LMFDB - Embedded newform 896.2.bh.a.625.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(81,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 9, 16]))

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

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

chi := DirichletCharacter("896.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.bh (of order $24$, degree $8$, 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:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			625.15
Character	$\chi$	$=$	896.625
Dual form			896.2.bh.a.529.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.118403 + 0.154306i) q^{3} +(2.39583 - 1.83839i) q^{5} +(-1.47323 + 2.19764i) q^{7} +(0.766666 + 2.86124i) q^{9} +O(q^{10})$	\(q+(-0.118403 + 0.154306i) q^{3} +(2.39583 - 1.83839i) q^{5} +(-1.47323 + 2.19764i) q^{7} +(0.766666 + 2.86124i) q^{9} +(-5.43183 + 0.715114i) q^{11} +(-5.50652 + 2.28087i) q^{13} +0.587363i q^{15} +(-3.70249 + 2.13763i) q^{17} +(-0.183696 + 1.39531i) q^{19} +(-0.164674 - 0.487536i) q^{21} +(0.326660 + 1.21911i) q^{23} +(1.06625 - 3.97929i) q^{25} +(-1.07136 - 0.443773i) q^{27} +(0.497218 + 1.20039i) q^{29} +(0.251275 + 0.435222i) q^{31} +(0.532801 - 0.922838i) q^{33} +(0.510497 + 7.97352i) q^{35} +(5.39866 - 4.14254i) q^{37} +(0.300037 - 1.11975i) q^{39} +(-3.02206 + 3.02206i) q^{41} +(3.49881 - 8.44689i) q^{43} +(7.09686 + 5.44561i) q^{45} +(7.99998 + 4.61879i) q^{47} +(-2.65920 - 6.47523i) q^{49} +(0.108537 - 0.824421i) q^{51} +(-7.09730 + 0.934377i) q^{53} +(-11.6991 + 11.6991i) q^{55} +(-0.193554 - 0.193554i) q^{57} +(-0.00968333 - 0.0735522i) q^{59} +(9.08657 + 1.19627i) q^{61} +(-7.41743 - 2.53040i) q^{63} +(-8.99956 + 15.5877i) q^{65} +(-0.469449 + 0.611798i) q^{67} +(-0.226794 - 0.0939414i) q^{69} +(7.84105 + 7.84105i) q^{71} +(-6.92569 - 1.85573i) q^{73} +(0.487783 + 0.635691i) q^{75} +(6.43076 - 12.9907i) q^{77} +(0.877666 + 0.506720i) q^{79} +(-7.50061 + 4.33048i) q^{81} +(6.18602 - 2.56233i) q^{83} +(-4.94075 + 11.9280i) q^{85} +(-0.244100 - 0.0654064i) q^{87} +(-13.9937 + 3.74960i) q^{89} +(3.09982 - 15.4616i) q^{91} +(-0.0969094 - 0.0127584i) q^{93} +(2.12501 + 3.68062i) q^{95} +0.451869 q^{97} +(-6.21051 - 14.9935i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9}+O(q^{10}) $ 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9	$ 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9} + 4 q^{11} - 16 q^{13} + 4 q^{19} - 8 q^{21} + 12 q^{23} - 4 q^{25} + 16 q^{27} - 16 q^{29} + 56 q^{31} - 8 q^{33} + 32 q^{35} - 4 q^{37} + 4 q^{39} - 16 q^{41} + 8 q^{45} + 28 q^{51} - 20 q^{53} + 16 q^{55} - 16 q^{57} + 36 q^{59} - 4 q^{61} + 16 q^{63} - 8 q^{65} - 36 q^{67} - 16 q^{69} - 48 q^{71} - 4 q^{73} - 16 q^{75} - 8 q^{77} + 96 q^{83} - 56 q^{85} + 4 q^{87} - 4 q^{89} + 56 q^{91} + 20 q^{93} + 8 q^{95} - 32 q^{97} - 8 q^{99}+O(q^{100}) $ 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9 + 4 * q^11 - 16 * q^13 + 4 * q^19 - 8 * q^21 + 12 * q^23 - 4 * q^25 + 16 * q^27 - 16 * q^29 + 56 * q^31 - 8 * q^33 + 32 * q^35 - 4 * q^37 + 4 * q^39 - 16 * q^41 + 8 * q^45 + 28 * q^51 - 20 * q^53 + 16 * q^55 - 16 * q^57 + 36 * q^59 - 4 * q^61 + 16 * q^63 - 8 * q^65 - 36 * q^67 - 16 * q^69 - 48 * q^71 - 4 * q^73 - 16 * q^75 - 8 * q^77 + 96 * q^83 - 56 * q^85 + 4 * q^87 - 4 * q^89 + 56 * q^91 + 20 * q^93 + 8 * q^95 - 32 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{8}\right)$

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
$3$	−0.118403	+	0.154306i	−0.0683603	+	0.0890888i	−0.826282	−	0.563257i	$-0.809548\pi$
$3$	−0.118403	+	0.154306i	−0.0683603	+	0.0890888i	0.757922	+	0.652346i	$0.226215\pi$
$4$		0			0
$5$	2.39583	−	1.83839i	1.07145	−	0.822151i	0.0867170	−	0.996233i	$-0.472362\pi$
$5$	2.39583	−	1.83839i	1.07145	−	0.822151i	0.984731	+	0.174082i	$0.0556958\pi$
$6$		0			0
$7$	−1.47323	+	2.19764i	−0.556828	+	0.830628i
$7$	−1.47323	+	2.19764i	−0.556828	+	0.830628i
$8$		0			0
$9$	0.766666	+	2.86124i	0.255555	+	0.953746i
$10$		0			0
$11$	−5.43183	+	0.715114i	−1.63776	+	0.215615i	−0.892464	−	0.451120i	$-0.851025\pi$
$11$	−5.43183	+	0.715114i	−1.63776	+	0.215615i	−0.745295	+	0.666735i	$0.767691\pi$
$12$		0			0
$13$	−5.50652	+	2.28087i	−1.52723	+	0.632601i	−0.979025	−	0.203741i	$-0.934690\pi$
$13$	−5.50652	+	2.28087i	−1.52723	+	0.632601i	−0.548209	+	0.836342i	$0.684690\pi$
$14$		0			0
$15$			0.587363i			0.151657i
$16$		0			0
$17$	−3.70249	+	2.13763i	−0.897986	+	0.518453i	−0.876546	−	0.481318i	$-0.840158\pi$
$17$	−3.70249	+	2.13763i	−0.897986	+	0.518453i	−0.0214399	+	0.999770i	$0.506825\pi$
$18$		0			0
$19$	−0.183696	+	1.39531i	−0.0421427	+	0.320105i	0.957369	+	0.288867i	$0.0932785\pi$
$19$	−0.183696	+	1.39531i	−0.0421427	+	0.320105i	−0.999512	+	0.0312385i	$0.990055\pi$
$20$		0			0
$21$	−0.164674	−	0.487536i	−0.0359348	−	0.106389i
$22$		0			0
$23$	0.326660	+	1.21911i	0.0681133	+	0.254202i	0.991584	−	0.129467i	$-0.0413267\pi$
$23$	0.326660	+	1.21911i	0.0681133	+	0.254202i	−0.923470	+	0.383670i	$0.874660\pi$
$24$		0			0
$25$	1.06625	−	3.97929i	0.213250	−	0.795859i
$26$		0			0
$27$	−1.07136	−	0.443773i	−0.206184	−	0.0854042i
$28$		0			0
$29$	0.497218	+	1.20039i	0.0923310	+	0.222907i	0.963298	−	0.268435i	$-0.0865065\pi$
$29$	0.497218	+	1.20039i	0.0923310	+	0.222907i	−0.870967	+	0.491342i	$0.836507\pi$
$30$		0			0
$31$	0.251275	+	0.435222i	0.0451304	+	0.0781682i	0.887708	−	0.460406i	$-0.152296\pi$
$31$	0.251275	+	0.435222i	0.0451304	+	0.0781682i	−0.842578	+	0.538575i	$0.818963\pi$
$32$		0			0
$33$	0.532801	−	0.922838i	0.0927487	−	0.160646i
$34$		0			0
$35$	0.510497	+	7.97352i	0.0862897	+	1.34777i
$36$		0			0
$37$	5.39866	−	4.14254i	0.887535	−	0.681029i	−0.0608517	−	0.998147i	$-0.519382\pi$
$37$	5.39866	−	4.14254i	0.887535	−	0.681029i	0.948386	+	0.317118i	$0.102715\pi$
$38$		0			0
$39$	0.300037	−	1.11975i	0.0480444	−	0.179304i
$40$		0			0
$41$	−3.02206	+	3.02206i	−0.471966	+	0.471966i	−0.902550	−	0.430584i	$-0.858308\pi$
$41$	−3.02206	+	3.02206i	−0.471966	+	0.471966i	0.430584	+	0.902550i	$0.358308\pi$
$42$		0			0
$43$	3.49881	−	8.44689i	0.533564	−	1.28814i	−0.395584	−	0.918430i	$-0.629458\pi$
$43$	3.49881	−	8.44689i	0.533564	−	1.28814i	0.929148	−	0.369708i	$-0.120542\pi$
$44$		0			0
$45$	7.09686	+	5.44561i	1.05794	+	0.811784i
$46$		0			0
$47$	7.99998	+	4.61879i	1.16692	+	0.673720i	0.952952	−	0.303121i	$-0.0980287\pi$
$47$	7.99998	+	4.61879i	1.16692	+	0.673720i	0.213965	+	0.976841i	$0.431362\pi$
$48$		0			0
$49$	−2.65920	−	6.47523i	−0.379886	−	0.925033i
$50$		0			0
$51$	0.108537	−	0.824421i	0.0151982	−	0.115442i
$52$		0			0
$53$	−7.09730	+	0.934377i	−0.974889	+	0.128347i	−0.601106	−	0.799169i	$-0.705273\pi$
$53$	−7.09730	+	0.934377i	−0.974889	+	0.128347i	−0.373783	+	0.927516i	$0.621940\pi$
$54$		0			0
$55$	−11.6991	+	11.6991i	−1.57751	+	1.57751i
$56$		0			0
$57$	−0.193554	−	0.193554i	−0.0256369	−	0.0256369i
$58$		0			0
$59$	−0.00968333	−	0.0735522i	−0.00126066	−	0.00957568i	0.990803	−	0.135313i	$-0.0432038\pi$
$59$	−0.00968333	−	0.0735522i	−0.00126066	−	0.00957568i	−0.992064	+	0.125737i	$0.959871\pi$
$60$		0			0
$61$	9.08657	+	1.19627i	1.16342	+	0.153167i	0.687406	−	0.726273i	$-0.258749\pi$
