LMFDB - Embedded newform 444.2.w.c.125.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [444,2,Mod(29,444)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("444.29"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(444, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 6, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 444 = 2^{2} \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	444.w (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.54535784974$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			125.4
Character	$\chi$	$=$	444.125
Dual form			444.2.w.c.341.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.526856 - 1.64998i) q^{3} +(-0.425223 + 1.58695i) q^{5} +(-1.24138 - 2.15014i) q^{7} +(-2.44485 + 1.73860i) q^{9} -5.53300 q^{11} +(1.40068 + 0.375311i) q^{13} +(2.84247 - 0.134487i) q^{15} +(-3.55279 + 0.951967i) q^{17} +(-1.73061 - 0.463714i) q^{19} +(-2.89365 + 3.18107i) q^{21} +(-1.79198 - 1.79198i) q^{23} +(1.99252 + 1.15038i) q^{25} +(4.15673 + 3.11795i) q^{27} +(0.643988 - 0.643988i) q^{29} +(-5.86660 - 5.86660i) q^{31} +(2.91509 + 9.12931i) q^{33} +(3.94004 - 1.05573i) q^{35} +(-4.93235 + 3.55977i) q^{37} +(-0.118701 - 2.50882i) q^{39} +(-1.33247 - 2.30791i) q^{41} +(-6.92135 + 6.92135i) q^{43} +(-1.71947 - 4.61915i) q^{45} +7.23726i q^{47} +(0.417927 - 0.723870i) q^{49} +(3.44253 + 5.36047i) q^{51} +(-3.61769 - 2.08867i) q^{53} +(2.35276 - 8.78061i) q^{55} +(0.146661 + 3.09977i) q^{57} +(9.30754 - 2.49395i) q^{59} +(0.753770 - 2.81311i) q^{61} +(6.77323 + 3.09850i) q^{63} +(-1.19120 + 2.06322i) q^{65} +(9.23364 - 5.33104i) q^{67} +(-2.01262 + 3.90085i) q^{69} +(11.7434 - 6.78003i) q^{71} -12.9564i q^{73} +(0.848334 - 3.89370i) q^{75} +(6.86858 + 11.8967i) q^{77} +(-10.2025 - 2.73375i) q^{79} +(2.95455 - 8.50121i) q^{81} +(-5.13079 - 2.96226i) q^{83} -6.04291i q^{85} +(-1.40185 - 0.723277i) q^{87} +(-1.69688 - 6.33284i) q^{89} +(-0.931811 - 3.47757i) q^{91} +(-6.58891 + 12.7706i) q^{93} +(1.47179 - 2.54921i) q^{95} +(-6.50678 + 6.50678i) q^{97} +(13.5273 - 9.61966i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 10 q^{9} - 24 q^{19} - 18 q^{21} + 32 q^{31} - 44 q^{37} + 62 q^{39} - 4 q^{43} - 54 q^{45} + 24 q^{49} + 14 q^{51} + 20 q^{55} + 34 q^{57} + 36 q^{61} - 36 q^{63} + 12 q^{67} - 50 q^{69} - 20 q^{75}+ \cdots - 12 q^{99}+O(q^{100}) $ 40 * q - 10 * q^9 - 24 * q^19 - 18 * q^21 + 32 * q^31 - 44 * q^37 + 62 * q^39 - 4 * q^43 - 54 * q^45 + 24 * q^49 + 14 * q^51 + 20 * q^55 + 34 * q^57 + 36 * q^61 - 36 * q^63 + 12 * q^67 - 50 * q^69 - 20 * q^75 + 8 * q^79 + 10 * q^81 - 32 * q^87 + 20 * q^91 - 30 * q^93 + 52 * q^97 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/444\mathbb{Z}\right)^\times$.

$n$	$149$	$223$	$409$
$\chi(n)$	$-1$	$1$	$e\left(\frac{11}{12}\right)$

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
$3$	−0.526856	−	1.64998i	−0.304180	−	0.952615i
$3$	−0.526856	−	1.64998i	−0.304180	−	0.952615i
$4$		0			0
$5$	−0.425223	+	1.58695i	−0.190165	+	0.709707i	0.803300	+	0.595574i	$0.203076\pi$
$5$	−0.425223	+	1.58695i	−0.190165	+	0.709707i	−0.993466	+	0.114133i	$0.963591\pi$
$6$		0			0
$7$	−1.24138	−	2.15014i	−0.469199	−	0.812677i	0.530181	−	0.847885i	$-0.322124\pi$
$7$	−1.24138	−	2.15014i	−0.469199	−	0.812677i	−0.999380	+	0.0352075i	$0.988791\pi$
$8$		0			0
$9$	−2.44485	+	1.73860i	−0.814949	+	0.579533i
$10$		0			0
$11$	−5.53300			−1.66826			−0.834130	−	0.551567i	$-0.814030\pi$
$11$	−5.53300			−1.66826			−0.834130	+	0.551567i	$0.814030\pi$
$12$		0			0
$13$	1.40068	+	0.375311i	0.388479	+	0.104093i	0.447771	−	0.894148i	$-0.352218\pi$
$13$	1.40068	+	0.375311i	0.388479	+	0.104093i	−0.0592927	+	0.998241i	$0.518885\pi$
$14$		0			0
$15$	2.84247	−	0.134487i	0.733922	−	0.0347245i
$16$		0			0
$17$	−3.55279	+	0.951967i	−0.861678	+	0.230886i	−0.662486	−	0.749075i	$-0.730498\pi$
$17$	−3.55279	+	0.951967i	−0.861678	+	0.230886i	−0.199192	+	0.979960i	$0.563832\pi$
$18$		0			0
$19$	−1.73061	−	0.463714i	−0.397028	−	0.106383i	0.0547801	−	0.998498i	$-0.482554\pi$
$19$	−1.73061	−	0.463714i	−0.397028	−	0.106383i	−0.451808	+	0.892115i	$0.649221\pi$
$20$		0			0
$21$	−2.89365	+	3.18107i	−0.631447	+	0.694166i
$22$		0			0
$23$	−1.79198	−	1.79198i	−0.373655	−	0.373655i	0.495152	−	0.868806i	$-0.335112\pi$
$23$	−1.79198	−	1.79198i	−0.373655	−	0.373655i	−0.868806	+	0.495152i	$0.835112\pi$
$24$		0			0
$25$	1.99252	+	1.15038i	0.398504	+	0.230076i
$26$		0			0
$27$	4.15673	+	3.11795i	0.799963	+	0.600050i
$28$		0			0
$29$	0.643988	−	0.643988i	0.119586	−	0.119586i	−0.644781	−	0.764367i	$-0.723052\pi$
$29$	0.643988	−	0.643988i	0.119586	−	0.119586i	0.764367	+	0.644781i	$0.223052\pi$
$30$		0			0
$31$	−5.86660	−	5.86660i	−1.05367	−	1.05367i	−0.998475	−	0.0551979i	$-0.982421\pi$
$31$	−5.86660	−	5.86660i	−1.05367	−	1.05367i	−0.0551979	−	0.998475i	$-0.517579\pi$
$32$		0			0
$33$	2.91509	+	9.12931i	0.507452	+	1.58921i
$34$		0			0
$35$	3.94004	−	1.05573i	0.665988	−	0.178451i
$36$		0			0
$37$	−4.93235	+	3.55977i	−0.810873	+	0.585222i
$37$	−4.93235	+	3.55977i	−0.810873	+	0.585222i
$38$		0			0
$39$	−0.118701	−	2.50882i	−0.0190074	−	0.401733i
$40$		0			0
$41$	−1.33247	−	2.30791i	−0.208097	−	0.360434i	0.743018	−	0.669271i	$-0.233394\pi$
$41$	−1.33247	−	2.30791i	−0.208097	−	0.360434i	−0.951115	+	0.308837i	$0.900060\pi$
$42$		0			0
$43$	−6.92135	+	6.92135i	−1.05550	+	1.05550i	−0.0571293	+	0.998367i	$0.518195\pi$
$43$	−6.92135	+	6.92135i	−1.05550	+	1.05550i	−0.998367	+	0.0571293i	$0.981805\pi$
$44$		0			0
$45$	−1.71947	−	4.61915i	−0.256324	−	0.688582i
$46$		0			0
$47$			7.23726i			1.05566i	0.849349	+	0.527831i	$0.176995\pi$
$47$			7.23726i			1.05566i	−0.849349	+	0.527831i	$0.823005\pi$
$48$		0			0
$49$	0.417927	−	0.723870i	0.0597038	−	0.103410i
$50$		0			0
$51$	3.44253	+	5.36047i	0.482051	+	0.750616i
$52$		0			0
$53$	−3.61769	−	2.08867i	−0.496928	−	0.286901i	0.230516	−	0.973069i	$-0.425959\pi$
$53$	−3.61769	−	2.08867i	−0.496928	−	0.286901i	−0.727444	+	0.686167i	$0.759292\pi$
$54$		0			0
$55$	2.35276	−	8.78061i	0.317246	−	1.18398i
$56$		0			0
$57$	0.146661	+	3.09977i	0.0194258	+	0.410574i
$58$		0			0
$59$	9.30754	−	2.49395i	1.21174	−	0.324684i	0.404294	−	0.914629i	$-0.367517\pi$
$59$	9.30754	−	2.49395i	1.21174	−	0.324684i	0.807444	+	0.589945i	$0.200850\pi$
$60$		0			0
$61$	0.753770	−	2.81311i	0.0965104	−	0.360182i	−0.900734	−	0.434372i	$-0.856970\pi$
$61$	0.753770	−	2.81311i	0.0965104	−	0.360182i	0.997244	+	0.0741900i	$0.0236371\pi$
$62$		0			0
$63$	6.77323	+	3.09850i	0.853347	+	0.390374i
$64$		0			0
$65$	−1.19120	+	2.06322i	−0.147750	+	0.255911i
$66$		0			0
$67$	9.23364	−	5.33104i	1.12807	−	0.651291i	0.184620	−	0.982810i	$-0.440895\pi$
$67$	9.23364	−	5.33104i	1.12807	−	0.651291i	0.943448	+	0.331519i	$0.107561\pi$
$68$		0			0
$69$	−2.01262	+	3.90085i	−0.242290	+	0.469607i
$70$		0			0
