LMFDB - Embedded newform 605.2.m.b.118.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(112,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 2]))

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

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

chi := DirichletCharacter("605.112");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.m (of order $20$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	$\Q(\zeta_{40})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{12} + x^{8} - x^{4} + 1 $ x^16 - x^12 + x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{4} $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			118.2
Root			$0.987688 - 0.156434i$ of defining polynomial
Character	$\chi$	$=$	605.118
Dual form			605.2.m.b.282.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.20854 + 0.349798i) q^{2} +(0.642040 - 1.26007i) q^{3} +(2.85317 + 0.927051i) q^{4} +(1.03025 + 1.98459i) q^{5} +(1.85874 - 2.55834i) q^{6} +(1.99235 + 1.01515i) q^{8} +(0.587785 + 0.809017i) q^{9} +O(q^{10})$	\(q+(2.20854 + 0.349798i) q^{2} +(0.642040 - 1.26007i) q^{3} +(2.85317 + 0.927051i) q^{4} +(1.03025 + 1.98459i) q^{5} +(1.85874 - 2.55834i) q^{6} +(1.99235 + 1.01515i) q^{8} +(0.587785 + 0.809017i) q^{9} +(1.58114 + 4.74342i) q^{10} +(3.00000 - 3.00000i) q^{12} +(-0.699596 + 4.41708i) q^{13} +(3.16219 - 0.0240055i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.699596 - 4.41708i) q^{17} +(1.01515 + 1.99235i) q^{18} +(-1.95440 - 6.01501i) q^{19} +(1.09966 + 6.61746i) q^{20} +(-1.00000 - 1.00000i) q^{23} +(2.55834 - 1.85874i) q^{24} +(-2.87718 + 4.08924i) q^{25} +(-3.09017 + 9.51057i) q^{26} +(5.58721 - 0.884927i) q^{27} +(1.95440 - 6.01501i) q^{29} +(6.99221 + 1.05311i) q^{30} +(-1.61803 + 1.17557i) q^{31} +(-4.74342 - 4.74342i) q^{32} -10.0000i q^{34} +(0.927051 + 2.85317i) q^{36} +(-1.92612 - 3.78022i) q^{37} +(-2.21232 - 13.9680i) q^{38} +(5.11667 + 3.71748i) q^{39} +(0.0379561 + 4.99986i) q^{40} +(-6.01501 + 1.95440i) q^{41} +(-1.00000 + 2.00000i) q^{45} +(-1.85874 - 2.55834i) q^{46} +(3.78022 + 1.92612i) q^{47} +(-1.26007 + 0.642040i) q^{48} +(-4.11450 + 5.66312i) q^{49} +(-7.78476 + 8.02481i) q^{50} +(-6.01501 - 1.95440i) q^{51} +(-6.09092 + 11.9541i) q^{52} +(1.39680 + 0.221232i) q^{53} +12.6491 q^{54} +(-8.83415 - 1.39919i) q^{57} +(6.42040 - 12.6007i) q^{58} +(5.70634 + 1.85410i) q^{59} +(9.04451 + 2.86302i) q^{60} +(-3.71748 + 5.11667i) q^{61} +(-3.98470 + 2.03031i) q^{62} +(-7.64121 - 10.5172i) q^{64} +(-9.48683 + 3.16228i) q^{65} +(3.00000 - 3.00000i) q^{67} +(2.09879 - 13.2512i) q^{68} +(-1.90211 + 0.618034i) q^{69} +(6.47214 + 4.70228i) q^{71} +(0.349798 + 2.20854i) q^{72} +(2.03031 + 3.98470i) q^{73} +(-2.93159 - 9.02251i) q^{74} +(3.30548 + 6.25090i) q^{75} -18.9737i q^{76} +(10.0000 + 10.0000i) q^{78} +(-5.11667 + 3.71748i) q^{79} +(0.333023 - 2.21113i) q^{80} +(1.54508 - 4.75528i) q^{81} +(-13.9680 + 2.21232i) q^{82} +(-8.83415 + 1.39919i) q^{83} +(8.04532 - 5.93910i) q^{85} +(-6.32456 - 6.32456i) q^{87} +6.00000i q^{89} +(-2.90813 + 4.06728i) q^{90} +(-1.92612 - 3.78022i) q^{92} +(0.442463 + 2.79360i) q^{93} +(7.67501 + 5.57622i) q^{94} +(9.92380 - 10.0756i) q^{95} +(-9.02251 + 2.93159i) q^{96} +(1.54862 - 9.77762i) q^{97} +(-11.0680 + 11.0680i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3} + 8 q^{5}+O(q^{10}) $ 16 * q + 4 * q^3 + 8 * q^5	$ 16 q + 4 q^{3} + 8 q^{5} + 48 q^{12} - 4 q^{15} - 4 q^{16} - 12 q^{20} - 16 q^{23} - 12 q^{25} + 40 q^{26} + 16 q^{27} - 8 q^{31} - 12 q^{36} - 12 q^{37} - 40 q^{38} - 16 q^{45} - 12 q^{47} + 4 q^{48} + 4 q^{53} + 40 q^{58} + 36 q^{60} + 48 q^{67} + 32 q^{71} - 4 q^{75} + 160 q^{78} + 8 q^{80} - 20 q^{81} - 40 q^{82} - 12 q^{92} + 8 q^{93} + 28 q^{97}+O(q^{100}) $ 16 * q + 4 * q^3 + 8 * q^5 + 48 * q^12 - 4 * q^15 - 4 * q^16 - 12 * q^20 - 16 * q^23 - 12 * q^25 + 40 * q^26 + 16 * q^27 - 8 * q^31 - 12 * q^36 - 12 * q^37 - 40 * q^38 - 16 * q^45 - 12 * q^47 + 4 * q^48 + 4 * q^53 + 40 * q^58 + 36 * q^60 + 48 * q^67 + 32 * q^71 - 4 * q^75 + 160 * q^78 + 8 * q^80 - 20 * q^81 - 40 * q^82 - 12 * q^92 + 8 * q^93 + 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	2.20854	+	0.349798i	1.56167	+	0.247345i	0.876632	−	0.481161i	$-0.159785\pi$
$2$	2.20854	+	0.349798i	1.56167	+	0.247345i	0.685040	+	0.728505i	$0.259785\pi$
$3$	0.642040	−	1.26007i	0.370682	−	0.727504i	−0.628033	−	0.778187i	$-0.716140\pi$
$3$	0.642040	−	1.26007i	0.370682	−	0.727504i	0.998715	+	0.0506828i	$0.0161398\pi$
$4$	2.85317	+	0.927051i	1.42658	+	0.463525i
$5$	1.03025	+	1.98459i	0.460741	+	0.887535i
$5$	1.03025	+	1.98459i	0.460741	+	0.887535i
$6$	1.85874	−	2.55834i	0.758827	−	1.04444i
$7$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$7$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$8$	1.99235	+	1.01515i	0.704403	+	0.358911i
$9$	0.587785	+	0.809017i	0.195928	+	0.269672i
$10$	1.58114	+	4.74342i	0.500000	+	1.50000i
$11$		0			0
$11$		0			0
$12$	3.00000	−	3.00000i	0.866025	−	0.866025i
$13$	−0.699596	+	4.41708i	−0.194033	+	1.22508i	0.677790	+	0.735256i	$0.262938\pi$
$13$	−0.699596	+	4.41708i	−0.194033	+	1.22508i	−0.871823	+	0.489821i	$0.837062\pi$
$14$		0			0
$15$	3.16219	−	0.0240055i	0.816473	−	0.00619820i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−0.699596	−	4.41708i	−0.169677	−	1.07130i	−0.914663	−	0.404218i	$-0.867544\pi$
$17$	−0.699596	−	4.41708i	−0.169677	−	1.07130i	0.744986	−	0.667080i	$-0.232456\pi$
$18$	1.01515	+	1.99235i	0.239274	+	0.469602i
$19$	−1.95440	−	6.01501i	−0.448369	−	1.37994i	−0.878746	−	0.477289i	$-0.841620\pi$
$19$	−1.95440	−	6.01501i	−0.448369	−	1.37994i	0.430377	−	0.902649i	$-0.358380\pi$
$20$	1.09966	+	6.61746i	0.245892	+	1.47971i
$21$		0			0
$22$		0			0
$23$	−1.00000	−	1.00000i	−0.208514	−	0.208514i	0.595121	−	0.803636i	$-0.297104\pi$
$23$	−1.00000	−	1.00000i	−0.208514	−	0.208514i	−0.803636	+	0.595121i	$0.797104\pi$
$24$	2.55834	−	1.85874i	0.522218	−	0.379414i
$25$	−2.87718	+	4.08924i	−0.575435	+	0.817848i
$26$	−3.09017	+	9.51057i	−0.606032	+	1.86518i
$27$	5.58721	−	0.884927i	1.07526	−	0.170304i
$28$		0			0
$29$	1.95440	−	6.01501i	0.362922	−	1.11696i	−0.588350	−	0.808606i	$-0.700222\pi$
$29$	1.95440	−	6.01501i	0.362922	−	1.11696i	0.951272	−	0.308353i	$-0.0997777\pi$
$30$	6.99221	+	1.05311i	1.27660	+	0.192271i
$31$	−1.61803	+	1.17557i	−0.290607	+	0.211139i	−0.723531	−	0.690292i	$-0.757482\pi$
$31$	−1.61803	+	1.17557i	−0.290607	+	0.211139i	0.432923	+	0.901431i	$0.357482\pi$
$32$	−4.74342	−	4.74342i	−0.838525	−	0.838525i
$33$		0			0
$34$		−	10.0000i		−	1.71499i
$35$		0			0
$36$	0.927051	+	2.85317i	0.154508	+	0.475528i
$37$	−1.92612	−	3.78022i	−0.316652	−	0.621464i	0.676742	−	0.736220i	$-0.263391\pi$
$37$	−1.92612	−	3.78022i	−0.316652	−	0.621464i	−0.993394	+	0.114756i	$0.963391\pi$
$38$	−2.21232	−	13.9680i	−0.358885	−	2.26591i
$39$	5.11667	+	3.71748i	0.819323	+	0.595273i
$40$	0.0379561	+	4.99986i	0.00600138	+	0.790547i
$41$	−6.01501	+	1.95440i	−0.939387	+	0.305225i	−0.738396	−	0.674368i	$-0.764416\pi$
$41$	−6.01501	+	1.95440i	−0.939387	+	0.305225i	−0.200991	+	0.979593i	$0.564416\pi$
$42$		0			0
$43$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$43$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$44$		0			0
$45$	−1.00000	+	2.00000i	−0.149071	+	0.298142i
$46$	−1.85874	−	2.55834i	−0.274056	−	0.377206i
$47$	3.78022	+	1.92612i	0.551402	+	0.280953i	0.707411	−	0.706802i	$-0.249863\pi$
$47$	3.78022	+	1.92612i	0.551402	+	0.280953i	−0.156009	+	0.987756i	$0.549863\pi$
$48$	−1.26007	+	0.642040i	−0.181876	+	0.0926704i
$49$	−4.11450	+	5.66312i	−0.587785	+	0.809017i
$50$	−7.78476	+	8.02481i	−1.10093	+	1.13488i
$51$	−6.01501	−	1.95440i	−0.842270	−	0.273670i
$52$	−6.09092	+	11.9541i	−0.844659	+	1.65774i
$53$	1.39680	+	0.221232i	0.191866	+	0.0303885i	0.251628	−	0.967824i	$-0.419034\pi$
$53$	1.39680	+	0.221232i	0.191866	+	0.0303885i	−0.0597620	+	0.998213i	$0.519034\pi$
$54$	12.6491			1.72133
$55$		0			0
$56$		0			0
$57$	−8.83415	−	1.39919i	−1.17011	−	0.185328i
$58$	6.42040	−	12.6007i	0.843039	−	1.65456i
$59$	5.70634	+	1.85410i	0.742902	+	0.241384i	0.655924	−	0.754827i	$-0.272279\pi$
$59$	5.70634	+	1.85410i	0.742902	+	0.241384i	0.0869778	+	0.996210i	$0.472279\pi$
$60$	9.04451	+	2.86302i	1.16764	+	0.369614i
$61$	−3.71748	+	5.11667i	−0.475975	+	0.655123i	−0.977725	−	0.209890i	$-0.932690\pi$
$61$	−3.71748	+	5.11667i	−0.475975	+	0.655123i	0.501751	+	0.865012i	$0.332690\pi$
