LMFDB - Embedded newform 1344.2.q.u.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(193,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, 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("1344.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.7318940317$
Analytic rank:	$0$
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:	no (minimal twist has level 672)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1344.193
Dual form			1344.2.q.u.961.1

$q$-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 $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			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	0.977672	+	0.210138i	$0.0673912\pi$
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	−0.306851	+	0.951757i	$0.599275\pi$
$6$		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	$-0.881504\pi$
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	0.780750	+	0.624844i	$0.214837\pi$
$12$		0			0
$13$	4.00000			1.10940			0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000			1.10940			0.554700	+	0.832050i	$0.312833\pi$
$14$		0			0
$15$	3.00000			0.774597
$16$		0			0
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	−0.999853	−	0.0171533i	$-0.994540\pi$
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	0.514782	+	0.857321i	$0.327873\pi$
$18$		0			0
$19$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$19$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$20$		0			0
$21$	2.50000	+	0.866025i	0.545545	+	0.188982i
$22$		0			0
$23$	−4.00000	−	6.92820i	−0.834058	−	1.44463i	−0.894795	−	0.446476i	$-0.852679\pi$
$23$	−4.00000	−	6.92820i	−0.834058	−	1.44463i	0.0607377	−	0.998154i	$-0.480655\pi$
$24$		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	$-0.274797\pi$
$29$	7.00000			1.29987			0.649934	+	0.759991i	$0.274797\pi$
$30$		0			0
$31$	−5.50000	+	9.52628i	−0.987829	+	1.71097i	−0.359211	+	0.933257i	$0.616954\pi$
$31$	−5.50000	+	9.52628i	−0.987829	+	1.71097i	−0.628619	+	0.777714i	$0.716379\pi$
$32$		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	$-0.0600231\pi$
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	−0.653476	+	0.756948i	$0.726690\pi$
$38$		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	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$		0			0
$45$	1.50000	−	2.59808i	0.223607	−	0.387298i
$46$		0			0
$47$	1.00000	+	1.73205i	0.145865	+	0.252646i	0.929695	−	0.368329i	$-0.120070\pi$
$47$	1.00000	+	1.73205i	0.145865	+	0.252646i	−0.783830	+	0.620975i	$0.786737\pi$
$48$		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	0.189651	+	0.981852i	$0.439264\pi$
$53$	−5.50000	+	9.52628i	−0.755483	+	1.30854i	−0.945134	+	0.326683i	$0.894069\pi$
$54$		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	$-0.682736\pi$
$59$	3.50000	−	6.06218i	0.455661	−	0.789228i	0.998726	+	0.0504625i	$0.0160695\pi$
$60$		0			0
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	0.985391	+	0.170305i	$0.0544754\pi$
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	−0.345207	+	0.938527i	$0.612191\pi$
$62$		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	−0.380251	−	0.924883i	$-0.624162\pi$
$67$	5.00000	−	8.66025i	0.610847	−	1.05802i	0.991098	−	0.133135i	$-0.0425044\pi$
$68$		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	−0.635323	−	0.772246i	$-0.719133\pi$
$73$	3.00000	−	5.19615i	0.351123	−	0.608164i	0.986447	+	0.164083i	$0.0524664\pi$
$74$		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	−0.989705	−	0.143120i	$-0.954286\pi$
$79$	−5.50000	−	9.52628i	−0.618798	−	1.07179i	0.370907	−	0.928670i	$-0.379047\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−11.0000			−1.20741			−0.603703	−	0.797209i	$-0.706309\pi$
