LMFDB - Embedded newform 512.2.o.a.141.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(5,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(128))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("512.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.o (of order $128$, degree $64$, 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:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$4032$
Relative dimension:	$63$ over $\Q(\zeta_{128})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{128}]$

Embedding invariants

Embedding label			141.19
Character	$\chi$	$=$	512.141
Dual form			512.2.o.a.69.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.882620 + 1.10498i) q^{2} +(-0.603125 + 1.82569i) q^{3} +(-0.441964 - 1.95056i) q^{4} +(0.147491 - 0.382356i) q^{5} +(-1.48502 - 2.27783i) q^{6} +(1.09882 - 1.83327i) q^{7} +(2.54541 + 1.23324i) q^{8} +(-0.559749 - 0.415138i) q^{9} +O(q^{10})$	\(q+(-0.882620 + 1.10498i) q^{2} +(-0.603125 + 1.82569i) q^{3} +(-0.441964 - 1.95056i) q^{4} +(0.147491 - 0.382356i) q^{5} +(-1.48502 - 2.27783i) q^{6} +(1.09882 - 1.83327i) q^{7} +(2.54541 + 1.23324i) q^{8} +(-0.559749 - 0.415138i) q^{9} +(0.292318 + 0.500450i) q^{10} +(0.0203509 + 0.165001i) q^{11} +(3.82766 + 0.369542i) q^{12} +(-0.156515 + 6.37572i) q^{13} +(1.05589 + 2.83226i) q^{14} +(0.609107 + 0.499881i) q^{15} +(-3.60934 + 1.72415i) q^{16} +(-2.24793 - 2.73910i) q^{17} +(0.952765 - 0.252103i) q^{18} +(3.95740 + 2.78712i) q^{19} +(-0.810993 - 0.118702i) q^{20} +(2.68425 + 3.11180i) q^{21} +(-0.200285 - 0.123146i) q^{22} +(-2.39281 + 5.05917i) q^{23} +(-3.78671 + 3.90333i) q^{24} +(3.58031 + 3.24501i) q^{25} +(-6.90690 - 5.80028i) q^{26} +(-3.62047 + 2.54983i) q^{27} +(-4.06154 - 1.33307i) q^{28} +(7.03456 - 1.94672i) q^{29} +(-1.08997 + 0.231846i) q^{30} +(-9.03093 + 1.79636i) q^{31} +(1.28052 - 5.51002i) q^{32} +(-0.313514 - 0.0623618i) q^{33} +(5.01072 - 0.0663252i) q^{34} +(-0.538897 - 0.690533i) q^{35} +(-0.562361 + 1.27530i) q^{36} +(-0.286706 - 1.27676i) q^{37} +(-6.57259 + 1.91289i) q^{38} +(-11.5457 - 4.13110i) q^{39} +(0.846962 - 0.791363i) q^{40} +(6.61349 - 5.99411i) q^{41} +(-5.80765 + 0.219515i) q^{42} +(-2.75230 + 5.46787i) q^{43} +(0.312849 - 0.112620i) q^{44} +(-0.241289 + 0.152794i) q^{45} +(-3.47835 - 7.10934i) q^{46} +(-5.22465 - 2.79264i) q^{47} +(-0.970879 - 7.62940i) q^{48} +(1.14630 + 2.14457i) q^{49} +(-6.74572 + 1.09207i) q^{50} +(6.35653 - 2.45198i) q^{51} +(12.5054 - 2.51255i) q^{52} +(-10.3088 - 2.85282i) q^{53} +(0.377995 - 6.25108i) q^{54} +(0.0660907 + 0.0165549i) q^{55} +(5.05781 - 3.31133i) q^{56} +(-7.47521 + 5.54400i) q^{57} +(-4.05775 + 9.49127i) q^{58} +(7.83324 - 0.192295i) q^{59} +(0.705843 - 1.40903i) q^{60} +(7.97696 + 6.88097i) q^{61} +(5.98593 - 11.5645i) q^{62} +(-1.37613 + 0.570010i) q^{63} +(4.95825 + 6.27820i) q^{64} +(2.41471 + 1.00021i) q^{65} +(0.345622 - 0.291385i) q^{66} +(-4.19395 + 0.309364i) q^{67} +(-4.34927 + 5.59529i) q^{68} +(-7.79330 - 7.41984i) q^{69} +(1.23867 + 0.0140072i) q^{70} +(-1.12248 + 7.56715i) q^{71} +(-0.912828 - 1.74700i) q^{72} +(6.86973 + 11.4614i) q^{73} +(1.66385 + 0.810089i) q^{74} +(-8.08374 + 4.57938i) q^{75} +(3.68740 - 8.95094i) q^{76} +(0.324854 + 0.143998i) q^{77} +(14.7552 - 9.11154i) q^{78} +(-12.0170 - 3.64533i) q^{79} +(0.126895 + 1.63435i) q^{80} +(-3.07847 - 10.1484i) q^{81} +(0.786185 + 12.5983i) q^{82} +(0.162928 - 0.725550i) q^{83} +(4.88339 - 6.61109i) q^{84} +(-1.37886 + 0.455515i) q^{85} +(-3.61266 - 7.86729i) q^{86} +(-0.688612 + 14.0170i) q^{87} +(-0.151684 + 0.445093i) q^{88} +(-2.12721 - 4.49761i) q^{89} +(0.0441314 - 0.401479i) q^{90} +(11.5164 + 7.29271i) q^{91} +(10.9257 + 2.43134i) q^{92} +(2.16719 - 17.5711i) q^{93} +(7.69719 - 3.30831i) q^{94} +(1.64935 - 1.10206i) q^{95} +(9.28725 + 5.66105i) q^{96} +(-4.21447 - 2.81602i) q^{97} +(-3.38145 - 0.626205i) q^{98} +(0.0571068 - 0.100808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) $ 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{79}{128}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.882620	+	1.10498i	−0.624107	+	0.781339i
$2$	−0.882620	+	1.10498i	−0.624107	+	0.781339i
$3$	−0.603125	+	1.82569i	−0.348215	+	1.05406i	0.615730	+	0.787957i	$0.288861\pi$
$3$	−0.603125	+	1.82569i	−0.348215	+	1.05406i	−0.963944	+	0.266103i	$0.914264\pi$
$4$	−0.441964	−	1.95056i	−0.220982	−	0.975278i
$5$	0.147491	−	0.382356i	0.0659600	−	0.170995i	−0.896087	−	0.443878i	$-0.853602\pi$
$5$	0.147491	−	0.382356i	0.0659600	−	0.170995i	0.962047	+	0.272883i	$0.0879773\pi$
$6$	−1.48502	−	2.27783i	−0.606256	−	0.929920i
$7$	1.09882	−	1.83327i	0.415315	−	0.692912i	−0.576987	−	0.816754i	$-0.695772\pi$
$7$	1.09882	−	1.83327i	0.415315	−	0.692912i	0.992302	+	0.123842i	$0.0395215\pi$
$8$	2.54541	+	1.23324i	0.899939	+	0.436015i
$9$	−0.559749	−	0.415138i	−0.186583	−	0.138379i
$10$	0.292318	+	0.500450i	0.0924390	+	0.158256i
$11$	0.0203509	+	0.165001i	0.00613603	+	0.0497497i	0.995236	−	0.0974974i	$-0.0310838\pi$
$11$	0.0203509	+	0.165001i	0.00613603	+	0.0497497i	−0.989100	+	0.147247i	$0.952959\pi$
$12$	3.82766	+	0.369542i	1.10495	+	0.106677i
$13$	−0.156515	+	6.37572i	−0.0434095	+	1.76831i	0.444848	+	0.895606i	$0.353258\pi$
$13$	−0.156515	+	6.37572i	−0.0434095	+	1.76831i	−0.488257	+	0.872700i	$0.662367\pi$
$14$	1.05589	+	2.83226i	0.282198	+	0.756953i
$15$	0.609107	+	0.499881i	0.157271	+	0.129069i
$16$	−3.60934	+	1.72415i	−0.902334	+	0.431038i
$17$	−2.24793	−	2.73910i	−0.545202	−	0.664330i	0.425404	−	0.905003i	$-0.360132\pi$
$17$	−2.24793	−	2.73910i	−0.545202	−	0.664330i	−0.970606	+	0.240673i	$0.922632\pi$
$18$	0.952765	−	0.252103i	0.224569	−	0.0594212i
$19$	3.95740	+	2.78712i	0.907890	+	0.639409i	0.932844	−	0.360280i	$-0.117319\pi$
$19$	3.95740	+	2.78712i	0.907890	+	0.639409i	−0.0249538	+	0.999689i	$0.507944\pi$
$20$	−0.810993	−	0.118702i	−0.181344	−	0.0265425i
$21$	2.68425	+	3.11180i	0.585752	+	0.679050i
$22$	−0.200285	−	0.123146i	−0.0427009	−	0.0262548i
$23$	−2.39281	+	5.05917i	−0.498935	+	1.05491i	0.484690	+	0.874686i	$0.338932\pi$
$23$	−2.39281	+	5.05917i	−0.498935	+	1.05491i	−0.983626	+	0.180224i	$0.942318\pi$
$24$	−3.78671	+	3.90333i	−0.772959	+	0.796764i
$25$	3.58031	+	3.24501i	0.716063	+	0.649001i
$26$	−6.90690	−	5.80028i	−1.35455	−	1.13753i
$27$	−3.62047	+	2.54983i	−0.696761	+	0.490714i
$28$	−4.06154	−	1.33307i	−0.767559	−	0.251927i
$29$	7.03456	−	1.94672i	1.30628	−	0.361498i	0.457016	−	0.889459i	$-0.348918\pi$
$29$	7.03456	−	1.94672i	1.30628	−	0.361498i	0.849269	+	0.527961i	$0.177043\pi$
$30$	−1.08997	+	0.231846i	−0.199000	+	0.0423292i
$31$	−9.03093	+	1.79636i	−1.62200	+	0.322636i	−0.920713	−	0.390240i	$-0.872392\pi$
$31$	−9.03093	+	1.79636i	−1.62200	+	0.322636i	−0.701290	+	0.712877i	$0.747392\pi$
$32$	1.28052	−	5.51002i	0.226366	−	0.974042i
$33$	−0.313514	−	0.0623618i	−0.0545758	−	0.0108558i
$34$	5.01072	−	0.0663252i	0.859332	−	0.0113747i
$35$	−0.538897	−	0.690533i	−0.0910902	−	0.116721i
$36$	−0.562361	+	1.27530i	−0.0937269	+	0.212550i
$37$	−0.286706	−	1.27676i	−0.0471342	−	0.209898i	0.946474	−	0.322779i	$-0.104617\pi$
$37$	−0.286706	−	1.27676i	−0.0471342	−	0.209898i	−0.993609	+	0.112881i	$0.963992\pi$
$38$	−6.57259	+	1.91289i	−1.06622	+	0.310311i
$39$	−11.5457	−	4.13110i	−1.84879	−	0.661506i
$40$	0.846962	−	0.791363i	0.133916	−	0.125125i
$41$	6.61349	−	5.99411i	1.03285	−	0.936123i	0.0348564	−	0.999392i	$-0.488903\pi$
$41$	6.61349	−	5.99411i	1.03285	−	0.936123i	0.997997	+	0.0632690i	$0.0201526\pi$
$42$	−5.80765	+	0.219515i	−0.896140	+	0.0338719i
$43$	−2.75230	+	5.46787i	−0.419721	+	0.833843i	0.580093	+	0.814551i	$0.303016\pi$
$43$	−2.75230	+	5.46787i	−0.419721	+	0.833843i	−0.999814	+	0.0192924i	$0.993859\pi$
$44$	0.312849	−	0.112620i	0.0471638	−	0.0169781i
$45$	−0.241289	+	0.152794i	−0.0359692	+	0.0227772i
$46$	−3.47835	−	7.10934i	−0.512854	−	1.04821i
$47$	−5.22465	−	2.79264i	−0.762094	−	0.407348i	0.0440786	−	0.999028i	$-0.485965\pi$
$47$	−5.22465	−	2.79264i	−0.762094	−	0.407348i	−0.806173	+	0.591680i	$0.798465\pi$
$48$	−0.970879	−	7.62940i	−0.140134	−	1.10121i
$49$	1.14630	+	2.14457i	0.163757	+	0.306367i
$50$	−6.74572	+	1.09207i	−0.953990	+	0.154442i
$51$	6.35653	−	2.45198i	0.890092	−	0.343346i
$52$	12.5054	−	2.51255i	1.73418	−	0.348428i
$53$	−10.3088	−	2.85282i	−1.41602	−	0.391865i	−0.527050	−	0.849835i	$-0.676702\pi$
$53$	−10.3088	−	2.85282i	−1.41602	−	0.391865i	−0.888968	+	0.457970i	$0.848577\pi$
$54$	0.377995	−	6.25108i	0.0514386	−	0.850664i
$55$	0.0660907	+	0.0165549i	0.00891167	+	0.00223226i
$56$	5.05781	−	3.31133i	0.675879	−	0.442495i
$57$	−7.47521	+	5.54400i	−0.990116	+	0.734320i
$58$	−4.05775	+	9.49127i	−0.532808	+	1.24626i
$59$	7.83324	−	0.192295i	1.01980	−	0.0250347i	0.488792	−	0.872400i	$-0.337438\pi$
$59$	7.83324	−	0.192295i	1.01980	−	0.0250347i	0.531010	+	0.847366i	$0.321813\pi$
$60$	0.705843	−	1.40903i	0.0911239	−	0.181905i
$61$	7.97696	+	6.88097i	1.02135	+	0.881018i	0.992945	−	0.118578i	$-0.0378336\pi$
$61$	7.97696	+	6.88097i	1.02135	+	0.881018i	0.0284005	+	0.999597i	$0.490959\pi$
$62$	5.98593	−	11.5645i	0.760214	−	1.46869i
$63$	−1.37613	+	0.570010i	−0.173376	+	0.0718145i
$64$	4.95825	+	6.27820i	0.619781	+	0.784775i
$65$	2.41471	+	1.00021i	0.299508	+	0.124060i
$66$	0.345622	−	0.291385i	0.0425432	−	0.0358670i
$67$	−4.19395	+	0.309364i	−0.512372	+	0.0377948i	−0.327282	−	0.944927i	$-0.606133\pi$
$67$	−4.19395	+	0.309364i	−0.512372	+	0.0377948i	−0.185090	+	0.982722i	$0.559258\pi$
$68$	−4.34927	+	5.59529i	−0.527427	+	0.678528i
$69$	−7.79330	−	7.41984i	−0.938203	−	0.893244i
$70$	1.23867	+	0.0140072i	0.148049	+	0.00167418i
$71$	−1.12248	+	7.56715i	−0.133214	+	0.898055i	0.814781	+	0.579769i	$0.196857\pi$
$71$	−1.12248	+	7.56715i	−0.133214	+	0.898055i	−0.947995	+	0.318286i	$0.896893\pi$
$72$	−0.912828	−	1.74700i	−0.107578	−	0.205886i
$73$	6.86973	+	11.4614i	0.804041	+	1.34146i	0.936641	+	0.350291i	$0.113917\pi$
