LMFDB - Embedded newform 224.2.be.a.3.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(3,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 9, 4]))

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

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

chi := DirichletCharacter("224.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.be (of order $24$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			3.15
Character	$\chi$	$=$	224.3
Dual form			224.2.be.a.75.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.124966 - 1.40868i) q^{2} +(2.48500 - 1.90681i) q^{3} +(-1.96877 + 0.352074i) q^{4} +(-2.71407 - 2.08258i) q^{5} +(-2.99663 - 3.26229i) q^{6} +(1.12555 + 2.39440i) q^{7} +(0.741988 + 2.72937i) q^{8} +(1.76286 - 6.57908i) q^{9} +O(q^{10})$	\(q+(-0.124966 - 1.40868i) q^{2} +(2.48500 - 1.90681i) q^{3} +(-1.96877 + 0.352074i) q^{4} +(-2.71407 - 2.08258i) q^{5} +(-2.99663 - 3.26229i) q^{6} +(1.12555 + 2.39440i) q^{7} +(0.741988 + 2.72937i) q^{8} +(1.76286 - 6.57908i) q^{9} +(-2.59452 + 4.08351i) q^{10} +(-2.02722 - 0.266888i) q^{11} +(-4.22105 + 4.62897i) q^{12} +(1.71462 + 0.710220i) q^{13} +(3.23229 - 1.88476i) q^{14} -10.7156 q^{15} +(3.75209 - 1.38630i) q^{16} +(0.0973921 - 0.168688i) q^{17} +(-9.48813 - 1.66115i) q^{18} +(7.47190 - 0.983695i) q^{19} +(6.07659 + 3.14456i) q^{20} +(7.36266 + 3.80387i) q^{21} +(-0.122628 + 2.88905i) q^{22} +(0.230374 + 0.0617284i) q^{23} +(7.04823 + 5.36766i) q^{24} +(1.73494 + 6.47489i) q^{25} +(0.786204 - 2.50411i) q^{26} +(-4.56833 - 11.0289i) q^{27} +(-3.05895 - 4.31773i) q^{28} +(-1.82864 - 0.757448i) q^{29} +(1.33908 + 15.0948i) q^{30} +(-1.75660 + 3.04252i) q^{31} +(-2.42174 - 5.11226i) q^{32} +(-5.54655 + 3.20230i) q^{33} +(-0.249798 - 0.116114i) q^{34} +(1.93170 - 8.84261i) q^{35} +(-1.15434 + 13.5733i) q^{36} +(2.06988 - 2.69752i) q^{37} +(-2.31944 - 10.4026i) q^{38} +(5.61510 - 1.50456i) q^{39} +(3.67032 - 8.95294i) q^{40} +(-3.44057 + 3.44057i) q^{41} +(4.43836 - 10.8470i) q^{42} +(-0.957734 - 2.31218i) q^{43} +(4.08508 - 0.188289i) q^{44} +(-18.4860 + 14.1848i) q^{45} +(0.0581669 - 0.332237i) q^{46} +(-0.188303 + 0.108717i) q^{47} +(6.68053 - 10.5995i) q^{48} +(-4.46627 + 5.39003i) q^{49} +(8.90425 - 3.25312i) q^{50} +(-0.0796364 - 0.604898i) q^{51} +(-3.62574 - 0.794583i) q^{52} +(-1.25208 + 9.51051i) q^{53} +(-14.9654 + 7.81357i) q^{54} +(4.94619 + 4.94619i) q^{55} +(-5.70004 + 4.84866i) q^{56} +(16.6920 - 16.6920i) q^{57} +(-0.838486 + 2.67063i) q^{58} +(8.24826 + 1.08590i) q^{59} +(21.0964 - 3.77267i) q^{60} +(6.57814 - 0.866029i) q^{61} +(4.50546 + 2.09428i) q^{62} +(17.7371 - 3.18411i) q^{63} +(-6.89891 + 4.05032i) q^{64} +(-3.17451 - 5.49842i) q^{65} +(5.20415 + 7.41314i) q^{66} +(-3.43269 - 4.47357i) q^{67} +(-0.132352 + 0.366397i) q^{68} +(0.690184 - 0.285883i) q^{69} +(-12.6978 - 1.61612i) q^{70} +(6.51746 + 6.51746i) q^{71} +(19.2648 - 0.0701089i) q^{72} +(3.54282 + 13.2220i) q^{73} +(-4.05861 - 2.57871i) q^{74} +(16.6577 + 12.7819i) q^{75} +(-14.3641 + 4.56733i) q^{76} +(-1.64270 - 5.15436i) q^{77} +(-2.82114 - 7.72186i) q^{78} +(-5.91609 - 10.2470i) q^{79} +(-13.0705 - 4.05150i) q^{80} +(-14.6865 - 8.47925i) q^{81} +(5.27663 + 4.41672i) q^{82} +(-1.39613 + 3.37055i) q^{83} +(-15.8346 - 4.89674i) q^{84} +(-0.615635 + 0.255004i) q^{85} +(-3.13743 + 1.63809i) q^{86} +(-5.98849 + 1.60461i) q^{87} +(-0.775735 - 5.73105i) q^{88} +(-0.410138 + 1.53066i) q^{89} +(22.2920 + 24.2682i) q^{90} +(0.229347 + 4.90487i) q^{91} +(-0.475285 - 0.0404204i) q^{92} +(1.43635 + 10.9102i) q^{93} +(0.176679 + 0.251674i) q^{94} +(-22.3279 - 12.8910i) q^{95} +(-15.7661 - 8.08617i) q^{96} +15.9978i q^{97} +(8.15097 + 5.61798i) q^{98} +(-5.32958 + 12.8667i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9	$ 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 12 q^{10} - 4 q^{11} - 12 q^{12} - 40 q^{14} - 32 q^{15} - 24 q^{16} + 16 q^{18} - 12 q^{19} - 8 q^{21} - 8 q^{22} + 4 q^{23} - 12 q^{24} - 4 q^{25} - 12 q^{26} + 12 q^{28} - 16 q^{29} - 52 q^{30} - 4 q^{32} - 24 q^{33} - 32 q^{35} + 64 q^{36} - 4 q^{37} - 12 q^{38} - 4 q^{39} - 12 q^{40} - 28 q^{42} - 32 q^{43} - 52 q^{44} - 48 q^{45} - 4 q^{46} - 24 q^{47} - 40 q^{50} + 20 q^{51} + 60 q^{52} - 20 q^{53} - 12 q^{54} - 48 q^{56} - 16 q^{57} - 36 q^{58} + 84 q^{59} + 28 q^{60} - 12 q^{61} - 136 q^{64} - 8 q^{65} + 132 q^{66} + 36 q^{67} - 12 q^{68} + 28 q^{70} - 80 q^{71} - 4 q^{72} - 12 q^{73} - 20 q^{74} - 72 q^{75} - 8 q^{77} - 216 q^{78} - 8 q^{79} + 24 q^{80} + 108 q^{82} + 12 q^{84} + 24 q^{85} - 4 q^{86} - 12 q^{87} - 48 q^{88} - 12 q^{89} + 40 q^{91} - 80 q^{92} + 20 q^{93} + 60 q^{94} + 312 q^{96} - 16 q^{98} - 40 q^{99}+O(q^{100}) $ 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 12 * q^10 - 4 * q^11 - 12 * q^12 - 40 * q^14 - 32 * q^15 - 24 * q^16 + 16 * q^18 - 12 * q^19 - 8 * q^21 - 8 * q^22 + 4 * q^23 - 12 * q^24 - 4 * q^25 - 12 * q^26 + 12 * q^28 - 16 * q^29 - 52 * q^30 - 4 * q^32 - 24 * q^33 - 32 * q^35 + 64 * q^36 - 4 * q^37 - 12 * q^38 - 4 * q^39 - 12 * q^40 - 28 * q^42 - 32 * q^43 - 52 * q^44 - 48 * q^45 - 4 * q^46 - 24 * q^47 - 40 * q^50 + 20 * q^51 + 60 * q^52 - 20 * q^53 - 12 * q^54 - 48 * q^56 - 16 * q^57 - 36 * q^58 + 84 * q^59 + 28 * q^60 - 12 * q^61 - 136 * q^64 - 8 * q^65 + 132 * q^66 + 36 * q^67 - 12 * q^68 + 28 * q^70 - 80 * q^71 - 4 * q^72 - 12 * q^73 - 20 * q^74 - 72 * q^75 - 8 * q^77 - 216 * q^78 - 8 * q^79 + 24 * q^80 + 108 * q^82 + 12 * q^84 + 24 * q^85 - 4 * q^86 - 12 * q^87 - 48 * q^88 - 12 * q^89 + 40 * q^91 - 80 * q^92 + 20 * q^93 + 60 * q^94 + 312 * q^96 - 16 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{8}\right)$

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 $

$2$	−0.124966	−	1.40868i	−0.0883641	−	0.996088i
$2$	−0.124966	−	1.40868i	−0.0883641	−	0.996088i
$3$	2.48500	−	1.90681i	1.43472	−	1.10090i	0.457365	−	0.889279i	$-0.348793\pi$
$3$	2.48500	−	1.90681i	1.43472	−	1.10090i	0.977352	−	0.211618i	$-0.0678734\pi$
$4$	−1.96877	+	0.352074i	−0.984384	+	0.176037i
$5$	−2.71407	−	2.08258i	−1.21377	−	0.931357i	−0.214795	−	0.976659i	$-0.568908\pi$
$5$	−2.71407	−	2.08258i	−1.21377	−	0.931357i	−0.998973	+	0.0453017i	$0.985575\pi$
$6$	−2.99663	−	3.26229i	−1.22337	−	1.33183i
$7$	1.12555	+	2.39440i	0.425418	+	0.904997i
$7$	1.12555	+	2.39440i	0.425418	+	0.904997i
$8$	0.741988	+	2.72937i	0.262333	+	0.964978i
$9$	1.76286	−	6.57908i	0.587620	−	2.19303i
$10$	−2.59452	+	4.08351i	−0.820461	+	1.29132i
$11$	−2.02722	−	0.266888i	−0.611229	−	0.0804698i	−0.181444	−	0.983401i	$-0.558077\pi$
$11$	−2.02722	−	0.266888i	−0.611229	−	0.0804698i	−0.429785	+	0.902931i	$0.641411\pi$
$12$	−4.22105	+	4.62897i	−1.21851	+	1.33627i
$13$	1.71462	+	0.710220i	0.475551	+	0.196979i	0.607568	−	0.794268i	$-0.292145\pi$
$13$	1.71462	+	0.710220i	0.475551	+	0.196979i	−0.132017	+	0.991247i	$0.542145\pi$
$14$	3.23229	−	1.88476i	0.863865	−	0.503723i
$15$	−10.7156			−2.76674
$16$	3.75209	−	1.38630i	0.938022	−	0.346576i
$17$	0.0973921	−	0.168688i	0.0236210	−	0.0409128i	−0.853973	−	0.520317i	$-0.825814\pi$
$17$	0.0973921	−	0.168688i	0.0236210	−	0.0409128i	0.877594	+	0.479404i	$0.159147\pi$
$18$	−9.48813	−	1.66115i	−2.23637	−	0.391536i
$19$	7.47190	−	0.983695i	1.71417	−	0.225675i	0.791475	−	0.611201i	$-0.209313\pi$
$19$	7.47190	−	0.983695i	1.71417	−	0.225675i	0.922697	+	0.385526i	$0.125980\pi$
$20$	6.07659	+	3.14456i	1.35877	+	0.703145i
$21$	7.36266	+	3.80387i	1.60666	+	0.830073i
$22$	−0.122628	+	2.88905i	−0.0261443	+	0.615948i
$23$	0.230374	+	0.0617284i	0.0480362	+	0.0128713i	0.282757	−	0.959192i	$-0.408751\pi$
$23$	0.230374	+	0.0617284i	0.0480362	+	0.0128713i	−0.234721	+	0.972063i	$0.575418\pi$
$24$	7.04823	+	5.36766i	1.43871	+	1.09567i
$25$	1.73494	+	6.47489i	0.346989	+	1.29498i
$26$	0.786204	−	2.50411i	0.154187	−	0.491096i
$27$	−4.56833	−	11.0289i	−0.879176	−	2.12252i
$28$	−3.05895	−	4.31773i	−0.578088	−	0.815975i
$29$	−1.82864	−	0.757448i	−0.339570	−	0.140655i	0.206381	−	0.978472i	$-0.433831\pi$
$29$	−1.82864	−	0.757448i	−0.339570	−	0.140655i	−0.545951	+	0.837817i	$0.683831\pi$
$30$	1.33908	+	15.0948i	0.244481	+	2.75592i
$31$	−1.75660	+	3.04252i	−0.315495	+	0.546453i	−0.979543	−	0.201237i	$-0.935504\pi$
$31$	−1.75660	+	3.04252i	−0.315495	+	0.546453i	0.664048	+	0.747690i	$0.268837\pi$
$32$	−2.42174	−	5.11226i	−0.428108	−	0.903728i
$33$	−5.54655	+	3.20230i	−0.965530	+	0.557449i
$34$	−0.249798	−	0.116114i	−0.0428401	−	0.0199134i
$35$	1.93170	−	8.84261i	0.326516	−	1.49467i
$36$	−1.15434	+	13.5733i	−0.192390	+	2.26222i
$37$	2.06988	−	2.69752i	0.340286	−	0.443470i	−0.591594	−	0.806236i	$-0.701501\pi$
$37$	2.06988	−	2.69752i	0.340286	−	0.443470i	0.931880	+	0.362766i	$0.118168\pi$
$38$	−2.31944	−	10.4026i	−0.376264	−	1.68752i
$39$	5.61510	−	1.50456i	0.899135	−	0.240922i
$40$	3.67032	−	8.95294i	0.580328	−	1.41558i
$41$	−3.44057	+	3.44057i	−0.537328	+	0.537328i	−0.922743	−	0.385416i	$-0.874058\pi$
$41$	−3.44057	+	3.44057i	−0.537328	+	0.537328i	0.385416	+	0.922743i	$0.374058\pi$
$42$	4.43836	−	10.8470i	0.684854	−	1.67373i
$43$	−0.957734	−	2.31218i	−0.146053	−	0.352603i	0.833875	−	0.551953i	$-0.186117\pi$
$43$	−0.957734	−	2.31218i	−0.146053	−	0.352603i	−0.979928	+	0.199349i	$0.936117\pi$
$44$	4.08508	−	0.188289i	0.615849	−	0.0283857i
$45$	−18.4860	+	14.1848i	−2.75573	+	2.11454i
$46$	0.0581669	−	0.332237i	0.00857624	−	0.0489857i
$47$	−0.188303	+	0.108717i	−0.0274669	+	0.0158580i	−0.513671	−	0.857988i	$-0.671715\pi$
$47$	−0.188303	+	0.108717i	−0.0274669	+	0.0158580i	0.486204	+	0.873846i	$0.338381\pi$
$48$	6.68053	−	10.5995i	0.964252	−	1.52990i
$49$	−4.46627	+	5.39003i	−0.638039	+	0.770004i
$50$	8.90425	−	3.25312i	1.25925	−	0.460061i
$51$	−0.0796364	−	0.604898i	−0.0111513	−	0.0847027i
$52$	−3.62574	−	0.794583i	−0.502800	−	0.110189i
$53$	−1.25208	+	9.51051i	−0.171987	+	1.30637i	0.659871	+	0.751379i	$0.270611\pi$
