LMFDB - Embedded newform 1440.2.cc.a.1391.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1440,2,Mod(911,1440)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1440, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))

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

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

chi := DirichletCharacter("1440.911");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1440 = 2^{5} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1440.cc (of order $6$, 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:	$11.4984578911$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 360)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1391.6
Character	$\chi$	$=$	1440.1391
Dual form			1440.2.cc.a.911.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36390 + 1.06761i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-1.02179 + 0.589933i) q^{7} +(0.720424 - 2.91221i) q^{9} +O(q^{10})$	\(q+(-1.36390 + 1.06761i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-1.02179 + 0.589933i) q^{7} +(0.720424 - 2.91221i) q^{9} +(-1.46604 + 0.846417i) q^{11} +(0.622400 + 0.359343i) q^{13} +(-0.242628 - 1.71497i) q^{15} -4.05527i q^{17} -5.64306 q^{19} +(0.763803 - 1.89548i) q^{21} +(2.06520 - 3.57703i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(2.12652 + 4.74109i) q^{27} +(1.77305 + 3.07101i) q^{29} +(0.580112 + 0.334928i) q^{31} +(1.09588 - 2.71958i) q^{33} -1.17987i q^{35} -11.3000i q^{37} +(-1.23253 + 0.174373i) q^{39} +(0.943354 + 0.544646i) q^{41} +(-1.39038 - 2.40820i) q^{43} +(2.16184 + 2.08001i) q^{45} +(2.66393 + 4.61407i) q^{47} +(-2.80396 + 4.85660i) q^{49} +(4.32944 + 5.53096i) q^{51} +9.15371 q^{53} -1.69283i q^{55} +(7.69655 - 6.02458i) q^{57} +(-6.11816 - 3.53232i) q^{59} +(2.33213 - 1.34646i) q^{61} +(0.981886 + 3.40068i) q^{63} +(-0.622400 + 0.359343i) q^{65} +(7.74884 - 13.4214i) q^{67} +(1.00215 + 7.08353i) q^{69} +10.1211 q^{71} -7.59376 q^{73} +(1.60652 + 0.647364i) q^{75} +(0.998659 - 1.72973i) q^{77} +(11.3263 - 6.53925i) q^{79} +(-7.96198 - 4.19606i) q^{81} +(12.0184 - 6.93884i) q^{83} +(3.51196 + 2.02763i) q^{85} +(-5.69690 - 2.29562i) q^{87} -4.96883i q^{89} -0.847953 q^{91} +(-1.14878 + 0.162526i) q^{93} +(2.82153 - 4.88703i) q^{95} +(-0.862865 - 1.49453i) q^{97} +(1.40878 + 4.87919i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{5}+O(q^{10}) $ 48 * q - 24 * q^5	$ 48 q - 24 q^{5} - 4 q^{21} - 24 q^{25} - 12 q^{27} - 8 q^{33} - 16 q^{39} + 12 q^{41} - 12 q^{47} + 24 q^{49} + 20 q^{51} + 4 q^{57} + 36 q^{59} + 12 q^{61} - 56 q^{63} - 40 q^{69} - 8 q^{81} + 60 q^{83} - 36 q^{87} + 16 q^{99}+O(q^{100}) $ 48 * q - 24 * q^5 - 4 * q^21 - 24 * q^25 - 12 * q^27 - 8 * q^33 - 16 * q^39 + 12 * q^41 - 12 * q^47 + 24 * q^49 + 20 * q^51 + 4 * q^57 + 36 * q^59 + 12 * q^61 - 56 * q^63 - 40 * q^69 - 8 * q^81 + 60 * q^83 - 36 * q^87 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times$.

$n$	$577$	$641$	$901$	$991$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.36390	+	1.06761i	−0.787446	+	0.616384i
$3$	−1.36390	+	1.06761i	−0.787446	+	0.616384i
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	−1.02179	+	0.589933i	−0.386202	+	0.222974i	−0.680513	−	0.732736i	$-0.738243\pi$
$7$	−1.02179	+	0.589933i	−0.386202	+	0.222974i	0.294311	+	0.955710i	$0.404910\pi$
$8$		0			0
$9$	0.720424	−	2.91221i	0.240141	−	0.970738i
$10$		0			0
$11$	−1.46604	+	0.846417i	−0.442027	+	0.255204i	−0.704457	−	0.709747i	$-0.748809\pi$
$11$	−1.46604	+	0.846417i	−0.442027	+	0.255204i	0.262430	+	0.964951i	$0.415476\pi$
$12$		0			0
$13$	0.622400	+	0.359343i	0.172623	+	0.0996638i	0.583822	−	0.811882i	$-0.301557\pi$
$13$	0.622400	+	0.359343i	0.172623	+	0.0996638i	−0.411199	+	0.911546i	$0.634890\pi$
$14$		0			0
$15$	−0.242628	−	1.71497i	−0.0626463	−	0.442804i
$16$		0			0
$17$		−	4.05527i		−	0.983547i	−0.870723	−	0.491773i	$-0.836349\pi$
$17$		−	4.05527i		−	0.983547i	0.870723	−	0.491773i	$-0.163651\pi$
$18$		0			0
$19$	−5.64306			−1.29461			−0.647303	−	0.762232i	$-0.724103\pi$
$19$	−5.64306			−1.29461			−0.647303	+	0.762232i	$0.724103\pi$
$20$		0			0
$21$	0.763803	−	1.89548i	0.166675	−	0.413628i
$22$		0			0
$23$	2.06520	−	3.57703i	0.430624	−	0.745863i	−0.566303	−	0.824197i	$-0.691627\pi$
$23$	2.06520	−	3.57703i	0.430624	−	0.745863i	0.996927	+	0.0783339i	$0.0249600\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	2.12652	+	4.74109i	0.409249	+	0.912423i
$28$		0			0
$29$	1.77305	+	3.07101i	0.329247	+	0.570273i	0.982363	−	0.186985i	$-0.0598717\pi$
$29$	1.77305	+	3.07101i	0.329247	+	0.570273i	−0.653115	+	0.757258i	$0.726538\pi$
$30$		0			0
$31$	0.580112	+	0.334928i	0.104191	+	0.0601548i	0.551190	−	0.834380i	$-0.314174\pi$
$31$	0.580112	+	0.334928i	0.104191	+	0.0601548i	−0.446999	+	0.894534i	$0.647507\pi$
$32$		0			0
$33$	1.09588	−	2.71958i	0.190768	−	0.473418i
$34$		0			0
$35$		−	1.17987i		−	0.199434i
$36$		0			0
$37$		−	11.3000i		−	1.85772i	−0.370437	−	0.928858i	$-0.620792\pi$
$37$		−	11.3000i		−	1.85772i	0.370437	−	0.928858i	$-0.379208\pi$
$38$		0			0
$39$	−1.23253	+	0.174373i	−0.197362	+	0.0279221i
$40$		0			0
$41$	0.943354	+	0.544646i	0.147327	+	0.0850593i	0.571851	−	0.820357i	$-0.306225\pi$
$41$	0.943354	+	0.544646i	0.147327	+	0.0850593i	−0.424524	+	0.905416i	$0.639559\pi$
$42$		0			0
$43$	−1.39038	−	2.40820i	−0.212030	−	0.367247i	0.740320	−	0.672255i	$-0.234674\pi$
$43$	−1.39038	−	2.40820i	−0.212030	−	0.367247i	−0.952350	+	0.305008i	$0.901341\pi$
$44$		0			0
$45$	2.16184	+	2.08001i	0.322268	+	0.310070i
$46$		0			0
$47$	2.66393	+	4.61407i	0.388575	+	0.673031i	0.992258	−	0.124193i	$-0.0396342\pi$
$47$	2.66393	+	4.61407i	0.388575	+	0.673031i	−0.603683	+	0.797224i	$0.706301\pi$
$48$		0			0
$49$	−2.80396	+	4.85660i	−0.400565	+	0.693800i
$50$		0			0
$51$	4.32944	+	5.53096i	0.606242	+	0.774490i
$52$		0			0
$53$	9.15371			1.25736			0.628680	−	0.777664i	$-0.283596\pi$
$53$	9.15371			1.25736			0.628680	+	0.777664i	$0.283596\pi$
$54$		0			0
$55$		−	1.69283i		−	0.228262i
$56$		0			0
$57$	7.69655	−	6.02458i	1.01943	−	0.797975i
$58$		0			0
$59$	−6.11816	−	3.53232i	−0.796516	−	0.459869i	0.0457354	−	0.998954i	$-0.485437\pi$
$59$	−6.11816	−	3.53232i	−0.796516	−	0.459869i	−0.842251	+	0.539085i	$0.818770\pi$
$60$		0			0
$61$	2.33213	−	1.34646i	0.298599	−	0.172396i	−0.343214	−	0.939257i	$-0.611516\pi$
$61$	2.33213	−	1.34646i	0.298599	−	0.172396i	0.641813	+	0.766861i	$0.278182\pi$
$62$		0			0
$63$	0.981886	+	3.40068i	0.123706	+	0.428446i
$64$		0			0
$65$	−0.622400	+	0.359343i	−0.0771993	+	0.0445710i
$66$		0			0
$67$	7.74884	−	13.4214i	0.946672	−	1.63968i	0.194303	−	0.980942i	$-0.437756\pi$
$67$	7.74884	−	13.4214i	0.946672	−	1.63968i	0.752369	−	0.658742i	$-0.228911\pi$
$68$		0			0
