LMFDB - Embedded newform 1232.2.q.k.529.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1232,2,Mod(177,1232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1232, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

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

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

chi := DirichletCharacter("1232.177");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1232 = 2^{4} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1232.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:	$9.83756952902$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1783323.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 $ x^6 - x^5 + 5x^4 - 2x^3 + 19x^2 - 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.1
Root			$1.09935 - 1.90412i$ of defining polynomial
Character	$\chi$	$=$	1232.529
Dual form			1232.2.q.k.177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09935 + 1.90412i) q^{3} +(0.317776 + 0.550404i) q^{5} +(-0.317776 - 2.62660i) q^{7} +(-0.917122 - 1.58850i) q^{9} +O(q^{10})$	\(q+(-1.09935 + 1.90412i) q^{3} +(0.317776 + 0.550404i) q^{5} +(-0.317776 - 2.62660i) q^{7} +(-0.917122 - 1.58850i) q^{9} +(-0.500000 + 0.866025i) q^{11} -1.80131 q^{13} -1.39738 q^{15} +(1.41712 - 2.45453i) q^{17} +(-2.78157 - 4.81782i) q^{19} +(5.35071 + 2.28245i) q^{21} +(1.08288 + 1.87560i) q^{23} +(2.29804 - 3.98032i) q^{25} -2.56314 q^{27} -10.4303 q^{29} +(3.21516 - 5.56882i) q^{31} +(-1.09935 - 1.90412i) q^{33} +(1.34471 - 1.00958i) q^{35} +(-3.03293 - 5.25320i) q^{37} +(1.98026 - 3.42991i) q^{39} +7.53566 q^{41} +4.86718 q^{43} +(0.582878 - 1.00958i) q^{45} +(-1.41712 - 2.45453i) q^{47} +(-6.79804 + 1.66934i) q^{49} +(3.11581 + 5.39675i) q^{51} +(-3.73490 + 6.46903i) q^{53} -0.635552 q^{55} +12.2316 q^{57} +(5.90338 - 10.2250i) q^{59} +(2.16576 + 3.75120i) q^{61} +(-3.88092 + 2.91370i) q^{63} +(-0.572413 - 0.991448i) q^{65} +(-0.801309 + 1.38791i) q^{67} -4.76183 q^{69} -4.29204 q^{71} +(7.99673 - 13.8507i) q^{73} +(5.05267 + 8.75149i) q^{75} +(2.43359 + 1.03810i) q^{77} +(2.38092 + 4.12387i) q^{79} +(5.56914 - 9.64603i) q^{81} +9.23163 q^{83} +1.80131 q^{85} +(11.4665 - 19.8606i) q^{87} +(-0.182224 - 0.315621i) q^{89} +(0.572413 + 4.73131i) q^{91} +(7.06914 + 12.2441i) q^{93} +(1.76783 - 3.06197i) q^{95} -2.59607 q^{97} +1.83424 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{3} + 2 q^{5} - 2 q^{7}+O(q^{10}) $ 6 * q - q^3 + 2 * q^5 - 2 * q^7	$ 6 q - q^{3} + 2 q^{5} - 2 q^{7} - 3 q^{11} - 22 q^{13} + 14 q^{15} + 3 q^{17} - 11 q^{19} + 10 q^{21} + 12 q^{23} - 3 q^{25} - 4 q^{27} - 18 q^{29} - 3 q^{31} - q^{33} - 9 q^{35} + 4 q^{37} - 5 q^{39} - 10 q^{41} - 4 q^{43} + 9 q^{45} - 3 q^{47} - 24 q^{49} + 2 q^{51} - 17 q^{53} - 4 q^{55} + 40 q^{57} + 8 q^{59} + 24 q^{61} - 12 q^{63} - 15 q^{65} - 16 q^{67} - 6 q^{69} - 14 q^{71} + 20 q^{73} + 25 q^{75} - 2 q^{77} + 3 q^{79} + 17 q^{81} + 22 q^{83} + 22 q^{85} + 30 q^{87} - q^{89} + 15 q^{91} + 26 q^{93} - 17 q^{95} + 18 q^{97}+O(q^{100}) $ 6 * q - q^3 + 2 * q^5 - 2 * q^7 - 3 * q^11 - 22 * q^13 + 14 * q^15 + 3 * q^17 - 11 * q^19 + 10 * q^21 + 12 * q^23 - 3 * q^25 - 4 * q^27 - 18 * q^29 - 3 * q^31 - q^33 - 9 * q^35 + 4 * q^37 - 5 * q^39 - 10 * q^41 - 4 * q^43 + 9 * q^45 - 3 * q^47 - 24 * q^49 + 2 * q^51 - 17 * q^53 - 4 * q^55 + 40 * q^57 + 8 * q^59 + 24 * q^61 - 12 * q^63 - 15 * q^65 - 16 * q^67 - 6 * q^69 - 14 * q^71 + 20 * q^73 + 25 * q^75 - 2 * q^77 + 3 * q^79 + 17 * q^81 + 22 * q^83 + 22 * q^85 + 30 * q^87 - q^89 + 15 * q^91 + 26 * q^93 - 17 * q^95 + 18 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times$.

$n$	$309$	$353$	$463$	$673$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	−1.09935	+	1.90412i	−0.634707	+	1.09935i	0.351870	+	0.936049i	$0.385546\pi$
$3$	−1.09935	+	1.90412i	−0.634707	+	1.09935i	−0.986577	+	0.163297i	$0.947787\pi$
$4$		0			0
$5$	0.317776	+	0.550404i	0.142114	+	0.246148i	0.928292	−	0.371851i	$-0.121277\pi$
$5$	0.317776	+	0.550404i	0.142114	+	0.246148i	−0.786179	+	0.617999i	$0.787943\pi$
$6$		0			0
$7$	−0.317776	−	2.62660i	−0.120108	−	0.992761i
$7$	−0.317776	−	2.62660i	−0.120108	−	0.992761i
$8$		0			0
$9$	−0.917122	−	1.58850i	−0.305707	−	0.529500i
$10$		0			0
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$		0			0
$13$	−1.80131			−0.499593			−0.249797	−	0.968298i	$-0.580364\pi$
$13$	−1.80131			−0.499593			−0.249797	+	0.968298i	$0.580364\pi$
$14$		0			0
$15$	−1.39738			−0.360803
$16$		0			0
$17$	1.41712	−	2.45453i	0.343702	−	0.595310i	−0.641415	−	0.767194i	$-0.721652\pi$
$17$	1.41712	−	2.45453i	0.343702	−	0.595310i	0.985117	+	0.171884i	$0.0549855\pi$
$18$		0			0
$19$	−2.78157	−	4.81782i	−0.638136	−	1.10528i	−0.985841	−	0.167680i	$-0.946372\pi$
$19$	−2.78157	−	4.81782i	−0.638136	−	1.10528i	0.347706	−	0.937604i	$-0.386961\pi$
$20$		0			0
$21$	5.35071	+	2.28245i	1.16762	+	0.498073i
$22$		0			0
$23$	1.08288	+	1.87560i	0.225796	+	0.391090i	0.956558	−	0.291542i	$-0.0941685\pi$
$23$	1.08288	+	1.87560i	0.225796	+	0.391090i	−0.730762	+	0.682632i	$0.760835\pi$
$24$		0			0
$25$	2.29804	−	3.98032i	0.459607	−	0.796063i
$26$		0			0
$27$	−2.56314			−0.493276
$28$		0			0
$29$	−10.4303			−1.93686			−0.968431	−	0.249283i	$-0.919805\pi$
$29$	−10.4303			−1.93686			−0.968431	+	0.249283i	$0.919805\pi$
$30$		0			0
$31$	3.21516	−	5.56882i	0.577460	−	1.00019i	−0.418310	−	0.908304i	$-0.637377\pi$
$31$	3.21516	−	5.56882i	0.577460	−	1.00019i	0.995770	−	0.0918849i	$-0.0292892\pi$
$32$		0			0
$33$	−1.09935	−	1.90412i	−0.191372	−	0.331465i
$34$		0			0
$35$	1.34471	−	1.00958i	0.227297	−	0.170649i
$36$		0			0
$37$	−3.03293	−	5.25320i	−0.498611	−	0.863620i	0.501387	−	0.865223i	$-0.332823\pi$
$37$	−3.03293	−	5.25320i	−0.498611	−	0.863620i	−0.999999	+	0.00160274i	$0.999490\pi$
$38$		0			0
$39$	1.98026	−	3.42991i	0.317096	−	0.549226i
$40$		0			0
$41$	7.53566			1.17687			0.588436	−	0.808543i	$-0.299744\pi$
$41$	7.53566			1.17687			0.588436	+	0.808543i	$0.299744\pi$
$42$		0			0
$43$	4.86718			0.742238			0.371119	−	0.928585i	$-0.378974\pi$
$43$	4.86718			0.742238			0.371119	+	0.928585i	$0.378974\pi$
$44$		0			0
$45$	0.582878	−	1.00958i	0.0868904	−	0.150499i
$46$		0			0
$47$	−1.41712	−	2.45453i	−0.206708	−	0.358030i	0.743967	−	0.668216i	$-0.232942\pi$
$47$	−1.41712	−	2.45453i	−0.206708	−	0.358030i	−0.950676	+	0.310187i	$0.899608\pi$
$48$		0			0
$49$	−6.79804	+	1.66934i	−0.971148	+	0.238477i
$50$		0			0
$51$	3.11581	+	5.39675i	0.436301	+	0.755696i
$52$		0			0
$53$	−3.73490	+	6.46903i	−0.513028	+	0.888590i	0.486858	+	0.873481i	$0.338143\pi$
$53$	−3.73490	+	6.46903i	−0.513028	+	0.888590i	−0.999886	+	0.0151089i	$0.995190\pi$
$54$		0			0
$55$	−0.635552			−0.0856978
$56$		0			0
$57$	12.2316			1.62012
$58$		0			0
$59$	5.90338	−	10.2250i	0.768555	−	1.33118i	−0.169791	−	0.985480i	$-0.554309\pi$
$59$	5.90338	−	10.2250i	0.768555	−	1.33118i	0.938346	−	0.345696i	$-0.112357\pi$
$60$		0			0
