LMFDB - Embedded newform 931.2.f.i.324.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [931,2,Mod(324,931)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("931.324"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(931, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.f (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 133)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			324.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	931.324
Dual form			931.2.f.i.704.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.20711 - 2.09077i) q^{2} +(0.707107 + 1.22474i) q^{3} +(-1.91421 - 3.31552i) q^{4} +(0.500000 - 0.866025i) q^{5} +3.41421 q^{6} -4.41421 q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.20711 - 2.09077i) q^{10} +(0.207107 + 0.358719i) q^{11} +(2.70711 - 4.68885i) q^{12} +2.24264 q^{13} +1.41421 q^{15} +(-1.50000 + 2.59808i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(-1.20711 - 2.09077i) q^{18} +(-0.500000 + 0.866025i) q^{19} -3.82843 q^{20} +1.00000 q^{22} +(2.79289 - 4.83743i) q^{23} +(-3.12132 - 5.40629i) q^{24} +(2.00000 + 3.46410i) q^{25} +(2.70711 - 4.68885i) q^{26} +5.65685 q^{27} -6.58579 q^{29} +(1.70711 - 2.95680i) q^{30} +(-3.12132 - 5.40629i) q^{31} +(-0.792893 - 1.37333i) q^{32} +(-0.292893 + 0.507306i) q^{33} -9.65685 q^{34} -3.82843 q^{36} +(-4.53553 + 7.85578i) q^{37} +(1.20711 + 2.09077i) q^{38} +(1.58579 + 2.74666i) q^{39} +(-2.20711 + 3.82282i) q^{40} +3.17157 q^{41} +8.07107 q^{43} +(0.792893 - 1.37333i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(-6.74264 - 11.6786i) q^{46} +(-2.20711 + 3.82282i) q^{47} -4.24264 q^{48} +9.65685 q^{50} +(2.82843 - 4.89898i) q^{51} +(-4.29289 - 7.43551i) q^{52} +(2.12132 + 3.67423i) q^{53} +(6.82843 - 11.8272i) q^{54} +0.414214 q^{55} -1.41421 q^{57} +(-7.94975 + 13.7694i) q^{58} +(3.41421 + 5.91359i) q^{59} +(-2.70711 - 4.68885i) q^{60} +(5.91421 - 10.2437i) q^{61} -15.0711 q^{62} -9.82843 q^{64} +(1.12132 - 1.94218i) q^{65} +(0.707107 + 1.22474i) q^{66} +(-0.585786 - 1.01461i) q^{67} +(-7.65685 + 13.2621i) q^{68} +7.89949 q^{69} -14.2426 q^{71} +(-2.20711 + 3.82282i) q^{72} +(7.57107 + 13.1135i) q^{73} +(10.9497 + 18.9655i) q^{74} +(-2.82843 + 4.89898i) q^{75} +3.82843 q^{76} +7.65685 q^{78} +(-0.707107 + 1.22474i) q^{79} +(1.50000 + 2.59808i) q^{80} +(2.50000 + 4.33013i) q^{81} +(3.82843 - 6.63103i) q^{82} -9.24264 q^{83} -4.00000 q^{85} +(9.74264 - 16.8747i) q^{86} +(-4.65685 - 8.06591i) q^{87} +(-0.914214 - 1.58346i) q^{88} +(-5.70711 + 9.88500i) q^{89} -2.41421 q^{90} -21.3848 q^{92} +(4.41421 - 7.64564i) q^{93} +(5.32843 + 9.22911i) q^{94} +(0.500000 + 0.866025i) q^{95} +(1.12132 - 1.94218i) q^{96} +3.17157 q^{97} +0.414214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} + 8 q^{6} - 12 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{11} + 8 q^{12} - 8 q^{13} - 6 q^{16} - 8 q^{17} - 2 q^{18} - 2 q^{19} - 4 q^{20} + 4 q^{22} + 14 q^{23} - 4 q^{24} + 8 q^{25}+ \cdots - 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 + 8 * q^6 - 12 * q^8 + 2 * q^9 - 2 * q^10 - 2 * q^11 + 8 * q^12 - 8 * q^13 - 6 * q^16 - 8 * q^17 - 2 * q^18 - 2 * q^19 - 4 * q^20 + 4 * q^22 + 14 * q^23 - 4 * q^24 + 8 * q^25 + 8 * q^26 - 32 * q^29 + 4 * q^30 - 4 * q^31 - 6 * q^32 - 4 * q^33 - 16 * q^34 - 4 * q^36 - 4 * q^37 + 2 * q^38 + 12 * q^39 - 6 * q^40 + 24 * q^41 + 4 * q^43 + 6 * q^44 - 2 * q^45 - 10 * q^46 - 6 * q^47 + 16 * q^50 - 20 * q^52 + 16 * q^54 - 4 * q^55 - 12 * q^58 + 8 * q^59 - 8 * q^60 + 18 * q^61 - 32 * q^62 - 28 * q^64 - 4 * q^65 - 8 * q^67 - 8 * q^68 - 8 * q^69 - 40 * q^71 - 6 * q^72 + 2 * q^73 + 24 * q^74 + 4 * q^76 + 8 * q^78 + 6 * q^80 + 10 * q^81 + 4 * q^82 - 20 * q^83 - 16 * q^85 + 22 * q^86 + 4 * q^87 + 2 * q^88 - 20 * q^89 - 4 * q^90 - 12 * q^92 + 12 * q^93 + 10 * q^94 + 2 * q^95 - 4 * q^96 + 24 * q^97 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/931\mathbb{Z}\right)^\times$.

$n$	$248$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.20711	−	2.09077i	0.853553	−	1.47840i	−0.0244272	−	0.999702i	$-0.507776\pi$
$2$	1.20711	−	2.09077i	0.853553	−	1.47840i	0.877981	−	0.478696i	$-0.158890\pi$
$3$	0.707107	+	1.22474i	0.408248	+	0.707107i	0.994694	−	0.102882i	$-0.0328064\pi$
$3$	0.707107	+	1.22474i	0.408248	+	0.707107i	−0.586445	+	0.809989i	$0.699473\pi$
$4$	−1.91421	−	3.31552i	−0.957107	−	1.65776i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	−0.732294	−	0.680989i	$-0.761550\pi$
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	0.955901	+	0.293691i	$0.0948835\pi$
$6$	3.41421			1.39385
$7$		0			0
$7$		0			0
$8$	−4.41421			−1.56066
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−1.20711	−	2.09077i	−0.381721	−	0.661160i
$11$	0.207107	+	0.358719i	0.0624450	+	0.108158i	0.895558	−	0.444945i	$-0.146777\pi$
$11$	0.207107	+	0.358719i	0.0624450	+	0.108158i	−0.833113	+	0.553103i	$0.813444\pi$
$12$	2.70711	−	4.68885i	0.781474	−	1.35355i
$13$	2.24264			0.621997			0.310998	−	0.950410i	$-0.399337\pi$
$13$	2.24264			0.621997			0.310998	+	0.950410i	$0.399337\pi$
$14$		0			0
$15$	1.41421			0.365148
$16$	−1.50000	+	2.59808i	−0.375000	+	0.649519i
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	0.514782	−	0.857321i	$-0.327873\pi$
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	−0.999853	+	0.0171533i	$0.994540\pi$
$18$	−1.20711	−	2.09077i	−0.284518	−	0.492799i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$20$	−3.82843			−0.856062
$21$		0			0
$22$	1.00000			0.213201
$23$	2.79289	−	4.83743i	0.582358	−	1.00867i	−0.412841	−	0.910803i	$-0.635463\pi$
$23$	2.79289	−	4.83743i	0.582358	−	1.00867i	0.995199	−	0.0978712i	$-0.0312033\pi$
$24$	−3.12132	−	5.40629i	−0.637137	−	1.10355i
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	2.70711	−	4.68885i	0.530907	−	0.919558i
$27$	5.65685			1.08866
$28$		0			0
$29$	−6.58579			−1.22295			−0.611475	−	0.791264i	$-0.709423\pi$
$29$	−6.58579			−1.22295			−0.611475	+	0.791264i	$0.709423\pi$
$30$	1.70711	−	2.95680i	0.311674	−	0.539835i
$31$	−3.12132	−	5.40629i	−0.560606	−	0.970998i	−0.997444	−	0.0714573i	$-0.977235\pi$
$31$	−3.12132	−	5.40629i	−0.560606	−	0.970998i	0.436838	−	0.899540i	$-0.356098\pi$
$32$	−0.792893	−	1.37333i	−0.140165	−	0.242773i
$33$	−0.292893	+	0.507306i	−0.0509862	+	0.0883106i
$34$	−9.65685			−1.65614
$35$		0			0
$36$	−3.82843			−0.638071
$37$	−4.53553	+	7.85578i	−0.745637	+	1.29148i	0.204259	+	0.978917i	$0.434521\pi$
$37$	−4.53553	+	7.85578i	−0.745637	+	1.29148i	−0.949896	+	0.312565i	$0.898812\pi$
$38$	1.20711	+	2.09077i	0.195819	+	0.339168i
$39$	1.58579	+	2.74666i	0.253929	+	0.439818i
$40$	−2.20711	+	3.82282i	−0.348974	+	0.604441i
$41$	3.17157			0.495316			0.247658	−	0.968847i	$-0.420339\pi$
$41$	3.17157			0.495316			0.247658	+	0.968847i	$0.420339\pi$
$42$		0			0
$43$	8.07107			1.23083			0.615413	−	0.788205i	$-0.288989\pi$
$43$	8.07107			1.23083			0.615413	+	0.788205i	$0.288989\pi$
$44$	0.792893	−	1.37333i	0.119533	−	0.207037i
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$	−6.74264	−	11.6786i	−0.994148	−	1.72192i
$47$	−2.20711	+	3.82282i	−0.321940	+	0.557616i	−0.980888	−	0.194572i	$-0.937668\pi$
$47$	−2.20711	+	3.82282i	−0.321940	+	0.557616i	0.658949	+	0.752188i	$0.271001\pi$
$48$	−4.24264			−0.612372
$49$		0			0
$50$	9.65685			1.36569
$51$	2.82843	−	4.89898i	0.396059	−	0.685994i
$52$	−4.29289	−	7.43551i	−0.595317	−	1.03112i
$53$	2.12132	+	3.67423i	0.291386	+	0.504695i	0.974138	−	0.225955i	$-0.0725503\pi$
$53$	2.12132	+	3.67423i	0.291386	+	0.504695i	−0.682752	+	0.730650i	$0.739217\pi$
$54$	6.82843	−	11.8272i	0.929231	−	1.60948i
$55$	0.414214			0.0558525
$56$		0			0
$57$	−1.41421			−0.187317
$58$	−7.94975	+	13.7694i	−1.04385	+	1.80801i
$59$	3.41421	+	5.91359i	0.444493	+	0.769884i	0.998017	−	0.0629492i	$-0.0200506\pi$
$59$	3.41421	+	5.91359i	0.444493	+	0.769884i	−0.553524	+	0.832833i	$0.686717\pi$
$60$	−2.70711	−	4.68885i	−0.349486	−	0.605327i
$61$	5.91421	−	10.2437i	0.757237	−	1.31157i	−0.187017	−	0.982357i	$-0.559882\pi$
