LMFDB - Embedded newform 768.2.o.b.287.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(95,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, 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("768.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.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:	$6.13251087523$
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			287.6
Character	$\chi$	$=$	768.287
Dual form			768.2.o.b.479.6

$q$-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 $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{8}\right)$

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	$-0.509843\pi$
$5$	1.56013	−	3.76650i	0.697713	−	1.68443i	0.728631	−	0.684906i	$-0.240157\pi$
$6$		0			0
$7$	−0.838552	+	0.838552i	−0.316943	+	0.316943i	−0.847592	−	0.530649i	$-0.821948\pi$
$7$	−0.838552	+	0.838552i	−0.316943	+	0.316943i	0.530649	+	0.847592i	$0.321948\pi$
$8$		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	−0.0786194	−	0.996905i	$-0.525051\pi$
$13$	2.05771	−	0.852332i	0.570706	−	0.236394i	0.649326	+	0.760510i	$0.275051\pi$
$14$		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	−0.384421	−	0.923158i	$-0.625599\pi$
$23$	2.58369	−	2.58369i	0.538737	−	0.538737i	0.923158	+	0.384421i	$0.125599\pi$
$24$		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	−0.0310857	−	0.999517i	$-0.509896\pi$
$29$	3.52027	−	1.45815i	0.653698	−	0.270771i	0.684784	+	0.728746i	$0.259896\pi$
$30$		0			0
$31$		−	7.63408i		−	1.37112i	−0.728015	−	0.685561i	$-0.759557\pi$
$31$		−	7.63408i		−	1.37112i	0.728015	−	0.685561i	$-0.240443\pi$
$32$		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	0.334570	−	0.942371i	$-0.391409\pi$
$37$	−0.579146	−	0.239890i	−0.0952110	−	0.0394377i	−0.429781	+	0.902933i	$0.641409\pi$
$38$		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	$-0.856693\pi$
$47$		−	5.96658i		−	0.870315i	0.900354	−	0.435158i	$-0.143307\pi$
$48$		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	0.329677	−	0.944094i	$-0.393060\pi$
$53$	−0.762825	−	0.315973i	−0.104782	−	0.0434022i	−0.434459	+	0.900692i	$0.643060\pi$
$54$		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	$-0.976871\pi$
$61$	−2.68247	−	6.47607i	−0.343456	−	0.829175i	0.653906	−	0.756576i	$-0.273129\pi$
$62$		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	$0.0775229\pi$
$71$	10.2094	+	10.2094i	1.21163	+	1.21163i	0.241145	+	0.970489i	$0.422477\pi$
$72$		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	$-0.724753\pi$
$79$	−11.5343			−1.29771			−0.648857	+	0.760910i	$0.724753\pi$
$80$		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	−0.822687	−	0.568494i	$-0.807526\pi$
$101$	1.61830	−	3.90691i	0.161026	−	0.388752i	0.983714	+	0.179742i	$0.0575262\pi$
$102$		0			0
$103$	−4.29846	+	4.29846i	−0.423540	+	0.423540i	−0.886421	−	0.462881i	$-0.846816\pi$
$103$	−4.29846	+	4.29846i	−0.423540	+	0.423540i	0.462881	+	0.886421i	$0.346816\pi$
$104$		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	−0.887085	−	0.461606i	$-0.847273\pi$
$109$	−12.4025	+	5.13729i	−1.18794	+	0.492063i	−0.300859	+	0.953669i	$0.597273\pi$
$110$		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	$-0.989766\pi$
$127$		−	0.724490i		−	0.0642881i	0.999483	−	0.0321441i	$-0.0102335\pi$
$128$		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	0.595423	−	0.803412i	$-0.296984\pi$
$149$	5.47285	+	2.26693i	0.448353	+	0.185714i	−0.147070	+	0.989126i	$0.546984\pi$
$150$		0			0
$151$	−5.81381	−	5.81381i	−0.473121	−	0.473121i	0.429802	−	0.902923i	$-0.358583\pi$
$151$	−5.81381	−	5.81381i	−0.473121	−	0.473121i	−0.902923	+	0.429802i	$0.858583\pi$
$152$		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	0.999446	−	0.0332797i	$-0.0105952\pi$
$157$	3.37305	+	8.14326i	0.269199	+	0.649903i	−0.730247	+	0.683183i	$0.760595\pi$
$158$		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	0.397157	−	0.917751i	$-0.369997\pi$
$167$	−6.72756	−	6.72756i	−0.520594	−	0.520594i	−0.917751	+	0.397157i	$0.869997\pi$
