LMFDB - Embedded newform 276.2.o.a.35.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(35,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 20]))

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

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

chi := DirichletCharacter("276.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.o (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$44$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			35.11
Character	$\chi$	$=$	276.35
Dual form			276.2.o.a.71.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00830 - 0.991633i) q^{2} +(-1.72667 - 0.136433i) q^{3} +(0.0333293 + 1.99972i) q^{4} +(-0.252117 - 0.858632i) q^{5} +(1.60571 + 1.84979i) q^{6} +(-1.92220 + 1.66560i) q^{7} +(1.94938 - 2.04937i) q^{8} +(2.96277 + 0.471148i) q^{9} +O(q^{10})$	\(q+(-1.00830 - 0.991633i) q^{2} +(-1.72667 - 0.136433i) q^{3} +(0.0333293 + 1.99972i) q^{4} +(-0.252117 - 0.858632i) q^{5} +(1.60571 + 1.84979i) q^{6} +(-1.92220 + 1.66560i) q^{7} +(1.94938 - 2.04937i) q^{8} +(2.96277 + 0.471148i) q^{9} +(-0.597239 + 1.11576i) q^{10} +(1.26700 + 0.814252i) q^{11} +(0.215279 - 3.45741i) q^{12} +(-0.796709 + 0.919451i) q^{13} +(3.58982 + 0.226700i) q^{14} +(0.318177 + 1.51697i) q^{15} +(-3.99778 + 0.133299i) q^{16} +(6.64432 - 3.03436i) q^{17} +(-2.52015 - 3.41304i) q^{18} +(5.60653 + 2.56042i) q^{19} +(1.70862 - 0.532782i) q^{20} +(3.54625 - 2.61369i) q^{21} +(-0.470075 - 2.07741i) q^{22} +(0.578761 - 4.76078i) q^{23} +(-3.64554 + 3.27262i) q^{24} +(3.53258 - 2.27025i) q^{25} +(1.71508 - 0.137038i) q^{26} +(-5.05145 - 1.21774i) q^{27} +(-3.39480 - 3.78836i) q^{28} +(-6.02903 + 2.75337i) q^{29} +(1.18346 - 1.84507i) q^{30} +(4.18222 - 0.601313i) q^{31} +(4.16313 + 3.82992i) q^{32} +(-2.07660 - 1.57880i) q^{33} +(-9.70842 - 3.52918i) q^{34} +(1.91476 + 1.23054i) q^{35} +(-0.843419 + 5.94042i) q^{36} +(5.30163 + 1.55670i) q^{37} +(-3.11406 - 8.14129i) q^{38} +(1.50110 - 1.47889i) q^{39} +(-2.25113 - 1.15712i) q^{40} +(1.90201 + 6.47765i) q^{41} +(-6.16750 - 0.881205i) q^{42} +(5.31318 + 0.763921i) q^{43} +(-1.58605 + 2.56079i) q^{44} +(-0.342423 - 2.66272i) q^{45} +(-5.30451 + 4.22637i) q^{46} +0.483749 q^{47} +(6.92103 + 0.315265i) q^{48} +(-0.0755561 + 0.525504i) q^{49} +(-5.81315 - 1.21393i) q^{50} +(-11.8865 + 4.33283i) q^{51} +(-1.86520 - 1.56255i) q^{52} +(-4.51572 + 3.91290i) q^{53} +(3.88582 + 6.23702i) q^{54} +(0.379710 - 1.29317i) q^{55} +(-0.333691 + 7.18619i) q^{56} +(-9.33130 - 5.18591i) q^{57} +(8.80939 + 3.20237i) q^{58} +(0.185128 - 0.213649i) q^{59} +(-3.02292 + 0.686826i) q^{60} +(1.15091 + 8.00476i) q^{61} +(-4.81321 - 3.54093i) q^{62} +(-6.47980 + 4.02915i) q^{63} +(-0.399804 - 7.99000i) q^{64} +(0.990335 + 0.452271i) q^{65} +(0.528238 + 3.65113i) q^{66} +(-2.83225 - 4.40707i) q^{67} +(6.28932 + 13.1857i) q^{68} +(-1.64886 + 8.14133i) q^{69} +(-0.710403 - 3.13949i) q^{70} +(6.21490 - 3.99407i) q^{71} +(6.74114 - 5.15336i) q^{72} +(-1.39548 + 3.05568i) q^{73} +(-3.80195 - 6.82688i) q^{74} +(-6.40934 + 3.43801i) q^{75} +(-4.93326 + 11.2968i) q^{76} +(-3.79165 + 0.545157i) q^{77} +(-2.98007 + 0.00262660i) q^{78} +(4.79347 + 4.15356i) q^{79} +(1.12236 + 3.39901i) q^{80} +(8.55604 + 2.79181i) q^{81} +(4.50566 - 8.41750i) q^{82} +(-11.1296 - 3.26795i) q^{83} +(5.34484 + 7.00441i) q^{84} +(-4.28054 - 4.94001i) q^{85} +(-4.59974 - 6.03899i) q^{86} +(10.7858 - 3.93159i) q^{87} +(4.13857 - 1.00926i) q^{88} +(7.29656 + 1.04909i) q^{89} +(-2.29517 + 3.02437i) q^{90} -3.09437i q^{91} +(9.53953 + 0.998688i) q^{92} +(-7.30335 + 0.467676i) q^{93} +(-0.487763 - 0.479701i) q^{94} +(0.784954 - 5.45948i) q^{95} +(-6.66583 - 7.18100i) q^{96} +(-7.46649 + 2.19236i) q^{97} +(0.597290 - 0.454941i) q^{98} +(3.37020 + 3.00939i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9}+O(q^{10}) $ 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9	$ 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9} - 30 q^{10} - 18 q^{12} - 36 q^{13} - 30 q^{16} - 10 q^{18} - 22 q^{21} - 48 q^{22} - 14 q^{24} - 8 q^{25} - 34 q^{28} - 21 q^{30} - 6 q^{33} - 32 q^{34} + 22 q^{36} - 36 q^{37} - 168 q^{40} + q^{42} - 44 q^{45} - 110 q^{46} - 6 q^{48} - 16 q^{49} - 94 q^{52} + 21 q^{54} - 46 q^{57} - 116 q^{58} - 47 q^{60} - 68 q^{61} - 28 q^{64} - 20 q^{66} - 22 q^{69} - 44 q^{70} - 23 q^{72} - 36 q^{73} - 74 q^{76} + 134 q^{78} - 130 q^{81} + 36 q^{82} + 105 q^{84} - 60 q^{85} + 38 q^{88} + 162 q^{90} - 332 q^{93} - 40 q^{94} + 225 q^{96} - 36 q^{97}+O(q^{100}) $ 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9 - 30 * q^10 - 18 * q^12 - 36 * q^13 - 30 * q^16 - 10 * q^18 - 22 * q^21 - 48 * q^22 - 14 * q^24 - 8 * q^25 - 34 * q^28 - 21 * q^30 - 6 * q^33 - 32 * q^34 + 22 * q^36 - 36 * q^37 - 168 * q^40 + q^42 - 44 * q^45 - 110 * q^46 - 6 * q^48 - 16 * q^49 - 94 * q^52 + 21 * q^54 - 46 * q^57 - 116 * q^58 - 47 * q^60 - 68 * q^61 - 28 * q^64 - 20 * q^66 - 22 * q^69 - 44 * q^70 - 23 * q^72 - 36 * q^73 - 74 * q^76 + 134 * q^78 - 130 * q^81 + 36 * q^82 + 105 * q^84 - 60 * q^85 + 38 * q^88 + 162 * q^90 - 332 * q^93 - 40 * q^94 + 225 * q^96 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$-1$	$-1$

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 $

$2$	−1.00830	−	0.991633i	−0.712974	−	0.701190i
$2$	−1.00830	−	0.991633i	−0.712974	−	0.701190i
$3$	−1.72667	−	0.136433i	−0.996893	−	0.0787695i
$3$	−1.72667	−	0.136433i	−0.996893	−	0.0787695i
$4$	0.0333293	+	1.99972i	0.0166647	+	0.999861i
$5$	−0.252117	−	0.858632i	−0.112750	−	0.383992i	0.883712	−	0.468031i	$-0.155036\pi$
$5$	−0.252117	−	0.858632i	−0.112750	−	0.383992i	−0.996463	+	0.0840385i	$0.973218\pi$
$6$	1.60571	+	1.84979i	0.655527	+	0.755172i
$7$	−1.92220	+	1.66560i	−0.726525	+	0.629537i	−0.937513	−	0.347951i	$-0.886877\pi$
$7$	−1.92220	+	1.66560i	−0.726525	+	0.629537i	0.210988	+	0.977489i	$0.432332\pi$
$8$	1.94938	−	2.04937i	0.689211	−	0.724560i
$9$	2.96277	+	0.471148i	0.987591	+	0.157049i
$10$	−0.597239	+	1.11576i	−0.188863	+	0.352836i
$11$	1.26700	+	0.814252i	0.382015	+	0.245506i	0.717528	−	0.696529i	$-0.245273\pi$
$11$	1.26700	+	0.814252i	0.382015	+	0.245506i	−0.335513	+	0.942035i	$0.608910\pi$
$12$	0.215279	−	3.45741i	0.0621457	−	0.998067i
$13$	−0.796709	+	0.919451i	−0.220967	+	0.255010i	−0.855400	−	0.517968i	$-0.826688\pi$
$13$	−0.796709	+	0.919451i	−0.220967	+	0.255010i	0.634432	+	0.772978i	$0.281234\pi$
$14$	3.58982	+	0.226700i	0.959419	+	0.0605882i
$15$	0.318177	+	1.51697i	0.0821531	+	0.391680i
$16$	−3.99778	+	0.133299i	−0.999445	+	0.0333247i
$17$	6.64432	−	3.03436i	1.61148	−	0.735940i	0.612952	−	0.790120i	$-0.289982\pi$
$17$	6.64432	−	3.03436i	1.61148	−	0.735940i	0.998531	+	0.0541802i	$0.0172545\pi$
$18$	−2.52015	−	3.41304i	−0.594005	−	0.804461i
$19$	5.60653	+	2.56042i	1.28623	+	0.587400i	0.936899	−	0.349600i	$-0.113683\pi$
$19$	5.60653	+	2.56042i	1.28623	+	0.587400i	0.349328	+	0.937001i	$0.386410\pi$
$20$	1.70862	−	0.532782i	0.382060	−	0.119134i
$21$	3.54625	−	2.61369i	0.773856	−	0.570353i
$22$	−0.470075	−	2.07741i	−0.100220	−	0.442905i
$23$	0.578761	−	4.76078i	0.120680	−	0.992691i
$23$	0.578761	−	4.76078i	0.120680	−	0.992691i
$24$	−3.64554	+	3.27262i	−0.744143	+	0.668020i
$25$	3.53258	−	2.27025i	0.706516	−	0.454050i
$26$	1.71508	−	0.137038i	0.336354	−	0.0268754i
$27$	−5.05145	−	1.21774i	−0.972151	−	0.234353i
$28$	−3.39480	−	3.78836i	−0.641557	−	0.715933i
$29$	−6.02903	+	2.75337i	−1.11956	+	0.511287i	−0.887220	−	0.461347i	$-0.847366\pi$
$29$	−6.02903	+	2.75337i	−1.11956	+	0.511287i	−0.232343	+	0.972634i	$0.574639\pi$
$30$	1.18346	−	1.84507i	0.216069	−	0.336863i
$31$	4.18222	−	0.601313i	0.751149	−	0.107999i	0.243902	−	0.969800i	$-0.421572\pi$
$31$	4.18222	−	0.601313i	0.751149	−	0.107999i	0.507247	+	0.861801i	$0.330663\pi$
$32$	4.16313	+	3.82992i	0.735945	+	0.677041i
$33$	−2.07660	−	1.57880i	−0.361490	−	0.274835i
$34$	−9.70842	−	3.52918i	−1.66498	−	0.605250i
$35$	1.91476	+	1.23054i	0.323653	+	0.207999i
$36$	−0.843419	+	5.94042i	−0.140570	+	0.990071i
$37$	5.30163	+	1.55670i	0.871582	+	0.255920i	0.686788	−	0.726858i	$-0.259020\pi$
$37$	5.30163	+	1.55670i	0.871582	+	0.255920i	0.184794	+	0.982777i	$0.440838\pi$
$38$	−3.11406	−	8.14129i	−0.505167	−	1.32069i
$39$	1.50110	−	1.47889i	0.240368	−	0.236812i
$40$	−2.25113	−	1.15712i	−0.355934	−	0.182957i
$41$	1.90201	+	6.47765i	0.297044	+	1.01164i	0.963858	+	0.266415i	$0.0858393\pi$
$41$	1.90201	+	6.47765i	0.297044	+	1.01164i	−0.666814	+	0.745224i	$0.732342\pi$
$42$	−6.16750	−	0.881205i	−0.951666	−	0.135973i
$43$	5.31318	+	0.763921i	0.810253	+	0.116497i	0.534975	−	0.844868i	$-0.320321\pi$
$43$	5.31318	+	0.763921i	0.810253	+	0.116497i	0.275278	+	0.961365i	$0.411230\pi$
$44$	−1.58605	+	2.56079i	−0.239106	+	0.386053i
$45$	−0.342423	−	2.66272i	−0.0510454	−	0.396934i
$46$	−5.30451	+	4.22637i	−0.782107	+	0.623144i
$47$	0.483749			0.0705620			0.0352810	−	0.999377i	$-0.488767\pi$
$47$	0.483749			0.0705620			0.0352810	+	0.999377i	$0.488767\pi$
$48$	6.92103	+	0.315265i	0.998964	+	0.0455046i
$49$	−0.0755561	+	0.525504i	−0.0107937	+	0.0750720i
$50$	−5.81315	−	1.21393i	−0.822104	−	0.171676i
$51$	−11.8865	+	4.33283i	−1.66445	+	0.606717i
$52$	−1.86520	−	1.56255i	−0.258657	−	0.216687i
$53$	−4.51572	+	3.91290i	−0.620282	+	0.537478i	−0.907320	−	0.420442i	$-0.861875\pi$
$53$	−4.51572	+	3.91290i	−0.620282	+	0.537478i	0.287037	+	0.957919i	$0.407330\pi$
$54$	3.88582	+	6.23702i	0.528793	+	0.848751i
$55$	0.379710	−	1.29317i	0.0512001	−	0.174372i
$56$	−0.333691	+	7.18619i	−0.0445914	+	0.960296i
$57$	−9.33130	−	5.18591i	−1.23596	−	0.686890i
$58$	8.80939	+	3.20237i	1.15673	+	0.420492i
$59$	0.185128	−	0.213649i	0.0241016	−	0.0278147i	−0.743571	−	0.668657i	$-0.766869\pi$
$59$	0.185128	−	0.213649i	0.0241016	−	0.0278147i	0.767672	+	0.640842i	$0.221415\pi$
