LMFDB - Embedded newform 550.2.ba.d.499.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [550,2,Mod(49,550)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(550, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("550.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	550.ba (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,2,0,2,0,0,-14,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			499.1
Root			$-0.587785 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	550.499
Dual form			550.2.ba.d.399.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.587785 + 0.809017i) q^{2} +(0.363271 + 0.118034i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.309017 + 0.224514i) q^{6} +(2.85317 - 0.927051i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-2.30902 - 1.67760i) q^{9} +(-1.23607 + 3.07768i) q^{11} -0.381966i q^{12} +(3.66547 - 5.04508i) q^{13} +(-0.927051 + 2.85317i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(2.57565 + 3.54508i) q^{17} +(2.71441 - 0.881966i) q^{18} +(1.80902 - 5.56758i) q^{19} +1.14590 q^{21} +(-1.76336 - 2.80902i) q^{22} -1.85410i q^{23} +(0.309017 + 0.224514i) q^{24} +(1.92705 + 5.93085i) q^{26} +(-1.31433 - 1.80902i) q^{27} +(-1.76336 - 2.42705i) q^{28} +(0.163119 + 0.502029i) q^{29} +(2.42705 + 1.76336i) q^{31} -1.00000i q^{32} +(-0.812299 + 0.972136i) q^{33} -4.38197 q^{34} +(-0.881966 + 2.71441i) q^{36} +(10.0453 - 3.26393i) q^{37} +(3.44095 + 4.73607i) q^{38} +(1.92705 - 1.40008i) q^{39} +(1.14590 - 3.52671i) q^{41} +(-0.673542 + 0.927051i) q^{42} +10.7082i q^{43} +(3.30902 + 0.224514i) q^{44} +(1.50000 + 1.08981i) q^{46} +(1.40008 + 0.454915i) q^{47} +(-0.363271 + 0.118034i) q^{48} +(1.61803 - 1.17557i) q^{49} +(0.517221 + 1.59184i) q^{51} +(-5.93085 - 1.92705i) q^{52} +(3.16344 - 4.35410i) q^{53} +2.23607 q^{54} +3.00000 q^{56} +(1.31433 - 1.80902i) q^{57} +(-0.502029 - 0.163119i) q^{58} +(2.07295 + 6.37988i) q^{59} +(-7.04508 + 5.11855i) q^{61} +(-2.85317 + 0.927051i) q^{62} +(-8.14324 - 2.64590i) q^{63} +(0.809017 + 0.587785i) q^{64} +(-0.309017 - 1.22857i) q^{66} +0.0901699i q^{67} +(2.57565 - 3.54508i) q^{68} +(0.218847 - 0.673542i) q^{69} +(10.7812 - 7.83297i) q^{71} +(-1.67760 - 2.30902i) q^{72} +(-10.9964 + 3.57295i) q^{73} +(-3.26393 + 10.0453i) q^{74} -5.85410 q^{76} +(-0.673542 + 9.92705i) q^{77} +2.38197i q^{78} +(-6.28115 - 4.56352i) q^{79} +(2.38197 + 7.33094i) q^{81} +(2.17963 + 3.00000i) q^{82} +(2.21238 + 3.04508i) q^{83} +(-0.354102 - 1.08981i) q^{84} +(-8.66312 - 6.29412i) q^{86} +0.201626i q^{87} +(-2.12663 + 2.54508i) q^{88} -11.1803 q^{89} +(5.78115 - 17.7926i) q^{91} +(-1.76336 + 0.572949i) q^{92} +(0.673542 + 0.927051i) q^{93} +(-1.19098 + 0.865300i) q^{94} +(0.118034 - 0.363271i) q^{96} +(0.555029 - 0.763932i) q^{97} +2.00000i q^{98} +(8.01722 - 5.03280i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} + 2 q^{6} - 14 q^{9} + 8 q^{11} + 6 q^{14} - 2 q^{16} + 10 q^{19} + 36 q^{21} - 2 q^{24} + 2 q^{26} - 30 q^{29} + 6 q^{31} - 44 q^{34} - 16 q^{36} + 2 q^{39} + 36 q^{41} + 22 q^{44} + 12 q^{46}+ \cdots + 6 q^{99}+O(q^{100}) $ 8 * q + 2 * q^4 + 2 * q^6 - 14 * q^9 + 8 * q^11 + 6 * q^14 - 2 * q^16 + 10 * q^19 + 36 * q^21 - 2 * q^24 + 2 * q^26 - 30 * q^29 + 6 * q^31 - 44 * q^34 - 16 * q^36 + 2 * q^39 + 36 * q^41 + 22 * q^44 + 12 * q^46 + 4 * q^49 - 54 * q^51 + 24 * q^56 + 30 * q^59 - 34 * q^61 + 2 * q^64 + 2 * q^66 + 42 * q^69 + 46 * q^71 - 44 * q^74 - 20 * q^76 - 10 * q^79 + 28 * q^81 + 24 * q^84 - 38 * q^86 + 6 * q^91 - 14 * q^94 - 8 * q^96 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$3$	0.363271	+	0.118034i	0.209735	+	0.0681470i	0.412000	−	0.911184i	$-0.364830\pi$
$3$	0.363271	+	0.118034i	0.209735	+	0.0681470i	−0.202265	+	0.979331i	$0.564830\pi$
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$		0			0
$5$		0			0
$6$	−0.309017	+	0.224514i	−0.126156	+	0.0916575i
$7$	2.85317	−	0.927051i	1.07840	−	0.350392i	0.284644	−	0.958633i	$-0.408125\pi$
$7$	2.85317	−	0.927051i	1.07840	−	0.350392i	0.793752	+	0.608241i	$0.208125\pi$
$8$	0.951057	+	0.309017i	0.336249	+	0.109254i
$9$	−2.30902	−	1.67760i	−0.769672	−	0.559200i
$10$		0			0
$11$	−1.23607	+	3.07768i	−0.372689	+	0.927957i
$11$	−1.23607	+	3.07768i	−0.372689	+	0.927957i
$12$		−	0.381966i		−	0.110264i
$13$	3.66547	−	5.04508i	1.01662	−	1.39925i	0.102070	−	0.994777i	$-0.467453\pi$
$13$	3.66547	−	5.04508i	1.01662	−	1.39925i	0.914548	−	0.404478i	$-0.132547\pi$
$14$	−0.927051	+	2.85317i	−0.247765	+	0.762542i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	2.57565	+	3.54508i	0.624688	+	0.859809i	0.997684	−	0.0680237i	$-0.0216694\pi$
$17$	2.57565	+	3.54508i	0.624688	+	0.859809i	−0.372996	+	0.927833i	$0.621669\pi$
$18$	2.71441	−	0.881966i	0.639793	−	0.207881i
$19$	1.80902	−	5.56758i	0.415017	−	1.27729i	−0.497219	−	0.867625i	$-0.665645\pi$
$19$	1.80902	−	5.56758i	0.415017	−	1.27729i	0.912236	−	0.409666i	$-0.134355\pi$
$20$		0			0
$21$	1.14590			0.250055
$22$	−1.76336	−	2.80902i	−0.375949	−	0.598884i
$23$		−	1.85410i		−	0.386607i	−0.981139	−	0.193303i	$-0.938080\pi$
$23$		−	1.85410i		−	0.386607i	0.981139	−	0.193303i	$-0.0619202\pi$
$24$	0.309017	+	0.224514i	0.0630778	+	0.0458287i
$25$		0			0
$26$	1.92705	+	5.93085i	0.377926	+	1.16314i
$27$	−1.31433	−	1.80902i	−0.252942	−	0.348145i
$28$	−1.76336	−	2.42705i	−0.333243	−	0.458670i
$29$	0.163119	+	0.502029i	0.0302904	+	0.0932244i	0.965059	−	0.262033i	$-0.0843931\pi$
$29$	0.163119	+	0.502029i	0.0302904	+	0.0932244i	−0.934768	+	0.355258i	$0.884393\pi$
$30$		0			0
$31$	2.42705	+	1.76336i	0.435911	+	0.316708i	0.784008	−	0.620750i	$-0.213172\pi$
$31$	2.42705	+	1.76336i	0.435911	+	0.316708i	−0.348097	+	0.937459i	$0.613172\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−0.812299	+	0.972136i	−0.141403	+	0.169227i
$34$	−4.38197			−0.751501
$35$		0			0
$36$	−0.881966	+	2.71441i	−0.146994	+	0.452402i
$37$	10.0453	−	3.26393i	1.65145	−	0.536587i	0.672393	−	0.740195i	$-0.265267\pi$
$37$	10.0453	−	3.26393i	1.65145	−	0.536587i	0.979053	+	0.203607i	$0.0652666\pi$
$38$	3.44095	+	4.73607i	0.558197	+	0.768292i
$39$	1.92705	−	1.40008i	0.308575	−	0.224193i
$40$		0			0
$41$	1.14590	−	3.52671i	0.178959	−	0.550780i	−0.820833	−	0.571168i	$-0.806490\pi$
$41$	1.14590	−	3.52671i	0.178959	−	0.550780i	0.999792	+	0.0203886i	$0.00649033\pi$
$42$	−0.673542	+	0.927051i	−0.103930	+	0.143047i
$43$			10.7082i			1.63299i	0.577355	+	0.816493i	$0.304085\pi$
$43$			10.7082i			1.63299i	−0.577355	+	0.816493i	$0.695915\pi$
$44$	3.30902	+	0.224514i	0.498853	+	0.0338468i
$45$		0			0
$46$	1.50000	+	1.08981i	0.221163	+	0.160684i
$47$	1.40008	+	0.454915i	0.204223	+	0.0663562i	0.409342	−	0.912381i	$-0.365758\pi$
$47$	1.40008	+	0.454915i	0.204223	+	0.0663562i	−0.205119	+	0.978737i	$0.565758\pi$
$48$	−0.363271	+	0.118034i	−0.0524337	+	0.0170367i
$49$	1.61803	−	1.17557i	0.231148	−	0.167939i
$50$		0			0
$51$	0.517221	+	1.59184i	0.0724254	+	0.222903i
$52$	−5.93085	−	1.92705i	−0.822461	−	0.267234i
$53$	3.16344	−	4.35410i	0.434532	−	0.598082i	−0.534454	−	0.845198i	$-0.679483\pi$
$53$	3.16344	−	4.35410i	0.434532	−	0.598082i	0.968986	+	0.247116i	$0.0794827\pi$
$54$	2.23607			0.304290
$55$		0			0
$56$	3.00000			0.400892
$57$	1.31433	−	1.80902i	0.174087	−	0.239610i
$58$	−0.502029	−	0.163119i	−0.0659196	−	0.0214186i
$59$	2.07295	+	6.37988i	0.269875	+	0.830590i	0.990530	+	0.137296i	$0.0438412\pi$
$59$	2.07295	+	6.37988i	0.269875	+	0.830590i	−0.720655	+	0.693294i	$0.756159\pi$
$60$		0			0
$61$	−7.04508	+	5.11855i	−0.902031	+	0.655364i	−0.938987	−	0.343953i	$-0.888234\pi$
$61$	−7.04508	+	5.11855i	−0.902031	+	0.655364i	0.0369561	+	0.999317i	$0.488234\pi$
$62$	−2.85317	+	0.927051i	−0.362353	+	0.117736i
$63$	−8.14324	−	2.64590i	−1.02595	−	0.333352i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$		0			0
$66$	−0.309017	−	1.22857i	−0.0380374	−	0.151227i
$67$			0.0901699i			0.0110160i	0.999985	+	0.00550801i	$0.00175326\pi$
$67$			0.0901699i			0.0110160i	−0.999985	+	0.00550801i	$0.998247\pi$
$68$	2.57565	−	3.54508i	0.312344	−	0.429905i
$69$	0.218847	−	0.673542i	0.0263461	−	0.0810849i
$70$		0			0
$71$	10.7812	−	7.83297i	1.27949	−	0.929602i	0.279950	−	0.960015i	$-0.409682\pi$