$69$	1.00215	+	7.08353i	0.120645	+	0.852757i
$70$		0			0
$71$	10.1211			1.20115			0.600576	−	0.799568i	$-0.294938\pi$
$71$	10.1211			1.20115			0.600576	+	0.799568i	$0.294938\pi$
$72$		0			0
$73$	−7.59376			−0.888782			−0.444391	−	0.895833i	$-0.646580\pi$
$73$	−7.59376			−0.888782			−0.444391	+	0.895833i	$0.646580\pi$
$74$		0			0
$75$	1.60652	+	0.647364i	0.185505	+	0.0747512i
$76$		0			0
$77$	0.998659	−	1.72973i	0.113808	−	0.197121i
$78$		0			0
$79$	11.3263	−	6.53925i	1.27431	−	0.735723i	0.298514	−	0.954405i	$-0.403509\pi$
$79$	11.3263	−	6.53925i	1.27431	−	0.735723i	0.975796	+	0.218682i	$0.0701757\pi$
$80$		0			0
$81$	−7.96198	−	4.19606i	−0.884664	−	0.466229i
$82$		0			0
$83$	12.0184	−	6.93884i	1.31919	−	0.761637i	0.335595	−	0.942006i	$-0.391063\pi$
$83$	12.0184	−	6.93884i	1.31919	−	0.761637i	0.983599	+	0.180369i	$0.0577293\pi$
$84$		0			0
$85$	3.51196	+	2.02763i	0.380926	+	0.219928i
$86$		0			0
$87$	−5.69690	−	2.29562i	−0.610772	−	0.246116i
$88$		0			0
$89$		−	4.96883i		−	0.526695i	−0.964701	−	0.263347i	$-0.915173\pi$
$89$		−	4.96883i		−	0.526695i	0.964701	−	0.263347i	$-0.0848265\pi$
$90$		0			0
$91$	−0.847953			−0.0888896
$92$		0			0
$93$	−1.14878	+	0.162526i	−0.119123	+	0.0168531i
$94$		0			0
$95$	2.82153	−	4.88703i	0.289483	−	0.501399i
$96$		0			0
$97$	−0.862865	−	1.49453i	−0.0876107	−	0.151746i	0.818890	−	0.573950i	$-0.194590\pi$
$97$	−0.862865	−	1.49453i	−0.0876107	−	0.151746i	−0.906501	+	0.422204i	$0.861256\pi$
$98$		0			0
$99$	1.40878	+	4.87919i	0.141588	+	0.490377i
$100$		0			0
$101$	6.41428	+	11.1099i	0.638244	+	1.10547i	0.985818	+	0.167819i	$0.0536724\pi$
$101$	6.41428	+	11.1099i	0.638244	+	1.10547i	−0.347573	+	0.937653i	$0.612994\pi$
$102$		0			0
$103$	−4.07102	−	2.35040i	−0.401129	−	0.231592i	0.285842	−	0.958277i	$-0.407727\pi$
$103$	−4.07102	−	2.35040i	−0.401129	−	0.231592i	−0.686971	+	0.726685i	$0.741060\pi$
$104$		0			0
$105$	1.25963	+	1.60921i	0.122928	+	0.157043i
$106$		0			0
$107$		−	10.3904i		−	1.00448i	−0.864728	−	0.502240i	$-0.832509\pi$
$107$		−	10.3904i		−	1.00448i	0.864728	−	0.502240i	$-0.167491\pi$
$108$		0			0
$109$			12.0084i			1.15020i	0.818085	+	0.575098i	$0.195036\pi$
$109$			12.0084i			1.15020i	−0.818085	+	0.575098i	$0.804964\pi$
$110$		0			0
$111$	12.0640	+	15.4121i	1.14507	+	1.46285i
$112$		0			0
$113$	5.20551	+	3.00540i	0.489693	+	0.282725i	0.724447	−	0.689330i	$-0.242095\pi$
$113$	5.20551	+	3.00540i	0.489693	+	0.282725i	−0.234754	+	0.972055i	$0.575428\pi$
$114$		0			0
$115$	2.06520	+	3.57703i	0.192581	+	0.333560i
$116$		0			0
$117$	1.49488	−	1.55368i	0.138201	−	0.143638i
$118$		0			0
$119$	2.39234	+	4.14365i	0.219305	+	0.379847i
$120$		0			0
$121$	−4.06716	+	7.04452i	−0.369741	+	0.640411i
$122$		0			0
$123$	−1.86810	+	0.264293i	−0.168441	+	0.0238305i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$			0.294527i			0.0261350i	0.999915	+	0.0130675i	$0.00415964\pi$
$127$			0.294527i			0.0261350i	−0.999915	+	0.0130675i	$0.995840\pi$
$128$		0			0
$129$	4.46734	+	1.80016i	0.393328	+	0.158495i
$130$		0			0
$131$	−14.7549	−	8.51875i	−1.28914	−	0.744287i	−0.310641	−	0.950527i	$-0.600544\pi$
$131$	−14.7549	−	8.51875i	−1.28914	−	0.744287i	−0.978501	+	0.206241i	$0.933877\pi$
$132$		0			0
$133$	5.76604	−	3.32903i	0.499979	−	0.288663i
$134$		0			0
$135$	−5.16916	−	0.528923i	−0.444891	−	0.0455224i
$136$		0			0
$137$	11.4836	−	6.63009i	0.981114	−	0.566447i	0.0785079	−	0.996913i	$-0.474984\pi$
$137$	11.4836	−	6.63009i	0.981114	−	0.566447i	0.902606	+	0.430467i	$0.141651\pi$
$138$		0			0
$139$	5.95041	−	10.3064i	0.504707	−	0.874179i	−0.495278	−	0.868735i	$-0.664934\pi$
$139$	5.95041	−	10.3064i	0.504707	−	0.874179i	0.999985	−	0.00544412i	$-0.00173293\pi$
$140$		0			0
$141$	−8.55935	−	3.44907i	−0.720827	−	0.290464i
$142$		0			0
$143$	−1.21662			−0.101739
$144$		0			0
$145$	−3.54610			−0.294488
$146$		0			0
$147$	−1.36064	−	9.61742i	−0.112224	−	0.793232i
$148$		0			0
$149$	9.19823	−	15.9318i	0.753548	−	1.30518i	−0.192545	−	0.981288i	$-0.561674\pi$
$149$	9.19823	−	15.9318i	0.753548	−	1.30518i	0.946093	−	0.323896i	$-0.104993\pi$
$150$		0			0
$151$	0.302444	−	0.174616i	0.0246126	−	0.0142101i	−0.487643	−	0.873043i	$-0.662143\pi$
$151$	0.302444	−	0.174616i	0.0246126	−	0.0142101i	0.512256	+	0.858833i	$0.328810\pi$
$152$		0			0
$153$	−11.8098	−	2.92151i	−0.954766	−	0.236190i
$154$		0			0
$155$	−0.580112	+	0.334928i	−0.0465957	+	0.0269020i
$156$		0			0
$157$	−18.6531	−	10.7693i	−1.48868	−	0.859488i	−0.488760	−	0.872418i	$-0.662551\pi$
$157$	−18.6531	−	10.7693i	−1.48868	−	0.859488i	−0.999916	+	0.0129307i	$0.995884\pi$
$158$		0			0
$159$	−12.4847	+	9.77258i	−0.990102	+	0.775016i
$160$		0			0
$161$			4.87332i			0.384072i
$162$		0			0
$163$	−7.31335			−0.572826			−0.286413	−	0.958106i	$-0.592463\pi$
$163$	−7.31335			−0.572826			−0.286413	+	0.958106i	$0.592463\pi$
$164$		0			0
$165$	1.80728	+	2.30885i	0.140697	+	0.179744i
$166$		0			0
$167$	7.04946	−	12.2100i	0.545504	−	0.944840i	−0.453071	−	0.891474i	$-0.649672\pi$
$167$	7.04946	−	12.2100i	0.545504	−	0.944840i	0.998575	−	0.0533657i	$-0.0169949\pi$
$168$		0			0
$169$	−6.24175	−	10.8110i	−0.480134	−	0.831617i
$170$		0			0
$171$	−4.06540	+	16.4338i	−0.310889	+	1.25672i
$172$		0			0
$173$	8.65925	+	14.9983i	0.658351	+	1.14030i	0.981043	+	0.193793i	$0.0620789\pi$
$173$	8.65925	+	14.9983i	0.658351	+	1.14030i	−0.322692	+	0.946504i	$0.604588\pi$
$174$		0			0
$175$	1.02179	+	0.589933i	0.0772404	+	0.0445947i
$176$		0			0
$177$	12.1157	−	1.71408i	0.910669	−	0.128838i
$178$		0			0
$179$			4.99037i			0.372998i	0.982455	+	0.186499i	$0.0597141\pi$
$179$			4.99037i			0.372998i	−0.982455	+	0.186499i	$0.940286\pi$
$180$		0			0
$181$		−	20.6992i		−	1.53856i	−0.638911	−	0.769281i	$-0.720615\pi$
$181$		−	20.6992i		−	1.53856i	0.638911	−	0.769281i	$-0.279385\pi$
$182$		0			0
$183$	−1.74330	+	4.32623i	−0.128868	+	0.319804i
$184$		0			0
$185$	9.78612	+	5.65002i	0.719490	+	0.415398i
$186$		0			0
$187$	3.43245	+	5.94517i	0.251005	+	0.434754i
$188$		0			0
$189$	−4.96979	−	3.58991i	−0.361499	−	0.261127i
$190$		0			0
$191$	9.61931	+	16.6611i	0.696029	+	1.20556i	0.969833	+	0.243772i	$0.0783849\pi$
$191$	9.61931	+	16.6611i	0.696029	+	1.20556i	−0.273803	+	0.961786i	$0.588282\pi$
$192$		0			0
$193$	−10.6944	+	18.5233i	−0.769801	+	1.33333i	0.167870	+	0.985809i	$0.446311\pi$
$193$	−10.6944	+	18.5233i	−0.769801	+	1.33333i	−0.937671	+	0.347525i	$0.887022\pi$
$194$		0			0
$195$	0.465252	−	1.15459i	0.0333174	−	0.0826816i
$196$		0			0
$197$	−18.9347			−1.34904			−0.674522	−	0.738255i	$-0.735650\pi$
$197$	−18.9347			−1.34904			−0.674522	+	0.738255i	$0.735650\pi$
$198$		0			0
$199$		−	24.2052i		−	1.71586i	−0.513765	−	0.857931i	$-0.671750\pi$
$199$		−	24.2052i		−	1.71586i	0.513765	−	0.857931i	$-0.328250\pi$