$53$	−1.25208	+	9.51051i	−0.171987	+	1.30637i	−0.831857	+	0.554989i	$0.812722\pi$
$54$	−14.9654	+	7.81357i	−2.03653	+	1.06329i
$55$	4.94619	+	4.94619i	0.666944	+	0.666944i
$56$	−5.70004	+	4.84866i	−0.761701	+	0.647929i
$57$	16.6920	−	16.6920i	2.21091	−	2.21091i
$58$	−0.838486	+	2.67063i	−0.110099	+	0.350671i
$59$	8.24826	+	1.08590i	1.07383	+	0.141373i	0.646645	−	0.762791i	$-0.276171\pi$
$59$	8.24826	+	1.08590i	1.07383	+	0.141373i	0.427187	+	0.904163i	$0.359505\pi$
$60$	21.0964	−	3.77267i	2.72354	−	0.487049i
$61$	6.57814	−	0.866029i	0.842245	−	0.110884i	0.302956	−	0.953005i	$-0.402026\pi$
$61$	6.57814	−	0.866029i	0.842245	−	0.110884i	0.539289	+	0.842121i	$0.318693\pi$
$62$	4.50546	+	2.09428i	0.572194	+	0.265974i
$63$	17.7371	−	3.18411i	2.23467	−	0.401160i
$64$	−6.89891	+	4.05032i	−0.862363	+	0.506290i
$65$	−3.17451	−	5.49842i	−0.393750	−	0.681995i
$66$	5.20415	+	7.41314i	0.640586	+	0.912494i
$67$	−3.43269	−	4.47357i	−0.419370	−	0.546533i	0.535120	−	0.844776i	$-0.320266\pi$
$67$	−3.43269	−	4.47357i	−0.419370	−	0.546533i	−0.954490	+	0.298243i	$0.903600\pi$
$68$	−0.132352	+	0.366397i	−0.0160500	+	0.0444321i
$69$	0.690184	−	0.285883i	0.0830883	−	0.0344163i
$70$	−12.6978	−	1.61612i	−1.51768	−	0.193163i
$71$	6.51746	+	6.51746i	0.773480	+	0.773480i	0.978713	−	0.205233i	$-0.0657953\pi$
$71$	6.51746	+	6.51746i	0.773480	+	0.773480i	−0.205233	+	0.978713i	$0.565795\pi$
$72$	19.2648	−	0.0701089i	2.27037	−	0.00826241i
$73$	3.54282	+	13.2220i	0.414655	+	1.54751i	0.785525	+	0.618830i	$0.212393\pi$
$73$	3.54282	+	13.2220i	0.414655	+	1.54751i	−0.370870	+	0.928685i	$0.620940\pi$
$74$	−4.05861	−	2.57871i	−0.471804	−	0.299769i
$75$	16.6577	+	12.7819i	1.92347	+	1.47593i
$76$	−14.3641	+	4.56733i	−1.64768	+	0.523908i
$77$	−1.64270	−	5.15436i	−0.187203	−	0.587393i
$78$	−2.82114	−	7.72186i	−0.319431	−	0.874329i
$79$	−5.91609	−	10.2470i	−0.665612	−	1.15287i	−0.979119	−	0.203288i	$-0.934837\pi$
$79$	−5.91609	−	10.2470i	−0.665612	−	1.15287i	0.313507	−	0.949586i	$-0.398496\pi$
$80$	−13.0705	−	4.05150i	−1.46133	−	0.452971i
$81$	−14.6865	−	8.47925i	−1.63183	−	0.942138i
$82$	5.27663	+	4.41672i	0.582706	+	0.487745i
$83$	−1.39613	+	3.37055i	−0.153245	+	0.369966i	−0.981794	−	0.189951i	$-0.939167\pi$
$83$	−1.39613	+	3.37055i	−0.153245	+	0.369966i	0.828549	+	0.559917i	$0.189167\pi$
$84$	−15.8346	−	4.89674i	−1.72770	−	0.534278i
$85$	−0.615635	+	0.255004i	−0.0667750	+	0.0276591i
$86$	−3.13743	+	1.63809i	−0.338318	+	0.176639i
$87$	−5.98849	+	1.60461i	−0.642034	+	0.172032i
$88$	−0.775735	−	5.73105i	−0.0826937	−	0.610932i
$89$	−0.410138	+	1.53066i	−0.0434746	+	0.162249i	−0.984250	−	0.176780i	$-0.943432\pi$
$89$	−0.410138	+	1.53066i	−0.0434746	+	0.162249i	0.940776	+	0.339029i	$0.110099\pi$
$90$	22.2920	+	24.2682i	2.34978	+	2.55810i
$91$	0.229347	+	4.90487i	0.0240421	+	0.514170i
$92$	−0.475285	−	0.0404204i	−0.0495519	−	0.00421411i
$93$	1.43635	+	10.9102i	0.148943	+	1.13133i
$94$	0.176679	+	0.251674i	0.0182231	+	0.0259581i
$95$	−22.3279	−	12.8910i	−2.29079	−	1.32259i
$96$	−15.7661	−	8.08617i	−1.60912	−	0.825292i
$97$			15.9978i			1.62433i	0.583430	+	0.812163i	$0.301710\pi$
$97$			15.9978i			1.62433i	−0.583430	+	0.812163i	$0.698290\pi$
$98$	8.15097	+	5.61798i	0.823372	+	0.567502i
$99$	−5.32958	+	12.8667i	−0.535643	+	1.29316i
$100$	−5.69534	−	12.1367i	−0.569534	−	1.21367i
$101$	0.347175	−	2.63705i	0.0345452	−	0.262397i	−0.965453	−	0.260577i	$-0.916087\pi$
$101$	0.347175	−	2.63705i	0.0345452	−	0.262397i	0.999998	−	0.00181996i	$-0.000579310\pi$
$102$	−0.842157	+	0.187774i	−0.0833860	+	0.0185924i
$103$	−19.1477	−	5.13061i	−1.88668	−	0.505534i	−0.998982	−	0.0451038i	$-0.985638\pi$
$103$	−19.1477	−	5.13061i	−1.88668	−	0.505534i	−0.887696	−	0.460430i	$-0.847695\pi$
$104$	−0.666222	+	5.20681i	−0.0653284	+	0.510570i
$105$	−12.0609	−	25.6573i	−1.17702	−	2.50389i
$106$	13.5537	+	0.575297i	1.31646	+	0.0558778i
$107$	4.14244	−	5.39853i	0.400465	−	0.521896i	−0.548978	−	0.835837i	$-0.684983\pi$
$107$	4.14244	−	5.39853i	0.400465	−	0.521896i	0.949442	+	0.313941i	$0.101649\pi$
$108$	12.8770	+	20.1050i	1.23909	+	1.93461i
$109$	3.29786	+	4.29786i	0.315878	+	0.411660i	0.924127	−	0.382086i	$-0.124794\pi$
$109$	3.29786	+	4.29786i	0.315878	+	0.411660i	−0.608249	+	0.793746i	$0.708128\pi$
$110$	6.34950	−	7.58571i	0.605401	−	0.723269i
$111$		−	10.6502i		−	1.01087i
$112$	7.54253	+	7.42363i	0.712702	+	0.701467i
$113$			3.51306i			0.330481i	0.986253	+	0.165240i	$0.0528400\pi$
$113$			3.51306i			0.330481i	−0.986253	+	0.165240i	$0.947160\pi$
$114$	−25.5996	−	21.4278i	−2.39762	−	2.00689i
$115$	−0.496696	−	0.647306i	−0.0463171	−	0.0603616i
$116$	3.86685	+	0.847422i	0.359028	+	0.0786812i
$117$	7.69523	−	10.0286i	0.711424	−	0.927146i
$118$	0.498943	−	11.7549i	0.0459314	−	1.08212i
$119$	0.513526	+	0.0433283i	0.0470748	+	0.00397189i
$120$	−7.95082	−	29.2467i	−0.725807	−	2.66985i
$121$	−6.58681	−	1.76493i	−0.598801	−	0.160448i
$122$	−2.04200	−	9.15828i	−0.184874	−	0.829152i
$123$	−1.98932	+	15.1104i	−0.179371	+	1.36246i
$124$	2.38715	−	6.60847i	0.214372	−	0.593458i
$125$	2.22990	−	5.38346i	0.199449	−	0.481511i
$126$	−6.70193	−	24.5880i	−0.597055	−	2.19048i
$127$		−	11.0271i		−	0.978498i	−0.872144	−	0.489249i	$-0.837271\pi$
$127$		−	11.0271i		−	0.978498i	0.872144	−	0.489249i	$-0.162729\pi$
$128$	6.56774	+	9.21221i	0.580512	+	0.814252i
$129$	−6.78885	−	3.91955i	−0.597725	−	0.345097i
$130$	−7.34882	+	5.15899i	−0.644534	+	0.452474i
$131$	0.725811	+	5.51308i	0.0634144	+	0.481680i	0.993455	+	0.114224i	$0.0364380\pi$
$131$	0.725811	+	5.51308i	0.0634144	+	0.481680i	−0.930041	+	0.367457i	$0.880229\pi$
$132$	9.79241	−	8.25738i	0.852320	−	0.718712i
$133$	10.7654	+	16.7835i	0.933475	+	1.45531i
$134$	−5.87286	+	5.39461i	−0.507338	+	0.466023i
$135$	−10.5698	+	39.4472i	−0.909708	+	3.39508i
$136$	0.532675	+	0.140654i	0.0456765	+	0.0120610i
$137$	5.93465	−	1.59019i	0.507032	−	0.135859i	0.00377010	−	0.999993i	$-0.498800\pi$
$137$	5.93465	−	1.59019i	0.507032	−	0.135859i	0.503261	+	0.864134i	$0.332133\pi$
$138$	−0.488968	−	0.936523i	−0.0416237	−	0.0797221i
$139$	−17.1308	+	7.09580i	−1.45301	+	0.601858i	−0.962914	−	0.269808i	$-0.913040\pi$
$139$	−17.1308	+	7.09580i	−1.45301	+	0.601858i	−0.490100	+	0.871666i	$0.663040\pi$
$140$	−0.689808	+	18.0891i	−0.0582994	+	1.52881i
$141$	−0.260632	+	0.629221i	−0.0219492	+	0.0529900i
$142$	8.36656	−	9.99548i	0.702106	−	0.838802i
$143$	−3.28636	−	1.89738i	−0.274819	−	0.158667i
$144$	−2.50620	−	27.1292i	−0.208850	−	2.26076i
$145$	3.38561	+	5.86406i	0.281160	+	0.486983i
$146$	18.1828	−	6.64299i	1.50482	−	0.549778i
$147$	−0.820929	+	21.9106i	−0.0677091	+	1.80715i
$148$	−3.12539	+	6.03955i	−0.256905	+	0.496448i
$149$	−8.59236	−	6.59315i	−0.703913	−	0.540132i	0.193621	−	0.981076i	$-0.437977\pi$
$149$	−8.59236	−	6.59315i	−0.703913	−	0.540132i	−0.897534	+	0.440945i	$0.854643\pi$
$150$	15.9240	−	25.0627i	1.30019	−	2.04636i
$151$	−0.0158912	−	0.0593067i	−0.00129321	−	0.00482631i	0.965276	−	0.261231i	$-0.0841286\pi$
$151$	−0.0158912	−	0.0593067i	−0.00129321	−	0.00482631i	−0.966569	+	0.256405i	$0.917462\pi$
$152$	8.22893	+	19.6637i	0.667454	+	1.59494i
$153$	−0.938124	−	0.938124i	−0.0758428	−	0.0758428i
$154$	−7.05557	+	2.95816i	−0.568554	+	0.238375i
$155$	11.1038	−	4.59936i	0.891881	−	0.369429i
$156$	−10.5251	+	4.93906i	−0.842682	+	0.395441i
$157$	−2.96368	−	3.86234i	−0.236528	−	0.308249i	0.659975	−	0.751288i	$-0.270567\pi$
$157$	−2.96368	−	3.86234i	−0.236528	−	0.308249i	−0.896502	+	0.443039i	$0.853900\pi$
$158$	−13.6954	+	9.61441i	−1.08955	+	0.764881i
$159$	15.0233	+	26.0211i	1.19143	+	2.06361i
$160$	−4.07390	+	18.9185i	−0.322070	+	1.49564i
$161$	0.111495	+	0.621084i	0.00878703	+	0.0489483i
$162$	−10.1092	+	21.7482i	−0.794258	+	1.70870i
$163$	−19.6749	+	2.59025i	−1.54106	+	0.202884i	−0.852666	−	0.522456i	$-0.825016\pi$
$163$	−19.6749	+	2.59025i	−1.54106	+	0.202884i	−0.688391	+	0.725340i	$0.741683\pi$
$164$	5.56235	−	7.98503i	0.434347	−	0.623526i
$165$	21.7227	+	2.85985i	1.69111	+	0.222639i
$166$	4.92250	+	1.54550i	0.382060	+	0.119954i
$167$	10.3198	−	10.3198i	0.798573	−	0.798573i	−0.184297	−	0.982871i	$-0.559001\pi$
$167$	10.3198	−	10.3198i	0.798573	−	0.798573i	0.982871	+	0.184297i	$0.0590009\pi$
$168$	−4.91916	+	22.9178i	−0.379521	+	1.76815i
$169$	−6.75687	−	6.75687i	−0.519759	−	0.519759i
$170$	0.436153	+	0.835366i	0.0334514	+	0.0640697i
$171$	6.70011	−	50.8924i	0.512370	−	3.89184i
$172$	2.69961	+	4.21494i	0.205844	+	0.321386i
$173$	2.05924	+	15.6415i	0.156561	+	1.18920i	0.871637	+	0.490152i	$0.163059\pi$
$173$	2.05924	+	15.6415i	0.156561	+	1.18920i	−0.715076	+	0.699047i	$0.753608\pi$
$174$	3.00874	+	8.23535i	0.228092	+	0.624321i
$175$	−13.5507	+	11.4420i	−1.02434	+	0.864931i
$176$	−7.97628	+	1.80895i	−0.601235	+	0.136355i
$177$	22.5676	−	13.0294i	1.69628	−	0.979349i
$178$	2.20746	+	0.386474i	0.165456	+	0.0289675i
$179$	12.9809	−	9.96058i	0.970236	−	0.744488i	0.00342864	−	0.999994i	$-0.498909\pi$
$179$	12.9809	−	9.96058i	0.970236	−	0.744488i	0.966808	+	0.255506i	$0.0822420\pi$
$180$	31.4005	−	34.4350i	2.34045	−	2.56663i
$181$	−1.73390	−	4.18600i	−0.128880	−	0.311143i	0.846247	−	0.532790i	$-0.178857\pi$
$181$	−1.73390	−	4.18600i	−0.128880	−	0.311143i	−0.975127	+	0.221647i	$0.928857\pi$
$182$	6.88074	−	0.936018i	0.510035	−	0.0693823i
$183$	14.6954	−	14.6954i	1.08631	−	1.08631i
$184$	0.00245494	+	0.674576i	0.000180980	+	0.0497304i
$185$	−11.2356	+	3.01057i	−0.826058	+	0.221342i
$186$	15.1895	−	3.38676i	1.11375	−	0.248329i
$187$	−0.242456	+	0.315974i	−0.0177301	+	0.0231063i
$188$	0.332449	−	0.280335i	0.0242463	−	0.0204455i
$189$	21.2658	−	23.3520i	1.54686	−	1.69861i
$190$	−15.3691	+	33.0638i	−1.11499	+	2.39870i
$191$	−18.2380	+	10.5297i	−1.31965	+	0.761902i	−0.983673	−	0.179966i	$-0.942401\pi$
$191$	−18.2380	+	10.5297i	−1.31965	+	0.761902i	−0.335981	+	0.941869i	$0.609068\pi$
