LMFDB - Embedded newform 930.2.bs.a.107.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(107,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([30, 15, 44]))

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

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

chi := DirichletCharacter("930.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bs (of order $60$, degree $16$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			107.17
Character	$\chi$	$=$	930.107
Dual form			930.2.bs.a.113.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453990 - 0.891007i) q^{2} +(0.0494968 + 1.73134i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(0.307868 + 2.21477i) q^{5} +(1.52017 - 0.830115i) q^{6} +(-0.186966 + 0.151402i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-2.99510 + 0.171392i) q^{9} +O(q^{10})$	\(q+(-0.453990 - 0.891007i) q^{2} +(0.0494968 + 1.73134i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(0.307868 + 2.21477i) q^{5} +(1.52017 - 0.830115i) q^{6} +(-0.186966 + 0.151402i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-2.99510 + 0.171392i) q^{9} +(1.83361 - 1.27980i) q^{10} +(-2.00620 - 4.50600i) q^{11} +(-1.42978 - 0.977614i) q^{12} +(-4.76348 + 3.09344i) q^{13} +(0.219782 + 0.0978530i) q^{14} +(-3.81929 + 0.642649i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(-2.25707 + 0.866406i) q^{17} +(1.51246 + 2.59084i) q^{18} +(0.204908 + 0.964018i) q^{19} +(-1.97275 - 1.05274i) q^{20} +(-0.271384 - 0.316209i) q^{21} +(-3.10408 + 3.83322i) q^{22} +(6.01819 + 0.953188i) q^{23} +(-0.221954 + 1.71777i) q^{24} +(-4.81043 + 1.36371i) q^{25} +(4.91885 + 2.83990i) q^{26} +(-0.444986 - 5.17706i) q^{27} +(-0.0125910 - 0.240251i) q^{28} +(1.31190 - 4.03761i) q^{29} +(2.30653 + 3.11126i) q^{30} +(-5.34641 - 1.55432i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(7.70213 - 3.69645i) q^{33} +(1.79666 + 1.61772i) q^{34} +(-0.392883 - 0.367476i) q^{35} +(1.62182 - 2.52383i) q^{36} +(1.11892 - 4.17587i) q^{37} +(0.765920 - 0.620230i) q^{38} +(-5.59158 - 8.09410i) q^{39} +(-0.0423894 + 2.23567i) q^{40} +(5.33500 - 4.80366i) q^{41} +(-0.158539 + 0.385361i) q^{42} +(-0.511917 + 0.788283i) q^{43} +(4.82464 + 1.02551i) q^{44} +(-1.30169 - 6.58070i) q^{45} +(-1.88291 - 5.79499i) q^{46} +(-10.0217 - 5.10633i) q^{47} +(1.63131 - 0.582089i) q^{48} +(-1.44335 + 6.79042i) q^{49} +(3.39897 + 3.66702i) q^{50} +(-1.61176 - 3.86487i) q^{51} +(0.297258 - 5.67201i) q^{52} +(-2.43739 + 3.00993i) q^{53} +(-4.41078 + 2.74682i) q^{54} +(9.36211 - 5.83053i) q^{55} +(-0.208349 + 0.120290i) q^{56} +(-1.65890 + 0.402483i) q^{57} +(-4.19313 + 0.664126i) q^{58} +(-1.77046 + 1.96630i) q^{59} +(1.72501 - 3.46761i) q^{60} -13.6901 q^{61} +(1.04231 + 5.46933i) q^{62} +(0.534034 - 0.485510i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-8.31779 - 9.59765i) q^{65} +(-6.79026 - 5.18449i) q^{66} +(11.6271 - 3.11548i) q^{67} +(0.625732 - 2.33526i) q^{68} +(-1.35241 + 10.4667i) q^{69} +(-0.149059 + 0.516892i) q^{70} +(-3.26073 + 0.342717i) q^{71} +(-2.98504 - 0.299255i) q^{72} +(0.255132 - 0.664641i) q^{73} +(-4.22871 + 0.898840i) q^{74} +(-2.59916 - 8.26102i) q^{75} +(-0.900349 - 0.400861i) q^{76} +(1.05731 + 0.538727i) q^{77} +(-4.67337 + 8.65678i) q^{78} +(-4.71809 + 10.5970i) q^{79} +(2.01124 - 0.977202i) q^{80} +(8.94125 - 1.02667i) q^{81} +(-6.70213 - 2.57271i) q^{82} +(-0.798229 + 15.2311i) q^{83} +(0.415334 - 0.0336911i) q^{84} +(-2.61377 - 4.73215i) q^{85} +(0.934771 + 0.0982484i) q^{86} +(7.05542 + 2.07150i) q^{87} +(-1.27661 - 4.76436i) q^{88} +(-6.00221 - 4.36086i) q^{89} +(-5.27249 + 4.14739i) q^{90} +(0.422257 - 1.29957i) q^{91} +(-4.30855 + 4.30855i) q^{92} +(2.42644 - 9.33340i) q^{93} +11.2477i q^{94} +(-2.07200 + 0.750616i) q^{95} +(-1.25924 - 1.18925i) q^{96} +(1.81288 + 11.4461i) q^{97} +(6.70557 - 1.79675i) q^{98} +(6.78106 + 13.1521i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q - 8 q^{3} + 24 q^{7}+O(q^{10}) $ 1024 * q - 8 * q^3 + 24 * q^7	$ 1024 q - 8 q^{3} + 24 q^{7} + 8 q^{10} + 8 q^{12} - 8 q^{15} + 256 q^{16} + 44 q^{22} + 16 q^{25} - 20 q^{27} + 4 q^{28} + 48 q^{30} - 32 q^{31} - 52 q^{33} + 112 q^{37} + 12 q^{42} + 40 q^{45} + 24 q^{46} - 12 q^{48} + 16 q^{51} - 20 q^{55} - 40 q^{57} - 56 q^{58} - 12 q^{60} + 32 q^{61} + 224 q^{63} - 32 q^{66} + 24 q^{67} - 24 q^{70} - 88 q^{73} + 224 q^{75} - 96 q^{76} - 32 q^{78} + 48 q^{81} - 24 q^{85} + 20 q^{87} - 36 q^{88} + 8 q^{90} - 80 q^{91} - 252 q^{93} - 32 q^{97}+O(q^{100}) $ 1024 * q - 8 * q^3 + 24 * q^7 + 8 * q^10 + 8 * q^12 - 8 * q^15 + 256 * q^16 + 44 * q^22 + 16 * q^25 - 20 * q^27 + 4 * q^28 + 48 * q^30 - 32 * q^31 - 52 * q^33 + 112 * q^37 + 12 * q^42 + 40 * q^45 + 24 * q^46 - 12 * q^48 + 16 * q^51 - 20 * q^55 - 40 * q^57 - 56 * q^58 - 12 * q^60 + 32 * q^61 + 224 * q^63 - 32 * q^66 + 24 * q^67 - 24 * q^70 - 88 * q^73 + 224 * q^75 - 96 * q^76 - 32 * q^78 + 48 * q^81 - 24 * q^85 + 20 * q^87 - 36 * q^88 + 8 * q^90 - 80 * q^91 - 252 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{11}{15}\right)$

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 $

$2$	−0.453990	−	0.891007i	−0.321020	−	0.630037i
$2$	−0.453990	−	0.891007i	−0.321020	−	0.630037i
$3$	0.0494968	+	1.73134i	0.0285770	+	0.999592i
$3$	0.0494968	+	1.73134i	0.0285770	+	0.999592i
$4$	−0.587785	+	0.809017i	−0.293893	+	0.404508i
$5$	0.307868	+	2.21477i	0.137683	+	0.990476i
$5$	0.307868	+	2.21477i	0.137683	+	0.990476i
$6$	1.52017	−	0.830115i	0.620606	−	0.338893i
$7$	−0.186966	+	0.151402i	−0.0706667	+	0.0572247i	−0.664003	−	0.747730i	$-0.731144\pi$
$7$	−0.186966	+	0.151402i	−0.0706667	+	0.0572247i	0.593336	+	0.804955i	$0.297810\pi$
$8$	0.987688	+	0.156434i	0.349201	+	0.0553079i
$9$	−2.99510	+	0.171392i	−0.998367	+	0.0571306i
$10$	1.83361	−	1.27980i	0.579838	−	0.404708i
$11$	−2.00620	−	4.50600i	−0.604892	−	1.35861i	−0.913274	−	0.407347i	$-0.866454\pi$
$11$	−2.00620	−	4.50600i	−0.604892	−	1.35861i	0.308382	−	0.951263i	$-0.400213\pi$
$12$	−1.42978	−	0.977614i	−0.412742	−	0.282213i
$13$	−4.76348	+	3.09344i	−1.32115	+	0.857966i	−0.996143	−	0.0877451i	$-0.972034\pi$
$13$	−4.76348	+	3.09344i	−1.32115	+	0.857966i	−0.325009	+	0.945711i	$0.605367\pi$
$14$	0.219782	+	0.0978530i	0.0587391	+	0.0261523i
$15$	−3.81929	+	0.642649i	−0.986137	+	0.165931i
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	−2.25707	+	0.866406i	−0.547419	+	0.210134i	−0.616329	−	0.787488i	$-0.711381\pi$
$17$	−2.25707	+	0.866406i	−0.547419	+	0.210134i	0.0689107	+	0.997623i	$0.478048\pi$
$18$	1.51246	+	2.59084i	0.356490	+	0.610668i
$19$	0.204908	+	0.964018i	0.0470092	+	0.221161i	0.995381	−	0.0959983i	$-0.0306044\pi$
$19$	0.204908	+	0.964018i	0.0470092	+	0.221161i	−0.948372	+	0.317159i	$0.897271\pi$
$20$	−1.97275	−	1.05274i	−0.441120	−	0.235400i
$21$	−0.271384	−	0.316209i	−0.0592208	−	0.0690025i
$22$	−3.10408	+	3.83322i	−0.661792	+	0.817245i
$23$	6.01819	+	0.953188i	1.25488	+	0.198753i	0.748254	−	0.663412i	$-0.230892\pi$
$23$	6.01819	+	0.953188i	1.25488	+	0.198753i	0.506626	+	0.862166i	$0.330892\pi$
$24$	−0.221954	+	1.71777i	−0.0453062	+	0.350638i
$25$	−4.81043	+	1.36371i	−0.962087	+	0.272743i
$26$	4.91885	+	2.83990i	0.964666	+	0.556950i
$27$	−0.444986	−	5.17706i	−0.0856376	−	0.996326i
$28$	−0.0125910	−	0.240251i	−0.00237948	−	0.0454032i
$29$	1.31190	−	4.03761i	0.243614	−	0.749765i	−0.752248	−	0.658880i	$-0.771030\pi$
$29$	1.31190	−	4.03761i	0.243614	−	0.749765i	0.995861	−	0.0908851i	$-0.0289696\pi$
$30$	2.30653	+	3.11126i	0.421112	+	0.568036i
$31$	−5.34641	−	1.55432i	−0.960243	−	0.279165i
$31$	−5.34641	−	1.55432i	−0.960243	−	0.279165i
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	7.70213	−	3.69645i	1.34077	−	0.643470i
$34$	1.79666	+	1.61772i	0.308125	+	0.277437i
$35$	−0.392883	−	0.367476i	−0.0664093	−	0.0621148i
$36$	1.62182	−	2.52383i	0.270303	−	0.420638i
$37$	1.11892	−	4.17587i	0.183950	−	0.686509i	−0.810903	−	0.585180i	$-0.801024\pi$
$37$	1.11892	−	4.17587i	0.183950	−	0.686509i	0.994853	−	0.101329i	$-0.0323096\pi$
$38$	0.765920	−	0.620230i	0.124249	−	0.100615i
$39$	−5.59158	−	8.09410i	−0.895370	−	1.29609i
$40$	−0.0423894	+	2.23567i	−0.00670235	+	0.353490i
$41$	5.33500	−	4.80366i	0.833187	−	0.750205i	−0.137513	−	0.990500i	$-0.543911\pi$
$41$	5.33500	−	4.80366i	0.833187	−	0.750205i	0.970700	+	0.240295i	$0.0772442\pi$
$42$	−0.158539	+	0.385361i	−0.0244631	+	0.0594624i
$43$	−0.511917	+	0.788283i	−0.0780666	+	0.120212i	−0.875547	−	0.483132i	$-0.839499\pi$
$43$	−0.511917	+	0.788283i	−0.0780666	+	0.120212i	0.797481	+	0.603345i	$0.206166\pi$
$44$	4.82464	+	1.02551i	0.727342	+	0.154601i
$45$	−1.30169	−	6.58070i	−0.194044	−	0.980993i
$46$	−1.88291	−	5.79499i	−0.277619	−	0.854424i
$47$	−10.0217	−	5.10633i	−1.46182	−	0.744835i	−0.471271	−	0.881989i	$-0.656205\pi$
$47$	−10.0217	−	5.10633i	−1.46182	−	0.744835i	−0.990550	+	0.137154i	$0.956205\pi$
$48$	1.63131	−	0.582089i	0.235459	−	0.0840173i
$49$	−1.44335	+	6.79042i	−0.206193	+	0.970060i
$50$	3.39897	+	3.66702i	0.480687	+	0.518594i
$51$	−1.61176	−	3.86487i	−0.225692	−	0.541190i
$52$	0.297258	−	5.67201i	0.0412222	−	0.786567i
$53$	−2.43739	+	3.00993i	−0.334802	+	0.413446i	−0.916548	−	0.399924i	$-0.869036\pi$
$53$	−2.43739	+	3.00993i	−0.334802	+	0.413446i	0.581746	+	0.813370i	$0.302370\pi$
$54$	−4.41078	+	2.74682i	−0.600231	+	0.373795i
$55$	9.36211	−	5.83053i	1.26239	−	0.786188i
$56$	−0.208349	+	0.120290i	−0.0278418	+	0.0160745i
$57$	−1.65890	+	0.402483i	−0.219727	+	0.0533101i
$58$	−4.19313	+	0.664126i	−0.550584	+	0.0872040i
$59$	−1.77046	+	1.96630i	−0.230494	+	0.255990i	−0.847287	−	0.531136i	$-0.821765\pi$
$59$	−1.77046	+	1.96630i	−0.230494	+	0.255990i	0.616792	+	0.787126i	$0.288432\pi$
$60$	1.72501	−	3.46761i	0.222698	−	0.447667i
$61$	−13.6901			−1.75283			−0.876416	−	0.481554i	$-0.840072\pi$
$61$	−13.6901			−1.75283			−0.876416	+	0.481554i	$0.840072\pi$
