LMFDB - Embedded newform 108.2.l.a.47.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,2,Mod(11,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("108.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	108.l (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.862384341830$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			47.3
Character	$\chi$	$=$	108.47
Dual form			108.2.l.a.23.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30706 - 0.540000i) q^{2} +(-1.71606 + 0.234845i) q^{3} +(1.41680 + 1.41162i) q^{4} +(0.137245 - 0.0242000i) q^{5} +(2.36980 + 0.619715i) q^{6} +(2.98823 - 3.56123i) q^{7} +(-1.08956 - 2.61015i) q^{8} +(2.88970 - 0.806015i) q^{9} +O(q^{10})$	\(q+(-1.30706 - 0.540000i) q^{2} +(-1.71606 + 0.234845i) q^{3} +(1.41680 + 1.41162i) q^{4} +(0.137245 - 0.0242000i) q^{5} +(2.36980 + 0.619715i) q^{6} +(2.98823 - 3.56123i) q^{7} +(-1.08956 - 2.61015i) q^{8} +(2.88970 - 0.806015i) q^{9} +(-0.192456 - 0.0424817i) q^{10} +(0.182573 - 1.03542i) q^{11} +(-2.76282 - 2.08970i) q^{12} +(-1.46220 - 0.532196i) q^{13} +(-5.82886 + 3.04109i) q^{14} +(-0.229837 + 0.0737600i) q^{15} +(0.0146392 + 3.99997i) q^{16} +(5.25631 - 3.03473i) q^{17} +(-4.21225 - 0.506929i) q^{18} +(3.80088 + 2.19444i) q^{19} +(0.228610 + 0.159452i) q^{20} +(-4.29163 + 6.81305i) q^{21} +(-0.797761 + 1.25477i) q^{22} +(-1.94128 + 1.62893i) q^{23} +(2.48273 + 4.22328i) q^{24} +(-4.68021 + 1.70346i) q^{25} +(1.62379 + 1.48520i) q^{26} +(-4.76959 + 2.06180i) q^{27} +(9.26084 - 0.827297i) q^{28} +(0.210458 + 0.578229i) q^{29} +(0.340241 + 0.0277036i) q^{30} +(-3.18818 - 3.79952i) q^{31} +(2.14085 - 5.23610i) q^{32} +(-0.0701412 + 1.81972i) q^{33} +(-8.50906 + 1.12816i) q^{34} +(0.323938 - 0.561078i) q^{35} +(5.23191 + 2.93720i) q^{36} +(-1.43991 - 2.49400i) q^{37} +(-3.78297 - 4.92073i) q^{38} +(2.63420 + 0.569889i) q^{39} +(-0.212703 - 0.331863i) q^{40} +(-2.25297 + 6.18999i) q^{41} +(9.28846 - 6.58756i) q^{42} +(-2.15530 - 0.380038i) q^{43} +(1.72029 - 1.20926i) q^{44} +(0.377091 - 0.180553i) q^{45} +(3.41698 - 1.08081i) q^{46} +(8.46639 + 7.10414i) q^{47} +(-0.964496 - 6.86074i) q^{48} +(-2.53733 - 14.3899i) q^{49} +(7.03718 + 0.300799i) q^{50} +(-8.30743 + 6.44219i) q^{51} +(-1.32038 - 2.81809i) q^{52} -8.73360i q^{53} +(7.34750 - 0.119308i) q^{54} -0.146525i q^{55} +(-12.5512 - 3.91953i) q^{56} +(-7.03787 - 2.87316i) q^{57} +(0.0371630 - 0.869426i) q^{58} +(1.42477 + 8.08025i) q^{59} +(-0.429755 - 0.219941i) q^{60} +(8.56477 + 7.18670i) q^{61} +(2.11539 + 6.68781i) q^{62} +(5.76467 - 12.6994i) q^{63} +(-5.62571 + 5.68782i) q^{64} +(-0.213559 - 0.0376562i) q^{65} +(1.07433 - 2.34060i) q^{66} +(-1.93034 + 5.30357i) q^{67} +(11.7310 + 3.12033i) q^{68} +(2.94880 - 3.25123i) q^{69} +(-0.726388 + 0.558434i) q^{70} +(-2.33277 - 4.04048i) q^{71} +(-5.25231 - 6.66432i) q^{72} +(-5.64518 + 9.77774i) q^{73} +(0.535287 + 4.03736i) q^{74} +(7.63146 - 4.02235i) q^{75} +(2.28736 + 8.47449i) q^{76} +(-3.14181 - 3.74426i) q^{77} +(-3.13531 - 2.16734i) q^{78} +(-0.572755 - 1.57363i) q^{79} +(0.0988087 + 0.548623i) q^{80} +(7.70068 - 4.65828i) q^{81} +(6.28736 - 6.87406i) q^{82} +(-2.20553 + 0.802749i) q^{83} +(-15.6978 + 3.59455i) q^{84} +(0.647964 - 0.543706i) q^{85} +(2.61188 + 1.66060i) q^{86} +(-0.496952 - 0.942848i) q^{87} +(-2.90152 + 0.651613i) q^{88} +(7.63741 + 4.40946i) q^{89} +(-0.590379 + 0.0323630i) q^{90} +(-6.26466 + 3.61690i) q^{91} +(-5.04983 - 0.432493i) q^{92} +(6.36339 + 5.77146i) q^{93} +(-7.22981 - 13.8574i) q^{94} +(0.574758 + 0.209195i) q^{95} +(-2.44415 + 9.48821i) q^{96} +(-0.978443 + 5.54902i) q^{97} +(-4.45412 + 20.1786i) q^{98} +(-0.306985 - 3.13921i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) $ 96 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 9 * q^8 - 12 * q^9	$ 96 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 15 q^{12} - 12 q^{13} - 21 q^{14} - 6 q^{16} - 18 q^{17} - 27 q^{18} - 27 q^{20} - 12 q^{21} - 6 q^{22} - 12 q^{24} - 12 q^{25} - 12 q^{28} - 24 q^{29} + 9 q^{30} + 24 q^{32} - 42 q^{33} - 12 q^{34} + 24 q^{36} - 6 q^{37} + 18 q^{38} - 21 q^{40} - 42 q^{41} + 54 q^{42} + 63 q^{44} - 24 q^{45} - 3 q^{46} + 69 q^{48} - 12 q^{49} + 87 q^{50} - 33 q^{52} + 78 q^{54} + 99 q^{56} - 24 q^{57} - 33 q^{58} + 102 q^{60} - 12 q^{61} + 90 q^{62} - 3 q^{64} + 12 q^{65} + 87 q^{66} + 51 q^{68} + 12 q^{69} - 21 q^{70} + 12 q^{72} - 6 q^{73} + 21 q^{74} - 18 q^{76} + 12 q^{77} - 24 q^{78} + 12 q^{81} - 12 q^{82} - 12 q^{84} - 42 q^{85} - 30 q^{86} + 18 q^{88} - 78 q^{90} - 123 q^{92} + 60 q^{93} + 21 q^{94} - 138 q^{96} - 30 q^{97} - 180 q^{98}+O(q^{100}) $ 96 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 15 * q^12 - 12 * q^13 - 21 * q^14 - 6 * q^16 - 18 * q^17 - 27 * q^18 - 27 * q^20 - 12 * q^21 - 6 * q^22 - 12 * q^24 - 12 * q^25 - 12 * q^28 - 24 * q^29 + 9 * q^30 + 24 * q^32 - 42 * q^33 - 12 * q^34 + 24 * q^36 - 6 * q^37 + 18 * q^38 - 21 * q^40 - 42 * q^41 + 54 * q^42 + 63 * q^44 - 24 * q^45 - 3 * q^46 + 69 * q^48 - 12 * q^49 + 87 * q^50 - 33 * q^52 + 78 * q^54 + 99 * q^56 - 24 * q^57 - 33 * q^58 + 102 * q^60 - 12 * q^61 + 90 * q^62 - 3 * q^64 + 12 * q^65 + 87 * q^66 + 51 * q^68 + 12 * q^69 - 21 * q^70 + 12 * q^72 - 6 * q^73 + 21 * q^74 - 18 * q^76 + 12 * q^77 - 24 * q^78 + 12 * q^81 - 12 * q^82 - 12 * q^84 - 42 * q^85 - 30 * q^86 + 18 * q^88 - 78 * q^90 - 123 * q^92 + 60 * q^93 + 21 * q^94 - 138 * q^96 - 30 * q^97 - 180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$-1$

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 $

$2$	−1.30706	−	0.540000i	−0.924229	−	0.381838i
$2$	−1.30706	−	0.540000i	−0.924229	−	0.381838i
$3$	−1.71606	+	0.234845i	−0.990765	+	0.135588i
$3$	−1.71606	+	0.234845i	−0.990765	+	0.135588i
$4$	1.41680	+	1.41162i	0.708400	+	0.705812i
$5$	0.137245	−	0.0242000i	0.0613780	−	0.0108226i	−0.142875	−	0.989741i	$-0.545635\pi$
$5$	0.137245	−	0.0242000i	0.0613780	−	0.0108226i	0.204253	+	0.978918i	$0.434524\pi$
$6$	2.36980	+	0.619715i	0.967467	+	0.252997i
$7$	2.98823	−	3.56123i	1.12944	−	1.34602i	0.198824	−	0.980035i	$-0.436288\pi$
$7$	2.98823	−	3.56123i	1.12944	−	1.34602i	0.930621	−	0.365984i	$-0.119268\pi$
$8$	−1.08956	−	2.61015i	−0.385218	−	0.922826i
$9$	2.88970	−	0.806015i	0.963232	−	0.268672i
$10$	−0.192456	−	0.0424817i	−0.0608598	−	0.0134339i
$11$	0.182573	−	1.03542i	0.0550477	−	0.312191i	−0.944834	−	0.327549i	$-0.893777\pi$
$11$	0.182573	−	1.03542i	0.0550477	−	0.312191i	0.999882	+	0.0153574i	$0.00488861\pi$
$12$	−2.76282	−	2.08970i	−0.797557	−	0.603243i
$13$	−1.46220	−	0.532196i	−0.405541	−	0.147605i	0.131192	−	0.991357i	$-0.458119\pi$
$13$	−1.46220	−	0.532196i	−0.405541	−	0.147605i	−0.536733	+	0.843752i	$0.680342\pi$
$14$	−5.82886	+	3.04109i	−1.55783	+	0.812766i
$15$	−0.229837	+	0.0737600i	−0.0593437	+	0.0190448i
$16$	0.0146392	+	3.99997i	0.00365980	+	0.999993i
$17$	5.25631	−	3.03473i	1.27484	−	0.736031i	0.298948	−	0.954269i	$-0.403364\pi$
$17$	5.25631	−	3.03473i	1.27484	−	0.736031i	0.975895	+	0.218238i	$0.0700310\pi$
$18$	−4.21225	−	0.506929i	−0.992836	−	0.119484i
$19$	3.80088	+	2.19444i	0.871981	+	0.503439i	0.868006	−	0.496553i	$-0.165401\pi$
$19$	3.80088	+	2.19444i	0.871981	+	0.503439i	0.00397518	+	0.999992i	$0.498735\pi$
$20$	0.228610	+	0.159452i	0.0511188	+	0.0356546i
$21$	−4.29163	+	6.81305i	−0.936510	+	1.48673i
$22$	−0.797761	+	1.25477i	−0.170083	+	0.267517i
$23$	−1.94128	+	1.62893i	−0.404785	+	0.339655i	−0.822340	−	0.568997i	$-0.807332\pi$
$23$	−1.94128	+	1.62893i	−0.404785	+	0.339655i	0.417555	+	0.908652i	$0.362887\pi$
$24$	2.48273	+	4.22328i	0.506785	+	0.862073i
$25$	−4.68021	+	1.70346i	−0.936042	+	0.340692i
$26$	1.62379	+	1.48520i	0.318451	+	0.291271i
$27$	−4.76959	+	2.06180i	−0.917908	+	0.396793i
$28$	9.26084	−	0.827297i	1.75013	−	0.156345i
$29$	0.210458	+	0.578229i	0.0390811	+	0.107374i	0.957698	−	0.287774i	$-0.0929153\pi$
$29$	0.210458	+	0.578229i	0.0390811	+	0.107374i	−0.918617	+	0.395149i	$0.870693\pi$
$30$	0.340241	+	0.0277036i	0.0621192	+	0.00505797i
$31$	−3.18818	−	3.79952i	−0.572613	−	0.682414i	0.399552	−	0.916711i	$-0.369166\pi$
$31$	−3.18818	−	3.79952i	−0.572613	−	0.682414i	−0.972165	+	0.234297i	$0.924721\pi$
$32$	2.14085	−	5.23610i	0.378453	−	0.925621i
$33$	−0.0701412	+	1.81972i	−0.0122100	+	0.316772i
$34$	−8.50906	+	1.12816i	−1.45929	+	0.193478i
$35$	0.323938	−	0.561078i	0.0547556	−	0.0948394i
$36$	5.23191	+	2.93720i	0.871985	+	0.489533i
$37$	−1.43991	−	2.49400i	−0.236720	−	0.410012i	0.723051	−	0.690795i	$-0.242739\pi$
$37$	−1.43991	−	2.49400i	−0.236720	−	0.410012i	−0.959771	+	0.280783i	$0.909406\pi$
$38$	−3.78297	−	4.92073i	−0.613679	−	0.798248i
$39$	2.63420	+	0.569889i	0.421809	+	0.0912552i
$40$	−0.212703	−	0.331863i	−0.0336313	−	0.0524721i
$41$	−2.25297	+	6.18999i	−0.351855	+	0.966713i	0.629919	+	0.776661i	$0.283088\pi$
$41$	−2.25297	+	6.18999i	−0.351855	+	0.966713i	−0.981774	+	0.190053i	$0.939134\pi$
$42$	9.28846	−	6.58756i	1.43324	−	1.01648i
$43$	−2.15530	−	0.380038i	−0.328681	−	0.0579553i	0.00687300	−	0.999976i	$-0.497812\pi$
$43$	−2.15530	−	0.380038i	−0.328681	−	0.0579553i	−0.335554	+	0.942021i	$0.608923\pi$
$44$	1.72029	−	1.20926i	0.259344	−	0.182303i
$45$	0.377091	−	0.180553i	0.0562135	−	0.0269152i
$46$	3.41698	−	1.08081i	0.503807	−	0.159357i
$47$	8.46639	+	7.10414i	1.23495	+	1.03625i	0.997902	+	0.0647475i	$0.0206242\pi$
$47$	8.46639	+	7.10414i	1.23495	+	1.03625i	0.237048	+	0.971498i	$0.423820\pi$
$48$	−0.964496	−	6.86074i	−0.139213	−	0.990262i
$49$	−2.53733	−	14.3899i	−0.362476	−	2.05570i
$50$	7.03718	+	0.300799i	0.995207	+	0.0425394i
$51$	−8.30743	+	6.44219i	−1.16327	+	0.902087i
$52$	−1.32038	−	2.81809i	−0.183104	−	0.390798i
$53$		−	8.73360i		−	1.19965i	−0.800130	−	0.599826i	$-0.795236\pi$
$53$		−	8.73360i		−	1.19965i	0.800130	−	0.599826i	$-0.204764\pi$
$54$	7.34750	−	0.119308i	0.999868	−	0.0162357i
$55$		−	0.146525i		−	0.0197574i
$56$	−12.5512	−	3.91953i	−1.67722	−	0.523770i
$57$	−7.03787	−	2.87316i	−0.932189	−	0.380559i
$58$	0.0371630	−	0.869426i	0.00487974	−	0.114161i
