LMFDB - Embedded newform 1152.2.p.e.959.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(191,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1152.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1152 = 2^{7} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1152.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.19876631285$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			959.1
Root			$0.500000 - 1.00333i$ of defining polynomial
Character	$\chi$	$=$	1152.959
Dual form			1152.2.p.e.191.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.65068 - 0.524648i) q^{3} +(-1.57313 + 2.72474i) q^{5} +(2.21650 - 1.27970i) q^{7} +(2.44949 + 1.73205i) q^{9} +O(q^{10})$	\(q+(-1.65068 - 0.524648i) q^{3} +(-1.57313 + 2.72474i) q^{5} +(2.21650 - 1.27970i) q^{7} +(2.44949 + 1.73205i) q^{9} +(-2.02166 + 1.16721i) q^{11} +(-2.59808 - 1.50000i) q^{13} +(4.02627 - 3.67234i) q^{15} +4.24264i q^{17} +8.08665 q^{19} +(-4.33013 + 0.949490i) q^{21} +(-0.642559 + 1.11295i) q^{23} +(-2.44949 - 4.24264i) q^{25} +(-3.13461 - 4.14418i) q^{27} +(-1.18386 - 2.05051i) q^{29} +(-7.64580 - 4.41431i) q^{31} +(3.94949 - 0.866025i) q^{33} +8.05254i q^{35} +7.34847i q^{37} +(3.50162 + 3.83909i) q^{39} +(-8.17423 - 4.71940i) q^{41} +(-1.11295 - 1.92768i) q^{43} +(-8.57277 + 3.94949i) q^{45} +(4.78674 + 8.29088i) q^{47} +(-0.224745 + 0.389270i) q^{49} +(2.22589 - 7.00324i) q^{51} -8.34242 q^{53} -7.34468i q^{55} +(-13.3485 - 4.24264i) q^{57} +(1.11295 + 0.642559i) q^{59} +(-7.79423 + 4.50000i) q^{61} +(7.64580 + 0.704487i) q^{63} +(8.17423 - 4.71940i) q^{65} +(-0.204229 + 0.353736i) q^{67} +(1.64456 - 1.50000i) q^{69} -14.5841 q^{71} -1.55051 q^{73} +(1.81743 + 8.28836i) q^{75} +(-2.98735 + 5.17423i) q^{77} +(-8.93092 + 5.15627i) q^{79} +(3.00000 + 8.48528i) q^{81} +(-2.93038 + 1.69185i) q^{83} +(-11.5601 - 6.67423i) q^{85} +(0.878383 + 4.00585i) q^{87} +6.14966i q^{89} -7.67819 q^{91} +(10.3048 + 11.2980i) q^{93} +(-12.7214 + 22.0341i) q^{95} +(6.62372 + 11.4726i) q^{97} +(-6.97370 - 0.642559i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 24 q^{33} - 72 q^{41} + 16 q^{49} - 96 q^{57} + 72 q^{65} - 64 q^{73} + 48 q^{81} + 8 q^{97}+O(q^{100}) $ 16 * q + 24 * q^33 - 72 * q^41 + 16 * q^49 - 96 * q^57 + 72 * q^65 - 64 * q^73 + 48 * q^81 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

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
$3$	−1.65068	−	0.524648i	−0.953021	−	0.302905i
$3$	−1.65068	−	0.524648i	−0.953021	−	0.302905i
$4$		0			0
$5$	−1.57313	+	2.72474i	−0.703526	+	1.21854i	0.263695	+	0.964606i	$0.415059\pi$
$5$	−1.57313	+	2.72474i	−0.703526	+	1.21854i	−0.967221	+	0.253937i	$0.918274\pi$
$6$		0			0
$7$	2.21650	−	1.27970i	0.837759	−	0.483680i	−0.0187428	−	0.999824i	$-0.505966\pi$
$7$	2.21650	−	1.27970i	0.837759	−	0.483680i	0.856502	+	0.516144i	$0.172633\pi$
$8$		0			0
$9$	2.44949	+	1.73205i	0.816497	+	0.577350i
$10$		0			0
$11$	−2.02166	+	1.16721i	−0.609554	+	0.351926i	−0.772791	−	0.634661i	$-0.781140\pi$
$11$	−2.02166	+	1.16721i	−0.609554	+	0.351926i	0.163237	+	0.986587i	$0.447807\pi$
$12$		0			0
$13$	−2.59808	−	1.50000i	−0.720577	−	0.416025i	0.0943882	−	0.995535i	$-0.469911\pi$
$13$	−2.59808	−	1.50000i	−0.720577	−	0.416025i	−0.814965	+	0.579510i	$0.803244\pi$
$14$		0			0
$15$	4.02627	−	3.67234i	1.03958	−	0.948195i
$16$		0			0
$17$			4.24264i			1.02899i	0.857493	+	0.514496i	$0.172021\pi$
$17$			4.24264i			1.02899i	−0.857493	+	0.514496i	$0.827979\pi$
$18$		0			0
$19$	8.08665			1.85520			0.927602	−	0.373570i	$-0.121866\pi$
$19$	8.08665			1.85520			0.927602	+	0.373570i	$0.121866\pi$
$20$		0			0
$21$	−4.33013	+	0.949490i	−0.944911	+	0.207196i
$22$		0			0
$23$	−0.642559	+	1.11295i	−0.133983	+	0.232065i	−0.925208	−	0.379459i	$-0.876110\pi$
$23$	−0.642559	+	1.11295i	−0.133983	+	0.232065i	0.791226	+	0.611524i	$0.209443\pi$
$24$		0			0
$25$	−2.44949	−	4.24264i	−0.489898	−	0.848528i
$26$		0			0
$27$	−3.13461	−	4.14418i	−0.603256	−	0.797548i
$28$		0			0
$29$	−1.18386	−	2.05051i	−0.219838	−	0.380770i	0.734920	−	0.678153i	$-0.237219\pi$
$29$	−1.18386	−	2.05051i	−0.219838	−	0.380770i	−0.954758	+	0.297383i	$0.903886\pi$
$30$		0			0
$31$	−7.64580	−	4.41431i	−1.37323	−	0.792833i	−0.381894	−	0.924206i	$-0.624728\pi$
$31$	−7.64580	−	4.41431i	−1.37323	−	0.792833i	−0.991333	+	0.131374i	$0.958061\pi$
$32$		0			0
$33$	3.94949	−	0.866025i	0.687518	−	0.150756i
$34$		0			0
$35$			8.05254i			1.36113i
$36$		0			0
$37$			7.34847i			1.20808i	0.796954	+	0.604040i	$0.206443\pi$
$37$			7.34847i			1.20808i	−0.796954	+	0.604040i	$0.793557\pi$
$38$		0			0
$39$	3.50162	+	3.83909i	0.560708	+	0.614747i
$40$		0			0
$41$	−8.17423	−	4.71940i	−1.27660	−	0.737046i	−0.300379	−	0.953820i	$-0.597113\pi$
$41$	−8.17423	−	4.71940i	−1.27660	−	0.737046i	−0.976222	+	0.216774i	$0.930447\pi$
$42$		0			0
$43$	−1.11295	−	1.92768i	−0.169723	−	0.293968i	0.768600	−	0.639730i	$-0.220954\pi$
$43$	−1.11295	−	1.92768i	−0.169723	−	0.293968i	−0.938322	+	0.345762i	$0.887621\pi$
$44$		0			0
$45$	−8.57277	+	3.94949i	−1.27795	+	0.588755i
$46$		0			0
$47$	4.78674	+	8.29088i	0.698218	+	1.20935i	0.969084	+	0.246732i	$0.0793566\pi$
$47$	4.78674	+	8.29088i	0.698218	+	1.20935i	−0.270866	+	0.962617i	$0.587310\pi$
$48$		0			0
$49$	−0.224745	+	0.389270i	−0.0321064	+	0.0556099i
$50$		0			0
$51$	2.22589	−	7.00324i	0.311687	−	0.980650i
$52$		0			0
$53$	−8.34242			−1.14592			−0.572960	−	0.819584i	$-0.694205\pi$
$53$	−8.34242			−1.14592			−0.572960	+	0.819584i	$0.694205\pi$
$54$		0			0
$55$		−	7.34468i		−	0.990357i
$56$		0			0
$57$	−13.3485	−	4.24264i	−1.76805	−	0.561951i
$58$		0			0
$59$	1.11295	+	0.642559i	0.144893	+	0.0836541i	0.570694	−	0.821163i	$-0.306674\pi$
$59$	1.11295	+	0.642559i	0.144893	+	0.0836541i	−0.425801	+	0.904817i	$0.640008\pi$
$60$		0			0
$61$	−7.79423	+	4.50000i	−0.997949	+	0.576166i	−0.907641	−	0.419748i	$-0.862118\pi$
$61$	−7.79423	+	4.50000i	−0.997949	+	0.576166i	−0.0903080	+	0.995914i	$0.528785\pi$
$62$		0			0
$63$	7.64580	+	0.704487i	0.963281	+	0.0887570i
$64$		0			0
$65$	8.17423	−	4.71940i	1.01389	−	0.585369i
$66$		0			0
$67$	−0.204229	+	0.353736i	−0.0249506	+	0.0432157i	−0.878231	−	0.478237i	$-0.841276\pi$
$67$	−0.204229	+	0.353736i	−0.0249506	+	0.0432157i	0.853281	+	0.521452i	$0.174610\pi$
$68$		0			0
$69$	1.64456	−	1.50000i	0.197982	−	0.180579i
$70$		0			0
$71$	−14.5841			−1.73082			−0.865409	−	0.501066i	$-0.832941\pi$
$71$	−14.5841			−1.73082			−0.865409	+	0.501066i	$0.832941\pi$
$72$		0			0
$73$	−1.55051			−0.181473			−0.0907367	−	0.995875i	$-0.528922\pi$
$73$	−1.55051			−0.181473			−0.0907367	+	0.995875i	$0.528922\pi$