$61$	2.16576	+	3.75120i	0.277297	+	0.480292i	0.970712	−	0.240246i	$-0.0772282\pi$
$61$	2.16576	+	3.75120i	0.277297	+	0.480292i	−0.693415	+	0.720538i	$0.743895\pi$
$62$		0			0
$63$	−3.88092	+	2.91370i	−0.488949	+	0.367091i
$64$		0			0
$65$	−0.572413	−	0.991448i	−0.0709990	−	0.122974i
$66$		0			0
$67$	−0.801309	+	1.38791i	−0.0978954	+	0.169560i	−0.910813	−	0.412818i	$-0.864544\pi$
$67$	−0.801309	+	1.38791i	−0.0978954	+	0.169560i	0.812918	+	0.582378i	$0.197878\pi$
$68$		0			0
$69$	−4.76183			−0.573257
$70$		0			0
$71$	−4.29204			−0.509371			−0.254685	−	0.967024i	$-0.581972\pi$
$71$	−4.29204			−0.509371			−0.254685	+	0.967024i	$0.581972\pi$
$72$		0			0
$73$	7.99673	−	13.8507i	0.935946	−	1.62111i	0.163008	−	0.986625i	$-0.447880\pi$
$73$	7.99673	−	13.8507i	0.935946	−	1.62111i	0.772938	−	0.634482i	$-0.218786\pi$
$74$		0			0
$75$	5.05267	+	8.75149i	0.583432	+	1.01053i
$76$		0			0
$77$	2.43359	+	1.03810i	0.277333	+	0.118302i
$78$		0			0
$79$	2.38092	+	4.12387i	0.267874	+	0.463971i	0.968313	−	0.249741i	$-0.0803456\pi$
$79$	2.38092	+	4.12387i	0.267874	+	0.463971i	−0.700439	+	0.713713i	$0.747012\pi$
$80$		0			0
$81$	5.56914	−	9.64603i	0.618793	−	1.07178i
$82$		0			0
$83$	9.23163			1.01330			0.506651	−	0.862151i	$-0.330883\pi$
$83$	9.23163			1.01330			0.506651	+	0.862151i	$0.330883\pi$
$84$		0			0
$85$	1.80131			0.195379
$86$		0			0
$87$	11.4665	−	19.8606i	1.22934	−	2.12928i
$88$		0			0
$89$	−0.182224	−	0.315621i	−0.0193157	−	0.0334558i	0.856206	−	0.516635i	$-0.172815\pi$
$89$	−0.182224	−	0.315621i	−0.0193157	−	0.0334558i	−0.875522	+	0.483179i	$0.839482\pi$
$90$		0			0
$91$	0.572413	+	4.73131i	0.0600051	+	0.495977i
$92$		0			0
$93$	7.06914	+	12.2441i	0.733036	+	1.26966i
$94$		0			0
$95$	1.76783	−	3.06197i	0.181376	−	0.314152i
$96$		0			0
$97$	−2.59607			−0.263591			−0.131796	−	0.991277i	$-0.542074\pi$
$97$	−2.59607			−0.263591			−0.131796	+	0.991277i	$0.542074\pi$
$98$		0			0
$99$	1.83424			0.184348
$100$		0			0
$101$	4.95006	−	8.57375i	0.492549	−	0.853120i	−0.507414	−	0.861702i	$-0.669399\pi$
$101$	4.95006	−	8.57375i	0.492549	−	0.853120i	0.999963	+	0.00858243i	$0.00273191\pi$
$102$		0			0
$103$	3.11581	+	5.39675i	0.307010	+	0.531757i	0.977707	−	0.209975i	$-0.0673381\pi$
$103$	3.11581	+	5.39675i	0.307010	+	0.531757i	−0.670697	+	0.741732i	$0.734005\pi$
$104$		0			0
$105$	0.444055	+	3.67036i	0.0433353	+	0.358191i
$106$		0			0
$107$	5.54940	+	9.61185i	0.536481	+	0.929212i	0.999090	+	0.0426499i	$0.0135800\pi$
$107$	5.54940	+	9.61185i	0.536481	+	0.929212i	−0.462609	+	0.886562i	$0.653087\pi$
$108$		0			0
$109$	7.15202	−	12.3877i	0.685039	−	1.18652i	−0.288385	−	0.957514i	$-0.593118\pi$
$109$	7.15202	−	12.3877i	0.685039	−	1.18652i	0.973424	−	0.229008i	$-0.0735483\pi$
$110$		0			0
$111$	13.3370			1.26589
$112$		0			0
$113$	−8.68942			−0.817432			−0.408716	−	0.912662i	$-0.634023\pi$
$113$	−8.68942			−0.817432			−0.408716	+	0.912662i	$0.634023\pi$
$114$		0			0
$115$	−0.688225	+	1.19204i	−0.0641774	+	0.111158i
$116$		0			0
$117$	1.65202	+	2.86138i	0.152729	+	0.264535i
$118$		0			0
$119$	−6.89738	−	2.94222i	−0.632282	−	0.269713i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$		0			0
$123$	−8.28430	+	14.3488i	−0.746970	+	1.29379i
$124$		0			0
$125$	6.09880			0.545494
$126$		0			0
$127$	−20.9989			−1.86335			−0.931676	−	0.363290i	$-0.881654\pi$
$127$	−20.9989			−1.86335			−0.931676	+	0.363290i	$0.881654\pi$
$128$		0			0
$129$	−5.35071	+	9.26770i	−0.471104	+	0.815976i
$130$		0			0
$131$	−6.85071	−	11.8658i	−0.598549	−	1.03672i	−0.993035	−	0.117816i	$-0.962411\pi$
$131$	−6.85071	−	11.8658i	−0.598549	−	1.03672i	0.394486	−	0.918902i	$-0.370923\pi$
$132$		0			0
$133$	−11.7706	+	8.83705i	−1.02064	+	0.766270i
$134$		0			0
$135$	−0.814504	−	1.41076i	−0.0701013	−	0.121419i
$136$		0			0
$137$	−3.63228	+	6.29129i	−0.310327	+	0.537501i	−0.978433	−	0.206564i	$-0.933772\pi$
$137$	−3.63228	+	6.29129i	−0.310327	+	0.537501i	0.668106	+	0.744066i	$0.267105\pi$
$138$		0			0
$139$	2.60262			0.220751			0.110376	−	0.993890i	$-0.464795\pi$
$139$	2.60262			0.220751			0.110376	+	0.993890i	$0.464795\pi$
$140$		0			0
$141$	6.23163			0.524798
$142$		0			0
$143$	0.900654	−	1.55998i	0.0753165	−	0.130452i
$144$		0			0
$145$	−3.31450	−	5.74089i	−0.275255	−	0.476755i
$146$		0			0
$147$	4.29476	−	14.7795i	0.354226	−	1.21899i
$148$		0			0
$149$	0.500000	+	0.866025i	0.0409616	+	0.0709476i	0.885779	−	0.464107i	$-0.153625\pi$
$149$	0.500000	+	0.866025i	0.0409616	+	0.0709476i	−0.844818	+	0.535054i	$0.820291\pi$
$150$		0			0
$151$	0.867720	−	1.50294i	0.0706140	−	0.122307i	−0.828557	−	0.559905i	$-0.810837\pi$
$151$	0.867720	−	1.50294i	0.0706140	−	0.122307i	0.899171	+	0.437598i	$0.144171\pi$
$152$		0			0
$153$	−5.19869			−0.420289
$154$		0			0
$155$	4.08680			0.328260
$156$		0			0
$157$	3.96980	−	6.87589i	0.316824	−	0.548756i	−0.662999	−	0.748620i	$-0.730717\pi$
$157$	3.96980	−	6.87589i	0.316824	−	0.548756i	0.979824	+	0.199864i	$0.0640502\pi$
$158$		0			0
$159$	−8.21189	−	14.2234i	−0.651245	−	1.12799i
$160$		0			0
$161$	4.58234	−	3.44031i	0.361139	−	0.271134i
$162$		0			0
$163$	−8.00273	−	13.8611i	−0.626822	−	1.08569i	−0.988185	−	0.153263i	$-0.951022\pi$
$163$	−8.00273	−	13.8611i	−0.626822	−	1.08569i	0.361363	−	0.932425i	$-0.382311\pi$
$164$		0			0
$165$	0.698691	−	1.21017i	0.0543930	−	0.0942115i
$166$		0			0
$167$	−1.15921			−0.0897026			−0.0448513	−	0.998994i	$-0.514281\pi$
$167$	−1.15921			−0.0897026			−0.0448513	+	0.998994i	$0.514281\pi$
$168$		0			0
$169$	−9.75529			−0.750407
$170$		0			0
$171$	−5.10208	+	8.83705i	−0.390165	+	0.675786i
$172$		0			0
$173$	0.496728	+	0.860358i	0.0377655	+	0.0654118i	0.884290	−	0.466937i	$-0.154643\pi$
$173$	0.496728	+	0.860358i	0.0377655	+	0.0654118i	−0.846525	+	0.532349i	$0.821309\pi$
$174$		0			0
$175$	−11.1850	−	4.77117i	−0.845503	−	0.360667i
$176$		0			0
$177$	12.9797	+	22.4815i	0.975615	+	1.68982i
$178$		0			0
$179$	−9.83097	+	17.0277i	−0.734801	+	1.27271i	0.220009	+	0.975498i	$0.429391\pi$
$179$	−9.83097	+	17.0277i	−0.734801	+	1.27271i	−0.954810	+	0.297215i	$0.903942\pi$
$180$		0			0
$181$	−23.8726			−1.77444			−0.887220	−	0.461347i	$-0.847366\pi$
$181$	−23.8726			−1.77444			−0.887220	+	0.461347i	$0.847366\pi$
$182$		0			0
$183$	−9.52366			−0.704009
$184$		0			0
$185$	1.92759	−	3.33868i	0.141719	−	0.245465i
$186$		0			0
$187$	1.41712	+	2.45453i	0.103630	+	0.179493i
$188$		0			0
$189$	0.814504	+	6.73234i	0.0592465	+	0.489705i
$190$		0			0
$191$	−5.56587	−	9.64037i	−0.402732	−	0.697553i	0.591322	−	0.806435i	$-0.298606\pi$
$191$	−5.56587	−	9.64037i	−0.402732	−	0.697553i	−0.994055	+	0.108883i	$0.965273\pi$
$192$		0			0
$193$	−1.80731	+	3.13035i	−0.130093	+	0.225328i	−0.923712	−	0.383087i	$-0.874861\pi$
$193$	−1.80731	+	3.13035i	−0.130093	+	0.225328i	0.793619	+	0.608415i	$0.208194\pi$
$194$		0			0
$195$	2.51712			0.180255
$196$		0			0
$197$	2.41831			0.172298			0.0861489	−	0.996282i	$-0.472544\pi$
