LMFDB - Embedded newform 261.2.x.a.2.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,2,Mod(2,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(84))

chi = DirichletCharacter(H, H._module([14, 3]))

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

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

chi := DirichletCharacter("261.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.x (of order $84$, degree $24$, 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:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$28$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			2.2
Character	$\chi$	$=$	261.2
Dual form			261.2.x.a.131.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.09871 - 1.54892i) q^{2} +(0.154284 - 1.72517i) q^{3} +(1.41592 + 4.59031i) q^{4} +(0.316022 - 0.805210i) q^{5} +(-2.99594 + 3.38165i) q^{6} +(0.806416 + 0.248746i) q^{7} +(2.41541 - 6.90284i) q^{8} +(-2.95239 - 0.532331i) q^{9} +O(q^{10})$	\(q+(-2.09871 - 1.54892i) q^{2} +(0.154284 - 1.72517i) q^{3} +(1.41592 + 4.59031i) q^{4} +(0.316022 - 0.805210i) q^{5} +(-2.99594 + 3.38165i) q^{6} +(0.806416 + 0.248746i) q^{7} +(2.41541 - 6.90284i) q^{8} +(-2.95239 - 0.532331i) q^{9} +(-1.91044 + 1.20041i) q^{10} +(-5.60376 - 1.06029i) q^{11} +(8.13751 - 1.73449i) q^{12} +(-3.77591 + 0.282965i) q^{13} +(-1.30715 - 1.77112i) q^{14} +(-1.34036 - 0.669421i) q^{15} +(-7.82313 + 5.33372i) q^{16} +(0.354593 + 0.354593i) q^{17} +(5.37168 + 5.69022i) q^{18} +(-3.63939 - 5.79205i) q^{19} +(4.14363 + 0.310522i) q^{20} +(0.553546 - 1.35282i) q^{21} +(10.1184 + 10.9050i) q^{22} +(-0.354747 + 2.35360i) q^{23} +(-11.5359 - 5.23198i) q^{24} +(3.11677 + 2.89194i) q^{25} +(8.36282 + 5.25471i) q^{26} +(-1.37387 + 5.01124i) q^{27} +4.05391i q^{28} +(4.65370 - 2.70981i) q^{29} +(1.77616 + 3.48103i) q^{30} +(-0.850723 - 1.94988i) q^{31} +(10.0637 + 0.376558i) q^{32} +(-2.69375 + 9.50384i) q^{33} +(-0.194952 - 1.29342i) q^{34} +(0.455138 - 0.570725i) q^{35} +(-1.73680 - 14.3062i) q^{36} +(-3.00215 - 1.05050i) q^{37} +(-1.33340 + 17.7929i) q^{38} +(-0.0944008 + 6.55772i) q^{39} +(-4.79492 - 4.12636i) q^{40} +(-5.84116 - 1.56513i) q^{41} +(-3.25715 + 1.98179i) q^{42} +(5.16563 + 2.25374i) q^{43} +(-3.06745 - 27.2243i) q^{44} +(-1.36166 + 2.20907i) q^{45} +(4.39004 - 4.39004i) q^{46} +(0.176761 - 0.934203i) q^{47} +(7.99456 + 14.3191i) q^{48} +(-5.19524 - 3.54205i) q^{49} +(-2.06181 - 10.8969i) q^{50} +(0.666440 - 0.557024i) q^{51} +(-6.64530 - 16.9319i) q^{52} +(5.52744 - 4.40798i) q^{53} +(10.6453 - 8.38912i) q^{54} +(-2.62467 + 4.17713i) q^{55} +(3.66488 - 4.96574i) q^{56} +(-10.5537 + 5.38492i) q^{57} +(-13.9640 - 1.52111i) q^{58} +(-9.57798 + 5.52985i) q^{59} +(1.17500 - 7.10054i) q^{60} +(10.8872 - 5.75405i) q^{61} +(-1.23478 + 5.40993i) q^{62} +(-2.24844 - 1.16368i) q^{63} +(-5.73224 - 4.57131i) q^{64} +(-0.965422 + 3.12982i) q^{65} +(20.3741 - 15.7734i) q^{66} +(6.11472 - 8.96864i) q^{67} +(-1.12562 + 2.12977i) q^{68} +(4.00561 + 0.975121i) q^{69} +(-1.83921 + 0.492815i) q^{70} +(-2.23829 - 1.07790i) q^{71} +(-10.8058 + 19.0941i) q^{72} +(6.40414 - 0.721574i) q^{73} +(4.67351 + 6.85478i) q^{74} +(5.46994 - 4.93076i) q^{75} +(21.4342 - 24.9070i) q^{76} +(-4.25522 - 2.24895i) q^{77} +(10.3555 - 13.6165i) q^{78} +(-10.3362 - 12.0109i) q^{79} +(1.82249 + 7.98483i) q^{80} +(8.43325 + 3.14330i) q^{81} +(9.83464 + 12.3322i) q^{82} +(3.83954 - 4.13804i) q^{83} +(6.99367 + 0.625454i) q^{84} +(0.397581 - 0.173463i) q^{85} +(-7.35029 - 12.7311i) q^{86} +(-3.95687 - 8.44649i) q^{87} +(-20.8544 + 36.1209i) q^{88} +(-0.611623 + 5.42831i) q^{89} +(6.27939 - 2.52710i) q^{90} +(-3.11534 - 0.711056i) q^{91} +(-11.3060 + 1.70411i) q^{92} +(-3.49512 + 1.16680i) q^{93} +(-1.81797 + 1.68683i) q^{94} +(-5.81394 + 1.10006i) q^{95} +(2.20230 - 17.3035i) q^{96} +(0.336663 + 8.99750i) q^{97} +(5.41695 + 15.4807i) q^{98} +(15.9801 + 6.11345i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9}+O(q^{10}) $ 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9	$ 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20} - 80 q^{21} - 14 q^{22} - 30 q^{23} - 16 q^{24} + 30 q^{25} + 36 q^{27} - 168 q^{30} - 12 q^{31} + 24 q^{32} - 70 q^{33} - 14 q^{34} + 128 q^{36} - 48 q^{37} - 42 q^{38} - 44 q^{39} - 2 q^{40} - 24 q^{41} - 28 q^{42} - 12 q^{43} + 24 q^{45} - 64 q^{46} - 42 q^{47} - 28 q^{48} + 22 q^{49} - 66 q^{50} - 28 q^{51} + 22 q^{52} - 36 q^{54} + 76 q^{55} - 42 q^{56} - 42 q^{58} - 132 q^{59} - 20 q^{60} - 28 q^{63} - 308 q^{64} - 66 q^{65} - 46 q^{66} - 14 q^{67} + 60 q^{68} - 64 q^{69} - 14 q^{70} + 56 q^{72} - 48 q^{73} + 66 q^{74} + 24 q^{75} - 28 q^{76} + 30 q^{77} + 72 q^{78} - 12 q^{79} + 140 q^{81} - 136 q^{82} + 246 q^{83} + 238 q^{84} + 34 q^{85} + 118 q^{87} + 8 q^{88} - 48 q^{90} - 56 q^{91} + 462 q^{92} + 28 q^{93} + 26 q^{94} - 246 q^{95} + 126 q^{96} - 36 q^{97} - 16 q^{99}+O(q^{100}) $ 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−2.09871	−	1.54892i	−1.48401	−	1.09525i	−0.971634	−	0.236491i	$-0.924003\pi$
$2$	−2.09871	−	1.54892i	−1.48401	−	1.09525i	−0.512378	−	0.858760i	$-0.671235\pi$
$3$	0.154284	−	1.72517i	0.0890760	−	0.996025i
$3$	0.154284	−	1.72517i	0.0890760	−	0.996025i
$4$	1.41592	+	4.59031i	0.707962	+	2.29516i
$5$	0.316022	−	0.805210i	0.141329	−	0.360101i	−0.842630	−	0.538492i	$-0.818994\pi$
$5$	0.316022	−	0.805210i	0.141329	−	0.360101i	0.983960	+	0.178391i	$0.0570893\pi$
$6$	−2.99594	+	3.38165i	−1.22309	+	1.38055i
$7$	0.806416	+	0.248746i	0.304797	+	0.0940173i	0.443381	−	0.896333i	$-0.353779\pi$
$7$	0.806416	+	0.248746i	0.304797	+	0.0940173i	−0.138584	+	0.990351i	$0.544255\pi$
$8$	2.41541	−	6.90284i	0.853976	−	2.44052i
$9$	−2.95239	−	0.532331i	−0.984131	−	0.177444i
$10$	−1.91044	+	1.20041i	−0.604135	+	0.379603i
$11$	−5.60376	−	1.06029i	−1.68960	−	0.319689i	−0.749863	−	0.661593i	$-0.769881\pi$
$11$	−5.60376	−	1.06029i	−1.68960	−	0.319689i	−0.939735	+	0.341903i	$0.888928\pi$
$12$	8.13751	−	1.73449i	2.34910	−	0.500705i
$13$	−3.77591	+	0.282965i	−1.04725	+	0.0784804i	−0.587223	−	0.809425i	$-0.699779\pi$
$13$	−3.77591	+	0.282965i	−1.04725	+	0.0784804i	−0.460025	+	0.887906i	$0.652160\pi$
$14$	−1.30715	−	1.77112i	−0.349349	−	0.473352i
$15$	−1.34036	−	0.669421i	−0.346081	−	0.172844i
$16$	−7.82313	+	5.33372i	−1.95578	+	1.33343i
$17$	0.354593	+	0.354593i	0.0860015	+	0.0860015i	0.748799	−	0.662797i	$-0.230631\pi$
$17$	0.354593	+	0.354593i	0.0860015	+	0.0860015i	−0.662797	+	0.748799i	$0.730631\pi$
$18$	5.37168	+	5.69022i	1.26612	+	1.34120i
$19$	−3.63939	−	5.79205i	−0.834932	−	1.32879i	−0.942369	−	0.334575i	$-0.891407\pi$
$19$	−3.63939	−	5.79205i	−0.834932	−	1.32879i	0.107437	−	0.994212i	$-0.465736\pi$
$20$	4.14363	+	0.310522i	0.926544	+	0.0694349i
$21$	0.553546	−	1.35282i	0.120794	−	0.295210i
$22$	10.1184	+	10.9050i	2.15724	+	2.32496i
$23$	−0.354747	+	2.35360i	−0.0739700	+	0.490759i	0.920917	+	0.389760i	$0.127442\pi$
$23$	−0.354747	+	2.35360i	−0.0739700	+	0.490759i	−0.994887	+	0.100999i	$0.967796\pi$
$24$	−11.5359	−	5.23198i	−2.35475	−	1.06797i
$25$	3.11677	+	2.89194i	0.623353	+	0.578387i
$26$	8.36282	+	5.25471i	1.64008	+	1.03053i
$27$	−1.37387	+	5.01124i	−0.264401	+	0.964413i
$28$			4.05391i			0.766117i
$29$	4.65370	−	2.70981i	0.864171	−	0.503198i
$29$	4.65370	−	2.70981i	0.864171	−	0.503198i
$30$	1.77616	+	3.48103i	0.324280	+	0.635547i
$31$	−0.850723	−	1.94988i	−0.152794	−	0.350209i	0.823283	−	0.567631i	$-0.192140\pi$
$31$	−0.850723	−	1.94988i	−0.152794	−	0.350209i	−0.976078	+	0.217422i	$0.930235\pi$
$32$	10.0637	+	0.376558i	1.77903	+	0.0665666i
$33$	−2.69375	+	9.50384i	−0.468921	+	1.65441i
$34$	−0.194952	−	1.29342i	−0.0334340	−	0.221820i
$35$	0.455138	−	0.570725i	0.0769324	−	0.0964702i
$36$	−1.73680	−	14.3062i	−0.289466	−	2.38436i
$37$	−3.00215	−	1.05050i	−0.493551	−	0.172701i	0.0720160	−	0.997403i	$-0.477057\pi$
$37$	−3.00215	−	1.05050i	−0.493551	−	0.172701i	−0.565567	+	0.824703i	$0.691342\pi$
$38$	−1.33340	+	17.7929i	−0.216305	+	2.88640i
$39$	−0.0944008	+	6.55772i	−0.0151162	+	1.05008i
$40$	−4.79492	−	4.12636i	−0.758143	−	0.652435i
$41$	−5.84116	−	1.56513i	−0.912236	−	0.244433i	−0.227973	−	0.973668i	$-0.573210\pi$
$41$	−5.84116	−	1.56513i	−0.912236	−	0.244433i	−0.684264	+	0.729235i	$0.739876\pi$
$42$	−3.25715	+	1.98179i	−0.502589	+	0.305796i
$43$	5.16563	+	2.25374i	0.787750	+	0.343692i	0.754961	−	0.655770i	$-0.227656\pi$
$43$	5.16563	+	2.25374i	0.787750	+	0.343692i	0.0327900	+	0.999462i	$0.489561\pi$
$44$	−3.06745	−	27.2243i	−0.462435	−	4.10422i
$45$	−1.36166	+	2.20907i	−0.202984	+	0.329309i
$46$	4.39004	−	4.39004i	0.647276	−	0.647276i
$47$	0.176761	−	0.934203i	0.0257832	−	0.136267i	−0.967310	−	0.253598i	$-0.918386\pi$
$47$	0.176761	−	0.934203i	0.0257832	−	0.136267i	0.993093	+	0.117330i	$0.0374336\pi$
$48$	7.99456	+	14.3191i	1.15392	+	2.06678i
$49$	−5.19524	−	3.54205i	−0.742177	−	0.506008i
$50$	−2.06181	−	10.8969i	−0.291585	−	1.54106i
$51$	0.666440	−	0.557024i	0.0933203	−	0.0779989i
$52$	−6.64530	−	16.9319i	−0.921537	−	2.34804i
$53$	5.52744	−	4.40798i	0.759252	−	0.605483i	−0.165431	−	0.986221i	$-0.552902\pi$
$53$	5.52744	−	4.40798i	0.759252	−	0.605483i	0.924683	+	0.380738i	$0.124330\pi$
$54$	10.6453	−	8.38912i	1.44865	−	1.14161i
$55$	−2.62467	+	4.17713i	−0.353910	+	0.563245i
$56$	3.66488	−	4.96574i	0.489741	−	0.663575i
$57$	−10.5537	+	5.38492i	−1.39788	+	0.713250i
$58$	−13.9640	−	1.52111i	−1.83357	−	0.199731i
$59$	−9.57798	+	5.52985i	−1.24695	+	0.719925i	−0.970499	−	0.241104i	$-0.922490\pi$
$59$	−9.57798	+	5.52985i	−1.24695	+	0.719925i	−0.276447	+	0.961029i	$0.589157\pi$
$60$	1.17500	−	7.10054i	0.151692	−	0.916676i
$61$	10.8872	−	5.75405i	1.39396	−	0.736730i	0.409497	−	0.912311i	$-0.365704\pi$
