LMFDB - Embedded newform 605.2.m.b.403.2

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			403.2
Root			$0.156434 - 0.987688i$ of defining polynomial
Character	$\chi$	$=$	605.403
Dual form			605.2.m.b.602.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.349798 + 2.20854i) q^{2} +(-1.26007 + 0.642040i) q^{3} +(-2.85317 + 0.927051i) q^{4} +(2.20582 - 0.366554i) q^{5} +(-1.85874 - 2.55834i) q^{6} +(-1.01515 - 1.99235i) q^{8} +(-0.587785 + 0.809017i) q^{9} +O(q^{10})$	\(q+(0.349798 + 2.20854i) q^{2} +(-1.26007 + 0.642040i) q^{3} +(-2.85317 + 0.927051i) q^{4} +(2.20582 - 0.366554i) q^{5} +(-1.85874 - 2.55834i) q^{6} +(-1.01515 - 1.99235i) q^{8} +(-0.587785 + 0.809017i) q^{9} +(1.58114 + 4.74342i) q^{10} +(3.00000 - 3.00000i) q^{12} +(-4.41708 + 0.699596i) q^{13} +(-2.54415 + 1.87811i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-4.41708 - 0.699596i) q^{17} +(-1.99235 - 1.01515i) q^{18} +(-1.95440 + 6.01501i) q^{19} +(-5.95376 + 3.09075i) q^{20} +(-1.00000 - 1.00000i) q^{23} +(2.55834 + 1.85874i) q^{24} +(4.73128 - 1.61710i) q^{25} +(-3.09017 - 9.51057i) q^{26} +(0.884927 - 5.58721i) q^{27} +(1.95440 + 6.01501i) q^{29} +(-5.03781 - 4.96190i) q^{30} +(-1.61803 - 1.17557i) q^{31} +(-4.74342 - 4.74342i) q^{32} -10.0000i q^{34} +(0.927051 - 2.85317i) q^{36} +(3.78022 + 1.92612i) q^{37} +(-13.9680 - 2.21232i) q^{38} +(5.11667 - 3.71748i) q^{39} +(-2.96955 - 4.02266i) q^{40} +(6.01501 + 1.95440i) q^{41} +(-1.00000 + 2.00000i) q^{45} +(1.85874 - 2.55834i) q^{46} +(-1.92612 - 3.78022i) q^{47} +(0.642040 - 1.26007i) q^{48} +(4.11450 + 5.66312i) q^{49} +(5.22642 + 9.88355i) q^{50} +(6.01501 - 1.95440i) q^{51} +(11.9541 - 6.09092i) q^{52} +(0.221232 + 1.39680i) q^{53} +12.6491 q^{54} +(-1.39919 - 8.83415i) q^{57} +(-12.6007 + 6.42040i) q^{58} +(-5.70634 + 1.85410i) q^{59} +(5.51780 - 7.71712i) q^{60} +(3.71748 + 5.11667i) q^{61} +(2.03031 - 3.98470i) q^{62} +(7.64121 - 10.5172i) q^{64} +(-9.48683 + 3.16228i) q^{65} +(3.00000 - 3.00000i) q^{67} +(13.2512 - 2.09879i) q^{68} +(1.90211 + 0.618034i) q^{69} +(6.47214 - 4.70228i) q^{71} +(2.20854 + 0.349798i) q^{72} +(-3.98470 - 2.03031i) q^{73} +(-2.93159 + 9.02251i) q^{74} +(-4.92351 + 5.07533i) q^{75} -18.9737i q^{76} +(10.0000 + 10.0000i) q^{78} +(-5.11667 - 3.71748i) q^{79} +(-1.56909 + 1.59310i) q^{80} +(1.54508 + 4.75528i) q^{81} +(-2.21232 + 13.9680i) q^{82} +(-1.39919 + 8.83415i) q^{83} +(-9.99971 + 0.0759122i) q^{85} +(-6.32456 - 6.32456i) q^{87} +6.00000i q^{89} +(-4.76687 - 1.50894i) q^{90} +(3.78022 + 1.92612i) q^{92} +(2.79360 + 0.442463i) q^{93} +(7.67501 - 5.57622i) q^{94} +(-2.10622 + 13.9844i) q^{95} +(9.02251 + 2.93159i) q^{96} +(9.77762 - 1.54862i) 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 $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.349798	+	2.20854i	0.247345	+	1.56167i	0.728505	+	0.685040i	$0.240215\pi$
$2$	0.349798	+	2.20854i	0.247345	+	1.56167i	−0.481161	+	0.876632i	$0.659785\pi$
$3$	−1.26007	+	0.642040i	−0.727504	+	0.370682i	−0.778187	−	0.628033i	$-0.783860\pi$
$3$	−1.26007	+	0.642040i	−0.727504	+	0.370682i	0.0506828	+	0.998715i	$0.483860\pi$
$4$	−2.85317	+	0.927051i	−1.42658	+	0.463525i
$5$	2.20582	−	0.366554i	0.986472	−	0.163928i
$5$	2.20582	−	0.366554i	0.986472	−	0.163928i
$6$	−1.85874	−	2.55834i	−0.758827	−	1.04444i
$7$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$7$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$8$	−1.01515	−	1.99235i	−0.358911	−	0.704403i
$9$	−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
$13$	−4.41708	+	0.699596i	−1.22508	+	0.194033i	−0.735256	−	0.677790i	$-0.762938\pi$
$13$	−4.41708	+	0.699596i	−1.22508	+	0.194033i	−0.489821	+	0.871823i	$0.662938\pi$
$14$		0			0
$15$	−2.54415	+	1.87811i	−0.656897	+	0.484925i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−4.41708	−	0.699596i	−1.07130	−	0.169677i	−0.404218	−	0.914663i	$-0.632456\pi$
$17$	−4.41708	−	0.699596i	−1.07130	−	0.169677i	−0.667080	+	0.744986i	$0.732456\pi$
$18$	−1.99235	−	1.01515i	−0.469602	−	0.239274i
$19$	−1.95440	+	6.01501i	−0.448369	+	1.37994i	0.430377	+	0.902649i	$0.358380\pi$
$19$	−1.95440	+	6.01501i	−0.448369	+	1.37994i	−0.878746	+	0.477289i	$0.841620\pi$
$20$	−5.95376	+	3.09075i	−1.33130	+	0.691112i
$21$		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
$25$	4.73128	−	1.61710i	0.946255	−	0.323420i
$26$	−3.09017	−	9.51057i	−0.606032	−	1.86518i
$27$	0.884927	−	5.58721i	0.170304	−	1.07526i
$28$		0			0
$29$	1.95440	+	6.01501i	0.362922	+	1.11696i	0.951272	+	0.308353i	$0.0997777\pi$
$29$	1.95440	+	6.01501i	0.362922	+	1.11696i	−0.588350	+	0.808606i	$0.700222\pi$
$30$	−5.03781	−	4.96190i	−0.919774	−	0.905915i
$31$	−1.61803	−	1.17557i	−0.290607	−	0.211139i	0.432923	−	0.901431i	$-0.357482\pi$
$31$	−1.61803	−	1.17557i	−0.290607	−	0.211139i	−0.723531	+	0.690292i	$0.757482\pi$
$32$	−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
$37$	3.78022	+	1.92612i	0.621464	+	0.316652i	0.736220	−	0.676742i	$-0.236609\pi$
$37$	3.78022	+	1.92612i	0.621464	+	0.316652i	−0.114756	+	0.993394i	$0.536609\pi$
$38$	−13.9680	−	2.21232i	−2.26591	−	0.358885i
$39$	5.11667	−	3.71748i	0.819323	−	0.595273i
$40$	−2.96955	−	4.02266i	−0.469527	−	0.636038i
$41$	6.01501	+	1.95440i	0.939387	+	0.305225i	0.738396	−	0.674368i	$-0.235584\pi$
$41$	6.01501	+	1.95440i	0.939387	+	0.305225i	0.200991	+	0.979593i	$0.435584\pi$
$42$		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
$47$	−1.92612	−	3.78022i	−0.280953	−	0.551402i	0.706802	−	0.707411i	$-0.250137\pi$
$47$	−1.92612	−	3.78022i	−0.280953	−	0.551402i	−0.987756	+	0.156009i	$0.950137\pi$
$48$	0.642040	−	1.26007i	0.0926704	−	0.181876i
$49$	4.11450	+	5.66312i	0.587785	+	0.809017i
$50$	5.22642	+	9.88355i	0.739128	+	1.39774i
$51$	6.01501	−	1.95440i	0.842270	−	0.273670i
$52$	11.9541	−	6.09092i	1.65774	−	0.844659i
$53$	0.221232	+	1.39680i	0.0303885	+	0.191866i	0.998213	−	0.0597620i	$-0.0190342\pi$
$53$	0.221232	+	1.39680i	0.0303885	+	0.191866i	−0.967824	+	0.251628i	$0.919034\pi$
$54$	12.6491			1.72133
$55$		0			0
$56$		0			0
$57$	−1.39919	−	8.83415i	−0.185328	−	1.17011i
$58$	−12.6007	+	6.42040i	−1.65456	+	0.843039i
$59$	−5.70634	+	1.85410i	−0.742902	+	0.241384i	−0.655924	−	0.754827i	$-0.727721\pi$
$59$	−5.70634	+	1.85410i	−0.742902	+	0.241384i	−0.0869778	+	0.996210i	$0.527721\pi$
$60$	5.51780	−	7.71712i	0.712345	−	0.996276i
$61$	3.71748	+	5.11667i	0.475975	+	0.655123i	0.977725	−	0.209890i	$-0.0673104\pi$
$61$	3.71748	+	5.11667i	0.475975	+	0.655123i	−0.501751	+	0.865012i	$0.667310\pi$
$62$	2.03031	−	3.98470i	0.257849	−	0.506058i
$63$		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	$0.166554\pi$
$68$	13.2512	−	2.09879i	1.60695	−	0.254516i
$69$	1.90211	+	0.618034i	0.228988	+	0.0744025i
$70$		0			0
$71$	6.47214	−	4.70228i	0.768101	−	0.558058i	−0.133283	−	0.991078i	$-0.542552\pi$
$71$	6.47214	−	4.70228i	0.768101	−	0.558058i	0.901384	+	0.433020i	$0.142552\pi$
$72$	2.20854	+	0.349798i	0.260279	+	0.0412241i
$73$	−3.98470	−	2.03031i	−0.466374	−	0.237629i	0.204980	−	0.978766i	$-0.434287\pi$
$73$	−3.98470	−	2.03031i	−0.466374	−	0.237629i	−0.671354	+	0.741137i	$0.734287\pi$
$74$	−2.93159	+	9.02251i	−0.340791	+	1.04885i