$197$	2.41831			0.172298			0.0861489	+	0.996282i	$0.472544\pi$
$198$		0			0
$199$	−9.24809	+	16.0182i	−0.655580	+	1.13550i	0.326168	+	0.945312i	$0.394242\pi$
$199$	−9.24809	+	16.0182i	−0.655580	+	1.13550i	−0.981748	+	0.190186i	$0.939091\pi$
$200$		0			0
$201$	−1.76183	−	3.05158i	−0.124270	−	0.215242i
$202$		0			0
$203$	3.31450	+	27.3963i	0.232633	+	1.92284i
$204$		0			0
$205$	2.39465	+	4.14766i	0.167250	+	0.289685i
$206$		0			0
$207$	1.98626	−	3.44031i	0.138055	−	0.239118i
$208$		0			0
$209$	5.56314			0.384810
$210$		0			0
$211$	7.85517			0.540773			0.270386	−	0.962752i	$-0.412849\pi$
$211$	7.85517			0.540773			0.270386	+	0.962752i	$0.412849\pi$
$212$		0			0
$213$	4.71843	−	8.17256i	0.323302	−	0.559975i
$214$		0			0
$215$	1.54667	+	2.67891i	0.105482	+	0.182700i
$216$		0			0
$217$	−15.6487	−	6.67529i	−1.06231	−	0.453148i
$218$		0			0
$219$	17.5823	+	30.4535i	1.18810	+	2.05786i
$220$		0			0
$221$	−2.55267	+	4.42136i	−0.171711	+	0.297413i
$222$		0			0
$223$	−20.3370			−1.36186			−0.680932	−	0.732346i	$-0.738425\pi$
$223$	−20.3370			−1.36186			−0.680932	+	0.732346i	$0.738425\pi$
$224$		0			0
$225$	−8.43032			−0.562021
$226$		0			0
$227$	3.60981	−	6.25238i	0.239592	−	0.414985i	−0.721006	−	0.692929i	$-0.756320\pi$
$227$	3.60981	−	6.25238i	0.239592	−	0.414985i	0.960597	+	0.277944i	$0.0896531\pi$
$228$		0			0
$229$	−6.03566	−	10.4541i	−0.398848	−	0.690825i	0.594736	−	0.803921i	$-0.297257\pi$
$229$	−6.03566	−	10.4541i	−0.398848	−	0.690825i	−0.993584	+	0.113096i	$0.963923\pi$
$230$		0			0
$231$	−4.65202	+	3.49262i	−0.306080	+	0.229798i
$232$		0			0
$233$	3.77110	+	6.53174i	0.247053	+	0.427909i	0.962707	−	0.270547i	$-0.0872044\pi$
$233$	3.77110	+	6.53174i	0.247053	+	0.427909i	−0.715654	+	0.698455i	$0.753871\pi$
$234$		0			0
$235$	0.900654	−	1.55998i	0.0587522	−	0.101762i
$236$		0			0
$237$	−10.4698			−0.680086
$238$		0			0
$239$	9.84625			0.636901			0.318450	−	0.947940i	$-0.396838\pi$
$239$	9.84625			0.636901			0.318450	+	0.947940i	$0.396838\pi$
$240$		0			0
$241$	0.837515	−	1.45062i	0.0539491	−	0.0934426i	−0.837790	−	0.545993i	$-0.816152\pi$
$241$	0.837515	−	1.45062i	0.0539491	−	0.0934426i	0.891739	+	0.452551i	$0.149486\pi$
$242$		0			0
$243$	8.40011	+	14.5494i	0.538867	+	0.933346i
$244$		0			0
$245$	−3.07906	−	3.21119i	−0.196714	−	0.205156i
$246$		0			0
$247$	5.01047	+	8.67838i	0.318808	+	0.552192i
$248$		0			0
$249$	−10.1487	+	17.5781i	−0.643151	+	1.11397i
$250$		0			0
$251$	−19.7738			−1.24811			−0.624057	−	0.781379i	$-0.714517\pi$
$251$	−19.7738			−1.24811			−0.624057	+	0.781379i	$0.714517\pi$
$252$		0			0
$253$	−2.16576			−0.136160
$254$		0			0
$255$	−1.98026	+	3.42991i	−0.124009	+	0.214789i
$256$		0			0
$257$	−1.35998	−	2.35556i	−0.0848335	−	0.146936i	0.820487	−	0.571665i	$-0.193702\pi$
$257$	−1.35998	−	2.35556i	−0.0848335	−	0.146936i	−0.905320	+	0.424730i	$0.860369\pi$
$258$		0			0
$259$	−12.8342	+	9.63564i	−0.797481	+	0.598730i
$260$		0			0
$261$	9.56587	+	16.5686i	0.592112	+	1.02557i
$262$		0			0
$263$	6.34744	−	10.9941i	0.391400	−	0.677924i	−0.601235	−	0.799073i	$-0.705324\pi$
$263$	6.34744	−	10.9941i	0.391400	−	0.677924i	0.992634	+	0.121148i	$0.0386576\pi$
$264$		0			0
$265$	−4.74744			−0.291633
$266$		0			0
$267$	0.801309			0.0490393
$268$		0			0
$269$	3.54667	−	6.14302i	0.216244	−	0.374546i	−0.737412	−	0.675443i	$-0.763953\pi$
$269$	3.54667	−	6.14302i	0.216244	−	0.374546i	0.953657	+	0.300896i	$0.0972859\pi$
$270$		0			0
$271$	−9.10808	−	15.7757i	−0.553276	−	0.958303i	−0.998035	−	0.0626524i	$-0.980044\pi$
$271$	−9.10808	−	15.7757i	−0.553276	−	0.958303i	0.444759	−	0.895650i	$-0.353289\pi$
$272$		0			0
$273$	−9.63828	−	4.11141i	−0.583335	−	0.248834i
$274$		0			0
$275$	2.29804	+	3.98032i	0.138577	+	0.240022i
$276$		0			0
$277$	−6.92432	+	11.9933i	−0.416042	+	0.720606i	−0.995537	−	0.0943700i	$-0.969916\pi$
$277$	−6.92432	+	11.9933i	−0.416042	+	0.720606i	0.579495	+	0.814976i	$0.303250\pi$
$278$		0			0
$279$	−11.7948			−0.706134
$280$		0			0
$281$	21.0329			1.25472			0.627360	−	0.778730i	$-0.284136\pi$
$281$	21.0329			1.25472			0.627360	+	0.778730i	$0.284136\pi$
$282$		0			0
$283$	0.176223	−	0.305226i	0.0104753	−	0.0181438i	−0.860740	−	0.509044i	$-0.829999\pi$
$283$	0.176223	−	0.305226i	0.0104753	−	0.0181438i	0.871216	+	0.490901i	$0.163332\pi$
$284$		0			0
$285$	3.88692	+	6.73234i	0.230241	+	0.398789i
$286$		0			0
$287$	−2.39465	−	19.7932i	−0.141352	−	1.16835i
$288$		0			0
$289$	4.48353	+	7.76571i	0.263737	+	0.456806i
$290$		0			0
$291$	2.85398	−	4.94324i	0.167303	−	0.289778i
$292$		0			0
$293$	−3.46325			−0.202325			−0.101163	−	0.994870i	$-0.532256\pi$
$293$	−3.46325			−0.202325			−0.101163	+	0.994870i	$0.532256\pi$
$294$		0			0
$295$	7.50381			0.436889
$296$		0			0
$297$	1.28157	−	2.21974i	0.0743642	−	0.128803i
$298$		0			0
$299$	−1.95060	−	3.37854i	−0.112806	−	0.195386i
$300$		0			0
$301$	−1.54667	−	12.7841i	−0.0891487	−	0.736864i
$302$		0			0
$303$	10.8836	+	18.8510i	0.625249	+	1.08296i
$304$		0			0
$305$	−1.37645	+	2.38408i	−0.0788154	+	0.136512i
$306$		0			0
$307$	6.51473			0.371815			0.185908	−	0.982567i	$-0.440477\pi$
$307$	6.51473			0.371815			0.185908	+	0.982567i	$0.440477\pi$
$308$		0			0
$309$	−13.7014			−0.779447
$310$		0			0
$311$	5.81505	−	10.0720i	0.329741	−	0.571128i	−0.652719	−	0.757600i	$-0.726372\pi$
$311$	5.81505	−	10.0720i	0.329741	−	0.571128i	0.982460	+	0.186472i	$0.0597052\pi$
$312$		0			0
$313$	13.5489	+	23.4673i	0.765827	+	1.32645i	0.939808	+	0.341702i	$0.111003\pi$
$313$	13.5489	+	23.4673i	0.765827	+	1.32645i	−0.173982	+	0.984749i	$0.555663\pi$
$314$		0			0
$315$	−2.83697	−	1.21017i	−0.159845	−	0.0681853i
$316$		0			0
$317$	−1.93086	−	3.34435i	−0.108448	−	0.187837i	0.806694	−	0.590970i	$-0.201255\pi$
$317$	−1.93086	−	3.34435i	−0.108448	−	0.187837i	−0.915142	+	0.403132i	$0.867921\pi$
$318$		0			0
$319$	5.21516	−	9.03292i	0.291993	−	0.505746i
$320$		0			0
$321$	−24.4028			−1.36203
$322$		0			0
$323$	−15.7673			−0.877315
$324$		0			0
$325$	−4.13947	+	7.16978i	−0.229617	+	0.397708i
$326$		0			0
$327$	15.7251	+	27.2366i	0.869599	+	1.50619i
$328$		0			0
$329$	−5.99673	+	4.50220i	−0.330610	+	0.248214i
$330$		0			0
$331$	3.07514	+	5.32630i	0.169025	+	0.292760i	0.938077	−	0.346426i	$-0.112605\pi$
$331$	3.07514	+	5.32630i	0.169025	+	0.292760i	−0.769052	+	0.639186i	$0.779271\pi$
$332$		0			0
$333$	−5.56314	+	9.63564i	−0.304858	+	0.528030i
$334$		0			0
$335$	−1.01855			−0.0556491
$336$		0			0
$337$	−11.7607			−0.640649			−0.320324	−	0.947308i	$-0.603792\pi$
$337$	−11.7607			−0.640649			−0.320324	+	0.947308i	$0.603792\pi$
$338$		0			0
$339$	9.55267	−	16.5457i	0.518830	−	0.898640i
$340$		0			0
$341$	3.21516	+	5.56882i	0.174111	+	0.301568i
$342$		0			0
$343$	6.54494	+	17.3252i	0.353393	+	0.935475i
$344$		0			0
$345$	−1.51320	−	2.62093i	−0.0814677	−	0.141106i
$346$		0			0
$347$	−0.420393	+	0.728143i	−0.0225679	+	0.0390888i	−0.877089	−	0.480328i	$-0.840518\pi$
