LMFDB - Embedded newform 513.2.h.c.334.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [513,2,Mod(235,513)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(513, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("513.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 513 = 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	513.h (of order $3$, degree $2$, 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:	$4.09632562369$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 171)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			334.3
Character	$\chi$	$=$	513.334
Dual form			513.2.h.c.235.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.95703 q^{2} +1.82996 q^{4} +(-0.0981173 - 0.169944i) q^{5} +(-2.23368 - 3.86885i) q^{7} +0.332766 q^{8} +O(q^{10})$	\(q-1.95703 q^{2} +1.82996 q^{4} +(-0.0981173 - 0.169944i) q^{5} +(-2.23368 - 3.86885i) q^{7} +0.332766 q^{8} +(0.192018 + 0.332586i) q^{10} +(-0.0755474 - 0.130852i) q^{11} +0.469111 q^{13} +(4.37138 + 7.57146i) q^{14} -4.31116 q^{16} +(-0.441434 + 0.764587i) q^{17} +(-0.132216 + 4.35689i) q^{19} +(-0.179551 - 0.310992i) q^{20} +(0.147849 + 0.256081i) q^{22} -5.15262 q^{23} +(2.48075 - 4.29678i) q^{25} -0.918063 q^{26} +(-4.08756 - 7.07986i) q^{28} +(-0.789052 + 1.36668i) q^{29} +(-1.37848 + 2.38759i) q^{31} +7.77154 q^{32} +(0.863900 - 1.49632i) q^{34} +(-0.438326 + 0.759203i) q^{35} -1.36950 q^{37} +(0.258751 - 8.52657i) q^{38} +(-0.0326501 - 0.0565516i) q^{40} +(-4.06669 - 7.04371i) q^{41} -8.19186 q^{43} +(-0.138249 - 0.239454i) q^{44} +10.0838 q^{46} +(-5.94010 + 10.2886i) q^{47} +(-6.47868 + 11.2214i) q^{49} +(-4.85489 + 8.40892i) q^{50} +0.858455 q^{52} +(-5.86701 - 10.1620i) q^{53} +(-0.0148250 + 0.0256777i) q^{55} +(-0.743293 - 1.28742i) q^{56} +(1.54420 - 2.67463i) q^{58} +(0.794340 + 1.37584i) q^{59} +(-4.56765 + 7.91140i) q^{61} +(2.69772 - 4.67258i) q^{62} -6.58680 q^{64} +(-0.0460278 - 0.0797226i) q^{65} -12.9376 q^{67} +(-0.807809 + 1.39917i) q^{68} +(0.857816 - 1.48578i) q^{70} +(-3.90988 + 6.77211i) q^{71} +(5.72527 - 9.91646i) q^{73} +2.68016 q^{74} +(-0.241951 + 7.97296i) q^{76} +(-0.337498 + 0.584564i) q^{77} -1.92868 q^{79} +(0.422999 + 0.732656i) q^{80} +(7.95863 + 13.7848i) q^{82} +(1.40773 + 2.43826i) q^{83} +0.173249 q^{85} +16.0317 q^{86} +(-0.0251396 - 0.0435430i) q^{88} +(-4.84774 - 8.39654i) q^{89} +(-1.04784 - 1.81492i) q^{91} -9.42910 q^{92} +(11.6250 - 20.1350i) q^{94} +(0.753401 - 0.405017i) q^{95} +15.2269 q^{97} +(12.6790 - 21.9606i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 34 q^{4} - 3 q^{5} + q^{7} + 36 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 34 * q^4 - 3 * q^5 + q^7 + 36 * q^8	$ 32 q + 2 q^{2} + 34 q^{4} - 3 q^{5} + q^{7} + 36 q^{8} - 8 q^{10} - 7 q^{11} + 8 q^{13} - q^{14} + 22 q^{16} + 7 q^{17} + 7 q^{19} + 3 q^{20} - 8 q^{22} + 10 q^{23} - 9 q^{25} + 4 q^{26} - 10 q^{28} - 10 q^{29} - 10 q^{31} + 34 q^{32} - 13 q^{34} + 3 q^{35} + 2 q^{37} + 46 q^{38} + 12 q^{40} - 6 q^{41} - 14 q^{43} - 20 q^{44} + 9 q^{47} - 13 q^{49} - q^{50} - 38 q^{52} - 16 q^{53} + 15 q^{55} + 6 q^{56} - 37 q^{59} - 12 q^{61} - 54 q^{62} - 64 q^{64} - 54 q^{65} + 22 q^{67} + 2 q^{68} + 24 q^{70} - 9 q^{71} - 10 q^{73} + 12 q^{74} - 40 q^{76} - 46 q^{77} + 16 q^{79} + 24 q^{80} + 7 q^{82} - 3 q^{83} + 54 q^{85} + 34 q^{86} + 9 q^{88} - 30 q^{89} - q^{91} - 34 q^{92} - 18 q^{94} - 3 q^{95} - 18 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 + 34 * q^4 - 3 * q^5 + q^7 + 36 * q^8 - 8 * q^10 - 7 * q^11 + 8 * q^13 - q^14 + 22 * q^16 + 7 * q^17 + 7 * q^19 + 3 * q^20 - 8 * q^22 + 10 * q^23 - 9 * q^25 + 4 * q^26 - 10 * q^28 - 10 * q^29 - 10 * q^31 + 34 * q^32 - 13 * q^34 + 3 * q^35 + 2 * q^37 + 46 * q^38 + 12 * q^40 - 6 * q^41 - 14 * q^43 - 20 * q^44 + 9 * q^47 - 13 * q^49 - q^50 - 38 * q^52 - 16 * q^53 + 15 * q^55 + 6 * q^56 - 37 * q^59 - 12 * q^61 - 54 * q^62 - 64 * q^64 - 54 * q^65 + 22 * q^67 + 2 * q^68 + 24 * q^70 - 9 * q^71 - 10 * q^73 + 12 * q^74 - 40 * q^76 - 46 * q^77 + 16 * q^79 + 24 * q^80 + 7 * q^82 - 3 * q^83 + 54 * q^85 + 34 * q^86 + 9 * q^88 - 30 * q^89 - q^91 - 34 * q^92 - 18 * q^94 - 3 * q^95 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/513\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.95703			−1.38383			−0.691914	−	0.721980i	$-0.743232\pi$
$2$	−1.95703			−1.38383			−0.691914	+	0.721980i	$0.743232\pi$
$3$		0			0
$3$		0			0
$4$	1.82996			0.914982
$5$	−0.0981173	−	0.169944i	−0.0438794	−	0.0760013i	0.843252	−	0.537519i	$-0.180638\pi$
$5$	−0.0981173	−	0.169944i	−0.0438794	−	0.0760013i	−0.887131	+	0.461518i	$0.847305\pi$
$6$		0			0
$7$	−2.23368	−	3.86885i	−0.844253	−	1.46229i	−0.886268	−	0.463172i	$-0.846711\pi$
$7$	−2.23368	−	3.86885i	−0.844253	−	1.46229i	0.0420154	−	0.999117i	$-0.486622\pi$
$8$	0.332766			0.117650
$9$		0			0
$10$	0.192018	+	0.332586i	0.0607215	+	0.105173i
$11$	−0.0755474	−	0.130852i	−0.0227784	−	0.0394534i	0.854412	−	0.519597i	$-0.173918\pi$
$11$	−0.0755474	−	0.130852i	−0.0227784	−	0.0394534i	−0.877190	+	0.480144i	$0.840585\pi$
$12$		0			0
$13$	0.469111			0.130108			0.0650539	−	0.997882i	$-0.479278\pi$
$13$	0.469111			0.130108			0.0650539	+	0.997882i	$0.479278\pi$
$14$	4.37138	+	7.57146i	1.16830	+	2.02356i
$15$		0			0
$16$	−4.31116			−1.07779
$17$	−0.441434	+	0.764587i	−0.107064	+	0.185440i	−0.914579	−	0.404406i	$-0.867478\pi$
$17$	−0.441434	+	0.764587i	−0.107064	+	0.185440i	0.807516	+	0.589846i	$0.200812\pi$
$18$		0			0
$19$	−0.132216	+	4.35689i	−0.0303325	+	0.999540i
$19$	−0.132216	+	4.35689i	−0.0303325	+	0.999540i
$20$	−0.179551	−	0.310992i	−0.0401488	−	0.0695398i
$21$		0			0
$22$	0.147849	+	0.256081i	0.0315214	+	0.0545967i
$23$	−5.15262			−1.07439			−0.537197	−	0.843457i	$-0.680517\pi$
$23$	−5.15262			−1.07439			−0.537197	+	0.843457i	$0.680517\pi$
$24$		0			0
$25$	2.48075	−	4.29678i	0.496149	−	0.859356i
$26$	−0.918063			−0.180047
$27$		0			0
$28$	−4.08756	−	7.07986i	−0.772476	−	1.33797i
$29$	−0.789052	+	1.36668i	−0.146523	+	0.253786i	−0.929940	−	0.367711i	$-0.880142\pi$
$29$	−0.789052	+	1.36668i	−0.146523	+	0.253786i	0.783417	+	0.621497i	$0.213475\pi$
$30$		0			0
$31$	−1.37848	+	2.38759i	−0.247582	+	0.428824i	−0.962854	−	0.270022i	$-0.912969\pi$
$31$	−1.37848	+	2.38759i	−0.247582	+	0.428824i	0.715273	+	0.698845i	$0.246302\pi$
$32$	7.77154			1.37383
$33$		0			0
$34$	0.863900	−	1.49632i	0.148158	−	0.256617i
$35$	−0.438326	+	0.759203i	−0.0740906	+	0.128329i
$36$		0			0
$37$	−1.36950			−0.225145			−0.112572	−	0.993644i	$-0.535909\pi$
$37$	−1.36950			−0.225145			−0.112572	+	0.993644i	$0.535909\pi$
$38$	0.258751	−	8.52657i	0.0419749	−	1.38319i
$39$		0			0
$40$	−0.0326501	−	0.0565516i	−0.00516243	−	0.00894159i
$41$	−4.06669	−	7.04371i	−0.635110	−	1.10004i	−0.986492	−	0.163811i	$-0.947621\pi$
$41$	−4.06669	−	7.04371i	−0.635110	−	1.10004i	0.351382	−	0.936232i	$-0.385712\pi$
$42$		0			0
$43$	−8.19186			−1.24925			−0.624623	−	0.780926i	$-0.714747\pi$
$43$	−8.19186			−1.24925			−0.624623	+	0.780926i	$0.714747\pi$
$44$	−0.138249	−	0.239454i	−0.0208418	−	0.0360991i
$45$		0			0
$46$	10.0838			1.48678
$47$	−5.94010	+	10.2886i	−0.866453	+	1.50074i	−0.000855324		1.00000i	$0.500272\pi$
$47$	−5.94010	+	10.2886i	−0.866453	+	1.50074i	−0.865597	+	0.500741i	$0.833061\pi$
$48$		0			0
$49$	−6.47868	+	11.2214i	−0.925526	+	1.60306i
$50$	−4.85489	+	8.40892i	−0.686586	+	1.18920i
$51$		0			0
$52$	0.858455			0.119046
$53$	−5.86701	−	10.1620i	−0.805895	−	1.39585i	−0.915685	−	0.401897i	$-0.868351\pi$