$200$		0			0
$201$	3.76017	+	26.5781i	0.265222	+	1.87467i
$202$		0			0
$203$	−3.62339	−	2.09196i	−0.254312	−	0.146827i
$204$		0			0
$205$	−0.943354	+	0.544646i	−0.0658867	+	0.0380397i
$206$		0			0
$207$	−8.92927	−	8.59129i	−0.620627	−	0.597136i
$208$		0			0
$209$	8.27294	−	4.77638i	0.572251	−	0.330389i
$210$		0			0
$211$	−9.25728	+	16.0341i	−0.637297	+	1.10383i	0.348726	+	0.937225i	$0.386614\pi$
$211$	−9.25728	+	16.0341i	−0.637297	+	1.10383i	−0.986023	+	0.166606i	$0.946719\pi$
$212$		0			0
$213$	−13.8041	+	10.8054i	−0.945842	+	0.740371i
$214$		0			0
$215$	2.78075			0.189646
$216$		0			0
$217$	−0.790340			−0.0536517
$218$		0			0
$219$	10.3571	−	8.10716i	0.699868	−	0.547831i
$220$		0			0
$221$	1.45723	−	2.52400i	0.0980240	−	0.169783i
$222$		0			0
$223$	−10.3230	+	5.95998i	−0.691278	+	0.399110i	−0.804091	−	0.594507i	$-0.797347\pi$
$223$	−10.3230	+	5.95998i	−0.691278	+	0.399110i	0.112813	+	0.993616i	$0.464014\pi$
$224$		0			0
$225$	−2.88226	+	0.832201i	−0.192151	+	0.0554801i
$226$		0			0
$227$	9.34236	−	5.39382i	0.620074	−	0.358000i	−0.156824	−	0.987627i	$-0.550125\pi$
$227$	9.34236	−	5.39382i	0.620074	−	0.358000i	0.776898	+	0.629627i	$0.216792\pi$
$228$		0			0
$229$	−22.7576	−	13.1391i	−1.50386	−	0.868257i	−0.999990	−	0.00448002i	$-0.998574\pi$
$229$	−22.7576	−	13.1391i	−1.50386	−	0.868257i	−0.503875	−	0.863777i	$-0.668093\pi$
$230$		0			0
$231$	0.484605	+	3.42535i	0.0318847	+	0.225371i
$232$		0			0
$233$		−	9.55605i		−	0.626037i	−0.949747	−	0.313019i	$-0.898660\pi$
$233$		−	9.55605i		−	0.626037i	0.949747	−	0.313019i	$-0.101340\pi$
$234$		0			0
$235$	−5.32787			−0.347552
$236$		0			0
$237$	−8.46656	+	21.0109i	−0.549962	+	1.36481i
$238$		0			0
$239$	−11.6389	+	20.1591i	−0.752856	+	1.30398i	0.193578	+	0.981085i	$0.437991\pi$
$239$	−11.6389	+	20.1591i	−0.752856	+	1.30398i	−0.946433	+	0.322899i	$0.895342\pi$
$240$		0			0
$241$	−3.37713	−	5.84936i	−0.217540	−	0.376791i	0.736515	−	0.676421i	$-0.236470\pi$
$241$	−3.37713	−	5.84936i	−0.217540	−	0.376791i	−0.954055	+	0.299630i	$0.903137\pi$
$242$		0			0
$243$	15.3391	−	2.77729i	0.984001	−	0.178163i
$244$		0			0
$245$	−2.80396	−	4.85660i	−0.179138	−	0.310277i
$246$		0			0
$247$	−3.51224	−	2.02779i	−0.223479	−	0.129025i
$248$		0			0
$249$	−8.98392	+	22.2948i	−0.569333	+	1.41288i
$250$		0			0
$251$			8.53803i			0.538916i	0.963012	+	0.269458i	$0.0868445\pi$
$251$			8.53803i			0.538916i	−0.963012	+	0.269458i	$0.913155\pi$
$252$		0			0
$253$			6.99209i			0.439589i
$254$		0			0
$255$	−6.95467	+	0.983922i	−0.435518	+	0.0616156i
$256$		0			0
$257$	−7.26049	−	4.19184i	−0.452897	−	0.261480i	0.256156	−	0.966635i	$-0.417544\pi$
$257$	−7.26049	−	4.19184i	−0.452897	−	0.261480i	−0.709053	+	0.705155i	$0.750877\pi$
$258$		0			0
$259$	6.66627	+	11.5463i	0.414222	+	0.717453i
$260$		0			0
$261$	10.2208	−	2.95107i	0.632652	−	0.182667i
$262$		0			0
$263$	−11.9363	−	20.6742i	−0.736022	−	1.27483i	−0.954274	−	0.298935i	$-0.903369\pi$
$263$	−11.9363	−	20.6742i	−0.736022	−	1.27483i	0.218252	−	0.975892i	$-0.429965\pi$
$264$		0			0
$265$	−4.57686	+	7.92735i	−0.281154	+	0.486973i
$266$		0			0
$267$	5.30476	+	6.77696i	0.324646	+	0.414743i
$268$		0			0
$269$	−2.11822			−0.129150			−0.0645752	−	0.997913i	$-0.520569\pi$
$269$	−2.11822			−0.129150			−0.0645752	+	0.997913i	$0.520569\pi$
$270$		0			0
$271$			3.47151i			0.210879i	0.994426	+	0.105440i	$0.0336250\pi$
$271$			3.47151i			0.210879i	−0.994426	+	0.105440i	$0.966375\pi$
$272$		0			0
$273$	1.15652	−	0.905282i	0.0699958	−	0.0547902i
$274$		0			0
$275$	1.46604	+	0.846417i	0.0884054	+	0.0510409i
$276$		0			0
$277$	15.4700	−	8.93161i	0.929502	−	0.536648i	0.0428481	−	0.999082i	$-0.486357\pi$
$277$	15.4700	−	8.93161i	0.929502	−	0.536648i	0.886654	+	0.462433i	$0.153024\pi$
$278$		0			0
$279$	1.39331	−	1.44812i	0.0834151	−	0.0866966i
$280$		0			0
$281$	−6.19927	+	3.57915i	−0.369817	+	0.213514i	−0.673379	−	0.739298i	$-0.735158\pi$
$281$	−6.19927	+	3.57915i	−0.369817	+	0.213514i	0.303561	+	0.952812i	$0.401824\pi$
$282$		0			0
$283$	−7.40809	+	12.8312i	−0.440365	+	0.762735i	−0.997716	−	0.0675418i	$-0.978484\pi$
$283$	−7.40809	+	12.8312i	−0.440365	+	0.762735i	0.557351	+	0.830277i	$0.311818\pi$
$284$		0			0
$285$	1.36917	+	9.67769i	0.0811023	+	0.573257i
$286$		0			0
$287$	−1.28522			−0.0758640
$288$		0			0
$289$	0.554813			0.0326361
$290$		0			0
$291$	2.77243	+	1.11718i	0.162523	+	0.0654900i
$292$		0			0
$293$	−2.14191	+	3.70990i	−0.125132	+	0.216735i	−0.921784	−	0.387703i	$-0.873269\pi$
$293$	−2.14191	+	3.70990i	−0.125132	+	0.216735i	0.796653	+	0.604437i	$0.206602\pi$
$294$		0			0
$295$	6.11816	−	3.53232i	0.356213	−	0.205660i
$296$		0			0
$297$	−7.13050	−	5.15069i	−0.413753	−	0.298873i
$298$		0			0
$299$	2.57076	−	1.48423i	0.148671	−	0.0858353i
$300$		0			0
$301$	2.84135	+	1.64046i	0.163773	+	0.0945543i
$302$		0			0
$303$	−20.6094	−	8.30475i	−1.18398	−	0.477095i
$304$		0			0
$305$			2.69292i			0.154196i
$306$		0			0
$307$	−6.72522			−0.383828			−0.191914	−	0.981412i	$-0.561470\pi$
$307$	−6.72522			−0.383828			−0.191914	+	0.981412i	$0.561470\pi$
$308$		0			0
$309$	8.06175	−	1.14055i	0.458617	−	0.0648835i
$310$		0			0
$311$	−1.29216	+	2.23808i	−0.0732715	+	0.126910i	−0.900333	−	0.435201i	$-0.856677\pi$
$311$	−1.29216	+	2.23808i	−0.0732715	+	0.126910i	0.827062	+	0.562111i	$0.190011\pi$
$312$		0			0
$313$	3.48570	+	6.03740i	0.197023	+	0.341254i	0.947562	−	0.319572i	$-0.103539\pi$
$313$	3.48570	+	6.03740i	0.197023	+	0.341254i	−0.750539	+	0.660826i	$0.770206\pi$
$314$		0			0
$315$	−3.43602	−	0.850004i	−0.193598	−	0.0478923i
$316$		0			0
$317$	0.840946	+	1.45656i	0.0472322	+	0.0818086i	0.888675	−	0.458538i	$-0.151627\pi$
$317$	0.840946	+	1.45656i	0.0472322	+	0.0818086i	−0.841443	+	0.540346i	$0.818293\pi$
$318$		0			0
$319$	−5.19872	−	3.00148i	−0.291072	−	0.168051i
$320$		0			0
$321$	11.0929	+	14.1714i	0.619145	+	0.790973i
$322$		0			0
$323$			22.8841i			1.27331i
$324$		0			0
$325$		−	0.718686i		−	0.0398655i
$326$		0			0
$327$	−12.8203	−	16.3782i	−0.708962	−	0.905716i
$328$		0			0
$329$	−5.44398	−	3.14309i	−0.300137	−	0.173284i
$330$		0			0
$331$	1.29513	+	2.24323i	0.0711868	+	0.123299i	0.899422	−	0.437082i	$-0.143988\pi$
$331$	1.29513	+	2.24323i	0.0711868	+	0.123299i	−0.828235	+	0.560381i	$0.810655\pi$
$332$		0			0
$333$	−32.9081	−	8.14082i	−1.80335	−	0.446114i
$334$		0			0
$335$	7.74884	+	13.4214i	0.423364	+	0.733289i
$336$		0			0
$337$	5.84149	−	10.1178i	0.318206	−	0.551150i	−0.661907	−	0.749586i	$-0.730253\pi$
$337$	5.84149	−	10.1178i	0.318206	−	0.551150i	0.980114	+	0.198436i	$0.0635862\pi$
$338$		0			0
$339$	−10.3084	+	1.45839i	−0.559874	+	0.0792089i
$340$		0			0
$341$	−1.13395			−0.0614071
$342$		0			0
$343$		−	14.8757i		−	0.803210i
$344$		0			0
