LMFDB - Embedded newform 430.2.q.b.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			31.1
Character	$\chi$	$=$	430.31
Dual form			430.2.q.b.111.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.900969 + 0.433884i) q^{2} +(-2.80831 + 1.91467i) q^{3} +(0.623490 - 0.781831i) q^{4} +(0.733052 + 0.680173i) q^{5} +(1.69945 - 2.94354i) q^{6} +(-0.338333 - 0.586011i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(3.12461 - 7.96138i) q^{9} +O(q^{10})$	\(q+(-0.900969 + 0.433884i) q^{2} +(-2.80831 + 1.91467i) q^{3} +(0.623490 - 0.781831i) q^{4} +(0.733052 + 0.680173i) q^{5} +(1.69945 - 2.94354i) q^{6} +(-0.338333 - 0.586011i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(3.12461 - 7.96138i) q^{9} +(-0.955573 - 0.294755i) q^{10} +(-1.25703 - 1.57626i) q^{11} +(-0.254001 + 3.38941i) q^{12} +(-0.583592 + 0.180014i) q^{13} +(0.559088 + 0.381180i) q^{14} +(-3.36095 - 0.506581i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(3.67091 - 3.40610i) q^{17} +(0.639135 + 8.52867i) q^{18} +(-1.95629 - 4.98454i) q^{19} +(0.988831 - 0.149042i) q^{20} +(2.07216 + 0.997902i) q^{21} +(1.81646 + 0.874761i) q^{22} +(2.91247 - 0.438985i) q^{23} +(-1.24176 - 3.16396i) q^{24} +(0.0747301 + 0.997204i) q^{25} +(0.447693 - 0.415399i) q^{26} +(4.19958 + 18.3996i) q^{27} +(-0.669109 - 0.100852i) q^{28} +(5.01953 + 3.42225i) q^{29} +(3.24791 - 1.00185i) q^{30} +(-0.624541 + 8.33393i) q^{31} +(0.623490 + 0.781831i) q^{32} +(6.54816 + 2.01984i) q^{33} +(-1.82952 + 4.66154i) q^{34} +(0.150573 - 0.659701i) q^{35} +(-4.27629 - 7.40676i) q^{36} +(-2.67054 + 4.62552i) q^{37} +(3.92526 + 3.64211i) q^{38} +(1.29424 - 1.62293i) q^{39} +(-0.826239 + 0.563320i) q^{40} +(9.86045 - 4.74854i) q^{41} -2.29993 q^{42} +(0.970879 - 6.48517i) q^{43} -2.01612 q^{44} +(7.70561 - 3.71083i) q^{45} +(-2.43358 + 1.65919i) q^{46} +(2.84652 - 3.56942i) q^{47} +(2.49158 + 2.31185i) q^{48} +(3.27106 - 5.66564i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-3.78747 + 16.5940i) q^{51} +(-0.223123 + 0.568508i) q^{52} +(-10.6271 - 3.27803i) q^{53} +(-11.7670 - 14.7553i) q^{54} +(0.150665 - 2.01048i) q^{55} +(0.646605 - 0.199451i) q^{56} +(15.0376 + 10.2525i) q^{57} +(-6.00730 - 0.905454i) q^{58} +(0.0146924 + 0.0643718i) q^{59} +(-2.49158 + 2.31185i) q^{60} +(0.0334112 + 0.445842i) q^{61} +(-3.05326 - 7.77959i) q^{62} +(-5.72261 + 0.862545i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(-0.550244 - 0.264984i) q^{65} +(-6.77606 + 1.02133i) q^{66} +(-2.81570 - 7.17429i) q^{67} +(-0.374226 - 4.99370i) q^{68} +(-7.33861 + 6.80924i) q^{69} +(0.150573 + 0.659701i) q^{70} +(5.48679 + 0.827001i) q^{71} +(7.06648 + 4.81784i) q^{72} +(3.00442 - 0.926740i) q^{73} +(0.399140 - 5.32615i) q^{74} +(-2.11919 - 2.65737i) q^{75} +(-5.11679 - 1.57832i) q^{76} +(-0.498413 + 1.26994i) q^{77} +(-0.461909 + 2.02375i) q^{78} +(1.56744 + 2.71489i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-28.2144 - 26.1791i) q^{81} +(-6.82364 + 8.55658i) q^{82} +(3.50456 - 2.38937i) q^{83} +(2.07216 - 0.997902i) q^{84} +5.00770 q^{85} +(1.93908 + 6.26418i) q^{86} -20.6489 q^{87} +(1.81646 - 0.874761i) q^{88} +(5.96064 - 4.06390i) q^{89} +(-5.33245 + 6.68668i) q^{90} +(0.302939 + 0.281086i) q^{91} +(1.47268 - 2.55076i) q^{92} +(-14.2028 - 24.6000i) q^{93} +(-1.01591 + 4.45099i) q^{94} +(1.95629 - 4.98454i) q^{95} +(-3.24791 - 1.00185i) q^{96} +(2.56120 + 3.21165i) q^{97} +(-0.488893 + 6.52383i) q^{98} +(-16.4770 + 5.08247i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9}+O(q^{10}) $ 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9	\( 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9} - 4 q^{10} - 9 q^{11} - q^{12} - 11 q^{13} + 7 q^{14} - 6 q^{15} - 8 q^{16} - 11 q^{17} - 15 q^{18} + 31 q^{19} - 4 q^{20} + 4 q^{21} + 12 q^{22} + 4 q^{23} + 6 q^{24} + 4 q^{25} + 31 q^{26} + 44 q^{27} + 13 q^{29} + q^{30} - q^{31} - 8 q^{32} - 30 q^{33} - 25 q^{34} + 14 q^{35} - 36 q^{36} - 27 q^{37} - 4 q^{38} + 4 q^{39} - 4 q^{40} + 16 q^{41} + 4 q^{42} - 7 q^{43} - 30 q^{44} + 12 q^{45} - 52 q^{46} - 43 q^{47} - q^{48} - 23 q^{49} - 24 q^{50} - 7 q^{51} - 25 q^{52} + 73 q^{53} - 61 q^{54} + 27 q^{55} + 7 q^{56} + 136 q^{57} - 36 q^{58} + 58 q^{59} + q^{60} - 61 q^{61} + 27 q^{62} + 32 q^{63} - 8 q^{64} - q^{65} + 12 q^{66} + 39 q^{67} + 17 q^{68} - 34 q^{69} + 14 q^{70} + 60 q^{71} + 27 q^{72} + 3 q^{73} + 29 q^{74} - 12 q^{75} + 17 q^{76} - 27 q^{77} - 17 q^{78} - 2 q^{79} + 24 q^{80} - 165 q^{81} + 2 q^{82} + 74 q^{83} + 4 q^{84} - 8 q^{85} + 14 q^{86} + 88 q^{87} + 12 q^{88} + 23 q^{89} - 2 q^{90} - 39 q^{91} + 4 q^{92} - 46 q^{93} + 55 q^{94} - 31 q^{95} - q^{96} - 85 q^{97} + 33 q^{98} - 168 q^{99}+O(q^{100}) \) 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9 - 4 * q^10 - 9 * q^11 - q^12 - 11 * q^13 + 7 * q^14 - 6 * q^15 - 8 * q^16 - 11 * q^17 - 15 * q^18 + 31 * q^19 - 4 * q^20 + 4 * q^21 + 12 * q^22 + 4 * q^23 + 6 * q^24 + 4 * q^25 + 31 * q^26 + 44 * q^27 + 13 * q^29 + q^30 - q^31 - 8 * q^32 - 30 * q^33 - 25 * q^34 + 14 * q^35 - 36 * q^36 - 27 * q^37 - 4 * q^38 + 4 * q^39 - 4 * q^40 + 16 * q^41 + 4 * q^42 - 7 * q^43 - 30 * q^44 + 12 * q^45 - 52 * q^46 - 43 * q^47 - q^48 - 23 * q^49 - 24 * q^50 - 7 * q^51 - 25 * q^52 + 73 * q^53 - 61 * q^54 + 27 * q^55 + 7 * q^56 + 136 * q^57 - 36 * q^58 + 58 * q^59 + q^60 - 61 * q^61 + 27 * q^62 + 32 * q^63 - 8 * q^64 - q^65 + 12 * q^66 + 39 * q^67 + 17 * q^68 - 34 * q^69 + 14 * q^70 + 60 * q^71 + 27 * q^72 + 3 * q^73 + 29 * q^74 - 12 * q^75 + 17 * q^76 - 27 * q^77 - 17 * q^78 - 2 * q^79 + 24 * q^80 - 165 * q^81 + 2 * q^82 + 74 * q^83 + 4 * q^84 - 8 * q^85 + 14 * q^86 + 88 * q^87 + 12 * q^88 + 23 * q^89 - 2 * q^90 - 39 * q^91 + 4 * q^92 - 46 * q^93 + 55 * q^94 - 31 * q^95 - q^96 - 85 * q^97 + 33 * q^98 - 168 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{17}{21}\right)$

Coefficient data

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

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

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

$2$	−0.900969	+	0.433884i	−0.637081	+	0.306802i
$2$	−0.900969	+	0.433884i	−0.637081	+	0.306802i
$3$	−2.80831	+	1.91467i	−1.62138	+	1.10544i	−0.701917	+	0.712259i	$0.747672\pi$
$3$	−2.80831	+	1.91467i	−1.62138	+	1.10544i	−0.919462	+	0.393178i	$0.871375\pi$
$4$	0.623490	−	0.781831i	0.311745	−	0.390916i
$5$	0.733052	+	0.680173i	0.327831	+	0.304182i
$5$	0.733052	+	0.680173i	0.327831	+	0.304182i
$6$	1.69945	−	2.94354i	0.693799	−	1.20170i
$7$	−0.338333	−	0.586011i	−0.127878	−	0.221491i	0.794976	−	0.606641i	$-0.207483\pi$
$7$	−0.338333	−	0.586011i	−0.127878	−	0.221491i	−0.922854	+	0.385149i	$0.874150\pi$
$8$	−0.222521	+	0.974928i	−0.0786730	+	0.344689i
$9$	3.12461	−	7.96138i	1.04154	−	2.65379i
$10$	−0.955573	−	0.294755i	−0.302179	−	0.0932098i
$11$	−1.25703	−	1.57626i	−0.379008	−	0.475262i	0.555339	−	0.831624i	$-0.312588\pi$
$11$	−1.25703	−	1.57626i	−0.379008	−	0.475262i	−0.934348	+	0.356362i	$0.884017\pi$
$12$	−0.254001	+	3.38941i	−0.0733237	+	0.978437i
$13$	−0.583592	+	0.180014i	−0.161859	+	0.0499270i	−0.374626	−	0.927176i	$-0.622229\pi$
$13$	−0.583592	+	0.180014i	−0.161859	+	0.0499270i	0.212766	+	0.977103i	$0.431753\pi$
$14$	0.559088	+	0.381180i	0.149423	+	0.101875i
$15$	−3.36095	−	0.506581i	−0.867793	−	0.130799i
$16$	−0.222521	−	0.974928i	−0.0556302	−	0.243732i
$17$	3.67091	−	3.40610i	0.890325	−	0.826101i	−0.0952300	−	0.995455i	$-0.530359\pi$
$17$	3.67091	−	3.40610i	0.890325	−	0.826101i	0.985555	+	0.169354i	$0.0541682\pi$
$18$	0.639135	+	8.52867i	0.150646	+	2.01023i
$19$	−1.95629	−	4.98454i	−0.448803	−	1.14353i	−0.958983	−	0.283463i	$-0.908517\pi$
$19$	−1.95629	−	4.98454i	−0.448803	−	1.14353i	0.510180	−	0.860067i	$-0.329579\pi$
$20$	0.988831	−	0.149042i	0.221109	−	0.0333269i
$21$	2.07216	+	0.997902i	0.452183	+	0.217760i
$22$	1.81646	+	0.874761i	0.387270	+	0.186500i
$23$	2.91247	−	0.438985i	0.607292	−	0.0915346i	0.161805	−	0.986823i	$-0.448268\pi$
$23$	2.91247	−	0.438985i	0.607292	−	0.0915346i	0.445488	+	0.895288i	$0.353030\pi$
$24$	−1.24176	−	3.16396i	−0.253473	−	0.645840i
$25$	0.0747301	+	0.997204i	0.0149460	+	0.199441i
$26$	0.447693	−	0.415399i	0.0877998	−	0.0814664i
$27$	4.19958	+	18.3996i	0.808209	+	3.54100i
$28$	−0.669109	−	0.100852i	−0.126450	−	0.0190592i
$29$	5.01953	+	3.42225i	0.932102	+	0.635497i	0.931202	−	0.364503i	$-0.118761\pi$
$29$	5.01953	+	3.42225i	0.932102	+	0.635497i	0.000900212		1.00000i	$0.499713\pi$
$30$	3.24791	−	1.00185i	0.592984	−	0.182911i
$31$	−0.624541	+	8.33393i	−0.112171	+	1.49682i	0.602929	+	0.797795i	$0.294000\pi$
$31$	−0.624541	+	8.33393i	−0.112171	+	1.49682i	−0.715100	+	0.699022i	$0.753619\pi$
$32$	0.623490	+	0.781831i	0.110218	+	0.138210i
$33$	6.54816	+	2.01984i	1.13989	+	0.351609i
$34$	−1.82952	+	4.66154i	−0.313760	+	0.799447i
$35$	0.150573	−	0.659701i	0.0254514	−	0.111510i
$36$	−4.27629	−	7.40676i	−0.712715	−	1.23446i
$37$	−2.67054	+	4.62552i	−0.439035	+	0.760430i	−0.997615	−	0.0690199i	$-0.978013\pi$
$37$	−2.67054	+	4.62552i	−0.439035	+	0.760430i	0.558581	+	0.829450i	$0.311346\pi$
$38$	3.92526	+	3.64211i	0.636761	+	0.590828i
$39$	1.29424	−	1.62293i	0.207244	−	0.259876i
$40$	−0.826239	+	0.563320i	−0.130640	+	0.0890687i
$41$	9.86045	−	4.74854i	1.53994	−	0.741597i	0.544664	−	0.838654i	$-0.316657\pi$
$41$	9.86045	−	4.74854i	1.53994	−	0.741597i	0.995279	+	0.0970567i	$0.0309428\pi$
$42$	−2.29993			−0.354887
$43$	0.970879	−	6.48517i	0.148058	−	0.988979i
$43$	0.970879	−	6.48517i	0.148058	−	0.988979i
$44$	−2.01612			−0.303941
$45$	7.70561	−	3.71083i	1.14868	−	0.553177i
$46$	−2.43358	+	1.65919i	−0.358812	+	0.244634i
$47$	2.84652	−	3.56942i	0.415207	−	0.520653i	−0.529615	−	0.848238i	$-0.677663\pi$
$47$	2.84652	−	3.56942i	0.415207	−	0.520653i	0.944822	+	0.327585i	$0.106235\pi$
$48$	2.49158	+	2.31185i	0.359628	+	0.333686i
$49$	3.27106	−	5.66564i	0.467294	−	0.809378i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−3.78747	+	16.5940i	−0.530352	+	2.32362i
