LMFDB - Embedded newform 245.2.e.f.226.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,2,Mod(116,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("245.116");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	245.e (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:	$1.95633484952$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	245.226
Dual form			245.2.e.f.116.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 1.22474i) q^{2} +(-1.20711 - 2.09077i) q^{3} +(-0.500000 + 0.866025i) q^{5} +3.41421 q^{6} -2.82843 q^{8} +(-1.41421 + 2.44949i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.20711 - 2.09077i) q^{3} +(-0.500000 + 0.866025i) q^{5} +3.41421 q^{6} -2.82843 q^{8} +(-1.41421 + 2.44949i) q^{9} +(-0.707107 - 1.22474i) q^{10} +(2.91421 + 5.04757i) q^{11} +1.58579 q^{13} +2.41421 q^{15} +(2.00000 - 3.46410i) q^{16} +(2.62132 + 4.54026i) q^{17} +(-2.00000 - 3.46410i) q^{18} +(-3.00000 + 5.19615i) q^{19} -8.24264 q^{22} +(-2.29289 + 3.97141i) q^{23} +(3.41421 + 5.91359i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.12132 + 1.94218i) q^{26} -0.414214 q^{27} +2.65685 q^{29} +(-1.70711 + 2.95680i) q^{30} +(-0.878680 - 1.52192i) q^{31} +(7.03553 - 12.1859i) q^{33} -7.41421 q^{34} +(3.12132 - 5.40629i) q^{37} +(-4.24264 - 7.34847i) q^{38} +(-1.91421 - 3.31552i) q^{39} +(1.41421 - 2.44949i) q^{40} +2.24264 q^{41} +2.00000 q^{43} +(-1.41421 - 2.44949i) q^{45} +(-3.24264 - 5.61642i) q^{46} +(-0.621320 + 1.07616i) q^{47} -9.65685 q^{48} +1.41421 q^{50} +(6.32843 - 10.9612i) q^{51} +(2.12132 + 3.67423i) q^{53} +(0.292893 - 0.507306i) q^{54} -5.82843 q^{55} +14.4853 q^{57} +(-1.87868 + 3.25397i) q^{58} +(-3.12132 - 5.40629i) q^{59} +(-1.41421 + 2.44949i) q^{61} +2.48528 q^{62} +8.00000 q^{64} +(-0.792893 + 1.37333i) q^{65} +(9.94975 + 17.2335i) q^{66} +(-0.121320 - 0.210133i) q^{67} +11.0711 q^{69} -8.82843 q^{71} +(4.00000 - 6.92820i) q^{72} +(-4.24264 - 7.34847i) q^{73} +(4.41421 + 7.64564i) q^{74} +(-1.20711 + 2.09077i) q^{75} +5.41421 q^{78} +(7.74264 - 13.4106i) q^{79} +(2.00000 + 3.46410i) q^{80} +(4.74264 + 8.21449i) q^{81} +(-1.58579 + 2.74666i) q^{82} -5.24264 q^{85} +(-1.41421 + 2.44949i) q^{86} +(-3.20711 - 5.55487i) q^{87} +(-8.24264 - 14.2767i) q^{88} +(4.00000 - 6.92820i) q^{89} +4.00000 q^{90} +(-2.12132 + 3.67423i) q^{93} +(-0.878680 - 1.52192i) q^{94} +(-3.00000 - 5.19615i) q^{95} +4.75736 q^{97} -16.4853 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 2 q^{5} + 8 q^{6}+O(q^{10}) $ 4 * q - 2 * q^3 - 2 * q^5 + 8 * q^6	$ 4 q - 2 q^{3} - 2 q^{5} + 8 q^{6} + 6 q^{11} + 12 q^{13} + 4 q^{15} + 8 q^{16} + 2 q^{17} - 8 q^{18} - 12 q^{19} - 16 q^{22} - 12 q^{23} + 8 q^{24} - 2 q^{25} + 4 q^{26} + 4 q^{27} - 12 q^{29} - 4 q^{30} - 12 q^{31} + 14 q^{33} - 24 q^{34} + 4 q^{37} - 2 q^{39} - 8 q^{41} + 8 q^{43} + 4 q^{46} + 6 q^{47} - 16 q^{48} + 14 q^{51} + 4 q^{54} - 12 q^{55} + 24 q^{57} - 16 q^{58} - 4 q^{59} - 24 q^{62} + 32 q^{64} - 6 q^{65} + 20 q^{66} + 8 q^{67} + 16 q^{69} - 24 q^{71} + 16 q^{72} + 12 q^{74} - 2 q^{75} + 16 q^{78} + 14 q^{79} + 8 q^{80} + 2 q^{81} - 12 q^{82} - 4 q^{85} - 10 q^{87} - 16 q^{88} + 16 q^{89} + 16 q^{90} - 12 q^{94} - 12 q^{95} + 36 q^{97} - 32 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - 2 * q^5 + 8 * q^6 + 6 * q^11 + 12 * q^13 + 4 * q^15 + 8 * q^16 + 2 * q^17 - 8 * q^18 - 12 * q^19 - 16 * q^22 - 12 * q^23 + 8 * q^24 - 2 * q^25 + 4 * q^26 + 4 * q^27 - 12 * q^29 - 4 * q^30 - 12 * q^31 + 14 * q^33 - 24 * q^34 + 4 * q^37 - 2 * q^39 - 8 * q^41 + 8 * q^43 + 4 * q^46 + 6 * q^47 - 16 * q^48 + 14 * q^51 + 4 * q^54 - 12 * q^55 + 24 * q^57 - 16 * q^58 - 4 * q^59 - 24 * q^62 + 32 * q^64 - 6 * q^65 + 20 * q^66 + 8 * q^67 + 16 * q^69 - 24 * q^71 + 16 * q^72 + 12 * q^74 - 2 * q^75 + 16 * q^78 + 14 * q^79 + 8 * q^80 + 2 * q^81 - 12 * q^82 - 4 * q^85 - 10 * q^87 - 16 * q^88 + 16 * q^89 + 16 * q^90 - 12 * q^94 - 12 * q^95 + 36 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	+	1.22474i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$2$	−0.707107	+	1.22474i	−0.500000	+	0.866025i	−1.00000			$\pi$
$3$	−1.20711	−	2.09077i	−0.696923	−	1.20711i	−0.969528	−	0.244981i	$-0.921218\pi$
$3$	−1.20711	−	2.09077i	−0.696923	−	1.20711i	0.272605	−	0.962126i	$-0.412115\pi$
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	3.41421			1.39385
$7$		0			0
$7$		0			0
$8$	−2.82843			−1.00000
$9$	−1.41421	+	2.44949i	−0.471405	+	0.816497i
$10$	−0.707107	−	1.22474i	−0.223607	−	0.387298i
$11$	2.91421	+	5.04757i	0.878668	+	1.52190i	0.852803	+	0.522233i	$0.174901\pi$
$11$	2.91421	+	5.04757i	0.878668	+	1.52190i	0.0258656	+	0.999665i	$0.491766\pi$
$12$		0			0
$13$	1.58579			0.439818			0.219909	−	0.975520i	$-0.429424\pi$
$13$	1.58579			0.439818			0.219909	+	0.975520i	$0.429424\pi$
$14$		0			0
$15$	2.41421			0.623347
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	2.62132	+	4.54026i	0.635764	+	1.10117i	0.986353	+	0.164645i	$0.0526480\pi$
$17$	2.62132	+	4.54026i	0.635764	+	1.10117i	−0.350589	+	0.936529i	$0.614019\pi$
$18$	−2.00000	−	3.46410i	−0.471405	−	0.816497i
$19$	−3.00000	+	5.19615i	−0.688247	+	1.19208i	0.284157	+	0.958778i	$0.408286\pi$
$19$	−3.00000	+	5.19615i	−0.688247	+	1.19208i	−0.972404	+	0.233301i	$0.925047\pi$
$20$		0			0
$21$		0			0
$22$	−8.24264			−1.75734
$23$	−2.29289	+	3.97141i	−0.478101	+	0.828096i	−0.999685	−	0.0251045i	$-0.992008\pi$
$23$	−2.29289	+	3.97141i	−0.478101	+	0.828096i	0.521584	+	0.853200i	$0.325341\pi$
$24$	3.41421	+	5.91359i	0.696923	+	1.20711i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.12132	+	1.94218i	−0.219909	+	0.380894i
$27$	−0.414214			−0.0797154
$28$		0			0
$29$	2.65685			0.493365			0.246683	−	0.969096i	$-0.420659\pi$
$29$	2.65685			0.493365			0.246683	+	0.969096i	$0.420659\pi$
$30$	−1.70711	+	2.95680i	−0.311674	+	0.539835i
$31$	−0.878680	−	1.52192i	−0.157816	−	0.273345i	0.776265	−	0.630407i	$-0.217112\pi$
$31$	−0.878680	−	1.52192i	−0.157816	−	0.273345i	−0.934081	+	0.357062i	$0.883778\pi$
$32$		0			0
$33$	7.03553	−	12.1859i	1.22473	−	2.12129i
$34$	−7.41421			−1.27153
$35$		0			0
$36$		0			0
$37$	3.12132	−	5.40629i	0.513142	−	0.888788i	−0.486742	−	0.873546i	$-0.661815\pi$
$37$	3.12132	−	5.40629i	0.513142	−	0.888788i	0.999884	−	0.0152420i	$-0.00485188\pi$
$38$	−4.24264	−	7.34847i	−0.688247	−	1.19208i
$39$	−1.91421	−	3.31552i	−0.306519	−	0.530907i
$40$	1.41421	−	2.44949i	0.223607	−	0.387298i
$41$	2.24264			0.350242			0.175121	−	0.984547i	$-0.443968\pi$
$41$	2.24264			0.350242			0.175121	+	0.984547i	$0.443968\pi$
$42$		0			0
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$		0			0
$45$	−1.41421	−	2.44949i	−0.210819	−	0.365148i
$46$	−3.24264	−	5.61642i	−0.478101	−	0.828096i
$47$	−0.621320	+	1.07616i	−0.0906289	+	0.156974i	−0.907776	−	0.419455i	$-0.862221\pi$
$47$	−0.621320	+	1.07616i	−0.0906289	+	0.156974i	0.817147	+	0.576429i	$0.195554\pi$
$48$	−9.65685			−1.39385
$49$		0			0
$50$	1.41421			0.200000
$51$	6.32843	−	10.9612i	0.886157	−	1.53487i
$52$		0			0
$53$	2.12132	+	3.67423i	0.291386	+	0.504695i	0.974138	−	0.225955i	$-0.0725503\pi$
$53$	2.12132	+	3.67423i	0.291386	+	0.504695i	−0.682752	+	0.730650i	$0.739217\pi$
$54$	0.292893	−	0.507306i	0.0398577	−	0.0690356i
$55$	−5.82843			−0.785905
$56$		0			0
$57$	14.4853			1.91862
$58$	−1.87868	+	3.25397i	−0.246683	+	0.427267i
$59$	−3.12132	−	5.40629i	−0.406361	−	0.703838i	0.588118	−	0.808775i	$-0.299869\pi$
$59$	−3.12132	−	5.40629i	−0.406361	−	0.703838i	−0.994479	+	0.104937i	$0.966536\pi$
$60$		0			0
$61$	−1.41421	+	2.44949i	−0.181071	+	0.313625i	−0.942246	−	0.334922i	$-0.891290\pi$