$62$	1.04231	+	5.46933i	0.132373	+	0.694606i
$63$	0.534034	−	0.485510i	0.0672820	−	0.0611685i
$64$	0.951057	+	0.309017i	0.118882	+	0.0386271i
$65$	−8.31779	−	9.59765i	−1.03169	−	1.19044i
$66$	−6.79026	−	5.18449i	−0.835823	−	0.638167i
$67$	11.6271	−	3.11548i	1.42048	−	0.380617i	0.534826	−	0.844962i	$-0.320377\pi$
$67$	11.6271	−	3.11548i	1.42048	−	0.380617i	0.885654	+	0.464345i	$0.153710\pi$
$68$	0.625732	−	2.33526i	0.0758812	−	0.283192i
$69$	−1.35241	+	10.4667i	−0.162812	+	1.26005i
$70$	−0.149059	+	0.516892i	−0.0178159	+	0.0617804i
$71$	−3.26073	+	0.342717i	−0.386978	+	0.0406730i	−0.296020	−	0.955182i	$-0.595660\pi$
$71$	−3.26073	+	0.342717i	−0.386978	+	0.0406730i	−0.0909579	+	0.995855i	$0.528993\pi$
$72$	−2.98504	−	0.299255i	−0.351790	−	0.0352676i
$73$	0.255132	−	0.664641i	0.0298609	−	0.0777904i	−0.917839	−	0.396952i	$-0.870068\pi$
$73$	0.255132	−	0.664641i	0.0298609	−	0.0777904i	0.947700	+	0.319162i	$0.103401\pi$
$74$	−4.22871	+	0.898840i	−0.491578	+	0.104488i
$75$	−2.59916	−	8.26102i	−0.300125	−	0.953900i
$76$	−0.900349	−	0.400861i	−0.103277	−	0.0459819i
$77$	1.05731	+	0.538727i	0.120492	+	0.0613936i
$78$	−4.67337	+	8.65678i	−0.529155	+	0.980188i
$79$	−4.71809	+	10.5970i	−0.530827	+	1.19226i	0.426827	+	0.904333i	$0.359631\pi$
$79$	−4.71809	+	10.5970i	−0.530827	+	1.19226i	−0.957654	+	0.287923i	$0.907035\pi$
$80$	2.01124	−	0.977202i	0.224863	−	0.109255i
$81$	8.94125	−	1.02667i	0.993472	−	0.114075i
$82$	−6.70213	−	2.57271i	−0.740126	−	0.284108i
$83$	−0.798229	+	15.2311i	−0.0876170	+	1.67183i	0.502548	+	0.864549i	$0.332396\pi$
$83$	−0.798229	+	15.2311i	−0.0876170	+	1.67183i	−0.590165	+	0.807282i	$0.700937\pi$
$84$	0.415334	−	0.0336911i	0.0453167	−	0.00367600i
$85$	−2.61377	−	4.73215i	−0.283503	−	0.513273i
$86$	0.934771	+	0.0982484i	0.100799	+	0.0105944i
$87$	7.05542	+	2.07150i	0.756421	+	0.222088i
$88$	−1.27661	−	4.76436i	−0.136087	−	0.507882i
$89$	−6.00221	−	4.36086i	−0.636233	−	0.462250i	0.222321	−	0.974974i	$-0.428637\pi$
$89$	−6.00221	−	4.36086i	−0.636233	−	0.462250i	−0.858554	+	0.512723i	$0.828637\pi$
$90$	−5.27249	+	4.14739i	−0.555769	+	0.437173i
$91$	0.422257	−	1.29957i	0.0442645	−	0.136232i
$92$	−4.30855	+	4.30855i	−0.449197	+	0.449197i
$93$	2.42644	−	9.33340i	0.251610	−	0.967829i
$94$			11.2477i			1.16011i
$95$	−2.07200	+	0.750616i	−0.212582	+	0.0770115i
$96$	−1.25924	−	1.18925i	−0.128521	−	0.121377i
$97$	1.81288	+	11.4461i	0.184070	+	1.16218i	0.890700	+	0.454592i	$0.150215\pi$
$97$	1.81288	+	11.4461i	0.184070	+	1.16218i	−0.706629	+	0.707584i	$0.749785\pi$
$98$	6.70557	−	1.79675i	0.677365	−	0.181499i
$99$	6.78106	+	13.1521i	0.681522	+	1.32183i
$100$	1.72423	−	4.69329i	0.172423	−	0.469329i
$101$	−3.32721	−	4.57951i	−0.331069	−	0.455678i	0.610737	−	0.791833i	$-0.290873\pi$
$101$	−3.32721	−	4.57951i	−0.331069	−	0.455678i	−0.941807	+	0.336155i	$0.890873\pi$
$102$	−2.71190	+	3.19071i	−0.268518	+	0.315927i
$103$	7.25081	+	0.379999i	0.714444	+	0.0374424i	0.406095	−	0.913831i	$-0.366890\pi$
$103$	7.25081	+	0.379999i	0.714444	+	0.0374424i	0.308349	+	0.951273i	$0.400224\pi$
$104$	−5.18875	+	2.31018i	−0.508799	+	0.226532i
$105$	0.616781	−	0.698404i	0.0601917	−	0.0681573i
$106$	3.78842	+	0.805254i	0.367964	+	0.0782132i
$107$	7.46029	−	2.86374i	0.721213	−	0.276848i	0.0300519	−	0.999548i	$-0.490433\pi$
$107$	7.46029	−	2.86374i	0.721213	−	0.276848i	0.691161	+	0.722701i	$0.257099\pi$
$108$	4.44989	+	2.68300i	0.428191	+	0.258172i
$109$	3.87238	−	1.25821i	0.370907	−	0.120515i	−0.117632	−	0.993057i	$-0.537530\pi$
$109$	3.87238	−	1.25821i	0.370907	−	0.120515i	0.488538	+	0.872542i	$0.337530\pi$
$110$	−9.44535	−	5.69470i	−0.900579	−	0.542969i
$111$	7.28525	+	1.73055i	0.691486	+	0.164256i
$112$	0.201768	+	0.131030i	0.0190653	+	0.0123811i
$113$	−18.7396	−	7.19345i	−1.76287	−	0.676703i	−0.999528	−	0.0307080i	$-0.990224\pi$
$113$	−18.7396	−	7.19345i	−1.76287	−	0.676703i	−0.763342	−	0.645995i	$-0.776443\pi$
$114$	1.11174	+	1.29537i	0.104124	+	0.121323i
$115$	−0.258287	+	13.6224i	−0.0240854	+	1.27029i
$116$	2.49538	+	3.43460i	0.231690	+	0.318894i
$117$	13.7369	−	10.0816i	1.26998	−	0.932043i
$118$	2.55576	+	0.684813i	0.235276	+	0.0630421i
$119$	0.290819	−	0.503714i	0.0266594	−	0.0461754i
$120$	−3.87280	+	0.0372677i	−0.353537	+	0.00340206i
$121$	−8.91874	+	9.90526i	−0.810794	+	0.900478i
$122$	6.21516	+	12.1979i	0.562694	+	1.10435i
$123$	8.58084	+	8.99895i	0.773708	+	0.811408i
$124$	4.40001	−	3.41173i	0.395133	−	0.306382i
$125$	−4.50129	−	10.2342i	−0.402608	−	0.915372i
$126$	−0.675039	−	0.255411i	−0.0601372	−	0.0227538i
$127$	1.13137	−	0.0592924i	0.100393	−	0.00526135i	−0.00207352	−	0.999998i	$-0.500660\pi$
$127$	1.13137	−	0.0592924i	0.100393	−	0.00526135i	0.102466	+	0.994736i	$0.467327\pi$
$128$	−0.156434	−	0.987688i	−0.0138270	−	0.0873001i
$129$	−1.39013	−	0.847287i	−0.122394	−	0.0745995i
$130$	−4.77538	+	11.7684i	−0.418828	+	1.03216i
$131$	−5.20248	−	0.546803i	−0.454543	−	0.0477744i	−0.125509	−	0.992092i	$-0.540056\pi$
$131$	−5.20248	−	0.546803i	−0.454543	−	0.0477744i	−0.329034	+	0.944318i	$0.606723\pi$
$132$	−1.53670	+	8.40387i	−0.133753	+	0.731463i
$133$	−0.184266	−	0.149215i	−0.0159779	−	0.0129386i
$134$	−8.05452	−	8.94545i	−0.695805	−	0.772770i
$135$	11.3290	−	2.57939i	0.975047	−	0.221999i
$136$	−2.36481	+	0.502656i	−0.202781	+	0.0431024i
$137$	−0.692680	+	0.449832i	−0.0591796	+	0.0384317i	−0.573890	−	0.818933i	$-0.694566\pi$
$137$	−0.692680	+	0.449832i	−0.0591796	+	0.0384317i	0.514710	+	0.857364i	$0.327900\pi$
$138$	9.93992	−	3.54679i	0.846142	−	0.301923i
$139$	−14.6670	+	4.76559i	−1.24404	+	0.404212i	−0.855780	−	0.517339i	$-0.826923\pi$
$139$	−14.6670	+	4.76559i	−1.24404	+	0.404212i	−0.388257	+	0.921551i	$0.626923\pi$
$140$	0.528225	−	0.101852i	0.0446432	−	0.00860805i
$141$	8.34477	−	17.6038i	0.702756	−	1.48251i
$142$	1.78571	+	2.74975i	0.149853	+	0.230754i
$143$	23.4955	+	15.2582i	1.96479	+	1.27595i
$144$	1.08854	+	2.79555i	0.0907117	+	0.232962i
$145$	9.34628	+	1.66251i	0.776166	+	0.138064i
$146$	−0.708027	+	0.0744167i	−0.0585968	+	0.00615877i
$147$	−11.8280	−	2.16283i	−0.975556	−	0.178387i
$148$	2.72067	+	3.35974i	0.223637	+	0.276169i
$149$	−4.63836	−	8.03388i	−0.379990	−	0.658161i	0.611071	−	0.791576i	$-0.290739\pi$
$149$	−4.63836	−	8.03388i	−0.379990	−	0.658161i	−0.991060	+	0.133415i	$0.957406\pi$
$150$	−6.18063	+	6.06629i	−0.504646	+	0.495310i
$151$	−3.39867	−	2.46927i	−0.276579	−	0.200947i	0.440845	−	0.897583i	$-0.354679\pi$
$151$	−3.39867	−	2.46927i	−0.276579	−	0.200947i	−0.717424	+	0.696637i	$0.754679\pi$
$152$	0.0515800	+	0.984204i	0.00418369	+	0.0798295i
$153$	6.61164	−	2.98182i	0.534519	−	0.241066i
$154$		−	1.18665i		−	0.0956228i
$155$	1.79648	−	12.3196i	0.144297	−	0.989534i
$156$	9.83492	+	0.233909i	0.787424	+	0.0187277i
$157$	−1.31130	+	0.668141i	−0.104653	+	0.0533235i	−0.505534	−	0.862807i	$-0.668704\pi$
$157$	−1.31130	+	0.668141i	−0.104653	+	0.0533235i	0.400880	+	0.916130i	$0.368704\pi$
$158$	11.5840	−	0.607090i	0.921571	−	0.0482975i
$159$	−5.33187	−	4.07098i	−0.422845	−	0.322850i
$160$	−1.78378	−	1.34839i	−0.141020	−	0.106599i
$161$	−1.26952	+	0.732955i	−0.100052	+	0.0577649i
$162$	−4.97401	−	7.50061i	−0.390795	−	0.589304i
$163$	−3.17516	+	20.0472i	−0.248698	+	1.57022i	0.474929	+	0.880024i	$0.342474\pi$
$163$	−3.17516	+	20.0472i	−0.248698	+	1.57022i	−0.723627	+	0.690191i	$0.757526\pi$
$164$	0.750405	+	7.13962i	0.0585968	+	0.557511i
$165$	10.5580	+	15.9204i	0.821942	+	1.23940i
$166$	13.9334	−	6.20355i	1.08144	−	0.481489i
$167$	−8.62187	+	13.2765i	−0.667180	+	1.02737i	0.329356	+	0.944206i	$0.393168\pi$
$167$	−8.62187	+	13.2765i	−0.667180	+	1.02737i	−0.996536	+	0.0831613i	$0.973498\pi$
$168$	−0.218577	−	0.354770i	−0.0168636	−	0.0273711i
$169$	7.83380	−	17.5950i	0.602600	−	1.35346i
$170$	−3.02975	+	4.47724i	−0.232371	+	0.343388i
$171$	−0.778946	−	2.85221i	−0.0595675	−	0.218114i
$172$	−0.336837	−	0.877491i	−0.0256836	−	0.0669081i
$173$	3.11391	+	4.79500i	0.236746	+	0.364557i	0.936996	−	0.349341i	$-0.113595\pi$
$173$	3.11391	+	4.79500i	0.236746	+	0.364557i	−0.700250	+	0.713898i	$0.746928\pi$
$174$	−1.35738	−	7.22687i	−0.102902	−	0.547868i
$175$	0.692920	−	0.983280i	0.0523798	−	0.0743290i
$176$	−3.66551	+	3.30044i	−0.276298	+	0.248780i
$177$	−3.49197	−	2.96795i	−0.262472	−	0.223085i
$178$	−1.16061	+	7.32780i	−0.0869913	+	0.549242i
$179$	−0.314152	+	2.98896i	−0.0234808	+	0.223405i	0.976488	+	0.215570i	$0.0691608\pi$
$179$	−0.314152	+	2.98896i	−0.0234808	+	0.223405i	−0.999969	+	0.00783552i	$0.997506\pi$
$180$	6.08901	+	2.81495i	0.453848	+	0.209814i
$181$	−7.60838	+	13.1781i	−0.565527	+	0.979521i	0.431474	+	0.902126i	$0.357994\pi$
$181$	−7.60838	+	13.1781i	−0.565527	+	0.979521i	−0.997000	+	0.0773956i	$0.975340\pi$
$182$	−1.34963	+	0.213760i	−0.100041	+	0.0158449i
$183$	−0.677614	−	23.7022i	−0.0500907	−	1.75212i
$184$	5.79499	+	1.88291i	0.427212	+	0.138810i
$185$	9.59309	+	1.19254i	0.705298	+	0.0876773i
$186$	−9.41770	+	2.07531i	−0.690539	+	0.152169i
$187$	8.43215	+	8.43215i	0.616620	+	0.616620i
$188$	10.0217	−	5.10633i	0.730910	−	0.372417i
$189$	0.867017	+	0.900565i	0.0630662	+	0.0655065i
$190$	1.60947	+	1.50539i	0.116763	+	0.109212i
$191$	−15.1155	−	8.72695i	−1.09372	−	0.631460i	−0.159156	−	0.987253i	$-0.550877\pi$
$191$	−15.1155	−	8.72695i	−1.09372	−	0.631460i	−0.934565	+	0.355794i	$0.884211\pi$
$192$	−0.487940	+	1.66190i	−0.0352141	+	0.119937i
$193$	2.66046	+	3.28540i	0.191504	+	0.236488i	0.863850	−	0.503749i	$-0.168046\pi$
$193$	2.66046	+	3.28540i	0.191504	+	0.236488i	−0.672346	+	0.740237i	$0.734713\pi$
$194$	9.37552	−	6.81171i	0.673123	−	0.489052i
$195$	16.2051	−	14.8760i	1.16047	−	1.06529i
$196$	−4.64519	−	5.15900i	−0.331799	−	0.368500i
$197$	−6.28134	+	16.3634i	−0.447527	+	1.16585i	0.505464	+	0.862848i	$0.331321\pi$
$197$	−6.28134	+	16.3634i	−0.447527	+	1.16585i	−0.952991	+	0.302999i	$0.902012\pi$
