LMFDB - Embedded newform 91.2.w.a.24.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(19,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 5]))

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

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

chi := DirichletCharacter("91.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.w (of order $12$, degree $4$, 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:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			24.6
Character	$\chi$	$=$	91.24
Dual form			91.2.w.a.19.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34471 - 0.360315i) q^{2} -1.44853i q^{3} +(-0.0536242 + 0.0309600i) q^{4} +(-0.643078 - 0.172312i) q^{5} +(-0.521927 - 1.94786i) q^{6} +(2.61524 - 0.400640i) q^{7} +(-2.02975 + 2.02975i) q^{8} +0.901760 q^{9} +O(q^{10})$	\(q+(1.34471 - 0.360315i) q^{2} -1.44853i q^{3} +(-0.0536242 + 0.0309600i) q^{4} +(-0.643078 - 0.172312i) q^{5} +(-0.521927 - 1.94786i) q^{6} +(2.61524 - 0.400640i) q^{7} +(-2.02975 + 2.02975i) q^{8} +0.901760 q^{9} -0.926843 q^{10} +(-3.40906 + 3.40906i) q^{11} +(0.0448464 + 0.0776763i) q^{12} +(-3.60544 - 0.0282257i) q^{13} +(3.37239 - 1.48106i) q^{14} +(-0.249600 + 0.931519i) q^{15} +(-1.93616 + 3.35353i) q^{16} +(0.233952 + 0.405217i) q^{17} +(1.21261 - 0.324918i) q^{18} +(2.38775 - 2.38775i) q^{19} +(0.0398194 - 0.0106696i) q^{20} +(-0.580338 - 3.78826i) q^{21} +(-3.35587 + 5.81255i) q^{22} +(6.02331 + 3.47756i) q^{23} +(2.94015 + 2.94015i) q^{24} +(-3.94627 - 2.27838i) q^{25} +(-4.85845 + 1.26114i) q^{26} -5.65182i q^{27} +(-0.127837 + 0.102452i) q^{28} +(-2.01911 - 3.49720i) q^{29} +1.34256i q^{30} +(-1.09883 - 4.10087i) q^{31} +(0.0906241 - 0.338214i) q^{32} +(4.93813 + 4.93813i) q^{33} +(0.460604 + 0.460604i) q^{34} +(-1.75084 - 0.192996i) q^{35} +(-0.0483562 + 0.0279185i) q^{36} +(-0.873807 - 3.26109i) q^{37} +(2.35049 - 4.07117i) q^{38} +(-0.0408858 + 5.22259i) q^{39} +(1.65504 - 0.955538i) q^{40} +(-3.68025 - 0.986119i) q^{41} +(-2.14535 - 4.88501i) q^{42} +(3.42191 + 1.97564i) q^{43} +(0.0772639 - 0.288353i) q^{44} +(-0.579902 - 0.155384i) q^{45} +(9.35265 + 2.50603i) q^{46} +(-2.58477 + 9.64648i) q^{47} +(4.85769 + 2.80459i) q^{48} +(6.67898 - 2.09554i) q^{49} +(-6.12753 - 1.64187i) q^{50} +(0.586968 - 0.338886i) q^{51} +(0.194213 - 0.110111i) q^{52} +(2.20051 - 3.81140i) q^{53} +(-2.03643 - 7.60007i) q^{54} +(2.77972 - 1.60487i) q^{55} +(-4.49509 + 6.12149i) q^{56} +(-3.45872 - 3.45872i) q^{57} +(-3.97522 - 3.97522i) q^{58} +(-1.58601 + 5.91907i) q^{59} +(-0.0154552 - 0.0576796i) q^{60} -4.87055i q^{61} +(-2.95521 - 5.11858i) q^{62} +(2.35832 - 0.361281i) q^{63} -8.23211i q^{64} +(2.31372 + 0.639413i) q^{65} +(8.41965 + 4.86109i) q^{66} +(6.61552 + 6.61552i) q^{67} +(-0.0250910 - 0.0144863i) q^{68} +(5.03735 - 8.72495i) q^{69} +(-2.42392 + 0.371330i) q^{70} +(3.19935 - 0.857263i) q^{71} +(-1.83035 + 1.83035i) q^{72} +(-0.112678 + 0.0301918i) q^{73} +(-2.35004 - 4.07039i) q^{74} +(-3.30030 + 5.71629i) q^{75} +(-0.0541165 + 0.201966i) q^{76} +(-7.54972 + 10.2813i) q^{77} +(1.82680 + 7.03762i) q^{78} +(0.194920 + 0.337611i) q^{79} +(1.82296 - 1.82296i) q^{80} -5.48155 q^{81} -5.30419 q^{82} +(-11.5572 + 11.5572i) q^{83} +(0.148404 + 0.185175i) q^{84} +(-0.0806256 - 0.300899i) q^{85} +(5.31334 + 1.42371i) q^{86} +(-5.06581 + 2.92474i) q^{87} -13.8391i q^{88} +(9.34114 - 2.50295i) q^{89} -0.835790 q^{90} +(-9.44041 + 1.37067i) q^{91} -0.430661 q^{92} +(-5.94024 + 1.59168i) q^{93} +13.9031i q^{94} +(-1.94695 + 1.12407i) q^{95} +(-0.489913 - 0.131272i) q^{96} +(4.61378 + 17.2188i) q^{97} +(8.22625 - 5.22443i) q^{98} +(-3.07416 + 3.07416i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} - 6 q^{4} - 6 q^{5} + 12 q^{6} + 2 q^{7} - 4 q^{8} - 12 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 - 6 * q^4 - 6 * q^5 + 12 * q^6 + 2 * q^7 - 4 * q^8 - 12 * q^9	\( 28 q - 2 q^{2} - 6 q^{4} - 6 q^{5} + 12 q^{6} + 2 q^{7} - 4 q^{8} - 12 q^{9} - 12 q^{10} + 2 q^{11} + 8 q^{12} - 20 q^{14} + 10 q^{15} - 2 q^{16} - 6 q^{17} - 4 q^{18} - 8 q^{19} - 36 q^{20} - 2 q^{21} - 8 q^{22} - 6 q^{23} + 12 q^{24} + 24 q^{26} - 18 q^{28} - 8 q^{29} - 38 q^{31} - 20 q^{32} + 18 q^{33} + 12 q^{34} - 2 q^{35} + 54 q^{36} - 16 q^{37} + 28 q^{39} + 48 q^{40} + 18 q^{41} - 4 q^{42} + 48 q^{43} - 6 q^{44} + 12 q^{45} + 18 q^{46} - 42 q^{47} + 12 q^{48} + 8 q^{49} + 10 q^{50} + 12 q^{51} - 28 q^{52} + 12 q^{53} - 30 q^{54} - 6 q^{55} - 24 q^{56} + 12 q^{57} + 62 q^{58} - 6 q^{59} + 16 q^{60} - 36 q^{62} - 38 q^{63} - 2 q^{65} + 66 q^{66} - 4 q^{67} + 30 q^{68} + 42 q^{69} + 68 q^{70} - 42 q^{71} - 38 q^{72} + 14 q^{73} - 6 q^{74} - 20 q^{75} + 52 q^{76} - 62 q^{78} + 4 q^{79} + 12 q^{80} + 12 q^{81} - 108 q^{82} - 66 q^{83} - 56 q^{84} - 54 q^{85} - 30 q^{86} + 42 q^{87} - 30 q^{89} - 72 q^{90} - 42 q^{91} - 156 q^{92} + 14 q^{93} - 6 q^{95} + 18 q^{96} + 62 q^{97} + 112 q^{98} - 36 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 - 6 * q^4 - 6 * q^5 + 12 * q^6 + 2 * q^7 - 4 * q^8 - 12 * q^9 - 12 * q^10 + 2 * q^11 + 8 * q^12 - 20 * q^14 + 10 * q^15 - 2 * q^16 - 6 * q^17 - 4 * q^18 - 8 * q^19 - 36 * q^20 - 2 * q^21 - 8 * q^22 - 6 * q^23 + 12 * q^24 + 24 * q^26 - 18 * q^28 - 8 * q^29 - 38 * q^31 - 20 * q^32 + 18 * q^33 + 12 * q^34 - 2 * q^35 + 54 * q^36 - 16 * q^37 + 28 * q^39 + 48 * q^40 + 18 * q^41 - 4 * q^42 + 48 * q^43 - 6 * q^44 + 12 * q^45 + 18 * q^46 - 42 * q^47 + 12 * q^48 + 8 * q^49 + 10 * q^50 + 12 * q^51 - 28 * q^52 + 12 * q^53 - 30 * q^54 - 6 * q^55 - 24 * q^56 + 12 * q^57 + 62 * q^58 - 6 * q^59 + 16 * q^60 - 36 * q^62 - 38 * q^63 - 2 * q^65 + 66 * q^66 - 4 * q^67 + 30 * q^68 + 42 * q^69 + 68 * q^70 - 42 * q^71 - 38 * q^72 + 14 * q^73 - 6 * q^74 - 20 * q^75 + 52 * q^76 - 62 * q^78 + 4 * q^79 + 12 * q^80 + 12 * q^81 - 108 * q^82 - 66 * q^83 - 56 * q^84 - 54 * q^85 - 30 * q^86 + 42 * q^87 - 30 * q^89 - 72 * q^90 - 42 * q^91 - 156 * q^92 + 14 * q^93 - 6 * q^95 + 18 * q^96 + 62 * q^97 + 112 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.34471	−	0.360315i	0.950856	−	0.254781i	0.250130	−	0.968212i	$-0.419527\pi$
$2$	1.34471	−	0.360315i	0.950856	−	0.254781i	0.700725	+	0.713431i	$0.252860\pi$
$3$		−	1.44853i		−	0.836309i	−0.908376	−	0.418155i	$-0.862677\pi$
$3$		−	1.44853i		−	0.836309i	0.908376	−	0.418155i	$-0.137323\pi$
$4$	−0.0536242	+	0.0309600i	−0.0268121	+	0.0154800i
$5$	−0.643078	−	0.172312i	−0.287593	−	0.0770604i	0.112138	−	0.993693i	$-0.464230\pi$
$5$	−0.643078	−	0.172312i	−0.287593	−	0.0770604i	−0.399732	+	0.916632i	$0.630897\pi$
$6$	−0.521927	−	1.94786i	−0.213076	−	0.795210i
$7$	2.61524	−	0.400640i	0.988468	−	0.151428i
$7$	2.61524	−	0.400640i	0.988468	−	0.151428i
$8$	−2.02975	+	2.02975i	−0.717625	+	0.717625i
$9$	0.901760			0.300587
$10$	−0.926843			−0.293093
$11$	−3.40906	+	3.40906i	−1.02787	+	1.02787i	−0.0282706	+	0.999600i	$0.509000\pi$
$11$	−3.40906	+	3.40906i	−1.02787	+	1.02787i	−0.999600	+	0.0282706i	$0.991000\pi$
$12$	0.0448464	+	0.0776763i	0.0129461	+	0.0224232i
$13$	−3.60544	−	0.0282257i	−0.999969	−	0.00782840i
$13$	−3.60544	−	0.0282257i	−0.999969	−	0.00782840i
$14$	3.37239	−	1.48106i	0.901310	−	0.395829i
$15$	−0.249600	+	0.931519i	−0.0644463	+	0.240517i
$16$	−1.93616	+	3.35353i	−0.484041	+	0.838383i
$17$	0.233952	+	0.405217i	0.0567417	+	0.0982794i	0.893001	−	0.450055i	$-0.148596\pi$
$17$	0.233952	+	0.405217i	0.0567417	+	0.0982794i	−0.836259	+	0.548334i	$0.815262\pi$
$18$	1.21261	−	0.324918i	0.285815	−	0.0765838i
$19$	2.38775	−	2.38775i	0.547787	−	0.547787i	−0.378014	−	0.925800i	$-0.623393\pi$
$19$	2.38775	−	2.38775i	0.547787	−	0.547787i	0.925800	+	0.378014i	$0.123393\pi$
$20$	0.0398194	−	0.0106696i	0.00890388	−	0.00238579i
$21$	−0.580338	−	3.78826i	−0.126640	−	0.826665i
$22$	−3.35587	+	5.81255i	−0.715475	+	1.23924i
$23$	6.02331	+	3.47756i	1.25595	+	0.725122i	0.972284	−	0.233802i	$-0.0751168\pi$
$23$	6.02331	+	3.47756i	1.25595	+	0.725122i	0.283663	+	0.958924i	$0.408450\pi$
$24$	2.94015	+	2.94015i	0.600157	+	0.600157i
$25$	−3.94627	−	2.27838i	−0.789254	−	0.455676i
$26$	−4.85845	+	1.26114i	−0.952821	+	0.247330i
$27$		−	5.65182i		−	1.08769i
$28$	−0.127837	+	0.102452i	−0.0241588	+	0.0193616i
$29$	−2.01911	−	3.49720i	−0.374940	−	0.649414i	0.615378	−	0.788232i	$-0.289003\pi$
$29$	−2.01911	−	3.49720i	−0.374940	−	0.649414i	−0.990318	+	0.138817i	$0.955670\pi$
$30$			1.34256i			0.245117i
$31$	−1.09883	−	4.10087i	−0.197355	−	0.736539i	−0.991645	−	0.129000i	$-0.958823\pi$
$31$	−1.09883	−	4.10087i	−0.197355	−	0.736539i	0.794290	−	0.607539i	$-0.207843\pi$
$32$	0.0906241	−	0.338214i	0.0160202	−	0.0597883i
$33$	4.93813	+	4.93813i	0.859618	+	0.859618i
$34$	0.460604	+	0.460604i	0.0789929	+	0.0789929i
$35$	−1.75084	−	0.192996i	−0.295946	−	0.0326222i
$36$	−0.0483562	+	0.0279185i	−0.00805937	+	0.00465308i
$37$	−0.873807	−	3.26109i	−0.143653	−	0.536120i	−0.999812	−	0.0194074i	$-0.993822\pi$
$37$	−0.873807	−	3.26109i	−0.143653	−	0.536120i	0.856159	−	0.516713i	$-0.172845\pi$
$38$	2.35049	−	4.07117i	0.381300	−	0.660432i
$39$	−0.0408858	+	5.22259i	−0.00654696	+	0.836284i
$40$	1.65504	−	0.955538i	0.261685	−	0.151084i
$41$	−3.68025	−	0.986119i	−0.574758	−	0.154006i	−0.0402801	−	0.999188i	$-0.512825\pi$
$41$	−3.68025	−	0.986119i	−0.574758	−	0.154006i	−0.534478	+	0.845182i	$0.679492\pi$
$42$	−2.14535	−	4.88501i	−0.331035	−	0.753774i
$43$	3.42191	+	1.97564i	0.521836	+	0.301282i	0.737686	−	0.675144i	$-0.235919\pi$
$43$	3.42191	+	1.97564i	0.521836	+	0.301282i	−0.215849	+	0.976427i	$0.569252\pi$
$44$	0.0772639	−	0.288353i	0.0116480	−	0.0434708i
$45$	−0.579902	−	0.155384i	−0.0864468	−	0.0231633i
$46$	9.35265	+	2.50603i	1.37897	+	0.369495i
$47$	−2.58477	+	9.64648i	−0.377027	+	1.40708i	0.473333	+	0.880883i	$0.343051\pi$
$47$	−2.58477	+	9.64648i	−0.377027	+	1.40708i	−0.850360	+	0.526201i	$0.823616\pi$