$74$		0			0
$75$	1.81743	+	8.28836i	0.209859	+	0.957058i
$76$		0			0
$77$	−2.98735	+	5.17423i	−0.340440	+	0.589659i
$78$		0			0
$79$	−8.93092	+	5.15627i	−1.00481	+	0.580126i	−0.909667	−	0.415338i	$-0.863663\pi$
$79$	−8.93092	+	5.15627i	−1.00481	+	0.580126i	−0.0951401	+	0.995464i	$0.530330\pi$
$80$		0			0
$81$	3.00000	+	8.48528i	0.333333	+	0.942809i
$82$		0			0
$83$	−2.93038	+	1.69185i	−0.321651	+	0.185705i	−0.652128	−	0.758109i	$-0.726124\pi$
$83$	−2.93038	+	1.69185i	−0.321651	+	0.185705i	0.330477	+	0.943814i	$0.392790\pi$
$84$		0			0
$85$	−11.5601	−	6.67423i	−1.25387	−	0.723922i
$86$		0			0
$87$	0.878383	+	4.00585i	0.0941726	+	0.429472i
$88$		0			0
$89$			6.14966i			0.651863i	0.945393	+	0.325932i	$0.105678\pi$
$89$			6.14966i			0.651863i	−0.945393	+	0.325932i	$0.894322\pi$
$90$		0			0
$91$	−7.67819			−0.804893
$92$		0			0
$93$	10.3048	+	11.2980i	1.06856	+	1.17154i
$94$		0			0
$95$	−12.7214	+	22.0341i	−1.30518	+	2.26065i
$96$		0			0
$97$	6.62372	+	11.4726i	0.672537	+	1.16487i	0.977182	+	0.212403i	$0.0681289\pi$
$97$	6.62372	+	11.4726i	0.672537	+	1.16487i	−0.304645	+	0.952466i	$0.598538\pi$
$98$		0			0
$99$	−6.97370	−	0.642559i	−0.700883	−	0.0645797i
$100$		0			0
$101$	1.57313	+	2.72474i	0.156533	+	0.271122i	0.933616	−	0.358275i	$-0.116635\pi$
$101$	1.57313	+	2.72474i	0.156533	+	0.271122i	−0.777083	+	0.629398i	$0.783302\pi$
$102$		0			0
$103$	−7.35698	−	4.24755i	−0.724905	−	0.418524i	0.0916506	−	0.995791i	$-0.470786\pi$
$103$	−7.35698	−	4.24755i	−0.724905	−	0.418524i	−0.816555	+	0.577267i	$0.804119\pi$
$104$		0			0
$105$	4.22474	−	13.2922i	0.412293	−	1.29718i
$106$		0			0
$107$		−	18.2037i		−	1.75981i	−0.475145	−	0.879907i	$-0.657604\pi$
$107$		−	18.2037i		−	1.75981i	0.475145	−	0.879907i	$-0.342396\pi$
$108$		0			0
$109$			1.34847i			0.129160i	0.997913	+	0.0645800i	$0.0205708\pi$
$109$			1.34847i			0.129160i	−0.997913	+	0.0645800i	$0.979429\pi$
$110$		0			0
$111$	3.85536	−	12.1300i	0.365934	−	1.15133i
$112$		0			0
$113$	4.50000	+	2.59808i	0.423324	+	0.244406i	0.696499	−	0.717558i	$-0.254740\pi$
$113$	4.50000	+	2.59808i	0.423324	+	0.244406i	−0.273174	+	0.961965i	$0.588074\pi$
$114$		0			0
$115$	−2.02166	−	3.50162i	−0.188521	−	0.326528i
$116$		0			0
$117$	−3.76588	−	8.17423i	−0.348156	−	0.755708i
$118$		0			0
$119$	5.42930	+	9.40382i	0.497703	+	0.862047i
$120$		0			0
$121$	−2.77526	+	4.80688i	−0.252296	+	0.436989i
$122$		0			0
$123$	11.0170	+	12.0788i	0.993372	+	1.08911i
$124$		0			0
$125$	−0.317837			−0.0284282
$126$		0			0
$127$		−	21.2921i		−	1.88937i	−0.327983	−	0.944684i	$-0.606369\pi$
$127$		−	21.2921i		−	1.88937i	0.327983	−	0.944684i	$-0.393631\pi$
$128$		0			0
$129$	0.825765	+	3.76588i	0.0727046	+	0.331568i
$130$		0			0
$131$	−1.52140	−	0.878383i	−0.132926	−	0.0767447i	0.432063	−	0.901844i	$-0.357786\pi$
$131$	−1.52140	−	0.878383i	−0.132926	−	0.0767447i	−0.564988	+	0.825099i	$0.691119\pi$
$132$		0			0
$133$	17.9241	−	10.3485i	1.55421	−	0.897326i
$134$		0			0
$135$	16.2230	−	2.02166i	1.39625	−	0.173997i
$136$		0			0
$137$	15.5227	−	8.96204i	1.32619	−	0.765679i	0.341485	−	0.939887i	$-0.389070\pi$
$137$	15.5227	−	8.96204i	1.32619	−	0.765679i	0.984709	+	0.174209i	$0.0557367\pi$
$138$		0			0
$139$	−8.79114	+	15.2267i	−0.745654	+	1.29151i	0.204234	+	0.978922i	$0.434530\pi$
$139$	−8.79114	+	15.2267i	−0.745654	+	1.29151i	−0.949888	+	0.312589i	$0.898804\pi$
$140$		0			0
$141$	−3.55159	−	16.1969i	−0.299098	−	1.36403i
$142$		0			0
$143$	7.00324			0.585641
$144$		0			0
$145$	7.44949			0.618646
$146$		0			0
$147$	0.575211	−	0.524648i	0.0474426	−	0.0432722i
$148$		0			0
$149$	5.74434	−	9.94949i	0.470595	−	0.815094i	−0.528840	−	0.848722i	$-0.677373\pi$
$149$	5.74434	−	9.94949i	0.470595	−	0.815094i	0.999434	+	0.0336278i	$0.0107061\pi$
$150$		0			0
$151$	−4.49792	+	2.59687i	−0.366035	+	0.211331i	−0.671725	−	0.740801i	$-0.734446\pi$
$151$	−4.49792	+	2.59687i	−0.366035	+	0.211331i	0.305690	+	0.952131i	$0.401113\pi$
$152$		0			0
$153$	−7.34847	+	10.3923i	−0.594089	+	0.840168i
$154$		0			0
$155$	24.0557	−	13.8886i	1.93220	−	1.11556i
$156$		0			0
$157$	6.62642	+	3.82577i	0.528846	+	0.305329i	0.740546	−	0.672005i	$-0.234567\pi$
$157$	6.62642	+	3.82577i	0.528846	+	0.305329i	−0.211700	+	0.977335i	$0.567900\pi$
$158$		0			0
$159$	13.7707	+	4.37683i	1.09208	+	0.347105i
$160$		0			0
$161$			3.28913i			0.259220i
$162$		0			0
$163$	3.63487			0.284705			0.142352	−	0.989816i	$-0.454533\pi$
$163$	3.63487			0.284705			0.142352	+	0.989816i	$0.454533\pi$
$164$		0			0
$165$	−3.85337	+	12.1237i	−0.299985	+	0.943831i
$166$		0			0
$167$	−6.07186	+	10.5168i	−0.469855	+	0.813812i	−0.999406	−	0.0344659i	$-0.989027\pi$
$167$	−6.07186	+	10.5168i	−0.469855	+	0.813812i	0.529551	+	0.848278i	$0.322360\pi$
$168$		0			0
$169$	−2.00000	−	3.46410i	−0.153846	−	0.266469i
$170$		0			0
$171$	19.8082	+	14.0065i	1.51477	+	1.07110i
$172$		0			0
$173$	2.52664	+	4.37628i	0.192097	+	0.332722i	0.945945	−	0.324327i	$-0.105138\pi$
$173$	2.52664	+	4.37628i	0.192097	+	0.332722i	−0.753848	+	0.657049i	$0.771804\pi$
$174$		0			0
$175$	−10.8586	−	6.26922i	−0.820833	−	0.473908i
$176$		0			0
$177$	−1.50000	−	1.64456i	−0.112747	−	0.123613i
$178$		0			0
$179$		−	3.04189i		−	0.227361i	−0.993517	−	0.113681i	$-0.963736\pi$
$179$		−	3.04189i		−	0.227361i	0.993517	−	0.113681i	$-0.0362641\pi$
$180$		0			0
$181$			19.3485i			1.43816i	0.694927	+	0.719080i	$0.255437\pi$
$181$			19.3485i			1.43816i	−0.694927	+	0.719080i	$0.744563\pi$
$182$		0			0
$183$	15.2267	−	3.33884i	1.12559	−	0.246814i
$184$		0			0
$185$	−20.0227	−	11.5601i	−1.47210	−	0.849916i
$186$		0			0
$187$	−4.95204	−	8.57719i	−0.362129	−	0.627226i
$188$		0			0
$189$	−12.2512	−	5.17423i	−0.891141	−	0.376370i
$190$		0			0
$191$	−5.36439	−	9.29139i	−0.388153	−	0.672302i	0.604048	−	0.796948i	$-0.293554\pi$
$191$	−5.36439	−	9.29139i	−0.388153	−	0.672302i	−0.992201	+	0.124647i	$0.960220\pi$
$192$		0			0
$193$	3.72474	−	6.45145i	0.268113	−	0.464385i	−0.700262	−	0.713886i	$-0.746933\pi$
$193$	3.72474	−	6.45145i	0.268113	−	0.464385i	0.968375	+	0.249501i	$0.0802666\pi$
$194$		0			0
$195$	−15.9691	+	3.50162i	−1.14357	+	0.250756i
$196$		0			0
$197$	16.6848			1.18875			0.594373	−	0.804190i	$-0.297400\pi$
$197$	16.6848			1.18875			0.594373	+	0.804190i	$0.297400\pi$
$198$		0			0
$199$		−	16.5068i		−	1.17014i	−0.810984	−	0.585068i	$-0.801068\pi$
$199$		−	16.5068i		−	1.17014i	0.810984	−	0.585068i	$-0.198932\pi$
$200$		0			0
$201$	0.522704	−	0.476756i	0.0368687	−	0.0336278i
$202$		0			0
$203$	−5.24807	−	3.02997i	−0.368342	−	0.212662i
$204$		0			0
$205$	25.7183	−	14.8485i	1.79624	−	1.03706i
$206$		0			0
