LMFDB - Embedded newform 288.2.bf.a.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(11,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 15, 4]))

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

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

chi := DirichletCharacter("288.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bf (of order $24$, degree $8$, 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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			11.1
Character	$\chi$	$=$	288.11
Dual form			288.2.bf.a.131.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41395 + 0.0275526i) q^{2} +(1.72268 - 0.179925i) q^{3} +(1.99848 - 0.0779158i) q^{4} +(-0.211536 - 1.60678i) q^{5} +(-2.43082 + 0.301868i) q^{6} +(0.419720 + 1.56642i) q^{7} +(-2.82360 + 0.165232i) q^{8} +(2.93525 - 0.619906i) q^{9} +O(q^{10})$	\(q+(-1.41395 + 0.0275526i) q^{2} +(1.72268 - 0.179925i) q^{3} +(1.99848 - 0.0779158i) q^{4} +(-0.211536 - 1.60678i) q^{5} +(-2.43082 + 0.301868i) q^{6} +(0.419720 + 1.56642i) q^{7} +(-2.82360 + 0.165232i) q^{8} +(2.93525 - 0.619906i) q^{9} +(0.343371 + 2.26607i) q^{10} +(4.18881 - 3.21419i) q^{11} +(3.42873 - 0.493801i) q^{12} +(-1.19629 + 1.55903i) q^{13} +(-0.636620 - 2.20326i) q^{14} +(-0.653508 - 2.72990i) q^{15} +(3.98786 - 0.311427i) q^{16} -3.66990 q^{17} +(-4.13321 + 0.957388i) q^{18} +(0.398863 - 0.165215i) q^{19} +(-0.547944 - 3.19463i) q^{20} +(1.00488 + 2.62291i) q^{21} +(-5.83419 + 4.66009i) q^{22} +(-3.12920 - 0.838465i) q^{23} +(-4.83442 + 0.792678i) q^{24} +(2.29265 - 0.614312i) q^{25} +(1.64853 - 2.23735i) q^{26} +(4.94497 - 1.59603i) q^{27} +(0.960851 + 3.09775i) q^{28} +(6.15042 + 0.809718i) q^{29} +(0.999241 + 3.84193i) q^{30} +(-1.59271 + 0.919554i) q^{31} +(-5.63003 + 0.550216i) q^{32} +(6.63766 - 6.29068i) q^{33} +(5.18904 - 0.101115i) q^{34} +(2.42809 - 1.00575i) q^{35} +(5.81775 - 1.46757i) q^{36} +(1.24490 - 3.00545i) q^{37} +(-0.559419 + 0.244594i) q^{38} +(-1.78031 + 2.90096i) q^{39} +(0.862784 + 4.50194i) q^{40} +(-1.46182 + 5.45559i) q^{41} +(-1.49311 - 3.68097i) q^{42} +(-3.53572 - 4.60784i) q^{43} +(8.12082 - 6.74987i) q^{44} +(-1.61696 - 4.58517i) q^{45} +(4.44761 + 1.09933i) q^{46} +(2.19382 + 1.26660i) q^{47} +(6.81377 - 1.25400i) q^{48} +(3.78468 - 2.18509i) q^{49} +(-3.22475 + 0.931773i) q^{50} +(-6.32206 + 0.660307i) q^{51} +(-2.26929 + 3.20891i) q^{52} +(-4.87033 + 11.7580i) q^{53} +(-6.94794 + 2.39294i) q^{54} +(-6.05056 - 6.05056i) q^{55} +(-1.44394 - 4.35357i) q^{56} +(0.657388 - 0.356377i) q^{57} +(-8.71866 - 0.975436i) q^{58} +(-9.75004 + 1.28362i) q^{59} +(-1.51873 - 5.40474i) q^{60} +(-1.45961 + 11.0868i) q^{61} +(2.22667 - 1.34408i) q^{62} +(2.20302 + 4.33764i) q^{63} +(7.94540 - 0.933098i) q^{64} +(2.75808 + 1.59238i) q^{65} +(-9.21197 + 9.07757i) q^{66} +(-0.643049 + 0.838037i) q^{67} +(-7.33423 + 0.285943i) q^{68} +(-5.54146 - 0.881387i) q^{69} +(-3.40548 + 1.48897i) q^{70} +(-11.7013 - 11.7013i) q^{71} +(-8.18555 + 2.23536i) q^{72} +(-9.39064 + 9.39064i) q^{73} +(-1.67741 + 4.28384i) q^{74} +(3.83896 - 1.47077i) q^{75} +(0.784248 - 0.361256i) q^{76} +(6.79288 + 5.21236i) q^{77} +(2.43734 - 4.15085i) q^{78} +(-1.60835 + 2.78574i) q^{79} +(-1.34397 - 6.34172i) q^{80} +(8.23143 - 3.63917i) q^{81} +(1.91662 - 7.75418i) q^{82} +(1.65688 + 0.218132i) q^{83} +(2.21260 + 5.16355i) q^{84} +(0.776316 + 5.89671i) q^{85} +(5.12628 + 6.41782i) q^{86} +(10.7409 + 0.288271i) q^{87} +(-11.2964 + 9.76769i) q^{88} +(-8.98232 + 8.98232i) q^{89} +(2.41263 + 6.43862i) q^{90} +(-2.94420 - 1.21953i) q^{91} +(-6.31897 - 1.43184i) q^{92} +(-2.57829 + 1.87067i) q^{93} +(-3.13684 - 1.73046i) q^{94} +(-0.349837 - 0.605936i) q^{95} +(-9.59975 + 1.96083i) q^{96} +(5.58932 - 9.68098i) q^{97} +(-5.29113 + 3.19387i) q^{98} +(10.3027 - 12.0311i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.41395	+	0.0275526i	−0.999810	+	0.0194827i
$2$	−1.41395	+	0.0275526i	−0.999810	+	0.0194827i
$3$	1.72268	−	0.179925i	0.994590	−	0.103880i
$3$	1.72268	−	0.179925i	0.994590	−	0.103880i
$4$	1.99848	−	0.0779158i	0.999241	−	0.0389579i
$5$	−0.211536	−	1.60678i	−0.0946018	−	0.718572i	−0.971355	−	0.237632i	$-0.923629\pi$
$5$	−0.211536	−	1.60678i	−0.0946018	−	0.718572i	0.876753	−	0.480940i	$-0.159705\pi$
$6$	−2.43082	+	0.301868i	−0.992377	+	0.123237i
$7$	0.419720	+	1.56642i	0.158639	+	0.592049i	0.998766	+	0.0496597i	$0.0158137\pi$
$7$	0.419720	+	1.56642i	0.158639	+	0.592049i	−0.840127	+	0.542390i	$0.817520\pi$
$8$	−2.82360	+	0.165232i	−0.998292	+	0.0584184i
$9$	2.93525	−	0.619906i	0.978418	−	0.206635i
$10$	0.343371	+	2.26607i	0.108584	+	0.716593i
$11$	4.18881	−	3.21419i	1.26297	−	0.969113i	0.262982	−	0.964801i	$-0.415294\pi$
$11$	4.18881	−	3.21419i	1.26297	−	0.969113i	0.999991	−	0.00431272i	$-0.00137279\pi$
$12$	3.42873	−	0.493801i	0.989788	−	0.142548i
$13$	−1.19629	+	1.55903i	−0.331791	+	0.432398i	−0.929222	−	0.369522i	$-0.879521\pi$
$13$	−1.19629	+	1.55903i	−0.331791	+	0.432398i	0.597431	+	0.801920i	$0.296188\pi$
$14$	−0.636620	−	2.20326i	−0.170144	−	0.588846i
$15$	−0.653508	−	2.72990i	−0.168735	−	0.704858i
$16$	3.98786	−	0.311427i	0.996965	−	0.0778567i
$17$	−3.66990			−0.890081			−0.445041	−	0.895510i	$-0.646811\pi$
$17$	−3.66990			−0.890081			−0.445041	+	0.895510i	$0.646811\pi$
$18$	−4.13321	+	0.957388i	−0.974206	+	0.225658i
$19$	0.398863	−	0.165215i	0.0915055	−	0.0379028i	−0.336461	−	0.941697i	$-0.609230\pi$
$19$	0.398863	−	0.165215i	0.0915055	−	0.0379028i	0.427967	+	0.903795i	$0.359230\pi$
$20$	−0.547944	−	3.19463i	−0.122524	−	0.714341i
$21$	1.00488	+	2.62291i	0.219283	+	0.572367i
$22$	−5.83419	+	4.66009i	−1.24385	+	0.993535i
$23$	−3.12920	−	0.838465i	−0.652482	−	0.174832i	−0.0826313	−	0.996580i	$-0.526332\pi$
$23$	−3.12920	−	0.838465i	−0.652482	−	0.174832i	−0.569851	+	0.821748i	$0.692999\pi$
$24$	−4.83442	+	0.792678i	−0.986823	+	0.161805i
$25$	2.29265	−	0.614312i	0.458529	−	0.122862i
$26$	1.64853	−	2.23735i	0.323303	−	0.438780i
$27$	4.94497	−	1.59603i	0.951659	−	0.307155i
$28$	0.960851	+	3.09775i	0.181584	+	0.585420i
$29$	6.15042	+	0.809718i	1.14210	+	0.150361i	0.677752	−	0.735290i	$-0.262954\pi$
$29$	6.15042	+	0.809718i	1.14210	+	0.150361i	0.464351	+	0.885651i	$0.346287\pi$
$30$	0.999241	+	3.84193i	0.182436	+	0.701436i
$31$	−1.59271	+	0.919554i	−0.286060	+	0.165157i	−0.636164	−	0.771554i	$-0.719480\pi$
$31$	−1.59271	+	0.919554i	−0.286060	+	0.165157i	0.350104	+	0.936711i	$0.386146\pi$
$32$	−5.63003	+	0.550216i	−0.995258	+	0.0972654i
$33$	6.63766	−	6.29068i	1.15547	−	1.09507i
$34$	5.18904	−	0.101115i	0.889912	−	0.0173411i
$35$	2.42809	−	1.00575i	0.410423	−	0.170003i
$36$	5.81775	−	1.46757i	0.969625	−	0.244596i
$37$	1.24490	−	3.00545i	0.204660	−	0.494093i	−0.787907	−	0.615795i	$-0.788835\pi$
$37$	1.24490	−	3.00545i	0.204660	−	0.494093i	0.992567	+	0.121702i	$0.0388351\pi$
$38$	−0.559419	+	0.244594i	−0.0907497	+	0.0396784i
$39$	−1.78031	+	2.90096i	−0.285078	+	0.464525i
$40$	0.862784	+	4.50194i	0.136418	+	0.711819i
$41$	−1.46182	+	5.45559i	−0.228298	+	0.852019i	0.752758	+	0.658297i	$0.228723\pi$
$41$	−1.46182	+	5.45559i	−0.228298	+	0.852019i	−0.981056	+	0.193723i	$0.937944\pi$
$42$	−1.49311	−	3.68097i	−0.230392	−	0.567986i
$43$	−3.53572	−	4.60784i	−0.539193	−	0.702690i	0.441717	−	0.897155i	$-0.354370\pi$
$43$	−3.53572	−	4.60784i	−0.539193	−	0.702690i	−0.980909	+	0.194465i	$0.937703\pi$
$44$	8.12082	−	6.74987i	1.22426	−	1.01758i
$45$	−1.61696	−	4.58517i	−0.241043	−	0.683516i
$46$	4.44761	+	1.09933i	0.655765	+	0.162087i
$47$	2.19382	+	1.26660i	0.320002	+	0.184753i	0.651393	−	0.758740i	$-0.274185\pi$
$47$	2.19382	+	1.26660i	0.320002	+	0.184753i	−0.331392	+	0.943493i	$0.607518\pi$
$48$	6.81377	−	1.25400i	0.983483	−	0.181000i
$49$	3.78468	−	2.18509i	0.540669	−	0.312156i
$50$	−3.22475	+	0.931773i	−0.456048	+	0.131773i
$51$	−6.32206	+	0.660307i	−0.885266	+	0.0924614i
$52$	−2.26929	+	3.20891i	−0.314693	+	0.444996i
$53$	−4.87033	+	11.7580i	−0.668992	+	1.61509i	0.114308	+	0.993445i	$0.463535\pi$
$53$	−4.87033	+	11.7580i	−0.668992	+	1.61509i	−0.783300	+	0.621644i	$0.786465\pi$
$54$	−6.94794	+	2.39294i	−0.945495	+	0.325638i
$55$	−6.05056	−	6.05056i	−0.815858	−	0.815858i
$56$	−1.44394	−	4.35357i	−0.192955	−	0.581771i
$57$	0.657388	−	0.356377i	0.0870732	−	0.0472034i
$58$	−8.71866	−	0.975436i	−1.14482	−	0.128081i
$59$	−9.75004	+	1.28362i	−1.26935	+	0.167113i	−0.734951	−	0.678121i	$-0.762795\pi$
$59$	−9.75004	+	1.28362i	−1.26935	+	0.167113i	−0.534397	+	0.845234i	$0.679461\pi$
$60$	−1.51873	−	5.40474i	−0.196067	−	0.697749i
$61$	−1.45961	+	11.0868i	−0.186884	+	1.41952i	0.598802	+	0.800897i	$0.295643\pi$
$61$	−1.45961	+	11.0868i	−0.186884	+	1.41952i	−0.785686	+	0.618625i	$0.787690\pi$
$62$	2.22667	−	1.34408i	0.282788	−	0.170699i
$63$	2.20302	+	4.33764i	0.277554	+	0.546491i
$64$	7.94540	−	0.933098i	0.993175	−	0.116637i
$65$	2.75808	+	1.59238i	0.342097	+	0.197510i
$66$	−9.21197	+	9.07757i	−1.13391	+	1.11737i
$67$	−0.643049	+	0.838037i	−0.0785609	+	0.102383i	−0.830981	−	0.556302i	$-0.812220\pi$
$67$	−0.643049	+	0.838037i	−0.0785609	+	0.102383i	0.752420	+	0.658684i	$0.228887\pi$
$68$	−7.33423	+	0.285943i	−0.889406	+	0.0346757i
$69$	−5.54146	−	0.881387i	−0.667114	−	0.106107i
$70$	−3.40548	+	1.48897i	−0.407033	+	0.177967i
$71$	−11.7013	−	11.7013i	−1.38869	−	1.38869i	−0.828081	−	0.560608i	$-0.810568\pi$
$71$	−11.7013	−	11.7013i	−1.38869	−	1.38869i	−0.560608	−	0.828081i	$-0.689432\pi$
