LMFDB - Embedded newform 1120.2.bz.d.591.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1120,2,Mod(271,1120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1120, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("1120.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1120 = 2^{5} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1120.bz (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:	$8.94324502638$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			591.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1120.591
Dual form			1120.2.bz.d.271.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(0.866025 + 2.50000i) q^{7} +O(q^{10})$	\(q+(1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(0.866025 + 2.50000i) q^{7} +(-0.732051 + 1.26795i) q^{11} +4.73205 q^{13} +1.73205i q^{15} +(-1.09808 - 0.633975i) q^{17} +(7.09808 - 4.09808i) q^{19} +(-0.866025 + 4.50000i) q^{21} +(-5.13397 + 2.96410i) q^{23} +(-0.500000 + 0.866025i) q^{25} -5.19615i q^{27} +10.4641i q^{29} +(-1.09808 + 1.90192i) q^{31} +(-2.19615 + 1.26795i) q^{33} +(-1.73205 + 2.00000i) q^{35} +(1.73205 - 1.00000i) q^{37} +(7.09808 + 4.09808i) q^{39} +5.19615i q^{41} -3.92820 q^{43} +(-1.26795 - 2.19615i) q^{47} +(-5.50000 + 4.33013i) q^{49} +(-1.09808 - 1.90192i) q^{51} +(0.169873 + 0.0980762i) q^{53} -1.46410 q^{55} +14.1962 q^{57} +(-4.09808 - 2.36603i) q^{59} +(2.13397 + 3.69615i) q^{61} +(2.36603 + 4.09808i) q^{65} +(5.69615 - 9.86603i) q^{67} -10.2679 q^{69} -5.26795i q^{71} +(-10.0981 - 5.83013i) q^{73} +(-1.50000 + 0.866025i) q^{75} +(-3.80385 - 0.732051i) q^{77} +(4.09808 - 2.36603i) q^{79} +(4.50000 - 7.79423i) q^{81} +14.6603i q^{83} -1.26795i q^{85} +(-9.06218 + 15.6962i) q^{87} +(12.6962 - 7.33013i) q^{89} +(4.09808 + 11.8301i) q^{91} +(-3.29423 + 1.90192i) q^{93} +(7.09808 + 4.09808i) q^{95} -3.46410i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} + 2 q^{5}+O(q^{10}) $ 4 * q + 6 * q^3 + 2 * q^5	$ 4 q + 6 q^{3} + 2 q^{5} + 4 q^{11} + 12 q^{13} + 6 q^{17} + 18 q^{19} - 24 q^{23} - 2 q^{25} + 6 q^{31} + 12 q^{33} + 18 q^{39} + 12 q^{43} - 12 q^{47} - 22 q^{49} + 6 q^{51} + 18 q^{53} + 8 q^{55} + 36 q^{57} - 6 q^{59} + 12 q^{61} + 6 q^{65} + 2 q^{67} - 48 q^{69} - 30 q^{73} - 6 q^{75} - 36 q^{77} + 6 q^{79} + 18 q^{81} - 12 q^{87} + 30 q^{89} + 6 q^{91} + 18 q^{93} + 18 q^{95}+O(q^{100}) $ 4 * q + 6 * q^3 + 2 * q^5 + 4 * q^11 + 12 * q^13 + 6 * q^17 + 18 * q^19 - 24 * q^23 - 2 * q^25 + 6 * q^31 + 12 * q^33 + 18 * q^39 + 12 * q^43 - 12 * q^47 - 22 * q^49 + 6 * q^51 + 18 * q^53 + 8 * q^55 + 36 * q^57 - 6 * q^59 + 12 * q^61 + 6 * q^65 + 2 * q^67 - 48 * q^69 - 30 * q^73 - 6 * q^75 - 36 * q^77 + 6 * q^79 + 18 * q^81 - 12 * q^87 + 30 * q^89 + 6 * q^91 + 18 * q^93 + 18 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times$.

$n$	$351$	$421$	$801$	$897$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	0.866025	+	2.50000i	0.327327	+	0.944911i
$7$	0.866025	+	2.50000i	0.327327	+	0.944911i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.732051	+	1.26795i	−0.220722	+	0.382301i	−0.955027	−	0.296518i	$-0.904175\pi$
$11$	−0.732051	+	1.26795i	−0.220722	+	0.382301i	0.734306	+	0.678819i	$0.237508\pi$
$12$		0			0
$13$	4.73205			1.31243			0.656217	−	0.754572i	$-0.272155\pi$
$13$	4.73205			1.31243			0.656217	+	0.754572i	$0.272155\pi$
$14$		0			0
$15$			1.73205i			0.447214i
$16$		0			0
$17$	−1.09808	−	0.633975i	−0.266323	−	0.153761i	0.360893	−	0.932607i	$-0.382472\pi$
$17$	−1.09808	−	0.633975i	−0.266323	−	0.153761i	−0.627215	+	0.778846i	$0.715805\pi$
$18$		0			0
$19$	7.09808	−	4.09808i	1.62841	−	0.940163i	0.643843	−	0.765158i	$-0.277339\pi$
$19$	7.09808	−	4.09808i	1.62841	−	0.940163i	0.984567	−	0.175005i	$-0.0559943\pi$
$20$		0			0
$21$	−0.866025	+	4.50000i	−0.188982	+	0.981981i
$22$		0			0
$23$	−5.13397	+	2.96410i	−1.07051	+	0.618058i	−0.928320	−	0.371782i	$-0.878747\pi$
$23$	−5.13397	+	2.96410i	−1.07051	+	0.618058i	−0.142188	+	0.989840i	$0.545414\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$		−	5.19615i		−	1.00000i
$28$		0			0
$29$			10.4641i			1.94313i	0.236763	+	0.971567i	$0.423914\pi$
$29$			10.4641i			1.94313i	−0.236763	+	0.971567i	$0.576086\pi$
$30$		0			0
$31$	−1.09808	+	1.90192i	−0.197220	+	0.341596i	−0.947626	−	0.319382i	$-0.896525\pi$
$31$	−1.09808	+	1.90192i	−0.197220	+	0.341596i	0.750406	+	0.660977i	$0.229858\pi$
$32$		0			0
$33$	−2.19615	+	1.26795i	−0.382301	+	0.220722i
$34$		0			0
$35$	−1.73205	+	2.00000i	−0.292770	+	0.338062i
$36$		0			0
$37$	1.73205	−	1.00000i	0.284747	−	0.164399i	−0.350823	−	0.936442i	$-0.614098\pi$
$37$	1.73205	−	1.00000i	0.284747	−	0.164399i	0.635571	+	0.772043i	$0.280765\pi$
$38$		0			0
$39$	7.09808	+	4.09808i	1.13660	+	0.656217i
$40$		0			0
$41$			5.19615i			0.811503i	0.913984	+	0.405751i	$0.132990\pi$
$41$			5.19615i			0.811503i	−0.913984	+	0.405751i	$0.867010\pi$
$42$		0			0
$43$	−3.92820			−0.599045			−0.299523	−	0.954089i	$-0.596827\pi$
$43$	−3.92820			−0.599045			−0.299523	+	0.954089i	$0.596827\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.26795	−	2.19615i	−0.184949	−	0.320342i	0.758610	−	0.651545i	$-0.225879\pi$
$47$	−1.26795	−	2.19615i	−0.184949	−	0.320342i	−0.943559	+	0.331203i	$0.892545\pi$
$48$		0			0
$49$	−5.50000	+	4.33013i	−0.785714	+	0.618590i
$50$		0			0
$51$	−1.09808	−	1.90192i	−0.153761	−	0.266323i
$52$		0			0
$53$	0.169873	+	0.0980762i	0.0233338	+	0.0134718i	0.511622	−	0.859211i	$-0.329045\pi$
$53$	0.169873	+	0.0980762i	0.0233338	+	0.0134718i	−0.488288	+	0.872683i	$0.662378\pi$
$54$		0			0
$55$	−1.46410			−0.197419
$56$		0			0
$57$	14.1962			1.88033
$58$		0			0
$59$	−4.09808	−	2.36603i	−0.533524	−	0.308030i	0.208926	−	0.977931i	$-0.433003\pi$
$59$	−4.09808	−	2.36603i	−0.533524	−	0.308030i	−0.742450	+	0.669901i	$0.766336\pi$
$60$		0			0
$61$	2.13397	+	3.69615i	0.273227	+	0.473244i	0.969686	−	0.244353i	$-0.0785755\pi$
$61$	2.13397	+	3.69615i	0.273227	+	0.473244i	−0.696459	+	0.717597i	$0.745242\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.36603	+	4.09808i	0.293469	+	0.508304i
$66$		0			0
$67$	5.69615	−	9.86603i	0.695896	−	1.20533i	−0.273982	−	0.961735i	$-0.588341\pi$
$67$	5.69615	−	9.86603i	0.695896	−	1.20533i	0.969878	−	0.243592i	$-0.0783258\pi$
$68$		0			0
$69$	−10.2679			−1.23612
$70$		0			0
$71$		−	5.26795i		−	0.625191i	−0.949886	−	0.312595i	$-0.898802\pi$
$71$		−	5.26795i		−	0.625191i	0.949886	−	0.312595i	$-0.101198\pi$