$207$	−3.50162	+	1.61320i	−0.243380	+	0.112125i
$208$		0			0
$209$	−16.3485	+	9.43879i	−1.13085	+	0.652895i
$210$		0			0
$211$	3.83909	−	6.64951i	0.264294	−	0.457771i	−0.703084	−	0.711107i	$-0.748194\pi$
$211$	3.83909	−	6.64951i	0.264294	−	0.457771i	0.967378	+	0.253336i	$0.0815277\pi$
$212$		0			0
$213$	24.0737	+	7.65153i	1.64951	+	0.524274i
$214$		0			0
$215$	7.00324			0.477617
$216$		0			0
$217$	−22.5959			−1.53391
$218$		0			0
$219$	2.55940	+	0.813472i	0.172948	+	0.0549693i
$220$		0			0
$221$	6.36396	−	11.0227i	0.428086	−	0.741467i
$222$		0			0
$223$	16.8006	−	9.69985i	1.12505	−	0.649550i	0.182367	−	0.983230i	$-0.441624\pi$
$223$	16.8006	−	9.69985i	1.12505	−	0.649550i	0.942686	+	0.333680i	$0.108291\pi$
$224$		0			0
$225$	1.34847	−	14.6349i	0.0898979	−	0.975663i
$226$		0			0
$227$	−20.4208	+	11.7900i	−1.35538	+	0.782529i	−0.988997	−	0.147936i	$-0.952737\pi$
$227$	−20.4208	+	11.7900i	−1.35538	+	0.782529i	−0.366382	+	0.930464i	$0.619404\pi$
$228$		0			0
$229$	−21.6900	−	12.5227i	−1.43331	−	0.827524i	−0.435941	−	0.899975i	$-0.643584\pi$
$229$	−21.6900	−	12.5227i	−1.43331	−	0.827524i	−0.997372	+	0.0724517i	$0.976918\pi$
$230$		0			0
$231$	7.64580	−	6.97370i	0.503057	−	0.458836i
$232$		0			0
$233$			8.48528i			0.555889i	0.960597	+	0.277945i	$0.0896532\pi$
$233$			8.48528i			0.555889i	−0.960597	+	0.277945i	$0.910347\pi$
$234$		0			0
$235$	−30.1207			−1.96486
$236$		0			0
$237$	17.4473	−	3.82577i	1.13333	−	0.248510i
$238$		0			0
$239$	−0.642559	+	1.11295i	−0.0415637	+	0.0719905i	−0.886059	−	0.463573i	$-0.846567\pi$
$239$	−0.642559	+	1.11295i	−0.0415637	+	0.0719905i	0.844495	+	0.535563i	$0.179901\pi$
$240$		0			0
$241$	−6.84847	−	11.8619i	−0.441149	−	0.764092i	0.556626	−	0.830763i	$-0.312096\pi$
$241$	−6.84847	−	11.8619i	−0.441149	−	0.764092i	−0.997775	+	0.0666710i	$0.978762\pi$
$242$		0			0
$243$	−0.500258	−	15.5804i	−0.0320915	−	0.999485i
$244$		0			0
$245$	−0.707107	−	1.22474i	−0.0451754	−	0.0782461i
$246$		0			0
$247$	−21.0097	−	12.1300i	−1.33682	−	0.771812i
$248$		0			0
$249$	5.72474	−	1.25529i	0.362791	−	0.0795511i
$250$		0			0
$251$			7.71071i			0.486696i	0.969939	+	0.243348i	$0.0782457\pi$
$251$			7.71071i			0.486696i	−0.969939	+	0.243348i	$0.921754\pi$
$252$		0			0
$253$		−	3.00000i		−	0.188608i
$254$		0			0
$255$	15.5804	+	17.0820i	0.975684	+	1.06972i
$256$		0			0
$257$	11.8485	+	6.84072i	0.739087	+	0.426712i	0.821737	−	0.569866i	$-0.193005\pi$
$257$	11.8485	+	6.84072i	0.739087	+	0.426712i	−0.0826501	+	0.996579i	$0.526338\pi$
$258$		0			0
$259$	9.40382	+	16.2879i	0.584325	+	1.01208i
$260$		0			0
$261$	0.651729	−	7.07321i	0.0403410	−	0.437821i
$262$		0			0
$263$	12.0788	+	20.9211i	0.744811	+	1.29005i	0.950283	+	0.311388i	$0.100794\pi$
$263$	12.0788	+	20.9211i	0.744811	+	1.29005i	−0.205472	+	0.978663i	$0.565873\pi$
$264$		0			0
$265$	13.1237	−	22.7310i	0.806184	−	1.39635i
$266$		0			0
$267$	3.22641	−	10.1511i	0.197453	−	0.621239i
$268$		0			0
$269$	3.32124			0.202499			0.101250	−	0.994861i	$-0.467716\pi$
$269$	3.32124			0.202499			0.101250	+	0.994861i	$0.467716\pi$
$270$		0			0
$271$			13.2054i			0.802173i	0.916040	+	0.401087i	$0.131367\pi$
$271$			13.2054i			0.802173i	−0.916040	+	0.401087i	$0.868633\pi$
$272$		0			0
$273$	12.6742	+	4.02834i	0.767080	+	0.243806i
$274$		0			0
$275$	9.90408	+	5.71812i	0.597239	+	0.344816i
$276$		0			0
$277$	21.6900	−	12.5227i	1.30322	−	0.752416i	0.322268	−	0.946649i	$-0.395555\pi$
$277$	21.6900	−	12.5227i	1.30322	−	0.752416i	0.980956	+	0.194232i	$0.0622215\pi$
$278$		0			0
$279$	−11.0825	−	24.0557i	−0.663493	−	1.44018i
$280$		0			0
$281$	−13.8712	+	8.00853i	−0.827485	+	0.477749i	−0.852991	−	0.521926i	$-0.825214\pi$
$281$	−13.8712	+	8.00853i	−0.827485	+	0.477749i	0.0255059	+	0.999675i	$0.491880\pi$
$282$		0			0
$283$	7.38216	−	12.7863i	0.438824	−	0.760065i	−0.558775	−	0.829319i	$-0.688729\pi$
$283$	7.38216	−	12.7863i	0.438824	−	0.760065i	0.997599	+	0.0692539i	$0.0220618\pi$
$284$		0			0
$285$	32.5590	−	29.6969i	1.92863	−	1.75909i
$286$		0			0
$287$	−24.1576			−1.42598
$288$		0			0
$289$	−1.00000			−0.0588235
$290$		0			0
$291$	−4.91456	−	22.4128i	−0.288097	−	1.31386i
$292$		0			0
$293$	−1.89097	+	3.27526i	−0.110472	+	0.191342i	−0.915961	−	0.401268i	$-0.868569\pi$
$293$	−1.89097	+	3.27526i	−0.110472	+	0.191342i	0.805489	+	0.592611i	$0.201903\pi$
$294$		0			0
$295$	−3.50162	+	2.02166i	−0.203872	+	0.117706i
$296$		0			0
$297$	11.1742	+	4.71940i	0.648395	+	0.273847i
$298$		0			0
$299$	3.33884	−	1.92768i	0.193090	−	0.111481i
$300$		0			0
$301$	−4.93369	−	2.84847i	−0.284373	−	0.164183i
$302$		0			0
$303$	−1.16721	−	5.32302i	−0.0670543	−	0.305800i
$304$		0			0
$305$		−	28.3164i		−	1.62139i
$306$		0			0
$307$	23.4430			1.33796			0.668982	−	0.743279i	$-0.266730\pi$
$307$	23.4430			1.33796			0.668982	+	0.743279i	$0.266730\pi$
$308$		0			0
$309$	9.91555	+	10.8712i	0.564076	+	0.618439i
$310$		0			0
$311$	−10.7937	+	18.6952i	−0.612054	+	1.06011i	0.378840	+	0.925462i	$0.376323\pi$
$311$	−10.7937	+	18.6952i	−0.612054	+	1.06011i	−0.990894	+	0.134646i	$0.957010\pi$
$312$		0			0
$313$	8.94949	+	15.5010i	0.505855	+	0.876167i	0.999977	+	0.00677410i	$0.00215628\pi$
$313$	8.94949	+	15.5010i	0.505855	+	0.876167i	−0.494122	+	0.869393i	$0.664510\pi$
$314$		0			0
$315$	−13.9474	+	19.7246i	−0.785847	+	1.11136i
$316$		0			0
$317$	−3.69445	−	6.39898i	−0.207501	−	0.359402i	0.743426	−	0.668819i	$-0.233200\pi$
$317$	−3.69445	−	6.39898i	−0.207501	−	0.359402i	−0.950927	+	0.309416i	$0.899866\pi$
$318$		0			0
$319$	4.78674	+	2.76363i	0.268006	+	0.154733i
$320$		0			0
$321$	−9.55051	+	30.0484i	−0.533058	+	1.67714i
$322$		0			0
$323$			34.3087i			1.90899i
$324$		0			0
$325$			14.6969i			0.815239i
$326$		0			0
$327$	0.707471	−	2.22589i	0.0391232	−	0.123092i
$328$		0			0
$329$	21.2196	+	12.2512i	1.16988	+	0.675429i
$330$		0			0
$331$	9.69985	+	16.8006i	0.533152	+	0.923446i	0.999250	+	0.0387135i	$0.0123260\pi$
$331$	9.69985	+	16.8006i	0.533152	+	0.923446i	−0.466098	+	0.884733i	$0.654341\pi$
$332$		0			0
$333$	−12.7279	+	18.0000i	−0.697486	+	0.986394i
$334$		0			0
$335$	−0.642559	−	1.11295i	−0.0351068	−	0.0608067i
$336$		0			0
$337$	−13.8485	+	23.9863i	−0.754374	+	1.30661i	0.191311	+	0.981530i	$0.438726\pi$
$337$	−13.8485	+	23.9863i	−0.754374	+	1.30661i	−0.945685	+	0.325085i	$0.894607\pi$
$338$		0			0
$339$	−6.06499	−	6.64951i	−0.329405	−	0.361152i
$340$		0			0
$341$	20.6096			1.11607
$342$		0			0
$343$			19.0662i			1.02948i
$344$		0			0
$345$	1.50000	+	6.84072i	0.0807573	+	0.368292i
$346$		0			0
$347$	−6.47344	−	3.73745i	−0.347513	−	0.200637i	0.316077	−	0.948734i	$-0.397634\pi$
