LMFDB - Embedded newform 912.2.q.l.577.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(49,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, 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("912.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	no (minimal twist has level 57)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			577.3
Root			$-1.62241 + 0.606458i$ of defining polynomial
Character	$\chi$	$=$	912.577
Dual form			912.2.q.l.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} +(1.33641 + 2.31473i) q^{5} +3.67282 q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{3} +(1.33641 + 2.31473i) q^{5} +3.67282 q^{7} +(-0.500000 + 0.866025i) q^{9} +3.81681 q^{11} +(-0.0719933 + 0.124696i) q^{13} +(-1.33641 + 2.31473i) q^{15} +(-4.24482 + 0.990721i) q^{19} +(1.83641 + 3.18076i) q^{21} +(3.76442 - 6.52016i) q^{23} +(-1.07199 + 1.85675i) q^{25} -1.00000 q^{27} +(2.67282 - 4.62947i) q^{29} -8.81681 q^{31} +(1.90841 + 3.30545i) q^{33} +(4.90841 + 8.50161i) q^{35} -1.00000 q^{37} -0.143987 q^{39} +(-2.67282 - 4.62947i) q^{41} +(1.40841 + 2.43943i) q^{43} -2.67282 q^{45} +(-3.00000 + 5.19615i) q^{47} +6.48963 q^{49} +(-4.00924 + 6.94420i) q^{53} +(5.10083 + 8.83490i) q^{55} +(-2.98040 - 3.18076i) q^{57} +(1.90841 + 3.30545i) q^{59} +(-5.74482 + 9.95031i) q^{61} +(-1.83641 + 3.18076i) q^{63} -0.384851 q^{65} +(2.69243 - 4.66342i) q^{67} +7.52884 q^{69} +(-6.81681 - 11.8071i) q^{71} +(0.172824 + 0.299339i) q^{73} -2.14399 q^{75} +14.0185 q^{77} +(3.26442 + 5.65414i) q^{79} +(-0.500000 - 0.866025i) q^{81} +2.28797 q^{83} +5.34565 q^{87} +(4.33641 - 7.51089i) q^{89} +(-0.264419 + 0.457986i) q^{91} +(-4.40841 - 7.63558i) q^{93} +(-7.96608 - 8.50161i) q^{95} +(2.95684 + 5.12140i) q^{97} +(-1.90841 + 3.30545i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{3} - 2 q^{5} + 2 q^{7} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^3 - 2 * q^5 + 2 * q^7 - 3 * q^9	$ 6 q + 3 q^{3} - 2 q^{5} + 2 q^{7} - 3 q^{9} + q^{13} + 2 q^{15} - 4 q^{19} + q^{21} + 14 q^{23} - 5 q^{25} - 6 q^{27} - 4 q^{29} - 30 q^{31} + 18 q^{35} - 6 q^{37} + 2 q^{39} + 4 q^{41} - 3 q^{43} + 4 q^{45} - 18 q^{47} - 4 q^{49} + 6 q^{53} + 12 q^{55} - 5 q^{57} - 13 q^{61} - q^{63} + 12 q^{65} + 9 q^{67} + 28 q^{69} - 18 q^{71} - 19 q^{73} - 10 q^{75} + 24 q^{77} + 11 q^{79} - 3 q^{81} + 8 q^{83} - 8 q^{87} + 16 q^{89} + 7 q^{91} - 15 q^{93} - 2 q^{95} + 2 q^{97}+O(q^{100}) $ 6 * q + 3 * q^3 - 2 * q^5 + 2 * q^7 - 3 * q^9 + q^13 + 2 * q^15 - 4 * q^19 + q^21 + 14 * q^23 - 5 * q^25 - 6 * q^27 - 4 * q^29 - 30 * q^31 + 18 * q^35 - 6 * q^37 + 2 * q^39 + 4 * q^41 - 3 * q^43 + 4 * q^45 - 18 * q^47 - 4 * q^49 + 6 * q^53 + 12 * q^55 - 5 * q^57 - 13 * q^61 - q^63 + 12 * q^65 + 9 * q^67 + 28 * q^69 - 18 * q^71 - 19 * q^73 - 10 * q^75 + 24 * q^77 + 11 * q^79 - 3 * q^81 + 8 * q^83 - 8 * q^87 + 16 * q^89 + 7 * q^91 - 15 * q^93 - 2 * q^95 + 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$

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
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$		0			0
$5$	1.33641	+	2.31473i	0.597662	+	1.03518i	0.993165	+	0.116716i	$0.0372367\pi$
$5$	1.33641	+	2.31473i	0.597662	+	1.03518i	−0.395504	+	0.918464i	$0.629430\pi$
$6$		0			0
$7$	3.67282			1.38820			0.694098	−	0.719880i	$-0.255803\pi$
$7$	3.67282			1.38820			0.694098	+	0.719880i	$0.255803\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	3.81681			1.15081			0.575406	−	0.817868i	$-0.304844\pi$
$11$	3.81681			1.15081			0.575406	+	0.817868i	$0.304844\pi$
$12$		0			0
$13$	−0.0719933	+	0.124696i	−0.0199673	+	0.0345844i	−0.875836	−	0.482608i	$-0.839690\pi$
$13$	−0.0719933	+	0.124696i	−0.0199673	+	0.0345844i	0.855869	+	0.517193i	$0.173023\pi$
$14$		0			0
$15$	−1.33641	+	2.31473i	−0.345060	+	0.597662i
$16$		0			0
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$		0			0
$19$	−4.24482	+	0.990721i	−0.973828	+	0.227287i
$19$	−4.24482	+	0.990721i	−0.973828	+	0.227287i
$20$		0			0
$21$	1.83641	+	3.18076i	0.400738	+	0.694098i
$22$		0			0
$23$	3.76442	−	6.52016i	0.784936	−	1.35955i	−0.144102	−	0.989563i	$-0.546029\pi$
$23$	3.76442	−	6.52016i	0.784936	−	1.35955i	0.929038	−	0.369985i	$-0.120637\pi$
$24$		0			0
$25$	−1.07199	+	1.85675i	−0.214399	+	0.371349i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	2.67282	−	4.62947i	0.496331	−	0.859670i	−0.503660	−	0.863902i	$-0.668014\pi$
$29$	2.67282	−	4.62947i	0.496331	−	0.859670i	0.999991	+	0.00423154i	$0.00134695\pi$
$30$		0			0
$31$	−8.81681			−1.58355			−0.791773	−	0.610816i	$-0.790842\pi$
$31$	−8.81681			−1.58355			−0.791773	+	0.610816i	$0.790842\pi$
$32$		0			0
$33$	1.90841	+	3.30545i	0.332211	+	0.575406i
$34$		0			0
$35$	4.90841	+	8.50161i	0.829672	+	1.43703i
$36$		0			0
$37$	−1.00000			−0.164399			−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000			−0.164399			−0.0821995	+	0.996616i	$0.526194\pi$
$38$		0			0
$39$	−0.143987			−0.0230563
$40$		0			0
$41$	−2.67282	−	4.62947i	−0.417425	−	0.723001i	0.578255	−	0.815856i	$-0.303734\pi$
$41$	−2.67282	−	4.62947i	−0.417425	−	0.723001i	−0.995680	+	0.0928551i	$0.970401\pi$
$42$		0			0
$43$	1.40841	+	2.43943i	0.214780	+	0.372009i	0.953204	−	0.302327i	$-0.0977633\pi$
$43$	1.40841	+	2.43943i	0.214780	+	0.372009i	−0.738425	+	0.674336i	$0.764430\pi$
$44$		0			0
$45$	−2.67282			−0.398441
$46$		0			0
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	−0.997503	−	0.0706177i	$-0.977503\pi$
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	0.559908	+	0.828554i	$0.310836\pi$
$48$		0			0
$49$	6.48963			0.927091
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−4.00924	+	6.94420i	−0.550711	+	0.953859i	0.447513	+	0.894278i	$0.352310\pi$
$53$	−4.00924	+	6.94420i	−0.550711	+	0.953859i	−0.998223	+	0.0595815i	$0.981023\pi$
$54$		0			0
$55$	5.10083	+	8.83490i	0.687796	+	1.19130i
$56$		0			0
$57$	−2.98040	−	3.18076i	−0.394763	−	0.421302i
$58$		0			0
$59$	1.90841	+	3.30545i	0.248453	+	0.430334i	0.963097	−	0.269155i	$-0.0867445\pi$
$59$	1.90841	+	3.30545i	0.248453	+	0.430334i	−0.714644	+	0.699489i	$0.753411\pi$
$60$		0			0
$61$	−5.74482	+	9.95031i	−0.735548	+	1.27401i	0.218934	+	0.975740i	$0.429742\pi$
$61$	−5.74482	+	9.95031i	−0.735548	+	1.27401i	−0.954482	+	0.298268i	$0.903591\pi$
$62$		0			0
$63$	−1.83641	+	3.18076i	−0.231366	+	0.400738i
$64$		0			0
$65$	−0.384851			−0.0477348
$66$		0			0
$67$	2.69243	−	4.66342i	0.328932	−	0.569727i	−0.653368	−	0.757040i	$-0.726645\pi$
$67$	2.69243	−	4.66342i	0.328932	−	0.569727i	0.982300	+	0.187313i	$0.0599779\pi$
