LMFDB - Embedded newform 384.2.o.a.143.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(47,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3, 4]))

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

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

chi := DirichletCharacter("384.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.o (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			143.6
Character	$\chi$	$=$	384.143
Dual form			384.2.o.a.239.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.345141 + 1.69731i) q^{3} +(-1.56013 + 3.76650i) q^{5} +(0.838552 - 0.838552i) q^{7} +(-2.76175 - 1.17163i) q^{9} +O(q^{10})$	\(q+(-0.345141 + 1.69731i) q^{3} +(-1.56013 + 3.76650i) q^{5} +(0.838552 - 0.838552i) q^{7} +(-2.76175 - 1.17163i) q^{9} +(-0.249049 + 0.601256i) q^{11} +(-2.05771 + 0.852332i) q^{13} +(-5.85446 - 3.94801i) q^{15} +3.23677 q^{17} +(-1.47818 - 3.56865i) q^{19} +(1.13387 + 1.71271i) q^{21} +(-2.58369 + 2.58369i) q^{23} +(-8.21694 - 8.21694i) q^{25} +(2.94182 - 4.28319i) q^{27} +(-3.52027 + 1.45815i) q^{29} +7.63408i q^{31} +(-0.934564 - 0.630232i) q^{33} +(1.85015 + 4.46665i) q^{35} +(0.579146 + 0.239890i) q^{37} +(-0.736474 - 3.78676i) q^{39} +(3.54554 + 3.54554i) q^{41} +(3.19595 + 1.32381i) q^{43} +(8.72163 - 8.57424i) q^{45} +5.96658i q^{47} +5.59366i q^{49} +(-1.11714 + 5.49382i) q^{51} +(0.762825 + 0.315973i) q^{53} +(-1.87608 - 1.87608i) q^{55} +(6.56731 - 1.27725i) q^{57} +(5.86827 + 2.43072i) q^{59} +(2.68247 + 6.47607i) q^{61} +(-3.29834 + 1.33340i) q^{63} -9.08011i q^{65} +(-4.78575 + 1.98232i) q^{67} +(-3.49360 - 5.27708i) q^{69} +(-10.2094 - 10.2094i) q^{71} +(8.09458 - 8.09458i) q^{73} +(16.7827 - 11.1107i) q^{75} +(0.295345 + 0.713025i) q^{77} +11.5343 q^{79} +(6.25458 + 6.47149i) q^{81} +(0.998651 - 0.413655i) q^{83} +(-5.04979 + 12.1913i) q^{85} +(-1.25994 - 6.47828i) q^{87} +(-10.4124 + 10.4124i) q^{89} +(-1.01077 + 2.44022i) q^{91} +(-12.9574 - 2.63484i) q^{93} +15.7475 q^{95} +9.21596 q^{97} +(1.39226 - 1.36873i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{3} + 8 q^{7} - 4 q^{9}+O(q^{10}) $ 56 * q + 4 * q^3 + 8 * q^7 - 4 * q^9	$ 56 q + 4 q^{3} + 8 q^{7} - 4 q^{9} - 8 q^{13} + 8 q^{15} + 8 q^{19} - 4 q^{21} - 8 q^{25} + 28 q^{27} - 8 q^{33} - 8 q^{37} + 28 q^{39} + 8 q^{43} - 4 q^{45} + 16 q^{51} - 24 q^{55} - 4 q^{57} - 40 q^{61} - 56 q^{67} - 4 q^{69} - 8 q^{73} - 16 q^{75} - 16 q^{79} - 48 q^{85} - 52 q^{87} - 40 q^{91} + 8 q^{93} - 16 q^{97} - 60 q^{99}+O(q^{100}) $ 56 * q + 4 * q^3 + 8 * q^7 - 4 * q^9 - 8 * q^13 + 8 * q^15 + 8 * q^19 - 4 * q^21 - 8 * q^25 + 28 * q^27 - 8 * q^33 - 8 * q^37 + 28 * q^39 + 8 * q^43 - 4 * q^45 + 16 * q^51 - 24 * q^55 - 4 * q^57 - 40 * q^61 - 56 * q^67 - 4 * q^69 - 8 * q^73 - 16 * q^75 - 16 * q^79 - 48 * q^85 - 52 * q^87 - 40 * q^91 + 8 * q^93 - 16 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$-1$	$e\left(\frac{1}{8}\right)$	$-1$

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
$3$	−0.345141	+	1.69731i	−0.199268	+	0.979945i
$3$	−0.345141	+	1.69731i	−0.199268	+	0.979945i
$4$		0			0
$5$	−1.56013	+	3.76650i	−0.697713	+	1.68443i	0.0309186	+	0.999522i	$0.490157\pi$
$5$	−1.56013	+	3.76650i	−0.697713	+	1.68443i	−0.728631	+	0.684906i	$0.759843\pi$
$6$		0			0
$7$	0.838552	−	0.838552i	0.316943	−	0.316943i	−0.530649	−	0.847592i	$-0.678052\pi$
$7$	0.838552	−	0.838552i	0.316943	−	0.316943i	0.847592	+	0.530649i	$0.178052\pi$
$8$		0			0
$9$	−2.76175	−	1.17163i	−0.920585	−	0.390542i
$10$		0			0
$11$	−0.249049	+	0.601256i	−0.0750910	+	0.181286i	−0.956968	−	0.290194i	$-0.906280\pi$
$11$	−0.249049	+	0.601256i	−0.0750910	+	0.181286i	0.881877	+	0.471480i	$0.156280\pi$
$12$		0			0
$13$	−2.05771	+	0.852332i	−0.570706	+	0.236394i	−0.649326	−	0.760510i	$-0.724949\pi$
$13$	−2.05771	+	0.852332i	−0.570706	+	0.236394i	0.0786194	+	0.996905i	$0.474949\pi$
$14$		0			0
$15$	−5.85446	−	3.94801i	−1.51162	−	1.01937i
$16$		0			0
$17$	3.23677			0.785032			0.392516	−	0.919745i	$-0.371605\pi$
$17$	3.23677			0.785032			0.392516	+	0.919745i	$0.371605\pi$
$18$		0			0
$19$	−1.47818	−	3.56865i	−0.339119	−	0.818705i	−0.997801	−	0.0662838i	$-0.978886\pi$
$19$	−1.47818	−	3.56865i	−0.339119	−	0.818705i	0.658682	−	0.752421i	$-0.271114\pi$
$20$		0			0
$21$	1.13387	+	1.71271i	0.247430	+	0.373743i
$22$		0			0
$23$	−2.58369	+	2.58369i	−0.538737	+	0.538737i	−0.923158	−	0.384421i	$-0.874401\pi$
$23$	−2.58369	+	2.58369i	−0.538737	+	0.538737i	0.384421	+	0.923158i	$0.374401\pi$
$24$		0			0
$25$	−8.21694	−	8.21694i	−1.64339	−	1.64339i
$26$		0			0
$27$	2.94182	−	4.28319i	0.566153	−	0.824300i
$28$		0			0
$29$	−3.52027	+	1.45815i	−0.653698	+	0.270771i	−0.684784	−	0.728746i	$-0.740104\pi$
$29$	−3.52027	+	1.45815i	−0.653698	+	0.270771i	0.0310857	+	0.999517i	$0.490104\pi$
$30$		0			0
$31$			7.63408i			1.37112i	0.728015	+	0.685561i	$0.240443\pi$
$31$			7.63408i			1.37112i	−0.728015	+	0.685561i	$0.759557\pi$
$32$		0			0
$33$	−0.934564	−	0.630232i	−0.162687	−	0.109709i
$34$		0			0
$35$	1.85015	+	4.46665i	0.312732	+	0.755002i
$36$		0			0
$37$	0.579146	+	0.239890i	0.0952110	+	0.0394377i	0.429781	−	0.902933i	$-0.358591\pi$
$37$	0.579146	+	0.239890i	0.0952110	+	0.0394377i	−0.334570	+	0.942371i	$0.608591\pi$
$38$		0			0
$39$	−0.736474	−	3.78676i	−0.117930	−	0.606367i
$40$		0			0
$41$	3.54554	+	3.54554i	0.553720	+	0.553720i	0.927512	−	0.373792i	$-0.121943\pi$
$41$	3.54554	+	3.54554i	0.553720	+	0.553720i	−0.373792	+	0.927512i	$0.621943\pi$
$42$		0			0
$43$	3.19595	+	1.32381i	0.487378	+	0.201879i	0.612820	−	0.790222i	$-0.290035\pi$
$43$	3.19595	+	1.32381i	0.487378	+	0.201879i	−0.125442	+	0.992101i	$0.540035\pi$
$44$		0			0
$45$	8.72163	−	8.57424i	1.30014	−	1.27817i
$46$		0			0
$47$			5.96658i			0.870315i	0.900354	+	0.435158i	$0.143307\pi$
$47$			5.96658i			0.870315i	−0.900354	+	0.435158i	$0.856693\pi$
$48$		0			0
$49$			5.59366i			0.799095i
$50$		0			0
$51$	−1.11714	+	5.49382i	−0.156431	+	0.769288i
$52$		0			0
$53$	0.762825	+	0.315973i	0.104782	+	0.0434022i	0.434459	−	0.900692i	$-0.356940\pi$
$53$	0.762825	+	0.315973i	0.104782	+	0.0434022i	−0.329677	+	0.944094i	$0.606940\pi$
$54$		0			0
$55$	−1.87608	−	1.87608i	−0.252971	−	0.252971i
$56$		0			0
$57$	6.56731	−	1.27725i	0.869862	−	0.169176i
$58$		0			0
$59$	5.86827	+	2.43072i	0.763984	+	0.316452i	0.730433	−	0.682985i	$-0.239318\pi$
$59$	5.86827	+	2.43072i	0.763984	+	0.316452i	0.0335508	+	0.999437i	$0.489318\pi$
$60$		0			0
$61$	2.68247	+	6.47607i	0.343456	+	0.829175i	0.997361	+	0.0725992i	$0.0231294\pi$
$61$	2.68247	+	6.47607i	0.343456	+	0.829175i	−0.653906	+	0.756576i	$0.726871\pi$
$62$		0			0
$63$	−3.29834	+	1.33340i	−0.415552	+	0.167993i
$64$		0			0
$65$		−	9.08011i		−	1.12625i
$66$		0			0
$67$	−4.78575	+	1.98232i	−0.584673	+	0.242179i	−0.655357	−	0.755319i	$-0.727482\pi$
$67$	−4.78575	+	1.98232i	−0.584673	+	0.242179i	0.0706842	+	0.997499i	$0.477482\pi$