$59$	1.42477	+	8.08025i	0.185489	+	1.05196i	0.925326	+	0.379173i	$0.123792\pi$
$59$	1.42477	+	8.08025i	0.185489	+	1.05196i	−0.739837	+	0.672786i	$0.765097\pi$
$60$	−0.429755	−	0.219941i	−0.0554811	−	0.0283942i
$61$	8.56477	+	7.18670i	1.09661	+	0.920162i	0.997192	−	0.0748840i	$-0.0238587\pi$
$61$	8.56477	+	7.18670i	1.09661	+	0.920162i	0.0994142	+	0.995046i	$0.468303\pi$
$62$	2.11539	+	6.68781i	0.268654	+	0.849353i
$63$	5.76467	−	12.6994i	0.726280	−	1.59998i
$64$	−5.62571	+	5.68782i	−0.703214	+	0.710978i
$65$	−0.213559	−	0.0376562i	−0.0264887	−	0.00467068i
$66$	1.07433	−	2.34060i	0.132240	−	0.288108i
$67$	−1.93034	+	5.30357i	−0.235829	+	0.647934i	0.764167	+	0.645019i	$0.223150\pi$
$67$	−1.93034	+	5.30357i	−0.235829	+	0.647934i	−0.999996	+	0.00291580i	$0.999072\pi$
$68$	11.7310	+	3.12033i	1.42260	+	0.378395i
$69$	2.94880	−	3.25123i	0.354994	−	0.391402i
$70$	−0.726388	+	0.558434i	−0.0868200	+	0.0667456i
$71$	−2.33277	−	4.04048i	−0.276849	−	0.479517i	0.693751	−	0.720215i	$-0.255957\pi$
$71$	−2.33277	−	4.04048i	−0.276849	−	0.479517i	−0.970600	+	0.240698i	$0.922624\pi$
$72$	−5.25231	−	6.66432i	−0.618991	−	0.785398i
$73$	−5.64518	+	9.77774i	−0.660718	+	1.14440i	0.319709	+	0.947516i	$0.396415\pi$
$73$	−5.64518	+	9.77774i	−0.660718	+	1.14440i	−0.980427	+	0.196882i	$0.936918\pi$
$74$	0.535287	+	4.03736i	0.0622258	+	0.469334i
$75$	7.63146	−	4.02235i	0.881205	−	0.464461i
$76$	2.28736	+	8.47449i	0.262378	+	0.972090i
$77$	−3.14181	−	3.74426i	−0.358042	−	0.426698i
$78$	−3.13531	−	2.16734i	−0.355004	−	0.245403i
$79$	−0.572755	−	1.57363i	−0.0644400	−	0.177047i	0.903294	−	0.429023i	$-0.141142\pi$
$79$	−0.572755	−	1.57363i	−0.0644400	−	0.177047i	−0.967734	+	0.251975i	$0.918920\pi$
$80$	0.0988087	+	0.548623i	0.0110471	+	0.0613379i
$81$	7.70068	−	4.65828i	0.855631	−	0.517586i
$82$	6.28736	−	6.87406i	0.694322	−	0.759113i
$83$	−2.20553	+	0.802749i	−0.242089	+	0.0881131i	−0.460215	−	0.887807i	$-0.652228\pi$
$83$	−2.20553	+	0.802749i	−0.242089	+	0.0881131i	0.218126	+	0.975921i	$0.430006\pi$
$84$	−15.6978	+	3.59455i	−1.71277	+	0.392198i
$85$	0.647964	−	0.543706i	0.0702815	−	0.0589732i
$86$	2.61188	+	1.66060i	0.281647	+	0.179067i
$87$	−0.496952	−	0.942848i	−0.0532788	−	0.101084i
$88$	−2.90152	+	0.651613i	−0.309303	+	0.0694622i
$89$	7.63741	+	4.40946i	0.809564	+	0.467402i	0.846804	−	0.531905i	$-0.178524\pi$
$89$	7.63741	+	4.40946i	0.809564	+	0.467402i	−0.0372408	+	0.999306i	$0.511857\pi$
$90$	−0.590379	+	0.0323630i	−0.0622314	+	0.00341136i
$91$	−6.26466	+	3.61690i	−0.656715	+	0.379154i
$92$	−5.04983	−	0.432493i	−0.526481	−	0.0450905i
$93$	6.36339	+	5.77146i	0.659853	+	0.598473i
$94$	−7.22981	−	13.8574i	−0.745698	−	1.42928i
$95$	0.574758	+	0.209195i	0.0589689	+	0.0214629i
$96$	−2.44415	+	9.48821i	−0.249455	+	0.968386i
$97$	−0.978443	+	5.54902i	−0.0993458	+	0.563418i	0.893983	+	0.448101i	$0.147899\pi$
$97$	−0.978443	+	5.54902i	−0.0993458	+	0.563418i	−0.993329	+	0.115317i	$0.963212\pi$
$98$	−4.45412	+	20.1786i	−0.449934	+	2.03835i
$99$	−0.306985	−	3.13921i	−0.0308532	−	0.315502i
$100$	−9.03556	−	4.19324i	−0.903556	−	0.419324i
$101$	−6.72190	+	8.01085i	−0.668854	+	0.797109i	−0.988628	−	0.150385i	$-0.951949\pi$
$101$	−6.72190	+	8.01085i	−0.668854	+	0.797109i	0.319773	+	0.947494i	$0.396393\pi$
$102$	14.3371	−	3.93430i	1.41958	−	0.389554i
$103$	1.52148	−	0.268277i	0.149915	−	0.0264341i	−0.0981867	−	0.995168i	$-0.531304\pi$
$103$	1.52148	−	0.268277i	0.149915	−	0.0264341i	0.248102	+	0.968734i	$0.420193\pi$
$104$	0.204043	+	4.39641i	0.0200081	+	0.431103i
$105$	−0.424130	+	1.03892i	−0.0413908	+	0.101388i
$106$	−4.71615	+	11.4153i	−0.458073	+	1.10875i
$107$	−7.89051			−0.762805			−0.381402	−	0.924409i	$-0.624559\pi$
$107$	−7.89051			−0.762805			−0.381402	+	0.924409i	$0.624559\pi$
$108$	−9.66803	−	3.81171i	−0.930307	−	0.366782i
$109$	1.78550			0.171020			0.0855098	−	0.996337i	$-0.472748\pi$
$109$	1.78550			0.171020			0.0855098	+	0.996337i	$0.472748\pi$
$110$	−0.0791235	+	0.191516i	−0.00754413	+	0.0182604i
$111$	3.05668	+	3.94169i	0.290127	+	0.374129i
$112$	14.2886	+	11.9007i	1.35014	+	1.12451i
$113$	−10.4607	+	1.84450i	−0.984057	+	0.173516i	−0.642451	−	0.766327i	$-0.722082\pi$
$113$	−10.4607	+	1.84450i	−0.984057	+	0.173516i	−0.341607	+	0.939843i	$0.610971\pi$
$114$	7.64740	+	7.55584i	0.716244	+	0.707669i
$115$	−0.227011	+	0.270542i	−0.0211689	+	0.0252281i
$116$	−0.518064	+	1.11632i	−0.0481011	+	0.103648i
$117$	−4.65426	−	0.359332i	−0.430287	−	0.0332203i
$118$	2.50109	−	11.3307i	0.230244	−	1.04308i
$119$	4.89968	−	27.7874i	0.449152	−	2.54727i
$120$	0.442946	+	0.519543i	0.0404353	+	0.0474275i
$121$	9.29786	+	3.38414i	0.845260	+	0.307649i
$122$	−7.31383	−	14.0184i	−0.662163	−	1.26917i
$123$	2.41253	−	11.1515i	0.217531	−	1.00549i
$124$	0.846487	−	9.88366i	0.0760167	−	0.887579i
$125$	−1.20457	+	0.695459i	−0.107740	+	0.0622038i
$126$	−14.3925	+	13.4860i	−1.28218	+	1.20143i
$127$	2.89596	+	1.67198i	0.256975	+	0.148364i	0.622954	−	0.782259i	$-0.285933\pi$
$127$	2.89596	+	1.67198i	0.256975	+	0.148364i	−0.365979	+	0.930623i	$0.619266\pi$
$128$	10.4246	−	4.39642i	0.921410	−	0.388593i
$129$	3.78787	+	0.146004i	0.333503	+	0.0128549i
$130$	0.258799	+	0.164541i	0.0226982	+	0.0144312i
$131$	−2.00847	+	1.68531i	−0.175481	+	0.147246i	−0.726298	−	0.687380i	$-0.758761\pi$
$131$	−2.00847	+	1.68531i	−0.175481	+	0.147246i	0.550817	+	0.834626i	$0.314316\pi$
$132$	−2.66813	+	2.47916i	−0.232231	+	0.215783i
$133$	19.1728	−	6.97833i	1.66249	−	0.605098i
$134$	5.38700	−	5.88969i	0.465366	−	0.508791i
$135$	−0.604708	+	0.398396i	−0.0520450	+	0.0342885i
$136$	−13.6482	−	10.4132i	−1.17032	−	0.892926i
$137$	3.04906	+	8.37723i	0.260499	+	0.715715i	0.999134	+	0.0416094i	$0.0132485\pi$
$137$	3.04906	+	8.37723i	0.260499	+	0.715715i	−0.738635	+	0.674106i	$0.764529\pi$
$138$	−5.60991	+	2.65719i	−0.477548	+	0.226195i
$139$	−9.64531	−	11.4948i	−0.818105	−	0.974979i	0.181860	−	0.983324i	$-0.441788\pi$
$139$	−9.64531	−	11.4948i	−0.818105	−	0.974979i	−0.999965	+	0.00834505i	$0.997344\pi$
$140$	1.25099	−	0.337655i	0.105728	−	0.0285371i
$141$	−16.1972	−	10.2028i	−1.36405	−	0.859232i
$142$	0.867207	+	6.54084i	0.0727744	+	0.548895i
$143$	−0.818005	+	1.41683i	−0.0684050	+	0.118481i
$144$	3.26634	+	11.5469i	0.272195	+	0.962242i
$145$	0.0428775	+	0.0742661i	0.00356079	+	0.00616746i
$146$	12.6586	−	9.73167i	1.04763	−	0.805398i
$147$	7.73360	+	24.0980i	0.637857	+	1.98757i
$148$	1.48053	−	5.56612i	0.121698	−	0.457532i
$149$	6.19266	−	17.0142i	0.507323	−	1.39386i	−0.376666	−	0.926349i	$-0.622929\pi$
$149$	6.19266	−	17.0142i	0.507323	−	1.39386i	0.883989	−	0.467509i	$-0.154848\pi$
$150$	−12.1468	+	1.13646i	−0.991784	+	0.0927915i
$151$	14.3804	+	2.53565i	1.17026	+	0.206348i	0.724803	−	0.688956i	$-0.241931\pi$
$151$	14.3804	+	2.53565i	1.17026	+	0.206348i	0.445456	+	0.895304i	$0.353042\pi$
$152$	1.58651	−	12.3118i	0.128683	−	0.998620i
$153$	12.7431	−	13.0061i	1.03022	−	1.05148i
$154$	2.08462	+	6.59054i	0.167983	+	0.531081i
$155$	−0.529511	−	0.444312i	−0.0425313	−	0.0356880i
$156$	2.92766	+	4.52591i	0.234400	+	0.362363i
$157$	0.0237965	+	0.134957i	0.00189917	+	0.0107707i	0.985743	−	0.168260i	$-0.0538149\pi$
$157$	0.0237965	+	0.134957i	0.00189917	+	0.0107707i	−0.983843	+	0.179031i	$0.942704\pi$
$158$	−0.101138	+	2.36612i	−0.00804610	+	0.188238i
$159$	2.05104	+	14.9873i	0.162658	+	1.18857i
$160$	0.167108	−	0.770439i	0.0132111	−	0.0609085i
$161$			11.7810i			0.928469i
$162$	−12.5807	+	1.93026i	−0.988433	+	0.151656i
$163$			12.0210i			0.941554i	0.882252	+	0.470777i	$0.156026\pi$
$163$			12.0210i			0.941554i	−0.882252	+	0.470777i	$0.843974\pi$
$164$	−11.9299	+	5.58962i	−0.931571	+	0.436476i
$165$	0.0344107	+	0.251445i	0.00267887	+	0.0195750i
$166$	3.31624	+	0.141750i	0.257390	+	0.0110020i
$167$	−1.95387	−	11.0810i	−0.151195	−	0.857471i	−0.962182	−	0.272407i	$-0.912180\pi$
$167$	−1.95387	−	11.0810i	−0.151195	−	0.857471i	0.810987	−	0.585064i	$-0.198931\pi$
$168$	22.4590	+	3.77855i	1.73275	+	0.291521i
$169$	−8.10379	−	6.79989i	−0.623368	−	0.523068i
$170$	−1.14053	+	0.360754i	−0.0874744	+	0.0276686i
$171$	12.7521	+	3.27769i	0.975180	+	0.250651i
$172$	−2.51716	−	3.58091i	−0.191932	−	0.273042i
$173$	5.61630	+	0.990305i	0.426999	+	0.0752915i	0.383018	−	0.923741i	$-0.374885\pi$
$173$	5.61630	+	0.990305i	0.426999	+	0.0752915i	0.0439813	+	0.999032i	$0.485996\pi$
$174$	0.140407	+	1.50071i	0.0106442	+	0.113769i
$175$	−7.91914	+	21.7577i	−0.598631	+	1.64472i
$176$	4.14433	+	0.715128i	0.312391	+	0.0539048i
$177$	−4.34259	−	13.5316i	−0.326409	−	1.01709i
$178$	−7.60142	−	9.88762i	−0.569751	−	0.741108i
$179$	−6.20187	−	10.7419i	−0.463549	−	0.802891i	0.535585	−	0.844481i	$-0.320091\pi$
$179$	−6.20187	−	10.7419i	−0.463549	−	0.802891i	−0.999135	+	0.0415901i	$0.986758\pi$
$180$	0.789135	+	0.276504i	0.0588186	+	0.0206094i
$181$	0.582122	−	1.00827i	0.0432688	−	0.0749437i	−0.843580	−	0.537004i	$-0.819556\pi$
$181$	0.582122	−	1.00827i	0.0432688	−	0.0749437i	0.886849	+	0.462060i	$0.152889\pi$
$182$	10.1414	−	1.34458i	0.751730	−	0.0996670i
$183$	−16.3854	−	10.3214i	−1.21124	−	0.762978i
$184$	6.36688	+	3.29221i	0.469372	+	0.242705i
$185$	−0.257976	−	0.307444i	−0.0189668	−	0.0226037i
$186$	−5.20072	−	10.9799i	−0.381335	−	0.805083i
$187$	−2.18257	−	5.99656i	−0.159605	−	0.438512i
$188$	1.96680	+	22.0165i	0.143443	+	1.60572i
$189$	−6.91009	+	23.1467i	−0.502635	+	1.68368i
$190$	−0.638277	−	0.583799i	−0.0463055	−	0.0423533i
$191$	−13.5161	+	4.91947i	−0.977993	+	0.355960i	−0.781060	−	0.624456i	$-0.785321\pi$
$191$	−13.5161	+	4.91947i	−0.977993	+	0.355960i	−0.196934	+	0.980417i	$0.563098\pi$
$192$	8.31828	−	11.0818i	0.600320	−	0.799760i
$193$	−14.0915	+	11.8242i	−1.01433	+	0.851125i	−0.988905	−	0.148551i	$-0.952539\pi$
$193$	−14.0915	+	11.8242i	−1.01433	+	0.851125i	−0.0254271	+	0.999677i	$0.508095\pi$
$194$	4.27536	−	6.72453i	0.306953	−	0.482793i
$195$	0.375322	+	0.0144669i	0.0268774	+	0.00103599i
$196$	16.7182	−	23.9694i	1.19416	−	1.71210i
$197$	−18.3471	−	10.5927i	−1.30718	−	0.754699i	−0.325553	−	0.945524i	$-0.605550\pi$