$61$	9.08657	+	1.19627i	1.16342	+	0.153167i	0.476010	+	0.879440i	$0.342083\pi$
$62$		0			0
$63$	−7.41743	−	2.53040i	−0.934508	−	0.318800i
$64$		0			0
$65$	−8.99956	+	15.5877i	−1.11626	+	1.93342i
$66$		0			0
$67$	−0.469449	+	0.611798i	−0.0573523	+	0.0747430i	−0.821149	−	0.570714i	$-0.806666\pi$
$67$	−0.469449	+	0.611798i	−0.0573523	+	0.0747430i	0.763796	+	0.645457i	$0.223333\pi$
$68$		0			0
$69$	−0.226794	−	0.0939414i	−0.0273028	−	0.0113092i
$70$		0			0
$71$	7.84105	+	7.84105i	0.930561	+	0.930561i	0.997741	−	0.0671798i	$-0.0214001\pi$
$71$	7.84105	+	7.84105i	0.930561	+	0.930561i	−0.0671798	+	0.997741i	$0.521400\pi$
$72$		0			0
$73$	−6.92569	−	1.85573i	−0.810591	−	0.217197i	−0.170362	−	0.985382i	$-0.554494\pi$
$73$	−6.92569	−	1.85573i	−0.810591	−	0.217197i	−0.640229	+	0.768184i	$0.721160\pi$
$74$		0			0
$75$	0.487783	+	0.635691i	0.0563243	+	0.0734033i
$76$		0			0
$77$	6.43076	−	12.9907i	0.732854	−	1.48043i
$78$		0			0
$79$	0.877666	+	0.506720i	0.0987451	+	0.0570105i	0.548559	−	0.836112i	$-0.315176\pi$
$79$	0.877666	+	0.506720i	0.0987451	+	0.0570105i	−0.449814	+	0.893122i	$0.648510\pi$
$80$		0			0
$81$	−7.50061	+	4.33048i	−0.833402	+	0.481165i
$82$		0			0
$83$	6.18602	−	2.56233i	0.679004	−	0.281253i	−0.0164063	−	0.999865i	$-0.505223\pi$
$83$	6.18602	−	2.56233i	0.679004	−	0.281253i	0.695411	+	0.718613i	$0.255223\pi$
$84$		0			0
$85$	−4.94075	+	11.9280i	−0.535899	+	1.29378i
$86$		0			0
$87$	−0.244100	−	0.0654064i	−0.0261703	−	0.00701231i
$88$		0			0
$89$	−13.9937	+	3.74960i	−1.48333	+	0.397456i	−0.907478	−	0.420100i	$-0.861995\pi$
$89$	−13.9937	+	3.74960i	−1.48333	+	0.397456i	−0.575849	+	0.817556i	$0.695328\pi$
$90$		0			0
$91$	3.09982	−	15.4616i	0.324950	−	1.62081i
$92$		0			0
$93$	−0.0969094	−	0.0127584i	−0.0100490	−	0.00132298i
$94$		0			0
$95$	2.12501	+	3.68062i	0.218021	+	0.377624i
$96$		0			0
$97$	0.451869			0.0458804			0.0229402	−	0.999737i	$-0.492697\pi$
$97$	0.451869			0.0458804			0.0229402	+	0.999737i	$0.492697\pi$
$98$		0			0
$99$	−6.21051	−	14.9935i	−0.624180	−	1.50690i
$100$		0			0
$101$	0.453155	+	3.44206i	0.0450906	+	0.342497i	0.999089	+	0.0426844i	$0.0135910\pi$
$101$	0.453155	+	3.44206i	0.0450906	+	0.342497i	−0.953998	+	0.299813i	$0.903076\pi$
$102$		0			0
$103$	−8.80466	+	2.35920i	−0.867549	+	0.232459i	−0.665028	−	0.746819i	$-0.731580\pi$
$103$	−8.80466	+	2.35920i	−0.867549	+	0.232459i	−0.202522	+	0.979278i	$0.564914\pi$
$104$		0			0
$105$	−1.29081	−	0.865320i	−0.125970	−	0.0844466i
$106$		0			0
$107$	−7.67351	−	10.0003i	−0.741826	−	0.966766i	−1.00000		0.000667722i	$-0.999787\pi$
$107$	−7.67351	−	10.0003i	−0.741826	−	0.966766i	0.258174	−	0.966098i	$-0.416879\pi$
$108$		0			0
$109$	11.0120	+	8.44984i	1.05476	+	0.809348i	0.982166	−	0.188014i	$-0.0602049\pi$
$109$	11.0120	+	8.44984i	1.05476	+	0.809348i	0.0725963	+	0.997361i	$0.476872\pi$
$110$		0			0
$111$			1.32354i			0.125625i
$112$		0			0
$113$			0.0684958i			0.00644354i	0.999995	+	0.00322177i	$0.00102552\pi$
$113$			0.0684958i			0.00644354i	−0.999995	+	0.00322177i	$0.998974\pi$
$114$		0			0
$115$	3.02382	+	2.32026i	0.281973	+	0.216365i
$116$		0			0
$117$	−10.7478	−	14.0068i	−0.993633	−	1.29493i
$118$		0			0
$119$	0.756872	−	11.2859i	0.0693823	−	1.03458i
$120$		0			0
$121$	18.3682	−	4.92175i	1.66984	−	0.447432i
$122$		0			0
$123$	−0.108501	−	0.824145i	−0.00978318	−	0.0743107i
$124$		0			0
$125$	1.01736	+	2.45613i	0.0909957	+	0.219683i
$126$		0			0
$127$	6.18288			0.548642			0.274321	−	0.961638i	$-0.411547\pi$
$127$	6.18288			0.548642			0.274321	+	0.961638i	$0.411547\pi$
$128$		0			0
$129$	0.889137	+	1.54003i	0.0782841	+	0.135592i
$130$		0			0
$131$	−8.65291	−	1.13918i	−0.756009	−	0.0995304i	−0.257337	−	0.966322i	$-0.582845\pi$
$131$	−8.65291	−	1.13918i	−0.756009	−	0.0995304i	−0.498671	+	0.866791i	$0.666178\pi$
$132$		0			0
$133$	−2.79575	−	2.45930i	−0.242422	−	0.213248i
$134$		0			0
$135$	−3.38263	+	0.906374i	−0.291131	+	0.0780082i
$136$		0			0
$137$	11.1426	+	2.98566i	0.951980	+	0.255082i	0.701202	−	0.712962i	$-0.252647\pi$
$137$	11.1426	+	2.98566i	0.951980	+	0.255082i	0.250778	+	0.968045i	$0.419314\pi$
$138$		0			0
$139$	−6.81777	+	16.4595i	−0.578275	+	1.39608i	0.316084	+	0.948731i	$0.397632\pi$
$139$	−6.81777	+	16.4595i	−0.578275	+	1.39608i	−0.894359	+	0.447349i	$0.852368\pi$
$140$		0			0
$141$	−1.65993	+	0.687567i	−0.139792	+	0.0579036i
$142$		0			0
$143$	28.2794	−	16.3271i	2.36484	−	1.36534i
$144$		0			0
$145$	3.39803	+	1.96185i	0.282191	+	0.162923i
$146$		0			0
$147$	1.31403	+	0.356358i	0.108379	+	0.0293919i
$148$		0			0
$149$	7.52295	+	9.80409i	0.616304	+	0.803183i	0.992355	−	0.123416i	$-0.0393850\pi$
$149$	7.52295	+	9.80409i	0.616304	+	0.803183i	−0.376051	+	0.926599i	$0.622718\pi$
$150$		0			0
$151$	6.48936	+	1.73882i	0.528097	+	0.141503i	0.513009	−	0.858383i	$-0.328531\pi$
$151$	6.48936	+	1.73882i	0.528097	+	0.141503i	0.0150875	+	0.999886i	$0.495197\pi$
$152$		0			0
$153$	−8.95485	−	8.95485i	−0.723957	−	0.723957i
$154$		0			0
$155$	1.40212	+	0.580777i	0.112621	+	0.0466491i
$156$		0			0
$157$	0.632229	−	0.823937i	0.0504574	−	0.0657573i	−0.767443	−	0.641117i	$-0.778471\pi$
$157$	0.632229	−	0.823937i	0.0504574	−	0.0657573i	0.817900	+	0.575360i	$0.195138\pi$
$158$		0			0
$159$	0.696164	−	1.20579i	0.0552094	−	0.0956255i
$160$		0			0
$161$	−3.16041	−	1.07815i	−0.249075	−	0.0849701i
$162$		0			0
$163$	−2.67408	−	0.352050i	−0.209450	−	0.0275747i	0.0250708	−	0.999686i	$-0.492019\pi$
$163$	−2.67408	−	0.352050i	−0.209450	−	0.0275747i	−0.234521	+	0.972111i	$0.575352\pi$
$164$		0			0
$165$	−0.420032	−	3.19046i	−0.0326994	−	0.248377i
$166$		0			0
$167$	−4.37579	−	4.37579i	−0.338609	−	0.338609i	0.517235	−	0.855843i	$-0.326961\pi$
$167$	−4.37579	−	4.37579i	−0.338609	−	0.338609i	−0.855843	+	0.517235i	$0.826961\pi$
$168$		0			0
$169$	15.9270	−	15.9270i	1.22515	−	1.22515i
$170$		0			0
$171$	−4.13313	+	0.544137i	−0.316069	+	0.0416112i
$172$		0			0
$173$	0.198608	−	1.50858i	0.0150999	−	0.114695i	−0.982235	−	0.187655i	$-0.939911\pi$
$173$	0.198608	−	1.50858i	0.0150999	−	0.114695i	0.997335	+	0.0729600i	$0.0232446\pi$
$174$		0			0
$175$	7.17421	+	8.20563i	0.542319	+	0.620287i
$176$		0			0
$177$	0.0124961	+	0.00721463i	0.000939265	+	0.000542285i
$178$		0			0
$179$	17.8811	+	13.7206i	1.33650	+	1.02553i	0.996368	+	0.0851496i	$0.0271368\pi$
$179$	17.8811	+	13.7206i	1.33650	+	1.02553i	0.340127	+	0.940379i	$0.389530\pi$
$180$		0			0
$181$	6.77001	−	16.3442i	0.503211	−	1.21486i	−0.444515	−	0.895772i	$-0.646624\pi$
$181$	6.77001	−	16.3442i	0.503211	−	1.21486i	0.947726	−	0.319087i	$-0.103376\pi$
$182$		0			0
$183$	−1.26047	+	1.26047i	−0.0931769	+	0.0931769i
$184$		0			0
$185$	5.31870	−	19.8496i	0.391038	−	1.45937i
$186$		0			0
$187$	18.5827	−	14.2590i	1.35890	−	1.04272i
$188$		0			0
$189$	2.55361	−	1.70069i	0.185748	−	0.123707i
$190$		0			0
$191$	−10.0442	+	17.3971i	−0.726772	+	1.25881i	0.231468	+	0.972843i	$0.425647\pi$
$191$	−10.0442	+	17.3971i	−0.726772	+	1.25881i	−0.958240	+	0.285964i	$0.907686\pi$
$192$		0			0
$193$	8.76441	+	15.1804i	0.630876	+	1.09271i	0.987373	+	0.158413i	$0.0506376\pi$
$193$	8.76441	+	15.1804i	0.630876	+	1.09271i	−0.356497	+	0.934296i	$0.616029\pi$