$75$	−4.92351	+	5.07533i	−0.568518	+	0.586049i
$76$		−	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	0.261490	−	0.965206i	$-0.415786\pi$
$79$	−5.11667	−	3.71748i	−0.575671	−	0.418249i	−0.837161	+	0.546957i	$0.815786\pi$
$80$	−1.56909	+	1.59310i	−0.175430	+	0.178114i
$81$	1.54508	+	4.75528i	0.171676	+	0.528365i
$82$	−2.21232	+	13.9680i	−0.244310	+	1.54251i
$83$	−1.39919	+	8.83415i	−0.153581	+	0.969674i	0.783710	+	0.621127i	$0.213325\pi$
$83$	−1.39919	+	8.83415i	−0.153581	+	0.969674i	−0.937291	+	0.348547i	$0.886675\pi$
$84$		0			0
$85$	−9.99971	+	0.0759122i	−1.08462	+	0.00823383i
$86$		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	$0.896989\pi$
$90$	−4.76687	−	1.50894i	−0.502473	−	0.159056i
$91$		0			0
$92$	3.78022	+	1.92612i	0.394115	+	0.200812i
$93$	2.79360	+	0.442463i	0.289683	+	0.0458813i
$94$	7.67501	−	5.57622i	0.791617	−	0.575143i
$95$	−2.10622	+	13.9844i	−0.216094	+	1.43477i
$96$	9.02251	+	2.93159i	0.920857	+	0.299204i
$97$	9.77762	−	1.54862i	0.992766	−	0.157239i	0.361140	−	0.932512i	$-0.382388\pi$
$97$	9.77762	−	1.54862i	0.992766	−	0.157239i	0.631626	+	0.775273i	$0.282388\pi$
$98$	−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	$-0.800000\pi$
$101$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$102$	6.42040	+	12.6007i	0.635714	+	1.24766i
$103$	−5.77836	+	11.3407i	−0.569358	+	1.11743i	0.409389	+	0.912360i	$0.365742\pi$
$103$	−5.77836	+	11.3407i	−0.569358	+	1.11743i	−0.978748	+	0.205069i	$0.934258\pi$
$104$	5.87785	+	8.09017i	0.576371	+	0.793306i
$105$		0			0
$106$	−3.00750	+	0.977198i	−0.292115	+	0.0949138i
$107$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$107$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$108$	2.65478	+	16.7616i	0.255456	+	1.61289i
$109$	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
$113$	11.3407	−	5.77836i	1.06684	−	0.543582i	0.169776	−	0.985483i	$-0.445696\pi$
$113$	11.3407	−	5.77836i	1.06684	−	0.543582i	0.897064	+	0.441901i	$0.145696\pi$
$114$	19.0211	−	6.18034i	1.78149	−	0.578842i
$115$	−2.57237	−	1.83927i	−0.239875	−	0.171512i
$116$	−11.1524	−	15.3500i	−1.03548	−	1.42521i
$117$	2.03031	−	3.98470i	0.187702	−	0.368386i
$118$	−6.09092	−	11.9541i	−0.560715	−	1.10046i
$119$		0			0
$120$	6.32456	+	3.16228i	0.577350	+	0.288675i
$121$		0			0
$122$	−10.0000	+	10.0000i	−0.905357	+	0.905357i
$123$	−8.83415	+	1.39919i	−0.796549	+	0.126161i
$124$	5.70634	+	1.85410i	0.512444	+	0.166503i
$125$	9.84359	−	5.30130i	0.880437	−	0.474163i
$126$		0			0
$127$	−8.83415	−	1.39919i	−0.783904	−	0.124158i	−0.248363	−	0.968667i	$-0.579892\pi$
$127$	−8.83415	−	1.39919i	−0.783904	−	0.124158i	−0.535542	+	0.844509i	$0.679892\pi$
$128$	13.9465	+	7.10608i	1.23270	+	0.628094i
$129$		0			0
$130$	−10.3025	−	19.8459i	−0.903588	−	1.74060i
$131$			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
$135$	−0.0960221	−	12.6487i	−0.00826427	−	1.08863i
$136$	3.09017	+	9.51057i	0.264980	+	0.815524i
$137$	−2.87601	+	18.1584i	−0.245714	+	1.55138i	0.488562	+	0.872529i	$0.337521\pi$
$137$	−2.87601	+	18.1584i	−0.245714	+	1.55138i	−0.734277	+	0.678850i	$0.762479\pi$
$138$	−0.699596	+	4.41708i	−0.0595536	+	0.376007i
$139$	−3.90879	−	12.0300i	−0.331539	−	1.02037i	−0.968402	−	0.249395i	$-0.919768\pi$
$139$	−3.90879	−	12.0300i	−0.331539	−	1.02037i	0.636862	−	0.770977i	$-0.280232\pi$
$140$		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
$145$	6.51587	+	12.5516i	0.541113	+	1.04236i
$146$	3.09017	−	9.51057i	0.255744	−	0.787100i
$147$	−8.82051	−	4.49428i	−0.727504	−	0.370682i
$148$	−12.5712	−	1.99109i	−1.03335	−	0.163666i
$149$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$149$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$150$	−12.9313	−	9.09843i	−1.05584	−	0.742883i
$151$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$151$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$152$	13.9680	−	2.21232i	1.13296	−	0.179443i
$153$	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
$157$	4.49428	+	8.82051i	0.358682	+	0.703954i	0.997879	−	0.0650892i	$-0.0207332\pi$
$157$	4.49428	+	8.82051i	0.358682	+	0.703954i	−0.639197	+	0.769043i	$0.720733\pi$
$158$	6.42040	−	12.6007i	0.510779	−	1.00246i
$159$	−1.17557	−	1.61803i	−0.0932288	−	0.128318i
$160$	−12.2018	−	8.72440i	−0.964640	−	0.689725i
$161$		0			0
$162$	−9.96176	+	5.07577i	−0.782669	+	0.398790i
$163$	0.221232	+	1.39680i	0.0173282	+	0.109406i	0.994836	−	0.101491i	$-0.0323614\pi$
$163$	0.221232	+	1.39680i	0.0173282	+	0.109406i	−0.977508	+	0.210897i	$0.932361\pi$
$164$	−18.9737			−1.48159
$165$		0			0
$166$	−20.0000			−1.55230
$167$	2.79838	+	17.6683i	0.216546	+	1.36721i	0.821161	+	0.570697i	$0.193327\pi$
$167$	2.79838	+	17.6683i	0.216546	+	1.36721i	−0.604615	+	0.796518i	$0.706673\pi$
$168$		0			0
$169$	6.65740	−	2.16312i	0.512107	−	0.166394i
$170$	−3.66554	−	22.0582i	−0.281134	−	1.69179i
$171$	−3.71748	−	5.11667i	−0.284283	−	0.391282i
$172$		0			0
$173$	2.03031	+	3.98470i	0.154361	+	0.302951i	0.955217	−	0.295906i	$-0.0956216\pi$
$173$	2.03031	+	3.98470i	0.154361	+	0.302951i	−0.800856	+	0.598857i	$0.795622\pi$
$174$	11.7557	−	16.1803i	0.891198	−	1.22663i
$175$		0			0
$176$		0			0
$177$	6.00000	−	6.00000i	0.450988	−	0.450988i
$178$	−13.2512	+	2.09879i	−0.993222	+	0.157311i
$179$	−3.80423	−	1.23607i	−0.284341	−	0.0923881i	0.163374	−	0.986564i	$-0.447762\pi$
$179$	−3.80423	−	1.23607i	−0.284341	−	0.0923881i	−0.447715	+	0.894176i	$0.647762\pi$
$180$	0.999068	−	6.63339i	0.0744661	−	0.494424i
$181$	6.47214	−	4.70228i	0.481070	−	0.349518i	−0.320670	−	0.947191i	$-0.603908\pi$
$181$	6.47214	−	4.70228i	0.481070	−	0.349518i	0.801740	+	0.597673i	$0.203908\pi$
$182$		0			0
$183$	−7.96940	−	4.06061i	−0.589115	−	0.300169i
$184$	−0.977198	+	3.00750i	−0.0720400	+	0.221716i
$185$	9.04451	+	2.86302i	0.664966	+	0.210493i
$186$			6.32456i			0.463739i
$187$		0			0
$188$	9.00000	+	9.00000i	0.656392	+	0.656392i
$189$		0			0
$190$	−31.6219	+	0.240055i	−2.29409	+	0.0174154i
$191$	6.79837	+	20.9232i	0.491913	+	1.51395i	0.821713	+	0.569902i	$0.193019\pi$
$191$	6.79837	+	20.9232i	0.491913	+	1.51395i	−0.329800	+	0.944051i	$0.606981\pi$
$192$	−2.87601	+	18.1584i	−0.207558	+	1.31047i
$193$	3.49798	−	22.0854i	0.251790	−	1.58974i	−0.460372	−	0.887726i	$-0.652284\pi$
$193$	3.49798	−	22.0854i	0.251790	−	1.58974i	0.712162	−	0.702015i	$-0.247716\pi$
$194$	6.84038	+	21.0525i	0.491111	+	1.51148i
$195$	9.92380	−	10.0756i	0.710658	−	0.721530i
$196$	−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	$0.931786\pi$
$200$	−8.02481	−	7.78476i	−0.567440	−	0.550466i
$201$	−1.85410	+	5.70634i	−0.130778	+	0.402494i
$202$		0			0
$203$		0			0
$204$	−15.3500	+	11.1524i	−1.07472	+	0.780827i
$205$	13.9844	+	2.10622i	0.976714	+	0.147105i
$206$	−27.0675	−	8.79478i	−1.88589	−	0.612761i
$207$	1.39680	−	0.221232i	0.0970845	−	0.0153767i
$208$	3.16228	−	3.16228i	0.219265	−	0.219265i
$209$		0			0
$210$		0			0
$211$	14.8699	−	20.4667i	1.02369	−	1.40899i	0.114102	−	0.993469i	$-0.463601\pi$
$211$	14.8699	−	20.4667i	1.02369	−	1.40899i	0.909586	−	0.415516i	$-0.136399\pi$
$212$	−1.92612	−	3.78022i	−0.132286	−	0.259627i
$213$	−5.13632	+	10.0806i	−0.351935	+	0.690711i