$72$	−8.18555	+	2.23536i	−0.964676	+	0.263440i
$73$	−9.39064	+	9.39064i	−1.09909	+	1.09909i	−0.104575	+	0.994517i	$0.533348\pi$
$73$	−9.39064	+	9.39064i	−1.09909	+	1.09909i	−0.994517	+	0.104575i	$0.966652\pi$
$74$	−1.67741	+	4.28384i	−0.194995	+	0.497986i
$75$	3.83896	−	1.47077i	0.443285	−	0.169830i
$76$	0.784248	−	0.361256i	0.0899595	−	0.0414389i
$77$	6.79288	+	5.21236i	0.774120	+	0.594003i
$78$	2.43734	−	4.15085i	0.275974	−	0.469991i
$79$	−1.60835	+	2.78574i	−0.180953	+	0.313420i	−0.942205	−	0.335036i	$-0.891252\pi$
$79$	−1.60835	+	2.78574i	−0.180953	+	0.313420i	0.761252	+	0.648456i	$0.224585\pi$
$80$	−1.34397	−	6.34172i	−0.150260	−	0.709026i
$81$	8.23143	−	3.63917i	0.914604	−	0.404352i
$82$	1.91662	−	7.75418i	0.211655	−	0.856306i
$83$	1.65688	+	0.218132i	0.181866	+	0.0239431i	0.220909	−	0.975294i	$-0.429098\pi$
$83$	1.65688	+	0.218132i	0.181866	+	0.0239431i	−0.0390431	+	0.999238i	$0.512431\pi$
$84$	2.21260	+	5.16355i	0.241415	+	0.563390i
$85$	0.776316	+	5.89671i	0.0842033	+	0.639588i
$86$	5.12628	+	6.41782i	0.552781	+	0.692051i
$87$	10.7409	+	0.288271i	1.15154	+	0.0309059i
$88$	−11.2964	+	9.76769i	−1.20420	+	1.04124i
$89$	−8.98232	+	8.98232i	−0.952124	+	0.952124i	−0.998905	−	0.0467811i	$-0.985104\pi$
$89$	−8.98232	+	8.98232i	−0.952124	+	0.952124i	0.0467811	+	0.998905i	$0.485104\pi$
$90$	2.41263	+	6.43862i	0.254314	+	0.678690i
$91$	−2.94420	−	1.21953i	−0.308636	−	0.127841i
$92$	−6.31897	−	1.43184i	−0.658798	−	0.149280i
$93$	−2.57829	+	1.87067i	−0.267356	+	0.193979i
$94$	−3.13684	−	1.73046i	−0.323540	−	0.178483i
$95$	−0.349837	−	0.605936i	−0.0358925	−	0.0621677i
$96$	−9.59975	+	1.96083i	−0.979770	+	0.200126i
$97$	5.58932	−	9.68098i	0.567509	−	0.982955i	−0.429302	−	0.903161i	$-0.641240\pi$
$97$	5.58932	−	9.68098i	0.567509	−	0.982955i	0.996811	−	0.0797940i	$-0.0254262\pi$
$98$	−5.29113	+	3.19387i	−0.534485	+	0.322630i
$99$	10.3027	−	12.0311i	1.03546	−	1.20917i
$100$	4.53395	−	1.40633i	0.453395	−	0.140633i
$101$	−11.0687	+	8.49335i	−1.10138	+	0.845120i	−0.988907	−	0.148535i	$-0.952544\pi$
$101$	−11.0687	+	8.49335i	−1.10138	+	0.845120i	−0.112474	+	0.993655i	$0.535878\pi$
$102$	8.92086	−	1.10783i	0.883296	−	0.109691i
$103$	−18.4054	−	4.93172i	−1.81354	−	0.485937i	−0.817586	−	0.575806i	$-0.804688\pi$
$103$	−18.4054	−	4.93172i	−1.81354	−	0.485937i	−0.995954	+	0.0898695i	$0.971355\pi$
$104$	3.12023	−	4.59975i	0.305964	−	0.451042i
$105$	4.00187	−	2.16946i	0.390543	−	0.211718i
$106$	6.56242	−	16.7594i	0.637399	−	1.62782i
$107$	10.4492	+	4.32822i	1.01017	+	0.418425i	0.825515	−	0.564380i	$-0.190885\pi$
$107$	10.4492	+	4.32822i	1.01017	+	0.418425i	0.184651	+	0.982804i	$0.440885\pi$
$108$	9.75807	−	3.57492i	0.938971	−	0.343997i
$109$	−2.70084	−	6.52041i	−0.258694	−	0.624542i	0.740159	−	0.672432i	$-0.234750\pi$
$109$	−2.70084	−	6.52041i	−0.258694	−	0.624542i	−0.998853	+	0.0478900i	$0.984750\pi$
$110$	8.72187	+	8.38845i	0.831598	+	0.799808i
$111$	1.60381	−	5.40142i	0.152227	−	0.512680i
$112$	2.16161	+	6.11593i	0.204253	+	0.577901i
$113$	5.34156	+	9.25185i	0.502492	+	0.870341i	0.999996	+	0.00287946i	$0.000916563\pi$
$113$	5.34156	+	9.25185i	0.502492	+	0.870341i	−0.497504	+	0.867462i	$0.665750\pi$
$114$	−0.919691	+	0.522011i	−0.0861370	+	0.0488908i
$115$	−0.685289	+	5.20528i	−0.0639035	+	0.485395i
$116$	12.3546	+	1.13899i	1.14709	+	0.105753i
$117$	−2.54495	+	5.31774i	−0.235281	+	0.491626i
$118$	13.7507	−	2.08360i	1.26585	−	0.191811i
$119$	−1.54033	−	5.74859i	−0.141202	−	0.526972i
$120$	2.29631	+	7.60016i	0.209624	+	0.693797i
$121$	4.36811	−	16.3020i	0.397101	−	1.48200i
$122$	1.75833	−	15.7164i	0.159192	−	1.42289i
$123$	−1.53665	+	9.66125i	−0.138555	+	0.871125i
$124$	−3.11136	+	1.96181i	−0.279408	+	0.176176i
$125$	−4.57300	−	11.0402i	−0.409022	−	0.987466i
$126$	−3.23446	−	6.07249i	−0.288148	−	0.540980i
$127$		−	5.67944i		−	0.503968i	−0.967731	−	0.251984i	$-0.918917\pi$
$127$		−	5.67944i		−	0.503968i	0.967731	−	0.251984i	$-0.0810831\pi$
$128$	−11.2086	+	1.53827i	−0.990714	+	0.135965i
$129$	−6.91999	−	7.30168i	−0.609271	−	0.642877i
$130$	−3.94364	−	2.17554i	−0.345880	−	0.190807i
$131$	13.5285	+	10.3808i	1.18199	+	0.906972i	0.997124	−	0.0757916i	$-0.0241484\pi$
$131$	13.5285	+	10.3808i	1.18199	+	0.906972i	0.184866	+	0.982764i	$0.440815\pi$
$132$	12.7751	−	13.0890i	1.11193	−	1.13925i
$133$	0.426206	+	0.555442i	0.0369567	+	0.0481629i
$134$	0.886145	−	1.20266i	0.0765513	−	0.103894i
$135$	−3.61050	−	7.60784i	−0.310742	−	0.654779i
$136$	10.3623	−	0.606385i	0.888561	−	0.0519971i
$137$	2.77942	−	0.744744i	0.237462	−	0.0636277i	−0.138125	−	0.990415i	$-0.544108\pi$
$137$	2.77942	−	0.744744i	0.237462	−	0.0636277i	0.375587	+	0.926787i	$0.377441\pi$
$138$	7.85961	+	1.09355i	0.669054	+	0.0930893i
$139$	−8.10807	+	1.06745i	−0.687717	+	0.0905397i	−0.466283	−	0.884636i	$-0.654407\pi$
$139$	−8.10807	+	1.06745i	−0.687717	+	0.0905397i	−0.221434	+	0.975175i	$0.571074\pi$
$140$	4.77414	−	2.19916i	0.403488	−	0.185863i
$141$	4.00714	+	1.78723i	0.337462	+	0.150512i
$142$	16.8674	+	16.2226i	1.41548	+	1.36137i
$143$			10.3756i			0.867650i
$144$	11.5123	−	3.38622i	0.959360	−	0.282185i
$145$		−	10.0536i		−	0.834909i
$146$	13.0191	−	13.5366i	1.07747	−	1.12030i
$147$	6.12665	−	4.44517i	0.505318	−	0.366631i
$148$	2.25373	−	6.10333i	0.185256	−	0.501691i
$149$	13.0985	−	1.72446i	1.07307	−	0.141273i	0.426776	−	0.904357i	$-0.359649\pi$
$149$	13.0985	−	1.72446i	1.07307	−	0.141273i	0.646299	+	0.763085i	$0.276316\pi$
$150$	−5.38756	+	2.18536i	−0.439893	+	0.178434i
$151$	−3.57732	+	0.958540i	−0.291118	+	0.0780049i	−0.401423	−	0.915893i	$-0.631484\pi$
$151$	−3.57732	+	0.958540i	−0.291118	+	0.0780049i	0.110304	+	0.993898i	$0.464817\pi$
$152$	−1.09893	+	0.532405i	−0.0891351	+	0.0431837i
$153$	−10.7721	+	2.27499i	−0.870872	+	0.183922i
$154$	−9.74837	−	7.18282i	−0.785546	−	0.578809i
$155$	1.81443	+	2.36462i	0.145739	+	0.189931i
$156$	−3.33189	+	5.93622i	−0.266765	+	0.475278i
$157$	11.1861	+	8.58340i	0.892748	+	0.685030i	0.949637	−	0.313351i	$-0.101452\pi$
$157$	11.1861	+	8.58340i	0.892748	+	0.685030i	−0.0568892	+	0.998380i	$0.518118\pi$
$158$	2.19736	−	3.98319i	0.174813	−	0.316886i
$159$	−6.27446	+	21.1316i	−0.497597	+	1.67585i
$160$	2.07503	+	8.92981i	0.164046	+	0.705964i
$161$		−	5.25354i		−	0.414037i
$162$	−11.5385	+	5.37238i	−0.906552	+	0.422094i
$163$	3.17637	+	7.66844i	0.248792	+	0.600638i	0.998102	−	0.0615817i	$-0.0196145\pi$
$163$	3.17637	+	7.66844i	0.248792	+	0.600638i	−0.749310	+	0.662220i	$0.769614\pi$
$164$	−2.49634	+	11.0168i	−0.194932	+	0.860267i
$165$	−11.5118	−	9.33454i	−0.896195	−	0.726693i
$166$	−2.34874	−	0.262775i	−0.182298	−	0.0203953i
$167$	3.30113	−	12.3200i	0.255449	−	0.953348i	−0.712392	−	0.701782i	$-0.752388\pi$
$167$	3.30113	−	12.3200i	0.255449	−	0.953348i	0.967840	−	0.251566i	$-0.0809454\pi$
$168$	−3.27077	−	7.24002i	−0.252345	−	0.558579i
$169$	2.36517	+	8.82693i	0.181936	+	0.678995i
$170$	−1.26014	−	8.31623i	−0.0966482	−	0.637826i
$171$	1.06835	−	0.732205i	0.0816986	−	0.0559931i
$172$	−7.42510	−	8.93320i	−0.566159	−	0.681150i
$173$	−0.540080	+	4.10232i	−0.0410616	+	0.311893i	0.958573	+	0.284848i	$0.0919432\pi$
$173$	−0.540080	+	4.10232i	−0.0410616	+	0.311893i	−0.999634	+	0.0270453i	$0.991390\pi$
$174$	−15.1950	−	0.111660i	−1.15193	−	0.00846489i
$175$	1.92454	+	3.33340i	0.145481	+	0.251981i
$176$	15.7034	−	14.1222i	1.18369	−	1.06450i
$177$	−16.5653	+	3.96554i	−1.24512	+	0.298068i
$178$	12.4530	−	12.9480i	0.933393	−	0.970493i
$179$	5.78361	+	13.9629i	0.432287	+	1.04363i	0.978548	+	0.206018i	$0.0660506\pi$
$179$	5.78361	+	13.9629i	0.432287	+	1.04363i	−0.546261	+	0.837615i	$0.683949\pi$
$180$	−3.58873	−	9.03738i	−0.267488	−	0.673607i
$181$	10.9599	+	4.53974i	0.814644	+	0.337437i	0.750805	−	0.660524i	$-0.229666\pi$
$181$	10.9599	+	4.53974i	0.814644	+	0.337437i	0.0638387	+	0.997960i	$0.479666\pi$
$182$	4.19654	+	1.64322i	0.311068	+	0.121804i
$183$	−0.519641	+	19.3617i	−0.0384130	+	1.43126i
$184$	8.97413	+	1.85044i	0.661581	+	0.136417i
$185$	−5.09243	−	1.36451i	−0.374403	−	0.100321i
$186$	3.59401	−	2.71606i	0.263526	−	0.199151i
$187$	−15.3725	+	11.7957i	−1.12415	+	0.862590i
$188$	4.48300	+	2.36035i	0.326956	+	0.172146i
$189$	4.57554	+	7.07599i	0.332822	+	0.514703i
$190$	0.511346	+	0.847121i	0.0370969	+	0.0614566i
$191$	9.91344	−	17.1706i	0.717312	−	1.24242i	−0.244750	−	0.969586i	$-0.578706\pi$
$191$	9.91344	−	17.1706i	0.717312	−	1.24242i	0.962061	−	0.272834i	$-0.0879609\pi$
$192$	13.5195	−	3.03700i	0.975685	−	0.219177i
$193$	−12.2923	−	21.2909i	−0.884818	−	1.53255i	−0.845922	−	0.533306i	$-0.820949\pi$
$193$	−12.2923	−	21.2909i	−0.884818	−	1.53255i	−0.0388957	−	0.999243i	$-0.512384\pi$
$194$	−7.63625	+	13.8424i	−0.548251	+	0.993825i
$195$	5.03779	+	2.24691i	0.360764	+	0.160904i
$196$	7.39337	−	4.66175i	0.528098	−	0.332982i
$197$	−4.34009	−	1.79773i	−0.309219	−	0.128083i	0.222677	−	0.974892i	$-0.428520\pi$
$197$	−4.34009	−	1.79773i	−0.309219	−	0.128083i	−0.531896	+	0.846810i	$0.678520\pi$
$198$	−14.2360	+	17.2952i	−1.01171	+	1.22912i
$199$	13.5922	−	13.5922i	0.963528	−	0.963528i	−0.0358298	−	0.999358i	$-0.511407\pi$
$199$	13.5922	−	13.5922i	0.963528	−	0.963528i	0.999358	+	0.0358298i	$0.0114074\pi$
$200$	−6.37200	+	2.11339i	−0.450569	+	0.149439i
$201$	−0.956983	+	1.55937i	−0.0675004	+	0.109990i
$202$	15.4166	−	12.3141i	1.08471	−	0.866417i
$203$	1.31310	+	9.97396i	0.0921614	+	0.700035i
$204$	−12.5831	+	1.81220i	−0.880992	+	0.126879i
