LMFDB - Embedded newform 672.2.q.a.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(193,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("672.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.36594701583$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	672.289
Dual form			672.2.q.a.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{3} +(-1.50000 + 2.59808i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{3} +(-1.50000 + 2.59808i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{11} -4.00000 q^{13} +3.00000 q^{15} +(-2.00000 - 3.46410i) q^{17} +(-2.50000 + 0.866025i) q^{21} +(-4.00000 + 6.92820i) q^{23} +(-2.00000 - 3.46410i) q^{25} +1.00000 q^{27} -7.00000 q^{29} +(-5.50000 - 9.52628i) q^{31} +(0.500000 - 0.866025i) q^{33} +(6.00000 + 5.19615i) q^{35} +(-2.00000 + 3.46410i) q^{37} +(2.00000 + 3.46410i) q^{39} -4.00000 q^{41} -2.00000 q^{43} +(-1.50000 - 2.59808i) q^{45} +(1.00000 - 1.73205i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(-2.00000 + 3.46410i) q^{51} +(5.50000 + 9.52628i) q^{53} -3.00000 q^{55} +(-3.50000 - 6.06218i) q^{59} +(-5.00000 + 8.66025i) q^{61} +(2.00000 + 1.73205i) q^{63} +(6.00000 - 10.3923i) q^{65} +(-5.00000 - 8.66025i) q^{67} +8.00000 q^{69} +6.00000 q^{71} +(3.00000 + 5.19615i) q^{73} +(-2.00000 + 3.46410i) q^{75} +(2.50000 - 0.866025i) q^{77} +(-5.50000 + 9.52628i) q^{79} +(-0.500000 - 0.866025i) q^{81} +11.0000 q^{83} +12.0000 q^{85} +(3.50000 + 6.06218i) q^{87} +(-3.00000 + 5.19615i) q^{89} +(-2.00000 + 10.3923i) q^{91} +(-5.50000 + 9.52628i) q^{93} +7.00000 q^{97} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{3} - 3 q^{5} + q^{7} - q^{9}+O(q^{10}) $ 2 * q - q^3 - 3 * q^5 + q^7 - q^9	$ 2 q - q^{3} - 3 q^{5} + q^{7} - q^{9} + q^{11} - 8 q^{13} + 6 q^{15} - 4 q^{17} - 5 q^{21} - 8 q^{23} - 4 q^{25} + 2 q^{27} - 14 q^{29} - 11 q^{31} + q^{33} + 12 q^{35} - 4 q^{37} + 4 q^{39} - 8 q^{41} - 4 q^{43} - 3 q^{45} + 2 q^{47} - 13 q^{49} - 4 q^{51} + 11 q^{53} - 6 q^{55} - 7 q^{59} - 10 q^{61} + 4 q^{63} + 12 q^{65} - 10 q^{67} + 16 q^{69} + 12 q^{71} + 6 q^{73} - 4 q^{75} + 5 q^{77} - 11 q^{79} - q^{81} + 22 q^{83} + 24 q^{85} + 7 q^{87} - 6 q^{89} - 4 q^{91} - 11 q^{93} + 14 q^{97} - 2 q^{99}+O(q^{100}) $ 2 * q - q^3 - 3 * q^5 + q^7 - q^9 + q^11 - 8 * q^13 + 6 * q^15 - 4 * q^17 - 5 * q^21 - 8 * q^23 - 4 * q^25 + 2 * q^27 - 14 * q^29 - 11 * q^31 + q^33 + 12 * q^35 - 4 * q^37 + 4 * q^39 - 8 * q^41 - 4 * q^43 - 3 * q^45 + 2 * q^47 - 13 * q^49 - 4 * q^51 + 11 * q^53 - 6 * q^55 - 7 * q^59 - 10 * q^61 + 4 * q^63 + 12 * q^65 - 10 * q^67 + 16 * q^69 + 12 * q^71 + 6 * q^73 - 4 * q^75 + 5 * q^77 - 11 * q^79 - q^81 + 22 * q^83 + 24 * q^85 + 7 * q^87 - 6 * q^89 - 4 * q^91 - 11 * q^93 + 14 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$		0			0
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	0.306851	+	0.951757i	$0.400725\pi$
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	−0.977672	+	0.210138i	$0.932609\pi$
$6$		0			0
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	0.931505	−	0.363727i	$-0.118496\pi$
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	−0.780750	+	0.624844i	$0.785163\pi$
$12$		0			0
$13$	−4.00000			−1.10940			−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000			−1.10940			−0.554700	+	0.832050i	$0.687167\pi$
$14$		0			0
$15$	3.00000			0.774597
$16$		0			0
$17$	−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	$0.994540\pi$
$18$		0			0
$19$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$19$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$20$		0			0
$21$	−2.50000	+	0.866025i	−0.545545	+	0.188982i
$22$		0			0
$23$	−4.00000	+	6.92820i	−0.834058	+	1.44463i	0.0607377	+	0.998154i	$0.480655\pi$
$23$	−4.00000	+	6.92820i	−0.834058	+	1.44463i	−0.894795	+	0.446476i	$0.852679\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−7.00000			−1.29987			−0.649934	−	0.759991i	$-0.725203\pi$
$29$	−7.00000			−1.29987			−0.649934	+	0.759991i	$0.725203\pi$
$30$		0			0
$31$	−5.50000	−	9.52628i	−0.987829	−	1.71097i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−5.50000	−	9.52628i	−0.987829	−	1.71097i	−0.359211	−	0.933257i	$-0.616954\pi$
$32$		0			0
$33$	0.500000	−	0.866025i	0.0870388	−	0.150756i
$34$		0			0
$35$	6.00000	+	5.19615i	1.01419	+	0.878310i
$36$		0			0
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	−0.982274	−	0.187453i	$-0.939977\pi$
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	0.653476	+	0.756948i	$0.273310\pi$
$38$		0			0
$39$	2.00000	+	3.46410i	0.320256	+	0.554700i
$40$		0			0
$41$	−4.00000			−0.624695			−0.312348	−	0.949968i	$-0.601115\pi$
$41$	−4.00000			−0.624695			−0.312348	+	0.949968i	$0.601115\pi$
$42$		0			0
$43$	−2.00000			−0.304997			−0.152499	−	0.988304i	$-0.548732\pi$
$43$	−2.00000			−0.304997			−0.152499	+	0.988304i	$0.548732\pi$
$44$		0			0
$45$	−1.50000	−	2.59808i	−0.223607	−	0.387298i
$46$		0			0
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	−0.783830	−	0.620975i	$-0.786737\pi$
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	0.929695	+	0.368329i	$0.120070\pi$
$48$		0			0
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$		0			0
$51$	−2.00000	+	3.46410i	−0.280056	+	0.485071i
$52$		0			0
$53$	5.50000	+	9.52628i	0.755483	+	1.30854i	0.945134	+	0.326683i	$0.105931\pi$
$53$	5.50000	+	9.52628i	0.755483	+	1.30854i	−0.189651	+	0.981852i	$0.560736\pi$
$54$		0			0
$55$	−3.00000			−0.404520
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.50000	−	6.06218i	−0.455661	−	0.789228i	0.543065	−	0.839691i	$-0.317264\pi$
$59$	−3.50000	−	6.06218i	−0.455661	−	0.789228i	−0.998726	+	0.0504625i	$0.983930\pi$
$60$		0			0
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	0.345207	+	0.938527i	$0.387809\pi$
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	−0.985391	+	0.170305i	$0.945525\pi$
$62$		0			0
$63$	2.00000	+	1.73205i	0.251976	+	0.218218i
$64$		0			0
$65$	6.00000	−	10.3923i	0.744208	−	1.28901i
$66$		0			0
$67$	−5.00000	−	8.66025i	−0.610847	−	1.05802i	−0.991098	−	0.133135i	$-0.957496\pi$
$67$	−5.00000	−	8.66025i	−0.610847	−	1.05802i	0.380251	−	0.924883i	$-0.375838\pi$
$68$		0			0
$69$	8.00000			0.963087
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$	3.00000	+	5.19615i	0.351123	+	0.608164i	0.986447	−	0.164083i	$-0.0524664\pi$
$73$	3.00000	+	5.19615i	0.351123	+	0.608164i	−0.635323	+	0.772246i	$0.719133\pi$
$74$		0			0
