0.0288418	−	0.0499554i
$815$	−8.46863	+	14.6681i	−0.296643	+	0.513801i
$816$	7.93725	−	13.7477i	0.277859	−	0.481267i
$817$	0.708497	+	1.22715i	0.0247872	+	0.0429327i
$818$	18.9373			0.662126
$819$		0			0
$820$	−18.0000			−0.628587
$821$	3.85425	+	6.67575i	0.134514	+	0.232985i	0.925412	−	0.378963i	$-0.123719\pi$
$821$	3.85425	+	6.67575i	0.134514	+	0.232985i	−0.790898	+	0.611949i	$0.790386\pi$
$822$	24.9686	−	43.2469i	0.870881	−	1.50841i
$823$	21.9373	−	37.9964i	0.764685	−	1.32447i	−0.175729	−	0.984439i	$-0.556228\pi$
$823$	21.9373	−	37.9964i	0.764685	−	1.32447i	0.940413	−	0.340034i	$-0.110439\pi$
$824$	−6.46863	−	11.2040i	−0.225345	−	0.390310i
$825$	21.9373			0.763757
$826$		0			0
$827$	−35.3948			−1.23080			−0.615398	−	0.788216i	$-0.711005\pi$
$827$	−35.3948			−1.23080			−0.615398	+	0.788216i	$0.711005\pi$
$828$	7.29150	+	12.6293i	0.253397	+	0.438897i
$829$	21.6974	−	37.5810i	0.753581	−	1.30524i	−0.192495	−	0.981298i	$-0.561658\pi$
$829$	21.6974	−	37.5810i	0.753581	−	1.30524i	0.946077	−	0.323943i	$-0.105009\pi$
$830$	24.2288	−	41.9654i	0.840992	−	1.45664i
$831$	15.4889	+	26.8275i	0.537304	+	0.930637i
$832$	−5.00000			−0.173344
$833$		0			0
$834$	−10.5830			−0.366460
$835$	−27.7601	−	48.0820i	−0.960679	−	1.66394i
$836$	−0.177124	+	0.306788i	−0.00612597	+	0.0106105i
$837$	−5.29150	+	9.16515i	−0.182901	+	0.316794i
$838$	−10.9373	−	18.9439i	−0.377821	−	0.654405i
$839$	−27.8745			−0.962335			−0.481167	−	0.876629i	$-0.659787\pi$
$839$	−27.8745			−0.962335			−0.481167	+	0.876629i	$0.659787\pi$
$840$		0			0
$841$	−10.5830			−0.364931
$842$	−16.5830	−	28.7226i	−0.571488	−	0.989846i
$843$	9.34313	−	16.1828i	0.321795	−	0.557365i
$844$	7.46863	−	12.9360i	0.257081	−	0.445277i
$845$	21.8745	+	37.8878i	0.752506	+	1.30338i
$846$	53.1660			1.82789
$847$		0			0
$848$	−3.64575			−0.125196
$849$	−10.1144	−	17.5186i	−0.347125	−	0.601237i
$850$	−24.8745	+	43.0839i	−0.853189	+	1.47777i
$851$	−3.00000	+	5.19615i	−0.102839	+	0.178122i
$852$	−12.7601	−	22.1012i	−0.437155	−	0.757174i
$853$	3.16601			0.108402			0.0542011	−	0.998530i	$-0.482739\pi$
$853$	3.16601			0.108402			0.0542011	+	0.998530i	$0.482739\pi$
$854$		0			0
$855$	−5.16601			−0.176674
$856$	2.46863	+	4.27579i	0.0843759	+	0.146143i
$857$	18.0000	−	31.1769i	0.614868	−	1.06498i	−0.375539	−	0.926806i	$-0.622542\pi$
$857$	18.0000	−	31.1769i	0.614868	−	1.06498i	0.990408	−	0.138177i	$-0.0441242\pi$
$858$	−6.61438	+	11.4564i	−0.225811	+	0.391116i
$859$	18.9059	+	32.7459i	0.645060	+	1.11728i	0.984288	+	0.176573i	$0.0565011\pi$