$61$	10.8872	−	5.75405i	1.39396	−	0.736730i	0.984465	+	0.175581i	$0.0561804\pi$
$62$	−1.23478	+	5.40993i	−0.156817	+	0.687062i
$63$	−2.24844	−	1.16368i	−0.283277	−	0.146610i
$64$	−5.73224	−	4.57131i	−0.716530	−	0.571414i
$65$	−0.965422	+	3.12982i	−0.119746	+	0.388207i
$66$	20.3741	−	15.7734i	2.50787	−	1.94157i
$67$	6.11472	−	8.96864i	0.747032	−	1.09569i	−0.244978	−	0.969529i	$-0.578781\pi$
$67$	6.11472	−	8.96864i	0.747032	−	1.09569i	0.992009	−	0.126165i	$-0.0402670\pi$
$68$	−1.12562	+	2.12977i	−0.136501	+	0.258273i
$69$	4.00561	+	0.975121i	0.482219	+	0.117391i
$70$	−1.83921	+	0.492815i	−0.219828	+	0.0589026i
$71$	−2.23829	−	1.07790i	−0.265636	−	0.127924i	0.296325	−	0.955087i	$-0.404239\pi$
$71$	−2.23829	−	1.07790i	−0.265636	−	0.127924i	−0.561962	+	0.827163i	$0.689953\pi$
$72$	−10.8058	+	19.0941i	−1.27348	+	2.25026i
$73$	6.40414	−	0.721574i	0.749548	−	0.0844538i	0.271078	−	0.962557i	$-0.412620\pi$
$73$	6.40414	−	0.721574i	0.749548	−	0.0844538i	0.478470	+	0.878104i	$0.341191\pi$
$74$	4.67351	+	6.85478i	0.543284	+	0.796852i
$75$	5.46994	−	4.93076i	0.631614	−	0.569355i
$76$	21.4342	−	24.9070i	2.45867	−	2.85703i
$77$	−4.25522	−	2.24895i	−0.484928	−	0.256292i
$78$	10.3555	−	13.6165i	1.17253	−	1.54177i
$79$	−10.3362	−	12.0109i	−1.16291	−	1.35133i	−0.924965	−	0.380052i	$-0.875906\pi$
$79$	−10.3362	−	12.0109i	−1.16291	−	1.35133i	−0.237948	−	0.971278i	$-0.576475\pi$
$80$	1.82249	+	7.98483i	0.203760	+	0.892732i
$81$	8.43325	+	3.14330i	0.937027	+	0.349256i
$82$	9.83464	+	12.3322i	1.08605	+	1.36187i
$83$	3.83954	−	4.13804i	0.421444	−	0.454209i	−0.486263	−	0.873812i	$-0.661640\pi$
$83$	3.83954	−	4.13804i	0.421444	−	0.454209i	0.907707	+	0.419604i	$0.137831\pi$
$84$	6.99367	+	0.625454i	0.763072	+	0.0682426i
$85$	0.397581	−	0.173463i	0.0431237	−	0.0188147i
$86$	−7.35029	−	12.7311i	−0.792602	−	1.37283i
$87$	−3.95687	−	8.44649i	−0.424221	−	0.905559i
$88$	−20.8544	+	36.1209i	−2.22309	+	3.85050i
$89$	−0.611623	+	5.42831i	−0.0648319	+	0.575399i	0.918737	+	0.394869i	$0.129210\pi$
$89$	−0.611623	+	5.42831i	−0.0648319	+	0.575399i	−0.983569	+	0.180530i	$0.942219\pi$
$90$	6.27939	−	2.52710i	0.661906	−	0.266379i
$91$	−3.11534	−	0.711056i	−0.326576	−	0.0745389i
$92$	−11.3060	+	1.70411i	−1.17874	+	0.177666i
$93$	−3.49512	+	1.16680i	−0.362427	+	0.120992i
$94$	−1.81797	+	1.68683i	−0.187510	+	0.173983i
$95$	−5.81394	+	1.10006i	−0.596498	+	0.112864i
$96$	2.20230	−	17.3035i	0.224771	−	1.76603i
$97$	0.336663	+	8.99750i	0.0341829	+	0.913558i	0.905886	+	0.423523i	$0.139207\pi$
$97$	0.336663	+	8.99750i	0.0341829	+	0.913558i	−0.871703	+	0.490035i	$0.836984\pi$
$98$	5.41695	+	15.4807i	0.547194	+	1.56379i
$99$	15.9801	+	6.11345i	1.60606	+	0.614425i
$100$	−8.86179	+	18.4017i	−0.886179	+	1.84017i
$101$	−5.11187	+	11.7165i	−0.508650	+	1.16584i	0.452988	+	0.891517i	$0.350358\pi$
$101$	−5.11187	+	11.7165i	−0.508650	+	1.16584i	−0.961638	+	0.274322i	$0.911547\pi$
$102$	−2.26145	+	0.136770i	−0.223917	+	0.0135423i
$103$	−0.534577	−	7.13344i	−0.0526735	−	0.702878i	−0.959560	−	0.281504i	$-0.909167\pi$
$103$	−0.534577	−	7.13344i	−0.0526735	−	0.702878i	0.906887	−	0.421375i	$-0.138452\pi$
$104$	−7.16710	+	26.7480i	−0.702792	+	2.62285i
$105$	−0.914375	−	0.873243i	−0.0892339	−	0.0852198i
$106$	−18.4281	+	0.689530i	−1.78989	+	0.0669731i
$107$	−7.07227	−	14.6857i	−0.683702	−	1.41972i	−0.896686	−	0.442667i	$-0.854032\pi$
$107$	−7.07227	−	14.6857i	−0.683702	−	1.41972i	0.212984	−	0.977056i	$-0.431682\pi$
$108$	−24.9484	+	0.789050i	−2.40066	+	0.0759264i
$109$	−10.0823	+	2.30122i	−0.965711	+	0.220417i	−0.676168	−	0.736748i	$-0.736361\pi$
$109$	−10.0823	+	2.30122i	−0.965711	+	0.220417i	−0.289543	+	0.957165i	$0.593503\pi$
$110$	11.9785	−	4.70120i	1.14210	−	0.448242i
$111$	−2.27547	+	5.01713i	−0.215978	+	0.476205i
$112$	−7.63544	+	2.35522i	−0.721481	+	0.222548i
$113$	−0.0330073	+	0.882137i	−0.00310506	+	0.0829845i	0.996886	+	0.0788512i	$0.0251252\pi$
$113$	−0.0330073	+	0.882137i	−0.00310506	+	0.0829845i	−0.999991	+	0.00413330i	$0.998684\pi$
$114$	30.4900	+	5.04550i	2.85565	+	0.472554i
$115$	1.78303	+	1.02943i	0.166269	+	0.0959952i
$116$	19.0282	+	17.5251i	1.76672	+	1.62716i
$117$	11.2986	+	1.17461i	1.04456	+	0.108593i
$118$	28.6667	+	3.22996i	2.63898	+	0.297342i
$119$	0.197746	+	0.374154i	0.0181273	+	0.0342986i
$120$	−7.85844	+	7.63540i	−0.717374	+	0.697013i
$121$	20.0384	+	7.86447i	1.82167	+	0.714952i
$122$	−31.7616	−	4.78729i	−2.87556	−	0.433421i
$123$	−3.60132	+	9.83550i	−0.324720	+	0.886837i
$124$	7.74599	−	6.66597i	0.695611	−	0.598622i
$125$	7.21029	−	3.47230i	0.644908	−	0.310572i
$126$	2.91639	+	5.92488i	0.259812	+	0.527830i
$127$	11.1504	−	3.90168i	0.989435	−	0.346218i	0.213439	−	0.976956i	$-0.431533\pi$
$127$	11.1504	−	3.90168i	0.989435	−	0.346218i	0.775996	+	0.630738i	$0.217248\pi$
$128$	−0.263286	−	0.982595i	−0.0232714	−	0.0868500i
$129$	4.68505	−	8.56384i	0.412495	−	0.754004i
$130$	6.87398	−	5.07323i	0.602888	−	0.444952i
$131$	13.5117	−	9.97210i	1.18052	−	0.871266i	0.186720	−	0.982413i	$-0.440214\pi$
$131$	13.5117	−	9.97210i	1.18052	−	0.871266i	0.993804	+	0.111147i	$0.0354524\pi$
$132$	−47.4397	+	1.09157i	−4.12910	+	0.0950089i
$133$	−1.49411	−	5.57609i	−0.129556	−	0.483508i
$134$	−26.7247	+	9.35138i	−2.30866	+	0.807836i
$135$	3.60093	+	2.68991i	0.309918	+	0.231511i
$136$	3.30419	−	1.59121i	0.283332	−	0.136445i
$137$	−4.26039	+	3.66636i	−0.363990	+	0.313239i	−0.815200	−	0.579179i	$-0.803373\pi$
$137$	−4.26039	+	3.66636i	−0.363990	+	0.313239i	0.451211	+	0.892417i	$0.350992\pi$
$138$	−6.89623	−	8.25086i	−0.587046	−	0.702360i
$139$	−17.4741	−	2.63380i	−1.48213	−	0.223396i	−0.642390	−	0.766378i	$-0.722057\pi$
$139$	−17.4741	−	2.63380i	−1.48213	−	0.223396i	−0.839744	+	0.542982i	$0.817295\pi$
$140$	3.26425	+	1.28112i	0.275880	+	0.108275i
$141$	−1.58438	−	0.449074i	−0.133429	−	0.0378189i
$142$	3.02794	+	5.72914i	0.254099	+	0.480779i
$143$	21.4593	+	2.41788i	1.79452	+	0.202194i
$144$	25.9363	−	11.5827i	2.16135	−	0.965228i
$145$	−0.711293	−	4.60357i	−0.0590697	−	0.382305i
$146$	−14.5581	−	8.40512i	−1.20484	−	0.695613i
$147$	−6.91217	+	8.41617i	−0.570106	+	0.694154i
$148$	0.571297	−	15.2682i	0.0469603	−	1.25504i
$149$	17.9685	−	5.54255i	1.47204	−	0.454063i	0.548036	−	0.836455i	$-0.315376\pi$
$149$	17.9685	−	5.54255i	1.47204	−	0.454063i	0.924000	+	0.382392i	$0.124899\pi$
$150$	−19.1171	+	1.87574i	−1.56091	+	0.153154i
$151$	2.65905	−	1.04360i	0.216390	−	0.0849270i	−0.254670	−	0.967028i	$-0.581967\pi$
$151$	2.65905	−	1.04360i	0.216390	−	0.0849270i	0.471060	+	0.882101i	$0.343872\pi$
$152$	−48.7722	+	11.1319i	−3.95595	+	0.902920i
$153$	−0.858137	−	1.23566i	−0.0693763	−	0.0998972i
$154$	5.44704	+	11.3109i	0.438935	+	0.911457i
$155$	−1.83891	+	0.0688071i	−0.147705	+	0.00552672i
$156$	−30.2357	+	8.85191i	−2.42079	+	0.708720i
$157$	−1.28534	+	4.79696i	−0.102581	+	0.382839i	−0.998060	−	0.0622663i	$-0.980167\pi$
$157$	−1.28534	+	4.79696i	−0.102581	+	0.382839i	0.895478	+	0.445106i	$0.146834\pi$
$158$	3.08881	+	41.2173i	0.245732	+	3.27907i
$159$	−6.75171	−	10.2158i	−0.535445	−	0.810168i
$160$	3.48356	−	7.98441i	0.275400	−	0.631223i
$161$	−0.871523	+	1.80974i	−0.0686856	+	0.142627i
$162$	−12.8302	−	19.6593i	−1.00804	−	1.54458i
$163$	−3.25576	−	9.30442i	−0.255011	−	0.728778i	−0.998215	−	0.0597145i	$-0.980981\pi$
$163$	−3.25576	−	9.30442i	−0.255011	−	0.728778i	0.743205	−	0.669064i	$-0.233305\pi$
$164$	−1.08618	−	29.0289i	−0.0848167	−	2.26677i
$165$	6.80130	+	5.17245i	0.529481	+	0.402675i
$166$	−14.4676	+	2.73741i	−1.12290	+	0.212464i
$167$	4.50625	−	4.18119i	0.348704	−	0.323550i	−0.486302	−	0.873791i	$-0.661655\pi$
$167$	4.50625	−	4.18119i	0.348704	−	0.323550i	0.835006	+	0.550241i	$0.185464\pi$
$168$	−8.00129	−	7.08867i	−0.617313	−	0.546902i
$169$	1.32260	−	0.199350i	0.101738	−	0.0153346i
$170$	−1.10309	−	0.251773i	−0.0846030	−	0.0193101i
$171$	7.66161	+	19.0378i	0.585898	+	1.45585i
$172$	−3.03124	+	26.9030i	−0.231130	+	2.05133i
$173$	0.0930057	−	0.161091i	0.00707109	−	0.0122475i	−0.862468	−	0.506111i	$-0.831083\pi$
$173$	0.0930057	−	0.161091i	0.00707109	−	0.0122475i	0.869539	+	0.493864i	$0.164416\pi$
$174$	−4.77859	+	23.8556i	−0.362264	+	1.80849i
$175$	1.79405	+	3.10739i	0.135618	+	0.234896i
$176$	49.4943	−	21.5941i	3.73077	−	1.62772i
$177$	8.06217	+	17.3768i	0.605990	+	1.30612i
$178$	9.69162	−	10.4451i	0.726418	−	0.782892i
$179$	−5.04611	−	6.32763i	−0.377164	−	0.472949i	0.556629	−	0.830761i	$-0.312094\pi$
$179$	−5.04611	−	6.32763i	−0.377164	−	0.472949i	−0.933794	+	0.357812i	$0.883523\pi$
$180$	−12.0683	−	3.12257i	−0.899520	−	0.232742i
$181$	−3.87154	−	16.9623i	−0.287770	−	1.26080i	−0.887578	−	0.460657i	$-0.847614\pi$
$181$	−3.87154	−	16.9623i	−0.287770	−	1.26080i	0.599809	−	0.800144i	$-0.295243\pi$
$182$	5.43682	+	6.31770i	0.403004	+	0.468299i
$183$	−8.24697	−	19.6700i	−0.609633	−	1.45405i
$184$	15.3896	+	8.13366i	1.13454	+	0.599622i
$185$	−1.79462	+	2.08538i	−0.131943	+	0.153320i
$186$	9.14252	+	2.96487i	0.670362	+	0.217395i
$187$	−1.61109	−	2.36303i	−0.117814	−	0.172802i
$188$	4.53856	−	0.511373i	0.331009	−	0.0372957i
$189$	−2.35444	+	3.69940i	−0.171260	+	0.269092i
$190$	13.9057	+	6.69662i	1.00882	+	0.485824i
$191$	9.25740	−	2.48051i	0.669842	−	0.179484i	0.0921582	−	0.995744i	$-0.470623\pi$
$191$	9.25740	−	2.48051i	0.669842	−	0.179484i	0.577684	+	0.816261i	$0.303957\pi$
$192$	−8.77066	+	9.18378i	−0.632968	+	0.662782i
$193$	−0.101027	+	0.191153i	−0.00727210	+	0.0137595i	−0.887725	−	0.460375i	$-0.847715\pi$
$193$	−0.101027	+	0.191153i	−0.00727210	+	0.0137595i	0.880453	+	0.474134i	$0.157239\pi$
$194$	13.2298	−	19.4046i	0.949847	−	1.39317i
$195$	5.25051	+	2.14840i	0.375997	+	0.153850i
$196$	8.90307	−	28.8631i	0.635934	−	2.06165i
$197$	7.99768	+	6.37794i	0.569811	+	0.454409i	0.865524	−	0.500868i	$-0.166986\pi$