$62$	−3.98470	+	2.03031i	−0.506058	+	0.257849i
$63$		0			0
$64$	−7.64121	−	10.5172i	−0.955151	−	1.31465i
$65$	−9.48683	+	3.16228i	−1.17670	+	0.392232i
$66$		0			0
$67$	3.00000	−	3.00000i	0.366508	−	0.366508i	−0.499694	−	0.866202i	$-0.666554\pi$
$67$	3.00000	−	3.00000i	0.366508	−	0.366508i	0.866202	+	0.499694i	$0.166554\pi$
$68$	2.09879	−	13.2512i	0.254516	−	1.60695i
$69$	−1.90211	+	0.618034i	−0.228988	+	0.0744025i
$70$		0			0
$71$	6.47214	+	4.70228i	0.768101	+	0.558058i	0.901384	−	0.433020i	$-0.142552\pi$
$71$	6.47214	+	4.70228i	0.768101	+	0.558058i	−0.133283	+	0.991078i	$0.542552\pi$
$72$	0.349798	+	2.20854i	0.0412241	+	0.260279i
$73$	2.03031	+	3.98470i	0.237629	+	0.466374i	0.978766	−	0.204980i	$-0.0657130\pi$
$73$	2.03031	+	3.98470i	0.237629	+	0.466374i	−0.741137	+	0.671354i	$0.765713\pi$
$74$	−2.93159	−	9.02251i	−0.340791	−	1.04885i
$75$	3.30548	+	6.25090i	0.381684	+	0.721792i
$76$		−	18.9737i		−	2.17643i
$77$		0			0
$78$	10.0000	+	10.0000i	1.13228	+	1.13228i
$79$	−5.11667	+	3.71748i	−0.575671	+	0.418249i	−0.837161	−	0.546957i	$-0.815786\pi$
$79$	−5.11667	+	3.71748i	−0.575671	+	0.418249i	0.261490	+	0.965206i	$0.415786\pi$
$80$	0.333023	−	2.21113i	0.0372331	−	0.247212i
$81$	1.54508	−	4.75528i	0.171676	−	0.528365i
$82$	−13.9680	+	2.21232i	−1.54251	+	0.244310i
$83$	−8.83415	+	1.39919i	−0.969674	+	0.153581i	−0.621127	−	0.783710i	$-0.713325\pi$
$83$	−8.83415	+	1.39919i	−0.969674	+	0.153581i	−0.348547	+	0.937291i	$0.613325\pi$
$84$		0			0
$85$	8.04532	−	5.93910i	0.872637	−	0.644186i
$86$		0			0
$87$	−6.32456	−	6.32456i	−0.678064	−	0.678064i
$88$		0			0
$89$			6.00000i			0.635999i	0.948091	+	0.317999i	$0.103011\pi$
$89$			6.00000i			0.635999i	−0.948091	+	0.317999i	$0.896989\pi$
$90$	−2.90813	+	4.06728i	−0.306544	+	0.428729i
$91$		0			0
$92$	−1.92612	−	3.78022i	−0.200812	−	0.394115i
$93$	0.442463	+	2.79360i	0.0458813	+	0.289683i
$94$	7.67501	+	5.57622i	0.791617	+	0.575143i
$95$	9.92380	−	10.0756i	1.01816	−	1.03374i
$96$	−9.02251	+	2.93159i	−0.920857	+	0.299204i
$97$	1.54862	−	9.77762i	0.157239	−	0.992766i	−0.775273	−	0.631626i	$-0.782388\pi$
$97$	1.54862	−	9.77762i	0.157239	−	0.992766i	0.932512	−	0.361140i	$-0.117612\pi$
$98$	−11.0680	+	11.0680i	−1.11803	+	1.11803i
$99$		0			0
$100$	−12.0000	+	9.00000i	−1.20000	+	0.900000i
$101$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$101$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$102$	−12.6007	−	6.42040i	−1.24766	−	0.635714i
$103$	11.3407	−	5.77836i	1.11743	−	0.569358i	0.205069	−	0.978748i	$-0.434258\pi$
$103$	11.3407	−	5.77836i	1.11743	−	0.569358i	0.912360	+	0.409389i	$0.134258\pi$
$104$	−5.87785	+	8.09017i	−0.576371	+	0.793306i
$105$		0			0
$106$	3.00750	+	0.977198i	0.292115	+	0.0949138i
$107$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$107$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$108$	16.7616	+	2.65478i	1.61289	+	0.255456i
$109$	12.6491			1.21157			0.605783	−	0.795630i	$-0.292860\pi$
$109$	12.6491			1.21157			0.605783	+	0.795630i	$0.292860\pi$
$110$		0			0
$111$	−6.00000			−0.569495
$112$		0			0
$113$	−5.77836	+	11.3407i	−0.543582	+	1.06684i	0.441901	+	0.897064i	$0.354304\pi$
$113$	−5.77836	+	11.3407i	−0.543582	+	1.06684i	−0.985483	+	0.169776i	$0.945696\pi$
$114$	−19.0211	−	6.18034i	−1.78149	−	0.578842i
$115$	0.954339	−	3.01484i	0.0889925	−	0.281135i
$116$	11.1524	−	15.3500i	1.03548	−	1.42521i
$117$	−3.98470	+	2.03031i	−0.368386	+	0.187702i
$118$	11.9541	+	6.09092i	1.10046	+	0.560715i
$119$		0			0
$120$	6.32456	+	3.16228i	0.577350	+	0.288675i
$121$		0			0
$122$	−10.0000	+	10.0000i	−0.905357	+	0.905357i
$123$	−1.39919	+	8.83415i	−0.126161	+	0.796549i
$124$	−5.70634	+	1.85410i	−0.512444	+	0.166503i
$125$	−11.0797	−	1.49707i	−0.990995	−	0.133902i
$126$		0			0
$127$	−1.39919	−	8.83415i	−0.124158	−	0.783904i	−0.968667	−	0.248363i	$-0.920108\pi$
$127$	−1.39919	−	8.83415i	−0.124158	−	0.783904i	0.844509	−	0.535542i	$-0.179892\pi$
$128$	−7.10608	−	13.9465i	−0.628094	−	1.23270i
$129$		0			0
$130$	−22.0582	+	3.66554i	−1.93463	+	0.321489i
$131$			12.6491i			1.10516i	0.833461	+	0.552579i	$0.186356\pi$
$131$			12.6491i			1.10516i	−0.833461	+	0.552579i	$0.813644\pi$
$132$		0			0
$133$		0			0
$134$	7.67501	−	5.57622i	0.663020	−	0.481712i
$135$	7.51243	+	10.1766i	0.646567	+	0.875863i
$136$	3.09017	−	9.51057i	0.264980	−	0.815524i
$137$	−18.1584	+	2.87601i	−1.55138	+	0.245714i	−0.872529	−	0.488562i	$-0.837521\pi$
$137$	−18.1584	+	2.87601i	−1.55138	+	0.245714i	−0.678850	+	0.734277i	$0.737521\pi$
$138$	−4.41708	+	0.699596i	−0.376007	+	0.0595536i
$139$	−3.90879	+	12.0300i	−0.331539	+	1.02037i	0.636862	+	0.770977i	$0.280232\pi$
$139$	−3.90879	+	12.0300i	−0.331539	+	1.02037i	−0.968402	+	0.249395i	$0.919768\pi$
$140$		0			0
$141$	4.85410	−	3.52671i	0.408789	−	0.297003i
$142$	12.6491	+	12.6491i	1.06149	+	1.06149i
$143$		0			0
$144$		−	1.00000i		−	0.0833333i
$145$	13.9508	−	2.31829i	1.15855	−	0.192523i
$146$	3.09017	+	9.51057i	0.255744	+	0.787100i
$147$	4.49428	+	8.82051i	0.370682	+	0.727504i
$148$	−1.99109	−	12.5712i	−0.163666	−	1.03335i
$149$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$149$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$150$	5.11372	+	14.9616i	0.417534	+	1.22161i
$151$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$151$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$152$	2.21232	−	13.9680i	0.179443	−	1.13296i
$153$	3.16228	−	3.16228i	0.255655	−	0.255655i
$154$		0			0
$155$	−4.00000	−	2.00000i	−0.321288	−	0.160644i
$156$	11.1524	+	15.3500i	0.892910	+	1.22899i
$157$	−8.82051	−	4.49428i	−0.703954	−	0.358682i	0.0650892	−	0.997879i	$-0.479267\pi$
$157$	−8.82051	−	4.49428i	−0.703954	−	0.358682i	−0.769043	+	0.639197i	$0.779267\pi$
$158$	−12.6007	+	6.42040i	−1.00246	+	0.510779i
$159$	1.17557	−	1.61803i	0.0932288	−	0.128318i
$160$	4.52683	−	14.3006i	0.357877	−	1.13056i
$161$		0			0
$162$	5.07577	−	9.96176i	0.398790	−	0.782669i
$163$	1.39680	+	0.221232i	0.109406	+	0.0173282i	0.210897	−	0.977508i	$-0.432361\pi$
$163$	1.39680	+	0.221232i	0.109406	+	0.0173282i	−0.101491	+	0.994836i	$0.532361\pi$
$164$	−18.9737			−1.48159
$165$		0			0
$166$	−20.0000			−1.55230
$167$	17.6683	+	2.79838i	1.36721	+	0.216546i	0.796518	−	0.604615i	$-0.206673\pi$
$167$	17.6683	+	2.79838i	1.36721	+	0.216546i	0.570697	+	0.821161i	$0.306673\pi$
$168$		0			0
$169$	−6.65740	−	2.16312i	−0.512107	−	0.166394i
$170$	19.8459	−	10.3025i	1.52211	−	0.790165i
$171$	3.71748	−	5.11667i	0.284283	−	0.391282i
$172$		0			0
$173$	−3.98470	−	2.03031i	−0.302951	−	0.154361i	0.295906	−	0.955217i	$-0.404378\pi$
$173$	−3.98470	−	2.03031i	−0.302951	−	0.154361i	−0.598857	+	0.800856i	$0.704378\pi$
$174$	−11.7557	−	16.1803i	−0.891198	−	1.22663i
$175$		0			0
$176$		0			0
$177$	6.00000	−	6.00000i	0.450988	−	0.450988i
$178$	−2.09879	+	13.2512i	−0.157311	+	0.993222i
$179$	3.80423	−	1.23607i	0.284341	−	0.0923881i	−0.163374	−	0.986564i	$-0.552238\pi$
$179$	3.80423	−	1.23607i	0.284341	−	0.0923881i	0.447715	+	0.894176i	$0.352238\pi$
$180$	−4.70727	+	4.77929i	−0.350859	+	0.356227i
$181$	6.47214	+	4.70228i	0.481070	+	0.349518i	0.801740	−	0.597673i	$-0.203908\pi$
$181$	6.47214	+	4.70228i	0.481070	+	0.349518i	−0.320670	+	0.947191i	$0.603908\pi$
$182$		0			0
$183$	4.06061	+	7.96940i	0.300169	+	0.589115i
$184$	−0.977198	−	3.00750i	−0.0720400	−	0.221716i
$185$	5.51780	−	7.71712i	0.405677	−	0.567374i
$186$			6.32456i			0.463739i
$187$		0			0
$188$	9.00000	+	9.00000i	0.656392	+	0.656392i
$189$		0			0
$190$	25.4415	−	18.7811i	1.84572	−	1.36252i
$191$	6.79837	−	20.9232i	0.491913	−	1.51395i	−0.329800	−	0.944051i	$-0.606981\pi$
$191$	6.79837	−	20.9232i	0.491913	−	1.51395i	0.821713	−	0.569902i	$-0.193019\pi$
$192$	−18.1584	+	2.87601i	−1.31047	+	0.207558i
$193$	22.0854	−	3.49798i	1.58974	−	0.251790i	0.702015	−	0.712162i	$-0.252284\pi$
$193$	22.0854	−	3.49798i	1.58974	−	0.251790i	0.887726	+	0.460372i	$0.152284\pi$
$194$	6.84038	−	21.0525i	0.491111	−	1.51148i
$195$	−2.10622	+	13.9844i	−0.150830	+	1.00144i
$196$	−16.9894	+	12.3435i	−1.21353	+	0.881678i
$197$	−3.16228	−	3.16228i	−0.225303	−	0.225303i	0.585424	−	0.810727i	$-0.300928\pi$
$197$	−3.16228	−	3.16228i	−0.225303	−	0.225303i	−0.810727	+	0.585424i	$0.800928\pi$
$198$		0			0
$199$			6.00000i			0.425329i	0.977125	+	0.212664i	$0.0682141\pi$
$199$			6.00000i			0.425329i	−0.977125	+	0.212664i	$0.931786\pi$
$200$	−9.88355	+	5.22642i	−0.698872	+	0.369564i