$83$	−11.0000			−1.20741			−0.603703	+	0.797209i	$0.706309\pi$
$84$		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	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$		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	$-0.736843\pi$
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	0.975796	+	0.218685i	$0.0701767\pi$
$102$		0			0
$103$	8.00000	+	13.8564i	0.788263	+	1.36531i	0.927030	+	0.374987i	$0.122353\pi$
$103$	8.00000	+	13.8564i	0.788263	+	1.36531i	−0.138767	+	0.990325i	$0.544314\pi$
$104$		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	$-0.276538\pi$
$107$	−3.50000	−	6.06218i	−0.338358	−	0.586053i	−0.984124	+	0.177482i	$0.943205\pi$
$108$		0			0
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	−0.520794	−	0.853682i	$-0.674364\pi$
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	0.999708	+	0.0241802i	$0.00769755\pi$
$110$		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	$-0.124830\pi$
$131$	1.50000	+	2.59808i	0.131056	+	0.226995i	−0.793028	+	0.609185i	$0.791497\pi$
$132$		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	−0.820141	−	0.572161i	$-0.806105\pi$
$137$	1.00000	−	1.73205i	0.0854358	−	0.147979i	0.905577	+	0.424182i	$0.139438\pi$
$138$		0			0
$139$	22.0000			1.86602			0.933008	−	0.359856i	$-0.117174\pi$
$139$	22.0000			1.86602			0.933008	+	0.359856i	$0.117174\pi$
$140$		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	$-0.245707\pi$
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	−0.962348	+	0.271821i	$0.912374\pi$
$150$		0			0
$151$	−5.50000	+	9.52628i	−0.447584	+	0.775238i	−0.998228	−	0.0595022i	$-0.981049\pi$
$151$	−5.50000	+	9.52628i	−0.447584	+	0.775238i	0.550645	+	0.834740i	$0.314382\pi$
$152$		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	$-0.992280\pi$
$157$	−6.00000	+	10.3923i	−0.478852	+	0.829396i	0.520854	+	0.853646i	$0.325614\pi$
$158$		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	$-0.268103\pi$
$163$	−4.00000	−	6.92820i	−0.313304	−	0.542659i	−0.979076	+	0.203497i	$0.934769\pi$
$164$		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	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$		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	$-0.981361\pi$
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	0.549825	+	0.835280i	$0.314694\pi$
$180$		0			0
$181$	−12.0000			−0.891953			−0.445976	−	0.895045i	$-0.647144\pi$
$181$	−12.0000			−0.891953			−0.445976	+	0.895045i	$0.647144\pi$
$182$		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	−0.863743	−	0.503932i	$-0.831886\pi$
$191$	−12.0000	−	20.7846i	−0.868290	−	1.50392i	−0.00454614	−	0.999990i	$-0.501447\pi$
$192$		0			0
$193$	9.50000	−	16.4545i	0.683825	−	1.18442i	−0.289980	−	0.957033i	$-0.593649\pi$
$193$	9.50000	−	16.4545i	0.683825	−	1.18442i	0.973805	−	0.227387i	$-0.0730182\pi$
$194$		0			0
$195$	12.0000			0.859338
$196$		0			0
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$		0			0
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	−0.256391	−	0.966573i	$-0.582534\pi$
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	0.965272	−	0.261245i	$-0.0841331\pi$
$200$		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	$-0.521931\pi$
$211$	−2.00000			−0.137686			−0.0688428	+	0.997628i	$0.521931\pi$
$212$		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	$-0.907959\pi$
$227$	−3.50000	+	6.06218i	−0.232303	+	0.402361i	0.726182	+	0.687502i	$0.241293\pi$
$228$		0			0
$229$	−4.00000	−	6.92820i	−0.264327	−	0.457829i	0.703060	−	0.711131i	$-0.251817\pi$
$229$	−4.00000	−	6.92820i	−0.264327	−	0.457829i	−0.967387	+	0.253302i	$0.918483\pi$
$230$		0			0
$231$	−2.00000	+	1.73205i	−0.131590	+	0.113961i
$232$		0			0
$233$	−6.00000	−	10.3923i	−0.393073	−	0.680823i	0.599780	−	0.800165i	$-0.295255\pi$
