LMFDB - Embedded newform 1232.2.q.k.529.2

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			529.2
Root			$0.356769 - 0.617942i$ of defining polynomial
Character	$\chi$	$=$	1232.529
Dual form			1232.2.q.k.177.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.356769 + 0.617942i) q^{3} +(-1.10220 - 1.90907i) q^{5} +(1.10220 + 2.40523i) q^{7} +(1.24543 + 2.15715i) q^{9} +O(q^{10})$	\(q+(-0.356769 + 0.617942i) q^{3} +(-1.10220 - 1.90907i) q^{5} +(1.10220 + 2.40523i) q^{7} +(1.24543 + 2.15715i) q^{9} +(-0.500000 + 0.866025i) q^{11} -3.28646 q^{13} +1.57292 q^{15} +(-0.745432 + 1.29113i) q^{17} +(-3.45897 - 5.99111i) q^{19} +(-1.87953 - 0.177017i) q^{21} +(3.24543 + 5.62125i) q^{23} +(0.0703069 - 0.121775i) q^{25} -3.91794 q^{27} -1.64975 q^{29} +(-1.17512 + 2.03538i) q^{31} +(-0.356769 - 0.617942i) q^{33} +(3.37691 - 4.75523i) q^{35} +(2.77733 + 4.81047i) q^{37} +(1.17251 - 2.03084i) q^{39} -11.2499 q^{41} -5.26819 q^{43} +(2.74543 - 4.75523i) q^{45} +(0.745432 + 1.29113i) q^{47} +(-4.57031 + 5.30210i) q^{49} +(-0.531894 - 0.921267i) q^{51} +(-0.152367 + 0.263908i) q^{53} +2.20440 q^{55} +4.93621 q^{57} +(-6.32936 + 10.9628i) q^{59} +(6.49086 + 11.2425i) q^{61} +(-3.81574 + 5.37317i) q^{63} +(3.62234 + 6.27408i) q^{65} +(-2.28646 + 3.96027i) q^{67} -4.63148 q^{69} -11.3267 q^{71} +(4.28384 - 7.41984i) q^{73} +(0.0501666 + 0.0868912i) q^{75} +(-2.63409 - 0.248083i) q^{77} +(2.31574 + 4.01098i) q^{79} +(-2.33850 + 4.05039i) q^{81} +1.93621 q^{83} +3.28646 q^{85} +(0.588580 - 1.01945i) q^{87} +(-1.60220 - 2.77509i) q^{89} +(-3.62234 - 7.90471i) q^{91} +(-0.838496 - 1.45232i) q^{93} +(-7.62496 + 13.2068i) q^{95} +1.85939 q^{97} -2.49086 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.356769	+	0.617942i	−0.205981	+	0.356769i	−0.950445	−	0.310894i	$-0.899372\pi$
$3$	−0.356769	+	0.617942i	−0.205981	+	0.356769i	0.744464	+	0.667663i	$0.232705\pi$
$4$		0			0
$5$	−1.10220	−	1.90907i	−0.492919	−	0.853761i	0.507048	−	0.861918i	$-0.330737\pi$
$5$	−1.10220	−	1.90907i	−0.492919	−	0.853761i	−0.999967	+	0.00815703i	$0.997404\pi$
$6$		0			0
$7$	1.10220	+	2.40523i	0.416593	+	0.909093i
$7$	1.10220	+	2.40523i	0.416593	+	0.909093i
$8$		0			0
$9$	1.24543	+	2.15715i	0.415144	+	0.719050i
$10$		0			0
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$		0			0
$13$	−3.28646			−0.911501			−0.455750	−	0.890108i	$-0.650629\pi$
$13$	−3.28646			−0.911501			−0.455750	+	0.890108i	$0.650629\pi$
$14$		0			0
$15$	1.57292			0.406127
$16$		0			0
$17$	−0.745432	+	1.29113i	−0.180794	+	0.313144i	−0.942151	−	0.335189i	$-0.891200\pi$
$17$	−0.745432	+	1.29113i	−0.180794	+	0.313144i	0.761357	+	0.648333i	$0.224533\pi$
$18$		0			0
$19$	−3.45897	−	5.99111i	−0.793542	−	1.37446i	−0.923761	−	0.382970i	$-0.874901\pi$
$19$	−3.45897	−	5.99111i	−0.793542	−	1.37446i	0.130219	−	0.991485i	$-0.458432\pi$
$20$		0			0
$21$	−1.87953	−	0.177017i	−0.410146	−	0.0386283i
$22$		0			0
$23$	3.24543	+	5.62125i	0.676719	+	1.17211i	0.975963	+	0.217936i	$0.0699323\pi$
$23$	3.24543	+	5.62125i	0.676719	+	1.17211i	−0.299244	+	0.954177i	$0.596734\pi$
$24$		0			0
$25$	0.0703069	−	0.121775i	0.0140614	−	0.0243550i
$26$		0			0
$27$	−3.91794			−0.754008
$28$		0			0
$29$	−1.64975			−0.306351			−0.153175	−	0.988199i	$-0.548950\pi$
$29$	−1.64975			−0.306351			−0.153175	+	0.988199i	$0.548950\pi$
$30$		0			0
$31$	−1.17512	+	2.03538i	−0.211059	+	0.365564i	−0.952046	−	0.305955i	$-0.901024\pi$
$31$	−1.17512	+	2.03538i	−0.211059	+	0.365564i	0.740987	+	0.671519i	$0.234358\pi$
$32$		0			0
$33$	−0.356769	−	0.617942i	−0.0621055	−	0.107570i
$34$		0			0
$35$	3.37691	−	4.75523i	0.570802	−	0.803780i
$36$		0			0
$37$	2.77733	+	4.81047i	0.456590	+	0.790836i	0.998778	−	0.0494206i	$-0.0157375\pi$
$37$	2.77733	+	4.81047i	0.456590	+	0.790836i	−0.542189	+	0.840257i	$0.682404\pi$
$38$		0			0
$39$	1.17251	−	2.03084i	0.187751	−	0.325195i
$40$		0			0
$41$	−11.2499			−1.75694			−0.878471	−	0.477796i	$-0.841436\pi$
$41$	−11.2499			−1.75694			−0.878471	+	0.477796i	$0.841436\pi$
$42$		0			0
$43$	−5.26819			−0.803391			−0.401696	−	0.915773i	$-0.631579\pi$
$43$	−5.26819			−0.803391			−0.401696	+	0.915773i	$0.631579\pi$
$44$		0			0
$45$	2.74543	−	4.75523i	0.409265	−	0.708867i
$46$		0			0
$47$	0.745432	+	1.29113i	0.108732	+	0.188330i	0.915257	−	0.402871i	$-0.131988\pi$
$47$	0.745432	+	1.29113i	0.108732	+	0.188330i	−0.806525	+	0.591201i	$0.798654\pi$
$48$		0			0
$49$	−4.57031	+	5.30210i	−0.652901	+	0.757443i
$50$		0			0
$51$	−0.531894	−	0.921267i	−0.0744800	−	0.129003i
$52$		0			0
$53$	−0.152367	+	0.263908i	−0.0209293	+	0.0362506i	−0.876300	−	0.481765i	$-0.839996\pi$
$53$	−0.152367	+	0.263908i	−0.0209293	+	0.0362506i	0.855371	+	0.518016i	$0.173329\pi$
$54$		0			0
$55$	2.20440			0.297241
$56$		0			0
$57$	4.93621			0.653817
$58$		0			0
$59$	−6.32936	+	10.9628i	−0.824012	+	1.42723i	0.0786592	+	0.996902i	$0.474936\pi$
$59$	−6.32936	+	10.9628i	−0.824012	+	1.42723i	−0.902672	+	0.430330i	$0.858397\pi$
$60$		0			0
$61$	6.49086	+	11.2425i	0.831070	+	1.43946i	0.897191	+	0.441644i	$0.145604\pi$
$61$	6.49086	+	11.2425i	0.831070	+	1.43946i	−0.0661206	+	0.997812i	$0.521062\pi$
$62$		0			0
$63$	−3.81574	+	5.37317i	−0.480738	+	0.676956i
$64$		0			0
$65$	3.62234	+	6.27408i	0.449296	+	0.778204i
$66$		0			0
$67$	−2.28646	+	3.96027i	−0.279336	+	0.483824i	−0.971220	−	0.238185i	$-0.923448\pi$
$67$	−2.28646	+	3.96027i	−0.279336	+	0.483824i	0.691884	+	0.722009i	$0.256781\pi$
$68$		0			0
$69$	−4.63148			−0.557564
$70$		0			0
$71$	−11.3267			−1.34424			−0.672119	−	0.740444i	$-0.734615\pi$
$71$	−11.3267			−1.34424			−0.672119	+	0.740444i	$0.734615\pi$
$72$		0			0
$73$	4.28384	−	7.41984i	0.501386	−	0.868426i	−0.498613	−	0.866825i	$-0.666157\pi$
$73$	4.28384	−	7.41984i	0.501386	−	0.868426i	0.999999	−	0.00160129i	$-0.000509706\pi$
$74$		0			0
$75$	0.0501666	+	0.0868912i	0.00579274	+	0.0100333i
$76$		0			0
$77$	−2.63409	−	0.248083i	−0.300183	−	0.0282717i
$78$		0			0
$79$	2.31574	+	4.01098i	0.260541	+	0.451270i	0.966386	−	0.257096i	$-0.0827658\pi$
$79$	2.31574	+	4.01098i	0.260541	+	0.451270i	−0.705845	+	0.708366i	$0.749432\pi$
$80$		0			0
$81$	−2.33850	+	4.05039i	−0.259833	+	0.450044i
$82$		0			0
$83$	1.93621			0.212527			0.106263	−	0.994338i	$-0.466111\pi$
$83$	1.93621			0.212527			0.106263	+	0.994338i	$0.466111\pi$
$84$		0			0
$85$	3.28646			0.356467
$86$		0			0
$87$	0.588580	−	1.01945i	0.0631024	−	0.109297i
$88$		0			0
$89$	−1.60220	−	2.77509i	−0.169833	−	0.294159i	0.768528	−	0.639816i	$-0.220989\pi$