$71$	10.7812	−	7.83297i	1.27949	−	0.929602i	0.999537	+	0.0304125i	$0.00968210\pi$
$72$	−1.67760	−	2.30902i	−0.197707	−	0.272120i
$73$	−10.9964	+	3.57295i	−1.28703	+	0.418182i	−0.871052	−	0.491192i	$-0.836562\pi$
$73$	−10.9964	+	3.57295i	−1.28703	+	0.418182i	−0.415980	+	0.909374i	$0.636562\pi$
$74$	−3.26393	+	10.0453i	−0.379424	+	1.16775i
$75$		0			0
$76$	−5.85410			−0.671512
$77$	−0.673542	+	9.92705i	−0.0767572	+	1.13129i
$78$			2.38197i			0.269705i
$79$	−6.28115	−	4.56352i	−0.706685	−	0.513437i	0.175418	−	0.984494i	$-0.443872\pi$
$79$	−6.28115	−	4.56352i	−0.706685	−	0.513437i	−0.882103	+	0.471057i	$0.843872\pi$
$80$		0			0
$81$	2.38197	+	7.33094i	0.264663	+	0.814549i
$82$	2.17963	+	3.00000i	0.240700	+	0.331295i
$83$	2.21238	+	3.04508i	0.242841	+	0.334241i	0.912988	−	0.407987i	$-0.133769\pi$
$83$	2.21238	+	3.04508i	0.242841	+	0.334241i	−0.670147	+	0.742228i	$0.733769\pi$
$84$	−0.354102	−	1.08981i	−0.0386357	−	0.118908i
$85$		0			0
$86$	−8.66312	−	6.29412i	−0.934168	−	0.678713i
$87$			0.201626i			0.0216166i
$88$	−2.12663	+	2.54508i	−0.226699	+	0.271307i
$89$	−11.1803			−1.18511			−0.592557	−	0.805529i	$-0.701881\pi$
$89$	−11.1803			−1.18511			−0.592557	+	0.805529i	$0.701881\pi$
$90$		0			0
$91$	5.78115	−	17.7926i	0.606029	−	1.86517i
$92$	−1.76336	+	0.572949i	−0.183843	+	0.0597341i
$93$	0.673542	+	0.927051i	0.0698430	+	0.0961307i
$94$	−1.19098	+	0.865300i	−0.122841	+	0.0892489i
$95$		0			0
$96$	0.118034	−	0.363271i	0.0120468	−	0.0370762i
$97$	0.555029	−	0.763932i	0.0563547	−	0.0775655i	−0.779910	−	0.625892i	$-0.784735\pi$
$97$	0.555029	−	0.763932i	0.0563547	−	0.0775655i	0.836264	+	0.548327i	$0.184735\pi$
$98$			2.00000i			0.202031i
$99$	8.01722	−	5.03280i	0.805761	−	0.505815i
$100$		0			0
$101$	−10.6631	−	7.74721i	−1.06102	−	0.770876i	−0.0867432	−	0.996231i	$-0.527646\pi$
$101$	−10.6631	−	7.74721i	−1.06102	−	0.770876i	−0.974277	+	0.225355i	$0.927646\pi$
$102$	−1.59184	−	0.517221i	−0.157616	−	0.0512125i
$103$	−0.673542	+	0.218847i	−0.0663661	+	0.0215636i	−0.342012	−	0.939696i	$-0.611108\pi$
$103$	−0.673542	+	0.218847i	−0.0663661	+	0.0215636i	0.275646	+	0.961259i	$0.411108\pi$
$104$	5.04508	−	3.66547i	0.494711	−	0.359429i
$105$		0			0
$106$	1.66312	+	5.11855i	0.161536	+	0.497158i
$107$	−0.726543	−	0.236068i	−0.0702375	−	0.0228216i	0.273687	−	0.961819i	$-0.411757\pi$
$107$	−0.726543	−	0.236068i	−0.0702375	−	0.0228216i	−0.343925	+	0.938997i	$0.611757\pi$
$108$	−1.31433	+	1.80902i	−0.126471	+	0.174073i
$109$	9.14590			0.876018			0.438009	−	0.898971i	$-0.355684\pi$
$109$	9.14590			0.876018			0.438009	+	0.898971i	$0.355684\pi$
$110$		0			0
$111$	4.03444			0.382932
$112$	−1.76336	+	2.42705i	−0.166621	+	0.229335i
$113$	−3.57971	−	1.16312i	−0.336751	−	0.109417i	0.135760	−	0.990742i	$-0.456652\pi$
$113$	−3.57971	−	1.16312i	−0.336751	−	0.109417i	−0.472511	+	0.881325i	$0.656652\pi$
$114$	0.690983	+	2.12663i	0.0647165	+	0.199177i
$115$		0			0
$116$	0.427051	−	0.310271i	0.0396507	−	0.0288079i
$117$	−16.9273	+	5.50000i	−1.56493	+	0.508475i
$118$	−6.37988	−	2.07295i	−0.587316	−	0.190830i
$119$	10.6353	+	7.72696i	0.974932	+	0.708330i
$120$		0			0
$121$	−7.94427	−	7.60845i	−0.722207	−	0.691677i
$122$		−	8.70820i		−	0.788404i
$123$	0.832544	−	1.14590i	0.0750679	−	0.103322i
$124$	0.927051	−	2.85317i	0.0832516	−	0.256222i
$125$		0			0
$126$	6.92705	−	5.03280i	0.617111	−	0.448357i
$127$	1.26133	+	1.73607i	0.111925	+	0.154051i	0.861304	−	0.508090i	$-0.169648\pi$
$127$	1.26133	+	1.73607i	0.111925	+	0.154051i	−0.749380	+	0.662141i	$0.769648\pi$
$128$	−0.951057	+	0.309017i	−0.0840623	+	0.0273135i
$129$	−1.26393	+	3.88998i	−0.111283	+	0.342494i
$130$		0			0
$131$	−20.5623			−1.79654			−0.898269	−	0.439447i	$-0.855174\pi$
$131$	−20.5623			−1.79654			−0.898269	+	0.439447i	$0.855174\pi$
$132$	1.17557	+	0.472136i	0.102320	+	0.0410942i
$133$		−	17.5623i		−	1.52285i
$134$	−0.0729490	−	0.0530006i	−0.00630184	−	0.00457855i
$135$		0			0
$136$	1.35410	+	4.16750i	0.116113	+	0.357360i
$137$	−1.86936	−	2.57295i	−0.159710	−	0.219822i	0.721661	−	0.692246i	$-0.243379\pi$
$137$	−1.86936	−	2.57295i	−0.159710	−	0.219822i	−0.881371	+	0.472425i	$0.843379\pi$
$138$	0.416272	+	0.572949i	0.0354354	+	0.0487727i
$139$	2.50000	+	7.69421i	0.212047	+	0.652614i	0.999350	+	0.0360478i	$0.0114769\pi$
$139$	2.50000	+	7.69421i	0.212047	+	0.652614i	−0.787303	+	0.616566i	$0.788523\pi$
$140$		0			0
$141$	0.454915	+	0.330515i	0.0383108	+	0.0278344i
$142$			13.3262i			1.11831i
$143$	10.9964	+	17.5172i	0.919566	+	1.46486i
$144$	2.85410			0.237842
$145$		0			0
$146$	3.57295	−	10.9964i	0.295699	−	0.910069i
$147$	0.726543	−	0.236068i	0.0599242	−	0.0194706i
$148$	−6.20837	−	8.54508i	−0.510325	−	0.702402i
$149$	−17.1353	+	12.4495i	−1.40377	+	1.01990i	−0.409584	+	0.912273i	$0.634326\pi$
$149$	−17.1353	+	12.4495i	−1.40377	+	1.01990i	−0.994191	+	0.107630i	$0.965674\pi$
$150$		0			0
$151$	6.20820	−	19.1069i	0.505216	−	1.55490i	−0.295190	−	0.955439i	$-0.595383\pi$
$151$	6.20820	−	19.1069i	0.505216	−	1.55490i	0.800406	−	0.599458i	$-0.204617\pi$
$152$	3.44095	−	4.73607i	0.279098	−	0.384146i
$153$		−	12.5066i		−	1.01110i
$154$	−7.63525	−	6.37988i	−0.615266	−	0.514105i
$155$		0			0
$156$	−1.92705	−	1.40008i	−0.154288	−	0.112096i
$157$	−18.7436	−	6.09017i	−1.49590	−	0.486048i	−0.557083	−	0.830457i	$-0.688080\pi$
$157$	−18.7436	−	6.09017i	−1.49590	−	0.486048i	−0.938820	+	0.344408i	$0.888080\pi$
$158$	7.38394	−	2.39919i	0.587435	−	0.190869i
$159$	1.66312	−	1.20833i	0.131894	−	0.0958265i
$160$		0			0
$161$	−1.71885	−	5.29007i	−0.135464	−	0.416916i
$162$	−7.33094	−	2.38197i	−0.575973	−	0.187145i
$163$	−7.15942	+	9.85410i	−0.560769	+	0.771833i	−0.991424	−	0.130684i	$-0.958283\pi$
$163$	−7.15942	+	9.85410i	−0.560769	+	0.771833i	0.430655	+	0.902517i	$0.358283\pi$
$164$	−3.70820			−0.289562
$165$		0			0
$166$	−3.76393			−0.292138
$167$	3.49396	−	4.80902i	0.270370	−	0.372133i	−0.652144	−	0.758095i	$-0.726130\pi$
$167$	3.49396	−	4.80902i	0.270370	−	0.372133i	0.922515	+	0.385962i	$0.126130\pi$
$168$	1.08981	+	0.354102i	0.0840810	+	0.0273196i
$169$	−8.00000	−	24.6215i	−0.615385	−	1.89396i
$170$		0			0
$171$	−13.5172	+	9.82084i	−1.03369	+	0.751018i
$172$	10.1841	−	3.30902i	0.776531	−	0.252310i
$173$	−8.14324	−	2.64590i	−0.619119	−	0.201164i	−0.0173698	−	0.999849i	$-0.505529\pi$
$173$	−8.14324	−	2.64590i	−0.619119	−	0.201164i	−0.601749	+	0.798685i	$0.705529\pi$
$174$	−0.163119	−	0.118513i	−0.0123660	−	0.00898444i
$175$		0			0
$176$	−0.809017	−	3.21644i	−0.0609820	−	0.242448i
$177$			2.56231i			0.192595i
$178$	6.57164	−	9.04508i	0.492565	−	0.677958i
$179$	−3.29180	+	10.1311i	−0.246040	+	0.757234i	0.749423	+	0.662091i	$0.230331\pi$
$179$	−3.29180	+	10.1311i	−0.246040	+	0.757234i	−0.995464	+	0.0951432i	$0.969669\pi$
$180$		0			0
$181$	−9.70820	+	7.05342i	−0.721605	+	0.524277i	−0.886897	−	0.461968i	$-0.847144\pi$
$181$	−9.70820	+	7.05342i	−0.721605	+	0.524277i	0.165292	+	0.986245i	$0.447144\pi$
$182$	10.9964	+	15.1353i	0.815108	+	1.12190i
$183$	−3.16344	+	1.02786i	−0.233848	+	0.0759819i
$184$	0.572949	−	1.76336i	0.0422384	−	0.129996i
$185$		0			0
$186$	−1.14590			−0.0840213
$187$	−14.0943	+	3.54508i	−1.03068	+	0.259242i
$188$		−	1.47214i		−	0.107367i
$189$	−5.42705	−	3.94298i	−0.394760	−	0.286810i
$190$		0			0
$191$	7.42705	+	22.8581i	0.537403	+	1.65395i	0.738400	+	0.674363i	$0.235582\pi$
$191$	7.42705	+	22.8581i	0.537403	+	1.65395i	−0.200997	+	0.979592i	$0.564418\pi$
$192$	0.224514	+	0.309017i	0.0162029	+	0.0223014i
$193$	1.08981	+	1.50000i	0.0784465	+	0.107972i	0.846437	−	0.532489i	$-0.178743\pi$
$193$	1.08981	+	1.50000i	0.0784465	+	0.107972i	−0.767990	+	0.640461i	$0.778743\pi$
$194$	0.291796	+	0.898056i	0.0209497	+	0.0644767i
$195$		0			0
$196$	−1.61803	−	1.17557i	−0.115574	−	0.0839693i
$197$			4.76393i			0.339416i	0.985494	+	0.169708i	$0.0542825\pi$
$197$			4.76393i			0.339416i	−0.985494	+	0.169708i	$0.945718\pi$
$198$	−0.640786	+	9.44427i	−0.0455387	+	0.671175i
$199$	3.94427			0.279602			0.139801	−	0.990180i	$-0.455354\pi$
$199$	3.94427			0.279602			0.139801	+	0.990180i	$0.455354\pi$
$200$		0			0
$201$	−0.0106431	+	0.0327561i	−0.000750708	+	0.00231044i
$202$	12.5352	−	4.07295i	0.881977	−	0.286572i
