LMFDB - Embedded newform 264.2.k.b.155.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [264,2,Mod(155,264)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(264, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("264.155"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 264 = 2^{3} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	264.k (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.10805061336$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			155.5
Character	$\chi$	$=$	264.155
Dual form			264.2.k.b.155.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.26755 - 0.627142i) q^{2} +(1.64971 + 0.527693i) q^{3} +(1.21339 + 1.58987i) q^{4} +1.66805 q^{5} +(-1.76016 - 1.70348i) q^{6} -0.635429i q^{7} +(-0.540958 - 2.77621i) q^{8} +(2.44308 + 1.74108i) q^{9} +(-2.11434 - 1.04610i) q^{10} -1.00000i q^{11} +(1.16277 + 3.26312i) q^{12} +0.0696073i q^{13} +(-0.398504 + 0.805441i) q^{14} +(2.75179 + 0.880216i) q^{15} +(-1.05539 + 3.85826i) q^{16} +2.97439i q^{17} +(-2.00483 - 3.73907i) q^{18} -2.49500 q^{19} +(2.02398 + 2.65198i) q^{20} +(0.335311 - 1.04827i) q^{21} +(-0.627142 + 1.26755i) q^{22} +3.91504 q^{23} +(0.572565 - 4.86541i) q^{24} -2.21762 q^{25} +(0.0436536 - 0.0882310i) q^{26} +(3.11162 + 4.16147i) q^{27} +(1.01025 - 0.771021i) q^{28} +3.31887 q^{29} +(-2.93602 - 2.84148i) q^{30} -9.67793i q^{31} +(3.75743 - 4.22868i) q^{32} +(0.527693 - 1.64971i) q^{33} +(1.86537 - 3.77020i) q^{34} -1.05992i q^{35} +(0.196308 + 5.99679i) q^{36} +5.28989i q^{37} +(3.16255 + 1.56472i) q^{38} +(-0.0367313 + 0.114832i) q^{39} +(-0.902343 - 4.63085i) q^{40} -5.12939i q^{41} +(-1.08244 + 1.11846i) q^{42} -5.47572 q^{43} +(1.58987 - 1.21339i) q^{44} +(4.07517 + 2.90420i) q^{45} +(-4.96252 - 2.45528i) q^{46} -7.10838 q^{47} +(-3.77706 + 5.80809i) q^{48} +6.59623 q^{49} +(2.81096 + 1.39076i) q^{50} +(-1.56957 + 4.90688i) q^{51} +(-0.110667 + 0.0844605i) q^{52} -6.81429 q^{53} +(-1.33431 - 7.22631i) q^{54} -1.66805i q^{55} +(-1.76409 + 0.343741i) q^{56} +(-4.11603 - 1.31660i) q^{57} +(-4.20685 - 2.08140i) q^{58} -0.0187615i q^{59} +(1.93955 + 5.44304i) q^{60} +14.0256i q^{61} +(-6.06943 + 12.2673i) q^{62} +(1.10633 - 1.55240i) q^{63} +(-7.41473 + 3.00363i) q^{64} +0.116108i q^{65} +(-1.70348 + 1.76016i) q^{66} -9.82150 q^{67} +(-4.72890 + 3.60909i) q^{68} +(6.45867 + 2.06594i) q^{69} +(-0.664723 + 1.34351i) q^{70} -14.1364 q^{71} +(3.51200 - 7.72437i) q^{72} -3.15463 q^{73} +(3.31751 - 6.70522i) q^{74} +(-3.65844 - 1.17022i) q^{75} +(-3.02740 - 3.96674i) q^{76} -0.635429 q^{77} +(0.118575 - 0.122520i) q^{78} -16.2269i q^{79} +(-1.76043 + 6.43575i) q^{80} +(2.93728 + 8.50719i) q^{81} +(-3.21686 + 6.50178i) q^{82} +8.26737i q^{83} +(2.07348 - 0.738858i) q^{84} +4.96142i q^{85} +(6.94077 + 3.43405i) q^{86} +(5.47517 + 1.75134i) q^{87} +(-2.77621 + 0.540958i) q^{88} -9.87741i q^{89} +(-3.34415 - 6.23694i) q^{90} +0.0442305 q^{91} +(4.75045 + 6.22441i) q^{92} +(5.10698 - 15.9658i) q^{93} +(9.01025 + 4.45796i) q^{94} -4.16178 q^{95} +(8.43011 - 4.99331i) q^{96} +9.27138 q^{97} +(-8.36108 - 4.13677i) q^{98} +(1.74108 - 2.44308i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{3} + 2 q^{6} + 8 q^{9} + 12 q^{10} - 12 q^{12} + 2 q^{18} - 32 q^{19} + 4 q^{22} + 12 q^{24} - 64 q^{27} + 40 q^{28} - 22 q^{30} - 64 q^{34} - 20 q^{36} + 32 q^{40} + 20 q^{42} - 16 q^{43} - 28 q^{46}+ \cdots - 16 q^{97}+O(q^{100}) $ 32 * q + 8 * q^3 + 2 * q^6 + 8 * q^9 + 12 * q^10 - 12 * q^12 + 2 * q^18 - 32 * q^19 + 4 * q^22 + 12 * q^24 - 64 * q^27 + 40 * q^28 - 22 * q^30 - 64 * q^34 - 20 * q^36 + 32 * q^40 + 20 * q^42 - 16 * q^43 - 28 * q^46 - 32 * q^49 + 8 * q^51 + 40 * q^52 - 8 * q^54 + 16 * q^57 - 40 * q^58 + 68 * q^60 - 14 * q^66 + 8 * q^70 - 8 * q^72 + 64 * q^73 - 16 * q^75 + 8 * q^76 + 16 * q^78 + 72 * q^81 + 88 * q^82 - 60 * q^84 + 8 * q^88 - 58 * q^90 + 80 * q^91 - 72 * q^94 - 4 * q^96 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/264\mathbb{Z}\right)^\times$.

$n$	$89$	$133$	$145$	$199$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

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 $

$2$	−1.26755	−	0.627142i	−0.896296	−	0.443456i
$2$	−1.26755	−	0.627142i	−0.896296	−	0.443456i
$3$	1.64971	+	0.527693i	0.952460	+	0.304664i
$3$	1.64971	+	0.527693i	0.952460	+	0.304664i
$4$	1.21339	+	1.58987i	0.606693	+	0.794936i
$5$	1.66805			0.745973			0.372986	−	0.927837i	$-0.378334\pi$
$5$	1.66805			0.745973			0.372986	+	0.927837i	$0.378334\pi$
$6$	−1.76016	−	1.70348i	−0.718581	−	0.695443i
$7$		−	0.635429i		−	0.240170i	−0.992764	−	0.120085i	$-0.961683\pi$
$7$		−	0.635429i		−	0.240170i	0.992764	−	0.120085i	$-0.0383166\pi$
$8$	−0.540958	−	2.77621i	−0.191258	−	0.981540i
$9$	2.44308	+	1.74108i	0.814360	+	0.580360i
$10$	−2.11434	−	1.04610i	−0.668612	−	0.330806i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	1.16277	+	3.26312i	0.335663	+	0.941982i
$13$			0.0696073i			0.0193056i	0.999953	+	0.00965279i	$0.00307263\pi$
$13$			0.0696073i			0.0193056i	−0.999953	+	0.00965279i	$0.996927\pi$
$14$	−0.398504	+	0.805441i	−0.106505	+	0.215263i
$15$	2.75179	+	0.880216i	0.710509	+	0.227271i
$16$	−1.05539	+	3.85826i	−0.263846	+	0.964565i
$17$			2.97439i			0.721396i	0.932683	+	0.360698i	$0.117461\pi$
$17$			2.97439i			0.721396i	−0.932683	+	0.360698i	$0.882539\pi$
$18$	−2.00483	−	3.73907i	−0.472544	−	0.881307i
$19$	−2.49500			−0.572393			−0.286197	−	0.958171i	$-0.592391\pi$
$19$	−2.49500			−0.572393			−0.286197	+	0.958171i	$0.592391\pi$
$20$	2.02398	+	2.65198i	0.452577	+	0.593000i
$21$	0.335311	−	1.04827i	0.0731709	−	0.228752i
$22$	−0.627142	+	1.26755i	−0.133707	+	0.270243i
$23$	3.91504			0.816342			0.408171	−	0.912906i	$-0.366167\pi$
$23$	3.91504			0.816342			0.408171	+	0.912906i	$0.366167\pi$
$24$	0.572565	−	4.86541i	0.116874	−	0.993147i
$25$	−2.21762			−0.443525
$26$	0.0436536	−	0.0882310i	0.00856118	−	0.0173035i
$27$	3.11162	+	4.16147i	0.598831	+	0.800875i
$28$	1.01025	−	0.771021i	0.190919	−	0.145709i
$29$	3.31887			0.616299			0.308149	−	0.951338i	$-0.400290\pi$
$29$	3.31887			0.616299			0.308149	+	0.951338i	$0.400290\pi$
$30$	−2.93602	−	2.84148i	−0.536042	−	0.518781i
$31$		−	9.67793i		−	1.73821i	−0.494629	−	0.869104i	$-0.664696\pi$
$31$		−	9.67793i		−	1.73821i	0.494629	−	0.869104i	$-0.335304\pi$
$32$	3.75743	−	4.22868i	0.664227	−	0.747531i
$33$	0.527693	−	1.64971i	0.0918595	−	0.287177i
$34$	1.86537	−	3.77020i	0.319907	−	0.646584i
$35$		−	1.05992i		−	0.179160i
$36$	0.196308	+	5.99679i	0.0327179	+	0.999465i
$37$			5.28989i			0.869652i	0.900514	+	0.434826i	$0.143190\pi$
$37$			5.28989i			0.869652i	−0.900514	+	0.434826i	$0.856810\pi$
$38$	3.16255	+	1.56472i	0.513034	+	0.253831i
$39$	−0.0367313	+	0.114832i	−0.00588171	+	0.0183878i
$40$	−0.902343	−	4.63085i	−0.142673	−	0.732202i
$41$		−	5.12939i		−	0.801077i	−0.916280	−	0.400538i	$-0.868823\pi$
$41$		−	5.12939i		−	0.801077i	0.916280	−	0.400538i	$-0.131177\pi$
$42$	−1.08244	+	1.11846i	−0.167024	+	0.172581i
$43$	−5.47572			−0.835040			−0.417520	−	0.908668i	$-0.637101\pi$
$43$	−5.47572			−0.835040			−0.417520	+	0.908668i	$0.637101\pi$
$44$	1.58987	−	1.21339i	0.239682	−	0.182925i
$45$	4.07517	+	2.90420i	0.607490	+	0.432933i
$46$	−4.96252	−	2.45528i	−0.731684	−	0.362012i
$47$	−7.10838			−1.03686			−0.518432	−	0.855119i	$-0.673484\pi$
$47$	−7.10838			−1.03686			−0.518432	+	0.855119i	$0.673484\pi$
$48$	−3.77706	+	5.80809i	−0.545171	+	0.838325i
$49$	6.59623			0.942319
$50$	2.81096	+	1.39076i	0.397530	+	0.196684i
$51$	−1.56957	+	4.90688i	−0.219783	+	0.687101i
$52$	−0.110667	+	0.0844605i	−0.0153467	+	0.0117126i
$53$	−6.81429			−0.936015			−0.468008	−	0.883724i	$-0.655028\pi$
$53$	−6.81429			−0.936015			−0.468008	+	0.883724i	$0.655028\pi$
$54$	−1.33431	−	7.22631i	−0.181577	−	0.983377i
$55$		−	1.66805i		−	0.224919i
$56$	−1.76409	+	0.343741i	−0.235736	+	0.0459343i
$57$	−4.11603	−	1.31660i	−0.545181	−	0.174387i
$58$	−4.20685	−	2.08140i	−0.552386	−	0.273302i
$59$		−	0.0187615i		−	0.00244255i	−0.999999	−	0.00122127i	$-0.999611\pi$
$59$		−	0.0187615i		−	0.00244255i	0.999999	−	0.00122127i	$-0.000388743\pi$
$60$	1.93955	+	5.44304i	0.250395	+	0.702693i
$61$			14.0256i			1.79579i	0.440210	+	0.897895i	$0.354904\pi$
$61$			14.0256i			1.79579i	−0.440210	+	0.897895i	$0.645096\pi$
$62$	−6.06943	+	12.2673i	−0.770819	+	1.55795i
$63$	1.10633	−	1.55240i	0.139385	−	0.195585i
$64$	−7.41473	+	3.00363i	−0.926841	+	0.375454i