$205$	9.07514	+	1.19476i	0.633835	+	0.0834460i
$206$	26.1601	+	6.46606i	1.82266	+	0.450512i
$207$	−9.70475	−	0.521300i	−0.674527	−	0.0362329i
$208$	−4.28510	+	6.58976i	−0.297118	+	0.456918i
$209$	1.13973	−	1.97407i	0.0788369	−	0.136550i
$210$	−5.59865	+	3.17776i	−0.386344	+	0.219286i
$211$	−18.8312	−	14.4497i	−1.29640	−	0.994760i	−0.999202	−	0.0399425i	$-0.987283\pi$
$211$	−18.8312	−	14.4497i	−1.29640	−	0.994760i	−0.297194	−	0.954817i	$-0.596051\pi$
$212$	−8.81714	+	23.8777i	−0.605563	+	1.63993i
$213$	−22.2630	−	18.0522i	−1.52543	−	1.23692i
$214$	−14.8939	−	5.83196i	−1.01813	−	0.398664i
$215$	−6.65584	+	6.65584i	−0.453925	+	0.453925i
$216$	−13.6989	+	5.32360i	−0.932091	+	0.362225i
$217$	−2.10890	−	2.10890i	−0.143161	−	0.143161i
$218$	3.99850	+	9.14509i	0.270812	+	0.619384i
$219$	−14.4875	+	17.8667i	−0.978972	+	1.20732i
$220$	−12.5634	−	11.6205i	−0.847022	−	0.783454i
$221$	4.39026	−	5.72149i	0.295321	−	0.384869i
$222$	−2.11887	+	7.68150i	−0.142209	+	0.515548i
$223$	7.58987	+	4.38201i	0.508255	+	0.293441i	0.732116	−	0.681180i	$-0.238533\pi$
$223$	7.58987	+	4.38201i	0.508255	+	0.293441i	−0.223861	+	0.974621i	$0.571866\pi$
$224$	−3.22490	−	8.58803i	−0.215473	−	0.573812i
$225$	6.34868	−	3.22439i	0.423245	−	0.214959i
$226$	−7.80758	−	12.9344i	−0.519353	−	0.860386i
$227$	1.24080	−	9.42479i	0.0823546	−	0.625546i	−0.899639	−	0.436634i	$-0.856171\pi$
$227$	1.24080	−	9.42479i	0.0823546	−	0.625546i	0.981994	−	0.188912i	$-0.0604961\pi$
$228$	1.28601	−	0.763435i	0.0851681	−	0.0505597i
$229$	3.31154	−	0.435972i	0.218833	−	0.0288099i	−0.0203126	−	0.999794i	$-0.506466\pi$
$229$	3.31154	−	0.435972i	0.218833	−	0.0288099i	0.239145	+	0.970984i	$0.423133\pi$
$230$	0.825541	−	7.37887i	0.0544346	−	0.486548i
$231$	12.6398	+	7.75702i	0.831637	+	0.510374i
$232$	−17.5001	−	1.27007i	−1.14894	−	0.0833842i
$233$	−10.6845	−	10.6845i	−0.699963	−	0.699963i	0.264439	−	0.964402i	$-0.414813\pi$
$233$	−10.6845	−	10.6845i	−0.699963	−	0.699963i	−0.964402	+	0.264439i	$0.914813\pi$
$234$	3.45191	−	7.58912i	0.225658	−	0.496116i
$235$	1.57108	−	3.79291i	0.102486	−	0.247422i
$236$	−19.3853	+	3.32497i	−1.26187	+	0.216437i
$237$	−2.26944	+	5.08832i	−0.147416	+	0.330522i
$238$	2.33633	+	8.08575i	0.151442	+	0.524121i
$239$	−8.67910	+	5.01088i	−0.561404	+	0.324127i	−0.753709	−	0.657208i	$-0.771737\pi$
$239$	−8.67910	+	5.01088i	−0.561404	+	0.324127i	0.192305	+	0.981335i	$0.438404\pi$
$240$	−3.45626	−	10.6829i	−0.223101	−	0.689581i
$241$	−5.33915	−	3.08256i	−0.343925	−	0.198565i	0.318081	−	0.948063i	$-0.396962\pi$
$241$	−5.33915	−	3.08256i	−0.343925	−	0.198565i	−0.662006	+	0.749498i	$0.730295\pi$
$242$	−5.72711	+	23.1705i	−0.368153	+	1.48946i
$243$	13.5253	−	7.75016i	0.867651	−	0.497173i
$244$	−2.05316	+	22.2705i	−0.131440	+	1.42573i
$245$	−4.31155	−	5.61892i	−0.275455	−	0.358980i
$246$	1.90655	−	13.7028i	0.121557	−	0.873660i
$247$	−0.219580	+	0.819485i	−0.0139716	+	0.0521426i
$248$	4.34524	−	2.85962i	0.275923	−	0.181586i
$249$	2.89352	+	0.0776580i	0.183369	+	0.00492138i
$250$	6.77016	+	15.4842i	0.428183	+	0.979310i
$251$	7.57951	−	18.2986i	0.478415	−	1.15500i	−0.481937	−	0.876206i	$-0.660067\pi$
$251$	7.57951	−	18.2986i	0.478415	−	1.15500i	0.960352	−	0.278790i	$-0.0899332\pi$
$252$	4.74066	+	8.49705i	0.298633	+	0.535264i
$253$	−15.8026	+	6.54564i	−0.993500	+	0.411521i
$254$	0.156483	+	8.03041i	0.00981864	+	0.503873i
$255$	2.39831	+	10.0185i	0.150188	+	0.627381i
$256$	15.8060	−	2.48385i	0.987877	−	0.155241i
$257$	−19.2022	+	11.0864i	−1.19780	+	0.691551i	−0.960065	−	0.279778i	$-0.909739\pi$
$257$	−19.2022	+	11.0864i	−1.19780	+	0.691551i	−0.237737	+	0.971330i	$0.576406\pi$
$258$	9.98566	+	10.1335i	0.621680	+	0.630885i
$259$	5.23029	+	0.688581i	0.324995	+	0.0427863i
$260$	5.63604	+	2.96744i	0.349532	+	0.184033i
$261$	18.5550	−	1.43596i	1.14852	−	0.0888834i
$262$	−19.4146	−	14.3051i	−1.19944	−	0.883772i
$263$	3.79051	−	1.01566i	0.233733	−	0.0626285i	−0.140051	−	0.990144i	$-0.544727\pi$
$263$	3.79051	−	1.01566i	0.233733	−	0.0626285i	0.373784	+	0.927516i	$0.378060\pi$
$264$	−17.7027	+	18.8591i	−1.08952	+	1.16070i
$265$	19.9228	+	5.33829i	1.22385	+	0.327929i
$266$	−0.617935	−	0.773621i	−0.0378880	−	0.0474338i
$267$	−13.8575	+	17.0898i	−0.848067	+	1.04588i
$268$	−1.21982	+	1.72491i	−0.0745126	+	0.105365i
$269$	15.6487	−	6.48189i	0.954116	−	0.395208i	0.149340	−	0.988786i	$-0.452285\pi$
$269$	15.6487	−	6.48189i	0.954116	−	0.395208i	0.804776	+	0.593578i	$0.202285\pi$
$270$	5.31466	+	10.6576i	0.323440	+	0.648600i
$271$	20.1319			1.22292			0.611462	−	0.791274i	$-0.290582\pi$
$271$	20.1319			1.22292			0.611462	+	0.791274i	$0.290582\pi$
$272$	−14.6350	+	1.14290i	−0.887379	+	0.0692988i
$273$	−5.29134	−	1.57112i	−0.320246	−	0.0950885i
$274$	−3.90943	+	1.12961i	−0.236177	+	0.0682421i
$275$	7.62894	−	9.94222i	0.460042	−	0.599539i
$276$	−11.1432	−	1.32967i	−0.670741	−	0.0800366i
$277$	12.6966	−	9.74248i	0.762867	−	0.585369i	−0.152351	−	0.988326i	$-0.548685\pi$
$277$	12.6966	−	9.74248i	0.762867	−	0.585369i	0.915219	+	0.402958i	$0.132018\pi$
$278$	11.4350	−	1.73271i	0.685823	−	0.103921i
$279$	−4.10498	+	3.68646i	−0.245759	+	0.220702i
$280$	−6.68978	+	3.24103i	−0.399791	+	0.193689i
$281$	−0.116398	−	0.434404i	−0.00694373	−	0.0259144i	0.962367	−	0.271753i	$-0.0876034\pi$
$281$	−0.116398	−	0.434404i	−0.00694373	−	0.0259144i	−0.969311	+	0.245839i	$0.920937\pi$
$282$	−5.71513	−	2.41664i	−0.340331	−	0.143909i
$283$	3.46648	+	26.3305i	0.206061	+	1.56519i	0.711726	+	0.702457i	$0.247914\pi$
$283$	3.46648	+	26.3305i	0.206061	+	1.56519i	−0.505665	+	0.862730i	$0.668753\pi$
$284$	−24.2966	−	22.4731i	−1.44174	−	1.33353i
$285$	−0.711680	−	0.980889i	−0.0421563	−	0.0581028i
$286$	−0.285875	−	14.6705i	−0.0169041	−	0.867485i
$287$	−9.15927			−0.540655
$288$	−16.1845	+	5.10512i	−0.953680	+	0.300822i
$289$	−3.53184			−0.207755
$290$	0.277004	+	14.2153i	0.0162662	+	0.834750i
$291$	7.88676	−	17.6829i	0.462330	−	1.03659i
$292$	−18.0353	+	19.4987i	−1.05544	+	1.14108i
$293$	−1.84657	−	14.0261i	−0.107878	−	0.819414i	−0.956770	−	0.290847i	$-0.906063\pi$
$293$	−1.84657	−	14.0261i	−0.107878	−	0.819414i	0.848892	−	0.528567i	$-0.177270\pi$
$294$	−8.54027	+	6.45403i	−0.498079	+	0.376407i
$295$	4.12497	+	15.3946i	0.240165	+	0.896309i
$296$	−3.01849	+	8.69188i	−0.175446	+	0.505205i
$297$	15.5836	−	22.5795i	0.904252	−	1.31019i
$298$	−18.4731	+	2.79919i	−1.07012	+	0.162152i
$299$	5.05061	−	3.87547i	0.292085	−	0.224124i
$300$	7.55750	−	3.23842i	0.436333	−	0.186970i
$301$	5.73379	−	7.47241i	0.330490	−	0.430703i
$302$	5.03172	−	1.45389i	0.289543	−	0.0836618i
$303$	−17.5397	+	16.6229i	−1.00763	+	0.954959i
$304$	1.53916	−	0.783069i	0.0882768	−	0.0449121i
$305$	18.1228			1.03771
$306$	15.1685	−	3.51352i	0.867123	−	0.200854i
$307$	20.0797	−	8.31727i	1.14601	−	0.474692i	0.272815	−	0.962067i	$-0.412045\pi$
$307$	20.0797	−	8.31727i	1.14601	−	0.474692i	0.873193	+	0.487375i	$0.162045\pi$
$308$	13.9816	+	9.88753i	0.796673	+	0.563394i
$309$	−32.5940	−	5.18418i	−1.85421	−	0.294918i
$310$	−2.63066	−	3.29344i	−0.149412	−	0.187055i
$311$	15.2541	+	4.08732i	0.864981	+	0.231771i	0.663916	−	0.747807i	$-0.268893\pi$
$311$	15.2541	+	4.08732i	0.864981	+	0.231771i	0.201065	+	0.979578i	$0.435560\pi$
$312$	4.54755	−	8.48530i	0.257455	−	0.480385i
$313$	13.5097	−	3.61990i	0.763611	−	0.204609i	0.144064	−	0.989568i	$-0.453983\pi$
$313$	13.5097	−	3.61990i	0.763611	−	0.204609i	0.619547	+	0.784960i	$0.287316\pi$
$314$	−16.0530	−	11.8282i	−0.905925	−	0.667507i
$315$	6.50360	−	4.45732i	0.366436	−	0.251142i
$316$	−2.99720	+	5.69256i	−0.168606	+	0.320232i
$317$	−14.9622	−	1.96982i	−0.840363	−	0.110636i	−0.301957	−	0.953321i	$-0.597640\pi$
$317$	−14.9622	−	1.96982i	−0.840363	−	0.110636i	−0.538406	+	0.842686i	$0.680973\pi$
$318$	8.28952	−	30.0518i	0.464853	−	1.68522i
$319$	28.3655	−	16.3768i	1.58816	−	0.916926i
$320$	−3.18002	−	12.5691i	−0.177768	−	0.702634i
$321$	18.7795	+	5.57605i	1.04817	+	0.311225i
$322$	0.144749	+	7.42822i	0.00806654	+	0.413958i
$323$	−1.46379	+	0.606321i	−0.0814474	+	0.0337366i
$324$	16.1668	−	7.91416i	0.898157	−	0.439676i
$325$	−1.78493	+	4.30920i	−0.0990101	+	0.239032i
$326$	−4.70250	−	10.7552i	−0.260447	−	0.595677i
$327$	−5.82587	−	10.7466i	−0.322172	−	0.594290i
$328$	3.22615	−	15.6459i	0.178134	−	0.863901i
$329$	−1.06324	+	3.96805i	−0.0586181	+	0.218766i
$330$	16.5343	+	12.8813i	0.910183	+	0.709095i
$331$	−12.0065	−	15.6471i	−0.659935	−	0.860044i	0.336734	−	0.941600i	$-0.390678\pi$
$331$	−12.0065	−	15.6471i	−0.659935	−	0.860044i	−0.996669	+	0.0815562i	$0.974011\pi$
$332$	3.32823	+	0.306836i	0.182660	+	0.0168398i
$333$	1.79099	−	9.59348i	0.0981459	−	0.525719i
$334$	−4.32816	+	17.5107i	−0.236827	+	0.958144i
$335$	1.48257	+	0.855960i	0.0810013	+	0.0467661i
$336$	4.82417	+	10.1469i	0.263180	+	0.553557i
$337$	−5.05922	+	2.92094i	−0.275593	+	0.159114i	−0.631427	−	0.775435i	$-0.717530\pi$
$337$	−5.05922	+	2.92094i	−0.275593	+	0.159114i	0.355833	+	0.934549i	$0.384197\pi$
$338$	−3.58742	−	12.4156i	−0.195130	−	0.675321i
$339$	10.8664	+	14.9769i	0.590184	+	0.813434i
$340$	2.01090	+	11.7240i	0.109056	+	0.635822i
$341$	−3.71596	+	8.97111i	−0.201230	+	0.485813i
$342$	−1.49041	+	1.06473i	−0.0805922	+	0.0575742i
$343$	13.0381	+	13.0381i	0.703993	+	0.703993i
$344$	10.7448	+	12.4265i	0.579322	+	0.669991i
$345$	−0.243972	+	9.09034i	−0.0131350	+	0.489407i
$346$	0.650614	−	5.81533i	0.0349772	−	0.312634i
$347$	14.7402	−	1.94058i	0.791293	−	0.104176i	0.275964	−	0.961168i	$-0.411003\pi$