$347$	−6.47344	−	3.73745i	−0.347513	−	0.200637i	−0.663589	+	0.748097i	$0.730968\pi$
$348$		0			0
$349$	−1.43027	+	0.825765i	−0.0765605	+	0.0442022i	−0.537792	−	0.843078i	$-0.680741\pi$
$349$	−1.43027	+	0.825765i	−0.0765605	+	0.0442022i	0.461231	+	0.887280i	$0.347408\pi$
$350$		0			0
$351$	1.92768	+	15.4688i	0.102892	+	0.825664i
$352$		0			0
$353$	−9.82577	+	5.67291i	−0.522973	+	0.301938i	−0.738150	−	0.674637i	$-0.764300\pi$
$353$	−9.82577	+	5.67291i	−0.522973	+	0.301938i	0.215177	+	0.976575i	$0.430967\pi$
$354$		0			0
$355$	22.9428	−	39.7380i	1.21768	−	2.10908i
$356$		0			0
$357$	−4.02834	−	18.3712i	−0.213203	−	0.972306i
$358$		0			0
$359$	2.57024			0.135652			0.0678260	−	0.997697i	$-0.478394\pi$
$359$	2.57024			0.135652			0.0678260	+	0.997697i	$0.478394\pi$
$360$		0			0
$361$	46.3939			2.44178
$362$		0			0
$363$	7.10298	−	6.47860i	0.372810	−	0.340038i
$364$		0			0
$365$	2.43916	−	4.22474i	0.127671	−	0.221133i
$366$		0			0
$367$	−2.50533	+	1.44645i	−0.130777	+	0.0755041i	−0.563961	−	0.825801i	$-0.690723\pi$
$367$	−2.50533	+	1.44645i	−0.130777	+	0.0755041i	0.433184	+	0.901305i	$0.357390\pi$
$368$		0			0
$369$	−11.8485	−	25.7183i	−0.616807	−	1.33884i
$370$		0			0
$371$	−18.4910	+	10.6758i	−0.960004	+	0.554259i
$372$		0			0
$373$	0.262459	+	0.151531i	0.0135896	+	0.00784597i	0.506779	−	0.862076i	$-0.330836\pi$
$373$	0.262459	+	0.151531i	0.0135896	+	0.00784597i	−0.493190	+	0.869922i	$0.664169\pi$
$374$		0			0
$375$	0.524648	+	0.166753i	0.0270927	+	0.00861106i
$376$		0			0
$377$			7.10318i			0.365832i
$378$		0			0
$379$	6.26922			0.322028			0.161014	−	0.986952i	$-0.448524\pi$
$379$	6.26922			0.322028			0.161014	+	0.986952i	$0.448524\pi$
$380$		0			0
$381$	−11.1708	+	35.1464i	−0.572300	+	1.80061i
$382$		0			0
$383$	4.78674	−	8.29088i	0.244591	−	0.423644i	−0.717426	−	0.696635i	$-0.754680\pi$
$383$	4.78674	−	8.29088i	0.244591	−	0.423644i	0.962017	+	0.272991i	$0.0880130\pi$
$384$		0			0
$385$	−9.39898	−	16.2795i	−0.479016	−	0.829681i
$386$		0			0
$387$	0.612688	−	6.64951i	0.0311447	−	0.338013i
$388$		0			0
$389$	−11.0119	−	19.0732i	−0.558327	−	0.967050i	−0.997636	−	0.0687146i	$-0.978110\pi$
$389$	−11.0119	−	19.0732i	−0.558327	−	0.967050i	0.439310	−	0.898336i	$-0.355223\pi$
$390$		0			0
$391$	−4.72183	−	2.72615i	−0.238793	−	0.137867i
$392$		0			0
$393$	2.05051	+	2.24813i	0.103435	+	0.113403i
$394$		0			0
$395$		−	32.4460i		−	1.63253i
$396$		0			0
$397$			28.0454i			1.40756i	0.710419	+	0.703779i	$0.248506\pi$
$397$			28.0454i			1.40756i	−0.710419	+	0.703779i	$0.751494\pi$
$398$		0			0
$399$	−35.0162	+	7.67819i	−1.75300	+	0.384390i
$400$		0			0
$401$	11.4773	+	6.62642i	0.573149	+	0.330908i	0.758406	−	0.651782i	$-0.225978\pi$
$401$	11.4773	+	6.62642i	0.573149	+	0.330908i	−0.185257	+	0.982690i	$0.559312\pi$
$402$		0			0
$403$	13.2429	+	22.9374i	0.659677	+	1.14259i
$404$		0			0
$405$	−27.8396	−	5.17423i	−1.38336	−	0.257110i
$406$		0			0
$407$	−8.57719	−	14.8561i	−0.425155	−	0.736391i
$408$		0			0
$409$	−13.2980	+	23.0327i	−0.657542	+	1.13890i	0.323708	+	0.946157i	$0.395070\pi$
$409$	−13.2980	+	23.0327i	−0.657542	+	1.13890i	−0.981250	+	0.192739i	$0.938263\pi$
$410$		0			0
$411$	−30.3249	+	6.64951i	−1.49582	+	0.327996i
$412$		0			0
$413$	3.28913			0.161847
$414$		0			0
$415$		−	10.6460i		−	0.522594i
$416$		0			0
$417$	22.5000	−	20.5222i	1.10183	−	1.00497i
$418$		0			0
$419$	13.7432	+	7.93463i	0.671398	+	0.387632i	0.796606	−	0.604499i	$-0.206627\pi$
$419$	13.7432	+	7.93463i	0.671398	+	0.387632i	−0.125208	+	0.992131i	$0.539960\pi$
$420$		0			0
$421$	15.3260	−	8.84847i	0.746943	−	0.431248i	−0.0776450	−	0.996981i	$-0.524740\pi$
$421$	15.3260	−	8.84847i	0.746943	−	0.431248i	0.824588	+	0.565733i	$0.191407\pi$
$422$		0			0
$423$	−2.63515	+	28.5993i	−0.128125	+	1.39055i
$424$		0			0
$425$	18.0000	−	10.3923i	0.873128	−	0.504101i
$426$		0			0
$427$	−11.5173	+	19.9485i	−0.557360	+	0.965377i
$428$		0			0
$429$	−11.5601	−	3.67423i	−0.558128	−	0.177394i
$430$		0			0
$431$	2.57024			0.123804			0.0619020	−	0.998082i	$-0.480283\pi$
$431$	2.57024			0.123804			0.0619020	+	0.998082i	$0.480283\pi$
$432$		0			0
$433$	−22.4495			−1.07885			−0.539427	−	0.842032i	$-0.681359\pi$
$433$	−22.4495			−1.07885			−0.539427	+	0.842032i	$0.681359\pi$
$434$		0			0
$435$	−12.2967	−	3.90836i	−0.589583	−	0.187391i
$436$		0			0
$437$	−5.19615	+	9.00000i	−0.248566	+	0.430528i
$438$		0			0
$439$	−13.9416	+	8.04917i	−0.665395	+	0.384166i	−0.794330	−	0.607487i	$-0.792178\pi$
$439$	−13.9416	+	8.04917i	−0.665395	+	0.384166i	0.128935	+	0.991653i	$0.458844\pi$
$440$		0			0
$441$	−1.22474	+	0.564242i	−0.0583212	+	0.0268687i
$442$		0			0
$443$	−10.0165	+	5.78304i	−0.475899	+	0.274760i	−0.718706	−	0.695314i	$-0.755265\pi$
$443$	−10.0165	+	5.78304i	−0.475899	+	0.274760i	0.242807	+	0.970075i	$0.421932\pi$
$444$		0			0
$445$	−16.7563	−	9.67423i	−0.794323	−	0.458603i
$446$		0			0
$447$	−14.7020	+	13.4097i	−0.695383	+	0.634256i
$448$		0			0
$449$		−	31.6055i		−	1.49156i	−0.666194	−	0.745778i	$-0.732078\pi$
$449$		−	31.6055i		−	1.49156i	0.666194	−	0.745778i	$-0.267922\pi$
$450$		0			0
$451$	22.0341			1.03754
$452$		0			0
$453$	8.78706	−	1.92679i	0.412852	−	0.0905283i
$454$		0			0
$455$	12.0788	−	20.9211i	0.566263	−	0.980797i
$456$		0			0
$457$	−0.926786	−	1.60524i	−0.0433532	−	0.0750900i	0.843535	−	0.537075i	$-0.180471\pi$
$457$	−0.926786	−	1.60524i	−0.0433532	−	0.0750900i	−0.886888	+	0.461985i	$0.847137\pi$
$458$		0			0
$459$	17.5823	−	13.2990i	0.820670	−	0.620745i
$460$		0			0
$461$	12.1797	+	21.0959i	0.567267	+	0.982535i	0.996835	+	0.0795004i	$0.0253325\pi$
$461$	12.1797	+	21.0959i	0.567267	+	0.982535i	−0.429568	+	0.903034i	$0.641334\pi$
$462$		0			0
$463$	21.6523	+	12.5010i	1.00627	+	0.580969i	0.910097	−	0.414396i	$-0.136007\pi$
$463$	21.6523	+	12.5010i	1.00627	+	0.580969i	0.0961706	+	0.995365i	$0.469341\pi$
$464$		0			0
$465$	−46.9949	+	10.3048i	−2.17934	+	0.477875i
$466$		0			0
$467$			25.9144i			1.19917i	0.800309	+	0.599587i	$0.204669\pi$
$467$			25.9144i			1.19917i	−0.800309	+	0.599587i	$0.795331\pi$
$468$		0			0
$469$			1.04541i			0.0482724i
$470$		0			0
$471$	−8.93092	−	9.79165i	−0.411515	−	0.451175i
$472$		0			0
$473$	4.50000	+	2.59808i	0.206910	+	0.119460i
$474$		0			0
$475$	−19.8082	−	34.3087i	−0.908861	−	1.57419i
$476$		0			0
$477$	−20.4347	−	14.4495i	−0.935639	−	0.661597i
$478$		0			0
$479$	1.22021	+	2.11346i	0.0557527	+	0.0965665i	0.892555	−	0.450939i	$-0.148911\pi$
$479$	1.22021	+	2.11346i	0.0557527	+	0.0965665i	−0.836802	+	0.547506i	$0.815577\pi$
$480$		0			0
$481$	11.0227	−	19.0919i	0.502592	−	0.870515i
$482$		0			0
$483$	1.72563	−	5.42930i	0.0785191	−	0.247042i