$214$		0			0
$215$		0			0
$216$	−12.0300	+	3.90879i	−0.818539	+	0.265959i
$217$		0			0
$218$	4.42463	+	27.9360i	0.299674	+	1.89207i
$219$	6.32456			0.427374
$220$		0			0
$221$	20.0000			1.34535
$222$	−2.09879	−	13.2512i	−0.140861	−	0.889364i
$223$	−13.8608	+	7.06243i	−0.928188	+	0.472936i	−0.851638	−	0.524130i	$-0.824391\pi$
$223$	−13.8608	+	7.06243i	−0.928188	+	0.472936i	−0.0765502	+	0.997066i	$0.524391\pi$
$224$		0			0
$225$	−1.47271	+	4.77819i	−0.0981808	+	0.318546i
$226$	16.7287	+	23.0250i	1.11277	+	1.53160i
$227$	−4.06061	+	7.96940i	−0.269512	+	0.528948i	−0.985606	−	0.169056i	$-0.945928\pi$
$227$	−4.06061	+	7.96940i	−0.269512	+	0.528948i	0.716094	+	0.698004i	$0.245928\pi$
$228$	12.1818	+	23.9082i	0.806762	+	1.58336i
$229$	−2.35114	+	3.23607i	−0.155368	+	0.213845i	−0.879604	−	0.475706i	$-0.842192\pi$
$229$	−2.35114	+	3.23607i	−0.155368	+	0.213845i	0.724236	+	0.689552i	$0.242192\pi$
$230$	3.16228	−	6.32456i	0.208514	−	0.417029i
$231$		0			0
$232$	10.0000	−	10.0000i	0.656532	−	0.656532i
$233$	13.2512	−	2.09879i	0.868117	−	0.137496i	0.293540	−	0.955947i	$-0.405167\pi$
$233$	13.2512	−	2.09879i	0.868117	−	0.137496i	0.574577	+	0.818451i	$0.305167\pi$
$234$	9.51057	+	3.09017i	0.621725	+	0.202011i
$235$	−5.63432	−	7.63246i	−0.367543	−	0.497887i
$236$	14.5623	−	10.5801i	0.947925	−	0.688708i
$237$	8.83415	+	1.39919i	0.573840	+	0.0908873i
$238$		0			0
$239$	5.86319	−	18.0450i	0.379258	−	1.16724i	−0.561303	−	0.827610i	$-0.689700\pi$
$239$	5.86319	−	18.0450i	0.379258	−	1.16724i	0.940561	−	0.339625i	$-0.110300\pi$
$240$	0.954339	−	3.01484i	0.0616023	−	0.194607i
$241$			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
$245$	11.1517	+	10.9836i	0.712454	+	0.701719i
$246$	−6.18034	−	19.0211i	−0.394044	−	1.21274i
$247$	4.42463	−	27.9360i	0.281533	−	1.77753i
$248$	−0.699596	+	4.41708i	−0.0444244	+	0.280485i
$249$	−3.90879	−	12.0300i	−0.247710	−	0.762371i
$250$	15.1514	+	19.8856i	0.958258	+	1.25767i
$251$	−9.70820	−	7.05342i	−0.612776	−	0.445208i	0.237614	−	0.971360i	$-0.423635\pi$
$251$	−9.70820	−	7.05342i	−0.612776	−	0.445208i	−0.850391	+	0.526151i	$0.823635\pi$
$252$		0			0
$253$		0			0
$254$		−	20.0000i		−	1.25491i
$255$	12.5516	−	6.51587i	0.786014	−	0.408039i
$256$	−2.78115	+	8.55951i	−0.173822	+	0.534969i
$257$	−8.82051	−	4.49428i	−0.550209	−	0.280345i	0.156705	−	0.987646i	$-0.449913\pi$
$257$	−8.82051	−	4.49428i	−0.550209	−	0.280345i	−0.706913	+	0.707300i	$0.749913\pi$
$258$		0			0
$259$		0			0
$260$	24.1360	−	17.8173i	1.49685	−	1.10498i
$261$	−6.01501	−	1.95440i	−0.372320	−	0.120974i
$262$	−27.9360	+	4.42463i	−1.72589	+	0.273355i
$263$	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
$267$	−3.85224	−	7.56044i	−0.235753	−	0.462691i
$268$	−5.77836	+	11.3407i	−0.352969	+	0.692741i
$269$	14.1068	+	19.4164i	0.860110	+	1.18384i	0.981543	+	0.191240i	$0.0612508\pi$
$269$	14.1068	+	19.4164i	0.860110	+	1.18384i	−0.121434	+	0.992600i	$0.538749\pi$
$270$	27.9017	−	4.63658i	1.69804	−	0.282173i
$271$	12.0300	−	3.90879i	0.730772	−	0.237442i	0.0800845	−	0.996788i	$-0.474481\pi$
$271$	12.0300	−	3.90879i	0.730772	−	0.237442i	0.650687	+	0.759346i	$0.274481\pi$
$272$	3.98470	−	2.03031i	0.241608	−	0.123105i
$273$		0			0
$274$	−41.1096			−2.48352
$275$		0			0
$276$	−6.00000			−0.361158
$277$	2.09879	+	13.2512i	0.126104	+	0.796189i	0.966960	+	0.254930i	$0.0820523\pi$
$277$	2.09879	+	13.2512i	0.126104	+	0.796189i	−0.840856	+	0.541260i	$0.817948\pi$
$278$	25.2015	−	12.8408i	1.51148	−	0.770139i
$279$	1.90211	−	0.618034i	0.113877	−	0.0370007i
$280$		0			0
$281$	11.1524	+	15.3500i	0.665299	+	0.915705i	0.999642	−	0.0267460i	$-0.00851453\pi$
$281$	11.1524	+	15.3500i	0.665299	+	0.915705i	−0.334343	+	0.942451i	$0.608515\pi$
$282$	−6.09092	+	11.9541i	−0.362709	+	0.711857i
$283$	−4.06061	−	7.96940i	−0.241378	−	0.473732i	0.738256	−	0.674520i	$-0.235650\pi$
$283$	−4.06061	−	7.96940i	−0.241378	−	0.473732i	−0.979635	+	0.200789i	$0.935650\pi$
$284$	−14.1068	+	19.4164i	−0.837087	+	1.15215i
$285$	−6.32456	−	18.9737i	−0.374634	−	1.12390i
$286$		0			0
$287$		0			0
$288$	6.62561	−	1.04939i	0.390418	−	0.0618362i
$289$	2.85317	+	0.927051i	0.167834	+	0.0545324i
$290$	−25.4415	+	18.7811i	−1.49398	+	1.10286i
$291$	−11.3262	+	8.22899i	−0.663956	+	0.482392i
$292$	13.2512	+	2.09879i	0.775470	+	0.122822i
$293$	−19.9235	−	10.1515i	−1.16394	−	0.593059i	−0.238202	−	0.971216i	$-0.576558\pi$
$293$	−19.9235	−	10.1515i	−1.16394	−	0.593059i	−0.925742	+	0.378156i	$0.876558\pi$
$294$	6.84038	−	21.0525i	0.398939	−	1.22781i
$295$	−11.9075	+	6.18149i	−0.693283	+	0.359900i
$296$		−	9.48683i		−	0.551411i
$297$		0			0
$298$		0			0
$299$	5.11667	+	3.71748i	0.295905	+	0.214987i
$300$	9.34253	−	19.0451i	0.539391	−	1.09957i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−1.95440	−	6.01501i	−0.112092	−	0.344984i
$305$	10.0756	+	9.92380i	0.576929	+	0.568235i
$306$	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
$310$	3.01788	−	9.53375i	0.171404	−	0.541481i
$311$	−2.47214	+	7.60845i	−0.140182	+	0.431436i	−0.996360	−	0.0852452i	$-0.972833\pi$
$311$	−2.47214	+	7.60845i	−0.140182	+	0.431436i	0.856178	+	0.516681i	$0.172833\pi$
$312$	−12.6007	−	6.42040i	−0.713376	−	0.363483i
$313$	−12.5712	−	1.99109i	−0.710567	−	0.112543i	−0.209320	−	0.977847i	$-0.567125\pi$
$313$	−12.5712	−	1.99109i	−0.710567	−	0.112543i	−0.501247	+	0.865304i	$0.667125\pi$
$314$	−17.9084	+	13.0112i	−1.01063	+	0.734263i
$315$		0			0
$316$	18.0450	+	5.86319i	1.01511	+	0.329830i
$317$	23.7456	−	3.76094i	1.33369	−	0.211235i	0.551446	−	0.834210i	$-0.314076\pi$
$317$	23.7456	−	3.76094i	1.33369	−	0.211235i	0.782242	+	0.622975i	$0.214076\pi$
$318$	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
$323$	12.8408	−	25.2015i	0.714481	−	1.40225i
$324$	−8.81678	−	12.1353i	−0.489821	−	0.674181i
$325$	−19.7671	+	10.4528i	−1.09648	+	0.579820i
$326$	−3.00750	+	0.977198i	−0.166570	+	0.0541220i
$327$	−15.9388	+	8.12123i	−0.881418	+	0.449105i
$328$	−2.21232	−	13.9680i	−0.122155	−	0.771255i
$329$		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	$0.664716\pi$
$332$	−4.19758	−	26.5025i	−0.230372	−	1.45451i
$333$	−3.78022	+	1.92612i	−0.207155	+	0.105551i
$334$	−38.0423	+	12.3607i	−2.08158	+	0.676346i
$335$	5.51780	−	7.71712i	0.301469	−	0.421631i
$336$		0			0
$337$	−6.09092	+	11.9541i	−0.331794	+	0.651182i	−0.995284	−	0.0970031i	$-0.969074\pi$
$337$	−6.09092	+	11.9541i	−0.331794	+	0.651182i	0.663490	+	0.748185i	$0.269074\pi$
$338$	7.10608	+	13.9465i	0.386520	+	0.758587i
$339$	−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
$345$	4.42226	+	0.666045i	0.238086	+	0.0358587i
$346$	−8.09017	+	5.87785i	−0.434930	+	0.315995i
$347$	26.5025	+	4.19758i	1.42273	+	0.225338i	0.819887	−	0.572525i	$-0.194036\pi$
$347$	26.5025	+	4.19758i	1.42273	+	0.225338i	0.602839	+	0.797863i	$0.294036\pi$
$348$	23.9082	+	12.1818i	1.28161	+	0.653015i
$349$	9.77198	−	30.0750i	0.523082	−	1.60988i	−0.244996	−	0.969524i	$-0.578787\pi$
$349$	9.77198	−	30.0750i	0.523082	−	1.60988i	0.768078	−	0.640356i	$-0.221213\pi$
$350$		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
$355$	12.5527	−	12.7448i	0.666229	−	0.676422i
$356$	−5.56231	−	17.1190i	−0.294802	−	0.907306i