$194$		0			0
$195$	−1.33970	−	3.23433i	−0.0959380	−	0.231615i
$196$		0			0
$197$	−8.32147	−	3.44687i	−0.592880	−	0.245579i	0.0660089	−	0.997819i	$-0.478973\pi$
$197$	−8.32147	−	3.44687i	−0.592880	−	0.245579i	−0.658889	+	0.752240i	$0.728973\pi$
$198$		0			0
$199$	2.15738	−	8.05144i	0.152932	−	0.570751i	−0.846341	−	0.532641i	$-0.821200\pi$
$199$	2.15738	−	8.05144i	0.152932	−	0.570751i	0.999274	−	0.0381102i	$-0.0121338\pi$
$200$		0			0
$201$	−0.0388199	−	0.144878i	−0.00273815	−	0.0102189i
$202$		0			0
$203$	−3.37053	−	0.675744i	−0.236565	−	0.0474279i
$204$		0			0
$205$	−1.68463	+	12.7960i	−0.117660	+	0.893715i
$206$		0			0
$207$	−3.23773	+	1.86930i	−0.225038	+	0.129926i
$208$		0			0
$209$		−	7.71043i		−	0.533342i
$210$		0			0
$211$	0.534006	−	0.221193i	0.0367625	−	0.0152275i	−0.364226	−	0.931310i	$-0.618667\pi$
$211$	0.534006	−	0.221193i	0.0367625	−	0.0152275i	0.400989	+	0.916083i	$0.368667\pi$
$212$		0			0
$213$	−2.13833	+	0.281517i	−0.146516	+	0.0192892i
$214$		0			0
$215$	−7.14607	−	26.6695i	−0.487358	−	1.81884i
$216$		0			0
$217$	−1.32664	−	0.0889691i	−0.0900585	−	0.00603961i
$218$		0			0
$219$	1.10638	−	0.848953i	0.0747620	−	0.0573669i
$220$		0			0
$221$	15.5122	−	20.2158i	1.04346	−	1.35986i
$222$		0			0
$223$	5.07246			0.339677			0.169839	−	0.985472i	$-0.445675\pi$
$223$	5.07246			0.339677			0.169839	+	0.985472i	$0.445675\pi$
$224$		0			0
$225$	12.2032			0.813544
$226$		0			0
$227$	−6.69399	+	8.72378i	−0.444296	+	0.579018i	−0.960791	−	0.277272i	$-0.910570\pi$
$227$	−6.69399	+	8.72378i	−0.444296	+	0.579018i	0.516496	+	0.856290i	$0.327236\pi$
$228$		0			0
$229$	12.5005	−	9.59199i	0.826058	−	0.633856i	−0.106728	−	0.994288i	$-0.534037\pi$
$229$	12.5005	−	9.59199i	0.826058	−	0.633856i	0.932786	+	0.360432i	$0.117371\pi$
$230$		0			0
$231$	1.24312	+	2.53045i	0.0817916	+	0.166492i
$232$		0			0
$233$	−3.50730	−	13.0894i	−0.229771	−	0.857516i	−0.980437	−	0.196834i	$-0.936934\pi$
$233$	−3.50730	−	13.0894i	−0.229771	−	0.857516i	0.750666	−	0.660682i	$-0.229733\pi$
$234$		0			0
$235$	27.6577	−	3.64121i	1.80419	−	0.237526i
$236$		0			0
$237$	−0.182109	+	0.0754319i	−0.0118292	+	0.00489983i
$238$		0			0
$239$		−	5.02121i		−	0.324795i	−0.986725	−	0.162397i	$-0.948077\pi$
$239$		−	5.02121i		−	0.324795i	0.986725	−	0.162397i	$-0.0519227\pi$
$240$		0			0
$241$	−20.7477	+	11.9787i	−1.33648	+	0.771615i	−0.986283	−	0.165062i	$-0.947218\pi$
$241$	−20.7477	+	11.9787i	−1.33648	+	0.771615i	−0.350194	+	0.936677i	$0.613884\pi$
$242$		0			0
$243$	0.673966	−	5.11928i	0.0432349	−	0.328402i
$244$		0			0
$245$	−18.2750	−	10.6249i	−1.16755	−	0.678802i
$246$		0			0
$247$	−2.17100	−	8.10227i	−0.138137	−	0.515535i
$248$		0			0
$249$	−0.337062	+	1.25793i	−0.0213604	+	0.0797182i
$250$		0			0
$251$	−15.8433	−	6.56249i	−1.00002	−	0.414221i	−0.178214	−	0.983992i	$-0.557032\pi$
$251$	−15.8433	−	6.56249i	−1.00002	−	0.414221i	−0.821803	+	0.569771i	$0.807032\pi$
$252$		0			0
$253$	−2.64617	−	6.38841i	−0.166363	−	0.401636i
$254$		0			0
$255$	−1.25557	−	2.17471i	−0.0786267	−	0.136185i
$256$		0			0
$257$	1.21717	−	2.10820i	0.0759249	−	0.131506i	−0.825563	−	0.564310i	$-0.809142\pi$
$257$	1.21717	−	2.10820i	0.0759249	−	0.131506i	0.901488	+	0.432804i	$0.142476\pi$
$258$		0			0
$259$	1.15033	+	17.9672i	0.0714782	+	1.11643i
$260$		0			0
$261$	−3.05340	+	2.34296i	−0.189001	+	0.145025i
$262$		0			0
$263$	−7.18443	+	26.8126i	−0.443011	+	1.65334i	0.278125	+	0.960545i	$0.410287\pi$
$263$	−7.18443	+	26.8126i	−0.443011	+	1.65334i	−0.721136	+	0.692794i	$0.756380\pi$
$264$		0			0
$265$	−15.2862	+	15.2862i	−0.939023	+	0.939023i
$266$		0			0
$267$	1.07831	−	2.60328i	0.0659917	−	0.159318i
$268$		0			0
$269$	−7.77004	−	5.96216i	−0.473747	−	0.363519i	0.344120	−	0.938926i	$-0.388177\pi$
$269$	−7.77004	−	5.96216i	−0.473747	−	0.363519i	−0.817868	+	0.575406i	$0.804844\pi$
$270$		0			0
$271$	−23.9839	−	13.8471i	−1.45692	−	0.841152i	−0.458059	−	0.888922i	$-0.651455\pi$
$271$	−23.9839	−	13.8471i	−1.45692	−	0.841152i	−0.998858	+	0.0477701i	$0.984789\pi$
$272$		0			0
$273$	2.01879	+	2.30903i	0.122183	+	0.139749i
$274$		0			0
$275$	−2.94603	+	22.3773i	−0.177652	+	1.34940i
$276$		0			0
$277$	1.11886	−	0.147300i	0.0672256	−	0.00885042i	−0.0968384	−	0.995300i	$-0.530873\pi$
$277$	1.11886	−	0.147300i	0.0672256	−	0.00885042i	0.164064	+	0.986450i	$0.447540\pi$
$278$		0			0
$279$	−1.05263	+	1.05263i	−0.0630192	+	0.0630192i
$280$		0			0
$281$	6.68419	+	6.68419i	0.398746	+	0.398746i	0.877790	−	0.479045i	$-0.159017\pi$
$281$	6.68419	+	6.68419i	0.398746	+	0.398746i	−0.479045	+	0.877790i	$0.659017\pi$
$282$		0			0
$283$	2.81117	+	21.3530i	0.167107	+	1.26930i	0.845250	+	0.534372i	$0.179452\pi$
$283$	2.81117	+	21.3530i	0.167107	+	1.26930i	−0.678143	+	0.734930i	$0.737215\pi$
$284$		0			0
$285$	−0.819552	−	0.107896i	−0.0485460	−	0.00639121i
$286$		0			0
$287$	−2.18920	−	11.0936i	−0.129225	−	0.654832i
$288$		0			0
$289$	0.638965	−	1.10672i	0.0375862	−	0.0651012i
$290$		0			0
$291$	−0.0535029	+	0.0697263i	−0.00313639	+	0.00408743i
$292$		0			0
$293$	−11.8675	−	4.91570i	−0.693309	−	0.287178i	0.00806883	−	0.999967i	$-0.497432\pi$
$293$	−11.8675	−	4.91570i	−0.693309	−	0.287178i	−0.701378	+	0.712789i	$0.747432\pi$
$294$		0			0
$295$	−0.158417	−	0.158417i	−0.00922339	−	0.00922339i
$296$		0			0
$297$	6.13682	+	1.64435i	0.356094	+	0.0954151i
$298$		0			0
$299$	−4.57940	−	5.96799i	−0.264834	−	0.345138i
$300$		0			0
$301$	13.4086	+	20.1333i	0.772860	+	1.16046i
$302$		0			0
$303$	−0.584787	−	0.337627i	−0.0335951	−	0.0193961i
$304$		0			0
$305$	23.9691	−	13.8386i	1.37247	−	0.792394i
$306$		0			0
$307$	−18.8697	+	7.81608i	−1.07695	+	0.446087i	−0.849438	−	0.527688i	$-0.823059\pi$
$307$	−18.8697	+	7.81608i	−1.07695	+	0.446087i	−0.227512	+	0.973775i	$0.573059\pi$
$308$		0			0
$309$	0.678463	−	1.63795i	0.0385964	−	0.0931799i
$310$		0			0
$311$	−2.85627	−	0.765335i	−0.161964	−	0.0433981i	0.176926	−	0.984224i	$-0.443385\pi$
$311$	−2.85627	−	0.765335i	−0.161964	−	0.0433981i	−0.338890	+	0.940826i	$0.610051\pi$
$312$		0			0
$313$	26.9261	−	7.21483i	1.52195	−	0.407806i	0.601569	−	0.798821i	$-0.294542\pi$
$313$	26.9261	−	7.21483i	1.52195	−	0.407806i	0.920384	+	0.391015i	$0.127876\pi$
$314$		0			0
$315$	−22.4228	+	7.57368i	−1.26338	+	0.426729i
$316$		0			0
$317$	−32.5474	−	4.28495i	−1.82805	−	0.240667i	−0.863457	−	0.504422i	$-0.831705\pi$
$317$	−32.5474	−	4.28495i	−1.82805	−	0.240667i	−0.964590	+	0.263756i	$0.915039\pi$
$318$		0			0
$319$	−3.55922	−	6.16475i	−0.199278	−	0.345160i
$320$		0			0
$321$	2.45168			0.136839
$322$		0			0
$323$	−2.30252	−	5.55878i	−0.128116	−	0.309299i
$324$		0			0
$325$	3.20495	+	24.3440i	0.177779	+	1.35036i
$326$		0			0
$327$	−2.60773	+	0.698739i	−0.144208	+	0.0386403i
$328$		0			0
$329$	−21.9362	+	10.7765i	−1.20938	+	0.594128i
$330$		0			0
$331$	−3.65442	−	4.76253i	−0.200865	−	0.261772i	0.682050	−	0.731306i	$-0.261089\pi$
$331$	−3.65442	−	4.76253i	−0.200865	−	0.261772i	−0.882915	+	0.469534i	$0.844422\pi$
$332$		0			0
$333$	15.9918	+	12.2709i	0.876343	+	0.672441i
$334$		0			0
$335$			2.32879i			0.127236i
$336$		0			0
$337$			8.26077i			0.449993i	0.974360	+	0.224996i	$0.0722370\pi$