$73$	6.86973	+	11.4614i	0.804041	+	1.34146i	−0.132600	+	0.991170i	$0.542333\pi$
$74$	1.66385	+	0.810089i	0.193418	+	0.0941710i
$75$	−8.08374	+	4.57938i	−0.933430	+	0.528782i
$76$	3.68740	−	8.95094i	0.422973	−	1.02674i
$77$	0.324854	+	0.143998i	0.0370205	+	0.0164101i
$78$	14.7552	−	9.11154i	1.67070	−	1.03168i
$79$	−12.0170	−	3.64533i	−1.35202	−	0.410132i	−0.470553	−	0.882372i	$-0.655946\pi$
$79$	−12.0170	−	3.64533i	−1.35202	−	0.410132i	−0.881470	+	0.472240i	$0.843446\pi$
$80$	0.126895	+	1.63435i	0.0141873	+	0.182726i
$81$	−3.07847	−	10.1484i	−0.342053	−	1.12760i
$82$	0.786185	+	12.5983i	0.0868197	+	1.39125i
$83$	0.162928	−	0.725550i	0.0178836	−	0.0796395i	−0.965947	−	0.258738i	$-0.916693\pi$
$83$	0.162928	−	0.725550i	0.0178836	−	0.0796395i	0.983831	+	0.179099i	$0.0573182\pi$
$84$	4.88339	−	6.61109i	0.532821	−	0.721329i
$85$	−1.37886	+	0.455515i	−0.149559	+	0.0494075i
$86$	−3.61266	−	7.86729i	−0.389563	−	0.848352i
$87$	−0.688612	+	14.0170i	−0.0738269	+	1.50278i
$88$	−0.151684	+	0.445093i	−0.0161696	+	0.0474471i
$89$	−2.12721	−	4.49761i	−0.225484	−	0.476745i	0.759253	−	0.650796i	$-0.225565\pi$
$89$	−2.12721	−	4.49761i	−0.225484	−	0.476745i	−0.984737	+	0.174050i	$0.944315\pi$
$90$	0.0441314	−	0.401479i	0.00465186	−	0.0423196i
$91$	11.5164	+	7.29271i	1.20725	+	0.764484i
$92$	10.9257	+	2.43134i	1.13909	+	0.253484i
$93$	2.16719	−	17.5711i	0.224727	−	1.82204i
$94$	7.69719	−	3.30831i	0.793905	−	0.341226i
$95$	1.64935	−	1.10206i	0.169220	−	0.113069i
$96$	9.28725	+	5.66105i	0.947876	+	0.577779i
$97$	−4.21447	−	2.81602i	−0.427914	−	0.285923i	0.322904	−	0.946432i	$-0.395341\pi$
$97$	−4.21447	−	2.81602i	−0.427914	−	0.285923i	−0.750819	+	0.660508i	$0.770341\pi$
$98$	−3.38145	−	0.626205i	−0.341578	−	0.0632562i
$99$	0.0571068	−	0.100808i	0.00573945	−	0.0101315i
$100$	4.74720	−	8.41778i	0.474720	−	0.841778i
$101$	7.67442	+	1.33164i	0.763634	+	0.132503i	0.539420	−	0.842037i	$-0.318644\pi$
$101$	7.67442	+	1.33164i	0.763634	+	0.132503i	0.224214	+	0.974540i	$0.428019\pi$
$102$	−2.90100	+	9.18801i	−0.287242	+	0.909748i
$103$	11.0582	−	0.543252i	1.08959	−	0.0535282i	0.503670	−	0.863896i	$-0.331983\pi$
$103$	11.0582	−	0.543252i	1.08959	−	0.0535282i	0.585922	+	0.810368i	$0.300733\pi$
$104$	−8.26117	+	16.0358i	−0.810074	+	1.57244i
$105$	1.58572	−	0.567379i	0.154750	−	0.0553705i
$106$	12.2510	−	8.87303i	1.18992	−	0.861825i
$107$	1.15622	+	0.0852880i	0.111776	+	0.00824510i	0.129337	−	0.991601i	$-0.458715\pi$
$107$	1.15622	+	0.0852880i	0.111776	+	0.00824510i	−0.0175609	+	0.999846i	$0.505590\pi$
$108$	6.57370	+	5.93501i	0.632554	+	0.571096i
$109$	0.828297	+	4.77359i	0.0793364	+	0.457227i	0.998056	+	0.0623174i	$0.0198491\pi$
$109$	0.828297	+	4.77359i	0.0793364	+	0.457227i	−0.918720	+	0.394910i	$0.870776\pi$
$110$	−0.0766258	+	0.0584173i	−0.00730598	+	0.00556987i
$111$	2.50388	+	0.246611i	0.237658	+	0.0234073i
$112$	−0.805175	+	8.51143i	−0.0760819	+	0.804255i
$113$	1.63768	+	16.6276i	0.154060	+	1.56420i	0.692429	+	0.721486i	$0.256541\pi$
$113$	1.63768	+	16.6276i	0.154060	+	1.56420i	−0.538369	+	0.842709i	$0.680959\pi$
$114$	0.471764	−	13.1532i	0.0441848	−	1.23191i
$115$	1.58149	+	1.66109i	0.147475	+	0.154897i
$116$	−6.90622	−	12.8609i	−0.641226	−	1.19411i
$117$	2.73441	−	3.50383i	0.252797	−	0.323929i
$118$	−6.70129	+	8.82531i	−0.616904	+	0.812435i
$119$	−7.49159	+	1.11127i	−0.686753	+	0.101870i
$120$	0.933956	+	2.02358i	0.0852582	+	0.184727i
$121$	10.6435	−	2.66607i	0.967594	−	0.242370i
$122$	−14.6440	+	2.74110i	−1.32580	+	0.248168i
$123$	6.95461	+	15.6894i	0.627076	+	1.41466i
$124$	7.49525	+	16.8214i	0.673094	+	1.51061i
$125$	3.59910	−	1.81164i	0.321914	−	0.162038i
$126$	0.584746	−	2.02369i	0.0520933	−	0.180285i
$127$	15.0845	−	15.0845i	1.33854	−	1.33854i	0.441058	−	0.897479i	$-0.354603\pi$
$127$	15.0845	−	15.0845i	1.33854	−	1.33854i	0.897479	−	0.441058i	$-0.145397\pi$
$128$	−11.3135	−	0.0624910i	−0.999985	−	0.00552348i
$129$	−8.32264	−	8.32264i	−0.732768	−	0.732768i
$130$	−3.23648	+	1.78541i	−0.283858	+	0.156591i
$131$	0.244544	+	0.485826i	0.0213659	+	0.0424468i	0.903655	−	0.428261i	$-0.140874\pi$
$131$	0.244544	+	0.485826i	0.0213659	+	0.0424468i	−0.882289	+	0.470708i	$0.843999\pi$
$132$	0.0169218	+	0.639089i	0.00147285	+	0.0556255i
$133$	9.45802	−	4.19245i	0.820115	−	0.363532i
$134$	3.35982	−	4.90728i	0.290244	−	0.423925i
$135$	0.440954	+	1.76039i	0.0379513	+	0.151510i
$136$	−2.34393	−	9.74438i	−0.200990	−	0.835573i
$137$	−2.33959	−	15.7723i	−0.199885	−	1.34751i	−0.824181	−	0.566327i	$-0.808364\pi$
$137$	−2.33959	−	15.7723i	−0.199885	−	1.34751i	0.624296	−	0.781188i	$-0.285386\pi$
$138$	15.0773	−	2.06255i	1.28346	−	0.175576i
$139$	3.29363	+	2.57037i	0.279362	+	0.218016i	0.745178	−	0.666865i	$-0.232364\pi$
$139$	3.29363	+	2.57037i	0.279362	+	0.218016i	−0.465817	+	0.884881i	$0.654239\pi$
$140$	−1.10875	+	1.35634i	−0.0937064	+	0.114632i
$141$	8.24960	−	7.85427i	0.694742	−	0.661449i
$142$	−7.37083	−	7.91923i	−0.618546	−	0.664567i
$143$	−1.05518	+	0.103927i	−0.0882390	+	0.00869078i
$144$	2.73608	+	0.533281i	0.228007	+	0.0444401i
$145$	0.293192	−	2.97683i	0.0243483	−	0.247212i
$146$	−18.7280	−	2.52519i	−1.54994	−	0.208986i
$147$	−4.60667	+	0.799334i	−0.379952	+	0.0659279i
$148$	−2.36368	+	1.12352i	−0.194293	+	0.0923527i
$149$	0.614134	−	8.32561i	0.0503118	−	0.682061i	−0.912013	−	0.410160i	$-0.865473\pi$
$149$	0.614134	−	8.32561i	0.0503118	−	0.682061i	0.962325	−	0.271901i	$-0.0876522\pi$
$150$	2.07474	−	12.9742i	0.169402	−	1.05934i
$151$	−7.47738	−	20.8979i	−0.608501	−	1.70065i	−0.708548	−	0.705663i	$-0.750649\pi$
$151$	−7.47738	−	20.8979i	−0.608501	−	1.70065i	0.100047	−	0.994983i	$-0.468101\pi$
$152$	6.63604	+	11.9748i	0.538254	+	0.971283i
$153$	0.121167	+	2.46641i	0.00979577	+	0.199398i
$154$	−0.445837	+	0.231862i	−0.0359266	+	0.0186840i
$155$	−0.645131	+	3.71798i	−0.0518181	+	0.298635i
$156$	−2.95518	+	24.3463i	−0.236604	+	1.94926i
$157$	11.3079	+	6.40587i	0.902473	+	0.511244i	0.872669	−	0.488311i	$-0.162387\pi$
$157$	11.3079	+	6.40587i	0.902473	+	0.511244i	0.0298031	+	0.999556i	$0.490512\pi$
$158$	14.6345	−	10.0612i	1.16426	−	0.800423i
$159$	11.4258	−	17.1000i	0.906127	−	1.35612i
$160$	−1.91792	−	1.30229i	−0.151625	−	0.102955i
$161$	6.64557	+	9.94580i	0.523744	+	0.783839i
$162$	13.9309	+	5.55550i	1.09451	+	0.436481i
$163$	10.4142	+	1.28447i	0.815703	+	0.100607i	0.519449	−	0.854502i	$-0.326137\pi$
$163$	10.4142	+	1.28447i	0.815703	+	0.100607i	0.296255	+	0.955109i	$0.404262\pi$
$164$	−14.6148	−	10.2508i	−1.14122	−	0.800452i
$165$	−0.0700850	+	0.110676i	−0.00545611	+	0.00861614i
$166$	0.657916	+	0.820417i	0.0510642	+	0.0636767i
$167$	0.147268	−	0.0696525i	0.0113959	−	0.00538988i	−0.421849	−	0.906666i	$-0.638619\pi$
$167$	0.147268	−	0.0696525i	0.0113959	−	0.00538988i	0.433245	+	0.901276i	$0.357369\pi$
$168$	2.99495	+	11.2311i	0.231065	+	0.866501i
$169$	−27.6409	−	1.35791i	−2.12623	−	0.104455i
$170$	0.713677	−	1.92566i	0.0547365	−	0.147692i
$171$	−1.05811	−	3.20296i	−0.0809160	−	0.244936i
$172$	11.8818	+	2.95190i	0.905979	+	0.225081i
$173$	−5.27954	−	1.18556i	−0.401396	−	0.0901365i	0.0137178	−	0.999906i	$-0.495633\pi$
$173$	−5.27954	−	1.18556i	−0.401396	−	0.0901365i	−0.415114	+	0.909769i	$0.636258\pi$
$174$	−14.8807	−	13.1326i	−1.12811	−	0.995580i
$175$	9.88311	−	2.99801i	0.747093	−	0.226628i
$176$	−0.357940	−	0.560456i	−0.0269807	−	0.0422459i
$177$	−4.37336	+	14.4170i	−0.328722	+	1.08365i
$178$	6.84729	+	1.61915i	0.513226	+	0.121361i
$179$	4.86750	−	10.9809i	0.363814	−	0.820751i	−0.635021	−	0.772495i	$-0.719009\pi$
$179$	4.86750	−	10.9809i	0.363814	−	0.820751i	0.998835	−	0.0482562i	$-0.0153664\pi$
$180$	0.404675	+	0.403117i	0.0301627	+	0.0300466i
$181$	−9.14668	−	16.1462i	−0.679868	−	1.20013i	−0.969990	−	0.243145i	$-0.921821\pi$
$181$	−9.14668	−	16.1462i	−0.679868	−	1.20013i	0.290122	−	0.956990i	$-0.406304\pi$
$182$	−18.2229	+	6.28876i	−1.35077	+	0.466154i
$183$	−17.3736	+	10.4133i	−1.28429	+	0.769776i
$184$	−12.3299	+	9.92678i	−0.908969	+	0.731812i
$185$	−0.530464	−	0.0786869i	−0.0390005	−	0.00578517i
$186$	17.5029	+	17.9033i	1.28337	+	1.31273i
$187$	0.406207	−	0.426653i	0.0297048	−	0.0312000i
$188$	−3.13808	+	11.4252i	−0.228868	+	0.833270i
$189$	0.696271	+	9.43912i	0.0506463	+	0.686595i
$190$	−0.237994	+	2.79521i	−0.0172659	+	0.202786i
$191$	−3.06733	+	7.40519i	−0.221944	+	0.535820i	−0.995154	−	0.0983299i	$-0.968650\pi$
$191$	−3.06733	+	7.40519i	−0.221944	+	0.535820i	0.773210	+	0.634150i	$0.218650\pi$
$192$	−14.4525	+	5.26567i	−1.04302	+	0.380017i
$193$	−5.14755	−	12.4273i	−0.370529	−	0.894536i	−0.993661	−	0.112419i	$-0.964140\pi$
$193$	−5.14755	−	12.4273i	−0.370529	−	0.894536i	0.623132	−	0.782117i	$-0.285860\pi$
$194$	6.83141	−	2.17143i	0.490467	−	0.155900i
$195$	−3.28244	+	3.80526i	−0.235060	+	0.272500i
$196$	3.67648	−	3.18374i	0.262606	−	0.227410i
$197$	−0.0476105	−	1.93944i	−0.00339211	−	0.138179i	−0.999005	−	0.0446070i	$-0.985796\pi$
$197$	−0.0476105	−	1.93944i	−0.00339211	−	0.138179i	0.995613	−	0.0935721i	$-0.0298286\pi$
$198$	0.0609868	+	0.152077i	0.00433415	+	0.0108076i
$199$	3.15990	+	4.26063i	0.223999	+	0.302028i	0.900883	−	0.434062i	$-0.142920\pi$
$199$	3.15990	+	4.26063i	0.223999	+	0.302028i	−0.676884	+	0.736090i	$0.736670\pi$
$200$	5.11151	+	12.6753i	0.361438	+	0.896276i
$201$	1.96467	−	7.84342i	0.138577	−	0.553232i
$202$	−8.24503	+	7.30476i	−0.580118	+	0.513961i
$203$	4.16085	−	15.0354i	0.292034	−	1.05528i
$204$	−7.59209	−	11.3151i	−0.531552	−	0.792214i
$205$	−1.31646	−	3.41279i	−0.0919453	−	0.238359i
$206$	−9.15986	+	12.6985i	−0.638198	+	0.884748i
$207$	3.43963	−	1.83852i	0.239071	−	0.127786i
$208$	−10.4278	−	23.2820i	−0.723037	−	1.61431i
$209$	−0.379340	+	0.709695i	−0.0262395	+	0.0490907i
$210$	−0.772644	+	2.25297i	−0.0533175	+	0.155470i
$211$	0.946608	+	1.49486i	0.0651672	+	0.102910i	0.875869	−	0.482549i	$-0.160289\pi$