$203$	0.930812	+	1.28115i	0.0653302	+	0.0899193i
$204$	1.35410	−	0.983813i	0.0948061	−	0.0688807i
$205$		0			0
$206$	0.218847	−	0.673542i	0.0152478	−	0.0469279i
$207$	−3.11044	+	4.28115i	−0.216191	+	0.297561i
$208$			6.23607i			0.432394i
$209$	14.8992	+	12.4495i	1.03060	+	0.861149i
$210$		0			0
$211$	22.0623	+	16.0292i	1.51883	+	1.10350i	0.962063	+	0.272829i	$0.0879592\pi$
$211$	22.0623	+	16.0292i	1.51883	+	1.10350i	0.556769	+	0.830667i	$0.312041\pi$
$212$	−5.11855	−	1.66312i	−0.351544	−	0.114223i
$213$	4.84104	−	1.57295i	0.331703	−	0.107777i
$214$	0.618034	−	0.449028i	0.0422479	−	0.0306949i
$215$		0			0
$216$	−0.690983	−	2.12663i	−0.0470154	−	0.144699i
$217$	8.55951	+	2.78115i	0.581057	+	0.188797i
$218$	−5.37582	+	7.39919i	−0.364097	+	0.501136i
$219$	−4.41641			−0.298433
$220$		0			0
$221$	27.3262			1.83816
$222$	−2.37139	+	3.26393i	−0.159157	+	0.219061i
$223$	19.6947	+	6.39919i	1.31885	+	0.428521i	0.882101	−	0.471061i	$-0.156129\pi$
$223$	19.6947	+	6.39919i	1.31885	+	0.428521i	0.436752	+	0.899582i	$0.356129\pi$
$224$	−0.927051	−	2.85317i	−0.0619412	−	0.190635i
$225$		0			0
$226$	3.04508	−	2.21238i	0.202556	−	0.147166i
$227$	17.4293	−	5.66312i	1.15682	−	0.375874i	0.333113	−	0.942887i	$-0.391901\pi$
$227$	17.4293	−	5.66312i	1.15682	−	0.375874i	0.823709	+	0.567012i	$0.191901\pi$
$228$	−2.12663	−	0.690983i	−0.140839	−	0.0457615i
$229$	0.427051	+	0.310271i	0.0282203	+	0.0205033i	0.601806	−	0.798642i	$-0.294448\pi$
$229$	0.427051	+	0.310271i	0.0282203	+	0.0205033i	−0.573586	+	0.819146i	$0.694448\pi$
$230$		0			0
$231$	−1.41641	+	3.52671i	−0.0931928	+	0.232041i
$232$			0.527864i			0.0346560i
$233$	9.04129	−	12.4443i	0.592315	−	0.815251i	−0.402663	−	0.915348i	$-0.631915\pi$
$233$	9.04129	−	12.4443i	0.592315	−	0.815251i	0.994978	+	0.100097i	$0.0319153\pi$
$234$	5.50000	−	16.9273i	0.359546	−	1.10657i
$235$		0			0
$236$	5.42705	−	3.94298i	0.353271	−	0.256666i
$237$	−1.74311	−	2.39919i	−0.113227	−	0.155844i
$238$	−12.5025	+	4.06231i	−0.810416	+	0.263320i
$239$	−4.83688	+	14.8864i	−0.312872	+	0.962920i	0.663750	+	0.747955i	$0.268964\pi$
$239$	−4.83688	+	14.8864i	−0.312872	+	0.962920i	−0.976622	+	0.214966i	$0.931036\pi$
$240$		0			0
$241$	−18.0000			−1.15948			−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000			−1.15948			−0.579741	+	0.814801i	$0.696846\pi$
$242$	10.8249	−	1.95492i	0.695850	−	0.125667i
$243$			9.65248i			0.619207i
$244$	7.04508	+	5.11855i	0.451015	+	0.327682i
$245$		0			0
$246$	0.437694	+	1.34708i	0.0279064	+	0.0858869i
$247$	−21.4580	−	29.5344i	−1.36534	−	1.87923i
$248$	1.76336	+	2.42705i	0.111973	+	0.154118i
$249$	0.444272	+	1.36733i	0.0281546	+	0.0866509i
$250$		0			0
$251$	11.7361	+	8.52675i	0.740774	+	0.538204i	0.892953	−	0.450149i	$-0.148629\pi$
$251$	11.7361	+	8.52675i	0.740774	+	0.538204i	−0.152179	+	0.988353i	$0.548629\pi$
$252$			8.56231i			0.539375i
$253$	5.70634	+	2.29180i	0.358754	+	0.144084i
$254$	−2.14590			−0.134646
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	30.1891	−	9.80902i	1.88314	−	0.611870i	0.898035	−	0.439925i	$-0.144995\pi$
$257$	30.1891	−	9.80902i	1.88314	−	0.611870i	0.985107	−	0.171945i	$-0.0550051\pi$
$258$	−2.40414	−	3.30902i	−0.149675	−	0.206010i
$259$	25.6353	−	18.6251i	1.59290	−	1.15731i
$260$		0			0
$261$	0.465558	−	1.43284i	0.0288173	−	0.0886906i
$262$	12.0862	−	16.6353i	0.746689	−	1.02773i
$263$			11.0344i			0.680413i	0.940351	+	0.340206i	$0.110497\pi$
$263$			11.0344i			0.680413i	−0.940351	+	0.340206i	$0.889503\pi$
$264$	−1.07295	+	0.673542i	−0.0660354	+	0.0414536i
$265$		0			0
$266$	14.2082	+	10.3229i	0.871161	+	0.632935i
$267$	−4.06150	−	1.31966i	−0.248560	−	0.0807619i
$268$	0.0857567	−	0.0278640i	0.00523842	−	0.00170207i
$269$	−14.6353	+	10.6331i	−0.892327	+	0.648314i	−0.936484	−	0.350711i	$-0.885940\pi$
$269$	−14.6353	+	10.6331i	−0.892327	+	0.648314i	0.0441565	+	0.999025i	$0.485940\pi$
$270$		0			0
$271$	5.02786	+	15.4742i	0.305421	+	0.939989i	0.979520	+	0.201348i	$0.0645322\pi$
$271$	5.02786	+	15.4742i	0.305421	+	0.939989i	−0.674099	+	0.738641i	$0.735468\pi$
$272$	−4.16750	−	1.35410i	−0.252692	−	0.0821045i
$273$	4.20025	−	5.78115i	0.254211	−	0.349891i
$274$	3.18034			0.192131
$275$		0			0
$276$	−0.708204			−0.0426289
$277$	−3.69822	+	5.09017i	−0.222205	+	0.305839i	−0.905536	−	0.424270i	$-0.860531\pi$
$277$	−3.69822	+	5.09017i	−0.222205	+	0.305839i	0.683331	+	0.730109i	$0.260531\pi$
$278$	−7.69421	−	2.50000i	−0.461468	−	0.149940i
$279$	−2.64590	−	8.14324i	−0.158406	−	0.487523i
$280$		0			0
$281$	−14.7082	+	10.6861i	−0.877418	+	0.637481i	−0.932567	−	0.360997i	$-0.882437\pi$
$281$	−14.7082	+	10.6861i	−0.877418	+	0.637481i	0.0551492	+	0.998478i	$0.482437\pi$
$282$	−0.534785	+	0.173762i	−0.0318460	+	0.0103474i
$283$	−17.4620	−	5.67376i	−1.03801	−	0.337270i	−0.260058	−	0.965593i	$-0.583742\pi$
$283$	−17.4620	−	5.67376i	−1.03801	−	0.337270i	−0.777953	+	0.628323i	$0.783742\pi$
$284$	−10.7812	−	7.83297i	−0.639744	−	0.464801i
$285$		0			0
$286$	−20.6353	−	1.40008i	−1.22019	−	0.0827887i
$287$		−	11.1246i		−	0.656665i
$288$	−1.67760	+	2.30902i	−0.0988535	+	0.136060i
$289$	−0.680340	+	2.09387i	−0.0400200	+	0.123169i
$290$		0			0
$291$	0.291796	−	0.212002i	0.0171054	−	0.0124278i
$292$	6.79615	+	9.35410i	0.397715	+	0.547407i
$293$	18.1558	−	5.89919i	1.06067	−	0.344634i	0.273826	−	0.961779i	$-0.411711\pi$
$293$	18.1558	−	5.89919i	1.06067	−	0.344634i	0.786849	+	0.617145i	$0.211711\pi$
$294$	−0.236068	+	0.726543i	−0.0137678	+	0.0423728i
$295$		0			0
$296$	10.5623			0.613922
$297$	7.19218	−	1.80902i	0.417333	−	0.104970i
$298$		−	21.1803i		−	1.22694i
$299$	−9.35410	−	6.79615i	−0.540962	−	0.393032i
$300$		0			0
$301$	9.92705	+	30.5523i	0.572186	+	1.76101i
$302$	11.8087	+	16.2533i	0.679515	+	0.935272i
$303$	−2.95917	−	4.07295i	−0.170000	−	0.233985i
$304$	1.80902	+	5.56758i	0.103754	+	0.319323i
$305$		0			0
$306$	10.1180	+	7.35118i	0.578410	+	0.420239i
$307$			9.56231i			0.545750i	0.962050	+	0.272875i	$0.0879745\pi$
$307$			9.56231i			0.545750i	−0.962050	+	0.272875i	$0.912026\pi$
$308$	9.64932	−	2.42705i	0.549821	−	0.138294i
$309$	−0.270510			−0.0153888
$310$		0			0
$311$	0.781153	−	2.40414i	0.0442951	−	0.136326i	−0.926463	−	0.376385i	$-0.877167\pi$
$311$	0.781153	−	2.40414i	0.0442951	−	0.136326i	0.970758	+	0.240059i	$0.0771668\pi$
$312$	2.26538	−	0.736068i	0.128252	−	0.0416716i
$313$	11.7229	+	16.1353i	0.662620	+	0.912019i	0.999565	−	0.0295060i	$-0.00939343\pi$
$313$	11.7229	+	16.1353i	0.662620	+	0.912019i	−0.336944	+	0.941525i	$0.609393\pi$
$314$	15.9443	−	11.5842i	0.899787	−	0.653734i
$315$		0			0
$316$	−2.39919	+	7.38394i	−0.134965	+	0.415379i
$317$	−18.6579	+	25.6803i	−1.04793	+	1.44235i	−0.157340	+	0.987545i	$0.550292\pi$
$317$	−18.6579	+	25.6803i	−1.04793	+	1.44235i	−0.890590	+	0.454807i	$0.849708\pi$
$318$			2.05573i			0.115280i
$319$	−1.74671	−	0.118513i	−0.0977970	−	0.00663545i
$320$		0			0
$321$	−0.236068	−	0.171513i	−0.0131760	−	0.00957295i
$322$	5.29007	+	1.71885i	0.294804	+	0.0957876i
$323$	24.3970	−	7.92705i	1.35748	−	0.441073i
$324$	6.23607	−	4.53077i	0.346448	−	0.251709i
$325$		0			0
$326$	−3.76393	−	11.5842i	−0.208465	−	0.641589i
$327$	3.32244	+	1.07953i	0.183731	+	0.0596980i
$328$	2.17963	−	3.00000i	0.120350	−	0.165647i
$329$	4.41641			0.243484
$330$		0			0
$331$	12.0000			0.659580			0.329790	−	0.944054i	$-0.393022\pi$
$331$	12.0000			0.659580			0.329790	+	0.944054i	$0.393022\pi$
$332$	2.21238	−	3.04508i	0.121420	−	0.167121i
$333$	−28.6705	−	9.31559i	−1.57113	−	0.510491i
$334$	1.83688	+	5.65334i	0.100510	+	0.309337i
$335$		0			0
$336$	−0.927051	+	0.673542i	−0.0505748	+	0.0367447i
$337$	1.22857	−	0.399187i	0.0669245	−	0.0217451i	−0.275363	−	0.961340i	$-0.588798\pi$
$337$	1.22857	−	0.399187i	0.0669245	−	0.0217451i	0.342288	+	0.939595i	$0.388798\pi$
$338$	24.6215	+	8.00000i	1.33923	+	0.435143i
$339$	−1.16312	−	0.845055i	−0.0631720	−	0.0458971i
$340$		0			0
$341$	−8.42705	+	5.29007i	−0.456350	+	0.286473i
$342$		−	16.7082i		−	0.903476i
$343$	−8.81678	+	12.1353i	−0.476061	+	0.655242i
$344$	−3.30902	+	10.1841i	−0.178410	+	0.549090i
$345$		0			0
$346$	6.92705	−	5.03280i	0.372401	−	0.270565i
$347$	−8.55951	−	11.7812i	−0.459498	−	0.632445i	0.514906	−	0.857247i	$-0.327827\pi$