$68$		0			0
$69$	7.52884			0.906365
$70$		0			0
$71$	−6.81681	−	11.8071i	−0.809007	−	1.40124i	−0.913553	−	0.406720i	$-0.866672\pi$
$71$	−6.81681	−	11.8071i	−0.809007	−	1.40124i	0.104546	−	0.994520i	$-0.466661\pi$
$72$		0			0
$73$	0.172824	+	0.299339i	0.0202275	+	0.0350350i	0.875962	−	0.482380i	$-0.160228\pi$
$73$	0.172824	+	0.299339i	0.0202275	+	0.0350350i	−0.855734	+	0.517415i	$0.826894\pi$
$74$		0			0
$75$	−2.14399			−0.247566
$76$		0			0
$77$	14.0185			1.59755
$78$		0			0
$79$	3.26442	+	5.65414i	0.367276	+	0.636140i	0.989139	−	0.146986i	$-0.0469572\pi$
$79$	3.26442	+	5.65414i	0.367276	+	0.636140i	−0.621863	+	0.783126i	$0.713624\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	2.28797			0.251138			0.125569	−	0.992085i	$-0.459924\pi$
$83$	2.28797			0.251138			0.125569	+	0.992085i	$0.459924\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	5.34565			0.573114
$88$		0			0
$89$	4.33641	−	7.51089i	0.459659	−	0.796152i	−0.539284	−	0.842124i	$-0.681305\pi$
$89$	4.33641	−	7.51089i	0.459659	−	0.796152i	0.998943	+	0.0459717i	$0.0146384\pi$
$90$		0			0
$91$	−0.264419	+	0.457986i	−0.0277186	+	0.0480100i
$92$		0			0
$93$	−4.40841	−	7.63558i	−0.457130	−	0.791773i
$94$		0			0
$95$	−7.96608	−	8.50161i	−0.817303	−	0.872246i
$96$		0			0
$97$	2.95684	+	5.12140i	0.300222	+	0.520000i	0.976186	−	0.216935i	$-0.0696059\pi$
$97$	2.95684	+	5.12140i	0.300222	+	0.520000i	−0.675964	+	0.736935i	$0.736273\pi$
$98$		0			0
$99$	−1.90841	+	3.30545i	−0.191802	+	0.332211i
$100$		0			0
$101$	−4.14399	+	7.17760i	−0.412342	+	0.714197i	−0.995145	−	0.0984158i	$-0.968622\pi$
$101$	−4.14399	+	7.17760i	−0.412342	+	0.714197i	0.582803	+	0.812613i	$0.301956\pi$
$102$		0			0
$103$	−14.6521			−1.44371			−0.721857	−	0.692043i	$-0.756711\pi$
$103$	−14.6521			−1.44371			−0.721857	+	0.692043i	$0.756711\pi$
$104$		0			0
$105$	−4.90841	+	8.50161i	−0.479011	+	0.829672i
$106$		0			0
$107$	16.6913			1.61361			0.806804	−	0.590819i	$-0.201195\pi$
$107$	16.6913			1.61361			0.806804	+	0.590819i	$0.201195\pi$
$108$		0			0
$109$	−3.91764	−	6.78555i	−0.375242	−	0.649938i	0.615121	−	0.788432i	$-0.289107\pi$
$109$	−3.91764	−	6.78555i	−0.375242	−	0.649938i	−0.990363	+	0.138494i	$0.955774\pi$
$110$		0			0
$111$	−0.500000	−	0.866025i	−0.0474579	−	0.0821995i
$112$		0			0
$113$	−6.38485			−0.600636			−0.300318	−	0.953839i	$-0.597093\pi$
$113$	−6.38485			−0.600636			−0.300318	+	0.953839i	$0.597093\pi$
$114$		0			0
$115$	20.1233			1.87650
$116$		0			0
$117$	−0.0719933	−	0.124696i	−0.00665578	−	0.0115281i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	3.56804			0.324367
$122$		0			0
$123$	2.67282	−	4.62947i	0.241000	−	0.417425i
$124$		0			0
$125$	7.63362			0.682772
$126$		0			0
$127$	1.32718	−	2.29874i	0.117768	−	0.203980i	−0.801115	−	0.598511i	$-0.795759\pi$
$127$	1.32718	−	2.29874i	0.117768	−	0.203980i	0.918883	+	0.394531i	$0.129093\pi$
$128$		0			0
$129$	−1.40841	+	2.43943i	−0.124003	+	0.214780i
$130$		0			0
$131$	−5.67282	−	9.82562i	−0.495637	−	0.858468i	0.504350	−	0.863499i	$-0.331732\pi$
$131$	−5.67282	−	9.82562i	−0.495637	−	0.858468i	−0.999987	+	0.00503076i	$0.998399\pi$
$132$		0			0
$133$	−15.5905	+	3.63875i	−1.35186	+	0.315519i
$134$		0			0
$135$	−1.33641	−	2.31473i	−0.115020	−	0.199221i
$136$		0			0
$137$	0.816810	−	1.41476i	0.0697848	−	0.120871i	−0.829022	−	0.559216i	$-0.811102\pi$
$137$	0.816810	−	1.41476i	0.0697848	−	0.120871i	0.898806	+	0.438346i	$0.144435\pi$
$138$		0			0
$139$	3.75405	−	6.50221i	0.318415	−	0.551510i	−0.661743	−	0.749731i	$-0.730183\pi$
$139$	3.75405	−	6.50221i	0.318415	−	0.551510i	0.980157	+	0.198221i	$0.0635163\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$		0			0
$143$	−0.274785	+	0.475941i	−0.0229786	+	0.0398002i
$144$		0			0
$145$	14.2880			1.18655
$146$		0			0
$147$	3.24482	+	5.62019i	0.267628	+	0.463545i
$148$		0			0
$149$	−7.00924	−	12.1404i	−0.574219	−	0.994576i	−0.996126	−	0.0879373i	$-0.971972\pi$
$149$	−7.00924	−	12.1404i	−0.574219	−	0.994576i	0.421907	−	0.906639i	$-0.361361\pi$
$150$		0			0
$151$	−11.0577			−0.899861			−0.449930	−	0.893064i	$-0.648551\pi$
$151$	−11.0577			−0.899861			−0.449930	+	0.893064i	$0.648551\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−11.7829	−	20.4086i	−0.946424	−	1.63926i
$156$		0			0
$157$	−7.02884	−	12.1743i	−0.560962	−	0.971615i	−0.997413	−	0.0718869i	$-0.977098\pi$
$157$	−7.02884	−	12.1743i	−0.560962	−	0.971615i	0.436451	−	0.899728i	$-0.356235\pi$
$158$		0			0
$159$	−8.01847			−0.635906
$160$		0			0
$161$	13.8260	−	23.9474i	1.08965	−	1.88732i
$162$		0			0
$163$	−4.61515			−0.361486			−0.180743	−	0.983530i	$-0.557850\pi$
$163$	−4.61515			−0.361486			−0.180743	+	0.983530i	$0.557850\pi$
$164$		0			0
$165$	−5.10083	+	8.83490i	−0.397099	+	0.687796i
$166$		0			0
$167$	−6.11007	+	10.5829i	−0.472811	+	0.818933i	−0.999516	−	0.0311155i	$-0.990094\pi$
$167$	−6.11007	+	10.5829i	−0.472811	+	0.818933i	0.526705	+	0.850048i	$0.323427\pi$
$168$		0			0
$169$	6.48963	+	11.2404i	0.499203	+	0.864644i
$170$		0			0
$171$	1.26442	−	4.17148i	0.0966925	−	0.319001i
$172$		0			0
$173$	−7.52884	−	13.0403i	−0.572407	−	0.991438i	−0.996318	−	0.0857340i	$-0.972676\pi$
$173$	−7.52884	−	13.0403i	−0.572407	−	0.991438i	0.423911	−	0.905704i	$-0.360657\pi$
$174$		0			0
$175$	−3.93724	+	6.81950i	−0.297628	+	0.515506i
$176$		0			0
$177$	−1.90841	+	3.30545i	−0.143445	+	0.248453i
$178$		0			0
$179$	15.1625			1.13330			0.566648	−	0.823960i	$-0.308240\pi$
$179$	15.1625			1.13330			0.566648	+	0.823960i	$0.308240\pi$
$180$		0			0
$181$	−6.10083	+	10.5669i	−0.453471	+	0.785435i	−0.998599	−	0.0529179i	$-0.983148\pi$
$181$	−6.10083	+	10.5669i	−0.453471	+	0.785435i	0.545128	+	0.838353i	$0.316481\pi$
$182$		0			0
$183$	−11.4896			−0.849338
$184$		0			0
$185$	−1.33641	−	2.31473i	−0.0982550	−	0.170183i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−3.67282			−0.267159
$190$		0			0
$191$	−5.45043			−0.394379			−0.197190	−	0.980365i	$-0.563181\pi$
$191$	−5.45043			−0.394379			−0.197190	+	0.980365i	$0.563181\pi$
$192$		0			0
$193$	0.255183	+	0.441990i	0.0183685	+	0.0318151i	0.875064	−	0.484008i	$-0.160819\pi$
$193$	0.255183	+	0.441990i	0.0183685	+	0.0318151i	−0.856695	+	0.515823i	$0.827486\pi$
$194$		0			0
$195$	−0.192425	−	0.333290i	−0.0137799	−	0.0238674i
$196$		0			0
$197$	22.9608			1.63589			0.817945	−	0.575297i	$-0.195114\pi$
$197$	22.9608			1.63589			0.817945	+	0.575297i	$0.195114\pi$
$198$		0			0