$347$	14.7402	−	1.94058i	0.791293	−	0.104176i	0.515329	+	0.856992i	$0.327670\pi$
$348$	21.4879	−	0.260781i	1.15187	−	0.0139793i
$349$	0.795501	−	6.04243i	0.0425822	−	0.323444i	−0.956875	−	0.290500i	$-0.906178\pi$
$349$	0.795501	−	6.04243i	0.0425822	−	0.323444i	0.999457	−	0.0329438i	$-0.0104882\pi$
$350$	−2.81303	−	4.66021i	−0.150363	−	0.249099i
$351$	−3.42735	+	9.61867i	−0.182938	+	0.513407i
$352$	−21.8146	+	20.4007i	−1.16272	+	1.08736i
$353$	2.38713	+	1.37821i	0.127054	+	0.0733548i	0.562180	−	0.827015i	$-0.309963\pi$
$353$	2.38713	+	1.37821i	0.127054	+	0.0733548i	−0.435126	+	0.900370i	$0.643296\pi$
$354$	23.3131	−	6.06347i	1.23908	−	0.322270i
$355$	−16.3261	+	21.2766i	−0.866501	+	1.12925i
$356$	−17.2511	+	18.6509i	−0.914308	+	0.988494i
$357$	−3.68781	−	9.62583i	−0.195180	−	0.509453i
$358$	−8.56241	−	19.5834i	−0.452538	−	1.03501i
$359$	−19.7072	−	19.7072i	−1.04011	−	1.04011i	−0.999161	−	0.0409452i	$-0.986963\pi$
$359$	−19.7072	−	19.7072i	−1.04011	−	1.04011i	−0.0409452	−	0.999161i	$-0.513037\pi$
$360$	5.32327	+	12.6795i	0.280561	+	0.668267i
$361$	−13.3032	+	13.3032i	−0.700170	+	0.700170i
$362$	−15.6218	−	6.11697i	−0.821063	−	0.321501i
$363$	4.59172	−	28.8691i	0.241003	−	1.51524i
$364$	−5.97895	−	2.20780i	−0.313382	−	0.115720i
$365$	17.0751	+	13.1022i	0.893753	+	0.685801i
$366$	0.201279	−	27.3907i	0.0105210	−	1.43173i
$367$	0.783024	−	1.35624i	0.0408735	−	0.0707950i	−0.844865	−	0.534980i	$-0.820319\pi$
$367$	0.783024	−	1.35624i	0.0408735	−	0.0707950i	0.885738	+	0.464185i	$0.153653\pi$
$368$	−12.7399	−	2.36917i	−0.664114	−	0.123501i
$369$	−0.908860	+	16.9197i	−0.0473134	+	0.880806i
$370$	7.23801	+	1.78904i	0.376286	+	0.0930075i
$371$	−20.4621	−	2.69389i	−1.06234	−	0.139860i
$372$	−5.00690	+	3.93938i	−0.259596	+	0.204247i
$373$	3.70295	+	28.1267i	0.191732	+	1.45635i	0.768716	+	0.639591i	$0.220896\pi$
$373$	3.70295	+	28.1267i	0.191732	+	1.45635i	−0.576984	+	0.816755i	$0.695770\pi$
$374$	21.4109	−	17.1021i	1.10713	−	0.884327i
$375$	−9.86423	−	18.1959i	−0.509387	−	0.939635i
$376$	−6.40375	−	3.21389i	−0.330248	−	0.165744i
$377$	−8.62005	+	8.62005i	−0.443955	+	0.443955i
$378$	−6.66453	−	9.87899i	−0.342786	−	0.508121i
$379$	−11.1998	−	4.63910i	−0.575294	−	0.238294i	0.0760158	−	0.997107i	$-0.475780\pi$
$379$	−11.1998	−	4.63910i	−0.575294	−	0.238294i	−0.651310	+	0.758812i	$0.725780\pi$
$380$	−0.746355	−	1.18369i	−0.0382872	−	0.0607222i
$381$	−1.02187	−	9.78385i	−0.0523521	−	0.501242i
$382$	−13.5440	+	24.5514i	−0.692970	+	1.25616i
$383$	0.977138	+	1.69245i	0.0499294	+	0.0864803i	0.889910	−	0.456136i	$-0.150767\pi$
$383$	0.977138	+	1.69245i	0.0499294	+	0.0864803i	−0.839981	+	0.542617i	$0.817434\pi$
$384$	−19.0321	+	4.66666i	−0.971230	+	0.238144i
$385$	6.93815	−	12.0172i	0.353601	−	0.612455i
$386$	17.9672	+	29.7654i	0.914508	+	1.51502i
$387$	−13.2347	−	11.3334i	−0.672756	−	0.576108i
$388$	10.4158	−	19.7828i	0.528785	−	1.00432i
$389$	11.7005	−	8.97810i	0.593238	−	0.455208i	−0.267993	−	0.963421i	$-0.586360\pi$
$389$	11.7005	−	8.97810i	0.593238	−	0.455208i	0.861231	+	0.508213i	$0.169694\pi$
$390$	−7.18507	−	3.03820i	−0.363830	−	0.153845i
$391$	11.4838	+	3.07708i	0.580762	+	0.155615i
$392$	−10.3254	+	6.79516i	−0.521510	+	0.343207i
$393$	25.1730	+	15.4486i	1.26981	+	0.779281i
$394$	6.18619	+	2.42230i	0.311656	+	0.122034i
$395$	4.81628	+	1.99497i	0.242333	+	0.100378i
$396$	19.6524	−	24.8467i	0.987569	−	1.24859i
$397$	5.45203	+	13.1624i	0.273630	+	0.660601i	0.999633	−	0.0270906i	$-0.00862425\pi$
$397$	5.45203	+	13.1624i	0.273630	+	0.660601i	−0.726003	+	0.687691i	$0.758624\pi$
$398$	−18.8442	+	19.5932i	−0.944573	+	0.982117i
$399$	0.834154	+	0.880164i	0.0417599	+	0.0440633i
$400$	8.95143	−	3.16378i	0.447572	−	0.158189i
$401$	9.39308	+	16.2693i	0.469068	+	0.812449i	0.999375	−	0.0353565i	$-0.0112567\pi$
$401$	9.39308	+	16.2693i	0.469068	+	0.812449i	−0.530307	+	0.847806i	$0.677923\pi$
$402$	1.31016	−	2.23123i	0.0653447	−	0.111284i
$403$	0.471730	−	3.58314i	0.0234985	−	0.178489i
$404$	−21.4589	+	17.8362i	−1.06762	+	0.887386i
$405$	−7.58857	−	12.4563i	−0.377079	−	0.618956i
$406$	−2.13146	−	14.0665i	−0.105782	−	0.698107i
$407$	−4.44543	−	16.5906i	−0.220352	−	0.822365i
$408$	17.7419	−	2.90905i	0.878352	−	0.144019i
$409$	−8.07690	+	30.1434i	−0.399377	+	1.49050i	0.414818	+	0.909904i	$0.363845\pi$
$409$	−8.07690	+	30.1434i	−0.399377	+	1.49050i	−0.814195	+	0.580591i	$0.802821\pi$
$410$	−12.8647	−	1.43929i	−0.635341	−	0.0710813i
$411$	4.65406	−	1.78304i	0.229568	−	0.0879510i
$412$	−37.1672	−	8.42187i	−1.83109	−	0.414916i
$413$	−6.10297	−	14.7339i	−0.300307	−	0.725006i
$414$	13.7364	+	0.469699i	0.675105	+	0.0230844i
$415$		−	2.70837i		−	0.132949i
$416$	5.87733	−	9.43562i	0.288160	−	0.462619i
$417$	−13.7756	+	3.29772i	−0.674592	+	0.161490i
$418$	−1.55713	+	2.82263i	−0.0761616	+	0.138060i
$419$	−27.1000	−	20.7946i	−1.32392	−	1.01588i	−0.997501	−	0.0706576i	$-0.977490\pi$
$419$	−27.1000	−	20.7946i	−1.32392	−	1.01588i	−0.326422	−	0.945224i	$-0.605843\pi$
$420$	7.82863	−	4.64743i	0.381998	−	0.226772i
$421$	−17.9981	−	23.4556i	−0.877175	−	1.14316i	−0.988776	−	0.149403i	$-0.952265\pi$
$421$	−17.9981	−	23.4556i	−0.877175	−	1.14316i	0.111602	−	0.993753i	$-0.464402\pi$
$422$	27.0245	+	19.9123i	1.31553	+	0.969314i
$423$	7.22460	+	2.35784i	0.351272	+	0.114642i
$424$	11.8091	−	34.0047i	0.573498	−	1.65141i
$425$	−8.41378	+	2.25446i	−0.408128	+	0.109358i
$426$	31.9760	+	24.9115i	1.54924	+	1.20697i
$427$	−17.9792	+	2.36701i	−0.870074	+	0.114547i
$428$	21.2199	+	7.83570i	1.02570	+	0.378753i
$429$	1.86683	+	17.8738i	0.0901312	+	0.862956i
$430$	9.22761	−	9.59438i	0.444995	−	0.462682i
$431$			28.6786i			1.38140i	0.723141	+	0.690700i	$0.242698\pi$
$431$			28.6786i			1.38140i	−0.723141	+	0.690700i	$0.757302\pi$
$432$	19.2228	−	7.90472i	0.924857	−	0.380316i
$433$		−	8.79379i		−	0.422602i	−0.977421	−	0.211301i	$-0.932230\pi$
$433$		−	8.79379i		−	0.422602i	0.977421	−	0.211301i	$-0.0677701\pi$
$434$	3.03997	+	2.92376i	0.145923	+	0.140345i
$435$	−1.80890	−	17.3192i	−0.0867301	−	0.830392i
$436$	−5.90563	−	12.8205i	−0.282828	−	0.613990i
$437$	−1.38665	+	0.182556i	−0.0663324	+	0.00873282i
$438$	19.9922	−	25.6617i	0.955264	−	1.22616i
$439$	0.0681566	−	0.0182625i	0.00325294	−	0.000871622i	−0.257192	−	0.966360i	$-0.582797\pi$
$439$	0.0681566	−	0.0182625i	0.00325294	−	0.000871622i	0.260445	+	0.965489i	$0.416131\pi$
$440$	18.0841	+	16.0846i	0.862125	+	0.766803i
$441$	9.75446	−	8.75994i	0.464498	−	0.417140i
$442$	−6.04994	+	8.21084i	−0.287766	+	0.390550i
$443$	−2.36007	−	3.07570i	−0.112130	−	0.146131i	0.733916	−	0.679240i	$-0.237690\pi$
$443$	−2.36007	−	3.07570i	−0.112130	−	0.146131i	−0.846047	+	0.533109i	$0.821024\pi$
$444$	2.78432	−	10.9196i	0.132138	−	0.518221i
$445$	16.3327	+	12.5325i	0.774243	+	0.594097i
$446$	−10.8524	−	5.98681i	−0.513876	−	0.283483i
$447$	22.2543	−	5.32744i	1.05259	−	0.251979i
$448$	4.79646	+	12.0542i	0.226611	+	0.569505i
$449$			5.68282i			0.268189i	0.990969	+	0.134094i	$0.0428125\pi$
$449$			5.68282i			0.268189i	−0.990969	+	0.134094i	$0.957187\pi$
$450$	−8.88785	+	4.73403i	−0.418977	+	0.223164i
$451$	11.4120	+	27.5510i	0.537369	+	1.29732i
$452$	11.3959	+	18.0735i	0.536017	+	0.850104i
$453$	−5.99011	+	2.29491i	−0.281440	+	0.107824i
$454$	−1.49474	+	13.3603i	−0.0701517	+	0.627031i
$455$	−1.33670	+	4.98864i	−0.0626656	+	0.233871i
$456$	−1.79731	+	1.11489i	−0.0841669	+	0.0522094i
$457$	−6.21816	−	23.2065i	−0.290873	−	1.08555i	−0.944440	−	0.328684i	$-0.893395\pi$
$457$	−6.21816	−	23.2065i	−0.290873	−	1.08555i	0.653567	−	0.756869i	$-0.273272\pi$
$458$	−4.67032	+	0.707683i	−0.218230	+	0.0330678i
$459$	−18.1475	+	5.85725i	−0.847054	+	0.273393i
$460$	−0.963963	+	10.4561i	−0.0449450	+	0.487516i
$461$	3.37722	−	25.6526i	0.157293	−	1.19476i	−0.712619	−	0.701551i	$-0.752491\pi$
$461$	3.37722	−	25.6526i	0.157293	−	1.19476i	0.869912	−	0.493207i	$-0.164176\pi$
$462$	−18.0857	−	10.6197i	−0.841422	−	0.494075i
$463$	−3.10991	−	5.38653i	−0.144530	−	0.250333i	0.784668	−	0.619917i	$-0.212834\pi$
$463$	−3.10991	−	5.38653i	−0.144530	−	0.250333i	−0.929197	+	0.369584i	$0.879500\pi$
$464$	24.7792	+	1.31364i	1.15034	+	0.0609840i
$465$	3.55114	+	3.74701i	0.164680	+	0.173764i
$466$	15.4016	+	14.8129i	0.713467	+	0.686193i
$467$	−5.66274	−	13.6711i	−0.262040	−	0.632621i	0.737024	−	0.675866i	$-0.236230\pi$
$467$	−5.66274	−	13.6711i	−0.262040	−	0.632621i	−0.999064	+	0.0432451i	$0.986230\pi$
$468$	−4.67171	+	10.8257i	−0.215950	+	0.500418i
$469$	−1.58261	−	0.655541i	−0.0730784	−	0.0302701i
$470$	−2.11691	+	5.40626i	−0.0976458	+	0.249372i
$471$	20.8144	+	12.7738i	0.959079	+	0.588585i
$472$	27.3181	−	5.23544i	1.25742	−	0.240981i
$473$	−29.6209	−	7.93690i	−1.36197	−	0.364939i
$474$	3.06867	−	7.25713i	0.140949	−	0.333331i
$475$	0.812959	−	0.623805i	0.0373011	−	0.0286222i
$476$	−3.52623	−	11.3684i	−0.161624	−	0.521071i
$477$	−7.00679	+	37.5319i	−0.320819	+	1.71847i
$478$	12.1337	−	7.32424i	0.554983	−	0.335003i
$479$	4.67076	−	8.08999i	0.213412	−	0.369641i	−0.739368	−	0.673302i	$-0.764876\pi$
$479$	4.67076	−	8.08999i	0.213412	−	0.369641i	0.952780	+	0.303661i	$0.0982089\pi$
$480$	5.18131	+	15.0099i	0.236493	+	0.685103i
$481$	3.19634	+	5.53622i	0.145740	+	0.252430i
$482$	7.63420	+	4.21147i	0.347728	+	0.191827i
$483$	−0.945243	−	9.05017i	−0.0430101	−	0.411797i
$484$	7.45941	−	32.9196i	0.339064	−	1.49635i
$485$	−16.7375	−	6.93291i	−0.760012	−	0.314807i