$53$	−5.86701	−	10.1620i	−0.805895	−	1.39585i	0.109790	−	0.993955i	$-0.464982\pi$
$54$		0			0
$55$	−0.0148250	+	0.0256777i	−0.00199900	+	0.00346238i
$56$	−0.743293	−	1.28742i	−0.0993267	−	0.172039i
$57$		0			0
$58$	1.54420	−	2.67463i	0.202763	−	0.351196i
$59$	0.794340	+	1.37584i	0.103414	+	0.179119i	0.913089	−	0.407760i	$-0.133690\pi$
$59$	0.794340	+	1.37584i	0.103414	+	0.179119i	−0.809675	+	0.586879i	$0.800357\pi$
$60$		0			0
$61$	−4.56765	+	7.91140i	−0.584828	+	1.01295i	0.410069	+	0.912054i	$0.365505\pi$
$61$	−4.56765	+	7.91140i	−0.584828	+	1.01295i	−0.994897	+	0.100897i	$0.967829\pi$
$62$	2.69772	−	4.67258i	0.342610	−	0.593419i
$63$		0			0
$64$	−6.58680			−0.823350
$65$	−0.0460278	−	0.0797226i	−0.00570905	−	0.00988837i
$66$		0			0
$67$	−12.9376			−1.58058			−0.790289	−	0.612734i	$-0.790070\pi$
$67$	−12.9376			−1.58058			−0.790289	+	0.612734i	$0.790070\pi$
$68$	−0.807809	+	1.39917i	−0.0979612	+	0.169674i
$69$		0			0
$70$	0.857816	−	1.48578i	0.102529	−	0.177585i
$71$	−3.90988	+	6.77211i	−0.464017	+	0.803702i	−0.999157	−	0.0410621i	$-0.986926\pi$
$71$	−3.90988	+	6.77211i	−0.464017	+	0.803702i	0.535139	+	0.844764i	$0.320259\pi$
$72$		0			0
$73$	5.72527	−	9.91646i	0.670092	−	1.16063i	−0.307785	−	0.951456i	$-0.599588\pi$
$73$	5.72527	−	9.91646i	0.670092	−	1.16063i	0.977878	−	0.209178i	$-0.0670788\pi$
$74$	2.68016			0.311562
$75$		0			0
$76$	−0.241951	+	7.97296i	−0.0277537	+	0.914561i
$77$	−0.337498	+	0.584564i	−0.0384615	+	0.0666172i
$78$		0			0
$79$	−1.92868			−0.216994			−0.108497	−	0.994097i	$-0.534604\pi$
$79$	−1.92868			−0.216994			−0.108497	+	0.994097i	$0.534604\pi$
$80$	0.422999	+	0.732656i	0.0472928	+	0.0819134i
$81$		0			0
$82$	7.95863	+	13.7848i	0.878884	+	1.52227i
$83$	1.40773	+	2.43826i	0.154518	+	0.267633i	0.932884	−	0.360178i	$-0.117284\pi$
$83$	1.40773	+	2.43826i	0.154518	+	0.267633i	−0.778365	+	0.627812i	$0.783951\pi$
$84$		0			0
$85$	0.173249			0.0187915
$86$	16.0317			1.72874
$87$		0			0
$88$	−0.0251396	−	0.0435430i	−0.00267989	−	0.00464170i
$89$	−4.84774	−	8.39654i	−0.513860	−	0.890031i	−0.999871	−	0.0160786i	$-0.994882\pi$
$89$	−4.84774	−	8.39654i	−0.513860	−	0.890031i	0.486011	−	0.873953i	$-0.338452\pi$
$90$		0			0
$91$	−1.04784	−	1.81492i	−0.109844	−	0.190255i
$92$	−9.42910			−0.983052
$93$		0			0
$94$	11.6250	−	20.1350i	1.19902	−	2.07677i
$95$	0.753401	−	0.405017i	0.0772973	−	0.0415539i
$96$		0			0
$97$	15.2269			1.54605			0.773026	−	0.634374i	$-0.218742\pi$
$97$	15.2269			1.54605			0.773026	+	0.634374i	$0.218742\pi$
$98$	12.6790	−	21.9606i	1.28077	−	2.21836i
$99$		0			0
$100$	4.53968	−	7.86295i	0.453968	−	0.786295i
$101$	−7.34668	+	12.7248i	−0.731022	+	1.26617i	0.225424	+	0.974261i	$0.427623\pi$
$101$	−7.34668	+	12.7248i	−0.731022	+	1.26617i	−0.956447	+	0.291907i	$0.905710\pi$
$102$		0			0
$103$	5.86742	−	10.1627i	0.578134	−	1.00136i	−0.417560	−	0.908650i	$-0.637114\pi$
$103$	5.86742	−	10.1627i	0.578134	−	1.00136i	0.995693	−	0.0927076i	$-0.0295522\pi$
$104$	0.156104			0.0153072
$105$		0			0
$106$	11.4819	+	19.8872i	1.11522	+	1.93162i
$107$	7.10478			0.686845			0.343422	−	0.939181i	$-0.388414\pi$
$107$	7.10478			0.686845			0.343422	+	0.939181i	$0.388414\pi$
$108$		0			0
$109$	−5.92520	+	10.2627i	−0.567531	+	0.982992i	0.429278	+	0.903172i	$0.358768\pi$
$109$	−5.92520	+	10.2627i	−0.567531	+	0.982992i	−0.996809	+	0.0798200i	$0.974565\pi$
$110$	0.0290130	−	0.0502520i	0.00276628	−	0.00479134i
$111$		0			0
$112$	9.62977	+	16.6792i	0.909927	+	1.57604i
$113$	4.99898	−	8.65848i	0.470264	−	0.814521i	−0.529158	−	0.848524i	$-0.677492\pi$
$113$	4.99898	−	8.65848i	0.470264	−	0.814521i	0.999422	+	0.0340022i	$0.0108253\pi$
$114$		0			0
$115$	0.505561	+	0.875656i	0.0471438	+	0.0816554i
$116$	−1.44394	+	2.50097i	−0.134066	+	0.232209i
$117$		0			0
$118$	−1.55455	−	2.69255i	−0.143108	−	0.247870i
$119$	3.94410			0.361555
$120$		0			0
$121$	5.48859	−	9.50651i	0.498962	−	0.864228i
$122$	8.93903	−	15.4828i	0.809301	−	1.40175i
$123$		0			0
$124$	−2.52256	+	4.36920i	−0.226533	+	0.392366i
$125$	−1.95479			−0.174842
$126$		0			0
$127$	1.43057	+	2.47782i	0.126943	+	0.219871i	0.922491	−	0.386020i	$-0.126150\pi$
$127$	1.43057	+	2.47782i	0.126943	+	0.219871i	−0.795548	+	0.605891i	$0.792817\pi$
$128$	−2.65250			−0.234451
$129$		0			0
$130$	0.0900778	+	0.156019i	0.00790035	+	0.0136838i
$131$	1.35114	+	2.34025i	0.118050	+	0.204468i	0.918995	−	0.394270i	$-0.129002\pi$
$131$	1.35114	+	2.34025i	0.118050	+	0.204468i	−0.800945	+	0.598738i	$0.795669\pi$
$132$		0			0
$133$	17.1515	−	9.22040i	1.48722	−	0.799510i
$134$	25.3192			2.18725
$135$		0			0
$136$	−0.146894	+	0.254428i	−0.0125961	+	0.0218170i
$137$	7.90307	−	13.6885i	0.675205	−	1.16949i	−0.301204	−	0.953560i	$-0.597389\pi$
$137$	7.90307	−	13.6885i	0.675205	−	1.16949i	0.976409	−	0.215929i	$-0.0692781\pi$
$138$		0			0
$139$	2.47481			0.209911			0.104956	−	0.994477i	$-0.466530\pi$
$139$	2.47481			0.209911			0.104956	+	0.994477i	$0.466530\pi$
$140$	−0.802120	+	1.38931i	−0.0677915	+	0.117418i
$141$		0			0
$142$	7.65175	−	13.2532i	0.642121	−	1.11219i
$143$	−0.0354401	−	0.0613840i	−0.00296365	−	0.00513319i
$144$		0			0
$145$	0.309679			0.0257174
$146$	−11.2045	+	19.4068i	−0.927293	+	1.60612i
$147$		0			0
$148$	−2.50614			−0.206004
$149$	8.34869	+	14.4604i	0.683952	+	1.18464i	0.973765	+	0.227556i	$0.0730734\pi$
$149$	8.34869	+	14.4604i	0.683952	+	1.18464i	−0.289814	+	0.957083i	$0.593593\pi$
$150$		0			0
$151$	−5.32769	−	9.22783i	−0.433561	−	0.750950i	0.563616	−	0.826037i	$-0.309410\pi$
$151$	−5.32769	−	9.22783i	−0.433561	−	0.750950i	−0.997177	+	0.0750871i	$0.976077\pi$
$152$	−0.0439970	+	1.44982i	−0.00356863	+	0.117596i
$153$		0			0
$154$	0.660494	−	1.14401i	0.0532241	−	0.0921868i
$155$	0.541009			0.0434549
$156$		0			0
$157$	4.36994	+	7.56897i	0.348760	+	0.604069i	0.986029	−	0.166572i	$-0.0532697\pi$
$157$	4.36994	+	7.56897i	0.348760	+	0.604069i	−0.637270	+	0.770641i	$0.719936\pi$
$158$	3.77449			0.300282
$159$		0			0
$160$	−0.762522	−	1.32073i	−0.0602826	−	0.104413i
$161$	11.5093	+	19.9347i	0.907061	+	1.57108i
$162$		0			0
$163$	−6.73838			−0.527791			−0.263895	−	0.964551i	$-0.585007\pi$
$163$	−6.73838			−0.527791			−0.263895	+	0.964551i	$0.585007\pi$
$164$	−7.44190	−	12.8897i	−0.581114	−	1.00652i
$165$		0			0
$166$	−2.75497	−	4.77174i	−0.213827	−	0.370359i
$167$	−10.7777			−0.834007			−0.417004	−	0.908905i	$-0.636920\pi$
$167$	−10.7777			−0.834007			−0.417004	+	0.908905i	$0.636920\pi$
$168$		0			0
$169$	−12.7799			−0.983072
$170$	−0.339054			−0.0260043
$171$		0			0
$172$	−14.9908			−1.14304
$173$	21.7578			1.65422			0.827109	−	0.562042i	$-0.189984\pi$
$173$	21.7578			1.65422			0.827109	+	0.562042i	$0.189984\pi$
$174$		0			0
$175$	−22.1648			−1.67550
$176$	0.325697	+	0.564124i	0.0245503	+	0.0425224i
$177$		0			0
$178$	9.48718	+	16.4323i	0.711094	+	1.23165i
$179$	14.4126			1.07725			0.538623	−	0.842547i	$-0.318945\pi$
$179$	14.4126			1.07725			0.538623	+	0.842547i	$0.318945\pi$
$180$		0			0
$181$	0.775446	+	1.34311i	0.0576384	+	0.0998327i	0.893405	−	0.449252i	$-0.148310\pi$
$181$	0.775446	+	1.34311i	0.0576384	+	0.0998327i	−0.835766	+	0.549085i	$0.814976\pi$
$182$	2.05066	+	3.55185i	0.152005	+	0.263281i
$183$		0			0
$184$	−1.71461			−0.126403
$185$	0.134372	+	0.232739i	0.00987922	+	0.0171113i
$186$		0			0
$187$	0.133397			0.00975495
$188$	−10.8702	+	18.8277i	−0.792789	+	1.37315i
$189$		0			0
$190$	−1.47443	+	0.792630i	−0.106966	+	0.0575034i
$191$	−2.32553	−	4.02794i	−0.168270	−	0.291452i	0.769542	−	0.638596i	$-0.220485\pi$