$65$			0.116108i			0.0144014i
$66$	−1.70348	+	1.76016i	−0.209684	+	0.216660i
$67$	−9.82150			−1.19989			−0.599944	−	0.800042i	$-0.704810\pi$
$67$	−9.82150			−1.19989			−0.599944	+	0.800042i	$0.704810\pi$
$68$	−4.72890	+	3.60909i	−0.573464	+	0.437666i
$69$	6.45867	+	2.06594i	0.777533	+	0.248710i
$70$	−0.664723	+	1.34351i	−0.0794496	+	0.160580i
$71$	−14.1364			−1.67769			−0.838843	−	0.544373i	$-0.816768\pi$
$71$	−14.1364			−1.67769			−0.838843	+	0.544373i	$0.816768\pi$
$72$	3.51200	−	7.72437i	0.413894	−	0.910325i
$73$	−3.15463			−0.369222			−0.184611	−	0.982812i	$-0.559102\pi$
$73$	−3.15463			−0.369222			−0.184611	+	0.982812i	$0.559102\pi$
$74$	3.31751	−	6.70522i	0.385653	−	0.779466i
$75$	−3.65844	−	1.17022i	−0.422440	−	0.135126i
$76$	−3.02740	−	3.96674i	−0.347267	−	0.455016i
$77$	−0.635429			−0.0724139
$78$	0.118575	−	0.122520i	0.0134259	−	0.0138726i
$79$		−	16.2269i		−	1.82567i	−0.408328	−	0.912835i	$-0.633888\pi$
$79$		−	16.2269i		−	1.82567i	0.408328	−	0.912835i	$-0.366112\pi$
$80$	−1.76043	+	6.43575i	−0.196822	+	0.719539i
$81$	2.93728	+	8.50719i	0.326365	+	0.945244i
$82$	−3.21686	+	6.50178i	−0.355242	+	0.718002i
$83$			8.26737i			0.907462i	0.891139	+	0.453731i	$0.149907\pi$
$83$			8.26737i			0.907462i	−0.891139	+	0.453731i	$0.850093\pi$
$84$	2.07348	−	0.738858i	0.226235	−	0.0806161i
$85$			4.96142i			0.538142i
$86$	6.94077	+	3.43405i	0.748443	+	0.370303i
$87$	5.47517	+	1.75134i	0.587000	+	0.187764i
$88$	−2.77621	+	0.540958i	−0.295945	+	0.0576663i
$89$		−	9.87741i		−	1.04700i	−0.852025	−	0.523502i	$-0.824625\pi$
$89$		−	9.87741i		−	1.04700i	0.852025	−	0.523502i	$-0.175375\pi$
$90$	−3.34415	−	6.23694i	−0.352505	−	0.657431i
$91$	0.0442305			0.00463661
$92$	4.75045	+	6.22441i	0.495269	+	0.648939i
$93$	5.10698	−	15.9658i	0.529569	−	1.65557i
$94$	9.01025	+	4.45796i	0.929337	+	0.459803i
$95$	−4.16178			−0.426989
$96$	8.43011	−	4.99331i	0.860395	−	0.509628i
$97$	9.27138			0.941366			0.470683	−	0.882302i	$-0.344008\pi$
$97$	9.27138			0.941366			0.470683	+	0.882302i	$0.344008\pi$
$98$	−8.36108	−	4.13677i	−0.844596	−	0.417877i
$99$	1.74108	−	2.44308i	0.174985	−	0.245539i
$100$	−2.69084	−	3.52574i	−0.269084	−	0.352574i
$101$	−5.68774			−0.565951			−0.282976	−	0.959127i	$-0.591322\pi$
$101$	−5.68774			−0.565951			−0.282976	+	0.959127i	$0.591322\pi$
$102$	5.06682	−	5.23540i	0.501690	−	0.518382i
$103$		−	5.77992i		−	0.569512i	−0.958600	−	0.284756i	$-0.908087\pi$
$103$		−	5.77992i		−	0.569512i	0.958600	−	0.284756i	$-0.0919126\pi$
$104$	0.193245	−	0.0376546i	0.0189492	−	0.00369234i
$105$	0.559315	−	1.74857i	0.0545835	−	0.170643i
$106$	8.63749	+	4.27353i	0.838947	+	0.415082i
$107$		−	14.8038i		−	1.43113i	−0.698544	−	0.715567i	$-0.746168\pi$
$107$		−	14.8038i		−	1.43113i	0.698544	−	0.715567i	$-0.253832\pi$
$108$	−2.84061	+	9.99655i	−0.273338	+	0.961918i
$109$			4.61080i			0.441635i	0.975315	+	0.220817i	$0.0708725\pi$
$109$			4.61080i			0.441635i	−0.975315	+	0.220817i	$0.929127\pi$
$110$	−1.04610	+	2.11434i	−0.0997418	+	0.201594i
$111$	−2.79144	+	8.72677i	−0.264951	+	0.828309i
$112$	2.45165	+	0.670623i	0.231659	+	0.0633679i
$113$			9.37547i			0.881970i	0.897515	+	0.440985i	$0.145371\pi$
$113$			9.37547i			0.881970i	−0.897515	+	0.440985i	$0.854629\pi$
$114$	4.39160	+	4.25019i	0.411311	+	0.398067i
$115$	6.53046			0.608968
$116$	4.02707	+	5.27658i	0.373904	+	0.489918i
$117$	−0.121192	+	0.170056i	−0.0112042	+	0.0157217i
$118$	−0.0117661	+	0.0237813i	−0.00108316	+	0.00218924i
$119$	1.89002			0.173257
$120$	0.955064	−	8.11572i	0.0871850	−	0.740860i
$121$	−1.00000			−0.0909091
$122$	8.79602	−	17.7782i	0.796354	−	1.60956i
$123$	2.70674	−	8.46201i	0.244059	−	0.762994i
$124$	15.3867	−	11.7431i	1.38176	−	1.05456i
$125$	−12.0393			−1.07683
$126$	−2.37591	+	1.27393i	−0.211663	+	0.113491i
$127$			15.1058i			1.34042i	0.742170	+	0.670212i	$0.233797\pi$
$127$			15.1058i			1.34042i	−0.742170	+	0.670212i	$0.766203\pi$
$128$	11.2823	+	0.842820i	0.997221	+	0.0744955i
$129$	−9.03335	−	2.88950i	−0.795342	−	0.254406i
$130$	0.0728162	−	0.147173i	0.00638640	−	0.0129079i
$131$		−	2.64263i		−	0.230888i	−0.993314	−	0.115444i	$-0.963171\pi$
$131$		−	2.64263i		−	0.230888i	0.993314	−	0.115444i	$-0.0368290\pi$
$132$	3.26312	−	1.16277i	0.284018	−	0.101206i
$133$			1.58540i			0.137471i
$134$	12.4493	+	6.15947i	1.07545	+	0.532097i
$135$	5.19032	+	6.94152i	0.446711	+	0.597431i
$136$	8.25755	−	1.60902i	0.708079	−	0.137972i
$137$		−	19.7144i		−	1.68431i	−0.539233	−	0.842157i	$-0.681286\pi$
$137$		−	19.7144i		−	1.68431i	0.539233	−	0.842157i	$-0.318714\pi$
$138$	−6.89108	−	6.66919i	−0.586608	−	0.567719i
$139$	1.78947			0.151781			0.0758906	−	0.997116i	$-0.475820\pi$
$139$	1.78947			0.151781			0.0758906	+	0.997116i	$0.475820\pi$
$140$	1.68514	−	1.28610i	0.142421	−	0.108695i
$141$	−11.7268	−	3.75104i	−0.987571	−	0.315895i
$142$	17.9187	+	8.86555i	1.50370	+	0.743980i
$143$	0.0696073			0.00582085
$144$	−9.29593	+	7.58853i	−0.774661	+	0.632377i
$145$	5.53603			0.459742
$146$	3.99867	+	1.97840i	0.330932	+	0.163734i
$147$	10.8819	+	3.48078i	0.897521	+	0.287090i
$148$	−8.41024	+	6.41868i	−0.691318	+	0.527612i
$149$	15.3672			1.25893			0.629466	−	0.777028i	$-0.283274\pi$
$149$	15.3672			1.25893			0.629466	+	0.777028i	$0.283274\pi$
$150$	3.90337	+	3.77768i	0.318709	+	0.308446i
$151$			7.47089i			0.607973i	0.952676	+	0.303986i	$0.0983177\pi$
$151$			7.47089i			0.607973i	−0.952676	+	0.303986i	$0.901682\pi$
$152$	1.34969	+	6.92666i	0.109475	+	0.561827i
$153$	−5.17865	+	7.26668i	−0.418669	+	0.587476i
$154$	0.805441	+	0.398504i	0.0649043	+	0.0321124i
$155$		−	16.1432i		−	1.29666i
$156$	−0.227137	+	0.0809373i	−0.0181855	+	0.00648017i
$157$			2.02167i			0.161347i	0.996741	+	0.0806736i	$0.0257071\pi$
$157$			2.02167i			0.161347i	−0.996741	+	0.0806736i	$0.974293\pi$
$158$	−10.1766	+	20.5685i	−0.809605	+	1.63634i
$159$	−11.2416	−	3.59585i	−0.891517	−	0.285170i
$160$	6.26757	−	7.05362i	0.495495	−	0.557638i
$161$		−	2.48773i		−	0.196060i
$162$	1.61205	−	12.6254i	0.126655	−	0.991947i
$163$	5.59623			0.438331			0.219165	−	0.975688i	$-0.429667\pi$
$163$	5.59623			0.438331			0.219165	+	0.975688i	$0.429667\pi$
$164$	8.15508	−	6.22394i	0.636805	−	0.486008i
$165$	0.880216	−	2.75179i	0.0685247	−	0.214227i
$166$	5.18481	−	10.4793i	0.402420	−	0.813355i
$167$	5.64224			0.436610			0.218305	−	0.975881i	$-0.429947\pi$
$167$	5.64224			0.436610			0.218305	+	0.975881i	$0.429947\pi$
$168$	−3.09162	−	0.363824i	−0.238524	−	0.0280696i
$169$	12.9952			0.999627
$170$	3.11151	−	6.28887i	0.238642	−	0.482334i
$171$	−6.09549	−	4.34400i	−0.466134	−	0.332194i
$172$	−6.64417	−	8.70570i	−0.506613	−	0.663803i
$173$	−10.1560			−0.772149			−0.386074	−	0.922468i	$-0.626169\pi$
$173$	−10.1560			−0.772149			−0.386074	+	0.922468i	$0.626169\pi$
$174$	−5.84174	−	5.65363i	−0.442861	−	0.428601i
$175$			1.40914i			0.106521i
$176$	3.85826	+	1.05539i	0.290827	+	0.0795527i
$177$	0.00990034	−	0.0309511i	0.000744155	−	0.00232643i
$178$	−6.19453	+	12.5201i	−0.464300	+	0.938425i
$179$			22.4437i			1.67752i	0.544502	+	0.838760i	$0.316719\pi$
$179$			22.4437i			1.67752i	−0.544502	+	0.838760i	$0.683281\pi$
$180$	0.327450	+	10.0029i	0.0244067	+	0.745573i
$181$		−	18.7296i		−	1.39216i	−0.717965	−	0.696079i	$-0.754926\pi$
$181$		−	18.7296i		−	1.39216i	0.717965	−	0.696079i	$-0.245074\pi$
$182$	−0.0560645	−	0.0277388i	−0.00415578	−	0.00205613i
$183$	−7.40119	+	23.1381i	−0.547112	+	1.71042i
$184$	−2.11787	−	10.8690i	−0.156132	−	0.801272i
$185$			8.82377i			0.648737i
$186$	−16.4862	+	17.0347i	−1.20882	+	1.24904i
$187$	2.97439			0.217509
$188$	−8.62521	−	11.3014i	−0.629058	−	0.824240i
$189$	2.64432	−	1.97721i	0.192346	−	0.143821i
$190$	5.27528	+	2.61002i	0.382709	+	0.189351i
$191$	13.8554			1.00254			0.501272	−	0.865290i	$-0.332866\pi$
$191$	13.8554			1.00254			0.501272	+	0.865290i	$0.332866\pi$
$192$	−13.8171	+	1.04242i	−0.997166	+	0.0752301i
$193$	−22.6500			−1.63038			−0.815190	−	0.579194i	$-0.803367\pi$
$193$	−22.6500			−1.63038			−0.815190	+	0.579194i	$0.803367\pi$
$194$	−11.7520	−	5.81447i	−0.843743	−	0.417455i
$195$	−0.0612694	+	0.191545i	−0.00438759	+	0.0137168i
$196$	8.00378	+	10.4872i	0.571698	+	0.749083i
$197$	−15.4248			−1.09897			−0.549487	−	0.835502i	$-0.685177\pi$
$197$	−15.4248			−1.09897			−0.549487	+	0.835502i	$0.685177\pi$
$198$	−3.73907	+	2.00483i	−0.265724	+	0.142477i
$199$		−	5.49102i		−	0.389248i	−0.980878	−	0.194624i	$-0.937651\pi$