$197$	7.99768	+	6.37794i	0.569811	+	0.454409i	−0.295713	+	0.955277i	$0.595557\pi$
$198$	−24.0683	−	37.5822i	−1.71046	−	2.67085i
$199$	−4.84165	+	21.2127i	−0.343216	+	1.50373i	0.449026	+	0.893518i	$0.351771\pi$
$199$	−4.84165	+	21.2127i	−0.343216	+	1.50373i	−0.792242	+	0.610207i	$0.791086\pi$
$200$	27.4908	−	14.5293i	1.94390	−	1.02738i
$201$	−14.5290	−	11.9326i	−1.02480	−	0.841662i
$202$	28.8763	−	16.6717i	2.03173	−	1.17302i
$203$	4.42688	−	1.02764i	0.310706	−	0.0721262i
$204$	3.50054	+	2.27047i	0.245087	+	0.158964i
$205$	−3.10620	+	4.20875i	−0.216946	+	0.293952i
$206$	−9.92719	+	15.7990i	−0.691660	+	1.10077i
$207$	2.30025	−	6.75990i	0.159878	−	0.469845i
$208$	28.0301	−	22.3533i	1.94354	−	1.54992i
$209$	14.2530	+	36.3161i	0.985901	+	2.51204i
$210$	0.566426	+	3.24898i	0.0390871	+	0.224201i
$211$	−0.820531	−	4.33661i	−0.0564877	−	0.298545i	0.942918	−	0.333026i	$-0.108070\pi$
$211$	−0.820531	−	4.33661i	−0.0564877	−	0.298545i	−0.999405	+	0.0344813i	$0.989022\pi$
$212$	28.0605	+	19.1313i	1.92720	+	1.31394i
$213$	−2.20490	+	3.69512i	−0.151077	+	0.253186i
$214$	−7.90434	+	41.7754i	−0.540330	+	2.85571i
$215$	3.44718	−	3.44718i	0.235096	−	0.235096i
$216$	31.2733	+	21.5878i	2.12788	+	1.46886i
$217$	−0.201012	−	1.78403i	−0.0136456	−	0.121108i
$218$	24.7243	+	10.7871i	1.67454	+	0.730594i
$219$	−0.256776	−	11.1595i	−0.0173513	−	0.754091i
$220$	−22.8907	−	6.13354i	−1.54329	−	0.413523i
$221$	−1.43925	−	1.23857i	−0.0968143	−	0.0833155i
$222$	12.5467	−	7.00499i	0.842078	−	0.470144i
$223$	−0.397742	+	5.30750i	−0.0266348	+	0.355417i	0.967924	+	0.251242i	$0.0808391\pi$
$223$	−0.397742	+	5.30750i	−0.0266348	+	0.355417i	−0.994559	+	0.104174i	$0.966780\pi$
$224$	8.02188	+	2.80698i	0.535984	+	0.187549i
$225$	−7.66245	−	10.1973i	−0.510830	−	0.679819i
$226$	1.43563	−	1.80022i	0.0954968	−	0.119749i
$227$	1.42348	+	9.44415i	0.0944794	+	0.626830i	0.985087	+	0.172057i	$0.0550414\pi$
$227$	1.42348	+	9.44415i	0.0944794	+	0.626830i	−0.890608	+	0.454773i	$0.849720\pi$
$228$	−39.6618	−	40.8203i	−2.62667	−	2.70339i
$229$	−23.5910	−	0.882714i	−1.55894	−	0.0583314i	−0.756072	−	0.654488i	$-0.772884\pi$
$229$	−23.5910	−	0.882714i	−1.55894	−	0.0583314i	−0.802868	+	0.596157i	$0.796694\pi$
$230$	−2.14756	−	4.92225i	−0.141606	−	0.324564i
$231$	−4.53633	+	6.99399i	−0.298468	+	0.460171i
$232$	−7.46477	−	38.6691i	−0.490086	−	2.53875i
$233$		−	1.06482i		−	0.0697584i	−0.999392	−	0.0348792i	$-0.988895\pi$
$233$		−	1.06482i		−	0.0697584i	0.999392	−	0.0348792i	$-0.0111047\pi$
$234$	−21.8931	−	19.9658i	−1.43120	−	1.30520i
$235$	−0.696369	−	0.437558i	−0.0454261	−	0.0285431i
$236$	−38.9454	−	36.1361i	−2.53513	−	2.35226i
$237$	−22.3155	+	15.9786i	−1.44955	+	1.03792i
$238$	0.164522	−	1.09153i	0.0106644	−	0.0707535i
$239$	−14.7866	−	15.9362i	−0.956467	−	1.03083i	−0.999496	−	0.0317522i	$-0.989891\pi$
$239$	−14.7866	−	15.9362i	−0.956467	−	1.03083i	0.0430290	−	0.999074i	$-0.486299\pi$
$240$	14.0563	−	1.91216i	0.907333	−	0.123429i
$241$	4.61369	+	0.345749i	0.297194	+	0.0222716i	0.222493	−	0.974934i	$-0.428581\pi$
$241$	4.61369	+	0.345749i	0.297194	+	0.0222716i	0.0747013	+	0.997206i	$0.476200\pi$
$242$	−29.8733	−	47.5430i	−1.92033	−	3.05618i
$243$	6.72383	−	14.0638i	0.431334	−	0.902192i
$244$	41.8283	+	41.8283i	2.67778	+	2.67778i
$245$	−4.49391	+	3.06389i	−0.287105	+	0.195745i
$246$	22.7925	−	15.0637i	1.45320	−	0.960427i
$247$	15.3809	+	20.8404i	0.978665	+	1.32604i
$248$	−15.5146	+	1.16265i	−0.985175	+	0.0738287i
$249$	−6.54642	−	7.26227i	−0.414863	−	0.460228i
$250$	−20.5106	−	3.88082i	−1.29721	−	0.245444i
$251$	17.8977	−	11.2458i	1.12969	−	0.709832i	0.168496	−	0.985702i	$-0.446109\pi$
$251$	17.8977	−	11.2458i	1.12969	−	0.709832i	0.961195	+	0.275871i	$0.0889662\pi$
$252$	2.15802	−	11.9687i	0.135943	−	0.753959i
$253$	4.48341	−	12.8129i	0.281870	−	0.805538i
$254$	−29.4448	−	9.08251i	−1.84753	−	0.569887i
$255$	−0.237912	−	0.712656i	−0.0148986	−	0.0446283i
$256$	−6.32662	+	16.1200i	−0.395414	+	1.00750i
$257$	4.92272	+	15.9591i	0.307071	+	0.995500i	0.969234	+	0.246140i	$0.0791624\pi$
$257$	4.92272	+	15.9591i	0.307071	+	0.995500i	−0.662163	+	0.749360i	$0.730361\pi$
$258$	−23.0972	+	10.7163i	−1.43797	+	0.667166i
$259$	−2.15968	−	1.59391i	−0.134196	−	0.0990410i
$260$	−15.7338			−0.975771
$261$	−15.1821	+	5.52310i	−0.939747	+	0.341871i
$262$	−43.8031			−2.70617
$263$	−21.1033	−	15.5749i	−1.30128	−	0.960390i	−0.999976	−	0.00686248i	$-0.997816\pi$
$263$	−21.1033	−	15.5749i	−1.30128	−	0.960390i	−0.301306	−	0.953528i	$-0.597423\pi$
$264$	59.0970	+	41.5502i	3.63717	+	2.55724i
$265$	−1.80256	−	5.84377i	−0.110731	−	0.358980i
$266$	−5.50120	+	14.0168i	−0.337300	+	0.859427i
$267$	9.27037	+	1.89265i	0.567337	+	0.115828i
$268$	49.8269	+	15.3696i	3.04366	+	0.938845i
$269$	−0.303849	+	0.868351i	−0.0185260	+	0.0529443i	−0.952775	−	0.303677i	$-0.901786\pi$
$269$	−0.303849	+	0.868351i	−0.0185260	+	0.0529443i	0.934249	+	0.356621i	$0.116071\pi$
$270$	−3.39085	−	11.2229i	−0.206360	−	0.683003i
$271$	−4.65501	+	2.92494i	−0.282772	+	0.177677i	−0.665948	−	0.745998i	$-0.731973\pi$
$271$	−4.65501	+	2.92494i	−0.282772	+	0.177677i	0.383177	+	0.923675i	$0.374830\pi$
$272$	−4.66533	−	0.882728i	−0.282877	−	0.0535232i
$273$	−1.70734	+	5.26477i	−0.103333	+	0.318638i
$274$	14.6202	−	1.09563i	0.883240	−	0.0661897i
$275$	−14.3993	−	19.5104i	−0.868312	−	1.17652i
$276$	1.19553	+	19.7677i	0.0719625	+	1.18988i
$277$	−5.04558	+	3.44002i	−0.303159	+	0.206691i	−0.705339	−	0.708870i	$-0.749205\pi$
$277$	−5.04558	+	3.44002i	−0.303159	+	0.206691i	0.402180	+	0.915561i	$0.368253\pi$
$278$	32.5935	+	32.5935i	1.95483	+	1.95483i
$279$	1.47369	+	6.20967i	0.0882274	+	0.371763i
$280$	−2.84028	−	4.52028i	−0.169739	−	0.270139i
$281$	12.7177	+	0.953058i	0.758673	+	0.0568547i	0.448448	−	0.893809i	$-0.351977\pi$
$281$	12.7177	+	0.953058i	0.758673	+	0.0568547i	0.310224	+	0.950663i	$0.399596\pi$
$282$	2.62958	+	3.39656i	0.156589	+	0.202262i
$283$	18.8974	+	20.3666i	1.12334	+	1.21067i	0.975111	+	0.221715i	$0.0711655\pi$
$283$	18.8974	+	20.3666i	1.12334	+	1.21067i	0.148225	+	0.988954i	$0.452644\pi$
$284$	1.77867	−	11.8007i	0.105545	−	0.700243i
$285$	1.00078	+	10.1997i	0.0592812	+	0.604180i
$286$	−41.2918	−	38.3132i	−2.44163	−	2.26550i
$287$	−4.32109	−	2.71512i	−0.255066	−	0.160268i
$288$	−29.5116	−	6.46898i	−1.73899	−	0.381188i
$289$		−	16.7485i		−	0.985207i
$290$	−5.63775	+	10.7633i	−0.331060	+	0.632042i
$291$	15.5741	+	0.807372i	0.912971	+	0.0473290i
$292$	12.3800	+	28.3753i	0.724486	+	1.66054i
$293$	−5.27457	−	0.197361i	−0.308144	−	0.0115299i	−0.117128	−	0.993117i	$-0.537369\pi$
$293$	−5.27457	−	0.197361i	−0.308144	−	0.0115299i	−0.191016	+	0.981587i	$0.561178\pi$
$294$	27.5426	−	6.95670i	1.60632	−	0.405723i
$295$	1.42584	+	9.45984i	0.0830157	+	0.550773i
$296$	−14.5028	+	18.1860i	−0.842961	+	1.05704i
$297$	13.0122	−	26.6251i	0.755044	−	1.54494i
$298$	−46.2956	−	16.1995i	−2.68183	−	0.938414i
$299$	0.673508	−	8.98734i	0.0389500	−	0.519751i
$300$	30.3787	+	18.1271i	1.75392	+	1.04657i
$301$	3.60503	+	3.10238i	0.207791	+	0.178818i
$302$	−7.19702	−	1.92844i	−0.414142	−	0.110969i
$303$	19.4243	+	10.6265i	1.11590	+	0.610477i
$304$	59.3645	+	25.9005i	3.40479	+	1.48549i
$305$	−1.19263	−	10.5849i	−0.0682898	−	0.606089i
$306$	−0.112954	+	3.92248i	−0.00645717	+	0.224233i
$307$	−6.15510	+	6.15510i	−0.351290	+	0.351290i	−0.860590	−	0.509299i	$-0.829905\pi$
$307$	−6.15510	+	6.15510i	−0.351290	+	0.351290i	0.509299	+	0.860590i	$0.329905\pi$
$308$	4.29832	−	22.7172i	0.244919	−	1.29443i
$309$	−12.3888	−	0.178342i	−0.704776	−	0.0101455i
$310$	3.96591	+	2.70391i	0.225249	+	0.153572i
$311$	5.32950	+	28.1671i	0.302208	+	1.59721i	0.723527	+	0.690296i	$0.242520\pi$
$311$	5.32950	+	28.1671i	0.302208	+	1.59721i	−0.421319	+	0.906912i	$0.638433\pi$
$312$	45.0389	+	16.4912i	2.54983	+	0.933631i
$313$	9.93119	+	25.3043i	0.561344	+	1.43028i	0.876574	+	0.481266i	$0.159823\pi$
$313$	9.93119	+	25.3043i	0.561344	+	1.43028i	−0.315230	+	0.949015i	$0.602082\pi$
$314$	10.1277	−	8.07654i	0.571537	−	0.455786i
$315$	−1.64756	+	1.44272i	−0.0928296	+	0.0812881i
$316$	40.4984	−	64.4529i	2.27822	−	3.62576i
$317$	−7.94820	+	10.7694i	−0.446415	+	0.604871i	−0.968802	−	0.247838i	$-0.920280\pi$
$317$	−7.94820	+	10.7694i	−0.446415	+	0.604871i	0.522386	+	0.852709i	$0.325042\pi$
$318$	−1.65361	+	31.8979i	−0.0927297	+	1.78874i
$319$	−28.9514	+	10.2508i	−1.62097	+	0.573937i
$320$	−5.49238	+	3.17103i	−0.307033	+	0.177266i
$321$	−26.4264	+	9.93507i	−1.47498	+	0.554521i
$322$	4.63221	−	2.44819i	0.258143	−	0.136432i
$323$	0.763320	−	3.34432i	0.0424722	−	0.186083i
$324$	−2.48791	+	43.1619i	−0.138217	+	2.39788i
$325$	−12.5869	−	10.0377i	−0.698197	−	0.556794i
$326$	−7.57890	+	24.5702i	−0.419756	+	1.36082i
$327$	2.41445	+	17.7487i	0.133519	+	0.981506i
$328$	−24.9127	+	36.5402i	−1.37557	+	2.01759i
$329$	0.374922	−	0.709388i	0.0206701	−	0.0391098i
$330$	−6.26226	−	21.3901i	−0.344726	−	1.17749i
$331$	3.46506	−	0.928461i	0.190457	−	0.0510328i	−0.162330	−	0.986737i	$-0.551901\pi$
$331$	3.46506	−	0.928461i	0.190457	−	0.0510328i	0.352787	+	0.935704i	$0.385234\pi$
$332$	24.4314	+	11.7655i	1.34085	+	0.645718i
$333$	8.30432	+	4.69962i	0.455074	+	0.257538i
$334$	−15.9336	+	1.79529i	−0.871849	+	0.0982338i
$335$	−5.28926	−	7.75792i	−0.288983	−	0.423860i
$336$	2.88512	+	13.5358i	0.157396	+	0.738437i
$337$	−5.26636	+	6.11962i	−0.286877	+	0.333357i	−0.882857	−	0.469643i	$-0.844383\pi$
$337$	−5.26636	+	6.11962i	−0.286877	+	0.333357i	0.595980	+	0.802999i	$0.296764\pi$
$338$	−3.08453	−	1.63022i	−0.167776	−	0.0886723i
$339$	1.51674	+	0.193043i	0.0823780	+	0.0104846i
$340$	1.35919	+	1.57941i	0.0737127	+	0.0856557i
$341$	2.69982	+	11.8287i	0.146203	+	0.640559i