$859$	18.9059	+	32.7459i	0.645060	+	1.11728i	−0.339227	+	0.940704i	$0.610166\pi$
$860$	14.5830			0.497276
$861$		0			0
$862$	−2.77124			−0.0943889
$863$	24.7601	+	42.8858i	0.842845	+	1.45985i	0.887480	+	0.460846i	$0.152454\pi$
$863$	24.7601	+	42.8858i	0.842845	+	1.45985i	−0.0446353	+	0.999003i	$0.514213\pi$
$864$	1.32288	−	2.29129i	0.0450051	−	0.0779512i
$865$	−18.7601	+	32.4935i	−0.637864	+	1.10481i
$866$	8.00000	+	13.8564i	0.271851	+	0.470860i
$867$	50.2693			1.70723
$868$		0			0
$869$	2.64575			0.0897510
$870$	20.6974	+	35.8489i	0.701707	+	1.21539i
$871$	9.84313	−	17.0488i	0.333522	−	0.577677i
$872$	5.29150	−	9.16515i	0.179193	−	0.310371i
$873$	−11.4170	−	19.7748i	−0.386407	−	0.669276i
$874$	1.29150			0.0436857
$875$		0			0
$876$	−14.9373			−0.504683
$877$	−4.43725	−	7.68555i	−0.149835	−	0.259523i	0.781331	−	0.624117i	$-0.214541\pi$
$877$	−4.43725	−	7.68555i	−0.149835	−	0.259523i	−0.931167	+	0.364594i	$0.881208\pi$
$878$	5.96863	−	10.3380i	0.201431	−	0.348889i
$879$	15.8745	−	27.4955i	0.535434	−	0.927399i
$880$	1.82288	+	3.15731i	0.0614491	+	0.106433i
$881$	−6.87451			−0.231608			−0.115804	−	0.993272i	$-0.536944\pi$
$881$	−6.87451			−0.231608			−0.115804	+	0.993272i	$0.536944\pi$
$882$		0			0
$883$	6.06275			0.204028			0.102014	−	0.994783i	$-0.467471\pi$
$883$	6.06275			0.204028			0.102014	+	0.994783i	$0.467471\pi$
$884$	−15.0000	−	25.9808i	−0.504505	−	0.873828i
$885$	3.11438	−	5.39426i	0.104689	−	0.181326i
$886$	−9.22876	+	15.9847i	−0.310046	+	0.537016i
$887$	−6.55163	−	11.3478i	−0.219982	−	0.381020i	0.734820	−	0.678262i	$-0.237267\pi$
$887$	−6.55163	−	11.3478i	−0.219982	−	0.381020i	−0.954802	+	0.297242i	$0.903933\pi$
$888$	4.35425			0.146119
$889$		0			0
$890$	53.1660			1.78213
$891$	2.50000	+	4.33013i	0.0837532	+	0.145065i
$892$	−6.17712	+	10.6991i	−0.206825	+	0.358232i
$893$	2.35425	−	4.07768i	0.0787819	−	0.136454i
$894$	−6.22876	−	10.7885i	−0.208321	−	0.360822i
$895$	14.8118			0.495103
$896$		0			0
$897$	48.2288			1.61031
$898$	4.93725	+	8.55157i	0.164758	+	0.285370i
$899$	8.58301	−	14.8662i	0.286259	−	0.495816i
$900$	−16.5830	+	28.7226i	−0.552767	+	0.957420i
$901$	−10.9373	−	18.9439i	−0.364373	−	0.631112i
$902$	−4.93725			−0.164393
$903$		0			0
$904$	7.70850			0.256381
$905$	18.2288	+	31.5731i	0.605944	+	1.04953i
$906$	−4.43725	+	7.68555i	−0.147418	+	0.255335i
$907$	5.22876	−	9.05647i	0.173618	−	0.300715i	−0.766064	−	0.642764i	$-0.777788\pi$
$907$	5.22876	−	9.05647i	0.173618	−	0.300715i	0.939682	+	0.342049i	$0.111121\pi$