$345$	−6.63559	−	2.67388i	−0.357248	−	0.143957i
$346$		0			0
$347$	−5.55078	−	3.20475i	−0.297982	−	0.172040i	0.343554	−	0.939133i	$-0.388369\pi$
$347$	−5.55078	−	3.20475i	−0.297982	−	0.172040i	−0.641536	+	0.767093i	$0.721702\pi$
$348$		0			0
$349$	−17.5635	+	10.1403i	−0.940153	+	0.542797i	−0.890008	−	0.455945i	$-0.849302\pi$
$349$	−17.5635	+	10.1403i	−0.940153	+	0.542797i	−0.0501445	+	0.998742i	$0.515968\pi$
$350$		0			0
$351$	−0.380129	+	3.71500i	−0.0202898	+	0.198292i
$352$		0			0
$353$	10.1091	−	5.83648i	0.538052	−	0.310645i	−0.206237	−	0.978502i	$-0.566122\pi$
$353$	10.1091	−	5.83648i	0.538052	−	0.310645i	0.744289	+	0.667858i	$0.232788\pi$
$354$		0			0
$355$	−5.06054	+	8.76512i	−0.268586	+	0.465204i
$356$		0			0
$357$	−7.68669	−	3.09742i	−0.406823	−	0.163933i
$358$		0			0
$359$	−6.88907			−0.363591			−0.181796	−	0.983336i	$-0.558191\pi$
$359$	−6.88907			−0.363591			−0.181796	+	0.983336i	$0.558191\pi$
$360$		0			0
$361$	12.8441			0.676007
$362$		0			0
$363$	−1.97361	−	13.9501i	−0.103588	−	0.732192i
$364$		0			0
$365$	3.79688	−	6.57639i	0.198738	−	0.344224i
$366$		0			0
$367$	−30.5870	+	17.6594i	−1.59663	+	0.921812i	−0.604495	+	0.796609i	$0.706625\pi$
$367$	−30.5870	+	17.6594i	−1.59663	+	0.921812i	−0.992131	+	0.125203i	$0.960042\pi$
$368$		0			0
$369$	2.26574	−	2.35487i	0.117950	−	0.122590i
$370$		0			0
$371$	−9.35321	+	5.40008i	−0.485594	+	0.280358i
$372$		0			0
$373$	17.8589	+	10.3108i	0.924699	+	0.533875i	0.885131	−	0.465342i	$-0.154068\pi$
$373$	17.8589	+	10.3108i	0.924699	+	0.533875i	0.0395680	+	0.999217i	$0.487402\pi$
$374$		0			0
$375$	−1.36390	+	1.06761i	−0.0704313	+	0.0551311i
$376$		0			0
$377$			2.54853i			0.131256i
$378$		0			0
$379$	−9.47680			−0.486791			−0.243395	−	0.969927i	$-0.578261\pi$
$379$	−9.47680			−0.486791			−0.243395	+	0.969927i	$0.578261\pi$
$380$		0			0
$381$	−0.314439	−	0.401704i	−0.0161092	−	0.0205799i
$382$		0			0
$383$	13.6393	−	23.6240i	0.696938	−	1.20713i	−0.272585	−	0.962132i	$-0.587879\pi$
$383$	13.6393	−	23.6240i	0.696938	−	1.20713i	0.969523	−	0.245000i	$-0.0787879\pi$
$384$		0			0
$385$	0.998659	+	1.72973i	0.0508964	+	0.0881551i
$386$		0			0
$387$	−8.01485	+	2.31414i	−0.407418	+	0.117635i
$388$		0			0
$389$	−6.12156	−	10.6029i	−0.310375	−	0.537586i	0.668068	−	0.744100i	$-0.267121\pi$
$389$	−6.12156	−	10.6029i	−0.310375	−	0.537586i	−0.978444	+	0.206514i	$0.933788\pi$
$390$		0			0
$391$	−14.5058	−	8.37494i	−0.733591	−	0.423539i
$392$		0			0
$393$	29.2188	−	4.13378i	1.47390	−	0.208521i
$394$		0			0
$395$			13.0785i			0.658051i
$396$		0			0
$397$			3.50428i			0.175875i	0.996126	+	0.0879373i	$0.0280275\pi$
$397$			3.50428i			0.175875i	−0.996126	+	0.0879373i	$0.971972\pi$
$398$		0			0
$399$	−4.31019	+	10.6963i	−0.215779	+	0.535486i
$400$		0			0
$401$	−34.5002	−	19.9187i	−1.72286	−	0.994691i	−0.912881	−	0.408226i	$-0.866148\pi$
$401$	−34.5002	−	19.9187i	−1.72286	−	0.994691i	−0.809975	−	0.586465i	$-0.800519\pi$
$402$		0			0
$403$	0.240708	+	0.416918i	0.0119905	+	0.0207682i
$404$		0			0
$405$	7.61488	−	4.79725i	0.378387	−	0.238377i
$406$		0			0
$407$	9.56455	+	16.5663i	0.474097	+	0.821160i
$408$		0			0
$409$	12.4218	−	21.5152i	0.614219	−	1.06386i	−0.376301	−	0.926497i	$-0.622804\pi$
$409$	12.4218	−	21.5152i	0.614219	−	1.06386i	0.990521	−	0.137362i	$-0.0438624\pi$
$410$		0			0
$411$	−8.58416	+	21.3028i	−0.423426	+	1.05079i
$412$		0			0
$413$	8.33533			0.410155
$414$		0			0
$415$			13.8777i			0.681229i
$416$		0			0
$417$	2.88747	+	20.4096i	0.141400	+	0.999462i
$418$		0			0
$419$	1.15450	+	0.666549i	0.0564009	+	0.0325631i	0.527935	−	0.849285i	$-0.322966\pi$
$419$	1.15450	+	0.666549i	0.0564009	+	0.0325631i	−0.471534	+	0.881848i	$0.656300\pi$
$420$		0			0
$421$	−5.60932	+	3.23854i	−0.273381	+	0.157837i	−0.630423	−	0.776252i	$-0.717119\pi$
$421$	−5.60932	+	3.23854i	−0.273381	+	0.157837i	0.357042	+	0.934088i	$0.383785\pi$
$422$		0			0
$423$	15.3563	−	4.43386i	0.746650	−	0.215582i
$424$		0			0
$425$	−3.51196	+	2.02763i	−0.170355	+	0.0983547i
$426$		0			0
$427$	−1.58864	+	2.75160i	−0.0768797	+	0.133159i
$428$		0			0
$429$	1.65934	−	1.29887i	0.0801136	−	0.0627100i
$430$		0			0
$431$	−16.0064			−0.771000			−0.385500	−	0.922708i	$-0.625971\pi$
$431$	−16.0064			−0.771000			−0.385500	+	0.922708i	$0.625971\pi$
$432$		0			0
$433$	17.9579			0.863003			0.431501	−	0.902112i	$-0.357984\pi$
$433$	17.9579			0.863003			0.431501	+	0.902112i	$0.357984\pi$
$434$		0			0
$435$	4.83651	−	3.78585i	0.231893	−	0.181518i
$436$		0			0
$437$	−11.6541	+	20.1854i	−0.557489	+	0.965600i
$438$		0			0
$439$	7.75341	−	4.47643i	0.370050	−	0.213648i	−0.303430	−	0.952854i	$-0.598132\pi$
$439$	7.75341	−	4.47643i	0.370050	−	0.213648i	0.673480	+	0.739205i	$0.264799\pi$
$440$		0			0
$441$	12.1234	+	11.6645i	0.577305	+	0.555454i
$442$		0			0
$443$	30.8234	−	17.7959i	1.46447	−	0.845509i	0.465252	−	0.885178i	$-0.345964\pi$
$443$	30.8234	−	17.7959i	1.46447	−	0.845509i	0.999213	+	0.0396689i	$0.0126303\pi$
$444$		0			0
$445$	4.30313	+	2.48441i	0.203988	+	0.117772i
$446$		0			0
$447$	4.46350	+	31.5494i	0.211116	+	1.49224i
$448$		0			0
$449$		−	7.62925i		−	0.360047i	−0.983662	−	0.180023i	$-0.942383\pi$
$449$		−	7.62925i		−	0.360047i	0.983662	−	0.180023i	$-0.0576173\pi$
$450$		0			0
$451$	−1.84399			−0.0868301
$452$		0			0
$453$	−0.226081	+	0.561051i	−0.0106222	+	0.0263605i
$454$		0			0
$455$	0.423977	−	0.734349i	0.0198763	−	0.0344268i
$456$		0			0
$457$	−15.0212	−	26.0174i	−0.702660	−	1.21704i	−0.967529	−	0.252759i	$-0.918662\pi$
$457$	−15.0212	−	26.0174i	−0.702660	−	1.21704i	0.264869	−	0.964284i	$-0.414671\pi$
$458$		0			0
$459$	19.2264	−	8.62361i	0.897410	−	0.402516i
$460$		0			0
$461$	16.1809	+	28.0261i	0.753618	+	1.30531i	0.946058	+	0.323997i	$0.105027\pi$
$461$	16.1809	+	28.0261i	0.753618	+	1.30531i	−0.192440	+	0.981309i	$0.561640\pi$
$462$		0			0
$463$	13.9061	+	8.02871i	0.646273	+	0.373126i	0.787027	−	0.616919i	$-0.211619\pi$
$463$	13.9061	+	8.02871i	0.646273	+	0.373126i	−0.140754	+	0.990045i	$0.544953\pi$
$464$		0			0
$465$	0.433640	−	1.07614i	0.0201096	−	0.0499047i
$466$		0			0
$467$		−	14.7880i		−	0.684308i	−0.939644	−	0.342154i	$-0.888844\pi$
$467$		−	14.7880i		−	0.684308i	0.939644	−	0.342154i	$-0.111156\pi$
$468$		0			0
$469$			18.2852i			0.844332i
$470$		0			0
$471$	36.9383	−	5.22589i	1.70203	−	0.240797i
$472$		0			0
$473$	4.07668	+	2.35367i	0.187446	+	0.108222i
$474$		0			0
$475$	2.82153	+	4.88703i	0.129461	+	0.224232i
$476$		0			0
$477$	6.59456	−	26.6576i	0.301944	−	1.22057i
$478$		0			0
$479$	13.3061	+	23.0468i	0.607969	+	1.05303i	0.991575	+	0.129536i	$0.0413489\pi$
$479$	13.3061	+	23.0468i	0.607969	+	1.05303i	−0.383606	+	0.923497i	$0.625318\pi$
$480$		0			0
$481$	4.06059	−	7.03315i	0.185147	−	0.320684i
$482$		0			0