$342$	13.4084	−	51.8219i	0.725046	−	2.80221i
$343$	−6.99163	−	8.76723i	−0.377513	−	0.473386i
$344$	28.0343	−	30.2138i	1.51151	−	1.62902i
$345$	2.05104	−	2.91720i	0.110424	−	0.157057i
$346$	−0.444708	+	0.194024i	−0.0239076	+	0.0104308i
$347$	0.651269	+	1.12803i	0.0349619	+	0.0605558i	0.882977	−	0.469416i	$-0.155536\pi$
$347$	0.651269	+	1.12803i	0.0349619	+	0.0605558i	−0.848015	+	0.529972i	$0.822202\pi$
$348$	33.1694	−	30.1229i	1.77807	−	1.61476i
$349$	8.48505	−	14.6965i	0.454195	−	0.786688i	−0.544447	−	0.838795i	$-0.683260\pi$
$349$	8.48505	−	14.6965i	0.454195	−	0.786688i	0.998641	+	0.0521072i	$0.0165938\pi$
$350$	1.04790	−	9.30035i	0.0560125	−	0.497124i
$351$	3.76959	−	19.3107i	0.201206	−	1.03073i
$352$	−55.9955	−	12.7806i	−2.98457	−	0.681208i
$353$	17.6805	−	2.66490i	0.941037	−	0.141838i	0.339430	−	0.940631i	$-0.389766\pi$
$353$	17.6805	−	2.66490i	0.941037	−	0.141838i	0.601606	+	0.798793i	$0.294528\pi$
$354$	9.99502	−	48.9564i	0.531230	−	2.60200i
$355$	−1.57529	+	1.46165i	−0.0836077	+	0.0775766i
$356$	−25.7836	+	4.87853i	−1.36653	+	0.258562i
$357$	0.675986	−	0.283419i	0.0357770	−	0.0150001i
$358$	0.789352	+	21.0959i	0.0417185	+	1.11495i
$359$	5.17376	+	14.7858i	0.273061	+	0.780362i	0.995992	+	0.0894426i	$0.0285086\pi$
$359$	5.17376	+	14.7858i	0.273061	+	0.780362i	−0.722931	+	0.690920i	$0.757206\pi$
$360$	11.9599	+	14.7351i	0.630342	+	0.776609i
$361$	−12.0589	+	25.0406i	−0.634680	+	1.31793i
$362$	−18.1480	+	41.5957i	−0.953839	+	2.18622i
$363$	16.6591	−	33.3561i	0.874377	−	1.75074i
$364$	−1.14711	−	15.3072i	−0.0601252	−	0.802314i
$365$	1.44283	−	5.38471i	0.0755212	−	0.281849i
$366$	−13.1592	+	54.0554i	−0.687841	+	2.82552i
$367$	−19.3069	+	0.722413i	−1.00781	+	0.0377096i	−0.536195	−	0.844094i	$-0.680139\pi$
$367$	−19.3069	+	0.722413i	−1.00781	+	0.0377096i	−0.471616	+	0.881804i	$0.656329\pi$
$368$	−9.77818	−	20.3046i	−0.509723	−	1.05845i
$369$	16.4122	+	7.73033i	0.854387	+	0.402425i
$370$	6.99647	−	1.59690i	0.363729	−	0.0830188i
$371$	5.55388	−	2.17974i	0.288343	−	0.113166i
$372$	−10.3048	−	14.3916i	−0.534280	−	0.746168i
$373$	5.10504	−	1.57470i	0.264329	−	0.0815347i	−0.159758	−	0.987156i	$-0.551071\pi$
$373$	5.10504	−	1.57470i	0.264329	−	0.0815347i	0.424087	+	0.905622i	$0.360595\pi$
$374$	−0.278937	+	7.45475i	−0.0144235	+	0.385476i
$375$	−4.87785	−	12.9747i	−0.251891	−	0.670009i
$376$	−6.02171	−	3.47663i	−0.310546	−	0.179294i
$377$	−16.8052	+	11.5488i	−0.865510	+	0.594794i
$378$	10.6713	−	4.11713i	0.548875	−	0.211762i
$379$	7.33263	+	0.826189i	0.376652	+	0.0424385i	0.298261	−	0.954484i	$-0.403593\pi$
$379$	7.33263	+	0.826189i	0.376652	+	0.0424385i	0.0783905	+	0.996923i	$0.475022\pi$
$380$	−13.2817	−	25.1302i	−0.681337	−	1.28915i
$381$	−5.01072	−	19.8382i	−0.256707	−	1.01634i
$382$	−23.2707	−	9.13308i	−1.19063	−	0.467289i
$383$	19.9066	+	3.00044i	1.01718	+	0.153315i	0.636407	−	0.771353i	$-0.280420\pi$
$383$	19.9066	+	3.00044i	1.01718	+	0.153315i	0.380773	+	0.924669i	$0.375658\pi$
$384$	−1.73576	+	0.302612i	−0.0885776	+	0.0154426i
$385$	−3.15562	+	2.71563i	−0.160825	+	0.138401i
$386$	0.508107	−	0.244692i	0.0258620	−	0.0124545i
$387$	−14.0512	−	9.40375i	−0.714264	−	0.478019i
$388$	−40.8247	+	14.2852i	−2.07256	+	0.725219i
$389$	3.24498	+	12.1104i	0.164527	+	0.614024i	0.998100	+	0.0616143i	$0.0196249\pi$
$389$	3.24498	+	12.1104i	0.164527	+	0.614024i	−0.833573	+	0.552410i	$0.813708\pi$
$390$	−7.69161	−	12.6415i	−0.389480	−	0.640126i
$391$	−0.960360	+	0.708778i	−0.0485675	+	0.0358444i
$392$	−36.9989	+	27.3064i	−1.86873	+	1.37918i
$393$	−15.1189	−	24.8485i	−0.762646	−	1.25344i
$394$	−6.90590	−	25.7732i	−0.347914	−	1.29843i
$395$	−12.9378	+	4.52712i	−0.650969	+	0.227784i
$396$	−5.43606	+	82.0098i	−0.273172	+	4.12115i
$397$	−4.77647	+	2.30023i	−0.239724	+	0.115445i	−0.549889	−	0.835238i	$-0.685330\pi$
$397$	−4.77647	+	2.30023i	−0.239724	+	0.115445i	0.310165	+	0.950683i	$0.399616\pi$
$398$	43.0179	−	37.0199i	2.15629	−	1.85564i
$399$	−9.85019	+	1.71728i	−0.493126	+	0.0859716i
$400$	−39.8076	−	6.00003i	−1.99038	−	0.300002i
$401$	31.3843	+	12.3174i	1.56726	+	0.615104i	0.980825	−	0.194892i	$-0.0624357\pi$
$401$	31.3843	+	12.3174i	1.56726	+	0.615104i	0.586435	+	0.809996i	$0.300531\pi$
$402$	12.0095	+	47.5473i	0.598978	+	2.37144i
$403$	3.76400	+	7.12183i	0.187498	+	0.354764i
$404$	−61.0206	−	6.87537i	−3.03589	−	0.342062i
$405$	5.19611	−	5.79719i	0.258197	−	0.288064i
$406$	−10.8825	−	4.70015i	−0.540087	−	0.233265i
$407$	15.7095	+	9.06989i	0.778692	+	0.449578i
$408$	−2.23532	−	5.94577i	−0.110665	−	0.294360i
$409$	0.646414	−	17.2758i	0.0319631	−	0.854232i	−0.887442	−	0.460920i	$-0.847520\pi$
$409$	0.646414	−	17.2758i	0.0319631	−	0.854232i	0.919405	−	0.393312i	$-0.128671\pi$
$410$	13.0380	−	4.02169i	0.643902	−	0.198617i
$411$	5.66777	+	7.91554i	0.279571	+	0.390445i
$412$	31.9878	−	12.5543i	1.57593	−	0.618505i
$413$	−9.09936	+	2.07687i	−0.447750	+	0.102196i
$414$	−15.2981	+	10.6242i	−0.751859	+	0.522149i
$415$	−2.11861	−	4.39935i	−0.103999	−	0.215955i
$416$	−38.1062	+	1.42583i	−1.86831	+	0.0699073i
$417$	−7.23972	+	29.7394i	−0.354530	+	1.45634i
$418$	26.3377	−	98.2937i	1.28822	−	4.80770i
$419$	−0.532340	−	7.10359i	−0.0260065	−	0.347033i	−0.994995	−	0.0999264i	$-0.968139\pi$
$419$	−0.532340	−	7.10359i	−0.0260065	−	0.347033i	0.968988	−	0.247107i	$-0.0794798\pi$
$420$	2.71377	−	5.43372i	0.132419	−	0.265138i
$421$	0.288511	−	0.661275i	0.0140612	−	0.0322286i	−0.909390	−	0.415944i	$-0.863451\pi$
$421$	0.288511	−	0.661275i	0.0140612	−	0.0322286i	0.923451	+	0.383716i	$0.125356\pi$
$422$	−4.99500	+	10.3722i	−0.243153	+	0.504912i
$423$	−1.01917	+	2.66404i	−0.0495539	+	0.129530i
$424$	−17.0766	−	48.8021i	−0.829313	−	2.37004i
$425$	0.0797231	+	2.13064i	0.00386714	+	0.103351i
$426$	10.3509	−	4.33978i	0.501502	−	0.210263i
$427$	10.2109	−	1.93201i	0.494140	−	0.0934964i
$428$	57.3983	−	53.2578i	2.77445	−	2.57431i
$429$	7.48208	−	36.6478i	0.361238	−	1.76937i
$430$	−12.5740	+	1.89523i	−0.606374	+	0.0913962i
$431$	5.36995	+	1.22566i	0.258661	+	0.0590377i	0.349885	−	0.936793i	$-0.386221\pi$
$431$	5.36995	+	1.22566i	0.258661	+	0.0590377i	−0.0912237	+	0.995830i	$0.529078\pi$
$432$	−15.9806	−	46.5314i	−0.768866	−	2.23874i
$433$	−0.118714	+	1.05361i	−0.00570502	+	0.0506334i	−0.996242	−	0.0866114i	$-0.972396\pi$
$433$	−0.118714	+	1.05361i	−0.00570502	+	0.0506334i	0.990537	+	0.137245i	$0.0438247\pi$
$434$	−2.34145	+	4.05551i	−0.112393	+	0.194671i
$435$	−8.05166	+	0.516841i	−0.386047	+	0.0247806i
$436$	−24.8391	−	43.0227i	−1.18958	−	2.06041i
$437$	14.9232	−	6.51093i	0.713874	−	0.311460i
$438$	−16.7463	+	23.8183i	−0.800169	+	1.13808i
$439$	−18.2637	+	19.6836i	−0.871681	+	0.939449i	−0.998623	−	0.0524614i	$-0.983293\pi$
$439$	−18.2637	+	19.6836i	−0.871681	+	0.939449i	0.126942	+	0.991910i	$0.459484\pi$
$440$	22.4945	+	28.2072i	1.07238	+	1.34472i
$441$	13.4528	+	13.2231i	0.640611	+	0.629673i
$442$	1.10212	+	4.82868i	0.0524223	+	0.229677i
$443$	9.54526	+	11.0918i	0.453509	+	0.526987i	0.937453	−	0.348112i	$-0.113177\pi$
$443$	9.54526	+	11.0918i	0.453509	+	0.526987i	−0.483944	+	0.875099i	$0.660796\pi$
$444$	−26.2521	−	3.34123i	−1.24587	−	0.158568i
$445$	4.17764	+	2.20795i	0.198039	+	0.104667i
$446$	9.05563	−	10.5228i	0.428797	−	0.498271i
$447$	−6.78956	−	31.8538i	−0.321135	−	1.50663i
$448$	−3.48547	−	5.11225i	−0.164673	−	0.241531i
$449$	−5.07584	+	0.571909i	−0.239544	+	0.0269901i	−0.230920	−	0.972973i	$-0.574174\pi$
$449$	−5.07584	+	0.571909i	−0.239544	+	0.0269901i	−0.00862355	+	0.999963i	$0.502745\pi$
$450$	0.286497	+	33.2696i	0.0135056	+	1.56835i
$451$	31.0730	+	14.9640i	1.46317	+	0.704626i
$452$	−4.09602	+	1.09753i	−0.192661	+	0.0516233i
$453$	−1.39013	−	4.74831i	−0.0653142	−	0.223095i
$454$	11.6407	−	22.0254i	0.546327	−	1.03370i
$455$	−1.55706	+	2.28379i	−0.0729963	+	0.107066i
$456$	11.6797	+	85.8576i	0.546950	+	4.02065i
$457$	9.00417	−	29.1908i	0.421197	−	1.36549i	−0.457967	−	0.888969i	$-0.651422\pi$
$457$	9.00417	−	29.1908i	0.421197	−	1.36549i	0.879164	−	0.476519i	$-0.158102\pi$
$458$	48.1435	+	38.3932i	2.24960	+	1.79399i
$459$	−2.26411	+	1.28979i	−0.105680	+	0.0602021i
$460$	−2.20079	+	9.64228i	−0.102612	+	0.449573i
$461$	−28.9486	+	15.2998i	−1.34827	+	0.712582i	−0.976454	−	0.215724i	$-0.930789\pi$
$461$	−28.9486	+	15.2998i	−1.34827	+	0.712582i	−0.371817	+	0.928306i	$0.621265\pi$
$462$	20.3535	−	7.65195i	0.946933	−	0.356001i
$463$	−18.3681	+	10.6048i	−0.853639	+	0.492849i	−0.861877	−	0.507117i	$-0.830711\pi$
$463$	−18.3681	+	10.6048i	−0.853639	+	0.492849i	0.00823786	+	0.999966i	$0.497378\pi$
$464$	−21.9532	+	46.0207i	−1.01915	+	2.13646i
$465$	−0.165011	+	3.18304i	−0.00765219	+	0.147610i
$466$	−1.64931	+	2.23474i	−0.0764030	+	0.103522i
$467$	12.0718	−	19.2121i	0.558616	−	0.889032i	−0.441350	−	0.897335i	$-0.645500\pi$
$467$	12.0718	−	19.2121i	0.558616	−	0.889032i	0.999966	+	0.00830336i	$0.00264307\pi$
$468$	10.6061	+	53.5272i	0.490268	+	2.47430i
$469$	7.16193	−	5.71144i	0.330707	−	0.263730i
$470$	0.783736	+	1.99693i	0.0361510	+	0.0921113i
$471$	8.07725	+	2.95752i	0.372180	+	0.136275i
$472$	15.0369	+	79.4721i	0.692131	+	3.65800i
$473$	−26.5573	−	18.1065i	−1.22111	−	0.832537i
$474$	71.5832	+	1.03047i	3.28793	+	0.0473309i
$475$	5.40712	−	28.5773i	0.248096	−	1.31122i
$476$	−1.43749	+	1.43749i	−0.0658872	+	0.0658872i
$477$	−18.6657	+	10.0717i	−0.854642	+	0.461150i
$478$	6.34897	+	56.3487i	0.290395	+	2.57733i
$479$	−7.74305	−	3.37826i	−0.353789	−	0.154357i	0.215479	−	0.976508i	$-0.430869\pi$
$479$	−7.74305	−	3.37826i	−0.353789	−	0.154357i	−0.569268	+	0.822152i	$0.692773\pi$
$480$	−13.2370	−	7.24159i	−0.604182	−	0.330532i
$481$	11.6331	+	3.11708i	0.530424	+	0.142127i
$482$	−9.14727	−	7.87186i	−0.416647	−	0.358553i
$483$	2.98763	+	1.78273i	0.135942	+	0.0811172i