$197$	−18.3471	−	10.5927i	−1.30718	−	0.754699i	−0.981624	+	0.190825i	$0.938884\pi$
$198$	−1.29393	+	4.26890i	−0.0919553	+	0.303377i
$199$	5.80763	−	3.35304i	0.411692	−	0.237691i	−0.279824	−	0.960051i	$-0.590276\pi$
$199$	5.80763	−	3.35304i	0.411692	−	0.237691i	0.691517	+	0.722361i	$0.256943\pi$
$200$	9.54565	+	10.3600i	0.674979	+	0.732564i
$201$	2.06706	−	9.55456i	0.145799	−	0.673926i
$202$	13.1118	−	6.84081i	0.922541	−	0.481318i
$203$	2.68810	+	0.978390i	0.188668	+	0.0686695i
$204$	−20.8639	−	2.59968i	−1.46077	−	0.182014i
$205$	−0.159412	+	0.904068i	−0.0111338	+	0.0631429i
$206$	−2.13353	−	0.470944i	−0.148650	−	0.0328122i
$207$	−4.29677	+	6.27180i	−0.298646	+	0.435920i
$208$	2.10737	−	5.85654i	0.146120	−	0.406078i
$209$	2.96610	−	3.53486i	0.205170	−	0.244512i
$210$	1.11538	−	1.12889i	0.0769684	−	0.0779010i
$211$	17.3303	−	3.05581i	1.19307	−	0.210370i	0.458369	−	0.888762i	$-0.348434\pi$
$211$	17.3303	−	3.05581i	1.19307	−	0.210370i	0.734701	+	0.678391i	$0.237323\pi$
$212$	12.3286	−	12.3738i	0.846729	−	0.849833i
$213$	4.95205	+	6.38585i	0.339309	+	0.437551i
$214$	10.3134	+	4.26088i	0.705006	+	0.291268i
$215$	−0.305002			−0.0208010
$216$	10.5783	+	10.2029i	0.719766	+	0.694217i
$217$	−23.0580			−1.56528
$218$	−2.33375	−	0.964170i	−0.158061	−	0.0653018i
$219$	7.39119	−	18.1049i	0.499450	−	1.22341i
$220$	0.206838	−	0.207596i	0.0139450	−	0.0139961i
$221$	−9.30084	+	1.63999i	−0.625643	+	0.110318i
$222$	−1.86674	−	6.80263i	−0.125287	−	0.456562i
$223$	−5.95915	+	7.10184i	−0.399054	+	0.475574i	−0.927731	−	0.373249i	$-0.878244\pi$
$223$	−5.95915	+	7.10184i	−0.399054	+	0.475574i	0.528677	+	0.848823i	$0.322688\pi$
$224$	−12.2496	−	23.2707i	−0.818462	−	1.55484i
$225$	−12.1514	+	8.69480i	−0.810092	+	0.579653i
$226$	14.6687	+	3.23790i	0.975749	+	0.215382i
$227$	−3.87558	+	21.9795i	−0.257231	+	1.45883i	0.533049	+	0.846085i	$0.321046\pi$
$227$	−3.87558	+	21.9795i	−0.257231	+	1.45883i	−0.790280	+	0.612746i	$0.790065\pi$
$228$	−5.91543	−	14.0055i	−0.391759	−	0.927538i
$229$	24.7476	+	9.00740i	1.63537	+	0.595226i	0.986221	−	0.165435i	$-0.0529028\pi$
$229$	24.7476	+	9.00740i	1.63537	+	0.595226i	0.649149	+	0.760661i	$0.275125\pi$
$230$	0.442809	−	0.231027i	0.0291980	−	0.0152335i
$231$	6.27084	+	5.68752i	0.412591	+	0.374211i
$232$	1.27995	−	1.17934i	0.0840331	−	0.0774276i
$233$	−6.49629	+	3.75063i	−0.425586	+	0.245712i	−0.697464	−	0.716619i	$-0.745688\pi$
$233$	−6.49629	+	3.75063i	−0.425586	+	0.245712i	0.271878	+	0.962332i	$0.412355\pi$
$234$	5.88935	+	2.98297i	0.384999	+	0.195003i
$235$	1.33389	+	0.770123i	0.0870135	+	0.0502373i
$236$	−9.38767	+	13.4593i	−0.611085	+	0.876128i
$237$	1.35244	+	2.56593i	0.0878504	+	0.166675i
$238$	−21.4094	+	33.6740i	−1.38776	+	2.18276i
$239$	−2.63068	+	2.20740i	−0.170165	+	0.142785i	−0.723893	−	0.689912i	$-0.757649\pi$
$239$	−2.63068	+	2.20740i	−0.170165	+	0.142785i	0.553728	+	0.832697i	$0.313205\pi$
$240$	−0.298403	−	0.918263i	−0.0192618	−	0.0592736i
$241$	1.59962	−	0.582213i	0.103040	−	0.0375036i	−0.289986	−	0.957031i	$-0.593650\pi$
$241$	1.59962	−	0.582213i	0.103040	−	0.0375036i	0.393026	+	0.919527i	$0.371428\pi$
$242$	−10.3254	−	9.44411i	−0.663741	−	0.607091i
$243$	−12.1208	+	9.80233i	−0.777551	+	0.628820i
$244$	1.98965	+	22.2723i	0.127374	+	1.42584i
$245$	−0.696473	−	1.91354i	−0.0444960	−	0.122252i
$246$	−9.17512	+	13.2728i	−0.584984	+	0.846245i
$247$	−4.38976	−	5.23152i	−0.279314	−	0.332873i
$248$	−6.44359	+	12.4614i	−0.409168	+	0.791300i
$249$	3.59630	−	1.89552i	0.227906	−	0.120124i
$250$	1.94999	−	0.258537i	0.123328	−	0.0163513i
$251$	7.79783	−	13.5062i	0.492195	−	0.852506i	−0.507765	−	0.861496i	$-0.669528\pi$
$251$	7.79783	−	13.5062i	0.492195	−	0.852506i	0.999960	+	0.00898943i	$0.00286146\pi$
$252$	26.0942	−	9.85501i	1.64378	−	0.620807i
$253$	1.33220	+	2.30744i	0.0837547	+	0.145067i
$254$	−2.88231	−	3.74919i	−0.180852	−	0.235245i
$255$	−0.984255	+	1.08520i	−0.0616364	+	0.0679579i
$256$	−15.9996	+	0.117113i	−0.999973	+	0.00731954i
$257$	−3.39598	+	9.33039i	−0.211836	+	0.582014i	−0.999415	−	0.0341995i	$-0.989112\pi$
$257$	−3.39598	+	9.33039i	−0.211836	+	0.582014i	0.787579	+	0.616213i	$0.211334\pi$
$258$	−4.87212	−	2.23629i	−0.303325	−	0.139225i
$259$	−13.1845	−	2.32479i	−0.819246	−	0.144455i
$260$	−0.249414	−	0.354816i	−0.0154680	−	0.0220048i
$261$	1.07422	+	1.50127i	0.0664926	+	0.0929264i
$262$	3.53526	−	1.11822i	0.218409	−	0.0690839i
$263$	20.0312	+	16.8082i	1.23518	+	1.03644i	0.997885	+	0.0649985i	$0.0207043\pi$
$263$	20.0312	+	16.8082i	1.23518	+	1.03644i	0.237292	+	0.971438i	$0.423740\pi$
$264$	4.82615	−	1.79961i	0.297029	−	0.110759i
$265$	−0.211354	−	1.19865i	−0.0129833	−	0.0736322i
$266$	−28.8283	−	1.23224i	−1.76757	−	0.0755537i
$267$	−14.1418	−	5.77327i	−0.865462	−	0.353318i
$268$	−10.2216	+	4.78918i	−0.624381	+	0.292546i
$269$			0.465194i			0.0283634i	0.999899	+	0.0141817i	$0.00451432\pi$
$269$			0.465194i			0.0283634i	−0.999899	+	0.0141817i	$0.995486\pi$
$270$	1.00552	−	0.194184i	0.0611942	−	0.0118177i
$271$		−	15.6578i		−	0.951143i	−0.879677	−	0.475571i	$-0.842241\pi$
$271$		−	15.6578i		−	0.951143i	0.879677	−	0.475571i	$-0.157759\pi$
$272$	12.2158	+	20.9807i	0.740692	+	1.27214i
$273$	9.90109	−	7.67803i	0.599241	−	0.464696i
$274$	0.538408	−	12.5960i	0.0325264	−	0.760953i
$275$	0.909317	+	5.15699i	0.0548339	+	0.310978i
$276$	8.76736	−	0.443747i	0.527733	−	0.0267104i
$277$	−7.55460	−	6.33906i	−0.453912	−	0.380877i	0.386973	−	0.922091i	$-0.373521\pi$
$277$	−7.55460	−	6.33906i	−0.453912	−	0.380877i	−0.840885	+	0.541214i	$0.817965\pi$
$278$	6.39976	+	20.2329i	0.383832	+	1.21349i
$279$	−12.2753	−	8.40974i	−0.734905	−	0.503478i
$280$	−1.81744	−	0.234198i	−0.108613	−	0.0139960i
$281$	16.8051	+	2.96320i	1.00251	+	0.176770i	0.650727	−	0.759312i	$-0.274464\pi$
$281$	16.8051	+	2.96320i	1.00251	+	0.176770i	0.351783	+	0.936081i	$0.385575\pi$
$282$	15.6611	+	22.0821i	0.932605	+	1.31497i
$283$	3.24599	−	8.91828i	0.192954	−	0.530137i	−0.805056	−	0.593199i	$-0.797865\pi$
$283$	3.24599	−	8.91828i	0.192954	−	0.530137i	0.998010	+	0.0630625i	$0.0200868\pi$
$284$	2.39857	−	9.01754i	0.142329	−	0.535093i
$285$	−1.03545	−	0.224011i	−0.0613345	−	0.0132693i
$286$	1.83427	−	1.41015i	0.108462	−	0.0833839i
$287$	15.3116	+	26.5204i	0.903814	+	1.56545i
$288$	1.96604	−	16.8563i	0.115850	−	0.993267i
$289$	9.91922	−	17.1806i	0.583484	−	1.01062i
$290$	−0.0159397	−	0.120224i	−0.000936011	−	0.00705979i
$291$	0.375901	−	9.75222i	0.0220357	−	0.571685i
$292$	−21.8006	+	5.88422i	−1.27578	+	0.344348i
$293$	1.45797	+	1.73754i	0.0851753	+	0.101508i	0.806949	−	0.590621i	$-0.201117\pi$
$293$	1.45797	+	1.73754i	0.0851753	+	0.101508i	−0.721774	+	0.692129i	$0.756673\pi$
$294$	2.90467	−	35.6736i	0.169404	−	2.08053i
$295$	0.391085	+	1.07450i	0.0227699	+	0.0625597i
$296$	−4.94084	+	6.47575i	−0.287180	+	0.376395i
$297$	1.26403	+	5.31496i	0.0733466	+	0.308405i
$298$	−17.2818	+	18.8945i	−1.00111	+	1.09453i
$299$	3.70544	−	1.34867i	0.214291	−	0.0779957i
$300$	16.4903	+	5.07387i	0.952067	+	0.292940i
$301$	−7.79394	+	6.53989i	−0.449235	+	0.376953i
$302$	−17.4267	−	11.0797i	−1.00280	−	0.637562i
$303$	9.65385	−	15.3257i	0.554599	−	0.880437i
$304$	−8.72205	+	15.2355i	−0.500244	+	0.873818i
$305$	1.34939	+	0.779072i	0.0772660	+	0.0446095i
$306$	−23.6793	+	10.1185i	−1.35365	+	0.578435i
$307$	10.5153	−	6.07100i	0.600138	−	0.346490i	−0.168958	−	0.985623i	$-0.554040\pi$
$307$	10.5153	−	6.07100i	0.600138	−	0.346490i	0.769096	+	0.639133i	$0.220707\pi$
$308$	0.834175	−	9.73991i	0.0475315	−	0.554983i
$309$	−2.54793	+	0.817690i	−0.144947	+	0.0465168i
$310$	0.452172	+	0.866678i	0.0256817	+	0.0492240i
$311$	−16.3253	−	5.94192i	−0.925723	−	0.336936i	−0.165210	−	0.986258i	$-0.552830\pi$
$311$	−16.3253	−	5.94192i	−0.925723	−	0.336936i	−0.760513	+	0.649323i	$0.775052\pi$
$312$	−1.38263	−	7.49656i	−0.0782757	−	0.424409i
$313$	2.82602	−	16.0272i	0.159736	−	0.905909i	−0.794591	−	0.607145i	$-0.792315\pi$
$313$	2.82602	−	16.0272i	0.159736	−	0.905909i	0.954327	−	0.298764i	$-0.0965743\pi$
$314$	0.0417733	−	0.189246i	0.00235740	−	0.0106798i
$315$	0.483846	−	1.88244i	0.0272616	−	0.106064i
$316$	1.40990	−	3.03804i	0.0793129	−	0.170903i
$317$	18.7298	−	22.3213i	1.05197	−	1.25369i	0.0856578	−	0.996325i	$-0.472701\pi$
$317$	18.7298	−	22.3213i	1.05197	−	1.25369i	0.966314	−	0.257366i	$-0.0828547\pi$
$318$	5.41234	−	20.6969i	0.303509	−	1.16062i
$319$	0.637134	−	0.112344i	0.0356727	−	0.00629005i
$320$	−0.634457	+	0.916769i	−0.0354672	+	0.0512490i
$321$	13.5406	−	1.85305i	0.755760	−	0.103427i
$322$	6.36172	−	15.3984i	0.354525	−	0.858118i
$323$	26.6381			1.48219
$324$	17.4860	+	4.27062i	0.971447	+	0.237257i
$325$	7.74997			0.429891
$326$	6.49132	−	15.7121i	0.359521	−	0.870212i
$327$	−3.06401	+	0.419316i	−0.169440	+	0.0231882i
$328$	18.6115	−	0.863785i	1.02765	−	0.0476946i
$329$	50.5990	−	8.92197i	2.78961	−	0.491884i
$330$	0.0908036	−	0.347235i	0.00499858	−	0.0191146i
$331$	1.75836	−	2.09553i	0.0966481	−	0.115181i	−0.715553	−	0.698559i	$-0.753825\pi$
$331$	1.75836	−	2.09553i	0.0966481	−	0.115181i	0.812201	+	0.583378i	$0.198269\pi$
$332$	−4.25798	−	1.97605i	−0.233687	−	0.108450i
$333$	−6.17112	−	6.04632i	−0.338175	−	0.331336i
$334$	−3.42990	+	15.5386i	−0.187676	+	0.850232i
$335$	−0.136584	+	0.774604i	−0.00746236	+	0.0423212i
$336$	−27.3148	−	17.0667i	−1.49015	−	0.931063i
$337$	−6.48096	−	2.35888i	−0.353040	−	0.128496i	0.159411	−	0.987212i	$-0.449040\pi$
$337$	−6.48096	−	2.35888i	−0.353040	−	0.128496i	−0.512452	+	0.858716i	$0.671263\pi$
$338$	6.92018	+	13.2639i	0.376408	+	0.721461i
$339$	17.5179	−	5.62190i	0.951443	−	0.305340i
$340$	1.68554	+	0.144358i	0.0914114	+	0.00782893i
$341$	−4.51618	+	2.60742i	−0.244565	+	0.141199i
$342$	−14.8978	−	11.1703i	−0.805582	−	0.604020i
$343$	−30.6457	−	17.6933i	−1.65471	−	0.955349i
$344$	1.35638	+	6.03973i	0.0731310	+	0.325640i
$345$	0.326029	−	0.517577i	0.0175528	−	0.0278654i
$346$	−6.80606	−	4.32719i	−0.365896	−	0.232631i
$347$	17.5469	−	14.7236i	0.941964	−	0.790402i	−0.0359618	−	0.999353i	$-0.511449\pi$