$191$	−2.32553	−	4.02794i	−0.168270	−	0.291452i	−0.937812	+	0.347145i	$0.887151\pi$
$192$		0			0
$193$	−4.60127	−	7.96963i	−0.331207	−	0.573667i	0.651542	−	0.758612i	$-0.274122\pi$
$193$	−4.60127	−	7.96963i	−0.331207	−	0.573667i	−0.982749	+	0.184946i	$0.940789\pi$
$194$	−29.7994			−2.13947
$195$		0			0
$196$	−11.8558	+	20.5348i	−0.846840	+	1.46677i
$197$	−22.3492			−1.59232			−0.796158	−	0.605089i	$-0.793138\pi$
$197$	−22.3492			−1.59232			−0.796158	+	0.605089i	$0.793138\pi$
$198$		0			0
$199$	−9.48803	−	16.4337i	−0.672588	−	1.16496i	−0.977168	−	0.212470i	$-0.931849\pi$
$199$	−9.48803	−	16.4337i	−0.672588	−	1.16496i	0.304579	−	0.952487i	$-0.401484\pi$
$200$	0.825507	−	1.42982i	0.0583722	−	0.101104i
$201$		0			0
$202$	14.3777	−	24.9029i	1.01161	−	1.75216i
$203$	7.04997			0.494811
$204$		0			0
$205$	−0.798025	+	1.38222i	−0.0557365	+	0.0965384i
$206$	−11.4827	+	19.8886i	−0.800038	+	1.38571i
$207$		0			0
$208$	−2.02241			−0.140229
$209$	0.580097	−	0.311851i	0.0401261	−	0.0215712i
$210$		0			0
$211$	−3.45858	−	5.99044i	−0.238099	−	0.412399i	0.722070	−	0.691820i	$-0.243191\pi$
$211$	−3.45858	−	5.99044i	−0.238099	−	0.412399i	−0.960169	+	0.279421i	$0.909857\pi$
$212$	−10.7364	−	18.5960i	−0.737380	−	1.27718i
$213$		0			0
$214$	−13.9043			−0.950475
$215$	0.803763	+	1.39216i	0.0548162	+	0.0949444i
$216$		0			0
$217$	12.3163			0.836086
$218$	11.5958	−	20.0845i	0.785365	−	1.36029i
$219$		0			0
$220$	−0.0271292	+	0.0469892i	−0.00182905	+	0.00316801i
$221$	−0.207082	+	0.358676i	−0.0139298	+	0.0241271i
$222$		0			0
$223$	12.5270			0.838873			0.419436	−	0.907785i	$-0.362228\pi$
$223$	12.5270			0.838873			0.419436	+	0.907785i	$0.362228\pi$
$224$	−17.3591	−	30.0669i	−1.15986	−	2.00893i
$225$		0			0
$226$	−9.78314	+	16.9449i	−0.650765	+	1.12716i
$227$	−2.70163	−	4.67937i	−0.179314	−	0.310581i	0.762332	−	0.647186i	$-0.224054\pi$
$227$	−2.70163	−	4.67937i	−0.179314	−	0.310581i	−0.941646	+	0.336606i	$0.890721\pi$
$228$		0			0
$229$	−4.76720	+	8.25703i	−0.315025	+	0.545640i	−0.979443	−	0.201722i	$-0.935346\pi$
$229$	−4.76720	+	8.25703i	−0.315025	+	0.545640i	0.664417	+	0.747362i	$0.268680\pi$
$230$	−0.989397	−	1.71369i	−0.0652389	−	0.112997i
$231$		0			0
$232$	−0.262570	+	0.454784i	−0.0172385	+	0.0298580i
$233$	−0.398324	+	0.689917i	−0.0260951	+	0.0451980i	−0.878778	−	0.477231i	$-0.841641\pi$
$233$	−0.398324	+	0.689917i	−0.0260951	+	0.0451980i	0.852683	+	0.522429i	$0.174974\pi$
$234$		0			0
$235$	2.33131			0.152078
$236$	1.45361	+	2.51773i	0.0946222	+	0.163890i
$237$		0			0
$238$	−7.71872			−0.500330
$239$	−4.00503	+	6.93691i	−0.259064	+	0.448711i	−0.965991	−	0.258574i	$-0.916747\pi$
$239$	−4.00503	+	6.93691i	−0.259064	+	0.448711i	0.706928	+	0.707286i	$0.250081\pi$
$240$		0			0
$241$	8.29543	−	14.3681i	0.534356	−	0.925531i	−0.464838	−	0.885396i	$-0.653888\pi$
$241$	8.29543	−	14.3681i	0.534356	−	0.925531i	0.999194	−	0.0401359i	$-0.0127791\pi$
$242$	−10.7413	+	18.6045i	−0.690478	+	1.19594i
$243$		0			0
$244$	−8.35864	+	14.4776i	−0.535107	+	0.926832i
$245$	2.54268			0.162446
$246$		0			0
$247$	−0.0620240	+	2.04386i	−0.00394649	+	0.130048i
$248$	−0.458709	+	0.794508i	−0.0291281	+	0.0504513i
$249$		0			0
$250$	3.82558			0.241951
$251$	−11.2878	−	19.5511i	−0.712480	−	1.23405i	−0.963923	−	0.266180i	$-0.914239\pi$
$251$	−11.2878	−	19.5511i	−0.712480	−	1.23405i	0.251443	−	0.967872i	$-0.419095\pi$
$252$		0			0
$253$	0.389267	+	0.674230i	0.0244730	+	0.0423885i
$254$	−2.79967	−	4.84917i	−0.175667	−	0.304264i
$255$		0			0
$256$	18.3646			1.14779
$257$	−18.2749			−1.13996			−0.569980	−	0.821659i	$-0.693049\pi$
$257$	−18.2749			−1.13996			−0.569980	+	0.821659i	$0.693049\pi$
$258$		0			0
$259$	3.05904	+	5.29841i	0.190079	+	0.329227i
$260$	−0.0842293	−	0.145889i	−0.00522368	−	0.00904768i
$261$		0			0
$262$	−2.64422	−	4.57993i	−0.163361	−	0.282949i
$263$	13.7568			0.848279			0.424139	−	0.905597i	$-0.360577\pi$
$263$	13.7568			0.848279			0.424139	+	0.905597i	$0.360577\pi$
$264$		0			0
$265$	−1.15131	+	1.99413i	−0.0707244	+	0.122498i
$266$	−33.5660	+	18.0446i	−2.05806	+	1.10638i
$267$		0			0
$268$	−23.6753			−1.44620
$269$	6.63512	−	11.4924i	0.404551	−	0.700702i	−0.589718	−	0.807609i	$-0.700761\pi$
$269$	6.63512	−	11.4924i	0.404551	−	0.700702i	0.994269	+	0.106907i	$0.0340946\pi$
$270$		0			0
$271$	−11.4102	+	19.7630i	−0.693119	+	1.20052i	0.277691	+	0.960670i	$0.410431\pi$
$271$	−11.4102	+	19.7630i	−0.693119	+	1.20052i	−0.970811	+	0.239847i	$0.922903\pi$
$272$	1.90309	−	3.29626i	0.115392	−	0.199865i
$273$		0			0
$274$	−15.4665	+	26.7888i	−0.934368	+	1.61837i
$275$	−0.749656			−0.0452059
$276$		0			0
$277$	2.60433	+	4.51083i	0.156479	+	0.271030i	0.933597	−	0.358326i	$-0.116652\pi$
$277$	2.60433	+	4.51083i	0.156479	+	0.271030i	−0.777118	+	0.629355i	$0.783319\pi$
$278$	−4.84328			−0.290481
$279$		0			0
$280$	−0.145860	+	0.252637i	−0.00871679	+	0.0150979i
$281$	−4.76015	+	8.24483i	−0.283967	+	0.491845i	−0.972358	−	0.233494i	$-0.924984\pi$
$281$	−4.76015	+	8.24483i	−0.283967	+	0.491845i	0.688391	+	0.725340i	$0.258317\pi$
$282$		0			0
$283$	−5.28849	−	9.15994i	−0.314368	−	0.544502i	0.664935	−	0.746902i	$-0.268459\pi$
$283$	−5.28849	−	9.15994i	−0.314368	−	0.544502i	−0.979303	+	0.202400i	$0.935126\pi$
$284$	−7.15494	+	12.3927i	−0.424568	+	0.735373i
$285$		0			0
$286$	0.0693573	+	0.120130i	0.00410118	+	0.00710346i
$287$	−18.1674	+	31.4669i	−1.07239	+	1.85743i
$288$		0			0
$289$	8.11027	+	14.0474i	0.477075	+	0.826318i
$290$	−0.606050			−0.0355885
$291$		0			0
$292$	10.4770	−	18.1468i	0.613122	−	1.06196i
$293$	−7.26863	+	12.5896i	−0.424638	+	0.735494i	−0.996387	−	0.0849345i	$-0.972932\pi$
$293$	−7.26863	+	12.5896i	−0.424638	+	0.735494i	0.571749	+	0.820429i	$0.306265\pi$
$294$		0			0
$295$	0.155877	−	0.269987i	0.00907551	−	0.0157192i
$296$	−0.455724			−0.0264884
$297$		0			0
$298$	−16.3386	−	28.2993i	−0.946472	−	1.63934i
$299$	−2.41715			−0.139787
$300$		0			0
$301$	18.2980	+	31.6931i	1.05468	+	1.82676i
$302$	10.4264	+	18.0591i	0.599974	+	1.03919i
$303$		0			0
$304$	0.570005	−	18.7833i	0.0326920	−	1.07729i
$305$	1.79266			0.102648
$306$		0			0
$307$	11.2958	−	19.5649i	0.644687	−	1.11663i	−0.339687	−	0.940539i	$-0.610321\pi$
$307$	11.2958	−	19.5649i	0.644687	−	1.11663i	0.984374	−	0.176092i	$-0.0563456\pi$
$308$	−0.617609	+	1.06973i	−0.0351915	+	0.0609536i
$309$		0			0
$310$	−1.05877			−0.0601341
$311$	16.6494	−	28.8377i	0.944103	−	1.63523i	0.186564	−	0.982443i	$-0.440265\pi$
$311$	16.6494	−	28.8377i	0.944103	−	1.63523i	0.757538	−	0.652791i	$-0.226402\pi$
$312$		0			0
$313$	−7.37888	+	12.7806i	−0.417079	+	0.722402i	−0.995644	−	0.0932343i	$-0.970279\pi$
$313$	−7.37888	+	12.7806i	−0.417079	+	0.722402i	0.578565	+	0.815636i	$0.303613\pi$
$314$	−8.55211	−	14.8127i	−0.482623	−	0.835928i
$315$		0			0
$316$	−3.52942			−0.198545
$317$	3.80715	−	6.59418i	0.213831	−	0.370366i	−0.739079	−	0.673618i	$-0.764739\pi$
$317$	3.80715	−	6.59418i	0.213831	−	0.370366i	0.952910	+	0.303252i	$0.0980725\pi$
$318$		0			0
$319$	0.238443			0.0133503
$320$	0.646279	+	1.11939i	0.0361281	+	0.0625757i
$321$		0			0
$322$	−22.5241	−	39.0128i	−1.25522	−	2.17410i
$323$	−3.27286	−	2.02437i	−0.182107	−	0.112639i
$324$		0			0
$325$	1.16374	−	2.01566i	0.0645529	−	0.111809i
$326$	13.1872			0.730372
$327$		0			0
$328$	−1.35325	−	2.34391i	−0.0747210	−	0.129421i
$329$	53.0732			2.92602
$330$		0			0
$331$	−0.881101	−	1.52611i	−0.0484297	−	0.0838826i	0.840794	−	0.541355i	$-0.182088\pi$