$61$	−1.41421	+	2.44949i	−0.181071	+	0.313625i	0.761174	+	0.648547i	$0.224623\pi$
$62$	2.48528			0.315631
$63$		0			0
$64$	8.00000			1.00000
$65$	−0.792893	+	1.37333i	−0.0983463	+	0.170341i
$66$	9.94975	+	17.2335i	1.22473	+	2.12129i
$67$	−0.121320	−	0.210133i	−0.0148216	−	0.0256718i	0.858519	−	0.512781i	$-0.171385\pi$
$67$	−0.121320	−	0.210133i	−0.0148216	−	0.0256718i	−0.873341	+	0.487109i	$0.838051\pi$
$68$		0			0
$69$	11.0711			1.33280
$70$		0			0
$71$	−8.82843			−1.04774			−0.523871	−	0.851798i	$-0.675513\pi$
$71$	−8.82843			−1.04774			−0.523871	+	0.851798i	$0.675513\pi$
$72$	4.00000	−	6.92820i	0.471405	−	0.816497i
$73$	−4.24264	−	7.34847i	−0.496564	−	0.860073i	0.503429	−	0.864037i	$-0.332072\pi$
$73$	−4.24264	−	7.34847i	−0.496564	−	0.860073i	−0.999992	+	0.00396356i	$0.998738\pi$
$74$	4.41421	+	7.64564i	0.513142	+	0.888788i
$75$	−1.20711	+	2.09077i	−0.139385	+	0.241421i
$76$		0			0
$77$		0			0
$78$	5.41421			0.613039
$79$	7.74264	−	13.4106i	0.871115	−	1.50882i	0.0102708	−	0.999947i	$-0.496731\pi$
$79$	7.74264	−	13.4106i	0.871115	−	1.50882i	0.860844	−	0.508868i	$-0.169936\pi$
$80$	2.00000	+	3.46410i	0.223607	+	0.387298i
$81$	4.74264	+	8.21449i	0.526960	+	0.912722i
$82$	−1.58579	+	2.74666i	−0.175121	+	0.303318i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	−5.24264			−0.568644
$86$	−1.41421	+	2.44949i	−0.152499	+	0.264135i
$87$	−3.20711	−	5.55487i	−0.343838	−	0.595545i
$88$	−8.24264	−	14.2767i	−0.878668	−	1.52190i
$89$	4.00000	−	6.92820i	0.423999	−	0.734388i	−0.572327	−	0.820025i	$-0.693959\pi$
$89$	4.00000	−	6.92820i	0.423999	−	0.734388i	0.996326	+	0.0856373i	$0.0272926\pi$
$90$	4.00000			0.421637
$91$		0			0
$92$		0			0
$93$	−2.12132	+	3.67423i	−0.219971	+	0.381000i
$94$	−0.878680	−	1.52192i	−0.0906289	−	0.156974i
$95$	−3.00000	−	5.19615i	−0.307794	−	0.533114i
$96$		0			0
$97$	4.75736			0.483037			0.241518	−	0.970396i	$-0.422355\pi$
$97$	4.75736			0.483037			0.241518	+	0.970396i	$0.422355\pi$
$98$		0			0
$99$	−16.4853			−1.65683
$100$		0			0
$101$	7.24264	+	12.5446i	0.720670	+	1.24824i	0.960732	+	0.277479i	$0.0894989\pi$
$101$	7.24264	+	12.5446i	0.720670	+	1.24824i	−0.240062	+	0.970758i	$0.577168\pi$
$102$	8.94975	+	15.5014i	0.886157	+	1.53487i
$103$	−5.37868	+	9.31615i	−0.529977	+	0.917947i	0.469411	+	0.882980i	$0.344466\pi$
$103$	−5.37868	+	9.31615i	−0.529977	+	0.917947i	−0.999388	+	0.0349676i	$0.988867\pi$
$104$	−4.48528			−0.439818
$105$		0			0
$106$	−6.00000			−0.582772
$107$	−7.24264	+	12.5446i	−0.700173	+	1.21273i	0.268233	+	0.963354i	$0.413560\pi$
$107$	−7.24264	+	12.5446i	−0.700173	+	1.21273i	−0.968406	+	0.249380i	$0.919773\pi$
$108$		0			0
$109$	−2.50000	−	4.33013i	−0.239457	−	0.414751i	0.721102	−	0.692829i	$-0.243636\pi$
$109$	−2.50000	−	4.33013i	−0.239457	−	0.414751i	−0.960558	+	0.278078i	$0.910303\pi$
$110$	4.12132	−	7.13834i	0.392952	−	0.680614i
$111$	−15.0711			−1.43048
$112$		0			0
$113$	1.07107			0.100758			0.0503788	−	0.998730i	$-0.483957\pi$
$113$	1.07107			0.100758			0.0503788	+	0.998730i	$0.483957\pi$
$114$	−10.2426	+	17.7408i	−0.959311	+	1.66158i
$115$	−2.29289	−	3.97141i	−0.213813	−	0.370336i
$116$		0			0
$117$	−2.24264	+	3.88437i	−0.207332	+	0.359110i
$118$	8.82843			0.812723
$119$		0			0
$120$	−6.82843			−0.623347
$121$	−11.4853	+	19.8931i	−1.04412	+	1.80846i
$122$	−2.00000	−	3.46410i	−0.181071	−	0.313625i
$123$	−2.70711	−	4.68885i	−0.244092	−	0.422779i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−0.242641			−0.0215309			−0.0107654	−	0.999942i	$-0.503427\pi$
$127$	−0.242641			−0.0215309			−0.0107654	+	0.999942i	$0.503427\pi$
$128$	−5.65685	+	9.79796i	−0.500000	+	0.866025i
$129$	−2.41421	−	4.18154i	−0.212560	−	0.368164i
$130$	−1.12132	−	1.94218i	−0.0983463	−	0.170341i
$131$	−1.87868	+	3.25397i	−0.164141	+	0.284301i	−0.936350	−	0.351068i	$-0.885819\pi$
$131$	−1.87868	+	3.25397i	−0.164141	+	0.284301i	0.772209	+	0.635369i	$0.219152\pi$
$132$		0			0
$133$		0			0
$134$	0.343146			0.0296433
$135$	0.207107	−	0.358719i	0.0178249	−	0.0308737i
$136$	−7.41421	−	12.8418i	−0.635764	−	1.10117i
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	−0.999893	−	0.0146279i	$-0.995344\pi$
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	0.487278	−	0.873247i	$-0.337990\pi$
$138$	−7.82843	+	13.5592i	−0.666400	+	1.15424i
$139$	16.2426			1.37768			0.688841	−	0.724912i	$-0.258120\pi$
$139$	16.2426			1.37768			0.688841	+	0.724912i	$0.258120\pi$
$140$		0			0
$141$	3.00000			0.252646
$142$	6.24264	−	10.8126i	0.523871	−	0.907371i
$143$	4.62132	+	8.00436i	0.386454	+	0.669358i
$144$	5.65685	+	9.79796i	0.471405	+	0.816497i
$145$	−1.32843	+	2.30090i	−0.110320	+	0.191080i
$146$	12.0000			0.993127
$147$		0			0
$148$		0			0
$149$	7.41421	−	12.8418i	0.607396	−	1.05204i	−0.384272	−	0.923220i	$-0.625547\pi$
$149$	7.41421	−	12.8418i	0.607396	−	1.05204i	0.991668	−	0.128821i	$-0.0411192\pi$
$150$	−1.70711	−	2.95680i	−0.139385	−	0.241421i
$151$	−4.74264	−	8.21449i	−0.385951	−	0.668486i	0.605950	−	0.795503i	$-0.292793\pi$
$151$	−4.74264	−	8.21449i	−0.385951	−	0.668486i	−0.991901	+	0.127017i	$0.959460\pi$
$152$	8.48528	−	14.6969i	0.688247	−	1.19208i
$153$	−14.8284			−1.19881
$154$		0			0
$155$	1.75736			0.141154
$156$		0			0
$157$	10.4142	+	18.0379i	0.831145	+	1.43958i	0.897131	+	0.441764i	$0.145647\pi$
$157$	10.4142	+	18.0379i	0.831145	+	1.43958i	−0.0659864	+	0.997821i	$0.521019\pi$
$158$	10.9497	+	18.9655i	0.871115	+	1.50882i
$159$	5.12132	−	8.87039i	0.406147	−	0.703467i
$160$		0			0
$161$		0			0
$162$	−13.4142			−1.05392
$163$	0.878680	−	1.52192i	0.0688235	−	0.119206i	−0.829560	−	0.558417i	$-0.811409\pi$
$163$	0.878680	−	1.52192i	0.0688235	−	0.119206i	0.898384	+	0.439212i	$0.144742\pi$
$164$		0			0
$165$	7.03553	+	12.1859i	0.547716	+	0.948671i
$166$		0			0
$167$	9.24264			0.715217			0.357609	−	0.933872i	$-0.383592\pi$
$167$	9.24264			0.715217			0.357609	+	0.933872i	$0.383592\pi$
$168$		0			0
$169$	−10.4853			−0.806560
$170$	3.70711	−	6.42090i	0.284322	−	0.492460i
$171$	−8.48528	−	14.6969i	−0.648886	−	1.12390i
$172$		0			0
$173$	−0.621320	+	1.07616i	−0.0472381	+	0.0818188i	−0.888678	−	0.458532i	$-0.848375\pi$
$173$	−0.621320	+	1.07616i	−0.0472381	+	0.0818188i	0.841440	+	0.540351i	$0.181709\pi$
$174$	9.07107			0.687676
$175$		0			0
$176$	23.3137			1.75734
$177$	−7.53553	+	13.0519i	−0.566405	+	0.981043i
$178$	5.65685	+	9.79796i	0.423999	+	0.734388i
$179$	−1.24264	−	2.15232i	−0.0928793	−	0.160872i	0.815842	−	0.578275i	$-0.196274\pi$
$179$	−1.24264	−	2.15232i	−0.0928793	−	0.160872i	−0.908722	+	0.417403i	$0.862940\pi$
$180$		0			0
$181$	6.72792			0.500083			0.250041	−	0.968235i	$-0.419556\pi$
$181$	6.72792			0.500083			0.250041	+	0.968235i	$0.419556\pi$
$182$		0			0
$183$	6.82843			0.504772
$184$	6.48528	−	11.2328i	0.478101	−	0.828096i
$185$	3.12132	+	5.40629i	0.229484	+	0.397478i
$186$	−3.00000	−	5.19615i	−0.219971	−	0.381000i
$187$	−15.2782	+	26.4626i	−1.11725	+	1.93514i
$188$		0			0
$189$		0			0
$190$	8.48528			0.615587
$191$	9.98528	−	17.2950i	0.722510	−	1.25142i	−0.237481	−	0.971392i	$-0.576322\pi$
$191$	9.98528	−	17.2950i	0.722510	−	1.25142i	0.959991	−	0.280031i	$-0.0903448\pi$
$192$	−9.65685	−	16.7262i	−0.696923	−	1.20711i
$193$	8.00000	+	13.8564i	0.575853	+	0.997406i	0.995948	+	0.0899262i	$0.0286631\pi$
$193$	8.00000	+	13.8564i	0.575853	+	0.997406i	−0.420096	+	0.907480i	$0.638004\pi$
$194$	−3.36396	+	5.82655i	−0.241518	+	0.418322i
$195$	3.82843			0.274159
$196$		0			0
$197$	10.5858			0.754206			0.377103	−	0.926171i	$-0.376920\pi$
$197$	10.5858			0.754206			0.377103	+	0.926171i	$0.376920\pi$
$198$	11.6569	−	20.1903i	0.828417	−	1.43486i