$347$	−8.55951	−	11.7812i	−0.459498	−	0.632445i	−0.974405	+	0.224801i	$0.927827\pi$
$348$	0.191758	−	0.0623059i	0.0102793	−	0.00333995i
$349$	2.23607	−	6.88191i	0.119694	−	0.368380i	−0.873203	−	0.487356i	$-0.837961\pi$
$349$	2.23607	−	6.88191i	0.119694	−	0.368380i	0.992897	+	0.118976i	$0.0379612\pi$
$350$		0			0
$351$	−13.9443			−0.744290
$352$	3.07768	+	1.23607i	0.164041	+	0.0658826i
$353$		−	23.5623i		−	1.25410i	−0.778981	−	0.627048i	$-0.784263\pi$
$353$		−	23.5623i		−	1.25410i	0.778981	−	0.627048i	$-0.215737\pi$
$354$	−2.07295	−	1.50609i	−0.110176	−	0.0800475i
$355$		0			0
$356$	3.45492	+	10.6331i	0.183110	+	0.563555i
$357$	2.95144	+	4.06231i	0.156207	+	0.215000i
$358$	−6.26137	−	8.61803i	−0.330924	−	0.455477i
$359$	−2.76393	−	8.50651i	−0.145875	−	0.448956i	0.851248	−	0.524764i	$-0.175846\pi$
$359$	−2.76393	−	8.50651i	−0.145875	−	0.448956i	−0.997122	+	0.0758078i	$0.975846\pi$
$360$		0			0
$361$	−12.3541	−	8.97578i	−0.650216	−	0.472409i
$362$		−	12.0000i		−	0.630706i
$363$	−1.98787	−	3.70163i	−0.104336	−	0.194285i
$364$	−18.7082			−0.980576
$365$		0			0
$366$	1.02786	−	3.16344i	0.0537273	−	0.165356i
$367$	9.23305	−	3.00000i	0.481961	−	0.156599i	−0.0579520	−	0.998319i	$-0.518457\pi$
$367$	9.23305	−	3.00000i	0.481961	−	0.156599i	0.539913	+	0.841721i	$0.318457\pi$
$368$	1.08981	+	1.50000i	0.0568105	+	0.0781929i
$369$	−8.56231	+	6.22088i	−0.445736	+	0.323846i
$370$		0			0
$371$	4.98936	−	15.3557i	0.259035	−	0.797226i
$372$	0.673542	−	0.927051i	0.0349215	−	0.0480654i
$373$			29.9787i			1.55224i	0.630586	+	0.776119i	$0.282815\pi$
$373$			29.9787i			1.55224i	−0.630586	+	0.776119i	$0.717185\pi$
$374$	5.41641	−	13.4863i	0.280076	−	0.697360i
$375$		0			0
$376$	1.19098	+	0.865300i	0.0614203	+	0.0446244i
$377$	3.13068	+	1.01722i	0.161238	+	0.0523895i
$378$	6.37988	−	2.07295i	0.328146	−	0.106621i
$379$	−6.54508	+	4.75528i	−0.336198	+	0.244262i	−0.743056	−	0.669229i	$-0.766624\pi$
$379$	−6.54508	+	4.75528i	−0.336198	+	0.244262i	0.406858	+	0.913492i	$0.366624\pi$
$380$		0			0
$381$	0.253289	+	0.779543i	0.0129764	+	0.0399372i
$382$	−22.8581	−	7.42705i	−1.16952	−	0.380001i
$383$	3.73871	−	5.14590i	0.191039	−	0.262943i	−0.702743	−	0.711444i	$-0.748042\pi$
$383$	3.73871	−	5.14590i	0.191039	−	0.262943i	0.893783	+	0.448500i	$0.148042\pi$
$384$	−0.381966			−0.0194921
$385$		0			0
$386$	−1.85410			−0.0943713
$387$	17.9641	−	24.7254i	0.913165	−	1.25686i
$388$	−0.898056	−	0.291796i	−0.0455919	−	0.0148137i
$389$	7.92705	+	24.3970i	0.401917	+	1.23697i	0.923442	+	0.383738i	$0.125364\pi$
$389$	7.92705	+	24.3970i	0.401917	+	1.23697i	−0.521524	+	0.853236i	$0.674636\pi$
$390$		0			0
$391$	6.57295	−	4.77553i	0.332408	−	0.241509i
$392$	1.90211	−	0.618034i	0.0960712	−	0.0312154i
$393$	−7.46969	−	2.42705i	−0.376796	−	0.122429i
$394$	−3.85410	−	2.80017i	−0.194167	−	0.141070i
$395$		0			0
$396$	−7.26393	−	6.06961i	−0.365026	−	0.305009i
$397$		−	6.41641i		−	0.322030i	−0.986952	−	0.161015i	$-0.948523\pi$
$397$		−	6.41641i		−	0.322030i	0.986952	−	0.161015i	$-0.0514768\pi$
$398$	−2.31838	+	3.19098i	−0.116210	+	0.159950i
$399$	2.07295	−	6.37988i	0.103777	−	0.319394i
$400$		0			0
$401$	12.4894	−	9.07405i	0.623689	−	0.453136i	−0.230519	−	0.973068i	$-0.574042\pi$
$401$	12.4894	−	9.07405i	0.623689	−	0.453136i	0.854208	+	0.519931i	$0.174042\pi$
$402$	−0.0202444	−	0.0278640i	−0.00100970	−	0.00138973i
$403$	17.7926	−	5.78115i	0.886311	−	0.287980i
$404$	−4.07295	+	12.5352i	−0.202637	+	0.623652i
$405$		0			0
$406$	−1.58359			−0.0785924
$407$	−2.37139	+	34.9508i	−0.117545	+	1.73245i
$408$			1.67376i			0.0828636i
$409$	−16.4443	−	11.9475i	−0.813117	−	0.590764i	0.101616	−	0.994824i	$-0.467599\pi$
$409$	−16.4443	−	11.9475i	−0.813117	−	0.590764i	−0.914733	+	0.404060i	$0.867599\pi$
$410$		0			0
$411$	−0.375388	−	1.15533i	−0.0185165	−	0.0569880i
$412$	0.416272	+	0.572949i	0.0205082	+	0.0282272i
$413$	11.8290	+	16.2812i	0.582065	+	0.801143i
$414$	−1.63525	−	5.03280i	−0.0803684	−	0.247348i
$415$		0			0
$416$	−5.04508	−	3.66547i	−0.247356	−	0.179714i
$417$			3.09017i			0.151326i
$418$	−18.8294	+	4.73607i	−0.920975	+	0.231649i
$419$	23.9443			1.16975			0.584877	−	0.811122i	$-0.301143\pi$
$419$	23.9443			1.16975			0.584877	+	0.811122i	$0.301143\pi$
$420$		0			0
$421$	−1.39261	+	4.28601i	−0.0678716	+	0.208887i	−0.979240	−	0.202704i	$-0.935027\pi$
$421$	−1.39261	+	4.28601i	−0.0678716	+	0.208887i	0.911368	+	0.411592i	$0.135027\pi$
$422$	−25.9358	+	8.42705i	−1.26253	+	0.410222i
$423$	−2.46965	−	3.39919i	−0.120079	−	0.165274i
$424$	4.35410	−	3.16344i	0.211454	−	0.153630i
$425$		0			0
$426$	−1.57295	+	4.84104i	−0.0762096	+	0.234549i
$427$	−15.3557	+	21.1353i	−0.743113	+	1.02281i
$428$			0.763932i			0.0369260i
$429$	1.92705	+	7.66145i	0.0930389	+	0.369898i
$430$		0			0
$431$	−19.6074	−	14.2456i	−0.944455	−	0.686187i	0.00503407	−	0.999987i	$-0.498398\pi$
$431$	−19.6074	−	14.2456i	−0.944455	−	0.686187i	−0.949489	+	0.313801i	$0.898398\pi$
$432$	2.12663	+	0.690983i	0.102317	+	0.0332449i
$433$	10.9637	−	3.56231i	0.526879	−	0.171193i	−0.0334857	−	0.999439i	$-0.510661\pi$
$433$	10.9637	−	3.56231i	0.526879	−	0.171193i	0.560365	+	0.828246i	$0.310661\pi$
$434$	−7.28115	+	5.29007i	−0.349507	+	0.253931i
$435$		0			0
$436$	−2.82624	−	8.69827i	−0.135352	−	0.416571i
$437$	−10.3229	−	3.35410i	−0.493810	−	0.160448i
$438$	2.59590	−	3.57295i	0.124037	−	0.170722i
$439$	3.94427			0.188250			0.0941249	−	0.995560i	$-0.469995\pi$
$439$	3.94427			0.188250			0.0941249	+	0.995560i	$0.469995\pi$
$440$		0			0
$441$	−5.70820			−0.271819
$442$	−16.0620	+	22.1074i	−0.763990	+	1.05154i
$443$	−16.5312	−	5.37132i	−0.785423	−	0.255199i	−0.111269	−	0.993790i	$-0.535491\pi$
$443$	−16.5312	−	5.37132i	−0.785423	−	0.255199i	−0.674154	+	0.738591i	$0.735491\pi$
$444$	−1.24671	−	3.83698i	−0.0591663	−	0.182095i
$445$		0			0
$446$	−16.7533	+	12.1720i	−0.793291	+	0.576360i
$447$	−7.69421	+	2.50000i	−0.363924	+	0.118246i
$448$	2.85317	+	0.927051i	0.134800	+	0.0437990i
$449$	−21.1803	−	15.3884i	−0.999562	−	0.726224i	−0.0375678	−	0.999294i	$-0.511961\pi$
$449$	−21.1803	−	15.3884i	−0.999562	−	0.726224i	−0.961994	+	0.273070i	$0.911961\pi$
$450$		0			0
$451$	9.43769	+	7.88597i	0.444404	+	0.371336i
$452$			3.76393i			0.177040i
$453$	4.51052	−	6.20820i	0.211923	−	0.291687i
$454$	−5.66312	+	17.4293i	−0.265783	+	0.817997i
$455$		0			0
$456$	1.80902	−	1.31433i	0.0847150	−	0.0615490i
$457$	−3.73098	−	5.13525i	−0.174528	−	0.240217i	0.712788	−	0.701380i	$-0.247432\pi$
$457$	−3.73098	−	5.13525i	−0.174528	−	0.240217i	−0.887315	+	0.461163i	$0.847432\pi$
$458$	−0.502029	+	0.163119i	−0.0234583	+	0.00762205i
$459$	3.02786	−	9.31881i	0.141329	−	0.434965i
$460$		0			0
$461$	−7.47214			−0.348012			−0.174006	−	0.984745i	$-0.555671\pi$
$461$	−7.47214			−0.348012			−0.174006	+	0.984745i	$0.555671\pi$
$462$	−2.02063	−	3.21885i	−0.0940080	−	0.149754i
$463$		−	4.41641i		−	0.205248i	−0.994720	−	0.102624i	$-0.967276\pi$
$463$		−	4.41641i		−	0.205248i	0.994720	−	0.102624i	$-0.0327238\pi$
$464$	−0.427051	−	0.310271i	−0.0198253	−	0.0144040i
$465$		0			0
$466$	4.75329	+	14.6291i	0.220192	+	0.677681i
$467$	8.95554	+	12.3262i	0.414413	+	0.570390i	0.964288	−	0.264857i	$-0.0853247\pi$
$467$	8.95554	+	12.3262i	0.414413	+	0.570390i	−0.549875	+	0.835247i	$0.685325\pi$
$468$	10.4616	+	14.3992i	0.483589	+	0.665603i
$469$	0.0835921	+	0.257270i	0.00385993	+	0.0118796i
$470$		0			0
$471$	−6.09017	−	4.42477i	−0.280620	−	0.203883i
$472$			6.70820i			0.308770i
$473$	−32.9565	−	13.2361i	−1.51534	−	0.608595i
$474$	2.96556			0.136213
$475$		0			0
$476$	4.06231	−	12.5025i	0.186195	−	0.573051i
$477$	−14.6089	+	4.74671i	−0.668894	+	0.217337i
$478$	−9.20029	−	12.6631i	−0.420812	−	0.579198i
$479$	−20.7533	+	15.0781i	−0.948242	+	0.688938i	−0.950390	−	0.311060i	$-0.899316\pi$
$479$	−20.7533	+	15.0781i	−0.948242	+	0.688938i	0.00214844	+	0.999998i	$0.499316\pi$
$480$		0			0
$481$	20.3541	−	62.6435i	0.928067	−	2.85630i
$482$	10.5801	−	14.5623i	0.481912	−	0.663295i
$483$		−	2.12461i		−	0.0966732i
$484$	−4.78115	+	9.90659i	−0.217325	+	0.450300i
$485$		0			0
$486$	−7.80902	−	5.67358i	−0.354224	−	0.257359i
$487$	8.28199	+	2.69098i	0.375293	+	0.121940i	0.490589	−	0.871391i	$-0.336782\pi$
