LMFDB - Embedded newform 43.2.g.a.9.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,2,Mod(9,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("43.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	43.g (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.343356728692$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			9.3
Character	$\chi$	$=$	43.9
Dual form			43.2.g.a.24.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.06016 + 1.32939i) q^{2} +(-1.14296 - 0.172273i) q^{3} +(-0.198316 + 0.868879i) q^{4} +(-1.45700 - 0.993363i) q^{5} +(-0.982695 - 1.70208i) q^{6} +(-0.297283 + 0.514909i) q^{7} +(1.69861 - 0.818009i) q^{8} +(-1.59004 - 0.490464i) q^{9} +O(q^{10})$	\(q+(1.06016 + 1.32939i) q^{2} +(-1.14296 - 0.172273i) q^{3} +(-0.198316 + 0.868879i) q^{4} +(-1.45700 - 0.993363i) q^{5} +(-0.982695 - 1.70208i) q^{6} +(-0.297283 + 0.514909i) q^{7} +(1.69861 - 0.818009i) q^{8} +(-1.59004 - 0.490464i) q^{9} +(-0.224073 - 2.99004i) q^{10} +(0.967034 + 4.23685i) q^{11} +(0.376351 - 0.958927i) q^{12} +(0.242325 - 3.23360i) q^{13} +(-0.999683 + 0.150678i) q^{14} +(1.49415 + 1.38637i) q^{15} +(4.49418 + 2.16428i) q^{16} +(-4.57863 + 3.12166i) q^{17} +(-1.03368 - 2.63377i) q^{18} +(2.59725 - 0.801147i) q^{19} +(1.15206 - 1.06895i) q^{20} +(0.428486 - 0.537305i) q^{21} +(-4.60724 + 5.77730i) q^{22} +(-3.88284 + 3.60275i) q^{23} +(-2.08236 + 0.642324i) q^{24} +(-0.690639 - 1.75972i) q^{25} +(4.55564 - 3.10598i) q^{26} +(4.85706 + 2.33904i) q^{27} +(-0.388437 - 0.360417i) q^{28} +(9.75088 - 1.46971i) q^{29} +(-0.258998 + 3.45609i) q^{30} +(1.36275 - 3.47222i) q^{31} +(1.04831 + 4.59293i) q^{32} +(-0.375383 - 5.00913i) q^{33} +(-9.00399 - 2.77736i) q^{34} +(0.944631 - 0.454910i) q^{35} +(0.741485 - 1.28429i) q^{36} +(-0.673012 - 1.16569i) q^{37} +(3.81854 + 2.60343i) q^{38} +(-0.834030 + 3.65413i) q^{39} +(-3.28745 - 0.495504i) q^{40} +(-6.99273 - 8.76860i) q^{41} +1.16855 q^{42} +(-4.98246 - 4.26323i) q^{43} -3.87309 q^{44} +(1.82948 + 2.29409i) q^{45} +(-8.90590 - 1.34235i) q^{46} +(-0.909600 + 3.98522i) q^{47} +(-4.76381 - 3.24791i) q^{48} +(3.32325 + 5.75603i) q^{49} +(1.60718 - 2.78371i) q^{50} +(5.77096 - 2.77915i) q^{51} +(2.76155 + 0.851826i) q^{52} +(-0.180172 - 2.40423i) q^{53} +(2.03974 + 8.93670i) q^{54} +(2.79977 - 7.13369i) q^{55} +(-0.0837683 + 1.11781i) q^{56} +(-3.10657 + 0.468240i) q^{57} +(12.2913 + 11.4047i) q^{58} +(0.662333 + 0.318963i) q^{59} +(-1.50090 + 1.02330i) q^{60} +(1.86879 + 4.76159i) q^{61} +(6.06068 - 1.86947i) q^{62} +(0.725237 - 0.672921i) q^{63} +(1.22570 - 1.53698i) q^{64} +(-3.56521 + 4.47063i) q^{65} +(6.26115 - 5.80950i) q^{66} +(-3.67807 + 1.13454i) q^{67} +(-1.80433 - 4.59735i) q^{68} +(5.05858 - 3.44888i) q^{69} +(1.60621 + 0.773511i) q^{70} +(2.81309 + 2.61017i) q^{71} +(-3.10208 + 0.467563i) q^{72} +(-0.557170 + 7.43491i) q^{73} +(0.836166 - 2.13052i) q^{74} +(0.486219 + 2.13026i) q^{75} +(0.181023 + 2.41558i) q^{76} +(-2.46907 - 0.761608i) q^{77} +(-5.74198 + 2.76519i) q^{78} +(-6.69672 + 11.5991i) q^{79} +(-4.39809 - 7.61771i) q^{80} +(-1.02395 - 0.698119i) q^{81} +(4.24355 - 18.5922i) q^{82} +(-7.70597 - 1.16149i) q^{83} +(0.381877 + 0.478859i) q^{84} +9.77199 q^{85} +(0.385325 - 11.1433i) q^{86} -11.3980 q^{87} +(5.10840 + 6.40573i) q^{88} +(-4.45907 - 0.672097i) q^{89} +(-1.11022 + 4.86420i) q^{90} +(1.59297 + 1.08607i) q^{91} +(-2.36033 - 4.08820i) q^{92} +(-2.15573 + 3.73383i) q^{93} +(-6.26225 + 3.01574i) q^{94} +(-4.58002 - 1.41275i) q^{95} +(-0.406931 - 5.43011i) q^{96} +(-0.0411575 - 0.180323i) q^{97} +(-4.12888 + 10.5202i) q^{98} +(0.540395 - 7.21108i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9}+O(q^{10}) $ 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9} - 7 q^{10} - 4 q^{11} + 2 q^{12} + 18 q^{14} - 3 q^{15} - 10 q^{16} - 10 q^{17} + 11 q^{18} + 10 q^{19} - 3 q^{20} - 21 q^{21} - 3 q^{22} + 4 q^{23} + 31 q^{24} - 2 q^{25} - 15 q^{26} - 4 q^{27} + 20 q^{28} + 9 q^{29} + 88 q^{30} + 40 q^{31} + 48 q^{32} - 11 q^{33} - 42 q^{34} + 11 q^{35} - 47 q^{36} - 19 q^{37} - 21 q^{38} - q^{39} - 97 q^{40} - 28 q^{41} + 2 q^{42} - 8 q^{43} + 14 q^{44} - 46 q^{45} - 61 q^{46} - 30 q^{47} - 97 q^{48} + 6 q^{49} - 3 q^{50} + 57 q^{51} - 8 q^{52} - 24 q^{53} + 6 q^{54} + 14 q^{55} + 39 q^{56} + 52 q^{57} + 64 q^{58} - q^{59} + 111 q^{60} - 14 q^{61} + 33 q^{62} + 47 q^{63} + 48 q^{64} + 38 q^{65} + 79 q^{66} + 66 q^{67} + 66 q^{68} - 7 q^{69} + 47 q^{70} - 33 q^{71} + 26 q^{72} + 29 q^{73} - 40 q^{74} - 55 q^{75} - 39 q^{76} - 27 q^{77} - 126 q^{78} - 17 q^{79} + 8 q^{80} + 38 q^{81} - 54 q^{82} - 23 q^{83} - 155 q^{84} - 56 q^{85} - 45 q^{86} - 86 q^{87} - 17 q^{88} - 19 q^{89} - 127 q^{90} - 13 q^{91} - 18 q^{92} - 30 q^{93} + 44 q^{94} + q^{95} - 36 q^{96} - 31 q^{97} - 5 q^{98} - 31 q^{99}+O(q^{100}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9 - 7 * q^10 - 4 * q^11 + 2 * q^12 + 18 * q^14 - 3 * q^15 - 10 * q^16 - 10 * q^17 + 11 * q^18 + 10 * q^19 - 3 * q^20 - 21 * q^21 - 3 * q^22 + 4 * q^23 + 31 * q^24 - 2 * q^25 - 15 * q^26 - 4 * q^27 + 20 * q^28 + 9 * q^29 + 88 * q^30 + 40 * q^31 + 48 * q^32 - 11 * q^33 - 42 * q^34 + 11 * q^35 - 47 * q^36 - 19 * q^37 - 21 * q^38 - q^39 - 97 * q^40 - 28 * q^41 + 2 * q^42 - 8 * q^43 + 14 * q^44 - 46 * q^45 - 61 * q^46 - 30 * q^47 - 97 * q^48 + 6 * q^49 - 3 * q^50 + 57 * q^51 - 8 * q^52 - 24 * q^53 + 6 * q^54 + 14 * q^55 + 39 * q^56 + 52 * q^57 + 64 * q^58 - q^59 + 111 * q^60 - 14 * q^61 + 33 * q^62 + 47 * q^63 + 48 * q^64 + 38 * q^65 + 79 * q^66 + 66 * q^67 + 66 * q^68 - 7 * q^69 + 47 * q^70 - 33 * q^71 + 26 * q^72 + 29 * q^73 - 40 * q^74 - 55 * q^75 - 39 * q^76 - 27 * q^77 - 126 * q^78 - 17 * q^79 + 8 * q^80 + 38 * q^81 - 54 * q^82 - 23 * q^83 - 155 * q^84 - 56 * q^85 - 45 * q^86 - 86 * q^87 - 17 * q^88 - 19 * q^89 - 127 * q^90 - 13 * q^91 - 18 * q^92 - 30 * q^93 + 44 * q^94 + q^95 - 36 * q^96 - 31 * q^97 - 5 * q^98 - 31 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{21}\right)$

Coefficient data

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

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

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

$2$	1.06016	+	1.32939i	0.749644	+	0.940024i	0.999601	−	0.0282328i	$-0.00898797\pi$
$2$	1.06016	+	1.32939i	0.749644	+	0.940024i	−0.249957	+	0.968257i	$0.580417\pi$
$3$	−1.14296	−	0.172273i	−0.659887	−	0.0994619i	−0.189443	−	0.981892i	$-0.560668\pi$
$3$	−1.14296	−	0.172273i	−0.659887	−	0.0994619i	−0.470444	+	0.882430i	$0.655906\pi$
$4$	−0.198316	+	0.868879i	−0.0991580	+	0.434439i
$5$	−1.45700	−	0.993363i	−0.651588	−	0.444245i	0.191884	−	0.981418i	$-0.438540\pi$
$5$	−1.45700	−	0.993363i	−0.651588	−	0.444245i	−0.843473	+	0.537172i	$0.819493\pi$
$6$	−0.982695	−	1.70208i	−0.401184	−	0.694871i
$7$	−0.297283	+	0.514909i	−0.112362	+	0.194617i	−0.916722	−	0.399525i	$-0.869175\pi$
$7$	−0.297283	+	0.514909i	−0.112362	+	0.194617i	0.804360	+	0.594142i	$0.202508\pi$
$8$	1.69861	−	0.818009i	0.600551	−	0.289210i
$9$	−1.59004	−	0.490464i	−0.530015	−	0.163488i
$10$	−0.224073	−	2.99004i	−0.0708580	−	0.945535i
$11$	0.967034	+	4.23685i	0.291572	+	1.27746i	0.882338	+	0.470616i	$0.155968\pi$
$11$	0.967034	+	4.23685i	0.291572	+	1.27746i	−0.590767	+	0.806843i	$0.701175\pi$
$12$	0.376351	−	0.958927i	0.108643	−	0.276818i
$13$	0.242325	−	3.23360i	0.0672089	−	0.896840i	−0.857089	−	0.515168i	$-0.827729\pi$
$13$	0.242325	−	3.23360i	0.0672089	−	0.896840i	0.924298	−	0.381672i	$-0.124652\pi$
$14$	−0.999683	+	0.150678i	−0.267177	+	0.0402704i
$15$	1.49415	+	1.38637i	0.385789	+	0.357960i
$16$	4.49418	+	2.16428i	1.12355	+	0.541071i
$17$	−4.57863	+	3.12166i	−1.11048	+	0.757113i	−0.972403	−	0.233308i	$-0.925045\pi$
$17$	−4.57863	+	3.12166i	−1.11048	+	0.757113i	−0.138078	+	0.990421i	$0.544093\pi$
$18$	−1.03368	−	2.63377i	−0.243640	−	0.620785i
$19$	2.59725	−	0.801147i	0.595851	−	0.183796i	0.0178622	−	0.999840i	$-0.494314\pi$
$19$	2.59725	−	0.801147i	0.595851	−	0.183796i	0.577989	+	0.816045i	$0.303838\pi$
$20$	1.15206	−	1.06895i	0.257608	−	0.239025i
$21$	0.428486	−	0.537305i	0.0935034	−	0.117250i
$22$	−4.60724	+	5.77730i	−0.982267	+	1.23172i
$23$	−3.88284	+	3.60275i	−0.809629	+	0.751226i	−0.971868	−	0.235526i	$-0.924319\pi$
$23$	−3.88284	+	3.60275i	−0.809629	+	0.751226i	0.162239	+	0.986751i	$0.448128\pi$
$24$	−2.08236	+	0.642324i	−0.425061	+	0.131114i
$25$	−0.690639	−	1.75972i	−0.138128	−	0.351944i
$26$	4.55564	−	3.10598i	0.893434	−	0.609133i
$27$	4.85706	+	2.33904i	0.934742	+	0.450148i
$28$	−0.388437	−	0.360417i	−0.0734078	−	0.0681125i
$29$	9.75088	−	1.46971i	1.81069	−	0.272918i	0.845409	−	0.534119i	$-0.179357\pi$
$29$	9.75088	−	1.46971i	1.81069	−	0.272918i	0.965284	+	0.261201i	$0.0841186\pi$
$30$	−0.258998	+	3.45609i	−0.0472864	+	0.630993i
$31$	1.36275	−	3.47222i	0.244756	−	0.623629i	−0.754718	−	0.656049i	$-0.772226\pi$
$31$	1.36275	−	3.47222i	0.244756	−	0.623629i	0.999474	+	0.0324203i	$0.0103215\pi$
$32$	1.04831	+	4.59293i	0.185316	+	0.811922i
$33$	−0.375383	−	5.00913i	−0.0653457	−	0.871978i
$34$	−9.00399	−	2.77736i	−1.54417	−	0.476314i
$35$	0.944631	−	0.454910i	0.159672	−	0.0768938i
$36$	0.741485	−	1.28429i	0.123581	−	0.214048i
$37$	−0.673012	−	1.16569i	−0.110643	−	0.191639i	0.805387	−	0.592749i	$-0.201958\pi$
$37$	−0.673012	−	1.16569i	−0.110643	−	0.191639i	−0.916030	+	0.401111i	$0.868624\pi$
$38$	3.81854	+	2.60343i	0.619449	+	0.422333i
$39$	−0.834030	+	3.65413i	−0.133552	+	0.585128i
$40$	−3.28745	−	0.495504i	−0.519792	−	0.0783460i
$41$	−6.99273	−	8.76860i	−1.09208	−	1.36943i	−0.923438	−	0.383748i	$-0.874633\pi$
$41$	−6.99273	−	8.76860i	−1.09208	−	1.36943i	−0.168643	−	0.985677i	$-0.553938\pi$
$42$	1.16855			0.180312
$43$	−4.98246	−	4.26323i	−0.759818	−	0.650136i
$43$	−4.98246	−	4.26323i	−0.759818	−	0.650136i
$44$	−3.87309			−0.583890
$45$	1.82948	+	2.29409i	0.272723	+	0.341983i
$46$	−8.90590	−	1.34235i	−1.31310	−	0.197919i
$47$	−0.909600	+	3.98522i	−0.132679	+	0.581304i	0.864255	+	0.503054i	$0.167790\pi$