$199$		−	5.49102i		−	0.389248i	0.980878	−	0.194624i	$-0.0623487\pi$
$200$	1.19964	+	6.15660i	0.0848275	+	0.435337i
$201$	−16.2026	−	5.18274i	−1.14284	−	0.365562i
$202$	7.20951	+	3.56702i	0.507260	+	0.250974i
$203$		−	2.10891i		−	0.148016i
$204$	−9.70580	+	3.45854i	−0.679542	+	0.242146i
$205$		−	8.55606i		−	0.597581i
$206$	−3.62483	+	7.32636i	−0.252554	+	0.510452i
$207$	9.56475	+	6.81639i	0.664796	+	0.473772i
$208$	−0.268563	−	0.0734625i	−0.0186215	−	0.00509371i
$209$			2.49500i			0.172583i
$210$	−1.80556	+	1.86563i	−0.124596	+	0.128741i
$211$	16.8200			1.15794			0.578968	−	0.815350i	$-0.303456\pi$
$211$	16.8200			1.15794			0.578968	+	0.815350i	$0.303456\pi$
$212$	−8.26837	−	10.8339i	−0.567874	−	0.744072i
$213$	−23.3210	−	7.45970i	−1.59793	−	0.511130i
$214$	−9.28406	+	18.7646i	−0.634645	+	1.28272i
$215$	−9.13375			−0.622917
$216$	9.86988	−	10.8897i	0.671560	−	0.740950i
$217$	−6.14964			−0.417465
$218$	2.89163	−	5.84444i	0.195846	−	0.395836i
$219$	−5.20423	−	1.66468i	−0.351669	−	0.112488i
$220$	2.65198	−	2.02398i	0.178796	−	0.136457i
$221$	−0.207039			−0.0139270
$222$	9.01122	−	9.31103i	0.604793	−	0.624916i
$223$			7.10997i			0.476119i	0.971251	+	0.238059i	$0.0765113\pi$
$223$			7.10997i			0.476119i	−0.971251	+	0.238059i	$0.923489\pi$
$224$	−2.68702	−	2.38758i	−0.179534	−	0.159527i
$225$	−5.41784	−	3.86106i	−0.361189	−	0.257404i
$226$	5.87974	−	11.8839i	0.391115	−	0.790506i
$227$			19.0669i			1.26552i	0.774350	+	0.632758i	$0.218077\pi$
$227$			19.0669i			1.26552i	−0.774350	+	0.632758i	$0.781923\pi$
$228$	−2.90112	−	8.14150i	−0.192131	−	0.539184i
$229$			3.57807i			0.236445i	0.992987	+	0.118223i	$0.0377197\pi$
$229$			3.57807i			0.236445i	−0.992987	+	0.118223i	$0.962280\pi$
$230$	−8.27771	−	4.09552i	−0.545816	−	0.270051i
$231$	−1.04827	−	0.335311i	−0.0689713	−	0.0220619i
$232$	−1.79537	−	9.21390i	−0.117872	−	0.604922i
$233$			8.52538i			0.558516i	0.960216	+	0.279258i	$0.0900885\pi$
$233$			8.52538i			0.558516i	−0.960216	+	0.279258i	$0.909912\pi$
$234$	0.260266	−	0.139551i	0.0170141	−	0.00912273i
$235$	−11.8571			−0.773472
$236$	0.0298285	−	0.0227650i	0.00194167	−	0.00148188i
$237$	8.56283	−	26.7697i	0.556215	−	1.73888i
$238$	−2.39570	−	1.18531i	−0.155290	−	0.0768321i
$239$	29.8677			1.93198			0.965991	−	0.258575i	$-0.0832529\pi$
$239$	29.8677			1.93198			0.965991	+	0.258575i	$0.0832529\pi$
$240$	−6.30030	+	9.68815i	−0.406683	+	0.625367i
$241$	14.6085			0.941013			0.470507	−	0.882396i	$-0.344071\pi$
$241$	14.6085			0.941013			0.470507	+	0.882396i	$0.344071\pi$
$242$	1.26755	+	0.627142i	0.0814815	+	0.0403142i
$243$	0.356479	+	15.5844i	0.0228681	+	0.999738i
$244$	−22.2989	+	17.0184i	−1.42754	+	1.08949i
$245$	11.0028			0.702944
$246$	−8.73782	+	9.02854i	−0.557103	+	0.575639i
$247$		−	0.173670i		−	0.0110504i
$248$	−26.8680	+	5.23536i	−1.70612	+	0.332445i
$249$	−4.36263	+	13.6388i	−0.276471	+	0.864321i
$250$	15.2605	+	7.55036i	0.965158	+	0.477527i
$251$		−	6.87598i		−	0.434008i	−0.976171	−	0.217004i	$-0.930371\pi$
$251$		−	6.87598i		−	0.434008i	0.976171	−	0.217004i	$-0.0696285\pi$
$252$	3.81053	−	0.124740i	0.240041	−	0.00785786i
$253$		−	3.91504i		−	0.246136i
$254$	9.47348	−	19.1474i	0.594419	−	1.20142i
$255$	−2.61811	+	8.18490i	−0.163952	+	0.512558i
$256$	−13.7723	−	8.14390i	−0.860770	−	0.508994i
$257$			24.1578i			1.50692i	0.657492	+	0.753462i	$0.271617\pi$
$257$			24.1578i			1.50692i	−0.657492	+	0.753462i	$0.728383\pi$
$258$	9.63813	+	9.32779i	0.600044	+	0.580723i
$259$	3.36135			0.208864
$260$	−0.184597	+	0.140884i	−0.0114482	+	0.00873725i
$261$	8.10827	+	5.77842i	0.501889	+	0.357675i
$262$	−1.65730	+	3.34968i	−0.102389	+	0.206944i
$263$	26.3147			1.62263			0.811317	−	0.584607i	$-0.198751\pi$
$263$	26.3147			1.62263			0.811317	+	0.584607i	$0.198751\pi$
$264$	−4.86541	−	0.572565i	−0.299445	−	0.0352389i
$265$	−11.3666			−0.698242
$266$	0.994269	−	2.00958i	0.0609625	−	0.123215i
$267$	5.21224	−	16.2948i	0.318984	−	0.997229i
$268$	−11.9173	−	15.6149i	−0.727964	−	0.953834i
$269$	29.9670			1.82712			0.913560	−	0.406703i	$-0.133322\pi$
$269$	29.9670			1.82712			0.913560	+	0.406703i	$0.133322\pi$
$270$	−2.22569	−	12.0538i	−0.135451	−	0.733572i
$271$			6.16891i			0.374735i	0.982290	+	0.187367i	$0.0599955\pi$
$271$			6.16891i			0.374735i	−0.982290	+	0.187367i	$0.940005\pi$
$272$	−11.4760	−	3.13913i	−0.695833	−	0.190338i
$273$	0.0729674	+	0.0233401i	0.00441619	+	0.00141261i
$274$	−12.3637	+	24.9890i	−0.746919	+	1.50964i
$275$			2.21762i			0.133728i
$276$	4.55229	+	12.7752i	0.274016	+	0.768979i
$277$		−	14.2818i		−	0.858107i	−0.903279	−	0.429054i	$-0.858847\pi$
$277$		−	14.2818i		−	0.858107i	0.903279	−	0.429054i	$-0.141153\pi$
$278$	−2.26825	−	1.12225i	−0.136041	−	0.0673083i
$279$	16.8500	−	23.6440i	1.00879	−	1.41553i
$280$	−2.94258	+	0.573375i	−0.175853	+	0.0342657i
$281$		−	9.03376i		−	0.538909i	−0.963013	−	0.269455i	$-0.913157\pi$
$281$		−	9.03376i		−	0.538909i	0.963013	−	0.269455i	$-0.0868434\pi$
$282$	12.5119	+	12.1090i	0.745071	+	0.721079i
$283$	−25.4937			−1.51544			−0.757721	−	0.652579i	$-0.773687\pi$
$283$	−25.4937			−1.51544			−0.757721	+	0.652579i	$0.773687\pi$
$284$	−17.1530	−	22.4751i	−1.01784	−	1.33365i
$285$	−6.86572	−	2.19614i	−0.406690	−	0.130088i
$286$	−0.0882310	−	0.0436536i	−0.00521721	−	0.00258129i
$287$	−3.25937			−0.192394
$288$	16.5422	−	3.78900i	0.974757	−	0.223269i
$289$	8.15299			0.479588
$290$	−7.01721	−	3.47187i	−0.412065	−	0.203875i
$291$	15.2951	+	4.89244i	0.896614	+	0.286800i
$292$	−3.82779	−	5.01546i	−0.224004	−	0.293508i
$293$	21.9276			1.28102			0.640511	−	0.767949i	$-0.278722\pi$
$293$	21.9276			1.28102			0.640511	+	0.767949i	$0.278722\pi$
$294$	−11.6104	−	11.2365i	−0.677132	−	0.655329i
$295$		−	0.0312951i		−	0.00182207i
$296$	14.6859	−	2.86161i	0.853598	−	0.166328i
$297$	4.16147	−	3.11162i	0.241473	−	0.180554i
$298$	−19.4788	−	9.63743i	−1.12838	−	0.558281i
$299$			0.272515i			0.0157599i
$300$	−2.57859	−	7.23638i	−0.148875	−	0.417793i
$301$			3.47943i			0.200551i
$302$	4.68531	−	9.46976i	0.269609	−	0.544924i
$303$	−9.38311	−	3.00138i	−0.539046	−	0.172425i
$304$	2.63319	−	9.62637i	0.151024	−	0.552110i
$305$			23.3953i			1.33961i
$306$	11.1215	−	5.96316i	0.635772	−	0.340891i
$307$	18.6318			1.06337			0.531686	−	0.846942i	$-0.321559\pi$
$307$	18.6318			1.06337			0.531686	+	0.846942i	$0.321559\pi$
$308$	−0.771021	−	1.01025i	−0.0439330	−	0.0575644i
$309$	3.05002	−	9.53518i	0.173510	−	0.542438i
$310$	−10.1241	+	20.4624i	−0.575010	+	1.16219i
$311$	−13.4100			−0.760411			−0.380205	−	0.924902i	$-0.624147\pi$
$311$	−13.4100			−0.760411			−0.380205	+	0.924902i	$0.624147\pi$
$312$	0.338668	+	0.0398547i	0.0191733	+	0.00225633i
$313$	8.61462			0.486927			0.243464	−	0.969910i	$-0.421716\pi$
$313$	8.61462			0.486927			0.243464	+	0.969910i	$0.421716\pi$
$314$	1.26788	−	2.56258i	0.0715504	−	0.144615i
$315$	1.84541	−	2.58948i	0.103977	−	0.145901i
$316$	25.7987	−	19.6895i	1.45129	−	1.10762i
$317$	14.1325			0.793758			0.396879	−	0.917871i	$-0.370093\pi$
$317$	14.1325			0.793758			0.396879	+	0.917871i	$0.370093\pi$
$318$	11.9942	+	11.6080i	0.672603	+	0.650945i
$319$		−	3.31887i		−	0.185821i
$320$	−12.3681	+	5.01019i	−0.691398	+	0.280078i
$321$	7.81184	−	24.4219i	0.436015	−	1.36310i
$322$	−1.56016	+	3.15333i	−0.0869442	+	0.175728i
$323$		−	7.42112i		−	0.412922i
$324$	−9.96129	+	14.9924i	−0.553405	+	0.832912i
$325$		−	0.154363i		−	0.00856251i
$326$	−7.09352	−	3.50963i	−0.392874	−	0.194380i
$327$	−2.43309	+	7.60649i	−0.134550	+	0.420640i
$328$	−14.2403	+	2.77479i	−0.786289	+	0.153212i
$329$			4.51687i			0.249023i
$330$	−2.84148	+	2.93602i	−0.156418	+	0.161623i
$331$	8.67374			0.476752			0.238376	−	0.971173i	$-0.423385\pi$
$331$	8.67374			0.476752			0.238376	+	0.971173i	$0.423385\pi$
$332$	−13.1441	+	10.0315i	−0.721374	+	0.550551i
$333$	−9.21011	+	12.9236i	−0.504711	+	0.708210i
$334$	−7.15184	−	3.53848i	−0.391331	−	0.193617i
$335$	−16.3827			−0.895083
$336$	3.69063	+	2.40005i	0.201340	+	0.130933i
$337$	−8.73386			−0.475764			−0.237882	−	0.971294i	$-0.576453\pi$
$337$	−8.73386			−0.475764			−0.237882	+	0.971294i	$0.576453\pi$
$338$	−16.4721	−	8.14980i	−0.895962	−	0.443291i
$339$	−4.94737	+	15.4668i	−0.268704	+	0.840041i
$340$	−7.88802	+	6.02012i	−0.427788	+	0.326487i
$341$	−9.67793			−0.524089
$342$	5.00207	+	9.32899i	0.270481	+	0.504454i
$343$		−	8.63944i		−	0.466486i
$344$	2.96214	+	15.2018i	0.159708	+	0.819625i