$357$		0			0
$358$	1.39919	−	8.83415i	0.0739496	−	0.466899i
$359$	−5.86319	−	18.0450i	−0.309447	−	0.952380i	−0.977980	−	0.208698i	$-0.933077\pi$
$359$	−5.86319	−	18.0450i	−0.309447	−	0.952380i	0.668533	−	0.743682i	$-0.266923\pi$
$360$	4.99986	−	0.0379561i	0.263516	−	0.00200046i
$361$	−16.9894	−	12.3435i	−0.894177	−	0.649657i
$362$	12.6491	+	12.6491i	0.664822	+	0.664822i
$363$		0			0
$364$		0			0
$365$	−9.53375	−	3.01788i	−0.499019	−	0.157963i
$366$	6.18034	−	19.0211i	0.323052	−	0.994250i
$367$	3.78022	+	1.92612i	0.197326	+	0.100543i	0.549862	−	0.835256i	$-0.314680\pi$
$367$	3.78022	+	1.92612i	0.197326	+	0.100543i	−0.352536	+	0.935798i	$0.614680\pi$
$368$	1.39680	+	0.221232i	0.0728134	+	0.0115325i
$369$	−5.11667	+	3.71748i	−0.266363	+	0.193524i
$370$	−3.15933	+	20.9766i	−0.164246	+	1.09052i
$371$		0			0
$372$	−8.38081	+	1.32739i	−0.434525	+	0.0688220i
$373$	−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
$377$	−12.8408	−	25.2015i	−0.661334	−	1.29794i
$378$		0			0
$379$	−15.2824	−	21.0344i	−0.785005	−	1.08047i	−0.994712	−	0.102702i	$-0.967251\pi$
$379$	−15.2824	−	21.0344i	−0.785005	−	1.08047i	0.209707	−	0.977764i	$-0.432749\pi$
$380$	−6.95486	−	41.8525i	−0.356777	−	2.14699i
$381$	12.0300	−	3.90879i	0.616317	−	0.200253i
$382$	−43.8317	+	22.3334i	−2.24263	+	1.14268i
$383$	−4.20340	−	26.5392i	−0.214784	−	1.35609i	−0.825572	−	0.564298i	$-0.809147\pi$
$383$	−4.20340	−	26.5392i	−0.214784	−	1.35609i	0.610788	−	0.791794i	$-0.290853\pi$
$384$	−22.1359			−1.12962
$385$		0			0
$386$	50.0000			2.54493
$387$		0			0
$388$	−26.4615	+	13.4828i	−1.34338	+	0.684487i
$389$	−15.2169	+	4.94427i	−0.771528	+	0.250685i	−0.668219	−	0.743965i	$-0.732943\pi$
$389$	−15.2169	+	4.94427i	−0.771528	+	0.250685i	−0.103309	+	0.994649i	$0.532943\pi$
$390$	25.7237	+	18.3927i	1.30257	+	0.931348i
$391$	3.71748	+	5.11667i	0.188001	+	0.258761i
$392$	7.10608	−	13.9465i	0.358911	−	0.704403i
$393$	−8.12123	−	15.9388i	−0.409662	−	0.804007i
$394$	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	$0.0973643\pi$
$398$	−13.2512	+	2.09879i	−0.664224	+	0.105203i
$399$		0			0
$400$	−2.87718	+	4.08924i	−0.143859	+	0.204462i
$401$	−9.70820	+	7.05342i	−0.484805	+	0.352231i	−0.803183	−	0.595733i	$-0.796862\pi$
$401$	−9.70820	+	7.05342i	−0.484805	+	0.352231i	0.318378	+	0.947964i	$0.396862\pi$
$402$	−13.2512	−	2.09879i	−0.660911	−	0.104678i
$403$	7.96940	+	4.06061i	0.396984	+	0.202274i
$404$		0			0
$405$	5.15124	+	9.92294i	0.255967	+	0.493075i
$406$		0			0
$407$		0			0
$408$	−10.0000	−	10.0000i	−0.495074	−	0.495074i
$409$	−10.2333	−	7.43496i	−0.506006	−	0.367635i	0.305300	−	0.952256i	$-0.401243\pi$
$409$	−10.2333	−	7.43496i	−0.506006	−	0.367635i	−0.811307	+	0.584621i	$0.801243\pi$
$410$	0.240055	+	31.6219i	0.0118555	+	1.56169i
$411$	−8.03444	−	24.7275i	−0.396310	−	1.21972i
$412$	5.97326	−	37.7137i	0.294281	−	1.85802i
$413$		0			0
$414$	0.977198	+	3.00750i	0.0480266	+	0.147811i
$415$	0.151824	+	19.9994i	0.00745276	+	0.981733i
$416$	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	0.484427	+	0.874832i	$0.339028\pi$
$421$	−8.65248	+	26.6296i	−0.421696	+	1.29785i	−0.906123	+	0.423015i	$0.860972\pi$
$422$	50.4029	+	25.6816i	2.45358	+	1.25016i
$423$	4.19041	+	0.663695i	0.203745	+	0.0322700i
$424$	2.55834	−	1.85874i	0.124244	−	0.0902684i
$425$	−22.0297	+	3.83288i	−1.06860	+	0.185922i
$426$	−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	$-0.951063\pi$
$431$	−11.1524	+	15.3500i	−0.537194	+	0.739384i	0.451011	+	0.892518i	$0.351063\pi$
$432$	2.56816	+	5.04029i	0.123561	+	0.242501i
$433$	0.642040	−	1.26007i	0.0308545	−	0.0605553i	−0.875065	−	0.484006i	$-0.839181\pi$
$433$	0.642040	−	1.26007i	0.0308545	−	0.0605553i	0.905919	+	0.423451i	$0.139181\pi$
$434$		0			0
$435$	−16.2691	−	11.6325i	−0.780044	−	0.557738i
$436$	−36.0901	+	11.7264i	−1.72840	+	0.561591i
$437$	7.96940	−	4.06061i	0.381228	−	0.194246i
$438$	2.21232	+	13.9680i	0.105709	+	0.667418i
$439$	−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
$442$	6.99596	+	44.1708i	0.332764	+	2.10099i
$443$	−13.8608	+	7.06243i	−0.658547	+	0.335546i	−0.751126	−	0.660159i	$-0.770489\pi$
$443$	−13.8608	+	7.06243i	−0.658547	+	0.335546i	0.0925790	+	0.995705i	$0.470489\pi$
$444$	17.1190	−	5.56231i	0.812433	−	0.263975i
$445$	2.19932	+	13.2349i	0.104258	+	0.627395i
$446$	−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	$-0.754782\pi$
$449$	3.52671	−	4.85410i	0.166436	−	0.229079i	0.884086	+	0.467325i	$0.154782\pi$
$450$	−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
$457$	−22.0854	−	3.49798i	−1.03311	−	0.163629i	−0.383221	−	0.923657i	$-0.625185\pi$
$457$	−22.0854	−	3.49798i	−1.03311	−	0.163629i	−0.649890	+	0.760028i	$0.725185\pi$
$458$	−7.96940	−	4.06061i	−0.372386	−	0.189740i
$459$	−7.81758	+	24.0600i	−0.364893	+	1.12303i
$460$	9.04451	+	2.86302i	0.421702	+	0.133489i
$461$			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
$465$	6.32437	−	0.0480111i	0.293286	−	0.00222646i
$466$	9.27051	+	28.5317i	0.429448	+	1.32171i
$467$	1.54862	−	9.77762i	0.0716617	−	0.452454i	−0.925600	−	0.378503i	$-0.876439\pi$
$467$	1.54862	−	9.77762i	0.0716617	−	0.452454i	0.997262	−	0.0739513i	$-0.0235609\pi$
$468$	−2.09879	+	13.2512i	−0.0970165	+	0.612538i
$469$		0			0
$470$	14.8857	−	15.1134i	0.686626	−	0.697131i
$471$	−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
$475$	0.480097	+	31.6191i	0.0220284	+	1.45079i
$476$		0			0
$477$	−1.26007	−	0.642040i	−0.0576948	−	0.0293970i
$478$	41.9041	+	6.63695i	1.91665	+	0.303567i
$479$	−5.11667	+	3.71748i	−0.233787	+	0.169856i	−0.698511	−	0.715600i	$-0.746154\pi$
$479$	−5.11667	+	3.71748i	−0.233787	+	0.169856i	0.464724	+	0.885456i	$0.346154\pi$
$480$	20.9766	+	3.15933i	0.957447	+	0.144203i
$481$	−18.0450	−	5.86319i	−0.822782	−	0.267338i
$482$	−13.9680	+	2.21232i	−0.636226	+	0.100768i
$483$		0			0
$484$		0			0
$485$	21.0000	−	7.00000i	0.953561	−	0.317854i
$486$	−13.0112	+	17.9084i	−0.590199	+	0.812339i
$487$	−1.92612	−	3.78022i	−0.0872808	−	0.171298i	0.843240	−	0.537537i	$-0.180645\pi$
$487$	−1.92612	−	3.78022i	−0.0872808	−	0.171298i	−0.930521	+	0.366239i	$0.880645\pi$
$488$	6.42040	−	12.6007i	0.290638	−	0.570408i
$489$	−1.17557	−	1.61803i	−0.0531611	−	0.0731700i
$490$	−20.3569	+	28.4709i	−0.919633	+	1.28619i
$491$	−6.01501	+	1.95440i	−0.271454	+	0.0882006i	−0.441581	−	0.897221i	$-0.645582\pi$
$491$	−6.01501	+	1.95440i	−0.271454	+	0.0882006i	0.170127	+	0.985422i	$0.445582\pi$
$492$	23.9082	−	12.1818i	1.07787	−	0.549200i
$493$	−4.42463	−	27.9360i	−0.199276	−	1.25818i
$494$	63.2456			2.84555
$495$		0			0
$496$	2.00000			0.0898027
$497$		0			0
$498$	25.2015	−	12.8408i	1.12930	−	0.575410i
$499$	32.3359	−	10.5066i	1.44755	−	0.470339i	0.523311	−	0.852142i	$-0.324697\pi$
$499$	32.3359	−	10.5066i	1.44755	−	0.470339i	0.924244	+	0.381803i	$0.124697\pi$
$500$	−23.1708	+	24.2510i	−1.03623	+	1.08454i
$501$	−14.8699	−	20.4667i	−0.664339	−	0.914384i
$502$	12.1818	−	23.9082i	0.543702	−	1.06708i
$503$	4.06061	+	7.96940i	0.181054	+	0.355338i	0.963640	−	0.267204i	$-0.0860998\pi$
$503$	4.06061	+	7.96940i	0.181054	+	0.355338i	−0.782586	+	0.622542i	$0.786100\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−7.00000	+	7.00000i	−0.310881	+	0.310881i