$60$	−3.02292	+	0.686826i	−0.390257	+	0.0886689i
$61$	1.15091	+	8.00476i	0.147359	+	1.02490i	0.920520	+	0.390695i	$0.127765\pi$
$61$	1.15091	+	8.00476i	0.147359	+	1.02490i	−0.773161	+	0.634210i	$0.781326\pi$
$62$	−4.81321	−	3.54093i	−0.611278	−	0.449698i
$63$	−6.47980	+	4.02915i	−0.816378	+	0.507625i
$64$	−0.399804	−	7.99000i	−0.0499754	−	0.998750i
$65$	0.990335	+	0.452271i	0.122836	+	0.0560973i
$66$	0.528238	+	3.65113i	0.0650216	+	0.449423i
$67$	−2.83225	−	4.40707i	−0.346014	−	0.538409i	0.624010	−	0.781416i	$-0.285502\pi$
$67$	−2.83225	−	4.40707i	−0.346014	−	0.538409i	−0.970024	+	0.243007i	$0.921866\pi$
$68$	6.28932	+	13.1857i	0.762692	+	1.59900i
$69$	−1.64886	+	8.14133i	−0.198499	+	0.980101i
$70$	−0.710403	−	3.13949i	−0.0849094	−	0.375241i
$71$	6.21490	−	3.99407i	0.737573	−	0.474009i	−0.117137	−	0.993116i	$-0.537372\pi$
$71$	6.21490	−	3.99407i	0.737573	−	0.474009i	0.854710	+	0.519106i	$0.173735\pi$
$72$	6.74114	−	5.15336i	0.794451	−	0.607329i
$73$	−1.39548	+	3.05568i	−0.163329	+	0.357640i	−0.973546	−	0.228489i	$-0.926621\pi$
$73$	−1.39548	+	3.05568i	−0.163329	+	0.357640i	0.810218	+	0.586129i	$0.199349\pi$
$74$	−3.80195	−	6.82688i	−0.441967	−	0.793609i
$75$	−6.40934	+	3.43801i	−0.740086	+	0.396988i
$76$	−4.93326	+	11.2968i	−0.565884	+	1.29584i
$77$	−3.79165	+	0.545157i	−0.432099	+	0.0621264i
$78$	−2.98007	+	0.00262660i	−0.337426	+	0.000297404i
$79$	4.79347	+	4.15356i	0.539307	+	0.467312i	0.881411	−	0.472350i	$-0.156594\pi$
$79$	4.79347	+	4.15356i	0.539307	+	0.467312i	−0.342104	+	0.939662i	$0.611140\pi$
$80$	1.12236	+	3.39901i	0.125484	+	0.380021i
$81$	8.55604	+	2.79181i	0.950671	+	0.310201i
$82$	4.50566	−	8.41750i	0.497567	−	0.929557i
$83$	−11.1296	−	3.26795i	−1.22163	−	0.358704i	−0.393547	−	0.919305i	$-0.628752\pi$
$83$	−11.1296	−	3.26795i	−1.22163	−	0.358704i	−0.828086	+	0.560601i	$0.810570\pi$
$84$	5.34484	+	7.00441i	0.583170	+	0.764244i
$85$	−4.28054	−	4.94001i	−0.464290	−	0.535819i
$86$	−4.59974	−	6.03899i	−0.496003	−	0.651201i
$87$	10.7858	−	3.93159i	1.15636	−	0.421511i
$88$	4.13857	−	1.00926i	0.441173	−	0.107587i
$89$	7.29656	+	1.04909i	0.773434	+	0.111203i	0.517721	−	0.855550i	$-0.326781\pi$
$89$	7.29656	+	1.04909i	0.773434	+	0.111203i	0.255713	+	0.966753i	$0.417690\pi$
$90$	−2.29517	+	3.02437i	−0.241932	+	0.318796i
$91$		−	3.09437i		−	0.324378i
$92$	9.53953	+	0.998688i	0.994565	+	0.104120i
$93$	−7.30335	+	0.467676i	−0.757322	+	0.0484958i
$94$	−0.487763	−	0.479701i	−0.0503089	−	0.0494774i
$95$	0.784954	−	5.45948i	0.0805346	−	0.560130i
$96$	−6.66583	−	7.18100i	−0.680328	−	0.732907i
$97$	−7.46649	+	2.19236i	−0.758107	+	0.222600i	−0.637869	−	0.770145i	$-0.720184\pi$
$97$	−7.46649	+	2.19236i	−0.758107	+	0.222600i	−0.120238	+	0.992745i	$0.538366\pi$
$98$	0.597290	−	0.454941i	0.0603354	−	0.0459560i
$99$	3.37020	+	3.00939i	0.338718	+	0.302455i
$100$	4.65761	+	6.98852i	0.465761	+	0.698852i
$101$	3.58738	−	12.2175i	0.356958	−	1.21569i	−0.563918	−	0.825831i	$-0.690706\pi$
$101$	3.58738	−	12.2175i	0.356958	−	1.21569i	0.920876	−	0.389856i	$-0.127475\pi$
$102$	16.2817	+	7.41828i	1.61213	+	0.734519i
$103$	−3.64636	+	5.67385i	−0.359287	+	0.559061i	−0.973098	−	0.230392i	$-0.925999\pi$
$103$	−3.64636	+	5.67385i	−0.359287	+	0.559061i	0.613811	+	0.789453i	$0.289636\pi$
$104$	0.331200	+	3.42511i	0.0324769	+	0.335860i
$105$	−3.13827	−	2.38597i	−0.306264	−	0.232847i
$106$	8.43335	+	0.532573i	0.819119	+	0.0517281i
$107$	−0.939439	−	6.53395i	−0.0908190	−	0.631660i	−0.983491	−	0.180954i	$-0.942081\pi$
$107$	−0.939439	−	6.53395i	−0.0908190	−	0.631660i	0.892672	−	0.450706i	$-0.148828\pi$
$108$	2.26677	−	10.1421i	0.218120	−	0.975922i
$109$	−5.11245	−	11.1947i	−0.489684	−	1.07226i	−0.979686	−	0.200537i	$-0.935731\pi$
$109$	−5.11245	−	11.1947i	−0.489684	−	1.07226i	0.490002	−	0.871721i	$-0.336996\pi$
$110$	−1.66522	+	0.927372i	−0.158772	+	0.0884215i
$111$	−8.94177	−	3.41122i	−0.848715	−	0.323778i
$112$	7.46252	−	6.91493i	0.705142	−	0.653399i
$113$	1.98229	+	3.08450i	0.186478	+	0.290165i	0.921888	−	0.387458i	$-0.126647\pi$
$113$	1.98229	+	3.08450i	0.186478	+	0.290165i	−0.735410	+	0.677623i	$0.763010\pi$
$114$	4.26622	+	14.4822i	0.399568	+	1.35638i
$115$	−4.23368	+	0.703332i	−0.394792	+	0.0655860i
$116$	−5.70691	−	11.9646i	−0.529873	−	1.11089i
$117$	−2.79367	+	2.34876i	−0.258274	+	0.217143i
$118$	−0.398525	+	0.0318429i	−0.0366872	+	0.00293138i
$119$	−7.71771	+	16.8994i	−0.707481	+	1.54917i
$120$	3.72908	+	2.30510i	0.340417	+	0.210426i
$121$	−3.62728	−	7.94264i	−0.329753	−	0.722058i
$122$	6.77732	−	9.21246i	0.613590	−	0.834057i
$123$	−2.40038	−	11.4443i	−0.216435	−	1.03189i
$124$	1.34185	+	8.34324i	0.120502	+	0.749245i
$125$	−6.22147	−	5.39093i	−0.556465	−	0.482180i
$126$	10.5290	+	2.36300i	0.937998	+	0.210513i
$127$	11.3815	−	17.7100i	1.00995	−	1.57151i	0.204477	−	0.978871i	$-0.434451\pi$
$127$	11.3815	−	17.7100i	1.00995	−	1.57151i	0.805470	−	0.592637i	$-0.201913\pi$
$128$	−7.52003	+	8.45276i	−0.664683	+	0.747126i
$129$	−9.06989	−	2.04393i	−0.798559	−	0.179958i
$130$	−0.550066	−	1.43807i	−0.0482440	−	0.126127i
$131$	13.0644	+	15.0771i	1.14144	+	1.31729i	0.941318	+	0.337520i	$0.109588\pi$
$131$	13.0644	+	15.0771i	1.14144	+	1.31729i	0.200121	+	0.979771i	$0.435866\pi$
$132$	3.08796	−	4.20525i	0.268772	−	0.366020i
$133$	−15.0415	+	4.41659i	−1.30427	+	0.382967i
$134$	−1.51444	+	7.25219i	−0.130828	+	0.626494i
$135$	0.227969	+	4.64435i	0.0196204	+	0.399722i
$136$	6.73381	−	19.5318i	0.577420	−	1.67484i
$137$		−	19.0753i		−	1.62971i	−0.579662	−	0.814857i	$-0.696815\pi$
$137$		−	19.0753i		−	1.62971i	0.579662	−	0.814857i	$-0.303185\pi$
$138$	9.73575	−	6.57383i	0.828762	−	0.559601i
$139$		−	12.2140i		−	1.03598i	−0.855388	−	0.517988i	$-0.826681\pi$
$139$		−	12.2140i		−	1.03598i	0.855388	−	0.517988i	$-0.173319\pi$
$140$	−2.39692	+	3.87000i	−0.202577	+	0.327075i
$141$	−0.835274	−	0.0659991i	−0.0703427	−	0.00555813i
$142$	−10.2271	−	2.13568i	−0.858241	−	0.179222i
$143$	−1.75810	+	0.516224i	−0.147019	+	0.0431688i
$144$	−11.9073	−	1.48861i	−0.992276	−	0.124051i
$145$	3.88415	+	4.48255i	0.322561	+	0.372255i
$146$	4.43717	−	1.69723i	0.367223	−	0.140464i
$147$	0.202156	−	0.897063i	0.0166736	−	0.0739885i
$148$	−2.93626	+	10.6537i	−0.241359	+	0.875726i
$149$	−0.114192	+	0.177686i	−0.00935495	+	0.0145566i	−0.845900	−	0.533342i	$-0.820936\pi$
$149$	−0.114192	+	0.177686i	−0.00935495	+	0.0145566i	0.836545	+	0.547899i	$0.184572\pi$
$150$	9.87177	+	2.88916i	0.806026	+	0.235899i
$151$	8.38713	+	7.26749i	0.682535	+	0.591420i	0.925560	−	0.378600i	$-0.123594\pi$
$151$	8.38713	+	7.26749i	0.682535	+	0.591420i	−0.243025	+	0.970020i	$0.578140\pi$
$152$	16.1765	−	6.49860i	1.31209	−	0.527106i
$153$	21.1152	−	5.85965i	1.70707	−	0.473725i
$154$	4.36371	+	3.21025i	0.351638	+	0.258689i
$155$	−1.57072	−	3.43939i	−0.126163	−	0.276258i
$156$	3.00740	+	2.95248i	0.240785	+	0.236388i
$157$	1.67861	−	3.67565i	0.133968	−	0.293349i	−0.830745	−	0.556654i	$-0.812085\pi$
$157$	1.67861	−	3.67565i	0.133968	−	0.293349i	0.964713	+	0.263304i	$0.0848124\pi$
$158$	−0.714434	−	8.94139i	−0.0568373	−	0.711338i
$159$	8.33101	−	6.14019i	0.660692	−	0.486948i
$160$	2.23890	−	4.54019i	0.177000	−	0.358934i
$161$	6.81706	+	10.1152i	0.537259	+	0.797188i
$162$	−5.85859	−	11.2994i	−0.460294	−	0.887767i
$163$	6.30664	+	9.81332i	0.493974	+	0.768639i	0.995323	−	0.0966068i	$-0.0307989\pi$
$163$	6.30664	+	9.81332i	0.493974	+	0.768639i	−0.501349	+	0.865245i	$0.667163\pi$
$164$	−12.8901	+	4.01939i	−1.00655	+	0.313862i
$165$	−0.832066	+	2.18108i	−0.0647762	+	0.169797i
$166$	7.98135	+	14.3315i	0.619473	+	1.11234i
$167$	8.32163	+	18.2218i	0.643947	+	1.41005i	0.896753	+	0.442531i	$0.145919\pi$
$167$	8.32163	+	18.2218i	0.643947	+	1.41005i	−0.252806	+	0.967517i	$0.581354\pi$
$168$	1.55661	−	12.3627i	0.120095	−	0.953799i
$169$	1.63945	+	11.4026i	0.126111	+	0.877124i
$170$	−0.582613	+	9.22573i	−0.0446844	+	0.707581i
$171$	15.4045	+	10.2274i	1.17801	+	0.782112i
$172$	−1.35054	+	10.6504i	−0.102978	+	0.812082i
$173$	−7.98798	+	12.4295i	−0.607315	+	0.945001i	0.392368	+	0.919808i	$0.371656\pi$
$173$	−7.98798	+	12.4295i	−0.607315	+	0.945001i	−0.999683	+	0.0251920i	$0.991980\pi$
$174$	−14.7740	−	6.73132i	−1.12001	−	0.510300i
$175$	−3.00901	+	10.2478i	−0.227460	+	0.774657i
$176$	−5.17373	−	3.08631i	−0.389984	−	0.232639i
$177$	−0.348803	+	0.343643i	−0.0262176	+	0.0258298i
$178$	−6.31680	−	8.29330i	−0.473464	−	0.621609i
$179$	−11.7452	+	3.44870i	−0.877878	+	0.257768i	−0.689463	−	0.724321i	$-0.742153\pi$
$179$	−11.7452	+	3.44870i	−0.877878	+	0.257768i	−0.188415	+	0.982089i	$0.560335\pi$
$180$	5.31328	−	0.773497i	0.396029	−	0.0576530i
$181$	−0.701366	+	4.87811i	−0.0521321	+	0.362587i	0.947011	+	0.321201i	$0.104086\pi$
$181$	−0.701366	+	4.87811i	−0.0521321	+	0.362587i	−0.999143	+	0.0413861i	$0.986823\pi$
$182$	−3.06848	+	3.12005i	−0.227451	+	0.231273i
$183$	−0.895131	−	13.9786i	−0.0661700	−	1.03333i
$184$	−8.62836	−	10.4667i	−0.636091	−	0.771614i
$185$		−	4.94462i		−	0.363536i
$186$	7.82772	+	6.77068i	0.573956	+	0.496451i
$187$	10.8891	+	1.56561i	0.796289	+	0.114489i
$188$	0.0161230	+	0.967363i	0.00117589	+	0.0705522i
$189$	11.7382	−	6.07295i	0.853827	−	0.441742i
$190$	−6.20526	+	4.72639i	−0.450177	+	0.342889i
$191$	−11.5586	−	13.3393i	−0.836350	−	0.965200i	0.163421	−	0.986556i	$-0.447747\pi$
$191$	−11.5586	−	13.3393i	−0.836350	−	0.965200i	−0.999772	+	0.0213564i	$0.993202\pi$
$192$	−0.399770	+	13.8506i	−0.0288509	+	0.999584i
$193$	−0.269554	−	0.0791481i	−0.0194029	−	0.00569720i	0.272017	−	0.962293i	$-0.412309\pi$
$193$	−0.269554	−	0.0791481i	−0.0194029	−	0.00569720i	−0.291420	+	0.956595i	$0.594128\pi$
$194$	9.70246	+	5.19346i	0.696596	+	0.372869i
$195$	−1.64828	−	0.916036i	−0.118035	−	0.0655987i
$196$	−1.05338	−	0.133576i	−0.0752415	−	0.00954118i