$68$		0			0
$69$	−3.49360	−	5.27708i	−0.420580	−	0.635285i
$70$		0			0
$71$	−10.2094	−	10.2094i	−1.21163	−	1.21163i	−0.970489	−	0.241145i	$-0.922477\pi$
$71$	−10.2094	−	10.2094i	−1.21163	−	1.21163i	−0.241145	−	0.970489i	$-0.577523\pi$
$72$		0			0
$73$	8.09458	−	8.09458i	0.947399	−	0.947399i	−0.0512851	−	0.998684i	$-0.516332\pi$
$73$	8.09458	−	8.09458i	0.947399	−	0.947399i	0.998684	+	0.0512851i	$0.0163317\pi$
$74$		0			0
$75$	16.7827	−	11.1107i	1.93790	−	1.28296i
$76$		0			0
$77$	0.295345	+	0.713025i	0.0336576	+	0.0812567i
$78$		0			0
$79$	11.5343			1.29771			0.648857	−	0.760910i	$-0.275247\pi$
$79$	11.5343			1.29771			0.648857	+	0.760910i	$0.275247\pi$
$80$		0			0
$81$	6.25458	+	6.47149i	0.694953	+	0.719055i
$82$		0			0
$83$	0.998651	−	0.413655i	0.109616	−	0.0454045i	−0.327201	−	0.944955i	$-0.606106\pi$
$83$	0.998651	−	0.413655i	0.109616	−	0.0454045i	0.436818	+	0.899550i	$0.356106\pi$
$84$		0			0
$85$	−5.04979	+	12.1913i	−0.547727	+	1.32233i
$86$		0			0
$87$	−1.25994	−	6.47828i	−0.135080	−	0.694544i
$88$		0			0
$89$	−10.4124	+	10.4124i	−1.10372	+	1.10372i	−0.109759	+	0.993958i	$0.535008\pi$
$89$	−10.4124	+	10.4124i	−1.10372	+	1.10372i	−0.993958	+	0.109759i	$0.964992\pi$
$90$		0			0
$91$	−1.01077	+	2.44022i	−0.105958	+	0.255805i
$92$		0			0
$93$	−12.9574	−	2.63484i	−1.34362	−	0.273220i
$94$		0			0
$95$	15.7475			1.61566
$96$		0			0
$97$	9.21596			0.935739			0.467870	−	0.883797i	$-0.345022\pi$
$97$	9.21596			0.935739			0.467870	+	0.883797i	$0.345022\pi$
$98$		0			0
$99$	1.39226	−	1.36873i	0.139927	−	0.137563i
$100$		0			0
$101$	−1.61830	+	3.90691i	−0.161026	+	0.388752i	−0.983714	−	0.179742i	$-0.942474\pi$
$101$	−1.61830	+	3.90691i	−0.161026	+	0.388752i	0.822687	+	0.568494i	$0.192474\pi$
$102$		0			0
$103$	4.29846	−	4.29846i	0.423540	−	0.423540i	−0.462881	−	0.886421i	$-0.653184\pi$
$103$	4.29846	−	4.29846i	0.423540	−	0.423540i	0.886421	+	0.462881i	$0.153184\pi$
$104$		0			0
$105$	−8.21988	+	1.59866i	−0.802178	+	0.156013i
$106$		0			0
$107$	−2.82811	+	6.82767i	−0.273404	+	0.660055i	−0.999624	−	0.0274065i	$-0.991275\pi$
$107$	−2.82811	+	6.82767i	−0.273404	+	0.660055i	0.726221	+	0.687462i	$0.241275\pi$
$108$		0			0
$109$	12.4025	−	5.13729i	1.18794	−	0.492063i	0.300859	−	0.953669i	$-0.402727\pi$
$109$	12.4025	−	5.13729i	1.18794	−	0.492063i	0.887085	+	0.461606i	$0.152727\pi$
$110$		0			0
$111$	−0.607056	+	0.900196i	−0.0576192	+	0.0854429i
$112$		0			0
$113$	−3.42949			−0.322619			−0.161310	−	0.986904i	$-0.551572\pi$
$113$	−3.42949			−0.322619			−0.161310	+	0.986904i	$0.551572\pi$
$114$		0			0
$115$	−5.70056	−	13.7624i	−0.531580	−	1.28335i
$116$		0			0
$117$	6.68151	+	0.0569391i	0.617706	+	0.00526402i
$118$		0			0
$119$	2.71420	−	2.71420i	0.248810	−	0.248810i
$120$		0			0
$121$	7.47869	+	7.47869i	0.679881	+	0.679881i
$122$		0			0
$123$	−7.24160	+	4.79418i	−0.652953	+	0.432277i
$124$		0			0
$125$	24.9361	−	10.3289i	2.23035	−	0.923842i
$126$		0			0
$127$			0.724490i			0.0642881i	0.999483	+	0.0321441i	$0.0102335\pi$
$127$			0.724490i			0.0642881i	−0.999483	+	0.0321441i	$0.989766\pi$
$128$		0			0
$129$	−3.34997	+	4.96764i	−0.294949	+	0.437376i
$130$		0			0
$131$	−1.44273	−	3.48306i	−0.126052	−	0.304317i	0.848238	−	0.529616i	$-0.177664\pi$
$131$	−1.44273	−	3.48306i	−0.126052	−	0.304317i	−0.974290	+	0.225299i	$0.927664\pi$
$132$		0			0
$133$	−4.23204	−	1.75297i	−0.366964	−	0.152001i
$134$		0			0
$135$	11.5430	+	17.7627i	0.993462	+	1.52877i
$136$		0			0
$137$	−2.20990	−	2.20990i	−0.188805	−	0.188805i	0.606375	−	0.795179i	$-0.292623\pi$
$137$	−2.20990	−	2.20990i	−0.188805	−	0.188805i	−0.795179	+	0.606375i	$0.792623\pi$
$138$		0			0
$139$	−4.01991	−	1.66510i	−0.340964	−	0.141232i	0.205629	−	0.978630i	$-0.434076\pi$
$139$	−4.01991	−	1.66510i	−0.340964	−	0.141232i	−0.546594	+	0.837398i	$0.684076\pi$
$140$		0			0
$141$	−10.1272	−	2.05931i	−0.852861	−	0.173426i
$142$		0			0
$143$		−	1.44948i		−	0.121212i
$144$		0			0
$145$		−	15.5340i		−	1.29003i
$146$		0			0
$147$	−9.49420	−	1.93060i	−0.783069	−	0.159234i
$148$		0			0
$149$	−5.47285	−	2.26693i	−0.448353	−	0.185714i	0.147070	−	0.989126i	$-0.453016\pi$
$149$	−5.47285	−	2.26693i	−0.448353	−	0.185714i	−0.595423	+	0.803412i	$0.703016\pi$
$150$		0			0
$151$	5.81381	+	5.81381i	0.473121	+	0.473121i	0.902923	−	0.429802i	$-0.141417\pi$
$151$	5.81381	+	5.81381i	0.473121	+	0.473121i	−0.429802	+	0.902923i	$0.641417\pi$
$152$		0			0
$153$	−8.93916	−	3.79229i	−0.722688	−	0.306588i
$154$		0			0
$155$	−28.7537	−	11.9102i	−2.30956	−	0.956649i
$156$		0			0
$157$	−3.37305	−	8.14326i	−0.269199	−	0.649903i	0.730247	−	0.683183i	$-0.239405\pi$
$157$	−3.37305	−	8.14326i	−0.269199	−	0.649903i	−0.999446	+	0.0332797i	$0.989405\pi$
$158$		0			0
$159$	−0.799588	+	1.18570i	−0.0634114	+	0.0940321i
$160$		0			0
$161$			4.33312i			0.341498i
$162$		0			0
$163$	−13.8401	+	5.73275i	−1.08404	+	0.449024i	−0.851924	−	0.523665i	$-0.824564\pi$
$163$	−13.8401	+	5.73275i	−1.08404	+	0.449024i	−0.232114	+	0.972688i	$0.574564\pi$
$164$		0			0
$165$	3.83181	−	2.53679i	0.298306	−	0.197489i
$166$		0			0
$167$	6.72756	+	6.72756i	0.520594	+	0.520594i	0.917751	−	0.397157i	$-0.130003\pi$
$167$	6.72756	+	6.72756i	0.520594	+	0.520594i	−0.397157	+	0.917751i	$0.630003\pi$
$168$		0			0
$169$	−5.68468	+	5.68468i	−0.437283	+	0.437283i
$170$		0			0
$171$	−0.0987485	+	11.5876i	−0.00755148	+	0.886128i
$172$		0			0
$173$	−0.275804	−	0.665850i	−0.0209690	−	0.0506236i	0.913048	−	0.407852i	$-0.133722\pi$
$173$	−0.275804	−	0.665850i	−0.0209690	−	0.0506236i	−0.934017	+	0.357228i	$0.883722\pi$
$174$		0			0
$175$	−13.7807			−1.04172
$176$		0			0
$177$	−6.15107	+	9.12136i	−0.462343	+	0.685603i
$178$		0			0
$179$	11.9198	−	4.93735i	0.890928	−	0.369035i	0.110203	−	0.993909i	$-0.464850\pi$
$179$	11.9198	−	4.93735i	0.890928	−	0.369035i	0.780725	+	0.624875i	$0.214850\pi$
$180$		0			0
$181$	−2.66842	+	6.44214i	−0.198342	+	0.478841i	−0.991489	−	0.130190i	$-0.958441\pi$
$181$	−2.66842	+	6.44214i	−0.198342	+	0.478841i	0.793147	+	0.609030i	$0.208441\pi$
$182$		0			0
$183$	−11.9178	+	2.31784i	−0.880986	+	0.171340i
$184$		0			0
$185$	−1.80709	+	1.80709i	−0.132860	+	0.132860i
$186$		0			0
$187$	−0.806113	+	1.94613i	−0.0589488	+	0.142315i
$188$		0			0
$189$	−1.12481	−	6.05854i	−0.0818180	−	0.440694i
$190$		0			0
$191$	−1.62308			−0.117442			−0.0587210	−	0.998274i	$-0.518702\pi$
$191$	−1.62308			−0.117442			−0.0587210	+	0.998274i	$0.518702\pi$
$192$		0			0
$193$	−10.3575			−0.745548			−0.372774	−	0.927922i	$-0.621593\pi$
$193$	−10.3575			−0.745548			−0.372774	+	0.927922i	$0.621593\pi$
$194$		0			0
$195$	15.4118	+	3.13392i	1.10366	+	0.224425i
$196$		0			0
$197$	0.784033	−	1.89282i	0.0558601	−	0.134858i	−0.893486	−	0.449092i	$-0.851748\pi$
$197$	0.784033	−	1.89282i	0.0558601	−	0.134858i	0.949346	+	0.314234i	$0.101748\pi$
$198$		0			0
$199$	8.78498	−	8.78498i	0.622751	−	0.622751i	−0.323483	−	0.946234i	$-0.604854\pi$