$52$	−0.223123	+	0.568508i	−0.0309416	+	0.0788379i
$53$	−10.6271	−	3.27803i	−1.45975	−	0.450272i	−0.539625	−	0.841906i	$-0.681434\pi$
$53$	−10.6271	−	3.27803i	−1.45975	−	0.450272i	−0.920121	+	0.391634i	$0.871910\pi$
$54$	−11.7670	−	14.7553i	−1.60128	−	2.00794i
$55$	0.150665	−	2.01048i	0.0203156	−	0.271093i
$56$	0.646605	−	0.199451i	0.0864062	−	0.0266528i
$57$	15.0376	+	10.2525i	1.99178	+	1.35797i
$58$	−6.00730	−	0.905454i	−0.788797	−	0.118892i
$59$	0.0146924	+	0.0643718i	0.00191279	+	0.00838049i	0.975875	−	0.218329i	$-0.0700605\pi$
$59$	0.0146924	+	0.0643718i	0.00191279	+	0.00838049i	−0.973963	+	0.226709i	$0.927203\pi$
$60$	−2.49158	+	2.31185i	−0.321661	+	0.298458i
$61$	0.0334112	+	0.445842i	0.00427787	+	0.0570842i	0.998934	−	0.0461574i	$-0.0146976\pi$
$61$	0.0334112	+	0.445842i	0.00427787	+	0.0570842i	−0.994656	+	0.103242i	$0.967079\pi$
$62$	−3.05326	−	7.77959i	−0.387765	−	0.988008i
$63$	−5.72261	+	0.862545i	−0.720981	+	0.108670i
$64$	−0.900969	−	0.433884i	−0.112621	−	0.0542355i
$65$	−0.550244	−	0.264984i	−0.0682494	−	0.0328672i
$66$	−6.77606	+	1.02133i	−0.834076	+	0.125717i
$67$	−2.81570	−	7.17429i	−0.343993	−	0.876479i	−0.993259	−	0.115918i	$-0.963019\pi$
$67$	−2.81570	−	7.17429i	−0.343993	−	0.876479i	0.649266	−	0.760561i	$-0.275076\pi$
$68$	−0.374226	−	4.99370i	−0.0453816	−	0.605575i
$69$	−7.33861	+	6.80924i	−0.883465	+	0.819736i
$70$	0.150573	+	0.659701i	0.0179969	+	0.0788494i
$71$	5.48679	+	0.827001i	0.651162	+	0.0981469i	0.466313	−	0.884620i	$-0.345582\pi$
$71$	5.48679	+	0.827001i	0.651162	+	0.0981469i	0.184849	+	0.982767i	$0.440820\pi$
$72$	7.06648	+	4.81784i	0.832792	+	0.567788i
$73$	3.00442	−	0.926740i	0.351640	−	0.108467i	−0.113903	−	0.993492i	$-0.536335\pi$
$73$	3.00442	−	0.926740i	0.351640	−	0.108467i	0.465543	+	0.885025i	$0.345859\pi$
$74$	0.399140	−	5.32615i	0.0463991	−	0.619153i
$75$	−2.11919	−	2.65737i	−0.244702	−	0.306847i
$76$	−5.11679	−	1.57832i	−0.586936	−	0.181046i
$77$	−0.498413	+	1.26994i	−0.0567994	+	0.144723i
$78$	−0.461909	+	2.02375i	−0.0523009	+	0.229145i
$79$	1.56744	+	2.71489i	0.176351	+	0.305449i	0.940628	−	0.339439i	$-0.110237\pi$
$79$	1.56744	+	2.71489i	0.176351	+	0.305449i	−0.764277	+	0.644888i	$0.776904\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−28.2144	−	26.1791i	−3.13493	−	2.90879i
$82$	−6.82364	+	8.55658i	−0.753545	+	0.944916i
$83$	3.50456	−	2.38937i	0.384675	−	0.262267i	−0.355507	−	0.934674i	$-0.615692\pi$
$83$	3.50456	−	2.38937i	0.384675	−	0.262267i	0.740182	+	0.672406i	$0.234739\pi$
$84$	2.07216	−	0.997902i	0.226092	−	0.108880i
$85$	5.00770			0.543162
$86$	1.93908	+	6.26418i	0.209096	+	0.675484i
$87$	−20.6489			−2.21379
$88$	1.81646	−	0.874761i	0.193635	−	0.0932498i
$89$	5.96064	−	4.06390i	0.631827	−	0.430772i	−0.204604	−	0.978845i	$-0.565591\pi$
$89$	5.96064	−	4.06390i	0.631827	−	0.430772i	0.836431	+	0.548073i	$0.184638\pi$
$90$	−5.33245	+	6.68668i	−0.562089	+	0.704838i
$91$	0.302939	+	0.281086i	0.0317567	+	0.0294659i
$92$	1.47268	−	2.55076i	0.153538	−	0.265936i
$93$	−14.2028	−	24.6000i	−1.47277	−	2.55091i
$94$	−1.01591	+	4.45099i	−0.104783	+	0.459085i
$95$	1.95629	−	4.98454i	0.200711	−	0.511403i
$96$	−3.24791	−	1.00185i	−0.331488	−	0.102250i
$97$	2.56120	+	3.21165i	0.260051	+	0.326093i	0.894667	−	0.446734i	$-0.147413\pi$
$97$	2.56120	+	3.21165i	0.260051	+	0.326093i	−0.634616	+	0.772828i	$0.718842\pi$
$98$	−0.488893	+	6.52383i	−0.0493857	+	0.659006i
$99$	−16.4770	+	5.08247i	−1.65600	+	0.510807i
$100$	0.826239	+	0.563320i	0.0826239	+	0.0563320i
$101$	13.0661	+	1.96940i	1.30013	+	0.195963i	0.762373	−	0.647138i	$-0.224034\pi$
$101$	13.0661	+	1.96940i	1.30013	+	0.195963i	0.537755	+	0.843101i	$0.319272\pi$
$102$	−3.78747	−	16.5940i	−0.375015	−	1.64305i
$103$	−0.813124	+	0.754469i	−0.0801195	+	0.0743400i	−0.719216	−	0.694786i	$-0.755499\pi$
$103$	−0.813124	+	0.754469i	−0.0801195	+	0.0743400i	0.639097	+	0.769126i	$0.279308\pi$
$104$	−0.0456395	−	0.609017i	−0.00447533	−	0.0597191i
$105$	0.840259	+	2.14094i	0.0820008	+	0.208935i
$106$	10.9970	−	1.65753i	1.06812	−	0.160993i
$107$	12.7775	+	6.15330i	1.23524	+	0.594862i	0.933517	−	0.358533i	$-0.116723\pi$
$107$	12.7775	+	6.15330i	1.23524	+	0.594862i	0.301726	+	0.953395i	$0.402437\pi$
$108$	17.0037	+	8.18857i	1.63619	+	0.787946i
$109$	−15.0090	+	2.26225i	−1.43761	+	0.216684i	−0.821153	−	0.570708i	$-0.806669\pi$
$109$	−15.0090	+	2.26225i	−1.43761	+	0.216684i	−0.616453	+	0.787392i	$0.711431\pi$
$110$	0.736570	+	1.87675i	0.0702292	+	0.178941i
$111$	−1.35664	−	18.1031i	−0.128767	−	1.71827i
$112$	−0.496032	+	0.460250i	−0.0468706	+	0.0434896i
$113$	−4.54126	−	19.8966i	−0.427206	−	1.87171i	−0.486838	−	0.873492i	$-0.661850\pi$
$113$	−4.54126	−	19.8966i	−0.427206	−	1.87171i	0.0596320	−	0.998220i	$-0.481007\pi$
$114$	−17.9968	−	2.71258i	−1.68556	−	0.254057i
$115$	2.43358	+	1.65919i	0.226932	+	0.154720i
$116$	5.80525	−	1.79068i	0.539004	−	0.166261i
$117$	−0.390336	+	5.20867i	−0.0360866	+	0.481542i
$118$	−0.0411673	−	0.0516222i	−0.00378976	−	0.00475221i
$119$	−3.23800	−	0.998792i	−0.296827	−	0.0915591i
$120$	1.24176	−	3.16396i	0.113357	−	0.288828i
$121$	1.54324	−	6.76139i	0.140295	−	0.614672i
$122$	−0.223546	−	0.387193i	−0.0202389	−	0.0350548i
$123$	−18.5993	+	32.2149i	−1.67704	+	2.90472i
$124$	6.12633	+	5.68440i	0.550161	+	0.510475i
$125$	−0.623490	+	0.781831i	−0.0557666	+	0.0699291i
$126$	4.78165	−	3.26007i	0.425983	−	0.290431i
$127$	−0.304891	+	0.146828i	−0.0270547	+	0.0130289i	−0.447362	−	0.894353i	$-0.647637\pi$
$127$	−0.304891	+	0.146828i	−0.0270547	+	0.0130289i	0.420307	+	0.907382i	$0.361922\pi$
$128$	1.00000			0.0883883
$129$	9.69045	+	20.0713i	0.853196	+	1.76718i
$130$	0.610725			0.0535641
$131$	13.6393	−	6.56835i	1.19167	−	0.573880i	0.270382	−	0.962753i	$-0.412850\pi$
$131$	13.6393	−	6.56835i	1.19167	−	0.573880i	0.921291	+	0.388873i	$0.127136\pi$
$132$	5.66188	−	3.86021i	0.492804	−	0.335988i
$133$	−2.25911	+	2.83284i	−0.195890	+	0.245638i
$134$	5.64967	+	5.24213i	0.488057	+	0.452851i
$135$	−9.43637	+	16.3443i	−0.812153	+	1.40669i
$136$	2.50385	+	4.33680i	0.214703	+	0.371877i
$137$	−1.54235	+	6.75746i	−0.131772	+	0.577329i	0.865327	+	0.501208i	$0.167111\pi$
$137$	−1.54235	+	6.75746i	−0.131772	+	0.577329i	−0.997099	+	0.0761212i	$0.975746\pi$
$138$	3.65745	−	9.31902i	0.311342	−	0.793287i
$139$	5.63867	+	1.73930i	0.478266	+	0.147526i	0.524509	−	0.851405i	$-0.324249\pi$
$139$	5.63867	+	1.73930i	0.478266	+	0.147526i	−0.0462434	+	0.998930i	$0.514725\pi$
$140$	−0.421895	−	0.529040i	−0.0356566	−	0.0447120i
$141$	−1.15963	+	15.4742i	−0.0976584	+	1.30316i
$142$	−5.30225	+	1.63553i	−0.444955	+	0.137250i
$143$	1.01734	+	0.693612i	0.0850744	+	0.0580028i
$144$	−8.45706	−	1.27470i	−0.704755	−	0.106225i
$145$	1.35185	+	5.92283i	0.112265	+	0.491865i
$146$	−2.30479	+	2.13853i	−0.190746	+	0.176986i
$147$	1.66170	+	22.1739i	0.137055	+	1.82887i
$148$	1.95132	+	4.97188i	0.160397	+	0.408686i
$149$	−4.35274	+	0.656071i	−0.356591	+	0.0537474i	−0.324895	−	0.945750i	$-0.605329\pi$
$149$	−4.35274	+	0.656071i	−0.356591	+	0.0537474i	−0.0316959	+	0.999498i	$0.510091\pi$
$150$	3.06231	+	1.47473i	0.250037	+	0.120411i
$151$	2.06013	+	0.992107i	0.167651	+	0.0807366i	0.515827	−	0.856693i	$-0.327485\pi$
$151$	2.06013	+	0.992107i	0.167651	+	0.0807366i	−0.348176	+	0.937429i	$0.613199\pi$
$152$	5.29488	−	0.798074i	0.429471	−	0.0647324i
$153$	−15.6471	−	39.8682i	−1.26499	−	3.22315i
$154$	−0.101950	−	1.36043i	−0.00821535	−	0.109626i
$155$	−6.12633	+	5.68440i	−0.492079	+	0.456582i
$156$	−0.461909	−	2.02375i	−0.0369823	−	0.162030i
$157$	16.9372	+	2.55288i	1.35174	+	0.203742i	0.784662	−	0.619924i	$-0.212837\pi$
$157$	16.9372	+	2.55288i	1.35174	+	0.203742i	0.567076	+	0.823666i	$0.308075\pi$
$158$	−2.59016	−	1.76594i	−0.206062	−	0.140491i
$159$	36.1206	−	11.1417i	2.86455	−	0.883596i
$160$	−0.0747301	+	0.997204i	−0.00590793	+	0.0788359i
$161$	−1.24264	−	1.55822i	−0.0979335	−	0.122805i
$162$	36.7790	+	11.3448i	2.88963	+	0.891333i
$163$	5.77362	−	14.7109i	0.452225	−	1.15225i	−0.505056	−	0.863087i	$-0.668528\pi$
$163$	5.77362	−	14.7109i	0.452225	−	1.15225i	0.957280	−	0.289162i	$-0.0933768\pi$
$164$	2.43533	−	10.6699i	0.190167	−	0.833177i
$165$	3.42630	+	5.93453i	0.266737	+	0.462002i
$166$	−2.12079	+	3.67332i	−0.164605	+	0.285105i
$167$	−18.5491	−	17.2110i	−1.43537	−	1.33183i	−0.856223	−	0.516607i	$-0.827195\pi$
$167$	−18.5491	−	17.2110i	−1.43537	−	1.33183i	−0.579148	−	0.815222i	$-0.696615\pi$
$168$	−1.43398	+	1.79816i	−0.110634	+	0.138731i
$169$	−10.4329	+	7.11305i	−0.802533	+	0.547158i
$170$	−4.51178	+	2.17276i	−0.346038	+	0.166643i
$171$	−45.7964			−3.50214
$172$	−4.46497	−	4.80250i	−0.340451	−	0.366187i
$173$	19.2896			1.46656			0.733281	−	0.679926i	$-0.237988\pi$
$173$	19.2896			1.46656			0.733281	+	0.679926i	$0.237988\pi$
$174$	18.6040	−	8.95922i	1.41037	−	0.679196i
$175$	0.559088	−	0.381180i	0.0422631	−	0.0288145i
$176$	−1.25703	+	1.57626i	−0.0947521	+	0.118815i
$177$	−0.164512	−	0.152645i	−0.0123655	−	0.0114735i
$178$	−3.60709	+	6.24767i	−0.270363	+	0.468283i
$179$	−3.98138	−	6.89596i	−0.297583	−	0.515428i	0.678000	−	0.735062i	$-0.262847\pi$
$179$	−3.98138	−	6.89596i	−0.297583	−	0.515428i	−0.975582	+	0.219634i	$0.929514\pi$
$180$	1.90313	−	8.33815i	0.141851	−	0.621489i
$181$	−1.32655	+	3.38000i	−0.0986018	+	0.251233i	−0.971660	−	0.236383i	$-0.924038\pi$
$181$	−1.32655	+	3.38000i	−0.0986018	+	0.251233i	0.873058	+	0.487616i	$0.162133\pi$
$182$	−0.394898	−	0.121810i	−0.0292718	−	0.00902914i
$183$	−0.947470	−	1.18809i	−0.0700390	−	0.0878262i
$184$	−0.220108	+	2.93713i	−0.0162266	+	0.216528i
$185$	−5.10380	+	1.57431i	−0.375239	+	0.115746i
$186$	23.4699	+	16.0015i	1.72090	+	1.17329i
$187$	−9.98335	−	1.50475i	−0.730055	−	0.110038i
$188$	−1.01591	−	4.45099i	−0.0740928	−	0.324622i
$189$	9.36148	−	8.68618i	0.680947	−	0.631827i
$190$	0.400156	+	5.33971i	0.0290304	+	0.387383i