$347$	−0.420393	+	0.728143i	−0.0225679	+	0.0390888i	0.854521	+	0.519417i	$0.173851\pi$
$348$		0			0
$349$	9.13174			0.488811			0.244405	−	0.969673i	$-0.421407\pi$
$349$	9.13174			0.488811			0.244405	+	0.969673i	$0.421407\pi$
$350$		0			0
$351$	4.61701			0.246438
$352$		0			0
$353$	−11.3639	+	19.6829i	−0.604840	+	1.04761i	0.387237	+	0.921980i	$0.373429\pi$
$353$	−11.3639	+	19.6829i	−0.604840	+	1.04761i	−0.992077	+	0.125633i	$0.959904\pi$
$354$		0			0
$355$	−1.36391	−	2.36235i	−0.0723886	−	0.125381i
$356$		0			0
$357$	13.1850	−	9.89894i	0.697822	−	0.523908i
$358$		0			0
$359$	−13.1093	−	22.7059i	−0.691881	−	1.19837i	−0.971221	−	0.238180i	$-0.923449\pi$
$359$	−13.1093	−	22.7059i	−0.691881	−	1.19837i	0.279340	−	0.960192i	$-0.409884\pi$
$360$		0			0
$361$	−5.97426	+	10.3477i	−0.314435	+	0.544617i
$362$		0			0
$363$	2.19869			0.115401
$364$		0			0
$365$	10.1647			0.532043
$366$		0			0
$367$	−1.91112	+	3.31016i	−0.0997597	+	0.172789i	−0.911585	−	0.411111i	$-0.865141\pi$
$367$	−1.91112	+	3.31016i	−0.0997597	+	0.172789i	0.811825	+	0.583900i	$0.198474\pi$
$368$		0			0
$369$	−6.91112	−	11.9704i	−0.359779	−	0.623155i
$370$		0			0
$371$	18.1784	+	7.75437i	0.943776	+	0.402587i
$372$		0			0
$373$	−7.55387	−	13.0837i	−0.391124	−	0.677447i	0.601474	−	0.798893i	$-0.294580\pi$
$373$	−7.55387	−	13.0837i	−0.391124	−	0.677447i	−0.992598	+	0.121445i	$0.961247\pi$
$374$		0			0
$375$	−6.70469	+	11.6129i	−0.346229	+	0.599686i
$376$		0			0
$377$	18.7882			0.967643
$378$		0			0
$379$	11.3765			0.584369			0.292185	−	0.956362i	$-0.405618\pi$
$379$	11.3765			0.584369			0.292185	+	0.956362i	$0.405618\pi$
$380$		0			0
$381$	23.0851	−	39.9845i	1.18268	−	2.04847i
$382$		0			0
$383$	4.44286	+	7.69526i	0.227020	+	0.393210i	0.956923	−	0.290340i	$-0.0937685\pi$
$383$	4.44286	+	7.69526i	0.227020	+	0.393210i	−0.729904	+	0.683550i	$0.760435\pi$
$384$		0			0
$385$	0.201963	+	1.66934i	0.0102930	+	0.0850774i
$386$		0			0
$387$	−4.46379	−	7.73152i	−0.226907	−	0.393015i
$388$		0			0
$389$	9.94951	−	17.2331i	0.504460	−	0.873751i	−0.495526	−	0.868593i	$-0.665025\pi$
$389$	9.94951	−	17.2331i	0.504460	−	0.873751i	0.999987	−	0.00515807i	$-0.00164187\pi$
$390$		0			0
$391$	6.13828			0.310426
$392$		0			0
$393$	30.1252			1.51962
$394$		0			0
$395$	−1.51320	+	2.62093i	−0.0761371	+	0.131873i
$396$		0			0
$397$	17.4303	+	30.1902i	0.874803	+	1.51520i	0.856973	+	0.515361i	$0.172342\pi$
$397$	17.4303	+	30.1902i	0.874803	+	1.51520i	0.0178296	+	0.999841i	$0.494324\pi$
$398$		0			0
$399$	−3.88692	−	32.1276i	−0.194589	−	1.60839i
$400$		0			0
$401$	−5.69815	−	9.86948i	−0.284552	−	0.492858i	0.687948	−	0.725760i	$-0.258511\pi$
$401$	−5.69815	−	9.86948i	−0.284552	−	0.492858i	−0.972500	+	0.232901i	$0.925178\pi$
$402$		0			0
$403$	−5.79149	+	10.0312i	−0.288495	+	0.499688i
$404$		0			0
$405$	7.07896			0.351756
$406$		0			0
$407$	6.06587			0.300674
$408$		0			0
$409$	2.04394	−	3.54021i	0.101066	−	0.175052i	−0.811058	−	0.584966i	$-0.801108\pi$
$409$	2.04394	−	3.54021i	0.101066	−	0.175052i	0.912124	+	0.409914i	$0.134441\pi$
$410$		0			0
$411$	−7.98626	−	13.8326i	−0.393933	−	0.682312i
$412$		0			0
$413$	−28.7328	−	12.2566i	−1.41385	−	0.603106i
$414$		0			0
$415$	2.93359	+	5.08112i	0.144004	+	0.249423i
$416$		0			0
$417$	−2.86118	+	4.95570i	−0.140112	+	0.242682i
$418$		0			0
$419$	−32.8002			−1.60240			−0.801198	−	0.598399i	$-0.795804\pi$
$419$	−32.8002			−1.60240			−0.801198	+	0.598399i	$0.795804\pi$
$420$		0			0
$421$	−8.52128			−0.415302			−0.207651	−	0.978203i	$-0.566582\pi$
$421$	−8.52128			−0.415302			−0.207651	+	0.978203i	$0.566582\pi$
$422$		0			0
$423$	−2.59935	+	4.50220i	−0.126385	+	0.218904i
$424$		0			0
$425$	−6.51320	−	11.2812i	−0.315936	−	0.547218i
$426$		0			0
$427$	9.16467	−	6.88061i	0.443510	−	0.332976i
$428$		0			0
$429$	1.98026	+	3.42991i	0.0956079	+	0.165598i
$430$		0			0
$431$	−8.36718	+	14.4924i	−0.403033	+	0.698073i	−0.994090	−	0.108556i	$-0.965377\pi$
$431$	−8.36718	+	14.4924i	−0.403033	+	0.698073i	0.591058	+	0.806629i	$0.298711\pi$
$432$		0			0
$433$	−25.8661			−1.24305			−0.621523	−	0.783396i	$-0.713486\pi$
$433$	−25.8661			−1.24305			−0.621523	+	0.783396i	$0.713486\pi$
$434$		0			0
$435$	14.5751			0.698825
$436$		0			0
$437$	6.02420	−	10.4342i	0.288177	−	0.499137i
$438$		0			0
$439$	−4.78430	−	8.28665i	−0.228342	−	0.395500i	0.728975	−	0.684541i	$-0.239997\pi$
$439$	−4.78430	−	8.28665i	−0.228342	−	0.395500i	−0.957317	+	0.289040i	$0.906664\pi$
$440$		0			0
$441$	8.88637	+	9.26770i	0.423161	+	0.441319i
$442$		0			0
$443$	9.51647	+	16.4830i	0.452141	+	0.783131i	0.998519	−	0.0544076i	$-0.0173270\pi$
$443$	9.51647	+	16.4830i	0.452141	+	0.783131i	−0.546378	+	0.837539i	$0.683994\pi$
$444$		0			0
$445$	0.115813	−	0.200594i	0.00549005	−	0.00950905i
$446$		0			0
$447$	−2.19869			−0.103995
$448$		0			0
$449$	33.3424			1.57353			0.786763	−	0.617255i	$-0.211755\pi$
$449$	33.3424			1.57353			0.786763	+	0.617255i	$0.211755\pi$
$450$		0			0
$451$	−3.76783	+	6.52608i	−0.177420	+	0.307301i
$452$		0			0
$453$	1.90785	+	3.30449i	0.0896385	+	0.155258i
$454$		0			0
$455$	−2.42224	+	1.81856i	−0.113556	+	0.0852552i
$456$		0			0
$457$	−5.98026	−	10.3581i	−0.279745	−	0.484532i	0.691576	−	0.722303i	$-0.256917\pi$
$457$	−5.98026	−	10.3581i	−0.279745	−	0.484532i	−0.971321	+	0.237771i	$0.923583\pi$
$458$		0			0
$459$	−3.63228	+	6.29129i	−0.169540	+	0.293652i
$460$		0			0
$461$	12.4896			0.581701			0.290850	−	0.956769i	$-0.406062\pi$
$461$	12.4896			0.581701			0.290850	+	0.956769i	$0.406062\pi$
$462$		0			0
$463$	−12.3095			−0.572071			−0.286035	−	0.958219i	$-0.592338\pi$
$463$	−12.3095			−0.572071			−0.286035	+	0.958219i	$0.592338\pi$
$464$		0			0
$465$	−4.49281	+	7.78177i	−0.208349	+	0.360871i
$466$		0			0
$467$	16.3804	+	28.3716i	0.757993	+	1.31288i	0.943872	+	0.330310i	$0.107153\pi$
$467$	16.3804	+	28.3716i	0.757993	+	1.31288i	−0.185879	+	0.982573i	$0.559513\pi$
$468$		0			0
$469$	3.90011	+	1.66367i	0.180090	+	0.0768213i
$470$		0			0
$471$	8.72835	+	15.1180i	0.402181	+	0.696598i
$472$		0			0
$473$	−2.43359	+	4.21510i	−0.111897	+	0.193810i
$474$		0			0
$475$	−25.5686			−1.17317
$476$		0			0
$477$	13.7014			0.627345
$478$		0			0
$479$	12.9890	−	22.4976i	0.593482	−	1.02794i	−0.400277	−	0.916394i	$-0.631086\pi$
$479$	12.9890	−	22.4976i	0.593482	−	1.02794i	0.993759	−	0.111547i	$-0.0355806\pi$
$480$		0			0
$481$	5.46325	+	9.46263i	0.249103	+	0.431459i
$482$		0			0
$483$	1.51320	+	12.5074i	0.0688528	+	0.569107i
$484$		0			0
$485$	−0.824970	−	1.42889i	−0.0374600	−	0.0648825i
$486$		0			0
$487$	7.26783	−	12.5883i	0.329337	−	0.570428i	−0.653044	−	0.757320i	$-0.726508\pi$
$487$	7.26783	−	12.5883i	0.329337	−	0.570428i	0.982380	+	0.186892i	$0.0598415\pi$
$488$		0			0
$489$	35.1911			1.59139
$490$		0			0
$491$	39.3952			1.77788			0.888941	−	0.458023i	$-0.151442\pi$
$491$	39.3952			1.77788			0.888941	+	0.458023i	$0.151442\pi$
$492$		0			0
$493$	−14.7810	+	25.6015i	−0.665704	+	1.15303i
$494$		0			0