$168$		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	0.934017	−	0.357228i	$-0.116278\pi$
$173$	0.275804	+	0.665850i	0.0209690	+	0.0506236i	−0.913048	+	0.407852i	$0.866278\pi$
$174$		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	−0.793147	−	0.609030i	$-0.791559\pi$
$181$	2.66842	−	6.44214i	0.198342	−	0.478841i	0.991489	+	0.130190i	$0.0415587\pi$
$182$		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	$-0.481298\pi$
$191$	1.62308			0.117442			0.0587210	+	0.998274i	$0.481298\pi$
$192$		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	−0.949346	−	0.314234i	$-0.898252\pi$
$197$	−0.784033	+	1.89282i	−0.0558601	+	0.134858i	0.893486	+	0.449092i	$0.148252\pi$
$198$		0			0
$199$	−8.78498	+	8.78498i	−0.622751	+	0.622751i	−0.946234	−	0.323483i	$-0.895146\pi$
$199$	−8.78498	+	8.78498i	−0.622751	+	0.622751i	0.323483	+	0.946234i	$0.395146\pi$
$200$		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	$0.184830\pi$
$223$			16.3840i			1.09715i	−0.836101	+	0.548576i	$0.815170\pi$
$224$		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	0.722206	−	0.691678i	$-0.243128\pi$
$229$	11.2556	+	4.66223i	0.743792	+	0.308089i	0.0215864	+	0.999767i	$0.493128\pi$
$230$		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	$-0.787829\pi$
$239$		−	19.1168i		−	1.23657i	0.785956	−	0.618283i	$-0.212171\pi$
$240$		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	0.952264	−	0.305276i	$-0.0987488\pi$
$263$	10.4924	+	10.4924i	0.646988	+	0.646988i	−0.305276	+	0.952264i	$0.598749\pi$
$264$		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	$0.00398337\pi$
$269$	4.94856	+	11.9469i	0.301719	+	0.728414i	−0.698203	+	0.715900i	$0.746017\pi$
$270$		0			0
$271$	7.03570			0.427388			0.213694	−	0.976901i	$-0.431450\pi$
$271$	7.03570			0.427388			0.213694	+	0.976901i	$0.431450\pi$
$272$		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	$0.389368\pi$
$277$	−9.40456	+	22.7046i	−0.565065	+	1.36419i	−0.905671	+	0.423982i	$0.860632\pi$
$278$		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	−0.997109	−	0.0759896i	$-0.975788\pi$
$293$	−4.07927	+	9.84823i	−0.238314	+	0.575340i	0.758795	+	0.651329i	$0.225788\pi$
$294$		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	$0.566764\pi$
$311$	−20.9205	+	20.9205i	−1.18629	+	1.18629i	−0.978084	+	0.208210i	$0.933236\pi$
$312$		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	−0.396191	−	0.918168i	$-0.629668\pi$
$317$	−0.482452	+	0.199838i	−0.0270972	+	0.0112240i	0.369094	+	0.929392i	$0.379668\pi$
$318$		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	$-0.717239\pi$
$349$	−13.7021	−	33.0798i	−0.733457	−	1.77072i	−0.102741	−	0.994708i	$-0.532761\pi$
$350$		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	0.778689	−	0.627410i	$-0.215885\pi$
$359$	2.86633	+	2.86633i	0.151279	+	0.151279i	−0.627410	+	0.778689i	$0.715885\pi$
$360$		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	$-0.773276\pi$
$367$	−28.9994			−1.51376			−0.756878	+	0.653557i	$0.773276\pi$
$368$		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	$0.295859\pi$
$373$	−7.55879	+	18.2485i	−0.391379	+	0.944873i	−0.989640	+	0.143572i	$0.954141\pi$
$374$		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	$-0.345805\pi$
$383$	18.2276			0.931388			0.465694	+	0.884946i	$0.345805\pi$
$384$		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	−0.941706	−	0.336436i	$-0.890779\pi$
$389$	−0.747968	+	1.80575i	−0.0379235	+	0.0915554i	0.903783	+	0.427991i	$0.140779\pi$
$390$		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	−0.187872	−	0.982193i	$-0.560159\pi$
$397$	7.44786	−	3.08500i	0.373797	−	0.154832i	0.561670	+	0.827361i	$0.310159\pi$
$398$		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	−0.0375773	−	0.999294i	$-0.511964\pi$
$421$	−15.8146	−	6.55062i	−0.770756	−	0.319258i	−0.733179	+	0.680036i	$0.761964\pi$
$422$		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	$0.170625\pi$
$431$			21.2060i			1.02146i	−0.859742	+	0.510729i	$0.829375\pi$