$47$	−0.909600	+	3.98522i	−0.132679	+	0.581304i	−0.996934	+	0.0782499i	$0.975067\pi$
$48$	−4.76381	−	3.24791i	−0.687597	−	0.468796i
$49$	3.32325	+	5.75603i	0.474749	+	0.822290i
$50$	1.60718	−	2.78371i	0.227289	−	0.393676i
$51$	5.77096	−	2.77915i	0.808096	−	0.389159i
$52$	2.76155	+	0.851826i	0.382958	+	0.118127i
$53$	−0.180172	−	2.40423i	−0.0247485	−	0.330246i	−0.995812	−	0.0914247i	$-0.970858\pi$
$53$	−0.180172	−	2.40423i	−0.0247485	−	0.330246i	0.971063	−	0.238822i	$-0.0767611\pi$
$54$	2.03974	+	8.93670i	0.277574	+	1.21613i
$55$	2.79977	−	7.13369i	0.377520	−	0.961906i
$56$	−0.0837683	+	1.11781i	−0.0111940	+	0.149374i
$57$	−3.10657	+	0.468240i	−0.411475	+	0.0620199i
$58$	12.2913	+	11.4047i	1.61393	+	1.49750i
$59$	0.662333	+	0.318963i	0.0862285	+	0.0415254i	0.476501	−	0.879174i	$-0.341905\pi$
$59$	0.662333	+	0.318963i	0.0862285	+	0.0415254i	−0.390272	+	0.920699i	$0.627619\pi$
$60$	−1.50090	+	1.02330i	−0.193766	+	0.132107i
$61$	1.86879	+	4.76159i	0.239273	+	0.609659i	0.999185	−	0.0403678i	$-0.0128530\pi$
$61$	1.86879	+	4.76159i	0.239273	+	0.609659i	−0.759911	+	0.650027i	$0.774758\pi$
$62$	6.06068	−	1.86947i	0.769707	−	0.237423i
$63$	0.725237	−	0.672921i	0.0913713	−	0.0847801i
$64$	1.22570	−	1.53698i	0.153212	−	0.192122i
$65$	−3.56521	+	4.47063i	−0.442210	+	0.554513i
$66$	6.26115	−	5.80950i	0.770695	−	0.715100i
$67$	−3.67807	+	1.13454i	−0.449348	+	0.138606i	−0.511166	−	0.859482i	$-0.670786\pi$
$67$	−3.67807	+	1.13454i	−0.449348	+	0.138606i	0.0618180	+	0.998087i	$0.480310\pi$
$68$	−1.80433	−	4.59735i	−0.218807	−	0.557511i
$69$	5.05858	−	3.44888i	0.608982	−	0.415197i
$70$	1.60621	+	0.773511i	0.191979	+	0.0924522i
$71$	2.81309	+	2.61017i	0.333852	+	0.309770i	0.829229	−	0.558908i	$-0.188780\pi$
$71$	2.81309	+	2.61017i	0.333852	+	0.309770i	−0.495377	+	0.868678i	$0.664970\pi$
$72$	−3.10208	+	0.467563i	−0.365583	+	0.0551028i
$73$	−0.557170	+	7.43491i	−0.0652118	+	0.870191i	0.864672	+	0.502337i	$0.167526\pi$
$73$	−0.557170	+	7.43491i	−0.0652118	+	0.870191i	−0.929884	+	0.367854i	$0.880093\pi$
$74$	0.836166	−	2.13052i	0.0972023	−	0.247667i
$75$	0.486219	+	2.13026i	0.0561437	+	0.245982i
$76$	0.181023	+	2.41558i	0.0207647	+	0.277086i
$77$	−2.46907	−	0.761608i	−0.281377	−	0.0867933i
$78$	−5.74198	+	2.76519i	−0.650151	+	0.313096i
$79$	−6.69672	+	11.5991i	−0.753440	+	1.30500i	0.192706	+	0.981257i	$0.438274\pi$
$79$	−6.69672	+	11.5991i	−0.753440	+	1.30500i	−0.946146	+	0.323740i	$0.895060\pi$
$80$	−4.39809	−	7.61771i	−0.491721	−	0.851686i
$81$	−1.02395	−	0.698119i	−0.113772	−	0.0775687i
$82$	4.24355	−	18.5922i	0.468621	−	2.05316i
$83$	−7.70597	−	1.16149i	−0.845840	−	0.127490i	−0.288198	−	0.957571i	$-0.593056\pi$
$83$	−7.70597	−	1.16149i	−0.845840	−	0.127490i	−0.557643	+	0.830081i	$0.688294\pi$
$84$	0.381877	+	0.478859i	0.0416662	+	0.0522478i
$85$	9.77199			1.05992
$86$	0.385325	−	11.1433i	0.0415507	−	1.20162i
$87$	−11.3980			−1.22200
$88$	5.10840	+	6.40573i	0.544557	+	0.682853i
$89$	−4.45907	−	0.672097i	−0.472661	−	0.0712421i	−0.0916073	−	0.995795i	$-0.529200\pi$
$89$	−4.45907	−	0.672097i	−0.472661	−	0.0712421i	−0.381053	+	0.924553i	$0.624439\pi$
$90$	−1.11022	+	4.86420i	−0.117028	+	0.512732i
$91$	1.59297	+	1.08607i	0.166989	+	0.113851i
$92$	−2.36033	−	4.08820i	−0.246081	−	0.426225i
$93$	−2.15573	+	3.73383i	−0.223539	+	0.387181i
$94$	−6.26225	+	3.01574i	−0.645902	+	0.311050i
$95$	−4.58002	−	1.41275i	−0.469900	−	0.144945i
$96$	−0.406931	−	5.43011i	−0.0415322	−	0.554209i
$97$	−0.0411575	−	0.180323i	−0.00417891	−	0.0183090i	0.972795	−	0.231666i	$-0.0744175\pi$
$97$	−0.0411575	−	0.180323i	−0.00417891	−	0.0183090i	−0.976974	+	0.213357i	$0.931560\pi$
$98$	−4.12888	+	10.5202i	−0.417079	+	1.06270i
$99$	0.540395	−	7.21108i	0.0543118	−	0.724740i
$100$	1.66595	−	0.251101i	0.166595	−	0.0251101i
$101$	−3.02611	−	2.80782i	−0.301109	−	0.279388i	0.515119	−	0.857119i	$-0.327748\pi$
$101$	−3.02611	−	2.80782i	−0.301109	−	0.279388i	−0.816227	+	0.577731i	$0.803938\pi$
$102$	9.81271	+	4.72555i	0.971603	+	0.467899i
$103$	12.9998	−	8.86308i	1.28090	−	0.873305i	0.284553	−	0.958660i	$-0.408155\pi$
$103$	12.9998	−	8.86308i	1.28090	−	0.873305i	0.996351	+	0.0853552i	$0.0272025\pi$
$104$	−2.23350	−	5.69087i	−0.219013	−	0.558036i
$105$	−1.15804	+	0.357208i	−0.113013	+	0.0348600i
$106$	3.00516	−	2.78838i	0.291887	−	0.270831i
$107$	0.0333463	−	0.0418149i	0.00322371	−	0.00404240i	−0.780217	−	0.625509i	$-0.784891\pi$
$107$	0.0333463	−	0.0418149i	0.00322371	−	0.00404240i	0.783441	+	0.621467i	$0.213463\pi$
$108$	−2.99557	+	3.75633i	−0.288249	+	0.361453i
$109$	3.84855	−	3.57093i	0.368624	−	0.342033i	−0.474010	−	0.880519i	$-0.657194\pi$
$109$	3.84855	−	3.57093i	0.368624	−	0.342033i	0.842635	+	0.538486i	$0.181003\pi$
$110$	12.4517	−	3.84083i	1.18722	−	0.366209i
$111$	0.568407	+	1.44828i	0.0539508	+	0.137464i
$112$	−2.45045	+	1.67069i	−0.231546	+	0.157865i
$113$	−2.32635	−	1.12031i	−0.218844	−	0.105390i	0.321250	−	0.946995i	$-0.395897\pi$
$113$	−2.32635	−	1.12031i	−0.218844	−	0.105390i	−0.540094	+	0.841605i	$0.681611\pi$
$114$	−3.91592	−	3.63345i	−0.366760	−	0.340303i
$115$	9.23613	−	1.39212i	0.861273	−	0.129816i
$116$	−0.656756	+	8.76380i	−0.0609783	+	0.813699i
$117$	−1.97127	+	5.02272i	−0.182244	+	0.464351i
$118$	0.278150	+	1.21865i	0.0256058	+	0.112186i
$119$	−0.246221	−	3.28559i	−0.0225711	−	0.301190i
$120$	3.67206	+	1.13268i	0.335211	+	0.103399i
$121$	−7.10509	+	3.42163i	−0.645917	+	0.311057i
$122$	−4.34882	+	7.53239i	−0.393724	+	0.681950i
$123$	6.48180	+	11.2268i	0.584444	+	1.01229i
$124$	2.74668	+	1.87266i	0.246659	+	0.168170i
$125$	−2.70376	+	11.8459i	−0.241831	+	1.05953i
$126$	1.66344	+	0.250724i	0.148191	+	0.0223362i
$127$	−8.14586	−	10.2146i	−0.722828	−	0.906397i	0.275666	−	0.961253i	$-0.411101\pi$
$127$	−8.14586	−	10.2146i	−0.722828	−	0.906397i	−0.998494	+	0.0548559i	$0.982530\pi$
$128$	12.7648			1.12826
$129$	4.96030	+	5.73103i	0.436730	+	0.504589i
$130$	−9.72291			−0.852756
$131$	−6.71788	−	8.42396i	−0.586944	−	0.736004i	0.396336	−	0.918106i	$-0.370282\pi$
$131$	−6.71788	−	8.42396i	−0.586944	−	0.736004i	−0.983280	+	0.182101i	$0.941710\pi$
$132$	4.42677	+	0.667229i	0.385301	+	0.0580748i
$133$	−0.359601	+	1.57552i	−0.0311814	+	0.136615i
$134$	−5.40758	−	3.68683i	−0.467144	−	0.318493i
$135$	−4.75320	−	8.23279i	−0.409091	−	0.708566i
$136$	−5.22378	+	9.04785i	−0.447936	+	0.775847i
$137$	7.24128	−	3.48722i	0.618664	−	0.297933i	−0.0981775	−	0.995169i	$-0.531301\pi$
$137$	7.24128	−	3.48722i	0.618664	−	0.297933i	0.716842	+	0.697236i	$0.245587\pi$
$138$	9.94782	+	3.06850i	0.846815	+	0.261208i
$139$	1.63572	+	21.8272i	0.138740	+	1.85136i	0.440227	+	0.897887i	$0.354898\pi$
$139$	1.63572	+	21.8272i	0.138740	+	1.85136i	−0.301487	+	0.953470i	$0.597483\pi$
$140$	0.207926	+	0.910985i	0.0175730	+	0.0769923i
$141$	1.72618	−	4.39824i	0.145371	−	0.370398i
$142$	−0.487624	+	6.50690i	−0.0409205	+	0.546047i
$143$	13.9346	−	2.10031i	1.16527	−	0.175637i
$144$	−6.08445	−	5.64554i	−0.507037	−	0.470462i
$145$	−15.6669	−	7.54480i	−1.30107	−	0.626562i
$146$	−10.4746	+	7.14148i	−0.866886	+	0.591033i
$147$	−2.80672	−	7.15140i	−0.231494	−	0.589838i
$148$	1.14631	−	0.353591i	0.0942264	−	0.0290650i
$149$	12.1022	−	11.2292i	0.991453	−	0.919934i	−0.00533774	−	0.999986i	$-0.501699\pi$
$149$	12.1022	−	11.2292i	0.991453	−	0.919934i	0.996791	+	0.0800518i	$0.0255086\pi$
$150$	−2.31649	+	2.90479i	−0.189141	+	0.237175i
$151$	9.89432	−	12.4071i	0.805188	−	1.00967i	−0.194398	−	0.980923i	$-0.562275\pi$
$151$	9.89432	−	12.4071i	0.805188	−	1.00967i	0.999587	−	0.0287513i	$-0.00915309\pi$
$152$	3.75639	−	3.48542i	0.304683	−	0.282705i
$153$	8.81129	−	2.71792i	0.712351	−	0.219731i
$154$	−1.60513	−	4.08980i	−0.129345	−	0.329565i
$155$	−5.43469	+	3.70531i	−0.436525	+	0.297617i
$156$	−3.00959	−	1.44934i	−0.240960	−	0.116040i
$157$	4.81341	+	4.46619i	0.384152	+	0.356441i	0.848485	−	0.529220i	$-0.177515\pi$
$157$	4.81341	+	4.46619i	0.384152	+	0.356441i	−0.464333	+	0.885661i	$0.653706\pi$
$158$	−22.5193	+	3.39424i	−1.79154	+	0.270031i
$159$	−0.208255	+	2.77897i	−0.0165157	+	0.220387i
$160$	3.03507	−	7.73322i	0.239943	−	0.611365i
$161$	−0.700786	−	3.07035i	−0.0552297	−	0.241977i
$162$	−0.157475	−	2.10135i	−0.0123724	−	0.165098i
$163$	−12.1383	−	3.74416i	−0.950742	−	0.293265i	−0.219677	−	0.975573i	$-0.570500\pi$
$163$	−12.1383	−	3.74416i	−0.950742	−	0.293265i	−0.731065	+	0.682308i	$0.760976\pi$
$164$	9.00562	−	4.33688i	0.703221	−	0.338653i
$165$	−4.42896	+	7.67118i	−0.344794	+	0.597200i
$166$	−6.62546	−	11.4756i	−0.514236	−	0.890682i
$167$	13.7745	+	9.39128i	1.06590	+	0.726719i	0.963415	−	0.268015i	$-0.0863678\pi$
$167$	13.7745	+	9.39128i	1.06590	+	0.726719i	0.102487	+	0.994734i	$0.467320\pi$
$168$	0.288312	−	1.26318i	0.0222438	−	0.0974564i
$169$	2.45733	+	0.370383i	0.189025	+	0.0284910i
$170$	10.3598	+	12.9908i	0.794563	+	0.996351i
$171$	−4.52268			−0.345858
$172$	4.69233	−	3.48369i	0.357787	−	0.265629i
$173$	8.10129			0.615930			0.307965	−	0.951398i	$-0.400352\pi$
$173$	8.10129			0.615930			0.307965	+	0.951398i	$0.400352\pi$
$174$	−12.0837	−	15.1525i	−0.916064	−	1.14871i
$175$	1.11141	+	0.167518i	0.0840147	+	0.0126632i
$176$	−4.82373	+	21.1341i	−0.363602	+	1.59304i
$177$	−0.702070	−	0.478663i	−0.0527708	−	0.0359785i
$178$	−3.83383	−	6.64039i	−0.287358	−	0.497719i
$179$	8.72484	−	15.1119i	0.652125	−	1.12951i	−0.330481	−	0.943813i	$-0.607211\pi$
$179$	8.72484	−	15.1119i	0.652125	−	1.12951i	0.982606	−	0.185702i	$-0.0594558\pi$
$180$	−2.35610	+	1.13464i	−0.175614	+	0.0845711i
$181$	13.4876	+	4.16037i	1.00252	+	0.309238i	0.752207	−	0.658927i	$-0.228989\pi$
$181$	13.4876	+	4.16037i	1.00252	+	0.309238i	0.250316	+	0.968164i	$0.419465\pi$
$182$	0.244985	+	3.26909i	0.0181595	+	0.242321i
$183$	−1.31565	−	5.76423i	−0.0972556	−	0.426104i
$184$	−3.64837	+	9.29589i	−0.268961	+	0.685302i
$185$	−0.177379	+	2.36695i	−0.0130411	+	0.174022i
$186$	−7.24915	+	1.09263i	−0.531534	+	0.0801158i
$187$	−17.6537	−	16.3802i	−1.29097	−	1.19784i
$188$	−3.28228	−	1.58066i	−0.239385	−	0.115282i
$189$	−2.64831	+	1.80559i	−0.192636	+	0.131337i