$495$	0.582878	+	1.00958i	0.0261984	+	0.0453770i
$496$		0			0
$497$	1.36391	+	11.2735i	0.0611795	+	0.505683i
$498$		0			0
$499$	−13.1153	−	22.7163i	−0.587120	−	1.01692i	−0.994607	−	0.103711i	$-0.966928\pi$
$499$	−13.1153	−	22.7163i	−0.587120	−	1.01692i	0.407487	−	0.913211i	$-0.366405\pi$
$500$		0			0
$501$	1.27438	−	2.20728i	0.0569349	−	0.0986142i
$502$		0			0
$503$	−3.94613			−0.175949			−0.0879747	−	0.996123i	$-0.528039\pi$
$503$	−3.94613			−0.175949			−0.0879747	+	0.996123i	$0.528039\pi$
$504$		0			0
$505$	6.29204			0.279992
$506$		0			0
$507$	10.7244	−	18.5753i	0.476289	−	0.824956i
$508$		0			0
$509$	−8.45279	−	14.6407i	−0.374663	−	0.648936i	0.615613	−	0.788048i	$-0.288908\pi$
$509$	−8.45279	−	14.6407i	−0.374663	−	0.648936i	−0.990277	+	0.139113i	$0.955575\pi$
$510$		0			0
$511$	−38.9215	−	16.6028i	−1.72179	−	0.734463i
$512$		0			0
$513$	7.12955	+	12.3487i	0.314777	+	0.545210i
$514$		0			0
$515$	−1.98026	+	3.42991i	−0.0872607	+	0.151140i
$516$		0			0
$517$	2.83424			0.124650
$518$		0			0
$519$	−2.18430			−0.0958803
$520$		0			0
$521$	−0.778840	+	1.34899i	−0.0341216	+	0.0591004i	−0.882582	−	0.470159i	$-0.844197\pi$
$521$	−0.778840	+	1.34899i	−0.0341216	+	0.0591004i	0.848460	+	0.529259i	$0.177530\pi$
$522$		0			0
$523$	−6.25136	−	10.8277i	−0.273353	−	0.473461i	0.696365	−	0.717688i	$-0.254799\pi$
$523$	−6.25136	−	10.8277i	−0.273353	−	0.473461i	−0.969718	+	0.244226i	$0.921466\pi$
$524$		0			0
$525$	21.3810	−	16.0524i	0.933144	−	0.700582i
$526$		0			0
$527$	−9.11254	−	15.7834i	−0.396949	−	0.687535i
$528$		0			0
$529$	9.15475	−	15.8565i	0.398033	−	0.689413i
$530$		0			0
$531$	−21.6565			−0.939811
$532$		0			0
$533$	−13.5741			−0.587958
$534$		0			0
$535$	−3.52693	+	6.10883i	−0.152483	+	0.264108i
$536$		0			0
$537$	−21.6153	−	37.4387i	−0.932768	−	1.61560i
$538$		0			0
$539$	1.95333	−	6.72194i	0.0841358	−	0.289535i
$540$		0			0
$541$	8.28103	+	14.3432i	0.356029	+	0.616661i	0.987294	−	0.158907i	$-0.0507970\pi$
$541$	8.28103	+	14.3432i	0.356029	+	0.616661i	−0.631264	+	0.775568i	$0.717464\pi$
$542$		0			0
$543$	26.2443	−	45.4564i	1.12625	−	1.95072i
$544$		0			0
$545$	9.09096			0.389414
$546$		0			0
$547$	6.64448			0.284097			0.142049	−	0.989860i	$-0.454631\pi$
$547$	6.64448			0.284097			0.142049	+	0.989860i	$0.454631\pi$
$548$		0			0
$549$	3.97252	−	6.88061i	0.169543	−	0.293657i
$550$		0			0
$551$	29.0127	+	50.2514i	1.23598	+	2.14078i
$552$		0			0
$553$	10.0751	−	7.56417i	0.428439	−	0.321661i
$554$		0			0
$555$	4.23817	+	7.34072i	0.179900	+	0.311596i
$556$		0			0
$557$	−6.55595	+	11.3552i	−0.277784	+	0.481137i	−0.970834	−	0.239753i	$-0.922933\pi$
$557$	−6.55595	+	11.3552i	−0.277784	+	0.481137i	0.693049	+	0.720890i	$0.256267\pi$
$558$		0			0
$559$	−8.76729			−0.370817
$560$		0			0
$561$	−6.23163			−0.263099
$562$		0			0
$563$	15.2443	−	26.4039i	0.642470	−	1.11279i	−0.342410	−	0.939551i	$-0.611243\pi$
$563$	15.2443	−	26.4039i	0.642470	−	1.11279i	0.984880	−	0.173240i	$-0.0554235\pi$
$564$		0			0
$565$	−2.76129	−	4.78269i	−0.116168	−	0.201209i
$566$		0			0
$567$	−27.1060	−	11.5626i	−1.13834	−	0.485584i
$568$		0			0
$569$	17.6790	+	30.6208i	0.741140	+	1.28369i	0.951976	+	0.306171i	$0.0990480\pi$
$569$	17.6790	+	30.6208i	0.741140	+	1.28369i	−0.210836	+	0.977521i	$0.567619\pi$
$570$		0			0
$571$	−20.6422	+	35.7533i	−0.863849	+	1.49623i	0.00433587	+	0.999991i	$0.498620\pi$
$571$	−20.6422	+	35.7533i	−0.863849	+	1.49623i	−0.868185	+	0.496240i	$0.834713\pi$
$572$		0			0
$573$	24.4753			1.02247
$574$		0			0
$575$	9.95398			0.415110
$576$		0			0
$577$	−4.35125	+	7.53659i	−0.181145	+	0.313752i	−0.942271	−	0.334852i	$-0.891314\pi$
$577$	−4.35125	+	7.53659i	−0.181145	+	0.313752i	0.761126	+	0.648604i	$0.224647\pi$
$578$		0			0
$579$	−3.97372	−	6.88268i	−0.165142	−	0.286034i
$580$		0			0
$581$	−2.93359	−	24.2478i	−0.121706	−	1.00597i
$582$		0			0
$583$	−3.73490	−	6.46903i	−0.154684	−	0.267920i
$584$		0			0
$585$	−1.04994	+	1.81856i	−0.0434098	+	0.0751881i
$586$		0			0
$587$	23.0539			0.951535			0.475767	−	0.879571i	$-0.342170\pi$
$587$	23.0539			0.951535			0.475767	+	0.879571i	$0.342170\pi$
$588$		0			0
$589$	−35.7727			−1.47399
$590$		0			0
$591$	−2.65856	+	4.60477i	−0.109359	+	0.189415i
$592$		0			0
$593$	−15.0494	−	26.0663i	−0.618005	−	1.07042i	−0.989849	−	0.142121i	$-0.954608\pi$
$593$	−15.0494	−	26.0663i	−0.618005	−	1.07042i	0.371844	−	0.928295i	$-0.378725\pi$
$594$		0			0
$595$	−0.572413	−	4.73131i	−0.0234666	−	0.193965i
$596$		0			0
$597$	−20.3337	−	35.2190i	−0.832203	−	1.44142i
$598$		0			0
$599$	14.6257	−	25.3325i	0.597591	−	1.03506i	−0.395584	−	0.918430i	$-0.629458\pi$
$599$	14.6257	−	25.3325i	0.597591	−	1.03506i	0.993176	−	0.116629i	$-0.0372088\pi$
$600$		0			0
$601$	−26.8222			−1.09410			−0.547051	−	0.837099i	$-0.684250\pi$
$601$	−26.8222			−1.09410			−0.547051	+	0.837099i	$0.684250\pi$
$602$		0			0
$603$	2.93959			0.119709
$604$		0			0
$605$	0.317776	−	0.550404i	0.0129194	−	0.0223771i
$606$		0			0
$607$	16.1048	+	27.8943i	0.653674	+	1.13220i	0.982224	+	0.187710i	$0.0601065\pi$
$607$	16.1048	+	27.8943i	0.653674	+	1.13220i	−0.328551	+	0.944486i	$0.606560\pi$
$608$		0			0
$609$	−55.8096	−	23.8067i	−2.26152	−	0.964697i
$610$		0			0
$611$	2.55267	+	4.42136i	0.103270	+	0.178869i
$612$		0			0
$613$	−22.2975	+	38.6204i	−0.900587	+	1.55986i	−0.0738539	+	0.997269i	$0.523530\pi$
$613$	−22.2975	+	38.6204i	−0.900587	+	1.55986i	−0.826733	+	0.562594i	$0.809803\pi$
$614$		0			0
$615$	−10.5302			−0.424619
$616$		0			0
$617$	−0.531290			−0.0213889			−0.0106945	−	0.999943i	$-0.503404\pi$
$617$	−0.531290			−0.0213889			−0.0106945	+	0.999943i	$0.503404\pi$
$618$		0			0
$619$	20.8726	−	36.1525i	0.838942	−	1.45309i	−0.0518379	−	0.998656i	$-0.516508\pi$
$619$	20.8726	−	36.1525i	0.838942	−	1.45309i	0.890780	−	0.454435i	$-0.150159\pi$
$620$		0			0
$621$	−2.77557	−	4.80743i	−0.111380	−	0.192915i
$622$		0			0
$623$	−0.771104	+	0.578926i	−0.0308936	+	0.0231942i
$624$		0			0
$625$	−9.55213	−	16.5448i	−0.382085	−	0.661791i
$626$		0			0
$627$	−6.11581	+	10.5929i	−0.244242	+	0.423040i
$628$		0			0
$629$	−17.1921			−0.685496
$630$		0			0
$631$	0.217238			0.00864810			0.00432405	−	0.999991i	$-0.498624\pi$
$631$	0.217238			0.00864810			0.00432405	+	0.999991i	$0.498624\pi$
$632$		0			0
$633$	−8.63555	+	14.9572i	−0.343232	+	0.594496i
$634$		0			0
$635$	−6.67295	−	11.5579i	−0.264808	−	0.458661i
$636$		0			0
$637$	12.2454	−	3.00700i	0.485179	−	0.119142i
$638$		0			0
$639$	3.93632	+	6.81790i	0.155718	+	0.269712i
$640$		0			0
$641$	4.84525	−	8.39222i	0.191376	−	0.331473i	−0.754331	−	0.656495i	$-0.772038\pi$
$641$	4.84525	−	8.39222i	0.191376	−	0.331473i	0.945706	+	0.325022i	$0.105372\pi$
$642$		0			0
$643$	−16.4633			−0.649247			−0.324624	−	0.945843i	$-0.605238\pi$
$643$	−16.4633			−0.649247			−0.324624	+	0.945843i	$0.605238\pi$
$644$		0			0
$645$	−6.80131			−0.267801
$646$		0			0
$647$	0.436861	−	0.756665i	0.0171748	−	0.0297476i	−0.857310	−	0.514800i	$-0.827866\pi$