$201$	−1.85410	−	5.70634i	−0.130778	−	0.402494i
$202$		0			0
$203$		0			0
$204$	−15.3500	−	11.1524i	−1.07472	−	0.780827i
$205$	−10.0756	−	9.92380i	−0.703712	−	0.693108i
$206$	27.0675	−	8.79478i	1.88589	−	0.612761i
$207$	0.221232	−	1.39680i	0.0153767	−	0.0970845i
$208$	3.16228	−	3.16228i	0.219265	−	0.219265i
$209$		0			0
$210$		0			0
$211$	−14.8699	−	20.4667i	−1.02369	−	1.40899i	−0.909586	−	0.415516i	$-0.863601\pi$
$211$	−14.8699	−	20.4667i	−1.02369	−	1.40899i	−0.114102	−	0.993469i	$-0.536399\pi$
$212$	3.78022	+	1.92612i	0.259627	+	0.132286i
$213$	10.0806	−	5.13632i	0.690711	−	0.351935i
$214$		0			0
$215$		0			0
$216$	12.0300	+	3.90879i	0.818539	+	0.265959i
$217$		0			0
$218$	27.9360	+	4.42463i	1.89207	+	0.299674i
$219$	6.32456			0.427374
$220$		0			0
$221$	20.0000			1.34535
$222$	−13.2512	−	2.09879i	−0.889364	−	0.140861i
$223$	7.06243	−	13.8608i	0.472936	−	0.928188i	−0.524130	−	0.851638i	$-0.675609\pi$
$223$	7.06243	−	13.8608i	0.472936	−	0.928188i	0.997066	−	0.0765502i	$-0.0243905\pi$
$224$		0			0
$225$	−4.99942	+	0.0759100i	−0.333295	+	0.00506066i
$226$	−16.7287	+	23.0250i	−1.11277	+	1.53160i
$227$	7.96940	−	4.06061i	0.528948	−	0.269512i	−0.169056	−	0.985606i	$-0.554072\pi$
$227$	7.96940	−	4.06061i	0.528948	−	0.269512i	0.698004	+	0.716094i	$0.254072\pi$
$228$	−23.9082	−	12.1818i	−1.58336	−	0.806762i
$229$	2.35114	+	3.23607i	0.155368	+	0.213845i	0.879604	−	0.475706i	$-0.157808\pi$
$229$	2.35114	+	3.23607i	0.155368	+	0.213845i	−0.724236	+	0.689552i	$0.757808\pi$
$230$	3.16228	−	6.32456i	0.208514	−	0.417029i
$231$		0			0
$232$	10.0000	−	10.0000i	0.656532	−	0.656532i
$233$	2.09879	−	13.2512i	0.137496	−	0.868117i	−0.818451	−	0.574577i	$-0.805167\pi$
$233$	2.09879	−	13.2512i	0.137496	−	0.868117i	0.955947	−	0.293540i	$-0.0948334\pi$
$234$	−9.51057	+	3.09017i	−0.621725	+	0.202011i
$235$	0.0720166	+	9.48656i	0.00469784	+	0.618835i
$236$	14.5623	+	10.5801i	0.947925	+	0.688708i
$237$	1.39919	+	8.83415i	0.0908873	+	0.573840i
$238$		0			0
$239$	5.86319	+	18.0450i	0.379258	+	1.16724i	0.940561	+	0.339625i	$0.110300\pi$
$239$	5.86319	+	18.0450i	0.379258	+	1.16724i	−0.561303	+	0.827610i	$0.689700\pi$
$240$	−2.57237	−	1.83927i	−0.166046	−	0.118724i
$241$			6.32456i			0.407400i	0.979033	+	0.203700i	$0.0652968\pi$
$241$			6.32456i			0.407400i	−0.979033	+	0.203700i	$0.934703\pi$
$242$		0			0
$243$	7.00000	+	7.00000i	0.449050	+	0.449050i
$244$	−15.3500	+	11.1524i	−0.982684	+	0.713962i
$245$	−15.4779	−	2.33116i	−0.988847	−	0.148932i
$246$	−6.18034	+	19.0211i	−0.394044	+	1.21274i
$247$	27.9360	−	4.42463i	1.77753	−	0.281533i
$248$	−4.41708	+	0.699596i	−0.280485	+	0.0444244i
$249$	−3.90879	+	12.0300i	−0.247710	+	0.762371i
$250$	−23.9462	−	7.18199i	−1.51449	−	0.454229i
$251$	−9.70820	+	7.05342i	−0.612776	+	0.445208i	−0.850391	−	0.526151i	$-0.823635\pi$
$251$	−9.70820	+	7.05342i	−0.612776	+	0.445208i	0.237614	+	0.971360i	$0.423635\pi$
$252$		0			0
$253$		0			0
$254$		−	20.0000i		−	1.25491i
$255$	−2.31829	−	13.9508i	−0.145177	−	0.873635i
$256$	−2.78115	−	8.55951i	−0.173822	−	0.534969i
$257$	4.49428	+	8.82051i	0.280345	+	0.550209i	0.987646	−	0.156705i	$-0.0500871\pi$
$257$	4.49428	+	8.82051i	0.280345	+	0.550209i	−0.707300	+	0.706913i	$0.750087\pi$
$258$		0			0
$259$		0			0
$260$	−29.9991	+	0.227736i	−1.86047	+	0.0141236i
$261$	6.01501	−	1.95440i	0.372320	−	0.120974i
$262$	−4.42463	+	27.9360i	−0.273355	+	1.72589i
$263$	18.9737	−	18.9737i	1.16997	−	1.16997i	0.187749	−	0.982217i	$-0.439881\pi$
$263$	18.9737	−	18.9737i	1.16997	−	1.16997i	0.982217	−	0.187749i	$-0.0601193\pi$
$264$		0			0
$265$	1.00000	+	3.00000i	0.0614295	+	0.184289i
$266$		0			0
$267$	7.56044	+	3.85224i	0.462691	+	0.235753i
$268$	11.3407	−	5.77836i	0.692741	−	0.352969i
$269$	−14.1068	+	19.4164i	−0.860110	+	1.18384i	0.121434	+	0.992600i	$0.461251\pi$
$269$	−14.1068	+	19.4164i	−0.860110	+	1.18384i	−0.981543	+	0.191240i	$0.938749\pi$
$270$	13.0317	+	25.1033i	0.793086	+	1.52774i
$271$	−12.0300	−	3.90879i	−0.730772	−	0.237442i	−0.0800845	−	0.996788i	$-0.525519\pi$
$271$	−12.0300	−	3.90879i	−0.730772	−	0.237442i	−0.650687	+	0.759346i	$0.725519\pi$
$272$	−2.03031	+	3.98470i	−0.123105	+	0.241608i
$273$		0			0
$274$	−41.1096			−2.48352
$275$		0			0
$276$	−6.00000			−0.361158
$277$	13.2512	+	2.09879i	0.796189	+	0.126104i	0.541260	−	0.840856i	$-0.317948\pi$
$277$	13.2512	+	2.09879i	0.796189	+	0.126104i	0.254930	+	0.966960i	$0.417948\pi$
$278$	−12.8408	+	25.2015i	−0.770139	+	1.51148i
$279$	−1.90211	−	0.618034i	−0.113877	−	0.0370007i
$280$		0			0
$281$	−11.1524	+	15.3500i	−0.665299	+	0.915705i	−0.999642	−	0.0267460i	$-0.991485\pi$
$281$	−11.1524	+	15.3500i	−0.665299	+	0.915705i	0.334343	+	0.942451i	$0.391485\pi$
$282$	11.9541	−	6.09092i	0.711857	−	0.362709i
$283$	7.96940	+	4.06061i	0.473732	+	0.241378i	0.674520	−	0.738256i	$-0.264350\pi$
$283$	7.96940	+	4.06061i	0.473732	+	0.241378i	−0.200789	+	0.979635i	$0.564350\pi$
$284$	14.1068	+	19.4164i	0.837087	+	1.15215i
$285$	−6.32456	−	18.9737i	−0.374634	−	1.12390i
$286$		0			0
$287$		0			0
$288$	1.04939	−	6.62561i	0.0618362	−	0.390418i
$289$	−2.85317	+	0.927051i	−0.167834	+	0.0545324i
$290$	31.6219	−	0.240055i	1.85690	−	0.0140965i
$291$	−11.3262	−	8.22899i	−0.663956	−	0.482392i
$292$	2.09879	+	13.2512i	0.122822	+	0.775470i
$293$	10.1515	+	19.9235i	0.593059	+	1.16394i	0.971216	+	0.238202i	$0.0765581\pi$
$293$	10.1515	+	19.9235i	0.593059	+	1.16394i	−0.378156	+	0.925742i	$0.623442\pi$
$294$	6.84038	+	21.0525i	0.398939	+	1.22781i
$295$	2.19932	+	13.2349i	0.128049	+	0.770567i
$296$		−	9.48683i		−	0.551411i
$297$		0			0
$298$		0			0
$299$	5.11667	−	3.71748i	0.295905	−	0.214987i
$300$	3.63619	+	20.8992i	0.209935	+	1.20662i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−1.95440	+	6.01501i	−0.112092	+	0.344984i
$305$	−13.9844	−	2.10622i	−0.800745	−	0.120602i
$306$	8.09017	−	5.87785i	0.462484	−	0.336014i
$307$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$307$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$308$		0			0
$309$		−	18.0000i		−	1.02398i
$310$	−8.13456	−	5.81627i	−0.462012	−	0.330342i
$311$	−2.47214	−	7.60845i	−0.140182	−	0.431436i	0.856178	−	0.516681i	$-0.172833\pi$
$311$	−2.47214	−	7.60845i	−0.140182	−	0.431436i	−0.996360	+	0.0852452i	$0.972833\pi$
$312$	6.42040	+	12.6007i	0.363483	+	0.713376i
$313$	−1.99109	−	12.5712i	−0.112543	−	0.710567i	−0.977847	−	0.209320i	$-0.932875\pi$
$313$	−1.99109	−	12.5712i	−0.112543	−	0.710567i	0.865304	−	0.501247i	$-0.167125\pi$
$314$	−17.9084	−	13.0112i	−1.01063	−	0.734263i
$315$		0			0
$316$	−18.0450	+	5.86319i	−1.01511	+	0.329830i
$317$	3.76094	−	23.7456i	0.211235	−	1.33369i	−0.622975	−	0.782242i	$-0.714076\pi$
$317$	3.76094	−	23.7456i	0.211235	−	1.33369i	0.834210	−	0.551446i	$-0.185924\pi$
$318$	3.16228	−	3.16228i	0.177332	−	0.177332i
$319$		0			0
$320$	13.0000	−	26.0000i	0.726722	−	1.45344i
$321$		0			0
$322$		0			0
$323$	−25.2015	+	12.8408i	−1.40225	+	0.714481i
$324$	8.81678	−	12.1353i	0.489821	−	0.674181i
$325$	−16.0496	−	15.5695i	−0.890272	−	0.863641i
$326$	3.00750	+	0.977198i	0.166570	+	0.0541220i
$327$	8.12123	−	15.9388i	0.449105	−	0.881418i
$328$	−13.9680	−	2.21232i	−0.771255	−	0.122155i
$329$		0			0
$330$		0			0
$331$	−18.0000			−0.989369			−0.494685	−	0.869072i	$-0.664716\pi$
$331$	−18.0000			−0.989369			−0.494685	+	0.869072i	$0.664716\pi$
$332$	−26.5025	−	4.19758i	−1.45451	−	0.230372i
$333$	1.92612	−	3.78022i	0.105551	−	0.207155i
$334$	38.0423	+	12.3607i	2.08158	+	0.676346i
$335$	9.04451	+	2.86302i	0.494154	+	0.156423i
$336$		0			0
$337$	11.9541	−	6.09092i	0.651182	−	0.331794i	−0.0970031	−	0.995284i	$-0.530926\pi$
$337$	11.9541	−	6.09092i	0.651182	−	0.331794i	0.748185	+	0.663490i	$0.230926\pi$
$338$	−13.9465	−	7.10608i	−0.758587	−	0.386520i
$339$	10.5801	+	14.5623i	0.574634	+	0.790916i
$340$	28.4605	−	9.48683i	1.54349	−	0.514496i
$341$		0			0
$342$	10.0000	−	10.0000i	0.540738	−	0.540738i
$343$		0			0
$344$		0			0
$345$	−3.18619	−	3.13818i	−0.171539	−	0.168954i
$346$	−8.09017	−	5.87785i	−0.434930	−	0.315995i
$347$	4.19758	+	26.5025i	0.225338	+	1.42273i	0.797863	+	0.602839i	$0.205964\pi$
$347$	4.19758	+	26.5025i	0.225338	+	1.42273i	−0.572525	+	0.819887i	$0.694036\pi$
$348$	−12.1818	−	23.9082i	−0.653015	−	1.28161i
$349$	9.77198	+	30.0750i	0.523082	+	1.60988i	0.768078	+	0.640356i	$0.221213\pi$
$349$	9.77198	+	30.0750i	0.523082	+	1.60988i	−0.244996	+	0.969524i	$0.578787\pi$
$350$		0			0
$351$			25.2982i			1.35032i
$352$		0			0