$211$	0.946608	+	1.49486i	0.0651672	+	0.102910i	−0.810702	+	0.585460i	$0.800914\pi$
$212$	−1.00848	+	21.3687i	−0.0692626	+	1.46761i
$213$	−13.1382	−	6.61324i	−0.900218	−	0.453132i
$214$	−1.11474	+	1.20232i	−0.0762024	+	0.0821892i
$215$	1.68474	+	1.85882i	0.114898	+	0.126770i
$216$	−12.3601	+	2.02545i	−0.841001	+	0.137815i
$217$	−6.63015	+	18.5300i	−0.450084	+	1.25790i
$218$	−6.00580	−	3.29801i	−0.406764	−	0.223370i
$219$	−25.0683	+	5.62928i	−1.69396	+	0.380391i
$220$	0.00308145	−	0.136230i	0.000207752	−	0.00918464i
$221$	17.8156	−	13.9034i	1.19841	−	0.935245i
$222$	−2.48248	+	2.54908i	−0.166613	+	0.171083i
$223$	0.301907	−	1.51779i	0.0202172	−	0.101639i	−0.969359	−	0.245648i	$-0.920999\pi$
$223$	0.301907	−	1.51779i	0.0202172	−	0.101639i	0.989576	+	0.144009i	$0.0459994\pi$
$224$	−8.69430	−	8.40206i	−0.580912	−	0.561386i
$225$	−0.656951	−	3.30271i	−0.0437967	−	0.220181i
$226$	−19.8187	−	12.8663i	−1.31832	−	0.855852i
$227$	−1.39182	−	5.02940i	−0.0923785	−	0.333813i	0.903024	−	0.429589i	$-0.141342\pi$
$227$	−1.39182	−	5.02940i	−0.0923785	−	0.333813i	−0.995403	+	0.0957763i	$0.969467\pi$
$228$	14.1176	+	12.1306i	0.934964	+	0.803367i
$229$	1.31282	+	1.86407i	0.0867538	+	0.123181i	0.858639	−	0.512582i	$-0.171311\pi$
$229$	1.31282	+	1.86407i	0.0867538	+	0.123181i	−0.771885	+	0.635763i	$0.780686\pi$
$230$	−3.23132	+	0.281403i	−0.213067	+	0.0185552i
$231$	−0.458822	+	0.506232i	−0.0301883	+	0.0333076i
$232$	20.3066	+	3.72006i	1.33320	+	0.244234i
$233$	11.3639	+	5.37474i	0.744475	+	0.352111i	0.761863	−	0.647738i	$-0.224285\pi$
$233$	11.3639	+	5.37474i	0.744475	+	0.352111i	−0.0173876	+	0.999849i	$0.505535\pi$
$234$	1.45821	+	6.11402i	0.0953264	+	0.399686i
$235$	−1.83837	+	1.58579i	−0.119922	+	0.103446i
$236$	−3.83710	−	15.1942i	−0.249774	−	0.989058i
$237$	13.9030	−	19.7408i	0.903098	−	1.28230i
$238$	5.38429	−	9.25890i	0.349012	−	0.600165i
$239$	10.4769	−	8.59817i	0.677694	−	0.556169i	−0.231349	−	0.972871i	$-0.574314\pi$
$239$	10.4769	−	8.59817i	0.677694	−	0.556169i	0.909043	+	0.416702i	$0.136814\pi$
$240$	−3.06034	−	0.754046i	−0.197544	−	0.0486735i
$241$	7.86134	−	9.57907i	0.506393	−	0.617042i	−0.455577	−	0.890196i	$-0.650567\pi$
$241$	7.86134	−	9.57907i	0.506393	−	0.617042i	0.961970	+	0.273154i	$0.0880670\pi$
$242$	−6.44824	+	14.1140i	−0.414509	+	0.907284i
$243$	7.10369	+	0.174386i	0.455702	+	0.0111868i
$244$	9.89619	−	18.6007i	0.633539	−	1.19078i
$245$	0.989058	−	0.121989i	0.0631886	−	0.00779357i
$246$	−23.4747	−	6.16303i	−1.49669	−	0.392940i
$247$	−18.3893	+	24.7951i	−1.17008	+	1.57767i
$248$	−25.2028	−	6.56479i	−1.60038	−	0.416865i
$249$	1.22636	+	0.735053i	0.0777175	+	0.0465821i
$250$	−1.17482	+	5.57593i	−0.0743020	+	0.352653i
$251$	16.8926	+	6.51619i	1.06625	+	0.411299i	0.828478	−	0.560022i	$-0.189207\pi$
$251$	16.8926	+	6.51619i	1.06625	+	0.411299i	0.237774	+	0.971321i	$0.423582\pi$
$252$	1.72003	+	2.43229i	0.108352	+	0.153220i
$253$	−0.883464	−	0.291857i	−0.0555429	−	0.0183489i
$254$	3.35421	+	29.9820i	0.210462	+	1.88124i
$255$		−	2.79210i		−	0.174848i
$256$	10.0546	−	12.4461i	0.628413	−	0.777880i
$257$			1.34510i			0.0839048i	0.999120	+	0.0419524i	$0.0133578\pi$
$257$			1.34510i			0.0839048i	−0.999120	+	0.0419524i	$0.986642\pi$
$258$	16.5421	−	1.85063i	1.02987	−	0.115215i
$259$	−2.65569	−	0.877321i	−0.165016	−	0.0545141i
$260$	0.883742	−	5.15208i	0.0548073	−	0.319519i
$261$	−4.74575	−	1.83064i	−0.293754	−	0.113314i
$262$	−0.752667	−	0.158583i	−0.0465000	−	0.00979729i
$263$	−22.9940	−	13.7821i	−1.41787	−	0.849840i	−0.419549	−	0.907733i	$-0.637812\pi$
$263$	−22.9940	−	13.7821i	−1.41787	−	0.849840i	−0.998323	+	0.0578927i	$0.981562\pi$
$264$	−0.721116	−	0.545374i	−0.0443816	−	0.0335655i
$265$	−2.61124	+	3.52085i	−0.160407	+	0.216284i
$266$	−3.71526	+	14.1513i	−0.227797	+	0.867670i
$267$	9.49420	−	1.17100i	0.581035	−	0.0716639i
$268$	2.45701	+	8.04380i	0.150086	+	0.491353i
$269$	−20.7326	−	0.508957i	−1.26409	−	0.0310317i	−0.613031	−	0.790059i	$-0.710050\pi$
$269$	−20.7326	−	0.508957i	−1.26409	−	0.0310317i	−0.651059	+	0.759027i	$0.725675\pi$
$270$	−2.33439	−	1.06651i	−0.142066	−	0.0649056i
$271$	−7.64487	+	9.31530i	−0.464393	+	0.565864i	−0.951567	−	0.307440i	$-0.900528\pi$
$271$	−7.64487	+	9.31530i	−0.464393	+	0.565864i	0.487175	+	0.873305i	$0.338028\pi$
$272$	12.8361	+	6.01058i	0.778306	+	0.364445i
$273$	−20.2601	+	16.6270i	−1.22619	+	1.00631i
$274$	19.4930	+	11.3357i	1.17762	+	0.684815i
$275$	−0.462566	+	0.656794i	−0.0278938	+	0.0396062i
$276$	−11.0284	+	18.4806i	−0.663835	+	1.11240i
$277$	6.50255	−	5.60914i	0.390700	−	0.337020i	−0.435712	−	0.900086i	$-0.643503\pi$
$277$	6.50255	−	5.60914i	0.390700	−	0.337020i	0.826412	+	0.563066i	$0.190378\pi$
$278$	−5.74723	+	1.37073i	−0.344696	+	0.0822110i
$279$	5.80079	+	2.74357i	0.347284	+	0.164253i
$280$	−0.520124	−	2.42228i	−0.0310834	−	0.144759i
$281$	−19.0955	+	21.0686i	−1.13914	+	1.25685i	−0.177027	+	0.984206i	$0.556648\pi$
$281$	−19.0955	+	21.0686i	−1.13914	+	1.25685i	−0.962115	+	0.272644i	$0.912102\pi$
$282$	1.39756	+	16.0480i	0.0832233	+	0.955644i
$283$	6.36420	+	9.03648i	0.378313	+	0.537163i	0.961367	−	0.275271i	$-0.0887674\pi$
$283$	6.36420	+	9.03648i	0.378313	+	0.537163i	−0.583054	+	0.812433i	$0.698142\pi$
$284$	15.2562	−	1.15495i	0.905291	−	0.0685335i
$285$	1.01725	+	3.67588i	0.0602569	+	0.217741i
$286$	0.816490	−	1.25769i	0.0482801	−	0.0743685i
$287$	−3.72181	−	18.7108i	−0.219691	−	1.10446i
$288$	−3.00419	+	2.55263i	−0.177023	+	0.150415i
$289$	0.867008	−	4.35875i	0.0510005	−	0.256397i
$290$	3.03056	+	2.95138i	0.177961	+	0.173311i
$291$	7.68301	−	5.99588i	0.450386	−	0.351485i
$292$	19.3200	−	18.4653i	1.13062	−	1.08060i
$293$	−0.328632	+	0.0737967i	−0.0191989	+	0.00431125i	−0.228690	−	0.973499i	$-0.573444\pi$
$293$	−0.328632	+	0.0737967i	−0.0191989	+	0.00431125i	0.209491	+	0.977811i	$0.432819\pi$
$294$	3.18269	−	5.79579i	0.185619	−	0.338018i
$295$	1.08181	−	3.02345i	0.0629853	−	0.176032i
$296$	0.844763	−	3.60346i	0.0491009	−	0.209447i
$297$	−0.494404	−	0.545490i	−0.0286882	−	0.0316526i
$298$	8.65759	+	8.02696i	0.501521	+	0.464989i
$299$	−31.8813	−	16.0477i	−1.84375	−	0.928064i
$300$	12.5051	+	13.7439i	0.721980	+	0.793503i
$301$	6.99982	+	11.0539i	0.403463	+	0.637138i
$302$	29.6914	+	10.1825i	1.70855	+	0.585938i
$303$	−7.05979	+	13.2079i	−0.405575	+	0.758777i
$304$	−19.0890	−	3.23648i	−1.09483	−	0.185625i
$305$	3.80751	−	2.03516i	0.218018	−	0.116533i
$306$	−2.83228	−	2.04302i	−0.161911	−	0.116791i
$307$	5.87884	+	15.2403i	0.335523	+	0.869811i	0.993190	+	0.116502i	$0.0371682\pi$
$307$	5.87884	+	15.2403i	0.335523	+	0.869811i	−0.657667	+	0.753308i	$0.728457\pi$
$308$	0.137302	−	0.697287i	0.00782350	−	0.0397316i
$309$	−5.67764	+	20.5164i	−0.322990	+	1.16714i
$310$	−3.53889	−	3.99442i	−0.200995	−	0.226868i
$311$	6.20669	−	24.7785i	0.351949	−	1.40506i	−0.492915	−	0.870077i	$-0.664069\pi$
$311$	6.20669	−	24.7785i	0.351949	−	1.40506i	0.844864	−	0.534981i	$-0.179681\pi$
$312$	−24.2938	−	24.7539i	−1.37537	−	1.40141i
$313$	14.9652	+	20.1783i	0.845885	+	1.14054i	0.988568	+	0.150775i	$0.0481769\pi$
$313$	14.9652	+	20.1783i	0.845885	+	1.14054i	−0.142683	+	0.989768i	$0.545573\pi$
$314$	−17.0590	+	6.84111i	−0.962694	+	0.386066i
$315$	0.0149806	+	0.610242i	0.000844061	+	0.0343832i
$316$	−1.79932	+	25.0510i	−0.101220	+	1.40923i
$317$	14.0358	−	16.2714i	0.788329	−	0.913893i	−0.209628	−	0.977781i	$-0.567225\pi$
$317$	14.0358	−	16.2714i	0.788329	−	0.913893i	0.997957	+	0.0638884i	$0.0203502\pi$
$318$	8.81046	+	27.7181i	0.494066	+	1.55435i
$319$	0.464371	+	1.12109i	0.0259998	+	0.0627690i
$320$	3.13181	−	0.969840i	0.175073	−	0.0542157i
$321$	−0.853055	+	2.05946i	−0.0476129	+	0.114948i
$322$	−16.8554	−	1.43513i	−0.939316	−	0.0799769i
$323$	−1.26174	−	17.1050i	−0.0702050	−	0.951746i
$324$	−18.4344	+	10.4900i	−1.02413	+	0.582775i
$325$	−21.2496	+	22.3192i	−1.17872	+	1.23804i
$326$	−10.6111	+	10.3738i	−0.587694	+	0.574551i
$327$	−9.21465	−	1.36686i	−0.509571	−	0.0755877i
$328$	24.2262	−	7.10149i	1.33767	−	0.392114i
$329$	−10.8606	+	6.50961i	−0.598766	+	0.358886i
$330$	−0.0604367	−	0.175128i	−0.00332693	−	0.00964046i
$331$	−11.3366	−	20.0119i	−0.623116	−	1.09995i	−0.985781	−	0.168034i	$-0.946258\pi$
$331$	−11.3366	−	20.0119i	−0.623116	−	1.09995i	0.362665	−	0.931919i	$-0.381867\pi$
$332$	−1.48723	+	0.00286754i	−0.0816226	+	0.000157377i
$333$	−0.369549	+	0.833688i	−0.0202511	+	0.0456858i
$334$	−0.0530169	+	0.224205i	−0.00290096	+	0.0122679i
$335$	−0.500282	+	1.64921i	−0.0273334	+	0.0901060i
$336$	−15.0536	−	6.60346i	−0.821240	−	0.360248i
$337$	12.7982	−	3.88228i	0.697161	−	0.211481i	0.0782397	−	0.996935i	$-0.475070\pi$
$337$	12.7982	−	3.88228i	0.697161	−	0.211481i	0.618921	+	0.785453i	$0.287570\pi$
$338$	25.8969	−	29.3442i	1.40861	−	1.59611i
$339$	−31.3446	−	7.03866i	−1.70240	−	0.382287i
$340$	1.49791	+	2.48823i	0.0812358	+	0.134943i
$341$	−0.480189	−	1.45355i	−0.0260037	−	0.0787144i
$342$	4.47312	+	1.65780i	0.241878	+	0.0896434i
$343$	20.1346	+	0.989151i	1.08717	+	0.0534092i
$344$	−13.7489	+	10.5238i	−0.741292	+	0.567403i
$345$	−3.98646	+	1.88546i	−0.214624	+	0.101510i
$346$	5.96985	−	4.78739i	0.320941	−	0.257372i
$347$	−1.30804	+	2.06562i	−0.0702192	+	0.110888i	−0.878142	−	0.478400i	$-0.841217\pi$
$347$	−1.30804	+	2.06562i	−0.0702192	+	0.110888i	0.807923	+	0.589288i	$0.200592\pi$
$348$	27.6453	−	4.85184i	1.48194	−	0.260086i
$349$	−12.0470	−	1.48585i	−0.644859	−	0.0795358i	−0.206659	−	0.978413i	$-0.566259\pi$
$349$	−12.0470	−	1.48585i	−0.644859	−	0.0795358i	−0.438200	+	0.898877i	$0.644384\pi$
$350$	−5.41029	+	13.5667i	−0.289192	+	0.725173i
$351$	−15.6903	−	23.4822i	−0.837487	−	1.25339i
$352$	0.935217	+	0.0991526i	0.0498473	+	0.00528485i
$353$	16.5120	−	24.7120i	0.878848	−	1.31529i	−0.0693451	−	0.997593i	$-0.522091\pi$
$353$	16.5120	−	24.7120i	0.878848	−	1.31529i	0.948193	−	0.317696i	$-0.102909\pi$
