LMFDB - Embedded newform 2214.2.i.b.1639.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2214,2,Mod(901,2214)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2214.901"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2214, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2214 = 2 \cdot 3^{3} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2214.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [36] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$17.6788790075$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 738)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1639.13
Character	$\chi$	$=$	2214.1639
Dual form			2214.2.i.b.901.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.18467 + 2.05191i) q^{5} +(-4.22182 - 2.43747i) q^{7} -1.00000 q^{8} +2.36934 q^{10} +(-3.26477 - 1.88492i) q^{11} +(0.883519 - 0.510100i) q^{13} +(-4.22182 + 2.43747i) q^{14} +(-0.500000 + 0.866025i) q^{16} -1.79124i q^{17} +8.27391i q^{19} +(1.18467 - 2.05191i) q^{20} +(-3.26477 + 1.88492i) q^{22} +(3.96640 + 6.87000i) q^{23} +(-0.306879 + 0.531530i) q^{25} -1.02020i q^{26} +4.87494i q^{28} +(7.89342 + 4.55727i) q^{29} +(2.79358 + 4.83863i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.55126 - 0.895620i) q^{34} -11.5504i q^{35} -6.27081 q^{37} +(7.16542 + 4.13696i) q^{38} +(-1.18467 - 2.05191i) q^{40} +(5.17282 - 3.77385i) q^{41} +(3.17911 - 5.50637i) q^{43} +3.76984i q^{44} +7.93279 q^{46} +(-0.755744 - 0.436329i) q^{47} +(8.38252 + 14.5189i) q^{49} +(0.306879 + 0.531530i) q^{50} +(-0.883519 - 0.510100i) q^{52} -2.59870i q^{53} -8.93201i q^{55} +(4.22182 + 2.43747i) q^{56} +(7.89342 - 4.55727i) q^{58} +(1.99784 + 3.46037i) q^{59} +(-0.584806 + 1.01291i) q^{61} +5.58717 q^{62} +1.00000 q^{64} +(2.09335 + 1.20860i) q^{65} +(-3.06655 + 1.77047i) q^{67} +(-1.55126 + 0.895620i) q^{68} +(-10.0029 - 5.77519i) q^{70} +4.65070i q^{71} +2.14855 q^{73} +(-3.13541 + 5.43068i) q^{74} +(7.16542 - 4.13696i) q^{76} +(9.18886 + 15.9156i) q^{77} +(2.47565 + 1.42931i) q^{79} -2.36934 q^{80} +(-0.681841 - 6.36672i) q^{82} +(-7.31381 + 12.6679i) q^{83} +(3.67546 - 2.12203i) q^{85} +(-3.17911 - 5.50637i) q^{86} +(3.26477 + 1.88492i) q^{88} +13.5197i q^{89} -4.97341 q^{91} +(3.96640 - 6.87000i) q^{92} +(-0.755744 + 0.436329i) q^{94} +(-16.9773 + 9.80184i) q^{95} +(-1.48001 - 0.854487i) q^{97} +16.7650 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 18 q^{2} - 18 q^{4} - 4 q^{5} - 36 q^{8} - 8 q^{10} - 18 q^{16} - 4 q^{20} + 4 q^{23} - 26 q^{25} + 8 q^{31} + 18 q^{32} - 60 q^{37} + 4 q^{40} + 6 q^{41} + 6 q^{43} + 8 q^{46} + 38 q^{49} + 26 q^{50}+ \cdots + 76 q^{98}+O(q^{100}) $ 36 * q + 18 * q^2 - 18 * q^4 - 4 * q^5 - 36 * q^8 - 8 * q^10 - 18 * q^16 - 4 * q^20 + 4 * q^23 - 26 * q^25 + 8 * q^31 + 18 * q^32 - 60 * q^37 + 4 * q^40 + 6 * q^41 + 6 * q^43 + 8 * q^46 + 38 * q^49 + 26 * q^50 - 22 * q^59 - 46 * q^61 + 16 * q^62 + 36 * q^64 + 64 * q^73 - 30 * q^74 + 2 * q^77 + 8 * q^80 + 12 * q^82 - 68 * q^83 - 6 * q^86 + 36 * q^91 + 4 * q^92 + 76 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2214\mathbb{Z}\right)^\times$.

$n$	$83$	$703$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.18467	+	2.05191i	0.529800	+	0.917640i	0.999396	+	0.0347588i	$0.0110663\pi$
$5$	1.18467	+	2.05191i	0.529800	+	0.917640i	−0.469596	+	0.882881i	$0.655600\pi$
$6$		0			0
$7$	−4.22182	−	2.43747i	−1.59570	−	0.921277i	−0.992303	−	0.123835i	$-0.960481\pi$
$7$	−4.22182	−	2.43747i	−1.59570	−	0.921277i	−0.603396	−	0.797442i	$-0.706186\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	2.36934			0.749250
$11$	−3.26477	−	1.88492i	−0.984366	−	0.568324i	−0.0807808	−	0.996732i	$-0.525741\pi$
$11$	−3.26477	−	1.88492i	−0.984366	−	0.568324i	−0.903586	+	0.428408i	$0.859075\pi$
$12$		0			0
$13$	0.883519	−	0.510100i	0.245044	−	0.141476i	−0.372449	−	0.928053i	$-0.621482\pi$
$13$	0.883519	−	0.510100i	0.245044	−	0.141476i	0.617493	+	0.786577i	$0.288148\pi$
$14$	−4.22182	+	2.43747i	−1.12833	+	0.651441i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		−	1.79124i		−	0.434440i	−0.976123	−	0.217220i	$-0.930301\pi$
$17$		−	1.79124i		−	0.434440i	0.976123	−	0.217220i	$-0.0696988\pi$
$18$		0			0
$19$			8.27391i			1.89817i	0.315027	+	0.949083i	$0.397986\pi$
$19$			8.27391i			1.89817i	−0.315027	+	0.949083i	$0.602014\pi$
$20$	1.18467	−	2.05191i	0.264900	−	0.458820i
$21$		0			0
$22$	−3.26477	+	1.88492i	−0.696052	+	0.401866i
$23$	3.96640	+	6.87000i	0.827051	+	1.43249i	0.900342	+	0.435183i	$0.143316\pi$
$23$	3.96640	+	6.87000i	0.827051	+	1.43249i	−0.0732914	+	0.997311i	$0.523350\pi$
$24$		0			0
$25$	−0.306879	+	0.531530i	−0.0613758	+	0.106306i
$26$		−	1.02020i		−	0.200078i
$27$		0			0
$28$			4.87494i			0.921277i
$29$	7.89342	+	4.55727i	1.46577	+	0.846263i	0.999268	−	0.0382562i	$-0.0121803\pi$
$29$	7.89342	+	4.55727i	1.46577	+	0.846263i	0.466503	+	0.884520i	$0.345514\pi$
$30$		0			0
$31$	2.79358	+	4.83863i	0.501743	+	0.869044i	0.999998	+	0.00201334i	$0.000640866\pi$
$31$	2.79358	+	4.83863i	0.501743	+	0.869044i	−0.498255	+	0.867030i	$0.666026\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−1.55126	−	0.895620i	−0.266039	−	0.153598i
$35$		−	11.5504i		−	1.95237i
$36$		0			0
$37$	−6.27081			−1.03092			−0.515458	−	0.856915i	$-0.672378\pi$
$37$	−6.27081			−1.03092			−0.515458	+	0.856915i	$0.672378\pi$
$38$	7.16542	+	4.13696i	1.16238	+	0.671103i
$39$		0			0
$40$	−1.18467	−	2.05191i	−0.187313	−	0.324435i
$41$	5.17282	−	3.77385i	0.807859	−	0.589376i
$41$	5.17282	−	3.77385i	0.807859	−	0.589376i
$42$		0			0
$43$	3.17911	−	5.50637i	0.484809	−	0.839714i	−0.515038	−	0.857167i	$-0.672222\pi$
$43$	3.17911	−	5.50637i	0.484809	−	0.839714i	0.999848	+	0.0174529i	$0.00555570\pi$
$44$			3.76984i			0.568324i
$45$		0			0
$46$	7.93279			1.16963
$47$	−0.755744	−	0.436329i	−0.110237	−	0.0636452i	0.443868	−	0.896092i	$-0.353606\pi$
$47$	−0.755744	−	0.436329i	−0.110237	−	0.0636452i	−0.554105	+	0.832447i	$0.686939\pi$
$48$		0			0
$49$	8.38252	+	14.5189i	1.19750	+	2.07413i
$50$	0.306879	+	0.531530i	0.0433992	+	0.0751697i
$51$		0			0
$52$	−0.883519	−	0.510100i	−0.122522	−	0.0707381i
$53$		−	2.59870i		−	0.356959i	−0.983944	−	0.178479i	$-0.942882\pi$
$53$		−	2.59870i		−	0.356959i	0.983944	−	0.178479i	$-0.0571178\pi$
$54$		0			0
$55$		−	8.93201i		−	1.20439i
$56$	4.22182	+	2.43747i	0.564165	+	0.325721i
$57$		0			0
$58$	7.89342	−	4.55727i	1.03646	−	0.598399i
$59$	1.99784	+	3.46037i	0.260097	+	0.450501i	0.966267	−	0.257541i	$-0.0829121\pi$
$59$	1.99784	+	3.46037i	0.260097	+	0.450501i	−0.706170	+	0.708042i	$0.749579\pi$
$60$		0			0
$61$	−0.584806	+	1.01291i	−0.0748768	+	0.129690i	−0.901033	−	0.433751i	$-0.857190\pi$
$61$	−0.584806	+	1.01291i	−0.0748768	+	0.129690i	0.826156	+	0.563442i	$0.190523\pi$
$62$	5.58717			0.709571
$63$		0			0
$64$	1.00000			0.125000
$65$	2.09335	+	1.20860i	0.259649	+	0.149908i
$66$		0			0
$67$	−3.06655	+	1.77047i	−0.374638	+	0.216297i	−0.675483	−	0.737376i	$-0.736065\pi$
$67$	−3.06655	+	1.77047i	−0.374638	+	0.216297i	0.300845	+	0.953673i	$0.402731\pi$
$68$	−1.55126	+	0.895620i	−0.188118	+	0.108610i
$69$		0			0
$70$	−10.0029	−	5.77519i	−1.19558	−	0.690267i