$353$	−21.0000	−	21.0000i	−1.11772	−	1.11772i	−0.992076	−	0.125642i	$-0.959901\pi$
$353$	−21.0000	−	21.0000i	−1.11772	−	1.11772i	−0.125642	−	0.992076i	$-0.540099\pi$
$354$	15.3500	−	11.1524i	0.815844	−	0.592746i
$355$	−2.66418	+	17.6890i	−0.141400	+	0.938837i
$356$	−5.56231	+	17.1190i	−0.294802	+	0.907306i
$357$		0			0
$358$	8.83415	−	1.39919i	0.466899	−	0.0739496i
$359$	−5.86319	+	18.0450i	−0.309447	+	0.952380i	0.668533	+	0.743682i	$0.266923\pi$
$359$	−5.86319	+	18.0450i	−0.309447	+	0.952380i	−0.977980	+	0.208698i	$0.933077\pi$
$360$	−4.02266	+	2.96955i	−0.212013	+	0.156509i
$361$	−16.9894	+	12.3435i	−0.894177	+	0.649657i
$362$	12.6491	+	12.6491i	0.664822	+	0.664822i
$363$		0			0
$364$		0			0
$365$	−5.81627	+	8.13456i	−0.304437	+	0.425782i
$366$	6.18034	+	19.0211i	0.323052	+	0.994250i
$367$	−1.92612	−	3.78022i	−0.100543	−	0.197326i	0.835256	−	0.549862i	$-0.185320\pi$
$367$	−1.92612	−	3.78022i	−0.100543	−	0.197326i	−0.935798	+	0.352536i	$0.885320\pi$
$368$	0.221232	+	1.39680i	0.0115325	+	0.0728134i
$369$	−5.11667	−	3.71748i	−0.266363	−	0.193524i
$370$	14.8857	−	15.1134i	0.773871	−	0.785710i
$371$		0			0
$372$	−1.32739	+	8.38081i	−0.0688220	+	0.434525i
$373$	−3.16228	+	3.16228i	−0.163737	+	0.163737i	−0.784220	−	0.620483i	$-0.786937\pi$
$373$	−3.16228	+	3.16228i	−0.163737	+	0.163737i	0.620483	+	0.784220i	$0.286937\pi$
$374$		0			0
$375$	−9.00000	+	13.0000i	−0.464758	+	0.671317i
$376$	5.57622	+	7.67501i	0.287572	+	0.395808i
$377$	25.2015	+	12.8408i	1.29794	+	0.661334i
$378$		0			0
$379$	15.2824	−	21.0344i	0.785005	−	1.08047i	−0.209707	−	0.977764i	$-0.567251\pi$
$379$	15.2824	−	21.0344i	0.785005	−	1.08047i	0.994712	−	0.102702i	$-0.0327490\pi$
$380$	37.6549	−	19.5476i	1.93166	−	1.00277i
$381$	−12.0300	−	3.90879i	−0.616317	−	0.200253i
$382$	22.3334	−	43.8317i	1.14268	−	2.24263i
$383$	−26.5392	−	4.20340i	−1.35609	−	0.214784i	−0.564298	−	0.825572i	$-0.690853\pi$
$383$	−26.5392	−	4.20340i	−1.35609	−	0.214784i	−0.791794	+	0.610788i	$0.790853\pi$
$384$	−22.1359			−1.12962
$385$		0			0
$386$	50.0000			2.54493
$387$		0			0
$388$	13.4828	−	26.4615i	0.684487	−	1.34338i
$389$	15.2169	+	4.94427i	0.771528	+	0.250685i	0.668219	−	0.743965i	$-0.267057\pi$
$389$	15.2169	+	4.94427i	0.771528	+	0.250685i	0.103309	+	0.994649i	$0.467057\pi$
$390$	−9.54339	+	30.1484i	−0.483248	+	1.52662i
$391$	−3.71748	+	5.11667i	−0.188001	+	0.258761i
$392$	−13.9465	+	7.10608i	−0.704403	+	0.358911i
$393$	15.9388	+	8.12123i	0.804007	+	0.409662i
$394$	−5.87785	−	8.09017i	−0.296122	−	0.407577i
$395$	−12.6491	−	6.32456i	−0.636446	−	0.318223i
$396$		0			0
$397$	13.0000	−	13.0000i	0.652451	−	0.652451i	−0.301131	−	0.953583i	$-0.597364\pi$
$397$	13.0000	−	13.0000i	0.652451	−	0.652451i	0.953583	+	0.301131i	$0.0973643\pi$
$398$	−2.09879	+	13.2512i	−0.105203	+	0.664224i
$399$		0			0
$400$	4.73128	−	1.61710i	0.236564	−	0.0808551i
$401$	−9.70820	−	7.05342i	−0.484805	−	0.352231i	0.318378	−	0.947964i	$-0.396862\pi$
$401$	−9.70820	−	7.05342i	−0.484805	−	0.352231i	−0.803183	+	0.595733i	$0.796862\pi$
$402$	−2.09879	−	13.2512i	−0.104678	−	0.660911i
$403$	−4.06061	−	7.96940i	−0.202274	−	0.396984i
$404$		0			0
$405$	11.0291	−	1.83277i	0.548040	−	0.0910710i
$406$		0			0
$407$		0			0
$408$	−10.0000	−	10.0000i	−0.495074	−	0.495074i
$409$	−10.2333	+	7.43496i	−0.506006	+	0.367635i	−0.811307	−	0.584621i	$-0.801243\pi$
$409$	−10.2333	+	7.43496i	−0.506006	+	0.367635i	0.305300	+	0.952256i	$0.401243\pi$
$410$	−18.7811	−	25.4415i	−0.927531	−	1.25647i
$411$	−8.03444	+	24.7275i	−0.396310	+	1.21972i
$412$	37.7137	−	5.97326i	1.85802	−	0.294281i
$413$		0			0
$414$	0.977198	−	3.00750i	0.0480266	−	0.147811i
$415$	−11.8782	−	16.0906i	−0.583078	−	0.789858i
$416$	24.2705	−	17.6336i	1.18996	−	0.864556i
$417$	12.6491	+	12.6491i	0.619430	+	0.619430i
$418$		0			0
$419$			36.0000i			1.75872i	0.476162	+	0.879358i	$0.342028\pi$
$419$			36.0000i			1.75872i	−0.476162	+	0.879358i	$0.657972\pi$
$420$		0			0
$421$	−8.65248	−	26.6296i	−0.421696	−	1.29785i	−0.906123	−	0.423015i	$-0.860972\pi$
$421$	−8.65248	−	26.6296i	−0.421696	−	1.29785i	0.484427	−	0.874832i	$-0.339028\pi$
$422$	−25.6816	−	50.4029i	−1.25016	−	2.45358i
$423$	0.663695	+	4.19041i	0.0322700	+	0.203745i
$424$	2.55834	+	1.85874i	0.124244	+	0.0902684i
$425$	20.0753	+	9.84789i	0.973797	+	0.477693i
$426$	24.0600	−	7.81758i	1.16571	−	0.378763i
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	11.1524	+	15.3500i	0.537194	+	0.739384i	0.988205	−	0.153134i	$-0.0489366\pi$
$431$	11.1524	+	15.3500i	0.537194	+	0.739384i	−0.451011	+	0.892518i	$0.648937\pi$
$432$	−5.04029	−	2.56816i	−0.242501	−	0.123561i
$433$	−1.26007	+	0.642040i	−0.0605553	+	0.0308545i	−0.484006	−	0.875065i	$-0.660819\pi$
$433$	−1.26007	+	0.642040i	−0.0605553	+	0.0308545i	0.423451	+	0.905919i	$0.360819\pi$
$434$		0			0
$435$	6.03577	−	19.0675i	0.289393	−	0.914217i
$436$	36.0901	+	11.7264i	1.72840	+	0.561591i
$437$	−4.06061	+	7.96940i	−0.194246	+	0.381228i
$438$	13.9680	+	2.21232i	0.667418	+	0.105709i
$439$	−12.6491			−0.603709			−0.301855	−	0.953354i	$-0.597606\pi$
$439$	−12.6491			−0.603709			−0.301855	+	0.953354i	$0.597606\pi$
$440$		0			0
$441$	−7.00000			−0.333333
$442$	44.1708	+	6.99596i	2.10099	+	0.332764i
$443$	7.06243	−	13.8608i	0.335546	−	0.658547i	−0.660159	−	0.751126i	$-0.729511\pi$
$443$	7.06243	−	13.8608i	0.335546	−	0.658547i	0.995705	+	0.0925790i	$0.0295111\pi$
$444$	−17.1190	−	5.56231i	−0.812433	−	0.263975i
$445$	−11.9075	+	6.18149i	−0.564471	+	0.293031i
$446$	20.4461	−	28.1417i	0.968153	−	1.33255i
$447$		0			0
$448$		0			0
$449$	−3.52671	−	4.85410i	−0.166436	−	0.229079i	0.717650	−	0.696404i	$-0.245218\pi$
$449$	−3.52671	−	4.85410i	−0.166436	−	0.229079i	−0.884086	+	0.467325i	$0.845218\pi$
$450$	−11.0680	−	1.58114i	−0.521749	−	0.0745356i
$451$		0			0
$452$	−27.0000	+	27.0000i	−1.26997	+	1.26997i
$453$		0			0
$454$	19.0211	−	6.18034i	0.892706	−	0.290058i
$455$		0			0
$456$	−16.1803	−	11.7557i	−0.757714	−	0.550511i
$457$	−3.49798	−	22.0854i	−0.163629	−	1.03311i	−0.923657	−	0.383221i	$-0.874815\pi$
$457$	−3.49798	−	22.0854i	−0.163629	−	1.03311i	0.760028	−	0.649890i	$-0.225185\pi$
$458$	4.06061	+	7.96940i	0.189740	+	0.372386i
$459$	−7.81758	−	24.0600i	−0.364893	−	1.12303i
$460$	5.51780	−	7.71712i	0.257269	−	0.359812i
$461$			25.2982i			1.17826i	0.808040	+	0.589128i	$0.200529\pi$
$461$			25.2982i			1.17826i	−0.808040	+	0.589128i	$0.799471\pi$
$462$		0			0
$463$	9.00000	+	9.00000i	0.418265	+	0.418265i	0.884606	−	0.466340i	$-0.154428\pi$
$463$	9.00000	+	9.00000i	0.418265	+	0.418265i	−0.466340	+	0.884606i	$0.654428\pi$
$464$	−5.11667	+	3.71748i	−0.237536	+	0.172580i
$465$	−5.08831	+	3.75621i	−0.235964	+	0.174190i
$466$	9.27051	−	28.5317i	0.429448	−	1.32171i
$467$	9.77762	−	1.54862i	0.452454	−	0.0716617i	0.0739513	−	0.997262i	$-0.476439\pi$
$467$	9.77762	−	1.54862i	0.452454	−	0.0716617i	0.378503	+	0.925600i	$0.376439\pi$
$468$	−13.2512	+	2.09879i	−0.612538	+	0.0970165i
$469$		0			0
$470$	−3.15933	+	20.9766i	−0.145729	+	0.967579i
$471$	−11.3262	+	8.22899i	−0.521885	+	0.379172i
$472$	9.48683	+	9.48683i	0.436667	+	0.436667i
$473$		0			0
$474$			20.0000i			0.918630i
$475$	30.2199	+	9.31425i	1.38659	+	0.427367i
$476$		0			0
$477$	0.642040	+	1.26007i	0.0293970	+	0.0576948i
$478$	6.63695	+	41.9041i	0.303567	+	1.91665i
$479$	−5.11667	−	3.71748i	−0.233787	−	0.169856i	0.464724	−	0.885456i	$-0.346154\pi$
$479$	−5.11667	−	3.71748i	−0.233787	−	0.169856i	−0.698511	+	0.715600i	$0.746154\pi$
$480$	−15.1134	−	14.8857i	−0.689831	−	0.679436i
$481$	18.0450	−	5.86319i	0.822782	−	0.267338i
$482$	−2.21232	+	13.9680i	−0.100768	+	0.636226i
$483$		0			0
$484$		0			0
$485$	21.0000	−	7.00000i	0.953561	−	0.317854i
$486$	13.0112	+	17.9084i	0.590199	+	0.812339i
$487$	3.78022	+	1.92612i	0.171298	+	0.0872808i	0.537537	−	0.843240i	$-0.319355\pi$
$487$	3.78022	+	1.92612i	0.171298	+	0.0872808i	−0.366239	+	0.930521i	$0.619355\pi$
$488$	−12.6007	+	6.42040i	−0.570408	+	0.290638i
$489$	1.17557	−	1.61803i	0.0531611	−	0.0731700i
$490$	−33.3681	−	10.5626i	−1.50742	−	0.477169i
$491$	6.01501	+	1.95440i	0.271454	+	0.0882006i	0.441581	−	0.897221i	$-0.354418\pi$
$491$	6.01501	+	1.95440i	0.271454	+	0.0882006i	−0.170127	+	0.985422i	$0.554418\pi$
$492$	−12.1818	+	23.9082i	−0.549200	+	1.07787i
$493$	−27.9360	−	4.42463i	−1.25818	−	0.199276i
$494$	63.2456			2.84555
$495$		0			0
$496$	2.00000			0.0898027
$497$		0			0
$498$	−12.8408	+	25.2015i	−0.575410	+	1.12930i
