LMFDB - Embedded newform 115.2.g.c.26.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(6,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("115.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.g (of order $11$, degree $10$, 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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			26.5
Character	$\chi$	$=$	115.26
Dual form			115.2.g.c.31.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.395474 + 2.75058i) q^{2} +(0.0237855 - 0.0520830i) q^{3} +(-5.49030 + 1.61210i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(0.152665 + 0.0448264i) q^{6} +(1.15709 - 0.743614i) q^{7} +(-4.29671 - 9.40848i) q^{8} +(1.96244 + 2.26477i) q^{9} +O(q^{10})$	\(q+(0.395474 + 2.75058i) q^{2} +(0.0237855 - 0.0520830i) q^{3} +(-5.49030 + 1.61210i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(0.152665 + 0.0448264i) q^{6} +(1.15709 - 0.743614i) q^{7} +(-4.29671 - 9.40848i) q^{8} +(1.96244 + 2.26477i) q^{9} +(-2.33773 - 1.50237i) q^{10} +(-0.191163 + 1.32957i) q^{11} +(-0.0466267 + 0.324296i) q^{12} +(3.77568 + 2.42648i) q^{13} +(2.50297 + 2.88858i) q^{14} +(0.0237855 + 0.0520830i) q^{15} +(14.5521 - 9.35205i) q^{16} +(-4.59136 - 1.34814i) q^{17} +(-5.45334 + 6.29349i) q^{18} +(4.28580 - 1.25843i) q^{19} +(2.37704 - 5.20499i) q^{20} +(-0.0112078 - 0.0779517i) q^{21} -3.73268 q^{22} +(-1.09795 - 4.66846i) q^{23} -0.592221 q^{24} +(-0.142315 - 0.989821i) q^{25} +(-5.18105 + 11.3449i) q^{26} +(0.329447 - 0.0967344i) q^{27} +(-5.15397 + 5.94800i) q^{28} +(0.946733 + 0.277986i) q^{29} +(-0.133852 + 0.0860213i) q^{30} +(0.902580 + 1.97638i) q^{31} +(17.9319 + 20.6945i) q^{32} +(0.0647009 + 0.0415808i) q^{33} +(1.89242 - 13.1621i) q^{34} +(-0.195744 + 1.36143i) q^{35} +(-14.4254 - 9.27064i) q^{36} +(-2.99668 - 3.45835i) q^{37} +(5.15632 + 11.2908i) q^{38} +(0.216185 - 0.138934i) q^{39} +(9.92420 + 2.91401i) q^{40} +(1.68289 - 1.94216i) q^{41} +(0.209980 - 0.0616557i) q^{42} +(3.33639 - 7.30568i) q^{43} +(-1.09385 - 7.60790i) q^{44} -2.99672 q^{45} +(12.4068 - 4.86625i) q^{46} -3.65973 q^{47} +(-0.140954 - 0.980359i) q^{48} +(-2.12202 + 4.64657i) q^{49} +(2.66630 - 0.782896i) q^{50} +(-0.179423 + 0.207065i) q^{51} +(-24.6414 - 7.23536i) q^{52} +(0.752147 - 0.483375i) q^{53} +(0.396363 + 0.867914i) q^{54} +(-0.879635 - 1.01515i) q^{55} +(-11.9679 - 7.69133i) q^{56} +(0.0363974 - 0.253150i) q^{57} +(-0.390214 + 2.71400i) q^{58} +(2.03565 + 1.30824i) q^{59} +(-0.214552 - 0.247607i) q^{60} +(-3.37105 - 7.38156i) q^{61} +(-5.07923 + 3.26422i) q^{62} +(3.95482 + 1.16124i) q^{63} +(-27.1745 + 31.3611i) q^{64} +(-4.30636 + 1.26446i) q^{65} +(-0.0887837 + 0.194409i) q^{66} +(-1.68495 - 11.7191i) q^{67} +27.3813 q^{68} +(-0.269262 - 0.0538571i) q^{69} -3.82214 q^{70} +(-1.07551 - 7.48031i) q^{71} +(12.8760 - 28.1946i) q^{72} +(-8.00567 + 2.35068i) q^{73} +(8.32736 - 9.61028i) q^{74} +(-0.0549379 - 0.0161312i) q^{75} +(-21.5016 + 13.8183i) q^{76} +(0.767493 + 1.68058i) q^{77} +(0.467643 + 0.539689i) q^{78} +(11.4753 + 7.37474i) q^{79} +(-2.46178 + 17.1220i) q^{80} +(-1.27664 + 8.87920i) q^{81} +(6.00761 + 3.86086i) q^{82} +(2.84808 + 3.28686i) q^{83} +(0.187200 + 0.409910i) q^{84} +(4.02556 - 2.58707i) q^{85} +(21.4143 + 6.28780i) q^{86} +(0.0369968 - 0.0426966i) q^{87} +(13.3306 - 3.91421i) q^{88} +(-6.62960 + 14.5168i) q^{89} +(-1.18512 - 8.24272i) q^{90} +6.17316 q^{91} +(13.5541 + 23.8612i) q^{92} +0.124404 q^{93} +(-1.44733 - 10.0664i) q^{94} +(-1.85555 + 4.06309i) q^{95} +(1.50435 - 0.441716i) q^{96} +(-11.2852 + 13.0238i) q^{97} +(-13.6200 - 3.99918i) q^{98} +(-3.38631 + 2.17625i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) $ 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9	\( 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9} - 5 q^{10} - 16 q^{11} - 9 q^{12} - 14 q^{13} - 12 q^{14} - 2 q^{15} + 27 q^{16} + 38 q^{17} - 42 q^{18} - 5 q^{19} - 11 q^{20} - 9 q^{21} + 6 q^{22} - 8 q^{23} + 102 q^{24} - 5 q^{25} - 19 q^{26} + 7 q^{27} - 34 q^{28} - 38 q^{29} - 11 q^{30} + 2 q^{31} + 49 q^{32} - 2 q^{33} - 31 q^{34} + 6 q^{35} - 59 q^{36} - 35 q^{37} + 30 q^{38} + 32 