$71$			4.65070i			0.551937i	0.961167	+	0.275968i	$0.0889985\pi$
$71$			4.65070i			0.551937i	−0.961167	+	0.275968i	$0.911001\pi$
$72$		0			0
$73$	2.14855			0.251468			0.125734	−	0.992064i	$-0.459871\pi$
$73$	2.14855			0.251468			0.125734	+	0.992064i	$0.459871\pi$
$74$	−3.13541	+	5.43068i	−0.364484	+	0.631304i
$75$		0			0
$76$	7.16542	−	4.13696i	0.821930	−	0.474541i
$77$	9.18886	+	15.9156i	1.04717	+	1.81375i
$78$		0			0
$79$	2.47565	+	1.42931i	0.278532	+	0.160810i	0.632759	−	0.774349i	$-0.281923\pi$
$79$	2.47565	+	1.42931i	0.278532	+	0.160810i	−0.354227	+	0.935160i	$0.615256\pi$
$80$	−2.36934			−0.264900
$81$		0			0
$82$	−0.681841	−	6.36672i	−0.0752967	−	0.703086i
$83$	−7.31381	+	12.6679i	−0.802794	+	1.39048i	0.114976	+	0.993368i	$0.463321\pi$
$83$	−7.31381	+	12.6679i	−0.802794	+	1.39048i	−0.917770	+	0.397112i	$0.870012\pi$
$84$		0			0
$85$	3.67546	−	2.12203i	0.398659	−	0.230166i
$86$	−3.17911	−	5.50637i	−0.342812	−	0.593768i
$87$		0			0
$88$	3.26477	+	1.88492i	0.348026	+	0.200933i
$89$			13.5197i			1.43309i	0.697542	+	0.716543i	$0.254277\pi$
$89$			13.5197i			1.43309i	−0.697542	+	0.716543i	$0.745723\pi$
$90$		0			0
$91$	−4.97341			−0.521355
$92$	3.96640	−	6.87000i	0.413525	−	0.716247i
$93$		0			0
$94$	−0.755744	+	0.436329i	−0.0779491	+	0.0450039i
$95$	−16.9773	+	9.80184i	−1.74183	+	1.00565i
$96$		0			0
$97$	−1.48001	−	0.854487i	−0.150273	−	0.0867600i	0.422978	−	0.906140i	$-0.360985\pi$
$97$	−1.48001	−	0.854487i	−0.150273	−	0.0867600i	−0.573251	+	0.819380i	$0.694318\pi$
$98$	16.7650			1.69352
$99$		0			0
$100$	0.613758			0.0613758
$101$	4.29909	+	2.48208i	0.427775	+	0.246976i	0.698398	−	0.715709i	$-0.253896\pi$
$101$	4.29909	+	2.48208i	0.427775	+	0.246976i	−0.270623	+	0.962685i	$0.587230\pi$
$102$		0			0
$103$	−6.24403	−	10.8150i	−0.615242	−	1.06563i	−0.990342	−	0.138646i	$-0.955725\pi$
$103$	−6.24403	−	10.8150i	−0.615242	−	1.06563i	0.375100	−	0.926984i	$-0.377608\pi$
$104$	−0.883519	+	0.510100i	−0.0866361	+	0.0500194i
$105$		0			0
$106$	−2.25054	−	1.29935i	−0.218592	−	0.126204i
$107$	−2.56768			−0.248227			−0.124113	−	0.992268i	$-0.539609\pi$
$107$	−2.56768			−0.248227			−0.124113	+	0.992268i	$0.539609\pi$
$108$		0			0
$109$			12.8485i			1.23066i	0.788269	+	0.615330i	$0.210977\pi$
$109$			12.8485i			1.23066i	−0.788269	+	0.615330i	$0.789023\pi$
$110$	−7.73535	−	4.46601i	−0.737537	−	0.425817i
$111$		0			0
$112$	4.22182	−	2.43747i	0.398925	−	0.230319i
$113$	6.06365	+	10.5025i	0.570420	+	0.987996i	0.996523	+	0.0833216i	$0.0265529\pi$
$113$	6.06365	+	10.5025i	0.570420	+	0.987996i	−0.426103	+	0.904675i	$0.640114\pi$
$114$		0			0
$115$	−9.39773	+	16.2773i	−0.876343	+	1.51787i
$116$		−	9.11454i		−	0.846263i
$117$		0			0
$118$	3.99569			0.367833
$119$	−4.36609	+	7.56230i	−0.400239	+	0.693235i
$120$		0			0
$121$	1.60583	+	2.78138i	0.145985	+	0.252853i
$122$	0.584806	+	1.01291i	0.0529459	+	0.0917050i
$123$		0			0
$124$	2.79358	−	4.83863i	0.250871	−	0.434522i
$125$	10.3925			0.929532
$126$		0			0
$127$	19.9429			1.76965			0.884824	−	0.465925i	$-0.154278\pi$
$127$	19.9429			1.76965			0.884824	+	0.465925i	$0.154278\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	2.09335	−	1.20860i	0.183599	−	0.106001i
$131$	2.06415	+	3.57521i	0.180345	+	0.312367i	0.941998	−	0.335618i	$-0.108945\pi$
$131$	2.06415	+	3.57521i	0.180345	+	0.312367i	−0.761653	+	0.647985i	$0.775612\pi$
$132$		0			0
$133$	20.1674	−	34.9310i	1.74874	−	3.02890i
$134$			3.54094i			0.305891i
$135$		0			0
$136$			1.79124i			0.153598i
$137$	−5.91355	−	3.41419i	−0.505228	−	0.291694i	0.225642	−	0.974210i	$-0.427552\pi$
$137$	−5.91355	−	3.41419i	−0.505228	−	0.291694i	−0.730870	+	0.682517i	$0.760885\pi$
$138$		0			0
$139$	−9.29993	−	16.1080i	−0.788810	−	1.36626i	−0.926696	−	0.375811i	$-0.877364\pi$
$139$	−9.29993	−	16.1080i	−0.788810	−	1.36626i	0.137886	−	0.990448i	$-0.455969\pi$
$140$	−10.0029	+	5.77519i	−0.845401	+	0.488092i
$141$		0			0
$142$	4.02763	+	2.32535i	0.337991	+	0.195139i
$143$	−3.84599			−0.321617
$144$		0			0
$145$			21.5954i			1.79340i
$146$	1.07427	−	1.86070i	0.0889075	−	0.153992i
$147$		0			0
$148$	3.13541	+	5.43068i	0.257729	+	0.446399i
$149$	3.24993	−	1.87635i	0.266245	−	0.153716i	−0.360935	−	0.932591i	$-0.617542\pi$
$149$	3.24993	−	1.87635i	0.266245	−	0.153716i	0.627180	+	0.778874i	$0.284209\pi$
$150$		0			0
$151$	−10.6094	−	6.12536i	−0.863384	−	0.498475i	0.00176024	−	0.999998i	$-0.499440\pi$
$151$	−10.6094	−	6.12536i	−0.863384	−	0.498475i	−0.865144	+	0.501524i	$0.832773\pi$
$152$		−	8.27391i		−	0.671103i
$153$		0			0
$154$	18.3777			1.48092
$155$	−6.61894	+	11.4643i	−0.531646	+	0.920838i
$156$		0			0
$157$	−1.69151	+	0.976594i	−0.134997	+	0.0779407i	−0.565978	−	0.824421i	$-0.691501\pi$
$157$	−1.69151	+	0.976594i	−0.134997	+	0.0779407i	0.430980	+	0.902361i	$0.358168\pi$
$158$	2.47565	−	1.42931i	0.196952	−	0.113710i
$159$		0			0
$160$	−1.18467	+	2.05191i	−0.0936563	+	0.162217i
$161$		−	38.6719i		−	3.04777i
$162$		0			0
$163$	−15.0198			−1.17644			−0.588220	−	0.808701i	$-0.700171\pi$
$163$	−15.0198			−1.17644			−0.588220	+	0.808701i	$0.700171\pi$
$164$	−5.85466	−	2.59287i	−0.457172	−	0.202469i
$165$		0			0
$166$	7.31381	+	12.6679i	0.567661	+	0.983218i
$167$	−14.0692	+	8.12285i	−1.08871	+	0.628565i	−0.933232	−	0.359275i	$-0.883024\pi$
$167$	−14.0692	+	8.12285i	−1.08871	+	0.628565i	−0.155474	+	0.987840i	$0.549691\pi$
$168$		0			0
$169$	−5.97960	+	10.3570i	−0.459969	+	0.796690i
$170$		−	4.24405i		−	0.325504i
$171$		0			0
$172$	−6.35821			−0.484809
$173$	3.45113	−	5.97753i	0.262385	−	0.454464i	−0.704490	−	0.709713i	$-0.748824\pi$
$173$	3.45113	−	5.97753i	0.262385	−	0.454464i	0.966875	+	0.255250i	$0.0821577\pi$
$174$		0			0
$175$	2.59118	−	1.49602i	0.195874	−	0.113088i
$176$	3.26477	−	1.88492i	0.246092	−	0.142081i
$177$		0			0
$178$	11.7084	+	6.75986i	0.877583	+	0.506673i
$179$			14.8852i			1.11257i	0.830990	+	0.556287i	$0.187775\pi$
$179$			14.8852i			1.11257i	−0.830990	+	0.556287i	$0.812225\pi$
$180$		0			0
$181$			0.411674i			0.0305995i	0.999883	+	0.0152997i	$0.00487025\pi$
$181$			0.411674i			0.0305995i	−0.999883	+	0.0152997i	$0.995130\pi$
$182$	−2.48671	+	4.30710i	−0.184327	+	0.319264i
$183$		0			0
$184$	−3.96640	−	6.87000i	−0.292407	−	0.506463i
$185$	−7.42884	−	12.8671i	−0.546179	−	0.946010i
$186$		0			0
$187$	−3.37634	+	5.84799i	−0.246902	+	0.427648i
$188$			0.872659i			0.0636452i
$189$		0			0
$190$			19.6037i			1.42220i
$191$	3.79497	+	2.19103i	0.274594	+	0.158537i	0.630974	−	0.775804i	$-0.282656\pi$
$191$	3.79497	+	2.19103i	0.274594	+	0.158537i	−0.356379	+	0.934341i	$0.615989\pi$
$192$		0			0
$193$	−11.6920	+	6.75038i	−0.841608	+	0.485903i	−0.857811	−	0.513966i	$-0.828176\pi$
$193$	−11.6920	+	6.75038i	−0.841608	+	0.485903i	0.0162022	+	0.999869i	$0.494842\pi$
$194$	−1.48001	+	0.854487i	−0.106259	+	0.0613486i
$195$		0			0
$196$	8.38252	−	14.5189i	0.598751	−	1.03707i
$197$	11.8168			0.841911			0.420955	−	0.907081i	$-0.361695\pi$
$197$	11.8168			0.841911			0.420955	+	0.907081i	$0.361695\pi$
$198$		0			0
$199$		−	0.995626i		−	0.0705780i	−0.999377	−	0.0352890i	$-0.988765\pi$
$199$		−	0.995626i		−	0.0705780i	0.999377	−	0.0352890i	$-0.0112352\pi$
$200$	0.306879	−	0.531530i	0.0216996	−	0.0375848i