$197$	−16.1860	−	14.0252i	−1.15320	−	0.999255i	−0.999939	−	0.0110696i	$-0.996476\pi$
$197$	−16.1860	−	14.0252i	−1.15320	−	0.999255i	−0.153263	−	0.988185i	$-0.548978\pi$
$198$	−0.413959	−	6.37636i	−0.0294188	−	0.453148i
$199$	−6.76489	+	0.972645i	−0.479551	+	0.0689490i	−0.377851	−	0.925866i	$-0.623337\pi$
$199$	−6.76489	+	0.972645i	−0.479551	+	0.0689490i	−0.101699	+	0.994815i	$0.532428\pi$
$200$	2.23378	−	11.6651i	0.157952	−	0.824850i
$201$	4.28909	+	7.99596i	0.302529	+	0.563991i
$202$	−15.7324	+	8.76152i	−1.10693	+	0.616458i
$203$	7.00302	−	15.3345i	0.491516	−	1.07627i
$204$	−9.06062	−	23.6253i	−0.634371	−	1.65410i
$205$	5.08239	−	3.26626i	0.354970	−	0.228125i
$206$	9.30300	−	2.10508i	0.648171	−	0.146668i
$207$	3.95777	−	13.8324i	0.275084	−	0.961420i
$208$	3.06250	−	3.78196i	0.212346	−	0.262232i
$209$	5.01866	+	7.80918i	0.347148	+	0.540172i
$210$	0.798301	+	5.51778i	0.0550880	+	0.380763i
$211$	−14.6613	−	6.69561i	−1.00933	−	0.460945i	−0.159045	−	0.987271i	$-0.550842\pi$
$211$	−14.6613	−	6.69561i	−1.00933	−	0.460945i	−0.850282	+	0.526327i	$0.823569\pi$
$212$	−7.97521	−	8.89978i	−0.547740	−	0.611239i
$213$	−11.2760	+	6.04853i	−0.772619	+	0.414438i
$214$	−5.53204	+	7.51974i	−0.378162	+	0.514039i
$215$	−0.683618	−	4.75467i	−0.0466224	−	0.324266i
$216$	−12.3428	+	7.97843i	−0.839821	+	0.542863i
$217$	−7.03754	+	8.12175i	−0.477739	+	0.551340i
$218$	−5.94616	+	16.3573i	−0.402725	+	1.10785i
$219$	2.82643	−	5.08575i	0.190992	−	0.343663i
$220$	2.59865	+	0.716215i	0.175201	+	0.0482872i
$221$	−2.50364	+	8.52662i	−0.168413	+	0.573563i
$222$	5.63329	+	12.3065i	0.378082	+	0.825957i
$223$	−6.92303	+	5.99884i	−0.463600	+	0.401712i	−0.855097	−	0.518467i	$-0.826503\pi$
$223$	−6.92303	+	5.99884i	−0.463600	+	0.401712i	0.391497	+	0.920179i	$0.371957\pi$
$224$	−14.3815	−	0.427779i	−0.960905	−	0.0285822i
$225$	11.5359	−	5.06187i	0.769057	−	0.337458i
$226$	1.05995	−	5.07579i	0.0705071	−	0.337637i
$227$	−3.23806	+	22.5212i	−0.214918	+	1.49479i	0.541502	+	0.840699i	$0.317856\pi$
$227$	−3.23806	+	22.5212i	−0.214918	+	1.49479i	−0.756420	+	0.654086i	$0.773053\pi$
$228$	10.0594	−	18.8329i	0.666198	−	1.24724i
$229$	15.4954			1.02397			0.511983	−	0.858995i	$-0.328911\pi$
$229$	15.4954			1.02397			0.511983	+	0.858995i	$0.328911\pi$
$230$	4.96625	+	3.48908i	0.327465	+	0.230063i
$231$	6.62131	−	0.424001i	0.435650	−	0.0278972i
$232$	−6.11024	+	17.7231i	−0.401157	+	1.16358i
$233$	14.5695	+	2.09478i	0.954479	+	0.137233i	0.601920	−	0.798556i	$-0.294403\pi$
$233$	14.5695	+	2.09478i	0.954479	+	0.137233i	0.352559	+	0.935790i	$0.385312\pi$
$234$	5.14595	+	0.402044i	0.336401	+	0.0262824i
$235$	−0.121961	−	0.415362i	−0.00795588	−	0.0270952i
$236$	0.433408	+	0.363083i	0.0282125	+	0.0236347i
$237$	−7.71005	−	7.82581i	−0.500821	−	0.508341i
$238$	24.5398	−	9.38652i	1.59068	−	0.608438i
$239$	−4.90891	−	1.44139i	−0.317531	−	0.0932355i	0.119083	−	0.992884i	$-0.462004\pi$
$239$	−4.90891	−	1.44139i	−0.317531	−	0.0932355i	−0.436614	+	0.899649i	$0.643823\pi$
$240$	−1.47421	−	6.02210i	−0.0951600	−	0.388725i
$241$	−1.20704	−	0.775718i	−0.0777523	−	0.0499684i	0.501187	−	0.865339i	$-0.332897\pi$
$241$	−1.20704	−	0.775718i	−0.0777523	−	0.0499684i	−0.578939	+	0.815371i	$0.696533\pi$
$242$	−4.21880	+	11.6055i	−0.271195	+	0.746028i
$243$	−14.3926	−	5.98786i	−0.923283	−	0.384121i
$244$	−15.9689	+	2.56830i	−1.02231	+	0.164418i
$245$	0.470264	−	0.0676137i	0.0300441	−	0.00431968i
$246$	−8.92821	+	13.9195i	−0.569242	+	0.887476i
$247$	−6.82095	+	3.11503i	−0.434007	+	0.198204i
$248$	6.92045	−	9.74309i	0.439449	−	0.618687i
$249$	18.7713	+	7.16110i	1.18958	+	0.453817i
$250$	0.927268	+	11.6051i	0.0586456	+	0.733969i
$251$	15.1964	−	9.76612i	0.959187	−	0.616432i	0.0354141	−	0.999373i	$-0.488725\pi$
$251$	15.1964	−	9.76612i	0.959187	−	0.616432i	0.923773	+	0.382941i	$0.125089\pi$
$252$	−8.27315	−	12.8235i	−0.521159	−	0.807805i
$253$	4.60977	−	5.56066i	0.289814	−	0.349595i
$254$	−29.0378	+	6.57066i	−1.82199	+	0.412280i
$255$	6.71710	+	9.11377i	0.420641	+	0.570726i
$256$	15.9645	−	1.06580i	0.997779	−	0.0666123i
$257$	1.35868	+	0.620488i	0.0847520	+	0.0387050i	0.457340	−	0.889292i	$-0.348802\pi$
$257$	1.35868	+	0.620488i	0.0847520	+	0.0387050i	−0.372588	+	0.927997i	$0.621530\pi$
$258$	7.11832	+	11.0549i	0.443167	+	0.688247i
$259$	−12.7836	+	5.83810i	−0.794337	+	0.362762i
$260$	−0.871409	+	1.99547i	−0.0540425	+	0.123754i
$261$	−19.1599	+	5.31703i	−1.18597	+	0.329116i
$262$	1.77816	−	28.1573i	0.109855	−	1.73956i
$263$	−17.6809	+	20.4048i	−1.09025	+	1.25822i	−0.126341	+	0.991987i	$0.540323\pi$
$263$	−17.6809	+	20.4048i	−1.09025	+	1.25822i	−0.963910	+	0.266229i	$0.914222\pi$
$264$	−7.28364	+	1.17802i	−0.448277	+	0.0725021i
$265$	4.49823	+	2.89084i	0.276324	+	0.177583i
$266$	19.5460	+	10.4624i	1.19844	+	0.641493i
$267$	−12.4556	−	2.80692i	−0.762271	−	0.171780i
$268$	8.71851	−	5.81060i	0.532568	−	0.354939i
$269$	−19.9009	+	17.2443i	−1.21338	+	1.05140i	−0.216202	+	0.976349i	$0.569367\pi$
$269$	−19.9009	+	17.2443i	−1.21338	+	1.05140i	−0.997180	+	0.0750520i	$0.976088\pi$
$270$	4.37563	−	4.90895i	0.266292	−	0.298749i
$271$	−0.989518	−	3.36999i	−0.0601089	−	0.204712i	0.923963	−	0.382481i	$-0.124930\pi$
$271$	−0.989518	−	3.36999i	−0.0601089	−	0.204712i	−0.984072	+	0.177769i	$0.943112\pi$
$272$	−26.1580	+	13.0164i	−1.58606	+	0.789233i
$273$	−0.422174	+	5.34296i	−0.0255511	+	0.323370i
$274$	−18.9157	+	19.2336i	−1.14274	+	1.16194i
$275$	6.32434			0.381372
$276$	−16.3354	−	3.02591i	−0.983273	−	0.182138i
$277$	23.2924			1.39950			0.699752	−	0.714386i	$-0.253294\pi$
$277$	23.2924			1.39950			0.699752	+	0.714386i	$0.253294\pi$
$278$	−12.1118	+	12.3153i	−0.726417	+	0.738625i
$279$	12.6743	+	0.188894i	0.758789	+	0.0113088i
$280$	6.25443	−	1.52525i	0.373774	−	0.0911508i
$281$	−4.53568	−	15.4471i	−0.270576	−	0.921498i	−0.976916	−	0.213625i	$-0.931473\pi$
$281$	−4.53568	−	15.4471i	−0.270576	−	0.921498i	0.706340	−	0.707873i	$-0.250345\pi$
$282$	0.776758	+	0.894831i	0.0462553	+	0.0532864i
$283$	−20.0340	+	17.3595i	−1.19090	+	1.03192i	−0.192174	+	0.981361i	$0.561554\pi$
$283$	−20.0340	+	17.3595i	−1.19090	+	1.03192i	−0.998721	+	0.0505561i	$0.983901\pi$
$284$	8.19418	+	12.2950i	0.486235	+	0.729571i
$285$	−2.10021	+	9.31962i	−0.124406	+	0.552046i
$286$	2.28459	+	1.22288i	0.135091	+	0.0723103i
$287$	−14.4452	−	9.28339i	−0.852675	−	0.547981i
$288$	10.5300	+	13.3086i	0.620484	+	0.784219i
$289$	23.8070	−	27.4747i	1.40041	−	1.61616i
$290$	0.528661	−	8.37140i	0.0310440	−	0.491585i
$291$	13.1913	−	2.76681i	0.773286	−	0.162193i
$292$	−6.15701	−	2.68873i	−0.360312	−	0.157346i
$293$	2.87530	−	1.31311i	0.167977	−	0.0767125i	−0.329652	−	0.944103i	$-0.606931\pi$
$293$	2.87530	−	1.31311i	0.167977	−	0.0767125i	0.497629	+	0.867390i	$0.334204\pi$
$294$	−1.09339	+	0.704042i	−0.0637679	+	0.0410606i
$295$	−0.230120	−	0.105092i	−0.0133981	−	0.00611870i
$296$	13.5252	−	7.83037i	0.786133	−	0.455131i
$297$	−5.40864	−	5.65602i	−0.313841	−	0.328196i
$298$	0.291338	−	0.0659240i	0.0168768	−	0.00381887i
$299$	3.91620	+	4.32510i	0.226480	+	0.250127i
$300$	−7.08869	−	12.7023i	−0.409266	−	0.733368i
$301$	−11.4854	+	7.38123i	−0.662008	+	0.425447i
$302$	−1.25005	−	15.6447i	−0.0719321	−	0.900254i
$303$	−7.86109	+	20.6062i	−0.451608	+	1.18379i
$304$	−22.7550	−	9.48864i	−1.30509	−	0.544211i
$305$	6.58298	−	3.00635i	0.376940	−	0.172143i
$306$	−27.1011	−	15.0303i	−1.54926	−	0.859224i
$307$	23.9785	−	3.44759i	1.36853	−	0.196764i	0.581431	−	0.813596i	$-0.302493\pi$
$307$	23.9785	−	3.44759i	1.36853	−	0.196764i	0.787095	+	0.616832i	$0.211584\pi$
$308$	−1.21654	−	7.56408i	−0.0693186	−	0.431004i
$309$	7.07016	−	9.29938i	0.402207	−	0.529023i
$310$	−1.82686	+	5.02550i	−0.103759	+	0.285429i
$311$	−29.4574	−	18.9311i	−1.67038	−	1.07349i	−0.899992	−	0.435906i	$-0.856428\pi$
$311$	−29.4574	−	18.9311i	−1.67038	−	1.07349i	−0.770384	−	0.637580i	$-0.779936\pi$
$312$	−0.104576	−	5.95922i	−0.00592045	−	0.337374i
$313$	−14.9268	−	4.38289i	−0.843711	−	0.247736i	−0.168814	−	0.985648i	$-0.553994\pi$
$313$	−14.9268	−	4.38289i	−0.843711	−	0.247736i	−0.674897	+	0.737912i	$0.735812\pi$
$314$	−5.33744	+	2.04158i	−0.301209	+	0.115213i
$315$	5.09323	+	4.54795i	0.286971	+	0.256248i
$316$	−8.14621	+	9.72404i	−0.458260	+	0.547020i
$317$	3.54627	+	12.0775i	0.199179	+	0.678340i	0.997136	+	0.0756264i	$0.0240957\pi$
$317$	3.54627	+	12.0775i	0.199179	+	0.678340i	−0.797958	+	0.602714i	$0.794086\pi$
$318$	−14.4889	−	2.07016i	−0.812500	−	0.116089i
$319$	−9.88072	−	1.42063i	−0.553214	−	0.0795402i
$320$	−6.75968	+	2.35770i	−0.377878	+	0.131800i
$321$	0.730657	+	11.4101i	0.0407813	+	0.636851i
$322$	3.15692	−	16.9591i	0.175928	−	0.945095i
$323$	45.0208			2.50502
$324$	−5.29768	+	17.2027i	−0.294315	+	0.955708i
$325$	−0.727053	+	5.05677i	−0.0403297	+	0.280499i
$326$	3.37224	−	16.1486i	0.186771	−	0.894389i
$327$	7.30019	+	20.0271i	0.403701	+	1.10750i
$328$	16.9828	+	8.72952i	0.937720	+	0.482007i
$329$	−0.929864	+	0.805731i	−0.0512650	+	0.0444214i
$330$	3.00180	−	1.37408i	0.165244	−	0.0756403i
$331$	3.55143	−	12.0950i	0.195204	−	0.664804i	−0.802473	−	0.596688i	$-0.796483\pi$
$331$	3.55143	−	12.0950i	0.195204	−	0.664804i	0.997677	−	0.0681159i	$-0.0216988\pi$
$332$	6.16404	−	22.3650i	0.338296	−	1.22744i
$333$	14.9741	+	7.10999i	0.820574	+	0.389625i
$334$	9.67868	−	26.6250i	0.529594	−	1.45686i
$335$	−3.06999	+	3.54296i	−0.167732	+	0.193573i
$336$	−13.8287	+	10.9217i	−0.754419	+	0.595825i
$337$	−0.974611	−	6.77857i	−0.0530905	−	0.369252i	−0.998996	−	0.0448089i	$-0.985732\pi$
$337$	−0.974611	−	6.77857i	−0.0530905	−	0.369252i	0.945905	−	0.324443i	$-0.105177\pi$
$338$	9.65415	−	13.1230i	0.525116	−	0.713795i
$339$	−3.00193	−	5.59636i	−0.163042	−	0.303952i
$340$	9.73598	−	8.72455i	0.528008	−	0.473155i
$341$	5.78850	+	2.64352i	0.313465	+	0.143155i
