LMFDB - Embedded newform 585.2.bu.b.316.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [585,2,Mod(316,585)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(585, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("585.316"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bu (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-6,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.56070144.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 $ x^8 - 4x^7 + 16x^6 - 34x^5 + 63x^4 - 74x^3 + 70x^2 - 38*x + 13
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			316.1
Root			$0.500000 - 1.56488i$ of defining polynomial
Character	$\chi$	$=$	585.316
Dual form			585.2.bu.b.361.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.10523 - 1.21545i) q^{2} +(1.95466 + 3.38556i) q^{4} +1.00000i q^{5} +(1.12682 - 0.650571i) q^{7} -4.64136i q^{8} +(1.21545 - 2.10523i) q^{10} +(2.75159 + 1.58863i) q^{11} +(-3.40216 + 1.19386i) q^{13} -3.16296 q^{14} +(-1.73205 + 3.00000i) q^{16} +(-0.325680 - 0.564094i) q^{17} +(2.17511 - 1.25580i) q^{19} +(-3.38556 + 1.95466i) q^{20} +(-3.86182 - 6.68886i) q^{22} +(-0.889774 + 1.54113i) q^{23} -1.00000 q^{25} +(8.61341 + 1.62182i) q^{26} +(4.40510 + 2.54329i) q^{28} +(-4.18965 + 7.25669i) q^{29} +8.50318i q^{31} +(-0.746354 + 0.430908i) q^{32} +1.58340i q^{34} +(0.650571 + 1.12682i) q^{35} +(1.21046 + 0.698857i) q^{37} -6.10547 q^{38} +4.64136 q^{40} +(10.0658 + 5.81147i) q^{41} +(1.63692 + 2.83522i) q^{43} +12.4209i q^{44} +(3.74635 - 2.16296i) q^{46} -12.2105i q^{47} +(-2.65351 + 4.59602i) q^{49} +(2.10523 + 1.21545i) q^{50} +(-10.6919 - 9.18465i) q^{52} +6.35452 q^{53} +(-1.58863 + 2.75159i) q^{55} +(-3.01954 - 5.22999i) q^{56} +(17.6403 - 10.1847i) q^{58} +(5.18377 - 2.99285i) q^{59} +(-6.49373 - 11.2475i) q^{61} +(10.3352 - 17.9011i) q^{62} +9.02320 q^{64} +(-1.19386 - 3.40216i) q^{65} +(11.3922 + 6.57727i) q^{67} +(1.27318 - 2.20522i) q^{68} -3.16296i q^{70} +(0.949658 - 0.548286i) q^{71} +12.2293i q^{73} +(-1.69886 - 2.94251i) q^{74} +(8.50318 + 4.90931i) q^{76} +4.13407 q^{77} -1.33022 q^{79} +(-3.00000 - 1.73205i) q^{80} +(-14.1272 - 24.4690i) q^{82} +14.2668i q^{83} +(0.564094 - 0.325680i) q^{85} -7.95839i q^{86} +(7.37341 - 12.7711i) q^{88} +(8.31719 + 4.80193i) q^{89} +(-3.05694 + 3.55862i) q^{91} -6.95681 q^{92} +(-14.8412 + 25.7058i) q^{94} +(1.25580 + 2.17511i) q^{95} +(6.88214 - 3.97341i) q^{97} +(11.1725 - 6.45045i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{2} + 4 q^{4} + 6 q^{7} + 2 q^{10} - 12 q^{11} + 6 q^{13} + 4 q^{14} + 2 q^{17} + 12 q^{19} - 4 q^{23} - 8 q^{25} + 4 q^{26} - 12 q^{28} + 6 q^{29} - 12 q^{32} + 6 q^{35} - 12 q^{37} + 16 q^{38}+ \cdots + 12 q^{98}+O(q^{100}) $ 8 * q - 6 * q^2 + 4 * q^4 + 6 * q^7 + 2 * q^10 - 12 * q^11 + 6 * q^13 + 4 * q^14 + 2 * q^17 + 12 * q^19 - 4 * q^23 - 8 * q^25 + 4 * q^26 - 12 * q^28 + 6 * q^29 - 12 * q^32 + 6 * q^35 - 12 * q^37 + 16 * q^38 + 30 * q^41 + 6 * q^43 + 36 * q^46 - 8 * q^49 + 6 * q^50 - 20 * q^52 + 32 * q^53 - 8 * q^55 - 4 * q^56 + 12 * q^58 + 30 * q^59 + 30 * q^62 + 32 * q^64 + 6 * q^65 + 30 * q^67 - 16 * q^68 - 18 * q^71 - 12 * q^74 + 8 * q^77 + 56 * q^79 - 24 * q^80 - 24 * q^82 + 6 * q^85 + 8 * q^88 + 18 * q^89 - 16 * q^91 - 40 * q^92 - 16 * q^94 - 6 * q^97 + 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−2.10523	−	1.21545i	−1.48862	−	0.859456i	−0.488705	−	0.872449i	$-0.662531\pi$
$2$	−2.10523	−	1.21545i	−1.48862	−	0.859456i	−0.999916	+	0.0129932i	$0.995864\pi$
$3$		0			0
$3$		0			0
$4$	1.95466	+	3.38556i	0.977328	+	1.69278i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$	1.12682	−	0.650571i	0.425899	−	0.245893i	−0.271699	−	0.962382i	$-0.587586\pi$
$7$	1.12682	−	0.650571i	0.425899	−	0.245893i	0.697598	+	0.716489i	$0.254252\pi$
$8$		−	4.64136i		−	1.64097i
$9$		0			0
$10$	1.21545	−	2.10523i	0.384360	−	0.665732i
$11$	2.75159	+	1.58863i	0.829636	+	0.478990i	0.853728	−	0.520719i	$-0.174336\pi$
$11$	2.75159	+	1.58863i	0.829636	+	0.478990i	−0.0240923	+	0.999710i	$0.507670\pi$
$12$		0			0
$13$	−3.40216	+	1.19386i	−0.943590	+	0.331117i
$13$	−3.40216	+	1.19386i	−0.943590	+	0.331117i
$14$	−3.16296			−0.845336
$15$		0			0
$16$	−1.73205	+	3.00000i	−0.433013	+	0.750000i
$17$	−0.325680	−	0.564094i	−0.0789890	−	0.136813i	0.823825	−	0.566844i	$-0.191836\pi$
$17$	−0.325680	−	0.564094i	−0.0789890	−	0.136813i	−0.902814	+	0.430031i	$0.858503\pi$
$18$		0			0
$19$	2.17511	−	1.25580i	0.499004	−	0.288100i	−0.229298	−	0.973356i	$-0.573643\pi$
$19$	2.17511	−	1.25580i	0.499004	−	0.288100i	0.728302	+	0.685256i	$0.240310\pi$
$20$	−3.38556	+	1.95466i	−0.757035	+	0.437074i
$21$		0			0
$22$	−3.86182	−	6.68886i	−0.823342	−	1.42607i
$23$	−0.889774	+	1.54113i	−0.185531	+	0.321349i	−0.943755	−	0.330645i	$-0.892734\pi$
$23$	−0.889774	+	1.54113i	−0.185531	+	0.321349i	0.758225	+	0.651994i	$0.226067\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	8.61341	+	1.62182i	1.68923	+	0.318066i
$27$		0			0
$28$	4.40510	+	2.54329i	0.832486	+	0.480636i
$29$	−4.18965	+	7.25669i	−0.777998	+	1.34753i	0.155095	+	0.987899i	$0.450431\pi$
$29$	−4.18965	+	7.25669i	−0.777998	+	1.34753i	−0.933094	+	0.359633i	$0.882902\pi$
$30$		0			0
$31$			8.50318i			1.52722i	0.645680	+	0.763608i	$0.276574\pi$
$31$			8.50318i			1.52722i	−0.645680	+	0.763608i	$0.723426\pi$
$32$	−0.746354	+	0.430908i	−0.131938	+	0.0761745i
$33$		0			0
$34$			1.58340i			0.271550i
$35$	0.650571	+	1.12682i	0.109967	+	0.190468i
$36$		0			0
$37$	1.21046	+	0.698857i	0.198998	+	0.114891i	0.596188	−	0.802845i	$-0.296681\pi$
$37$	1.21046	+	0.698857i	0.198998	+	0.114891i	−0.397190	+	0.917736i	$0.630015\pi$
$38$	−6.10547			−0.990437
$39$		0			0
$40$	4.64136			0.733864
$41$	10.0658	+	5.81147i	1.57201	+	0.907600i	0.995923	+	0.0902108i	$0.0287541\pi$
$41$	10.0658	+	5.81147i	1.57201	+	0.907600i	0.576086	+	0.817389i	$0.304579\pi$
$42$		0			0
$43$	1.63692	+	2.83522i	0.249627	+	0.432367i	0.963422	−	0.267987i	$-0.0863585\pi$
$43$	1.63692	+	2.83522i	0.249627	+	0.432367i	−0.713795	+	0.700355i	$0.753025\pi$
$44$			12.4209i			1.87252i
$45$		0			0
$46$	3.74635	−	2.16296i	0.552370	−	0.318911i
$47$		−	12.2105i		−	1.78108i	−0.454907	−	0.890539i	$-0.650327\pi$
$47$		−	12.2105i		−	1.78108i	0.454907	−	0.890539i	$-0.349673\pi$
$48$		0			0
$49$	−2.65351	+	4.59602i	−0.379073	+	0.656574i
$50$	2.10523	+	1.21545i	0.297724	+	0.171891i
$51$		0			0
$52$	−10.6919	−	9.18465i	−1.48271	−	1.27368i
$53$	6.35452			0.872861			0.436431	−	0.899738i	$-0.356242\pi$
$53$	6.35452			0.872861			0.436431	+	0.899738i	$0.356242\pi$
$54$		0			0
$55$	−1.58863	+	2.75159i	−0.214211	+	0.371024i
$56$	−3.01954	−	5.22999i	−0.403503	−	0.698887i
$57$		0			0
$58$	17.6403	−	10.1847i	2.31629	−	1.33731i
$59$	5.18377	−	2.99285i	0.674869	−	0.389636i	−0.123050	−	0.992400i	$-0.539268\pi$
$59$	5.18377	−	2.99285i	0.674869	−	0.389636i	0.797919	+	0.602765i	$0.205934\pi$
$60$		0			0
$61$	−6.49373	−	11.2475i	−0.831437	−	1.44009i	−0.896898	−	0.442237i	$-0.854185\pi$
$61$	−6.49373	−	11.2475i	−0.831437	−	1.44009i	0.0654609	−	0.997855i	$-0.479148\pi$
$62$	10.3352	−	17.9011i	1.31257	−	2.27345i
$63$		0			0
$64$	9.02320			1.12790
$65$	−1.19386	−	3.40216i	−0.148080	−	0.421986i
$66$		0			0
$67$	11.3922	+	6.57727i	1.39177	+	0.803541i	0.993512	−	0.113730i	$-0.0362799\pi$