q^{39} + 42 q^{40} - 11 q^{41} - 102 q^{42} + 6 q^{43} - 55 q^{44} + 58 q^{45} + 153 q^{46} - 10 q^{47} + 84 q^{48} + 6 q^{50} - 20 q^{51} - 97 q^{52} - 29 q^{53} + 19 q^{54} + 17 q^{55} + 77 q^{56} - 49 q^{57} - 12 q^{58} - 50 q^{59} + 2 q^{60} + 4 q^{61} + 126 q^{62} + 74 q^{63} - 44 q^{64} - 14 q^{65} - 144 q^{66} - 43 q^{67} + 54 q^{68} - 50 q^{69} - 12 q^{70} - 25 q^{71} - 14 q^{72} - 20 q^{73} - 47 q^{74} - 2 q^{75} - 26 q^{76} + 150 q^{77} + 174 q^{78} + 72 q^{79} - 28 q^{80} - 71 q^{81} - 11 q^{82} + 36 q^{83} + 100 q^{84} - 6 q^{85} - 20 q^{86} + 85 q^{87} - 45 q^{88} - 24 q^{89} - 42 q^{90} + 38 q^{91} + 74 q^{92} + 100 q^{93} + 150 q^{94} - 5 q^{95} - 169 q^{96} - 14 q^{97} - 44 q^{98} + 36 q^{99}+O(q^{100}) \) 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9 - 5 * q^10 - 16 * q^11 - 9 * q^12 - 14 * q^13 - 12 * q^14 - 2 * q^15 + 27 * q^16 + 38 * q^17 - 42 * q^18 - 5 * q^19 - 11 * q^20 - 9 * q^21 + 6 * q^22 - 8 * q^23 + 102 * q^24 - 5 * q^25 - 19 * q^26 + 7 * q^27 - 34 * q^28 - 38 * q^29 - 11 * q^30 + 2 * q^31 + 49 * q^32 - 2 * q^33 - 31 * q^34 + 6 * q^35 - 59 * q^36 - 35 * q^37 + 30 * q^38 + 32 * q^39 + 42 * q^40 - 11 * q^41 - 102 * q^42 + 6 * q^43 - 55 * q^44 + 58 * q^45 + 153 * q^46 - 10 * q^47 + 84 * q^48 + 6 * q^50 - 20 * q^51 - 97 * q^52 - 29 * q^53 + 19 * q^54 + 17 * q^55 + 77 * q^56 - 49 * q^57 - 12 * q^58 - 50 * q^59 + 2 * q^60 + 4 * q^61 + 126 * q^62 + 74 * q^63 - 44 * q^64 - 14 * q^65 - 144 * q^66 - 43 * q^67 + 54 * q^68 - 50 * q^69 - 12 * q^70 - 25 * q^71 - 14 * q^72 - 20 * q^73 - 47 * q^74 - 2 * q^75 - 26 * q^76 + 150 * q^77 + 174 * q^78 + 72 * q^79 - 28 * q^80 - 71 * q^81 - 11 * q^82 + 36 * q^83 + 100 * q^84 - 6 * q^85 - 20 * q^86 + 85 * q^87 - 45 * q^88 - 24 * q^89 - 42 * q^90 + 38 * q^91 + 74 * q^92 + 100 * q^93 + 150 * q^94 - 5 * q^95 - 169 * q^96 - 14 * q^97 - 44 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{8}{11}\right)$

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 $

$2$	0.395474	+	2.75058i	0.279642	+	1.94495i	0.324309	+	0.945951i	$0.394868\pi$
$2$	0.395474	+	2.75058i	0.279642	+	1.94495i	−0.0446667	+	0.999002i	$0.514223\pi$
$3$	0.0237855	−	0.0520830i	0.0137326	−	0.0300701i	−0.902641	−	0.430393i	$-0.858375\pi$
$3$	0.0237855	−	0.0520830i	0.0137326	−	0.0300701i	0.916374	+	0.400323i	$0.131102\pi$
$4$	−5.49030	+	1.61210i	−2.74515	+	0.806049i
$5$	−0.654861	+	0.755750i	−0.292863	+	0.337981i
$5$	−0.654861	+	0.755750i	−0.292863	+	0.337981i
$6$	0.152665	+	0.0448264i	0.0623252	+	0.0183003i
$7$	1.15709	−	0.743614i	0.437337	−	0.281060i	−0.303389	−	0.952867i	$-0.598118\pi$
$7$	1.15709	−	0.743614i	0.437337	−	0.281060i	0.740726	+	0.671807i	$0.234482\pi$
$8$	−4.29671	−	9.40848i	−1.51912	−	3.32640i
$9$	1.96244	+	2.26477i	0.654145	+	0.754924i
$10$	−2.33773	−	1.50237i	−0.739255	−	0.475090i
$11$	−0.191163	+	1.32957i	−0.0576378	+	0.400880i	0.940495	+	0.339806i	$0.110362\pi$
$11$	−0.191163	+	1.32957i	−0.0576378	+	0.400880i	−0.998133	+	0.0610736i	$0.980548\pi$
$12$	−0.0466267	+	0.324296i	−0.0134600	+	0.0936161i
$13$	3.77568	+	2.42648i	1.04719	+	0.672985i	0.946754	−	0.321959i	$-0.104341\pi$
$13$	3.77568	+	2.42648i	1.04719	+	0.672985i	0.100432	+	0.994944i	$0.467978\pi$
$14$	2.50297	+	2.88858i	0.668946	+	0.772005i
$15$	0.0237855	+	0.0520830i	0.00614139	+	0.0134478i
$16$	14.5521	−	9.35205i	3.63802	−	2.33801i
$17$	−4.59136	−	1.34814i	−1.11357	−	0.326973i	−0.327338	−	0.944907i	$-0.606152\pi$
$17$	−4.59136	−	1.34814i	−1.11357	−	0.326973i	−0.786230	+	0.617934i	$0.787970\pi$
$18$	−5.45334	+	6.29349i	−1.28536	+	1.48339i
$19$	4.28580	−	1.25843i	0.983231	−	0.288703i	0.249673	−	0.968330i	$-0.419677\pi$
$19$	4.28580	−	1.25843i	0.983231	−	0.288703i	0.733557	+	0.679628i	$0.237859\pi$
$20$	2.37704	−	5.20499i	0.531522	−	1.16387i
$21$	−0.0112078	−	0.0779517i	−0.00244573	−	0.0170105i
$22$	−3.73268			−0.795811
$23$	−1.09795	−	4.66846i	−0.228939	−	0.973441i
$23$	−1.09795	−	4.66846i	−0.228939	−	0.973441i
$24$	−0.592221			−0.120887
$25$	−0.142315	−	0.989821i	−0.0284630	−	0.197964i
$26$	−5.18105	+	11.3449i	−1.01609	+	2.22492i
$27$	0.329447	−	0.0967344i	0.0634021	−	0.0186165i
$28$	−5.15397	+	5.94800i	−0.974009	+	1.12407i