$647$	0.436861	−	0.756665i	0.0171748	−	0.0297476i	0.874485	+	0.485052i	$0.161199\pi$
$648$		0			0
$649$	5.90338	+	10.2250i	0.231728	+	0.401365i
$650$		0			0
$651$	29.9140	−	22.4587i	1.17242	−	0.880225i
$652$		0			0
$653$	19.9665	+	34.5830i	0.781350	+	1.35334i	0.931155	+	0.364623i	$0.118802\pi$
$653$	19.9665	+	34.5830i	0.781350	+	1.35334i	−0.149805	+	0.988716i	$0.547865\pi$
$654$		0			0
$655$	4.35398	−	7.54132i	0.170124	−	0.294664i
$656$		0			0
$657$	−29.3359			−1.14450
$658$		0			0
$659$	6.89465			0.268578			0.134289	−	0.990942i	$-0.457125\pi$
$659$	6.89465			0.268578			0.134289	+	0.990942i	$0.457125\pi$
$660$		0			0
$661$	20.0072	−	34.6535i	0.778190	−	1.34786i	−0.154795	−	0.987947i	$-0.549472\pi$
$661$	20.0072	−	34.6535i	0.778190	−	1.34786i	0.932984	−	0.359917i	$-0.117195\pi$
$662$		0			0
$663$	−5.61254	−	9.72121i	−0.217973	−	0.377540i
$664$		0			0
$665$	−8.60435	−	3.67036i	−0.333662	−	0.142331i
$666$		0			0
$667$	−11.2948	−	19.5631i	−0.437335	−	0.757487i
$668$		0			0
$669$	22.3574	−	38.7241i	0.864386	−	1.49716i
$670$		0			0
$671$	−4.33151			−0.167216
$672$		0			0
$673$	31.3788			1.20957			0.604783	−	0.796391i	$-0.293260\pi$
$673$	31.3788			1.20957			0.604783	+	0.796391i	$0.293260\pi$
$674$		0			0
$675$	−5.89019	+	10.2021i	−0.226713	+	0.392679i
$676$		0			0
$677$	18.2658	+	31.6372i	0.702010	+	1.21592i	0.967760	+	0.251875i	$0.0810471\pi$
$677$	18.2658	+	31.6372i	0.702010	+	1.21592i	−0.265750	+	0.964042i	$0.585620\pi$
$678$		0			0
$679$	0.824970	+	6.81884i	0.0316594	+	0.261683i
$680$		0			0
$681$	7.93686	+	13.7470i	0.304141	+	0.526788i
$682$		0			0
$683$	−7.63501	+	13.2242i	−0.292146	+	0.506011i	−0.974317	−	0.225181i	$-0.927702\pi$
$683$	−7.63501	+	13.2242i	−0.292146	+	0.506011i	0.682171	+	0.731192i	$0.261036\pi$
$684$		0			0
$685$	−4.61701			−0.176407
$686$		0			0
$687$	26.5411			1.01261
$688$		0			0
$689$	6.72770	−	11.6527i	0.256305	−	0.443933i
$690$		0			0
$691$	−19.1921	−	33.2418i	−0.730104	−	1.26458i	−0.956839	−	0.290620i	$-0.906138\pi$
$691$	−19.1921	−	33.2418i	−0.730104	−	1.26458i	0.226735	−	0.973957i	$-0.427195\pi$
$692$		0			0
$693$	−0.582878	−	4.81782i	−0.0221417	−	0.183014i
$694$		0			0
$695$	0.827049	+	1.43249i	0.0313718	+	0.0543375i
$696$		0			0
$697$	10.6790	−	18.4965i	0.404494	−	0.700604i
$698$		0			0
$699$	−16.5830			−0.627226
$700$		0			0
$701$	17.9056			0.676284			0.338142	−	0.941095i	$-0.390202\pi$
$701$	17.9056			0.676284			0.338142	+	0.941095i	$0.390202\pi$
$702$		0			0
$703$	−16.8726	+	29.2243i	−0.636364	+	1.10221i
$704$		0			0
$705$	1.98026	+	3.42991i	0.0745809	+	0.129178i
$706$		0			0
$707$	−24.0928	−	10.2773i	−0.906103	−	0.386517i
$708$		0			0
$709$	−17.1997	−	29.7907i	−0.645948	−	1.11881i	−0.984082	−	0.177716i	$-0.943129\pi$
$709$	−17.1997	−	29.7907i	−0.645948	−	1.11881i	0.338134	−	0.941098i	$-0.390204\pi$
$710$		0			0
$711$	4.36718	−	7.56417i	0.163782	−	0.283679i
$712$		0			0
$713$	13.9265			0.521552
$714$		0			0
$715$	1.14483			0.0428140
$716$		0			0
$717$	−10.8244	+	18.7485i	−0.404246	+	0.700174i
$718$		0			0
$719$	24.7086	+	42.7966i	0.921476	+	1.59604i	0.797133	+	0.603804i	$0.206349\pi$
$719$	24.7086	+	42.7966i	0.921476	+	1.59604i	0.124343	+	0.992239i	$0.460318\pi$
$720$		0			0
$721$	13.1850	−	9.89894i	0.491033	−	0.368656i
$722$		0			0
$723$	1.84144	+	3.18946i	0.0684838	+	0.118617i
$724$		0			0
$725$	−23.9693	+	41.5160i	−0.890196	+	1.54186i
$726$		0			0
$727$	19.8201			0.735086			0.367543	−	0.930007i	$-0.380199\pi$
$727$	19.8201			0.735086			0.367543	+	0.930007i	$0.380199\pi$
$728$		0			0
$729$	−3.52366			−0.130506
$730$		0			0
$731$	6.89738	−	11.9466i	0.255109	−	0.441862i
$732$		0			0
$733$	15.3238	+	26.5416i	0.565997	+	0.980335i	0.996956	+	0.0779637i	$0.0248418\pi$
$733$	15.3238	+	26.5416i	0.565997	+	0.980335i	−0.430960	+	0.902371i	$0.641825\pi$
$734$		0			0
$735$	9.49946	−	2.33271i	0.350393	−	0.0860432i
$736$		0			0
$737$	−0.801309	−	1.38791i	−0.0295166	−	0.0511242i
$738$		0			0
$739$	8.55094	−	14.8107i	0.314551	−	0.544819i	−0.664791	−	0.747030i	$-0.731479\pi$
$739$	8.55094	−	14.8107i	0.314551	−	0.544819i	0.979342	+	0.202211i	$0.0648126\pi$
$740$		0			0
$741$	−22.0329			−0.809400
$742$		0			0
$743$	6.97252			0.255797			0.127899	−	0.991787i	$-0.459177\pi$
$743$	6.97252			0.255797			0.127899	+	0.991787i	$0.459177\pi$
$744$		0			0
$745$	−0.317776	+	0.550404i	−0.0116424	+	0.0201652i
$746$		0			0
$747$	−8.46652	−	14.6644i	−0.309774	−	0.536544i
$748$		0			0
$749$	23.4830	−	17.6305i	0.858050	−	0.644203i
$750$		0			0
$751$	7.61636	+	13.1919i	0.277925	+	0.481380i	0.970869	−	0.239612i	$-0.0770201\pi$
$751$	7.61636	+	13.1919i	0.277925	+	0.481380i	−0.692944	+	0.720991i	$0.743687\pi$
$752$		0			0
$753$	21.7383	−	37.6518i	0.792187	−	1.37211i
$754$		0			0
$755$	1.10296			0.0401409
$756$		0			0
$757$	−14.5326			−0.528196			−0.264098	−	0.964496i	$-0.585074\pi$
$757$	−14.5326			−0.528196			−0.264098	+	0.964496i	$0.585074\pi$
$758$		0			0
$759$	2.38092	−	4.12387i	0.0864217	−	0.149687i
$760$		0			0
$761$	0.856712	+	1.48387i	0.0310558	+	0.0537902i	0.881136	−	0.472864i	$-0.156780\pi$
$761$	0.856712	+	1.48387i	0.0310558	+	0.0537902i	−0.850080	+	0.526654i	$0.823446\pi$
$762$		0			0
$763$	−34.8101	−	14.8490i	−1.26021	−	0.537569i
$764$		0			0
$765$	−1.65202	−	2.86138i	−0.0597289	−	0.103453i
$766$		0			0
$767$	−10.6338	+	18.4183i	−0.383965	+	0.665047i
$768$		0			0
$769$	−36.5874			−1.31937			−0.659687	−	0.751540i	$-0.729311\pi$
$769$	−36.5874			−1.31937			−0.659687	+	0.751540i	$0.729311\pi$
$770$		0			0
$771$	5.98037			0.215378
$772$		0			0
$773$	−13.4106	+	23.2278i	−0.482345	+	0.835446i	−0.999795	−	0.0202677i	$-0.993548\pi$
$773$	−13.4106	+	23.2278i	−0.482345	+	0.835446i	0.517450	+	0.855714i	$0.326881\pi$
$774$		0			0
$775$	−14.7771	−	25.5947i	−0.530809	−	0.919389i
$776$		0			0
$777$	−4.23817	−	35.0309i	−0.152043	−	1.25673i
$778$		0			0
$779$	−20.9610	−	36.3055i	−0.751005	−	1.30078i
$780$		0			0
$781$	2.14602	−	3.71701i	0.0767906	−	0.133005i
$782$		0			0
$783$	26.7344			0.955408
$784$		0			0
$785$	5.04602			0.180100
$786$		0			0
$787$	2.47580	−	4.28821i	0.0882526	−	0.152858i	−0.818520	−	0.574478i	$-0.805205\pi$
$787$	2.47580	−	4.28821i	0.0882526	−	0.152858i	0.906773	+	0.421620i	$0.138538\pi$
$788$		0			0
$789$	13.9561	+	24.1726i	0.496849	+	0.860567i
$790$		0			0
$791$	2.76129	+	22.8236i	0.0981801	+	0.811514i
$792$		0			0
$793$	−3.90120	−	6.75707i	−0.138536	−	0.239951i
$794$		0			0
$795$	5.21908	−	9.03971i	0.185102	−	0.320606i
$796$		0			0
$797$	−26.6818			−0.945117			−0.472559	−	0.881299i	$-0.656670\pi$
$797$	−26.6818			−0.945117			−0.472559	+	0.881299i	$0.656670\pi$
$798$		0			0
$799$	−8.03293			−0.284185
$800$		0			0
$801$	−0.334243	+	0.578926i	−0.0118099	+	0.0204554i
$802$		0			0
$803$	7.99673	+	13.8507i	0.282198	+	0.488782i
$804$		0			0
$805$	3.34972	+	1.42889i	0.118062	+	0.0503617i
$806$		0			0
$807$	7.79804	+	13.5066i	0.274504	+	0.475455i