$337$			8.26077i			0.449993i	−0.974360	+	0.224996i	$0.927763\pi$
$338$		0			0
$339$	−0.0105693	−	0.00811014i	−0.000574048	−	0.000440482i
$340$		0			0
$341$	−1.67612	−	2.18436i	−0.0907670	−	0.118290i
$342$		0			0
$343$	18.1478	+	3.69554i	0.979890	+	0.199540i
$344$		0			0
$345$	−0.716062	+	0.191868i	−0.0385515	+	0.0103298i
$346$		0			0
$347$	−3.23389	−	24.5639i	−0.173605	−	1.31866i	−0.827240	−	0.561848i	$-0.810090\pi$
$347$	−3.23389	−	24.5639i	−0.173605	−	1.31866i	0.653636	−	0.756809i	$-0.273243\pi$
$348$		0			0
$349$	7.17014	+	17.3102i	0.383809	+	0.926596i	0.991222	+	0.132210i	$0.0422073\pi$
$349$	7.17014	+	17.3102i	0.383809	+	0.926596i	−0.607413	+	0.794386i	$0.707793\pi$
$350$		0			0
$351$	6.91168			0.368918
$352$		0			0
$353$	−1.24335	−	2.15355i	−0.0661769	−	0.114622i	0.831039	−	0.556215i	$-0.187747\pi$
$353$	−1.24335	−	2.15355i	−0.0661769	−	0.114622i	−0.897215	+	0.441593i	$0.854413\pi$
$354$		0			0
$355$	33.2007	+	4.37095i	1.76211	+	0.231986i
$356$		0			0
$357$	1.65188	+	1.45309i	0.0874266	+	0.0769054i
$358$		0			0
$359$	16.1733	−	4.33362i	0.853594	−	0.228720i	0.194614	−	0.980880i	$-0.437655\pi$
$359$	16.1733	−	4.33362i	0.853594	−	0.228720i	0.658980	+	0.752160i	$0.270988\pi$
$360$		0			0
$361$	16.4395	+	4.40494i	0.865234	+	0.231839i
$362$		0			0
$363$	−1.41540	+	3.41709i	−0.0742894	+	0.179350i
$364$		0			0
$365$	−20.0043	+	8.28607i	−1.04707	+	0.433712i
$366$		0			0
$367$	6.07154	−	3.50540i	0.316932	−	0.182981i	−0.333092	−	0.942894i	$-0.608092\pi$
$367$	6.07154	−	3.50540i	0.316932	−	0.182981i	0.650024	+	0.759914i	$0.274759\pi$
$368$		0			0
$369$	−10.9637	−	6.32991i	−0.570749	−	0.329522i
$370$		0			0
$371$	8.40252	−	16.9738i	0.436237	−	0.881237i
$372$		0			0
$373$	10.9932	+	14.3266i	0.569207	+	0.741805i	0.985917	−	0.167234i	$-0.0534836\pi$
$373$	10.9932	+	14.3266i	0.569207	+	0.741805i	−0.416710	+	0.909039i	$0.636817\pi$
$374$		0			0
$375$	−0.499456	−	0.133829i	−0.0257918	−	0.00691089i
$376$		0			0
$377$	−5.47588	−	5.47588i	−0.282022	−	0.282022i
$378$		0			0
$379$	3.29244	+	1.36377i	0.169121	+	0.0700523i	0.465638	−	0.884975i	$-0.345825\pi$
$379$	3.29244	+	1.36377i	0.169121	+	0.0700523i	−0.296516	+	0.955028i	$0.595825\pi$
$380$		0			0
$381$	−0.732074	+	0.954058i	−0.0375053	+	0.0488779i
$382$		0			0
$383$	10.0023	−	17.3246i	0.511096	−	0.885244i	−0.488821	−	0.872384i	$-0.662573\pi$
$383$	10.0023	−	17.3246i	0.511096	−	0.885244i	0.999917	−	0.0128604i	$-0.00409371\pi$
$384$		0			0
$385$	−8.47491	−	42.9458i	−0.431922	−	2.18872i
$386$		0			0
$387$	26.8510	+	3.53500i	1.36491	+	0.179694i
$388$		0			0
$389$	−0.604023	−	4.58801i	−0.0306252	−	0.232621i	0.969286	−	0.245936i	$-0.0790952\pi$
$389$	−0.604023	−	4.58801i	−0.0306252	−	0.232621i	−0.999911	+	0.0133142i	$0.995762\pi$
$390$		0			0
$391$	−3.81547	−	3.81547i	−0.192957	−	0.192957i
$392$		0			0
$393$	1.20032	−	1.20032i	0.0605480	−	0.0605480i
$394$		0			0
$395$	3.03429	−	0.399471i	0.152671	−	0.0200996i
$396$		0			0
$397$	3.56041	−	27.0440i	0.178692	−	1.35730i	−0.633425	−	0.773804i	$-0.718352\pi$
$397$	3.56041	−	27.0440i	0.178692	−	1.35730i	0.812117	−	0.583495i	$-0.198315\pi$
$398$		0			0
$399$	0.710512	−	0.140212i	0.0355701	−	0.00701940i
$400$		0			0
$401$	1.09372	+	0.631459i	0.0546177	+	0.0315336i	0.527060	−	0.849828i	$-0.323294\pi$
$401$	1.09372	+	0.631459i	0.0546177	+	0.0315336i	−0.472442	+	0.881362i	$0.656628\pi$
$402$		0			0
$403$	−2.37634	−	1.82343i	−0.118374	−	0.0908315i
$404$		0			0
$405$	−10.0091	+	24.1641i	−0.497357	+	1.20072i
$406$		0			0
$407$	−26.3622	+	26.3622i	−1.30673	+	1.30673i
$408$		0			0
$409$	−2.26792	+	8.46400i	−0.112142	+	0.418518i	−0.999057	−	0.0434134i	$-0.986177\pi$
$409$	−2.26792	+	8.46400i	−0.112142	+	0.418518i	0.886916	+	0.461931i	$0.152843\pi$
$410$		0			0
$411$	−1.78003	+	1.36587i	−0.0878026	+	0.0673733i
$412$		0			0
$413$	0.175907	+	0.0870787i	0.00865580	+	0.00428486i
$414$		0			0
$415$	10.1101	−	17.5112i	0.496286	−	0.859592i
$416$		0			0
$417$	−1.73257	−	3.00089i	−0.0848441	−	0.146954i
$418$		0			0
$419$	−0.789499	−	1.90602i	−0.0385696	−	0.0931152i	0.903421	−	0.428755i	$-0.141048\pi$
$419$	−0.789499	−	1.90602i	−0.0385696	−	0.0931152i	−0.941990	+	0.335640i	$0.891048\pi$
$420$		0			0
$421$	8.35055	+	3.45891i	0.406981	+	0.168577i	0.576776	−	0.816902i	$-0.304311\pi$
$421$	8.35055	+	3.45891i	0.406981	+	0.168577i	−0.169795	+	0.985479i	$0.554311\pi$
$422$		0			0
$423$	−7.08214	+	26.4309i	−0.344346	+	1.28512i
$424$		0			0
$425$	4.55850	+	17.0126i	0.221120	+	0.825230i
$426$		0			0
$427$	−16.0156	+	18.2066i	−0.775047	+	0.881079i
$428$		0			0
$429$	−0.829000	+	6.29688i	−0.0400245	+	0.304016i
$430$		0			0
$431$	−2.36261	+	1.36406i	−0.113803	+	0.0657043i	−0.555821	−	0.831302i	$-0.687596\pi$
$431$	−2.36261	+	1.36406i	−0.113803	+	0.0657043i	0.442018	+	0.897006i	$0.354263\pi$
$432$		0			0
$433$			23.1713i			1.11354i	0.830666	+	0.556771i	$0.187960\pi$
$433$			23.1713i			1.11354i	−0.830666	+	0.556771i	$0.812040\pi$
$434$		0			0
$435$	−0.705065	+	0.292047i	−0.0338053	+	0.0140026i
$436$		0			0
$437$	−1.76104	+	0.231845i	−0.0842420	+	0.0110907i
$438$		0			0
$439$	4.54888	+	16.9766i	0.217106	+	0.810251i	0.985415	+	0.170171i	$0.0544320\pi$
$439$	4.54888	+	16.9766i	0.217106	+	0.810251i	−0.768308	+	0.640080i	$0.778901\pi$
$440$		0			0
$441$	16.4885	−	12.5729i	0.785165	−	0.598712i
$442$		0			0
$443$	−5.38327	+	4.13073i	−0.255767	+	0.196257i	−0.728684	−	0.684850i	$-0.759868\pi$
$443$	−5.38327	+	4.13073i	−0.255767	+	0.196257i	0.472917	+	0.881107i	$0.343201\pi$
$444$		0			0
$445$	−26.6333	+	34.7092i	−1.26254	+	1.64537i
$446$		0			0
$447$	−2.40358			−0.113685
$448$		0			0
$449$	18.3637			0.866635			0.433318	−	0.901241i	$-0.357343\pi$
$449$	18.3637			0.866635			0.433318	+	0.901241i	$0.357343\pi$
$450$		0			0
$451$	14.2542	−	18.5764i	0.671204	−	0.874730i
$452$		0			0
$453$	−1.03667	+	0.795468i	−0.0487072	+	0.0373743i
$454$		0			0
$455$	−20.9977	−	42.7420i	−0.984386	−	2.00377i
$456$		0			0
$457$	−6.02250	−	22.4763i	−0.281720	−	1.05140i	−0.951203	−	0.308567i	$-0.900151\pi$
$457$	−6.02250	−	22.4763i	−0.281720	−	1.05140i	0.669482	−	0.742828i	$-0.266516\pi$
$458$		0			0
$459$	4.91534	−	0.647117i	0.229428	−	0.0302048i
$460$		0			0
$461$	−25.1245	+	10.4069i	−1.17016	+	0.484698i	−0.881247	−	0.472657i	$-0.843295\pi$
$461$	−25.1245	+	10.4069i	−1.17016	+	0.484698i	−0.288917	+	0.957354i	$0.593295\pi$
$462$		0			0
$463$			11.5497i			0.536761i	0.963313	+	0.268381i	$0.0864885\pi$
$463$			11.5497i			0.536761i	−0.963313	+	0.268381i	$0.913512\pi$
$464$		0			0
$465$	−0.255633	+	0.147590i	−0.0118547	+	0.00684432i
$466$		0			0
$467$	−1.34169	+	10.1912i	−0.0620861	+	0.471590i	0.931954	+	0.362576i	$0.118103\pi$
$467$	−1.34169	+	10.1912i	−0.0620861	+	0.471590i	−0.994040	+	0.109014i	$0.965231\pi$
$468$		0			0
$469$	−0.652903	−	1.93299i	−0.0301483	−	0.0892574i
$470$		0			0
$471$	0.0522806	+	0.195114i	0.00240896	+	0.00899037i
$472$		0			0
$473$	−12.9645	+	48.3841i	−0.596108	+	2.22470i
$474$		0			0
$475$	5.35647	+	2.21872i	0.245772	+	0.101802i
$476$		0			0
$477$	−8.11473	−	19.5907i	−0.371548	−	0.896997i
$478$		0			0
$479$	8.77291	+	15.1951i	0.400844	+	0.694283i	0.993828	−	0.110932i	$-0.0353834\pi$