$75$	−2.00000	+	3.46410i	−0.230940	+	0.400000i
$76$		0			0
$77$	2.50000	−	0.866025i	0.284901	−	0.0986928i
$78$		0			0
$79$	−5.50000	+	9.52628i	−0.618798	+	1.07179i	0.370907	+	0.928670i	$0.379047\pi$
$79$	−5.50000	+	9.52628i	−0.618798	+	1.07179i	−0.989705	+	0.143120i	$0.954286\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	11.0000			1.20741			0.603703	−	0.797209i	$-0.293691\pi$
$83$	11.0000			1.20741			0.603703	+	0.797209i	$0.293691\pi$
$84$		0			0
$85$	12.0000			1.30158
$86$		0			0
$87$	3.50000	+	6.06218i	0.375239	+	0.649934i
$88$		0			0
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$		0			0
$91$	−2.00000	+	10.3923i	−0.209657	+	1.08941i
$92$		0			0
$93$	−5.50000	+	9.52628i	−0.570323	+	0.987829i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	7.00000			0.710742			0.355371	−	0.934725i	$-0.384354\pi$
$97$	7.00000			0.710742			0.355371	+	0.934725i	$0.384354\pi$
$98$		0			0
$99$	−1.00000			−0.100504
$100$		0			0
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$		0			0
$103$	8.00000	−	13.8564i	0.788263	−	1.36531i	−0.138767	−	0.990325i	$-0.544314\pi$
$103$	8.00000	−	13.8564i	0.788263	−	1.36531i	0.927030	−	0.374987i	$-0.122353\pi$
$104$		0			0
$105$	1.50000	−	7.79423i	0.146385	−	0.760639i
$106$		0			0
$107$	3.50000	−	6.06218i	0.338358	−	0.586053i	−0.645766	−	0.763535i	$-0.723462\pi$
$107$	3.50000	−	6.06218i	0.338358	−	0.586053i	0.984124	+	0.177482i	$0.0567953\pi$
$108$		0			0
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	0.520794	−	0.853682i	$-0.325636\pi$
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	−0.999708	+	0.0241802i	$0.992302\pi$
$110$		0			0
$111$	4.00000			0.379663
$112$		0			0
$113$	12.0000			1.12887			0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000			1.12887			0.564433	+	0.825479i	$0.309095\pi$
$114$		0			0
$115$	−12.0000	−	20.7846i	−1.11901	−	1.93817i
$116$		0			0
$117$	2.00000	−	3.46410i	0.184900	−	0.320256i
$118$		0			0
$119$	−10.0000	+	3.46410i	−0.916698	+	0.317554i
$120$		0			0
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$		0			0
$123$	2.00000	+	3.46410i	0.180334	+	0.312348i
$124$		0			0
$125$	−3.00000			−0.268328
$126$		0			0
$127$	17.0000			1.50851			0.754253	−	0.656584i	$-0.227999\pi$
$127$	17.0000			1.50851			0.754253	+	0.656584i	$0.227999\pi$
$128$		0			0
$129$	1.00000	+	1.73205i	0.0880451	+	0.152499i
$130$		0			0
$131$	−1.50000	+	2.59808i	−0.131056	+	0.226995i	−0.924084	−	0.382190i	$-0.875170\pi$
$131$	−1.50000	+	2.59808i	−0.131056	+	0.226995i	0.793028	+	0.609185i	$0.208503\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−1.50000	+	2.59808i	−0.129099	+	0.223607i
$136$		0			0
$137$	1.00000	+	1.73205i	0.0854358	+	0.147979i	0.905577	−	0.424182i	$-0.139438\pi$
$137$	1.00000	+	1.73205i	0.0854358	+	0.147979i	−0.820141	+	0.572161i	$0.806105\pi$
$138$		0			0
$139$	−22.0000			−1.86602			−0.933008	−	0.359856i	$-0.882826\pi$
$139$	−22.0000			−1.86602			−0.933008	+	0.359856i	$0.882826\pi$
$140$		0			0
$141$	−2.00000			−0.168430
$142$		0			0
$143$	−2.00000	−	3.46410i	−0.167248	−	0.289683i
$144$		0			0
$145$	10.5000	−	18.1865i	0.871978	−	1.51031i
$146$		0			0
$147$	1.00000	+	6.92820i	0.0824786	+	0.571429i
$148$		0			0
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$		0			0
$151$	−5.50000	−	9.52628i	−0.447584	−	0.775238i	0.550645	−	0.834740i	$-0.314382\pi$
$151$	−5.50000	−	9.52628i	−0.447584	−	0.775238i	−0.998228	+	0.0595022i	$0.981049\pi$
$152$		0			0
$153$	4.00000			0.323381
$154$		0			0
$155$	33.0000			2.65062
$156$		0			0
$157$	6.00000	+	10.3923i	0.478852	+	0.829396i	0.999706	−	0.0242497i	$-0.00771967\pi$
$157$	6.00000	+	10.3923i	0.478852	+	0.829396i	−0.520854	+	0.853646i	$0.674386\pi$
$158$		0			0
$159$	5.50000	−	9.52628i	0.436178	−	0.755483i
$160$		0			0
$161$	16.0000	+	13.8564i	1.26098	+	1.09204i
$162$		0			0
$163$	4.00000	−	6.92820i	0.313304	−	0.542659i	−0.665771	−	0.746156i	$-0.731897\pi$
$163$	4.00000	−	6.92820i	0.313304	−	0.542659i	0.979076	+	0.203497i	$0.0652307\pi$
$164$		0			0
$165$	1.50000	+	2.59808i	0.116775	+	0.202260i
$166$		0			0
$167$	−22.0000			−1.70241			−0.851206	−	0.524832i	$-0.824128\pi$
$167$	−22.0000			−1.70241			−0.851206	+	0.524832i	$0.824128\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$		0			0
$171$		0			0
$172$		0			0
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$		0			0
$175$	−10.0000	+	3.46410i	−0.755929	+	0.261861i
$176$		0			0
$177$	−3.50000	+	6.06218i	−0.263076	+	0.455661i
$178$		0			0
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	0.998286	−	0.0585225i	$-0.0186389\pi$
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	−0.549825	+	0.835280i	$0.685306\pi$
$180$		0			0
$181$	12.0000			0.891953			0.445976	−	0.895045i	$-0.352856\pi$
$181$	12.0000			0.891953			0.445976	+	0.895045i	$0.352856\pi$
$182$		0			0
$183$	10.0000			0.739221
$184$		0			0
$185$	−6.00000	−	10.3923i	−0.441129	−	0.764057i
$186$		0			0
$187$	2.00000	−	3.46410i	0.146254	−	0.253320i
$188$		0			0
$189$	0.500000	−	2.59808i	0.0363696	−	0.188982i
$190$		0			0
$191$	−12.0000	+	20.7846i	−0.868290	+	1.50392i	−0.00454614	+	0.999990i	$0.501447\pi$
$191$	−12.0000	+	20.7846i	−0.868290	+	1.50392i	−0.863743	+	0.503932i	$0.831886\pi$
$192$		0			0
$193$	9.50000	+	16.4545i	0.683825	+	1.18442i	0.973805	+	0.227387i	$0.0730182\pi$
$193$	9.50000	+	16.4545i	0.683825	+	1.18442i	−0.289980	+	0.957033i	$0.593649\pi$
$194$		0			0
$195$	−12.0000			−0.859338
$196$		0			0
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$		0			0
$199$	10.0000	+	17.3205i	0.708881	+	1.22782i	0.965272	+	0.261245i	$0.0841331\pi$
$199$	10.0000	+	17.3205i	0.708881	+	1.22782i	−0.256391	+	0.966573i	$0.582534\pi$
$200$		0			0
$201$	−5.00000	+	8.66025i	−0.352673	+	0.610847i
$202$		0			0
$203$	−3.50000	+	18.1865i	−0.245652	+	1.27644i
$204$		0			0
$205$	6.00000	−	10.3923i	0.419058	−	0.725830i
$206$		0			0
$207$	−4.00000	−	6.92820i	−0.278019	−	0.481543i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	2.00000			0.137686			0.0688428	−	0.997628i	$-0.478069\pi$
$211$	2.00000			0.137686			0.0688428	+	0.997628i	$0.478069\pi$
$212$		0			0
$213$	−3.00000	−	5.19615i	−0.205557	−	0.356034i
$214$		0			0
$215$	3.00000	−	5.19615i	0.204598	−	0.354375i
$216$		0			0
$217$	−27.5000	+	9.52628i	−1.86682	+	0.646686i
$218$		0			0
$219$	3.00000	−	5.19615i	0.202721	−	0.351123i
$220$		0			0
$221$	8.00000	+	13.8564i	0.538138	+	0.932083i
$222$		0			0