$347$	17.5469	−	14.7236i	0.941964	−	0.790402i	0.977926	+	0.208951i	$0.0670050\pi$
$348$	0.626865	−	2.03733i	0.0336035	−	0.109213i
$349$	−25.4917	+	9.27824i	−1.36454	+	0.496653i	−0.917456	−	0.397838i	$-0.869760\pi$
$349$	−25.4917	+	9.27824i	−1.36454	+	0.496653i	−0.447086	+	0.894491i	$0.647538\pi$
$350$	22.0999	−	24.1622i	1.18129	−	1.29152i
$351$	8.07137	−	0.476397i	0.430818	−	0.0254282i
$352$	−5.03071	−	3.17265i	−0.268138	−	0.169103i
$353$	−2.30370	−	6.32935i	−0.122613	−	0.336877i	0.863166	−	0.504919i	$-0.168478\pi$
$353$	−2.30370	−	6.32935i	−0.122613	−	0.336877i	−0.985780	+	0.168042i	$0.946256\pi$
$354$	−1.63104	+	20.0315i	−0.0866888	+	1.06466i
$355$	−0.417942	−	0.498084i	−0.0221820	−	0.0264355i
$356$	4.59618	+	17.0285i	0.243597	+	0.902507i
$357$	−1.88237	+	48.8355i	−0.0996256	+	2.58465i
$358$	2.30554	+	17.3894i	0.121852	+	0.919056i
$359$	−14.3604	+	24.8729i	−0.757913	+	1.31274i	0.186000	+	0.982550i	$0.440448\pi$
$359$	−14.3604	+	24.8729i	−0.757913	+	1.31274i	−0.943913	+	0.330194i	$0.892886\pi$
$360$	−0.882132	−	0.787541i	−0.0464925	−	0.0415070i
$361$	0.131118	+	0.227104i	0.00690097	+	0.0119528i
$362$	−1.30533	+	1.00351i	−0.0686067	+	0.0527435i
$363$	−16.7504	−	3.62382i	−0.879167	−	0.190201i
$364$	−13.9815	−	3.71891i	−0.732828	−	0.194924i
$365$	−0.538153	+	1.47856i	−0.0281682	+	0.0773915i
$366$	15.8431	+	22.3387i	0.828132	+	1.16767i
$367$	3.84637	+	0.678219i	0.200779	+	0.0354027i	0.273133	−	0.961976i	$-0.411940\pi$
$367$	3.84637	+	0.678219i	0.200779	+	0.0354027i	−0.0723541	+	0.997379i	$0.523051\pi$
$368$	−6.54408	−	7.74122i	−0.341134	−	0.403539i
$369$	−1.52118	+	19.7031i	−0.0791894	+	1.02570i
$370$	0.171170	+	0.541155i	0.00889870	+	0.0281333i
$371$	−31.1024	−	26.0980i	−1.61476	−	1.35494i
$372$	0.868512	+	17.1597i	0.0450302	+	0.889689i
$373$	−1.89369	−	10.7397i	−0.0980518	−	0.556079i	−0.993769	−	0.111456i	$-0.964449\pi$
$373$	−1.89369	−	10.7397i	−0.0980518	−	0.556079i	0.895718	−	0.444623i	$-0.146662\pi$
$374$	−0.385401	+	9.01643i	−0.0199286	+	0.466229i
$375$	1.90379	−	1.47633i	0.0983111	−	0.0762376i
$376$	9.31820	−	29.8389i	0.480549	−	1.53882i
$377$		−	0.957490i		−	0.0493132i
$378$	21.5311	−	26.5227i	1.10744	−	1.36418i
$379$			5.95264i			0.305766i	0.988244	+	0.152883i	$0.0488558\pi$
$379$			5.95264i			0.305766i	−0.988244	+	0.152883i	$0.951144\pi$
$380$	0.519012	+	1.10773i	0.0266248	+	0.0568253i
$381$	−5.36228	−	2.18911i	−0.274718	−	0.112152i
$382$	20.3229	+	0.868687i	1.03981	+	0.0444459i
$383$	1.15926	+	6.57451i	0.0592356	+	0.335942i	0.999995	−	0.00313275i	$-0.000997186\pi$
$383$	1.15926	+	6.57451i	0.0592356	+	0.335942i	−0.940759	+	0.339075i	$0.889886\pi$
$384$	−16.8566	+	9.99267i	−0.860212	+	0.509936i
$385$	−0.521809	−	0.437850i	−0.0265939	−	0.0223149i
$386$	24.8035	−	7.84548i	1.26247	−	0.399325i
$387$	−6.53448	+	0.639012i	−0.332167	+	0.0324828i
$388$	−9.21939	+	6.48066i	−0.468043	+	0.329006i
$389$	−30.0164	−	5.29270i	−1.52189	−	0.268351i	−0.650716	−	0.759321i	$-0.725531\pi$
$389$	−30.0164	−	5.29270i	−1.52189	−	0.268351i	−0.871176	+	0.490970i	$0.836642\pi$
$390$	−0.482756	−	0.221583i	−0.0244453	−	0.0112203i
$391$	−5.26061	+	14.4534i	−0.266041	+	0.730941i
$392$	−34.7952	+	22.3015i	−1.75742	+	1.12639i
$393$	3.05087	−	3.36377i	0.153896	−	0.169680i
$394$	18.2607	+	23.7527i	0.919958	+	1.19664i
$395$	−0.116690	−	0.202113i	−0.00587131	−	0.0101694i
$396$	3.99644	−	4.88097i	0.200829	−	0.245278i
$397$	7.87633	−	13.6422i	0.395302	−	0.684683i	−0.597838	−	0.801617i	$-0.703973\pi$
$397$	7.87633	−	13.6422i	0.395302	−	0.684683i	0.993140	+	0.116934i	$0.0373067\pi$
$398$	−9.40155	+	1.24649i	−0.471257	+	0.0624809i
$399$	−31.2628	+	16.4778i	−1.56510	+	0.824924i
$400$	−6.88230	−	18.6958i	−0.344115	−	0.934789i
$401$	−1.99200	−	2.37398i	−0.0994758	−	0.118551i	0.714010	−	0.700136i	$-0.246877\pi$
$401$	−1.99200	−	2.37398i	−0.0994758	−	0.118551i	−0.813486	+	0.581585i	$0.802433\pi$
$402$	−7.86123	+	11.3721i	−0.392082	+	0.567191i
$403$	2.63965	+	7.25239i	0.131490	+	0.361267i
$404$	−20.8319	+	1.86097i	−1.03643	+	0.0925868i
$405$	0.944151	−	0.825683i	0.0469153	−	0.0410285i
$406$	−2.98518	−	2.73039i	−0.148152	−	0.135507i
$407$	−2.84523	+	1.03558i	−0.141033	+	0.0513318i
$408$	25.8665	+	14.6644i	1.28058	+	0.725998i
$409$	−20.1116	+	16.8756i	−0.994454	+	0.834446i	−0.986206	−	0.165520i	$-0.947070\pi$
$409$	−20.1116	+	16.8756i	−0.994454	+	0.834446i	−0.00824757	+	0.999966i	$0.502625\pi$
$410$	0.696557	−	1.09559i	0.0344005	−	0.0541072i
$411$	−7.19971	−	13.6597i	−0.355136	−	0.673785i
$412$	2.53433	+	1.76766i	0.124858	+	0.0870862i
$413$	33.0332	+	19.0717i	1.62546	+	0.938458i
$414$	9.00290	−	5.87735i	0.442468	−	0.288856i
$415$	−0.283273	+	0.163547i	−0.0139053	+	0.00802823i
$416$	−5.91698	+	6.51686i	−0.290104	+	0.319515i
$417$	19.2514	+	17.4606i	0.942745	+	0.855051i
$418$	−5.78570	+	3.01857i	−0.282988	+	0.147643i
$419$	33.9869	+	12.3702i	1.66037	+	0.604325i	0.990421	−	0.138082i	$-0.0440939\pi$
$419$	33.9869	+	12.3702i	1.66037	+	0.604325i	0.669949	+	0.742407i	$0.266316\pi$
$420$	−2.06747	+	0.873224i	−0.100882	+	0.0426089i
$421$	2.20155	−	12.4856i	0.107297	−	0.608511i	−0.882981	−	0.469409i	$-0.844467\pi$
$421$	2.20155	−	12.4856i	0.107297	−	0.608511i	0.990278	−	0.139103i	$-0.0444218\pi$
$422$	−24.3019	−	5.36428i	−1.18300	−	0.261129i
$423$	30.1913	+	13.7048i	1.46795	+	0.666349i
$424$	−22.7960	+	9.51579i	−1.10707	+	0.462128i
$425$	−19.4311	+	23.1571i	−0.942548	+	1.12328i
$426$	−3.02426	−	11.0208i	−0.146526	−	0.533959i
$427$	51.1870	−	9.02565i	2.47711	−	0.436782i
$428$	−11.1793	−	11.1384i	−0.540370	−	0.538396i
$429$	1.07101	−	2.62346i	0.0517087	−	0.126662i
$430$	0.398655	+	0.164701i	0.0192249	+	0.00794260i
$431$	−11.3033			−0.544463			−0.272231	−	0.962232i	$-0.587762\pi$
$431$	−11.3033			−0.544463			−0.272231	+	0.962232i	$0.587762\pi$
$432$	−8.31696	−	19.0480i	−0.400150	−	0.916450i
$433$	18.1058			0.870111			0.435056	−	0.900404i	$-0.356729\pi$
$433$	18.1058			0.870111			0.435056	+	0.900404i	$0.356729\pi$
$434$	30.1381	+	12.4513i	1.44668	+	0.597682i
$435$	−0.0910213	−	0.117375i	−0.00436414	−	0.00562771i
$436$	2.52969	+	2.52045i	0.121150	+	0.120708i
$437$	−10.9531	+	1.93133i	−0.523960	+	0.0923883i
$438$	−19.4374	+	19.6729i	−0.928753	+	0.940007i
$439$	8.79038	−	10.4760i	0.419542	−	0.499991i	−0.514333	−	0.857591i	$-0.671960\pi$
$439$	8.79038	−	10.4760i	0.419542	−	0.499991i	0.933875	+	0.357600i	$0.116405\pi$
$440$	−0.382451	+	0.159648i	−0.0182326	+	0.00761091i
$441$	−18.9306	−	39.5373i	−0.901457	−	1.88273i
$442$	13.0423	+	2.87890i	0.620361	+	0.136935i
$443$	−1.88953	+	10.7160i	−0.0897742	+	0.509135i	0.906450	+	0.422314i	$0.138782\pi$
$443$	−1.88953	+	10.7160i	−0.0897742	+	0.509135i	−0.996224	+	0.0868210i	$0.972329\pi$
$444$	−1.23349	+	9.89946i	−0.0585388	+	0.469808i
$445$	1.15491	+	0.420352i	0.0547479	+	0.0199266i
$446$	11.6239	−	6.06457i	0.550410	−	0.287166i
$447$	−6.63125	+	30.6516i	−0.313647	+	1.44977i
$448$	3.44474	+	37.0310i	0.162749	+	1.74955i
$449$	−6.10203	+	3.52301i	−0.287973	+	0.166261i	−0.637027	−	0.770841i	$-0.719836\pi$
$449$	−6.10203	+	3.52301i	−0.287973	+	0.166261i	0.349055	+	0.937102i	$0.386503\pi$
$450$	20.5777	−	4.80285i	0.970044	−	0.226409i
$451$	5.99791	+	3.46289i	0.282431	+	0.163061i
$452$	−17.4244	−	12.1532i	−0.819575	−	0.571641i
$453$	−25.2730	−	0.974152i	−1.18743	−	0.0457697i
$454$	16.9345	−	26.6357i	0.794778	−	1.25007i
$455$	−0.772266	+	0.648008i	−0.0362044	+	0.0303791i
$456$	0.168825	+	21.5004i	0.00790593	+	1.00685i
$457$	−23.9184	+	8.70557i	−1.11885	+	0.407229i	−0.834234	−	0.551411i	$-0.814090\pi$
$457$	−23.9184	+	8.70557i	−1.11885	+	0.407229i	−0.284620	+	0.958641i	$0.591867\pi$
$458$	−27.4826	−	25.1369i	−1.28418	−	1.17457i
$459$	−18.8135	+	25.3119i	−0.878137	+	1.18146i
$460$	−0.703532	+	0.0628485i	−0.0328024	+	0.00293033i
$461$	−13.4094	−	36.8420i	−0.624538	−	1.71590i	−0.695597	−	0.718432i	$-0.744860\pi$
$461$	−13.4094	−	36.8420i	−0.624538	−	1.71590i	0.0710586	−	0.997472i	$-0.477362\pi$
$462$	−5.12508	−	10.8202i	−0.238440	−	0.503400i
$463$	−4.80801	−	5.72997i	−0.223447	−	0.266294i	0.642661	−	0.766151i	$-0.277830\pi$
$463$	−4.80801	−	5.72997i	−0.223447	−	0.266294i	−0.866108	+	0.499857i	$0.833386\pi$
$464$	−2.30982	+	0.850291i	−0.107231	+	0.0394738i
$465$	1.01301	+	0.638112i	0.0469774	+	0.0295917i
$466$	10.5164	−	1.39430i	0.487161	−	0.0645895i
$467$	−0.689932	+	1.19500i	−0.0319262	+	0.0552979i	−0.881547	−	0.472096i	$-0.843498\pi$
$467$	−0.689932	+	1.19500i	−0.0319262	+	0.0552979i	0.849621	+	0.527394i	$0.176831\pi$
$468$	−6.08692	−	7.07917i	−0.281368	−	0.327235i
$469$	13.1189	+	22.7227i	0.605777	+	1.04924i
$470$	−1.32761	−	1.72690i	−0.0612379	−	0.0796558i
$471$	−0.0725301	−	0.226005i	−0.00334201	−	0.0104138i
$472$	19.5383	−	12.5228i	0.899322	−	0.576408i
$473$	−0.786999	+	2.16226i	−0.0361862	+	0.0994209i
$474$	−0.382113	−	4.08414i	−0.0175510	−	0.187591i
$475$	−21.5271	−	3.79580i	−0.987729	−	0.174163i
$476$	46.1673	−	32.4527i	2.11607	−	1.48747i
$477$	−7.03941	−	25.2374i	−0.322313	−	1.15554i
$478$	4.63045	−	1.46463i	0.211792	−	0.0669908i
$479$	−9.74905	−	8.18042i	−0.445445	−	0.373773i	0.392297	−	0.919839i	$-0.371681\pi$
$479$	−9.74905	−	8.18042i	−0.445445	−	0.373773i	−0.837742	+	0.546066i	$0.816125\pi$
$480$	−0.105833	+	1.36136i	−0.00483059	+	0.0621373i
$481$	0.778139	+	4.41304i	0.0354801	+	0.201217i
$482$	−2.40519	−	0.102808i	−0.109553	−	0.00468277i
$483$	−2.76670	−	20.2168i	−0.125889	−	0.919895i
$484$	8.39606	+	17.9197i	0.381639	+	0.814533i
$485$			0.785256i			0.0356566i
$486$	21.1359	−	6.26696i	0.958743	−	0.284275i
$487$		−	12.3932i		−	0.561588i	−0.959768	−	0.280794i	$-0.909402\pi$
$487$		−	12.3932i		−	0.561588i	0.959768	−	0.280794i	$-0.0905979\pi$
$488$	9.42648	−	30.1856i	0.426717	−	1.36644i
$489$	−2.82306	−	20.6286i	−0.127663	−	0.932859i
$490$	−0.122984	+	2.87721i	−0.00555586	+	0.129979i
$491$	−4.61221	−	26.1572i	−0.208146	−	1.18046i	−0.892411	−	0.451223i	$-0.850988\pi$
$491$	−4.61221	−	26.1572i	−0.208146	−	1.18046i	0.684265	−	0.729233i	$-0.260123\pi$
$492$	19.1597	−	12.3938i	0.863788	−	0.558755i