$191$	−2.70339	−	6.88812i	−0.195610	−	0.498407i	0.799092	−	0.601209i	$-0.205314\pi$
$191$	−2.70339	−	6.88812i	−0.195610	−	0.498407i	−0.994702	+	0.102803i	$0.967219\pi$
$192$	3.36095	−	0.506581i	0.242555	−	0.0365593i
$193$	−4.41667	−	2.12695i	−0.317919	−	0.153102i	0.268118	−	0.963386i	$-0.413598\pi$
$193$	−4.41667	−	2.12695i	−0.317919	−	0.153102i	−0.586037	+	0.810285i	$0.699313\pi$
$194$	−3.70104	−	1.78233i	−0.265720	−	0.127964i
$195$	2.05261	−	0.309382i	0.146991	−	0.0221553i
$196$	−2.39011	−	6.08989i	−0.170722	−	0.434992i
$197$	0.310566	+	4.14421i	0.0221269	+	0.295263i	0.997279	+	0.0737248i	$0.0234887\pi$
$197$	0.310566	+	4.14421i	0.0221269	+	0.295263i	−0.975152	+	0.221538i	$0.928892\pi$
$198$	12.6400	−	11.7282i	0.898287	−	0.833489i
$199$	2.46485	+	10.7992i	0.174729	+	0.765536i	0.984010	+	0.178114i	$0.0569997\pi$
$199$	2.46485	+	10.7992i	0.174729	+	0.765536i	−0.809281	+	0.587421i	$0.800143\pi$
$200$	−0.988831	−	0.149042i	−0.0699209	−	0.0105389i
$201$	21.6438	+	14.7565i	1.52664	+	1.04084i
$202$	−12.6267	+	3.89481i	−0.888409	+	0.274038i
$203$	0.307204	−	4.09936i	0.0215615	−	0.287719i
$204$	10.6122	+	13.3073i	0.743006	+	0.931700i
$205$	10.4580	+	3.22588i	0.730422	+	0.225305i
$206$	0.405248	−	1.03255i	0.0282349	−	0.0719415i
$207$	5.60542	−	24.5589i	0.389604	−	1.70696i
$208$	0.305363	+	0.528903i	0.0211731	+	0.0366729i
$209$	−5.39784	+	9.34933i	−0.373376	+	0.646706i
$210$	−1.68597	−	1.56435i	−0.116343	−	0.107950i
$211$	−14.3123	+	17.9470i	−0.985296	+	1.23552i	−0.0134492	+	0.999910i	$0.504281\pi$
$211$	−14.3123	+	17.9470i	−0.985296	+	1.23552i	−0.971847	+	0.235613i	$0.924290\pi$
$212$	−9.18876	+	6.26479i	−0.631087	+	0.430268i
$213$	−16.9920	+	8.18294i	−1.16428	+	0.560686i
$214$	−14.1819			−0.969455
$215$	5.12274	−	4.09360i	0.349368	−	0.279181i
$216$	−18.8727			−1.28413
$217$	5.09507	−	2.45366i	0.345876	−	0.166565i
$218$	12.5411	−	8.55040i	0.849392	−	0.579106i
$219$	−6.66293	+	8.35505i	−0.450239	+	0.564582i
$220$	−1.47792	−	1.37131i	−0.0996413	−	0.0924536i
$221$	−1.52916	+	2.64859i	−0.102863	+	0.178163i
$222$	9.07693	+	15.7217i	0.609204	+	1.05517i
$223$	2.35459	−	10.3161i	0.157675	−	0.690818i	−0.832852	−	0.553496i	$-0.813293\pi$
$223$	2.35459	−	10.3161i	0.157675	−	0.690818i	0.990526	−	0.137322i	$-0.0438495\pi$
$224$	0.247214	−	0.629891i	0.0165177	−	0.0420864i
$225$	8.17262	+	2.52092i	0.544841	+	0.168061i
$226$	12.7243	+	15.9558i	0.846410	+	1.06137i
$227$	1.03825	−	13.8545i	0.0689111	−	0.919554i	−0.850429	−	0.526090i	$-0.823657\pi$
$227$	1.03825	−	13.8545i	0.0689111	−	0.919554i	0.919340	−	0.393464i	$-0.128723\pi$
$228$	17.3915	−	5.36457i	1.15178	−	0.355277i
$229$	−13.7534	−	9.37694i	−0.908853	−	0.619646i	0.0160403	−	0.999871i	$-0.494894\pi$
$229$	−13.7534	−	9.37694i	−0.908853	−	0.619646i	−0.924894	+	0.380226i	$0.875846\pi$
$230$	−2.91247	−	0.438985i	−0.192043	−	0.0289458i
$231$	−1.03181	−	4.52067i	−0.0678884	−	0.297438i
$232$	−4.45340	+	4.13215i	−0.292380	+	0.271289i
$233$	0.759631	+	10.1366i	0.0497651	+	0.664069i	0.965185	+	0.261569i	$0.0842398\pi$
$233$	0.759631	+	10.1366i	0.0497651	+	0.664069i	−0.915420	+	0.402501i	$0.868141\pi$
$234$	−1.90828	−	4.86221i	−0.124748	−	0.317853i
$235$	4.51446	−	0.680446i	0.294491	−	0.0443874i
$236$	0.0594885	+	0.0286481i	0.00387237	+	0.00186484i
$237$	−9.59998	−	4.62311i	−0.623586	−	0.300303i
$238$	3.35070	−	0.505037i	0.217194	−	0.0327367i
$239$	−3.25102	−	8.28347i	−0.210291	−	0.535813i	0.786343	−	0.617790i	$-0.211972\pi$
$239$	−3.25102	−	8.28347i	−0.210291	−	0.535813i	−0.996634	+	0.0819769i	$0.973877\pi$
$240$	0.254001	+	3.38941i	0.0163957	+	0.218785i
$241$	−11.9404	+	11.0791i	−0.769149	+	0.713666i	−0.963630	−	0.267241i	$-0.913888\pi$
$241$	−11.9404	+	11.0791i	−0.769149	+	0.713666i	0.194481	+	0.980906i	$0.437698\pi$
$242$	1.54324	+	6.76139i	0.0992034	+	0.434639i
$243$	73.3735	+	11.0593i	4.70691	+	0.709453i
$244$	0.369405	+	0.251856i	0.0236487	+	0.0161234i
$245$	6.25147	−	1.92832i	0.399392	−	0.123196i
$246$	2.77985	−	37.0946i	0.177237	−	2.36506i
$247$	2.03896	+	2.55678i	0.129736	+	0.162684i
$248$	−7.98600	−	2.46336i	−0.507112	−	0.156423i
$249$	−5.26703	+	13.4202i	−0.333785	+	0.850469i
$250$	0.222521	−	0.974928i	0.0140735	−	0.0616599i
$251$	11.7434	+	20.3401i	0.741234	+	1.28385i	0.951934	+	0.306304i	$0.0990924\pi$
$251$	11.7434	+	20.3401i	0.741234	+	1.28385i	−0.210700	+	0.977551i	$0.567574\pi$
$252$	−2.89363	+	5.01191i	−0.182281	+	0.315720i
$253$	−4.35302	−	4.03901i	−0.273672	−	0.253930i
$254$	0.210991	−	0.264575i	0.0132388	−	0.0166009i
$255$	−14.0632	+	9.58811i	−0.880671	+	0.600431i
$256$	−0.900969	+	0.433884i	−0.0563106	+	0.0271177i
$257$	−1.16821			−0.0728712			−0.0364356	−	0.999336i	$-0.511600\pi$
$257$	−1.16821			−0.0728712			−0.0364356	+	0.999336i	$0.511600\pi$
$258$	−17.4394	−	13.8791i	−1.08573	−	0.864073i
$259$	3.61414			0.224572
$260$	−0.550244	+	0.264984i	−0.0341247	+	0.0164336i
$261$	42.9299	−	29.2691i	2.65729	−	1.81171i
$262$	−9.43871	+	11.8358i	−0.583125	+	0.731216i
$263$	11.2564	+	10.4444i	0.694101	+	0.644031i	0.946167	−	0.323679i	$-0.104920\pi$
$263$	11.2564	+	10.4444i	0.694101	+	0.644031i	−0.252066	+	0.967710i	$0.581110\pi$
$264$	−3.42630	+	5.93453i	−0.210874	+	0.365245i
$265$	−5.56060	−	9.63124i	−0.341585	−	0.591642i
$266$	0.806269	−	3.53249i	0.0494355	−	0.216591i
$267$	−8.95830	+	22.8254i	−0.548239	+	1.39689i
$268$	−7.36465	−	2.27169i	−0.449868	−	0.138766i
$269$	−17.0720	−	21.4076i	−1.04090	−	1.30524i	−0.950966	−	0.309295i	$-0.899907\pi$
$269$	−17.0720	−	21.4076i	−1.04090	−	1.30524i	−0.0899308	−	0.995948i	$-0.528665\pi$
$270$	1.41036	−	18.8200i	0.0858318	−	1.14535i
$271$	15.8984	−	4.90399i	0.965756	−	0.297896i	0.228526	−	0.973538i	$-0.426609\pi$
$271$	15.8984	−	4.90399i	0.965756	−	0.297896i	0.737230	+	0.675641i	$0.236133\pi$
$272$	−4.13756	−	2.82094i	−0.250876	−	0.171045i
$273$	−1.38894	−	0.209348i	−0.0840622	−	0.0126703i
$274$	−1.54235	−	6.75746i	−0.0931765	−	0.408233i
$275$	1.47792	−	1.37131i	0.0891219	−	0.0826930i
$276$	0.748126	+	9.98305i	0.0450319	+	0.600909i
$277$	−11.4180	−	29.0927i	−0.686044	−	1.74801i	−0.663396	−	0.748268i	$-0.730886\pi$
$277$	−11.4180	−	29.0927i	−0.686044	−	1.74801i	−0.0226478	−	0.999744i	$-0.507210\pi$
$278$	−5.83492	+	0.879473i	−0.349955	+	0.0527473i
$279$	64.3981	+	31.0125i	3.85541	+	1.85667i
$280$	0.609656	+	0.293595i	0.0364339	+	0.0175456i
$281$	−3.08255	+	0.464620i	−0.183889	+	0.0277169i	−0.240341	−	0.970688i	$-0.577259\pi$
$281$	−3.08255	+	0.464620i	−0.183889	+	0.0277169i	0.0564518	+	0.998405i	$0.482021\pi$
$282$	−5.66921	−	14.4449i	−0.337596	−	0.860181i
$283$	−1.13496	−	15.1449i	−0.0674661	−	0.900272i	−0.923560	−	0.383453i	$-0.874735\pi$
$283$	−1.13496	−	15.1449i	−0.0674661	−	0.900272i	0.856094	−	0.516819i	$-0.172884\pi$
$284$	4.06753	−	3.77412i	0.241364	−	0.223953i
$285$	4.04990	+	17.7438i	0.239895	+	1.05105i
$286$	−1.21754	−	0.183515i	−0.0719947	−	0.0108515i
$287$	−6.11882	−	4.17174i	−0.361182	−	0.246250i
$288$	8.17262	−	2.52092i	0.481576	−	0.148547i
$289$	0.603601	−	8.05449i	0.0355059	−	0.473794i
$290$	−3.78779	−	4.74974i	−0.222427	−	0.278915i
$291$	−13.3419	−	4.11543i	−0.782116	−	0.241251i
$292$	1.14867	−	2.92676i	0.0672208	−	0.171276i
$293$	−6.71275	+	29.4105i	−0.392163	+	1.71818i	0.264842	+	0.964292i	$0.414680\pi$
$293$	−6.71275	+	29.4105i	−0.392163	+	1.71818i	−0.657005	+	0.753887i	$0.728177\pi$
$294$	−11.1180	−	19.2570i	−0.648417	−	1.12309i
$295$	−0.0330136	+	0.0571813i	−0.00192213	+	0.00332922i
$296$	−3.91529	−	3.63286i	−0.227572	−	0.211156i
$297$	23.7236	−	29.7484i	1.37658	−	1.72618i
$298$	3.63703	−	2.47968i	0.210687	−	0.143644i
$299$	−1.62067	+	0.780475i	−0.0937259	+	0.0451360i
$300$	−3.39891			−0.196236
$301$	−4.12886	+	1.62520i	−0.237983	+	0.0936752i
$302$	−2.28657			−0.131578
$303$	−40.4645	+	19.4867i	−2.32462	+	1.11948i
$304$	−4.42425	+	3.01640i	−0.253748	+	0.173002i
$305$	−0.278757	+	0.349550i	−0.0159616	+	0.0200152i
$306$	31.3957	+	29.1310i	1.79477	+	1.66531i
$307$	−0.381384	+	0.660576i	−0.0217667	+	0.0377011i	−0.876704	−	0.481031i	$-0.840262\pi$
$307$	−0.381384	+	0.660576i	−0.0217667	+	0.0377011i	0.854937	+	0.518732i	$0.173596\pi$
$308$	0.682120	+	1.18147i	0.0388674	+	0.0673203i
$309$	0.838943	−	3.67565i	0.0477258	−	0.209100i
$310$	3.05326	−	7.77959i	0.173414	−	0.441851i
$311$	11.2114	+	3.45825i	0.635738	+	0.196099i	0.595838	−	0.803104i	$-0.296820\pi$
$311$	11.2114	+	3.45825i	0.635738	+	0.196099i	0.0398998	+	0.999204i	$0.487296\pi$
$312$	1.29424	+	1.62293i	0.0732719	+	0.0918800i
$313$	−2.40374	+	32.0757i	−0.135868	+	1.81303i	0.347576	+	0.937652i	$0.387005\pi$
$313$	−2.40374	+	32.0757i	−0.135868	+	1.81303i	−0.483444	+	0.875375i	$0.660614\pi$
$314$	−16.3676	+	5.04872i	−0.923675	+	0.284916i
$315$	−4.78165	−	3.26007i	−0.269416	−	0.183684i
$316$	3.09987	+	0.467230i	0.174381	+	0.0262837i
$317$	3.44155	+	15.0784i	0.193297	+	0.846888i	0.974817	+	0.223008i	$0.0715875\pi$
$317$	3.44155	+	15.0784i	0.193297	+	0.846888i	−0.781520	+	0.623880i	$0.785555\pi$
$318$	−27.7093	+	25.7105i	−1.55386	+	1.44177i
$319$	−0.915311	−	12.2140i	−0.0512476	−	0.683851i
$320$	−0.365341	−	0.930874i	−0.0204232	−	0.0520374i
$321$	−47.6646	+	7.18429i	−2.66038	+	0.400988i
$322$	1.79566	+	0.864745i	0.100068	+	0.0481904i
$323$	−24.1592	−	11.6344i	−1.34425	−	0.647358i
$324$	−38.0591	+	5.73648i	−2.11439	+	0.318693i
$325$	−0.223123	−	0.568508i	−0.0123766	−	0.0315351i
$326$	1.18099	+	15.7592i	0.0654088	+	0.872820i
$327$	37.8186	−	35.0905i	2.09137	−	1.94051i
$328$	2.43533	+	10.6699i	0.134469	+	0.589145i
$329$	−3.05479	−	0.460435i	−0.168416	−	0.0253846i
$330$	−5.66188	−	3.86021i	−0.311676	−	0.212497i
$331$	−7.95805	+	2.45473i	−0.437414	+	0.134924i	−0.505638	−	0.862746i	$-0.668743\pi$
$331$	−7.95805	+	2.45473i	−0.437414	+	0.134924i	0.0682240	+	0.997670i	$0.478267\pi$
$332$	0.316974	−	4.22972i	0.0173962	−	0.232136i
$333$	28.4811	+	35.7141i	1.56075	+	1.95712i
$334$	24.1797	+	7.45846i	1.32306	+	0.408109i
$335$	2.81570	−	7.17429i	0.153838	−	0.391973i