$223$	9.00000			0.602685			0.301342	−	0.953516i	$-0.402565\pi$
$223$	9.00000			0.602685			0.301342	+	0.953516i	$0.402565\pi$
$224$		0			0
$225$	4.00000			0.266667
$226$		0			0
$227$	3.50000	+	6.06218i	0.232303	+	0.402361i	0.958485	−	0.285141i	$-0.0920405\pi$
$227$	3.50000	+	6.06218i	0.232303	+	0.402361i	−0.726182	+	0.687502i	$0.758707\pi$
$228$		0			0
$229$	4.00000	−	6.92820i	0.264327	−	0.457829i	−0.703060	−	0.711131i	$-0.748183\pi$
$229$	4.00000	−	6.92820i	0.264327	−	0.457829i	0.967387	+	0.253302i	$0.0815167\pi$
$230$		0			0
$231$	−2.00000	−	1.73205i	−0.131590	−	0.113961i
$232$		0			0
$233$	−6.00000	+	10.3923i	−0.393073	+	0.680823i	−0.992853	−	0.119342i	$-0.961921\pi$
$233$	−6.00000	+	10.3923i	−0.393073	+	0.680823i	0.599780	+	0.800165i	$0.295255\pi$
$234$		0			0
$235$	3.00000	+	5.19615i	0.195698	+	0.338960i
$236$		0			0
$237$	11.0000			0.714527
$238$		0			0
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	12.5000	+	21.6506i	0.805196	+	1.39464i	0.916159	+	0.400815i	$0.131273\pi$
$241$	12.5000	+	21.6506i	0.805196	+	1.39464i	−0.110963	+	0.993825i	$0.535394\pi$
$242$		0			0
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	16.5000	−	12.9904i	1.05415	−	0.829925i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−5.50000	−	9.52628i	−0.348548	−	0.603703i
$250$		0			0
$251$	−25.0000			−1.57799			−0.788993	−	0.614402i	$-0.789397\pi$
$251$	−25.0000			−1.57799			−0.788993	+	0.614402i	$0.789397\pi$
$252$		0			0
$253$	−8.00000			−0.502956
$254$		0			0
$255$	−6.00000	−	10.3923i	−0.375735	−	0.650791i
$256$		0			0
$257$	−7.00000	+	12.1244i	−0.436648	+	0.756297i	−0.997429	−	0.0716680i	$-0.977168\pi$
$257$	−7.00000	+	12.1244i	−0.436648	+	0.756297i	0.560781	+	0.827964i	$0.310501\pi$
$258$		0			0
$259$	8.00000	+	6.92820i	0.497096	+	0.430498i
$260$		0			0
$261$	3.50000	−	6.06218i	0.216645	−	0.375239i
$262$		0			0
$263$	−13.0000	−	22.5167i	−0.801614	−	1.38844i	−0.918553	−	0.395298i	$-0.870641\pi$
$263$	−13.0000	−	22.5167i	−0.801614	−	1.38844i	0.116939	−	0.993139i	$-0.462692\pi$
$264$		0			0
$265$	−33.0000			−2.02717
$266$		0			0
$267$	6.00000			0.367194
$268$		0			0
$269$	−10.5000	−	18.1865i	−0.640196	−	1.10885i	−0.985389	−	0.170321i	$-0.945520\pi$
$269$	−10.5000	−	18.1865i	−0.640196	−	1.10885i	0.345192	−	0.938532i	$-0.387814\pi$
$270$		0			0
$271$	0.500000	−	0.866025i	0.0303728	−	0.0526073i	−0.850439	−	0.526073i	$-0.823664\pi$
$271$	0.500000	−	0.866025i	0.0303728	−	0.0526073i	0.880812	+	0.473466i	$0.156997\pi$
$272$		0			0
$273$	10.0000	−	3.46410i	0.605228	−	0.209657i
$274$		0			0
$275$	2.00000	−	3.46410i	0.120605	−	0.208893i
$276$		0			0
$277$	−16.0000	−	27.7128i	−0.961347	−	1.66510i	−0.719125	−	0.694881i	$-0.755457\pi$
$277$	−16.0000	−	27.7128i	−0.961347	−	1.66510i	−0.242222	−	0.970221i	$-0.577876\pi$
$278$		0			0
$279$	11.0000			0.658553
$280$		0			0
$281$	−30.0000			−1.78965			−0.894825	−	0.446417i	$-0.852700\pi$
$281$	−30.0000			−1.78965			−0.894825	+	0.446417i	$0.852700\pi$
$282$		0			0
$283$	1.00000	+	1.73205i	0.0594438	+	0.102960i	0.894216	−	0.447636i	$-0.147734\pi$
$283$	1.00000	+	1.73205i	0.0594438	+	0.102960i	−0.834772	+	0.550596i	$0.814401\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.00000	+	10.3923i	−0.118056	+	0.613438i
$288$		0			0
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$		0			0
$291$	−3.50000	−	6.06218i	−0.205174	−	0.355371i
$292$		0			0
$293$	−7.00000			−0.408944			−0.204472	−	0.978872i	$-0.565548\pi$
$293$	−7.00000			−0.408944			−0.204472	+	0.978872i	$0.565548\pi$
$294$		0			0
$295$	21.0000			1.22267
$296$		0			0
$297$	0.500000	+	0.866025i	0.0290129	+	0.0502519i
$298$		0			0
$299$	16.0000	−	27.7128i	0.925304	−	1.60267i
$300$		0			0
$301$	−1.00000	+	5.19615i	−0.0576390	+	0.299501i
$302$		0			0
$303$	−3.00000	+	5.19615i	−0.172345	+	0.298511i
$304$		0			0
$305$	−15.0000	−	25.9808i	−0.858898	−	1.48765i
$306$		0			0
$307$	−8.00000			−0.456584			−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000			−0.456584			−0.228292	+	0.973593i	$0.573314\pi$
$308$		0			0
$309$	−16.0000			−0.910208
$310$		0			0
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	0.644246	−	0.764818i	$-0.277171\pi$
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	−0.984475	+	0.175525i	$0.943838\pi$
$312$		0			0
$313$	−0.500000	+	0.866025i	−0.0282617	+	0.0489506i	−0.879810	−	0.475325i	$-0.842331\pi$
$313$	−0.500000	+	0.866025i	−0.0282617	+	0.0489506i	0.851549	+	0.524276i	$0.175664\pi$
$314$		0			0
$315$	−7.50000	+	2.59808i	−0.422577	+	0.146385i
$316$		0			0
$317$	−8.50000	+	14.7224i	−0.477408	+	0.826894i	−0.999665	−	0.0258939i	$-0.991757\pi$
$317$	−8.50000	+	14.7224i	−0.477408	+	0.826894i	0.522257	+	0.852788i	$0.325090\pi$
$318$		0			0
$319$	−3.50000	−	6.06218i	−0.195962	−	0.339417i
$320$		0			0
$321$	−7.00000			−0.390702
$322$		0			0
$323$		0			0
$324$		0			0
$325$	8.00000	+	13.8564i	0.443760	+	0.768615i
$326$		0			0
$327$	−5.00000	+	8.66025i	−0.276501	+	0.478913i
$328$		0			0
$329$	−4.00000	−	3.46410i	−0.220527	−	0.190982i
$330$		0			0
$331$	−6.00000	+	10.3923i	−0.329790	+	0.571213i	−0.982470	−	0.186421i	$-0.940311\pi$
$331$	−6.00000	+	10.3923i	−0.329790	+	0.571213i	0.652680	+	0.757634i	$0.273645\pi$
$332$		0			0
$333$	−2.00000	−	3.46410i	−0.109599	−	0.189832i
$334$		0			0
$335$	30.0000			1.63908
$336$		0			0
$337$	−15.0000			−0.817102			−0.408551	−	0.912735i	$-0.633966\pi$
$337$	−15.0000			−0.817102			−0.408551	+	0.912735i	$0.633966\pi$
$338$		0			0
$339$	−6.00000	−	10.3923i	−0.325875	−	0.564433i
$340$		0			0
$341$	5.50000	−	9.52628i	0.297842	−	0.515877i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		0			0
$345$	−12.0000	+	20.7846i	−0.646058	+	1.11901i
$346$		0			0
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	0.658824	−	0.752297i	$-0.271054\pi$
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	−0.980921	+	0.194409i	$0.937721\pi$
$348$		0			0
$349$	−34.0000			−1.81998			−0.909989	−	0.414632i	$-0.863910\pi$
$349$	−34.0000			−1.81998			−0.909989	+	0.414632i	$0.863910\pi$
$350$		0			0
$351$	−4.00000			−0.213504
$352$		0			0
$353$	12.0000	+	20.7846i	0.638696	+	1.10625i	0.985719	+	0.168397i	$0.0538590\pi$
$353$	12.0000	+	20.7846i	0.638696	+	1.10625i	−0.347024	+	0.937856i	$0.612808\pi$
$354$		0			0
$355$	−9.00000	+	15.5885i	−0.477670	+	0.827349i
$356$		0			0
$357$	8.00000	+	6.92820i	0.423405	+	0.366679i
$358$		0			0
$359$	−1.00000	+	1.73205i	−0.0527780	+	0.0914141i	−0.891207	−	0.453596i	$-0.850141\pi$