$508$	26.5025	−	4.19758i	1.17586	−	0.186237i
$509$	−3.80423	−	1.23607i	−0.168619	−	0.0547877i	0.223491	−	0.974706i	$-0.428255\pi$
$509$	−3.80423	−	1.23607i	−0.168619	−	0.0547877i	−0.392110	+	0.919918i	$0.628255\pi$
$510$	18.7811	+	25.4415i	0.831640	+	1.12657i
$511$		0			0
$512$	11.0427	+	1.74899i	0.488023	+	0.0772952i
$513$	31.8776	+	16.2425i	1.40743	+	0.717122i
$514$	6.84038	−	21.0525i	0.301716	−	0.928587i
$515$	−8.58905	+	27.1335i	−0.378479	+	1.19565i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−5.11667	−	3.71748i	−0.224597	−	0.163179i
$520$	15.9310	+	15.6909i	0.698619	+	0.688092i
$521$	−8.65248	−	26.6296i	−0.379072	−	1.16666i	−0.940690	−	0.339267i	$-0.889821\pi$
$521$	−8.65248	−	26.6296i	−0.379072	−	1.16666i	0.561618	−	0.827396i	$-0.310179\pi$
$522$	2.21232	−	13.9680i	0.0968305	−	0.611364i
$523$	4.19758	−	26.5025i	0.183547	−	1.15887i	−0.708090	−	0.706122i	$-0.750443\pi$
$523$	4.19758	−	26.5025i	0.183547	−	1.15887i	0.891638	−	0.452750i	$-0.149557\pi$
$524$	−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
$530$	−6.27582	+	3.25793i	−0.272604	+	0.141516i
$531$	1.85410	−	5.70634i	0.0804612	−	0.247634i
$532$		0			0
$533$	−27.9360	−	4.42463i	−1.21004	−	0.191652i
$534$	15.3500	−	11.1524i	0.664260	−	0.482613i
$535$		0			0
$536$	−9.02251	−	2.93159i	−0.389713	−	0.126626i
$537$	5.58721	−	0.884927i	0.241106	−	0.0381874i
$538$	−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	0.0115321	−	0.999934i	$-0.496329\pi$
$541$	22.3049	−	30.7000i	0.958962	−	1.31990i	0.947430	−	0.319964i	$-0.103671\pi$
$542$	12.8408	+	25.2015i	0.551559	+	1.08250i
$543$	−5.13632	+	10.0806i	−0.220420	+	0.432599i
$544$	17.6336	+	24.2705i	0.756033	+	1.04059i
$545$	27.9017	−	4.63658i	1.19518	−	0.198609i
$546$		0			0
$547$	15.9388	−	8.12123i	0.681494	−	0.347239i	−0.0787331	−	0.996896i	$-0.525088\pi$
$547$	15.9388	−	8.12123i	0.681494	−	0.347239i	0.760227	+	0.649657i	$0.225088\pi$
$548$	−8.62804	−	54.4753i	−0.368572	−	2.32707i
$549$	−6.32456			−0.269925
$550$		0			0
$551$	−40.0000			−1.70406
$552$	−0.699596	−	4.41708i	−0.0297768	−	0.188003i
$553$		0			0
$554$	−28.5317	+	9.27051i	−1.21220	+	0.393866i
$555$	−13.2349	+	2.19932i	−0.561791	+	0.0933560i
$556$	22.3049	+	30.7000i	0.945938	+	1.30197i
$557$	−10.1515	+	19.9235i	−0.430134	+	0.844186i	0.569617	+	0.821910i	$0.307091\pi$
$557$	−10.1515	+	19.9235i	−0.430134	+	0.844186i	−0.999752	+	0.0222763i	$0.992909\pi$
$558$	2.03031	+	3.98470i	0.0859498	+	0.168686i
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−30.0000	+	30.0000i	−1.26547	+	1.26547i
$563$	−26.5025	+	4.19758i	−1.11695	+	0.176907i	−0.687499	−	0.726185i	$-0.741291\pi$
$563$	−26.5025	+	4.19758i	−1.11695	+	0.176907i	−0.429447	+	0.903092i	$0.641291\pi$
$564$	−17.1190	−	5.56231i	−0.720841	−	0.234215i
$565$	22.8974	−	16.9030i	0.963300	−	0.711113i
$566$	16.1803	−	11.7557i	0.680110	−	0.494129i
$567$		0			0
$568$	−15.9388	−	8.12123i	−0.668778	−	0.340759i
$569$	−11.7264	+	36.0901i	−0.491595	+	1.51297i	0.330602	+	0.943770i	$0.392748\pi$
$569$	−11.7264	+	36.0901i	−0.491595	+	1.51297i	−0.822197	+	0.569204i	$0.807252\pi$
$570$	39.6917	−	20.6050i	1.66250	−	0.863047i
$571$		−	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
$575$	−6.34838	−	3.11418i	−0.264746	−	0.129870i
$576$	4.01722	+	12.3637i	0.167384	+	0.515156i
$577$	−5.08833	+	32.1265i	−0.211830	+	1.33744i	0.620956	+	0.783846i	$0.286745\pi$
$577$	−5.08833	+	32.1265i	−0.211830	+	1.33744i	−0.832785	+	0.553596i	$0.813255\pi$
$578$	−1.04939	+	6.62561i	−0.0436490	+	0.275589i
$579$	9.77198	+	30.0750i	0.406109	+	1.24988i
$580$	−30.2269	−	29.7714i	−1.25510	−	1.23619i
$581$		0			0
$582$	−22.1359	−	22.1359i	−0.917564	−	0.917564i
$583$		0			0
$584$			10.0000i			0.413803i
$585$	3.01788	−	9.53375i	0.124774	−	0.394172i
$586$	15.4508	−	47.5528i	0.638269	−	1.96439i
$587$	−8.82051	−	4.49428i	−0.364062	−	0.185499i	0.262384	−	0.964963i	$-0.415491\pi$
$587$	−8.82051	−	4.49428i	−0.364062	−	0.185499i	−0.626446	+	0.779465i	$0.715491\pi$
$588$	29.3328	+	4.64587i	1.20967	+	0.191592i
$589$	10.2333	−	7.43496i	0.421658	−	0.306352i
$590$	−17.8173	−	24.1360i	−0.733526	−	0.993661i
$591$	6.01501	+	1.95440i	0.247424	+	0.0803931i
$592$	−4.19041	+	0.663695i	−0.172225	+	0.0272777i
$593$	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
$597$	−3.85224	−	7.56044i	−0.157662	−	0.309428i
$598$	−6.42040	+	12.6007i	−0.262549	+	0.515282i
$599$	−9.40456	−	12.9443i	−0.384260	−	0.528889i	0.572447	−	0.819942i	$-0.305994\pi$
$599$	−9.40456	−	12.9443i	−0.384260	−	0.528889i	−0.956707	+	0.291053i	$0.905994\pi$
$600$	15.1100	+	4.65712i	0.616862	+	0.190126i
$601$	30.0750	−	9.77198i	1.22679	−	0.398607i	0.377238	−	0.926117i	$-0.376874\pi$
$601$	30.0750	−	9.77198i	1.22679	−	0.398607i	0.849549	+	0.527509i	$0.176874\pi$
$602$		0			0
$603$	0.663695	+	4.19041i	0.0270278	+	0.170647i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−6.99596	−	44.1708i	−0.283957	−	1.79284i	−0.556663	−	0.830739i	$-0.687918\pi$
$607$	−6.99596	−	44.1708i	−0.283957	−	1.79284i	0.272706	−	0.962098i	$-0.412082\pi$
$608$	37.8022	−	19.2612i	1.53308	−	0.781144i
$609$		0			0
$610$	−18.3927	+	25.7237i	−0.744697	+	1.04152i
$611$	11.1524	+	15.3500i	0.451179	+	0.620995i
$612$	−6.09092	+	11.9541i	−0.246211	+	0.483216i
$613$	18.2728	+	35.8623i	0.738030	+	1.44847i	0.888033	+	0.459780i	$0.152072\pi$
$613$	18.2728	+	35.8623i	0.738030	+	1.44847i	−0.150003	+	0.988686i	$0.547928\pi$
$614$		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	$0.410795\pi$
$618$	39.7537	−	6.29637i	1.59913	−	0.253277i
$619$	34.2380	+	11.1246i	1.37614	+	0.447136i	0.901399	−	0.432988i	$-0.142541\pi$
$619$	34.2380	+	11.1246i	1.37614	+	0.447136i	0.474743	+	0.880124i	$0.342541\pi$
$620$	13.2668	+	1.99814i	0.532807	+	0.0802470i
$621$	−6.47214	+	4.70228i	−0.259718	+	0.188696i
$622$	−17.6683	−	2.79838i	−0.708435	−	0.112205i
$623$		0			0
$624$	−1.95440	+	6.01501i	−0.0782384	+	0.240793i
$625$	19.7700	−	15.3019i	0.790799	−	0.612076i
$626$		−	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	0.930003	+	0.367553i	$0.119804\pi$
$631$	9.88854	+	30.4338i	0.393657	+	1.21155i	−0.536346	+	0.843998i	$0.680196\pi$
$632$	−2.21232	+	13.9680i	−0.0880013	+	0.555618i
$633$	−5.59677	+	35.3366i	−0.222452	+	1.40450i
$634$	16.6124	+	51.1276i	0.659761	+	2.03054i
$635$	−19.9994	+	0.151824i	−0.793653	+	0.00602496i
$636$	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
$640$	33.3681	+	10.5626i	1.31899	+	0.417523i
$641$	−2.47214	+	7.60845i	−0.0976435	+	0.300516i	−0.987934	−	0.154878i	$-0.950502\pi$
$641$	−2.47214	+	7.60845i	−0.0976435	+	0.300516i	0.890290	+	0.455394i	$0.150502\pi$
$642$		0			0
$643$	15.3648	+	2.43355i	0.605930	+	0.0959698i	0.451858	−	0.892090i	$-0.350761\pi$
$643$	15.3648	+	2.43355i	0.605930	+	0.0959698i	0.154072	+	0.988060i	$0.450761\pi$
$644$		0			0
$645$		0			0
$646$	60.1501	+	19.5440i	2.36657	+	0.768946i
$647$	−18.1584	+	2.87601i	−0.713882	+	0.113068i	−0.502803	−	0.864401i	$-0.667698\pi$
$647$	−18.1584	+	2.87601i	−0.713882	+	0.113068i	−0.211079	+	0.977469i	$0.567698\pi$
$648$	7.90569	−	7.90569i	0.310565	−	0.310565i
$649$		0			0