$499$	−32.3359	−	10.5066i	−1.44755	−	0.470339i	−0.523311	−	0.852142i	$-0.675303\pi$
$499$	−32.3359	−	10.5066i	−1.44755	−	0.470339i	−0.924244	+	0.381803i	$0.875303\pi$
$500$	−30.2243	−	14.5428i	−1.35167	−	0.650374i
$501$	14.8699	−	20.4667i	0.664339	−	0.914384i
$502$	−23.9082	+	12.1818i	−1.06708	+	0.543702i
$503$	−7.96940	−	4.06061i	−0.355338	−	0.181054i	0.267204	−	0.963640i	$-0.413900\pi$
$503$	−7.96940	−	4.06061i	−0.355338	−	0.181054i	−0.622542	+	0.782586i	$0.713900\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−7.00000	+	7.00000i	−0.310881	+	0.310881i
$508$	4.19758	−	26.5025i	0.186237	−	1.17586i
$509$	3.80423	−	1.23607i	0.168619	−	0.0547877i	−0.223491	−	0.974706i	$-0.571745\pi$
$509$	3.80423	−	1.23607i	0.168619	−	0.0547877i	0.392110	+	0.919918i	$0.371745\pi$
$510$	−0.240055	−	31.6219i	−0.0106298	−	1.40024i
$511$		0			0
$512$	1.74899	+	11.0427i	0.0772952	+	0.488023i
$513$	−16.2425	−	31.8776i	−0.717122	−	1.40743i
$514$	6.84038	+	21.0525i	0.301716	+	0.928587i
$515$	23.1514	+	16.5534i	1.02017	+	0.729430i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−5.11667	+	3.71748i	−0.224597	+	0.163179i
$520$	−22.1113	−	3.33023i	−0.969645	−	0.146040i
$521$	−8.65248	+	26.6296i	−0.379072	+	1.16666i	0.561618	+	0.827396i	$0.310179\pi$
$521$	−8.65248	+	26.6296i	−0.379072	+	1.16666i	−0.940690	+	0.339267i	$0.889821\pi$
$522$	13.9680	−	2.21232i	0.611364	−	0.0968305i
$523$	26.5025	−	4.19758i	1.15887	−	0.183547i	0.452750	−	0.891638i	$-0.350443\pi$
$523$	26.5025	−	4.19758i	1.15887	−	0.183547i	0.706122	+	0.708090i	$0.250443\pi$
$524$	−11.7264	+	36.0901i	−0.512269	+	1.57660i
$525$		0			0
$526$	48.5410	−	35.2671i	2.11649	−	1.53772i
$527$	6.32456	+	6.32456i	0.275502	+	0.275502i
$528$		0			0
$529$		−	21.0000i		−	0.913043i
$530$	1.15914	+	6.97541i	0.0503500	+	0.302993i
$531$	1.85410	+	5.70634i	0.0804612	+	0.247634i
$532$		0			0
$533$	−4.42463	−	27.9360i	−0.191652	−	1.21004i
$534$	15.3500	+	11.1524i	0.664260	+	0.482613i
$535$		0			0
$536$	9.02251	−	2.93159i	0.389713	−	0.126626i
$537$	0.884927	−	5.58721i	0.0381874	−	0.241106i
$538$	−37.9473	+	37.9473i	−1.63603	+	1.63603i
$539$		0			0
$540$	12.0000	+	36.0000i	0.516398	+	1.54919i
$541$	−22.3049	−	30.7000i	−0.958962	−	1.31990i	−0.947430	−	0.319964i	$-0.896329\pi$
$541$	−22.3049	−	30.7000i	−0.958962	−	1.31990i	−0.0115321	−	0.999934i	$-0.503671\pi$
$542$	−25.2015	−	12.8408i	−1.08250	−	0.551559i
$543$	10.0806	−	5.13632i	0.432599	−	0.220420i
$544$	−17.6336	+	24.2705i	−0.756033	+	1.04059i
$545$	13.0317	+	25.1033i	0.558218	+	1.07531i
$546$		0			0
$547$	−8.12123	+	15.9388i	−0.347239	+	0.681494i	−0.996896	−	0.0787331i	$-0.974912\pi$
$547$	−8.12123	+	15.9388i	−0.347239	+	0.681494i	0.649657	+	0.760227i	$0.274912\pi$
$548$	−54.4753	−	8.62804i	−2.32707	−	0.368572i
$549$	−6.32456			−0.269925
$550$		0			0
$551$	−40.0000			−1.70406
$552$	−4.41708	−	0.699596i	−0.188003	−	0.0297768i
$553$		0			0
$554$	28.5317	+	9.27051i	1.21220	+	0.393866i
$555$	−6.18149	−	11.9075i	−0.262390	−	0.505446i
$556$	−22.3049	+	30.7000i	−0.945938	+	1.30197i
$557$	19.9235	−	10.1515i	0.844186	−	0.430134i	0.0222763	−	0.999752i	$-0.492909\pi$
$557$	19.9235	−	10.1515i	0.844186	−	0.430134i	0.821910	+	0.569617i	$0.192909\pi$
$558$	−3.98470	−	2.03031i	−0.168686	−	0.0859498i
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−30.0000	+	30.0000i	−1.26547	+	1.26547i
$563$	−4.19758	+	26.5025i	−0.176907	+	1.11695i	0.726185	+	0.687499i	$0.241291\pi$
$563$	−4.19758	+	26.5025i	−0.176907	+	1.11695i	−0.903092	+	0.429447i	$0.858709\pi$
$564$	17.1190	−	5.56231i	0.720841	−	0.234215i
$565$	−28.4597	+	0.216050i	−1.19731	+	0.00908928i
$566$	16.1803	+	11.7557i	0.680110	+	0.494129i
$567$		0			0
$568$	8.12123	+	15.9388i	0.340759	+	0.668778i
$569$	−11.7264	−	36.0901i	−0.491595	−	1.51297i	−0.822197	−	0.569204i	$-0.807252\pi$
$569$	−11.7264	−	36.0901i	−0.491595	−	1.51297i	0.330602	−	0.943770i	$-0.392748\pi$
$570$	−7.33107	−	44.1164i	−0.307065	−	1.84783i
$571$		−	44.2719i		−	1.85272i	−0.376638	−	0.926360i	$-0.622920\pi$
$571$		−	44.2719i		−	1.85272i	0.376638	−	0.926360i	$-0.377080\pi$
$572$		0			0
$573$	−22.0000	−	22.0000i	−0.919063	−	0.919063i
$574$		0			0
$575$	6.96641	−	1.21206i	0.290519	−	0.0505465i
$576$	4.01722	−	12.3637i	0.167384	−	0.515156i
$577$	−32.1265	+	5.08833i	−1.33744	+	0.211830i	−0.783846	−	0.620956i	$-0.786745\pi$
$577$	−32.1265	+	5.08833i	−1.33744	+	0.211830i	−0.553596	+	0.832785i	$0.686745\pi$
$578$	−6.62561	+	1.04939i	−0.275589	+	0.0436490i
$579$	9.77198	−	30.0750i	0.406109	−	1.24988i
$580$	41.9532	+	6.31866i	1.74201	+	0.262368i
$581$		0			0
$582$	−22.1359	−	22.1359i	−0.917564	−	0.917564i
$583$		0			0
$584$			10.0000i			0.413803i
$585$	−8.13456	−	5.81627i	−0.336323	−	0.240473i
$586$	15.4508	+	47.5528i	0.638269	+	1.96439i
$587$	4.49428	+	8.82051i	0.185499	+	0.364062i	0.964963	−	0.262384i	$-0.0845089\pi$
$587$	4.49428	+	8.82051i	0.185499	+	0.364062i	−0.779465	+	0.626446i	$0.784509\pi$
$588$	4.64587	+	29.3328i	0.191592	+	1.20967i
$589$	10.2333	+	7.43496i	0.421658	+	0.306352i
$590$	0.227736	+	29.9991i	0.00937576	+	1.23504i
$591$	−6.01501	+	1.95440i	−0.247424	+	0.0803931i
$592$	−0.663695	+	4.19041i	−0.0272777	+	0.172225i
$593$	15.8114	−	15.8114i	0.649296	−	0.649296i	−0.303527	−	0.952823i	$-0.598164\pi$
$593$	15.8114	−	15.8114i	0.649296	−	0.649296i	0.952823	+	0.303527i	$0.0981642\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	7.56044	+	3.85224i	0.309428	+	0.157662i
$598$	12.6007	−	6.42040i	0.515282	−	0.262549i
$599$	9.40456	−	12.9443i	0.384260	−	0.528889i	−0.572447	−	0.819942i	$-0.694006\pi$
$599$	9.40456	−	12.9443i	0.384260	−	0.528889i	0.956707	+	0.291053i	$0.0940057\pi$
$600$	0.240048	+	15.8096i	0.00979994	+	0.645423i
$601$	−30.0750	−	9.77198i	−1.22679	−	0.398607i	−0.377238	−	0.926117i	$-0.623126\pi$
$601$	−30.0750	−	9.77198i	−1.22679	−	0.398607i	−0.849549	+	0.527509i	$0.823126\pi$
$602$		0			0
$603$	4.19041	+	0.663695i	0.170647	+	0.0270278i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−44.1708	−	6.99596i	−1.79284	−	0.283957i	−0.830739	−	0.556663i	$-0.812082\pi$
$607$	−44.1708	−	6.99596i	−1.79284	−	0.283957i	−0.962098	+	0.272706i	$0.912082\pi$
$608$	−19.2612	+	37.8022i	−0.781144	+	1.53308i
$609$		0			0
$610$	−30.1484	−	9.54339i	−1.22067	−	0.386400i
$611$	−11.1524	+	15.3500i	−0.451179	+	0.620995i
$612$	11.9541	−	6.09092i	0.483216	−	0.246211i
$613$	−35.8623	−	18.2728i	−1.44847	−	0.738030i	−0.459780	−	0.888033i	$-0.652072\pi$
$613$	−35.8623	−	18.2728i	−1.44847	−	0.738030i	−0.988686	+	0.150003i	$0.952072\pi$
$614$		0			0
$615$	−18.9737	+	6.32456i	−0.765092	+	0.255031i
$616$		0			0
$617$	−17.0000	+	17.0000i	−0.684394	+	0.684394i	−0.960987	−	0.276593i	$-0.910795\pi$
$617$	−17.0000	+	17.0000i	−0.684394	+	0.684394i	0.276593	+	0.960987i	$0.410795\pi$
$618$	6.29637	−	39.7537i	0.253277	−	1.59913i
$619$	−34.2380	+	11.1246i	−1.37614	+	0.447136i	−0.901399	−	0.432988i	$-0.857459\pi$
$619$	−34.2380	+	11.1246i	−1.37614	+	0.447136i	−0.474743	+	0.880124i	$0.657459\pi$
$620$	−9.55858	−	9.41454i	−0.383882	−	0.378097i
$621$	−6.47214	−	4.70228i	−0.259718	−	0.188696i
$622$	−2.79838	−	17.6683i	−0.112205	−	0.708435i
$623$		0			0
$624$	−1.95440	−	6.01501i	−0.0782384	−	0.240793i
$625$	−8.44373	−	23.5309i	−0.337749	−	0.941236i
$626$		−	28.4605i		−	1.13751i
$627$		0			0
$628$	−21.0000	−	21.0000i	−0.837991	−	0.837991i
$629$	−15.3500	+	11.1524i	−0.612045	+	0.444677i
$630$		0			0
$631$	9.88854	−	30.4338i	0.393657	−	1.21155i	−0.536346	−	0.843998i	$-0.680196\pi$
$631$	9.88854	−	30.4338i	0.393657	−	1.21155i	0.930003	−	0.367553i	$-0.119804\pi$
$632$	−13.9680	+	2.21232i	−0.555618	+	0.0880013i
$633$	−35.3366	+	5.59677i	−1.40450	+	0.222452i
$634$	16.6124	−	51.1276i	0.659761	−	2.03054i
$635$	16.0906	−	11.8782i	0.638537	−	0.471372i
$636$	4.85410	−	3.52671i	0.192478	−	0.139843i
$637$	−22.1359	−	22.1359i	−0.877058	−	0.877058i
$638$		0			0
$639$			8.00000i			0.316475i
$640$	20.3569	−	28.4709i	0.804679	−	1.12541i
$641$	−2.47214	−	7.60845i	−0.0976435	−	0.300516i	0.890290	−	0.455394i	$-0.150502\pi$
$641$	−2.47214	−	7.60845i	−0.0976435	−	0.300516i	−0.987934	+	0.154878i	$0.950502\pi$
$642$		0			0
$643$	2.43355	+	15.3648i	0.0959698	+	0.605930i	0.988060	+	0.154072i	$0.0492386\pi$
$643$	2.43355	+	15.3648i	0.0959698	+	0.605930i	−0.892090	+	0.451858i	$0.850761\pi$
$644$		0			0
$645$		0			0
$646$	−60.1501	+	19.5440i	−2.36657	+	0.768946i
$647$	−2.87601	+	18.1584i	−0.113068	+	0.713882i	0.864401	+	0.502803i	$0.167698\pi$