$345$	10.7734	+	3.44608i	0.580018	+	0.185531i
$346$	12.8733	+	6.36927i	0.692074	+	0.342414i
$347$			12.5262i			0.672441i	0.941783	+	0.336220i	$0.109149\pi$
$347$			12.5262i			0.672441i	−0.941783	+	0.336220i	$0.890851\pi$
$348$	3.85909	+	10.8299i	0.206869	+	0.580543i
$349$			35.4264i			1.89633i	0.317779	+	0.948165i	$0.397063\pi$
$349$			35.4264i			1.89633i	−0.317779	+	0.948165i	$0.602937\pi$
$350$	0.883732	−	1.78617i	0.0472375	−	0.0954745i
$351$	−0.289669	+	0.216591i	−0.0154614	+	0.0115608i
$352$	−4.22868	−	3.75743i	−0.225389	−	0.200272i
$353$		−	2.28109i		−	0.121410i	−0.998156	−	0.0607050i	$-0.980665\pi$
$353$		−	2.28109i		−	0.121410i	0.998156	−	0.0607050i	$-0.0193349\pi$
$354$	−0.0319599	+	0.0330233i	−0.00169865	+	0.00175517i
$355$	−23.5802			−1.25151
$356$	15.7038	−	11.9851i	0.832300	−	0.635210i
$357$	3.11798	+	0.997347i	0.165021	+	0.0527852i
$358$	14.0754	−	28.4486i	0.743906	−	1.50355i
$359$	−3.43694			−0.181395			−0.0906973	−	0.995879i	$-0.528910\pi$
$359$	−3.43694			−0.181395			−0.0906973	+	0.995879i	$0.528910\pi$
$360$	5.85818	−	12.8846i	0.308753	−	0.679078i
$361$	−12.7750			−0.672366
$362$	−11.7461	+	23.7408i	−0.617361	+	1.24779i
$363$	−1.64971	−	0.527693i	−0.0865873	−	0.0276967i
$364$	0.0536687	+	0.0703208i	0.00281300	+	0.00368581i
$365$	−5.26207			−0.275429
$366$	23.8923	−	24.6872i	1.24887	−	1.29042i
$367$		−	8.27404i		−	0.431901i	−0.976404	−	0.215951i	$-0.930715\pi$
$367$		−	8.27404i		−	0.431901i	0.976404	−	0.215951i	$-0.0692850\pi$
$368$	−4.13187	+	15.1052i	−0.215389	+	0.787414i
$369$	8.93068	−	12.5315i	0.464913	−	0.652365i
$370$	5.53375	−	11.1846i	0.287686	−	0.581460i
$371$			4.33000i			0.224802i
$372$	31.5803	−	11.2532i	1.63736	−	0.583452i
$373$		−	2.81935i		−	0.145980i	−0.997333	−	0.0729902i	$-0.976746\pi$
$373$		−	2.81935i		−	0.145980i	0.997333	−	0.0729902i	$-0.0232542\pi$
$374$	−3.77020	−	1.86537i	−0.194953	−	0.0964557i
$375$	−19.8614	−	6.35307i	−1.02564	−	0.328071i
$376$	3.84533	+	19.7344i	0.198308	+	1.01772i
$377$			0.231018i			0.0118980i
$378$	−4.59181	+	0.847860i	−0.236177	+	0.0436092i
$379$	5.93196			0.304704			0.152352	−	0.988326i	$-0.451315\pi$
$379$	5.93196			0.304704			0.152352	+	0.988326i	$0.451315\pi$
$380$	−5.04985	−	6.61670i	−0.259052	−	0.339429i
$381$	−7.97123	+	24.9202i	−0.408378	+	1.27670i
$382$	−17.5625	−	8.68932i	−0.898576	−	0.444584i
$383$	2.60459			0.133088			0.0665442	−	0.997783i	$-0.478803\pi$
$383$	2.60459			0.133088			0.0665442	+	0.997783i	$0.478803\pi$
$384$	18.1677	+	7.34398i	0.927117	+	0.374771i
$385$	−1.05992			−0.0540188
$386$	28.7101	+	14.2047i	1.46130	+	0.723002i
$387$	−13.3776	−	9.53367i	−0.680023	−	0.484624i
$388$	11.2498	+	14.7403i	0.571121	+	0.748326i
$389$	−11.1278			−0.564200			−0.282100	−	0.959385i	$-0.591031\pi$
$389$	−11.1278			−0.564200			−0.282100	+	0.959385i	$0.591031\pi$
$390$	0.197788	−	0.204368i	0.0100154	−	0.0103486i
$391$			11.6449i			0.588906i
$392$	−3.56828	−	18.3125i	−0.180226	−	0.924923i
$393$	1.39450	−	4.35957i	0.0703430	−	0.219911i
$394$	19.5518	+	9.67356i	0.985006	+	0.487347i
$395$		−	27.0672i		−	1.36190i
$396$	5.99679	−	0.196308i	0.301350	−	0.00986483i
$397$		−	10.8070i		−	0.542388i	−0.962525	−	0.271194i	$-0.912581\pi$
$397$		−	10.8070i		−	0.542388i	0.962525	−	0.271194i	$-0.0874185\pi$
$398$	−3.44365	+	6.96017i	−0.172615	+	0.348882i
$399$	−0.836603	+	2.61544i	−0.0418825	+	0.130936i
$400$	2.34045	−	8.55617i	0.117022	−	0.427809i
$401$		−	3.69508i		−	0.184523i	−0.995735	−	0.0922616i	$-0.970590\pi$
$401$		−	3.69508i		−	0.184523i	0.995735	−	0.0922616i	$-0.0294096\pi$
$402$	17.2874	+	16.7307i	0.862216	+	0.834453i
$403$	0.673654			0.0335571
$404$	−6.90142	−	9.04277i	−0.343359	−	0.449895i
$405$	4.89952	+	14.1904i	0.243459	+	0.705126i
$406$	−1.32258	+	2.67315i	−0.0656387	+	0.132666i
$407$	5.28989			0.262210
$408$	14.4716	+	1.70303i	0.716452	+	0.0843126i
$409$	25.7240			1.27197			0.635985	−	0.771701i	$-0.280594\pi$
$409$	25.7240			1.27197			0.635985	+	0.771701i	$0.280594\pi$
$410$	−5.36586	+	10.8453i	−0.265001	+	0.535610i
$411$	10.4031	−	32.5230i	0.513149	−	1.60424i
$412$	9.18933	−	7.01327i	0.452726	−	0.345519i
$413$	−0.0119216			−0.000586625
$414$	−7.84900	−	14.6386i	−0.385757	−	0.719448i
$415$			13.7904i			0.676942i
$416$	0.294347	+	0.261545i	0.0144315	+	0.0128233i
$417$	2.95211	+	0.944292i	0.144565	+	0.0462422i
$418$	1.56472	−	3.16255i	0.0765330	−	0.154685i
$419$			18.4592i			0.901793i	0.892576	+	0.450896i	$0.148896\pi$
$419$			18.4592i			0.901793i	−0.892576	+	0.450896i	$0.851104\pi$
$420$	3.45866	−	1.23245i	0.168765	−	0.0601374i
$421$			0.178746i			0.00871155i	0.999991	+	0.00435578i	$0.00138649\pi$
$421$			0.178746i			0.00871155i	−0.999991	+	0.00435578i	$0.998614\pi$
$422$	−21.3203	−	10.5485i	−1.03785	−	0.513494i
$423$	−17.3663	−	12.3763i	−0.844380	−	0.601754i
$424$	3.68625	+	18.9179i	0.179020	+	0.918736i
$425$		−	6.59609i		−	0.319957i
$426$	24.8824	+	24.0812i	1.20555	+	1.16674i
$427$	8.91225			0.431294
$428$	23.5361	−	17.9627i	1.13766	−	0.868260i
$429$	0.114832	+	0.0367313i	0.00554413	+	0.00177340i
$430$	11.5775	+	5.72816i	0.558318	+	0.276236i
$431$	−12.6286			−0.608298			−0.304149	−	0.952624i	$-0.598372\pi$
$431$	−12.6286			−0.608298			−0.304149	+	0.952624i	$0.598372\pi$
$432$	−19.3400	+	7.61347i	−0.930496	+	0.366303i
$433$	−23.1371			−1.11190			−0.555950	−	0.831216i	$-0.687645\pi$
$433$	−23.1371			−1.11190			−0.555950	+	0.831216i	$0.687645\pi$
$434$	7.79500	+	3.85670i	0.374172	+	0.185127i
$435$	9.13284	+	2.92132i	0.437886	+	0.140067i
$436$	−7.33059	+	5.59469i	−0.351071	+	0.267937i
$437$	−9.76803			−0.467268
$438$	5.55265	+	5.37386i	0.265316	+	0.256773i
$439$		−	31.7464i		−	1.51517i	−0.652736	−	0.757586i	$-0.726379\pi$
$439$		−	31.7464i		−	1.51517i	0.652736	−	0.757586i	$-0.273621\pi$
$440$	−4.63085	+	0.902343i	−0.220767	+	0.0430175i
$441$	16.1151	+	11.4846i	0.767387	+	0.546884i
$442$	0.262433	+	0.129843i	0.0124827	+	0.00617600i
$443$			14.6046i			0.693887i	0.937886	+	0.346943i	$0.112780\pi$
$443$			14.6046i			0.693887i	−0.937886	+	0.346943i	$0.887220\pi$
$444$	−17.2615	+	6.15093i	−0.819197	+	0.291910i
$445$		−	16.4760i		−	0.781036i
$446$	4.45896	−	9.01227i	0.211138	−	0.426743i
$447$	25.3515	+	8.10917i	1.19908	+	0.383551i
$448$	1.90859	+	4.71153i	0.0901726	+	0.222599i
$449$		−	24.3408i		−	1.14871i	−0.818605	−	0.574356i	$-0.805252\pi$
$449$		−	24.3408i		−	1.14871i	0.818605	−	0.574356i	$-0.194748\pi$
$450$	4.44597	+	8.29185i	0.209585	+	0.390882i
$451$	−5.12939			−0.241534
$452$	−14.9058	+	11.3761i	−0.701109	+	0.535085i
$453$	−3.94234	+	12.3248i	−0.185227	+	0.579070i
$454$	11.9577	−	24.1683i	0.561201	−	1.13428i
$455$	0.0737784			0.00345879
$456$	−1.42855	+	12.1392i	−0.0668980	+	0.568470i
$457$	−2.35640			−0.110228			−0.0551140	−	0.998480i	$-0.517552\pi$
$457$	−2.35640			−0.110228			−0.0551140	+	0.998480i	$0.517552\pi$
$458$	2.24396	−	4.53540i	0.104853	−	0.211925i
$459$	−12.3778	+	9.25517i	−0.577748	+	0.431994i
$460$	7.92397	+	10.3826i	0.369457	+	0.484091i
$461$	−34.3334			−1.59906			−0.799532	−	0.600623i	$-0.794919\pi$
$461$	−34.3334			−1.59906			−0.799532	+	0.600623i	$0.794919\pi$
$462$	1.11846	+	1.08244i	0.0520352	+	0.0503597i
$463$			8.37349i			0.389149i	0.980888	+	0.194575i	$0.0623326\pi$
$463$			8.37349i			0.389149i	−0.980888	+	0.194575i	$0.937667\pi$
$464$	−3.50269	+	12.8051i	−0.162608	+	0.594460i
$465$	8.51867	−	26.6316i	0.395044	−	1.23501i
$466$	5.34662	−	10.8064i	0.247677	−	0.500596i
$467$			18.2946i			0.846574i	0.905996	+	0.423287i	$0.139124\pi$
$467$			18.2946i			0.846574i	−0.905996	+	0.423287i	$0.860876\pi$
$468$	−0.417420	+	0.0136644i	−0.0192952	+	0.000631639i
$469$			6.24087i			0.288176i
$470$	15.0295	+	7.43608i	0.693260	+	0.343001i
$471$	−1.06682	+	3.33518i	−0.0491566	+	0.153677i
$472$	−0.0520861	+	0.0101492i	−0.00239746	+	0.000467155i
$473$			5.47572i			0.251774i
$474$	−27.6422	+	28.5619i	−1.26965	+	1.31189i
$475$	5.53298			0.253871
$476$	2.29332	+	3.00488i	0.105114	+	0.137729i
$477$	−16.6479	−	11.8642i	−0.762254	−	0.543226i
$478$	−37.8590	−	18.7313i	−1.73163	−	0.856749i
$479$	−25.4823			−1.16432			−0.582158	−	0.813076i	$-0.697791\pi$
$479$	−25.4823			−1.16432			−0.582158	+	0.813076i	$0.697791\pi$
$480$	14.0618	−	8.32907i	0.641831	−	0.380168i
$481$	−0.368215			−0.0167891
$482$	−18.5170	−	9.16157i	−0.843427	−	0.417298i
$483$	1.31276	−	4.10403i	0.0597325	−	0.186740i
$484$	−1.21339	−	1.58987i	−0.0551539	−	0.0722669i
$485$	15.4651			0.702233