$192$	−9.42061	+	23.2200i	−0.679874	+	1.67576i
$193$	4.10420	−	7.10868i	0.295427	−	0.511694i	−0.679657	−	0.733530i	$-0.737872\pi$
$193$	4.10420	−	7.10868i	0.295427	−	0.511694i	0.975084	+	0.221836i	$0.0712049\pi$
$194$	22.5357	−	1.99917i	1.61797	−	0.143532i
$195$	−18.3731	−	7.61040i	−1.31573	−	0.544992i
$196$	6.89536	−	12.1842i	0.492525	−	0.870298i
$197$	−5.75586	−	13.8959i	−0.410088	−	0.990041i	−0.985114	−	0.171905i	$-0.945008\pi$
$197$	−5.75586	−	13.8959i	−0.410088	−	0.990041i	0.575025	−	0.818136i	$-0.304992\pi$
$198$	18.7911	+	5.89978i	1.33543	+	0.419279i
$199$	−0.753624	−	2.81256i	−0.0534230	−	0.199377i	0.934056	−	0.357126i	$-0.116243\pi$
$199$	−0.753624	−	2.81256i	−0.0534230	−	0.199377i	−0.987479	+	0.157748i	$0.949577\pi$
$200$	−16.3851	+	9.53959i	−1.15860	+	0.674551i
$201$	−17.0605	−	4.57134i	−1.20335	−	0.322438i
$202$	−3.75815	−	0.159517i	−0.264423	−	0.0112236i
$203$	−0.244598	−	5.23104i	−0.0171674	−	0.367147i
$204$	0.369754	+	1.16287i	0.0258880	+	0.0814169i
$205$	16.5032	−	2.17269i	1.15264	−	0.151747i
$206$	−4.83459	+	27.6142i	−0.336842	+	1.92397i
$207$	0.812233	−	1.40683i	0.0564541	−	0.0977813i
$208$	7.41799	+	0.287821i	0.514345	+	0.0199568i
$209$	−15.4097			−1.06591
$210$	−34.6357	+	20.1962i	−2.39009	+	1.39367i
$211$	−6.43362	−	2.66489i	−0.442909	−	0.183459i	0.150073	−	0.988675i	$-0.452049\pi$
$211$	−6.43362	−	2.66489i	−0.442909	−	0.183459i	−0.592981	+	0.805216i	$0.702049\pi$
$212$	−0.883343	−	19.1648i	−0.0606683	−	1.31624i
$213$	28.6235	+	3.76835i	1.96125	+	0.258203i
$214$	−8.12248	−	5.16075i	−0.555241	−	0.352782i
$215$	−2.21593	+	8.26996i	−0.151125	+	0.564007i
$216$	26.7124	−	20.6520i	1.81755	−	1.40519i
$217$	−9.26215	−	0.781485i	−0.628756	−	0.0530507i
$218$	5.64219	−	5.18272i	0.382137	−	0.351018i
$219$	34.0157	+	26.1012i	2.29857	+	1.76375i
$220$	−11.4793	−	7.99647i	−0.773936	−	0.539122i
$221$	0.286796	−	0.220066i	0.0192920	−	0.0148033i
$222$	−15.0028	+	1.33091i	−1.00692	+	0.0893251i
$223$	24.3303			1.62928			0.814639	−	0.579968i	$-0.196935\pi$
$223$	24.3303			1.62928			0.814639	+	0.579968i	$0.196935\pi$
$224$	9.51498	−	11.5527i	0.635746	−	0.771898i
$225$	45.6573			3.04382
$226$	4.94878	−	0.439012i	0.329188	−	0.0292026i
$227$	−14.2164	+	10.9087i	−0.943578	+	0.724033i	−0.961212	−	0.275812i	$-0.911053\pi$
$227$	−14.2164	+	10.9087i	−0.943578	+	0.724033i	0.0176338	+	0.999845i	$0.494387\pi$
$228$	−26.9858	+	38.7394i	−1.78718	+	2.56558i
$229$	−11.3873	−	8.73779i	−0.752495	−	0.577410i	0.159700	−	0.987166i	$-0.448947\pi$
$229$	−11.3873	−	8.73779i	−0.752495	−	0.577410i	−0.912195	+	0.409756i	$0.865614\pi$
$230$	−0.849778	+	0.780577i	−0.0560327	+	0.0514697i
$231$	−13.9105	−	9.67628i	−0.915243	−	0.636652i
$232$	0.710524	−	5.55305i	0.0466482	−	0.364576i
$233$	3.00503	−	11.2149i	0.196866	−	0.734715i	−0.794909	−	0.606728i	$-0.792482\pi$
$233$	3.00503	−	11.2149i	0.196866	−	0.734715i	0.991776	−	0.127987i	$-0.0408516\pi$
$234$	−15.0888	−	9.58690i	−0.986384	−	0.626715i
$235$	0.737480	+	0.0970911i	0.0481079	+	0.00633352i
$236$	−16.6212	+	0.766105i	−1.08195	+	0.0498692i
$237$	−34.2405	−	14.1829i	−2.22416	−	0.921278i
$238$	−0.00313740	−	0.728809i	−0.000203368	−	0.0472416i
$239$	11.3929			0.736945			0.368472	−	0.929639i	$-0.379881\pi$
$239$	11.3929			0.736945			0.368472	+	0.929639i	$0.379881\pi$
$240$	−40.2057	+	14.8550i	−2.59527	+	0.958886i
$241$	−4.47218	+	7.74605i	−0.288079	+	0.498967i	−0.973351	−	0.229320i	$-0.926350\pi$
$241$	−4.47218	+	7.74605i	−0.288079	+	0.498967i	0.685272	+	0.728287i	$0.259683\pi$
$242$	−1.66310	+	9.49927i	−0.106908	+	0.610636i
$243$	−17.1578	+	2.25886i	−1.10067	+	0.144906i
$244$	−12.6459	+	4.02100i	−0.809572	+	0.257418i
$245$	23.3469	−	5.32756i	1.49158	−	0.340365i
$246$	21.5343	+	0.914036i	1.37298	+	0.0582768i
$247$	13.5101	+	3.62003i	0.859629	+	0.230337i
$248$	−9.60754	−	2.53690i	−0.610080	−	0.161093i
$249$	2.95762	+	11.0380i	0.187432	+	0.699504i
$250$	−7.86224	−	2.46847i	−0.497252	−	0.156120i
$251$	−1.17069	−	2.82630i	−0.0738933	−	0.178394i	0.882617	−	0.470093i	$-0.155780\pi$
$251$	−1.17069	−	2.82630i	−0.0738933	−	0.178394i	−0.956510	+	0.291699i	$0.905780\pi$
$252$	−33.7992	+	12.5135i	−2.12915	+	0.788279i
$253$	−0.450543	−	0.186621i	−0.0283254	−	0.0117328i
$254$	−15.5337	+	1.37801i	−0.974671	+	0.0864642i
$255$	−1.04361	+	1.80758i	−0.0653534	+	0.113195i
$256$	12.1563	−	10.4031i	0.759770	−	0.650191i
$257$	9.02303	−	5.20945i	0.562841	−	0.324956i	−0.191444	−	0.981504i	$-0.561317\pi$
$257$	9.02303	−	5.20945i	0.562841	−	0.324956i	0.754285	+	0.656547i	$0.227984\pi$
$258$	−4.67302	+	10.0531i	−0.290929	+	0.625881i
$259$	8.78870	+	1.91992i	0.546103	+	0.119298i
$260$	8.18573	+	9.70744i	0.507657	+	0.602030i
$261$	−8.20695	+	10.6955i	−0.507998	+	0.662035i
$262$	7.67547	−	1.71138i	0.474192	−	0.105730i
$263$	16.3420	−	4.37882i	1.00769	−	0.270010i	0.283026	−	0.959112i	$-0.408662\pi$
$263$	16.3420	−	4.37882i	1.00769	−	0.270010i	0.724664	+	0.689102i	$0.241995\pi$
$264$	−12.8557	−	12.7625i	−0.791215	−	0.785477i
$265$	23.2046	−	23.2046i	1.42545	−	1.42545i
$266$	22.2973	−	17.2623i	1.36714	−	1.05842i
$267$	1.89948	+	4.58574i	0.116246	+	0.280643i
$268$	8.33319	+	7.59885i	0.509031	+	0.464174i
$269$	13.3782	−	10.2654i	0.815683	−	0.625895i	−0.114322	−	0.993444i	$-0.536469\pi$
$269$	13.3782	−	10.2654i	0.815683	−	0.625895i	0.930004	+	0.367549i	$0.119803\pi$
$270$	56.8894	+	9.96000i	3.46218	+	0.606146i
$271$	12.9189	−	7.45872i	0.784766	−	0.453085i	−0.0533505	−	0.998576i	$-0.516990\pi$
$271$	12.9189	−	7.45872i	0.784766	−	0.453085i	0.838117	+	0.545491i	$0.183657\pi$
$272$	0.131571	−	0.767947i	0.00797766	−	0.0465636i
$273$	9.92259	+	11.7513i	0.600542	+	0.711221i
$274$	−2.98169	−	8.16132i	−0.180131	−	0.493043i
$275$	−1.78903	−	13.5890i	−0.107883	−	0.819450i
$276$	−1.25816	+	0.805833i	−0.0757322	+	0.0485055i
$277$	−0.244478	+	1.85700i	−0.0146893	+	0.111576i	−0.997219	−	0.0745313i	$-0.976254\pi$
$277$	−0.244478	+	1.85700i	−0.0146893	+	0.111576i	0.982529	+	0.186107i	$0.0595873\pi$
$278$	12.1365	+	23.2451i	0.727898	+	1.39415i
$279$	16.9204	+	16.9204i	1.01300	+	1.01300i
$280$	25.5680	−	1.28880i	1.52798	−	0.0770207i
$281$	−21.3597	+	21.3597i	−1.27421	+	1.27421i	−0.330358	+	0.943856i	$0.607169\pi$
$281$	−21.3597	+	21.3597i	−1.27421	+	1.27421i	−0.943856	+	0.330358i	$0.892831\pi$
$282$	0.918942	+	0.288516i	0.0547222	+	0.0171809i
$283$	18.7402	+	2.46720i	1.11399	+	0.146660i	0.664976	−	0.746865i	$-0.268442\pi$
$283$	18.7402	+	2.46720i	1.11399	+	0.146660i	0.449015	+	0.893524i	$0.351775\pi$
$284$	−15.1260	−	10.5367i	−0.897562	−	0.625240i
$285$	−80.0656	+	10.5408i	−4.74267	+	0.624385i
$286$	−2.26212	+	4.86654i	−0.133762	+	0.287765i
$287$	−12.1106	−	4.36556i	−0.714869	−	0.257691i
$288$	−37.9031	+	6.92065i	−2.23346	+	0.407803i
$289$	8.48103	+	14.6896i	0.498884	+	0.864093i
$290$	7.83750	−	5.50206i	0.460234	−	0.323092i
$291$	30.5047	+	39.7545i	1.78822	+	2.33045i
$292$	−11.6301	−	24.7837i	−0.680600	−	1.45035i
$293$	−19.9130	+	8.24822i	−1.16333	+	0.481866i	−0.878981	−	0.476856i	$-0.841776\pi$
$293$	−19.9130	+	8.24822i	−1.16333	+	0.481866i	−0.284346	+	0.958722i	$0.591776\pi$
$294$	30.9676	−	1.58164i	1.80607	−	0.0922433i
$295$	−20.1249	−	20.1249i	−1.17172	−	1.17172i
$296$	8.89836	+	3.64794i	0.517207	+	0.212032i
$297$	6.31751	+	23.5773i	0.366579	+	1.36809i
$298$	−8.21389	+	12.9278i	−0.475818	+	0.748888i
$299$	0.351163	+	0.269457i	0.0203083	+	0.0155831i
$300$	−37.2954	−	19.2999i	−2.15325	−	1.11428i
$301$	4.45829	−	4.89567i	0.256971	−	0.282182i
$302$	−0.0815584	+	0.0297969i	−0.00469316	+	0.00171462i
$303$	−4.16563	−	7.21508i	−0.239309	−	0.414496i
$304$	26.6715	−	14.0492i	1.52972	−	0.805779i
$305$	−19.6571	−	11.3490i	−1.12556	−	0.649844i
$306$	−1.20428	+	1.43875i	−0.0688443	+	0.0822479i
$307$	4.44124	−	10.7221i	0.253475	−	0.611943i	−0.745005	−	0.667059i	$-0.767553\pi$
$307$	4.44124	−	10.7221i	0.253475	−	0.611943i	0.998480	+	0.0551162i	$0.0175529\pi$
$308$	5.04881	+	9.56938i	0.287683	+	0.545266i
$309$	−57.3652	+	23.7614i	−3.26339	+	1.35174i
$310$	−7.86663	−	15.0670i	−0.446794	−	0.855748i
$311$	−8.82225	+	2.36391i	−0.500264	+	0.134045i	−0.500122	−	0.865955i	$-0.666712\pi$
$311$	−8.82225	+	2.36391i	−0.500264	+	0.134045i	−0.000141327		1.00000i	$0.500045\pi$
$312$	8.27284	+	14.2093i	0.468357	+	0.804443i
$313$	4.01196	−	14.9729i	0.226770	−	0.846316i	−0.754918	−	0.655819i	$-0.772323\pi$
$313$	4.01196	−	14.9729i	0.226770	−	0.846316i	0.981688	−	0.190497i	$-0.0610098\pi$
$314$	−5.07046	+	4.65754i	−0.286142	+	0.262840i
$315$	−54.7709	−	28.2971i	−3.08599	−	1.59436i
$316$	15.2551	+	18.0910i	0.858166	+	1.01770i
$317$	0.243513	+	1.84967i	0.0136771	+	0.103888i	0.996922	−	0.0784031i	$-0.0249821\pi$
$317$	0.243513	+	1.84967i	0.0136771	+	0.103888i	−0.983245	+	0.182291i	$0.941649\pi$
$318$	34.7781	−	24.4148i	1.95026	−	1.36911i
$319$	3.50490	+	2.02355i	0.196237	+	0.113297i
$320$	27.1592	+	3.37467i	1.51825	+	0.188650i
$321$		−	21.3142i		−	1.18964i
$322$	0.860977	−	0.234675i	0.0479804	−	0.0130779i
$323$	0.561766	−	1.35622i	0.0312575	−	0.0754623i
$324$	31.8996	+	11.5229i	1.77220	+	0.640163i
$325$	−1.62383	+	12.3342i	−0.0900737	+	0.684177i
$326$	6.10753	+	27.3920i	0.338265	+	1.51710i
$327$	16.3904	+	4.39179i	0.906391	+	0.242867i
$328$	−11.9435	−	6.83773i	−0.659467	−	0.377550i
$329$	−0.472257	−	0.328506i	−0.0260363	−	0.0181111i
$330$	1.31402	−	30.9578i	0.0723346	−	1.70417i
$331$	10.3779	−	13.5248i	0.570423	−	0.743390i	−0.415683	−	0.909510i	$-0.636457\pi$
$331$	10.3779	−	13.5248i	0.570423	−	0.743390i	0.986106	+	0.166120i	$0.0531240\pi$
$332$	1.56197	−	7.12737i	0.0857242	−	0.391165i
$333$	−14.0983	−	18.3733i	−0.772583	−	1.00685i
$334$	−15.8270	−	13.2477i	−0.866015	−	0.724884i
$335$			19.2904i			1.05395i
$336$	32.8987	+	4.06559i	1.79477	+	0.221796i
$337$			21.1213i			1.15055i	0.817960	+	0.575275i	$0.195105\pi$
$337$			21.1213i			1.15055i	−0.817960	+	0.575275i	$0.804895\pi$