$67$	11.3922	+	6.57727i	1.39177	+	0.803541i	0.398263	+	0.917271i	$0.369613\pi$
$68$	1.27318	−	2.20522i	0.154396	−	0.267422i
$69$		0			0
$70$		−	3.16296i		−	0.378046i
$71$	0.949658	−	0.548286i	0.112704	−	0.0650695i	−0.442589	−	0.896725i	$-0.645940\pi$
$71$	0.949658	−	0.548286i	0.112704	−	0.0650695i	0.555292	+	0.831655i	$0.312606\pi$
$72$		0			0
$73$			12.2293i			1.43134i	0.698440	+	0.715668i	$0.253878\pi$
$73$			12.2293i			1.43134i	−0.698440	+	0.715668i	$0.746122\pi$
$74$	−1.69886	−	2.94251i	−0.197488	−	0.342059i
$75$		0			0
$76$	8.50318	+	4.90931i	0.975382	+	0.563137i
$77$	4.13407			0.471121
$78$		0			0
$79$	−1.33022			−0.149662			−0.0748310	−	0.997196i	$-0.523842\pi$
$79$	−1.33022			−0.149662			−0.0748310	+	0.997196i	$0.523842\pi$
$80$	−3.00000	−	1.73205i	−0.335410	−	0.193649i
$81$		0			0
$82$	−14.1272	−	24.4690i	−1.56008	−	2.70214i
$83$			14.2668i			1.56599i	0.622028	+	0.782995i	$0.286309\pi$
$83$			14.2668i			1.56599i	−0.622028	+	0.782995i	$0.713691\pi$
$84$		0			0
$85$	0.564094	−	0.325680i	0.0611846	−	0.0353249i
$86$		−	7.95839i		−	0.858175i
$87$		0			0
$88$	7.37341	−	12.7711i	0.786009	−	1.36141i
$89$	8.31719	+	4.80193i	0.881620	+	0.509004i	0.871192	−	0.490942i	$-0.163347\pi$
$89$	8.31719	+	4.80193i	0.881620	+	0.509004i	0.0104280	+	0.999946i	$0.496681\pi$
$90$		0			0
$91$	−3.05694	+	3.55862i	−0.320455	+	0.373044i
$92$	−6.95681			−0.725298
$93$		0			0
$94$	−14.8412	+	25.7058i	−1.53076	+	2.65135i
$95$	1.25580	+	2.17511i	0.128842	+	0.223161i
$96$		0			0
$97$	6.88214	−	3.97341i	0.698776	−	0.403438i	−0.108116	−	0.994138i	$-0.534482\pi$
$97$	6.88214	−	3.97341i	0.698776	−	0.403438i	0.806891	+	0.590700i	$0.201148\pi$
$98$	11.1725	−	6.45045i	1.12859	−	0.651594i
$99$		0			0
$100$	−1.95466	−	3.38556i	−0.195466	−	0.338556i
$101$	1.06273	−	1.84070i	0.105745	−	0.183157i	−0.808297	−	0.588775i	$-0.799610\pi$
$101$	1.06273	−	1.84070i	0.105745	−	0.183157i	0.914043	+	0.405618i	$0.132944\pi$
$102$		0			0
$103$	0.985697			0.0971236			0.0485618	−	0.998820i	$-0.484536\pi$
$103$	0.985697			0.0971236			0.0485618	+	0.998820i	$0.484536\pi$
$104$	5.54113	+	15.7907i	0.543353	+	1.54840i
$105$		0			0
$106$	−13.3777	−	7.72363i	−1.29936	−	0.750185i
$107$	−6.16796	+	10.6832i	−0.596279	+	1.03279i	0.397086	+	0.917781i	$0.370021\pi$
$107$	−6.16796	+	10.6832i	−0.596279	+	1.03279i	−0.993365	+	0.115004i	$0.963312\pi$
$108$		0			0
$109$			0.870235i			0.0833534i	0.999131	+	0.0416767i	$0.0132700\pi$
$109$			0.870235i			0.0833534i	−0.999131	+	0.0416767i	$0.986730\pi$
$110$	6.68886	−	3.86182i	0.637758	−	0.368210i
$111$		0			0
$112$			4.50729i			0.425899i
$113$	−7.55068	−	13.0782i	−0.710308	−	1.23029i	−0.964742	−	0.263199i	$-0.915222\pi$
$113$	−7.55068	−	13.0782i	−0.710308	−	1.23029i	0.254434	−	0.967090i	$-0.418111\pi$
$114$		0			0
$115$	−1.54113	−	0.889774i	−0.143711	−	0.0829719i
$116$	−32.7573			−3.04144
$117$		0			0
$118$	−14.5507			−1.33950
$119$	−0.733967	−	0.423756i	−0.0672827	−	0.0388457i
$120$		0			0
$121$	−0.452503	−	0.783758i	−0.0411366	−	0.0712507i
$122$			31.5713i			2.85833i
$123$		0			0
$124$	−28.7881	+	16.6208i	−2.58524	+	1.49259i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$	−1.44815	+	2.50828i	−0.128503	+	0.222573i	−0.923097	−	0.384568i	$-0.874350\pi$
$127$	−1.44815	+	2.50828i	−0.128503	+	0.222573i	0.794594	+	0.607141i	$0.207684\pi$
$128$	−17.5032	−	10.1055i	−1.54708	−	0.893205i
$129$		0			0
$130$	−1.62182	+	8.61341i	−0.142243	+	0.755446i
$131$	−15.7570			−1.37670			−0.688349	−	0.725380i	$-0.741664\pi$
$131$	−15.7570			−1.37670			−0.688349	+	0.725380i	$0.741664\pi$
$132$		0			0
$133$	1.63397	−	2.83013i	0.141684	−	0.245403i
$134$	−15.9887	−	27.6933i	−1.38122	−	2.39234i
$135$		0			0
$136$	−2.61817	+	1.51160i	−0.224506	+	0.129619i
$137$	−0.638901	+	0.368870i	−0.0545850	+	0.0315147i	−0.527044	−	0.849838i	$-0.676700\pi$
$137$	−0.638901	+	0.368870i	−0.0545850	+	0.0315147i	0.472459	+	0.881353i	$0.343366\pi$
$138$		0			0
$139$	9.87341	+	17.1013i	0.837452	+	1.45051i	0.892018	+	0.451999i	$0.149289\pi$
$139$	9.87341	+	17.1013i	0.837452	+	1.45051i	−0.0545661	+	0.998510i	$0.517378\pi$
$140$	−2.54329	+	4.40510i	−0.214947	+	0.372299i
$141$		0			0
$142$	−2.66566			−0.223697
$143$	−11.2580	−	2.11977i	−0.941437	−	0.177264i
$144$		0			0
$145$	−7.25669	−	4.18965i	−0.602635	−	0.347931i
$146$	14.8642	−	25.7456i	1.23017	−	2.13072i
$147$		0			0
$148$			5.46410i			0.449146i
$149$	2.74140	−	1.58275i	0.224584	−	0.129664i	−0.383487	−	0.923546i	$-0.625277\pi$
$149$	2.74140	−	1.58275i	0.224584	−	0.129664i	0.608071	+	0.793883i	$0.291944\pi$
$150$		0			0
$151$		−	0.168843i		−	0.0137402i	−0.999976	−	0.00687011i	$-0.997813\pi$
$151$		−	0.168843i		−	0.0137402i	0.999976	−	0.00687011i	$-0.00218684\pi$
$152$	−5.82862	−	10.0955i	−0.472764	−	0.818851i
$153$		0			0
$154$	−8.70316	−	5.02477i	−0.701321	−	0.404908i
$155$	−8.50318			−0.682992
$156$		0			0
$157$	13.5512			1.08150			0.540750	−	0.841183i	$-0.318141\pi$
$157$	13.5512			1.08150			0.540750	+	0.841183i	$0.318141\pi$
$158$	2.80043	+	1.61683i	0.222790	+	0.128628i
$159$		0			0
$160$	−0.430908	−	0.746354i	−0.0340663	−	0.0590045i
$161$			2.31545i			0.182483i
$162$		0			0
$163$	−13.1689	+	7.60307i	−1.03147	+	0.595519i	−0.917405	−	0.397955i	$-0.869720\pi$
$163$	−13.1689	+	7.60307i	−1.03147	+	0.595519i	−0.114064	+	0.993473i	$0.536387\pi$
$164$			45.4377i			3.54809i
$165$		0			0
$166$	17.3407	−	30.0350i	1.34590	−	2.33117i
$167$	−6.47429	−	3.73793i	−0.500996	−	0.289250i	0.228129	−	0.973631i	$-0.426739\pi$
$167$	−6.47429	−	3.73793i	−0.500996	−	0.289250i	−0.729125	+	0.684381i	$0.760073\pi$
$168$		0			0
$169$	10.1494	−	8.12340i	0.780723	−	0.624877i
$170$	−1.58340			−0.121441
$171$		0			0
$172$	−6.39922	+	11.0838i	−0.487936	+	0.845130i
$173$	4.64701	+	8.04886i	0.353306	+	0.611943i	0.986826	−	0.161782i	$-0.0517242\pi$
$173$	4.64701	+	8.04886i	0.353306	+	0.611943i	−0.633521	+	0.773726i	$0.718391\pi$
$174$		0			0
$175$	−1.12682	+	0.650571i	−0.0851798	+	0.0491786i
$176$	−9.53179	+	5.50318i	−0.718485	+	0.414818i
$177$		0			0
$178$	−11.6731	−	20.2183i	−0.874932	−	1.51543i
$179$	−5.42376	+	9.39422i	−0.405391	+	0.702157i	−0.994367	−	0.105993i	$-0.966198\pi$
$179$	−5.42376	+	9.39422i	−0.405391	+	0.702157i	0.588976	+	0.808150i	$0.299531\pi$
$180$		0			0
$181$	−0.759361			−0.0564428			−0.0282214	−	0.999602i	$-0.508984\pi$
$181$	−0.759361			−0.0564428			−0.0282214	+	0.999602i	$0.508984\pi$
$182$	10.7609	−	3.77613i	0.797651	−	0.279905i
$183$		0			0
$184$	7.15296	+	4.12976i	0.527323	+	0.304450i
$185$	−0.698857	+	1.21046i	−0.0513810	+	0.0889945i
$186$		0			0
$187$		−	2.06954i		−	0.151340i
$188$	41.3393	−	23.8672i	3.01498	−	1.74070i
$189$		0			0
$190$		−	6.10547i		−	0.442937i
$191$	3.34149	+	5.78763i	0.241782	+	0.418778i	0.961222	−	0.275776i	$-0.0889349\pi$
$191$	3.34149	+	5.78763i	0.241782	+	0.418778i	−0.719440	+	0.694554i	$0.755602\pi$
$192$		0			0
$193$	−13.7082	−	7.91441i	−0.986735	−	0.569692i	−0.0824381	−	0.996596i	$-0.526271\pi$
$193$	−13.7082	−	7.91441i	−0.986735	−	0.569692i	−0.904297	+	0.426905i	$0.859604\pi$
$194$	−19.3180			−1.38695
$195$		0			0
$196$	−20.7468			−1.48192
$197$	−5.91886	−	3.41725i	−0.421701	−	0.243469i	0.274104	−	0.961700i	$-0.411619\pi$
$197$	−5.91886	−	3.41725i	−0.421701	−	0.243469i	−0.695805	+	0.718231i	$0.744952\pi$
$198$		0			0