$199$	2.29289	+	3.97141i	0.162539	+	0.281526i	0.935779	−	0.352588i	$-0.114698\pi$
$199$	2.29289	+	3.97141i	0.162539	+	0.281526i	−0.773240	+	0.634114i	$0.781365\pi$
$200$	1.41421	+	2.44949i	0.100000	+	0.173205i
$201$	−0.292893	+	0.507306i	−0.0206591	+	0.0357826i
$202$	−20.4853			−1.44134
$203$		0			0
$204$		0			0
$205$	−1.12132	+	1.94218i	−0.0783164	+	0.135648i
$206$	−7.60660	−	13.1750i	−0.529977	−	0.917947i
$207$	−6.48528	−	11.2328i	−0.450758	−	0.780736i
$208$	3.17157	−	5.49333i	0.219909	−	0.380894i
$209$	−34.9706			−2.41896
$210$		0			0
$211$	9.00000			0.619586			0.309793	−	0.950804i	$-0.399740\pi$
$211$	9.00000			0.619586			0.309793	+	0.950804i	$0.399740\pi$
$212$		0			0
$213$	10.6569	+	18.4582i	0.730196	+	1.26474i
$214$	−10.2426	−	17.7408i	−0.700173	−	1.21273i
$215$	−1.00000	+	1.73205i	−0.0681994	+	0.118125i
$216$	1.17157			0.0797154
$217$		0			0
$218$	7.07107			0.478913
$219$	−10.2426	+	17.7408i	−0.692134	+	1.19881i
$220$		0			0
$221$	4.15685	+	7.19988i	0.279620	+	0.484317i
$222$	10.6569	−	18.4582i	0.715241	−	1.23883i
$223$	18.2132			1.21965			0.609823	−	0.792538i	$-0.291240\pi$
$223$	18.2132			1.21965			0.609823	+	0.792538i	$0.291240\pi$
$224$		0			0
$225$	2.82843			0.188562
$226$	−0.757359	+	1.31178i	−0.0503788	+	0.0872586i
$227$	4.86396	+	8.42463i	0.322832	+	0.559162i	0.981071	−	0.193647i	$-0.0620316\pi$
$227$	4.86396	+	8.42463i	0.322832	+	0.559162i	−0.658239	+	0.752809i	$0.728698\pi$
$228$		0			0
$229$	15.0208	−	26.0168i	0.992603	−	1.71924i	0.391164	−	0.920321i	$-0.372072\pi$
$229$	15.0208	−	26.0168i	0.992603	−	1.71924i	0.601439	−	0.798919i	$-0.294594\pi$
$230$	6.48528			0.427627
$231$		0			0
$232$	−7.51472			−0.493365
$233$	7.41421	−	12.8418i	0.485721	−	0.841294i	−0.514144	−	0.857704i	$-0.671890\pi$
$233$	7.41421	−	12.8418i	0.485721	−	0.841294i	0.999865	+	0.0164099i	$0.00522367\pi$
$234$	−3.17157	−	5.49333i	−0.207332	−	0.359110i
$235$	−0.621320	−	1.07616i	−0.0405305	−	0.0702008i
$236$		0			0
$237$	−37.3848			−2.42840
$238$		0			0
$239$	−0.514719			−0.0332944			−0.0166472	−	0.999861i	$-0.505299\pi$
$239$	−0.514719			−0.0332944			−0.0166472	+	0.999861i	$0.505299\pi$
$240$	4.82843	−	8.36308i	0.311674	−	0.539835i
$241$	−12.3640	−	21.4150i	−0.796433	−	1.37946i	−0.921925	−	0.387367i	$-0.873384\pi$
$241$	−12.3640	−	21.4150i	−0.796433	−	1.37946i	0.125493	−	0.992095i	$-0.459949\pi$
$242$	−16.2426	−	28.1331i	−1.04412	−	1.80846i
$243$	10.8284	−	18.7554i	0.694644	−	1.20316i
$244$		0			0
$245$		0			0
$246$	7.65685			0.488183
$247$	−4.75736	+	8.23999i	−0.302704	+	0.524298i
$248$	2.48528	+	4.30463i	0.157816	+	0.273345i
$249$		0			0
$250$	−0.707107	+	1.22474i	−0.0447214	+	0.0774597i
$251$	−25.2132			−1.59144			−0.795722	−	0.605663i	$-0.792908\pi$
$251$	−25.2132			−1.59144			−0.795722	+	0.605663i	$0.792908\pi$
$252$		0			0
$253$	−26.7279			−1.68037
$254$	0.171573	−	0.297173i	0.0107654	−	0.0186463i
$255$	6.32843	+	10.9612i	0.396301	+	0.686414i
$256$		0			0
$257$	13.2426	−	22.9369i	0.826053	−	1.43077i	−0.0750585	−	0.997179i	$-0.523914\pi$
$257$	13.2426	−	22.9369i	0.826053	−	1.43077i	0.901112	−	0.433587i	$-0.142752\pi$
$258$	6.82843			0.425119
$259$		0			0
$260$		0			0
$261$	−3.75736	+	6.50794i	−0.232575	+	0.402831i
$262$	−2.65685	−	4.60181i	−0.164141	−	0.284301i
$263$	−14.3137	−	24.7921i	−0.882621	−	1.52874i	−0.848416	−	0.529330i	$-0.822443\pi$
$263$	−14.3137	−	24.7921i	−0.882621	−	1.52874i	−0.0342049	−	0.999415i	$-0.510890\pi$
$264$	−19.8995	+	34.4669i	−1.22473	+	2.12129i
$265$	−4.24264			−0.260623
$266$		0			0
$267$	−19.3137			−1.18198
$268$		0			0
$269$	3.87868	+	6.71807i	0.236487	+	0.409608i	0.959704	−	0.281013i	$-0.0906705\pi$
$269$	3.87868	+	6.71807i	0.236487	+	0.409608i	−0.723217	+	0.690621i	$0.757337\pi$
$270$	0.292893	+	0.507306i	0.0178249	+	0.0308737i
$271$	11.6569	−	20.1903i	0.708103	−	1.22647i	−0.257456	−	0.966290i	$-0.582884\pi$
$271$	11.6569	−	20.1903i	0.708103	−	1.22647i	0.965560	−	0.260181i	$-0.0837823\pi$
$272$	20.9706			1.27153
$273$		0			0
$274$	16.9706			1.02523
$275$	2.91421	−	5.04757i	0.175734	−	0.304380i
$276$		0			0
$277$	13.6066	+	23.5673i	0.817541	+	1.41602i	0.907489	+	0.420077i	$0.137997\pi$
$277$	13.6066	+	23.5673i	0.817541	+	1.41602i	−0.0899471	+	0.995947i	$0.528670\pi$
$278$	−11.4853	+	19.8931i	−0.688841	+	1.19311i
$279$	4.97056			0.297580
$280$		0			0
$281$	−20.3137			−1.21181			−0.605907	−	0.795535i	$-0.707190\pi$
$281$	−20.3137			−1.21181			−0.605907	+	0.795535i	$0.707190\pi$
$282$	−2.12132	+	3.67423i	−0.126323	+	0.218797i
$283$	3.27817	+	5.67796i	0.194867	+	0.337520i	0.946857	−	0.321655i	$-0.104239\pi$
$283$	3.27817	+	5.67796i	0.194867	+	0.337520i	−0.751990	+	0.659175i	$0.770906\pi$
$284$		0			0
$285$	−7.24264	+	12.5446i	−0.429017	+	0.743079i
$286$	−13.0711			−0.772908
$287$		0			0
$288$		0			0
$289$	−5.24264	+	9.08052i	−0.308391	+	0.534148i
$290$	−1.87868	−	3.25397i	−0.110320	−	0.191080i
$291$	−5.74264	−	9.94655i	−0.336640	−	0.583077i
$292$		0			0
$293$	0.272078			0.0158950			0.00794748	−	0.999968i	$-0.497470\pi$
$293$	0.272078			0.0158950			0.00794748	+	0.999968i	$0.497470\pi$
$294$		0			0
$295$	6.24264			0.363461
$296$	−8.82843	+	15.2913i	−0.513142	+	0.888788i
$297$	−1.20711	−	2.09077i	−0.0700434	−	0.121319i
$298$	10.4853	+	18.1610i	0.607396	+	1.05204i
$299$	−3.63604	+	6.29780i	−0.210278	+	0.364211i
$300$		0			0
$301$		0			0
$302$	13.4142			0.771901
$303$	17.4853	−	30.2854i	1.00450	−	1.73985i
$304$	12.0000	+	20.7846i	0.688247	+	1.19208i
$305$	−1.41421	−	2.44949i	−0.0809776	−	0.140257i
$306$	10.4853	−	18.1610i	0.599404	−	1.03820i
$307$	11.1005			0.633539			0.316770	−	0.948503i	$-0.397402\pi$
$307$	11.1005			0.633539			0.316770	+	0.948503i	$0.397402\pi$
$308$		0			0
$309$	25.9706			1.47741
$310$	−1.24264	+	2.15232i	−0.0705772	+	0.122243i
$311$	5.00000	+	8.66025i	0.283524	+	0.491078i	0.972250	−	0.233944i	$-0.0751631\pi$
$311$	5.00000	+	8.66025i	0.283524	+	0.491078i	−0.688726	+	0.725022i	$0.741830\pi$
$312$	5.41421	+	9.37769i	0.306519	+	0.530907i
$313$	−12.1066	+	20.9692i	−0.684306	+	1.18525i	0.289349	+	0.957224i	$0.406561\pi$
$313$	−12.1066	+	20.9692i	−0.684306	+	1.18525i	−0.973654	+	0.228028i	$0.926772\pi$
$314$	−29.4558			−1.66229
$315$		0			0
$316$		0			0
$317$	5.82843	−	10.0951i	0.327357	−	0.566999i	−0.654629	−	0.755950i	$-0.727175\pi$
$317$	5.82843	−	10.0951i	0.327357	−	0.566999i	0.981987	+	0.188951i	$0.0605087\pi$
$318$	7.24264	+	12.5446i	0.406147	+	0.703467i
$319$	7.74264	+	13.4106i	0.433505	+	0.750852i
$320$	−4.00000	+	6.92820i	−0.223607	+	0.387298i
$321$	34.9706			1.95187
$322$		0			0
$323$	−31.4558			−1.75025
$324$		0			0
$325$	−0.792893	−	1.37333i	−0.0439818	−	0.0761787i
$326$	1.24264	+	2.15232i	0.0688235	+	0.119206i
$327$	−6.03553	+	10.4539i	−0.333766	+	0.578099i
$328$	−6.34315			−0.350242
$329$		0			0
$330$	−19.8995			−1.09543
$331$	−11.7279	+	20.3134i	−0.644625	+	1.11652i	0.339763	+	0.940511i	$0.389653\pi$
$331$	−11.7279	+	20.3134i	−0.644625	+	1.11652i	−0.984388	+	0.176012i	$0.943680\pi$
$332$		0			0
$333$	8.82843	+	15.2913i	0.483795	+	0.837957i
$334$	−6.53553	+	11.3199i	−0.357609	+	0.619396i
$335$	0.242641			0.0132569
$336$		0			0
$337$	13.7574			0.749411			0.374706	−	0.927144i	$-0.377744\pi$
$337$	13.7574			0.749411			0.374706	+	0.927144i	$0.377744\pi$
$338$	7.41421	−	12.8418i	0.403280	−	0.698502i
$339$	−1.29289	−	2.23936i	−0.0702203	−	0.121625i
$340$		0			0
$341$	5.12132	−	8.87039i	0.277335	−	0.480358i
$342$	24.0000			1.29777
$343$		0			0
$344$	−5.65685			−0.304997
$345$	−5.53553	+	9.58783i	−0.298023	+	0.516191i
$346$	−0.878680	−	1.52192i	−0.0472381	−	0.0818188i