$484$	−7.72761	+	103.118i	−0.351255	+	4.68717i
$485$	7.35127	+	2.57232i	0.333804	+	0.116803i
$486$	−35.8950	+	19.1011i	−1.62823	+	0.866445i
$487$	23.9647	−	30.0508i	1.08594	−	1.36173i	0.158678	−	0.987330i	$-0.449277\pi$
$487$	23.9647	−	30.0508i	1.08594	−	1.36173i	0.927267	−	0.374401i	$-0.122152\pi$
$488$	−13.4223	−	89.0510i	−0.607598	−	4.03115i
$489$	−16.5540	+	4.18120i	−0.748597	+	0.189080i
$490$	14.1771	+	0.530471i	0.640457	+	0.0239642i
$491$	0.0861176	+	0.197384i	0.00388643	+	0.00890780i	0.918495	−	0.395433i	$-0.129406\pi$
$491$	0.0861176	+	0.197384i	0.00388643	+	0.00890780i	−0.914608	+	0.404341i	$0.867501\pi$
$492$	−50.2472	−	2.60485i	−2.26532	−	0.117436i
$493$	2.61105	+	0.689292i	0.117596	+	0.0310442i
$494$		−	67.5618i		−	3.03975i
$495$	9.97267	−	10.9354i	0.448238	−	0.491507i
$496$	17.0554	+	10.7166i	0.765811	+	0.481191i
$497$	−1.53687	−	1.42601i	−0.0689381	−	0.0639652i
$498$	2.49037	+	25.3813i	0.111596	+	1.13736i
$499$	−2.45361	+	16.2787i	−0.109839	+	0.728733i	0.864332	+	0.502921i	$0.167741\pi$
$499$	−2.45361	+	16.2787i	−0.109839	+	0.728733i	−0.974171	+	0.225812i	$0.927497\pi$
$500$	26.1482	+	28.1810i	1.16938	+	1.26029i
$501$	−6.51800	−	8.41911i	−0.291203	−	0.376138i
$502$	−54.9809	−	4.12025i	−2.45392	−	0.183896i
$503$	−5.35826	−	8.52763i	−0.238913	−	0.380228i	0.705649	−	0.708562i	$-0.250656\pi$
$503$	−5.35826	−	8.52763i	−0.238913	−	0.380228i	−0.944562	+	0.328334i	$0.893513\pi$
$504$	−13.4636	+	12.7099i	−0.599716	+	0.566143i
$505$	7.81881	+	7.81881i	0.347933	+	0.347933i
$506$	−29.2555	+	19.9460i	−1.30056	+	0.886709i
$507$	−0.139855	−	2.31246i	−0.00621119	−	0.102700i
$508$	33.6980	+	45.6592i	1.49511	+	2.02580i
$509$	−20.7163	+	1.55247i	−0.918235	+	0.0688122i	−0.525456	−	0.850821i	$-0.676105\pi$
$509$	−20.7163	+	1.55247i	−0.918235	+	0.0688122i	−0.392779	+	0.919633i	$0.628486\pi$
$510$	−0.604538	+	1.86416i	−0.0267694	+	0.0825466i
$511$	5.34389	+	1.01112i	0.236400	+	0.0447293i
$512$	36.5236	−	22.9493i	1.61413	−	1.01422i
$513$	34.0254	−	10.2803i	1.50226	−	0.453887i
$514$	14.3879	−	41.1184i	0.634625	−	1.81365i
$515$	−5.91285	−	1.82387i	−0.260552	−	0.0803695i
$516$	45.9444	+	9.38008i	2.02259	+	0.412935i
$517$	−1.98105	+	5.04763i	−0.0871265	+	0.221995i
$518$	2.06369	+	6.69032i	0.0906734	+	0.293956i
$519$	−0.263559	−	0.185304i	−0.0115689	−	0.00813394i
$520$	19.2728	+	14.2240i	0.845167	+	0.623762i
$521$	−18.3922			−0.805775			−0.402888	−	0.915249i	$-0.631993\pi$
$521$	−18.3922			−0.805775			−0.402888	+	0.915249i	$0.631993\pi$
$522$	40.4176	+	11.9244i	1.76903	+	0.521917i
$523$	2.19388			0.0959316			0.0479658	−	0.998849i	$-0.484726\pi$
$523$	2.19388			0.0959316			0.0479658	+	0.998849i	$0.484726\pi$
$524$	64.9066	+	47.9033i	2.83546	+	2.09266i
$525$	5.63755	−	2.61562i	0.246043	−	0.114155i
$526$	20.1653	+	65.3744i	0.879251	+	2.85046i
$527$	0.389753	−	0.993074i	0.0169779	−	0.0432590i
$528$	−29.6173	−	88.7174i	−1.28893	−	3.86093i
$529$	16.5646	+	5.10950i	0.720200	+	0.222152i
$530$	−5.26846	+	15.0564i	−0.228847	+	0.654008i
$531$	31.2217	−	11.2276i	1.35490	−	0.487237i
$532$	23.4804	−	14.7537i	1.01801	−	0.639656i
$533$	22.4986	+	4.25696i	0.974521	+	0.184389i
$534$	−16.5242	−	18.3312i	−0.715074	−	0.793267i
$535$	−14.0601	+	1.05366i	−0.607871	+	0.0455536i
$536$	−47.1396	−	63.8719i	−2.03612	−	2.75884i
$537$	−11.6947	+	7.72913i	−0.504665	+	0.333537i
$538$	1.98270	−	1.35178i	0.0854801	−	0.0582794i
$539$	25.3573	+	25.3573i	1.09222	+	1.09222i
$540$	−7.24890	+	20.3381i	−0.311943	+	0.875212i
$541$	−12.9596	−	20.6250i	−0.557176	−	0.886740i	0.442775	−	0.896633i	$-0.353994\pi$
$541$	−12.9596	−	20.6250i	−0.557176	−	0.886740i	−0.999951	+	0.00989253i	$0.996851\pi$
$542$	14.3000	+	1.07164i	0.614238	+	0.0460308i
$543$	−29.8602	+	4.06203i	−1.28142	+	0.174319i
$544$	3.43500	+	3.70205i	0.147274	+	0.158724i
$545$	−1.33326	+	8.84563i	−0.0571107	+	0.378905i
$546$	11.7379	−	8.40470i	0.502336	−	0.359688i
$547$	−8.41029	−	7.80361i	−0.359598	−	0.333658i	0.479597	−	0.877489i	$-0.340783\pi$
$547$	−8.41029	−	7.80361i	−0.359598	−	0.333658i	−0.839195	+	0.543831i	$0.816973\pi$
$548$	−22.8622	−	14.3652i	−0.976623	−	0.613653i
$549$	−35.2063	+	11.1926i	−1.50257	+	0.477689i
$550$			63.2501i			2.69699i
$551$	−32.6319	−	17.0924i	−1.39017	−	0.728163i
$552$	16.4063	−	25.2948i	0.698298	−	1.07662i
$553$	−5.34762	−	12.2569i	−0.227404	−	0.521215i
$554$	15.9175	+	0.595591i	0.676270	+	0.0253042i
$555$	3.32075	+	3.41775i	0.140958	+	0.145076i
$556$	−12.6521	−	83.9409i	−0.536567	−	3.55989i
$557$	26.9258	−	33.7639i	1.14088	−	1.43062i	0.254860	−	0.966978i	$-0.417971\pi$
$557$	26.9258	−	33.7639i	1.14088	−	1.43062i	0.886022	−	0.463643i	$-0.153458\pi$
$558$	6.52543	−	15.3149i	0.276244	−	0.648333i
$559$	−20.1426	−	7.04822i	−0.851943	−	0.298108i
$560$	−0.516517	+	6.89244i	−0.0218268	+	0.291259i
$561$	−4.32518	+	2.41481i	−0.182609	+	0.101953i
$562$	−25.2145	−	21.6988i	−1.06361	−	0.915310i
$563$	5.64380	+	1.51225i	0.237858	+	0.0637338i	0.375779	−	0.926709i	$-0.377375\pi$
$563$	5.64380	+	1.51225i	0.237858	+	0.0637338i	−0.137921	+	0.990443i	$0.544042\pi$
$564$	−0.181975	−	7.90867i	−0.00766254	−	0.333015i
$565$	0.699875	+	0.305352i	0.0294440	+	0.0128463i
$566$	−8.11405	−	72.0142i	−0.341059	−	3.02698i
$567$	6.01882	+	4.63255i	0.252767	+	0.194549i
$568$	−12.8470	+	12.8470i	−0.539048	+	0.539048i
$569$	8.01297	−	42.3496i	0.335921	−	1.77539i	−0.253274	−	0.967395i	$-0.581507\pi$
$569$	8.01297	−	42.3496i	0.335921	−	1.77539i	0.589195	−	0.807991i	$-0.299445\pi$
$570$	13.6982	−	22.9564i	0.573755	−	0.961538i
$571$	3.72639	+	2.54061i	0.155945	+	0.106321i	0.638778	−	0.769391i	$-0.279440\pi$
$571$	3.72639	+	2.54061i	0.155945	+	0.106321i	−0.482834	+	0.875712i	$0.660392\pi$
$572$	19.2859	+	101.929i	0.806385	+	4.26185i
$573$	−2.85103	−	16.3532i	−0.119103	−	0.683167i
$574$	4.86321	+	12.3913i	0.202986	+	0.517201i
$575$	−7.91211	+	6.30970i	−0.329958	+	0.263133i
$576$	14.4904	+	16.5478i	0.603766	+	0.689490i
$577$	−16.1983	+	25.7795i	−0.674344	+	1.07321i	0.317805	+	0.948156i	$0.397054\pi$
$577$	−16.1983	+	25.7795i	−0.674344	+	1.07321i	−0.992150	+	0.125057i	$0.960089\pi$
$578$	−25.9421	+	35.1503i	−1.07905	+	1.46206i
$579$	0.314184	+	0.203781i	0.0130570	+	0.00846883i
$580$	20.1247	−	9.78336i	0.835632	−	0.406232i
$581$	4.12559	−	2.38191i	0.171158	−	0.0988183i
$582$	−31.4350	−	25.8175i	−1.30302	−	1.07017i
$583$	−35.6482	+	18.8406i	−1.47640	+	0.780299i
$584$	10.4877	−	45.9497i	0.433985	−	1.90141i
$585$	4.51641	−	8.72654i	0.186730	−	0.360798i
$586$	10.7641	+	8.58409i	0.444661	+	0.354605i
$587$	1.73183	−	5.61447i	0.0714805	−	0.231734i	−0.912782	−	0.408447i	$-0.866070\pi$
$587$	1.73183	−	5.61447i	0.0714805	−	0.231734i	0.984262	+	0.176713i	$0.0565465\pi$
$588$	−48.4200	−	19.8124i	−1.99681	−	0.817049i
$589$	−8.19768	+	12.0238i	−0.337780	+	0.495432i
$590$	11.6601	−	22.0620i	0.480038	−	0.908277i
$591$	12.2369	−	12.8133i	0.503359	−	0.527069i
$592$	29.0893	−	7.79445i	1.19556	−	0.320350i
$593$	−16.6369	−	8.01191i	−0.683196	−	0.329010i	0.0598910	−	0.998205i	$-0.480925\pi$
$593$	−16.6369	−	8.01191i	−0.683196	−	0.329010i	−0.743087	+	0.669195i	$0.766639\pi$
$594$	−68.5489	+	35.7235i	−2.81260	+	1.46575i
$595$	0.363764	−	0.0409864i	0.0149129	−	0.00168028i
$596$	50.8841	+	74.6332i	2.08429	+	3.05710i
$597$	35.8484	+	11.6254i	1.46718	+	0.475797i
$598$	−15.3341	+	17.8186i	−0.627060	+	0.728657i
$599$	−39.7063	−	20.9854i	−1.62236	−	0.857440i	−0.997025	−	0.0770810i	$-0.975440\pi$
$599$	−39.7063	−	20.9854i	−1.62236	−	0.857440i	−0.625331	−	0.780359i	$-0.715036\pi$
$600$	−20.8241	−	49.6679i	−0.850141	−	2.02768i
$601$	15.8122	+	18.3741i	0.644993	+	0.749495i	0.981348	−	0.192240i	$-0.0615753\pi$
$601$	15.8122	+	18.3741i	0.644993	+	0.749495i	−0.336355	+	0.941735i	$0.609194\pi$
$602$	−2.76058	−	12.0949i	−0.112513	−	0.492952i
$603$	−22.8273	+	23.2239i	−0.929601	+	0.945750i
$604$	8.55546	+	10.7282i	0.348117	+	0.436525i
$605$	12.6651	−	13.6497i	0.514910	−	0.554941i
$606$	−24.3063	−	52.3886i	−0.987378	−	2.12814i
$607$	19.5803	−	8.54280i	0.794740	−	0.346742i	0.0370145	−	0.999315i	$-0.488215\pi$
$607$	19.5803	−	8.54280i	0.794740	−	0.346742i	0.757726	+	0.652573i	$0.226310\pi$
$608$	−34.4447	−	59.6600i	−1.39692	−	2.41953i
$609$	−1.08985	−	7.79564i	−0.0441630	−	0.315895i
$610$	−13.8921	+	24.0619i	−0.562476	+	0.974237i
$611$	−0.403085	+	3.57748i	−0.0163071	+	0.144729i
$612$	4.45701	−	5.68872i	0.180164	−	0.229953i
$613$	20.8020	+	4.74793i	0.840186	+	0.191767i	0.620896	−	0.783893i	$-0.286769\pi$
$613$	20.8020	+	4.74793i	0.840186	+	0.191767i	0.219290	+	0.975660i	$0.429626\pi$
$614$	22.4515	−	3.38402i	0.906070	−	0.136568i
$615$	6.78155	+	6.00805i	0.273458	+	0.242268i
$616$	−25.8023	+	23.9410i	−1.03960	+	0.964611i
$617$	13.1209	−	2.48262i	0.528229	−	0.0999463i	0.0850453	−	0.996377i	$-0.472897\pi$
$617$	13.1209	−	2.48262i	0.528229	−	0.0999463i	0.443184	+	0.896431i	$0.353849\pi$
$618$	25.7243	+	19.5636i	1.03478	+	0.786963i
$619$	0.199139	+	5.32210i	0.00800407	+	0.213913i	0.997562	+	0.0697802i	$0.0222298\pi$
$619$	0.199139	+	5.32210i	0.00800407	+	0.213913i	−0.989558	+	0.144133i	$0.953961\pi$
$620$	−2.91960	−	8.34375i	−0.117254	−	0.335093i
$621$	−11.3070	−	5.01125i	−0.453736	−	0.201095i
$622$	32.4434	−	67.3695i	1.30086	−	2.70127i
$623$	−1.84350	+	4.22534i	−0.0738581	+	0.169285i
$624$	−34.2385	−	51.8054i	−1.37064	−	2.07388i
$625$	1.07136	+	14.2963i	0.0428543	+	0.571851i
$626$	18.3515	−	68.4889i	0.733475	−	2.73737i
$627$	64.8503	−	18.9858i	2.58987	−	0.758220i
$628$	−23.8395	+	0.892012i	−0.951300	+	0.0355951i
$629$	−0.692043	−	1.43704i	−0.0275936	−	0.0572986i
$630$	5.69241	−	0.475914i	0.226791	−	0.0189609i
$631$	−27.5171	+	6.28060i	−1.09544	+	0.250027i	−0.731804	−	0.681515i	$-0.761321\pi$