$359$	−1.00000	+	1.73205i	−0.0527780	+	0.0914141i	0.838429	+	0.545010i	$0.183474\pi$
$360$		0			0
$361$	9.50000	+	16.4545i	0.500000	+	0.866025i
$362$		0			0
$363$	−10.0000			−0.524864
$364$		0			0
$365$	−18.0000			−0.942163
$366$		0			0
$367$	−8.50000	−	14.7224i	−0.443696	−	0.768505i	0.554264	−	0.832341i	$-0.313000\pi$
$367$	−8.50000	−	14.7224i	−0.443696	−	0.768505i	−0.997960	+	0.0638362i	$0.979666\pi$
$368$		0			0
$369$	2.00000	−	3.46410i	0.104116	−	0.180334i
$370$		0			0
$371$	27.5000	−	9.52628i	1.42773	−	0.494580i
$372$		0			0
$373$	6.00000	−	10.3923i	0.310668	−	0.538093i	−0.667839	−	0.744306i	$-0.732781\pi$
$373$	6.00000	−	10.3923i	0.310668	−	0.538093i	0.978507	+	0.206213i	$0.0661139\pi$
$374$		0			0
$375$	1.50000	+	2.59808i	0.0774597	+	0.134164i
$376$		0			0
$377$	28.0000			1.44207
$378$		0			0
$379$	28.0000			1.43826			0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000			1.43826			0.719132	+	0.694874i	$0.244540\pi$
$380$		0			0
$381$	−8.50000	−	14.7224i	−0.435468	−	0.754253i
$382$		0			0
$383$	−1.00000	+	1.73205i	−0.0510976	+	0.0885037i	−0.890443	−	0.455095i	$-0.849605\pi$
$383$	−1.00000	+	1.73205i	−0.0510976	+	0.0885037i	0.839345	+	0.543599i	$0.182939\pi$
$384$		0			0
$385$	−1.50000	+	7.79423i	−0.0764471	+	0.397231i
$386$		0			0
$387$	1.00000	−	1.73205i	0.0508329	−	0.0880451i
$388$		0			0
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	0.932002	−	0.362454i	$-0.118061\pi$
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	−0.779895	+	0.625910i	$0.784728\pi$
$390$		0			0
$391$	32.0000			1.61831
$392$		0			0
$393$	3.00000			0.151330
$394$		0			0
$395$	−16.5000	−	28.5788i	−0.830205	−	1.43796i
$396$		0			0
$397$	2.00000	−	3.46410i	0.100377	−	0.173858i	−0.811463	−	0.584404i	$-0.801328\pi$
$397$	2.00000	−	3.46410i	0.100377	−	0.173858i	0.911840	+	0.410546i	$0.134662\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−8.00000	+	13.8564i	−0.399501	+	0.691956i	−0.993664	−	0.112388i	$-0.964150\pi$
$401$	−8.00000	+	13.8564i	−0.399501	+	0.691956i	0.594163	+	0.804344i	$0.297483\pi$
$402$		0			0
$403$	22.0000	+	38.1051i	1.09590	+	1.89815i
$404$		0			0
$405$	3.00000			0.149071
$406$		0			0
$407$	−4.00000			−0.198273
$408$		0			0
$409$	−3.50000	−	6.06218i	−0.173064	−	0.299755i	0.766426	−	0.642333i	$-0.222033\pi$
$409$	−3.50000	−	6.06218i	−0.173064	−	0.299755i	−0.939490	+	0.342578i	$0.888700\pi$
$410$		0			0
$411$	1.00000	−	1.73205i	0.0493264	−	0.0854358i
$412$		0			0
$413$	−17.5000	+	6.06218i	−0.861119	+	0.298300i
$414$		0			0
$415$	−16.5000	+	28.5788i	−0.809953	+	1.40288i
$416$		0			0
$417$	11.0000	+	19.0526i	0.538672	+	0.933008i
$418$		0			0
$419$	−24.0000			−1.17248			−0.586238	−	0.810139i	$-0.699392\pi$
$419$	−24.0000			−1.17248			−0.586238	+	0.810139i	$0.699392\pi$
$420$		0			0
$421$	30.0000			1.46211			0.731055	−	0.682318i	$-0.239028\pi$
$421$	30.0000			1.46211			0.731055	+	0.682318i	$0.239028\pi$
$422$		0			0
$423$	1.00000	+	1.73205i	0.0486217	+	0.0842152i
$424$		0			0
$425$	−8.00000	+	13.8564i	−0.388057	+	0.672134i
$426$		0			0
$427$	20.0000	+	17.3205i	0.967868	+	0.838198i
$428$		0			0
$429$	−2.00000	+	3.46410i	−0.0965609	+	0.167248i
$430$		0			0
$431$	−4.00000	−	6.92820i	−0.192673	−	0.333720i	0.753462	−	0.657491i	$-0.228382\pi$
$431$	−4.00000	−	6.92820i	−0.192673	−	0.333720i	−0.946135	+	0.323772i	$0.895049\pi$
$432$		0			0
$433$	−2.00000			−0.0961139			−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000			−0.0961139			−0.0480569	+	0.998845i	$0.515303\pi$
$434$		0			0
$435$	−21.0000			−1.00687
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−7.50000	+	12.9904i	−0.357955	+	0.619997i	−0.987619	−	0.156871i	$-0.949859\pi$
$439$	−7.50000	+	12.9904i	−0.357955	+	0.619997i	0.629664	+	0.776868i	$0.283193\pi$
$440$		0			0
$441$	5.50000	−	4.33013i	0.261905	−	0.206197i
$442$		0			0
$443$	10.5000	−	18.1865i	0.498870	−	0.864068i	−0.501129	−	0.865373i	$-0.667082\pi$
$443$	10.5000	−	18.1865i	0.498870	−	0.864068i	0.999999	+	0.00130426i	$0.000415158\pi$
$444$		0			0
$445$	−9.00000	−	15.5885i	−0.426641	−	0.738964i
$446$		0			0
$447$	−6.00000			−0.283790
$448$		0			0
$449$	−12.0000			−0.566315			−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000			−0.566315			−0.283158	+	0.959073i	$0.591382\pi$
$450$		0			0
$451$	−2.00000	−	3.46410i	−0.0941763	−	0.163118i
$452$		0			0
$453$	−5.50000	+	9.52628i	−0.258413	+	0.447584i
$454$		0			0
$455$	−24.0000	−	20.7846i	−1.12514	−	0.974398i
$456$		0			0
$457$	8.50000	−	14.7224i	0.397613	−	0.688686i	−0.595818	−	0.803120i	$-0.703172\pi$
$457$	8.50000	−	14.7224i	0.397613	−	0.688686i	0.993431	+	0.114433i	$0.0365053\pi$
$458$		0			0
$459$	−2.00000	−	3.46410i	−0.0933520	−	0.161690i
$460$		0			0
$461$	−2.00000			−0.0931493			−0.0465746	−	0.998915i	$-0.514831\pi$
$461$	−2.00000			−0.0931493			−0.0465746	+	0.998915i	$0.514831\pi$
$462$		0			0
$463$		0			0			−	1.00000i	$-0.5\pi$
$463$		0			0				1.00000i	$0.5\pi$
$464$		0			0
$465$	−16.5000	−	28.5788i	−0.765169	−	1.32531i
$466$		0			0
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	−0.970799	−	0.239892i	$-0.922888\pi$
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	0.693153	+	0.720791i	$0.256221\pi$
$468$		0			0
$469$	−25.0000	+	8.66025i	−1.15439	+	0.399893i
$470$		0			0
$471$	6.00000	−	10.3923i	0.276465	−	0.478852i
$472$		0			0
$473$	−1.00000	−	1.73205i	−0.0459800	−	0.0796398i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−11.0000			−0.503655
$478$		0			0
$479$	−3.00000	−	5.19615i	−0.137073	−	0.237418i	0.789314	−	0.613990i	$-0.210436\pi$
$479$	−3.00000	−	5.19615i	−0.137073	−	0.237418i	−0.926388	+	0.376571i	$0.877103\pi$
$480$		0			0
$481$	8.00000	−	13.8564i	0.364769	−	0.631798i
$482$		0			0
$483$	4.00000	−	20.7846i	0.182006	−	0.945732i
$484$		0			0
$485$	−10.5000	+	18.1865i	−0.476780	+	0.825808i
$486$		0			0
$487$	1.50000	+	2.59808i	0.0679715	+	0.117730i	0.898008	−	0.439979i	$-0.145014\pi$
$487$	1.50000	+	2.59808i	0.0679715	+	0.117730i	−0.830037	+	0.557709i	$0.811681\pi$
$488$		0			0
$489$	−8.00000			−0.361773
$490$		0			0
$491$	−37.0000			−1.66979			−0.834893	−	0.550412i	$-0.814471\pi$
$491$	−37.0000			−1.66979			−0.834893	+	0.550412i	$0.814471\pi$
$492$		0			0
$493$	14.0000	+	24.2487i	0.630528	+	1.09211i
$494$		0			0
$495$	1.50000	−	2.59808i	0.0674200	−	0.116775i
$496$		0			0
$497$	3.00000	−	15.5885i	0.134568	−	0.699238i
$498$		0			0