$331$	−0.881101	−	1.52611i	−0.0484297	−	0.0838826i	−0.889224	+	0.457472i	$0.848755\pi$
$332$	2.57609	+	4.46192i	0.141381	+	0.244880i
$333$		0			0
$334$	21.0924			1.15412
$335$	1.26940	+	2.19867i	0.0693548	+	0.120126i
$336$		0			0
$337$	7.43162	+	12.8719i	0.404826	+	0.701179i	0.994301	−	0.106607i	$-0.0339987\pi$
$337$	7.43162	+	12.8719i	0.404826	+	0.701179i	−0.589475	+	0.807787i	$0.700665\pi$
$338$	25.0107			1.36040
$339$		0			0
$340$	0.317040			0.0171939
$341$	0.416561			0.0225580
$342$		0			0
$343$	26.6137			1.43701
$344$	−2.72597			−0.146974
$345$		0			0
$346$	−42.5807			−2.28915
$347$	−8.90705	−	15.4275i	−0.478155	−	0.828189i	0.521531	−	0.853232i	$-0.325361\pi$
$347$	−8.90705	−	15.4275i	−0.478155	−	0.828189i	−0.999686	+	0.0250431i	$0.992028\pi$
$348$		0			0
$349$	−8.22239	−	14.2416i	−0.440134	−	0.762335i	0.557565	−	0.830134i	$-0.311736\pi$
$349$	−8.22239	−	14.2416i	−0.440134	−	0.762335i	−0.997699	+	0.0677984i	$0.978403\pi$
$350$	43.3772			2.31861
$351$		0			0
$352$	−0.587119	−	1.01692i	−0.0312936	−	0.0542021i
$353$	−5.08611	−	8.80940i	−0.270706	−	0.468877i	0.698337	−	0.715770i	$-0.253924\pi$
$353$	−5.08611	−	8.80940i	−0.270706	−	0.468877i	−0.969043	+	0.246892i	$0.920591\pi$
$354$		0			0
$355$	1.53451			0.0814432
$356$	−8.87120	−	15.3654i	−0.470173	−	0.814363i
$357$		0			0
$358$	−28.2058			−1.49072
$359$	−17.4994	+	30.3098i	−0.923580	+	1.59969i	−0.129752	+	0.991546i	$0.541418\pi$
$359$	−17.4994	+	30.3098i	−0.923580	+	1.59969i	−0.793828	+	0.608142i	$0.791915\pi$
$360$		0			0
$361$	−18.9650	−	1.15210i	−0.998160	−	0.0606370i
$362$	−1.51757	−	2.62851i	−0.0797617	−	0.138151i
$363$		0			0
$364$	−1.91752	−	3.32124i	−0.100505	−	0.174080i
$365$	−2.24699			−0.117613
$366$		0			0
$367$	−0.857408	+	1.48507i	−0.0447564	+	0.0775203i	−0.887536	−	0.460739i	$-0.847584\pi$
$367$	−0.857408	+	1.48507i	−0.0447564	+	0.0775203i	0.842779	+	0.538259i	$0.180918\pi$
$368$	22.2137			1.15797
$369$		0			0
$370$	−0.262970	−	0.455477i	−0.0136711	−	0.0236791i
$371$	−26.2101	+	45.3972i	−1.36076	+	2.35690i
$372$		0			0
$373$	16.8990	−	29.2699i	0.874996	−	1.51554i	0.0182282	−	0.999834i	$-0.494197\pi$
$373$	16.8990	−	29.2699i	0.874996	−	1.51554i	0.856767	−	0.515703i	$-0.172469\pi$
$374$	−0.261062			−0.0134992
$375$		0			0
$376$	−1.97666	+	3.42368i	−0.101939	+	0.176563i
$377$	−0.370153	+	0.641123i	−0.0190638	+	0.0330195i
$378$		0			0
$379$	16.5713			0.851211			0.425605	−	0.904909i	$-0.360061\pi$
$379$	16.5713			0.851211			0.425605	+	0.904909i	$0.360061\pi$
$380$	1.37870	−	0.741167i	0.0707256	−	0.0380210i
$381$		0			0
$382$	4.55114	+	7.88280i	0.232856	+	0.403319i
$383$	−5.84177	−	10.1182i	−0.298501	−	0.517018i	0.677292	−	0.735714i	$-0.263153\pi$
$383$	−5.84177	−	10.1182i	−0.298501	−	0.517018i	−0.975793	+	0.218696i	$0.929820\pi$
$384$		0			0
$385$	0.132458			0.00675066
$386$	9.00482	+	15.5968i	0.458333	+	0.793856i
$387$		0			0
$388$	27.8646			1.41461
$389$	12.8495	−	22.2560i	0.651496	−	1.12842i	−0.331264	−	0.943538i	$-0.607475\pi$
$389$	12.8495	−	22.2560i	0.651496	−	1.12842i	0.982760	−	0.184886i	$-0.0591915\pi$
$390$		0			0
$391$	2.27454	−	3.93962i	0.115029	−	0.199235i
$392$	−2.15588	+	3.73410i	−0.108889	+	0.188601i
$393$		0			0
$394$	43.7381			2.20349
$395$	0.189237	+	0.327768i	0.00952155	+	0.0164918i
$396$		0			0
$397$	1.27823	−	2.21396i	0.0641525	−	0.111115i	−0.832165	−	0.554528i	$-0.812899\pi$
$397$	1.27823	−	2.21396i	0.0641525	−	0.111115i	0.896318	+	0.443412i	$0.146232\pi$
$398$	18.5683	+	32.1613i	0.930747	+	1.61210i
$399$		0			0
$400$	−10.6949	+	18.5241i	−0.534745	+	0.926205i
$401$	−11.2209	−	19.4353i	−0.560347	−	0.970550i	−0.997466	−	0.0711462i	$-0.977334\pi$
$401$	−11.2209	−	19.4353i	−0.560347	−	0.970550i	0.437119	−	0.899404i	$-0.355999\pi$
$402$		0			0
$403$	−0.646657	+	1.12004i	−0.0322123	+	0.0557933i
$404$	−13.4442	+	23.2860i	−0.668872	+	1.15852i
$405$		0			0
$406$	−13.7970			−0.684734
$407$	0.103462	+	0.179202i	0.00512844	+	0.00888272i
$408$		0			0
$409$	8.57885			0.424197			0.212098	−	0.977248i	$-0.431970\pi$
$409$	8.57885			0.424197			0.212098	+	0.977248i	$0.431970\pi$
$410$	1.56176	−	2.70504i	0.0771297	−	0.133593i
$411$		0			0
$412$	10.7372	−	18.5973i	0.528982	−	0.916224i
$413$	3.54861	−	6.14637i	0.174616	−	0.302443i
$414$		0			0
$415$	0.276245	−	0.478470i	0.0135603	−	0.0234872i
$416$	3.64571			0.178746
$417$		0			0
$418$	−1.13527	+	0.610302i	−0.0555277	+	0.0298509i
$419$	10.3066	−	17.8516i	0.503511	−	0.872106i	−0.496481	−	0.868048i	$-0.665375\pi$
$419$	10.3066	−	17.8516i	0.503511	−	0.872106i	0.999992	−	0.00405866i	$-0.00129192\pi$
$420$		0			0
$421$	7.13762			0.347866			0.173933	−	0.984757i	$-0.444352\pi$
$421$	7.13762			0.347866			0.173933	+	0.984757i	$0.444352\pi$
$422$	6.76854	+	11.7235i	0.329488	+	0.570689i
$423$		0			0
$424$	−1.95234	−	3.38155i	−0.0948139	−	0.164223i
$425$	2.19017	+	3.79349i	0.106239	+	0.184011i
$426$		0			0
$427$	40.8107			1.97497
$428$	13.0015			0.628450
$429$		0			0
$430$	−1.57299	−	2.72449i	−0.0758562	−	0.131387i
$431$	−3.59358	−	6.22427i	−0.173097	−	0.299813i	0.766404	−	0.642359i	$-0.222044\pi$
$431$	−3.59358	−	6.22427i	−0.173097	−	0.299813i	−0.939501	+	0.342546i	$0.888711\pi$
$432$		0			0
$433$	−12.0394	−	20.8529i	−0.578578	−	1.00213i	−0.995643	−	0.0932498i	$-0.970274\pi$
$433$	−12.0394	−	20.8529i	−0.578578	−	1.00213i	0.417065	−	0.908877i	$-0.363059\pi$
$434$	−24.1034			−1.15700
$435$		0			0
$436$	−10.8429	+	18.7804i	−0.519280	+	0.899420i
$437$	0.681259	−	22.4494i	0.0325890	−	1.07390i
$438$		0			0
$439$	−14.2545			−0.680332			−0.340166	−	0.940365i	$-0.610483\pi$
$439$	−14.2545			−0.680332			−0.340166	+	0.940365i	$0.610483\pi$
$440$	−0.00493326	+	0.00854465i	−0.000235184	+	0.000407350i
$441$		0			0
$442$	0.405265	−	0.701939i	0.0192765	−	0.0333878i
$443$	5.99954	−	10.3915i	0.285047	−	0.493715i	−0.687574	−	0.726114i	$-0.741324\pi$
$443$	5.99954	−	10.3915i	0.285047	−	0.493715i	0.972620	+	0.232399i	$0.0746576\pi$
$444$		0			0
$445$	−0.951295	+	1.64769i	−0.0450957	+	0.0781080i
$446$	−24.5158			−1.16086
$447$		0			0
$448$	14.7128	+	25.4834i	0.695116	+	1.20398i
$449$	16.5849			0.782689			0.391345	−	0.920244i	$-0.372010\pi$
$449$	16.5849			0.782689			0.391345	+	0.920244i	$0.372010\pi$
$450$		0			0
$451$	−0.614456	+	1.06427i	−0.0289336	+	0.0501145i
$452$	9.14795	−	15.8447i	0.430283	−	0.745272i
$453$		0			0
$454$	5.28718	+	9.15766i	0.248140	+	0.429790i
$455$	−0.205623	+	0.356150i	−0.00963977	+	0.0166966i
$456$		0			0
$457$	−1.23271	−	2.13512i	−0.0576639	−	0.0998768i	0.835752	−	0.549106i	$-0.185032\pi$
$457$	−1.23271	−	2.13512i	−0.0576639	−	0.0998768i	−0.893416	+	0.449230i	$0.851699\pi$
$458$	9.32955	−	16.1593i	0.435941	−	0.755072i
$459$		0			0
$460$	0.925157	+	1.60242i	0.0431357	+	0.0747132i
$461$	26.4680			1.23274			0.616368	−	0.787458i	$-0.288603\pi$
$461$	26.4680			1.23274			0.616368	+	0.787458i	$0.288603\pi$
$462$		0			0
$463$	−7.78625	+	13.4862i	−0.361858	+	0.626756i	−0.988267	−	0.152739i	$-0.951191\pi$
$463$	−7.78625	+	13.4862i	−0.361858	+	0.626756i	0.626409	+	0.779495i	$0.284524\pi$
$464$	3.40173	−	5.89197i	0.157921	−	0.273528i
$465$		0			0
$466$	0.779532	−	1.35019i	0.0361111	−	0.0625463i
$467$	0.796236			0.0368454			0.0184227	−	0.999830i	$-0.494136\pi$
$467$	0.796236			0.0368454			0.0184227	+	0.999830i	$0.494136\pi$
$468$		0			0
$469$	28.8985	+	50.0536i	1.33441	+	2.31126i
$470$	−4.56243			−0.210449
$471$		0			0
$472$	0.264329	+	0.457832i	0.0121667	+	0.0210734i
$473$	0.618874	+	1.07192i	0.0284558	+	0.0492870i
$474$		0			0
$475$	18.3926	+	11.3764i	0.843911	+	0.521987i