$631$	−27.5171	+	6.28060i	−1.09544	+	0.250027i	−0.363634	+	0.931542i	$0.618464\pi$
$632$	−107.875	+	42.3380i	−4.29105	+	1.68411i
$633$	−7.60797	+	0.746482i	−0.302390	+	0.0296700i
$634$	33.3619	−	10.2908i	1.32497	−	0.408700i
$635$	0.382084	−	10.2114i	0.0151625	−	0.405227i
$636$	37.3339	−	45.4573i	1.48039	−	1.80250i
$637$	20.6190	+	11.9044i	0.816955	+	0.471669i
$638$	76.6384	+	23.3299i	3.03414	+	0.923638i
$639$	6.03452	+	4.37391i	0.238722	+	0.173029i
$640$	−0.874400	−	0.0985212i	−0.0345637	−	0.00389439i
$641$	4.33208	+	8.19670i	0.171107	+	0.323750i	0.954723	−	0.297495i	$-0.0961511\pi$
$641$	4.33208	+	8.19670i	0.171107	+	0.323750i	−0.783617	+	0.621245i	$0.786627\pi$
$642$	70.8500	+	20.0816i	2.79623	+	0.792557i
$643$	−25.2423	−	9.90686i	−0.995457	−	0.390688i	−0.188998	−	0.981977i	$-0.560524\pi$
$643$	−25.2423	−	9.90686i	−0.995457	−	0.390688i	−0.806460	+	0.591289i	$0.798619\pi$
$644$	−9.54126	−	1.43811i	−0.375979	−	0.0566696i
$645$	−5.41512	−	6.47881i	−0.213220	−	0.255103i
$646$	−6.78207	+	5.83644i	−0.266837	+	0.229632i
$647$	−9.56723	+	4.60733i	−0.376127	+	0.181133i	−0.612390	−	0.790556i	$-0.709792\pi$
$647$	−9.56723	+	4.60733i	−0.376127	+	0.181133i	0.236263	+	0.971689i	$0.424077\pi$
$648$	42.0675	−	50.6210i	1.65257	−	1.98858i
$649$	59.5360	−	20.8325i	2.33699	−	0.817748i
$650$	10.8687	+	40.5624i	0.426304	+	1.59099i
$651$	−3.10876	+	0.0715313i	−0.121842	+	0.00280353i
$652$	38.1003	−	28.1193i	1.49212	−	1.10124i
$653$	−6.03719	+	4.45565i	−0.236253	+	0.174363i	−0.705512	−	0.708698i	$-0.749283\pi$
$653$	−6.03719	+	4.45565i	−0.236253	+	0.174363i	0.469259	+	0.883061i	$0.344521\pi$
$654$	22.4241	−	40.9892i	0.876851	−	1.60280i
$655$	−3.75964	−	14.0312i	−0.146901	−	0.548243i
$656$	54.0441	−	18.9109i	2.11007	−	0.738345i
$657$	−19.2917	−	1.27876i	−0.752639	−	0.0498891i
$658$	−1.88564	+	0.908075i	−0.0735098	+	0.0354004i
$659$	−1.91497	+	1.64797i	−0.0745967	+	0.0641957i	−0.688796	−	0.724956i	$-0.741860\pi$
$659$	−1.91497	+	1.64797i	−0.0745967	+	0.0641957i	0.614199	+	0.789151i	$0.289479\pi$
$660$	−14.1130	+	38.5439i	−0.549350	+	1.50032i
$661$	−5.83139	−	0.878941i	−0.226815	−	0.0341868i	0.0346514	−	0.999399i	$-0.488968\pi$
$661$	−5.83139	−	0.878941i	−0.226815	−	0.0341868i	−0.261466	+	0.965213i	$0.584206\pi$
$662$	−8.71027	−	3.41853i	−0.338534	−	0.132865i
$663$	−2.35880	+	2.29185i	−0.0916081	+	0.0890081i
$664$	−19.2902	−	36.4988i	−0.748604	−	1.41643i
$665$	−4.96209	−	0.559094i	−0.192422	−	0.0216807i
$666$	−10.1490	−	22.7258i	−0.393266	−	0.880609i
$667$	4.72690	+	11.9142i	0.183026	+	0.461321i
$668$	25.5735	+	14.7648i	0.989467	+	0.571269i
$669$	9.09496	+	1.50503i	0.351631	+	0.0581880i
$670$	−0.915762	+	24.4743i	−0.0353790	+	0.945523i
$671$	−67.1102	+	20.7008i	−2.59076	+	0.799144i
$672$	6.08015	−	13.4060i	0.234547	−	0.517148i
$673$	40.5387	−	15.9103i	1.56265	−	0.613296i	0.582728	−	0.812667i	$-0.301985\pi$
$673$	40.5387	−	15.9103i	1.56265	−	0.613296i	0.979924	+	0.199371i	$0.0638899\pi$
$674$	20.5313	−	4.68614i	0.790838	−	0.180504i
$675$	−18.7742	+	11.6457i	−0.722619	+	0.448244i
$676$	2.78778	+	5.78888i	0.107222	+	0.222649i
$677$	−41.0348	+	1.53541i	−1.57709	+	0.0590107i	−0.811515	−	0.584331i	$-0.801357\pi$
$677$	−41.0348	+	1.53541i	−1.57709	+	0.0590107i	−0.765579	+	0.643342i	$0.777547\pi$
$678$	−2.88419	−	2.75445i	−0.110767	−	0.105784i
$679$	−1.96661	+	7.33947i	−0.0754714	+	0.281663i
$680$	−0.237066	−	3.16343i	−0.00909107	−	0.121312i
$681$	16.5123	−	0.998650i	0.632754	−	0.0382684i
$682$	12.6555	−	29.0067i	0.484605	−	1.11073i
$683$	−3.18257	+	6.60868i	−0.121778	+	0.252874i	−0.952942	−	0.303153i	$-0.901961\pi$
$683$	−3.18257	+	6.60868i	−0.121778	+	0.252874i	0.831164	+	0.556027i	$0.187675\pi$
$684$	−76.5410	+	62.1252i	−2.92662	+	2.37542i
$685$	1.60582	+	4.58916i	0.0613551	+	0.175343i
$686$	1.09368	+	29.2293i	0.0417571	+	1.11598i
$687$	−5.16255	+	40.5623i	−0.196964	+	1.54755i
$688$	−52.4322	+	9.92070i	−1.99896	+	0.378223i
$689$	−19.6238	+	18.2082i	−0.747606	+	0.693677i
$690$	−8.82304	+	2.94547i	−0.335887	+	0.112132i
$691$	17.8334	−	2.68796i	0.678416	−	0.102255i	0.199209	−	0.979957i	$-0.436163\pi$
$691$	17.8334	−	2.68796i	0.678416	−	0.102255i	0.479206	+	0.877702i	$0.340925\pi$
$692$	0.871145	+	0.198833i	0.0331160	+	0.00755850i
$693$	11.3659	+	8.90498i	0.431755	+	0.338272i
$694$	0.380403	−	3.37617i	0.0144399	−	0.128158i
$695$	−7.64296	+	13.2380i	−0.289914	+	0.502146i
$696$	−67.8623	+	6.91195i	−2.57231	+	0.261997i
$697$	−1.51625	−	2.62622i	−0.0574321	−	0.0994753i
$698$	−40.5714	+	17.7011i	−1.53565	+	0.669998i
$699$	−1.83698	−	0.164284i	−0.0694811	−	0.00621380i
$700$	−11.7236	+	12.6351i	−0.443112	+	0.477561i
$701$	9.33306	+	11.7033i	0.352505	+	0.442027i	0.926195	−	0.377046i	$-0.123060\pi$
$701$	9.33306	+	11.7033i	0.352505	+	0.442027i	−0.573690	+	0.819073i	$0.694489\pi$
$702$	−37.8220	+	34.6888i	−1.42750	+	1.30924i
$703$	4.84145	+	21.2118i	0.182599	+	0.800017i
$704$	27.2752	+	31.6944i	1.02797	+	1.19453i
$705$	−0.862299	+	1.13384i	−0.0324760	+	0.0427030i
$706$	−41.2339	−	21.7928i	−1.55186	−	0.820181i
$707$	−7.03674	+	8.17684i	−0.264644	+	0.307522i
$708$	−68.3494	+	61.6121i	−2.56873	+	2.31552i
$709$	8.26053	+	12.1160i	0.310231	+	0.455025i	0.949413	−	0.314030i	$-0.101679\pi$
$709$	8.26053	+	12.1160i	0.310231	+	0.455025i	−0.639182	+	0.769055i	$0.720727\pi$
$710$	5.57006	−	0.627595i	0.209041	−	0.0235532i
$711$	24.1228	+	40.9631i	0.904674	+	1.53624i
$712$	35.9934	+	17.3335i	1.34891	+	0.649601i
$713$	4.89102	−	1.31054i	0.183170	−	0.0490803i
$714$	−1.85769	−	0.452234i	−0.0695223	−	0.0169244i
$715$	8.72852	−	16.5152i	0.326428	−	0.617632i
$716$	21.9009	−	32.1227i	0.818474	−	1.20048i
$717$	−29.7739	+	23.0507i	−1.11193	+	0.860843i
$718$	12.0437	−	39.0447i	0.449467	−	1.45714i
$719$	−26.1906	−	20.8863i	−0.976746	−	0.778929i	−0.00148791	−	0.999999i	$-0.500474\pi$
$719$	−26.1906	−	20.8863i	−0.976746	−	0.778929i	−0.975258	+	0.221070i	$0.929045\pi$
$720$	−1.13012	−	24.5445i	−0.0421170	−	0.914721i
$721$	1.34333	−	5.88549i	0.0500281	−	0.219187i
$722$	64.0940	−	33.8747i	2.38533	−	1.26068i
$723$	1.30829	−	7.90604i	0.0486560	−	0.294029i
$724$	72.3806	−	41.7890i	2.69001	−	1.55308i
$725$	22.3411	+	5.01238i	0.829727	+	0.186155i
$726$	−86.6286	+	44.2012i	−3.21509	+	1.64046i
$727$	−4.67875	+	6.33948i	−0.173525	+	0.235118i	−0.882726	−	0.469888i	$-0.844294\pi$
$727$	−4.67875	+	6.33948i	−0.173525	+	0.235118i	0.709201	+	0.705007i	$0.249056\pi$
$728$	−12.4331	+	19.7872i	−0.460802	+	0.733363i
$729$	−23.2250	−	13.7695i	−0.860184	−	0.509983i
$730$	−11.3686	+	9.06613i	−0.420769	+	0.335552i
$731$	1.03254	+	2.63086i	0.0381897	+	0.0973057i
$732$	78.6142	−	65.7073i	2.90567	−	2.42861i
$733$	−3.95273	−	20.8907i	−0.145997	−	0.771614i	−0.976652	−	0.214827i	$-0.931081\pi$
$733$	−3.95273	−	20.8907i	−0.145997	−	0.771614i	0.830655	−	0.556788i	$-0.187966\pi$
$734$	41.6385	+	28.3887i	1.53691	+	1.04784i
$735$	4.59239	+	8.22544i	0.169393	+	0.303400i
$736$	−4.45634	+	23.5523i	−0.164263	+	0.868151i
$737$	−43.7748	+	43.7748i	−1.61247	+	1.61247i
$738$	−22.4709	−	41.6449i	−0.827164	−	1.53297i
$739$	2.43311	+	21.5945i	0.0895036	+	0.794366i	0.955636	+	0.294551i	$0.0951701\pi$
$739$	2.43311	+	21.5945i	0.0895036	+	0.794366i	−0.866132	+	0.499815i	$0.833401\pi$
$740$	−12.1136	−	5.28511i	−0.445305	−	0.194285i
$741$	38.3262	−	23.3193i	1.40795	−	0.856656i
$742$	−15.0322	−	4.02787i	−0.551850	−	0.147868i
$743$	−26.5034	−	22.8080i	−0.972316	−	0.836746i	0.0142847	−	0.999898i	$-0.495453\pi$
$743$	−26.5034	−	22.8080i	−0.972316	−	0.836746i	−0.986601	+	0.163152i	$0.947834\pi$
$744$	−0.387877	+	26.9446i	−0.0142203	+	0.987835i
$745$	1.21552	−	16.2200i	0.0445332	−	0.594254i
$746$	−13.1531	−	4.60246i	−0.481568	−	0.168508i
$747$	−13.5386	+	10.1732i	−0.495353	+	0.372218i
$748$	8.56587	−	10.7413i	0.313199	−	0.392739i
$749$	−2.05017	−	13.6020i	−0.0749117	−	0.497007i
$750$	−9.85952	+	34.7855i	−0.360019	+	1.27019i
$751$	−0.732291	−	0.0274004i	−0.0267217	−	0.000999854i	0.0240270	−	0.999711i	$-0.492351\pi$
$751$	−0.732291	−	0.0274004i	−0.0267217	−	0.000999854i	−0.0507487	+	0.998711i	$0.516161\pi$
$752$	3.59995	+	8.25118i	0.131277	+	0.300889i
$753$	−16.6396	−	32.6115i	−0.606382	−	1.18843i
$754$	53.1573	+	1.79222i	1.93588	+	0.0652690i
$755$		−	2.47089i		−	0.0899250i
$756$	−20.3151	−	5.56953i	−0.738853	−	0.202562i
$757$	−24.7977	−	15.5814i	−0.901286	−	0.566316i	−0.000221513	−	1.00000i	$-0.500071\pi$
$757$	−24.7977	−	15.5814i	−0.901286	−	0.566316i	−0.901065	+	0.433684i	$0.857213\pi$
$758$	−14.1094	−	13.0916i	−0.512475	−	0.475507i
$759$	−21.4126	−	9.71145i	−0.777228	−	0.352503i
$760$	−6.44953	+	42.7898i	−0.233949	+	1.55215i
$761$	−2.85101	−	3.07266i	−0.103349	−	0.111384i	0.679259	−	0.733899i	$-0.262301\pi$
$761$	−2.85101	−	3.07266i	−0.103349	−	0.111384i	−0.782608	+	0.622515i	$0.786111\pi$
$762$	−20.2117	+	49.3958i	−0.732192	+	1.78942i
$763$	−8.70297	−	0.652197i	−0.315069	−	0.0236111i
$764$	24.4941	+	38.9821i	0.886166	+	1.41032i
$765$	−1.26616	+	0.300486i	−0.0457780	+	0.0108641i
$766$	−37.1307	−	37.1307i	−1.34159	−	1.34159i
$767$	34.6008	−	23.5904i	1.24936	−	0.851801i
$768$	26.8335	+	13.4015i	0.968271	+	0.483586i
$769$	−12.8433	−	17.4021i	−0.463142	−	0.627535i	0.509325	−	0.860574i	$-0.329895\pi$
$769$	−12.8433	−	17.4021i	−0.463142	−	0.627535i	−0.972467	+	0.233039i	$0.925133\pi$
$770$	10.8290	−	0.811523i	0.390251	−	0.0292453i
$771$	28.2916	−	6.03028i	1.01890	−	0.217175i
$772$	−1.02050	−	0.193089i	−0.0367286	−	0.00694942i
$773$	12.6095	−	7.92307i	0.453532	−	0.284973i	−0.285831	−	0.958280i	$-0.592270\pi$
$773$	12.6095	−	7.92307i	0.453532	−	0.284973i	0.739363	+	0.673307i	$0.235127\pi$
$774$	14.9238	+	41.4999i	0.536425	+	1.49168i
$775$	2.98742	−	8.53755i	0.107311	−	0.306678i
$776$	62.9215	+	19.4087i	2.25875	+	0.696732i