$487$	8.28199	+	2.69098i	0.375293	+	0.121940i	−0.115296	+	0.993331i	$0.536782\pi$
$488$	−8.28199	+	2.69098i	−0.374908	+	0.121815i
$489$	−3.76393	+	2.73466i	−0.170211	+	0.123665i
$490$		0			0
$491$	−8.52786	−	26.2461i	−0.384857	−	1.18447i	−0.936584	−	0.350443i	$-0.886031\pi$
$491$	−8.52786	−	26.2461i	−0.384857	−	1.18447i	0.551727	−	0.834025i	$-0.313969\pi$
$492$	−1.34708	−	0.437694i	−0.0607312	−	0.0197328i
$493$	−1.35960	+	1.87132i	−0.0612331	+	0.0842801i
$494$	36.5066			1.64251
$495$		0			0
$496$	−3.00000			−0.134704
$497$	23.4989	−	32.3435i	1.05407	−	1.45080i
$498$	−1.36733	−	0.444272i	−0.0612714	−	0.0199083i
$499$	−7.46149	−	22.9641i	−0.334022	−	1.02801i	−0.967202	−	0.254010i	$-0.918250\pi$
$499$	−7.46149	−	22.9641i	−0.334022	−	1.02801i	0.633179	−	0.774005i	$-0.281750\pi$
$500$		0			0
$501$	1.83688	−	1.33457i	0.0820658	−	0.0596243i
$502$	−13.7966	+	4.48278i	−0.615771	+	0.200076i
$503$	−8.52675	−	2.77051i	−0.380189	−	0.123531i	0.112687	−	0.993631i	$-0.464054\pi$
$503$	−8.52675	−	2.77051i	−0.380189	−	0.123531i	−0.492876	+	0.870100i	$0.664054\pi$
$504$	−6.92705	−	5.03280i	−0.308555	−	0.224179i
$505$		0			0
$506$	−5.20820	+	3.26944i	−0.231533	+	0.145344i
$507$		−	9.88854i		−	0.439166i
$508$	1.26133	−	1.73607i	0.0559623	−	0.0770256i
$509$	0.0623059	−	0.191758i	0.00276166	−	0.00849952i	−0.949666	−	0.313264i	$-0.898578\pi$
$509$	0.0623059	−	0.191758i	0.00276166	−	0.00849952i	0.952428	+	0.304764i	$0.0985776\pi$
$510$		0			0
$511$	−28.0623	+	20.3885i	−1.24140	+	0.901932i
$512$	0.587785	+	0.809017i	0.0259767	+	0.0357538i
$513$	−12.4495	+	4.04508i	−0.549658	+	0.178595i
$514$	−9.80902	+	30.1891i	−0.432657	+	1.33158i
$515$		0			0
$516$	4.09017			0.180060
$517$	−3.13068	+	3.74671i	−0.137687	+	0.164780i
$518$			31.6869i			1.39224i
$519$	−2.64590	−	1.92236i	−0.116142	−	0.0843821i
$520$		0			0
$521$	−5.46149	−	16.8087i	−0.239272	−	0.736405i	−0.996526	−	0.0832835i	$-0.973459\pi$
$521$	−5.46149	−	16.8087i	−0.239272	−	0.736405i	0.757254	−	0.653121i	$-0.226541\pi$
$522$	0.885544	+	1.21885i	0.0387592	+	0.0533475i
$523$	2.02063	+	2.78115i	0.0883558	+	0.121611i	0.850907	−	0.525317i	$-0.176053\pi$
$523$	2.02063	+	2.78115i	0.0883558	+	0.121611i	−0.762551	+	0.646928i	$0.776053\pi$
$524$	6.35410	+	19.5559i	0.277580	+	0.854304i
$525$		0			0
$526$	−8.92705	−	6.48588i	−0.389238	−	0.282798i
$527$			13.1459i			0.572644i
$528$	0.0857567	−	1.26393i	0.00373208	−	0.0550056i
$529$	19.5623			0.850535
$530$		0			0
$531$	5.91641	−	18.2088i	0.256750	−	0.790196i
$532$	−16.7027	+	5.42705i	−0.724156	+	0.235293i
$533$	−13.5923	−	18.7082i	−0.588748	−	0.810342i
$534$	3.45492	−	2.51014i	0.149509	−	0.108624i
$535$		0			0
$536$	−0.0278640	+	0.0857567i	−0.00120354	+	0.00370413i
$537$	−2.39163	+	3.29180i	−0.103206	+	0.142051i
$538$		−	18.0902i		−	0.779923i
$539$	1.61803	+	6.43288i	0.0696937	+	0.277084i
$540$		0			0
$541$	3.11803	+	2.26538i	0.134055	+	0.0973965i	0.652792	−	0.757537i	$-0.273598\pi$
$541$	3.11803	+	2.26538i	0.134055	+	0.0973965i	−0.518737	+	0.854934i	$0.673598\pi$
$542$	−15.4742	−	5.02786i	−0.664673	−	0.215965i
$543$	−4.35926	+	1.41641i	−0.187074	+	0.0607839i
$544$	3.54508	−	2.57565i	0.151994	−	0.110430i
$545$		0			0
$546$	2.20820	+	6.79615i	0.0945024	+	0.290848i
$547$	2.02063	+	0.656541i	0.0863957	+	0.0280717i	0.351896	−	0.936039i	$-0.385537\pi$
$547$	2.02063	+	0.656541i	0.0863957	+	0.0280717i	−0.265500	+	0.964111i	$0.585537\pi$
$548$	−1.86936	+	2.57295i	−0.0798550	+	0.109911i
$549$	24.8541			1.06075
$550$		0			0
$551$	3.09017			0.131646
$552$	0.416272	−	0.572949i	0.0177177	−	0.0243863i
$553$	−22.1518	−	7.19756i	−0.941991	−	0.306071i
$554$	−1.94427	−	5.98385i	−0.0826042	−	0.254230i
$555$		0			0
$556$	6.54508	−	4.75528i	0.277573	−	0.201669i
$557$	−0.898056	+	0.291796i	−0.0380519	+	0.0123638i	−0.327981	−	0.944684i	$-0.606368\pi$
$557$	−0.898056	+	0.291796i	−0.0380519	+	0.0123638i	0.289929	+	0.957048i	$0.406368\pi$
$558$	8.14324	+	2.64590i	0.344731	+	0.112010i
$559$	54.0238	+	39.2506i	2.28496	+	1.66012i
$560$		0			0
$561$	−5.53851	−	0.375783i	−0.233836	−	0.0158656i
$562$		−	18.1803i		−	0.766891i
$563$	−21.0418	+	28.9615i	−0.886804	+	1.22058i	0.0876852	+	0.996148i	$0.472053\pi$
$563$	−21.0418	+	28.9615i	−0.886804	+	1.22058i	−0.974489	+	0.224433i	$0.927947\pi$
$564$	0.173762	−	0.534785i	0.00731670	−	0.0225185i
$565$		0			0
$566$	14.8541	−	10.7921i	0.624364	−	0.453627i
$567$	13.5923	+	18.7082i	0.570823	+	0.785671i
$568$	12.6740	−	4.11803i	0.531789	−	0.172789i
$569$	12.8262	−	39.4751i	0.537704	−	1.65488i	−0.200029	−	0.979790i	$-0.564104\pi$
$569$	12.8262	−	39.4751i	0.537704	−	1.65488i	0.737733	−	0.675092i	$-0.235896\pi$
$570$		0			0
$571$	18.7082			0.782914			0.391457	−	0.920196i	$-0.371971\pi$
$571$	18.7082			0.782914			0.391457	+	0.920196i	$0.371971\pi$
$572$	13.2618	−	15.8713i	0.554503	−	0.663613i
$573$			9.18034i			0.383514i
$574$	9.00000	+	6.53888i	0.375653	+	0.272928i
$575$		0			0
$576$	−0.881966	−	2.71441i	−0.0367486	−	0.113101i
$577$	−16.8743	−	23.2254i	−0.702485	−	0.966887i	−0.999926	−	0.0121471i	$-0.996133\pi$
$577$	−16.8743	−	23.2254i	−0.702485	−	0.966887i	0.297442	−	0.954740i	$-0.403867\pi$
$578$	−1.29408	−	1.78115i	−0.0538268	−	0.0740862i
$579$	0.218847	+	0.673542i	0.00909497	+	0.0279914i
$580$		0			0
$581$	9.13525	+	6.63715i	0.378994	+	0.275355i
$582$			0.360680i			0.0149507i
$583$	9.49032	+	15.1180i	0.393049	+	0.626125i
$584$	−11.5623			−0.478452
$585$		0			0
$586$	−5.89919	+	18.1558i	−0.243693	+	0.750010i
$587$	21.0620	−	6.84346i	0.869322	−	0.282460i	0.159805	−	0.987149i	$-0.448913\pi$
$587$	21.0620	−	6.84346i	0.869322	−	0.282460i	0.709517	+	0.704689i	$0.248913\pi$
$588$	−0.449028	−	0.618034i	−0.0185176	−	0.0254873i
$589$	14.2082	−	10.3229i	0.585439	−	0.425346i
$590$		0			0
$591$	−0.562306	+	1.73060i	−0.0231302	+	0.0711874i
$592$	−6.20837	+	8.54508i	−0.255162	+	0.351201i
$593$			38.3951i			1.57670i	0.615228	+	0.788349i	$0.289064\pi$
$593$			38.3951i			1.57670i	−0.615228	+	0.788349i	$0.710936\pi$
$594$	−2.76393	+	6.88191i	−0.113406	+	0.282368i
$595$		0			0
$596$	17.1353	+	12.4495i	0.701887	+	0.509951i
$597$	1.43284	+	0.465558i	0.0586423	+	0.0190540i
$598$	10.9964	−	3.57295i	0.449676	−	0.146109i
$599$	7.23607	−	5.25731i	0.295658	−	0.214808i	−0.430060	−	0.902800i	$-0.641508\pi$
$599$	7.23607	−	5.25731i	0.295658	−	0.214808i	0.725718	+	0.687992i	$0.241508\pi$
$600$		0			0
$601$	−6.02786	−	18.5519i	−0.245882	−	0.756746i	−0.995490	−	0.0948646i	$-0.969758\pi$
$601$	−6.02786	−	18.5519i	−0.245882	−	0.756746i	0.749608	−	0.661881i	$-0.230242\pi$
$602$	−30.5523	−	9.92705i	−1.24522	−	0.404596i
$603$	0.151269	−	0.208204i	0.00616015	−	0.00847872i
$604$	−20.0902			−0.817457
$605$		0			0
$606$	5.03444			0.204510
$607$	−11.7759	+	16.2082i	−0.477971	+	0.657871i	−0.978113	−	0.208072i	$-0.933281\pi$
$607$	−11.7759	+	16.2082i	−0.477971	+	0.657871i	0.500142	+	0.865943i	$0.333281\pi$
$608$	−5.56758	−	1.80902i	−0.225795	−	0.0733653i
$609$	0.186918	+	0.575274i	0.00757429	+	0.0233113i
$610$		0			0
$611$	7.42705	−	5.39607i	0.300466	−	0.218302i
$612$	−11.8945	+	3.86475i	−0.480805	+	0.156223i
$613$	19.6947	+	6.39919i	0.795460	+	0.258461i	0.678428	−	0.734667i	$-0.262662\pi$
$613$	19.6947	+	6.39919i	0.795460	+	0.258461i	0.117033	+	0.993128i	$0.462662\pi$
$614$	−7.73607	−	5.62058i	−0.312202	−	0.226828i
$615$		0			0
$616$	−3.70820	+	9.23305i	−0.149408	+	0.372010i
$617$			48.6312i			1.95782i	0.204297	+	0.978909i	$0.434509\pi$
$617$			48.6312i			1.95782i	−0.204297	+	0.978909i	$0.565491\pi$
$618$	0.159002	−	0.218847i	0.00639599	−	0.00880332i
$619$	−9.83688	+	30.2748i	−0.395378	+	1.21685i	0.533289	+	0.845933i	$0.320956\pi$
$619$	−9.83688	+	30.2748i	−0.395378	+	1.21685i	−0.928667	+	0.370914i	$0.879044\pi$
$620$		0			0
$621$	−3.35410	+	2.43690i	−0.134595	+	0.0977893i
$622$	1.48584	+	2.04508i	0.0595768	+	0.0820004i
$623$	−31.8994	+	10.3647i	−1.27802	+	0.415255i
$624$	−0.736068	+	2.26538i	−0.0294663	+	0.0906880i
$625$		0			0
$626$	−19.9443			−0.797133
$627$	3.94298	+	6.28115i	0.157468	+	0.250845i
$628$			19.7082i			0.786443i
$629$	37.4443	+	27.2049i	1.49300	+	1.08473i
$630$		0			0
$631$	−6.12868	−	18.8621i	−0.243979	−	0.750889i	−0.995803	−	0.0915256i	$-0.970826\pi$