$338$	−8.67390	+	10.3627i	−0.471798	+	0.563654i
$339$	6.69873	+	8.72996i	0.363825	+	0.474146i
$340$	1.12226	−	0.718793i	0.0608631	−	0.0389820i
$341$	4.37302	−	5.69904i	0.236813	−	0.308620i
$342$	−72.5284	−	3.07851i	−3.92189	−	0.166467i
$343$	−17.9329	−	4.62727i	−0.968285	−	0.249849i
$344$	5.60015	−	4.32962i	0.301940	−	0.233437i
$345$	−2.46858	−	0.661454i	−0.132904	−	0.0356115i
$346$	21.7765	−	4.85546i	1.17071	−	0.261031i
$347$	2.89518	−	21.9911i	0.155422	−	1.18054i	−0.718871	−	0.695144i	$-0.755341\pi$
$347$	2.89518	−	21.9911i	0.155422	−	1.18054i	0.874292	−	0.485400i	$-0.161326\pi$
$348$	11.2250	−	5.26750i	0.601723	−	0.282367i
$349$	11.1334	−	26.8783i	0.595955	−	1.43876i	−0.281715	−	0.959498i	$-0.590903\pi$
$349$	11.1334	−	26.8783i	0.595955	−	1.43876i	0.877670	−	0.479265i	$-0.159097\pi$
$350$	17.8115	+	17.6588i	0.952062	+	0.943901i
$351$		−	22.1550i		−	1.18255i
$352$	3.54499	+	11.0100i	0.188949	+	0.586834i
$353$	17.1120	+	9.87963i	0.910781	+	0.525840i	0.880682	−	0.473707i	$-0.157084\pi$
$353$	17.1120	+	9.87963i	0.910781	+	0.525840i	0.0300987	+	0.999547i	$0.490418\pi$
$354$	−21.1744	−	30.1623i	−1.12541	−	1.60311i
$355$	−4.11571	−	31.2619i	−0.218439	−	1.65921i
$356$	0.268562	−	3.15791i	0.0142338	−	0.167369i
$357$	1.35873	−	0.871525i	0.0719117	−	0.0461260i
$358$	−15.6534	−	17.0412i	−0.827310	−	0.900655i
$359$	−1.44986	+	5.41096i	−0.0765209	+	0.285580i	−0.993574	−	0.113186i	$-0.963895\pi$
$359$	−1.44986	+	5.41096i	−0.0765209	+	0.285580i	0.917053	+	0.398765i	$0.130561\pi$
$360$	−52.4319	−	39.9301i	−2.76340	−	2.10450i
$361$	36.5091	−	9.78258i	1.92153	−	0.514873i
$362$	−5.68007	+	2.96562i	−0.298538	+	0.155869i
$363$	−19.7336	+	8.17393i	−1.03575	+	0.429020i
$364$	−2.17841	−	9.57581i	−0.114180	−	0.501909i
$365$	17.9203	−	43.2635i	0.937994	−	2.26452i
$366$	−22.5375	−	18.8647i	−1.17805	−	0.986071i
$367$	−12.0577	−	6.96154i	−0.629409	−	0.363389i	0.151114	−	0.988516i	$-0.451714\pi$
$367$	−12.0577	−	6.96154i	−0.629409	−	0.363389i	−0.780523	+	0.625127i	$0.785047\pi$
$368$	0.949956	−	0.0877572i	0.0495199	−	0.00457466i
$369$	16.5706	+	28.7011i	0.862630	+	1.49412i
$370$	5.64500	+	15.4512i	0.293470	+	0.803268i
$371$	−24.1812	+	7.70658i	−1.25543	+	0.400106i
$372$	−6.66903	−	20.9739i	−0.345773	−	1.08745i
$373$	−1.44361	−	1.10772i	−0.0747473	−	0.0573556i	0.570712	−	0.821150i	$-0.306667\pi$
$373$	−1.44361	−	1.10772i	−0.0747473	−	0.0573556i	−0.645459	+	0.763795i	$0.723334\pi$
$374$	0.475406	+	0.302057i	0.0245826	+	0.0156190i
$375$	−4.72392	−	17.6299i	−0.243942	−	0.910405i
$376$	−0.436448	−	0.433282i	−0.0225081	−	0.0223448i
$377$	−2.59747	−	2.59747i	−0.133777	−	0.133777i
$378$	−35.5531	−	27.0385i	−1.82865	−	1.39071i
$379$	−12.4823	+	5.17035i	−0.641174	+	0.265583i	−0.679492	−	0.733683i	$-0.737800\pi$
$379$	−12.4823	+	5.17035i	−0.641174	+	0.265583i	0.0383184	+	0.999266i	$0.487800\pi$
$380$	48.4970	+	17.5183i	2.48784	+	0.898671i
$381$	−21.0266	−	27.4024i	−1.07723	−	1.40387i
$382$	17.1121	+	24.3756i	0.875532	+	1.24717i
$383$	5.49456	+	9.51685i	0.280759	+	0.486288i	0.971572	−	0.236745i	$-0.0760806\pi$
$383$	5.49456	+	9.51685i	0.280759	+	0.486288i	−0.690813	+	0.723033i	$0.742747\pi$
$384$	33.8868	+	10.3689i	1.72928	+	0.529138i
$385$	−6.27595	+	17.4103i	−0.319852	+	0.887313i
$386$	−10.5267	−	4.89316i	−0.535797	−	0.249056i
$387$	−16.9003	+	2.22497i	−0.859093	+	0.113102i
$388$	−5.63239	−	31.4959i	−0.285941	−	1.59896i
$389$	−14.9419	−	1.96714i	−0.757585	−	0.0997379i	−0.258168	−	0.966100i	$-0.583119\pi$
$389$	−14.9419	−	1.96714i	−0.757585	−	0.0997379i	−0.499416	+	0.866362i	$0.666452\pi$
$390$	−8.42461	+	26.8329i	−0.426597	+	1.35874i
$391$	0.0328494	−	0.0328494i	0.00166127	−	0.00166127i
$392$	−18.0253	−	8.19076i	−0.910415	−	0.413696i
$393$	12.3160	+	12.3160i	0.621262	+	0.621262i
$394$	−18.8556	+	9.84469i	−0.949931	+	0.495968i
$395$	−5.28344	+	40.1317i	−0.265839	+	2.01925i
$396$	5.96265	−	27.2080i	0.299635	−	1.36725i
$397$	1.41849	+	10.7745i	0.0711922	+	0.540758i	0.989461	+	0.144800i	$0.0462540\pi$
$397$	1.41849	+	10.7745i	0.0711922	+	0.540758i	−0.918269	+	0.395958i	$0.870413\pi$
$398$	−3.86783	+	1.41309i	−0.193877	+	0.0708318i
$399$	58.7549	+	21.1795i	2.94142	+	1.06030i
$400$	15.4858	+	21.8892i	0.774291	+	1.09446i
$401$	−6.71494	+	3.87687i	−0.335328	+	0.193602i	−0.658204	−	0.752839i	$-0.728684\pi$
$401$	−6.71494	+	3.87687i	−0.335328	+	0.193602i	0.322876	+	0.946441i	$0.395350\pi$
$402$	−4.30759	+	24.6041i	−0.214843	+	1.22714i
$403$	−5.17277	+	3.96920i	−0.257674	+	0.197720i
$404$	0.244931	+	5.31397i	0.0121858	+	0.264380i
$405$	22.2014	+	53.5990i	1.10320	+	2.66336i
$406$	−7.33830	+	0.998262i	−0.364194	+	0.0495429i
$407$	−4.91604	+	4.91604i	−0.243679	+	0.243679i
$408$	1.59190	−	0.666185i	0.0788109	−	0.0329811i
$409$	18.8128	−	5.04087i	0.930232	−	0.249255i	0.238279	−	0.971197i	$-0.423417\pi$
$409$	18.8128	−	5.04087i	0.930232	−	0.249255i	0.691954	+	0.721942i	$0.256750\pi$
$410$	−5.12297	−	22.9763i	−0.253005	−	1.13472i
$411$	11.7154	−	15.2679i	0.577881	−	0.753109i
$412$	39.5037	+	3.35957i	1.94621	+	0.165514i
$413$	6.68375	+	20.9719i	0.328886	+	1.03196i
$414$	−2.08327	−	0.968372i	−0.102387	−	0.0475929i
$415$	10.8086	−	6.24037i	0.530575	−	0.306327i
$416$	−0.521547	−	10.4856i	−0.0255709	−	0.514097i
$417$	−29.0397	+	50.2982i	−1.42208	+	2.46311i
$418$	1.92568	+	21.7074i	0.0941883	+	1.06174i
$419$	−20.2892	−	8.40406i	−0.991192	−	0.410565i	−0.172632	−	0.984986i	$-0.555227\pi$
$419$	−20.2892	−	8.40406i	−0.991192	−	0.410565i	−0.818560	+	0.574421i	$0.805227\pi$
$420$	32.7784	+	46.2669i	1.59942	+	2.25759i
$421$	1.26152	+	3.04559i	0.0614830	+	0.148433i	0.951635	−	0.307230i	$-0.0994022\pi$
$421$	1.26152	+	3.04559i	0.0614830	+	0.148433i	−0.890152	+	0.455663i	$0.849402\pi$
$422$	−2.95000	+	9.39595i	−0.143604	+	0.457388i
$423$	0.383306	+	1.43052i	0.0186370	+	0.0695541i
$424$	−26.8867	+	3.63929i	−1.30573	+	0.176740i
$425$	1.26121	+	0.337939i	0.0611775	+	0.0163925i
$426$	1.73145	−	40.7923i	0.0838892	−	1.97639i
$427$	9.47765	+	14.7759i	0.458656	+	0.715057i
$428$	−6.25482	+	12.0869i	−0.302338	+	0.584243i
$429$	−11.7846	+	1.55147i	−0.568964	+	0.0749055i
$430$	11.9267	+	2.08808i	0.575154	+	0.100696i
$431$	−3.87691	+	6.71501i	−0.186744	+	0.323451i	−0.944163	−	0.329479i	$-0.893127\pi$
$431$	−3.87691	+	6.71501i	−0.186744	+	0.323451i	0.757419	+	0.652930i	$0.226460\pi$
$432$	−32.4302	−	35.0484i	−1.56030	−	1.68627i
$433$	−11.4499			−0.550249			−0.275125	−	0.961409i	$-0.588719\pi$
$433$	−11.4499			−0.550249			−0.275125	+	0.961409i	$0.588719\pi$
$434$	0.0565874	+	13.1451i	0.00271628	+	0.630984i
$435$	19.5949	+	8.11648i	0.939504	+	0.389155i
$436$	−8.00588	−	7.30039i	−0.383412	−	0.349625i
$437$	1.78205	+	0.234611i	0.0852471	+	0.0112230i
$438$	32.5174	−	51.1790i	1.55374	−	2.44543i
$439$	6.70938	−	25.0397i	0.320221	−	1.19508i	−0.598808	−	0.800892i	$-0.704359\pi$
$439$	6.70938	−	25.0397i	0.320221	−	1.19508i	0.919029	−	0.394189i	$-0.128975\pi$
$440$	−9.82996	+	17.1700i	−0.468625	+	0.818547i
$441$	27.5880	+	38.8858i	1.31372	+	1.85171i
$442$	−0.345843	−	0.376504i	−0.0164501	−	0.0179084i
$443$	−15.9559	−	12.2434i	−0.758085	−	0.581699i	0.155744	−	0.987797i	$-0.450222\pi$
$443$	−15.9559	−	12.2434i	−0.758085	−	0.581699i	−0.913830	+	0.406098i	$0.866889\pi$
$444$	3.74967	+	20.9678i	0.177951	+	0.995088i
$445$	4.30086	−	3.30016i	0.203880	−	0.156443i
$446$	−3.04046	−	34.2737i	−0.143970	−	1.62291i
$447$	−33.9239			−1.60455
$448$	−17.4631	−	11.9599i	−0.825056	−	0.565051i
$449$	−26.1862			−1.23580			−0.617902	−	0.786255i	$-0.712017\pi$
$449$	−26.1862			−1.23580			−0.617902	+	0.786255i	$0.712017\pi$
$450$	−5.70560	−	64.3166i	−0.268965	−	3.03191i
$451$	7.89304	−	6.05654i	0.371669	−	0.285191i
$452$	−1.23686	−	6.91639i	−0.0581768	−	0.325320i
$453$	−0.152576	−	0.117076i	−0.00716866	−	0.00550071i
$454$	17.1434	+	18.6632i	0.804579	+	0.875908i
$455$	9.59232	−	13.7898i	0.449695	−	0.646476i
$456$	57.9438	+	33.1733i	2.71347	+	1.55348i
$457$	−3.56542	+	13.3063i	−0.166783	+	0.622444i	0.831023	+	0.556239i	$0.187756\pi$
$457$	−3.56542	+	13.3063i	−0.166783	+	0.622444i	−0.997806	+	0.0662056i	$0.978911\pi$
$458$	−10.8857	+	17.1330i	−0.508657	+	0.800573i
$459$	−2.30537	−	0.303508i	−0.107605	−	0.0141665i
$460$	1.20578	+	1.09952i	0.0562197	+	0.0512655i
$461$	9.48431	+	3.92853i	0.441728	+	0.182970i	0.592451	−	0.805606i	$-0.298160\pi$
$461$	9.48431	+	3.92853i	0.441728	+	0.182970i	−0.150723	+	0.988576i	$0.548160\pi$
$462$	−11.8925	+	20.8047i	−0.553287	+	0.967920i
$463$	−9.01476			−0.418952			−0.209476	−	0.977814i	$-0.567176\pi$
$463$	−9.01476			−0.418952			−0.209476	+	0.977814i	$0.567176\pi$
$464$	−7.91128	−	0.306961i	−0.367272	−	0.0142503i
$465$	18.8229	−	32.6023i	0.872893	−	1.51190i
$466$	−16.1738	−	2.83165i	−0.749237	−	0.131174i
$467$	−8.79254	+	1.15756i	−0.406870	+	0.0535655i	−0.331184	−	0.943566i	$-0.607448\pi$
$467$	−8.79254	+	1.15756i	−0.406870	+	0.0535655i	−0.0756862	+	0.997132i	$0.524115\pi$
$468$	−11.6193	+	22.4533i	−0.537102	+	1.03790i
$469$	6.84783	−	13.2544i	0.316203	−	0.612034i
$470$	0.0446107	−	1.05101i	0.00205774	−	0.0484794i
$471$	−14.7295	−	3.94676i	−0.678700	−	0.181857i
$472$	3.15628	+	23.3183i	0.145280	+	1.07331i
$473$	1.32444	+	4.94289i	0.0608979	+	0.227274i
$474$	−15.7003	+	50.0064i	−0.721138	+	2.29687i
$475$	19.3326	+	46.6731i	0.887042	+	2.14151i
$476$	−1.02627	+	0.0954957i	−0.0470389	+	0.00437704i
$477$	60.3632	+	25.0032i	2.76384	+	1.14482i
$478$	−1.42372	−	16.0490i	−0.0651195	−	0.734062i
$479$	2.80856	−	4.86457i	0.128326	−	0.222268i	−0.794702	−	0.607000i	$-0.792373\pi$
$479$	2.80856	−	4.86457i	0.128326	−	0.222268i	0.923028	+	0.384732i	$0.125706\pi$
$480$	25.9503	+	54.7807i	1.18446	+	2.50038i
$481$	5.46490	−	3.15516i	0.249178	−	0.143863i
$482$	11.4706	+	5.33189i	0.522471	+	0.242861i
$483$	1.46135	+	1.33080i	0.0664940	+	0.0605533i
$484$	13.5893	+	1.15569i	0.617694	+	0.0525315i