$190$	−2.97744	−	7.58638i	−0.216006	−	0.550374i
$191$	−18.1083	+	5.58567i	−1.31027	+	0.404165i	−0.869713	−	0.493558i	$-0.835696\pi$
$191$	−18.1083	+	5.58567i	−1.31027	+	0.404165i	−0.440559	+	0.897724i	$0.645220\pi$
$192$	−1.66570	+	1.54555i	−0.120212	+	0.111540i
$193$	−13.2105	+	16.5654i	−0.950912	+	1.19241i	0.0303130	+	0.999540i	$0.490350\pi$
$193$	−13.2105	+	16.5654i	−0.950912	+	1.19241i	−0.981225	+	0.192866i	$0.938222\pi$
$194$	0.196087	−	0.245885i	0.0140782	−	0.0176535i
$195$	4.84505	−	4.49555i	0.346961	−	0.321933i
$196$	−5.66035	+	1.74599i	−0.404310	+	0.124713i
$197$	1.03126	+	2.62761i	0.0734742	+	0.187209i	0.962893	−	0.269885i	$-0.0869856\pi$
$197$	1.03126	+	2.62761i	0.0734742	+	0.187209i	−0.889418	+	0.457094i	$0.848890\pi$
$198$	10.1593	−	6.92647i	0.721988	−	0.492243i
$199$	0.0117039	+	0.00563631i	0.000829669	+	0.000399547i	0.434299	−	0.900769i	$-0.356996\pi$
$199$	0.0117039	+	0.00563631i	0.000829669	+	0.000399547i	−0.433469	+	0.901169i	$0.642711\pi$
$200$	−2.61259	−	2.42413i	−0.184738	−	0.171412i
$201$	4.39933	−	0.663093i	0.310305	−	0.0467710i
$202$	0.524549	−	6.99961i	0.0369071	−	0.492491i
$203$	−2.14200	+	5.45773i	−0.150339	+	0.383058i
$204$	1.27027	+	5.56541i	0.0889366	+	0.389657i
$205$	1.47797	+	19.7221i	0.103226	+	1.37745i
$206$	25.5643	+	7.88554i	1.78115	+	0.549412i
$207$	7.94091	−	3.82414i	0.551932	−	0.265796i
$208$	8.08749	−	14.0080i	0.560767	−	0.971277i
$209$	5.90597	+	10.2294i	0.408525	+	0.707585i
$210$	−1.70258	−	1.16080i	−0.117489	−	0.0801026i
$211$	0.482505	−	2.11399i	0.0332170	−	0.145533i	−0.955600	−	0.294667i	$-0.904791\pi$
$211$	0.482505	−	2.11399i	0.0332170	−	0.145533i	0.988817	+	0.149134i	$0.0476485\pi$
$212$	2.12471	+	0.320249i	0.145926	+	0.0219948i
$213$	−2.76558	−	3.46793i	−0.189495	−	0.237619i
$214$	0.0909409			0.00621659
$215$	3.02449	+	11.1609i	0.206268	+	0.761166i
$216$	10.1636			0.691547
$217$	1.38276	+	1.73392i	0.0938676	+	0.117706i
$218$	8.82725	+	1.33049i	0.597857	+	0.0901124i
$219$	1.91766	−	8.40181i	0.129583	−	0.567741i
$220$	5.64307	+	3.84738i	0.380456	+	0.259390i
$221$	8.98469	+	15.5619i	0.604376	+	1.04681i
$222$	−1.32273	+	2.29104i	−0.0887760	+	0.153765i
$223$	−3.40210	+	1.63836i	−0.227821	+	0.109713i	−0.544313	−	0.838882i	$-0.683209\pi$
$223$	−3.40210	+	1.63836i	−0.227821	+	0.109713i	0.316491	+	0.948595i	$0.397495\pi$
$224$	−2.67658	−	0.825616i	−0.178837	−	0.0551638i
$225$	0.235068	+	3.13677i	0.0156712	+	0.209118i
$226$	−0.976960	−	4.28034i	−0.0649864	−	0.284724i
$227$	−6.05732	+	15.4338i	−0.402039	+	1.02438i	0.576276	+	0.817255i	$0.304505\pi$
$227$	−6.05732	+	15.4338i	−0.402039	+	1.02438i	−0.978315	+	0.207123i	$0.933590\pi$
$228$	0.209238	−	2.79209i	0.0138571	−	0.184911i
$229$	0.765334	−	0.115355i	0.0505747	−	0.00762291i	−0.123706	−	0.992319i	$-0.539478\pi$
$229$	0.765334	−	0.115355i	0.0505747	−	0.00762291i	0.174281	+	0.984696i	$0.444240\pi$
$230$	11.6424	+	10.8026i	0.767679	+	0.712302i
$231$	2.69084	+	1.29584i	0.177044	+	0.0852601i
$232$	15.3607	−	10.4728i	1.00848	−	0.687572i
$233$	−9.49014	−	24.1805i	−0.621720	−	1.58412i	−0.799910	−	0.600120i	$-0.795119\pi$
$233$	−9.49014	−	24.1805i	−0.621720	−	1.58412i	0.178190	−	0.983996i	$-0.442976\pi$
$234$	−8.76704	+	2.70427i	−0.573119	+	0.176784i
$235$	5.28405	−	4.90288i	0.344694	−	0.319829i
$236$	−0.408491	+	0.512232i	−0.0265905	+	0.0333435i
$237$	9.65227	−	12.1036i	0.626983	−	0.786211i
$238$	4.10682	−	3.81057i	0.266205	−	0.247003i
$239$	3.36898	−	1.03919i	0.217921	−	0.0672198i	−0.183872	−	0.982950i	$-0.558863\pi$
$239$	3.36898	−	1.03919i	0.217921	−	0.0672198i	0.401793	+	0.915730i	$0.368387\pi$
$240$	3.71450	+	9.46439i	0.239770	+	0.610924i
$241$	−16.1244	+	10.9934i	−1.03866	+	0.708149i	−0.957465	−	0.288549i	$-0.906827\pi$
$241$	−16.1244	+	10.9934i	−1.03866	+	0.708149i	−0.0811985	+	0.996698i	$0.525875\pi$
$242$	−12.0812	−	5.81801i	−0.776610	−	0.373996i
$243$	−10.8054	−	10.0260i	−0.693169	−	0.643167i
$244$	−4.50785	+	0.679449i	−0.288586	+	0.0434973i
$245$	0.875872	−	11.6877i	0.0559574	−	0.746700i
$246$	−8.05313	+	20.5190i	−0.513449	+	1.30825i
$247$	−1.96121	−	8.59263i	−0.124789	−	0.546736i
$248$	−0.525529	−	7.01270i	−0.0333711	−	0.445307i
$249$	8.60750	+	2.65506i	0.545478	+	0.168258i
$250$	−18.6143	+	8.96419i	−1.17727	+	0.566945i
$251$	−4.45344	+	7.71359i	−0.281099	+	0.486878i	−0.971656	−	0.236401i	$-0.924032\pi$
$251$	−4.45344	+	7.71359i	−0.281099	+	0.486878i	0.690557	+	0.723278i	$0.257366\pi$
$252$	0.440861	+	0.763594i	0.0277716	+	0.0481019i
$253$	−19.0192	−	12.9670i	−1.19572	−	0.815231i
$254$	4.94332	−	21.6581i	0.310172	−	1.35895i
$255$	−11.1690	−	1.68345i	−0.699428	−	0.105422i
$256$	11.0813	+	13.8955i	0.692579	+	0.868466i
$257$	0.0980769			0.00611787			0.00305893	−	0.999995i	$-0.499026\pi$
$257$	0.0980769			0.00611787			0.00305893	+	0.999995i	$0.499026\pi$
$258$	−2.36011	+	12.6700i	−0.146934	+	0.788799i
$259$	0.800300			0.0497282
$260$	−3.17740	−	3.98433i	−0.197054	−	0.247098i
$261$	−16.2252	−	2.44555i	−1.00431	−	0.151376i
$262$	4.07676	−	17.8614i	0.251863	−	1.10348i
$263$	−0.383264	−	0.261305i	−0.0236331	−	0.0161128i	0.551446	−	0.834211i	$-0.314076\pi$
$263$	−0.383264	−	0.261305i	−0.0236331	−	0.0161128i	−0.575079	+	0.818098i	$0.695029\pi$
$264$	−4.73515	−	8.20152i	−0.291428	−	0.504768i
$265$	−2.12576	+	3.68193i	−0.130584	+	0.226179i
$266$	−2.47572	+	1.19224i	−0.151796	+	0.0731011i
$267$	4.98074	+	1.53636i	0.304817	+	0.0940235i
$268$	−0.256353	−	3.42080i	−0.0156593	−	0.208958i
$269$	−4.76797	−	20.8899i	−0.290709	−	1.27368i	−0.883542	−	0.468352i	$-0.844848\pi$
$269$	−4.76797	−	20.8899i	−0.290709	−	1.27368i	0.592833	−	0.805325i	$-0.298009\pi$
$270$	5.90549	−	15.0469i	0.359397	−	0.915727i
$271$	−0.706856	+	9.43234i	−0.0429385	+	0.572974i	0.933696	+	0.358067i	$0.116564\pi$
$271$	−0.706856	+	9.43234i	−0.0429385	+	0.572974i	−0.976634	+	0.214907i	$0.931055\pi$
$272$	−27.3334	+	4.11984i	−1.65733	+	0.249802i
$273$	−1.63360	−	1.51576i	−0.0988699	−	0.0917378i
$274$	12.3128	+	5.92952i	0.743842	+	0.358216i
$275$	6.78780	−	4.62784i	0.409319	−	0.279069i
$276$	1.99346	+	5.07926i	0.119992	+	0.305736i
$277$	12.1472	−	3.74690i	0.729852	−	0.225130i	0.0925114	−	0.995712i	$-0.470511\pi$
$277$	12.1472	−	3.74690i	0.729852	−	0.225130i	0.637341	+	0.770582i	$0.280034\pi$
$278$	−27.2828	+	25.3148i	−1.63631	+	1.51828i
$279$	−3.86982	+	4.85261i	−0.231680	+	0.290518i
$280$	1.23244	−	1.54543i	0.0736525	−	0.0923573i
$281$	−14.2546	+	13.2263i	−0.850356	+	0.789015i	−0.979253	−	0.202643i	$-0.935047\pi$
$281$	−14.2546	+	13.2263i	−0.850356	+	0.789015i	0.128896	+	0.991658i	$0.458857\pi$
$282$	7.67702	−	2.36805i	0.457160	−	0.141015i
$283$	0.901034	+	2.29580i	0.0535609	+	0.136471i	0.955150	−	0.296123i	$-0.0956937\pi$
$283$	0.901034	+	2.29580i	0.0535609	+	0.136471i	−0.901589	+	0.432594i	$0.857598\pi$
$284$	−2.82580	+	1.92660i	−0.167680	+	0.114323i
$285$	4.99139	+	2.40372i	0.295664	+	0.142384i
$286$	17.5650	+	16.2980i	1.03864	+	0.963719i
$287$	6.59385	−	0.993862i	0.389222	−	0.0586658i
$288$	0.585812	−	7.81711i	0.0345193	−	0.460628i
$289$	5.00832	−	12.7610i	0.294607	−	0.750647i
$290$	−6.57940	−	28.8262i	−0.386356	−	1.69273i
$291$	0.0159765	+	0.213191i	0.000936558	+	0.0124975i
$292$	−6.34954	−	1.95858i	−0.371579	−	0.114617i
$293$	19.6328	−	9.45465i	1.14696	−	0.552347i	0.238841	−	0.971059i	$-0.423233\pi$
$293$	19.6328	−	9.45465i	1.14696	−	0.552347i	0.908119	+	0.418712i	$0.137518\pi$
$294$	6.53148	−	11.3129i	0.380923	−	0.659779i
$295$	−0.648171	−	1.12266i	−0.0377380	−	0.0653641i
$296$	−2.09673	−	1.42953i	−0.121870	−	0.0830897i
$297$	−5.21321	+	22.8406i	−0.302501	+	1.32534i
$298$	27.7583	+	4.18390i	1.60800	+	0.242367i
$299$	10.7090	+	13.4286i	0.619315	+	0.776597i
$300$	−1.94736			−0.112431
$301$	3.67637	−	1.29813i	0.211903	−	0.0748228i
$302$	26.9834			1.55272
$303$	2.97500	+	3.73053i	0.170909	+	0.214313i
$304$	13.4064	+	2.02070i	0.768912	+	0.115895i
$305$	2.00717	−	8.79399i	0.114930	−	0.503543i
$306$	12.9545	+	8.83226i	0.740562	+	0.504907i
$307$	9.96776	+	17.2647i	0.568890	+	0.985346i	0.996676	+	0.0814663i	$0.0259603\pi$
$307$	9.96776	+	17.2647i	0.568890	+	0.985346i	−0.427786	+	0.903880i	$0.640706\pi$
$308$	1.15140	−	1.99429i	0.0656072	−	0.113635i
$309$	−16.3850	+	7.89062i	−0.932112	+	0.448881i
$310$	−10.6874	−	3.29664i	−0.607006	−	0.187236i
$311$	−0.440535	−	5.87853i	−0.0249805	−	0.333341i	−0.995667	−	0.0929916i	$-0.970357\pi$
$311$	−0.440535	−	5.87853i	−0.0249805	−	0.333341i	0.970686	−	0.240349i	$-0.0772620\pi$
$312$	1.57241	+	6.88919i	0.0890204	+	0.390024i
$313$	7.65823	−	19.5129i	0.432869	−	1.10293i	−0.533506	−	0.845796i	$-0.679126\pi$
$313$	7.65823	−	19.5129i	0.432869	−	1.10293i	0.966375	−	0.257136i	$-0.0827788\pi$
$314$	−0.834362	+	11.1338i	−0.0470858	+	0.628316i
$315$	−1.72512	+	0.260020i	−0.0971996	+	0.0146505i
$316$	−8.75011	−	8.11892i	−0.492232	−	0.456725i
$317$	−19.5710	−	9.42489i	−1.09922	−	0.529355i	−0.205805	−	0.978593i	$-0.565981\pi$
$317$	−19.5710	−	9.42489i	−1.09922	−	0.529355i	−0.893412	+	0.449238i	$0.851695\pi$
$318$	−3.91513	+	2.66929i	−0.219550	+	0.149686i
$319$	15.6564	+	39.8918i	0.876588	+	2.23351i
$320$	−3.31261	+	1.02181i	−0.185181	+	0.0571207i
$321$	−0.0453170	+	0.0420480i	−0.00252935	+	0.00234689i
$322$	3.33876	−	4.18667i	0.186062	−	0.233314i
$323$	−9.39096	+	11.7759i	−0.522527	+	0.655228i
$324$	0.809647	−	0.751242i	0.0449804	−	0.0417357i
$325$	−5.85759	+	1.80683i	−0.324921	+	0.100225i
$326$	−7.89100	−	20.1059i	−0.437042	−	1.11356i
$327$	−5.01391	+	3.41842i	−0.277270	+	0.189039i
$328$	−19.0507	−	9.17435i	−1.05190	−	0.506569i
$329$	−1.78162	−	1.65310i	−0.0982237	−	0.0911382i
$330$	−14.8934	+	2.24482i	−0.819855	+	0.123573i
$331$	−0.708671	+	9.45655i	−0.0389521	+	0.519779i	0.943266	+	0.332037i	$0.107736\pi$
$331$	−0.708671	+	9.45655i	−0.0389521	+	0.519779i	−0.982218	+	0.187742i	$0.939883\pi$
$332$	2.53741	−	6.46521i	0.139258	−	0.354825i
$333$	0.498390	+	2.18359i	0.0273116	+	0.119660i
$334$	2.11839	+	28.2680i	0.115913	+	1.54675i
$335$	6.48594	+	2.00065i	0.354365	+	0.109307i