$201$		0			0
$202$	4.29909	−	2.48208i	0.302483	−	0.174638i
$203$	−22.2164	−	38.4799i	−1.55929	−	2.70076i
$204$		0			0
$205$	13.8717	+	6.14338i	0.968839	+	0.429072i
$206$	−12.4881			−0.870084
$207$		0			0
$208$			1.02020i			0.0707381i
$209$	15.5956	−	27.0124i	1.07877	−	1.86849i
$210$		0			0
$211$	3.63947	−	2.10125i	0.250552	−	0.144656i	−0.369465	−	0.929245i	$-0.620459\pi$
$211$	3.63947	−	2.10125i	0.250552	−	0.144656i	0.620017	+	0.784588i	$0.287126\pi$
$212$	−2.25054	+	1.29935i	−0.154568	+	0.0892397i
$213$		0			0
$214$	−1.28384	+	2.22368i	−0.0877615	+	0.152007i
$215$	15.0647			1.02741
$216$		0			0
$217$		−	27.2371i		−	1.84898i
$218$	11.1271	+	6.42424i	0.753623	+	0.435104i
$219$		0			0
$220$	−7.73535	+	4.46601i	−0.521517	+	0.301098i
$221$	−0.913711	−	1.58259i	−0.0614629	−	0.106457i
$222$		0			0
$223$	−6.73892	+	11.6721i	−0.451271	+	0.781625i	−0.998465	−	0.0553810i	$-0.982363\pi$
$223$	−6.73892	+	11.6721i	−0.451271	+	0.781625i	0.547194	+	0.837006i	$0.315696\pi$
$224$		−	4.87494i		−	0.325721i
$225$		0			0
$226$	12.1273			0.806696
$227$	−13.4763	−	7.78057i	−0.894456	−	0.516414i	−0.0190585	−	0.999818i	$-0.506067\pi$
$227$	−13.4763	−	7.78057i	−0.894456	−	0.516414i	−0.875397	+	0.483404i	$0.839400\pi$
$228$		0			0
$229$	19.7946	−	11.4284i	1.30806	−	0.755212i	0.326292	−	0.945269i	$-0.394201\pi$
$229$	19.7946	−	11.4284i	1.30806	−	0.755212i	0.981773	+	0.190058i	$0.0608675\pi$
$230$	9.39773	+	16.2773i	0.619668	+	1.07330i
$231$		0			0
$232$	−7.89342	−	4.55727i	−0.518228	−	0.299199i
$233$			6.30922i			0.413331i	0.978412	+	0.206665i	$0.0662612\pi$
$233$			6.30922i			0.413331i	−0.978412	+	0.206665i	$0.933739\pi$
$234$		0			0
$235$		−	2.06762i		−	0.134877i
$236$	1.99784	−	3.46037i	0.130049	−	0.225251i
$237$		0			0
$238$	4.36609	+	7.56230i	0.283012	+	0.490191i
$239$	−15.9212	+	9.19209i	−1.02985	+	0.594587i	−0.916943	−	0.399018i	$-0.869351\pi$
$239$	−15.9212	+	9.19209i	−1.02985	+	0.594587i	−0.112912	+	0.993605i	$0.536018\pi$
$240$		0			0
$241$	9.73255	−	16.8573i	0.626929	−	1.08587i	−0.361236	−	0.932475i	$-0.617645\pi$
$241$	9.73255	−	16.8573i	0.626929	−	1.08587i	0.988164	−	0.153398i	$-0.0490217\pi$
$242$	3.21166			0.206454
$243$		0			0
$244$	1.16961			0.0748768
$245$	−19.8610	+	34.4003i	−1.26887	+	2.19775i
$246$		0			0
$247$	4.22052	+	7.31016i	0.268545	+	0.465134i
$248$	−2.79358	−	4.83863i	−0.177393	−	0.307253i
$249$		0			0
$250$	5.19624	−	9.00016i	0.328639	−	0.569220i
$251$	1.76288			0.111272			0.0556361	−	0.998451i	$-0.482281\pi$
$251$	1.76288			0.111272			0.0556361	+	0.998451i	$0.482281\pi$
$252$		0			0
$253$		−	29.9053i		−	1.88013i
$254$	9.97146	−	17.2711i	0.625665	−	1.08368i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.28762	−	3.63016i	0.392211	−	0.226443i	−0.290907	−	0.956751i	$-0.593957\pi$
$257$	6.28762	−	3.63016i	0.392211	−	0.226443i	0.683118	+	0.730308i	$0.260624\pi$
$258$		0			0
$259$	26.4743	+	15.2849i	1.64503	+	0.949759i
$260$		−	2.41720i		−	0.149908i
$261$		0			0
$262$	4.12829			0.255047
$263$	−4.65782	−	2.68919i	−0.287213	−	0.165823i	0.349471	−	0.936947i	$-0.386361\pi$
$263$	−4.65782	−	2.68919i	−0.287213	−	0.165823i	−0.636685	+	0.771124i	$0.719695\pi$
$264$		0			0
$265$	5.33229	−	3.07860i	0.327560	−	0.189117i
$266$	−20.1674	−	34.9310i	−1.23654	−	2.14176i
$267$		0			0
$268$	3.06655	+	1.77047i	0.187319	+	0.108149i
$269$	−1.23141			−0.0750805			−0.0375403	−	0.999295i	$-0.511952\pi$
$269$	−1.23141			−0.0750805			−0.0375403	+	0.999295i	$0.511952\pi$
$270$		0			0
$271$	−7.39532			−0.449233			−0.224617	−	0.974447i	$-0.572113\pi$
$271$	−7.39532			−0.449233			−0.224617	+	0.974447i	$0.572113\pi$
$272$	1.55126	+	0.895620i	0.0940589	+	0.0543049i
$273$		0			0
$274$	−5.91355	+	3.41419i	−0.357250	+	0.206259i
$275$	2.00378	−	1.15688i	0.120832	−	0.0697627i
$276$		0			0
$277$	−8.51360	+	14.7460i	−0.511532	+	0.886000i	0.488378	+	0.872632i	$0.337589\pi$
$277$	−8.51360	+	14.7460i	−0.511532	+	0.886000i	−0.999911	+	0.0133682i	$0.995745\pi$
$278$	−18.5999			−1.11555
$279$		0			0
$280$			11.5504i			0.690267i
$281$	19.5785	+	11.3037i	1.16796	+	0.674320i	0.953198	−	0.302347i	$-0.0977702\pi$
$281$	19.5785	+	11.3037i	1.16796	+	0.674320i	0.214759	+	0.976667i	$0.431103\pi$
$282$		0			0
$283$	−2.14984	−	3.72362i	−0.127794	−	0.221346i	0.795027	−	0.606574i	$-0.207456\pi$
$283$	−2.14984	−	3.72362i	−0.127794	−	0.221346i	−0.922822	+	0.385227i	$0.874123\pi$
$284$	4.02763	−	2.32535i	0.238996	−	0.137984i
$285$		0			0
$286$	−1.92299	+	3.33072i	−0.113709	+	0.196950i
$287$	−31.0374	+	3.32393i	−1.83208	+	0.196206i
$288$		0			0
$289$	13.7915			0.811262
$290$	18.7022	+	10.7977i	1.09823	+	0.634063i
$291$		0			0
$292$	−1.07427	−	1.86070i	−0.0628671	−	0.108889i
$293$	−9.22331	+	5.32508i	−0.538832	+	0.311095i	−0.744605	−	0.667505i	$-0.767362\pi$
$293$	−9.22331	+	5.32508i	−0.538832	+	0.311095i	0.205774	+	0.978600i	$0.434029\pi$
$294$		0			0
$295$	−4.73356	+	8.19877i	−0.275599	+	0.477351i
$296$	6.27081			0.364484
$297$		0			0
$298$		−	3.75270i		−	0.217388i
$299$	7.00877	+	4.04652i	0.405328	+	0.234016i
$300$		0			0
$301$	−26.8432	+	15.4980i	−1.54722	+	0.893287i
$302$	−10.6094	+	6.12536i	−0.610504	+	0.352475i
$303$		0			0
$304$	−7.16542	−	4.13696i	−0.410965	−	0.237271i
$305$	−2.77121			−0.158679
$306$		0			0
$307$	14.6398			0.835535			0.417768	−	0.908554i	$-0.362813\pi$
$307$	14.6398			0.835535			0.417768	+	0.908554i	$0.362813\pi$
$308$	9.18886	−	15.9156i	0.523584	−	0.906874i
$309$		0			0
$310$	6.61894	+	11.4643i	0.375931	+	0.651131i
$311$	8.57490	−	4.95072i	0.486238	−	0.280730i	−0.236775	−	0.971565i	$-0.576090\pi$
$311$	8.57490	−	4.95072i	0.486238	−	0.280730i	0.723012	+	0.690835i	$0.242757\pi$
$312$		0			0
$313$	−16.8234	−	9.71299i	−0.950915	−	0.549011i	−0.0575498	−	0.998343i	$-0.518329\pi$
$313$	−16.8234	−	9.71299i	−0.950915	−	0.549011i	−0.893365	+	0.449332i	$0.851662\pi$
$314$			1.95319i			0.110225i
$315$		0			0
$316$		−	2.85863i		−	0.160810i
$317$	26.8971	+	15.5290i	1.51069	+	0.872197i	0.999922	+	0.0124789i	$0.00397226\pi$
$317$	26.8971	+	15.5290i	1.51069	+	0.872197i	0.510768	+	0.859719i	$0.329361\pi$
$318$		0			0
$319$	−17.1802	−	29.7569i	−0.961904	−	1.66607i
$320$	1.18467	+	2.05191i	0.0662250	+	0.114705i
$321$		0			0
$322$	−33.4908	−	19.3359i	−1.86637	−	1.07755i
$323$	14.8206			0.824638
$324$		0			0
$325$			0.626155i			0.0347329i
$326$	−7.50989	+	13.0075i	−0.415934	+	0.720419i
$327$		0			0
$328$	−5.17282	+	3.77385i	−0.285621	+	0.208376i
$329$	2.12708	+	3.68421i	0.117270	+	0.203117i
$330$		0			0
$331$	22.0103	+	12.7077i	1.20980	+	0.698477i	0.962715	−	0.270518i	$-0.0871950\pi$
$331$	22.0103	+	12.7077i	1.20980	+	0.698477i	0.247082	+	0.968995i	$0.420528\pi$
$332$	14.6276			0.802794
$333$		0			0
$334$			16.2457i			0.888925i
$335$	−7.26568	−	4.19484i	−0.396967	−	0.229189i
$336$		0			0
$337$	−11.4954	−	19.9107i	−0.626195	−	1.08460i	−0.988308	−	0.152468i	$-0.951278\pi$
$337$	−11.4954	−	19.9107i	−0.626195	−	1.08460i	0.362113	−	0.932134i	$-0.382055\pi$
$338$	5.97960	+	10.3570i	0.325247	+	0.563345i
$339$		0			0
$340$	−3.67546	−	2.12203i	−0.199330	−	0.115083i
$341$		−	21.0627i		−	1.14061i
$342$		0			0
$343$		−	47.6039i		−	2.57037i
$344$	−3.17911	+	5.50637i	−0.171406	+	0.296884i