$342$	−5.39050	−	25.5880i	−0.291485	−	1.38364i
$343$	−10.3557	−	16.1137i	−0.559153	−	0.870059i
$344$	11.9230	−	9.39949i	0.642844	−	0.506786i
$345$	7.40612	−	0.636809i	0.398732	−	0.0342846i
$346$	20.3798	−	4.61154i	1.09563	−	0.247918i
$347$	23.6115	−	15.1742i	1.26753	−	0.814593i	0.278235	−	0.960513i	$-0.410251\pi$
$347$	23.6115	−	15.1742i	1.26753	−	0.814593i	0.989296	+	0.145920i	$0.0466143\pi$
$348$	8.22158	+	21.4375i	0.440723	+	1.14917i
$349$	10.2308	−	22.4024i	0.547645	−	1.19917i	−0.410229	−	0.911983i	$-0.634551\pi$
$349$	10.2308	−	22.4024i	0.547645	−	1.19917i	0.957873	−	0.287192i	$-0.0927216\pi$
$350$	13.1960	−	7.34895i	0.705355	−	0.392818i
$351$	5.14418	−	3.67438i	0.274576	−	0.196124i
$352$	2.15617	+	8.24236i	0.114924	+	0.439319i
$353$	−7.08525	+	1.01870i	−0.377110	+	0.0542202i	−0.328264	−	0.944586i	$-0.606463\pi$
$353$	−7.08525	+	1.01870i	−0.377110	+	0.0542202i	−0.0488460	+	0.998806i	$0.515554\pi$
$354$	0.692465		0.000610331i	0.0368041		3.24387e-5i
$355$	−4.99632	−	4.32934i	−0.265177	−	0.229778i
$356$	−1.85469	+	14.6261i	−0.0982986	+	0.775180i
$357$	15.6316	−	28.1268i	0.827310	−	1.48863i
$358$	15.2625	+	8.16961i	0.806649	+	0.431777i
$359$	−15.8738	−	4.66096i	−0.837786	−	0.245996i	−0.165428	−	0.986222i	$-0.552900\pi$
$359$	−15.8738	−	4.66096i	−0.837786	−	0.245996i	−0.672358	+	0.740226i	$0.734719\pi$
$360$	−6.12439	−	4.48891i	−0.322784	−	0.236586i
$361$	12.4351	+	14.3509i	0.654480	+	0.755310i
$362$	5.54448	−	4.22309i	0.291411	−	0.221961i
$363$	5.17948	+	14.2092i	0.271852	+	0.745789i
$364$	6.18788	−	0.103133i	0.324333	−	0.00540565i
$365$	2.97553	+	0.427816i	0.155746	+	0.0223929i
$366$	−12.9591	+	14.9822i	−0.677382	+	0.783134i
$367$			0.0283362i			0.00147914i	1.00000		0.000739568i	$0.000235412\pi$
$367$			0.0283362i			0.00147914i	−1.00000		0.000739568i	$0.999765\pi$
$368$	−1.67915	+	19.1097i	−0.0875319	+	0.996162i
$369$	2.58329	+	20.0879i	0.134481	+	1.04574i
$370$	−4.90325	+	4.98565i	−0.254908	+	0.259192i
$371$	2.16282	−	15.0428i	0.112288	−	0.780982i
$372$	−1.17864	−	14.5891i	−0.0611095	−	0.756409i
$373$	−16.2386	+	4.76807i	−0.840801	+	0.246882i	−0.673651	−	0.739050i	$-0.735275\pi$
$373$	−16.2386	+	4.76807i	−0.840801	+	0.246882i	−0.167151	+	0.985931i	$0.553457\pi$
$374$	−9.42693	−	12.3766i	−0.487455	−	0.639978i
$375$	10.0069	+	10.1572i	0.516755	+	0.524514i
$376$	0.943012	−	0.991378i	0.0486321	−	0.0511264i
$377$	2.27180	−	7.73703i	0.117003	−	0.398477i
$378$	−17.8577	−	5.51662i	−0.918502	−	0.283744i
$379$	−9.71366	+	15.1148i	−0.498957	+	0.776393i	−0.995810	−	0.0914418i	$-0.970852\pi$
$379$	−9.71366	+	15.1148i	−0.498957	+	0.776393i	0.496853	+	0.867835i	$0.334489\pi$
$380$	10.9436	+	1.38773i	0.561395	+	0.0711890i
$381$	−22.0683	+	29.0265i	−1.13060	+	1.48707i
$382$	−1.57321	+	24.9119i	−0.0804923	+	1.27460i
$383$	−0.754662	−	5.24879i	−0.0385614	−	0.268201i	0.961415	−	0.275103i	$-0.0887120\pi$
$383$	−0.754662	−	5.24879i	−0.0385614	−	0.268201i	−0.999976	+	0.00690243i	$0.997803\pi$
$384$	14.1378	−	13.5691i	0.721468	−	0.692448i
$385$	1.42403	+	3.11819i	0.0725753	+	0.158918i
$386$	0.193304	+	0.347103i	0.00983894	+	0.0176671i
$387$	15.3818	+	4.76662i	0.781903	+	0.242301i
$388$	−4.63296	−	14.8578i	−0.235203	−	0.754292i
$389$	−4.03413	−	6.27723i	−0.204539	−	0.318268i	0.723796	−	0.690014i	$-0.242396\pi$
$389$	−4.03413	−	6.27723i	−0.204539	−	0.318268i	−0.928335	+	0.371746i	$0.878759\pi$
$390$	0.753582	+	2.55812i	0.0381591	+	0.129535i
$391$	−10.6004	−	33.3883i	−0.536087	−	1.68852i
$392$	0.929663	+	1.17925i	0.0469550	+	0.0595612i
$393$	−20.5008	−	27.8156i	−1.03413	−	1.40311i
$394$	2.41241	+	30.1921i	0.121535	+	1.52106i
$395$	2.35787	−	5.16301i	0.118637	−	0.259779i
$396$	−5.90562	+	6.83977i	−0.296768	+	0.343711i
$397$	3.95821	+	8.66727i	0.198657	+	0.434998i	0.982575	−	0.185866i	$-0.0595091\pi$
$397$	3.95821	+	8.66727i	0.198657	+	0.434998i	−0.783918	+	0.620864i	$0.786782\pi$
$398$	7.78553	+	5.72757i	0.390254	+	0.287097i
$399$	26.5743	−	5.57384i	1.33038	−	0.279041i
$400$	−13.8199	+	9.54685i	−0.690993	+	0.477343i
$401$	11.1679	+	9.67704i	0.557699	+	0.483249i	0.887504	−	0.460800i	$-0.152438\pi$
$401$	11.1679	+	9.67704i	0.557699	+	0.483249i	−0.329805	+	0.944049i	$0.606983\pi$
$402$	3.60437	−	12.3155i	0.179770	−	0.614242i
$403$	−2.77914	+	4.32442i	−0.138439	+	0.215415i
$404$	24.5512	+	6.76657i	1.22147	+	0.336649i
$405$	0.240014	−	8.05035i	0.0119264	−	0.400025i
$406$	−22.2673	+	8.51730i	−1.10511	+	0.422706i
$407$	5.44962	+	6.28920i	0.270128	+	0.311744i
$408$	−14.2918	+	32.8062i	−0.707552	+	1.62415i
$409$	16.1986	−	4.75634i	0.800970	−	0.235186i	0.144467	−	0.989510i	$-0.453853\pi$
$409$	16.1986	−	4.75634i	0.800970	−	0.235186i	0.656503	+	0.754324i	$0.272035\pi$
$410$	−8.36349	−	1.74651i	−0.413043	−	0.0862539i
$411$	−2.60250	+	32.9368i	−0.128372	+	1.62465i
$412$	−11.4677	−	7.10261i	−0.564971	−	0.349920i
$413$			0.719025i			0.0353809i
$414$	−17.7073	+	10.0226i	−0.870266	+	0.492582i
$415$			10.3801i			0.509541i
$416$	−6.83823	+	0.776465i	−0.335272	+	0.0380693i
$417$	−1.66639	+	21.0895i	−0.0816033	+	1.03276i
$418$	2.68354	−	12.8506i	0.131256	−	0.628546i
$419$	−7.24752	+	2.12806i	−0.354064	+	0.103963i	−0.453928	−	0.891038i	$-0.649978\pi$
$419$	−7.24752	+	2.12806i	−0.354064	+	0.103963i	0.0998634	+	0.995001i	$0.468159\pi$
$420$	4.66669	−	6.35519i	0.227711	−	0.310101i
$421$	−10.1793	−	11.7476i	−0.496111	−	0.572543i	0.451377	−	0.892333i	$-0.350933\pi$
$421$	−10.1793	−	11.7476i	−0.496111	−	0.572543i	−0.947488	+	0.319791i	$0.896387\pi$
$422$	8.14341	+	21.2898i	0.396415	+	1.03637i
$423$	1.43324	+	0.227917i	0.0696864	+	0.0110817i
$424$	−0.783921	+	16.8821i	−0.0380706	+	0.819868i
$425$	16.5828	−	25.8034i	0.804385	−	1.25165i
$426$	17.3675	+	5.08293i	0.841457	+	0.246269i
$427$	−15.5450	−	13.4698i	−0.752276	−	0.651851i
$428$	13.0348	−	2.09639i	0.630059	−	0.101333i
$429$	3.10608	−	0.651485i	0.149963	−	0.0314540i
$430$	−4.02559	+	5.47202i	−0.194131	+	0.263884i
$431$	12.5112	+	27.3957i	0.602643	+	1.31960i	0.927494	+	0.373839i	$0.121959\pi$
$431$	12.5112	+	27.3957i	0.602643	+	1.31960i	−0.324851	+	0.945765i	$0.605314\pi$
$432$	20.3569	+	4.19489i	0.979421	+	0.201827i
$433$	−11.8115	+	25.8636i	−0.567624	+	1.24292i	0.380429	+	0.924810i	$0.375777\pi$
$433$	−11.8115	+	25.8636i	−0.567624	+	1.24292i	−0.948053	+	0.318113i	$0.896951\pi$
$434$	15.1497	−	1.21049i	0.727210	−	0.0581055i
$435$	−6.09508	−	8.26980i	−0.292237	−	0.396507i
$436$	22.2159	−	10.5966i	1.06395	−	0.507485i
$437$	15.4344	−	25.2096i	0.738329	−	1.20594i
$438$	−7.89308	+	2.32517i	−0.377146	+	0.111101i
$439$	1.88020	+	2.92565i	0.0897370	+	0.139634i	0.883220	−	0.468959i	$-0.155371\pi$
$439$	1.88020	+	2.92565i	0.0897370	+	0.139634i	−0.793483	+	0.608593i	$0.791734\pi$
$440$	−1.90999	−	3.29906i	−0.0910551	−	0.157277i
$441$	−0.471446	+	1.52135i	−0.0224498	+	0.0724453i
$442$	10.9797	−	6.11468i	0.522251	−	0.290846i
$443$	9.42060	+	20.6282i	0.447586	+	0.980077i	0.990143	+	0.140058i	$0.0447290\pi$
$443$	9.42060	+	20.6282i	0.447586	+	0.980077i	−0.542557	+	0.840019i	$0.682544\pi$
$444$	6.52347	−	17.9948i	0.309590	−	0.853993i
$445$	−0.938808	−	6.52956i	−0.0445038	−	0.309531i
$446$	12.9291	+	0.816485i	0.612212	+	0.0386617i
$447$	0.221413	−	0.291225i	0.0104725	−	0.0137745i
$448$	14.0767	+	14.6925i	0.665059	+	0.694156i
$449$	−0.151898	+	0.236358i	−0.00716852	+	0.0111544i	−0.844819	−	0.535052i	$-0.820292\pi$
$449$	−0.151898	+	0.236358i	−0.00716852	+	0.0111544i	0.837651	+	0.546206i	$0.183928\pi$
$450$	−16.6511	−	6.33546i	−0.784940	−	0.298657i
$451$	−2.86459	+	9.75591i	−0.134888	+	0.459388i
$452$	−6.10207	+	4.06683i	−0.287017	+	0.191287i
$453$	−13.4903	−	13.6928i	−0.633829	−	0.643345i
$454$	25.5977	−	19.4971i	1.20136	−	0.915046i
$455$	−2.65693	+	0.780144i	−0.124559	+	0.0365737i
$456$	−28.8181	+	9.01393i	−1.34953	+	0.422116i
$457$	4.82992	−	33.5929i	0.225934	−	1.57141i	−0.489043	−	0.872260i	$-0.662654\pi$
$457$	4.82992	−	33.5929i	0.225934	−	1.57141i	0.714977	−	0.699148i	$-0.246437\pi$
$458$	−15.6240	−	15.3658i	−0.730062	−	0.717996i
$459$	−37.2585	+	7.23687i	−1.73908	+	0.337788i
$460$	−1.54757	−	8.44274i	−0.0721560	−	0.393645i
$461$			14.0254i			0.653227i	0.945158	+	0.326614i	$0.105908\pi$
$461$			14.0254i			0.653227i	−0.945158	+	0.326614i	$0.894092\pi$
$462$	−7.09670	−	6.13838i	−0.330168	−	0.285584i
$463$	−7.89428	−	1.13503i	−0.366878	−	0.0527491i	−0.0435896	−	0.999050i	$-0.513879\pi$
$463$	−7.89428	−	1.13503i	−0.366878	−	0.0527491i	−0.323289	+	0.946300i	$0.604788\pi$
$464$	23.7357	−	11.8110i	1.10190	−	0.548312i
$465$	2.24286	+	6.15298i	0.104010	+	0.285338i
$466$	−12.6131	−	16.5597i	−0.584292	−	0.767115i
$467$	10.6309	+	12.2687i	0.491937	+	0.567726i	0.946382	−	0.323049i	$-0.104708\pi$
$467$	10.6309	+	12.2687i	0.491937	+	0.567726i	−0.454445	+	0.890775i	$0.650162\pi$
$468$	−4.78997	−	5.50827i	−0.221417	−	0.254620i
$469$	12.7846	+	3.75389i	0.590337	+	0.173339i
$470$	−0.288913	+	0.539750i	−0.0133266	+	0.0248968i
$471$	−3.39989	+	6.11762i	−0.156659	+	0.281885i
$472$	−0.0769596	−	0.795878i	−0.00354235	−	0.0366333i
$473$	6.10979	+	5.29416i	0.280928	+	0.243426i
$474$	0.0136935	+	15.5363i	0.000628964	+	0.713605i
$475$	25.6183	−	3.68336i	1.17545	−	0.169004i
$476$	−34.0514	−	14.8700i	−1.56074	−	0.681567i
$477$	−15.2226	+	9.46545i	−0.696996	+	0.433393i
$478$	3.52032	+	6.32118i	0.161016	+	0.289124i
$479$	15.9635	−	34.9552i	0.729392	−	1.59715i	−0.0708636	−	0.997486i	$-0.522576\pi$
$479$	15.9635	−	34.9552i	0.729392	−	1.59715i	0.800255	−	0.599659i	$-0.204697\pi$
$480$	−4.48527	+	7.53395i	−0.204723	+	0.343876i
$481$	−5.65516	+	3.63435i	−0.257853	+	0.165712i
$482$	0.447829	+	1.97910i	0.0203981	+	0.0901453i
$483$	−10.3908	−	18.3956i	−0.472796	−	0.837030i
$484$	15.7622	−	7.51828i	0.716462	−	0.341740i
$485$	3.76486	+	5.85824i	0.170954	+	0.266009i