$233$	−6.00000	−	10.3923i	−0.393073	−	0.680823i	−0.992853	+	0.119342i	$0.961921\pi$
$234$		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	−0.110963	−	0.993825i	$-0.535394\pi$
$241$	12.5000	−	21.6506i	0.805196	−	1.39464i	0.916159	−	0.400815i	$-0.131273\pi$
$242$		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	$-0.210603\pi$
$251$	25.0000			1.57799			0.788993	+	0.614402i	$0.210603\pi$
$252$		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	0.560781	−	0.827964i	$-0.310501\pi$
$257$	−7.00000	−	12.1244i	−0.436648	−	0.756297i	−0.997429	+	0.0716680i	$0.977168\pi$
$258$		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	0.116939	+	0.993139i	$0.462692\pi$
$263$	−13.0000	+	22.5167i	−0.801614	+	1.38844i	−0.918553	+	0.395298i	$0.870641\pi$
$264$		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	−0.345192	−	0.938532i	$-0.612186\pi$
$269$	10.5000	−	18.1865i	0.640196	−	1.10885i	0.985389	−	0.170321i	$-0.0544803\pi$
$270$		0			0
$271$	0.500000	+	0.866025i	0.0303728	+	0.0526073i	0.880812	−	0.473466i	$-0.156997\pi$
$271$	0.500000	+	0.866025i	0.0303728	+	0.0526073i	−0.850439	+	0.526073i	$0.823664\pi$
$272$		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	0.242222	−	0.970221i	$-0.422124\pi$
$277$	16.0000	−	27.7128i	0.961347	−	1.66510i	0.719125	−	0.694881i	$-0.244543\pi$
$278$		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	$-0.852266\pi$
$283$	−1.00000	+	1.73205i	−0.0594438	+	0.102960i	0.834772	+	0.550596i	$0.185599\pi$
$284$		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	$-0.434452\pi$
$293$	7.00000			0.408944			0.204472	+	0.978872i	$0.434452\pi$
$294$		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	$-0.426686\pi$
$307$	8.00000			0.456584			0.228292	+	0.973593i	$0.426686\pi$
$308$		0			0
$309$	16.0000			0.910208
$310$		0			0
$311$	−6.00000	+	10.3923i	−0.340229	+	0.589294i	−0.984475	−	0.175525i	$-0.943838\pi$
$311$	−6.00000	+	10.3923i	−0.340229	+	0.589294i	0.644246	+	0.764818i	$0.277171\pi$
$312$		0			0
$313$	−0.500000	−	0.866025i	−0.0282617	−	0.0489506i	0.851549	−	0.524276i	$-0.175664\pi$
$313$	−0.500000	−	0.866025i	−0.0282617	−	0.0489506i	−0.879810	+	0.475325i	$0.842331\pi$
$314$		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	$-0.00824321\pi$
$317$	8.50000	+	14.7224i	0.477408	+	0.826894i	−0.522257	+	0.852788i	$0.674910\pi$
$318$		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	$-0.0596888\pi$
$331$	6.00000	+	10.3923i	0.329790	+	0.571213i	−0.652680	+	0.757634i	$0.726355\pi$
$332$		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	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		0			0
$349$	34.0000			1.81998			0.909989	−	0.414632i	$-0.136090\pi$
$349$	34.0000			1.81998			0.909989	+	0.414632i	$0.136090\pi$
$350$		0			0
$351$	−4.00000			−0.213504
$352$		0			0
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	−0.347024	−	0.937856i	$-0.612808\pi$
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	0.985719	−	0.168397i	$-0.0538590\pi$
$354$		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	0.838429	−	0.545010i	$-0.183474\pi$
$359$	−1.00000	−	1.73205i	−0.0527780	−	0.0914141i	−0.891207	+	0.453596i	$0.850141\pi$
$360$		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	−0.997960	−	0.0638362i	$-0.979666\pi$
$367$	−8.50000	+	14.7224i	−0.443696	+	0.768505i	0.554264	+	0.832341i	$0.313000\pi$
$368$		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	$-0.267219\pi$
$373$	−6.00000	−	10.3923i	−0.310668	−	0.538093i	−0.978507	+	0.206213i	$0.933886\pi$
$374$		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	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$		0			0
$381$	8.50000	−	14.7224i	0.435468	−	0.754253i
$382$		0			0