$808$		0			0
$809$	19.7700	−	34.2427i	0.695077	−	1.20391i	−0.275078	−	0.961422i	$-0.588704\pi$
$809$	19.7700	−	34.2427i	0.695077	−	1.20391i	0.970155	−	0.242487i	$-0.0779630\pi$
$810$		0			0
$811$	33.4543			1.17474			0.587370	−	0.809318i	$-0.300163\pi$
$811$	33.4543			1.17474			0.587370	+	0.809318i	$0.300163\pi$
$812$		0			0
$813$	40.0517			1.40467
$814$		0			0
$815$	5.08615	−	8.80947i	0.178160	−	0.308582i
$816$		0			0
$817$	−13.5384	−	23.4492i	−0.473648	−	0.820383i
$818$		0			0
$819$	6.99073	−	5.24847i	0.244276	−	0.183396i
$820$		0			0
$821$	−28.4310	−	49.2439i	−0.992248	−	1.71862i	−0.603751	−	0.797173i	$-0.706328\pi$
$821$	−28.4310	−	49.2439i	−0.992248	−	1.71862i	−0.388497	−	0.921450i	$-0.627006\pi$
$822$		0			0
$823$	−20.0878	+	34.7931i	−0.700217	+	1.21281i	0.268174	+	0.963371i	$0.413580\pi$
$823$	−20.0878	+	34.7931i	−0.700217	+	1.21281i	−0.968390	+	0.249440i	$0.919753\pi$
$824$		0			0
$825$	−10.1053			−0.351823
$826$		0			0
$827$	5.73544			0.199441			0.0997204	−	0.995015i	$-0.468205\pi$
$827$	5.73544			0.199441			0.0997204	+	0.995015i	$0.468205\pi$
$828$		0			0
$829$	17.7980	−	30.8271i	0.618151	−	1.07067i	−0.371671	−	0.928364i	$-0.621215\pi$
$829$	17.7980	−	30.8271i	0.618151	−	1.07067i	0.989823	−	0.142305i	$-0.0454515\pi$
$830$		0			0
$831$	−15.2244	−	26.3695i	−0.528130	−	0.914747i
$832$		0			0
$833$	−5.53621	+	19.0516i	−0.191818	+	0.660099i
$834$		0			0
$835$	−0.368370	−	0.638036i	−0.0127480	−	0.0220801i
$836$		0			0
$837$	−8.24090	+	14.2737i	−0.284847	+	0.493370i
$838$		0			0
$839$	41.7727			1.44216			0.721078	−	0.692854i	$-0.243647\pi$
$839$	41.7727			1.44216			0.721078	+	0.692854i	$0.243647\pi$
$840$		0			0
$841$	79.7915			2.75143
$842$		0			0
$843$	−23.1225	+	40.0493i	−0.796380	+	1.37937i
$844$		0			0
$845$	−3.10000	−	5.36935i	−0.106643	−	0.184711i
$846$		0			0
$847$	−2.11581	+	1.58850i	−0.0727002	+	0.0545815i
$848$		0			0
$849$	0.387459	+	0.671099i	0.0132976	+	0.0230321i
$850$		0			0
$851$	6.56860	−	11.3771i	0.225169	−	0.390004i
$852$		0			0
$853$	49.7871			1.70468			0.852340	−	0.522989i	$-0.175183\pi$
$853$	49.7871			1.70468			0.852340	+	0.522989i	$0.175183\pi$
$854$		0			0
$855$	−6.48527			−0.221791
$856$		0			0
$857$	−12.7394	+	22.0652i	−0.435168	+	0.753734i	−0.997309	−	0.0733077i	$-0.976644\pi$
$857$	−12.7394	+	22.0652i	−0.435168	+	0.753734i	0.562141	+	0.827041i	$0.309978\pi$
$858$		0			0
$859$	8.08080	+	13.9964i	0.275713	+	0.477549i	0.970315	−	0.241845i	$-0.0777526\pi$
$859$	8.08080	+	13.9964i	0.275713	+	0.477549i	−0.694602	+	0.719395i	$0.744419\pi$
$860$		0			0
$861$	40.3212	+	17.1998i	1.37414	+	0.586168i
$862$		0			0
$863$	1.44951	+	2.51063i	0.0493420	+	0.0854629i	0.889642	−	0.456660i	$-0.150954\pi$
$863$	1.44951	+	2.51063i	0.0493420	+	0.0854629i	−0.840300	+	0.542122i	$0.817621\pi$
$864$		0			0
$865$	−0.315697	+	0.546802i	−0.0107340	+	0.0185918i
$866$		0			0
$867$	−19.7158			−0.669584
$868$		0			0
$869$	−4.76183			−0.161534
$870$		0			0
$871$	1.44340	−	2.50005i	0.0489079	−	0.0847110i
$872$		0			0
$873$	2.38092	+	4.12387i	0.0805818	+	0.139572i
$874$		0			0
$875$	−1.93805	−	16.0191i	−0.0655182	−	0.541545i
$876$		0			0
$877$	4.20742	+	7.28747i	0.142075	+	0.246080i	0.928278	−	0.371888i	$-0.121289\pi$
$877$	4.20742	+	7.28747i	0.142075	+	0.246080i	−0.786203	+	0.617968i	$0.787956\pi$
$878$		0			0
$879$	3.80731	−	6.59445i	0.128417	−	0.222425i
$880$		0			0
$881$	41.5335			1.39930			0.699649	−	0.714486i	$-0.253340\pi$
$881$	41.5335			1.39930			0.699649	+	0.714486i	$0.253340\pi$
$882$		0			0
$883$	56.4753			1.90054			0.950272	−	0.311422i	$-0.100805\pi$
$883$	56.4753			1.90054			0.950272	+	0.311422i	$0.100805\pi$
$884$		0			0
$885$	−8.24929	+	14.2882i	−0.277297	+	0.480292i
$886$		0			0
$887$	−17.2898	−	29.9467i	−0.580533	−	1.00551i	−0.995416	−	0.0956383i	$-0.969511\pi$
$887$	−17.2898	−	29.9467i	−0.580533	−	1.00551i	0.414883	−	0.909875i	$-0.363823\pi$
$888$		0			0
$889$	6.67295	+	55.1557i	0.223804	+	1.84986i
$890$		0			0
$891$	5.56914	+	9.64603i	0.186573	+	0.323154i
$892$		0			0
$893$	−7.88364	+	13.6549i	−0.263816	+	0.456943i
$894$		0			0
$895$	−12.4962			−0.417701
$896$		0			0
$897$	8.57753			0.286395
$898$		0			0
$899$	−33.5351	+	58.0845i	−1.11846	+	1.93723i
$900$		0			0
$901$	10.5856	+	18.3348i	0.352658	+	0.610821i
$902$		0			0
$903$	26.0429	+	11.1091i	0.866652	+	0.369688i
$904$		0			0
$905$	−7.58615	−	13.1396i	−0.252172	−	0.436775i
$906$		0			0
$907$	4.20142	−	7.27707i	0.139506	−	0.241631i	−0.787804	−	0.615926i	$-0.788782\pi$
$907$	4.20142	−	7.27707i	0.139506	−	0.241631i	0.927310	+	0.374295i	$0.122115\pi$
$908$		0			0
$909$	−18.1592			−0.602303
$910$		0			0
$911$	0.593689			0.0196698			0.00983489	−	0.999952i	$-0.496869\pi$
$911$	0.593689			0.0196698			0.00983489	+	0.999952i	$0.496869\pi$
$912$		0			0
$913$	−4.61581	+	7.99482i	−0.152761	+	0.264590i
$914$		0			0
$915$	−3.02639	−	5.24186i	−0.100049	−	0.173291i
$916$		0			0
$917$	−28.9896	+	21.7647i	−0.957322	+	0.718734i
$918$		0			0
$919$	−8.16849	−	14.1482i	−0.269454	−	0.466707i	0.699267	−	0.714860i	$-0.253510\pi$
$919$	−8.16849	−	14.1482i	−0.269454	−	0.466707i	−0.968721	+	0.248153i	$0.920176\pi$
$920$		0			0
$921$	−7.16194	+	12.4048i	−0.235994	+	0.408754i
$922$		0			0
$923$	7.73128			0.254478
$924$		0			0
$925$	−27.8792			−0.916662
$926$		0			0
$927$	5.71516	−	9.89894i	0.187710	−	0.325124i
$928$		0			0
$929$	−4.45060	−	7.70866i	−0.146019	−	0.252913i	0.783733	−	0.621097i	$-0.213313\pi$
$929$	−4.45060	−	7.70866i	−0.146019	−	0.252913i	−0.929753	+	0.368184i	$0.879980\pi$
$930$		0			0
$931$	26.9518	+	28.1083i	0.883309	+	0.921213i
$932$		0			0
$933$	12.7855	+	22.1451i	0.418578	+	0.724999i
$934$		0			0
$935$	−0.900654	+	1.55998i	−0.0294545	+	0.0510168i
$936$		0			0
$937$	45.2360			1.47780			0.738898	−	0.673817i	$-0.235347\pi$
$937$	45.2360			1.47780			0.738898	+	0.673817i	$0.235347\pi$
$938$		0			0
$939$	−59.5795			−1.94430
$940$		0			0
$941$	3.46652	−	6.00419i	0.113005	−	0.195731i	−0.803975	−	0.594663i	$-0.797286\pi$
$941$	3.46652	−	6.00419i	0.113005	−	0.195731i	0.916981	+	0.398932i	$0.130619\pi$
$942$		0			0
$943$	8.16021	+	14.1339i	0.265733	+	0.460263i
$944$		0			0
$945$	−3.44668	+	2.58768i	−0.112120	+	0.0841773i
$946$		0			0
$947$	10.3716	+	17.9642i	0.337033	+	0.583758i	0.983873	−	0.178867i	$-0.0572432\pi$
$947$	10.3716	+	17.9642i	0.337033	+	0.583758i	−0.646840	+	0.762626i	$0.723910\pi$
$948$		0			0
$949$	−14.4046	+	24.9495i	−0.467592	+	0.809894i
$950$		0			0
$951$	8.49073			0.275331
$952$		0			0
$953$	20.2076			0.654589			0.327295	−	0.944922i	$-0.393863\pi$
$953$	20.2076			0.654589			0.327295	+	0.944922i	$0.393863\pi$
$954$		0			0
$955$	3.53740	−	6.12695i	0.114468	−	0.198264i
$956$		0			0
$957$	11.4665	+	19.8606i	0.370660	+	0.642002i
$958$		0			0
$959$	17.6790	+	7.54132i	0.570883	+	0.243522i
$960$		0			0
$961$	−5.17449	−	8.96248i	−0.166919	−	0.289112i
$962$		0			0
$963$	10.1790	−	17.6305i	0.328012	−	0.568134i
$964$		0			0