$198$	8.64004	−	12.0129i	0.614021	−	0.853718i
$199$	−0.738703	+	3.47532i	−0.0523652	+	0.246359i	−0.996543	−	0.0830770i	$-0.973525\pi$
$199$	−0.738703	+	3.47532i	−0.0523652	+	0.246359i	0.944178	+	0.329436i	$0.106859\pi$
$200$	−4.96454	+	0.594407i	−0.351046	+	0.0420309i
$201$	5.96947	+	19.9764i	0.421054	+	1.40902i
$202$	−2.56985	+	5.04362i	−0.180814	+	0.354868i
$203$	0.366023	+	0.953522i	0.0256898	+	0.0669241i
$204$	4.07412	+	0.967769i	0.285245	+	0.0677574i
$205$	12.2815	+	10.3369i	0.857776	+	0.721962i
$206$	−2.95322	−	6.63304i	−0.205760	−	0.462145i
$207$	−18.1885	−	1.82342i	−1.26419	−	0.126737i
$208$	4.41403	+	3.57441i	0.306058	+	0.247841i
$209$	3.93278	−	2.85733i	0.272036	−	0.197646i
$210$	−0.902295	−	0.232487i	−0.0622643	−	0.0160431i
$211$	12.3582	+	21.4050i	0.850773	+	1.47358i	0.880512	+	0.474024i	$0.157199\pi$
$211$	12.3582	+	21.4050i	0.850773	+	1.47358i	−0.0297396	+	0.999558i	$0.509468\pi$
$212$	−1.00242	−	3.74109i	−0.0688466	−	0.256939i
$213$	−0.754757	−	5.62849i	−0.0517151	−	0.385658i
$214$	−5.93851	−	5.34706i	−0.405948	−	0.365517i
$215$	−1.90347	−	0.891093i	−0.129816	−	0.0607720i
$216$	0.370364	−	5.18294i	0.0252001	−	0.352654i
$217$	1.23493	−	0.518853i	0.0838323	−	0.0352220i
$218$	−2.87910	−	2.87910i	−0.194997	−	0.194997i
$219$	1.16335	+	0.408823i	0.0786120	+	0.0276257i
$220$	−0.785918	+	11.0012i	−0.0529866	+	0.741701i
$221$	8.07131	−	11.1092i	0.542935	−	0.747286i
$222$	−1.76551	−	7.27686i	−0.118493	−	0.488391i
$223$	−11.7301	−	3.14307i	−0.785505	−	0.210475i	−0.156295	−	0.987710i	$-0.549955\pi$
$223$	−11.7301	−	3.14307i	−0.785505	−	0.210475i	−0.629210	+	0.777235i	$0.716622\pi$
$224$	0.0251475	−	0.239263i	0.00168024	−	0.0159864i
$225$	14.1740	−	4.90893i	0.944934	−	0.327262i
$226$	2.09818	+	19.9628i	0.139569	+	1.32791i
$227$	25.6155	+	1.34245i	1.70016	+	0.0891018i	0.877546	−	0.479493i	$-0.159179\pi$
$227$	25.6155	+	1.34245i	1.70016	+	0.0891018i	0.822618	+	0.568595i	$0.192513\pi$
$228$	0.649464	−	1.57865i	0.0430118	−	0.104549i
$229$	−1.26298	−	5.94184i	−0.0834598	−	0.392648i	0.916513	−	0.400005i	$-0.130992\pi$
$229$	−1.26298	−	5.94184i	−0.0834598	−	0.392648i	−0.999973	+	0.00735701i	$0.997658\pi$
$230$	12.2549	−	5.95430i	0.808064	−	0.392615i
$231$	−0.880388	+	1.85723i	−0.0579252	+	0.122197i
$232$	1.92737	−	3.78267i	0.126538	−	0.248345i
$233$	8.89523	−	17.4579i	0.582746	−	1.14370i	−0.391912	−	0.920003i	$-0.628186\pi$
$233$	8.89523	−	17.4579i	0.582746	−	1.14370i	0.974658	−	0.223700i	$-0.0718137\pi$
$234$	−15.2192	−	7.66273i	−0.994909	−	0.500928i
$235$	8.22399	−	23.7679i	0.536474	−	1.55045i
$236$	−0.550116	−	2.58809i	−0.0358095	−	0.168471i
$237$	−18.5806	−	7.64412i	−1.20694	−	0.496539i
$238$	−0.580842	−	0.0304406i	−0.0376504	−	0.00197317i
$239$	1.14773	+	10.9199i	0.0742406	+	0.706352i	0.966819	+	0.255461i	$0.0822271\pi$
$239$	1.14773	+	10.9199i	0.0742406	+	0.706352i	−0.892579	+	0.450891i	$0.851106\pi$
$240$	1.79142	+	3.43377i	0.115636	+	0.221649i
$241$	1.81346	−	17.2540i	0.116815	−	1.11142i	−0.766369	−	0.642400i	$-0.777939\pi$
$241$	1.81346	−	17.2540i	0.116815	−	1.11142i	0.883185	−	0.469025i	$-0.155395\pi$
$242$	12.8747	+	3.44976i	0.827616	+	0.221759i
$243$	2.22008	+	15.4296i	0.142418	+	0.989807i
$244$	8.04681	−	11.0755i	0.515145	−	0.709036i
$245$	−15.4836	−	1.10614i	−0.989211	−	0.0706685i
$246$	4.12250	−	11.7310i	0.262841	−	0.747943i
$247$	−3.95821	−	3.95821i	−0.251855	−	0.251855i
$248$	−5.03744	−	2.37155i	−0.319877	−	0.150594i
$249$	−26.4098	−	0.628117i	−1.67365	−	0.0398053i
$250$	−7.07517	+	8.65690i	−0.447473	+	0.547510i
$251$	17.2033	+	15.4899i	1.08586	+	0.977714i	0.999827	−	0.0185778i	$-0.00591384\pi$
$251$	17.2033	+	15.4899i	1.08586	+	0.977714i	0.0860344	+	0.996292i	$0.472581\pi$
$252$	0.0788885	+	0.717418i	0.00496951	+	0.0451931i
$253$	−7.77863	−	29.0302i	−0.489038	−	1.82512i
$254$	−0.566460	−	0.981137i	−0.0355428	−	0.0615620i
$255$	8.06360	−	4.75956i	0.504962	−	0.298055i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−2.98354	−	2.41602i	−0.186108	−	0.150707i	0.531739	−	0.846908i	$-0.321539\pi$
$257$	−2.98354	−	2.41602i	−0.186108	−	0.150707i	−0.717847	+	0.696201i	$0.754872\pi$
$258$	−0.123834	+	1.62327i	−0.00770954	+	0.101061i
$259$	0.423037	+	0.950156i	0.0262862	+	0.0590398i
$260$	12.6537	−	1.08787i	0.784752	−	0.0674670i
$261$	−3.23726	+	12.3179i	−0.200381	+	0.762459i
$262$	1.87467	+	4.88369i	0.115818	+	0.301715i
$263$	5.84332	−	11.4682i	0.360315	−	0.707157i	−0.637690	−	0.770293i	$-0.720110\pi$
$263$	5.84332	−	11.4682i	0.360315	−	0.707157i	0.998005	+	0.0631356i	$0.0201101\pi$
$264$	8.18555	−	2.44606i	0.503786	−	0.150545i
$265$	−7.41671	−	4.47161i	−0.455605	−	0.274689i
$266$	−0.0492970	+	0.231924i	−0.00302259	+	0.0142202i
$267$	7.25306	−	10.6077i	0.443880	−	0.649183i
$268$	−4.31378	+	11.2378i	−0.263506	+	0.686457i
$269$	−0.251739	−	0.279585i	−0.0153488	−	0.0170466i	0.735422	−	0.677610i	$-0.236984\pi$
$269$	−0.251739	−	0.279585i	−0.0153488	−	0.0170466i	−0.750770	+	0.660563i	$0.770318\pi$
$270$	−7.44152	−	8.92321i	−0.452877	−	0.543049i
$271$	8.97835	−	6.52315i	0.545396	−	0.396253i	−0.280689	−	0.959799i	$-0.590563\pi$
$271$	8.97835	−	6.52315i	0.545396	−	0.396253i	0.826085	+	0.563545i	$0.190563\pi$
$272$	1.52147	+	1.87886i	0.0922528	+	0.113923i
$273$	2.27091	+	0.666746i	0.137441	+	0.0403533i
$274$	0.715273	+	0.412963i	0.0432112	+	0.0249480i
$275$	15.7956	+	18.9399i	0.952509	+	1.14212i
$276$	−7.67284	−	7.24632i	−0.461851	−	0.436177i
$277$	14.1720	−	7.22102i	0.851516	−	0.433869i	0.0269513	−	0.999637i	$-0.491420\pi$
$277$	14.1720	−	7.22102i	0.851516	−	0.433869i	0.824565	+	0.565768i	$0.191420\pi$
$278$	10.9048	+	10.9048i	0.654029	+	0.654029i
$279$	16.2794	+	3.73902i	0.974624	+	0.223849i
$280$	−0.330560	−	0.424412i	−0.0197547	−	0.0253635i
$281$	−14.4489	−	4.69473i	−0.861949	−	0.280064i	−0.155507	−	0.987835i	$-0.549701\pi$
$281$	−14.4489	−	4.69473i	−0.861949	−	0.280064i	−0.706442	+	0.707770i	$0.749701\pi$
$282$	−19.4736	+	0.556723i	−1.15963	+	0.0331524i
$283$	18.5300	−	2.93486i	1.10149	−	0.174459i	0.420890	−	0.907112i	$-0.361718\pi$
$283$	18.5300	−	2.93486i	1.10149	−	0.174459i	0.680603	+	0.732652i	$0.261718\pi$
$284$	1.63935	−	2.83943i	0.0972774	−	0.168489i
$285$	−1.40213	−	3.55018i	−0.0830550	−	0.210295i
$286$	2.92839	−	27.8617i	0.173159	−	1.64750i
$287$	−0.270181	+	1.70585i	−0.0159483	+	0.100693i
$288$	1.99666	−	2.23905i	0.117655	−	0.131937i
$289$	−8.28978	+	7.46415i	−0.487634	+	0.439068i
$290$	−2.76182	−	9.08236i	−0.162179	−	0.533334i
$291$	−19.7274	+	3.70527i	−1.15644	+	0.217207i
$292$	0.387743	+	0.597072i	0.0226910	+	0.0349410i
$293$	7.47023	+	19.4606i	0.436416	+	1.13690i	0.958773	+	0.284175i	$0.0917195\pi$
$293$	7.47023	+	19.4606i	0.436416	+	1.13690i	−0.522357	+	0.852727i	$0.674947\pi$
$294$	3.44270	+	11.5207i	0.200782	+	0.671902i
$295$	−4.89997	−	3.31581i	−0.285287	−	0.193054i
$296$	1.75840	−	3.94942i	0.102205	−	0.229556i
$297$	−22.4351	+	12.3913i	−1.30182	+	0.719018i
$298$	−5.05247	+	7.78012i	−0.292682	+	0.450690i
$299$	−31.6162	+	14.0764i	−1.82841	+	0.814061i
$300$	8.21105	+	2.75294i	0.474065	+	0.158941i
$301$	−0.0236367	−	0.224888i	−0.00136240	−	0.0129623i
$302$	−0.657178	+	4.14926i	−0.0378164	+	0.238763i
$303$	7.76401	−	5.98721i	0.446031	−	0.343956i
$304$	0.853516	−	0.492777i	0.0489525	−	0.0282627i
$305$	−4.21473	−	30.3204i	−0.241335	−	1.73614i
$306$	−5.65844	−	4.53730i	−0.323471	−	0.259380i
$307$	32.6594	−	1.71161i	1.86397	−	0.0976866i	0.913187	−	0.407540i	$-0.133613\pi$
$307$	32.6594	−	1.71161i	1.86397	−	0.0976866i	0.950784	+	0.309853i	$0.100280\pi$
$308$	−1.05731	+	0.538727i	−0.0602459	+	0.0306968i
$309$	−0.299017	+	12.5725i	−0.0170105	+	0.715222i
$310$	−11.7924	+	3.99230i	−0.669765	+	0.226748i
$311$			16.5976i			0.941162i	0.882357	+	0.470581i	$0.155956\pi$
$311$			16.5976i			0.941162i	−0.882357	+	0.470581i	$0.844044\pi$
$312$	−4.25655	−	8.86917i	−0.240979	−	0.502118i
$313$	0.489533	+	9.34085i	0.0276701	+	0.527976i	0.976940	+	0.213514i	$0.0684909\pi$
$313$	0.489533	+	9.34085i	0.0276701	+	0.527976i	−0.949270	+	0.314462i	$0.898176\pi$
$314$	1.19064	+	0.865048i	0.0671915	+	0.0488175i
$315$	1.23971	+	1.03329i	0.0698495	+	0.0582194i
$316$	−5.79993	−	10.0458i	−0.326272	−	0.565119i
$317$	16.5421	+	20.4279i	0.929100	+	1.14734i	0.988818	+	0.149127i	$0.0476464\pi$
$317$	16.5421	+	20.4279i	0.929100	+	1.14734i	−0.0597183	+	0.998215i	$0.519020\pi$
$318$	−1.20666	+	6.59892i	−0.0676659	+	0.370049i
$319$	−20.8254	+	2.18884i	−1.16600	+	0.122551i
$320$	−0.391603	+	2.20151i	−0.0218913	+	0.123068i
$321$	5.32737	+	12.7746i	0.297345	+	0.713007i
$322$	1.22942	+	0.798392i	0.0685126	+	0.0444926i
$323$	−1.29772	−	1.99832i	−0.0722072	−	0.111189i
$324$	−4.42494	+	7.83709i	−0.245830	+	0.435394i
$325$	18.6958	−	21.3768i	1.03706	−	1.18577i
$326$	19.3036	−	6.27214i	1.06913	−	0.347381i
$327$	2.37007	+	6.64214i	0.131065	+	0.367311i
$328$	6.02077	−	3.90994i	0.332442	−	0.215890i
$329$	2.64684	−	0.562603i	0.145925	−	0.0310173i
$330$	9.39197	−	16.6350i	0.517011	−	0.915727i
$331$	19.5743	+	21.7395i	1.07590	+	1.19491i	0.979892	+	0.199529i	$0.0639413\pi$
$331$	19.5743	+	21.7395i	1.07590	+	1.19491i	0.0960096	+	0.995380i	$0.469392\pi$
$332$	−11.8530	−	9.59840i	−0.650520	−	0.526781i
$333$	−2.63557	+	12.6989i	−0.144428	+	0.695897i
$334$	15.7437	+	1.65473i	0.861457	+	0.0905428i
$335$	10.4797	+	24.7923i	0.572567	+	1.35455i
$336$	−0.216871	+	0.355815i	−0.0118313	+	0.0194113i
$337$	−1.84383	−	11.6415i	−0.100440	−	0.634152i	−0.985630	−	0.168921i	$-0.945972\pi$
$337$	−1.84383	−	11.6415i	−0.100440	−	0.634152i	0.885190	−	0.465230i	$-0.154028\pi$
$338$	−19.2337	+	1.00800i	−1.04618	+	0.0548278i
$339$	11.5268	−	32.8007i	0.626049	−	1.78149i
$340$	5.36472	+	0.666902i	0.290943	+	0.0361678i
$341$	3.72219	+	27.2092i	0.201568	+	1.47346i
$342$	−2.18770	+	1.98892i	−0.118298	+	0.107549i
$343$	−1.52278	−	2.98862i	−0.0822223	−	0.161370i