$199$	8.78498	−	8.78498i	0.622751	−	0.622751i	0.946234	+	0.323483i	$0.104854\pi$
$200$		0			0
$201$	−1.71287	−	8.80711i	−0.120816	−	0.621206i
$202$		0			0
$203$	−1.72920	+	4.17466i	−0.121366	+	0.293004i
$204$		0			0
$205$	−18.8858	+	7.82274i	−1.31904	+	0.546364i
$206$		0			0
$207$	10.1626	−	4.10840i	0.706353	−	0.285553i
$208$		0			0
$209$	2.51382			0.173884
$210$		0			0
$211$	9.81540	+	23.6965i	0.675720	+	1.63133i	0.771729	+	0.635951i	$0.219392\pi$
$211$	9.81540	+	23.6965i	0.675720	+	1.63133i	−0.0960096	+	0.995380i	$0.530608\pi$
$212$		0			0
$213$	20.8523	−	13.8049i	1.42877	−	0.945896i
$214$		0			0
$215$	−9.97223	+	9.97223i	−0.680100	+	0.680100i
$216$		0			0
$217$	6.40157	+	6.40157i	0.434567	+	0.434567i
$218$		0			0
$219$	10.9453	+	16.5328i	0.739613	+	1.11718i
$220$		0			0
$221$	−6.66034	+	2.75880i	−0.448023	+	0.185577i
$222$		0			0
$223$		−	16.3840i		−	1.09715i	−0.836101	−	0.548576i	$-0.815170\pi$
$223$		−	16.3840i		−	1.09715i	0.836101	−	0.548576i	$-0.184830\pi$
$224$		0			0
$225$	13.0660	+	32.3204i	0.871065	+	2.15469i
$226$		0			0
$227$	−9.61652	−	23.2163i	−0.638271	−	1.54092i	−0.828981	−	0.559276i	$-0.811079\pi$
$227$	−9.61652	−	23.2163i	−0.638271	−	1.54092i	0.190710	−	0.981646i	$-0.438921\pi$
$228$		0			0
$229$	−11.2556	−	4.66223i	−0.743792	−	0.308089i	−0.0215864	−	0.999767i	$-0.506872\pi$
$229$	−11.2556	−	4.66223i	−0.743792	−	0.308089i	−0.722206	+	0.691678i	$0.756872\pi$
$230$		0			0
$231$	−1.31216	+	0.255198i	−0.0863340	+	0.0167908i
$232$		0			0
$233$	13.5410	+	13.5410i	0.887101	+	0.887101i	0.994244	−	0.107143i	$-0.0341701\pi$
$233$	13.5410	+	13.5410i	0.887101	+	0.887101i	−0.107143	+	0.994244i	$0.534170\pi$
$234$		0			0
$235$	−22.4731	−	9.30866i	−1.46598	−	0.607230i
$236$		0			0
$237$	−3.98098	+	19.5774i	−0.258592	+	1.27169i
$238$		0			0
$239$			19.1168i			1.23657i	0.785956	+	0.618283i	$0.212171\pi$
$239$			19.1168i			1.23657i	−0.785956	+	0.618283i	$0.787829\pi$
$240$		0			0
$241$			1.71219i			0.110292i	0.998478	+	0.0551460i	$0.0175624\pi$
$241$			1.71219i			0.110292i	−0.998478	+	0.0551460i	$0.982438\pi$
$242$		0			0
$243$	−13.1429	+	8.38241i	−0.843116	+	0.537732i
$244$		0			0
$245$	−21.0685	−	8.72686i	−1.34602	−	0.557539i
$246$		0			0
$247$	6.08335	+	6.08335i	0.387075	+	0.387075i
$248$		0			0
$249$	0.357427	+	1.83780i	0.0226510	+	0.116466i
$250$		0			0
$251$	25.5253	+	10.5729i	1.61115	+	0.667358i	0.992936	−	0.118655i	$-0.0378582\pi$
$251$	25.5253	+	10.5729i	1.61115	+	0.667358i	0.618210	+	0.786013i	$0.287858\pi$
$252$		0			0
$253$	−0.909996	−	2.19693i	−0.0572110	−	0.138120i
$254$		0			0
$255$	−18.9495	−	12.7788i	−1.18667	−	0.800239i
$256$		0			0
$257$		−	21.5264i		−	1.34278i	−0.741104	−	0.671391i	$-0.765697\pi$
$257$		−	21.5264i		−	1.34278i	0.741104	−	0.671391i	$-0.234303\pi$
$258$		0			0
$259$	0.686804	−	0.284483i	0.0426759	−	0.0176769i
$260$		0			0
$261$	11.4305	+	0.0974097i	0.707532	+	0.00602951i
$262$		0			0
$263$	−10.4924	−	10.4924i	−0.646988	−	0.646988i	0.305276	−	0.952264i	$-0.401251\pi$
$263$	−10.4924	−	10.4924i	−0.646988	−	0.646988i	−0.952264	+	0.305276i	$0.901251\pi$
$264$		0			0
$265$	−2.38022	+	2.38022i	−0.146216	+	0.146216i
$266$		0			0
$267$	−14.0794	−	21.2670i	−0.861647	−	1.30152i
$268$		0			0
$269$	−4.94856	−	11.9469i	−0.301719	−	0.728414i	−0.999922	−	0.0125138i	$-0.996017\pi$
$269$	−4.94856	−	11.9469i	−0.301719	−	0.728414i	0.698203	−	0.715900i	$-0.253983\pi$
$270$		0			0
$271$	−7.03570			−0.427388			−0.213694	−	0.976901i	$-0.568550\pi$
$271$	−7.03570			−0.427388			−0.213694	+	0.976901i	$0.568550\pi$
$272$		0			0
$273$	−3.79296	−	2.55782i	−0.229561	−	0.154806i
$274$		0			0
$275$	6.98690	−	2.89407i	0.421326	−	0.174519i
$276$		0			0
$277$	9.40456	−	22.7046i	0.565065	−	1.36419i	−0.340606	−	0.940206i	$-0.610632\pi$
$277$	9.40456	−	22.7046i	0.565065	−	1.36419i	0.905671	−	0.423982i	$-0.139368\pi$
$278$		0			0
$279$	8.94430	−	21.0835i	0.535481	−	1.26223i
$280$		0			0
$281$	13.7076	−	13.7076i	0.817727	−	0.817727i	−0.168051	−	0.985778i	$-0.553747\pi$
$281$	13.7076	−	13.7076i	0.817727	−	0.817727i	0.985778	+	0.168051i	$0.0537473\pi$
$282$		0			0
$283$	11.3422	−	27.3825i	0.674224	−	1.62772i	−0.100134	−	0.994974i	$-0.531927\pi$
$283$	11.3422	−	27.3825i	0.674224	−	1.62772i	0.774358	−	0.632747i	$-0.218073\pi$
$284$		0			0
$285$	−5.43511	+	26.7284i	−0.321948	+	1.58326i
$286$		0			0
$287$	5.94623			0.350995
$288$		0			0
$289$	−6.52333			−0.383725
$290$		0			0
$291$	−3.18081	+	15.6424i	−0.186462	+	0.916973i
$292$		0			0
$293$	4.07927	−	9.84823i	0.238314	−	0.575340i	−0.758795	−	0.651329i	$-0.774212\pi$
$293$	4.07927	−	9.84823i	0.238314	−	0.575340i	0.997109	+	0.0759896i	$0.0242116\pi$
$294$		0			0
$295$	−18.3106	+	18.3106i	−1.06608	+	1.06608i
$296$		0			0
$297$	1.84264	+	2.83551i	0.106921	+	0.164533i
$298$		0			0
$299$	3.11433	−	7.51865i	0.180106	−	0.434815i
$300$		0			0
$301$	3.79005	−	1.56989i	0.218455	−	0.0904871i
$302$		0			0
$303$	−6.07272	−	4.09520i	−0.348869	−	0.235263i
$304$		0			0
$305$	−28.5771			−1.63632
$306$		0			0
$307$	8.04114	+	19.4130i	0.458932	+	1.10796i	0.968830	+	0.247725i	$0.0796830\pi$
$307$	8.04114	+	19.4130i	0.458932	+	1.10796i	−0.509898	+	0.860235i	$0.670317\pi$
$308$		0			0
$309$	5.81226	+	8.77941i	0.330648	+	0.499443i
$310$		0			0
$311$	20.9205	−	20.9205i	1.18629	−	1.18629i	0.208210	−	0.978084i	$-0.433236\pi$
$311$	20.9205	−	20.9205i	1.18629	−	1.18629i	0.978084	−	0.208210i	$-0.0667638\pi$
$312$		0			0
$313$	−8.91198	−	8.91198i	−0.503735	−	0.503735i	0.408861	−	0.912596i	$-0.365926\pi$
$313$	−8.91198	−	8.91198i	−0.503735	−	0.503735i	−0.912596	+	0.408861i	$0.865926\pi$
$314$		0			0
$315$	0.123597	−	14.5035i	0.00696391	−	0.817179i
$316$		0			0
$317$	0.482452	−	0.199838i	0.0270972	−	0.0112240i	−0.369094	−	0.929392i	$-0.620332\pi$
$317$	0.482452	−	0.199838i	0.0270972	−	0.0112240i	0.396191	+	0.918168i	$0.370332\pi$
$318$		0			0
$319$		−	2.47974i		−	0.138839i
$320$		0			0
$321$	−10.6126	−	7.15671i	−0.592337	−	0.399448i
$322$		0			0
$323$	−4.78454	−	11.5509i	−0.266219	−	0.642710i
$324$		0			0
$325$	23.9116	+	9.90452i	1.32638	+	0.549404i
$326$		0			0
$327$	4.43897	+	22.8240i	0.245476	+	1.26217i
$328$		0			0
$329$	5.00329	+	5.00329i	0.275840	+	0.275840i
$330$		0			0
$331$	19.5132	+	8.08262i	1.07254	+	0.444261i	0.847887	−	0.530177i	$-0.177875\pi$
$331$	19.5132	+	8.08262i	1.07254	+	0.444261i	0.224654	+	0.974439i	$0.427875\pi$
$332$		0			0
$333$	−1.31840	−	1.34106i	−0.0722477	−	0.0734896i
$334$		0			0
$335$		−	21.1182i		−	1.15381i
$336$		0			0
$337$		−	10.2626i		−	0.559037i	−0.960140	−	0.279519i	$-0.909825\pi$
$337$		−	10.2626i		−	0.559037i	0.960140	−	0.279519i	$-0.0901749\pi$
$338$		0			0
$339$	1.18366	−	5.82092i	0.0642875	−	0.316149i
$340$		0			0
$341$	−4.59004	−	1.90126i	−0.248565	−	0.102959i
$342$		0			0
$343$	10.5604	+	10.5604i	0.570210	+	0.570210i
$344$		0			0
$345$	25.3266	−	4.92568i	1.36354	−	0.265190i