$199$	−0.0627577	+	0.108700i	−0.00444878	+	0.00770551i	−0.868241	−	0.496142i	$-0.834749\pi$
$199$	−0.0627577	+	0.108700i	−0.00444878	+	0.00770551i	0.863792	+	0.503848i	$0.168083\pi$
$200$		0			0
$201$	5.38485			0.379818
$202$		0			0
$203$	9.81681	−	17.0032i	0.689005	−	1.19339i
$204$		0			0
$205$	7.14399	−	12.3737i	0.498958	−	0.864220i
$206$		0			0
$207$	3.76442	+	6.52016i	0.261645	+	0.453183i
$208$		0			0
$209$	−16.2017	+	3.78140i	−1.12069	+	0.261565i
$210$		0			0
$211$	12.4269	+	21.5240i	0.855501	+	1.48177i	0.876179	+	0.481986i	$0.160084\pi$
$211$	12.4269	+	21.5240i	0.855501	+	1.48177i	−0.0206776	+	0.999786i	$0.506582\pi$
$212$		0			0
$213$	6.81681	−	11.8071i	0.467080	−	0.809007i
$214$		0			0
$215$	−3.76442	+	6.52016i	−0.256731	+	0.444672i
$216$		0			0
$217$	−32.3826			−2.19827
$218$		0			0
$219$	−0.172824	+	0.299339i	−0.0116783	+	0.0202275i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−11.8980	−	20.6080i	−0.796752	−	1.38001i	−0.921721	−	0.387854i	$-0.873217\pi$
$223$	−11.8980	−	20.6080i	−0.796752	−	1.38001i	0.124969	−	0.992161i	$-0.460117\pi$
$224$		0			0
$225$	−1.07199	−	1.85675i	−0.0714662	−	0.123783i
$226$		0			0
$227$	−9.81681			−0.651565			−0.325782	−	0.945445i	$-0.605628\pi$
$227$	−9.81681			−0.651565			−0.325782	+	0.945445i	$0.605628\pi$
$228$		0			0
$229$	0.143987			0.00951490			0.00475745	−	0.999989i	$-0.498486\pi$
$229$	0.143987			0.00951490			0.00475745	+	0.999989i	$0.498486\pi$
$230$		0			0
$231$	7.00924	+	12.1404i	0.461174	+	0.798777i
$232$		0			0
$233$	−5.28797	−	9.15904i	−0.346427	−	0.600029i	0.639185	−	0.769053i	$-0.279272\pi$
$233$	−5.28797	−	9.15904i	−0.346427	−	0.600029i	−0.985612	+	0.169024i	$0.945938\pi$
$234$		0			0
$235$	−16.0369			−1.04613
$236$		0			0
$237$	−3.26442	+	5.65414i	−0.212047	+	0.367276i
$238$		0			0
$239$	9.81681			0.634997			0.317498	−	0.948259i	$-0.397157\pi$
$239$	9.81681			0.634997			0.317498	+	0.948259i	$0.397157\pi$
$240$		0			0
$241$	−0.971163	+	1.68210i	−0.0625581	+	0.108354i	−0.895608	−	0.444844i	$-0.853259\pi$
$241$	−0.971163	+	1.68210i	−0.0625581	+	0.108354i	0.833050	+	0.553198i	$0.186593\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$	8.67282	+	15.0218i	0.554086	+	0.959706i
$246$		0			0
$247$	0.182059	−	0.600637i	0.0115842	−	0.0382176i
$248$		0			0
$249$	1.14399	+	1.98144i	0.0724972	+	0.125569i
$250$		0			0
$251$	6.81681	−	11.8071i	0.430273	−	0.745255i	−0.566623	−	0.823977i	$-0.691751\pi$
$251$	6.81681	−	11.8071i	0.430273	−	0.745255i	0.996897	+	0.0787218i	$0.0250839\pi$
$252$		0			0
$253$	14.3681	−	24.8862i	0.903313	−	1.56458i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.29721	−	10.9071i	0.392809	−	0.680365i	−0.600010	−	0.799993i	$-0.704837\pi$
$257$	6.29721	−	10.9071i	0.392809	−	0.680365i	0.992819	+	0.119627i	$0.0381700\pi$
$258$		0			0
$259$	−3.67282			−0.228218
$260$		0			0
$261$	2.67282	+	4.62947i	0.165444	+	0.286557i
$262$		0			0
$263$	−0.816810	−	1.41476i	−0.0503667	−	0.0872376i	0.839743	−	0.542984i	$-0.182706\pi$
$263$	−0.816810	−	1.41476i	−0.0503667	−	0.0872376i	−0.890110	+	0.455747i	$0.849372\pi$
$264$		0			0
$265$	−21.4320			−1.31655
$266$		0			0
$267$	8.67282			0.530768
$268$		0			0
$269$	10.8260	+	18.7513i	0.660076	+	1.14328i	0.980595	+	0.196043i	$0.0628091\pi$
$269$	10.8260	+	18.7513i	0.660076	+	1.14328i	−0.320520	+	0.947242i	$0.603858\pi$
$270$		0			0
$271$	−10.7776	−	18.6674i	−0.654693	−	1.13396i	−0.981971	−	0.189033i	$-0.939465\pi$
$271$	−10.7776	−	18.6674i	−0.654693	−	1.13396i	0.327278	−	0.944928i	$-0.393869\pi$
$272$		0			0
$273$	−0.528837			−0.0320067
$274$		0			0
$275$	−4.09159	+	7.08685i	−0.246732	+	0.427353i
$276$		0			0
$277$	7.62571			0.458185			0.229092	−	0.973405i	$-0.426424\pi$
$277$	7.62571			0.458185			0.229092	+	0.973405i	$0.426424\pi$
$278$		0			0
$279$	4.40841	−	7.63558i	0.263924	−	0.457130i
$280$		0			0
$281$	0.846778	−	1.46666i	0.0505145	−	0.0874937i	−0.839663	−	0.543109i	$-0.817247\pi$
$281$	0.846778	−	1.46666i	0.0505145	−	0.0874937i	0.890177	+	0.455615i	$0.150581\pi$
$282$		0			0
$283$	5.14399	+	8.90965i	0.305778	+	0.529623i	0.977434	−	0.211240i	$-0.0677500\pi$
$283$	5.14399	+	8.90965i	0.305778	+	0.529623i	−0.671656	+	0.740863i	$0.734417\pi$
$284$		0			0
$285$	3.37957	−	11.1496i	0.200188	−	0.660447i
$286$		0			0
$287$	−9.81681	−	17.0032i	−0.579468	−	1.00367i
$288$		0			0
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$		0			0
$291$	−2.95684	+	5.12140i	−0.173333	+	0.300222i
$292$		0			0
$293$	12.1153			0.707786			0.353893	−	0.935286i	$-0.384858\pi$
$293$	12.1153			0.707786			0.353893	+	0.935286i	$0.384858\pi$
$294$		0			0
$295$	−5.10083	+	8.83490i	−0.296982	+	0.514388i
$296$		0			0
$297$	−3.81681			−0.221474
$298$		0			0
$299$	0.542026	+	0.938816i	0.0313461	+	0.0542931i
$300$		0			0
$301$	5.17282	+	8.95959i	0.298157	+	0.516422i
$302$		0			0
$303$	−8.28797			−0.476132
$304$		0			0
$305$	−30.7098			−1.75844
$306$		0			0
$307$	−2.24482	−	3.88814i	−0.128118	−	0.221908i	0.794829	−	0.606833i	$-0.207560\pi$
$307$	−2.24482	−	3.88814i	−0.128118	−	0.221908i	−0.922948	+	0.384926i	$0.874227\pi$
$308$		0			0
$309$	−7.32605	−	12.6891i	−0.416764	−	0.721857i
$310$		0			0
$311$	−0.759136			−0.0430466			−0.0215233	−	0.999768i	$-0.506852\pi$
$311$	−0.759136			−0.0430466			−0.0215233	+	0.999768i	$0.506852\pi$
$312$		0			0
$313$	−5.71598	+	9.90037i	−0.323086	+	0.559602i	−0.981123	−	0.193384i	$-0.938054\pi$
$313$	−5.71598	+	9.90037i	−0.323086	+	0.559602i	0.658037	+	0.752986i	$0.271387\pi$
$314$		0			0
$315$	−9.81681			−0.553115
$316$		0			0
$317$	5.80757	−	10.0590i	0.326186	−	0.564971i	−0.655566	−	0.755138i	$-0.727570\pi$
$317$	5.80757	−	10.0590i	0.326186	−	0.564971i	0.981752	+	0.190168i	$0.0609031\pi$
$318$		0			0
$319$	10.2017	−	17.6698i	0.571183	−	0.989319i
$320$		0			0
$321$	8.34565	+	14.4551i	0.465809	+	0.806804i
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−0.154353	−	0.267347i	−0.00856194	−	0.0148297i
$326$		0			0
$327$	3.91764	−	6.78555i	0.216646	−	0.375242i
$328$		0			0
$329$	−11.0185	+	19.0846i	−0.607468	+	1.05217i
$330$		0			0
$331$	11.4712			0.630512			0.315256	−	0.949007i	$-0.397910\pi$
$331$	11.4712			0.630512			0.315256	+	0.949007i	$0.397910\pi$
$332$		0			0
$333$	0.500000	−	0.866025i	0.0273998	−	0.0474579i
$334$		0			0
$335$	14.3928			0.786360
$336$		0			0
$337$	−3.78402	−	6.55412i	−0.206129	−	0.357025i	0.744363	−	0.667775i	$-0.232753\pi$
$337$	−3.78402	−	6.55412i	−0.206129	−	0.357025i	−0.950492	+	0.310750i	$0.899420\pi$
$338$		0			0
$339$	−3.19243	−	5.52944i	−0.173389	−	0.300318i