$485$	33.3166	−	43.4190i	1.51283	−	1.97156i
$486$	5.32615	+	23.8875i	0.241599	+	1.08356i
$487$	11.9215	−	3.19437i	0.540217	−	0.144751i	0.0216147	−	0.999766i	$-0.493119\pi$
$487$	11.9215	−	3.19437i	0.540217	−	0.144751i	0.518602	+	0.855016i	$0.326453\pi$
$488$	7.24462	+	17.3116i	0.327948	+	0.783659i
$489$	−43.9531	+	43.9531i	−1.98763	+	1.98763i
$490$	−10.4224	−	32.2226i	−0.470836	−	1.45567i
$491$	−10.7179	−	25.8753i	−0.483692	−	1.16773i	−0.957843	−	0.287292i	$-0.907245\pi$
$491$	−10.7179	−	25.8753i	−0.483692	−	1.16773i	0.474151	−	0.880443i	$-0.342755\pi$
$492$	−1.40346	−	30.4492i	−0.0632730	−	1.37275i
$493$	−0.305868	+	0.234700i	−0.0137756	+	0.0105704i
$494$	3.41116	−	19.4838i	0.153475	−	0.876620i
$495$	41.2608	−	23.8220i	1.85454	−	1.07072i
$496$	−2.37306	+	13.8510i	−0.106554	+	0.621928i
$497$	−8.26965	+	22.9411i	−0.370944	+	1.02905i
$498$	15.1794	−	5.54571i	0.680206	−	0.248509i
$499$	1.71413	+	13.0201i	0.0767350	+	0.582860i	0.986013	+	0.166670i	$0.0533016\pi$
$499$	1.71413	+	13.0201i	0.0767350	+	0.582860i	−0.909278	+	0.416190i	$0.863365\pi$
$500$	−2.49478	+	11.3839i	−0.111570	+	0.509102i
$501$	5.96686	−	45.3228i	0.266580	−	2.02487i
$502$	−3.83506	+	2.00232i	−0.171167	+	0.0893679i
$503$	18.1004	+	18.1004i	0.807058	+	0.807058i	0.984188	−	0.177129i	$-0.0566811\pi$
$503$	18.1004	+	18.1004i	0.807058	+	0.807058i	−0.177129	+	0.984188i	$0.556681\pi$
$504$	21.8513	+	46.0486i	0.973336	+	2.05117i
$505$	−6.43412	+	6.43412i	−0.286315	+	0.286315i
$506$	−0.206587	+	0.657992i	−0.00918391	+	0.0292513i
$507$	−29.6749	−	3.90678i	−1.31791	−	0.173506i
$508$	3.88236	+	21.7098i	0.172252	+	0.963218i
$509$	3.10757	−	0.409120i	0.137741	−	0.0181339i	−0.0613405	−	0.998117i	$-0.519538\pi$
$509$	3.10757	−	0.409120i	0.137741	−	0.0181339i	0.199081	+	0.979983i	$0.436204\pi$
$510$	2.67673	+	1.24423i	0.118527	+	0.0550953i
$511$	−27.6710	+	23.3649i	−1.22409	+	1.03360i
$512$	−16.1737	−	15.8244i	−0.714784	−	0.699345i
$513$	−44.9833	−	77.9133i	−1.98606	−	3.43996i
$514$	−8.46602	−	12.0596i	−0.373420	−	0.531925i
$515$	41.2833	+	53.8014i	1.81916	+	2.37077i
$516$	14.7456	+	5.32650i	0.649141	+	0.234486i
$517$	0.410747	−	0.170137i	0.0180646	−	0.00748261i
$518$	1.60627	−	12.6204i	0.0705754	−	0.554508i
$519$	34.9425	+	34.9425i	1.53381	+	1.53381i
$520$	12.6518	−	12.7442i	0.554816	−	0.558869i
$521$	1.67288	+	6.24328i	0.0732903	+	0.273523i	0.992840	−	0.119450i	$-0.0381131\pi$
$521$	1.67288	+	6.24328i	0.0732903	+	0.273523i	−0.919550	+	0.392973i	$0.871446\pi$
$522$	16.0922	+	10.2244i	0.704334	+	0.447510i
$523$	3.72391	+	2.85746i	0.162835	+	0.124948i	0.686965	−	0.726691i	$-0.258943\pi$
$523$	3.72391	+	2.85746i	0.162835	+	0.124948i	−0.524130	+	0.851639i	$0.675609\pi$
$524$	−3.36996	−	10.5984i	−0.147218	−	0.462995i
$525$	−11.8559	+	54.2719i	−0.517433	+	2.36862i
$526$	−8.21056	−	22.4735i	−0.357997	−	0.979890i
$527$	0.342158	+	0.592635i	0.0149046	+	0.0258156i
$528$	−16.3718	+	19.7045i	−0.712490	+	0.857528i
$529$	−19.8693	−	11.4716i	−0.863884	−	0.498763i
$530$	−35.5877	−	29.7881i	−1.54583	−	1.29391i
$531$	21.6848	−	52.3517i	0.941039	−	2.27187i
$532$	−27.1035	−	29.2526i	−1.17509	−	1.26826i
$533$	−8.34285	+	3.45572i	−0.361369	+	0.149684i
$534$	6.22248	−	3.24882i	0.269273	−	0.140590i
$535$	−22.4857	+	6.02504i	−0.972144	+	0.260485i
$536$	9.66300	−	12.6884i	0.417378	−	0.548056i
$537$	13.2646	−	49.5041i	0.572409	−	2.13626i
$538$	−16.1326	−	17.5628i	−0.695524	−	0.757185i
$539$	10.4926	−	9.73477i	0.451950	−	0.419306i
$540$	6.92124	−	81.3837i	0.297843	−	3.50220i
$541$	2.85960	+	21.7208i	0.122944	+	0.933852i	0.936082	+	0.351781i	$0.114424\pi$
$541$	2.85960	+	21.7208i	0.122944	+	0.933852i	−0.813138	+	0.582071i	$0.802243\pi$
$542$	−12.1214	−	17.2665i	−0.520658	−	0.741660i
$543$	−12.2907	−	7.09601i	−0.527443	−	0.304519i
$544$	−1.09823	−	0.0893744i	−0.0470864	−	0.00383190i
$545$		−	18.5327i		−	0.793855i
$546$	15.3139	−	15.4463i	0.655373	−	0.661040i
$547$	5.04442	−	12.1783i	0.215684	−	0.520707i	−0.778595	−	0.627527i	$-0.784067\pi$
$547$	5.04442	−	12.1783i	0.215684	−	0.520707i	0.994278	+	0.106821i	$0.0340671\pi$
$548$	−11.1241	+	5.22014i	−0.475197	+	0.222993i
$549$	5.89867	−	44.8048i	0.251749	−	1.91222i
$550$	−18.9191	+	4.21834i	−0.806712	+	0.179871i
$551$	−14.4085	−	3.86075i	−0.613824	−	0.164474i
$552$	1.29239	+	1.67164i	0.0550077	+	0.0711499i
$553$	17.8765	−	25.6990i	0.760184	−	1.09283i
$554$	2.64647	+	0.112331i	0.112438	+	0.00477249i
$555$	−22.1799	+	28.9054i	−0.941485	+	1.22697i
$556$	31.2283	−	20.0013i	1.32437	−	0.848243i
$557$	15.0816	+	19.6547i	0.639026	+	0.832795i	0.994808	−	0.101774i	$-0.0324519\pi$
$557$	15.0816	+	19.6547i	0.639026	+	0.832795i	−0.355781	+	0.934569i	$0.615785\pi$
$558$	21.7209	−	25.9499i	0.919520	−	1.09855i
$559$		−	4.64471i		−	0.196450i
$560$	−5.01064	−	35.8561i	−0.211738	−	1.51520i
$561$			1.24751i			0.0526701i
$562$	32.7583	+	27.4198i	1.38182	+	1.15663i
$563$	−18.8149	−	24.5201i	−0.792954	−	1.03340i	−0.998500	−	0.0547503i	$-0.982564\pi$
$563$	−18.8149	−	24.5201i	−0.792954	−	1.03340i	0.205546	−	0.978647i	$-0.434103\pi$
$564$	0.291591	−	1.33055i	0.0122782	−	0.0560263i
$565$	7.31622	−	9.53468i	0.307796	−	0.401127i
$566$	1.13361	−	26.7073i	0.0476492	−	1.12259i
$567$	3.77229	−	44.7091i	0.158421	−	1.87761i
$568$	−12.9527	+	22.6244i	−0.543482	+	0.949300i
$569$	−29.8787	−	8.00596i	−1.25258	−	0.335627i	−0.429247	−	0.903187i	$-0.641221\pi$
$569$	−29.8787	−	8.00596i	−1.25258	−	0.335627i	−0.823332	+	0.567560i	$0.807888\pi$
$570$	24.8541	+	111.470i	1.04102	+	4.66895i
$571$	−4.31154	+	32.7494i	−0.180432	+	1.37052i	0.626291	+	0.779589i	$0.284572\pi$
$571$	−4.31154	+	32.7494i	−0.180432	+	1.37052i	−0.806723	+	0.590930i	$0.798761\pi$
$572$	7.13810	+	2.57846i	0.298459	+	0.107811i
$573$	−25.2433	+	60.9427i	−1.05455	+	2.54592i
$574$	−4.63626	+	17.6056i	−0.193514	+	0.734843i
$575$			1.59874i			0.0666721i
$576$	14.4856	+	52.5286i	0.603566	+	2.18869i
$577$	24.7620	+	14.2964i	1.03086	+	0.595165i	0.917230	−	0.398358i	$-0.130420\pi$
$577$	24.7620	+	14.2964i	1.03086	+	0.595165i	0.113626	+	0.993524i	$0.463753\pi$
$578$	19.6331	−	13.7828i	0.816629	−	0.573287i
$579$	−3.35596	−	25.4910i	−0.139469	−	1.05937i
$580$	−8.73007	−	10.3530i	−0.362496	−	0.429884i
$581$	−9.64185	+	0.450844i	−0.400012	+	0.0187041i
$582$	52.1894	−	47.9393i	2.16332	−	1.98715i
$583$	5.07648	−	18.9457i	0.210246	−	0.784650i
$584$	−33.4589	+	19.4802i	−1.38454	+	0.806097i
$585$	−41.7708	+	11.1924i	−1.72701	+	0.462751i
$586$	14.1075	+	27.0203i	0.582777	+	1.11620i
$587$	41.5584	−	17.2140i	1.71530	−	0.710500i	0.715367	−	0.698749i	$-0.246259\pi$
$587$	41.5584	−	17.2140i	1.71530	−	0.710500i	0.999931	−	0.0117512i	$-0.00374060\pi$
$588$	−6.09792	−	43.4258i	−0.251474	−	1.79085i
$589$	−10.1322	+	24.4614i	−0.417492	+	1.00791i
$590$	−25.8346	+	30.8645i	−1.06359	+	1.27067i
$591$	−40.8001	−	23.5560i	−1.67829	−	0.968963i
$592$	4.02680	−	12.9908i	0.165500	−	0.533920i
$593$	−11.6641	−	20.2028i	−0.478987	−	0.829630i	0.520723	−	0.853726i	$-0.325663\pi$
$593$	−11.6641	−	20.2028i	−0.478987	−	0.829630i	−0.999710	+	0.0240960i	$0.992329\pi$
$594$	32.4234	−	11.8457i	1.33035	−	0.486036i
$595$	−1.30351	−	1.18705i	−0.0534387	−	0.0486644i
$596$	19.2376	+	9.95523i	0.788004	+	0.407782i
$597$	−7.23578	−	5.55221i	−0.296141	−	0.227237i
$598$	0.335695	−	0.528350i	0.0137276	−	0.0216058i
$599$	−7.13898	−	26.6430i	−0.291691	−	1.08860i	−0.943810	−	0.330488i	$-0.892787\pi$
$599$	−7.13898	−	26.6430i	−0.291691	−	1.08860i	0.652119	−	0.758116i	$-0.273880\pi$
$600$	−22.5267	+	54.9491i	−0.919651	+	2.24329i
$601$	34.1101	+	34.1101i	1.39138	+	1.39138i	0.822240	+	0.569141i	$0.192724\pi$
$601$	34.1101	+	34.1101i	1.39138	+	1.39138i	0.569141	+	0.822240i	$0.307276\pi$
$602$	−7.45357	−	5.66851i	−0.303785	−	0.231031i
$603$	−35.4833	+	14.6977i	−1.44499	+	0.598535i
$604$	0.0521664	+	0.111166i	0.00212262	+	0.00452329i
$605$	14.2014	+	18.5077i	0.577371	+	0.752444i
$606$	−9.64319	+	6.76968i	−0.391728	+	0.275000i
$607$	11.9233	+	20.6517i	0.483951	+	0.838228i	0.999830	−	0.0184338i	$-0.00586799\pi$
$607$	11.9233	+	20.6517i	0.483951	+	0.838228i	−0.515879	+	0.856661i	$0.672535\pi$
$608$	−23.1239	−	35.8160i	−0.937799	−	1.45253i
$609$	−10.5824	−	12.5327i	−0.428822	−	0.507853i
$610$	−13.5307	+	29.1088i	−0.547842	+	1.17858i
$611$	−0.400082	+	0.0526718i	−0.0161856	+	0.00213087i
$612$	2.17724	+	1.51666i	0.0880095	+	0.0613073i
$613$	−47.4156	−	6.24238i	−1.91510	−	0.252128i	−0.923711	−	0.383089i	$-0.874860\pi$
$613$	−47.4156	−	6.24238i	−1.91510	−	0.252128i	−0.991387	+	0.130961i	$0.958194\pi$
$614$	−15.6590	−	4.91640i	−0.631947	−	0.198410i
$615$	36.8677	−	36.8677i	1.48665	−	1.48665i
$616$	12.8493	−	8.30801i	0.517712	−	0.334739i
$617$	−1.26891	−	1.26891i	−0.0510843	−	0.0510843i	0.681103	−	0.732187i	$-0.261501\pi$
$617$	−1.26891	−	1.26891i	−0.0510843	−	0.0510843i	−0.732187	+	0.681103i	$0.761501\pi$
$618$	40.6410	+	77.8399i	1.63482	+	3.13118i
$619$	4.30023	−	32.6635i	0.172841	−	1.31286i	−0.656590	−	0.754248i	$-0.728002\pi$
$619$	4.30023	−	32.6635i	0.172841	−	1.31286i	0.829431	−	0.558610i	$-0.188665\pi$
$620$	−20.2415	+	12.9644i	−0.812920	+	0.520664i
$621$	−0.371625	−	2.82277i	−0.0149128	−	0.113274i
$622$	4.43248	+	12.1323i	0.177726	+	0.486462i
$623$	−4.12663	+	0.740799i	−0.165330	+	0.0296795i
$624$	18.9826	−	13.4295i	0.759910	−	0.537609i
$625$	11.7626	−	6.79112i	0.470503	−	0.271645i
$626$	−21.5933	−	3.78048i	−0.863043	−	0.151099i
$627$	−38.2932	+	29.3834i	−1.52928	+	1.17346i
$628$	7.19463	+	6.56062i	0.287097	+	0.261797i
$629$	−0.253450	−	0.611881i	−0.0101057	−	0.0243973i
$630$	−33.0170	+	80.6909i	−1.31543	+	3.21480i
$631$	0.719141	−	0.719141i	0.0286286	−	0.0286286i	−0.692648	−	0.721276i	$-0.743556\pi$
$631$	0.719141	−	0.719141i	0.0286286	−	0.0286286i	0.721276	+	0.692648i	$0.243556\pi$
$632$	23.5781	−	23.7503i	0.937886	−	0.944737i
$633$	−21.0690	+	5.64543i	−0.837419	+	0.224386i