$484$		0			0
$485$	−41.6800			−1.89259
$486$		0			0
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$		0			0
$489$	−6.00000	−	1.90702i	−0.271329	−	0.0862386i
$490$		0			0
$491$	−7.97422	−	4.60392i	−0.359871	−	0.207772i	0.309153	−	0.951012i	$-0.399954\pi$
$491$	−7.97422	−	4.60392i	−0.359871	−	0.207772i	−0.669024	+	0.743240i	$0.733288\pi$
$492$		0			0
$493$	8.69958	−	5.02270i	0.391809	−	0.226211i
$494$		0			0
$495$	12.7214	−	17.9907i	0.571783	−	0.808623i
$496$		0			0
$497$	−32.3258	+	18.6633i	−1.45001	+	0.837163i
$498$		0			0
$499$	−9.19959	+	15.9342i	−0.411830	+	0.713311i	−0.995090	−	0.0989747i	$-0.968444\pi$
$499$	−9.19959	+	15.9342i	−0.411830	+	0.713311i	0.583260	+	0.812286i	$0.301777\pi$
$500$		0			0
$501$	15.5403	−	14.1742i	0.694289	−	0.633258i
$502$		0			0
$503$	20.8799			0.930989			0.465494	−	0.885051i	$-0.345877\pi$
$503$	20.8799			0.930989			0.465494	+	0.885051i	$0.345877\pi$
$504$		0			0
$505$	−9.89898			−0.440499
$506$		0			0
$507$	1.48393	+	6.76742i	0.0659035	+	0.300552i
$508$		0			0
$509$	−11.2262	+	19.4444i	−0.497594	+	0.861857i	−0.999996	−	0.00277650i	$-0.999116\pi$
$509$	−11.2262	+	19.4444i	−0.497594	+	0.861857i	0.502403	+	0.864634i	$0.332450\pi$
$510$		0			0
$511$	−3.43671	+	1.98419i	−0.152031	+	0.0877752i
$512$		0			0
$513$	−25.3485	−	33.5125i	−1.11916	−	1.47961i
$514$		0			0
$515$	23.1470	−	13.3639i	1.01998	−	0.588885i
$516$		0			0
$517$	−19.3543	−	11.1742i	−0.851203	−	0.491442i
$518$		0			0
$519$	−1.87468	−	8.54943i	−0.0822892	−	0.375278i
$520$		0			0
$521$		−	18.8776i		−	0.827042i	−0.910495	−	0.413521i	$-0.864299\pi$
$521$		−	18.8776i		−	0.827042i	0.910495	−	0.413521i	$-0.135701\pi$
$522$		0			0
$523$	−22.4425			−0.981343			−0.490671	−	0.871345i	$-0.663248\pi$
$523$	−22.4425			−0.981343			−0.490671	+	0.871345i	$0.663248\pi$
$524$		0			0
$525$	14.6349	+	16.0454i	0.638721	+	0.700279i
$526$		0			0
$527$	18.7283	−	32.4384i	0.815818	−	1.41304i
$528$		0			0
$529$	10.6742	+	18.4883i	0.464097	+	0.803840i
$530$		0			0
$531$	1.61320	+	3.50162i	0.0700071	+	0.151957i
$532$		0			0
$533$	14.1582	+	24.5227i	0.613259	+	1.06220i
$534$		0			0
$535$	49.6003	+	28.6368i	2.14441	+	1.23808i
$536$		0			0
$537$	−1.59592	+	5.02118i	−0.0688689	+	0.216680i
$538$		0			0
$539$		−	1.04930i		−	0.0451963i
$540$		0			0
$541$			8.69694i			0.373911i	0.982368	+	0.186955i	$0.0598620\pi$
$541$			8.69694i			0.373911i	−0.982368	+	0.186955i	$0.940138\pi$
$542$		0			0
$543$	10.1511	−	31.9381i	0.435627	−	1.37060i
$544$		0			0
$545$	−3.67423	−	2.12132i	−0.157387	−	0.0908674i
$546$		0			0
$547$	−7.88242	−	13.6527i	−0.337028	−	0.583749i	0.646844	−	0.762622i	$-0.276088\pi$
$547$	−7.88242	−	13.6527i	−0.337028	−	0.583749i	−0.983872	+	0.178873i	$0.942755\pi$
$548$		0			0
$549$	−26.8861	−	2.47730i	−1.14747	−	0.105728i
$550$		0			0
$551$	−9.57348	−	16.5818i	−0.407844	−	0.706407i
$552$		0			0
$553$	−13.1969	+	22.8578i	−0.561191	+	0.972011i
$554$		0			0
$555$	26.9861	+	29.5869i	1.14550	+	1.25589i
$556$		0			0
$557$	−20.6417			−0.874619			−0.437309	−	0.899311i	$-0.644069\pi$
$557$	−20.6417			−0.874619			−0.437309	+	0.899311i	$0.644069\pi$
$558$		0			0
$559$			6.67767i			0.282436i
$560$		0			0
$561$	3.67423	+	16.7563i	0.155126	+	0.707450i
$562$		0			0
$563$	−36.5941	−	21.1276i	−1.54226	−	0.890424i	−0.998696	−	0.0510558i	$-0.983741\pi$
$563$	−36.5941	−	21.1276i	−1.54226	−	0.890424i	−0.543564	−	0.839368i	$-0.682925\pi$
$564$		0			0
$565$	−14.1582	+	8.17423i	−0.595640	+	0.343893i
$566$		0			0
$567$	17.5081	+	14.9686i	0.735271	+	0.628620i
$568$		0			0
$569$	13.5000	−	7.79423i	0.565949	−	0.326751i	−0.189580	−	0.981865i	$-0.560713\pi$
$569$	13.5000	−	7.79423i	0.565949	−	0.326751i	0.755530	+	0.655114i	$0.227379\pi$
$570$		0			0
$571$	−6.47344	+	11.2123i	−0.270905	+	0.469222i	−0.969094	−	0.246692i	$-0.920656\pi$
$571$	−6.47344	+	11.2123i	−0.270905	+	0.469222i	0.698189	+	0.715914i	$0.253990\pi$
$572$		0			0
$573$	3.98018	+	18.1515i	0.166274	+	0.758291i
$574$		0			0
$575$	6.29577			0.262552
$576$		0			0
$577$	9.34847			0.389182			0.194591	−	0.980884i	$-0.437662\pi$
$577$	9.34847			0.389182			0.194591	+	0.980884i	$0.437662\pi$
$578$		0			0
$579$	−9.53310	+	8.69510i	−0.396182	+	0.361356i
$580$		0			0
$581$	−4.33013	+	7.50000i	−0.179644	+	0.311152i
$582$		0			0
$583$	16.8655	−	9.73733i	0.698500	−	0.403279i
$584$		0			0
$585$	28.1969	+	2.59808i	1.16580	+	0.107417i
$586$		0			0
$587$	16.2857	−	9.40257i	0.672184	−	0.388086i	−0.124720	−	0.992192i	$-0.539803\pi$
$587$	16.2857	−	9.40257i	0.672184	−	0.388086i	0.796904	+	0.604106i	$0.206470\pi$
$588$		0			0
$589$	−61.8289	−	35.6969i	−2.54762	−	1.47087i
$590$		0			0
$591$	−27.5413	−	8.75366i	−1.13290	−	0.360077i
$592$		0			0
$593$		−	25.0273i		−	1.02775i	−0.857866	−	0.513873i	$-0.828210\pi$
$593$		−	25.0273i		−	1.02775i	0.857866	−	0.513873i	$-0.171790\pi$
$594$		0			0
$595$	−34.1640			−1.40059
$596$		0			0
$597$	−8.66025	+	27.2474i	−0.354441	+	1.11516i
$598$		0			0
$599$	15.6453	−	27.0985i	0.639251	−	1.10722i	−0.346346	−	0.938107i	$-0.612578\pi$
$599$	15.6453	−	27.0985i	0.639251	−	1.10722i	0.985597	−	0.169109i	$-0.0540889\pi$
$600$		0			0
$601$	−0.623724	−	1.08032i	−0.0254422	−	0.0440673i	0.853024	−	0.521872i	$-0.174766\pi$
$601$	−0.623724	−	1.08032i	−0.0254422	−	0.0440673i	−0.878466	+	0.477805i	$0.841433\pi$
$602$		0			0
$603$	−1.11295	+	0.512736i	−0.0453227	+	0.0208802i
$604$		0			0
$605$	−8.73169	−	15.1237i	−0.354994	−	0.614867i
$606$		0			0
$607$	10.5049	+	6.06499i	0.426379	+	0.246170i	0.697803	−	0.716290i	$-0.254161\pi$
$607$	10.5049	+	6.06499i	0.426379	+	0.246170i	−0.271424	+	0.962460i	$0.587494\pi$
$608$		0			0
$609$	7.07321	+	7.75490i	0.286621	+	0.314245i
$610$		0			0
$611$		−	28.7204i		−	1.16190i
$612$		0			0
$613$			40.0454i			1.61742i	0.588208	+	0.808709i	$0.299833\pi$
$613$			40.0454i			1.61742i	−0.588208	+	0.808709i	$0.700167\pi$
$614$		0			0
$615$	−50.2429	+	11.0170i	−2.02599	+	0.444249i
$616$		0			0
$617$	13.8712	+	8.00853i	0.558432	+	0.322411i	0.752516	−	0.658574i	$-0.228840\pi$
$617$	13.8712	+	8.00853i	0.558432	+	0.322411i	−0.194084	+	0.980985i	$0.562173\pi$
$618$		0			0
$619$	−0.612688	−	1.06121i	−0.0246260	−	0.0426535i	0.853450	−	0.521175i	$-0.174506\pi$
$619$	−0.612688	−	1.06121i	−0.0246260	−	0.0426535i	−0.878076	+	0.478522i	$0.841173\pi$
$620$		0			0
$621$	6.62642	−	0.825765i	0.265909	−	0.0331368i
$622$		0			0
$623$	7.86971	+	13.6307i	0.315293	+	0.546104i
$624$		0			0
$625$	12.7474	−	22.0792i	0.509898	−	0.883169i
$626$		0			0
$627$	31.9381	−	7.00324i	1.27549	−	0.279683i
$628$		0			0
$629$	−31.1769			−1.24310
$630$		0			0