$432$		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	$0.0779983\pi$
$439$	25.4093	+	25.4093i	1.21272	+	1.21272i	0.242594	+	0.970128i	$0.422002\pi$
$440$		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	$0.0457618\pi$
$461$	8.39897	+	20.2769i	0.391179	+	0.944389i	−0.598505	+	0.801119i	$0.704238\pi$
$462$		0			0
$463$	24.1790			1.12369			0.561847	−	0.827241i	$-0.310091\pi$
$463$	24.1790			1.12369			0.561847	+	0.827241i	$0.310091\pi$
$464$		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	$-0.318049\pi$
$479$	23.6803			1.08198			0.540991	+	0.841028i	$0.318049\pi$
$480$		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	−0.252623	−	0.967565i	$-0.581293\pi$
$487$	15.7774	−	15.7774i	0.714942	−	0.714942i	0.967565	+	0.252623i	$0.0812931\pi$
$488$		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	−0.476802	−	0.879011i	$-0.658204\pi$
$503$	9.02060	−	9.02060i	0.402208	−	0.402208i	0.879011	+	0.476802i	$0.158204\pi$
$504$		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	−0.668873	−	0.743376i	$-0.733223\pi$
$509$	−13.9019	+	5.75836i	−0.616192	+	0.255235i	0.0526815	+	0.998611i	$0.483223\pi$
$510$		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	$-0.911499\pi$
$541$	−11.0650	−	26.7133i	−0.475722	−	1.14849i	0.485875	−	0.874028i	$-0.338501\pi$
$542$		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	$-0.984611\pi$
$557$	−7.71096	−	18.6159i	−0.326724	−	0.788781i	0.672108	−	0.740453i	$-0.265389\pi$
$558$		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	−0.204028	−	0.978965i	$-0.565403\pi$
$599$	18.9662	−	18.9662i	0.774937	−	0.774937i	0.978965	+	0.204028i	$0.0654033\pi$
$600$		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	$-0.942995\pi$
$607$		−	8.77741i		−	0.356264i	0.984007	−	0.178132i	$-0.0570054\pi$
$608$		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	0.463738	−	0.885972i	$-0.346508\pi$
$613$	4.08951	+	1.69393i	0.165174	+	0.0684172i	−0.298564	+	0.954389i	$0.596508\pi$
$614$		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	0.920005	−	0.391907i	$-0.128185\pi$
$631$	13.2657	+	13.2657i	0.528098	+	0.528098i	−0.391907	+	0.920005i	$0.628185\pi$
$632$		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	0.0675491	−	0.997716i	$-0.478482\pi$
$647$	−23.6599	−	23.6599i	−0.930167	−	0.930167i	−0.997716	+	0.0675491i	$0.978482\pi$
$648$		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	$0.0889058\pi$
$653$	12.1760	+	29.3955i	0.476484	+	1.15033i	−0.484763	+	0.874646i	$0.661094\pi$
$654$		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	−0.962893	−	0.269882i	$-0.913015\pi$
$661$	−2.34448	+	5.66007i	−0.0911896	+	0.220151i	0.871704	+	0.490033i	$0.163015\pi$
$662$		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	$0.535369\pi$
$677$	−19.1300	+	46.1838i	−0.735224	+	1.77499i	−0.624338	+	0.781155i	$0.714631\pi$
$678$		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	−0.192182	−	0.981359i	$-0.561556\pi$
$701$	9.68643	−	4.01225i	0.365851	−	0.151541i	0.558033	+	0.829819i	$0.311556\pi$
$702$		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	0.958088	−	0.286473i	$-0.0924827\pi$
$709$	38.1564	+	15.8049i	1.43299	+	0.593565i	0.474904	+	0.880038i	$0.342483\pi$
$710$		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	$-0.664519\pi$
$719$		−	46.6233i		−	1.73876i	0.494147	−	0.869378i	$-0.335481\pi$
$720$		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	0.0630153	−	0.998013i	$-0.479928\pi$
$727$	−25.2103	−	25.2103i	−0.934997	−	0.934997i	−0.998013	+	0.0630153i	$0.979928\pi$
$728$		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	0.959973	−	0.280094i	$-0.0903657\pi$
$733$	2.25020	+	5.43246i	0.0831129	+	0.200652i	−0.876860	+	0.480747i	$0.840366\pi$
$734$		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	0.364139	−	0.931345i	$-0.381363\pi$
$743$	−15.4609	−	15.4609i	−0.567205	−	0.567205i	−0.931345	+	0.364139i	$0.881363\pi$
$744$		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	$-0.282627\pi$