$634$	2.57516	−	0.574178i	0.102273	−	0.0228035i
$635$	−22.9648	+	29.9284i	−0.911332	+	1.18767i
$636$	−38.7387	−	45.9402i	−1.53609	−	1.82165i
$637$	−11.4861	+	6.06983i	−0.455095	+	0.240496i
$638$	2.41255	−	5.19016i	0.0955138	−	0.205480i
$639$	54.3683	−	31.3895i	2.15078	−	1.24175i
$640$	1.35986	−	38.6804i	0.0537530	−	1.52898i
$641$	−16.4168	+	28.4348i	−0.648425	+	1.12311i	0.335074	+	0.942192i	$0.391239\pi$
$641$	−16.4168	+	28.4348i	−0.648425	+	1.12311i	−0.983499	+	0.180913i	$0.942095\pi$
$642$	−30.0250	+	2.66355i	−1.18499	+	0.105122i
$643$	21.3561	+	8.84600i	0.842204	+	0.348852i	0.761722	−	0.647904i	$-0.224354\pi$
$643$	21.3561	+	8.84600i	0.842204	+	0.348852i	0.0804817	+	0.996756i	$0.474354\pi$
$644$	−0.438175	−	1.18352i	−0.0172665	−	0.0466371i
$645$	10.2627	+	24.7762i	0.404092	+	0.975563i
$646$	−1.98069	−	0.621868i	−0.0779292	−	0.0244671i
$647$	12.8657	+	48.0155i	0.505804	+	1.88769i	0.458263	+	0.888817i	$0.348472\pi$
$647$	12.8657	+	48.0155i	0.505804	+	1.88769i	0.0475412	+	0.998869i	$0.484861\pi$
$648$	12.2458	−	46.3763i	0.481060	−	1.82183i
$649$	−16.4312	−	4.40273i	−0.644981	−	0.172822i
$650$	17.5779	+	0.746103i	0.689460	+	0.0292646i
$651$	−24.5066	+	15.7192i	−0.960490	+	0.616083i
$652$	37.8233	−	12.0266i	1.48128	−	0.470999i
$653$	36.5679	−	4.81426i	1.43101	−	0.188397i	0.625154	−	0.780502i	$-0.285036\pi$
$653$	36.5679	−	4.81426i	1.43101	−	0.188397i	0.805861	+	0.592105i	$0.201703\pi$
$654$	4.13840	−	23.6377i	0.161824	−	0.924306i
$655$	9.51152	−	16.4744i	0.371646	−	0.643710i
$656$	−8.13966	+	17.6790i	−0.317800	+	0.690250i
$657$	93.2339			3.63740
$658$	−0.403745	+	0.706311i	−0.0157396	+	0.0275349i
$659$	18.9409	+	7.84558i	0.737833	+	0.305620i	0.719766	−	0.694216i	$-0.244249\pi$
$659$	18.9409	+	7.84558i	0.737833	+	0.305620i	0.0180667	+	0.999837i	$0.494249\pi$
$660$	−43.7739	+	2.01763i	−1.70390	+	0.0785360i
$661$	−43.5474	−	5.73313i	−1.69380	−	0.222993i	−0.779035	−	0.626981i	$-0.784290\pi$
$661$	−43.5474	−	5.73313i	−1.69380	−	0.222993i	−0.914764	+	0.403988i	$0.867624\pi$
$662$	−20.3490	−	12.9291i	−0.790886	−	0.502502i
$663$	0.293064	−	1.09373i	0.0113817	−	0.0424770i
$664$	−10.2354	−	1.30964i	−0.397210	−	0.0508238i
$665$	5.73502	−	67.9713i	0.222394	−	2.63581i
$666$	−24.1203	+	22.1561i	−0.934642	+	0.858530i
$667$	−0.374515	−	0.287375i	−0.0145013	−	0.0111272i
$668$	−16.6840	+	23.9507i	−0.645524	+	0.926681i
$669$	60.4609	−	46.3933i	2.33755	−	1.79367i
$670$	27.1741	−	2.41064i	1.04983	−	0.0931312i
$671$	−13.5665			−0.523727
$672$	1.61591	−	46.8518i	0.0623350	−	1.80735i
$673$	−28.9666			−1.11658			−0.558291	−	0.829645i	$-0.688543\pi$
$673$	−28.9666			−1.11658			−0.558291	+	0.829645i	$0.688543\pi$
$674$	29.7531	−	2.63944i	1.14605	−	0.101667i
$675$	63.4854	−	48.7141i	2.44355	−	1.87500i
$676$	15.6816	+	10.9238i	0.603139	+	0.420146i
$677$	7.69151	+	5.90190i	0.295609	+	0.226829i	0.745908	−	0.666049i	$-0.232016\pi$
$677$	7.69151	+	5.90190i	0.295609	+	0.226829i	−0.450299	+	0.892878i	$0.648683\pi$
$678$	11.4606	−	10.5273i	0.440142	−	0.404300i
$679$	−38.3050	+	18.0063i	−1.47001	+	0.691018i
$680$	−1.15279	−	1.49108i	−0.0442076	−	0.0571805i
$681$	−14.5272	+	54.2161i	−0.556682	+	2.07756i
$682$	−8.57460	−	5.44801i	−0.328339	−	0.208615i
$683$	23.7383	+	3.12520i	0.908320	+	0.119583i	0.570186	−	0.821516i	$-0.306871\pi$
$683$	23.7383	+	3.12520i	0.908320	+	0.119583i	0.338134	+	0.941098i	$0.390204\pi$
$684$	4.72692	+	102.554i	0.180738	+	3.92126i
$685$	−19.4187	−	8.04351i	−0.741952	−	0.307327i
$686$	−4.27735	+	25.8400i	−0.163310	+	0.986575i
$687$	−44.9588			−1.71529
$688$	−6.79888	−	7.34777i	−0.259205	−	0.280131i
$689$	−8.90140	+	15.4177i	−0.339116	+	0.587366i
$690$	−0.623290	+	3.56010i	−0.0237282	+	0.135531i
$691$	40.5175	−	5.33423i	1.54136	−	0.202924i	0.688567	−	0.725173i	$-0.258240\pi$
$691$	40.5175	−	5.33423i	1.54136	−	0.202924i	0.852793	+	0.522249i	$0.174907\pi$
$692$	−9.56112	−	30.0694i	−0.363459	−	1.14307i
$693$	−36.8068	+	1.72105i	−1.39817	+	0.0653772i
$694$	−31.3403	−	1.33026i	−1.18966	−	0.0504959i
$695$	61.2717	+	16.4177i	2.32417	+	0.622759i
$696$	−8.82297	−	15.1542i	−0.334434	−	0.574418i
$697$	0.245299	+	0.915468i	0.00929136	+	0.0346758i
$698$	−39.2543	−	12.3245i	−1.48580	−	0.466489i
$699$	−13.9172	−	33.5992i	−0.526398	−	1.27084i
$700$	22.6497	−	27.2974i	0.856080	−	1.03175i
$701$	−40.4355	−	16.7489i	−1.52723	−	0.632598i	−0.548203	−	0.836345i	$-0.684688\pi$
$701$	−40.4355	−	16.7489i	−1.52723	−	0.632598i	−0.979024	+	0.203747i	$0.934688\pi$
$702$	−31.2093	+	2.76861i	−1.17792	+	0.104495i
$703$	12.8124	−	22.1918i	0.483229	−	0.836978i
$704$	15.0666	−	6.36964i	0.567842	−	0.240065i
$705$	2.01777	−	1.16496i	0.0759938	−	0.0438750i
$706$	11.7788	−	25.3400i	0.443302	−	0.953684i
$707$	6.70491	−	2.13686i	0.252164	−	0.0803650i
$708$	−39.8430	+	33.5973i	−1.49739	+	1.26266i
$709$	−19.4917	+	25.4021i	−0.732027	+	0.953996i	−0.999955	−	0.00944253i	$-0.996994\pi$
$709$	−19.4917	+	25.4021i	−0.732027	+	0.953996i	0.267928	+	0.963439i	$0.413661\pi$
$710$	−43.5238	+	9.70440i	−1.63342	+	0.364200i
$711$	−77.8449	+	20.8585i	−2.91941	+	0.782254i
$712$	−4.48204	+	0.0163112i	−0.167972	+	0.000611288i
$713$	−0.592485	+	0.592485i	−0.0221887	+	0.0221887i
$714$	−1.39750	−	1.80511i	−0.0523000	−	0.0675545i
$715$	4.96796	+	11.9937i	0.185791	+	0.448540i
$716$	−22.0495	+	24.1803i	−0.824027	+	0.903660i
$717$	28.3114	−	21.7241i	1.05731	−	0.811301i
$718$	7.80351	+	1.36621i	0.291224	+	0.0509865i
$719$	−39.8460	+	23.0051i	−1.48601	+	0.857946i	−0.999873	−	0.0159389i	$-0.994926\pi$
$719$	−39.8460	+	23.0051i	−1.48601	+	0.857946i	−0.486133	+	0.873885i	$0.661593\pi$
$720$	−49.6966	+	78.8497i	−1.85208	+	2.93856i
$721$	−9.26699	−	51.6219i	−0.345121	−	1.92250i
$722$	−18.3429	−	50.2072i	−0.682653	−	1.86852i
$723$	3.65685	+	27.7766i	0.136000	+	1.03302i
$724$	4.88743	+	7.63080i	0.181640	+	0.283597i
$725$	1.73181	−	13.1544i	0.0643177	−	0.488542i
$726$	13.9805	+	26.7769i	0.518865	+	0.993785i
$727$	−5.99713	−	5.99713i	−0.222421	−	0.222421i	0.587096	−	0.809517i	$-0.300271\pi$
$727$	−5.99713	−	5.99713i	−0.222421	−	0.222421i	−0.809517	+	0.587096i	$0.800271\pi$
$728$	−13.2170	+	4.26533i	−0.489856	+	0.158084i
$729$	−2.35547	+	2.35547i	−0.0872397	+	0.0872397i
$730$	−63.1840	−	19.8376i	−2.33854	−	0.734222i
$731$	−0.483312	−	0.0636292i	−0.0178759	−	0.00235341i
$732$	−23.7579	+	34.1056i	−0.878116	+	1.26058i
$733$	18.9690	−	2.49732i	0.700637	−	0.0922406i	0.228212	−	0.973611i	$-0.426712\pi$
$733$	18.9690	−	2.49732i	0.700637	−	0.0922406i	0.472425	+	0.881371i	$0.343379\pi$
$734$	−8.29978	+	17.8555i	−0.306351	+	0.659057i
$735$	47.8585	−	57.7572i	1.76529	−	2.13040i
$736$	−0.242334	−	1.32722i	−0.00893255	−	0.0489219i
$737$	5.76486	+	9.98503i	0.212351	+	0.367803i
$738$	38.3599	−	26.9293i	1.41205	−	0.991282i
$739$	−17.1971	−	22.4117i	−0.632605	−	0.824427i	0.361554	−	0.932351i	$-0.382246\pi$
$739$	−17.1971	−	22.4117i	−0.632605	−	0.824427i	−0.994159	+	0.107924i	$0.965580\pi$
$740$	21.0603	−	9.88288i	0.774194	−	0.363302i
$741$	40.4754	−	16.7655i	1.48690	−	0.615895i
$742$	13.8779	+	33.1006i	0.509475	+	1.21516i
$743$	19.1599	+	19.1599i	0.702910	+	0.702910i	0.965034	−	0.262124i	$-0.0844231\pi$
$743$	19.1599	+	19.1599i	0.702910	+	0.702910i	−0.262124	+	0.965034i	$0.584423\pi$
$744$	−28.7122	+	12.0156i	−1.05264	+	0.440512i
$745$	9.58950	+	35.7885i	0.351332	+	1.31119i
$746$	−1.38002	+	2.17201i	−0.0505262	+	0.0795230i
$747$	19.7140	+	15.1271i	0.721296	+	0.553470i
$748$	0.366092	−	0.707442i	0.0133857	−	0.0258666i
$749$	17.5888	+	3.84232i	0.642679	+	0.140395i
$750$	−24.2446	+	8.85764i	−0.885288	+	0.323435i
$751$	−1.70859	−	2.95936i	−0.0623473	−	0.107989i	0.833167	−	0.553022i	$-0.186525\pi$
$751$	−1.70859	−	2.95936i	−0.0623473	−	0.107989i	−0.895514	+	0.445033i	$0.853192\pi$
$752$	−0.555816	+	0.668961i	−0.0202685	+	0.0243945i
$753$	−8.29838	−	4.79107i	−0.302410	−	0.174596i
$754$	−3.33442	+	3.98361i	−0.121432	+	0.145075i
$755$	−0.0803811	+	0.194057i	−0.00292537	+	0.00706246i
$756$	−33.6457	+	53.4618i	−1.22368	+	1.94439i
$757$	3.33601	−	1.38182i	0.121250	−	0.0502232i	−0.321234	−	0.947000i	$-0.604098\pi$
$757$	3.33601	−	1.38182i	0.121250	−	0.0502232i	0.442483	+	0.896777i	$0.354098\pi$
$758$	8.84324	+	16.9375i	0.321201	+	0.615198i
$759$	−1.47545	+	0.395346i	−0.0535555	+	0.0143501i
$760$	18.6173	−	70.5060i	0.675320	−	2.55752i
$761$	−10.6853	+	39.8780i	−0.387341	+	1.44558i	0.447102	+	0.894483i	$0.352456\pi$
$761$	−10.6853	+	39.8780i	−0.387341	+	1.44558i	−0.834443	+	0.551094i	$0.814210\pi$
$762$	−35.9737	+	33.0442i	−1.30319	+	1.19706i
$763$	−6.57886	+	12.7338i	−0.238171	+	0.460996i
$764$	32.1991	−	27.1516i	1.16492	−	0.982312i
$765$	0.592416	+	4.49985i	0.0214189	+	0.162692i
$766$	12.7196	−	8.92936i	0.459577	−	0.322631i
$767$	13.3714	+	7.71999i	0.482814	+	0.278753i
$768$	10.3719	−	49.0315i	0.374262	−	1.76927i
$769$		−	41.7574i		−	1.50581i	−0.658129	−	0.752905i	$-0.728652\pi$
$769$		−	41.7574i		−	1.50581i	0.658129	−	0.752905i	$-0.271348\pi$
$770$	25.3099	+	6.66512i	0.912105	+	0.240194i
$771$	12.4888	−	30.1507i	0.449774	−	1.08585i
$772$	−5.57743	+	15.4403i	−0.200736	+	0.555709i
$773$	0.691493	−	5.25241i	0.0248713	−	0.188916i	−0.974499	−	0.224390i	$-0.927961\pi$
$773$	0.691493	−	5.25241i	0.0248713	−	0.188916i	0.999371	+	0.0354744i	$0.0112942\pi$
$774$	5.24624	+	23.5292i	0.188572	+	0.845738i
$775$	−22.7476	−	6.09520i	−0.817118	−	0.218946i
$776$	−43.6638	+	11.8702i	−1.56744	+	0.426114i
$777$	25.5009	−	11.9874i	0.914838	−	0.430045i
$778$	−0.903846	+	21.2942i	−0.0324044	+	0.763434i
$779$	−22.3232	+	29.0921i	−0.799810	+	1.04233i
$780$	38.8518	+	8.51440i	1.39112	+	0.304864i
$781$	−11.4729	−	14.9517i	−0.410531	−	0.535015i
$782$	−0.0503794	−	0.0421693i	−0.00180156	−	0.00150797i
$783$			23.6282i			0.844405i
$784$	−9.28562	+	26.4155i	−0.331629	+	0.943410i
$785$			16.6548i			0.594434i
$786$	15.8103	−	18.8885i	0.563935	−	0.673729i