$72$		0			0
$73$	−10.0981	−	5.83013i	−1.18189	−	0.682365i	−0.225439	−	0.974257i	$-0.572382\pi$
$73$	−10.0981	−	5.83013i	−1.18189	−	0.682365i	−0.956451	+	0.291892i	$0.905715\pi$
$74$		0			0
$75$	−1.50000	+	0.866025i	−0.173205	+	0.100000i
$76$		0			0
$77$	−3.80385	−	0.732051i	−0.433489	−	0.0834249i
$78$		0			0
$79$	4.09808	−	2.36603i	0.461070	−	0.266199i	−0.251424	−	0.967877i	$-0.580899\pi$
$79$	4.09808	−	2.36603i	0.461070	−	0.266199i	0.712494	+	0.701678i	$0.247566\pi$
$80$		0			0
$81$	4.50000	−	7.79423i	0.500000	−	0.866025i
$82$		0			0
$83$			14.6603i			1.60917i	0.593836	+	0.804586i	$0.297613\pi$
$83$			14.6603i			1.60917i	−0.593836	+	0.804586i	$0.702387\pi$
$84$		0			0
$85$		−	1.26795i		−	0.137528i
$86$		0			0
$87$	−9.06218	+	15.6962i	−0.971567	+	1.68280i
$88$		0			0
$89$	12.6962	−	7.33013i	1.34579	−	0.776992i	0.358139	−	0.933668i	$-0.383411\pi$
$89$	12.6962	−	7.33013i	1.34579	−	0.776992i	0.987650	+	0.156676i	$0.0500779\pi$
$90$		0			0
$91$	4.09808	+	11.8301i	0.429595	+	1.24013i
$92$		0			0
$93$	−3.29423	+	1.90192i	−0.341596	+	0.197220i
$94$		0			0
$95$	7.09808	+	4.09808i	0.728247	+	0.420454i
$96$		0			0
$97$		−	3.46410i		−	0.351726i	−0.984415	−	0.175863i	$-0.943728\pi$
$97$		−	3.46410i		−	0.351726i	0.984415	−	0.175863i	$-0.0562716\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.59808	−	9.69615i	0.557029	−	0.964803i	−0.440713	−	0.897648i	$-0.645274\pi$
$101$	5.59808	−	9.69615i	0.557029	−	0.964803i	0.997743	−	0.0671552i	$-0.0213923\pi$
$102$		0			0
$103$	−1.33013	−	2.30385i	−0.131061	−	0.227005i	0.793025	−	0.609190i	$-0.208505\pi$
$103$	−1.33013	−	2.30385i	−0.131061	−	0.227005i	−0.924086	+	0.382185i	$0.875172\pi$
$104$		0			0
$105$	−4.33013	+	1.50000i	−0.422577	+	0.146385i
$106$		0			0
$107$	3.50000	+	6.06218i	0.338358	+	0.586053i	0.984124	−	0.177482i	$-0.0567953\pi$
$107$	3.50000	+	6.06218i	0.338358	+	0.586053i	−0.645766	+	0.763535i	$0.723462\pi$
$108$		0			0
$109$	−15.0622	−	8.69615i	−1.44269	−	0.832940i	−0.444666	−	0.895696i	$-0.646678\pi$
$109$	−15.0622	−	8.69615i	−1.44269	−	0.832940i	−0.998029	+	0.0627561i	$0.980011\pi$
$110$		0			0
$111$	3.46410			0.328798
$112$		0			0
$113$	−3.26795			−0.307423			−0.153711	−	0.988116i	$-0.549123\pi$
$113$	−3.26795			−0.307423			−0.153711	+	0.988116i	$0.549123\pi$
$114$		0			0
$115$	−5.13397	−	2.96410i	−0.478746	−	0.276404i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.633975	−	3.29423i	0.0581164	−	0.301981i
$120$		0			0
$121$	4.42820	+	7.66987i	0.402564	+	0.697261i
$122$		0			0
$123$	−4.50000	+	7.79423i	−0.405751	+	0.702782i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$		−	15.4641i		−	1.37222i	−0.727499	−	0.686109i	$-0.759317\pi$
$127$		−	15.4641i		−	1.37222i	0.727499	−	0.686109i	$-0.240683\pi$
$128$		0			0
$129$	−5.89230	−	3.40192i	−0.518789	−	0.299523i
$130$		0			0
$131$	10.3923	−	6.00000i	0.907980	−	0.524222i	0.0281993	−	0.999602i	$-0.491023\pi$
$131$	10.3923	−	6.00000i	0.907980	−	0.524222i	0.879781	+	0.475380i	$0.157689\pi$
$132$		0			0
$133$	16.3923	+	14.1962i	1.42139	+	1.23096i
$134$		0			0
$135$	4.50000	−	2.59808i	0.387298	−	0.223607i
$136$		0			0
$137$	6.19615	−	10.7321i	0.529373	−	0.916901i	−0.470040	−	0.882645i	$-0.655761\pi$
$137$	6.19615	−	10.7321i	0.529373	−	0.916901i	0.999413	−	0.0342559i	$-0.0109061\pi$
$138$		0			0
$139$			9.46410i			0.802735i	0.915917	+	0.401367i	$0.131465\pi$
$139$			9.46410i			0.802735i	−0.915917	+	0.401367i	$0.868535\pi$
$140$		0			0
$141$		−	4.39230i		−	0.369899i
$142$		0			0
$143$	−3.46410	+	6.00000i	−0.289683	+	0.501745i
$144$		0			0
$145$	−9.06218	+	5.23205i	−0.752573	+	0.434498i
$146$		0			0
$147$	−12.0000	+	1.73205i	−0.989743	+	0.142857i
$148$		0			0
$149$	2.13397	−	1.23205i	0.174822	−	0.100934i	−0.410036	−	0.912070i	$-0.634484\pi$
$149$	2.13397	−	1.23205i	0.174822	−	0.100934i	0.584858	+	0.811136i	$0.301150\pi$
$150$		0			0
$151$	5.02628	+	2.90192i	0.409033	+	0.236155i	0.690374	−	0.723453i	$-0.257446\pi$
$151$	5.02628	+	2.90192i	0.409033	+	0.236155i	−0.281341	+	0.959608i	$0.590779\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−2.19615			−0.176399
$156$		0			0
$157$	1.26795	−	2.19615i	0.101193	−	0.175272i	−0.810983	−	0.585069i	$-0.801067\pi$
$157$	1.26795	−	2.19615i	0.101193	−	0.175272i	0.912177	+	0.409797i	$0.134401\pi$
$158$		0			0
$159$	0.169873	+	0.294229i	0.0134718	+	0.0233338i
$160$		0			0
$161$	−11.8564	−	10.2679i	−0.934416	−	0.809228i
$162$		0			0
$163$	−5.00000	−	8.66025i	−0.391630	−	0.678323i	0.601035	−	0.799223i	$-0.294755\pi$
$163$	−5.00000	−	8.66025i	−0.391630	−	0.678323i	−0.992665	+	0.120900i	$0.961422\pi$
$164$		0			0
$165$	−2.19615	−	1.26795i	−0.170970	−	0.0987097i
$166$		0			0
$167$	−3.33975			−0.258437			−0.129219	−	0.991616i	$-0.541247\pi$
$167$	−3.33975			−0.258437			−0.129219	+	0.991616i	$0.541247\pi$
$168$		0			0
$169$	9.39230			0.722485
$170$		0			0
$171$		0			0
$172$		0			0
$173$	0.803848	+	1.39230i	0.0611154	+	0.105855i	0.894964	−	0.446138i	$-0.147201\pi$
$173$	0.803848	+	1.39230i	0.0611154	+	0.105855i	−0.833849	+	0.551993i	$0.813868\pi$
$174$		0			0
$175$	−2.59808	−	0.500000i	−0.196396	−	0.0377964i
$176$		0			0
$177$	−4.09808	−	7.09808i	−0.308030	−	0.533524i
$178$		0			0
$179$	9.09808	−	15.7583i	0.680022	−	1.17783i	−0.294951	−	0.955512i	$-0.595303\pi$
$179$	9.09808	−	15.7583i	0.680022	−	1.17783i	0.974974	−	0.222321i	$-0.0713632\pi$
$180$		0			0
$181$	1.73205			0.128742			0.0643712	−	0.997926i	$-0.479496\pi$
$181$	1.73205			0.128742			0.0643712	+	0.997926i	$0.479496\pi$
$182$		0			0
$183$			7.39230i			0.546455i
$184$		0			0
$185$	1.73205	+	1.00000i	0.127343	+	0.0735215i
$186$		0			0
$187$	1.60770	−	0.928203i	0.117566	−	0.0678769i
$188$		0			0
$189$	12.9904	−	4.50000i	0.944911	−	0.327327i
$190$		0			0
$191$	−21.1244	+	12.1962i	−1.52850	+	0.882483i	−0.529080	+	0.848572i	$0.677463\pi$
$191$	−21.1244	+	12.1962i	−1.52850	+	0.882483i	−0.999425	+	0.0339106i	$0.989204\pi$
$192$		0			0
$193$	−6.92820	+	12.0000i	−0.498703	+	0.863779i	−0.999999	−	0.00149702i	$-0.999523\pi$
$193$	−6.92820	+	12.0000i	−0.498703	+	0.863779i	0.501296	+	0.865276i	$0.332857\pi$
$194$		0			0
$195$			8.19615i			0.586939i
$196$		0			0
$197$		−	4.92820i		−	0.351120i	−0.984469	−	0.175560i	$-0.943826\pi$
$197$		−	4.92820i		−	0.351120i	0.984469	−	0.175560i	$-0.0561736\pi$
$198$		0			0
$199$	9.00000	−	15.5885i	0.637993	−	1.10504i	−0.347879	−	0.937539i	$-0.613098\pi$