$29$	0.946733	+	0.277986i	0.175804	+	0.0516207i	0.368450	−	0.929648i	$-0.379889\pi$
$29$	0.946733	+	0.277986i	0.175804	+	0.0516207i	−0.192646	+	0.981268i	$0.561707\pi$
$30$	−0.133852	+	0.0860213i	−0.0244379	+	0.0157053i
$31$	0.902580	+	1.97638i	0.162108	+	0.354968i	0.973203	−	0.229947i	$-0.0738553\pi$
$31$	0.902580	+	1.97638i	0.162108	+	0.354968i	−0.811095	+	0.584915i	$0.801128\pi$
$32$	17.9319	+	20.6945i	3.16993	+	3.65830i
$33$	0.0647009	+	0.0415808i	0.0112630	+	0.00723828i
$34$	1.89242	−	13.1621i	0.324547	−	2.25727i
$35$	−0.195744	+	1.36143i	−0.0330868	+	0.230124i
$36$	−14.4254	−	9.27064i	−2.40423	−	1.54511i
$37$	−2.99668	−	3.45835i	−0.492651	−	0.568549i	0.453921	−	0.891042i	$-0.350025\pi$
$37$	−2.99668	−	3.45835i	−0.492651	−	0.568549i	−0.946572	+	0.322493i	$0.895479\pi$
$38$	5.15632	+	11.2908i	0.836466	+	1.83160i
$39$	0.216185	−	0.138934i	0.0346173	−	0.0222472i
$40$	9.92420	+	2.91401i	1.56915	+	0.460745i
$41$	1.68289	−	1.94216i	0.262824	−	0.303315i	−0.608965	−	0.793197i	$-0.708415\pi$
$41$	1.68289	−	1.94216i	0.262824	−	0.303315i	0.871788	+	0.489882i	$0.162960\pi$
$42$	0.209980	−	0.0616557i	0.0324006	−	0.00951367i
$43$	3.33639	−	7.30568i	0.508795	−	1.11411i	−0.464715	−	0.885460i	$-0.653843\pi$
$43$	3.33639	−	7.30568i	0.508795	−	1.11411i	0.973510	−	0.228645i	$-0.0734295\pi$
$44$	−1.09385	−	7.60790i	−0.164904	−	1.14693i
$45$	−2.99672			−0.446725
$46$	12.4068	−	4.86625i	1.82928	−	0.717490i
$47$	−3.65973			−0.533826			−0.266913	−	0.963721i	$-0.586004\pi$
$47$	−3.65973			−0.533826			−0.266913	+	0.963721i	$0.586004\pi$
$48$	−0.140954	−	0.980359i	−0.0203450	−	0.141503i
$49$	−2.12202	+	4.64657i	−0.303146	+	0.663796i
$50$	2.66630	−	0.782896i	0.377072	−	0.110718i
$51$	−0.179423	+	0.207065i	−0.0251243	+	0.0289949i
$52$	−24.6414	−	7.23536i	−3.41714	−	1.00336i
$53$	0.752147	−	0.483375i	0.103315	−	0.0663967i	−0.487963	−	0.872864i	$-0.662260\pi$
$53$	0.752147	−	0.483375i	0.103315	−	0.0663967i	0.591278	+	0.806468i	$0.298624\pi$
$54$	0.396363	+	0.867914i	0.0539382	+	0.118108i
$55$	−0.879635	−	1.01515i	−0.118610	−	0.136883i
$56$	−11.9679	−	7.69133i	−1.59928	−	1.02780i
$57$	0.0363974	−	0.253150i	0.00482095	−	0.0335305i
$58$	−0.390214	+	2.71400i	−0.0512376	+	0.356366i
$59$	2.03565	+	1.30824i	0.265020	+	0.170318i	0.666402	−	0.745593i	$-0.267834\pi$
$59$	2.03565	+	1.30824i	0.265020	+	0.170318i	−0.401382	+	0.915911i	$0.631470\pi$
$60$	−0.214552	−	0.247607i	−0.0276986	−	0.0319659i
$61$	−3.37105	−	7.38156i	−0.431618	−	0.945113i	−0.993061	−	0.117597i	$-0.962481\pi$
$61$	−3.37105	−	7.38156i	−0.431618	−	0.945113i	0.561443	−	0.827515i	$-0.310246\pi$
$62$	−5.07923	+	3.26422i	−0.645063	+	0.414557i
$63$	3.95482	+	1.16124i	0.498261	+	0.146303i
$64$	−27.1745	+	31.3611i	−3.39681	+	3.92013i
$65$	−4.30636	+	1.26446i	−0.534138	+	0.156837i
$66$	−0.0887837	+	0.194409i	−0.0109285	+	0.0239301i
$67$	−1.68495	−	11.7191i	−0.205849	−	1.43171i	−0.786516	−	0.617570i	$-0.788117\pi$
$67$	−1.68495	−	11.7191i	−0.205849	−	1.43171i	0.580667	−	0.814142i	$-0.302792\pi$
$68$	27.3813			3.32047
$69$	−0.269262	−	0.0538571i	−0.0324154	−	0.00648363i
$70$	−3.82214			−0.456833
$71$	−1.07551	−	7.48031i	−0.127639	−	0.887750i	−0.948535	−	0.316672i	$-0.897435\pi$
$71$	−1.07551	−	7.48031i	−0.127639	−	0.887750i	0.820896	−	0.571078i	$-0.193474\pi$
$72$	12.8760	−	28.1946i	1.51746	−	3.32276i
$73$	−8.00567	+	2.35068i	−0.936993	+	0.275126i	−0.714362	−	0.699777i	$-0.753283\pi$
$73$	−8.00567	+	2.35068i	−0.936993	+	0.275126i	−0.222631	+	0.974903i	$0.571465\pi$
$74$	8.32736	−	9.61028i	0.968036	−	1.11717i
$75$	−0.0549379	−	0.0161312i	−0.00634368	−	0.00186267i
$76$	−21.5016	+	13.8183i	−2.46641	+	1.58506i
$77$	0.767493	+	1.68058i	0.0874640	+	0.191519i
$78$	0.467643	+	0.539689i	0.0529502	+	0.0611077i
$79$	11.4753	+	7.37474i	1.29107	+	0.829723i	0.992211	−	0.124572i	$-0.0397558\pi$
$79$	11.4753	+	7.37474i	1.29107	+	0.829723i	0.298864	+	0.954296i	$0.403392\pi$
$80$	−2.46178	+	17.1220i	−0.275235	+	1.91430i
$81$	−1.27664	+	8.87920i	−0.141848	+	0.986578i
$82$	6.00761	+	3.86086i	0.663430	+	0.426361i
$83$	2.84808	+	3.28686i	0.312617	+	0.360780i	0.890214	−	0.455543i	$-0.150555\pi$