$48$	4.85769	+	2.80459i	0.701148	+	0.404808i
$49$	6.67898	−	2.09554i	0.954139	−	0.299363i
$50$	−6.12753	−	1.64187i	−0.866564	−	0.232195i
$51$	0.586968	−	0.338886i	0.0821920	−	0.0474536i
$52$	0.194213	−	0.110111i	0.0269325	−	0.0152696i
$53$	2.20051	−	3.81140i	0.302264	−	0.523537i	−0.674384	−	0.738380i	$-0.735591\pi$
$53$	2.20051	−	3.81140i	0.302264	−	0.523537i	0.976648	+	0.214844i	$0.0689243\pi$
$54$	−2.03643	−	7.60007i	−0.277123	−	1.03424i
$55$	2.77972	−	1.60487i	0.374817	−	0.216401i
$56$	−4.49509	+	6.12149i	−0.600682	+	0.818018i
$57$	−3.45872	−	3.45872i	−0.458119	−	0.458119i
$58$	−3.97522	−	3.97522i	−0.521972	−	0.521972i
$59$	−1.58601	+	5.91907i	−0.206481	+	0.770598i	0.782512	+	0.622635i	$0.213938\pi$
$59$	−1.58601	+	5.91907i	−0.206481	+	0.770598i	−0.988993	+	0.147962i	$0.952729\pi$
$60$	−0.0154552	−	0.0576796i	−0.00199526	−	0.00744640i
$61$		−	4.87055i		−	0.623610i	−0.950146	−	0.311805i	$-0.899066\pi$
$61$		−	4.87055i		−	0.623610i	0.950146	−	0.311805i	$-0.100934\pi$
$62$	−2.95521	−	5.11858i	−0.375312	−	0.650060i
$63$	2.35832	−	0.361281i	0.297120	−	0.0455171i
$64$		−	8.23211i		−	1.02901i
$65$	2.31372	+	0.639413i	0.286981	+	0.0793095i
$66$	8.41965	+	4.86109i	1.03639	+	0.598358i
$67$	6.61552	+	6.61552i	0.808215	+	0.808215i	0.984364	−	0.176149i	$-0.0563640\pi$
$67$	6.61552	+	6.61552i	0.808215	+	0.808215i	−0.176149	+	0.984364i	$0.556364\pi$
$68$	−0.0250910	−	0.0144863i	−0.00304273	−	0.00175672i
$69$	5.03735	−	8.72495i	0.606426	−	1.05036i
$70$	−2.42392	+	0.371330i	−0.289714	+	0.0443824i
$71$	3.19935	−	0.857263i	0.379693	−	0.101738i	−0.0639244	−	0.997955i	$-0.520362\pi$
$71$	3.19935	−	0.857263i	0.379693	−	0.101738i	0.443617	+	0.896216i	$0.353695\pi$
$72$	−1.83035	+	1.83035i	−0.215709	+	0.215709i
$73$	−0.112678	+	0.0301918i	−0.0131879	+	0.00353369i	−0.265407	−	0.964136i	$-0.585506\pi$
$73$	−0.112678	+	0.0301918i	−0.0131879	+	0.00353369i	0.252219	+	0.967670i	$0.418840\pi$
$74$	−2.35004	−	4.07039i	−0.273187	−	0.473173i
$75$	−3.30030	+	5.71629i	−0.381086	+	0.660060i
$76$	−0.0541165	+	0.201966i	−0.00620759	+	0.0231670i
$77$	−7.54972	+	10.2813i	−0.860370	+	1.17167i
$78$	1.82680	+	7.03762i	0.206844	+	0.796853i
$79$	0.194920	+	0.337611i	0.0219302	+	0.0379842i	0.876782	−	0.480888i	$-0.159686\pi$
$79$	0.194920	+	0.337611i	0.0219302	+	0.0379842i	−0.854852	+	0.518872i	$0.826352\pi$
$80$	1.82296	−	1.82296i	0.203813	−	0.203813i
$81$	−5.48155			−0.609061
$82$	−5.30419			−0.585750
$83$	−11.5572	+	11.5572i	−1.26857	+	1.26857i	−0.321741	+	0.946828i	$0.604268\pi$
$83$	−11.5572	+	11.5572i	−1.26857	+	1.26857i	−0.946828	+	0.321741i	$0.895732\pi$
$84$	0.148404	+	0.185175i	0.0161923	+	0.0202043i
$85$	−0.0806256	−	0.300899i	−0.00874507	−	0.0326371i
$86$	5.31334	+	1.42371i	0.572952	+	0.153522i
$87$	−5.06581	+	2.92474i	−0.543111	+	0.313565i
$88$		−	13.8391i		−	1.47525i
$89$	9.34114	−	2.50295i	0.990159	−	0.265312i	0.272842	−	0.962059i	$-0.412036\pi$
$89$	9.34114	−	2.50295i	0.990159	−	0.265312i	0.717317	+	0.696747i	$0.245370\pi$
$90$	−0.835790			−0.0881000
$91$	−9.44041	+	1.37067i	−0.989624	+	0.143685i
$92$	−0.430661			−0.0448995
$93$	−5.94024	+	1.59168i	−0.615974	+	0.165050i
$94$			13.9031i			1.43399i
$95$	−1.94695	+	1.12407i	−0.199752	+	0.115327i
$96$	−0.489913	−	0.131272i	−0.0500015	−	0.0133979i
$97$	4.61378	+	17.2188i	0.468458	+	1.74831i	0.645163	+	0.764045i	$0.276790\pi$
$97$	4.61378	+	17.2188i	0.468458	+	1.74831i	−0.176705	+	0.984264i	$0.556544\pi$
$98$	8.22625	−	5.22443i	0.830977	−	0.527747i
$99$	−3.07416	+	3.07416i	−0.308964	+	0.308964i
$100$	0.282154			0.0282154
$101$	−11.1459			−1.10905			−0.554527	−	0.832166i	$-0.687101\pi$
$101$	−11.1459			−1.10905			−0.554527	+	0.832166i	$0.687101\pi$
$102$	0.667198	−	0.667198i	0.0660625	−	0.0660625i
$103$	−3.73616	−	6.47122i	−0.368135	−	0.637628i	0.621139	−	0.783700i	$-0.286670\pi$
$103$	−3.73616	−	6.47122i	−0.368135	−	0.637628i	−0.989274	+	0.146072i	$0.953337\pi$
$104$	7.37544	−	7.26085i	0.723221	−	0.711985i
$105$	−0.279560	+	2.53615i	−0.0272823	+	0.247502i
$106$	1.58576	−	5.91812i	0.154022	−	0.574819i
$107$	2.07553	−	3.59492i	0.200649	−	0.347534i	−0.748089	−	0.663598i	$-0.769028\pi$
$107$	2.07553	−	3.59492i	0.200649	−	0.347534i	0.948738	+	0.316065i	$0.102362\pi$
$108$	0.174980	+	0.303074i	0.0168375	+	0.0291633i
$109$	5.94172	−	1.59208i	0.569113	−	0.152493i	0.0372233	−	0.999307i	$-0.488149\pi$
$109$	5.94172	−	1.59208i	0.569113	−	0.152493i	0.531890	+	0.846814i	$0.321482\pi$
$110$	3.15966	−	3.15966i	0.301262	−	0.301262i
$111$	−4.72379	+	1.26574i	−0.448363	+	0.120138i
$112$	−3.71998	+	9.54600i	−0.351505	+	0.902012i
$113$	−0.554932	+	0.961171i	−0.0522036	+	0.0904194i	−0.890946	−	0.454109i	$-0.849958\pi$
$113$	−0.554932	+	0.961171i	−0.0522036	+	0.0904194i	0.838743	+	0.544528i	$0.183291\pi$
$114$	−5.89722	−	3.40476i	−0.552325	−	0.318885i
$115$	−3.27424	−	3.27424i	−0.305324	−	0.305324i
$116$	0.216547	+	0.125023i	0.0201058	+	0.0116081i
$117$	−3.25124	−	0.0254528i	−0.300577	−	0.00235311i
$118$			8.53092i			0.785335i
$119$	0.774186	+	0.966009i	0.0709695	+	0.0885539i
$120$	−1.38413	−	2.39738i	−0.126353	−	0.218849i
$121$		−	12.2434i		−	1.11304i
$122$	−1.75493	−	6.54950i	−0.158884	−	0.592963i
$123$	−1.42842	+	5.33095i	−0.128797	+	0.480675i
$124$	0.185887	+	0.185887i	0.0166931	+	0.0166931i
$125$	4.49900	+	4.49900i	0.402403	+	0.402403i
$126$	3.04109	−	1.33556i	0.270922	−	0.118981i
$127$	17.2552	−	9.96228i	1.53115	−	0.884009i	0.531840	−	0.846845i	$-0.321501\pi$
$127$	17.2552	−	9.96228i	1.53115	−	0.884009i	0.999309	−	0.0371647i	$-0.0118326\pi$
$128$	−2.78490	−	10.3934i	−0.246153	−	0.918655i
$129$	2.86178	−	4.95674i	0.251965	−	0.436417i
$130$	3.34168	+	0.0261608i	0.293084	+	0.00229445i
$131$	6.61385	−	3.81851i	0.577855	−	0.333625i	−0.182426	−	0.983220i	$-0.558395\pi$
$131$	6.61385	−	3.81851i	0.577855	−	0.333625i	0.760280	+	0.649595i	$0.225062\pi$
$132$	−0.417688	−	0.111919i	−0.0363550	−	0.00974131i
$133$	5.28791	−	7.20116i	0.458520	−	0.624420i
$134$	11.2797	+	6.51231i	0.974414	+	0.562578i
$135$	−0.973878	+	3.63456i	−0.0838181	+	0.312813i
$136$	−1.29735	−	0.347625i	−0.111247	−	0.0298086i
$137$	−12.7196	−	3.40822i	−1.08671	−	0.291184i	−0.329369	−	0.944201i	$-0.606836\pi$
$137$	−12.7196	−	3.40822i	−1.08671	−	0.291184i	−0.757343	+	0.653018i	$0.773503\pi$
$138$	3.63007	−	13.5476i	0.309012	−	1.15325i
$139$	14.9082	+	8.60724i	1.26449	+	0.730056i	0.973941	−	0.226802i	$-0.0728272\pi$
$139$	14.9082	+	8.60724i	1.26449	+	0.730056i	0.290554	+	0.956859i	$0.406161\pi$
$140$	0.0998626	−	0.0438567i	0.00843993	−	0.00370657i
$141$	13.9732	+	3.74411i	1.17676	+	0.315311i
$142$	3.99332	−	2.30555i	0.335112	−	0.193477i
$143$	12.3874	−	12.1949i	1.03589	−	1.01979i
$144$	−1.74595	+	3.02408i	−0.145496	+	0.252007i
$145$	0.695836	+	2.59689i	0.0577860	+	0.215660i
$146$	−0.140640	+	0.0811987i	−0.0116395	+	0.00672006i
$147$	−3.03545	−	9.67470i	−0.250360	−	0.797956i
$148$	0.147821	+	0.147821i	0.0121508	+	0.0121508i
$149$	2.66059	+	2.66059i	0.217964	+	0.217964i	0.807640	−	0.589676i	$-0.200745\pi$
$149$	2.66059	+	2.66059i	0.217964	+	0.217964i	−0.589676	+	0.807640i	$0.700745\pi$
$150$	−2.37829	+	8.87592i	−0.194187	+	0.724716i
$151$	−1.95684	−	7.30304i	−0.159246	−	0.594313i	−0.998704	−	0.0508895i	$-0.983794\pi$
$151$	−1.95684	−	7.30304i	−0.159246	−	0.594313i	0.839459	−	0.543424i	$-0.182872\pi$
$152$			9.69306i			0.786211i
$153$	0.210968	+	0.365408i	0.0170558	+	0.0295415i
$154$	−6.44769	+	16.5457i	−0.519569	+	1.33329i
$155$			2.82653i			0.227032i
$156$	−0.159499	−	0.281323i	−0.0127701	−	0.0225239i
$157$	−21.3379	−	12.3194i	−1.70295	−	0.983199i	−0.942744	−	0.333518i	$-0.891764\pi$
$157$	−21.3379	−	12.3194i	−1.70295	−	0.983199i	−0.760207	−	0.649681i	$-0.774903\pi$
$158$	0.383757	+	0.383757i	0.0305301	+	0.0305301i
$159$	−5.52093	−	3.18751i	−0.437838	−	0.252786i
$160$	−0.116557	+	0.201882i	−0.00921463	+	0.0159602i
$161$	17.1457	+	6.68149i	1.35127	+	0.526575i
$162$	−7.37111	+	1.97508i	−0.579129	+	0.155177i
$163$	−14.6811	+	14.6811i	−1.14991	+	1.14991i	−0.163340	+	0.986570i	$0.552227\pi$
$163$	−14.6811	+	14.6811i	−1.14991	+	1.14991i	−0.986570	+	0.163340i	$0.947773\pi$
$164$	0.227881	−	0.0610604i	0.0177945	−	0.00476802i
$165$	−2.32470	−	4.02651i	−0.180978	−	0.313463i
$166$	−11.3769	+	19.7054i	−0.883018	+	1.52943i
$167$	4.53457	−	16.9233i	0.350896	−	1.30956i	−0.534676	−	0.845057i	$-0.679566\pi$
$167$	4.53457	−	16.9233i	0.350896	−	1.30956i	0.885571	−	0.464503i	$-0.153767\pi$
$168$	8.86716	+	6.51127i	0.684116	+	0.502356i
$169$	12.9984	+	0.203532i	0.999877	+	0.0156563i
$170$	−0.216837	−	0.375572i	−0.0166306	−	0.0288051i
$171$	2.15317	−	2.15317i	0.164657	−	0.164657i
$172$	−0.244663			−0.0186554
$173$	5.92061			0.450135			0.225068	−	0.974343i	$-0.427740\pi$
$173$	5.92061			0.450135			0.225068	+	0.974343i	$0.427740\pi$
$174$	−5.75823	+	5.75823i	−0.436530	+	0.436530i
$175$	−11.2333	−	4.37748i	−0.849154	−	0.330906i
$176$	−4.83190	−	18.0329i	−0.364218	−	1.35928i
$177$	8.57396	+	2.29738i	0.644458	+	0.172682i
$178$	11.6593	−	6.73150i	0.873902	−	0.504548i
$179$		−	3.77015i		−	0.281794i	−0.990024	−	0.140897i	$-0.955001\pi$
$179$		−	3.77015i		−	0.281794i	0.990024	−	0.140897i	$-0.0449987\pi$
$180$	0.0359075	−	0.00962139i	0.00267639	−	0.000717136i
$181$	−5.68899			−0.422859			−0.211430	−	0.977393i	$-0.567812\pi$
$181$	−5.68899			−0.422859			−0.211430	+	0.977393i	$0.567812\pi$
$182$	−12.2008	+	5.24467i	−0.904381	+	0.388761i
$183$	−7.05514			−0.521531
$184$	−19.2844	+	5.16724i	−1.42167	+	0.380934i
$185$			2.24771i			0.165255i
$186$	−7.41441	+	4.28071i	−0.543651	+	0.313877i
$187$	−2.17896	−	0.583852i	−0.159342	−	0.0426955i
$188$	−0.160049	−	0.597309i	−0.0116727	−	0.0435633i
$189$	−2.26434	−	14.7809i	−0.164707	−	1.07515i
$190$	−2.21307	+	2.21307i	−0.160553	+	0.160553i
$191$	−9.16764			−0.663347			−0.331674	−	0.943394i	$-0.607613\pi$