$347$	0.535534	+	0.927572i	0.0287490	+	0.0497947i	0.880042	−	0.474896i	$-0.157514\pi$
$347$	0.535534	+	0.927572i	0.0287490	+	0.0497947i	−0.851293	+	0.524691i	$0.824181\pi$
$348$		0			0
$349$	22.9706			1.22959			0.614793	−	0.788688i	$-0.289240\pi$
$349$	22.9706			1.22959			0.614793	+	0.788688i	$0.289240\pi$
$350$		0			0
$351$	−0.656854			−0.0350603
$352$		0			0
$353$	−18.1066	−	31.3616i	−0.963717	−	1.66921i	−0.713023	−	0.701141i	$-0.752674\pi$
$353$	−18.1066	−	31.3616i	−0.963717	−	1.66921i	−0.250694	−	0.968066i	$-0.580659\pi$
$354$	−10.6569	−	18.4582i	−0.566405	−	0.981043i
$355$	4.41421	−	7.64564i	0.234282	−	0.405789i
$356$		0			0
$357$		0			0
$358$	3.51472			0.185759
$359$	−5.65685	+	9.79796i	−0.298557	+	0.517116i	−0.975806	−	0.218638i	$-0.929839\pi$
$359$	−5.65685	+	9.79796i	−0.298557	+	0.517116i	0.677249	+	0.735754i	$0.263172\pi$
$360$	4.00000	+	6.92820i	0.210819	+	0.365148i
$361$	−8.50000	−	14.7224i	−0.447368	−	0.774865i
$362$	−4.75736	+	8.23999i	−0.250041	+	0.433084i
$363$	55.4558			2.91068
$364$		0			0
$365$	8.48528			0.444140
$366$	−4.82843	+	8.36308i	−0.252386	+	0.437145i
$367$	−14.9350	−	25.8682i	−0.779602	−	1.35031i	−0.932171	−	0.362018i	$-0.882088\pi$
$367$	−14.9350	−	25.8682i	−0.779602	−	1.35031i	0.152569	−	0.988293i	$-0.451245\pi$
$368$	9.17157	+	15.8856i	0.478101	+	0.828096i
$369$	−3.17157	+	5.49333i	−0.165105	+	0.285971i
$370$	−8.82843			−0.458968
$371$		0			0
$372$		0			0
$373$	−0.242641	+	0.420266i	−0.0125635	+	0.0217605i	−0.872239	−	0.489080i	$-0.837333\pi$
$373$	−0.242641	+	0.420266i	−0.0125635	+	0.0217605i	0.859675	+	0.510841i	$0.170666\pi$
$374$	−21.6066	−	37.4237i	−1.11725	−	1.93514i
$375$	−1.20711	−	2.09077i	−0.0623347	−	0.107967i
$376$	1.75736	−	3.04384i	0.0906289	−	0.156974i
$377$	4.21320			0.216991
$378$		0			0
$379$	2.00000			0.102733			0.0513665	−	0.998680i	$-0.483642\pi$
$379$	2.00000			0.102733			0.0513665	+	0.998680i	$0.483642\pi$
$380$		0			0
$381$	0.292893	+	0.507306i	0.0150054	+	0.0259901i
$382$	14.1213	+	24.4588i	0.722510	+	1.25142i
$383$	6.24264	−	10.8126i	0.318984	−	0.552497i	−0.661292	−	0.750128i	$-0.729992\pi$
$383$	6.24264	−	10.8126i	0.318984	−	0.552497i	0.980276	+	0.197632i	$0.0633250\pi$
$384$	27.3137			1.39385
$385$		0			0
$386$	−22.6274			−1.15171
$387$	−2.82843	+	4.89898i	−0.143777	+	0.249029i
$388$		0			0
$389$	17.5711	+	30.4340i	0.890889	+	1.54306i	0.838812	+	0.544421i	$0.183251\pi$
$389$	17.5711	+	30.4340i	0.890889	+	1.54306i	0.0520764	+	0.998643i	$0.483416\pi$
$390$	−2.70711	+	4.68885i	−0.137080	+	0.237429i
$391$	−24.0416			−1.21584
$392$		0			0
$393$	9.07107			0.457575
$394$	−7.48528	+	12.9649i	−0.377103	+	0.653162i
$395$	7.74264	+	13.4106i	0.389575	+	0.674763i
$396$		0			0
$397$	−2.20711	+	3.82282i	−0.110772	+	0.191862i	−0.916082	−	0.400992i	$-0.868666\pi$
$397$	−2.20711	+	3.82282i	−0.110772	+	0.191862i	0.805310	+	0.592854i	$0.201999\pi$
$398$	−6.48528			−0.325078
$399$		0			0
$400$	−4.00000			−0.200000
$401$	−3.08579	+	5.34474i	−0.154097	+	0.266904i	−0.932730	−	0.360576i	$-0.882580\pi$
$401$	−3.08579	+	5.34474i	−0.154097	+	0.266904i	0.778633	+	0.627480i	$0.215913\pi$
$402$	−0.414214	−	0.717439i	−0.0206591	−	0.0357826i
$403$	−1.39340	−	2.41344i	−0.0694101	−	0.120222i
$404$		0			0
$405$	−9.48528			−0.471327
$406$		0			0
$407$	36.3848			1.80353
$408$	−17.8995	+	31.0028i	−0.886157	+	1.53487i
$409$	7.24264	+	12.5446i	0.358126	+	0.620292i	0.987648	−	0.156691i	$-0.0500826\pi$
$409$	7.24264	+	12.5446i	0.358126	+	0.620292i	−0.629522	+	0.776983i	$0.716749\pi$
$410$	−1.58579	−	2.74666i	−0.0783164	−	0.135648i
$411$	−14.4853	+	25.0892i	−0.714506	+	1.23756i
$412$		0			0
$413$		0			0
$414$	18.3431			0.901516
$415$		0			0
$416$		0			0
$417$	−19.6066	−	33.9596i	−0.960139	−	1.66301i
$418$	24.7279	−	42.8300i	1.20948	−	2.09488i
$419$	−6.72792			−0.328681			−0.164340	−	0.986404i	$-0.552550\pi$
$419$	−6.72792			−0.328681			−0.164340	+	0.986404i	$0.552550\pi$
$420$		0			0
$421$	−19.0000			−0.926003			−0.463002	−	0.886357i	$-0.653228\pi$
$421$	−19.0000			−0.926003			−0.463002	+	0.886357i	$0.653228\pi$
$422$	−6.36396	+	11.0227i	−0.309793	+	0.536577i
$423$	−1.75736	−	3.04384i	−0.0854457	−	0.147996i
$424$	−6.00000	−	10.3923i	−0.291386	−	0.504695i
$425$	2.62132	−	4.54026i	0.127153	−	0.220235i
$426$	−30.1421			−1.46039
$427$		0			0
$428$		0			0
$429$	11.1569	−	19.3242i	0.538658	−	0.932983i
$430$	−1.41421	−	2.44949i	−0.0681994	−	0.118125i
$431$	−5.39949	−	9.35220i	−0.260085	−	0.450480i	0.706180	−	0.708033i	$-0.250417\pi$
$431$	−5.39949	−	9.35220i	−0.260085	−	0.450480i	−0.966264	+	0.257553i	$0.917084\pi$
$432$	−0.828427	+	1.43488i	−0.0398577	+	0.0690356i
$433$	−22.9706			−1.10389			−0.551947	−	0.833879i	$-0.686115\pi$
$433$	−22.9706			−1.10389			−0.551947	+	0.833879i	$0.686115\pi$
$434$		0			0
$435$	6.41421			0.307538
$436$		0			0
$437$	−13.7574	−	23.8284i	−0.658104	−	1.13987i
$438$	−14.4853	−	25.0892i	−0.692134	−	1.19881i
$439$	−3.19239	+	5.52938i	−0.152364	+	0.263903i	−0.932096	−	0.362211i	$-0.882022\pi$
$439$	−3.19239	+	5.52938i	−0.152364	+	0.263903i	0.779732	+	0.626114i	$0.215355\pi$
$440$	16.4853			0.785905
$441$		0			0
$442$	−11.7574			−0.559241
$443$	−10.4142	+	18.0379i	−0.494794	+	0.857009i	−0.999982	−	0.00600072i	$-0.998090\pi$
$443$	−10.4142	+	18.0379i	−0.494794	+	0.857009i	0.505188	+	0.863009i	$0.331423\pi$
$444$		0			0
$445$	4.00000	+	6.92820i	0.189618	+	0.328428i
$446$	−12.8787	+	22.3065i	−0.609823	+	1.05624i
$447$	−35.7990			−1.69323
$448$		0			0
$449$	−29.8284			−1.40769			−0.703845	−	0.710353i	$-0.748535\pi$
$449$	−29.8284			−1.40769			−0.703845	+	0.710353i	$0.748535\pi$
$450$	−2.00000	+	3.46410i	−0.0942809	+	0.163299i
$451$	6.53553	+	11.3199i	0.307746	+	0.533032i
$452$		0			0
$453$	−11.4497	+	19.8315i	−0.537956	+	0.931767i
$454$	−13.7574			−0.645665
$455$		0			0
$456$	−40.9706			−1.91862
$457$	10.1213	−	17.5306i	0.473455	−	0.820049i	−0.526083	−	0.850433i	$-0.676340\pi$
$457$	10.1213	−	17.5306i	0.473455	−	0.820049i	0.999538	+	0.0303845i	$0.00967317\pi$
$458$	21.2426	+	36.7933i	0.992603	+	1.71924i
$459$	−1.08579	−	1.88064i	−0.0506802	−	0.0877806i
$460$		0			0
$461$	36.9706			1.72189			0.860945	−	0.508697i	$-0.169873\pi$
$461$	36.9706			1.72189			0.860945	+	0.508697i	$0.169873\pi$
$462$		0			0
$463$	29.4558			1.36893			0.684465	−	0.729046i	$-0.260036\pi$
$463$	29.4558			1.36893			0.684465	+	0.729046i	$0.260036\pi$
$464$	5.31371	−	9.20361i	0.246683	−	0.427267i
$465$	−2.12132	−	3.67423i	−0.0983739	−	0.170389i
$466$	10.4853	+	18.1610i	0.485721	+	0.841294i
$467$	−9.86396	+	17.0849i	−0.456450	+	0.790594i	−0.998770	−	0.0495776i	$-0.984212\pi$
$467$	−9.86396	+	17.0849i	−0.456450	+	0.790594i	0.542321	+	0.840172i	$0.317546\pi$
$468$		0			0
$469$		0			0
$470$	1.75736			0.0810609
$471$	25.1421	−	43.5475i	1.15849	−	2.00656i
$472$	8.82843	+	15.2913i	0.406361	+	0.703838i
$473$	5.82843	+	10.0951i	0.267991	+	0.464175i
$474$	26.4350	−	45.7868i	1.21420	−	2.10306i
$475$	6.00000			0.275299
$476$		0			0
$477$	−12.0000			−0.549442
$478$	0.363961	−	0.630399i	0.0166472	−	0.0288338i
$479$	−10.1213	−	17.5306i	−0.462455	−	0.800995i	0.536628	−	0.843819i	$-0.319698\pi$
$479$	−10.1213	−	17.5306i	−0.462455	−	0.800995i	−0.999083	+	0.0428237i	$0.986365\pi$
$480$		0			0
$481$	4.94975	−	8.57321i	0.225689	−	0.390905i
$482$	34.9706			1.59287
$483$		0			0
$484$		0			0
$485$	−2.37868	+	4.11999i	−0.108010	+	0.187079i
$486$	15.3137	+	26.5241i	0.694644	+	1.20316i
$487$	15.8492	+	27.4517i	0.718198	+	1.24395i	0.961713	+	0.274058i	$0.0883660\pi$
$487$	15.8492	+	27.4517i	0.718198	+	1.24395i	−0.243515	+	0.969897i	$0.578301\pi$