$199$	−8.62135	−	14.9326i	−0.611151	−	1.05854i	−0.991047	−	0.133515i	$-0.957373\pi$
$199$	−8.62135	−	14.9326i	−0.611151	−	1.05854i	0.379896	−	0.925029i	$-0.375960\pi$
$200$			4.64136i			0.328194i
$201$		0			0
$202$	−4.47457	+	2.58340i	−0.314830	+	0.181767i
$203$			10.9027i			0.765217i
$204$		0			0
$205$	−5.81147	+	10.0658i	−0.405891	+	0.703024i
$206$	−2.07512	−	1.19807i	−0.144580	−	0.0834734i
$207$		0			0
$208$	2.31114	−	12.2743i	0.160249	−	0.851070i
$209$	7.98001			0.551989
$210$		0			0
$211$	11.9066	−	20.6229i	0.819685	−	1.41974i	−0.0862299	−	0.996275i	$-0.527482\pi$
$211$	11.9066	−	20.6229i	0.819685	−	1.41974i	0.905915	−	0.423460i	$-0.139185\pi$
$212$	12.4209	+	21.5137i	0.853072	+	1.47756i
$213$		0			0
$214$	25.9699	−	14.9937i	1.77527	−	1.02495i
$215$	−2.83522	+	1.63692i	−0.193361	+	0.111637i
$216$		0			0
$217$	5.53193	+	9.58158i	0.375532	+	0.650440i
$218$	1.05773	−	1.83204i	0.0716386	−	0.124082i
$219$		0			0
$220$	−12.4209			−0.837418
$221$	1.78146	+	1.53032i	0.119834	+	0.102941i
$222$		0			0
$223$	−9.34911	−	5.39771i	−0.626063	−	0.361458i	0.153163	−	0.988201i	$-0.451054\pi$
$223$	−9.34911	−	5.39771i	−0.626063	−	0.361458i	−0.779226	+	0.626743i	$0.784387\pi$
$224$	−0.560673	+	0.971114i	−0.0374615	+	0.0648853i
$225$		0			0
$226$			36.7100i			2.44191i
$227$	9.13935	−	5.27661i	0.606600	−	0.350221i	−0.165034	−	0.986288i	$-0.552773\pi$
$227$	9.13935	−	5.27661i	0.606600	−	0.350221i	0.771634	+	0.636067i	$0.219440\pi$
$228$		0			0
$229$		−	15.3248i		−	1.01269i	−0.862330	−	0.506346i	$-0.830996\pi$
$229$		−	15.3248i		−	1.01269i	0.862330	−	0.506346i	$-0.169004\pi$
$230$	2.16296	+	3.74635i	0.142621	+	0.247027i
$231$		0			0
$232$	33.6809	+	19.4457i	2.21126	+	1.27667i
$233$	−9.96092			−0.652562			−0.326281	−	0.945273i	$-0.605796\pi$
$233$	−9.96092			−0.652562			−0.326281	+	0.945273i	$0.605796\pi$
$234$		0			0
$235$	12.2105			0.796522
$236$	20.2650	+	11.7000i	1.31914	+	0.761604i
$237$		0			0
$238$	1.03011	+	1.78421i	0.0667722	+	0.115653i
$239$		−	2.47998i		−	0.160417i	−0.996778	−	0.0802083i	$-0.974441\pi$
$239$		−	2.47998i		−	0.160417i	0.996778	−	0.0802083i	$-0.0255586\pi$
$240$		0			0
$241$	24.6599	−	14.2374i	1.58848	−	0.917111i	0.594924	−	0.803782i	$-0.297182\pi$
$241$	24.6599	−	14.2374i	1.58848	−	0.917111i	0.993558	−	0.113329i	$-0.0361514\pi$
$242$			2.19999i			0.141420i
$243$		0			0
$244$	25.3860	−	43.9699i	1.62517	−	2.81489i
$245$	−4.59602	−	2.65351i	−0.293629	−	0.169527i
$246$		0			0
$247$	−5.90082	+	6.86920i	−0.375460	+	0.437077i
$248$	39.4663			2.50612
$249$		0			0
$250$	−1.21545	+	2.10523i	−0.0768721	+	0.133146i
$251$	−13.4795	−	23.3472i	−0.850820	−	1.47366i	−0.880469	−	0.474104i	$-0.842772\pi$
$251$	−13.4795	−	23.3472i	−0.850820	−	1.47366i	0.0296488	−	0.999560i	$-0.490561\pi$
$252$		0			0
$253$	−4.89659	+	2.82705i	−0.307846	+	0.177735i
$254$	6.09739	−	3.52033i	0.382584	−	0.220885i
$255$		0			0
$256$	15.5423	+	26.9200i	0.971391	+	1.68250i
$257$	4.29614	−	7.44114i	0.267986	−	0.464166i	−0.700356	−	0.713794i	$-0.746975\pi$
$257$	4.29614	−	7.44114i	0.267986	−	0.464166i	0.968342	+	0.249629i	$0.0803085\pi$
$258$		0			0
$259$	1.81863			0.113004
$260$	9.18465	−	10.6919i	0.569608	−	0.663086i
$261$		0			0
$262$	33.1721	+	19.1519i	2.04938	+	1.18321i
$263$	−7.31726	+	12.6739i	−0.451202	+	0.781504i	−0.998461	−	0.0554590i	$-0.982338\pi$
$263$	−7.31726	+	12.6739i	−0.451202	+	0.781504i	0.547259	+	0.836963i	$0.315671\pi$
$264$		0			0
$265$			6.35452i			0.390355i
$266$	−6.87978	+	3.97204i	−0.421826	+	0.243541i
$267$		0			0
$268$			51.4252i			3.14129i
$269$	3.68759	+	6.38710i	0.224837	+	0.389428i	0.956270	−	0.292484i	$-0.0944819\pi$
$269$	3.68759	+	6.38710i	0.224837	+	0.389428i	−0.731434	+	0.681912i	$0.761149\pi$
$270$		0			0
$271$	−10.2106	−	5.89511i	−0.620251	−	0.358102i	0.156716	−	0.987644i	$-0.449909\pi$
$271$	−10.2106	−	5.89511i	−0.620251	−	0.358102i	−0.776967	+	0.629542i	$0.783243\pi$
$272$	2.25638			0.136813
$273$		0			0
$274$	1.79338			0.108342
$275$	−2.75159	−	1.58863i	−0.165927	−	0.0957981i
$276$		0			0
$277$	−9.62548	−	16.6718i	−0.578339	−	1.00171i	−0.995670	−	0.0929583i	$-0.970368\pi$
$277$	−9.62548	−	16.6718i	−0.578339	−	1.00171i	0.417331	−	0.908755i	$-0.362966\pi$
$278$		−	48.0027i		−	2.87901i
$279$		0			0
$280$	5.22999	−	3.01954i	0.312552	−	0.180452i
$281$		−	25.4911i		−	1.52067i	−0.649529	−	0.760336i	$-0.725034\pi$
$281$		−	25.4911i		−	1.52067i	0.649529	−	0.760336i	$-0.274966\pi$
$282$		0			0
$283$	−2.58634	+	4.47967i	−0.153742	+	0.266289i	−0.932600	−	0.360911i	$-0.882466\pi$
$283$	−2.58634	+	4.47967i	−0.153742	+	0.266289i	0.778858	+	0.627200i	$0.215799\pi$
$284$	3.71251	+	2.14342i	0.220297	+	0.127189i
$285$		0			0
$286$	21.1241	+	18.1461i	1.24909	+	1.07300i
$287$	15.1231			0.892689
$288$		0			0
$289$	8.28787	−	14.3550i	0.487521	−	0.844412i
$290$	10.1847	+	17.6403i	0.598063	+	1.03588i
$291$		0			0
$292$	−41.4032	+	23.9042i	−2.42294	+	1.39889i
$293$	22.5099	−	12.9961i	1.31505	−	0.759242i	0.332118	−	0.943238i	$-0.392237\pi$
$293$	22.5099	−	12.9961i	1.31505	−	0.759242i	0.982927	+	0.183996i	$0.0589033\pi$
$294$		0			0
$295$	2.99285	+	5.18377i	0.174250	+	0.301810i
$296$	3.24365	−	5.61817i	0.188533	−	0.326549i
$297$		0			0
$298$	−7.69502			−0.445761
$299$	1.18726	−	6.30545i	0.0686609	−	0.364654i
$300$		0			0
$301$	3.68903	+	2.12986i	0.212632	+	0.122763i
$302$	−0.205220	+	0.355452i	−0.0118091	+	0.0204540i
$303$		0			0
$304$			8.70043i			0.499004i
$305$	11.2475	−	6.49373i	0.644029	−	0.371830i
$306$		0			0
$307$			20.7454i			1.18400i	0.805937	+	0.592001i	$0.201662\pi$
$307$			20.7454i			1.18400i	−0.805937	+	0.592001i	$0.798338\pi$
$308$	8.08069	+	13.9962i	0.460440	+	0.797506i
$309$		0			0
$310$	17.9011	+	10.3352i	1.01672	+	0.587001i
$311$	−1.72617			−0.0978819			−0.0489410	−	0.998802i	$-0.515585\pi$
$311$	−1.72617			−0.0978819			−0.0489410	+	0.998802i	$0.515585\pi$
$312$		0			0
$313$	6.29703			0.355929			0.177965	−	0.984037i	$-0.443049\pi$
$313$	6.29703			0.355929			0.177965	+	0.984037i	$0.443049\pi$
$314$	−28.5283	−	16.4708i	−1.60994	−	0.929501i
$315$		0			0
$316$	−2.60013	−	4.50356i	−0.146269	−	0.253345i
$317$			10.5750i			0.593950i	0.954885	+	0.296975i	$0.0959778\pi$
$317$			10.5750i			0.593950i	−0.954885	+	0.296975i	$0.904022\pi$
$318$		0			0
$319$	−23.0564	+	13.3116i	−1.29091	+	0.745307i
$320$			9.02320i			0.504412i
$321$		0			0
$322$	2.81432	−	4.87454i	0.156836	−	0.271648i
$323$	−1.41678	−	0.817977i	−0.0788316	−	0.0455135i
$324$		0			0
$325$	3.40216	−	1.19386i	0.188718	−	0.0662234i
$326$	36.9647			2.04729
$327$		0			0
$328$	26.9732	−	46.7189i	1.48934	−	2.57962i
$329$	−7.94377	−	13.7590i	−0.437954	−	0.758559i
$330$		0			0
$331$	−4.99907	+	2.88621i	−0.274774	+	0.158641i	−0.631055	−	0.775738i	$-0.717378\pi$
$331$	−4.99907	+	2.88621i	−0.274774	+	0.158641i	0.356281	+	0.934379i	$0.384044\pi$
$332$	−48.3013	+	27.8868i	−2.65088	+	1.53049i
$333$		0			0
$334$	9.08658	+	15.7384i	0.497195	+	0.861167i
$335$	−6.57727	+	11.3922i	−0.359355	+	0.622420i
$336$		0			0
$337$	2.08610			0.113637			0.0568186	−	0.998385i	$-0.481904\pi$
$337$	2.08610			0.113637			0.0568186	+	0.998385i	$0.481904\pi$
$338$	−31.2404	+	4.76548i	−1.69926	+	0.259208i
$339$		0			0
$340$	2.20522	+	1.27318i	0.119595	+	0.0690481i
$341$	−13.5084	+	23.3973i	−0.731522	+	1.26703i
$342$		0			0
$343$			16.0132i			0.864632i