$908$	−6.64575	−	11.5108i	−0.220547	−	0.381999i
$909$	−12.0000			−0.398015
$910$		0			0
$911$	−1.29150			−0.0427894			−0.0213947	−	0.999771i	$-0.506811\pi$
$911$	−1.29150			−0.0427894			−0.0213947	+	0.999771i	$0.506811\pi$
$912$	−0.468627	−	0.811686i	−0.0155178	−	0.0268776i
$913$	6.64575	−	11.5108i	0.219942	−	0.380951i
$914$	−19.5830	+	33.9188i	−0.647748	+	1.12193i
$915$	−17.8856	−	30.9788i	−0.591280	−	1.02413i
$916$	16.0000			0.528655
$917$		0			0
$918$	15.8745			0.523937
$919$	17.6458	+	30.5633i	0.582080	+	1.00819i	0.995233	+	0.0975298i	$0.0310941\pi$
$919$	17.6458	+	30.5633i	0.582080	+	1.00819i	−0.413153	+	0.910662i	$0.635573\pi$
$920$	6.64575	−	11.5108i	0.219104	−	0.379499i
$921$	−5.59412	+	9.68930i	−0.184332	+	0.319273i
$922$	16.0830	+	27.8566i	0.529666	+	0.917408i
$923$	−48.2288			−1.58747
$924$		0			0
$925$	−13.6458			−0.448670
$926$	−11.2288	−	19.4488i	−0.369000	−	0.639126i
$927$	25.8745	−	44.8160i	0.849830	−	1.47195i
$928$	−2.14575	+	3.71655i	−0.0704377	+	0.122002i
$929$	17.7915	+	30.8158i	0.583720	+	1.01103i	0.995034	+	0.0995392i	$0.0317369\pi$
$929$	17.7915	+	30.8158i	0.583720	+	1.01103i	−0.411313	+	0.911494i	$0.634930\pi$
$930$	38.5830			1.26519
$931$		0			0
$932$	16.9373			0.554798
$933$	22.4059	+	38.8081i	0.733536	+	1.27052i
$934$	−5.35425	+	9.27383i	−0.175196	+	0.303449i
$935$	−10.9373	+	18.9439i	−0.357686	+	0.619531i
$936$	−10.0000	−	17.3205i	−0.326860	−	0.566139i
$937$	46.6863			1.52517			0.762587	−	0.646886i	$-0.223929\pi$
$937$	46.6863			1.52517			0.762587	+	0.646886i	$0.223929\pi$
$938$		0			0
$939$	−6.39477			−0.208685
$940$	−24.2288	−	41.9654i	−0.790255	−	1.36876i
$941$	−22.3118	+	38.6451i	−0.727343	+	1.25979i	0.230660	+	0.973034i	$0.425912\pi$
$941$	−22.3118	+	38.6451i	−0.727343	+	1.25979i	−0.958002	+	0.286760i	$0.907422\pi$
$942$	28.0000	−	48.4974i	0.912289	−	1.58013i
$943$	9.00000	+	15.5885i	0.293080	+	0.507630i
$944$	0.645751			0.0210174
$945$		0			0
$946$	4.00000			0.130051
$947$	16.9373	+	29.3362i	0.550387	+	0.953298i	0.998246	+	0.0591941i	$0.0188531\pi$
$947$	16.9373	+	29.3362i	0.550387	+	0.953298i	−0.447860	+	0.894104i	$0.647814\pi$
$948$	−3.50000	+	6.06218i	−0.113675	+	0.196890i
$949$	−14.1144	+	24.4468i	−0.458172	+	0.793577i
$950$	1.46863	+	2.54374i	0.0476486	+	0.0825297i
$951$	31.7490			1.02953
$952$		0			0
$953$	−25.5203			−0.826682			−0.413341	−	0.910576i	$-0.635638\pi$
$953$	−25.5203			−0.826682			−0.413341	+	0.910576i	$0.635638\pi$