$336$	0.511782	−	2.24227i	0.0279200	−	0.122326i
$337$	−8.32099	−	14.4124i	−0.453273	−	0.785092i	0.545314	−	0.838232i	$-0.316411\pi$
$337$	−8.32099	−	14.4124i	−0.453273	−	0.785092i	−0.998587	+	0.0531396i	$0.983077\pi$
$338$	6.31351	−	10.9353i	0.343410	−	0.594803i
$339$	50.8487	+	47.1807i	2.76172	+	2.56251i
$340$	3.12225	−	3.91518i	0.169328	−	0.212330i
$341$	13.9215	−	9.49154i	0.753893	−	0.513996i
$342$	41.2611	−	19.8703i	2.23115	−	1.07446i
$343$	−9.16351			−0.494783
$344$	6.10653	+	2.38962i	0.329242	+	0.128840i
$345$	−10.0110			−0.538976
$346$	−17.3793	+	8.36944i	−0.934318	+	0.449944i
$347$	−13.2092	+	9.00590i	−0.709108	+	0.483462i	−0.863372	−	0.504568i	$-0.831652\pi$
$347$	−13.2092	+	9.00590i	−0.709108	+	0.483462i	0.154264	+	0.988030i	$0.450699\pi$
$348$	−12.8744	+	16.1440i	−0.690139	+	0.865407i
$349$	14.7178	+	13.6561i	0.787827	+	0.730997i	0.967539	−	0.252723i	$-0.0813261\pi$
$349$	14.7178	+	13.6561i	0.787827	+	0.730997i	−0.179712	+	0.983719i	$0.557517\pi$
$350$	−0.338333	+	0.586011i	−0.0180847	+	0.0313236i
$351$	−5.76302	−	9.98185i	−0.307607	−	0.532792i
$352$	0.448628	−	1.96557i	0.0239120	−	0.104765i
$353$	−12.2552	+	31.2258i	−0.652280	+	1.66198i	0.0933598	+	0.995632i	$0.470239\pi$
$353$	−12.2552	+	31.2258i	−0.652280	+	1.66198i	−0.745640	+	0.666349i	$0.767856\pi$
$354$	0.214450	+	0.0661491i	0.0113979	+	0.00351579i
$355$	3.45960	+	4.33820i	0.183616	+	0.230248i
$356$	0.539117	−	7.19402i	0.0285731	−	0.381282i
$357$	11.0057	−	3.39480i	0.582482	−	0.179672i
$358$	6.57915	+	4.48559i	0.347719	+	0.237071i
$359$	−14.2987	−	2.15518i	−0.754657	−	0.113746i	−0.239564	−	0.970881i	$-0.577005\pi$
$359$	−14.2987	−	2.15518i	−0.754657	−	0.113746i	−0.515093	+	0.857134i	$0.672243\pi$
$360$	1.90313	+	8.33815i	0.100304	+	0.439459i
$361$	−7.09055	+	6.57907i	−0.373187	+	0.346267i
$362$	−0.271345	−	3.62084i	−0.0142616	−	0.190307i
$363$	8.61195	+	21.9429i	0.452010	+	1.15170i
$364$	0.408642	−	0.0615928i	0.0214186	−	0.00322834i
$365$	2.83274	+	1.36417i	0.148272	+	0.0714041i
$366$	1.36913	+	0.659340i	0.0715658	+	0.0344643i
$367$	−22.2505	+	3.35372i	−1.16147	+	0.175063i	−0.701364	−	0.712803i	$-0.747425\pi$
$367$	−22.2505	+	3.35372i	−1.16147	+	0.175063i	−0.460102	+	0.887866i	$0.652187\pi$
$368$	−1.07606	−	2.74177i	−0.0560937	−	0.142924i
$369$	−6.99487	−	93.3401i	−0.364138	−	4.85909i
$370$	3.91529	−	3.63286i	0.203546	−	0.188863i
$371$	1.67455	+	7.33667i	0.0869381	+	0.380901i
$372$	−28.0884	−	4.23365i	−1.45632	−	0.219504i
$373$	−9.76591	−	6.65829i	−0.505660	−	0.344753i	0.283468	−	0.958982i	$-0.408515\pi$
$373$	−9.76591	−	6.65829i	−0.505660	−	0.344753i	−0.789128	+	0.614229i	$0.789467\pi$
$374$	9.64757	−	2.97588i	0.498864	−	0.153879i
$375$	0.254001	−	3.38941i	0.0131165	−	0.175028i
$376$	2.84652	+	3.56942i	0.146798	+	0.184079i
$377$	−3.54541	−	1.09361i	−0.182598	−	0.0563240i
$378$	−4.66561	+	11.8878i	−0.239973	+	0.611441i
$379$	3.67319	−	16.0933i	0.188679	−	0.826657i	−0.788635	−	0.614862i	$-0.789212\pi$
$379$	3.67319	−	16.0933i	0.188679	−	0.826657i	0.977314	−	0.211795i	$-0.0679310\pi$
$380$	−2.67734	−	4.63729i	−0.137345	−	0.237888i
$381$	0.575102	−	0.996105i	0.0294633	−	0.0510320i
$382$	5.42431	+	5.03302i	0.277532	+	0.257512i
$383$	−2.69505	+	3.37948i	−0.137710	+	0.172683i	−0.845904	−	0.533334i	$-0.820939\pi$
$383$	−2.69505	+	3.37948i	−0.137710	+	0.172683i	0.708194	+	0.706018i	$0.249510\pi$
$384$	−2.80831	+	1.91467i	−0.143311	+	0.0977078i
$385$	−1.22914	+	0.591922i	−0.0626427	+	0.0301671i
$386$	4.90213			0.249512
$387$	−48.5972	−	27.9932i	−2.47034	−	1.42297i
$388$	4.10785			0.208544
$389$	−27.6261	+	13.3040i	−1.40070	+	0.674540i	−0.973303	−	0.229525i	$-0.926283\pi$
$389$	−27.6261	+	13.3040i	−1.40070	+	0.674540i	−0.427394	+	0.904065i	$0.640568\pi$
$390$	−1.71511	+	1.16934i	−0.0868478	+	0.0592118i
$391$	9.19618	−	11.5316i	0.465071	−	0.583181i
$392$	4.79571	+	4.44977i	0.242220	+	0.224747i
$393$	−25.7272	+	44.5608i	−1.29777	+	2.24780i
$394$	−2.07792	−	3.59906i	−0.104684	−	0.181318i
$395$	−0.697577	+	3.05628i	−0.0350989	+	0.153778i
$396$	−6.29958	+	16.0511i	−0.316566	+	0.806597i
$397$	8.12544	+	2.50637i	0.407804	+	0.125791i	0.491869	−	0.870669i	$-0.336314\pi$
$397$	8.12544	+	2.50637i	0.407804	+	0.125791i	−0.0840645	+	0.996460i	$0.526790\pi$
$398$	−6.90635	−	8.66029i	−0.346184	−	0.434101i
$399$	0.920331	−	12.2810i	0.0460742	−	0.614817i
$400$	0.955573	−	0.294755i	0.0477786	−	0.0147378i
$401$	7.07177	+	4.82145i	0.353147	+	0.240772i	0.726880	−	0.686765i	$-0.240970\pi$
$401$	7.07177	+	4.82145i	0.353147	+	0.240772i	−0.373732	+	0.927537i	$0.621922\pi$
$402$	−25.9030	−	3.90425i	−1.29192	−	0.194726i
$403$	−1.13575	−	4.97604i	−0.0565757	−	0.247874i
$404$	9.68634	−	8.98761i	0.481913	−	0.447150i
$405$	−2.87628	−	38.3813i	−0.142924	−	1.90718i
$406$	1.50186	+	3.82669i	0.0745362	+	0.189915i
$407$	10.6480	−	1.60493i	0.527801	−	0.0795532i
$408$	−15.3351	−	7.38502i	−0.759203	−	0.365613i
$409$	−28.2101	−	13.5853i	−1.39490	−	0.671748i	−0.422780	−	0.906232i	$-0.638946\pi$
$409$	−28.2101	−	13.5853i	−1.39490	−	0.671748i	−0.972120	+	0.234484i	$0.924660\pi$
$410$	−10.8220	+	1.63116i	−0.534462	+	0.0805572i
$411$	−8.60695	−	21.9301i	−0.424549	−	1.08173i
$412$	0.0828930	+	1.10613i	0.00408384	+	0.0544951i
$413$	0.0327516	−	0.0303891i	0.00161160	−	0.00149535i
$414$	5.60542	+	24.5589i	0.275491	+	1.20701i
$415$	4.19421	+	0.632175i	0.205886	+	0.0310323i
$416$	−0.504605	−	0.344034i	−0.0247403	−	0.0168676i
$417$	−19.1653	+	5.91172i	−0.938530	+	0.289498i
$418$	0.806762	−	10.7655i	0.0394600	−	0.526557i
$419$	−16.3468	−	20.4983i	−0.798595	−	1.00141i	−0.999761	−	0.0218489i	$-0.993045\pi$
$419$	−16.3468	−	20.4983i	−0.798595	−	1.00141i	0.201167	−	0.979557i	$-0.435527\pi$
$420$	2.19775	+	0.677916i	0.107239	+	0.0330789i
$421$	13.5345	−	34.4853i	0.659631	−	1.68071i	−0.0705926	−	0.997505i	$-0.522489\pi$
$421$	13.5345	−	34.4853i	0.659631	−	1.68071i	0.730224	−	0.683208i	$-0.239416\pi$
$422$	5.10798	−	22.3795i	0.248653	−	1.08942i
$423$	−19.5232	−	33.8152i	−0.949252	−	1.64415i
$424$	5.56060	−	9.63124i	0.270046	−	0.467734i
$425$	3.67091	+	3.40610i	0.178065	+	0.165220i
$426$	11.7589	−	14.7451i	0.569719	−	0.714405i
$427$	0.249964	−	0.170422i	0.0120966	−	0.00824732i
$428$	12.7775	−	6.15330i	0.617622	−	0.297431i
$429$	−4.18505			−0.202056
$430$	−2.83928	+	5.91088i	−0.136922	+	0.285048i
$431$	21.9435			1.05698			0.528491	−	0.848939i	$-0.322758\pi$
$431$	21.9435			1.05698			0.528491	+	0.848939i	$0.322758\pi$
$432$	17.0037	−	8.18857i	0.818093	−	0.393973i
$433$	23.3004	−	15.8859i	1.11974	−	0.763429i	0.145598	−	0.989344i	$-0.453490\pi$
$433$	23.3004	−	15.8859i	1.11974	−	0.763429i	0.974147	+	0.225915i	$0.0725371\pi$
$434$	−3.52590	+	4.42134i	−0.169249	+	0.212231i
$435$	−15.1367	−	14.0448i	−0.725749	−	0.673397i
$436$	−7.58929	+	13.1450i	−0.363461	+	0.629533i
$437$	−7.88576	−	13.6585i	−0.377227	−	0.653377i
$438$	2.37797	−	10.4186i	0.113624	−	0.497819i
$439$	2.81838	−	7.18111i	0.134514	−	0.342736i	−0.847707	−	0.530465i	$-0.822017\pi$
$439$	2.81838	−	7.18111i	0.134514	−	0.342736i	0.982221	+	0.187729i	$0.0601127\pi$
$440$	1.92655	+	0.594261i	0.0918445	+	0.0283303i
$441$	−34.8855	−	43.7451i	−1.66122	−	2.08310i
$442$	0.228549	−	3.04978i	0.0108710	−	0.145063i
$443$	20.6987	−	6.38470i	0.983425	−	0.303346i	0.238976	−	0.971026i	$-0.423188\pi$
$443$	20.6987	−	6.38470i	0.983425	−	0.303346i	0.744449	+	0.667679i	$0.232712\pi$
$444$	−14.9994	−	10.2264i	−0.711841	−	0.485325i
$445$	7.13361	+	1.07522i	0.338166	+	0.0509703i
$446$	2.35459	+	10.3161i	0.111493	+	0.488482i
$447$	10.9677	−	10.1765i	0.518754	−	0.481334i
$448$	0.0505674	+	0.674775i	0.00238908	+	0.0318801i
$449$	−5.28592	−	13.4683i	−0.249458	−	0.635608i	0.750215	−	0.661194i	$-0.229950\pi$
$449$	−5.28592	−	13.4683i	−0.249458	−	0.635608i	−0.999673	+	0.0255859i	$0.991855\pi$
$450$	−8.45706	+	1.27470i	−0.398670	+	0.0600898i
$451$	−19.8798	−	9.57362i	−0.936104	−	0.450804i
$452$	−18.3872	−	8.85481i	−0.864861	−	0.416495i
$453$	−7.68505	+	1.15834i	−0.361075	+	0.0544234i
$454$	5.07580	+	12.9329i	0.238219	+	0.606973i
$455$	0.0308828	+	0.412102i	0.00144781	+	0.0193196i
$456$	−13.3416	+	12.3792i	−0.624778	+	0.579709i
$457$	3.28516	+	14.3932i	0.153674	+	0.673288i	0.991799	+	0.127810i	$0.0407947\pi$
$457$	3.28516	+	14.3932i	0.153674	+	0.673288i	−0.838125	+	0.545478i	$0.816348\pi$
$458$	16.4599	+	2.48094i	0.769122	+	0.115927i
$459$	78.0870	+	53.2388i	3.64479	+	2.48498i
$460$	2.81452	−	0.868163i	0.131227	−	0.0404783i
$461$	−1.94067	+	25.8964i	−0.0903858	+	1.20611i	0.748997	+	0.662574i	$0.230536\pi$
$461$	−1.94067	+	25.8964i	−0.0903858	+	1.20611i	−0.839383	+	0.543541i	$0.817083\pi$
$462$	2.89108	+	3.62530i	0.134505	+	0.168664i
$463$	11.4169	+	3.52165i	0.530589	+	0.163665i	0.548462	−	0.836175i	$-0.315213\pi$
$463$	11.4169	+	3.52165i	0.530589	+	0.163665i	−0.0178735	+	0.999840i	$0.505690\pi$
$464$	2.21950	−	5.65520i	0.103038	−	0.262536i
$465$	6.32086	−	27.6935i	0.293123	−	1.28426i
$466$	−5.08250	−	8.80315i	−0.235442	−	0.407798i
$467$	7.50242	−	12.9946i	0.347170	−	0.601317i	−0.638575	−	0.769559i	$-0.720476\pi$
$467$	7.50242	−	12.9946i	0.347170	−	0.601317i	0.985746	+	0.168243i	$0.0538092\pi$
$468$	3.82893	+	3.55273i	0.176993	+	0.164225i
$469$	−3.25157	+	4.07733i	−0.150143	+	0.188274i
$470$	−3.77216	+	2.57181i	−0.173997	+	0.118629i
$471$	−52.4529	+	25.2600i	−2.41690	+	1.16392i
$472$	−0.0660272			−0.00303915
$473$	−11.4428	+	6.62168i	−0.526139	+	0.304465i
$474$	10.6552			0.489408
$475$	4.82440	−	2.32331i	0.221359	−	0.106601i
$476$	−2.79975	+	1.90884i	−0.128326	+	0.0874914i
$477$	−59.3032	+	74.3639i	−2.71531	+	3.40489i
$478$	6.52313	+	6.05258i	0.298361	+	0.276839i
$479$	−16.1154	+	27.9127i	−0.736331	+	1.27536i	0.217806	+	0.975992i	$0.430110\pi$
$479$	−16.1154	+	27.9127i	−0.736331	+	1.27536i	−0.954137	+	0.299371i	$0.903223\pi$
$480$	−1.69945	−	2.94354i	−0.0775691	−	0.134354i
$481$	0.725849	−	3.18015i	0.0330959	−	0.145002i
$482$	5.95090	−	15.1626i	0.271056	−	0.690639i