$493$	2.86100	+	2.40067i	0.128853	+	0.108121i
$494$	2.91265	+	9.20837i	0.131046	+	0.414304i
$495$	−0.118101	−	0.423412i	−0.00530826	−	0.0190310i
$496$	15.1513	−	12.8082i	0.680314	−	0.575107i
$497$	−21.3599	−	3.76634i	−0.958125	−	0.168943i
$498$	−5.72415	+	0.535552i	−0.256505	+	0.0239987i
$499$	3.29755	−	9.05994i	0.147619	−	0.405579i	−0.843741	−	0.536750i	$-0.819652\pi$
$499$	3.29755	−	9.05994i	0.147619	−	0.405579i	0.991360	+	0.131172i	$0.0418739\pi$
$500$	−2.68836	−	0.715074i	−0.120227	−	0.0319791i
$501$	5.95527	+	18.5567i	0.266062	+	0.829052i
$502$	−17.4856	+	13.4426i	−0.780420	+	0.599973i
$503$	4.28642	+	7.42429i	0.191122	+	0.331033i	0.945622	−	0.325267i	$-0.105454\pi$
$503$	4.28642	+	7.42429i	0.191122	+	0.331033i	−0.754500	+	0.656300i	$0.772121\pi$
$504$	−39.4283	−	1.20981i	−1.75628	−	0.0538891i
$505$	−0.728686	+	1.26212i	−0.0324261	+	0.0561637i
$506$	−0.495245	−	3.73534i	−0.0220163	−	0.166056i
$507$	15.5035	+	9.76585i	0.688533	+	0.433717i
$508$	1.74278	+	6.45686i	0.0773234	+	0.286477i
$509$	19.9295	+	23.7511i	0.883360	+	1.05275i	0.998236	+	0.0593674i	$0.0189083\pi$
$509$	19.9295	+	23.7511i	0.883360	+	1.05275i	−0.114876	+	0.993380i	$0.536647\pi$
$510$	1.87249	−	0.886922i	0.0829151	−	0.0392736i
$511$	17.9517	+	49.3219i	0.794137	+	2.18187i
$512$	20.9756	+	8.48670i	0.926999	+	0.375063i
$513$	−22.6531	−	2.62993i	−1.00016	−	0.116114i
$514$	9.47716	−	10.3615i	0.418020	−	0.457027i
$515$	0.202323	−	0.0736396i	0.00891542	−	0.00324495i
$516$	5.16055	+	5.55390i	0.227180	+	0.244497i
$517$	8.90151	−	7.46925i	0.391488	−	0.328497i
$518$	15.9775	+	10.1583i	0.702013	+	0.446329i
$519$	−9.87045	−	0.380458i	−0.433265	−	0.0167003i
$520$	0.134397	+	0.598448i	0.00589371	+	0.0262437i
$521$	−25.2374	−	14.5708i	−1.10567	−	0.638359i	−0.167966	−	0.985793i	$-0.553720\pi$
$521$	−25.2374	−	14.5708i	−1.10567	−	0.638359i	−0.937705	+	0.347433i	$0.887053\pi$
$522$	−0.593380	−	2.54233i	−0.0259716	−	0.111275i
$523$	4.50959	−	2.60361i	0.197190	−	0.113848i	−0.398154	−	0.917319i	$-0.630349\pi$
$523$	4.50959	−	2.60361i	0.197190	−	0.113848i	0.595344	+	0.803471i	$0.297016\pi$
$524$	−5.22463	−	0.447464i	−0.228239	−	0.0195475i
$525$	8.48000	−	39.1971i	0.370098	−	1.71070i
$526$	−17.1055	−	32.7861i	−0.745836	−	1.42954i
$527$	−28.2886	−	10.2962i	−1.23227	−	0.448510i
$528$	−7.27984	−	0.253924i	−0.316815	−	0.0110506i
$529$	−2.87875	+	16.3262i	−0.125163	+	0.709834i
$530$	−0.371018	+	1.68083i	−0.0161160	+	0.0730106i
$531$	10.6299	+	22.2011i	0.461300	+	0.963445i
$532$	37.0148	+	17.1779i	1.60479	+	0.744756i
$533$	6.58858	−	7.85196i	0.285383	−	0.340106i
$534$	15.3665	+	15.1826i	0.664974	+	0.657013i
$535$	−1.08294	+	0.190951i	−0.0468194	+	0.00825552i
$536$	15.9463	−	0.740090i	0.688776	−	0.0319670i
$537$	13.1654	+	16.9773i	0.568131	+	0.732625i
$538$	0.251205	−	0.608035i	0.0108302	−	0.0262143i
$539$	−15.3629			−0.661725
$540$	−1.41914	−	0.289173i	−0.0610699	−	0.0124440i
$541$	24.3664			1.04759			0.523797	−	0.851843i	$-0.324515\pi$
$541$	24.3664			1.04759			0.523797	+	0.851843i	$0.324515\pi$
$542$	−8.45521	+	20.4656i	−0.363182	+	0.879074i
$543$	−0.762168	+	1.86695i	−0.0327078	+	0.0801184i
$544$	−4.63718	−	34.0195i	−0.198817	−	1.45857i
$545$	0.245051	−	0.0432091i	0.0104968	−	0.00185088i
$546$	−17.0874	+	4.68903i	−0.731275	+	0.200672i
$547$	−22.9927	+	27.4016i	−0.983097	+	1.17161i	0.00206780	+	0.999998i	$0.499342\pi$
$547$	−22.9927	+	27.4016i	−0.983097	+	1.17161i	−0.985165	+	0.171611i	$0.945103\pi$
$548$	−7.50558	+	16.1730i	−0.320623	+	0.690875i
$549$	30.5422	+	13.8640i	1.30351	+	0.591702i
$550$	1.59625	−	7.23152i	0.0680643	−	0.308353i
$551$	−0.468962	+	2.65961i	−0.0199784	+	0.113303i
$552$	−11.6991	−	4.15438i	−0.497946	−	0.176822i
$553$	−7.31560	−	2.66266i	−0.311091	−	0.113228i
$554$	6.45120	+	12.3650i	0.274085	+	0.525339i
$555$	0.514904	+	0.467007i	0.0218564	+	0.0198233i
$556$	2.56091	−	29.9014i	0.108607	−	1.26810i
$557$	10.4040	−	6.00674i	0.440831	−	0.254514i	−0.263119	−	0.964763i	$-0.584751\pi$
$557$	10.4040	−	6.00674i	0.440831	−	0.254514i	0.703950	+	0.710250i	$0.251418\pi$
$558$	11.5033	+	17.6207i	0.486973	+	0.745944i
$559$	2.94922	+	1.70274i	0.124739	+	0.0720180i
$560$	2.24904	+	1.28753i	0.0950392	+	0.0544081i
$561$	5.15367	+	9.77786i	0.217588	+	0.412822i
$562$	−20.3651	−	12.9478i	−0.859052	−	0.546172i
$563$	−3.65854	+	3.06988i	−0.154189	+	0.129380i	−0.716619	−	0.697465i	$-0.754311\pi$
$563$	−3.65854	+	3.06988i	−0.154189	+	0.129380i	0.562430	+	0.826845i	$0.309867\pi$
$564$	−8.54560	−	37.3196i	−0.359835	−	1.57144i
$565$	−1.39104	+	0.506297i	−0.0585215	+	0.0213001i
$566$	−9.05857	+	9.90387i	−0.380760	+	0.416291i
$567$	6.42219	−	41.3439i	0.269707	−	1.73628i
$568$	−8.00454	+	10.4912i	−0.335863	+	0.440202i
$569$	2.71384	+	7.45620i	0.113770	+	0.312580i	0.983489	−	0.180966i	$-0.0579225\pi$
$569$	2.71384	+	7.45620i	0.113770	+	0.312580i	−0.869719	+	0.493547i	$0.835700\pi$
$570$	1.23242	+	0.851936i	0.0516204	+	0.0356837i
$571$	10.4105	+	12.4067i	0.435666	+	0.519206i	0.938548	−	0.345149i	$-0.112172\pi$
$571$	10.4105	+	12.4067i	0.435666	+	0.519206i	−0.502882	+	0.864355i	$0.667727\pi$
$572$	−3.15897	+	0.852643i	−0.132083	+	0.0356508i
$573$	22.0391	−	11.6163i	0.920698	−	0.485277i
$574$	−5.69207	−	42.9320i	−0.237583	−	1.79195i
$575$	6.31079	−	10.9306i	0.263178	−	0.455838i
$576$	−11.6721	+	20.9705i	−0.486339	+	0.873770i
$577$	−8.09164	−	14.0151i	−0.336859	−	0.583458i	0.646981	−	0.762506i	$-0.276031\pi$
$577$	−8.09164	−	14.0151i	−0.336859	−	0.583458i	−0.983840	+	0.179049i	$0.942698\pi$
$578$	−22.2425	+	17.0996i	−0.925167	+	0.711251i
$579$	21.4050	−	23.6003i	0.889562	−	0.980797i
$580$	−0.0440869	+	0.165747i	−0.00183061	+	0.00688227i
$581$	−3.73187	+	10.2532i	−0.154824	+	0.425375i
$582$	−5.75753	+	12.5437i	−0.238657	+	0.519954i
$583$	−9.04295	−	1.59452i	−0.374521	−	0.0660381i
$584$	31.6721	+	4.08130i	1.31060	+	0.168885i
$585$	−0.647472	+	0.0633167i	−0.0267697	+	0.00261782i
$586$	−0.967376	−	3.05836i	−0.0399619	−	0.126340i
$587$	−19.9180	−	16.7132i	−0.822103	−	0.689826i	0.131361	−	0.991335i	$-0.458065\pi$
$587$	−19.9180	−	16.7132i	−0.822103	−	0.689826i	−0.953464	+	0.301508i	$0.902510\pi$
$588$	−23.0604	+	45.0590i	−0.950993	+	1.85820i
$589$	−3.78006	−	21.4378i	−0.155755	−	0.883328i
$590$	0.0690583	−	1.61562i	0.00284309	−	0.0665139i
$591$	33.9723	+	13.8689i	1.39743	+	0.570492i
$592$	9.95487	−	5.79613i	0.409143	−	0.238219i
$593$			7.68968i			0.315778i	0.987457	+	0.157889i	$0.0504687\pi$
$593$			7.68968i			0.315778i	−0.987457	+	0.157889i	$0.949531\pi$
$594$	1.21792	−	7.62954i	0.0499718	−	0.313044i
$595$		−	3.93227i		−	0.161207i
$596$	32.7914	−	15.3640i	1.34319	−	0.629334i
$597$	−9.17878	+	7.11789i	−0.375662	+	0.291316i
$598$	−5.57151	−	0.238150i	−0.227836	−	0.00973869i
$599$	−5.26567	−	29.8631i	−0.215150	−	1.22017i	−0.880647	−	0.473773i	$-0.842892\pi$
$599$	−5.26567	−	29.8631i	−0.215150	−	1.22017i	0.665497	−	0.746400i	$-0.268220\pi$
$600$	−18.8139	−	15.5366i	−0.768073	−	0.634279i
$601$	14.0780	+	11.8129i	0.574254	+	0.481857i	0.883055	−	0.469270i	$-0.155483\pi$
$601$	14.0780	+	11.8129i	0.574254	+	0.481857i	−0.308800	+	0.951127i	$0.599927\pi$
$602$	13.7187	−	4.33929i	0.559132	−	0.176856i
$603$	−1.30334	+	16.8816i	−0.0530762	+	0.687471i
$604$	16.7947	+	23.8922i	0.683368	+	0.972159i
$605$	1.35798	+	0.239449i	0.0552099	+	0.00973499i
$606$	−20.8940	+	14.8185i	−0.848761	+	0.601959i
$607$	−1.94501	+	5.34387i	−0.0789455	+	0.216901i	−0.972886	−	0.231284i	$-0.925707\pi$
$607$	−1.94501	+	5.34387i	−0.0789455	+	0.216901i	0.893941	+	0.448185i	$0.147930\pi$
$608$	19.6274	−	15.2038i	0.795997	−	0.616596i
$609$	−4.84271	−	1.04768i	−0.196236	−	0.0424543i
$610$	−1.34303	−	1.74696i	−0.0543779	−	0.0707325i
$611$	−8.59873	−	14.8934i	−0.347867	−	0.602524i
$612$	36.4142	−	0.438601i	1.47196	−	0.0177294i
$613$	−4.98728	+	8.63823i	−0.201434	+	0.348895i	−0.948991	−	0.315304i	$-0.897894\pi$
$613$	−4.98728	+	8.63823i	−0.201434	+	0.348895i	0.747556	+	0.664198i	$0.231227\pi$
$614$	−17.0224	+	2.25689i	−0.686969	+	0.0910806i
$615$	0.0612432	−	1.58887i	0.00246956	−	0.0640694i
$616$	−6.34987	+	12.2802i	−0.255844	+	0.494782i
$617$	12.6243	+	15.0451i	0.508236	+	0.605692i	0.957757	−	0.287577i	$-0.0928498\pi$
$617$	12.6243	+	15.0451i	0.508236	+	0.605692i	−0.449521	+	0.893270i	$0.648405\pi$
$618$	3.77185	+	0.307118i	0.151726	+	0.0123541i
$619$	−11.9916	−	32.9466i	−0.481983	−	1.32424i	−0.907791	−	0.419423i	$-0.862232\pi$
$619$	−11.9916	−	32.9466i	−0.481983	−	1.32424i	0.425808	−	0.904814i	$-0.359990\pi$
$620$	−0.123009	−	1.37697i	−0.00494015	−	0.0553005i
$621$	5.90059	−	11.7718i	0.236782	−	0.472388i
$622$	18.1295	+	16.5821i	0.726926	+	0.664882i
$623$	38.5254	−	14.0221i	1.54349	−	0.561784i
$624$	−2.24098	+	10.5451i	−0.0897109	+	0.422140i
$625$	18.9282	−	15.8827i	0.757129	−	0.635307i
$626$	−12.3485	+	19.4224i	−0.493543	+	0.776274i
$627$	−4.25985	+	6.76260i	−0.170122	+	0.270072i
$628$	−0.156793	+	0.224798i	−0.00625673	+	0.00897043i
$629$	−15.1373	−	8.73951i	−0.603563	−	0.348467i
$630$	−1.64893	+	2.19918i	−0.0656951	+	0.0876176i
$631$	−20.6478	+	11.9210i	−0.821976	+	0.474568i	−0.851097	−	0.525008i	$-0.824062\pi$
$631$	−20.6478	+	11.9210i	−0.821976	+	0.474568i	0.0291214	+	0.999576i	$0.490729\pi$
$632$	−3.48336	+	3.20954i	−0.138561	+	0.127669i
$633$	−29.0222	+	9.31389i	−1.15353	+	0.370194i
$634$	−36.5345	+	19.0612i	−1.45097	+	0.757015i
$635$	0.437918	+	0.159389i	0.0173783	+	0.00632517i
$636$	−18.2506	+	24.1294i	−0.723682	+	0.956791i
$637$	−3.94818	+	22.3913i	−0.156433	+	0.887174i
$638$	−0.893437	−	0.197213i	−0.0353715	−	0.00780772i
$639$	−9.99769	−	9.79551i	−0.395502	−	0.387504i
$640$	1.32433	−	0.855663i	0.0523487	−	0.0338231i
$641$	11.9138	−	14.1983i	0.470568	−	0.560801i	−0.477598	−	0.878579i	$-0.658492\pi$
$641$	11.9138	−	14.1983i	0.470568	−	0.560801i	0.948165	+	0.317778i	$0.102937\pi$
$642$	−18.6989	−	4.88987i	−0.737988	−	0.192988i
$643$	−35.2470	+	6.21500i	−1.39001	+	0.245096i	−0.818031	−	0.575175i	$-0.804934\pi$
$643$	−35.2470	+	6.21500i	−1.39001	+	0.245096i	−0.571976	+	0.820270i	$0.693823\pi$