$191$	−9.16764			−0.663347			−0.331674	+	0.943394i	$0.607613\pi$
$192$	−11.9245			−0.860573
$193$	−17.9686	+	17.9686i	−1.29340	+	1.29340i	−0.360738	+	0.932667i	$0.617475\pi$
$193$	−17.9686	+	17.9686i	−1.29340	+	1.29340i	−0.932667	+	0.360738i	$0.882525\pi$
$194$	12.4084	+	21.4920i	0.890872	+	1.54304i
$195$	0.926209	−	3.35149i	0.0663272	−	0.240005i
$196$	−0.293277	+	0.319152i	−0.0209484	+	0.0227966i
$197$	−0.371638	+	1.38697i	−0.0264781	+	0.0988175i	−0.977900	−	0.209071i	$-0.932956\pi$
$197$	−0.371638	+	1.38697i	−0.0264781	+	0.0988175i	0.951422	+	0.307889i	$0.0996225\pi$
$198$	−3.02619	+	5.24152i	−0.215062	+	0.372499i
$199$	5.50792	+	9.53999i	0.390446	+	0.676272i	0.992508	−	0.122177i	$-0.0389875\pi$
$199$	5.50792	+	9.53999i	0.390446	+	0.676272i	−0.602062	+	0.798449i	$0.705654\pi$
$200$	12.6345	−	3.38540i	0.893393	−	0.239384i
$201$	9.58279	−	9.58279i	0.675918	−	0.675918i
$202$	−14.9880	+	4.01602i	−1.05455	+	0.282566i
$203$	−6.68158	−	8.33710i	−0.468955	−	0.585149i
$204$	−0.0209838	+	0.0363450i	−0.00146916	+	0.00254466i
$205$	2.19677	+	1.26830i	0.153429	+	0.0885822i
$206$	−7.35574	−	7.35574i	−0.512499	−	0.512499i
$207$	5.43158	+	3.13593i	0.377521	+	0.217962i
$208$	7.07538	−	12.0363i	0.490589	−	0.834568i
$209$			16.2800i			1.12611i
$210$	0.537882	+	3.51112i	0.0371174	+	0.242290i
$211$	11.5485	+	20.0025i	0.795029	+	1.37703i	0.922821	+	0.385229i	$0.125878\pi$
$211$	11.5485	+	20.0025i	0.795029	+	1.37703i	−0.127792	+	0.991801i	$0.540789\pi$
$212$			0.272511i			0.0187162i
$213$	−1.24177	−	4.63435i	−0.0850848	−	0.317541i
$214$	1.49569	−	5.58197i	0.102243	−	0.381576i
$215$	−1.86013	−	1.86013i	−0.126860	−	0.126860i
$216$	11.4718	+	11.4718i	0.780556	+	0.780556i
$217$	−4.51667	−	10.2845i	−0.306611	−	0.698160i
$218$	7.41625	−	4.28178i	0.502292	−	0.289998i
$219$	0.0437338	+	0.163217i	0.00295526	+	0.0110292i
$220$	−0.0993735	+	0.172120i	−0.00669976	+	0.0116043i
$221$	−0.832062	−	1.46759i	−0.0559706	−	0.0987206i
$222$	−5.89608	+	3.40410i	−0.395719	+	0.228469i
$223$	3.57776	+	0.958657i	0.239584	+	0.0641964i	0.376613	−	0.926371i	$-0.377089\pi$
$223$	3.57776	+	0.958657i	0.239584	+	0.0641964i	−0.137029	+	0.990567i	$0.543755\pi$
$224$	0.101502	−	0.920819i	0.00678190	−	0.0615248i
$225$	−3.55859	−	2.05455i	−0.237239	−	0.136970i
$226$	−0.399901	+	1.49245i	−0.0266010	+	0.0992763i
$227$	23.2863	+	6.23954i	1.54556	+	0.414133i	0.928059	−	0.372433i	$-0.121476\pi$
$227$	23.2863	+	6.23954i	1.54556	+	0.414133i	0.617506	+	0.786566i	$0.288143\pi$
$228$	0.292553	+	0.0783894i	0.0193748	+	0.00519147i
$229$	4.82564	−	18.0095i	0.318887	−	1.19010i	−0.601429	−	0.798926i	$-0.705402\pi$
$229$	4.82564	−	18.0095i	0.318887	−	1.19010i	0.920316	−	0.391176i	$-0.127932\pi$
$230$	−5.58266	−	3.22315i	−0.368110	−	0.212528i
$231$	14.8928	+	10.9360i	0.979875	+	0.719535i
$232$	11.1967	+	3.00016i	0.735102	+	0.196970i
$233$	3.91672	−	2.26132i	0.256593	−	0.148144i	−0.366187	−	0.930541i	$-0.619337\pi$
$233$	3.91672	−	2.26132i	0.256593	−	0.148144i	0.622779	+	0.782398i	$0.286003\pi$
$234$	−4.38116	+	1.13724i	−0.286405	+	0.0743440i
$235$	3.32442	−	5.75806i	0.216861	−	0.375614i
$236$	−0.0982057	−	0.366509i	−0.00639264	−	0.0238577i
$237$	0.489040	−	0.282347i	0.0317665	−	0.0183404i
$238$	1.38913	+	1.02005i	0.0900437	+	0.0661203i
$239$	−11.1608	−	11.1608i	−0.721931	−	0.721931i	0.247067	−	0.968998i	$-0.420533\pi$
$239$	−11.1608	−	11.1608i	−0.721931	−	0.721931i	−0.968998	+	0.247067i	$0.920533\pi$
$240$	−2.64061	−	2.64061i	−0.170451	−	0.170451i
$241$	1.95884	−	7.31049i	0.126180	−	0.470910i	−0.873699	−	0.486467i	$-0.838285\pi$
$241$	1.95884	−	7.31049i	0.126180	−	0.470910i	0.999879	+	0.0155569i	$0.00495211\pi$
$242$	−4.41148	−	16.4639i	−0.283581	−	1.05834i
$243$		−	9.01526i		−	0.578329i
$244$	0.150792	+	0.261180i	0.00965348	+	0.0167203i
$245$	−4.65619	+	0.196725i	−0.297473	+	0.0125683i
$246$			7.68328i			0.489868i
$247$	−8.67627	+	8.54148i	−0.552058	+	0.543481i
$248$	10.5541	+	6.09341i	0.670186	+	0.386932i
$249$	16.7410	+	16.7410i	1.06092	+	1.06092i
$250$	7.67092	+	4.42881i	0.485151	+	0.280102i
$251$	10.6165	−	18.3883i	0.670106	−	1.16066i	−0.307767	−	0.951462i	$-0.599582\pi$
$251$	10.6165	−	18.3883i	0.670106	−	1.16066i	0.977874	−	0.209197i	$-0.0670849\pi$
$252$	−0.115278	+	0.0923869i	−0.00726182	+	0.00581983i
$253$	−32.3891	+	8.67863i	−2.03628	+	0.545621i
$254$	19.6137	−	19.6137i	1.23067	−	1.23067i
$255$	−0.435861	+	0.116789i	−0.0272947	+	0.00731359i
$256$	0.742320	+	1.28574i	0.0463950	+	0.0803584i
$257$	−12.6205	+	21.8594i	−0.787245	+	1.36355i	0.140403	+	0.990094i	$0.455160\pi$
$257$	−12.6205	+	21.8594i	−0.787245	+	1.36355i	−0.927648	+	0.373455i	$0.878173\pi$
$258$	2.06228	−	7.69653i	0.128392	−	0.479165i
$259$	−3.59174	−	8.17846i	−0.223180	−	0.508185i
$260$	−0.143868	+	0.0373446i	−0.00892229	+	0.00231601i
$261$	−1.82075	−	3.15364i	−0.112702	−	0.195205i
$262$	7.51786	−	7.51786i	0.464455	−	0.464455i
$263$	0.304035			0.0187476			0.00937381	−	0.999956i	$-0.497016\pi$
$263$	0.304035			0.0187476			0.00937381	+	0.999956i	$0.497016\pi$
$264$	−20.0463			−1.23377
$265$	−2.07186	+	2.07186i	−0.127273	+	0.127273i
$266$	4.51603	−	11.5888i	0.276896	−	0.710555i
$267$	−3.62560	−	13.5309i	−0.221883	−	0.828079i
$268$	−0.559569	−	0.149936i	−0.0341811	−	0.00915880i
$269$	−15.5352	+	8.96926i	−0.947199	+	0.546865i	−0.892210	−	0.451622i	$-0.850846\pi$
$269$	−15.5352	+	8.96926i	−0.947199	+	0.546865i	−0.0549891	+	0.998487i	$0.517512\pi$
$270$			5.23835i			0.318796i
$271$	−12.5421	+	3.36065i	−0.761879	+	0.204145i	−0.618781	−	0.785563i	$-0.712373\pi$
$271$	−12.5421	+	3.36065i	−0.761879	+	0.204145i	−0.143098	+	0.989708i	$0.545707\pi$
$272$	−1.81188			−0.109861
$273$	1.98545	+	13.6747i	0.120165	+	0.827631i
$274$	−18.3323			−1.10749
$275$	21.2202	−	5.68594i	1.27963	−	0.342875i
$276$			0.623825i			0.0375499i
$277$	−5.38051	+	3.10644i	−0.323283	+	0.186648i	−0.652855	−	0.757483i	$-0.726429\pi$
$277$	−5.38051	+	3.10644i	−0.323283	+	0.186648i	0.329572	+	0.944130i	$0.393096\pi$
$278$	23.1485	+	6.20263i	1.38836	+	0.372009i
$279$	−0.990877	−	3.69801i	−0.0593223	−	0.221394i
$280$	3.94550	−	3.16204i	0.235789	−	0.188968i
$281$	1.72841	−	1.72841i	0.103108	−	0.103108i	−0.653671	−	0.756779i	$-0.726772\pi$
$281$	1.72841	−	1.72841i	0.103108	−	0.103108i	0.756779	+	0.653671i	$0.226772\pi$
$282$	20.1390			1.19926
$283$	−18.0162			−1.07095			−0.535475	−	0.844551i	$-0.679868\pi$
$283$	−18.0162			−1.07095			−0.535475	+	0.844551i	$0.679868\pi$
$284$	−0.145022	+	0.145022i	−0.00860546	+	0.00860546i
$285$	1.62825	+	2.82021i	0.0964492	+	0.167055i
$286$	12.2635	−	20.8621i	0.725154	−	1.23360i
$287$	−10.0198	−	1.10449i	−0.591451	−	0.0651958i
$288$	0.0817212	−	0.304988i	0.00481547	−	0.0179716i
$289$	8.39053	−	14.5328i	0.493561	−	0.854872i
$290$	1.87140	+	3.24136i	0.109892	+	0.190339i
$291$	24.9420	−	6.68319i	1.46213	−	0.391776i
$292$	0.00510751	−	0.00510751i	0.000298894	−	0.000298894i
$293$	−4.38187	+	1.17412i	−0.255992	+	0.0685927i	−0.384532	−	0.923111i	$-0.625637\pi$
$293$	−4.38187	+	1.17412i	−0.255992	+	0.0685927i	0.128541	+	0.991704i	$0.458971\pi$
$294$	−7.56775	−	11.9160i	−0.441360	−	0.694954i
$295$	2.03986	−	3.53314i	0.118765	−	0.205707i
$296$	8.39282	+	4.84559i	0.487823	+	0.281644i
$297$	19.2674	+	19.2674i	1.11801	+	1.11801i
$298$	4.53638	+	2.61908i	0.262785	+	0.151719i
$299$	−21.6185	−	12.7082i	−1.25023	−	0.734932i
$300$		−	0.408709i		−	0.0235968i
$301$	9.74064	+	3.79583i	0.561441	+	0.218788i
$302$	−5.26279	−	9.11542i	−0.302839	−	0.524533i
$303$			16.1451i			0.927512i
$304$	3.38432	+	12.6305i	0.194104	+	0.724406i
$305$	−0.839256	+	3.13215i	−0.0480557	+	0.179346i
$306$	0.415354	+	0.415354i	0.0237442	+	0.0237442i
$307$	−11.5340	−	11.5340i	−0.658282	−	0.658282i	0.296691	−	0.954973i	$-0.404117\pi$
$307$	−11.5340	−	11.5340i	−0.658282	−	0.658282i	−0.954973	+	0.296691i	$0.904117\pi$
$308$	0.0865382	−	0.785067i	0.00493097	−	0.0447333i
$309$	−9.37376	+	5.41194i	−0.533254	+	0.307875i
$310$	1.01844	+	3.80087i	0.0578434	+	0.215875i
$311$	−5.42435	+	9.39525i	−0.307587	+	0.532756i	−0.977834	−	0.209382i	$-0.932855\pi$
$311$	−5.42435	+	9.39525i	−0.307587	+	0.532756i	0.670247	+	0.742138i	$0.266188\pi$
$312$	−10.5176	−	10.6835i	−0.595440	−	0.604836i
$313$	−6.22407	+	3.59347i	−0.351805	+	0.203115i	−0.665480	−	0.746416i	$-0.731773\pi$
$313$	−6.22407	+	3.59347i	−0.351805	+	0.203115i	0.313675	+	0.949530i	$0.398440\pi$
$314$	−33.1322	−	8.87776i	−1.86976	−	0.501001i
$315$	−1.57884	−	0.174036i	−0.0889574	−	0.00980581i
$316$	−0.0209048	−	0.0120694i	−0.00117599	−	0.000678958i
$317$	−2.45087	+	9.14677i	−0.137655	+	0.513734i	0.862318	+	0.506367i	$0.169012\pi$
$317$	−2.45087	+	9.14677i	−0.137655	+	0.513734i	−0.999973	+	0.00736711i	$0.997655\pi$
$318$	−8.57258	−	2.29702i	−0.480726	−	0.128810i
$319$	18.8055	+	5.03891i	1.05290	+	0.282125i
$320$	−1.41849	+	5.29389i	−0.0792962	+	0.295937i
$321$	−5.20734	−	3.00646i	−0.290646	−	0.167804i
$322$	25.4634	+	2.80684i	1.41902	+	0.156419i
$323$	1.52617	+	0.408937i	0.0849185	+	0.0227538i
$324$	0.293944	−	0.169709i	0.0163302	−	0.00942825i
$325$	14.1637	+	8.32595i	0.785662	+	0.461840i
$326$	−14.4520	+	25.0316i	−0.800423	+	1.38637i
$327$	−2.30617	−	8.60675i	−0.127532	−	0.475955i
$328$	9.47156	−	5.46841i	0.522979	−	0.301942i
$329$	−2.89503	+	26.2634i	−0.159608	+	1.44795i
$330$	−4.57687	−	4.57687i	−0.251948	−	0.251948i
$331$	4.19587	+	4.19587i	0.230626	+	0.230626i	0.812954	−	0.582328i	$-0.197858\pi$
$331$	4.19587	+	4.19587i	0.230626	+	0.230626i	−0.582328	+	0.812954i	$0.697858\pi$
$332$	0.261936	−	0.977557i	0.0143756	−	0.0536504i
$333$	−0.787965	−	2.94072i	−0.0431802	−	0.161151i
$334$		−	24.3908i		−	1.33460i
$335$	−3.11436	−	5.39424i	−0.170156	−	0.294719i
$336$	13.8277	+	5.38850i	0.754361	+	0.293967i
$337$			16.0448i			0.874014i	0.899458	+	0.437007i	$0.143961\pi$
$337$			16.0448i			0.874014i	−0.899458	+	0.437007i	$0.856039\pi$