$486$	9.32176	−	19.9776i	0.422844	−	0.906203i
$487$			14.4438i			0.654511i	0.944936	+	0.327256i	$0.106124\pi$
$487$			14.4438i			0.654511i	−0.944936	+	0.327256i	$0.893876\pi$
$488$	38.9380	−	7.58724i	1.76264	−	0.343458i
$489$	9.23215	+	2.95309i	0.417492	+	0.133543i
$490$	−13.9467	−	6.90032i	−0.630046	−	0.311725i
$491$		−	38.9968i		−	1.75990i	−0.475068	−	0.879949i	$-0.657576\pi$
$491$		−	38.9968i		−	1.75990i	0.475068	−	0.879949i	$-0.342424\pi$
$492$	16.7378	−	5.96431i	0.754600	−	0.268892i
$493$			9.87162i			0.444596i
$494$	−0.108916	+	0.220137i	−0.00490036	+	0.00990441i
$495$	2.90420	−	4.07517i	0.130534	−	0.183165i
$496$	37.3400	+	10.2140i	1.67661	+	0.458620i
$497$			8.98270i			0.402929i
$498$	14.0833	−	14.5519i	0.631088	−	0.652085i
$499$	−17.7796			−0.795922			−0.397961	−	0.917402i	$-0.630282\pi$
$499$	−17.7796			−0.795922			−0.397961	+	0.917402i	$0.630282\pi$
$500$	−14.6084	−	19.1410i	−0.653306	−	0.856011i
$501$	9.30805	+	2.97737i	0.415853	+	0.133019i
$502$	−4.31222	+	8.71568i	−0.192464	+	0.389000i
$503$	23.6893			1.05625			0.528127	−	0.849165i	$-0.322894\pi$
$503$	23.6893			1.05625			0.528127	+	0.849165i	$0.322894\pi$
$504$	−4.90829	−	2.23163i	−0.218632	−	0.0994047i
$505$	−9.48740			−0.422184
$506$	−2.45528	+	4.96252i	−0.109151	+	0.220611i
$507$	21.4382	+	6.85745i	0.952105	+	0.304550i
$508$	−24.0163	+	18.3292i	−1.06555	+	0.813226i
$509$	32.8416			1.45568			0.727839	−	0.685748i	$-0.240525\pi$
$509$	32.8416			1.45568			0.727839	+	0.685748i	$0.240525\pi$
$510$	8.45168	−	8.73288i	0.374247	−	0.386698i
$511$			2.00455i			0.0886759i
$512$	12.3498	+	18.9600i	0.545788	+	0.837923i
$513$	−7.76349	−	10.3829i	−0.342767	−	0.458416i
$514$	15.1504	−	30.6213i	0.668254	−	1.35065i
$515$		−	9.64116i		−	0.424840i
$516$	−6.36701	−	17.8679i	−0.280292	−	0.786592i
$517$			7.10838i			0.312626i
$518$	−4.26069	−	2.10804i	−0.187204	−	0.0926220i
$519$	−16.7545	−	5.35927i	−0.735441	−	0.235246i
$520$	0.322341	−	0.0628096i	0.0141356	−	0.00275438i
$521$		−	43.0008i		−	1.88390i	−0.335756	−	0.941949i	$-0.608992\pi$
$521$		−	43.0008i		−	1.88390i	0.335756	−	0.941949i	$-0.391008\pi$
$522$	−6.65378	−	12.4095i	−0.291228	−	0.543149i
$523$	−23.8463			−1.04273			−0.521363	−	0.853335i	$-0.674576\pi$
$523$	−23.8463			−1.04273			−0.521363	+	0.853335i	$0.674576\pi$
$524$	4.20144	−	3.20653i	0.183541	−	0.140078i
$525$	−0.743595	+	2.32468i	−0.0324531	+	0.101457i
$526$	−33.3553	−	16.5030i	−1.45436	−	0.719567i
$527$	28.7860			1.25394
$528$	5.80809	+	3.77706i	0.252764	+	0.164375i
$529$	−7.67249			−0.333586
$530$	14.4077	+	7.12844i	0.625831	+	0.309640i
$531$	0.0326653	−	0.0458360i	0.00141756	−	0.00198911i
$532$	−2.52058	+	1.92370i	−0.109281	+	0.0834030i
$533$	0.357043			0.0154653
$534$	−16.8260	+	17.3858i	−0.728131	+	0.752357i
$535$		−	24.6934i		−	1.06759i
$536$	5.31302	+	27.2666i	0.229488	+	1.17774i
$537$	−11.8434	+	37.0255i	−0.511079	+	1.59777i
$538$	−37.9848	−	18.7936i	−1.63764	−	0.810248i
$539$		−	6.59623i		−	0.284120i
$540$	−4.73827	+	16.6747i	−0.203903	+	0.717564i
$541$		−	38.6555i		−	1.66193i	−0.556323	−	0.830966i	$-0.687788\pi$
$541$		−	38.6555i		−	1.66193i	0.556323	−	0.830966i	$-0.312212\pi$
$542$	3.86878	−	7.81943i	0.166178	−	0.335873i
$543$	9.88347	−	30.8984i	0.424140	−	1.32598i
$544$	12.5777	+	11.1761i	0.539266	+	0.479170i
$545$			7.69103i			0.329448i
$546$	−0.0778526	−	0.0753458i	−0.00333178	−	0.00322450i
$547$	8.82567			0.377358			0.188679	−	0.982039i	$-0.439579\pi$
$547$	8.82567			0.377358			0.188679	+	0.982039i	$0.439579\pi$
$548$	31.3433	−	23.9212i	1.33892	−	1.02186i
$549$	−24.4196	+	34.2656i	−1.04220	+	1.46242i
$550$	1.39076	−	2.81096i	0.0593024	−	0.119860i
$551$	−8.28060			−0.352765
$552$	2.24161	−	19.0482i	0.0954093	−	0.810747i
$553$	−10.3111			−0.438470
$554$	−8.95668	+	18.1029i	−0.380533	+	0.769118i
$555$	−4.65624	+	14.5567i	−0.197646	+	0.617896i
$556$	2.17132	+	2.84503i	0.0920846	+	0.120656i
$557$	−15.1216			−0.640723			−0.320362	−	0.947295i	$-0.603804\pi$
$557$	−15.1216			−0.640723			−0.320362	+	0.947295i	$0.603804\pi$
$558$	−36.1865	+	19.4026i	−1.53190	+	0.821379i
$559$		−	0.381150i		−	0.0161209i
$560$	4.08946	+	1.11863i	0.172811	+	0.0472707i
$561$	4.90688	+	1.56957i	0.207169	+	0.0662671i
$562$	−5.66545	+	11.4508i	−0.238983	+	0.483022i
$563$			37.9812i			1.60072i	0.599523	+	0.800358i	$0.295357\pi$
$563$			37.9812i			1.60072i	−0.599523	+	0.800358i	$0.704643\pi$
$564$	−8.26541	−	23.1955i	−0.348037	−	0.976707i
$565$			15.6387i			0.657925i
$566$	32.3146	+	15.9881i	1.35828	+	0.672032i
$567$	5.40572	−	1.86644i	0.227019	−	0.0783829i
$568$	7.64722	+	39.2458i	0.320870	+	1.64672i
$569$			35.2488i			1.47771i	0.673865	+	0.738854i	$0.264633\pi$
$569$			35.2488i			1.47771i	−0.673865	+	0.738854i	$0.735367\pi$
$570$	7.32539	+	7.08951i	0.306827	+	0.296947i
$571$	−14.3624			−0.601047			−0.300523	−	0.953774i	$-0.597161\pi$
$571$	−14.3624			−0.601047			−0.300523	+	0.953774i	$0.597161\pi$
$572$	0.0844605	+	0.110667i	0.00353147	+	0.00462720i
$573$	22.8574	+	7.31141i	0.954883	+	0.305439i
$574$	4.13142	+	2.04408i	0.172442	+	0.0853184i
$575$	−8.68208			−0.362068
$576$	−23.3443	−	5.57152i	−0.972681	−	0.232147i
$577$	−15.6727			−0.652462			−0.326231	−	0.945290i	$-0.605779\pi$
$577$	−15.6727			−0.652462			−0.326231	+	0.945290i	$0.605779\pi$
$578$	−10.3344	−	5.11308i	−0.429853	−	0.212676i
$579$	−37.3658	−	11.9522i	−1.55287	−	0.496717i
$580$	6.71734	+	8.80158i	0.278922	+	0.365466i
$581$	5.25333			0.217945
$582$	−16.3191	−	15.7936i	−0.676448	−	0.654667i
$583$			6.81429i			0.282219i
$584$	1.70652	+	8.75794i	0.0706165	+	0.362406i
$585$	−0.202153	+	0.283661i	−0.00835801	+	0.0117280i
$586$	−27.7944	−	13.7517i	−1.14818	−	0.568077i
$587$		−	14.3808i		−	0.593558i	−0.954946	−	0.296779i	$-0.904088\pi$
$587$		−	14.3808i		−	0.593558i	0.954946	−	0.296779i	$-0.0959125\pi$
$588$	7.66990	+	21.5243i	0.316302	+	0.887647i
$589$			24.1465i			0.994938i
$590$	−0.0196265	+	0.0396682i	−0.000808009	+	0.00163312i
$591$	−25.4465	−	8.13958i	−1.04673	−	0.334817i
$592$	−20.4098	−	5.58287i	−0.838836	−	0.229455i
$593$			4.09363i			0.168105i	0.996461	+	0.0840526i	$0.0267864\pi$
$593$			4.09363i			0.168105i	−0.996461	+	0.0840526i	$0.973214\pi$
$594$	−7.22631	+	1.33431i	−0.296499	+	0.0547474i
$595$	3.15263			0.129245
$596$	18.6464	+	24.4319i	0.763786	+	1.00077i
$597$	2.89757	−	9.05859i	0.118590	−	0.370743i
$598$	0.170906	−	0.345427i	0.00698885	−	0.0141256i
$599$	−17.0416			−0.696301			−0.348151	−	0.937439i	$-0.613190\pi$
$599$	−17.0416			−0.696301			−0.348151	+	0.937439i	$0.613190\pi$
$600$	−1.26973	+	10.7896i	−0.0518367	+	0.440485i
$601$	25.0332			1.02113			0.510563	−	0.859841i	$-0.329437\pi$
$601$	25.0332			1.02113			0.510563	+	0.859841i	$0.329437\pi$
$602$	2.18210	−	4.41037i	0.0889356	−	0.179753i
$603$	−23.9947	−	17.1000i	−0.977140	−	0.696366i
$604$	−11.8778	+	9.06508i	−0.483299	+	0.368853i
$605$	−1.66805			−0.0678157
$606$	10.0113	+	9.68895i	0.406682	+	0.393587i
$607$		−	2.23540i		−	0.0907323i	−0.998970	−	0.0453661i	$-0.985555\pi$
$607$		−	2.23540i		−	0.0907323i	0.998970	−	0.0453661i	$-0.0144455\pi$
$608$	−9.37481	+	10.5506i	−0.380199	+	0.427882i
$609$	1.11286	−	3.47908i	0.0450952	−	0.140980i
$610$	14.6722	−	29.6548i	0.594058	−	1.20069i
$611$		−	0.494795i		−	0.0200173i
$612$	−17.8368	+	0.583896i	−0.721010	+	0.0236026i
$613$		−	20.4350i		−	0.825361i	−0.910876	−	0.412681i	$-0.864593\pi$
$613$		−	20.4350i		−	0.825361i	0.910876	−	0.412681i	$-0.135407\pi$
$614$	−23.6168	−	11.6848i	−0.953095	−	0.471558i
$615$	4.51497	−	14.1150i	0.182061	−	0.569172i
$616$	0.343741	+	1.76409i	0.0138497	+	0.0710771i
$617$		−	11.3875i		−	0.458442i	−0.973374	−	0.229221i	$-0.926382\pi$
$617$		−	11.3875i		−	0.458442i	0.973374	−	0.229221i	$-0.0736179\pi$
$618$	−9.84598	+	10.1736i	−0.396063	+	0.409241i
$619$	3.01307			0.121106			0.0605528	−	0.998165i	$-0.480714\pi$
$619$	3.01307			0.121106			0.0605528	+	0.998165i	$0.480714\pi$
$620$	25.6657	−	19.5880i	1.03076	−	0.786672i
$621$	12.1821	+	16.2923i	0.488851	+	0.653788i
$622$	16.9979	+	8.40996i	0.681553	+	0.337209i
$623$	−6.27639			−0.251458
$624$	−0.404285	−	0.262910i	−0.0161843	−	0.0105248i
$625$	−8.99402			−0.359761
$626$	−10.9195	−	5.40259i	−0.436431	−	0.215931i
$627$	−1.31660	+	4.11603i	−0.0525798	+	0.164378i
$628$	−3.21420	+	2.45307i	−0.128261	+	0.0978883i
$629$	−15.7342			−0.627363
$630$	−3.96313	+	2.12497i	−0.157895	+	0.0846609i
$631$			45.8357i			1.82469i	0.409424	+	0.912344i	$0.365730\pi$