$336$	3.08858	−	1.48738i	0.168496	−	0.0811433i
$337$	12.4992	−	21.6492i	0.680872	−	1.17931i	−0.293843	−	0.955854i	$-0.594934\pi$
$337$	12.4992	−	21.6492i	0.680872	−	1.17931i	0.974715	−	0.223452i	$-0.0717325\pi$
$338$	2.11277	+	3.65942i	0.114919	+	0.199046i
$339$	2.46592	+	1.68123i	0.133930	+	0.0913121i
$340$	−1.93794	+	8.49067i	−0.105100	+	0.460471i
$341$	16.0291	+	2.41600i	0.868024	+	0.130834i
$342$	−4.79475	−	6.01243i	−0.259271	−	0.325115i
$343$	−8.11373			−0.438100
$344$	−11.9506	−	3.16588i	−0.644335	−	0.170693i
$345$	−10.7963			−0.581255
$346$	8.58864	+	10.7698i	0.461728	+	0.578989i
$347$	10.1285	+	1.52662i	0.543726	+	0.0819535i	0.415162	−	0.909748i	$-0.363725\pi$
$347$	10.1285	+	1.52662i	0.543726	+	0.0819535i	0.128564	+	0.991701i	$0.458963\pi$
$348$	2.26041	−	9.90351i	0.121171	−	0.530884i
$349$	−12.2273	−	8.33643i	−0.654512	−	0.446239i	0.189994	−	0.981785i	$-0.439153\pi$
$349$	−12.2273	−	8.33643i	−0.654512	−	0.446239i	−0.844506	+	0.535547i	$0.820106\pi$
$350$	0.955571	+	1.65510i	0.0510774	+	0.0884687i
$351$	8.74051	−	15.1390i	0.466534	−	0.808060i
$352$	−18.4458	+	8.88303i	−0.983164	+	0.473467i
$353$	−11.4923	−	3.54492i	−0.611675	−	0.188677i	−0.0265870	−	0.999647i	$-0.508464\pi$
$353$	−11.4923	−	3.54492i	−0.611675	−	0.188677i	−0.585088	+	0.810970i	$0.698940\pi$
$354$	−0.107972	−	1.44079i	−0.00573865	−	0.0765770i
$355$	−1.50582	−	6.59742i	−0.0799205	−	0.350155i
$356$	1.46828	−	3.74110i	0.0778184	−	0.198278i
$357$	−0.284599	+	3.79771i	−0.0150626	+	0.200996i
$358$	29.3393	−	4.42220i	1.55063	−	0.233720i
$359$	−5.64703	−	5.23968i	−0.298039	−	0.276540i	0.516951	−	0.856015i	$-0.327067\pi$
$359$	−5.64703	−	5.23968i	−0.298039	−	0.276540i	−0.814990	+	0.579475i	$0.803257\pi$
$360$	4.98417	+	2.40025i	0.262689	+	0.126504i
$361$	−9.59465	+	6.54152i	−0.504981	+	0.344290i
$362$	8.76818	+	22.3410i	0.460845	+	1.17421i
$363$	8.71027	−	2.68676i	0.457171	−	0.141019i
$364$	−1.25957	+	1.16871i	−0.0660197	+	0.0612573i
$365$	8.19736	−	10.2792i	0.429069	−	0.538036i
$366$	6.26815	−	7.86001i	0.327641	−	0.410849i
$367$	−2.35699	+	2.18697i	−0.123034	+	0.114159i	−0.739290	−	0.673387i	$-0.764839\pi$
$367$	−2.35699	+	2.18697i	−0.123034	+	0.114159i	0.616256	+	0.787546i	$0.288648\pi$
$368$	−25.2476	+	7.78785i	−1.31612	+	0.405970i
$369$	6.81807	+	17.3721i	0.354934	+	0.904358i
$370$	−3.33466	+	2.27354i	−0.173361	+	0.118195i
$371$	1.29152	+	0.621963i	0.0670524	+	0.0322907i
$372$	−2.81673	−	2.61355i	−0.146041	−	0.135506i
$373$	17.4202	−	2.62567i	0.901984	−	0.135952i	0.318354	−	0.947972i	$-0.396870\pi$
$373$	17.4202	−	2.62567i	0.901984	−	0.135952i	0.583630	+	0.812020i	$0.301632\pi$
$374$	3.06011	−	40.8343i	0.158235	−	2.11149i
$375$	5.13101	−	13.0736i	0.264964	−	0.675118i
$376$	1.71489	+	7.51341i	0.0884385	+	0.387474i
$377$	−2.38957	−	31.8866i	−0.123069	−	1.64225i
$378$	−5.20797	−	1.60644i	−0.267869	−	0.0826266i
$379$	−15.9289	+	7.67093i	−0.818210	+	0.394029i	−0.795680	−	0.605717i	$-0.792886\pi$
$379$	−15.9289	+	7.67093i	−0.818210	+	0.394029i	−0.0225300	+	0.999746i	$0.507172\pi$
$380$	2.13580	−	3.69931i	0.109564	−	0.189771i
$381$	7.55067	+	13.0781i	0.386833	+	0.670014i
$382$	−26.6232	−	18.1514i	−1.36216	−	0.928707i
$383$	−5.53953	+	24.2703i	−0.283057	+	1.24015i	0.610795	+	0.791789i	$0.290850\pi$
$383$	−5.53953	+	24.2703i	−0.283057	+	1.24015i	−0.893851	+	0.448364i	$0.852007\pi$
$384$	−14.5896	−	2.19903i	−0.744522	−	0.112219i
$385$	2.84088	+	3.56235i	0.144784	+	0.181554i
$386$	−36.0272			−1.83374
$387$	5.83137	+	9.22244i	0.296425	+	0.468803i
$388$	0.164841			0.00836852
$389$	−4.19252	−	5.25726i	−0.212569	−	0.266554i	0.664103	−	0.747641i	$-0.268813\pi$
$389$	−4.19252	−	5.25726i	−0.212569	−	0.266554i	−0.876673	+	0.481087i	$0.840242\pi$
$390$	11.1129	+	1.67500i	0.562722	+	0.0848167i
$391$	6.53155	−	28.6166i	0.330315	−	1.44720i
$392$	10.3534	+	7.05883i	0.522926	+	0.356525i
$393$	6.22703	+	10.7855i	0.314112	+	0.544058i
$394$	−2.39983	+	4.15663i	−0.120902	+	0.209408i
$395$	21.2792	−	10.2475i	1.07067	−	0.515608i
$396$	6.15838	+	1.89961i	0.309470	+	0.0954590i
$397$	−1.52068	−	20.2921i	−0.0763210	−	1.01843i	−0.895548	−	0.444964i	$-0.853216\pi$
$397$	−1.52068	−	20.2921i	−0.0763210	−	1.01843i	0.819227	−	0.573469i	$-0.194403\pi$
$398$	0.00491511	+	0.0215345i	0.000246372	+	0.00107943i
$399$	0.682428	−	1.73880i	0.0341641	−	0.0870488i
$400$	0.704675	−	9.40324i	0.0352338	−	0.470162i
$401$	−0.190899	+	0.0287734i	−0.00953303	+	0.00143687i	−0.153807	−	0.988101i	$-0.549153\pi$
$401$	−0.190899	+	0.0287734i	−0.00953303	+	0.00143687i	0.144274	+	0.989538i	$0.453915\pi$
$402$	5.54550	+	5.14547i	0.276584	+	0.256633i
$403$	−10.8976	−	5.24799i	−0.542846	−	0.261421i
$404$	3.03978	−	2.07248i	0.151234	−	0.103110i
$405$	0.798408	+	2.03431i	0.0396732	+	0.101086i
$406$	−9.52634	+	2.93849i	−0.472784	+	0.145835i
$407$	4.28804	−	3.97872i	0.212550	−	0.197218i
$408$	7.52926	−	9.44140i	0.372754	−	0.467419i
$409$	−0.306947	+	0.384900i	−0.0151776	+	0.0190321i	−0.789362	−	0.613928i	$-0.789589\pi$
$409$	−0.306947	+	0.384900i	−0.0151776	+	0.0190321i	0.774185	+	0.632960i	$0.218160\pi$
$410$	−24.6516	+	22.8734i	−1.21746	+	1.12963i
$411$	−8.87723	+	2.73826i	−0.437881	+	0.135069i
$412$	5.12288	+	13.0529i	0.252386	+	0.643070i
$413$	−0.361137	+	0.246219i	−0.0177704	+	0.0121157i
$414$	13.5024	+	6.50242i	0.663607	+	0.319576i
$415$	10.0738	+	9.34711i	0.494503	+	0.458831i
$416$	15.1057	−	2.27682i	0.740620	−	0.111630i
$417$	1.89068	−	25.2293i	0.0925868	−	1.23549i
$418$	−7.33771	+	18.6962i	−0.358899	+	0.914460i
$419$	3.57770	+	15.6749i	0.174782	+	0.765770i	0.983986	+	0.178243i	$0.0570413\pi$
$419$	3.57770	+	15.6749i	0.174782	+	0.765770i	−0.809204	+	0.587527i	$0.800102\pi$
$420$	−0.0807128	−	1.07704i	−0.00393838	−	0.0525541i
$421$	−34.8128	−	10.7383i	−1.69667	−	0.523355i	−0.712670	−	0.701500i	$-0.752514\pi$
$421$	−34.8128	−	10.7383i	−1.69667	−	0.523355i	−0.984004	+	0.178145i	$0.942990\pi$
$422$	3.32186	−	1.59972i	0.161706	−	0.0778734i
$423$	3.40091	−	5.89055i	0.165358	−	0.286408i
$424$	−2.27272	−	3.93647i	−0.110373	−	0.191172i
$425$	8.65542	+	5.90117i	0.419850	+	0.286249i
$426$	1.67830	−	7.35310i	0.0813138	−	0.356259i
$427$	−3.00734	−	0.453284i	−0.145535	−	0.0219359i
$428$	0.0297190	+	0.0372665i	0.00143652	+	0.00180134i
$429$	−16.2885			−0.786417
$430$	−11.6308	+	15.8530i	−0.560887	+	0.764501i
$431$	8.13149			0.391680			0.195840	−	0.980636i	$-0.437257\pi$
$431$	8.13149			0.391680			0.195840	+	0.980636i	$0.437257\pi$
$432$	16.7662	+	21.0241i	0.806663	+	1.01152i
$433$	27.2335	+	4.10478i	1.30876	+	0.197263i	0.766116	−	0.642702i	$-0.222187\pi$
$433$	27.2335	+	4.10478i	1.30876	+	0.197263i	0.542640	+	0.839965i	$0.317425\pi$
$434$	−0.839127	+	3.67646i	−0.0402794	+	0.176476i
$435$	16.6069	+	11.3224i	0.796239	+	0.542867i
$436$	2.33948	+	4.05210i	0.112041	+	0.194060i
$437$	−7.19840	+	12.4680i	−0.344346	+	0.596425i
$438$	13.2023	−	6.35791i	0.630832	−	0.303793i
$439$	−35.6148	−	10.9857i	−1.69980	−	0.524320i	−0.715170	−	0.698951i	$-0.753651\pi$
$439$	−35.6148	−	10.9857i	−1.69980	−	0.524320i	−0.984634	+	0.174631i	$0.944127\pi$
$440$	−1.07970	−	14.4076i	−0.0514727	−	0.686856i
$441$	−2.46098	−	10.7823i	−0.117190	−	0.513442i
$442$	−11.1628	+	28.4423i	−0.530959	+	1.35286i
$443$	−0.409109	+	5.45918i	−0.0194373	+	0.259373i	0.979016	+	0.203782i	$0.0653234\pi$
$443$	−0.409109	+	5.45918i	−0.0194373	+	0.259373i	−0.998454	+	0.0555912i	$0.982296\pi$
$444$	−1.37110	+	0.206660i	−0.0650696	+	0.00980767i
$445$	5.82921	+	5.40872i	0.276331	+	0.256398i
$446$	−5.78479	−	2.78581i	−0.273918	−	0.131912i
$447$	−15.7668	+	10.7496i	−0.745745	+	0.508440i
$448$	0.427024	+	1.08804i	0.0201750	+	0.0514050i
$449$	21.7205	−	6.69990i	1.02506	−	0.316188i	0.263757	−	0.964589i	$-0.415038\pi$
$449$	21.7205	−	6.69990i	1.02506	−	0.316188i	0.761298	+	0.648402i	$0.224562\pi$
$450$	−3.92079	+	3.63796i	−0.184828	+	0.171495i
$451$	30.3891	−	38.1067i	1.43096	−	1.79437i
$452$	1.43477	−	1.79914i	0.0674857	−	0.0846244i
$453$	−13.4462	+	12.4762i	−0.631757	+	0.586185i
$454$	−26.9393	+	8.30968i	−1.26433	+	0.389993i
$455$	−1.24209	−	3.16480i	−0.0582301	−	0.148368i
$456$	−4.89383	+	3.33656i	−0.229175	+	0.156249i
$457$	29.8326	+	14.3666i	1.39551	+	0.672042i	0.972245	−	0.233964i	$-0.0751699\pi$
$457$	29.8326	+	14.3666i	1.39551	+	0.672042i	0.423264	+	0.906006i	$0.360884\pi$
$458$	0.964727	+	0.895136i	0.0450787	+	0.0418269i
$459$	−29.5404	+	4.45250i	−1.37883	+	0.207825i
$460$	−0.622085	+	8.30115i	−0.0290049	+	0.387043i
$461$	−5.47361	+	13.9465i	−0.254931	+	0.649555i	−0.999845	−	0.0176063i	$-0.994395\pi$
$461$	−5.47361	+	13.9465i	−0.254931	+	0.649555i	0.744914	+	0.667161i	$0.232491\pi$
$462$	1.13003	+	4.95099i	0.0525738	+	0.230341i
$463$	1.36296	+	18.1874i	0.0633419	+	0.845239i	0.934892	+	0.354932i	$0.115496\pi$
$463$	1.36296	+	18.1874i	0.0633419	+	0.845239i	−0.871550	+	0.490307i	$0.836885\pi$
$464$	47.0031	+	14.4985i	2.18207	+	0.673078i
$465$	6.84994	−	3.29876i	0.317658	−	0.152976i
$466$	22.0844	−	38.2513i	1.02304	−	1.77196i
$467$	−1.73991	−	3.01362i	−0.0805135	−	0.139454i	0.822957	−	0.568104i	$-0.192323\pi$
$467$	−1.73991	−	3.01362i	−0.0805135	−	0.139454i	−0.903471	+	0.428650i	$0.858989\pi$
$468$	−3.97320	−	2.70888i	−0.183661	−	0.125218i
$469$	0.509246	−	2.23115i	0.0235148	−	0.103025i
$470$	12.1198	+	1.82676i	0.559044	+	0.0842624i
$471$	−4.73212	−	5.93389i	−0.218044	−	0.273419i
$472$	1.38596			0.0637941
$473$	13.2445	−	25.2326i	0.608981	−	1.16020i
$474$	26.3233			1.20907
$475$	−3.20356	−	4.01713i	−0.146989	−	0.184319i
$476$	2.90361	+	0.437649i	0.133087	+	0.0200596i
$477$	−0.892706	+	3.91120i	−0.0408742	+	0.179082i
$478$	4.95314	+	3.37700i	0.226552	+	0.154460i
$479$	−11.9934	−	20.7733i	−0.547994	−	0.949154i	−0.998412	−	0.0563362i	$-0.982058\pi$
$479$	−11.9934	−	20.7733i	−0.547994	−	0.949154i	0.450417	−	0.892818i	$-0.351275\pi$
$480$	−4.80118	+	8.31588i	−0.219143	+	0.379566i
$481$	−3.93247	+	1.89378i	−0.179305	+	0.0863489i
$482$	−31.7090	−	9.78093i	−1.44431	−	0.445509i
$483$	0.272031	+	3.63000i	0.0123778	+	0.165171i