$89$	−1.60220	−	2.77509i	−0.169833	−	0.294159i	−0.938361	+	0.345657i	$0.887656\pi$
$90$		0			0
$91$	−3.62234	−	7.90471i	−0.379725	−	0.828639i
$92$		0			0
$93$	−0.838496	−	1.45232i	−0.0869480	−	0.150598i
$94$		0			0
$95$	−7.62496	+	13.2068i	−0.782304	+	1.35499i
$96$		0			0
$97$	1.85939			0.188792			0.0943960	−	0.995535i	$-0.469908\pi$
$97$	1.85939			0.188792			0.0943960	+	0.995535i	$0.469908\pi$
$98$		0			0
$99$	−2.49086			−0.250341
$100$		0			0
$101$	−3.02276	+	5.23557i	−0.300776	+	0.520959i	−0.976312	−	0.216368i	$-0.930579\pi$
$101$	−3.02276	+	5.23557i	−0.300776	+	0.520959i	0.675536	+	0.737327i	$0.263912\pi$
$102$		0			0
$103$	−0.531894	−	0.921267i	−0.0524091	−	0.0907752i	0.838631	−	0.544700i	$-0.183357\pi$
$103$	−0.531894	−	0.921267i	−0.0524091	−	0.0907752i	−0.891040	+	0.453925i	$0.850023\pi$
$104$		0			0
$105$	1.73368	+	3.78325i	0.169190	+	0.369208i
$106$		0			0
$107$	−3.16599	−	5.48365i	−0.306068	−	0.530125i	0.671431	−	0.741067i	$-0.265680\pi$
$107$	−3.16599	−	5.48365i	−0.306068	−	0.530125i	−0.977498	+	0.210943i	$0.932347\pi$
$108$		0			0
$109$	1.40694	−	2.43688i	0.134760	−	0.233411i	−0.790746	−	0.612145i	$-0.790307\pi$
$109$	1.40694	−	2.43688i	0.134760	−	0.233411i	0.925506	+	0.378734i	$0.123640\pi$
$110$		0			0
$111$	−3.96345			−0.376194
$112$		0			0
$113$	−12.7538			−1.19978			−0.599889	−	0.800083i	$-0.704789\pi$
$113$	−12.7538			−1.19978			−0.599889	+	0.800083i	$0.704789\pi$
$114$		0			0
$115$	7.15423	−	12.3915i	0.667136	−	1.15551i
$116$		0			0
$117$	−4.09306	−	7.08940i	−0.378404	−	0.655415i
$118$		0			0
$119$	−3.92708	−	0.369859i	−0.359994	−	0.0339049i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$		0			0
$123$	4.01362	−	6.95180i	0.361896	−	0.626822i
$124$		0			0
$125$	−11.3320			−1.01356
$126$		0			0
$127$	12.3775			1.09832			0.549162	−	0.835716i	$-0.314947\pi$
$127$	12.3775			1.09832			0.549162	+	0.835716i	$0.314947\pi$
$128$		0			0
$129$	1.87953	−	3.25544i	0.165483	−	0.286625i
$130$		0			0
$131$	0.379526	+	0.657359i	0.0331594	+	0.0574337i	0.882129	−	0.471008i	$-0.156110\pi$
$131$	0.379526	+	0.657359i	0.0331594	+	0.0574337i	−0.848969	+	0.528442i	$0.822776\pi$
$132$		0			0
$133$	10.5975	−	14.9230i	0.918924	−	1.29399i
$134$		0			0
$135$	4.31836	+	7.47961i	0.371665	+	0.643742i
$136$		0			0
$137$	2.92056	−	5.05855i	0.249520	−	0.432181i	−0.713873	−	0.700275i	$-0.753060\pi$
$137$	2.92056	−	5.05855i	0.249520	−	0.432181i	0.963393	+	0.268094i	$0.0863938\pi$
$138$		0			0
$139$	5.57292			0.472689			0.236345	−	0.971669i	$-0.424051\pi$
$139$	5.57292			0.472689			0.236345	+	0.971669i	$0.424051\pi$
$140$		0			0
$141$	−1.06379			−0.0895871
$142$		0			0
$143$	1.64323	−	2.84616i	0.137414	−	0.238008i
$144$		0			0
$145$	1.81836	+	3.14948i	0.151006	+	0.261550i
$146$		0			0
$147$	−1.64585	−	4.71581i	−0.135747	−	0.388953i
$148$		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
$151$	7.42056	−	12.8528i	0.603876	−	1.04594i	−0.388352	−	0.921511i	$-0.626955\pi$
$151$	7.42056	−	12.8528i	0.603876	−	1.04594i	0.992228	−	0.124433i	$-0.0397113\pi$
$152$		0			0
$153$	−3.71354			−0.300222
$154$		0			0
$155$	5.18089			0.416139
$156$		0			0
$157$	−3.19527	+	5.53436i	−0.255010	+	0.441690i	−0.964898	−	0.262624i	$-0.915412\pi$
$157$	−3.19527	+	5.53436i	−0.255010	+	0.441690i	0.709888	+	0.704314i	$0.248745\pi$
$158$		0			0
$159$	−0.108720	−	0.188308i	−0.00862205	−	0.0149338i
$160$		0			0
$161$	−9.94331	+	14.0018i	−0.783643	+	1.10349i
$162$		0			0
$163$	4.97259	+	8.61278i	0.389483	+	0.674605i	0.992380	−	0.123214i	$-0.0393202\pi$
$163$	4.97259	+	8.61278i	0.389483	+	0.674605i	−0.602897	+	0.797819i	$0.705987\pi$
$164$		0			0
$165$	−0.786462	+	1.36219i	−0.0612260	+	0.106047i
$166$		0			0
$167$	1.94145			0.150234			0.0751168	−	0.997175i	$-0.476067\pi$
$167$	1.94145			0.150234			0.0751168	+	0.997175i	$0.476067\pi$
$168$		0			0
$169$	−2.19917			−0.169167
$170$		0			0
$171$	8.61582	−	14.9230i	0.658868	−	1.14119i
$172$		0			0
$173$	−3.21616	−	5.57054i	−0.244520	−	0.423521i	0.717477	−	0.696582i	$-0.245297\pi$
$173$	−3.21616	−	5.57054i	−0.244520	−	0.423521i	−0.961996	+	0.273062i	$0.911964\pi$
$174$		0			0
$175$	0.370390	+	0.0348840i	0.0279989	+	0.00263698i
$176$		0			0
$177$	−4.51624	−	7.82235i	−0.339461	−	0.587964i
$178$		0			0
$179$	−1.79298	+	3.10553i	−0.134014	+	0.232119i	−0.925220	−	0.379430i	$-0.876120\pi$
$179$	−1.79298	+	3.10553i	−0.134014	+	0.232119i	0.791207	+	0.611549i	$0.209453\pi$
$180$		0			0
$181$	12.2134			0.907813			0.453906	−	0.891049i	$-0.350030\pi$
$181$	12.2134			0.907813			0.453906	+	0.891049i	$0.350030\pi$
$182$		0			0
$183$	−9.26295			−0.684737
$184$		0			0
$185$	6.12234	−	10.6042i	0.450123	−	0.779637i
$186$		0			0
$187$	−0.745432	−	1.29113i	−0.0545114	−	0.0944165i
$188$		0			0
$189$	−4.31836	−	9.42356i	−0.314114	−	0.685463i
$190$		0			0
$191$	6.05465	+	10.4870i	0.438099	+	0.758810i	0.997543	−	0.0700583i	$-0.0223185\pi$
$191$	6.05465	+	10.4870i	0.438099	+	0.758810i	−0.559444	+	0.828868i	$0.688985\pi$
$192$		0			0
$193$	5.96997	−	10.3403i	0.429728	−	0.744311i	−0.567121	−	0.823635i	$-0.691943\pi$
$193$	5.96997	−	10.3403i	0.429728	−	0.744311i	0.996849	+	0.0793237i	$0.0252761\pi$
$194$		0			0
$195$	−5.16936			−0.370185
$196$		0			0
$197$	12.1626			0.866551			0.433275	−	0.901262i	$-0.357358\pi$
$197$	12.1626			0.866551			0.433275	+	0.901262i	$0.357358\pi$
$198$		0			0
$199$	0.952451	−	1.64969i	0.0675174	−	0.116944i	−0.830290	−	0.557331i	$-0.811826\pi$
$199$	0.952451	−	1.64969i	0.0675174	−	0.116944i	0.897808	+	0.440387i	$0.145159\pi$
$200$		0			0
$201$	−1.63148	−	2.82580i	−0.115076	−	0.199317i
$202$		0			0
$203$	−1.81836	−	3.96804i	−0.127624	−	0.278502i
$204$		0			0
$205$	12.3997	+	21.4769i	0.866030	+	1.50001i
$206$		0			0
$207$	−8.08393	+	14.0018i	−0.561872	+	0.973191i
$208$		0			0
$209$	6.91794			0.478524
$210$		0			0
$211$	16.2447			1.11833			0.559165	−	0.829056i	$-0.311122\pi$
$211$	16.2447			1.11833			0.559165	+	0.829056i	$0.311122\pi$
$212$		0			0
$213$	4.04103	−	6.99927i	0.276887	−	0.479582i
$214$		0			0
$215$	5.80660	+	10.0573i	0.396007	+	0.685904i
$216$		0			0
$217$	−6.19078	−	0.583058i	−0.420258	−	0.0395806i
$218$		0			0
$219$	3.05669	+	5.29434i	0.206552	+	0.357758i
$220$		0			0
$221$	2.44983	−	4.24324i	0.164794	−	0.285431i
$222$		0			0
$223$	−3.03655			−0.203342			−0.101671	−	0.994818i	$-0.532419\pi$
$223$	−3.03655			−0.203342			−0.101671	+	0.994818i	$0.532419\pi$
$224$		0			0
$225$	0.350250			0.0233500
$226$		0			0
$227$	9.22454	−	15.9774i	0.612254	−	1.06046i	−0.378605	−	0.925558i	$-0.623596\pi$
$227$	9.22454	−	15.9774i	0.612254	−	1.06046i	0.990860	−	0.134897i	$-0.0430705\pi$