$787$	−16.4153	−	21.3929i	−0.585143	−	0.762573i	0.403151	−	0.915133i	$-0.367915\pi$
$787$	−16.4153	−	21.3929i	−0.585143	−	0.762573i	−0.988294	+	0.152560i	$0.951248\pi$
$788$	16.2243	+	25.3313i	0.577968	+	0.902389i
$789$	32.2603	−	42.0425i	1.14850	−	1.49675i
$790$	57.1931	+	2.42759i	2.03484	+	0.0863699i
$791$	−8.41165	+	3.95412i	−0.299084	+	0.140592i
$792$	−39.0726	−	4.99941i	−1.38838	−	0.177646i
$793$	11.8941	+	3.18701i	0.422372	+	0.113174i
$794$	15.0006	−	3.34465i	0.532352	−	0.118697i
$795$	13.4167	−	101.910i	0.475843	−	3.61439i
$796$	2.47394	+	5.27195i	0.0876865	+	0.186859i
$797$	2.83752	−	6.85037i	0.100510	−	0.242653i	−0.865623	−	0.500696i	$-0.833078\pi$
$797$	2.83752	−	6.85037i	0.100510	−	0.242653i	0.966133	+	0.258043i	$0.0830776\pi$
$798$	22.4929	−	85.4137i	0.796240	−	3.02361i
$799$			0.0423527i			0.00149833i
$800$	28.8997	−	24.5500i	1.02176	−	0.867973i
$801$	9.34730	+	5.39667i	0.330271	+	0.190682i
$802$	6.30042	+	8.97474i	0.222476	+	0.316909i
$803$	−3.65327	−	27.7493i	−0.128921	−	0.979253i
$804$	35.1976	+	2.99336i	1.24132	+	0.105568i
$805$	0.990852	−	1.91786i	0.0349229	−	0.0675958i
$806$	6.23776	+	6.79076i	0.219716	+	0.239194i
$807$	13.6706	−	51.0193i	0.481228	−	1.79597i
$808$	7.45509	−	1.00910i	0.262269	−	0.0354998i
$809$	−10.5567	+	2.82867i	−0.371155	+	0.0994508i	−0.439575	−	0.898206i	$-0.644871\pi$
$809$	−10.5567	+	2.82867i	−0.371155	+	0.0994508i	0.0684198	+	0.997657i	$0.478204\pi$
$810$	72.7295	−	37.9728i	2.55545	−	1.33423i
$811$	−46.7592	+	19.3683i	−1.64194	+	0.680113i	−0.996492	−	0.0836921i	$-0.973329\pi$
$811$	−46.7592	+	19.3683i	−1.64194	+	0.680113i	−0.645447	+	0.763805i	$0.723329\pi$
$812$	2.32327	+	10.2126i	0.0815308	+	0.358391i
$813$	17.8811	−	43.1688i	0.627118	−	1.51400i
$814$	7.53946	+	6.31079i	0.264258	+	0.221193i
$815$	58.7934	+	33.9444i	2.05944	+	1.18902i
$816$	−1.13738	−	2.15923i	−0.0398161	−	0.0755882i
$817$	−9.43057	−	16.3342i	−0.329934	−	0.571462i
$818$	−9.45194	−	25.8713i	−0.330479	−	0.904568i
$819$	32.6739	+	7.13771i	1.14172	+	0.249412i
$820$	−31.7261	+	10.0879i	−1.10792	+	0.352284i
$821$	−26.9007	−	20.6417i	−0.938843	−	0.720399i	0.0213400	−	0.999772i	$-0.493207\pi$
$821$	−26.9007	−	20.6417i	−0.938843	−	0.720399i	−0.960183	+	0.279373i	$0.909873\pi$
$822$	−22.9716	−	14.5954i	−0.801226	−	0.509072i
$823$	6.80754	+	25.4061i	0.237296	+	0.885600i	0.977100	+	0.212778i	$0.0682512\pi$
$823$	6.80754	+	25.4061i	0.237296	+	0.885600i	−0.739805	+	0.672822i	$0.765082\pi$
$824$	−0.204044	−	56.0680i	−0.00710822	−	1.95322i
$825$	−30.3575	−	30.3575i	−1.05691	−	1.05691i
$826$	28.7074	−	12.0360i	0.998859	−	0.418788i
$827$	26.5258	−	10.9873i	0.922391	−	0.382067i	0.129604	−	0.991566i	$-0.458629\pi$
$827$	26.5258	−	10.9873i	0.922391	−	0.382067i	0.792787	+	0.609499i	$0.208629\pi$
$828$	−1.10379	+	3.05568i	−0.0383593	+	0.106192i
$829$	1.89219	+	2.46594i	0.0657183	+	0.0856458i	0.825056	−	0.565051i	$-0.191144\pi$
$829$	1.89219	+	2.46594i	0.0657183	+	0.0856458i	−0.759338	+	0.650697i	$0.774477\pi$
$830$	−10.1414	−	14.4461i	−0.352013	−	0.501431i
$831$	2.93341	+	5.08082i	0.101759	+	0.176252i
$832$	−14.7056	+	2.04503i	−0.509826	+	0.0708986i
$833$	0.474254	+	1.27835i	0.0164319	+	0.0442923i
$834$	74.4832	+	34.6221i	2.57914	+	1.19887i
$835$	−49.5006	+	6.51688i	−1.71304	+	0.225526i
$836$	30.3381	−	5.42535i	1.04927	−	0.187640i
$837$	41.5805	+	5.47418i	1.43723	+	0.189215i
$838$	−9.30318	+	29.6312i	−0.321373	+	1.02359i
$839$	13.3529	−	13.3529i	0.460993	−	0.460993i	−0.437988	−	0.898981i	$-0.644309\pi$
$839$	13.3529	−	13.3529i	0.460993	−	0.460993i	0.898981	+	0.437988i	$0.144309\pi$
$840$	61.0791	−	51.9561i	2.10743	−	1.79265i
$841$	−17.7359	−	17.7359i	−0.611583	−	0.611583i
$842$	4.13262	−	2.15768i	0.142419	−	0.0743586i
$843$	−12.3500	+	93.8079i	−0.425358	+	3.23091i
$844$	13.6045	+	2.98145i	0.468288	+	0.102626i
$845$	4.26690	+	32.4103i	0.146786	+	1.11495i
$846$	1.96724	−	0.718721i	0.0676351	−	0.0247101i
$847$	−3.18785	−	17.7579i	−0.109536	−	0.610170i
$848$	8.48652	+	37.4200i	0.291428	+	1.28501i
$849$	51.2740	−	29.6031i	1.75972	−	1.01597i
$850$	0.318441	−	1.81887i	0.0109224	−	0.0623867i
$851$	0.643360	−	0.493667i	0.0220541	−	0.0169227i
$852$	−57.6797	+	2.65857i	−1.97607	+	0.0910811i
$853$	15.2552	+	36.8293i	0.522328	+	1.26101i	0.936453	+	0.350792i	$0.114088\pi$
$853$	15.2552	+	36.8293i	0.522328	+	1.26101i	−0.414125	+	0.910220i	$0.635912\pi$
$854$	19.6302	−	15.1975i	0.671731	−	0.520047i
$855$	−124.172	+	124.172i	−4.24659	+	4.24659i
$856$	17.8082	+	7.30060i	0.608673	+	0.249529i
$857$	7.18165	−	1.92432i	0.245320	−	0.0657334i	−0.134063	−	0.990973i	$-0.542803\pi$
$857$	7.18165	−	1.92432i	0.245320	−	0.0657334i	0.379384	+	0.925239i	$0.376136\pi$
$858$	3.65819	+	16.4068i	0.124889	+	0.560119i
$859$	−11.9609	+	15.5878i	−0.408102	+	0.531849i	−0.951509	−	0.307620i	$-0.900467\pi$
$859$	−11.9609	+	15.5878i	−0.408102	+	0.531849i	0.543407	+	0.839469i	$0.317134\pi$
$860$	1.45101	−	17.0618i	0.0494791	−	0.581802i
$861$	−38.4193	+	12.2443i	−1.30933	+	0.417284i
$862$	9.94379	+	4.62219i	0.338687	+	0.157432i
$863$	−26.7965	+	15.4710i	−0.912164	+	0.526638i	−0.881127	−	0.472880i	$-0.843214\pi$
$863$	−26.7965	+	15.4710i	−0.912164	+	0.526638i	−0.0310371	+	0.999518i	$0.509881\pi$
$864$	−45.3194	+	50.0637i	−1.54180	+	1.70320i
$865$	26.9857	−	46.7406i	0.917541	−	1.58923i
$866$	1.43085	+	16.1293i	0.0486223	+	0.548097i
$867$	49.0856	+	20.3319i	1.66703	+	0.690508i
$868$	18.5102	−	1.72240i	0.628276	−	0.0584620i
$869$	9.25841	+	22.3518i	0.314070	+	0.758232i
$870$	8.98484	−	28.6173i	0.304614	−	0.970216i
$871$	−2.70855	−	10.1084i	−0.0917757	−	0.342511i
$872$	−9.28346	+	12.1900i	−0.314378	+	0.412807i
$873$	105.251	+	28.2018i	3.56219	+	0.954486i
$874$	0.107797	−	2.53966i	0.00364630	−	0.0859053i
$875$	15.4000	−	0.720089i	0.520615	−	0.0243435i
$876$	−76.1585	−	39.4111i	−2.57316	−	1.33158i
$877$	3.88985	−	0.512109i	0.131351	−	0.0172927i	−0.0645640	−	0.997914i	$-0.520566\pi$
$877$	3.88985	−	0.512109i	0.131351	−	0.0172927i	0.195915	+	0.980621i	$0.437232\pi$
$878$	−36.1115	−	6.32227i	−1.21870	−	0.213366i
$879$	−33.7560	+	58.4671i	−1.13856	+	1.97205i
$880$	25.4155	+	11.7016i	0.856755	+	0.394462i
$881$	49.8727			1.68025			0.840126	−	0.542391i	$-0.182481\pi$
$881$	49.8727			1.68025			0.840126	+	0.542391i	$0.182481\pi$
$882$	51.3302	−	43.7222i	1.72838	−	1.47220i
$883$	−2.81245	−	1.16495i	−0.0946465	−	0.0392038i	0.334858	−	0.942269i	$-0.391312\pi$
$883$	−2.81245	−	1.16495i	−0.0946465	−	0.0392038i	−0.429504	+	0.903065i	$0.641312\pi$
$884$	−0.487155	+	0.534233i	−0.0163848	+	0.0179682i
$885$	−88.3847	−	11.6361i	−2.97102	−	0.391142i
$886$	−15.2531	+	24.0067i	−0.512436	+	0.806521i
$887$	−5.64552	+	21.0694i	−0.189558	+	0.707440i	0.804051	+	0.594561i	$0.202674\pi$
$887$	−5.64552	+	21.0694i	−0.189558	+	0.707440i	−0.993609	+	0.112879i	$0.963993\pi$
$888$	29.0684	−	7.90234i	0.975471	−	0.265185i
$889$	26.4033	−	12.4116i	0.885538	−	0.416271i
$890$	−5.18634	−	5.64613i	−0.173846	−	0.189259i
$891$	27.5097	+	21.1089i	0.921609	+	0.707175i
$892$	−47.9007	+	8.56607i	−1.60384	+	0.286813i
$893$	−1.30004	+	0.997556i	−0.0435042	+	0.0333819i
$894$	4.23933	+	47.7880i	0.141784	+	1.59827i
$895$	−55.9747			−1.87103
$896$	−14.6654	+	26.0946i	−0.489935	+	0.871759i
$897$	1.38644			0.0462920
$898$	3.27238	+	36.8880i	0.109201	+	1.23097i
$899$	5.51675	−	4.23315i	0.183994	−	0.141183i
$900$	−89.8886	+	16.0747i	−2.99629	+	0.535825i
$901$	1.48237	+	1.13746i	0.0493847	+	0.0378942i
$902$	−9.51810	−	10.3619i	−0.316918	−	0.345014i
$903$	1.74375	−	20.6669i	0.0580283	−	0.687750i
$904$	−9.58843	+	2.60665i	−0.318906	+	0.0866958i
$905$	−4.01176	+	14.9721i	−0.133355	+	0.497689i
$906$	−0.145856	+	0.229562i	−0.00484574	+	0.00762668i
$907$	9.79565	+	1.28962i	0.325259	+	0.0428212i	0.291388	−	0.956605i	$-0.405883\pi$
$907$	9.79565	+	1.28962i	0.325259	+	0.0428212i	0.0338714	+	0.999426i	$0.489216\pi$
$908$	24.1482	−	26.4818i	0.801386	−	0.878831i
$909$	−16.7374	−	6.93284i	−0.555143	−	0.229948i
$910$	−20.6241	−	11.7893i	−0.683684	−	0.390811i
$911$	35.9240			1.19022			0.595108	−	0.803646i	$-0.297109\pi$
$911$	35.9240			1.19022			0.595108	+	0.803646i	$0.297109\pi$
$912$	39.4896	−	85.7699i	1.30763	−	2.84013i
$913$	3.72982	−	6.46023i	0.123439	−	0.213802i
$914$	19.1899	+	3.35971i	0.634747	+	0.111129i
$915$	−70.4884	+	9.27998i	−2.33028	+	0.306787i
$916$	25.4953	+	13.1935i	0.842389	+	0.435926i
$917$	−12.3836	+	7.94313i	−0.408941	+	0.262305i
$918$	−0.139453	+	3.28546i	−0.00460265	+	0.108436i
$919$	4.69180	+	1.25716i	0.154768	+	0.0414700i	0.335371	−	0.942086i	$-0.391138\pi$
$919$	4.69180	+	1.25716i	0.154768	+	0.0414700i	−0.180603	+	0.983556i	$0.557805\pi$
$920$	1.39819	−	1.83596i	0.0460971	−	0.0605298i
$921$	−9.40852	−	35.1131i	−0.310021	−	1.15701i
$922$	4.34883	−	13.8513i	0.143221	−	0.456168i
$923$	6.54615	+	15.8038i	0.215469	+	0.520189i
$924$	30.7933	+	14.1528i	1.01302	+	0.465593i
$925$	21.0573	+	8.72222i	0.692360	+	0.286785i
$926$	1.12654	+	12.6989i	0.0370203	+	0.417313i
$927$	−67.5094	+	116.930i	−2.21730	+	3.84048i
$928$	0.556229	+	11.1828i	0.0182591	+	0.367094i
$929$	−32.9857	+	19.0443i	−1.08223	+	0.624823i	−0.931496	−	0.363752i	$-0.881496\pi$
$929$	−32.9857	+	19.0443i	−1.08223	+	0.624823i	−0.150729	+	0.988575i	$0.548162\pi$
$930$	−48.2785	−	22.4414i	−1.58311	−	0.735881i
$931$	−28.0694	+	44.6672i	−0.919937	+	1.46391i
$932$	−1.96772	+	23.1376i	−0.0644550	+	0.757897i
$933$	−17.4158	+	22.6967i	−0.570167	+	0.743056i
$934$	2.72940	+	12.2412i	0.0893087	+	0.400545i
$935$	1.31608	−	0.352643i	0.0430405	−	0.0115327i
$936$	33.0816	+	13.5620i	1.08131	+	0.443288i
$937$	24.5985	−	24.5985i	0.803598	−	0.803598i	−0.180058	−	0.983656i	$-0.557628\pi$
$937$	24.5985	−	24.5985i	0.803598	−	0.803598i	0.983656	+	0.180058i	$0.0576284\pi$
$938$	−19.5270	−	7.99006i	−0.637580	−	0.260885i
$939$	−18.5806	−	44.8576i	−0.606356	−	1.46387i