$486$	8.57423	+	20.3097i	0.388935	+	0.921265i
$487$	10.0628	+	4.59553i	0.455989	+	0.208243i	0.630149	−	0.776474i	$-0.282994\pi$
$487$	10.0628	+	4.59553i	0.455989	+	0.208243i	−0.174160	+	0.984717i	$0.555721\pi$
$488$	18.6483	+	13.2457i	0.844167	+	0.599605i
$489$	−9.55062	−	17.8048i	−0.431894	−	0.805160i
$490$	−0.541214	−	0.398154i	−0.0244496	−	0.0179868i
$491$	−2.11883	−	14.7368i	−0.0956212	−	0.665060i	−0.980104	−	0.198487i	$-0.936397\pi$
$491$	−2.11883	−	14.7368i	−0.0956212	−	0.665060i	0.884482	−	0.466574i	$-0.154512\pi$
$492$	22.8053	−	5.18152i	1.02814	−	0.233601i
$493$	−31.7041	+	36.5885i	−1.42788	+	1.64786i
$494$	9.96652	+	3.62301i	0.448415	+	0.163007i
$495$	1.73427	−	3.65248i	0.0779498	−	0.164167i
$496$	−16.6394	+	2.96140i	−0.747133	+	0.132971i
$497$	−5.29378	+	18.0290i	−0.237459	+	0.808710i
$498$	−11.8259	−	25.8347i	−0.529930	−	1.15768i
$499$	−8.61943	+	7.46878i	−0.385859	+	0.334348i	−0.826092	−	0.563535i	$-0.809441\pi$
$499$	−8.61943	+	7.46878i	−0.385859	+	0.334348i	0.440234	+	0.897883i	$0.354896\pi$
$500$	10.5730	−	12.6209i	0.472839	−	0.564423i
$501$	−11.8826	−	32.5984i	−0.530878	−	1.45639i
$502$	−25.0069	−	5.22207i	−1.11611	−	0.233072i
$503$	−3.35735	+	23.3509i	−0.149697	+	1.04117i	0.767019	+	0.641625i	$0.221739\pi$
$503$	−3.35735	+	23.3509i	−0.149697	+	1.04117i	−0.916716	+	0.399541i	$0.869170\pi$
$504$	−4.37441	+	21.1338i	−0.194852	+	0.941376i
$505$	−11.3948			−0.507061
$506$	−10.1621	+	1.03560i	−0.451763	+	0.0460382i
$507$	−1.27509	−	19.9122i	−0.0566289	−	0.884332i
$508$	35.7944	+	22.1696i	1.58812	+	0.983618i
$509$	−3.51588	−	0.505508i	−0.155839	−	0.0224062i	0.0639538	−	0.997953i	$-0.479629\pi$
$509$	−3.51588	−	0.505508i	−0.155839	−	0.0224062i	−0.219793	+	0.975547i	$0.570538\pi$
$510$	2.26467	−	15.8503i	0.100281	−	0.701863i
$511$	−2.40713	−	8.19794i	−0.106485	−	0.362656i
$512$	−17.1538	−	14.7562i	−0.758099	−	0.652140i
$513$	−25.2032	−	19.7611i	−1.11275	−	0.872474i
$514$	−0.754657	−	1.97295i	−0.0332865	−	0.0870229i
$515$	5.79106	+	1.70041i	0.255185	+	0.0749290i
$516$	3.78500	−	18.2054i	0.166625	−	0.801447i
$517$	0.612910	+	0.393893i	0.0269557	+	0.0173234i
$518$	18.6790	+	6.79014i	0.820707	+	0.298342i
$519$	15.4884	−	20.3719i	0.679865	−	0.894226i
$520$	2.85741	−	1.14791i	0.125306	−	0.0503391i
$521$	−32.8173	+	4.71842i	−1.43775	+	0.206718i	−0.816705	−	0.577056i	$-0.804202\pi$
$521$	−32.8173	+	4.71842i	−1.43775	+	0.206718i	−0.621047	+	0.783773i	$0.713292\pi$
$522$	24.5914	+	13.6384i	1.07634	+	0.596937i
$523$	6.44512	−	2.94339i	0.281826	−	0.128705i	−0.269487	−	0.963004i	$-0.586854\pi$
$523$	6.44512	−	2.94339i	0.281826	−	0.128705i	0.551313	+	0.834298i	$0.314127\pi$
$524$	−29.7146	+	26.6276i	−1.29809	+	1.16323i
$525$	6.59370	−	17.2840i	0.287773	−	0.754334i
$526$	38.0617	−	3.04120i	1.65957	−	0.132603i
$527$	25.9634	−	16.6857i	1.13098	−	0.726839i
$528$	8.51224	+	6.03490i	0.370448	+	0.262635i
$529$	−22.3301	−	5.51071i	−0.970873	−	0.239596i
$530$	−1.66891	−	7.37542i	−0.0724927	−	0.320368i
$531$	0.649152	−	0.545770i	0.0281708	−	0.0236844i
$532$	−9.33328	−	29.9317i	−0.404649	−	1.29770i
$533$	−7.47124	−	3.41200i	−0.323615	−	0.147790i
$534$	9.77554	+	15.1816i	0.423029	+	0.656972i
$535$	−5.37341	+	2.45395i	−0.232313	+	0.106094i
$536$	−14.5528	−	2.78675i	−0.628587	−	0.120369i
$537$	20.7506	−	4.35234i	0.895455	−	0.187817i
$538$	37.1660	+	2.34707i	1.60234	+	0.101189i
$539$	−0.523622	+	0.604292i	−0.0225540	+	0.0260287i
$540$	−9.27981	+	0.610667i	−0.399339	+	0.0262789i
$541$	−23.8046	−	15.2983i	−1.02344	−	0.657724i	−0.0826016	−	0.996583i	$-0.526323\pi$
$541$	−23.8046	−	15.2983i	−1.02344	−	0.657724i	−0.940837	+	0.338858i	$0.889959\pi$
$542$	−2.34406	+	4.37919i	−0.100686	+	0.188102i
$543$	1.87656	−	8.32719i	0.0805309	−	0.357354i
$544$	39.2825	+	12.8148i	1.68422	+	0.549429i
$545$	−8.32320	+	7.21209i	−0.356527	+	0.308932i
$546$	5.72393	−	4.96865i	0.244961	−	0.212639i
$547$	−1.19561	−	4.07189i	−0.0511207	−	0.174101i	0.929976	−	0.367621i	$-0.119828\pi$
$547$	−1.19561	−	4.07189i	−0.0511207	−	0.174101i	−0.981096	+	0.193520i	$0.938010\pi$
$548$	38.1453	−	0.635767i	1.62949	−	0.0271586i
$549$	−0.361543	+	24.2585i	−0.0154303	+	1.03533i
$550$	−6.37682	−	6.27142i	−0.271909	−	0.267414i
$551$	−40.8517			−1.74034
$552$	13.4703	+	19.2497i	0.573335	+	0.819321i
$553$	−16.1322			−0.686011
$554$	−23.4856	−	23.0975i	−0.997810	−	0.981318i
$555$	−0.674608	+	8.53772i	−0.0286355	+	0.362406i
$556$	24.4246	−	0.407084i	1.03583	−	0.0172642i
$557$	5.26734	+	17.9389i	0.223184	+	0.760096i	0.992609	+	0.121358i	$0.0387249\pi$
$557$	5.26734	+	17.9389i	0.223184	+	0.760096i	−0.769424	+	0.638738i	$0.779457\pi$
$558$	−12.5921	−	12.7587i	−0.533067	−	0.540118i
$559$	−4.93545	+	4.27659i	−0.208747	+	0.180881i
$560$	−7.81881	−	4.66419i	−0.330405	−	0.197098i
$561$	−18.5882	−	4.18893i	−0.784796	−	0.176857i
$562$	−10.7445	+	20.0730i	−0.453231	+	0.846729i
$563$	−27.1735	−	17.4633i	−1.14523	−	0.735991i	−0.176542	−	0.984293i	$-0.556491\pi$
$563$	−27.1735	−	17.4633i	−1.14523	−	0.735991i	−0.968683	+	0.248302i	$0.920128\pi$
$564$	0.104141	−	1.67252i	0.00438512	−	0.0704256i
$565$	2.14868	−	2.47971i	0.0903957	−	0.104322i
$566$	37.4145	+	2.36276i	1.57265	+	0.0993141i
$567$	−21.0965	+	8.88450i	−0.885969	+	0.373114i
$568$	3.92991	−	20.5226i	0.164895	−	0.861109i
$569$	−0.615380	+	0.281035i	−0.0257981	+	0.0117816i	−0.428272	−	0.903650i	$-0.640878\pi$
$569$	−0.615380	+	0.281035i	−0.0257981	+	0.0117816i	0.402474	+	0.915431i	$0.368150\pi$
$570$	11.3593	−	7.31431i	0.475787	−	0.306363i
$571$	−32.8804	−	15.0160i	−1.37600	−	0.628399i	−0.416251	−	0.909250i	$-0.636656\pi$
$571$	−32.8804	−	15.0160i	−1.37600	−	0.628399i	−0.959752	+	0.280851i	$0.909383\pi$
$572$	−1.09090	−	3.49850i	−0.0456128	−	0.146280i
$573$	18.1379	+	24.6096i	0.757724	+	1.02808i
$574$	5.35939	+	23.6848i	0.223697	+	0.988584i
$575$	−8.76365	−	18.1318i	−0.365470	−	0.756147i
$576$	2.57995	−	23.8609i	0.107498	−	0.994205i
$577$	−25.1184	+	16.1426i	−1.04569	+	0.672026i	−0.946388	−	0.323031i	$-0.895298\pi$
$577$	−25.1184	+	16.1426i	−1.04569	+	0.672026i	−0.0993047	+	0.995057i	$0.531662\pi$
$578$	−51.2494	+	4.09492i	−2.13169	+	0.170326i
$579$	0.454631	+	0.173438i	0.0188938	+	0.00720786i
$580$	−8.83440	+	7.91662i	−0.366828	+	0.328720i
$581$	26.8365	−	12.2558i	1.11336	−	0.508456i
$582$	−16.0444	−	10.2911i	−0.665061	−	0.426581i
$583$	−8.90751	+	1.28071i	−0.368911	+	0.0530414i
$584$	3.54187	+	8.81653i	0.146564	+	0.364831i
$585$	2.72105	+	1.80657i	0.112502	+	0.0746925i
$586$	−4.20128	−	1.52724i	−0.173553	−	0.0630898i
$587$	−12.8654	−	8.26810i	−0.531013	−	0.341261i	0.247502	−	0.968887i	$-0.420390\pi$
$587$	−12.8654	−	8.26810i	−0.531013	−	0.341261i	−0.778515	+	0.627626i	$0.784027\pi$
$588$	1.80062	+	0.374358i	0.0742561	+	0.0154383i
$589$	24.9874	+	7.33695i	1.02959	+	0.302314i
$590$	0.127816	+	0.334158i	0.00526212	+	0.0137571i
$591$	26.0343	+	26.4252i	1.07091	+	1.08699i
$592$	−21.4022	−	5.51663i	−0.879626	−	0.226732i
$593$	4.46501	+	15.2064i	0.183356	+	0.624453i	0.998949	+	0.0458275i	$0.0145925\pi$
$593$	4.46501	+	15.2064i	0.183356	+	0.624453i	−0.815593	+	0.578625i	$0.803589\pi$
$594$	−0.155174	+	11.0663i	−0.00636688	+	0.454058i
$595$	16.4562	+	2.36604i	0.674637	+	0.0969981i
$596$	−0.359128	−	0.222430i	−0.0147105	−	0.00911107i
$597$	11.8134	−	0.756483i	0.483492	−	0.0309608i
$598$	0.340213	−	8.24442i	0.0139123	−	0.337140i
$599$	27.9464			1.14186			0.570929	−	0.821000i	$-0.306583\pi$
$599$	27.9464			1.14186			0.570929	+	0.821000i	$0.306583\pi$
$600$	−5.44851	+	19.8371i	−0.222434	+	0.809846i
$601$	2.97472	−	20.6896i	0.121341	−	0.843948i	−0.834698	−	0.550709i	$-0.814358\pi$
$601$	2.97472	−	20.6896i	0.121341	−	0.843948i	0.956039	−	0.293240i	$-0.0947334\pi$
$602$	18.9002	+	3.94683i	0.770314	+	0.160861i
$603$	−6.31493	−	14.3915i	−0.257164	−	0.586069i
$604$	−14.2534	+	17.0142i	−0.579964	+	0.692296i
$605$	−5.90530	+	5.11698i	−0.240085	+	0.208035i
$606$	28.3601	−	12.9818i	1.15205	−	0.527351i
$607$	−5.93201	+	20.2026i	−0.240773	+	0.819997i	0.747097	+	0.664715i	$0.231447\pi$
$607$	−5.93201	+	20.2026i	−0.240773	+	0.819997i	−0.987870	+	0.155282i	$0.950371\pi$
$608$	13.5346	+	32.1320i	0.548898	+	1.30312i
$609$	−14.1840	+	25.5221i	−0.574766	+	1.03421i
$610$	−9.61880	−	3.49661i	−0.389454	−	0.141573i
$611$	−0.385407	+	0.444783i	−0.0155919	+	0.0179940i
$612$	12.4214	+	42.0293i	0.502107	+	1.69893i
$613$	−1.52458	−	10.6037i	−0.0615772	−	0.428279i	−0.997169	−	0.0751948i	$-0.976042\pi$
$613$	−1.52458	−	10.6037i	−0.0615772	−	0.428279i	0.935592	−	0.353084i	$-0.114867\pi$
$614$	−27.5962	−	20.3017i	−1.11369	−	0.819309i
$615$	−9.22124	+	4.94634i	−0.371836	+	0.199456i
$616$	−6.27416	+	8.83321i	−0.252793	+	0.355900i
$617$	−33.9727	−	15.5148i	−1.36769	−	0.624603i	−0.409915	−	0.912124i	$-0.634442\pi$
$617$	−33.9727	−	15.5148i	−1.36769	−	0.624603i	−0.957774	+	0.287521i	$0.907169\pi$
$618$	−16.3504	+	2.36554i	−0.657710	+	0.0951561i
$619$	3.57908	+	5.56916i	0.143856	+	0.223844i	0.905703	−	0.423913i	$-0.139344\pi$
$619$	3.57908	+	5.56916i	0.143856	+	0.223844i	−0.761847	+	0.647757i	$0.775707\pi$
$620$	6.82547	−	3.25563i	0.274118	−	0.130749i
$621$	−8.72096	+	23.3441i	−0.349960	+	0.936765i
$622$	10.9291	+	48.2991i	0.438218	+	1.93662i
$623$	−15.7728	+	10.1366i	−0.631926	+	0.406114i
$624$	−5.80392	+	6.11237i	−0.232343	+	0.244691i
$625$	5.66174	−	12.3975i	0.226470	−	0.495899i
$626$	10.7044	+	19.2211i	0.427834	+	0.768231i
$627$	−7.60013	−	14.1686i	−0.303520	−	0.565839i
$628$	7.40623	+	3.23426i	0.295541	+	0.129061i
$629$	39.9493	−	5.74384i	1.59288	−	0.229022i
$630$	−0.625597	−	9.63629i	−0.0249244	−	0.383919i
$631$	27.9037	+	24.1787i	1.11083	+	0.962538i	0.999512	−	0.0312466i	$-0.00994772\pi$
$631$	27.9037	+	24.1787i	1.11083	+	0.962538i	0.111317	+	0.993785i	$0.464493\pi$
$632$	17.8565	−	1.72668i	0.710292	−	0.0686836i