$354$	−12.0705	−	17.5572i	−0.641541	−	0.933156i
$355$	2.72779	+	1.54527i	0.144776	+	0.0820146i
$356$	−7.83268	+	6.13702i	−0.415131	+	0.325262i
$357$	2.48953	−	14.3475i	0.131760	−	0.759352i
$358$	7.83753	+	15.0705i	0.414226	+	0.796498i
$359$	−0.0503004	−	1.02389i	−0.00265475	−	0.0540387i	0.997103	−	0.0760691i	$-0.0242370\pi$
$359$	−0.0503004	−	1.02389i	−0.00265475	−	0.0540387i	−0.999757	+	0.0220304i	$0.992987\pi$
$360$	−0.802611	+	0.0913585i	−0.0423013	+	0.00481501i
$361$	1.49210	+	4.17015i	0.0785318	+	0.219482i
$362$	25.9142	+	4.14401i	1.36202	+	0.217804i
$363$	−1.55198	+	21.0397i	−0.0814580	+	1.10430i
$364$	9.13498	−	25.6866i	0.478803	−	1.34634i
$365$	5.39558	−	0.936222i	0.282417	−	0.0490041i
$366$	3.82775	−	28.3885i	0.200080	−	1.48389i
$367$	1.83942	−	18.6759i	0.0960167	−	0.974874i	−0.819631	−	0.572892i	$-0.805821\pi$
$367$	1.83942	−	18.6759i	0.0960167	−	0.974874i	0.915648	−	0.401982i	$-0.131679\pi$
$368$	−0.0863245	−	22.3858i	−0.00449998	−	1.16694i
$369$	−6.19028	+	0.609689i	−0.322253	+	0.0317392i
$370$	0.555145	−	0.516702i	0.0288606	−	0.0268620i
$371$	−16.5575	+	15.7640i	−0.859622	+	0.818428i
$372$	−35.2312	+	3.53857i	−1.82665	+	0.183466i
$373$	−6.75633	−	5.27269i	−0.349830	−	0.273010i	0.424982	−	0.905202i	$-0.360280\pi$
$373$	−6.75633	−	5.27269i	−0.349830	−	0.273010i	−0.774812	+	0.632192i	$0.782155\pi$
$374$	0.112917	+	0.825424i	0.00583877	+	0.0426816i
$375$	1.13677	+	7.66348i	0.0587026	+	0.395741i
$376$	−9.85492	−	13.5516i	−0.508229	−	0.698873i
$377$	11.3107	+	45.1550i	0.582533	+	2.32560i
$378$	−11.0446	−	7.56179i	−0.568072	−	0.388936i
$379$	25.4528	−	11.2824i	1.30742	−	0.579540i	0.370420	−	0.928865i	$-0.379214\pi$
$379$	25.4528	−	11.2824i	1.30742	−	0.579540i	0.937002	+	0.349324i	$0.113589\pi$
$380$	−2.87859	−	2.73008i	−0.147669	−	0.140050i
$381$	18.4418	+	36.6375i	0.944801	+	1.87700i
$382$	−5.47530	−	9.92530i	−0.280141	−	0.507823i
$383$	10.4200	+	10.4200i	0.532435	+	0.532435i	0.921296	−	0.388861i	$-0.127131\pi$
$383$	10.4200	+	10.4200i	0.532435	+	0.532435i	−0.388861	+	0.921296i	$0.627131\pi$
$384$	6.93757	−	20.6173i	0.354031	−	1.05212i
$385$	0.102971	−	0.102971i	0.00524791	−	0.00524791i
$386$	18.2752	+	5.28063i	0.930185	+	0.268777i
$387$	3.81052	−	1.91805i	0.193700	−	0.0975002i
$388$	−3.63015	+	9.46513i	−0.184293	+	0.480519i
$389$	−4.16688	−	9.40033i	−0.211269	−	0.476616i	0.776969	−	0.629539i	$-0.216756\pi$
$389$	−4.16688	−	9.40033i	−0.211269	−	0.476616i	−0.988238	+	0.152923i	$0.951131\pi$
$390$	−1.30759	−	6.98562i	−0.0662124	−	0.353731i
$391$	19.2365	−	4.81848i	0.972830	−	0.243681i
$392$	0.273033	+	6.87247i	0.0137903	+	0.347112i
$393$	−1.03446	+	0.153447i	−0.0521814	+	0.00774038i
$394$	2.18506	+	1.65918i	0.110082	+	0.0835881i
$395$	−3.16622	+	4.05714i	−0.159310	+	0.204137i
$396$	−0.221870	−	0.0668366i	−0.0111494	−	0.00335867i
$397$	11.9853	+	12.5885i	0.601524	+	0.631801i	0.952484	−	0.304590i	$-0.0985195\pi$
$397$	11.9853	+	12.5885i	0.601524	+	0.631801i	−0.350959	+	0.936391i	$0.614144\pi$
$398$	−7.49690	−	0.268890i	−0.375785	−	0.0134782i
$399$	1.94973	+	19.7960i	0.0976087	+	0.991038i
$400$	−18.5174	−	5.53931i	−0.925872	−	0.276966i
$401$	4.61435	+	0.454474i	0.230430	+	0.0226954i	0.212573	−	0.977145i	$-0.431816\pi$
$401$	4.61435	+	0.454474i	0.230430	+	0.0226954i	0.0178568	+	0.999841i	$0.494316\pi$
$402$	6.93277	+	9.09369i	0.345775	+	0.453552i
$403$	−10.0396	−	57.8598i	−0.500110	−	2.88220i
$404$	−0.794384	−	15.5579i	−0.0395221	−	0.774036i
$405$	−4.33434	−	0.319720i	−0.215375	−	0.0158870i
$406$	12.9413	+	17.8682i	0.642268	+	0.886782i
$407$	0.204832	−	0.0732900i	0.0101531	−	0.00363285i
$408$	19.2039	+	1.59780i	0.950733	+	0.0791029i
$409$	−18.6069	+	0.914100i	−0.920053	+	0.0451993i	−0.503580	−	0.863949i	$-0.667984\pi$
$409$	−18.6069	+	0.914100i	−0.920053	+	0.0451993i	−0.416473	+	0.909148i	$0.636734\pi$
$410$	4.93299	+	1.55753i	0.243623	+	0.0769211i
$411$	30.2063	+	5.24128i	1.48997	+	0.258533i
$412$	−5.94695	−	21.3294i	−0.292985	−	1.05083i
$413$	8.25481	−	14.5718i	0.406192	−	0.717030i
$414$	−1.00436	+	5.42344i	−0.0493614	+	0.266547i
$415$	−0.253388	−	0.169309i	−0.0124383	−	0.00831104i
$416$	34.9299	+	9.02662i	1.71258	+	0.442566i
$417$	−6.67916	+	4.46287i	−0.327080	+	0.218548i
$418$	−0.449387	−	1.04555i	−0.0219802	−	0.0511398i
$419$	0.595508	−	4.82825i	0.0290925	−	0.235876i	−0.970901	−	0.239481i	$-0.923023\pi$
$419$	0.595508	−	4.82825i	0.0290925	−	0.235876i	0.999993	+	0.00360558i	$0.00114769\pi$
$420$	−1.80754	−	2.84227i	−0.0881987	−	0.138689i
$421$	−13.5361	−	8.57165i	−0.659710	−	0.417757i	0.162682	−	0.986679i	$-0.447986\pi$
$421$	−13.5361	−	8.57165i	−0.659710	−	0.417757i	−0.822392	+	0.568922i	$0.807361\pi$
$422$	−2.48728	−	0.273407i	−0.121079	−	0.0133093i
$423$	1.76517	+	3.73213i	0.0858253	+	0.181462i
$424$	−22.7218	−	19.9748i	−1.10347	−	0.970060i
$425$	0.840137	−	17.1014i	0.0407526	−	0.829539i
$426$	18.9036	−	8.68053i	0.915881	−	0.420573i
$427$	21.3800	−	7.06298i	1.03465	−	0.341802i
$428$	−0.344649	−	2.29297i	−0.0166592	−	0.110835i
$429$	0.446671	−	1.98912i	0.0215655	−	0.0960355i
$430$	−3.54094	+	0.220969i	−0.170759	+	0.0106561i
$431$	−4.64470	−	15.3115i	−0.223727	−	0.737530i	−0.994897	−	0.100900i	$-0.967828\pi$
$431$	−4.64470	−	15.3115i	−0.223727	−	0.737530i	0.771169	−	0.636630i	$-0.219672\pi$
$432$	8.67122	−	15.4454i	0.417194	−	0.743118i
$433$	−10.7307	−	3.25512i	−0.515685	−	0.156431i	0.0217065	−	0.999764i	$-0.493090\pi$
$433$	−10.7307	−	3.25512i	−0.515685	−	0.156431i	−0.537391	+	0.843333i	$0.680590\pi$
$434$	−14.6234	−	23.6812i	−0.701947	−	1.13673i
$435$	5.25793	+	2.33068i	0.252098	+	0.111748i
$436$	8.94508	−	3.72539i	0.428392	−	0.178414i
$437$	−23.5698	+	13.3521i	−1.12750	+	0.638719i
$438$	15.9055	−	32.6685i	0.759997	−	1.56096i
$439$	5.65892	+	9.44133i	0.270085	+	0.450610i	0.962651	−	0.270744i	$-0.0872698\pi$
$439$	5.65892	+	9.44133i	0.270085	+	0.450610i	−0.692566	+	0.721355i	$0.743520\pi$
$440$	0.147812	+	0.123645i	0.00704666	+	0.00589452i
$441$	0.248655	−	1.67629i	0.0118407	−	0.0798235i
$442$	−0.361382	+	31.9573i	−0.0171892	+	1.52005i
$443$	21.4349	+	20.4077i	1.01840	+	0.969599i	0.999543	−	0.0302234i	$-0.00962188\pi$
$443$	21.4349	+	20.4077i	1.01840	+	0.969599i	0.0188582	+	0.999822i	$0.493997\pi$
$444$	−0.625598	−	4.99296i	−0.0296896	−	0.236955i
$445$	−2.03343	+	0.149995i	−0.0963940	+	0.00711045i
$446$	1.41066	+	1.67323i	0.0667965	+	0.0792297i
$447$	14.8296	+	6.14261i	0.701414	+	0.290535i
$448$	16.9579	−	2.19121i	0.801184	−	0.103525i
$449$	13.1082	−	5.42960i	0.618615	−	0.256239i	−0.0512919	−	0.998684i	$-0.516334\pi$
$449$	13.1082	−	5.42960i	0.618615	−	0.256239i	0.669907	+	0.742445i	$0.266334\pi$
$450$	4.22927	+	2.18912i	0.199370	+	0.103196i
$451$	1.12362	+	0.969246i	0.0529094	+	0.0456400i
$452$	31.7093	−	10.5432i	1.49148	−	0.495910i
$453$	42.6628	−	1.04731i	2.00447	−	0.0492070i
$454$	6.78584	+	2.90111i	0.318475	+	0.136156i
$455$	4.48699	−	3.32778i	0.210353	−	0.156009i
$456$	−25.8646	+	4.89304i	−1.21122	+	0.229138i
$457$	−30.8526	−	7.72818i	−1.44322	−	0.361509i	−0.559233	−	0.829011i	$-0.688904\pi$
$457$	−30.8526	−	7.72818i	−1.44322	−	0.361509i	−0.883992	+	0.467502i	$0.845154\pi$
$458$	−3.21848	−	0.194617i	−0.150390	−	0.00909388i
$459$	15.1228	+	4.18504i	0.705872	+	0.195341i
$460$	2.54109	−	3.81892i	0.118479	−	0.178058i
$461$	−7.04131	+	2.71613i	−0.327947	+	0.126503i	−0.518267	−	0.855219i	$-0.673422\pi$
$461$	−7.04131	+	2.71613i	−0.327947	+	0.126503i	0.190320	+	0.981722i	$0.439047\pi$
$462$	−0.154411	−	0.953801i	−0.00718386	−	0.0443748i
$463$	7.83055	+	14.6499i	0.363917	+	0.680840i	0.995530	−	0.0944433i	$-0.0301071\pi$
$463$	7.83055	+	14.6499i	0.363917	+	0.680840i	−0.631614	+	0.775283i	$0.717607\pi$
$464$	−22.0336	+	19.1550i	−1.02289	+	0.889250i
$465$	−6.39877	−	3.42021i	−0.296736	−	0.158609i
$466$	−15.9690	+	7.81307i	−0.739750	+	0.361933i
$467$	−10.7616	+	6.81474i	−0.497990	+	0.315349i	−0.760230	−	0.649654i	$-0.774914\pi$
$467$	−10.7616	+	6.81474i	−0.497990	+	0.315349i	0.262240	+	0.965003i	$0.415539\pi$
$468$	−8.04292	−	3.78506i	−0.371784	−	0.174964i
$469$	−4.04125	+	8.02859i	−0.186608	+	0.370726i
$470$	−0.129684	−	3.43101i	−0.00598188	−	0.158261i
$471$	−18.5152	+	16.7812i	−0.853137	+	0.773238i
$472$	20.1760	+	9.17078i	0.928675	+	0.422119i
$473$	−0.958216	−	0.342855i	−0.0440588	−	0.0157645i
$474$	9.54209	+	32.7862i	0.438283	+	1.50592i
$475$	5.12453	+	22.8205i	0.235129	+	1.04708i
$476$	5.47862	+	14.1216i	0.251112	+	0.647264i
$477$	4.58601	+	5.87642i	0.209979	+	0.269063i
$478$	0.253690	+	19.1657i	0.0116035	+	0.876618i
$479$	28.5330	+	5.67557i	1.30371	+	0.259323i	0.797620	−	0.603160i	$-0.206092\pi$
$479$	28.5330	+	5.67557i	1.30371	+	0.259323i	0.506086	+	0.862483i	$0.331092\pi$
$480$	3.53433	−	2.71608i	0.161319	−	0.123972i
$481$	8.18514	−	1.62813i	0.373210	−	0.0742361i
$482$	3.64611	+	17.1413i	0.166076	+	0.780765i
$483$	−22.1660	+	6.13417i	−1.00859	+	0.279114i
$484$	−9.90437	−	19.5825i	−0.450199	−	0.890114i
$485$	−1.69832	+	1.19609i	−0.0771166	+	0.0543116i
$486$	−6.46255	+	7.69552i	−0.293147	+	0.349076i
$487$	−22.7880	−	20.6538i	−1.03262	−	0.935914i	−0.0346393	−	0.999400i	$-0.511028\pi$
$487$	−22.7880	−	20.6538i	−1.03262	−	0.935914i	−0.997983	+	0.0634858i	$0.979778\pi$
$488$	11.8188	+	27.3524i	0.535011	+	1.23819i
$489$	−8.62611	+	18.2384i	−0.390086	+	0.824768i
$490$	−0.738167	+	1.20056i	−0.0333470	+	0.0542358i
$491$	−7.45797	−	8.64586i	−0.336574	−	0.390182i	0.563358	−	0.826213i	$-0.309509\pi$
$491$	−7.45797	−	8.64586i	−0.336574	−	0.390182i	−0.899932	+	0.436030i	$0.856384\pi$
$492$	27.5293	−	20.4995i	1.24112	−	0.924189i
$493$	−21.1454	−	14.8923i	−0.952343	−	0.670715i
$494$	−11.1673	−	42.2044i	−0.502442	−	1.89887i
$495$	−0.0301217	−	0.0367034i	−0.00135387	−	0.00164969i
$496$	29.4984	−	22.0544i	1.32452	−	0.990270i
$497$	12.6392	+	10.3728i	0.566947	+	0.465282i
$498$	−1.89463	+	0.706334i	−0.0849004	+	0.0316516i
$499$	−0.812140	+	33.0829i	−0.0363564	+	1.48100i	0.653432	+	0.756985i	$0.273328\pi$