$344$	13.1593	−	7.59753i	0.709502	−	0.409631i
$345$		0			0
$346$		−	22.5929i		−	1.21460i
$347$	−3.84163	−	6.65390i	−0.206229	−	0.357200i	0.744294	−	0.667852i	$-0.232786\pi$
$347$	−3.84163	−	6.65390i	−0.206229	−	0.357200i	−0.950524	+	0.310652i	$0.899453\pi$
$348$		0			0
$349$	−14.5469	−	8.39867i	−0.778679	−	0.449570i	0.0572831	−	0.998358i	$-0.481756\pi$
$349$	−14.5469	−	8.39867i	−0.778679	−	0.449570i	−0.835962	+	0.548788i	$0.815090\pi$
$350$	3.16296			0.169067
$351$		0			0
$352$	−2.73821			−0.145947
$353$	−0.140884	−	0.0813396i	−0.00749851	−	0.00432927i	0.496246	−	0.868182i	$-0.334711\pi$
$353$	−0.140884	−	0.0813396i	−0.00749851	−	0.00432927i	−0.503745	+	0.863853i	$0.668045\pi$
$354$		0			0
$355$	0.548286	+	0.949658i	0.0291000	+	0.0504026i
$356$			37.5445i			1.98985i
$357$		0			0
$358$	22.8365	−	13.1847i	1.20695	−	0.696830i
$359$		−	19.3374i		−	1.02059i	−0.860000	−	0.510295i	$-0.829536\pi$
$359$		−	19.3374i		−	1.02059i	0.860000	−	0.510295i	$-0.170464\pi$
$360$		0			0
$361$	−6.34594	+	10.9915i	−0.333997	+	0.578499i
$362$	1.59863	+	0.922968i	0.0840220	+	0.0485101i
$363$		0			0
$364$	−18.0232	−	3.39360i	−0.944672	−	0.177873i
$365$	−12.2293			−0.640113
$366$		0			0
$367$	1.13421	−	1.96451i	0.0592054	−	0.102547i	−0.834904	−	0.550396i	$-0.814477\pi$
$367$	1.13421	−	1.96451i	0.0592054	−	0.102547i	0.894109	+	0.447850i	$0.147810\pi$
$368$	−3.08227	−	5.33864i	−0.160674	−	0.278296i
$369$		0			0
$370$	2.94251	−	1.69886i	0.152974	−	0.0883194i
$371$	7.16042	−	4.13407i	0.371751	−	0.214630i
$372$		0			0
$373$	5.96434	+	10.3305i	0.308822	+	0.534895i	0.978105	−	0.208112i	$-0.0667320\pi$
$373$	5.96434	+	10.3305i	0.308822	+	0.534895i	−0.669283	+	0.743007i	$0.733399\pi$
$374$	−2.51543	+	4.35686i	−0.130070	+	0.225288i
$375$		0			0
$376$	−56.6732			−2.92270
$377$	5.59040	−	29.6903i	0.287920	−	1.52913i
$378$		0			0
$379$	−9.97692	−	5.76018i	−0.512480	−	0.295880i	0.221372	−	0.975189i	$-0.428946\pi$
$379$	−9.97692	−	5.76018i	−0.512480	−	0.295880i	−0.733853	+	0.679309i	$0.762280\pi$
$380$	−4.90931	+	8.50318i	−0.251842	+	0.436204i
$381$		0			0
$382$		−	16.2457i		−	0.831202i
$383$	11.9602	−	6.90524i	0.611139	−	0.352841i	−0.162272	−	0.986746i	$-0.551882\pi$
$383$	11.9602	−	6.90524i	0.611139	−	0.352841i	0.773411	+	0.633905i	$0.218549\pi$
$384$		0			0
$385$			4.13407i			0.210692i
$386$	19.2392	+	33.3233i	0.979249	+	1.69611i
$387$		0			0
$388$	26.9044	+	15.5333i	1.36587	+	0.788583i
$389$	13.9037			0.704946			0.352473	−	0.935822i	$-0.385341\pi$
$389$	13.9037			0.704946			0.352473	+	0.935822i	$0.385341\pi$
$390$		0			0
$391$	1.15913			0.0586195
$392$	21.3318	+	12.3159i	1.07742	+	0.622048i
$393$		0			0
$394$	8.30703	+	14.3882i	0.418502	+	0.724867i
$395$		−	1.33022i		−	0.0669309i
$396$		0			0
$397$	21.6274	−	12.4866i	1.08545	−	0.626684i	0.153087	−	0.988213i	$-0.451079\pi$
$397$	21.6274	−	12.4866i	1.08545	−	0.626684i	0.932361	+	0.361529i	$0.117745\pi$
$398$			41.9154i			2.10103i
$399$		0			0
$400$	1.73205	−	3.00000i	0.0866025	−	0.150000i
$401$	7.91663	+	4.57067i	0.395338	+	0.228248i	0.684470	−	0.729041i	$-0.260034\pi$
$401$	7.91663	+	4.57067i	0.395338	+	0.228248i	−0.289133	+	0.957289i	$0.593367\pi$
$402$		0			0
$403$	−10.1516	−	28.9292i	−0.505687	−	1.44107i
$404$	8.30908			0.413392
$405$		0			0
$406$	13.2517	−	22.9526i	0.657670	−	1.13912i
$407$	2.22045	+	3.84594i	0.110064	+	0.190636i
$408$		0			0
$409$	−21.1456	+	12.2084i	−1.04558	+	0.603667i	−0.921409	−	0.388594i	$-0.872961\pi$
$409$	−21.1456	+	12.2084i	−1.04558	+	0.603667i	−0.124172	+	0.992261i	$0.539627\pi$
$410$	24.4690	−	14.1272i	1.20844	−	0.697691i
$411$		0			0
$412$	1.92670	+	3.33714i	0.0949216	+	0.164409i
$413$	3.89412	−	6.74482i	0.191617	−	0.331891i
$414$		0			0
$415$	−14.2668			−0.700332
$416$	2.02477	−	2.35706i	0.0992727	−	0.115564i
$417$		0			0
$418$	−16.7997	−	9.69933i	−0.821702	−	0.474410i
$419$	3.48713	−	6.03989i	0.170358	−	0.295068i	−0.768187	−	0.640225i	$-0.778841\pi$
$419$	3.48713	−	6.03989i	0.170358	−	0.295068i	0.938545	+	0.345157i	$0.112174\pi$
$420$		0			0
$421$		−	0.673176i		−	0.0328086i	−0.999865	−	0.0164043i	$-0.994778\pi$
$421$		−	0.673176i		−	0.0328086i	0.999865	−	0.0164043i	$-0.00522189\pi$
$422$	−50.1322	+	28.9439i	−2.44040	+	1.40897i
$423$		0			0
$424$		−	29.4937i		−	1.43234i
$425$	0.325680	+	0.564094i	0.0157978	+	0.0273626i
$426$		0			0
$427$	−14.6346	−	8.44928i	−0.708217	−	0.408889i
$428$	−48.2249			−2.33104
$429$		0			0
$430$	7.95839			0.383787
$431$	−24.2754	−	14.0154i	−1.16931	−	0.675099i	−0.215790	−	0.976440i	$-0.569233\pi$
$431$	−24.2754	−	14.0154i	−1.16931	−	0.675099i	−0.953517	+	0.301340i	$0.902566\pi$
$432$		0			0
$433$	1.33317	+	2.30911i	0.0640679	+	0.110969i	0.896280	−	0.443488i	$-0.146259\pi$
$433$	1.33317	+	2.30911i	0.0640679	+	0.110969i	−0.832212	+	0.554457i	$0.812926\pi$
$434$		−	26.8952i		−	1.29101i
$435$		0			0
$436$	−2.94624	+	1.70101i	−0.141099	+	0.0814636i
$437$			4.46951i			0.213806i
$438$		0			0
$439$	11.0370	−	19.1166i	0.526765	−	0.912384i	−0.472749	−	0.881197i	$-0.656738\pi$
$439$	11.0370	−	19.1166i	0.526765	−	0.912384i	0.999514	−	0.0311863i	$-0.00992851\pi$
$440$	12.7711	+	7.37341i	0.608840	+	0.351514i
$441$		0			0
$442$	−1.89035	−	5.38697i	−0.0899148	−	0.256232i
$443$	−14.6927			−0.698070			−0.349035	−	0.937110i	$-0.613491\pi$
$443$	−14.6927			−0.698070			−0.349035	+	0.937110i	$0.613491\pi$
$444$		0			0
$445$	−4.80193	+	8.31719i	−0.227633	+	0.394273i
$446$	13.1213	+	22.7268i	0.621314	+	1.07615i
$447$		0			0
$448$	10.1675	−	5.87024i	0.480371	−	0.277343i
$449$	4.88200	−	2.81863i	0.230396	−	0.133019i	−0.380359	−	0.924839i	$-0.624199\pi$
$449$	4.88200	−	2.81863i	0.230396	−	0.133019i	0.610755	+	0.791820i	$0.290866\pi$
$450$		0			0
$451$	18.4646	+	31.9816i	0.869463	+	1.50595i
$452$	29.5180	−	51.1266i	1.38841	−	2.40479i
$453$		0			0
$454$	−25.6539			−1.20400
$455$	−3.55862	−	3.05694i	−0.166831	−	0.143312i
$456$		0			0
$457$	−4.39355	−	2.53662i	−0.205521	−	0.118658i	0.393707	−	0.919236i	$-0.371192\pi$
$457$	−4.39355	−	2.53662i	−0.205521	−	0.118658i	−0.599228	+	0.800578i	$0.704526\pi$
$458$	−18.6266	+	32.2622i	−0.870364	+	1.50751i
$459$		0			0
$460$		−	6.95681i		−	0.324363i
$461$	−28.6562	+	16.5446i	−1.33465	+	0.770561i	−0.986009	−	0.166695i	$-0.946691\pi$
$461$	−28.6562	+	16.5446i	−1.33465	+	0.770561i	−0.348642	+	0.937256i	$0.613357\pi$
$462$		0			0
$463$		−	24.4976i		−	1.13850i	−0.822164	−	0.569251i	$-0.807233\pi$
$463$		−	24.4976i		−	1.13850i	0.822164	−	0.569251i	$-0.192767\pi$
$464$	−14.5134	−	25.1379i	−0.673766	−	1.16700i
$465$		0			0
$466$	20.9700	+	12.1070i	0.971417	+	0.560848i
$467$	30.5932			1.41569			0.707843	−	0.706370i	$-0.249668\pi$
$467$	30.5932			1.41569			0.707843	+	0.706370i	$0.249668\pi$
$468$		0			0
$469$	17.1159			0.790341
$470$	−25.7058	−	14.8412i	−1.18572	−	0.684576i
$471$		0			0
$472$	−13.8909	−	24.0597i	−0.639380	−	1.10744i
$473$			10.4018i			0.478276i
$474$		0			0
$475$	−2.17511	+	1.25580i	−0.0998008	+	0.0576200i
$476$		−	3.31319i		−	0.151860i
$477$		0			0
$478$	−3.01430	+	5.22093i	−0.137871	+	0.238800i
$479$	−12.0534	−	6.95901i	−0.550732	−	0.317965i	0.198685	−	0.980063i	$-0.436333\pi$
$479$	−12.0534	−	6.95901i	−0.550732	−	0.317965i	−0.749417	+	0.662098i	$0.769666\pi$
$480$		0			0
$481$	−4.95250	−	0.932511i	−0.225815	−	0.0425188i
$482$	−69.2195			−3.15286
$483$		0			0