$338$	17.5525	−	4.40983i	0.954728	−	0.239863i
$339$	1.39229	+	0.803836i	0.0756185	+	0.0436584i
$340$	0.0136393	+	0.0136393i	0.000739695	+	0.000739695i
$341$	17.7261	+	10.2342i	0.959922	+	0.554211i
$342$	2.11958	−	3.67122i	0.114614	−	0.198517i
$343$	16.6276	−	8.15620i	0.897805	−	0.440393i
$344$	−10.9557	+	2.93557i	−0.590691	+	0.158275i
$345$	−4.74283	+	4.74283i	−0.255345	+	0.255345i
$346$	7.96152	−	2.13328i	0.428014	−	0.114686i
$347$	−11.4687	−	19.8644i	−0.615673	−	1.06638i	−0.990266	−	0.139187i	$-0.955551\pi$
$347$	−11.4687	−	19.8644i	−0.615673	−	1.06638i	0.374593	−	0.927189i	$-0.377782\pi$
$348$	0.181100	−	0.313674i	0.00970798	−	0.0168147i
$349$	3.69715	−	13.7979i	0.197904	−	0.738587i	−0.793592	−	0.608450i	$-0.791792\pi$
$349$	3.69715	−	13.7979i	0.197904	−	0.738587i	0.991496	−	0.130137i	$-0.0415417\pi$
$350$	−16.6828	−	1.83895i	−0.891732	−	0.0982959i
$351$	−0.159526	+	20.3773i	−0.00851489	+	1.08766i
$352$	0.844049	+	1.46194i	0.0449880	+	0.0779214i
$353$	−3.28863	+	3.28863i	−0.175036	+	0.175036i	−0.789188	−	0.614152i	$-0.789498\pi$
$353$	−3.28863	+	3.28863i	−0.175036	+	0.175036i	0.614152	+	0.789188i	$0.289498\pi$
$354$	12.3573			0.656783
$355$	−2.20515			−0.117037
$356$	−0.423420	+	0.423420i	−0.0224412	+	0.0224412i
$357$	1.39929	−	1.12143i	0.0740584	−	0.0593525i
$358$	−1.35844	−	5.06977i	−0.0717959	−	0.267946i
$359$	−17.5557	−	4.70405i	−0.926557	−	0.248270i	−0.236171	−	0.971711i	$-0.575893\pi$
$359$	−17.5557	−	4.70405i	−0.926557	−	0.248270i	−0.690386	+	0.723441i	$0.742559\pi$
$360$	1.49245	−	0.861666i	0.0786590	−	0.0454138i
$361$			7.59733i			0.399860i
$362$	−7.65006	+	2.04983i	−0.402078	+	0.107736i
$363$	−17.7349			−0.930843
$364$	0.463799	−	0.365776i	0.0243097	−	0.0191718i
$365$	0.0776629			0.00406506
$366$	−9.48714	+	2.54207i	−0.495901	+	0.132876i
$367$			14.6545i			0.764957i	0.923964	+	0.382478i	$0.124929\pi$
$367$			14.6545i			0.764957i	−0.923964	+	0.382478i	$0.875071\pi$
$368$	−23.3242	+	13.4663i	−1.21586	+	0.701977i
$369$	−3.31870	−	0.889243i	−0.172765	−	0.0462921i
$370$	0.809882	+	3.02252i	0.0421038	+	0.157133i
$371$	4.22788	−	10.8494i	0.219501	−	0.563270i
$372$	0.269262	−	0.269262i	0.0139606	−	0.0139606i
$373$	−5.72519			−0.296439			−0.148220	−	0.988954i	$-0.547354\pi$
$373$	−5.72519			−0.296439			−0.148220	+	0.988954i	$0.547354\pi$
$374$	−3.14045			−0.162389
$375$	6.51693	−	6.51693i	0.336533	−	0.336533i
$376$	−14.3335	−	24.8264i	−0.739195	−	1.28032i
$377$	7.18108	+	12.6660i	0.369844	+	0.652330i
$378$	−8.37066	−	19.0602i	−0.430540	−	0.980348i
$379$	−0.283332	+	1.05741i	−0.0145538	+	0.0543156i	−0.972821	−	0.231559i	$-0.925617\pi$
$379$	−0.283332	+	1.05741i	−0.0145538	+	0.0543156i	0.958267	+	0.285875i	$0.0922840\pi$
$380$	0.0696023	−	0.120555i	0.00357052	−	0.00618433i
$381$	−14.4307	−	24.9946i	−0.739305	−	1.28051i
$382$	−12.3278	+	3.30324i	−0.630747	+	0.169008i
$383$	−0.360580	+	0.360580i	−0.0184248	+	0.0184248i	−0.716259	−	0.697834i	$-0.754147\pi$
$383$	−0.360580	+	0.360580i	−0.0184248	+	0.0184248i	0.697834	+	0.716259i	$0.254147\pi$
$384$	−15.0551	+	4.03401i	−0.768280	+	0.205860i
$385$	6.62666	−	5.31079i	0.337726	−	0.270663i
$386$	−17.6882	+	30.6369i	−0.900306	+	1.55938i
$387$	3.08574	+	1.78155i	0.156857	+	0.0905615i
$388$	−0.780505	−	0.780505i	−0.0396241	−	0.0396241i
$389$	17.8137	+	10.2847i	0.903191	+	0.521457i	0.878234	−	0.478231i	$-0.158722\pi$
$389$	17.8137	+	10.2847i	0.903191	+	0.521457i	0.0249566	+	0.999689i	$0.492055\pi$
$390$	0.0378947	−	4.84052i	0.00191887	−	0.245109i
$391$			3.25433i			0.164578i
$392$	−9.30323	+	17.8101i	−0.469884	+	0.899545i
$393$	−5.53122	−	9.58036i	−0.279013	−	0.483265i
$394$			1.99898i			0.100707i
$395$	−0.0671742	−	0.250697i	−0.00337990	−	0.0126140i
$396$	0.0696735	−	0.260025i	0.00350122	−	0.0130667i
$397$	20.9004	+	20.9004i	1.04896	+	1.04896i	0.998738	+	0.0502241i	$0.0159936\pi$
$397$	20.9004	+	20.9004i	1.04896	+	1.04896i	0.0502241	+	0.998738i	$0.484006\pi$
$398$	10.8440	+	10.8440i	0.543559	+	0.543559i
$399$	−10.4311	−	7.65969i	−0.522208	−	0.383464i
$400$	15.2812	−	8.82263i	0.764062	−	0.441131i
$401$	−1.71146	−	6.38727i	−0.0854664	−	0.318965i	0.909936	−	0.414749i	$-0.136131\pi$
$401$	−1.71146	−	6.38727i	−0.0854664	−	0.318965i	−0.995402	+	0.0957844i	$0.969464\pi$
$402$	9.43328	−	16.3389i	0.470489	−	0.814911i
$403$	3.84600	+	14.8165i	0.191583	+	0.738061i
$404$	0.597688	−	0.345075i	0.0297361	−	0.0171681i
$405$	3.52507	+	0.944538i	0.175162	+	0.0469345i
$406$	−11.9888	−	8.80353i	−0.594994	−	0.436912i
$407$	14.0961	+	8.13841i	0.698719	+	0.403406i
$408$	−0.503545	+	1.87925i	−0.0249292	+	0.0930369i
$409$	2.30851	+	0.618563i	0.114148	+	0.0305860i	0.315441	−	0.948945i	$-0.397848\pi$
$409$	2.30851	+	0.618563i	0.114148	+	0.0305860i	−0.201293	+	0.979531i	$0.564514\pi$
$410$	3.41101	+	0.913977i	0.168458	+	0.0451381i
$411$	−4.93690	+	18.4248i	−0.243520	+	0.908827i
$412$	0.400697	+	0.231343i	0.0197409	+	0.0113974i
$413$	−1.77639	+	16.1152i	−0.0874103	+	0.792978i
$414$	8.43384	+	2.25984i	0.414501	+	0.111065i
$415$	9.42364	−	5.44074i	0.462588	−	0.267076i
$416$	−0.336286	+	1.21685i	−0.0164878	+	0.0596611i
$417$	12.4678	−	21.5949i	0.610553	−	1.05751i
$418$	5.86591	+	21.8919i	0.286911	+	1.07077i
$419$	−13.1791	+	7.60897i	−0.643842	+	0.371722i	−0.786093	−	0.618108i	$-0.787899\pi$
$419$	−13.1791	+	7.60897i	−0.643842	+	0.371722i	0.142251	+	0.989831i	$0.454566\pi$
$420$	−0.0635278	−	0.144654i	−0.00309984	−	0.00705839i
$421$	−15.0076	−	15.0076i	−0.731425	−	0.731425i	0.239477	−	0.970902i	$-0.423024\pi$
$421$	−15.0076	−	15.0076i	−0.731425	−	0.731425i	−0.970902	+	0.239477i	$0.923024\pi$
$422$	22.7366	+	22.7366i	1.10680	+	1.10680i
$423$	−2.33084	+	8.69881i	−0.113329	+	0.422951i
$424$	3.26970	+	12.2027i	0.158791	+	0.592615i
$425$		−	2.13212i		−	0.103423i
$426$	−3.33965	−	5.78445i	−0.161807	−	0.280257i
$427$	−1.95134	−	12.7377i	−0.0944318	−	0.616419i
$428$			0.257033i			0.0124241i
$429$	−17.6648	−	17.9435i	−0.852862	−	0.866321i
$430$	−3.17157	−	1.83111i	−0.152947	−	0.0883039i
$431$	−21.2427	−	21.2427i	−1.02322	−	1.02322i	−0.999724	−	0.0234994i	$-0.992519\pi$
$431$	−21.2427	−	21.2427i	−1.02322	−	1.02322i	−0.0234994	−	0.999724i	$-0.507481\pi$
$432$	18.9536	+	10.9428i	0.911903	+	0.526488i
$433$	7.75396	−	13.4302i	0.372631	−	0.645417i	−0.617338	−	0.786698i	$-0.711789\pi$
$433$	7.75396	−	13.4302i	0.372631	−	0.645417i	0.989969	+	0.141281i	$0.0451222\pi$
$434$	−9.77930	−	12.2023i	−0.469421	−	0.585731i
$435$	3.76168	−	1.00794i	0.180359	−	0.0483270i
$436$	−0.269329	+	0.269329i	−0.0128985	+	0.0128985i
$437$	22.6857	−	6.07861i	1.08520	−	0.290779i
$438$	0.117619	+	0.203722i	0.00562005	+	0.00973420i
$439$	7.21696	−	12.5001i	0.344447	−	0.596599i	−0.640806	−	0.767703i	$-0.721400\pi$
$439$	7.21696	−	12.5001i	0.344447	−	0.596599i	0.985253	+	0.171103i	$0.0547332\pi$
$440$	−2.38465	+	8.89962i	−0.113684	+	0.424273i
$441$	6.02283	−	1.88967i	0.286802	−	0.0899844i
$442$	−1.64768	−	1.67368i	−0.0783721	−	0.0796088i
$443$	6.23855	+	10.8055i	0.296403	+	0.513384i	0.975310	−	0.220839i	$-0.0708797\pi$
$443$	6.23855	+	10.8055i	0.296403	+	0.513384i	−0.678908	+	0.734224i	$0.737546\pi$
$444$	0.214123	−	0.214123i	0.0101618	−	0.0101618i
$445$	−6.43838			−0.305208
$446$	5.15648			0.244166
$447$	3.85394	−	3.85394i	0.182285	−	0.182285i
$448$	−3.29811	−	21.5289i	−0.155821	−	1.01715i
$449$	−7.24956	−	27.0557i	−0.342128	−	1.27684i	−0.895932	−	0.444191i	$-0.853491\pi$
$449$	−7.24956	−	27.0557i	−0.342128	−	1.27684i	0.553804	−	0.832647i	$-0.313176\pi$
$450$	−5.52556	−	1.48057i	−0.260478	−	0.0697948i
$451$	15.9079	−	9.18445i	0.749075	−	0.432479i
$452$		−	0.0687227i		−	0.00323245i
$453$	−10.5787	+	2.83455i	−0.497030	+	0.133179i
$454$	33.5616			1.57512
$455$	6.30710	+	0.745253i	0.295682	+	0.0349380i
$456$	14.0407			0.657515
$457$	17.0148	−	4.55910i	0.795919	−	0.213266i	0.162128	−	0.986770i	$-0.448164\pi$
$457$	17.0148	−	4.55910i	0.795919	−	0.213266i	0.633791	+	0.773504i	$0.281498\pi$
$458$		−	25.9564i		−	1.21286i
$459$	2.29021	−	1.32225i	0.106898	−	0.0617175i
$460$	0.276949	+	0.0742082i	0.0129128	+	0.00345997i
$461$	−1.39627	−	5.21097i	−0.0650310	−	0.242699i	0.925757	−	0.378118i	$-0.123429\pi$
$461$	−1.39627	−	5.21097i	−0.0650310	−	0.242699i	−0.990788	+	0.135419i	$0.956762\pi$
$462$	23.9670	+	9.33967i	1.11504	+	0.434521i
$463$	−19.4789	+	19.4789i	−0.905259	+	0.905259i	−0.995885	−	0.0906259i	$-0.971113\pi$
$463$	−19.4789	+	19.4789i	−0.905259	+	0.905259i	0.0906259	+	0.995885i	$0.471113\pi$
$464$	15.6373			0.725944
$465$	4.09431			0.189869
$466$	4.45207	−	4.45207i	0.206238	−	0.206238i
$467$	−4.79805	−	8.31047i	−0.222027	−	0.384563i	0.733396	−	0.679802i	$-0.237934\pi$
$467$	−4.79805	−	8.31047i	−0.222027	−	0.384563i	−0.955423	+	0.295239i	$0.904601\pi$
$468$	0.175133	−	0.0992935i	0.00809554	−	0.00458984i
$469$	19.9516	+	14.6508i	0.921281	+	0.676509i
$470$	2.39567	−	8.94077i	0.110504	−	0.412407i
$471$	−17.8451	+	30.9086i	−0.822259	+	1.42419i
$472$	−8.79503	−	15.2334i	−0.404824	−	0.701176i
$473$	−18.4006	+	4.93042i	−0.846060	+	0.226701i
$474$	0.555884	−	0.555884i	0.0255326	−	0.0255326i
$475$	−14.8629	+	3.98250i	−0.681956	+	0.182729i
$476$	−0.0714227	−	0.0278327i	−0.00327366	−	0.00127571i
$477$	1.98434	−	3.43697i	0.0908565	−	0.157368i
$478$	−19.0295	−	10.9867i	−0.870387	−	0.502518i
$479$	−21.8842	−	21.8842i	−0.999915	−	0.999915i	8.46616e−5	−	1.00000i	$-0.499973\pi$
$479$	−21.8842	−	21.8842i	−0.999915	−	0.999915i	−1.00000		8.46616e-5i	$0.999973\pi$
$480$	0.292433	+	0.168836i	0.0133477	+	0.00770628i
$481$	3.05841	+	11.7823i	0.139452	+	0.537229i
$482$		−	10.5363i		−	0.479916i
$483$	9.67833	−	24.8360i	0.440379	−	1.13008i
$484$	0.379055	+	0.656543i	0.0172298	+	0.0298429i
$485$		−	11.8681i		−	0.538902i
$486$	−3.24833	−	12.1229i	−0.147347	−	0.549908i
$487$	1.44837	−	5.40538i	0.0656318	−	0.244941i	−0.925314	−	0.379201i	$-0.876199\pi$