$486$	−18.9106	+	11.3310i	−0.857801	+	0.513983i
$487$	−12.5361	+	12.5361i	−0.568065	+	0.568065i	−0.931586	−	0.363521i	$-0.881574\pi$
$487$	−12.5361	+	12.5361i	−0.568065	+	0.568065i	0.363521	+	0.931586i	$0.381574\pi$
$488$	2.28944	−	31.5459i	0.103638	−	1.42802i
$489$	6.85161	+	12.6388i	0.309841	+	0.571544i
$490$	6.25111	+	7.82605i	0.282396	+	0.353545i
$491$	2.67263	+	20.3007i	0.120614	+	0.916156i	0.939584	+	0.342319i	$0.111212\pi$
$491$	2.67263	+	20.3007i	0.120614	+	0.916156i	−0.818970	+	0.573837i	$0.805454\pi$
$492$	−2.31821	+	19.4276i	−0.104513	+	0.875862i
$493$	−22.5714	−	2.97158i	−1.01657	−	0.133833i
$494$	0.287896	−	1.16476i	0.0129530	−	0.0524049i
$495$	−21.5107	−	14.0092i	−0.966835	−	0.629665i
$496$	−6.06514	+	4.16306i	−0.272333	+	0.186927i
$497$	13.4178	−	23.2404i	0.601872	−	1.04247i
$498$	−4.09341	−	0.0300802i	−0.183430	−	0.00134793i
$499$	−1.15428	−	0.885710i	−0.0516726	−	0.0396498i	0.582602	−	0.812757i	$-0.302035\pi$
$499$	−1.15428	−	0.885710i	−0.0516726	−	0.0396498i	−0.634275	+	0.773108i	$0.718701\pi$
$500$	−9.99927	−	21.7073i	−0.447181	−	0.970782i
$501$	3.47011	−	21.8173i	0.155033	−	0.974726i
$502$	−10.2128	+	26.0820i	−0.455822	+	1.16410i
$503$	7.61248	−	7.61248i	0.339424	−	0.339424i	−0.516727	−	0.856150i	$-0.672850\pi$
$503$	7.61248	−	7.61248i	0.339424	−	0.339424i	0.856150	+	0.516727i	$0.172850\pi$
$504$	−6.93714	−	11.8837i	−0.309005	−	0.529344i
$505$	15.9884	+	15.9884i	0.711472	+	0.711472i
$506$	22.1636	−	9.69058i	0.985294	−	0.430799i
$507$	5.66262	+	14.7804i	0.251486	+	0.656422i
$508$	−0.442518	−	11.3502i	−0.0196336	−	0.503586i
$509$	15.4897	−	20.1866i	0.686569	−	0.894754i	−0.311898	−	0.950116i	$-0.600965\pi$
$509$	15.4897	−	20.1866i	0.686569	−	0.894754i	0.998466	+	0.0553621i	$0.0176313\pi$
$510$	−3.66711	−	14.0995i	−0.162383	−	0.624335i
$511$	−18.6511	−	10.7682i	−0.825075	−	0.476358i
$512$	−22.2804	+	3.94753i	−0.984665	+	0.174458i
$513$	1.70868	−	1.45358i	0.0754401	−	0.0641770i
$514$	26.8454	−	16.2046i	1.18410	−	0.714756i
$515$	−4.03076	+	30.6166i	−0.177616	+	1.34913i
$516$	−14.3984	−	14.0531i	−0.633853	−	0.618653i
$517$	13.2606	−	1.74579i	0.583200	−	0.0767797i
$518$	−7.41432	−	0.829507i	−0.325766	−	0.0364465i
$519$	−0.192276	+	7.16416i	−0.00843999	+	0.314472i
$520$	−8.05081	−	4.04050i	−0.353051	−	0.177188i
$521$	6.93436	+	6.93436i	0.303800	+	0.303800i	0.842499	−	0.538699i	$-0.181084\pi$
$521$	6.93436	+	6.93436i	0.303800	+	0.303800i	−0.538699	+	0.842499i	$0.681084\pi$
$522$	−26.1962	+	2.54160i	−1.14658	+	0.111243i
$523$	−2.57284	+	6.21138i	−0.112502	+	0.271605i	−0.970095	−	0.242724i	$-0.921959\pi$
$523$	−2.57284	+	6.21138i	−0.112502	+	0.271605i	0.857593	+	0.514329i	$0.171959\pi$
$524$	27.8453	+	19.6917i	1.21643	+	0.860236i
$525$	3.91512	+	5.39610i	0.170870	+	0.235505i
$526$	−5.33159	+	1.54053i	−0.232468	+	0.0671703i
$527$	5.84510	−	3.37467i	0.254616	−	0.147003i
$528$	24.5110	−	27.1535i	1.06670	−	1.18170i
$529$	−10.8297	−	6.25256i	−0.470859	−	0.271850i
$530$	−28.3168	−	6.99913i	−1.23000	−	0.304023i
$531$	−27.8231	+	9.81186i	−1.20742	+	0.425798i
$532$	0.895042	+	1.07683i	0.0388050	+	0.0466866i
$533$	−6.75668	−	8.80548i	−0.292664	−	0.381408i
$534$	19.1229	−	24.5459i	0.827529	−	1.06220i
$535$	4.74409	−	17.7052i	0.205105	−	0.765461i
$536$	1.67724	−	2.47253i	0.0724457	−	0.106797i
$537$	12.4756	+	23.0129i	0.538361	+	0.993081i
$538$	−21.9478	+	9.59620i	−0.946236	+	0.413722i
$539$	8.83004	−	21.3176i	0.380337	−	0.918214i
$540$	−7.80828	−	14.9228i	−0.336015	−	0.642176i
$541$	−1.62610	+	0.673552i	−0.0699115	+	0.0289583i	−0.417365	−	0.908739i	$-0.637046\pi$
$541$	−1.62610	+	0.673552i	−0.0699115	+	0.0289583i	0.347454	+	0.937697i	$0.387046\pi$
$542$	−28.4654	+	0.554686i	−1.22269	+	0.0238258i
$543$	19.6972	+	5.84857i	0.845289	+	0.250986i
$544$	20.6616	−	2.01924i	0.885861	−	0.0865741i
$545$	−9.90552	+	5.71895i	−0.424306	+	0.244973i
$546$	7.52495	+	2.07569i	0.322038	+	0.0888312i
$547$	36.8430	+	4.85048i	1.57529	+	0.207391i	0.866920	−	0.498447i	$-0.166096\pi$
$547$	36.8430	+	4.85048i	1.57529	+	0.207391i	0.708373	+	0.705838i	$0.249429\pi$
$548$	5.49659	−	1.70492i	0.234803	−	0.0728305i
$549$	2.58847	+	33.4475i	0.110473	+	1.42750i
$550$	−10.5130	+	14.2680i	−0.448274	+	0.608388i
$551$	2.58695	−	0.693172i	0.110208	−	0.0295301i
$552$	15.7925	+	1.57305i	0.672173	+	0.0669536i
$553$	−5.03868	−	1.35011i	−0.214266	−	0.0574125i
$554$	−17.6839	+	14.1252i	−0.751318	+	0.600120i
$555$	−9.01813	−	1.43436i	−0.382798	−	0.0608853i
$556$	−16.1207	+	2.76502i	−0.683668	+	0.117263i
$557$	28.9414	−	11.9879i	1.22628	−	0.507944i	0.326882	−	0.945065i	$-0.394002\pi$
$557$	28.9414	−	11.9879i	1.22628	−	0.507944i	0.899402	+	0.437121i	$0.144002\pi$
$558$	5.70265	−	5.32555i	0.241412	−	0.225449i
$559$	11.4135			0.482741
$560$	9.36968	−	4.76696i	0.395941	−	0.201441i
$561$	−24.3596	+	23.0862i	−1.02846	+	0.974699i
$562$	0.176550	+	0.611016i	0.00744729	+	0.0257742i
$563$	−9.97300	+	12.9971i	−0.420312	+	0.547761i	−0.954736	−	0.297456i	$-0.903862\pi$
$563$	−9.97300	+	12.9971i	−0.420312	+	0.547761i	0.534424	+	0.845217i	$0.320529\pi$
$564$	8.14746	+	3.25952i	0.343070	+	0.137251i
$565$	13.7357	−	10.5398i	0.577866	−	0.443412i
$566$	−5.62688	−	37.1344i	−0.236516	−	1.56087i
$567$	9.15534	+	11.3664i	0.384488	+	0.477344i
$568$	34.9732	+	31.1063i	1.46744	+	1.30519i
$569$	5.75421	+	21.4750i	0.241229	+	0.900279i	0.975241	+	0.221143i	$0.0709788\pi$
$569$	5.75421	+	21.4750i	0.241229	+	0.900279i	−0.734012	+	0.679136i	$0.762355\pi$
$570$	1.03330	+	1.36731i	0.0432803	+	0.0572705i
$571$	−4.90573	−	37.2627i	−0.205298	−	1.55940i	−0.715050	−	0.699073i	$-0.753596\pi$
$571$	−4.90573	−	37.2627i	−0.205298	−	1.55940i	0.509752	−	0.860322i	$-0.329737\pi$
$572$	0.808422	+	20.7354i	0.0338018	+	0.866991i
$573$	13.9883	−	31.3631i	0.584369	−	1.31021i
$574$	12.9507	−	0.252362i	0.540552	−	0.0105334i
$575$	−7.68921			−0.320662
$576$	22.7433	−	7.66428i	0.947638	−	0.319345i
$577$	17.5720			0.731533			0.365766	−	0.930707i	$-0.380807\pi$
$577$	17.5720			0.731533			0.365766	+	0.930707i	$0.380807\pi$
$578$	4.99383	−	0.0973115i	0.207716	−	0.00404763i
$579$	−25.0064	−	34.4657i	−1.03923	−	1.43234i
$580$	−0.783337	−	20.0920i	−0.0325263	−	0.834275i
$581$	0.353739	+	2.68691i	0.0146755	+	0.111472i
$582$	−10.6642	+	25.2199i	−0.442047	+	1.04540i
$583$	17.3916	+	64.9063i	0.720286	+	2.68814i
$584$	24.9638	−	28.0670i	1.03301	−	1.16142i
$585$	9.08278	+	2.96428i	0.375527	+	0.122558i
$586$	2.99741	+	19.7813i	0.123822	+	0.817157i
$587$	−21.3419	+	16.3762i	−0.880876	+	0.675920i	−0.946771	−	0.321907i	$-0.895676\pi$
$587$	−21.3419	+	16.3762i	−0.880876	+	0.675920i	0.0658957	+	0.997827i	$0.479010\pi$
$588$	11.8976	−	9.36095i	0.490651	−	0.386039i
$589$	−0.483351	+	0.629916i	−0.0199161	+	0.0259552i
$590$	−6.25665	−	21.6535i	−0.257582	−	0.891460i
$591$	−7.80005	−	2.31602i	−0.320851	−	0.0952681i
$592$	4.02850	−	12.3730i	0.165570	−	0.508527i
$593$	−14.8605			−0.610249			−0.305125	−	0.952312i	$-0.598698\pi$
$593$	−14.8605			−0.610249			−0.305125	+	0.952312i	$0.598698\pi$
$594$	−21.4122	+	32.3555i	−0.878554	+	1.32756i
$595$	−8.91086	+	3.69100i	−0.365310	+	0.151316i
$596$	26.0428	−	4.46688i	1.06676	−	0.182970i
$597$	20.9695	−	25.8607i	0.858224	−	1.05841i
$598$	−7.03451	+	5.61886i	−0.287663	+	0.229772i
$599$	−22.1978	−	5.94789i	−0.906979	−	0.243024i	−0.224968	−	0.974366i	$-0.572228\pi$
$599$	−22.1978	−	5.94789i	−0.906979	−	0.243024i	−0.682011	+	0.731342i	$0.738894\pi$
$600$	−10.5967	+	4.78718i	−0.432607	+	0.195436i
$601$	−18.1994	+	4.87651i	−0.742368	+	0.198917i	−0.610130	−	0.792301i	$-0.708883\pi$
$601$	−18.1994	+	4.87651i	−0.742368	+	0.198917i	−0.132238	+	0.991218i	$0.542216\pi$
$602$	−7.90137	+	10.7236i	−0.322036	+	0.437060i
$603$	−1.36801	+	2.85848i	−0.0557095	+	0.116406i
$604$	−7.07452	+	2.19435i	−0.287858	+	0.0892870i
$605$	−27.1177	−	3.57012i	−1.10249	−	0.145146i
$606$	24.3422	−	23.9871i	0.988836	−	0.974409i
$607$	−7.11457	+	4.10760i	−0.288771	+	0.166722i	−0.637388	−	0.770543i	$-0.719985\pi$
$607$	−7.11457	+	4.10760i	−0.288771	+	0.166722i	0.348616	+	0.937266i	$0.386652\pi$
$608$	−2.15471	+	1.14962i	−0.0873850	+	0.0466234i
$609$	4.05661	+	16.9457i	0.164382	+	0.686674i
$610$	−25.6247	+	0.499331i	−1.03751	+	0.0202173i
$611$	−4.59912	+	1.90502i	−0.186060	+	0.0770687i
$612$	−21.3506	+	5.38585i	−0.863045	+	0.217710i
$613$	−8.28038	+	19.9906i	−0.334442	+	0.807413i	0.663787	+	0.747921i	$0.268948\pi$
$613$	−8.28038	+	19.9906i	−0.334442	+	0.807413i	−0.998229	+	0.0594919i	$0.981052\pi$
$614$	−28.1624	+	12.3134i	−1.13654	+	0.496929i
$615$	15.8485	+	0.425353i	0.639074	+	0.0171519i
$616$	−20.0416	−	13.5952i	−0.807499	−	0.547766i
$617$	−0.197720	+	0.737900i	−0.00795990	+	0.0297067i	−0.969792	−	0.243935i	$-0.921562\pi$
$617$	−0.197720	+	0.737900i	−0.00795990	+	0.0297067i	0.961832	+	0.273642i	$0.0882283\pi$
$618$	46.2290	+	6.43209i	1.85960	+	0.258737i
$619$	−8.10422	−	10.5616i	−0.325736	−	0.424508i	0.601565	−	0.798824i	$-0.294544\pi$
$619$	−8.10422	−	10.5616i	−0.325736	−	0.424508i	−0.927301	+	0.374316i	$0.877877\pi$
$620$	3.81035	+	4.58427i	0.153027	+	0.184109i
$621$	−16.8120	+	0.848094i	−0.674641	+	0.0340328i
$622$	−21.6811	−	5.35896i	−0.869332	−	0.214875i
$623$	−17.8401	−	10.3000i	−0.714749	−	0.412660i
$624$	−6.19620	+	12.1230i	−0.248046	+	0.485310i
$625$	−6.49414	+	3.74940i	−0.259766	+	0.149976i
$626$	−19.0022	+	5.49057i	−0.759479	+	0.219447i
$627$	1.60821	−	3.60576i	0.0642257	−	0.144000i
$628$	23.0240	+	16.2822i	0.918758	+	0.649730i