$71$	11.7434	−	6.78003i	1.39368	−	0.804642i	0.399960	−	0.916533i	$-0.369024\pi$
$71$	11.7434	−	6.78003i	1.39368	−	0.804642i	0.993720	+	0.111891i	$0.0356908\pi$
$72$		0			0
$73$		−	12.9564i		−	1.51643i	−0.652004	−	0.758216i	$-0.726071\pi$
$73$		−	12.9564i		−	1.51643i	0.652004	−	0.758216i	$-0.273929\pi$
$74$		0			0
$75$	0.848334	−	3.89370i	0.0979571	−	0.449606i
$76$		0			0
$77$	6.86858	+	11.8967i	0.782747	+	1.35576i
$78$		0			0
$79$	−10.2025	−	2.73375i	−1.14787	−	0.307571i	−0.365760	−	0.930709i	$-0.619191\pi$
$79$	−10.2025	−	2.73375i	−1.14787	−	0.307571i	−0.782112	+	0.623138i	$0.785857\pi$
$80$		0			0
$81$	2.95455	−	8.50121i	0.328283	−	0.944579i
$82$		0			0
$83$	−5.13079	−	2.96226i	−0.563177	−	0.325150i	0.191243	−	0.981543i	$-0.438748\pi$
$83$	−5.13079	−	2.96226i	−0.563177	−	0.325150i	−0.754420	+	0.656392i	$0.772082\pi$
$84$		0			0
$85$		−	6.04291i		−	0.655445i
$86$		0			0
$87$	−1.40185	−	0.723277i	−0.150295	−	0.0775434i
$88$		0			0
$89$	−1.69688	−	6.33284i	−0.179869	−	0.671280i	−0.995671	−	0.0929487i	$-0.970371\pi$
$89$	−1.69688	−	6.33284i	−0.179869	−	0.671280i	0.815802	−	0.578331i	$-0.196296\pi$
$90$		0			0
$91$	−0.931811	−	3.47757i	−0.0976803	−	0.364548i
$92$		0			0
$93$	−6.58891	+	12.7706i	−0.683238	+	1.32425i
$94$		0			0
$95$	1.47179	−	2.54921i	0.151002	−	0.261543i
$96$		0			0
$97$	−6.50678	+	6.50678i	−0.660664	+	0.660664i	−0.955536	−	0.294873i	$-0.904723\pi$
$97$	−6.50678	+	6.50678i	−0.660664	+	0.660664i	0.294873	+	0.955536i	$0.404723\pi$
$98$		0			0
$99$	13.5273	−	9.61966i	1.35955	−	0.966812i
$100$		0			0
$101$	1.54896			0.154127			0.0770636	−	0.997026i	$-0.475446\pi$
$101$	1.54896			0.154127			0.0770636	+	0.997026i	$0.475446\pi$
$102$		0			0
$103$	3.44999	+	3.44999i	0.339937	+	0.339937i	0.856344	−	0.516406i	$-0.172731\pi$
$103$	3.44999	+	3.44999i	0.339937	+	0.339937i	−0.516406	+	0.856344i	$0.672731\pi$
$104$		0			0
$105$	−3.81776	−	5.94476i	−0.372575	−	0.580149i
$106$		0			0
$107$	12.2358	−	7.06434i	1.18288	−	0.682936i	0.226200	−	0.974081i	$-0.427370\pi$
$107$	12.2358	−	7.06434i	1.18288	−	0.682936i	0.956679	+	0.291145i	$0.0940363\pi$
$108$		0			0
$109$	−0.390674	−	1.45802i	−0.0374198	−	0.139653i	0.944689	−	0.327968i	$-0.106364\pi$
$109$	−0.390674	−	1.45802i	−0.0374198	−	0.139653i	−0.982109	+	0.188316i	$0.939697\pi$
$110$		0			0
$111$	8.47217	+	6.26278i	0.804142	+	0.594437i
$112$		0			0
$113$	−2.73122	−	10.1930i	−0.256931	−	0.958881i	−0.967006	−	0.254755i	$-0.918005\pi$
$113$	−2.73122	−	10.1930i	−0.256931	−	0.958881i	0.710074	−	0.704127i	$-0.248661\pi$
$114$		0			0
$115$	3.60579	−	2.08180i	0.336241	−	0.194129i
$116$		0			0
$117$	−4.07696	+	1.51764i	−0.376915	+	0.140306i
$118$		0			0
$119$	6.45724	+	6.45724i	0.591934	+	0.591934i
$120$		0			0
$121$	19.6140			1.78309
$122$		0			0
$123$	−3.10597	+	3.41448i	−0.280056	+	0.307873i
$124$		0			0
$125$	−8.48152	+	8.48152i	−0.758610	+	0.758610i
$126$		0			0
$127$	−5.69658	+	9.86677i	−0.505490	+	0.875534i	0.494490	+	0.869183i	$0.335355\pi$
$127$	−5.69658	+	9.86677i	−0.505490	+	0.875534i	−0.999980	+	0.00635095i	$0.997978\pi$
$128$		0			0
$129$	15.0666	+	7.77352i	1.32654	+	0.684420i
$130$		0			0
$131$	2.53558	+	9.46291i	0.221534	+	0.826778i	0.983763	+	0.179470i	$0.0574384\pi$
$131$	2.53558	+	9.46291i	0.221534	+	0.826778i	−0.762229	+	0.647308i	$0.775895\pi$
$132$		0			0
$133$	1.15130	+	4.29669i	0.0998300	+	0.372571i
$134$		0			0
$135$	−6.71558	+	5.27071i	−0.577985	+	0.453631i
$136$		0			0
$137$		−	1.01452i		−	0.0866765i	−0.999060	−	0.0433383i	$-0.986201\pi$
$137$		−	1.01452i		−	0.0866765i	0.999060	−	0.0433383i	$-0.0137993\pi$
$138$		0			0
$139$	−3.54499	−	2.04670i	−0.300682	−	0.173599i	0.342067	−	0.939676i	$-0.388873\pi$
$139$	−3.54499	−	2.04670i	−0.300682	−	0.173599i	−0.642749	+	0.766076i	$0.722206\pi$
$140$		0			0
$141$	11.9413	−	3.81299i	1.00564	−	0.321112i
$142$		0			0
$143$	−7.74996	−	2.07659i	−0.648084	−	0.173654i
$144$		0			0
$145$	0.748140	+	1.29582i	0.0621297	+	0.107612i
$146$		0			0
$147$	−1.41456	−	0.308194i	−0.116671	−	0.0254194i
$148$		0			0
$149$			17.2324i			1.41173i	0.708346	+	0.705865i	$0.249441\pi$
$149$			17.2324i			1.41173i	−0.708346	+	0.705865i	$0.750559\pi$
$150$		0			0
$151$	−10.0609	+	5.80867i	−0.818746	+	0.472703i	−0.849984	−	0.526809i	$-0.823388\pi$
$151$	−10.0609	+	5.80867i	−0.818746	+	0.472703i	0.0312380	+	0.999512i	$0.490055\pi$
$152$		0			0
$153$	7.03094	−	8.50429i	0.568417	−	0.687531i
$154$		0			0
$155$	11.8046	−	6.81541i	0.948172	−	0.547427i
$156$		0			0
$157$	−2.44604	+	4.23666i	−0.195215	+	0.338122i	−0.946971	−	0.321319i	$-0.895874\pi$
$157$	−2.44604	+	4.23666i	−0.195215	+	0.338122i	0.751756	+	0.659441i	$0.229207\pi$
$158$		0			0
$159$	−1.54026	+	7.06953i	−0.122151	+	0.560651i
$160$		0			0
$161$	−1.62848	+	6.07756i	−0.128342	+	0.478979i
$162$		0			0
$163$	−21.1321	+	5.66234i	−1.65520	+	0.443509i	−0.961061	−	0.276335i	$-0.910880\pi$
$163$	−21.1321	+	5.66234i	−1.65520	+	0.443509i	−0.694136	+	0.719844i	$0.744213\pi$
$164$		0			0
$165$	−15.7274	+	0.744118i	−1.22437	+	0.0579295i
$166$		0			0
$167$	1.57877	−	5.89204i	0.122169	−	0.455940i	−0.877554	−	0.479477i	$-0.840826\pi$
$167$	1.57877	−	5.89204i	0.122169	−	0.455940i	0.999723	+	0.0235376i	$0.00749294\pi$
$168$		0			0
$169$	−9.43728	−	5.44862i	−0.725945	−	0.419125i
$170$		0			0
$171$	5.03728	−	1.87512i	0.385210	−	0.143394i
$172$		0			0
$173$	−0.104248	+	0.180563i	−0.00792583	+	0.0137279i	−0.869961	−	0.493120i	$-0.835856\pi$
$173$	−0.104248	+	0.180563i	−0.00792583	+	0.0137279i	0.862035	+	0.506848i	$0.169190\pi$
$174$		0			0
$175$		−	5.71227i		−	0.431807i
$176$		0			0
$177$	−9.01868	−	14.0433i	−0.677886	−	1.05556i
$178$		0			0
$179$	−9.26755	+	9.26755i	−0.692689	+	0.692689i	−0.962823	−	0.270134i	$-0.912932\pi$
$179$	−9.26755	+	9.26755i	−0.692689	+	0.692689i	0.270134	+	0.962823i	$0.412932\pi$
$180$		0			0
$181$	9.90041	+	17.1480i	0.735892	+	1.27460i	0.954331	+	0.298751i	$0.0965700\pi$
$181$	9.90041	+	17.1480i	0.735892	+	1.27460i	−0.218440	+	0.975850i	$0.570097\pi$
$182$		0			0
$183$	−5.03869	+	0.238399i	−0.372471	+	0.0176229i
$184$		0			0
$185$	−3.55183	−	9.34110i	−0.261136	−	0.686771i
$186$		0			0
$187$	19.6576	−	5.26723i	1.43750	−	0.385178i
$188$		0			0
$189$	1.54393	−	12.8081i	0.112305	−	0.931654i
$190$		0			0
$191$	−3.25885	−	3.25885i	−0.235802	−	0.235802i	0.579307	−	0.815109i	$-0.303323\pi$
$191$	−3.25885	−	3.25885i	−0.235802	−	0.235802i	−0.815109	+	0.579307i	$0.803323\pi$
$192$		0			0
$193$	7.31034	−	7.31034i	0.526210	−	0.526210i	−0.393230	−	0.919440i	$-0.628642\pi$
$193$	7.31034	−	7.31034i	0.526210	−	0.526210i	0.919440	+	0.393230i	$0.128642\pi$
$194$		0			0
$195$	4.03186	+	0.878436i	0.288728	+	0.0629061i
$196$		0			0
$197$	−17.1897	−	9.92450i	−1.22472	−	0.707091i	−0.258798	−	0.965931i	$-0.583326\pi$
$197$	−17.1897	−	9.92450i	−1.22472	−	0.707091i	−0.965920	+	0.258840i	$0.916660\pi$