$484$	−1.56393	−	6.85203i	−0.0710878	−	0.311456i
$485$	−0.119160	+	0.303614i	−0.00541076	+	0.0137864i
$486$	1.87303	−	24.9938i	0.0849622	−	1.13374i
$487$	4.37068	−	0.658774i	0.198054	−	0.0298519i	−0.0492658	−	0.998786i	$-0.515688\pi$
$487$	4.37068	−	0.658774i	0.198054	−	0.0298519i	0.247320	+	0.968934i	$0.420450\pi$
$488$	7.06937	+	6.55941i	0.320015	+	0.296931i
$489$	13.2285	+	6.37051i	0.598213	+	0.288084i
$490$	16.4661	−	11.2264i	0.743864	−	0.507158i
$491$	5.72014	+	14.5747i	0.258146	+	0.657746i	0.999917	−	0.0129076i	$-0.00410874\pi$
$491$	5.72014	+	14.5747i	0.258146	+	0.657746i	−0.741770	+	0.670654i	$0.766014\pi$
$492$	−11.0402	+	3.40544i	−0.497729	+	0.153529i
$493$	−40.0578	+	37.1682i	−1.80411	+	1.67397i
$494$	9.34380	−	11.7168i	0.420398	−	0.527162i
$495$	−7.95057	+	9.96970i	−0.357351	+	0.448105i
$496$	13.6393	−	12.6554i	0.612423	−	0.568245i
$497$	−2.18028	+	0.672528i	−0.0977990	+	0.0301670i
$498$	5.59568	+	14.2576i	0.250748	+	0.638896i
$499$	31.1162	−	21.2146i	1.39295	−	0.949698i	0.393411	−	0.919363i	$-0.371295\pi$
$499$	31.1162	−	21.2146i	1.39295	−	0.949698i	0.999540	−	0.0303356i	$-0.00965760\pi$
$500$	−9.75648	−	4.69847i	−0.436323	−	0.210122i
$501$	−14.1258	−	13.1068i	−0.631093	−	0.585569i
$502$	−14.9758	+	2.25723i	−0.668401	+	0.100745i
$503$	−2.31985	+	30.9562i	−0.103437	+	1.38027i	0.668093	+	0.744077i	$0.267111\pi$
$503$	−2.31985	+	30.9562i	−0.103437	+	1.38027i	−0.771530	+	0.636193i	$0.780508\pi$
$504$	0.681441	−	1.73628i	0.0303538	−	0.0773402i
$505$	1.61984	+	7.09699i	0.0720820	+	0.315812i
$506$	−2.92498	−	39.0311i	−0.130031	−	1.73514i
$507$	−2.74481	−	0.846663i	−0.121901	−	0.0376016i
$508$	10.4907	−	5.05205i	0.465449	−	0.224148i
$509$	−2.32607	+	4.02888i	−0.103101	+	0.178577i	−0.912961	−	0.408047i	$-0.866210\pi$
$509$	−2.32607	+	4.02888i	−0.103101	+	0.178577i	0.809860	+	0.586624i	$0.199543\pi$
$510$	−9.60289	−	16.6327i	−0.425223	−	0.736508i
$511$	−3.66267	−	2.49716i	−0.162027	−	0.110468i
$512$	−1.04382	+	4.57329i	−0.0461309	+	0.202113i
$513$	14.4889	+	2.18386i	0.639702	+	0.0964196i
$514$	0.103977	+	0.130383i	0.00458622	+	0.00575094i
$515$	−27.7448			−1.22258
$516$	−5.96328	+	3.17334i	−0.262519	+	0.139699i
$517$	−17.7644			−0.781277
$518$	0.848443	+	1.06391i	0.0372785	+	0.0467457i
$519$	−9.25943	−	1.39563i	−0.406444	−	0.0612616i
$520$	−2.39889	+	10.5102i	−0.105198	+	0.460905i
$521$	−5.84633	−	3.98596i	−0.256132	−	0.174628i	0.428446	−	0.903567i	$-0.359061\pi$
$521$	−5.84633	−	3.98596i	−0.256132	−	0.174628i	−0.684578	+	0.728939i	$0.740014\pi$
$522$	−13.9501	−	24.1623i	−0.610581	−	1.05756i
$523$	−2.20635	+	3.82151i	−0.0964770	+	0.167103i	−0.910224	−	0.414116i	$-0.864091\pi$
$523$	−2.20635	+	3.82151i	−0.0964770	+	0.167103i	0.813747	+	0.581219i	$0.197424\pi$
$524$	8.65166	−	4.16642i	0.377949	−	0.182011i
$525$	−1.24144	−	0.382932i	−0.0541807	−	0.0167125i
$526$	−0.0589425	−	0.786533i	−0.00257002	−	0.0342945i
$527$	4.59957	+	20.1520i	0.200361	+	0.877837i
$528$	9.15415	−	23.3244i	0.398383	−	1.01506i
$529$	0.377858	−	5.04216i	0.0164286	−	0.219224i
$530$	−7.14838	+	1.07744i	−0.310506	+	0.0468012i
$531$	−0.896700	−	0.832016i	−0.0389135	−	0.0361064i
$532$	−1.29762	−	0.624900i	−0.0562589	−	0.0270928i
$533$	−30.0487	+	20.4869i	−1.30155	+	0.887384i
$534$	3.23795	+	8.25016i	0.140120	+	0.357019i
$535$	−0.0901228	+	0.0277992i	−0.00389635	+	0.00120186i
$536$	−5.31957	+	4.93584i	−0.229770	+	0.213196i
$537$	−12.5755	+	15.7692i	−0.542673	+	0.680490i
$538$	22.7161	−	28.4851i	0.979360	−	1.22808i
$539$	−21.1738	+	19.6464i	−0.912018	+	0.846229i
$540$	8.09593	−	2.49726i	0.348394	−	0.107465i
$541$	−6.23494	−	15.8864i	−0.268061	−	0.683009i	−0.999999	−	0.00163693i	$-0.999479\pi$
$541$	−6.23494	−	15.8864i	−0.268061	−	0.683009i	0.731937	−	0.681372i	$-0.238616\pi$
$542$	−13.2887	+	9.06007i	−0.570798	+	0.389163i
$543$	−14.6990	−	7.07867i	−0.630795	−	0.303775i
$544$	−19.1374	−	17.7569i	−0.820507	−	0.761320i
$545$	−9.15456	+	1.37983i	−0.392138	+	0.0591053i
$546$	0.283170	−	3.77864i	0.0121185	−	0.161711i
$547$	3.72664	−	9.49533i	0.159340	−	0.405991i	−0.828801	−	0.559544i	$-0.810976\pi$
$547$	3.72664	−	9.49533i	0.159340	−	0.405991i	0.988140	+	0.153553i	$0.0490715\pi$
$548$	1.59391	+	6.98336i	0.0680883	+	0.298315i
$549$	−0.636066	−	8.48771i	−0.0271466	−	0.362247i
$550$	13.3484	+	4.11742i	0.569176	+	0.175568i
$551$	24.1481	−	11.6291i	1.02874	−	0.495416i
$552$	5.77136	−	9.99629i	0.245645	−	0.425470i
$553$	−3.98164	−	6.89640i	−0.169316	−	0.293265i
$554$	17.8590	+	12.1761i	0.758757	+	0.517312i
$555$	0.610499	−	2.67477i	0.0259142	−	0.113538i
$556$	−19.2896	−	2.90743i	−0.818060	−	0.123303i
$557$	19.5750	+	24.5463i	0.829419	+	1.04006i	0.998516	+	0.0544591i	$0.0173435\pi$
$557$	19.5750	+	24.5463i	0.829419	+	1.04006i	−0.169097	+	0.985599i	$0.554085\pi$
$558$	−10.5537			−0.446772
$559$	−14.9930	+	15.0782i	−0.634135	+	0.637740i
$560$	5.22990			0.221004
$561$	17.3555	+	21.7632i	0.732752	+	0.918842i
$562$	−32.6951	−	4.92799i	−1.37916	−	0.207875i
$563$	8.39490	−	36.7805i	0.353803	−	1.55011i	−0.414515	−	0.910043i	$-0.636049\pi$
$563$	8.39490	−	36.7805i	0.353803	−	1.55011i	0.768317	−	0.640069i	$-0.221094\pi$
$564$	3.47921	+	2.37208i	0.146501	+	0.0998827i
$565$	2.27660	+	3.94319i	0.0957775	+	0.165891i
$566$	−2.09678	+	3.63174i	−0.0881344	+	0.152653i
$567$	0.663871	−	0.319703i	0.0278799	−	0.0134263i
$568$	6.91349	+	2.13253i	0.290084	+	0.0894790i
$569$	0.270303	+	3.60694i	0.0113317	+	0.151211i	0.999999	+	0.00109048i	$0.000347110\pi$
$569$	0.270303	+	3.60694i	0.0113317	+	0.151211i	−0.988668	+	0.150120i	$0.952034\pi$
$570$	2.09615	+	9.18385i	0.0877982	+	0.384669i
$571$	5.62048	−	14.3207i	0.235210	−	0.599304i	−0.763721	−	0.645547i	$-0.776629\pi$
$571$	5.62048	−	14.3207i	0.235210	−	0.599304i	0.998930	+	0.0462426i	$0.0147247\pi$
$572$	−0.938546	+	12.5240i	−0.0392426	+	0.523656i
$573$	21.6593	−	3.26461i	0.904830	−	0.136381i
$574$	8.31175	+	7.71218i	0.346926	+	0.321900i
$575$	9.02147	+	4.34451i	0.376221	+	0.181179i
$576$	−2.70275	+	1.84270i	−0.112614	+	0.0767792i
$577$	11.6350	+	29.6454i	0.484370	+	1.23416i	0.939136	+	0.343545i	$0.111628\pi$
$577$	11.6350	+	29.6454i	0.484370	+	1.23416i	−0.454766	+	0.890611i	$0.650277\pi$
$578$	22.2740	−	6.87062i	0.926477	−	0.285780i
$579$	17.9528	−	16.6578i	0.746093	−	0.692274i
$580$	9.66252	−	12.1164i	0.401214	−	0.503107i
$581$	2.88891	−	3.62258i	0.119852	−	0.150290i
$582$	−0.266478	+	0.247255i	−0.0110459	+	0.0102491i
$583$	10.0121	−	3.08833i	0.414660	−	0.127906i
$584$	5.13541	+	13.0848i	0.212505	+	0.541454i
$585$	7.86152	−	5.35989i	0.325034	−	0.221604i
$586$	33.3828	+	16.0763i	1.37903	+	0.664106i
$587$	−13.6300	−	12.6468i	−0.562570	−	0.521989i	0.346821	−	0.937931i	$-0.387261\pi$
$587$	−13.6300	−	12.6468i	−0.562570	−	0.521989i	−0.909391	+	0.415943i	$0.863452\pi$
$588$	6.77032	−	1.02046i	0.279203	−	0.0420831i
$589$	0.757639	−	10.1100i	0.0312180	−	0.416575i
$590$	0.805302	−	2.05188i	0.0331538	−	0.0844744i
$591$	−0.726020	−	3.18090i	−0.0298645	−	0.130845i
$592$	−0.501753	−	6.69542i	−0.0206219	−	0.275180i
$593$	3.28071	+	1.01197i	0.134723	+	0.0415564i	0.361383	−	0.932417i	$-0.382305\pi$
$593$	3.28071	+	1.01197i	0.134723	+	0.0415564i	−0.226661	+	0.973974i	$0.572781\pi$
$594$	−35.8910	+	17.2842i	−1.47262	+	0.709178i
$595$	−2.90504	+	5.03168i	−0.119095	+	0.206279i
$596$	7.35677	+	12.7423i	0.301345	+	0.521945i
$597$	−0.0124061	−	0.00845833i	−0.000507748	−	0.000346177i
$598$	−6.49875	+	28.4729i	−0.265754	+	1.16434i
$599$	−18.5193	−	2.79133i	−0.756677	−	0.114051i	−0.240637	−	0.970615i	$-0.577356\pi$
$599$	−18.5193	−	2.79133i	−0.756677	−	0.114051i	−0.516040	+	0.856564i	$0.672594\pi$
$600$	2.56847	+	3.22076i	0.104857	+	0.131487i
$601$	−4.01565			−0.163802			−0.0819010	−	0.996640i	$-0.526099\pi$
$601$	−4.01565			−0.163802			−0.0819010	+	0.996640i	$0.526099\pi$
$602$	5.62326	+	3.51113i	0.229187	+	0.143103i
$603$	6.40475			0.260822
$604$	8.81805	+	11.0575i	0.358801	+	0.449923i
$605$	13.7510	+	2.07263i	0.559058	+	0.0842644i
$606$	−1.80538	+	7.90990i	−0.0733386	+	0.321318i
$607$	21.0791	+	14.3715i	0.855573	+	0.583319i	0.909724	−	0.415213i	$-0.136293\pi$
$607$	21.0791	+	14.3715i	0.855573	+	0.583319i	−0.0541516	+	0.998533i	$0.517245\pi$
$608$	6.40232	+	11.0892i	0.259649	+	0.449724i
$609$	3.38844	−	5.86895i	0.137306	−	0.237822i
$610$	13.8186	−	6.65469i	0.559499	−	0.269441i
$611$	12.6662	+	3.90701i	0.512420	+	0.158061i
$612$	0.614127	+	8.19495i	0.0248246	+	0.331261i
$613$	3.94359	+	17.2780i	0.159280	+	0.697851i	0.989989	+	0.141144i	$0.0450781\pi$
$613$	3.94359	+	17.2780i	0.159280	+	0.697851i	−0.830709	+	0.556707i	$0.812065\pi$
$614$	−12.3842	+	31.5543i	−0.499784	+	1.27343i
$615$	1.70834	−	22.7962i	0.0688868	−	0.919230i
$616$	−4.81700	+	0.726047i	−0.194083	+	0.0292533i
$617$	−9.87536	−	9.16299i	−0.397567	−	0.368888i	0.455904	−	0.890029i	$-0.349316\pi$
$617$	−9.87536	−	9.16299i	−0.397567	−	0.368888i	−0.853471	+	0.521141i	$0.825507\pi$
$618$	−27.8605	−	13.4169i	−1.12071	−	0.539706i
$619$	25.1021	−	17.1143i	1.00894	−	0.687882i	0.0583365	−	0.998297i	$-0.481420\pi$
$619$	25.1021	−	17.1143i	1.00894	−	0.687882i	0.950601	+	0.310415i	$0.100468\pi$
$620$	−2.14168	−	5.45691i	−0.0860119	−	0.219155i
$621$	−27.2862	+	8.41667i	−1.09496	+	0.337749i
$622$	7.34786	−	6.81781i	0.294622	−	0.273369i
$623$	1.67167	−	2.09621i	0.0669742	−	0.0839830i
$624$	−11.6569	+	14.6172i	−0.466648	+	0.585158i
$625$	8.77788	−	8.14468i	0.351115	−	0.325787i
$626$	34.0592	−	10.5059i	1.36128	−	0.419899i
$627$	−4.98802	−	12.7093i	−0.199202	−	0.507559i
$628$	−4.83515	+	3.29655i	−0.192944	+	0.131547i
$629$	6.72037	+	3.23636i	0.267959	+	0.129042i
$630$	−2.17457	−	2.01771i	−0.0866369	−	0.0803873i
$631$	5.70762	−	0.860285i	0.227217	−	0.0342474i	−0.0344469	−	0.999407i	$-0.510967\pi$
$631$	5.70762	−	0.860285i	0.227217	−	0.0342474i	0.261664	+	0.965159i	$0.415729\pi$
$632$	−1.88700	+	25.1803i	−0.0750609	+	1.00162i
$633$	−0.915667	+	2.33308i	−0.0363945	+	0.0927317i
$634$	−8.21892	−	36.0094i	−0.326415	−	1.43012i
$635$	1.72169	+	22.9744i	0.0683233	+	0.911711i