$383$	−1.00000	−	1.73205i	−0.0510976	−	0.0885037i	0.839345	−	0.543599i	$-0.182939\pi$
$383$	−1.00000	−	1.73205i	−0.0510976	−	0.0885037i	−0.890443	+	0.455095i	$0.849605\pi$
$384$		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	$-0.881939\pi$
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	0.779895	+	0.625910i	$0.215272\pi$
$390$		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	$-0.198672\pi$
$397$	−2.00000	−	3.46410i	−0.100377	−	0.173858i	−0.911840	+	0.410546i	$0.865338\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−8.00000	−	13.8564i	−0.399501	−	0.691956i	0.594163	−	0.804344i	$-0.297483\pi$
$401$	−8.00000	−	13.8564i	−0.399501	−	0.691956i	−0.993664	+	0.112388i	$0.964150\pi$
$402$		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	−0.939490	−	0.342578i	$-0.888700\pi$
$409$	−3.50000	+	6.06218i	−0.173064	+	0.299755i	0.766426	+	0.642333i	$0.222033\pi$
$410$		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	$-0.300608\pi$
$419$	24.0000			1.17248			0.586238	+	0.810139i	$0.300608\pi$
$420$		0			0
$421$	−30.0000			−1.46211			−0.731055	−	0.682318i	$-0.760972\pi$
$421$	−30.0000			−1.46211			−0.731055	+	0.682318i	$0.760972\pi$
$422$		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	−0.946135	−	0.323772i	$-0.895049\pi$
$431$	−4.00000	+	6.92820i	−0.192673	+	0.333720i	0.753462	+	0.657491i	$0.228382\pi$
$432$		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	0.629664	−	0.776868i	$-0.283193\pi$
$439$	−7.50000	−	12.9904i	−0.357955	−	0.619997i	−0.987619	+	0.156871i	$0.949859\pi$
$440$		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	$-0.332918\pi$
$443$	−10.5000	−	18.1865i	−0.498870	−	0.864068i	−0.999999	+	0.00130426i	$0.999585\pi$
$444$		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	0.993431	−	0.114433i	$-0.0365053\pi$
$457$	8.50000	+	14.7224i	0.397613	+	0.688686i	−0.595818	+	0.803120i	$0.703172\pi$
$458$		0			0
$459$	2.00000	−	3.46410i	0.0933520	−	0.161690i
$460$		0			0
$461$	2.00000			0.0931493			0.0465746	−	0.998915i	$-0.485169\pi$
$461$	2.00000			0.0931493			0.0465746	+	0.998915i	$0.485169\pi$
$462$		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	$-0.0771121\pi$
$467$	6.00000	+	10.3923i	0.277647	+	0.480899i	−0.693153	+	0.720791i	$0.743779\pi$
$468$		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	−0.926388	−	0.376571i	$-0.877103\pi$
$479$	−3.00000	+	5.19615i	−0.137073	+	0.237418i	0.789314	+	0.613990i	$0.210436\pi$
$480$		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	−0.830037	−	0.557709i	$-0.811681\pi$
$487$	1.50000	−	2.59808i	0.0679715	−	0.117730i	0.898008	+	0.439979i	$0.145014\pi$
$488$		0			0
$489$	−8.00000			−0.361773
$490$		0			0
$491$	37.0000			1.66979			0.834893	−	0.550412i	$-0.185529\pi$
$491$	37.0000			1.66979			0.834893	+	0.550412i	$0.185529\pi$
$492$		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	$-0.0948104\pi$
$499$	5.00000	+	8.66025i	0.223831	+	0.387686i	−0.732137	+	0.681157i	$0.761477\pi$
$500$		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	−0.738945	−	0.673766i	$-0.764676\pi$
$509$	−21.5000	−	37.2391i	−0.952971	−	1.65059i	−0.214026	−	0.976828i	$-0.568658\pi$
$510$		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	−0.977633	−	0.210318i	$-0.932550\pi$
$521$	−7.00000	+	12.1244i	−0.306676	+	0.531178i	0.670957	+	0.741496i	$0.265883\pi$
$522$		0			0
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	0.560208	−	0.828352i	$-0.310721\pi$
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	−0.997478	+	0.0709788i	$0.977388\pi$
$524$		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	−0.984325	−	0.176367i	$-0.943566\pi$
$541$	−15.0000	−	25.9808i	−0.644900	−	1.11700i	0.339424	−	0.940633i	$-0.389768\pi$