$499$	−5.00000	+	8.66025i	−0.223831	+	0.387686i	−0.955968	−	0.293471i	$-0.905190\pi$
$499$	−5.00000	+	8.66025i	−0.223831	+	0.387686i	0.732137	+	0.681157i	$0.238523\pi$
$500$		0			0
$501$	11.0000	+	19.0526i	0.491444	+	0.851206i
$502$		0			0
$503$	32.0000			1.42681			0.713405	−	0.700752i	$-0.247152\pi$
$503$	32.0000			1.42681			0.713405	+	0.700752i	$0.247152\pi$
$504$		0			0
$505$	18.0000			0.800989
$506$		0			0
$507$	−1.50000	−	2.59808i	−0.0666173	−	0.115385i
$508$		0			0
$509$	21.5000	−	37.2391i	0.952971	−	1.65059i	0.214026	−	0.976828i	$-0.431342\pi$
$509$	21.5000	−	37.2391i	0.952971	−	1.65059i	0.738945	−	0.673766i	$-0.235324\pi$
$510$		0			0
$511$	15.0000	−	5.19615i	0.663561	−	0.229864i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	24.0000	+	41.5692i	1.05757	+	1.83176i
$516$		0			0
$517$	2.00000			0.0879599
$518$		0			0
$519$	−6.00000			−0.263371
$520$		0			0
$521$	−7.00000	−	12.1244i	−0.306676	−	0.531178i	0.670957	−	0.741496i	$-0.265883\pi$
$521$	−7.00000	−	12.1244i	−0.306676	−	0.531178i	−0.977633	+	0.210318i	$0.932550\pi$
$522$		0			0
$523$	10.0000	−	17.3205i	0.437269	−	0.757373i	−0.560208	−	0.828352i	$-0.689279\pi$
$523$	10.0000	−	17.3205i	0.437269	−	0.757373i	0.997478	+	0.0709788i	$0.0226123\pi$
$524$		0			0
$525$	8.00000	+	6.92820i	0.349149	+	0.302372i
$526$		0			0
$527$	−22.0000	+	38.1051i	−0.958335	+	1.65989i
$528$		0			0
$529$	−20.5000	−	35.5070i	−0.891304	−	1.54378i
$530$		0			0
$531$	7.00000			0.303774
$532$		0			0
$533$	16.0000			0.693037
$534$		0			0
$535$	10.5000	+	18.1865i	0.453955	+	0.786272i
$536$		0			0
$537$	6.00000	−	10.3923i	0.258919	−	0.448461i
$538$		0			0
$539$	−1.00000	−	6.92820i	−0.0430730	−	0.298419i
$540$		0			0
$541$	15.0000	−	25.9808i	0.644900	−	1.11700i	−0.339424	−	0.940633i	$-0.610232\pi$
$541$	15.0000	−	25.9808i	0.644900	−	1.11700i	0.984325	−	0.176367i	$-0.0564345\pi$
$542$		0			0
$543$	−6.00000	−	10.3923i	−0.257485	−	0.445976i
$544$		0			0
$545$	30.0000			1.28506
$546$		0			0
$547$	−20.0000			−0.855138			−0.427569	−	0.903983i	$-0.640630\pi$
$547$	−20.0000			−0.855138			−0.427569	+	0.903983i	$0.640630\pi$
$548$		0			0
$549$	−5.00000	−	8.66025i	−0.213395	−	0.369611i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	22.0000	+	19.0526i	0.935535	+	0.810197i
$554$		0			0
$555$	−6.00000	+	10.3923i	−0.254686	+	0.441129i
$556$		0			0
$557$	−1.50000	−	2.59808i	−0.0635570	−	0.110084i	0.832496	−	0.554031i	$-0.186911\pi$
$557$	−1.50000	−	2.59808i	−0.0635570	−	0.110084i	−0.896053	+	0.443947i	$0.853578\pi$
$558$		0			0
$559$	8.00000			0.338364
$560$		0			0
$561$	−4.00000			−0.168880
$562$		0			0
$563$	−9.50000	−	16.4545i	−0.400377	−	0.693474i	0.593394	−	0.804912i	$-0.297788\pi$
$563$	−9.50000	−	16.4545i	−0.400377	−	0.693474i	−0.993771	+	0.111438i	$0.964454\pi$
$564$		0			0
$565$	−18.0000	+	31.1769i	−0.757266	+	1.31162i
$566$		0			0
$567$	−2.50000	+	0.866025i	−0.104990	+	0.0363696i
$568$		0			0
$569$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$569$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$570$		0			0
$571$	11.0000	+	19.0526i	0.460336	+	0.797325i	0.998978	−	0.0452101i	$-0.0143957\pi$
$571$	11.0000	+	19.0526i	0.460336	+	0.797325i	−0.538642	+	0.842535i	$0.681062\pi$
$572$		0			0
$573$	24.0000			1.00261
$574$		0			0
$575$	32.0000			1.33449
$576$		0			0
$577$	8.50000	+	14.7224i	0.353860	+	0.612903i	0.986922	−	0.161198i	$-0.0515357\pi$
$577$	8.50000	+	14.7224i	0.353860	+	0.612903i	−0.633062	+	0.774101i	$0.718202\pi$
$578$		0			0
$579$	9.50000	−	16.4545i	0.394807	−	0.683825i
$580$		0			0
$581$	5.50000	−	28.5788i	0.228178	−	1.18565i
$582$		0			0
$583$	−5.50000	+	9.52628i	−0.227787	+	0.394538i
$584$		0			0
$585$	6.00000	+	10.3923i	0.248069	+	0.429669i
$586$		0			0
$587$	−15.0000			−0.619116			−0.309558	−	0.950881i	$-0.600181\pi$
$587$	−15.0000			−0.619116			−0.309558	+	0.950881i	$0.600181\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	−3.00000	−	5.19615i	−0.123404	−	0.213741i
$592$		0			0
$593$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$593$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$594$		0			0
$595$	6.00000	−	31.1769i	0.245976	−	1.27813i
$596$		0			0
$597$	10.0000	−	17.3205i	0.409273	−	0.708881i
$598$		0			0
$599$	−9.00000	−	15.5885i	−0.367730	−	0.636927i	0.621480	−	0.783430i	$-0.286532\pi$
$599$	−9.00000	−	15.5885i	−0.367730	−	0.636927i	−0.989210	+	0.146503i	$0.953198\pi$
$600$		0			0
$601$	−37.0000			−1.50926			−0.754631	−	0.656150i	$-0.772184\pi$
$601$	−37.0000			−1.50926			−0.754631	+	0.656150i	$0.772184\pi$
$602$		0			0
$603$	10.0000			0.407231
$604$		0			0
$605$	15.0000	+	25.9808i	0.609837	+	1.05627i
$606$		0			0
$607$	13.5000	−	23.3827i	0.547948	−	0.949074i	−0.450467	−	0.892793i	$-0.648742\pi$
$607$	13.5000	−	23.3827i	0.547948	−	0.949074i	0.998415	−	0.0562808i	$-0.0179242\pi$
$608$		0			0
$609$	17.5000	−	6.06218i	0.709136	−	0.245652i
$610$		0			0
$611$	−4.00000	+	6.92820i	−0.161823	+	0.280285i
$612$		0			0
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	0.981129	−	0.193352i	$-0.0619359\pi$
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	−0.658012	+	0.753007i	$0.728603\pi$
$614$		0			0
$615$	−12.0000			−0.483887
$616$		0			0
$617$	22.0000			0.885687			0.442843	−	0.896599i	$-0.353970\pi$
$617$	22.0000			0.885687			0.442843	+	0.896599i	$0.353970\pi$
$618$		0			0
$619$	11.0000	+	19.0526i	0.442127	+	0.765787i	0.997847	−	0.0655827i	$-0.0208906\pi$
$619$	11.0000	+	19.0526i	0.442127	+	0.765787i	−0.555720	+	0.831370i	$0.687557\pi$
$620$		0			0
$621$	−4.00000	+	6.92820i	−0.160514	+	0.278019i
$622$		0			0
$623$	12.0000	+	10.3923i	0.480770	+	0.416359i
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	16.0000			0.637962
$630$		0			0
$631$	−43.0000			−1.71180			−0.855901	−	0.517139i	$-0.826997\pi$
$631$	−43.0000			−1.71180			−0.855901	+	0.517139i	$0.826997\pi$
$632$		0			0
$633$	−1.00000	−	1.73205i	−0.0397464	−	0.0688428i
$634$		0			0
$635$	−25.5000	+	44.1673i	−1.01194	+	1.75273i
$636$		0			0
$637$	26.0000	+	10.3923i	1.03016	+	0.411758i
$638$		0			0
$639$	−3.00000	+	5.19615i	−0.118678	+	0.205557i
$640$		0			0
$641$	5.00000	+	8.66025i	0.197488	+	0.342059i	0.947713	−	0.319123i	$-0.103388\pi$
$641$	5.00000	+	8.66025i	0.197488	+	0.342059i	−0.750225	+	0.661182i	$0.770055\pi$
$642$		0			0
$643$	2.00000			0.0788723			0.0394362	−	0.999222i	$-0.487444\pi$
$643$	2.00000			0.0788723			0.0394362	+	0.999222i	$0.487444\pi$
$644$		0			0