$479$	8.77291	+	15.1951i	0.400844	+	0.694283i	−0.592984	+	0.805215i	$0.702050\pi$
$480$		0			0
$481$	−20.2792	+	35.1246i	−0.924653	+	1.60155i
$482$		0			0
$483$	0.540569	−	0.360015i	0.0245967	−	0.0163812i
$484$		0			0
$485$	1.08260	−	0.830710i	0.0491584	−	0.0377206i
$486$		0			0
$487$	3.33054	−	12.4297i	0.150921	−	0.563245i	−0.848499	−	0.529197i	$-0.822493\pi$
$487$	3.33054	−	12.4297i	0.150921	−	0.563245i	0.999420	−	0.0340483i	$-0.0108400\pi$
$488$		0			0
$489$	0.370944	−	0.370944i	0.0167747	−	0.0167747i
$490$		0			0
$491$	−15.2024	+	36.7019i	−0.686076	+	1.65633i	0.0664663	+	0.997789i	$0.478828\pi$
$491$	−15.2024	+	36.7019i	−0.686076	+	1.65633i	−0.752542	+	0.658544i	$0.771172\pi$
$492$		0			0
$493$	−4.40694	−	3.38156i	−0.198479	−	0.152298i
$494$		0			0
$495$	−42.4432	−	24.5046i	−1.90768	−	1.10140i
$496$		0			0
$497$	−28.7834	+	5.68011i	−1.29111	+	0.254788i
$498$		0			0
$499$	−3.23014	+	24.5353i	−0.144601	+	1.09835i	0.753150	+	0.657849i	$0.228533\pi$
$499$	−3.23014	+	24.5353i	−0.144601	+	1.09835i	−0.897751	+	0.440504i	$0.854800\pi$
$500$		0			0
$501$	1.19332	−	0.157104i	0.0533136	−	0.00701887i
$502$		0			0
$503$	13.6066	−	13.6066i	0.606689	−	0.606689i	−0.335390	−	0.942079i	$-0.608868\pi$
$503$	13.6066	−	13.6066i	0.606689	−	0.606689i	0.942079	+	0.335390i	$0.108868\pi$
$504$		0			0
$505$	7.41351	+	7.41351i	0.329897	+	0.329897i
$506$		0			0
$507$	0.571825	+	4.34344i	0.0253956	+	0.192899i
$508$		0			0
$509$	−24.1716	−	3.18225i	−1.07139	−	0.141051i	−0.425861	−	0.904789i	$-0.640029\pi$
$509$	−24.1716	−	3.18225i	−1.07139	−	0.141051i	−0.645527	+	0.763738i	$0.723362\pi$
$510$		0			0
$511$	14.2813	−	12.4862i	0.631769	−	0.552358i
$512$		0			0
$513$	0.816005	−	1.41336i	0.0360275	−	0.0624014i
$514$		0			0
$515$	−16.7574	+	21.8386i	−0.738418	+	0.962324i
$516$		0			0
$517$	−46.7575	−	19.3676i	−2.05639	−	0.851786i
$518$		0			0
$519$	0.209268	+	0.209268i	0.00918583	+	0.00918583i
$520$		0			0
$521$	19.7383	+	5.28886i	0.864750	+	0.231709i	0.663816	−	0.747896i	$-0.268936\pi$
$521$	19.7383	+	5.28886i	0.864750	+	0.231709i	0.200934	+	0.979605i	$0.435602\pi$
$522$		0			0
$523$	21.5776	+	28.1205i	0.943525	+	1.22963i	0.973175	+	0.230065i	$0.0738939\pi$
$523$	21.5776	+	28.1205i	0.943525	+	1.22963i	−0.0296506	+	0.999560i	$0.509439\pi$
$524$		0			0
$525$	−2.11563	+	0.135451i	−0.0923338	+	0.00591158i
$526$		0			0
$527$	−1.86069	−	1.07427i	−0.0810530	−	0.0467960i
$528$		0			0
$529$	18.5391	−	10.7035i	0.806046	−	0.465371i
$530$		0			0
$531$	0.203026	−	0.0840963i	0.00881059	−	0.00364947i
$532$		0			0
$533$	9.74808	−	23.5340i	0.422236	−	1.01937i
$534$		0			0
$535$	−36.7688	−	9.85218i	−1.58966	−	0.425947i
$536$		0			0
$537$	−4.23437	+	1.13459i	−0.182726	+	0.0489614i
$538$		0			0
$539$	19.0749	+	33.2707i	0.821613	+	1.43307i
$540$		0			0
$541$	9.81306	+	1.29191i	0.421896	+	0.0555437i	0.338486	−	0.940972i	$-0.390085\pi$
$541$	9.81306	+	1.29191i	0.421896	+	0.0555437i	0.0834107	+	0.996515i	$0.473419\pi$
$542$		0			0
$543$	1.72043	+	2.97987i	0.0738307	+	0.127878i
$544$		0			0
$545$	41.9171			1.79553
$546$		0			0
$547$	2.30920	+	5.57491i	0.0987344	+	0.238366i	0.965527	−	0.260303i	$-0.0838224\pi$
$547$	2.30920	+	5.57491i	0.0987344	+	0.238366i	−0.866793	+	0.498669i	$0.833822\pi$
$548$		0			0
$549$	3.54356	+	26.9160i	0.151235	+	1.14875i
$550$		0			0
$551$	−1.76625	+	0.473265i	−0.0752447	+	0.0201618i
$552$		0			0
$553$	−2.40659	+	1.18227i	−0.102339	+	0.0502754i
$554$		0			0
$555$	2.43317	+	3.17098i	0.103283	+	0.134600i
$556$		0			0
$557$	−26.1993	−	20.1034i	−1.11010	−	0.851810i	−0.120085	−	0.992764i	$-0.538317\pi$
$557$	−26.1993	−	20.1034i	−1.11010	−	0.851810i	−0.990016	+	0.140953i	$0.954983\pi$
$558$		0			0
$559$			54.4933i			2.30482i
$560$		0			0
$561$			4.55574i			0.192343i
$562$		0			0
$563$	−33.6425	−	25.8148i	−1.41786	−	1.08797i	−0.982196	−	0.187858i	$-0.939846\pi$
$563$	−33.6425	−	25.8148i	−1.41786	−	1.08797i	−0.435668	−	0.900108i	$-0.643488\pi$
$564$		0			0
$565$	0.125922	+	0.164104i	0.00529757	+	0.00690392i
$566$		0			0
$567$	1.53329	−	22.8634i	0.0643922	−	0.960172i
$568$		0			0
$569$	−0.667826	+	0.178943i	−0.0279967	+	0.00750170i	−0.272790	−	0.962074i	$-0.587946\pi$
$569$	−0.667826	+	0.178943i	−0.0279967	+	0.00750170i	0.244794	+	0.969575i	$0.421280\pi$
$570$		0			0
$571$	0.400155	+	3.03948i	0.0167460	+	0.127198i	0.997776	−	0.0666583i	$-0.0212337\pi$
$571$	0.400155	+	3.03948i	0.0167460	+	0.127198i	−0.981030	+	0.193856i	$0.937900\pi$
$572$		0			0
$573$	−1.49521	−	3.60975i	−0.0624633	−	0.150800i
$574$		0			0
$575$	5.19951			0.216834
$576$		0			0
$577$	−23.0936	−	39.9993i	−0.961399	−	1.66519i	−0.718993	−	0.695017i	$-0.755397\pi$
$577$	−23.0936	−	39.9993i	−0.961399	−	1.66519i	−0.242406	−	0.970175i	$-0.577936\pi$
$578$		0			0
$579$	−3.38017	−	0.445008i	−0.140475	−	0.0184939i
$580$		0			0
$581$	−3.48234	+	17.3695i	−0.144472	+	0.720609i
$582$		0			0
$583$	37.8832	−	10.1508i	1.56896	−	0.420402i
$584$		0			0
$585$	−51.4997	−	13.7993i	−2.12925	−	0.570531i
$586$		0			0
$587$	0.997077	−	2.40716i	0.0411538	−	0.0993540i	−0.901966	−	0.431807i	$-0.857876\pi$
$587$	0.997077	−	2.40716i	0.0411538	−	0.0993540i	0.943120	+	0.332453i	$0.107876\pi$
$588$		0			0
$589$	−0.653426	+	0.270658i	−0.0269239	+	0.0111523i
$590$		0			0
$591$	1.51716	−	0.875935i	0.0624078	−	0.0360312i
$592$		0			0
$593$	19.2249	+	11.0995i	0.789473	+	0.455802i	0.839777	−	0.542932i	$-0.182686\pi$
$593$	19.2249	+	11.0995i	0.789473	+	0.455802i	−0.0503042	+	0.998734i	$0.516019\pi$
$594$		0			0
$595$	−18.9346	−	28.4306i	−0.776243	−	1.16554i
$596$		0			0
$597$	0.986948	+	1.28622i	0.0403931	+	0.0526413i
$598$		0			0
$599$	19.3702	+	5.19023i	0.791446	+	0.212067i	0.631825	−	0.775111i	$-0.282306\pi$
$599$	19.3702	+	5.19023i	0.791446	+	0.212067i	0.159621	+	0.987178i	$0.448973\pi$
$600$		0			0
$601$	17.5555	+	17.5555i	0.716102	+	0.716102i	0.967805	−	0.251703i	$-0.0809905\pi$
$601$	17.5555	+	17.5555i	0.716102	+	0.716102i	−0.251703	+	0.967805i	$0.580991\pi$
$602$		0			0
$603$	−2.11041	−	0.874160i	−0.0859425	−	0.0355985i
$604$		0			0
$605$	34.9591	−	45.5596i	1.42129	−	1.85226i
$606$		0			0
$607$	−15.1703	+	26.2757i	−0.615742	+	1.06650i	0.374512	+	0.927222i	$0.377810\pi$
$607$	−15.1703	+	26.2757i	−0.615742	+	1.06650i	−0.990254	+	0.139274i	$0.955523\pi$
$608$		0			0
$609$	0.503355	−	0.440084i	0.0203970	−	0.0178331i
$610$		0			0
$611$	−54.5869	−	7.18651i	−2.20835	−	0.290735i
$612$		0			0
$613$	−0.908361	−	6.89968i	−0.0366883	−	0.278676i	−0.999949	−	0.0101071i	$-0.996783\pi$
$613$	−0.908361	−	6.89968i	−0.0366883	−	0.278676i	0.963261	−	0.268569i	$-0.0865506\pi$
$614$		0			0
$615$	−1.77505	−	1.77505i	−0.0715768	−	0.0715768i
$616$		0			0
$617$	3.00134	−	3.00134i	0.120829	−	0.120829i	−0.644106	−	0.764936i	$-0.722771\pi$
$617$	3.00134	−	3.00134i	0.120829	−	0.120829i	0.764936	+	0.644106i	$0.222771\pi$
$618$		0			0
$619$	−0.367838	+	0.0484268i	−0.0147847	+	0.00194644i	−0.137915	−	0.990444i	$-0.544040\pi$
$619$	−0.367838	+	0.0484268i	−0.0147847	+	0.00194644i	0.123130	+	0.992391i	$0.460707\pi$
$620$		0			0
$621$	0.191038	−	1.45108i	0.00766608	−	0.0582297i
$622$		0			0
$623$	12.3756	−	36.2770i	0.495819	−	1.45341i
$624$		0			0