$61$	5.91421	−	10.2437i	0.757237	−	1.31157i	0.944254	−	0.329217i	$-0.106785\pi$
$62$	−15.0711			−1.91403
$63$		0			0
$64$	−9.82843			−1.22855
$65$	1.12132	−	1.94218i	0.139083	−	0.240898i
$66$	0.707107	+	1.22474i	0.0870388	+	0.150756i
$67$	−0.585786	−	1.01461i	−0.0715652	−	0.123955i	0.828022	−	0.560695i	$-0.189466\pi$
$67$	−0.585786	−	1.01461i	−0.0715652	−	0.123955i	−0.899587	+	0.436741i	$0.856133\pi$
$68$	−7.65685	+	13.2621i	−0.928530	+	1.60826i
$69$	7.89949			0.950987
$70$		0			0
$71$	−14.2426			−1.69029			−0.845145	−	0.534537i	$-0.820486\pi$
$71$	−14.2426			−1.69029			−0.845145	+	0.534537i	$0.820486\pi$
$72$	−2.20711	+	3.82282i	−0.260110	+	0.450524i
$73$	7.57107	+	13.1135i	0.886126	+	1.53482i	0.844417	+	0.535686i	$0.179947\pi$
$73$	7.57107	+	13.1135i	0.886126	+	1.53482i	0.0417094	+	0.999130i	$0.486720\pi$
$74$	10.9497	+	18.9655i	1.27288	+	2.20470i
$75$	−2.82843	+	4.89898i	−0.326599	+	0.565685i
$76$	3.82843			0.439151
$77$		0			0
$78$	7.65685			0.866968
$79$	−0.707107	+	1.22474i	−0.0795557	+	0.137795i	−0.903058	−	0.429518i	$-0.858683\pi$
$79$	−0.707107	+	1.22474i	−0.0795557	+	0.137795i	0.823503	+	0.567312i	$0.192017\pi$
$80$	1.50000	+	2.59808i	0.167705	+	0.290474i
$81$	2.50000	+	4.33013i	0.277778	+	0.481125i
$82$	3.82843	−	6.63103i	0.422779	−	0.732275i
$83$	−9.24264			−1.01451			−0.507256	−	0.861796i	$-0.669340\pi$
$83$	−9.24264			−1.01451			−0.507256	+	0.861796i	$0.669340\pi$
$84$		0			0
$85$	−4.00000			−0.433861
$86$	9.74264	−	16.8747i	1.05058	−	1.81965i
$87$	−4.65685	−	8.06591i	−0.499267	−	0.864756i
$88$	−0.914214	−	1.58346i	−0.0974555	−	0.168798i
$89$	−5.70711	+	9.88500i	−0.604952	+	1.04781i	0.387107	+	0.922035i	$0.373474\pi$
$89$	−5.70711	+	9.88500i	−0.604952	+	1.04781i	−0.992059	+	0.125773i	$0.959859\pi$
$90$	−2.41421			−0.254480
$91$		0			0
$92$	−21.3848			−2.22952
$93$	4.41421	−	7.64564i	0.457733	−	0.792816i
$94$	5.32843	+	9.22911i	0.549585	+	0.951910i
$95$	0.500000	+	0.866025i	0.0512989	+	0.0888523i
$96$	1.12132	−	1.94218i	0.114444	−	0.198223i
$97$	3.17157			0.322024			0.161012	−	0.986952i	$-0.448524\pi$
$97$	3.17157			0.322024			0.161012	+	0.986952i	$0.448524\pi$
$98$		0			0
$99$	0.414214			0.0416300
$100$	7.65685	−	13.2621i	0.765685	−	1.32621i
$101$	9.15685	+	15.8601i	0.911141	+	1.57814i	0.812455	+	0.583024i	$0.198131\pi$
$101$	9.15685	+	15.8601i	0.911141	+	1.57814i	0.0986861	+	0.995119i	$0.468536\pi$
$102$	−6.82843	−	11.8272i	−0.676115	−	1.17107i
$103$	−3.00000	+	5.19615i	−0.295599	+	0.511992i	−0.975124	−	0.221660i	$-0.928852\pi$
$103$	−3.00000	+	5.19615i	−0.295599	+	0.511992i	0.679525	+	0.733652i	$0.262186\pi$
$104$	−9.89949			−0.970725
$105$		0			0
$106$	10.2426			0.994853
$107$	6.94975	−	12.0373i	0.671857	−	1.16369i	−0.305519	−	0.952186i	$-0.598830\pi$
$107$	6.94975	−	12.0373i	0.671857	−	1.16369i	0.977377	−	0.211505i	$-0.0678366\pi$
$108$	−10.8284	−	18.7554i	−1.04197	−	1.80474i
$109$	4.82843	+	8.36308i	0.462479	+	0.801038i	0.999084	−	0.0427961i	$-0.0136266\pi$
$109$	4.82843	+	8.36308i	0.462479	+	0.801038i	−0.536604	+	0.843834i	$0.680293\pi$
$110$	0.500000	−	0.866025i	0.0476731	−	0.0825723i
$111$	−12.8284			−1.21762
$112$		0			0
$113$	−0.242641			−0.0228257			−0.0114129	−	0.999935i	$-0.503633\pi$
$113$	−0.242641			−0.0228257			−0.0114129	+	0.999935i	$0.503633\pi$
$114$	−1.70711	+	2.95680i	−0.159885	+	0.276929i
$115$	−2.79289	−	4.83743i	−0.260439	−	0.451093i
$116$	12.6066	+	21.8353i	1.17049	+	2.02735i
$117$	1.12132	−	1.94218i	0.103666	−	0.179555i
$118$	16.4853			1.51759
$119$		0			0
$120$	−6.24264			−0.569873
$121$	5.41421	−	9.37769i	0.492201	−	0.852518i
$122$	−14.2782	−	24.7305i	−1.29269	−	2.23900i
$123$	2.24264	+	3.88437i	0.202212	+	0.350242i
$124$	−11.9497	+	20.6976i	−1.07312	+	1.85870i
$125$	9.00000			0.804984
$126$		0			0
$127$	4.24264			0.376473			0.188237	−	0.982124i	$-0.439723\pi$
$127$	4.24264			0.376473			0.188237	+	0.982124i	$0.439723\pi$
$128$	−10.2782	+	17.8023i	−0.908471	+	1.57352i
$129$	5.70711	+	9.88500i	0.502483	+	0.870326i
$130$	−2.70711	−	4.68885i	−0.237429	−	0.411239i
$131$	1.75736	−	3.04384i	0.153541	−	0.265941i	−0.778986	−	0.627042i	$-0.784266\pi$
$131$	1.75736	−	3.04384i	0.153541	−	0.265941i	0.932527	+	0.361101i	$0.117599\pi$
$132$	2.24264			0.195197
$133$		0			0
$134$	−2.82843			−0.244339
$135$	2.82843	−	4.89898i	0.243432	−	0.421637i
$136$	8.82843	+	15.2913i	0.757031	+	1.31122i
$137$	9.91421	+	17.1719i	0.847028	+	1.46710i	0.883848	+	0.467774i	$0.154944\pi$
$137$	9.91421	+	17.1719i	0.847028	+	1.46710i	−0.0368195	+	0.999322i	$0.511723\pi$
$138$	9.53553	−	16.5160i	0.811719	−	1.40594i
$139$	6.07107			0.514941			0.257471	−	0.966286i	$-0.417111\pi$
$139$	6.07107			0.514941			0.257471	+	0.966286i	$0.417111\pi$
$140$		0			0
$141$	−6.24264			−0.525725
$142$	−17.1924	+	29.7781i	−1.44275	+	2.49892i
$143$	0.464466	+	0.804479i	0.0388406	+	0.0672739i
$144$	1.50000	+	2.59808i	0.125000	+	0.216506i
$145$	−3.29289	+	5.70346i	−0.273460	+	0.473646i
$146$	36.5563			3.02542
$147$		0			0
$148$	34.7279			2.85462
$149$	0.0857864	−	0.148586i	0.00702790	−	0.0121727i	−0.862490	−	0.506074i	$-0.831096\pi$
$149$	0.0857864	−	0.148586i	0.00702790	−	0.0121727i	0.869518	+	0.493901i	$0.164430\pi$
$150$	6.82843	+	11.8272i	0.557539	+	0.965685i
$151$	8.65685	+	14.9941i	0.704485	+	1.22020i	0.966877	+	0.255242i	$0.0821552\pi$
$151$	8.65685	+	14.9941i	0.704485	+	1.22020i	−0.262392	+	0.964961i	$0.584511\pi$
$152$	2.20711	−	3.82282i	0.179020	−	0.310072i
$153$	−4.00000			−0.323381
$154$		0			0
$155$	−6.24264			−0.501421
$156$	6.07107	−	10.5154i	0.486074	−	0.841906i
$157$	3.08579	+	5.34474i	0.246273	+	0.426557i	0.962489	−	0.271322i	$-0.0874608\pi$
$157$	3.08579	+	5.34474i	0.246273	+	0.426557i	−0.716216	+	0.697879i	$0.754127\pi$
$158$	1.70711	+	2.95680i	0.135810	+	0.235230i
$159$	−3.00000	+	5.19615i	−0.237915	+	0.412082i
$160$	−1.58579			−0.125367
$161$		0			0
$162$	12.0711			0.948393
$163$	−1.96447	+	3.40256i	−0.153869	+	0.266509i	−0.932647	−	0.360791i	$-0.882507\pi$
$163$	−1.96447	+	3.40256i	−0.153869	+	0.266509i	0.778778	+	0.627300i	$0.215840\pi$
$164$	−6.07107	−	10.5154i	−0.474071	−	0.821115i
$165$	0.292893	+	0.507306i	0.0228017	+	0.0394937i
$166$	−11.1569	+	19.3242i	−0.865940	+	1.49985i
$167$	−13.0711			−1.01147			−0.505735	−	0.862689i	$-0.668779\pi$
$167$	−13.0711			−1.01147			−0.505735	+	0.862689i	$0.668779\pi$
$168$		0			0
$169$	−7.97056			−0.613120
$170$	−4.82843	+	8.36308i	−0.370323	+	0.641419i
$171$	0.500000	+	0.866025i	0.0382360	+	0.0662266i
$172$	−15.4497	−	26.7597i	−1.17803	−	2.04041i
$173$	−3.65685	+	6.33386i	−0.278025	+	0.481554i	−0.970894	−	0.239510i	$-0.923013\pi$
$173$	−3.65685	+	6.33386i	−0.278025	+	0.481554i	0.692868	+	0.721064i	$0.256347\pi$
$174$	−22.4853			−1.70460
$175$		0			0
$176$	−1.24264			−0.0936676
$177$	−4.82843	+	8.36308i	−0.362927	+	0.628608i
$178$	13.7782	+	23.8645i	1.03272	+	1.78872i
$179$	−8.89949	−	15.4144i	−0.665179	−	1.15212i	−0.979237	−	0.202721i	$-0.935022\pi$
$179$	−8.89949	−	15.4144i	−0.665179	−	1.15212i	0.314057	−	0.949404i	$-0.398312\pi$
$180$	−1.91421	+	3.31552i	−0.142677	+	0.247124i
$181$	−9.89949			−0.735824			−0.367912	−	0.929861i	$-0.619927\pi$
$181$	−9.89949			−0.735824			−0.367912	+	0.929861i	$0.619927\pi$
$182$		0			0
$183$	16.7279			1.23656
$184$	−12.3284	+	21.3535i	−0.908864	+	1.57420i
$185$	4.53553	+	7.85578i	0.333459	+	0.577568i
$186$	−10.6569	−	18.4582i	−0.781398	−	1.35342i
$187$	0.828427	−	1.43488i	0.0605806	−	0.104929i
$188$	16.8995			1.23252
$189$		0			0
$190$	2.41421			0.175145
$191$	−4.20711	+	7.28692i	−0.304416	+	0.527263i	−0.977131	−	0.212638i	$-0.931794\pi$
$191$	−4.20711	+	7.28692i	−0.304416	+	0.527263i	0.672715	+	0.739901i	$0.265128\pi$
$192$	−6.94975	−	12.0373i	−0.501555	−	0.868718i
$193$	−3.94975	−	6.84116i	−0.284309	−	0.492438i	0.688132	−	0.725585i	$-0.258431\pi$
$193$	−3.94975	−	6.84116i	−0.284309	−	0.492438i	−0.972441	+	0.233147i	$0.925098\pi$
$194$	3.82843	−	6.63103i	0.274865	−	0.476080i
$195$	3.17157			0.227121
$196$		0			0
$197$	4.51472			0.321660			0.160830	−	0.986982i	$-0.448583\pi$