$228$		0			0
$229$	12.7499	+	22.0835i	0.842538	+	1.45932i	0.887742	+	0.460341i	$0.152273\pi$
$229$	12.7499	+	22.0835i	0.842538	+	1.45932i	−0.0452039	+	0.998978i	$0.514394\pi$
$230$		0			0
$231$	1.09306	−	1.53921i	0.0719184	−	0.101273i
$232$		0			0
$233$	−1.90880	−	3.30614i	−0.125050	−	0.216593i	0.796703	−	0.604372i	$-0.206576\pi$
$233$	−1.90880	−	3.30614i	−0.125050	−	0.216593i	−0.921752	+	0.387779i	$0.873242\pi$
$234$		0			0
$235$	1.64323	−	2.84616i	0.107193	−	0.185663i
$236$		0			0
$237$	−3.30473			−0.214666
$238$		0			0
$239$	−13.0037			−0.841142			−0.420571	−	0.907260i	$-0.638170\pi$
$239$	−13.0037			−0.841142			−0.420571	+	0.907260i	$0.638170\pi$
$240$		0			0
$241$	0.225292	−	0.390216i	0.0145123	−	0.0251360i	−0.858678	−	0.512515i	$-0.828714\pi$
$241$	0.225292	−	0.390216i	0.0145123	−	0.0251360i	0.873190	+	0.487379i	$0.162047\pi$
$242$		0			0
$243$	−7.54551	−	13.0692i	−0.484045	−	0.838391i
$244$		0			0
$245$	15.1595	+	2.88104i	0.968503	+	0.184063i
$246$		0			0
$247$	11.3678	+	19.6896i	0.723314	+	1.25282i
$248$		0			0
$249$	−0.690780	+	1.19647i	−0.0437764	+	0.0758230i
$250$		0			0
$251$	−1.11861			−0.0706058			−0.0353029	−	0.999377i	$-0.511240\pi$
$251$	−1.11861			−0.0706058			−0.0353029	+	0.999377i	$0.511240\pi$
$252$		0			0
$253$	−6.49086			−0.408077
$254$		0			0
$255$	−1.17251	+	2.03084i	−0.0734253	+	0.127176i
$256$		0			0
$257$	11.4198	+	19.7797i	0.712348	+	1.23382i	0.963974	+	0.265998i	$0.0857015\pi$
$257$	11.4198	+	19.7797i	0.712348	+	1.23382i	−0.251626	+	0.967825i	$0.580965\pi$
$258$		0			0
$259$	−8.50914	+	11.9822i	−0.528732	+	0.744539i
$260$		0			0
$261$	−2.05465	−	3.55876i	−0.127180	−	0.220282i
$262$		0			0
$263$	−4.59568	+	7.95995i	−0.283382	+	0.490832i	−0.972215	−	0.234088i	$-0.924790\pi$
$263$	−4.59568	+	7.95995i	−0.283382	+	0.490832i	0.688834	+	0.724919i	$0.258123\pi$
$264$		0			0
$265$	0.671758			0.0412658
$266$		0			0
$267$	2.28646			0.139929
$268$		0			0
$269$	7.80660	−	13.5214i	0.475977	−	0.824416i	−0.523644	−	0.851937i	$-0.675428\pi$
$269$	7.80660	−	13.5214i	0.475977	−	0.824416i	0.999621	+	0.0275208i	$0.00876123\pi$
$270$		0			0
$271$	13.8723	+	24.0275i	0.842680	+	1.45956i	0.887621	+	0.460574i	$0.152357\pi$
$271$	13.8723	+	24.0275i	0.842680	+	1.45956i	−0.0449415	+	0.998990i	$0.514310\pi$
$272$		0			0
$273$	6.17699	+	0.581759i	0.373849	+	0.0352097i
$274$		0			0
$275$	0.0703069	+	0.121775i	0.00423967	+	0.00734332i
$276$		0			0
$277$	−7.40619	+	12.8279i	−0.444995	+	0.770753i	−0.998052	−	0.0623900i	$-0.980128\pi$
$277$	−7.40619	+	12.8279i	−0.444995	+	0.770753i	0.553057	+	0.833143i	$0.313461\pi$
$278$		0			0
$279$	−5.85415			−0.350479
$280$		0			0
$281$	15.2227			0.908109			0.454054	−	0.890974i	$-0.349977\pi$
$281$	15.2227			0.908109			0.454054	+	0.890974i	$0.349977\pi$
$282$		0			0
$283$	10.8586	−	18.8077i	0.645479	−	1.11800i	−0.338712	−	0.940890i	$-0.609991\pi$
$283$	10.8586	−	18.8077i	0.645479	−	1.11800i	0.984191	−	0.177112i	$-0.0566755\pi$
$284$		0			0
$285$	−5.44070	−	9.42356i	−0.322279	−	0.558204i
$286$		0			0
$287$	−12.3997	−	27.0587i	−0.731929	−	1.59722i
$288$		0			0
$289$	7.38866	+	12.7975i	0.434627	+	0.752796i
$290$		0			0
$291$	−0.663371	+	1.14899i	−0.0388875	+	0.0673551i
$292$		0			0
$293$	11.1276			0.650080			0.325040	−	0.945700i	$-0.394622\pi$
$293$	11.1276			0.650080			0.325040	+	0.945700i	$0.394622\pi$
$294$		0			0
$295$	27.9049			1.62469
$296$		0			0
$297$	1.95897	−	3.39304i	0.113671	−	0.196884i
$298$		0			0
$299$	−10.6660	−	18.4740i	−0.616830	−	1.06838i
$300$		0			0
$301$	−5.80660	−	12.6712i	−0.334687	−	0.730358i
$302$		0			0
$303$	−2.15685	−	3.73578i	−0.123908	−	0.214615i
$304$		0			0
$305$	14.3085	−	24.7830i	0.819301	−	1.41907i
$306$		0			0
$307$	−24.9855			−1.42600			−0.712998	−	0.701166i	$-0.752663\pi$
$307$	−24.9855			−1.42600			−0.712998	+	0.701166i	$0.752663\pi$
$308$		0			0
$309$	0.759053			0.0431810
$310$		0			0
$311$	17.3704	−	30.0864i	0.984984	−	1.70604i	0.342979	−	0.939343i	$-0.388564\pi$
$311$	17.3704	−	30.0864i	0.984984	−	1.70604i	0.642005	−	0.766700i	$-0.278103\pi$
$312$		0			0
$313$	−11.8547	−	20.5330i	−0.670069	−	1.16059i	−0.977884	−	0.209148i	$-0.932931\pi$
$313$	−11.8547	−	20.5330i	−0.670069	−	1.16059i	0.307815	−	0.951446i	$-0.400402\pi$
$314$		0			0
$315$	14.4635	+	1.36219i	0.814923	+	0.0767508i
$316$		0			0
$317$	−9.83850	−	17.0408i	−0.552585	−	0.957105i	−0.998087	−	0.0618244i	$-0.980308\pi$
$317$	−9.83850	−	17.0408i	−0.552585	−	0.957105i	0.445502	−	0.895281i	$-0.353025\pi$
$318$		0			0
$319$	0.824875	−	1.42873i	0.0461841	−	0.0799933i
$320$		0			0
$321$	4.51811			0.252176
$322$		0			0
$323$	10.3137			0.573870
$324$		0			0
$325$	−0.231061	+	0.400209i	−0.0128170	+	0.0221996i
$326$		0			0
$327$	1.00390	+	1.73881i	0.0555159	+	0.0961564i
$328$		0			0
$329$	−2.28384	+	3.21602i	−0.125912	+	0.177305i
$330$		0			0
$331$	−14.0949	−	24.4131i	−0.774728	−	1.34187i	−0.934947	−	0.354786i	$-0.884554\pi$
$331$	−14.0949	−	24.4131i	−0.774728	−	1.34187i	0.160220	−	0.987081i	$-0.448780\pi$
$332$		0			0
$333$	−6.91794	+	11.9822i	−0.379101	+	0.656622i
$334$		0			0
$335$	10.0806			0.550760
$336$		0			0
$337$	21.7460			1.18458			0.592290	−	0.805725i	$-0.298224\pi$
$337$	21.7460			1.18458			0.592290	+	0.805725i	$0.298224\pi$
$338$		0			0
$339$	4.55017	−	7.88112i	0.247131	−	0.428044i
$340$		0			0
$341$	−1.17512	−	2.03538i	−0.0636366	−	0.110222i
$342$		0			0
$343$	−17.7902	−	5.14868i	−0.960580	−	0.278003i
$344$		0			0
$345$	5.10482	+	8.84180i	0.274834	+	0.476027i
$346$		0			0
$347$	−1.97072	+	3.41339i	−0.105794	+	0.183241i	−0.914062	−	0.405574i	$-0.867072\pi$
$347$	−1.97072	+	3.41339i	−0.105794	+	0.183241i	0.808268	+	0.588814i	$0.200405\pi$
$348$		0			0
$349$	−14.1093			−0.755254			−0.377627	−	0.925958i	$-0.623260\pi$
$349$	−14.1093			−0.755254			−0.377627	+	0.925958i	$0.623260\pi$
$350$		0			0
$351$	12.8762			0.687279
$352$		0			0
$353$	2.48434	−	4.30301i	0.132228	−	0.229026i	−0.792307	−	0.610123i	$-0.791120\pi$
$353$	2.48434	−	4.30301i	0.132228	−	0.229026i	0.924535	+	0.381097i	$0.124453\pi$
$354$		0			0
$355$	12.4843	+	21.6235i	0.662600	+	1.14766i
$356$		0			0
$357$	1.62961	−	2.29475i	0.0862481	−	0.121451i
$358$		0			0
$359$	−2.03580	−	3.52610i	−0.107445	−	0.186101i	0.807289	−	0.590156i	$-0.200934\pi$
$359$	−2.03580	−	3.52610i	−0.107445	−	0.186101i	−0.914735	+	0.404055i	$0.867600\pi$
$360$		0			0
$361$	−14.4289	+	24.9917i	−0.759418	+	1.31535i
$362$		0			0
$363$	0.713538			0.0374510
$364$		0			0
$365$	−18.8866			−0.988571
$366$		0			0