$650$	−30.0000	−	40.0000i	−1.17670	−	1.56893i
$651$		0			0
$652$	−1.92612	−	3.78022i	−0.0754326	−	0.148045i
$653$	0.642040	−	1.26007i	0.0251249	−	0.0493105i	−0.878103	−	0.478472i	$-0.841191\pi$
$653$	0.642040	−	1.26007i	0.0251249	−	0.0493105i	0.903228	+	0.429161i	$0.141191\pi$
$654$	−23.5114	−	32.3607i	−0.919369	−	1.26540i
$655$	4.63658	+	27.9017i	0.181166	+	1.09021i
$656$	−6.01501	+	1.95440i	−0.234847	+	0.0763063i
$657$	3.98470	−	2.03031i	0.155458	−	0.0792098i
$658$		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	$0.195743\pi$
$662$	−6.29637	−	39.7537i	−0.244715	−	1.54507i
$663$	−25.2015	+	12.8408i	−0.978744	+	0.498695i
$664$	19.0211	−	6.18034i	0.738163	−	0.239844i
$665$		0			0
$666$	−5.57622	−	7.67501i	−0.216074	−	0.297401i
$667$	4.06061	−	7.96940i	0.157228	−	0.308577i
$668$	−24.3637	−	47.8164i	−0.942659	−	1.85007i
$669$	12.9313	−	17.7984i	0.499952	−	0.688125i
$670$	18.9737	+	9.48683i	0.733017	+	0.366508i
$671$		0			0
$672$		0			0
$673$	−39.7537	+	6.29637i	−1.53239	+	0.242707i	−0.864913	−	0.501922i	$-0.832627\pi$
$673$	−39.7537	+	6.29637i	−1.53239	+	0.242707i	−0.667479	+	0.744629i	$0.732627\pi$
$674$	−28.5317	−	9.27051i	−1.09900	−	0.357087i
$675$	−4.84825	−	27.8657i	−0.186609	−	1.07255i
$676$	−16.9894	+	12.3435i	−0.653437	+	0.474750i
$677$	13.2512	+	2.09879i	0.509286	+	0.0806630i	0.405789	−	0.913967i	$-0.366997\pi$
$677$	13.2512	+	2.09879i	0.509286	+	0.0806630i	0.103497	+	0.994630i	$0.466997\pi$
$678$	−35.8623	−	18.2728i	−1.37728	−	0.701761i
$679$		0			0
$680$	10.3025	+	19.8459i	0.395082	+	0.761055i
$681$		−	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
$685$	0.312072	+	41.1084i	0.0119237	+	1.57067i
$686$		0			0
$687$	0.884927	−	5.58721i	0.0337621	−	0.213165i
$688$		0			0
$689$	−1.95440	−	6.01501i	−0.0744565	−	0.229154i
$690$	0.0759122	+	9.99971i	0.00288993	+	0.380683i
$691$	22.6525	+	16.4580i	0.861741	+	0.626091i	0.928358	−	0.371687i	$-0.121221\pi$
$691$	22.6525	+	16.4580i	0.861741	+	0.626091i	−0.0666172	+	0.997779i	$0.521221\pi$
$692$	−9.48683	−	9.48683i	−0.360635	−	0.360635i
$693$		0			0
$694$			60.0000i			2.27757i
$695$	−13.0317	−	25.1033i	−0.494322	−	0.952221i
$696$	−6.18034	+	19.0211i	−0.234265	+	0.720994i
$697$	−25.2015	−	12.8408i	−0.954574	−	0.486380i
$698$	69.8401	+	11.0616i	2.64349	+	0.418687i
$699$	−15.3500	+	11.1524i	−0.580591	+	0.421824i
$700$		0			0
$701$	30.0750	+	9.77198i	1.13592	+	0.369082i	0.815822	−	0.578303i	$-0.196285\pi$
$701$	30.0750	+	9.77198i	1.13592	+	0.369082i	0.320096	+	0.947385i	$0.396285\pi$
$702$	−55.8721	+	8.84927i	−2.10876	+	0.333994i
$703$	−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
$708$	−11.5567	+	22.6813i	−0.434328	+	0.852416i
$709$	−3.52671	−	4.85410i	−0.132448	−	0.182300i	0.737642	−	0.675192i	$-0.235939\pi$
$709$	−3.52671	−	4.85410i	−0.132448	−	0.182300i	−0.870090	+	0.492893i	$0.835939\pi$
$710$	32.5382	+	23.2651i	1.22114	+	0.873123i
$711$	6.01501	−	1.95440i	0.225580	−	0.0732955i
$712$	11.9541	−	6.09092i	0.447999	−	0.228267i
$713$	0.442463	+	2.79360i	0.0165704	+	0.104621i
$714$		0			0
$715$		0			0
$716$	12.0000			0.448461
$717$	4.19758	+	26.5025i	0.156761	+	0.989752i
$718$	37.8022	−	19.2612i	1.41077	−	0.718821i
$719$	22.8254	−	7.41641i	0.851242	−	0.276585i	0.149276	−	0.988796i	$-0.452306\pi$
$719$	22.8254	−	7.41641i	0.851242	−	0.276585i	0.701966	+	0.712210i	$0.252306\pi$
$720$	−0.366554	−	2.20582i	−0.0136606	−	0.0822060i
$721$		0			0
$722$	21.3182	−	41.8394i	0.793382	−	1.55710i
$723$	−4.06061	−	7.96940i	−0.151016	−	0.296385i
$724$	−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
$730$	3.33023	−	22.1113i	0.123257	−	0.818376i
$731$		0			0
$732$	26.5025	+	4.19758i	0.979559	+	0.155147i
$733$	−11.9541	−	6.09092i	−0.441535	−	0.224973i	0.219067	−	0.975710i	$-0.429699\pi$
$733$	−11.9541	−	6.09092i	−0.441535	−	0.224973i	−0.660602	+	0.750737i	$0.729699\pi$
$734$	−2.93159	+	9.02251i	−0.108207	+	0.333027i
$735$	−21.1039	−	6.68037i	−0.778427	−	0.246409i
$736$			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	0.759876	−	0.650068i	$-0.225260\pi$
$739$	10.2333	+	7.43496i	0.376440	+	0.273499i	−0.383437	+	0.923567i	$0.625260\pi$
$740$	−28.4597	+	0.216050i	−1.04620	+	0.00794215i
$741$	12.3607	+	38.0423i	0.454081	+	1.39752i
$742$		0			0
$743$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$743$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$744$	−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
$750$	−31.8592	−	15.3295i	−1.16333	−	0.559753i
$751$	−2.47214	+	7.60845i	−0.0902095	+	0.277636i	−0.985976	−	0.166889i	$-0.946628\pi$
$751$	−2.47214	+	7.60845i	−0.0902095	+	0.277636i	0.895766	+	0.444526i	$0.146628\pi$
$752$	3.78022	+	1.92612i	0.137850	+	0.0702383i
$753$	16.7616	+	2.65478i	0.610828	+	0.0967456i
$754$	51.1667	−	37.1748i	1.86338	−	1.35383i
$755$		0			0
$756$		0			0
$757$	37.7137	−	5.97326i	1.37073	−	0.217102i	0.572720	−	0.819751i	$-0.305888\pi$
$757$	37.7137	−	5.97326i	1.37073	−	0.217102i	0.798006	+	0.602649i	$0.205888\pi$
$758$	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	0.182994	+	0.983114i	$0.441421\pi$
$761$	−22.3049	+	30.7000i	−0.808551	+	1.11288i	−0.991545	+	0.129761i	$0.958579\pi$
$762$	12.8408	+	25.2015i	0.465173	+	0.912953i
$763$		0			0
$764$	−38.7938	−	53.3951i	−1.40351	−	1.93177i
$765$	5.81627	−	8.13456i	0.210288	−	0.294106i
$766$	57.1426	−	18.5668i	2.06465	−	0.670844i
$767$	23.9082	−	12.1818i	0.863276	−	0.439861i
$768$	−1.99109	−	12.5712i	−0.0718471	−	0.453625i
$769$	−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
$772$	10.4939	+	66.2561i	0.377685	+	2.38461i
$773$	−13.8608	+	7.06243i	−0.498539	+	0.254018i	−0.685132	−	0.728419i	$-0.740255\pi$
$773$	−13.8608	+	7.06243i	−0.498539	+	0.254018i	0.186593	+	0.982437i	$0.440255\pi$
$774$		0			0
$775$	−9.55638	−	2.94542i	−0.343275	−	0.105803i
$776$	−13.0112	−	17.9084i	−0.467074	−	0.642872i
$777$		0			0
$778$	−16.2425	−	31.8776i	−0.582320	−	1.14287i
$779$	−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
$783$	35.3366	−	5.59677i	1.26283	−	0.200012i
$784$	−6.65740	−	2.16312i	−0.237764	−	0.0772542i
$785$	13.1468	+	17.8091i	0.469228	+	0.635633i
$786$	32.3607	−	23.5114i	1.15427	−	0.838624i
$787$	−35.3366	−	5.59677i	−1.25961	−	0.199503i	−0.509303	−	0.860588i	$-0.670097\pi$
$787$	−35.3366	−	5.59677i	−1.25961	−	0.199503i	−0.750312	+	0.661084i	$0.770097\pi$
$788$	11.9541	+	6.09092i	0.425847	+	0.216980i
$789$	−11.7264	+	36.0901i	−0.417470	+	1.28484i
$790$	9.54339	−	30.1484i	0.339538	−	1.07263i
$791$		0			0
$792$		0			0
$793$	−20.0000	−	20.0000i	−0.710221	−	0.710221i
$794$	33.2584	+	24.1636i	1.18030	+	0.857535i
$795$	−3.18619	−	3.13818i	−0.113003	−	0.111300i
$796$	−5.56231	−	17.1190i	−0.197151	−	0.606767i
$797$	−2.87601	+	18.1584i	−0.101874	+	0.643205i	0.882926	+	0.469512i	$0.155570\pi$
$797$	−2.87601	+	18.1584i	−0.101874	+	0.643205i	−0.984800	+	0.173693i	$0.944430\pi$
$798$		0			0
$799$	5.86319	+	18.0450i	0.207425	+	0.638387i
$800$	−30.1130	−	14.7718i	−1.06466	−	0.522263i
$801$	−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
$807$	−30.2418	−	15.4089i	−1.06456	−	0.542421i
$808$		0			0
$809$	15.3500	−	11.1524i	0.539678	−	0.392099i	−0.284287	−	0.958739i	$-0.591757\pi$