$631$			45.8357i			1.82469i	−0.409424	+	0.912344i	$0.634270\pi$
$632$	−45.0494	+	8.77808i	−1.79197	+	0.349173i
$633$	27.7481	+	8.87579i	1.10289	+	0.352781i
$634$	−17.9136	−	8.86305i	−0.711442	−	0.351997i
$635$			25.1972i			0.999919i
$636$	−7.92346	−	22.2359i	−0.314186	−	0.881710i
$637$			0.459146i			0.0181920i
$638$	−2.08140	+	4.20685i	−0.0824035	+	0.166551i
$639$	−34.5365	−	24.6127i	−1.36624	−	0.973662i
$640$	18.8193	+	1.40586i	0.743900	+	0.0555716i
$641$		−	23.3467i		−	0.922139i	−0.887364	−	0.461070i	$-0.847466\pi$
$641$		−	23.3467i		−	0.922139i	0.887364	−	0.461070i	$-0.152534\pi$
$642$	−25.2179	+	26.0570i	−0.995272	+	1.02839i
$643$	15.5799			0.614413			0.307207	−	0.951643i	$-0.400606\pi$
$643$	15.5799			0.614413			0.307207	+	0.951643i	$0.400606\pi$
$644$	3.95517	−	3.01858i	0.155856	−	0.118949i
$645$	−15.0680	−	4.81982i	−0.593303	−	0.189780i
$646$	−4.65409	+	9.40667i	−0.183113	+	0.370100i
$647$	−15.4112			−0.605876			−0.302938	−	0.953010i	$-0.597968\pi$
$647$	−15.4112			−0.605876			−0.302938	+	0.953010i	$0.597968\pi$
$648$	22.0288	−	12.7566i	0.865375	−	0.501125i
$649$	−0.0187615			−0.000736455
$650$	−0.0968073	+	0.195663i	−0.00379710	+	0.00767454i
$651$	−10.1451	−	3.24512i	−0.397618	−	0.127186i
$652$	6.79039	+	8.89729i	0.265932	+	0.348445i
$653$	24.4686			0.957532			0.478766	−	0.877943i	$-0.341084\pi$
$653$	24.4686			0.957532			0.478766	+	0.877943i	$0.341084\pi$
$654$	7.85442	−	8.11574i	0.307132	−	0.317351i
$655$		−	4.40803i		−	0.172236i
$656$	19.7905	+	5.41349i	0.772690	+	0.211361i
$657$	−7.70702	−	5.49247i	−0.300680	−	0.214282i
$658$	2.83272	−	5.72538i	0.110431	−	0.223198i
$659$		−	20.8400i		−	0.811811i	−0.913915	−	0.405906i	$-0.866956\pi$
$659$		−	20.8400i		−	0.811811i	0.913915	−	0.405906i	$-0.133044\pi$
$660$	5.44304	−	1.93955i	0.211870	−	0.0754971i
$661$			26.6750i			1.03754i	0.854915	+	0.518769i	$0.173609\pi$
$661$			26.6750i			1.03754i	−0.854915	+	0.518769i	$0.826391\pi$
$662$	−10.9944	−	5.43966i	−0.427311	−	0.211418i
$663$	−0.341555	−	0.109253i	−0.0132649	−	0.00424304i
$664$	22.9520	−	4.47230i	0.890710	−	0.173559i
$665$			2.64452i			0.102550i
$666$	19.7793	−	10.6053i	0.766431	−	0.410949i
$667$	12.9935			0.503110
$668$	6.84622	+	8.97044i	0.264888	+	0.347077i
$669$	−3.75188	+	11.7294i	−0.145056	+	0.453484i
$670$	20.7660	+	10.2743i	0.802259	+	0.396930i
$671$	14.0256			0.541451
$672$	−3.17290	−	5.35674i	−0.122397	−	0.206641i
$673$	12.3082			0.474445			0.237223	−	0.971455i	$-0.423763\pi$
$673$	12.3082			0.474445			0.237223	+	0.971455i	$0.423763\pi$
$674$	11.0706	+	5.47737i	0.426425	+	0.210980i
$675$	−6.90040	−	9.22858i	−0.265596	−	0.355208i
$676$	15.7681	+	20.6606i	0.606467	+	0.794640i
$677$	13.5649			0.521341			0.260670	−	0.965428i	$-0.416056\pi$
$677$	13.5649			0.521341			0.260670	+	0.965428i	$0.416056\pi$
$678$	15.9709	−	16.5023i	0.613360	−	0.633767i
$679$		−	5.89131i		−	0.226088i
$680$	13.7740	−	2.68392i	0.528207	−	0.102924i
$681$	−10.0615	+	31.4549i	−0.385557	+	1.20535i
$682$	12.2673	+	6.06943i	0.469739	+	0.232411i
$683$		−	18.6981i		−	0.715464i	−0.933824	−	0.357732i	$-0.883550\pi$
$683$		−	18.6981i		−	0.715464i	0.933824	−	0.357732i	$-0.116450\pi$
$684$	−0.489788	−	14.9620i	−0.0187275	−	0.572087i
$685$		−	32.8845i		−	1.25645i
$686$	−5.41815	+	10.9510i	−0.206866	+	0.418109i
$687$	−1.88812	+	5.90277i	−0.0720363	+	0.225205i
$688$	5.77900	−	21.1268i	0.220322	−	0.805450i
$689$		−	0.474324i		−	0.0180703i
$690$	−11.4946	−	11.1245i	−0.437593	−	0.423503i
$691$	8.29275			0.315471			0.157736	−	0.987481i	$-0.449581\pi$
$691$	8.29275			0.315471			0.157736	+	0.987481i	$0.449581\pi$
$692$	−12.3232	−	16.1468i	−0.468458	−	0.613809i
$693$	−1.55240	−	1.10633i	−0.0589710	−	0.0420261i
$694$	7.85569	−	15.8776i	0.298198	−	0.602706i
$695$	2.98492			0.113225
$696$	1.90027	−	16.1477i	0.0720295	−	0.612075i
$697$	15.2568			0.577894
$698$	22.2173	−	44.9048i	0.840939	−	1.69967i
$699$	−4.49878	+	14.0644i	−0.170159	+	0.531964i
$700$	−2.24036	+	1.70984i	−0.0846775	+	0.0646257i
$701$	−44.9157			−1.69644			−0.848222	−	0.529641i	$-0.822327\pi$
$701$	−44.9157			−1.69644			−0.848222	+	0.529641i	$0.822327\pi$
$702$	0.503004	−	0.0928777i	0.0189847	−	0.00350544i
$703$		−	13.1983i		−	0.497783i
$704$	3.00363	+	7.41473i	0.113204	+	0.279453i
$705$	−19.5608	−	6.25690i	−0.736701	−	0.235649i
$706$	−1.43056	+	2.89140i	−0.0538400	+	0.108819i
$707$			3.61415i			0.135924i
$708$	0.0612212	−	0.0218154i	0.00230083	−	0.000819872i
$709$			18.6639i			0.700938i	0.936574	+	0.350469i	$0.113978\pi$
$709$			18.6639i			0.700938i	−0.936574	+	0.350469i	$0.886022\pi$
$710$	29.8892	+	14.7881i	1.12172	+	0.554989i
$711$	28.2523	−	39.6437i	1.05955	−	1.48675i
$712$	−27.4218	+	5.34326i	−1.02768	+	0.200247i
$713$		−	37.8895i		−	1.41897i
$714$	−3.32672	−	3.21960i	−0.124500	−	0.120491i
$715$	0.116108			0.00434220
$716$	−35.6826	+	27.2329i	−1.33352	+	1.01774i
$717$	49.2731	+	15.7610i	1.84014	+	0.588605i
$718$	4.35650	+	2.15545i	0.162583	+	0.0804406i
$719$	−4.48410			−0.167229			−0.0836143	−	0.996498i	$-0.526646\pi$
$719$	−4.48410			−0.167229			−0.0836143	+	0.996498i	$0.526646\pi$
$720$	−15.5060	+	12.6580i	−0.577876	+	0.471736i
$721$	−3.67273			−0.136780
$722$	16.1929	+	8.01171i	0.602639	+	0.298165i
$723$	24.0997	+	7.70878i	0.896278	+	0.286693i
$724$	29.7776	−	22.7262i	1.10668	−	0.844613i
$725$	−7.36001			−0.273344
$726$	1.76016	+	1.70348i	0.0653256	+	0.0632221i
$727$			31.1454i			1.15512i	0.816348	+	0.577560i	$0.195995\pi$
$727$			31.1454i			1.15512i	−0.816348	+	0.577560i	$0.804005\pi$
$728$	−0.0239268	−	0.122793i	−0.000886788	−	0.00455102i
$729$	−7.63568	+	25.8978i	−0.282803	+	0.959178i
$730$	6.66996	+	3.30006i	0.246866	+	0.122141i
$731$		−	16.2869i		−	0.602394i
$732$	−45.7671	+	16.3085i	−1.69160	+	0.602780i
$733$			4.13928i			0.152888i	0.997074	+	0.0764439i	$0.0243566\pi$
$733$			4.13928i			0.152888i	−0.997074	+	0.0764439i	$0.975643\pi$
$734$	−5.18899	+	10.4878i	−0.191529	+	0.387111i
$735$	18.1514	+	5.80610i	0.669526	+	0.214161i
$736$	14.7105	−	16.5554i	0.542236	−	0.610241i
$737$			9.82150i			0.361780i
$738$	−19.1792	+	10.2836i	−0.705995	+	0.378544i
$739$	8.86355			0.326051			0.163025	−	0.986622i	$-0.447875\pi$
$739$	8.86355			0.326051			0.163025	+	0.986622i	$0.447875\pi$
$740$	−14.0287	+	10.7066i	−0.515704	+	0.393584i
$741$	0.0916446	−	0.286506i	0.00336665	−	0.0105250i
$742$	2.71552	−	5.48851i	0.0996900	−	0.201490i
$743$	−1.05947			−0.0388680			−0.0194340	−	0.999811i	$-0.506186\pi$
$743$	−1.05947			−0.0388680			−0.0194340	+	0.999811i	$0.506186\pi$
$744$	−47.0871	−	5.54124i	−1.72630	−	0.203152i
$745$	25.6332			0.939129
$746$	−1.76813	+	3.57368i	−0.0647359	+	0.130842i
$747$	−14.3942	+	20.1979i	−0.526655	+	0.739001i
$748$	3.60909	+	4.72890i	0.131961	+	0.172906i
$749$	−9.40675			−0.343715
$750$	21.1911	+	20.5088i	0.773790	+	0.748874i
$751$		−	0.342250i		−	0.0124889i	−0.999981	−	0.00624444i	$-0.998012\pi$
$751$		−	0.342250i		−	0.0124889i	0.999981	−	0.00624444i	$-0.00198768\pi$
$752$	7.50208	−	27.4260i	0.273573	−	1.00012i
$753$	3.62841	−	11.3434i	0.132227	−	0.413376i
$754$	0.144881	−	0.292827i	0.00527625	−	0.0106641i
$755$			12.4618i			0.453531i
$756$	6.35210	+	1.80501i	0.231023	+	0.0656475i
$757$		−	49.5286i		−	1.80015i	−0.435736	−	0.900074i	$-0.643512\pi$
$757$		−	49.5286i		−	1.80015i	0.435736	−	0.900074i	$-0.356488\pi$
$758$	−7.51908	−	3.72018i	−0.273105	−	0.135123i
$759$	2.06594	−	6.45867i	0.0749888	−	0.234435i
$760$	2.25135	+	11.5540i	0.0816650	+	0.419107i
$761$			15.5394i			0.563302i	0.959517	+	0.281651i	$0.0908820\pi$
$761$			15.5394i			0.563302i	−0.959517	+	0.281651i	$0.909118\pi$
$762$	25.7325	−	26.5886i	0.932188	−	0.963203i
$763$	2.92984			0.106067
$764$	16.8120	+	22.0284i	0.608237	+	0.796958i
$765$	−8.63823	+	12.1211i	−0.312316	+	0.438241i
$766$	−3.30146	−	1.63345i	−0.119287	−	0.0590189i
$767$	0.00130594			4.71548e−5
$768$	−18.4228	−	20.7026i	−0.664777	−	0.747042i
$769$	38.3405			1.38259			0.691296	−	0.722571i	$-0.257040\pi$
$769$	38.3405			1.38259			0.691296	+	0.722571i	$0.257040\pi$
$770$	1.34351	+	0.664723i	0.0484168	+	0.0239549i
$771$	−12.7479	+	39.8534i	−0.459105	+	1.43528i
$772$	−27.4832	−	36.0105i	−0.989141	−	1.29605i
$773$	31.6334			1.13777			0.568887	−	0.822416i	$-0.307374\pi$
$773$	31.6334			1.13777			0.568887	+	0.822416i	$0.307374\pi$
$774$	10.9779	+	20.4741i	0.394593	+	0.735927i
$775$			21.4620i			0.770939i
$776$	−5.01543	−	25.7393i	−0.180043	−	0.923989i