$629$	−4.56865	+	11.0297i	−0.182164	+	0.439783i
$630$	−9.07293	+	6.48160i	−0.361474	+	0.258233i
$631$	−23.9131	−	23.9131i	−0.951966	−	0.951966i	0.0469323	−	0.998898i	$-0.485056\pi$
$631$	−23.9131	−	23.9131i	−0.951966	−	0.951966i	−0.998898	+	0.0469323i	$0.985056\pi$
$632$	4.08103	−	8.13155i	0.162335	−	0.323456i
$633$	−35.0401	−	21.5040i	−1.39272	−	0.854709i
$634$	21.2101	+	2.37296i	0.842359	+	0.0942424i
$635$	−9.12559	+	1.20141i	−0.362138	+	0.0476763i
$636$	−10.8929	+	42.7200i	−0.431932	+	1.69396i
$637$	−1.12095	+	8.51444i	−0.0444136	+	0.337355i
$638$	−39.6560	+	23.9375i	−1.57000	+	0.947694i
$639$	−41.6000	−	27.0926i	−1.64567	−	1.07177i
$640$	4.84268	+	17.6844i	0.191424	+	0.699037i
$641$	35.0291	+	20.2241i	1.38357	+	0.798803i	0.992580	−	0.121592i	$-0.0388001\pi$
$641$	35.0291	+	20.2241i	1.38357	+	0.798803i	0.390988	+	0.920396i	$0.372133\pi$
$642$	−26.7068	−	7.36681i	−1.05403	−	0.290745i
$643$	15.7221	−	20.4895i	0.620020	−	0.808026i	−0.372766	−	0.927925i	$-0.621591\pi$
$643$	15.7221	−	20.4895i	0.620020	−	0.808026i	0.992786	+	0.119899i	$0.0382572\pi$
$644$	−0.409334	−	10.4991i	−0.0161300	−	0.413723i
$645$	−10.2683	+	12.6634i	−0.404315	+	0.498623i
$646$	2.05301	−	0.897636i	0.0807746	−	0.0353170i
$647$	−10.7004	−	10.7004i	−0.420678	−	0.420678i	0.464759	−	0.885437i	$-0.346141\pi$
$647$	−10.7004	−	10.7004i	−0.420678	−	0.420678i	−0.885437	+	0.464759i	$0.846141\pi$
$648$	−22.6409	+	11.6356i	−0.889420	+	0.457091i
$649$	−36.7153	+	36.7153i	−1.44120	+	1.44120i
$650$	2.40506	−	6.14216i	0.0943344	−	0.240915i
$651$	−4.01240	−	3.25351i	−0.157258	−	0.127515i
$652$	6.94541	+	15.0777i	0.272003	+	0.590490i
$653$	−10.0587	−	7.71829i	−0.393626	−	0.302040i	0.392918	−	0.919573i	$-0.371465\pi$
$653$	−10.0587	−	7.71829i	−0.393626	−	0.302040i	−0.786545	+	0.617533i	$0.788132\pi$
$654$	8.53356	+	15.0346i	0.333689	+	0.587901i
$655$	13.8178	−	23.9332i	0.539907	−	0.935146i
$656$	−4.13052	+	22.2114i	−0.161270	+	0.867208i
$657$	−21.7426	+	33.3852i	−0.848260	+	1.30248i
$658$	1.39403	−	5.63990i	0.0543449	−	0.219866i
$659$	2.79804	+	0.368369i	0.108996	+	0.0143496i	0.184827	−	0.982771i	$-0.440828\pi$
$659$	2.79804	+	0.368369i	0.108996	+	0.0143496i	−0.0758308	+	0.997121i	$0.524161\pi$
$660$	−23.7335	−	17.7579i	−0.923825	−	0.691227i
$661$	2.28824	+	17.3809i	0.0890021	+	0.676038i	0.976545	+	0.215313i	$0.0690773\pi$
$661$	2.28824	+	17.3809i	0.0890021	+	0.676038i	−0.887543	+	0.460725i	$0.847589\pi$
$662$	17.4076	+	21.7934i	0.676565	+	0.847023i
$663$	6.53357	−	10.6462i	0.253743	−	0.413465i
$664$	−4.71439	−	0.342147i	−0.182954	−	0.0132779i
$665$	0.802313	−	0.802313i	0.0311124	−	0.0311124i
$666$	−2.26804	+	13.6140i	−0.0878848	+	0.527532i
$667$	−18.5669	−	7.69068i	−0.718915	−	0.297784i
$668$	5.63732	−	24.8784i	0.218114	−	0.962576i
$669$	13.8634	+	6.18320i	0.535988	+	0.239056i
$670$	−2.11985	−	1.16943i	−0.0818970	−	0.0451791i
$671$	29.5211	+	51.1320i	1.13965	+	1.97393i
$672$	−7.10068	−	14.2142i	−0.273915	−	0.548324i
$673$	−9.15047	+	15.8491i	−0.352725	+	0.610937i	−0.986726	−	0.162395i	$-0.948078\pi$
$673$	−9.15047	+	15.8491i	−0.352725	+	0.610937i	0.634001	+	0.773332i	$0.281411\pi$
$674$	7.07299	−	4.26945i	0.272441	−	0.164453i
$675$	10.3566	−	6.69688i	0.398626	−	0.257763i
$676$	5.41450	+	17.4562i	0.208250	+	0.671391i
$677$	17.6689	−	13.5578i	0.679069	−	0.521068i	−0.210659	−	0.977560i	$-0.567561\pi$
$677$	17.6689	−	13.5578i	0.679069	−	0.521068i	0.889728	+	0.456492i	$0.150894\pi$
$678$	−15.7772	−	20.8771i	−0.605920	−	0.801781i
$679$	17.5104	+	4.69189i	0.671987	+	0.180058i
$680$	−3.16633	−	16.5217i	−0.121423	−	0.633576i
$681$	0.441742	−	16.4592i	0.0169276	−	0.630716i
$682$	5.00698	−	12.7870i	0.191727	−	0.489641i
$683$	22.5717	+	9.34950i	0.863682	+	0.357749i	0.770146	−	0.637867i	$-0.220183\pi$
$683$	22.5717	+	9.34950i	0.863682	+	0.357749i	0.0935354	+	0.995616i	$0.470183\pi$
$684$	2.07802	−	1.54654i	0.0794552	−	0.0591334i
$685$	−1.78458	−	4.30837i	−0.0681855	−	0.164614i
$686$	−18.7944	−	18.0760i	−0.717575	−	0.690144i
$687$	5.62628	−	1.34687i	0.214656	−	0.0513863i
$688$	−15.5350	−	17.2743i	−0.592265	−	0.658577i
$689$	−12.5048	−	21.6590i	−0.476396	−	0.825142i
$690$	0.0945009	−	12.8600i	0.00359759	−	0.489570i
$691$	−1.39983	+	10.6328i	−0.0532522	+	0.404491i	0.943972	+	0.330027i	$0.107058\pi$
$691$	−1.39983	+	10.6328i	−0.0532522	+	0.404491i	−0.997224	+	0.0744637i	$0.976276\pi$
$692$	−0.759705	+	8.24049i	−0.0288797	+	0.313256i
$693$	23.1700	+	11.0886i	0.880155	+	0.421223i
$694$	−20.7883	+	3.15000i	−0.789113	+	0.119572i
$695$	3.43030	+	12.8021i	0.130119	+	0.485610i
$696$	−30.3756	+	0.960779i	−1.15138	+	0.0364182i
$697$	5.36473	−	20.0215i	0.203204	−	0.758367i
$698$	−0.958309	+	8.56558i	−0.0362725	+	0.324212i
$699$	−20.3283	−	16.4835i	−0.768888	−	0.623464i
$700$	4.10588	+	6.51178i	0.155188	+	0.246122i
$701$	1.30158	+	3.14230i	0.0491601	+	0.118683i	0.946552	−	0.322552i	$-0.104541\pi$
$701$	1.30158	+	3.14230i	0.0491601	+	0.118683i	−0.897392	+	0.441235i	$0.854541\pi$
$702$	4.58106	−	13.6947i	0.172901	−	0.516873i
$703$		−	1.40444i		−	0.0529694i
$704$	30.2826	−	29.4465i	1.14132	−	1.10981i
$705$	2.02402	−	6.81665i	0.0762290	−	0.256730i
$706$	−3.41325	−	1.88294i	−0.128459	−	0.0708656i
$707$	−17.9499	−	13.7734i	−0.675075	−	0.518003i
$708$	−32.7964	+	9.21575i	−1.23256	+	0.346349i
$709$	26.3185	+	34.2989i	0.988411	+	1.28812i	0.957449	+	0.288602i	$0.0931905\pi$
$709$	26.3185	+	34.2989i	0.988411	+	1.28812i	0.0309622	+	0.999521i	$0.490143\pi$
$710$	22.4980	−	30.5338i	0.844336	−	1.14591i
$711$	−2.99401	+	9.17387i	−0.112284	+	0.344047i
$712$	23.8783	−	26.8466i	0.894876	−	1.00612i
$713$	5.75492	−	1.54203i	0.215524	−	0.0577494i
$714$	5.47958	+	13.5088i	0.205068	+	0.505554i
$715$	16.6712	−	2.19481i	0.623469	−	0.0820813i
$716$	12.6464	+	27.4539i	0.472617	+	1.02600i
$717$	−14.0497	+	10.1937i	−0.524697	+	0.380692i
$718$	28.4079	+	27.3219i	1.06017	+	1.01965i
$719$			6.15692i			0.229614i	0.993388	+	0.114807i	$0.0366250\pi$
$719$			6.15692i			0.229614i	−0.993388	+	0.114807i	$0.963375\pi$
$720$	−7.87616	−	17.7814i	−0.293527	−	0.662674i
$721$		−	30.9005i		−	1.15079i
$722$	18.4435	−	19.1766i	0.686396	−	0.713678i
$723$	−9.75228	−	4.34962i	−0.362691	−	0.161764i
$724$	22.2569	+	8.21865i	0.827171	+	0.305444i
$725$	14.5981	−	1.92188i	0.542161	−	0.0713769i
$726$	−5.69702	+	40.9459i	−0.211436	+	1.51964i
$727$	15.8867	−	4.25684i	0.589207	−	0.157877i	0.0481161	−	0.998842i	$-0.484678\pi$
$727$	15.8867	−	4.25684i	0.589207	−	0.157877i	0.541091	+	0.840964i	$0.318012\pi$
$728$	8.51474	+	2.95698i	0.315577	+	0.109593i
$729$	21.9054	−	15.7846i	0.811311	−	0.584615i
$730$	−24.5043	−	18.0553i	−0.906945	−	0.668258i
$731$	12.9757	+	16.9103i	0.479925	+	0.625451i
$732$	0.470087	+	38.7344i	0.0173749	+	1.43167i
$733$	−15.0971	−	11.5844i	−0.557625	−	0.427880i	0.291118	−	0.956687i	$-0.405973\pi$
$733$	−15.0971	−	11.5844i	−0.557625	−	0.427880i	−0.848742	+	0.528807i	$0.822640\pi$
$734$	−1.06978	+	1.93922i	−0.0394865	+	0.0715779i
$735$	−8.43840	−	8.90384i	−0.311255	−	0.328423i
$736$	18.0788	+	2.99885i	0.666394	+	0.110539i
$737$			5.57726i			0.205441i
$738$	0.818895	−	23.9486i	0.0301439	−	0.881560i
$739$	5.22780	+	12.6210i	0.192308	+	0.464272i	0.990394	−	0.138271i	$-0.0441544\pi$
$739$	5.22780	+	12.6210i	0.192308	+	0.464272i	−0.798087	+	0.602542i	$0.794154\pi$
$740$	−10.2834	−	2.33017i	−0.378027	−	0.0856588i
$741$	−0.230821	+	1.45122i	−0.00847942	+	0.0533119i
$742$	29.0066	+	3.24523i	1.06486	+	0.119136i
$743$	7.77741	−	29.0257i	0.285325	−	1.06485i	−0.663276	−	0.748375i	$-0.730834\pi$
$743$	7.77741	−	29.0257i	0.285325	−	1.06485i	0.948601	−	0.316474i	$-0.102499\pi$
$744$	6.97094	−	5.70802i	0.255567	−	0.209266i
$745$	−5.54163	−	20.6816i	−0.203030	−	0.757717i
$746$	−6.01074	−	39.6676i	−0.220069	−	1.45233i
$747$	4.99857	−	0.386836i	0.182888	−	0.0141536i
$748$	−29.8026	+	24.7713i	−1.08969	+	0.905729i
$749$	−2.39403	+	18.1845i	−0.0874761	+	0.664447i
$750$	14.4488	+	25.4563i	0.527597	+	0.929532i
$751$	−9.89541	−	17.1394i	−0.361089	−	0.625424i	0.627052	−	0.778978i	$-0.284262\pi$
$751$	−9.89541	−	17.1394i	−0.361089	−	0.625424i	−0.988140	+	0.153554i	$0.950928\pi$
$752$	9.14310	+	4.36782i	0.333415	+	0.159278i
$753$	9.76471	−	32.8863i	0.355846	−	1.19844i
$754$	11.9508	−	12.4258i	0.435221	−	0.452520i
$755$	2.29689	+	5.54519i	0.0835925	+	0.201810i
$756$	9.69547	+	13.7847i	0.352621	+	0.501346i
$757$	−6.55875	−	2.71672i	−0.238382	−	0.0987410i	0.260294	−	0.965529i	$-0.416180\pi$
$757$	−6.55875	−	2.71672i	−0.238382	−	0.0987410i	−0.498676	+	0.866788i	$0.666180\pi$
$758$	15.9637	+	6.25085i	0.579827	+	0.227041i
$759$	−26.0451	+	14.1193i	−0.945376	+	0.512499i
$760$	1.08792	+	1.65311i	0.0394630	+	0.0599647i
$761$	−1.21771	−	0.326284i	−0.0441419	−	0.0118278i	0.236681	−	0.971588i	$-0.423941\pi$
$761$	−1.21771	−	0.326284i	−0.0441419	−	0.0118278i	−0.280822	+	0.959760i	$0.590607\pi$
$762$	1.71444	+	13.8057i	0.0621077	+	0.500127i
$763$	9.08008	−	6.96739i	0.328721	−	0.252236i
$764$	18.4740	−	35.0875i	0.668365	−	1.26942i
$765$	5.93409	+	16.8271i	0.214548	+	0.608385i
$766$	−1.42825	−	2.36611i	−0.0516048	−	0.0854911i
$767$	9.66266	−	16.7362i	0.348898	−	0.604310i
$768$	26.7818	−	7.12278i	0.966406	−	0.257021i
$769$	14.2525	+	24.6861i	0.513960	+	0.890204i	0.999869	+	0.0161951i	$0.00515529\pi$
$769$	14.2525	+	24.6861i	0.513960	+	0.890204i	−0.485909	+	0.874009i	$0.661511\pi$
$770$	−9.47906	+	17.1829i	−0.341602	+	0.619228i