$199$	9.00000	−	15.5885i	0.637993	−	1.10504i	0.985873	−	0.167497i	$-0.0535685\pi$
$200$		0			0
$201$	17.0885	−	9.86603i	1.20533	−	0.695896i
$202$		0			0
$203$	−26.1603	+	9.06218i	−1.83609	+	0.636040i
$204$		0			0
$205$	−4.50000	+	2.59808i	−0.314294	+	0.181458i
$206$		0			0
$207$		0			0
$208$		0			0
$209$			12.0000i			0.830057i
$210$		0			0
$211$	18.5885			1.27968			0.639841	−	0.768507i	$-0.279000\pi$
$211$	18.5885			1.27968			0.639841	+	0.768507i	$0.279000\pi$
$212$		0			0
$213$	4.56218	−	7.90192i	0.312595	−	0.541431i
$214$		0			0
$215$	−1.96410	−	3.40192i	−0.133951	−	0.232009i
$216$		0			0
$217$	−5.70577	−	1.09808i	−0.387333	−	0.0745423i
$218$		0			0
$219$	−10.0981	−	17.4904i	−0.682365	−	1.18189i
$220$		0			0
$221$	−5.19615	−	3.00000i	−0.349531	−	0.201802i
$222$		0			0
$223$	13.8564			0.927894			0.463947	−	0.885863i	$-0.346433\pi$
$223$	13.8564			0.927894			0.463947	+	0.885863i	$0.346433\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.39230	+	2.53590i	0.291528	+	0.168313i	0.638631	−	0.769514i	$-0.279501\pi$
$227$	4.39230	+	2.53590i	0.291528	+	0.168313i	−0.347103	+	0.937827i	$0.612835\pi$
$228$		0			0
$229$	−7.73205	−	13.3923i	−0.510948	−	0.884988i	−0.999919	−	0.0126885i	$-0.995961\pi$
$229$	−7.73205	−	13.3923i	−0.510948	−	0.884988i	0.488971	−	0.872300i	$-0.337372\pi$
$230$		0			0
$231$	−5.07180	−	4.39230i	−0.333700	−	0.288992i
$232$		0			0
$233$	2.63397	+	4.56218i	0.172557	+	0.298878i	0.939313	−	0.343061i	$-0.111464\pi$
$233$	2.63397	+	4.56218i	0.172557	+	0.298878i	−0.766756	+	0.641939i	$0.778130\pi$
$234$		0			0
$235$	1.26795	−	2.19615i	0.0827119	−	0.143261i
$236$		0			0
$237$	8.19615			0.532397
$238$		0			0
$239$		−	1.80385i		−	0.116681i	−0.998297	−	0.0583406i	$-0.981419\pi$
$239$		−	1.80385i		−	0.116681i	0.998297	−	0.0583406i	$-0.0185809\pi$
$240$		0			0
$241$	−6.80385	−	3.92820i	−0.438274	−	0.253038i	0.264591	−	0.964361i	$-0.414763\pi$
$241$	−6.80385	−	3.92820i	−0.438274	−	0.253038i	−0.702865	+	0.711323i	$0.748096\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−6.50000	−	2.59808i	−0.415270	−	0.165985i
$246$		0			0
$247$	33.5885	−	19.3923i	2.13718	−	1.23390i
$248$		0			0
$249$	−12.6962	+	21.9904i	−0.804586	+	1.39358i
$250$		0			0
$251$		−	15.8038i		−	0.997530i	−0.866737	−	0.498765i	$-0.833787\pi$
$251$		−	15.8038i		−	0.997530i	0.866737	−	0.498765i	$-0.166213\pi$
$252$		0			0
$253$		−	8.67949i		−	0.545675i
$254$		0			0
$255$	1.09808	−	1.90192i	0.0687642	−	0.119103i
$256$		0			0
$257$	5.19615	−	3.00000i	0.324127	−	0.187135i	−0.329104	−	0.944294i	$-0.606747\pi$
$257$	5.19615	−	3.00000i	0.324127	−	0.187135i	0.653231	+	0.757159i	$0.273413\pi$
$258$		0			0
$259$	4.00000	+	3.46410i	0.248548	+	0.215249i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−13.9186	−	8.03590i	−0.858257	−	0.495515i	0.00517143	−	0.999987i	$-0.498354\pi$
$263$	−13.9186	−	8.03590i	−0.858257	−	0.495515i	−0.863428	+	0.504472i	$0.831687\pi$
$264$		0			0
$265$			0.196152i			0.0120495i
$266$		0			0
$267$	25.3923			1.55398
$268$		0			0
$269$	−4.33013	+	7.50000i	−0.264013	+	0.457283i	−0.967304	−	0.253618i	$-0.918379\pi$
$269$	−4.33013	+	7.50000i	−0.264013	+	0.457283i	0.703292	+	0.710901i	$0.251713\pi$
$270$		0			0
$271$	−7.09808	−	12.2942i	−0.431177	−	0.746821i	0.565798	−	0.824544i	$-0.308568\pi$
$271$	−7.09808	−	12.2942i	−0.431177	−	0.746821i	−0.996975	+	0.0777230i	$0.975235\pi$
$272$		0			0
$273$	−4.09808	+	21.2942i	−0.248027	+	1.28879i
$274$		0			0
$275$	−0.732051	−	1.26795i	−0.0441443	−	0.0764602i
$276$		0			0
$277$	1.90192	+	1.09808i	0.114276	+	0.0659770i	0.556048	−	0.831150i	$-0.312317\pi$
$277$	1.90192	+	1.09808i	0.114276	+	0.0659770i	−0.441773	+	0.897127i	$0.645650\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	21.8564			1.30384			0.651922	−	0.758286i	$-0.273963\pi$
$281$	21.8564			1.30384			0.651922	+	0.758286i	$0.273963\pi$
$282$		0			0
$283$	−3.00000	−	1.73205i	−0.178331	−	0.102960i	0.408177	−	0.912903i	$-0.366165\pi$
$283$	−3.00000	−	1.73205i	−0.178331	−	0.102960i	−0.586509	+	0.809943i	$0.699498\pi$
$284$		0			0
$285$	7.09808	+	12.2942i	0.420454	+	0.728247i
$286$		0			0
$287$	−12.9904	+	4.50000i	−0.766798	+	0.265627i
$288$		0			0
$289$	−7.69615	−	13.3301i	−0.452715	−	0.784125i
$290$		0			0
$291$	3.00000	−	5.19615i	0.175863	−	0.304604i
$292$		0			0
$293$	−13.8564			−0.809500			−0.404750	−	0.914427i	$-0.632641\pi$
$293$	−13.8564			−0.809500			−0.404750	+	0.914427i	$0.632641\pi$
$294$		0			0
$295$		−	4.73205i		−	0.275511i
$296$		0			0
$297$	6.58846	+	3.80385i	0.382301	+	0.220722i
$298$		0			0
$299$	−24.2942	+	14.0263i	−1.40497	+	0.811161i
$300$		0			0
$301$	−3.40192	−	9.82051i	−0.196084	−	0.566045i
$302$		0			0
$303$	16.7942	−	9.69615i	0.964803	−	0.557029i
$304$		0			0
$305$	−2.13397	+	3.69615i	−0.122191	+	0.211641i
$306$		0			0
$307$			6.12436i			0.349535i	0.984610	+	0.174768i	$0.0559175\pi$
$307$			6.12436i			0.349535i	−0.984610	+	0.174768i	$0.944083\pi$
$308$		0			0
$309$		−	4.60770i		−	0.262123i
$310$		0			0
$311$	1.90192	−	3.29423i	0.107848	−	0.186799i	−0.807050	−	0.590483i	$-0.798937\pi$
$311$	1.90192	−	3.29423i	0.107848	−	0.186799i	0.914898	+	0.403684i	$0.132271\pi$
$312$		0			0
$313$	−15.0000	+	8.66025i	−0.847850	+	0.489506i	−0.859925	−	0.510421i	$-0.829490\pi$
$313$	−15.0000	+	8.66025i	−0.847850	+	0.489506i	0.0120748	+	0.999927i	$0.496156\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.02628	+	4.63397i	−0.450801	+	0.260270i	−0.708168	−	0.706044i	$-0.750478\pi$
$317$	−8.02628	+	4.63397i	−0.450801	+	0.260270i	0.257368	+	0.966314i	$0.417145\pi$
$318$		0			0
$319$	−13.2679	−	7.66025i	−0.742863	−	0.428892i
$320$		0			0
$321$			12.1244i			0.676716i
$322$		0			0
$323$	−10.3923			−0.578243
$324$		0			0
$325$	−2.36603	+	4.09808i	−0.131243	+	0.227320i
$326$		0			0
$327$	−15.0622	−	26.0885i	−0.832940	−	1.44269i
$328$		0			0
$329$	4.39230	−	5.07180i	0.242156	−	0.279617i
$330$		0			0
$331$	−11.3660	−	19.6865i	−0.624733	−	1.08207i	−0.988592	−	0.150616i	$-0.951874\pi$
$331$	−11.3660	−	19.6865i	−0.624733	−	1.08207i	0.363859	−	0.931454i	$-0.381459\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	11.3923			0.622428
$336$		0			0
$337$	−28.9808			−1.57868			−0.789341	−	0.613955i	$-0.789578\pi$
$337$	−28.9808			−1.57868			−0.789341	+	0.613955i	$0.789578\pi$
$338$		0			0
$339$	−4.90192	−	2.83013i	−0.266236	−	0.153711i
$340$		0			0
$341$	−1.60770	−	2.78461i	−0.0870616	−	0.150795i
$342$		0			0