$625$	24.7914	+	14.3133i	0.991657	+	0.572534i
$626$		0			0
$627$	1.18977	+	0.912942i	0.0475148	+	0.0364594i
$628$		0			0
$629$	−11.1333	+	26.8781i	−0.443912	+	1.07170i
$630$		0			0
$631$	34.5848	−	34.5848i	1.37680	−	1.37680i	0.526830	−	0.849971i	$-0.323381\pi$
$631$	34.5848	−	34.5848i	1.37680	−	1.37680i	0.849971	−	0.526830i	$-0.176619\pi$
$632$		0			0
$633$	−0.0290967	+	0.108591i	−0.00115649	+	0.00431609i
$634$		0			0
$635$	14.8131	−	11.3665i	0.587841	−	0.451067i
$636$		0			0
$637$	29.4121	+	29.5907i	1.16535	+	1.17243i
$638$		0			0
$639$	−16.4236	+	28.4466i	−0.649709	+	1.12533i
$640$		0			0
$641$	3.23073	+	5.59579i	0.127606	+	0.221021i	0.922749	−	0.385402i	$-0.125937\pi$
$641$	3.23073	+	5.59579i	0.127606	+	0.221021i	−0.795142	+	0.606423i	$0.792604\pi$
$642$		0			0
$643$	−2.82466	−	6.81934i	−0.111394	−	0.268929i	0.858345	−	0.513073i	$-0.171493\pi$
$643$	−2.82466	−	6.81934i	−0.111394	−	0.268929i	−0.969739	+	0.244144i	$0.921493\pi$
$644$		0			0
$645$	4.96139	+	2.05508i	0.195355	+	0.0809185i
$646$		0			0
$647$	0.271500	−	1.01325i	0.0106738	−	0.0398351i	−0.960384	−	0.278682i	$-0.910103\pi$
$647$	0.271500	−	1.01325i	0.0106738	−	0.0398351i	0.971057	+	0.238846i	$0.0767693\pi$
$648$		0			0
$649$	0.105196	+	0.392598i	0.00412932	+	0.0154108i
$650$		0			0
$651$	0.170808	−	0.194176i	0.00669449	−	0.00761034i
$652$		0			0
$653$	1.71660	−	13.0389i	0.0671757	−	0.510250i	−0.924470	−	0.381256i	$-0.875492\pi$
$653$	1.71660	−	13.0389i	0.0671757	−	0.510250i	0.991645	−	0.128994i	$-0.0411749\pi$
$654$		0			0
$655$	−22.8252	+	13.1781i	−0.891853	+	0.514912i
$656$		0			0
$657$		−	21.2388i		−	0.828603i
$658$		0			0
$659$	9.08982	−	3.76512i	0.354089	−	0.146668i	−0.198547	−	0.980091i	$-0.563622\pi$
$659$	9.08982	−	3.76512i	0.354089	−	0.146668i	0.552636	+	0.833423i	$0.313622\pi$
$660$		0			0
$661$	26.6893	−	3.51371i	1.03809	−	0.136668i	0.407837	−	0.913055i	$-0.366283\pi$
$661$	26.6893	−	3.51371i	1.03809	−	0.136668i	0.630256	+	0.776387i	$0.282950\pi$
$662$		0			0
$663$	1.28274	+	4.78725i	0.0498175	+	0.185921i
$664$		0			0
$665$	−11.2193	−	0.752401i	−0.435065	−	0.0291769i
$666$		0			0
$667$	−1.30099	+	0.998284i	−0.0503745	+	0.0386537i
$668$		0			0
$669$	−0.600597	+	0.782713i	−0.0232204	+	0.0302614i
$670$		0			0
$671$	−50.2122			−1.93842
$672$		0			0
$673$	−28.1530			−1.08522			−0.542609	−	0.839985i	$-0.682563\pi$
$673$	−28.1530			−1.08522			−0.542609	+	0.839985i	$0.682563\pi$
$674$		0			0
$675$	−2.90824	+	3.79010i	−0.111938	+	0.145881i
$676$		0			0
$677$	20.6879	−	15.8744i	0.795102	−	0.610103i	−0.129264	−	0.991610i	$-0.541261\pi$
$677$	20.6879	−	15.8744i	0.795102	−	0.610103i	0.924366	+	0.381507i	$0.124595\pi$
$678$		0			0
$679$	−0.665706	+	0.993044i	−0.0255475	+	0.0381095i
$680$		0			0
$681$	−0.553543	−	2.06585i	−0.0212118	−	0.0791636i
$682$		0			0
$683$	−3.51722	+	0.463050i	−0.134583	+	0.0177181i	−0.197516	−	0.980300i	$-0.563288\pi$
$683$	−3.51722	+	0.463050i	−0.134583	+	0.0177181i	0.0629339	+	0.998018i	$0.479954\pi$
$684$		0			0
$685$	32.1847	−	13.3313i	1.22971	−	0.509364i
$686$		0			0
$687$			3.06463i			0.116923i
$688$		0			0
$689$	36.9502	−	21.3332i	1.40769	−	0.812731i
$690$		0			0
$691$	0.159432	−	1.21101i	0.00606507	−	0.0460688i	−0.988145	−	0.153525i	$-0.950937\pi$
$691$	0.159432	−	1.21101i	0.00606507	−	0.0460688i	0.994210	+	0.107457i	$0.0342707\pi$
$692$		0			0
$693$	42.0997	+	8.44040i	1.59924	+	0.320624i
$694$		0			0
$695$	13.9248	+	51.9680i	0.528197	+	1.97126i
$696$		0			0
$697$	4.72909	−	17.6492i	0.179127	−	0.668511i
$698$		0			0
$699$	2.43506	+	1.00863i	0.0921023	+	0.0381500i
$700$		0			0
$701$	9.67092	+	23.3477i	0.365266	+	0.881830i	0.994512	+	0.104623i	$0.0333637\pi$
$701$	9.67092	+	23.3477i	0.365266	+	0.881830i	−0.629246	+	0.777206i	$0.716636\pi$
$702$		0			0
$703$	4.78840	+	8.29375i	0.180598	+	0.312805i
$704$		0			0
$705$	−2.71291	+	4.69890i	−0.102174	+	0.176971i
$706$		0			0
$707$	−8.23199	−	4.07506i	−0.309596	−	0.153259i
$708$		0			0
$709$	−1.27025	+	0.974694i	−0.0477051	+	0.0366054i	−0.632339	−	0.774692i	$-0.717905\pi$
$709$	−1.27025	+	0.974694i	−0.0477051	+	0.0366054i	0.584634	+	0.811297i	$0.301238\pi$
$710$		0			0
$711$	−0.776971	+	2.89969i	−0.0291387	+	0.108747i
$712$		0			0
$713$	−0.448503	+	0.448503i	−0.0167966	+	0.0167966i
$714$		0			0
$715$	37.7371	−	91.1054i	1.41129	−	3.40715i
$716$		0			0
$717$	0.774804	+	0.594528i	0.0289356	+	0.0222031i
$718$		0			0
$719$	6.32208	+	3.65005i	0.235774	+	0.136124i	0.613233	−	0.789902i	$-0.289869\pi$
$719$	6.32208	+	3.65005i	0.235774	+	0.136124i	−0.377459	+	0.926026i	$0.623202\pi$
$720$		0			0
$721$	7.78661	−	22.8251i	0.289988	−	0.850050i
$722$		0			0
$723$	0.608211	−	4.61982i	0.0226196	−	0.171813i
$724$		0			0
$725$	5.30686	−	0.698662i	0.197092	−	0.0259476i
$726$		0			0
$727$	15.9338	−	15.9338i	0.590952	−	0.590952i	−0.346937	−	0.937888i	$-0.612778\pi$
$727$	15.9338	−	15.9338i	0.590952	−	0.590952i	0.937888	+	0.346937i	$0.112778\pi$
$728$		0			0
$729$	−17.6625	−	17.6625i	−0.654168	−	0.654168i
$730$		0			0
$731$	5.10202	+	38.7537i	0.188705	+	1.43336i
$732$		0			0
$733$	8.04946	+	1.05973i	0.297314	+	0.0391421i	0.277707	−	0.960666i	$-0.410425\pi$
$733$	8.04946	+	1.05973i	0.297314	+	0.0391421i	0.0196063	+	0.999808i	$0.493759\pi$
$734$		0			0
$735$	3.80331	−	1.56192i	0.140287	−	0.0576122i
$736$		0			0
$737$	2.11246	−	3.65889i	0.0778135	−	0.134777i
$738$		0			0
$739$	24.1438	−	31.4648i	0.888143	−	1.15745i	−0.0985941	−	0.995128i	$-0.531435\pi$
$739$	24.1438	−	31.4648i	0.888143	−	1.15745i	0.986738	−	0.162323i	$-0.0518988\pi$
$740$		0			0
$741$	1.50728	+	0.624338i	0.0553715	+	0.0229356i
$742$		0			0
$743$	33.9729	+	33.9729i	1.24634	+	1.24634i	0.957323	+	0.289020i	$0.0933295\pi$
$743$	33.9729	+	33.9729i	1.24634	+	1.24634i	0.289020	+	0.957323i	$0.406671\pi$
$744$		0			0
$745$	36.0474	+	9.65887i	1.32067	+	0.353874i
$746$		0			0
$747$	12.0741	+	15.7352i	0.441767	+	0.575722i
$748$		0			0
$749$	33.2818	−	2.13084i	1.21609	−	0.0778591i
$750$		0			0
$751$	−9.05161	−	5.22595i	−0.330298	−	0.190698i	0.325675	−	0.945482i	$-0.394408\pi$
$751$	−9.05161	−	5.22595i	−0.330298	−	0.190698i	−0.655973	+	0.754784i	$0.727742\pi$
$752$		0			0
$753$	2.88853	−	1.66769i	0.105264	−	0.0607741i
$754$		0			0
$755$	18.7440	−	7.76403i	0.682165	−	0.282562i
$756$		0			0
$757$	2.64470	−	6.38487i	0.0961232	−	0.232062i	−0.868503	−	0.495684i	$-0.834917\pi$
$757$	2.64470	−	6.38487i	0.0961232	−	0.232062i	0.964626	+	0.263622i	$0.0849173\pi$
$758$		0			0
$759$	1.29909	+	0.348090i	0.0471539	+	0.0126349i
$760$		0			0
$761$	−43.3060	+	11.6038i	−1.56984	+	0.420637i	−0.935762	−	0.352632i	$-0.885287\pi$
$761$	−43.3060	+	11.6038i	−1.56984	+	0.420637i	−0.634078	+	0.773269i	$0.718620\pi$
$762$		0			0
$763$	−34.7929	+	11.7519i	−1.25959	+	0.425448i
$764$		0			0
$765$	−37.9168	−	4.99184i	−1.37088	−	0.180480i
$766$		0			0
$767$	0.221085	+	0.382930i	0.00798291	+	0.0138268i
$768$		0			0
$769$	−24.3333			−0.877480			−0.438740	−	0.898614i	$-0.644575\pi$
$769$	−24.3333			−0.877480			−0.438740	+	0.898614i	$0.644575\pi$
$770$		0			0
$771$	0.181191	+	0.437435i	0.00652545	+	0.0157538i
$772$		0			0
$773$	1.78908	+	13.5894i	0.0643486	+	0.488776i	0.993027	+	0.117890i	$0.0376129\pi$