$488$	4.00000	−	6.92820i	0.181071	−	0.313625i
$489$	−4.24264			−0.191859
$490$		0			0
$491$	19.2843			0.870287			0.435143	−	0.900361i	$-0.356698\pi$
$491$	19.2843			0.870287			0.435143	+	0.900361i	$0.356698\pi$
$492$		0			0
$493$	6.96447	+	12.0628i	0.313664	+	0.543282i
$494$	−6.72792	−	11.6531i	−0.302704	−	0.524298i
$495$	8.24264	−	14.2767i	0.370479	−	0.641689i
$496$	−7.02944			−0.315631
$497$		0			0
$498$		0			0
$499$	−1.50000	+	2.59808i	−0.0671492	+	0.116306i	−0.897645	−	0.440719i	$-0.854724\pi$
$499$	−1.50000	+	2.59808i	−0.0671492	+	0.116306i	0.830496	+	0.557024i	$0.188057\pi$
$500$		0			0
$501$	−11.1569	−	19.3242i	−0.498451	−	0.863343i
$502$	17.8284	−	30.8797i	0.795722	−	1.37823i
$503$	−32.7574			−1.46058			−0.730289	−	0.683138i	$-0.760615\pi$
$503$	−32.7574			−1.46058			−0.730289	+	0.683138i	$0.760615\pi$
$504$		0			0
$505$	−14.4853			−0.644587
$506$	18.8995	−	32.7349i	0.840185	−	1.45524i
$507$	12.6569	+	21.9223i	0.562111	+	0.973604i
$508$		0			0
$509$	−8.60660	+	14.9071i	−0.381481	+	0.660744i	−0.991274	−	0.131816i	$-0.957919\pi$
$509$	−8.60660	+	14.9071i	−0.381481	+	0.660744i	0.609793	+	0.792561i	$0.291252\pi$
$510$	−17.8995			−0.792603
$511$		0			0
$512$	−22.6274			−1.00000
$513$	1.24264	−	2.15232i	0.0548639	−	0.0950271i
$514$	18.7279	+	32.4377i	0.826053	+	1.43077i
$515$	−5.37868	−	9.31615i	−0.237013	−	0.410518i
$516$		0			0
$517$	−7.24264			−0.318531
$518$		0			0
$519$	3.00000			0.131685
$520$	2.24264	−	3.88437i	0.0983463	−	0.170341i
$521$	9.48528	+	16.4290i	0.415558	+	0.719767i	0.995487	−	0.0948999i	$-0.0302531\pi$
$521$	9.48528	+	16.4290i	0.415558	+	0.719767i	−0.579929	+	0.814667i	$0.696920\pi$
$522$	−5.31371	−	9.20361i	−0.232575	−	0.402831i
$523$	−7.75736	+	13.4361i	−0.339206	+	0.587521i	−0.984284	−	0.176595i	$-0.943492\pi$
$523$	−7.75736	+	13.4361i	−0.339206	+	0.587521i	0.645078	+	0.764117i	$0.276825\pi$
$524$		0			0
$525$		0			0
$526$	40.4853			1.76524
$527$	4.60660	−	7.97887i	0.200667	−	0.347565i
$528$	−28.1421	−	48.7436i	−1.22473	−	2.12129i
$529$	0.985281	+	1.70656i	0.0428383	+	0.0741981i
$530$	3.00000	−	5.19615i	0.130312	−	0.225706i
$531$	17.6569			0.766242
$532$		0			0
$533$	3.55635			0.154043
$534$	13.6569	−	23.6544i	0.590990	−	1.02362i
$535$	−7.24264	−	12.5446i	−0.313127	−	0.542351i
$536$	0.343146	+	0.594346i	0.0148216	+	0.0256718i
$537$	−3.00000	+	5.19615i	−0.129460	+	0.224231i
$538$	−10.9706			−0.472975
$539$		0			0
$540$		0			0
$541$	−5.98528	+	10.3668i	−0.257327	+	0.445704i	−0.965525	−	0.260310i	$-0.916175\pi$
$541$	−5.98528	+	10.3668i	−0.257327	+	0.445704i	0.708198	+	0.706014i	$0.249509\pi$
$542$	16.4853	+	28.5533i	0.708103	+	1.22647i
$543$	−8.12132	−	14.0665i	−0.348519	−	0.603653i
$544$		0			0
$545$	5.00000			0.214176
$546$		0			0
$547$	−7.51472			−0.321306			−0.160653	−	0.987011i	$-0.551360\pi$
$547$	−7.51472			−0.321306			−0.160653	+	0.987011i	$0.551360\pi$
$548$		0			0
$549$	−4.00000	−	6.92820i	−0.170716	−	0.295689i
$550$	4.12132	+	7.13834i	0.175734	+	0.304380i
$551$	−7.97056	+	13.8054i	−0.339557	+	0.588131i
$552$	−31.3137			−1.33280
$553$		0			0
$554$	−38.4853			−1.63508
$555$	7.53553	−	13.0519i	0.319866	−	0.554023i
$556$		0			0
$557$	−15.8995	−	27.5387i	−0.673683	−	1.16685i	−0.976852	−	0.213917i	$-0.931378\pi$
$557$	−15.8995	−	27.5387i	−0.673683	−	1.16685i	0.303169	−	0.952937i	$-0.401955\pi$
$558$	−3.51472	+	6.08767i	−0.148790	+	0.257712i
$559$	3.17157			0.134143
$560$		0			0
$561$	73.7696			3.11455
$562$	14.3640	−	24.8791i	0.605907	−	1.04946i
$563$	−17.9706	−	31.1259i	−0.757369	−	1.31180i	−0.944188	−	0.329407i	$-0.893151\pi$
$563$	−17.9706	−	31.1259i	−0.757369	−	1.31180i	0.186819	−	0.982394i	$-0.440182\pi$
$564$		0			0
$565$	−0.535534	+	0.927572i	−0.0225301	+	0.0390232i
$566$	−9.27208			−0.389735
$567$		0			0
$568$	24.9706			1.04774
$569$	1.07107	−	1.85514i	0.0449015	−	0.0777717i	−0.842701	−	0.538382i	$-0.819036\pi$
$569$	1.07107	−	1.85514i	0.0449015	−	0.0777717i	0.887603	+	0.460610i	$0.152369\pi$
$570$	−10.2426	−	17.7408i	−0.429017	−	0.743079i
$571$	17.2426	+	29.8651i	0.721582	+	1.24982i	0.960365	+	0.278744i	$0.0899181\pi$
$571$	17.2426	+	29.8651i	0.721582	+	1.24982i	−0.238783	+	0.971073i	$0.576749\pi$
$572$		0			0
$573$	−48.2132			−2.01414
$574$		0			0
$575$	4.58579			0.191241
$576$	−11.3137	+	19.5959i	−0.471405	+	0.816497i
$577$	4.86396	+	8.42463i	0.202489	+	0.350722i	0.949330	−	0.314281i	$-0.101764\pi$
$577$	4.86396	+	8.42463i	0.202489	+	0.350722i	−0.746841	+	0.665003i	$0.768430\pi$
$578$	−7.41421	−	12.8418i	−0.308391	−	0.534148i
$579$	19.3137	−	33.4523i	0.802650	−	1.39023i
$580$		0			0
$581$		0			0
$582$	16.2426			0.673279
$583$	−12.3640	+	21.4150i	−0.512063	+	0.886919i
$584$	12.0000	+	20.7846i	0.496564	+	0.860073i
$585$	−2.24264	−	3.88437i	−0.0927218	−	0.160599i
$586$	−0.192388	+	0.333226i	−0.00794748	+	0.0137654i
$587$	13.4558			0.555382			0.277691	−	0.960670i	$-0.410431\pi$
$587$	13.4558			0.555382			0.277691	+	0.960670i	$0.410431\pi$
$588$		0			0
$589$	10.5442			0.434464
$590$	−4.41421	+	7.64564i	−0.181730	+	0.314766i
$591$	−12.7782	−	22.1324i	−0.525624	−	0.910407i
$592$	−12.4853	−	21.6251i	−0.513142	−	0.888788i
$593$	−5.37868	+	9.31615i	−0.220876	+	0.382568i	−0.955074	−	0.296367i	$-0.904225\pi$
$593$	−5.37868	+	9.31615i	−0.220876	+	0.382568i	0.734198	+	0.678935i	$0.237558\pi$
$594$	3.41421			0.140087
$595$		0			0
$596$		0			0
$597$	5.53553	−	9.58783i	0.226554	−	0.392404i
$598$	−5.14214	−	8.90644i	−0.210278	−	0.364211i
$599$	6.08579	+	10.5409i	0.248658	+	0.430689i	0.963154	−	0.268951i	$-0.0866770\pi$
$599$	6.08579	+	10.5409i	0.248658	+	0.430689i	−0.714495	+	0.699640i	$0.753344\pi$
$600$	3.41421	−	5.91359i	0.139385	−	0.241421i
$601$	22.9706			0.936989			0.468494	−	0.883466i	$-0.344797\pi$
$601$	22.9706			0.936989			0.468494	+	0.883466i	$0.344797\pi$
$602$		0			0
$603$	0.686292			0.0279480
$604$		0			0
$605$	−11.4853	−	19.8931i	−0.466943	−	0.808769i
$606$	24.7279	+	42.8300i	1.00450	+	1.73985i
$607$	12.4497	−	21.5636i	0.505320	−	0.875239i	−0.494661	−	0.869086i	$-0.664708\pi$
$607$	12.4497	−	21.5636i	0.505320	−	0.875239i	0.999981	−	0.00615355i	$-0.00195875\pi$
$608$		0			0
$609$		0			0
$610$	4.00000			0.161955
$611$	−0.985281	+	1.70656i	−0.0398602	+	0.0690399i
$612$		0			0
$613$	−21.9706	−	38.0541i	−0.887383	−	1.53699i	−0.842958	−	0.537979i	$-0.819188\pi$
$613$	−21.9706	−	38.0541i	−0.887383	−	1.53699i	−0.0444245	−	0.999013i	$-0.514145\pi$
$614$	−7.84924	+	13.5953i	−0.316770	+	0.548661i
$615$	5.41421			0.218322
$616$		0			0
$617$	7.41421			0.298485			0.149242	−	0.988801i	$-0.452316\pi$
$617$	7.41421			0.298485			0.149242	+	0.988801i	$0.452316\pi$
$618$	−18.3640	+	31.8073i	−0.738707	+	1.27948i
$619$	−15.5355	−	26.9083i	−0.624426	−	1.08154i	−0.988652	−	0.150227i	$-0.952000\pi$
$619$	−15.5355	−	26.9083i	−0.624426	−	1.08154i	0.364226	−	0.931311i	$-0.381334\pi$
$620$		0			0
$621$	0.949747	−	1.64501i	0.0381121	−	0.0660120i
$622$	−14.1421			−0.567048
$623$		0			0
$624$	−15.3137			−0.613039
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−17.1213	−	29.6550i	−0.684306	−	1.18525i
$627$	42.2132	+	73.1154i	1.68583	+	2.91995i
$628$		0			0
$629$	32.7279			1.30495
$630$		0			0
$631$	8.45584			0.336622			0.168311	−	0.985734i	$-0.446169\pi$
$631$	8.45584			0.336622			0.168311	+	0.985734i	$0.446169\pi$
$632$	−21.8995	+	37.9310i	−0.871115	+	1.50882i
$633$	−10.8640	−	18.8169i	−0.431804	−	0.747906i
$634$	8.24264	+	14.2767i	0.327357	+	0.566999i
$635$	0.121320	−	0.210133i	0.00481445	−	0.00833887i
$636$		0			0
$637$		0			0
$638$	−21.8995			−0.867009
$639$	12.4853	−	21.6251i	0.493910	−	0.855477i
$640$	−5.65685	−	9.79796i	−0.223607	−	0.387298i