$809$	15.3500	−	11.1524i	0.539678	−	0.392099i	0.823965	+	0.566640i	$0.191757\pi$
$810$	−20.1133	+	14.8477i	−0.706709	+	0.521697i
$811$	−6.01501	−	1.95440i	−0.211216	−	0.0686281i	0.201498	−	0.979489i	$-0.435419\pi$
$811$	−6.01501	−	1.95440i	−0.211216	−	0.0686281i	−0.412714	+	0.910861i	$0.635419\pi$
$812$		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
$818$	12.8408	−	25.2015i	0.448968	−	0.881149i
$819$		0			0
$820$	−41.8525	+	6.95486i	−1.46155	+	0.242874i
$821$	−18.0450	+	5.86319i	−0.629776	+	0.204627i	−0.606476	−	0.795102i	$-0.707417\pi$
$821$	−18.0450	+	5.86319i	−0.629776	+	0.204627i	−0.0233000	+	0.999729i	$0.507417\pi$
$822$	51.8011	−	26.3940i	1.80677	−	0.920596i
$823$	2.43355	+	15.3648i	0.0848282	+	0.535584i	0.993106	+	0.117217i	$0.0373974\pi$
$823$	2.43355	+	15.3648i	0.0848282	+	0.535584i	−0.908278	+	0.418367i	$0.862603\pi$
$824$	28.4605			0.991468
$825$		0			0
$826$		0			0
$827$	−1.39919	−	8.83415i	−0.0486547	−	0.307194i	0.951345	−	0.308128i	$-0.0997025\pi$
$827$	−1.39919	−	8.83415i	−0.0486547	−	0.307194i	−1.00000		0.000934498i	$0.999703\pi$
$828$	−3.78022	+	1.92612i	−0.131372	+	0.0669372i
$829$	−5.70634	+	1.85410i	−0.198189	+	0.0643956i	−0.406430	−	0.913682i	$-0.633226\pi$
$829$	−5.70634	+	1.85410i	−0.198189	+	0.0643956i	0.208240	+	0.978078i	$0.433226\pi$
$830$	−44.1164	+	7.33107i	−1.53130	+	0.254465i
$831$	−11.1524	−	15.3500i	−0.386874	−	0.532486i
$832$	−26.3940	+	51.8011i	−0.915047	+	1.79588i
$833$	−14.2122	−	27.8929i	−0.492422	−	0.966432i
$834$	−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
$838$	−79.5074	+	12.5927i	−2.74654	+	0.435009i
$839$	5.70634	+	1.85410i	0.197005	+	0.0640107i	0.405857	−	0.913936i	$-0.366973\pi$
$839$	5.70634	+	1.85410i	0.197005	+	0.0640107i	−0.208853	+	0.977947i	$0.566973\pi$
$840$		0			0
$841$	−8.89919	+	6.46564i	−0.306869	+	0.222953i
$842$	−61.8391	−	9.79435i	−2.13112	−	0.337535i
$843$	−23.9082	−	12.1818i	−0.823443	−	0.419565i
$844$	−23.4527	+	72.1801i	−0.807277	+	2.48454i
$845$	13.8921	−	7.21174i	0.477903	−	0.248091i
$846$			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
$850$	−16.1710	−	47.3128i	−0.554661	−	1.62281i
$851$	−1.85410	−	5.70634i	−0.0635578	−	0.195611i
$852$	5.30956	−	33.5233i	0.181903	−	1.14849i
$853$	−2.09879	+	13.2512i	−0.0718612	+	0.453713i	0.925352	+	0.379109i	$0.123769\pi$
$853$	−2.09879	+	13.2512i	−0.0718612	+	0.453713i	−0.997213	+	0.0746045i	$0.976231\pi$
$854$		0			0
$855$	−10.0756	−	9.92380i	−0.344579	−	0.339387i
$856$		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
$862$	−37.8022	−	19.2612i	−1.28755	−	0.656039i
$863$	1.39680	+	0.221232i	0.0475477	+	0.00753082i	0.180163	−	0.983637i	$-0.442337\pi$
$863$	1.39680	+	0.221232i	0.0475477	+	0.00753082i	−0.132615	+	0.991168i	$0.542337\pi$
$864$	−30.7000	+	22.3049i	−1.04444	+	0.758827i
$865$	5.93910	+	8.04532i	0.201935	+	0.273549i
$866$	3.00750	+	0.977198i	0.102199	+	0.0332065i
$867$	−4.19041	+	0.663695i	−0.142314	+	0.0225403i
$868$		0			0
$869$		0			0
$870$	20.0000	−	40.0000i	0.678064	−	1.35613i
$871$	−11.1524	+	15.3500i	−0.377886	+	0.520116i
$872$	−12.8408	−	25.2015i	−0.434844	−	0.853429i
$873$	−4.49428	+	8.82051i	−0.152108	+	0.298529i
$874$	11.7557	+	16.1803i	0.397643	+	0.547308i
$875$		0			0
$876$	−18.0450	+	5.86319i	−0.609685	+	0.198099i
$877$	−51.8011	+	26.3940i	−1.74920	+	0.891262i	−0.787879	+	0.615830i	$0.788821\pi$
$877$	−51.8011	+	26.3940i	−1.74920	+	0.891262i	−0.961320	+	0.275432i	$0.911179\pi$
$878$	−4.42463	−	27.9360i	−0.149324	−	0.942796i
$879$	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	$0.489274\pi$
$882$	−2.44859	−	15.4598i	−0.0824482	−	0.520557i
$883$	23.9414	−	12.1988i	0.805692	−	0.410521i	−0.00209290	−	0.999998i	$-0.500666\pi$
$883$	23.9414	−	12.1988i	0.805692	−	0.410521i	0.807785	+	0.589477i	$0.200666\pi$
$884$	−57.0634	+	18.5410i	−1.91925	+	0.623602i
$885$	11.0356	−	15.4342i	0.370957	−	0.518816i
$886$	−20.4461	−	28.1417i	−0.686902	−	0.945439i
$887$	4.06061	−	7.96940i	0.136342	−	0.267586i	−0.812733	−	0.582636i	$-0.802021\pi$
$887$	4.06061	−	7.96940i	0.136342	−	0.267586i	0.949075	+	0.315050i	$0.102021\pi$
$888$	6.09092	+	11.9541i	0.204398	+	0.401154i
$889$		0			0
$890$	−28.4605	+	9.48683i	−0.953998	+	0.317999i
$891$		0			0
$892$	33.0000	−	33.0000i	1.10492	−	1.10492i
$893$	26.5025	−	4.19758i	0.886871	−	0.140467i
$894$		0			0
$895$	−8.84452	−	1.33209i	−0.295640	−	0.0445269i
$896$		0			0
$897$	−8.83415	−	1.39919i	−0.294964	−	0.0467177i
$898$	11.9541	+	6.09092i	0.398914	+	0.203257i
$899$	3.90879	−	12.0300i	0.130365	−	0.401224i
$900$	−0.227730	−	14.9983i	−0.00759100	−	0.499942i
$901$		−	6.32456i		−	0.210701i
$902$		0			0
$903$		0			0
$904$	−23.0250	−	16.7287i	−0.765801	−	0.556387i
$905$	12.5527	−	12.7448i	0.417267	−	0.423650i
$906$		0			0
$907$	3.76094	−	23.7456i	0.124880	−	0.788461i	−0.843160	−	0.537663i	$-0.819307\pi$
$907$	3.76094	−	23.7456i	0.124880	−	0.788461i	0.968040	−	0.250798i	$-0.0806929\pi$
$908$	4.19758	−	26.5025i	0.139301	−	0.879515i
$909$		0			0
$910$		0			0
$911$	−33.9787	−	24.6870i	−1.12577	−	0.817916i	−0.140692	−	0.990053i	$-0.544933\pi$
$911$	−33.9787	−	24.6870i	−1.12577	−	0.817916i	−0.985073	+	0.172137i	$0.944933\pi$
$912$	6.32456	+	6.32456i	0.209427	+	0.209427i
$913$		0			0
$914$		−	50.0000i		−	1.65385i
$915$	−19.0675	−	6.03577i	−0.630352	−	0.199536i
$916$	3.70820	−	11.4127i	0.122523	−	0.377086i
$917$		0			0
$918$	−55.8721	−	8.84927i	−1.84405	−	0.292069i
$919$	30.7000	−	22.3049i	1.01270	−	0.735770i	0.0479269	−	0.998851i	$-0.484739\pi$
$919$	30.7000	−	22.3049i	1.01270	−	0.735770i	0.964774	+	0.263081i	$0.0847385\pi$
$920$	−1.05311	+	6.99221i	−0.0347200	+	0.230526i
$921$		0			0
$922$	−55.8721	+	8.84927i	−1.84005	+	0.291435i
$923$	−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
$927$	−5.77836	−	11.3407i	−0.189786	−	0.372476i
$928$	19.2612	−	37.8022i	0.632279	−	1.24092i
$929$	2.35114	+	3.23607i	0.0771384	+	0.106172i	0.845843	−	0.533432i	$-0.179098\pi$
$929$	2.35114	+	3.23607i	0.0771384	+	0.106172i	−0.768704	+	0.639604i	$0.779098\pi$
$930$	2.31829	+	13.9508i	0.0760197	+	0.457466i
$931$	−42.1051	+	13.6808i	−1.37994	+	0.448369i
$932$	−35.8623	+	18.2728i	−1.17471	+	0.598544i
$933$	−1.76985	−	11.1744i	−0.0579424	−	0.365834i
$934$	22.1359			0.724310
$935$		0			0
$936$	−10.0000			−0.326860
$937$	−2.09879	−	13.2512i	−0.0685644	−	0.432899i	−0.997962	−	0.0638176i	$-0.979672\pi$
$937$	−2.09879	−	13.2512i	−0.0685644	−	0.432899i	0.929397	−	0.369081i	$-0.120328\pi$
$938$		0			0
$939$	17.1190	−	5.56231i	0.558658	−	0.181519i
$940$	23.1514	+	16.5534i	0.755114	+	0.539912i
$941$	−22.3049	−	30.7000i	−0.727118	−	1.00079i	−0.999257	−	0.0385346i	$-0.987731\pi$
$941$	−22.3049	−	30.7000i	−0.727118	−	1.00079i	0.272139	−	0.962258i	$-0.412269\pi$
$942$	14.2122	−	27.8929i	0.463057	−	0.908800i
$943$	−4.06061	−	7.96940i	−0.132232	−	0.259520i
$944$	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	$0.301422\pi$
$948$	−26.5025	+	4.19758i	−0.860760	+	0.136331i
$949$	19.0211	+	6.18034i	0.617452	+	0.200622i
$950$	−69.6641	+	12.1206i	−2.26020	+	0.393245i
$951$	−27.5066	+	19.9847i	−0.891962	+	0.648048i
$952$		0			0
$953$	11.9541	+	6.09092i	0.387232	+	0.197304i	0.636758	−	0.771064i	$-0.280275\pi$