$340$		0			0
$341$	−33.6521			−1.82236
$342$		0			0
$343$	−1.87448			−0.101213
$344$		0			0
$345$	10.0616	+	17.4272i	0.541700	+	0.938252i
$346$		0			0
$347$	10.9084	+	18.8939i	0.585594	+	1.01428i	0.994801	+	0.101837i	$0.0324720\pi$
$347$	10.9084	+	18.8939i	0.585594	+	1.01428i	−0.409207	+	0.912441i	$0.634195\pi$
$348$		0			0
$349$	−4.54731			−0.243412			−0.121706	−	0.992566i	$-0.538836\pi$
$349$	−4.54731			−0.243412			−0.121706	+	0.992566i	$0.538836\pi$
$350$		0			0
$351$	0.0719933	−	0.124696i	0.00384272	−	0.00665578i
$352$		0			0
$353$	−8.99774			−0.478901			−0.239451	−	0.970909i	$-0.576967\pi$
$353$	−8.99774			−0.478901			−0.239451	+	0.970909i	$0.576967\pi$
$354$		0			0
$355$	18.2201	−	31.5582i	0.967024	−	1.67494i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	6.48963	+	11.2404i	0.342510	+	0.593244i	0.984898	−	0.173135i	$-0.0553897\pi$
$359$	6.48963	+	11.2404i	0.342510	+	0.593244i	−0.642388	+	0.766379i	$0.722056\pi$
$360$		0			0
$361$	17.0369	−	8.41086i	0.896681	−	0.442677i
$362$		0			0
$363$	1.78402	+	3.09001i	0.0936368	+	0.162184i
$364$		0			0
$365$	−0.461927	+	0.800082i	−0.0241784	+	0.0418782i
$366$		0			0
$367$	−2.02355	+	3.50490i	−0.105629	+	0.182954i	−0.913995	−	0.405726i	$-0.867019\pi$
$367$	−2.02355	+	3.50490i	−0.105629	+	0.182954i	0.808366	+	0.588680i	$0.200352\pi$
$368$		0			0
$369$	5.34565			0.278283
$370$		0			0
$371$	−14.7252	+	25.5048i	−0.764495	+	1.32414i
$372$		0			0
$373$	3.79834			0.196671			0.0983353	−	0.995153i	$-0.468648\pi$
$373$	3.79834			0.196671			0.0983353	+	0.995153i	$0.468648\pi$
$374$		0			0
$375$	3.81681	+	6.61091i	0.197099	+	0.341386i
$376$		0			0
$377$	0.384851	+	0.666581i	0.0198208	+	0.0343307i
$378$		0			0
$379$	−4.89522			−0.251450			−0.125725	−	0.992065i	$-0.540126\pi$
$379$	−4.89522			−0.251450			−0.125725	+	0.992065i	$0.540126\pi$
$380$		0			0
$381$	2.65435			0.135987
$382$		0			0
$383$	17.0709	+	29.5676i	0.872280	+	1.51083i	0.859632	+	0.510914i	$0.170693\pi$
$383$	17.0709	+	29.5676i	0.872280	+	1.51083i	0.0126484	+	0.999920i	$0.495974\pi$
$384$		0			0
$385$	18.7345	+	32.4490i	0.954796	+	1.65376i
$386$		0			0
$387$	−2.81681			−0.143187
$388$		0			0
$389$	−13.4412	+	23.2808i	−0.681496	+	1.18039i	0.293029	+	0.956104i	$0.405337\pi$
$389$	−13.4412	+	23.2808i	−0.681496	+	1.18039i	−0.974524	+	0.224281i	$0.927997\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	5.67282	−	9.82562i	0.286156	−	0.495637i
$394$		0			0
$395$	−8.72522	+	15.1125i	−0.439013	+	0.760393i
$396$		0			0
$397$	−12.6193	−	21.8573i	−0.633345	−	1.09699i	−0.986863	−	0.161558i	$-0.948348\pi$
$397$	−12.6193	−	21.8573i	−0.633345	−	1.09699i	0.353519	−	0.935427i	$-0.384985\pi$
$398$		0			0
$399$	−10.9465	−	11.6824i	−0.548009	−	0.584850i
$400$		0			0
$401$	1.66359	+	2.88142i	0.0830756	+	0.143891i	0.904570	−	0.426326i	$-0.140192\pi$
$401$	1.66359	+	2.88142i	0.0830756	+	0.143891i	−0.821494	+	0.570217i	$0.806859\pi$
$402$		0			0
$403$	0.634751	−	1.09942i	0.0316192	−	0.0547661i
$404$		0			0
$405$	1.33641	−	2.31473i	0.0664068	−	0.115020i
$406$		0			0
$407$	−3.81681			−0.189192
$408$		0			0
$409$	−17.0616	+	29.5516i	−0.843643	+	1.46123i	0.0431512	+	0.999069i	$0.486260\pi$
$409$	−17.0616	+	29.5516i	−0.843643	+	1.46123i	−0.886794	+	0.462164i	$0.847073\pi$
$410$		0			0
$411$	1.63362			0.0805806
$412$		0			0
$413$	7.00924	+	12.1404i	0.344902	+	0.597388i
$414$		0			0
$415$	3.05767	+	5.29605i	0.150095	+	0.259973i
$416$		0			0
$417$	7.50811			0.367673
$418$		0			0
$419$	9.16246			0.447615			0.223808	−	0.974633i	$-0.428151\pi$
$419$	9.16246			0.447615			0.223808	+	0.974633i	$0.428151\pi$
$420$		0			0
$421$	7.91764	+	13.7138i	0.385882	+	0.668368i	0.991891	−	0.127090i	$-0.0405638\pi$
$421$	7.91764	+	13.7138i	0.385882	+	0.668368i	−0.606009	+	0.795458i	$0.707230\pi$
$422$		0			0
$423$	−3.00000	−	5.19615i	−0.145865	−	0.252646i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−21.0997	+	36.5458i	−1.02109	+	1.76857i
$428$		0			0
$429$	−0.549569			−0.0265335
$430$		0			0
$431$	−4.63362	+	8.02567i	−0.223194	+	0.386583i	−0.955776	−	0.294096i	$-0.904982\pi$
$431$	−4.63362	+	8.02567i	−0.223194	+	0.386583i	0.732582	+	0.680678i	$0.238315\pi$
$432$		0			0
$433$	9.90727	−	17.1599i	0.476113	−	0.824652i	−0.523512	−	0.852018i	$-0.675379\pi$
$433$	9.90727	−	17.1599i	0.476113	−	0.824652i	0.999625	+	0.0273658i	$0.00871190\pi$
$434$		0			0
$435$	7.14399	+	12.3737i	0.342528	+	0.593276i
$436$		0			0
$437$	−9.51960	+	31.4064i	−0.455384	+	1.50237i
$438$		0			0
$439$	3.45156	+	5.97828i	0.164734	+	0.285328i	0.936561	−	0.350505i	$-0.113990\pi$
$439$	3.45156	+	5.97828i	0.164734	+	0.285328i	−0.771827	+	0.635833i	$0.780657\pi$
$440$		0			0
$441$	−3.24482	+	5.62019i	−0.154515	+	0.267628i
$442$		0			0
$443$	−9.81681	+	17.0032i	−0.466411	+	0.807847i	−0.999264	−	0.0383606i	$-0.987786\pi$
$443$	−9.81681	+	17.0032i	−0.466411	+	0.807847i	0.532853	+	0.846208i	$0.321120\pi$
$444$		0			0
$445$	23.1809			1.09888
$446$		0			0
$447$	7.00924	−	12.1404i	0.331525	−	0.574219i
$448$		0			0
$449$	29.0162			1.36936			0.684680	−	0.728844i	$-0.259942\pi$
$449$	29.0162			1.36936			0.684680	+	0.728844i	$0.259942\pi$
$450$		0			0
$451$	−10.2017	−	17.6698i	−0.480377	−	0.832038i
$452$		0			0
$453$	−5.52884	−	9.57623i	−0.259767	−	0.449930i
$454$		0			0
$455$	−1.41349			−0.0662654
$456$		0			0
$457$	32.5473			1.52250			0.761249	−	0.648459i	$-0.224586\pi$
$457$	32.5473			1.52250			0.761249	+	0.648459i	$0.224586\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	4.82605	+	8.35896i	0.224771	+	0.389315i	0.956251	−	0.292548i	$-0.0945031\pi$
$461$	4.82605	+	8.35896i	0.224771	+	0.389315i	−0.731479	+	0.681863i	$0.761170\pi$
$462$		0			0
$463$	31.0554			1.44327			0.721634	−	0.692275i	$-0.243392\pi$
$463$	31.0554			1.44327			0.721634	+	0.692275i	$0.243392\pi$
$464$		0			0
$465$	11.7829	−	20.4086i	0.546418	−	0.946424i
$466$		0			0
$467$	−8.61289			−0.398557			−0.199278	−	0.979943i	$-0.563860\pi$
$467$	−8.61289			−0.398557			−0.199278	+	0.979943i	$0.563860\pi$
$468$		0			0
$469$	9.88880	−	17.1279i	0.456623	−	0.790893i
$470$		0			0
$471$	7.02884	−	12.1743i	0.323872	−	0.560962i
$472$		0			0
$473$	5.37562	+	9.31084i	0.247171	+	0.428113i
$474$		0			0
$475$	2.71090	−	8.94360i	0.124384	−	0.410360i
$476$		0			0
$477$	−4.00924	−	6.94420i	−0.183570	−	0.317953i
$478$		0			0
$479$	8.73050	−	15.1217i	0.398907	−	0.690927i	−0.594685	−	0.803959i	$-0.702723\pi$
$479$	8.73050	−	15.1217i	0.398907	−	0.690927i	0.993591	+	0.113032i	$0.0360564\pi$
$480$		0			0