$367$	−9.01100	+	15.6075i	−0.470371	+	0.814706i	−0.999426	−	0.0338816i	$-0.989213\pi$
$367$	−9.01100	+	15.6075i	−0.470371	+	0.814706i	0.529055	+	0.848587i	$0.322546\pi$
$368$		0			0
$369$	−14.0110	−	24.2678i	−0.729384	−	1.26333i
$370$		0			0
$371$	−0.802700	−	0.0755997i	−0.0416741	−	0.00392494i
$372$		0			0
$373$	−14.4582	−	25.0424i	−0.748618	−	1.29664i	−0.948485	−	0.316822i	$-0.897384\pi$
$373$	−14.4582	−	25.0424i	−0.748618	−	1.29664i	0.199867	−	0.979823i	$-0.435949\pi$
$374$		0			0
$375$	4.04290	−	7.00250i	0.208774	−	0.361608i
$376$		0			0
$377$	5.42184			0.279239
$378$		0			0
$379$	−4.30847			−0.221311			−0.110656	−	0.993859i	$-0.535295\pi$
$379$	−4.30847			−0.221311			−0.110656	+	0.993859i	$0.535295\pi$
$380$		0			0
$381$	−4.41591	+	7.64857i	−0.226234	+	0.391848i
$382$		0			0
$383$	−6.17438	−	10.6943i	−0.315496	−	0.546455i	0.664047	−	0.747691i	$-0.268837\pi$
$383$	−6.17438	−	10.6943i	−0.315496	−	0.546455i	−0.979543	+	0.201236i	$0.935504\pi$
$384$		0			0
$385$	2.42969	+	5.30210i	0.123829	+	0.270220i
$386$		0			0
$387$	−6.56117	−	11.3643i	−0.333523	−	0.577679i
$388$		0			0
$389$	−14.7115	+	25.4811i	−0.745903	+	1.29194i	0.203869	+	0.978998i	$0.434648\pi$
$389$	−14.7115	+	25.4811i	−0.745903	+	1.29194i	−0.949772	+	0.312943i	$0.898685\pi$
$390$		0			0
$391$	−9.67699			−0.489387
$392$		0			0
$393$	−0.541613			−0.0273208
$394$		0			0
$395$	5.10482	−	8.84180i	0.256851	−	0.444879i
$396$		0			0
$397$	8.64975	+	14.9818i	0.434119	+	0.751915i	0.997223	−	0.0744702i	$-0.0237266\pi$
$397$	8.64975	+	14.9818i	0.434119	+	0.751915i	−0.563105	+	0.826386i	$0.690393\pi$
$398$		0			0
$399$	5.44070	+	11.8727i	0.272376	+	0.594381i
$400$		0			0
$401$	12.4752	+	21.6077i	0.622982	+	1.07904i	0.988927	+	0.148400i	$0.0474124\pi$
$401$	12.4752	+	21.6077i	0.622982	+	1.07904i	−0.365945	+	0.930636i	$0.619254\pi$
$402$		0			0
$403$	3.86200	−	6.68919i	0.192380	−	0.333212i
$404$		0			0
$405$	10.3100			0.512306
$406$		0			0
$407$	−5.55465			−0.275334
$408$		0			0
$409$	19.2792	−	33.3925i	0.953295	−	1.65115i	0.215072	−	0.976598i	$-0.431001\pi$
$409$	19.2792	−	33.3925i	0.953295	−	1.65115i	0.738223	−	0.674557i	$-0.235665\pi$
$410$		0			0
$411$	2.08393	+	3.60947i	0.102793	+	0.178042i
$412$		0			0
$413$	−33.3443	−	3.14042i	−1.64076	−	0.154530i
$414$		0			0
$415$	−2.13409	−	3.69636i	−0.104759	−	0.181447i
$416$		0			0
$417$	−1.98825	+	3.44374i	−0.0973648	+	0.168641i
$418$		0			0
$419$	−0.908970			−0.0444061			−0.0222030	−	0.999753i	$-0.507068\pi$
$419$	−0.908970			−0.0444061			−0.0222030	+	0.999753i	$0.507068\pi$
$420$		0			0
$421$	15.5532			0.758014			0.379007	−	0.925394i	$-0.376266\pi$
$421$	15.5532			0.758014			0.379007	+	0.925394i	$0.376266\pi$
$422$		0			0
$423$	−1.85677	+	3.21602i	−0.0902792	+	0.156368i
$424$		0			0
$425$	0.104818	+	0.181550i	0.00508442	+	0.00880647i
$426$		0			0
$427$	−19.8866	+	28.0035i	−0.962381	+	1.35519i
$428$		0			0
$429$	1.17251	+	2.03084i	0.0566092	+	0.0980500i
$430$		0			0
$431$	1.76819	−	3.06259i	0.0851707	−	0.147520i	−0.820293	−	0.571943i	$-0.806190\pi$
$431$	1.76819	−	3.06259i	0.0851707	−	0.147520i	0.905464	+	0.424423i	$0.139523\pi$
$432$		0			0
$433$	17.6457			0.847997			0.423999	−	0.905663i	$-0.360626\pi$
$433$	17.6457			0.847997			0.423999	+	0.905663i	$0.360626\pi$
$434$		0			0
$435$	−2.59493			−0.124417
$436$		0			0
$437$	22.4517	−	38.8875i	1.07401	−	1.86024i
$438$		0			0
$439$	7.51362	+	13.0140i	0.358606	+	0.621123i	0.987728	−	0.156183i	$-0.0499190\pi$
$439$	7.51362	+	13.0140i	0.358606	+	0.621123i	−0.629123	+	0.777306i	$0.716586\pi$
$440$		0			0
$441$	−17.1294	−	3.25544i	−0.815688	−	0.155021i
$442$		0			0
$443$	6.61134	+	11.4512i	0.314114	+	0.544062i	0.979249	−	0.202662i	$-0.0649592\pi$
$443$	6.61134	+	11.4512i	0.314114	+	0.544062i	−0.665135	+	0.746723i	$0.731626\pi$
$444$		0			0
$445$	−3.53189	+	6.11742i	−0.167428	+	0.289994i
$446$		0			0
$447$	−0.713538			−0.0337492
$448$		0			0
$449$	−9.90864			−0.467617			−0.233809	−	0.972283i	$-0.575119\pi$
$449$	−9.90864			−0.467617			−0.233809	+	0.972283i	$0.575119\pi$
$450$		0			0
$451$	5.62496	−	9.74271i	0.264869	−	0.458766i
$452$		0			0
$453$	5.29485	+	9.17095i	0.248774	+	0.430889i
$454$		0			0
$455$	−11.0981	+	15.6279i	−0.520286	+	0.732646i
$456$		0			0
$457$	−5.17251	−	8.95905i	−0.241960	−	0.419087i	0.719313	−	0.694686i	$-0.244457\pi$
$457$	−5.17251	−	8.95905i	−0.241960	−	0.419087i	−0.961272	+	0.275600i	$0.911124\pi$
$458$		0			0
$459$	2.92056	−	5.05855i	0.136320	−	0.236113i
$460$		0			0
$461$	−15.3372			−0.714325			−0.357163	−	0.934042i	$-0.616256\pi$
$461$	−15.3372			−0.714325			−0.357163	+	0.934042i	$0.616256\pi$
$462$		0			0
$463$	25.1313			1.16795			0.583976	−	0.811771i	$-0.301496\pi$
$463$	25.1313			1.16795			0.583976	+	0.811771i	$0.301496\pi$
$464$		0			0
$465$	−1.84838	+	3.20149i	−0.0857167	+	0.148466i
$466$		0			0
$467$	−0.373007	−	0.646068i	−0.0172607	−	0.0298964i	0.857266	−	0.514874i	$-0.172161\pi$
$467$	−0.373007	−	0.646068i	−0.0172607	−	0.0298964i	−0.874527	+	0.484977i	$0.838828\pi$
$468$		0			0
$469$	−12.0455	−	1.13447i	−0.556210	−	0.0523848i
$470$		0			0
$471$	−2.27994	−	3.94898i	−0.105054	−	0.181959i
$472$		0			0
$473$	2.63409	−	4.56239i	0.121116	−	0.209779i
$474$		0			0
$475$	−0.972758			−0.0446332
$476$		0			0
$477$	−0.759053			−0.0347546
$478$		0			0
$479$	−10.0565	+	17.4184i	−0.459494	+	0.795867i	−0.998934	−	0.0461569i	$-0.985303\pi$
$479$	−10.0565	+	17.4184i	−0.459494	+	0.795867i	0.539440	+	0.842024i	$0.318636\pi$
$480$		0			0
$481$	−9.12758	−	15.8094i	−0.416182	−	0.720848i
$482$		0			0
$483$	−5.10482	−	11.1398i	−0.232277	−	0.506878i
$484$		0			0
$485$	−2.04942	−	3.54969i	−0.0930592	−	0.161183i
$486$		0			0
$487$	−2.12496	+	3.68054i	−0.0962911	+	0.166781i	−0.910147	−	0.414286i	$-0.864031\pi$
$487$	−2.12496	+	3.68054i	−0.0962911	+	0.166781i	0.813856	+	0.581067i	$0.197365\pi$
$488$		0			0
$489$	−7.09626			−0.320904
$490$		0			0
$491$	−30.3279			−1.36868			−0.684340	−	0.729163i	$-0.739909\pi$
$491$	−30.3279			−1.36868			−0.684340	+	0.729163i	$0.739909\pi$
$492$		0			0
$493$	1.22978	−	2.13003i	0.0553863	−	0.0959320i
$494$		0			0
$495$	2.74543	+	4.75523i	0.123398	+	0.213732i
$496$		0			0
$497$	−12.4843	−	27.2435i	−0.559999	−	1.22204i
$498$		0			0
$499$	7.22064	+	12.5065i	0.323240	+	0.559869i	0.981155	−	0.193224i	$-0.0618945\pi$
$499$	7.22064	+	12.5065i	0.323240	+	0.559869i	−0.657914	+	0.753093i	$0.728561\pi$
$500$		0			0
$501$	−0.692648	+	1.19970i	−0.0309452	+	0.0535987i
$502$		0			0
$503$	2.95822			0.131901			0.0659503	−	0.997823i	$-0.478992\pi$