$644$	−16.6303	+	16.6912i	−0.655324	+	0.657727i
$645$	0.523401	−	0.0716283i	0.0206089	−	0.00282036i
$646$	−34.8176	−	14.3846i	−1.36988	−	0.565955i
$647$	31.4863			1.23785			0.618926	−	0.785449i	$-0.287568\pi$
$647$	31.4863			1.23785			0.618926	+	0.785449i	$0.287568\pi$
$648$	−20.5491	−	15.0244i	−0.807246	−	0.590215i
$649$	8.62659			0.338623
$650$	−10.1297	−	4.18499i	−0.397318	−	0.164149i
$651$	39.5688	−	5.41506i	1.55082	−	0.212233i
$652$	−16.9691	+	17.0313i	−0.664560	+	0.666996i
$653$	−26.5025	+	4.67310i	−1.03712	+	0.182873i	−0.666186	−	0.745786i	$-0.732074\pi$
$653$	−26.5025	+	4.67310i	−1.03712	+	0.182873i	−0.370936	+	0.928658i	$0.620963\pi$
$654$	4.23127	+	1.10650i	0.165456	+	0.0432675i
$655$	−0.234869	+	0.279906i	−0.00917709	+	0.0109368i
$656$	−24.7928	−	8.92121i	−0.967995	−	0.348315i
$657$	−8.43185	+	32.8048i	−0.328958	+	1.27984i
$658$	−70.9537	−	15.6620i	−2.76606	−	0.610567i
$659$	−7.78431	+	44.1470i	−0.303234	+	1.71972i	0.328471	+	0.944514i	$0.393467\pi$
$659$	−7.78431	+	44.1470i	−0.303234	+	1.71972i	−0.631705	+	0.775209i	$0.717645\pi$
$660$	−0.306193	+	0.404822i	−0.0119185	+	0.0157577i
$661$	19.0048	+	6.91718i	0.739201	+	0.269047i	0.684054	−	0.729431i	$-0.260215\pi$
$661$	19.0048	+	6.91718i	0.739201	+	0.269047i	0.0551465	+	0.998478i	$0.482437\pi$
$662$	−3.42986	+	1.78946i	−0.133305	+	0.0695495i
$663$	15.5756	−	4.99857i	0.604907	−	0.194128i
$664$	4.49835	+	4.88212i	0.174570	+	0.189463i
$665$	2.46250	−	1.42173i	0.0954917	−	0.0551322i
$666$	4.80099	+	11.2353i	0.186035	+	0.435359i
$667$	−1.35045	−	0.779683i	−0.0522896	−	0.0301894i
$668$	12.8739	−	18.4576i	0.498106	−	0.714147i
$669$	8.55840	−	13.5866i	0.330887	−	0.525289i
$670$	0.596809	−	0.938697i	0.0230568	−	0.0362650i
$671$	9.00495	−	7.55605i	0.347632	−	0.291698i
$672$	26.4860	+	37.0571i	1.02172	+	1.42951i
$673$	40.4201	−	14.7117i	1.55808	−	0.567094i	0.587784	−	0.809018i	$-0.300001\pi$
$673$	40.4201	−	14.7117i	1.55808	−	0.567094i	0.970295	+	0.241924i	$0.0777784\pi$
$674$	7.19720	+	6.58291i	0.277226	+	0.253564i
$675$	18.8105	−	17.7744i	0.724017	−	0.684139i
$676$	−1.88256	−	21.0736i	−0.0724062	−	0.810522i
$677$	6.79083	+	18.6577i	0.260993	+	0.717072i	0.999101	+	0.0423898i	$0.0134971\pi$
$677$	6.79083	+	18.6577i	0.260993	+	0.717072i	−0.738108	+	0.674682i	$0.764281\pi$
$678$	−25.9328	−	2.11154i	−0.995942	−	0.0810932i
$679$	16.8376	+	20.0662i	0.646166	+	0.770071i
$680$	−2.12515	−	1.09888i	−0.0814957	−	0.0421401i
$681$	1.48893	−	38.6282i	0.0570559	−	1.48024i
$682$	7.31091	−	0.969305i	0.279949	−	0.0371166i
$683$	16.6637	−	28.8624i	0.637618	−	1.10439i	−0.348336	−	0.937370i	$-0.613253\pi$
$683$	16.6637	−	28.8624i	0.637618	−	1.10439i	0.985954	−	0.167017i	$-0.0534136\pi$
$684$	13.4403	+	22.6450i	0.513904	+	0.865855i
$685$	0.621199	+	1.07595i	0.0237348	+	0.0411098i
$686$	30.5013	+	39.6749i	1.16455	+	1.51479i
$687$	−44.5837	−	9.64534i	−1.70097	−	0.367993i
$688$	1.48859	−	8.62672i	0.0567520	−	0.328890i
$689$	−4.64799	+	12.7703i	−0.177074	+	0.486508i
$690$	−0.705630	+	0.500447i	−0.0268629	+	0.0190517i
$691$	1.92394	+	0.339243i	0.0731902	+	0.0129054i	0.210123	−	0.977675i	$-0.432613\pi$
$691$	1.92394	+	0.339243i	0.0731902	+	0.0129054i	−0.136933	+	0.990580i	$0.543725\pi$
$692$	6.55923	+	9.33116i	0.249345	+	0.354718i
$693$	−12.0968	−	8.28743i	−0.459519	−	0.314813i
$694$	−30.8855	+	9.76923i	−1.17240	+	0.370835i
$695$	−1.60195	−	1.34420i	−0.0607654	−	0.0509882i
$696$	−1.91951	+	2.32441i	−0.0727588	+	0.0881064i
$697$	6.94264	+	39.3737i	0.262971	+	1.49138i
$698$	38.3294	+	1.63836i	1.45079	+	0.0620130i
$699$	10.2672	−	7.96192i	0.388340	−	0.301147i
$700$	−41.9334	+	19.6474i	−1.58493	+	0.742601i
$701$			15.9132i			0.601032i	0.953777	+	0.300516i	$0.0971588\pi$
$701$			15.9132i			0.601032i	−0.953777	+	0.300516i	$0.902841\pi$
$702$	−10.8070	−	3.73586i	−0.407884	−	0.141001i
$703$		−	12.6392i		−	0.476697i
$704$	4.86219	+	6.86342i	0.183251	+	0.258675i
$705$	−2.46989	−	1.00832i	−0.0930216	−	0.0379754i
$706$	−0.406790	+	9.51682i	−0.0153097	+	0.358170i
$707$	8.44192	+	47.8765i	0.317491	+	1.80058i
$708$	12.9489	−	25.3016i	0.486650	−	0.950893i
$709$	−25.2965	−	21.2262i	−0.950028	−	0.797169i	0.0292739	−	0.999571i	$-0.490681\pi$
$709$	−25.2965	−	21.2262i	−0.950028	−	0.797169i	−0.979302	+	0.202403i	$0.935125\pi$
$710$	0.277309	+	0.876713i	0.0104072	+	0.0329024i
$711$	−2.92346	−	4.08567i	−0.109638	−	0.153225i
$712$	3.18791	−	24.7391i	0.119472	−	0.927137i
$713$	12.3783	+	2.18262i	0.463570	+	0.0817399i
$714$	28.8315	−	62.8143i	1.07899	−	2.35077i
$715$	−0.0779800	+	0.214248i	−0.00291629	+	0.00801244i
$716$	6.37679	−	23.9739i	0.238312	−	0.895946i
$717$	3.99600	−	4.40583i	0.149233	−	0.164539i
$718$	32.2013	−	24.7558i	1.20174	−	0.923876i
$719$	−4.06158	−	7.03487i	−0.151471	−	0.262356i	0.780297	−	0.625409i	$-0.215068\pi$
$719$	−4.06158	−	7.03487i	−0.151471	−	0.262356i	−0.931769	+	0.363053i	$0.881734\pi$
$720$	0.727726	+	1.50571i	0.0271207	+	0.0561146i
$721$	3.59112	−	6.22000i	0.133740	−	0.231645i
$722$	−0.0487432	−	0.367642i	−0.00181403	−	0.0136822i
$723$	−2.60830	+	1.37477i	−0.0970038	+	0.0511283i
$724$	2.24804	−	0.606772i	0.0835478	−	0.0225505i
$725$	−1.96998	−	2.34773i	−0.0731631	−	0.0871924i
$726$	19.9369	+	13.7818i	0.739926	+	0.511489i
$727$	−12.8952	−	35.4294i	−0.478258	−	1.31400i	−0.910971	−	0.412470i	$-0.864666\pi$
$727$	−12.8952	−	35.4294i	−0.478258	−	1.31400i	0.432713	−	0.901532i	$-0.357556\pi$
$728$	16.2664	+	12.4108i	0.602872	+	0.459976i
$729$	18.4980	−	19.6679i	0.685110	−	0.728439i
$730$	1.50182	−	1.64196i	0.0555849	−	0.0607718i
$731$	−12.4823	+	4.54317i	−0.461673	+	0.168035i
$732$	−8.64490	−	37.7533i	−0.319525	−	1.39540i
$733$	−22.3955	+	18.7921i	−0.827198	+	0.694101i	−0.954646	−	0.297744i	$-0.903766\pi$
$733$	−22.3955	+	18.7921i	−0.827198	+	0.694101i	0.127448	+	0.991845i	$0.459321\pi$
$734$	−4.66119	−	2.96351i	−0.172048	−	0.109385i
$735$	1.64457	+	3.12018i	0.0606610	+	0.115090i
$736$	4.37323	+	13.6520i	0.161199	+	0.503220i
$737$	5.13900	+	2.96700i	0.189298	+	0.109291i
$738$	12.6279	−	24.9317i	0.464841	−	0.917747i
$739$	−34.0829	+	19.6778i	−1.25376	+	0.723858i	−0.971854	−	0.235584i	$-0.924300\pi$
$739$	−34.0829	+	19.6778i	−1.25376	+	0.723858i	−0.281905	+	0.959442i	$0.590966\pi$
$740$	0.0684948	−	0.799752i	0.00251792	−	0.0293995i
$741$	8.76168	+	7.94666i	0.321868	+	0.291928i
$742$	26.5597	+	50.9069i	0.975036	+	1.86885i
$743$	−10.4717	−	3.81140i	−0.384171	−	0.139827i	0.142713	−	0.989764i	$-0.454417\pi$
$743$	−10.4717	−	3.81140i	−0.384171	−	0.139827i	−0.526884	+	0.849937i	$0.676640\pi$
$744$	8.13105	−	22.8977i	0.298099	−	0.839471i
$745$	0.438169	−	2.48498i	0.0160533	−	0.0910427i
$746$	−3.32426	+	15.0600i	−0.121710	+	0.551385i
$747$	−5.72629	+	4.09739i	−0.209514	+	0.149916i
$748$	5.37262	−	11.5769i	0.196442	−	0.423293i
$749$	−23.5787	+	28.0999i	−0.861545	+	1.02675i
$750$	−3.28558	+	0.901609i	−0.119972	+	0.0329221i
$751$	−28.7902	+	5.07650i	−1.05057	+	0.185244i	−0.672169	−	0.740397i	$-0.734637\pi$
$751$	−28.7902	+	5.07650i	−1.05057	+	0.185244i	−0.378402	+	0.925641i	$0.623526\pi$
$752$	−28.2924	+	33.9693i	−1.03172	+	1.23873i
$753$	−10.2096	+	25.0087i	−0.372060	+	0.911369i
$754$	−0.517045	+	1.25149i	−0.0188297	+	0.0455767i
$755$	2.03500			0.0740613
$756$	−42.4647	+	23.0398i	−1.54443	+	0.837951i
$757$	−8.57552			−0.311682			−0.155841	−	0.987782i	$-0.549809\pi$
$757$	−8.57552			−0.311682			−0.155841	+	0.987782i	$0.549809\pi$
$758$	3.21443	−	7.78044i	0.116753	−	0.282598i
$759$	−2.82802	−	3.64683i	−0.102651	−	0.132372i
$760$	−0.0802050	−	1.72813i	−0.00290934	−	0.0626860i
$761$	−5.54033	+	0.976910i	−0.200837	+	0.0354130i	−0.273161	−	0.961968i	$-0.588069\pi$
$761$	−5.54033	+	0.976910i	−0.200837	+	0.0354130i	0.0723247	+	0.997381i	$0.476958\pi$
$762$	5.82669	+	5.75693i	0.211079	+	0.208552i
$763$	5.33548	−	6.35857i	0.193157	−	0.230196i
$764$	−26.0941	−	12.1098i	−0.944051	−	0.438117i
$765$	1.43418	−	2.09341i	0.0518530	−	0.0756875i
$766$	2.03501	−	9.21927i	0.0735281	−	0.333106i
$767$	2.21699	−	12.5732i	0.0800509	−	0.453991i
$768$	27.4287	−	3.95839i	0.989746	−	0.142836i
$769$	−2.35854	−	0.858439i	−0.0850512	−	0.0309561i	0.299144	−	0.954208i	$-0.403299\pi$
$769$	−2.35854	−	0.858439i	−0.0850512	−	0.0309561i	−0.384195	+	0.923252i	$0.625521\pi$
$770$	0.445596	+	0.854072i	0.0160582	+	0.0307786i
$771$	3.63650	−	16.8090i	0.130965	−	0.605361i
$772$	−36.6562	−	3.13942i	−1.31929	−	0.112990i
$773$	0.0355587	−	0.0205298i	0.00127896	−	0.000738407i	−0.499360	−	0.866394i	$-0.666432\pi$
$773$	0.0355587	−	0.0205298i	0.00127896	−	0.000738407i	0.500639	+	0.865656i	$0.333098\pi$
$774$	8.88601	+	2.69340i	0.319401	+	0.0968122i
$775$	21.3937	+	12.3516i	0.768483	+	0.443684i
$776$	15.5498	−	3.49212i	0.558206	−	0.125360i
$777$	23.1713	+	0.893143i	0.831267	+	0.0320413i
$778$	36.3751	+	23.1267i	1.30411	+	0.829134i
$779$	−22.1468	+	18.5834i	−0.793492	+	0.665819i
$780$	0.511335	+	0.550311i	0.0183087	+	0.0197043i
$781$	−4.60950	+	1.67772i	−0.164941	+	0.0600335i
$782$	14.6808	−	16.0507i	0.524983	−	0.573972i
$783$	−2.19599	−	2.32399i	−0.0784783	−	0.0830527i
$784$	57.5221	−	10.3599i	2.05436	−	0.369997i
$785$	0.00653192	+	0.0179463i	0.000233134	+	0.000640531i
$786$	−5.80410	+	2.74917i	−0.207025	+	0.0980596i
$787$	−27.9726	−	33.3365i	−0.997116	−	1.18832i	−0.982087	−	0.188429i	$-0.939660\pi$
$787$	−27.9726	−	33.3365i	−0.997116	−	1.18832i	−0.0150289	−	0.999887i	$-0.504784\pi$
$788$	−11.0412	−	40.9069i	−0.393328	−	1.45725i
$789$	−38.3220	−	24.1395i	−1.36430	−	0.859391i
$790$	0.0433794	+	0.327186i	0.00154337	+	0.0116407i
$791$	−24.6902	+	42.7647i	−0.877882	+	1.52054i
$792$	−7.85931	+	4.22163i	−0.279268	+	0.150009i
$793$	−8.69865	−	15.0665i	−0.308898	−	0.535028i
$794$	−17.6616	+	13.5779i	−0.626787	+	0.481863i
$795$	0.644191	+	2.00731i	0.0228471	+	0.0711918i
$796$	12.9615	+	3.44761i	0.459407	+	0.122197i
$797$	15.3705	−	42.2300i	0.544450	−	1.49586i	−0.296652	−	0.954986i	$-0.595870\pi$
$797$	15.3705	−	42.2300i	0.544450	−	1.49586i	0.841102	−	0.540877i	$-0.181908\pi$