$953$	11.9541	+	6.09092i	0.387232	+	0.197304i	−0.249527	+	0.968368i	$0.580275\pi$
$954$	0.977198	−	3.00750i	0.0316379	−	0.0973716i
$955$	22.6655	+	43.6609i	0.733437	+	1.41283i
$956$			56.9210i			1.84096i
$957$		0			0
$958$	−10.0000	−	10.0000i	−0.323085	−	0.323085i
$959$		0			0
$960$	0.312072	+	41.1084i	0.0100721	+	1.32677i
$961$	−8.34346	−	25.6785i	−0.269144	−	0.828340i
$962$	6.63695	−	41.9041i	0.213984	−	1.35104i
$963$		0			0
$964$	−5.86319	−	18.0450i	−0.188840	−	0.581191i
$965$	−0.379561	−	49.9986i	−0.0122185	−	1.60951i
$966$		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
$970$	22.8055	+	43.9307i	0.732241	+	1.41053i
$971$	12.9787	−	39.9444i	0.416507	−	1.28188i	−0.494389	−	0.869240i	$-0.664608\pi$
$971$	12.9787	−	39.9444i	0.416507	−	1.28188i	0.910896	−	0.412635i	$-0.135392\pi$
$972$	−26.4615	−	13.4828i	−0.848754	−	0.432462i
$973$		0			0
$974$	7.67501	−	5.57622i	0.245923	−	0.178674i
$975$	18.1969	−	25.8626i	0.582766	−	0.828266i
$976$	−6.01501	−	1.95440i	−0.192536	−	0.0625587i
$977$	23.7456	−	3.76094i	0.759690	−	0.120323i	0.235442	−	0.971888i	$-0.424346\pi$
$977$	23.7456	−	3.76094i	0.759690	−	0.120323i	0.524248	+	0.851565i	$0.324346\pi$
$978$	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
$982$	−6.42040	−	12.6007i	−0.204883	−	0.402106i
$983$	−18.6191	+	36.5421i	−0.593859	+	1.16551i	0.377079	+	0.926181i	$0.376928\pi$
$983$	−18.6191	+	36.5421i	−0.593859	+	1.16551i	−0.970938	+	0.239332i	$0.923072\pi$
$984$	11.7557	+	16.1803i	0.374758	+	0.515810i
$985$	−8.13456	−	5.81627i	−0.259189	−	0.185322i
$986$	60.1501	−	19.5440i	1.91557	−	0.622406i
$987$		0			0
$988$	13.2739	+	83.8081i	0.422299	+	2.66629i
$989$		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	$0.872802\pi$
$992$	2.09879	+	13.2512i	0.0666366	+	0.420727i
$993$	22.6813	−	11.5567i	0.719770	−	0.366741i
$994$		0			0
$995$	2.19932	+	13.2349i	0.0697232	+	0.419575i
$996$	22.3049	+	30.7000i	0.706757	+	0.972768i
$997$	22.3334	−	43.8317i	0.707305	−	1.38816i	−0.205044	−	0.978753i	$-0.565734\pi$
$997$	22.3334	−	43.8317i	0.707305	−	1.38816i	0.912350	−	0.409412i	$-0.134266\pi$
$998$	34.5152	+	67.7399i	1.09256	+	2.14427i
$999$	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.403.2		16
5.2	odd	4	inner	605.2.m.b.282.1		16
11.2	odd	10	inner	605.2.m.b.578.1		16
11.3	even	5	inner	605.2.m.b.118.2		16
11.4	even	5	inner	605.2.m.b.233.1		16
11.5	even	5		55.2.e.a.43.1	yes	4
11.6	odd	10		55.2.e.a.43.2	yes	4
11.7	odd	10	inner	605.2.m.b.233.2		16
11.8	odd	10	inner	605.2.m.b.118.1		16
11.9	even	5	inner	605.2.m.b.578.2		16
11.10	odd	2	inner	605.2.m.b.403.1		16
33.5	odd	10		495.2.k.b.208.2		4
33.17	even	10		495.2.k.b.208.1		4
44.27	odd	10		880.2.bd.e.593.2		4
44.39	even	10		880.2.bd.e.593.1		4
55.2	even	20	inner	605.2.m.b.457.1		16
55.7	even	20	inner	605.2.m.b.112.2		16
55.17	even	20		55.2.e.a.32.1	✓	4
55.27	odd	20		55.2.e.a.32.2	yes	4
55.28	even	20		275.2.e.b.32.2		4
55.32	even	4	inner	605.2.m.b.282.2		16
55.37	odd	20	inner	605.2.m.b.112.1		16
55.38	odd	20		275.2.e.b.32.1		4
55.39	odd	10		275.2.e.b.43.1		4
55.42	odd	20	inner	605.2.m.b.457.2		16
55.47	odd	20	inner	605.2.m.b.602.1		16
55.49	even	10		275.2.e.b.43.2		4
55.52	even	20	inner	605.2.m.b.602.2		16
165.17	odd	20		495.2.k.b.307.2		4
165.137	even	20		495.2.k.b.307.1		4
220.27	even	20		880.2.bd.e.417.2		4
220.127	odd	20		880.2.bd.e.417.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.e.a.32.1	✓	4	55.17	even	20
55.2.e.a.32.2	yes	4	55.27	odd	20
55.2.e.a.43.1	yes	4	11.5	even	5
55.2.e.a.43.2	yes	4	11.6	odd	10
275.2.e.b.32.1		4	55.38	odd	20
275.2.e.b.32.2		4	55.28	even	20
275.2.e.b.43.1		4	55.39	odd	10
275.2.e.b.43.2		4	55.49	even	10
495.2.k.b.208.1		4	33.17	even	10
495.2.k.b.208.2		4	33.5	odd	10
495.2.k.b.307.1		4	165.137	even	20
495.2.k.b.307.2		4	165.17	odd	20
605.2.m.b.112.1		16	55.37	odd	20	inner
605.2.m.b.112.2		16	55.7	even	20	inner
605.2.m.b.118.1		16	11.8	odd	10	inner
605.2.m.b.118.2		16	11.3	even	5	inner
605.2.m.b.233.1		16	11.4	even	5	inner
605.2.m.b.233.2		16	11.7	odd	10	inner
605.2.m.b.282.1		16	5.2	odd	4	inner
605.2.m.b.282.2		16	55.32	even	4	inner
605.2.m.b.403.1		16	11.10	odd	2	inner
605.2.m.b.403.2		16	1.1	even	1	trivial
605.2.m.b.457.1		16	55.2	even	20	inner
605.2.m.b.457.2		16	55.42	odd	20	inner
605.2.m.b.578.1		16	11.2	odd	10	inner
605.2.m.b.578.2		16	11.9	even	5	inner
605.2.m.b.602.1		16	55.47	odd	20	inner
605.2.m.b.602.2		16	55.52	even	20	inner
880.2.bd.e.417.1		4	220.127	odd	20
880.2.bd.e.417.2		4	220.27	even	20
880.2.bd.e.593.1		4	44.39	even	10
880.2.bd.e.593.2		4	44.27	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)

\(f(q)\)	\(=\)	\(q+(0.349798 + 2.20854i) q^{2} +(-1.26007 + 0.642040i) q^{3} +(-2.85317 + 0.927051i) q^{4} +(2.20582 - 0.366554i) q^{5} +(-1.85874 - 2.55834i) q^{6} +(-1.01515 - 1.99235i) q^{8} +(-0.587785 + 0.809017i) q^{9} +O(q^{10})\)	\(q+(0.349798 + 2.20854i) q^{2} +(-1.26007 + 0.642040i) q^{3} +(-2.85317 + 0.927051i) q^{4} +(2.20582 - 0.366554i) q^{5} +(-1.85874 - 2.55834i) q^{6} +(-1.01515 - 1.99235i) q^{8} +(-0.587785 + 0.809017i) q^{9} +(1.58114 + 4.74342i) q^{10} +(3.00000 - 3.00000i) q^{12} +(-4.41708 + 0.699596i) q^{13} +(-2.54415 + 1.87811i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-4.41708 - 0.699596i) q^{17} +(-1.99235 - 1.01515i) q^{18} +(-1.95440 + 6.01501i) q^{19} +(-5.95376 + 3.09075i) q^{20} +(-1.00000 - 1.00000i) q^{23} +(2.55834 + 1.85874i) q^{24} +(4.73128 - 1.61710i) q^{25} +(-3.09017 - 9.51057i) q^{26} +(0.884927 - 5.58721i) q^{27} +(1.95440 + 6.01501i) q^{29} +(-5.03781 - 4.96190i) q^{30} +(-1.61803 - 1.17557i) q^{31} +(-4.74342 - 4.74342i) q^{32} -10.0000i q^{34} +(0.927051 - 2.85317i) q^{36} +(3.78022 + 1.92612i) q^{37} +(-13.9680 - 2.21232i) q^{38} +(5.11667 - 3.71748i) q^{39} +(-2.96955 - 4.02266i) q^{40} +(6.01501 + 1.95440i) q^{41} +(-1.00000 + 2.00000i) q^{45} +(1.85874 - 2.55834i) q^{46} +(-1.92612 - 3.78022i) q^{47} +(0.642040 - 1.26007i) q^{48} +(4.11450 + 5.66312i) q^{49} +(5.22642 + 9.88355i) q^{50} +(6.01501 - 1.95440i) q^{51} +(11.9541 - 6.09092i) q^{52} +(0.221232 + 1.39680i) q^{53} +12.6491 q^{54} +(-1.39919 - 8.83415i) q^{57} +(-12.6007 + 6.42040i) q^{58} +(-5.70634 + 1.85410i) q^{59} +(5.51780 - 7.71712i) q^{60} +(3.71748 + 5.11667i) q^{61} +(2.03031 - 3.98470i) q^{62} +(7.64121 - 10.5172i) q^{64} +(-9.48683 + 3.16228i) q^{65} +(3.00000 - 3.00000i) q^{67} +(13.2512 - 2.09879i) q^{68} +(1.90211 + 0.618034i) q^{69} +(6.47214 - 4.70228i) q^{71} +(2.20854 + 0.349798i) q^{72} +(-3.98470 - 2.03031i) q^{73} +(-2.93159 + 9.02251i) q^{74} +(-4.92351 + 5.07533i) q^{75} -18.9737i q^{76} +(10.0000 + 10.0000i) q^{78} +(-5.11667 - 3.71748i) q^{79} +(-1.56909 + 1.59310i) q^{80} +(1.54508 + 4.75528i) q^{81} +(-2.21232 + 13.9680i) q^{82} +(-1.39919 + 8.83415i) q^{83} +(-9.99971 + 0.0759122i) q^{85} +(-6.32456 - 6.32456i) q^{87} +6.00000i q^{89} +(-4.76687 - 1.50894i) q^{90} +(3.78022 + 1.92612i) q^{92} +(2.79360 + 0.442463i) q^{93} +(7.67501 - 5.57622i) q^{94} +(-2.10622 + 13.9844i) q^{95} +(9.02251 + 2.93159i) q^{96} +(9.77762 - 1.54862i) 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