$346$		0			0
$347$	−4.24383	−	1.75785i	−0.227821	−	0.0943665i	0.265853	−	0.964014i	$-0.414346\pi$
$347$	−4.24383	−	1.75785i	−0.227821	−	0.0943665i	−0.493674	+	0.869647i	$0.664346\pi$
$348$		0			0
$349$	13.7021	+	33.0798i	0.733457	+	1.77072i	0.630716	+	0.776014i	$0.282761\pi$
$349$	13.7021	+	33.0798i	0.733457	+	1.77072i	0.102741	+	0.994708i	$0.467239\pi$
$350$		0			0
$351$	−2.40271	+	11.3210i	−0.128247	+	0.604269i
$352$		0			0
$353$		−	4.53983i		−	0.241631i	−0.992675	−	0.120815i	$-0.961449\pi$
$353$		−	4.53983i		−	0.241631i	0.992675	−	0.120815i	$-0.0385509\pi$
$354$		0			0
$355$	54.3817	−	22.5257i	2.88628	−	1.19554i
$356$		0			0
$357$	3.67007	+	5.54363i	0.194241	+	0.293400i
$358$		0			0
$359$	−2.86633	−	2.86633i	−0.151279	−	0.151279i	0.627410	−	0.778689i	$-0.284115\pi$
$359$	−2.86633	−	2.86633i	−0.151279	−	0.151279i	−0.778689	+	0.627410i	$0.784115\pi$
$360$		0			0
$361$	2.88477	−	2.88477i	0.151830	−	0.151830i
$362$		0			0
$363$	−15.2749	+	10.1125i	−0.801724	+	0.530768i
$364$		0			0
$365$	17.8596	+	43.1168i	0.934813	+	2.25684i
$366$		0			0
$367$	28.9994			1.51376			0.756878	−	0.653557i	$-0.226724\pi$
$367$	28.9994			1.51376			0.756878	+	0.653557i	$0.226724\pi$
$368$		0			0
$369$	−5.63786	−	13.9460i	−0.293495	−	0.725997i
$370$		0			0
$371$	0.904628	−	0.374709i	0.0469659	−	0.0194539i
$372$		0			0
$373$	7.55879	−	18.2485i	0.391379	−	0.944873i	−0.598261	−	0.801302i	$-0.704141\pi$
$373$	7.55879	−	18.2485i	0.391379	−	0.944873i	0.989640	−	0.143572i	$-0.0458587\pi$
$374$		0			0
$375$	8.92486	+	45.8893i	0.460878	+	2.36971i
$376$		0			0
$377$	6.00088	−	6.00088i	0.309061	−	0.309061i
$378$		0			0
$379$	−7.21366	+	17.4153i	−0.370541	+	0.894564i	0.623118	+	0.782128i	$0.285866\pi$
$379$	−7.21366	+	17.4153i	−0.370541	+	0.894564i	−0.993659	+	0.112437i	$0.964134\pi$
$380$		0			0
$381$	−1.22969	−	0.250052i	−0.0629988	−	0.0128105i
$382$		0			0
$383$	−18.2276			−0.931388			−0.465694	−	0.884946i	$-0.654195\pi$
$383$	−18.2276			−0.931388			−0.465694	+	0.884946i	$0.654195\pi$
$384$		0			0
$385$	−3.14638			−0.160354
$386$		0			0
$387$	−7.27543	−	7.40050i	−0.369831	−	0.376189i
$388$		0			0
$389$	0.747968	−	1.80575i	0.0379235	−	0.0915554i	−0.903783	−	0.427991i	$-0.859221\pi$
$389$	0.747968	−	1.80575i	0.0379235	−	0.0915554i	0.941706	+	0.336436i	$0.109221\pi$
$390$		0			0
$391$	−8.36281	+	8.36281i	−0.422926	+	0.422926i
$392$		0			0
$393$	6.40980	−	1.24662i	0.323332	−	0.0628837i
$394$		0			0
$395$	−17.9951	+	43.4440i	−0.905432	+	2.18591i
$396$		0			0
$397$	−7.44786	+	3.08500i	−0.373797	+	0.154832i	−0.561670	−	0.827361i	$-0.689841\pi$
$397$	−7.44786	+	3.08500i	−0.373797	+	0.154832i	0.187872	+	0.982193i	$0.439841\pi$
$398$		0			0
$399$	4.43599	−	6.57807i	0.222077	−	0.329316i
$400$		0			0
$401$	33.1951			1.65768			0.828842	−	0.559482i	$-0.189000\pi$
$401$	33.1951			1.65768			0.828842	+	0.559482i	$0.189000\pi$
$402$		0			0
$403$	−6.50677	−	15.7087i	−0.324125	−	0.782508i
$404$		0			0
$405$	−34.1328	+	13.4614i	−1.69607	+	0.668905i
$406$		0			0
$407$	−0.288471	+	0.288471i	−0.0142990	+	0.0142990i
$408$		0			0
$409$	24.3278	+	24.3278i	1.20293	+	1.20293i	0.973270	+	0.229664i	$0.0737629\pi$
$409$	24.3278	+	24.3278i	1.20293	+	1.20293i	0.229664	+	0.973270i	$0.426237\pi$
$410$		0			0
$411$	4.51363	−	2.98817i	0.222641	−	0.147396i
$412$		0			0
$413$	6.95913	−	2.88257i	0.342436	−	0.141842i
$414$		0			0
$415$			4.40677i			0.216320i
$416$		0			0
$417$	4.21364	−	6.24836i	0.206343	−	0.305983i
$418$		0			0
$419$	8.96150	+	21.6350i	0.437798	+	1.05694i	0.976708	+	0.214574i	$0.0688363\pi$
$419$	8.96150	+	21.6350i	0.437798	+	1.05694i	−0.538910	+	0.842363i	$0.681164\pi$
$420$		0			0
$421$	15.8146	+	6.55062i	0.770756	+	0.319258i	0.733179	−	0.680036i	$-0.238036\pi$
$421$	15.8146	+	6.55062i	0.770756	+	0.319258i	0.0375773	+	0.999294i	$0.488036\pi$
$422$		0			0
$423$	6.99061	−	16.4782i	0.339895	−	0.801199i
$424$		0			0
$425$	−26.5963	−	26.5963i	−1.29011	−	1.29011i
$426$		0			0
$427$	7.67991	+	3.18112i	0.371657	+	0.153945i
$428$		0			0
$429$	2.46023	+	0.500277i	0.118781	+	0.0241536i
$430$		0			0
$431$		−	21.2060i		−	1.02146i	−0.859742	−	0.510729i	$-0.829375\pi$
$431$		−	21.2060i		−	1.02146i	0.859742	−	0.510729i	$-0.170625\pi$
$432$		0			0
$433$			7.73016i			0.371488i	0.982598	+	0.185744i	$0.0594695\pi$
$433$			7.73016i			0.371488i	−0.982598	+	0.185744i	$0.940531\pi$
$434$		0			0
$435$	26.3661	+	5.36143i	1.26416	+	0.257061i
$436$		0			0
$437$	13.0395	+	5.40113i	0.623763	+	0.258371i
$438$		0			0
$439$	−25.4093	−	25.4093i	−1.21272	−	1.21272i	−0.970128	−	0.242594i	$-0.922002\pi$
$439$	−25.4093	−	25.4093i	−1.21272	−	1.21272i	−0.242594	−	0.970128i	$-0.577998\pi$
$440$		0			0
$441$	6.55369	−	15.4483i	0.312080	−	0.735634i
$442$		0			0
$443$	4.74325	+	1.96472i	0.225359	+	0.0933467i	0.492506	−	0.870309i	$-0.336081\pi$
$443$	4.74325	+	1.96472i	0.225359	+	0.0933467i	−0.267147	+	0.963656i	$0.586081\pi$
$444$		0			0
$445$	−22.9736	−	55.4632i	−1.08905	−	2.62921i
$446$		0			0
$447$	5.73660	−	8.50674i	0.271332	−	0.402355i
$448$		0			0
$449$		−	13.4003i		−	0.632399i	−0.948693	−	0.316199i	$-0.897593\pi$
$449$		−	13.4003i		−	0.632399i	0.948693	−	0.316199i	$-0.102407\pi$
$450$		0			0
$451$	−3.01479	+	1.24877i	−0.141961	+	0.0588021i
$452$		0			0
$453$	−11.8745	+	7.86128i	−0.557911	+	0.369355i
$454$		0			0
$455$	−7.61414	−	7.61414i	−0.356957	−	0.356957i
$456$		0			0
$457$	−21.8591	+	21.8591i	−1.02253	+	1.02253i	−0.0227865	+	0.999740i	$0.507254\pi$
$457$	−21.8591	+	21.8591i	−1.02253	+	1.02253i	−0.999740	+	0.0227865i	$0.992746\pi$
$458$		0			0
$459$	9.52198	−	13.8637i	0.444448	−	0.647102i
$460$		0			0
$461$	−8.39897	−	20.2769i	−0.391179	−	0.944389i	−0.989684	−	0.143270i	$-0.954238\pi$
$461$	−8.39897	−	20.2769i	−0.391179	−	0.944389i	0.598505	−	0.801119i	$-0.295762\pi$
$462$		0			0
$463$	−24.1790			−1.12369			−0.561847	−	0.827241i	$-0.689909\pi$
$463$	−24.1790			−1.12369			−0.561847	+	0.827241i	$0.689909\pi$
$464$		0			0
$465$	30.1394	−	44.6934i	1.39768	−	2.07261i
$466$		0			0
$467$	22.1546	−	9.17674i	1.02519	−	0.424649i	0.194218	−	0.980958i	$-0.437783\pi$
$467$	22.1546	−	9.17674i	1.02519	−	0.424649i	0.830975	+	0.556309i	$0.187783\pi$
$468$		0			0
$469$	−2.35082	+	5.67538i	−0.108551	+	0.262065i
$470$		0			0
$471$	14.9859	−	2.91455i	0.690512	−	0.134295i
$472$		0			0
$473$	−1.59190	+	1.59190i	−0.0731954	+	0.0731954i
$474$		0			0
$475$	−17.1772	+	41.4695i	−0.788146	+	1.90275i
$476$		0			0
$477$	−1.73653	−	1.76639i	−0.0795105	−	0.0808773i
$478$		0			0
$479$	−23.6803			−1.08198			−0.540991	−	0.841028i	$-0.681951\pi$
$479$	−23.6803			−1.08198			−0.540991	+	0.841028i	$0.681951\pi$
$480$		0			0
$481$	−1.39618			−0.0636603
$482$		0			0
$483$	−7.35467	−	1.49554i	−0.334649	−	0.0680494i
$484$		0			0
$485$	−14.3781	+	34.7119i	−0.652877	+	1.57619i
$486$		0			0
$487$	−15.7774	+	15.7774i	−0.714942	+	0.714942i	−0.967565	−	0.252623i	$-0.918707\pi$