$633$	24.4018	+	13.5614i	0.969883	+	0.539017i
$634$	8.40074	−	15.6943i	0.333636	−	0.623301i
$635$	−18.0759	−	5.30755i	−0.717318	−	0.210624i
$636$	12.5563	+	16.4551i	0.497891	+	0.652485i
$637$	−0.422979	−	0.488144i	−0.0167590	−	0.0193410i
$638$	8.55396	+	11.2305i	0.338655	+	0.444618i
$639$	20.2951	−	8.90539i	0.802863	−	0.352292i
$640$	9.15374	+	4.32585i	0.361833	+	0.170994i
$641$	−43.6092	−	6.27005i	−1.72246	−	0.247652i	−0.791083	−	0.611709i	$-0.790482\pi$
$641$	−43.6092	−	6.27005i	−1.72246	−	0.247652i	−0.931377	+	0.364057i	$0.881391\pi$
$642$	10.5779	−	12.2294i	0.417478	−	0.482654i
$643$		−	42.1685i		−	1.66296i	−0.555553	−	0.831481i	$-0.687494\pi$
$643$		−	42.1685i		−	1.66296i	0.555553	−	0.831481i	$-0.312506\pi$
$644$	−20.0003	+	13.9694i	−0.788124	+	0.550470i
$645$	0.531690	+	8.30301i	0.0209353	+	0.326931i
$646$	−45.3944	−	44.6441i	−1.78602	−	1.75650i
$647$	−2.84386	+	19.7795i	−0.111804	+	0.777612i	0.854360	+	0.519682i	$0.173950\pi$
$647$	−2.84386	+	19.7795i	−0.111804	+	0.777612i	−0.966164	+	0.257930i	$0.916959\pi$
$648$	22.4004	−	12.0921i	0.879973	−	0.475024i
$649$	0.408521	−	0.119953i	0.0160358	−	0.00470855i
$650$	5.74754	−	4.37776i	0.225437	−	0.171710i
$651$	13.2596	−	13.0634i	0.519684	−	0.511996i
$652$	−19.4137	+	12.9386i	−0.760300	+	0.506715i
$653$	0.199242	−	0.678557i	0.00779695	−	0.0265540i	−0.955503	−	0.294983i	$-0.904686\pi$
$653$	0.199242	−	0.678557i	0.00779695	−	0.0265540i	0.963300	+	0.268429i	$0.0865043\pi$
$654$	12.4987	−	27.4323i	0.488739	−	1.07269i
$655$	9.65192	−	15.0187i	0.377132	−	0.586829i
$656$	−8.46728	−	25.6427i	−0.330592	−	1.00118i
$657$	−5.57417	+	8.39579i	−0.217469	+	0.327551i
$658$	1.73657	+	0.109666i	0.0676985	+	0.00427522i
$659$	1.83098	+	12.7347i	0.0713247	+	0.496074i	0.993902	+	0.110263i	$0.0351693\pi$
$659$	1.83098	+	12.7347i	0.0713247	+	0.496074i	−0.922578	+	0.385811i	$0.873922\pi$
$660$	−4.38929	−	1.59121i	−0.170853	−	0.0619376i
$661$	−3.16875	−	6.93859i	−0.123250	−	0.269880i	0.837942	−	0.545759i	$-0.183758\pi$
$661$	−3.16875	−	6.93859i	−0.123250	−	0.269880i	−0.961192	+	0.275879i	$0.911031\pi$
$662$	−15.5747	+	8.67370i	−0.605329	+	0.337113i
$663$	5.48627	−	14.3811i	0.213069	−	0.558515i
$664$	−28.3931	+	16.4382i	−1.10187	+	0.637924i
$665$	7.58446	+	11.8016i	0.294113	+	0.457648i
$666$	−8.04783	−	22.0178i	−0.311847	−	0.853171i
$667$	9.61880	+	30.2964i	0.372441	+	1.17308i
$668$	−36.1612	+	17.2483i	−1.39912	+	0.667356i
$669$	12.7722	−	9.41348i	0.493803	−	0.363946i
$670$	6.60878	−	0.528054i	0.255319	−	0.0204005i
$671$	−5.05969	+	11.0792i	−0.195327	+	0.427707i
$672$	24.7738	+	2.70074i	0.955668	+	0.104183i
$673$	13.9697	+	30.5894i	0.538493	+	1.17913i	0.961952	+	0.273219i	$0.0880885\pi$
$673$	13.9697	+	30.5894i	0.538493	+	1.17913i	−0.423459	+	0.905915i	$0.639184\pi$
$674$	−5.73915	+	7.80127i	−0.221064	+	0.300494i
$675$	−20.6092	+	7.16631i	−0.793249	+	0.275831i
$676$	−22.7474	+	3.65848i	−0.874900	+	0.140711i
$677$	−7.55804	−	6.54908i	−0.290479	−	0.251702i	0.497414	−	0.867513i	$-0.334283\pi$
$677$	−7.55804	−	6.54908i	−0.290479	−	0.251702i	−0.787894	+	0.615811i	$0.788828\pi$
$678$	−2.52269	+	8.61960i	−0.0968835	+	0.331034i
$679$	10.7005	−	16.6503i	0.410649	−	0.638982i
$680$	−18.4683	−	0.857577i	−0.708228	−	0.0328866i
$681$	8.66369	−	38.4449i	0.331993	−	1.47321i
$682$	−3.21513	−	8.40552i	−0.123114	−	0.321864i
$683$	2.01654	+	2.32721i	0.0771607	+	0.0890482i	0.793017	−	0.609199i	$-0.208509\pi$
$683$	2.01654	+	2.32721i	0.0771607	+	0.0890482i	−0.715857	+	0.698247i	$0.753964\pi$
$684$	−19.9386	+	31.1457i	−0.762372	+	1.19088i
$685$	−16.3787	+	4.80922i	−0.625797	+	0.183751i
$686$	−5.53730	+	26.5164i	−0.211415	+	1.01240i
$687$	−26.7555	−	2.11408i	−1.02079	−	0.0806573i
$688$	−21.3428	−	2.34574i	−0.813685	−	0.0894307i
$689$		−	7.26943i		−	0.276943i
$690$	−8.09905	−	6.70205i	−0.308326	−	0.255143i
$691$			34.1984i			1.30097i	0.759519	+	0.650485i	$0.225434\pi$
$691$			34.1984i			1.30097i	−0.759519	+	0.650485i	$0.774566\pi$
$692$	−25.1219	−	15.5595i	−0.954990	−	0.591483i
$693$	−11.4907	−	0.171254i	−0.436494	−	0.00650539i
$694$	−38.8546	−	8.11383i	−1.47490	−	0.307997i
$695$	−10.4873	+	3.07936i	−0.397807	+	0.116807i
$696$	12.9684	−	29.7682i	0.491565	−	1.12836i
$697$	32.2931	+	37.2682i	1.22319	+	1.41163i
$698$	−32.5307	+	12.4431i	−1.23131	+	0.470977i
$699$	−24.8709	−	5.60474i	−0.940703	−	0.211991i
$700$	−20.5930	−	5.67564i	−0.778340	−	0.214519i
$701$	7.87469	−	12.2533i	0.297423	−	0.462799i	−0.660091	−	0.751186i	$-0.729482\pi$
$701$	7.87469	−	12.2533i	0.297423	−	0.462799i	0.957514	+	0.288386i	$0.0931187\pi$
$702$	−8.83050	−	1.39627i	−0.333286	−	0.0526989i
$703$	25.7379	+	22.3021i	0.970725	+	0.841138i
$704$	5.99933	−	10.4489i	0.226108	−	0.393807i
$705$	0.153918	+	0.733833i	0.00579688	+	0.0276377i
$706$	8.15422	+	5.99880i	0.306888	+	0.225768i
$707$	13.4538	+	29.4597i	0.505982	+	1.10795i
$708$	−0.698816	−	0.686056i	−0.0262631	−	0.0257836i
$709$	2.69486	−	5.90093i	0.101208	−	0.221614i	−0.852254	−	0.523128i	$-0.824765\pi$
$709$	2.69486	−	5.90093i	0.101208	−	0.221614i	0.953462	+	0.301514i	$0.0974921\pi$
$710$	0.744669	+	9.31978i	0.0279469	+	0.349765i
$711$	12.2450	+	14.5645i	0.459224	+	0.546211i
$712$	16.3738	−	12.9083i	0.613633	−	0.483757i
$713$	−0.442210	−	20.2587i	−0.0165609	−	0.758693i
$714$	−43.6527	+	12.8594i	−1.63366	+	0.481251i
$715$	0.886493	+	1.37941i	0.0331529	+	0.0515870i
$716$	−7.28791	−	23.3722i	−0.272362	−	0.873461i
$717$	8.27941	+	3.15853i	0.309200	+	0.117958i
$718$	11.3835	+	20.4406i	0.424830	+	0.762836i
$719$	−12.0750	−	26.4406i	−0.450323	−	0.986070i	−0.989587	−	0.143933i	$-0.954025\pi$
$719$	−12.0750	−	26.4406i	−0.450323	−	0.986070i	0.539265	−	0.842136i	$-0.318702\pi$
$720$	1.72387	+	10.5993i	0.0642447	+	0.395013i
$721$	−2.44131	−	16.9797i	−0.0909191	−	0.632357i
$722$	1.69251	−	26.8010i	0.0629887	−	0.997432i
$723$	1.97833	+	1.50409i	0.0735748	+	0.0559376i
$724$	−9.77824	−	1.23995i	−0.363405	−	0.0460825i
$725$	−15.0472	+	23.4139i	−0.558839	+	0.869571i
$726$	8.86783	−	19.4632i	0.329116	−	0.722348i
$727$	6.61631	−	22.5331i	0.245385	−	0.835706i	−0.741035	−	0.671466i	$-0.765665\pi$
$727$	6.61631	−	22.5331i	0.245385	−	0.835706i	0.986421	−	0.164239i	$-0.0525169\pi$
$728$	−6.34150	−	6.03212i	−0.235032	−	0.223565i
$729$	24.0342	+	12.3027i	0.890157	+	0.455654i
$730$	−2.57598	−	3.38199i	−0.0953413	−	0.125173i
$731$	37.6205	−	11.0464i	1.39144	−	0.408565i
$732$	27.9235	−	2.25591i	1.03208	−	0.0833808i
$733$	−3.65831	+	25.4441i	−0.135123	+	0.939800i	0.803610	+	0.595156i	$0.202910\pi$
$733$	−3.65831	+	25.4441i	−0.135123	+	0.939800i	−0.938733	+	0.344644i	$0.887999\pi$
$734$	0.0280991	−	0.0285713i	0.00103716	−	0.00105459i
$735$	−0.821215	+	0.0525872i	−0.0302910	+	0.00193971i
$736$	20.6429	−	17.6032i	0.760907	−	0.648861i
$737$		−	7.88992i		−	0.290629i
$738$	17.3151	−	22.8163i	0.637379	−	0.839880i
$739$	24.0773	+	3.46180i	0.885699	+	0.127344i	0.570126	−	0.821557i	$-0.306894\pi$
$739$	24.0773	+	3.46180i	0.885699	+	0.127344i	0.315572	+	0.948901i	$0.397803\pi$
$740$	9.88786	−	0.164801i	0.363485	−	0.00605819i
$741$	12.2025	−	4.44802i	0.448271	−	0.163402i
$742$	−17.0977	+	13.0229i	−0.627676	+	0.478085i
$743$	16.4886	+	19.0288i	0.604907	+	0.698100i	0.972768	−	0.231781i	$-0.0744553\pi$
$743$	16.4886	+	19.0288i	0.604907	+	0.698100i	−0.367861	+	0.929881i	$0.619910\pi$
$744$	−13.2786	+	15.8789i	−0.486817	+	0.582149i
$745$	0.181356	+	0.0532511i	0.00664439	+	0.00195097i
$746$	21.1015	+	11.2951i	0.772581	+	0.413541i
$747$	−31.4348	−	14.9259i	−1.15014	−	0.546109i
$748$	−2.76787	+	21.8273i	−0.101203	+	0.798086i
$749$	12.6887	+	10.9948i	0.463636	+	0.401743i
$750$	−0.0177729	−	20.1646i	−0.000648974	−	0.736308i
$751$	−10.2521	+	1.47403i	−0.374105	+	0.0537881i	−0.326803	−	0.945093i	$-0.605971\pi$
$751$	−10.2521	+	1.47403i	−0.374105	+	0.0537881i	−0.0473018	+	0.998881i	$0.515062\pi$
$752$	−1.93392	+	0.0644831i	−0.0705228	+	0.00235145i
$753$	−27.5715	+	14.7896i	−1.00476	+	0.538962i
$754$	−9.96294	+	5.54844i	−0.362829	+	0.202062i
$755$	4.12556	−	9.03372i	0.150145	−	0.328771i
$756$	12.5354	+	23.2707i	0.455910	+	0.846347i
$757$	−17.4925	+	11.2418i	−0.635776	+	0.408589i	−0.818444	−	0.574586i	$-0.805163\pi$
$757$	−17.4925	+	11.2418i	−0.635776	+	0.408589i	0.182668	+	0.983175i	$0.441527\pi$
$758$	24.7826	−	5.60779i	0.900143	−	0.203684i
$759$	−8.71820	+	8.97249i	−0.316451	+	0.325681i
$760$	−9.65829	−	12.2513i	−0.350343	−	0.444400i
$761$	20.0730	+	31.2342i	0.727646	+	1.13224i	0.986090	+	0.166213i	$0.0531540\pi$
$761$	20.0730	+	31.2342i	0.727646	+	1.13224i	−0.258444	+	0.966026i	$0.583210\pi$
$762$	51.0351	−	7.38366i	1.84881	−	0.267482i
$763$	28.4731	+	13.0032i	1.03079	+	0.470748i
$764$	26.2897	−	23.5586i	0.951128	−	0.852319i
$765$	−10.3548	−	16.6529i	−0.374379	−	0.602087i
$766$	−4.44395	+	6.04069i	−0.160566	+	0.218259i
$767$	0.0489467	+	0.340432i	0.00176736	+	0.0122923i
$768$	−27.7108	−	0.337796i	−0.999926	−	0.0121892i
$769$	26.3502	−	30.4098i	0.950214	−	1.09660i	−0.0450103	−	0.998987i	$-0.514332\pi$
$769$	26.3502	−	30.4098i	0.950214	−	1.09660i	0.995224	−	0.0976185i	$-0.0311225\pi$
$770$	1.65625	−	4.55618i	0.0596873	−	0.164193i
$771$	−2.26133	−	1.25675i	−0.0814399	−	0.0452606i
$772$	0.149290	−	0.541670i	0.00537307	−	0.0194951i
$773$	7.98788	−	27.2042i	0.287304	−	0.978468i	−0.681743	−	0.731592i	$-0.738778\pi$
$773$	7.98788	−	27.2042i	0.287304	−	0.978468i	0.969047	−	0.246876i	$-0.0794041\pi$
$774$	−10.7827	−	20.0593i	−0.387577	−	0.721017i
$775$	13.4089	−	11.6189i	0.481662	−	0.417363i
$776$	−10.0621	+	19.5753i	−0.361209	+	0.702713i
$777$	22.8696	−	8.33635i	0.820444	−	0.299065i
$778$	−2.15710	+	10.3297i	−0.0773358	+	0.370338i
$779$	−5.92181	+	41.1871i	−0.212171	+	1.47568i
$780$	1.77688	−	3.32662i	0.0636226	−	0.119112i
$781$	11.1265			0.398136