$542$		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	$-0.359370\pi$
$547$	20.0000			0.855138			0.427569	+	0.903983i	$0.359370\pi$
$548$		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	$-0.813089\pi$
$557$	1.50000	−	2.59808i	0.0635570	−	0.110084i	0.896053	+	0.443947i	$0.146422\pi$
$558$		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	$-0.702212\pi$
$563$	9.50000	−	16.4545i	0.400377	−	0.693474i	0.993771	+	0.111438i	$0.0355457\pi$
$564$		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	$-0.166667\pi$
$569$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$570$		0			0
$571$	−11.0000	+	19.0526i	−0.460336	+	0.797325i	−0.998978	−	0.0452101i	$-0.985604\pi$
$571$	−11.0000	+	19.0526i	−0.460336	+	0.797325i	0.538642	+	0.842535i	$0.318938\pi$
$572$		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	−0.633062	−	0.774101i	$-0.718202\pi$
$577$	8.50000	−	14.7224i	0.353860	−	0.612903i	0.986922	+	0.161198i	$0.0515357\pi$
$578$		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	$-0.399819\pi$
$587$	15.0000			0.619116			0.309558	+	0.950881i	$0.399819\pi$
$588$		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	$-0.166667\pi$
$593$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$594$		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	−0.989210	−	0.146503i	$-0.953198\pi$
$599$	−9.00000	+	15.5885i	−0.367730	+	0.636927i	0.621480	+	0.783430i	$0.286532\pi$
$600$		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	0.998415	+	0.0562808i	$0.0179242\pi$
$607$	13.5000	+	23.3827i	0.547948	+	0.949074i	−0.450467	+	0.892793i	$0.648742\pi$
$608$		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	$-0.938064\pi$
$613$	−8.00000	+	13.8564i	−0.323117	+	0.559655i	0.658012	+	0.753007i	$0.271397\pi$
$614$		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	$-0.979109\pi$
$619$	−11.0000	+	19.0526i	−0.442127	+	0.765787i	0.555720	+	0.831370i	$0.312443\pi$
$620$		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	−0.750225	−	0.661182i	$-0.770055\pi$
$641$	5.00000	−	8.66025i	0.197488	−	0.342059i	0.947713	+	0.319123i	$0.103388\pi$
$642$		0			0
$643$	−2.00000			−0.0788723			−0.0394362	−	0.999222i	$-0.512556\pi$
$643$	−2.00000			−0.0788723			−0.0394362	+	0.999222i	$0.512556\pi$
$644$		0			0
$645$	6.00000			0.236250
$646$		0			0
$647$	15.0000	−	25.9808i	0.589711	−	1.02141i	−0.404559	−	0.914512i	$-0.632575\pi$
$647$	15.0000	−	25.9808i	0.589711	−	1.02141i	0.994270	−	0.106897i	$-0.0340916\pi$
$648$		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	0.888745	+	0.458402i	$0.151578\pi$
$653$	21.5000	+	37.2391i	0.841360	+	1.45728i	−0.0473852	+	0.998877i	$0.515089\pi$
$654$		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	0.0912190	+	0.995831i	$0.470924\pi$
$661$	−21.0000	+	36.3731i	−0.816805	+	1.41475i	−0.908024	+	0.418917i	$0.862410\pi$
$662$		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	$-0.0735938\pi$
$677$	7.50000	+	12.9904i	0.288248	+	0.499261i	−0.685143	+	0.728408i	$0.740260\pi$
$678$		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	$-0.701728\pi$
$683$	10.5000	−	18.1865i	0.401771	−	0.695888i	0.993940	+	0.109926i	$0.0350613\pi$
$684$		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	$-0.0424468\pi$
$691$	10.0000	+	17.3205i	0.380418	+	0.658903i	−0.610704	+	0.791859i	$0.709113\pi$
$692$		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	$-0.714166\pi$
$701$	−33.0000			−1.24639			−0.623196	+	0.782065i	$0.714166\pi$
$702$		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	−0.985773	−	0.168080i	$-0.946243\pi$
$709$	−17.0000	−	29.4449i	−0.638448	−	1.10583i	0.347325	−	0.937745i	$-0.387090\pi$
$710$		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	0.983608	−	0.180319i	$-0.0577130\pi$