$198$		0			0
$199$	−12.5690	−	12.5690i	−0.890990	−	0.890990i	0.103626	−	0.994616i	$-0.466955\pi$
$199$	−12.5690	−	12.5690i	−0.890990	−	0.890990i	−0.994616	+	0.103626i	$0.966955\pi$
$200$		0			0
$201$	−13.6609	−	12.4266i	−0.963565	−	0.876505i
$202$		0			0
$203$	−2.18410	−	0.585229i	−0.153294	−	0.0410750i
$204$		0			0
$205$	4.22914	−	1.13319i	0.295376	−	0.0791457i
$206$		0			0
$207$	7.49667	+	1.26558i	0.521054	+	0.0879642i
$208$		0			0
$209$	9.57543	+	2.56573i	0.662346	+	0.177475i
$210$		0			0
$211$	26.9548			1.85564			0.927822	−	0.373023i	$-0.121679\pi$
$211$	26.9548			1.85564			0.927822	+	0.373023i	$0.121679\pi$
$212$		0			0
$213$	−17.3739	−	15.8042i	−1.19044	−	1.08288i
$214$		0			0
$215$	−8.04074	−	13.9270i	−0.548374	−	0.949812i
$216$		0			0
$217$	−5.33132	+	19.8967i	−0.361913	+	1.35068i
$218$		0			0
$219$	−21.3778	+	6.82615i	−1.44457	+	0.461268i
$220$		0			0
$221$	−5.33360			−0.358777
$222$		0			0
$223$	3.34158			0.223769			0.111884	−	0.993721i	$-0.464311\pi$
$223$	3.34158			0.223769			0.111884	+	0.993721i	$0.464311\pi$
$224$		0			0
$225$	−6.87146	+	0.651686i	−0.458097	+	0.0434457i
$226$		0			0
$227$	−7.68219	+	28.6703i	−0.509885	+	1.90292i	−0.0883919	+	0.996086i	$0.528173\pi$
$227$	−7.68219	+	28.6703i	−0.509885	+	1.90292i	−0.421493	+	0.906832i	$0.638494\pi$
$228$		0			0
$229$	8.61118	+	14.9150i	0.569043	+	0.985611i	0.996661	+	0.0816514i	$0.0260194\pi$
$229$	8.61118	+	14.9150i	0.569043	+	0.985611i	−0.427618	+	0.903959i	$0.640647\pi$
$230$		0			0
$231$	16.0106	−	17.6008i	1.05342	−	1.15805i
$232$		0			0
$233$	−7.22299			−0.473194			−0.236597	−	0.971608i	$-0.576032\pi$
$233$	−7.22299			−0.473194			−0.236597	+	0.971608i	$0.576032\pi$
$234$		0			0
$235$	−11.4852	−	3.07745i	−0.749211	−	0.200750i
$236$		0			0
$237$	0.864618	+	18.2742i	0.0561629	+	1.18704i
$238$		0			0
$239$	−26.2747	+	7.04028i	−1.69957	+	0.455398i	−0.972831	−	0.231518i	$-0.925631\pi$
$239$	−26.2747	+	7.04028i	−1.69957	+	0.455398i	−0.726737	+	0.686916i	$0.758964\pi$
$240$		0			0
$241$	−4.08602	−	1.09485i	−0.263204	−	0.0705252i	0.124804	−	0.992181i	$-0.460170\pi$
$241$	−4.08602	−	1.09485i	−0.263204	−	0.0705252i	−0.388007	+	0.921656i	$0.626837\pi$
$242$		0			0
$243$	−15.5834	−	0.396024i	−0.999677	−	0.0254050i
$244$		0			0
$245$	0.971037	+	0.971037i	0.0620373	+	0.0620373i
$246$		0			0
$247$	−2.24999	−	1.29903i	−0.143163	−	0.0826553i
$248$		0			0
$249$	−2.18448	+	10.0264i	−0.138436	+	0.635395i
$250$		0			0
$251$	5.48883	−	5.48883i	0.346452	−	0.346452i	−0.512334	−	0.858786i	$-0.671219\pi$
$251$	5.48883	−	5.48883i	0.346452	−	0.346452i	0.858786	+	0.512334i	$0.171219\pi$
$252$		0			0
$253$	9.91504	+	9.91504i	0.623353	+	0.623353i
$254$		0			0
$255$	−9.97066	+	3.18374i	−0.624387	+	0.199374i
$256$		0			0
$257$	19.5592	−	5.24088i	1.22007	−	0.326917i	0.409365	−	0.912371i	$-0.365750\pi$
$257$	19.5592	−	5.24088i	1.22007	−	0.326917i	0.810706	+	0.585454i	$0.199084\pi$
$258$		0			0
$259$	13.7769	+	6.18621i	0.856058	+	0.384393i
$260$		0			0
$261$	−0.454815	+	2.69409i	−0.0281523	+	0.166760i
$262$		0			0
$263$	−10.5847	−	18.3332i	−0.652679	−	1.13047i	−0.982470	−	0.186420i	$-0.940312\pi$
$263$	−10.5847	−	18.3332i	−0.652679	−	1.13047i	0.329791	−	0.944054i	$-0.393022\pi$
$264$		0			0
$265$	4.85295	−	4.85295i	0.298115	−	0.298115i
$266$		0			0
$267$	−9.55503	+	6.13631i	−0.584759	+	0.375536i
$268$		0			0
$269$			0.480089i			0.0292716i	0.999893	+	0.0146358i	$0.00465888\pi$
$269$			0.480089i			0.0292716i	−0.999893	+	0.0146358i	$0.995341\pi$
$270$		0			0
$271$	2.63631	−	4.56622i	0.160144	−	0.277378i	−0.774776	−	0.632236i	$-0.782137\pi$
$271$	2.63631	−	4.56622i	0.160144	−	0.277378i	0.934920	+	0.354858i	$0.115471\pi$
$272$		0			0
$273$	−5.24697	+	3.36964i	−0.317561	+	0.203940i
$274$		0			0
$275$	−11.0246	−	6.36506i	−0.664809	−	0.383828i
$276$		0			0
$277$	1.84071	−	6.86962i	0.110597	−	0.412755i	−0.888322	−	0.459220i	$-0.848129\pi$
$277$	1.84071	−	6.86962i	0.110597	−	0.412755i	0.998920	+	0.0464648i	$0.0147955\pi$
$278$		0			0
$279$	24.5426	+	4.14328i	1.46933	+	0.248051i
$280$		0			0
$281$	23.1370	−	6.19953i	1.38024	−	0.369833i	0.509029	−	0.860749i	$-0.330005\pi$
$281$	23.1370	−	6.19953i	1.38024	−	0.369833i	0.871207	+	0.490916i	$0.163338\pi$
$282$		0			0
$283$	−7.68728	+	28.6893i	−0.456961	+	1.70540i	0.225296	+	0.974290i	$0.427665\pi$
$283$	−7.68728	+	28.6893i	−0.456961	+	1.70540i	−0.682257	+	0.731112i	$0.739001\pi$
$284$		0			0
$285$	−4.98155	−	1.08535i	−0.295082	−	0.0642905i
$286$		0			0
$287$	−3.30822	+	5.73000i	−0.195278	+	0.338231i
$288$		0			0
$289$	−3.00636	+	1.73572i	−0.176845	+	0.102101i
$290$		0			0
$291$	14.1642	+	7.30790i	0.830319	+	0.428397i
$292$		0			0
$293$	−26.6034	+	15.3595i	−1.55419	+	0.897312i	−0.556396	+	0.830917i	$0.687816\pi$
$293$	−26.6034	+	15.3595i	−1.55419	+	0.897312i	−0.997793	+	0.0663946i	$0.978850\pi$
$294$		0			0
$295$			15.8311i			0.921723i
$296$		0			0
$297$	−22.9992	−	17.2516i	−1.33455	−	1.00104i
$298$		0			0
$299$	−1.83744	−	3.18255i	−0.106262	−	0.184051i
$300$		0			0
$301$	23.4739	+	6.28982i	1.35302	+	0.362539i
$302$		0			0
$303$	−0.816078	−	2.55575i	−0.0468824	−	0.146824i
$304$		0			0
$305$	4.14375	+	2.39240i	0.237271	+	0.136988i
$306$		0			0
$307$			2.45030i			0.139846i	0.997552	+	0.0699231i	$0.0222754\pi$
$307$			2.45030i			0.139846i	−0.997552	+	0.0699231i	$0.977725\pi$
$308$		0			0
$309$	3.87475	−	7.51004i	0.220427	−	0.427231i
$310$		0			0
$311$	−6.41896	−	23.9559i	−0.363986	−	1.35841i	−0.868790	−	0.495180i	$-0.835102\pi$
$311$	−6.41896	−	23.9559i	−0.363986	−	1.35841i	0.504804	−	0.863234i	$-0.331565\pi$
$312$		0			0
$313$	4.73126	+	17.6573i	0.267426	+	0.998049i	0.960748	+	0.277421i	$0.0894797\pi$
$313$	4.73126	+	17.6573i	0.267426	+	0.998049i	−0.693322	+	0.720628i	$0.743854\pi$
$314$		0			0
$315$	−7.79730	+	9.43125i	−0.439328	+	0.531391i
$316$		0			0
$317$	15.2556	−	26.4235i	0.856842	−	1.48409i	−0.0180831	−	0.999836i	$-0.505756\pi$
$317$	15.2556	−	26.4235i	0.856842	−	1.48409i	0.874925	−	0.484258i	$-0.160910\pi$
$318$		0			0
$319$	−3.56318	+	3.56318i	−0.199500	+	0.199500i
$320$		0			0
$321$	−18.1025	−	16.4669i	−1.01038	−	0.919092i
$322$		0			0
$323$	6.58992			0.366673
$324$		0			0
$325$	2.35913	+	2.35913i	0.130861	+	0.130861i
$326$		0			0
$327$	−2.19986	+	1.41277i	−0.121653	+	0.0781262i
$328$		0			0
$329$	15.5611	−	8.98422i	0.857913	−	0.495316i
$330$		0			0
$331$	−7.92800	−	29.5877i	−0.435762	−	1.62629i	−0.739236	−	0.673447i	$-0.764813\pi$
$331$	−7.92800	−	29.5877i	−0.435762	−	1.62629i	0.303474	−	0.952840i	$-0.401854\pi$
$332$		0			0
$333$	5.86983	−	17.2785i	0.321665	−	0.946854i
$334$		0			0
$335$	4.53376	+	16.9202i	0.247706	+	0.924451i
$336$		0			0
$337$	9.08801	−	5.24696i	0.495055	−	0.285820i	−0.231614	−	0.972808i	$-0.574401\pi$
$337$	9.08801	−	5.24696i	0.495055	−	0.285820i	0.726669	+	0.686987i	$0.241067\pi$