$345$		0			0
$346$	−3.45113	−	5.97753i	−0.185534	−	0.321354i
$347$	25.5614	−	14.7579i	1.37221	−	0.792244i	0.381001	−	0.924575i	$-0.375580\pi$
$347$	25.5614	−	14.7579i	1.37221	−	0.792244i	0.991206	+	0.132331i	$0.0422462\pi$
$348$		0			0
$349$	4.54328	−	7.86919i	0.243196	−	0.421228i	−0.718427	−	0.695603i	$-0.755137\pi$
$349$	4.54328	−	7.86919i	0.243196	−	0.421228i	0.961623	+	0.274375i	$0.0884708\pi$
$350$		−	2.99203i		−	0.159931i
$351$		0			0
$352$		−	3.76984i		−	0.200933i
$353$	−10.5516	+	18.2760i	−0.561607	+	0.972732i	0.435749	+	0.900068i	$0.356483\pi$
$353$	−10.5516	+	18.2760i	−0.561607	+	0.972732i	−0.997356	+	0.0726642i	$0.976850\pi$
$354$		0			0
$355$	−9.54280	+	5.50954i	−0.506479	+	0.292416i
$356$	11.7084	−	6.75986i	0.620545	−	0.358272i
$357$		0			0
$358$	12.8910	+	7.44262i	0.681310	+	0.393355i
$359$	−17.0214			−0.898354			−0.449177	−	0.893443i	$-0.648283\pi$
$359$	−17.0214			−0.898354			−0.449177	+	0.893443i	$0.648283\pi$
$360$		0			0
$361$	−49.4576			−2.60303
$362$	0.356520	+	0.205837i	0.0187383	+	0.0108185i
$363$		0			0
$364$	2.48671	+	4.30710i	0.130339	+	0.225753i
$365$	2.54532	+	4.40862i	0.133228	+	0.230757i
$366$		0			0
$367$	7.18379	−	12.4427i	0.374991	−	0.649503i	−0.615335	−	0.788266i	$-0.710979\pi$
$367$	7.18379	−	12.4427i	0.374991	−	0.649503i	0.990326	+	0.138763i	$0.0443125\pi$
$368$	−7.93279			−0.413525
$369$		0			0
$370$	−14.8577			−0.772414
$371$	−6.33425	+	10.9712i	−0.328858	+	0.569599i
$372$		0			0
$373$	15.6241	+	27.0617i	0.808983	+	1.40120i	0.913569	+	0.406684i	$0.133315\pi$
$373$	15.6241	+	27.0617i	0.808983	+	1.40120i	−0.104585	+	0.994516i	$0.533352\pi$
$374$	3.37634	+	5.84799i	0.174586	+	0.302393i
$375$		0			0
$376$	0.755744	+	0.436329i	0.0389745	+	0.0225020i
$377$	9.29865			0.478905
$378$		0			0
$379$	10.8106			0.555303			0.277651	−	0.960682i	$-0.410444\pi$
$379$	10.8106			0.555303			0.277651	+	0.960682i	$0.410444\pi$
$380$	16.9773	+	9.80184i	0.870917	+	0.502824i
$381$		0			0
$382$	3.79497	−	2.19103i	0.194167	−	0.112103i
$383$	9.04861	−	5.22422i	0.462362	−	0.266945i	−0.250675	−	0.968071i	$-0.580652\pi$
$383$	9.04861	−	5.22422i	0.462362	−	0.266945i	0.713037	+	0.701126i	$0.247319\pi$
$384$		0			0
$385$	−21.7715	+	37.7094i	−1.10958	+	1.92185i
$386$			13.5008i			0.687170i
$387$		0			0
$388$			1.70897i			0.0867600i
$389$	8.03655	−	13.9197i	0.407469	−	0.705757i	−0.587136	−	0.809488i	$-0.699745\pi$
$389$	8.03655	−	13.9197i	0.407469	−	0.705757i	0.994605	+	0.103731i	$0.0330781\pi$
$390$		0			0
$391$	12.3058	−	7.10477i	0.622332	−	0.359304i
$392$	−8.38252	−	14.5189i	−0.423381	−	0.733317i
$393$		0			0
$394$	5.90839	−	10.2336i	0.297660	−	0.515563i
$395$			6.77305i			0.340789i
$396$		0			0
$397$			27.5081i			1.38059i	0.723528	+	0.690295i	$0.242519\pi$
$397$			27.5081i			1.38059i	−0.723528	+	0.690295i	$0.757481\pi$
$398$	−0.862237	−	0.497813i	−0.0432200	−	0.0249531i
$399$		0			0
$400$	−0.306879	−	0.531530i	−0.0153439	−	0.0265765i
$401$	5.26643	+	9.12173i	0.262993	+	0.455517i	0.967036	−	0.254640i	$-0.0819570\pi$
$401$	5.26643	+	9.12173i	0.262993	+	0.455517i	−0.704043	+	0.710158i	$0.748624\pi$
$402$		0			0
$403$	4.93637	+	2.85001i	0.245898	+	0.141969i
$404$		−	4.96416i		−	0.246976i
$405$		0			0
$406$	−44.4328			−2.20516
$407$	20.4728	+	11.8200i	1.01480	+	0.585894i
$408$		0			0
$409$	7.41896	+	12.8500i	0.366844	+	0.635392i	0.989070	−	0.147445i	$-0.0471049\pi$
$409$	7.41896	+	12.8500i	0.366844	+	0.635392i	−0.622226	+	0.782837i	$0.713772\pi$
$410$	12.2562	−	8.94152i	0.605288	−	0.441590i
$411$		0			0
$412$	−6.24403	+	10.8150i	−0.307621	+	0.532815i
$413$		−	19.4787i		−	0.958486i
$414$		0			0
$415$	−34.6577			−1.70128
$416$	0.883519	+	0.510100i	0.0433181	+	0.0250097i
$417$		0			0
$418$	−15.5956	−	27.0124i	−0.762808	−	1.32122i
$419$	−10.8374	−	18.7709i	−0.529442	−	0.917020i	−0.999410	−	0.0343369i	$-0.989068\pi$
$419$	−10.8374	−	18.7709i	−0.529442	−	0.917020i	0.469969	−	0.882683i	$-0.344265\pi$
$420$		0			0
$421$	−34.1977	−	19.7441i	−1.66669	−	0.962267i	−0.969402	−	0.245480i	$-0.921054\pi$
$421$	−34.1977	−	19.7441i	−1.66669	−	0.962267i	−0.697293	−	0.716786i	$-0.745612\pi$
$422$		−	4.20250i		−	0.204575i
$423$		0			0
$424$			2.59870i			0.126204i
$425$	0.952098	+	0.549694i	0.0461835	+	0.0266641i
$426$		0			0
$427$	4.93790	−	2.85090i	0.238962	−	0.137965i
$428$	1.28384	+	2.22368i	0.0620567	+	0.107485i
$429$		0			0
$430$	7.53237	−	13.0465i	0.363243	−	0.629156i
$431$	−14.1510			−0.681627			−0.340814	−	0.940131i	$-0.610703\pi$
$431$	−14.1510			−0.681627			−0.340814	+	0.940131i	$0.610703\pi$
$432$		0			0
$433$	−36.1991			−1.73962			−0.869810	−	0.493387i	$-0.835759\pi$
$433$	−36.1991			−1.73962			−0.869810	+	0.493387i	$0.835759\pi$
$434$	−23.5880	−	13.6186i	−1.13226	−	0.653712i
$435$		0			0
$436$	11.1271	−	6.42424i	0.532892	−	0.307665i
$437$	−56.8418	+	32.8176i	−2.71911	+	1.56988i
$438$		0			0
$439$	7.35009	+	4.24358i	0.350801	+	0.202535i	0.665038	−	0.746810i	$-0.268415\pi$
$439$	7.35009	+	4.24358i	0.350801	+	0.202535i	−0.314237	+	0.949345i	$0.601749\pi$
$440$			8.93201i			0.425817i
$441$		0			0
$442$	−1.82742			−0.0869216
$443$	2.05505	−	3.55945i	0.0976385	−	0.169115i	−0.813068	−	0.582168i	$-0.802204\pi$
$443$	2.05505	−	3.55945i	0.0976385	−	0.169115i	0.910707	+	0.413054i	$0.135538\pi$
$444$		0			0
$445$	−27.7412	+	16.0164i	−1.31506	+	0.759249i
$446$	6.73892	+	11.6721i	0.319097	+	0.552692i
$447$		0			0
$448$	−4.22182	−	2.43747i	−0.199462	−	0.115160i
$449$	−22.2112			−1.04821			−0.524106	−	0.851653i	$-0.675601\pi$
$449$	−22.2112			−1.04821			−0.524106	+	0.851653i	$0.675601\pi$
$450$		0			0
$451$	−24.0015	+	2.57043i	−1.13019	+	0.121037i
$452$	6.06365	−	10.5025i	0.285210	−	0.493998i
$453$		0			0
$454$	−13.4763	+	7.78057i	−0.632476	+	0.365160i
$455$	−5.89184	−	10.2050i	−0.276214	−	0.478416i
$456$		0			0
$457$	−5.18852	−	2.99559i	−0.242709	−	0.140128i	0.373712	−	0.927545i	$-0.378085\pi$
$457$	−5.18852	−	2.99559i	−0.242709	−	0.140128i	−0.616421	+	0.787417i	$0.711418\pi$
$458$		−	22.8568i		−	1.06803i
$459$		0			0
$460$	18.7955			0.876343
$461$	10.3050	−	17.8487i	0.479950	−	0.831299i	−0.519785	−	0.854297i	$-0.673988\pi$
$461$	10.3050	−	17.8487i	0.479950	−	0.831299i	0.999735	+	0.0229985i	$0.00732130\pi$
$462$		0			0
$463$	−2.61596	+	1.51032i	−0.121574	+	0.0701907i	−0.559554	−	0.828794i	$-0.689027\pi$
$463$	−2.61596	+	1.51032i	−0.121574	+	0.0701907i	0.437980	+	0.898985i	$0.355694\pi$
$464$	−7.89342	+	4.55727i	−0.366443	+	0.211566i
$465$		0			0
$466$	5.46395	+	3.15461i	0.253112	+	0.146135i
$467$	−38.3929			−1.77661			−0.888306	−	0.459252i	$-0.848118\pi$
$467$	−38.3929			−1.77661			−0.888306	+	0.459252i	$0.848118\pi$
$468$		0			0
$469$	17.2619			0.797079
$470$	−1.79061	−	1.03381i	−0.0825948	−	0.0476861i
$471$		0			0
$472$	−1.99784	−	3.46037i	−0.0919582	−	0.159276i
$473$	−20.7581	+	11.9847i	−0.954460	+	0.551058i
$474$		0			0
$475$	−4.39783	−	2.53909i	−0.201786	−	0.116501i
$476$	8.73219			0.400239
$477$		0			0
$478$			18.3842i			0.840873i
$479$	−14.8658	−	8.58280i	−0.679237	−	0.392158i	0.120330	−	0.992734i	$-0.461605\pi$
$479$	−14.8658	−	8.58280i	−0.679237	−	0.392158i	−0.799568	+	0.600576i	$0.794938\pi$
$480$		0			0
$481$	−5.54038	+	3.19874i	−0.252620	+	0.145850i