$343$	−15.5885	−	10.0000i	−0.841698	−	0.539949i
$344$		0			0
$345$	−5.13397	−	8.89230i	−0.276404	−	0.478746i
$346$		0			0
$347$	8.62436	−	14.9378i	0.462980	−	0.801904i	−0.536128	−	0.844137i	$-0.680114\pi$
$347$	8.62436	−	14.9378i	0.462980	−	0.801904i	0.999108	+	0.0422323i	$0.0134470\pi$
$348$		0			0
$349$	34.5167			1.84763			0.923817	−	0.382834i	$-0.125052\pi$
$349$	34.5167			1.84763			0.923817	+	0.382834i	$0.125052\pi$
$350$		0			0
$351$		−	24.5885i		−	1.31243i
$352$		0			0
$353$	−30.0788	−	17.3660i	−1.60094	−	0.924300i	−0.991301	−	0.131618i	$-0.957983\pi$
$353$	−30.0788	−	17.3660i	−1.60094	−	0.924300i	−0.609634	−	0.792683i	$-0.708684\pi$
$354$		0			0
$355$	4.56218	−	2.63397i	0.242135	−	0.139797i
$356$		0			0
$357$	3.80385	−	4.39230i	0.201321	−	0.232465i
$358$		0			0
$359$	−23.9545	+	13.8301i	−1.26427	+	0.729926i	−0.973898	−	0.226988i	$-0.927112\pi$
$359$	−23.9545	+	13.8301i	−1.26427	+	0.729926i	−0.290372	+	0.956914i	$0.593779\pi$
$360$		0			0
$361$	24.0885	−	41.7224i	1.26781	−	2.19592i
$362$		0			0
$363$			15.3397i			0.805128i
$364$		0			0
$365$		−	11.6603i		−	0.610326i
$366$		0			0
$367$	−9.86603	+	17.0885i	−0.515002	+	0.892010i	0.484846	+	0.874599i	$0.338876\pi$
$367$	−9.86603	+	17.0885i	−0.515002	+	0.892010i	−0.999848	+	0.0174107i	$0.994458\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.0980762	+	0.509619i	−0.00509186	+	0.0264581i
$372$		0			0
$373$	0.803848	−	0.464102i	0.0416216	−	0.0240303i	−0.479045	−	0.877790i	$-0.659017\pi$
$373$	0.803848	−	0.464102i	0.0416216	−	0.0240303i	0.520666	+	0.853760i	$0.325684\pi$
$374$		0			0
$375$	−1.50000	−	0.866025i	−0.0774597	−	0.0447214i
$376$		0			0
$377$			49.5167i			2.55024i
$378$		0			0
$379$	26.4449			1.35838			0.679191	−	0.733962i	$-0.262331\pi$
$379$	26.4449			1.35838			0.679191	+	0.733962i	$0.262331\pi$
$380$		0			0
$381$	13.3923	−	23.1962i	0.686109	−	1.18837i
$382$		0			0
$383$	8.59808	+	14.8923i	0.439341	+	0.760961i	0.997639	−	0.0686795i	$-0.0218786\pi$
$383$	8.59808	+	14.8923i	0.439341	+	0.760961i	−0.558298	+	0.829641i	$0.688545\pi$
$384$		0			0
$385$	−1.26795	−	3.66025i	−0.0646207	−	0.186544i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−21.7128	−	12.5359i	−1.10088	−	0.635595i	−0.164430	−	0.986389i	$-0.552579\pi$
$389$	−21.7128	−	12.5359i	−1.10088	−	0.635595i	−0.936453	+	0.350793i	$0.885912\pi$
$390$		0			0
$391$	7.51666			0.380134
$392$		0			0
$393$	20.7846			1.04844
$394$		0			0
$395$	4.09808	+	2.36603i	0.206197	+	0.119048i
$396$		0			0
$397$	−13.3923	−	23.1962i	−0.672141	−	1.16418i	−0.977296	−	0.211879i	$-0.932042\pi$
$397$	−13.3923	−	23.1962i	−0.672141	−	1.16418i	0.305155	−	0.952303i	$-0.401292\pi$
$398$		0			0
$399$	12.2942	+	35.4904i	0.615481	+	1.77674i
$400$		0			0
$401$	−4.23205	−	7.33013i	−0.211339	−	0.366049i	0.740795	−	0.671731i	$-0.234449\pi$
$401$	−4.23205	−	7.33013i	−0.211339	−	0.366049i	−0.952134	+	0.305682i	$0.901116\pi$
$402$		0			0
$403$	−5.19615	+	9.00000i	−0.258839	+	0.448322i
$404$		0			0
$405$	9.00000			0.447214
$406$		0			0
$407$			2.92820i			0.145146i
$408$		0			0
$409$	17.8923	+	10.3301i	0.884718	+	0.510792i	0.872211	−	0.489130i	$-0.162686\pi$
$409$	17.8923	+	10.3301i	0.884718	+	0.510792i	0.0125066	+	0.999922i	$0.496019\pi$
$410$		0			0
$411$	18.5885	−	10.7321i	0.916901	−	0.529373i
$412$		0			0
$413$	2.36603	−	12.2942i	0.116424	−	0.604959i
$414$		0			0
$415$	−12.6962	+	7.33013i	−0.623230	+	0.359822i
$416$		0			0
$417$	−8.19615	+	14.1962i	−0.401367	+	0.695189i
$418$		0			0
$419$			11.3205i			0.553043i	0.961008	+	0.276522i	$0.0891817\pi$
$419$			11.3205i			0.553043i	−0.961008	+	0.276522i	$0.910818\pi$
$420$		0			0
$421$			21.2487i			1.03560i	0.855502	+	0.517799i	$0.173249\pi$
$421$			21.2487i			1.03560i	−0.855502	+	0.517799i	$0.826751\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.09808	−	0.633975i	0.0532645	−	0.0307523i
$426$		0			0
$427$	−7.39230	+	8.53590i	−0.357739	+	0.413081i
$428$		0			0
$429$	−10.3923	+	6.00000i	−0.501745	+	0.289683i
$430$		0			0
$431$	−6.92820	−	4.00000i	−0.333720	−	0.192673i	0.323772	−	0.946135i	$-0.395049\pi$
$431$	−6.92820	−	4.00000i	−0.333720	−	0.192673i	−0.657491	+	0.753462i	$0.728382\pi$
$432$		0			0
$433$			28.9808i			1.39273i	0.717689	+	0.696363i	$0.245200\pi$
$433$			28.9808i			1.39273i	−0.717689	+	0.696363i	$0.754800\pi$
$434$		0			0
$435$	−18.1244			−0.868996
$436$		0			0
$437$	−24.2942	+	42.0788i	−1.16215	+	2.01290i
$438$		0			0
$439$	6.92820	+	12.0000i	0.330665	+	0.572729i	0.982642	−	0.185510i	$-0.0593936\pi$
$439$	6.92820	+	12.0000i	0.330665	+	0.572729i	−0.651977	+	0.758238i	$0.726060\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	3.50000	+	6.06218i	0.166290	+	0.288023i	0.937113	−	0.349027i	$-0.113488\pi$
$443$	3.50000	+	6.06218i	0.166290	+	0.288023i	−0.770823	+	0.637050i	$0.780155\pi$
$444$		0			0
$445$	12.6962	+	7.33013i	0.601855	+	0.347481i
$446$		0			0
$447$	4.26795			0.201867
$448$		0			0
$449$	19.5359			0.921956			0.460978	−	0.887412i	$-0.347499\pi$
$449$	19.5359			0.921956			0.460978	+	0.887412i	$0.347499\pi$
$450$		0			0
$451$	−6.58846	−	3.80385i	−0.310238	−	0.179116i
$452$		0			0
$453$	5.02628	+	8.70577i	0.236155	+	0.409033i
$454$		0			0
$455$	−8.19615	+	9.46410i	−0.384242	+	0.443684i
$456$		0			0
$457$	−20.3205	−	35.1962i	−0.950553	−	1.64641i	−0.744231	−	0.667923i	$-0.767184\pi$
$457$	−20.3205	−	35.1962i	−0.950553	−	1.64641i	−0.206322	−	0.978484i	$-0.566150\pi$
$458$		0			0
$459$	−3.29423	+	5.70577i	−0.153761	+	0.266323i
$460$		0			0
$461$	−10.1436			−0.472434			−0.236217	−	0.971700i	$-0.575908\pi$
$461$	−10.1436			−0.472434			−0.236217	+	0.971700i	$0.575908\pi$
$462$		0			0
$463$			19.3923i			0.901237i	0.892717	+	0.450618i	$0.148796\pi$
$463$			19.3923i			0.901237i	−0.892717	+	0.450618i	$0.851204\pi$
$464$		0			0
$465$	−3.29423	−	1.90192i	−0.152766	−	0.0881996i
$466$		0			0
$467$	−24.4808	+	14.1340i	−1.13283	+	0.654042i	−0.944646	−	0.328091i	$-0.893595\pi$
$467$	−24.4808	+	14.1340i	−1.13283	+	0.654042i	−0.188188	+	0.982133i	$0.560262\pi$
$468$		0			0
$469$	29.5981	+	5.69615i	1.36671	+	0.263024i
$470$		0			0
$471$	3.80385	−	2.19615i	0.175272	−	0.101193i
$472$		0			0
$473$	2.87564	−	4.98076i	0.132222	−	0.229016i
$474$		0			0
$475$			8.19615i			0.376065i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	2.83013	−	4.90192i	0.129312	−	0.223975i	−0.794098	−	0.607789i	$-0.792057\pi$
$479$	2.83013	−	4.90192i	0.129312	−	0.223975i	0.923410	+	0.383815i	$0.125390\pi$