$631$			2.96786i			0.118148i	0.998254	+	0.0590742i	$0.0188149\pi$
$631$			2.96786i			0.118148i	−0.998254	+	0.0590742i	$0.981185\pi$
$632$		0			0
$633$	−9.82577	+	8.96204i	−0.390539	+	0.356209i
$634$		0			0
$635$	58.0155	+	33.4953i	2.30228	+	1.32922i
$636$		0			0
$637$	1.16781	−	0.674235i	0.0462703	−	0.0267141i
$638$		0			0
$639$	−35.7237	−	25.2605i	−1.41321	−	0.999288i
$640$		0			0
$641$	−19.1969	+	11.0834i	−0.758233	+	0.437766i	−0.828661	−	0.559751i	$-0.810897\pi$
$641$	−19.1969	+	11.0834i	−0.758233	+	0.437766i	0.0704277	+	0.997517i	$0.477564\pi$
$642$		0			0
$643$	−0.204229	+	0.353736i	−0.00805402	+	0.0139500i	−0.870024	−	0.493009i	$-0.835897\pi$
$643$	−0.204229	+	0.353736i	−0.00805402	+	0.0139500i	0.861970	+	0.506959i	$0.169230\pi$
$644$		0			0
$645$	−11.5601	−	3.67423i	−0.455179	−	0.144673i
$646$		0			0
$647$	−19.1470			−0.752745			−0.376372	−	0.926468i	$-0.622829\pi$
$647$	−19.1470			−0.752745			−0.376372	+	0.926468i	$0.622829\pi$
$648$		0			0
$649$	−3.00000			−0.117760
$650$		0			0
$651$	37.2986	+	11.8549i	1.46185	+	0.464630i
$652$		0			0
$653$	15.2546	−	26.4217i	0.596957	−	1.03396i	−0.396310	−	0.918117i	$-0.629710\pi$
$653$	15.2546	−	26.4217i	0.596957	−	1.03396i	0.993267	−	0.115844i	$-0.0369572\pi$
$654$		0			0
$655$	4.78674	−	2.76363i	0.187033	−	0.107984i
$656$		0			0
$657$	−3.79796	−	2.68556i	−0.148172	−	0.104774i
$658$		0			0
$659$	1.20474	−	0.695560i	0.0469302	−	0.0270952i	−0.476351	−	0.879255i	$-0.658041\pi$
$659$	1.20474	−	0.695560i	0.0469302	−	0.0270952i	0.523282	+	0.852160i	$0.324708\pi$
$660$		0			0
$661$	8.96204	+	5.17423i	0.348583	+	0.201254i	0.664061	−	0.747678i	$-0.268832\pi$
$661$	8.96204	+	5.17423i	0.348583	+	0.201254i	−0.315478	+	0.948933i	$0.602165\pi$
$662$		0			0
$663$	−16.2879	+	14.8561i	−0.632570	+	0.576964i
$664$		0			0
$665$			65.1180i			2.52517i
$666$		0			0
$667$	3.04281			0.117818
$668$		0			0
$669$	−32.8215	+	7.19694i	−1.26895	+	0.278250i
$670$		0			0
$671$	10.5049	−	18.1950i	0.405536	−	0.702409i
$672$		0			0
$673$	−9.62372	−	16.6688i	−0.370967	−	0.642534i	0.618747	−	0.785590i	$-0.287640\pi$
$673$	−9.62372	−	16.6688i	−0.370967	−	0.642534i	−0.989715	+	0.143056i	$0.954307\pi$
$674$		0			0
$675$	−9.90408	+	23.4501i	−0.381208	+	0.902596i
$676$		0			0
$677$	5.18010	+	8.97219i	0.199087	+	0.344829i	0.948233	−	0.317576i	$-0.102869\pi$
$677$	5.18010	+	8.97219i	0.199087	+	0.344829i	−0.749145	+	0.662406i	$0.769536\pi$
$678$		0			0
$679$	29.3630	+	16.9527i	1.12685	+	0.650586i
$680$		0			0
$681$	39.8939	−	8.74774i	1.52874	−	0.335214i
$682$		0			0
$683$		−	31.7385i		−	1.21444i	−0.794534	−	0.607220i	$-0.792285\pi$
$683$		−	31.7385i		−	1.21444i	0.794534	−	0.607220i	$-0.207715\pi$
$684$		0			0
$685$			56.3939i			2.15470i
$686$		0			0
$687$	29.2332	+	32.0506i	1.11532	+	1.22281i
$688$		0			0
$689$	21.6742	+	12.5136i	0.825723	+	0.476731i
$690$		0			0
$691$	−3.74730	−	6.49051i	−0.142554	−	0.246911i	0.785904	−	0.618349i	$-0.212198\pi$
$691$	−3.74730	−	6.49051i	−0.142554	−	0.246911i	−0.928458	+	0.371438i	$0.878865\pi$
$692$		0			0
$693$	−16.2795	+	7.50000i	−0.618407	+	0.284901i
$694$		0			0
$695$	−27.6592	−	47.9072i	−1.04917	−	1.81722i
$696$		0			0
$697$	20.0227	−	34.6803i	0.758414	−	1.31361i
$698$		0			0
$699$	4.45178	−	14.0065i	0.168382	−	0.529774i
$700$		0			0
$701$	1.76416			0.0666314			0.0333157	−	0.999445i	$-0.489393\pi$
$701$	1.76416			0.0666314			0.0333157	+	0.999445i	$0.489393\pi$
$702$		0			0
$703$			59.4245i			2.24124i
$704$		0			0
$705$	49.7196	+	15.8028i	1.87255	+	0.595166i
$706$		0			0
$707$	6.97370	+	4.02627i	0.262273	+	0.151423i
$708$		0			0
$709$	−8.96204	+	5.17423i	−0.336576	+	0.194322i	−0.658757	−	0.752356i	$-0.728917\pi$
$709$	−8.96204	+	5.17423i	−0.336576	+	0.194322i	0.322181	+	0.946678i	$0.395584\pi$
$710$		0			0
$711$	−30.8071	−	2.83858i	−1.15536	−	0.106455i
$712$		0			0
$713$	9.82577	−	5.67291i	0.367978	−	0.212452i
$714$		0			0
$715$	−11.0170	+	19.0820i	−0.412013	+	0.713628i
$716$		0			0
$717$	1.64456	−	1.50000i	0.0614174	−	0.0560185i
$718$		0			0
$719$	28.0130			1.04471			0.522354	−	0.852729i	$-0.325054\pi$
$719$	28.0130			1.04471			0.522354	+	0.852729i	$0.325054\pi$
$720$		0			0
$721$	−21.7423			−0.809727
$722$		0			0
$723$	5.08132	+	23.1732i	0.188976	+	0.861822i
$724$		0			0
$725$	−5.79972	+	10.0454i	−0.215396	+	0.373077i
$726$		0			0
$727$	32.5109	−	18.7702i	1.20576	−	0.696147i	0.243931	−	0.969792i	$-0.421563\pi$
$727$	32.5109	−	18.7702i	1.20576	−	0.696147i	0.961831	+	0.273645i	$0.0882295\pi$
$728$		0			0
$729$	−7.34847	+	25.9808i	−0.272166	+	0.962250i
$730$		0			0
$731$	8.17845	−	4.72183i	0.302491	−	0.174643i
$732$		0			0
$733$	12.9904	+	7.50000i	0.479811	+	0.277019i	0.720338	−	0.693624i	$-0.243987\pi$
$733$	12.9904	+	7.50000i	0.479811	+	0.277019i	−0.240527	+	0.970642i	$0.577320\pi$
$734$		0			0
$735$	0.524648	+	2.39264i	0.0193519	+	0.0882540i
$736$		0			0
$737$		−	0.953512i		−	0.0351231i
$738$		0			0
$739$	−1.00052			−0.0368046			−0.0184023	−	0.999831i	$-0.505858\pi$
$739$	−1.00052			−0.0368046			−0.0184023	+	0.999831i	$0.505858\pi$
$740$		0			0
$741$	28.3164	+	31.0454i	1.04023	+	1.14048i
$742$		0			0
$743$	18.7932	−	32.5508i	0.689457	−	1.19417i	−0.282557	−	0.959250i	$-0.591183\pi$
$743$	18.7932	−	32.5508i	0.689457	−	1.19417i	0.972014	−	0.234923i	$-0.0754839\pi$
$744$		0			0
$745$	18.0732	+	31.3037i	0.662151	+	1.14688i
$746$		0			0
$747$	−10.1083	−	0.931383i	−0.369844	−	0.0340775i
$748$		0			0
$749$	−23.2952	−	40.3485i	−0.851188	−	1.47430i
$750$		0			0
$751$	−14.8080	−	8.54943i	−0.540353	−	0.311973i	0.204869	−	0.978789i	$-0.434323\pi$
$751$	−14.8080	−	8.54943i	−0.540353	−	0.311973i	−0.745222	+	0.666816i	$0.767657\pi$
$752$		0			0
$753$	4.04541	−	12.7279i	0.147423	−	0.463831i
$754$		0			0
$755$		−	16.3409i		−	0.594706i
$756$		0			0
$757$		−	12.0000i		−	0.436147i	−0.975932	−	0.218074i	$-0.930023\pi$
$757$		−	12.0000i		−	0.436147i	0.975932	−	0.218074i	$-0.0699773\pi$
$758$		0			0
$759$	−1.57394	+	4.95204i	−0.0571305	+	0.179748i
$760$		0			0
$761$	−42.5227	−	24.5505i	−1.54145	−	0.889955i	−0.998748	−	0.0500275i	$-0.984069\pi$
$761$	−42.5227	−	24.5505i	−1.54145	−	0.889955i	−0.542699	−	0.839927i	$-0.682598\pi$
$762$		0			0
$763$	1.72563	+	2.98889i	0.0624721	+	0.108205i
$764$		0			0
$765$	−16.7563	−	36.3712i	−0.605824	−	1.31500i
$766$		0			0
$767$	−1.92768	−	3.33884i	−0.0696044	−	0.120558i
$768$		0			0
$769$	−13.2980	+	23.0327i	−0.479537	+	0.830582i	−0.999725	−	0.0234700i	$-0.992529\pi$
$769$	−13.2980	+	23.0327i	−0.479537	+	0.830582i	0.520188	+	0.854052i	$0.325862\pi$
$770$		0			0
$771$	−15.9691	−	17.5081i	−0.575112	−	0.630539i
$772$		0			0