$719$	9.00000	+	15.5885i	0.335643	+	0.581351i	−0.647965	+	0.761670i	$0.724380\pi$
$720$		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	$-0.0834217\pi$
$733$	7.00000	+	12.1244i	0.258551	+	0.447823i	−0.707303	+	0.706910i	$0.750088\pi$
$734$		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	−0.363117	−	0.931744i	$-0.618287\pi$
$739$	17.0000	−	29.4449i	0.625355	−	1.08315i	0.988472	−	0.151403i	$-0.0483792\pi$
$740$		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	0.892095	−	0.451848i	$-0.149235\pi$
$751$	1.50000	+	2.59808i	0.0547358	+	0.0948051i	−0.837359	+	0.546653i	$0.815902\pi$
$752$		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	$-0.418116\pi$
$757$	14.0000			0.508839			0.254419	+	0.967094i	$0.418116\pi$
$758$		0			0
$759$	4.00000	−	6.92820i	0.145191	−	0.251478i
$760$		0			0
$761$	6.00000	+	10.3923i	0.217500	+	0.376721i	0.954043	−	0.299670i	$-0.0968765\pi$
$761$	6.00000	+	10.3923i	0.217500	+	0.376721i	−0.736543	+	0.676391i	$0.763543\pi$
$762$		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	−0.459418	−	0.888220i	$-0.651942\pi$
$773$	15.0000	−	25.9808i	0.539513	−	0.934463i	0.998930	−	0.0462427i	$-0.0147248\pi$
$774$		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	0.385911	+	0.922536i	$0.373887\pi$
$787$	−17.0000	+	29.4449i	−0.605985	+	1.04960i	−0.991895	+	0.127060i	$0.959446\pi$
$788$		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	$-0.353995\pi$
$797$	25.0000			0.885545			0.442773	+	0.896634i	$0.353995\pi$
$798$		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	0.264188	+	0.964471i	$0.414896\pi$
$809$	−20.0000	+	34.6410i	−0.703163	+	1.21791i	−0.967351	+	0.253442i	$0.918437\pi$
$810$		0			0
$811$	2.00000			0.0702295			0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000			0.0702295			0.0351147	+	0.999383i	$0.488820\pi$
$812$		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	0.984150	+	0.177338i	$0.0567487\pi$
$821$	18.5000	+	32.0429i	0.645654	+	1.11831i	−0.338495	+	0.940968i	$0.609918\pi$
$822$		0			0
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	−0.692240	−	0.721668i	$-0.743376\pi$
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	0.971102	+	0.238664i	$0.0767093\pi$
$824$		0			0
$825$	−4.00000			−0.139262
$826$		0			0
$827$	21.0000			0.730242			0.365121	−	0.930960i	$-0.381028\pi$
$827$	21.0000			0.730242			0.365121	+	0.930960i	$0.381028\pi$
$828$		0			0
$829$	12.0000	−	20.7846i	0.416777	−	0.721879i	−0.578836	−	0.815444i	$-0.696493\pi$
$829$	12.0000	−	20.7846i	0.416777	−	0.721879i	0.995613	+	0.0935647i	$0.0298262\pi$
$830$		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	$-0.328315\pi$
$853$	30.0000			1.02718			0.513590	+	0.858036i	$0.328315\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−21.0000	+	36.3731i	−0.717346	+	1.24248i	0.244701	+	0.969599i	$0.421310\pi$
$857$	−21.0000	+	36.3731i	−0.717346	+	1.24248i	−0.962048	+	0.272882i	$0.912023\pi$
$858$		0			0
$859$	17.0000	+	29.4449i	0.580033	+	1.00465i	0.995475	+	0.0950262i	$0.0302935\pi$
$859$	17.0000	+	29.4449i	0.580033	+	1.00465i	−0.415442	+	0.909620i	$0.636373\pi$
$860$		0			0
$861$	−10.0000	−	3.46410i	−0.340799	−	0.118056i
$862$		0			0
$863$	9.00000	+	15.5885i	0.306364	+	0.530637i	0.977564	−	0.210639i	$-0.0675543\pi$
$863$	9.00000	+	15.5885i	0.306364	+	0.530637i	−0.671200	+	0.741276i	$0.734221\pi$
$864$		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	−0.998888	−	0.0471555i	$-0.984984\pi$
$877$	−16.0000	−	27.7128i	−0.540282	−	0.935795i	0.458606	−	0.888640i	$-0.348349\pi$
$878$		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	$-0.160881\pi$
$883$	52.0000			1.74994			0.874970	+	0.484178i	$0.160881\pi$
$884$		0			0
$885$	10.5000	−	18.1865i	0.352954	−	0.611334i