$636$	−2.37329	−	0.732062i	−0.0941070	−	0.0290282i
$637$	19.4180	−	9.35123i	0.769370	−	0.370509i
$638$	−36.4337	+	63.1050i	−1.44242	+	2.49835i
$639$	−3.19275	−	5.53000i	−0.126303	−	0.218763i
$640$	−18.5982	−	12.6800i	−0.735159	−	0.501223i
$641$	2.67792	−	11.7327i	0.105772	−	0.463415i	−0.894107	−	0.447853i	$-0.852189\pi$
$641$	2.67792	−	11.7327i	0.105772	−	0.463415i	0.999879	−	0.0155626i	$-0.00495394\pi$
$642$	−0.103942	−	0.0156667i	−0.00410225	−	0.000618314i
$643$	−26.5269	−	33.2637i	−1.04612	−	1.31179i	−0.948572	−	0.316563i	$-0.897471\pi$
$643$	−26.5269	−	33.2637i	−1.04612	−	1.31179i	−0.0975487	−	0.995231i	$-0.531100\pi$
$644$	2.80674			0.110601
$645$	−1.53414	−	13.2775i	−0.0604067	−	0.522800i
$646$	−25.6107			−1.00764
$647$	−18.0570	−	22.6428i	−0.709894	−	0.890179i	0.287825	−	0.957683i	$-0.407068\pi$
$647$	−18.0570	−	22.6428i	−0.709894	−	0.890179i	−0.997719	+	0.0675040i	$0.978496\pi$
$648$	−2.31037	−	0.348232i	−0.0907598	−	0.0136798i
$649$	−0.710900	+	3.11466i	−0.0279053	+	0.122261i
$650$	−8.61196	−	5.87153i	−0.337789	−	0.230300i
$651$	−1.28172	−	2.22001i	−0.0502347	−	0.0870090i
$652$	5.66043	−	9.80415i	0.221679	−	0.383960i
$653$	2.42189	−	1.16632i	0.0947758	−	0.0456416i	−0.385895	−	0.922543i	$-0.626107\pi$
$653$	2.42189	−	1.16632i	0.0947758	−	0.0456416i	0.480671	+	0.876901i	$0.340393\pi$
$654$	−9.85997	−	3.04140i	−0.385555	−	0.118928i
$655$	1.41988	+	18.9470i	0.0554792	+	0.740319i
$656$	−12.4488	−	54.5420i	−0.486046	−	2.12951i
$657$	4.53248	−	11.5486i	0.176829	−	0.450553i
$658$	0.308827	−	4.12101i	0.0120393	−	0.160654i
$659$	−7.71731	+	1.16320i	−0.300624	+	0.0453117i	−0.297622	−	0.954684i	$-0.596194\pi$
$659$	−7.71731	+	1.16320i	−0.300624	+	0.0453117i	−0.00300156	+	0.999995i	$0.500955\pi$
$660$	−5.78699	−	5.36954i	−0.225258	−	0.209009i
$661$	−3.05815	−	1.47273i	−0.118948	−	0.0572824i	0.373463	−	0.927645i	$-0.378170\pi$
$661$	−3.05815	−	1.47273i	−0.118948	−	0.0572824i	−0.492411	+	0.870363i	$0.663884\pi$
$662$	−13.3228	+	9.08333i	−0.517805	+	0.353034i
$663$	−7.58821	−	19.3345i	−0.294702	−	0.750888i
$664$	−14.0396	+	4.33064i	−0.544841	+	0.168061i
$665$	2.08900	−	1.93830i	0.0810078	−	0.0751642i
$666$	−2.37448	+	2.97751i	−0.0920093	+	0.115376i
$667$	−32.5662	+	40.8367i	−1.26097	+	1.58120i
$668$	−10.8916	+	10.1059i	−0.421408	+	0.391010i
$669$	4.17070	−	1.28649i	0.161248	−	0.0497386i
$670$	4.21647	+	10.7434i	0.162896	+	0.415053i
$671$	−18.3670	+	12.5224i	−0.709049	+	0.483421i
$672$	2.91699	+	1.40475i	0.112525	+	0.0541893i
$673$	11.9248	+	11.0646i	0.459669	+	0.426510i	0.875712	−	0.482835i	$-0.160393\pi$
$673$	11.9248	+	11.0646i	0.459669	+	0.426510i	−0.416043	+	0.909345i	$0.636583\pi$
$674$	42.0314	−	6.33521i	1.61899	−	0.244023i
$675$	0.761574	−	10.1625i	0.0293130	−	0.391155i
$676$	−0.809145	+	2.06167i	−0.0311209	+	0.0792949i
$677$	−0.535224	−	2.34497i	−0.0205703	−	0.0901246i	0.963601	−	0.267345i	$-0.0861465\pi$
$677$	−0.535224	−	2.34497i	−0.0205703	−	0.0901246i	−0.984171	+	0.177221i	$0.943289\pi$
$678$	0.379236	+	5.06055i	0.0145645	+	0.194349i
$679$	0.105085	+	0.0324145i	0.00403280	+	0.00124395i
$680$	16.5988	−	7.99357i	0.636536	−	0.306540i
$681$	9.58209	−	16.5967i	0.367187	−	0.635986i
$682$	13.7815	+	23.8703i	0.527723	+	0.914042i
$683$	3.95745	+	2.69814i	0.151428	+	0.103242i	0.636664	−	0.771142i	$-0.280314\pi$
$683$	3.95745	+	2.69814i	0.151428	+	0.103242i	−0.485236	+	0.874383i	$0.661266\pi$
$684$	0.896920	−	3.92966i	0.0342946	−	0.150254i
$685$	−14.0146	−	2.11236i	−0.535470	−	0.0807091i
$686$	−8.60183	−	10.7864i	−0.328419	−	0.411825i
$687$	−0.894617			−0.0341318
$688$	−13.1652	−	29.9432i	−0.501920	−	1.14157i
$689$	−7.81798			−0.297841
$690$	−11.4458	−	14.3526i	−0.435734	−	0.546393i
$691$	17.5752	+	2.64903i	0.668591	+	0.100774i	0.474562	−	0.880222i	$-0.342606\pi$
$691$	17.5752	+	2.64903i	0.668591	+	0.100774i	0.194029	+	0.980996i	$0.437844\pi$
$692$	−1.60662	+	7.03904i	−0.0610743	+	0.267584i
$693$	3.55240	+	2.42198i	0.134944	+	0.0920035i
$694$	8.70830	+	15.0832i	0.330563	+	0.572551i
$695$	19.2991	−	33.4270i	0.732055	−	1.26796i
$696$	−19.3609	+	9.32370i	−0.733871	+	0.353414i
$697$	59.3897	+	18.3193i	2.24955	+	0.693893i
$698$	−1.88045	−	25.0928i	−0.0711760	−	0.949777i
$699$	6.68118	+	29.2722i	0.252706	+	1.10718i
$700$	−0.365963	+	0.932459i	−0.0138321	+	0.0352436i
$701$	0.194278	−	2.59246i	0.00733777	−	0.0979157i	−0.992332	−	0.123598i	$-0.960557\pi$
$701$	0.194278	−	2.59246i	0.00733777	−	0.0979157i	0.999670	+	0.0256821i	$0.00817577\pi$
$702$	29.3920	−	4.43014i	1.10933	−	0.167205i
$703$	−2.68187	−	2.48842i	−0.101149	−	0.0938524i
$704$	7.69724	+	3.70679i	0.290100	+	0.139705i
$705$	−6.88408	+	4.69349i	−0.259270	+	0.176767i
$706$	−7.47109	−	19.0360i	−0.281178	−	0.716430i
$707$	2.34538	−	0.723453i	0.0882070	−	0.0272083i
$708$	0.555132	−	0.515087i	0.0208631	−	0.0193582i
$709$	−23.9515	+	30.0342i	−0.899517	+	1.12796i	0.0917101	+	0.995786i	$0.470767\pi$
$709$	−23.9515	+	30.0342i	−0.899517	+	1.12796i	−0.991227	+	0.132172i	$0.957805\pi$
$710$	7.17417	−	8.99613i	0.269242	−	0.337619i
$711$	16.3370	−	15.1585i	0.612686	−	0.568489i
$712$	−8.12402	+	2.50593i	−0.304461	+	0.0939136i
$713$	7.21822	+	18.3917i	0.270324	+	0.688775i
$714$	−5.35038	+	3.64782i	−0.200233	+	0.136516i
$715$	−22.3891	−	10.7820i	−0.837304	−	0.403224i
$716$	11.4001	+	10.5778i	0.426042	+	0.395309i
$717$	−4.02963	+	0.607368i	−0.150489	+	0.0226826i
$718$	0.978863	−	13.0620i	0.0365308	−	0.487470i
$719$	12.1950	−	31.0723i	0.454795	−	1.15880i	−0.501177	−	0.865345i	$-0.667100\pi$
$719$	12.1950	−	31.0723i	0.454795	−	1.15880i	0.955973	−	0.293455i	$-0.0948052\pi$
$720$	3.25694	+	14.2696i	0.121379	+	0.531796i
$721$	0.699076	+	9.32852i	0.0260350	+	0.347412i
$722$	−18.8681	−	5.82004i	−0.702198	−	0.216599i
$723$	20.3234	−	9.78722i	0.755834	−	0.363991i
$724$	−6.28965	+	10.8940i	−0.233753	+	0.404872i
$725$	−9.32061	−	16.1438i	−0.346159	−	0.599565i
$726$	12.8060	+	8.73100i	0.475276	+	0.324038i
$727$	8.20631	−	35.9542i	0.304355	−	1.33347i	−0.559125	−	0.829084i	$-0.688863\pi$
$727$	8.20631	−	35.9542i	0.304355	−	1.33347i	0.863480	−	0.504384i	$-0.168280\pi$
$728$	3.59426	+	0.541747i	0.133212	+	0.0200785i
$729$	12.9410	+	16.2275i	0.479296	+	0.601019i
$730$	22.3556			0.827416
$731$	36.1212	+	3.96622i	1.33599	+	0.146696i
$732$	5.26934			0.194760
$733$	−16.6422	−	20.8687i	−0.614695	−	0.770803i	0.372893	−	0.927875i	$-0.378366\pi$
$733$	−16.6422	−	20.8687i	−0.614695	−	0.770803i	−0.987587	+	0.157072i	$0.949795\pi$
$734$	−5.40613	−	0.814842i	−0.199544	−	0.0300764i
$735$	−3.01456	+	13.2077i	−0.111194	+	0.487172i
$736$	−20.6176	−	14.0568i	−0.759974	−	0.518142i
$737$	−8.36368	−	14.4863i	−0.308080	−	0.533610i
$738$	−15.8662	+	27.4811i	−0.584044	+	1.01159i
$739$	−45.9243	+	22.1160i	−1.68935	+	0.813550i	−0.693716	+	0.720249i	$0.744028\pi$
$739$	−45.9243	+	22.1160i	−1.68935	+	0.813550i	−0.995638	+	0.0933007i	$0.970258\pi$
$740$	−2.02142	−	0.623525i	−0.0743088	−	0.0229212i
$741$	0.761302	+	10.1589i	0.0279671	+	0.373196i
$742$	0.542379	+	2.37632i	0.0199114	+	0.0872374i
$743$	−7.59718	+	19.3573i	−0.278714	+	0.710150i	0.721136	+	0.692794i	$0.243620\pi$
$743$	−7.59718	+	19.3573i	−0.278714	+	0.710150i	−0.999849	+	0.0173567i	$0.994475\pi$
$744$	−0.607442	+	8.10575i	−0.0222699	+	0.297171i
$745$	−28.7876	+	4.33903i	−1.05470	+	0.158970i
$746$	21.9587	+	20.3747i	0.803966	+	0.745971i
$747$	11.6832	+	5.62632i	0.427465	+	0.205856i
$748$	17.7334	−	12.0905i	0.648399	−	0.442071i
$749$	0.0116176	+	0.0296012i	0.000424498	+	0.00108160i
$750$	22.8197	−	7.03894i	0.833257	−	0.257026i
$751$	−7.85716	+	7.29038i	−0.286712	+	0.266030i	−0.810396	−	0.585883i	$-0.800748\pi$
$751$	−7.85716	+	7.29038i	−0.286712	+	0.266030i	0.523684	+	0.851913i	$0.324557\pi$
$752$	−12.7131	+	15.9417i	−0.463598	+	0.581333i
$753$	6.41894	−	8.04910i	0.233919	−	0.293325i
$754$	39.8566	−	36.9815i	1.45149	−	1.34679i
$755$	−26.7407	+	8.24842i	−0.973194	+	0.300191i
$756$	−1.04363	−	2.65914i	−0.0379566	−	0.0967119i
$757$	−2.76234	+	1.88333i	−0.100399	+	0.0684508i	−0.612479	−	0.790487i	$-0.709828\pi$
$757$	−2.76234	+	1.88333i	−0.100399	+	0.0684508i	0.512080	+	0.858938i	$0.328875\pi$
$758$	−27.0848	−	13.0433i	−0.983764	−	0.473756i
$759$	19.5042	+	18.0973i	0.707958	+	0.656889i
$760$	−8.93532	+	1.34678i	−0.324118	+	0.0488529i
$761$	−2.86710	+	38.2588i	−0.103932	+	1.38688i	0.664662	+	0.747144i	$0.268575\pi$
$761$	−2.86710	+	38.2588i	−0.103932	+	1.38688i	−0.768595	+	0.639736i	$0.779044\pi$
$762$	−9.38112	+	23.9027i	−0.339842	+	0.865904i
$763$	0.694597	+	3.04323i	0.0251461	+	0.110172i
$764$	−1.26211	−	16.8417i	−0.0456615	−	0.609310i
$765$	−15.5379	−	4.79281i	−0.561774	−	0.173284i
$766$	−38.1375	+	18.3661i	−1.37797	+	0.663593i
$767$	1.19190	−	2.06443i	0.0430370	−	0.0745423i
$768$	−10.2716	−	17.7909i	−0.370644	−	0.641975i
$769$	−0.538943	−	0.367445i	−0.0194348	−	0.0132504i	0.553564	−	0.832807i	$-0.313268\pi$
$769$	−0.538943	−	0.367445i	−0.0194348	−	0.0132504i	−0.572998	+	0.819556i	$0.694220\pi$
$770$	−1.72399	+	7.55329i	−0.0621283	+	0.272202i
$771$	−0.112098	−	0.0168960i	−0.00403710	−	0.000608495i
$772$	−11.7735	−	14.7635i	−0.423738	−	0.531350i
$773$	43.3995			1.56097			0.780486	−	0.625174i	$-0.214972\pi$
$773$	43.3995			1.56097			0.780486	+	0.625174i	$0.214972\pi$
$774$	−6.07809	+	17.5294i	−0.218472	+	0.630082i
$775$	−7.05130			−0.253290
$776$	−0.217416	−	0.272631i	−0.00780479	−	0.00978689i
$777$	−0.914709	−	0.137870i	−0.0328150	−	0.00494606i
$778$	2.54424	−	11.1470i	0.0912154	−	0.399641i
$779$	−25.1868	−	17.1721i	−0.902412	−	0.615254i
$780$	2.94524	+	5.10130i	0.105456	+	0.182656i
$781$	−8.33853	+	14.4428i	−0.298376	+	0.516803i
$782$	44.9672	−	21.6551i	1.60802	−	0.774384i
$783$	50.7983	+	15.6692i	1.81538	+	0.559972i
$784$	2.47759	+	33.0611i	0.0884853	+	1.18075i
$785$	−2.57657	−	11.2887i	−0.0919616	−	0.402910i
$786$	−7.73660	+	19.7125i	−0.275955	+	0.703123i
$787$	−2.49920	+	33.3495i	−0.0890868	+	1.18878i	0.756153	+	0.654394i	$0.227076\pi$
$787$	−2.49920	+	33.3495i	−0.0890868	+	1.18878i	−0.845240	+	0.534387i	$0.820543\pi$