$83$	2.84808	+	3.28686i	0.312617	+	0.360780i	−0.577597	+	0.816322i	$0.696009\pi$
$84$	0.187200	+	0.409910i	0.0204252	+	0.0447249i
$85$	4.02556	−	2.58707i	0.436633	−	0.280607i
$86$	21.4143	+	6.28780i	2.30916	+	0.678031i
$87$	0.0369968	−	0.0426966i	0.00396648	−	0.00457756i
$88$	13.3306	−	3.91421i	1.42104	−	0.417256i
$89$	−6.62960	+	14.5168i	−0.702736	+	1.53878i	0.133887	+	0.990997i	$0.457254\pi$
$89$	−6.62960	+	14.5168i	−0.702736	+	1.53878i	−0.836623	+	0.547780i	$0.815473\pi$
$90$	−1.18512	−	8.24272i	−0.124923	−	0.868859i
$91$	6.17316			0.647123
$92$	13.5541	+	23.8612i	1.41311	+	2.48771i
$93$	0.124404			0.0129001
$94$	−1.44733	−	10.0664i	−0.149280	−	1.03827i
$95$	−1.85555	+	4.06309i	−0.190375	+	0.416864i
$96$	1.50435	−	0.441716i	0.153537	−	0.0450825i
$97$	−11.2852	+	13.0238i	−1.14583	+	1.32236i	−0.206863	+	0.978370i	$0.566325\pi$
$97$	−11.2852	+	13.0238i	−1.14583	+	1.32236i	−0.938972	+	0.343994i	$0.888220\pi$
$98$	−13.6200	−	3.99918i	−1.37582	−	0.403979i
$99$	−3.38631	+	2.17625i	−0.340337	+	0.218721i
$100$	2.37704	+	5.20499i	0.237704	+	0.520499i
$101$	−6.19001	−	7.14365i	−0.615929	−	0.710820i	0.359000	−	0.933338i	$-0.383118\pi$
$101$	−6.19001	−	7.14365i	−0.615929	−	0.710820i	−0.974929	+	0.222518i	$0.928572\pi$
$102$	−0.640507	−	0.411629i	−0.0634196	−	0.0407573i
$103$	1.26746	−	8.81535i	0.124886	−	0.868602i	−0.827011	−	0.562185i	$-0.809961\pi$
$103$	1.26746	−	8.81535i	0.124886	−	0.868602i	0.951897	−	0.306417i	$-0.0991301\pi$
$104$	6.60651	−	45.9493i	0.647822	−	4.50570i
$105$	0.0662515	+	0.0425772i	0.00646548	+	0.00415511i
$106$	1.62702	+	1.87768i	0.158030	+	0.182376i
$107$	−2.62099	−	5.73916i	−0.253380	−	0.554826i	0.739608	−	0.673038i	$-0.235011\pi$
$107$	−2.62099	−	5.73916i	−0.253380	−	0.554826i	−0.992988	+	0.118212i	$0.962284\pi$
$108$	−1.65282	+	1.06220i	−0.159042	+	0.102210i
$109$	−0.904128	−	0.265476i	−0.0865998	−	0.0254280i	0.238146	−	0.971229i	$-0.423460\pi$
$109$	−0.904128	−	0.265476i	−0.0865998	−	0.0254280i	−0.324745	+	0.945801i	$0.605279\pi$
$110$	2.44439	−	2.82097i	0.233063	−	0.268969i
$111$	−0.251399	+	0.0738173i	−0.0238617	+	0.00700642i
$112$	9.88369	−	21.6423i	0.933921	−	2.04500i
$113$	1.27711	+	8.88246i	0.120140	+	0.835592i	0.957395	+	0.288780i	$0.0932496\pi$
$113$	1.27711	+	8.88246i	0.120140	+	0.835592i	−0.837255	+	0.546812i	$0.815841\pi$
$114$	0.710702			0.0665633
$115$	4.24719	+	2.22741i	0.396053	+	0.207707i
$116$	−5.64599			−0.524217
$117$	1.91410	+	13.3129i	0.176959	+	1.23078i
$118$	−2.79336	+	6.11660i	−0.257149	+	0.563079i
$119$	−6.31510	+	1.85428i	−0.578904	+	0.169982i
$120$	0.387822	−	0.447570i	0.0354031	−	0.0408574i
$121$	8.82321	+	2.59073i	0.802110	+	0.235521i
$122$	18.9704	−	12.1915i	1.71750	−	1.10377i
$123$	−0.0611251	−	0.133845i	−0.00551147	−	0.0120684i
$124$	−8.14155	−	9.39585i	−0.731133	−	0.843772i
$125$	0.841254	+	0.540641i	0.0752440	+	0.0483564i
$126$	−1.63006	+	11.3373i	−0.145217	+	1.01001i
$127$	−0.343569	+	2.38958i	−0.0304868	+	0.212041i	−0.999371	−	0.0354758i	$-0.988705\pi$
$127$	−0.343569	+	2.38958i	−0.0304868	+	0.212041i	0.968884	+	0.247516i	$0.0796144\pi$
$128$	−50.9363	−	32.7348i	−4.50217	−	2.89337i
$129$	−0.301144	−	0.347538i	−0.0265142	−	0.0305990i
$130$	−5.18105	−	11.3449i	−0.454408	−	0.995015i
$131$	−9.24697	+	5.94266i	−0.807911	+	0.519213i	−0.878189	−	0.478315i	$-0.841248\pi$
$131$	−9.24697	+	5.94266i	−0.807911	+	0.519213i	0.0702774	+	0.997527i	$0.477612\pi$
$132$	−0.422260	−	0.123987i	−0.0367530	−	0.0107917i
$133$	4.02326	−	4.64309i	0.348861	−	0.402607i
$134$	31.5679	−	9.26916i	2.72705	−	0.800734i
$135$	−0.142635	+	0.312327i	−0.0122761	+	0.0268808i
$136$	7.04374	+	48.9903i	0.603996	+	4.20088i
$137$	1.43118			0.122274			0.0611371	−	0.998129i	$-0.480527\pi$
$137$	1.43118			0.122274			0.0611371	+	0.998129i	$0.480527\pi$
$138$	0.0416519	−	0.761927i	0.00354565	−	0.0648595i
$139$	−1.70367			−0.144503			−0.0722517	−	0.997386i	$-0.523018\pi$
$139$	−1.70367			−0.144503			−0.0722517	+	0.997386i	$0.523018\pi$
$140$	−1.12007	−	7.79022i	−0.0946628	−	0.658394i
$141$	−0.0870484	+	0.190609i	−0.00733080	+	0.0160522i
$142$	20.1499	−	5.91653i	1.69094	−	0.496504i
$143$	−3.94795	+	4.55617i	−0.330144	+	0.381006i
$144$	49.7378	+	14.6043i	4.14481	+	1.21703i