$483$	6.47319	+	1.99671i	0.294540	+	0.0908536i
$484$	−4.32407	−	5.42221i	−0.196549	−	0.246464i
$485$	−0.306980	+	4.09636i	−0.0139392	+	0.186006i
$486$	−70.9056	+	21.8715i	−3.21635	+	0.992111i
$487$	18.5994	+	12.6808i	0.842818	+	0.574624i	0.905952	−	0.423381i	$-0.139157\pi$
$487$	18.5994	+	12.6808i	0.842818	+	0.574624i	−0.0631332	+	0.998005i	$0.520109\pi$
$488$	−0.442098	−	0.0666356i	−0.0200128	−	0.00301645i
$489$	11.9525	+	52.3675i	0.540512	+	2.36814i
$490$	−4.79571	+	4.44977i	−0.216648	+	0.201020i
$491$	1.15988	+	15.4775i	0.0523446	+	0.698490i	0.960219	+	0.279248i	$0.0900851\pi$
$491$	1.15988	+	15.4775i	0.0523446	+	0.698490i	−0.907874	+	0.419242i	$0.862296\pi$
$492$	13.5902	+	34.6272i	0.612692	+	1.56111i
$493$	30.0827	−	4.53424i	1.35486	−	0.204212i
$494$	−2.94638	−	1.41890i	−0.132564	−	0.0638395i
$495$	−15.5354	−	7.48146i	−0.698265	−	0.336267i
$496$	8.26395	−	1.24559i	0.371062	−	0.0559287i
$497$	−1.37173	−	3.49512i	−0.0615307	−	0.156778i
$498$	−1.07737	−	14.3764i	−0.0482779	−	0.644224i
$499$	5.14486	−	4.77373i	0.230315	−	0.213702i	−0.556570	−	0.830801i	$-0.687883\pi$
$499$	5.14486	−	4.77373i	0.230315	−	0.213702i	0.786885	+	0.617099i	$0.211692\pi$
$500$	0.222521	+	0.974928i	0.00995144	+	0.0436001i
$501$	85.0451	+	12.8185i	3.79953	+	0.572688i
$502$	−19.4056	−	13.2305i	−0.866116	−	0.590508i
$503$	−23.1293	+	7.13444i	−1.03128	+	0.318109i	−0.763800	−	0.645454i	$-0.776668\pi$
$503$	−23.1293	+	7.13444i	−1.03128	+	0.318109i	−0.267484	+	0.963562i	$0.586192\pi$
$504$	0.432482	−	5.77107i	0.0192643	−	0.257064i
$505$	8.23861	+	10.3309i	0.366613	+	0.459719i
$506$	5.67439	+	1.75032i	0.252258	+	0.0778111i
$507$	15.6797	−	39.9513i	0.696361	−	1.77430i
$508$	−0.0753019	+	0.329919i	−0.00334098	+	0.0146378i
$509$	3.94090	+	6.82585i	0.174677	+	0.302550i	0.940050	−	0.341038i	$-0.110778\pi$
$509$	3.94090	+	6.82585i	0.174677	+	0.302550i	−0.765372	+	0.643588i	$0.777445\pi$
$510$	8.51036	−	14.7404i	0.376845	−	0.652715i
$511$	−1.55957	−	1.44707i	−0.0689915	−	0.0640148i
$512$	0.623490	−	0.781831i	0.0275546	−	0.0345524i
$513$	83.4976	−	56.9277i	3.68651	−	2.51342i
$514$	1.05252	−	0.506869i	0.0464248	−	0.0223570i
$515$	−1.10923			−0.0488786
$516$	21.7343	+	4.93794i	0.956797	+	0.217381i
$517$	−9.20450			−0.404813
$518$	−3.25622	+	1.56812i	−0.143070	+	0.0688990i
$519$	−54.1712	+	36.9333i	−2.37785	+	1.62119i
$520$	0.380781	−	0.477484i	0.0166983	−	0.0209391i
$521$	1.85788	+	1.72386i	0.0813951	+	0.0755236i	0.719821	−	0.694159i	$-0.244224\pi$
$521$	1.85788	+	1.72386i	0.0813951	+	0.0755236i	−0.638426	+	0.769683i	$0.720414\pi$
$522$	−25.9791	+	44.9972i	−1.13708	+	1.96947i
$523$	4.63743	+	8.03227i	0.202781	+	0.351226i	0.949423	−	0.313999i	$-0.101669\pi$
$523$	4.63743	+	8.03227i	0.202781	+	0.351226i	−0.746643	+	0.665225i	$0.768335\pi$
$524$	3.36864	−	14.7590i	0.147160	−	0.644748i
$525$	−0.840259	+	2.14094i	−0.0366719	+	0.0934385i
$526$	−14.6734	−	4.52613i	−0.639789	−	0.197349i
$527$	26.0936	+	32.7203i	1.13665	+	1.42532i
$528$	0.512095	−	6.83344i	0.0222861	−	0.297387i
$529$	−13.6884	+	4.22231i	−0.595147	+	0.183579i
$530$	9.18876	+	6.26479i	0.399134	+	0.272125i
$531$	0.558396	+	0.0841647i	0.0242323	+	0.00365244i
$532$	0.806269	+	3.53249i	0.0349562	+	0.153153i
$533$	−4.89967	+	4.54623i	−0.212228	+	0.196919i
$534$	−1.83241	−	24.4518i	−0.0792961	−	1.05813i
$535$	5.18123	+	13.2016i	0.224004	+	0.570753i
$536$	7.62097	−	1.14868i	0.329176	−	0.0496153i
$537$	24.3845	+	11.7429i	1.05227	+	0.506745i
$538$	24.6697	+	11.8803i	1.06359	+	0.512197i
$539$	−13.0424	+	1.96582i	−0.561775	+	0.0846739i
$540$	6.89498	+	17.5681i	0.296713	+	0.756012i
$541$	1.55260	+	20.7181i	0.0667516	+	0.890739i	0.925599	+	0.378506i	$0.123562\pi$
$541$	1.55260	+	20.7181i	0.0667516	+	0.890739i	−0.858847	+	0.512232i	$0.828819\pi$
$542$	−12.1962	+	11.3164i	−0.523870	+	0.486080i
$543$	−2.74622	−	12.0320i	−0.117852	−	0.516342i
$544$	4.95177	+	0.746359i	0.212305	+	0.0319999i
$545$	−12.5411	−	8.55040i	−0.537203	−	0.366259i
$546$	1.34222	−	0.414020i	0.0574418	−	0.0177184i
$547$	−1.76800	+	23.5923i	−0.0755940	+	1.00873i	0.822453	+	0.568833i	$0.192605\pi$
$547$	−1.76800	+	23.5923i	−0.0755940	+	1.00873i	−0.898047	+	0.439899i	$0.855014\pi$
$548$	4.32156	+	5.41906i	0.184608	+	0.231491i
$549$	3.65391	+	1.12708i	0.155945	+	0.0481027i
$550$	−0.736570	+	1.87675i	−0.0314075	+	0.0800249i
$551$	7.23872	−	31.7149i	0.308380	−	1.35110i
$552$	−5.00552	−	8.66982i	−0.213049	−	0.369012i
$553$	1.06064	−	1.83707i	0.0451028	−	0.0781203i
$554$	22.9102	+	21.2575i	0.973360	+	0.903146i
$555$	11.3188	−	14.1933i	0.480454	−	0.602471i
$556$	4.87549	−	3.32406i	0.206767	−	0.140971i
$557$	−1.78595	+	0.860069i	−0.0756732	+	0.0364423i	−0.471338	−	0.881953i	$-0.656229\pi$
$557$	−1.78595	+	0.860069i	−0.0756732	+	0.0364423i	0.395664	+	0.918395i	$0.370514\pi$
$558$	−71.4765			−3.02584
$559$	0.600826	+	3.95947i	0.0254122	+	0.167468i
$560$	−0.676667			−0.0285944
$561$	30.9174	−	14.8891i	1.30534	−	0.628617i
$562$	2.57569	−	1.75608i	0.108649	−	0.0740756i
$563$	25.4107	−	31.8640i	1.07093	−	1.34291i	0.134954	−	0.990852i	$-0.456911\pi$
$563$	25.4107	−	31.8640i	1.07093	−	1.34291i	0.935979	−	0.352056i	$-0.114517\pi$
$564$	11.3752	+	10.5546i	0.478982	+	0.444430i
$565$	10.2041	−	17.6741i	0.429291	−	0.743554i
$566$	7.59370	+	13.1527i	0.319187	+	0.552848i
$567$	−5.79538	+	25.3912i	−0.243383	+	1.06633i
$568$	−2.02719	+	5.16520i	−0.0850591	+	0.216727i
$569$	39.2402	+	12.1040i	1.64503	+	0.507426i	0.972551	−	0.232688i	$-0.0747520\pi$
$569$	39.2402	+	12.1040i	1.64503	+	0.507426i	0.672482	+	0.740113i	$0.265228\pi$
$570$	−11.3476	−	14.2294i	−0.475297	−	0.596004i
$571$	−0.552907	+	7.37803i	−0.0231384	+	0.308761i	0.973612	+	0.228210i	$0.0732871\pi$
$571$	−0.552907	+	7.37803i	−0.0231384	+	0.308761i	−0.996750	+	0.0805513i	$0.974332\pi$
$572$	1.17659	−	0.362930i	0.0491957	−	0.0151749i
$573$	20.7804	+	14.1679i	0.868116	+	0.591871i
$574$	7.32291	+	1.10375i	0.305652	+	0.0460697i
$575$	0.655406	+	2.87152i	0.0273323	+	0.119751i
$576$	−6.26949	+	5.81723i	−0.261229	+	0.242385i
$577$	0.713900	+	9.52634i	0.0297201	+	0.396587i	0.992150	+	0.125056i	$0.0399109\pi$
$577$	0.713900	+	9.52634i	0.0297201	+	0.396587i	−0.962430	+	0.271531i	$0.912470\pi$
$578$	2.95089	+	7.51874i	0.122741	+	0.312738i
$579$	16.4758	−	2.48333i	0.684711	−	0.103204i
$580$	5.47352	+	2.63591i	0.227276	+	0.109450i
$581$	−2.58591	−	1.24531i	−0.107281	−	0.0516640i
$582$	13.8063	−	2.08096i	0.572288	−	0.0862585i
$583$	8.19154	+	20.8717i	0.339259	+	0.864418i
$584$	0.234959	+	3.13531i	0.00972267	+	0.129740i
$585$	−3.82893	+	3.55273i	−0.158307	+	0.146887i
$586$	−6.71275	−	29.4105i	−0.277301	−	1.21494i
$587$	−28.3775	−	4.27721i	−1.17126	−	0.176539i	−0.465540	−	0.885027i	$-0.654140\pi$
$587$	−28.3775	−	4.27721i	−1.17126	−	0.176539i	−0.705723	+	0.708488i	$0.749378\pi$
$588$	18.3723	+	12.5260i	0.757661	+	0.516565i
$589$	42.7625	−	13.1905i	1.76200	−	0.543505i
$590$	0.00493422	−	0.0658426i	0.000203139	−	0.00271070i
$591$	−8.80698	−	11.0436i	−0.362271	−	0.454273i
$592$	5.10380	+	1.57431i	0.209765	+	0.0647039i
$593$	6.39644	−	16.2979i	0.262670	−	0.669273i	−0.737310	−	0.675555i	$-0.763904\pi$
$593$	6.39644	−	16.2979i	0.262670	−	0.669273i	0.999980	+	0.00628170i	$0.00199954\pi$
$594$	−8.46684	+	37.0957i	−0.347399	+	1.52205i
$595$	−1.69427	−	2.93457i	−0.0694584	−	0.120306i
$596$	−2.20095	+	3.81217i	−0.0901546	+	0.156152i
$597$	−27.5990	−	25.6082i	−1.12955	−	1.04807i
$598$	1.12154	−	1.40637i	0.0458632	−	0.0575106i
$599$	−13.6385	+	9.29856i	−0.557253	+	0.379929i	−0.808950	−	0.587877i	$-0.799964\pi$
$599$	−13.6385	+	9.29856i	−0.557253	+	0.379929i	0.251697	+	0.967806i	$0.419011\pi$
$600$	3.06231	−	1.47473i	0.125018	−	0.0602057i
$601$	6.20739			0.253205			0.126602	−	0.991954i	$-0.459593\pi$
$601$	6.20739			0.253205			0.126602	+	0.991954i	$0.459593\pi$
$602$	3.01482	−	3.25570i	0.122875	−	0.132693i
$603$	−65.9152			−2.68427
$604$	2.06013	−	0.992107i	0.0838256	−	0.0403683i
$605$	5.73019	−	3.90678i	0.232965	−	0.158833i
$606$	28.0023	−	35.1138i	1.13752	−	1.42640i
$607$	−20.5114	−	19.0318i	−0.832533	−	0.772478i	0.143603	−	0.989635i	$-0.454131\pi$
$607$	−20.5114	−	19.0318i	−0.832533	−	0.772478i	−0.976137	+	0.217157i	$0.930322\pi$
$608$	2.67734	−	4.63729i	0.108581	−	0.188067i
$609$	6.98621	+	12.1005i	0.283096	+	0.490336i
$610$	0.0994873	−	0.435882i	0.00402812	−	0.0176484i
$611$	−1.01866	+	2.59550i	−0.0412105	+	0.105003i
$612$	−40.9260	−	12.6240i	−1.65434	−	0.510295i
$613$	10.1046	+	12.6707i	0.408120	+	0.511766i	0.942832	−	0.333268i	$-0.108151\pi$
$613$	10.1046	+	12.6707i	0.408120	+	0.511766i	−0.534712	+	0.845034i	$0.679580\pi$
$614$	0.0570017	−	0.760635i	0.00230040	−	0.0306967i
$615$	−35.5460	+	10.9645i	−1.43335	+	0.442130i
$616$	−1.12719	−	0.768504i	−0.0454157	−	0.0309639i
$617$	18.9339	+	2.85382i	0.762250	+	0.114891i	0.518652	−	0.854986i	$-0.326434\pi$
$617$	18.9339	+	2.85382i	0.762250	+	0.114891i	0.243598	+	0.969876i	$0.421672\pi$
$618$	0.838943	+	3.67565i	0.0337473	+	0.147856i
$619$	9.22450	−	8.55909i	0.370764	−	0.344019i	−0.472682	−	0.881233i	$-0.656714\pi$
$619$	9.22450	−	8.55909i	0.370764	−	0.344019i	0.843446	+	0.537215i	$0.180523\pi$
$620$	0.624541	+	8.33393i	0.0250822	+	0.334699i
$621$	20.3083	+	51.7446i	0.814943	+	2.07644i
$622$	−11.6016	+	1.74865i	−0.465180	+	0.0701147i
$623$	−4.39817	−	2.11805i	−0.176209	−	0.0848578i
$624$	−1.87023	−	0.900655i	−0.0748691	−	0.0360551i
$625$	−0.988831	+	0.149042i	−0.0395532	+	0.00596169i
$626$	−11.7514	−	29.9422i	−0.469682	−	1.19673i
$627$	−2.74211	−	36.5909i	−0.109509	−	1.46130i
$628$	12.5561	−	11.6504i	0.501043	−	0.464900i
$629$	5.95167	+	26.0760i	0.237309	+	1.03972i
$630$	5.72261	+	0.862545i	0.227994	+	0.0343646i
$631$	−12.6265	−	8.60864i	−0.502655	−	0.342704i	0.285299	−	0.958439i	$-0.407907\pi$
$631$	−12.6265	−	8.60864i	−0.502655	−	0.342704i	−0.787954	+	0.615734i	$0.788859\pi$
$632$	−2.99561	+	0.924022i	−0.119159	+	0.0367556i