$771$	−31.0846	+	22.5533i	−1.11948	+	0.812237i
$772$	−26.2248	−	41.5916i	−0.943851	−	1.49692i
$773$	50.9849	+	21.1186i	1.83380	+	0.759584i	0.963852	+	0.266437i	$0.0858463\pi$
$773$	50.9849	+	21.1186i	1.83380	+	0.759584i	0.869946	+	0.493147i	$0.164154\pi$
$774$	19.0254	+	15.6601i	0.683853	+	0.562891i
$775$	−3.08663	+	3.08663i	−0.110875	+	0.110875i
$776$	−14.1824	+	28.2587i	−0.509117	+	1.01443i
$777$	9.13401	+	0.245145i	0.327681	+	0.00879451i
$778$	−16.2965	+	13.0169i	−0.584257	+	0.466679i
$779$	0.318276	+	2.41755i	0.0114034	+	0.0866176i
$780$	10.2430	+	4.09788i	0.366758	+	0.146728i
$781$	−86.6247	−	11.4044i	−3.09967	−	0.408080i
$782$	−16.3223	−	4.03442i	−0.583684	−	0.144270i
$783$	31.7059	−	5.81220i	1.13308	−	0.207711i
$784$	14.4123	−	9.89248i	0.514725	−	0.353303i
$785$	11.4253	−	19.7893i	0.407788	−	0.706309i
$786$	−36.0189	−	21.1499i	−1.28475	−	0.754393i
$787$	−15.6457	−	12.0054i	−0.557710	−	0.427946i	0.291063	−	0.956704i	$-0.405991\pi$
$787$	−15.6457	−	12.0054i	−0.557710	−	0.427946i	−0.848772	+	0.528758i	$0.822658\pi$
$788$	−8.81367	−	3.25456i	−0.313974	−	0.115939i
$789$	6.34709	−	2.43167i	0.225962	−	0.0865698i
$790$	−6.86493	−	2.68808i	−0.244243	−	0.0956375i
$791$	−12.2503	+	12.2503i	−0.435570	+	0.435570i
$792$	−27.1028	+	35.6734i	−0.963056	+	1.26760i
$793$	−15.5386	−	15.5386i	−0.551792	−	0.551792i
$794$	−8.07154	−	18.4607i	−0.286448	−	0.655144i
$795$	35.2811	+	5.61156i	1.25129	+	0.199022i
$796$	26.1048	−	28.2229i	0.925260	−	1.00033i
$797$	15.2344	−	19.8538i	0.539630	−	0.703259i	−0.441358	−	0.897331i	$-0.645503\pi$
$797$	15.2344	−	19.8538i	0.539630	−	0.703259i	0.980987	+	0.194072i	$0.0621696\pi$
$798$	−1.20370	−	1.22152i	−0.0426105	−	0.0432414i
$799$	−8.05110	−	4.64830i	−0.284827	−	0.164445i
$800$	−12.5697	+	4.72005i	−0.444405	+	0.166879i
$801$	−20.7972	+	31.9336i	−0.734833	+	1.12832i
$802$	−13.7296	−	22.7451i	−0.484807	−	0.803156i
$803$	−9.15233	+	69.5189i	−0.322979	+	2.45327i
$804$	−1.79101	+	3.19094i	−0.0631642	+	0.112536i
$805$	−8.44127	+	1.11131i	−0.297516	+	0.0391687i
$806$	−0.568275	+	5.07937i	−0.0200166	+	0.178913i
$807$	25.7914	−	13.9818i	0.907900	−	0.492183i
$808$	29.8503	−	25.8107i	1.05013	−	0.908017i
$809$	−32.7842	−	32.7842i	−1.15263	−	1.15263i	−0.986023	−	0.166607i	$-0.946719\pi$
$809$	−32.7842	−	32.7842i	−1.15263	−	1.15263i	−0.166607	−	0.986023i	$-0.553281\pi$
$810$	11.0730	+	17.4034i	0.389067	+	0.611492i
$811$	19.0081	−	45.8896i	0.667464	−	1.61140i	−0.118375	−	0.992969i	$-0.537769\pi$
$811$	19.0081	−	45.8896i	0.667464	−	1.61140i	0.785839	−	0.618431i	$-0.212231\pi$
$812$	3.40133	+	19.8305i	0.119363	+	0.695913i
$813$	34.6808	−	3.62223i	1.21631	−	0.127037i
$814$	6.74271	+	23.3357i	0.236332	+	0.817916i
$815$	11.6495	−	6.72587i	0.408066	−	0.235597i
$816$	−25.0059	+	4.60207i	−0.875380	+	0.161105i
$817$	−2.17155	−	1.25375i	−0.0759731	−	0.0438631i
$818$	10.5898	−	42.8437i	0.370263	−	1.49799i
$819$	−9.39796	−	1.75449i	−0.328391	−	0.0613070i
$820$	18.2296	+	1.68062i	0.636605	+	0.0586897i
$821$	24.3061	+	31.6763i	0.848287	+	1.10551i	0.993241	+	0.116071i	$0.0370301\pi$
$821$	24.3061	+	31.6763i	0.848287	+	1.10551i	−0.144953	+	0.989438i	$0.546303\pi$
$822$	−6.53145	+	2.64936i	−0.227811	+	0.0924069i
$823$	2.00017	−	7.46475i	0.0697217	−	0.260205i	−0.922263	−	0.386563i	$-0.873662\pi$
$823$	2.00017	−	7.46475i	0.0697217	−	0.260205i	0.991985	+	0.126358i	$0.0403288\pi$
$824$	52.7844	+	10.8840i	1.83883	+	0.379163i
$825$	11.3534	−	18.4999i	0.395273	−	0.644084i
$826$	9.03521	+	20.6647i	0.314375	+	0.719018i
$827$	−1.05481	+	2.54654i	−0.0366793	+	0.0885517i	−0.941158	−	0.337968i	$-0.890260\pi$
$827$	−1.05481	+	2.54654i	−0.0366793	+	0.0885517i	0.904478	+	0.426520i	$0.140260\pi$
$828$	−19.4354	−	0.285656i	−0.675426	−	0.00992722i
$829$	−9.02140	+	3.73678i	−0.313326	+	0.129784i	−0.533804	−	0.845608i	$-0.679238\pi$
$829$	−9.02140	+	3.73678i	−0.313326	+	0.129784i	0.220478	+	0.975392i	$0.429238\pi$
$830$	0.0746228	+	3.82949i	0.00259020	+	0.132924i
$831$	20.1193	−	19.0676i	0.697932	−	0.661448i
$832$	−8.05025	+	13.5034i	−0.279092	+	0.468146i
$833$	−13.8894	+	8.01906i	−0.481240	+	0.277844i
$834$	19.3870	−	5.04234i	0.671317	−	0.174602i
$835$	−20.4937	−	2.69805i	−0.709215	−	0.0933700i
$836$	2.12392	−	4.03395i	0.0734574	−	0.139517i
$837$	−6.40828	+	7.08917i	−0.221503	+	0.245038i
$838$	38.8909	+	28.6557i	1.34346	+	0.989895i
$839$	−32.0659	+	8.59203i	−1.10704	+	0.296630i	−0.765627	−	0.643285i	$-0.777571\pi$
$839$	−32.0659	+	8.59203i	−1.10704	+	0.296630i	−0.341410	+	0.939914i	$0.610904\pi$
$840$	−10.9412	+	6.78692i	−0.377507	+	0.234171i
$841$	9.16014	+	2.45445i	0.315867	+	0.0846363i
$842$	26.0946	+	32.6690i	0.899280	+	1.12585i
$843$	−0.278677	−	0.727396i	−0.00959814	−	0.0250528i
$844$	−38.7597	−	27.4102i	−1.33417	−	0.943500i
$845$	13.6826	−	5.66751i	0.470695	−	0.194968i
$846$	−10.2801	−	3.13480i	−0.353439	−	0.107777i
$847$	27.3691			0.940414
$848$	−15.7604	+	48.4061i	−0.541216	+	1.66227i
$849$	10.7092	+	44.7353i	0.367537	+	1.53531i
$850$	11.8345	−	3.41951i	0.405920	−	0.117288i
$851$	−6.41549	+	8.36083i	−0.219920	+	0.286606i
$852$	−45.8987	−	34.3424i	−1.57246	−	1.17655i
$853$	35.7582	−	27.4382i	1.22434	−	0.939467i	0.224946	−	0.974371i	$-0.427779\pi$
$853$	35.7582	−	27.4382i	1.22434	−	0.939467i	0.999391	+	0.0349046i	$0.0111127\pi$
$854$	25.3564	−	3.84219i	0.867678	−	0.131477i
$855$	−1.40248	−	1.56171i	−0.0479639	−	0.0534093i
$856$	−30.2196	−	10.4946i	−1.03288	−	0.358698i
$857$	5.06530	+	18.9039i	0.173027	+	0.645747i	0.996879	+	0.0789416i	$0.0251541\pi$
$857$	5.06530	+	18.9039i	0.173027	+	0.645747i	−0.823852	+	0.566805i	$0.808179\pi$
$858$	−3.13206	−	25.2211i	−0.106927	−	0.861036i
$859$	1.98781	+	15.0989i	0.0678233	+	0.515169i	0.991311	+	0.131540i	$0.0419923\pi$
$859$	1.98781	+	15.0989i	0.0678233	+	0.515169i	−0.923488	+	0.383628i	$0.874674\pi$
$860$	−12.7830	+	13.8202i	−0.435896	+	0.471264i
$861$	−15.7785	+	1.64798i	−0.537730	+	0.0561631i
$862$	−0.790171	−	40.5500i	−0.0269133	−	1.38114i
$863$	−37.7012			−1.28336			−0.641681	−	0.766972i	$-0.721763\pi$
$863$	−37.7012			−1.28336			−0.641681	+	0.766972i	$0.721763\pi$
$864$	−26.9622	+	11.7065i	−0.917271	+	0.398263i
$865$	6.70576			0.228003
$866$	0.242292	+	12.4339i	0.00823342	+	0.422522i
$867$	−6.08423	+	0.635467i	−0.206631	+	0.0215816i
$868$	−4.37891	−	4.05027i	−0.148630	−	0.137475i
$869$	2.21682	+	16.8384i	0.0752006	+	0.571205i
$870$	3.03487	+	24.4385i	0.102892	+	0.828544i
$871$	−0.537256	−	2.00507i	−0.0182042	−	0.0679391i
$872$	8.70347	+	17.9647i	0.294737	+	0.608363i
$873$	10.4048	−	31.8810i	0.352148	−	1.07901i
$874$	1.95561	−	0.296330i	0.0661497	−	0.0100235i
$875$	15.3742	−	11.7970i	0.519742	−	0.398812i
$876$	−27.5608	+	36.8350i	−0.931194	+	1.24454i
$877$	18.5817	−	24.2162i	0.627460	−	0.817722i	−0.366154	−	0.930554i	$-0.619326\pi$
$877$	18.5817	−	24.2162i	0.627460	−	0.817722i	0.993614	+	0.112832i	$0.0359923\pi$
$878$	−0.0958666	+	0.0277001i	−0.00323534	+	0.000934833i
$879$	−5.70470	−	23.8303i	−0.192415	−	0.803774i
$880$	−26.0131	−	22.2445i	−0.876901	−	0.749861i
$881$	33.0415			1.11320			0.556599	−	0.830781i	$-0.312106\pi$
$881$	33.0415			1.11320			0.556599	+	0.830781i	$0.312106\pi$
$882$	−13.5509	+	12.6548i	−0.456283	+	0.426111i
$883$	25.4881	−	10.5575i	0.857742	−	0.355289i	0.0899183	−	0.995949i	$-0.471339\pi$
$883$	25.4881	−	10.5575i	0.857742	−	0.355289i	0.767824	+	0.640661i	$0.221339\pi$
$884$	8.32805	−	11.7764i	0.280103	−	0.396082i
$885$	9.87589	+	25.7778i	0.331974	+	0.866512i
$886$	3.42175	+	4.28385i	0.114956	+	0.143919i
$887$	41.5709	+	11.1389i	1.39581	+	0.374007i	0.876840	−	0.480783i	$-0.159648\pi$
$887$	41.5709	+	11.1389i	1.39581	+	0.374007i	0.518974	+	0.854790i	$0.326314\pi$
$888$	−3.63601	+	15.5164i	−0.122017	+	0.520697i
$889$	8.89636	−	2.38377i	0.298374	−	0.0799491i
$890$	−23.4388	−	17.2703i	−0.785670	−	0.578900i
$891$	22.7829	−	41.7011i	0.763257	−	1.39704i
$892$	15.5096	+	8.16600i	0.519301	+	0.273418i
$893$	1.08430	+	0.142750i	0.0362846	+	0.00477696i
$894$	−31.3196	+	8.14588i	−1.04748	+	0.272439i
$895$	21.2118	−	12.2466i	0.709031	−	0.409359i
$896$	−7.11405	−	16.9118i	−0.237664	−	0.564982i
$897$	8.00330	−	7.58493i	0.267222	−	0.253253i
$898$	−0.156577	−	8.03520i	−0.00522503	−	0.268138i
$899$	−10.5404	+	4.36599i	−0.351543	+	0.145614i
$900$	12.4365	−	6.93854i	0.414550	−	0.231285i
$901$	17.8736	−	43.1508i	0.595457	−	1.43756i
$902$	−16.8950	−	38.6411i	−0.562543	−	1.28661i
$903$	8.53300	−	13.9042i	0.283961	−	0.462704i
$904$	−16.6111	−	25.2409i	−0.552477	−	0.839500i
$905$	4.97594	−	18.5705i	0.165406	−	0.617303i
$906$	8.40646	−	3.40992i	0.279286	−	0.113287i
$907$	14.0565	+	18.3188i	0.466738	+	0.608265i	0.966113	−	0.258121i	$-0.0831034\pi$
$907$	14.0565	+	18.3188i	0.466738	+	0.608265i	−0.499374	+	0.866386i	$0.666437\pi$
$908$	1.74537	−	18.9320i	0.0579222	−	0.628279i
$909$	−27.2245	+	31.7917i	−0.902980	+	1.05446i
$910$	1.75257	−	7.09050i	0.0580973	−	0.235048i
$911$	42.7753	+	24.6963i	1.41721	+	0.818226i	0.996053	−	0.0887624i	$-0.0282912\pi$
$911$	42.7753	+	24.6963i	1.41721	+	0.818226i	0.421156	+	0.906988i	$0.361625\pi$
$912$	2.51058	−	1.62591i	0.0831338	−	0.0538393i
$913$	7.64145	−	4.41179i	0.252895	−	0.146009i
$914$	9.43153	+	32.6414i	0.311967	+	1.07968i
$915$	31.2198	−	3.26075i	1.03209	−	0.107797i
$916$	6.58408	−	1.12930i	0.217544	−	0.0373133i
$917$	−10.5824	+	25.5482i	−0.349463	+	0.843677i
$918$	25.4982	−	8.78185i	0.841567	−	0.289844i
$919$	−42.1113	−	42.1113i	−1.38912	−	1.38912i	−0.827169	−	0.561954i	$-0.810050\pi$