$645$	−6.00000			−0.236250
$646$		0			0
$647$	15.0000	+	25.9808i	0.589711	+	1.02141i	0.994270	+	0.106897i	$0.0340916\pi$
$647$	15.0000	+	25.9808i	0.589711	+	1.02141i	−0.404559	+	0.914512i	$0.632575\pi$
$648$		0			0
$649$	3.50000	−	6.06218i	0.137387	−	0.237961i
$650$		0			0
$651$	22.0000	+	19.0526i	0.862248	+	0.746729i
$652$		0			0
$653$	−21.5000	+	37.2391i	−0.841360	+	1.45728i	0.0473852	+	0.998877i	$0.484911\pi$
$653$	−21.5000	+	37.2391i	−0.841360	+	1.45728i	−0.888745	+	0.458402i	$0.848422\pi$
$654$		0			0
$655$	−4.50000	−	7.79423i	−0.175830	−	0.304546i
$656$		0			0
$657$	−6.00000			−0.234082
$658$		0			0
$659$		0			0			−	1.00000i	$-0.5\pi$
$659$		0			0				1.00000i	$0.5\pi$
$660$		0			0
$661$	21.0000	+	36.3731i	0.816805	+	1.41475i	0.908024	+	0.418917i	$0.137590\pi$
$661$	21.0000	+	36.3731i	0.816805	+	1.41475i	−0.0912190	+	0.995831i	$0.529076\pi$
$662$		0			0
$663$	8.00000	−	13.8564i	0.310694	−	0.538138i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	28.0000	−	48.4974i	1.08416	−	1.87783i
$668$		0			0
$669$	−4.50000	−	7.79423i	−0.173980	−	0.301342i
$670$		0			0
$671$	−10.0000			−0.386046
$672$		0			0
$673$	45.0000			1.73462			0.867311	−	0.497766i	$-0.165846\pi$
$673$	45.0000			1.73462			0.867311	+	0.497766i	$0.165846\pi$
$674$		0			0
$675$	−2.00000	−	3.46410i	−0.0769800	−	0.133333i
$676$		0			0
$677$	−7.50000	+	12.9904i	−0.288248	+	0.499261i	−0.973392	−	0.229147i	$-0.926406\pi$
$677$	−7.50000	+	12.9904i	−0.288248	+	0.499261i	0.685143	+	0.728408i	$0.259740\pi$
$678$		0			0
$679$	3.50000	−	18.1865i	0.134318	−	0.697935i
$680$		0			0
$681$	3.50000	−	6.06218i	0.134120	−	0.232303i
$682$		0			0
$683$	−10.5000	−	18.1865i	−0.401771	−	0.695888i	0.592168	−	0.805814i	$-0.298272\pi$
$683$	−10.5000	−	18.1865i	−0.401771	−	0.695888i	−0.993940	+	0.109926i	$0.964939\pi$
$684$		0			0
$685$	−6.00000			−0.229248
$686$		0			0
$687$	−8.00000			−0.305219
$688$		0			0
$689$	−22.0000	−	38.1051i	−0.838133	−	1.45169i
$690$		0			0
$691$	−10.0000	+	17.3205i	−0.380418	+	0.658903i	−0.991122	−	0.132956i	$-0.957553\pi$
$691$	−10.0000	+	17.3205i	−0.380418	+	0.658903i	0.610704	+	0.791859i	$0.290887\pi$
$692$		0			0
$693$	−0.500000	+	2.59808i	−0.0189934	+	0.0986928i
$694$		0			0
$695$	33.0000	−	57.1577i	1.25176	−	2.16811i
$696$		0			0
$697$	8.00000	+	13.8564i	0.303022	+	0.524849i
$698$		0			0
$699$	12.0000			0.453882
$700$		0			0
$701$	33.0000			1.24639			0.623196	−	0.782065i	$-0.285834\pi$
$701$	33.0000			1.24639			0.623196	+	0.782065i	$0.285834\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	3.00000	−	5.19615i	0.112987	−	0.195698i
$706$		0			0
$707$	−15.0000	+	5.19615i	−0.564133	+	0.195421i
$708$		0			0
$709$	17.0000	−	29.4449i	0.638448	−	1.10583i	−0.347325	−	0.937745i	$-0.612910\pi$
$709$	17.0000	−	29.4449i	0.638448	−	1.10583i	0.985773	−	0.168080i	$-0.0537568\pi$
$710$		0			0
$711$	−5.50000	−	9.52628i	−0.206266	−	0.357263i
$712$		0			0
$713$	88.0000			3.29563
$714$		0			0
$715$	12.0000			0.448775
$716$		0			0
$717$		0			0
$718$		0			0
$719$	9.00000	−	15.5885i	0.335643	−	0.581351i	−0.647965	−	0.761670i	$-0.724380\pi$
$719$	9.00000	−	15.5885i	0.335643	−	0.581351i	0.983608	+	0.180319i	$0.0577130\pi$
$720$		0			0
$721$	−32.0000	−	27.7128i	−1.19174	−	1.03208i
$722$		0			0
$723$	12.5000	−	21.6506i	0.464880	−	0.805196i
$724$		0			0
$725$	14.0000	+	24.2487i	0.519947	+	0.900575i
$726$		0			0
$727$	7.00000			0.259616			0.129808	−	0.991539i	$-0.458564\pi$
$727$	7.00000			0.259616			0.129808	+	0.991539i	$0.458564\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	4.00000	+	6.92820i	0.147945	+	0.256249i
$732$		0			0
$733$	−7.00000	+	12.1244i	−0.258551	+	0.447823i	−0.965854	−	0.259087i	$-0.916578\pi$
$733$	−7.00000	+	12.1244i	−0.258551	+	0.447823i	0.707303	+	0.706910i	$0.249912\pi$
$734$		0			0
$735$	−19.5000	−	7.79423i	−0.719268	−	0.287494i
$736$		0			0
$737$	5.00000	−	8.66025i	0.184177	−	0.319005i
$738$		0			0
$739$	−17.0000	−	29.4449i	−0.625355	−	1.08315i	−0.988472	−	0.151403i	$-0.951621\pi$
$739$	−17.0000	−	29.4449i	−0.625355	−	1.08315i	0.363117	−	0.931744i	$-0.381713\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−50.0000			−1.83432			−0.917161	−	0.398517i	$-0.869525\pi$
$743$	−50.0000			−1.83432			−0.917161	+	0.398517i	$0.869525\pi$
$744$		0			0
$745$	9.00000	+	15.5885i	0.329734	+	0.571117i
$746$		0			0
$747$	−5.50000	+	9.52628i	−0.201234	+	0.348548i
$748$		0			0
$749$	−14.0000	−	12.1244i	−0.511549	−	0.443014i
$750$		0			0
$751$	1.50000	−	2.59808i	0.0547358	−	0.0948051i	−0.837359	−	0.546653i	$-0.815902\pi$
$751$	1.50000	−	2.59808i	0.0547358	−	0.0948051i	0.892095	+	0.451848i	$0.149235\pi$
$752$		0			0
$753$	12.5000	+	21.6506i	0.455525	+	0.788993i
$754$		0			0
$755$	33.0000			1.20099
$756$		0			0
$757$	−14.0000			−0.508839			−0.254419	−	0.967094i	$-0.581884\pi$
$757$	−14.0000			−0.508839			−0.254419	+	0.967094i	$0.581884\pi$
$758$		0			0
$759$	4.00000	+	6.92820i	0.145191	+	0.251478i
$760$		0			0
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	−0.736543	−	0.676391i	$-0.763543\pi$
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	0.954043	+	0.299670i	$0.0968765\pi$
$762$		0			0
$763$	−25.0000	+	8.66025i	−0.905061	+	0.313522i
$764$		0			0
$765$	−6.00000	+	10.3923i	−0.216930	+	0.375735i
$766$		0			0
$767$	14.0000	+	24.2487i	0.505511	+	0.875570i
$768$		0			0
$769$	−3.00000			−0.108183			−0.0540914	−	0.998536i	$-0.517226\pi$
$769$	−3.00000			−0.108183			−0.0540914	+	0.998536i	$0.517226\pi$
$770$		0			0
$771$	14.0000			0.504198
$772$		0			0
$773$	−15.0000	−	25.9808i	−0.539513	−	0.934463i	−0.998930	−	0.0462427i	$-0.985275\pi$
$773$	−15.0000	−	25.9808i	−0.539513	−	0.934463i	0.459418	−	0.888220i	$-0.348058\pi$
$774$		0			0
$775$	−22.0000	+	38.1051i	−0.790263	+	1.36878i
$776$		0			0
$777$	2.00000	−	10.3923i	0.0717496	−	0.372822i
$778$		0			0
$779$		0			0
$780$		0			0
$781$	3.00000	+	5.19615i	0.107348	+	0.185933i
$782$		0			0
$783$	−7.00000			−0.250160
$784$		0			0
$785$	−36.0000			−1.28490
$786$		0			0
$787$	17.0000	+	29.4449i	0.605985	+	1.04960i	0.991895	+	0.127060i	$0.0405540\pi$
$787$	17.0000	+	29.4449i	0.605985	+	1.04960i	−0.385911	+	0.922536i	$0.626113\pi$
$788$		0			0
$789$	−13.0000	+	22.5167i	−0.462812	+	0.801614i
$790$		0			0
$791$	6.00000	−	31.1769i	0.213335	−	1.10852i
$792$		0			0
$793$	20.0000	−	34.6410i	0.710221	−	1.23014i
$794$		0			0
$795$	16.5000	+	28.5788i	0.585195	+	1.01359i
$796$		0			0