$503$	2.95822			0.131901			0.0659503	+	0.997823i	$0.478992\pi$
$504$		0			0
$505$	13.3267			0.593032
$506$		0			0
$507$	0.784595	−	1.35896i	0.0348451	−	0.0603534i
$508$		0			0
$509$	12.4953	+	21.6426i	0.553847	+	0.959290i	0.997992	+	0.0633358i	$0.0201739\pi$
$509$	12.4953	+	21.6426i	0.553847	+	0.959290i	−0.444146	+	0.895955i	$0.646493\pi$
$510$		0			0
$511$	22.5681	+	2.12550i	0.998354	+	0.0940267i
$512$		0			0
$513$	13.5520	+	23.4728i	0.598337	+	1.03635i
$514$		0			0
$515$	−1.17251	+	2.03084i	−0.0516669	+	0.0894896i
$516$		0			0
$517$	−1.49086			−0.0655681
$518$		0			0
$519$	4.58970			0.201465
$520$		0			0
$521$	−14.4316	+	24.9962i	−0.632258	+	1.09510i	0.354831	+	0.934931i	$0.384538\pi$
$521$	−14.4316	+	24.9962i	−0.632258	+	1.09510i	−0.987089	+	0.160173i	$0.948795\pi$
$522$		0			0
$523$	0.236295	+	0.409276i	0.0103325	+	0.0178964i	0.871145	−	0.491025i	$-0.163378\pi$
$523$	0.236295	+	0.409276i	0.0103325	+	0.0178964i	−0.860813	+	0.508921i	$0.830044\pi$
$524$		0			0
$525$	−0.153700	+	0.216434i	−0.00670802	+	0.00944596i
$526$		0			0
$527$	−1.75195	−	3.03447i	−0.0763162	−	0.132184i
$528$		0			0
$529$	−9.56566	+	16.5682i	−0.415898	+	0.720357i
$530$		0			0
$531$	−31.5311			−1.36834
$532$		0			0
$533$	36.9724			1.60145
$534$		0			0
$535$	−6.97911	+	12.0882i	−0.301733	+	0.522617i
$536$		0			0
$537$	−1.27936	−	2.21592i	−0.0552085	−	0.0956239i
$538$		0			0
$539$	−2.30660	−	6.60905i	−0.0993524	−	0.284672i
$540$		0			0
$541$	−7.72978	−	13.3884i	−0.332329	−	0.575611i	0.650639	−	0.759387i	$-0.274501\pi$
$541$	−7.72978	−	13.3884i	−0.332329	−	0.575611i	−0.982968	+	0.183776i	$0.941168\pi$
$542$		0			0
$543$	−4.35735	+	7.54715i	−0.186992	+	0.323879i
$544$		0			0
$545$	−6.20290			−0.265703
$546$		0			0
$547$	35.0440			1.49837			0.749187	−	0.662359i	$-0.230444\pi$
$547$	35.0440			1.49837			0.749187	+	0.662359i	$0.230444\pi$
$548$		0			0
$549$	−16.1679	+	28.0035i	−0.690027	+	1.19516i
$550$		0			0
$551$	5.70644	+	9.88384i	0.243102	+	0.421066i
$552$		0			0
$553$	−7.09493	+	9.99080i	−0.301707	+	0.424852i
$554$		0			0
$555$	4.36852	+	7.56650i	0.185433	+	0.321180i
$556$		0			0
$557$	−5.26632	+	9.12154i	−0.223141	+	0.386492i	−0.955760	−	0.294147i	$-0.904964\pi$
$557$	−5.26632	+	9.12154i	−0.223141	+	0.386492i	0.732619	+	0.680639i	$0.238298\pi$
$558$		0			0
$559$	17.3137			0.732292
$560$		0			0
$561$	1.06379			0.0449132
$562$		0			0
$563$	−15.3574	+	26.5997i	−0.647235	+	1.12104i	0.336545	+	0.941667i	$0.390742\pi$
$563$	−15.3574	+	26.5997i	−0.647235	+	1.12104i	−0.983780	+	0.179377i	$0.942592\pi$
$564$		0			0
$565$	14.0573	+	24.3479i	0.591394	+	1.02432i
$566$		0			0
$567$	−12.3196	−	1.16028i	−0.517376	−	0.0487274i
$568$		0			0
$569$	15.3860	+	26.6494i	0.645017	+	1.11720i	0.984298	+	0.176516i	$0.0564829\pi$
$569$	15.3860	+	26.6494i	0.645017	+	1.11720i	−0.339281	+	0.940685i	$0.610184\pi$
$570$		0			0
$571$	−3.75847	+	6.50986i	−0.157287	+	0.272429i	−0.933889	−	0.357562i	$-0.883608\pi$
$571$	−3.75847	+	6.50986i	−0.157287	+	0.272429i	0.776602	+	0.629991i	$0.216941\pi$
$572$		0			0
$573$	−8.64045			−0.360960
$574$		0			0
$575$	0.912705			0.0380624
$576$		0			0
$577$	−13.8092	+	23.9183i	−0.574885	+	0.995731i	0.421169	+	0.906982i	$0.361620\pi$
$577$	−13.8092	+	23.9183i	−0.574885	+	0.995731i	−0.996054	+	0.0887483i	$0.971713\pi$
$578$		0			0
$579$	4.25980	+	7.37819i	0.177031	+	0.306627i
$580$		0			0
$581$	2.13409	+	4.65704i	0.0885372	+	0.193207i
$582$		0			0
$583$	−0.152367	−	0.263908i	−0.00631041	−	0.0109300i
$584$		0			0
$585$	−9.02276	+	15.6279i	−0.373045	+	0.646133i
$586$		0			0
$587$	29.9582			1.23651			0.618254	−	0.785978i	$-0.287840\pi$
$587$	29.9582			1.23651			0.618254	+	0.785978i	$0.287840\pi$
$588$		0			0
$589$	16.2589			0.669936
$590$		0			0
$591$	−4.33925	+	7.51579i	−0.178493	+	0.309158i
$592$		0			0
$593$	−6.33401	−	10.9708i	−0.260107	−	0.450518i	0.706163	−	0.708049i	$-0.250424\pi$
$593$	−6.33401	−	10.9708i	−0.260107	−	0.450518i	−0.966270	+	0.257531i	$0.917091\pi$
$594$		0			0
$595$	3.62234	+	7.90471i	0.148502	+	0.324062i
$596$		0			0
$597$	0.679610	+	1.17712i	0.0278146	+	0.0481762i
$598$		0			0
$599$	0.647133	−	1.12087i	0.0264411	−	0.0457974i	−0.852502	−	0.522724i	$-0.824916\pi$
$599$	0.647133	−	1.12087i	0.0264411	−	0.0457974i	0.878943	+	0.476926i	$0.158249\pi$
$600$		0			0
$601$	−41.0220			−1.67332			−0.836661	−	0.547721i	$-0.815496\pi$
$601$	−41.0220			−1.67332			−0.836661	+	0.547721i	$0.815496\pi$
$602$		0			0
$603$	−11.3905			−0.463858
$604$		0			0
$605$	−1.10220	+	1.90907i	−0.0448108	+	0.0776146i
$606$		0			0
$607$	−10.5884	−	18.3397i	−0.429770	−	0.744384i	0.567082	−	0.823661i	$-0.308072\pi$
$607$	−10.5884	−	18.3397i	−0.429770	−	0.744384i	−0.996853	+	0.0792770i	$0.974739\pi$
$608$		0			0
$609$	3.10075	+	0.292034i	0.125649	+	0.0118338i
$610$		0			0
$611$	−2.44983	−	4.24324i	−0.0991096	−	0.171663i
$612$		0			0
$613$	−3.38156	+	5.85704i	−0.136580	+	0.236563i	−0.926200	−	0.377033i	$-0.876944\pi$
$613$	−3.38156	+	5.85704i	−0.136580	+	0.236563i	0.789620	+	0.613596i	$0.210278\pi$
$614$		0			0
$615$	−17.6953			−0.713542
$616$		0			0
$617$	−41.0728			−1.65353			−0.826763	−	0.562550i	$-0.809820\pi$
$617$	−41.0728			−1.65353			−0.826763	+	0.562550i	$0.809820\pi$
$618$		0			0
$619$	−15.2134	+	26.3503i	−0.611477	+	1.05911i	0.379515	+	0.925186i	$0.376091\pi$
$619$	−15.2134	+	26.3503i	−0.611477	+	1.05911i	−0.990992	+	0.133924i	$0.957242\pi$
$620$		0			0
$621$	−12.7154	−	22.0237i	−0.510252	−	0.883782i
$622$		0			0
$623$	4.90880	−	6.91238i	0.196667	−	0.276939i
$624$		0			0
$625$	12.1386	+	21.0246i	0.485543	+	0.840985i
$626$		0			0
$627$	−2.46811	+	4.27489i	−0.0985667	+	0.170722i
$628$		0			0
$629$	−8.28123			−0.330194
$630$		0			0
$631$	−12.3670			−0.492323			−0.246162	−	0.969229i	$-0.579169\pi$
$631$	−12.3670			−0.492323			−0.246162	+	0.969229i	$0.579169\pi$
$632$		0			0
$633$	−5.79560	+	10.0383i	−0.230354	+	0.398985i
$634$		0			0
$635$	−13.6425	−	23.6295i	−0.541385	−	0.937707i
$636$		0			0
$637$	15.0201	−	17.4252i	0.595120	−	0.690410i
$638$		0			0
$639$	−14.1067	−	24.4335i	−0.558052	−	0.966574i
$640$		0			0
$641$	23.5657	−	40.8169i	0.930787	−	1.61217i	0.148809	−	0.988866i	$-0.452456\pi$
$641$	23.5657	−	40.8169i	0.930787	−	1.61217i	0.781979	−	0.623305i	$-0.214211\pi$
$642$		0			0
$643$	−1.87242			−0.0738412			−0.0369206	−	0.999318i	$-0.511755\pi$
$643$	−1.87242			−0.0738412			−0.0369206	+	0.999318i	$0.511755\pi$
$644$		0			0
$645$	−8.28646			−0.326279
$646$		0			0
$647$	−0.917939	+	1.58992i	−0.0360879	+	0.0625061i	−0.883505	−	0.468421i	$-0.844823\pi$