$499$	−0.812140	+	33.0829i	−0.0363564	+	1.48100i	−0.689789	+	0.724011i	$0.742297\pi$
$500$	−5.12437	−	6.21958i	−0.229169	−	0.278148i
$501$	0.0383427	+	0.310874i	0.00171302	+	0.0138888i
$502$	−22.1100	+	12.9147i	−0.986818	+	0.576410i
$503$	−6.43259	−	4.77073i	−0.286815	−	0.212716i	0.442720	−	0.896660i	$-0.354013\pi$
$503$	−6.43259	−	4.77073i	−0.286815	−	0.212716i	−0.729535	+	0.683943i	$0.760263\pi$
$504$	−4.20577	−	0.246179i	−0.187340	−	0.0109657i
$505$	1.64107	−	2.73796i	0.0730266	−	0.121838i
$506$	1.10226	−	0.718612i	0.0490014	−	0.0319462i
$507$	19.1501	−	49.6447i	0.850485	−	2.20480i
$508$	−36.0901	−	22.7564i	−1.60124	−	1.00965i
$509$	0.915579	−	2.77150i	0.0405823	−	0.122845i	−0.927248	−	0.374447i	$-0.877833\pi$
$509$	0.915579	−	2.77150i	0.0405823	−	0.122845i	0.967831	+	0.251603i	$0.0809576\pi$
$510$	3.08522	+	2.46437i	0.136616	+	0.109124i
$511$	28.5606			1.26344
$512$	4.87829	+	22.0953i	0.215592	+	0.976484i
$513$	−21.4343			−0.946349
$514$	−1.48631	−	1.18721i	−0.0655581	−	0.0523655i
$515$	1.42326	−	4.30828i	0.0627164	−	0.189845i
$516$	−12.5555	+	19.9121i	−0.552724	+	0.876581i
$517$	0.354461	−	0.918905i	0.0155892	−	0.0404134i
$518$	3.31339	−	2.16014i	0.145582	−	0.0949113i
$519$	5.34869	−	8.92375i	0.234781	−	0.391709i
$520$	4.91294	+	5.52385i	0.215447	+	0.242237i
$521$	13.2615	+	9.83543i	0.580999	+	0.430898i	0.845873	−	0.533385i	$-0.179080\pi$
$521$	13.2615	+	9.83543i	0.580999	+	0.430898i	−0.264874	+	0.964283i	$0.585330\pi$
$522$	6.21151	−	3.62820i	0.271870	−	0.158802i
$523$	5.05816	+	41.0105i	0.221178	+	1.79326i	0.536109	+	0.844149i	$0.319894\pi$
$523$	5.05816	+	41.0105i	0.221178	+	1.79326i	−0.314931	+	0.949115i	$0.601981\pi$
$524$	0.839550	−	0.691714i	0.0366759	−	0.0302177i
$525$	−0.487330	+	19.8516i	−0.0212688	+	0.866396i
$526$	35.5239	−	13.2436i	1.54892	−	0.577449i
$527$	25.2213	+	20.6986i	1.09866	+	0.901644i
$528$	1.23910	−	0.315461i	0.0539249	−	0.0137287i
$529$	−5.27864	−	6.43204i	−0.229506	−	0.279654i
$530$	−1.58574	−	5.99295i	−0.0688801	−	0.260317i
$531$	−4.46448	−	3.14424i	−0.193742	−	0.136448i
$532$	−12.3577	−	16.5955i	−0.535775	−	0.719506i
$533$	37.1817	+	43.1039i	1.61052	+	1.86704i
$534$	−7.08584	+	11.5244i	−0.306634	+	0.498712i
$535$	0.203143	−	0.429509i	0.00878262	−	0.0185693i
$536$	−11.0568	−	4.38467i	−0.477583	−	0.189389i
$537$	17.1120	+	15.5094i	0.738436	+	0.669279i
$538$	18.8614	−	22.4599i	0.813173	−	0.968316i
$539$	−0.330528	+	0.232784i	−0.0142368	+	0.0100267i
$540$	3.23885	−	1.63813i	0.139378	−	0.0704940i
$541$	26.6879	−	7.38553i	1.14740	−	0.317529i	0.359389	−	0.933188i	$-0.382985\pi$
$541$	26.6879	−	7.38553i	1.14740	−	0.317529i	0.788013	+	0.615659i	$0.211110\pi$
$542$	−3.54571	−	16.6693i	−0.152301	−	0.716008i
$543$	34.9944	−	6.96082i	1.50175	−	0.298717i
$544$	−17.9710	+	8.87863i	−0.770501	+	0.380668i
$545$	1.94738	+	0.387358i	0.0834165	+	0.0165926i
$546$	−0.490581	−	37.0623i	−0.0209949	−	1.58612i
$547$	−10.6194	−	13.6075i	−0.454051	−	0.581813i	0.505684	−	0.862719i	$-0.331240\pi$
$547$	−10.6194	−	13.6075i	−0.454051	−	0.581813i	−0.959735	+	0.280906i	$0.909365\pi$
$548$	−29.7306	+	11.5343i	−1.27003	+	0.492720i
$549$	−1.60854	−	7.16316i	−0.0686509	−	0.305716i
$550$	−0.317474	−	1.09083i	−0.0135371	−	0.0465130i
$551$	33.2643	+	11.9022i	1.41711	+	0.507049i
$552$	−10.6867	−	28.4975i	−0.454858	−	1.21294i
$553$	−19.8875	+	18.0250i	−0.845702	+	0.766499i
$554$	0.458708	+	12.1359i	0.0194887	+	0.515606i
$555$	0.463594	−	0.921003i	0.0196785	−	0.0390944i
$556$	3.55799	−	7.56041i	0.150892	−	0.320633i
$557$	−27.0532	+	17.1312i	−1.14628	+	0.725873i	−0.966204	−	0.257779i	$-0.917009\pi$
$557$	−27.0532	+	17.1312i	−1.14628	+	0.725873i	−0.180076	+	0.983653i	$0.557634\pi$
$558$	−8.15149	+	3.98823i	−0.345080	+	0.168835i
$559$	−34.4308	−	18.4037i	−1.45627	−	0.778392i
$560$	3.13564	+	1.56322i	0.132505	+	0.0660583i
$561$	0.533941	+	0.998933i	0.0225430	+	0.0421750i
$562$	−6.42637	−	39.6958i	−0.271080	−	1.67446i
$563$	6.02224	−	2.32303i	0.253807	−	0.0979041i	−0.229647	−	0.973274i	$-0.573757\pi$
$563$	6.02224	−	2.32303i	0.253807	−	0.0979041i	0.483454	+	0.875370i	$0.339382\pi$
$564$	−18.9662	−	12.6200i	−0.798622	−	0.531398i
$565$	6.59922	+	1.82625i	0.277631	+	0.0768309i
$566$	−15.6023	−	0.943451i	−0.655814	−	0.0396562i
$567$	−21.9874	−	5.50756i	−0.923385	−	0.231296i
$568$	−12.1893	+	17.8772i	−0.511450	+	0.750112i
$569$	37.2395	−	27.6187i	1.56116	−	1.15783i	0.640180	−	0.768225i	$-0.278860\pi$
$569$	37.2395	−	27.6187i	1.56116	−	1.15783i	0.920980	−	0.389610i	$-0.127390\pi$
$570$	−4.95963	−	2.12036i	−0.207736	−	0.0888122i
$571$	−17.2127	+	0.422547i	−0.720328	+	0.0176831i	−0.383057	−	0.923725i	$-0.625129\pi$
$571$	−17.2127	+	0.422547i	−0.720328	+	0.0176831i	−0.337271	+	0.941408i	$0.609504\pi$
$572$	0.669068	+	2.01226i	0.0279752	+	0.0841370i
$573$	−11.6696	−	10.0662i	−0.487503	−	0.420523i
$574$	23.9600	+	12.4020i	1.00007	+	0.517649i
$575$	−24.9841	+	10.3487i	−1.04191	+	0.431572i
$576$	−0.169057	−	5.57257i	−0.00704403	−	0.232191i
$577$	−7.52849	−	3.11840i	−0.313415	−	0.129821i	0.220431	−	0.975403i	$-0.429254\pi$
$577$	−7.52849	−	3.11840i	−0.313415	−	0.129821i	−0.533846	+	0.845582i	$0.679254\pi$
$578$	4.05109	+	4.80514i	0.168503	+	0.199868i
$579$	25.7930	−	1.90260i	1.07192	−	0.0790695i
$580$	−5.93606	+	0.743765i	−0.246481	+	0.0308832i
$581$	−1.15110	−	1.09594i	−0.0477558	−	0.0454673i
$582$	−0.155847	+	13.7817i	−0.00646006	+	0.571268i
$583$	0.260925	−	1.75901i	0.0108064	−	0.0728509i
$584$	3.35160	+	37.6461i	0.138690	+	1.55781i
$585$	−0.936409	−	1.56230i	−0.0387157	−	0.0645933i
$586$	0.208513	−	0.428266i	0.00861359	−	0.0176915i
$587$	−1.61499	+	0.914878i	−0.0666576	+	0.0377611i	−0.525865	−	0.850568i	$-0.676258\pi$
$587$	−1.61499	+	0.914878i	−0.0666576	+	0.0377611i	0.459208	+	0.888329i	$0.348133\pi$
$588$	3.59513	+	8.63230i	0.148261	+	0.355990i
$589$	−40.7457	−	18.0613i	−1.67890	−	0.744204i
$590$	2.38603	+	3.86394i	0.0982313	+	0.159076i
$591$	3.56952	+	1.08280i	0.146830	+	0.0445405i
$592$	3.23615	+	4.11393i	0.133005	+	0.169082i
$593$	−7.86379	−	25.9235i	−0.322927	−	1.06455i	−0.956711	−	0.291039i	$-0.905999\pi$
$593$	−7.86379	−	25.9235i	−0.322927	−	1.06455i	0.633784	−	0.773510i	$-0.281501\pi$
$594$	1.03913	−	0.0648458i	0.0426359	−	0.00266065i
$595$	−0.680041	+	3.02836i	−0.0278790	+	0.124151i
$596$	−16.5110	+	2.48172i	−0.676317	+	0.101655i
$597$	−9.68438	+	3.19929i	−0.396355	+	0.130938i
$598$	45.8715	−	21.0642i	1.87583	−	0.861380i
$599$	0.00546028	−	0.111147i	0.000223101	−	0.00454133i	−0.998681	−	0.0513382i	$-0.983651\pi$
$599$	0.00546028	−	0.111147i	0.000223101	−	0.00454133i	0.998904	+	0.0467969i	$0.0149014\pi$
$600$	−26.2239	+	1.68725i	−1.07059	+	0.0688815i
$601$	6.34426	+	13.4138i	0.258788	+	0.547161i	0.990992	−	0.133925i	$-0.0427580\pi$
$601$	6.34426	+	13.4138i	0.258788	+	0.547161i	−0.732204	+	0.681086i	$0.761508\pi$
$602$	−18.3926	−	2.02175i	−0.749625	−	0.0824003i
$603$	2.47599	+	1.56790i	0.100830	+	0.0638499i
$604$	−37.4577	+	23.8212i	−1.52413	+	0.969269i
$605$	0.550439	−	4.46284i	0.0223785	−	0.181440i
$606$	−8.36341	−	19.4585i	−0.339740	−	0.790449i
$607$	27.8106	−	18.5825i	1.12880	−	0.754240i	0.156430	−	0.987689i	$-0.450001\pi$
$607$	27.8106	−	18.5825i	1.12880	−	0.754240i	0.972369	+	0.233449i	$0.0750013\pi$
$608$	20.4246	−	18.2364i	0.828326	−	0.739584i
$609$	24.9404	+	16.6646i	1.01063	+	0.675284i
$610$	−1.11178	+	6.00350i	−0.0450145	+	0.243075i
$611$	18.6228	−	32.8738i	0.753398	−	1.32993i
$612$	4.75732	−	1.32641i	0.192303	−	0.0536169i
$613$	−9.08690	−	1.57673i	−0.367016	−	0.0636834i	−0.0155377	−	0.999879i	$-0.504946\pi$
$613$	−9.08690	−	1.57673i	−0.367016	−	0.0636834i	−0.351479	+	0.936196i	$0.614321\pi$
$614$	−22.0290	−	6.95540i	−0.889019	−	0.280697i
$615$	7.02467	−	0.345100i	0.283262	−	0.0139158i
$616$	0.649303	+	0.767156i	0.0261612	+	0.0309096i
$617$	0.0351771	−	0.0125866i	0.00141618	−	0.000506716i	−0.336182	−	0.941797i	$-0.609136\pi$
$617$	0.0351771	−	0.0125866i	0.00141618	−	0.000506716i	0.337598	+	0.941290i	$0.390386\pi$
$618$	−17.6590	−	24.3818i	−0.710349	−	0.980782i
$619$	8.40546	+	0.620024i	0.337844	+	0.0249209i	0.241424	−	0.970420i	$-0.422386\pi$
$619$	8.40546	+	0.620024i	0.337844	+	0.0249209i	0.0964204	+	0.995341i	$0.469261\pi$
$620$	7.53725	−	0.384850i	0.302703	−	0.0154560i
$621$	−4.23690	−	24.4179i	−0.170021	−	0.979855i
$622$	21.9016	+	28.7282i	0.878174	+	1.15190i
$623$	−10.5828	−	1.04231i	−0.423989	−	0.0417593i
$624$	48.7948	−	4.99593i	1.95336	−	0.199997i
$625$	2.20626	+	22.4006i	0.0882506	+	0.896023i
$626$	−35.5052	−	1.27346i	−1.41907	−	0.0508977i
$627$	−1.06689	−	1.12059i	−0.0426076	−	0.0447521i
$628$	7.49731	−	24.8879i	0.299175	−	0.993137i
$629$	−2.85269	+	3.65538i	−0.113744	+	0.145750i
$630$	−0.687527	−	0.522058i	−0.0273917	−	0.0207993i
$631$	−27.1362	+	4.02528i	−1.08028	+	0.160244i	−0.663062	−	0.748565i	$-0.730743\pi$
$631$	−27.1362	+	4.02528i	−1.08028	+	0.160244i	−0.417213	+	0.908809i	$0.636993\pi$
$632$	−26.0928	−	24.0987i	−1.03792	−	0.958597i
$633$	−3.30006	+	0.826623i	−0.131166	+	0.0328553i
$634$	5.59130	+	29.8708i	0.222059	+	1.18632i
$635$	−3.54283	−	7.99250i	−0.140593	−	0.317173i
$636$	−38.4042	−	14.7291i	−1.52283	−	0.584049i
$637$	−13.8526	+	6.97281i	−0.548860	+	0.276273i
$638$	−1.64865	−	0.476376i	−0.0652706	−	0.0188599i
$639$	3.76972	−	3.76972i	0.149128	−	0.149128i
$640$	−1.69254	+	4.31658i	−0.0669035	+	0.170628i
$641$	−3.85677	−	3.85677i	−0.152333	−	0.152333i	0.626826	−	0.779159i	$-0.284354\pi$
$641$	−3.85677	−	3.85677i	−0.152333	−	0.152333i	−0.779159	+	0.626826i	$0.784354\pi$
$642$	−1.52274	−	2.76033i	−0.0600976	−	0.108941i
$643$	−16.0387	−	31.8634i	−0.632504	−	1.25657i	−0.951160	−	0.308699i	$-0.900106\pi$
$643$	−16.0387	−	31.8634i	−0.632504	−	1.25657i	0.318656	−	0.947870i	$-0.396769\pi$
$644$	16.4627	−	17.3582i	0.648723	−	0.684011i
$645$	−4.40973	+	1.95470i	−0.173633	+	0.0769662i