$197$	4.51472			0.321660			0.160830	+	0.986982i	$0.448583\pi$
$198$	0.500000	−	0.866025i	0.0355335	−	0.0615457i
$199$	8.03553	+	13.9180i	0.569624	+	0.986618i	0.996603	+	0.0823560i	$0.0262445\pi$
$199$	8.03553	+	13.9180i	0.569624	+	0.986618i	−0.426979	+	0.904262i	$0.640422\pi$
$200$	−8.82843	−	15.2913i	−0.624264	−	1.08126i
$201$	0.828427	−	1.43488i	0.0584327	−	0.101208i
$202$	44.2132			3.11083
$203$		0			0
$204$	−21.6569			−1.51628
$205$	1.58579	−	2.74666i	0.110756	−	0.191835i
$206$	7.24264	+	12.5446i	0.504619	+	0.874025i
$207$	−2.79289	−	4.83743i	−0.194119	−	0.336225i
$208$	−3.36396	+	5.82655i	−0.233249	+	0.403999i
$209$	−0.414214			−0.0286518
$210$		0			0
$211$	−1.17157			−0.0806544			−0.0403272	−	0.999187i	$-0.512840\pi$
$211$	−1.17157			−0.0806544			−0.0403272	+	0.999187i	$0.512840\pi$
$212$	8.12132	−	14.0665i	0.557775	−	0.966094i
$213$	−10.0711	−	17.4436i	−0.690058	−	1.19522i
$214$	−16.7782	−	29.0607i	−1.14693	−	1.98655i
$215$	4.03553	−	6.98975i	0.275221	−	0.476697i
$216$	−24.9706			−1.69903
$217$		0			0
$218$	23.3137			1.57900
$219$	−10.7071	+	18.5453i	−0.723519	+	1.25317i
$220$	−0.792893	−	1.37333i	−0.0534568	−	0.0925900i
$221$	−4.48528	−	7.76874i	−0.301713	−	0.522582i
$222$	−15.4853	+	26.8213i	−1.03930	+	1.80013i
$223$	−2.24264			−0.150178			−0.0750892	−	0.997177i	$-0.523924\pi$
$223$	−2.24264			−0.150178			−0.0750892	+	0.997177i	$0.523924\pi$
$224$		0			0
$225$	4.00000			0.266667
$226$	−0.292893	+	0.507306i	−0.0194830	+	0.0337455i
$227$	−10.1213	−	17.5306i	−0.671776	−	1.16355i	−0.977400	−	0.211397i	$-0.932199\pi$
$227$	−10.1213	−	17.5306i	−0.671776	−	1.16355i	0.305625	−	0.952152i	$-0.401135\pi$
$228$	2.70711	+	4.68885i	0.179283	+	0.310526i
$229$	6.24264	−	10.8126i	0.412525	−	0.714515i	−0.582640	−	0.812730i	$-0.697980\pi$
$229$	6.24264	−	10.8126i	0.412525	−	0.714515i	0.995165	+	0.0982157i	$0.0313135\pi$
$230$	−13.4853			−0.889193
$231$		0			0
$232$	29.0711			1.90861
$233$	−0.242641	+	0.420266i	−0.0158959	+	0.0275325i	−0.873864	−	0.486171i	$-0.838393\pi$
$233$	−0.242641	+	0.420266i	−0.0158959	+	0.0275325i	0.857968	+	0.513703i	$0.171727\pi$
$234$	−2.70711	−	4.68885i	−0.176969	−	0.306519i
$235$	2.20711	+	3.82282i	0.143976	+	0.249373i
$236$	13.0711	−	22.6398i	0.850854	−	1.47372i
$237$	−2.00000			−0.129914
$238$		0			0
$239$	2.00000			0.129369			0.0646846	−	0.997906i	$-0.479396\pi$
$239$	2.00000			0.129369			0.0646846	+	0.997906i	$0.479396\pi$
$240$	−2.12132	+	3.67423i	−0.136931	+	0.237171i
$241$	−13.0208	−	22.5527i	−0.838744	−	1.45275i	−0.890945	−	0.454111i	$-0.849957\pi$
$241$	−13.0208	−	22.5527i	−0.838744	−	1.45275i	0.0522005	−	0.998637i	$-0.483377\pi$
$242$	−13.0711	−	22.6398i	−0.840240	−	1.45534i
$243$	4.94975	−	8.57321i	0.317526	−	0.549972i
$244$	−45.2843			−2.89903
$245$		0			0
$246$	10.8284			0.690395
$247$	−1.12132	+	1.94218i	−0.0713479	+	0.123578i
$248$	13.7782	+	23.8645i	0.874915	+	1.51540i
$249$	−6.53553	−	11.3199i	−0.414173	−	0.717368i
$250$	10.8640	−	18.8169i	0.687097	−	1.19009i
$251$	13.7279			0.866499			0.433249	−	0.901274i	$-0.357367\pi$
$251$	13.7279			0.866499			0.433249	+	0.901274i	$0.357367\pi$
$252$		0			0
$253$	2.31371			0.145462
$254$	5.12132	−	8.87039i	0.321340	−	0.556578i
$255$	−2.82843	−	4.89898i	−0.177123	−	0.306786i
$256$	14.9853	+	25.9553i	0.936580	+	1.62220i
$257$	4.65685	−	8.06591i	0.290487	−	0.503138i	−0.683438	−	0.730008i	$-0.739516\pi$
$257$	4.65685	−	8.06591i	0.290487	−	0.503138i	0.973925	+	0.226871i	$0.0728495\pi$
$258$	27.5563			1.71558
$259$		0			0
$260$	−8.58579			−0.532468
$261$	−3.29289	+	5.70346i	−0.203825	+	0.353035i
$262$	−4.24264	−	7.34847i	−0.262111	−	0.453990i
$263$	−8.24264	−	14.2767i	−0.508263	−	0.880337i	−0.999954	−	0.00956772i	$-0.996954\pi$
$263$	−8.24264	−	14.2767i	−0.508263	−	0.880337i	0.491691	−	0.870770i	$-0.336379\pi$
$264$	1.29289	−	2.23936i	0.0795721	−	0.137823i
$265$	4.24264			0.260623
$266$		0			0
$267$	−16.1421			−0.987883
$268$	−2.24264	+	3.88437i	−0.136991	+	0.237276i
$269$	−2.00000	−	3.46410i	−0.121942	−	0.211210i	0.798591	−	0.601874i	$-0.205579\pi$
$269$	−2.00000	−	3.46410i	−0.121942	−	0.211210i	−0.920534	+	0.390664i	$0.872246\pi$
$270$	−6.82843	−	11.8272i	−0.415565	−	0.719779i
$271$	−7.62132	+	13.2005i	−0.462962	+	0.801874i	−0.999107	−	0.0422519i	$-0.986547\pi$
$271$	−7.62132	+	13.2005i	−0.462962	+	0.801874i	0.536145	+	0.844126i	$0.319880\pi$
$272$	12.0000			0.727607
$273$		0			0
$274$	47.8701			2.89194
$275$	−0.828427	+	1.43488i	−0.0499560	+	0.0865264i
$276$	−15.1213	−	26.1909i	−0.910197	−	1.57651i
$277$	11.2279	+	19.4473i	0.674620	+	1.16848i	0.976580	+	0.215156i	$0.0690260\pi$
$277$	11.2279	+	19.4473i	0.674620	+	1.16848i	−0.301959	+	0.953321i	$0.597641\pi$
$278$	7.32843	−	12.6932i	0.439530	−	0.761288i
$279$	−6.24264			−0.373737
$280$		0			0
$281$	−28.2426			−1.68481			−0.842407	−	0.538841i	$-0.818862\pi$
$281$	−28.2426			−1.68481			−0.842407	+	0.538841i	$0.818862\pi$
$282$	−7.53553	+	13.0519i	−0.448735	+	0.777231i
$283$	15.0355	+	26.0423i	0.893770	+	1.54805i	0.835320	+	0.549764i	$0.185282\pi$
$283$	15.0355	+	26.0423i	0.893770	+	1.54805i	0.0584498	+	0.998290i	$0.481384\pi$
$284$	27.2635	+	47.2217i	1.61779	+	2.80209i
$285$	−0.707107	+	1.22474i	−0.0418854	+	0.0725476i
$286$	2.24264			0.132610
$287$		0			0
$288$	−1.58579			−0.0934434
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$	7.94975	+	13.7694i	0.466825	+	0.808565i
$291$	2.24264	+	3.88437i	0.131466	+	0.227706i
$292$	28.9853	−	50.2040i	1.69624	−	2.93797i
$293$	−3.17157			−0.185285			−0.0926426	−	0.995699i	$-0.529531\pi$
$293$	−3.17157			−0.185285			−0.0926426	+	0.995699i	$0.529531\pi$
$294$		0			0
$295$	6.82843			0.397566
$296$	20.0208	−	34.6771i	1.16369	−	2.01556i
$297$	1.17157	+	2.02922i	0.0679816	+	0.117748i
$298$	−0.207107	−	0.358719i	−0.0119974	−	0.0207801i
$299$	6.26346	−	10.8486i	0.362225	−	0.627392i
$300$	21.6569			1.25036
$301$		0			0
$302$	41.7990			2.40526
$303$	−12.9497	+	22.4296i	−0.743944	+	1.28855i
$304$	−1.50000	−	2.59808i	−0.0860309	−	0.149010i
$305$	−5.91421	−	10.2437i	−0.338647	−	0.586554i
$306$	−4.82843	+	8.36308i	−0.276023	+	0.478086i
$307$	−29.3137			−1.67302			−0.836511	−	0.547950i	$-0.815408\pi$
$307$	−29.3137			−1.67302			−0.836511	+	0.547950i	$0.815408\pi$
$308$		0			0
$309$	−8.48528			−0.482711
$310$	−7.53553	+	13.0519i	−0.427990	+	0.741300i
$311$	−11.8995	−	20.6105i	−0.674758	−	1.16872i	−0.976539	−	0.215339i	$-0.930914\pi$
$311$	−11.8995	−	20.6105i	−0.674758	−	1.16872i	0.301781	−	0.953377i	$-0.402419\pi$
$312$	−7.00000	−	12.1244i	−0.396297	−	0.686406i
$313$	−3.32843	+	5.76500i	−0.188134	+	0.325857i	−0.944628	−	0.328143i	$-0.893577\pi$
$313$	−3.32843	+	5.76500i	−0.188134	+	0.325857i	0.756494	+	0.654000i	$0.226911\pi$
$314$	14.8995			0.840827
$315$		0			0
$316$	5.41421			0.304573
$317$	10.1213	−	17.5306i	0.568470	−	0.984619i	−0.428248	−	0.903661i	$-0.640869\pi$
$317$	10.1213	−	17.5306i	0.568470	−	0.984619i	0.996718	−	0.0809574i	$-0.0257978\pi$
$318$	7.24264	+	12.5446i	0.406147	+	0.703467i
$319$	−1.36396	−	2.36245i	−0.0763672	−	0.132272i
$320$	−4.91421	+	8.51167i	−0.274713	+	0.475817i
$321$	19.6569			1.09714
$322$		0			0
$323$	4.00000			0.222566
$324$	9.57107	−	16.5776i	0.531726	−	0.920976i
$325$	4.48528	+	7.76874i	0.248799	+	0.430932i
$326$	4.74264	+	8.21449i	0.262671	+	0.454959i
$327$	−6.82843	+	11.8272i	−0.377613	+	0.654045i
$328$	−14.0000			−0.773021
$329$		0			0
$330$	1.41421			0.0778499
$331$	15.7279	−	27.2416i	0.864485	−	1.49733i	−0.00307307	−	0.999995i	$-0.500978\pi$
$331$	15.7279	−	27.2416i	0.864485	−	1.49733i	0.867558	−	0.497336i	$-0.165688\pi$
$332$	17.6924	+	30.6441i	0.970996	+	1.68181i
$333$	4.53553	+	7.85578i	0.248546	+	0.430494i
$334$	−15.7782	+	27.3286i	−0.863343	+	1.49535i
$335$	−1.17157			−0.0640099
$336$		0			0
$337$	19.5563			1.06530			0.532651	−	0.846335i	$-0.321196\pi$
$337$	19.5563			1.06530			0.532651	+	0.846335i	$0.321196\pi$
$338$	−9.62132	+	16.6646i	−0.523331	+	0.906436i
$339$	−0.171573	−	0.297173i	−0.00931856	−	0.0161402i