$641$	0.343146	+	0.594346i	0.0135534	+	0.0234753i	0.872723	−	0.488216i	$-0.162352\pi$
$641$	0.343146	+	0.594346i	0.0135534	+	0.0234753i	−0.859169	+	0.511692i	$0.829019\pi$
$642$	−24.7279	+	42.8300i	−0.975933	+	1.69037i
$643$	27.7279			1.09348			0.546741	−	0.837302i	$-0.315868\pi$
$643$	27.7279			1.09348			0.546741	+	0.837302i	$0.315868\pi$
$644$		0			0
$645$	4.82843			0.190119
$646$	22.2426	−	38.5254i	0.875125	−	1.51576i
$647$	14.2426	+	24.6690i	0.559936	+	0.969838i	0.997501	+	0.0706508i	$0.0225076\pi$
$647$	14.2426	+	24.6690i	0.559936	+	0.969838i	−0.437565	+	0.899187i	$0.644159\pi$
$648$	−13.4142	−	23.2341i	−0.526960	−	0.912722i
$649$	18.1924	−	31.5101i	0.714114	−	1.23688i
$650$	2.24264			0.0879636
$651$		0			0
$652$		0			0
$653$	−0.514719	+	0.891519i	−0.0201425	+	0.0348878i	−0.875921	−	0.482455i	$-0.839745\pi$
$653$	−0.514719	+	0.891519i	−0.0201425	+	0.0348878i	0.855778	+	0.517342i	$0.173079\pi$
$654$	−8.53553	−	14.7840i	−0.333766	−	0.578099i
$655$	−1.87868	−	3.25397i	−0.0734061	−	0.127143i
$656$	4.48528	−	7.76874i	0.175121	−	0.303318i
$657$	24.0000			0.936329
$658$		0			0
$659$	−13.9706			−0.544216			−0.272108	−	0.962267i	$-0.587721\pi$
$659$	−13.9706			−0.544216			−0.272108	+	0.962267i	$0.587721\pi$
$660$		0			0
$661$	18.7279	+	32.4377i	0.728432	+	1.26168i	0.957546	+	0.288281i	$0.0930838\pi$
$661$	18.7279	+	32.4377i	0.728432	+	1.26168i	−0.229114	+	0.973400i	$0.573583\pi$
$662$	−16.5858	−	28.7274i	−0.644625	−	1.11652i
$663$	10.0355	−	17.3821i	0.389748	−	0.675063i
$664$		0			0
$665$		0			0
$666$	−24.9706			−0.967590
$667$	−6.09188	+	10.5515i	−0.235879	+	0.408554i
$668$		0			0
$669$	−21.9853	−	38.0796i	−0.850000	−	1.47224i
$670$	−0.171573	+	0.297173i	−0.00662844	+	0.0114808i
$671$	−16.4853			−0.636407
$672$		0			0
$673$	20.4853			0.789650			0.394825	−	0.918756i	$-0.370805\pi$
$673$	20.4853			0.789650			0.394825	+	0.918756i	$0.370805\pi$
$674$	−9.72792	+	16.8493i	−0.374706	+	0.649009i
$675$	0.207107	+	0.358719i	0.00797154	+	0.0138071i
$676$		0			0
$677$	−0.893398	+	1.54741i	−0.0343361	+	0.0594718i	−0.882683	−	0.469969i	$-0.844265\pi$
$677$	−0.893398	+	1.54741i	−0.0343361	+	0.0594718i	0.848347	+	0.529441i	$0.177598\pi$
$678$	3.65685			0.140441
$679$		0			0
$680$	14.8284			0.568644
$681$	11.7426	−	20.3389i	0.449979	−	0.779386i
$682$	7.24264	+	12.5446i	0.277335	+	0.480358i
$683$	3.89949	+	6.75412i	0.149210	+	0.258439i	0.930936	−	0.365183i	$-0.118994\pi$
$683$	3.89949	+	6.75412i	0.149210	+	0.258439i	−0.781726	+	0.623622i	$0.785660\pi$
$684$		0			0
$685$	12.0000			0.458496
$686$		0			0
$687$	−72.5269			−2.76707
$688$	4.00000	−	6.92820i	0.152499	−	0.264135i
$689$	3.36396	+	5.82655i	0.128157	+	0.221974i
$690$	−7.82843	−	13.5592i	−0.298023	−	0.516191i
$691$	−4.58579	+	7.94282i	−0.174452	+	0.302159i	−0.939971	−	0.341253i	$-0.889149\pi$
$691$	−4.58579	+	7.94282i	−0.174452	+	0.302159i	0.765520	+	0.643412i	$0.222482\pi$
$692$		0			0
$693$		0			0
$694$	−1.51472			−0.0574979
$695$	−8.12132	+	14.0665i	−0.308059	+	0.533574i
$696$	9.07107	+	15.7116i	0.343838	+	0.595545i
$697$	5.87868	+	10.1822i	0.222671	+	0.385677i
$698$	−16.2426	+	28.1331i	−0.614793	+	1.06485i
$699$	−35.7990			−1.35404
$700$		0			0
$701$	−4.45584			−0.168295			−0.0841475	−	0.996453i	$-0.526817\pi$
$701$	−4.45584			−0.168295			−0.0841475	+	0.996453i	$0.526817\pi$
$702$	0.464466	−	0.804479i	0.0175301	−	0.0303631i
$703$	18.7279	+	32.4377i	0.706337	+	1.22341i
$704$	23.3137	+	40.3805i	0.878668	+	1.52190i
$705$	−1.50000	+	2.59808i	−0.0564933	+	0.0978492i
$706$	51.2132			1.92743
$707$		0			0
$708$		0			0
$709$	−8.50000	+	14.7224i	−0.319224	+	0.552913i	−0.980326	−	0.197383i	$-0.936756\pi$
$709$	−8.50000	+	14.7224i	−0.319224	+	0.552913i	0.661102	+	0.750296i	$0.270089\pi$
$710$	6.24264	+	10.8126i	0.234282	+	0.405789i
$711$	21.8995	+	37.9310i	0.821295	+	1.42253i
$712$	−11.3137	+	19.5959i	−0.423999	+	0.734388i
$713$	8.05887			0.301807
$714$		0			0
$715$	−9.24264			−0.345655
$716$		0			0
$717$	0.621320	+	1.07616i	0.0232036	+	0.0401899i
$718$	−8.00000	−	13.8564i	−0.298557	−	0.517116i
$719$	−8.60660	+	14.9071i	−0.320972	+	0.555940i	−0.980689	−	0.195574i	$-0.937343\pi$
$719$	−8.60660	+	14.9071i	−0.320972	+	0.555940i	0.659717	+	0.751514i	$0.270676\pi$
$720$	−11.3137			−0.421637
$721$		0			0
$722$	24.0416			0.894737
$723$	−29.8492	+	51.7004i	−1.11011	+	1.92276i
$724$		0			0
$725$	−1.32843	−	2.30090i	−0.0493365	−	0.0854534i
$726$	−39.2132	+	67.9193i	−1.45534	+	2.52072i
$727$	−29.3137			−1.08719			−0.543593	−	0.839349i	$-0.682936\pi$
$727$	−29.3137			−1.08719			−0.543593	+	0.839349i	$0.682936\pi$
$728$		0			0
$729$	−23.8284			−0.882534
$730$	−6.00000	+	10.3923i	−0.222070	+	0.384636i
$731$	5.24264	+	9.08052i	0.193906	+	0.335855i
$732$		0			0
$733$	22.3492	−	38.7100i	0.825488	−	1.42979i	−0.0760576	−	0.997103i	$-0.524233\pi$
$733$	22.3492	−	38.7100i	0.825488	−	1.42979i	0.901546	−	0.432684i	$-0.142433\pi$
$734$	42.2426			1.55920
$735$		0			0
$736$		0			0
$737$	0.707107	−	1.22474i	0.0260466	−	0.0451141i
$738$	−4.48528	−	7.76874i	−0.165105	−	0.285971i
$739$	1.98528	+	3.43861i	0.0730298	+	0.126491i	0.900228	−	0.435419i	$-0.143400\pi$
$739$	1.98528	+	3.43861i	0.0730298	+	0.126491i	−0.827198	+	0.561911i	$0.810067\pi$
$740$		0			0
$741$	22.9706			0.843845
$742$		0			0
$743$	36.7279			1.34742			0.673708	−	0.738997i	$-0.264700\pi$
$743$	36.7279			1.34742			0.673708	+	0.738997i	$0.264700\pi$
$744$	6.00000	−	10.3923i	0.219971	−	0.381000i
$745$	7.41421	+	12.8418i	0.271636	+	0.470487i
$746$	−0.343146	−	0.594346i	−0.0125635	−	0.0217605i
$747$		0			0
$748$		0			0
$749$		0			0
$750$	3.41421			0.124669
$751$	−6.25736	+	10.8381i	−0.228334	+	0.395487i	−0.957315	−	0.289048i	$-0.906661\pi$
$751$	−6.25736	+	10.8381i	−0.228334	+	0.395487i	0.728980	+	0.684535i	$0.239995\pi$
$752$	2.48528	+	4.30463i	0.0906289	+	0.156974i
$753$	30.4350	+	52.7150i	1.10911	+	1.92104i
$754$	−2.97918	+	5.16010i	−0.108496	+	0.187920i
$755$	9.48528			0.345205
$756$		0			0
$757$	−16.4853			−0.599168			−0.299584	−	0.954070i	$-0.596848\pi$
$757$	−16.4853			−0.599168			−0.299584	+	0.954070i	$0.596848\pi$
$758$	−1.41421	+	2.44949i	−0.0513665	+	0.0889695i
$759$	32.2635	+	55.8819i	1.17109	+	2.02839i
$760$	8.48528	+	14.6969i	0.307794	+	0.533114i
$761$	−6.36396	+	11.0227i	−0.230693	+	0.399573i	−0.958012	−	0.286727i	$-0.907433\pi$
$761$	−6.36396	+	11.0227i	−0.230693	+	0.399573i	0.727319	+	0.686300i	$0.240766\pi$
$762$	−0.828427			−0.0300107
$763$		0			0
$764$		0			0
$765$	7.41421	−	12.8418i	0.268061	−	0.464296i
$766$	8.82843	+	15.2913i	0.318984	+	0.552497i
$767$	−4.94975	−	8.57321i	−0.178725	−	0.309561i
$768$		0			0
$769$	−3.17157			−0.114370			−0.0571849	−	0.998364i	$-0.518212\pi$
$769$	−3.17157			−0.114370			−0.0571849	+	0.998364i	$0.518212\pi$
$770$		0			0
$771$	−63.9411			−2.30278
$772$		0			0
$773$	−18.1066	−	31.3616i	−0.651249	−	1.12800i	−0.982820	−	0.184566i	$-0.940912\pi$
$773$	−18.1066	−	31.3616i	−0.651249	−	1.12800i	0.331571	−	0.943430i	$-0.392421\pi$
$774$	−4.00000	−	6.92820i	−0.143777	−	0.249029i
$775$	−0.878680	+	1.52192i	−0.0315631	+	0.0546689i
$776$	−13.4558			−0.483037
$777$		0			0
$778$	−49.6985			−1.78178
$779$	−6.72792	+	11.6531i	−0.241053	+	0.417516i
$780$		0			0
$781$	−25.7279	−	44.5621i	−0.920617	−	1.59456i
$782$	17.0000	−	29.4449i	0.607919	−	1.05295i
$783$	−1.10051			−0.0393288
$784$		0			0
$785$	−20.8284			−0.743398
$786$	−6.41421	+	11.1097i	−0.228787	+	0.396271i
$787$	−22.8640	−	39.6015i	−0.815012	−	1.41164i	−0.909319	−	0.416099i	$-0.863397\pi$
$787$	−22.8640	−	39.6015i	−0.815012	−	1.41164i	0.0943070	−	0.995543i	$-0.469936\pi$