$487$	1.44837	−	5.40538i	0.0656318	−	0.244941i	0.990946	+	0.134260i	$0.0428656\pi$
$488$	9.88601	+	9.88601i	0.447518	+	0.447518i
$489$	21.2660	+	21.2660i	0.961680	+	0.961680i
$490$	−6.19036	+	1.94223i	−0.279652	+	0.0877412i
$491$	12.0113	−	6.93474i	0.542063	−	0.312960i	−0.203851	−	0.979002i	$-0.565346\pi$
$491$	12.0113	−	6.93474i	0.542063	−	0.312960i	0.745915	+	0.666041i	$0.232013\pi$
$492$	−0.0884479	−	0.330092i	−0.00398754	−	0.0148817i
$493$	0.944750	−	1.63635i	0.0425494	−	0.0736977i
$494$	−8.58948	+	14.6120i	−0.386459	+	0.657426i
$495$	2.50664	−	1.44721i	0.112665	−	0.0650472i
$496$	15.8799	+	4.25501i	0.713030	+	0.191056i
$497$	8.02362	−	3.52374i	0.359908	−	0.158061i
$498$	28.5438	+	16.4798i	1.27908	+	0.738477i
$499$	−2.36642	+	8.83159i	−0.105935	+	0.395356i	−0.998450	−	0.0556630i	$-0.982273\pi$
$499$	−2.36642	+	8.83159i	−0.105935	+	0.395356i	0.892514	+	0.451019i	$0.148939\pi$
$500$	−0.380544	−	0.101966i	−0.0170184	−	0.00456008i
$501$	−24.5138	−	6.56846i	−1.09520	−	0.293457i
$502$	7.65055	−	28.5522i	0.341461	−	1.27435i
$503$	27.9587	+	16.1420i	1.24662	+	0.719736i	0.970434	−	0.241369i	$-0.0775963\pi$
$503$	27.9587	+	16.1420i	1.24662	+	0.719736i	0.276185	+	0.961104i	$0.410930\pi$
$504$	−4.05349	+	5.52011i	−0.180557	+	0.245885i
$505$	7.16766	+	1.92057i	0.318957	+	0.0854642i
$506$	−40.4270	+	23.3405i	−1.79720	+	1.03761i
$507$	0.294822	−	18.8286i	0.0130935	−	0.836207i
$508$	−0.616864	+	1.06844i	−0.0273689	+	0.0474043i
$509$	3.12559	+	11.6648i	0.138539	+	0.517035i	0.999958	+	0.00914032i	$0.00290950\pi$
$509$	3.12559	+	11.6648i	0.138539	+	0.517035i	−0.861419	+	0.507895i	$0.830424\pi$
$510$	−0.544027	+	0.314094i	−0.0240899	+	0.0139083i
$511$	−0.282583	+	0.124102i	−0.0125007	+	0.00548995i
$512$	16.6785	+	16.6785i	0.737091	+	0.737091i
$513$	−13.4951	−	13.4951i	−0.595824	−	0.595824i
$514$	−9.09471	+	33.9419i	−0.401150	+	1.49711i
$515$	1.28757	+	4.80529i	0.0567372	+	0.211746i
$516$			0.354402i			0.0156017i
$517$	−24.0738	−	41.6971i	−1.05877	−	1.83384i
$518$	−7.77668	−	9.70353i	−0.341688	−	0.426349i
$519$		−	8.57618i		−	0.376452i
$520$	−5.99412	+	3.39842i	−0.262859	+	0.149031i
$521$	10.1929	+	5.88486i	0.446558	+	0.257821i	0.706376	−	0.707837i	$-0.250329\pi$
$521$	10.1929	+	5.88486i	0.446558	+	0.257821i	−0.259817	+	0.965658i	$0.583662\pi$
$522$	−3.58469	−	3.58469i	−0.156898	−	0.156898i
$523$	−13.2762	−	7.66503i	−0.580529	−	0.335168i	0.180815	−	0.983517i	$-0.442127\pi$
$523$	−13.2762	−	7.66503i	−0.580529	−	0.335168i	−0.761344	+	0.648349i	$0.775460\pi$
$524$	−0.236442	+	0.409529i	−0.0103290	+	0.0178904i
$525$	−6.34091	+	16.2717i	−0.276740	+	0.710156i
$526$	0.408840	−	0.109548i	0.0178263	−	0.00477654i
$527$	1.40467	−	1.40467i	0.0611884	−	0.0611884i
$528$	−26.1212	+	6.99916i	−1.13678	+	0.304599i
$529$	12.6869	+	21.9743i	0.551603	+	0.955404i
$530$	−2.03953	+	3.53257i	−0.0885916	+	0.153445i
$531$	−1.43020	+	5.33758i	−0.0620654	+	0.231631i
$532$	−0.0606124	+	0.549870i	−0.00262788	+	0.0238399i
$533$	13.2411	+	3.65927i	0.573535	+	0.158501i
$534$	−9.75079	−	16.8889i	−0.421958	−	0.730852i
$535$	−1.95417	+	1.95417i	−0.0844863	+	0.0844863i
$536$	−26.8557			−1.15999
$537$	−5.46118			−0.235667
$538$	−17.6586	+	17.6586i	−0.761318	+	0.761318i
$539$	−15.6252	+	29.9129i	−0.673026	+	1.28844i
$540$	−0.0603024	−	0.225052i	−0.00259500	−	0.00968469i
$541$	14.5150	+	3.88929i	0.624050	+	0.167214i	0.556968	−	0.830534i	$-0.311964\pi$
$541$	14.5150	+	3.88929i	0.624050	+	0.167214i	0.0670818	+	0.997747i	$0.478631\pi$
$542$	−15.6547	+	9.03822i	−0.672425	+	0.388225i
$543$			8.24067i			0.353641i
$544$	0.158252	−	0.0424034i	0.00678498	−	0.00181803i
$545$	−4.09532			−0.175424
$546$	7.59706	+	17.6732i	0.325124	+	0.756342i
$547$	20.0277			0.856322			0.428161	−	0.903702i	$-0.359162\pi$
$547$	20.0277			0.856322			0.428161	+	0.903702i	$0.359162\pi$
$548$	0.787599	−	0.211036i	0.0336446	−	0.00901503i
$549$		−	4.39207i		−	0.187449i
$550$	26.4864	−	15.2919i	1.12938	−	0.652049i
$551$	−13.1716	−	3.52931i	−0.561127	−	0.150354i
$552$	7.48490	+	27.9340i	0.318579	+	1.18895i
$553$	0.645022	+	0.804841i	0.0274291	+	0.0342253i
$554$	−6.11594	+	6.11594i	−0.259841	+	0.259841i
$555$	3.25587			0.138204
$556$	−1.06592			−0.0452050
$557$	1.76207	−	1.76207i	0.0746611	−	0.0746611i	−0.668790	−	0.743451i	$-0.733188\pi$
$557$	1.76207	−	1.76207i	0.0746611	−	0.0746611i	0.743451	+	0.668790i	$0.233188\pi$
$558$	−2.66489	−	4.61573i	−0.112814	−	0.195399i
$559$	−12.2817	−	7.21964i	−0.519462	−	0.305358i
$560$	4.03713	−	5.49783i	0.170600	−	0.232326i
$561$	−0.845727	+	3.15630i	−0.0357066	+	0.133259i
$562$	1.70144	−	2.94698i	0.0717710	−	0.124311i
$563$	9.85804	+	17.0746i	0.415467	+	0.719609i	0.995477	−	0.0949995i	$-0.0302849\pi$
$563$	9.85804	+	17.0746i	0.415467	+	0.719609i	−0.580011	+	0.814609i	$0.696952\pi$
$564$	−0.865221	+	0.231835i	−0.0364324	+	0.00976202i
$565$	0.522487	−	0.522487i	0.0219812	−	0.0219812i
$566$	−24.2266	+	6.49150i	−1.01832	+	0.272858i
$567$	−14.3356	+	2.19613i	−0.602037	+	0.0922286i
$568$	−4.75385	+	8.23391i	−0.199467	+	0.345487i
$569$	−38.6991	−	22.3429i	−1.62235	−	0.936664i	−0.986290	−	0.165023i	$-0.947230\pi$
$569$	−38.6991	−	22.3429i	−1.62235	−	0.936664i	−0.636059	−	0.771640i	$-0.719437\pi$
$570$	3.20569	+	3.20569i	0.134272	+	0.134272i
$571$	−23.8503	−	13.7700i	−0.998103	−	0.576255i	−0.0904162	−	0.995904i	$-0.528820\pi$
$571$	−23.8503	−	13.7700i	−0.998103	−	0.576255i	−0.907686	+	0.419649i	$0.862153\pi$
$572$	−0.286709	+	1.03746i	−0.0119879	+	0.0433783i
$573$			13.2796i			0.554763i
$574$	−13.8717	+	2.12507i	−0.578995	+	0.0886986i
$575$	−15.8464	−	27.4468i	−0.660841	−	1.14461i
$576$		−	7.42338i		−	0.309308i
$577$	4.76139	+	17.7698i	0.198219	+	0.739765i	0.991410	+	0.130791i	$0.0417518\pi$
$577$	4.76139	+	17.7698i	0.198219	+	0.739765i	−0.793190	+	0.608974i	$0.791582\pi$
$578$	6.04647	−	22.5657i	0.251500	−	0.938610i
$579$	26.0280	+	26.0280i	1.08169	+	1.08169i
$580$	−0.117713	−	0.117713i	−0.00488778	−	0.00488778i
$581$	−25.5946	+	34.8552i	−1.06184	+	1.44604i
$582$	31.1318	−	17.9740i	1.29046	−	0.745045i
$583$	5.49162	+	20.4950i	0.227440	+	0.848816i
$584$	0.167425	−	0.289989i	0.00692811	−	0.0119998i
$585$	2.08642	+	0.576597i	0.0862628	+	0.0238394i
$586$	−5.46930	+	3.15770i	−0.225935	+	0.130444i
$587$	20.1767	+	5.40633i	0.832781	+	0.223143i	0.649927	−	0.759997i	$-0.274800\pi$
$587$	20.1767	+	5.40633i	0.832781	+	0.223143i	0.182855	+	0.983140i	$0.441466\pi$
$588$	0.462302	+	0.424821i	0.0190650	+	0.0175193i
$589$	−12.4156	−	7.16813i	−0.511574	−	0.295358i
$590$	1.46998	−	5.48605i	0.0605182	−	0.225857i
$591$	2.00907	+	0.538328i	0.0826420	+	0.0221439i
$592$	12.6280	+	3.38367i	0.519008	+	0.139068i
$593$	2.29261	−	8.55614i	0.0941462	−	0.351358i	−0.902742	−	0.430182i	$-0.858450\pi$
$593$	2.29261	−	8.55614i	0.0941462	−	0.351358i	0.996889	+	0.0788231i	$0.0251162\pi$
$594$	32.8514	+	18.9668i	1.34791	+	0.778217i
$595$	−0.331407	−	0.754621i	−0.0135864	−	0.0309365i
$596$	−0.225044	−	0.0603003i	−0.00921815	−	0.00247000i
$597$	13.8190	−	7.97838i	0.565573	−	0.326534i
$598$	−33.6497	−	9.29934i	−1.37604	−	0.380278i
$599$	18.1377	−	31.4154i	0.741087	−	1.28360i	−0.210914	−	0.977505i	$-0.567644\pi$
$599$	18.1377	−	31.4154i	0.741087	−	1.28360i	0.952001	−	0.306096i	$-0.0990227\pi$
$600$	−4.90385	−	18.3014i	−0.200199	−	0.747153i
$601$	−30.7163	+	17.7340i	−1.25294	+	0.723387i	−0.971693	−	0.236248i	$-0.924082\pi$
$601$	−30.7163	+	17.7340i	−1.25294	+	0.723387i	−0.281250	+	0.959635i	$0.590749\pi$
$602$	14.4661	+	1.59460i	0.589593	+	0.0649910i
$603$	5.96562	+	5.96562i	0.242939	+	0.242939i
$604$	0.331036	+	0.331036i	0.0134697	+	0.0134697i
$605$	−2.10969	+	7.87347i	−0.0857711	+	0.320102i
$606$	5.81732	+	21.7105i	0.236313	+	0.881930i
$607$			25.7091i			1.04350i	0.853099	+	0.521749i	$0.174720\pi$
$607$			25.7091i			1.04350i	−0.853099	+	0.521749i	$0.825280\pi$
$608$	−0.591182	−	1.02396i	−0.0239756	−	0.0415269i
$609$	−12.0765	+	9.67847i	−0.489366	+	0.392192i
$610$			4.51424i			0.182776i
$611$	9.59150	−	34.7069i	0.388031	−	1.40409i
$612$	−0.0226260	−	0.0130632i	−0.000914604	−	0.000528047i
$613$	−32.2606	−	32.2606i	−1.30299	−	1.30299i	−0.926364	−	0.376628i	$-0.877083\pi$
$613$	−32.2606	−	32.2606i	−1.30299	−	1.30299i	−0.376628	−	0.926364i	$-0.622917\pi$
$614$	−19.6659	−	11.3541i	−0.793649	−	0.458214i
$615$	1.83718	−	3.18208i	0.0740821	−	0.128314i
$616$	−5.54449	−	36.1926i	−0.223394	−	1.45824i
$617$	35.5733	−	9.53183i	1.43213	−	0.383737i	0.542357	−	0.840148i	$-0.317532\pi$
$617$	35.5733	−	9.53183i	1.43213	−	0.383737i	0.889769	+	0.456411i	$0.150865\pi$
$618$	−10.6550	+	10.6550i	−0.428607	+	0.428607i
$619$	−5.13248	+	1.37524i	−0.206292	+	0.0552757i	−0.360485	−	0.932765i	$-0.617389\pi$
$619$	−5.13248	+	1.37524i	−0.206292	+	0.0552757i	0.154193	+	0.988041i	$0.450722\pi$
$620$	−0.0875091	−	0.151570i	−0.00351445	−	0.00608721i
$621$	19.6545	−	34.0427i	0.788710	−	1.36609i
$622$	−3.90895	+	14.5884i	−0.156734	+	0.584941i
$623$	23.4266	−	10.2883i	0.938565	−	0.412190i
$624$	−17.4350	−	10.2489i	−0.697957	−	0.410284i
$625$	9.27392	+	16.0629i	0.370957	+	0.642516i
$626$	−7.07481	+	7.07481i	−0.282766	+	0.282766i
$627$	23.5820			0.941774
$628$	1.52564			0.0608796
$629$	1.11702	−	1.11702i	0.0445385	−	0.0445385i
$630$	−2.18579	+	0.334850i	−0.0870840	+	0.0133408i
$631$	−3.50380	−	13.0763i	−0.139484	−	0.520561i	−0.999939	−	0.0110350i	$-0.996487\pi$
$631$	−3.50380	−	13.0763i	−0.139484	−	0.520561i	0.860455	−	0.509526i	$-0.170179\pi$
$632$	−1.08090	−	0.289627i	−0.0429961	−	0.0115208i
$633$	28.9743	−	16.7283i	1.15162	−	0.664890i
$634$			13.1829i			0.523558i
$635$	−12.8131	+	3.43325i	−0.508471	+	0.136244i
$636$	0.394741			0.0156525
$637$	−24.1398	+	7.36682i	−0.956454	+	0.291884i
$638$	27.1035			1.07304
$639$	2.88505	−	0.773046i	0.114131	−	0.0305812i
$640$			7.16364i			0.283168i