$777$	−3.08297	+	3.47988i	−0.110601	+	0.124840i
$778$	11.9478	−	30.4425i	0.428350	−	1.09142i
$779$	12.1929	+	39.5284i	0.436856	+	1.41625i
$780$	−2.42748	+	27.1435i	−0.0869177	+	0.971892i
$781$	11.4000	+	8.41356i	0.407923	+	0.301061i
$782$	3.11336			0.111333
$783$	7.18591	+	27.0437i	0.256804	+	0.966464i
$784$	59.5353			2.12626
$785$	3.45637	+	2.55092i	0.123363	+	0.0910461i
$786$	−6.75813	+	75.5676i	−0.241054	+	2.69541i
$787$	0.698286	+	2.26379i	0.0248912	+	0.0806954i	0.967166	−	0.254145i	$-0.0817939\pi$
$787$	0.698286	+	2.26379i	0.0248912	+	0.0806954i	−0.942275	+	0.334840i	$0.891318\pi$
$788$	−17.9526	+	45.7425i	−0.639536	+	1.62951i
$789$	−30.1252	+	34.0036i	−1.07249	+	1.21056i
$790$	34.1647	+	10.5384i	1.21553	+	0.374940i
$791$	−0.246046	+	0.703160i	−0.00874839	+	0.0250015i
$792$	80.7987	−	95.5416i	2.87106	−	3.39492i
$793$	−39.4808	+	24.8074i	−1.40201	+	0.880938i
$794$	13.5873	+	2.57085i	0.482195	+	0.0912362i
$795$	−10.3596	+	2.20812i	−0.367416	+	0.0783139i
$796$	−104.228	+	7.81082i	−3.69427	+	0.276847i
$797$	−13.3997	−	18.1559i	−0.474641	−	0.643116i	0.500228	−	0.865894i	$-0.333249\pi$
$797$	−13.3997	−	18.1559i	−0.474641	−	0.643116i	−0.974869	+	0.222778i	$0.928488\pi$
$798$	23.3326	+	11.6531i	0.825966	+	0.412514i
$799$	0.393940	−	0.268584i	0.0139366	−	0.00950181i
$800$	30.2773	+	30.2773i	1.07046	+	1.07046i
$801$	4.69541	−	15.7009i	0.165904	−	0.554764i
$802$	−46.7879	−	74.4625i	−1.65214	−	2.62936i
$803$	−36.6524	−	2.74672i	−1.29343	−	0.0969295i
$804$	34.2025	−	83.5883i	1.20623	−	2.94793i
$805$	1.18180	+	1.27368i	0.0416529	+	0.0448911i
$806$	3.13160	−	20.7768i	0.110306	−	0.731831i
$807$	1.45117	+	0.658163i	0.0510836	+	0.0231684i
$808$	68.5301	+	63.5867i	2.41088	+	2.23697i
$809$	−1.27379	−	0.800372i	−0.0447839	−	0.0281396i	0.509454	−	0.860498i	$-0.329847\pi$
$809$	−1.27379	−	0.800372i	−0.0447839	−	0.0281396i	−0.554238	+	0.832358i	$0.686990\pi$
$810$	−19.8845	+	4.11826i	−0.698670	+	0.144701i
$811$		−	0.866241i		−	0.0304178i	−0.999884	−	0.0152089i	$-0.995159\pi$
$811$		−	0.866241i		−	0.0304178i	0.999884	−	0.0152089i	$-0.00484134\pi$
$812$	10.9853	+	18.8657i	0.385509	+	0.662056i
$813$	4.32781	+	8.48194i	0.151783	+	0.297475i
$814$	−18.9212	−	43.3678i	−0.663187	−	1.52004i
$815$	−8.52090	−	0.318830i	−0.298474	−	0.0111681i
$816$	−2.24264	+	7.91227i	−0.0785080	+	0.276985i
$817$	−5.74593	−	38.1218i	−0.201025	−	1.33371i
$818$	−28.1154	+	35.2556i	−0.983031	+	1.23268i
$819$	8.81919	+	3.75771i	0.308167	+	0.131305i
$820$	−23.7176	−	8.29915i	−0.828255	−	0.289819i
$821$	2.46643	−	32.9123i	0.0860791	−	1.14865i	−0.772171	−	0.635415i	$-0.780829\pi$
$821$	2.46643	−	32.9123i	0.0860791	−	1.14865i	0.858250	−	0.513232i	$-0.171552\pi$
$822$	0.365518	−	25.3913i	0.0127489	−	0.885625i
$823$	38.2814	+	32.9439i	1.33441	+	1.14835i	0.976722	+	0.214508i	$0.0688149\pi$
$823$	38.2814	+	32.9439i	1.33441	+	1.14835i	0.357685	+	0.933842i	$0.383566\pi$
$824$	−50.5322	−	13.5401i	−1.76037	−	0.471691i
$825$	−35.8803	+	21.8311i	−1.24919	+	0.760061i
$826$	22.3138	+	9.73542i	0.776397	+	0.338739i
$827$	4.98076	+	44.2055i	0.173198	+	1.53717i	0.716470	+	0.697618i	$0.245757\pi$
$827$	4.98076	+	44.2055i	0.173198	+	1.53717i	−0.543272	+	0.839557i	$0.682815\pi$
$828$	34.2870	+	0.987353i	1.19156	+	0.0343129i
$829$	14.4211	−	14.4211i	0.500866	−	0.500866i	−0.410841	−	0.911707i	$-0.634765\pi$
$829$	14.4211	−	14.4211i	0.500866	−	0.500866i	0.911707	+	0.410841i	$0.134765\pi$
$830$	−2.36787	+	12.5145i	−0.0821901	+	0.434385i
$831$	5.15615	+	9.23520i	0.178865	+	0.320365i
$832$	22.9379	+	15.6388i	0.795229	+	0.542178i
$833$	−0.586208	−	3.09818i	−0.0203109	−	0.107346i
$834$	61.2579	−	51.2006i	2.12119	−	1.77293i
$835$	−1.94266	−	4.94982i	−0.0672286	−	0.171296i
$836$	−146.521	+	116.847i	−5.06754	+	4.04122i
$837$	10.9401	−	1.58430i	0.378145	−	0.0547615i
$838$	−9.88565	+	15.7329i	−0.341494	+	0.543485i
$839$	−0.149354	+	0.202367i	−0.00515627	+	0.00698650i	−0.807168	−	0.590321i	$-0.799001\pi$
$839$	−0.149354	+	0.202367i	−0.00515627	+	0.00698650i	0.802012	+	0.597308i	$0.203763\pi$
$840$	−8.23645	+	4.20255i	−0.284185	+	0.145002i
$841$	14.3139	−	25.2213i	0.493583	−	0.869699i
$842$	−1.62976	+	0.940944i	−0.0561653	+	0.0324271i
$843$	3.60632	−	21.7931i	0.124208	−	0.750593i
$844$	18.7446	−	9.90681i	0.645216	−	0.341007i
$845$	0.257452	−	1.12797i	0.00885661	−	0.0388033i
$846$	6.26532	−	4.01243i	0.215406	−	0.137950i
$847$	14.2030	+	11.3265i	0.488021	+	0.389183i
$848$	−19.7309	+	63.9660i	−0.677562	+	2.19660i
$849$	38.0513	−	29.4590i	1.30592	−	1.01103i
$850$	3.13288	−	4.59509i	0.107457	−	0.157610i
$851$	3.53745	−	6.69319i	0.121262	−	0.229440i
$852$	−20.0837	−	4.88916i	−0.688057	−	0.167500i
$853$	−8.34959	+	2.23727i	−0.285884	+	0.0766025i	−0.398912	−	0.916989i	$-0.630612\pi$
$853$	−8.34959	+	2.23727i	−0.285884	+	0.0766025i	0.113027	+	0.993592i	$0.463945\pi$
$854$	−24.4223	−	11.7611i	−0.835712	−	0.402458i
$855$	17.7506	−	0.152857i	0.607059	−	0.00522761i
$856$	−118.456	+	13.3468i	−4.04873	+	0.456183i
$857$	−14.6490	−	21.4862i	−0.500401	−	0.733953i	0.490069	−	0.871684i	$-0.336972\pi$
$857$	−14.6490	−	21.4862i	−0.500401	−	0.733953i	−0.990470	+	0.137731i	$0.956019\pi$
$858$	−72.4672	+	65.3240i	−2.47399	+	2.23013i
$859$	−23.1304	+	26.8780i	−0.789199	+	0.917066i	−0.998146	−	0.0608606i	$-0.980615\pi$
$859$	−23.1304	+	26.8780i	−0.789199	+	0.917066i	0.208947	+	0.977927i	$0.432996\pi$
$860$	20.7046	+	10.9427i	0.706021	+	0.373143i
$861$	−5.35070	+	7.03569i	−0.182352	+	0.239776i
$862$	−9.37152	−	10.8899i	−0.319195	−	0.370911i
$863$	11.0456	+	48.3939i	0.375996	+	1.64735i	0.709579	+	0.704626i	$0.248885\pi$
$863$	11.0456	+	48.3939i	0.375996	+	1.64735i	−0.333583	+	0.942721i	$0.608258\pi$
$864$	−15.7132	+	49.9143i	−0.534575	+	1.69812i
$865$	−0.100320	−	0.125797i	−0.00341098	−	0.00427723i
$866$	1.88111	−	2.02735i	0.0639226	−	0.0688922i
$867$	−28.8940	−	2.58403i	−0.981291	−	0.0877583i
$868$	7.90463	−	3.44876i	0.268301	−	0.117058i
$869$	45.1866	+	78.2655i	1.53285	+	2.65498i
$870$	17.6986	+	11.3867i	0.600040	+	0.386044i
$871$	−20.5508	+	35.5950i	−0.696337	+	1.20609i
$872$	−8.46795	+	75.1551i	−0.286761	+	2.54507i
$873$	3.79569	−	26.7434i	0.128465	−	0.905126i
$874$	−41.4044	−	9.45028i	−1.40052	−	0.319660i
$875$	6.67822	−	1.00658i	0.225765	−	0.0340286i
$876$	50.8622	−	16.9797i	1.71847	−	0.573692i
$877$	36.0879	−	33.4847i	1.21860	−	1.13070i	0.231127	−	0.972924i	$-0.425759\pi$
$877$	36.0879	−	33.4847i	1.21860	−	1.13070i	0.987475	−	0.157774i	$-0.0504317\pi$
$878$	68.8186	−	13.0212i	2.32252	−	0.439444i
$879$	−1.15426	+	9.06906i	−0.0389323	+	0.305892i
$880$	−1.74655	−	46.6775i	−0.0588761	−	1.57350i
$881$	−2.42820	−	6.93941i	−0.0818083	−	0.233795i	0.895713	−	0.444634i	$-0.146666\pi$
$881$	−2.42820	−	6.93941i	−0.0818083	−	0.233795i	−0.977521	+	0.210839i	$0.932380\pi$
$882$	−7.75207	−	48.5888i	−0.261026	−	1.63607i
$883$	−13.9991	+	29.0694i	−0.471106	+	0.978262i	0.521082	+	0.853507i	$0.325529\pi$
$883$	−13.9991	+	29.0694i	−0.471106	+	0.978262i	−0.992188	+	0.124755i	$0.960186\pi$
$884$	3.64757	−	8.36033i	0.122681	−	0.281188i
$885$	16.5398	−	1.00031i	0.555978	−	0.0336250i
$886$	−2.85245	−	38.0633i	−0.0958299	−	1.27876i
$887$	8.31797	−	31.0431i	0.279290	−	1.04232i	−0.673621	−	0.739077i	$-0.735262\pi$
$887$	8.31797	−	31.0431i	0.279290	−	1.04232i	0.952912	−	0.303248i	$-0.0980712\pi$
$888$	29.1363	+	27.8256i	0.977750	+	0.933767i
$889$	9.96237	−	0.372766i	0.334127	−	0.0125022i
$890$	−5.34773	−	11.1047i	−0.179256	−	0.372229i
$891$	−43.9251	−	26.5560i	−1.47155	−	0.889660i
$892$	−24.9263	+	5.68926i	−0.834593	+	0.190491i
$893$	−6.05425	+	2.37612i	−0.202598	+	0.0795137i
$894$	−35.0896	+	77.3683i	−1.17357	+	2.58758i
$895$	−6.68975	+	2.06352i	−0.223614	+	0.0689757i
$896$	0.0320993	−	0.857872i	0.00107236	−	0.0286595i
$897$	−15.4007	−	2.54852i	−0.514216	−	0.0850925i
$898$	11.5385	+	6.66178i	0.385046	+	0.222307i
$899$	−9.24281	−	6.76886i	−0.308265	−	0.225754i
$900$	35.9593	−	49.6116i	1.19864	−	1.65372i
$901$	3.52303	+	0.396950i	0.117369	+	0.0132243i
$902$	−42.0352	−	79.5346i	−1.39962	−	2.64821i
$903$	5.90832	−	5.74063i	0.196617	−	0.191036i
$904$	6.00953	+	2.35857i	0.199874	+	0.0784448i
$905$	−14.8817	−	2.24306i	−0.494686	−	0.0745619i
$906$	−4.43726	+	12.1185i	−0.147418	+	0.402611i
$907$	2.73045	−	2.34974i	0.0906630	−	0.0780218i	−0.605788	−	0.795626i	$-0.707142\pi$
$907$	2.73045	−	2.34974i	0.0906630	−	0.0780218i	0.696451	+	0.717604i	$0.254761\pi$
$908$	−41.3361	+	19.9064i	−1.37179	+	0.660617i
$909$	21.3293	−	31.8706i	0.707449	−	1.05708i
$910$	6.80524	−	2.38126i	0.225591	−	0.0789378i
$911$	−4.16633	−	15.5490i	−0.138037	−	0.515160i	−0.999967	−	0.00813294i	$-0.997411\pi$
$911$	−4.16633	−	15.5490i	−0.138037	−	0.515160i	0.861930	−	0.507027i	$-0.169255\pi$
$912$	53.8416	−	98.4176i	1.78287	−	3.25893i
$913$	−25.9034	+	19.1176i	−0.857277	+	0.632699i
$914$	−64.1113	+	47.3163i	−2.12061	+	1.56508i
$915$	−18.4447	+	0.424405i	−0.609762	+	0.0140304i
$916$	−29.3512	−	109.540i	−0.969791	−	3.61931i
$917$	13.3766	−	4.68067i	0.441734	−	0.154569i
$918$	6.74949	+	0.800041i	0.222766	+	0.0264053i
$919$	2.51008	−	1.20879i	0.0828000	−	0.0398744i	−0.392025	−	0.919954i	$-0.628225\pi$
$919$	2.51008	−	1.20879i	0.0828000	−	0.0398744i	0.474825	+	0.880080i	$0.342511\pi$
$920$	11.4128	−	9.82149i	0.376268	−	0.323805i
$921$	9.66894	+	11.5682i	0.318602	+	0.381185i
$922$	84.4528	+	12.7292i	2.78131	+	0.419214i
$923$	8.75659	+	3.43671i	0.288227	+	0.113121i
$924$	−38.5277	−	10.9202i	−1.26747	−	0.359248i
$925$	−6.31903	−	11.9562i	−0.207768	−	0.393117i
$926$	54.9754	+	6.19424i	1.80660	+	0.203555i
$927$	−2.21907	+	21.3453i	−0.0728838	+	0.701071i
$928$	47.8540	−	25.5183i	1.57088	−	0.837681i
$929$	19.1022	+	11.0286i	0.626721	+	0.361838i	0.779481	−	0.626426i	$-0.215483\pi$