$633$	5.83061	−	77.8040i	0.231746	−	3.09243i
$634$	−9.64300	−	12.0919i	−0.382973	−	0.480232i
$635$	−0.323369	−	0.0997462i	−0.0128325	−	0.00395831i
$636$	13.8099	−	35.1870i	0.547597	−	1.39525i
$637$	−0.889069	+	3.89526i	−0.0352262	+	0.154336i
$638$	6.12411	+	10.6073i	0.242456	+	0.419946i
$639$	23.7281	−	41.0983i	0.938671	−	1.62583i
$640$	0.733052	+	0.680173i	0.0289764	+	0.0268862i
$641$	6.56145	−	8.22780i	0.259162	−	0.324979i	−0.635179	−	0.772365i	$-0.719074\pi$
$641$	6.56145	−	8.22780i	0.259162	−	0.324979i	0.894341	+	0.447386i	$0.147645\pi$
$642$	39.8272	−	27.1537i	1.57185	−	1.07167i
$643$	21.4511	−	10.3303i	0.845949	−	0.407387i	0.0398764	−	0.999205i	$-0.487304\pi$
$643$	21.4511	−	10.3303i	0.845949	−	0.407387i	0.806072	+	0.591817i	$0.201589\pi$
$644$	−1.99303			−0.0785365
$645$	−6.54834	+	21.3045i	−0.257841	+	0.838863i
$646$	26.8147			1.05501
$647$	−29.0099	+	13.9704i	−1.14050	+	0.549234i	−0.906165	−	0.422924i	$-0.861004\pi$
$647$	−29.0099	+	13.9704i	−1.14050	+	0.549234i	−0.234330	+	0.972157i	$0.575290\pi$
$648$	31.8011	−	21.6816i	1.24926	−	0.851733i
$649$	0.0829981	−	0.104076i	0.00325796	−	0.00408535i
$650$	0.447693	+	0.415399i	0.0175600	+	0.0162933i
$651$	−9.61059	+	16.6460i	−0.376669	+	0.652410i
$652$	−7.90168	−	13.6861i	−0.309454	−	0.535990i
$653$	−8.50538	+	37.2645i	−0.332841	+	1.45827i	0.480762	+	0.876851i	$0.340360\pi$
$653$	−8.50538	+	37.2645i	−0.332841	+	1.45827i	−0.813603	+	0.581421i	$0.802497\pi$
$654$	−18.8482	+	48.0243i	−0.737022	+	1.87790i
$655$	14.4660	+	4.46215i	0.565231	+	0.174351i
$656$	−6.82364	−	8.55658i	−0.266418	−	0.334078i
$657$	2.00951	−	26.8150i	0.0783983	−	1.04615i
$658$	2.95204	−	0.910585i	0.115083	−	0.0354983i
$659$	5.56906	+	3.79692i	0.216940	+	0.147907i	0.666915	−	0.745134i	$-0.267615\pi$
$659$	5.56906	+	3.79692i	0.216940	+	0.147907i	−0.449975	+	0.893041i	$0.648567\pi$
$660$	6.77606	+	1.02133i	0.263758	+	0.0397551i
$661$	−3.50454	−	15.3544i	−0.136311	−	0.597216i	−0.996227	−	0.0867815i	$-0.972342\pi$
$661$	−3.50454	−	15.3544i	−0.136311	−	0.597216i	0.859917	−	0.510434i	$-0.170515\pi$
$662$	6.10489	−	5.66451i	0.237273	−	0.220157i
$663$	−0.776818	−	10.3659i	−0.0301691	−	0.402579i
$664$	1.54962	+	3.94838i	0.0601371	+	0.153227i
$665$	−3.58287	+	0.540031i	−0.138938	+	0.0209415i
$666$	−41.1563	−	19.8199i	−1.59478	−	0.768004i
$667$	16.1215	+	7.76373i	0.624229	+	0.300613i
$668$	−25.0213	+	3.77135i	−0.968103	+	0.145918i
$669$	13.1396	+	33.4791i	0.508006	+	1.29438i
$670$	0.575949	+	7.68550i	0.0222508	+	0.296917i
$671$	0.660765	−	0.613101i	0.0255086	−	0.0236685i
$672$	0.511782	+	2.24227i	0.0197424	+	0.0864973i
$673$	−37.3087	−	5.62337i	−1.43814	−	0.216765i	−0.616764	−	0.787148i	$-0.711557\pi$
$673$	−37.3087	−	5.62337i	−1.43814	−	0.216765i	−0.821379	+	0.570383i	$0.806795\pi$
$674$	13.7503	+	9.37476i	0.529640	+	0.361102i
$675$	−18.0343	+	5.56283i	−0.694139	+	0.214114i
$676$	−0.943618	+	12.5917i	−0.0362930	+	0.484296i
$677$	19.2485	+	24.1369i	0.739781	+	0.927656i	0.999274	−	0.0380888i	$-0.0121270\pi$
$677$	19.2485	+	24.1369i	0.739781	+	0.927656i	−0.259493	+	0.965745i	$0.583556\pi$
$678$	−66.2841	−	20.4459i	−2.54562	−	0.785221i
$679$	1.01552	−	2.58750i	0.0389720	−	0.0992991i
$680$	−1.11432	+	4.88215i	−0.0427322	+	0.187222i
$681$	23.6111	+	40.8956i	0.904779	+	1.56712i
$682$	−8.42464	+	14.5919i	−0.322596	+	0.558753i
$683$	7.41269	+	6.87797i	0.283639	+	0.263178i	0.809142	−	0.587613i	$-0.199932\pi$
$683$	7.41269	+	6.87797i	0.283639	+	0.263178i	−0.525503	+	0.850792i	$0.676123\pi$
$684$	−28.5536	+	35.8051i	−1.09177	+	1.36904i
$685$	−5.72686	+	3.90451i	−0.218812	+	0.149184i
$686$	8.25603	−	3.97590i	0.315217	−	0.151800i
$687$	56.5777			2.15858
$688$	−6.53861	+	0.496548i	−0.249282	+	0.0189307i
$689$	6.79199			0.258754
$690$	9.01964	−	4.34363i	0.343372	−	0.165359i
$691$	−8.48423	+	5.78445i	−0.322755	+	0.220051i	−0.713848	−	0.700300i	$-0.753049\pi$
$691$	−8.48423	+	5.78445i	−0.322755	+	0.220051i	0.391093	+	0.920351i	$0.372097\pi$
$692$	12.0269	−	15.0812i	0.457193	−	0.573302i
$693$	8.55309	+	7.93610i	0.324905	+	0.301468i
$694$	7.99359	−	13.8453i	0.303433	−	0.525561i
$695$	2.95041	+	5.11027i	0.111916	+	0.193844i
$696$	4.59481	−	20.1312i	0.174166	−	0.763070i
$697$	20.0227	−	51.0171i	0.758416	−	1.93241i
$698$	−19.1855	−	5.91794i	−0.726181	−	0.223997i
$699$	−21.5415	−	27.0122i	−0.814775	−	1.02170i
$700$	0.0505674	−	0.674775i	0.00191127	−	0.0255041i
$701$	−11.5522	+	3.56339i	−0.436322	+	0.134588i	−0.505132	−	0.863042i	$-0.668556\pi$
$701$	−11.5522	+	3.56339i	−0.436322	+	0.134588i	0.0688096	+	0.997630i	$0.478080\pi$
$702$	9.52327	+	6.49285i	0.359433	+	0.245057i
$703$	28.2804	+	4.26258i	1.06662	+	0.160766i
$704$	0.448628	+	1.96557i	0.0169083	+	0.0740802i
$705$	−11.3752	+	10.5546i	−0.428414	+	0.397510i
$706$	−2.50679	−	33.4508i	−0.0943444	−	1.25894i
$707$	−3.26662	−	8.32320i	−0.122854	−	0.313026i
$708$	−0.221914	+	0.0334481i	−0.00834004	+	0.00125706i
$709$	−23.1373	−	11.1423i	−0.868938	−	0.418459i	−0.0543664	−	0.998521i	$-0.517314\pi$
$709$	−23.1373	−	11.1423i	−0.868938	−	0.418459i	−0.814572	+	0.580062i	$0.803028\pi$
$710$	−4.99927	−	2.40752i	−0.187619	−	0.0903526i
$711$	26.5119	−	3.99602i	0.994273	−	0.149863i
$712$	2.63564	+	6.71550i	0.0987747	+	0.251674i
$713$	1.83951	+	24.5465i	0.0688900	+	0.919273i
$714$	−8.44282	+	7.83379i	−0.315965	+	0.293172i
$715$	0.273989	+	1.20042i	0.0102466	+	0.0448933i
$716$	−7.87383	−	1.18679i	−0.294259	−	0.0443524i
$717$	24.9900	+	17.0379i	0.933270	+	0.636293i
$718$	13.8178	−	4.26223i	0.515676	−	0.159065i
$719$	−0.717222	+	9.57066i	−0.0267479	+	0.356925i	0.967731	+	0.251986i	$0.0810838\pi$
$719$	−0.717222	+	9.57066i	−0.0267479	+	0.356925i	−0.994479	+	0.104939i	$0.966535\pi$
$720$	−5.33245	−	6.68668i	−0.198729	−	0.249198i
$721$	0.717234	+	0.221237i	0.0267112	+	0.00823931i
$722$	3.53381	−	9.00401i	0.131515	−	0.335095i
$723$	12.3195	−	53.9754i	0.458169	−	2.00737i
$724$	1.81550	+	3.14453i	0.0674724	+	0.116866i
$725$	−3.03758	+	5.26124i	−0.112813	+	0.195397i
$726$	−17.2798	−	16.0333i	−0.641312	−	0.595051i
$727$	18.2902	−	22.9352i	0.678347	−	0.850621i	−0.316854	−	0.948474i	$-0.602626\pi$
$727$	18.2902	−	22.9352i	0.678347	−	0.850621i	0.995201	+	0.0978539i	$0.0311978\pi$
$728$	−0.341449	+	0.232796i	−0.0126550	+	0.00862800i
$729$	−123.198	+	59.3292i	−4.56290	+	2.19738i
$730$	−3.14410			−0.116368
$731$	−18.5251	−	27.1133i	−0.685177	−	1.00282i
$732$	−1.51962			−0.0561669
$733$	−2.93873	+	1.41522i	−0.108545	+	0.0522723i	−0.487368	−	0.873197i	$-0.662043\pi$
$733$	−2.93873	+	1.41522i	−0.108545	+	0.0522723i	0.378824	+	0.925469i	$0.376329\pi$
$734$	18.5919	−	12.6757i	0.686239	−	0.467870i
$735$	−13.8640	+	17.3849i	−0.511380	+	0.641250i
$736$	2.15911	+	2.00336i	0.0795858	+	0.0738448i
$737$	−7.76916	+	13.4566i	−0.286181	+	0.495680i
$738$	46.8009	+	81.0615i	1.72276	+	2.98392i
$739$	−9.66102	+	42.3277i	−0.355386	+	1.55705i	0.409149	+	0.912467i	$0.365825\pi$
$739$	−9.66102	+	42.3277i	−0.355386	+	1.55705i	−0.764536	+	0.644581i	$0.777032\pi$
$740$	−1.95132	+	4.97188i	−0.0717319	+	0.182770i
$741$	−10.6214	−	3.27628i	−0.390188	−	0.120357i
$742$	−4.69198	−	5.88355i	−0.172248	−	0.215992i
$743$	2.67394	−	35.6813i	0.0980975	−	1.30902i	−0.703302	−	0.710891i	$-0.748292\pi$
$743$	2.67394	−	35.6813i	0.0980975	−	1.30902i	0.801400	−	0.598129i	$-0.204089\pi$
$744$	27.1437	−	8.37272i	0.995136	−	0.306959i
$745$	−3.63703	−	2.47968i	−0.133250	−	0.0908486i
$746$	11.6877	+	1.76164i	0.427917	+	0.0644982i
$747$	−8.07228	−	35.3670i	−0.295349	−	1.29401i
$748$	−7.40098	+	6.86710i	−0.270606	+	0.251086i
$749$	−0.717142	−	9.56959i	−0.0262038	−	0.349665i
$750$	1.24176	+	3.16396i	0.0453427	+	0.115531i
$751$	−20.3871	+	3.07286i	−0.743935	+	0.112130i	−0.510063	−	0.860137i	$-0.670378\pi$
$751$	−20.3871	+	3.07286i	−0.743935	+	0.112130i	−0.233872	+	0.972267i	$0.575140\pi$
$752$	−4.11333	−	1.98088i	−0.149998	−	0.0722352i
$753$	−71.9236	−	34.6366i	−2.62104	−	1.26223i
$754$	3.66881	−	0.552984i	0.133610	−	0.0201385i
$755$	0.835379	+	2.12851i	0.0304026	+	0.0774645i
$756$	−0.954345	−	12.7348i	−0.0347092	−	0.463162i
$757$	33.9161	−	31.4696i	1.23270	−	1.14378i	0.248144	−	0.968723i	$-0.420179\pi$
$757$	33.9161	−	31.4696i	1.23270	−	1.14378i	0.984558	−	0.175058i	$-0.0560112\pi$
$758$	3.67319	+	16.0933i	0.133416	+	0.584535i
$759$	19.9580	+	3.00819i	0.724430	+	0.109190i
$760$	4.42425	+	3.01640i	0.160484	+	0.109416i
$761$	35.4423	−	10.9325i	1.28478	−	0.396303i	0.424180	−	0.905578i	$-0.360563\pi$
$761$	35.4423	−	10.9325i	1.28478	−	0.396303i	0.860604	+	0.509275i	$0.170086\pi$
$762$	−0.0859548	+	1.14699i	−0.00311381	+	0.0415509i
$763$	6.40376	+	8.03007i	0.231832	+	0.290708i
$764$	−7.07088	−	2.18108i	−0.255815	−	0.0789086i
$765$	15.6471	−	39.8682i	0.565723	−	1.44144i
$766$	0.961851	−	4.21414i	0.0347531	−	0.152263i
$767$	−0.0201622	−	0.0349220i	−0.000728016	−	0.00126096i
$768$	1.69945	−	2.94354i	0.0613238	−	0.106216i
$769$	1.71814	+	1.59420i	0.0619576	+	0.0574883i	0.710544	−	0.703653i	$-0.248449\pi$
$769$	1.71814	+	1.59420i	0.0619576	+	0.0574883i	−0.648586	+	0.761141i	$0.724639\pi$
$770$	0.850590	−	1.06661i	0.0306531	−	0.0384378i
$771$	3.28071	−	2.23675i	0.118152	−	0.0805545i
$772$	−4.41667	+	2.12695i	−0.158959	+	0.0765508i
$773$	−4.58192			−0.164800			−0.0824001	−	0.996599i	$-0.526259\pi$
$773$	−4.58192			−0.164800			−0.0824001	+	0.996599i	$0.526259\pi$
$774$	55.9304	+	4.13541i	2.01038	+	0.148644i
$775$	−8.35730			−0.300203
$776$	−3.70104	+	1.78233i	−0.132860	+	0.0639819i
$777$	−10.1496	+	6.91989i	−0.364116	+	0.248250i
$778$	19.1178	−	23.9730i	0.685407	−	0.859474i
$779$	−42.9591	−	39.8602i	−1.53917	−	1.42814i
$780$	1.03790	−	1.79769i	0.0371628	−	0.0643678i
$781$	−5.59348	−	9.68819i	−0.200151	−	0.346671i
$782$	−3.28208	+	14.3797i	−0.117367	+	0.514218i
$783$	−41.8881	+	106.729i	−1.49696	+	3.81418i
$784$	−6.25147	−	1.92832i	−0.223267	−	0.0688687i
$785$	10.6795	+	13.3916i	0.381166	+	0.477968i
$786$	3.84519	−	51.3106i	0.137154	−	1.83019i