$940$	−1.48611	+	0.0684977i	−0.0484715	+	0.00223415i
$941$	0.133605	−	0.102519i	0.00435540	−	0.00334202i	−0.606581	−	0.795021i	$-0.707460\pi$
$941$	0.133605	−	0.102519i	0.00435540	−	0.00334202i	0.610937	+	0.791679i	$0.290793\pi$
$942$	−3.71905	+	21.2424i	−0.121173	+	0.692115i
$943$	−1.00500	+	0.580236i	−0.0327273	+	0.0188951i
$944$	32.4536	−	7.36018i	1.05627	−	0.239554i
$945$	−106.349	+	19.0914i	−3.45954	+	0.621045i
$946$	6.79744	−	2.48341i	0.221004	−	0.0807426i
$947$	−3.82121	−	29.0250i	−0.124173	−	0.943185i	−0.934189	−	0.356778i	$-0.883875\pi$
$947$	−3.82121	−	29.0250i	−0.124173	−	0.943185i	0.810016	−	0.586407i	$-0.199458\pi$
$948$	72.4051	+	15.8676i	2.35161	+	0.515356i
$949$	−3.31591	+	25.1869i	−0.107639	+	0.817600i
$950$	63.3316	−	33.0661i	2.05475	−	1.07281i
$951$	4.13210	+	4.13210i	0.133992	+	0.133992i
$952$	0.262771	+	1.43375i	0.00851647	+	0.0464681i
$953$	21.4447	−	21.4447i	0.694661	−	0.694661i	−0.268593	−	0.963254i	$-0.586559\pi$
$953$	21.4447	−	21.4447i	0.694661	−	0.694661i	0.963254	+	0.268593i	$0.0865586\pi$
$954$	27.6783	−	88.1570i	0.896117	−	2.85419i
$955$	71.4281	+	9.40368i	2.31136	+	0.304296i
$956$	−22.4300	+	4.01114i	−0.725437	+	0.129730i
$957$	12.5682	−	1.65464i	0.406273	−	0.0534868i
$958$	−7.20360	−	3.34846i	−0.232738	−	0.108184i
$959$	10.4873	+	12.4201i	0.338652	+	0.401065i
$960$	73.9256	−	43.4014i	2.38594	−	1.40077i
$961$	9.32871	+	16.1578i	0.300926	+	0.521219i
$962$	−5.12754	−	7.30401i	−0.165319	−	0.235491i
$963$	−28.2149	−	36.7703i	−0.909211	−	1.18491i
$964$	6.07751	−	16.8247i	0.195743	−	0.541887i
$965$	−25.9435	+	10.7461i	−0.835149	+	0.345930i
$966$	1.69205	−	2.22489i	0.0544408	−	0.0715846i
$967$	11.9447	+	11.9447i	0.384117	+	0.384117i	0.872583	−	0.488466i	$-0.162443\pi$
$967$	11.9447	+	11.9447i	0.384117	+	0.384117i	−0.488466	+	0.872583i	$0.662443\pi$
$968$	−0.0701912	−	19.2874i	−0.00225603	−	0.619920i
$969$	−1.19007	−	4.44140i	−0.0382306	−	0.142678i
$970$	−65.3270	−	41.5066i	−2.09752	−	1.33270i
$971$	−17.1629	−	13.1696i	−0.550784	−	0.422632i	0.295516	−	0.955338i	$-0.404508\pi$
$971$	−17.1629	−	13.1696i	−0.550784	−	0.422632i	−0.846300	+	0.532706i	$0.821175\pi$
$972$	32.9843	−	10.4880i	1.05797	−	0.336402i
$973$	−36.2717	−	33.0312i	−1.16282	−	1.05893i
$974$	−5.98963	−	16.3945i	−0.191920	−	0.525313i
$975$	19.4837	+	33.7468i	0.623979	+	1.08076i
$976$	23.4812	−	12.3687i	0.751615	−	0.395913i
$977$	33.6586	+	19.4328i	1.07683	+	0.621710i	0.930040	−	0.367458i	$-0.119772\pi$
$977$	33.6586	+	19.4328i	1.07683	+	0.621710i	0.146793	+	0.989167i	$0.453105\pi$
$978$	67.4085	+	56.4233i	2.15549	+	1.80422i
$979$	1.23995	−	2.99351i	0.0396291	−	0.0956730i
$980$	−44.0890	+	18.7086i	−1.40837	+	0.597623i
$981$	34.0896	−	14.1204i	1.08840	−	0.450829i
$982$	−35.1107	+	18.3316i	−1.12043	+	0.584985i
$983$	45.6589	−	12.2343i	1.45629	−	0.390212i	0.558085	−	0.829784i	$-0.311536\pi$
$983$	45.6589	−	12.2343i	1.45629	−	0.390212i	0.898208	+	0.439571i	$0.144870\pi$
$984$	−42.7178	+	5.78214i	−1.36179	+	0.184328i
$985$	−13.3175	+	49.7014i	−0.424329	+	1.58362i
$986$	0.368841	+	0.401540i	0.0117463	+	0.0127877i
$987$	−1.79996	+	0.0841643i	−0.0572933	+	0.00267898i
$988$	−27.8728	−	2.37043i	−0.886752	−	0.0754134i
$989$	−0.0779098	−	0.591784i	−0.00247739	−	0.0188176i
$990$	−38.7137	−	55.1464i	−1.23040	−	1.75267i
$991$	3.69395	+	2.13270i	0.117342	+	0.0677475i	0.557522	−	0.830162i	$-0.311752\pi$
$991$	3.69395	+	2.13270i	0.117342	+	0.0677475i	−0.440180	+	0.897909i	$0.645085\pi$
$992$	19.8082	+	1.61199i	0.628911	+	0.0511808i
$993$		−	53.3979i		−	1.69453i
$994$	33.3501	+	8.78245i	1.05780	+	0.278562i
$995$	−3.81200	+	9.20297i	−0.120848	+	0.291754i
$996$	−9.70905	−	20.6899i	−0.307643	−	0.655585i
$997$	−4.14327	+	31.4713i	−0.131219	+	0.996705i	0.791483	+	0.611191i	$0.209309\pi$
$997$	−4.14327	+	31.4713i	−0.131219	+	0.996705i	−0.922702	+	0.385514i	$0.874024\pi$
$998$	18.1270	−	4.04173i	0.573800	−	0.127939i
$999$	−39.2067	−	10.5054i	−1.24045	−	0.332376i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.be.a.3.15	✓	240
4.3	odd	2		896.2.bi.a.815.1		240
7.5	odd	6	inner	224.2.be.a.131.6	yes	240
28.19	even	6		896.2.bi.a.47.30		240
32.11	odd	8	inner	224.2.be.a.171.6	yes	240
32.21	even	8		896.2.bi.a.591.30		240
224.75	even	24	inner	224.2.be.a.75.15	yes	240
224.117	odd	24		896.2.bi.a.719.1		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.be.a.3.15	✓	240	1.1	even	1	trivial
224.2.be.a.75.15	yes	240	224.75	even	24	inner
224.2.be.a.131.6	yes	240	7.5	odd	6	inner
224.2.be.a.171.6	yes	240	32.11	odd	8	inner
896.2.bi.a.47.30		240	28.19	even	6
896.2.bi.a.591.30		240	32.21	even	8
896.2.bi.a.719.1		240	224.117	odd	24
896.2.bi.a.815.1		240	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.be (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.124966 - 1.40868i) q^{2} +(2.48500 - 1.90681i) q^{3} +(-1.96877 + 0.352074i) q^{4} +(-2.71407 - 2.08258i) q^{5} +(-2.99663 - 3.26229i) q^{6} +(1.12555 + 2.39440i) q^{7} +(0.741988 + 2.72937i) q^{8} +(1.76286 - 6.57908i) q^{9} +O(q^{10})\)	\(q+(-0.124966 - 1.40868i) q^{2} +(2.48500 - 1.90681i) q^{3} +(-1.96877 + 0.352074i) q^{4} +(-2.71407 - 2.08258i) q^{5} +(-2.99663 - 3.26229i) q^{6} +(1.12555 + 2.39440i) q^{7} +(0.741988 + 2.72937i) q^{8} +(1.76286 - 6.57908i) q^{9} +(-2.59452 + 4.08351i) q^{10} +(-2.02722 - 0.266888i) q^{11} +(-4.22105 + 4.62897i) q^{12} +(1.71462 + 0.710220i) q^{13} +(3.23229 - 1.88476i) q^{14} -10.7156 q^{15} +(3.75209 - 1.38630i) q^{16} +(0.0973921 - 0.168688i) q^{17} +(-9.48813 - 1.66115i) q^{18} +(7.47190 - 0.983695i) q^{19} +(6.07659 + 3.14456i) q^{20} +(7.36266 + 3.80387i) q^{21} +(-0.122628 + 2.88905i) q^{22} +(0.230374 + 0.0617284i) q^{23} +(7.04823 + 5.36766i) q^{24} +(1.73494 + 6.47489i) q^{25} +(0.786204 - 2.50411i) q^{26} +(-4.56833 - 11.0289i) q^{27} +(-3.05895 - 4.31773i) q^{28} +(-1.82864 - 0.757448i) q^{29} +(1.33908 + 15.0948i) q^{30} +(-1.75660 + 3.04252i) q^{31} +(-2.42174 - 5.11226i) q^{32} +(-5.54655 + 3.20230i) q^{33} +(-0.249798 - 0.116114i) q^{34} +(1.93170 - 8.84261i) q^{35} +(-1.15434 + 13.5733i) q^{36} +(2.06988 - 2.69752i) q^{37} +(-2.31944 - 10.4026i) q^{38} +(5.61510 - 1.50456i) q^{39} +(3.67032 - 8.95294i) q^{40} +(-3.44057 + 3.44057i) q^{41} +(4.43836 - 10.8470i) q^{42} +(-0.957734 - 2.31218i) q^{43} +(4.08508 - 0.188289i) q^{44} +(-18.4860 + 14.1848i) q^{45} +(0.0581669 - 0.332237i) q^{46} +(-0.188303 + 0.108717i) q^{47} +(6.68053 - 10.5995i) q^{48} +(-4.46627 + 5.39003i) q^{49} +(8.90425 - 3.25312i) q^{50} +(-0.0796364 - 0.604898i) q^{51} +(-3.62574 - 0.794583i) q^{52} +(-1.25208 + 9.51051i) q^{53} +(-14.9654 + 7.81357i) q^{54} +(4.94619 + 4.94619i) q^{55} +(-5.70004 + 4.84866i) q^{56} +(16.6920 - 16.6920i) q^{57} +(-0.838486 + 2.67063i) q^{58} +(8.24826 + 1.08590i) q^{59} +(21.0964 - 3.77267i) q^{60} +(6.57814 - 0.866029i) q^{61} +(4.50546 + 2.09428i) q^{62} +(17.7371 - 3.18411i) q^{63} +(-6.89891 + 4.05032i) q^{64} +(-3.17451 - 5.49842i) q^{65} +(5.20415 + 7.41314i) q^{66} +(-3.43269 - 4.47357i) q^{67} +(-0.132352 + 0.366397i) q^{68} +(0.690184 - 0.285883i) q^{69} +(-12.6978 - 1.61612i) q^{70} +(6.51746 + 6.51746i) q^{71} +(19.2648 - 0.0701089i) q^{72} +(3.54282 + 13.2220i) q^{73} +(-4.05861 - 2.57871i) q^{74} +(16.6577 + 12.7819i) q^{75} +(-14.3641 + 4.56733i) q^{76} +(-1.64270 - 5.15436i) q^{77} +(-2.82114 - 7.72186i) q^{78} +(-5.91609 - 10.2470i) q^{79} +(-13.0705 - 4.05150i) q^{80} +(-14.6865 - 8.47925i) q^{81} +(5.27663 + 4.41672i) q^{82} +(-1.39613 + 3.37055i) q^{83} +(-15.8346 - 4.89674i) q^{84} +(-0.615635 + 0.255004i) q^{85} +(-3.13743 + 1.63809i) q^{86} +(-5.98849 + 1.60461i) q^{87} +(-0.775735 - 5.73105i) q^{88} +(-0.410138 + 1.53066i) q^{89} +(22.2920 + 24.2682i) q^{90} +(0.229347 + 4.90487i) q^{91} +(-0.475285 - 0.0404204i) q^{92} +(1.43635 + 10.9102i) q^{93} +(0.176679 + 0.251674i) q^{94} +(-22.3279 - 12.8910i) q^{95} +(-15.7661 - 8.08617i) q^{96} +15.9978i q^{97} +(8.15097 + 5.61798i) q^{98} +(-5.32958 + 12.8667i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 12 q^{10} - 4 q^{11} - 12 q^{12} - 40 q^{14} - 32 q^{15} - 24 q^{16} + 16 q^{18} - 12 q^{19} - 8 q^{21} - 8 q^{22} + 4 q^{23} - 12 q^{24} - 4 q^{25} - 12 q^{26} + 12 q^{28} - 16 q^{29} - 52 q^{30} - 4 q^{32} - 24 q^{33} - 32 q^{35} + 64 q^{36} - 4 q^{37} - 12 q^{38} - 4 q^{39} - 12 q^{40} - 28 q^{42} - 32 q^{43} - 52 q^{44} - 48 q^{45} - 4 q^{46} - 24 q^{47} - 40 q^{50} + 20 q^{51} + 60 q^{52} - 20 q^{53} - 12 q^{54} - 48 q^{56} - 16 q^{57} - 36 q^{58} + 84 q^{59} + 28 q^{60} - 12 q^{61} - 136 q^{64} - 8 q^{65} + 132 q^{66} + 36 q^{67} - 12 q^{68} + 28 q^{70} - 80 q^{71} - 4 q^{72} - 12 q^{73} - 20 q^{74} - 72 q^{75} - 8 q^{77} - 216 q^{78} - 8 q^{79} + 24 q^{80} + 108 q^{82} + 12 q^{84} + 24 q^{85} - 4 q^{86} - 12 q^{87} - 48 q^{88} - 12 q^{89} + 40 q^{91} - 80 q^{92} + 20 q^{93} + 60 q^{94} + 312 q^{96} - 16 q^{98} - 40 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 12 * q^10 - 4 * q^11 - 12 * q^12 - 40 * q^14 - 32 * q^15 - 24 * q^16 + 16 * q^18 - 12 * q^19 - 8 * q^21 - 8 * q^22 + 4 * q^23 - 12 * q^24 - 4 * q^25 - 12 * q^26 + 12 * q^28 - 16 * q^29 - 52 * q^30 - 4 * q^32 - 24 * q^33 - 32 * q^35 + 64 * q^36 - 4 * q^37 - 12 * q^38 - 4 * q^39 - 12 * q^40 - 28 * q^42 - 32 * q^43 - 52 * q^44 - 48 * q^45 - 4 * q^46 - 24 * q^47 - 40 * q^50 + 20 * q^51 + 60 * q^52 - 20 * q^53 - 12 * q^54 - 48 * q^56 - 16 * q^57 - 36 * q^58 + 84 * q^59 + 28 * q^60 - 12 * q^61 - 136 * q^64 - 8 * q^65 + 132 * q^66 + 36 * q^67 - 12 * q^68 + 28 * q^70 - 80 * q^71 - 4 * q^72 - 12 * q^73 - 20 * q^74 - 72 * q^75 - 8 * q^77 - 216 * q^78 - 8 * q^79 + 24 * q^80 + 108 * q^82 + 12 * q^84 + 24 * q^85 - 4 * q^86 - 12 * q^87 - 48 * q^88 - 12 * q^89 + 40 * q^91 - 80 * q^92 + 20 * q^93 + 60 * q^94 + 312 * q^96 - 16 * q^98 - 40 * q^99

Introduction

L-functions

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