$487$	−15.7774	+	15.7774i	−0.714942	+	0.714942i	0.252623	+	0.967565i	$0.418707\pi$
$488$		0			0
$489$	−4.95349	−	25.4696i	−0.224005	−	1.15177i
$490$		0			0
$491$	1.45911	−	3.52259i	0.0658486	−	0.158972i	−0.887530	−	0.460751i	$-0.847580\pi$
$491$	1.45911	−	3.52259i	0.0658486	−	0.158972i	0.953378	+	0.301778i	$0.0975802\pi$
$492$		0			0
$493$	−11.3943	+	4.71968i	−0.513174	+	0.212564i
$494$		0			0
$495$	2.98321	+	7.37934i	0.134085	+	0.331677i
$496$		0			0
$497$	−17.1222			−0.768037
$498$		0			0
$499$	−12.0066	−	28.9865i	−0.537490	−	1.29761i	−0.926470	−	0.376369i	$-0.877173\pi$
$499$	−12.0066	−	28.9865i	−0.537490	−	1.29761i	0.388980	−	0.921246i	$-0.372827\pi$
$500$		0			0
$501$	−13.7407	+	9.09682i	−0.613891	+	0.406416i
$502$		0			0
$503$	−9.02060	+	9.02060i	−0.402208	+	0.402208i	−0.879011	−	0.476802i	$-0.841796\pi$
$503$	−9.02060	+	9.02060i	−0.402208	+	0.402208i	0.476802	+	0.879011i	$0.341796\pi$
$504$		0			0
$505$	−12.1906	−	12.1906i	−0.542475	−	0.542475i
$506$		0			0
$507$	−7.68668	−	11.6107i	−0.341377	−	0.515650i
$508$		0			0
$509$	13.9019	−	5.75836i	0.616192	−	0.255235i	−0.0526815	−	0.998611i	$-0.516777\pi$
$509$	13.9019	−	5.75836i	0.616192	−	0.255235i	0.668873	+	0.743376i	$0.266777\pi$
$510$		0			0
$511$		−	13.5754i		−	0.600543i
$512$		0			0
$513$	−19.6338	−	4.16698i	−0.866852	−	0.183977i
$514$		0			0
$515$	9.48396	+	22.8963i	0.417913	+	1.00893i
$516$		0			0
$517$	−3.58745	−	1.48597i	−0.157776	−	0.0653528i
$518$		0			0
$519$	1.22535	−	0.238314i	0.0537868	−	0.0104608i
$520$		0			0
$521$	24.3052	+	24.3052i	1.06483	+	1.06483i	0.997747	+	0.0670849i	$0.0213698\pi$
$521$	24.3052	+	24.3052i	1.06483	+	1.06483i	0.0670849	+	0.997747i	$0.478630\pi$
$522$		0			0
$523$	−11.5224	−	4.77273i	−0.503839	−	0.208697i	0.116262	−	0.993219i	$-0.462909\pi$
$523$	−11.5224	−	4.77273i	−0.503839	−	0.208697i	−0.620102	+	0.784522i	$0.712909\pi$
$524$		0			0
$525$	4.75627	−	23.3901i	0.207581	−	1.02083i
$526$		0			0
$527$			24.7098i			1.07637i
$528$		0			0
$529$			9.64908i			0.419525i
$530$		0			0
$531$	−13.3588	−	13.5885i	−0.579724	−	0.589689i
$532$		0			0
$533$	−10.3177	−	4.27372i	−0.446908	−	0.185115i
$534$		0			0
$535$	−21.3041	−	21.3041i	−0.921058	−	0.921058i
$536$		0			0
$537$	4.26621	+	21.9357i	0.184101	+	0.946597i
$538$		0			0
$539$	−3.36323	−	1.39309i	−0.144864	−	0.0600048i
$540$		0			0
$541$	11.0650	+	26.7133i	0.475722	+	1.14849i	0.961597	+	0.274466i	$0.0885010\pi$
$541$	11.0650	+	26.7133i	0.475722	+	1.14849i	−0.485875	+	0.874028i	$0.661499\pi$
$542$		0			0
$543$	−10.0134	−	6.75260i	−0.429714	−	0.289782i
$544$		0			0
$545$			54.7288i			2.34433i
$546$		0			0
$547$	−5.80786	+	2.40569i	−0.248326	+	0.102860i	−0.503375	−	0.864068i	$-0.667909\pi$
$547$	−5.80786	+	2.40569i	−0.248326	+	0.102860i	0.255049	+	0.966928i	$0.417909\pi$
$548$		0			0
$549$	0.179200	−	21.0282i	0.00764806	−	0.897460i
$550$		0			0
$551$	10.4072	+	10.4072i	0.443363	+	0.443363i
$552$		0			0
$553$	9.67214	−	9.67214i	0.411301	−	0.411301i
$554$		0			0
$555$	−2.44350	−	3.69090i	−0.103721	−	0.156670i
$556$		0			0
$557$	7.71096	+	18.6159i	0.326724	+	0.788781i	0.998832	+	0.0483277i	$0.0153892\pi$
$557$	7.71096	+	18.6159i	0.326724	+	0.788781i	−0.672108	+	0.740453i	$0.734611\pi$
$558$		0			0
$559$	−7.70467			−0.325873
$560$		0			0
$561$	−3.02497	−	2.03992i	−0.127714	−	0.0861253i
$562$		0			0
$563$	−11.4466	+	4.74136i	−0.482419	+	0.199824i	−0.610620	−	0.791924i	$-0.709080\pi$
$563$	−11.4466	+	4.74136i	−0.482419	+	0.199824i	0.128201	+	0.991748i	$0.459080\pi$
$564$		0			0
$565$	5.35046	−	12.9172i	0.225096	−	0.543429i
$566$		0			0
$567$	10.6715	+	0.181895i	0.448160	+	0.00763889i
$568$		0			0
$569$	−27.9002	+	27.9002i	−1.16964	+	1.16964i	−0.187343	+	0.982295i	$0.559987\pi$
$569$	−27.9002	+	27.9002i	−1.16964	+	1.16964i	−0.982295	+	0.187343i	$0.940013\pi$
$570$		0			0
$571$	9.45224	−	22.8197i	0.395564	−	0.954976i	−0.593141	−	0.805099i	$-0.702112\pi$
$571$	9.45224	−	22.8197i	0.395564	−	0.954976i	0.988705	−	0.149877i	$-0.0478878\pi$
$572$		0			0
$573$	0.560193	−	2.75488i	0.0234024	−	0.115087i
$574$		0			0
$575$	42.4601			1.77071
$576$		0			0
$577$	−16.6076			−0.691383			−0.345691	−	0.938348i	$-0.612356\pi$
$577$	−16.6076			−0.691383			−0.345691	+	0.938348i	$0.612356\pi$
$578$		0			0
$579$	3.57479	−	17.5799i	0.148563	−	0.730596i
$580$		0			0
$581$	0.490550	−	1.18429i	0.0203514	−	0.0491327i
$582$		0			0
$583$	−0.379961	+	0.379961i	−0.0157364	+	0.0157364i
$584$		0			0
$585$	−10.6385	+	25.0770i	−0.439848	+	1.03681i
$586$		0			0
$587$	5.82661	−	14.0667i	0.240490	−	0.580594i	−0.756842	−	0.653598i	$-0.773259\pi$
$587$	5.82661	−	14.0667i	0.240490	−	0.580594i	0.997332	+	0.0730041i	$0.0232586\pi$
$588$		0			0
$589$	27.2434	−	11.2846i	1.12254	−	0.464973i
$590$		0			0
$591$	2.94212	+	1.98404i	0.121022	+	0.0816126i
$592$		0			0
$593$	−0.760076			−0.0312126			−0.0156063	−	0.999878i	$-0.504968\pi$
$593$	−0.760076			−0.0312126			−0.0156063	+	0.999878i	$0.504968\pi$
$594$		0			0
$595$	5.98850	+	14.4575i	0.245505	+	0.592701i
$596$		0			0
$597$	11.8788	+	17.9429i	0.486168	+	0.734356i
$598$		0			0
$599$	−18.9662	+	18.9662i	−0.774937	+	0.774937i	−0.978965	−	0.204028i	$-0.934597\pi$
$599$	−18.9662	+	18.9662i	−0.774937	+	0.774937i	0.204028	+	0.978965i	$0.434597\pi$
$600$		0			0
$601$	−15.3756	−	15.3756i	−0.627183	−	0.627183i	0.320175	−	0.947358i	$-0.396258\pi$
$601$	−15.3756	−	15.3756i	−0.627183	−	0.627183i	−0.947358	+	0.320175i	$0.896258\pi$
$602$		0			0
$603$	15.5396	+	0.132427i	0.632822	+	0.00539284i
$604$		0			0
$605$	−39.8362	+	16.5007i	−1.61957	+	0.670849i
$606$		0			0
$607$			8.77741i			0.356264i	0.984007	+	0.178132i	$0.0570054\pi$
$607$			8.77741i			0.356264i	−0.984007	+	0.178132i	$0.942995\pi$
$608$		0			0
$609$	−6.48890	−	4.37585i	−0.262943	−	0.177318i
$610$		0			0
$611$	−5.08551	−	12.2775i	−0.205738	−	0.496695i
$612$		0			0
$613$	−4.08951	−	1.69393i	−0.165174	−	0.0684172i	0.298564	−	0.954389i	$-0.403492\pi$
$613$	−4.08951	−	1.69393i	−0.165174	−	0.0684172i	−0.463738	+	0.885972i	$0.653492\pi$
$614$		0			0
$615$	−6.75939	−	34.7550i	−0.272565	−	1.40146i
$616$		0			0
$617$	10.3859	+	10.3859i	0.418123	+	0.418123i	0.884556	−	0.466434i	$-0.154461\pi$
$617$	10.3859	+	10.3859i	0.418123	+	0.418123i	−0.466434	+	0.884556i	$0.654461\pi$
$618$		0			0
$619$	20.6486	+	8.55293i	0.829937	+	0.343771i	0.756878	−	0.653556i	$-0.226724\pi$
$619$	20.6486	+	8.55293i	0.829937	+	0.343771i	0.0730593	+	0.997328i	$0.476724\pi$
$620$		0			0
$621$	3.46570	+	18.6672i	0.139074	+	0.749088i
$622$		0			0
$623$			17.4628i			0.699630i
$624$		0			0
$625$			51.9336i			2.07734i
$626$		0			0
$627$	−0.867622	+	4.26674i	−0.0346495	+	0.170397i
$628$		0			0
$629$	1.87456	+	0.776468i	0.0747436	+	0.0309598i
$630$		0			0
$631$	−13.2657	−	13.2657i	−0.528098	−	0.528098i	0.391907	−	0.920005i	$-0.371815\pi$
$631$	−13.2657	−	13.2657i	−0.528098	−	0.528098i	−0.920005	+	0.391907i	$0.871815\pi$