$338$		0			0
$339$	−15.3793	+	9.87671i	−0.835291	+	0.536429i
$340$		0			0
$341$	32.4599	+	32.4599i	1.75780	+	1.75780i
$342$		0			0
$343$	−19.4546			−1.05045
$344$		0			0
$345$	−5.33466	−	4.85266i	−0.287208	−	0.261258i
$346$		0			0
$347$	−12.4634	+	12.4634i	−0.669070	+	0.669070i	−0.957501	−	0.288430i	$-0.906867\pi$
$347$	−12.4634	+	12.4634i	−0.669070	+	0.669070i	0.288430	+	0.957501i	$0.406867\pi$
$348$		0			0
$349$	−0.783243	+	1.35662i	−0.0419260	+	0.0726180i	−0.886227	−	0.463251i	$-0.846683\pi$
$349$	−0.783243	+	1.35662i	−0.0419260	+	0.0726180i	0.844301	+	0.535869i	$0.180016\pi$
$350$		0			0
$351$	4.65205	+	5.92732i	0.248308	+	0.316377i
$352$		0			0
$353$	−2.91033	−	10.8615i	−0.154901	−	0.578099i	−0.999114	−	0.0420905i	$-0.986598\pi$
$353$	−2.91033	−	10.8615i	−0.154901	−	0.578099i	0.844213	−	0.536008i	$-0.180068\pi$
$354$		0			0
$355$	5.76605	+	21.5192i	0.306030	+	1.14212i
$356$		0			0
$357$	7.25227	−	14.0563i	0.383831	−	0.743940i
$358$		0			0
$359$			28.1419i			1.48527i	0.669695	+	0.742636i	$0.266425\pi$
$359$			28.1419i			1.48527i	−0.669695	+	0.742636i	$0.733575\pi$
$360$		0			0
$361$	−13.6745	−	7.89499i	−0.719712	−	0.415526i
$362$		0			0
$363$	−10.3338	−	32.3627i	−0.542382	−	1.69860i
$364$		0			0
$365$	20.5612	+	5.50936i	1.07622	+	0.288373i
$366$		0			0
$367$	2.41872	+	4.18935i	0.126256	+	0.218683i	0.922223	−	0.386658i	$-0.126370\pi$
$367$	2.41872	+	4.18935i	0.126256	+	0.218683i	−0.795967	+	0.605340i	$0.793037\pi$
$368$		0			0
$369$	7.27021	+	3.32585i	0.378472	+	0.173137i
$370$		0			0
$371$			10.3714i			0.538456i
$372$		0			0
$373$	6.86406	−	3.96297i	0.355407	−	0.205195i	−0.311657	−	0.950195i	$-0.600884\pi$
$373$	6.86406	−	3.96297i	0.355407	−	0.205195i	0.667064	+	0.745000i	$0.267551\pi$
$374$		0			0
$375$	18.4628	+	9.52578i	0.953417	+	0.491909i
$376$		0			0
$377$	1.14372	−	0.660325i	0.0589044	−	0.0340085i
$378$		0			0
$379$	6.49086	−	11.2425i	0.333413	−	0.577488i	−0.649766	−	0.760135i	$-0.725133\pi$
$379$	6.49086	−	11.2425i	0.333413	−	0.577488i	0.983179	+	0.182646i	$0.0584663\pi$
$380$		0			0
$381$	19.2812	+	4.20087i	0.987807	+	0.215217i
$382$		0			0
$383$	−4.18684	+	15.6255i	−0.213938	+	0.798426i	0.772600	+	0.634893i	$0.218956\pi$
$383$	−4.18684	+	15.6255i	−0.213938	+	0.798426i	−0.986538	+	0.163533i	$0.947711\pi$
$384$		0			0
$385$	−21.8002	+	5.84135i	−1.11104	+	0.297703i
$386$		0			0
$387$	4.88819	−	28.9551i	0.248481	−	1.47187i
$388$		0			0
$389$	−4.34679	+	16.2224i	−0.220391	+	0.822510i	0.763808	+	0.645444i	$0.223327\pi$
$389$	−4.34679	+	16.2224i	−0.220391	+	0.822510i	−0.984199	+	0.177067i	$0.943339\pi$
$390$		0			0
$391$	8.07245	+	4.66063i	0.408241	+	0.235698i
$392$		0			0
$393$	14.2777	−	9.16923i	0.720214	−	0.462526i
$394$		0			0
$395$	8.67668	−	15.0284i	0.436571	−	0.756163i
$396$		0			0
$397$			16.5459i			0.830413i	0.909727	+	0.415206i	$0.136291\pi$
$397$			16.5459i			0.830413i	−0.909727	+	0.415206i	$0.863709\pi$
$398$		0			0
$399$	6.48288	−	4.16335i	0.324550	−	0.208428i
$400$		0			0
$401$	−0.568565	+	0.568565i	−0.0283928	+	0.0283928i	−0.721161	−	0.692768i	$-0.756391\pi$
$401$	−0.568565	+	0.568565i	−0.0283928	+	0.0283928i	0.692768	+	0.721161i	$0.256391\pi$
$402$		0			0
$403$	−6.01543	−	10.4190i	−0.299650	−	0.519009i
$404$		0			0
$405$	12.2347	+	8.30364i	0.607947	+	0.412611i
$406$		0			0
$407$	27.2907	−	19.6962i	1.35275	−	0.976303i
$408$		0			0
$409$	28.6941	−	7.68856i	1.41883	−	0.380175i	0.533763	−	0.845634i	$-0.320778\pi$
$409$	28.6941	−	7.68856i	1.41883	−	0.380175i	0.885069	+	0.465460i	$0.154111\pi$
$410$		0			0
$411$	−1.67394	+	0.534507i	−0.0825693	+	0.0263653i
$412$		0			0
$413$	−16.9166	−	16.9166i	−0.832410	−	0.832410i
$414$		0			0
$415$	6.88270	−	6.88270i	0.337858	−	0.337858i
$416$		0			0
$417$	−1.50931	+	6.92747i	−0.0739114	+	0.339240i
$418$		0			0
$419$	−8.84354	−	5.10582i	−0.432035	−	0.249436i	0.268178	−	0.963369i	$-0.413578\pi$
$419$	−8.84354	−	5.10582i	−0.432035	−	0.249436i	−0.700213	+	0.713934i	$0.746912\pi$
$420$		0			0
$421$	−21.4079	−	21.4079i	−1.04336	−	1.04336i	−0.999017	−	0.0443398i	$-0.985882\pi$
$421$	−21.4079	−	21.4079i	−1.04336	−	1.04336i	−0.0443398	−	0.999017i	$-0.514118\pi$
$422$		0			0
$423$	−12.5827	−	17.6940i	−0.611791	−	0.860311i
$424$		0			0
$425$	−8.17413	−	2.19025i	−0.396504	−	0.106243i
$426$		0			0
$427$	−6.98430	+	1.87144i	−0.337994	+	0.0905652i
$428$		0			0
$429$	0.656775	+	13.8813i	0.0317094	+	0.670196i
$430$		0			0
$431$	26.0516	+	6.98051i	1.25486	+	0.336240i	0.824213	−	0.566280i	$-0.191618\pi$
$431$	26.0516	+	6.98051i	1.25486	+	0.336240i	0.430650	+	0.902519i	$0.358284\pi$
$432$		0			0
$433$	4.62604			0.222313			0.111157	−	0.993803i	$-0.464544\pi$
$433$	4.62604			0.222313			0.111157	+	0.993803i	$0.464544\pi$
$434$		0			0
$435$	1.74391	−	1.91712i	0.0836139	−	0.0919190i
$436$		0			0
$437$	2.27025	+	3.93219i	0.108601	+	0.188102i
$438$		0			0
$439$	2.24373	−	8.37373i	0.107088	−	0.399656i	−0.891486	−	0.453048i	$-0.850337\pi$
$439$	2.24373	−	8.37373i	0.107088	−	0.399656i	0.998574	+	0.0533918i	$0.0170032\pi$
$440$		0			0
$441$	0.236753	+	2.49636i	0.0112740	+	0.118874i
$442$		0			0
$443$	−8.56590			−0.406978			−0.203489	−	0.979077i	$-0.565228\pi$
$443$	−8.56590			−0.406978			−0.203489	+	0.979077i	$0.565228\pi$
$444$		0			0
$445$	10.7715			0.510617
$446$		0			0
$447$	28.4330	−	9.07896i	1.34483	−	0.429420i
$448$		0			0
$449$	7.83122	−	29.2265i	0.369578	−	1.37928i	−0.491529	−	0.870861i	$-0.663562\pi$
$449$	7.83122	−	29.2265i	0.369578	−	1.37928i	0.861107	−	0.508423i	$-0.169771\pi$
$450$		0			0
$451$	7.37255	+	12.7696i	0.347160	+	0.601299i
$452$		0			0
$453$	14.8848	+	13.5399i	0.699350	+	0.636162i
$454$		0			0
$455$	5.91496			0.277298
$456$		0			0
$457$	17.2510	+	4.62240i	0.806969	+	0.216227i	0.638641	−	0.769504i	$-0.279497\pi$
$457$	17.2510	+	4.62240i	0.806969	+	0.216227i	0.168328	+	0.985731i	$0.446163\pi$
$458$		0			0
$459$	−17.7362	−	7.12035i	−0.827853	−	0.332349i
$460$		0			0
$461$	−23.2177	+	6.22115i	−1.08135	+	0.289748i	−0.755151	−	0.655551i	$-0.772436\pi$
$461$	−23.2177	+	6.22115i	−1.08135	+	0.289748i	−0.326204	+	0.945299i	$0.605770\pi$
$462$		0			0
$463$	−1.37252	−	0.367764i	−0.0637862	−	0.0170915i	0.226785	−	0.973945i	$-0.427179\pi$
$463$	−1.37252	−	0.367764i	−0.0637862	−	0.0170915i	−0.290571	+	0.956853i	$0.593845\pi$
$464$		0			0
$465$	−17.4646	−	15.8866i	−0.809902	−	0.736726i
$466$		0			0
$467$	19.5181	+	19.5181i	0.903190	+	0.903190i	0.995711	−	0.0925203i	$-0.0294923\pi$
$467$	19.5181	+	19.5181i	0.903190	+	0.903190i	−0.0925203	+	0.995711i	$0.529492\pi$
$468$		0			0
$469$	−22.9250	−	13.2358i	−1.05858	−	0.611170i
$470$		0			0
$471$	8.27909	+	1.80380i	0.381481	+	0.0831145i
$472$		0			0
$473$	38.2958	−	38.2958i	1.76084	−	1.76084i
$474$		0			0
$475$	−2.91482	−	2.91482i	−0.133741	−	0.133741i
$476$		0			0
$477$	12.4761	−	1.18322i	0.571240	−	0.0541761i