$798$	49.7603	−	4.65558i	1.76150	−	0.164806i
$799$	66.0612	+	11.6484i	2.33708	+	0.412090i
$800$	−1.10017	+	28.1529i	−0.0388969	+	0.995356i
$801$	25.6239	+	6.58613i	0.905375	+	0.232709i
$802$	1.32171	+	4.17860i	0.0466713	+	0.147552i
$803$	9.09342	+	7.63028i	0.320900	+	0.269267i
$804$	16.4160	−	10.6190i	0.578949	−	0.374503i
$805$	0.285100	+	1.61688i	0.0100484	+	0.0569875i
$806$	0.466114	−	10.9047i	0.0164182	−	0.384102i
$807$	−0.109249	−	0.798299i	−0.00384573	−	0.0281014i
$808$	28.2334	+	8.81683i	0.993248	+	0.310175i
$809$		−	39.4534i		−	1.38711i	−0.720405	−	0.693553i	$-0.756044\pi$
$809$		−	39.4534i		−	1.38711i	0.720405	−	0.693553i	$-0.243956\pi$
$810$	−1.67993	+	0.569373i	−0.0590267	+	0.0200057i
$811$			49.4348i			1.73589i	0.496659	+	0.867946i	$0.334560\pi$
$811$			49.4348i			1.73589i	−0.496659	+	0.867946i	$0.665440\pi$
$812$	2.42739	+	5.18077i	0.0851845	+	0.181809i
$813$	3.67716	+	26.8696i	0.128964	+	0.942359i
$814$	4.27810	+	0.182864i	0.149947	+	0.00640938i
$815$	0.290908	+	1.64982i	0.0101900	+	0.0577906i
$816$	−25.8902	−	33.1352i	−0.906339	−	1.15996i
$817$	−7.35807	−	6.17416i	−0.257426	−	0.216006i
$818$	35.3998	−	11.1971i	1.23773	−	0.391499i
$819$	−15.1877	+	15.5012i	−0.530700	+	0.541654i
$820$	−1.50206	+	1.05585i	−0.0524541	+	0.0368720i
$821$	21.7656	+	3.83786i	0.759624	+	0.133942i	0.540026	−	0.841648i	$-0.318414\pi$
$821$	21.7656	+	3.83786i	0.759624	+	0.133942i	0.219598	+	0.975590i	$0.429525\pi$
$822$	2.03418	+	21.7419i	0.0709500	+	0.758336i
$823$	−6.69131	+	18.3842i	−0.233244	+	0.640833i	−0.999999	−	0.00110635i	$-0.999648\pi$
$823$	−6.69131	+	18.3842i	−0.233244	+	0.640833i	0.766755	+	0.641940i	$0.221870\pi$
$824$	−2.35798	−	3.67897i	−0.0821442	−	0.128163i
$825$	−2.77153	−	8.63614i	−0.0964925	−	0.300672i
$826$	−32.8776	−	42.7658i	−1.14396	−	1.48801i
$827$	8.39197	+	14.5353i	0.291817	+	0.505442i	0.974239	−	0.225516i	$-0.0724068\pi$
$827$	8.39197	+	14.5353i	0.291817	+	0.505442i	−0.682422	+	0.730958i	$0.739073\pi$
$828$	−14.9411	+	2.82047i	−0.519238	+	0.0980180i
$829$	−18.8116	+	32.5827i	−0.653355	+	1.13164i	0.328949	+	0.944348i	$0.393306\pi$
$829$	−18.8116	+	32.5827i	−0.653355	+	1.13164i	−0.982304	+	0.187296i	$0.940028\pi$
$830$	0.458569	−	0.0607987i	0.0159172	−	0.00211035i
$831$	14.4528	+	9.10402i	0.501363	+	0.315815i
$832$	11.2529	−	5.32274i	0.390126	−	0.184533i
$833$	−57.0065	−	67.9377i	−1.97516	−	2.35390i
$834$	−15.7339	−	33.2178i	−0.544822	−	1.15024i
$835$	−0.536320	−	1.47353i	−0.0185601	−	0.0509935i
$836$	9.19227	−	0.821172i	0.317921	−	0.0284008i
$837$	23.0401	+	11.5488i	0.796384	+	0.399184i
$838$	−37.7429	−	34.5215i	−1.30381	−	1.19253i
$839$	51.7302	−	18.8283i	1.78592	−	0.650024i	0.786449	−	0.617655i	$-0.211917\pi$
$839$	51.7302	−	18.8283i	1.78592	−	0.650024i	0.999476	−	0.0323683i	$-0.0103049\pi$
$840$	3.17384	−	0.0249215i	0.109508	−	0.000859874i
$841$	21.9252	−	18.3975i	0.756043	−	0.634395i
$842$	−9.61979	+	15.1306i	−0.331520	+	0.521434i
$843$	−29.5344	−	1.13841i	−1.01722	−	0.0392089i
$844$	28.8673	+	20.1345i	0.993652	+	0.693057i
$845$	−1.27676	−	0.737140i	−0.0439220	−	0.0253584i
$846$	−32.0612	−	34.2163i	−1.10229	−	1.17638i
$847$	39.8358	−	22.9992i	1.36878	−	0.790263i
$848$	34.9342	−	0.127853i	1.19964	−	0.00439048i
$849$	−3.47588	+	16.0666i	−0.119292	+	0.551404i
$850$	37.9024	−	19.7749i	1.30004	−	0.678272i
$851$	6.85782	+	2.49604i	0.235083	+	0.0855633i
$852$	−1.99835	+	16.0379i	−0.0684622	+	0.549449i
$853$	1.97889	−	11.2229i	0.0677560	−	0.384263i	−0.932006	−	0.362443i	$-0.881943\pi$
$853$	1.97889	−	11.2229i	0.0677560	−	0.384263i	0.999762	−	0.0218204i	$-0.00694619\pi$
$854$	−71.7782	−	15.8440i	−2.45620	−	0.542169i
$855$	1.82949	+	0.141246i	0.0625672	+	0.00483050i
$856$	8.59719	+	20.5954i	0.293846	+	0.703936i
$857$	17.0466	−	20.3153i	0.582300	−	0.693958i	−0.391807	−	0.920048i	$-0.628150\pi$
$857$	17.0466	−	20.3153i	0.582300	−	0.693958i	0.974106	+	0.226090i	$0.0725943\pi$
$858$	−2.81654	+	2.85066i	−0.0961549	+	0.0973201i
$859$	−7.71712	+	1.36074i	−0.263305	+	0.0464277i	−0.303742	−	0.952754i	$-0.598236\pi$
$859$	−7.71712	+	1.36074i	−0.263305	+	0.0464277i	0.0404372	+	0.999182i	$0.487125\pi$
$860$	−0.432127	−	0.430548i	−0.0147354	−	0.0146816i
$861$	−32.5037	−	41.9147i	−1.10772	−	1.42845i
$862$	14.7741	+	6.10381i	0.503208	+	0.207896i
$863$	−32.9090			−1.12023			−0.560117	−	0.828413i	$-0.689244\pi$
$863$	−32.9090			−1.12023			−0.560117	+	0.828413i	$0.689244\pi$
$864$	0.584789	+	29.3881i	0.0198949	+	0.999802i
$865$	0.794776			0.0270232
$866$	−23.6654	−	9.77716i	−0.804182	−	0.332242i
$867$	−12.9872	+	31.8123i	−0.441067	+	1.08040i
$868$	−32.6685	−	32.5492i	−1.10884	−	1.10479i
$869$	−1.73394	+	0.305741i	−0.0588199	+	0.0103715i
$870$	0.0555874	+	0.202568i	0.00188459	+	0.00686768i
$871$	5.64508	−	6.72755i	0.191276	−	0.227954i
$872$	−1.94541	−	4.66041i	−0.0658798	−	0.157821i
$873$	1.64519	+	16.8236i	0.0556814	+	0.569394i
$874$	15.3593	+	3.39034i	0.519536	+	0.114680i
$875$	−1.12284	+	6.36795i	−0.0379590	+	0.215276i
$876$	36.0291	−	15.2174i	1.21731	−	0.514149i
$877$	−37.2032	−	13.5408i	−1.25626	−	0.457242i	−0.373748	−	0.927530i	$-0.621928\pi$
$877$	−37.2032	−	13.5408i	−1.25626	−	0.457242i	−0.882513	+	0.470288i	$0.844150\pi$
$878$	−17.1466	+	8.94588i	−0.578668	+	0.301909i
$879$	−2.91000	−	2.63931i	−0.0981520	−	0.0890219i
$880$	0.586096	−	0.00214500i	0.0197573	−	7.23081e-5i
$881$	−20.1797	+	11.6507i	−0.679870	+	0.392523i	−0.799806	−	0.600259i	$-0.795064\pi$
$881$	−20.1797	+	11.6507i	−0.679870	+	0.392523i	0.119936	+	0.992782i	$0.461731\pi$
$882$	3.39320	+	61.9001i	0.114255	+	2.08428i
$883$	44.2753	+	25.5624i	1.48998	+	0.860242i	0.999934	−	0.0114524i	$-0.00364550\pi$
$883$	44.2753	+	25.5624i	1.48998	+	0.860242i	0.490049	+	0.871695i	$0.336979\pi$
$884$	−15.4925	−	10.8058i	−0.521068	−	0.363437i
$885$	−0.923464	−	1.75205i	−0.0310419	−	0.0588946i
$886$	8.25639	−	12.9861i	0.277379	−	0.436278i
$887$	5.23482	−	4.39254i	0.175768	−	0.147487i	−0.550659	−	0.834730i	$-0.685624\pi$
$887$	5.23482	−	4.39254i	0.175768	−	0.147487i	0.726428	+	0.687243i	$0.241179\pi$
$888$	6.95795	−	12.2731i	0.233494	−	0.411858i
$889$	14.6081	−	5.31691i	0.489940	−	0.178324i
$890$	−1.28254	−	1.17307i	−0.0429908	−	0.0393215i
$891$	−3.41734	−	8.82392i	−0.114485	−	0.295612i
$892$	−18.4680	+	1.64980i	−0.618356	+	0.0552395i
$893$	16.5901	+	45.5809i	0.555167	+	1.52531i
$894$	25.2193	−	36.4826i	0.843460	−	1.22016i
$895$	−1.11113	−	1.32420i	−0.0371411	−	0.0442630i
$896$	15.4943	−	50.2618i	0.517628	−	1.67913i
$897$	−6.04202	+	3.18460i	−0.201737	+	0.106331i
$898$	9.87813	−	1.30968i	0.329638	−	0.0437045i
$899$	1.52601	−	2.64313i	0.0508954	−	0.0881535i
$900$	−29.4898	−	4.83439i	−0.982995	−	0.161146i
$901$	−26.5042	−	45.9065i	−0.882981	−	1.52937i
$902$	−5.96965	−	7.76508i	−0.198768	−	0.258549i
$903$	11.8390	−	13.0532i	0.393977	−	0.434383i
$904$	16.2119	+	25.2942i	0.539201	+	0.841272i
$905$	0.0554934	−	0.152467i	0.00184466	−	0.00506817i
$906$	32.5073	+	14.9207i	1.07998	+	0.495708i
$907$	−7.37773	−	1.30089i	−0.244974	−	0.0431955i	0.0498130	−	0.998759i	$-0.484137\pi$
$907$	−7.37773	−	1.30089i	−0.244974	−	0.0431955i	−0.294787	+	0.955563i	$0.595249\pi$
$908$	−36.5177	+	25.6697i	−1.21188	+	0.851878i
$909$	−12.9674	+	28.5669i	−0.430101	+	0.947503i
$910$	1.35932	−	0.429960i	0.0450610	−	0.0142530i
$911$	−19.8453	−	16.6521i	−0.657503	−	0.551710i	0.251835	−	0.967770i	$-0.418966\pi$
$911$	−19.8453	−	16.6521i	−0.657503	−	0.551710i	−0.909337	+	0.416060i	$0.863411\pi$
$912$	11.3895	−	28.1934i	0.377145	−	0.933576i
$913$	0.428513	+	2.43022i	0.0141817	+	0.0804284i
$914$	35.9637	+	1.53724i	1.18957	+	0.0508474i
$915$	−2.49859	−	1.02003i	−0.0826010	−	0.0337213i
$916$	22.3474	+	47.6960i	0.738378	+	1.57592i
$917$			12.1887i			0.402508i
$918$	38.2587	−	22.9248i	1.26273	−	0.756632i
$919$		−	37.4197i		−	1.23436i	−0.786821	−	0.617182i	$-0.788274\pi$
$919$		−	37.4197i		−	1.23436i	0.786821	−	0.617182i	$-0.211726\pi$
$920$	0.953495	+	0.297761i	0.0314358	+	0.00981689i
$921$	−16.6191	+	12.8876i	−0.547616	+	0.424662i
$922$	−2.36785	+	55.3957i	−0.0779810	+	1.82436i
$923$	1.26065	+	7.14947i	0.0414946	+	0.235328i
$924$	0.855880	+	16.9101i	0.0281564	+	0.556302i
$925$	10.9875	+	9.21963i	0.361268	+	0.303140i
$926$	3.19017	+	10.0857i	0.104835	+	0.331438i
$927$	4.18037	−	2.00157i	0.137301	−	0.0657403i
$928$	3.47822	+	0.135923i	0.114178	+	0.00446190i
$929$	−12.0979	−	2.13318i	−0.396919	−	0.0699875i	−0.0283738	−	0.999597i	$-0.509033\pi$
$929$	−12.0979	−	2.13318i	−0.396919	−	0.0699875i	−0.368545	+	0.929610i	$0.620144\pi$
$930$	−0.979488	−	1.38108i	−0.0321187	−	0.0452873i
$931$	21.9337	−	60.2623i	0.718848	−	1.97502i
$932$	−14.4984	−	3.85642i	−0.474911	−	0.126321i
$933$	29.4106	+	6.36276i	0.962859	+	0.208307i
$934$	1.54708	−	1.18937i	0.0506220	−	0.0389173i
$935$	−0.444664	−	0.770181i	−0.0145421	−	0.0251876i
$936$	4.13319	+	12.5398i	0.135098	+	0.409877i
$937$	−20.8028	+	36.0316i	−0.679599	+	1.17710i	0.295503	+	0.955342i	$0.404513\pi$
$937$	−20.8028	+	36.0316i	−0.679599	+	1.17710i	−0.975102	+	0.221758i	$0.928821\pi$
$938$	−4.87696	−	36.7841i	−0.159238	−	1.20104i
$939$	−1.08571	+	28.1672i	−0.0354308	+	0.919202i
$940$	0.802734	+	2.97406i	0.0261823	+	0.0970032i
$941$	33.5803	+	40.0194i	1.09469	+	1.30460i	0.949004	+	0.315265i	$0.102093\pi$
$941$	33.5803	+	40.0194i	1.09469	+	1.30460i	0.145682	+	0.989331i	$0.453462\pi$
$942$	−0.0272417	+	0.334568i	−0.000887582	+	0.0109008i
$943$	−5.70939	−	15.6864i	−0.185923	−	0.510820i
$944$	−32.2999	+	5.81732i	−1.05127	+	0.189338i
$945$	−0.388224	+	3.34401i	−0.0126289	+	0.108781i
$946$	2.19627	−	2.40122i	0.0714070	−	0.0780704i
$947$	−16.5986	+	6.04138i	−0.539380	+	0.196318i	−0.597322	−	0.802002i	$-0.703769\pi$
$947$	−16.5986	+	6.04138i	−0.539380	+	0.196318i	0.0579415	+	0.998320i	$0.481546\pi$
$948$	−1.70599	+	5.54455i	−0.0554081	+	0.180079i
$949$	13.4580	−	11.2926i	0.436867	−	0.366575i
$950$	26.0874	+	16.5859i	0.846386	+	0.538119i
$951$	−26.8994	+	42.7033i	−0.872272	+	1.38475i
$952$	−77.8677	+	17.4872i	−2.52371	+	0.566765i
$953$	47.6750	+	27.5252i	1.54435	+	0.891628i	0.998557	+	0.0537052i	$0.0171031\pi$