$929$	19.1022	+	11.0286i	0.626721	+	0.361838i	−0.152760	+	0.988263i	$0.548816\pi$
$930$	5.27658	−	6.42469i	0.173026	−	0.210674i
$931$	−1.60827	+	42.9820i	−0.0527090	+	1.40868i
$932$	4.88784	−	1.50770i	0.160107	−	0.0493863i
$933$	49.4151	−	4.84853i	1.61778	−	0.158734i
$934$	−55.0932	+	21.6225i	−1.80270	+	0.707510i
$935$	−2.41187	+	0.550494i	−0.0788767	+	0.0180031i
$936$	35.3989	−	75.1552i	1.15705	−	2.45653i
$937$	−17.6467	−	36.6437i	−0.576492	−	1.19710i	−0.961658	−	0.274251i	$-0.911570\pi$
$937$	−17.6467	−	36.6437i	−0.576492	−	1.19710i	0.385166	−	0.922847i	$-0.374144\pi$
$938$	−23.8774	+	0.893428i	−0.779624	+	0.0291715i
$939$	45.1863	−	13.2289i	1.47460	−	0.431709i
$940$	1.02252	−	3.81610i	0.0333510	−	0.124468i
$941$	−1.05897	−	14.1309i	−0.0345213	−	0.460655i	−0.987500	−	0.157618i	$-0.949619\pi$
$941$	−1.05897	−	14.1309i	−0.0345213	−	0.460655i	0.952979	−	0.303037i	$-0.0980005\pi$
$942$	−12.3708	−	18.7180i	−0.403064	−	0.609865i
$943$	5.75583	−	13.1925i	0.187436	−	0.429607i
$944$	45.4351	−	94.3469i	1.47879	−	3.07073i
$945$	2.23474	+	3.06491i	0.0726961	+	0.0997014i
$946$	27.6907	+	79.1354i	0.900301	+	2.57291i
$947$	−1.81242	−	48.4379i	−0.0588957	−	1.57402i	−0.645254	−	0.763968i	$-0.723248\pi$
$947$	−1.81242	−	48.4379i	−0.0588957	−	1.57402i	0.586358	−	0.810052i	$-0.300561\pi$
$948$	−104.944	−	79.8106i	−3.40841	−	2.59213i
$949$	−23.9773	+	4.53674i	−0.778335	+	0.147269i
$950$	−55.6119	+	51.6003i	−1.80429	+	1.67414i
$951$	17.3528	+	15.3735i	0.562702	+	0.498520i
$952$	3.06036	−	0.461275i	0.0991869	−	0.0149500i
$953$	−30.8786	−	7.04783i	−1.00025	−	0.228302i	−0.309117	−	0.951024i	$-0.600033\pi$
$953$	−30.8786	−	7.04783i	−1.00025	−	0.228302i	−0.691138	+	0.722722i	$0.742890\pi$
$954$	54.7740	+	7.77408i	1.77337	+	0.251695i
$955$	0.928205	−	8.23805i	0.0300360	−	0.266577i
$956$	52.2154	−	90.4396i	1.68877	−	2.92503i
$957$	13.2177	+	51.5276i	0.427266	+	1.66565i
$958$	11.0178	+	19.0833i	0.355968	+	0.616554i
$959$	−4.34764	+	1.89686i	−0.140393	+	0.0612527i
$960$	4.62316	+	9.96450i	0.149212	+	0.321603i
$961$	18.0071	−	19.4070i	0.580873	−	0.626032i
$962$	−19.5864	−	24.5606i	−0.631491	−	0.791864i
$963$	13.0625	+	47.1228i	0.420932	+	1.51851i
$964$	4.94555	+	21.6679i	0.159285	+	0.697875i
$965$	0.121992	+	0.141757i	0.00392705	+	0.00456331i
$966$	−3.50886	−	8.36904i	−0.112896	−	0.269269i
$967$	2.43518	+	1.28703i	0.0783102	+	0.0413881i	0.505965	−	0.862554i	$-0.331136\pi$
$967$	2.43518	+	1.28703i	0.0783102	+	0.0413881i	−0.427655	+	0.903942i	$0.640660\pi$
$968$	102.688	−	119.326i	3.30052	−	3.83527i
$969$	−5.65174	−	1.83283i	−0.181560	−	0.0588789i
$970$	−11.4439	−	16.7851i	−0.367441	−	0.538936i
$971$	40.8639	−	4.60426i	1.31139	−	0.147758i	0.571562	−	0.820559i	$-0.306338\pi$
$971$	40.8639	−	4.60426i	1.31139	−	0.147758i	0.739823	+	0.672801i	$0.234909\pi$
$972$	74.0776	+	10.9512i	2.37604	+	0.351261i
$973$	−13.4363	−	6.47056i	−0.430747	−	0.207437i
$974$	−96.8412	+	25.9485i	−3.10299	+	0.831444i
$975$	−19.2587	+	20.1659i	−0.616773	+	0.645825i
$976$	−54.4814	+	103.084i	−1.74391	+	3.29963i
$977$	13.6508	−	20.0220i	0.436726	−	0.640560i	−0.543274	−	0.839555i	$-0.682816\pi$
$977$	13.6508	−	20.0220i	0.436726	−	0.640560i	0.980000	+	0.198995i	$0.0637679\pi$
$978$	41.2183	+	16.8656i	1.31802	+	0.539304i
$979$	9.18297	−	29.7705i	0.293489	−	0.951468i
$980$	−20.4273	−	16.2902i	−0.652525	−	0.520371i
$981$	30.9920	−	1.42698i	0.989498	−	0.0455600i
$982$	0.124995	−	0.547640i	0.00398876	−	0.0174759i
$983$	−1.15341	+	0.609596i	−0.0367882	+	0.0194431i	−0.485562	−	0.874202i	$-0.661385\pi$
$983$	−1.15341	+	0.609596i	−0.0367882	+	0.0194431i	0.448773	+	0.893646i	$0.351861\pi$
$984$	59.1942	+	48.6161i	1.88704	+	1.54982i
$985$	7.66302	−	4.42425i	0.244164	−	0.140968i
$986$	−4.41218	−	5.49093i	−0.140512	−	0.174867i
$987$	−1.16597	−	0.756250i	−0.0371131	−	0.0240717i
$988$	−73.8858	+	100.112i	−2.35062	+	3.18498i
$989$	−7.13688	+	11.3583i	−0.226940	+	0.361172i
$990$	−37.8677	+	7.50327i	−1.20351	+	0.238470i
$991$	10.3858	−	8.28236i	0.329914	−	0.263098i	−0.444497	−	0.895780i	$-0.646618\pi$
$991$	10.3858	−	8.28236i	0.329914	−	0.263098i	0.774411	+	0.632682i	$0.218046\pi$
$992$	−7.82720	−	19.9434i	−0.248514	−	0.633203i
$993$	−1.06714	−	6.12105i	−0.0338648	−	0.194246i
$994$	1.01668	+	5.37326i	0.0322470	+	0.170430i
$995$	15.5506	+	10.6022i	0.492987	+	0.336113i
$996$	24.0669	−	40.3330i	0.762588	−	1.27800i
$997$	2.02584	−	10.7068i	0.0641591	−	0.339089i	−0.935749	−	0.352668i	$-0.885275\pi$
$997$	2.02584	−	10.7068i	0.0641591	−	0.339089i	0.999908	+	0.0135784i	$0.00432228\pi$
$998$	30.3637	−	30.3637i	0.961147	−	0.961147i
$999$	9.38885	−	13.6012i	0.297050	−	0.430324i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.x.a.2.2	✓	672
3.2	odd	2		783.2.be.a.89.27		672
9.4	even	3		783.2.be.a.611.27		672
9.5	odd	6	inner	261.2.x.a.176.2	yes	672
29.15	odd	28	inner	261.2.x.a.218.2	yes	672
87.44	even	28		783.2.be.a.305.27		672
261.131	even	84	inner	261.2.x.a.131.2	yes	672
261.247	odd	84		783.2.be.a.44.27		672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.x.a.2.2	✓	672	1.1	even	1	trivial
261.2.x.a.131.2	yes	672	261.131	even	84	inner
261.2.x.a.176.2	yes	672	9.5	odd	6	inner
261.2.x.a.218.2	yes	672	29.15	odd	28	inner
783.2.be.a.44.27		672	261.247	odd	84
783.2.be.a.89.27		672	3.2	odd	2
783.2.be.a.305.27		672	87.44	even	28
783.2.be.a.611.27		672	9.4	even	3

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.x (of order \(84\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.09871 - 1.54892i) q^{2} +(0.154284 - 1.72517i) q^{3} +(1.41592 + 4.59031i) q^{4} +(0.316022 - 0.805210i) q^{5} +(-2.99594 + 3.38165i) q^{6} +(0.806416 + 0.248746i) q^{7} +(2.41541 - 6.90284i) q^{8} +(-2.95239 - 0.532331i) q^{9} +O(q^{10})\)	\(q+(-2.09871 - 1.54892i) q^{2} +(0.154284 - 1.72517i) q^{3} +(1.41592 + 4.59031i) q^{4} +(0.316022 - 0.805210i) q^{5} +(-2.99594 + 3.38165i) q^{6} +(0.806416 + 0.248746i) q^{7} +(2.41541 - 6.90284i) q^{8} +(-2.95239 - 0.532331i) q^{9} +(-1.91044 + 1.20041i) q^{10} +(-5.60376 - 1.06029i) q^{11} +(8.13751 - 1.73449i) q^{12} +(-3.77591 + 0.282965i) q^{13} +(-1.30715 - 1.77112i) q^{14} +(-1.34036 - 0.669421i) q^{15} +(-7.82313 + 5.33372i) q^{16} +(0.354593 + 0.354593i) q^{17} +(5.37168 + 5.69022i) q^{18} +(-3.63939 - 5.79205i) q^{19} +(4.14363 + 0.310522i) q^{20} +(0.553546 - 1.35282i) q^{21} +(10.1184 + 10.9050i) q^{22} +(-0.354747 + 2.35360i) q^{23} +(-11.5359 - 5.23198i) q^{24} +(3.11677 + 2.89194i) q^{25} +(8.36282 + 5.25471i) q^{26} +(-1.37387 + 5.01124i) q^{27} +4.05391i q^{28} +(4.65370 - 2.70981i) q^{29} +(1.77616 + 3.48103i) q^{30} +(-0.850723 - 1.94988i) q^{31} +(10.0637 + 0.376558i) q^{32} +(-2.69375 + 9.50384i) q^{33} +(-0.194952 - 1.29342i) q^{34} +(0.455138 - 0.570725i) q^{35} +(-1.73680 - 14.3062i) q^{36} +(-3.00215 - 1.05050i) q^{37} +(-1.33340 + 17.7929i) q^{38} +(-0.0944008 + 6.55772i) q^{39} +(-4.79492 - 4.12636i) q^{40} +(-5.84116 - 1.56513i) q^{41} +(-3.25715 + 1.98179i) q^{42} +(5.16563 + 2.25374i) q^{43} +(-3.06745 - 27.2243i) q^{44} +(-1.36166 + 2.20907i) q^{45} +(4.39004 - 4.39004i) q^{46} +(0.176761 - 0.934203i) q^{47} +(7.99456 + 14.3191i) q^{48} +(-5.19524 - 3.54205i) q^{49} +(-2.06181 - 10.8969i) q^{50} +(0.666440 - 0.557024i) q^{51} +(-6.64530 - 16.9319i) q^{52} +(5.52744 - 4.40798i) q^{53} +(10.6453 - 8.38912i) q^{54} +(-2.62467 + 4.17713i) q^{55} +(3.66488 - 4.96574i) q^{56} +(-10.5537 + 5.38492i) q^{57} +(-13.9640 - 1.52111i) q^{58} +(-9.57798 + 5.52985i) q^{59} +(1.17500 - 7.10054i) q^{60} +(10.8872 - 5.75405i) q^{61} +(-1.23478 + 5.40993i) q^{62} +(-2.24844 - 1.16368i) q^{63} +(-5.73224 - 4.57131i) q^{64} +(-0.965422 + 3.12982i) q^{65} +(20.3741 - 15.7734i) q^{66} +(6.11472 - 8.96864i) q^{67} +(-1.12562 + 2.12977i) q^{68} +(4.00561 + 0.975121i) q^{69} +(-1.83921 + 0.492815i) q^{70} +(-2.23829 - 1.07790i) q^{71} +(-10.8058 + 19.0941i) q^{72} +(6.40414 - 0.721574i) q^{73} +(4.67351 + 6.85478i) q^{74} +(5.46994 - 4.93076i) q^{75} +(21.4342 - 24.9070i) q^{76} +(-4.25522 - 2.24895i) q^{77} +(10.3555 - 13.6165i) q^{78} +(-10.3362 - 12.0109i) q^{79} +(1.82249 + 7.98483i) q^{80} +(8.43325 + 3.14330i) q^{81} +(9.83464 + 12.3322i) q^{82} +(3.83954 - 4.13804i) q^{83} +(6.99367 + 0.625454i) q^{84} +(0.397581 - 0.173463i) q^{85} +(-7.35029 - 12.7311i) q^{86} +(-3.95687 - 8.44649i) q^{87} +(-20.8544 + 36.1209i) q^{88} +(-0.611623 + 5.42831i) q^{89} +(6.27939 - 2.52710i) q^{90} +(-3.11534 - 0.711056i) q^{91} +(-11.3060 + 1.70411i) q^{92} +(-3.49512 + 1.16680i) q^{93} +(-1.81797 + 1.68683i) q^{94} +(-5.81394 + 1.10006i) q^{95} +(2.20230 - 17.3035i) q^{96} +(0.336663 + 8.99750i) q^{97} +(5.41695 + 15.4807i) q^{98} +(15.9801 + 6.11345i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9}+O(q^{10}) \) 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9	\( 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20} - 80 q^{21} - 14 q^{22} - 30 q^{23} - 16 q^{24} + 30 q^{25} + 36 q^{27} - 168 q^{30} - 12 q^{31} + 24 q^{32} - 70 q^{33} - 14 q^{34} + 128 q^{36} - 48 q^{37} - 42 q^{38} - 44 q^{39} - 2 q^{40} - 24 q^{41} - 28 q^{42} - 12 q^{43} + 24 q^{45} - 64 q^{46} - 42 q^{47} - 28 q^{48} + 22 q^{49} - 66 q^{50} - 28 q^{51} + 22 q^{52} - 36 q^{54} + 76 q^{55} - 42 q^{56} - 42 q^{58} - 132 q^{59} - 20 q^{60} - 28 q^{63} - 308 q^{64} - 66 q^{65} - 46 q^{66} - 14 q^{67} + 60 q^{68} - 64 q^{69} - 14 q^{70} + 56 q^{72} - 48 q^{73} + 66 q^{74} + 24 q^{75} - 28 q^{76} + 30 q^{77} + 72 q^{78} - 12 q^{79} + 140 q^{81} - 136 q^{82} + 246 q^{83} + 238 q^{84} + 34 q^{85} + 118 q^{87} + 8 q^{88} - 48 q^{90} - 56 q^{91} + 462 q^{92} + 28 q^{93} + 26 q^{94} - 246 q^{95} + 126 q^{96} - 36 q^{97} - 16 q^{99}+O(q^{100}) \) 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more