$482$	−9.73255	−	16.8573i	−0.443306	−	0.767828i
$483$		0			0
$484$	1.60583	−	2.78138i	0.0729923	−	0.126426i
$485$		−	4.04913i		−	0.183862i
$486$		0			0
$487$	8.83968			0.400564			0.200282	−	0.979738i	$-0.435814\pi$
$487$	8.83968			0.400564			0.200282	+	0.979738i	$0.435814\pi$
$488$	0.584806	−	1.01291i	0.0264729	−	0.0458525i
$489$		0			0
$490$	19.8610	+	34.4003i	0.897229	+	1.55405i
$491$	18.4092	+	31.8858i	0.830798	+	1.43898i	0.897406	+	0.441205i	$0.145449\pi$
$491$	18.4092	+	31.8858i	0.830798	+	1.43898i	−0.0666087	+	0.997779i	$0.521218\pi$
$492$		0			0
$493$	8.16316	−	14.1390i	0.367650	−	0.636789i
$494$	8.44104			0.379780
$495$		0			0
$496$	−5.58717			−0.250871
$497$	11.3359	−	19.6344i	0.508487	−	0.880725i
$498$		0			0
$499$	−0.131128	+	0.0757069i	−0.00587010	+	0.00338910i	−0.502932	−	0.864326i	$-0.667745\pi$
$499$	−0.131128	+	0.0757069i	−0.00587010	+	0.00338910i	0.497062	+	0.867715i	$0.334412\pi$
$500$	−5.19624	−	9.00016i	−0.232383	−	0.402499i
$501$		0			0
$502$	0.881442	−	1.52670i	0.0393407	−	0.0681401i
$503$		−	17.8020i		−	0.793750i	−0.917873	−	0.396875i	$-0.870095\pi$
$503$		−	17.8020i		−	0.793750i	0.917873	−	0.396875i	$-0.129905\pi$
$504$		0			0
$505$			11.7618i			0.523391i
$506$	−25.8988	−	14.9527i	−1.15134	−	0.664727i
$507$		0			0
$508$	−9.97146	−	17.2711i	−0.442412	−	0.766280i
$509$	−12.7907	+	7.38472i	−0.566939	+	0.327322i	−0.755926	−	0.654657i	$-0.772813\pi$
$509$	−12.7907	+	7.38472i	−0.566939	+	0.327322i	0.188987	+	0.981980i	$0.439480\pi$
$510$		0			0
$511$	−9.07078	−	5.23702i	−0.401268	−	0.231672i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$		−	7.26031i		−	0.320239i
$515$	14.7942	−	25.6243i	0.651910	−	1.12914i
$516$		0			0
$517$	1.64489	+	2.84903i	0.0723422	+	0.125300i
$518$	26.4743	−	15.2849i	1.16321	−	0.671581i
$519$		0			0
$520$	−2.09335	−	1.20860i	−0.0917996	−	0.0530005i
$521$			35.9628i			1.57556i	0.615958	+	0.787779i	$0.288769\pi$
$521$			35.9628i			1.57556i	−0.615958	+	0.787779i	$0.711231\pi$
$522$		0			0
$523$	31.3935			1.37274			0.686371	−	0.727252i	$-0.259203\pi$
$523$	31.3935			1.37274			0.686371	+	0.727252i	$0.259203\pi$
$524$	2.06415	−	3.57521i	0.0901727	−	0.156184i
$525$		0			0
$526$	−4.65782	+	2.68919i	−0.203091	+	0.117254i
$527$	8.66715	−	5.00398i	0.377547	−	0.217977i
$528$		0			0
$529$	−19.9646	+	34.5797i	−0.868025	+	1.50346i
$530$		−	6.15720i		−	0.267452i
$531$		0			0
$532$	−40.3348			−1.74874
$533$	2.64524	−	5.97292i	0.114578	−	0.258716i
$534$		0			0
$535$	−3.04185	−	5.26864i	−0.131511	−	0.227783i
$536$	3.06655	−	1.77047i	0.132455	−	0.0764727i
$537$		0			0
$538$	−0.615706	+	1.06643i	−0.0265450	+	0.0459772i
$539$		−	63.2014i		−	2.72228i
$540$		0			0
$541$	35.1456			1.51103			0.755514	−	0.655133i	$-0.227387\pi$
$541$	35.1456			1.51103			0.755514	+	0.655133i	$0.227387\pi$
$542$	−3.69766	+	6.40453i	−0.158828	+	0.275098i
$543$		0			0
$544$	1.55126	−	0.895620i	0.0665097	−	0.0383994i
$545$	−26.3639	+	15.2212i	−1.12930	+	0.652004i
$546$		0			0
$547$	28.0707	+	16.2066i	1.20022	+	0.692946i	0.960604	−	0.277922i	$-0.0896457\pi$
$547$	28.0707	+	16.2066i	1.20022	+	0.692946i	0.239614	+	0.970868i	$0.422979\pi$
$548$			6.82838i			0.291694i
$549$		0			0
$550$		−	2.31377i		−	0.0986593i
$551$	−37.7064	+	65.3095i	−1.60635	+	2.78228i
$552$		0			0
$553$	−6.96782	−	12.0686i	−0.296302	−	0.513210i
$554$	8.51360	+	14.7460i	0.361708	+	0.626497i
$555$		0			0
$556$	−9.29993	+	16.1080i	−0.394405	+	0.683130i
$557$			10.9092i			0.462237i	0.972926	+	0.231118i	$0.0742384\pi$
$557$			10.9092i			0.462237i	−0.972926	+	0.231118i	$0.925762\pi$
$558$		0			0
$559$		−	6.48665i		−	0.274356i
$560$	10.0029	+	5.77519i	0.422700	+	0.244046i
$561$		0			0
$562$	19.5785	−	11.3037i	0.825870	−	0.476816i
$563$	3.87933	−	2.23973i	0.163494	−	0.0943935i	−0.416020	−	0.909355i	$-0.636575\pi$
$563$	3.87933	−	2.23973i	0.163494	−	0.0943935i	0.579515	+	0.814962i	$0.303242\pi$
$564$		0			0
$565$	−14.3668	+	24.8841i	−0.604417	+	1.04688i
$566$	−4.29967			−0.180729
$567$		0			0
$568$		−	4.65070i		−	0.195139i
$569$	14.7509	−	25.5493i	0.618390	−	1.07108i	−0.371390	−	0.928477i	$-0.621119\pi$
$569$	14.7509	−	25.5493i	0.618390	−	1.07108i	0.989780	−	0.142606i	$-0.0455481\pi$
$570$		0			0
$571$	7.52372	−	4.34382i	0.314858	−	0.181783i	−0.334240	−	0.942488i	$-0.608480\pi$
$571$	7.52372	−	4.34382i	0.314858	−	0.181783i	0.649098	+	0.760705i	$0.275146\pi$
$572$	1.92299	+	3.33072i	0.0804044	+	0.139264i
$573$		0			0
$574$	−12.6401	+	28.5411i	−0.527586	+	1.19128i
$575$	−4.86881			−0.203044
$576$		0			0
$577$		−	31.3335i		−	1.30443i	−0.758034	−	0.652215i	$-0.773840\pi$
$577$		−	31.3335i		−	1.30443i	0.758034	−	0.652215i	$-0.226160\pi$
$578$	6.89573	−	11.9438i	0.286825	−	0.496795i
$579$		0			0
$580$	18.7022	−	10.7977i	0.776565	−	0.448350i
$581$	61.7552	−	35.6544i	2.56204	−	1.47919i
$582$		0			0
$583$	−4.89834	+	8.48417i	−0.202868	+	0.351378i
$584$	−2.14855			−0.0889075
$585$		0			0
$586$			10.6502i			0.439954i
$587$	10.0003	+	5.77368i	0.412757	+	0.238305i	0.691974	−	0.721923i	$-0.256741\pi$
$587$	10.0003	+	5.77368i	0.412757	+	0.238305i	−0.279217	+	0.960228i	$0.590075\pi$
$588$		0			0
$589$	−40.0344	+	23.1139i	−1.64959	+	0.952390i
$590$	4.73356	+	8.19877i	0.194878	+	0.337538i
$591$		0			0
$592$	3.13541	−	5.43068i	0.128864	−	0.223200i
$593$		−	2.38737i		−	0.0980375i	−0.998798	−	0.0490187i	$-0.984391\pi$
$593$		−	2.38737i		−	0.0980375i	0.998798	−	0.0490187i	$-0.0156094\pi$
$594$		0			0
$595$	−20.6895			−0.848187
$596$	−3.24993	−	1.87635i	−0.133122	−	0.0768582i
$597$		0			0
$598$	7.00877	−	4.04652i	0.286610	−	0.165474i
$599$	−12.4875	−	21.6290i	−0.510225	−	0.883736i	−0.999930	−	0.0118473i	$-0.996229\pi$
$599$	−12.4875	−	21.6290i	−0.510225	−	0.883736i	0.489705	−	0.871888i	$-0.337105\pi$
$600$		0			0
$601$	2.68855	+	1.55223i	0.109668	+	0.0633169i	0.553831	−	0.832629i	$-0.313165\pi$
$601$	2.68855	+	1.55223i	0.109668	+	0.0633169i	−0.444163	+	0.895946i	$0.646499\pi$
$602$			30.9959i			1.26330i
$603$		0			0
$604$			12.2507i			0.498475i
$605$	−3.80476	+	6.59003i	−0.154685	+	0.267923i
$606$		0			0
$607$	−15.9613	−	27.6458i	−0.647850	−	1.12211i	−0.983635	−	0.180170i	$-0.942335\pi$
$607$	−15.9613	−	27.6458i	−0.647850	−	1.12211i	0.335786	−	0.941938i	$-0.390998\pi$
$608$	−7.16542	+	4.13696i	−0.290596	+	0.167776i
$609$		0			0
$610$	−1.38560	+	2.39994i	−0.0561014	+	0.0971706i
$611$	−0.890286			−0.0360171
$612$		0			0
$613$	40.2200			1.62447			0.812236	−	0.583330i	$-0.198250\pi$
$613$	40.2200			1.62447			0.812236	+	0.583330i	$0.198250\pi$
$614$	7.31988	−	12.6784i	0.295406	−	0.511659i
$615$		0			0
$616$	−9.18886	−	15.9156i	−0.370230	−	0.641257i
$617$	−9.19582	−	15.9276i	−0.370210	−	0.641222i	0.619388	−	0.785085i	$-0.287381\pi$
$617$	−9.19582	−	15.9276i	−0.370210	−	0.641222i	−0.989598	+	0.143863i	$0.954048\pi$
$618$		0			0
$619$	−8.32782	+	14.4242i	−0.334723	+	0.579758i	−0.983432	−	0.181279i	$-0.941976\pi$
$619$	−8.32782	+	14.4242i	−0.334723	+	0.579758i	0.648708	+	0.761037i	$0.275310\pi$
$620$	13.2379			0.531646
$621$		0			0
$622$		−	9.90144i		−	0.397012i
$623$	32.9539	−	57.0778i	1.32027	−	2.28677i
$624$		0			0
$625$	13.8460	+	23.9821i	0.553842	+	0.959282i