$478$		0			0
$479$	−0.375141	+	0.100519i	−0.0171406	+	0.00459281i	−0.267379	−	0.963591i	$-0.586158\pi$
$479$	−0.375141	+	0.100519i	−0.0171406	+	0.00459281i	0.250239	+	0.968184i	$0.419491\pi$
$480$		0			0
$481$	−8.24466	+	3.13493i	−0.375924	+	0.142940i
$482$		0			0
$483$	10.8858	−	0.515047i	0.495321	−	0.0234354i
$484$		0			0
$485$	−7.55913	−	13.0928i	−0.343242	−	0.594513i
$486$		0			0
$487$	−10.5633	+	10.5633i	−0.478670	+	0.478670i	−0.904706	−	0.426036i	$-0.859910\pi$
$487$	−10.5633	+	10.5633i	−0.478670	+	0.478670i	0.426036	+	0.904706i	$0.359910\pi$
$488$		0			0
$489$	20.4763	+	31.8843i	0.925971	+	1.44186i
$490$		0			0
$491$		−	7.71538i		−	0.348190i	−0.984729	−	0.174095i	$-0.944300\pi$
$491$		−	7.71538i		−	0.348190i	0.984729	−	0.174095i	$-0.0557000\pi$
$492$		0			0
$493$	−1.67490	+	2.90101i	−0.0754336	+	0.130655i
$494$		0			0
$495$	9.51382	+	25.5577i	0.427615	+	1.14873i
$496$		0			0
$497$	−29.1561	−	16.8333i	−1.30783	−	0.755075i
$498$		0			0
$499$	10.3334	−	38.5646i	0.462585	−	1.72639i	−0.202189	−	0.979346i	$-0.564806\pi$
$499$	10.3334	−	38.5646i	0.462585	−	1.72639i	0.664774	−	0.747044i	$-0.268528\pi$
$500$		0			0
$501$	−10.5535	+	0.499325i	−0.471496	+	0.0223082i
$502$		0			0
$503$	−33.5910	+	9.00069i	−1.49775	+	0.401321i	−0.912346	−	0.409420i	$-0.865731\pi$
$503$	−33.5910	+	9.00069i	−1.49775	+	0.401321i	−0.585405	+	0.810741i	$0.699064\pi$
$504$		0			0
$505$	−0.658653	+	2.45813i	−0.0293097	+	0.109385i
$506$		0			0
$507$	−4.01801	+	18.4419i	−0.178446	+	0.819035i
$508$		0			0
$509$	3.36694	−	5.83171i	0.149237	−	0.258486i	−0.781709	−	0.623644i	$-0.785652\pi$
$509$	3.36694	−	5.83171i	0.149237	−	0.258486i	0.930946	+	0.365158i	$0.118985\pi$
$510$		0			0
$511$	−27.8581	+	16.0839i	−1.23237	+	0.711509i
$512$		0			0
$513$	−5.74782	−	7.32347i	−0.253772	−	0.323339i
$514$		0			0
$515$	−6.94198	+	4.00795i	−0.305900	+	0.176612i
$516$		0			0
$517$		−	40.0437i		−	1.76112i
$518$		0			0
$519$	0.352848	+	0.0768763i	0.0154883	+	0.00337449i
$520$		0			0
$521$	14.9951	+	25.9722i	0.656946	+	1.13786i	0.981402	+	0.191964i	$0.0614855\pi$
$521$	14.9951	+	25.9722i	0.656946	+	1.13786i	−0.324456	+	0.945901i	$0.605181\pi$
$522$		0			0
$523$	4.65390	+	1.24701i	0.203501	+	0.0545279i	0.359130	−	0.933288i	$-0.383074\pi$
$523$	4.65390	+	1.24701i	0.203501	+	0.0545279i	−0.155629	+	0.987816i	$0.549740\pi$
$524$		0			0
$525$	−9.42511	+	3.00954i	−0.411346	+	0.131347i
$526$		0			0
$527$	26.4276	+	15.2580i	1.15121	+	0.664649i
$528$		0			0
$529$		−	16.5776i		−	0.720765i
$530$		0			0
$531$	−18.4195	+	22.2794i	−0.799339	+	0.966843i
$532$		0			0
$533$	−1.00018	−	3.73273i	−0.0433227	−	0.161682i
$534$		0			0
$535$	6.00784	+	22.4216i	0.259741	+	0.969368i
$536$		0			0
$537$	20.1739	+	10.4086i	0.870568	+	0.449163i
$538$		0			0
$539$	−2.31239	+	4.00517i	−0.0996016	+	0.172515i
$540$		0			0
$541$	−0.778680	+	0.778680i	−0.0334781	+	0.0334781i	−0.723648	−	0.690170i	$-0.757536\pi$
$541$	−0.778680	+	0.778680i	−0.0334781	+	0.0334781i	0.690170	+	0.723648i	$0.257536\pi$
$542$		0			0
$543$	23.0777	−	25.3700i	0.990360	−	1.08873i
$544$		0			0
$545$	2.47993			0.106228
$546$		0			0
$547$	−7.57357	−	7.57357i	−0.323822	−	0.323822i	0.526409	−	0.850231i	$-0.323538\pi$
$547$	−7.57357	−	7.57357i	−0.323822	−	0.323822i	−0.850231	+	0.526409i	$0.823538\pi$
$548$		0			0
$549$	3.04801	+	8.18812i	0.130086	+	0.349461i
$550$		0			0
$551$	−1.41312	+	0.815863i	−0.0602007	+	0.0347569i
$552$		0			0
$553$	6.78728	+	25.3305i	0.288624	+	1.07716i
$554$		0			0
$555$	−13.5413	+	10.7819i	−0.574796	+	0.457664i
$556$		0			0
$557$	1.67402	+	6.24751i	0.0709303	+	0.264716i	0.992280	−	0.124020i	$-0.0395787\pi$
$557$	1.67402	+	6.24751i	0.0709303	+	0.264716i	−0.921349	+	0.388735i	$0.872912\pi$
$558$		0			0
$559$	−12.2923	+	7.09694i	−0.519907	+	0.300168i
$560$		0			0
$561$	−19.0475	−	29.6595i	−0.804186	−	1.25222i
$562$		0			0
$563$	9.50717	+	9.50717i	0.400679	+	0.400679i	0.878472	−	0.477793i	$-0.158563\pi$
$563$	9.50717	+	9.50717i	0.400679	+	0.400679i	−0.477793	+	0.878472i	$0.658563\pi$
$564$		0			0
$565$	17.3373			0.729384
$566$		0			0
$567$	−21.9465	+	4.20058i	−0.921668	+	0.176408i
$568$		0			0
$569$	3.48152	−	3.48152i	0.145953	−	0.145953i	−0.630354	−	0.776307i	$-0.717090\pi$
$569$	3.48152	−	3.48152i	0.145953	−	0.145953i	0.776307	+	0.630354i	$0.217090\pi$
$570$		0			0
$571$	7.53745	−	13.0552i	0.315432	−	0.546345i	−0.664097	−	0.747647i	$-0.731184\pi$
$571$	7.53745	−	13.0552i	0.315432	−	0.546345i	0.979529	+	0.201301i	$0.0645171\pi$
$572$		0			0
$573$	−3.66009	+	7.09397i	−0.152902	+	0.296355i
$574$		0			0
$575$	−1.50910	−	5.63203i	−0.0629338	−	0.234872i
$576$		0			0
$577$	−7.88716	−	29.4353i	−0.328347	−	1.22541i	−0.910905	−	0.412617i	$-0.864615\pi$
$577$	−7.88716	−	29.4353i	−0.328347	−	1.22541i	0.582558	−	0.812789i	$-0.302052\pi$
$578$		0			0
$579$	−15.9134	−	8.21040i	−0.661338	−	0.341213i
$580$		0			0
$581$			14.7092i			0.610241i
$582$		0			0
$583$	20.0167	+	11.5566i	0.829005	+	0.478627i
$584$		0			0
$585$	−0.674810	−	7.11529i	−0.0279000	−	0.294181i
$586$		0			0
$587$	−27.3162	−	7.31936i	−1.12746	−	0.302102i	−0.353562	−	0.935411i	$-0.615030\pi$
$587$	−27.3162	−	7.31936i	−1.12746	−	0.302102i	−0.773899	+	0.633309i	$0.781696\pi$
$588$		0			0
$589$	7.43235	+	12.8732i	0.306245	+	0.530431i
$590$		0			0
$591$	−7.31869	+	33.5915i	−0.301051	+	1.38177i
$592$		0			0
$593$		−	1.36215i		−	0.0559367i	−0.999609	−	0.0279683i	$-0.991096\pi$
$593$		−	1.36215i		−	0.0559367i	0.999609	−	0.0279683i	$-0.00890376\pi$
$594$		0			0
$595$	−12.9931	+	7.50158i	−0.532666	+	0.307535i
$596$		0			0
$597$	−14.1165	+	27.3605i	−0.577748	+	1.11979i
$598$		0			0
$599$	2.89762	−	1.67294i	0.118393	−	0.0683545i	−0.439634	−	0.898177i	$-0.644892\pi$
$599$	2.89762	−	1.67294i	0.118393	−	0.0683545i	0.558027	+	0.829823i	$0.311558\pi$
$600$		0			0
$601$	−13.8410	+	23.9733i	−0.564586	+	0.977891i	0.432502	+	0.901633i	$0.357631\pi$
$601$	−13.8410	+	23.9733i	−0.564586	+	0.977891i	−0.997088	+	0.0762586i	$0.975703\pi$
$602$		0			0
$603$	−13.3063	+	29.0872i	−0.541874	+	1.18452i
$604$		0			0
$605$	−8.34034	+	31.1266i	−0.339083	+	1.26547i
$606$		0			0
$607$	11.3079	−	3.02994i	0.458973	−	0.122982i	−0.0219217	−	0.999760i	$-0.506978\pi$
$607$	11.3079	−	3.02994i	0.458973	−	0.122982i	0.480895	+	0.876778i	$0.340312\pi$
$608$		0			0
$609$	0.185093	+	3.91205i	0.00750035	+	0.158524i
$610$		0			0
$611$	−2.71622	+	10.1371i	−0.109887	+	0.410102i
$612$		0			0
$613$	1.82741	+	1.05506i	0.0738085	+	0.0426134i	0.536450	−	0.843932i	$-0.319765\pi$
$613$	1.82741	+	1.05506i	0.0738085	+	0.0426134i	−0.462642	+	0.886545i	$0.653098\pi$
$614$		0			0
$615$	−4.09789	−	6.38095i	−0.165243	−	0.257305i
$616$		0			0
$617$	5.53931	−	9.59437i	0.223004	−	0.386255i	−0.732714	−	0.680536i	$-0.761747\pi$
$617$	5.53931	−	9.59437i	0.223004	−	0.386255i	0.955719	+	0.294281i	$0.0950802\pi$