$647$	−2.87601	+	18.1584i	−0.113068	+	0.713882i	−0.977469	+	0.211079i	$0.932302\pi$
$648$	7.90569	−	7.90569i	0.310565	−	0.310565i
$649$		0			0
$650$	−30.0000	−	40.0000i	−1.17670	−	1.56893i
$651$		0			0
$652$	3.78022	+	1.92612i	0.148045	+	0.0754326i
$653$	−1.26007	+	0.642040i	−0.0493105	+	0.0251249i	−0.478472	−	0.878103i	$-0.658809\pi$
$653$	−1.26007	+	0.642040i	−0.0493105	+	0.0251249i	0.429161	+	0.903228i	$0.358809\pi$
$654$	23.5114	−	32.3607i	0.919369	−	1.26540i
$655$	−25.1033	+	13.0317i	−0.980866	+	0.509192i
$656$	6.01501	+	1.95440i	0.234847	+	0.0763063i
$657$	−2.03031	+	3.98470i	−0.0792098	+	0.155458i
$658$		0			0
$659$	12.6491			0.492739			0.246370	−	0.969176i	$-0.420762\pi$
$659$	12.6491			0.492739			0.246370	+	0.969176i	$0.420762\pi$
$660$		0			0
$661$	42.0000			1.63361			0.816805	−	0.576913i	$-0.195743\pi$
$661$	42.0000			1.63361			0.816805	+	0.576913i	$0.195743\pi$
$662$	−39.7537	−	6.29637i	−1.54507	−	0.244715i
$663$	12.8408	−	25.2015i	0.498695	−	0.978744i
$664$	−19.0211	−	6.18034i	−0.738163	−	0.239844i
$665$		0			0
$666$	5.57622	−	7.67501i	0.216074	−	0.297401i
$667$	−7.96940	+	4.06061i	−0.308577	+	0.157228i
$668$	47.8164	+	24.3637i	1.85007	+	0.942659i
$669$	−12.9313	−	17.7984i	−0.499952	−	0.688125i
$670$	18.9737	+	9.48683i	0.733017	+	0.366508i
$671$		0			0
$672$		0			0
$673$	−6.29637	+	39.7537i	−0.242707	+	1.53239i	0.501922	+	0.864913i	$0.332627\pi$
$673$	−6.29637	+	39.7537i	−0.242707	+	1.53239i	−0.744629	+	0.667479i	$0.767373\pi$
$674$	28.5317	−	9.27051i	1.09900	−	0.357087i
$675$	−12.4567	+	25.3935i	−0.479459	+	0.977397i
$676$	−16.9894	−	12.3435i	−0.653437	−	0.474750i
$677$	2.09879	+	13.2512i	0.0806630	+	0.509286i	0.994630	+	0.103497i	$0.0330032\pi$
$677$	2.09879	+	13.2512i	0.0806630	+	0.509286i	−0.913967	+	0.405789i	$0.866997\pi$
$678$	18.2728	+	35.8623i	0.701761	+	1.37728i
$679$		0			0
$680$	22.0582	−	3.66554i	0.845893	−	0.140567i
$681$		−	12.6491i		−	0.484715i
$682$		0			0
$683$	29.0000	+	29.0000i	1.10965	+	1.10965i	0.993196	+	0.116459i	$0.0371542\pi$
$683$	29.0000	+	29.0000i	1.10965	+	1.10965i	0.116459	+	0.993196i	$0.462846\pi$
$684$	15.3500	−	11.1524i	0.586923	−	0.426424i
$685$	−24.4154	−	33.0740i	−0.932864	−	1.26369i
$686$		0			0
$687$	5.58721	−	0.884927i	0.213165	−	0.0337621i
$688$		0			0
$689$	−1.95440	+	6.01501i	−0.0744565	+	0.229154i
$690$	−5.93910	−	8.04532i	−0.226098	−	0.306280i
$691$	22.6525	−	16.4580i	0.861741	−	0.626091i	−0.0666172	−	0.997779i	$-0.521221\pi$
$691$	22.6525	−	16.4580i	0.861741	−	0.626091i	0.928358	+	0.371687i	$0.121221\pi$
$692$	−9.48683	−	9.48683i	−0.360635	−	0.360635i
$693$		0			0
$694$			60.0000i			2.27757i
$695$	−27.9017	+	4.63658i	−1.05837	+	0.175875i
$696$	−6.18034	−	19.0211i	−0.234265	−	0.720994i
$697$	12.8408	+	25.2015i	0.486380	+	0.954574i
$698$	11.0616	+	69.8401i	0.418687	+	2.64349i
$699$	−15.3500	−	11.1524i	−0.580591	−	0.421824i
$700$		0			0
$701$	−30.0750	+	9.77198i	−1.13592	+	0.369082i	−0.815822	−	0.578303i	$-0.803715\pi$
$701$	−30.0750	+	9.77198i	−1.13592	+	0.369082i	−0.320096	+	0.947385i	$0.603715\pi$
$702$	−8.84927	+	55.8721i	−0.333994	+	2.10876i
$703$	−18.9737	+	18.9737i	−0.715605	+	0.715605i
$704$		0			0
$705$	12.0000	+	6.00000i	0.451946	+	0.225973i
$706$	−39.0335	−	53.7251i	−1.46905	−	2.02197i
$707$		0			0
$708$	22.6813	−	11.5567i	0.852416	−	0.434328i
$709$	3.52671	−	4.85410i	0.132448	−	0.182300i	−0.737642	−	0.675192i	$-0.764061\pi$
$709$	3.52671	−	4.85410i	0.132448	−	0.182300i	0.870090	+	0.492893i	$0.164061\pi$
$710$	−12.0715	+	38.1350i	−0.453037	+	1.43118i
$711$	−6.01501	−	1.95440i	−0.225580	−	0.0732955i
$712$	−6.09092	+	11.9541i	−0.228267	+	0.447999i
$713$	2.79360	+	0.442463i	0.104621	+	0.0165704i
$714$		0			0
$715$		0			0
$716$	12.0000			0.448461
$717$	26.5025	+	4.19758i	0.989752	+	0.156761i
$718$	−19.2612	+	37.8022i	−0.718821	+	1.41077i
$719$	−22.8254	−	7.41641i	−0.851242	−	0.276585i	−0.149276	−	0.988796i	$-0.547694\pi$
$719$	−22.8254	−	7.41641i	−0.851242	−	0.276585i	−0.701966	+	0.712210i	$0.747694\pi$
$720$	1.98459	−	1.03025i	0.0739612	−	0.0383951i
$721$		0			0
$722$	−41.8394	+	21.3182i	−1.55710	+	0.793382i
$723$	7.96940	+	4.06061i	0.296385	+	0.151016i
$724$	14.1068	+	19.4164i	0.524277	+	0.721605i
$725$	18.9737	+	25.2982i	0.704664	+	0.939552i
$726$		0			0
$727$	23.0000	−	23.0000i	0.853023	−	0.853023i	−0.137482	−	0.990504i	$-0.543901\pi$
$727$	23.0000	−	23.0000i	0.853023	−	0.853023i	0.990504	+	0.137482i	$0.0439008\pi$
$728$		0			0
$729$	27.5806	−	8.96149i	1.02151	−	0.331907i
$730$	−15.6909	+	15.9310i	−0.580746	+	0.589631i
$731$		0			0
$732$	4.19758	+	26.5025i	0.155147	+	0.979559i
$733$	6.09092	+	11.9541i	0.224973	+	0.441535i	0.975710	−	0.219067i	$-0.0703012\pi$
$733$	6.09092	+	11.9541i	0.224973	+	0.441535i	−0.750737	+	0.660602i	$0.770301\pi$
$734$	−2.93159	−	9.02251i	−0.108207	−	0.333027i
$735$	−12.8749	+	18.0066i	−0.474896	+	0.664184i
$736$			9.48683i			0.349689i
$737$		0			0
$738$	−10.0000	−	10.0000i	−0.368105	−	0.368105i
$739$	10.2333	−	7.43496i	0.376440	−	0.273499i	−0.383437	−	0.923567i	$-0.625260\pi$
$739$	10.2333	−	7.43496i	0.376440	−	0.273499i	0.759876	+	0.650068i	$0.225260\pi$
$740$	22.8974	−	16.9030i	0.841724	−	0.621365i
$741$	12.3607	−	38.0423i	0.454081	−	1.39752i
$742$		0			0
$743$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$743$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$744$	−1.95440	+	6.01501i	−0.0716516	+	0.220521i
$745$		0			0
$746$	−8.09017	+	5.87785i	−0.296202	+	0.215203i
$747$	−6.32456	−	6.32456i	−0.231403	−	0.231403i
$748$		0			0
$749$		0			0
$750$	−24.4242	+	25.5628i	−0.891846	+	0.933422i
$751$	−2.47214	−	7.60845i	−0.0902095	−	0.277636i	0.895766	−	0.444526i	$-0.146628\pi$
$751$	−2.47214	−	7.60845i	−0.0902095	−	0.277636i	−0.985976	+	0.166889i	$0.946628\pi$
$752$	−1.92612	−	3.78022i	−0.0702383	−	0.137850i
$753$	2.65478	+	16.7616i	0.0967456	+	0.610828i
$754$	51.1667	+	37.1748i	1.86338	+	1.35383i
$755$		0			0
$756$		0			0
$757$	5.97326	−	37.7137i	0.217102	−	1.37073i	−0.602649	−	0.798006i	$-0.705888\pi$
$757$	5.97326	−	37.7137i	0.217102	−	1.37073i	0.819751	−	0.572720i	$-0.194112\pi$
$758$	41.1096	−	41.1096i	1.49317	−	1.49317i
$759$		0			0
$760$	30.0000	−	10.0000i	1.08821	−	0.362738i
$761$	22.3049	+	30.7000i	0.808551	+	1.11288i	0.991545	+	0.129761i	$0.0414211\pi$
$761$	22.3049	+	30.7000i	0.808551	+	1.11288i	−0.182994	+	0.983114i	$0.558579\pi$
$762$	−25.2015	−	12.8408i	−0.912953	−	0.465173i
$763$		0			0
$764$	38.7938	−	53.3951i	1.40351	−	1.93177i
$765$	9.53375	+	3.01788i	0.344693	+	0.109112i
$766$	−57.1426	−	18.5668i	−2.06465	−	0.670844i
$767$	−12.1818	+	23.9082i	−0.439861	+	0.863276i
$768$	−12.5712	−	1.99109i	−0.453625	−	0.0718471i
$769$	−6.32456			−0.228069			−0.114035	−	0.993477i	$-0.536377\pi$
$769$	−6.32456			−0.228069			−0.114035	+	0.993477i	$0.536377\pi$
$770$		0			0
$771$	14.0000			0.504198
$772$	66.2561	+	10.4939i	2.38461	+	0.377685i
$773$	7.06243	−	13.8608i	0.254018	−	0.498539i	−0.728419	−	0.685132i	$-0.759745\pi$
$773$	7.06243	−	13.8608i	0.254018	−	0.498539i	0.982437	+	0.186593i	$0.0597446\pi$
$774$		0			0
$775$	−0.151820	−	9.99885i	−0.00545353	−	0.359169i
$776$	13.0112	−	17.9084i	0.467074	−	0.642872i
$777$		0			0
$778$	31.8776	+	16.2425i	1.14287	+	0.582320i
$779$	23.5114	+	32.3607i	0.842384	+	1.15944i
$780$	−18.9737	+	37.9473i	−0.679366	+	1.35873i
$781$		0			0
$782$	−10.0000	+	10.0000i	−0.357599	+	0.357599i
$783$	5.59677	−	35.3366i	0.200012	−	1.26283i
$784$	6.65740	−	2.16312i	0.237764	−	0.0772542i
$785$	−0.168039	−	22.1353i	−0.00599756	−	0.790043i
$786$	32.3607	+	23.5114i	1.15427	+	0.838624i
$787$	−5.59677	−	35.3366i	−0.199503	−	1.25961i	−0.860588	−	0.509303i	$-0.829903\pi$
$787$	−5.59677	−	35.3366i	−0.199503	−	1.25961i	0.661084	−	0.750312i	$-0.270097\pi$
$788$	−6.09092	−	11.9541i	−0.216980	−	0.425847i
$789$	−11.7264	−	36.0901i	−0.417470	−	1.28484i
$790$	−25.7237	−	18.3927i	−0.915209	−	0.654381i
$791$		0			0
$792$		0			0
$793$	−20.0000	−	20.0000i	−0.710221	−	0.710221i
$794$	33.2584	−	24.1636i	1.18030	−	0.857535i
$795$	4.42226	+	0.666045i	0.156841	+	0.0236222i
$796$	−5.56231	+	17.1190i	−0.197151	+	0.606767i
$797$	−18.1584	+	2.87601i	−0.643205	+	0.101874i	−0.469512	−	0.882926i	$-0.655570\pi$
$797$	−18.1584	+	2.87601i	−0.643205	+	0.101874i	−0.173693	+	0.984800i	$0.555570\pi$
$798$		0			0
$799$	5.86319	−	18.0450i	0.207425	−	0.638387i
$800$	33.0446	−	5.74932i	1.16830	−	0.203269i