$340$	7.65685	+	13.2621i	0.415251	+	0.719236i
$341$	1.29289	−	2.23936i	0.0700141	−	0.121268i
$342$	2.41421			0.130546
$343$		0			0
$344$	−35.6274			−1.92090
$345$	3.94975	−	6.84116i	0.212647	−	0.368316i
$346$	8.82843	+	15.2913i	0.474619	+	0.822065i
$347$	−13.5208	−	23.4187i	−0.725835	−	1.25718i	−0.958629	−	0.284658i	$-0.908120\pi$
$347$	−13.5208	−	23.4187i	−0.725835	−	1.25718i	0.232794	−	0.972526i	$-0.425213\pi$
$348$	−17.8284	+	30.8797i	−0.955704	+	1.65533i
$349$	−4.48528			−0.240092			−0.120046	−	0.992768i	$-0.538304\pi$
$349$	−4.48528			−0.240092			−0.120046	+	0.992768i	$0.538304\pi$
$350$		0			0
$351$	12.6863			0.677144
$352$	0.328427	−	0.568852i	0.0175052	−	0.0303199i
$353$	0.242641	+	0.420266i	0.0129145	+	0.0223685i	0.872410	−	0.488774i	$-0.162556\pi$
$353$	0.242641	+	0.420266i	0.0129145	+	0.0223685i	−0.859496	+	0.511143i	$0.829222\pi$
$354$	11.6569	+	20.1903i	0.619555	+	1.07310i
$355$	−7.12132	+	12.3345i	−0.377960	+	0.654647i
$356$	43.6985			2.31602
$357$		0			0
$358$	−42.9706			−2.27106
$359$	−2.62132	+	4.54026i	−0.138348	+	0.239626i	−0.926871	−	0.375379i	$-0.877513\pi$
$359$	−2.62132	+	4.54026i	−0.138348	+	0.239626i	0.788523	+	0.615005i	$0.210846\pi$
$360$	2.20711	+	3.82282i	0.116325	+	0.201480i
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$	−11.9497	+	20.6976i	−0.628065	+	1.08784i
$363$	15.3137			0.803761
$364$		0			0
$365$	15.1421			0.792576
$366$	20.1924	−	34.9742i	1.05547	−	1.82813i
$367$	−12.1716	−	21.0818i	−0.635351	−	1.10046i	−0.986441	−	0.164118i	$-0.947522\pi$
$367$	−12.1716	−	21.0818i	−0.635351	−	1.10046i	0.351090	−	0.936342i	$-0.385811\pi$
$368$	8.37868	+	14.5123i	0.436769	+	0.756506i
$369$	1.58579	−	2.74666i	0.0825527	−	0.142986i
$370$	21.8995			1.13850
$371$		0			0
$372$	−33.7990			−1.75240
$373$	−5.65685	+	9.79796i	−0.292901	+	0.507319i	−0.974494	−	0.224412i	$-0.927954\pi$
$373$	−5.65685	+	9.79796i	−0.292901	+	0.507319i	0.681594	+	0.731731i	$0.261287\pi$
$374$	−2.00000	−	3.46410i	−0.103418	−	0.179124i
$375$	6.36396	+	11.0227i	0.328634	+	0.569210i
$376$	9.74264	−	16.8747i	0.502438	−	0.870249i
$377$	−14.7696			−0.760671
$378$		0			0
$379$	4.24264			0.217930			0.108965	−	0.994046i	$-0.465246\pi$
$379$	4.24264			0.217930			0.108965	+	0.994046i	$0.465246\pi$
$380$	1.91421	−	3.31552i	0.0981971	−	0.170082i
$381$	3.00000	+	5.19615i	0.153695	+	0.266207i
$382$	10.1569	+	17.5922i	0.519670	+	0.900095i
$383$	9.87868	−	17.1104i	0.504777	−	0.874299i	−0.495208	−	0.868775i	$-0.664908\pi$
$383$	9.87868	−	17.1104i	0.504777	−	0.874299i	0.999985	−	0.00552476i	$-0.00175859\pi$
$384$	−29.0711			−1.48353
$385$		0			0
$386$	−19.0711			−0.970692
$387$	4.03553	−	6.98975i	0.205138	−	0.355309i
$388$	−6.07107	−	10.5154i	−0.308212	−	0.533838i
$389$	5.75736	+	9.97204i	0.291910	+	0.505602i	0.974261	−	0.225422i	$-0.0723760\pi$
$389$	5.75736	+	9.97204i	0.291910	+	0.505602i	−0.682352	+	0.731024i	$0.739043\pi$
$390$	3.82843	−	6.63103i	0.193860	−	0.335775i
$391$	−22.3431			−1.12994
$392$		0			0
$393$	4.97056			0.250732
$394$	5.44975	−	9.43924i	0.274554	−	0.475542i
$395$	0.707107	+	1.22474i	0.0355784	+	0.0616236i
$396$	−0.792893	−	1.37333i	−0.0398444	−	0.0690125i
$397$	−4.31371	+	7.47156i	−0.216499	+	0.374987i	−0.953735	−	0.300648i	$-0.902797\pi$
$397$	−4.31371	+	7.47156i	−0.216499	+	0.374987i	0.737236	+	0.675635i	$0.236130\pi$
$398$	38.7990			1.94482
$399$		0			0
$400$	−12.0000			−0.600000
$401$	−0.242641	+	0.420266i	−0.0121169	+	0.0209871i	−0.872020	−	0.489470i	$-0.837190\pi$
$401$	−0.242641	+	0.420266i	−0.0121169	+	0.0209871i	0.859903	+	0.510457i	$0.170524\pi$
$402$	−2.00000	−	3.46410i	−0.0997509	−	0.172774i
$403$	−7.00000	−	12.1244i	−0.348695	−	0.603957i
$404$	35.0563	−	60.7194i	1.74412	−	3.02090i
$405$	5.00000			0.248452
$406$		0			0
$407$	−3.75736			−0.186245
$408$	−12.4853	+	21.6251i	−0.618114	+	1.07060i
$409$	−1.34315	−	2.32640i	−0.0664143	−	0.115033i	0.830906	−	0.556413i	$-0.187823\pi$
$409$	−1.34315	−	2.32640i	−0.0664143	−	0.115033i	−0.897320	+	0.441380i	$0.854489\pi$
$410$	−3.82843	−	6.63103i	−0.189073	−	0.327483i
$411$	−14.0208	+	24.2848i	−0.691596	+	1.19788i
$412$	22.9706			1.13168
$413$		0			0
$414$	−13.4853			−0.662765
$415$	−4.62132	+	8.00436i	−0.226852	+	0.392919i
$416$	−1.77817	−	3.07989i	−0.0871822	−	0.151004i
$417$	4.29289	+	7.43551i	0.210224	+	0.364118i
$418$	−0.500000	+	0.866025i	−0.0244558	+	0.0423587i
$419$	−6.07107			−0.296591			−0.148296	−	0.988943i	$-0.547379\pi$
$419$	−6.07107			−0.296591			−0.148296	+	0.988943i	$0.547379\pi$
$420$		0			0
$421$	−37.2132			−1.81366			−0.906830	−	0.421496i	$-0.861505\pi$
$421$	−37.2132			−1.81366			−0.906830	+	0.421496i	$0.861505\pi$
$422$	−1.41421	+	2.44949i	−0.0688428	+	0.119239i
$423$	2.20711	+	3.82282i	0.107313	+	0.185872i
$424$	−9.36396	−	16.2189i	−0.454754	−	0.787657i
$425$	8.00000	−	13.8564i	0.388057	−	0.672134i
$426$	−48.6274			−2.35601
$427$		0			0
$428$	−53.2132			−2.57216
$429$	−0.656854	+	1.13770i	−0.0317132	+	0.0549289i
$430$	−9.74264	−	16.8747i	−0.469832	−	0.813773i
$431$	5.02082	+	8.69631i	0.241844	+	0.418886i	0.961240	−	0.275714i	$-0.0889144\pi$
$431$	5.02082	+	8.69631i	0.241844	+	0.418886i	−0.719395	+	0.694601i	$0.755581\pi$
$432$	−8.48528	+	14.6969i	−0.408248	+	0.707107i
$433$	−28.0000			−1.34559			−0.672797	−	0.739827i	$-0.734907\pi$
$433$	−28.0000			−1.34559			−0.672797	+	0.739827i	$0.734907\pi$
$434$		0			0
$435$	−9.31371			−0.446558
$436$	18.4853	−	32.0174i	0.885284	−	1.53336i
$437$	2.79289	+	4.83743i	0.133602	+	0.231406i
$438$	25.8492	+	44.7722i	1.23512	+	2.13930i
$439$	−12.2426	+	21.2049i	−0.584309	+	1.01205i	0.410652	+	0.911792i	$0.365301\pi$
$439$	−12.2426	+	21.2049i	−0.584309	+	1.01205i	−0.994961	+	0.100261i	$0.968032\pi$
$440$	−1.82843			−0.0871668
$441$		0			0
$442$	−21.6569			−1.03011
$443$	−8.82843	+	15.2913i	−0.419451	+	0.726511i	−0.995884	−	0.0906335i	$-0.971111\pi$
$443$	−8.82843	+	15.2913i	−0.419451	+	0.726511i	0.576433	+	0.817144i	$0.304444\pi$
$444$	24.5563	+	42.5328i	1.16539	+	2.01852i
$445$	5.70711	+	9.88500i	0.270543	+	0.468594i
$446$	−2.70711	+	4.68885i	−0.128185	+	0.222023i
$447$	0.242641			0.0114765
$448$		0			0
$449$	9.65685			0.455735			0.227868	−	0.973692i	$-0.426825\pi$
$449$	9.65685			0.455735			0.227868	+	0.973692i	$0.426825\pi$
$450$	4.82843	−	8.36308i	0.227614	−	0.394239i
$451$	0.656854	+	1.13770i	0.0309301	+	0.0535724i
$452$	0.464466	+	0.804479i	0.0218466	+	0.0378395i
$453$	−12.2426	+	21.2049i	−0.575209	+	0.996292i
$454$	−48.8701			−2.29359
$455$		0			0
$456$	6.24264			0.292338
$457$	3.91421	−	6.77962i	0.183099	−	0.317137i	−0.759835	−	0.650116i	$-0.774720\pi$
$457$	3.91421	−	6.77962i	0.183099	−	0.317137i	0.942934	+	0.332979i	$0.108054\pi$
$458$	−15.0711	−	26.1039i	−0.704225	−	1.21975i
$459$	−11.3137	−	19.5959i	−0.528079	−	0.914659i
$460$	−10.6924	+	18.5198i	−0.498535	+	0.863488i
$461$	−29.9706			−1.39587			−0.697934	−	0.716162i	$-0.745897\pi$
$461$	−29.9706			−1.39587			−0.697934	+	0.716162i	$0.745897\pi$
$462$		0			0
$463$	−4.07107			−0.189199			−0.0945993	−	0.995515i	$-0.530157\pi$
$463$	−4.07107			−0.189199			−0.0945993	+	0.995515i	$0.530157\pi$
$464$	9.87868	−	17.1104i	0.458606	−	0.794329i
$465$	−4.41421	−	7.64564i	−0.204704	−	0.354558i
$466$	0.585786	+	1.01461i	0.0271360	+	0.0470010i
$467$	9.55025	−	16.5415i	0.441933	−	0.765450i	−0.555900	−	0.831249i	$-0.687626\pi$
$467$	9.55025	−	16.5415i	0.441933	−	0.765450i	0.997833	+	0.0657988i	$0.0209596\pi$
$468$	−8.58579			−0.396878
$469$		0			0
$470$	10.6569			0.491564
$471$	−4.36396	+	7.55860i	−0.201081	+	0.348282i
$472$	−15.0711	−	26.1039i	−0.693702	−	1.20153i
$473$	1.67157	+	2.89525i	0.0768590	+	0.133124i
$474$	−2.41421	+	4.18154i	−0.110889	+	0.192065i
$475$	−4.00000			−0.183533
$476$		0			0
$477$	4.24264			0.194257
$478$	2.41421	−	4.18154i	0.110424	−	0.191259i
$479$	−12.6924	−	21.9839i	−0.579930	−	1.00447i	−0.995487	−	0.0949010i	$-0.969747\pi$
$479$	−12.6924	−	21.9839i	−0.579930	−	1.00447i	0.415557	−	0.909567i	$-0.363587\pi$
$480$	−1.12132	−	1.94218i	−0.0511810	−	0.0886482i