$631$	−6.12868	−	18.8621i	−0.243979	−	0.750889i	0.751824	−	0.659364i	$-0.229174\pi$
$632$	−4.56352	−	6.28115i	−0.181527	−	0.249851i
$633$	6.12261	+	8.42705i	0.243352	+	0.334945i
$634$	−9.80902	−	30.1891i	−0.389566	−	1.19896i
$635$		0			0
$636$	−1.66312	−	1.20833i	−0.0659470	−	0.0479133i
$637$		−	12.4721i		−	0.494164i
$638$	1.12257	−	1.34346i	0.0444430	−	0.0531880i
$639$	−38.0344			−1.50462
$640$		0			0
$641$	−8.52786	+	26.2461i	−0.336830	+	1.03666i	0.628983	+	0.777419i	$0.283471\pi$
$641$	−8.52786	+	26.2461i	−0.336830	+	1.03666i	−0.965813	+	0.259238i	$0.916529\pi$
$642$	0.277515	−	0.0901699i	0.0109526	−	0.00355872i
$643$	−8.53926	−	11.7533i	−0.336756	−	0.463504i	0.606735	−	0.794904i	$-0.292479\pi$
$643$	−8.53926	−	11.7533i	−0.336756	−	0.463504i	−0.943490	+	0.331400i	$0.892479\pi$
$644$	−4.50000	+	3.26944i	−0.177325	+	0.128834i
$645$		0			0
$646$	−7.92705	+	24.3970i	−0.311886	+	0.959885i
$647$	25.4540	−	35.0344i	1.00070	−	1.37735i	0.0758058	−	0.997123i	$-0.475847\pi$
$647$	25.4540	−	35.0344i	1.00070	−	1.37735i	0.924895	−	0.380223i	$-0.124153\pi$
$648$			7.70820i			0.302807i
$649$	−22.1976	−	1.50609i	−0.871330	−	0.0591190i
$650$		0			0
$651$	2.78115	+	2.02063i	0.109002	+	0.0791946i
$652$	11.5842	+	3.76393i	0.453672	+	0.147407i
$653$	−17.5680	+	5.70820i	−0.687491	+	0.223379i	−0.631872	−	0.775073i	$-0.717713\pi$
$653$	−17.5680	+	5.70820i	−0.687491	+	0.223379i	−0.0556188	+	0.998452i	$0.517713\pi$
$654$	−2.82624	+	2.05338i	−0.110515	+	0.0802936i
$655$		0			0
$656$	1.14590	+	3.52671i	0.0447398	+	0.137695i
$657$	31.3849	+	10.1976i	1.22444	+	0.397845i
$658$	−2.59590	+	3.57295i	−0.101199	+	0.139288i
$659$	−45.4508			−1.77051			−0.885257	−	0.465102i	$-0.846017\pi$
$659$	−45.4508			−1.77051			−0.885257	+	0.465102i	$0.846017\pi$
$660$		0			0
$661$	30.2918			1.17821			0.589107	−	0.808055i	$-0.299480\pi$
$661$	30.2918			1.17821			0.589107	+	0.808055i	$0.299480\pi$
$662$	−7.05342	+	9.70820i	−0.274139	+	0.377320i
$663$	9.92684	+	3.22542i	0.385526	+	0.125265i
$664$	1.16312	+	3.57971i	0.0451378	+	0.138920i
$665$		0			0
$666$	24.3885	−	17.7193i	0.945037	−	0.686609i
$667$	0.930812	−	0.302439i	0.0360412	−	0.0117105i
$668$	−5.65334	−	1.83688i	−0.218734	−	0.0710711i
$669$	6.39919	+	4.64928i	0.247407	+	0.179752i
$670$		0			0
$671$	−7.04508	−	28.0094i	−0.271972	−	1.08129i
$672$		−	1.14590i		−	0.0442040i
$673$	−14.3516	+	19.7533i	−0.553214	+	0.761433i	−0.990444	−	0.137916i	$-0.955960\pi$
$673$	−14.3516	+	19.7533i	−0.553214	+	0.761433i	0.437230	+	0.899350i	$0.355960\pi$
$674$	−0.399187	+	1.22857i	−0.0153761	+	0.0473228i
$675$		0			0
$676$	−20.9443	+	15.2169i	−0.805549	+	0.585266i
$677$	−7.05342	−	9.70820i	−0.271085	−	0.373117i	0.651671	−	0.758502i	$-0.274068\pi$
$677$	−7.05342	−	9.70820i	−0.271085	−	0.373117i	−0.922756	+	0.385386i	$0.874068\pi$
$678$	1.36733	−	0.444272i	0.0525119	−	0.0170622i
$679$	0.875388	−	2.69417i	0.0335943	−	0.103393i
$680$		0			0
$681$	7.00000			0.268241
$682$	0.673542	−	9.92705i	0.0257913	−	0.380126i
$683$		−	33.8885i		−	1.29671i	−0.761339	−	0.648355i	$-0.775457\pi$
$683$		−	33.8885i		−	1.29671i	0.761339	−	0.648355i	$-0.224543\pi$
$684$	13.5172	+	9.82084i	0.516844	+	0.375509i
$685$		0			0
$686$	−4.63525	−	14.2658i	−0.176975	−	0.544673i
$687$	0.118513	+	0.163119i	0.00452155	+	0.00622338i
$688$	−6.29412	−	8.66312i	−0.239961	−	0.330278i
$689$	−10.3713	−	31.9196i	−0.395116	−	1.21604i
$690$		0			0
$691$	0.0278640	+	0.0202444i	0.00106000	+	0.000770134i	0.588315	−	0.808632i	$-0.299791\pi$
$691$	0.0278640	+	0.0202444i	0.00106000	+	0.000770134i	−0.587255	+	0.809402i	$0.699791\pi$
$692$			8.56231i			0.325490i
$693$	18.2088	−	21.7918i	0.691696	−	0.827802i
$694$	14.5623			0.552778
$695$		0			0
$696$	−0.0623059	+	0.191758i	−0.00236170	+	0.00726856i
$697$	15.4539	−	5.02129i	0.585359	−	0.190195i
$698$	4.25325	+	5.85410i	0.160988	+	0.221581i
$699$	4.75329	−	3.45347i	0.179786	−	0.130622i
$700$		0			0
$701$	−4.07953	+	12.5555i	−0.154082	+	0.474214i	−0.998067	−	0.0621522i	$-0.980204\pi$
$701$	−4.07953	+	12.5555i	−0.154082	+	0.474214i	0.843985	+	0.536367i	$0.180204\pi$
$702$	8.19624	−	11.2812i	0.309347	−	0.425780i
$703$		−	61.8328i		−	2.33207i
$704$	−2.80902	+	1.76336i	−0.105869	+	0.0664590i
$705$		0			0
$706$	19.0623	+	13.8496i	0.717419	+	0.521236i
$707$	−37.6057	−	12.2188i	−1.41431	−	0.459537i
$708$	2.43690	−	0.791796i	0.0915842	−	0.0297575i
$709$	−5.42705	+	3.94298i	−0.203817	+	0.148082i	−0.685012	−	0.728532i	$-0.740203\pi$
$709$	−5.42705	+	3.94298i	−0.203817	+	0.148082i	0.481195	+	0.876614i	$0.340203\pi$
$710$		0			0
$711$	6.84752	+	21.0745i	0.256802	+	0.790356i
$712$	−10.6331	−	3.45492i	−0.398494	−	0.129478i
$713$	3.26944	−	4.50000i	0.122442	−	0.168526i
$714$	−5.02129			−0.187917
$715$		0			0
$716$	10.6525			0.398102
$717$	−3.51420	+	4.83688i	−0.131240	+	0.180637i
$718$	8.50651	+	2.76393i	0.317460	+	0.103149i
$719$	−14.1074	−	43.4181i	−0.526117	−	1.61922i	−0.762097	−	0.647463i	$-0.775830\pi$
$719$	−14.1074	−	43.4181i	−0.526117	−	1.61922i	0.235980	−	0.971758i	$-0.424170\pi$
$720$		0			0
$721$	−1.71885	+	1.24882i	−0.0640132	+	0.0465083i
$722$	14.5231	−	4.71885i	0.540494	−	0.175617i
$723$	−6.53888	−	2.12461i	−0.243184	−	0.0790152i
$724$	9.70820	+	7.05342i	0.360803	+	0.262138i
$725$		0			0
$726$	4.16312	+	0.567541i	0.154508	+	0.0210634i
$727$			14.7639i			0.547564i	0.961792	+	0.273782i	$0.0882747\pi$
$727$			14.7639i			0.547564i	−0.961792	+	0.273782i	$0.911725\pi$
$728$	10.9964	−	15.1353i	0.407554	−	0.560950i
$729$	6.00658	−	18.4863i	0.222466	−	0.684679i
$730$		0			0
$731$	−37.9615	+	27.5806i	−1.40406	+	1.02011i
$732$	1.95511	+	2.69098i	0.0722631	+	0.0994616i
$733$	34.9771	−	11.3647i	1.29191	−	0.419766i	0.419149	−	0.907917i	$-0.362328\pi$
$733$	34.9771	−	11.3647i	1.29191	−	0.419766i	0.872759	+	0.488151i	$0.162328\pi$
$734$	−3.00000	+	9.23305i	−0.110732	+	0.340798i
$735$		0			0
$736$	−1.85410			−0.0683431
$737$	−0.277515	−	0.111456i	−0.0102224	−	0.00410554i
$738$		−	10.5836i		−	0.389587i
$739$	17.5623	+	12.7598i	0.646040	+	0.469375i	0.861920	−	0.507044i	$-0.169262\pi$
$739$	17.5623	+	12.7598i	0.646040	+	0.469375i	−0.215880	+	0.976420i	$0.569262\pi$
$740$		0			0
$741$	−4.30902	−	13.2618i	−0.158296	−	0.487184i
$742$	9.49032	+	13.0623i	0.348401	+	0.479532i
$743$	19.8459	+	27.3156i	0.728077	+	1.00211i	0.999217	+	0.0395720i	$0.0125994\pi$
$743$	19.8459	+	27.3156i	0.728077	+	1.00211i	−0.271140	+	0.962540i	$0.587401\pi$
$744$	0.354102	+	1.08981i	0.0129820	+	0.0399545i
$745$		0			0
$746$	−24.2533	−	17.6210i	−0.887976	−	0.645152i
$747$		−	10.7426i		−	0.393053i
$748$	7.72696	+	12.3090i	0.282526	+	0.450062i
$749$	−2.29180			−0.0837404
$750$		0			0
$751$	3.15654	−	9.71483i	0.115184	−	0.354499i	−0.876802	−	0.480853i	$-0.840327\pi$
$751$	3.15654	−	9.71483i	0.115184	−	0.354499i	0.991985	+	0.126353i	$0.0403272\pi$
$752$	−1.40008	+	0.454915i	−0.0510558	+	0.0165890i
$753$	3.25693	+	4.48278i	0.118689	+	0.163362i
$754$	−2.66312	+	1.93487i	−0.0969851	+	0.0704638i
$755$		0			0
$756$	−2.07295	+	6.37988i	−0.0753924	+	0.232034i
$757$	−9.07405	+	12.4894i	−0.329802	+	0.453933i	−0.941428	−	0.337213i	$-0.890516\pi$
$757$	−9.07405	+	12.4894i	−0.329802	+	0.453933i	0.611626	+	0.791147i	$0.290516\pi$
$758$		−	8.09017i		−	0.293848i
$759$	1.80244	+	1.50609i	0.0654244	+	0.0546674i
$760$		0			0
$761$	19.9894	+	14.5231i	0.724614	+	0.526463i	0.887855	−	0.460124i	$-0.152195\pi$
$761$	19.9894	+	14.5231i	0.724614	+	0.526463i	−0.163241	+	0.986586i	$0.552195\pi$
$762$	−0.779543	−	0.253289i	−0.0282399	−	0.00917569i
$763$	26.0948	−	8.47871i	0.944695	−	0.306950i
$764$	19.4443	−	14.1271i	0.703469	−	0.511100i
$765$		0			0
$766$	1.96556	+	6.04937i	0.0710185	+	0.218572i
$767$	39.7854	+	12.9271i	1.43657	+	0.466769i
$768$	0.224514	−	0.309017i	0.00810145	−	0.0111507i
$769$	−12.2361			−0.441244			−0.220622	−	0.975359i	$-0.570809\pi$
$769$	−12.2361			−0.441244			−0.220622	+	0.975359i	$0.570809\pi$
$770$		0			0
$771$	12.1246			0.436657
$772$	1.08981	−	1.50000i	0.0392233	−	0.0539862i
$773$	27.0786	+	8.79837i	0.973950	+	0.316456i	0.752409	−	0.658696i	$-0.228892\pi$
$773$	27.0786	+	8.79837i	0.973950	+	0.316456i	0.221540	+	0.975151i	$0.428892\pi$
$774$	9.44427	+	29.0665i	0.339467	+	1.04477i