$618$		0			0
$619$		−	25.1797i		−	1.01206i	−0.862516	−	0.506030i	$-0.831113\pi$
$619$		−	25.1797i		−	1.01206i	0.862516	−	0.506030i	$-0.168887\pi$
$620$		0			0
$621$	−1.86148	−	13.0361i	−0.0746985	−	0.523121i
$622$		0			0
$623$	−11.5100	+	11.5100i	−0.461140	+	0.461140i
$624$		0			0
$625$	−4.10133	−	7.10371i	−0.164053	−	0.284148i
$626$		0			0
$627$	−0.811476	−	17.1510i	−0.0324072	−	0.684945i
$628$		0			0
$629$	14.1348	−	17.3425i	0.563592	−	0.691492i
$630$		0			0
$631$	−43.2003	+	11.5755i	−1.71978	+	0.460813i	−0.977787	−	0.209600i	$-0.932784\pi$
$631$	−43.2003	+	11.5755i	−1.71978	+	0.460813i	−0.741989	+	0.670413i	$0.766117\pi$
$632$		0			0
$633$	−14.2013	−	44.4748i	−0.564450	−	1.76771i
$634$		0			0
$635$	−13.2358	−	13.2358i	−0.525246	−	0.525246i
$636$		0			0
$637$	0.857058	−	0.857058i	0.0339579	−	0.0339579i
$638$		0			0
$639$	−16.9230	+	36.9931i	−0.669462	+	1.46343i
$640$		0			0
$641$	13.1965	+	7.61901i	0.521231	+	0.300933i	0.737438	−	0.675415i	$-0.236035\pi$
$641$	13.1965	+	7.61901i	0.521231	+	0.300933i	−0.216207	+	0.976347i	$0.569369\pi$
$642$		0			0
$643$	12.1271	+	12.1271i	0.478245	+	0.478245i	0.904570	−	0.426325i	$-0.140192\pi$
$643$	12.1271	+	12.1271i	0.478245	+	0.478245i	−0.426325	+	0.904570i	$0.640192\pi$
$644$		0			0
$645$	−18.7429	+	20.6045i	−0.738000	+	0.811303i
$646$		0			0
$647$	26.8294	+	7.18892i	1.05477	+	0.282625i	0.744223	−	0.667932i	$-0.232820\pi$
$647$	26.8294	+	7.18892i	1.05477	+	0.282625i	0.310550	+	0.950557i	$0.399487\pi$
$648$		0			0
$649$	−51.4986	+	13.7990i	−2.02150	+	0.541658i
$650$		0			0
$651$	35.6380	−	1.68616i	1.39676	−	0.0660859i
$652$		0			0
$653$	−34.7723	−	9.31720i	−1.36074	−	0.364610i	−0.496655	−	0.867948i	$-0.665438\pi$
$653$	−34.7723	−	9.31720i	−1.36074	−	0.364610i	−0.864090	+	0.503338i	$0.832105\pi$
$654$		0			0
$655$	−16.0954			−0.628898
$656$		0			0
$657$	22.5260	+	31.6764i	0.878822	+	1.23581i
$658$		0			0
$659$	−22.9807	−	39.8038i	−0.895202	−	1.55054i	−0.833554	−	0.552438i	$-0.813697\pi$
$659$	−22.9807	−	39.8038i	−0.895202	−	1.55054i	−0.0616487	−	0.998098i	$-0.519636\pi$
$660$		0			0
$661$	11.5791	−	43.2137i	0.450374	−	1.68082i	−0.250969	−	0.967995i	$-0.580749\pi$
$661$	11.5791	−	43.2137i	0.450374	−	1.68082i	0.701343	−	0.712824i	$-0.252584\pi$
$662$		0			0
$663$	2.81004	+	8.80032i	0.109133	+	0.341776i
$664$		0			0
$665$	−7.30821			−0.283400
$666$		0			0
$667$	−2.30803			−0.0893674
$668$		0			0
$669$	−1.76053	−	5.51353i	−0.0680661	−	0.213166i
$670$		0			0
$671$	−4.17061	+	15.5649i	−0.161004	+	0.600877i
$672$		0			0
$673$	−6.32887	−	10.9619i	−0.243960	−	0.422551i	0.717879	−	0.696168i	$-0.245113\pi$
$673$	−6.32887	−	10.9619i	−0.243960	−	0.422551i	−0.961839	+	0.273617i	$0.911780\pi$
$674$		0			0
$675$	4.69553	+	10.9944i	0.180731	+	0.423175i
$676$		0			0
$677$	−35.1546			−1.35110			−0.675550	−	0.737314i	$-0.736094\pi$
$677$	−35.1546			−1.35110			−0.675550	+	0.737314i	$0.736094\pi$
$678$		0			0
$679$	22.0679	+	5.91308i	0.846889	+	0.226923i
$680$		0			0
$681$	51.3528	−	2.42969i	1.96784	−	0.0931058i
$682$		0			0
$683$	−30.7910	+	8.25042i	−1.17818	+	0.315693i	−0.794206	−	0.607649i	$-0.792113\pi$
$683$	−30.7910	+	8.25042i	−1.17818	+	0.315693i	−0.383978	+	0.923342i	$0.625446\pi$
$684$		0			0
$685$	1.61000	+	0.431398i	0.0615149	+	0.0164829i
$686$		0			0
$687$	20.0726	−	22.0663i	0.765816	−	0.841882i
$688$		0			0
$689$	−4.28332	−	4.28332i	−0.163182	−	0.163182i
$690$		0			0
$691$	11.9909	+	6.92293i	0.456154	+	0.263361i	0.710426	−	0.703772i	$-0.248502\pi$
$691$	11.9909	+	6.92293i	0.456154	+	0.263361i	−0.254272	+	0.967133i	$0.581836\pi$
$692$		0			0
$693$	−37.4762	−	17.1440i	−1.42361	−	0.651245i
$694$		0			0
$695$	4.75544	−	4.75544i	0.180384	−	0.180384i
$696$		0			0
$697$	6.93104	+	6.93104i	0.262532	+	0.262532i
$698$		0			0
$699$	3.80547	+	11.9178i	0.143936	+	0.450771i
$700$		0			0
$701$	32.4256	−	8.68841i	1.22470	−	0.328157i	0.412185	−	0.911100i	$-0.364766\pi$
$701$	32.4256	−	8.68841i	1.22470	−	0.328157i	0.812513	+	0.582943i	$0.198099\pi$
$702$		0			0
$703$	10.1867	−	3.87335i	0.384197	−	0.146086i
$704$		0			0
$705$	0.973319	+	20.5717i	0.0366573	+	0.774774i
$706$		0			0
$707$	−1.92285	−	3.33048i	−0.0723164	−	0.125256i
$708$		0			0
$709$	−0.0989368	+	0.0989368i	−0.00371565	+	0.00371565i	−0.708962	−	0.705247i	$-0.750836\pi$
$709$	−0.0989368	+	0.0989368i	−0.00371565	+	0.00371565i	0.705247	+	0.708962i	$0.250836\pi$
$710$		0			0
$711$	29.6965	−	11.0545i	1.11370	−	0.414575i
$712$		0			0
$713$			21.0257i			0.787420i
$714$		0			0
$715$	6.59092	−	11.4158i	0.246486	−	0.426927i
$716$		0			0
$717$	25.4593	+	39.6434i	0.950793	+	1.48051i
$718$		0			0
$719$	−11.3925	−	6.57748i	−0.424870	−	0.245299i	0.272289	−	0.962216i	$-0.412219\pi$
$719$	−11.3925	−	6.57748i	−0.424870	−	0.245299i	−0.697159	+	0.716917i	$0.745553\pi$
$720$		0			0
$721$	3.13520	−	11.7007i	0.116761	−	0.435758i
$722$		0			0
$723$	0.346272	+	7.31866i	0.0128780	+	0.272184i
$724$		0			0
$725$	2.02399	−	0.542327i	0.0751692	−	0.0201415i
$726$		0			0
$727$	1.22263	−	4.56293i	0.0453450	−	0.169230i	−0.939540	−	0.342439i	$-0.888747\pi$
$727$	1.22263	−	4.56293i	0.0453450	−	0.169230i	0.984885	+	0.173209i	$0.0554137\pi$
$728$		0			0
$729$	7.55678	+	25.9209i	0.279881	+	0.960035i
$730$		0			0
$731$	18.0012	−	31.1790i	0.665798	−	1.15320i
$732$		0			0
$733$	4.95739	−	2.86215i	0.183105	−	0.105716i	−0.405646	−	0.914030i	$-0.632953\pi$
$733$	4.95739	−	2.86215i	0.183105	−	0.105716i	0.588751	+	0.808315i	$0.299620\pi$
$734$		0			0
$735$	1.09059	−	2.11378i	0.0402271	−	0.0779681i
$736$		0			0
$737$	−51.0897	+	29.4966i	−1.88191	+	1.08652i
$738$		0			0
$739$		−	43.1595i		−	1.58765i	−0.608147	−	0.793824i	$-0.708087\pi$
$739$		−	43.1595i		−	1.58765i	0.608147	−	0.793824i	$-0.291913\pi$
$740$		0			0
$741$	−0.957952	+	4.39683i	−0.0351913	+	0.161522i
$742$		0			0
$743$	−14.8034	−	25.6403i	−0.543086	−	0.940652i	−0.998725	−	0.0504876i	$-0.983922\pi$
$743$	−14.8034	−	25.6403i	−0.543086	−	0.940652i	0.455639	−	0.890165i	$-0.349411\pi$
$744$		0			0
$745$	−27.3469	−	7.32759i	−1.00191	−	0.268462i
$746$		0			0
$747$	17.6942	−	1.67811i	0.647396	−	0.0613987i
$748$		0			0
$749$	−30.3787	−	17.5391i	−1.11001	−	0.640866i
$750$		0			0
$751$		−	22.0382i		−	0.804187i	−0.915599	−	0.402093i	$-0.868283\pi$
$751$		−	22.0382i		−	0.804187i	0.915599	−	0.402093i	$-0.131717\pi$
$752$		0			0
$753$	−11.9483	−	6.16462i	−0.435419	−	0.224651i
$754$		0			0
$755$	−4.93996	−	18.4362i	−0.179784	−	0.670961i
$756$		0			0
$757$	−4.62210	−	17.2499i	−0.167993	−	0.626958i	−0.997639	−	0.0686692i	$-0.978125\pi$
$757$	−4.62210	−	17.2499i	−0.167993	−	0.626958i	0.829647	−	0.558289i	$-0.188542\pi$
$758$		0			0
$759$	11.1358	−	21.5834i	0.404204	−	0.783427i
$760$		0			0
$761$	−12.0812	+	20.9252i	−0.437942	+	0.758537i	−0.997531	−	0.0702329i	$-0.977626\pi$