$801$	−4.85410	+	3.52671i	−0.171511	+	0.124610i
$802$	−18.9737	−	18.9737i	−0.669983	−	0.669983i
$803$		0			0
$804$		−	18.0000i		−	0.634811i
$805$		0			0
$806$	−6.18034	−	19.0211i	−0.217693	−	0.669991i
$807$	15.4089	+	30.2418i	0.542421	+	1.06456i
$808$		0			0
$809$	15.3500	+	11.1524i	0.539678	+	0.392099i	0.823965	−	0.566640i	$-0.191757\pi$
$809$	15.3500	+	11.1524i	0.539678	+	0.392099i	−0.284287	+	0.958739i	$0.591757\pi$
$810$	24.9993	−	0.189780i	0.878385	−	0.00666820i
$811$	6.01501	−	1.95440i	0.211216	−	0.0686281i	−0.201498	−	0.979489i	$-0.564581\pi$
$811$	6.01501	−	1.95440i	0.211216	−	0.0686281i	0.412714	+	0.910861i	$0.364581\pi$
$812$		0			0
$813$	−12.6491	+	12.6491i	−0.443624	+	0.443624i
$814$		0			0
$815$	1.00000	+	3.00000i	0.0350285	+	0.105085i
$816$	3.71748	+	5.11667i	0.130138	+	0.179119i
$817$		0			0
$818$	−25.2015	+	12.8408i	−0.881149	+	0.448968i
$819$		0			0
$820$	−19.5476	−	37.6549i	−0.682632	−	1.31497i
$821$	18.0450	+	5.86319i	0.629776	+	0.204627i	0.606476	−	0.795102i	$-0.292583\pi$
$821$	18.0450	+	5.86319i	0.629776	+	0.204627i	0.0233000	+	0.999729i	$0.492583\pi$
$822$	−26.3940	+	51.8011i	−0.920596	+	1.80677i
$823$	15.3648	+	2.43355i	0.535584	+	0.0848282i	0.418367	−	0.908278i	$-0.362603\pi$
$823$	15.3648	+	2.43355i	0.535584	+	0.0848282i	0.117217	+	0.993106i	$0.462603\pi$
$824$	28.4605			0.991468
$825$		0			0
$826$		0			0
$827$	−8.83415	−	1.39919i	−0.307194	−	0.0486547i	0.000934498	−	1.00000i	$-0.499703\pi$
$827$	−8.83415	−	1.39919i	−0.307194	−	0.0486547i	−0.308128	+	0.951345i	$0.599703\pi$
$828$	1.92612	−	3.78022i	0.0669372	−	0.131372i
$829$	5.70634	+	1.85410i	0.198189	+	0.0643956i	0.406430	−	0.913682i	$-0.366774\pi$
$829$	5.70634	+	1.85410i	0.198189	+	0.0643956i	−0.208240	+	0.978078i	$0.566774\pi$
$830$	−20.6050	−	39.6917i	−0.715209	−	1.37772i
$831$	11.1524	−	15.3500i	0.386874	−	0.532486i
$832$	51.8011	−	26.3940i	1.79588	−	0.915047i
$833$	27.8929	+	14.2122i	0.966432	+	0.492422i
$834$	23.5114	+	32.3607i	0.814134	+	1.12056i
$835$	12.6491	+	37.9473i	0.437741	+	1.31322i
$836$		0			0
$837$	−8.00000	+	8.00000i	−0.276520	+	0.276520i
$838$	−12.5927	+	79.5074i	−0.435009	+	2.74654i
$839$	−5.70634	+	1.85410i	−0.197005	+	0.0640107i	−0.405857	−	0.913936i	$-0.633027\pi$
$839$	−5.70634	+	1.85410i	−0.197005	+	0.0640107i	0.208853	+	0.977947i	$0.433027\pi$
$840$		0			0
$841$	−8.89919	−	6.46564i	−0.306869	−	0.222953i
$842$	−9.79435	−	61.8391i	−0.337535	−	2.13112i
$843$	12.1818	+	23.9082i	0.419565	+	0.823443i
$844$	−23.4527	−	72.1801i	−0.807277	−	2.48454i
$845$	−2.56587	−	15.4407i	−0.0882688	−	0.531177i
$846$			9.48683i			0.326164i
$847$		0			0
$848$	−1.00000	−	1.00000i	−0.0343401	−	0.0343401i
$849$	10.2333	−	7.43496i	0.351208	−	0.255167i
$850$	40.8924	+	28.7718i	1.40260	+	0.986863i
$851$	−1.85410	+	5.70634i	−0.0635578	+	0.195611i
$852$	33.5233	−	5.30956i	1.14849	−	0.181903i
$853$	−13.2512	+	2.09879i	−0.453713	+	0.0718612i	−0.379109	−	0.925352i	$-0.623769\pi$
$853$	−13.2512	+	2.09879i	−0.453713	+	0.0718612i	−0.0746045	+	0.997213i	$0.523769\pi$
$854$		0			0
$855$	13.9844	+	2.10622i	0.478257	+	0.0720312i
$856$		0			0
$857$	−15.8114	−	15.8114i	−0.540107	−	0.540107i	0.383453	−	0.923560i	$-0.374735\pi$
$857$	−15.8114	−	15.8114i	−0.540107	−	0.540107i	−0.923560	+	0.383453i	$0.874735\pi$
$858$		0			0
$859$		−	44.0000i		−	1.50126i	−0.660722	−	0.750630i	$-0.729750\pi$
$859$		−	44.0000i		−	1.50126i	0.660722	−	0.750630i	$-0.270250\pi$
$860$		0			0
$861$		0			0
$862$	19.2612	+	37.8022i	0.656039	+	1.28755i
$863$	0.221232	+	1.39680i	0.00753082	+	0.0475477i	0.991168	−	0.132615i	$-0.0423375\pi$
$863$	0.221232	+	1.39680i	0.00753082	+	0.0475477i	−0.983637	+	0.180163i	$0.942337\pi$
$864$	−30.7000	−	22.3049i	−1.04444	−	0.758827i
$865$	−0.0759122	−	9.99971i	−0.00258109	−	0.340000i
$866$	−3.00750	+	0.977198i	−0.102199	+	0.0332065i
$867$	−0.663695	+	4.19041i	−0.0225403	+	0.142314i
$868$		0			0
$869$		0			0
$870$	20.0000	−	40.0000i	0.678064	−	1.35613i
$871$	11.1524	+	15.3500i	0.377886	+	0.520116i
$872$	25.2015	+	12.8408i	0.853429	+	0.434844i
$873$	8.82051	−	4.49428i	0.298529	−	0.152108i
$874$	−11.7557	+	16.1803i	−0.397643	+	0.547308i
$875$		0			0
$876$	18.0450	+	5.86319i	0.609685	+	0.198099i
$877$	26.3940	−	51.8011i	0.891262	−	1.74920i	0.275432	−	0.961320i	$-0.411179\pi$
$877$	26.3940	−	51.8011i	0.891262	−	1.74920i	0.615830	−	0.787879i	$-0.288821\pi$
$878$	−27.9360	−	4.42463i	−0.942796	−	0.149324i
$879$	31.6228			1.06661
$880$		0			0
$881$	2.00000			0.0673817			0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000			0.0673817			0.0336909	+	0.999432i	$0.489274\pi$
$882$	−15.4598	−	2.44859i	−0.520557	−	0.0824482i
$883$	−12.1988	+	23.9414i	−0.410521	+	0.805692i	−0.999998	−	0.00209290i	$-0.999334\pi$
$883$	−12.1988	+	23.9414i	−0.410521	+	0.805692i	0.589477	+	0.807785i	$0.299334\pi$
$884$	57.0634	+	18.5410i	1.91925	+	0.623602i
$885$	18.0890	+	5.72603i	0.608056	+	0.192478i
$886$	20.4461	−	28.1417i	0.686902	−	0.945439i
$887$	−7.96940	+	4.06061i	−0.267586	+	0.136342i	−0.582636	−	0.812733i	$-0.697979\pi$
$887$	−7.96940	+	4.06061i	−0.267586	+	0.136342i	0.315050	+	0.949075i	$0.397979\pi$
$888$	−11.9541	−	6.09092i	−0.401154	−	0.204398i
$889$		0			0
$890$	−28.4605	+	9.48683i	−0.953998	+	0.317999i
$891$		0			0
$892$	33.0000	−	33.0000i	1.10492	−	1.10492i
$893$	4.19758	−	26.5025i	0.140467	−	0.886871i
$894$		0			0
$895$	6.37238	+	6.27636i	0.213005	+	0.209796i
$896$		0			0
$897$	−1.39919	−	8.83415i	−0.0467177	−	0.294964i
$898$	−6.09092	−	11.9541i	−0.203257	−	0.398914i
$899$	3.90879	+	12.0300i	0.130365	+	0.401224i
$900$	−14.3346	−	4.41814i	−0.477819	−	0.147271i
$901$		−	6.32456i		−	0.210701i
$902$		0			0
$903$		0			0
$904$	−23.0250	+	16.7287i	−0.765801	+	0.556387i
$905$	−2.66418	+	17.6890i	−0.0885603	+	0.588004i
$906$		0			0
$907$	23.7456	−	3.76094i	0.788461	−	0.124880i	0.250798	−	0.968040i	$-0.419307\pi$
$907$	23.7456	−	3.76094i	0.788461	−	0.124880i	0.537663	+	0.843160i	$0.319307\pi$
$908$	26.5025	−	4.19758i	0.879515	−	0.139301i
$909$		0			0
$910$		0			0
$911$	−33.9787	+	24.6870i	−1.12577	+	0.817916i	−0.985073	−	0.172137i	$-0.944933\pi$
$911$	−33.9787	+	24.6870i	−1.12577	+	0.817916i	−0.140692	+	0.990053i	$0.544933\pi$
$912$	6.32456	+	6.32456i	0.209427	+	0.209427i
$913$		0			0
$914$		−	50.0000i		−	1.65385i
$915$	−11.6325	+	16.2691i	−0.384560	+	0.537840i
$916$	3.70820	+	11.4127i	0.122523	+	0.377086i
$917$		0			0
$918$	−8.84927	−	55.8721i	−0.292069	−	1.84405i
$919$	30.7000	+	22.3049i	1.01270	+	0.735770i	0.964774	−	0.263081i	$-0.0847385\pi$
$919$	30.7000	+	22.3049i	1.01270	+	0.735770i	0.0479269	+	0.998851i	$0.484739\pi$
$920$	4.96190	−	5.03781i	0.163589	−	0.166092i
$921$		0			0
$922$	−8.84927	+	55.8721i	−0.291435	+	1.84005i
$923$	−25.2982	+	25.2982i	−0.832701	+	0.832701i
$924$		0			0
$925$	21.0000	+	3.00000i	0.690476	+	0.0986394i
$926$	16.7287	+	23.0250i	0.549738	+	0.756649i
$927$	11.3407	+	5.77836i	0.372476	+	0.189786i
$928$	−37.8022	+	19.2612i	−1.24092	+	0.632279i
$929$	−2.35114	+	3.23607i	−0.0771384	+	0.106172i	−0.845843	−	0.533432i	$-0.820902\pi$
$929$	−2.35114	+	3.23607i	−0.0771384	+	0.106172i	0.768704	+	0.639604i	$0.220902\pi$
$930$	−12.5516	+	6.51587i	−0.411584	+	0.213664i
$931$	42.1051	+	13.6808i	1.37994	+	0.448369i
$932$	18.2728	−	35.8623i	0.598544	−	1.17471i
$933$	−11.1744	−	1.76985i	−0.365834	−	0.0579424i
$934$	22.1359			0.724310
$935$		0			0
$936$	−10.0000			−0.326860
$937$	−13.2512	−	2.09879i	−0.432899	−	0.0685644i	−0.0638176	−	0.997962i	$-0.520328\pi$
$937$	−13.2512	−	2.09879i	−0.432899	−	0.0685644i	−0.369081	+	0.929397i	$0.620328\pi$
$938$		0			0
$939$	−17.1190	−	5.56231i	−0.558658	−	0.181519i
$940$	−8.58905	+	27.1335i	−0.280144	+	0.884998i
$941$	22.3049	−	30.7000i	0.727118	−	1.00079i	−0.272139	−	0.962258i	$-0.587731\pi$
$941$	22.3049	−	30.7000i	0.727118	−	1.00079i	0.999257	−	0.0385346i	$-0.0122690\pi$
$942$	−27.8929	+	14.2122i	−0.908800	+	0.463057i
$943$	7.96940	+	4.06061i	0.259520	+	0.132232i
$944$	−3.52671	−	4.85410i	−0.114785	−	0.157988i
$945$		0			0
$946$		0			0
$947$	−7.00000	+	7.00000i	−0.227469	+	0.227469i	−0.811635	−	0.584165i	$-0.801422\pi$
$947$	−7.00000	+	7.00000i	−0.227469	+	0.227469i	0.584165	+	0.811635i	$0.301422\pi$
$948$	−4.19758	+	26.5025i	−0.136331	+	0.860760i
$949$	−19.0211	+	6.18034i	−0.617452	+	0.200622i
$950$	63.4838	+	31.1418i	2.05969	+	1.01037i
$951$	−27.5066	−	19.9847i	−0.891962	−	0.648048i
$952$		0			0
$953$	−6.09092	−	11.9541i	−0.197304	−	0.387232i	0.771064	−	0.636758i	$-0.219725\pi$