$775$		0			0
$776$	0.763932	−	0.555029i	0.0274236	−	0.0199244i
$777$	11.5109	−	3.74013i	0.412953	−	0.134177i
$778$	−24.3970	−	7.92705i	−0.874673	−	0.284199i
$779$	−17.5623	−	12.7598i	−0.629235	−	0.457166i
$780$		0			0
$781$	10.7812	+	42.8631i	0.385780	+	1.53376i
$782$			8.12461i			0.290536i
$783$	0.693786	−	0.954915i	0.0247939	−	0.0341259i
$784$	−0.618034	+	1.90211i	−0.0220726	+	0.0679326i
$785$		0			0
$786$	6.35410	−	4.61653i	0.226643	−	0.164666i
$787$	−14.9394	−	20.5623i	−0.532532	−	0.732967i	0.454982	−	0.890501i	$-0.349646\pi$
$787$	−14.9394	−	20.5623i	−0.532532	−	0.732967i	−0.987514	+	0.157534i	$0.949646\pi$
$788$	4.53077	−	1.47214i	0.161402	−	0.0524427i
$789$	−1.30244	+	4.00850i	−0.0463681	+	0.142706i
$790$		0			0
$791$	−11.2918			−0.401490
$792$	9.18005	−	2.30902i	0.326199	−	0.0820473i
$793$			54.3050i			1.92843i
$794$	5.19098	+	3.77147i	0.184221	+	0.133844i
$795$		0			0
$796$	−1.21885	−	3.75123i	−0.0432009	−	0.132959i
$797$	−11.6169	−	15.9894i	−0.411493	−	0.566372i	0.552088	−	0.833786i	$-0.313831\pi$
$797$	−11.6169	−	15.9894i	−0.411493	−	0.566372i	−0.963582	+	0.267413i	$0.913831\pi$
$798$	3.94298	+	5.42705i	0.139580	+	0.192116i
$799$	1.99342	+	6.13512i	0.0705222	+	0.217045i
$800$		0			0
$801$	25.8156	+	18.7561i	0.912149	+	0.662715i
$802$			15.4377i			0.545124i
$803$	2.59590	−	38.2599i	0.0916073	−	1.35016i
$804$	0.0344419			0.00121467
$805$		0			0
$806$	−5.78115	+	17.7926i	−0.203632	+	0.626716i
$807$	−6.57164	+	2.13525i	−0.231333	+	0.0751645i
$808$	−7.74721	−	10.6631i	−0.272546	−	0.375127i
$809$	15.2254	−	11.0619i	0.535297	−	0.388916i	−0.287038	−	0.957919i	$-0.592671\pi$
$809$	15.2254	−	11.0619i	0.535297	−	0.388916i	0.822336	+	0.569003i	$0.192671\pi$
$810$		0			0
$811$	−13.3647	+	41.1325i	−0.469300	+	1.44436i	0.384194	+	0.923252i	$0.374479\pi$
$811$	−13.3647	+	41.1325i	−0.469300	+	1.44436i	−0.853494	+	0.521103i	$0.825521\pi$
$812$	0.930812	−	1.28115i	0.0326651	−	0.0449597i
$813$			6.21478i			0.217962i
$814$	−26.8820	−	22.4621i	−0.942212	−	0.787296i
$815$		0			0
$816$	−1.35410	−	0.983813i	−0.0474031	−	0.0344403i
$817$	59.6188	+	19.3713i	2.08580	+	0.677717i
$818$	19.3314	−	6.28115i	0.675907	−	0.219615i
$819$	−43.1976	+	31.3849i	−1.50944	+	1.09668i
$820$		0			0
$821$	9.07295	+	27.9237i	0.316648	+	0.974543i	0.975071	+	0.221894i	$0.0712240\pi$
$821$	9.07295	+	27.9237i	0.316648	+	0.974543i	−0.658423	+	0.752648i	$0.728776\pi$
$822$	1.15533	+	0.375388i	0.0402966	+	0.0130932i
$823$	23.8092	−	32.7705i	0.829935	−	1.14231i	−0.158000	−	0.987439i	$-0.550504\pi$
$823$	23.8092	−	32.7705i	0.829935	−	1.14231i	0.987935	−	0.154869i	$-0.0494955\pi$
$824$	−0.708204			−0.0246715
$825$		0			0
$826$	−20.1246			−0.700225
$827$	8.75127	−	12.0451i	0.304311	−	0.418849i	−0.629285	−	0.777174i	$-0.716652\pi$
$827$	8.75127	−	12.0451i	0.304311	−	0.418849i	0.933597	+	0.358326i	$0.116652\pi$
$828$	5.03280	+	1.63525i	0.174902	+	0.0568290i
$829$	−1.50658	−	4.63677i	−0.0523256	−	0.161042i	0.921479	−	0.388428i	$-0.126982\pi$
$829$	−1.50658	−	4.63677i	−0.0523256	−	0.161042i	−0.973805	+	0.227387i	$0.926982\pi$
$830$		0			0
$831$	−1.94427	+	1.41260i	−0.0674460	+	0.0490024i
$832$	5.93085	−	1.92705i	0.205615	−	0.0668085i
$833$	8.33499	+	2.70820i	0.288790	+	0.0938337i
$834$	−2.50000	−	1.81636i	−0.0865679	−	0.0628953i
$835$		0			0
$836$	7.23607	−	18.0171i	0.250265	−	0.623134i
$837$		−	6.70820i		−	0.231869i
$838$	−14.0741	+	19.3713i	−0.486181	+	0.669171i
$839$	15.1631	−	46.6673i	0.523489	−	1.61113i	−0.243796	−	0.969827i	$-0.578393\pi$
$839$	15.1631	−	46.6673i	0.523489	−	1.61113i	0.767285	−	0.641307i	$-0.221607\pi$
$840$		0			0
$841$	23.2361	−	16.8820i	0.801244	−	0.582138i
$842$	−2.64890	−	3.64590i	−0.0912871	−	0.125646i
$843$	−6.60440	+	2.14590i	−0.227467	+	0.0739087i
$844$	8.42705	−	25.9358i	0.290071	−	0.892747i
$845$		0			0
$846$	4.20163			0.144455
$847$	−29.7198	−	14.3435i	−1.02118	−	0.492847i
$848$			5.38197i			0.184817i
$849$	−5.67376	−	4.12223i	−0.194723	−	0.141475i
$850$		0			0
$851$	−6.05166	−	18.6251i	−0.207448	−	0.638460i
$852$	−2.99193	−	4.11803i	−0.102502	−	0.141082i
$853$	−9.23305	−	12.7082i	−0.316134	−	0.435121i	0.621148	−	0.783693i	$-0.286667\pi$
$853$	−9.23305	−	12.7082i	−0.316134	−	0.435121i	−0.937282	+	0.348573i	$0.886667\pi$
$854$	−8.07295	−	24.8460i	−0.276251	−	0.850212i
$855$		0			0
$856$	−0.618034	−	0.449028i	−0.0211240	−	0.0153475i
$857$		−	41.3394i		−	1.41213i	−0.708149	−	0.706063i	$-0.750469\pi$
$857$		−	41.3394i		−	1.41213i	0.708149	−	0.706063i	$-0.249531\pi$
$858$	−7.33094	−	2.94427i	−0.250274	−	0.100516i
$859$	6.30495			0.215122			0.107561	−	0.994198i	$-0.465696\pi$
$859$	6.30495			0.215122			0.107561	+	0.994198i	$0.465696\pi$
$860$		0			0
$861$	1.31308	−	4.04125i	0.0447497	−	0.137725i
$862$	23.0499	−	7.48936i	0.785082	−	0.255089i
$863$	−8.30224	−	11.4271i	−0.282611	−	0.388981i	0.643985	−	0.765038i	$-0.277280\pi$
$863$	−8.30224	−	11.4271i	−0.282611	−	0.388981i	−0.926597	+	0.376057i	$0.877280\pi$
$864$	−1.80902	+	1.31433i	−0.0615440	+	0.0447143i
$865$		0			0
$866$	−3.56231	+	10.9637i	−0.121052	+	0.372560i
$867$	−0.494296	+	0.680340i	−0.0167872	+	0.0231056i
$868$		−	9.00000i		−	0.305480i
$869$	21.8090	−	13.6906i	0.739820	−	0.464421i
$870$		0			0
$871$	0.454915	+	0.330515i	0.0154142	+	0.0111991i
$872$	8.69827	+	2.82624i	0.294560	+	0.0957085i
$873$	−2.56314	+	0.832816i	−0.0867493	+	0.0281865i
$874$	8.78115	−	6.37988i	0.297027	−	0.215803i
$875$		0			0
$876$	1.36475	+	4.20025i	0.0461105	+	0.141913i
$877$	20.9232	+	6.79837i	0.706528	+	0.229565i	0.640172	−	0.768231i	$-0.278863\pi$
$877$	20.9232	+	6.79837i	0.706528	+	0.229565i	0.0663553	+	0.997796i	$0.478863\pi$
$878$	−2.31838	+	3.19098i	−0.0782417	+	0.107690i
$879$	7.29180			0.245946
$880$		0			0
$881$	−42.7984			−1.44191			−0.720957	−	0.692980i	$-0.756297\pi$
$881$	−42.7984			−1.44191			−0.720957	+	0.692980i	$0.756297\pi$
$882$	3.35520	−	4.61803i	0.112975	−	0.155497i
$883$	46.0997	+	14.9787i	1.55138	+	0.504074i	0.954488	−	0.298248i	$-0.0964023\pi$
$883$	46.0997	+	14.9787i	1.55138	+	0.504074i	0.596891	+	0.802322i	$0.296402\pi$
$884$	−8.44427	−	25.9888i	−0.284012	−	0.874098i
$885$		0			0
$886$	14.0623	−	10.2169i	0.472432	−	0.343242i
$887$	−35.4994	+	11.5344i	−1.19195	+	0.387289i	−0.836794	−	0.547518i	$-0.815573\pi$
$887$	−35.4994	+	11.5344i	−1.19195	+	0.387289i	−0.355158	+	0.934806i	$0.615573\pi$
$888$	3.83698	+	1.24671i	0.128761	+	0.0418369i
$889$	5.20820	+	3.78398i	0.174678	+	0.126911i
$890$		0			0
$891$	−25.5066	−	1.73060i	−0.854503	−	0.0579773i
$892$		−	20.7082i		−	0.693362i
$893$	5.06555	−	6.97214i	0.169512	−	0.233314i
$894$	2.50000	−	7.69421i	0.0836125	−	0.257333i
$895$		0			0
$896$	−2.42705	+	1.76336i	−0.0810821	+	0.0589096i
$897$	−2.59590	−	3.57295i	−0.0866746	−	0.119297i
$898$	24.8990	−	8.09017i	0.830890	−	0.269972i
$899$	−0.489357	+	1.50609i	−0.0163210	+	0.0502308i
$900$		0			0
$901$	23.5836			0.785683
$902$	−11.9272	+	3.00000i	−0.397133	+	0.0998891i
$903$			12.2705i			0.408337i
$904$	−3.04508	−	2.21238i	−0.101278	−	0.0735828i
$905$		0			0
$906$	2.37132	+	7.29818i	0.0787819	+	0.242466i
$907$	24.7275	+	34.0344i	0.821062	+	1.13010i	0.989521	+	0.144386i	$0.0461208\pi$
$907$	24.7275	+	34.0344i	0.821062	+	1.13010i	−0.168459	+	0.985709i	$0.553879\pi$
$908$	−10.7719	−	14.8262i	−0.357478	−	0.492026i
$909$	11.6246	+	35.7769i	0.385564	+	1.18664i
$910$		0			0
$911$	43.8328	+	31.8464i	1.45225	+	1.05512i	0.985300	+	0.170833i	$0.0546457\pi$
$911$	43.8328	+	31.8464i	1.45225	+	1.05512i	0.466946	+	0.884286i	$0.345354\pi$
$912$			2.23607i			0.0740436i
$913$	−12.1065	+	3.04508i	−0.400665	+	0.100778i
$914$	6.34752			0.209957
$915$		0			0
$916$	0.163119	−	0.502029i	0.00538960	−	0.0165875i
$917$	−58.6677	+	19.0623i	−1.93738	+	0.629493i
$918$	5.75934	+	7.92705i	0.190087	+	0.261632i
$919$	−29.0066	+	21.0745i	−0.956839	+	0.695184i	−0.952414	−	0.304806i	$-0.901408\pi$
$919$	−29.0066	+	21.0745i	−0.956839	+	0.695184i	−0.00442432	+	0.999990i	$0.501408\pi$
$920$		0			0
$921$	−1.12868	+	3.47371i	−0.0371912	+	0.114463i
$922$	4.39201	−	6.04508i	0.144643	−	0.199084i
$923$		−	83.1033i		−	2.73538i
$924$	3.79180	+	0.257270i	0.124741	+	0.00846357i
$925$		0			0
$926$	3.57295	+	2.59590i	0.117414	+	0.0853065i