$626$	−16.8234	+	9.71299i	−0.672398	+	0.388209i
$627$		0			0
$628$	1.69151	+	0.976594i	0.0674986	+	0.0389703i
$629$			11.2325i			0.447870i
$630$		0			0
$631$	1.18152			0.0470356			0.0235178	−	0.999723i	$-0.492513\pi$
$631$	1.18152			0.0470356			0.0235178	+	0.999723i	$0.492513\pi$
$632$	−2.47565	−	1.42931i	−0.0984759	−	0.0568551i
$633$		0			0
$634$	26.8971	−	15.5290i	1.06822	−	0.616737i
$635$	23.6258	+	40.9210i	0.937560	+	1.62390i
$636$		0			0
$637$	14.8122	+	8.55184i	0.586882	+	0.338836i
$638$	−34.3603			−1.36034
$639$		0			0
$640$	2.36934			0.0936563
$641$	14.2317	+	8.21670i	0.562120	+	0.324540i	0.753996	−	0.656879i	$-0.228124\pi$
$641$	14.2317	+	8.21670i	0.562120	+	0.324540i	−0.191876	+	0.981419i	$0.561457\pi$
$642$		0			0
$643$	14.0501	−	8.11186i	0.554084	−	0.319900i	−0.196684	−	0.980467i	$-0.563017\pi$
$643$	14.0501	−	8.11186i	0.554084	−	0.319900i	0.750767	+	0.660567i	$0.229684\pi$
$644$	−33.4908	+	19.3359i	−1.31972	+	0.761943i
$645$		0			0
$646$	7.41028	−	12.8350i	0.291554	−	0.504986i
$647$	−2.79497			−0.109882			−0.0549408	−	0.998490i	$-0.517497\pi$
$647$	−2.79497			−0.109882			−0.0549408	+	0.998490i	$0.517497\pi$
$648$		0			0
$649$		−	15.0631i		−	0.591278i
$650$	0.542267	+	0.313078i	0.0212694	+	0.0122799i
$651$		0			0
$652$	7.50989	+	13.0075i	0.294110	+	0.509413i
$653$	−29.2270	+	16.8742i	−1.14374	+	0.660340i	−0.947355	−	0.320186i	$-0.896255\pi$
$653$	−29.2270	+	16.8742i	−1.14374	+	0.660340i	−0.196388	+	0.980526i	$0.562921\pi$
$654$		0			0
$655$	−4.89066	+	8.47087i	−0.191094	+	0.330984i
$656$	0.681841	+	6.36672i	0.0266214	+	0.248579i
$657$		0			0
$658$	4.25416			0.165844
$659$	11.6023	+	6.69857i	0.451960	+	0.260939i	0.708658	−	0.705553i	$-0.249301\pi$
$659$	11.6023	+	6.69857i	0.451960	+	0.260939i	−0.256698	+	0.966492i	$0.582634\pi$
$660$		0			0
$661$	−3.00112	−	5.19808i	−0.116730	−	0.202182i	0.801740	−	0.597673i	$-0.203908\pi$
$661$	−3.00112	−	5.19808i	−0.116730	−	0.202182i	−0.918470	+	0.395491i	$0.870575\pi$
$662$	22.0103	−	12.7077i	0.855456	−	0.493898i
$663$		0			0
$664$	7.31381	−	12.6679i	0.283831	−	0.491609i
$665$	95.5668			3.70592
$666$		0			0
$667$			72.3037i			2.79961i
$668$	14.0692	+	8.12285i	0.544353	+	0.314282i
$669$		0			0
$670$	−7.26568	+	4.19484i	−0.280698	+	0.162061i
$671$	3.81852	−	2.20462i	0.147412	−	0.0851086i
$672$		0			0
$673$	17.1253	+	9.88732i	0.660134	+	0.381128i	0.792328	−	0.610095i	$-0.208869\pi$
$673$	17.1253	+	9.88732i	0.660134	+	0.381128i	−0.132194	+	0.991224i	$0.542202\pi$
$674$	−22.9908			−0.885574
$675$		0			0
$676$	11.9592			0.459969
$677$	−1.57334	+	2.72511i	−0.0604684	+	0.104734i	−0.894675	−	0.446718i	$-0.852593\pi$
$677$	−1.57334	+	2.72511i	−0.0604684	+	0.104734i	0.834206	+	0.551452i	$0.185926\pi$
$678$		0			0
$679$	4.16557	+	7.21498i	0.159860	+	0.276886i
$680$	−3.67546	+	2.12203i	−0.140947	+	0.0813760i
$681$		0			0
$682$	−18.2408	−	10.5314i	−0.698478	−	0.403266i
$683$			27.0410i			1.03470i	0.855775	+	0.517348i	$0.173081\pi$
$683$			27.0410i			1.03470i	−0.855775	+	0.517348i	$0.826919\pi$
$684$		0			0
$685$		−	16.1787i		−	0.618157i
$686$	−41.2262	−	23.8020i	−1.57402	−	0.908764i
$687$		0			0
$688$	3.17911	+	5.50637i	0.121202	+	0.209929i
$689$	−1.32560	−	2.29600i	−0.0505012	−	0.0874707i
$690$		0			0
$691$	5.89775	+	3.40506i	0.224361	+	0.129535i	0.607968	−	0.793962i	$-0.291985\pi$
$691$	5.89775	+	3.40506i	0.224361	+	0.129535i	−0.383607	+	0.923496i	$0.625318\pi$
$692$	−6.90226			−0.262385
$693$		0			0
$694$		−	29.5157i		−	1.12040i
$695$	22.0347	−	38.1652i	0.835823	−	1.44769i
$696$		0			0
$697$	−6.75987	−	9.26576i	−0.256048	−	0.350966i
$698$	−4.54328	−	7.86919i	−0.171966	−	0.297853i
$699$		0			0
$700$	−2.59118	−	1.49602i	−0.0979372	−	0.0565441i
$701$	−24.5252			−0.926303			−0.463151	−	0.886279i	$-0.653281\pi$
$701$	−24.5252			−0.926303			−0.463151	+	0.886279i	$0.653281\pi$
$702$		0			0
$703$		−	51.8842i		−	1.95685i
$704$	−3.26477	−	1.88492i	−0.123046	−	0.0710405i
$705$		0			0
$706$	10.5516	+	18.2760i	0.397116	+	0.687826i
$707$	−12.1000	−	20.9578i	−0.455067	−	0.788199i
$708$		0			0
$709$	−8.31381	−	4.79998i	−0.312232	−	0.180267i	0.335693	−	0.941971i	$-0.391030\pi$
$709$	−8.31381	−	4.79998i	−0.312232	−	0.180267i	−0.647925	+	0.761704i	$0.724363\pi$
$710$			11.0191i			0.413539i
$711$		0			0
$712$		−	13.5197i		−	0.506673i
$713$	−22.1609	+	38.3838i	−0.829933	+	1.43749i
$714$		0			0
$715$	−4.55622	−	7.89160i	−0.170393	−	0.295129i
$716$	12.8910	−	7.44262i	0.481759	−	0.278144i
$717$		0			0
$718$	−8.51069	+	14.7409i	−0.317616	+	0.550127i
$719$			50.1862i			1.87163i	0.352495	+	0.935814i	$0.385333\pi$
$719$			50.1862i			1.87163i	−0.352495	+	0.935814i	$0.614667\pi$
$720$		0			0
$721$			60.8785i			2.26723i
$722$	−24.7288	+	42.8315i	−0.920311	+	1.59403i
$723$		0			0
$724$	0.356520	−	0.205837i	0.0132500	−	0.00764987i
$725$	−4.84465	+	2.79706i	−0.179926	+	0.103880i
$726$		0			0
$727$	38.0592	+	21.9735i	1.41154	+	0.814952i	0.995533	−	0.0944103i	$-0.0300965\pi$
$727$	38.0592	+	21.9735i	1.41154	+	0.814952i	0.416005	+	0.909362i	$0.363430\pi$
$728$	4.97341			0.184327
$729$		0			0
$730$	5.09063			0.188413
$731$	−9.86324	−	5.69454i	−0.364805	−	0.210620i
$732$		0			0
$733$	−21.8748	−	37.8883i	−0.807964	−	1.39943i	−0.914272	−	0.405101i	$-0.867236\pi$
$733$	−21.8748	−	37.8883i	−0.807964	−	1.39943i	0.106308	−	0.994333i	$-0.466097\pi$
$734$	−7.18379	−	12.4427i	−0.265159	−	0.459268i
$735$		0			0
$736$	−3.96640	+	6.87000i	−0.146203	+	0.253231i
$737$	13.3488			0.491708
$738$		0			0
$739$	15.0259			0.552738			0.276369	−	0.961052i	$-0.410869\pi$
$739$	15.0259			0.552738			0.276369	+	0.961052i	$0.410869\pi$
$740$	−7.42884	+	12.8671i	−0.273089	+	0.473005i
$741$		0			0
$742$	6.33425	+	10.9712i	0.232538	+	0.402767i
$743$	−3.10453	−	5.37720i	−0.113894	−	0.197270i	0.803443	−	0.595382i	$-0.202999\pi$
$743$	−3.10453	−	5.37720i	−0.113894	−	0.197270i	−0.917337	+	0.398111i	$0.869666\pi$
$744$		0			0
$745$	7.70018	+	4.44570i	0.282113	+	0.162878i
$746$	31.2481			1.14408
$747$		0			0
$748$	6.75268			0.246902
$749$	10.8403	+	6.25864i	0.396095	+	0.228686i
$750$		0			0
$751$	−13.3710	+	7.71976i	−0.487915	+	0.281698i	−0.723709	−	0.690105i	$-0.757564\pi$
$751$	−13.3710	+	7.71976i	−0.487915	+	0.281698i	0.235794	+	0.971803i	$0.424231\pi$
$752$	0.755744	−	0.436329i	0.0275592	−	0.0159113i
$753$		0			0
$754$	4.64932	−	8.05286i	0.169318	−	0.293268i
$755$		−	29.0261i		−	1.05637i
$756$		0			0
$757$		−	51.1223i		−	1.85807i	−0.369992	−	0.929035i	$-0.620639\pi$
$757$		−	51.1223i		−	1.85807i	0.369992	−	0.929035i	$-0.379361\pi$
$758$	5.40529	−	9.36225i	0.196329	−	0.340052i
$759$		0			0
$760$	16.9773	−	9.80184i	0.615831	−	0.355550i
$761$	−10.2952	−	17.8318i	−0.373201	−	0.646403i	0.616855	−	0.787077i	$-0.288406\pi$
$761$	−10.2952	−	17.8318i	−0.373201	−	0.646403i	−0.990056	+	0.140674i	$0.955073\pi$
$762$		0			0
$763$	31.3178	−	54.2440i	1.13378	−	1.96376i
$764$		−	4.38205i		−	0.158537i
$765$		0			0
$766$		−	10.4484i		−	0.377517i
$767$	3.53026	+	2.03820i	0.127470	+	0.0735951i
$768$		0			0
$769$	15.5878	+	26.9989i	0.562111	+	0.973605i	0.997312	+	0.0732713i	$0.0233439\pi$
$769$	15.5878	+	26.9989i	0.562111	+	0.973605i	−0.435201	+	0.900333i	$0.643323\pi$
$770$	21.7715	+	37.7094i	0.784591	+	1.35895i