$484$	1.76897	−	3.06395i	0.0804079	−	0.139271i
$485$	3.97341	+	6.88214i	0.180423	+	0.312502i
$486$		0			0
$487$	−26.4585	+	15.2758i	−1.19895	+	0.692213i	−0.960321	−	0.278898i	$-0.910031\pi$
$487$	−26.4585	+	15.2758i	−1.19895	+	0.692213i	−0.238628	+	0.971111i	$0.576698\pi$
$488$	−52.2036	+	30.1398i	−2.36315	+	1.36436i
$489$		0			0
$490$	6.45045	+	11.1725i	0.291401	+	0.504722i
$491$	7.34214	−	12.7170i	0.331346	−	0.573908i	−0.651430	−	0.758709i	$-0.725831\pi$
$491$	7.34214	−	12.7170i	0.331346	−	0.573908i	0.982776	+	0.184801i	$0.0591639\pi$
$492$		0			0
$493$	5.45794			0.245813
$494$	20.7718	−	7.28906i	0.934566	−	0.327951i
$495$		0			0
$496$	−25.5095	−	14.7279i	−1.14541	−	0.661304i
$497$	0.713398	−	1.23564i	0.0320003	−	0.0554261i
$498$		0			0
$499$		−	16.1489i		−	0.722922i	−0.932387	−	0.361461i	$-0.882278\pi$
$499$		−	16.1489i		−	0.722922i	0.932387	−	0.361461i	$-0.117722\pi$
$500$	3.38556	−	1.95466i	0.151407	−	0.0874149i
$501$		0			0
$502$			65.5350i			2.92497i
$503$	−1.00431	−	1.73951i	−0.0447799	−	0.0775610i	0.842767	−	0.538279i	$-0.180925\pi$
$503$	−1.00431	−	1.73951i	−0.0447799	−	0.0775610i	−0.887547	+	0.460718i	$0.847592\pi$
$504$		0			0
$505$	1.84070	+	1.06273i	0.0819101	+	0.0472908i
$506$	13.7446			0.611021
$507$		0			0
$508$	−11.3226			−0.502358
$509$	33.2529	+	19.1986i	1.47391	+	0.850962i	0.999568	−	0.0293796i	$-0.00935315\pi$
$509$	33.2529	+	19.1986i	1.47391	+	0.850962i	0.474341	+	0.880341i	$0.342686\pi$
$510$		0			0
$511$	7.95606	+	13.7803i	0.351956	+	0.609605i
$512$		−	35.1417i		−	1.55306i
$513$		0			0
$514$	−18.0887	+	10.4435i	−0.797860	+	0.460644i
$515$			0.985697i			0.0434350i
$516$		0			0
$517$	19.3979	−	33.5982i	0.853119	−	1.47765i
$518$	−3.82862	−	2.21046i	−0.168220	−	0.0971219i
$519$		0			0
$520$	−15.7907	+	5.54113i	−0.692467	+	0.242995i
$521$	−31.2138			−1.36750			−0.683751	−	0.729716i	$-0.739652\pi$
$521$	−31.2138			−1.36750			−0.683751	+	0.729716i	$0.739652\pi$
$522$		0			0
$523$	−16.6041	+	28.7591i	−0.726045	+	1.25755i	0.232498	+	0.972597i	$0.425310\pi$
$523$	−16.6041	+	28.7591i	−0.726045	+	1.25755i	−0.958543	+	0.284949i	$0.908023\pi$
$524$	−30.7996	−	53.3464i	−1.34549	−	2.33045i
$525$		0			0
$526$	30.8090	−	17.7876i	1.34334	−	0.775576i
$527$	4.79659	−	2.76931i	0.208943	−	0.120633i
$528$		0			0
$529$	9.91660	+	17.1761i	0.431157	+	0.746785i
$530$	7.72363	−	13.3777i	0.335493	−	0.581091i
$531$		0			0
$532$	12.7754			0.553885
$533$	−41.1834	−	7.75446i	−1.78385	−	0.335883i
$534$		0			0
$535$	−10.6832	−	6.16796i	−0.461876	−	0.266664i
$536$	30.5275	−	52.8752i	1.31859	−	2.28386i
$537$		0			0
$538$		−	17.9284i		−	0.772948i
$539$	−14.6028	+	8.43091i	−0.628985	+	0.363145i
$540$		0			0
$541$		−	39.1911i		−	1.68496i	−0.538731	−	0.842478i	$-0.681096\pi$
$541$		−	39.1911i		−	1.68496i	0.538731	−	0.842478i	$-0.318904\pi$
$542$	14.3305	+	24.8211i	0.615546	+	1.06616i
$543$		0			0
$544$	0.486145	+	0.280676i	0.0208433	+	0.0120339i
$545$	−0.870235			−0.0372768
$546$		0			0
$547$	8.26842			0.353532			0.176766	−	0.984253i	$-0.443436\pi$
$547$	8.26842			0.353532			0.176766	+	0.984253i	$0.443436\pi$
$548$	−2.49766	−	1.44203i	−0.106695	−	0.0616004i
$549$		0			0
$550$	3.86182	+	6.68886i	0.164668	+	0.285214i
$551$			21.0454i			0.896566i
$552$		0			0
$553$	−1.49893	+	0.865406i	−0.0637409	+	0.0368008i
$554$			46.7973i			1.98823i
$555$		0			0
$556$	−38.5983	+	66.8542i	−1.63693	+	2.83525i
$557$	39.0259	+	22.5316i	1.65358	+	0.954695i	0.975583	+	0.219631i	$0.0704852\pi$
$557$	39.0259	+	22.5316i	1.65358	+	0.954695i	0.677997	+	0.735064i	$0.262848\pi$
$558$		0			0
$559$	−8.95391	−	7.69164i	−0.378710	−	0.325322i
$560$	−4.50729			−0.190468
$561$		0			0
$562$	−30.9833	+	53.6646i	−1.30695	+	2.26371i
$563$	22.9389	+	39.7313i	0.966758	+	1.67447i	0.704816	+	0.709391i	$0.251030\pi$
$563$	22.9389	+	39.7313i	0.966758	+	1.67447i	0.261943	+	0.965083i	$0.415637\pi$
$564$		0			0
$565$	13.0782	−	7.55068i	0.550202	−	0.317659i
$566$	10.8897	−	6.28715i	0.457727	−	0.264269i
$567$		0			0
$568$	−2.54479	−	4.40771i	−0.106777	−	0.184943i
$569$	−3.06034	+	5.30066i	−0.128296	+	0.222215i	−0.923017	−	0.384760i	$-0.874284\pi$
$569$	−3.06034	+	5.30066i	−0.128296	+	0.222215i	0.794720	+	0.606976i	$0.207617\pi$
$570$		0			0
$571$	−19.2267			−0.804611			−0.402306	−	0.915505i	$-0.631791\pi$
$571$	−19.2267			−0.804611			−0.402306	+	0.915505i	$0.631791\pi$
$572$	−14.8288	−	42.2579i	−0.620024	−	1.76689i
$573$		0			0
$574$	−31.8376	−	18.3815i	−1.32888	−	0.767227i
$575$	0.889774	−	1.54113i	0.0371061	−	0.0642697i
$576$		0			0
$577$			9.40689i			0.391614i	0.980642	+	0.195807i	$0.0627326\pi$
$577$			9.40689i			0.391614i	−0.980642	+	0.195807i	$0.937267\pi$
$578$	−34.8957	+	20.1470i	−1.45147	+	0.838006i
$579$		0			0
$580$		−	32.7573i		−	1.36017i
$581$	9.28160	+	16.0762i	0.385066	+	0.666954i
$582$		0			0
$583$	17.4850	+	10.0950i	0.724157	+	0.418092i
$584$	56.7608			2.34878
$585$		0			0
$586$	−63.1848			−2.61014
$587$	32.2409	+	18.6143i	1.33072	+	0.768294i	0.985411	−	0.170193i	$-0.0544392\pi$
$587$	32.2409	+	18.6143i	1.33072	+	0.768294i	0.345314	+	0.938487i	$0.387773\pi$
$588$		0			0
$589$	10.6783	+	18.4953i	0.439991	+	0.762087i
$590$		−	14.5507i		−	0.599042i
$591$		0			0
$592$	−4.19314	+	2.42091i	−0.172337	+	0.0994989i
$593$		−	18.1214i		−	0.744157i	−0.928201	−	0.372078i	$-0.878645\pi$
$593$		−	18.1214i		−	0.744157i	0.928201	−	0.372078i	$-0.121355\pi$
$594$		0			0
$595$	0.423756	−	0.733967i	0.0173723	−	0.0300897i
$596$	10.7170	+	6.18745i	0.438985	+	0.253448i
$597$		0			0
$598$	−10.1634	+	11.8314i	−0.415614	+	0.483820i
$599$	7.18204			0.293450			0.146725	−	0.989177i	$-0.453127\pi$
$599$	7.18204			0.293450			0.146725	+	0.989177i	$0.453127\pi$
$600$		0			0
$601$	16.5370	−	28.6428i	0.674556	−	1.16837i	−0.302042	−	0.953295i	$-0.597668\pi$
$601$	16.5370	−	28.6428i	0.674556	−	1.16837i	0.976598	−	0.215071i	$-0.0689983\pi$
$602$	−5.17750	−	8.96769i	−0.211019	−	0.365496i
$603$		0			0
$604$	0.571628	−	0.330029i	0.0232592	−	0.0134287i
$605$	0.783758	−	0.452503i	0.0318643	−	0.0183969i
$606$		0			0
$607$	−10.8071	−	18.7185i	−0.438648	−	0.759760i	0.558938	−	0.829210i	$-0.311209\pi$
$607$	−10.8071	−	18.7185i	−0.438648	−	0.759760i	−0.997585	+	0.0694496i	$0.977876\pi$
$608$	−1.08227	+	1.87454i	−0.0438917	+	0.0760227i
$609$		0			0
$610$	−31.5713			−1.27829
$611$	14.5776	+	41.5419i	0.589745	+	1.68061i
$612$		0			0
$613$	−23.6890	−	13.6769i	−0.956790	−	0.552403i	−0.0616062	−	0.998101i	$-0.519622\pi$
$613$	−23.6890	−	13.6769i	−0.956790	−	0.552403i	−0.895184	+	0.445698i	$0.852956\pi$
$614$	25.2151	−	43.6738i	1.01760	−	1.76253i
$615$		0			0
$616$		−	19.1877i		−	0.773096i
$617$	14.1425	−	8.16518i	0.569356	−	0.328718i	−0.187536	−	0.982258i	$-0.560050\pi$
$617$	14.1425	−	8.16518i	0.569356	−	0.328718i	0.756892	+	0.653540i	$0.226717\pi$
$618$		0			0
$619$			35.8801i			1.44214i	0.692860	+	0.721072i	$0.256350\pi$
$619$			35.8801i			1.44214i	−0.692860	+	0.721072i	$0.743650\pi$
$620$	−16.6208	−	28.7881i	−0.667507	−	1.15616i
$621$		0			0
$622$	3.63397	+	2.09808i	0.145709	+	0.0841252i
$623$	12.4960			0.500642
$624$		0			0
$625$	1.00000			0.0400000
$626$	−13.2567	−	7.65375i	−0.529844	−	0.305905i
$627$		0			0
$628$	26.4878	+	45.8783i	1.05698	+	1.83074i
$629$		−	0.910415i		−	0.0363006i
$630$		0			0
$631$	−6.10348	+	3.52385i	−0.242976	+	0.140282i	−0.616544	−	0.787321i	$-0.711468\pi$