$646$	20.0143	+	13.7030i	0.787452	+	0.539137i
$647$	−4.75857	−	18.9973i	−0.187079	−	0.746860i	−0.988811	−	0.149176i	$-0.952338\pi$
$647$	−4.75857	−	18.9973i	−0.187079	−	0.746860i	0.801732	−	0.597684i	$-0.203912\pi$
$648$	4.67936	−	29.6283i	0.183823	−	1.16391i
$649$	0.191143	+	1.28858i	0.00750301	+	0.0505812i
$650$	−5.90692	−	43.1798i	−0.231688	−	1.69365i
$651$	−29.8312	−	23.2805i	−1.16918	−	0.912435i
$652$	−2.09728	−	20.8812i	−0.0821356	−	0.817770i
$653$	−16.4588	+	15.6701i	−0.644082	+	0.613217i	−0.939663	−	0.342100i	$-0.888862\pi$
$653$	−16.4588	+	15.6701i	−0.644082	+	0.613217i	0.295581	+	0.955318i	$0.404487\pi$
$654$	9.64339	−	8.97559i	0.377086	−	0.350973i
$655$	0.221827	−	0.0218480i	0.00866748	−	0.000853672i
$656$	−13.5355	+	33.0374i	−0.528474	+	1.28989i
$657$	0.912761	−	9.26742i	0.0356102	−	0.361556i
$658$	2.39281	−	17.7463i	0.0932816	−	0.691822i
$659$	−40.5919	+	7.04336i	−1.58123	+	0.274370i	−0.892638	−	0.450775i	$-0.851148\pi$
$659$	−40.5919	+	7.04336i	−1.58123	+	0.274370i	−0.688596	+	0.725145i	$0.741773\pi$
$660$	0.246855	+	0.0877897i	0.00960883	+	0.00341721i
$661$	−2.92304	+	39.6267i	−0.113693	+	1.54130i	0.576152	+	0.817342i	$0.304554\pi$
$661$	−2.92304	+	39.6267i	−0.113693	+	1.54130i	−0.689845	+	0.723957i	$0.742321\pi$
$662$	32.1187	+	5.13618i	1.24833	+	0.199623i
$663$	14.6383	+	40.9112i	0.568503	+	1.58886i
$664$	1.30949	−	1.64590i	0.0508182	−	0.0638732i
$665$	−0.208037	−	4.23468i	−0.00806732	−	0.164214i
$666$	−0.595038	−	1.14417i	−0.0230573	−	0.0443358i
$667$	−6.98355	+	40.2472i	−0.270404	+	1.55838i
$668$	−0.200948	−	0.256470i	−0.00777492	−	0.00992314i
$669$	2.58892	+	1.46660i	0.100093	+	0.0567021i
$670$	−1.38079	−	2.00843i	−0.0533444	−	0.0775924i
$671$	−0.973029	+	1.45624i	−0.0375634	+	0.0562175i
$672$	20.5833	−	10.8056i	0.794017	−	0.416834i
$673$	−1.51230	−	2.26332i	−0.0582950	−	0.0872446i	0.801177	−	0.598427i	$-0.204208\pi$
$673$	−1.51230	−	2.26332i	−0.0582950	−	0.0872446i	−0.859472	+	0.511183i	$0.829208\pi$
$674$	−7.00607	+	17.5683i	−0.269864	+	0.676706i
$675$	−21.2366	−	2.61929i	−0.817398	−	0.100816i
$676$	9.56762	+	54.5153i	0.367985	+	2.09674i
$677$	−24.0332	+	37.9526i	−0.923672	+	1.45864i	−0.0353723	+	0.999374i	$0.511262\pi$
$677$	−24.0332	+	37.9526i	−0.923672	+	1.45864i	−0.888300	+	0.459264i	$0.848113\pi$
$678$	35.4429	−	28.4227i	1.36118	−	1.09157i
$679$	−9.79347	+	4.63197i	−0.375839	+	0.177759i
$680$	−4.07153	−	0.540992i	−0.156136	−	0.0207461i
$681$	10.0216	+	0.492327i	0.384027	+	0.0188660i
$682$	2.02997	+	0.752336i	0.0777317	+	0.0288084i
$683$	7.79019	+	23.5812i	0.298083	+	0.902311i	0.984543	+	0.175143i	$0.0560389\pi$
$683$	7.79019	+	23.5812i	0.298083	+	0.902311i	−0.686459	+	0.727168i	$0.740836\pi$
$684$	−5.77990	+	3.47950i	−0.221000	+	0.133042i
$685$	−6.37569	−	1.43171i	−0.243603	−	0.0547028i
$686$	−18.8642	+	21.3753i	−0.720240	+	0.816114i
$687$	−4.19500	+	1.27254i	−0.160049	+	0.0485504i
$688$	0.506518	−	24.4808i	0.0193108	−	0.933320i
$689$	19.8022	−	65.2792i	0.754405	−	2.48694i
$690$	1.43514	−	6.06911i	0.0546348	−	0.231047i
$691$	0.229339	−	0.517381i	0.00872448	−	0.0196821i	−0.909795	−	0.415059i	$-0.863761\pi$
$691$	0.229339	−	0.517381i	0.00872448	−	0.0196821i	0.918519	+	0.395377i	$0.129386\pi$
$692$	0.0208659	+	10.8220i	0.000793204	+	0.411391i
$693$	−0.122058	−	0.215462i	−0.00463659	−	0.00818472i
$694$	−1.12797	−	3.26852i	−0.0428171	−	0.124071i
$695$	1.46858	−	0.880231i	0.0557063	−	0.0333891i
$696$	−19.0391	+	34.8299i	−0.721676	+	1.32022i
$697$	−31.2851	−	4.64071i	−1.18501	−	0.175779i
$698$	12.2747	−	12.0002i	0.464605	−	0.454215i
$699$	−16.6665	+	17.5053i	−0.630383	+	0.662112i
$700$	−10.2158	−	17.9525i	−0.386119	−	0.678542i
$701$	3.17301	+	43.0154i	0.119843	+	1.62467i	0.638454	+	0.769660i	$0.279574\pi$
$701$	3.17301	+	43.0154i	0.119843	+	1.62467i	−0.518611	+	0.855011i	$0.673551\pi$
$702$	39.7960	+	3.38838i	1.50200	+	0.127886i
$703$	2.42387	−	5.85174i	0.0914180	−	0.220702i
$704$	−0.935003	+	0.945883i	−0.0352393	+	0.0356493i
$705$	−1.78639	−	4.31272i	−0.0672792	−	0.162426i
$706$	12.7324	+	40.0568i	0.479192	+	1.50756i
$707$	10.8741	−	12.6061i	0.408962	−	0.474100i
$708$	30.0541	+	2.15867i	1.12950	+	0.0811277i
$709$	−0.371843	−	15.1472i	−0.0139649	−	0.568865i	−0.965364	−	0.260906i	$-0.915979\pi$
$709$	−0.371843	−	15.1472i	−0.0139649	−	0.568865i	0.951399	−	0.307959i	$-0.0996461\pi$
$710$	−4.11510	+	1.65027i	−0.154437	+	0.0619334i
$711$	5.21322	+	7.02921i	0.195511	+	0.263616i
$712$	0.131991	−	14.0716i	0.00494659	−	0.527356i
$713$	12.5212	−	49.9874i	0.468922	−	1.87204i
$714$	13.6564	+	15.4143i	0.511079	+	0.576866i
$715$	−0.115893	+	0.418785i	−0.00433416	+	0.0156617i
$716$	−23.5701	−	4.64116i	−0.880857	−	0.173448i
$717$	9.37867	+	24.3133i	0.350253	+	0.907997i
$718$	1.17577	+	0.848122i	0.0438794	+	0.0316516i
$719$	−25.4052	+	13.5794i	−0.947456	+	0.506426i	−0.871343	−	0.490674i	$-0.836751\pi$
$719$	−25.4052	+	13.5794i	−0.947456	+	0.506426i	−0.0761123	+	0.997099i	$0.524251\pi$
$720$	0.607451	−	0.967504i	0.0226384	−	0.0360568i
$721$	11.1550	−	20.8695i	0.415434	−	0.777222i
$722$	−5.92490	−	2.03191i	−0.220502	−	0.0756200i
$723$	12.7470	+	20.1297i	0.474066	+	0.748632i
$724$	−27.4515	+	24.9771i	−1.02023	+	0.928268i
$725$	31.5031	+	15.8573i	1.16999	+	0.588925i
$726$	−21.8787	−	20.2850i	−0.811994	−	0.752847i
$727$	6.65609	+	7.34387i	0.246861	+	0.272369i	0.851759	−	0.523934i	$-0.175536\pi$
$727$	6.65609	+	7.34387i	0.246861	+	0.272369i	−0.604898	+	0.796303i	$0.706786\pi$
$728$	20.3205	+	32.7655i	0.753127	+	1.21437i
$729$	6.11538	−	17.0913i	0.226496	−	0.633013i
$730$	−3.72774	+	6.78834i	−0.137970	+	0.251248i
$731$	21.1640	−	4.75254i	0.782780	−	0.175779i
$732$	27.9903	+	29.2859i	1.03455	+	1.08244i
$733$	−31.6979	+	24.7373i	−1.17079	+	0.913692i	−0.997464	−	0.0711734i	$-0.977326\pi$
$733$	−31.6979	+	24.7373i	−1.17079	+	0.913692i	−0.173324	+	0.984865i	$0.555451\pi$
$734$	19.0130	+	18.5162i	0.701783	+	0.683447i
$735$	−0.373813	+	1.87929i	−0.0137883	+	0.0693185i
$736$	24.8121	+	19.6628i	0.914586	+	0.724780i
$737$	−0.136396	−	0.685709i	−0.00502421	−	0.0252584i
$738$	4.78997	−	7.37826i	0.176321	−	0.271598i
$739$	8.45101	+	30.5380i	0.310875	+	1.12336i	0.938624	+	0.344943i	$0.112102\pi$
$739$	8.45101	+	30.5380i	0.310875	+	1.12336i	−0.627749	+	0.778416i	$0.716023\pi$
$740$	0.0809629	+	1.06948i	0.00297625	+	0.0393147i
$741$	−34.1770	−	48.5276i	−1.25552	−	1.78270i
$742$	−2.80499	−	32.2093i	−0.102974	−	1.18244i
$743$	−13.0589	+	14.4083i	−0.479084	+	0.528588i	−0.931754	−	0.363090i	$-0.881722\pi$
$743$	−13.0589	+	14.4083i	−0.479084	+	0.528588i	0.452670	+	0.891678i	$0.350472\pi$
$744$	27.1857	−	42.0530i	0.996676	−	1.54174i
$745$	−3.09277	−	1.46277i	−0.113310	−	0.0535918i
$746$	11.7895	−	2.81183i	0.431644	−	0.102948i
$747$	−0.392402	+	0.338489i	−0.0143573	+	0.0123847i
$748$	−1.01174	−	0.603765i	−0.0369929	−	0.0220758i
$749$	1.42684	−	2.02595i	0.0521355	−	0.0740267i
$750$	−9.47134	−	5.50783i	−0.345844	−	0.201118i
$751$	−13.4444	+	11.0335i	−0.490592	+	0.402619i	−0.846902	−	0.531749i	$-0.821535\pi$
$751$	−13.4444	+	11.0335i	−0.490592	+	0.402619i	0.356310	+	0.934368i	$0.384035\pi$
$752$	23.6725	+	1.07146i	0.863246	+	0.0390723i
$753$	−22.0849	+	26.9105i	−0.804818	+	0.980674i
$754$	−59.8785	−	27.3566i	−2.18065	−	0.996268i
$755$	−9.09328	−	0.223228i	−0.330938	−	0.00812408i
$756$	18.1038	−	5.52987i	0.658429	−	0.201119i
$757$	−45.3406	+	5.59223i	−1.64793	+	0.203253i	−0.892204	−	0.451633i	$-0.850842\pi$
$757$	−45.3406	+	5.59223i	−1.64793	+	0.203253i	−0.755728	+	0.654886i	$0.772717\pi$
$758$	−9.99825	+	38.0829i	−0.363153	+	1.38323i
$759$	1.06568	−	1.43690i	0.0386817	−	0.0521562i
$760$	5.55739	−	0.771160i	0.201588	−	0.0279729i
$761$	40.7991	+	24.4541i	1.47897	+	0.886459i	0.999963	+	0.00864673i	$0.00275237\pi$
$761$	40.7991	+	24.4541i	1.47897	+	0.886459i	0.479005	+	0.877812i	$0.340998\pi$
$762$	−56.7608	−	11.9592i	−2.05623	−	0.433236i
$763$	9.66144	+	3.72683i	0.349768	+	0.134920i
$764$	15.7999	+	2.71017i	0.571619	+	0.0980504i
$765$	0.960919	+	0.317445i	0.0347421	+	0.0114772i
$766$	−20.7107	+	2.31699i	−0.748309	+	0.0837163i
$767$			49.9726i			1.80441i
$768$	16.6585	+	25.8631i	0.601110	+	0.933254i
$769$		−	37.1599i		−	1.34002i	−0.742352	−	0.670011i	$-0.766290\pi$
$769$		−	37.1599i		−	1.34002i	0.742352	−	0.670011i	$-0.233710\pi$
$770$	0.0228968	+	0.204666i	0.000825144	+	0.00737566i
$771$	−2.45572	−	0.811262i	−0.0884408	−	0.0292169i
$772$	−21.9651	+	15.5330i	−0.790541	+	0.559045i
$773$	−33.8113	−	13.0425i	−1.21611	−	0.469104i	−0.335089	−	0.942186i	$-0.608766\pi$
$773$	−33.8113	−	13.0425i	−1.21611	−	0.469104i	−0.881018	+	0.473082i	$0.843141\pi$
$774$	−1.24383	+	5.90346i	−0.0447085	+	0.212196i
$775$	−38.1628	−	22.8739i	−1.37085	−	0.821654i
$776$	−7.25474	−	12.3654i	−0.260430	−	0.443891i
$777$	3.20343	−	4.31932i	0.114922	−	0.154955i
$778$	14.0650	+	3.69260i	0.504253	+	0.132386i
$779$	42.8785	−	5.28856i	1.53628	−	0.189482i
$780$	8.87308	+	4.72079i	0.317707	+	0.169031i
$781$	−1.27143	−	0.0312119i	−0.0454953	−	0.00111685i
$782$	−11.6542	+	25.5088i	−0.416752	+	0.912193i
$783$	−20.5046	+	24.9850i	−0.732776	+	0.892890i
$784$	−7.83493	−	5.76408i	−0.279819	−	0.205860i
$785$	4.11715	−	3.37886i	0.146947	−	0.120597i
$786$	0.743476	−	1.27849i	0.0265189	−	0.0456022i
$787$	6.73295	−	9.56005i	0.240004	−	0.340779i	−0.679631	−	0.733554i	$-0.737860\pi$
$787$	6.73295	−	9.56005i	0.240004	−	0.340779i	0.919634	+	0.392775i	$0.128485\pi$
$788$	−3.76194	+	0.950029i	−0.134013	+	0.0338434i
$789$	39.0301	−	33.6676i	1.38951	−	1.19860i
$790$	−1.68849	−	7.07953i	−0.0600737	−	0.251878i
$791$	32.2825	+	15.2685i	1.14783	+	0.542885i
$792$	0.269680	−	0.186171i	0.00958266	−	0.00661529i
$793$	−45.1197	+	49.7819i	−1.60225	+	1.76781i
$794$	−24.4885	+	2.13261i	−0.869066	+	0.0756836i
$795$	−4.85307	−	6.89083i	−0.172121	−	0.244393i
$796$	6.91403	−	8.04660i	0.245061	−	0.285204i