$773$	1.78908	+	13.5894i	0.0643486	+	0.488776i	−0.928678	+	0.370887i	$0.879054\pi$
$774$		0			0
$775$	1.99980	−	0.535844i	0.0718349	−	0.0192481i
$776$		0			0
$777$	−2.90866	−	1.94987i	−0.104347	−	0.0699513i
$778$		0			0
$779$	−3.66156	−	4.77184i	−0.131189	−	0.170969i
$780$		0			0
$781$	−48.1985	−	36.9840i	−1.72468	−	1.32339i
$782$		0			0
$783$		−	1.50671i		−	0.0538453i
$784$		0			0
$785$		−	3.13629i		−	0.111939i
$786$		0			0
$787$	−43.4167	−	33.3148i	−1.54764	−	1.18754i	−0.908076	−	0.418804i	$-0.862449\pi$
$787$	−43.4167	−	33.3148i	−1.54764	−	1.18754i	−0.639561	−	0.768740i	$-0.720884\pi$
$788$		0			0
$789$	−3.28670	−	4.28331i	−0.117010	−	0.152490i
$790$		0			0
$791$	−0.150529	−	0.100910i	−0.00535219	−	0.00358794i
$792$		0			0
$793$	−52.7639	+	14.1381i	−1.87370	+	0.502057i
$794$		0			0
$795$	−0.548819	−	4.16869i	−0.0194646	−	0.147848i
$796$		0			0
$797$	13.4980	+	32.5870i	0.478122	+	1.15429i	0.960489	+	0.278320i	$0.0897774\pi$
$797$	13.4980	+	32.5870i	0.478122	+	1.15429i	−0.482366	+	0.875970i	$0.660223\pi$
$798$		0			0
$799$	−39.4932			−1.39717
$800$		0			0
$801$	−21.4570	−	37.1645i	−0.758144	−	1.31314i
$802$		0			0
$803$	38.9462	+	5.12737i	1.37438	+	0.180941i
$804$		0			0
$805$	−9.55386	+	3.22699i	−0.336729	+	0.113736i
$806$		0			0
$807$	1.84000	−	0.493026i	0.0647710	−	0.0173553i
$808$		0			0
$809$	23.5700	+	6.31557i	0.828678	+	0.222043i	0.648137	−	0.761524i	$-0.275549\pi$
$809$	23.5700	+	6.31557i	0.828678	+	0.222043i	0.180541	+	0.983567i	$0.442215\pi$
$810$		0			0
$811$	16.1023	−	38.8745i	0.565429	−	1.36507i	−0.339942	−	0.940446i	$-0.610407\pi$
$811$	16.1023	−	38.8745i	0.565429	−	1.36507i	0.905371	−	0.424621i	$-0.139593\pi$
$812$		0			0
$813$	4.97647	−	2.06132i	0.174532	−	0.0722937i
$814$		0			0
$815$	−7.05385	+	4.07254i	−0.247086	+	0.142655i
$816$		0			0
$817$	11.1433	+	6.43357i	0.389854	+	0.225082i
$818$		0			0
$819$	46.6157	−	2.98453i	1.62889	−	0.104288i
$820$		0			0
$821$	0.799478	+	1.04190i	0.0279020	+	0.0363625i	0.807096	−	0.590420i	$-0.201038\pi$
$821$	0.799478	+	1.04190i	0.0279020	+	0.0363625i	−0.779194	+	0.626783i	$0.784371\pi$
$822$		0			0
$823$	−8.10536	−	2.17183i	−0.282535	−	0.0757051i	0.114768	−	0.993392i	$-0.463387\pi$
$823$	−8.10536	−	2.17183i	−0.282535	−	0.0757051i	−0.397304	+	0.917687i	$0.630054\pi$
$824$		0			0
$825$	−3.10415	−	3.10415i	−0.108072	−	0.108072i
$826$		0			0
$827$	9.70756	+	4.02100i	0.337565	+	0.139824i	0.545026	−	0.838419i	$-0.316520\pi$
$827$	9.70756	+	4.02100i	0.337565	+	0.139824i	−0.207461	+	0.978243i	$0.566520\pi$
$828$		0			0
$829$	−9.33231	+	12.1621i	−0.324125	+	0.422407i	−0.926786	−	0.375589i	$-0.877440\pi$
$829$	−9.33231	+	12.1621i	−0.324125	+	0.422407i	0.602661	+	0.797997i	$0.294107\pi$
$830$		0			0
$831$	−0.109747	+	0.190088i	−0.00380709	+	0.00659407i
$832$		0			0
$833$	23.6874	+	18.2901i	0.820718	+	0.633714i
$834$		0			0
$835$	−18.5280	−	2.43926i	−0.641189	−	0.0844141i
$836$		0			0
$837$	−0.0760675	−	0.577790i	−0.00262928	−	0.0199714i
$838$		0			0
$839$	−13.7601	−	13.7601i	−0.475050	−	0.475050i	0.428494	−	0.903545i	$-0.359044\pi$
$839$	−13.7601	−	13.7601i	−0.475050	−	0.475050i	−0.903545	+	0.428494i	$0.859044\pi$
$840$		0			0
$841$	19.3124	−	19.3124i	0.665944	−	0.665944i
$842$		0			0
$843$	−1.82285	+	0.239982i	−0.0627821	+	0.00826542i
$844$		0			0
$845$	8.87841	−	67.4382i	0.305427	−	2.31995i
$846$		0			0
$847$	−16.2444	+	47.6175i	−0.558163	+	1.63616i
$848$		0			0
$849$	−3.62775	−	2.09448i	−0.124504	−	0.0718825i
$850$		0			0
$851$	6.81375	+	5.22837i	0.233572	+	0.179226i
$852$		0			0
$853$	18.5187	−	44.7080i	0.634067	−	1.53077i	−0.200400	−	0.979714i	$-0.564224\pi$
$853$	18.5187	−	44.7080i	0.634067	−	1.53077i	0.834467	−	0.551058i	$-0.185776\pi$
$854$		0			0
$855$	−8.90196	+	8.90196i	−0.304441	+	0.304441i
$856$		0			0
$857$	−6.34114	+	23.6655i	−0.216609	+	0.808397i	0.768985	+	0.639267i	$0.220762\pi$
$857$	−6.34114	+	23.6655i	−0.216609	+	0.808397i	−0.985594	+	0.169129i	$0.945904\pi$
$858$		0			0
$859$	−4.83863	+	3.71281i	−0.165092	+	0.126680i	−0.688003	−	0.725708i	$-0.741513\pi$
$859$	−4.83863	+	3.71281i	−0.165092	+	0.126680i	0.522911	+	0.852387i	$0.324846\pi$
$860$		0			0
$861$	1.97102	+	0.975708i	0.0671721	+	0.0332520i
$862$		0			0
$863$	24.9061	−	43.1386i	0.847814	−	1.46846i	−0.0353411	−	0.999375i	$-0.511252\pi$
$863$	24.9061	−	43.1386i	0.847814	−	1.46846i	0.883155	−	0.469081i	$-0.155415\pi$
$864$		0			0
$865$	−2.29752	−	3.97942i	−0.0781181	−	0.135304i
$866$		0			0
$867$	0.0951183	+	0.229636i	0.00323039	+	0.00779884i
$868$		0			0
$869$	−5.12969	−	2.12479i	−0.174013	−	0.0720785i
$870$		0			0
$871$	1.18960	−	4.43963i	0.0403079	−	0.150431i
$872$		0			0
$873$	0.346433	+	1.29290i	0.0117250	+	0.0437582i
$874$		0			0
$875$	−6.89649	−	1.38265i	−0.233144	−	0.0467420i
$876$		0			0
$877$	−4.30096	+	32.6691i	−0.145233	+	1.10316i	0.751231	+	0.660039i	$0.229460\pi$
$877$	−4.30096	+	32.6691i	−0.145233	+	1.10316i	−0.896464	+	0.443116i	$0.853873\pi$
$878$		0			0
$879$	2.16368	−	1.24920i	0.0729792	−	0.0421345i
$880$		0			0
$881$		−	6.14703i		−	0.207099i	−0.994624	−	0.103549i	$-0.966980\pi$
$881$		−	6.14703i		−	0.207099i	0.994624	−	0.103549i	$-0.0330200\pi$
$882$		0			0
$883$	−36.8658	+	15.2703i	−1.24063	+	0.513887i	−0.903913	−	0.427717i	$-0.859318\pi$
$883$	−36.8658	+	15.2703i	−1.24063	+	0.513887i	−0.336721	+	0.941604i	$0.609318\pi$
$884$		0			0
$885$	0.0432018	−	0.00568763i	0.00145221	−	0.000191188i
$886$		0			0
$887$	7.05302	+	26.3222i	0.236817	+	0.883814i	0.977321	+	0.211762i	$0.0679202\pi$
$887$	7.05302	+	26.3222i	0.236817	+	0.883814i	−0.740504	+	0.672052i	$0.765413\pi$
$888$		0			0
$889$	−9.10879	+	13.5877i	−0.305499	+	0.455717i
$890$		0			0
$891$	37.6453	−	28.8862i	1.26116	−	0.967725i
$892$		0			0
$893$	−7.91419	+	10.3140i	−0.264838	+	0.345144i
$894$		0			0
$895$	68.0639			2.27513
$896$		0			0
$897$	1.46312			0.0488520
$898$		0			0
$899$	−0.397497	+	0.518029i	−0.0132573	+	0.0172772i
$900$		0			0
$901$	24.2803	−	18.6310i	0.808895	−	0.620687i
$902$		0			0
$903$	−4.69432	−	0.314816i	−0.156217	−	0.0104764i
$904$		0			0
$905$	−13.8272	−	51.6039i	−0.459633	−	1.71537i
$906$		0			0
$907$	−19.5273	+	2.57082i	−0.648394	+	0.0853627i	−0.447548	−	0.894260i	$-0.647703\pi$
$907$	−19.5273	+	2.57082i	−0.648394	+	0.0853627i	−0.200847	+	0.979623i	$0.564369\pi$
$908$		0			0
$909$	−9.50112	+	3.93549i	−0.315132	+	0.130532i
$910$		0			0
$911$		−	15.2338i		−	0.504719i	−0.967634	−	0.252360i	$-0.918793\pi$
$911$		−	15.2338i		−	0.504719i	0.967634	−	0.252360i	$-0.0812066\pi$
$912$		0			0
$913$	−31.7691	+	18.3419i	−1.05140	+	0.607028i
$914$		0			0
$915$	−0.702645	+	5.33712i	−0.0232287	+	0.176440i
$916$		0			0
$917$	15.2512	−	17.3377i	0.503639	−	0.572541i
$918$		0			0
$919$	13.9437	+	52.0387i	0.459961	+	1.71660i	0.673079	+	0.739571i	$0.264971\pi$
$919$	13.9437	+	52.0387i	0.459961	+	1.71660i	−0.213118	+	0.977026i	$0.568362\pi$
$920$		0			0
$921$	1.02816	−	3.83716i	0.0338792	−	0.126439i
$922$		0			0
$923$	−61.0613	−	25.2924i	−2.00986	−	0.832510i
$924$		0			0
$925$	−10.7281	−	25.8998i	−0.352737	−	0.851581i
$926$		0			0
$927$	−13.5005	−	23.3835i	−0.443414	−	0.768015i
$928$		0			0