$787$	12.4727	−	3.84731i	0.444603	−	0.137142i	−0.0643667	−	0.997926i	$-0.520503\pi$
$787$	12.4727	−	3.84731i	0.444603	−	0.137142i	0.508970	+	0.860784i	$0.330027\pi$
$788$	3.43371	+	2.34106i	0.122321	+	0.0833969i
$789$	−51.6092	−	7.77884i	−1.83734	−	0.276934i
$790$	−0.697577	−	3.05628i	−0.0248187	−	0.108738i
$791$	−10.1231	+	9.39291i	−0.359938	+	0.333973i
$792$	−1.28857	−	17.1948i	−0.0457874	−	0.610991i
$793$	−0.0997564	−	0.254175i	−0.00354245	−	0.00902603i
$794$	−8.40824	+	1.26734i	−0.298397	+	0.0449762i
$795$	34.0566	+	16.4008i	1.20786	+	0.581676i
$796$	9.97997	+	4.80610i	0.353731	+	0.170348i
$797$	13.1145	−	1.97669i	0.464538	−	0.0700179i	0.0873968	−	0.996174i	$-0.472145\pi$
$797$	13.1145	−	1.97669i	0.464538	−	0.0700179i	0.377141	+	0.926156i	$0.376907\pi$
$798$	4.49932	+	11.4641i	0.159274	+	0.405824i
$799$	−1.70851	−	22.7985i	−0.0604428	−	0.806553i
$800$	−0.733052	+	0.680173i	−0.0259173	+	0.0240477i
$801$	−13.7295	−	60.1530i	−0.485109	−	2.12540i
$802$	−8.46339	−	1.27565i	−0.298853	−	0.0450448i
$803$	−5.23742	−	3.57082i	−0.184825	−	0.126011i
$804$	25.0318	−	7.72128i	0.882803	−	0.272309i
$805$	0.148940	−	1.98746i	0.00524943	−	0.0700488i
$806$	3.18230	+	3.99048i	0.112092	+	0.140558i
$807$	88.9320	+	27.4319i	3.13055	+	0.965648i
$808$	−4.82751	+	12.3003i	−0.169831	+	0.432723i
$809$	1.72577	−	7.56107i	0.0606747	−	0.265833i	−0.935488	−	0.353360i	$-0.885039\pi$
$809$	1.72577	−	7.56107i	0.0606747	−	0.265833i	0.996162	+	0.0875267i	$0.0278963\pi$
$810$	19.2445	+	33.3324i	0.676182	+	1.17118i
$811$	−15.6600	+	27.1239i	−0.549897	+	0.952449i	0.448384	+	0.893841i	$0.352000\pi$
$811$	−15.6600	+	27.1239i	−0.549897	+	0.952449i	−0.998281	+	0.0586081i	$0.981334\pi$
$812$	−3.01347	−	2.79609i	−0.105752	−	0.0981235i
$813$	−35.2580	+	44.2121i	−1.23655	+	1.55059i
$814$	−8.89715	+	6.06598i	−0.311845	+	0.212612i
$815$	14.2383	−	6.85682i	0.498747	−	0.240184i
$816$	17.0207			0.595845
$817$	−34.2249	+	7.84746i	−1.19738	+	0.274548i
$818$	31.3108			1.09476
$819$	3.18440	−	1.53353i	0.111272	−	0.0535858i
$820$	9.04258	−	6.16513i	0.315781	−	0.215296i
$821$	−5.78256	+	7.25110i	−0.201813	+	0.253065i	−0.872431	−	0.488738i	$-0.837457\pi$
$821$	−5.78256	+	7.25110i	−0.201813	+	0.253065i	0.670618	+	0.741803i	$0.266029\pi$
$822$	17.2697	+	16.0240i	0.602351	+	0.558900i
$823$	13.8418	−	23.9747i	0.482495	−	0.835705i	−0.517303	−	0.855802i	$-0.673064\pi$
$823$	13.8418	−	23.9747i	0.482495	−	0.835705i	0.999798	+	0.0200970i	$0.00639749\pi$
$824$	−0.554616	−	0.960623i	−0.0193210	−	0.0334649i
$825$	−1.52485	+	6.68079i	−0.0530884	+	0.232595i
$826$	−0.0163229	+	0.0415900i	−0.000567945	+	0.00144710i
$827$	−9.28717	−	2.86471i	−0.322947	−	0.0996159i	0.129043	−	0.991639i	$-0.458809\pi$
$827$	−9.28717	−	2.86471i	−0.322947	−	0.0996159i	−0.451990	+	0.892023i	$0.649286\pi$
$828$	−15.7060	−	19.6947i	−0.545822	−	0.684440i
$829$	−3.27140	+	43.6538i	−0.113620	+	1.51616i	0.591055	+	0.806631i	$0.298711\pi$
$829$	−3.27140	+	43.6538i	−0.113620	+	1.51616i	−0.704676	+	0.709529i	$0.748908\pi$
$830$	−4.05314	+	1.25023i	−0.140687	+	0.0433961i
$831$	87.7685	+	59.8395i	3.04466	+	2.07581i
$832$	0.603904	+	0.0910238i	0.0209366	+	0.00315568i
$833$	−7.29001	−	31.9396i	−0.252584	−	1.10664i
$834$	14.7024	−	13.6418i	0.509101	−	0.472377i
$835$	−1.89096	−	25.2332i	−0.0654395	−	0.873229i
$836$	3.94410	+	10.0494i	0.136410	+	0.347566i
$837$	−155.963	+	23.5077i	−5.39088	+	0.812545i
$838$	23.6218	+	11.3757i	0.816003	+	0.392966i
$839$	6.92239	+	3.33365i	0.238988	+	0.115090i	0.549545	−	0.835464i	$-0.314801\pi$
$839$	6.92239	+	3.33365i	0.238988	+	0.115090i	−0.310557	+	0.950555i	$0.600516\pi$
$840$	−2.27424	+	0.342787i	−0.0784688	+	0.0118273i
$841$	2.88892	+	7.36085i	0.0996179	+	0.253822i
$842$	2.76847	+	36.9426i	0.0954077	+	1.27313i
$843$	7.76716	−	7.20687i	0.267515	−	0.248218i
$844$	5.10798	+	22.3795i	0.175824	+	0.770336i
$845$	−12.4860	−	1.88196i	−0.429531	−	0.0647414i
$846$	32.2617	+	21.9956i	1.10918	+	0.756226i
$847$	−4.48438	+	1.38325i	−0.154085	+	0.0475289i
$848$	−0.831088	+	11.0901i	−0.0285397	+	0.380836i
$849$	32.1849	+	40.3586i	1.10458	+	1.38510i
$850$	−4.78522	−	1.47605i	−0.164132	−	0.0506280i
$851$	−5.74735	+	14.6440i	−0.197017	+	0.501990i
$852$	−4.19669	+	18.3869i	−0.143776	+	0.629925i
$853$	−13.9181	−	24.1069i	−0.476548	−	0.825405i	0.523091	−	0.852277i	$-0.324779\pi$
$853$	−13.9181	−	24.1069i	−0.476548	−	0.825405i	−0.999639	+	0.0268719i	$0.991445\pi$
$854$	−0.151266	+	0.262001i	−0.00517622	+	0.00896548i
$855$	−33.5711	−	31.1495i	−1.14811	−	1.06529i
$856$	−8.84227	+	11.0879i	−0.302223	+	0.378975i
$857$	14.1157	−	9.62392i	0.482183	−	0.328747i	−0.297713	−	0.954655i	$-0.596224\pi$
$857$	14.1157	−	9.62392i	0.482183	−	0.328747i	0.779897	+	0.625908i	$0.215272\pi$
$858$	3.77060	−	1.81583i	0.128726	−	0.0619913i
$859$	32.4749			1.10803			0.554014	−	0.832507i	$-0.313095\pi$
$859$	32.4749			1.10803			0.554014	+	0.832507i	$0.313095\pi$
$860$	−0.00652849	−	6.55744i	−0.000222620	−	0.223607i
$861$	25.1711			0.857827
$862$	−19.7704	+	9.52094i	−0.673384	+	0.324285i
$863$	−28.6858	+	19.5577i	−0.976478	+	0.665751i	−0.942687	−	0.333678i	$-0.891710\pi$
$863$	−28.6858	+	19.5577i	−0.976478	+	0.665751i	−0.0337904	+	0.999429i	$0.510758\pi$
$864$	−11.7670	+	14.7553i	−0.400320	+	0.501985i
$865$	14.1403	+	13.1203i	0.480784	+	0.446102i
$866$	−14.1003	+	24.4224i	−0.479147	+	0.829906i
$867$	13.7266	+	23.7752i	0.466181	+	0.807448i
$868$	1.25838	−	5.51332i	0.0427122	−	0.187134i
$869$	2.30906	−	5.88339i	0.0783295	−	0.199580i
$870$	19.7315	+	6.08637i	0.668961	+	0.206347i
$871$	2.93470	+	3.67999i	0.0994384	+	0.124692i
$872$	1.13430	−	15.1361i	0.0384121	−	0.512574i
$873$	33.5719	−	10.3556i	1.13624	−	0.350482i
$874$	13.0310	+	8.88442i	0.440782	+	0.300520i
$875$	0.669109	+	0.100852i	0.0226200	+	0.00340942i
$876$	2.37797	+	10.4186i	0.0803442	+	0.352011i
$877$	−41.1278	+	38.1610i	−1.38879	+	1.28860i	−0.476427	+	0.879214i	$0.658068\pi$
$877$	−41.1278	+	38.1610i	−1.38879	+	1.28860i	−0.912359	+	0.409391i	$0.865741\pi$
$878$	0.576496	+	7.69281i	0.0194558	+	0.259620i
$879$	−37.4600	−	95.4465i	−1.26349	−	3.21933i
$880$	−1.99360	+	0.300487i	−0.0672042	+	0.0101294i
$881$	4.20107	+	2.02313i	0.141538	+	0.0681610i	0.503312	−	0.864105i	$-0.332115\pi$
$881$	4.20107	+	2.02313i	0.141538	+	0.0681610i	−0.361774	+	0.932266i	$0.617829\pi$
$882$	50.4111	+	24.2767i	1.69743	+	0.817438i
$883$	35.2640	−	5.31519i	1.18673	−	0.178870i	0.474137	−	0.880451i	$-0.342760\pi$
$883$	35.2640	−	5.31519i	1.18673	−	0.178870i	0.712590	+	0.701580i	$0.247522\pi$
$884$	1.11733	+	2.84692i	0.0375800	+	0.0957522i
$885$	−0.0167710	−	0.223793i	−0.000563750	−	0.00752272i
$886$	−15.8787	+	14.7332i	−0.533454	+	0.494973i
$887$	−1.12561	−	4.93160i	−0.0377941	−	0.165587i	0.952509	−	0.304511i	$-0.0984929\pi$
$887$	−1.12561	−	4.93160i	−0.0377941	−	0.165587i	−0.990303	+	0.138924i	$0.955636\pi$
$888$	17.9511	+	2.70569i	0.602400	+	0.0907971i
$889$	0.189198	+	0.128993i	0.00634548	+	0.00432628i
$890$	−6.89368	+	2.12642i	−0.231077	+	0.0712777i
$891$	−5.79892	+	77.3813i	−0.194271	+	2.59237i
$892$	−6.59740	−	8.27288i	−0.220897	−	0.276996i
$893$	−23.3605	−	7.20576i	−0.781729	−	0.241131i
$894$	−5.46612	+	13.9274i	−0.182814	+	0.465803i
$895$	1.77188	−	7.76312i	0.0592275	−	0.259493i
$896$	−0.338333	−	0.586011i	−0.0113029	−	0.0195772i
$897$	3.05700	−	5.29488i	0.102070	−	0.176791i
$898$	10.6061	+	9.84104i	0.353931	+	0.328400i
$899$	−31.6557	+	39.6950i	−1.05578	+	1.32390i
$900$	7.06648	−	4.81784i	0.235549	−	0.160595i
$901$	−50.1764	+	24.1637i	−1.67162	+	0.805009i
$902$	22.0649			0.734682
$903$	8.48338	−	12.4695i	0.282309	−	0.414959i
$904$	20.4083			0.678768
$905$	−3.27141	+	1.57543i	−0.108745	+	0.0523691i
$906$	6.42141	−	4.37804i	0.213337	−	0.145451i
$907$	−1.54948	+	1.94299i	−0.0514496	+	0.0645158i	−0.806891	−	0.590701i	$-0.798851\pi$
$907$	−1.54948	+	1.94299i	−0.0514496	+	0.0645158i	0.755441	+	0.655217i	$0.227423\pi$
$908$	−10.1845	−	9.44986i	−0.337986	−	0.313605i
$909$	56.5057	−	97.8707i	1.87418	−	3.24617i
$910$	−0.206629	−	0.357891i	−0.00684968	−	0.0118640i
$911$	3.70581	−	16.2362i	0.122779	−	0.537930i	−0.875703	−	0.482850i	$-0.839602\pi$
$911$	3.70581	−	16.2362i	0.122779	−	0.537930i	0.998482	−	0.0550797i	$-0.0175413\pi$
$912$	6.64924	−	16.9420i	0.220178	−	0.561005i
$913$	−8.17161	−	2.52061i	−0.270441	−	0.0834199i
$914$	−9.20483	−	11.5425i	−0.304469	−	0.381792i
$915$	0.113562	−	1.51538i	0.00375423	−	0.0500968i
$916$	−15.9063	+	4.90645i	−0.525560	+	0.162114i
$917$	−8.46377	−	5.77050i	−0.279498	−	0.190559i
$918$	−93.4534	−	14.0858i	−3.08442	−	0.464902i
$919$	−1.12428	−	4.92581i	−0.0370867	−	0.162487i	0.952994	−	0.302991i	$-0.0979851\pi$
$919$	−1.12428	−	4.92581i	−0.0370867	−	0.162487i	−0.990080	+	0.140503i	$0.955128\pi$
$920$	−2.15911	+	2.00336i	−0.0711837	+	0.0660488i
$921$	−0.193744	−	2.58533i	−0.00638407	−	0.0851894i
$922$	−9.48754	−	24.1739i	−0.312455	−	0.796123i
$923$	−3.35092	+	0.505070i	−0.110297	+	0.0166246i
$924$	−4.17773	−	2.01189i	−0.137437	−	0.0661862i
$925$	−4.81215	−	2.31741i	−0.158223	−	0.0761960i
$926$	−11.8143	+	1.78071i	−0.388241	+	0.0585179i
$927$	3.46592	+	8.83101i	0.113836	+	0.290048i
$928$	0.453997	+	6.05816i	0.0149032	+	0.198869i
$929$	−30.0121	+	27.8471i	−0.984664	+	0.913635i	−0.996269	−	0.0862980i	$-0.972496\pi$
$929$	−30.0121	+	27.8471i	−0.984664	+	0.913635i	0.0116054	+	0.999933i	$0.496306\pi$
$930$	6.32086	+	27.6935i	0.207269	+	0.908106i
$931$	−34.6397	−	5.22110i	−1.13527	−	0.171115i
$932$	8.39872	+	5.72615i	0.275109	+	0.187566i
$933$	−38.1064	+	11.7543i	−1.24755	+	0.384817i
$934$	−1.12131	+	14.9629i	−0.0366905	+	0.489600i
$935$	−6.29482	−	7.89346i	−0.205863	−	0.258144i
$936$	−4.99122	−	1.53959i	−0.163143	−	0.0503230i
$937$	4.82298	−	12.2888i	0.157560	−	0.401456i	−0.830194	−	0.557474i	$-0.811771\pi$
$937$	4.82298	−	12.2888i	0.157560	−	0.401456i	0.987754	+	0.156018i	$0.0498658\pi$
$938$	1.16047	−	5.08435i	0.0378907	−	0.166010i