$771$		0			0
$772$	11.6920	+	6.75038i	0.420804	+	0.242951i
$773$		−	37.8592i		−	1.36170i	−0.732423	−	0.680850i	$-0.761611\pi$
$773$		−	37.8592i		−	1.36170i	0.732423	−	0.680850i	$-0.238389\pi$
$774$		0			0
$775$	−3.42917			−0.123179
$776$	1.48001	+	0.854487i	0.0531294	+	0.0306743i
$777$		0			0
$778$	−8.03655	−	13.9197i	−0.288124	−	0.499046i
$779$	31.2245	+	42.7994i	1.11873	+	1.53345i
$780$		0			0
$781$	8.76619	−	15.1835i	0.313679	−	0.543308i
$782$		−	14.2095i		−	0.508132i
$783$		0			0
$784$	−16.7650			−0.598751
$785$	−4.00776	−	2.31388i	−0.143043	−	0.0825859i
$786$		0			0
$787$	1.00283	+	1.73695i	0.0357470	+	0.0619156i	0.883345	−	0.468723i	$-0.155286\pi$
$787$	1.00283	+	1.73695i	0.0357470	+	0.0619156i	−0.847598	+	0.530638i	$0.821952\pi$
$788$	−5.90839	−	10.2336i	−0.210478	−	0.364558i
$789$		0			0
$790$	5.86564	+	3.38653i	0.208690	+	0.120487i
$791$		−	59.1198i		−	2.10206i
$792$		0			0
$793$			1.19324i			0.0423731i
$794$	23.8227	+	13.7540i	0.845435	+	0.488112i
$795$		0			0
$796$	−0.862237	+	0.497813i	−0.0305612	+	0.0176445i
$797$	−11.7865	−	20.4149i	−0.417501	−	0.723132i	0.578187	−	0.815904i	$-0.303760\pi$
$797$	−11.7865	−	20.4149i	−0.417501	−	0.723132i	−0.995687	+	0.0927722i	$0.970427\pi$
$798$		0			0
$799$	−0.781571	+	1.35372i	−0.0276500	+	0.0478912i
$800$	−0.613758			−0.0216996
$801$		0			0
$802$	10.5329			0.371928
$803$	−7.01452	−	4.04983i	−0.247537	−	0.142916i
$804$		0			0
$805$	79.3511	−	45.8134i	2.79676	−	1.61471i
$806$	4.93637	−	2.85001i	0.173876	−	0.100387i
$807$		0			0
$808$	−4.29909	−	2.48208i	−0.151241	−	0.0873192i
$809$		−	6.06955i		−	0.213394i	−0.994292	−	0.106697i	$-0.965973\pi$
$809$		−	6.06955i		−	0.213394i	0.994292	−	0.106697i	$-0.0340275\pi$
$810$		0			0
$811$	−39.1375			−1.37430			−0.687152	−	0.726514i	$-0.741139\pi$
$811$	−39.1375			−1.37430			−0.687152	+	0.726514i	$0.741139\pi$
$812$	−22.2164	+	38.4799i	−0.779643	+	1.35038i
$813$		0			0
$814$	20.4728	−	11.8200i	0.717571	−	0.414290i
$815$	−17.7935	−	30.8192i	−0.623277	−	1.07955i
$816$		0			0
$817$	45.5593	+	26.3036i	1.59392	+	0.920248i
$818$	14.8379			0.518796
$819$		0			0
$820$	−1.61551	−	15.0849i	−0.0564161	−	0.526788i
$821$	−3.20799	+	5.55640i	−0.111960	+	0.193920i	−0.916560	−	0.399896i	$-0.869046\pi$
$821$	−3.20799	+	5.55640i	−0.111960	+	0.193920i	0.804601	+	0.593816i	$0.202379\pi$
$822$		0			0
$823$	−34.8428	+	20.1165i	−1.21454	+	0.701217i	−0.963746	−	0.266823i	$-0.914026\pi$
$823$	−34.8428	+	20.1165i	−1.21454	+	0.701217i	−0.250797	+	0.968040i	$0.580693\pi$
$824$	6.24403	+	10.8150i	0.217521	+	0.376757i
$825$		0			0
$826$	−16.8691	−	9.73936i	−0.586950	−	0.338876i
$827$			42.8896i			1.49142i	0.666272	+	0.745709i	$0.267889\pi$
$827$			42.8896i			1.49142i	−0.666272	+	0.745709i	$0.732111\pi$
$828$		0			0
$829$	−14.0068			−0.486476			−0.243238	−	0.969967i	$-0.578210\pi$
$829$	−14.0068			−0.486476			−0.243238	+	0.969967i	$0.578210\pi$
$830$	−17.3289	+	30.0145i	−0.601494	+	1.04182i
$831$		0			0
$832$	0.883519	−	0.510100i	0.0306305	−	0.0176845i
$833$	26.0069	−	15.0151i	0.901086	−	0.520242i
$834$		0			0
$835$	−33.3346	−	19.2458i	−1.15359	−	0.666027i
$836$	−31.1913			−1.07877
$837$		0			0
$838$	−21.6748			−0.748744
$839$	13.0827	+	7.55328i	0.451664	+	0.260768i	0.708533	−	0.705678i	$-0.249358\pi$
$839$	13.0827	+	7.55328i	0.451664	+	0.260768i	−0.256869	+	0.966446i	$0.582691\pi$
$840$		0			0
$841$	27.0374	+	46.8301i	0.932323	+	1.61483i
$842$	−34.1977	+	19.7441i	−1.17853	+	0.680425i
$843$		0			0
$844$	−3.63947	−	2.10125i	−0.125276	−	0.0723281i
$845$	−28.3354			−0.974766
$846$		0			0
$847$		−	15.6567i		−	0.537969i
$848$	2.25054	+	1.29935i	0.0772839	+	0.0446199i
$849$		0			0
$850$	0.952098	−	0.549694i	0.0326567	−	0.0188543i
$851$	−24.8725	−	43.0805i	−0.852619	−	1.47678i
$852$		0			0
$853$	12.8734	−	22.2974i	0.440776	−	0.763447i	−0.556971	−	0.830532i	$-0.688036\pi$
$853$	12.8734	−	22.2974i	0.440776	−	0.763447i	0.997747	+	0.0670849i	$0.0213698\pi$
$854$		−	5.70179i		−	0.195111i
$855$		0			0
$856$	2.56768			0.0877615
$857$	−13.3942	+	23.1994i	−0.457536	+	0.792475i	−0.998830	−	0.0483583i	$-0.984601\pi$
$857$	−13.3942	+	23.1994i	−0.457536	+	0.792475i	0.541295	+	0.840833i	$0.317934\pi$
$858$		0			0
$859$	−15.0584	−	26.0819i	−0.513786	−	0.889903i	−0.999872	−	0.0159924i	$-0.994909\pi$
$859$	−15.0584	−	26.0819i	−0.513786	−	0.889903i	0.486086	−	0.873911i	$-0.338424\pi$
$860$	−7.53237	−	13.0465i	−0.256852	−	0.444880i
$861$		0			0
$862$	−7.07548	+	12.2551i	−0.240992	+	0.417410i
$863$	36.4107			1.23943			0.619717	−	0.784825i	$-0.287247\pi$
$863$	36.4107			1.23943			0.619717	+	0.784825i	$0.287247\pi$
$864$		0			0
$865$	16.3538			0.556045
$866$	−18.0996	+	31.3494i	−0.615048	+	1.06530i
$867$		0			0
$868$	−23.5880	+	13.6186i	−0.800630	+	0.462244i
$869$	−5.38828	−	9.33278i	−0.182785	−	0.316593i
$870$		0			0
$871$	−1.80623	+	3.12849i	−0.0612019	+	0.106005i
$872$		−	12.8485i		−	0.435104i
$873$		0			0
$874$			65.6352i			2.22014i
$875$	−43.8752	−	25.3314i	−1.48325	−	0.856357i
$876$		0			0
$877$	21.4618	+	37.1729i	0.724713	+	1.25524i	0.959092	+	0.283095i	$0.0913611\pi$
$877$	21.4618	+	37.1729i	0.724713	+	1.25524i	−0.234379	+	0.972145i	$0.575306\pi$
$878$	7.35009	−	4.24358i	0.248054	−	0.143214i
$879$		0			0
$880$	7.73535	+	4.46601i	0.260759	+	0.150549i
$881$	8.22436			0.277086			0.138543	−	0.990356i	$-0.455758\pi$
$881$	8.22436			0.277086			0.138543	+	0.990356i	$0.455758\pi$
$882$		0			0
$883$		−	0.0492990i		−	0.00165904i	−1.00000		0.000829522i	$-0.999736\pi$
$883$		−	0.0492990i		−	0.00165904i	1.00000		0.000829522i	$-0.000264045\pi$
$884$	−0.913711	+	1.58259i	−0.0307314	+	0.0532284i
$885$		0			0
$886$	−2.05505	−	3.55945i	−0.0690408	−	0.119582i
$887$	−11.9207	+	6.88244i	−0.400259	+	0.231090i	−0.686596	−	0.727039i	$-0.740896\pi$
$887$	−11.9207	+	6.88244i	−0.400259	+	0.231090i	0.286337	+	0.958129i	$0.407562\pi$
$888$		0			0
$889$	−84.1955	−	48.6103i	−2.82383	−	1.63034i
$890$			32.0328i			1.07374i
$891$		0			0
$892$	13.4778			0.451271
$893$	3.61015	−	6.25296i	0.120809	−	0.209247i
$894$		0			0
$895$	−30.5431	+	17.6341i	−1.02094	+	0.589442i
$896$	−4.22182	+	2.43747i	−0.141041	+	0.0814301i
$897$		0			0
$898$	−11.1056	+	19.2355i	−0.370599	+	0.641896i
$899$			50.9244i			1.69843i
$900$		0			0
$901$	−4.65490			−0.155077
$902$	−9.77468	+	22.0711i	−0.325461	+	0.734887i
$903$		0			0
$904$	−6.06365	−	10.5025i	−0.201674	−	0.349309i
$905$	−0.844716	+	0.487697i	−0.0280793	+	0.0162116i
$906$		0			0
$907$	−18.1325	+	31.4065i	−0.602081	+	1.04284i	0.390424	+	0.920635i	$0.372328\pi$
$907$	−18.1325	+	31.4065i	−0.602081	+	1.04284i	−0.992505	+	0.122200i	$0.961005\pi$
$908$			15.5611i			0.516414i
$909$		0			0
$910$	−11.7837			−0.390625
$911$	11.9582	−	20.7121i	0.396192	−	0.686224i	−0.597061	−	0.802196i	$-0.703665\pi$
$911$	11.9582	−	20.7121i	0.396192	−	0.686224i	0.993253	+	0.115972i	$0.0369982\pi$
$912$		0			0
$913$	47.7558	−	27.5718i	1.58049	−	0.912495i
$914$	−5.18852	+	2.99559i	−0.171621	+	0.0990854i
$915$		0			0
$916$	−19.7946	−	11.4284i	−0.654032	−	0.377606i
$917$		−	20.1252i		−	0.664592i
$918$		0			0
$919$		−	22.1114i		−	0.729387i	−0.931128	−	0.364693i	$-0.881174\pi$