$761$	−12.0812	+	20.9252i	−0.437942	+	0.758537i	0.559589	+	0.828770i	$0.310959\pi$
$762$		0			0
$763$	−2.64996	+	2.64996i	−0.0959352	+	0.0959352i
$764$		0			0
$765$	10.5062	+	14.7740i	0.379852	+	0.534154i
$766$		0			0
$767$	13.9729			0.504532
$768$		0			0
$769$	−9.70494	−	9.70494i	−0.349969	−	0.349969i	0.510129	−	0.860098i	$-0.329598\pi$
$769$	−9.70494	−	9.70494i	−0.349969	−	0.349969i	−0.860098	+	0.510129i	$0.829598\pi$
$770$		0			0
$771$	−18.9522	−	29.5111i	−0.682547	−	1.06282i
$772$		0			0
$773$	−18.1079	+	10.4546i	−0.651296	+	0.376026i	−0.788953	−	0.614454i	$-0.789376\pi$
$773$	−18.1079	+	10.4546i	−0.651296	+	0.376026i	0.137656	+	0.990480i	$0.456043\pi$
$774$		0			0
$775$	−4.94049	−	18.4382i	−0.177468	−	0.662319i
$776$		0			0
$777$	2.94865	−	25.9909i	0.105782	−	0.932418i
$778$		0			0
$779$	1.23577	+	4.61196i	0.0442761	+	0.165241i
$780$		0			0
$781$	−64.9759	+	37.5139i	−2.32502	+	1.34235i
$782$		0			0
$783$	4.68481	−	0.668961i	0.167421	−	0.0239067i
$784$		0			0
$785$	−5.68327	−	5.68327i	−0.202845	−	0.202845i
$786$		0			0
$787$	17.7312			0.632049			0.316025	−	0.948751i	$-0.397652\pi$
$787$	17.7312			0.632049			0.316025	+	0.948751i	$0.397652\pi$
$788$		0			0
$789$	−24.6728	+	27.1234i	−0.878373	+	0.965619i
$790$		0			0
$791$	−18.5260	+	18.5260i	−0.658709	+	0.658709i
$792$		0			0
$793$	2.11158	−	3.65737i	0.0749844	−	0.129877i
$794$		0			0
$795$	−10.5641	−	5.45045i	−0.374669	−	0.193308i
$796$		0			0
$797$	14.2083	+	53.0262i	0.503285	+	1.87829i	0.477526	+	0.878617i	$0.341533\pi$
$797$	14.2083	+	53.0262i	0.503285	+	1.87829i	0.0257586	+	0.999668i	$0.491800\pi$
$798$		0			0
$799$	−6.88963	−	25.7124i	−0.243738	−	0.909641i
$800$		0			0
$801$	15.1589	+	12.5326i	0.535613	+	0.442819i
$802$		0			0
$803$			71.6877i			2.52980i
$804$		0			0
$805$	−8.95234	−	5.16864i	−0.315529	−	0.182171i
$806$		0			0
$807$	0.792136	−	0.252938i	0.0278845	−	0.00890383i
$808$		0			0
$809$	4.66860	+	1.25095i	0.164139	+	0.0439810i	0.339953	−	0.940442i	$-0.389589\pi$
$809$	4.66860	+	1.25095i	0.164139	+	0.0439810i	−0.175813	+	0.984423i	$0.556256\pi$
$810$		0			0
$811$	20.0693	+	34.7610i	0.704727	+	1.22062i	0.966790	+	0.255572i	$0.0822639\pi$
$811$	20.0693	+	34.7610i	0.704727	+	1.22062i	−0.262063	+	0.965051i	$0.584403\pi$
$812$		0			0
$813$	−8.92311	−	1.94411i	−0.312947	−	0.0681828i
$814$		0			0
$815$		−	35.9435i		−	1.25905i
$816$		0			0
$817$	15.1877	−	8.76860i	0.531349	−	0.306774i
$818$		0			0
$819$	8.32423	+	6.88207i	0.290872	+	0.240479i
$820$		0			0
$821$	21.9154	−	12.6529i	0.764854	−	0.441589i	−0.0661818	−	0.997808i	$-0.521082\pi$
$821$	21.9154	−	12.6529i	0.764854	−	0.441589i	0.831036	+	0.556219i	$0.187748\pi$
$822$		0			0
$823$	−13.3502	+	23.1232i	−0.465359	+	0.806025i	−0.999218	−	0.0395487i	$-0.987408\pi$
$823$	−13.3502	+	23.1232i	−0.465359	+	0.806025i	0.533859	+	0.845574i	$0.320741\pi$
$824$		0			0
$825$	−4.69383	+	21.5438i	−0.163418	+	0.750059i
$826$		0			0
$827$	5.34553	−	19.9498i	0.185882	−	0.693722i	−0.808558	−	0.588417i	$-0.799751\pi$
$827$	5.34553	−	19.9498i	0.185882	−	0.693722i	0.994440	−	0.105305i	$-0.0335819\pi$
$828$		0			0
$829$	−4.57491	+	1.22584i	−0.158893	+	0.0425753i	−0.337389	−	0.941365i	$-0.609544\pi$
$829$	−4.57491	+	1.22584i	−0.158893	+	0.0425753i	0.178496	+	0.983941i	$0.442877\pi$
$830$		0			0
$831$	−12.3045	+	0.582170i	−0.426838	+	0.0201953i
$832$		0			0
$833$	−0.795705	+	2.96961i	−0.0275695	+	0.102891i
$834$		0			0
$835$	8.67906	+	5.01086i	0.300351	+	0.173408i
$836$		0			0
$837$	−6.09411	−	42.6777i	−0.210643	−	1.47516i
$838$		0			0
$839$	25.6817	−	44.4820i	0.886630	−	1.53569i	0.0427960	−	0.999084i	$-0.486373\pi$
$839$	25.6817	−	44.4820i	0.886630	−	1.53569i	0.843834	−	0.536604i	$-0.180293\pi$
$840$		0			0
$841$			28.1706i			0.971399i
$842$		0			0
$843$	−22.4189	−	34.9092i	−0.772149	−	1.20234i
$844$		0			0
$845$	12.6597	−	12.6597i	0.435505	−	0.435505i
$846$		0			0
$847$	−24.3486	−	42.1730i	−0.836627	−	1.44908i
$848$		0			0
$849$	51.3868	−	2.43129i	1.76359	−	0.0834418i
$850$		0			0
$851$	15.2177	+	2.45965i	0.521657	+	0.0843157i
$852$		0			0
$853$	−52.0438	+	13.9451i	−1.78195	+	0.477471i	−0.990937	−	0.134331i	$-0.957111\pi$
$853$	−52.0438	+	13.9451i	−1.78195	+	0.477471i	−0.791011	+	0.611802i	$0.790445\pi$
$854$		0			0
$855$	0.833759	+	8.79127i	0.0285140	+	0.300655i
$856$		0			0
$857$	3.10757	+	3.10757i	0.106153	+	0.106153i	0.758188	−	0.652036i	$-0.226085\pi$
$857$	3.10757	+	3.10757i	0.106153	+	0.106153i	−0.652036	+	0.758188i	$0.726085\pi$
$858$		0			0
$859$	19.6609	−	19.6609i	0.670823	−	0.670823i	−0.287083	−	0.957906i	$-0.592686\pi$
$859$	19.6609	−	19.6609i	0.670823	−	0.670823i	0.957906	+	0.287083i	$0.0926856\pi$
$860$		0			0
$861$	11.1973	+	2.43960i	0.381604	+	0.0831413i
$862$		0			0
$863$	−4.07270	−	2.35137i	−0.138636	−	0.0800416i	0.429078	−	0.903268i	$-0.358839\pi$
$863$	−4.07270	−	2.35137i	−0.138636	−	0.0800416i	−0.567714	+	0.823226i	$0.692172\pi$
$864$		0			0
$865$	−0.242216	−	0.242216i	−0.00823560	−	0.00823560i
$866$		0			0
$867$	4.44782	+	4.04595i	0.151056	+	0.137408i
$868$		0			0
$869$	56.4504	+	15.1258i	1.91495	+	0.513109i
$870$		0			0
$871$	14.9342	−	4.00160i	0.506025	−	0.135589i
$872$		0			0
$873$	4.59540	−	27.2208i	0.155531	−	0.921283i
$874$		0			0
$875$	28.7653	+	7.70764i	0.972445	+	0.260566i
$876$		0			0
$877$	26.3715			0.890504			0.445252	−	0.895405i	$-0.353114\pi$
$877$	26.3715			0.890504			0.445252	+	0.895405i	$0.353114\pi$
$878$		0			0
$879$	39.3590	+	35.8028i	1.32755	+	1.20760i
$880$		0			0
$881$	11.6859	+	20.2405i	0.393707	+	0.681920i	0.992935	−	0.118658i	$-0.0378593\pi$
$881$	11.6859	+	20.2405i	0.393707	+	0.681920i	−0.599229	+	0.800578i	$0.704526\pi$
$882$		0			0
$883$	−6.21035	+	23.1773i	−0.208995	+	0.779979i	0.779200	+	0.626776i	$0.215626\pi$
$883$	−6.21035	+	23.1773i	−0.208995	+	0.779979i	−0.988195	+	0.153204i	$0.951041\pi$
$884$		0			0
$885$	26.1210	−	8.34071i	0.878047	−	0.280370i
$886$		0			0
$887$	21.8215			0.732693			0.366347	−	0.930478i	$-0.380608\pi$
$887$	21.8215			0.732693			0.366347	+	0.930478i	$0.380608\pi$
$888$		0			0
$889$	28.2866			0.948702
$890$		0			0
$891$	−16.3475	+	47.0372i	−0.547662	+	1.57580i
$892$		0			0
$893$	3.35602	−	12.5248i	0.112305	−	0.419128i
$894$		0			0
$895$	−10.7664	−	18.6479i	−0.359881	−	0.623332i
$896$		0			0
$897$	−4.28306	+	4.70848i	−0.143007	+	0.157212i
$898$		0			0
$899$	−7.55605			−0.252008
$900$		0			0
$901$	14.8412	+	3.97670i	0.494433	+	0.132483i
$902$		0			0
$903$	−1.98931	−	42.0453i	−0.0662002	−	1.39918i
$904$		0			0
$905$	−31.4230	+	8.41976i	−1.04453	+	0.279882i
$906$		0			0
$907$	13.6425	+	3.65549i	0.452990	+	0.121378i	0.478098	−	0.878306i	$-0.341326\pi$
$907$	13.6425	+	3.65549i	0.452990	+	0.121378i	−0.0251079	+	0.999685i	$0.507993\pi$
$908$		0			0
$909$	−3.78697	+	2.69302i	−0.125606	+	0.0893218i
$910$		0			0
$911$	29.4855	+	29.4855i	0.976899	+	0.976899i	0.999739	−	0.0228400i	$-0.00727083\pi$