$145$	−0.830066	+	0.533451i	−0.0689332	+	0.0443007i
$146$	−9.63176	−	21.0906i	−0.797130	−	1.74547i
$147$	0.191534	+	0.221042i	0.0157975	+	0.0182312i
$148$	22.0279	+	14.1564i	1.81068	+	1.16365i
$149$	1.13160	−	7.87047i	0.0927045	−	0.644774i	−0.889497	−	0.456942i	$-0.848945\pi$
$149$	1.13160	−	7.87047i	0.0927045	−	0.644774i	0.982201	−	0.187832i	$-0.0601461\pi$
$150$	0.0226437	−	0.157490i	0.00184885	−	0.0128590i
$151$	8.45022	+	5.43063i	0.687669	+	0.441938i	0.837257	−	0.546810i	$-0.184158\pi$
$151$	8.45022	+	5.43063i	0.687669	+	0.441938i	−0.149587	+	0.988749i	$0.547794\pi$
$152$	−30.2547	−	34.9158i	−2.45398	−	2.83204i
$153$	−5.95701	−	13.0440i	−0.481595	−	1.05455i
$154$	−4.31903	+	2.77567i	−0.348038	+	0.223670i
$155$	−2.08471	−	0.612126i	−0.167448	−	0.0491671i
$156$	−0.962945	+	1.11130i	−0.0770973	+	0.0889751i
$157$	9.52091	−	2.79559i	0.759851	−	0.223112i	0.121220	−	0.992626i	$-0.461319\pi$
$157$	9.52091	−	2.79559i	0.759851	−	0.223112i	0.638631	+	0.769513i	$0.279501\pi$
$158$	−15.7466	+	34.4803i	−1.25273	+	2.74311i
$159$	−0.00728544	−	0.0506713i	−0.000577773	−	0.00401850i
$160$	−27.3827			−2.16479
$161$	−4.74195	−	4.58536i	−0.373718	−	0.361377i
$162$	−24.9278			−1.95851
$163$	−0.337865	−	2.34990i	−0.0264636	−	0.184058i	0.972302	−	0.233728i	$-0.0750924\pi$
$163$	−0.337865	−	2.34990i	−0.0264636	−	0.184058i	−0.998766	+	0.0496691i	$0.984183\pi$
$164$	−6.10864	+	13.3761i	−0.477004	+	1.04449i
$165$	−0.0737947	+	0.0216681i	−0.00574491	+	0.00168686i
$166$	−7.91443	+	9.13374i	−0.614279	+	0.708916i
$167$	−3.79183	−	1.11338i	−0.293421	−	0.0861561i	0.131709	−	0.991288i	$-0.457953\pi$
$167$	−3.79183	−	1.11338i	−0.293421	−	0.0861561i	−0.425130	+	0.905132i	$0.639772\pi$
$168$	−0.685250	+	0.440384i	−0.0528682	+	0.0339763i
$169$	2.96756	+	6.49804i	0.228274	+	0.499849i
$170$	8.70795	+	10.0495i	0.667869	+	0.770762i
$171$	11.2607	+	7.23678i	0.861124	+	0.553411i
$172$	−6.54032	+	45.4889i	−0.498695	+	3.46850i
$173$	−0.00901048	+	0.0626692i	−0.000685054	+	0.00476465i	−0.990161	−	0.139932i	$-0.955312\pi$
$173$	−0.00901048	+	0.0626692i	−0.000685054	+	0.00476465i	0.989476	+	0.144697i	$0.0462207\pi$
$174$	0.132072	+	0.0848773i	0.0100123	+	0.00643453i
$175$	−0.900716	−	1.03948i	−0.0680877	−	0.0785774i
$176$	9.65237	+	21.1357i	0.727575	+	1.59317i
$177$	0.116556	−	0.0749059i	0.00876087	−	0.00563027i
$178$	−42.5514	−	12.4942i	−3.18936	−	0.936481i
$179$	−3.81649	+	4.40447i	−0.285258	+	0.329205i	−0.880236	−	0.474537i	$-0.842615\pi$
$179$	−3.81649	+	4.40447i	−0.285258	+	0.329205i	0.594978	+	0.803742i	$0.297161\pi$
$180$	16.4529	−	4.83101i	1.22633	−	0.360082i
$181$	3.75100	−	8.21354i	0.278809	−	0.610508i	−0.717479	−	0.696580i	$-0.754704\pi$
$181$	3.75100	−	8.21354i	0.278809	−	0.610508i	0.996289	+	0.0860721i	$0.0274316\pi$
$182$	2.44132	+	16.9798i	0.180963	+	1.25862i
$183$	−0.464636			−0.0343469
$184$	−39.2055	+	30.3890i	−2.89027	+	2.24031i
$185$	4.57605			0.336438
$186$	0.0491984	+	0.342182i	0.00360740	+	0.0250900i
$187$	2.67015	−	5.84681i	0.195261	−	0.427561i
$188$	20.0930	−	5.89984i	1.46543	−	0.430290i
$189$	0.309265	−	0.356911i	0.0224958	−	0.0259615i
$190$	−11.9097	−	3.49699i	−0.864018	−	0.253699i
$191$	11.4811	−	7.37846i	0.830744	−	0.533887i	−0.0547703	−	0.998499i	$-0.517443\pi$
$191$	11.4811	−	7.37846i	0.830744	−	0.533887i	0.885514	+	0.464612i	$0.153806\pi$
$192$	0.987018	+	2.16127i	0.0712319	+	0.155976i
$193$	−9.41083	−	10.8607i	−0.677406	−	0.781769i	0.308110	−	0.951351i	$-0.400304\pi$
$193$	−9.41083	−	10.8607i	−0.677406	−	0.781769i	−0.985516	+	0.169582i	$0.945758\pi$
$194$	−40.2859	−	25.8902i	−2.89236	−	1.85881i
$195$	−0.0365720	+	0.254364i	−0.00261897	+	0.0182154i
$196$	4.15979	−	28.9320i	0.297128	−	2.06657i
$197$	16.3987	+	10.5388i	1.16836	+	0.750858i	0.973210	−	0.229916i	$-0.0738452\pi$
$197$	16.3987	+	10.5388i	1.16836	+	0.750858i	0.195147	+	0.980774i	$0.437482\pi$
$198$	−7.32515	−	8.45367i	−0.520576	−	0.600776i
$199$	−8.49813	−	18.6083i	−0.602417	−	1.31911i	−0.927641	−	0.373472i	$-0.878167\pi$
$199$	−8.49813	−	18.6083i	−0.602417	−	1.31911i	0.325225	−	0.945637i	$-0.394560\pi$
$200$	−8.70123	+	5.59194i	−0.615270	+	0.395410i