$631$	−6.10348	+	3.52385i	−0.242976	+	0.140282i	0.373568	+	0.927603i	$0.378134\pi$
$632$			6.17406i			0.245591i
$633$		0			0
$634$	12.8534	−	22.2627i	0.510474	−	0.884166i
$635$	−2.50828	−	1.44815i	−0.0995379	−	0.0574682i
$636$		0			0
$637$	3.54068	−	18.8043i	0.140287	−	0.745054i
$638$	64.7186			2.56223
$639$		0			0
$640$	10.1055	−	17.5032i	0.399454	−	0.691874i
$641$	−20.4752	−	35.4641i	−0.808723	−	1.40075i	−0.913749	−	0.406279i	$-0.866826\pi$
$641$	−20.4752	−	35.4641i	−0.808723	−	1.40075i	0.105026	−	0.994469i	$-0.466507\pi$
$642$		0			0
$643$	30.5004	−	17.6094i	1.20282	−	0.694448i	0.241638	−	0.970366i	$-0.422315\pi$
$643$	30.5004	−	17.6094i	1.20282	−	0.694448i	0.961181	+	0.275918i	$0.0889819\pi$
$644$	−7.83909	+	4.52590i	−0.308904	+	0.178346i
$645$		0			0
$646$	1.98843	+	3.44406i	0.0782336	+	0.135505i
$647$	−14.2359	+	24.6573i	−0.559670	+	0.969377i	0.437854	+	0.899046i	$0.355739\pi$
$647$	−14.2359	+	24.6573i	−0.559670	+	0.969377i	−0.997524	+	0.0703308i	$0.977595\pi$
$648$		0			0
$649$	19.0181			0.746527
$650$	−8.61341	−	1.62182i	−0.337846	−	0.0636132i
$651$		0			0
$652$	−51.4814	−	29.7228i	−2.01617	−	1.16403i
$653$	15.6332	−	27.0775i	0.611774	−	1.05962i	−0.379168	−	0.925328i	$-0.623790\pi$
$653$	15.6332	−	27.0775i	0.611774	−	1.05962i	0.990941	−	0.134295i	$-0.0428770\pi$
$654$		0			0
$655$		−	15.7570i		−	0.615678i
$656$	−34.8688	+	20.1315i	−1.36140	+	0.786004i
$657$		0			0
$658$			38.6212i			1.50561i
$659$	−1.61118	−	2.79065i	−0.0627627	−	0.108708i	0.832937	−	0.553368i	$-0.186658\pi$
$659$	−1.61118	−	2.79065i	−0.0627627	−	0.108708i	−0.895699	+	0.444660i	$0.853324\pi$
$660$		0			0
$661$	25.9416	+	14.9774i	1.00901	+	0.582552i	0.910902	−	0.412623i	$-0.135387\pi$
$661$	25.9416	+	14.9774i	1.00901	+	0.582552i	0.0981086	+	0.995176i	$0.468721\pi$
$662$	14.0322			0.545378
$663$		0			0
$664$	66.2176			2.56974
$665$	2.83013	+	1.63397i	0.109748	+	0.0633628i
$666$		0			0
$667$	−7.45568	−	12.9136i	−0.288685	−	0.500017i
$668$		−	29.2255i		−	1.13077i
$669$		0			0
$670$	27.6933	−	15.9887i	1.06989	−	0.617699i
$671$		−	41.2646i		−	1.59300i
$672$		0			0
$673$	−14.8836	+	25.7792i	−0.573722	+	0.993716i	0.422457	+	0.906383i	$0.361168\pi$
$673$	−14.8836	+	25.7792i	−0.573722	+	0.993716i	−0.996179	+	0.0873333i	$0.972165\pi$
$674$	−4.39172	−	2.53556i	−0.169163	−	0.0976661i
$675$		0			0
$676$	47.3409	+	18.4830i	1.82080	+	0.710884i
$677$	−24.8749			−0.956019			−0.478010	−	0.878355i	$-0.658642\pi$
$677$	−24.8749			−0.956019			−0.478010	+	0.878355i	$0.658642\pi$
$678$		0			0
$679$	5.16997	−	8.95465i	0.198405	−	0.343648i
$680$	−1.51160	−	2.61817i	−0.0579672	−	0.100402i
$681$		0			0
$682$	56.8766	−	32.8377i	2.17792	−	1.25742i
$683$	7.90797	−	4.56567i	0.302590	−	0.174701i	−0.341016	−	0.940058i	$-0.610771\pi$
$683$	7.90797	−	4.56567i	0.302590	−	0.174701i	0.643606	+	0.765357i	$0.277438\pi$
$684$		0			0
$685$	−0.368870	−	0.638901i	−0.0140938	−	0.0244112i
$686$	19.4633	−	33.7114i	0.743113	−	1.28711i
$687$		0			0
$688$	−11.3409			−0.432367
$689$	−21.6191	+	7.58641i	−0.823623	+	0.289019i
$690$		0			0
$691$	−28.5679	−	16.4937i	−1.08677	−	0.627449i	−0.154057	−	0.988062i	$-0.549234\pi$
$691$	−28.5679	−	16.4937i	−1.08677	−	0.627449i	−0.932715	+	0.360613i	$0.882567\pi$
$692$	−18.1666	+	31.4655i	−0.690591	+	1.19614i
$693$		0			0
$694$			18.6773i			0.708980i
$695$	−17.1013	+	9.87341i	−0.648688	+	0.374520i
$696$		0			0
$697$		−	7.57072i		−	0.286762i
$698$	20.4164	+	35.3622i	0.772772	+	1.33848i
$699$		0			0
$700$	−4.40510	−	2.54329i	−0.166497	−	0.0961272i
$701$	24.6223			0.929971			0.464985	−	0.885318i	$-0.346060\pi$
$701$	24.6223			0.929971			0.464985	+	0.885318i	$0.346060\pi$
$702$		0			0
$703$	3.51050			0.132401
$704$	24.8281	+	14.3345i	0.935746	+	0.540253i
$705$		0			0
$706$	0.197729	+	0.342477i	0.00744163	+	0.0128893i
$707$		−	2.76552i		−	0.104008i
$708$		0			0
$709$	43.1727	−	24.9258i	1.62138	−	0.936107i	0.634834	−	0.772648i	$-0.281068\pi$
$709$	43.1727	−	24.9258i	1.62138	−	0.936107i	0.986550	−	0.163458i	$-0.0522650\pi$
$710$		−	2.66566i		−	0.100041i
$711$		0			0
$712$	22.2875	−	38.6031i	0.835260	−	1.44671i
$713$	−13.1045	−	7.56591i	−0.490769	−	0.283345i
$714$		0			0
$715$	2.11977	−	11.2580i	0.0792749	−	0.421024i
$716$	−42.4063			−1.58480
$717$		0			0
$718$	−23.5037	+	40.7096i	−0.877151	+	1.51927i
$719$	6.33625	+	10.9747i	0.236302	+	0.409288i	0.959650	−	0.281196i	$-0.0907311\pi$
$719$	6.33625	+	10.9747i	0.236302	+	0.409288i	−0.723348	+	0.690484i	$0.757398\pi$
$720$		0			0
$721$	1.11071	−	0.641266i	0.0413648	−	0.0238820i
$722$	26.7193	−	15.4264i	0.994389	−	0.574111i
$723$		0			0
$724$	−1.48429	−	2.57086i	−0.0551632	−	0.0955454i
$725$	4.18965	−	7.25669i	0.155600	−	0.269507i
$726$		0			0
$727$	26.0757			0.967093			0.483547	−	0.875319i	$-0.339348\pi$
$727$	26.0757			0.967093			0.483547	+	0.875319i	$0.339348\pi$
$728$	16.5168	+	14.1884i	0.612155	+	0.525856i
$729$		0			0
$730$	25.7456	+	14.8642i	0.952886	+	0.550149i
$731$	1.06622	−	1.84675i	0.0394356	−	0.0683045i
$732$		0			0
$733$		−	3.39408i		−	0.125363i	−0.998034	−	0.0626815i	$-0.980035\pi$
$733$		−	3.39408i		−	0.125363i	0.998034	−	0.0626815i	$-0.0199652\pi$
$734$	−4.77555	+	2.75716i	−0.176269	+	0.101769i
$735$		0			0
$736$		−	1.53364i		−	0.0565308i
$737$	20.8977	+	36.1959i	0.769777	+	1.33329i
$738$		0			0
$739$	−5.88277	−	3.39642i	−0.216401	−	0.124939i	0.387882	−	0.921709i	$-0.373207\pi$
$739$	−5.88277	−	3.39642i	−0.216401	−	0.124939i	−0.604283	+	0.796770i	$0.706540\pi$
$740$	−5.46410			−0.200864
$741$		0			0
$742$	−20.0991			−0.737861
$743$	11.8937	+	6.86681i	0.436336	+	0.251919i	0.702042	−	0.712135i	$-0.252272\pi$
$743$	11.8937	+	6.86681i	0.436336	+	0.251919i	−0.265706	+	0.964054i	$0.585605\pi$
$744$		0			0
$745$	1.58275	+	2.74140i	0.0579874	+	0.100437i
$746$		−	28.9975i		−	1.06167i
$747$		0			0
$748$	7.00656	−	4.04524i	0.256185	−	0.147909i
$749$			16.0508i			0.586483i
$750$		0			0
$751$	−20.3873	+	35.3119i	−0.743944	+	1.28855i	0.206742	+	0.978396i	$0.433714\pi$
$751$	−20.3873	+	35.3119i	−0.743944	+	1.28855i	−0.950686	+	0.310154i	$0.899619\pi$
$752$	36.6314	+	21.1491i	1.33581	+	0.771229i
$753$		0			0
$754$	−47.8562	+	55.7099i	−1.74282	+	2.02883i
$755$	0.168843			0.00614481
$756$		0			0
$757$	6.79693	−	11.7726i	0.247039	−	0.427884i	−0.715664	−	0.698445i	$-0.753876\pi$
$757$	6.79693	−	11.7726i	0.247039	−	0.427884i	0.962703	+	0.270561i	$0.0872092\pi$
$758$	14.0025	+	24.2530i	0.508592	+	0.880908i
$759$		0			0
$760$	10.0955	−	5.82862i	0.366201	−	0.211426i
$761$	−8.49411	+	4.90408i	−0.307911	+	0.177773i	−0.645991	−	0.763345i	$-0.723556\pi$
$761$	−8.49411	+	4.90408i	−0.307911	+	0.177773i	0.338080	+	0.941117i	$0.390223\pi$
$762$		0			0
$763$	0.566150	+	0.980601i	0.0204960	+	0.0355001i
$764$	−13.0629	+	22.6256i	−0.472600	+	0.818567i
$765$		0			0
$766$	−33.5720			−1.21301
$767$	−14.0630	+	16.3708i	−0.507784	+	0.591117i
$768$		0			0
$769$	37.4841	+	21.6415i	1.35171	+	0.780411i	0.988489	−	0.151292i	$-0.0483433\pi$
$769$	37.4841	+	21.6415i	1.35171	+	0.780411i	0.363222	+	0.931703i	$0.381677\pi$
$770$	5.02477	−	8.70316i	0.181080	−	0.313640i
$771$		0			0
$772$		−	61.8798i		−	2.22710i
$773$	20.9759	−	12.1104i	0.754449	−	0.435582i	−0.0728499	−	0.997343i	$-0.523209\pi$
$773$	20.9759	−	12.1104i	0.754449	−	0.435582i	0.827299	+	0.561761i	$0.189876\pi$