$788$		0			0
$789$	−34.5563	+	59.8534i	−1.23024	+	2.13084i
$790$	−21.8995			−0.779149
$791$		0			0
$792$	46.6274			1.65683
$793$	−2.24264	+	3.88437i	−0.0796385	+	0.137938i
$794$	−3.12132	−	5.40629i	−0.110772	−	0.191862i
$795$	5.12132	+	8.87039i	0.181635	+	0.314600i
$796$		0			0
$797$	55.1838			1.95471			0.977355	−	0.211608i	$-0.0678700\pi$
$797$	55.1838			1.95471			0.977355	+	0.211608i	$0.0678700\pi$
$798$		0			0
$799$	−6.51472			−0.230474
$800$		0			0
$801$	11.3137	+	19.5959i	0.399750	+	0.692388i
$802$	−4.36396	−	7.55860i	−0.154097	−	0.266904i
$803$	24.7279	−	42.8300i	0.872629	−	1.51144i
$804$		0			0
$805$		0			0
$806$	3.94113			0.138820
$807$	9.36396	−	16.2189i	0.329627	−	0.570931i
$808$	−20.4853	−	35.4815i	−0.720670	−	1.24824i
$809$	−15.2990	−	26.4986i	−0.537884	−	0.931642i	−0.999018	−	0.0443116i	$-0.985891\pi$
$809$	−15.2990	−	26.4986i	−0.537884	−	0.931642i	0.461134	−	0.887331i	$-0.347443\pi$
$810$	6.70711	−	11.6170i	0.235664	−	0.408182i
$811$	−23.3553			−0.820117			−0.410058	−	0.912059i	$-0.634492\pi$
$811$	−23.3553			−0.820117			−0.410058	+	0.912059i	$0.634492\pi$
$812$		0			0
$813$	−56.2843			−1.97398
$814$	−25.7279	+	44.5621i	−0.901763	+	1.56190i
$815$	0.878680	+	1.52192i	0.0307788	+	0.0533105i
$816$	−25.3137	−	43.8446i	−0.886157	−	1.53487i
$817$	−6.00000	+	10.3923i	−0.209913	+	0.363581i
$818$	−20.4853			−0.716251
$819$		0			0
$820$		0			0
$821$	3.25736	−	5.64191i	0.113683	−	0.196904i	−0.803570	−	0.595211i	$-0.797069\pi$
$821$	3.25736	−	5.64191i	0.113683	−	0.196904i	0.917252	+	0.398307i	$0.130402\pi$
$822$	−20.4853	−	35.4815i	−0.714506	−	1.23756i
$823$	4.36396	+	7.55860i	0.152118	+	0.263476i	0.932006	−	0.362443i	$-0.118057\pi$
$823$	4.36396	+	7.55860i	0.152118	+	0.263476i	−0.779888	+	0.625919i	$0.784724\pi$
$824$	15.2132	−	26.3500i	0.529977	−	0.917947i
$825$	−14.0711			−0.489892
$826$		0			0
$827$	−6.04163			−0.210088			−0.105044	−	0.994468i	$-0.533498\pi$
$827$	−6.04163			−0.210088			−0.105044	+	0.994468i	$0.533498\pi$
$828$		0			0
$829$	−27.0208	−	46.8014i	−0.938472	−	1.62548i	−0.768323	−	0.640062i	$-0.778909\pi$
$829$	−27.0208	−	46.8014i	−0.938472	−	1.62548i	−0.170149	−	0.985418i	$-0.554425\pi$
$830$		0			0
$831$	32.8492	−	56.8966i	1.13953	−	1.97372i
$832$	12.6863			0.439818
$833$		0			0
$834$	55.4558			1.92028
$835$	−4.62132	+	8.00436i	−0.159927	+	0.277002i
$836$		0			0
$837$	0.363961	+	0.630399i	0.0125803	+	0.0217898i
$838$	4.75736	−	8.23999i	0.164340	−	0.284646i
$839$	−48.7279			−1.68227			−0.841137	−	0.540822i	$-0.818113\pi$
$839$	−48.7279			−1.68227			−0.841137	+	0.540822i	$0.818113\pi$
$840$		0			0
$841$	−21.9411			−0.756591
$842$	13.4350	−	23.2702i	0.463002	−	0.801942i
$843$	24.5208	+	42.4713i	0.844542	+	1.46279i
$844$		0			0
$845$	5.24264	−	9.08052i	0.180352	−	0.312379i
$846$	4.97056			0.170891
$847$		0			0
$848$	16.9706			0.582772
$849$	7.91421	−	13.7078i	0.271615	−	0.470451i
$850$	3.70711	+	6.42090i	0.127153	+	0.220235i
$851$	14.3137	+	24.7921i	0.490668	+	0.849861i
$852$		0			0
$853$	−22.9706			−0.786497			−0.393249	−	0.919432i	$-0.628649\pi$
$853$	−22.9706			−0.786497			−0.393249	+	0.919432i	$0.628649\pi$
$854$		0			0
$855$	16.9706			0.580381
$856$	20.4853	−	35.4815i	0.700173	−	1.21273i
$857$	2.75736	+	4.77589i	0.0941896	+	0.163141i	0.909270	−	0.416207i	$-0.136641\pi$
$857$	2.75736	+	4.77589i	0.0941896	+	0.163141i	−0.815080	+	0.579348i	$0.803307\pi$
$858$	15.7782	+	27.3286i	0.538658	+	0.932983i
$859$	−24.3848	+	42.2357i	−0.831998	+	1.44106i	0.0644537	+	0.997921i	$0.479470\pi$
$859$	−24.3848	+	42.2357i	−0.831998	+	1.44106i	−0.896452	+	0.443142i	$0.853864\pi$
$860$		0			0
$861$		0			0
$862$	15.2721			0.520169
$863$	9.19239	−	15.9217i	0.312913	−	0.541980i	−0.666079	−	0.745881i	$-0.732029\pi$
$863$	9.19239	−	15.9217i	0.312913	−	0.541980i	0.978992	+	0.203901i	$0.0653620\pi$
$864$		0			0
$865$	−0.621320	−	1.07616i	−0.0211255	−	0.0365905i
$866$	16.2426	−	28.1331i	0.551947	−	0.956001i
$867$	25.3137			0.859699
$868$		0			0
$869$	90.2548			3.06169
$870$	−4.53553	+	7.85578i	−0.153769	+	0.266336i
$871$	−0.192388	−	0.333226i	−0.00651882	−	0.0112909i
$872$	7.07107	+	12.2474i	0.239457	+	0.414751i
$873$	−6.72792	+	11.6531i	−0.227706	+	0.394398i
$874$	38.9117			1.31621
$875$		0			0
$876$		0			0
$877$	−23.4853	+	40.6777i	−0.793042	+	1.37359i	0.131034	+	0.991378i	$0.458170\pi$
$877$	−23.4853	+	40.6777i	−0.793042	+	1.37359i	−0.924075	+	0.382210i	$0.875163\pi$
$878$	−4.51472	−	7.81972i	−0.152364	−	0.263903i
$879$	−0.328427	−	0.568852i	−0.0110776	−	0.0191869i
$880$	−11.6569	+	20.1903i	−0.392952	+	0.680614i
$881$	−19.0294			−0.641118			−0.320559	−	0.947229i	$-0.603871\pi$
$881$	−19.0294			−0.641118			−0.320559	+	0.947229i	$0.603871\pi$
$882$		0			0
$883$	48.4853			1.63166			0.815830	−	0.578292i	$-0.196281\pi$
$883$	48.4853			1.63166			0.815830	+	0.578292i	$0.196281\pi$
$884$		0			0
$885$	−7.53553	−	13.0519i	−0.253304	−	0.438736i
$886$	−14.7279	−	25.5095i	−0.494794	−	0.857009i
$887$	15.4853	−	26.8213i	0.519945	−	0.900571i	−0.479786	−	0.877385i	$-0.659286\pi$
$887$	15.4853	−	26.8213i	0.519945	−	0.900571i	0.999731	−	0.0231855i	$-0.00738085\pi$
$888$	42.6274			1.43048
$889$		0			0
$890$	−11.3137			−0.379236
$891$	−27.6421	+	47.8776i	−0.926046	+	1.60396i
$892$		0			0
$893$	−3.72792	−	6.45695i	−0.124750	−	0.216074i
$894$	25.3137	−	43.8446i	0.846617	−	1.46638i
$895$	2.48528			0.0830738
$896$		0			0
$897$	17.5563			0.586189
$898$	21.0919	−	36.5322i	0.703845	−	1.21910i
$899$	−2.33452	−	4.04351i	−0.0778607	−	0.134859i
$900$		0			0
$901$	−11.1213	+	19.2627i	−0.370505	+	0.641733i
$902$	−18.4853			−0.615493
$903$		0			0
$904$	−3.02944			−0.100758
$905$	−3.36396	+	5.82655i	−0.111822	+	0.193681i
$906$	−16.1924	−	28.0460i	−0.537956	−	0.931767i
$907$	−16.0919	−	27.8720i	−0.534322	−	0.925473i	−0.999196	−	0.0400962i	$-0.987234\pi$
$907$	−16.0919	−	27.8720i	−0.534322	−	0.925473i	0.464874	−	0.885377i	$-0.346100\pi$
$908$		0			0
$909$	−40.9706			−1.35891
$910$		0			0
$911$	−5.65685			−0.187420			−0.0937100	−	0.995600i	$-0.529873\pi$
$911$	−5.65685			−0.187420			−0.0937100	+	0.995600i	$0.529873\pi$
$912$	28.9706	−	50.1785i	0.959311	−	1.66158i
$913$		0			0
$914$	14.3137	+	24.7921i	0.473455	+	0.820049i
$915$	−3.41421	+	5.91359i	−0.112870	+	0.195497i
$916$		0			0
$917$		0			0
$918$	3.07107			0.101360
$919$	19.2279	−	33.3037i	0.634271	−	1.09859i	−0.352399	−	0.935850i	$-0.614634\pi$
$919$	19.2279	−	33.3037i	0.634271	−	1.09859i	0.986669	−	0.162739i	$-0.0520328\pi$
$920$	6.48528	+	11.2328i	0.213813	+	0.370336i
$921$	−13.3995	−	23.2086i	−0.441528	−	0.764750i
$922$	−26.1421	+	45.2795i	−0.860945	+	1.49120i
$923$	−14.0000			−0.460816
$924$		0			0
$925$	−6.24264			−0.205257
$926$	−20.8284	+	36.0759i	−0.684465	+	1.18553i
$927$	−15.2132	−	26.3500i	−0.499667	−	0.865449i
$928$		0			0
$929$	−27.3640	+	47.3958i	−0.897782	+	1.55500i	−0.0674597	+	0.997722i	$0.521489\pi$
$929$	−27.3640	+	47.3958i	−0.897782	+	1.55500i	−0.830323	+	0.557283i	$0.811844\pi$
$930$	6.00000			0.196748
$931$		0			0
$932$		0			0
$933$	12.0711	−	20.9077i	0.395189	−	0.684487i
$934$	−13.9497	−	24.1617i	−0.456450	−	0.790594i
$935$	−15.2782	−	26.4626i	−0.499650	−	0.865419i
$936$	6.34315	−	10.9867i	0.207332	−	0.359110i
$937$	−17.4437			−0.569859			−0.284930	−	0.958548i	$-0.591970\pi$
$937$	−17.4437			−0.569859			−0.284930	+	0.958548i	$0.591970\pi$
$938$		0			0
$939$	58.4558			1.90763
$940$		0			0
$941$	2.48528	+	4.30463i	0.0810179	+	0.140327i	0.903687	−	0.428193i	$-0.140850\pi$
$941$	2.48528	+	4.30463i	0.0810179	+	0.140327i	−0.822670	+	0.568520i	$0.807516\pi$
$942$	35.5563	+	61.5854i	1.15849	+	2.00656i