$481$	0.0719933	−	0.124696i	0.00328261	−	0.00568565i
$482$		0			0
$483$	27.6521			1.25821
$484$		0			0
$485$	−7.90312	+	13.6886i	−0.358862	+	0.621568i
$486$		0			0
$487$	11.6336			0.527170			0.263585	−	0.964636i	$-0.415095\pi$
$487$	11.6336			0.527170			0.263585	+	0.964636i	$0.415095\pi$
$488$		0			0
$489$	−2.30757	−	3.99684i	−0.104352	−	0.180743i
$490$		0			0
$491$	−12.1625	−	21.0660i	−0.548884	−	0.950695i	−0.998351	−	0.0573983i	$-0.981720\pi$
$491$	−12.1625	−	21.0660i	−0.548884	−	0.950695i	0.449467	−	0.893297i	$-0.351614\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−10.2017			−0.458531
$496$		0			0
$497$	−25.0369	−	43.3653i	−1.12306	−	1.94520i
$498$		0			0
$499$	19.0565	+	33.0069i	0.853088	+	1.47759i	0.878407	+	0.477912i	$0.158606\pi$
$499$	19.0565	+	33.0069i	0.853088	+	1.47759i	−0.0253194	+	0.999679i	$0.508060\pi$
$500$		0			0
$501$	−12.2201			−0.545955
$502$		0			0
$503$	2.18319	−	3.78140i	0.0973436	−	0.168604i	−0.813241	−	0.581927i	$-0.802299\pi$
$503$	2.18319	−	3.78140i	0.0973436	−	0.168604i	0.910584	+	0.413323i	$0.135632\pi$
$504$		0			0
$505$	−22.1523			−0.985764
$506$		0			0
$507$	−6.48963	+	11.2404i	−0.288215	+	0.499203i
$508$		0			0
$509$	7.85601	−	13.6070i	0.348212	−	0.603120i	−0.637720	−	0.770268i	$-0.720122\pi$
$509$	7.85601	−	13.6070i	0.348212	−	0.603120i	0.985932	+	0.167148i	$0.0534557\pi$
$510$		0			0
$511$	0.634751	+	1.09942i	0.0280797	+	0.0486355i
$512$		0			0
$513$	4.24482	−	0.990721i	0.187413	−	0.0437414i
$514$		0			0
$515$	−19.5812	−	33.9157i	−0.862852	−	1.49450i
$516$		0			0
$517$	−11.4504	+	19.8327i	−0.503589	+	0.872242i
$518$		0			0
$519$	7.52884	−	13.0403i	0.330479	−	0.572407i
$520$		0			0
$521$	33.4425			1.46514			0.732572	−	0.680690i	$-0.238320\pi$
$521$	33.4425			1.46514			0.732572	+	0.680690i	$0.238320\pi$
$522$		0			0
$523$	−14.7109	+	25.4800i	−0.643263	+	1.11416i	0.341437	+	0.939905i	$0.389086\pi$
$523$	−14.7109	+	25.4800i	−0.643263	+	1.11416i	−0.984700	+	0.174259i	$0.944247\pi$
$524$		0			0
$525$	−7.87448			−0.343671
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−16.8417	−	29.1707i	−0.732248	−	1.26829i
$530$		0			0
$531$	−3.81681			−0.165635
$532$		0			0
$533$	0.769701			0.0333395
$534$		0			0
$535$	22.3064	+	38.6359i	0.964392	+	1.67038i
$536$		0			0
$537$	7.58123	+	13.1311i	0.327154	+	0.566648i
$538$		0			0
$539$	24.7697			1.06691
$540$		0			0
$541$	−13.0865	+	22.6665i	−0.562633	+	0.974509i	0.434632	+	0.900608i	$0.356878\pi$
$541$	−13.0865	+	22.6665i	−0.562633	+	0.974509i	−0.997266	+	0.0739012i	$0.976455\pi$
$542$		0			0
$543$	−12.2017			−0.523623
$544$		0			0
$545$	10.4712	−	18.1366i	0.448535	−	0.776886i
$546$		0			0
$547$	10.9557	−	18.9759i	0.468432	−	0.811349i	−0.530917	−	0.847424i	$-0.678152\pi$
$547$	10.9557	−	18.9759i	0.468432	−	0.811349i	0.999349	+	0.0360752i	$0.0114856\pi$
$548$		0			0
$549$	−5.74482	−	9.95031i	−0.245183	−	0.424669i
$550$		0			0
$551$	−6.75914	+	22.2993i	−0.287949	+	0.949980i
$552$		0			0
$553$	11.9896	+	20.7667i	0.509851	+	0.883088i
$554$		0			0
$555$	1.33641	−	2.31473i	0.0567275	−	0.0982550i
$556$		0			0
$557$	−17.0185	+	29.4769i	−0.721096	+	1.24897i	0.239465	+	0.970905i	$0.423028\pi$
$557$	−17.0185	+	29.4769i	−0.721096	+	1.24897i	−0.960561	+	0.278070i	$0.910305\pi$
$558$		0			0
$559$	−0.405583			−0.0171543
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−11.5552			−0.486994			−0.243497	−	0.969902i	$-0.578295\pi$
$563$	−11.5552			−0.486994			−0.243497	+	0.969902i	$0.578295\pi$
$564$		0			0
$565$	−8.53279	−	14.7792i	−0.358977	−	0.621767i
$566$		0			0
$567$	−1.83641	−	3.18076i	−0.0771220	−	0.133579i
$568$		0			0
$569$	39.7075			1.66463			0.832313	−	0.554307i	$-0.187016\pi$
$569$	39.7075			1.66463			0.832313	+	0.554307i	$0.187016\pi$
$570$		0			0
$571$	−14.6521			−0.613171			−0.306585	−	0.951843i	$-0.599187\pi$
$571$	−14.6521			−0.613171			−0.306585	+	0.951843i	$0.599187\pi$
$572$		0			0
$573$	−2.72522	−	4.72021i	−0.113848	−	0.197190i
$574$		0			0
$575$	8.07086	+	13.9791i	0.336578	+	0.582971i
$576$		0			0
$577$	20.8145			0.866521			0.433261	−	0.901269i	$-0.357363\pi$
$577$	20.8145			0.866521			0.433261	+	0.901269i	$0.357363\pi$
$578$		0			0
$579$	−0.255183	+	0.441990i	−0.0106050	+	0.0183685i
$580$		0			0
$581$	8.40332			0.348629
$582$		0			0
$583$	−15.3025	+	26.5047i	−0.633764	+	1.09771i
$584$		0			0
$585$	0.192425	−	0.333290i	0.00795581	−	0.0137799i
$586$		0			0
$587$	9.82209	+	17.0124i	0.405401	+	0.702175i	0.994368	−	0.105982i	$-0.0337985\pi$
$587$	9.82209	+	17.0124i	0.405401	+	0.702175i	−0.588967	+	0.808157i	$0.700465\pi$
$588$		0			0
$589$	37.4257	−	8.73500i	1.54210	−	0.359920i
$590$		0			0
$591$	11.4804	+	19.8846i	0.472240	+	0.817945i
$592$		0			0
$593$	−10.8260	+	18.7513i	−0.444572	+	0.770022i	−0.998022	−	0.0628605i	$-0.979978\pi$
$593$	−10.8260	+	18.7513i	−0.444572	+	0.770022i	0.553450	+	0.832882i	$0.313311\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.125515			−0.00513700
$598$		0			0
$599$	−5.88993	+	10.2017i	−0.240656	+	0.416829i	−0.960901	−	0.276891i	$-0.910696\pi$
$599$	−5.88993	+	10.2017i	−0.240656	+	0.416829i	0.720245	+	0.693720i	$0.244029\pi$
$600$		0			0
$601$	−11.4112			−0.465474			−0.232737	−	0.972540i	$-0.574768\pi$
$601$	−11.4112			−0.465474			−0.232737	+	0.972540i	$0.574768\pi$
$602$		0			0
$603$	2.69243	+	4.66342i	0.109644	+	0.189909i
$604$		0			0
$605$	4.76837	+	8.25906i	0.193862	+	0.335779i
$606$		0			0
$607$	1.10478			0.0448418			0.0224209	−	0.999749i	$-0.492863\pi$
$607$	1.10478			0.0448418			0.0224209	+	0.999749i	$0.492863\pi$
$608$		0			0
$609$	19.6336			0.795594
$610$		0			0
$611$	−0.431960	−	0.748176i	−0.0174752	−	0.0302680i
$612$		0			0
$613$	−2.38880	−	4.13753i	−0.0964829	−	0.167113i	0.813744	−	0.581224i	$-0.197426\pi$
$613$	−2.38880	−	4.13753i	−0.0964829	−	0.167113i	−0.910227	+	0.414111i	$0.864093\pi$
$614$		0			0
$615$	14.2880			0.576147
$616$		0			0
$617$	−18.7397	+	32.4582i	−0.754433	+	1.30672i	0.191222	+	0.981547i	$0.438755\pi$
$617$	−18.7397	+	32.4582i	−0.754433	+	1.30672i	−0.945656	+	0.325170i	$0.894578\pi$
$618$		0			0
$619$	0.615149			0.0247249			0.0123625	−	0.999924i	$-0.496065\pi$
$619$	0.615149			0.0247249			0.0123625	+	0.999924i	$0.496065\pi$
$620$		0			0
$621$	−3.76442	+	6.52016i	−0.151061	+	0.261645i
$622$		0			0
$623$	15.9269	−	27.5862i	0.638097	−	1.10522i
$624$		0			0
$625$	15.5616	+	26.9535i	0.622465	+	1.07814i
$626$		0			0
$627$	−11.3756	−	12.1404i	−0.454298	−	0.484839i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	10.6532	−	18.4519i	0.424098	−	0.734559i	−0.572238	−	0.820088i	$-0.693925\pi$