$788$	−2.48759	+	0.374944i	−0.0886167	+	0.0133568i
$789$	0.393039	+	0.364686i	0.0139925	+	0.0129832i
$790$	36.1822	+	17.4244i	1.28731	+	0.619934i
$791$	1.26844	−	0.864808i	0.0451006	−	0.0307490i
$792$	−4.98080	−	12.6909i	−0.176985	−	0.450951i
$793$	15.8499	−	4.88906i	0.562848	−	0.173616i
$794$	25.3641	−	23.5344i	0.900138	−	0.835206i
$795$	3.06395	−	3.84207i	0.108667	−	0.136264i
$796$	−0.00721834	+	0.00905152i	−0.000255847	+	0.000320822i
$797$	25.1690	−	23.3534i	0.891531	−	0.827220i	−0.0941987	−	0.995553i	$-0.530029\pi$
$797$	25.1690	−	23.3534i	0.891531	−	0.827220i	0.985730	+	0.168333i	$0.0538384\pi$
$798$	3.03503	−	0.936183i	0.107439	−	0.0331405i
$799$	−8.27577	−	21.0863i	−0.292776	−	0.745980i
$800$	7.35826	−	5.01678i	0.260154	−	0.177370i
$801$	6.76048	+	3.25568i	0.238870	+	0.115034i
$802$	−0.240634	−	0.223276i	−0.00849708	−	0.00788414i
$803$	−32.0394	+	4.82917i	−1.13065	+	0.170418i
$804$	−0.296311	+	3.95399i	−0.0104501	+	0.139446i
$805$	−2.02892	+	5.16962i	−0.0715102	+	0.182205i
$806$	−4.57647	−	20.0508i	−0.161199	−	0.706261i
$807$	1.85083	+	24.6976i	0.0651523	+	0.869397i
$808$	−7.43700	−	2.29401i	−0.261633	−	0.0807030i
$809$	−42.0700	+	20.2599i	−1.47910	+	0.712299i	−0.987368	−	0.158445i	$-0.949352\pi$
$809$	−42.0700	+	20.2599i	−1.47910	+	0.712299i	−0.491736	+	0.870744i	$0.663638\pi$
$810$	−1.85796	+	3.21809i	−0.0652822	+	0.113072i
$811$	12.4749	+	21.6071i	0.438052	+	0.758728i	0.997539	−	0.0701106i	$-0.0223352\pi$
$811$	12.4749	+	21.6071i	0.438052	+	0.758728i	−0.559487	+	0.828839i	$0.689002\pi$
$812$	−4.31732	−	2.94350i	−0.151508	−	0.103296i
$813$	2.43285	−	10.6590i	0.0853236	−	0.373827i
$814$	9.83528	+	1.48243i	0.344726	+	0.0519591i
$815$	13.9661	+	17.5129i	0.489211	+	0.613451i
$816$	31.9506			1.11850
$817$	−16.3562	−	7.08100i	−0.572230	−	0.247733i
$818$	−0.837096			−0.0292684
$819$	−2.00022	−	2.50819i	−0.0698933	−	0.0876434i
$820$	−17.4292	−	2.62704i	−0.608656	−	0.0917401i
$821$	−12.2059	+	53.4774i	−0.425988	+	1.86637i	0.0692223	+	0.997601i	$0.477948\pi$
$821$	−12.2059	+	53.4774i	−0.425988	+	1.86637i	−0.495210	+	0.868773i	$0.664909\pi$
$822$	−13.0515	−	8.89835i	−0.455223	−	0.310366i
$823$	−13.5728	−	23.5087i	−0.473117	−	0.819462i	0.526410	−	0.850231i	$-0.323538\pi$
$823$	−13.5728	−	23.5087i	−0.473117	−	0.819462i	−0.999527	+	0.0307686i	$0.990205\pi$
$824$	14.8315	−	25.6889i	0.516679	−	0.894914i
$825$	−8.55541	+	4.12007i	−0.297861	+	0.143442i
$826$	−0.710184	−	0.219063i	−0.0247105	−	0.00762217i
$827$	−0.301792	−	4.02714i	−0.0104944	−	0.140037i	0.989495	−	0.144564i	$-0.0461781\pi$
$827$	−0.301792	−	4.02714i	−0.0104944	−	0.140037i	−0.999990	+	0.00452696i	$0.998559\pi$
$828$	1.74791	+	7.65808i	0.0607440	+	0.266137i
$829$	4.52216	−	11.5223i	0.157061	−	0.400185i	−0.830584	−	0.556894i	$-0.811993\pi$
$829$	4.52216	−	11.5223i	0.157061	−	0.400185i	0.987645	+	0.156709i	$0.0500884\pi$
$830$	−1.74620	+	23.3014i	−0.0606115	+	0.808805i
$831$	−14.5292	+	2.18992i	−0.504012	+	0.0759675i
$832$	−4.67296	−	4.33587i	−0.162006	−	0.150319i
$833$	−33.1843	−	15.9807i	−1.14977	−	0.553699i
$834$	35.5442	−	24.2336i	1.23079	−	0.839141i
$835$	−10.7404	−	27.3661i	−0.371687	−	0.947043i
$836$	−10.0594	+	3.10291i	−0.347911	+	0.107316i
$837$	14.7406	−	13.6773i	0.509509	−	0.472756i
$838$	−17.0452	+	21.3741i	−0.588818	+	0.738355i
$839$	20.3816	−	25.5577i	0.703651	−	0.882351i	−0.293639	−	0.955916i	$-0.594866\pi$
$839$	20.3816	−	25.5577i	0.703651	−	0.882351i	0.997290	+	0.0735654i	$0.0234378\pi$
$840$	−1.67487	+	1.55405i	−0.0577883	+	0.0536197i
$841$	65.2081	−	20.1140i	2.24855	−	0.693587i
$842$	−22.6316	−	57.6643i	−0.779936	−	1.98724i
$843$	18.5709	−	12.6614i	0.639616	−	0.436083i
$844$	1.74112	+	0.838477i	0.0599317	+	0.0288616i
$845$	−3.21239	−	2.98066i	−0.110510	−	0.102538i
$846$	11.4364	−	1.72375i	0.393190	−	0.0592639i
$847$	0.350393	−	4.67567i	0.0120396	−	0.160658i
$848$	4.39371	−	11.1950i	0.150881	−	0.384438i
$849$	−0.634339	−	2.77922i	−0.0217705	−	0.0953827i
$850$	1.33113	+	17.7626i	0.0456572	+	0.609253i
$851$	6.81290	+	2.10150i	0.233543	+	0.0720385i
$852$	3.56167	−	1.71521i	0.122021	−	0.0587621i
$853$	−4.58177	+	7.93585i	−0.156877	+	0.271718i	−0.933741	−	0.357950i	$-0.883476\pi$
$853$	−4.58177	+	7.93585i	−0.156877	+	0.271718i	0.776864	+	0.629668i	$0.216809\pi$
$854$	−2.58566	−	4.47850i	−0.0884795	−	0.153251i
$855$	6.58953	+	4.49266i	0.225357	+	0.153646i
$856$	0.0224375	−	0.0983050i	0.000766897	−	0.00336000i
$857$	12.4074	+	1.87011i	0.423829	+	0.0638819i	0.357494	−	0.933916i	$-0.383631\pi$
$857$	12.4074	+	1.87011i	0.423829	+	0.0638819i	0.0663349	+	0.997797i	$0.478869\pi$
$858$	−17.2684	−	21.6539i	−0.589533	−	0.739251i
$859$	13.4029			0.457302			0.228651	−	0.973508i	$-0.426568\pi$
$859$	13.4029			0.457302			0.228651	+	0.973508i	$0.426568\pi$
$860$	−10.2973	+	0.414531i	−0.351134	+	0.0141354i
$861$	−7.70770			−0.262678
$862$	8.62066	+	10.8100i	0.293621	+	0.368189i
$863$	−32.7567	−	4.93727i	−1.11505	−	0.168067i	−0.434432	−	0.900705i	$-0.643051\pi$
$863$	−32.7567	−	4.93727i	−1.11505	−	0.168067i	−0.680619	+	0.732638i	$0.738289\pi$
$864$	−5.65134	+	24.7602i	−0.192263	+	0.842358i
$865$	−11.8035	−	8.04752i	−0.401333	−	0.273624i
$866$	23.4149	+	40.5557i	0.795669	+	1.37814i
$867$	−7.92268	+	13.7225i	−0.269068	+	0.466040i
$868$	−1.78079	+	0.857583i	−0.0604439	+	0.0291083i
$869$	−55.6194	−	17.1563i	−1.88676	−	0.581989i
$870$	2.55399	+	34.0806i	0.0865883	+	1.15544i
$871$	2.77735	+	12.1684i	0.0941069	+	0.412309i
$872$	3.61615	−	9.21379i	0.122458	−	0.312018i
$873$	−0.0229995	+	0.306907i	−0.000778416	+	0.0103872i
$874$	−24.2063	+	3.64851i	−0.818791	+	0.123413i
$875$	−5.29579	−	4.91378i	−0.179031	−	0.166116i
$876$	6.91985	+	3.33242i	0.233800	+	0.112592i
$877$	−0.226534	+	0.154449i	−0.00764952	+	0.00521536i	−0.567139	−	0.823622i	$-0.691950\pi$
$877$	−0.226534	+	0.154449i	−0.00764952	+	0.00521536i	0.559489	+	0.828838i	$0.310997\pi$
$878$	−23.1530	−	58.9928i	−0.781374	−	1.99091i
$879$	−24.0682	+	7.42406i	−0.811801	+	0.250407i
$880$	28.0220	−	26.0006i	0.944621	−	0.876480i
$881$	−22.6315	+	28.3791i	−0.762476	+	0.956115i	−0.999883	−	0.0152957i	$-0.995131\pi$
$881$	−22.6315	+	28.3791i	−0.762476	+	0.956115i	0.237407	+	0.971410i	$0.423702\pi$
$882$	11.7249	−	14.7025i	0.394797	−	0.495060i
$883$	1.58488	−	1.47056i	0.0533356	−	0.0494882i	−0.653055	−	0.757311i	$-0.726513\pi$
$883$	1.58488	−	1.47056i	0.0533356	−	0.0494882i	0.706390	+	0.707823i	$0.250322\pi$
$884$	−15.3032	+	4.72043i	−0.514704	+	0.158765i
$885$	0.547427	+	1.39482i	0.0184016	+	0.0468864i
$886$	−7.69112	+	5.24372i	−0.258388	+	0.176166i
$887$	−32.9093	−	15.8483i	−1.10499	−	0.532134i	−0.209764	−	0.977752i	$-0.567270\pi$
$887$	−32.9093	−	15.8483i	−1.10499	−	0.532134i	−0.895223	+	0.445619i	$0.852984\pi$
$888$	2.15021	+	1.99510i	0.0721563	+	0.0669513i
$889$	7.68120	−	1.15775i	0.257619	−	0.0388298i
$890$	−1.01044	+	13.4834i	−0.0338701	+	0.451965i
$891$	1.96763	−	5.01344i	0.0659180	−	0.167956i
$892$	−0.748849	−	3.28092i	−0.0250733	−	0.109853i
$893$	0.830282	+	11.0793i	0.0277843	+	0.370756i
$894$	−31.0058	−	9.56403i	−1.03699	−	0.319869i
$895$	−27.7236	+	13.3510i	−0.926699	+	0.446275i
$896$	−3.79474	+	6.57269i	−0.126774	+	0.219578i
$897$	−9.92650	−	17.1932i	−0.331436	−	0.574064i
$898$	31.9340	+	21.7722i	1.06565	+	0.726548i
$899$	8.18482	−	35.8600i	0.272979	−	1.19600i
$900$	−2.77209	−	0.417825i	−0.0924029	−	0.0139275i
$901$	8.33012	+	10.4456i	0.277517	+	0.347995i
$902$	82.8760			2.75947
$903$	−4.42557	+	0.850364i	−0.147274	+	0.0282984i
$904$	−4.86799			−0.161907
$905$	−15.5186	−	19.4597i	−0.515855	−	0.646862i
$906$	−30.8409	−	4.64852i	−1.02462	−	0.154437i
$907$	−5.32086	+	23.3122i	−0.176676	+	0.774069i	0.806474	+	0.591270i	$0.201373\pi$
$907$	−5.32086	+	23.3122i	−0.176676	+	0.774069i	−0.983150	+	0.182799i	$0.941484\pi$
$908$	−12.2088	−	8.32385i	−0.405165	−	0.276237i
$909$	3.43451	+	5.94875i	0.113916	+	0.197307i
$910$	2.89045	−	5.00641i	0.0958176	−	0.165961i
$911$	18.7823	−	9.04509i	0.622286	−	0.299677i	−0.0960468	−	0.995377i	$-0.530620\pi$
$911$	18.7823	−	9.04509i	0.622286	−	0.299677i	0.718333	+	0.695700i	$0.244906\pi$
$912$	−14.9749	−	4.61914i	−0.495868	−	0.152955i
$913$	−2.53088	−	33.7722i	−0.0837599	−	1.11770i
$914$	12.5283	+	54.8902i	0.414400	+	1.81560i
$915$	−3.80908	+	9.70538i	−0.125924	+	0.320850i
$916$	−0.0515479	+	0.687859i	−0.00170319	+	0.0227275i
$917$	6.33468	−	0.954799i	0.209189	−	0.0315302i
$918$	−37.2366	−	34.5505i	−1.22899	−	1.14034i
$919$	23.5089	+	11.3213i	0.775486	+	0.373454i	0.779391	−	0.626538i	$-0.215529\pi$
$919$	23.5089	+	11.3213i	0.775486	+	0.373454i	−0.00390486	+	0.999992i	$0.501243\pi$
$920$	14.5498	−	9.91991i	0.479694	−	0.327050i
$921$	−8.41849	−	21.4500i	−0.277399	−	0.706800i
$922$	−24.3433	+	7.50892i	−0.801705	+	0.247293i
$923$	9.12193	−	8.46391i	0.300252	−	0.278593i
$924$	−1.65957	+	2.08103i	−0.0545957	+	0.0684608i
$925$	−1.58648	+	1.98938i	−0.0521632	+	0.0654106i
$926$	−22.7333	+	21.0934i	−0.747061	+	0.693171i
$927$	−25.0172	+	7.71678i	−0.821673	+	0.253452i
$928$	16.9722	+	43.2444i	0.557139	+	1.41957i
$929$	8.57866	−	5.84883i	0.281457	−	0.191894i	−0.414361	−	0.910113i	$-0.635995\pi$
$929$	8.57866	−	5.84883i	0.281457	−	0.191894i	0.695817	+	0.718219i	$0.255042\pi$
$930$	11.6474	+	5.60908i	0.381932	+	0.183929i
$931$	13.2427	+	12.2875i	0.434013	+	0.402705i
$932$	22.8920	−	3.45041i	0.749851	−	0.113022i
$933$	−0.509200	+	6.79481i	−0.0166705	+	0.222452i
$934$	2.16171	−	5.50794i	0.0707332	−	0.180225i
$935$	9.44984	+	41.4024i	0.309043	+	1.35400i
$936$	0.760202	+	10.1442i	0.0248480	+	0.331573i
$937$	22.6423	+	6.98421i	0.739690	+	0.228164i	0.641628	−	0.767016i	$-0.278259\pi$
$937$	22.6423	+	6.98421i	0.739690	+	0.228164i	0.0980624	+	0.995180i	$0.468736\pi$
$938$	3.50596	−	1.68838i	0.114474	−	0.0551276i
$939$	−12.1146	+	20.9831i	−0.395344	+	0.684756i
$940$	3.21210	+	5.56352i	0.104767	+	0.181462i
$941$	−20.3425	−	13.8692i	−0.663145	−	0.452125i	0.184398	−	0.982852i	$-0.440967\pi$
$941$	−20.3425	−	13.8692i	−0.663145	−	0.452125i	−0.847543	+	0.530727i	$0.821919\pi$