$777$	5.54525	+	1.77376i	0.198935	+	0.0636333i
$778$	14.1051	+	6.97869i	0.505691	+	0.250198i
$779$			12.7979i			0.458531i
$780$	−0.378875	+	0.135007i	−0.0135659	+	0.00483403i
$781$			14.1364i			0.505842i
$782$	7.30297	−	14.7605i	0.261154	−	0.527834i
$783$	10.3271	+	13.8114i	0.369059	+	0.493579i
$784$	−6.96157	+	25.4500i	−0.248627	+	0.908927i
$785$			3.37224i			0.120361i
$786$	−4.50167	+	4.65144i	−0.160569	+	0.165911i
$787$	29.3603			1.04658			0.523291	−	0.852154i	$-0.324704\pi$
$787$	29.3603			1.04658			0.523291	+	0.852154i	$0.324704\pi$
$788$	−18.7163	−	24.5235i	−0.666740	−	0.873614i
$789$	43.4116	+	13.8861i	1.54549	+	0.494357i
$790$	−16.9750	+	34.3092i	−0.603943	+	1.22067i
$791$	5.95744			0.211822
$792$	−7.72437	−	3.51200i	−0.274473	−	0.124794i
$793$	−0.976281			−0.0346688
$794$	−6.77752	+	13.6985i	−0.240525	+	0.486140i
$795$	−18.7515	−	5.99805i	−0.665047	−	0.212729i
$796$	8.73002	−	6.66273i	0.309428	−	0.236154i
$797$	17.6347			0.624652			0.312326	−	0.949975i	$-0.398892\pi$
$797$	17.6347			0.624652			0.312326	+	0.949975i	$0.398892\pi$
$798$	2.70069	−	2.79055i	0.0956035	−	0.0987844i
$799$		−	21.1431i		−	0.747989i
$800$	−8.33258	+	9.37762i	−0.294601	+	0.331549i
$801$	17.1974	−	24.1313i	0.607639	−	0.852638i
$802$	−2.31734	+	4.68371i	−0.0818280	+	0.165387i
$803$			3.15463i			0.111325i
$804$	−11.4202	−	32.0488i	−0.402758	−	1.13027i
$805$		−	4.14964i		−	0.146256i
$806$	−0.853893	−	0.422477i	−0.0300771	−	0.0148811i
$807$	49.4368	+	15.8134i	1.74026	+	0.556657i
$808$	3.07683	+	15.7904i	0.108242	+	0.555503i
$809$		−	27.8266i		−	0.978331i	−0.872191	−	0.489165i	$-0.837301\pi$
$809$		−	27.8266i		−	0.978331i	0.872191	−	0.489165i	$-0.162699\pi$
$810$	2.68897	−	21.0598i	0.0944808	−	0.739965i
$811$	25.6977			0.902367			0.451184	−	0.892431i	$-0.351002\pi$
$811$	25.6977			0.902367			0.451184	+	0.892431i	$0.351002\pi$
$812$	3.35289	−	2.55892i	0.117663	−	0.0898005i
$813$	−3.25529	+	10.1769i	−0.114168	+	0.356920i
$814$	−6.70522	−	3.31751i	−0.235018	−	0.116279i
$815$	9.33477			0.326983
$816$	−17.2755	−	11.2344i	−0.604764	−	0.393284i
$817$	13.6619			0.477971
$818$	−32.6066	−	16.1326i	−1.14006	−	0.564063i
$819$	0.108059	+	0.0770088i	0.00377587	+	0.00269090i
$820$	13.6030	−	10.3818i	0.475039	−	0.362549i
$821$	−21.0808			−0.735726			−0.367863	−	0.929880i	$-0.619910\pi$
$821$	−21.0808			−0.735726			−0.367863	+	0.929880i	$0.619910\pi$
$822$	−33.5831	+	34.7004i	−1.17134	+	1.21032i
$823$		−	29.6426i		−	1.03328i	−0.856204	−	0.516638i	$-0.827183\pi$
$823$		−	29.6426i		−	1.03328i	0.856204	−	0.516638i	$-0.172817\pi$
$824$	−16.0463	+	3.12669i	−0.558999	+	0.108924i
$825$	−1.17022	+	3.65844i	−0.0407420	+	0.127370i
$826$	0.0151113	+	0.00747655i	0.000525790	+	0.000260143i
$827$			1.85013i			0.0643353i	0.999482	+	0.0321676i	$0.0102410\pi$
$827$			1.85013i			0.0643353i	−0.999482	+	0.0321676i	$0.989759\pi$
$828$	0.768552	+	23.4776i	0.0267090	+	0.815905i
$829$			24.2891i			0.843594i	0.906690	+	0.421797i	$0.138600\pi$
$829$			24.2891i			0.843594i	−0.906690	+	0.421797i	$0.861400\pi$
$830$	8.64850	−	17.4800i	0.300194	−	0.606740i
$831$	7.53638	−	23.5607i	0.261434	−	0.817313i
$832$	−0.209075	−	0.516119i	−0.00724836	−	0.0178932i
$833$			19.6198i			0.679785i
$834$	−3.14975	−	3.04833i	−0.109067	−	0.105555i
$835$	9.41151			0.325699
$836$	−3.96674	+	3.02740i	−0.137192	+	0.104705i
$837$	40.2744	−	30.1140i	1.39209	−	1.04089i
$838$	11.5766	−	23.3981i	0.399906	−	0.808273i
$839$	−26.6793			−0.921073			−0.460537	−	0.887641i	$-0.652343\pi$
$839$	−26.6793			−0.921073			−0.460537	+	0.887641i	$0.652343\pi$
$840$	−5.15696	−	0.606875i	−0.177932	−	0.0209392i
$841$	−17.9851			−0.620176
$842$	0.112099	−	0.226570i	0.00386319	−	0.00780813i
$843$	4.76705	−	14.9031i	0.164186	−	0.513289i
$844$	20.4092	+	26.7416i	0.702512	+	0.920485i
$845$	21.6765			0.745695
$846$	14.2511	+	26.5787i	0.489963	+	0.913795i
$847$			0.635429i			0.0218336i
$848$	7.19171	−	26.2913i	0.246964	−	0.902847i
$849$	−42.0572	−	13.4528i	−1.44340	−	0.461700i
$850$	−4.13668	+	8.36089i	−0.141887	+	0.286776i
$851$			20.7101i			0.709933i
$852$	−16.4374	−	46.1289i	−0.563137	−	1.58035i
$853$		−	17.3896i		−	0.595408i	−0.954658	−	0.297704i	$-0.903779\pi$
$853$		−	17.3896i		−	0.595408i	0.954658	−	0.297704i	$-0.0962209\pi$
$854$	−11.2968	−	5.58924i	−0.386567	−	0.191260i
$855$	−10.1676	−	7.24599i	−0.347723	−	0.247808i
$856$	−41.0984	+	8.00822i	−1.40472	+	0.273715i
$857$			28.3201i			0.967396i	0.875235	+	0.483698i	$0.160707\pi$
$857$			28.3201i			0.967396i	−0.875235	+	0.483698i	$0.839293\pi$
$858$	−0.122520	−	0.118575i	−0.00418275	−	0.00404807i
$859$	22.0179			0.751243			0.375621	−	0.926773i	$-0.377429\pi$
$859$	22.0179			0.751243			0.375621	+	0.926773i	$0.377429\pi$
$860$	−11.0828	−	14.5215i	−0.377919	−	0.495179i
$861$	−5.37701	−	1.71994i	−0.183248	−	0.0586155i
$862$	16.0074	+	7.91992i	0.545215	+	0.269753i
$863$	7.39300			0.251660			0.125830	−	0.992052i	$-0.459841\pi$
$863$	7.39300			0.251660			0.125830	+	0.992052i	$0.459841\pi$
$864$	29.2892	+	2.47843i	0.996439	+	0.0843180i
$865$	−16.9407			−0.576002
$866$	29.3276	+	14.5103i	0.996591	+	0.493079i
$867$	13.4501	+	4.30228i	0.456788	+	0.146113i
$868$	−7.46189	−	9.77714i	−0.253273	−	0.331858i
$869$	−16.2269			−0.550460
$870$	−9.74428	−	9.43052i	−0.330362	−	0.319724i
$871$		−	0.683648i		−	0.0231645i
$872$	12.8006	−	2.49425i	0.433482	−	0.0844660i
$873$	22.6507	+	16.1422i	0.766611	+	0.546331i
$874$	12.3815	+	6.12594i	0.418811	+	0.207213i
$875$			7.65014i			0.258622i
$876$	−3.66812	−	10.2940i	−0.123934	−	0.347800i
$877$		−	50.8000i		−	1.71539i	−0.514155	−	0.857697i	$-0.671894\pi$
$877$		−	50.8000i		−	1.71539i	0.514155	−	0.857697i	$-0.328106\pi$
$878$	−19.9095	+	40.2402i	−0.671912	+	1.35804i
$879$	36.1741	+	11.5710i	1.22012	+	0.390281i
$880$	6.43575	+	1.76043i	0.216949	+	0.0593441i
$881$			25.7026i			0.865944i	0.901407	+	0.432972i	$0.142535\pi$
$881$			25.7026i			0.865944i	−0.901407	+	0.432972i	$0.857465\pi$
$882$	−13.2243	−	24.6638i	−0.445287	−	0.830472i
$883$	28.9835			0.975374			0.487687	−	0.873019i	$-0.337841\pi$
$883$	28.9835			0.975374			0.487687	+	0.873019i	$0.337841\pi$
$884$	−0.251219	−	0.329166i	−0.00844940	−	0.0110710i
$885$	0.0165142	−	0.0516278i	0.000555119	−	0.00173545i
$886$	9.15917	−	18.5122i	0.307708	−	0.621928i
$887$	28.2276			0.947789			0.473895	−	0.880582i	$-0.342848\pi$
$887$	28.2276			0.947789			0.473895	+	0.880582i	$0.342848\pi$
$888$	25.7374	+	3.02880i	0.863692	+	0.101640i
$889$	9.59867			0.321929
$890$	−10.3328	+	20.8842i	−0.346355	+	0.700039i
$891$	8.50719	−	2.93728i	0.285002	−	0.0984027i
$892$	−11.3039	+	8.62714i	−0.378484	+	0.288858i
$893$	17.7354			0.593493
$894$	−27.0487	−	26.1778i	−0.904645	−	0.875516i
$895$			37.4371i			1.25138i
$896$	0.535552	−	7.16908i	0.0178915	−	0.239502i
$897$	−0.143804	+	0.449570i	−0.00480148	+	0.0150107i
$898$	−15.2651	+	30.8533i	−0.509404	+	1.02959i
$899$		−	32.1198i		−	1.07126i
$900$	−0.435337	−	13.2986i	−0.0145112	−	0.443288i
$901$		−	20.2684i		−	0.675238i
$902$	6.50178	+	3.21686i	0.216486	+	0.107110i
$903$	−1.83607	+	5.74005i	−0.0611006	+	0.191017i
$904$	26.0283	−	5.07173i	0.865688	−	0.168683i
$905$		−	31.2418i		−	1.03851i
$906$	12.7265	−	13.1499i	0.422810	−	0.436878i
$907$	−43.8772			−1.45692			−0.728459	−	0.685089i	$-0.759763\pi$
$907$	−43.8772			−1.45692			−0.728459	+	0.685089i	$0.759763\pi$
$908$	−30.3140	+	23.1355i	−1.00600	+	0.767780i
$909$	−13.8956	−	9.90280i	−0.460888	−	0.328455i
$910$	−0.0935182	−	0.0462695i	−0.00310010	−	0.00153382i
$911$	−50.2102			−1.66354			−0.831768	−	0.555123i	$-0.812671\pi$
$911$	−50.2102			−1.66354			−0.831768	+	0.555123i	$0.812671\pi$
$912$	9.42377	−	14.4912i	0.312052	−	0.479851i
$913$	8.26737			0.273610
$914$	2.98687	+	1.47780i	0.0987969	+	0.0488813i
$915$	−12.3455	+	38.5954i	−0.408130	+	1.27592i
$916$	−5.68867	+	4.34158i	−0.187959	+	0.143450i
$917$	−1.67920			−0.0554522
$918$	21.4939	−	3.96876i	0.709404	−	0.130989i
$919$			36.7376i			1.21186i	0.795517	+	0.605931i	$0.207199\pi$
$919$			36.7376i			1.21186i	−0.795517	+	0.605931i	$0.792801\pi$
$920$	−3.53271	−	18.1300i	−0.116470	−	0.597727i
$921$	30.7370	+	9.83185i	1.01282	+	0.323970i
$922$	43.5194	+	21.5319i	1.43324	+	0.709115i
$923$		−	0.983999i		−	0.0323887i
$924$	−0.738858	−	2.07348i	−0.0243067	−	0.0682126i
$925$		−	11.7310i		−	0.385712i
$926$	5.25136	−	10.6139i	0.172571	−	0.348793i
$927$	10.0633	−	14.1208i	0.330522	−	0.463788i
$928$	12.4704	−	14.0344i	0.409362	−	0.460703i