$782$	−22.4205	+	44.1771i	−0.801757	+	1.57977i
$783$	33.8082	−	6.56671i	1.20821	−	0.234675i
$784$	0.232007	−	2.11092i	0.00828598	−	0.0753900i
$785$	−3.57924	−	0.514617i	−0.127749	−	0.0183675i
$786$	−6.91186	+	48.3757i	−0.246538	+	1.72550i
$787$	−2.30422	−	7.84746i	−0.0821367	−	0.279732i	0.908176	−	0.418589i	$-0.137475\pi$
$787$	−2.30422	−	7.84746i	−0.0821367	−	0.279732i	−0.990312	+	0.138857i	$0.955657\pi$
$788$	27.5071	−	32.8349i	0.979899	−	1.16969i
$789$	33.3129	−	32.8202i	1.18597	−	1.16843i
$790$	−7.49724	+	2.86771i	−0.266740	+	0.102029i
$791$	−8.94790	−	2.62734i	−0.318151	−	0.0934175i
$792$	12.7372	−	1.04032i	0.452595	−	0.0369663i
$793$	−8.27693	−	5.31926i	−0.293922	−	0.188892i
$794$	4.60369	−	12.6643i	0.163379	−	0.449438i
$795$	−7.37255	−	5.60523i	−0.261477	−	0.198797i
$796$	−2.17049	−	13.4955i	−0.0769309	−	0.478335i
$797$	−16.5836	+	2.38435i	−0.587420	+	0.0844582i	−0.429615	−	0.903012i	$-0.641351\pi$
$797$	−16.5836	+	2.38435i	−0.587420	+	0.0844582i	−0.157805	+	0.987470i	$0.550442\pi$
$798$	−32.3220	−	20.7319i	−1.14419	−	0.733900i
$799$	3.21418	−	1.46787i	0.113709	−	0.0519294i
$800$	23.4015	+	4.07815i	0.827368	+	0.144184i
$801$	21.1238	+	6.54597i	0.746372	+	0.231290i
$802$	−1.66450	−	20.8318i	−0.0587756	−	0.735596i
$803$	−4.25616	+	2.73527i	−0.150197	+	0.0965256i
$804$	−15.8467	+	8.84349i	−0.558872	+	0.311886i
$805$	6.96652	−	8.40356i	0.245538	−	0.296186i
$806$	7.09043	−	1.60442i	0.249750	−	0.0565133i
$807$	36.7150	−	27.0600i	1.29243	−	0.952557i
$808$	−18.0450	−	31.1685i	−0.634819	−	1.09650i
$809$	−20.8546	−	9.52397i	−0.733208	−	0.334845i	0.0135793	−	0.999908i	$-0.495677\pi$
$809$	−20.8546	−	9.52397i	−0.733208	−	0.334845i	−0.746787	+	0.665063i	$0.768405\pi$
$810$	−8.22500	+	7.87915i	−0.288997	+	0.276845i
$811$	−10.3706	+	4.73609i	−0.364160	+	0.166306i	−0.589088	−	0.808069i	$-0.700513\pi$
$811$	−10.3706	+	4.73609i	−0.364160	+	0.166306i	0.224927	+	0.974376i	$0.427786\pi$
$812$	30.8981	+	13.4930i	1.08431	+	0.473512i
$813$	1.24879	+	5.95386i	0.0437971	+	0.208811i
$814$	0.741733	−	11.7454i	0.0259977	−	0.411676i
$815$	6.83602	−	7.88919i	0.239455	−	0.276346i
$816$	46.9421	−	18.9061i	1.64330	−	0.661848i
$817$	27.8326	+	17.8869i	0.973739	+	0.625784i
$818$	−21.0496	−	11.2673i	−0.735981	−	0.393951i
$819$	1.45791	−	9.16792i	0.0509434	−	0.320353i
$820$	6.70100	+	10.0545i	0.234009	+	0.351119i
$821$	35.6784	−	30.9155i	1.24518	−	1.07896i	0.251371	−	0.967891i	$-0.419119\pi$
$821$	35.6784	−	30.9155i	1.24518	−	1.07896i	0.993813	−	0.111067i	$-0.0354267\pi$
$822$	35.2853	−	30.6293i	1.23071	−	1.06832i
$823$	−3.77705	−	12.8635i	−0.131660	−	0.448392i	0.867103	−	0.498130i	$-0.165980\pi$
$823$	−3.77705	−	12.8635i	−0.131660	−	0.448392i	−0.998762	+	0.0497377i	$0.984161\pi$
$824$	4.51964	+	18.5333i	0.157449	+	0.645636i
$825$	−10.9200	−	0.862847i	−0.380187	−	0.0300405i
$826$	0.713009	−	0.724992i	0.0248088	−	0.0252257i
$827$	−32.8908			−1.14373			−0.571863	−	0.820349i	$-0.693779\pi$
$827$	−32.8908			−1.14373			−0.571863	+	0.820349i	$0.693779\pi$
$828$	27.7929	+	7.45342i	0.965871	+	0.259024i
$829$	23.5541			0.818066			0.409033	−	0.912520i	$-0.365866\pi$
$829$	23.5541			0.818066			0.409033	+	0.912520i	$0.365866\pi$
$830$	10.2933	−	10.4663i	0.357285	−	0.363290i
$831$	−40.2182	−	3.17784i	−1.39515	−	0.110238i
$832$	7.66495	+	5.99811i	0.265734	+	0.207947i
$833$	1.09255	+	3.72088i	0.0378546	+	0.128921i
$834$	22.5933	−	19.6121i	0.782341	−	0.679110i
$835$	13.5478	−	11.7393i	0.468842	−	0.406254i
$836$	−15.4489	+	10.2962i	−0.534312	+	0.356101i
$837$	−21.8585	−	2.05534i	−0.755541	−	0.0710431i
$838$	9.41791	+	5.04115i	0.325336	+	0.174144i
$839$	10.5978	+	6.81077i	0.365875	+	0.235134i	0.710641	−	0.703555i	$-0.248405\pi$
$839$	10.5978	+	6.81077i	0.365875	+	0.235134i	−0.344765	+	0.938689i	$0.612042\pi$
$840$	−11.0074	+	1.78029i	−0.379792	+	0.0614257i
$841$	9.77721	−	11.2835i	0.337145	−	0.389086i
$842$	−1.38548	+	21.9392i	−0.0477469	+	0.756076i
$843$	5.72413	+	27.2909i	0.197150	+	0.939948i
$844$	12.9007	−	29.5418i	0.444060	−	1.01687i
$845$	9.37732	−	4.28248i	0.322589	−	0.147322i
$846$	−1.21912	−	1.65105i	−0.0419142	−	0.0567644i
$847$	20.2016	+	9.22577i	0.694136	+	0.317001i
$848$	17.5313	−	16.2448i	0.602027	−	0.557850i
$849$	36.9604	−	27.2409i	1.26848	−	0.934904i
$850$	−42.3079	+	9.57343i	−1.45115	+	0.328366i
$851$	10.4795	−	24.3389i	0.359232	−	0.834328i
$852$	−12.4712	−	22.3473i	−0.427256	−	0.765605i
$853$	41.5108	−	26.6774i	1.42130	−	0.913415i	0.421323	−	0.906911i	$-0.361566\pi$
$853$	41.5108	−	26.6774i	1.42130	−	0.913415i	0.999979	−	0.00650434i	$-0.00207041\pi$
$854$	2.31688	+	28.9965i	0.0792820	+	0.992241i
$855$	4.89786	−	15.8054i	0.167503	−	0.540532i
$856$	−15.2218	−	10.8119i	−0.520270	−	0.369544i
$857$	19.3900	−	8.85510i	0.662348	−	0.302484i	−0.0557308	−	0.998446i	$-0.517749\pi$
$857$	19.3900	−	8.85510i	0.662348	−	0.302484i	0.718079	+	0.695961i	$0.245022\pi$
$858$	−3.77789	−	2.42320i	−0.128975	−	0.0827266i
$859$	−26.4229	+	3.79904i	−0.901538	+	0.129622i	−0.577470	−	0.816412i	$-0.695960\pi$
$859$	−26.4229	+	3.79904i	−0.901538	+	0.129622i	−0.324068	+	0.946034i	$0.605051\pi$
$860$	9.48523	−	1.52552i	0.323444	−	0.0520197i
$861$	23.6756	+	18.0001i	0.806862	+	0.613443i
$862$	14.5515	−	40.0295i	0.495624	−	1.36341i
$863$	−10.9390	−	7.03006i	−0.372368	−	0.239306i	0.341050	−	0.940045i	$-0.389217\pi$
$863$	−10.9390	−	7.03006i	−0.372368	−	0.239306i	−0.713418	+	0.700739i	$0.752854\pi$
$864$	−16.3660	−	24.4163i	−0.556783	−	0.830658i
$865$	12.6863	+	3.72504i	0.431348	+	0.126655i
$866$	37.5567	−	14.3655i	1.27623	−	0.488160i
$867$	−44.8552	+	44.1917i	−1.52336	+	1.50083i
$868$	−16.4758	−	13.8024i	−0.559225	−	0.468485i
$869$	2.69128	+	9.16566i	0.0912954	+	0.310924i
$870$	−2.05495	+	14.3825i	−0.0696695	+	0.487613i
$871$	6.30856	+	0.907034i	0.213757	+	0.0307337i
$872$	−32.9082	−	11.3455i	−1.11441	−	0.384207i
$873$	−23.1544	+	2.97764i	−0.783659	+	0.100778i
$874$	−40.5612	+	10.1135i	−1.37200	+	0.342094i
$875$	20.9381			0.707836
$876$	10.2643	+	5.48256i	0.346798	+	0.185239i
$877$	6.58241	−	45.7817i	0.222272	−	1.54594i	−0.507140	−	0.861864i	$-0.669297\pi$
$877$	6.58241	−	45.7817i	0.222272	−	1.54594i	0.729412	−	0.684074i	$-0.239794\pi$
$878$	1.00537	−	4.81439i	0.0339295	−	0.162478i
$879$	−5.14385	+	1.87502i	−0.173498	+	0.0632427i
$880$	−1.34562	+	5.22044i	−0.0453608	+	0.175981i
$881$	−6.99947	+	6.06508i	−0.235818	+	0.204338i	−0.764751	−	0.644326i	$-0.777138\pi$
$881$	−6.99947	+	6.06508i	−0.235818	+	0.204338i	0.528933	+	0.848664i	$0.322592\pi$
$882$	1.98398	−	1.06647i	0.0668041	−	0.0359100i
$883$	4.42183	−	15.0594i	0.148806	−	0.506788i	−0.851026	−	0.525124i	$-0.824019\pi$
$883$	4.42183	−	15.0594i	0.148806	−	0.506788i	0.999832	+	0.0183366i	$0.00583703\pi$
$884$	−17.1343	−	4.72240i	−0.576290	−	0.158832i
$885$	0.383002	+	0.212855i	0.0128745	+	0.00715505i
$886$	10.9569	−	30.1412i	0.368103	−	1.01261i
$887$	−7.37544	+	8.51171i	−0.247643	+	0.285795i	−0.865939	−	0.500150i	$-0.833278\pi$
$887$	−7.37544	+	8.51171i	−0.247643	+	0.285795i	0.618295	+	0.785946i	$0.287824\pi$
$888$	−24.4218	+	11.6752i	−0.819541	+	0.391794i
$889$	7.62015	+	52.9993i	0.255572	+	1.77754i
$890$	−5.52832	+	7.51469i	−0.185310	+	0.251893i
$891$	8.56727	+	10.5040i	0.287014	+	0.351897i
$892$	−12.2268	−	13.6442i	−0.409382	−	0.456842i
$893$	2.71215	+	1.23860i	0.0907587	+	0.0414481i
$894$	−0.512039	+	0.0740808i	−0.0171251	+	0.00247763i
$895$	5.92234	+	9.21534i	0.197962	+	0.308035i
$896$	0.376113	−	28.7733i	0.0125650	−	0.961248i
$897$	−6.17190	−	8.00231i	−0.206074	−	0.267189i
$898$	0.387539	−	0.0876922i	0.0129323	−	0.00292633i
$899$	−23.5591	+	15.1405i	−0.785740	+	0.504964i
$900$	10.5068	+	22.8998i	0.350227	+	0.763327i
$901$	−18.1308	+	39.7008i	−0.604023	+	1.32263i
$902$	12.5626	−	6.99624i	0.418290	−	0.232949i
$903$	20.8385	−	11.1779i	0.693463	−	0.371979i
$904$	10.1855	+	1.95044i	0.338765	+	0.0648707i
$905$	4.36533	−	0.627639i	0.145108	−	0.0208634i
$906$	0.0239595	+	27.1839i	0.000796003	+	0.903123i
$907$	−27.8499	−	24.1321i	−0.924740	−	0.801292i	0.0556316	−	0.998451i	$-0.482283\pi$
$907$	−27.8499	−	24.1321i	−0.924740	−	0.801292i	−0.980371	+	0.197160i	$0.936828\pi$
$908$	−45.1441	−	5.72461i	−1.49816	−	0.189978i
$909$	16.3849	−	34.5075i	0.543451	−	1.14454i
$910$	3.45259	+	1.84808i	0.114452	+	0.0612632i
$911$	−12.7033	−	3.73003i	−0.420880	−	0.123582i	0.0644329	−	0.997922i	$-0.479476\pi$
$911$	−12.7033	−	3.73003i	−0.420880	−	0.123582i	−0.485313	+	0.874340i	$0.661294\pi$
$912$	37.9958	+	19.4883i	1.25817	+	0.645321i
$913$	−11.4403	−	13.2028i	−0.378618	−	0.436949i
$914$	−38.1818	+	29.0821i	−1.26294	+	0.961950i
$915$	−11.7768	+	4.29283i	−0.389329	+	0.141917i
$916$	0.516452	+	30.9866i	0.0170641	+	1.02382i
$917$	−50.2248	−	7.22123i	−1.65857	−	0.238466i
$918$	44.7439	+	29.6498i	1.47677	+	0.978589i
$919$			52.5903i			1.73479i	0.497617	+	0.867397i	$0.334208\pi$
$919$			52.5903i			1.73479i	−0.497617	+	0.867397i	$0.665792\pi$
$920$	−6.81168	+	10.0474i	−0.224574	+	0.331254i
$921$	−41.8733	+	2.68139i	−1.37977	+	0.0883549i
$922$	13.9080	−	14.1418i	0.458036	−	0.465734i
$923$	−1.27911	+	8.89641i	−0.0421025	+	0.292829i
$924$	1.06857	+	13.2266i	0.0351533	+	0.435125i
$925$	22.2625	−	6.53687i	0.731987	−	0.214931i
$926$	6.83426	+	8.97267i	0.224588	+	0.294860i
$927$	−13.4766	+	15.0924i	−0.442629	+	0.495698i
$928$	−35.6448	−	11.6281i	−1.17010	−	0.381711i
$929$	−8.54254	+	29.0932i	−0.280272	+	0.954518i	0.692241	+	0.721667i	$0.256624\pi$
$929$	−8.54254	+	29.0932i	−0.280272	+	0.954518i	−0.972512	+	0.232851i	$0.925195\pi$
$930$	3.84003	−	8.42814i	0.125919	−	0.276369i
$931$	−1.76912	+	2.75280i	−0.0579805	+	0.0902194i
$932$	−3.70338	+	29.2047i	−0.121308	+	0.956633i
$933$	48.2804	+	36.7067i	1.58063	+	1.20173i
$934$	1.44694	−	22.9124i	0.0473452	−	0.749716i
$935$	−1.40104	−	9.74444i	−0.0458189	−	0.318677i