$927$	1.92236	+	0.624612i	0.0631385	+	0.0205149i
$928$	0.502029	−	0.163119i	0.0164799	−	0.00535464i
$929$	−4.47214	+	3.24920i	−0.146726	+	0.106603i	−0.658727	−	0.752382i	$-0.728905\pi$
$929$	−4.47214	+	3.24920i	−0.146726	+	0.106603i	0.512001	+	0.858985i	$0.328905\pi$
$930$		0			0
$931$	−3.61803	−	11.1352i	−0.118576	−	0.364940i
$932$	−14.6291	−	4.75329i	−0.479193	−	0.155699i
$933$	0.567541	−	0.781153i	0.0185805	−	0.0255738i
$934$	−15.2361			−0.498539
$935$		0			0
$936$	−17.7984			−0.581758
$937$	24.7602	−	34.0795i	0.808881	−	1.11333i	−0.182614	−	0.983185i	$-0.558456\pi$
$937$	24.7602	−	34.0795i	0.808881	−	1.11333i	0.991495	−	0.130145i	$-0.0415442\pi$
$938$	−0.257270	−	0.0835921i	−0.00840017	−	0.00272938i
$939$	2.35410	+	7.24518i	0.0768232	+	0.236438i
$940$		0			0
$941$	8.60739	−	6.25364i	0.280593	−	0.203863i	−0.438583	−	0.898691i	$-0.644519\pi$
$941$	8.60739	−	6.25364i	0.280593	−	0.203863i	0.719176	+	0.694828i	$0.244519\pi$
$942$	7.15942	−	2.32624i	0.233267	−	0.0757929i
$943$	−6.53888	−	2.12461i	−0.212935	−	0.0691869i
$944$	−5.42705	−	3.94298i	−0.176635	−	0.128333i
$945$		0			0
$946$	30.0795	−	18.8824i	0.977970	−	0.613919i
$947$			43.3050i			1.40722i	0.710585	+	0.703611i	$0.248430\pi$
$947$			43.3050i			1.40722i	−0.710585	+	0.703611i	$0.751570\pi$
$948$	−1.74311	+	2.39919i	−0.0566136	+	0.0779220i
$949$	−22.2812	+	68.5743i	−0.723277	+	2.22602i
$950$		0			0
$951$	−9.80902	+	7.12667i	−0.318079	+	0.231098i
$952$	7.72696	+	10.6353i	0.250432	+	0.344691i
$953$	−15.9434	+	5.18034i	−0.516459	+	0.167808i	−0.555638	−	0.831425i	$-0.687526\pi$
$953$	−15.9434	+	5.18034i	−0.516459	+	0.167808i	0.0391788	+	0.999232i	$0.487526\pi$
$954$	4.74671	−	14.6089i	0.153680	−	0.472980i
$955$		0			0
$956$	15.6525			0.506237
$957$	−0.620541	−	0.249224i	−0.0200593	−	0.00805625i
$958$		−	25.6525i		−	0.828794i
$959$	−7.71885	−	5.60807i	−0.249255	−	0.181094i
$960$		0			0
$961$	−6.79837	−	20.9232i	−0.219302	−	0.674943i
$962$	38.7158	+	53.2877i	1.24825	+	1.71807i
$963$	1.28157	+	1.76393i	0.0412981	+	0.0568419i
$964$	5.56231	+	17.1190i	0.179150	+	0.551366i
$965$		0			0
$966$	1.71885	+	1.24882i	0.0553030	+	0.0401800i
$967$			13.1803i			0.423851i	0.977286	+	0.211926i	$0.0679734\pi$
$967$			13.1803i			0.423851i	−0.977286	+	0.211926i	$0.932027\pi$
$968$	−5.20431	−	9.69098i	−0.167273	−	0.311480i
$969$	9.79837			0.314769
$970$		0			0
$971$	−12.7599	+	39.2708i	−0.409484	+	1.26026i	0.507609	+	0.861587i	$0.330529\pi$
$971$	−12.7599	+	39.2708i	−0.409484	+	1.26026i	−0.917093	+	0.398674i	$0.869471\pi$
$972$	9.18005	−	2.98278i	0.294450	−	0.0956727i
$973$	14.2658	+	19.6353i	0.457342	+	0.629477i
$974$	−7.04508	+	5.11855i	−0.225739	+	0.164009i
$975$		0			0
$976$	2.69098	−	8.28199i	0.0861363	−	0.265100i
$977$	5.31031	−	7.30902i	0.169892	−	0.233836i	−0.715578	−	0.698533i	$-0.753837\pi$
$977$	5.31031	−	7.30902i	0.169892	−	0.233836i	0.885470	+	0.464697i	$0.153837\pi$
$978$		−	4.65248i		−	0.148770i
$979$	13.8197	−	34.4095i	0.441678	−	1.09973i
$980$		0			0
$981$	−21.1180	−	15.3431i	−0.674247	−	0.489869i
$982$	26.2461	+	8.52786i	0.837546	+	0.272135i
$983$	−19.1926	+	6.23607i	−0.612150	+	0.198900i	−0.598652	−	0.801009i	$-0.704297\pi$
$983$	−19.1926	+	6.23607i	−0.612150	+	0.198900i	−0.0134983	+	0.999909i	$0.504297\pi$
$984$	1.14590	−	0.832544i	0.0365299	−	0.0265405i
$985$		0			0
$986$	−0.714782	−	2.19987i	−0.0227633	−	0.0700582i
$987$	1.60435	+	0.521286i	0.0510672	+	0.0165927i
$988$	−21.4580	+	29.5344i	−0.682671	+	0.939616i
$989$	19.8541			0.631324
$990$		0			0
$991$	−28.0000			−0.889449			−0.444725	−	0.895667i	$-0.646698\pi$
$991$	−28.0000			−0.889449			−0.444725	+	0.895667i	$0.646698\pi$
$992$	1.76336	−	2.42705i	0.0559866	−	0.0770589i
$993$	4.35926	+	1.41641i	0.138337	+	0.0449483i
$994$	12.3541	+	38.0220i	0.391848	+	1.20599i
$995$		0			0
$996$	1.16312	−	0.845055i	0.0368548	−	0.0267766i
$997$	−0.587785	+	0.190983i	−0.0186153	+	0.00604849i	−0.318310	−	0.947987i	$-0.603115\pi$
$997$	−0.587785	+	0.190983i	−0.0186153	+	0.00604849i	0.299695	+	0.954035i	$0.403115\pi$
$998$	22.9641	+	7.46149i	0.726916	+	0.236189i
$999$	−19.1074	−	13.8823i	−0.604531	−	0.439218i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	550.2.ba.d.499.1		8
5.2	odd	4		550.2.h.a.301.1	yes	4
5.3	odd	4		550.2.h.i.301.1	yes	4
5.4	even	2	inner	550.2.ba.d.499.2		8
11.3	even	5	inner	550.2.ba.d.399.2		8
55.3	odd	20		550.2.h.i.201.1	yes	4
55.14	even	10	inner	550.2.ba.d.399.1		8
55.17	even	20		6050.2.a.cg.1.1		2
55.27	odd	20		6050.2.a.cx.1.1		2
55.28	even	20		6050.2.a.cj.1.2		2
55.38	odd	20		6050.2.a.br.1.2		2
55.47	odd	20		550.2.h.a.201.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
550.2.h.a.201.1	✓	4	55.47	odd	20
550.2.h.a.301.1	yes	4	5.2	odd	4
550.2.h.i.201.1	yes	4	55.3	odd	20
550.2.h.i.301.1	yes	4	5.3	odd	4
550.2.ba.d.399.1		8	55.14	even	10	inner
550.2.ba.d.399.2		8	11.3	even	5	inner
550.2.ba.d.499.1		8	1.1	even	1	trivial
550.2.ba.d.499.2		8	5.4	even	2	inner
6050.2.a.br.1.2		2	55.38	odd	20
6050.2.a.cg.1.1		2	55.17	even	20
6050.2.a.cj.1.2		2	55.28	even	20
6050.2.a.cx.1.1		2	55.27	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.ba (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(0.363271 + 0.118034i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.309017 + 0.224514i) q^{6} +(2.85317 - 0.927051i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-2.30902 - 1.67760i) q^{9} +(-1.23607 + 3.07768i) q^{11} -0.381966i q^{12} +(3.66547 - 5.04508i) q^{13} +(-0.927051 + 2.85317i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(2.57565 + 3.54508i) q^{17} +(2.71441 - 0.881966i) q^{18} +(1.80902 - 5.56758i) q^{19} +1.14590 q^{21} +(-1.76336 - 2.80902i) q^{22} -1.85410i q^{23} +(0.309017 + 0.224514i) q^{24} +(1.92705 + 5.93085i) q^{26} +(-1.31433 - 1.80902i) q^{27} +(-1.76336 - 2.42705i) q^{28} +(0.163119 + 0.502029i) q^{29} +(2.42705 + 1.76336i) q^{31} -1.00000i q^{32} +(-0.812299 + 0.972136i) q^{33} -4.38197 q^{34} +(-0.881966 + 2.71441i) q^{36} +(10.0453 - 3.26393i) q^{37} +(3.44095 + 4.73607i) q^{38} +(1.92705 - 1.40008i) q^{39} +(1.14590 - 3.52671i) q^{41} +(-0.673542 + 0.927051i) q^{42} +10.7082i q^{43} +(3.30902 + 0.224514i) q^{44} +(1.50000 + 1.08981i) q^{46} +(1.40008 + 0.454915i) q^{47} +(-0.363271 + 0.118034i) q^{48} +(1.61803 - 1.17557i) q^{49} +(0.517221 + 1.59184i) q^{51} +(-5.93085 - 1.92705i) q^{52} +(3.16344 - 4.35410i) q^{53} +2.23607 q^{54} +3.00000 q^{56} +(1.31433 - 1.80902i) q^{57} +(-0.502029 - 0.163119i) q^{58} +(2.07295 + 6.37988i) q^{59} +(-7.04508 + 5.11855i) q^{61} +(-2.85317 + 0.927051i) q^{62} +(-8.14324 - 2.64590i) q^{63} +(0.809017 + 0.587785i) q^{64} +(-0.309017 - 1.22857i) q^{66} +0.0901699i q^{67} +(2.57565 - 3.54508i) q^{68} +(0.218847 - 0.673542i) q^{69} +(10.7812 - 7.83297i) q^{71} +(-1.67760 - 2.30902i) q^{72} +(-10.9964 + 3.57295i) q^{73} +(-3.26393 + 10.0453i) q^{74} -5.85410 q^{76} +(-0.673542 + 9.92705i) q^{77} +2.38197i q^{78} +(-6.28115 - 4.56352i) q^{79} +(2.38197 + 7.33094i) q^{81} +(2.17963 + 3.00000i) q^{82} +(2.21238 + 3.04508i) q^{83} +(-0.354102 - 1.08981i) q^{84} +(-8.66312 - 6.29412i) q^{86} +0.201626i q^{87} +(-2.12663 + 2.54508i) q^{88} -11.1803 q^{89} +(5.78115 - 17.7926i) q^{91} +(-1.76336 + 0.572949i) q^{92} +(0.673542 + 0.927051i) q^{93} +(-1.19098 + 0.865300i) q^{94} +(0.118034 - 0.363271i) q^{96} +(0.555029 - 0.763932i) q^{97} +2.00000i q^{98} +(8.01722 - 5.03280i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} + 2 q^{6} - 14 q^{9} + 8 q^{11} + 6 q^{14} - 2 q^{16} + 10 q^{19} + 36 q^{21} - 2 q^{24} + 2 q^{26} - 30 q^{29} + 6 q^{31} - 44 q^{34} - 16 q^{36} + 2 q^{39} + 36 q^{41} + 22 q^{44} + 12 q^{46}+ \cdots + 6 q^{99}+O(q^{100}) \) 8 * q + 2 * q^4 + 2 * q^6 - 14 * q^9 + 8 * q^11 + 6 * q^14 - 2 * q^16 + 10 * q^19 + 36 * q^21 - 2 * q^24 + 2 * q^26 - 30 * q^29 + 6 * q^31 - 44 * q^34 - 16 * q^36 + 2 * q^39 + 36 * q^41 + 22 * q^44 + 12 * q^46 + 4 * q^49 - 54 * q^51 + 24 * q^56 + 30 * q^59 - 34 * q^61 + 2 * q^64 + 2 * q^66 + 42 * q^69 + 46 * q^71 - 44 * q^74 - 20 * q^76 - 10 * q^79 + 28 * q^81 + 24 * q^84 - 38 * q^86 + 6 * q^91 - 14 * q^94 - 8 * q^96 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more