$751$	34.5867			1.26209			0.631043	+	0.775748i	$0.282627\pi$
$752$		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	−0.749882	−	0.661571i	$-0.769890\pi$
$757$	6.82795	−	16.4841i	0.248166	−	0.599126i	0.998048	+	0.0624455i	$0.0198900\pi$
$758$		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	$-0.706290\pi$
$773$	10.7578	−	25.9715i	0.386929	−	0.934130i	0.990587	−	0.136886i	$-0.0437095\pi$
$774$		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	−0.365089	−	0.930973i	$-0.618961\pi$
$797$	0.989560	−	0.409889i	0.0350520	−	0.0145190i	0.400141	+	0.916454i	$0.368961\pi$
$798$		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	−0.217155	−	0.976137i	$-0.569678\pi$
$821$	−30.3992	−	12.5918i	−1.06094	−	0.439455i	−0.843785	+	0.536682i	$0.819678\pi$
$822$		0			0
$823$	−7.58486	−	7.58486i	−0.264392	−	0.264392i	0.562444	−	0.826835i	$-0.309861\pi$
$823$	−7.58486	−	7.58486i	−0.264392	−	0.264392i	−0.826835	+	0.562444i	$0.809861\pi$
$824$		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	0.949407	−	0.314047i	$-0.101685\pi$
$829$	1.61267	+	3.89332i	0.0560102	+	0.135221i	−0.893397	+	0.449268i	$0.851685\pi$
$830$		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	0.902940	−	0.429767i	$-0.141404\pi$
$839$	13.7057	+	13.7057i	0.473173	+	0.473173i	−0.429767	+	0.902940i	$0.641404\pi$
$840$		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	$-0.662988\pi$
$853$	13.8120	−	33.3450i	0.472913	−	1.14171i	0.962870	−	0.269966i	$-0.0870124\pi$
$854$		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	$-0.723021\pi$
$863$	−37.8790			−1.28942			−0.644708	+	0.764429i	$0.723021\pi$
$864$		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	−0.527789	−	0.849376i	$-0.676979\pi$
$877$	−8.89587	+	3.68479i	−0.300392	+	0.124426i	0.227397	+	0.973802i	$0.426979\pi$
$878$		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	−0.450885	−	0.892582i	$-0.648891\pi$
$887$	13.1549	−	13.1549i	0.441698	−	0.441698i	0.892582	+	0.450885i	$0.148891\pi$
$888$		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	$0.336218\pi$
$911$			52.5495i			1.74104i	−0.492132	+	0.870520i	$0.663782\pi$
$912$		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	$-0.977315\pi$
$919$	−32.3967	−	32.3967i	−1.06867	−	1.06867i	−0.0712063	−	0.997462i	$-0.522685\pi$
$920$		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	$0.110463\pi$
$941$	15.8263	+	38.2081i	0.515924	+	1.24555i	−0.424464	+	0.905445i	$0.639537\pi$
$942$		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	−0.169265	−	0.985571i	$-0.554139\pi$
$967$	25.3843	−	25.3843i	0.816305	−	0.816305i	0.985571	+	0.169265i	$0.0541395\pi$
$968$		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	−0.964424	−	0.264361i	$-0.914839\pi$
$983$	−21.9489	+	21.9489i	−0.700063	+	0.700063i	0.264361	+	0.964424i	$0.414839\pi$
$984$		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	$0.169696\pi$
$991$			31.9976i			1.01644i	−0.861229	+	0.508218i	$0.830304\pi$
$992$		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	−0.137529	−	0.990498i	$-0.543916\pi$
$997$	−29.5281	−	12.2309i	−0.935164	−	0.387358i	−0.797635	+	0.603140i	$0.793916\pi$
$998$		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	768.2.o.b.287.6		56
3.2	odd	2	inner	768.2.o.b.287.3		56
4.3	odd	2		768.2.o.a.287.9		56
8.3	odd	2		384.2.o.a.143.6		56
8.5	even	2		96.2.o.a.59.13	yes	56
12.11	even	2		768.2.o.a.287.12		56
24.5	odd	2		96.2.o.a.59.2	✓	56
24.11	even	2		384.2.o.a.143.3		56
32.3	odd	8		96.2.o.a.83.2	yes	56
32.13	even	8		768.2.o.a.479.12		56
32.19	odd	8	inner	768.2.o.b.479.3		56
32.29	even	8		384.2.o.a.239.3		56
96.29	odd	8		384.2.o.a.239.6		56
96.35	even	8		96.2.o.a.83.13	yes	56
96.77	odd	8		768.2.o.a.479.9		56
96.83	even	8	inner	768.2.o.b.479.6		56

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

Level:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.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

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