$929$		−	8.81754i		−	0.289294i	−0.989483	−	0.144647i	$-0.953795\pi$
$929$		−	8.81754i		−	0.289294i	0.989483	−	0.144647i	$-0.0462047\pi$
$930$	−27.4997	+	28.4146i	−0.901750	+	0.931752i
$931$	−16.4576			−0.539377
$932$	−13.5543	+	10.3446i	−0.443984	+	0.338848i
$933$	−22.1226	−	7.07636i	−0.724261	−	0.231670i
$934$	11.4733	−	23.1894i	0.375419	−	0.758781i
$935$	4.96142			0.162256
$936$	0.537672	+	0.244461i	0.0175744	+	0.00799046i
$937$	−38.1300			−1.24565			−0.622827	−	0.782360i	$-0.714016\pi$
$937$	−38.1300			−1.24565			−0.622827	+	0.782360i	$0.714016\pi$
$938$	3.91391	−	7.91064i	0.127794	−	0.258291i
$939$	14.2116	+	4.54587i	0.463779	+	0.148349i
$940$	−14.3872	−	18.8513i	−0.469260	−	0.614860i
$941$	5.47079			0.178343			0.0891714	−	0.996016i	$-0.471578\pi$
$941$	5.47079			0.178343			0.0891714	+	0.996016i	$0.471578\pi$
$942$	3.44388	−	3.55847i	0.112208	−	0.115941i
$943$		−	20.0818i		−	0.653952i
$944$	0.0723869	+	0.0198007i	0.00235599	+	0.000644457i
$945$	4.41084	−	3.29808i	0.143485	−	0.107287i
$946$	3.43405	−	6.94077i	0.111651	−	0.225664i
$947$			0.612227i			0.0198947i	0.999951	+	0.00994736i	$0.00316639\pi$
$947$			0.612227i			0.0198947i	−0.999951	+	0.00994736i	$0.996834\pi$
$948$	52.9504	−	18.8682i	1.71975	−	0.612810i
$949$		−	0.219585i		−	0.00712804i
$950$	−7.01335	−	3.46996i	−0.227543	−	0.112580i
$951$	23.3144	+	7.45759i	0.756022	+	0.241829i
$952$	−1.02242	−	5.24709i	−0.0331368	−	0.170059i
$953$		−	2.38824i		−	0.0773626i	−0.999252	−	0.0386813i	$-0.987684\pi$
$953$		−	2.38824i		−	0.0773626i	0.999252	−	0.0386813i	$-0.0123157\pi$
$954$	13.6615	+	25.4791i	0.442308	+	0.824917i
$955$	23.1115			0.747870
$956$	36.2411	+	47.4859i	1.17212	+	1.53580i
$957$	1.75134	−	5.47517i	0.0566129	−	0.176987i
$958$	32.3002	+	15.9810i	1.04357	+	0.516323i
$959$	−12.5271			−0.404521
$960$	−23.0476	+	1.73880i	−0.743859	+	0.0561196i
$961$	−62.6624			−2.02137
$962$	0.466732	+	0.230923i	0.0150480	+	0.00744525i
$963$	25.7745	−	36.1668i	0.830573	−	1.16546i
$964$	17.7257	+	23.2256i	0.570906	+	0.748045i
$965$	−37.7812			−1.21622
$966$	−4.23780	+	4.37879i	−0.136349	+	0.140885i
$967$			21.4389i			0.689428i	0.938708	+	0.344714i	$0.112024\pi$
$967$			21.4389i			0.689428i	−0.938708	+	0.344714i	$0.887976\pi$
$968$	0.540958	+	2.77621i	0.0173871	+	0.0892309i
$969$	3.91607	−	12.2427i	0.125802	−	0.393292i
$970$	−19.6028	−	9.69880i	−0.629409	−	0.311410i
$971$		−	33.9504i		−	1.08952i	−0.838592	−	0.544760i	$-0.816621\pi$
$971$		−	33.9504i		−	1.08952i	0.838592	−	0.544760i	$-0.183379\pi$
$972$	−24.3446	+	19.4766i	−0.780854	+	0.624713i
$973$		−	1.13708i		−	0.0364532i
$974$	9.05831	−	18.3083i	0.290247	−	0.586636i
$975$	0.0814561	−	0.254654i	0.00260868	−	0.00815545i
$976$	−54.1143	−	14.8024i	−1.73216	−	0.473813i
$977$			24.8966i			0.796511i	0.917274	+	0.398256i	$0.130384\pi$
$977$			24.8966i			0.796511i	−0.917274	+	0.398256i	$0.869616\pi$
$978$	−9.85025	−	9.53307i	−0.314976	−	0.304834i
$979$	−9.87741			−0.315683
$980$	13.3507	+	17.4931i	0.426471	+	0.558795i
$981$	−8.02778	+	11.2646i	−0.256307	+	0.359650i
$982$	−24.4565	+	49.4305i	−0.780438	+	1.57739i
$983$	−26.1512			−0.834095			−0.417048	−	0.908885i	$-0.636935\pi$
$983$	−26.1512			−0.834095			−0.417048	+	0.908885i	$0.636935\pi$
$984$	−24.9566	−	2.93691i	−0.795587	−	0.0936253i
$985$	−25.7293			−0.819804
$986$	6.19091	−	12.5128i	0.197159	−	0.398489i
$987$	−2.38352	+	7.45152i	−0.0758683	+	0.237185i
$988$	0.276114	−	0.210729i	0.00878434	−	0.00670419i
$989$	−21.4377			−0.681678
$990$	−6.23694	+	3.34415i	−0.198223	+	0.106284i
$991$			54.3769i			1.72734i	0.504057	+	0.863670i	$0.331840\pi$
$991$			54.3769i			1.72734i	−0.504057	+	0.863670i	$0.668160\pi$
$992$	−40.9248	−	36.3642i	−1.29936	−	1.15456i
$993$	14.3091	+	4.57707i	0.454087	+	0.145249i
$994$	5.63343	−	11.3861i	0.178681	−	0.361144i
$995$		−	9.15928i		−	0.290369i
$996$	−26.9774	+	9.61306i	−0.854813	+	0.304601i
$997$		−	12.6342i		−	0.400128i	−0.979783	−	0.200064i	$-0.935885\pi$
$997$		−	12.6342i		−	0.400128i	0.979783	−	0.200064i	$-0.0641150\pi$
$998$	22.5365	+	11.1503i	0.713382	+	0.352957i
$999$	−22.0137	+	16.4601i	−0.696483	+	0.520775i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	264.2.k.b.155.5	✓	32
3.2	odd	2	inner	264.2.k.b.155.28	yes	32
4.3	odd	2		1056.2.k.b.815.2		32
8.3	odd	2	inner	264.2.k.b.155.27	yes	32
8.5	even	2		1056.2.k.b.815.1		32
12.11	even	2		1056.2.k.b.815.3		32
24.5	odd	2		1056.2.k.b.815.4		32
24.11	even	2	inner	264.2.k.b.155.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
264.2.k.b.155.5	✓	32	1.1	even	1	trivial
264.2.k.b.155.6	yes	32	24.11	even	2	inner
264.2.k.b.155.27	yes	32	8.3	odd	2	inner
264.2.k.b.155.28	yes	32	3.2	odd	2	inner
1056.2.k.b.815.1		32	8.5	even	2
1056.2.k.b.815.2		32	4.3	odd	2
1056.2.k.b.815.3		32	12.11	even	2
1056.2.k.b.815.4		32	24.5	odd	2

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:	\( N \)	\(=\)	\( 264 = 2^{3} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	264.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26755 - 0.627142i) q^{2} +(1.64971 + 0.527693i) q^{3} +(1.21339 + 1.58987i) q^{4} +1.66805 q^{5} +(-1.76016 - 1.70348i) q^{6} -0.635429i q^{7} +(-0.540958 - 2.77621i) q^{8} +(2.44308 + 1.74108i) q^{9} +(-2.11434 - 1.04610i) q^{10} -1.00000i q^{11} +(1.16277 + 3.26312i) q^{12} +0.0696073i q^{13} +(-0.398504 + 0.805441i) q^{14} +(2.75179 + 0.880216i) q^{15} +(-1.05539 + 3.85826i) q^{16} +2.97439i q^{17} +(-2.00483 - 3.73907i) q^{18} -2.49500 q^{19} +(2.02398 + 2.65198i) q^{20} +(0.335311 - 1.04827i) q^{21} +(-0.627142 + 1.26755i) q^{22} +3.91504 q^{23} +(0.572565 - 4.86541i) q^{24} -2.21762 q^{25} +(0.0436536 - 0.0882310i) q^{26} +(3.11162 + 4.16147i) q^{27} +(1.01025 - 0.771021i) q^{28} +3.31887 q^{29} +(-2.93602 - 2.84148i) q^{30} -9.67793i q^{31} +(3.75743 - 4.22868i) q^{32} +(0.527693 - 1.64971i) q^{33} +(1.86537 - 3.77020i) q^{34} -1.05992i q^{35} +(0.196308 + 5.99679i) q^{36} +5.28989i q^{37} +(3.16255 + 1.56472i) q^{38} +(-0.0367313 + 0.114832i) q^{39} +(-0.902343 - 4.63085i) q^{40} -5.12939i q^{41} +(-1.08244 + 1.11846i) q^{42} -5.47572 q^{43} +(1.58987 - 1.21339i) q^{44} +(4.07517 + 2.90420i) q^{45} +(-4.96252 - 2.45528i) q^{46} -7.10838 q^{47} +(-3.77706 + 5.80809i) q^{48} +6.59623 q^{49} +(2.81096 + 1.39076i) q^{50} +(-1.56957 + 4.90688i) q^{51} +(-0.110667 + 0.0844605i) q^{52} -6.81429 q^{53} +(-1.33431 - 7.22631i) q^{54} -1.66805i q^{55} +(-1.76409 + 0.343741i) q^{56} +(-4.11603 - 1.31660i) q^{57} +(-4.20685 - 2.08140i) q^{58} -0.0187615i q^{59} +(1.93955 + 5.44304i) q^{60} +14.0256i q^{61} +(-6.06943 + 12.2673i) q^{62} +(1.10633 - 1.55240i) q^{63} +(-7.41473 + 3.00363i) q^{64} +0.116108i q^{65} +(-1.70348 + 1.76016i) q^{66} -9.82150 q^{67} +(-4.72890 + 3.60909i) q^{68} +(6.45867 + 2.06594i) q^{69} +(-0.664723 + 1.34351i) q^{70} -14.1364 q^{71} +(3.51200 - 7.72437i) q^{72} -3.15463 q^{73} +(3.31751 - 6.70522i) q^{74} +(-3.65844 - 1.17022i) q^{75} +(-3.02740 - 3.96674i) q^{76} -0.635429 q^{77} +(0.118575 - 0.122520i) q^{78} -16.2269i q^{79} +(-1.76043 + 6.43575i) q^{80} +(2.93728 + 8.50719i) q^{81} +(-3.21686 + 6.50178i) q^{82} +8.26737i q^{83} +(2.07348 - 0.738858i) q^{84} +4.96142i q^{85} +(6.94077 + 3.43405i) q^{86} +(5.47517 + 1.75134i) q^{87} +(-2.77621 + 0.540958i) q^{88} -9.87741i q^{89} +(-3.34415 - 6.23694i) q^{90} +0.0442305 q^{91} +(4.75045 + 6.22441i) q^{92} +(5.10698 - 15.9658i) q^{93} +(9.01025 + 4.45796i) q^{94} -4.16178 q^{95} +(8.43011 - 4.99331i) q^{96} +9.27138 q^{97} +(-8.36108 - 4.13677i) q^{98} +(1.74108 - 2.44308i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{3} + 2 q^{6} + 8 q^{9} + 12 q^{10} - 12 q^{12} + 2 q^{18} - 32 q^{19} + 4 q^{22} + 12 q^{24} - 64 q^{27} + 40 q^{28} - 22 q^{30} - 64 q^{34} - 20 q^{36} + 32 q^{40} + 20 q^{42} - 16 q^{43} - 28 q^{46}+ \cdots - 16 q^{97}+O(q^{100}) \) 32 * q + 8 * q^3 + 2 * q^6 + 8 * q^9 + 12 * q^10 - 12 * q^12 + 2 * q^18 - 32 * q^19 + 4 * q^22 + 12 * q^24 - 64 * q^27 + 40 * q^28 - 22 * q^30 - 64 * q^34 - 20 * q^36 + 32 * q^40 + 20 * q^42 - 16 * q^43 - 28 * q^46 - 32 * q^49 + 8 * q^51 + 40 * q^52 - 8 * q^54 + 16 * q^57 - 40 * q^58 + 68 * q^60 - 14 * q^66 + 8 * q^70 - 8 * q^72 + 64 * q^73 - 16 * q^75 + 8 * q^76 + 16 * q^78 + 72 * q^81 + 88 * q^82 - 60 * q^84 + 8 * q^88 - 58 * q^90 + 80 * q^91 - 72 * q^94 - 4 * q^96 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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