$965$	−2.29728			−0.0739520
$966$		0			0
$967$	7.98254			0.256701			0.128351	−	0.991729i	$-0.459032\pi$
$967$	7.98254			0.256701			0.128351	+	0.991729i	$0.459032\pi$
$968$		0			0
$969$	17.3337	−	30.0229i	0.556839	−	0.964473i
$970$		0			0
$971$	−6.88965	−	11.9332i	−0.221099	−	0.382955i	0.734043	−	0.679103i	$-0.237631\pi$
$971$	−6.88965	−	11.9332i	−0.221099	−	0.382955i	−0.955142	+	0.296148i	$0.904298\pi$
$972$		0			0
$973$	−0.827049	−	6.83603i	−0.0265140	−	0.219153i
$974$		0			0
$975$	−9.10143	−	15.7641i	−0.291479	−	0.504856i
$976$		0			0
$977$	−6.01047	+	10.4104i	−0.192292	+	0.333059i	−0.946009	−	0.324139i	$-0.894925\pi$
$977$	−6.01047	+	10.4104i	−0.192292	+	0.333059i	0.753718	+	0.657199i	$0.228259\pi$
$978$		0			0
$979$	0.364448			0.0116478
$980$		0			0
$981$	−26.2371			−0.837686
$982$		0			0
$983$	−22.3272	+	38.6718i	−0.712126	+	1.23344i	0.251932	+	0.967745i	$0.418934\pi$
$983$	−22.3272	+	38.6718i	−0.712126	+	1.23344i	−0.964058	+	0.265693i	$0.914399\pi$
$984$		0			0
$985$	0.768482	+	1.33105i	0.0244859	+	0.0424108i
$986$		0			0
$987$	−1.98026	−	16.3680i	−0.0630324	−	0.520998i
$988$		0			0
$989$	5.27056	+	9.12888i	0.167594	+	0.290282i
$990$		0			0
$991$	−11.4830	+	19.8891i	−0.364769	+	0.631799i	−0.988739	−	0.149650i	$-0.952185\pi$
$991$	−11.4830	+	19.8891i	−0.364769	+	0.631799i	0.623970	+	0.781448i	$0.285519\pi$
$992$		0			0
$993$	−13.5226			−0.429126
$994$		0			0
$995$	−11.7553			−0.372668
$996$		0			0
$997$	−0.674488	+	1.16825i	−0.0213612	+	0.0369988i	−0.876508	−	0.481387i	$-0.840133\pi$
$997$	−0.674488	+	1.16825i	−0.0213612	+	0.0369988i	0.855147	+	0.518385i	$0.173467\pi$
$998$		0			0
$999$	7.77383	+	13.4647i	0.245953	+	0.426003i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.q.k.529.1		6
4.3	odd	2		77.2.e.b.67.1	yes	6
7.2	even	3	inner	1232.2.q.k.177.1		6
7.3	odd	6		8624.2.a.ck.1.1		3
7.4	even	3		8624.2.a.cl.1.3		3
12.11	even	2		693.2.i.g.298.3		6
28.3	even	6		539.2.a.i.1.3		3
28.11	odd	6		539.2.a.h.1.3		3
28.19	even	6		539.2.e.l.177.1		6
28.23	odd	6		77.2.e.b.23.1	✓	6
28.27	even	2		539.2.e.l.67.1		6
44.3	odd	10		847.2.n.e.130.1		24
44.7	even	10		847.2.n.d.753.1		24
44.15	odd	10		847.2.n.e.753.3		24
44.19	even	10		847.2.n.d.130.3		24
44.27	odd	10		847.2.n.e.487.3		24
44.31	odd	10		847.2.n.e.81.1		24
44.35	even	10		847.2.n.d.81.3		24
44.39	even	10		847.2.n.d.487.1		24
44.43	even	2		847.2.e.d.606.3		6
84.11	even	6		4851.2.a.bo.1.1		3
84.23	even	6		693.2.i.g.100.3		6
84.59	odd	6		4851.2.a.bn.1.1		3
308.51	even	30		847.2.n.d.632.3		24
308.79	even	30		847.2.n.d.807.1		24
308.87	odd	6		5929.2.a.w.1.1		3
308.107	even	30		847.2.n.d.9.1		24
308.135	odd	30		847.2.n.e.9.3		24
308.163	odd	30		847.2.n.e.807.3		24
308.191	odd	30		847.2.n.e.632.1		24
308.219	even	6		847.2.e.d.485.3		6
308.247	odd	30		847.2.n.e.366.1		24
308.263	even	6		5929.2.a.v.1.1		3
308.303	even	30		847.2.n.d.366.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.b.23.1	✓	6	28.23	odd	6
77.2.e.b.67.1	yes	6	4.3	odd	2
539.2.a.h.1.3		3	28.11	odd	6
539.2.a.i.1.3		3	28.3	even	6
539.2.e.l.67.1		6	28.27	even	2
539.2.e.l.177.1		6	28.19	even	6
693.2.i.g.100.3		6	84.23	even	6
693.2.i.g.298.3		6	12.11	even	2
847.2.e.d.485.3		6	308.219	even	6
847.2.e.d.606.3		6	44.43	even	2
847.2.n.d.9.1		24	308.107	even	30
847.2.n.d.81.3		24	44.35	even	10
847.2.n.d.130.3		24	44.19	even	10
847.2.n.d.366.3		24	308.303	even	30
847.2.n.d.487.1		24	44.39	even	10
847.2.n.d.632.3		24	308.51	even	30
847.2.n.d.753.1		24	44.7	even	10
847.2.n.d.807.1		24	308.79	even	30
847.2.n.e.9.3		24	308.135	odd	30
847.2.n.e.81.1		24	44.31	odd	10
847.2.n.e.130.1		24	44.3	odd	10
847.2.n.e.366.1		24	308.247	odd	30
847.2.n.e.487.3		24	44.27	odd	10
847.2.n.e.632.1		24	308.191	odd	30
847.2.n.e.753.3		24	44.15	odd	10
847.2.n.e.807.3		24	308.163	odd	30
1232.2.q.k.177.1		6	7.2	even	3	inner
1232.2.q.k.529.1		6	1.1	even	1	trivial
4851.2.a.bn.1.1		3	84.59	odd	6
4851.2.a.bo.1.1		3	84.11	even	6
5929.2.a.v.1.1		3	308.263	even	6
5929.2.a.w.1.1		3	308.87	odd	6
8624.2.a.ck.1.1		3	7.3	odd	6
8624.2.a.cl.1.3		3	7.4	even	3

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:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1232.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.09935 + 1.90412i) q^{3} +(0.317776 + 0.550404i) q^{5} +(-0.317776 - 2.62660i) q^{7} +(-0.917122 - 1.58850i) q^{9} +O(q^{10})\)	\(q+(-1.09935 + 1.90412i) q^{3} +(0.317776 + 0.550404i) q^{5} +(-0.317776 - 2.62660i) q^{7} +(-0.917122 - 1.58850i) q^{9} +(-0.500000 + 0.866025i) q^{11} -1.80131 q^{13} -1.39738 q^{15} +(1.41712 - 2.45453i) q^{17} +(-2.78157 - 4.81782i) q^{19} +(5.35071 + 2.28245i) q^{21} +(1.08288 + 1.87560i) q^{23} +(2.29804 - 3.98032i) q^{25} -2.56314 q^{27} -10.4303 q^{29} +(3.21516 - 5.56882i) q^{31} +(-1.09935 - 1.90412i) q^{33} +(1.34471 - 1.00958i) q^{35} +(-3.03293 - 5.25320i) q^{37} +(1.98026 - 3.42991i) q^{39} +7.53566 q^{41} +4.86718 q^{43} +(0.582878 - 1.00958i) q^{45} +(-1.41712 - 2.45453i) q^{47} +(-6.79804 + 1.66934i) q^{49} +(3.11581 + 5.39675i) q^{51} +(-3.73490 + 6.46903i) q^{53} -0.635552 q^{55} +12.2316 q^{57} +(5.90338 - 10.2250i) q^{59} +(2.16576 + 3.75120i) q^{61} +(-3.88092 + 2.91370i) q^{63} +(-0.572413 - 0.991448i) q^{65} +(-0.801309 + 1.38791i) q^{67} -4.76183 q^{69} -4.29204 q^{71} +(7.99673 - 13.8507i) q^{73} +(5.05267 + 8.75149i) q^{75} +(2.43359 + 1.03810i) q^{77} +(2.38092 + 4.12387i) q^{79} +(5.56914 - 9.64603i) q^{81} +9.23163 q^{83} +1.80131 q^{85} +(11.4665 - 19.8606i) q^{87} +(-0.182224 - 0.315621i) q^{89} +(0.572413 + 4.73131i) q^{91} +(7.06914 + 12.2441i) q^{93} +(1.76783 - 3.06197i) q^{95} -2.59607 q^{97} +1.83424 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{3} + 2 q^{5} - 2 q^{7}+O(q^{10}) \) 6 * q - q^3 + 2 * q^5 - 2 * q^7	\( 6 q - q^{3} + 2 q^{5} - 2 q^{7} - 3 q^{11} - 22 q^{13} + 14 q^{15} + 3 q^{17} - 11 q^{19} + 10 q^{21} + 12 q^{23} - 3 q^{25} - 4 q^{27} - 18 q^{29} - 3 q^{31} - q^{33} - 9 q^{35} + 4 q^{37} - 5 q^{39} - 10 q^{41} - 4 q^{43} + 9 q^{45} - 3 q^{47} - 24 q^{49} + 2 q^{51} - 17 q^{53} - 4 q^{55} + 40 q^{57} + 8 q^{59} + 24 q^{61} - 12 q^{63} - 15 q^{65} - 16 q^{67} - 6 q^{69} - 14 q^{71} + 20 q^{73} + 25 q^{75} - 2 q^{77} + 3 q^{79} + 17 q^{81} + 22 q^{83} + 22 q^{85} + 30 q^{87} - q^{89} + 15 q^{91} + 26 q^{93} - 17 q^{95} + 18 q^{97}+O(q^{100}) \) 6 * q - q^3 + 2 * q^5 - 2 * q^7 - 3 * q^11 - 22 * q^13 + 14 * q^15 + 3 * q^17 - 11 * q^19 + 10 * q^21 + 12 * q^23 - 3 * q^25 - 4 * q^27 - 18 * q^29 - 3 * q^31 - q^33 - 9 * q^35 + 4 * q^37 - 5 * q^39 - 10 * q^41 - 4 * q^43 + 9 * q^45 - 3 * q^47 - 24 * q^49 + 2 * q^51 - 17 * q^53 - 4 * q^55 + 40 * q^57 + 8 * q^59 + 24 * q^61 - 12 * q^63 - 15 * q^65 - 16 * q^67 - 6 * q^69 - 14 * q^71 + 20 * q^73 + 25 * q^75 - 2 * q^77 + 3 * q^79 + 17 * q^81 + 22 * q^83 + 22 * q^85 + 30 * q^87 - q^89 + 15 * q^91 + 26 * q^93 - 17 * q^95 + 18 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more