$201$	−0.650441	−	0.190987i	−0.0458786	−	0.0134712i
$202$	17.2012	−	19.8512i	1.21027	−	1.39673i
$203$	1.30217	−	0.382350i	0.0913941	−	0.0268357i
$204$	0.651277	−	1.42610i	0.0455985	−	0.0998469i
$205$	0.365728	+	2.54369i	0.0255435	+	0.177659i
$206$	24.7486			1.72431
$207$	8.41833	−	11.6482i	0.585115	−	0.809603i
$208$	77.6366			5.38313
$209$	0.853875	+	5.93883i	0.0590638	+	0.410798i
$210$	−0.0909113	+	0.199068i	−0.00627348	+	0.0137370i
$211$	−16.8716	+	4.95394i	−1.16149	+	0.341043i	−0.805010	−	0.593261i	$-0.797840\pi$
$211$	−16.8716	+	4.95394i	−1.16149	+	0.341043i	−0.356476	+	0.934304i	$0.616022\pi$
$212$	−3.35026	+	3.86641i	−0.230097	+	0.265546i
$213$	−0.415178	−	0.121907i	−0.0284475	−	0.00835295i
$214$	14.7495	−	9.47892i	1.00825	−	0.647966i
$215$	3.33639	+	7.30568i	0.227540	+	0.498243i
$216$	−2.32566	−	2.68396i	−0.158241	−	0.182620i
$217$	2.51402	+	1.61566i	0.170663	+	0.109678i
$218$	0.372654	−	2.59186i	0.0252393	−	0.175543i
$219$	−0.0679886	+	0.472871i	−0.00459424	+	0.0319537i
$220$	6.46599	+	4.15544i	0.435937	+	0.280160i
$221$	−14.0643	−	16.2310i	−0.946065	−	1.09182i
$222$	−0.302462	−	0.662299i	−0.0202999	−	0.0444506i
$223$	6.95767	−	4.47142i	0.465920	−	0.299429i	−0.286538	−	0.958069i	$-0.592504\pi$
$223$	6.95767	−	4.47142i	0.465920	−	0.299429i	0.752458	+	0.658640i	$0.228868\pi$
$224$	36.1374	+	10.6109i	2.41453	+	0.708970i
$225$	1.96244	−	2.26477i	0.130829	−	0.150985i
$226$	−23.9269	+	7.02556i	−1.59159	+	0.467333i
$227$	1.88705	−	4.13206i	0.125248	−	0.274254i	−0.836613	−	0.547795i	$-0.815467\pi$
$227$	1.88705	−	4.13206i	0.125248	−	0.274254i	0.961860	+	0.273541i	$0.0881948\pi$
$228$	0.208269	+	1.44854i	0.0137930	+	0.0959321i
$229$	−9.25944			−0.611881			−0.305941	−	0.952051i	$-0.598971\pi$
$229$	−9.25944			−0.611881			−0.305941	+	0.952051i	$0.598971\pi$
$230$	−4.44703	+	12.5631i	−0.293228	+	0.828387i
$231$	0.105785			0.00696011
$232$	−1.45241	−	10.1017i	−0.0953554	−	0.663212i
$233$	−0.651928	+	1.42752i	−0.0427092	+	0.0935201i	−0.929784	−	0.368106i	$-0.880006\pi$
$233$	−0.651928	+	1.42752i	−0.0427092	+	0.0935201i	0.887075	+	0.461626i	$0.152734\pi$
$234$	−35.8611	+	10.5298i	−2.34432	+	0.688353i
$235$	2.39661	−	2.76584i	0.156338	−	0.180423i
$236$	−13.2854	−	3.90093i	−0.864803	−	0.253929i
$237$	0.657045	−	0.422257i	0.0426796	−	0.0274285i
$238$	−7.59780	−	16.6369i	−0.492492	−	1.07841i
$239$	−12.3633	−	14.2680i	−0.799712	−	0.922917i	0.198653	−	0.980070i	$-0.436343\pi$
$239$	−12.3633	−	14.2680i	−0.799712	−	0.922917i	−0.998365	+	0.0571528i	$0.981798\pi$
$240$	0.833211	+	0.535472i	0.0537835	+	0.0345646i
$241$	2.23804	−	15.5659i	0.144165	−	1.00269i	−0.781381	−	0.624055i	$-0.785484\pi$
$241$	2.23804	−	15.5659i	0.144165	−	1.00269i	0.925546	−	0.378636i	$-0.123607\pi$
$242$	−3.63666	+	25.2935i	−0.233773	+	1.62593i
$243$	1.29864	+	0.834583i	0.0833075	+	0.0535385i
$244$	30.4079	+	35.0926i	1.94666	+	2.24657i
$245$	−2.12202	−	4.64657i	−0.135571	−	0.296859i
$246$	0.343979	−	0.221062i	0.0219313	−	0.0140944i
$247$	19.2354	+	5.64802i	1.22392	+	0.359375i
$248$	14.7166	−	16.9838i	0.934503	−	1.07847i
$249$	0.238932	−	0.0701569i	0.0151417	−	0.00444601i
$250$	−1.15438	+	2.52774i	−0.0730095	+	0.159869i
$251$	−0.896052	−	6.23218i	−0.0565583	−	0.393372i	−0.998362	−	0.0572089i	$-0.981780\pi$
$251$	−0.896052	−	6.23218i	−0.0565583	−	0.393372i	0.941804	−	0.336163i	$-0.109129\pi$
$252$	−23.5852			−1.48573
$253$	6.41692	−	0.567363i	0.403428	−	0.0356698i
$254$	−6.70859			−0.420934
$255$	−0.0389924	−	0.271198i	−0.00244180	−	0.0169831i
$256$	35.4190	−	77.5567i	2.21369	−	4.84730i
$257$	−2.15270	+	0.632091i	−0.134282	+	0.0394287i	−0.348183	−	0.937427i	$-0.613201\pi$
$257$	−2.15270	+	0.632091i	−0.134282	+	0.0394287i	0.213901	+	0.976855i	$0.431383\pi$
$258$	0.836837	−	0.965761i	0.0520992	−	0.0601257i
$259$	−6.03909	−	1.77324i	−0.375251	−	0.110184i
$260$	21.6048	−	13.8845i	1.33987	−	0.861083i
$261$	1.22833	+	2.68966i	0.0760316	+	0.166486i
$262$	−20.0027	−	23.0843i	−1.23577	−	1.42616i
$263$	2.50513	+	1.60995i	0.154473	+	0.0992735i	0.615594	−	0.788064i	$-0.288916\pi$
$263$	2.50513	+	1.60995i	0.154473	+	0.0992735i	−0.461121	+	0.887337i	$0.652553\pi$
$264$	0.113211	−	0.787398i	0.00696764	−	0.0484610i