$631$	10.6532	−	18.4519i	0.424098	−	0.734559i	0.996336	+	0.0855284i	$0.0272578\pi$
$632$		0			0
$633$	−12.4269	+	21.5240i	−0.493924	+	0.855501i
$634$		0			0
$635$	7.09462			0.281541
$636$		0			0
$637$	−0.467210	+	0.809231i	−0.0185115	+	0.0320629i
$638$		0			0
$639$	13.6336			0.539338
$640$		0			0
$641$	−19.9608	−	34.5731i	−0.788404	−	1.36556i	−0.926944	−	0.375199i	$-0.877574\pi$
$641$	−19.9608	−	34.5731i	−0.788404	−	1.36556i	0.138540	−	0.990357i	$-0.455759\pi$
$642$		0			0
$643$	−18.6924	−	32.3762i	−0.737157	−	1.27679i	−0.953770	−	0.300536i	$-0.902834\pi$
$643$	−18.6924	−	32.3762i	−0.737157	−	1.27679i	0.216613	−	0.976258i	$-0.430499\pi$
$644$		0			0
$645$	−7.52884			−0.296448
$646$		0			0
$647$	−16.0369			−0.630477			−0.315239	−	0.949012i	$-0.602085\pi$
$647$	−16.0369			−0.630477			−0.315239	+	0.949012i	$0.602085\pi$
$648$		0			0
$649$	7.28402	+	12.6163i	0.285923	+	0.495233i
$650$		0			0
$651$	−16.1913	−	28.0441i	−0.634587	−	1.09914i
$652$		0			0
$653$	13.4241			0.525324			0.262662	−	0.964888i	$-0.415400\pi$
$653$	13.4241			0.525324			0.262662	+	0.964888i	$0.415400\pi$
$654$		0			0
$655$	15.1625	−	26.2621i	0.592446	−	1.02615i
$656$		0			0
$657$	−0.345647			−0.0134850
$658$		0			0
$659$	−9.27252	+	16.0605i	−0.361206	+	0.625628i	−0.988160	−	0.153429i	$-0.950968\pi$
$659$	−9.27252	+	16.0605i	−0.361206	+	0.625628i	0.626953	+	0.779057i	$0.284302\pi$
$660$		0			0
$661$	−3.28797	+	5.69494i	−0.127887	+	0.221507i	−0.922858	−	0.385141i	$-0.874153\pi$
$661$	−3.28797	+	5.69494i	−0.127887	+	0.221507i	0.794971	+	0.606648i	$0.207486\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−29.2580	−	31.2249i	−1.13458	−	1.21085i
$666$		0			0
$667$	−20.1233	−	34.8545i	−0.779176	−	1.34957i
$668$		0			0
$669$	11.8980	−	20.6080i	0.460005	−	0.796752i
$670$		0			0
$671$	−21.9269	+	37.9785i	−0.846478	+	1.46614i
$672$		0			0
$673$	−39.2386			−1.51254			−0.756268	−	0.654261i	$-0.772980\pi$
$673$	−39.2386			−1.51254			−0.756268	+	0.654261i	$0.772980\pi$
$674$		0			0
$675$	1.07199	−	1.85675i	0.0412610	−	0.0714662i
$676$		0			0
$677$	−25.8432			−0.993234			−0.496617	−	0.867970i	$-0.665425\pi$
$677$	−25.8432			−0.993234			−0.496617	+	0.867970i	$0.665425\pi$
$678$		0			0
$679$	10.8600	+	18.8100i	0.416767	+	0.721862i
$680$		0			0
$681$	−4.90841	−	8.50161i	−0.188090	−	0.325782i
$682$		0			0
$683$	−42.9898			−1.64496			−0.822480	−	0.568794i	$-0.807410\pi$
$683$	−42.9898			−1.64496			−0.822480	+	0.568794i	$0.807410\pi$
$684$		0			0
$685$	4.36638			0.166831
$686$		0			0
$687$	0.0719933	+	0.124696i	0.00274671	+	0.00475745i
$688$		0			0
$689$	−0.577276	−	0.999871i	−0.0219925	−	0.0380921i
$690$		0			0
$691$	48.4033			1.84135			0.920675	−	0.390331i	$-0.127639\pi$
$691$	48.4033			1.84135			0.920675	+	0.390331i	$0.127639\pi$
$692$		0			0
$693$	−7.00924	+	12.1404i	−0.266259	+	0.461174i
$694$		0			0
$695$	20.0678			0.761217
$696$		0			0
$697$		0			0
$698$		0			0
$699$	5.28797	−	9.15904i	0.200010	−	0.346427i
$700$		0			0
$701$	1.60591	+	2.78152i	0.0606545	+	0.105057i	0.894758	−	0.446551i	$-0.147348\pi$
$701$	1.60591	+	2.78152i	0.0606545	+	0.105057i	−0.834104	+	0.551608i	$0.814015\pi$
$702$		0			0
$703$	4.24482	−	0.990721i	0.160096	−	0.0373658i
$704$		0			0
$705$	−8.01847	−	13.8884i	−0.301993	−	0.523067i
$706$		0			0
$707$	−15.2201	+	26.3620i	−0.572412	+	0.991447i
$708$		0			0
$709$	−11.0328	+	19.1094i	−0.414345	+	0.717667i	−0.995359	−	0.0962265i	$-0.969323\pi$
$709$	−11.0328	+	19.1094i	−0.414345	+	0.717667i	0.581014	+	0.813893i	$0.302656\pi$
$710$		0			0
$711$	−6.52884			−0.244851
$712$		0			0
$713$	−33.1902	+	57.4871i	−1.24298	+	2.15291i
$714$		0			0
$715$	−1.46890			−0.0549338
$716$		0			0
$717$	4.90841	+	8.50161i	0.183308	+	0.317498i
$718$		0			0
$719$	8.83000	+	15.2940i	0.329303	+	0.570370i	0.982374	−	0.186927i	$-0.0598528\pi$
$719$	8.83000	+	15.2940i	0.329303	+	0.570370i	−0.653070	+	0.757297i	$0.726519\pi$
$720$		0			0
$721$	−53.8145			−2.00416
$722$		0			0
$723$	−1.94233			−0.0722359
$724$		0			0
$725$	5.73050	+	9.92551i	0.212825	+	0.368624i
$726$		0			0
$727$	−20.1966	−	34.9815i	−0.749050	−	1.29739i	−0.948279	−	0.317439i	$-0.897177\pi$
$727$	−20.1966	−	34.9815i	−0.749050	−	1.29739i	0.199229	−	0.979953i	$-0.436156\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−17.9137			−0.661657			−0.330829	−	0.943691i	$-0.607328\pi$
$733$	−17.9137			−0.661657			−0.330829	+	0.943691i	$0.607328\pi$
$734$		0			0
$735$	−8.67282	+	15.0218i	−0.319902	+	0.554086i
$736$		0			0
$737$	10.2765	−	17.7994i	0.378539	−	0.655649i
$738$		0			0
$739$	−8.48850	−	14.7025i	−0.312255	−	0.540841i	0.666595	−	0.745420i	$-0.267751\pi$
$739$	−8.48850	−	14.7025i	−0.312255	−	0.540841i	−0.978850	+	0.204579i	$0.934418\pi$
$740$		0			0
$741$	0.611196	−	0.142651i	0.0224529	−	0.00524040i
$742$		0			0
$743$	−25.3588	−	43.9228i	−0.930325	−	1.61137i	−0.782765	−	0.622318i	$-0.786191\pi$
$743$	−25.3588	−	43.9228i	−0.930325	−	1.61137i	−0.147561	−	0.989053i	$-0.547142\pi$
$744$		0			0
$745$	18.7345	−	32.4490i	0.686377	−	1.18884i
$746$		0			0
$747$	−1.14399	+	1.98144i	−0.0418563	+	0.0724972i
$748$		0			0
$749$	61.3042			2.24001
$750$		0			0
$751$	−12.7972	+	22.1654i	−0.466977	+	0.808828i	−0.999288	−	0.0377210i	$-0.987990\pi$
$751$	−12.7972	+	22.1654i	−0.466977	+	0.808828i	0.532312	+	0.846549i	$0.321324\pi$
$752$		0			0
$753$	13.6336			0.496837
$754$		0			0
$755$	−14.7776	−	25.5956i	−0.537812	−	0.931518i
$756$		0			0
$757$	−22.8681	−	39.6087i	−0.831154	−	1.43960i	−0.897124	−	0.441780i	$-0.854347\pi$
$757$	−22.8681	−	39.6087i	−0.831154	−	1.43960i	0.0659694	−	0.997822i	$-0.478986\pi$
$758$		0			0
$759$	28.7361			1.04306
$760$		0			0
$761$	−44.1338			−1.59985			−0.799925	−	0.600100i	$-0.795127\pi$
$761$	−44.1338			−1.59985			−0.799925	+	0.600100i	$0.795127\pi$
$762$		0			0
$763$	−14.3888	−	24.9221i	−0.520910	−	0.902242i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.549569			−0.0198438
$768$		0			0
$769$	22.0473	−	38.1871i	0.795046	−	1.37706i	−0.127764	−	0.991805i	$-0.540780\pi$
$769$	22.0473	−	38.1871i	0.795046	−	1.37706i	0.922810	−	0.385256i	$-0.125887\pi$
$770$		0			0
$771$	12.5944			0.453577
$772$		0			0
$773$	−2.45043	+	4.24427i	−0.0881359	+	0.152656i	−0.906723	−	0.421726i	$-0.861424\pi$
$773$	−2.45043	+	4.24427i	−0.0881359	+	0.152656i	0.818587	+	0.574382i	$0.194758\pi$
$774$		0			0
$775$	9.45156	−	16.3706i	0.339510	−	0.588049i
$776$		0			0
$777$	−1.83641	−	3.18076i	−0.0658809	−	0.114109i