$953$	−6.09092	−	11.9541i	−0.197304	−	0.387232i	−0.968368	+	0.249527i	$0.919725\pi$
$954$	0.977198	+	3.00750i	0.0316379	+	0.0973716i
$955$	48.5280	−	8.06418i	1.57033	−	0.260951i
$956$			56.9210i			1.84096i
$957$		0			0
$958$	−10.0000	−	10.0000i	−0.323085	−	0.323085i
$959$		0			0
$960$	−24.4154	−	33.0740i	−0.788004	−	1.06746i
$961$	−8.34346	+	25.6785i	−0.269144	+	0.828340i
$962$	41.9041	−	6.63695i	1.35104	−	0.213984i
$963$		0			0
$964$	−5.86319	+	18.0450i	−0.188840	+	0.581191i
$965$	29.6955	+	40.2266i	0.955932	+	1.29494i
$966$		0			0
$967$	18.9737	+	18.9737i	0.610152	+	0.610152i	0.942986	−	0.332834i	$-0.108005\pi$
$967$	18.9737	+	18.9737i	0.610152	+	0.610152i	−0.332834	+	0.942986i	$0.608005\pi$
$968$		0			0
$969$			40.0000i			1.28499i
$970$	48.8279	−	8.11401i	1.56777	−	0.260525i
$971$	12.9787	+	39.9444i	0.416507	+	1.28188i	0.910896	+	0.412635i	$0.135392\pi$
$971$	12.9787	+	39.9444i	0.416507	+	1.28188i	−0.494389	+	0.869240i	$0.664608\pi$
$972$	13.4828	+	26.4615i	0.432462	+	0.848754i
$973$		0			0
$974$	7.67501	+	5.57622i	0.245923	+	0.178674i
$975$	−29.9232	+	10.2274i	−0.958310	+	0.327540i
$976$	6.01501	−	1.95440i	0.192536	−	0.0625587i
$977$	3.76094	−	23.7456i	0.120323	−	0.759690i	−0.851565	−	0.524248i	$-0.824346\pi$
$977$	3.76094	−	23.7456i	0.120323	−	0.759690i	0.971888	−	0.235442i	$-0.0756537\pi$
$978$	3.16228	−	3.16228i	0.101118	−	0.101118i
$979$		0			0
$980$	−42.0000	−	21.0000i	−1.34164	−	0.670820i
$981$	7.43496	+	10.2333i	0.237380	+	0.326726i
$982$	12.6007	+	6.42040i	0.402106	+	0.204883i
$983$	36.5421	−	18.6191i	1.16551	−	0.593859i	0.239332	−	0.970938i	$-0.423072\pi$
$983$	36.5421	−	18.6191i	1.16551	−	0.593859i	0.926181	+	0.377079i	$0.123072\pi$
$984$	−11.7557	+	16.1803i	−0.374758	+	0.515810i
$985$	3.01788	−	9.53375i	0.0961578	−	0.303771i
$986$	−60.1501	−	19.5440i	−1.91557	−	0.622406i
$987$		0			0
$988$	83.8081	+	13.2739i	2.66629	+	0.422299i
$989$		0			0
$990$		0			0
$991$	−58.0000			−1.84243			−0.921215	−	0.389053i	$-0.872802\pi$
$991$	−58.0000			−1.84243			−0.921215	+	0.389053i	$0.872802\pi$
$992$	13.2512	+	2.09879i	0.420727	+	0.0666366i
$993$	−11.5567	+	22.6813i	−0.366741	+	0.719770i
$994$		0			0
$995$	−11.9075	+	6.18149i	−0.377494	+	0.195966i
$996$	−22.3049	+	30.7000i	−0.706757	+	0.972768i
$997$	−43.8317	+	22.3334i	−1.38816	+	0.707305i	−0.978753	−	0.205044i	$-0.934266\pi$
$997$	−43.8317	+	22.3334i	−1.38816	+	0.707305i	−0.409412	+	0.912350i	$0.634266\pi$
$998$	−67.7399	−	34.5152i	−2.14427	−	1.09256i
$999$	−14.1068	−	19.4164i	−0.446321	−	0.614308i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.m.b.118.2		16
5.2	odd	4	inner	605.2.m.b.602.1		16
11.2	odd	10		55.2.e.a.43.2	yes	4
11.3	even	5	inner	605.2.m.b.578.2		16
11.4	even	5	inner	605.2.m.b.403.2		16
11.5	even	5	inner	605.2.m.b.233.1		16
11.6	odd	10	inner	605.2.m.b.233.2		16
11.7	odd	10	inner	605.2.m.b.403.1		16
11.8	odd	10	inner	605.2.m.b.578.1		16
11.9	even	5		55.2.e.a.43.1	yes	4
11.10	odd	2	inner	605.2.m.b.118.1		16
33.2	even	10		495.2.k.b.208.1		4
33.20	odd	10		495.2.k.b.208.2		4
44.31	odd	10		880.2.bd.e.593.2		4
44.35	even	10		880.2.bd.e.593.1		4
55.2	even	20		55.2.e.a.32.1	✓	4
55.7	even	20	inner	605.2.m.b.282.2		16
55.9	even	10		275.2.e.b.43.2		4
55.13	even	20		275.2.e.b.32.2		4
55.17	even	20	inner	605.2.m.b.112.2		16
55.24	odd	10		275.2.e.b.43.1		4
55.27	odd	20	inner	605.2.m.b.112.1		16
55.32	even	4	inner	605.2.m.b.602.2		16
55.37	odd	20	inner	605.2.m.b.282.1		16
55.42	odd	20		55.2.e.a.32.2	yes	4
55.47	odd	20	inner	605.2.m.b.457.2		16
55.52	even	20	inner	605.2.m.b.457.1		16
55.53	odd	20		275.2.e.b.32.1		4
165.2	odd	20		495.2.k.b.307.2		4
165.152	even	20		495.2.k.b.307.1		4
220.167	odd	20		880.2.bd.e.417.1		4
220.207	even	20		880.2.bd.e.417.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.e.a.32.1	✓	4	55.2	even	20
55.2.e.a.32.2	yes	4	55.42	odd	20
55.2.e.a.43.1	yes	4	11.9	even	5
55.2.e.a.43.2	yes	4	11.2	odd	10
275.2.e.b.32.1		4	55.53	odd	20
275.2.e.b.32.2		4	55.13	even	20
275.2.e.b.43.1		4	55.24	odd	10
275.2.e.b.43.2		4	55.9	even	10
495.2.k.b.208.1		4	33.2	even	10
495.2.k.b.208.2		4	33.20	odd	10
495.2.k.b.307.1		4	165.152	even	20
495.2.k.b.307.2		4	165.2	odd	20
605.2.m.b.112.1		16	55.27	odd	20	inner
605.2.m.b.112.2		16	55.17	even	20	inner
605.2.m.b.118.1		16	11.10	odd	2	inner
605.2.m.b.118.2		16	1.1	even	1	trivial
605.2.m.b.233.1		16	11.5	even	5	inner
605.2.m.b.233.2		16	11.6	odd	10	inner
605.2.m.b.282.1		16	55.37	odd	20	inner
605.2.m.b.282.2		16	55.7	even	20	inner
605.2.m.b.403.1		16	11.7	odd	10	inner
605.2.m.b.403.2		16	11.4	even	5	inner
605.2.m.b.457.1		16	55.52	even	20	inner
605.2.m.b.457.2		16	55.47	odd	20	inner
605.2.m.b.578.1		16	11.8	odd	10	inner
605.2.m.b.578.2		16	11.3	even	5	inner
605.2.m.b.602.1		16	5.2	odd	4	inner
605.2.m.b.602.2		16	55.32	even	4	inner
880.2.bd.e.417.1		4	220.167	odd	20
880.2.bd.e.417.2		4	220.207	even	20
880.2.bd.e.593.1		4	44.35	even	10
880.2.bd.e.593.2		4	44.31	odd	10

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.m (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.20854 + 0.349798i) q^{2} +(0.642040 - 1.26007i) q^{3} +(2.85317 + 0.927051i) q^{4} +(1.03025 + 1.98459i) q^{5} +(1.85874 - 2.55834i) q^{6} +(1.99235 + 1.01515i) q^{8} +(0.587785 + 0.809017i) q^{9} +O(q^{10})\)	\(q+(2.20854 + 0.349798i) q^{2} +(0.642040 - 1.26007i) q^{3} +(2.85317 + 0.927051i) q^{4} +(1.03025 + 1.98459i) q^{5} +(1.85874 - 2.55834i) q^{6} +(1.99235 + 1.01515i) q^{8} +(0.587785 + 0.809017i) q^{9} +(1.58114 + 4.74342i) q^{10} +(3.00000 - 3.00000i) q^{12} +(-0.699596 + 4.41708i) q^{13} +(3.16219 - 0.0240055i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.699596 - 4.41708i) q^{17} +(1.01515 + 1.99235i) q^{18} +(-1.95440 - 6.01501i) q^{19} +(1.09966 + 6.61746i) q^{20} +(-1.00000 - 1.00000i) q^{23} +(2.55834 - 1.85874i) q^{24} +(-2.87718 + 4.08924i) q^{25} +(-3.09017 + 9.51057i) q^{26} +(5.58721 - 0.884927i) q^{27} +(1.95440 - 6.01501i) q^{29} +(6.99221 + 1.05311i) q^{30} +(-1.61803 + 1.17557i) q^{31} +(-4.74342 - 4.74342i) q^{32} -10.0000i q^{34} +(0.927051 + 2.85317i) q^{36} +(-1.92612 - 3.78022i) q^{37} +(-2.21232 - 13.9680i) q^{38} +(5.11667 + 3.71748i) q^{39} +(0.0379561 + 4.99986i) q^{40} +(-6.01501 + 1.95440i) q^{41} +(-1.00000 + 2.00000i) q^{45} +(-1.85874 - 2.55834i) q^{46} +(3.78022 + 1.92612i) q^{47} +(-1.26007 + 0.642040i) q^{48} +(-4.11450 + 5.66312i) q^{49} +(-7.78476 + 8.02481i) q^{50} +(-6.01501 - 1.95440i) q^{51} +(-6.09092 + 11.9541i) q^{52} +(1.39680 + 0.221232i) q^{53} +12.6491 q^{54} +(-8.83415 - 1.39919i) q^{57} +(6.42040 - 12.6007i) q^{58} +(5.70634 + 1.85410i) q^{59} +(9.04451 + 2.86302i) q^{60} +(-3.71748 + 5.11667i) q^{61} +(-3.98470 + 2.03031i) q^{62} +(-7.64121 - 10.5172i) q^{64} +(-9.48683 + 3.16228i) q^{65} +(3.00000 - 3.00000i) q^{67} +(2.09879 - 13.2512i) q^{68} +(-1.90211 + 0.618034i) q^{69} +(6.47214 + 4.70228i) q^{71} +(0.349798 + 2.20854i) q^{72} +(2.03031 + 3.98470i) q^{73} +(-2.93159 - 9.02251i) q^{74} +(3.30548 + 6.25090i) q^{75} -18.9737i q^{76} +(10.0000 + 10.0000i) q^{78} +(-5.11667 + 3.71748i) q^{79} +(0.333023 - 2.21113i) q^{80} +(1.54508 - 4.75528i) q^{81} +(-13.9680 + 2.21232i) q^{82} +(-8.83415 + 1.39919i) q^{83} +(8.04532 - 5.93910i) q^{85} +(-6.32456 - 6.32456i) q^{87} +6.00000i q^{89} +(-2.90813 + 4.06728i) q^{90} +(-1.92612 - 3.78022i) q^{92} +(0.442463 + 2.79360i) q^{93} +(7.67501 + 5.57622i) q^{94} +(9.92380 - 10.0756i) q^{95} +(-9.02251 + 2.93159i) q^{96} +(1.54862 - 9.77762i) q^{97} +(-11.0680 + 11.0680i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3} + 8 q^{5}+O(q^{10}) \) 16 * q + 4 * q^3 + 8 * q^5	\( 16 q + 4 q^{3} + 8 q^{5} + 48 q^{12} - 4 q^{15} - 4 q^{16} - 12 q^{20} - 16 q^{23} - 12 q^{25} + 40 q^{26} + 16 q^{27} - 8 q^{31} - 12 q^{36} - 12 q^{37} - 40 q^{38} - 16 q^{45} - 12 q^{47} + 4 q^{48} + 4 q^{53} + 40 q^{58} + 36 q^{60} + 48 q^{67} + 32 q^{71} - 4 q^{75} + 160 q^{78} + 8 q^{80} - 20 q^{81} - 40 q^{82} - 12 q^{92} + 8 q^{93} + 28 q^{97}+O(q^{100}) \) 16 * q + 4 * q^3 + 8 * q^5 + 48 * q^12 - 4 * q^15 - 4 * q^16 - 12 * q^20 - 16 * q^23 - 12 * q^25 + 40 * q^26 + 16 * q^27 - 8 * q^31 - 12 * q^36 - 12 * q^37 - 40 * q^38 - 16 * q^45 - 12 * q^47 + 4 * q^48 + 4 * q^53 + 40 * q^58 + 36 * q^60 + 48 * q^67 + 32 * q^71 - 4 * q^75 + 160 * q^78 + 8 * q^80 - 20 * q^81 - 40 * q^82 - 12 * q^92 + 8 * q^93 + 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more