$954$	−7.29150	−	12.6293i	−0.236071	−	0.408887i
$955$	−24.2288	+	41.9654i	−0.784024	+	1.35797i
$956$	−4.61438	+	7.99234i	−0.149240	+	0.258491i
$957$	5.67712	+	9.83307i	0.183515	+	0.317858i
$958$	−25.9373			−0.837995
$959$		0			0
$960$	−9.64575			−0.311315
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	4.11438	−	7.12631i	0.132653	−	0.229762i
$963$	−9.87451	+	17.1031i	−0.318202	+	0.551141i
$964$	11.4059	+	19.7556i	0.367359	+	0.636284i
$965$	42.0000			1.35203
$966$		0			0
$967$	−26.3320			−0.846781			−0.423390	−	0.905947i	$-0.639160\pi$
$967$	−26.3320			−0.846781			−0.423390	+	0.905947i	$0.639160\pi$
$968$	0.500000	+	0.866025i	0.0160706	+	0.0278351i
$969$	2.81176	−	4.87011i	0.0903268	−	0.156451i
$970$	−10.4059	+	18.0235i	−0.334113	+	0.578700i
$971$	−12.9686	−	22.4623i	−0.416183	−	0.720850i	0.579369	−	0.815066i	$-0.303299\pi$
$971$	−12.9686	−	22.4623i	−0.416183	−	0.720850i	−0.995552	+	0.0942153i	$0.969966\pi$
$972$	−21.1660			−0.678900
$973$		0			0
$974$	30.5830			0.979943
$975$	54.8431	+	94.9911i	1.75639	+	3.04215i
$976$	1.85425	−	3.21165i	0.0593531	−	0.102803i
$977$	−18.2288	+	31.5731i	−0.583190	+	1.01011i	0.411909	+	0.911225i	$0.364862\pi$
$977$	−18.2288	+	31.5731i	−0.583190	+	1.01011i	−0.995098	+	0.0988890i	$0.968471\pi$
$978$	−6.14575	−	10.6448i	−0.196519	−	0.340382i
$979$	14.5830			0.466075
$980$		0			0
$981$	42.3320			1.35156
$982$	5.35425	+	9.27383i	0.170861	+	0.295940i
$983$	−18.6458	+	32.2954i	−0.594707	+	1.03006i	0.398881	+	0.917003i	$0.369399\pi$
$983$	−18.6458	+	32.2954i	−0.594707	+	1.03006i	−0.993588	+	0.113060i	$0.963935\pi$
$984$	6.53137	−	11.3127i	0.208213	−	0.360635i
$985$	34.4059	+	59.5927i	1.09626	+	1.89878i
$986$	−25.7490			−0.820016
$987$		0			0
$988$	−1.77124			−0.0563508
$989$	−7.29150	−	12.6293i	−0.231856	−	0.401587i
$990$	−7.29150	+	12.6293i	−0.231739	+	0.401384i
$991$	−28.3431	+	49.0917i	−0.900349	+	1.55945i	−0.0733083	+	0.997309i	$0.523356\pi$
$991$	−28.3431	+	49.0917i	−0.900349	+	1.55945i	−0.827041	+	0.562141i	$0.809978\pi$
$992$	2.00000	+	3.46410i	0.0635001	+	0.109985i
$993$	−40.6235			−1.28915
$994$		0			0
$995$	−81.0405			−2.56916
$996$	17.5830	+	30.4547i	0.557139	+	0.964993i
$997$	−21.2915	+	36.8780i	−0.674309	+	1.16794i	0.302362	+	0.953193i	$0.402225\pi$
$997$	−21.2915	+	36.8780i	−0.674309	+	1.16794i	−0.976670	+	0.214744i	$0.931108\pi$
$998$	8.93725	−	15.4798i	0.282904	−	0.490004i
$999$	2.17712	+	3.77089i	0.0688812	+	0.119306i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.e.v.67.1		4