$647$	−0.917939	+	1.58992i	−0.0360879	+	0.0625061i	0.847417	+	0.530927i	$0.178156\pi$
$648$		0			0
$649$	−6.32936	−	10.9628i	−0.248449	−	0.430326i
$650$		0			0
$651$	2.56897	−	3.61753i	0.100686	−	0.141782i
$652$		0			0
$653$	9.08858	+	15.7419i	0.355664	+	0.616027i	0.987231	−	0.159293i	$-0.0509216\pi$
$653$	9.08858	+	15.7419i	0.355664	+	0.616027i	−0.631568	+	0.775321i	$0.717588\pi$
$654$		0			0
$655$	0.836629	−	1.44908i	0.0326898	−	0.0566204i
$656$		0			0
$657$	21.3409			0.832590
$658$		0			0
$659$	16.8997			0.658318			0.329159	−	0.944275i	$-0.393235\pi$
$659$	16.8997			0.658318			0.329159	+	0.944275i	$0.393235\pi$
$660$		0			0
$661$	22.6516	−	39.2338i	0.881046	−	1.52602i	0.0308661	−	0.999524i	$-0.490173\pi$
$661$	22.6516	−	39.2338i	0.881046	−	1.52602i	0.850180	−	0.526493i	$-0.176493\pi$
$662$		0			0
$663$	1.74805	+	3.02771i	0.0678886	+	0.117587i
$664$		0			0
$665$	−40.1697	−	3.78325i	−1.55772	−	0.146708i
$666$		0			0
$667$	−5.35415	−	9.27366i	−0.207314	−	0.359078i
$668$		0			0
$669$	1.08335	−	1.87641i	0.0418845	−	0.0725462i
$670$		0			0
$671$	−12.9817			−0.501154
$672$		0			0
$673$	39.5076			1.52291			0.761454	−	0.648219i	$-0.224486\pi$
$673$	39.5076			1.52291			0.761454	+	0.648219i	$0.224486\pi$
$674$		0			0
$675$	−0.275458	+	0.477108i	−0.0106024	+	0.0183639i
$676$		0			0
$677$	17.0669	+	29.5608i	0.655936	+	1.13611i	0.981658	+	0.190649i	$0.0610591\pi$
$677$	17.0669	+	29.5608i	0.655936	+	1.13611i	−0.325723	+	0.945465i	$0.605608\pi$
$678$		0			0
$679$	2.04942	+	4.47226i	0.0786494	+	0.171630i
$680$		0			0
$681$	6.58206	+	11.4005i	0.252225	+	0.436867i
$682$		0			0
$683$	11.8931	−	20.5995i	0.455079	−	0.788219i	−0.543614	−	0.839335i	$-0.682944\pi$
$683$	11.8931	−	20.5995i	0.455079	−	0.788219i	0.998693	+	0.0511160i	$0.0162778\pi$
$684$		0			0
$685$	−12.8762			−0.491973
$686$		0			0
$687$	−18.1951			−0.694186
$688$		0			0
$689$	0.500750	−	0.867324i	0.0190770	−	0.0330424i
$690$		0			0
$691$	−10.2812	−	17.8076i	−0.391116	−	0.677433i	0.601481	−	0.798887i	$-0.294578\pi$
$691$	−10.2812	−	17.8076i	−0.391116	−	0.677433i	−0.992597	+	0.121454i	$0.961244\pi$
$692$		0			0
$693$	−2.74543	−	5.99111i	−0.104290	−	0.227584i
$694$		0			0
$695$	−6.14248	−	10.6391i	−0.232998	−	0.403564i
$696$		0			0
$697$	8.38605	−	14.5251i	0.317644	−	0.550176i
$698$		0			0
$699$	2.72401			0.103031
$700$		0			0
$701$	−23.9907			−0.906116			−0.453058	−	0.891481i	$-0.649667\pi$
$701$	−23.9907			−0.906116			−0.453058	+	0.891481i	$0.649667\pi$
$702$		0			0
$703$	19.2134	−	33.2785i	0.724646	−	1.25512i
$704$		0			0
$705$	1.17251	+	2.03084i	0.0441592	+	0.0764860i
$706$		0			0
$707$	−15.9245	−	1.49979i	−0.598901	−	0.0564055i
$708$		0			0
$709$	25.8559	+	44.7836i	0.971037	+	1.68189i	0.692437	+	0.721478i	$0.256537\pi$
$709$	25.8559	+	44.7836i	0.971037	+	1.68189i	0.278599	+	0.960407i	$0.410130\pi$
$710$		0			0
$711$	−5.76819	+	9.99080i	−0.216324	+	0.374684i
$712$		0			0
$713$	−15.2552			−0.571310
$714$		0			0
$715$	−7.24468			−0.270936
$716$		0			0
$717$	4.63933	−	8.03555i	0.173259	−	0.300093i
$718$		0			0
$719$	12.8926	+	22.3306i	0.480812	+	0.832790i	0.999758	−	0.0220170i	$-0.00700879\pi$
$719$	12.8926	+	22.3306i	0.480812	+	0.832790i	−0.518946	+	0.854807i	$0.673675\pi$
$720$		0			0
$721$	1.62961	−	2.29475i	0.0606898	−	0.0854610i
$722$		0			0
$723$	0.160754	+	0.278434i	0.00597851	+	0.0103551i
$724$		0			0
$725$	−0.115989	+	0.200899i	−0.00430772	+	0.00746118i
$726$		0			0
$727$	−32.7330			−1.21400			−0.606999	−	0.794702i	$-0.707627\pi$
$727$	−32.7330			−1.21400			−0.606999	+	0.794702i	$0.707627\pi$
$728$		0			0
$729$	−3.26295			−0.120850
$730$		0			0
$731$	3.92708	−	6.80189i	0.145248	−	0.251577i
$732$		0			0
$733$	4.64136	+	8.03908i	0.171433	+	0.296930i	0.938921	−	0.344133i	$-0.111827\pi$
$733$	4.64136	+	8.03908i	0.171433	+	0.296930i	−0.767488	+	0.641063i	$0.778494\pi$
$734$		0			0
$735$	−7.18875	+	8.33981i	−0.265161	+	0.307618i
$736$		0			0
$737$	−2.28646	−	3.96027i	−0.0842229	−	0.145878i
$738$		0			0
$739$	−25.0466	+	43.3820i	−0.921355	+	1.59583i	−0.124035	+	0.992278i	$0.539583\pi$
$739$	−25.0466	+	43.3820i	−0.921355	+	1.59583i	−0.797320	+	0.603556i	$0.793750\pi$
$740$		0			0
$741$	−16.2227			−0.595955
$742$		0			0
$743$	−13.1679			−0.483082			−0.241541	−	0.970391i	$-0.577653\pi$
$743$	−13.1679			−0.483082			−0.241541	+	0.970391i	$0.577653\pi$
$744$		0			0
$745$	1.10220	−	1.90907i	0.0403815	−	0.0699428i
$746$		0			0
$747$	2.41142	+	4.17670i	0.0882293	+	0.152818i
$748$		0			0
$749$	9.69992	−	13.6590i	0.354427	−	0.499090i
$750$		0			0
$751$	20.6569	+	35.7787i	0.753779	+	1.30558i	0.945979	+	0.324228i	$0.105105\pi$
$751$	20.6569	+	35.7787i	0.753779	+	1.30558i	−0.192200	+	0.981356i	$0.561562\pi$
$752$		0			0
$753$	0.399084	−	0.691234i	0.0145434	−	0.0251900i
$754$		0			0
$755$	−32.7158			−1.19065
$756$		0			0
$757$	−45.5114			−1.65414			−0.827069	−	0.562100i	$-0.809994\pi$
$757$	−45.5114			−1.65414			−0.827069	+	0.562100i	$0.809994\pi$
$758$		0			0
$759$	2.31574	−	4.01098i	0.0840560	−	0.145589i
$760$		0			0
$761$	−15.6360	−	27.0823i	−0.566803	−	0.981732i	−0.996879	−	0.0789393i	$-0.974847\pi$
$761$	−15.6360	−	27.0823i	−0.566803	−	0.981732i	0.430076	−	0.902793i	$-0.358487\pi$
$762$		0			0
$763$	7.41200	+	0.698075i	0.268333	+	0.0252720i
$764$		0			0
$765$	4.09306	+	7.08940i	0.147985	+	0.256318i
$766$		0			0
$767$	20.8012	−	36.0287i	0.751088	−	1.30092i
$768$		0			0
$769$	42.0467			1.51624			0.758121	−	0.652114i	$-0.226118\pi$
$769$	42.0467			1.51624			0.758121	+	0.652114i	$0.226118\pi$
$770$		0			0
$771$	−16.2969			−0.586920
$772$		0			0
$773$	−3.82226	+	6.62034i	−0.137477	+	0.238117i	−0.926541	−	0.376194i	$-0.877233\pi$
$773$	−3.82226	+	6.62034i	−0.137477	+	0.238117i	0.789064	+	0.614311i	$0.210566\pi$
$774$		0			0
$775$	0.165239	+	0.286202i	0.00593555	+	0.0102807i
$776$		0			0
$777$	−4.36852	−	9.53304i	−0.156720	−	0.341996i
$778$		0			0
$779$	38.9131	+	67.3995i	1.39421	+	2.41484i
$780$		0			0
$781$	5.66337	−	9.80925i	0.202651	−	0.351002i
$782$		0			0
$783$	6.46362			0.230991
$784$		0			0
$785$	14.0873			0.502797
$786$		0			0
$787$	−13.9517	+	24.1651i	−0.497324	+	0.861391i	−0.999995	−	0.00308674i	$-0.999017\pi$
$787$	−13.9517	+	24.1651i	−0.497324	+	0.861391i	0.502671	+	0.864478i	$0.332351\pi$
$788$		0			0
$789$	−3.27919	−	5.67973i	−0.116742	−	0.202204i
$790$		0			0
$791$	−14.0573	−	30.6759i	−0.499819	−	1.09071i
$792$		0			0
$793$	−21.3320	−	36.9481i	−0.757521	−	1.31206i
$794$		0			0
$795$	−0.239662	+	0.415107i	−0.00849995	+	0.0147223i
$796$		0			0