$778$		0			0
$779$	15.9322	+	17.0032i	0.570829	+	0.609203i
$780$		0			0
$781$	−26.0185	−	45.0653i	−0.931014	−	1.61256i
$782$		0			0
$783$	−2.67282	+	4.62947i	−0.0955189	+	0.165444i
$784$		0			0
$785$	18.7868	−	32.5398i	0.670531	−	1.16139i
$786$		0			0
$787$	−35.0554			−1.24959			−0.624795	−	0.780789i	$-0.714818\pi$
$787$	−35.0554			−1.24959			−0.624795	+	0.780789i	$0.714818\pi$
$788$		0			0
$789$	0.816810	−	1.41476i	0.0290792	−	0.0503667i
$790$		0			0
$791$	−23.4504			−0.833801
$792$		0			0
$793$	−0.827176	−	1.43271i	−0.0293739	−	0.0508771i
$794$		0			0
$795$	−10.7160	−	18.5606i	−0.380057	−	0.658277i
$796$		0			0
$797$	−5.67056			−0.200862			−0.100431	−	0.994944i	$-0.532022\pi$
$797$	−5.67056			−0.200862			−0.100431	+	0.994944i	$0.532022\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	4.33641	+	7.51089i	0.153220	+	0.265384i
$802$		0			0
$803$	0.659635	+	1.14252i	0.0232780	+	0.0403187i
$804$		0			0
$805$	73.9092			2.60496
$806$		0			0
$807$	−10.8260	+	18.7513i	−0.381095	+	0.660076i
$808$		0			0
$809$	10.6359			0.373938			0.186969	−	0.982366i	$-0.440134\pi$
$809$	10.6359			0.373938			0.186969	+	0.982366i	$0.440134\pi$
$810$		0			0
$811$	13.6521	−	23.6461i	0.479390	−	0.830327i	−0.520331	−	0.853965i	$-0.674191\pi$
$811$	13.6521	−	23.6461i	0.479390	−	0.830327i	0.999721	+	0.0236373i	$0.00752470\pi$
$812$		0			0
$813$	10.7776	−	18.6674i	0.377987	−	0.654693i
$814$		0			0
$815$	−6.16774	−	10.6828i	−0.216047	−	0.374204i
$816$		0			0
$817$	−8.39522	−	8.95959i	−0.293711	−	0.313456i
$818$		0			0
$819$	−0.264419	−	0.457986i	−0.00923953	−	0.0160033i
$820$		0			0
$821$	−10.5865	+	18.3364i	−0.369472	+	0.639944i	−0.989483	−	0.144649i	$-0.953795\pi$
$821$	−10.5865	+	18.3364i	−0.369472	+	0.639944i	0.620011	+	0.784593i	$0.287128\pi$
$822$		0			0
$823$	23.3641	−	40.4678i	0.814422	−	1.41062i	−0.0953202	−	0.995447i	$-0.530388\pi$
$823$	23.3641	−	40.4678i	0.814422	−	1.41062i	0.909742	−	0.415174i	$-0.136279\pi$
$824$		0			0
$825$	−8.18319			−0.284902
$826$		0			0
$827$	−2.83754	+	4.91477i	−0.0986710	+	0.170903i	−0.911135	−	0.412108i	$-0.864792\pi$
$827$	−2.83754	+	4.91477i	−0.0986710	+	0.170903i	0.812464	+	0.583012i	$0.198126\pi$
$828$		0			0
$829$	−22.3377			−0.775822			−0.387911	−	0.921697i	$-0.626803\pi$
$829$	−22.3377			−0.775822			−0.387911	+	0.921697i	$0.626803\pi$
$830$		0			0
$831$	3.81286	+	6.60406i	0.132267	+	0.229092i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−32.6623			−1.13032
$836$		0			0
$837$	8.81681			0.304754
$838$		0			0
$839$	−6.54203	−	11.3311i	−0.225856	−	0.391194i	0.730720	−	0.682677i	$-0.239184\pi$
$839$	−6.54203	−	11.3311i	−0.225856	−	0.391194i	−0.956576	+	0.291484i	$0.905851\pi$
$840$		0			0
$841$	0.212027	+	0.367241i	0.00731127	+	0.0126635i
$842$		0			0
$843$	1.69356			0.0583292
$844$		0			0
$845$	−17.3456	+	30.0435i	−0.596708	+	1.03353i
$846$		0			0
$847$	13.1048			0.450286
$848$		0			0
$849$	−5.14399	+	8.90965i	−0.176541	+	0.305778i
$850$		0			0
$851$	−3.76442	+	6.52016i	−0.129043	+	0.223508i
$852$		0			0
$853$	−20.1129	−	34.8365i	−0.688652	−	1.19278i	−0.972274	−	0.233844i	$-0.924869\pi$
$853$	−20.1129	−	34.8365i	−0.688652	−	1.19278i	0.283622	−	0.958936i	$-0.408464\pi$
$854$		0			0
$855$	11.3456	−	2.64802i	0.388013	−	0.0905605i
$856$		0			0
$857$	3.00000	+	5.19615i	0.102478	+	0.177497i	0.912705	−	0.408619i	$-0.133990\pi$
$857$	3.00000	+	5.19615i	0.102478	+	0.177497i	−0.810227	+	0.586116i	$0.800656\pi$
$858$		0			0
$859$	−10.9412	+	18.9507i	−0.373309	+	0.646590i	−0.990072	−	0.140559i	$-0.955110\pi$
$859$	−10.9412	+	18.9507i	−0.373309	+	0.646590i	0.616764	+	0.787148i	$0.288443\pi$
$860$		0			0
$861$	9.81681	−	17.0032i	0.334556	−	0.579468i
$862$		0			0
$863$	10.5759			0.360009			0.180005	−	0.983666i	$-0.442389\pi$
$863$	10.5759			0.360009			0.180005	+	0.983666i	$0.442389\pi$
$864$		0			0
$865$	20.1233	−	34.8545i	0.684211	−	1.18509i
$866$		0			0
$867$	17.0000			0.577350
$868$		0			0
$869$	12.4597	+	21.5808i	0.422665	+	0.732078i
$870$		0			0
$871$	0.387673	+	0.671469i	0.0131358	+	0.0227519i
$872$		0			0
$873$	−5.91369			−0.200148
$874$		0			0
$875$	28.0369			0.947822
$876$		0			0
$877$	21.7672	+	37.7020i	0.735028	+	1.27310i	0.954711	+	0.297534i	$0.0961641\pi$
$877$	21.7672	+	37.7020i	0.735028	+	1.27310i	−0.219684	+	0.975571i	$0.570503\pi$
$878$		0			0
$879$	6.05767	+	10.4922i	0.204320	+	0.353893i
$880$		0			0
$881$	4.96080			0.167133			0.0835667	−	0.996502i	$-0.473369\pi$
$881$	4.96080			0.167133			0.0835667	+	0.996502i	$0.473369\pi$
$882$		0			0
$883$	−6.50528	+	11.2675i	−0.218920	+	0.379181i	−0.954478	−	0.298281i	$-0.903587\pi$
$883$	−6.50528	+	11.2675i	−0.218920	+	0.379181i	0.735558	+	0.677462i	$0.236920\pi$
$884$		0			0
$885$	−10.2017			−0.342925
$886$		0			0
$887$	17.0709	−	29.5676i	0.573183	−	0.992783i	−0.423053	−	0.906105i	$-0.639042\pi$
$887$	17.0709	−	29.5676i	0.573183	−	0.992783i	0.996236	−	0.0866779i	$-0.0276251\pi$
$888$		0			0
$889$	4.87448	−	8.44285i	0.163485	−	0.283164i
$890$		0			0
$891$	−1.90841	−	3.30545i	−0.0639340	−	0.110737i
$892$		0			0
$893$	7.58651	−	25.0289i	0.253873	−	0.837560i
$894$		0			0
$895$	20.2633	+	35.0970i	0.677327	+	1.17316i
$896$		0			0
$897$	−0.542026	+	0.938816i	−0.0180977	+	0.0313461i
$898$		0			0
$899$	−23.5658	+	40.8171i	−0.785963	+	1.36133i
$900$		0			0
$901$		0			0
$902$		0			0
$903$	−5.17282	+	8.95959i	−0.172141	+	0.298157i
$904$		0			0
$905$	−32.6129			−1.08409
$906$		0			0
$907$	23.7490	+	41.1344i	0.788572	+	1.36585i	0.926842	+	0.375452i	$0.122512\pi$
$907$	23.7490	+	41.1344i	0.788572	+	1.36585i	−0.138270	+	0.990395i	$0.544154\pi$
$908$		0			0
$909$	−4.14399	−	7.17760i	−0.137447	−	0.238066i
$910$		0			0
$911$	46.1523			1.52909			0.764547	−	0.644568i	$-0.222963\pi$
$911$	46.1523			1.52909			0.764547	+	0.644568i	$0.222963\pi$
$912$		0			0
$913$	8.73276			0.289012
$914$		0			0
$915$	−15.3549	−	26.5954i	−0.507617	−	0.879218i
$916$		0			0
$917$	−20.8353	−	36.0878i	−0.688042	−	1.19172i
$918$		0			0
$919$	29.5160			0.973643			0.486822	−	0.873501i	$-0.338156\pi$
$919$	29.5160			0.973643			0.486822	+	0.873501i	$0.338156\pi$
$920$		0			0
$921$	2.24482	−	3.88814i	0.0739692	−	0.128118i
$922$		0			0
$923$	1.96306			0.0646148
$924$		0			0
$925$	1.07199	−	1.85675i	0.0352469	−	0.0610495i
$926$		0			0
$927$	7.32605	−	12.6891i	0.240619	−	0.416764i
$928$		0			0
$929$	19.7213	+	34.1582i	0.647034	+	1.12070i	0.983828	+	0.179117i	$0.0573240\pi$
$929$	19.7213	+	34.1582i	0.647034	+	1.12070i	−0.336794	+	0.941578i	$0.609343\pi$