$344$	−0.628929	+	0.698497i	−0.0339096	+	0.0376604i
$345$	−23.5978	+	0.227080i	−1.27046	+	0.0122256i
$346$	2.85869	−	4.95140i	0.153684	−	0.266189i
$347$	−9.02424	−	2.41804i	−0.484447	−	0.129807i	0.00832567	−	0.999965i	$-0.497350\pi$
$347$	−9.02424	−	2.41804i	−0.484447	−	0.129807i	−0.492772	+	0.870158i	$0.664016\pi$
$348$	−5.82295	+	4.49036i	−0.312143	+	0.240709i
$349$	−1.36324	−	1.87633i	−0.0729723	−	0.100438i	0.770971	−	0.636871i	$-0.219771\pi$
$349$	−1.36324	−	1.87633i	−0.0729723	−	0.100438i	−0.843943	+	0.536433i	$0.819771\pi$
$350$	−1.19069	−	0.170997i	−0.0636450	−	0.00914015i
$351$	18.1346	+	23.2843i	0.967954	+	1.24282i
$352$	4.60482	+	1.76762i	0.245438	+	0.0942147i
$353$	−12.1227	−	7.87257i	−0.645226	−	0.419015i	0.180118	−	0.983645i	$-0.442352\pi$
$353$	−12.1227	−	7.87257i	−0.645226	−	0.419015i	−0.825344	+	0.564630i	$0.809019\pi$
$354$	−1.05914	+	4.45879i	−0.0562929	+	0.236982i
$355$	−1.76292	−	7.11627i	−0.0935658	−	0.377693i
$356$	7.05602	−	2.29264i	0.373968	−	0.121510i
$357$	0.886497	+	0.478576i	0.0469184	+	0.0253289i
$358$	2.80580	−	1.07705i	0.148291	−	0.0569237i
$359$	8.39374	+	1.78414i	0.443005	+	0.0941635i	0.424013	−	0.905656i	$-0.360621\pi$
$359$	8.39374	+	1.78414i	0.443005	+	0.0941635i	0.0189916	+	0.999820i	$0.493954\pi$
$360$	−0.256215	−	6.70331i	−0.0135037	−	0.353295i
$361$	16.4700	−	7.33293i	0.866843	−	0.385943i
$362$	15.1959	+	0.796384i	0.798680	+	0.0418570i
$363$	−17.5909	−	14.9511i	−0.923281	−	0.784730i
$364$	0.803180	+	1.10548i	0.0420980	+	0.0579430i
$365$	1.55058	+	0.360438i	0.0811609	+	0.0188662i
$366$	−20.8112	+	11.3643i	−1.08782	+	0.594023i
$367$	−10.5443	+	2.82535i	−0.550410	+	0.147482i	−0.523297	−	0.852151i	$-0.675298\pi$
$367$	−10.5443	+	2.82535i	−0.550410	+	0.147482i	−0.0271130	+	0.999632i	$0.508631\pi$
$368$	−0.953188	−	6.01819i	−0.0496884	−	0.313720i
$369$	−15.1555	+	15.3018i	−0.788966	+	0.796580i
$370$	−3.29261	−	9.08891i	−0.171175	−	0.472510i
$371$		−	0.931783i		−	0.0483758i
$372$	6.12466	+	7.44906i	0.317549	+	0.386216i
$373$	−14.7887	+	14.7887i	−0.765729	+	0.765729i	−0.977351	−	0.211623i	$-0.932125\pi$
$373$	−14.7887	+	14.7887i	−0.765729	+	0.765729i	0.211623	+	0.977351i	$0.432125\pi$
$374$	3.68498	−	11.3412i	0.190546	−	0.586440i
$375$	17.4961	−	8.29985i	0.903493	−	0.428602i
$376$	−9.09955	−	6.61121i	−0.469273	−	0.340947i
$377$	6.24090	+	23.2914i	0.321423	+	1.19957i
$378$	0.408792	−	1.18137i	0.0210260	−	0.0607629i
$379$	−30.9747	−	3.25557i	−1.59106	−	0.167227i	−0.732802	−	0.680442i	$-0.761788\pi$
$379$	−30.9747	−	3.25557i	−1.59106	−	0.167227i	−0.858260	+	0.513214i	$0.828455\pi$
$380$	0.610628	−	2.11748i	0.0313246	−	0.108624i
$381$	0.158655	+	1.95585i	0.00812812	+	0.100201i
$382$	−0.913466	+	17.4300i	−0.0467370	+	0.891795i
$383$	−17.8865	−	6.86600i	−0.913959	−	0.350836i	−0.144480	−	0.989508i	$-0.546151\pi$
$383$	−17.8865	−	6.86600i	−0.913959	−	0.350836i	−0.769479	+	0.638672i	$0.779484\pi$
$384$	1.70228	−	0.319729i	0.0868694	−	0.0163161i
$385$	−0.867645	+	2.50756i	−0.0442193	+	0.127797i
$386$	1.71949	−	3.86203i	0.0875195	−	0.196572i
$387$	1.39814	−	2.44873i	0.0710713	−	0.124476i
$388$	−10.3257	−	5.26119i	−0.524207	−	0.267097i
$389$	−7.41612	−	3.30187i	−0.376012	−	0.167412i	0.210024	−	0.977696i	$-0.432646\pi$
$389$	−7.41612	−	3.30187i	−0.376012	−	0.167412i	−0.586036	+	0.810285i	$0.699312\pi$
$390$	−20.6116	−	7.68532i	−1.04371	−	0.389161i
$391$	−14.4093	+	3.06279i	−0.728710	+	0.154892i
$392$	−2.48783	+	6.48103i	−0.125655	+	0.327341i
$393$	0.689198	−	9.03435i	0.0347654	−	0.455723i
$394$	17.4316	−	1.83213i	0.878191	−	0.0923016i
$395$	−24.9225	−	7.18702i	−1.25399	−	0.361618i
$396$	−14.6261	−	2.24460i	−0.734987	−	0.112795i
$397$	−9.49446	+	35.4338i	−0.476513	+	1.77837i	0.139052	+	0.990285i	$0.455594\pi$
$397$	−9.49446	+	35.4338i	−0.476513	+	1.77837i	−0.615565	+	0.788086i	$0.711072\pi$
$398$	3.43190	−	0.919575i	0.172026	−	0.0460941i
$399$	0.249223	−	0.326413i	0.0124767	−	0.0163411i
$400$	2.78348	+	4.15358i	0.139174	+	0.207679i
$401$	−12.9730	−	4.21517i	−0.647839	−	0.210496i	−0.0333780	−	0.999443i	$-0.510627\pi$
$401$	−12.9730	−	4.21517i	−0.647839	−	0.210496i	−0.614461	+	0.788947i	$0.710627\pi$
$402$	15.0890	−	14.3879i	0.752570	−	0.717604i
$403$	30.2757	−	9.13481i	1.50814	−	0.455037i
$404$	5.66058			0.281624
$405$	5.02657	+	19.4868i	0.249772	+	0.968305i
$406$	0.683424	−	0.759019i	0.0339177	−	0.0376695i
$407$	−21.0613	+	3.33578i	−1.04397	+	0.165348i
$408$	−0.987322	−	4.06942i	−0.0488797	−	0.201466i
$409$	28.1769	−	16.2679i	1.39326	−	0.804398i	0.399584	−	0.916697i	$-0.369155\pi$
$409$	28.1769	−	16.2679i	1.39326	−	0.804398i	0.993675	+	0.112298i	$0.0358212\pi$
$410$	3.63459	−	15.6357i	0.179500	−	0.772194i
$411$	−0.813098	−	1.17700i	−0.0401072	−	0.0580572i
$412$	−4.56935	+	5.64267i	−0.225115	+	0.277994i
$413$	0.0333148	−	0.635684i	0.00163931	−	0.0312799i
$414$	6.63270	+	17.0339i	0.325980	+	0.837168i
$415$	−33.9792	+	2.92127i	−1.66797	+	0.143400i
$416$	1.18090	−	5.55568i	0.0578982	−	0.272390i
$417$	−8.97684	−	25.1577i	−0.439598	−	1.23198i
$418$	−4.33134	−	2.20693i	−0.211853	−	0.107944i
$419$	−6.42102	−	19.7619i	−0.313687	−	0.965431i	−0.976291	−	0.216461i	$-0.930549\pi$
$419$	−6.42102	−	19.7619i	−0.313687	−	0.965431i	0.662604	−	0.748970i	$-0.269451\pi$
$420$	0.202486	+	0.909498i	0.00988030	+	0.0443790i
$421$	−17.4622	−	3.71171i	−0.851057	−	0.180898i	−0.238322	−	0.971186i	$-0.576597\pi$
$421$	−17.4622	−	3.71171i	−0.851057	−	0.180898i	−0.612735	+	0.790289i	$0.709931\pi$
$422$	13.4615	−	20.7289i	0.655296	−	1.00907i
$423$	30.8913	+	13.5763i	1.50199	+	0.660103i
$424$	−2.87824	+	2.59158i	−0.139780	+	0.125858i
$425$	9.67593	−	7.24578i	0.469352	−	0.351472i
$426$	−4.67237	+	3.22777i	−0.226377	+	0.156386i
$427$	2.55958	−	2.07271i	0.123867	−	0.100305i
$428$	−2.06824	+	7.71876i	−0.0999719	+	0.373100i
$429$	−25.2542	+	41.4341i	−1.21928	+	2.00045i
$430$	0.0701880	+	2.10055i	0.00338477	+	0.101298i
$431$	8.65037	+	7.78883i	0.416674	+	0.375175i	0.850635	−	0.525757i	$-0.176218\pi$
$431$	8.65037	+	7.78883i	0.416674	+	0.375175i	−0.433961	+	0.900932i	$0.642885\pi$
$432$	−4.78617	+	2.02301i	−0.230275	+	0.0973320i
$433$	−24.0137	+	24.0137i	−1.15403	+	1.15403i	−0.168289	+	0.985738i	$0.553824\pi$
$433$	−24.0137	+	24.0137i	−1.15403	+	1.15403i	−0.985738	+	0.168289i	$0.946176\pi$
$434$	−1.02295	−	0.864774i	−0.0491030	−	0.0415105i
$435$	−2.41576	+	16.2639i	−0.115827	+	0.779795i
$436$	−1.25821	+	3.87238i	−0.0602574	+	0.185453i
$437$	0.314288	+	5.99696i	0.0150344	+	0.286874i
$438$	−0.163886	−	1.22215i	−0.00783077	−	0.0583968i
$439$	−2.58192	−	1.49067i	−0.123229	−	0.0711460i	0.437119	−	0.899404i	$-0.355999\pi$
$439$	−2.58192	−	1.49067i	−0.123229	−	0.0711460i	−0.560347	+	0.828258i	$0.689332\pi$
$440$	10.1589	−	4.29419i	0.484309	−	0.204717i
$441$	3.15915	−	20.5854i	0.150436	−	0.980255i
$442$	−13.5627	−	2.14812i	−0.645110	−	0.102175i
$443$	7.17460	−	8.85990i	0.340876	−	0.420946i	−0.577664	−	0.816274i	$-0.696036\pi$
$443$	7.17460	−	8.85990i	0.340876	−	0.420946i	0.918540	+	0.395328i	$0.129369\pi$
$444$	−5.68221	+	4.87671i	−0.269666	+	0.231438i
$445$	7.81043	−	14.6361i	0.370250	−	0.693817i
$446$	2.52486	+	11.8785i	0.119555	+	0.562464i
$447$	13.6798	−	8.42825i	0.647034	−	0.398643i
$448$	−0.224602	+	0.0862165i	−0.0106114	+	0.00407334i
$449$	−11.0233	−	33.9262i	−0.520221	−	1.60108i	−0.773577	−	0.633703i	$-0.781534\pi$
$449$	−11.0233	−	33.9262i	−0.520221	−	1.60108i	0.253356	−	0.967373i	$-0.418466\pi$
$450$	−10.8088	−	10.4005i	−0.509529	−	0.490285i
$451$	−32.3483	−	14.4024i	−1.52322	−	0.678183i
$452$	16.8345	−	10.9324i	0.791827	−	0.514218i
$453$	4.10694	−	6.00648i	0.192961	−	0.282209i
$454$	−10.4331	−	23.4331i	−0.489649	−	1.09977i
$455$	3.00826	+	0.535106i	0.141029	+	0.0250861i
$456$	−1.70144	+	0.138018i	−0.0796773	+	0.00646326i
$457$	−15.7167	−	2.48927i	−0.735194	−	0.116443i	−0.222401	−	0.974955i	$-0.571389\pi$
$457$	−15.7167	−	2.48927i	−0.735194	−	0.116443i	−0.512793	+	0.858512i	$0.671389\pi$
$458$	−4.72084	+	3.82286i	−0.220590	+	0.178630i
$459$	5.48980	+	11.2994i	0.256242	+	0.527412i
$460$	−10.8689	−	8.21600i	−0.506766	−	0.383073i
$461$	7.00043	−	9.63527i	0.326043	−	0.448759i	−0.614257	−	0.789106i	$-0.710544\pi$
$461$	7.00043	−	9.63527i	0.326043	−	0.448759i	0.940300	+	0.340347i	$0.110544\pi$
$462$	2.05449	−	0.0587353i	0.0955837	−	0.00273261i
$463$	−18.1431	−	35.6078i	−0.843181	−	1.65484i	−0.752153	−	0.658989i	$-0.770985\pi$
$463$	−18.1431	−	35.6078i	−0.843181	−	1.65484i	−0.0910285	−	0.995848i	$-0.529015\pi$
$464$	−4.24539			−0.197087
$465$	21.4184	+	2.50055i	0.993254	+	0.115960i
$466$	−19.5934			−0.907648
$467$	8.10625	+	15.9094i	0.375113	+	0.736200i	0.998972	−	0.0453369i	$-0.0144361\pi$
$467$	8.10625	+	15.9094i	0.375113	+	0.736200i	−0.623859	+	0.781537i	$0.714436\pi$
$468$	0.0818208	+	17.0392i	0.00378217	+	0.787637i
$469$	−1.70219	+	2.34287i	−0.0785999	+	0.108184i
$470$	−24.9110	+	3.46279i	−1.14906	+	0.159727i
$471$	−1.22169	−	2.23724i	−0.0562924	−	0.103087i
$472$	−2.05626	+	1.66513i	−0.0946471	+	0.0766437i
$473$	4.57901	+	0.725244i	0.210543	+	0.0333468i
$474$	1.62445	+	20.0258i	0.0746135	+	0.919815i
$475$	−2.30034	−	4.35791i	−0.105547	−	0.199955i
$476$	0.236574	+	0.531353i	0.0108433	+	0.0243545i
$477$	6.78436	−	9.43280i	0.310635	−	0.431898i
$478$	9.20867	−	5.98018i	0.421195	−	0.273527i
$479$	18.4319	+	8.20640i	0.842174	+	0.374960i	0.782038	−	0.623230i	$-0.214180\pi$
$479$	18.4319	+	8.20640i	0.842174	+	0.374960i	0.0601356	+	0.998190i	$0.480847\pi$
$480$	2.24623	−	3.15507i	0.102526	−	0.144009i
$481$	7.58785	+	23.3530i	0.345976	+	1.06481i
$482$	−16.1967	+	6.21732i	−0.737739	+	0.283191i
$483$	−1.33183	−	2.16169i	−0.0606005	−	0.0983602i
$484$	−2.77122	−	13.0376i	−0.125965	−	0.592617i
$485$	−24.7924	+	7.53901i	−1.12576	+	0.342329i
$486$	12.7399	−	8.98298i	0.577895	−	0.407476i