$774$		0			0
$775$		−	8.50318i		−	0.305443i
$776$	−18.4420	−	31.9425i	−0.662030	−	1.14667i
$777$		0			0
$778$	−29.2705	−	16.8993i	−1.04940	−	0.605870i
$779$	29.1922			1.04592
$780$		0			0
$781$	3.48409			0.124671
$782$	−2.44022	−	1.40886i	−0.0872623	−	0.0503809i
$783$		0			0
$784$	−9.19204	−	15.9211i	−0.328287	−	0.568610i
$785$			13.5512i			0.483661i
$786$		0			0
$787$	9.07378	−	5.23875i	0.323445	−	0.186741i	−0.329482	−	0.944162i	$-0.606874\pi$
$787$	9.07378	−	5.23875i	0.323445	−	0.186741i	0.652927	+	0.757421i	$0.273541\pi$
$788$		−	26.7182i		−	0.951797i
$789$		0			0
$790$	−1.61683	+	2.80043i	−0.0575241	+	0.0996347i
$791$	−17.0166	−	9.82451i	−0.605039	−	0.349319i
$792$		0			0
$793$	35.5206	+	30.5131i	1.26137	+	1.08355i
$794$	−60.7075			−2.15443
$795$		0			0
$796$	33.7035	−	58.3762i	1.19459	−	2.06909i
$797$	−23.1068	−	40.0222i	−0.818486	−	1.41766i	−0.906798	−	0.421566i	$-0.861481\pi$
$797$	−23.1068	−	40.0222i	−0.818486	−	1.41766i	0.0883119	−	0.996093i	$-0.471853\pi$
$798$		0			0
$799$	−6.88785	+	3.97670i	−0.243674	+	0.140686i
$800$	0.746354	−	0.430908i	0.0263876	−	0.0152349i
$801$		0			0
$802$	−11.1109	−	19.2446i	−0.392339	−	0.679550i
$803$	−19.4279	+	33.6501i	−0.685596	+	1.18749i
$804$		0			0
$805$	−2.31545			−0.0816088
$806$	−13.7907	+	73.2413i	−0.485756	+	2.57982i
$807$		0			0
$808$	−8.54336	−	4.93251i	−0.300554	−	0.173525i
$809$	3.60640	−	6.24646i	0.126794	−	0.219614i	−0.795639	−	0.605772i	$-0.792865\pi$
$809$	3.60640	−	6.24646i	0.126794	−	0.219614i	0.922433	+	0.386158i	$0.126198\pi$
$810$		0			0
$811$			44.8652i			1.57543i	0.616040	+	0.787714i	$0.288736\pi$
$811$			44.8652i			1.57543i	−0.616040	+	0.787714i	$0.711264\pi$
$812$	−36.9117	+	21.3110i	−1.29535	+	0.747868i
$813$		0			0
$814$		−	10.7954i		−	0.378380i
$815$	−7.60307	−	13.1689i	−0.266324	−	0.461287i
$816$		0			0
$817$	7.12094	+	4.11128i	0.249130	+	0.143835i
$818$	59.3550			2.07530
$819$		0			0
$820$	−45.4377			−1.58675
$821$	−39.5195	−	22.8166i	−1.37924	−	0.796304i	−0.387171	−	0.922008i	$-0.626548\pi$
$821$	−39.5195	−	22.8166i	−1.37924	−	0.796304i	−0.992068	+	0.125704i	$0.959881\pi$
$822$		0			0
$823$	−6.96523	−	12.0641i	−0.242793	−	0.420529i	0.718716	−	0.695304i	$-0.244730\pi$
$823$	−6.96523	−	12.0641i	−0.242793	−	0.420529i	−0.961509	+	0.274775i	$0.911397\pi$
$824$		−	4.57498i		−	0.159377i
$825$		0			0
$826$	−16.3960	+	9.46626i	−0.570491	+	0.329373i
$827$		−	17.8737i		−	0.621530i	−0.950487	−	0.310765i	$-0.899415\pi$
$827$		−	17.8737i		−	0.621530i	0.950487	−	0.310765i	$-0.100585\pi$
$828$		0			0
$829$	−17.7236	+	30.6981i	−0.615565	+	1.06619i	0.374721	+	0.927138i	$0.377739\pi$
$829$	−17.7236	+	30.6981i	−0.615565	+	1.06619i	−0.990285	+	0.139051i	$0.955595\pi$
$830$	30.0350	+	17.3407i	1.04253	+	0.601904i
$831$		0			0
$832$	−30.6984	+	10.7724i	−1.06427	+	0.373467i
$833$	3.45678			0.119770
$834$		0			0
$835$	3.73793	−	6.47429i	0.129357	−	0.224052i
$836$	15.5982	+	27.0168i	0.539474	+	0.934397i
$837$		0			0
$838$	−14.6824	+	8.47690i	−0.507196	+	0.292830i
$839$	6.08860	−	3.51526i	0.210202	−	0.121360i	−0.391203	−	0.920304i	$-0.627941\pi$
$839$	6.08860	−	3.51526i	0.210202	−	0.121360i	0.601405	+	0.798944i	$0.294608\pi$
$840$		0			0
$841$	−20.6063	−	35.6912i	−0.710563	−	1.23073i
$842$	−0.818215	+	1.41719i	−0.0281975	+	0.0488396i
$843$		0			0
$844$	93.0933			3.20440
$845$	8.12340	+	10.1494i	0.279454	+	0.349150i
$846$		0			0
$847$	−1.01978	−	0.588771i	−0.0350401	−	0.0202304i
$848$	−11.0064	+	19.0636i	−0.377960	+	0.654646i
$849$		0			0
$850$		−	1.58340i		−	0.0543100i
$851$	−2.15406	+	1.24365i	−0.0738404	+	0.0426318i
$852$		0			0
$853$		−	25.7138i		−	0.880425i	−0.897894	−	0.440212i	$-0.854903\pi$
$853$		−	25.7138i		−	0.880425i	0.897894	−	0.440212i	$-0.145097\pi$
$854$	20.5394	+	35.5753i	0.702844	+	1.21736i
$855$		0			0
$856$	49.5847	+	28.6277i	1.69477	+	0.978476i
$857$	20.7578			0.709072			0.354536	−	0.935042i	$-0.384639\pi$
$857$	20.7578			0.709072			0.354536	+	0.935042i	$0.384639\pi$
$858$		0			0
$859$	−9.79466			−0.334190			−0.167095	−	0.985941i	$-0.553439\pi$
$859$	−9.79466			−0.334190			−0.167095	+	0.985941i	$0.553439\pi$
$860$	−11.0838	−	6.39922i	−0.377954	−	0.218212i
$861$		0			0
$862$	34.0702	+	59.0113i	1.16044	+	2.00993i
$863$			23.1995i			0.789720i	0.918741	+	0.394860i	$0.129207\pi$
$863$			23.1995i			0.789720i	−0.918741	+	0.394860i	$0.870793\pi$
$864$		0			0
$865$	−8.04886	+	4.64701i	−0.273669	+	0.158003i
$866$		−	6.48161i		−	0.220254i
$867$		0			0
$868$	−21.6260	+	37.4574i	−0.734035	+	1.27139i
$869$	−3.66023	−	2.11324i	−0.124165	−	0.0716866i
$870$		0			0
$871$	−46.6103	−	8.77629i	−1.57933	−	0.297373i
$872$	4.03908			0.136780
$873$		0			0
$874$	5.43248	−	9.40934i	0.183757	−	0.318276i
$875$	−0.650571	−	1.12682i	−0.0219933	−	0.0380936i
$876$		0			0
$877$	−49.7414	+	28.7182i	−1.67965	+	0.969745i	−0.717765	+	0.696285i	$0.754835\pi$
$877$	−49.7414	+	28.7182i	−1.67965	+	0.969745i	−0.961883	+	0.273460i	$0.911832\pi$
$878$	−46.4706	+	26.8298i	−1.56831	+	0.905462i
$879$		0			0
$880$	−5.50318	−	9.53179i	−0.185512	−	0.321316i
$881$	−10.4314	+	18.0677i	−0.351442	+	0.608716i	−0.986502	−	0.163747i	$-0.947642\pi$
$881$	−10.4314	+	18.0677i	−0.351442	+	0.608716i	0.635060	+	0.772463i	$0.280975\pi$
$882$		0			0
$883$	39.9752			1.34527			0.672637	−	0.739973i	$-0.265162\pi$
$883$	39.9752			1.34527			0.672637	+	0.739973i	$0.265162\pi$
$884$	−1.69886	+	9.02252i	−0.0571387	+	0.303460i
$885$		0			0
$886$	30.9314	+	17.8583i	1.03916	+	0.599961i
$887$	4.85794	−	8.41420i	0.163114	−	0.282521i	−0.772870	−	0.634564i	$-0.781180\pi$
$887$	4.85794	−	8.41420i	0.163114	−	0.282521i	0.935984	+	0.352043i	$0.114513\pi$
$888$		0			0
$889$			3.76851i			0.126392i
$890$	20.2183	−	11.6731i	0.677720	−	0.391282i
$891$		0			0
$892$		−	42.2027i		−	1.41305i
$893$	−15.3339	−	26.5591i	−0.513129	−	0.888765i
$894$		0			0
$895$	−9.39422	−	5.42376i	−0.314014	−	0.181296i
$896$	−26.2973			−0.878531
$897$		0			0
$898$	−13.7036			−0.457296
$899$	−61.7049	−	35.6253i	−2.05797	−	1.18817i
$900$		0			0
$901$	−2.06954	−	3.58455i	−0.0689464	−	0.119419i
$902$		−	89.7714i		−	2.98906i
$903$		0			0
$904$	−60.7005	+	35.0454i	−2.01887	+	1.16559i
$905$		−	0.759361i		−	0.0252420i
$906$		0			0
$907$	4.94812	−	8.57040i	0.164300	−	0.284576i	−0.772107	−	0.635493i	$-0.780797\pi$
$907$	4.94812	−	8.57040i	0.164300	−	0.284576i	0.936406	+	0.350917i	$0.114130\pi$
$908$	35.7286	+	20.6279i	1.18569	+	0.684561i
$909$		0			0
$910$	3.77613	+	10.7609i	0.125177	+	0.356720i
$911$	48.9981			1.62338			0.811690	−	0.584088i	$-0.198548\pi$
$911$	48.9981			1.62338			0.811690	+	0.584088i	$0.198548\pi$
$912$		0			0
$913$	−22.6648	+	39.2565i	−0.750094	+	1.29920i
$914$	6.16628	+	10.6803i	0.203962	+	0.353273i
$915$		0			0
$916$	51.8831	−	29.9547i	1.71427	−	0.989733i
$917$	−17.7554	+	10.2511i	−0.586334	+	0.338520i
$918$		0			0
$919$	−2.80648	−	4.86096i	−0.0925771	−	0.160348i	0.816018	−	0.578027i	$-0.196177\pi$
$919$	−2.80648	−	4.86096i	−0.0925771	−	0.160348i	−0.908595	+	0.417679i	$0.862844\pi$
$920$	−4.12976	+	7.15296i	−0.136154	+	0.235826i
$921$		0			0
$922$	80.4370			2.64905
$923$	−2.57632	+	2.99911i	−0.0848005	+	0.0987170i
$924$		0			0
$925$	−1.21046	−	0.698857i	−0.0397995	−	0.0229783i
$926$	−29.7757	+	51.5731i	−0.978492	+	1.69480i
$927$		0			0
$928$		−	7.22141i		−	0.237054i