$481$	−10.1716	+	17.6177i	−0.463784	+	0.803297i
$482$	−62.8701			−2.86365
$483$		0			0
$484$	−41.4558			−1.88436
$485$	1.58579	−	2.74666i	0.0720069	−	0.124720i
$486$	−11.9497	−	20.6976i	−0.542052	−	0.938861i
$487$	−7.58579	−	13.1390i	−0.343745	−	0.595383i	0.641380	−	0.767223i	$-0.278362\pi$
$487$	−7.58579	−	13.1390i	−0.343745	−	0.595383i	−0.985125	+	0.171840i	$0.945029\pi$
$488$	−26.1066	+	45.2180i	−1.18179	+	2.04692i
$489$	−5.55635			−0.251267
$490$		0			0
$491$	−1.44365			−0.0651510			−0.0325755	−	0.999469i	$-0.510371\pi$
$491$	−1.44365			−0.0651510			−0.0325755	+	0.999469i	$0.510371\pi$
$492$	8.58579	−	14.8710i	0.387077	−	0.670437i
$493$	13.1716	+	22.8138i	0.593218	+	1.02748i
$494$	2.70711	+	4.68885i	0.121798	+	0.210961i
$495$	0.207107	−	0.358719i	0.00930876	−	0.0161232i
$496$	18.7279			0.840909
$497$		0			0
$498$	−31.5563			−1.41407
$499$	−17.2782	+	29.9267i	−0.773477	+	1.33970i	0.162169	+	0.986763i	$0.448151\pi$
$499$	−17.2782	+	29.9267i	−0.773477	+	1.33970i	−0.935646	+	0.352939i	$0.885182\pi$
$500$	−17.2279	−	29.8396i	−0.770456	−	1.33447i
$501$	−9.24264	−	16.0087i	−0.412931	−	0.715217i
$502$	16.5711	−	28.7019i	0.739603	−	1.28103i
$503$	29.0416			1.29490			0.647451	−	0.762107i	$-0.275835\pi$
$503$	29.0416			1.29490			0.647451	+	0.762107i	$0.275835\pi$
$504$		0			0
$505$	18.3137			0.814949
$506$	2.79289	−	4.83743i	0.124159	−	0.215050i
$507$	−5.63604	−	9.76191i	−0.250305	−	0.433541i
$508$	−8.12132	−	14.0665i	−0.360325	−	0.624102i
$509$	−7.48528	+	12.9649i	−0.331779	+	0.574659i	−0.982861	−	0.184349i	$-0.940982\pi$
$509$	−7.48528	+	12.9649i	−0.331779	+	0.574659i	0.651082	+	0.759008i	$0.274316\pi$
$510$	−13.6569			−0.604736
$511$		0			0
$512$	31.2426			1.38074
$513$	−2.82843	+	4.89898i	−0.124878	+	0.216295i
$514$	−11.2426	−	19.4728i	−0.495892	−	0.858909i
$515$	3.00000	+	5.19615i	0.132196	+	0.228970i
$516$	21.8492	−	37.8440i	0.961859	−	1.66599i
$517$	−1.82843			−0.0804141
$518$		0			0
$519$	−10.3431			−0.454014
$520$	−4.94975	+	8.57321i	−0.217061	+	0.375960i
$521$	20.7782	+	35.9889i	0.910308	+	1.57670i	0.813629	+	0.581385i	$0.197489\pi$
$521$	20.7782	+	35.9889i	0.910308	+	1.57670i	0.0966796	+	0.995316i	$0.469178\pi$
$522$	7.94975	+	13.7694i	0.347951	+	0.602669i
$523$	−6.17157	+	10.6895i	−0.269864	+	0.467418i	−0.968827	−	0.247740i	$-0.920312\pi$
$523$	−6.17157	+	10.6895i	−0.269864	+	0.467418i	0.698962	+	0.715158i	$0.253645\pi$
$524$	−13.4558			−0.587821
$525$		0			0
$526$	−39.7990			−1.73532
$527$	−12.4853	+	21.6251i	−0.543867	+	0.942006i
$528$	−0.878680	−	1.52192i	−0.0382396	−	0.0662330i
$529$	−4.10051	−	7.10228i	−0.178283	−	0.308795i
$530$	5.12132	−	8.87039i	0.222456	−	0.385305i
$531$	6.82843			0.296328
$532$		0			0
$533$	7.11270			0.308085
$534$	−19.4853	+	33.7495i	−0.843211	+	1.46048i
$535$	−6.94975	−	12.0373i	−0.300464	−	0.520419i
$536$	2.58579	+	4.47871i	0.111689	+	0.193451i
$537$	12.5858	−	21.7992i	0.543117	−	0.940706i
$538$	−9.65685			−0.416337
$539$		0			0
$540$	−21.6569			−0.931963
$541$	11.5711	−	20.0417i	0.497479	−	0.861659i	−0.502517	−	0.864567i	$-0.667592\pi$
$541$	11.5711	−	20.0417i	0.497479	−	0.861659i	0.999996	+	0.00290849i	$0.000925802\pi$
$542$	18.3995	+	31.8689i	0.790326	+	1.36888i
$543$	−7.00000	−	12.1244i	−0.300399	−	0.520306i
$544$	−3.17157	+	5.49333i	−0.135980	+	0.235524i
$545$	9.65685			0.413654
$546$		0			0
$547$	−1.55635			−0.0665447			−0.0332723	−	0.999446i	$-0.510593\pi$
$547$	−1.55635			−0.0665447			−0.0332723	+	0.999446i	$0.510593\pi$
$548$	37.9558	−	65.7415i	1.62139	−	2.80834i
$549$	−5.91421	−	10.2437i	−0.252412	−	0.437191i
$550$	2.00000	+	3.46410i	0.0852803	+	0.147710i
$551$	3.29289	−	5.70346i	0.140282	−	0.242975i
$552$	−34.8701			−1.48417
$553$		0			0
$554$	54.2132			2.30330
$555$	−6.41421	+	11.1097i	−0.272268	+	0.471582i
$556$	−11.6213	−	20.1287i	−0.492854	−	0.853648i
$557$	−7.91421	−	13.7078i	−0.335336	−	0.580819i	0.648213	−	0.761459i	$-0.275517\pi$
$557$	−7.91421	−	13.7078i	−0.335336	−	0.580819i	−0.983549	+	0.180640i	$0.942183\pi$
$558$	−7.53553	+	13.0519i	−0.319005	+	0.552532i
$559$	18.1005			0.765570
$560$		0			0
$561$	2.34315			0.0989277
$562$	−34.0919	+	59.0489i	−1.43808	+	2.49083i
$563$	2.94975	+	5.10911i	0.124317	+	0.215323i	0.921466	−	0.388460i	$-0.126993\pi$
$563$	2.94975	+	5.10911i	0.124317	+	0.215323i	−0.797149	+	0.603783i	$0.793659\pi$
$564$	11.9497	+	20.6976i	0.503175	+	0.871525i
$565$	−0.121320	+	0.210133i	−0.00510399	+	0.00884036i
$566$	72.5980			3.05152
$567$		0			0
$568$	62.8701			2.63797
$569$	4.51472	−	7.81972i	0.189267	−	0.327820i	−0.755739	−	0.654873i	$-0.772722\pi$
$569$	4.51472	−	7.81972i	0.189267	−	0.327820i	0.945006	+	0.327053i	$0.106056\pi$
$570$	1.70711	+	2.95680i	0.0715028	+	0.123847i
$571$	−0.449747	−	0.778985i	−0.0188213	−	0.0325995i	0.856461	−	0.516211i	$-0.172658\pi$
$571$	−0.449747	−	0.778985i	−0.0188213	−	0.0325995i	−0.875283	+	0.483612i	$0.839325\pi$
$572$	1.77817	−	3.07989i	0.0743492	−	0.128777i
$573$	−11.8995			−0.497109
$574$		0			0
$575$	22.3431			0.931774
$576$	−4.91421	+	8.51167i	−0.204759	+	0.354653i
$577$	−2.98528	−	5.17066i	−0.124279	−	0.215257i	0.797172	−	0.603752i	$-0.206328\pi$
$577$	−2.98528	−	5.17066i	−0.124279	−	0.215257i	−0.921451	+	0.388495i	$0.872995\pi$
$578$	−1.20711	−	2.09077i	−0.0502090	−	0.0869646i
$579$	5.58579	−	9.67487i	0.232137	−	0.402074i
$580$	25.2132			1.04692
$581$		0			0
$582$	10.8284			0.448853
$583$	−0.878680	+	1.52192i	−0.0363912	+	0.0630314i
$584$	−33.4203	−	57.8857i	−1.38294	−	2.39533i
$585$	−1.12132	−	1.94218i	−0.0463609	−	0.0802994i
$586$	−3.82843	+	6.63103i	−0.158151	+	0.273925i
$587$	−14.0000			−0.577842			−0.288921	−	0.957353i	$-0.593296\pi$
$587$	−14.0000			−0.577842			−0.288921	+	0.957353i	$0.593296\pi$
$588$		0			0
$589$	6.24264			0.257224
$590$	8.24264	−	14.2767i	0.339344	−	0.587761i
$591$	3.19239	+	5.52938i	0.131317	+	0.227448i
$592$	−13.6066	−	23.5673i	−0.559228	−	0.968611i
$593$	5.91421	−	10.2437i	0.242868	−	0.420659i	−0.718662	−	0.695359i	$-0.755245\pi$
$593$	5.91421	−	10.2437i	0.242868	−	0.420659i	0.961530	+	0.274700i	$0.0885786\pi$
$594$	5.65685			0.232104
$595$		0			0
$596$	−0.656854			−0.0269058
$597$	−11.3640	+	19.6830i	−0.465096	+	0.805570i
$598$	−15.1213	−	26.1909i	−0.618357	−	1.07103i
$599$	−13.8492	−	23.9876i	−0.565865	−	0.980106i	−0.996969	−	0.0778042i	$-0.975209\pi$
$599$	−13.8492	−	23.9876i	−0.565865	−	0.980106i	0.431104	−	0.902302i	$-0.358124\pi$
$600$	12.4853	−	21.6251i	0.509709	−	0.882843i
$601$	34.7279			1.41658			0.708291	−	0.705921i	$-0.249467\pi$
$601$	34.7279			1.41658			0.708291	+	0.705921i	$0.249467\pi$
$602$		0			0
$603$	−1.17157			−0.0477101
$604$	33.1421	−	57.4039i	1.34853	−	2.33573i
$605$	−5.41421	−	9.37769i	−0.220119	−	0.381257i
$606$	31.2635	+	54.1499i	1.26999	+	2.19969i
$607$	−16.2635	+	28.1691i	−0.660113	+	1.14335i	0.320472	+	0.947258i	$0.396158\pi$
$607$	−16.2635	+	28.1691i	−0.660113	+	1.14335i	−0.980586	+	0.196092i	$0.937175\pi$
$608$	1.58579			0.0643121
$609$		0			0
$610$	−28.5563			−1.15621
$611$	−4.94975	+	8.57321i	−0.200245	+	0.346835i
$612$	7.65685	+	13.2621i	0.309510	+	0.536087i
$613$	15.6569	+	27.1185i	0.632374	+	1.09530i	0.987065	+	0.160321i	$0.0512529\pi$
$613$	15.6569	+	27.1185i	0.632374	+	1.09530i	−0.354691	+	0.934984i	$0.615414\pi$
$614$	−35.3848	+	61.2882i	−1.42801	+	2.47339i
$615$	4.48528			0.180864
$616$		0			0
$617$	8.45584			0.340419			0.170210	−	0.985408i	$-0.445555\pi$
$617$	8.45584			0.340419			0.170210	+	0.985408i	$0.445555\pi$
$618$	−10.2426	+	17.7408i	−0.412019	+	0.713639i
$619$	17.2782	+	29.9267i	0.694468	+	1.20285i	0.970360	+	0.241666i	$0.0776938\pi$
$619$	17.2782	+	29.9267i	0.694468	+	1.20285i	−0.275891	+	0.961189i	$0.588973\pi$
$620$	11.9497	+	20.6976i	0.479913	+	0.831234i
$621$	15.7990	−	27.3647i	0.633992	−	1.09811i
$622$	−57.4558			−2.30377
$623$		0			0
$624$	−9.51472			−0.380894
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	8.03553	+	13.9180i	0.321165	+	0.556273i
$627$	−0.292893	−	0.507306i	−0.0116970	−	0.0202598i