$797$	12.0514	+	43.5480i	0.426881	+	1.54255i	0.791367	+	0.611342i	$0.209370\pi$
$797$	12.0514	+	43.5480i	0.426881	+	1.54255i	−0.364485	+	0.931209i	$0.618755\pi$
$798$	−23.5950	−	15.3179i	−0.835255	−	0.542248i
$799$	4.09531	+	20.5885i	0.144882	+	0.728369i
$800$	22.4647	−	15.5723i	0.794247	−	0.550564i
$801$	−0.676425	+	3.40062i	−0.0239003	+	0.120155i
$802$	−4.57490	+	4.69764i	−0.161545	+	0.165880i
$803$	−1.75134	+	1.36676i	−0.0618036	+	0.0482320i
$804$	−16.1673	−	0.365696i	−0.570178	−	0.0128971i
$805$	4.78300	−	1.07406i	0.168579	−	0.0378556i
$806$	72.7951	+	39.9746i	2.56410	+	1.40805i
$807$	13.4336	−	37.5443i	0.472884	−	1.32162i
$808$	17.8923	+	12.8540i	0.629450	+	0.452201i
$809$	−11.4399	−	12.6220i	−0.402205	−	0.443765i	0.505847	−	0.862623i	$-0.331180\pi$
$809$	−11.4399	−	12.6220i	−0.402205	−	0.443765i	−0.908051	+	0.418859i	$0.862430\pi$
$810$	4.17886	−	4.50717i	0.146830	−	0.158366i
$811$	47.8482	+	24.0848i	1.68018	+	0.845730i	0.992848	+	0.119385i	$0.0380922\pi$
$811$	47.8482	+	24.0848i	1.68018	+	0.845730i	0.687330	+	0.726346i	$0.258783\pi$
$812$	−31.1663	−	1.47087i	−1.09372	−	0.0516174i
$813$	−12.3960	−	19.5754i	−0.434747	−	0.686540i
$814$	−0.0998047	+	0.291023i	−0.00349815	+	0.0102003i
$815$	2.02713	−	3.79249i	0.0710071	−	0.132845i
$816$	−18.7152	+	19.8096i	−0.655165	+	0.693476i
$817$	−26.1316	+	13.9676i	−0.914227	+	0.488665i
$818$	15.4128	−	21.3671i	0.538895	−	0.747083i
$819$	−3.41884	−	8.86301i	−0.119464	−	0.309698i
$820$	−6.07500	+	4.07615i	−0.212148	+	0.142345i
$821$	0.290979	−	1.05146i	0.0101552	−	0.0366963i	−0.958524	−	0.285013i	$-0.908002\pi$
$821$	0.290979	−	1.05146i	0.0101552	−	0.0366963i	0.968679	+	0.248316i	$0.0798772\pi$
$822$	−32.4522	+	28.7513i	−1.13190	+	1.00282i
$823$	2.95482	−	11.7963i	0.102999	−	0.411194i	−0.896494	−	0.443057i	$-0.853894\pi$
$823$	2.95482	−	11.7963i	0.102999	−	0.411194i	0.999492	+	0.0318629i	$0.0101440\pi$
$824$	28.8175	+	12.2545i	1.00391	+	0.426907i
$825$	−0.920114	−	1.24063i	−0.0320343	−	0.0431932i
$826$	8.81567	+	21.9827i	0.306736	+	0.764877i
$827$	−0.866264	−	35.2877i	−0.0301230	−	1.22707i	−0.804346	−	0.594161i	$-0.797484\pi$
$827$	−0.866264	−	35.2877i	−0.0301230	−	1.22707i	0.774223	−	0.632913i	$-0.218141\pi$
$828$	−5.10633	−	5.89663i	−0.177457	−	0.204922i
$829$	−7.43652	+	8.62100i	−0.258281	+	0.299420i	−0.871402	−	0.490569i	$-0.836789\pi$
$829$	−7.43652	+	8.62100i	−0.258281	+	0.299420i	0.613121	+	0.789989i	$0.289914\pi$
$830$	0.410728	−	0.130554i	0.0142566	−	0.00453160i
$831$	6.31867	+	15.2546i	0.219192	+	0.529177i
$832$	−40.8040	+	30.6298i	−1.41463	+	1.06190i
$833$	3.29741	−	7.96066i	0.114249	−	0.275821i
$834$	0.963773	−	11.3194i	0.0333727	−	0.391957i
$835$	−0.00491138	−	0.0665819i	−0.000169965	−	0.00230416i
$836$	1.55196	+	0.426264i	0.0536755	+	0.0147427i
$837$	28.1158	−	29.5310i	0.971825	−	1.02074i
$838$	4.80952	+	4.91954i	0.166142	+	0.169943i
$839$	15.8353	+	2.34894i	0.546694	+	0.0810944i	0.414364	−	0.910111i	$-0.364004\pi$
$839$	15.8353	+	2.34894i	0.546694	+	0.0810944i	0.132330	+	0.991206i	$0.457754\pi$
$840$	4.73602	+	0.511354i	0.163408	+	0.0176434i
$841$	20.8211	−	12.4797i	0.717970	−	0.430335i
$842$	21.4188	−	7.39164i	0.738139	−	0.254733i
$843$	−26.9478	−	47.5694i	−0.928130	−	1.63838i
$844$	2.49744	−	2.50708i	0.0859653	−	0.0862974i
$845$	−4.59600	+	10.3684i	−0.158107	+	0.356684i
$846$	−5.68190	−	1.34358i	−0.195348	−	0.0461932i
$847$	6.80771	−	22.4420i	0.233916	−	0.771117i
$848$	42.1265	−	7.47709i	1.44663	−	0.256764i
$849$	−20.3362	+	6.16892i	−0.697936	+	0.211717i
$850$	18.1552	+	16.0224i	0.622717	+	0.549562i
$851$	7.14538	+	1.60455i	0.244941	+	0.0550033i
$852$	−7.09285	+	28.5497i	−0.242997	+	0.978096i
$853$	5.64071	+	17.0747i	0.193134	+	0.584626i	0.999981	−	0.00613474i	$-0.00195276\pi$
$853$	5.64071	+	17.0747i	0.193134	+	0.584626i	−0.806847	+	0.590761i	$0.798828\pi$
$854$	−11.0659	+	29.8584i	−0.378668	+	1.02173i
$855$	−1.38073	−	0.0678310i	−0.0472201	−	0.00231977i
$856$	2.83788	+	1.64299i	0.0969967	+	0.0561562i
$857$	16.4910	−	7.79968i	0.563323	−	0.266432i	−0.124610	−	0.992206i	$-0.539768\pi$
$857$	16.4910	−	7.79968i	0.563323	−	0.266432i	0.687933	+	0.725774i	$0.258518\pi$
$858$	1.80369	+	2.24920i	0.0615771	+	0.0767863i
$859$	−1.94760	+	3.07560i	−0.0664513	+	0.104938i	−0.876448	−	0.481496i	$-0.840094\pi$
$859$	−1.94760	+	3.07560i	−0.0664513	+	0.104938i	0.809997	+	0.586434i	$0.199469\pi$
$860$	2.88114	−	4.10770i	0.0982460	−	0.140072i
$861$	36.4047	+	4.49010i	1.24067	+	0.153022i
$862$	21.0184	+	8.38195i	0.715891	+	0.285490i
$863$	0.885284	+	1.32492i	0.0301354	+	0.0451008i	0.846231	−	0.532815i	$-0.178866\pi$
$863$	0.885284	+	1.32492i	0.0301354	+	0.0451008i	−0.816096	+	0.577916i	$0.803866\pi$
$864$	9.41350	+	23.2140i	0.320254	+	0.789755i
$865$	−1.23199	+	1.84381i	−0.0418890	+	0.0626913i
$866$	13.0680	−	8.98418i	0.444068	−	0.305295i
$867$	7.43479	+	4.21176i	0.252499	+	0.143039i
$868$	39.0742	+	4.74287i	1.32626	+	0.160984i
$869$	0.356925	−	2.05701i	0.0121079	−	0.0697793i
$870$	−7.21611	+	3.75281i	−0.244649	+	0.127232i
$871$	−1.31600	−	26.7878i	−0.0445910	−	0.907671i
$872$	−3.77861	+	13.1722i	−0.127960	+	0.446068i
$873$	1.19001	+	3.32585i	0.0402757	+	0.112563i
$874$	6.04934	−	37.8291i	0.204622	−	1.27959i
$875$	0.633548	−	8.58881i	0.0214178	−	0.290355i
$876$	22.0595	+	46.4092i	0.745322	+	1.56802i
$877$	49.9394	−	8.66530i	1.68633	−	0.292607i	0.754717	−	0.656050i	$-0.227774\pi$
$877$	49.9394	−	8.66530i	1.68633	−	0.292607i	0.931616	+	0.363444i	$0.118399\pi$
$878$	−15.4272	−	2.08012i	−0.520642	−	0.0702005i
$879$	0.0634765	−	0.644487i	0.00214101	−	0.0217380i
$880$	−0.267087	+	0.0541984i	−0.00900349	+	0.00182703i
$881$	31.4522	−	3.09777i	1.05965	−	0.104366i	0.446853	−	0.894607i	$-0.352545\pi$
$881$	31.4522	−	3.09777i	1.05965	−	0.104366i	0.612796	+	0.790241i	$0.290045\pi$
$882$	1.63280	+	1.75429i	0.0549794	+	0.0590700i
$883$	3.63746	−	3.46315i	0.122410	−	0.116544i	−0.625869	−	0.779928i	$-0.715255\pi$
$883$	3.63746	−	3.46315i	0.122410	−	0.116544i	0.748279	+	0.663384i	$0.230880\pi$
$884$	−34.9933	−	28.6055i	−1.17695	−	0.962107i
$885$	4.86741	+	3.79856i	0.163616	+	0.127687i
$886$	−41.4689	+	5.67288i	−1.39318	+	0.190584i
$887$	0.490058	+	3.30370i	0.0164545	+	0.110927i	0.995848	−	0.0910359i	$-0.0290178\pi$
$887$	0.490058	+	3.30370i	0.0164545	+	0.110927i	−0.979393	+	0.201963i	$0.935268\pi$
$888$	6.06929	+	3.71561i	0.203672	+	0.124688i
$889$	−11.0789	−	44.2293i	−0.371573	−	1.48340i
$890$	1.62901	−	2.37929i	0.0546044	−	0.0797541i
$891$	1.61184	−	0.714480i	0.0539987	−	0.0239360i
$892$	−3.09396	+	0.0819218i	−0.103593	+	0.00274294i
$893$	−12.8927	−	25.6133i	−0.431436	−	0.857117i
$894$	−19.8763	+	10.9648i	−0.664764	+	0.366717i
$895$	−3.48070	−	3.48070i	−0.116347	−	0.116347i
$896$	−12.5461	+	20.6721i	−0.419136	+	0.690607i
$897$	48.5266	−	48.5266i	1.62025	−	1.62025i
$898$	−5.56997	+	19.2766i	−0.185872	+	0.643269i
$899$	−60.0316	+	30.2173i	−2.00216	+	1.00780i
$900$	−6.15178	+	2.74110i	−0.205059	+	0.0913700i
$901$	15.3592	+	34.6497i	0.511688	+	1.15435i
$902$	−2.06273	+	0.386108i	−0.0686814	+	0.0128560i
$903$	−24.4028	+	6.11258i	−0.812074	+	0.203414i
$904$	−16.3372	+	44.3438i	−0.543369	+	1.47485i
$905$	−7.52264	+	1.11588i	−0.250061	+	0.0370930i
$906$	−36.4978	+	48.0659i	−1.21256	+	1.59688i
$907$	−0.890606	+	1.14121i	−0.0295721	+	0.0378931i	−0.802905	−	0.596107i	$-0.796713\pi$
$907$	−0.890606	+	1.14121i	−0.0295721	+	0.0378931i	0.773333	+	0.634000i	$0.218588\pi$
$908$	−9.19499	+	4.93764i	−0.305146	+	0.163861i
$909$	−3.74294	−	3.93133i	−0.124145	−	0.130394i
$910$	−0.283176	+	7.89519i	−0.00938719	+	0.261723i
$911$	−0.502136	−	5.09827i	−0.0166365	−	0.168913i	0.983276	−	0.182120i	$-0.0582960\pi$
$911$	−0.502136	−	5.09827i	−0.0166365	−	0.168913i	−0.999913	+	0.0132069i	$0.995796\pi$
$912$	17.4219	−	32.8985i	0.576896	−	1.08938i
$913$	0.123032	+	0.0121176i	0.00407177	+	0.000401035i
$914$	35.7706	−	27.2705i	1.18319	−	0.902028i
$915$	1.41915	+	8.17878i	0.0469158	+	0.270382i
$916$	3.05574	−	3.38459i	0.100965	−	0.111830i
$917$	1.15936	+	0.0855196i	0.0382855	+	0.00282411i
$918$	−17.9721	+	13.0166i	−0.593167	+	0.429612i
$919$	28.2483	−	10.1074i	0.931824	−	0.333412i	0.173160	−	0.984894i	$-0.444602\pi$
$919$	28.2483	−	10.1074i	0.931824	−	0.333412i	0.758664	+	0.651482i	$0.225852\pi$
$920$	1.97702	+	6.17851i	0.0651805	+	0.203699i
$921$	−31.3697	+	1.54110i	−1.03367	+	0.0507808i
$922$	3.21353	−	10.1778i	0.105832	−	0.335189i
$923$	−48.0703	−	8.34099i	−1.58225	−	0.274547i
$924$	1.19022	+	0.671222i	0.0391553	+	0.0220816i
$925$	3.11660	−	5.50156i	0.102473	−	0.180890i
$926$	−23.0993	−	4.27771i	−0.759090	−	0.140574i
$927$	−6.41532	−	4.28658i	−0.210707	−	0.140790i
$928$	−1.71861	−	41.2533i	−0.0564161	−	1.35421i
$929$	0.207636	−	0.138738i	0.00681233	−	0.00455185i	−0.552159	−	0.833739i	$-0.686196\pi$
$929$	0.207636	−	0.138738i	0.00681233	−	0.00455185i	0.558972	+	0.829187i	$0.311196\pi$
$930$	9.42695	−	4.05177i	0.309122	−	0.132863i
$931$	−1.44081	+	11.6818i	−0.0472207	+	0.382855i
$932$	5.46127	−	24.5414i	0.178890	−	0.803881i
$933$	41.4943	+	26.2760i	1.35846	+	0.860238i
$934$	1.96829	−	17.9062i	0.0644045	−	0.585910i
$935$	−0.103221	−	0.218243i	−0.00337570	−	0.00713732i
$936$	11.2813	−	5.54650i	0.368740	−	0.181293i
$937$	0.525556	−	10.6979i	0.0171692	−	0.349486i	−0.974806	−	0.223054i	$-0.928397\pi$
$937$	0.525556	−	10.6979i	0.0171692	−	0.349486i	0.991975	−	0.126432i	$-0.0403526\pi$
$938$	−5.30454	−	11.5517i	−0.173199	−	0.377176i
$939$	−45.8651	+	15.1518i	−1.49675	+	0.494460i
$940$	3.90567	+	2.88498i	0.127389	+	0.0940978i
$941$	5.17111	−	23.0280i	0.168573	−	0.750691i	−0.816330	−	0.577586i	$-0.803995\pi$
$941$	5.17111	−	23.0280i	0.168573	−	0.750691i	0.984903	−	0.173105i	$-0.0553801\pi$
$942$	−2.20102	−	35.2704i	−0.0717131	−	1.14917i
$943$	14.5004	+	47.8015i	0.472199	+	1.55663i
$944$	−27.9413	+	14.1998i	−0.909410	+	0.462163i
$945$	3.71180	+	1.12596i	0.120745	+	0.0366276i