$487$	9.20278	−	11.3645i	0.417018	−	0.514974i	−0.524742	−	0.851262i	$-0.675838\pi$
$487$	9.20278	−	11.3645i	0.417018	−	0.514974i	0.941759	+	0.336287i	$0.109171\pi$
$488$	−13.5215	−	2.14160i	−0.612090	−	0.0969455i
$489$	−34.8657	−	4.50502i	−1.57668	−	0.203724i
$490$	6.04383	+	14.2982i	0.273032	+	0.645925i
$491$	−8.40161	−	4.85067i	−0.379160	−	0.218908i	0.298293	−	0.954474i	$-0.403583\pi$
$491$	−8.40161	−	4.85067i	−0.379160	−	0.218908i	−0.677453	+	0.735566i	$0.736916\pi$
$492$	−12.3240	+	1.65260i	−0.555609	+	0.0745048i
$493$	0.537169	+	10.2498i	0.0241929	+	0.461627i
$494$	−1.72980	+	5.32378i	−0.0778274	+	0.239528i
$495$	−27.0412	+	19.0676i	−1.21541	+	0.857025i
$496$	0.173882	+	5.56505i	0.00780754	+	0.249878i
$497$	0.557760	−	0.557760i	0.0250189	−	0.0250189i
$498$	11.4301	+	23.8165i	0.512197	+	1.06724i
$499$	5.48237	+	4.93635i	0.245425	+	0.220981i	0.782657	−	0.622453i	$-0.213864\pi$
$499$	5.48237	+	4.93635i	0.245425	+	0.220981i	−0.537233	+	0.843434i	$0.680530\pi$
$500$	10.9254	+	2.37387i	0.488599	+	0.106163i
$501$	−23.4130	−	14.2703i	−1.04601	−	0.637548i
$502$	5.99148	−	22.3605i	0.267413	−	0.997998i
$503$	−27.9839	+	22.6610i	−1.24774	+	1.01040i	−0.248616	+	0.968602i	$0.579976\pi$
$503$	−27.9839	+	22.6610i	−1.24774	+	1.01040i	−0.999126	+	0.0417998i	$0.986691\pi$
$504$	0.603410	−	0.395991i	0.0268780	−	0.0176388i
$505$	9.11823	−	8.77889i	0.405756	−	0.390655i
$506$	−22.3347	+	20.1103i	−0.992899	+	0.894010i
$507$	30.8507	+	12.6921i	1.37013	+	0.563676i
$508$	−0.617032	+	0.950146i	−0.0273764	+	0.0421559i
$509$	1.47600	+	0.313733i	0.0654224	+	0.0139060i	0.240507	−	0.970648i	$-0.422686\pi$
$509$	1.47600	+	0.313733i	0.0654224	+	0.0139060i	−0.175084	+	0.984553i	$0.556020\pi$
$510$	−7.90160	−	5.02392i	−0.349889	−	0.222463i
$511$	0.0529272	+	0.162893i	0.00234136	+	0.00720597i
$512$	0.891007	+	0.453990i	0.0393773	+	0.0200637i
$513$	4.89960	−	1.48980i	0.216323	−	0.0657762i
$514$	−0.798192	+	3.75520i	−0.0352068	+	0.165635i
$515$	1.39068	+	16.1759i	0.0612807	+	0.712795i
$516$	1.50257	−	0.626614i	0.0661468	−	0.0275851i
$517$	−2.90351	+	55.4022i	−0.127696	+	2.43659i
$518$	0.654540	−	0.808290i	0.0287589	−	0.0355142i
$519$	−8.14766	+	5.62858i	−0.357643	+	0.247067i
$520$	−6.71398	−	10.7807i	−0.294427	−	0.472764i
$521$	−30.3541	+	17.5250i	−1.32984	+	0.767782i	−0.985274	−	0.170981i	$-0.945306\pi$
$521$	−30.3541	+	17.5250i	−1.32984	+	0.767782i	−0.344563	+	0.938763i	$0.611973\pi$
$522$	12.4450	−	2.70779i	0.544703	−	0.118517i
$523$	−18.3047	+	2.89919i	−0.800410	+	0.126773i	−0.543222	−	0.839589i	$-0.682796\pi$
$523$	−18.3047	+	2.89919i	−0.800410	+	0.126773i	−0.257188	+	0.966361i	$0.582796\pi$
$524$	3.50032	−	3.88749i	0.152912	−	0.169826i
$525$	1.73669	+	1.15101i	0.0757955	+	0.0502344i
$526$	−12.8710			−0.561203
$527$	13.4139	−	1.12395i	0.584317	−	0.0489602i
$528$	−5.89562	−	6.18289i	−0.256574	−	0.269076i
$529$	13.4358	+	4.36555i	0.584164	+	0.189807i
$530$	−0.617121	+	8.63841i	−0.0268060	+	0.375228i
$531$	4.96570	−	6.19270i	0.215493	−	0.268740i
$532$	0.229026	−	0.0613674i	0.00992956	−	0.00266062i
$533$	−10.5533	+	39.3856i	−0.457116	+	1.70598i
$534$	−12.7444	−	1.64671i	−0.551503	−	0.0712601i
$535$	8.63931	+	15.6412i	0.373510	+	0.676227i
$536$	11.9714	−	1.25824i	0.517084	−	0.0543477i
$537$	−5.19046	−	0.395961i	−0.223985	−	0.0170870i
$538$	−0.134825	+	0.351230i	−0.00581271	+	0.0151426i
$539$	33.4933	−	7.11921i	1.44266	−	0.306646i
$540$	−4.57226	+	10.6815i	−0.196759	+	0.459659i
$541$	18.3136	+	8.15376i	0.787365	+	0.350557i	0.760714	−	0.649087i	$-0.224849\pi$
$541$	18.3136	+	8.15376i	0.787365	+	0.350557i	0.0266510	+	0.999645i	$0.491516\pi$
$542$	−9.88825	−	5.03832i	−0.424737	−	0.216414i
$543$	−23.1924	−	12.5205i	−0.995282	−	0.537304i
$544$	0.983344	−	2.20863i	0.0421605	−	0.0946941i
$545$	3.97883	+	8.18907i	0.170434	+	0.350781i
$546$	−0.436894	−	2.32609i	−0.0186973	−	0.0995474i
$547$	−9.02061	−	3.46269i	−0.385693	−	0.148054i	0.157792	−	0.987472i	$-0.449562\pi$
$547$	−9.02061	−	3.46269i	−0.385693	−	0.148054i	−0.543486	+	0.839419i	$0.682896\pi$
$548$	0.0432256	−	0.824794i	0.00184651	−	0.0352335i
$549$	41.0031	−	2.34637i	1.74997	−	0.100140i
$550$	9.70455	−	22.6725i	0.413803	−	0.966759i
$551$	4.16115	+	0.437354i	0.177271	+	0.0186319i
$552$	−2.97312	+	10.1263i	−0.126545	+	0.431004i
$553$	−0.722288	−	2.69561i	−0.0307148	−	0.114629i
$554$	−12.8680	−	9.34911i	−0.546707	−	0.397206i
$555$	−1.58987	+	16.6680i	−0.0674862	+	0.707516i
$556$	4.76559	−	14.6670i	0.202106	−	0.622019i
$557$	7.59945	−	7.59945i	0.321999	−	0.321999i	−0.527534	−	0.849534i	$-0.676883\pi$
$557$	7.59945	−	7.59945i	0.321999	−	0.321999i	0.849534	+	0.527534i	$0.176883\pi$
$558$	−4.05921	−	16.2026i	−0.171840	−	0.685909i
$559$		−	5.33856i		−	0.225797i
$560$	−0.228083	+	0.487210i	−0.00963827	+	0.0205884i
$561$	−14.1816	+	15.0163i	−0.598747	+	0.633989i
$562$	2.37663	+	15.0054i	0.100252	+	0.632966i
$563$	22.8895	−	6.13322i	0.964677	−	0.258485i	0.258098	−	0.966119i	$-0.416904\pi$
$563$	22.8895	−	6.13322i	0.964677	−	0.258485i	0.706579	+	0.707634i	$0.250237\pi$
$564$	9.33685	+	17.0983i	0.393152	+	0.719969i
$565$	10.1625	−	43.7185i	0.427541	−	1.83925i
$566$	−11.0274	−	15.1779i	−0.463517	−	0.637977i
$567$	−1.51627	+	1.54568i	−0.0636775	+	0.0649125i
$568$	−3.27420	−	0.171594i	−0.137382	−	0.00719991i
$569$	4.96729	−	2.21158i	0.208240	−	0.0927143i	−0.299966	−	0.953950i	$-0.596975\pi$
$569$	4.96729	−	2.21158i	0.208240	−	0.0927143i	0.508206	+	0.861235i	$0.330309\pi$
$570$	−2.52668	+	2.86106i	−0.105831	+	0.119836i
$571$	−21.2619	−	4.51936i	−0.889784	−	0.189129i	−0.259730	−	0.965681i	$-0.583634\pi$
$571$	−21.2619	−	4.51936i	−0.889784	−	0.189129i	−0.630053	+	0.776552i	$0.716967\pi$
$572$	−26.1544	+	10.0397i	−1.09357	+	0.419783i
$573$	14.3612	−	26.6021i	0.599947	−	1.11132i
$574$	1.64259	−	0.533709i	0.0685602	−	0.0222766i
$575$	−30.2500	+	3.62185i	−1.26151	+	0.151041i
$576$	−2.90147	−	0.762533i	−0.120895	−	0.0317722i
$577$	−35.1493	−	22.8262i	−1.46328	−	0.950268i	−0.997874	−	0.0651724i	$-0.979240\pi$
$577$	−35.1493	−	22.8262i	−1.46328	−	0.950268i	−0.465410	−	0.885095i	$-0.654093\pi$
$578$	10.4141	+	3.99759i	0.433169	+	0.166278i
$579$	−5.55647	+	4.76879i	−0.230919	+	0.198184i
$580$	−6.83860	+	6.58410i	−0.283957	+	0.273390i
$581$	−2.15679	−	2.96856i	−0.0894785	−	0.123157i
$582$	12.2575	+	15.8951i	0.508089	+	0.658872i
$583$	18.4526	+	4.94437i	0.764230	+	0.204775i
$584$	0.355964	−	0.616547i	0.0147299	−	0.0255129i
$585$	26.5576	+	27.3203i	1.09802	+	1.12956i
$586$	13.9481	−	15.4910i	0.576192	−	0.639926i
$587$	3.80126	+	7.46040i	0.156895	+	0.307924i	0.956051	−	0.293200i	$-0.0947201\pi$
$587$	3.80126	+	7.46040i	0.156895	+	0.307924i	−0.799156	+	0.601123i	$0.794720\pi$
$588$	8.70208	−	8.29777i	0.358868	−	0.342194i
$589$	0.402872	−	5.47253i	0.0166000	−	0.225492i
$590$	−0.729870	+	5.87125i	−0.0300483	+	0.241716i
$591$	−28.6416	−	10.0652i	−1.17816	−	0.414027i
$592$	−4.31726	+	0.226258i	−0.177438	+	0.00929914i
$593$	3.26521	+	20.6157i	0.134086	+	0.846585i	0.959428	+	0.281953i	$0.0909821\pi$
$593$	3.26521	+	20.6157i	0.134086	+	0.846585i	−0.825342	+	0.564633i	$0.809018\pi$
$594$	21.2261	+	14.3643i	0.870916	+	0.589373i
$595$	1.20515	+	0.489022i	0.0494062	+	0.0200479i
$596$	9.22591	+	0.969682i	0.377908	+	0.0397197i
$597$	−6.05354	−	1.10693i	−0.247755	−	0.0453037i
$598$	26.8956	+	21.7797i	1.09984	+	0.890636i
$599$	0.481082	+	0.534295i	0.0196565	+	0.0218307i	0.752893	−	0.658143i	$-0.228658\pi$
$599$	0.481082	+	0.534295i	0.0196565	+	0.0218307i	−0.733236	+	0.679974i	$0.761991\pi$
$600$	−1.27485	−	8.56591i	−0.0520456	−	0.349702i
$601$	−3.56402	+	0.757555i	−0.145379	+	0.0309013i	−0.280026	−	0.959992i	$-0.590343\pi$
$601$	−3.56402	+	0.757555i	−0.145379	+	0.0309013i	0.134647	+	0.990894i	$0.457010\pi$
$602$	−0.189646	+	0.123157i	−0.00772939	+	0.00501952i
$603$	−34.2905	+	11.3240i	−1.39642	+	0.461148i
$604$	3.99537	−	1.29817i	0.162569	−	0.0528220i
$605$	−24.6837	−	16.7035i	−1.00353	−	0.679093i
$606$	−8.85943	−	4.19965i	−0.359890	−	0.170599i
$607$	−5.58770	−	8.60430i	−0.226798	−	0.349238i	0.706892	−	0.707322i	$-0.250097\pi$
$607$	−5.58770	−	8.60430i	−0.226798	−	0.349238i	−0.933689	+	0.358084i	$0.883430\pi$
$608$	−0.826556	−	0.536772i	−0.0335213	−	0.0217690i
$609$	−1.63276	+	0.680908i	−0.0661627	+	0.0275918i
$610$	−25.1022	+	17.5205i	−1.01636	+	0.709385i
$611$	63.5345	−	6.67774i	2.57033	−	0.270153i
$612$	−1.47389	+	7.10160i	−0.0595783	+	0.287065i
$613$	−17.2879	−	21.3488i	−0.698252	−	0.862270i	0.297464	−	0.954733i	$-0.403859\pi$
$613$	−17.2879	−	21.3488i	−0.698252	−	0.862270i	−0.995716	+	0.0924635i	$0.970526\pi$
$614$	−16.3521	−	28.3227i	−0.659918	−	1.14301i
$615$	−17.2889	+	21.7751i	−0.697154	+	0.878057i
$616$	0.960018	+	0.697494i	0.0386802	+	0.0281028i
$617$	−1.58031	−	30.1542i	−0.0636211	−	1.21396i	−0.824802	−	0.565422i	$-0.808713\pi$
$617$	−1.58031	−	30.1542i	−0.0636211	−	1.21396i	0.761180	−	0.648540i	$-0.224620\pi$
$618$	11.3379	−	5.44135i	0.456077	−	0.218883i
$619$		−	26.6231i		−	1.07007i	−0.844828	−	0.535037i	$-0.820298\pi$
$619$		−	26.6231i		−	1.07007i	0.844828	−	0.535037i	$-0.179702\pi$
$620$	8.91082	+	8.69467i	0.357867	+	0.349186i
$621$	2.25670	−	31.5807i	0.0905584	−	1.26729i
$622$	14.7885	−	7.53514i	0.592967	−	0.302132i
$623$	1.78246	−	0.0934146i	0.0714126	−	0.00374258i
$624$	−5.97006	+	7.81913i	−0.238994	+	0.313016i
$625$	21.2806	−	13.1201i	0.851223	−	0.524805i
$626$	8.10052	−	4.67684i	0.323762	−	0.186924i
$627$	5.14168	+	6.66756i	0.205339	+	0.266277i
$628$	0.230226	−	1.45359i	0.00918701	−	0.0580045i
$629$	1.09252	+	10.3947i	0.0435617	+	0.414462i
$630$	0.357854	−	1.57369i	0.0142573	−	0.0626973i
$631$	27.7521	−	12.3560i	1.10479	−	0.491886i	0.228443	−	0.973557i	$-0.426637\pi$
$631$	27.7521	−	12.3560i	1.10479	−	0.491886i	0.876352	+	0.481671i	$0.159970\pi$
$632$	−6.31774	+	9.72847i	−0.251306	+	0.386978i
$633$	−36.4477	+	22.4557i	−1.44867	+	0.892536i