$929$	0.661356	−	0.381834i	0.0216984	−	0.0125276i	−0.489112	−	0.872221i	$-0.662679\pi$
$929$	0.661356	−	0.381834i	0.0216984	−	0.0125276i	0.510810	+	0.859694i	$0.329346\pi$
$930$		0			0
$931$			13.3291i			0.436844i
$932$	−19.4702	−	33.7233i	−0.637767	−	1.10464i
$933$		0			0
$934$	−64.4057	−	37.1847i	−2.10742	−	1.21672i
$935$	2.06954			0.0676812
$936$		0			0
$937$	−23.8968			−0.780674			−0.390337	−	0.920672i	$-0.627641\pi$
$937$	−23.8968			−0.780674			−0.390337	+	0.920672i	$0.627641\pi$
$938$	−36.0329	−	20.8036i	−1.17652	−	0.679263i
$939$		0			0
$940$	23.8672	+	41.3393i	0.778464	+	1.34834i
$941$			5.76615i			0.187971i	0.995574	+	0.0939856i	$0.0299608\pi$
$941$			5.76615i			0.187971i	−0.995574	+	0.0939856i	$0.970039\pi$
$942$		0			0
$943$	−17.9125	+	10.3418i	−0.583312	+	0.336775i
$944$			20.7351i			0.674869i
$945$		0			0
$946$	12.6429	−	21.8982i	0.411057	−	0.711972i
$947$	−28.3284	−	16.3554i	−0.920549	−	0.531479i	−0.0367391	−	0.999325i	$-0.511697\pi$
$947$	−28.3284	−	16.3554i	−0.920549	−	0.531479i	−0.883810	+	0.467845i	$0.845030\pi$
$948$		0			0
$949$	−14.6001	−	41.6062i	−0.473940	−	1.35059i
$950$	6.10547			0.198087
$951$		0			0
$952$	−1.96681	+	3.40661i	−0.0637446	+	0.110409i
$953$	−21.7005	−	37.5863i	−0.702947	−	1.21754i	−0.967427	−	0.253148i	$-0.918534\pi$
$953$	−21.7005	−	37.5863i	−0.702947	−	1.21754i	0.264481	−	0.964391i	$-0.414799\pi$
$954$		0			0
$955$	−5.78763	+	3.34149i	−0.187283	+	0.108128i
$956$	8.39614	−	4.84751i	0.271550	−	0.156780i
$957$		0			0
$958$	16.9167	+	29.3006i	0.546554	+	0.946659i
$959$	−0.479952	+	0.831302i	−0.0154985	+	0.0268441i
$960$		0			0
$961$	−41.3041			−1.33239
$962$	9.29272	+	7.98269i	0.299609	+	0.257372i
$963$		0			0
$964$	96.4032	+	55.6584i	3.10494	+	1.79264i
$965$	7.91441	−	13.7082i	0.254774	−	0.441281i
$966$		0			0
$967$			43.6204i			1.40274i	0.712798	+	0.701369i	$0.247427\pi$
$967$			43.6204i			1.40274i	−0.712798	+	0.701369i	$0.752573\pi$
$968$	−3.63770	+	2.10023i	−0.116920	+	0.0675039i
$969$		0			0
$970$		−	19.3180i		−	0.620263i
$971$	18.5097	+	32.0598i	0.594005	+	1.02885i	0.993686	+	0.112193i	$0.0357874\pi$
$971$	18.5097	+	32.0598i	0.594005	+	1.02885i	−0.399682	+	0.916654i	$0.630879\pi$
$972$		0			0
$973$	22.2512	+	12.8467i	0.713340	+	0.411847i
$974$	74.2682			2.37971
$975$		0			0
$976$	44.9899			1.44009
$977$	−21.7180	−	12.5389i	−0.694821	−	0.401155i	0.110594	−	0.993866i	$-0.464725\pi$
$977$	−21.7180	−	12.5389i	−0.694821	−	0.401155i	−0.805416	+	0.592710i	$0.798058\pi$
$978$		0			0
$979$	15.2570	+	26.4259i	0.487616	+	0.844575i
$980$		−	20.7468i		−	0.662733i
$981$		0			0
$982$	−30.9137	+	17.8481i	−0.986497	+	0.569554i
$983$			21.0019i			0.669857i	0.942244	+	0.334928i	$0.108712\pi$
$983$			21.0019i			0.669857i	−0.942244	+	0.334928i	$0.891288\pi$
$984$		0			0
$985$	3.41725	−	5.91886i	0.108883	−	0.188590i
$986$	−11.4902	−	6.63387i	−0.365923	−	0.211266i
$987$		0			0
$988$	−34.7902	−	6.55068i	−1.10682	−	0.208405i
$989$	−5.82594			−0.185254
$990$		0			0
$991$	−1.51944	+	2.63175i	−0.0482666	+	0.0836003i	−0.889149	−	0.457617i	$-0.848703\pi$
$991$	−1.51944	+	2.63175i	−0.0482666	+	0.0836003i	0.840883	+	0.541217i	$0.182036\pi$
$992$	−3.66409	−	6.34638i	−0.116335	−	0.201498i
$993$		0			0
$994$	−3.00373	+	1.73420i	−0.0952725	+	0.0550056i
$995$	14.9326	−	8.62135i	0.473396	−	0.273315i
$996$		0			0
$997$	−5.15872	−	8.93516i	−0.163378	−	0.282979i	0.772700	−	0.634771i	$-0.218906\pi$
$997$	−5.15872	−	8.93516i	−0.163378	−	0.282979i	−0.936078	+	0.351792i	$0.885572\pi$
$998$	−19.6282	+	33.9970i	−0.621319	+	1.07616i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bu.b.316.1		8
3.2	odd	2		195.2.bb.c.121.4	✓	8
13.6	odd	12		7605.2.a.ck.1.4		4
13.7	odd	12		7605.2.a.cg.1.1		4
13.10	even	6	inner	585.2.bu.b.361.1		8
15.2	even	4		975.2.w.g.199.1		8
15.8	even	4		975.2.w.j.199.4		8
15.14	odd	2		975.2.bc.i.901.1		8
39.20	even	12		2535.2.a.bl.1.4		4
39.23	odd	6		195.2.bb.c.166.4	yes	8
39.32	even	12		2535.2.a.bi.1.1		4
195.23	even	12		975.2.w.g.49.1		8
195.62	even	12		975.2.w.j.49.4		8
195.179	odd	6		975.2.bc.i.751.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bb.c.121.4	✓	8	3.2	odd	2
195.2.bb.c.166.4	yes	8	39.23	odd	6
585.2.bu.b.316.1		8	1.1	even	1	trivial
585.2.bu.b.361.1		8	13.10	even	6	inner
975.2.w.g.49.1		8	195.23	even	12
975.2.w.g.199.1		8	15.2	even	4
975.2.w.j.49.4		8	195.62	even	12
975.2.w.j.199.4		8	15.8	even	4
975.2.bc.i.751.1		8	195.179	odd	6
975.2.bc.i.901.1		8	15.14	odd	2
2535.2.a.bi.1.1		4	39.32	even	12
2535.2.a.bl.1.4		4	39.20	even	12
7605.2.a.cg.1.1		4	13.7	odd	12
7605.2.a.ck.1.4		4	13.6	odd	12

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bu (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.10523 - 1.21545i) q^{2} +(1.95466 + 3.38556i) q^{4} +1.00000i q^{5} +(1.12682 - 0.650571i) q^{7} -4.64136i q^{8} +(1.21545 - 2.10523i) q^{10} +(2.75159 + 1.58863i) q^{11} +(-3.40216 + 1.19386i) q^{13} -3.16296 q^{14} +(-1.73205 + 3.00000i) q^{16} +(-0.325680 - 0.564094i) q^{17} +(2.17511 - 1.25580i) q^{19} +(-3.38556 + 1.95466i) q^{20} +(-3.86182 - 6.68886i) q^{22} +(-0.889774 + 1.54113i) q^{23} -1.00000 q^{25} +(8.61341 + 1.62182i) q^{26} +(4.40510 + 2.54329i) q^{28} +(-4.18965 + 7.25669i) q^{29} +8.50318i q^{31} +(-0.746354 + 0.430908i) q^{32} +1.58340i q^{34} +(0.650571 + 1.12682i) q^{35} +(1.21046 + 0.698857i) q^{37} -6.10547 q^{38} +4.64136 q^{40} +(10.0658 + 5.81147i) q^{41} +(1.63692 + 2.83522i) q^{43} +12.4209i q^{44} +(3.74635 - 2.16296i) q^{46} -12.2105i q^{47} +(-2.65351 + 4.59602i) q^{49} +(2.10523 + 1.21545i) q^{50} +(-10.6919 - 9.18465i) q^{52} +6.35452 q^{53} +(-1.58863 + 2.75159i) q^{55} +(-3.01954 - 5.22999i) q^{56} +(17.6403 - 10.1847i) q^{58} +(5.18377 - 2.99285i) q^{59} +(-6.49373 - 11.2475i) q^{61} +(10.3352 - 17.9011i) q^{62} +9.02320 q^{64} +(-1.19386 - 3.40216i) q^{65} +(11.3922 + 6.57727i) q^{67} +(1.27318 - 2.20522i) q^{68} -3.16296i q^{70} +(0.949658 - 0.548286i) q^{71} +12.2293i q^{73} +(-1.69886 - 2.94251i) q^{74} +(8.50318 + 4.90931i) q^{76} +4.13407 q^{77} -1.33022 q^{79} +(-3.00000 - 1.73205i) q^{80} +(-14.1272 - 24.4690i) q^{82} +14.2668i q^{83} +(0.564094 - 0.325680i) q^{85} -7.95839i q^{86} +(7.37341 - 12.7711i) q^{88} +(8.31719 + 4.80193i) q^{89} +(-3.05694 + 3.55862i) q^{91} -6.95681 q^{92} +(-14.8412 + 25.7058i) q^{94} +(1.25580 + 2.17511i) q^{95} +(6.88214 - 3.97341i) q^{97} +(11.1725 - 6.45045i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{2} + 4 q^{4} + 6 q^{7} + 2 q^{10} - 12 q^{11} + 6 q^{13} + 4 q^{14} + 2 q^{17} + 12 q^{19} - 4 q^{23} - 8 q^{25} + 4 q^{26} - 12 q^{28} + 6 q^{29} - 12 q^{32} + 6 q^{35} - 12 q^{37} + 16 q^{38}+ \cdots + 12 q^{98}+O(q^{100}) \) 8 * q - 6 * q^2 + 4 * q^4 + 6 * q^7 + 2 * q^10 - 12 * q^11 + 6 * q^13 + 4 * q^14 + 2 * q^17 + 12 * q^19 - 4 * q^23 - 8 * q^25 + 4 * q^26 - 12 * q^28 + 6 * q^29 - 12 * q^32 + 6 * q^35 - 12 * q^37 + 16 * q^38 + 30 * q^41 + 6 * q^43 + 36 * q^46 - 8 * q^49 + 6 * q^50 - 20 * q^52 + 32 * q^53 - 8 * q^55 - 4 * q^56 + 12 * q^58 + 30 * q^59 + 30 * q^62 + 32 * q^64 + 6 * q^65 + 30 * q^67 - 16 * q^68 - 18 * q^71 - 12 * q^74 + 8 * q^77 + 56 * q^79 - 24 * q^80 - 24 * q^82 + 6 * q^85 + 8 * q^88 + 18 * q^89 - 16 * q^91 - 40 * q^92 - 16 * q^94 - 6 * q^97 + 12 * q^98

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