$483$	−5.20280	−	6.64671i	−0.236736	−	0.302436i
$484$		0			0
$485$	1.72573			0.0783614
$486$		0			0
$487$		−	27.0627i		−	1.22633i	−0.789956	−	0.613164i	$-0.789896\pi$
$487$		−	27.0627i		−	1.22633i	0.789956	−	0.613164i	$-0.210104\pi$
$488$		0			0
$489$	9.97465	−	7.80779i	0.451069	−	0.353081i
$490$		0			0
$491$	20.3680	+	11.7595i	0.919194	+	0.530697i	0.883378	−	0.468661i	$-0.155263\pi$
$491$	20.3680	+	11.7595i	0.919194	+	0.530697i	0.0358165	+	0.999358i	$0.488597\pi$
$492$		0			0
$493$	12.4538	−	7.19019i	0.560890	−	0.323830i
$494$		0			0
$495$	−4.92990	−	1.21956i	−0.221582	−	0.0548151i
$496$		0			0
$497$	−10.3417	+	5.97076i	−0.463887	+	0.267825i
$498$		0			0
$499$	3.21984	−	5.57692i	0.144140	−	0.249657i	−0.784912	−	0.619607i	$-0.787292\pi$
$499$	3.21984	−	5.57692i	0.144140	−	0.249657i	0.929052	+	0.369950i	$0.120625\pi$
$500$		0			0
$501$	3.42079	+	24.1793i	0.152830	+	1.08025i
$502$		0			0
$503$	−15.9851			−0.712738			−0.356369	−	0.934345i	$-0.615985\pi$
$503$	−15.9851			−0.712738			−0.356369	+	0.934345i	$0.615985\pi$
$504$		0			0
$505$	−12.8286			−0.570863
$506$		0			0
$507$	20.0550	+	8.08137i	0.890675	+	0.358906i
$508$		0			0
$509$	21.0256	−	36.4174i	0.931944	−	1.61417i	0.151950	−	0.988388i	$-0.451445\pi$
$509$	21.0256	−	36.4174i	0.931944	−	1.61417i	0.779994	−	0.625787i	$-0.215222\pi$
$510$		0			0
$511$	7.75925	−	4.47981i	0.343249	−	0.198175i
$512$		0			0
$513$	−12.0001	−	26.7542i	−0.529817	−	1.18123i
$514$		0			0
$515$	4.07102	−	2.35040i	0.179390	−	0.103571i
$516$		0			0
$517$	−7.81086	−	4.50960i	−0.343521	−	0.198332i
$518$		0			0
$519$	−27.8226	−	11.2114i	−1.22128	−	0.492125i
$520$		0			0
$521$			26.0924i			1.14313i	0.820558	+	0.571563i	$0.193663\pi$
$521$			26.0924i			1.14313i	−0.820558	+	0.571563i	$0.806337\pi$
$522$		0			0
$523$	−29.9530			−1.30975			−0.654876	−	0.755737i	$-0.727279\pi$
$523$	−29.9530			−1.30975			−0.654876	+	0.755737i	$0.727279\pi$
$524$		0			0
$525$	−2.02344	+	0.286269i	−0.0883101	+	0.0124938i
$526$		0			0
$527$	1.35822	−	2.35251i	0.0591650	−	0.102477i
$528$		0			0
$529$	2.96988	+	5.14398i	0.129125	+	0.223651i
$530$		0			0
$531$	−14.6945	+	15.2726i	−0.637688	+	0.662775i
$532$		0			0
$533$	0.391429	+	0.677975i	0.0169547	+	0.0293664i
$534$		0			0
$535$	8.99837	+	5.19521i	0.389033	+	0.224608i
$536$		0			0
$537$	−5.32776	−	6.80634i	−0.229910	−	0.293715i
$538$		0			0
$539$		−	9.49327i		−	0.408904i
$540$		0			0
$541$			1.81980i			0.0782393i	0.999235	+	0.0391196i	$0.0124553\pi$
$541$			1.81980i			0.0782393i	−0.999235	+	0.0391196i	$0.987545\pi$
$542$		0			0
$543$	22.0987	+	28.2316i	0.948345	+	1.21153i
$544$		0			0
$545$	−10.3996	−	6.00420i	−0.445469	−	0.257191i
$546$		0			0
$547$	−6.93203	−	12.0066i	−0.296392	−	0.513367i	0.678915	−	0.734216i	$-0.262450\pi$
$547$	−6.93203	−	12.0066i	−0.296392	−	0.513367i	−0.975308	+	0.220850i	$0.929117\pi$
$548$		0			0
$549$	−2.24105	−	7.76169i	−0.0956456	−	0.331261i
$550$		0			0
$551$	−10.0054	−	17.3299i	−0.426246	−	0.738279i
$552$		0			0
$553$	−7.71544	+	13.3635i	−0.328094	+	0.568275i
$554$		0			0
$555$	−19.3793	+	2.74171i	−0.822604	+	0.116379i
$556$		0			0
$557$	13.1558			0.557428			0.278714	−	0.960374i	$-0.410092\pi$
$557$	13.1558			0.557428			0.278714	+	0.960374i	$0.410092\pi$
$558$		0			0
$559$		−	1.99849i		−	0.0845270i
$560$		0			0
$561$	−11.0286	−	4.44409i	−0.465629	−	0.187630i
$562$		0			0
$563$	28.3026	+	16.3405i	1.19281	+	0.688671i	0.958943	−	0.283598i	$-0.0915280\pi$
$563$	28.3026	+	16.3405i	1.19281	+	0.688671i	0.233869	+	0.972268i	$0.424861\pi$
$564$		0			0
$565$	−5.20551	+	3.00540i	−0.218998	+	0.126438i
$566$		0			0
$567$	10.6109	−	0.409527i	0.445616	−	0.0171985i
$568$		0			0
$569$	13.9164	−	8.03462i	0.583404	−	0.336829i	−0.179081	−	0.983834i	$-0.557312\pi$
$569$	13.9164	−	8.03462i	0.583404	−	0.336829i	0.762485	+	0.647006i	$0.223979\pi$
$570$		0			0
$571$	20.1991	−	34.9859i	0.845308	−	1.46412i	−0.0400464	−	0.999198i	$-0.512751\pi$
$571$	20.1991	−	34.9859i	0.845308	−	1.46412i	0.885354	−	0.464918i	$-0.153916\pi$
$572$		0			0
$573$	−30.9073	−	12.4544i	−1.29117	−	0.520290i
$574$		0			0
$575$	−4.13040			−0.172250
$576$		0			0
$577$	38.7400			1.61277			0.806384	−	0.591392i	$-0.201421\pi$
$577$	38.7400			1.61277			0.806384	+	0.591392i	$0.201421\pi$
$578$		0			0
$579$	−5.18953	−	36.6812i	−0.215670	−	1.52442i
$580$		0			0
$581$	−8.18691	+	14.1801i	−0.339650	+	0.588291i
$582$		0			0
$583$	−13.4197	+	7.74786i	−0.555787	+	0.320884i
$584$		0			0
$585$	0.598091	+	2.07144i	0.0247280	+	0.0856436i
$586$		0			0
$587$	−11.1211	+	6.42078i	−0.459018	+	0.265014i	−0.711631	−	0.702553i	$-0.752043\pi$
$587$	−11.1211	+	6.42078i	−0.459018	+	0.265014i	0.252613	+	0.967567i	$0.418710\pi$
$588$		0			0
$589$	−3.27361	−	1.89002i	−0.134887	−	0.0778768i
$590$		0			0
$591$	25.8250	−	20.2149i	1.06230	−	0.831529i
$592$		0			0
$593$			35.8596i			1.47258i	0.676668	+	0.736288i	$0.263423\pi$
$593$			35.8596i			1.47258i	−0.676668	+	0.736288i	$0.736577\pi$
$594$		0			0
$595$	−4.78467			−0.196152
$596$		0			0
$597$	25.8417	+	33.0134i	1.05763	+	1.35115i
$598$		0			0
$599$	0.760967	−	1.31803i	0.0310923	−	0.0538534i	−0.850061	−	0.526685i	$-0.823435\pi$
$599$	0.760967	−	1.31803i	0.0310923	−	0.0538534i	0.881153	+	0.472832i	$0.156768\pi$
$600$		0			0
$601$	13.4622	+	23.3172i	0.549135	+	0.951130i	0.998334	+	0.0576983i	$0.0183761\pi$
$601$	13.4622	+	23.3172i	0.549135	+	0.951130i	−0.449199	+	0.893432i	$0.648291\pi$
$602$		0			0
$603$	−33.5035	−	32.2354i	−1.36437	−	1.31273i
$604$		0			0
$605$	−4.06716	−	7.04452i	−0.165353	−	0.286400i
$606$		0			0
$607$	10.9753	+	6.33658i	0.445473	+	0.257194i	0.705916	−	0.708295i	$-0.250535\pi$
$607$	10.9753	+	6.33658i	0.445473	+	0.257194i	−0.260444	+	0.965489i	$0.583869\pi$
$608$		0			0
$609$	7.17532	−	1.01514i	0.290759	−	0.0411355i
$610$		0			0
$611$			3.82906i			0.154907i
$612$		0			0
$613$		−	22.4783i		−	0.907890i	−0.891030	−	0.453945i	$-0.850016\pi$
$613$		−	22.4783i		−	0.907890i	0.891030	−	0.453945i	$-0.149984\pi$
$614$		0			0
$615$	0.705168	−	1.74997i	0.0284351	−	0.0705657i
$616$		0			0
$617$	−35.8335	−	20.6885i	−1.44260	−	0.832886i	−0.444578	−	0.895740i	$-0.646647\pi$
$617$	−35.8335	−	20.6885i	−1.44260	−	0.832886i	−0.998023	+	0.0628537i	$0.979980\pi$
$618$		0			0
$619$	5.75193	+	9.96263i	0.231190	+	0.400432i	0.958158	−	0.286238i	$-0.0924049\pi$
$619$	5.75193	+	9.96263i	0.231190	+	0.400432i	−0.726969	+	0.686670i	$0.759072\pi$
$620$		0			0
$621$	21.3507	+	2.18466i	0.856775	+	0.0876676i
$622$		0			0
$623$	2.93127	+	5.07712i	0.117439	+	0.203410i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−6.18412	+	15.3467i	−0.246970	+	0.612890i
$628$		0			0
$629$	−45.8247			−1.82715
$630$		0			0
$631$			3.70901i			0.147654i	0.997271	+	0.0738268i	$0.0235212\pi$