$953$	47.6750	+	27.5252i	1.54435	+	0.891628i	0.545788	+	0.837923i	$0.316230\pi$
$954$	−4.42731	+	36.7881i	−0.143340	+	1.19106i
$955$	−1.73597	+	1.00227i	−0.0561748	+	0.0324325i
$956$	−6.84317	−	0.586084i	−0.221324	−	0.0189553i
$957$	−1.06697	+	0.342416i	−0.0344904	+	0.0110687i
$958$	8.32514	+	15.9568i	0.268973	+	0.515540i
$959$	38.9446	+	14.1747i	1.25759	+	0.457724i
$960$	0.873465	−	1.72223i	0.0281910	−	0.0555846i
$961$	1.11121	−	6.30196i	0.0358453	−	0.203289i
$962$	1.36597	−	6.18830i	0.0440407	−	0.199519i
$963$	−22.8012	+	6.35987i	−0.734758	+	0.204944i
$964$	3.08820	+	1.43318i	0.0994642	+	0.0461595i
$965$	−1.64785	+	1.96383i	−0.0530462	+	0.0632180i
$966$	−7.30083	+	27.9185i	−0.234900	+	0.898263i
$967$	−16.5590	+	2.91980i	−0.532502	+	0.0938945i	−0.433433	−	0.901186i	$-0.642698\pi$
$967$	−16.5590	+	2.91980i	−0.532502	+	0.0938945i	−0.0990696	+	0.995081i	$0.531587\pi$
$968$	−1.29748	−	27.9560i	−0.0417024	−	0.898539i
$969$	−45.7125	+	6.25584i	−1.46850	+	0.200967i
$970$	0.424038	−	1.02637i	0.0136151	−	0.0329549i
$971$	−22.4986			−0.722013			−0.361007	−	0.932563i	$-0.617567\pi$
$971$	−22.4986			−0.722013			−0.361007	+	0.932563i	$0.617567\pi$
$972$	−31.0100	−	3.22211i	−0.994645	−	0.103349i
$973$	−69.7582			−2.23635
$974$	−6.69232	+	16.1986i	−0.214436	+	0.519037i
$975$	−13.2994	+	1.82004i	−0.425921	+	0.0582880i
$976$	−28.6212	+	34.3641i	−0.916143	+	1.09997i
$977$	8.62912	−	1.52155i	0.276070	−	0.0486786i	−0.0338989	−	0.999425i	$-0.510792\pi$
$977$	8.62912	−	1.52155i	0.276070	−	0.0486786i	0.309969	+	0.950747i	$0.399681\pi$
$978$	−7.44956	+	28.4873i	−0.238211	+	0.910922i
$979$	5.96003	−	7.10288i	0.190483	−	0.227009i
$980$	1.71444	−	3.69426i	0.0547658	−	0.118009i
$981$	5.15955	−	1.43914i	0.164732	−	0.0459481i
$982$	−8.09645	+	36.6795i	−0.258368	+	1.17049i
$983$	−1.90169	+	10.7850i	−0.0606544	+	0.343988i	0.939345	+	0.342973i	$0.111434\pi$
$983$	−1.90169	+	10.7850i	−0.0606544	+	0.343988i	−0.999999	+	0.00101465i	$0.999677\pi$
$984$	−31.7355	+	5.85313i	−1.01169	+	0.186591i
$985$	−2.77440	−	1.00980i	−0.0883996	−	0.0321748i
$986$	−2.44314	−	4.68275i	−0.0778053	−	0.149129i
$987$	−84.7354	+	27.1935i	−2.69716	+	0.865580i
$988$	1.16552	−	13.6087i	0.0370801	−	0.432950i
$989$	4.80310	−	2.77307i	0.152730	−	0.0881785i
$990$	−0.0742777	+	0.617199i	−0.00236070	+	0.0196159i
$991$	−31.9842	−	18.4661i	−1.01601	−	0.586594i	−0.103065	−	0.994675i	$-0.532865\pi$
$991$	−31.9842	−	18.4661i	−1.01601	−	0.586594i	−0.912946	+	0.408081i	$0.866198\pi$
$992$	−26.7201	+	8.55940i	−0.848364	+	0.271761i
$993$	−2.52532	+	4.00899i	−0.0801385	+	0.127221i
$994$	25.8849	+	16.4572i	0.821018	+	0.521991i
$995$	0.715926	−	0.600734i	0.0226964	−	0.0190445i
$996$	7.77099	+	2.39105i	0.246233	+	0.0757632i
$997$	35.4190	−	12.8915i	1.12173	−	0.408276i	0.286447	−	0.958096i	$-0.407526\pi$
$997$	35.4190	−	12.8915i	1.12173	−	0.408276i	0.835283	+	0.549820i	$0.185304\pi$
$998$	−9.20246	+	10.0612i	−0.291299	+	0.318481i
$999$	12.0099	+	8.92656i	0.379977	+	0.282424i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.2.l.a.47.3	yes	96
3.2	odd	2		324.2.l.a.143.14		96
4.3	odd	2	inner	108.2.l.a.47.11	yes	96
9.2	odd	6		972.2.l.a.107.8		96
9.4	even	3		972.2.l.c.755.13		96
9.5	odd	6		972.2.l.b.755.4		96
9.7	even	3		972.2.l.d.107.9		96
12.11	even	2		324.2.l.a.143.6		96
27.4	even	9		324.2.l.a.179.6		96
27.5	odd	18		972.2.l.c.215.11		96
27.13	even	9		972.2.l.a.863.16		96
27.14	odd	18		972.2.l.d.863.1		96
27.22	even	9		972.2.l.b.215.6		96
27.23	odd	18	inner	108.2.l.a.23.11	yes	96
36.7	odd	6		972.2.l.d.107.1		96
36.11	even	6		972.2.l.a.107.16		96
36.23	even	6		972.2.l.b.755.6		96
36.31	odd	6		972.2.l.c.755.11		96
108.23	even	18	inner	108.2.l.a.23.3	✓	96
108.31	odd	18		324.2.l.a.179.14		96
108.59	even	18		972.2.l.c.215.13		96
108.67	odd	18		972.2.l.a.863.8		96
108.95	even	18		972.2.l.d.863.9		96
108.103	odd	18		972.2.l.b.215.4		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.3	✓	96	108.23	even	18	inner
108.2.l.a.23.11	yes	96	27.23	odd	18	inner
108.2.l.a.47.3	yes	96	1.1	even	1	trivial
108.2.l.a.47.11	yes	96	4.3	odd	2	inner
324.2.l.a.143.6		96	12.11	even	2
324.2.l.a.143.14		96	3.2	odd	2
324.2.l.a.179.6		96	27.4	even	9
324.2.l.a.179.14		96	108.31	odd	18
972.2.l.a.107.8		96	9.2	odd	6
972.2.l.a.107.16		96	36.11	even	6
972.2.l.a.863.8		96	108.67	odd	18
972.2.l.a.863.16		96	27.13	even	9
972.2.l.b.215.4		96	108.103	odd	18
972.2.l.b.215.6		96	27.22	even	9
972.2.l.b.755.4		96	9.5	odd	6
972.2.l.b.755.6		96	36.23	even	6
972.2.l.c.215.11		96	27.5	odd	18
972.2.l.c.215.13		96	108.59	even	18
972.2.l.c.755.11		96	36.31	odd	6
972.2.l.c.755.13		96	9.4	even	3
972.2.l.d.107.1		96	36.7	odd	6
972.2.l.d.107.9		96	9.7	even	3
972.2.l.d.863.1		96	27.14	odd	18
972.2.l.d.863.9		96	108.95	even	18

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	108.l (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30706 - 0.540000i) q^{2} +(-1.71606 + 0.234845i) q^{3} +(1.41680 + 1.41162i) q^{4} +(0.137245 - 0.0242000i) q^{5} +(2.36980 + 0.619715i) q^{6} +(2.98823 - 3.56123i) q^{7} +(-1.08956 - 2.61015i) q^{8} +(2.88970 - 0.806015i) q^{9} +O(q^{10})\)	\(q+(-1.30706 - 0.540000i) q^{2} +(-1.71606 + 0.234845i) q^{3} +(1.41680 + 1.41162i) q^{4} +(0.137245 - 0.0242000i) q^{5} +(2.36980 + 0.619715i) q^{6} +(2.98823 - 3.56123i) q^{7} +(-1.08956 - 2.61015i) q^{8} +(2.88970 - 0.806015i) q^{9} +(-0.192456 - 0.0424817i) q^{10} +(0.182573 - 1.03542i) q^{11} +(-2.76282 - 2.08970i) q^{12} +(-1.46220 - 0.532196i) q^{13} +(-5.82886 + 3.04109i) q^{14} +(-0.229837 + 0.0737600i) q^{15} +(0.0146392 + 3.99997i) q^{16} +(5.25631 - 3.03473i) q^{17} +(-4.21225 - 0.506929i) q^{18} +(3.80088 + 2.19444i) q^{19} +(0.228610 + 0.159452i) q^{20} +(-4.29163 + 6.81305i) q^{21} +(-0.797761 + 1.25477i) q^{22} +(-1.94128 + 1.62893i) q^{23} +(2.48273 + 4.22328i) q^{24} +(-4.68021 + 1.70346i) q^{25} +(1.62379 + 1.48520i) q^{26} +(-4.76959 + 2.06180i) q^{27} +(9.26084 - 0.827297i) q^{28} +(0.210458 + 0.578229i) q^{29} +(0.340241 + 0.0277036i) q^{30} +(-3.18818 - 3.79952i) q^{31} +(2.14085 - 5.23610i) q^{32} +(-0.0701412 + 1.81972i) q^{33} +(-8.50906 + 1.12816i) q^{34} +(0.323938 - 0.561078i) q^{35} +(5.23191 + 2.93720i) q^{36} +(-1.43991 - 2.49400i) q^{37} +(-3.78297 - 4.92073i) q^{38} +(2.63420 + 0.569889i) q^{39} +(-0.212703 - 0.331863i) q^{40} +(-2.25297 + 6.18999i) q^{41} +(9.28846 - 6.58756i) q^{42} +(-2.15530 - 0.380038i) q^{43} +(1.72029 - 1.20926i) q^{44} +(0.377091 - 0.180553i) q^{45} +(3.41698 - 1.08081i) q^{46} +(8.46639 + 7.10414i) q^{47} +(-0.964496 - 6.86074i) q^{48} +(-2.53733 - 14.3899i) q^{49} +(7.03718 + 0.300799i) q^{50} +(-8.30743 + 6.44219i) q^{51} +(-1.32038 - 2.81809i) q^{52} -8.73360i q^{53} +(7.34750 - 0.119308i) q^{54} -0.146525i q^{55} +(-12.5512 - 3.91953i) q^{56} +(-7.03787 - 2.87316i) q^{57} +(0.0371630 - 0.869426i) q^{58} +(1.42477 + 8.08025i) q^{59} +(-0.429755 - 0.219941i) q^{60} +(8.56477 + 7.18670i) q^{61} +(2.11539 + 6.68781i) q^{62} +(5.76467 - 12.6994i) q^{63} +(-5.62571 + 5.68782i) q^{64} +(-0.213559 - 0.0376562i) q^{65} +(1.07433 - 2.34060i) q^{66} +(-1.93034 + 5.30357i) q^{67} +(11.7310 + 3.12033i) q^{68} +(2.94880 - 3.25123i) q^{69} +(-0.726388 + 0.558434i) q^{70} +(-2.33277 - 4.04048i) q^{71} +(-5.25231 - 6.66432i) q^{72} +(-5.64518 + 9.77774i) q^{73} +(0.535287 + 4.03736i) q^{74} +(7.63146 - 4.02235i) q^{75} +(2.28736 + 8.47449i) q^{76} +(-3.14181 - 3.74426i) q^{77} +(-3.13531 - 2.16734i) q^{78} +(-0.572755 - 1.57363i) q^{79} +(0.0988087 + 0.548623i) q^{80} +(7.70068 - 4.65828i) q^{81} +(6.28736 - 6.87406i) q^{82} +(-2.20553 + 0.802749i) q^{83} +(-15.6978 + 3.59455i) q^{84} +(0.647964 - 0.543706i) q^{85} +(2.61188 + 1.66060i) q^{86} +(-0.496952 - 0.942848i) q^{87} +(-2.90152 + 0.651613i) q^{88} +(7.63741 + 4.40946i) q^{89} +(-0.590379 + 0.0323630i) q^{90} +(-6.26466 + 3.61690i) q^{91} +(-5.04983 - 0.432493i) q^{92} +(6.36339 + 5.77146i) q^{93} +(-7.22981 - 13.8574i) q^{94} +(0.574758 + 0.209195i) q^{95} +(-2.44415 + 9.48821i) q^{96} +(-0.978443 + 5.54902i) q^{97} +(-4.45412 + 20.1786i) q^{98} +(-0.306985 - 3.13921i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) 96 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 9 * q^8 - 12 * q^9	\( 96 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 15 q^{12} - 12 q^{13} - 21 q^{14} - 6 q^{16} - 18 q^{17} - 27 q^{18} - 27 q^{20} - 12 q^{21} - 6 q^{22} - 12 q^{24} - 12 q^{25} - 12 q^{28} - 24 q^{29} + 9 q^{30} + 24 q^{32} - 42 q^{33} - 12 q^{34} + 24 q^{36} - 6 q^{37} + 18 q^{38} - 21 q^{40} - 42 q^{41} + 54 q^{42} + 63 q^{44} - 24 q^{45} - 3 q^{46} + 69 q^{48} - 12 q^{49} + 87 q^{50} - 33 q^{52} + 78 q^{54} + 99 q^{56} - 24 q^{57} - 33 q^{58} + 102 q^{60} - 12 q^{61} + 90 q^{62} - 3 q^{64} + 12 q^{65} + 87 q^{66} + 51 q^{68} + 12 q^{69} - 21 q^{70} + 12 q^{72} - 6 q^{73} + 21 q^{74} - 18 q^{76} + 12 q^{77} - 24 q^{78} + 12 q^{81} - 12 q^{82} - 12 q^{84} - 42 q^{85} - 30 q^{86} + 18 q^{88} - 78 q^{90} - 123 q^{92} + 60 q^{93} + 21 q^{94} - 138 q^{96} - 30 q^{97} - 180 q^{98}+O(q^{100}) \) 96 * q - 6 * q^2 - 6 * q^4 - 12 * q^5 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 15 * q^12 - 12 * q^13 - 21 * q^14 - 6 * q^16 - 18 * q^17 - 27 * q^18 - 27 * q^20 - 12 * q^21 - 6 * q^22 - 12 * q^24 - 12 * q^25 - 12 * q^28 - 24 * q^29 + 9 * q^30 + 24 * q^32 - 42 * q^33 - 12 * q^34 + 24 * q^36 - 6 * q^37 + 18 * q^38 - 21 * q^40 - 42 * q^41 + 54 * q^42 + 63 * q^44 - 24 * q^45 - 3 * q^46 + 69 * q^48 - 12 * q^49 + 87 * q^50 - 33 * q^52 + 78 * q^54 + 99 * q^56 - 24 * q^57 - 33 * q^58 + 102 * q^60 - 12 * q^61 + 90 * q^62 - 3 * q^64 + 12 * q^65 + 87 * q^66 + 51 * q^68 + 12 * q^69 - 21 * q^70 + 12 * q^72 - 6 * q^73 + 21 * q^74 - 18 * q^76 + 12 * q^77 - 24 * q^78 + 12 * q^81 - 12 * q^82 - 12 * q^84 - 42 * q^85 - 30 * q^86 + 18 * q^88 - 78 * q^90 - 123 * q^92 + 60 * q^93 + 21 * q^94 - 138 * q^96 - 30 * q^97 - 180 * q^98

Introduction

L-functions

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