$641$	18.5489	−	10.7092i	0.732638	−	0.422989i	−0.0867484	−	0.996230i	$-0.527648\pi$
$641$	18.5489	−	10.7092i	0.732638	−	0.422989i	0.819386	+	0.573241i	$0.194314\pi$
$642$	−8.08566	−	2.16654i	−0.319115	−	0.0855067i
$643$	3.68080	+	13.7369i	0.145157	+	0.541732i	0.999748	+	0.0224315i	$0.00714075\pi$
$643$	3.68080	+	13.7369i	0.145157	+	0.541732i	−0.854592	+	0.519300i	$0.826193\pi$
$644$	−1.12628	+	0.172540i	−0.0443817	+	0.00679902i
$645$	−2.69445	+	2.69445i	−0.106094	+	0.106094i
$646$	2.19961			0.0865425
$647$	20.5476			0.807811			0.403906	−	0.914801i	$-0.367652\pi$
$647$	20.5476			0.807811			0.403906	+	0.914801i	$0.367652\pi$
$648$	11.1262	−	11.1262i	0.437077	−	0.437077i
$649$	−14.7717	−	25.5853i	−0.579839	−	1.00431i
$650$	22.0461	+	6.09261i	0.864720	+	0.238972i
$651$	−14.8975	+	6.54253i	−0.583878	+	0.256422i
$652$	0.332736	−	1.24179i	0.0130309	−	0.0486321i
$653$	21.8478	−	37.8415i	0.854972	−	1.48085i	−0.0216997	−	0.999765i	$-0.506908\pi$
$653$	21.8478	−	37.8415i	0.854972	−	1.48085i	0.876671	−	0.481090i	$-0.159759\pi$
$654$	−6.20228	−	10.7427i	−0.242528	−	0.420072i
$655$	−4.91120	+	1.31595i	−0.191896	+	0.0514185i
$656$	10.4325	−	10.4325i	0.407322	−	0.407322i
$657$	−0.101608	+	0.0272258i	−0.00396411	+	0.00106218i
$658$	5.57012	+	36.3599i	0.217146	+	1.41746i
$659$	−6.26381	+	10.8492i	−0.244003	+	0.422626i	−0.961851	−	0.273574i	$-0.911794\pi$
$659$	−6.26381	+	10.8492i	−0.244003	+	0.422626i	0.717848	+	0.696200i	$0.245127\pi$
$660$	0.249321	+	0.143945i	0.00970480	+	0.00560307i
$661$	16.2681	+	16.2681i	0.632756	+	0.632756i	0.948758	−	0.316002i	$-0.102341\pi$
$661$	16.2681	+	16.2681i	0.632756	+	0.632756i	−0.316002	+	0.948758i	$0.602341\pi$
$662$	7.15407	+	4.13040i	0.278051	+	0.160533i
$663$	−2.12585	+	1.20527i	−0.0825610	+	0.0468087i
$664$		−	46.9165i		−	1.82071i
$665$	−4.64139	+	3.71974i	−0.179985	+	0.144245i
$666$	−2.11917	−	3.67051i	−0.0821163	−	0.142230i
$667$		−	28.0863i		−	1.08751i
$668$	0.280780	+	1.04789i	0.0108637	+	0.0405439i
$669$	1.38864	−	5.18249i	0.0536881	−	0.200367i
$670$	−6.13155	−	6.13155i	−0.236882	−	0.236882i
$671$	16.6040	+	16.6040i	0.640991	+	0.640991i
$672$	−1.33383	−	0.147029i	−0.0514537	−	0.00567176i
$673$	−12.0684	+	6.96769i	−0.465202	+	0.268585i	−0.714229	−	0.699912i	$-0.753223\pi$
$673$	−12.0684	+	6.96769i	−0.465202	+	0.268585i	0.249027	+	0.968497i	$0.419889\pi$
$674$	5.78116	+	21.5756i	0.222682	+	0.831061i
$675$	−12.8770	+	22.3036i	−0.495635	+	0.858466i
$676$	−0.703331	+	0.391516i	−0.0270512	+	0.0150583i
$677$	44.8299	−	25.8826i	1.72295	−	0.994747i	0.810296	−	0.586020i	$-0.199306\pi$
$677$	44.8299	−	25.8826i	1.72295	−	0.994747i	0.912657	−	0.408727i	$-0.134027\pi$
$678$	2.16186	+	0.579268i	0.0830257	+	0.0222467i
$679$	18.9647	+	43.1830i	0.727798	+	1.65721i
$680$	0.774399	+	0.447100i	0.0296969	+	0.0171455i
$681$	9.03816	−	33.7309i	0.346343	−	1.29257i
$682$	27.5240	+	7.37505i	1.05395	+	0.282405i
$683$	27.5651	+	7.38605i	1.05475	+	0.282620i	0.744213	−	0.667942i	$-0.232825\pi$
$683$	27.5651	+	7.38605i	1.05475	+	0.282620i	0.310537	+	0.950561i	$0.399491\pi$
$684$	−0.0488001	+	0.182125i	−0.00186592	+	0.00696371i
$685$	7.59245	+	4.38350i	0.290092	+	0.167485i
$686$	19.4205	−	16.9589i	0.741479	−	0.647494i
$687$	−26.0873	−	6.99008i	−0.995294	−	0.266688i
$688$	−13.2508	+	7.65033i	−0.505180	+	0.291666i
$689$	−8.04141	+	13.6797i	−0.306353	+	0.521154i
$690$	−4.66883	+	8.08666i	−0.177739	+	0.307854i
$691$	4.84897	+	18.0966i	0.184463	+	0.688427i	0.994745	+	0.102386i	$0.0326476\pi$
$691$	4.84897	+	18.0966i	0.184463	+	0.688427i	−0.810281	+	0.586041i	$0.800686\pi$
$692$	−0.317488	+	0.183302i	−0.0120691	+	0.00696809i
$693$	−6.80803	+	9.27129i	−0.258616	+	0.352187i
$694$	−22.5796	−	22.5796i	−0.857108	−	0.857108i
$695$	−8.10399	−	8.10399i	−0.307402	−	0.307402i
$696$	4.34582	−	16.2188i	0.164728	−	0.614773i
$697$	−0.461409	−	1.72200i	−0.0174771	−	0.0652254i
$698$		−	19.8864i		−	0.752712i
$699$	−3.27559	−	5.67348i	−0.123894	−	0.214591i
$700$	0.737901	−	0.113042i	0.0278900	−	0.00427259i
$701$		−	20.1282i		−	0.760231i	−0.924939	−	0.380115i	$-0.875884\pi$
$701$		−	20.1282i		−	0.760231i	0.924939	−	0.380115i	$-0.124116\pi$
$702$	7.12772	+	27.4591i	0.269019	+	1.03638i
$703$	−9.87309	−	5.70023i	−0.372371	−	0.214988i
$704$	28.0638	+	28.0638i	1.05769	+	1.05769i
$705$	−8.34072	−	4.81552i	−0.314130	−	0.181363i
$706$	−3.23732	+	5.60721i	−0.121838	+	0.211030i
$707$	−29.1491	+	4.46547i	−1.09626	+	0.167941i
$708$	−0.530899	+	0.142254i	−0.0199524	+	0.00534623i
$709$	−3.04711	+	3.04711i	−0.114437	+	0.114437i	−0.762006	−	0.647570i	$-0.775785\pi$
$709$	−3.04711	+	3.04711i	−0.114437	+	0.114437i	0.647570	+	0.762006i	$0.275785\pi$
$710$	−2.96529	+	0.794548i	−0.111285	+	0.0298189i
$711$	0.175771	+	0.304444i	0.00659192	+	0.0114175i
$712$	−13.8798	+	24.0406i	−0.520168	+	0.900958i
$713$	7.64247	−	28.5221i	0.286213	−	1.06816i
$714$	1.47758	−	2.01219i	0.0552970	−	0.0753043i
$715$	−10.0674	+	5.70781i	−0.376500	+	0.213460i
$716$	0.116724	+	0.202172i	0.00436217	+	0.00755550i
$717$	−16.1667	+	16.1667i	−0.603758	+	0.603758i
$718$	−25.3024			−0.944277
$719$	−31.8460			−1.18765			−0.593827	−	0.804593i	$-0.702384\pi$
$719$	−31.8460			−1.18765			−0.593827	+	0.804593i	$0.702384\pi$
$720$	1.64387	−	1.64387i	0.0612635	−	0.0612635i
$721$	−12.3636	−	15.4269i	−0.460444	−	0.574530i
$722$	2.73743	+	10.2162i	0.101877	+	0.380209i
$723$	−10.5895	−	2.83744i	−0.393826	−	0.105525i
$724$	0.305068	−	0.176131i	0.0113377	−	0.00654585i
$725$			18.4012i			0.683404i
$726$	−23.8484	+	6.39016i	−0.885098	+	0.237161i
$727$	49.3169			1.82906			0.914531	−	0.404516i	$-0.132560\pi$
$727$	49.3169			1.82906			0.914531	+	0.404516i	$0.132560\pi$
$728$	16.3796	−	21.9438i	0.607067	−	0.813291i
$729$	−29.5035			−1.09272
$730$	0.104434	−	0.0279831i	0.00386529	−	0.00103570i
$731$			1.84882i			0.0683811i
$732$	0.378327	−	0.218427i	0.0139834	−	0.00807329i
$733$	15.7361	+	4.21647i	0.581226	+	0.155739i	0.537440	−	0.843302i	$-0.319391\pi$
$733$	15.7361	+	4.21647i	0.581226	+	0.155739i	0.0437858	+	0.999041i	$0.486058\pi$
$734$	5.28022	+	19.7061i	0.194896	+	0.727364i
$735$	0.284963	+	6.74464i	0.0105110	+	0.248780i
$736$	1.72202	−	1.72202i	0.0634744	−	0.0634744i
$737$	−45.1055			−1.66148
$738$	−4.78311			−0.176069
$739$	17.8507	−	17.8507i	0.656650	−	0.656650i	−0.297936	−	0.954586i	$-0.596298\pi$
$739$	17.8507	−	17.8507i	0.656650	−	0.656650i	0.954586	+	0.297936i	$0.0962982\pi$
$740$	−0.0695889	−	0.120532i	−0.00255814	−	0.00443083i
$741$	12.3726	+	12.5678i	0.454519	+	0.461691i
$742$	1.77610	−	16.1126i	0.0652027	−	0.591513i
$743$	2.17652	−	8.12290i	0.0798489	−	0.298000i	−0.914440	−	0.404721i	$-0.867369\pi$
$743$	2.17652	−	8.12290i	0.0798489	−	0.298000i	0.994289	+	0.106721i	$0.0340352\pi$
$744$	8.82649	−	15.2879i	0.323595	−	0.560483i
$745$	−1.25252	−	2.16942i	−0.0458886	−	0.0794814i
$746$	−7.69874	+	2.06287i	−0.281871	+	0.0755270i
$747$	−10.4218	+	10.4218i	−0.381315	+	0.381315i
$748$	0.134921	−	0.0361521i	0.00493321	−	0.00132185i
$749$	3.98773	−	10.2331i	0.145709	−	0.373910i
$750$	6.41526	−	11.1116i	0.234252	−	0.405737i
$751$	29.6007	+	17.0900i	1.08015	+	0.623623i	0.930936	−	0.365183i	$-0.118993\pi$
$751$	29.6007	+	17.0900i	1.08015	+	0.623623i	0.149211	+	0.988805i	$0.452327\pi$
$752$	−27.3453	−	27.3453i	−0.997179	−	0.997179i
$753$	−26.6360	−	15.3783i	−0.970669	−	0.560416i
$754$	14.2202	+	14.4446i	0.517870	+	0.526042i
$755$			5.03362i			0.183192i
$756$	0.579039	+	0.722509i	0.0210594	+	0.0262774i
$757$	−6.77459	−	11.7339i	−0.246227	−	0.426477i	0.716249	−	0.697845i	$-0.245857\pi$
$757$	−6.77459	−	11.7339i	−0.246227	−	0.426477i	−0.962476	+	0.271368i	$0.912524\pi$
$758$			1.52400i			0.0553543i
$759$	12.5713	+	46.9166i	0.456308	+	1.70296i
$760$	1.67023	−	6.23340i	0.0605857	−	0.226109i
$761$	14.1336	+	14.1336i	0.512343	+	0.512343i	0.915244	−	0.402901i	$-0.131998\pi$
$761$	14.1336	+	14.1336i	0.512343	+	0.512343i	−0.402901	+	0.915244i	$0.631998\pi$
$762$	−28.4110	−	28.4110i	−1.02922	−	1.02922i
$763$	14.9012	−	6.54415i	0.539459	−	0.236914i
$764$	0.491608	−	0.283830i	0.0177857	−	0.0102686i
$765$	−0.0727049	−	0.271339i	−0.00262865	−	0.00981027i
$766$	−0.354954	+	0.614799i	−0.0128250	+	0.0222136i
$767$	5.88534	−	21.2961i	0.212507	−	0.768958i
$768$	1.86243	−	1.07527i	0.0672045	−	0.0388005i
$769$	−30.3963	−	8.14467i	−1.09612	−	0.293704i	−0.334936	−	0.942241i	$-0.608715\pi$
$769$	−30.3963	−	8.14467i	−1.09612	−	0.293704i	−0.761184	+	0.648536i	$0.775381\pi$
$770$	6.99740	−	9.52917i	0.252169	−	0.343407i
$771$	31.6639	+	18.2812i	1.14035	+	0.658381i
$772$	0.407244	−	1.51986i	0.0146570	−	0.0547008i
$773$	−36.9885	−	9.91105i	−1.33039	−	0.356476i	−0.477527	−	0.878617i	$-0.658467\pi$
$773$	−36.9885	−	9.91105i	−1.33039	−	0.356476i	−0.852859	+	0.522142i	$0.825133\pi$
$774$	4.79136	+	1.28384i	0.172222	+	0.0461467i
$775$	−5.00708	+	18.6867i	−0.179860	+	0.671246i
$776$	−44.3148	−	25.5852i	−1.59081	−	0.918453i
$777$	−11.8468	+	5.20274i	−0.425000	+	0.186647i
$778$	27.6601	+	7.41149i	0.991661	+	0.265715i
$779$	−11.1421	+	6.43289i	−0.399207	+	0.230482i
$780$	0.0540947	+	0.208396i	0.00193690	+	0.00746179i
$781$	−7.98432	+	13.8292i	−0.285701	+	0.494849i
$782$	1.17258	+	4.37614i	0.0419315	+	0.156490i
$783$	−19.7656	+	11.4116i	−0.706363	+	0.407819i
$784$	−5.90413	+	26.4555i	−0.210862	+	0.944838i
$785$	11.5992	+	11.5992i	0.413992	+	0.413992i
$786$	−10.8899	−	10.8899i	−0.388428	−	0.388428i
$787$	5.74579	−	21.4436i	0.204815	−	0.764381i	−0.784690	−	0.619888i	$-0.787178\pi$
$787$	5.74579	−	21.4436i	0.204815	−	0.764381i	0.989506	−	0.144494i	$-0.0461553\pi$
$788$	−0.0230118	−	0.0858811i	−0.000819760	−	0.00305939i
$789$		−	0.440404i		−	0.0156788i
$790$	−0.180660	−	0.312912i	−0.00642759	−	0.0111329i
$791$	−1.06620	+	2.73602i	−0.0379097	+	0.0972817i
$792$		−	12.4795i		−	0.443441i
$793$	−0.137475	+	17.5605i	−0.00488187	+	0.623591i