$936$	−0.632465	+	10.3039i	−0.0206728	+	0.336793i
$937$	−15.4701	−	33.8748i	−0.505386	−	1.10664i	−0.974681	−	0.223600i	$-0.928219\pi$
$937$	−15.4701	−	33.8748i	−0.505386	−	1.10664i	0.469295	−	0.883042i	$-0.344508\pi$
$938$	−9.16818	−	16.4626i	−0.299352	−	0.537524i
$939$	25.1756	+	9.60431i	0.821575	+	0.313425i
$940$	0.826544	−	0.257733i	0.0269589	−	0.00840631i
$941$	−7.55222	−	11.7515i	−0.246195	−	0.383087i	0.696060	−	0.717984i	$-0.254935\pi$
$941$	−7.55222	−	11.7515i	−0.246195	−	0.383087i	−0.942255	+	0.334897i	$0.891299\pi$
$942$	9.49454	−	2.79694i	0.309349	−	0.0911292i
$943$	31.9395	−	5.30604i	1.04009	−	0.172788i
$944$	−0.711620	+	0.878798i	−0.0231613	+	0.0286024i
$945$	−8.17383	−	8.54768i	−0.265895	−	0.278056i
$946$	−0.910623	−	11.3968i	−0.0296069	−	0.370540i
$947$	−10.3291	+	22.6176i	−0.335651	+	0.734973i	−0.999922	−	0.0125191i	$-0.996015\pi$
$947$	−10.3291	+	22.6176i	−0.335651	+	0.734973i	0.664271	+	0.747492i	$0.268742\pi$
$948$	15.3925	−	15.6788i	0.499925	−	0.509223i
$949$	−1.69775	−	3.71756i	−0.0551114	−	0.120677i
$950$	−29.4834	−	21.6900i	−0.956569	−	0.703718i
$951$	−4.47548	−	21.3377i	−0.145127	−	0.691922i
$952$	19.5883	+	48.7599i	0.634862	+	1.58032i
$953$	−27.8415	−	24.1248i	−0.901876	−	0.781480i	0.0745762	−	0.997215i	$-0.476240\pi$
$953$	−27.8415	−	24.1248i	−0.901876	−	0.781480i	−0.976452	+	0.215736i	$0.930785\pi$
$954$	24.7352	+	5.55125i	0.800831	+	0.179728i
$955$	−8.53946	+	13.2877i	−0.276330	+	0.429978i
$956$	2.71876	−	9.86450i	0.0879310	−	0.319041i
$957$	16.8669	+	3.80102i	0.545230	+	0.122869i
$958$	−50.7587	+	19.4153i	−1.63994	+	0.627281i
$959$	31.7718	+	36.6667i	1.02597	+	1.18403i
$960$	11.9934	−	3.14873i	0.387085	−	0.101625i
$961$	−12.6149	+	3.70406i	−0.406932	+	0.119486i
$962$	9.30603	+	1.94333i	0.300038	+	0.0626556i
$963$	0.295112	−	19.8012i	0.00950986	−	0.638085i
$964$	1.51099	−	2.43960i	0.0486657	−	0.0785742i
$965$			0.251402i			0.00809292i
$966$	−7.76473	+	28.8521i	−0.249826	+	0.928301i
$967$			5.27841i			0.169742i	0.996392	+	0.0848711i	$0.0270478\pi$
$967$			5.27841i			0.169742i	−0.996392	+	0.0848711i	$0.972952\pi$
$968$	−23.3483	−	8.04962i	−0.750444	−	0.258725i
$969$	−77.7360	−	6.14231i	−2.49724	−	0.197319i
$970$	2.01312	−	9.64021i	0.0646374	−	0.309528i
$971$	35.4402	−	10.4062i	1.13733	−	0.333950i	0.341745	−	0.939793i	$-0.388982\pi$
$971$	35.4402	−	10.4062i	1.13733	−	0.333950i	0.795584	+	0.605843i	$0.207164\pi$
$972$	11.4944	−	28.9807i	0.368682	−	0.929556i
$973$	20.3436	+	23.4778i	0.652186	+	0.752663i
$974$	−5.58923	−	14.6123i	−0.179091	−	0.468207i
$975$	1.94529	−	8.63217i	0.0622991	−	0.276451i
$976$	−5.66811	−	31.8478i	−0.181432	−	1.01942i
$977$	−8.95434	+	13.9332i	−0.286475	+	0.445763i	−0.954429	−	0.298439i	$-0.903534\pi$
$977$	−8.95434	+	13.9332i	−0.286475	+	0.445763i	0.667954	+	0.744203i	$0.267170\pi$
$978$	−8.02594	+	27.4232i	−0.256641	+	0.876898i
$979$	8.39053	+	7.27043i	0.268162	+	0.232364i
$980$	0.150882	+	0.938144i	0.00481976	+	0.0299679i
$981$	−9.87266	−	35.5761i	−0.315210	−	1.13586i
$982$	−12.4770	+	16.9601i	−0.398158	+	0.541220i
$983$	−25.1195	−	55.0039i	−0.801186	−	1.75435i	−0.641407	−	0.767200i	$-0.721649\pi$
$983$	−25.1195	−	55.0039i	−0.801186	−	1.75435i	−0.159779	−	0.987153i	$-0.551078\pi$
$984$	−28.1327	−	17.3900i	−0.896839	−	0.554373i
$985$	−7.96174	+	17.4338i	−0.253682	+	0.555487i
$986$	68.2495	−	5.45327i	2.17351	−	0.173667i
$987$	1.71549	−	1.26437i	0.0546048	−	0.0402453i
$988$	−6.45652	−	13.5362i	−0.205409	−	0.430644i
$989$	6.71192	−	24.8528i	0.213427	−	0.790272i
$990$	−5.37058	+	1.96303i	−0.170688	+	0.0623892i
$991$	−16.2294	−	25.2535i	−0.515544	−	0.802202i	0.481704	−	0.876334i	$-0.340018\pi$
$991$	−16.2294	−	25.2535i	−0.515544	−	0.802202i	−0.997248	+	0.0741315i	$0.976382\pi$
$992$	19.7141	+	13.5142i	0.625924	+	0.429078i
$993$	−7.78230	+	20.3996i	−0.246964	+	0.647362i
$994$	23.2158	−	12.9291i	0.736361	−	0.410086i
$995$	2.54069	+	5.56334i	0.0805453	+	0.176370i
$996$	−13.6946	+	37.7760i	−0.433930	+	1.19698i
$997$	8.73142	+	60.7283i	0.276527	+	1.92329i	0.372762	+	0.927927i	$0.378411\pi$
$997$	8.73142	+	60.7283i	0.276527	+	1.92329i	−0.0962351	+	0.995359i	$0.530680\pi$
$998$	16.0972	+	1.01655i	0.509549	+	0.0321785i
$999$	−24.8852	−	14.3196i	−0.787334	−	0.453051i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.o.a.35.11	✓	440
3.2	odd	2	inner	276.2.o.a.35.34	yes	440
4.3	odd	2	inner	276.2.o.a.35.18	yes	440
12.11	even	2	inner	276.2.o.a.35.27	yes	440
23.2	even	11	inner	276.2.o.a.71.27	yes	440
69.2	odd	22	inner	276.2.o.a.71.18	yes	440
92.71	odd	22	inner	276.2.o.a.71.34	yes	440
276.71	even	22	inner	276.2.o.a.71.11	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.o.a.35.11	✓	440	1.1	even	1	trivial
276.2.o.a.35.18	yes	440	4.3	odd	2	inner
276.2.o.a.35.27	yes	440	12.11	even	2	inner
276.2.o.a.35.34	yes	440	3.2	odd	2	inner
276.2.o.a.71.11	yes	440	276.71	even	22	inner
276.2.o.a.71.18	yes	440	69.2	odd	22	inner
276.2.o.a.71.27	yes	440	23.2	even	11	inner
276.2.o.a.71.34	yes	440	92.71	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.o (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00830 - 0.991633i) q^{2} +(-1.72667 - 0.136433i) q^{3} +(0.0333293 + 1.99972i) q^{4} +(-0.252117 - 0.858632i) q^{5} +(1.60571 + 1.84979i) q^{6} +(-1.92220 + 1.66560i) q^{7} +(1.94938 - 2.04937i) q^{8} +(2.96277 + 0.471148i) q^{9} +O(q^{10})\)	\(q+(-1.00830 - 0.991633i) q^{2} +(-1.72667 - 0.136433i) q^{3} +(0.0333293 + 1.99972i) q^{4} +(-0.252117 - 0.858632i) q^{5} +(1.60571 + 1.84979i) q^{6} +(-1.92220 + 1.66560i) q^{7} +(1.94938 - 2.04937i) q^{8} +(2.96277 + 0.471148i) q^{9} +(-0.597239 + 1.11576i) q^{10} +(1.26700 + 0.814252i) q^{11} +(0.215279 - 3.45741i) q^{12} +(-0.796709 + 0.919451i) q^{13} +(3.58982 + 0.226700i) q^{14} +(0.318177 + 1.51697i) q^{15} +(-3.99778 + 0.133299i) q^{16} +(6.64432 - 3.03436i) q^{17} +(-2.52015 - 3.41304i) q^{18} +(5.60653 + 2.56042i) q^{19} +(1.70862 - 0.532782i) q^{20} +(3.54625 - 2.61369i) q^{21} +(-0.470075 - 2.07741i) q^{22} +(0.578761 - 4.76078i) q^{23} +(-3.64554 + 3.27262i) q^{24} +(3.53258 - 2.27025i) q^{25} +(1.71508 - 0.137038i) q^{26} +(-5.05145 - 1.21774i) q^{27} +(-3.39480 - 3.78836i) q^{28} +(-6.02903 + 2.75337i) q^{29} +(1.18346 - 1.84507i) q^{30} +(4.18222 - 0.601313i) q^{31} +(4.16313 + 3.82992i) q^{32} +(-2.07660 - 1.57880i) q^{33} +(-9.70842 - 3.52918i) q^{34} +(1.91476 + 1.23054i) q^{35} +(-0.843419 + 5.94042i) q^{36} +(5.30163 + 1.55670i) q^{37} +(-3.11406 - 8.14129i) q^{38} +(1.50110 - 1.47889i) q^{39} +(-2.25113 - 1.15712i) q^{40} +(1.90201 + 6.47765i) q^{41} +(-6.16750 - 0.881205i) q^{42} +(5.31318 + 0.763921i) q^{43} +(-1.58605 + 2.56079i) q^{44} +(-0.342423 - 2.66272i) q^{45} +(-5.30451 + 4.22637i) q^{46} +0.483749 q^{47} +(6.92103 + 0.315265i) q^{48} +(-0.0755561 + 0.525504i) q^{49} +(-5.81315 - 1.21393i) q^{50} +(-11.8865 + 4.33283i) q^{51} +(-1.86520 - 1.56255i) q^{52} +(-4.51572 + 3.91290i) q^{53} +(3.88582 + 6.23702i) q^{54} +(0.379710 - 1.29317i) q^{55} +(-0.333691 + 7.18619i) q^{56} +(-9.33130 - 5.18591i) q^{57} +(8.80939 + 3.20237i) q^{58} +(0.185128 - 0.213649i) q^{59} +(-3.02292 + 0.686826i) q^{60} +(1.15091 + 8.00476i) q^{61} +(-4.81321 - 3.54093i) q^{62} +(-6.47980 + 4.02915i) q^{63} +(-0.399804 - 7.99000i) q^{64} +(0.990335 + 0.452271i) q^{65} +(0.528238 + 3.65113i) q^{66} +(-2.83225 - 4.40707i) q^{67} +(6.28932 + 13.1857i) q^{68} +(-1.64886 + 8.14133i) q^{69} +(-0.710403 - 3.13949i) q^{70} +(6.21490 - 3.99407i) q^{71} +(6.74114 - 5.15336i) q^{72} +(-1.39548 + 3.05568i) q^{73} +(-3.80195 - 6.82688i) q^{74} +(-6.40934 + 3.43801i) q^{75} +(-4.93326 + 11.2968i) q^{76} +(-3.79165 + 0.545157i) q^{77} +(-2.98007 + 0.00262660i) q^{78} +(4.79347 + 4.15356i) q^{79} +(1.12236 + 3.39901i) q^{80} +(8.55604 + 2.79181i) q^{81} +(4.50566 - 8.41750i) q^{82} +(-11.1296 - 3.26795i) q^{83} +(5.34484 + 7.00441i) q^{84} +(-4.28054 - 4.94001i) q^{85} +(-4.59974 - 6.03899i) q^{86} +(10.7858 - 3.93159i) q^{87} +(4.13857 - 1.00926i) q^{88} +(7.29656 + 1.04909i) q^{89} +(-2.29517 + 3.02437i) q^{90} -3.09437i q^{91} +(9.53953 + 0.998688i) q^{92} +(-7.30335 + 0.467676i) q^{93} +(-0.487763 - 0.479701i) q^{94} +(0.784954 - 5.45948i) q^{95} +(-6.66583 - 7.18100i) q^{96} +(-7.46649 + 2.19236i) q^{97} +(0.597290 - 0.454941i) q^{98} +(3.37020 + 3.00939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9}+O(q^{10}) \) 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9	\( 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9} - 30 q^{10} - 18 q^{12} - 36 q^{13} - 30 q^{16} - 10 q^{18} - 22 q^{21} - 48 q^{22} - 14 q^{24} - 8 q^{25} - 34 q^{28} - 21 q^{30} - 6 q^{33} - 32 q^{34} + 22 q^{36} - 36 q^{37} - 168 q^{40} + q^{42} - 44 q^{45} - 110 q^{46} - 6 q^{48} - 16 q^{49} - 94 q^{52} + 21 q^{54} - 46 q^{57} - 116 q^{58} - 47 q^{60} - 68 q^{61} - 28 q^{64} - 20 q^{66} - 22 q^{69} - 44 q^{70} - 23 q^{72} - 36 q^{73} - 74 q^{76} + 134 q^{78} - 130 q^{81} + 36 q^{82} + 105 q^{84} - 60 q^{85} + 38 q^{88} + 162 q^{90} - 332 q^{93} - 40 q^{94} + 225 q^{96} - 36 q^{97}+O(q^{100}) \) 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9 - 30 * q^10 - 18 * q^12 - 36 * q^13 - 30 * q^16 - 10 * q^18 - 22 * q^21 - 48 * q^22 - 14 * q^24 - 8 * q^25 - 34 * q^28 - 21 * q^30 - 6 * q^33 - 32 * q^34 + 22 * q^36 - 36 * q^37 - 168 * q^40 + q^42 - 44 * q^45 - 110 * q^46 - 6 * q^48 - 16 * q^49 - 94 * q^52 + 21 * q^54 - 46 * q^57 - 116 * q^58 - 47 * q^60 - 68 * q^61 - 28 * q^64 - 20 * q^66 - 22 * q^69 - 44 * q^70 - 23 * q^72 - 36 * q^73 - 74 * q^76 + 134 * q^78 - 130 * q^81 + 36 * q^82 + 105 * q^84 - 60 * q^85 + 38 * q^88 + 162 * q^90 - 332 * q^93 - 40 * q^94 + 225 * q^96 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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