$919$		−	22.1114i		−	0.729387i	0.931128	−	0.364693i	$-0.118826\pi$
$920$	9.39773	−	16.2773i	0.309834	−	0.536648i
$921$		0			0
$922$	−10.3050	−	17.8487i	−0.339376	−	0.587817i
$923$	2.37232	+	4.10898i	0.0780859	+	0.135249i
$924$		0			0
$925$	1.92438	−	3.33312i	0.0632732	−	0.109592i
$926$			3.02065i			0.0992647i
$927$		0			0
$928$			9.11454i			0.299199i
$929$	−19.5249	−	11.2727i	−0.640591	−	0.369845i	0.144251	−	0.989541i	$-0.453923\pi$
$929$	−19.5249	−	11.2727i	−0.640591	−	0.369845i	−0.784842	+	0.619696i	$0.787256\pi$
$930$		0			0
$931$	−120.128	+	69.3562i	−3.93705	+	2.27306i
$932$	5.46395	−	3.15461i	0.178978	−	0.103333i
$933$		0			0
$934$	−19.1965	+	33.2492i	−0.628127	+	1.08795i
$935$	−15.9994			−0.523236
$936$		0			0
$937$		−	30.5206i		−	0.997063i	−0.866872	−	0.498532i	$-0.833873\pi$
$937$		−	30.5206i		−	0.997063i	0.866872	−	0.498532i	$-0.166127\pi$
$938$	8.63094	−	14.9492i	0.281810	−	0.488109i
$939$		0			0
$940$	−1.79061	+	1.03381i	−0.0584034	+	0.0337192i
$941$	−1.50505	−	2.60683i	−0.0490634	−	0.0849803i	0.840451	−	0.541888i	$-0.182290\pi$
$941$	−1.50505	−	2.60683i	−0.0490634	−	0.0849803i	−0.889514	+	0.456908i	$0.848957\pi$
$942$		0			0
$943$	46.4438	+	20.5687i	1.51242	+	0.669808i
$944$	−3.99569			−0.130049
$945$		0			0
$946$			23.9694i			0.779313i
$947$	11.2653	−	19.5120i	0.366072	−	0.634055i	−0.622876	−	0.782321i	$-0.714036\pi$
$947$	11.2653	−	19.5120i	0.366072	−	0.634055i	0.988948	+	0.148266i	$0.0473691\pi$
$948$		0			0
$949$	1.89828	−	1.09597i	0.0616208	−	0.0355768i
$950$	−4.39783	+	2.53909i	−0.142684	+	0.0823789i
$951$		0			0
$952$	4.36609	−	7.56230i	0.141506	−	0.245095i
$953$	8.27459			0.268040			0.134020	−	0.990979i	$-0.457211\pi$
$953$	8.27459			0.268040			0.134020	+	0.990979i	$0.457211\pi$
$954$		0			0
$955$			10.3826i			0.335972i
$956$	15.9212	+	9.19209i	0.514927	+	0.297293i
$957$		0			0
$958$	−14.8658	+	8.58280i	−0.480293	+	0.277298i
$959$	16.6440	+	28.8282i	0.537461	+	0.930911i
$960$		0			0
$961$	−0.108229	+	0.187458i	−0.00349125	+	0.00604702i
$962$			6.39748i			0.206263i
$963$		0			0
$964$	−19.4651			−0.626929
$965$	−27.7023	−	15.9939i	−0.891768	−	0.514863i
$966$		0			0
$967$	−2.43201	+	1.40412i	−0.0782082	+	0.0451535i	−0.538594	−	0.842565i	$-0.681044\pi$
$967$	−2.43201	+	1.40412i	−0.0782082	+	0.0451535i	0.460386	+	0.887719i	$0.347711\pi$
$968$	−1.60583	−	2.78138i	−0.0516134	−	0.0893970i
$969$		0			0
$970$	−3.50665	−	2.02457i	−0.112592	−	0.0650049i
$971$		−	33.4875i		−	1.07467i	−0.843370	−	0.537333i	$-0.819432\pi$
$971$		−	33.4875i		−	1.07467i	0.843370	−	0.537333i	$-0.180568\pi$
$972$		0			0
$973$			90.6732i			2.90685i
$974$	4.41984	−	7.65539i	0.141621	−	0.245294i
$975$		0			0
$976$	−0.584806	−	1.01291i	−0.0187192	−	0.0324226i
$977$	26.2539	−	15.1577i	0.839937	−	0.484938i	−0.0173059	−	0.999850i	$-0.505509\pi$
$977$	26.2539	−	15.1577i	0.839937	−	0.484938i	0.857243	+	0.514913i	$0.172176\pi$
$978$		0			0
$979$	25.4836	−	44.1388i	0.814458	−	1.41068i
$980$	39.7220			1.26887
$981$		0			0
$982$	36.8185			1.17493
$983$	−9.39214	+	16.2677i	−0.299563	+	0.518858i	−0.976036	−	0.217609i	$-0.930174\pi$
$983$	−9.39214	+	16.2677i	−0.299563	+	0.518858i	0.676473	+	0.736467i	$0.263507\pi$
$984$		0			0
$985$	13.9990	+	24.2469i	0.446044	+	0.772571i
$986$	−8.16316	−	14.1390i	−0.259968	−	0.450278i
$987$		0			0
$988$	4.22052	−	7.31016i	0.134273	−	0.232567i
$989$	50.4384			1.60385
$990$		0			0
$991$		−	9.81733i		−	0.311858i	−0.987768	−	0.155929i	$-0.950163\pi$
$991$		−	9.81733i		−	0.311858i	0.987768	−	0.155929i	$-0.0498371\pi$
$992$	−2.79358	+	4.83863i	−0.0886964	+	0.153627i
$993$		0			0
$994$	−11.3359	−	19.6344i	−0.359554	−	0.622766i
$995$	2.04293	−	1.17949i	0.0647652	−	0.0373922i
$996$		0			0
$997$	7.91332	+	4.56875i	0.250617	+	0.144694i	0.620047	−	0.784565i	$-0.287114\pi$
$997$	7.91332	+	4.56875i	0.250617	+	0.144694i	−0.369430	+	0.929259i	$0.620447\pi$
$998$			0.151414i			0.00479292i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2214.2.i.b.1639.13		36
3.2	odd	2		738.2.i.b.655.13	yes	36
9.4	even	3	inner	2214.2.i.b.901.14		36
9.5	odd	6		738.2.i.b.409.6	✓	36
41.40	even	2	inner	2214.2.i.b.1639.14		36
123.122	odd	2		738.2.i.b.655.6	yes	36
369.40	even	6	inner	2214.2.i.b.901.13		36
369.122	odd	6		738.2.i.b.409.13	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
738.2.i.b.409.6	✓	36	9.5	odd	6
738.2.i.b.409.13	yes	36	369.122	odd	6
738.2.i.b.655.6	yes	36	123.122	odd	2
738.2.i.b.655.13	yes	36	3.2	odd	2
2214.2.i.b.901.13		36	369.40	even	6	inner
2214.2.i.b.901.14		36	9.4	even	3	inner
2214.2.i.b.1639.13		36	1.1	even	1	trivial
2214.2.i.b.1639.14		36	41.40	even	2	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2214 = 2 \cdot 3^{3} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2214.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.18467 + 2.05191i) q^{5} +(-4.22182 - 2.43747i) q^{7} -1.00000 q^{8} +2.36934 q^{10} +(-3.26477 - 1.88492i) q^{11} +(0.883519 - 0.510100i) q^{13} +(-4.22182 + 2.43747i) q^{14} +(-0.500000 + 0.866025i) q^{16} -1.79124i q^{17} +8.27391i q^{19} +(1.18467 - 2.05191i) q^{20} +(-3.26477 + 1.88492i) q^{22} +(3.96640 + 6.87000i) q^{23} +(-0.306879 + 0.531530i) q^{25} -1.02020i q^{26} +4.87494i q^{28} +(7.89342 + 4.55727i) q^{29} +(2.79358 + 4.83863i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.55126 - 0.895620i) q^{34} -11.5504i q^{35} -6.27081 q^{37} +(7.16542 + 4.13696i) q^{38} +(-1.18467 - 2.05191i) q^{40} +(5.17282 - 3.77385i) q^{41} +(3.17911 - 5.50637i) q^{43} +3.76984i q^{44} +7.93279 q^{46} +(-0.755744 - 0.436329i) q^{47} +(8.38252 + 14.5189i) q^{49} +(0.306879 + 0.531530i) q^{50} +(-0.883519 - 0.510100i) q^{52} -2.59870i q^{53} -8.93201i q^{55} +(4.22182 + 2.43747i) q^{56} +(7.89342 - 4.55727i) q^{58} +(1.99784 + 3.46037i) q^{59} +(-0.584806 + 1.01291i) q^{61} +5.58717 q^{62} +1.00000 q^{64} +(2.09335 + 1.20860i) q^{65} +(-3.06655 + 1.77047i) q^{67} +(-1.55126 + 0.895620i) q^{68} +(-10.0029 - 5.77519i) q^{70} +4.65070i q^{71} +2.14855 q^{73} +(-3.13541 + 5.43068i) q^{74} +(7.16542 - 4.13696i) q^{76} +(9.18886 + 15.9156i) q^{77} +(2.47565 + 1.42931i) q^{79} -2.36934 q^{80} +(-0.681841 - 6.36672i) q^{82} +(-7.31381 + 12.6679i) q^{83} +(3.67546 - 2.12203i) q^{85} +(-3.17911 - 5.50637i) q^{86} +(3.26477 + 1.88492i) q^{88} +13.5197i q^{89} -4.97341 q^{91} +(3.96640 - 6.87000i) q^{92} +(-0.755744 + 0.436329i) q^{94} +(-16.9773 + 9.80184i) q^{95} +(-1.48001 - 0.854487i) q^{97} +16.7650 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{2} - 18 q^{4} - 4 q^{5} - 36 q^{8} - 8 q^{10} - 18 q^{16} - 4 q^{20} + 4 q^{23} - 26 q^{25} + 8 q^{31} + 18 q^{32} - 60 q^{37} + 4 q^{40} + 6 q^{41} + 6 q^{43} + 8 q^{46} + 38 q^{49} + 26 q^{50}+ \cdots + 76 q^{98}+O(q^{100}) \) 36 * q + 18 * q^2 - 18 * q^4 - 4 * q^5 - 36 * q^8 - 8 * q^10 - 18 * q^16 - 4 * q^20 + 4 * q^23 - 26 * q^25 + 8 * q^31 + 18 * q^32 - 60 * q^37 + 4 * q^40 + 6 * q^41 + 6 * q^43 + 8 * q^46 + 38 * q^49 + 26 * q^50 - 22 * q^59 - 46 * q^61 + 16 * q^62 + 36 * q^64 + 64 * q^73 - 30 * q^74 + 2 * q^77 + 8 * q^80 + 12 * q^82 - 68 * q^83 - 6 * q^86 + 36 * q^91 + 4 * q^92 + 76 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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