$939$	−54.6641	−	94.6810i	−1.78390	−	3.08980i
$940$	2.28273	−	3.95380i	0.0744544	−	0.128959i
$941$	−19.8264	−	18.3962i	−0.646321	−	0.599699i	0.287352	−	0.957825i	$-0.407225\pi$
$941$	−19.8264	−	18.3962i	−0.646321	−	0.599699i	−0.933673	+	0.358126i	$0.883416\pi$
$942$	36.2985	−	45.5169i	1.18267	−	1.48302i
$943$	26.6337	−	18.1586i	0.867314	−	0.591325i
$944$	0.0594885	−	0.0286481i	0.00193618	−	0.000932418i
$945$	12.7706			0.415426
$946$	7.43653	−	10.9308i	0.241782	−	0.355389i
$947$	39.3006			1.27710			0.638549	−	0.769581i	$-0.279535\pi$
$947$	39.3006			1.27710			0.638549	+	0.769581i	$0.279535\pi$
$948$	−9.59998	+	4.62311i	−0.311793	+	0.150152i
$949$	−1.58653	+	1.08168i	−0.0515009	+	0.0351127i
$950$	−3.33859	+	4.18646i	−0.108318	+	0.135827i
$951$	−38.5352	−	35.7554i	−1.24959	−	1.15945i
$952$	1.69427	−	2.93457i	0.0549117	−	0.0951099i
$953$	21.8555	+	37.8549i	0.707970	+	1.22624i	0.965609	+	0.259999i	$0.0837224\pi$
$953$	21.8555	+	37.8549i	0.707970	+	1.22624i	−0.257638	+	0.966241i	$0.582944\pi$
$954$	21.1651	−	92.7302i	0.685244	−	3.00225i
$955$	2.70339	−	6.88812i	0.0874795	−	0.222894i
$956$	−8.50326	−	2.62291i	−0.275015	−	0.0848309i
$957$	25.9562	+	32.5481i	0.839046	+	1.05213i
$958$	2.40861	−	32.1407i	0.0778187	−	1.03842i
$959$	4.48177	−	1.38244i	0.144724	−	0.0446414i
$960$	2.80831	+	1.91467i	0.0906378	+	0.0617958i
$961$	−38.4105	−	5.78945i	−1.23905	−	0.186757i
$962$	0.725849	+	3.18015i	0.0234023	+	0.102532i
$963$	88.9133	−	82.4995i	2.86519	−	2.65851i
$964$	1.21725	+	16.2431i	0.0392050	+	0.523154i
$965$	−1.79095	−	4.56326i	−0.0576527	−	0.146897i
$966$	−6.69848	+	1.00963i	−0.215520	+	0.0324844i
$967$	34.4353	+	16.5832i	1.10737	+	0.533279i	0.895967	−	0.444121i	$-0.146484\pi$
$967$	34.4353	+	16.5832i	1.10737	+	0.533279i	0.211399	+	0.977400i	$0.432198\pi$
$968$	6.24846	+	3.00910i	0.200833	+	0.0967162i
$969$	90.1226	−	13.5838i	2.89516	−	0.436375i
$970$	−1.50077	−	3.82389i	−0.0481867	−	0.122778i
$971$	−2.97035	−	39.6365i	−0.0953230	−	1.27200i	−0.815725	−	0.578440i	$-0.803662\pi$
$971$	−2.97035	−	39.6365i	−0.0953230	−	1.27200i	0.720402	−	0.693557i	$-0.243957\pi$
$972$	54.3941	−	50.4703i	1.74469	−	1.61884i
$973$	−0.888503	−	3.89279i	−0.0284841	−	0.124797i
$974$	−22.2595	−	3.35508i	−0.713240	−	0.107504i
$975$	1.71511	+	1.16934i	0.0549273	+	0.0374488i
$976$	0.427229	−	0.131783i	0.0136753	−	0.00421826i
$977$	−1.80896	+	24.1389i	−0.0578737	+	0.772271i	0.890473	+	0.455036i	$0.150373\pi$
$977$	−1.80896	+	24.1389i	−0.0578737	+	0.772271i	−0.948347	+	0.317235i	$0.897246\pi$
$978$	−33.4902	−	41.9954i	−1.07090	−	1.34287i
$979$	−13.8985	−	4.28711i	−0.444197	−	0.137017i
$980$	2.39011	−	6.08989i	0.0763491	−	0.194534i
$981$	−28.8868	+	126.561i	−0.922284	+	4.04079i
$982$	−7.76045	−	13.4415i	−0.247646	−	0.428935i
$983$	−24.8674	+	43.0716i	−0.793147	+	1.37377i	0.130861	+	0.991401i	$0.458226\pi$
$983$	−24.8674	+	43.0716i	−0.793147	+	1.37377i	−0.924009	+	0.382371i	$0.875108\pi$
$984$	−27.2685	−	25.3015i	−0.869288	−	0.806581i
$985$	−2.59112	+	3.24916i	−0.0825599	+	0.103527i
$986$	−25.1363	+	17.1376i	−0.800502	+	0.545773i
$987$	9.46038	−	4.55588i	0.301127	−	0.145015i
$988$	3.27024			0.104040
$989$	−0.0192288	−	19.3141i	−0.000611441	−	0.614152i
$990$	17.2430			0.548019
$991$	−17.9282	+	8.63377i	−0.569508	+	0.274261i	−0.696398	−	0.717656i	$-0.745215\pi$
$991$	−17.9282	+	8.63377i	−0.569508	+	0.274261i	0.126889	+	0.991917i	$0.459501\pi$
$992$	−6.90512	+	4.70783i	−0.219238	+	0.149474i
$993$	17.6487	−	22.1307i	0.560064	−	0.702298i
$994$	2.75237	+	2.55382i	0.0872997	+	0.0810023i
$995$	−5.53847	+	9.59290i	−0.175581	+	0.304116i
$996$	7.20838	+	12.4853i	0.228406	+	0.395611i
$997$	−6.75512	+	29.5961i	−0.213937	+	0.937319i	0.747925	+	0.663783i	$0.231050\pi$
$997$	−6.75512	+	29.5961i	−0.213937	+	0.937319i	−0.961862	+	0.273535i	$0.911807\pi$
$998$	−2.56411	+	6.53325i	−0.0811656	+	0.206806i
$999$	−96.3226	−	29.7116i	−3.04751	−	0.940033i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.b.31.1	✓	48
43.25	even	21	inner	430.2.q.b.111.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.b.31.1	✓	48	1.1	even	1	trivial
430.2.q.b.111.1	yes	48	43.25	even	21	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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.900969 + 0.433884i) q^{2} +(-2.80831 + 1.91467i) q^{3} +(0.623490 - 0.781831i) q^{4} +(0.733052 + 0.680173i) q^{5} +(1.69945 - 2.94354i) q^{6} +(-0.338333 - 0.586011i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(3.12461 - 7.96138i) q^{9} +O(q^{10})\)	\(q+(-0.900969 + 0.433884i) q^{2} +(-2.80831 + 1.91467i) q^{3} +(0.623490 - 0.781831i) q^{4} +(0.733052 + 0.680173i) q^{5} +(1.69945 - 2.94354i) q^{6} +(-0.338333 - 0.586011i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(3.12461 - 7.96138i) q^{9} +(-0.955573 - 0.294755i) q^{10} +(-1.25703 - 1.57626i) q^{11} +(-0.254001 + 3.38941i) q^{12} +(-0.583592 + 0.180014i) q^{13} +(0.559088 + 0.381180i) q^{14} +(-3.36095 - 0.506581i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(3.67091 - 3.40610i) q^{17} +(0.639135 + 8.52867i) q^{18} +(-1.95629 - 4.98454i) q^{19} +(0.988831 - 0.149042i) q^{20} +(2.07216 + 0.997902i) q^{21} +(1.81646 + 0.874761i) q^{22} +(2.91247 - 0.438985i) q^{23} +(-1.24176 - 3.16396i) q^{24} +(0.0747301 + 0.997204i) q^{25} +(0.447693 - 0.415399i) q^{26} +(4.19958 + 18.3996i) q^{27} +(-0.669109 - 0.100852i) q^{28} +(5.01953 + 3.42225i) q^{29} +(3.24791 - 1.00185i) q^{30} +(-0.624541 + 8.33393i) q^{31} +(0.623490 + 0.781831i) q^{32} +(6.54816 + 2.01984i) q^{33} +(-1.82952 + 4.66154i) q^{34} +(0.150573 - 0.659701i) q^{35} +(-4.27629 - 7.40676i) q^{36} +(-2.67054 + 4.62552i) q^{37} +(3.92526 + 3.64211i) q^{38} +(1.29424 - 1.62293i) q^{39} +(-0.826239 + 0.563320i) q^{40} +(9.86045 - 4.74854i) q^{41} -2.29993 q^{42} +(0.970879 - 6.48517i) q^{43} -2.01612 q^{44} +(7.70561 - 3.71083i) q^{45} +(-2.43358 + 1.65919i) q^{46} +(2.84652 - 3.56942i) q^{47} +(2.49158 + 2.31185i) q^{48} +(3.27106 - 5.66564i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-3.78747 + 16.5940i) q^{51} +(-0.223123 + 0.568508i) q^{52} +(-10.6271 - 3.27803i) q^{53} +(-11.7670 - 14.7553i) q^{54} +(0.150665 - 2.01048i) q^{55} +(0.646605 - 0.199451i) q^{56} +(15.0376 + 10.2525i) q^{57} +(-6.00730 - 0.905454i) q^{58} +(0.0146924 + 0.0643718i) q^{59} +(-2.49158 + 2.31185i) q^{60} +(0.0334112 + 0.445842i) q^{61} +(-3.05326 - 7.77959i) q^{62} +(-5.72261 + 0.862545i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(-0.550244 - 0.264984i) q^{65} +(-6.77606 + 1.02133i) q^{66} +(-2.81570 - 7.17429i) q^{67} +(-0.374226 - 4.99370i) q^{68} +(-7.33861 + 6.80924i) q^{69} +(0.150573 + 0.659701i) q^{70} +(5.48679 + 0.827001i) q^{71} +(7.06648 + 4.81784i) q^{72} +(3.00442 - 0.926740i) q^{73} +(0.399140 - 5.32615i) q^{74} +(-2.11919 - 2.65737i) q^{75} +(-5.11679 - 1.57832i) q^{76} +(-0.498413 + 1.26994i) q^{77} +(-0.461909 + 2.02375i) q^{78} +(1.56744 + 2.71489i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-28.2144 - 26.1791i) q^{81} +(-6.82364 + 8.55658i) q^{82} +(3.50456 - 2.38937i) q^{83} +(2.07216 - 0.997902i) q^{84} +5.00770 q^{85} +(1.93908 + 6.26418i) q^{86} -20.6489 q^{87} +(1.81646 - 0.874761i) q^{88} +(5.96064 - 4.06390i) q^{89} +(-5.33245 + 6.68668i) q^{90} +(0.302939 + 0.281086i) q^{91} +(1.47268 - 2.55076i) q^{92} +(-14.2028 - 24.6000i) q^{93} +(-1.01591 + 4.45099i) q^{94} +(1.95629 - 4.98454i) q^{95} +(-3.24791 - 1.00185i) q^{96} +(2.56120 + 3.21165i) q^{97} +(-0.488893 + 6.52383i) q^{98} +(-16.4770 + 5.08247i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9}+O(q^{10}) \) 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9	\( 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9} - 4 q^{10} - 9 q^{11} - q^{12} - 11 q^{13} + 7 q^{14} - 6 q^{15} - 8 q^{16} - 11 q^{17} - 15 q^{18} + 31 q^{19} - 4 q^{20} + 4 q^{21} + 12 q^{22} + 4 q^{23} + 6 q^{24} + 4 q^{25} + 31 q^{26} + 44 q^{27} + 13 q^{29} + q^{30} - q^{31} - 8 q^{32} - 30 q^{33} - 25 q^{34} + 14 q^{35} - 36 q^{36} - 27 q^{37} - 4 q^{38} + 4 q^{39} - 4 q^{40} + 16 q^{41} + 4 q^{42} - 7 q^{43} - 30 q^{44} + 12 q^{45} - 52 q^{46} - 43 q^{47} - q^{48} - 23 q^{49} - 24 q^{50} - 7 q^{51} - 25 q^{52} + 73 q^{53} - 61 q^{54} + 27 q^{55} + 7 q^{56} + 136 q^{57} - 36 q^{58} + 58 q^{59} + q^{60} - 61 q^{61} + 27 q^{62} + 32 q^{63} - 8 q^{64} - q^{65} + 12 q^{66} + 39 q^{67} + 17 q^{68} - 34 q^{69} + 14 q^{70} + 60 q^{71} + 27 q^{72} + 3 q^{73} + 29 q^{74} - 12 q^{75} + 17 q^{76} - 27 q^{77} - 17 q^{78} - 2 q^{79} + 24 q^{80} - 165 q^{81} + 2 q^{82} + 74 q^{83} + 4 q^{84} - 8 q^{85} + 14 q^{86} + 88 q^{87} + 12 q^{88} + 23 q^{89} - 2 q^{90} - 39 q^{91} + 4 q^{92} - 46 q^{93} + 55 q^{94} - 31 q^{95} - q^{96} - 85 q^{97} + 33 q^{98} - 168 q^{99}+O(q^{100}) \) 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9 - 4 * q^10 - 9 * q^11 - q^12 - 11 * q^13 + 7 * q^14 - 6 * q^15 - 8 * q^16 - 11 * q^17 - 15 * q^18 + 31 * q^19 - 4 * q^20 + 4 * q^21 + 12 * q^22 + 4 * q^23 + 6 * q^24 + 4 * q^25 + 31 * q^26 + 44 * q^27 + 13 * q^29 + q^30 - q^31 - 8 * q^32 - 30 * q^33 - 25 * q^34 + 14 * q^35 - 36 * q^36 - 27 * q^37 - 4 * q^38 + 4 * q^39 - 4 * q^40 + 16 * q^41 + 4 * q^42 - 7 * q^43 - 30 * q^44 + 12 * q^45 - 52 * q^46 - 43 * q^47 - q^48 - 23 * q^49 - 24 * q^50 - 7 * q^51 - 25 * q^52 + 73 * q^53 - 61 * q^54 + 27 * q^55 + 7 * q^56 + 136 * q^57 - 36 * q^58 + 58 * q^59 + q^60 - 61 * q^61 + 27 * q^62 + 32 * q^63 - 8 * q^64 - q^65 + 12 * q^66 + 39 * q^67 + 17 * q^68 - 34 * q^69 + 14 * q^70 + 60 * q^71 + 27 * q^72 + 3 * q^73 + 29 * q^74 - 12 * q^75 + 17 * q^76 - 27 * q^77 - 17 * q^78 - 2 * q^79 + 24 * q^80 - 165 * q^81 + 2 * q^82 + 74 * q^83 + 4 * q^84 - 8 * q^85 + 14 * q^86 + 88 * q^87 + 12 * q^88 + 23 * q^89 - 2 * q^90 - 39 * q^91 + 4 * q^92 - 46 * q^93 + 55 * q^94 - 31 * q^95 - q^96 - 85 * q^97 + 33 * q^98 - 168 * q^99

Introduction

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