$797$	−25.0000			−0.885545			−0.442773	−	0.896634i	$-0.646005\pi$
$797$	−25.0000			−0.885545			−0.442773	+	0.896634i	$0.646005\pi$
$798$		0			0
$799$	−8.00000			−0.283020
$800$		0			0
$801$	−3.00000	−	5.19615i	−0.106000	−	0.183597i
$802$		0			0
$803$	−3.00000	+	5.19615i	−0.105868	+	0.183368i
$804$		0			0
$805$	−60.0000	+	20.7846i	−2.11472	+	0.732561i
$806$		0			0
$807$	−10.5000	+	18.1865i	−0.369618	+	0.640196i
$808$		0			0
$809$	−20.0000	−	34.6410i	−0.703163	−	1.21791i	−0.967351	−	0.253442i	$-0.918437\pi$
$809$	−20.0000	−	34.6410i	−0.703163	−	1.21791i	0.264188	−	0.964471i	$-0.414896\pi$
$810$		0			0
$811$	−2.00000			−0.0702295			−0.0351147	−	0.999383i	$-0.511180\pi$
$811$	−2.00000			−0.0702295			−0.0351147	+	0.999383i	$0.511180\pi$
$812$		0			0
$813$	−1.00000			−0.0350715
$814$		0			0
$815$	12.0000	+	20.7846i	0.420342	+	0.728053i
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−8.00000	−	6.92820i	−0.279543	−	0.242091i
$820$		0			0
$821$	−18.5000	+	32.0429i	−0.645654	+	1.11831i	0.338495	+	0.940968i	$0.390082\pi$
$821$	−18.5000	+	32.0429i	−0.645654	+	1.11831i	−0.984150	+	0.177338i	$0.943251\pi$
$822$		0			0
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	0.971102	−	0.238664i	$-0.0767093\pi$
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	−0.692240	+	0.721668i	$0.743376\pi$
$824$		0			0
$825$	−4.00000			−0.139262
$826$		0			0
$827$	−21.0000			−0.730242			−0.365121	−	0.930960i	$-0.618972\pi$
$827$	−21.0000			−0.730242			−0.365121	+	0.930960i	$0.618972\pi$
$828$		0			0
$829$	−12.0000	−	20.7846i	−0.416777	−	0.721879i	0.578836	−	0.815444i	$-0.303507\pi$
$829$	−12.0000	−	20.7846i	−0.416777	−	0.721879i	−0.995613	+	0.0935647i	$0.970174\pi$
$830$		0			0
$831$	−16.0000	+	27.7128i	−0.555034	+	0.961347i
$832$		0			0
$833$	4.00000	+	27.7128i	0.138592	+	0.960192i
$834$		0			0
$835$	33.0000	−	57.1577i	1.14201	−	1.97802i
$836$		0			0
$837$	−5.50000	−	9.52628i	−0.190108	−	0.329276i
$838$		0			0
$839$	20.0000			0.690477			0.345238	−	0.938515i	$-0.387798\pi$
$839$	20.0000			0.690477			0.345238	+	0.938515i	$0.387798\pi$
$840$		0			0
$841$	20.0000			0.689655
$842$		0			0
$843$	15.0000	+	25.9808i	0.516627	+	0.894825i
$844$		0			0
$845$	−4.50000	+	7.79423i	−0.154805	+	0.268130i
$846$		0			0
$847$	−20.0000	−	17.3205i	−0.687208	−	0.595140i
$848$		0			0
$849$	1.00000	−	1.73205i	0.0343199	−	0.0594438i
$850$		0			0
$851$	−16.0000	−	27.7128i	−0.548473	−	0.949983i
$852$		0			0
$853$	−30.0000			−1.02718			−0.513590	−	0.858036i	$-0.671685\pi$
$853$	−30.0000			−1.02718			−0.513590	+	0.858036i	$0.671685\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−21.0000	−	36.3731i	−0.717346	−	1.24248i	−0.962048	−	0.272882i	$-0.912023\pi$
$857$	−21.0000	−	36.3731i	−0.717346	−	1.24248i	0.244701	−	0.969599i	$-0.421310\pi$
$858$		0			0
$859$	−17.0000	+	29.4449i	−0.580033	+	1.00465i	0.415442	+	0.909620i	$0.363627\pi$
$859$	−17.0000	+	29.4449i	−0.580033	+	1.00465i	−0.995475	+	0.0950262i	$0.969707\pi$
$860$		0			0
$861$	10.0000	−	3.46410i	0.340799	−	0.118056i
$862$		0			0
$863$	9.00000	−	15.5885i	0.306364	−	0.530637i	−0.671200	−	0.741276i	$-0.734221\pi$
$863$	9.00000	−	15.5885i	0.306364	−	0.530637i	0.977564	+	0.210639i	$0.0675543\pi$
$864$		0			0
$865$	9.00000	+	15.5885i	0.306009	+	0.530023i
$866$		0			0
$867$	−1.00000			−0.0339618
$868$		0			0
$869$	−11.0000			−0.373149
$870$		0			0
$871$	20.0000	+	34.6410i	0.677674	+	1.17377i
$872$		0			0
$873$	−3.50000	+	6.06218i	−0.118457	+	0.205174i
$874$		0			0
$875$	−1.50000	+	7.79423i	−0.0507093	+	0.263493i
$876$		0			0
$877$	16.0000	−	27.7128i	0.540282	−	0.935795i	−0.458606	−	0.888640i	$-0.651651\pi$
$877$	16.0000	−	27.7128i	0.540282	−	0.935795i	0.998888	−	0.0471555i	$-0.0150156\pi$
$878$		0			0
$879$	3.50000	+	6.06218i	0.118052	+	0.204472i
$880$		0			0
$881$	−2.00000			−0.0673817			−0.0336909	−	0.999432i	$-0.510726\pi$
$881$	−2.00000			−0.0673817			−0.0336909	+	0.999432i	$0.510726\pi$
$882$		0			0
$883$	−52.0000			−1.74994			−0.874970	−	0.484178i	$-0.839119\pi$
$883$	−52.0000			−1.74994			−0.874970	+	0.484178i	$0.839119\pi$
$884$		0			0
$885$	−10.5000	−	18.1865i	−0.352954	−	0.611334i
$886$		0			0
$887$	4.00000	−	6.92820i	0.134307	−	0.232626i	−0.791026	−	0.611783i	$-0.790453\pi$
$887$	4.00000	−	6.92820i	0.134307	−	0.232626i	0.925332	+	0.379157i	$0.123786\pi$
$888$		0			0
$889$	8.50000	−	44.1673i	0.285081	−	1.48132i
$890$		0			0
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−36.0000			−1.20335
$896$		0			0
$897$	−32.0000			−1.06845
$898$		0			0
$899$	38.5000	+	66.6840i	1.28405	+	2.22403i
$900$		0			0
$901$	22.0000	−	38.1051i	0.732926	−	1.26947i
$902$		0			0
$903$	5.00000	−	1.73205i	0.166390	−	0.0576390i
$904$		0			0
$905$	−18.0000	+	31.1769i	−0.598340	+	1.03636i
$906$		0			0
$907$	−16.0000	−	27.7128i	−0.531271	−	0.920189i	−0.999334	−	0.0364935i	$-0.988381\pi$
$907$	−16.0000	−	27.7128i	−0.531271	−	0.920189i	0.468063	−	0.883695i	$-0.344952\pi$
$908$		0			0
$909$	6.00000			0.199007
$910$		0			0
$911$	58.0000			1.92163			0.960813	−	0.277198i	$-0.0894057\pi$
$911$	58.0000			1.92163			0.960813	+	0.277198i	$0.0894057\pi$
$912$		0			0
$913$	5.50000	+	9.52628i	0.182023	+	0.315274i
$914$		0			0
$915$	−15.0000	+	25.9808i	−0.495885	+	0.858898i
$916$		0			0
$917$	6.00000	+	5.19615i	0.198137	+	0.171592i
$918$		0			0
$919$	−4.00000	+	6.92820i	−0.131948	+	0.228540i	−0.924427	−	0.381358i	$-0.875456\pi$
$919$	−4.00000	+	6.92820i	−0.131948	+	0.228540i	0.792480	+	0.609898i	$0.208790\pi$
$920$		0			0
$921$	4.00000	+	6.92820i	0.131804	+	0.228292i
$922$		0			0
$923$	−24.0000			−0.789970
$924$		0			0
$925$	16.0000			0.526077
$926$		0			0
$927$	8.00000	+	13.8564i	0.262754	+	0.455104i
$928$		0			0
$929$	−9.00000	+	15.5885i	−0.295280	+	0.511441i	−0.975050	−	0.221985i	$-0.928746\pi$
$929$	−9.00000	+	15.5885i	−0.295280	+	0.511441i	0.679770	+	0.733426i	$0.262080\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−6.00000	+	10.3923i	−0.196431	+	0.340229i
$934$		0			0
$935$	6.00000	+	10.3923i	0.196221	+	0.339865i
$936$		0			0
$937$	−13.0000			−0.424691			−0.212346	−	0.977195i	$-0.568110\pi$
$937$	−13.0000			−0.424691			−0.212346	+	0.977195i	$0.568110\pi$
$938$		0			0
$939$	1.00000			0.0326338
$940$		0			0
$941$	24.5000	+	42.4352i	0.798677	+	1.38335i	0.920478	+	0.390795i	$0.127800\pi$
$941$	24.5000	+	42.4352i	0.798677	+	1.38335i	−0.121801	+	0.992555i	$0.538867\pi$
$942$		0			0