$634$	10.6914	−	24.0132i	0.424609	−	0.953687i
$635$	0.479631	+	2.48747i	0.0190336	+	0.0987121i
$636$	6.42749	−	1.92071i	0.254867	−	0.0761610i
$637$	−14.1304	−	36.8109i	−0.559867	−	1.45850i
$638$	11.4048	+	17.5618i	0.451520	+	0.695280i
$639$	9.70749	−	1.58534i	0.384022	−	0.0627149i
$640$	2.13934	−	0.650544i	0.0845650	−	0.0257150i
$641$	26.3447	−	23.7208i	1.04055	−	0.936916i	0.0424863	−	0.999097i	$-0.486472\pi$
$641$	26.3447	−	23.7208i	1.04055	−	0.936916i	0.998065	+	0.0621806i	$0.0198055\pi$
$642$	8.96365	−	10.5463i	0.353767	−	0.416228i
$643$	4.17631	−	26.3682i	0.164698	−	1.03986i	−0.757414	−	0.652935i	$-0.773537\pi$
$643$	4.17631	−	26.3682i	0.164698	−	1.03986i	0.922111	−	0.386925i	$-0.126463\pi$
$644$	0.153229	−	1.45788i	0.00603808	−	0.0574485i
$645$	1.44857	−	3.33967i	0.0570375	−	0.131499i
$646$	−1.19136	+	2.06350i	−0.0468734	+	0.0811872i
$647$	3.74343	−	0.592901i	0.147169	−	0.0233093i	−0.0824150	−	0.996598i	$-0.526263\pi$
$647$	3.74343	−	0.592901i	0.147169	−	0.0233093i	0.229584	+	0.973289i	$0.426263\pi$
$648$	8.99177	+	0.384688i	0.353230	+	0.0151120i
$649$	12.4120	+	4.03291i	0.487215	+	0.158306i
$650$	−27.5346	−	6.95325i	−1.08000	−	0.272729i
$651$	0.959438	+	2.11240i	0.0376033	+	0.0827915i
$652$	−14.3522	−	14.3522i	−0.562075	−	0.562075i
$653$	17.2529	−	8.79077i	0.675156	−	0.344009i	−0.0825668	−	0.996586i	$-0.526312\pi$
$653$	17.2529	−	8.79077i	0.675156	−	0.344009i	0.757723	+	0.652576i	$0.226312\pi$
$654$	4.84220	−	5.12721i	0.189345	−	0.200490i
$655$	−0.390633	−	11.6907i	−0.0152633	−	0.456792i
$656$	−6.21715	−	3.58947i	−0.242739	−	0.140145i
$657$	−0.650231	+	2.03439i	−0.0253679	+	0.0793693i
$658$	−1.70292	−	2.10293i	−0.0663868	−	0.0819809i
$659$	22.4958	−	16.3442i	0.876312	−	0.636678i	−0.0559612	−	0.998433i	$-0.517822\pi$
$659$	22.4958	−	16.3442i	0.876312	−	0.636678i	0.932273	+	0.361755i	$0.117822\pi$
$660$	−19.0858	−	0.816170i	−0.742913	−	0.0317694i
$661$	30.6745	+	34.0675i	1.19310	+	1.32507i	0.933166	+	0.359446i	$0.117034\pi$
$661$	30.6745	+	34.0675i	1.19310	+	1.32507i	0.259935	+	0.965626i	$0.416299\pi$
$662$	10.4835	−	27.3104i	0.407451	−	1.06145i
$663$	19.6334	+	13.4243i	0.762496	+	0.521358i
$664$	−3.17107	+	14.9187i	−0.123061	+	0.578959i
$665$	0.273749	−	0.454045i	0.0106155	−	0.0176071i
$666$	12.5114	−	3.41688i	0.484805	−	0.132402i
$667$	11.7439	−	23.0486i	0.454724	−	0.892447i
$668$	−5.67312	−	14.7790i	−0.219499	−	0.571816i
$669$	4.86113	−	20.4644i	0.187942	−	0.791199i
$670$	17.3324	−	20.5930i	0.669610	−	0.795575i
$671$	27.4650	+	61.6874i	1.06027	+	2.38141i
$672$	0.415491	+	0.0316963i	0.0160279	+	0.00122271i
$673$	−33.7165	−	27.3031i	−1.29968	−	1.05246i	−0.994987	−	0.100005i	$-0.968114\pi$
$673$	−33.7165	−	27.3031i	−1.29968	−	1.05246i	−0.304689	−	0.952452i	$-0.598553\pi$
$674$	−9.53555	+	6.92798i	−0.367296	+	0.266856i
$675$	9.20061	+	24.2971i	0.354132	+	0.935196i
$676$	9.63006	+	16.6797i	0.370387	+	0.641529i
$677$	−0.965011	−	3.60147i	−0.0370884	−	0.138416i	0.944899	−	0.327362i	$-0.106160\pi$
$677$	−0.965011	−	3.60147i	−0.0370884	−	0.138416i	−0.981987	+	0.188946i	$0.939493\pi$
$678$	−34.4587	+	4.62076i	−1.32338	+	0.177459i
$679$	−2.07192	−	1.86556i	−0.0795128	−	0.0715937i
$680$	−1.84132	−	5.08277i	−0.0706114	−	0.194915i
$681$	−1.05636	+	44.4158i	−0.0404799	+	1.70202i
$682$	22.5537	−	15.6692i	0.863627	−	0.600005i
$683$	−32.1315	−	32.1315i	−1.22948	−	1.22948i	−0.964161	−	0.265319i	$-0.914523\pi$
$683$	−32.1315	−	32.1315i	−1.22948	−	1.22948i	−0.265319	−	0.964161i	$-0.585477\pi$
$684$	2.76534	+	1.04631i	0.105735	+	0.0400066i
$685$	−1.20953	−	1.39564i	−0.0462137	−	0.0533247i
$686$	−1.97155	+	2.71361i	−0.0752743	+	0.103606i
$687$	10.2248	−	2.48075i	0.390102	−	0.0946464i
$688$	0.907893	+	0.243269i	0.0346131	+	0.00927455i
$689$	2.29944	−	21.8777i	0.0876016	−	0.833473i
$690$	10.9155	+	20.9227i	0.415546	+	0.796514i
$691$	−0.824851	−	7.84793i	−0.0313788	−	0.298549i	−0.998945	−	0.0459304i	$-0.985375\pi$
$691$	−0.824851	−	7.84793i	−0.0313788	−	0.298549i	0.967566	−	0.252619i	$-0.0812919\pi$
$692$	−5.70954	−	0.299225i	−0.217044	−	0.0113748i
$693$	−3.25909	−	1.43233i	−0.123802	−	0.0544096i
$694$	1.94243	+	9.13843i	0.0737337	+	0.346890i
$695$	−15.0702	−	31.0169i	−0.571645	−	1.17654i
$696$	6.64451	+	3.14971i	0.251859	+	0.119389i
$697$	−7.87952	+	15.4644i	−0.298458	+	0.585757i
$698$	−1.05293	+	2.06649i	−0.0398539	+	0.0782178i
$699$	30.6659	+	14.5366i	1.15989	+	0.549824i
$700$	0.388202	+	1.13854i	0.0146727	+	0.0430328i
$701$	−0.132447	−	0.623116i	−0.00500247	−	0.0235348i	0.975576	−	0.219664i	$-0.0704961\pi$
$701$	−0.132447	−	0.623116i	−0.00500247	−	0.0235348i	−0.980578	+	0.196129i	$0.937163\pi$
$702$	12.5135	−	26.7289i	0.472292	−	1.00882i
$703$	4.25489	+	0.222990i	0.160476	+	0.00841021i
$704$	−0.515579	−	4.90541i	−0.0194316	−	0.184880i
$705$	41.5575	+	13.0621i	1.56515	+	0.491948i
$706$	−1.51092	+	14.3755i	−0.0568644	+	0.541028i
$707$	1.31542	+	0.352467i	0.0494716	+	0.0132559i
$708$	4.45365	−	1.08054i	0.167378	−	0.0406093i
$709$	−13.3689	+	18.4007i	−0.502078	+	0.691051i	−0.982558	−	0.185954i	$-0.940462\pi$
$709$	−13.3689	+	18.4007i	−0.502078	+	0.691051i	0.480480	+	0.877006i	$0.340462\pi$
$710$	−5.54030	+	4.80149i	−0.207924	+	0.180197i
$711$	12.3149	−	32.5477i	0.461845	−	1.22064i
$712$	−5.24612	−	5.24612i	−0.196607	−	0.196607i
$713$	−30.6942	−	14.4503i	−1.14951	−	0.541170i
$714$	0.0239534	−	1.00714i	0.000896432	−	0.0376914i
$715$	−26.5599	+	56.7347i	−0.993283	+	2.12176i
$716$	−2.23346	−	2.01102i	−0.0834684	−	0.0751553i
$717$	−18.8493	+	2.52762i	−0.703942	+	0.0943957i
$718$	−2.22099	−	8.28886i	−0.0828867	−	0.309337i
$719$	−6.57313	−	11.3850i	−0.245136	−	0.424589i	0.717034	−	0.697039i	$-0.245499\pi$
$719$	−6.57313	−	11.3850i	−0.245136	−	0.424589i	−0.962170	+	0.272450i	$0.912166\pi$
$720$	−5.85637	+	3.27153i	−0.218254	+	0.121923i
$721$	−1.41319	+	1.02674i	−0.0526300	+	0.0382379i
$722$	−14.0109	−	11.3458i	−0.521432	−	0.422248i
$723$	29.9623	+	2.28571i	1.11431	+	0.0850066i
$724$	−6.18922	−	13.9012i	−0.230020	−	0.516634i
$725$	−0.804659	+	21.2117i	−0.0298843	+	0.787783i
$726$	−5.33546	+	22.4612i	−0.198018	+	0.833615i
$727$	16.8430	+	43.8776i	0.624673	+	1.62733i	0.770072	+	0.637957i	$0.220220\pi$
$727$	16.8430	+	43.8776i	0.624673	+	1.62733i	−0.145399	+	0.989373i	$0.546447\pi$
$728$	0.620356	−	1.21752i	0.0229919	−	0.0451242i
$729$	−26.6040	+	4.60744i	−0.985332	+	0.170646i
$730$	−0.382795	−	1.54521i	−0.0141679	−	0.0571907i
$731$	0.472457	−	2.22274i	0.0174745	−	0.0822108i
$732$	19.5738	+	13.3836i	0.723467	+	0.494672i
$733$	−10.1715	+	26.4977i	−0.375694	+	0.978717i	0.607201	+	0.794549i	$0.292292\pi$
$733$	−10.1715	+	26.4977i	−0.375694	+	0.978717i	−0.982895	+	0.184168i	$0.941041\pi$
$734$	7.30443	+	8.11239i	0.269611	+	0.299434i
$735$	1.14871	−	26.8622i	0.0423710	−	0.990826i
$736$	−4.92951	+	3.58150i	−0.181704	+	0.132016i
$737$	−37.3647	−	46.1416i	−1.37635	−	1.69965i
$738$	20.5145	+	6.55682i	0.755149	+	0.241360i
$739$	7.26803	+	4.19620i	0.267359	+	0.154360i	0.627687	−	0.778466i	$-0.284002\pi$
$739$	7.26803	+	4.19620i	0.267359	+	0.154360i	−0.360328	+	0.932826i	$0.617335\pi$
$740$	−6.60346	+	7.06002i	−0.242748	+	0.259531i
$741$	6.65710	−	7.04894i	0.244555	−	0.258949i
$742$	−0.830225	+	0.423021i	−0.0304785	+	0.0155296i
$743$	−7.63369	−	7.63369i	−0.280053	−	0.280053i	0.553077	−	0.833130i	$-0.313453\pi$
$743$	−7.63369	−	7.63369i	−0.280053	−	0.280053i	−0.833130	+	0.553077i	$0.813453\pi$
$744$	3.85663	−	8.83891i	0.141391	−	0.324050i
$745$	16.3652	−	12.7463i	0.599575	−	0.466988i
$746$	19.8907	+	6.46289i	0.728251	+	0.236623i
$747$	−0.219714	−	45.7555i	−0.00803891	−	1.67411i
$748$	−11.7780	+	1.86546i	−0.430648	+	0.0682079i
$749$	−0.961247	+	1.66493i	−0.0351232	+	0.0608351i
$750$	−15.3383	−	11.8211i	−0.560074	−	0.431644i
$751$	2.12136	−	20.1834i	0.0774097	−	0.736504i	−0.885126	−	0.465351i	$-0.845928\pi$
$751$	2.12136	−	20.1834i	0.0774097	−	0.736504i	0.962536	−	0.271153i	$-0.0874051\pi$
$752$	−1.75952	+	11.1092i	−0.0641631	+	0.405110i
$753$	−25.9668	+	30.5515i	−0.946284	+	1.11336i
$754$	17.9194	−	16.1347i	0.652588	−	0.587592i
$755$	4.42254	−	8.28748i	0.160953	−	0.301612i
$756$	−1.23819	+	0.172093i	−0.0450326	+	0.00625896i
$757$	−5.07275	−	7.81135i	−0.184372	−	0.283908i	0.734384	−	0.678735i	$-0.237471\pi$
$757$	−5.07275	−	7.81135i	−0.184372	−	0.283908i	−0.918756	+	0.394827i	$0.870805\pi$
$758$	11.1615	+	29.0766i	0.405403	+	1.05611i
$759$	49.8763	−	14.9044i	1.81040	−	0.540995i
$760$	−2.16391	+	0.417243i	−0.0784932	+	0.0151350i
$761$	15.5510	−	34.9280i	0.563722	−	1.26614i	−0.376764	−	0.926309i	$-0.622963\pi$
$761$	15.5510	−	34.9280i	0.563722	−	1.26614i	0.940486	−	0.339832i	$-0.110370\pi$
$762$	1.67065	−	1.02930i	0.0605212	−	0.0372876i
$763$	−0.533508	+	0.821531i	−0.0193143	+	0.0297414i
$764$	15.9449	−	7.09914i	0.576867	−	0.256838i
$765$	8.63955	+	13.7253i	0.312364	+	0.496238i
$766$	2.00267	+	19.0541i	0.0723594	+	0.688453i
$767$	2.35094	−	14.8432i	0.0848874	−	0.535958i
$768$	−1.05770	−	1.37159i	−0.0381665	−	0.0494931i
$769$	1.95790	−	1.13039i	0.0706036	−	0.0407630i	−0.464283	−	0.885687i	$-0.653688\pi$
$769$	1.95790	−	1.13039i	0.0706036	−	0.0407630i	0.534886	+	0.844924i	$0.320354\pi$
$770$	2.62815	−	0.365331i	0.0947121	−	0.0131656i
$771$	4.03528	−	5.28511i	0.145327	−	0.190339i
$772$	−4.22172	+	0.221251i	−0.151943	+	0.00796300i
$773$	−6.68681	+	3.40710i	−0.240508	+	0.122545i	−0.570091	−	0.821582i	$-0.693092\pi$
$773$	−6.68681	+	3.40710i	−0.240508	+	0.122545i	0.329583	+	0.944127i	$0.393092\pi$
$774$	−2.81657	−	0.134052i	−0.101240	−	0.00481839i
$775$	27.8382	+	0.185996i	0.999978	+	0.00668119i
$776$			11.5888i			0.416013i
$777$	−1.62411	+	0.779451i	−0.0582645	+	0.0279627i
$778$	0.424861	+	8.10683i	0.0152320	+	0.290644i
$779$	5.72400	+	4.15873i	0.205083	+	0.149002i
$780$	2.50980	+	21.8541i	0.0898653	+	0.782503i
$781$	8.08597	+	14.0053i	0.289339	+	0.501149i