$929$	−11.2640	+	19.5098i	−0.369559	+	0.640095i	−0.989497	−	0.144556i	$-0.953824\pi$
$929$	−11.2640	+	19.5098i	−0.369559	+	0.640095i	0.619938	+	0.784651i	$0.287158\pi$
$930$		0			0
$931$	9.52342	−	2.52093i	0.312117	−	0.0826201i
$932$		0			0
$933$	0.456288	−	0.350122i	0.0149382	−	0.0114625i
$934$		0			0
$935$	18.3074	−	68.3242i	0.598716	−	2.23444i
$936$		0			0
$937$	−10.5179	+	10.5179i	−0.343606	+	0.343606i	−0.857721	−	0.514115i	$-0.828120\pi$
$937$	−10.5179	+	10.5179i	−0.343606	+	0.343606i	0.514115	+	0.857721i	$0.328120\pi$
$938$		0			0
$939$	−2.07485	+	5.00913i	−0.0677102	+	0.163467i
$940$		0			0
$941$	23.6476	+	18.1455i	0.770890	+	0.591525i	0.917531	−	0.397665i	$-0.130179\pi$
$941$	23.6476	+	18.1455i	0.770890	+	0.591525i	−0.146640	+	0.989190i	$0.546846\pi$
$942$		0			0
$943$	−4.67141	−	2.69704i	−0.152122	−	0.0878278i
$944$		0			0
$945$	2.99151	−	8.76909i	0.0973138	−	0.285258i
$946$		0			0
$947$	6.68210	−	50.7556i	0.217139	−	1.64934i	−0.441781	−	0.897123i	$-0.645653\pi$
$947$	6.68210	−	50.7556i	0.217139	−	1.64934i	0.658920	−	0.752213i	$-0.271013\pi$
$948$		0			0
$949$	42.3691	−	5.57800i	1.37536	−	0.181070i
$950$		0			0
$951$	4.51493	−	4.51493i	0.146406	−	0.146406i
$952$		0			0
$953$	−6.86940	−	6.86940i	−0.222522	−	0.222522i	0.587038	−	0.809560i	$-0.300294\pi$
$953$	−6.86940	−	6.86940i	−0.222522	−	0.222522i	−0.809560	+	0.587038i	$0.800294\pi$
$954$		0			0
$955$	7.91831	+	60.1455i	0.256230	+	1.94626i
$956$		0			0
$957$	1.37268	+	0.180717i	0.0443726	+	0.00584176i
$958$		0			0
$959$	−22.9770	+	20.0889i	−0.741967	+	0.648704i
$960$		0			0
$961$	15.3737	−	26.6281i	0.495926	−	0.858970i
$962$		0			0
$963$	22.7302	−	29.6226i	0.732471	−	0.954575i
$964$		0			0
$965$	48.9055	+	20.2573i	1.57432	+	0.652106i
$966$		0			0
$967$	−10.0451	−	10.0451i	−0.323029	−	0.323029i	0.526899	−	0.849928i	$-0.323355\pi$
$967$	−10.0451	−	10.0451i	−0.323029	−	0.323029i	−0.849928	+	0.526899i	$0.823355\pi$
$968$		0			0
$969$	1.13038	+	0.302885i	0.0363131	+	0.00973007i
$970$		0			0
$971$	−3.80805	−	4.96274i	−0.122206	−	0.159262i	0.728244	−	0.685318i	$-0.240337\pi$
$971$	−3.80805	−	4.96274i	−0.122206	−	0.159262i	−0.850450	+	0.526056i	$0.823670\pi$
$972$		0			0
$973$	−26.1280	−	39.2316i	−0.837624	−	1.25771i
$974$		0			0
$975$	−4.13592	−	2.38787i	−0.132455	−	0.0764731i
$976$		0			0
$977$	−42.1874	+	24.3569i	−1.34969	+	0.779246i	−0.988206	−	0.153131i	$-0.951064\pi$
$977$	−42.1874	+	24.3569i	−1.34969	+	0.779246i	−0.361488	+	0.932377i	$0.617731\pi$
$978$		0			0
$979$	73.3299	−	30.3743i	2.34363	−	0.970765i
$980$		0			0
$981$	−15.7344	+	37.9863i	−0.502362	+	1.21281i
$982$		0			0
$983$	49.5761	+	13.2839i	1.58123	+	0.423690i	0.939307	−	0.343078i	$-0.111470\pi$
$983$	49.5761	+	13.2839i	1.58123	+	0.423690i	0.641925	+	0.766768i	$0.278136\pi$
$984$		0			0
$985$	−26.2735	+	7.03997i	−0.837144	+	0.224312i
$986$		0			0
$987$	0.934439	−	4.66087i	0.0297435	−	0.148357i
$988$		0			0
$989$	11.4406	+	1.50619i	0.363791	+	0.0478940i
$990$		0			0
$991$	26.5712	+	46.0226i	0.844062	+	1.46196i	0.886434	+	0.462856i	$0.153175\pi$
$991$	26.5712	+	46.0226i	0.844062	+	1.46196i	−0.0423722	+	0.999102i	$0.513492\pi$
$992$		0			0
$993$	1.16758			0.0370522
$994$		0			0
$995$	−9.63294	−	23.2560i	−0.305385	−	0.737264i
$996$		0			0
$997$	4.40157	+	33.4332i	0.139399	+	1.05884i	0.907958	+	0.419062i	$0.137641\pi$
$997$	4.40157	+	33.4332i	0.139399	+	1.05884i	−0.768559	+	0.639779i	$0.779026\pi$
$998$		0			0
$999$	−7.62228	+	2.04238i	−0.241158	+	0.0646182i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.bh.a.625.15		240
4.3	odd	2		224.2.bd.a.37.15	✓	240
7.4	even	3	inner	896.2.bh.a.753.16		240
28.11	odd	6		224.2.bd.a.165.5	yes	240
32.13	even	8	inner	896.2.bh.a.401.16		240
32.19	odd	8		224.2.bd.a.205.5	yes	240
224.109	even	24	inner	896.2.bh.a.529.15		240
224.179	odd	24		224.2.bd.a.109.15	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.37.15	✓	240	4.3	odd	2
224.2.bd.a.109.15	yes	240	224.179	odd	24
224.2.bd.a.165.5	yes	240	28.11	odd	6
224.2.bd.a.205.5	yes	240	32.19	odd	8
896.2.bh.a.401.16		240	32.13	even	8	inner
896.2.bh.a.529.15		240	224.109	even	24	inner
896.2.bh.a.625.15		240	1.1	even	1	trivial
896.2.bh.a.753.16		240	7.4	even	3	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:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.bh (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.118403 + 0.154306i) q^{3} +(2.39583 - 1.83839i) q^{5} +(-1.47323 + 2.19764i) q^{7} +(0.766666 + 2.86124i) q^{9} +O(q^{10})\)	\(q+(-0.118403 + 0.154306i) q^{3} +(2.39583 - 1.83839i) q^{5} +(-1.47323 + 2.19764i) q^{7} +(0.766666 + 2.86124i) q^{9} +(-5.43183 + 0.715114i) q^{11} +(-5.50652 + 2.28087i) q^{13} +0.587363i q^{15} +(-3.70249 + 2.13763i) q^{17} +(-0.183696 + 1.39531i) q^{19} +(-0.164674 - 0.487536i) q^{21} +(0.326660 + 1.21911i) q^{23} +(1.06625 - 3.97929i) q^{25} +(-1.07136 - 0.443773i) q^{27} +(0.497218 + 1.20039i) q^{29} +(0.251275 + 0.435222i) q^{31} +(0.532801 - 0.922838i) q^{33} +(0.510497 + 7.97352i) q^{35} +(5.39866 - 4.14254i) q^{37} +(0.300037 - 1.11975i) q^{39} +(-3.02206 + 3.02206i) q^{41} +(3.49881 - 8.44689i) q^{43} +(7.09686 + 5.44561i) q^{45} +(7.99998 + 4.61879i) q^{47} +(-2.65920 - 6.47523i) q^{49} +(0.108537 - 0.824421i) q^{51} +(-7.09730 + 0.934377i) q^{53} +(-11.6991 + 11.6991i) q^{55} +(-0.193554 - 0.193554i) q^{57} +(-0.00968333 - 0.0735522i) q^{59} +(9.08657 + 1.19627i) q^{61} +(-7.41743 - 2.53040i) q^{63} +(-8.99956 + 15.5877i) q^{65} +(-0.469449 + 0.611798i) q^{67} +(-0.226794 - 0.0939414i) q^{69} +(7.84105 + 7.84105i) q^{71} +(-6.92569 - 1.85573i) q^{73} +(0.487783 + 0.635691i) q^{75} +(6.43076 - 12.9907i) q^{77} +(0.877666 + 0.506720i) q^{79} +(-7.50061 + 4.33048i) q^{81} +(6.18602 - 2.56233i) q^{83} +(-4.94075 + 11.9280i) q^{85} +(-0.244100 - 0.0654064i) q^{87} +(-13.9937 + 3.74960i) q^{89} +(3.09982 - 15.4616i) q^{91} +(-0.0969094 - 0.0127584i) q^{93} +(2.12501 + 3.68062i) q^{95} +0.451869 q^{97} +(-6.21051 - 14.9935i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9}+O(q^{10}) \) 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9	\( 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9} + 4 q^{11} - 16 q^{13} + 4 q^{19} - 8 q^{21} + 12 q^{23} - 4 q^{25} + 16 q^{27} - 16 q^{29} + 56 q^{31} - 8 q^{33} + 32 q^{35} - 4 q^{37} + 4 q^{39} - 16 q^{41} + 8 q^{45} + 28 q^{51} - 20 q^{53} + 16 q^{55} - 16 q^{57} + 36 q^{59} - 4 q^{61} + 16 q^{63} - 8 q^{65} - 36 q^{67} - 16 q^{69} - 48 q^{71} - 4 q^{73} - 16 q^{75} - 8 q^{77} + 96 q^{83} - 56 q^{85} + 4 q^{87} - 4 q^{89} + 56 q^{91} + 20 q^{93} + 8 q^{95} - 32 q^{97} - 8 q^{99}+O(q^{100}) \) 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9 + 4 * q^11 - 16 * q^13 + 4 * q^19 - 8 * q^21 + 12 * q^23 - 4 * q^25 + 16 * q^27 - 16 * q^29 + 56 * q^31 - 8 * q^33 + 32 * q^35 - 4 * q^37 + 4 * q^39 - 16 * q^41 + 8 * q^45 + 28 * q^51 - 20 * q^53 + 16 * q^55 - 16 * q^57 + 36 * q^59 - 4 * q^61 + 16 * q^63 - 8 * q^65 - 36 * q^67 - 16 * q^69 - 48 * q^71 - 4 * q^73 - 16 * q^75 - 8 * q^77 + 96 * q^83 - 56 * q^85 + 4 * q^87 - 4 * q^89 + 56 * q^91 + 20 * q^93 + 8 * q^95 - 32 * q^97 - 8 * q^99

Introduction

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