$797$	10.0560			0.356201			0.178101	−	0.984012i	$-0.443005\pi$
$797$	10.0560			0.356201			0.178101	+	0.984012i	$0.443005\pi$
$798$		0			0
$799$	−2.22267			−0.0786326
$800$		0			0
$801$	3.99086	−	6.91238i	0.141010	−	0.244237i
$802$		0			0
$803$	4.28384	+	7.41984i	0.151174	+	0.261840i
$804$		0			0
$805$	37.6899	+	3.54969i	1.32839	+	0.125110i
$806$		0			0
$807$	5.57031	+	9.64805i	0.196084	+	0.339628i
$808$		0			0
$809$	−19.2863	+	33.4048i	−0.678070	+	1.17445i	0.297491	+	0.954725i	$0.403850\pi$
$809$	−19.2863	+	33.4048i	−0.678070	+	1.17445i	−0.975561	+	0.219727i	$0.929483\pi$
$810$		0			0
$811$	−12.3760			−0.434580			−0.217290	−	0.976107i	$-0.569722\pi$
$811$	−12.3760			−0.434580			−0.217290	+	0.976107i	$0.569722\pi$
$812$		0			0
$813$	−19.7968			−0.694303
$814$		0			0
$815$	10.9616	−	18.9860i	0.383968	−	0.665051i
$816$		0			0
$817$	18.2225	+	31.5623i	0.637525	+	1.10423i
$818$		0			0
$819$	12.5403	−	17.6587i	0.438193	−	0.617046i
$820$		0			0
$821$	−14.8691	−	25.7540i	−0.518934	−	0.898820i	−0.999758	−	0.0220025i	$-0.992996\pi$
$821$	−14.8691	−	25.7540i	−0.518934	−	0.898820i	0.480824	−	0.876817i	$-0.340338\pi$
$822$		0			0
$823$	20.3885	−	35.3139i	0.710698	−	1.23097i	−0.253897	−	0.967231i	$-0.581712\pi$
$823$	20.3885	−	35.3139i	0.710698	−	1.23097i	0.964595	−	0.263734i	$-0.0849542\pi$
$824$		0			0
$825$	−0.100333			−0.00349316
$826$		0			0
$827$	18.8411			0.655170			0.327585	−	0.944822i	$-0.393765\pi$
$827$	18.8411			0.655170			0.327585	+	0.944822i	$0.393765\pi$
$828$		0			0
$829$	15.5703	−	26.9686i	0.540779	−	0.936657i	−0.458080	−	0.888911i	$-0.651463\pi$
$829$	15.5703	−	26.9686i	0.540779	−	0.936657i	0.998860	−	0.0477461i	$-0.0152038\pi$
$830$		0			0
$831$	−5.28459	−	9.15319i	−0.183321	−	0.317521i
$832$		0			0
$833$	−3.43883	−	9.85320i	−0.119148	−	0.341393i
$834$		0			0
$835$	−2.13986	−	3.70635i	−0.0740530	−	0.128264i
$836$		0			0
$837$	4.60407	−	7.97448i	0.159140	−	0.275638i
$838$		0			0
$839$	−10.2589			−0.354176			−0.177088	−	0.984195i	$-0.556668\pi$
$839$	−10.2589			−0.354176			−0.177088	+	0.984195i	$0.556668\pi$
$840$		0			0
$841$	−26.2783			−0.906149
$842$		0			0
$843$	−5.43098	+	9.40673i	−0.187053	+	0.323985i
$844$		0			0
$845$	2.42392	+	4.19836i	0.0833855	+	0.144428i
$846$		0			0
$847$	1.53189	−	2.15715i	0.0526365	−	0.0741206i
$848$		0			0
$849$	7.74805	+	13.4200i	0.265912	+	0.460574i
$850$		0			0
$851$	−18.0272	+	31.2241i	−0.617966	+	1.07035i
$852$		0			0
$853$	3.04435			0.104237			0.0521183	−	0.998641i	$-0.483403\pi$
$853$	3.04435			0.104237			0.0521183	+	0.998641i	$0.483403\pi$
$854$		0			0
$855$	−37.9855			−1.29908
$856$		0			0
$857$	−24.7766	+	42.9143i	−0.846352	+	1.46592i	0.0380904	+	0.999274i	$0.487873\pi$
$857$	−24.7766	+	42.9143i	−0.846352	+	1.46592i	−0.884442	+	0.466650i	$0.845461\pi$
$858$		0			0
$859$	18.4373	+	31.9344i	0.629074	+	1.08959i	0.987738	+	0.156121i	$0.0498989\pi$
$859$	18.4373	+	31.9344i	0.629074	+	1.08959i	−0.358664	+	0.933467i	$0.616768\pi$
$860$		0			0
$861$	21.1445	+	1.99143i	0.720603	+	0.0678676i
$862$		0			0
$863$	−23.2115	−	40.2035i	−0.790129	−	1.36854i	−0.925887	−	0.377801i	$-0.876680\pi$
$863$	−23.2115	−	40.2035i	−0.790129	−	1.36854i	0.135758	−	0.990742i	$-0.456653\pi$
$864$		0			0
$865$	−7.08970	+	12.2797i	−0.241057	+	0.417523i
$866$		0			0
$867$	−10.5442			−0.358099
$868$		0			0
$869$	−4.63148			−0.157112
$870$		0			0
$871$	7.51437	−	13.0153i	0.254615	−	0.441006i
$872$		0			0
$873$	2.31574	+	4.01098i	0.0783759	+	0.135751i
$874$		0			0
$875$	−12.4901	−	27.2561i	−0.422243	−	0.921423i
$876$		0			0
$877$	−19.5155	−	33.8018i	−0.658991	−	1.14141i	−0.980877	−	0.194628i	$-0.937650\pi$
$877$	−19.5155	−	33.8018i	−0.658991	−	1.14141i	0.321886	−	0.946778i	$-0.395683\pi$
$878$		0			0
$879$	−3.96997	+	6.87620i	−0.133904	+	0.231928i
$880$		0			0
$881$	−44.0049			−1.48256			−0.741281	−	0.671194i	$-0.765782\pi$
$881$	−44.0049			−1.48256			−0.741281	+	0.671194i	$0.765782\pi$
$882$		0			0
$883$	23.3596			0.786112			0.393056	−	0.919515i	$-0.371418\pi$
$883$	23.3596			0.786112			0.393056	+	0.919515i	$0.371418\pi$
$884$		0			0
$885$	−9.95560	+	17.2436i	−0.334654	+	0.579638i
$886$		0			0
$887$	20.9588	+	36.3017i	0.703728	+	1.21889i	0.967149	+	0.254211i	$0.0818158\pi$
$887$	20.9588	+	36.3017i	0.703728	+	1.21889i	−0.263421	+	0.964681i	$0.584851\pi$
$888$		0			0
$889$	13.6425	+	29.7708i	0.457554	+	0.998480i
$890$		0			0
$891$	−2.33850	−	4.05039i	−0.0783426	−	0.135693i
$892$		0			0
$893$	5.15685	−	8.93193i	0.172567	−	0.298896i
$894$		0			0
$895$	7.90490			0.264232
$896$		0			0
$897$	15.2212			0.508220
$898$		0			0
$899$	1.93866	−	3.35786i	0.0646580	−	0.111991i
$900$		0			0
$901$	−0.227159	−	0.393451i	−0.00756776	−	0.0131078i
$902$		0			0
$903$	9.90170	+	0.932559i	0.329508	+	0.0310336i
$904$		0			0
$905$	−13.4616	−	23.3162i	−0.447478	−	0.775055i
$906$		0			0
$907$	−10.2591	+	17.7692i	−0.340646	+	0.590017i	−0.984553	−	0.175087i	$-0.943979\pi$
$907$	−10.2591	+	17.7692i	−0.340646	+	0.590017i	0.643907	+	0.765104i	$0.277313\pi$
$908$		0			0
$909$	−15.0586			−0.499461
$910$		0			0
$911$	−27.6755			−0.916930			−0.458465	−	0.888712i	$-0.651601\pi$
$911$	−27.6755			−0.916930			−0.458465	+	0.888712i	$0.651601\pi$
$912$		0			0
$913$	−0.968106	+	1.67681i	−0.0320396	+	0.0554943i
$914$		0			0
$915$	10.2096	+	17.6836i	0.337520	+	0.584602i
$916$		0			0
$917$	−1.16279	+	1.63739i	−0.0383987	+	0.0540714i
$918$		0			0
$919$	0.481727	+	0.834376i	0.0158907	+	0.0275235i	0.873861	−	0.486175i	$-0.161608\pi$
$919$	0.481727	+	0.834376i	0.0158907	+	0.0275235i	−0.857971	+	0.513699i	$0.828275\pi$
$920$		0			0
$921$	8.91404	−	15.4396i	0.293728	−	0.508751i
$922$		0			0
$923$	37.2249			1.22527
$924$		0			0
$925$	0.781061			0.0256811
$926$		0			0
$927$	1.32488	−	2.29475i	0.0435146	−	0.0753695i
$928$		0			0
$929$	−13.1660	−	22.8042i	−0.431962	−	0.748180i	0.565080	−	0.825036i	$-0.308845\pi$
$929$	−13.1660	−	22.8042i	−0.431962	−	0.748180i	−0.997042	+	0.0768558i	$0.975512\pi$
$930$		0			0
$931$	47.5740	+	9.04140i	1.55918	+	0.296320i
$932$		0			0
$933$	12.3944	+	21.4678i	0.405775	+	0.702824i
$934$		0			0
$935$	−1.64323	+	2.84616i	−0.0537394	+	0.0930794i
$936$		0			0
$937$	−21.3865			−0.698665			−0.349333	−	0.936999i	$-0.613592\pi$
$937$	−21.3865			−0.698665			−0.349333	+	0.936999i	$0.613592\pi$
$938$		0			0
$939$	16.9176			0.552085
$940$		0			0
$941$	−7.41142	+	12.8370i	−0.241605	+	0.418473i	−0.961172	−	0.275951i	$-0.911007\pi$
$941$	−7.41142	+	12.8370i	−0.241605	+	0.418473i	0.719566	+	0.694424i	$0.244341\pi$
$942$		0			0
$943$	−36.5108	−	63.2386i	−1.18896	−	2.05933i