$480$		0			0
$481$	8.19615	−	4.73205i	0.373712	−	0.215763i
$482$		0			0
$483$	−8.89230	−	25.6699i	−0.404614	−	1.16802i
$484$		0			0
$485$	3.00000	−	1.73205i	0.136223	−	0.0786484i
$486$		0			0
$487$	21.4641	+	12.3923i	0.972631	+	0.561549i	0.900037	−	0.435813i	$-0.143539\pi$
$487$	21.4641	+	12.3923i	0.972631	+	0.561549i	0.0725939	+	0.997362i	$0.476872\pi$
$488$		0			0
$489$		−	17.3205i		−	0.783260i
$490$		0			0
$491$	26.7321			1.20640			0.603200	−	0.797590i	$-0.293892\pi$
$491$	26.7321			1.20640			0.603200	+	0.797590i	$0.293892\pi$
$492$		0			0
$493$	6.63397	−	11.4904i	0.298779	−	0.517501i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	13.1699	−	4.56218i	0.590750	−	0.204642i
$498$		0			0
$499$	11.1962	+	19.3923i	0.501209	+	0.868119i	0.999999	+	0.00139615i	$0.000444410\pi$
$499$	11.1962	+	19.3923i	0.501209	+	0.868119i	−0.498790	+	0.866723i	$0.666222\pi$
$500$		0			0
$501$	−5.00962	−	2.89230i	−0.223813	−	0.129219i
$502$		0			0
$503$	2.66025			0.118615			0.0593074	−	0.998240i	$-0.481111\pi$
$503$	2.66025			0.118615			0.0593074	+	0.998240i	$0.481111\pi$
$504$		0			0
$505$	11.1962			0.498222
$506$		0			0
$507$	14.0885	+	8.13397i	0.625690	+	0.361242i
$508$		0			0
$509$	14.2583	+	24.6962i	0.631989	+	1.09464i	0.987145	+	0.159830i	$0.0510947\pi$
$509$	14.2583	+	24.6962i	0.631989	+	1.09464i	−0.355155	+	0.934807i	$0.615572\pi$
$510$		0			0
$511$	5.83013	−	30.2942i	0.257910	−	1.34014i
$512$		0			0
$513$	−21.2942	−	36.8827i	−0.940163	−	1.62841i
$514$		0			0
$515$	1.33013	−	2.30385i	0.0586124	−	0.101520i
$516$		0			0
$517$	3.71281			0.163289
$518$		0			0
$519$			2.78461i			0.122231i
$520$		0			0
$521$	10.6077	+	6.12436i	0.464732	+	0.268313i	0.714032	−	0.700113i	$-0.246867\pi$
$521$	10.6077	+	6.12436i	0.464732	+	0.268313i	−0.249300	+	0.968426i	$0.580201\pi$
$522$		0			0
$523$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$523$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$524$		0			0
$525$	−3.46410	−	3.00000i	−0.151186	−	0.130931i
$526$		0			0
$527$	2.41154	−	1.39230i	0.105048	−	0.0606498i
$528$		0			0
$529$	6.07180	−	10.5167i	0.263991	−	0.457246i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			24.5885i			1.06504i
$534$		0			0
$535$	−3.50000	+	6.06218i	−0.151318	+	0.262091i
$536$		0			0
$537$	27.2942	−	15.7583i	1.17783	−	0.680022i
$538$		0			0
$539$	−1.46410	−	10.1436i	−0.0630633	−	0.436916i
$540$		0			0
$541$	−39.1865	+	22.6244i	−1.68476	+	0.972697i	−0.726341	+	0.687335i	$0.758781\pi$
$541$	−39.1865	+	22.6244i	−1.68476	+	0.972697i	−0.958420	+	0.285363i	$0.907886\pi$
$542$		0			0
$543$	2.59808	+	1.50000i	0.111494	+	0.0643712i
$544$		0			0
$545$		−	17.3923i		−	0.745004i
$546$		0			0
$547$	−1.00000			−0.0427569			−0.0213785	−	0.999771i	$-0.506805\pi$
$547$	−1.00000			−0.0427569			−0.0213785	+	0.999771i	$0.506805\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	42.8827	+	74.2750i	1.82686	+	3.16422i
$552$		0			0
$553$	9.46410	+	8.19615i	0.402455	+	0.348536i
$554$		0			0
$555$	1.73205	+	3.00000i	0.0735215	+	0.127343i
$556$		0			0
$557$	36.1244	+	20.8564i	1.53064	+	0.883714i	0.999332	+	0.0365341i	$0.0116318\pi$
$557$	36.1244	+	20.8564i	1.53064	+	0.883714i	0.531306	+	0.847180i	$0.321702\pi$
$558$		0			0
$559$	−18.5885			−0.786208
$560$		0			0
$561$	3.21539			0.135754
$562$		0			0
$563$	14.3038	+	8.25833i	0.602835	+	0.348047i	0.770156	−	0.637855i	$-0.220178\pi$
$563$	14.3038	+	8.25833i	0.602835	+	0.348047i	−0.167321	+	0.985902i	$0.553512\pi$
$564$		0			0
$565$	−1.63397	−	2.83013i	−0.0687418	−	0.119064i
$566$		0			0
$567$	23.3827	+	4.50000i	0.981981	+	0.188982i
$568$		0			0
$569$	−3.26795	−	5.66025i	−0.137000	−	0.237290i	0.789360	−	0.613931i	$-0.210413\pi$
$569$	−3.26795	−	5.66025i	−0.137000	−	0.237290i	−0.926360	+	0.376640i	$0.877079\pi$
$570$		0			0
$571$	1.29423	−	2.24167i	0.0541618	−	0.0938110i	−0.837673	−	0.546172i	$-0.816085\pi$
$571$	1.29423	−	2.24167i	0.0541618	−	0.0938110i	0.891835	+	0.452361i	$0.149418\pi$
$572$		0			0
$573$	−42.2487			−1.76497
$574$		0			0
$575$		−	5.92820i		−	0.247223i
$576$		0			0
$577$	14.7846	+	8.53590i	0.615491	+	0.355354i	0.775112	−	0.631824i	$-0.217694\pi$
$577$	14.7846	+	8.53590i	0.615491	+	0.355354i	−0.159620	+	0.987178i	$0.551027\pi$
$578$		0			0
$579$	−20.7846	+	12.0000i	−0.863779	+	0.498703i
$580$		0			0
$581$	−36.6506	+	12.6962i	−1.52052	+	0.526725i
$582$		0			0
$583$	−0.248711	+	0.143594i	−0.0103006	+	0.00594704i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			9.46410i			0.390625i	0.980741	+	0.195313i	$0.0625722\pi$
$587$			9.46410i			0.390625i	−0.980741	+	0.195313i	$0.937428\pi$
$588$		0			0
$589$			18.0000i			0.741677i
$590$		0			0
$591$	4.26795	−	7.39230i	0.175560	−	0.304079i
$592$		0			0
$593$	−35.2750	+	20.3660i	−1.44857	+	0.836332i	−0.998396	−	0.0566085i	$-0.981971\pi$
$593$	−35.2750	+	20.3660i	−1.44857	+	0.836332i	−0.450174	+	0.892941i	$0.648638\pi$
$594$		0			0
$595$	3.16987	−	1.09808i	0.129952	−	0.0450167i
$596$		0			0
$597$	27.0000	−	15.5885i	1.10504	−	0.637993i
$598$		0			0
$599$	−13.2679	−	7.66025i	−0.542114	−	0.312989i	0.203821	−	0.979008i	$-0.434664\pi$
$599$	−13.2679	−	7.66025i	−0.542114	−	0.312989i	−0.745935	+	0.666019i	$0.767997\pi$
$600$		0			0
$601$			1.60770i			0.0655793i	0.999462	+	0.0327896i	$0.0104391\pi$
$601$			1.60770i			0.0655793i	−0.999462	+	0.0327896i	$0.989561\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−4.42820	+	7.66987i	−0.180032	+	0.311825i
$606$		0			0
$607$	15.5263	+	26.8923i	0.630192	+	1.09152i	0.987512	+	0.157543i	$0.0503573\pi$
$607$	15.5263	+	26.8923i	0.630192	+	1.09152i	−0.357320	+	0.933982i	$0.616309\pi$
$608$		0			0
$609$	−47.0885	−	9.06218i	−1.90812	−	0.367218i
$610$		0			0
$611$	−6.00000	−	10.3923i	−0.242734	−	0.420428i
$612$		0			0
$613$	21.8827	+	12.6340i	0.883833	+	0.510281i	0.871920	−	0.489648i	$-0.162875\pi$
$613$	21.8827	+	12.6340i	0.883833	+	0.510281i	0.0119129	+	0.999929i	$0.496208\pi$
$614$		0			0
$615$	−9.00000			−0.362915
$616$		0			0
$617$	28.9282			1.16461			0.582303	−	0.812972i	$-0.302152\pi$
$617$	28.9282			1.16461			0.582303	+	0.812972i	$0.302152\pi$
$618$		0			0
$619$	−6.58846	−	3.80385i	−0.264812	−	0.152890i	0.361715	−	0.932289i	$-0.382191\pi$
$619$	−6.58846	−	3.80385i	−0.264812	−	0.152890i	−0.626528	+	0.779399i	$0.715525\pi$
$620$		0			0
$621$	15.4019	+	26.6769i	0.618058	+	1.07051i
$622$		0			0