$794$	35.6358	+	20.5743i	1.26467	+	0.730156i
$795$	3.00115	+	3.00115i	0.106440	+	0.106440i
$796$	−0.590716	−	0.341050i	−0.0209374	−	0.0120882i
$797$	−15.2784	+	26.4630i	−0.541189	+	0.937367i	0.457647	+	0.889134i	$0.348692\pi$
$797$	−15.2784	+	26.4630i	−0.541189	+	0.937367i	−0.998836	+	0.0482334i	$0.984641\pi$
$798$	−16.7867	−	6.54161i	−0.594244	−	0.231571i
$799$	−4.51362	+	1.20942i	−0.159681	+	0.0427863i
$800$	−1.12821	+	1.12821i	−0.0398881	+	0.0398881i
$801$	8.42347	−	2.25706i	0.297629	−	0.0797494i
$802$	−4.60285	−	7.97238i	−0.162532	−	0.281514i
$803$	0.281199	−	0.487050i	0.00992329	−	0.0171876i
$804$	−0.217187	+	0.810552i	−0.00765959	+	0.0285860i
$805$	−9.87471	−	7.25113i	−0.348038	−	0.255569i
$806$	10.5104	+	18.5381i	0.370212	+	0.652978i
$807$	12.9922	+	22.5032i	0.457349	+	0.792151i
$808$	22.6233	−	22.6233i	0.795885	−	0.795885i
$809$	26.7755			0.941376			0.470688	−	0.882300i	$-0.344006\pi$
$809$	26.7755			0.941376			0.470688	+	0.882300i	$0.344006\pi$
$810$	5.08053			0.178512
$811$	7.94016	−	7.94016i	0.278817	−	0.278817i	−0.553820	−	0.832637i	$-0.686830\pi$
$811$	7.94016	−	7.94016i	0.278817	−	0.278817i	0.832637	+	0.553820i	$0.186830\pi$
$812$	0.616411	+	0.240209i	0.0216318	+	0.00842968i
$813$	4.86800	+	18.1676i	0.170728	+	0.637167i
$814$	21.8876	+	5.86478i	0.767161	+	0.205560i
$815$	11.9708	−	6.91135i	0.419319	−	0.242094i
$816$			2.62456i			0.0918779i
$817$	12.8880	−	3.45332i	0.450893	−	0.120817i
$818$	3.32716			0.116331
$819$	−8.51298	+	1.23601i	−0.297468	+	0.0431897i
$820$	−0.157067			−0.00548500
$821$	−8.87838	+	2.37896i	−0.309858	+	0.0830261i	−0.410397	−	0.911907i	$-0.634610\pi$
$821$	−8.87838	+	2.37896i	−0.309858	+	0.0830261i	0.100539	+	0.994933i	$0.467943\pi$
$822$			26.5549i			0.926208i
$823$	−29.9975	+	17.3191i	−1.04565	+	0.603705i	−0.921428	−	0.388550i	$-0.872976\pi$
$823$	−29.9975	+	17.3191i	−1.04565	+	0.603705i	−0.124220	+	0.992255i	$0.539643\pi$
$824$	20.7184	+	5.55149i	0.721761	+	0.193395i
$825$	−8.23625	−	30.7381i	−0.286750	−	1.07016i
$826$	3.41782	+	22.3104i	0.118921	+	0.776278i
$827$	−18.6739	+	18.6739i	−0.649355	+	0.649355i	−0.952837	−	0.303482i	$-0.901851\pi$
$827$	−18.6739	+	18.6739i	−0.649355	+	0.649355i	0.303482	+	0.952837i	$0.401851\pi$
$828$	−0.388353			−0.0134962
$829$	32.6557			1.13418			0.567089	−	0.823656i	$-0.308069\pi$
$829$	32.6557			1.13418			0.567089	+	0.823656i	$0.308069\pi$
$830$	10.7117	−	10.7117i	0.371809	−	0.371809i
$831$	4.49977	+	7.79382i	0.156095	+	0.270365i
$832$	−0.232357	+	29.6804i	−0.00805552	+	1.02898i
$833$	2.41171	+	2.21618i	0.0835606	+	0.0767860i
$834$	8.98470	−	33.5313i	0.311115	−	1.16110i
$835$	−5.83217	+	10.1016i	−0.201831	+	0.349581i
$836$	−0.504027	−	0.873000i	−0.0174321	−	0.0301933i
$837$	−23.1774	+	6.21036i	−0.801128	+	0.214662i
$838$	−14.9805	+	14.9805i	−0.517493	+	0.517493i
$839$	38.6060	−	10.3444i	1.33283	−	0.357130i	0.479058	−	0.877783i	$-0.340978\pi$
$839$	38.6060	−	10.3444i	1.33283	−	0.357130i	0.853768	+	0.520654i	$0.174312\pi$
$840$	−4.58030	−	5.71518i	−0.158036	−	0.197192i
$841$	6.34638	−	10.9922i	0.218841	−	0.379043i
$842$	−25.5883	−	14.7734i	−0.881833	−	0.509126i
$843$	−2.50365	−	2.50365i	−0.0862303	−	0.0862303i
$844$	−1.23855	−	0.715080i	−0.0426328	−	0.0246141i
$845$	−8.32392	−	2.37067i	−0.286352	−	0.0815536i
$846$			12.5372i			0.431039i
$847$	−4.90519	−	32.0195i	−0.168544	−	1.10020i
$848$	8.52111	+	14.7590i	0.292616	+	0.506826i
$849$			26.0970i			0.895646i
$850$	−0.768236	−	2.86710i	−0.0263503	−	0.0983406i
$851$	6.07744	−	22.6813i	0.208332	−	0.777505i
$852$	0.210068	+	0.210068i	0.00719683	+	0.00719683i
$853$	−20.1071	−	20.1071i	−0.688454	−	0.688454i	0.273436	−	0.961890i	$-0.411840\pi$
$853$	−20.1071	−	20.1071i	−0.688454	−	0.688454i	−0.961890	+	0.273436i	$0.911840\pi$
$854$	−7.21356	−	16.4254i	−0.246843	−	0.562066i
$855$	−1.75568	+	1.01364i	−0.0600429	+	0.0346658i
$856$	3.08398	+	11.5096i	0.105408	+	0.393389i
$857$	−6.66400	+	11.5424i	−0.227638	+	0.394280i	−0.957108	−	0.289733i	$-0.906434\pi$
$857$	−6.66400	+	11.5424i	−0.227638	+	0.394280i	0.729470	+	0.684013i	$0.239767\pi$
$858$	−30.2193	−	17.7640i	−1.03167	−	0.606453i
$859$	−11.1463	+	6.43532i	−0.380307	+	0.219570i	−0.677952	−	0.735106i	$-0.737132\pi$
$859$	−11.1463	+	6.43532i	−0.380307	+	0.219570i	0.297645	+	0.954677i	$0.403799\pi$
$860$	0.157338	+	0.0421585i	0.00536517	+	0.00143759i
$861$	−1.59988	+	14.5140i	−0.0545239	+	0.494636i
$862$	−36.2193	−	20.9112i	−1.23364	−	0.712240i
$863$	−3.87766	+	14.4716i	−0.131997	+	0.492620i	−0.999992	−	0.00395268i	$-0.998742\pi$
$863$	−3.87766	+	14.4716i	−0.131997	+	0.492620i	0.867995	+	0.496573i	$0.165408\pi$
$864$	−1.91152	−	0.512191i	−0.0650313	−	0.0174251i
$865$	−3.80741	−	1.02019i	−0.129456	−	0.0346876i
$866$	5.58773	−	20.8537i	0.189879	−	0.708638i
$867$	−21.0512	−	12.1539i	−0.714938	−	0.412769i
$868$	0.560612	+	0.411665i	0.0190284	+	0.0139728i
$869$	−1.81543	−	0.486443i	−0.0615842	−	0.0165014i
$870$	4.69520	−	2.71078i	0.159182	−	0.0919040i
$871$	−23.6652	−	24.0386i	−0.801863	−	0.814517i
$872$	−8.82868	+	15.2917i	−0.298977	+	0.517843i
$873$	4.16052	+	15.5273i	0.140812	+	0.525518i
$874$	28.3155	−	16.3480i	0.957787	−	0.552978i
$875$	13.5684	+	9.96349i	0.458697	+	0.336827i
$876$	−0.00739838	−	0.00739838i	−0.000249968	−	0.000249968i
$877$	13.1631	+	13.1631i	0.444485	+	0.444485i	0.893516	−	0.449031i	$-0.148231\pi$
$877$	13.1631	+	13.1631i	0.444485	+	0.444485i	−0.449031	+	0.893516i	$0.648231\pi$
$878$	5.20076	−	19.4095i	0.175517	−	0.655038i
$879$	1.70075	+	6.34727i	0.0573647	+	0.214088i
$880$			12.4292i			0.418987i
$881$	4.17631	+	7.23358i	0.140703	+	0.243705i	0.927762	−	0.373173i	$-0.121730\pi$
$881$	4.17631	+	7.23358i	0.140703	+	0.243705i	−0.787058	+	0.616879i	$0.788397\pi$
$882$	7.41811	−	4.71118i	0.249781	−	0.158634i
$883$			44.6713i			1.50331i	0.659557	+	0.751655i	$0.270744\pi$
$883$			44.6713i			1.50331i	−0.659557	+	0.751655i	$0.729256\pi$
$884$	0.0900551	+	0.0529376i	0.00302888	+	0.00178049i
$885$	−5.11786	−	2.95480i	−0.172035	−	0.0993244i
$886$	12.2824	+	12.2824i	0.412637	+	0.412637i
$887$	1.68229	+	0.971270i	0.0564858	+	0.0326121i	0.527977	−	0.849259i	$-0.322951\pi$
$887$	1.68229	+	0.971270i	0.0564858	+	0.0326121i	−0.471491	+	0.881871i	$0.656284\pi$
$888$	7.01899	−	12.1572i	0.235542	−	0.407971i
$889$	41.1352	−	32.9669i	1.37963	−	1.10567i
$890$	−8.65777	+	2.31984i	−0.290209	+	0.0777613i
$891$	18.6869	−	18.6869i	0.626036	−	0.626036i
$892$	−0.221534	+	0.0593600i	−0.00741752	+	0.00198752i
$893$	16.8616	+	29.2051i	0.564251	+	0.977312i
$894$	3.79382	−	6.57108i	0.126884	−	0.219770i
$895$	−0.649644	+	2.42450i	−0.0217152	+	0.0810422i
$896$	−11.4472	−	26.0655i	−0.382424	−	0.870787i
$897$	−18.4081	+	31.3151i	−0.614630	+	1.04558i
$898$	−19.4972	−	33.7701i	−0.650628	−	1.12692i
$899$	−12.1229	+	12.1229i	−0.404323	+	0.404323i
$900$	0.254435			0.00848118
$901$	2.05926			0.0686038
$902$	18.0823	−	18.0823i	0.602075	−	0.602075i
$903$	5.49837	−	14.1096i	0.182974	−	0.469539i
$904$	−0.824563	−	3.07731i	−0.0274246	−	0.102350i
$905$	3.65847	+	0.980283i	0.121612	+	0.0325857i
$906$	−13.2040	+	7.62331i	−0.438672	+	0.253267i
$907$			52.0808i			1.72931i	0.502364	+	0.864656i	$0.332464\pi$
$907$			52.0808i			1.72931i	−0.502364	+	0.864656i	$0.667536\pi$
$908$	−1.44188	+	0.386352i	−0.0478506	+	0.0128215i
$909$	−10.0509			−0.333367
$910$	8.74977	−	1.27039i	0.290052	−	0.0421130i
$911$	−48.8065			−1.61703			−0.808516	−	0.588474i	$-0.799729\pi$
$911$	−48.8065			−1.61703			−0.808516	+	0.588474i	$0.799729\pi$
$912$	18.2956	−	4.90229i	0.605828	−	0.162331i
$913$		−	78.7985i		−	2.60785i
$914$	21.2373	−	12.2614i	0.702468	−	0.405570i
$915$	4.53701	+	1.21569i	0.149989	+	0.0401894i
$916$	0.298803	+	1.11515i	0.00987273	+	0.0368455i
$917$	15.7670	−	12.6361i	0.520671	−	0.417280i
$918$	2.60325	−	2.60325i	0.0859200	−	0.0859200i
$919$	7.45019			0.245759			0.122880	−	0.992422i	$-0.460787\pi$
$919$	7.45019			0.245759			0.122880	+	0.992422i	$0.460787\pi$
$920$	13.2918			0.438216
$921$	−16.7074	+	16.7074i	−0.550528	+	0.550528i
$922$	−3.75518	−	6.50415i	−0.123670	−	0.214203i
$923$	−11.5593	+	3.00051i	−0.380478	+	0.0987629i
$924$	−1.13719	−	0.125353i	−0.0374109	−	0.00412382i
$925$	−3.98173	+	14.8600i	−0.130918	+	0.488594i
$926$	−19.1750	+	33.2120i	−0.630128	+	1.09141i
$927$	−3.36912	−	5.83549i	−0.110656	−	0.191663i
$928$	−1.36578	+	0.365960i	−0.0448340	+	0.0120132i
$929$	10.5757	−	10.5757i	0.346976	−	0.346976i	−0.512006	−	0.858982i	$-0.671097\pi$
$929$	10.5757	−	10.5757i	0.346976	−	0.346976i	0.858982	+	0.512006i	$0.171097\pi$
$930$	5.50567	−	1.47524i	0.180538	−	0.0483750i
$931$	10.9441	−	20.9513i	0.358678	−	0.686652i
$932$	−0.140021	+	0.242523i	−0.00458653	+	0.00794410i
$933$	13.6093	+	7.85733i	0.445548	+	0.257238i
$934$	−9.44639	−	9.44639i	−0.309095	−	0.309095i
$935$	1.30064	+	0.750925i	0.0425355	+	0.0245579i
$936$	6.65087	−	6.54755i	0.217391	−	0.214013i
$937$			0.823290i			0.0268957i	0.999910	+	0.0134479i	$0.00428071\pi$
$937$			0.823290i			0.0268957i	−0.999910	+	0.0134479i	$0.995719\pi$
$938$	32.1081	+	12.5122i	1.04837	+	0.408537i
$939$	5.20525	+	9.01576i	0.169867	+	0.294218i
$940$			0.411695i			0.0134280i
$941$	−6.45688	−	24.0974i	−0.210488	−	0.785553i	−0.987706	−	0.156321i	$-0.950036\pi$
$941$	−6.45688	−	24.0974i	−0.210488	−	0.785553i	0.777218	−	0.629231i	$-0.216630\pi$
$942$	−12.8597	+	47.9931i	−0.418992	+	1.56370i
$943$	−18.7380	−	18.7380i	−0.610193	−	0.610193i
$944$	−16.7790	−	16.7790i	−0.546111	−	0.546111i
$945$	−1.09078	+	9.89543i	−0.0354830	+	0.321898i
$946$	−22.9670	+	13.2600i	−0.746722	+	0.431120i
$947$	3.19280	+	11.9157i	0.103752	+	0.387207i	0.998201	−	0.0599632i	$-0.0190983\pi$
$947$	3.19280	+	11.9157i	0.103752	+	0.387207i	−0.894449	+	0.447171i	$0.852432\pi$
$948$	−0.0174829	+	0.0302813i	−0.000567819	+	0.000983491i
$949$	0.407104	−	0.105675i	0.0132152	−	0.00343034i