$773$	42.9192			1.54370			0.771848	−	0.635807i	$-0.219332\pi$
$773$	42.9192			1.54370			0.771848	+	0.635807i	$0.219332\pi$
$774$		0			0
$775$			43.2512i			1.55363i
$776$		0			0
$777$	−6.97730	−	31.8198i	−0.250309	−	1.14153i
$778$		0			0
$779$	−66.1022	−	38.1641i	−2.36836	−	1.36737i
$780$		0			0
$781$	29.4842	−	17.0227i	1.05503	−	0.609120i
$782$		0			0
$783$	−4.78674	+	11.3337i	−0.171064	+	0.405033i
$784$		0			0
$785$	−20.8485	+	12.0369i	−0.744114	+	0.429614i
$786$		0			0
$787$	−19.1037	+	33.0885i	−0.680972	+	1.17948i	0.293712	+	0.955894i	$0.405109\pi$
$787$	−19.1037	+	33.0885i	−0.680972	+	1.17948i	−0.974684	+	0.223585i	$0.928224\pi$
$788$		0			0
$789$	−8.96204	−	40.8712i	−0.319057	−	1.45505i
$790$		0			0
$791$	13.2990			0.472859
$792$		0			0
$793$	27.0000			0.958798
$794$		0			0
$795$	−33.5888	+	30.6362i	−1.19127	+	1.08655i
$796$		0			0
$797$	−17.0902	+	29.6010i	−0.605364	+	1.04852i	0.386629	+	0.922235i	$0.373639\pi$
$797$	−17.0902	+	29.6010i	−0.605364	+	1.04852i	−0.991994	+	0.126287i	$0.959694\pi$
$798$		0			0
$799$	−35.1752	+	20.3084i	−1.24441	+	0.718460i
$800$		0			0
$801$	−10.6515	+	15.0635i	−0.376353	+	0.532244i
$802$		0			0
$803$	3.13461	−	1.80977i	0.110618	−	0.0638653i
$804$		0			0
$805$	−8.96204	−	5.17423i	−0.315870	−	0.182368i
$806$		0			0
$807$	−5.48230	−	1.74248i	−0.192986	−	0.0613382i
$808$		0			0
$809$			14.6349i			0.514537i	0.966340	+	0.257269i	$0.0828225\pi$
$809$			14.6349i			0.514537i	−0.966340	+	0.257269i	$0.917177\pi$
$810$		0			0
$811$	20.6251			0.724244			0.362122	−	0.932131i	$-0.382052\pi$
$811$	20.6251			0.724244			0.362122	+	0.932131i	$0.382052\pi$
$812$		0			0
$813$	6.92820	−	21.7980i	0.242983	−	0.764488i
$814$		0			0
$815$	−5.71812	+	9.90408i	−0.200297	+	0.346925i
$816$		0			0
$817$	−9.00000	−	15.5885i	−0.314870	−	0.545371i
$818$		0			0
$819$	−18.8076	−	13.2990i	−0.657192	−	0.464705i
$820$		0			0
$821$	−16.7402	−	28.9949i	−0.584237	−	1.01193i	−0.994970	−	0.100173i	$-0.968060\pi$
$821$	−16.7402	−	28.9949i	−0.584237	−	1.01193i	0.410733	−	0.911756i	$-0.365273\pi$
$822$		0			0
$823$	−8.80110	−	5.08132i	−0.306787	−	0.177124i	0.338701	−	0.940894i	$-0.390013\pi$
$823$	−8.80110	−	5.08132i	−0.306787	−	0.177124i	−0.645488	+	0.763771i	$0.723346\pi$
$824$		0			0
$825$	−13.3485	−	14.6349i	−0.464734	−	0.509523i
$826$		0			0
$827$			29.1683i			1.01428i	0.861864	+	0.507140i	$0.169297\pi$
$827$			29.1683i			1.01428i	−0.861864	+	0.507140i	$0.830703\pi$
$828$		0			0
$829$		−	34.6515i		−	1.20350i	−0.798685	−	0.601749i	$-0.794471\pi$
$829$		−	34.6515i		−	1.20350i	0.798685	−	0.601749i	$-0.205529\pi$
$830$		0			0
$831$	−42.3732	+	9.29139i	−1.46991	+	0.322315i
$832$		0			0
$833$	−1.65153	−	0.953512i	−0.0572221	−	0.0330372i
$834$		0			0
$835$	−19.1037	−	33.0885i	−0.661110	−	1.14508i
$836$		0			0
$837$	5.67291	+	45.5227i	0.196084	+	1.57349i
$838$		0			0
$839$	−2.92397	−	5.06447i	−0.100947	−	0.174845i	0.811128	−	0.584868i	$-0.198854\pi$
$839$	−2.92397	−	5.06447i	−0.100947	−	0.174845i	−0.912075	+	0.410023i	$0.865521\pi$
$840$		0			0
$841$	11.6969	−	20.2597i	0.403343	−	0.698610i
$842$		0			0
$843$	27.0985	−	5.94204i	0.933323	−	0.204655i
$844$		0			0
$845$	12.5851			0.432939
$846$		0			0
$847$			14.2060i			0.488122i
$848$		0			0
$849$	−18.8939	+	17.2330i	−0.648436	+	0.591436i
$850$		0			0
$851$	−8.17845	−	4.72183i	−0.280354	−	0.161862i
$852$		0			0
$853$	−15.8509	+	9.15153i	−0.542725	+	0.313342i	−0.746183	−	0.665741i	$-0.768115\pi$
$853$	−15.8509	+	9.15153i	−0.542725	+	0.313342i	0.203458	+	0.979084i	$0.434782\pi$
$854$		0			0
$855$	−69.3250	+	31.9381i	−2.37086	+	1.09226i
$856$		0			0
$857$	17.1742	−	9.91555i	0.586661	−	0.338709i	−0.177115	−	0.984190i	$-0.556677\pi$
$857$	17.1742	−	9.91555i	0.586661	−	0.338709i	0.763776	+	0.645481i	$0.223343\pi$
$858$		0			0
$859$	25.4647	−	44.1061i	0.868844	−	1.50488i	0.00566493	−	0.999984i	$-0.498197\pi$
$859$	25.4647	−	44.1061i	0.868844	−	1.50488i	0.863179	−	0.504898i	$-0.168470\pi$
$860$		0			0
$861$	39.8765	+	12.6742i	1.35899	+	0.431937i
$862$		0			0
$863$	25.4427			0.866081			0.433040	−	0.901375i	$-0.357441\pi$
$863$	25.4427			0.866081			0.433040	+	0.901375i	$0.357441\pi$
$864$		0			0
$865$	−15.8990			−0.540582
$866$		0			0
$867$	1.65068	+	0.524648i	0.0560600	+	0.0178180i
$868$		0			0
$869$	12.0369	−	20.8485i	0.408323	−	0.707236i
$870$		0			0
$871$	1.06121	−	0.612688i	0.0359576	−	0.0207601i
$872$		0			0
$873$	−3.64643	+	39.5747i	−0.123413	+	1.33940i
$874$		0			0
$875$	−0.704487	+	0.406736i	−0.0238160	+	0.0137502i
$876$		0			0
$877$	−12.4655	−	7.19694i	−0.420929	−	0.243023i	0.274546	−	0.961574i	$-0.411472\pi$
$877$	−12.4655	−	7.19694i	−0.420929	−	0.243023i	−0.695475	+	0.718551i	$0.744806\pi$
$878$		0			0
$879$	4.83974	−	4.41431i	0.163240	−	0.148891i
$880$		0			0
$881$		−	26.9343i		−	0.907439i	−0.891145	−	0.453719i	$-0.850097\pi$
$881$		−	26.9343i		−	0.907439i	0.891145	−	0.453719i	$-0.149903\pi$
$882$		0			0
$883$	15.3564			0.516783			0.258392	−	0.966040i	$-0.416808\pi$
$883$	15.3564			0.516783			0.258392	+	0.966040i	$0.416808\pi$
$884$		0			0
$885$	6.84072	−	1.50000i	0.229948	−	0.0504219i
$886$		0			0
$887$	−22.2299	+	38.5034i	−0.746408	+	1.29282i	0.203126	+	0.979153i	$0.434890\pi$
$887$	−22.2299	+	38.5034i	−0.746408	+	1.29282i	−0.949534	+	0.313664i	$0.898443\pi$
$888$		0			0
$889$	−27.2474	−	47.1940i	−0.913850	−	1.58283i
$890$		0			0
$891$	−15.9691	−	13.6527i	−0.534984	−	0.457384i
$892$		0			0
$893$	38.7087	+	67.0454i	1.29534	+	2.24359i
$894$		0			0
$895$	8.28836	+	4.78529i	0.277049	+	0.159955i
$896$		0			0
$897$	−6.52270	+	1.43027i	−0.217787	+	0.0477552i
$898$		0			0
$899$			20.9037i			0.697178i
$900$		0			0
$901$		−	35.3939i		−	1.17914i
$902$		0			0
$903$	6.64951	+	7.29036i	0.221282	+	0.242608i
$904$		0			0
$905$	−52.7196	−	30.4377i	−1.75246	−	1.01178i
$906$		0			0
$907$	22.3301	+	38.6768i	0.741458	+	1.28424i	0.951831	+	0.306622i	$0.0991988\pi$
$907$	22.3301	+	38.6768i	0.741458	+	1.28424i	−0.210373	+	0.977621i	$0.567468\pi$
$908$		0			0
$909$	−0.866025	+	9.39898i	−0.0287242	+	0.311744i
$910$		0			0
$911$	−20.3672	−	35.2770i	−0.674794	−	1.16878i	−0.976529	−	0.215386i	$-0.930899\pi$
$911$	−20.3672	−	35.2770i	−0.674794	−	1.16878i	0.301735	−	0.953392i	$-0.402434\pi$
$912$		0			0
$913$	3.94949	−	6.84072i	0.130709	−	0.226395i
$914$		0			0
$915$	−14.8561	+	46.7413i	−0.491128	+	1.54522i
$916$		0			0
$917$	−4.49626			−0.148480
$918$		0			0
$919$			18.4741i			0.609406i	0.952447	+	0.304703i	$0.0985572\pi$
$919$			18.4741i			0.609406i	−0.952447	+	0.304703i	$0.901443\pi$
$920$		0			0
$921$	−38.6969	−	12.2993i	−1.27511	−	0.405277i
$922$		0			0
$923$	37.8907	+	21.8762i	1.24719	+	0.720064i