$623$	29.3205	+	25.3923i	1.17470	+	1.01732i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−10.3923	+	18.0000i	−0.415029	+	0.718851i
$628$		0			0
$629$	−2.53590			−0.101113
$630$		0			0
$631$			21.4641i			0.854472i	0.904140	+	0.427236i	$0.140513\pi$
$631$			21.4641i			0.854472i	−0.904140	+	0.427236i	$0.859487\pi$
$632$		0			0
$633$	27.8827	+	16.0981i	1.10824	+	0.639841i
$634$		0			0
$635$	13.3923	−	7.73205i	0.531457	−	0.306837i
$636$		0			0
$637$	−26.0263	+	20.4904i	−1.03120	+	0.811858i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−17.2321	+	29.8468i	−0.680625	+	1.17888i	0.294165	+	0.955755i	$0.404958\pi$
$641$	−17.2321	+	29.8468i	−0.680625	+	1.17888i	−0.974790	+	0.223123i	$0.928375\pi$
$642$		0			0
$643$			19.6077i			0.773252i	0.922237	+	0.386626i	$0.126360\pi$
$643$			19.6077i			0.773252i	−0.922237	+	0.386626i	$0.873640\pi$
$644$		0			0
$645$		−	6.80385i		−	0.267901i
$646$		0			0
$647$	−13.7942	+	23.8923i	−0.542307	+	0.939303i	0.456464	+	0.889742i	$0.349116\pi$
$647$	−13.7942	+	23.8923i	−0.542307	+	0.939303i	−0.998771	+	0.0495615i	$0.984218\pi$
$648$		0			0
$649$	6.00000	−	3.46410i	0.235521	−	0.135978i
$650$		0			0
$651$	−7.60770	−	6.58846i	−0.298169	−	0.258222i
$652$		0			0
$653$	−16.4378	+	9.49038i	−0.643262	+	0.371387i	−0.785870	−	0.618392i	$-0.787784\pi$
$653$	−16.4378	+	9.49038i	−0.643262	+	0.371387i	0.142608	+	0.989779i	$0.454451\pi$
$654$		0			0
$655$	10.3923	+	6.00000i	0.406061	+	0.234439i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	17.8038			0.693539			0.346770	−	0.937950i	$-0.387279\pi$
$659$	17.8038			0.693539			0.346770	+	0.937950i	$0.387279\pi$
$660$		0			0
$661$	−1.79423	+	3.10770i	−0.0697874	+	0.120875i	−0.898808	−	0.438343i	$-0.855565\pi$
$661$	−1.79423	+	3.10770i	−0.0697874	+	0.120875i	0.829020	+	0.559219i	$0.188899\pi$
$662$		0			0
$663$	−5.19615	−	9.00000i	−0.201802	−	0.349531i
$664$		0			0
$665$	−4.09808	+	21.2942i	−0.158917	+	0.825755i
$666$		0			0
$667$	−31.0167	−	53.7224i	−1.20097	−	2.08014i
$668$		0			0
$669$	20.7846	+	12.0000i	0.803579	+	0.463947i
$670$		0			0
$671$	−6.24871			−0.241229
$672$		0			0
$673$	38.7846			1.49504			0.747518	−	0.664241i	$-0.231245\pi$
$673$	38.7846			1.49504			0.747518	+	0.664241i	$0.231245\pi$
$674$		0			0
$675$	4.50000	+	2.59808i	0.173205	+	0.100000i
$676$		0			0
$677$	−18.2942	−	31.6865i	−0.703104	−	1.21781i	−0.967371	−	0.253363i	$-0.918463\pi$
$677$	−18.2942	−	31.6865i	−0.703104	−	1.21781i	0.264267	−	0.964450i	$-0.414870\pi$
$678$		0			0
$679$	8.66025	−	3.00000i	0.332350	−	0.115129i
$680$		0			0
$681$	4.39230	+	7.60770i	0.168313	+	0.291528i
$682$		0			0
$683$	12.4282	−	21.5263i	0.475552	−	0.823680i	−0.524056	−	0.851684i	$-0.675582\pi$
$683$	12.4282	−	21.5263i	0.475552	−	0.823680i	0.999608	+	0.0280037i	$0.00891503\pi$
$684$		0			0
$685$	12.3923			0.473486
$686$		0			0
$687$		−	26.7846i		−	1.02190i
$688$		0			0
$689$	0.803848	+	0.464102i	0.0306242	+	0.0176809i
$690$		0			0
$691$	−19.3923	+	11.1962i	−0.737718	+	0.425922i	−0.821239	−	0.570584i	$-0.806717\pi$
$691$	−19.3923	+	11.1962i	−0.737718	+	0.425922i	0.0835210	+	0.996506i	$0.473383\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−8.19615	+	4.73205i	−0.310898	+	0.179497i
$696$		0			0
$697$	3.29423	−	5.70577i	0.124778	−	0.216122i
$698$		0			0
$699$			9.12436i			0.345115i
$700$		0			0
$701$		−	33.7846i		−	1.27603i	−0.770025	−	0.638014i	$-0.779756\pi$
$701$		−	33.7846i		−	1.27603i	0.770025	−	0.638014i	$-0.220244\pi$
$702$		0			0
$703$	8.19615	−	14.1962i	0.309124	−	0.535418i
$704$		0			0
$705$	3.80385	−	2.19615i	0.143261	−	0.0827119i
$706$		0			0
$707$	29.0885	+	5.59808i	1.09398	+	0.210537i
$708$		0			0
$709$	22.6699	−	13.0885i	0.851385	−	0.491547i	−0.00973296	−	0.999953i	$-0.503098\pi$
$709$	22.6699	−	13.0885i	0.851385	−	0.491547i	0.861118	+	0.508405i	$0.169765\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	13.0192i		−	0.487574i
$714$		0			0
$715$	−6.92820			−0.259100
$716$		0			0
$717$	1.56218	−	2.70577i	0.0583406	−	0.101049i
$718$		0			0
$719$	−21.4641	−	37.1769i	−0.800476	−	1.38646i	−0.919303	−	0.393550i	$-0.871247\pi$
$719$	−21.4641	−	37.1769i	−0.800476	−	1.38646i	0.118827	−	0.992915i	$-0.462087\pi$
$720$		0			0
$721$	4.60770	−	5.32051i	0.171600	−	0.198146i
$722$		0			0
$723$	−6.80385	−	11.7846i	−0.253038	−	0.438274i
$724$		0			0
$725$	−9.06218	−	5.23205i	−0.336561	−	0.194313i
$726$		0			0
$727$	−25.0526			−0.929148			−0.464574	−	0.885534i	$-0.653793\pi$
$727$	−25.0526			−0.929148			−0.464574	+	0.885534i	$0.653793\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	4.31347	+	2.49038i	0.159539	+	0.0921101i
$732$		0			0
$733$	−5.19615	−	9.00000i	−0.191924	−	0.332423i	0.753964	−	0.656916i	$-0.228139\pi$
$733$	−5.19615	−	9.00000i	−0.191924	−	0.332423i	−0.945888	+	0.324494i	$0.894806\pi$
$734$		0			0
$735$	−7.50000	−	9.52628i	−0.276642	−	0.351382i
$736$		0			0
$737$	8.33975	+	14.4449i	0.307198	+	0.532083i
$738$		0			0
$739$	2.80385	−	4.85641i	0.103141	−	0.178646i	−0.809836	−	0.586656i	$-0.800444\pi$
$739$	2.80385	−	4.85641i	0.103141	−	0.178646i	0.912977	+	0.408010i	$0.133777\pi$
$740$		0			0
$741$	67.1769			2.46781
$742$		0			0
$743$			9.39230i			0.344570i	0.985047	+	0.172285i	$0.0551150\pi$
$743$			9.39230i			0.344570i	−0.985047	+	0.172285i	$0.944885\pi$
$744$		0			0
$745$	2.13397	+	1.23205i	0.0781828	+	0.0451388i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−12.1244	+	14.0000i	−0.443014	+	0.511549i
$750$		0			0
$751$	−40.8564	+	23.5885i	−1.49087	+	0.860755i	−0.999945	−	0.0104462i	$-0.996675\pi$
$751$	−40.8564	+	23.5885i	−1.49087	+	0.860755i	−0.490926	+	0.871201i	$0.663341\pi$
$752$		0			0
$753$	13.6865	−	23.7058i	0.498765	−	0.863886i
$754$		0			0
$755$			5.80385i			0.211224i
$756$		0			0
$757$		−	18.1962i		−	0.661350i	−0.943745	−	0.330675i	$-0.892724\pi$
$757$		−	18.1962i		−	0.661350i	0.943745	−	0.330675i	$-0.107276\pi$
$758$		0			0
$759$	7.51666	−	13.0192i	0.272837	−	0.472568i
$760$		0			0
$761$	−30.8038	+	17.7846i	−1.11664	+	0.644692i	−0.940541	−	0.339681i	$-0.889681\pi$
$761$	−30.8038	+	17.7846i	−1.11664	+	0.644692i	−0.176098	+	0.984373i	$0.556348\pi$
$762$		0			0
$763$	8.69615	−	45.1865i	0.314822	−	1.63586i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−19.3923	−	11.1962i	−0.700216	−	0.404270i
$768$		0			0
$769$			10.3923i			0.374756i	0.982288	+	0.187378i	$0.0599989\pi$
$769$			10.3923i			0.374756i	−0.982288	+	0.187378i	$0.940001\pi$
$770$		0			0
$771$	10.3923			0.374270