$265$	−0.127241	+	0.884978i	−0.00781633	+	0.0543638i
$266$	14.3623	+	9.23007i	0.880608	+	0.565932i
$267$	0.598389	+	0.690578i	0.0366208	+	0.0422627i
$268$	28.1431	+	61.6249i	1.71912	+	3.76434i
$269$	0.953299	−	0.612648i	0.0581237	−	0.0373538i	−0.511256	−	0.859428i	$-0.670820\pi$
$269$	0.953299	−	0.612648i	0.0581237	−	0.0373538i	0.569380	+	0.822074i	$0.307183\pi$
$270$	−0.915488	−	0.268812i	−0.0557149	−	0.0163594i
$271$	−9.69109	+	11.1841i	−0.588692	+	0.679386i	−0.969450	−	0.245288i	$-0.921117\pi$
$271$	−9.69109	+	11.1841i	−0.588692	+	0.679386i	0.380759	+	0.924674i	$0.375663\pi$
$272$	−79.4218	+	23.3203i	−4.81565	+	1.41400i
$273$	0.146832	−	0.321516i	0.00888665	−	0.0194590i
$274$	0.565995	+	3.93658i	0.0341930	+	0.237818i
$275$	1.34324			0.0810004
$276$	1.56515	−	0.138386i	0.0942112	−	0.00832985i
$277$	4.80882			0.288934			0.144467	−	0.989510i	$-0.453853\pi$
$277$	4.80882			0.288934			0.144467	+	0.989510i	$0.453853\pi$
$278$	−0.673756	−	4.68608i	−0.0404092	−	0.281052i
$279$	−2.70478	+	5.92265i	−0.161931	+	0.354580i
$280$	13.6500	−	4.00802i	0.815746	−	0.239525i
$281$	−1.80054	+	2.07793i	−0.107411	+	0.123959i	−0.806909	−	0.590675i	$-0.798861\pi$
$281$	−1.80054	+	2.07793i	−0.107411	+	0.123959i	0.699498	+	0.714634i	$0.253407\pi$
$282$	−0.558712	−	0.164053i	−0.0332708	−	0.00976919i
$283$	−16.9762	+	10.9099i	−1.00913	+	0.648529i	−0.937168	−	0.348878i	$-0.886563\pi$
$283$	−16.9762	+	10.9099i	−1.00913	+	0.648529i	−0.0719627	+	0.997407i	$0.522926\pi$
$284$	17.9638	+	39.3353i	1.06596	+	2.33412i
$285$	0.167482	+	0.193285i	0.00992080	+	0.0114492i
$286$	−14.0934	−	9.05729i	−0.833361	−	0.535569i
$287$	0.503033	−	3.49867i	0.0296931	−	0.206520i
$288$	−11.6781	+	81.2231i	−0.688140	+	4.78612i
$289$	4.96178	+	3.18874i	0.291869	+	0.187573i
$290$	−1.79557	−	2.07220i	−0.105439	−	0.121684i
$291$	0.409894	+	0.897542i	0.0240284	+	0.0526148i
$292$	40.1640	−	25.8119i	2.35042	−	1.51052i
$293$	19.7136	+	5.78842i	1.15168	+	0.338163i	0.801194	−	0.598405i	$-0.204199\pi$
$293$	19.7136	+	5.78842i	1.15168	+	0.338163i	0.350485	+	0.936568i	$0.386017\pi$
$294$	−0.532247	+	0.614246i	−0.0310413	+	0.0358235i
$295$	−2.32177	+	0.681733i	−0.135179	+	0.0396920i
$296$	−19.6620	+	43.0537i	−1.14283	+	2.50244i
$297$	0.0656368	+	0.456514i	0.00380864	+	0.0264896i
$298$	22.0959			1.27998
$299$	7.18242	−	20.2908i	0.415370	−	1.17345i
$300$	0.327630			0.0189158
$301$	−1.57211	−	10.9343i	−0.0906151	−	0.630242i
$302$	−11.5955	+	25.3907i	−0.667248	+	1.46107i
$303$	−0.519295	+	0.152479i	−0.0298327	+	0.00875967i
$304$	50.5985	−	58.3938i	2.90202	−	3.34911i
$305$	7.78618	+	2.28623i	0.445835	+	0.130909i
$306$	33.5228	−	21.5438i	1.91637	−	1.23158i
$307$	9.83198	+	21.5290i	0.561141	+	1.22873i	0.951382	+	0.308014i	$0.0996645\pi$
$307$	9.83198	+	21.5290i	0.561141	+	1.22873i	−0.390241	+	0.920713i	$0.627608\pi$
$308$	−6.92302	−	7.98959i	−0.394476	−	0.455249i
$309$	−0.428982	−	0.275690i	−0.0244040	−	0.0156835i
$310$	0.859253	−	5.97624i	0.0488023	−	0.339428i
$311$	−4.50813	+	31.3547i	−0.255632	+	1.77796i	0.307453	+	0.951563i	$0.400523\pi$
$311$	−4.50813	+	31.3547i	−0.255632	+	1.77796i	−0.563085	+	0.826399i	$0.690386\pi$
$312$	−2.23604	−	1.43701i	−0.126591	−	0.0813549i
$313$	−8.43094	−	9.72982i	−0.476545	−	0.549962i	0.465676	−	0.884955i	$-0.345811\pi$
$313$	−8.43094	−	9.72982i	−0.476545	−	0.549962i	−0.942220	+	0.334993i	$0.891266\pi$
$314$	11.4548	+	25.0824i	0.646429	+	1.41548i
$315$	−3.46746	+	2.22840i	−0.195369	+	0.125556i
$316$	−74.8918	−	21.9902i	−4.21299	−	1.23705i
$317$	9.25227	−	10.6777i	0.519659	−	0.599719i	−0.433886	−	0.900968i	$-0.642858\pi$
$317$	9.25227	−	10.6777i	0.519659	−	0.599719i	0.953546	+	0.301249i	$0.0974034\pi$
$318$	0.136494	−	0.0400784i	0.00765422	−	0.00224748i
$319$	−0.550581	+	1.20560i	−0.0308266	+	0.0675009i
$320$	−5.90559	−	41.0743i	−0.330132	−	2.29612i
$321$	−0.361254			−0.0201632
$322$	10.7371	−	14.8565i	0.598353	−	0.827921i
$323$	−21.3742			−1.18929
$324$	−7.30502	−	50.8075i	−0.405834	−	2.82264i
$325$	1.86445	−	4.08258i	0.103421	−	0.226461i
$326$	6.32997	−	1.85865i	0.350585	−	0.102941i
$327$	−0.0353319	+	0.0407752i	−0.00195386	+	0.00225487i