$632$		0			0
$633$	−43.6081	+	8.48118i	−1.73326	+	0.337097i
$634$		0			0
$635$	−2.72879	−	1.13030i	−0.108289	−	0.0448546i
$636$		0			0
$637$	−4.76766	−	11.5101i	−0.188901	−	0.456048i
$638$		0			0
$639$	16.2343	+	40.1575i	0.642218	+	1.58861i
$640$		0			0
$641$		−	3.60149i		−	0.142250i	−0.997467	−	0.0711252i	$-0.977341\pi$
$641$		−	3.60149i		−	0.142250i	0.997467	−	0.0711252i	$-0.0226590\pi$
$642$		0			0
$643$	−16.5202	+	6.84287i	−0.651492	+	0.269857i	−0.683853	−	0.729620i	$-0.739697\pi$
$643$	−16.5202	+	6.84287i	−0.651492	+	0.269857i	0.0323617	+	0.999476i	$0.489697\pi$
$644$		0			0
$645$	−13.4842	−	20.3678i	−0.530939	−	0.801983i
$646$		0			0
$647$	23.6599	+	23.6599i	0.930167	+	0.930167i	0.997716	−	0.0675491i	$-0.0215179\pi$
$647$	23.6599	+	23.6599i	0.930167	+	0.930167i	−0.0675491	+	0.997716i	$0.521518\pi$
$648$		0			0
$649$	−2.92297	+	2.92297i	−0.114737	+	0.114737i
$650$		0			0
$651$	−13.0749	+	8.65604i	−0.512447	+	0.339257i
$652$		0			0
$653$	−12.1760	−	29.3955i	−0.476484	−	1.15033i	−0.961247	−	0.275689i	$-0.911094\pi$
$653$	−12.1760	−	29.3955i	−0.476484	−	1.15033i	0.484763	−	0.874646i	$-0.338906\pi$
$654$		0			0
$655$	15.3698			0.600547
$656$		0			0
$657$	−31.8391	+	12.8714i	−1.24216	+	0.502162i
$658$		0			0
$659$	−41.6508	+	17.2523i	−1.62248	+	0.672055i	−0.994360	−	0.106059i	$-0.966177\pi$
$659$	−41.6508	+	17.2523i	−1.62248	+	0.672055i	−0.628123	+	0.778114i	$0.716177\pi$
$660$		0			0
$661$	2.34448	−	5.66007i	0.0911896	−	0.220151i	−0.871704	−	0.490033i	$-0.836985\pi$
$661$	2.34448	−	5.66007i	0.0911896	−	0.220151i	0.962893	+	0.269882i	$0.0869847\pi$
$662$		0			0
$663$	−2.38380	−	12.2569i	−0.0925790	−	0.476017i
$664$		0			0
$665$	13.2051	−	13.2051i	0.512071	−	0.512071i
$666$		0			0
$667$	5.32790	−	12.8627i	0.206297	−	0.498046i
$668$		0			0
$669$	27.8087	+	5.65478i	1.07515	+	0.218627i
$670$		0			0
$671$	−4.56184			−0.176108
$672$		0			0
$673$	45.2206			1.74313			0.871563	−	0.490283i	$-0.163107\pi$
$673$	45.2206			1.74313			0.871563	+	0.490283i	$0.163107\pi$
$674$		0			0
$675$	−59.3674	+	11.0220i	−2.28505	+	0.424236i
$676$		0			0
$677$	19.1300	−	46.1838i	0.735224	−	1.77499i	0.110886	−	0.993833i	$-0.464631\pi$
$677$	19.1300	−	46.1838i	0.735224	−	1.77499i	0.624338	−	0.781155i	$-0.285369\pi$
$678$		0			0
$679$	7.72806	−	7.72806i	0.296576	−	0.296576i
$680$		0			0
$681$	42.7245	−	8.30935i	1.63721	−	0.318415i
$682$		0			0
$683$	14.1282	−	34.1085i	0.540600	−	1.30512i	−0.383700	−	0.923458i	$-0.625350\pi$
$683$	14.1282	−	34.1085i	0.540600	−	1.30512i	0.924300	−	0.381666i	$-0.124650\pi$
$684$		0			0
$685$	11.7713	−	4.87584i	0.449759	−	0.186296i
$686$		0			0
$687$	11.7981	−	17.4952i	0.450124	−	0.667484i
$688$		0			0
$689$	−1.83899			−0.0700599
$690$		0			0
$691$	1.84991	+	4.46608i	0.0703740	+	0.169898i	0.955153	−	0.296113i	$-0.0956906\pi$
$691$	1.84991	+	4.46608i	0.0703740	+	0.169898i	−0.884779	+	0.466011i	$0.845691\pi$
$692$		0			0
$693$	0.0197302	−	2.31523i	0.000749487	−	0.0879485i
$694$		0			0
$695$	12.5432	−	12.5432i	0.475791	−	0.475791i
$696$		0			0
$697$	11.4761	+	11.4761i	0.434688	+	0.434688i
$698$		0			0
$699$	−27.6569	+	18.3098i	−1.04608	+	0.692540i
$700$		0			0
$701$	−9.68643	+	4.01225i	−0.365851	+	0.151541i	−0.558033	−	0.829819i	$-0.688444\pi$
$701$	−9.68643	+	4.01225i	−0.365851	+	0.151541i	0.192182	+	0.981359i	$0.438444\pi$
$702$		0			0
$703$		−	2.42137i		−	0.0913238i
$704$		0			0
$705$	23.5561	−	34.9311i	0.887175	−	1.31558i
$706$		0			0
$707$	1.91912	+	4.63317i	0.0721761	+	0.174248i
$708$		0			0
$709$	−38.1564	−	15.8049i	−1.43299	−	0.593565i	−0.474904	−	0.880038i	$-0.657517\pi$
$709$	−38.1564	−	15.8049i	−1.43299	−	0.593565i	−0.958088	+	0.286473i	$0.907517\pi$
$710$		0			0
$711$	−31.8550	−	13.5139i	−1.19466	−	0.506812i
$712$		0			0
$713$	−19.7241	−	19.7241i	−0.738674	−	0.738674i
$714$		0			0
$715$	5.45948	+	2.26139i	0.204173	+	0.0845711i
$716$		0			0
$717$	−32.4473	−	6.59802i	−1.21177	−	0.246407i
$718$		0			0
$719$			46.6233i			1.73876i	0.494147	+	0.869378i	$0.335481\pi$
$719$			46.6233i			1.73876i	−0.494147	+	0.869378i	$0.664519\pi$
$720$		0			0
$721$		−	7.20896i		−	0.268476i
$722$		0			0
$723$	−2.90613	−	0.590948i	−0.108080	−	0.0219776i
$724$		0			0
$725$	40.9074	+	16.9444i	1.51926	+	0.629298i
$726$		0			0
$727$	25.2103	+	25.2103i	0.934997	+	0.934997i	0.998013	−	0.0630153i	$-0.0200717\pi$
$727$	25.2103	+	25.2103i	0.934997	+	0.934997i	−0.0630153	+	0.998013i	$0.520072\pi$
$728$		0			0
$729$	−9.69143	−	25.2007i	−0.358942	−	0.933360i
$730$		0			0
$731$	10.3446	+	4.28486i	0.382608	+	0.158481i
$732$		0			0
$733$	−2.25020	−	5.43246i	−0.0831129	−	0.200652i	0.876860	−	0.480747i	$-0.159634\pi$
$733$	−2.25020	−	5.43246i	−0.0831129	−	0.200652i	−0.959973	+	0.280094i	$0.909634\pi$
$734$		0			0
$735$	22.0838	−	32.7479i	0.814575	−	1.20792i
$736$		0			0
$737$		−	3.37116i		−	0.124178i
$738$		0			0
$739$	−10.5170	+	4.35630i	−0.386876	+	0.160249i	−0.567639	−	0.823277i	$-0.692143\pi$
$739$	−10.5170	+	4.35630i	−0.386876	+	0.160249i	0.180763	+	0.983527i	$0.442143\pi$
$740$		0			0
$741$	−12.4250	+	8.22575i	−0.456443	+	0.302180i
$742$		0			0
$743$	15.4609	+	15.4609i	0.567205	+	0.567205i	0.931345	−	0.364139i	$-0.118637\pi$
$743$	15.4609	+	15.4609i	0.567205	+	0.567205i	−0.364139	+	0.931345i	$0.618637\pi$
$744$		0			0
$745$	17.0768	−	17.0768i	0.625644	−	0.625644i
$746$		0			0
$747$	−3.24268	−	0.0276338i	−0.118643	−	0.00101107i
$748$		0			0
$749$	3.35383	+	8.09687i	0.122546	+	0.295853i
$750$		0			0
$751$	−34.5867			−1.26209			−0.631043	−	0.775748i	$-0.717373\pi$
$751$	−34.5867			−1.26209			−0.631043	+	0.775748i	$0.717373\pi$
$752$		0			0
$753$	−26.7555	+	39.6754i	−0.975023	+	1.44585i
$754$		0			0
$755$	−30.9680	+	12.8274i	−1.12704	+	0.466836i
$756$		0			0
$757$	−6.82795	+	16.4841i	−0.248166	+	0.599126i	−0.998048	−	0.0624455i	$-0.980110\pi$
$757$	−6.82795	+	16.4841i	−0.248166	+	0.599126i	0.749882	+	0.661571i	$0.230110\pi$
$758$		0			0
$759$	4.04295	−	0.786300i	0.146750	−	0.0285409i
$760$		0			0
$761$	10.6555	−	10.6555i	0.386261	−	0.386261i	−0.487090	−	0.873352i	$-0.661942\pi$
$761$	10.6555	−	10.6555i	0.386261	−	0.386261i	0.873352	+	0.487090i	$0.161942\pi$
$762$		0			0
$763$	6.09226	−	14.7080i	0.220555	−	0.532466i
$764$		0			0
$765$	28.2299	−	27.7528i	1.02065	−	1.00341i
$766$		0			0
$767$	−14.1470			−0.510818
$768$		0			0
$769$	4.53950			0.163699			0.0818493	−	0.996645i	$-0.473917\pi$
$769$	4.53950			0.163699			0.0818493	+	0.996645i	$0.473917\pi$
$770$		0			0
$771$	36.5371	+	7.42966i	1.31585	+	0.267573i
$772$		0			0
$773$	−10.7578	+	25.9715i	−0.386929	+	0.934130i	0.603657	+	0.797244i	$0.293710\pi$
$773$	−10.7578	+	25.9715i	−0.386929	+	0.934130i	−0.990587	+	0.136886i	$0.956290\pi$
$774$		0			0
$775$	62.7288	−	62.7288i	2.25328	−	2.25328i
$776$		0			0
$777$	0.245814	+	1.26391i	0.00881851	+	0.0453425i
$778$		0			0
$779$	7.41183	−	17.8938i	0.265557	−	0.641110i
$780$		0			0