$772$		0			0
$773$	−24.2942	+	42.0788i	−0.873803	+	1.51347i	−0.0157699	+	0.999876i	$0.505020\pi$
$773$	−24.2942	+	42.0788i	−0.873803	+	1.51347i	−0.858033	+	0.513595i	$0.828313\pi$
$774$		0			0
$775$	−1.09808	−	1.90192i	−0.0394441	−	0.0683191i
$776$		0			0
$777$	3.00000	+	8.66025i	0.107624	+	0.310685i
$778$		0			0
$779$	21.2942	+	36.8827i	0.762945	+	1.32146i
$780$		0			0
$781$	6.67949	+	3.85641i	0.239011	+	0.137993i
$782$		0			0
$783$	54.3731			1.94313
$784$		0			0
$785$	2.53590			0.0905101
$786$		0			0
$787$	−29.3038	−	16.9186i	−1.04457	−	0.603082i	−0.123445	−	0.992351i	$-0.539394\pi$
$787$	−29.3038	−	16.9186i	−1.04457	−	0.603082i	−0.921124	+	0.389269i	$0.872728\pi$
$788$		0			0
$789$	−13.9186	−	24.1077i	−0.495515	−	0.858257i
$790$		0			0
$791$	−2.83013	−	8.16987i	−0.100628	−	0.290487i
$792$		0			0
$793$	10.0981	+	17.4904i	0.358593	+	0.621102i
$794$		0			0
$795$	−0.169873	+	0.294229i	−0.00602477	+	0.0104352i
$796$		0			0
$797$	−5.32051			−0.188462			−0.0942310	−	0.995550i	$-0.530039\pi$
$797$	−5.32051			−0.188462			−0.0942310	+	0.995550i	$0.530039\pi$
$798$		0			0
$799$			3.21539i			0.113752i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	14.7846	−	8.53590i	0.521738	−	0.301225i
$804$		0			0
$805$	2.96410	−	15.4019i	0.104471	−	0.542846i
$806$		0			0
$807$	−12.9904	+	7.50000i	−0.457283	+	0.264013i
$808$		0			0
$809$	9.16025	−	15.8660i	0.322057	−	0.557820i	−0.658855	−	0.752270i	$-0.728959\pi$
$809$	9.16025	−	15.8660i	0.322057	−	0.557820i	0.980912	+	0.194450i	$0.0622923\pi$
$810$		0			0
$811$			17.6603i			0.620135i	0.950714	+	0.310068i	$0.100352\pi$
$811$			17.6603i			0.620135i	−0.950714	+	0.310068i	$0.899648\pi$
$812$		0			0
$813$		−	24.5885i		−	0.862355i
$814$		0			0
$815$	5.00000	−	8.66025i	0.175142	−	0.303355i
$816$		0			0
$817$	−27.8827	+	16.0981i	−0.975492	+	0.563200i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.73205	+	1.00000i	−0.0604490	+	0.0349002i	−0.529920	−	0.848048i	$-0.677778\pi$
$821$	−1.73205	+	1.00000i	−0.0604490	+	0.0349002i	0.469471	+	0.882948i	$0.344445\pi$
$822$		0			0
$823$	−20.3827	−	11.7679i	−0.710496	−	0.410205i	0.100749	−	0.994912i	$-0.467876\pi$
$823$	−20.3827	−	11.7679i	−0.710496	−	0.410205i	−0.811245	+	0.584707i	$0.801209\pi$
$824$		0			0
$825$		−	2.53590i		−	0.0882886i
$826$		0			0
$827$	8.85641			0.307967			0.153984	−	0.988073i	$-0.450790\pi$
$827$	8.85641			0.307967			0.153984	+	0.988073i	$0.450790\pi$
$828$		0			0
$829$	7.60770	−	13.1769i	0.264226	−	0.457653i	−0.703134	−	0.711057i	$-0.748217\pi$
$829$	7.60770	−	13.1769i	0.264226	−	0.457653i	0.967361	+	0.253404i	$0.0815501\pi$
$830$		0			0
$831$	1.90192	+	3.29423i	0.0659770	+	0.114276i
$832$		0			0
$833$	8.78461	−	1.26795i	0.304369	−	0.0439318i
$834$		0			0
$835$	−1.66987	−	2.89230i	−0.0577883	−	0.100092i
$836$		0			0
$837$	9.88269	+	5.70577i	0.341596	+	0.197220i
$838$		0			0
$839$	−44.5359			−1.53755			−0.768775	−	0.639519i	$-0.779133\pi$
$839$	−44.5359			−1.53755			−0.768775	+	0.639519i	$0.779133\pi$
$840$		0			0
$841$	−80.4974			−2.77577
$842$		0			0
$843$	32.7846	+	18.9282i	1.12916	+	0.651922i
$844$		0			0
$845$	4.69615	+	8.13397i	0.161553	+	0.279817i
$846$		0			0
$847$	−15.3397	+	17.7128i	−0.527080	+	0.608619i
$848$		0			0
$849$	−3.00000	−	5.19615i	−0.102960	−	0.178331i
$850$		0			0
$851$	−5.92820	+	10.2679i	−0.203216	+	0.351981i
$852$		0			0
$853$	1.51666			0.0519295			0.0259647	−	0.999663i	$-0.491734\pi$
$853$	1.51666			0.0519295			0.0259647	+	0.999663i	$0.491734\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−8.41154	−	4.85641i	−0.287333	−	0.165892i	0.349406	−	0.936972i	$-0.386384\pi$
$857$	−8.41154	−	4.85641i	−0.287333	−	0.165892i	−0.636738	+	0.771080i	$0.719717\pi$
$858$		0			0
$859$	43.9808	−	25.3923i	1.50060	−	0.866374i	0.500604	−	0.865676i	$-0.333111\pi$
$859$	43.9808	−	25.3923i	1.50060	−	0.866374i	1.00000		0.000698137i	$-0.000222224\pi$
$860$		0			0
$861$	−23.3827	−	4.50000i	−0.796880	−	0.153360i
$862$		0			0
$863$	−18.2776	+	10.5526i	−0.622176	+	0.359213i	−0.777716	−	0.628616i	$-0.783622\pi$
$863$	−18.2776	+	10.5526i	−0.622176	+	0.359213i	0.155540	+	0.987830i	$0.450288\pi$
$864$		0			0
$865$	−0.803848	+	1.39230i	−0.0273316	+	0.0473398i
$866$		0			0
$867$		−	26.6603i		−	0.905430i
$868$		0			0
$869$			6.92820i			0.235023i
$870$		0			0
$871$	26.9545	−	46.6865i	0.913318	−	1.58191i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.866025	−	2.50000i	−0.0292770	−	0.0845154i
$876$		0			0
$877$	36.8827	−	21.2942i	1.24544	−	0.719055i	0.275243	−	0.961375i	$-0.411242\pi$
$877$	36.8827	−	21.2942i	1.24544	−	0.719055i	0.970196	+	0.242320i	$0.0779082\pi$
$878$		0			0
$879$	−20.7846	−	12.0000i	−0.701047	−	0.404750i
$880$		0			0
$881$			26.6603i			0.898207i	0.893480	+	0.449103i	$0.148257\pi$
$881$			26.6603i			0.898207i	−0.893480	+	0.449103i	$0.851743\pi$
$882$		0			0
$883$	3.46410			0.116576			0.0582882	−	0.998300i	$-0.481436\pi$
$883$	3.46410			0.116576			0.0582882	+	0.998300i	$0.481436\pi$
$884$		0			0
$885$	4.09808	−	7.09808i	0.137755	−	0.238599i
$886$		0			0
$887$	−20.1340	−	34.8731i	−0.676033	−	1.17092i	−0.976166	−	0.217026i	$-0.930364\pi$
$887$	−20.1340	−	34.8731i	−0.676033	−	1.17092i	0.300133	−	0.953897i	$-0.402969\pi$
$888$		0			0
$889$	38.6603	−	13.3923i	1.29662	−	0.449163i
$890$		0			0
$891$	6.58846	+	11.4115i	0.220722	+	0.382301i
$892$		0			0
$893$	−18.0000	−	10.3923i	−0.602347	−	0.347765i
$894$		0			0
$895$	18.1962			0.608230
$896$		0			0
$897$	−48.5885			−1.62232
$898$		0			0
$899$	−19.9019	−	11.4904i	−0.663766	−	0.383226i
$900$		0			0
$901$	−0.124356	−	0.215390i	−0.00414289	−	0.00717569i
$902$		0			0
$903$	3.40192	−	17.6769i	0.113209	−	0.588251i
$904$		0			0
$905$	0.866025	+	1.50000i	0.0287877	+	0.0498617i
$906$		0			0
$907$	−17.0885	+	29.5981i	−0.567413	+	0.982788i	0.429408	+	0.903111i	$0.358722\pi$
$907$	−17.0885	+	29.5981i	−0.567413	+	0.982788i	−0.996821	+	0.0796773i	$0.974611\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			1.71281i			0.0567480i	0.999597	+	0.0283740i	$0.00903294\pi$
$911$			1.71281i			0.0567480i	−0.999597	+	0.0283740i	$0.990967\pi$
$912$		0			0
$913$	−18.5885	−	10.7321i	−0.615188	−	0.355179i
$914$		0			0
$915$	−6.40192	+	3.69615i	−0.211641	+	0.122191i
$916$		0			0
$917$	24.0000	+	20.7846i	0.792550	+	0.686368i
$918$		0			0
$919$	28.5622	−	16.4904i	0.942179	−	0.543967i	0.0515365	−	0.998671i	$-0.483588\pi$