$631$			3.70901i			0.147654i	−0.997271	+	0.0738268i	$0.976479\pi$
$632$		0			0
$633$	−4.49215	−	31.7520i	−0.178547	−	1.26203i
$634$		0			0
$635$	−0.255068	−	0.147263i	−0.0101221	−	0.00584397i
$636$		0			0
$637$	−3.49037	+	2.01517i	−0.138293	+	0.0798438i
$638$		0			0
$639$	7.29147	−	29.4748i	0.288446	−	1.16600i
$640$		0			0
$641$	−14.6920	+	8.48244i	−0.580300	+	0.335036i	−0.761252	−	0.648456i	$-0.775415\pi$
$641$	−14.6920	+	8.48244i	−0.580300	+	0.335036i	0.180953	+	0.983492i	$0.442082\pi$
$642$		0			0
$643$	−12.0107	+	20.8032i	−0.473657	+	0.820398i	−0.999545	−	0.0301558i	$-0.990400\pi$
$643$	−12.0107	+	20.8032i	−0.473657	+	0.820398i	0.525888	+	0.850554i	$0.323733\pi$
$644$		0			0
$645$	−3.79265	+	2.96875i	−0.149336	+	0.116895i
$646$		0			0
$647$	−31.1081			−1.22299			−0.611493	−	0.791250i	$-0.709431\pi$
$647$	−31.1081			−1.22299			−0.611493	+	0.791250i	$0.709431\pi$
$648$		0			0
$649$	11.9593			0.469442
$650$		0			0
$651$	1.07794	−	0.843773i	0.0422478	−	0.0330701i
$652$		0			0
$653$	24.2158	−	41.9430i	0.947638	−	1.64136i	0.197257	−	0.980352i	$-0.436797\pi$
$653$	24.2158	−	41.9430i	0.947638	−	1.64136i	0.750381	−	0.661005i	$-0.229870\pi$
$654$		0			0
$655$	14.7549	−	8.51875i	0.576522	−	0.332855i
$656$		0			0
$657$	−5.47073	+	22.1146i	−0.213433	+	0.862774i
$658$		0			0
$659$	14.3198	−	8.26752i	0.557819	−	0.322057i	−0.194451	−	0.980912i	$-0.562292\pi$
$659$	14.3198	−	8.26752i	0.557819	−	0.322057i	0.752270	+	0.658855i	$0.228959\pi$
$660$		0			0
$661$	19.9686	+	11.5289i	0.776687	+	0.448420i	0.835255	−	0.549863i	$-0.185320\pi$
$661$	19.9686	+	11.5289i	0.776687	+	0.448420i	−0.0585680	+	0.998283i	$0.518653\pi$
$662$		0			0
$663$	0.707131	+	4.99822i	0.0274627	+	0.194115i
$664$		0			0
$665$			6.65805i			0.258188i
$666$		0			0
$667$	14.6468			0.567128
$668$		0			0
$669$	7.71655	−	19.1497i	0.298339	−	0.740370i
$670$		0			0
$671$	−2.27933	+	3.94791i	−0.0879926	+	0.152408i
$672$		0			0
$673$	−14.6629	−	25.3969i	−0.565213	−	0.978977i	−0.997030	−	0.0770158i	$-0.975461\pi$
$673$	−14.6629	−	25.3969i	−0.565213	−	0.978977i	0.431817	−	0.901961i	$-0.357873\pi$
$674$		0			0
$675$	3.04264	−	4.21216i	0.117111	−	0.162126i
$676$		0			0
$677$	−3.94679	−	6.83604i	−0.151687	−	0.262730i	0.780161	−	0.625579i	$-0.215137\pi$
$677$	−3.94679	−	6.83604i	−0.151687	−	0.262730i	−0.931848	+	0.362849i	$0.881804\pi$
$678$		0			0
$679$	1.76334	+	1.01806i	0.0676708	+	0.0390697i
$680$		0			0
$681$	−6.98353	+	17.3306i	−0.267609	+	0.664110i
$682$		0			0
$683$			0.634665i			0.0242848i	0.999926	+	0.0121424i	$0.00386514\pi$
$683$			0.634665i			0.0242848i	−0.999926	+	0.0121424i	$0.996135\pi$
$684$		0			0
$685$			13.2602i			0.506645i
$686$		0			0
$687$	45.0664	−	6.37584i	1.71939	−	0.243253i
$688$		0			0
$689$	5.69727	+	3.28932i	0.217049	+	0.125313i
$690$		0			0
$691$	−16.0251	−	27.7562i	−0.609622	−	1.05590i	−0.991303	−	0.131602i	$-0.957988\pi$
$691$	−16.0251	−	27.7562i	−0.609622	−	1.05590i	0.381681	−	0.924294i	$-0.375345\pi$
$692$		0			0
$693$	−4.31788	−	4.15445i	−0.164023	−	0.157814i
$694$		0			0
$695$	5.95041	+	10.3064i	0.225712	+	0.390945i
$696$		0			0
$697$	2.20868	−	3.82555i	0.0836598	−	0.144903i
$698$		0			0
$699$	10.2021	+	13.0335i	0.385879	+	0.492970i
$700$		0			0
$701$	2.21948			0.0838288			0.0419144	−	0.999121i	$-0.486654\pi$
$701$	2.21948			0.0838288			0.0419144	+	0.999121i	$0.486654\pi$
$702$		0			0
$703$			63.7668i			2.40501i
$704$		0			0
$705$	7.26666	−	5.68808i	0.273678	−	0.214225i
$706$		0			0
$707$	−13.1081	−	7.56799i	−0.492982	−	0.284623i
$708$		0			0
$709$	18.5688	−	10.7207i	0.697364	−	0.402624i	−0.109001	−	0.994042i	$-0.534765\pi$
$709$	18.5688	−	10.7207i	0.697364	−	0.402624i	0.806365	+	0.591418i	$0.201432\pi$
$710$		0			0
$711$	−10.8839	−	37.6957i	−0.408180	−	1.41370i
$712$		0			0
$713$	2.39610	−	1.38339i	0.0897345	−	0.0518082i
$714$		0			0
$715$	0.608308	−	1.05362i	0.0227494	−	0.0394032i
$716$		0			0
$717$	−5.64783	−	39.9207i	−0.210922	−	1.49087i
$718$		0			0
$719$	11.0608			0.412498			0.206249	−	0.978499i	$-0.433874\pi$
$719$	11.0608			0.412498			0.206249	+	0.978499i	$0.433874\pi$
$720$		0			0
$721$	5.54632			0.206556
$722$		0			0
$723$	10.8509	+	4.37247i	0.403549	+	0.162614i
$724$		0			0
$725$	1.77305	−	3.07101i	0.0658495	−	0.114055i
$726$		0			0
$727$	−15.9631	+	9.21629i	−0.592038	+	0.341813i	−0.765903	−	0.642956i	$-0.777708\pi$
$727$	−15.9631	+	9.21629i	−0.592038	+	0.341813i	0.173865	+	0.984769i	$0.444374\pi$
$728$		0			0
$729$	−17.9558	+	20.1640i	−0.665030	+	0.746816i
$730$		0			0
$731$	−9.76589	+	5.63834i	−0.361205	+	0.208542i
$732$		0			0
$733$	18.9150	+	10.9206i	0.698641	+	0.403360i	0.806841	−	0.590769i	$-0.201175\pi$
$733$	18.9150	+	10.9206i	0.698641	+	0.403360i	−0.108200	+	0.994129i	$0.534509\pi$
$734$		0			0
$735$	9.00925	+	3.63036i	0.332311	+	0.133908i
$736$		0			0
$737$			26.2350i			0.966379i
$738$		0			0
$739$	17.2982			0.636326			0.318163	−	0.948036i	$-0.396934\pi$
$739$	17.2982			0.636326			0.318163	+	0.948036i	$0.396934\pi$
$740$		0			0
$741$	6.95522	−	0.984000i	0.255506	−	0.0361481i
$742$		0			0
$743$	25.2134	−	43.6709i	0.924990	−	1.60213i	0.133413	−	0.991061i	$-0.457406\pi$
$743$	25.2134	−	43.6709i	0.924990	−	1.60213i	0.791577	−	0.611069i	$-0.209260\pi$
$744$		0			0
$745$	9.19823	+	15.9318i	0.336997	+	0.583696i
$746$		0			0
$747$	−11.5490	−	39.9991i	−0.422557	−	1.46349i
$748$		0			0
$749$	6.12965	+	10.6169i	0.223973	+	0.387932i
$750$		0			0
$751$	−18.9397	−	10.9349i	−0.691120	−	0.399019i	0.112911	−	0.993605i	$-0.463982\pi$
$751$	−18.9397	−	10.9349i	−0.691120	−	0.399019i	−0.804032	+	0.594587i	$0.797316\pi$
$752$		0			0
$753$	−9.11528	−	11.6450i	−0.332179	−	0.424367i
$754$		0			0
$755$			0.349233i			0.0127099i
$756$		0			0
$757$			6.81492i			0.247693i	0.992301	+	0.123846i	$0.0395230\pi$
$757$			6.81492i			0.247693i	−0.992301	+	0.123846i	$0.960477\pi$
$758$		0			0
$759$	−7.46481	−	9.53648i	−0.270956	−	0.346152i
$760$		0			0
$761$	−33.8048	−	19.5172i	−1.22542	−	0.707498i	−0.259354	−	0.965782i	$-0.583510\pi$
$761$	−33.8048	−	19.5172i	−1.22542	−	0.707498i	−0.966069	+	0.258284i	$0.916843\pi$
$762$		0			0
$763$	−7.08415	−	12.2701i	−0.256463	−	0.444207i
$764$		0			0
$765$	8.43500	−	8.76683i	0.304968	−	0.316966i
$766$		0			0
$767$	−2.53863	−	4.39703i	−0.0916645	−	0.158768i
$768$		0			0
$769$	−3.96893	+	6.87439i	−0.143123	+	0.247897i	−0.928671	−	0.370904i	$-0.879048\pi$
$769$	−3.96893	+	6.87439i	−0.143123	+	0.247897i	0.785548	+	0.618801i	$0.212381\pi$
$770$		0			0
$771$	14.3778	−	2.03412i	0.517804	−	0.0732570i
$772$		0			0
$773$	−54.8377			−1.97238			−0.986188	−	0.165632i	$-0.947034\pi$
$773$	−54.8377			−1.97238			−0.986188	+	0.165632i	$0.947034\pi$
$774$		0			0
$775$		−	0.669855i		−	0.0240619i
$776$		0			0
$777$	−21.4190	−	8.63101i	−0.768404	−	0.309636i
$778$		0			0