$782$	9.27065	+	11.4483i	0.331518	+	0.409390i
$783$	−21.4867	−	4.99510i	−0.767873	−	0.178510i
$784$	6.90409	−	0.725649i	0.246575	−	0.0259160i
$785$	−1.88349	−	2.69854i	−0.0672246	−	0.0963149i
$786$	−8.36255	+	3.48743i	−0.298282	+	0.124392i
$787$	32.2104	+	20.9177i	1.14818	+	0.745636i	0.971126	−	0.238566i	$-0.0766772\pi$
$787$	32.2104	+	20.9177i	1.14818	+	0.745636i	0.177052	+	0.984201i	$0.443344\pi$
$788$	−9.54622	−	14.6999i	−0.340070	−	0.523662i
$789$	20.1446	+	9.54916i	0.717165	+	0.339959i
$790$	4.91090	+	25.4690i	0.174722	+	0.906145i
$791$	4.59278	−	1.49228i	0.163300	−	0.0530595i
$792$	4.64014	+	14.0509i	0.164880	+	0.499278i
$793$	65.2123	−	42.3494i	2.31576	−	1.50387i
$794$	35.8821	−	7.62698i	1.27341	−	0.270672i
$795$	7.37479	−	13.0622i	0.261557	−	0.463268i
$796$	−2.37740	−	2.64037i	−0.0842646	−	0.0935853i
$797$	0.203172	+	0.164525i	0.00719672	+	0.00582779i	0.632912	−	0.774224i	$-0.281859\pi$
$797$	0.203172	+	0.164525i	0.00719672	+	0.00582779i	−0.625715	+	0.780052i	$0.715193\pi$
$798$	−0.403981	−	0.0738706i	−0.0143008	−	0.00261499i
$799$	27.0439	+	2.84242i	0.956743	+	0.100558i
$800$	2.43720	−	4.36578i	0.0861680	−	0.154354i
$801$	18.7246	+	12.0325i	0.661602	+	0.425147i
$802$	2.13386	+	13.4726i	0.0753491	+	0.475736i
$803$	−3.50672	+	0.183779i	−0.123749	+	0.00648543i
$804$	−19.6700	−	6.91240i	−0.693707	−	0.243782i
$805$	−2.01417	−	2.58603i	−0.0709902	−	0.0911457i
$806$	−21.8841	−	22.8287i	−0.770833	−	0.804108i
$807$	0.471597	−	0.449686i	0.0166010	−	0.0158297i
$808$	−2.56985	−	5.04362i	−0.0904070	−	0.177434i
$809$	−19.4468	+	21.5978i	−0.683712	+	0.759339i	−0.980695	−	0.195544i	$-0.937353\pi$
$809$	−19.4468	+	21.5978i	−0.683712	+	0.759339i	0.296983	+	0.954883i	$0.404019\pi$
$810$	15.0808	−	13.3255i	0.529886	−	0.468211i
$811$	17.5365	−	30.3741i	0.615789	−	1.06658i	−0.374456	−	0.927245i	$-0.622171\pi$
$811$	17.5365	−	30.3741i	0.615789	−	1.06658i	0.990245	−	0.139334i	$-0.0444961\pi$
$812$	−0.986558	−	0.264348i	−0.0346214	−	0.00927678i
$813$	11.7382	+	15.2217i	0.411677	+	0.533849i
$814$	12.5338	+	17.2513i	0.439310	+	0.604658i
$815$	−45.3774	−	0.860379i	−1.58950	−	0.0301378i
$816$	−3.17765	+	2.72719i	−0.111240	+	0.0954707i
$817$	−0.864816	−	0.331972i	−0.0302561	−	0.0116142i
$818$	−27.2869	−	17.7203i	−0.954064	−	0.619576i
$819$	−1.04196	+	3.96472i	−0.0364092	+	0.138539i
$820$	−15.5816	+	3.86004i	−0.544134	+	0.134798i
$821$	24.6473	−	8.00839i	0.860197	−	0.279495i	0.154486	−	0.987995i	$-0.450628\pi$
$821$	24.6473	−	8.00839i	0.860197	−	0.279495i	0.705711	+	0.708500i	$0.250628\pi$
$822$	−0.679577	+	1.25882i	−0.0237030	+	0.0439065i
$823$	17.8896	−	6.86718i	0.623592	−	0.239375i	−0.0259945	−	0.999662i	$-0.508275\pi$
$823$	17.8896	−	6.86718i	0.623592	−	0.239375i	0.649587	+	0.760287i	$0.274942\pi$
$824$	7.10210	+	1.50960i	0.247413	+	0.0525893i
$825$	−32.0097	+	28.2850i	−1.11443	+	0.984759i
$826$	−0.581523	+	0.258911i	−0.0202338	+	0.00900865i
$827$	9.64540	+	0.505494i	0.335403	+	0.0175777i	0.219294	−	0.975659i	$-0.429624\pi$
$827$	9.64540	+	0.505494i	0.335403	+	0.0175777i	0.116109	+	0.993236i	$0.462958\pi$
$828$	12.1661	−	13.6430i	0.422801	−	0.474127i
$829$	−12.1482	−	16.7206i	−0.421924	−	0.580729i	0.544152	−	0.838987i	$-0.316852\pi$
$829$	−12.1482	−	16.7206i	−0.421924	−	0.580729i	−0.966076	+	0.258258i	$0.916852\pi$
$830$	18.0291	+	28.9495i	0.625799	+	1.00485i
$831$	13.2035	+	24.1793i	0.458026	+	0.838769i
$832$	−5.48626	+	1.47004i	−0.190202	+	0.0509645i
$833$	−2.62553	−	16.5769i	−0.0909692	−	0.574357i
$834$	−18.3403	+	19.4198i	−0.635072	+	0.672452i
$835$	−32.0588	−	15.0081i	−1.10944	−	0.519375i
$836$			4.86118i			0.168127i
$837$	−5.66775	+	28.3703i	−0.195906	+	0.980623i
$838$	−14.6929	+	14.6929i	−0.507557	+	0.507557i
$839$	8.77254	−	26.9991i	0.302862	−	0.932112i	−0.677605	−	0.735426i	$-0.736982\pi$
$839$	8.77254	−	26.9991i	0.302862	−	0.932112i	0.980467	−	0.196686i	$-0.0630179\pi$
$840$	0.718442	−	0.593320i	0.0247886	−	0.0204715i
$841$	8.88028	+	6.45190i	0.306216	+	0.222479i
$842$	4.62053	+	17.2440i	0.159234	+	0.594269i
$843$	7.41302	−	25.2484i	0.255318	−	0.869601i
$844$	−24.5810	−	2.58356i	−0.846112	−	0.0889299i
$845$	41.3807	+	11.9331i	1.42354	+	0.410513i
$846$	−1.92776	−	33.6879i	−0.0662777	−	1.15821i
$847$	0.167824	−	3.20227i	0.00576650	−	0.110031i
$848$	3.61581	+	1.38798i	0.124167	+	0.0476634i
$849$	5.99843	+	31.9365i	0.205866	+	1.09606i
$850$	−10.8488	−	5.33180i	−0.372111	−	0.182879i
$851$	10.7143	−	24.0647i	0.367281	−	0.824926i
$852$	4.99718	+	2.69773i	0.171200	+	0.0924228i
$853$	−0.287677	−	0.146579i	−0.00984988	−	0.00501876i	0.449059	−	0.893502i	$-0.351759\pi$
$853$	−0.287677	−	0.146579i	−0.00984988	−	0.00501876i	−0.458909	+	0.888484i	$0.651759\pi$
$854$	−3.00882	−	1.33961i	−0.102960	−	0.0458406i
$855$	6.07719	−	2.60329i	0.207835	−	0.0890307i
$856$	7.81643	−	1.66143i	0.267160	−	0.0567866i
$857$	4.85716	−	12.6533i	0.165918	−	0.432230i	−0.825263	−	0.564749i	$-0.808973\pi$
$857$	4.85716	−	12.6533i	0.165918	−	0.432230i	0.991181	+	0.132519i	$0.0423064\pi$
$858$	48.3832	+	3.69098i	1.65177	+	0.126008i
$859$	−15.3345	+	1.61172i	−0.523206	+	0.0549912i	−0.362450	−	0.932003i	$-0.618060\pi$
$859$	−15.3345	+	1.61172i	−0.523206	+	0.0549912i	−0.160756	+	0.986994i	$0.551393\pi$
$860$	1.83974	−	1.01617i	0.0627347	−	0.0346511i
$861$	−2.96679	−	0.383341i	−0.101108	−	0.0130642i
$862$	3.01271	−	11.2436i	0.102613	−	0.382958i
$863$	−17.8688	+	4.78793i	−0.608261	+	0.162983i	−0.549786	−	0.835306i	$-0.685291\pi$
$863$	−17.8688	+	4.78793i	−0.608261	+	0.162983i	−0.0584755	+	0.998289i	$0.518624\pi$
$864$	3.97539	+	3.34608i	0.135245	+	0.113836i
$865$	−9.66116	+	8.37282i	−0.328489	+	0.284685i
$866$	32.2984	+	10.4944i	1.09754	+	0.356614i
$867$	−13.3333	−	13.9830i	−0.452823	−	0.474888i
$868$	−0.306111	+	1.30405i	−0.0103901	+	0.0442624i
$869$	57.2155			1.94090
$870$	15.5880	−	5.23120i	0.528482	−	0.177354i
$871$	−45.7481	+	50.8084i	−1.55011	+	1.72158i
$872$	4.02153	−	0.636948i	0.136186	−	0.0215698i
$873$	−7.39154	−	33.9715i	−0.250166	−	1.14976i
$874$	5.20065	−	3.00260i	0.175915	−	0.101564i
$875$	2.39107	+	1.23194i	0.0808329	+	0.0416472i
$876$	−1.01455	+	0.700870i	−0.0342783	+	0.0236802i
$877$	−33.4915	+	41.3585i	−1.13093	+	1.39658i	−0.224365	+	0.974505i	$0.572031\pi$
$877$	−33.4915	+	41.3585i	−1.13093	+	1.39658i	−0.906562	+	0.422073i	$0.861303\pi$
$878$	−0.156032	+	2.97726i	−0.00526582	+	0.100478i
$879$	−33.3233	+	13.8968i	−1.12397	+	0.468727i
$880$	−8.43821	−	7.10217i	−0.284452	−	0.239414i
$881$	−8.19805	+	38.5688i	−0.276199	+	1.29942i	0.593099	+	0.805129i	$0.297904\pi$
$881$	−8.19805	+	38.5688i	−0.276199	+	1.29942i	−0.869299	+	0.494287i	$0.835429\pi$
$882$	−19.7759	+	6.53074i	−0.665890	+	0.219901i
$883$	19.7688	+	10.0727i	0.665273	+	0.338974i	0.753804	−	0.657100i	$-0.228217\pi$
$883$	19.7688	+	10.0727i	0.665273	+	0.338974i	−0.0885303	+	0.996073i	$0.528217\pi$
$884$	4.24334	+	13.0597i	0.142719	+	0.439244i
$885$	5.49827	−	8.64765i	0.184822	−	0.290688i
$886$	−11.1514	−	2.37031i	−0.374640	−	0.0796321i
$887$	−24.1224	+	37.1452i	−0.809950	+	1.24721i	0.155813	+	0.987787i	$0.450200\pi$
$887$	−24.1224	+	37.1452i	−0.809950	+	1.24721i	−0.965763	+	0.259427i	$0.916466\pi$
$888$	6.92484	+	2.84890i	0.232383	+	0.0956030i
$889$	−0.202551	+	0.182377i	−0.00679333	+	0.00611674i
$890$	−16.5867	−	0.314493i	−0.555988	−	0.0105418i
$891$	−22.5641	−	38.2295i	−0.755926	−	1.28074i
$892$	9.43757	−	7.64240i	0.315993	−	0.255886i
$893$	2.86906	−	10.7075i	0.0960093	−	0.358312i
$894$	−13.7201	−	8.36247i	−0.458870	−	0.279683i
$895$	−6.71658	+	0.224428i	−0.224510	+	0.00750181i
$896$	0.178786	+	0.160980i	0.00597283	+	0.00537796i
$897$	−25.9360	−	54.0417i	−0.865979	−	1.80440i
$898$	−25.2240	+	25.2240i	−0.841735	+	0.841735i
$899$	−13.2897	+	19.5476i	−0.443236	+	0.651949i
$900$	−4.35986	+	14.3524i	−0.145329	+	0.478414i
$901$	2.89353	−	8.90538i	0.0963976	−	0.296681i
$902$	1.85320	+	35.3611i	0.0617047	+	1.17740i
$903$	0.388188	−	0.0520545i	0.0129181	−	0.00173226i
$904$	−17.3836	−	10.0364i	−0.578168	−	0.333806i
$905$	−31.5289	−	12.7937i	−1.04806	−	0.425278i
$906$	−7.21632	−	0.932426i	−0.239746	−	0.0309778i
$907$	−9.02693	−	1.42973i	−0.299734	−	0.0474733i	0.00475597	−	0.999989i	$-0.498486\pi$
$907$	−9.02693	−	1.42973i	−0.299734	−	0.0474733i	−0.304490	+	0.952515i	$0.598486\pi$
$908$	−16.1425	+	19.9343i	−0.535708	+	0.661544i
$909$	10.7502	+	13.1458i	0.356562	+	0.436020i
$910$	−0.888937	−	2.92331i	−0.0294680	−	0.0969067i
$911$	−9.58213	−	45.0804i	−0.317470	−	1.49358i	−0.790461	−	0.612513i	$-0.790159\pi$
$911$	−9.58213	−	45.0804i	−0.317470	−	1.49358i	0.472991	−	0.881068i	$-0.343174\pi$
$912$	0.895413	+	1.45334i	0.0296501	+	0.0481248i
$913$	70.2327	−	26.9598i	2.32436	−	0.892240i
$914$	4.91725	+	15.1337i	0.162648	+	0.500580i
$915$	52.2864	−	8.79790i	1.72853	−	0.290850i
$916$	5.54941	+	2.47075i	0.183358	+	0.0816360i
$917$	1.05548	−	0.685435i	0.0348549	−	0.0226351i
$918$	7.57555	−	10.0213i	0.250030	−	0.330752i
$919$	−1.27689	−	2.86794i	−0.0421207	−	0.0946047i	0.891260	−	0.453493i	$-0.149822\pi$
$919$	−1.27689	−	2.86794i	−0.0421207	−	0.0946047i	−0.933380	+	0.358889i	$0.883156\pi$
$920$	−2.38612	+	13.4143i	−0.0786680	+	0.442255i
$921$	4.57992	+	56.4600i	0.150913	+	1.86042i
$922$	−11.7632	−	1.86311i	−0.387401	−	0.0613583i
$923$	14.4723	−	11.7194i	0.476361	−	0.385749i
$924$	−0.985055	−	1.80390i	−0.0324059	−	0.0593440i
$925$	0.312196	+	21.6137i	0.0102650	+	0.710653i
$926$	−23.4900	+	32.3312i	−0.771930	+	1.06247i
$927$	−21.7820	+	0.104595i	−0.715416	+	0.00343536i
$928$	1.92737	+	3.78267i	0.0632690	+	0.124172i
$929$	25.6149			0.840396			0.420198	−	0.907432i	$-0.361961\pi$
$929$	25.6149			0.840396			0.420198	+	0.907432i	$0.361961\pi$
$930$	−7.49574	−	20.2191i	−0.245795	−	0.663012i
$931$	−6.84184			−0.224232
$932$	8.89523	+	17.4579i	0.291373	+	0.571852i
$933$	−28.7361	+	0.821527i	−0.940778	+	0.0268956i