$946$	1.22459	−	0.756199i	0.0398148	−	0.0245862i
$947$	−3.79175	−	1.68077i	−0.123215	−	0.0546175i	0.342713	−	0.939440i	$-0.388654\pi$
$947$	−3.79175	−	1.68077i	−0.123215	−	0.0546175i	−0.465928	+	0.884823i	$0.654279\pi$
$948$	−44.6501	−	18.3939i	−1.45017	−	0.597406i
$949$	−74.1501	+	42.0055i	−2.40702	+	1.36356i
$950$	−29.7393	−	14.4794i	−0.964869	−	0.469773i
$951$	21.2411	+	35.4387i	0.688791	+	1.14918i
$952$	−20.4397	−	6.41027i	−0.662453	−	0.207758i
$953$	5.46551	−	36.8454i	0.177045	−	1.19354i	−0.700360	−	0.713790i	$-0.746977\pi$
$953$	5.46551	−	36.8454i	0.177045	−	1.19354i	0.877405	−	0.479751i	$-0.159273\pi$
$954$	−10.5410	−	0.119201i	−0.341279	−	0.00385927i
$955$	2.37902	+	2.26501i	0.0769831	+	0.0732940i
$956$	−21.4016	−	16.6357i	−0.692178	−	0.538037i
$957$	−2.32683	+	0.171638i	−0.0752159	+	0.00554826i
$958$	−31.4552	+	26.5190i	−1.01627	+	0.856791i
$959$	−31.4856	−	13.0418i	−1.01672	−	0.421141i
$960$	−0.118247	+	6.30263i	−0.00381642	+	0.203417i
$961$	49.6905	−	20.5825i	1.60292	−	0.663951i
$962$	−5.42532	+	10.4814i	−0.174919	+	0.337935i
$963$	−0.611787	−	0.527731i	−0.0197146	−	0.0170059i
$964$	−22.1589	−	11.1004i	−0.713691	−	0.357519i
$965$	−5.51087	+	0.135284i	−0.177401	+	0.00435495i
$966$	12.7860	−	29.9072i	0.411384	−	0.962247i
$967$	17.1767	−	12.7391i	0.552365	−	0.409662i	−0.283194	−	0.959063i	$-0.591394\pi$
$967$	17.1767	−	12.7391i	0.552365	−	0.409662i	0.835559	+	0.549401i	$0.185144\pi$
$968$	30.3801	+	6.33977i	0.976453	+	0.203768i
$969$	31.9893	+	8.01290i	1.02764	+	0.257412i
$970$	0.177312	−	2.93230i	0.00569316	−	0.0941505i
$971$	−43.9837	−	12.1719i	−1.41151	−	0.390616i	−0.524120	−	0.851645i	$-0.675606\pi$
$971$	−43.9837	−	12.1719i	−1.41151	−	0.390616i	−0.887385	+	0.461028i	$0.847481\pi$
$972$	−2.79943	−	13.9332i	−0.0897916	−	0.446908i
$973$	8.33130	−	3.21374i	0.267089	−	0.103028i
$974$	42.9352	−	6.95080i	1.37573	−	0.222718i
$975$	−27.9316	−	52.2564i	−0.894528	−	1.67354i
$976$	−40.6554	−	11.0823i	−1.30135	−	0.354734i
$977$	−26.2567	−	14.0345i	−0.840026	−	0.449003i	−0.00550827	−	0.999985i	$-0.501753\pi$
$977$	−26.2567	−	14.0345i	−0.840026	−	0.449003i	−0.834517	+	0.550982i	$0.814253\pi$
$978$	−12.5395	−	25.6292i	−0.400968	−	0.819533i
$979$	0.698819	−	0.442522i	0.0223343	−	0.0141431i
$980$	−0.675074	−	1.87530i	−0.0215645	−	0.0599042i
$981$	1.51806	−	3.01587i	0.0484680	−	0.0962894i
$982$	16.1361	−	0.609904i	0.514923	−	0.0194628i
$983$	19.9770	−	18.1061i	0.637166	−	0.577494i	−0.287731	−	0.957711i	$-0.592901\pi$
$983$	19.9770	−	18.1061i	0.637166	−	0.577494i	0.924897	+	0.380218i	$0.124151\pi$
$984$	−1.64634	+	48.5126i	−0.0524835	+	1.54652i
$985$	−0.748578	−	0.267845i	−0.0238517	−	0.00853427i
$986$	35.1191	−	10.2211i	1.11842	−	0.325505i
$987$	−5.33419	−	23.7542i	−0.169789	−	0.756105i
$988$	56.4915	+	24.9108i	1.79723	+	0.792517i
$989$	−21.0772	−	27.0079i	−0.670216	−	0.858802i
$990$	0.0671425		0.000888743i	0.00213393		2.82461e-5i
$991$	11.0027	+	2.18858i	0.349513	+	0.0695225i	0.366725	−	0.930329i	$-0.380479\pi$
$991$	11.0027	+	2.18858i	0.349513	+	0.0695225i	−0.0172120	+	0.999852i	$0.505479\pi$
$992$	−1.66627	+	52.0608i	−0.0529041	+	1.65293i
$993$	43.3729	−	8.62740i	1.37640	−	0.273782i
$994$	−22.6173	+	4.81091i	−0.717378	+	0.152593i
$995$	2.09513	−	0.579801i	0.0664202	−	0.0183809i
$996$	0.891754	−	2.71695i	0.0282563	−	0.0860900i
$997$	40.1553	−	28.2805i	1.27173	−	0.895654i	0.273918	−	0.961753i	$-0.411680\pi$
$997$	40.1553	−	28.2805i	1.27173	−	0.895654i	0.997813	+	0.0660991i	$0.0210554\pi$
$998$	−35.8392	−	30.0971i	−1.13447	−	0.952706i
$999$	4.29353	+	3.89143i	0.135841	+	0.123119i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.o.a.141.19	yes	4032
512.69	even	128	inner	512.2.o.a.69.19	✓	4032

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
512.2.o.a.69.19	✓	4032	512.69	even	128	inner
512.2.o.a.141.19	yes	4032	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.o (of order \(128\), degree \(64\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.882620 + 1.10498i) q^{2} +(-0.603125 + 1.82569i) q^{3} +(-0.441964 - 1.95056i) q^{4} +(0.147491 - 0.382356i) q^{5} +(-1.48502 - 2.27783i) q^{6} +(1.09882 - 1.83327i) q^{7} +(2.54541 + 1.23324i) q^{8} +(-0.559749 - 0.415138i) q^{9} +O(q^{10})\)	\(q+(-0.882620 + 1.10498i) q^{2} +(-0.603125 + 1.82569i) q^{3} +(-0.441964 - 1.95056i) q^{4} +(0.147491 - 0.382356i) q^{5} +(-1.48502 - 2.27783i) q^{6} +(1.09882 - 1.83327i) q^{7} +(2.54541 + 1.23324i) q^{8} +(-0.559749 - 0.415138i) q^{9} +(0.292318 + 0.500450i) q^{10} +(0.0203509 + 0.165001i) q^{11} +(3.82766 + 0.369542i) q^{12} +(-0.156515 + 6.37572i) q^{13} +(1.05589 + 2.83226i) q^{14} +(0.609107 + 0.499881i) q^{15} +(-3.60934 + 1.72415i) q^{16} +(-2.24793 - 2.73910i) q^{17} +(0.952765 - 0.252103i) q^{18} +(3.95740 + 2.78712i) q^{19} +(-0.810993 - 0.118702i) q^{20} +(2.68425 + 3.11180i) q^{21} +(-0.200285 - 0.123146i) q^{22} +(-2.39281 + 5.05917i) q^{23} +(-3.78671 + 3.90333i) q^{24} +(3.58031 + 3.24501i) q^{25} +(-6.90690 - 5.80028i) q^{26} +(-3.62047 + 2.54983i) q^{27} +(-4.06154 - 1.33307i) q^{28} +(7.03456 - 1.94672i) q^{29} +(-1.08997 + 0.231846i) q^{30} +(-9.03093 + 1.79636i) q^{31} +(1.28052 - 5.51002i) q^{32} +(-0.313514 - 0.0623618i) q^{33} +(5.01072 - 0.0663252i) q^{34} +(-0.538897 - 0.690533i) q^{35} +(-0.562361 + 1.27530i) q^{36} +(-0.286706 - 1.27676i) q^{37} +(-6.57259 + 1.91289i) q^{38} +(-11.5457 - 4.13110i) q^{39} +(0.846962 - 0.791363i) q^{40} +(6.61349 - 5.99411i) q^{41} +(-5.80765 + 0.219515i) q^{42} +(-2.75230 + 5.46787i) q^{43} +(0.312849 - 0.112620i) q^{44} +(-0.241289 + 0.152794i) q^{45} +(-3.47835 - 7.10934i) q^{46} +(-5.22465 - 2.79264i) q^{47} +(-0.970879 - 7.62940i) q^{48} +(1.14630 + 2.14457i) q^{49} +(-6.74572 + 1.09207i) q^{50} +(6.35653 - 2.45198i) q^{51} +(12.5054 - 2.51255i) q^{52} +(-10.3088 - 2.85282i) q^{53} +(0.377995 - 6.25108i) q^{54} +(0.0660907 + 0.0165549i) q^{55} +(5.05781 - 3.31133i) q^{56} +(-7.47521 + 5.54400i) q^{57} +(-4.05775 + 9.49127i) q^{58} +(7.83324 - 0.192295i) q^{59} +(0.705843 - 1.40903i) q^{60} +(7.97696 + 6.88097i) q^{61} +(5.98593 - 11.5645i) q^{62} +(-1.37613 + 0.570010i) q^{63} +(4.95825 + 6.27820i) q^{64} +(2.41471 + 1.00021i) q^{65} +(0.345622 - 0.291385i) q^{66} +(-4.19395 + 0.309364i) q^{67} +(-4.34927 + 5.59529i) q^{68} +(-7.79330 - 7.41984i) q^{69} +(1.23867 + 0.0140072i) q^{70} +(-1.12248 + 7.56715i) q^{71} +(-0.912828 - 1.74700i) q^{72} +(6.86973 + 11.4614i) q^{73} +(1.66385 + 0.810089i) q^{74} +(-8.08374 + 4.57938i) q^{75} +(3.68740 - 8.95094i) q^{76} +(0.324854 + 0.143998i) q^{77} +(14.7552 - 9.11154i) q^{78} +(-12.0170 - 3.64533i) q^{79} +(0.126895 + 1.63435i) q^{80} +(-3.07847 - 10.1484i) q^{81} +(0.786185 + 12.5983i) q^{82} +(0.162928 - 0.725550i) q^{83} +(4.88339 - 6.61109i) q^{84} +(-1.37886 + 0.455515i) q^{85} +(-3.61266 - 7.86729i) q^{86} +(-0.688612 + 14.0170i) q^{87} +(-0.151684 + 0.445093i) q^{88} +(-2.12721 - 4.49761i) q^{89} +(0.0441314 - 0.401479i) q^{90} +(11.5164 + 7.29271i) q^{91} +(10.9257 + 2.43134i) q^{92} +(2.16719 - 17.5711i) q^{93} +(7.69719 - 3.30831i) q^{94} +(1.64935 - 1.10206i) q^{95} +(9.28725 + 5.66105i) q^{96} +(-4.21447 - 2.81602i) q^{97} +(-3.38145 - 0.626205i) q^{98} +(0.0571068 - 0.100808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9}+O(q^{10}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9	\( 4032 q - 64 q^{2} - 64 q^{3} - 64 q^{4} - 64 q^{5} - 64 q^{6} - 64 q^{7} - 64 q^{8} - 64 q^{9} - 64 q^{10} - 64 q^{11} - 64 q^{12} - 64 q^{13} - 64 q^{14} - 64 q^{15} - 64 q^{16} - 64 q^{17} - 64 q^{18} - 64 q^{19} - 64 q^{20} - 64 q^{21} - 64 q^{22} - 64 q^{23} - 64 q^{24} - 64 q^{25} - 64 q^{26} - 64 q^{27} - 64 q^{28} - 64 q^{29} - 64 q^{30} - 64 q^{31} - 64 q^{32} - 64 q^{33} - 64 q^{34} - 64 q^{35} - 64 q^{36} - 64 q^{37} - 64 q^{38} - 64 q^{39} - 64 q^{40} - 64 q^{41} - 64 q^{42} - 64 q^{43} - 64 q^{44} - 64 q^{45} - 64 q^{46} - 64 q^{47} - 64 q^{48} - 64 q^{49} - 64 q^{50} - 64 q^{51} - 64 q^{52} - 64 q^{53} - 64 q^{54} - 64 q^{55} - 64 q^{56} - 64 q^{57} - 64 q^{58} - 64 q^{59} - 64 q^{60} - 64 q^{61} - 64 q^{62} - 64 q^{63} - 64 q^{64} - 64 q^{65} - 64 q^{66} - 64 q^{67} - 64 q^{68} - 64 q^{69} - 64 q^{70} - 64 q^{71} - 64 q^{72} - 64 q^{73} - 64 q^{74} - 64 q^{75} - 64 q^{76} - 64 q^{77} - 64 q^{78} - 64 q^{79} - 64 q^{80} - 64 q^{81} - 64 q^{82} - 64 q^{83} - 64 q^{84} - 64 q^{85} - 64 q^{86} - 64 q^{87} - 64 q^{88} - 64 q^{89} - 64 q^{90} - 64 q^{91} - 64 q^{92} - 64 q^{93} - 64 q^{94} - 64 q^{95} - 64 q^{96} - 64 q^{97} - 64 q^{98} - 64 q^{99}+O(q^{100}) \) 4032 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - 64 * q^5 - 64 * q^6 - 64 * q^7 - 64 * q^8 - 64 * q^9 - 64 * q^10 - 64 * q^11 - 64 * q^12 - 64 * q^13 - 64 * q^14 - 64 * q^15 - 64 * q^16 - 64 * q^17 - 64 * q^18 - 64 * q^19 - 64 * q^20 - 64 * q^21 - 64 * q^22 - 64 * q^23 - 64 * q^24 - 64 * q^25 - 64 * q^26 - 64 * q^27 - 64 * q^28 - 64 * q^29 - 64 * q^30 - 64 * q^31 - 64 * q^32 - 64 * q^33 - 64 * q^34 - 64 * q^35 - 64 * q^36 - 64 * q^37 - 64 * q^38 - 64 * q^39 - 64 * q^40 - 64 * q^41 - 64 * q^42 - 64 * q^43 - 64 * q^44 - 64 * q^45 - 64 * q^46 - 64 * q^47 - 64 * q^48 - 64 * q^49 - 64 * q^50 - 64 * q^51 - 64 * q^52 - 64 * q^53 - 64 * q^54 - 64 * q^55 - 64 * q^56 - 64 * q^57 - 64 * q^58 - 64 * q^59 - 64 * q^60 - 64 * q^61 - 64 * q^62 - 64 * q^63 - 64 * q^64 - 64 * q^65 - 64 * q^66 - 64 * q^67 - 64 * q^68 - 64 * q^69 - 64 * q^70 - 64 * q^71 - 64 * q^72 - 64 * q^73 - 64 * q^74 - 64 * q^75 - 64 * q^76 - 64 * q^77 - 64 * q^78 - 64 * q^79 - 64 * q^80 - 64 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^84 - 64 * q^85 - 64 * q^86 - 64 * q^87 - 64 * q^88 - 64 * q^89 - 64 * q^90 - 64 * q^91 - 64 * q^92 - 64 * q^93 - 64 * q^94 - 64 * q^95 - 64 * q^96 - 64 * q^97 - 64 * q^98 - 64 * q^99

Introduction

L-functions

Modular forms

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