$476$	7.21756			0.330816
$477$		0			0
$478$	7.83795	−	13.5757i	0.358500	−	0.620940i
$479$	5.02836	−	8.70937i	0.229751	−	0.397941i	−0.727983	−	0.685595i	$-0.759542\pi$
$479$	5.02836	−	8.70937i	0.229751	−	0.397941i	0.957734	+	0.287654i	$0.0928753\pi$
$480$		0			0
$481$	−0.642448			−0.0292931
$482$	−16.2344	+	28.1188i	−0.739457	+	1.28078i
$483$		0			0
$484$	10.0439	−	17.3966i	0.456541	−	0.790753i
$485$	−1.49402	−	2.58771i	−0.0678398	−	0.117502i
$486$		0			0
$487$	−17.6239			−0.798614			−0.399307	−	0.916817i	$-0.630749\pi$
$487$	−17.6239			−0.798614			−0.399307	+	0.916817i	$0.630749\pi$
$488$	−1.51996	+	2.63264i	−0.0688052	+	0.119174i
$489$		0			0
$490$	−4.97610			−0.224797
$491$	8.19141	+	14.1879i	0.369673	+	0.640293i	0.989514	−	0.144435i	$-0.0461363\pi$
$491$	8.19141	+	14.1879i	0.369673	+	0.640293i	−0.619841	+	0.784727i	$0.712803\pi$
$492$		0			0
$493$	−0.696630	−	1.20660i	−0.0313746	−	0.0543424i
$494$	0.121383	−	3.99990i	0.00546127	−	0.179964i
$495$		0			0
$496$	5.94283	−	10.2933i	0.266841	−	0.462182i
$497$	34.9337			1.56699
$498$		0			0
$499$	−9.00981	−	15.6054i	−0.403334	−	0.698596i	0.590792	−	0.806824i	$-0.298816\pi$
$499$	−9.00981	−	15.6054i	−0.403334	−	0.698596i	−0.994126	+	0.108229i	$0.965482\pi$
$500$	−3.57719			−0.159977
$501$		0			0
$502$	22.0906	+	38.2620i	0.985950	+	1.70772i
$503$	−18.7382	−	32.4554i	−0.835493	−	1.44712i	−0.893628	−	0.448808i	$-0.851849\pi$
$503$	−18.7382	−	32.4554i	−0.835493	−	1.44712i	0.0581348	−	0.998309i	$-0.481485\pi$
$504$		0			0
$505$	2.88335			0.128307
$506$	−0.761806	−	1.31949i	−0.0338664	−	0.0586584i
$507$		0			0
$508$	2.61789	+	4.53432i	0.116150	+	0.201178i
$509$	−37.6481			−1.66872			−0.834361	−	0.551218i	$-0.814163\pi$
$509$	−37.6481			−1.66872			−0.834361	+	0.551218i	$0.814163\pi$
$510$		0			0
$511$	−51.1538			−2.26291
$512$	−30.6351			−1.35389
$513$		0			0
$514$	35.7646			1.57751
$515$	−2.30278			−0.101473
$516$		0			0
$517$	1.79504			0.0789456
$518$	−5.98662	−	10.3691i	−0.263037	−	0.455594i
$519$		0			0
$520$	−0.0153165	−	0.0265289i	−0.000671672	−	0.00116337i
$521$	25.6456			1.12355			0.561776	−	0.827289i	$-0.310118\pi$
$521$	25.6456			1.12355			0.561776	+	0.827289i	$0.310118\pi$
$522$		0			0
$523$	8.31030	+	14.3939i	0.363384	+	0.629399i	0.988515	−	0.151120i	$-0.0482880\pi$
$523$	8.31030	+	14.3939i	0.363384	+	0.629399i	−0.625132	+	0.780519i	$0.714955\pi$
$524$	2.47254	+	4.28257i	0.108013	+	0.187085i
$525$		0			0
$526$	−26.9224			−1.17387
$527$	−1.21701	−	2.10793i	−0.0530139	−	0.0918228i
$528$		0			0
$529$	3.54944			0.154324
$530$	2.25315	−	3.90256i	0.0978704	−	0.169516i
$531$		0			0
$532$	31.3866	−	16.8730i	1.36078	−	0.731537i
$533$	−1.90773	−	3.30428i	−0.0826328	−	0.143124i
$534$		0			0
$535$	−0.697101	−	1.20741i	−0.0301383	−	0.0522011i
$536$	−4.30519			−0.185956
$537$		0			0
$538$	−12.9851	+	22.4909i	−0.559829	+	0.969652i
$539$	1.95779			0.0843280
$540$		0			0
$541$	−10.5384	−	18.2531i	−0.453083	−	0.784763i	0.545493	−	0.838116i	$-0.316343\pi$
$541$	−10.5384	−	18.2531i	−0.453083	−	0.784763i	−0.998576	+	0.0533527i	$0.983009\pi$
$542$	22.3301	−	38.6768i	0.959158	−	1.66131i
$543$		0			0
$544$	−3.43062	+	5.94201i	−0.147087	+	0.254762i
$545$	2.32546			0.0996116
$546$		0			0
$547$	−22.1896	+	38.4336i	−0.948761	+	1.64330i	−0.200720	+	0.979649i	$0.564328\pi$
$547$	−22.1896	+	38.4336i	−0.948761	+	1.64330i	−0.748041	+	0.663653i	$0.769005\pi$
$548$	14.4623	−	25.0495i	0.617800	−	1.07006i
$549$		0			0
$550$	1.46710			0.0625573
$551$	−5.85015	−	3.61851i	−0.249225	−	0.154154i
$552$		0			0
$553$	4.30807	+	7.46179i	0.183198	+	0.317308i
$554$	−5.09675	−	8.82783i	−0.216540	−	0.375059i
$555$		0			0
$556$	4.52882			0.192065
$557$	4.03714	+	6.99254i	0.171059	+	0.296283i	0.938790	−	0.344489i	$-0.111948\pi$
$557$	4.03714	+	6.99254i	0.171059	+	0.296283i	−0.767731	+	0.640772i	$0.778614\pi$
$558$		0			0
$559$	−3.84289			−0.162537
$560$	1.88969	−	3.27304i	0.0798541	−	0.138311i
$561$		0			0
$562$	9.31576	−	16.1354i	0.392962	−	0.680629i
$563$	2.37128	−	4.10718i	0.0999376	−	0.173097i	−0.811721	−	0.584045i	$-0.801469\pi$
$563$	2.37128	−	4.10718i	0.0999376	−	0.173097i	0.911659	+	0.410948i	$0.134802\pi$
$564$		0			0
$565$	−1.96194			−0.0825396
$566$	10.3497	+	17.9263i	0.435032	+	0.753497i
$567$		0			0
$568$	−1.30107	+	2.25353i	−0.0545919	+	0.0945559i
$569$	−8.96716	−	15.5316i	−0.375923	−	0.651118i	0.614542	−	0.788884i	$-0.289341\pi$
$569$	−8.96716	−	15.5316i	−0.375923	−	0.651118i	−0.990465	+	0.137767i	$0.956008\pi$
$570$		0			0
$571$	−16.8027	+	29.1031i	−0.703170	+	1.21793i	0.264178	+	0.964474i	$0.414900\pi$
$571$	−16.8027	+	29.1031i	−0.703170	+	1.21793i	−0.967348	+	0.253453i	$0.918434\pi$
$572$	−0.0648541	−	0.112331i	−0.00271169	−	0.00469678i
$573$		0			0
$574$	35.5541	−	61.5816i	1.48400	−	2.57036i
$575$	−12.7823	+	22.1396i	−0.533060	+	0.923287i
$576$		0			0
$577$	−21.7618			−0.905954			−0.452977	−	0.891522i	$-0.649638\pi$
$577$	−21.7618			−0.905954			−0.452977	+	0.891522i	$0.649638\pi$
$578$	−15.8720	−	27.4912i	−0.660190	−	1.14348i
$579$		0			0
$580$	0.566701			0.0235310
$581$	6.28884	−	10.8926i	0.260905	−	0.451901i
$582$		0			0
$583$	−0.886474	+	1.53542i	−0.0367140	+	0.0635905i
$584$	1.90517	−	3.29986i	0.0788366	−	0.136549i
$585$		0			0
$586$	14.2249	−	24.6383i	0.587626	−	1.01780i
$587$	−43.9694			−1.81481			−0.907406	−	0.420254i	$-0.861941\pi$
$587$	−43.9694			−1.81481			−0.907406	+	0.420254i	$0.861941\pi$
$588$		0			0
$589$	−10.2202	−	6.32155i	−0.421117	−	0.260475i
$590$	−0.305056	+	0.528372i	−0.0125589	+	0.0217527i
$591$		0			0
$592$	5.90415			0.242659
$593$	7.81848	+	13.5420i	0.321066	+	0.556103i	0.980708	−	0.195477i	$-0.0626254\pi$
$593$	7.81848	+	13.5420i	0.321066	+	0.556103i	−0.659642	+	0.751580i	$0.729292\pi$
$594$		0			0
$595$	−0.386984	−	0.670276i	−0.0158648	−	0.0274786i
$596$	15.2778	+	26.4619i	0.625803	+	1.08392i
$597$		0			0
$598$	4.73043			0.193441
$599$	13.4497			0.549540			0.274770	−	0.961510i	$-0.411398\pi$
$599$	13.4497			0.549540			0.274770	+	0.961510i	$0.411398\pi$
$600$		0			0
$601$	20.6960	+	35.8466i	0.844208	+	1.46221i	0.886307	+	0.463098i	$0.153262\pi$
$601$	20.6960	+	35.8466i	0.844208	+	1.46221i	−0.0420990	+	0.999113i	$0.513404\pi$
$602$	−35.8098	−	62.0243i	−1.45950	−	2.52792i
$603$		0			0
$604$	−9.74948	−	16.8866i	−0.396701	−	0.687106i
$605$	−2.15410			−0.0875766
$606$		0			0
$607$	3.77674	−	6.54150i	0.153293	−	0.265511i	−0.779143	−	0.626846i	$-0.784345\pi$
$607$	3.77674	−	6.54150i	0.153293	−	0.265511i	0.932436	+	0.361335i	$0.117679\pi$
$608$	−1.02752	+	33.8597i	−0.0416715	+	1.37319i
$609$		0			0
$610$	−3.50829			−0.142047
$611$	−2.78656	+	4.82647i	−0.112732	+	0.195258i
$612$		0			0
$613$	2.01301	−	3.48663i	0.0813047	−	0.140824i	−0.822506	−	0.568757i	$-0.807425\pi$
$613$	2.01301	−	3.48663i	0.0813047	−	0.140824i	0.903811	+	0.427933i	$0.140758\pi$
$614$	−22.1063	+	38.2892i	−0.892136	+	1.54523i
$615$		0			0
$616$	−0.112308	+	0.194523i	−0.00452501	+	0.00783755i
$617$	−24.3411			−0.979935			−0.489968	−	0.871741i	$-0.662991\pi$
$617$	−24.3411			−0.979935			−0.489968	+	0.871741i	$0.662991\pi$
$618$		0			0
$619$	−8.47222	−	14.6743i	−0.340527	−	0.589811i	0.644003	−	0.765023i	$-0.277272\pi$
$619$	−8.47222	−	14.6743i	−0.340527	−	0.589811i	−0.984531	+	0.175212i	$0.943939\pi$
$620$	0.990027			0.0397604
$621$		0			0
$622$	−32.5834	+	56.4361i	−1.30648	+	2.26288i
$623$	−21.6567	+	37.5104i	−0.867655	+	1.50282i
$624$		0			0
$625$	−12.2119	−	21.1517i	−0.488477	−	0.846067i
$626$	14.4407	−	25.0120i	0.577166	−	0.999680i