$924$		0			0
$925$	31.1769	−	18.0000i	1.02509	−	0.591836i
$926$		0			0
$927$	−10.6639	−	23.1470i	−0.350247	−	0.760247i
$928$		0			0
$929$	31.8712	−	18.4008i	1.04566	−	0.603712i	0.124228	−	0.992254i	$-0.460354\pi$
$929$	31.8712	−	18.4008i	1.04566	−	0.603712i	0.921431	+	0.388542i	$0.127021\pi$
$930$		0			0
$931$	−1.81743	+	3.14789i	−0.0595640	+	0.103168i
$932$		0			0
$933$	27.6253	−	25.1969i	0.904413	−	0.824911i
$934$		0			0
$935$	31.1609			1.01907
$936$		0			0
$937$	−43.1464			−1.40953			−0.704766	−	0.709440i	$-0.748948\pi$
$937$	−43.1464			−1.40953			−0.704766	+	0.709440i	$0.748948\pi$
$938$		0			0
$939$	−6.64020	−	30.2825i	−0.216695	−	0.988231i
$940$		0			0
$941$	−22.5006	+	38.9722i	−0.733499	+	1.27046i	0.221880	+	0.975074i	$0.428781\pi$
$941$	−22.5006	+	38.9722i	−0.733499	+	1.27046i	−0.955379	+	0.295383i	$0.904553\pi$
$942$		0			0
$943$	10.5049	−	6.06499i	0.342085	−	0.197503i
$944$		0			0
$945$	33.3712	−	25.2415i	1.08556	−	0.821108i
$946$		0			0
$947$	−15.1521	+	8.74810i	−0.492379	+	0.284275i	−0.725561	−	0.688158i	$-0.758420\pi$
$947$	−15.1521	+	8.74810i	−0.492379	+	0.284275i	0.233182	+	0.972433i	$0.425086\pi$
$948$		0			0
$949$	4.02834	+	2.32577i	0.130766	+	0.0754975i
$950$		0			0
$951$	2.74115	+	12.5010i	0.0888879	+	0.405371i
$952$		0			0
$953$			18.4490i			0.597621i	0.954312	+	0.298811i	$0.0965899\pi$
$953$			18.4490i			0.597621i	−0.954312	+	0.298811i	$0.903410\pi$
$954$		0			0
$955$	33.7556			1.09230
$956$		0			0
$957$	−6.45145	−	7.07321i	−0.208546	−	0.228645i
$958$		0			0
$959$	22.9374	−	39.7288i	0.740687	−	1.28291i
$960$		0			0
$961$	23.4722	+	40.6550i	0.757168	+	1.31145i
$962$		0			0
$963$	31.5297	−	44.5897i	1.01603	−	1.43688i
$964$		0			0
$965$	11.7190	+	20.2980i	0.377249	+	0.653414i
$966$		0			0
$967$	22.8076	+	13.1680i	0.733442	+	0.423453i	0.819680	−	0.572821i	$-0.194151\pi$
$967$	22.8076	+	13.1680i	0.733442	+	0.423453i	−0.0862378	+	0.996275i	$0.527484\pi$
$968$		0			0
$969$	18.0000	−	56.6328i	0.578243	−	1.81931i
$970$		0			0
$971$			44.6957i			1.43435i	0.696892	+	0.717177i	$0.254566\pi$
$971$			44.6957i			1.43435i	−0.696892	+	0.717177i	$0.745434\pi$
$972$		0			0
$973$			45.0000i			1.44263i
$974$		0			0
$975$	7.71071	−	24.2599i	0.246940	−	0.776940i
$976$		0			0
$977$	33.1515	+	19.1400i	1.06061	+	0.612344i	0.925601	−	0.378500i	$-0.123560\pi$
$977$	33.1515	+	19.1400i	1.06061	+	0.612344i	0.135010	+	0.990844i	$0.456893\pi$
$978$		0			0
$979$	−7.17793	−	12.4325i	−0.229408	−	0.397346i
$980$		0			0
$981$	−2.33562	+	3.30306i	−0.0745705	+	0.105459i
$982$		0			0
$983$	−8.93092	−	15.4688i	−0.284852	−	0.493378i	0.687721	−	0.725975i	$-0.258611\pi$
$983$	−8.93092	−	15.4688i	−0.284852	−	0.493378i	−0.972573	+	0.232597i	$0.925278\pi$
$984$		0			0
$985$	−26.2474	+	45.4619i	−0.836313	+	1.44854i
$986$		0			0
$987$	−28.5993	−	31.3556i	−0.910326	−	0.998059i
$988$		0			0
$989$	2.86054			0.0909597
$990$		0			0
$991$			2.30084i			0.0730887i	0.999332	+	0.0365444i	$0.0116350\pi$
$991$			2.30084i			0.0730887i	−0.999332	+	0.0365444i	$0.988365\pi$
$992$		0			0
$993$	−7.19694	−	32.8215i	−0.228388	−	1.04156i
$994$		0			0
$995$	44.9768	+	25.9674i	1.42586	+	0.823221i
$996$		0			0
$997$	21.6900	−	12.5227i	0.686928	−	0.396598i	−0.115532	−	0.993304i	$-0.536857\pi$
$997$	21.6900	−	12.5227i	0.686928	−	0.396598i	0.802460	+	0.596706i	$0.203524\pi$
$998$		0			0
$999$	30.4534	−	23.0346i	0.963502	−	0.728781i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.p.e.959.1	yes	16
3.2	odd	2		3456.2.p.e.2879.8		16
4.3	odd	2	inner	1152.2.p.e.959.7	yes	16
8.3	odd	2	inner	1152.2.p.e.959.2	yes	16
8.5	even	2	inner	1152.2.p.e.959.8	yes	16
9.2	odd	6	inner	1152.2.p.e.191.2	yes	16
9.7	even	3		3456.2.p.e.575.1		16
12.11	even	2		3456.2.p.e.2879.7		16
24.5	odd	2		3456.2.p.e.2879.2		16
24.11	even	2		3456.2.p.e.2879.1		16
36.7	odd	6		3456.2.p.e.575.2		16
36.11	even	6	inner	1152.2.p.e.191.8	yes	16
72.11	even	6	inner	1152.2.p.e.191.1	✓	16
72.29	odd	6	inner	1152.2.p.e.191.7	yes	16
72.43	odd	6		3456.2.p.e.575.8		16
72.61	even	6		3456.2.p.e.575.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.p.e.191.1	✓	16	72.11	even	6	inner
1152.2.p.e.191.2	yes	16	9.2	odd	6	inner
1152.2.p.e.191.7	yes	16	72.29	odd	6	inner
1152.2.p.e.191.8	yes	16	36.11	even	6	inner
1152.2.p.e.959.1	yes	16	1.1	even	1	trivial
1152.2.p.e.959.2	yes	16	8.3	odd	2	inner
1152.2.p.e.959.7	yes	16	4.3	odd	2	inner
1152.2.p.e.959.8	yes	16	8.5	even	2	inner
3456.2.p.e.575.1		16	9.7	even	3
3456.2.p.e.575.2		16	36.7	odd	6
3456.2.p.e.575.7		16	72.61	even	6
3456.2.p.e.575.8		16	72.43	odd	6
3456.2.p.e.2879.1		16	24.11	even	2
3456.2.p.e.2879.2		16	24.5	odd	2
3456.2.p.e.2879.7		16	12.11	even	2
3456.2.p.e.2879.8		16	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:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.65068 - 0.524648i) q^{3} +(-1.57313 + 2.72474i) q^{5} +(2.21650 - 1.27970i) q^{7} +(2.44949 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(-1.65068 - 0.524648i) q^{3} +(-1.57313 + 2.72474i) q^{5} +(2.21650 - 1.27970i) q^{7} +(2.44949 + 1.73205i) q^{9} +(-2.02166 + 1.16721i) q^{11} +(-2.59808 - 1.50000i) q^{13} +(4.02627 - 3.67234i) q^{15} +4.24264i q^{17} +8.08665 q^{19} +(-4.33013 + 0.949490i) q^{21} +(-0.642559 + 1.11295i) q^{23} +(-2.44949 - 4.24264i) q^{25} +(-3.13461 - 4.14418i) q^{27} +(-1.18386 - 2.05051i) q^{29} +(-7.64580 - 4.41431i) q^{31} +(3.94949 - 0.866025i) q^{33} +8.05254i q^{35} +7.34847i q^{37} +(3.50162 + 3.83909i) q^{39} +(-8.17423 - 4.71940i) q^{41} +(-1.11295 - 1.92768i) q^{43} +(-8.57277 + 3.94949i) q^{45} +(4.78674 + 8.29088i) q^{47} +(-0.224745 + 0.389270i) q^{49} +(2.22589 - 7.00324i) q^{51} -8.34242 q^{53} -7.34468i q^{55} +(-13.3485 - 4.24264i) q^{57} +(1.11295 + 0.642559i) q^{59} +(-7.79423 + 4.50000i) q^{61} +(7.64580 + 0.704487i) q^{63} +(8.17423 - 4.71940i) q^{65} +(-0.204229 + 0.353736i) q^{67} +(1.64456 - 1.50000i) q^{69} -14.5841 q^{71} -1.55051 q^{73} +(1.81743 + 8.28836i) q^{75} +(-2.98735 + 5.17423i) q^{77} +(-8.93092 + 5.15627i) q^{79} +(3.00000 + 8.48528i) q^{81} +(-2.93038 + 1.69185i) q^{83} +(-11.5601 - 6.67423i) q^{85} +(0.878383 + 4.00585i) q^{87} +6.14966i q^{89} -7.67819 q^{91} +(10.3048 + 11.2980i) q^{93} +(-12.7214 + 22.0341i) q^{95} +(6.62372 + 11.4726i) q^{97} +(-6.97370 - 0.642559i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 24 q^{33} - 72 q^{41} + 16 q^{49} - 96 q^{57} + 72 q^{65} - 64 q^{73} + 48 q^{81} + 8 q^{97}+O(q^{100}) \) 16 * q + 24 * q^33 - 72 * q^41 + 16 * q^49 - 96 * q^57 + 72 * q^65 - 64 * q^73 + 48 * q^81 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more