$628$	11.8137	−	20.4619i	0.471418	−	0.816520i
$629$	36.2843			1.44675
$630$		0			0
$631$	−36.5563			−1.45529			−0.727643	−	0.685956i	$-0.759384\pi$
$631$	−36.5563			−1.45529			−0.727643	+	0.685956i	$0.759384\pi$
$632$	3.12132	−	5.40629i	0.124159	−	0.215050i
$633$	−0.828427	−	1.43488i	−0.0329270	−	0.0570313i
$634$	−24.4350	−	42.3227i	−0.970439	−	1.68085i
$635$	2.12132	−	3.67423i	0.0841820	−	0.145808i
$636$	22.9706			0.910842
$637$		0			0
$638$	−6.58579			−0.260734
$639$	−7.12132	+	12.3345i	−0.281715	+	0.487945i
$640$	10.2782	+	17.8023i	0.406281	+	0.703699i
$641$	17.8995	+	31.0028i	0.706988	+	1.22454i	0.965969	+	0.258656i	$0.0832797\pi$
$641$	17.8995	+	31.0028i	0.706988	+	1.22454i	−0.258982	+	0.965882i	$0.583387\pi$
$642$	23.7279	−	41.0980i	0.936466	−	1.62201i
$643$	−1.85786			−0.0732670			−0.0366335	−	0.999329i	$-0.511663\pi$
$643$	−1.85786			−0.0732670			−0.0366335	+	0.999329i	$0.511663\pi$
$644$		0			0
$645$	11.4142			0.449434
$646$	4.82843	−	8.36308i	0.189972	−	0.329041i
$647$	−18.1066	−	31.3616i	−0.711844	−	1.23295i	−0.964164	−	0.265306i	$-0.914527\pi$
$647$	−18.1066	−	31.3616i	−0.711844	−	1.23295i	0.252320	−	0.967644i	$-0.418806\pi$
$648$	−11.0355	−	19.1141i	−0.433517	−	0.750873i
$649$	−1.41421	+	2.44949i	−0.0555127	+	0.0961509i
$650$	21.6569			0.849452
$651$		0			0
$652$	15.0416			0.589076
$653$	15.0711	−	26.1039i	0.589776	−	1.02152i	−0.404485	−	0.914545i	$-0.632549\pi$
$653$	15.0711	−	26.1039i	0.589776	−	1.02152i	0.994261	−	0.106978i	$-0.0341175\pi$
$654$	16.4853	+	28.5533i	0.644626	+	1.11652i
$655$	−1.75736	−	3.04384i	−0.0686657	−	0.118932i
$656$	−4.75736	+	8.23999i	−0.185744	+	0.321717i
$657$	15.1421			0.590751
$658$		0			0
$659$	10.0416			0.391166			0.195583	−	0.980687i	$-0.437340\pi$
$659$	10.0416			0.391166			0.195583	+	0.980687i	$0.437340\pi$
$660$	1.12132	−	1.94218i	0.0436473	−	0.0755994i
$661$	1.36396	+	2.36245i	0.0530519	+	0.0918886i	0.891332	−	0.453352i	$-0.149772\pi$
$661$	1.36396	+	2.36245i	0.0530519	+	0.0918886i	−0.838280	+	0.545240i	$0.816438\pi$
$662$	−37.9706	−	65.7669i	−1.47577	−	2.55610i
$663$	6.34315	−	10.9867i	0.246347	−	0.426686i
$664$	40.7990			1.58331
$665$		0			0
$666$	21.8995			0.848588
$667$	−18.3934	+	31.8583i	−0.712195	+	1.23356i
$668$	25.0208	+	43.3373i	0.968084	+	1.67677i
$669$	−1.58579	−	2.74666i	−0.0613100	−	0.106192i
$670$	−1.41421	+	2.44949i	−0.0546358	+	0.0946320i
$671$	4.89949			0.189143
$672$		0			0
$673$	−3.79899			−0.146440			−0.0732201	−	0.997316i	$-0.523328\pi$
$673$	−3.79899			−0.146440			−0.0732201	+	0.997316i	$0.523328\pi$
$674$	23.6066	−	40.8878i	0.909292	−	1.57494i
$675$	11.3137	+	19.5959i	0.435465	+	0.754247i
$676$	15.2574	+	26.4265i	0.586822	+	1.01640i
$677$	11.6569	−	20.1903i	0.448009	−	0.775975i	−0.550247	−	0.835002i	$-0.685466\pi$
$677$	11.6569	−	20.1903i	0.448009	−	0.775975i	0.998256	+	0.0590270i	$0.0187998\pi$
$678$	−0.828427			−0.0318156
$679$		0			0
$680$	17.6569			0.677109
$681$	14.3137	−	24.7921i	0.548503	−	0.950034i
$682$	−3.12132	−	5.40629i	−0.119522	−	0.207017i
$683$	3.24264	+	5.61642i	0.124076	+	0.214906i	0.921371	−	0.388683i	$-0.127070\pi$
$683$	3.24264	+	5.61642i	0.124076	+	0.214906i	−0.797295	+	0.603589i	$0.793737\pi$
$684$	1.91421	−	3.31552i	0.0731918	−	0.126772i
$685$	19.8284			0.757605
$686$		0			0
$687$	17.6569			0.673651
$688$	−12.1066	+	20.9692i	−0.461560	+	0.799445i
$689$	4.75736	+	8.23999i	0.181241	+	0.313919i
$690$	−9.53553	−	16.5160i	−0.363012	−	0.628754i
$691$	15.4853	−	26.8213i	0.589088	−	1.02033i	−0.405264	−	0.914200i	$-0.632821\pi$
$691$	15.4853	−	26.8213i	0.589088	−	1.02033i	0.994352	−	0.106131i	$-0.0338462\pi$
$692$	28.0000			1.06440
$693$		0			0
$694$	−65.2843			−2.47816
$695$	3.03553	−	5.25770i	0.115144	−	0.199436i
$696$	20.5563	+	35.6046i	0.779186	+	1.34959i
$697$	−6.34315	−	10.9867i	−0.240264	−	0.416149i
$698$	−5.41421	+	9.37769i	−0.204931	+	0.354951i
$699$	−0.686292			−0.0259579
$700$		0			0
$701$	−1.82843			−0.0690587			−0.0345294	−	0.999404i	$-0.510993\pi$
$701$	−1.82843			−0.0690587			−0.0345294	+	0.999404i	$0.510993\pi$
$702$	15.3137	−	26.5241i	0.577979	−	1.00109i
$703$	−4.53553	−	7.85578i	−0.171061	−	0.296286i
$704$	−2.03553	−	3.52565i	−0.0767171	−	0.132878i
$705$	−3.12132	+	5.40629i	−0.117556	+	0.203612i
$706$	1.17157			0.0440927
$707$		0			0
$708$	36.9706			1.38944
$709$	21.4706	−	37.1881i	0.806344	−	1.39663i	−0.109036	−	0.994038i	$-0.534776\pi$
$709$	21.4706	−	37.1881i	0.806344	−	1.39663i	0.915380	−	0.402591i	$-0.131890\pi$
$710$	17.1924	+	29.7781i	0.645219	+	1.11755i
$711$	0.707107	+	1.22474i	0.0265186	+	0.0459315i
$712$	25.1924	−	43.6345i	0.944125	−	1.63527i
$713$	−34.8701			−1.30589
$714$		0			0
$715$	0.928932			0.0347401
$716$	−34.0711	+	59.0128i	−1.27330	+	2.20541i
$717$	1.41421	+	2.44949i	0.0528148	+	0.0914779i
$718$	6.32843	+	10.9612i	0.236175	+	0.409067i
$719$	26.0416	−	45.1054i	0.971189	−	1.68215i	0.279211	−	0.960230i	$-0.409927\pi$
$719$	26.0416	−	45.1054i	0.971189	−	1.68215i	0.691978	−	0.721919i	$-0.256740\pi$
$720$	3.00000			0.111803
$721$		0			0
$722$	−2.41421			−0.0898477
$723$	18.4142	−	31.8944i	0.684832	−	1.18616i
$724$	18.9497	+	32.8219i	0.704262	+	1.21982i
$725$	−13.1716	−	22.8138i	−0.489180	−	0.847285i
$726$	18.4853	−	32.0174i	0.686053	−	1.18828i
$727$	−20.0711			−0.744395			−0.372197	−	0.928154i	$-0.621396\pi$
$727$	−20.0711			−0.744395			−0.372197	+	0.928154i	$0.621396\pi$
$728$		0			0
$729$	29.0000			1.07407
$730$	18.2782	−	31.6587i	0.676506	−	1.17174i
$731$	−16.1421	−	27.9590i	−0.597038	−	1.03410i
$732$	−32.0208	−	55.4617i	−1.18352	−	2.04992i
$733$	10.7279	−	18.5813i	0.396245	−	0.686316i	−0.597014	−	0.802231i	$-0.703646\pi$
$733$	10.7279	−	18.5813i	0.396245	−	0.686316i	0.993259	+	0.115914i	$0.0369798\pi$
$734$	−58.7696			−2.16922
$735$		0			0
$736$	−8.85786			−0.326505
$737$	0.242641	−	0.420266i	0.00893778	−	0.0154807i
$738$	−3.82843	−	6.63103i	−0.140926	−	0.244092i
$739$	4.17157	+	7.22538i	0.153454	+	0.265790i	0.932495	−	0.361183i	$-0.117627\pi$
$739$	4.17157	+	7.22538i	0.153454	+	0.265790i	−0.779041	+	0.626973i	$0.784294\pi$
$740$	17.3640	−	30.0753i	0.638312	−	1.10559i
$741$	−3.17157			−0.116511
$742$		0			0
$743$	−2.87006			−0.105292			−0.0526461	−	0.998613i	$-0.516766\pi$
$743$	−2.87006			−0.105292			−0.0526461	+	0.998613i	$0.516766\pi$
$744$	−19.4853	+	33.7495i	−0.714365	+	1.23732i
$745$	−0.0857864	−	0.148586i	−0.00314297	−	0.00544379i
$746$	13.6569	+	23.6544i	0.500013	+	0.866048i
$747$	−4.62132	+	8.00436i	−0.169085	+	0.292864i
$748$	−6.34315			−0.231928
$749$		0			0
$750$	30.7279			1.12203
$751$	−4.72792	+	8.18900i	−0.172524	+	0.298821i	−0.939302	−	0.343092i	$-0.888526\pi$
$751$	−4.72792	+	8.18900i	−0.172524	+	0.298821i	0.766777	+	0.641913i	$0.221859\pi$
$752$	−6.62132	−	11.4685i	−0.241455	−	0.418212i
$753$	9.70711	+	16.8132i	0.353747	+	0.612707i
$754$	−17.8284	+	30.8797i	−0.649273	+	1.12457i
$755$	17.3137			0.630110
$756$		0			0
$757$	−5.00000			−0.181728			−0.0908640	−	0.995863i	$-0.528963\pi$
$757$	−5.00000			−0.181728			−0.0908640	+	0.995863i	$0.528963\pi$
$758$	5.12132	−	8.87039i	0.186015	−	0.322187i
$759$	1.63604	+	2.83370i	0.0593845	+	0.102857i
$760$	−2.20711	−	3.82282i	−0.0800602	−	0.138668i
$761$	−17.0563	+	29.5425i	−0.618292	+	1.07091i	0.371505	+	0.928431i	$0.378842\pi$
$761$	−17.0563	+	29.5425i	−0.618292	+	1.07091i	−0.989797	+	0.142483i	$0.954492\pi$
$762$	14.4853			0.524746
$763$		0			0
$764$	32.2132			1.16543
$765$	−2.00000	+	3.46410i	−0.0723102	+	0.125245i
$766$	−23.8492	−	41.3081i	−0.861708	−	1.49252i
$767$	7.65685	+	13.2621i	0.276473	+	0.478865i
$768$	−21.1924	+	36.7063i	−0.764714	+	1.32452i
$769$	43.4264			1.56600			0.782998	−	0.622024i	$-0.213689\pi$
$769$	43.4264			1.56600			0.782998	+	0.622024i	$0.213689\pi$
$770$		0			0
$771$	13.1716			0.474363
$772$	−15.1213	+	26.1909i	−0.544228	+	0.942631i
$773$	−17.1213	−	29.6550i	−0.615811	−	1.06662i	−0.990242	−	0.139361i	$-0.955495\pi$
$773$	−17.1213	−	29.6550i	−0.615811	−	1.06662i	0.374431	−	0.927255i	$-0.377838\pi$
$774$	−9.74264	−	16.8747i	−0.350192	−	0.606550i