$779$	−5.32340	−	3.07347i	−0.190731	−	0.110118i
$780$		0			0
$781$	−14.8379	+	8.56666i	−0.530941	+	0.306539i
$782$		0			0
$783$	−10.7895	+	14.9368i	−0.385586	+	0.533796i
$784$		0			0
$785$	18.6531	−	10.7693i	0.665756	−	0.384375i
$786$		0			0
$787$	11.6878	−	20.2439i	0.416625	−	0.721616i	−0.578972	−	0.815347i	$-0.696546\pi$
$787$	11.6878	−	20.2439i	0.416625	−	0.721616i	0.995598	+	0.0937309i	$0.0298793\pi$
$788$		0			0
$789$	38.3518	+	15.4542i	1.36536	+	0.550185i
$790$		0			0
$791$	−7.09195			−0.252161
$792$		0			0
$793$	1.93536			0.0687267
$794$		0			0
$795$	−2.22095	−	15.6984i	−0.0787689	−	0.556764i
$796$		0			0
$797$	−11.2474	+	19.4810i	−0.398403	+	0.690054i	−0.993529	−	0.113578i	$-0.963769\pi$
$797$	−11.2474	+	19.4810i	−0.398403	+	0.690054i	0.595126	+	0.803632i	$0.297102\pi$
$798$		0			0
$799$	18.7113	−	10.8030i	0.661958	−	0.382181i
$800$		0			0
$801$	−14.4703	−	3.57966i	−0.511282	−	0.126481i
$802$		0			0
$803$	11.1327	−	6.42749i	0.392866	−	0.226821i
$804$		0			0
$805$	−4.22042	−	2.43666i	−0.148750	−	0.0858810i
$806$		0			0
$807$	2.88904	−	2.26143i	0.101699	−	0.0796062i
$808$		0			0
$809$			10.6019i			0.372744i	0.982479	+	0.186372i	$0.0596730\pi$
$809$			10.6019i			0.372744i	−0.982479	+	0.186372i	$0.940327\pi$
$810$		0			0
$811$	45.4705			1.59668			0.798342	−	0.602204i	$-0.205711\pi$
$811$	45.4705			1.59668			0.798342	+	0.602204i	$0.205711\pi$
$812$		0			0
$813$	−3.70621	−	4.73478i	−0.129983	−	0.166056i
$814$		0			0
$815$	3.65667	−	6.33355i	0.128088	−	0.221854i
$816$		0			0
$817$	7.84597	+	13.5896i	0.274496	+	0.475441i
$818$		0			0
$819$	−0.610886	+	2.46942i	−0.0213461	+	0.0862885i
$820$		0			0
$821$	6.79733	+	11.7733i	0.237229	+	0.410892i	0.959918	−	0.280281i	$-0.0904276\pi$
$821$	6.79733	+	11.7733i	0.237229	+	0.410892i	−0.722689	+	0.691173i	$0.757094\pi$
$822$		0			0
$823$	45.8629	+	26.4790i	1.59868	+	0.922998i	0.991742	+	0.128250i	$0.0409358\pi$
$823$	45.8629	+	26.4790i	1.59868	+	0.922998i	0.606938	+	0.794749i	$0.292397\pi$
$824$		0			0
$825$	−2.90316	+	0.410729i	−0.101075	+	0.0142998i
$826$		0			0
$827$			13.1858i			0.458517i	0.973366	+	0.229258i	$0.0736301\pi$
$827$			13.1858i			0.458517i	−0.973366	+	0.229258i	$0.926370\pi$
$828$		0			0
$829$			27.6691i			0.960987i	0.876998	+	0.480494i	$0.159542\pi$
$829$			27.6691i			0.960987i	−0.876998	+	0.480494i	$0.840458\pi$
$830$		0			0
$831$	−11.5640	+	28.6977i	−0.401151	+	0.995512i
$832$		0			0
$833$	19.6948	+	11.3708i	0.682384	+	0.393975i
$834$		0			0
$835$	7.04946	+	12.2100i	0.243957	+	0.422545i
$836$		0			0
$837$	−0.354302	+	3.46259i	−0.0122465	+	0.119685i
$838$		0			0
$839$	−7.30540	−	12.6533i	−0.252210	−	0.436841i	0.711924	−	0.702257i	$-0.247824\pi$
$839$	−7.30540	−	12.6533i	−0.252210	−	0.436841i	−0.964134	+	0.265416i	$0.914491\pi$
$840$		0			0
$841$	8.21258	−	14.2246i	0.283192	−	0.490504i
$842$		0			0
$843$	4.63403	−	11.5000i	0.159604	−	0.396080i
$844$		0			0
$845$	12.4835			0.429445
$846$		0			0
$847$		−	9.59740i		−	0.329770i
$848$		0			0
$849$	−3.59482	−	25.4093i	−0.123374	−	0.872047i
$850$		0			0
$851$	−40.4206	−	23.3369i	−1.38560	−	0.799978i
$852$		0			0
$853$	11.9267	−	6.88590i	0.408364	−	0.235769i	−0.281723	−	0.959496i	$-0.590906\pi$
$853$	11.9267	−	6.88590i	0.408364	−	0.235769i	0.690086	+	0.723727i	$0.257573\pi$
$854$		0			0
$855$	−12.1994	−	11.7376i	−0.417210	−	0.401419i
$856$		0			0
$857$	23.7045	−	13.6858i	0.809729	−	0.467497i	−0.0371325	−	0.999310i	$-0.511822\pi$
$857$	23.7045	−	13.6858i	0.809729	−	0.467497i	0.846862	+	0.531813i	$0.178489\pi$
$858$		0			0
$859$	−3.49539	+	6.05420i	−0.119261	+	0.206567i	−0.919475	−	0.393148i	$-0.871386\pi$
$859$	−3.49539	+	6.05420i	−0.119261	+	0.206567i	0.800214	+	0.599715i	$0.204719\pi$
$860$		0			0
$861$	1.75290	−	1.37211i	0.0597388	−	0.0467614i
$862$		0			0
$863$	5.01460			0.170699			0.0853495	−	0.996351i	$-0.472799\pi$
$863$	5.01460			0.170699			0.0853495	+	0.996351i	$0.472799\pi$
$864$		0			0
$865$	−17.3185			−0.588847
$866$		0			0
$867$	−0.756708	+	0.592324i	−0.0256991	+	0.0201164i
$868$		0			0
$869$	−11.0699	+	19.1736i	−0.375520	+	0.650419i
$870$		0			0
$871$	9.64576	−	5.56898i	0.326834	−	0.188698i
$872$		0			0
$873$	−4.97401	+	1.43615i	−0.168345	+	0.0486065i
$874$		0			0
$875$	−1.02179	+	0.589933i	−0.0345429	+	0.0199434i
$876$		0			0
$877$	44.3620	+	25.6124i	1.49800	+	0.864870i	0.999997	−	0.00230558i	$-0.000733889\pi$
$877$	44.3620	+	25.6124i	1.49800	+	0.864870i	0.498002	+	0.867176i	$0.334067\pi$
$878$		0			0
$879$	−1.03938	−	7.34664i	−0.0350573	−	0.247796i
$880$		0			0
$881$		−	37.2669i		−	1.25555i	−0.778394	−	0.627777i	$-0.783965\pi$
$881$		−	37.2669i		−	1.25555i	0.778394	−	0.627777i	$-0.216035\pi$
$882$		0			0
$883$	27.8819			0.938301			0.469151	−	0.883118i	$-0.344560\pi$
$883$	27.8819			0.938301			0.469151	+	0.883118i	$0.344560\pi$
$884$		0			0
$885$	−4.57339	+	11.3495i	−0.153733	+	0.381510i
$886$		0			0
$887$	7.74805	−	13.4200i	0.260154	−	0.450600i	−0.706129	−	0.708084i	$-0.749560\pi$
$887$	7.74805	−	13.4200i	0.260154	−	0.450600i	0.966283	+	0.257483i	$0.0828933\pi$
$888$		0			0
$889$	−0.173751	−	0.300946i	−0.00582742	−	0.0100934i
$890$		0			0
$891$	15.2242	−	0.587577i	0.510029	−	0.0196846i
$892$		0			0
$893$	−15.0327	−	26.0375i	−0.503052	−	0.871311i
$894$		0			0
$895$	−4.32179	−	2.49518i	−0.144461	−	0.0834048i
$896$		0			0
$897$	−1.92168	+	4.76891i	−0.0641629	+	0.159229i
$898$		0			0
$899$			2.37538i			0.0792232i
$900$		0			0
$901$		−	37.1207i		−	1.23667i
$902$		0			0
$903$	−5.62668	+	0.796042i	−0.187244	+	0.0264906i
$904$		0			0
$905$	17.9261	+	10.3496i	0.595882	+	0.344033i
$906$		0			0
$907$	2.14332	+	3.71233i	0.0711676	+	0.123266i	0.899413	−	0.437099i	$-0.143994\pi$
$907$	2.14332	+	3.71233i	0.0711676	+	0.123266i	−0.828246	+	0.560365i	$0.810661\pi$
$908$		0			0
$909$	36.9753	−	10.6759i	1.22639	−	0.354099i
$910$		0			0
$911$	3.66147	+	6.34185i	0.121310	+	0.210115i	0.920284	−	0.391250i	$-0.127957\pi$
$911$	3.66147	+	6.34185i	0.121310	+	0.210115i	−0.798975	+	0.601365i	$0.794624\pi$
$912$		0			0
$913$	−11.7463	+	20.3452i	−0.388746	+	0.673328i
$914$		0			0
$915$	−2.87498	−	3.67286i	−0.0950439	−	0.121421i
$916$		0			0
$917$	20.1020			0.663825
$918$		0			0
$919$			18.3957i			0.606818i	0.952860	+	0.303409i	$0.0981249\pi$
$919$			18.3957i			0.606818i	−0.952860	+	0.303409i	$0.901875\pi$
$920$		0			0
$921$	9.17250	−	7.17990i	0.302244	−	0.236586i
$922$		0			0
$923$	6.29937	+	3.63694i	0.207346	+	0.119711i
$924$		0			0
$925$	−9.78612	+	5.65002i	−0.321766	+	0.185772i
$926$		0			0
$927$	−9.77773	+	10.1624i	−0.321143	+	0.333776i
$928$		0			0
$929$	−17.9190	+	10.3455i	−0.587903	+	0.339426i	−0.764268	−	0.644899i	$-0.776899\pi$
$929$	−17.9190	+	10.3455i	−0.587903	+	0.339426i	0.176365	+	0.984325i	$0.443566\pi$