$911$	29.4855	+	29.4855i	0.976899	+	0.976899i	−0.0228400	+	0.999739i	$0.507271\pi$
$912$		0			0
$913$	28.3886	+	16.3902i	0.939526	+	0.542436i
$914$		0			0
$915$	1.76424	−	8.09754i	0.0583240	−	0.267696i
$916$		0			0
$917$	17.1990	−	17.1990i	0.567960	−	0.567960i
$918$		0			0
$919$	18.5284	+	18.5284i	0.611196	+	0.611196i	0.943258	−	0.332061i	$-0.107744\pi$
$919$	18.5284	+	18.5284i	0.611196	+	0.611196i	−0.332061	+	0.943258i	$0.607744\pi$
$920$		0			0
$921$	4.04294	−	1.29096i	0.133219	−	0.0425384i
$922$		0			0
$923$	18.9933	−	5.08924i	0.625172	−	0.167514i
$924$		0			0
$925$	−13.9229	+	1.41882i	−0.457782	+	0.0466504i
$926$		0			0
$927$	−14.4328	−	2.43654i	−0.474036	−	0.0800266i
$928$		0			0
$929$	5.75253	+	9.96368i	0.188734	+	0.326898i	0.944829	−	0.327565i	$-0.106228\pi$
$929$	5.75253	+	9.96368i	0.188734	+	0.326898i	−0.756094	+	0.654463i	$0.772895\pi$
$930$		0			0
$931$	−1.05894	+	1.05894i	−0.0347052	+	0.0347052i
$932$		0			0
$933$	−36.1448	+	23.2124i	−1.18333	+	0.759941i
$934$		0			0
$935$			33.4354i			1.09345i
$936$		0			0
$937$	4.20853	−	7.28938i	0.137487	−	0.238134i	−0.789058	−	0.614319i	$-0.789431\pi$
$937$	4.20853	−	7.28938i	0.137487	−	0.238134i	0.926545	+	0.376185i	$0.122764\pi$
$938$		0			0
$939$	26.6414	−	17.1093i	0.869410	−	0.558341i
$940$		0			0
$941$	−41.8479	−	24.1609i	−1.36420	−	0.787623i	−0.374023	−	0.927420i	$-0.622022\pi$
$941$	−41.8479	−	24.1609i	−1.36420	−	0.787623i	−0.990180	+	0.139797i	$0.955355\pi$
$942$		0			0
$943$	−1.74797	+	6.52350i	−0.0569216	+	0.212434i
$944$		0			0
$945$	19.6694	+	7.89646i	0.639845	+	0.256872i
$946$		0			0
$947$	28.3305	−	7.59113i	0.920617	−	0.246679i	0.232768	−	0.972532i	$-0.425222\pi$
$947$	28.3305	−	7.59113i	0.920617	−	0.246679i	0.687849	+	0.725854i	$0.258555\pi$
$948$		0			0
$949$	4.86268	−	18.1478i	0.157849	−	0.589101i
$950$		0			0
$951$	−51.6358	−	11.2501i	−1.67440	−	0.364808i
$952$		0			0
$953$	8.10811	−	14.0437i	0.262647	−	0.454919i	−0.704297	−	0.709905i	$-0.748738\pi$
$953$	8.10811	−	14.0437i	0.262647	−	0.454919i	0.966945	+	0.254987i	$0.0820711\pi$
$954$		0			0
$955$	6.55738	−	3.78591i	0.212192	−	0.122509i
$956$		0			0
$957$	7.75645	+	4.00189i	0.250730	+	0.129363i
$958$		0			0
$959$	−2.18137	+	1.25941i	−0.0704400	+	0.0406686i
$960$		0			0
$961$			37.8341i			1.22045i
$962$		0			0
$963$	−17.6326	+	38.5444i	−0.568202	+	1.24207i
$964$		0			0
$965$	8.49265	+	14.7097i	0.273388	+	0.473522i
$966$		0			0
$967$	−49.6497	−	13.3036i	−1.59663	−	0.427815i	−0.652604	−	0.757699i	$-0.726324\pi$
$967$	−49.6497	−	13.3036i	−1.59663	−	0.427815i	−0.944021	+	0.329884i	$0.892990\pi$
$968$		0			0
$969$	−3.47193	−	10.8732i	−0.111535	−	0.349298i
$970$		0			0
$971$	8.43329	+	4.86896i	0.270637	+	0.156252i	0.629177	−	0.777262i	$-0.283392\pi$
$971$	8.43329	+	4.86896i	0.270637	+	0.156252i	−0.358540	+	0.933514i	$0.616725\pi$
$972$		0			0
$973$			10.1630i			0.325810i
$974$		0			0
$975$	2.64959	−	5.13544i	0.0848548	−	0.164466i
$976$		0			0
$977$	−6.20625	−	23.1620i	−0.198555	−	0.741019i	−0.991318	−	0.131488i	$-0.958025\pi$
$977$	−6.20625	−	23.1620i	−0.198555	−	0.741019i	0.792762	−	0.609531i	$-0.208642\pi$
$978$		0			0
$979$	9.38883	+	35.0396i	0.300068	+	1.11987i
$980$		0			0
$981$	3.49004	+	2.88540i	0.111429	+	0.0921237i
$982$		0			0
$983$	30.1024	−	52.1389i	0.960117	−	1.66297i	0.237918	−	0.971285i	$-0.423535\pi$
$983$	30.1024	−	52.1389i	0.960117	−	1.66297i	0.722198	−	0.691686i	$-0.243132\pi$
$984$		0			0
$985$	23.0592	−	23.0592i	0.734727	−	0.734727i
$986$		0			0
$987$	−23.0222	−	20.9421i	−0.732805	−	0.666595i
$988$		0			0
$989$	24.8059			0.788782
$990$		0			0
$991$	21.2761	+	21.2761i	0.675857	+	0.675857i	0.959060	−	0.283203i	$-0.0913970\pi$
$991$	21.2761	+	21.2761i	0.675857	+	0.675857i	−0.283203	+	0.959060i	$0.591397\pi$
$992$		0			0
$993$	−44.6421	+	28.6694i	−1.41667	+	0.909797i
$994$		0			0
$995$	25.2910	−	14.6017i	0.801777	−	0.462906i
$996$		0			0
$997$	12.3876	+	46.2312i	0.392320	+	1.46416i	0.826297	+	0.563234i	$0.190443\pi$
$997$	12.3876	+	46.2312i	0.392320	+	1.46416i	−0.433977	+	0.900924i	$0.642890\pi$
$998$		0			0
$999$	−31.6016	−	0.581840i	−0.999831	−	0.0184086i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	444.2.w.c.125.4	✓	40
3.2	odd	2	inner	444.2.w.c.125.8	yes	40
37.8	odd	12	inner	444.2.w.c.341.8	yes	40
111.8	even	12	inner	444.2.w.c.341.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
444.2.w.c.125.4	✓	40	1.1	even	1	trivial
444.2.w.c.125.8	yes	40	3.2	odd	2	inner
444.2.w.c.341.4	yes	40	111.8	even	12	inner
444.2.w.c.341.8	yes	40	37.8	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 444 = 2^{2} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	444.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.526856 - 1.64998i) q^{3} +(-0.425223 + 1.58695i) q^{5} +(-1.24138 - 2.15014i) q^{7} +(-2.44485 + 1.73860i) q^{9} -5.53300 q^{11} +(1.40068 + 0.375311i) q^{13} +(2.84247 - 0.134487i) q^{15} +(-3.55279 + 0.951967i) q^{17} +(-1.73061 - 0.463714i) q^{19} +(-2.89365 + 3.18107i) q^{21} +(-1.79198 - 1.79198i) q^{23} +(1.99252 + 1.15038i) q^{25} +(4.15673 + 3.11795i) q^{27} +(0.643988 - 0.643988i) q^{29} +(-5.86660 - 5.86660i) q^{31} +(2.91509 + 9.12931i) q^{33} +(3.94004 - 1.05573i) q^{35} +(-4.93235 + 3.55977i) q^{37} +(-0.118701 - 2.50882i) q^{39} +(-1.33247 - 2.30791i) q^{41} +(-6.92135 + 6.92135i) q^{43} +(-1.71947 - 4.61915i) q^{45} +7.23726i q^{47} +(0.417927 - 0.723870i) q^{49} +(3.44253 + 5.36047i) q^{51} +(-3.61769 - 2.08867i) q^{53} +(2.35276 - 8.78061i) q^{55} +(0.146661 + 3.09977i) q^{57} +(9.30754 - 2.49395i) q^{59} +(0.753770 - 2.81311i) q^{61} +(6.77323 + 3.09850i) q^{63} +(-1.19120 + 2.06322i) q^{65} +(9.23364 - 5.33104i) q^{67} +(-2.01262 + 3.90085i) q^{69} +(11.7434 - 6.78003i) q^{71} -12.9564i q^{73} +(0.848334 - 3.89370i) q^{75} +(6.86858 + 11.8967i) q^{77} +(-10.2025 - 2.73375i) q^{79} +(2.95455 - 8.50121i) q^{81} +(-5.13079 - 2.96226i) q^{83} -6.04291i q^{85} +(-1.40185 - 0.723277i) q^{87} +(-1.69688 - 6.33284i) q^{89} +(-0.931811 - 3.47757i) q^{91} +(-6.58891 + 12.7706i) q^{93} +(1.47179 - 2.54921i) q^{95} +(-6.50678 + 6.50678i) q^{97} +(13.5273 - 9.61966i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 10 q^{9} - 24 q^{19} - 18 q^{21} + 32 q^{31} - 44 q^{37} + 62 q^{39} - 4 q^{43} - 54 q^{45} + 24 q^{49} + 14 q^{51} + 20 q^{55} + 34 q^{57} + 36 q^{61} - 36 q^{63} + 12 q^{67} - 50 q^{69} - 20 q^{75}+ \cdots - 12 q^{99}+O(q^{100}) \) 40 * q - 10 * q^9 - 24 * q^19 - 18 * q^21 + 32 * q^31 - 44 * q^37 + 62 * q^39 - 4 * q^43 - 54 * q^45 + 24 * q^49 + 14 * q^51 + 20 * q^55 + 34 * q^57 + 36 * q^61 - 36 * q^63 + 12 * q^67 - 50 * q^69 - 20 * q^75 + 8 * q^79 + 10 * q^81 - 32 * q^87 + 20 * q^91 - 30 * q^93 + 52 * q^97 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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