$942$	2.87169	−	12.5817i	0.0935648	−	0.409934i
$943$	58.7428	+	8.85405i	1.91293	+	0.288327i
$944$	2.28632	+	2.86696i	0.0744134	+	0.0933115i
$945$	5.65218			0.183865
$946$	47.5853	−	9.14342i	1.54713	−	0.297278i
$947$	−6.75858			−0.219624			−0.109812	−	0.993952i	$-0.535025\pi$
$947$	−6.75858			−0.219624			−0.109812	+	0.993952i	$0.535025\pi$
$948$	8.60233	+	10.7870i	0.279391	+	0.350345i
$949$	23.9066	+	3.60333i	0.776040	+	0.116969i
$950$	1.94408	−	8.51759i	0.0630744	−	0.276347i
$951$	20.7452	+	14.1438i	0.672708	+	0.458644i
$952$	−3.10588	−	5.37954i	−0.100662	−	0.174352i
$953$	−24.9228	+	43.1676i	−0.807329	+	1.39834i	0.107378	+	0.994218i	$0.465754\pi$
$953$	−24.9228	+	43.1676i	−0.807329	+	1.39834i	−0.914707	+	0.404117i	$0.867579\pi$
$954$	−6.14594	+	2.95973i	−0.198982	+	0.0958247i
$955$	31.9323	+	9.84982i	1.03331	+	0.318733i
$956$	0.234810	+	3.13332i	0.00759430	+	0.101339i
$957$	−11.0223	−	48.2918i	−0.356300	−	1.56105i
$958$	14.9009	−	37.9669i	0.481427	−	1.22666i
$959$	−0.357109	+	4.76529i	−0.0115316	+	0.153879i
$960$	3.96221	−	0.597206i	0.127880	−	0.0192748i
$961$	12.5254	+	11.6219i	0.404044	+	0.374898i
$962$	−6.68662	−	3.22011i	−0.215585	−	0.103820i
$963$	−0.0735308	+	0.0501325i	−0.00236950	+	0.00161550i
$964$	−6.35423	−	16.1903i	−0.204656	−	0.521455i
$965$	35.7031	−	11.0130i	1.14932	−	0.354519i
$966$	−4.53731	+	4.21001i	−0.145986	+	0.135455i
$967$	−14.1131	+	17.6973i	−0.453848	+	0.569107i	−0.955134	−	0.296175i	$-0.904289\pi$
$967$	−14.1131	+	17.6973i	−0.453848	+	0.569107i	0.501286	+	0.865282i	$0.332860\pi$
$968$	−9.26988	+	11.6241i	−0.297945	+	0.373611i
$969$	12.7621	−	11.8415i	0.409979	−	0.380405i
$970$	−0.529950	+	0.163468i	−0.0170157	+	0.00524864i
$971$	−21.8978	−	55.7948i	−0.702735	−	1.79054i	−0.606352	−	0.795196i	$-0.707368\pi$
$971$	−21.8978	−	55.7948i	−0.702735	−	1.79054i	−0.0963829	−	0.995344i	$-0.530727\pi$
$972$	10.8542	−	7.40030i	0.348150	−	0.237365i
$973$	−11.7253	−	5.64660i	−0.375895	−	0.181022i
$974$	5.50938	+	5.11195i	0.176532	+	0.163798i
$975$	7.00625	−	1.05602i	0.224380	−	0.0338198i
$976$	−1.90677	+	25.4440i	−0.0610341	+	0.814444i
$977$	−5.79096	+	14.7551i	−0.185269	+	0.472058i	−0.993088	−	0.117373i	$-0.962553\pi$
$977$	−5.79096	+	14.7551i	−0.185269	+	0.472058i	0.807819	+	0.589431i	$0.200648\pi$
$978$	5.55536	+	24.3396i	0.177641	+	0.778296i
$979$	−1.46450	−	19.5424i	−0.0468055	−	0.624576i
$980$	9.98149	+	3.07888i	0.318847	+	0.0983513i
$981$	−7.87078	+	3.79037i	−0.251295	+	0.121017i
$982$	−13.3113	+	23.0558i	−0.424780	+	0.735740i
$983$	13.2289	+	22.9131i	0.421935	+	0.730813i	0.996129	−	0.0879064i	$-0.0280176\pi$
$983$	13.2289	+	22.9131i	0.421935	+	0.730813i	−0.574194	+	0.818720i	$0.694684\pi$
$984$	20.1937	+	13.7678i	0.643751	+	0.438902i
$985$	1.10763	−	4.85283i	0.0352919	−	0.154624i
$986$	−91.8787	−	13.8485i	−2.92601	−	0.441026i
$987$	1.75153	+	2.19635i	0.0557517	+	0.0699104i
$988$	7.85489			0.249897
$989$	34.7055	−	1.39712i	1.10357	−	0.0444257i
$990$	−21.6825			−0.689116
$991$	−12.2046	−	15.3041i	−0.387691	−	0.486150i	0.549239	−	0.835665i	$-0.314918\pi$
$991$	−12.2046	−	15.3041i	−0.387691	−	0.486150i	−0.936931	+	0.349516i	$0.886346\pi$
$992$	17.3762	+	2.61904i	0.551696	+	0.0831547i
$993$	2.43909	−	10.6864i	0.0774022	−	0.339121i
$994$	−3.20549	−	2.18547i	−0.101672	−	0.0693189i
$995$	−0.0114537	−	0.0198383i	−0.000363105	−	0.000628917i
$996$	−4.01393	+	6.95234i	−0.127186	+	0.220293i
$997$	−16.2736	+	7.83696i	−0.515391	+	0.248199i	−0.673453	−	0.739230i	$-0.735190\pi$
$997$	−16.2736	+	7.83696i	−0.515391	+	0.248199i	0.158062	+	0.987429i	$0.449475\pi$
$998$	61.1907	+	18.8748i	1.93696	+	0.597472i
$999$	−0.542266	−	7.23604i	−0.0171565	−	0.228938i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.2.g.a.9.3	✓	36
3.2	odd	2		387.2.y.c.181.1		36
4.3	odd	2		688.2.bg.c.353.2		36
43.14	even	21		1849.2.a.n.1.15		18
43.24	even	21	inner	43.2.g.a.24.3	yes	36
43.29	odd	42		1849.2.a.o.1.4		18
129.110	odd	42		387.2.y.c.325.1		36
172.67	odd	42		688.2.bg.c.497.2		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.9.3	✓	36	1.1	even	1	trivial
43.2.g.a.24.3	yes	36	43.24	even	21	inner
387.2.y.c.181.1		36	3.2	odd	2
387.2.y.c.325.1		36	129.110	odd	42
688.2.bg.c.353.2		36	4.3	odd	2
688.2.bg.c.497.2		36	172.67	odd	42
1849.2.a.n.1.15		18	43.14	even	21
1849.2.a.o.1.4		18	43.29	odd	42

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	43.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.06016 + 1.32939i) q^{2} +(-1.14296 - 0.172273i) q^{3} +(-0.198316 + 0.868879i) q^{4} +(-1.45700 - 0.993363i) q^{5} +(-0.982695 - 1.70208i) q^{6} +(-0.297283 + 0.514909i) q^{7} +(1.69861 - 0.818009i) q^{8} +(-1.59004 - 0.490464i) q^{9} +O(q^{10})\)	\(q+(1.06016 + 1.32939i) q^{2} +(-1.14296 - 0.172273i) q^{3} +(-0.198316 + 0.868879i) q^{4} +(-1.45700 - 0.993363i) q^{5} +(-0.982695 - 1.70208i) q^{6} +(-0.297283 + 0.514909i) q^{7} +(1.69861 - 0.818009i) q^{8} +(-1.59004 - 0.490464i) q^{9} +(-0.224073 - 2.99004i) q^{10} +(0.967034 + 4.23685i) q^{11} +(0.376351 - 0.958927i) q^{12} +(0.242325 - 3.23360i) q^{13} +(-0.999683 + 0.150678i) q^{14} +(1.49415 + 1.38637i) q^{15} +(4.49418 + 2.16428i) q^{16} +(-4.57863 + 3.12166i) q^{17} +(-1.03368 - 2.63377i) q^{18} +(2.59725 - 0.801147i) q^{19} +(1.15206 - 1.06895i) q^{20} +(0.428486 - 0.537305i) q^{21} +(-4.60724 + 5.77730i) q^{22} +(-3.88284 + 3.60275i) q^{23} +(-2.08236 + 0.642324i) q^{24} +(-0.690639 - 1.75972i) q^{25} +(4.55564 - 3.10598i) q^{26} +(4.85706 + 2.33904i) q^{27} +(-0.388437 - 0.360417i) q^{28} +(9.75088 - 1.46971i) q^{29} +(-0.258998 + 3.45609i) q^{30} +(1.36275 - 3.47222i) q^{31} +(1.04831 + 4.59293i) q^{32} +(-0.375383 - 5.00913i) q^{33} +(-9.00399 - 2.77736i) q^{34} +(0.944631 - 0.454910i) q^{35} +(0.741485 - 1.28429i) q^{36} +(-0.673012 - 1.16569i) q^{37} +(3.81854 + 2.60343i) q^{38} +(-0.834030 + 3.65413i) q^{39} +(-3.28745 - 0.495504i) q^{40} +(-6.99273 - 8.76860i) q^{41} +1.16855 q^{42} +(-4.98246 - 4.26323i) q^{43} -3.87309 q^{44} +(1.82948 + 2.29409i) q^{45} +(-8.90590 - 1.34235i) q^{46} +(-0.909600 + 3.98522i) q^{47} +(-4.76381 - 3.24791i) q^{48} +(3.32325 + 5.75603i) q^{49} +(1.60718 - 2.78371i) q^{50} +(5.77096 - 2.77915i) q^{51} +(2.76155 + 0.851826i) q^{52} +(-0.180172 - 2.40423i) q^{53} +(2.03974 + 8.93670i) q^{54} +(2.79977 - 7.13369i) q^{55} +(-0.0837683 + 1.11781i) q^{56} +(-3.10657 + 0.468240i) q^{57} +(12.2913 + 11.4047i) q^{58} +(0.662333 + 0.318963i) q^{59} +(-1.50090 + 1.02330i) q^{60} +(1.86879 + 4.76159i) q^{61} +(6.06068 - 1.86947i) q^{62} +(0.725237 - 0.672921i) q^{63} +(1.22570 - 1.53698i) q^{64} +(-3.56521 + 4.47063i) q^{65} +(6.26115 - 5.80950i) q^{66} +(-3.67807 + 1.13454i) q^{67} +(-1.80433 - 4.59735i) q^{68} +(5.05858 - 3.44888i) q^{69} +(1.60621 + 0.773511i) q^{70} +(2.81309 + 2.61017i) q^{71} +(-3.10208 + 0.467563i) q^{72} +(-0.557170 + 7.43491i) q^{73} +(0.836166 - 2.13052i) q^{74} +(0.486219 + 2.13026i) q^{75} +(0.181023 + 2.41558i) q^{76} +(-2.46907 - 0.761608i) q^{77} +(-5.74198 + 2.76519i) q^{78} +(-6.69672 + 11.5991i) q^{79} +(-4.39809 - 7.61771i) q^{80} +(-1.02395 - 0.698119i) q^{81} +(4.24355 - 18.5922i) q^{82} +(-7.70597 - 1.16149i) q^{83} +(0.381877 + 0.478859i) q^{84} +9.77199 q^{85} +(0.385325 - 11.1433i) q^{86} -11.3980 q^{87} +(5.10840 + 6.40573i) q^{88} +(-4.45907 - 0.672097i) q^{89} +(-1.11022 + 4.86420i) q^{90} +(1.59297 + 1.08607i) q^{91} +(-2.36033 - 4.08820i) q^{92} +(-2.15573 + 3.73383i) q^{93} +(-6.26225 + 3.01574i) q^{94} +(-4.58002 - 1.41275i) q^{95} +(-0.406931 - 5.43011i) q^{96} +(-0.0411575 - 0.180323i) q^{97} +(-4.12888 + 10.5202i) q^{98} +(0.540395 - 7.21108i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9}+O(q^{10}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9} - 7 q^{10} - 4 q^{11} + 2 q^{12} + 18 q^{14} - 3 q^{15} - 10 q^{16} - 10 q^{17} + 11 q^{18} + 10 q^{19} - 3 q^{20} - 21 q^{21} - 3 q^{22} + 4 q^{23} + 31 q^{24} - 2 q^{25} - 15 q^{26} - 4 q^{27} + 20 q^{28} + 9 q^{29} + 88 q^{30} + 40 q^{31} + 48 q^{32} - 11 q^{33} - 42 q^{34} + 11 q^{35} - 47 q^{36} - 19 q^{37} - 21 q^{38} - q^{39} - 97 q^{40} - 28 q^{41} + 2 q^{42} - 8 q^{43} + 14 q^{44} - 46 q^{45} - 61 q^{46} - 30 q^{47} - 97 q^{48} + 6 q^{49} - 3 q^{50} + 57 q^{51} - 8 q^{52} - 24 q^{53} + 6 q^{54} + 14 q^{55} + 39 q^{56} + 52 q^{57} + 64 q^{58} - q^{59} + 111 q^{60} - 14 q^{61} + 33 q^{62} + 47 q^{63} + 48 q^{64} + 38 q^{65} + 79 q^{66} + 66 q^{67} + 66 q^{68} - 7 q^{69} + 47 q^{70} - 33 q^{71} + 26 q^{72} + 29 q^{73} - 40 q^{74} - 55 q^{75} - 39 q^{76} - 27 q^{77} - 126 q^{78} - 17 q^{79} + 8 q^{80} + 38 q^{81} - 54 q^{82} - 23 q^{83} - 155 q^{84} - 56 q^{85} - 45 q^{86} - 86 q^{87} - 17 q^{88} - 19 q^{89} - 127 q^{90} - 13 q^{91} - 18 q^{92} - 30 q^{93} + 44 q^{94} + q^{95} - 36 q^{96} - 31 q^{97} - 5 q^{98} - 31 q^{99}+O(q^{100}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9 - 7 * q^10 - 4 * q^11 + 2 * q^12 + 18 * q^14 - 3 * q^15 - 10 * q^16 - 10 * q^17 + 11 * q^18 + 10 * q^19 - 3 * q^20 - 21 * q^21 - 3 * q^22 + 4 * q^23 + 31 * q^24 - 2 * q^25 - 15 * q^26 - 4 * q^27 + 20 * q^28 + 9 * q^29 + 88 * q^30 + 40 * q^31 + 48 * q^32 - 11 * q^33 - 42 * q^34 + 11 * q^35 - 47 * q^36 - 19 * q^37 - 21 * q^38 - q^39 - 97 * q^40 - 28 * q^41 + 2 * q^42 - 8 * q^43 + 14 * q^44 - 46 * q^45 - 61 * q^46 - 30 * q^47 - 97 * q^48 + 6 * q^49 - 3 * q^50 + 57 * q^51 - 8 * q^52 - 24 * q^53 + 6 * q^54 + 14 * q^55 + 39 * q^56 + 52 * q^57 + 64 * q^58 - q^59 + 111 * q^60 - 14 * q^61 + 33 * q^62 + 47 * q^63 + 48 * q^64 + 38 * q^65 + 79 * q^66 + 66 * q^67 + 66 * q^68 - 7 * q^69 + 47 * q^70 - 33 * q^71 + 26 * q^72 + 29 * q^73 - 40 * q^74 - 55 * q^75 - 39 * q^76 - 27 * q^77 - 126 * q^78 - 17 * q^79 + 8 * q^80 + 38 * q^81 - 54 * q^82 - 23 * q^83 - 155 * q^84 - 56 * q^85 - 45 * q^86 - 86 * q^87 - 17 * q^88 - 19 * q^89 - 127 * q^90 - 13 * q^91 - 18 * q^92 - 30 * q^93 + 44 * q^94 + q^95 - 36 * q^96 - 31 * q^97 - 5 * q^98 - 31 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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