$930$		0			0
$931$	15.8229	−	27.4061i	0.518575	−	0.898198i
$932$		0			0
$933$	−0.627027	−	4.43203i	−0.0205280	−	0.145098i
$934$		0			0
$935$	−6.86489			−0.224506
$936$		0			0
$937$	−8.59458			−0.280773			−0.140386	−	0.990097i	$-0.544834\pi$
$937$	−8.59458			−0.280773			−0.140386	+	0.990097i	$0.544834\pi$
$938$		0			0
$939$	−11.1997	−	4.51303i	−0.365489	−	0.147277i
$940$		0			0
$941$	7.07610	−	12.2562i	0.230674	−	0.399540i	−0.727332	−	0.686285i	$-0.759240\pi$
$941$	7.07610	−	12.2562i	0.230674	−	0.399540i	0.958007	+	0.286746i	$0.0925735\pi$
$942$		0			0
$943$	3.89643	−	2.24961i	0.126885	−	0.0732573i
$944$		0			0
$945$	5.59385	−	2.50901i	0.181968	−	0.0816181i
$946$		0			0
$947$	−33.0703	+	19.0932i	−1.07464	+	0.620445i	−0.929446	−	0.368958i	$-0.879715\pi$
$947$	−33.0703	+	19.0932i	−1.07464	+	0.620445i	−0.145196	+	0.989403i	$0.546381\pi$
$948$		0			0
$949$	−4.72636	−	2.72876i	−0.153424	−	0.0885794i
$950$		0			0
$951$	−2.70200	−	1.08880i	−0.0876183	−	0.0353067i
$952$		0			0
$953$		−	1.88922i		−	0.0611978i	−0.999532	−	0.0305989i	$-0.990259\pi$
$953$		−	1.88922i		−	0.0611978i	0.999532	−	0.0305989i	$-0.00974145\pi$
$954$		0			0
$955$	−19.2386			−0.622547
$956$		0			0
$957$	10.2949	−	1.45649i	0.332787	−	0.0470816i
$958$		0			0
$959$	−7.82261	+	13.5492i	−0.252605	+	0.437525i
$960$		0			0
$961$	−15.2756	−	26.4582i	−0.492763	−	0.853490i
$962$		0			0
$963$	−30.2591	−	7.48551i	−0.975086	−	0.241217i
$964$		0			0
$965$	−10.6944	−	18.5233i	−0.344265	−	0.596285i
$966$		0			0
$967$	21.5058	+	12.4164i	0.691579	+	0.399283i	0.804203	−	0.594354i	$-0.202592\pi$
$967$	21.5058	+	12.4164i	0.691579	+	0.399283i	−0.112624	+	0.993638i	$0.535926\pi$
$968$		0			0
$969$	−24.4313	−	31.2115i	−0.784846	−	1.00266i
$970$		0			0
$971$		−	21.4099i		−	0.687075i	−0.939139	−	0.343538i	$-0.888375\pi$
$971$		−	21.4099i		−	0.687075i	0.939139	−	0.343538i	$-0.111625\pi$
$972$		0			0
$973$			14.0414i			0.450146i
$974$		0			0
$975$	0.767275	+	0.980213i	0.0245725	+	0.0313919i
$976$		0			0
$977$	11.0044	+	6.35337i	0.352061	+	0.203262i	0.665593	−	0.746315i	$-0.268179\pi$
$977$	11.0044	+	6.35337i	0.352061	+	0.203262i	−0.313532	+	0.949578i	$0.601512\pi$
$978$		0			0
$979$	4.20570	+	7.28449i	0.134415	+	0.232813i
$980$		0			0
$981$	34.9710	+	8.65113i	1.11654	+	0.276209i
$982$		0			0
$983$	−1.35255	−	2.34269i	−0.0431397	−	0.0747202i	0.843649	−	0.536895i	$-0.180403\pi$
$983$	−1.35255	−	2.34269i	−0.0431397	−	0.0747202i	−0.886789	+	0.462174i	$0.847069\pi$
$984$		0			0
$985$	9.46736	−	16.3980i	0.301655	−	0.522482i
$986$		0			0
$987$	10.7806	−	1.52520i	0.343151	−	0.0485477i
$988$		0			0
$989$	−11.4856			−0.365222
$990$		0			0
$991$			18.6055i			0.591024i	0.955339	+	0.295512i	$0.0954903\pi$
$991$			18.6055i			0.591024i	−0.955339	+	0.295512i	$0.904510\pi$
$992$		0			0
$993$	−4.16132	−	1.67684i	−0.132055	−	0.0532130i
$994$		0			0
$995$	20.9623	+	12.1026i	0.664550	+	0.383678i
$996$		0			0
$997$	−14.4956	+	8.36903i	−0.459080	+	0.265050i	−0.711657	−	0.702527i	$-0.752055\pi$
$997$	−14.4956	+	8.36903i	−0.459080	+	0.265050i	0.252578	+	0.967577i	$0.418722\pi$
$998$		0			0
$999$	53.5745	−	24.0298i	1.69502	−	0.760268i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1440.2.cc.a.1391.6		48
3.2	odd	2		4320.2.cc.b.3311.10		48
4.3	odd	2		360.2.bm.a.131.1	yes	48
8.3	odd	2		1440.2.cc.b.1391.6		48
8.5	even	2		360.2.bm.b.131.10	yes	48
9.2	odd	6		1440.2.cc.b.911.6		48
9.7	even	3		4320.2.cc.a.1871.15		48
12.11	even	2		1080.2.bm.b.611.24		48
24.5	odd	2		1080.2.bm.a.611.15		48
24.11	even	2		4320.2.cc.a.3311.15		48
36.7	odd	6		1080.2.bm.a.251.15		48
36.11	even	6		360.2.bm.b.11.10	yes	48
72.11	even	6	inner	1440.2.cc.a.911.6		48
72.29	odd	6		360.2.bm.a.11.1	✓	48
72.43	odd	6		4320.2.cc.b.1871.10		48
72.61	even	6		1080.2.bm.b.251.24		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bm.a.11.1	✓	48	72.29	odd	6
360.2.bm.a.131.1	yes	48	4.3	odd	2
360.2.bm.b.11.10	yes	48	36.11	even	6
360.2.bm.b.131.10	yes	48	8.5	even	2
1080.2.bm.a.251.15		48	36.7	odd	6
1080.2.bm.a.611.15		48	24.5	odd	2
1080.2.bm.b.251.24		48	72.61	even	6
1080.2.bm.b.611.24		48	12.11	even	2
1440.2.cc.a.911.6		48	72.11	even	6	inner
1440.2.cc.a.1391.6		48	1.1	even	1	trivial
1440.2.cc.b.911.6		48	9.2	odd	6
1440.2.cc.b.1391.6		48	8.3	odd	2
4320.2.cc.a.1871.15		48	9.7	even	3
4320.2.cc.a.3311.15		48	24.11	even	2
4320.2.cc.b.1871.10		48	72.43	odd	6
4320.2.cc.b.3311.10		48	3.2	odd	2

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:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1440.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.36390 + 1.06761i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-1.02179 + 0.589933i) q^{7} +(0.720424 - 2.91221i) q^{9} +O(q^{10})\)	\(q+(-1.36390 + 1.06761i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-1.02179 + 0.589933i) q^{7} +(0.720424 - 2.91221i) q^{9} +(-1.46604 + 0.846417i) q^{11} +(0.622400 + 0.359343i) q^{13} +(-0.242628 - 1.71497i) q^{15} -4.05527i q^{17} -5.64306 q^{19} +(0.763803 - 1.89548i) q^{21} +(2.06520 - 3.57703i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(2.12652 + 4.74109i) q^{27} +(1.77305 + 3.07101i) q^{29} +(0.580112 + 0.334928i) q^{31} +(1.09588 - 2.71958i) q^{33} -1.17987i q^{35} -11.3000i q^{37} +(-1.23253 + 0.174373i) q^{39} +(0.943354 + 0.544646i) q^{41} +(-1.39038 - 2.40820i) q^{43} +(2.16184 + 2.08001i) q^{45} +(2.66393 + 4.61407i) q^{47} +(-2.80396 + 4.85660i) q^{49} +(4.32944 + 5.53096i) q^{51} +9.15371 q^{53} -1.69283i q^{55} +(7.69655 - 6.02458i) q^{57} +(-6.11816 - 3.53232i) q^{59} +(2.33213 - 1.34646i) q^{61} +(0.981886 + 3.40068i) q^{63} +(-0.622400 + 0.359343i) q^{65} +(7.74884 - 13.4214i) q^{67} +(1.00215 + 7.08353i) q^{69} +10.1211 q^{71} -7.59376 q^{73} +(1.60652 + 0.647364i) q^{75} +(0.998659 - 1.72973i) q^{77} +(11.3263 - 6.53925i) q^{79} +(-7.96198 - 4.19606i) q^{81} +(12.0184 - 6.93884i) q^{83} +(3.51196 + 2.02763i) q^{85} +(-5.69690 - 2.29562i) q^{87} -4.96883i q^{89} -0.847953 q^{91} +(-1.14878 + 0.162526i) q^{93} +(2.82153 - 4.88703i) q^{95} +(-0.862865 - 1.49453i) q^{97} +(1.40878 + 4.87919i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{5}+O(q^{10}) \) 48 * q - 24 * q^5	\( 48 q - 24 q^{5} - 4 q^{21} - 24 q^{25} - 12 q^{27} - 8 q^{33} - 16 q^{39} + 12 q^{41} - 12 q^{47} + 24 q^{49} + 20 q^{51} + 4 q^{57} + 36 q^{59} + 12 q^{61} - 56 q^{63} - 40 q^{69} - 8 q^{81} + 60 q^{83} - 36 q^{87} + 16 q^{99}+O(q^{100}) \) 48 * q - 24 * q^5 - 4 * q^21 - 24 * q^25 - 12 * q^27 - 8 * q^33 - 16 * q^39 + 12 * q^41 - 12 * q^47 + 24 * q^49 + 20 * q^51 + 4 * q^57 + 36 * q^59 + 12 * q^61 - 56 * q^63 - 40 * q^69 - 8 * q^81 + 60 * q^83 - 36 * q^87 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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