$627$		0			0
$628$	7.99684	+	13.8509i	0.319109	+	0.552712i
$629$	0.604546	−	1.04710i	0.0241048	−	0.0417508i
$630$		0			0
$631$	5.70293	+	9.87777i	0.227030	+	0.393228i	0.956927	−	0.290330i	$-0.0937651\pi$
$631$	5.70293	+	9.87777i	0.227030	+	0.393228i	−0.729896	+	0.683558i	$0.760432\pi$
$632$	−0.641799			−0.0255294
$633$		0			0
$634$	−7.45070	+	12.9050i	−0.295905	+	0.512523i
$635$	0.280727	−	0.486234i	0.0111403	−	0.0192956i
$636$		0			0
$637$	−3.03922	+	5.26408i	−0.120418	+	0.208570i
$638$	−0.466641			−0.0184745
$639$		0			0
$640$	0.260256	+	0.450777i	0.0102875	+	0.0178185i
$641$	27.4117			1.08270			0.541348	−	0.840799i	$-0.317914\pi$
$641$	27.4117			1.08270			0.541348	+	0.840799i	$0.317914\pi$
$642$		0			0
$643$	−3.02593	−	5.24107i	−0.119331	−	0.206688i	0.800172	−	0.599771i	$-0.204742\pi$
$643$	−3.02593	−	5.24107i	−0.119331	−	0.206688i	−0.919503	+	0.393084i	$0.871408\pi$
$644$	21.0616	+	36.4798i	0.829944	+	1.43751i
$645$		0			0
$646$	6.40508	+	3.96176i	0.252004	+	0.155873i
$647$	−24.3919			−0.958945			−0.479473	−	0.877557i	$-0.659172\pi$
$647$	−24.3919			−0.958945			−0.479473	+	0.877557i	$0.659172\pi$
$648$		0			0
$649$	0.120021	−	0.207882i	0.00471122	−	0.00816008i
$650$	−2.27748	+	3.94471i	−0.0893302	+	0.154724i
$651$		0			0
$652$	−12.3310			−0.482919
$653$	−20.0350	+	34.7016i	−0.784029	+	1.35798i	0.145549	+	0.989351i	$0.453505\pi$
$653$	−20.0350	+	34.7016i	−0.784029	+	1.35798i	−0.929578	+	0.368626i	$0.879828\pi$
$654$		0			0
$655$	0.265141	−	0.459237i	0.0103599	−	0.0179439i
$656$	17.5322	+	30.3666i	0.684515	+	1.18562i
$657$		0			0
$658$	−103.866			−4.04911
$659$	−10.0934	+	17.4823i	−0.393184	+	0.681014i	−0.992868	−	0.119223i	$-0.961960\pi$
$659$	−10.0934	+	17.4823i	−0.393184	+	0.681014i	0.599684	+	0.800237i	$0.295293\pi$
$660$		0			0
$661$	20.5311			0.798569			0.399284	−	0.916827i	$-0.369259\pi$
$661$	20.5311			0.798569			0.399284	+	0.916827i	$0.369259\pi$
$662$	1.72434	+	2.98664i	0.0670184	+	0.116079i
$663$		0			0
$664$	0.468444	+	0.811368i	0.0181791	+	0.0314872i
$665$	−3.24981	−	2.01012i	−0.126022	−	0.0779490i
$666$		0			0
$667$	4.06568	−	7.04197i	0.157424	−	0.272666i
$668$	−19.7229			−0.763102
$669$		0			0
$670$	−2.48426	−	4.30286i	−0.0959752	−	0.166234i
$671$	1.38030			0.0532858
$672$		0			0
$673$	−5.67978	−	9.83766i	−0.218939	−	0.379214i	0.735545	−	0.677476i	$-0.236926\pi$
$673$	−5.67978	−	9.83766i	−0.218939	−	0.379214i	−0.954484	+	0.298262i	$0.903593\pi$
$674$	−14.5439	−	25.1908i	−0.560210	−	0.970312i
$675$		0			0
$676$	−23.3868			−0.899493
$677$	−5.92995	−	10.2710i	−0.227907	−	0.394746i	0.729281	−	0.684214i	$-0.239855\pi$
$677$	−5.92995	−	10.2710i	−0.227907	−	0.394746i	−0.957187	+	0.289469i	$0.906521\pi$
$678$		0			0
$679$	−34.0120	−	58.9105i	−1.30526	−	2.26078i
$680$	0.0576514			0.00221083
$681$		0			0
$682$	−0.815222			−0.0312165
$683$	27.7320			1.06114			0.530568	−	0.847642i	$-0.321979\pi$
$683$	27.7320			1.06114			0.530568	+	0.847642i	$0.321979\pi$
$684$		0			0
$685$	−3.10171			−0.118510
$686$	−52.0839			−1.98857
$687$		0			0
$688$	35.3164			1.34643
$689$	−2.75227	−	4.76708i	−0.104853	−	0.181611i
$690$		0			0
$691$	17.9088	+	31.0190i	0.681284	+	1.18002i	0.974589	+	0.223999i	$0.0719113\pi$
$691$	17.9088	+	31.0190i	0.681284	+	1.18002i	−0.293306	+	0.956019i	$0.594755\pi$
$692$	39.8161			1.51358
$693$		0			0
$694$	17.4313	+	30.1920i	0.661685	+	1.14607i
$695$	−0.242822	−	0.420580i	−0.00921077	−	0.0159535i
$696$		0			0
$697$	7.18071			0.271989
$698$	16.0915	+	27.8712i	0.609071	+	1.05494i
$699$		0			0
$700$	−40.5608			−1.53305
$701$	16.9108	−	29.2903i	0.638711	−	1.10628i	−0.347006	−	0.937863i	$-0.612801\pi$
$701$	16.9108	−	29.2903i	0.638711	−	1.10628i	0.985716	−	0.168416i	$-0.0538652\pi$
$702$		0			0
$703$	0.181070	−	5.96678i	0.00682920	−	0.225041i
$704$	0.497616	+	0.861896i	0.0187546	+	0.0324839i
$705$		0			0
$706$	9.95367	+	17.2403i	0.374611	+	0.648846i
$707$	65.6407			2.46867
$708$		0			0
$709$	4.00539	−	6.93754i	0.150426	−	0.260545i	−0.780958	−	0.624583i	$-0.785269\pi$
$709$	4.00539	−	6.93754i	0.150426	−	0.260545i	0.931384	+	0.364038i	$0.118602\pi$
$710$	−3.00308			−0.112703
$711$		0			0
$712$	−1.61316	−	2.79408i	−0.0604558	−	0.104713i
$713$	7.10275	−	12.3023i	0.266000	−	0.460726i
$714$		0			0
$715$	−0.00695457	+	0.0120457i	−0.000260086	+	0.000450482i
$716$	26.3745			0.985660
$717$		0			0
$718$	34.2467	−	59.3171i	1.27808	−	2.21369i
$719$	3.19388	−	5.53196i	0.119112	−	0.206307i	−0.800304	−	0.599594i	$-0.795329\pi$
$719$	3.19388	−	5.53196i	0.119112	−	0.206307i	0.919416	+	0.393287i	$0.128662\pi$
$720$		0			0
$721$	−52.4238			−1.95236
$722$	37.1151	+	2.25470i	1.38128	+	0.0839112i
$723$		0			0
$724$	1.41904	+	2.45785i	0.0527381	+	0.0913451i
$725$	3.91488	+	6.78077i	0.145395	+	0.251831i
$726$		0			0
$727$	−11.5614			−0.428789			−0.214394	−	0.976747i	$-0.568778\pi$
$727$	−11.5614			−0.428789			−0.214394	+	0.976747i	$0.568778\pi$
$728$	−0.348687	−	0.603943i	−0.0129232	−	0.0223836i
$729$		0			0
$730$	4.39743			0.162756
$731$	3.61617	−	6.26339i	0.133749	−	0.231660i
$732$		0			0
$733$	9.39109	−	16.2658i	0.346868	−	0.600792i	−0.638824	−	0.769353i	$-0.720579\pi$
$733$	9.39109	−	16.2658i	0.346868	−	0.600792i	0.985691	+	0.168561i	$0.0539120\pi$
$734$	1.67797	−	2.90634i	0.0619351	−	0.107275i
$735$		0			0
$736$	−40.0437			−1.47603
$737$	0.977402	+	1.69291i	0.0360031	+	0.0623591i
$738$		0			0
$739$	4.38969	−	7.60316i	0.161477	−	0.279687i	−0.773921	−	0.633282i	$-0.781708\pi$
$739$	4.38969	−	7.60316i	0.161477	−	0.279687i	0.935399	+	0.353595i	$0.115041\pi$
$740$	0.245896	+	0.425904i	0.00903930	+	0.0156565i
$741$		0			0
$742$	51.2939	−	88.8436i	1.88306	−	3.26155i
$743$	18.0153	+	31.2035i	0.660918	+	1.14474i	0.980375	+	0.197143i	$0.0631664\pi$
$743$	18.0153	+	31.2035i	0.660918	+	1.14474i	−0.319456	+	0.947601i	$0.603500\pi$
$744$		0			0
$745$	1.63830	−	2.83762i	0.0600227	−	0.103962i
$746$	−33.0718	+	57.2820i	−1.21084	+	2.09724i
$747$		0			0
$748$	0.244112			0.00892560
$749$	−15.8698	−	27.4873i	−0.579871	−	1.00437i
$750$		0			0
$751$	24.8622			0.907234			0.453617	−	0.891197i	$-0.350133\pi$
$751$	24.8622			0.907234			0.453617	+	0.891197i	$0.350133\pi$
$752$	25.6087	−	44.3556i	0.933854	−	1.61748i
$753$		0			0
$754$	0.724400	−	1.25470i	0.0263811	−	0.0456934i
$755$	−1.04548	+	1.81082i	−0.0380488	+	0.0659024i
$756$		0			0
$757$	7.93827	−	13.7495i	0.288521	−	0.499734i	−0.684936	−	0.728604i	$-0.740170\pi$
$757$	7.93827	−	13.7495i	0.288521	−	0.499734i	0.973457	+	0.228870i	$0.0735031\pi$
$758$	−32.4305			−1.17793
$759$		0			0
$760$	0.250706	−	0.134776i	0.00909406	−	0.00488883i
$761$	−24.0436	+	41.6448i	−0.871581	+	1.50962i	−0.0112194	+	0.999937i	$0.503571\pi$
$761$	−24.0436	+	41.6448i	−0.871581	+	1.50962i	−0.860361	+	0.509685i	$0.829762\pi$
$762$		0			0
$763$	52.9400			1.91656
$764$	−4.25564	−	7.37099i	−0.153964	−	0.266673i
$765$		0			0
$766$	11.4325	+	19.8017i	0.413074	+	0.715465i
$767$	0.372633	+	0.645420i	0.0134550	+	0.0233048i
$768$		0			0
$769$	−1.27806			−0.0460881			−0.0230441	−	0.999734i	$-0.507336\pi$
$769$	−1.27806			−0.0460881			−0.0230441	+	0.999734i	$0.507336\pi$
$770$	−0.259223			−0.00934176
$771$		0			0
$772$	−8.42015	−	14.5841i	−0.303048	−	0.524895i
$773$	7.15330	+	12.3899i	0.257286	+	0.445633i	0.965514	−	0.260351i	$-0.0838383\pi$
$773$	7.15330	+	12.3899i	0.257286	+	0.445633i	−0.708228	+	0.705984i	$0.750505\pi$
$774$		0			0
$775$	6.83929	+	11.8460i	0.245675	+	0.425521i
$776$	5.06697			0.181894
$777$		0			0
$778$	−25.1469	+	43.5556i	−0.901558	+	1.56155i