$919$	28.5622	−	16.4904i	0.942179	−	0.543967i	0.890643	+	0.454704i	$0.150255\pi$
$920$		0			0
$921$	−5.30385	+	9.18653i	−0.174768	+	0.302707i
$922$		0			0
$923$		−	24.9282i		−	0.820522i
$924$		0			0
$925$			2.00000i			0.0657596i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−26.8923	+	15.5263i	−0.882308	+	0.509401i	−0.871419	−	0.490540i	$-0.836800\pi$
$929$	−26.8923	+	15.5263i	−0.882308	+	0.509401i	−0.0108892	+	0.999941i	$0.503466\pi$
$930$		0			0
$931$	−21.2942	+	53.2750i	−0.697890	+	1.74602i
$932$		0			0
$933$	5.70577	−	3.29423i	0.186799	−	0.107848i
$934$		0			0
$935$	1.60770	+	0.928203i	0.0525773	+	0.0303555i
$936$		0			0
$937$		−	13.8564i		−	0.452669i	−0.974050	−	0.226335i	$-0.927326\pi$
$937$		−	13.8564i		−	0.452669i	0.974050	−	0.226335i	$-0.0726743\pi$
$938$		0			0
$939$	−30.0000			−0.979013
$940$		0			0
$941$	12.4641	−	21.5885i	0.406318	−	0.703764i	−0.588156	−	0.808748i	$-0.700146\pi$
$941$	12.4641	−	21.5885i	0.406318	−	0.703764i	0.994474	+	0.104984i	$0.0334792\pi$
$942$		0			0
$943$	−15.4019	−	26.6769i	−0.501556	−	0.868720i
$944$		0			0
$945$	10.3923	+	9.00000i	0.338062	+	0.292770i
$946$		0			0
$947$	−7.08846	−	12.2776i	−0.230344	−	0.398967i	0.727565	−	0.686038i	$-0.240652\pi$
$947$	−7.08846	−	12.2776i	−0.230344	−	0.398967i	−0.957909	+	0.287071i	$0.907318\pi$
$948$		0			0
$949$	−47.7846	−	27.5885i	−1.55115	−	0.895559i
$950$		0			0
$951$	−16.0526			−0.520540
$952$		0			0
$953$	30.1051			0.975200			0.487600	−	0.873067i	$-0.337872\pi$
$953$	30.1051			0.975200			0.487600	+	0.873067i	$0.337872\pi$
$954$		0			0
$955$	−21.1244	−	12.1962i	−0.683568	−	0.394658i
$956$		0			0
$957$	−13.2679	−	22.9808i	−0.428892	−	0.742863i
$958$		0			0
$959$	32.1962	+	6.19615i	1.03967	+	0.200084i
$960$		0			0
$961$	13.0885	+	22.6699i	0.422208	+	0.731286i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−13.8564			−0.446054
$966$		0			0
$967$			34.1769i			1.09906i	0.835475	+	0.549528i	$0.185192\pi$
$967$			34.1769i			1.09906i	−0.835475	+	0.549528i	$0.814808\pi$
$968$		0			0
$969$	−15.5885	−	9.00000i	−0.500773	−	0.289122i
$970$		0			0
$971$	−40.1769	+	23.1962i	−1.28934	+	0.744400i	−0.978536	−	0.206075i	$-0.933931\pi$
$971$	−40.1769	+	23.1962i	−1.28934	+	0.744400i	−0.310802	+	0.950475i	$0.600598\pi$
$972$		0			0
$973$	−23.6603	+	8.19615i	−0.758513	+	0.262757i
$974$		0			0
$975$	−7.09808	+	4.09808i	−0.227320	+	0.131243i
$976$		0			0
$977$	20.9282	−	36.2487i	0.669553	−	1.15970i	−0.308477	−	0.951232i	$-0.599819\pi$
$977$	20.9282	−	36.2487i	0.669553	−	1.15970i	0.978029	−	0.208467i	$-0.0668474\pi$
$978$		0			0
$979$			21.4641i			0.685996i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	22.3301	−	38.6769i	0.712220	−	1.23360i	−0.251801	−	0.967779i	$-0.581023\pi$
$983$	22.3301	−	38.6769i	0.712220	−	1.23360i	0.964022	−	0.265823i	$-0.0856437\pi$
$984$		0			0
$985$	4.26795	−	2.46410i	0.135988	−	0.0785128i
$986$		0			0
$987$	10.9808	−	3.80385i	0.349522	−	0.121078i
$988$		0			0
$989$	20.1673	−	11.6436i	0.641283	−	0.370245i
$990$		0			0
$991$	11.5814	+	6.68653i	0.367896	+	0.212405i	0.672539	−	0.740062i	$-0.265204\pi$
$991$	11.5814	+	6.68653i	0.367896	+	0.212405i	−0.304643	+	0.952467i	$0.598537\pi$
$992$		0			0
$993$		−	39.3731i		−	1.24947i
$994$		0			0
$995$	18.0000			0.570638
$996$		0			0
$997$	−22.5622	+	39.0788i	−0.714551	+	1.23764i	0.248581	+	0.968611i	$0.420036\pi$
$997$	−22.5622	+	39.0788i	−0.714551	+	1.23764i	−0.963132	+	0.269028i	$0.913298\pi$
$998$		0			0
$999$	−5.19615	−	9.00000i	−0.164399	−	0.284747i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1120.2.bz.d.591.2		4
4.3	odd	2		280.2.bj.d.171.2	yes	4
7.5	odd	6		1120.2.bz.a.271.1		4
8.3	odd	2		1120.2.bz.a.591.1		4
8.5	even	2		280.2.bj.a.171.2	yes	4
28.19	even	6		280.2.bj.a.131.1	✓	4
56.5	odd	6		280.2.bj.d.131.2	yes	4
56.19	even	6	inner	1120.2.bz.d.271.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bj.a.131.1	✓	4	28.19	even	6
280.2.bj.a.171.2	yes	4	8.5	even	2
280.2.bj.d.131.2	yes	4	56.5	odd	6
280.2.bj.d.171.2	yes	4	4.3	odd	2
1120.2.bz.a.271.1		4	7.5	odd	6
1120.2.bz.a.591.1		4	8.3	odd	2
1120.2.bz.d.271.2		4	56.19	even	6	inner
1120.2.bz.d.591.2		4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1120.bz (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(0.866025 + 2.50000i) q^{7} +O(q^{10})\)	\(q+(1.50000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(0.866025 + 2.50000i) q^{7} +(-0.732051 + 1.26795i) q^{11} +4.73205 q^{13} +1.73205i q^{15} +(-1.09808 - 0.633975i) q^{17} +(7.09808 - 4.09808i) q^{19} +(-0.866025 + 4.50000i) q^{21} +(-5.13397 + 2.96410i) q^{23} +(-0.500000 + 0.866025i) q^{25} -5.19615i q^{27} +10.4641i q^{29} +(-1.09808 + 1.90192i) q^{31} +(-2.19615 + 1.26795i) q^{33} +(-1.73205 + 2.00000i) q^{35} +(1.73205 - 1.00000i) q^{37} +(7.09808 + 4.09808i) q^{39} +5.19615i q^{41} -3.92820 q^{43} +(-1.26795 - 2.19615i) q^{47} +(-5.50000 + 4.33013i) q^{49} +(-1.09808 - 1.90192i) q^{51} +(0.169873 + 0.0980762i) q^{53} -1.46410 q^{55} +14.1962 q^{57} +(-4.09808 - 2.36603i) q^{59} +(2.13397 + 3.69615i) q^{61} +(2.36603 + 4.09808i) q^{65} +(5.69615 - 9.86603i) q^{67} -10.2679 q^{69} -5.26795i q^{71} +(-10.0981 - 5.83013i) q^{73} +(-1.50000 + 0.866025i) q^{75} +(-3.80385 - 0.732051i) q^{77} +(4.09808 - 2.36603i) q^{79} +(4.50000 - 7.79423i) q^{81} +14.6603i q^{83} -1.26795i q^{85} +(-9.06218 + 15.6962i) q^{87} +(12.6962 - 7.33013i) q^{89} +(4.09808 + 11.8301i) q^{91} +(-3.29423 + 1.90192i) q^{93} +(7.09808 + 4.09808i) q^{95} -3.46410i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} + 2 q^{5}+O(q^{10}) \) 4 * q + 6 * q^3 + 2 * q^5	\( 4 q + 6 q^{3} + 2 q^{5} + 4 q^{11} + 12 q^{13} + 6 q^{17} + 18 q^{19} - 24 q^{23} - 2 q^{25} + 6 q^{31} + 12 q^{33} + 18 q^{39} + 12 q^{43} - 12 q^{47} - 22 q^{49} + 6 q^{51} + 18 q^{53} + 8 q^{55} + 36 q^{57} - 6 q^{59} + 12 q^{61} + 6 q^{65} + 2 q^{67} - 48 q^{69} - 30 q^{73} - 6 q^{75} - 36 q^{77} + 6 q^{79} + 18 q^{81} - 12 q^{87} + 30 q^{89} + 6 q^{91} + 18 q^{93} + 18 q^{95}+O(q^{100}) \) 4 * q + 6 * q^3 + 2 * q^5 + 4 * q^11 + 12 * q^13 + 6 * q^17 + 18 * q^19 - 24 * q^23 - 2 * q^25 + 6 * q^31 + 12 * q^33 + 18 * q^39 + 12 * q^43 - 12 * q^47 - 22 * q^49 + 6 * q^51 + 18 * q^53 + 8 * q^55 + 36 * q^57 - 6 * q^59 + 12 * q^61 + 6 * q^65 + 2 * q^67 - 48 * q^69 - 30 * q^73 - 6 * q^75 - 36 * q^77 + 6 * q^79 + 18 * q^81 - 12 * q^87 + 30 * q^89 + 6 * q^91 + 18 * q^93 + 18 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more