$775$	12.4853	−	21.6251i	0.448485	−	0.776798i
$776$	−14.0000			−0.502571
$777$		0			0
$778$	27.7990			0.996642
$779$	−1.58579	+	2.74666i	−0.0568167	+	0.0984094i
$780$	−6.07107	−	10.5154i	−0.217379	−	0.376512i
$781$	−2.94975	−	5.10911i	−0.105550	−	0.182818i
$782$	−26.9706	+	46.7144i	−0.964465	+	1.67050i
$783$	−37.2548			−1.33138
$784$		0			0
$785$	6.17157			0.220273
$786$	6.00000	−	10.3923i	0.214013	−	0.370681i
$787$	20.5061	+	35.5176i	0.730963	+	1.26607i	0.956472	+	0.291825i	$0.0942623\pi$
$787$	20.5061	+	35.5176i	0.730963	+	1.26607i	−0.225508	+	0.974241i	$0.572404\pi$
$788$	−8.64214	−	14.9686i	−0.307863	−	0.533235i
$789$	11.6569	−	20.1903i	0.414995	−	0.718792i
$790$	3.41421			0.121472
$791$		0			0
$792$	−1.82843			−0.0649703
$793$	13.2635	−	22.9730i	0.470999	−	0.815794i
$794$	10.4142	+	18.0379i	0.369587	+	0.640143i
$795$	3.00000	+	5.19615i	0.106399	+	0.184289i
$796$	30.7635	−	53.2839i	1.09038	−	1.88860i
$797$	30.2426			1.07125			0.535625	−	0.844456i	$-0.320076\pi$
$797$	30.2426			1.07125			0.535625	+	0.844456i	$0.320076\pi$
$798$		0			0
$799$	17.6569			0.624655
$800$	3.17157	−	5.49333i	0.112132	−	0.194218i
$801$	5.70711	+	9.88500i	0.201651	+	0.349269i
$802$	0.585786	+	1.01461i	0.0206848	+	0.0358272i
$803$	−3.13604	+	5.43178i	−0.110668	+	0.191683i
$804$	−6.34315			−0.223706
$805$		0			0
$806$	−33.7990			−1.19052
$807$	2.82843	−	4.89898i	0.0995654	−	0.172452i
$808$	−40.4203	−	70.0100i	−1.42198	−	2.46294i
$809$	−15.5711	−	26.9699i	−0.547450	−	0.948211i	−0.998448	−	0.0556859i	$-0.982265\pi$
$809$	−15.5711	−	26.9699i	−0.547450	−	0.948211i	0.450999	−	0.892525i	$-0.351068\pi$
$810$	6.03553	−	10.4539i	0.212067	−	0.367311i
$811$	0.544156			0.0191079			0.00955395	−	0.999954i	$-0.496959\pi$
$811$	0.544156			0.0191079			0.00955395	+	0.999954i	$0.496959\pi$
$812$		0			0
$813$	−21.5563			−0.756014
$814$	−4.53553	+	7.85578i	−0.158970	+	0.275345i
$815$	1.96447	+	3.40256i	0.0688122	+	0.119186i
$816$	8.48528	+	14.6969i	0.297044	+	0.514496i
$817$	−4.03553	+	6.98975i	−0.141185	+	0.244540i
$818$	−6.48528			−0.226753
$819$		0			0
$820$	−12.1421			−0.424022
$821$	−5.05635	+	8.75785i	−0.176468	+	0.305651i	−0.940668	−	0.339328i	$-0.889800\pi$
$821$	−5.05635	+	8.75785i	−0.176468	+	0.305651i	0.764200	+	0.644979i	$0.223134\pi$
$822$	33.8492	+	58.6286i	1.18063	+	2.04491i
$823$	3.10660	+	5.38079i	0.108289	+	0.187563i	0.915077	−	0.403278i	$-0.132129\pi$
$823$	3.10660	+	5.38079i	0.108289	+	0.187563i	−0.806788	+	0.590841i	$0.798796\pi$
$824$	13.2426	−	22.9369i	0.461329	−	0.799046i
$825$	−2.34315			−0.0815779
$826$		0			0
$827$	12.2843			0.427166			0.213583	−	0.976925i	$-0.431487\pi$
$827$	12.2843			0.427166			0.213583	+	0.976925i	$0.431487\pi$
$828$	−10.6924	+	18.5198i	−0.371586	+	0.643606i
$829$	−14.1421	−	24.4949i	−0.491177	−	0.850743i	0.508772	−	0.860901i	$-0.330100\pi$
$829$	−14.1421	−	24.4949i	−0.491177	−	0.850743i	−0.999948	+	0.0101585i	$0.996766\pi$
$830$	11.1569	+	19.3242i	0.387260	+	0.670754i
$831$	−15.8787	+	27.5027i	−0.550825	+	0.954057i
$832$	−22.0416			−0.764156
$833$		0			0
$834$	20.7279			0.717749
$835$	−6.53553	+	11.3199i	−0.226171	+	0.391740i
$836$	0.792893	+	1.37333i	0.0274228	+	0.0474977i
$837$	−17.6569	−	30.5826i	−0.610310	−	1.05709i
$838$	−7.32843	+	12.6932i	−0.253156	+	0.438480i
$839$	19.7990			0.683537			0.341769	−	0.939784i	$-0.388974\pi$
$839$	19.7990			0.683537			0.341769	+	0.939784i	$0.388974\pi$
$840$		0			0
$841$	14.3726			0.495606
$842$	−44.9203	+	77.8043i	−1.54806	+	2.68131i
$843$	−19.9706	−	34.5900i	−0.687823	−	1.19134i
$844$	2.24264	+	3.88437i	0.0771949	+	0.133705i
$845$	−3.98528	+	6.90271i	−0.137098	+	0.237460i
$846$	10.6569			0.366390
$847$		0			0
$848$	−12.7279			−0.437079
$849$	−21.2635	+	36.8294i	−0.729760	+	1.26398i
$850$	−19.3137	−	33.4523i	−0.662455	−	1.14741i
$851$	25.3345	+	43.8807i	0.868456	+	1.50421i
$852$	−38.5563	+	66.7816i	−1.32092	+	2.28790i
$853$	−43.9706			−1.50552			−0.752762	−	0.658293i	$-0.771279\pi$
$853$	−43.9706			−1.50552			−0.752762	+	0.658293i	$0.771279\pi$
$854$		0			0
$855$	1.00000			0.0341993
$856$	−30.6777	+	53.1353i	−1.04854	+	1.81613i
$857$	−6.48528	−	11.2328i	−0.221533	−	0.383706i	0.733741	−	0.679430i	$-0.237773\pi$
$857$	−6.48528	−	11.2328i	−0.221533	−	0.383706i	−0.955274	+	0.295723i	$0.904439\pi$
$858$	1.58579	+	2.74666i	0.0541379	+	0.0937695i
$859$	−6.03553	+	10.4539i	−0.205930	+	0.356681i	−0.950429	−	0.310943i	$-0.899355\pi$
$859$	−6.03553	+	10.4539i	−0.205930	+	0.356681i	0.744499	+	0.667624i	$0.232689\pi$
$860$	−30.8995			−1.05366
$861$		0			0
$862$	24.2426			0.825708
$863$	−2.29289	+	3.97141i	−0.0780510	+	0.135188i	−0.902409	−	0.430881i	$-0.858203\pi$
$863$	−2.29289	+	3.97141i	−0.0780510	+	0.135188i	0.824358	+	0.566069i	$0.191536\pi$
$864$	−4.48528	−	7.76874i	−0.152592	−	0.264298i
$865$	3.65685	+	6.33386i	0.124337	+	0.215358i
$866$	−33.7990	+	58.5416i	−1.14854	+	1.98932i
$867$	1.41421			0.0480292
$868$		0			0
$869$	−0.585786			−0.0198714
$870$	−11.2426	+	19.4728i	−0.381161	+	0.660191i
$871$	−1.31371	−	2.27541i	−0.0445133	−	0.0770993i
$872$	−21.3137	−	36.9164i	−0.721773	−	1.25015i
$873$	1.58579	−	2.74666i	0.0536707	−	0.0929604i
$874$	13.4853			0.456146
$875$		0			0
$876$	81.9828			2.76994
$877$	13.9497	−	24.1617i	0.471050	−	0.815882i	−0.528402	−	0.848994i	$-0.677209\pi$
$877$	13.9497	−	24.1617i	0.471050	−	0.815882i	0.999452	+	0.0331126i	$0.0105420\pi$
$878$	29.5563	+	51.1931i	0.997478	+	1.72768i
$879$	−2.24264	−	3.88437i	−0.0756424	−	0.131016i
$880$	−0.621320	+	1.07616i	−0.0209447	+	0.0362773i
$881$	52.2843			1.76150			0.880751	−	0.473580i	$-0.157038\pi$
$881$	52.2843			1.76150			0.880751	+	0.473580i	$0.157038\pi$
$882$		0			0
$883$	−5.65685			−0.190368			−0.0951842	−	0.995460i	$-0.530344\pi$
$883$	−5.65685			−0.190368			−0.0951842	+	0.995460i	$0.530344\pi$
$884$	−17.1716	+	29.7420i	−0.577542	+	1.00033i
$885$	4.82843	+	8.36308i	0.162306	+	0.281122i
$886$	21.3137	+	36.9164i	0.716048	+	1.24023i
$887$	−10.6569	+	18.4582i	−0.357822	+	0.619766i	−0.987597	−	0.157012i	$-0.949814\pi$
$887$	−10.6569	+	18.4582i	−0.357822	+	0.619766i	0.629775	+	0.776778i	$0.283147\pi$
$888$	56.6274			1.90029
$889$		0			0
$890$	27.5563			0.923691
$891$	−1.03553	+	1.79360i	−0.0346917	+	0.0600878i
$892$	4.29289	+	7.43551i	0.143737	+	0.248959i
$893$	−2.20711	−	3.82282i	−0.0738580	−	0.127926i
$894$	0.292893	−	0.507306i	0.00979581	−	0.0169668i
$895$	−17.7990			−0.594955
$896$		0			0
$897$	17.7157			0.591511
$898$	11.6569	−	20.1903i	0.388994	−	0.673758i
$899$	20.5563	+	35.6046i	0.685593	+	1.18748i
$900$	−7.65685	−	13.2621i	−0.255228	−	0.442069i
$901$	8.48528	−	14.6969i	0.282686	−	0.489626i
$902$	3.17157			0.105602
$903$		0			0
$904$	1.07107			0.0356232
$905$	−4.94975	+	8.57321i	−0.164535	+	0.284983i
$906$	29.5563	+	51.1931i	0.981944	+	1.70078i
$907$	−15.7071	−	27.2055i	−0.521546	−	0.903344i	−0.999686	−	0.0250604i	$-0.992022\pi$
$907$	−15.7071	−	27.2055i	−0.521546	−	0.903344i	0.478140	−	0.878284i	$-0.341311\pi$
$908$	−38.7487	+	67.1148i	−1.28592	+	2.22728i
$909$	18.3137			0.607427
$910$		0			0
$911$	9.27208			0.307198			0.153599	−	0.988133i	$-0.450914\pi$
$911$	9.27208			0.307198			0.153599	+	0.988133i	$0.450914\pi$
$912$	2.12132	−	3.67423i	0.0702439	−	0.121666i
$913$	−1.91421	−	3.31552i	−0.0633512	−	0.109728i
$914$	−9.44975	−	16.3674i	−0.312570	−	0.541387i
$915$	8.36396	−	14.4868i	0.276504	−	0.478919i
$916$	−47.7990			−1.57932
$917$		0			0
$918$	−54.6274			−1.80297
$919$	9.52082	−	16.4905i	0.314063	−	0.543973i	−0.665175	−	0.746687i	$-0.731643\pi$
$919$	9.52082	−	16.4905i	0.314063	−	0.543973i	0.979238	+	0.202715i	$0.0649764\pi$
$920$	12.3284	+	21.3535i	0.406456	+	0.704003i
$921$	−20.7279	−	35.9018i	−0.683008	−	1.18300i
$922$	−36.1777	+	62.6616i	−1.19145	+	2.06365i
$923$	−31.9411			−1.05135
$924$		0			0
$925$	−36.2843			−1.19302
$926$	−4.91421	+	8.51167i	−0.161491	+	0.279711i
$927$	3.00000	+	5.19615i	0.0985329	+	0.170664i
$928$	5.22183	+	9.04447i	0.171415	+	0.296899i