$919$	−42.1113	−	42.1113i	−1.38912	−	1.38912i	−0.561954	−	0.827169i	$-0.689950\pi$
$920$	1.07490	−	14.8109i	0.0354384	−	0.488299i
$921$	33.0944	−	17.9408i	1.09050	−	0.591171i
$922$	−4.06841	+	36.3644i	−0.133986	+	1.19760i
$923$	32.2408	−	4.24459i	1.06122	−	0.139712i
$924$	25.8648	+	14.5174i	0.850889	+	0.477588i
$925$	1.00782	−	7.65519i	0.0331371	−	0.251701i
$926$	4.54566	+	7.53057i	0.149380	+	0.247470i
$927$	−57.0818	−	3.06620i	−1.87481	−	0.100707i
$928$	−35.0726	−	1.17468i	−1.15131	−	0.0385607i
$929$	−8.23505	−	4.75451i	−0.270183	−	0.155990i	0.358788	−	0.933419i	$-0.383190\pi$
$929$	−8.23505	−	4.75451i	−0.270183	−	0.155990i	−0.628971	+	0.777429i	$0.716524\pi$
$930$	−5.12436	−	5.20023i	−0.168034	−	0.170522i
$931$	1.14856	−	1.49684i	0.0376427	−	0.0490569i
$932$	−22.1852	−	20.5202i	−0.726701	−	0.672163i
$933$	27.0134	+	4.29656i	0.884377	+	0.140663i
$934$	8.38348	+	19.1741i	0.274316	+	0.627396i
$935$	22.2050	+	22.2050i	0.726180	+	0.726180i
$936$	6.30726	−	15.4357i	0.206159	−	0.504531i
$937$	−11.9823	+	11.9823i	−0.391446	+	0.391446i	−0.875202	−	0.483757i	$-0.839272\pi$
$937$	−11.9823	+	11.9823i	−0.391446	+	0.391446i	0.483757	+	0.875202i	$0.339272\pi$
$938$	2.25579	+	0.883293i	0.0736542	+	0.0288405i
$939$	22.6215	−	8.66665i	0.738225	−	0.282826i
$940$	2.84424	−	7.70248i	0.0927688	−	0.251227i
$941$	−25.0693	−	19.2364i	−0.817237	−	0.627088i	0.113187	−	0.993574i	$-0.463894\pi$
$941$	−25.0693	−	19.2364i	−0.817237	−	0.627088i	−0.930424	+	0.366486i	$0.880561\pi$
$942$	−29.7824	−	17.4879i	−0.970364	−	0.569788i
$943$	9.14864	−	15.8459i	0.297921	−	0.516014i
$944$	−38.4820	+	8.15531i	−1.25248	+	0.265433i
$945$	10.4016	−	8.84870i	0.338365	−	0.287848i
$946$	42.1011	+	10.4062i	1.36882	+	0.338335i
$947$	27.4726	+	3.61683i	0.892738	+	0.117531i	0.562918	−	0.826513i	$-0.309679\pi$
$947$	27.4726	+	3.61683i	0.892738	+	0.117531i	0.329820	+	0.944044i	$0.393012\pi$
$948$	−4.13898	+	10.3457i	−0.134428	+	0.336014i
$949$	−3.40641	−	25.8742i	−0.110577	−	0.839913i
$950$	−1.13229	+	0.904426i	−0.0367364	+	0.0293434i
$951$	−26.1296	−	0.701283i	−0.847310	−	0.0227407i
$952$	5.29912	+	15.9772i	0.171745	+	0.517823i
$953$	37.5423	−	37.5423i	1.21611	−	1.21611i	0.247133	−	0.968982i	$-0.420512\pi$
$953$	37.5423	−	37.5423i	1.21611	−	1.21611i	0.968982	−	0.247133i	$-0.0794884\pi$
$954$	8.87311	−	53.2612i	0.287278	−	1.72439i
$955$	−29.6864	−	12.2965i	−0.960628	−	0.397905i
$956$	−16.9546	+	10.6904i	−0.548351	+	0.345752i
$957$	45.9181	−	33.3157i	1.48432	−	1.07694i
$958$	−6.38129	+	11.5675i	−0.206170	+	0.373729i
$959$	2.33316	+	4.04114i	0.0753415	+	0.130495i
$960$	−7.73965	−	21.0804i	−0.249796	−	0.680366i
$961$	−13.8088	+	23.9176i	−0.445447	+	0.771536i
$962$	−4.67198	−	7.73984i	−0.150631	−	0.249543i
$963$	33.3543	+	6.22687i	1.07483	+	0.200658i
$964$	−10.9104	−	5.74444i	−0.351400	−	0.185016i
$965$	−31.6094	+	24.2547i	−1.01754	+	0.780788i
$966$	1.58588	+	12.7704i	0.0510248	+	0.410881i
$967$	−23.8605	−	6.39340i	−0.767302	−	0.205598i	−0.146123	−	0.989266i	$-0.546679\pi$
$967$	−23.8605	−	6.39340i	−0.767302	−	0.205598i	−0.621179	+	0.783668i	$0.713346\pi$
$968$	−9.64018	+	46.7521i	−0.309847	+	1.50267i
$969$	−2.41255	+	1.30787i	−0.0775022	+	0.0420148i
$970$	23.8570	+	9.34159i	0.766001	+	0.299940i
$971$	12.8054	+	5.30418i	0.410945	+	0.170219i	0.578572	−	0.815631i	$-0.303610\pi$
$971$	12.8054	+	5.30418i	0.410945	+	0.170219i	−0.167626	+	0.985851i	$0.553610\pi$
$972$	26.4263	−	16.5424i	0.847624	−	0.530597i
$973$	−5.07518	−	12.2526i	−0.162703	−	0.392800i
$974$	17.3800	−	18.0708i	0.556890	−	0.579025i
$975$	−2.29953	+	7.74453i	−0.0736439	+	0.248024i
$976$	−2.36798	+	44.6672i	−0.0757971	+	1.42976i
$977$	16.7079	+	28.9390i	0.534534	+	0.925840i	0.999186	+	0.0403467i	$0.0128462\pi$
$977$	16.7079	+	28.9390i	0.534534	+	0.925840i	−0.464652	+	0.885494i	$0.653820\pi$
$978$	−10.0360	−	17.6817i	−0.320917	−	0.565399i
$979$	−8.75437	+	66.4961i	−0.279791	+	2.12522i
$980$	−9.05435	−	10.8934i	−0.289231	−	0.347976i
$981$	−11.9697	−	17.4648i	−0.382163	−	0.557608i
$982$	−4.33829	−	28.6304i	−0.138440	−	0.913632i
$983$	1.92322	+	7.17754i	0.0613411	+	0.228928i	0.989790	−	0.142531i	$-0.0455242\pi$
$983$	1.92322	+	7.17754i	0.0613411	+	0.228928i	−0.928449	+	0.371459i	$0.878858\pi$
$984$	2.74254	−	27.5334i	0.0874289	−	0.877732i
$985$	−1.97046	+	7.35385i	−0.0627840	+	0.234313i
$986$	31.9966	+	3.57975i	1.01898	+	0.114003i
$987$	−1.11766	+	7.02699i	−0.0355757	+	0.223672i
$988$	−0.374977	+	1.65484i	−0.0119296	+	0.0526473i
$989$	7.20045	+	17.3834i	0.228961	+	0.552761i
$990$	30.8010	+	19.2155i	0.978919	+	0.610709i
$991$			22.9964i			0.730503i	0.930909	+	0.365252i	$0.119017\pi$
$991$			22.9964i			0.730503i	−0.930909	+	0.365252i	$0.880983\pi$
$992$	8.46107	−	6.05345i	0.268639	−	0.192197i
$993$	−23.4986	−	24.7947i	−0.745705	−	0.786837i
$994$	−18.3317	+	33.2303i	−0.581448	+	1.05400i
$995$	−24.7149	−	18.9644i	−0.783516	−	0.601213i
$996$	5.78869	−	0.0702524i	0.183422	−	0.00222603i
$997$	−15.9480	−	20.7838i	−0.505077	−	0.658229i	0.469330	−	0.883023i	$-0.344496\pi$
$997$	−15.9480	−	20.7838i	−0.505077	−	0.658229i	−0.974406	+	0.224794i	$0.927829\pi$
$998$	1.65649	+	1.22054i	0.0524353	+	0.0386356i
$999$	1.35920	−	16.8487i	0.0430033	−	0.533071i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bf.a.11.1	✓	368
3.2	odd	2		864.2.bn.a.683.46		368
9.4	even	3		864.2.bn.a.395.32		368
9.5	odd	6	inner	288.2.bf.a.203.15	yes	368
32.3	odd	8	inner	288.2.bf.a.227.15	yes	368
96.35	even	8		864.2.bn.a.35.32		368
288.67	odd	24		864.2.bn.a.611.46		368
288.131	even	24	inner	288.2.bf.a.131.1	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.1	✓	368	1.1	even	1	trivial
288.2.bf.a.131.1	yes	368	288.131	even	24	inner
288.2.bf.a.203.15	yes	368	9.5	odd	6	inner
288.2.bf.a.227.15	yes	368	32.3	odd	8	inner
864.2.bn.a.35.32		368	96.35	even	8
864.2.bn.a.395.32		368	9.4	even	3
864.2.bn.a.611.46		368	288.67	odd	24
864.2.bn.a.683.46		368	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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bf (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41395 + 0.0275526i) q^{2} +(1.72268 - 0.179925i) q^{3} +(1.99848 - 0.0779158i) q^{4} +(-0.211536 - 1.60678i) q^{5} +(-2.43082 + 0.301868i) q^{6} +(0.419720 + 1.56642i) q^{7} +(-2.82360 + 0.165232i) q^{8} +(2.93525 - 0.619906i) q^{9} +O(q^{10})\)	\(q+(-1.41395 + 0.0275526i) q^{2} +(1.72268 - 0.179925i) q^{3} +(1.99848 - 0.0779158i) q^{4} +(-0.211536 - 1.60678i) q^{5} +(-2.43082 + 0.301868i) q^{6} +(0.419720 + 1.56642i) q^{7} +(-2.82360 + 0.165232i) q^{8} +(2.93525 - 0.619906i) q^{9} +(0.343371 + 2.26607i) q^{10} +(4.18881 - 3.21419i) q^{11} +(3.42873 - 0.493801i) q^{12} +(-1.19629 + 1.55903i) q^{13} +(-0.636620 - 2.20326i) q^{14} +(-0.653508 - 2.72990i) q^{15} +(3.98786 - 0.311427i) q^{16} -3.66990 q^{17} +(-4.13321 + 0.957388i) q^{18} +(0.398863 - 0.165215i) q^{19} +(-0.547944 - 3.19463i) q^{20} +(1.00488 + 2.62291i) q^{21} +(-5.83419 + 4.66009i) q^{22} +(-3.12920 - 0.838465i) q^{23} +(-4.83442 + 0.792678i) q^{24} +(2.29265 - 0.614312i) q^{25} +(1.64853 - 2.23735i) q^{26} +(4.94497 - 1.59603i) q^{27} +(0.960851 + 3.09775i) q^{28} +(6.15042 + 0.809718i) q^{29} +(0.999241 + 3.84193i) q^{30} +(-1.59271 + 0.919554i) q^{31} +(-5.63003 + 0.550216i) q^{32} +(6.63766 - 6.29068i) q^{33} +(5.18904 - 0.101115i) q^{34} +(2.42809 - 1.00575i) q^{35} +(5.81775 - 1.46757i) q^{36} +(1.24490 - 3.00545i) q^{37} +(-0.559419 + 0.244594i) q^{38} +(-1.78031 + 2.90096i) q^{39} +(0.862784 + 4.50194i) q^{40} +(-1.46182 + 5.45559i) q^{41} +(-1.49311 - 3.68097i) q^{42} +(-3.53572 - 4.60784i) q^{43} +(8.12082 - 6.74987i) q^{44} +(-1.61696 - 4.58517i) q^{45} +(4.44761 + 1.09933i) q^{46} +(2.19382 + 1.26660i) q^{47} +(6.81377 - 1.25400i) q^{48} +(3.78468 - 2.18509i) q^{49} +(-3.22475 + 0.931773i) q^{50} +(-6.32206 + 0.660307i) q^{51} +(-2.26929 + 3.20891i) q^{52} +(-4.87033 + 11.7580i) q^{53} +(-6.94794 + 2.39294i) q^{54} +(-6.05056 - 6.05056i) q^{55} +(-1.44394 - 4.35357i) q^{56} +(0.657388 - 0.356377i) q^{57} +(-8.71866 - 0.975436i) q^{58} +(-9.75004 + 1.28362i) q^{59} +(-1.51873 - 5.40474i) q^{60} +(-1.45961 + 11.0868i) q^{61} +(2.22667 - 1.34408i) q^{62} +(2.20302 + 4.33764i) q^{63} +(7.94540 - 0.933098i) q^{64} +(2.75808 + 1.59238i) q^{65} +(-9.21197 + 9.07757i) q^{66} +(-0.643049 + 0.838037i) q^{67} +(-7.33423 + 0.285943i) q^{68} +(-5.54146 - 0.881387i) q^{69} +(-3.40548 + 1.48897i) q^{70} +(-11.7013 - 11.7013i) q^{71} +(-8.18555 + 2.23536i) q^{72} +(-9.39064 + 9.39064i) q^{73} +(-1.67741 + 4.28384i) q^{74} +(3.83896 - 1.47077i) q^{75} +(0.784248 - 0.361256i) q^{76} +(6.79288 + 5.21236i) q^{77} +(2.43734 - 4.15085i) q^{78} +(-1.60835 + 2.78574i) q^{79} +(-1.34397 - 6.34172i) q^{80} +(8.23143 - 3.63917i) q^{81} +(1.91662 - 7.75418i) q^{82} +(1.65688 + 0.218132i) q^{83} +(2.21260 + 5.16355i) q^{84} +(0.776316 + 5.89671i) q^{85} +(5.12628 + 6.41782i) q^{86} +(10.7409 + 0.288271i) q^{87} +(-11.2964 + 9.76769i) q^{88} +(-8.98232 + 8.98232i) q^{89} +(2.41263 + 6.43862i) q^{90} +(-2.94420 - 1.21953i) q^{91} +(-6.31897 - 1.43184i) q^{92} +(-2.57829 + 1.87067i) q^{93} +(-3.13684 - 1.73046i) q^{94} +(-0.349837 - 0.605936i) q^{95} +(-9.59975 + 1.96083i) q^{96} +(5.58932 - 9.68098i) q^{97} +(-5.29113 + 3.19387i) q^{98} +(10.3027 - 12.0311i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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