$943$	16.0000	−	27.7128i	0.521032	−	0.902453i
$944$		0			0
$945$	6.00000	+	5.19615i	0.195180	+	0.169031i
$946$		0			0
$947$	20.0000	−	34.6410i	0.649913	−	1.12568i	−0.333231	−	0.942845i	$-0.608139\pi$
$947$	20.0000	−	34.6410i	0.649913	−	1.12568i	0.983143	−	0.182836i	$-0.0585279\pi$
$948$		0			0
$949$	−12.0000	−	20.7846i	−0.389536	−	0.674697i
$950$		0			0
$951$	17.0000			0.551263
$952$		0			0
$953$	2.00000			0.0647864			0.0323932	−	0.999475i	$-0.489687\pi$
$953$	2.00000			0.0647864			0.0323932	+	0.999475i	$0.489687\pi$
$954$		0			0
$955$	−36.0000	−	62.3538i	−1.16493	−	2.01772i
$956$		0			0
$957$	−3.50000	+	6.06218i	−0.113139	+	0.195962i
$958$		0			0
$959$	5.00000	−	1.73205i	0.161458	−	0.0559308i
$960$		0			0
$961$	−45.0000	+	77.9423i	−1.45161	+	2.51427i
$962$		0			0
$963$	3.50000	+	6.06218i	0.112786	+	0.195351i
$964$		0			0
$965$	−57.0000			−1.83489
$966$		0			0
$967$	−5.00000			−0.160789			−0.0803946	−	0.996763i	$-0.525618\pi$
$967$	−5.00000			−0.160789			−0.0803946	+	0.996763i	$0.525618\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	13.5000	−	23.3827i	0.433236	−	0.750386i	−0.563914	−	0.825833i	$-0.690705\pi$
$971$	13.5000	−	23.3827i	0.433236	−	0.750386i	0.997150	+	0.0754473i	$0.0240385\pi$
$972$		0			0
$973$	−11.0000	+	57.1577i	−0.352644	+	1.83239i
$974$		0			0
$975$	8.00000	−	13.8564i	0.256205	−	0.443760i
$976$		0			0
$977$	−13.0000	−	22.5167i	−0.415907	−	0.720372i	0.579616	−	0.814890i	$-0.303202\pi$
$977$	−13.0000	−	22.5167i	−0.415907	−	0.720372i	−0.995523	+	0.0945177i	$0.969869\pi$
$978$		0			0
$979$	−6.00000			−0.191761
$980$		0			0
$981$	10.0000			0.319275
$982$		0			0
$983$	24.0000	+	41.5692i	0.765481	+	1.32585i	0.939992	+	0.341197i	$0.110832\pi$
$983$	24.0000	+	41.5692i	0.765481	+	1.32585i	−0.174511	+	0.984655i	$0.555834\pi$
$984$		0			0
$985$	−9.00000	+	15.5885i	−0.286764	+	0.496690i
$986$		0			0
$987$	−1.00000	+	5.19615i	−0.0318304	+	0.165395i
$988$		0			0
$989$	8.00000	−	13.8564i	0.254385	−	0.440608i
$990$		0			0
$991$	−11.5000	−	19.9186i	−0.365310	−	0.632735i	0.623516	−	0.781810i	$-0.285704\pi$
$991$	−11.5000	−	19.9186i	−0.365310	−	0.632735i	−0.988826	+	0.149076i	$0.952370\pi$
$992$		0			0
$993$	12.0000			0.380808
$994$		0			0
$995$	−60.0000			−1.90213
$996$		0			0
$997$	−1.00000	−	1.73205i	−0.0316703	−	0.0548546i	0.849756	−	0.527176i	$-0.176749\pi$
$997$	−1.00000	−	1.73205i	−0.0316703	−	0.0548546i	−0.881426	+	0.472322i	$0.843416\pi$
$998$		0			0
$999$	−2.00000	+	3.46410i	−0.0632772	+	0.109599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.q.a.289.1	yes	2
3.2	odd	2		2016.2.s.n.289.1		2
4.3	odd	2		672.2.q.f.289.1	yes	2
7.2	even	3		4704.2.a.bf.1.1		1
7.4	even	3	inner	672.2.q.a.193.1	✓	2
7.5	odd	6		4704.2.a.b.1.1		1
8.3	odd	2		1344.2.q.k.961.1		2
8.5	even	2		1344.2.q.u.961.1		2
12.11	even	2		2016.2.s.k.289.1		2
21.11	odd	6		2016.2.s.n.865.1		2
28.11	odd	6		672.2.q.f.193.1	yes	2
28.19	even	6		4704.2.a.s.1.1		1
28.23	odd	6		4704.2.a.o.1.1		1
56.5	odd	6		9408.2.a.dc.1.1		1
56.11	odd	6		1344.2.q.k.193.1		2
56.19	even	6		9408.2.a.bl.1.1		1
56.37	even	6		9408.2.a.e.1.1		1
56.51	odd	6		9408.2.a.bt.1.1		1
56.53	even	6		1344.2.q.u.193.1		2
84.11	even	6		2016.2.s.k.865.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.q.a.193.1	✓	2	7.4	even	3	inner
672.2.q.a.289.1	yes	2	1.1	even	1	trivial
672.2.q.f.193.1	yes	2	28.11	odd	6
672.2.q.f.289.1	yes	2	4.3	odd	2
1344.2.q.k.193.1		2	56.11	odd	6
1344.2.q.k.961.1		2	8.3	odd	2
1344.2.q.u.193.1		2	56.53	even	6
1344.2.q.u.961.1		2	8.5	even	2
2016.2.s.k.289.1		2	12.11	even	2
2016.2.s.k.865.1		2	84.11	even	6
2016.2.s.n.289.1		2	3.2	odd	2
2016.2.s.n.865.1		2	21.11	odd	6
4704.2.a.b.1.1		1	7.5	odd	6
4704.2.a.o.1.1		1	28.23	odd	6
4704.2.a.s.1.1		1	28.19	even	6
4704.2.a.bf.1.1		1	7.2	even	3
9408.2.a.e.1.1		1	56.37	even	6
9408.2.a.bl.1.1		1	56.19	even	6
9408.2.a.bt.1.1		1	56.51	odd	6
9408.2.a.dc.1.1		1	56.5	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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +(-1.50000 + 2.59808i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{3} +(-1.50000 + 2.59808i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{11} -4.00000 q^{13} +3.00000 q^{15} +(-2.00000 - 3.46410i) q^{17} +(-2.50000 + 0.866025i) q^{21} +(-4.00000 + 6.92820i) q^{23} +(-2.00000 - 3.46410i) q^{25} +1.00000 q^{27} -7.00000 q^{29} +(-5.50000 - 9.52628i) q^{31} +(0.500000 - 0.866025i) q^{33} +(6.00000 + 5.19615i) q^{35} +(-2.00000 + 3.46410i) q^{37} +(2.00000 + 3.46410i) q^{39} -4.00000 q^{41} -2.00000 q^{43} +(-1.50000 - 2.59808i) q^{45} +(1.00000 - 1.73205i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(-2.00000 + 3.46410i) q^{51} +(5.50000 + 9.52628i) q^{53} -3.00000 q^{55} +(-3.50000 - 6.06218i) q^{59} +(-5.00000 + 8.66025i) q^{61} +(2.00000 + 1.73205i) q^{63} +(6.00000 - 10.3923i) q^{65} +(-5.00000 - 8.66025i) q^{67} +8.00000 q^{69} +6.00000 q^{71} +(3.00000 + 5.19615i) q^{73} +(-2.00000 + 3.46410i) q^{75} +(2.50000 - 0.866025i) q^{77} +(-5.50000 + 9.52628i) q^{79} +(-0.500000 - 0.866025i) q^{81} +11.0000 q^{83} +12.0000 q^{85} +(3.50000 + 6.06218i) q^{87} +(-3.00000 + 5.19615i) q^{89} +(-2.00000 + 10.3923i) q^{91} +(-5.50000 + 9.52628i) q^{93} +7.00000 q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{3} - 3 q^{5} + q^{7} - q^{9}+O(q^{10}) \) 2 * q - q^3 - 3 * q^5 + q^7 - q^9	\( 2 q - q^{3} - 3 q^{5} + q^{7} - q^{9} + q^{11} - 8 q^{13} + 6 q^{15} - 4 q^{17} - 5 q^{21} - 8 q^{23} - 4 q^{25} + 2 q^{27} - 14 q^{29} - 11 q^{31} + q^{33} + 12 q^{35} - 4 q^{37} + 4 q^{39} - 8 q^{41} - 4 q^{43} - 3 q^{45} + 2 q^{47} - 13 q^{49} - 4 q^{51} + 11 q^{53} - 6 q^{55} - 7 q^{59} - 10 q^{61} + 4 q^{63} + 12 q^{65} - 10 q^{67} + 16 q^{69} + 12 q^{71} + 6 q^{73} - 4 q^{75} + 5 q^{77} - 11 q^{79} - q^{81} + 22 q^{83} + 24 q^{85} + 7 q^{87} - 6 q^{89} - 4 q^{91} - 11 q^{93} + 14 q^{97} - 2 q^{99}+O(q^{100}) \) 2 * q - q^3 - 3 * q^5 + q^7 - q^9 + q^11 - 8 * q^13 + 6 * q^15 - 4 * q^17 - 5 * q^21 - 8 * q^23 - 4 * q^25 + 2 * q^27 - 14 * q^29 - 11 * q^31 + q^33 + 12 * q^35 - 4 * q^37 + 4 * q^39 - 8 * q^41 - 4 * q^43 - 3 * q^45 + 2 * q^47 - 13 * q^49 - 4 * q^51 + 11 * q^53 - 6 * q^55 - 7 * q^59 - 10 * q^61 + 4 * q^63 + 12 * q^65 - 10 * q^67 + 16 * q^69 + 12 * q^71 + 6 * q^73 - 4 * q^75 + 5 * q^77 - 11 * q^79 - q^81 + 22 * q^83 + 24 * q^85 + 7 * q^87 - 6 * q^89 - 4 * q^91 - 11 * q^93 + 14 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more