$779$	31.2264	−	16.7868i	1.11880	−	0.601451i
$780$		0			0
$781$	1.18153			0.0422783
$782$	−4.45134	+	7.70995i	−0.159180	+	0.275707i
$783$		0			0
$784$	27.9306	−	48.3773i	0.997523	−	1.72776i
$785$	0.857534	−	1.48529i	0.0306067	−	0.0530124i
$786$		0			0
$787$	−10.1038	+	17.5003i	−0.360161	+	0.623818i	−0.987987	−	0.154536i	$-0.950612\pi$
$787$	−10.1038	+	17.5003i	−0.360161	+	0.623818i	0.627826	+	0.778354i	$0.283945\pi$
$788$	−40.8983			−1.45694
$789$		0			0
$790$	−0.370342	−	0.641452i	−0.0131762	−	0.0228218i
$791$	−44.6645			−1.58809
$792$		0			0
$793$	−2.14273	+	3.71132i	−0.0760907	+	0.131793i
$794$	−2.50153	+	4.33278i	−0.0887761	+	0.153765i
$795$		0			0
$796$	−17.3627	−	30.0732i	−0.615406	−	1.06591i
$797$	−6.56225	+	11.3661i	−0.232447	+	0.402610i	−0.958528	−	0.285000i	$-0.908006\pi$
$797$	−6.56225	+	11.3661i	−0.232447	+	0.402610i	0.726081	+	0.687609i	$0.241340\pi$
$798$		0			0
$799$	−5.24433	−	9.08344i	−0.185531	−	0.321349i
$800$	19.2792	−	33.3926i	0.681623	−	1.18061i
$801$		0			0
$802$	21.9597	+	38.0354i	0.775425	+	1.34308i
$803$	−1.73012			−0.0610545
$804$		0			0
$805$	2.25852	−	3.91188i	0.0796025	−	0.137876i
$806$	1.26553	−	2.19196i	0.0445763	−	0.0772084i
$807$		0			0
$808$	−2.44472	+	4.23439i	−0.0860051	+	0.148965i
$809$	36.7460			1.29192			0.645959	−	0.763372i	$-0.276458\pi$
$809$	36.7460			1.29192			0.645959	+	0.763372i	$0.276458\pi$
$810$		0			0
$811$	3.65981	+	6.33898i	0.128513	+	0.222592i	0.923101	−	0.384558i	$-0.125646\pi$
$811$	3.65981	+	6.33898i	0.128513	+	0.222592i	−0.794587	+	0.607150i	$0.792313\pi$
$812$	12.9012			0.452743
$813$		0			0
$814$	−0.202479	−	0.350704i	−0.00709688	−	0.0122922i
$815$	0.661152	+	1.14515i	0.0231591	+	0.0401128i
$816$		0			0
$817$	1.08310	−	35.6910i	0.0378927	−	1.24867i
$818$	−16.7891			−0.587016
$819$		0			0
$820$	−1.46036	+	2.52941i	−0.0509979	+	0.0883309i
$821$	−12.4259	+	21.5223i	−0.433668	+	0.751134i	−0.997186	−	0.0749693i	$-0.976114\pi$
$821$	−12.4259	+	21.5223i	−0.433668	+	0.751134i	0.563518	+	0.826104i	$0.309447\pi$
$822$		0			0
$823$	35.8649			1.25017			0.625086	−	0.780556i	$-0.285064\pi$
$823$	35.8649			1.25017			0.625086	+	0.780556i	$0.285064\pi$
$824$	1.95248	−	3.38179i	0.0680177	−	0.117810i
$825$		0			0
$826$	−6.94473	+	12.0286i	−0.241638	+	0.418529i
$827$	−21.3388	−	36.9598i	−0.742022	−	1.28522i	−0.951573	−	0.307422i	$-0.900534\pi$
$827$	−21.3388	−	36.9598i	−0.742022	−	1.28522i	0.209552	−	0.977798i	$-0.432800\pi$
$828$		0			0
$829$	15.8631			0.550949			0.275475	−	0.961308i	$-0.411165\pi$
$829$	15.8631			0.550949			0.275475	+	0.961308i	$0.411165\pi$
$830$	−0.540619	+	0.936380i	−0.0187652	+	0.0325022i
$831$		0			0
$832$	−3.08994			−0.107124
$833$	−5.71983	−	9.90703i	−0.198180	−	0.343258i
$834$		0			0
$835$	1.05748	+	1.83161i	0.0365957	+	0.0633856i
$836$	1.06156	−	0.570677i	0.0367147	−	0.0197373i
$837$		0			0
$838$	−20.1703	+	34.9360i	−0.696773	+	1.20685i
$839$	−13.9938			−0.483120			−0.241560	−	0.970386i	$-0.577659\pi$
$839$	−13.9938			−0.483120			−0.241560	+	0.970386i	$0.577659\pi$
$840$		0			0
$841$	13.2548	+	22.9580i	0.457062	+	0.791654i
$842$	−13.9685			−0.481388
$843$		0			0
$844$	−6.32908	−	10.9623i	−0.217856	−	0.377337i
$845$	1.25393	+	2.17187i	0.0431366	+	0.0747148i
$846$		0			0
$847$	−49.0390			−1.68500
$848$	25.2936	+	43.8098i	0.868586	+	1.50443i
$849$		0			0
$850$	−4.28623	−	7.42397i	−0.147017	−	0.254640i
$851$	7.05652			0.241894
$852$		0			0
$853$	−14.5671			−0.498767			−0.249384	−	0.968405i	$-0.580228\pi$
$853$	−14.5671			−0.498767			−0.249384	+	0.968405i	$0.580228\pi$
$854$	−79.8678			−2.73302
$855$		0			0
$856$	2.36423			0.0808076
$857$	26.5021			0.905295			0.452648	−	0.891689i	$-0.350480\pi$
$857$	26.5021			0.905295			0.452648	+	0.891689i	$0.350480\pi$
$858$		0			0
$859$	24.1413			0.823689			0.411845	−	0.911254i	$-0.364885\pi$
$859$	24.1413			0.823689			0.411845	+	0.911254i	$0.364885\pi$
$860$	1.47086	+	2.54760i	0.0501558	+	0.0868724i
$861$		0			0
$862$	7.03275	+	12.1811i	0.239536	+	0.414889i
$863$	−10.0162			−0.340956			−0.170478	−	0.985361i	$-0.554531\pi$
$863$	−10.0162			−0.340956			−0.170478	+	0.985361i	$0.554531\pi$
$864$		0			0
$865$	−2.13482	−	3.69762i	−0.0725860	−	0.125723i
$866$	23.5615	+	40.8097i	0.800653	+	1.38677i
$867$		0			0
$868$	22.5384			0.765003
$869$	0.145707	+	0.252372i	0.00494277	+	0.00856113i
$870$		0			0
$871$	−6.06916			−0.205646
$872$	−1.97170	+	3.41509i	−0.0667703	+	0.115649i
$873$		0			0
$874$	−1.33324	+	43.9341i	−0.0450976	+	1.48609i
$875$	4.36638	+	7.56279i	0.147611	+	0.255669i
$876$		0			0
$877$	11.6553	+	20.1875i	0.393570	+	0.681683i	0.992918	−	0.118806i	$-0.0379066\pi$
$877$	11.6553	+	20.1875i	0.393570	+	0.681683i	−0.599348	+	0.800489i	$0.704573\pi$
$878$	27.8965			0.941462
$879$		0			0
$880$	0.0639130	−	0.110701i	0.00215451	−	0.00373172i
$881$	5.49429			0.185107			0.0925537	−	0.995708i	$-0.470497\pi$
$881$	5.49429			0.185107			0.0925537	+	0.995708i	$0.470497\pi$
$882$		0			0
$883$	−17.4681	−	30.2556i	−0.587848	−	1.01818i	−0.994514	−	0.104606i	$-0.966642\pi$
$883$	−17.4681	−	30.2556i	−0.587848	−	1.01818i	0.406665	−	0.913577i	$-0.366692\pi$
$884$	−0.378952	+	0.656364i	−0.0127455	+	0.0220759i
$885$		0			0
$886$	−11.7413	+	20.3365i	−0.394456	+	0.683217i
$887$	−5.18763			−0.174184			−0.0870918	−	0.996200i	$-0.527757\pi$
$887$	−5.18763			−0.174184			−0.0870918	+	0.996200i	$0.527757\pi$
$888$		0			0
$889$	6.39088	−	11.0693i	0.214343	−	0.371253i
$890$	1.86171	−	3.22458i	0.0624047	−	0.108088i
$891$		0			0
$892$	22.9240			0.767553
$893$	−44.0408	−	27.2407i	−1.47377	−	0.911575i
$894$		0			0
$895$	−1.41412	−	2.44933i	−0.0472689	−	0.0818721i
$896$	5.92486	+	10.2622i	0.197936	+	0.342834i
$897$		0			0
$898$	−32.4571			−1.08311
$899$	−2.17538	−	3.76787i	−0.0725529	−	0.125665i
$900$		0			0
$901$	10.3596			0.345128
$902$	1.20251	−	2.08281i	0.0400391	−	0.0693498i
$903$		0			0
$904$	1.66349	−	2.88125i	0.0553268	−	0.0958288i
$905$	0.152169	−	0.263565i	0.00505828	−	0.00876119i
$906$		0			0
$907$	16.4256			0.545405			0.272702	−	0.962098i	$-0.412083\pi$
$907$	16.4256			0.545405			0.272702	+	0.962098i	$0.412083\pi$
$908$	−4.94389	−	8.56307i	−0.164069	−	0.284176i
$909$		0			0
$910$	0.402411	−	0.696996i	0.0133398	−	0.0231052i
$911$	11.4146	+	19.7707i	0.378184	+	0.655033i	0.990798	−	0.135349i	$-0.0432154\pi$
$911$	11.4146	+	19.7707i	0.378184	+	0.655033i	−0.612614	+	0.790382i	$0.709882\pi$
$912$		0			0
$913$	0.212700	−	0.368408i	0.00703936	−	0.0121925i
$914$	2.41246	+	4.17850i	0.0797970	+	0.138212i
$915$		0			0
$916$	−8.72380	+	15.1101i	−0.288243	+	0.499251i
$917$	6.03605	−	10.4547i	0.199328	−	0.345246i
$918$		0			0
$919$	−20.1717			−0.665404			−0.332702	−	0.943032i	$-0.607960\pi$
$919$	−20.1717			−0.665404			−0.332702	+	0.943032i	$0.607960\pi$
$920$	0.168233	+	0.291388i	0.00554648	+	0.00960679i
$921$		0			0
$922$	−51.7986			−1.70590
$923$	−1.83417	+	3.17687i	−0.0603723	+	0.104568i
$924$		0			0
$925$	−3.39739	+	5.88445i	−0.111705	+	0.193480i
$926$	15.2379	−	26.3928i	0.500749	−	0.867322i
$927$		0			0
$928$	−6.13215	+	10.6212i	−0.201298	+	0.348658i
$929$	−2.81217			−0.0922643			−0.0461322	−	0.998935i	$-0.514690\pi$
$929$	−2.81217			−0.0922643			−0.0461322	+	0.998935i	$0.514690\pi$
$930$		0			0
$931$	−48.0339	−	29.7106i	−1.57425	−	0.973725i
$932$	−0.728918	+	1.26252i	−0.0238765	+	0.0413553i
$933$		0			0
$934$	−1.55826			−0.0509878
$935$	−0.0130885	−	0.0226700i	−0.000428041	−	0.000741389i
$936$		0			0
$937$	−8.01674	−	13.8854i	−0.261896	−	0.453617i	0.704850	−	0.709356i	$-0.251014\pi$