7.2	even	3	inner	1078.2.e.v.177.1		4
7.3	odd	6		1078.2.a.s.1.1		2
7.4	even	3		1078.2.a.n.1.2		2
7.5	odd	6		154.2.e.f.23.2	✓	4
7.6	odd	2		154.2.e.f.67.2	yes	4
21.5	even	6		1386.2.k.s.793.2		4
21.11	odd	6		9702.2.a.dr.1.2		2
21.17	even	6		9702.2.a.cz.1.1		2
21.20	even	2		1386.2.k.s.991.2		4
28.3	even	6		8624.2.a.ca.1.2		2
28.11	odd	6		8624.2.a.bk.1.1		2
28.19	even	6		1232.2.q.g.177.1		4
28.27	even	2		1232.2.q.g.529.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.e.f.23.2	✓	4	7.5	odd	6
154.2.e.f.67.2	yes	4	7.6	odd	2
1078.2.a.n.1.2		2	7.4	even	3
1078.2.a.s.1.1		2	7.3	odd	6
1078.2.e.v.67.1		4	1.1	even	1	trivial
1078.2.e.v.177.1		4	7.2	even	3	inner
1232.2.q.g.177.1		4	28.19	even	6
1232.2.q.g.529.1		4	28.27	even	2
1386.2.k.s.793.2		4	21.5	even	6
1386.2.k.s.991.2		4	21.20	even	2
8624.2.a.bk.1.1		2	28.11	odd	6
8624.2.a.ca.1.2		2	28.3	even	6
9702.2.a.cz.1.1		2	21.17	even	6
9702.2.a.dr.1.2		2	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.32288 + 2.29129i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.82288 + 3.15731i) q^{5} -2.64575 q^{6} -1.00000 q^{8} +(-2.00000 - 3.46410i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.32288 + 2.29129i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.82288 + 3.15731i) q^{5} -2.64575 q^{6} -1.00000 q^{8} +(-2.00000 - 3.46410i) q^{9} +(-1.82288 + 3.15731i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(-1.32288 - 2.29129i) q^{12} -5.00000 q^{13} -9.64575 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(2.00000 - 3.46410i) q^{18} +(-0.177124 - 0.306788i) q^{19} -3.64575 q^{20} -1.00000 q^{22} +(1.82288 + 3.15731i) q^{23} +(1.32288 - 2.29129i) q^{24} +(-4.14575 + 7.18065i) q^{25} +(-2.50000 - 4.33013i) q^{26} +2.64575 q^{27} -4.29150 q^{29} +(-4.82288 - 8.35347i) q^{30} +(-2.00000 + 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.32288 - 2.29129i) q^{33} +6.00000 q^{34} +4.00000 q^{36} +(0.822876 + 1.42526i) q^{37} +(0.177124 - 0.306788i) q^{38} +(6.61438 - 11.4564i) q^{39} +(-1.82288 - 3.15731i) q^{40} +4.93725 q^{41} -4.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(7.29150 - 12.6293i) q^{45} +(-1.82288 + 3.15731i) q^{46} +(6.64575 + 11.5108i) q^{47} +2.64575 q^{48} -8.29150 q^{50} +(7.93725 + 13.7477i) q^{51} +(2.50000 - 4.33013i) q^{52} +(1.82288 - 3.15731i) q^{53} +(1.32288 + 2.29129i) q^{54} -3.64575 q^{55} +0.937254 q^{57} +(-2.14575 - 3.71655i) q^{58} +(-0.322876 + 0.559237i) q^{59} +(4.82288 - 8.35347i) q^{60} +(1.85425 + 