$950$	−18.5514	+	10.7106i	−0.601886	+	0.347499i
$951$	13.2494	+	3.55016i	0.429640	+	0.115122i
$952$	−3.53216	−	0.389351i	−0.114478	−	0.0126190i
$953$	−17.9140	−	10.3426i	−0.580291	−	0.335031i	0.180958	−	0.983491i	$-0.442080\pi$
$953$	−17.9140	−	10.3426i	−0.580291	−	0.335031i	−0.761249	+	0.648460i	$0.775414\pi$
$954$	1.42997	−	5.33673i	0.0462970	−	0.172783i
$955$	5.89551	+	1.57970i	0.190774	+	0.0511178i
$956$	0.944026	+	0.252951i	0.0305320	+	0.00818102i
$957$	7.29901	−	27.2403i	0.235943	−	0.880553i
$958$	−37.3132	−	21.5428i	−1.20553	−	0.696016i
$959$	−34.6304	−	3.81732i	−1.11827	−	0.123268i
$960$	7.66836	+	2.05473i	0.247495	+	0.0663161i
$961$	11.2370	−	6.48771i	0.362485	−	0.209281i
$962$	8.35804	+	14.7419i	0.269474	+	0.475297i
$963$	1.87163	−	3.24175i	0.0603123	−	0.104464i
$964$	0.121291	+	0.452665i	0.00390653	+	0.0145794i
$965$	14.6514	−	8.45899i	0.471645	−	0.272304i
$966$	4.06580	−	36.8846i	0.130815	−	1.18674i
$967$	6.39351	+	6.39351i	0.205601	+	0.205601i	0.802395	−	0.596793i	$-0.203559\pi$
$967$	6.39351	+	6.39351i	0.205601	+	0.205601i	−0.596793	+	0.802395i	$0.703559\pi$
$968$	24.8511	+	24.8511i	0.798743	+	0.798743i
$969$	0.592357	−	2.21071i	0.0190292	−	0.0710181i
$970$	−4.27624	−	15.9592i	−0.137302	−	0.512418i
$971$		−	17.2714i		−	0.554265i	−0.960832	−	0.277133i	$-0.910616\pi$
$971$		−	17.2714i		−	0.554265i	0.960832	−	0.277133i	$-0.0893841\pi$
$972$	0.279112	+	0.483437i	0.00895253	+	0.0155062i
$973$	42.4369	+	16.5372i	1.36046	+	0.530158i
$974$		−	7.79056i		−	0.249626i
$975$	12.0604	−	20.5166i	0.386242	−	0.657057i
$976$	16.3336	+	9.43018i	0.522824	+	0.301853i
$977$	−38.2614	−	38.2614i	−1.22409	−	1.22409i	−0.966165	−	0.257924i	$-0.916961\pi$
$977$	−38.2614	−	38.2614i	−1.22409	−	1.22409i	−0.257924	−	0.966165i	$-0.583039\pi$
$978$	36.2591	+	20.9342i	1.15944	+	0.669401i
$979$	−23.3118	+	40.3773i	−0.745049	+	1.29046i
$980$	0.243594	−	0.154705i	0.00778133	−	0.00494186i
$981$	5.35800	−	1.43567i	0.171068	−	0.0458375i
$982$	13.6531	−	13.6531i	0.435688	−	0.435688i
$983$	36.2359	−	9.70939i	1.15575	−	0.309681i	0.370481	−	0.928840i	$-0.379193\pi$
$983$	36.2359	−	9.70939i	1.15575	−	0.309681i	0.785266	+	0.619159i	$0.212526\pi$
$984$	−7.92115	−	13.7198i	−0.252517	−	0.437372i
$985$	0.477984	−	0.827893i	0.0152298	−	0.0263789i
$986$	0.680815	−	2.54083i	0.0216816	−	0.0809167i
$987$	38.0434	+	4.19354i	1.21093	+	0.133482i
$988$	0.200815	−	0.726648i	0.00638876	−	0.0231177i
$989$	13.7408	+	23.7998i	0.436933	+	0.756790i
$990$	2.84926	−	2.84926i	0.0905554	−	0.0905554i
$991$	34.8540			1.10717			0.553587	−	0.832791i	$-0.313259\pi$
$991$	34.8540			1.10717			0.553587	+	0.832791i	$0.313259\pi$
$992$	−1.48655			−0.0471981
$993$	6.07784	−	6.07784i	0.192874	−	0.192874i
$994$	9.51981	−	7.62944i	0.301950	−	0.241991i
$995$	−1.89816	−	7.08404i	−0.0601758	−	0.224579i
$996$	−1.41602	−	0.379422i	−0.0448683	−	0.0120224i
$997$	13.1836	−	7.61153i	0.417528	−	0.241060i	−0.276491	−	0.961016i	$-0.589172\pi$
$997$	13.1836	−	7.61153i	0.417528	−	0.241060i	0.694019	+	0.719957i	$0.255838\pi$
$998$			12.7286i			0.402917i
$999$	−18.4311	+	4.93860i	−0.583134	+	0.156250i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.2.w.a.24.6	yes	28
3.2	odd	2		819.2.gh.b.388.2		28
7.2	even	3		637.2.bb.a.362.2		28
7.3	odd	6		637.2.bd.b.440.2		28
7.4	even	3		637.2.bd.a.440.2		28
7.5	odd	6		91.2.ba.a.89.2	yes	28
7.6	odd	2		637.2.x.a.570.6		28
13.6	odd	12		91.2.ba.a.45.2	yes	28
21.5	even	6		819.2.et.b.271.6		28
39.32	even	12		819.2.et.b.136.6		28
91.6	even	12		637.2.bb.a.227.2		28
91.19	even	12	inner	91.2.w.a.19.6	✓	28
91.32	odd	12		637.2.bd.b.97.2		28
91.45	even	12		637.2.bd.a.97.2		28
91.58	odd	12		637.2.x.a.19.6		28
273.110	odd	12		819.2.gh.b.19.2		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.19.6	✓	28	91.19	even	12	inner
91.2.w.a.24.6	yes	28	1.1	even	1	trivial
91.2.ba.a.45.2	yes	28	13.6	odd	12
91.2.ba.a.89.2	yes	28	7.5	odd	6
637.2.x.a.19.6		28	91.58	odd	12
637.2.x.a.570.6		28	7.6	odd	2
637.2.bb.a.227.2		28	91.6	even	12
637.2.bb.a.362.2		28	7.2	even	3
637.2.bd.a.97.2		28	91.45	even	12
637.2.bd.a.440.2		28	7.4	even	3
637.2.bd.b.97.2		28	91.32	odd	12
637.2.bd.b.440.2		28	7.3	odd	6
819.2.et.b.136.6		28	39.32	even	12
819.2.et.b.271.6		28	21.5	even	6
819.2.gh.b.19.2		28	273.110	odd	12
819.2.gh.b.388.2		28	3.2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34471 - 0.360315i) q^{2} -1.44853i q^{3} +(-0.0536242 + 0.0309600i) q^{4} +(-0.643078 - 0.172312i) q^{5} +(-0.521927 - 1.94786i) q^{6} +(2.61524 - 0.400640i) q^{7} +(-2.02975 + 2.02975i) q^{8} +0.901760 q^{9} +O(q^{10})\)	\(q+(1.34471 - 0.360315i) q^{2} -1.44853i q^{3} +(-0.0536242 + 0.0309600i) q^{4} +(-0.643078 - 0.172312i) q^{5} +(-0.521927 - 1.94786i) q^{6} +(2.61524 - 0.400640i) q^{7} +(-2.02975 + 2.02975i) q^{8} +0.901760 q^{9} -0.926843 q^{10} +(-3.40906 + 3.40906i) q^{11} +(0.0448464 + 0.0776763i) q^{12} +(-3.60544 - 0.0282257i) q^{13} +(3.37239 - 1.48106i) q^{14} +(-0.249600 + 0.931519i) q^{15} +(-1.93616 + 3.35353i) q^{16} +(0.233952 + 0.405217i) q^{17} +(1.21261 - 0.324918i) q^{18} +(2.38775 - 2.38775i) q^{19} +(0.0398194 - 0.0106696i) q^{20} +(-0.580338 - 3.78826i) q^{21} +(-3.35587 + 5.81255i) q^{22} +(6.02331 + 3.47756i) q^{23} +(2.94015 + 2.94015i) q^{24} +(-3.94627 - 2.27838i) q^{25} +(-4.85845 + 1.26114i) q^{26} -5.65182i q^{27} +(-0.127837 + 0.102452i) q^{28} +(-2.01911 - 3.49720i) q^{29} +1.34256i q^{30} +(-1.09883 - 4.10087i) q^{31} +(0.0906241 - 0.338214i) q^{32} +(4.93813 + 4.93813i) q^{33} +(0.460604 + 0.460604i) q^{34} +(-1.75084 - 0.192996i) q^{35} +(-0.0483562 + 0.0279185i) q^{36} +(-0.873807 - 3.26109i) q^{37} +(2.35049 - 4.07117i) q^{38} +(-0.0408858 + 5.22259i) q^{39} +(1.65504 - 0.955538i) q^{40} +(-3.68025 - 0.986119i) q^{41} +(-2.14535 - 4.88501i) q^{42} +(3.42191 + 1.97564i) q^{43} +(0.0772639 - 0.288353i) q^{44} +(-0.579902 - 0.155384i) q^{45} +(9.35265 + 2.50603i) q^{46} +(-2.58477 + 9.64648i) q^{47} +(4.85769 + 2.80459i) q^{48} +(6.67898 - 2.09554i) q^{49} +(-6.12753 - 1.64187i) q^{50} +(0.586968 - 0.338886i) q^{51} +(0.194213 - 0.110111i) q^{52} +(2.20051 - 3.81140i) q^{53} +(-2.03643 - 7.60007i) q^{54} +(2.77972 - 1.60487i) q^{55} +(-4.49509 + 6.12149i) q^{56} +(-3.45872 - 3.45872i) q^{57} +(-3.97522 - 3.97522i) q^{58} +(-1.58601 + 5.91907i) q^{59} +(-0.0154552 - 0.0576796i) q^{60} -4.87055i q^{61} +(-2.95521 - 5.11858i) q^{62} +(2.35832 - 0.361281i) q^{63} -8.23211i q^{64} +(2.31372 + 0.639413i) q^{65} +(8.41965 + 4.86109i) q^{66} +(6.61552 + 6.61552i) q^{67} +(-0.0250910 - 0.0144863i) q^{68} +(5.03735 - 8.72495i) q^{69} +(-2.42392 + 0.371330i) q^{70} +(3.19935 - 0.857263i) q^{71} +(-1.83035 + 1.83035i) q^{72} +(-0.112678 + 0.0301918i) q^{73} +(-2.35004 - 4.07039i) q^{74} +(-3.30030 + 5.71629i) q^{75} +(-0.0541165 + 0.201966i) q^{76} +(-7.54972 + 10.2813i) q^{77} +(1.82680 + 7.03762i) q^{78} +(0.194920 + 0.337611i) q^{79} +(1.82296 - 1.82296i) q^{80} -5.48155 q^{81} -5.30419 q^{82} +(-11.5572 + 11.5572i) q^{83} +(0.148404 + 0.185175i) q^{84} +(-0.0806256 - 0.300899i) q^{85} +(5.31334 + 1.42371i) q^{86} +(-5.06581 + 2.92474i) q^{87} -13.8391i q^{88} +(9.34114 - 2.50295i) q^{89} -0.835790 q^{90} +(-9.44041 + 1.37067i) q^{91} -0.430661 q^{92} +(-5.94024 + 1.59168i) q^{93} +13.9031i q^{94} +(-1.94695 + 1.12407i) q^{95} +(-0.489913 - 0.131272i) q^{96} +(4.61378 + 17.2188i) q^{97} +(8.22625 - 5.22443i) q^{98} +(-3.07416 + 3.07416i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} - 6 q^{4} - 6 q^{5} + 12 q^{6} + 2 q^{7} - 4 q^{8} - 12 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 - 6 * q^4 - 6 * q^5 + 12 * q^6 + 2 * q^7 - 4 * q^8 - 12 * q^9	\( 28 q - 2 q^{2} - 6 q^{4} - 6 q^{5} + 12 q^{6} + 2 q^{7} - 4 q^{8} - 12 q^{9} - 12 q^{10} + 2 q^{11} + 8 q^{12} - 20 q^{14} + 10 q^{15} - 2 q^{16} - 6 q^{17} - 4 q^{18} - 8 q^{19} - 36 q^{20} - 2 q^{21} - 8 q^{22} - 6 q^{23} + 12 q^{24} + 24 q^{26} - 18 q^{28} - 8 q^{29} - 38 q^{31} - 20 q^{32} + 18 q^{33} + 12 q^{34} - 2 q^{35} + 54 q^{36} - 16 q^{37} + 28 q^{39} + 48 q^{40} + 18 q^{41} - 4 q^{42} + 48 q^{43} - 6 q^{44} + 12 q^{45} + 18 q^{46} - 42 q^{47} + 12 q^{48} + 8 q^{49} + 10 q^{50} + 12 q^{51} - 28 q^{52} + 12 q^{53} - 30 q^{54} - 6 q^{55} - 24 q^{56} + 12 q^{57} + 62 q^{58} - 6 q^{59} + 16 q^{60} - 36 q^{62} - 38 q^{63} - 2 q^{65} + 66 q^{66} - 4 q^{67} + 30 q^{68} + 42 q^{69} + 68 q^{70} - 42 q^{71} - 38 q^{72} + 14 q^{73} - 6 q^{74} - 20 q^{75} + 52 q^{76} - 62 q^{78} + 4 q^{79} + 12 q^{80} + 12 q^{81} - 108 q^{82} - 66 q^{83} - 56 q^{84} - 54 q^{85} - 30 q^{86} + 42 q^{87} - 30 q^{89} - 72 q^{90} - 42 q^{91} - 156 q^{92} + 14 q^{93} - 6 q^{95} + 18 q^{96} + 62 q^{97} + 112 q^{98} - 36 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 - 6 * q^4 - 6 * q^5 + 12 * q^6 + 2 * q^7 - 4 * q^8 - 12 * q^9 - 12 * q^10 + 2 * q^11 + 8 * q^12 - 20 * q^14 + 10 * q^15 - 2 * q^16 - 6 * q^17 - 4 * q^18 - 8 * q^19 - 36 * q^20 - 2 * q^21 - 8 * q^22 - 6 * q^23 + 12 * q^24 + 24 * q^26 - 18 * q^28 - 8 * q^29 - 38 * q^31 - 20 * q^32 + 18 * q^33 + 12 * q^34 - 2 * q^35 + 54 * q^36 - 16 * q^37 + 28 * q^39 + 48 * q^40 + 18 * q^41 - 4 * q^42 + 48 * q^43 - 6 * q^44 + 12 * q^45 + 18 * q^46 - 42 * q^47 + 12 * q^48 + 8 * q^49 + 10 * q^50 + 12 * q^51 - 28 * q^52 + 12 * q^53 - 30 * q^54 - 6 * q^55 - 24 * q^56 + 12 * q^57 + 62 * q^58 - 6 * q^59 + 16 * q^60 - 36 * q^62 - 38 * q^63 - 2 * q^65 + 66 * q^66 - 4 * q^67 + 30 * q^68 + 42 * q^69 + 68 * q^70 - 42 * q^71 - 38 * q^72 + 14 * q^73 - 6 * q^74 - 20 * q^75 + 52 * q^76 - 62 * q^78 + 4 * q^79 + 12 * q^80 + 12 * q^81 - 108 * q^82 - 66 * q^83 - 56 * q^84 - 54 * q^85 - 30 * q^86 + 42 * q^87 - 30 * q^89 - 72 * q^90 - 42 * q^91 - 156 * q^92 + 14 * q^93 - 6 * q^95 + 18 * q^96 + 62 * q^97 + 112 * q^98 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more