$934$	10.4952	−	14.4454i	0.343414	−	0.472669i
$935$	−16.0793	+	21.2713i	−0.525849	+	0.695645i
$936$	15.1449	−	7.80854i	0.495026	−	0.255230i
$937$	9.39014	−	7.60398i	0.306762	−	0.248411i	−0.463561	−	0.886065i	$-0.653428\pi$
$937$	9.39014	−	7.60398i	0.306762	−	0.248411i	0.770323	+	0.637654i	$0.220095\pi$
$938$	2.86029	+	0.453025i	0.0933917	+	0.0147918i
$939$	−16.1480	+	1.30989i	−0.526970	+	0.0427467i
$940$	14.3947	+	20.6238i	0.469504	+	0.672674i
$941$	1.22335	+	2.74768i	0.0398799	+	0.0895718i	0.932387	−	0.361462i	$-0.117722\pi$
$941$	1.22335	+	2.74768i	0.0398799	+	0.0895718i	−0.892507	+	0.451033i	$0.851056\pi$
$942$	−1.43876	+	2.10422i	−0.0468774	+	0.0685591i
$943$	36.6858	−	23.8241i	1.19466	−	0.775818i
$944$	2.41716	+	1.07619i	0.0786719	+	0.0350270i
$945$	−1.72762	+	2.19750i	−0.0561995	+	0.0714847i
$946$	−1.43263	−	4.40918i	−0.0465788	−	0.143355i
$947$	−32.5042	+	12.4772i	−1.05625	+	0.405455i	−0.823638	−	0.567116i	$-0.808059\pi$
$947$	−32.5042	+	12.4772i	−1.05625	+	0.405455i	−0.232608	+	0.972571i	$0.574726\pi$
$948$	17.1056	−	10.5389i	0.555565	−	0.342288i
$949$	0.840712	+	3.95524i	0.0272907	+	0.128393i
$950$	−2.83859	+	4.02807i	−0.0920961	+	0.130688i
$951$	−34.5488	+	29.6513i	−1.12032	+	0.961508i
$952$	0.366037	−	0.452018i	0.0118633	−	0.0146500i
$953$	−5.22763	−	0.827975i	−0.169340	−	0.0268208i	0.0711888	−	0.997463i	$-0.477321\pi$
$953$	−5.22763	−	0.827975i	−0.169340	−	0.0268208i	−0.240528	+	0.970642i	$0.577321\pi$
$954$	−11.4847	−	1.76251i	−0.371831	−	0.0570634i
$955$	14.6746	−	36.1642i	0.474860	−	1.17025i
$956$	−9.50903	−	5.49004i	−0.307544	−	0.177561i
$957$	−4.82042	−	35.9476i	−0.155822	−	1.16202i
$958$	−1.05594	−	20.1486i	−0.0341159	−	0.650970i
$959$	0.0614023	−	0.188977i	0.00198278	−	0.00610238i
$960$	−3.83095	−	0.569031i	−0.123643	−	0.0183654i
$961$	26.1682	+	16.6201i	0.844134	+	0.536132i
$962$	17.3629	−	17.3629i	0.559801	−	0.559801i
$963$	−21.8535	+	9.85581i	−0.704219	+	0.317599i
$964$	12.8928	+	11.6087i	0.415250	+	0.373892i
$965$	−6.45734	+	6.90379i	−0.207869	+	0.222241i
$966$	−1.32144	+	2.16806i	−0.0425166	+	0.0697561i
$967$	−7.79720	+	29.0995i	−0.250741	+	0.935778i	0.719670	+	0.694317i	$0.244293\pi$
$967$	−7.79720	+	29.0995i	−0.250741	+	0.935778i	−0.970410	+	0.241461i	$0.922373\pi$
$968$	−10.3585	+	8.38811i	−0.332933	+	0.269604i
$969$	3.39554	−	2.34571i	0.109081	−	0.0753552i
$970$	17.9728	+	18.6675i	0.577072	+	0.599378i
$971$	0.535490	−	0.482157i	0.0171847	−	0.0154732i	−0.660494	−	0.750832i	$-0.729653\pi$
$971$	0.535490	−	0.482157i	0.0171847	−	0.0154732i	0.677678	+	0.735359i	$0.262986\pi$
$972$	−13.7877	−	7.27318i	−0.442241	−	0.233287i
$973$	2.02071	−	3.11162i	0.0647810	−	0.0997540i
$974$	−14.3038	−	3.04037i	−0.458324	−	0.0974197i
$975$	37.9360	+	31.3108i	1.21492	+	1.00275i
$976$	4.23046	+	13.0200i	0.135414	+	0.416761i
$977$	32.2957	+	16.4555i	1.03323	+	0.526458i	0.886505	−	0.462720i	$-0.153126\pi$
$977$	32.2957	+	16.4555i	1.03323	+	0.526458i	0.146726	+	0.989177i	$0.453126\pi$
$978$	11.8147	+	33.1108i	0.377792	+	1.05877i
$979$	−7.60840	+	35.7947i	−0.243165	+	1.14400i
$980$	9.99591	−	11.8763i	0.319308	−	0.379375i
$981$	−11.3825	+	4.43216i	−0.363416	+	0.141508i
$982$	−0.507729	+	9.68805i	−0.0162023	+	0.309158i
$983$	−34.8069	+	42.9830i	−1.11017	+	1.37094i	−0.188909	+	0.981995i	$0.560495\pi$
$983$	−34.8069	+	42.9830i	−1.11017	+	1.37094i	−0.921259	+	0.388949i	$0.872838\pi$
$984$	7.06745	+	10.2305i	0.225302	+	0.326136i
$985$	−38.1751	−	8.87395i	−1.21636	−	0.282748i
$986$	8.88876	−	5.13193i	0.283076	−	0.163434i
$987$	1.10507	+	4.55474i	0.0351747	+	0.144979i
$988$	5.52884	−	0.875682i	0.175896	−	0.0278591i
$989$	−3.83220	+	4.25609i	−0.121857	+	0.135336i
$990$	29.2658	+	15.4373i	0.930128	+	0.490631i
$991$	−1.08928			−0.0346021			−0.0173010	−	0.999850i	$-0.505507\pi$
$991$	−1.08928			−0.0346021			−0.0173010	+	0.999850i	$0.505507\pi$
$992$	4.87955	−	2.68141i	0.154926	−	0.0851348i
$993$	−36.6696	+	34.9659i	−1.16368	+	1.10961i
$994$	−0.750185	−	0.243750i	−0.0237944	−	0.00773128i
$995$	−7.92447	−	0.566119i	−0.251223	−	0.0179472i
$996$	16.0314	−	20.9968i	0.507976	−	0.665308i
$997$	26.4717	−	7.09308i	0.838368	−	0.224640i	0.186007	−	0.982548i	$-0.440445\pi$
$997$	26.4717	−	7.09308i	0.838368	−	0.224640i	0.652361	+	0.757908i	$0.273779\pi$
$998$	1.90937	−	7.12588i	0.0604402	−	0.225566i
$999$	−22.1167	−	3.93452i	−0.699740	−	0.124483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bs.a.107.17	✓	1024
3.2	odd	2	inner	930.2.bs.a.107.50	yes	1024
5.3	odd	4	inner	930.2.bs.a.293.1	yes	1024
15.8	even	4	inner	930.2.bs.a.293.34	yes	1024
31.20	even	15	inner	930.2.bs.a.857.34	yes	1024
93.20	odd	30	inner	930.2.bs.a.857.1	yes	1024
155.113	odd	60	inner	930.2.bs.a.113.50	yes	1024
465.113	even	60	inner	930.2.bs.a.113.17	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bs.a.107.17	✓	1024	1.1	even	1	trivial
930.2.bs.a.107.50	yes	1024	3.2	odd	2	inner
930.2.bs.a.113.17	yes	1024	465.113	even	60	inner
930.2.bs.a.113.50	yes	1024	155.113	odd	60	inner
930.2.bs.a.293.1	yes	1024	5.3	odd	4	inner
930.2.bs.a.293.34	yes	1024	15.8	even	4	inner
930.2.bs.a.857.1	yes	1024	93.20	odd	30	inner
930.2.bs.a.857.34	yes	1024	31.20	even	15	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bs (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.453990 - 0.891007i) q^{2} +(0.0494968 + 1.73134i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(0.307868 + 2.21477i) q^{5} +(1.52017 - 0.830115i) q^{6} +(-0.186966 + 0.151402i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-2.99510 + 0.171392i) q^{9} +O(q^{10})\)	\(q+(-0.453990 - 0.891007i) q^{2} +(0.0494968 + 1.73134i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(0.307868 + 2.21477i) q^{5} +(1.52017 - 0.830115i) q^{6} +(-0.186966 + 0.151402i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-2.99510 + 0.171392i) q^{9} +(1.83361 - 1.27980i) q^{10} +(-2.00620 - 4.50600i) q^{11} +(-1.42978 - 0.977614i) q^{12} +(-4.76348 + 3.09344i) q^{13} +(0.219782 + 0.0978530i) q^{14} +(-3.81929 + 0.642649i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(-2.25707 + 0.866406i) q^{17} +(1.51246 + 2.59084i) q^{18} +(0.204908 + 0.964018i) q^{19} +(-1.97275 - 1.05274i) q^{20} +(-0.271384 - 0.316209i) q^{21} +(-3.10408 + 3.83322i) q^{22} +(6.01819 + 0.953188i) q^{23} +(-0.221954 + 1.71777i) q^{24} +(-4.81043 + 1.36371i) q^{25} +(4.91885 + 2.83990i) q^{26} +(-0.444986 - 5.17706i) q^{27} +(-0.0125910 - 0.240251i) q^{28} +(1.31190 - 4.03761i) q^{29} +(2.30653 + 3.11126i) q^{30} +(-5.34641 - 1.55432i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(7.70213 - 3.69645i) q^{33} +(1.79666 + 1.61772i) q^{34} +(-0.392883 - 0.367476i) q^{35} +(1.62182 - 2.52383i) q^{36} +(1.11892 - 4.17587i) q^{37} +(0.765920 - 0.620230i) q^{38} +(-5.59158 - 8.09410i) q^{39} +(-0.0423894 + 2.23567i) q^{40} +(5.33500 - 4.80366i) q^{41} +(-0.158539 + 0.385361i) q^{42} +(-0.511917 + 0.788283i) q^{43} +(4.82464 + 1.02551i) q^{44} +(-1.30169 - 6.58070i) q^{45} +(-1.88291 - 5.79499i) q^{46} +(-10.0217 - 5.10633i) q^{47} +(1.63131 - 0.582089i) q^{48} +(-1.44335 + 6.79042i) q^{49} +(3.39897 + 3.66702i) q^{50} +(-1.61176 - 3.86487i) q^{51} +(0.297258 - 5.67201i) q^{52} +(-2.43739 + 3.00993i) q^{53} +(-4.41078 + 2.74682i) q^{54} +(9.36211 - 5.83053i) q^{55} +(-0.208349 + 0.120290i) q^{56} +(-1.65890 + 0.402483i) q^{57} +(-4.19313 + 0.664126i) q^{58} +(-1.77046 + 1.96630i) q^{59} +(1.72501 - 3.46761i) q^{60} -13.6901 q^{61} +(1.04231 + 5.46933i) q^{62} +(0.534034 - 0.485510i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-8.31779 - 9.59765i) q^{65} +(-6.79026 - 5.18449i) q^{66} +(11.6271 - 3.11548i) q^{67} +(0.625732 - 2.33526i) q^{68} +(-1.35241 + 10.4667i) q^{69} +(-0.149059 + 0.516892i) q^{70} +(-3.26073 + 0.342717i) q^{71} +(-2.98504 - 0.299255i) q^{72} +(0.255132 - 0.664641i) q^{73} +(-4.22871 + 0.898840i) q^{74} +(-2.59916 - 8.26102i) q^{75} +(-0.900349 - 0.400861i) q^{76} +(1.05731 + 0.538727i) q^{77} +(-4.67337 + 8.65678i) q^{78} +(-4.71809 + 10.5970i) q^{79} +(2.01124 - 0.977202i) q^{80} +(8.94125 - 1.02667i) q^{81} +(-6.70213 - 2.57271i) q^{82} +(-0.798229 + 15.2311i) q^{83} +(0.415334 - 0.0336911i) q^{84} +(-2.61377 - 4.73215i) q^{85} +(0.934771 + 0.0982484i) q^{86} +(7.05542 + 2.07150i) q^{87} +(-1.27661 - 4.76436i) q^{88} +(-6.00221 - 4.36086i) q^{89} +(-5.27249 + 4.14739i) q^{90} +(0.422257 - 1.29957i) q^{91} +(-4.30855 + 4.30855i) q^{92} +(2.42644 - 9.33340i) q^{93} +11.2477i q^{94} +(-2.07200 + 0.750616i) q^{95} +(-1.25924 - 1.18925i) q^{96} +(1.81288 + 11.4461i) q^{97} +(6.70557 - 1.79675i) q^{98} +(6.78106 + 13.1521i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q - 8 q^{3} + 24 q^{7}+O(q^{10}) \) 1024 * q - 8 * q^3 + 24 * q^7	\( 1024 q - 8 q^{3} + 24 q^{7} + 8 q^{10} + 8 q^{12} - 8 q^{15} + 256 q^{16} + 44 q^{22} + 16 q^{25} - 20 q^{27} + 4 q^{28} + 48 q^{30} - 32 q^{31} - 52 q^{33} + 112 q^{37} + 12 q^{42} + 40 q^{45} + 24 q^{46} - 12 q^{48} + 16 q^{51} - 20 q^{55} - 40 q^{57} - 56 q^{58} - 12 q^{60} + 32 q^{61} + 224 q^{63} - 32 q^{66} + 24 q^{67} - 24 q^{70} - 88 q^{73} + 224 q^{75} - 96 q^{76} - 32 q^{78} + 48 q^{81} - 24 q^{85} + 20 q^{87} - 36 q^{88} + 8 q^{90} - 80 q^{91} - 252 q^{93} - 32 q^{97}+O(q^{100}) \) 1024 * q - 8 * q^3 + 24 * q^7 + 8 * q^10 + 8 * q^12 - 8 * q^15 + 256 * q^16 + 44 * q^22 + 16 * q^25 - 20 * q^27 + 4 * q^28 + 48 * q^30 - 32 * q^31 - 52 * q^33 + 112 * q^37 + 12 * q^42 + 40 * q^45 + 24 * q^46 - 12 * q^48 + 16 * q^51 - 20 * q^55 - 40 * q^57 - 56 * q^58 - 12 * q^60 + 32 * q^61 + 224 * q^63 - 32 * q^66 + 24 * q^67 - 24 * q^70 - 88 * q^73 + 224 * q^75 - 96 * q^76 - 32 * q^78 + 48 * q^81 - 24 * q^85 + 20 * q^87 - 36 * q^88 + 8 * q^90 - 80 * q^91 - 252 * q^93 - 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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