3.21165i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(-9.11438 - 15.7866i) q^{65} +(1.32288 - 2.29129i) q^{66} +(-1.96863 + 3.40976i) q^{67} +(3.00000 + 5.19615i) q^{68} -9.64575 q^{69} +9.64575 q^{71} +(2.00000 + 3.46410i) q^{72} +(2.82288 - 4.88936i) q^{73} +(-0.822876 + 1.42526i) q^{74} +(-10.9686 - 18.9982i) q^{75} +0.354249 q^{76} +13.2288 q^{78} +(-1.32288 - 2.29129i) q^{79} +(1.82288 - 3.15731i) q^{80} +(2.50000 - 4.33013i) q^{81} +(2.46863 + 4.27579i) q^{82} -13.2915 q^{83} +21.8745 q^{85} +(-2.00000 - 3.46410i) q^{86} +(5.67712 - 9.83307i) q^{87} +(0.500000 - 0.866025i) q^{88} +(-7.29150 - 12.6293i) q^{89} +14.5830 q^{90} -3.64575 q^{92} +(-5.29150 - 9.16515i) q^{93} +(-6.64575 + 11.5108i) q^{94} +(0.645751 - 1.11847i) q^{95} +(1.32288 + 2.29129i) q^{96} +5.70850 q^{97} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^8 - 8 * q^9	\( 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{8} - 8 q^{9} - 2 q^{10} - 2 q^{11} - 20 q^{13} - 28 q^{15} - 2 q^{16} + 12 q^{17} + 8 q^{18} - 6 q^{19} - 4 q^{20} - 4 q^{22} + 2 q^{23} - 6 q^{25} - 10 q^{26} + 4 q^{29} - 14 q^{30} - 8 q^{31} + 2 q^{32} + 24 q^{34} + 16 q^{36} - 2 q^{37} + 6 q^{38} - 2 q^{40} - 12 q^{41} - 16 q^{43} - 2 q^{44} + 8 q^{45} - 2 q^{46} + 16 q^{47} - 12 q^{50} + 10 q^{52} + 2 q^{53} - 4 q^{55} - 28 q^{57} + 2 q^{58} + 4 q^{59} + 14 q^{60} + 18 q^{61} - 16 q^{62} + 4 q^{64} - 10 q^{65} + 8 q^{67} + 12 q^{68} - 28 q^{69} + 28 q^{71} + 8 q^{72} + 6 q^{73} + 2 q^{74} - 28 q^{75} + 12 q^{76} + 2 q^{80} + 10 q^{81} - 6 q^{82} - 32 q^{83} + 24 q^{85} - 8 q^{86} + 28 q^{87} + 2 q^{88} - 8 q^{89} + 16 q^{90} - 4 q^{92} - 16 q^{94} - 8 q^{95} + 44 q^{97} + 16 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^8 - 8 * q^9 - 2 * q^10 - 2 * q^11 - 20 * q^13 - 28 * q^15 - 2 * q^16 + 12 * q^17 + 8 * q^18 - 6 * q^19 - 4 * q^20 - 4 * q^22 + 2 * q^23 - 6 * q^25 - 10 * q^26 + 4 * q^29 - 14 * q^30 - 8 * q^31 + 2 * q^32 + 24 * q^34 + 16 * q^36 - 2 * q^37 + 6 * q^38 - 2 * q^40 - 12 * q^41 - 16 * q^43 - 2 * q^44 + 8 * q^45 - 2 * q^46 + 16 * q^47 - 12 * q^50 + 10 * q^52 + 2 * q^53 - 4 * q^55 - 28 * q^57 + 2 * q^58 + 4 * q^59 + 14 * q^60 + 18 * q^61 - 16 * q^62 + 4 * q^64 - 10 * q^65 + 8 * q^67 + 12 * q^68 - 28 * q^69 + 28 * q^71 + 8 * q^72 + 6 * q^73 + 2 * q^74 - 28 * q^75 + 12 * q^76 + 2 * q^80 + 10 * q^81 - 6 * q^82 - 32 * q^83 + 24 * q^85 - 8 * q^86 + 28 * q^87 + 2 * q^88 - 8 * q^89 + 16 * q^90 - 4 * q^92 - 16 * q^94 - 8 * q^95 + 44 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more