$886$		0			0
$887$	4.00000	+	6.92820i	0.134307	+	0.232626i	0.925332	−	0.379157i	$-0.123786\pi$
$887$	4.00000	+	6.92820i	0.134307	+	0.232626i	−0.791026	+	0.611783i	$0.790453\pi$
$888$		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	−0.468063	−	0.883695i	$-0.655048\pi$
$907$	16.0000	−	27.7128i	0.531271	−	0.920189i	0.999334	−	0.0364935i	$-0.0116188\pi$
$908$		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	0.792480	−	0.609898i	$-0.208790\pi$
$919$	−4.00000	−	6.92820i	−0.131948	−	0.228540i	−0.924427	+	0.381358i	$0.875456\pi$
$920$		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	0.679770	−	0.733426i	$-0.262080\pi$
$929$	−9.00000	−	15.5885i	−0.295280	−	0.511441i	−0.975050	+	0.221985i	$0.928746\pi$
$930$		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	0.121801	+	0.992555i	$0.461133\pi$
$941$	−24.5000	+	42.4352i	−0.798677	+	1.38335i	−0.920478	+	0.390795i	$0.872200\pi$
$942$		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	−0.983143	−	0.182836i	$-0.941472\pi$
$947$	−20.0000	−	34.6410i	−0.649913	−	1.12568i	0.333231	−	0.942845i	$-0.391861\pi$
$948$		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	$-0.309295\pi$
$971$	−13.5000	−	23.3827i	−0.433236	−	0.750386i	−0.997150	+	0.0754473i	$0.975962\pi$
$972$		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	−0.995523	−	0.0945177i	$-0.969869\pi$
$977$	−13.0000	+	22.5167i	−0.415907	+	0.720372i	0.579616	+	0.814890i	$0.303202\pi$
$978$		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	−0.174511	−	0.984655i	$-0.555834\pi$
$983$	24.0000	−	41.5692i	0.765481	−	1.32585i	0.939992	−	0.341197i	$-0.110832\pi$
$984$		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	−0.988826	−	0.149076i	$-0.952370\pi$
$991$	−11.5000	+	19.9186i	−0.365310	+	0.632735i	0.623516	+	0.781810i	$0.285704\pi$
$992$		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	$-0.823251\pi$
$997$	1.00000	−	1.73205i	0.0316703	−	0.0548546i	0.881426	+	0.472322i	$0.156584\pi$
$998$		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	1344.2.q.u.193.1		2
4.3	odd	2		1344.2.q.k.193.1		2
7.2	even	3	inner	1344.2.q.u.961.1		2
7.3	odd	6		9408.2.a.dc.1.1		1
7.4	even	3		9408.2.a.e.1.1		1
8.3	odd	2		672.2.q.f.193.1	yes	2
8.5	even	2		672.2.q.a.193.1	✓	2
24.5	odd	2		2016.2.s.n.865.1		2
24.11	even	2		2016.2.s.k.865.1		2
28.3	even	6		9408.2.a.bl.1.1		1
28.11	odd	6		9408.2.a.bt.1.1		1
28.23	odd	6		1344.2.q.k.961.1		2
56.3	even	6		4704.2.a.s.1.1		1
56.11	odd	6		4704.2.a.o.1.1		1
56.37	even	6		672.2.q.a.289.1	yes	2
56.45	odd	6		4704.2.a.b.1.1		1
56.51	odd	6		672.2.q.f.289.1	yes	2
56.53	even	6		4704.2.a.bf.1.1		1
168.107	even	6		2016.2.s.k.289.1		2
168.149	odd	6		2016.2.s.n.289.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.q.a.193.1	✓	2	8.5	even	2
672.2.q.a.289.1	yes	2	56.37	even	6
672.2.q.f.193.1	yes	2	8.3	odd	2
672.2.q.f.289.1	yes	2	56.51	odd	6
1344.2.q.k.193.1		2	4.3	odd	2
1344.2.q.k.961.1		2	28.23	odd	6
1344.2.q.u.193.1		2	1.1	even	1	trivial
1344.2.q.u.961.1		2	7.2	even	3	inner
2016.2.s.k.289.1		2	168.107	even	6
2016.2.s.k.865.1		2	24.11	even	2
2016.2.s.n.289.1		2	168.149	odd	6
2016.2.s.n.865.1		2	24.5	odd	2
4704.2.a.b.1.1		1	56.45	odd	6
4704.2.a.o.1.1		1	56.11	odd	6
4704.2.a.s.1.1		1	56.3	even	6
4704.2.a.bf.1.1		1	56.53	even	6
9408.2.a.e.1.1		1	7.4	even	3
9408.2.a.bl.1.1		1	28.3	even	6
9408.2.a.bt.1.1		1	28.11	odd	6
9408.2.a.dc.1.1		1	7.3	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:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.q (of order \(3\), degree \(2\), not 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

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Representations

Groups

Database

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