$937$	−8.01674	−	13.8854i	−0.261896	−	0.453617i	−0.966746	+	0.255740i	$0.917681\pi$
$938$	−56.5552	−	97.9564i	−1.84659	−	3.19839i
$939$		0			0
$940$	4.26621			0.139148
$941$	11.0306			0.359586			0.179793	−	0.983704i	$-0.442457\pi$
$941$	11.0306			0.359586			0.179793	+	0.983704i	$0.442457\pi$
$942$		0			0
$943$	20.9541	+	36.2935i	0.682359	+	1.18188i
$944$	−3.42453	−	5.93146i	−0.111459	−	0.193052i
$945$		0			0
$946$	−1.21115	−	2.09778i	−0.0393780	−	0.0682047i
$947$	−14.7856			−0.480468			−0.240234	−	0.970715i	$-0.577224\pi$
$947$	−14.7856			−0.480468			−0.240234	+	0.970715i	$0.577224\pi$
$948$		0			0
$949$	2.68578	−	4.65192i	0.0871843	−	0.151008i
$950$	−35.9949	−	22.2640i	−1.16783	−	0.722341i
$951$		0			0
$952$	1.31246			0.0425371
$953$	−28.4287	+	49.2399i	−0.920895	+	1.59504i	−0.122862	+	0.992424i	$0.539207\pi$
$953$	−28.4287	+	49.2399i	−0.920895	+	1.59504i	−0.798033	+	0.602613i	$0.794126\pi$
$954$		0			0
$955$	−0.456350	+	0.790421i	−0.0147671	+	0.0255774i
$956$	−7.32905	+	12.6943i	−0.237039	+	0.410563i
$957$		0			0
$958$	−9.84064	+	17.0445i	−0.317937	+	0.550682i
$959$	−70.6118			−2.28017
$960$		0			0
$961$	11.6996	+	20.2643i	0.377407	+	0.653688i
$962$	1.25729			0.0405367
$963$		0			0
$964$	15.1803	−	26.2931i	0.488926	−	0.846845i
$965$	−0.902928	+	1.56392i	−0.0290663	+	0.0503443i
$966$		0			0
$967$	17.6662	+	30.5987i	0.568105	+	0.983987i	0.996753	+	0.0805155i	$0.0256567\pi$
$967$	17.6662	+	30.5987i	0.568105	+	0.983987i	−0.428648	+	0.903471i	$0.641010\pi$
$968$	1.82641	−	3.16344i	0.0587031	−	0.101677i
$969$		0			0
$970$	2.92384	+	5.06423i	0.0938787	+	0.162603i
$971$	10.3147	−	17.8656i	0.331015	−	0.573335i	−0.651696	−	0.758480i	$-0.725942\pi$
$971$	10.3147	−	17.8656i	0.331015	−	0.573335i	0.982711	+	0.185146i	$0.0592756\pi$
$972$		0			0
$973$	−5.52795	−	9.57469i	−0.177218	−	0.306951i
$974$	34.4904			1.10514
$975$		0			0
$976$	19.6919	−	34.1073i	0.630321	−	1.09175i
$977$	−25.5253	+	44.2111i	−0.816627	+	1.41444i	0.0915267	+	0.995803i	$0.470825\pi$
$977$	−25.5253	+	44.2111i	−0.816627	+	1.41444i	−0.908154	+	0.418637i	$0.862508\pi$
$978$		0			0
$979$	−0.732469	+	1.26867i	−0.0234098	+	0.0405470i
$980$	4.65302			0.148635
$981$		0			0
$982$	−16.0308	−	27.7662i	−0.511564	−	0.886056i
$983$	8.96843			0.286048			0.143024	−	0.989719i	$-0.454317\pi$
$983$	8.96843			0.286048			0.143024	+	0.989719i	$0.454317\pi$
$984$		0			0
$985$	2.19284	+	3.79812i	0.0698698	+	0.121018i
$986$	1.36332	+	2.36135i	0.0434171	+	0.0752006i
$987$		0			0
$988$	−0.113502	+	3.74020i	−0.00361097	+	0.118992i
$989$	42.2095			1.34218
$990$		0			0
$991$	17.2725	−	29.9168i	0.548678	−	0.950338i	−0.449687	−	0.893186i	$-0.648465\pi$
$991$	17.2725	−	29.9168i	0.548678	−	0.950338i	0.998365	−	0.0571522i	$-0.0182020\pi$
$992$	−10.7129	+	18.5552i	−0.340134	+	0.589129i
$993$		0			0
$994$	−68.3664			−2.16845
$995$	−1.86188	+	3.22487i	−0.0590255	+	0.102235i
$996$		0			0
$997$	−22.3313	+	38.6790i	−0.707241	+	1.22498i	0.258636	+	0.965975i	$0.416727\pi$
$997$	−22.3313	+	38.6790i	−0.707241	+	1.22498i	−0.965877	+	0.259002i	$0.916606\pi$
$998$	17.6325	+	30.5403i	0.558146	+	0.966737i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	513.2.h.c.334.3		32
3.2	odd	2		171.2.h.c.49.14	yes	32
9.2	odd	6		171.2.g.c.106.3	✓	32
9.7	even	3		513.2.g.c.505.14		32
19.7	even	3		513.2.g.c.64.14		32
57.26	odd	6		171.2.g.c.121.3	yes	32
171.7	even	3	inner	513.2.h.c.235.3		32
171.83	odd	6		171.2.h.c.7.14	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.g.c.106.3	✓	32	9.2	odd	6
171.2.g.c.121.3	yes	32	57.26	odd	6
171.2.h.c.7.14	yes	32	171.83	odd	6
171.2.h.c.49.14	yes	32	3.2	odd	2
513.2.g.c.64.14		32	19.7	even	3
513.2.g.c.505.14		32	9.7	even	3
513.2.h.c.235.3		32	171.7	even	3	inner
513.2.h.c.334.3		32	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 513 = 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	513.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.95703 q^{2} +1.82996 q^{4} +(-0.0981173 - 0.169944i) q^{5} +(-2.23368 - 3.86885i) q^{7} +0.332766 q^{8} +O(q^{10})\)	\(q-1.95703 q^{2} +1.82996 q^{4} +(-0.0981173 - 0.169944i) q^{5} +(-2.23368 - 3.86885i) q^{7} +0.332766 q^{8} +(0.192018 + 0.332586i) q^{10} +(-0.0755474 - 0.130852i) q^{11} +0.469111 q^{13} +(4.37138 + 7.57146i) q^{14} -4.31116 q^{16} +(-0.441434 + 0.764587i) q^{17} +(-0.132216 + 4.35689i) q^{19} +(-0.179551 - 0.310992i) q^{20} +(0.147849 + 0.256081i) q^{22} -5.15262 q^{23} +(2.48075 - 4.29678i) q^{25} -0.918063 q^{26} +(-4.08756 - 7.07986i) q^{28} +(-0.789052 + 1.36668i) q^{29} +(-1.37848 + 2.38759i) q^{31} +7.77154 q^{32} +(0.863900 - 1.49632i) q^{34} +(-0.438326 + 0.759203i) q^{35} -1.36950 q^{37} +(0.258751 - 8.52657i) q^{38} +(-0.0326501 - 0.0565516i) q^{40} +(-4.06669 - 7.04371i) q^{41} -8.19186 q^{43} +(-0.138249 - 0.239454i) q^{44} +10.0838 q^{46} +(-5.94010 + 10.2886i) q^{47} +(-6.47868 + 11.2214i) q^{49} +(-4.85489 + 8.40892i) q^{50} +0.858455 q^{52} +(-5.86701 - 10.1620i) q^{53} +(-0.0148250 + 0.0256777i) q^{55} +(-0.743293 - 1.28742i) q^{56} +(1.54420 - 2.67463i) q^{58} +(0.794340 + 1.37584i) q^{59} +(-4.56765 + 7.91140i) q^{61} +(2.69772 - 4.67258i) q^{62} -6.58680 q^{64} +(-0.0460278 - 0.0797226i) q^{65} -12.9376 q^{67} +(-0.807809 + 1.39917i) q^{68} +(0.857816 - 1.48578i) q^{70} +(-3.90988 + 6.77211i) q^{71} +(5.72527 - 9.91646i) q^{73} +2.68016 q^{74} +(-0.241951 + 7.97296i) q^{76} +(-0.337498 + 0.584564i) q^{77} -1.92868 q^{79} +(0.422999 + 0.732656i) q^{80} +(7.95863 + 13.7848i) q^{82} +(1.40773 + 2.43826i) q^{83} +0.173249 q^{85} +16.0317 q^{86} +(-0.0251396 - 0.0435430i) q^{88} +(-4.84774 - 8.39654i) q^{89} +(-1.04784 - 1.81492i) q^{91} -9.42910 q^{92} +(11.6250 - 20.1350i) q^{94} +(0.753401 - 0.405017i) q^{95} +15.2269 q^{97} +(12.6790 - 21.9606i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 34 q^{4} - 3 q^{5} + q^{7} + 36 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 34 * q^4 - 3 * q^5 + q^7 + 36 * q^8	\( 32 q + 2 q^{2} + 34 q^{4} - 3 q^{5} + q^{7} + 36 q^{8} - 8 q^{10} - 7 q^{11} + 8 q^{13} - q^{14} + 22 q^{16} + 7 q^{17} + 7 q^{19} + 3 q^{20} - 8 q^{22} + 10 q^{23} - 9 q^{25} + 4 q^{26} - 10 q^{28} - 10 q^{29} - 10 q^{31} + 34 q^{32} - 13 q^{34} + 3 q^{35} + 2 q^{37} + 46 q^{38} + 12 q^{40} - 6 q^{41} - 14 q^{43} - 20 q^{44} + 9 q^{47} - 13 q^{49} - q^{50} - 38 q^{52} - 16 q^{53} + 15 q^{55} + 6 q^{56} - 37 q^{59} - 12 q^{61} - 54 q^{62} - 64 q^{64} - 54 q^{65} + 22 q^{67} + 2 q^{68} + 24 q^{70} - 9 q^{71} - 10 q^{73} + 12 q^{74} - 40 q^{76} - 46 q^{77} + 16 q^{79} + 24 q^{80} + 7 q^{82} - 3 q^{83} + 54 q^{85} + 34 q^{86} + 9 q^{88} - 30 q^{89} - q^{91} - 34 q^{92} - 18 q^{94} - 3 q^{95} - 18 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 + 34 * q^4 - 3 * q^5 + q^7 + 36 * q^8 - 8 * q^10 - 7 * q^11 + 8 * q^13 - q^14 + 22 * q^16 + 7 * q^17 + 7 * q^19 + 3 * q^20 - 8 * q^22 + 10 * q^23 - 9 * q^25 + 4 * q^26 - 10 * q^28 - 10 * q^29 - 10 * q^31 + 34 * q^32 - 13 * q^34 + 3 * q^35 + 2 * q^37 + 46 * q^38 + 12 * q^40 - 6 * q^41 - 14 * q^43 - 20 * q^44 + 9 * q^47 - 13 * q^49 - q^50 - 38 * q^52 - 16 * q^53 + 15 * q^55 + 6 * q^56 - 37 * q^59 - 12 * q^61 - 54 * q^62 - 64 * q^64 - 54 * q^65 + 22 * q^67 + 2 * q^68 + 24 * q^70 - 9 * q^71 - 10 * q^73 + 12 * q^74 - 40 * q^76 - 46 * q^77 + 16 * q^79 + 24 * q^80 + 7 * q^82 - 3 * q^83 + 54 * q^85 + 34 * q^86 + 9 * q^88 - 30 * q^89 - q^91 - 34 * q^92 - 18 * q^94 - 3 * q^95 - 18 * q^98

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