$781$	8.68111	−	3.59583i	0.310635	−	0.128669i
$782$		0			0
$783$	−4.11049	+	19.3676i	−0.146897	+	0.692141i
$784$		0			0
$785$	35.9340			1.28254
$786$		0			0
$787$	18.2001	+	43.9390i	0.648764	+	1.56626i	0.814550	+	0.580093i	$0.196984\pi$
$787$	18.2001	+	43.9390i	0.648764	+	1.56626i	−0.165786	+	0.986162i	$0.553016\pi$
$788$		0			0
$789$	21.4302	−	14.1875i	0.762936	−	0.505089i
$790$		0			0
$791$	−2.87581	+	2.87581i	−0.102252	+	0.102252i
$792$		0			0
$793$	−11.0395	−	11.0395i	−0.392025	−	0.392025i
$794$		0			0
$795$	−3.21847	−	4.86149i	−0.114147	−	0.172419i
$796$		0			0
$797$	−0.989560	+	0.409889i	−0.0350520	+	0.0145190i	−0.400141	−	0.916454i	$-0.631039\pi$
$797$	−0.989560	+	0.409889i	−0.0350520	+	0.0145190i	0.365089	+	0.930973i	$0.381039\pi$
$798$		0			0
$799$			19.3124i			0.683225i
$800$		0			0
$801$	40.9561	−	16.5571i	1.44711	−	0.585017i
$802$		0			0
$803$	2.85097	+	6.88286i	0.100609	+	0.242891i
$804$		0			0
$805$	−16.3207	−	6.76024i	−0.575228	−	0.238267i
$806$		0			0
$807$	21.9856	−	4.27590i	0.773928	−	0.150519i
$808$		0			0
$809$	−16.4456	−	16.4456i	−0.578196	−	0.578196i	0.356210	−	0.934406i	$-0.384069\pi$
$809$	−16.4456	−	16.4456i	−0.578196	−	0.578196i	−0.934406	+	0.356210i	$0.884069\pi$
$810$		0			0
$811$	30.7926	+	12.7547i	1.08127	+	0.447878i	0.850956	−	0.525238i	$-0.176024\pi$
$811$	30.7926	+	12.7547i	1.08127	+	0.447878i	0.230317	+	0.973116i	$0.426024\pi$
$812$		0			0
$813$	2.42831	−	11.9418i	0.0851646	−	0.418817i
$814$		0			0
$815$		−	61.0725i		−	2.13927i
$816$		0			0
$817$		−	13.3621i		−	0.467480i
$818$		0			0
$819$	5.65054	−	5.55504i	0.197446	−	0.194109i
$820$		0			0
$821$	30.3992	+	12.5918i	1.06094	+	0.439455i	0.843785	−	0.536682i	$-0.180322\pi$
$821$	30.3992	+	12.5918i	1.06094	+	0.439455i	0.217155	+	0.976137i	$0.430322\pi$
$822$		0			0
$823$	7.58486	+	7.58486i	0.264392	+	0.264392i	0.826835	−	0.562444i	$-0.190139\pi$
$823$	7.58486	+	7.58486i	0.264392	+	0.264392i	−0.562444	+	0.826835i	$0.690139\pi$
$824$		0			0
$825$	2.50068	+	12.8578i	0.0870624	+	0.447652i
$826$		0			0
$827$	−34.9305	−	14.4687i	−1.21465	−	0.503126i	−0.318947	−	0.947773i	$-0.603329\pi$
$827$	−34.9305	−	14.4687i	−1.21465	−	0.503126i	−0.895706	+	0.444647i	$0.853329\pi$
$828$		0			0
$829$	−1.61267	−	3.89332i	−0.0560102	−	0.135221i	0.893397	−	0.449268i	$-0.148315\pi$
$829$	−1.61267	−	3.89332i	−0.0560102	−	0.135221i	−0.949407	+	0.314047i	$0.898315\pi$
$830$		0			0
$831$	35.2910	+	23.7988i	1.22423	+	0.825571i
$832$		0			0
$833$			18.1054i			0.627315i
$834$		0			0
$835$	−35.8352	+	14.8434i	−1.24013	+	0.513678i
$836$		0			0
$837$	32.6982	+	22.4581i	1.13022	+	0.776264i
$838$		0			0
$839$	−13.7057	−	13.7057i	−0.473173	−	0.473173i	0.429767	−	0.902940i	$-0.358596\pi$
$839$	−13.7057	−	13.7057i	−0.473173	−	0.473173i	−0.902940	+	0.429767i	$0.858596\pi$
$840$		0			0
$841$	−10.2400	+	10.2400i	−0.353102	+	0.353102i
$842$		0			0
$843$	18.5351	+	27.9972i	0.638381	+	0.964274i
$844$		0			0
$845$	−12.5425	−	30.2802i	−0.431474	−	1.04167i
$846$		0			0
$847$	12.5425			0.430967
$848$		0			0
$849$	42.5621	+	28.7021i	1.46073	+	0.985055i
$850$		0			0
$851$	−2.11614	+	0.876532i	−0.0725402	+	0.0300471i
$852$		0			0
$853$	−13.8120	+	33.3450i	−0.472913	+	1.14171i	0.489957	+	0.871746i	$0.337012\pi$
$853$	−13.8120	+	33.3450i	−0.472913	+	1.14171i	−0.962870	+	0.269966i	$0.912988\pi$
$854$		0			0
$855$	−43.4907	−	18.4502i	−1.48735	−	0.630983i
$856$		0			0
$857$	−24.4023	+	24.4023i	−0.833565	+	0.833565i	−0.988003	−	0.154438i	$-0.950643\pi$
$857$	−24.4023	+	24.4023i	−0.833565	+	0.833565i	0.154438	+	0.988003i	$0.450643\pi$
$858$		0			0
$859$	−1.51555	+	3.65886i	−0.0517099	+	0.124839i	−0.947623	−	0.319390i	$-0.896522\pi$
$859$	−1.51555	+	3.65886i	−0.0517099	+	0.124839i	0.895914	+	0.444228i	$0.146522\pi$
$860$		0			0
$861$	−2.05229	+	10.0926i	−0.0699419	+	0.343956i
$862$		0			0
$863$	37.8790			1.28942			0.644708	−	0.764429i	$-0.276979\pi$
$863$	37.8790			1.28942			0.644708	+	0.764429i	$0.276979\pi$
$864$		0			0
$865$	2.93821			0.0999021
$866$		0			0
$867$	2.25147	−	11.0721i	0.0764640	−	0.376030i
$868$		0			0
$869$	−2.87261	+	6.93509i	−0.0974466	+	0.235257i
$870$		0			0
$871$	8.15810	−	8.15810i	0.276427	−	0.276427i
$872$		0			0
$873$	−25.4522	−	10.7977i	−0.861427	−	0.365446i
$874$		0			0
$875$	12.2489	−	29.5715i	0.414089	−	0.999699i
$876$		0			0
$877$	8.89587	−	3.68479i	0.300392	−	0.124426i	−0.227397	−	0.973802i	$-0.573021\pi$
$877$	8.89587	−	3.68479i	0.300392	−	0.124426i	0.527789	+	0.849376i	$0.323021\pi$
$878$		0			0
$879$	15.3076	+	10.3228i	0.516313	+	0.348181i
$880$		0			0
$881$	8.66239			0.291843			0.145922	−	0.989296i	$-0.453385\pi$
$881$	8.66239			0.291843			0.145922	+	0.989296i	$0.453385\pi$
$882$		0			0
$883$	−10.6679	−	25.7547i	−0.359005	−	0.866715i	−0.995440	−	0.0953849i	$-0.969592\pi$
$883$	−10.6679	−	25.7547i	−0.359005	−	0.866715i	0.636435	−	0.771330i	$-0.280408\pi$
$884$		0			0
$885$	−24.7591	−	37.3985i	−0.832267	−	1.25714i
$886$		0			0
$887$	−13.1549	+	13.1549i	−0.441698	+	0.441698i	−0.892582	−	0.450885i	$-0.851109\pi$
$887$	−13.1549	+	13.1549i	−0.441698	+	0.441698i	0.450885	+	0.892582i	$0.351109\pi$
$888$		0			0
$889$	0.607523	+	0.607523i	0.0203757	+	0.0203757i
$890$		0			0
$891$	−5.44872	+	2.14889i	−0.182539	+	0.0719905i
$892$		0			0
$893$	21.2927	−	8.81971i	0.712532	−	0.295140i
$894$		0			0
$895$			52.5988i			1.75818i
$896$		0			0
$897$	11.6866	+	7.88099i	0.390205	+	0.263139i
$898$		0			0
$899$	−11.1316	−	26.8741i	−0.371260	−	0.896300i
$900$		0			0
$901$	2.46909	+	1.02273i	0.0822573	+	0.0340721i
$902$		0			0
$903$	1.35650	+	6.97475i	0.0451414	+	0.232105i
$904$		0			0
$905$	−20.1012	−	20.1012i	−0.668187	−	0.668187i
$906$		0			0
$907$	−24.0939	−	9.98004i	−0.800026	−	0.331382i	−0.0550594	−	0.998483i	$-0.517535\pi$
$907$	−24.0939	−	9.98004i	−0.800026	−	0.331382i	−0.744967	+	0.667101i	$0.767535\pi$
$908$		0			0
$909$	9.04678	−	8.89389i	0.300063	−	0.294992i
$910$		0			0
$911$		−	52.5495i		−	1.74104i	−0.492132	−	0.870520i	$-0.663782\pi$
$911$		−	52.5495i		−	1.74104i	0.492132	−	0.870520i	$-0.336218\pi$
$912$		0			0
$913$			0.703466i			0.0232813i
$914$		0			0
$915$	9.86314	−	48.5043i	0.326065	−	1.60350i
$916$		0			0
$917$	−4.13053	−	1.71092i	−0.136402	−	0.0564997i
$918$		0			0
$919$	32.3967	+	32.3967i	1.06867	+	1.06867i	0.997462	+	0.0712063i	$0.0226849\pi$
$919$	32.3967	+	32.3967i	1.06867	+	1.06867i	0.0712063	+	0.997462i	$0.477315\pi$
$920$		0			0
$921$	−35.7253	+	6.94810i	−1.17719	+	0.228948i
$922$		0			0
$923$	29.7098	+	12.3062i	0.977911	+	0.405064i
$924$		0			0
$925$	−2.78764	−	6.72996i	−0.0916571	−	0.221280i
$926$		0			0
$927$	−16.9075	+	6.83510i	−0.555315	+	0.224494i
$928$		0			0
$929$			45.9891i			1.50885i	0.656385	+	0.754426i	$0.272085\pi$
$929$			45.9891i			1.50885i	−0.656385	+	0.754426i	$0.727915\pi$
$930$		0			0
$931$	19.9618	−	8.26846i	0.654223	−	0.270988i
$932$		0			0
$933$	28.2882	+	42.7293i	0.926113	+	1.39889i