$943$	−5.14214	+	8.90644i	−0.167451	+	0.290034i
$944$	−24.9706			−0.812723
$945$		0			0
$946$	−16.4853			−0.535983
$947$	21.8787	−	37.8950i	0.710962	−	1.23142i	−0.253535	−	0.967326i	$-0.581593\pi$
$947$	21.8787	−	37.8950i	0.710962	−	1.23142i	0.964497	−	0.264095i	$-0.0850734\pi$
$948$		0			0
$949$	−6.72792	−	11.6531i	−0.218398	−	0.378276i
$950$	−4.24264	+	7.34847i	−0.137649	+	0.238416i
$951$	−28.1421			−0.912571
$952$		0			0
$953$	−29.0122			−0.939797			−0.469899	−	0.882720i	$-0.655710\pi$
$953$	−29.0122			−0.939797			−0.469899	+	0.882720i	$0.655710\pi$
$954$	8.48528	−	14.6969i	0.274721	−	0.475831i
$955$	9.98528	+	17.2950i	0.323116	+	0.559654i
$956$		0			0
$957$	18.6924	−	32.3762i	0.604239	−	1.04657i
$958$	28.6274			0.924910
$959$		0			0
$960$	19.3137			0.623347
$961$	13.9558	−	24.1722i	0.450189	−	0.779749i
$962$	7.00000	+	12.1244i	0.225689	+	0.390905i
$963$	−20.4853	−	35.4815i	−0.660129	−	1.14338i
$964$		0			0
$965$	−16.0000			−0.515058
$966$		0			0
$967$	24.4264			0.785500			0.392750	−	0.919645i	$-0.371524\pi$
$967$	24.4264			0.785500			0.392750	+	0.919645i	$0.371524\pi$
$968$	32.4853	−	56.2662i	1.04412	−	1.80846i
$969$	37.9706	+	65.7669i	1.21979	+	2.11274i
$970$	−3.36396	−	5.82655i	−0.108010	−	0.187079i
$971$	21.3640	−	37.0035i	0.685602	−	1.18750i	−0.287645	−	0.957737i	$-0.592872\pi$
$971$	21.3640	−	37.0035i	0.685602	−	1.18750i	0.973247	−	0.229761i	$-0.0737943\pi$
$972$		0			0
$973$		0			0
$974$	−44.8284			−1.43640
$975$	−1.91421	+	3.31552i	−0.0613039	+	0.106181i
$976$	5.65685	+	9.79796i	0.181071	+	0.313625i
$977$	15.3848	+	26.6472i	0.492203	+	0.852520i	0.999960	−	0.00898038i	$-0.00285858\pi$
$977$	15.3848	+	26.6472i	0.492203	+	0.852520i	−0.507757	+	0.861500i	$0.669525\pi$
$978$	3.00000	−	5.19615i	0.0959294	−	0.166155i
$979$	46.6274			1.49022
$980$		0			0
$981$	14.1421			0.451524
$982$	−13.6360	+	23.6183i	−0.435143	+	0.753691i
$983$	21.1066	+	36.5577i	0.673196	+	1.16601i	0.976993	+	0.213273i	$0.0684123\pi$
$983$	21.1066	+	36.5577i	0.673196	+	1.16601i	−0.303797	+	0.952737i	$0.598254\pi$
$984$	7.65685	+	13.2621i	0.244092	+	0.422779i
$985$	−5.29289	+	9.16756i	−0.168646	+	0.292103i
$986$	−19.6985			−0.627328
$987$		0			0
$988$		0			0
$989$	−4.58579	+	7.94282i	−0.145820	+	0.252567i
$990$	11.6569	+	20.1903i	0.370479	+	0.641689i
$991$	23.9706	+	41.5182i	0.761450	+	1.31887i	0.942103	+	0.335323i	$0.108846\pi$
$991$	23.9706	+	41.5182i	0.761450	+	1.31887i	−0.180653	+	0.983547i	$0.557821\pi$
$992$		0			0
$993$	56.6274			1.79702
$994$		0			0
$995$	−4.58579			−0.145379
$996$		0			0
$997$	−1.86396	−	3.22848i	−0.0590322	−	0.102247i	0.834999	−	0.550251i	$-0.185468\pi$
$997$	−1.86396	−	3.22848i	−0.0590322	−	0.102247i	−0.894031	+	0.448005i	$0.852135\pi$
$998$	−2.12132	−	3.67423i	−0.0671492	−	0.116306i
$999$	−1.29289	+	2.23936i	−0.0409053	+	0.0708501i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.2.e.f.226.1		4
7.2	even	3		245.2.a.f.1.2	yes	2
7.3	odd	6		245.2.e.g.116.1		4
7.4	even	3	inner	245.2.e.f.116.1		4
7.5	odd	6		245.2.a.e.1.2	✓	2
7.6	odd	2		245.2.e.g.226.1		4
21.2	odd	6		2205.2.a.t.1.1		2
21.5	even	6		2205.2.a.v.1.1		2
28.19	even	6		3920.2.a.bw.1.2		2
28.23	odd	6		3920.2.a.br.1.1		2
35.2	odd	12		1225.2.b.j.99.3		4
35.9	even	6		1225.2.a.p.1.1		2
35.12	even	12		1225.2.b.i.99.4		4
35.19	odd	6		1225.2.a.r.1.1		2
35.23	odd	12		1225.2.b.j.99.2		4
35.33	even	12		1225.2.b.i.99.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.2.a.e.1.2	✓	2	7.5	odd	6
245.2.a.f.1.2	yes	2	7.2	even	3
245.2.e.f.116.1		4	7.4	even	3	inner
245.2.e.f.226.1		4	1.1	even	1	trivial
245.2.e.g.116.1		4	7.3	odd	6
245.2.e.g.226.1		4	7.6	odd	2
1225.2.a.p.1.1		2	35.9	even	6
1225.2.a.r.1.1		2	35.19	odd	6
1225.2.b.i.99.1		4	35.33	even	12
1225.2.b.i.99.4		4	35.12	even	12
1225.2.b.j.99.2		4	35.23	odd	12
1225.2.b.j.99.3		4	35.2	odd	12
2205.2.a.t.1.1		2	21.2	odd	6
2205.2.a.v.1.1		2	21.5	even	6
3920.2.a.br.1.1		2	28.23	odd	6
3920.2.a.bw.1.2		2	28.19	even	6

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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.20711 - 2.09077i) q^{3} +(-0.500000 + 0.866025i) q^{5} +3.41421 q^{6} -2.82843 q^{8} +(-1.41421 + 2.44949i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.20711 - 2.09077i) q^{3} +(-0.500000 + 0.866025i) q^{5} +3.41421 q^{6} -2.82843 q^{8} +(-1.41421 + 2.44949i) q^{9} +(-0.707107 - 1.22474i) q^{10} +(2.91421 + 5.04757i) q^{11} +1.58579 q^{13} +2.41421 q^{15} +(2.00000 - 3.46410i) q^{16} +(2.62132 + 4.54026i) q^{17} +(-2.00000 - 3.46410i) q^{18} +(-3.00000 + 5.19615i) q^{19} -8.24264 q^{22} +(-2.29289 + 3.97141i) q^{23} +(3.41421 + 5.91359i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.12132 + 1.94218i) q^{26} -0.414214 q^{27} +2.65685 q^{29} +(-1.70711 + 2.95680i) q^{30} +(-0.878680 - 1.52192i) q^{31} +(7.03553 - 12.1859i) q^{33} -7.41421 q^{34} +(3.12132 - 5.40629i) q^{37} +(-4.24264 - 7.34847i) q^{38} +(-1.91421 - 3.31552i) q^{39} +(1.41421 - 2.44949i) q^{40} +2.24264 q^{41} +2.00000 q^{43} +(-1.41421 - 2.44949i) q^{45} +(-3.24264 - 5.61642i) q^{46} +(-0.621320 + 1.07616i) q^{47} -9.65685 q^{48} +1.41421 q^{50} +(6.32843 - 10.9612i) q^{51} +(2.12132 + 3.67423i) q^{53} +(0.292893 - 0.507306i) q^{54} -5.82843 q^{55} +14.4853 q^{57} +(-1.87868 + 3.25397i) q^{58} +(-3.12132 - 5.40629i) q^{59} +(-1.41421 + 2.44949i) q^{61} +2.48528 q^{62} +8.00000 q^{64} +(-0.792893 + 1.37333i) q^{65} +(9.94975 + 17.2335i) q^{66} +(-0.121320 - 0.210133i) q^{67} +11.0711 q^{69} -8.82843 q^{71} +(4.00000 - 6.92820i) q^{72} +(-4.24264 - 7.34847i) q^{73} +(4.41421 + 7.64564i) q^{74} +(-1.20711 + 2.09077i) q^{75} +5.41421 q^{78} +(7.74264 - 13.4106i) q^{79} +(2.00000 + 3.46410i) q^{80} +(4.74264 + 8.21449i) q^{81} +(-1.58579 + 2.74666i) q^{82} -5.24264 q^{85} +(-1.41421 + 2.44949i) q^{86} +(-3.20711 - 5.55487i) q^{87} +(-8.24264 - 14.2767i) q^{88} +(4.00000 - 6.92820i) q^{89} +4.00000 q^{90} +(-2.12132 + 3.67423i) q^{93} +(-0.878680 - 1.52192i) q^{94} +(-3.00000 - 5.19615i) q^{95} +4.75736 q^{97} -16.4853 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 2 q^{5} + 8 q^{6}+O(q^{10}) \) 4 * q - 2 * q^3 - 2 * q^5 + 8 * q^6	\( 4 q - 2 q^{3} - 2 q^{5} + 8 q^{6} + 6 q^{11} + 12 q^{13} + 4 q^{15} + 8 q^{16} + 2 q^{17} - 8 q^{18} - 12 q^{19} - 16 q^{22} - 12 q^{23} + 8 q^{24} - 2 q^{25} + 4 q^{26} + 4 q^{27} - 12 q^{29} - 4 q^{30} - 12 q^{31} + 14 q^{33} - 24 q^{34} + 4 q^{37} - 2 q^{39} - 8 q^{41} + 8 q^{43} + 4 q^{46} + 6 q^{47} - 16 q^{48} + 14 q^{51} + 4 q^{54} - 12 q^{55} + 24 q^{57} - 16 q^{58} - 4 q^{59} - 24 q^{62} + 32 q^{64} - 6 q^{65} + 20 q^{66} + 8 q^{67} + 16 q^{69} - 24 q^{71} + 16 q^{72} + 12 q^{74} - 2 q^{75} + 16 q^{78} + 14 q^{79} + 8 q^{80} + 2 q^{81} - 12 q^{82} - 4 q^{85} - 10 q^{87} - 16 q^{88} + 16 q^{89} + 16 q^{90} - 12 q^{94} - 12 q^{95} + 36 q^{97} - 32 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - 2 * q^5 + 8 * q^6 + 6 * q^11 + 12 * q^13 + 4 * q^15 + 8 * q^16 + 2 * q^17 - 8 * q^18 - 12 * q^19 - 16 * q^22 - 12 * q^23 + 8 * q^24 - 2 * q^25 + 4 * q^26 + 4 * q^27 - 12 * q^29 - 4 * q^30 - 12 * q^31 + 14 * q^33 - 24 * q^34 + 4 * q^37 - 2 * q^39 - 8 * q^41 + 8 * q^43 + 4 * q^46 + 6 * q^47 - 16 * q^48 + 14 * q^51 + 4 * q^54 - 12 * q^55 + 24 * q^57 - 16 * q^58 - 4 * q^59 - 24 * q^62 + 32 * q^64 - 6 * q^65 + 20 * q^66 + 8 * q^67 + 16 * q^69 - 24 * q^71 + 16 * q^72 + 12 * q^74 - 2 * q^75 + 16 * q^78 + 14 * q^79 + 8 * q^80 + 2 * q^81 - 12 * q^82 - 4 * q^85 - 10 * q^87 - 16 * q^88 + 16 * q^89 + 16 * q^90 - 12 * q^94 - 12 * q^95 + 36 * q^97 - 32 * q^99

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