$930$		0			0
$931$	−27.5473	+	6.42942i	−0.902827	+	0.210716i
$932$		0			0
$933$	−0.379568	−	0.657431i	−0.0124265	−	0.0215233i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−13.8681	+	24.0202i	−0.453050	+	0.784706i	−0.998574	−	0.0533896i	$-0.982997\pi$
$937$	−13.8681	+	24.0202i	−0.453050	+	0.784706i	0.545524	+	0.838095i	$0.316331\pi$
$938$		0			0
$939$	−11.4320			−0.373068
$940$		0			0
$941$	8.12325	−	14.0699i	0.264811	−	0.458665i	−0.702703	−	0.711483i	$-0.748024\pi$
$941$	8.12325	−	14.0699i	0.264811	−	0.458665i	0.967514	+	0.252818i	$0.0813573\pi$
$942$		0			0
$943$	−40.2465			−1.31061
$944$		0			0
$945$	−4.90841	−	8.50161i	−0.159670	−	0.276557i
$946$		0			0
$947$	−7.96080	−	13.7885i	−0.258691	−	0.448066i	0.707200	−	0.707013i	$-0.249958\pi$
$947$	−7.96080	−	13.7885i	−0.258691	−	0.448066i	−0.965892	+	0.258947i	$0.916625\pi$
$948$		0			0
$949$	−0.0497686			−0.00161556
$950$		0			0
$951$	11.6151			0.376647
$952$		0			0
$953$	−17.9700	−	31.1250i	−0.582106	−	1.00824i	−0.995229	−	0.0975627i	$-0.968895\pi$
$953$	−17.9700	−	31.1250i	−0.582106	−	1.00824i	0.413123	−	0.910675i	$-0.364438\pi$
$954$		0			0
$955$	−7.28402	−	12.6163i	−0.235705	−	0.408254i
$956$		0			0
$957$	20.4033			0.659546
$958$		0			0
$959$	3.00000	−	5.19615i	0.0968751	−	0.167793i
$960$		0			0
$961$	46.7361			1.50762
$962$		0			0
$963$	−8.34565	+	14.4551i	−0.268935	+	0.465809i
$964$		0			0
$965$	−0.682059	+	1.18136i	−0.0219563	+	0.0380294i
$966$		0			0
$967$	1.30362	+	2.25794i	0.0419217	+	0.0726104i	0.886225	−	0.463255i	$-0.153319\pi$
$967$	1.30362	+	2.25794i	0.0419217	+	0.0726104i	−0.844303	+	0.535866i	$0.819985\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	8.06558	+	13.9700i	0.258837	+	0.448318i	0.965931	−	0.258801i	$-0.0833275\pi$
$971$	8.06558	+	13.9700i	0.258837	+	0.448318i	−0.707094	+	0.707120i	$0.749994\pi$
$972$		0			0
$973$	13.7880	−	23.8815i	0.442022	−	0.765605i
$974$		0			0
$975$	0.154353	−	0.267347i	0.00494324	−	0.00856194i
$976$		0			0
$977$	−3.17302			−0.101514			−0.0507570	−	0.998711i	$-0.516163\pi$
$977$	−3.17302			−0.101514			−0.0507570	+	0.998711i	$0.516163\pi$
$978$		0			0
$979$	16.5513	−	28.6676i	0.528981	−	0.916221i
$980$		0			0
$981$	7.83528			0.250161
$982$		0			0
$983$	10.4165	+	18.0419i	0.332235	+	0.575448i	0.982950	−	0.183874i	$-0.0588639\pi$
$983$	10.4165	+	18.0419i	0.332235	+	0.575448i	−0.650715	+	0.759322i	$0.725531\pi$
$984$		0			0
$985$	30.6851	+	53.1481i	0.977708	+	1.69344i
$986$		0			0
$987$	−22.0369			−0.701444
$988$		0			0
$989$	21.2073			0.674353
$990$		0			0
$991$	−22.9165	−	39.6926i	−0.727967	−	1.26088i	−0.957741	−	0.287632i	$-0.907132\pi$
$991$	−22.9165	−	39.6926i	−0.727967	−	1.26088i	0.229774	−	0.973244i	$-0.426201\pi$
$992$		0			0
$993$	5.73558	+	9.93432i	0.182013	+	0.315256i
$994$		0			0
$995$	−0.335481			−0.0106355
$996$		0			0
$997$	−27.3168	+	47.3141i	−0.865132	+	1.49845i	0.00178393	+	0.999998i	$0.499432\pi$
$997$	−27.3168	+	47.3141i	−0.865132	+	1.49845i	−0.866916	+	0.498454i	$0.833901\pi$
$998$		0			0
$999$	1.00000			0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.q.l.577.3		6
3.2	odd	2		2736.2.s.z.577.1		6
4.3	odd	2		57.2.e.b.7.2	✓	6
12.11	even	2		171.2.f.b.64.2		6
19.11	even	3	inner	912.2.q.l.49.3		6
57.11	odd	6		2736.2.s.z.1873.1		6
76.7	odd	6		1083.2.a.l.1.2		3
76.11	odd	6		57.2.e.b.49.2	yes	6
76.31	even	6		1083.2.a.o.1.2		3
228.11	even	6		171.2.f.b.163.2		6
228.83	even	6		3249.2.a.y.1.2		3
228.107	odd	6		3249.2.a.t.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.e.b.7.2	✓	6	4.3	odd	2
57.2.e.b.49.2	yes	6	76.11	odd	6
171.2.f.b.64.2		6	12.11	even	2
171.2.f.b.163.2		6	228.11	even	6
912.2.q.l.49.3		6	19.11	even	3	inner
912.2.q.l.577.3		6	1.1	even	1	trivial
1083.2.a.l.1.2		3	76.7	odd	6
1083.2.a.o.1.2		3	76.31	even	6
2736.2.s.z.577.1		6	3.2	odd	2
2736.2.s.z.1873.1		6	57.11	odd	6
3249.2.a.t.1.2		3	228.107	odd	6
3249.2.a.y.1.2		3	228.83	even	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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +(1.33641 + 2.31473i) q^{5} +3.67282 q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} +(1.33641 + 2.31473i) q^{5} +3.67282 q^{7} +(-0.500000 + 0.866025i) q^{9} +3.81681 q^{11} +(-0.0719933 + 0.124696i) q^{13} +(-1.33641 + 2.31473i) q^{15} +(-4.24482 + 0.990721i) q^{19} +(1.83641 + 3.18076i) q^{21} +(3.76442 - 6.52016i) q^{23} +(-1.07199 + 1.85675i) q^{25} -1.00000 q^{27} +(2.67282 - 4.62947i) q^{29} -8.81681 q^{31} +(1.90841 + 3.30545i) q^{33} +(4.90841 + 8.50161i) q^{35} -1.00000 q^{37} -0.143987 q^{39} +(-2.67282 - 4.62947i) q^{41} +(1.40841 + 2.43943i) q^{43} -2.67282 q^{45} +(-3.00000 + 5.19615i) q^{47} +6.48963 q^{49} +(-4.00924 + 6.94420i) q^{53} +(5.10083 + 8.83490i) q^{55} +(-2.98040 - 3.18076i) q^{57} +(1.90841 + 3.30545i) q^{59} +(-5.74482 + 9.95031i) q^{61} +(-1.83641 + 3.18076i) q^{63} -0.384851 q^{65} +(2.69243 - 4.66342i) q^{67} +7.52884 q^{69} +(-6.81681 - 11.8071i) q^{71} +(0.172824 + 0.299339i) q^{73} -2.14399 q^{75} +14.0185 q^{77} +(3.26442 + 5.65414i) q^{79} +(-0.500000 - 0.866025i) q^{81} +2.28797 q^{83} +5.34565 q^{87} +(4.33641 - 7.51089i) q^{89} +(-0.264419 + 0.457986i) q^{91} +(-4.40841 - 7.63558i) q^{93} +(-7.96608 - 8.50161i) q^{95} +(2.95684 + 5.12140i) q^{97} +(-1.90841 + 3.30545i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{3} - 2 q^{5} + 2 q^{7} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^3 - 2 * q^5 + 2 * q^7 - 3 * q^9	\( 6 q + 3 q^{3} - 2 q^{5} + 2 q^{7} - 3 q^{9} + q^{13} + 2 q^{15} - 4 q^{19} + q^{21} + 14 q^{23} - 5 q^{25} - 6 q^{27} - 4 q^{29} - 30 q^{31} + 18 q^{35} - 6 q^{37} + 2 q^{39} + 4 q^{41} - 3 q^{43} + 4 q^{45} - 18 q^{47} - 4 q^{49} + 6 q^{53} + 12 q^{55} - 5 q^{57} - 13 q^{61} - q^{63} + 12 q^{65} + 9 q^{67} + 28 q^{69} - 18 q^{71} - 19 q^{73} - 10 q^{75} + 24 q^{77} + 11 q^{79} - 3 q^{81} + 8 q^{83} - 8 q^{87} + 16 q^{89} + 7 q^{91} - 15 q^{93} - 2 q^{95} + 2 q^{97}+O(q^{100}) \) 6 * q + 3 * q^3 - 2 * q^5 + 2 * q^7 - 3 * q^9 + q^13 + 2 * q^15 - 4 * q^19 + q^21 + 14 * q^23 - 5 * q^25 - 6 * q^27 - 4 * q^29 - 30 * q^31 + 18 * q^35 - 6 * q^37 + 2 * q^39 + 4 * q^41 - 3 * q^43 + 4 * q^45 - 18 * q^47 - 4 * q^49 + 6 * q^53 + 12 * q^55 - 5 * q^57 - 13 * q^61 - q^63 + 12 * q^65 + 9 * q^67 + 28 * q^69 - 18 * q^71 - 19 * q^73 - 10 * q^75 + 24 * q^77 + 11 * q^79 - 3 * q^81 + 8 * q^83 - 8 * q^87 + 16 * q^89 + 7 * q^91 - 15 * q^93 - 2 * q^95 + 2 * q^97

Introduction

L-functions

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