$934$		0			0
$935$	−6.07244	−	6.07244i	−0.198590	−	0.198590i
$936$		0			0
$937$	−19.7725	+	19.7725i	−0.645940	+	0.645940i	−0.952009	−	0.306069i	$-0.900986\pi$
$937$	−19.7725	+	19.7725i	−0.645940	+	0.645940i	0.306069	+	0.952009i	$0.400986\pi$
$938$		0			0
$939$	18.2023	−	12.0505i	0.594011	−	0.393255i
$940$		0			0
$941$	−15.8263	−	38.2081i	−0.515924	−	1.24555i	−0.940387	−	0.340105i	$-0.889537\pi$
$941$	−15.8263	−	38.2081i	−0.515924	−	1.24555i	0.424464	−	0.905445i	$-0.360463\pi$
$942$		0			0
$943$	−18.3211			−0.596619
$944$		0			0
$945$	24.5743	+	5.21554i	0.799403	+	0.169661i
$946$		0			0
$947$	29.7644	−	12.3288i	0.967213	−	0.400633i	0.157539	−	0.987513i	$-0.449644\pi$
$947$	29.7644	−	12.3288i	0.967213	−	0.400633i	0.809674	+	0.586880i	$0.199644\pi$
$948$		0			0
$949$	−9.75704	+	23.5556i	−0.316727	+	0.764646i
$950$		0			0
$951$	0.172674	+	0.887846i	0.00559934	+	0.0287904i
$952$		0			0
$953$	12.6032	−	12.6032i	0.408259	−	0.408259i	−0.472872	−	0.881131i	$-0.656783\pi$
$953$	12.6032	−	12.6032i	0.408259	−	0.408259i	0.881131	+	0.472872i	$0.156783\pi$
$954$		0			0
$955$	2.53222	−	6.11333i	0.0819408	−	0.197823i
$956$		0			0
$957$	4.20889	+	0.855860i	0.136054	+	0.0276660i
$958$		0			0
$959$	−3.70623			−0.119681
$960$		0			0
$961$	−27.2792			−0.879975
$962$		0			0
$963$	15.8100	−	15.5428i	0.509471	−	0.500861i
$964$		0			0
$965$	16.1590	−	39.0114i	0.520178	−	1.25582i
$966$		0			0
$967$	−25.3843	+	25.3843i	−0.816305	+	0.816305i	−0.985571	−	0.169265i	$-0.945861\pi$
$967$	−25.3843	+	25.3843i	−0.816305	+	0.816305i	0.169265	+	0.985571i	$0.445861\pi$
$968$		0			0
$969$	21.2569	−	4.13418i	0.682869	−	0.132809i
$970$		0			0
$971$	−2.40697	+	5.81095i	−0.0772435	+	0.186482i	−0.957784	−	0.287488i	$-0.907180\pi$
$971$	−2.40697	+	5.81095i	−0.0772435	+	0.186482i	0.880541	+	0.473971i	$0.157180\pi$
$972$		0			0
$973$	−4.76718	+	1.97463i	−0.152829	+	0.0633037i
$974$		0			0
$975$	−25.0640	+	37.1671i	−0.802690	+	1.19030i
$976$		0			0
$977$	−23.9584			−0.766497			−0.383249	−	0.923645i	$-0.625195\pi$
$977$	−23.9584			−0.766497			−0.383249	+	0.923645i	$0.625195\pi$
$978$		0			0
$979$	−3.66735	−	8.85376i	−0.117209	−	0.282967i
$980$		0			0
$981$	−40.2717	−	0.343191i	−1.28578	−	0.0109572i
$982$		0			0
$983$	21.9489	−	21.9489i	0.700063	−	0.700063i	−0.264361	−	0.964424i	$-0.585161\pi$
$983$	21.9489	−	21.9489i	0.700063	−	0.700063i	0.964424	+	0.264361i	$0.0851611\pi$
$984$		0			0
$985$	5.90611	+	5.90611i	0.188184	+	0.188184i
$986$		0			0
$987$	−10.2190	+	6.76531i	−0.325274	+	0.215342i
$988$		0			0
$989$	−11.6777	+	4.83705i	−0.371328	+	0.153809i
$990$		0			0
$991$		−	31.9976i		−	1.01644i	−0.861229	−	0.508218i	$-0.830304\pi$
$991$		−	31.9976i		−	1.01644i	0.861229	−	0.508218i	$-0.169696\pi$
$992$		0			0
$993$	−20.4536	+	30.3304i	−0.649074	+	0.962505i
$994$		0			0
$995$	19.3829	+	46.7944i	0.614478	+	1.48348i
$996$		0			0
$997$	29.5281	+	12.2309i	0.935164	+	0.387358i	0.797635	−	0.603140i	$-0.206084\pi$
$997$	29.5281	+	12.2309i	0.935164	+	0.387358i	0.137529	+	0.990498i	$0.456084\pi$
$998$		0			0
$999$	2.73123	−	1.77488i	0.0864124	−	0.0561547i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.o.a.143.6		56
3.2	odd	2	inner	384.2.o.a.143.3		56
4.3	odd	2		96.2.o.a.59.13	yes	56
8.3	odd	2		768.2.o.b.287.6		56
8.5	even	2		768.2.o.a.287.9		56
12.11	even	2		96.2.o.a.59.2	✓	56
24.5	odd	2		768.2.o.a.287.12		56
24.11	even	2		768.2.o.b.287.3		56
32.3	odd	8		768.2.o.a.479.12		56
32.13	even	8		96.2.o.a.83.2	yes	56
32.19	odd	8	inner	384.2.o.a.239.3		56
32.29	even	8		768.2.o.b.479.3		56
96.29	odd	8		768.2.o.b.479.6		56
96.35	even	8		768.2.o.a.479.9		56
96.77	odd	8		96.2.o.a.83.13	yes	56
96.83	even	8	inner	384.2.o.a.239.6		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.o.a.59.2	✓	56	12.11	even	2
96.2.o.a.59.13	yes	56	4.3	odd	2
96.2.o.a.83.2	yes	56	32.13	even	8
96.2.o.a.83.13	yes	56	96.77	odd	8
384.2.o.a.143.3		56	3.2	odd	2	inner
384.2.o.a.143.6		56	1.1	even	1	trivial
384.2.o.a.239.3		56	32.19	odd	8	inner
384.2.o.a.239.6		56	96.83	even	8	inner
768.2.o.a.287.9		56	8.5	even	2
768.2.o.a.287.12		56	24.5	odd	2
768.2.o.a.479.9		56	96.35	even	8
768.2.o.a.479.12		56	32.3	odd	8
768.2.o.b.287.3		56	24.11	even	2
768.2.o.b.287.6		56	8.3	odd	2
768.2.o.b.479.3		56	32.29	even	8
768.2.o.b.479.6		56	96.29	odd	8

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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.o (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.345141 + 1.69731i) q^{3} +(-1.56013 + 3.76650i) q^{5} +(0.838552 - 0.838552i) q^{7} +(-2.76175 - 1.17163i) q^{9} +O(q^{10})\)	\(q+(-0.345141 + 1.69731i) q^{3} +(-1.56013 + 3.76650i) q^{5} +(0.838552 - 0.838552i) q^{7} +(-2.76175 - 1.17163i) q^{9} +(-0.249049 + 0.601256i) q^{11} +(-2.05771 + 0.852332i) q^{13} +(-5.85446 - 3.94801i) q^{15} +3.23677 q^{17} +(-1.47818 - 3.56865i) q^{19} +(1.13387 + 1.71271i) q^{21} +(-2.58369 + 2.58369i) q^{23} +(-8.21694 - 8.21694i) q^{25} +(2.94182 - 4.28319i) q^{27} +(-3.52027 + 1.45815i) q^{29} +7.63408i q^{31} +(-0.934564 - 0.630232i) q^{33} +(1.85015 + 4.46665i) q^{35} +(0.579146 + 0.239890i) q^{37} +(-0.736474 - 3.78676i) q^{39} +(3.54554 + 3.54554i) q^{41} +(3.19595 + 1.32381i) q^{43} +(8.72163 - 8.57424i) q^{45} +5.96658i q^{47} +5.59366i q^{49} +(-1.11714 + 5.49382i) q^{51} +(0.762825 + 0.315973i) q^{53} +(-1.87608 - 1.87608i) q^{55} +(6.56731 - 1.27725i) q^{57} +(5.86827 + 2.43072i) q^{59} +(2.68247 + 6.47607i) q^{61} +(-3.29834 + 1.33340i) q^{63} -9.08011i q^{65} +(-4.78575 + 1.98232i) q^{67} +(-3.49360 - 5.27708i) q^{69} +(-10.2094 - 10.2094i) q^{71} +(8.09458 - 8.09458i) q^{73} +(16.7827 - 11.1107i) q^{75} +(0.295345 + 0.713025i) q^{77} +11.5343 q^{79} +(6.25458 + 6.47149i) q^{81} +(0.998651 - 0.413655i) q^{83} +(-5.04979 + 12.1913i) q^{85} +(-1.25994 - 6.47828i) q^{87} +(-10.4124 + 10.4124i) q^{89} +(-1.01077 + 2.44022i) q^{91} +(-12.9574 - 2.63484i) q^{93} +15.7475 q^{95} +9.21596 q^{97} +(1.39226 - 1.36873i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{3} + 8 q^{7} - 4 q^{9}+O(q^{10}) \) 56 * q + 4 * q^3 + 8 * q^7 - 4 * q^9	\( 56 q + 4 q^{3} + 8 q^{7} - 4 q^{9} - 8 q^{13} + 8 q^{15} + 8 q^{19} - 4 q^{21} - 8 q^{25} + 28 q^{27} - 8 q^{33} - 8 q^{37} + 28 q^{39} + 8 q^{43} - 4 q^{45} + 16 q^{51} - 24 q^{55} - 4 q^{57} - 40 q^{61} - 56 q^{67} - 4 q^{69} - 8 q^{73} - 16 q^{75} - 16 q^{79} - 48 q^{85} - 52 q^{87} - 40 q^{91} + 8 q^{93} - 16 q^{97} - 60 q^{99}+O(q^{100}) \) 56 * q + 4 * q^3 + 8 * q^7 - 4 * q^9 - 8 * q^13 + 8 * q^15 + 8 * q^19 - 4 * q^21 - 8 * q^25 + 28 * q^27 - 8 * q^33 - 8 * q^37 + 28 * q^39 + 8 * q^43 - 4 * q^45 + 16 * q^51 - 24 * q^55 - 4 * q^57 - 40 * q^61 - 56 * q^67 - 4 * q^69 - 8 * q^73 - 16 * q^75 - 16 * q^79 - 48 * q^85 - 52 * q^87 - 40 * q^91 + 8 * q^93 - 16 * q^97 - 60 * q^99

Introduction

L-functions

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