$929$	7.50000	−	12.9904i	0.246067	−	0.426201i	−0.716364	−	0.697727i	$-0.754195\pi$
$929$	7.50000	−	12.9904i	0.246067	−	0.426201i	0.962431	+	0.271526i	$0.0875283\pi$
$930$	−21.3137			−0.698904
$931$		0			0
$932$	1.85786			0.0608564
$933$	16.8284	−	29.1477i	0.550938	−	0.954253i
$934$	−23.0563	−	39.9348i	−0.754427	−	1.30671i
$935$	−0.828427	−	1.43488i	−0.0270925	−	0.0469255i
$936$	−4.94975	+	8.57321i	−0.161788	+	0.280224i
$937$	33.6863			1.10048			0.550242	−	0.835006i	$-0.314536\pi$
$937$	33.6863			1.10048			0.550242	+	0.835006i	$0.314536\pi$
$938$		0			0
$939$	−9.41421			−0.307221
$940$	8.44975	−	14.6354i	0.275600	−	0.477354i
$941$	2.02082	+	3.50015i	0.0658767	+	0.114102i	0.897083	−	0.441863i	$-0.145682\pi$
$941$	2.02082	+	3.50015i	0.0658767	+	0.114102i	−0.831206	+	0.555965i	$0.812349\pi$
$942$	10.5355	+	18.2481i	0.343266	+	0.594555i
$943$	8.85786	−	15.3423i	0.288452	−	0.499613i
$944$	−20.4853			−0.666739
$945$		0			0
$946$	8.07107			0.262413
$947$	−1.82843	+	3.16693i	−0.0594159	+	0.102911i	−0.894203	−	0.447661i	$-0.852257\pi$
$947$	−1.82843	+	3.16693i	−0.0594159	+	0.102911i	0.834787	+	0.550572i	$0.185590\pi$
$948$	3.82843	+	6.63103i	0.124342	+	0.215366i
$949$	16.9792	+	29.4088i	0.551168	+	0.954650i
$950$	−4.82843	+	8.36308i	−0.156655	+	0.271334i
$951$	28.6274			0.928308
$952$		0			0
$953$	−3.41421			−0.110597			−0.0552986	−	0.998470i	$-0.517611\pi$
$953$	−3.41421			−0.110597			−0.0552986	+	0.998470i	$0.517611\pi$
$954$	5.12132	−	8.87039i	0.165809	−	0.287189i
$955$	4.20711	+	7.28692i	0.136139	+	0.235799i
$956$	−3.82843	−	6.63103i	−0.123820	−	0.214463i
$957$	1.92893	−	3.34101i	0.0623535	−	0.107999i
$958$	−61.2843			−1.98000
$959$		0			0
$960$	−13.8995			−0.448604
$961$	−3.98528	+	6.90271i	−0.128557	+	0.222668i
$962$	24.5563	+	42.5328i	0.791728	+	1.37131i
$963$	−6.94975	−	12.0373i	−0.223952	−	0.387897i
$964$	−49.8492	+	86.3414i	−1.60554	+	2.78087i
$965$	−7.89949			−0.254294
$966$		0			0
$967$	−36.2843			−1.16682			−0.583412	−	0.812177i	$-0.698283\pi$
$967$	−36.2843			−1.16682			−0.583412	+	0.812177i	$0.698283\pi$
$968$	−23.8995	+	41.3951i	−0.768159	+	1.33049i
$969$	2.82843	+	4.89898i	0.0908622	+	0.157378i
$970$	−3.82843	−	6.63103i	−0.122923	−	0.212910i
$971$	13.4350	−	23.2702i	0.431151	−	0.746775i	−0.565822	−	0.824527i	$-0.691441\pi$
$971$	13.4350	−	23.2702i	0.431151	−	0.746775i	0.996973	+	0.0777526i	$0.0247744\pi$
$972$	−37.8995			−1.21563
$973$		0			0
$974$	−36.6274			−1.17362
$975$	−6.34315	+	10.9867i	−0.203143	+	0.351854i
$976$	17.7426	+	30.7312i	0.567928	+	0.983680i
$977$	22.3848	+	38.7716i	0.716152	+	1.24041i	0.962513	+	0.271234i	$0.0874318\pi$
$977$	22.3848	+	38.7716i	0.716152	+	1.24041i	−0.246361	+	0.969178i	$0.579235\pi$
$978$	−6.70711	+	11.6170i	−0.214470	+	0.371472i
$979$	−4.72792			−0.151105
$980$		0			0
$981$	9.65685			0.308320
$982$	−1.74264	+	3.01834i	−0.0556099	+	0.0963192i
$983$	−23.0000	−	39.8372i	−0.733586	−	1.27061i	−0.955341	−	0.295506i	$-0.904512\pi$
$983$	−23.0000	−	39.8372i	−0.733586	−	1.27061i	0.221755	−	0.975102i	$-0.428822\pi$
$984$	−9.89949	−	17.1464i	−0.315584	−	0.546608i
$985$	2.25736	−	3.90986i	0.0719254	−	0.124579i
$986$	63.5980			2.02537
$987$		0			0
$988$	8.58579			0.273150
$989$	22.5416	−	39.0432i	0.716782	−	1.24150i
$990$	−0.500000	−	0.866025i	−0.0158910	−	0.0275241i
$991$	−1.89949	−	3.29002i	−0.0603394	−	0.104511i	0.834278	−	0.551344i	$-0.185885\pi$
$991$	−1.89949	−	3.29002i	−0.0603394	−	0.104511i	−0.894617	+	0.446833i	$0.852552\pi$
$992$	−4.94975	+	8.57321i	−0.157155	+	0.272200i
$993$	44.4853			1.41170
$994$		0			0
$995$	16.0711			0.509487
$996$	−25.0208	+	43.3373i	−0.792815	+	1.37320i
$997$	−14.1421	−	24.4949i	−0.447886	−	0.775761i	0.550362	−	0.834926i	$-0.314490\pi$
$997$	−14.1421	−	24.4949i	−0.447886	−	0.775761i	−0.998248	+	0.0591648i	$0.981156\pi$
$998$	41.7132	+	72.2494i	1.32041	+	2.28701i
$999$	−25.6569	+	44.4390i	−0.811747	+	1.40599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.f.i.324.2		4
7.2	even	3		931.2.a.e.1.1		2
7.3	odd	6		133.2.f.c.39.2	✓	4
7.4	even	3	inner	931.2.f.i.704.2		4
7.5	odd	6		931.2.a.f.1.1		2
7.6	odd	2		133.2.f.c.58.2	yes	4
21.2	odd	6		8379.2.a.bl.1.2		2
21.5	even	6		8379.2.a.bi.1.2		2
21.17	even	6		1197.2.j.e.172.1		4
21.20	even	2		1197.2.j.e.856.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.f.c.39.2	✓	4	7.3	odd	6
133.2.f.c.58.2	yes	4	7.6	odd	2
931.2.a.e.1.1		2	7.2	even	3
931.2.a.f.1.1		2	7.5	odd	6
931.2.f.i.324.2		4	1.1	even	1	trivial
931.2.f.i.704.2		4	7.4	even	3	inner
1197.2.j.e.172.1		4	21.17	even	6
1197.2.j.e.856.1		4	21.20	even	2
8379.2.a.bi.1.2		2	21.5	even	6
8379.2.a.bl.1.2		2	21.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.20711 - 2.09077i) q^{2} +(0.707107 + 1.22474i) q^{3} +(-1.91421 - 3.31552i) q^{4} +(0.500000 - 0.866025i) q^{5} +3.41421 q^{6} -4.41421 q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.20711 - 2.09077i) q^{10} +(0.207107 + 0.358719i) q^{11} +(2.70711 - 4.68885i) q^{12} +2.24264 q^{13} +1.41421 q^{15} +(-1.50000 + 2.59808i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(-1.20711 - 2.09077i) q^{18} +(-0.500000 + 0.866025i) q^{19} -3.82843 q^{20} +1.00000 q^{22} +(2.79289 - 4.83743i) q^{23} +(-3.12132 - 5.40629i) q^{24} +(2.00000 + 3.46410i) q^{25} +(2.70711 - 4.68885i) q^{26} +5.65685 q^{27} -6.58579 q^{29} +(1.70711 - 2.95680i) q^{30} +(-3.12132 - 5.40629i) q^{31} +(-0.792893 - 1.37333i) q^{32} +(-0.292893 + 0.507306i) q^{33} -9.65685 q^{34} -3.82843 q^{36} +(-4.53553 + 7.85578i) q^{37} +(1.20711 + 2.09077i) q^{38} +(1.58579 + 2.74666i) q^{39} +(-2.20711 + 3.82282i) q^{40} +3.17157 q^{41} +8.07107 q^{43} +(0.792893 - 1.37333i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(-6.74264 - 11.6786i) q^{46} +(-2.20711 + 3.82282i) q^{47} -4.24264 q^{48} +9.65685 q^{50} +(2.82843 - 4.89898i) q^{51} +(-4.29289 - 7.43551i) q^{52} +(2.12132 + 3.67423i) q^{53} +(6.82843 - 11.8272i) q^{54} +0.414214 q^{55} -1.41421 q^{57} +(-7.94975 + 13.7694i) q^{58} +(3.41421 + 5.91359i) q^{59} +(-2.70711 - 4.68885i) q^{60} +(5.91421 - 10.2437i) q^{61} -15.0711 q^{62} -9.82843 q^{64} +(1.12132 - 1.94218i) q^{65} +(0.707107 + 1.22474i) q^{66} +(-0.585786 - 1.01461i) q^{67} +(-7.65685 + 13.2621i) q^{68} +7.89949 q^{69} -14.2426 q^{71} +(-2.20711 + 3.82282i) q^{72} +(7.57107 + 13.1135i) q^{73} +(10.9497 + 18.9655i) q^{74} +(-2.82843 + 4.89898i) q^{75} +3.82843 q^{76} +7.65685 q^{78} +(-0.707107 + 1.22474i) q^{79} +(1.50000 + 2.59808i) q^{80} +(2.50000 + 4.33013i) q^{81} +(3.82843 - 6.63103i) q^{82} -9.24264 q^{83} -4.00000 q^{85} +(9.74264 - 16.8747i) q^{86} +(-4.65685 - 8.06591i) q^{87} +(-0.914214 - 1.58346i) q^{88} +(-5.70711 + 9.88500i) q^{89} -2.41421 q^{90} -21.3848 q^{92} +(4.41421 - 7.64564i) q^{93} +(5.32843 + 9.22911i) q^{94} +(0.500000 + 0.866025i) q^{95} +(1.12132 - 1.94218i) q^{96} +3.17157 q^{97} +0.414214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} + 2 q^{5} + 8 q^{6} - 12 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{11} + 8 q^{12} - 8 q^{13} - 6 q^{16} - 8 q^{17} - 2 q^{18} - 2 q^{19} - 4 q^{20} + 4 q^{22} + 14 q^{23} - 4 q^{24} + 8 q^{25}+ \cdots - 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 + 8 * q^6 - 12 * q^8 + 2 * q^9 - 2 * q^10 - 2 * q^11 + 8 * q^12 - 8 * q^13 - 6 * q^16 - 8 * q^17 - 2 * q^18 - 2 * q^19 - 4 * q^20 + 4 * q^22 + 14 * q^23 - 4 * q^24 + 8 * q^25 + 8 * q^26 - 32 * q^29 + 4 * q^30 - 4 * q^31 - 6 * q^32 - 4 * q^33 - 16 * q^34 - 4 * q^36 - 4 * q^37 + 2 * q^38 + 12 * q^39 - 6 * q^40 + 24 * q^41 + 4 * q^43 + 6 * q^44 - 2 * q^45 - 10 * q^46 - 6 * q^47 + 16 * q^50 - 20 * q^52 + 16 * q^54 - 4 * q^55 - 12 * q^58 + 8 * q^59 - 8 * q^60 + 18 * q^61 - 32 * q^62 - 28 * q^64 - 4 * q^65 - 8 * q^67 - 8 * q^68 - 8 * q^69 - 40 * q^71 - 6 * q^72 + 2 * q^73 + 24 * q^74 + 4 * q^76 + 8 * q^78 + 6 * q^80 + 10 * q^81 + 4 * q^82 - 20 * q^83 - 16 * q^85 + 22 * q^86 + 4 * q^87 + 2 * q^88 - 20 * q^89 - 4 * q^90 - 12 * q^92 + 12 * q^93 + 10 * q^94 + 2 * q^95 - 4 * q^96 + 24 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more