$944$		0			0
$945$	−13.2305	+	18.6307i	−0.430389	+	0.606056i
$946$		0			0
$947$	15.8560	+	27.4634i	0.515251	+	0.892442i	0.999843	+	0.0177013i	$0.00563478\pi$
$947$	15.8560	+	27.4634i	0.515251	+	0.892442i	−0.484592	+	0.874740i	$0.661032\pi$
$948$		0			0
$949$	−14.0787	+	24.3850i	−0.457014	+	0.791571i
$950$		0			0
$951$	14.0403			0.455287
$952$		0			0
$953$	49.9620			1.61843			0.809213	−	0.587515i	$-0.199894\pi$
$953$	49.9620			1.61843			0.809213	+	0.587515i	$0.199894\pi$
$954$		0			0
$955$	13.3469	−	23.1175i	0.431895	−	0.748064i
$956$		0			0
$957$	0.588580	+	1.01945i	0.0190261	+	0.0329541i
$958$		0			0
$959$	15.3860	+	1.44908i	0.496841	+	0.0467933i
$960$		0			0
$961$	12.7382	+	22.0631i	0.410908	+	0.711714i
$962$		0			0
$963$	7.88605	−	13.6590i	0.254124	−	0.440156i
$964$		0			0
$965$	−26.3204			−0.847285
$966$		0			0
$967$	52.4581			1.68694			0.843469	−	0.537178i	$-0.180510\pi$
$967$	52.4581			1.68694			0.843469	+	0.537178i	$0.180510\pi$
$968$		0			0
$969$	−3.67961	+	6.37327i	−0.118206	+	0.204739i
$970$		0			0
$971$	15.4133	+	26.6966i	0.494636	+	0.856735i	0.999981	−	0.00618284i	$-0.00196807\pi$
$971$	15.4133	+	26.6966i	0.494636	+	0.856735i	−0.505345	+	0.862917i	$0.668635\pi$
$972$		0			0
$973$	6.14248	+	13.4042i	0.196919	+	0.429719i
$974$		0			0
$975$	−0.164871	−	0.285565i	−0.00528009	−	0.00914538i
$976$		0			0
$977$	−12.3678	+	21.4216i	−0.395680	+	0.685338i	−0.993188	−	0.116525i	$-0.962824\pi$
$977$	−12.3678	+	21.4216i	−0.395680	+	0.685338i	0.597508	+	0.801863i	$0.296158\pi$
$978$		0			0
$979$	3.20440			0.102413
$980$		0			0
$981$	7.00897			0.223779
$982$		0			0
$983$	6.11192	−	10.5862i	0.194940	−	0.337646i	−0.751941	−	0.659231i	$-0.770882\pi$
$983$	6.11192	−	10.5862i	0.194940	−	0.337646i	0.946881	+	0.321585i	$0.104215\pi$
$984$		0			0
$985$	−13.4057	−	23.2193i	−0.427140	−	0.739827i
$986$		0			0
$987$	−1.17251	−	2.55866i	−0.0373213	−	0.0814430i
$988$		0			0
$989$	−17.0975	−	29.6138i	−0.543670	−	0.941665i
$990$		0			0
$991$	2.30008	−	3.98386i	0.0730645	−	0.126552i	−0.827178	−	0.561939i	$-0.810055\pi$
$991$	2.30008	−	3.98386i	0.0730645	−	0.126552i	0.900243	+	0.435388i	$0.143389\pi$
$992$		0			0
$993$	20.1145			0.638316
$994$		0			0
$995$	−4.19917			−0.133123
$996$		0			0
$997$	17.2382	−	29.8574i	0.545938	−	0.945593i	−0.452609	−	0.891709i	$-0.649507\pi$
$997$	17.2382	−	29.8574i	0.545938	−	0.945593i	0.998547	−	0.0538835i	$-0.0171600\pi$
$998$		0			0
$999$	−10.8814	−	18.8471i	−0.344272	−	0.596297i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.q.k.529.2		6
4.3	odd	2		77.2.e.b.67.3	yes	6
7.2	even	3	inner	1232.2.q.k.177.2		6
7.3	odd	6		8624.2.a.ck.1.2		3
7.4	even	3		8624.2.a.cl.1.2		3
12.11	even	2		693.2.i.g.298.1		6
28.3	even	6		539.2.a.i.1.1		3
28.11	odd	6		539.2.a.h.1.1		3
28.19	even	6		539.2.e.l.177.3		6
28.23	odd	6		77.2.e.b.23.3	✓	6
28.27	even	2		539.2.e.l.67.3		6
44.3	odd	10		847.2.n.e.130.3		24
44.7	even	10		847.2.n.d.753.3		24
44.15	odd	10		847.2.n.e.753.1		24
44.19	even	10		847.2.n.d.130.1		24
44.27	odd	10		847.2.n.e.487.1		24
44.31	odd	10		847.2.n.e.81.3		24
44.35	even	10		847.2.n.d.81.1		24
44.39	even	10		847.2.n.d.487.3		24
44.43	even	2		847.2.e.d.606.1		6
84.11	even	6		4851.2.a.bo.1.3		3
84.23	even	6		693.2.i.g.100.1		6
84.59	odd	6		4851.2.a.bn.1.3		3
308.51	even	30		847.2.n.d.632.1		24
308.79	even	30		847.2.n.d.807.3		24
308.87	odd	6		5929.2.a.w.1.3		3
308.107	even	30		847.2.n.d.9.3		24
308.135	odd	30		847.2.n.e.9.1		24
308.163	odd	30		847.2.n.e.807.1		24
308.191	odd	30		847.2.n.e.632.3		24
308.219	even	6		847.2.e.d.485.1		6
308.247	odd	30		847.2.n.e.366.3		24
308.263	even	6		5929.2.a.v.1.3		3
308.303	even	30		847.2.n.d.366.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.b.23.3	✓	6	28.23	odd	6
77.2.e.b.67.3	yes	6	4.3	odd	2
539.2.a.h.1.1		3	28.11	odd	6
539.2.a.i.1.1		3	28.3	even	6
539.2.e.l.67.3		6	28.27	even	2
539.2.e.l.177.3		6	28.19	even	6
693.2.i.g.100.1		6	84.23	even	6
693.2.i.g.298.1		6	12.11	even	2
847.2.e.d.485.1		6	308.219	even	6
847.2.e.d.606.1		6	44.43	even	2
847.2.n.d.9.3		24	308.107	even	30
847.2.n.d.81.1		24	44.35	even	10
847.2.n.d.130.1		24	44.19	even	10
847.2.n.d.366.1		24	308.303	even	30
847.2.n.d.487.3		24	44.39	even	10
847.2.n.d.632.1		24	308.51	even	30
847.2.n.d.753.3		24	44.7	even	10
847.2.n.d.807.3		24	308.79	even	30
847.2.n.e.9.1		24	308.135	odd	30
847.2.n.e.81.3		24	44.31	odd	10
847.2.n.e.130.3		24	44.3	odd	10
847.2.n.e.366.3		24	308.247	odd	30
847.2.n.e.487.1		24	44.27	odd	10
847.2.n.e.632.3		24	308.191	odd	30
847.2.n.e.753.1		24	44.15	odd	10
847.2.n.e.807.1		24	308.163	odd	30
1232.2.q.k.177.2		6	7.2	even	3	inner
1232.2.q.k.529.2		6	1.1	even	1	trivial
4851.2.a.bn.1.3		3	84.59	odd	6
4851.2.a.bo.1.3		3	84.11	even	6
5929.2.a.v.1.3		3	308.263	even	6
5929.2.a.w.1.3		3	308.87	odd	6
8624.2.a.ck.1.2		3	7.3	odd	6
8624.2.a.cl.1.2		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)

\(f(q)\)	\(=\)	\(q+(-0.356769 + 0.617942i) q^{3} +(-1.10220 - 1.90907i) q^{5} +(1.10220 + 2.40523i) q^{7} +(1.24543 + 2.15715i) q^{9} +O(q^{10})\)	\(q+(-0.356769 + 0.617942i) q^{3} +(-1.10220 - 1.90907i) q^{5} +(1.10220 + 2.40523i) q^{7} +(1.24543 + 2.15715i) q^{9} +(-0.500000 + 0.866025i) q^{11} -3.28646 q^{13} +1.57292 q^{15} +(-0.745432 + 1.29113i) q^{17} +(-3.45897 - 5.99111i) q^{19} +(-1.87953 - 0.177017i) q^{21} +(3.24543 + 5.62125i) q^{23} +(0.0703069 - 0.121775i) q^{25} -3.91794 q^{27} -1.64975 q^{29} +(-1.17512 + 2.03538i) q^{31} +(-0.356769 - 0.617942i) q^{33} +(3.37691 - 4.75523i) q^{35} +(2.77733 + 4.81047i) q^{37} +(1.17251 - 2.03084i) q^{39} -11.2499 q^{41} -5.26819 q^{43} +(2.74543 - 4.75523i) q^{45} +(0.745432 + 1.29113i) q^{47} +(-4.57031 + 5.30210i) q^{49} +(-0.531894 - 0.921267i) q^{51} +(-0.152367 + 0.263908i) q^{53} +2.20440 q^{55} +4.93621 q^{57} +(-6.32936 + 10.9628i) q^{59} +(6.49086 + 11.2425i) q^{61} +(-3.81574 + 5.37317i) q^{63} +(3.62234 + 6.27408i) q^{65} +(-2.28646 + 3.96027i) q^{67} -4.63148 q^{69} -11.3267 q^{71} +(4.28384 - 7.41984i) q^{73} +(0.0501666 + 0.0868912i) q^{75} +(-2.63409 - 0.248083i) q^{77} +(2.31574 + 4.01098i) q^{79} +(-2.33850 + 4.05039i) q^{81} +1.93621 q^{83} +3.28646 q^{85} +(0.588580 - 1.01945i) q^{87} +(-1.60220 - 2.77509i) q^{89} +(-3.62234 - 7.90471i) q^{91} +(-0.838496 - 1.45232i) q^{93} +(-7.62496 + 13.2068i) q^{95} +1.85939 q^{97} -2.49086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{3} + 2 q^{5} - 2 q^{7}+O(q^{10}) \) 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

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