$328$	−25.5037	−	7.48856i	−1.40821	−	0.413487i
$329$	−4.23462	+	2.72143i	−0.233462	+	0.150037i
$330$	−0.0887837	−	0.194409i	−0.00488738	−	0.0107019i
$331$	20.4528	+	23.6038i	1.12419	+	1.29738i	0.949853	+	0.312698i	$0.101233\pi$
$331$	20.4528	+	23.6038i	1.12419	+	1.29738i	0.174337	+	0.984686i	$0.444222\pi$
$332$	−20.9356	−	13.4545i	−1.14899	−	0.738410i
$333$	1.95159	−	13.5736i	0.106946	−	0.743827i
$334$	1.56288	−	10.8700i	0.0855168	−	0.594782i
$335$	9.96009	+	6.40096i	0.544178	+	0.349722i
$336$	−0.892105	−	1.02954i	−0.0486683	−	0.0561662i
$337$	9.83740	+	21.5409i	0.535877	+	1.17341i	0.963071	+	0.269247i	$0.0867750\pi$
$337$	9.83740	+	21.5409i	0.535877	+	1.17341i	−0.427194	+	0.904160i	$0.640498\pi$
$338$	−16.6998	+	10.7323i	−0.908349	+	0.583760i
$339$	0.493002	+	0.144758i	0.0267762	+	0.00786219i
$340$	−17.9309	+	20.6934i	−0.972441	+	1.12226i
$341$	−2.80027	+	0.822232i	−0.151643	+	0.0445264i
$342$	−15.4521	+	33.8353i	−0.835551	+	1.82960i
$343$	2.37011	+	16.4845i	0.127974	+	0.890077i
$344$	−83.0708			−4.47888
$345$	0.217032	−	0.168226i	0.0116846	−	0.00905699i
$346$	−0.175940			−0.00945860
$347$	−2.89231	−	20.1165i	−0.155267	−	1.07991i	−0.907209	−	0.420679i	$-0.861792\pi$
$347$	−2.89231	−	20.1165i	−0.155267	−	1.07991i	0.751942	−	0.659229i	$-0.229117\pi$
$348$	−0.134293	+	0.294060i	−0.00719884	+	0.0157633i
$349$	18.8607	−	5.53800i	1.00959	−	0.296442i	0.265204	−	0.964192i	$-0.414561\pi$
$349$	18.8607	−	5.53800i	1.00959	−	0.296442i	0.744385	+	0.667750i	$0.232743\pi$
$350$	2.50297	−	2.88858i	0.133789	−	0.154401i
$351$	1.47861	+	0.434159i	0.0789224	+	0.0231737i
$352$	−30.9426	+	19.8856i	−1.64925	+	1.05991i
$353$	8.40026	+	18.3940i	0.447101	+	0.979015i	0.990240	+	0.139372i	$0.0445083\pi$
$353$	8.40026	+	18.3940i	0.447101	+	0.979015i	−0.543139	+	0.839643i	$0.682764\pi$
$354$	0.252129	+	0.290973i	0.0134005	+	0.0154650i
$355$	6.35755	+	4.08575i	0.337424	+	0.216849i
$356$	12.9960	−	90.3891i	0.688786	−	4.79061i
$357$	−0.0536313	+	0.373014i	−0.00283847	+	0.0197420i
$358$	−13.6242	−	8.75571i	−0.720059	−	0.462754i
$359$	−7.89436	−	9.11057i	−0.416648	−	0.480838i	0.508165	−	0.861260i	$-0.330324\pi$
$359$	−7.89436	−	9.11057i	−0.416648	−	0.480838i	−0.924813	+	0.380422i	$0.875779\pi$
$360$	12.8760	+	28.1946i	0.678627	+	1.48599i
$361$	0.800653	−	0.514549i	0.0421396	−	0.0270815i
$362$	24.0754	+	7.06918i	1.26538	+	0.371548i
$363$	0.344797	−	0.397917i	0.0180972	−	0.0208852i
$364$	−33.8925	+	9.95173i	−1.77645	+	0.521612i
$365$	3.46608	−	7.58965i	0.181423	−	0.397260i
$366$	−0.183751	−	1.27802i	−0.00960483	−	0.0668030i
$367$	−29.4350			−1.53649			−0.768247	−	0.640154i	$-0.778871\pi$
$367$	−29.4350			−1.53649			−0.768247	+	0.640154i	$0.778871\pi$
$368$	−59.6371	−	57.6677i	−3.10880	−	3.00614i
$369$	7.70113			0.400905
$370$	1.80971	+	12.5868i	0.0940822	+	0.654356i
$371$	0.510854	−	1.11861i	0.0265222	−	0.0580755i
$372$	−0.683014	+	0.200551i	−0.0354126	+	0.0103981i
$373$	−19.5046	+	22.5095i	−1.00991	+	1.16550i	−0.0237471	+	0.999718i	$0.507560\pi$
$373$	−19.5046	+	22.5095i	−1.00991	+	1.16550i	−0.986163	+	0.165780i	$0.946986\pi$
$374$	17.1381	+	5.03220i	0.886189	+	0.260209i
$375$	0.0481678	−	0.0309556i	0.00248737	−	0.00159854i
$376$	15.7248	+	34.4325i	0.810944	+	1.77572i
$377$	2.90003	+	3.34682i	0.149359	+	0.172370i
$378$	1.10402	+	0.709510i	0.0567846	+	0.0364933i
$379$	0.390306	−	2.71464i	0.0200487	−	0.139442i	−0.977339	−	0.211682i	$-0.932106\pi$
$379$	0.390306	−	2.71464i	0.0200487	−	0.139442i	0.997387	+	0.0722405i	$0.0230149\pi$
$380$	3.63743	−	25.2989i	0.186596	−	1.29781i
$381$	0.116284	+	0.0747313i	0.00595742	+	0.00382860i
$382$	24.8355	+	28.6617i	1.27070	+	1.46646i
$383$	−3.46772	−	7.59326i	−0.177192	−	0.387997i	0.800108	−	0.599856i	$-0.204776\pi$
$383$	−3.46772	−	7.59326i	−0.177192	−	0.387997i	−0.977300	+	0.211859i	$0.932048\pi$
$384$	−2.91647	+	1.87430i	−0.148830	+	0.0956475i
$385$	−1.77270	−	0.520510i	−0.0903449	−	0.0265277i
$386$	26.1514	−	30.1803i	1.33107	−	1.53614i
$387$	23.0931	−	6.78076i	1.17389	−	0.344685i
$388$	40.9634	−	89.6972i	2.07960	−	4.55369i
$389$	−2.69359	−	18.7343i	−0.136570	−	0.949867i	−0.936723	−	0.350071i	$-0.886157\pi$
$389$	−2.69359	−	18.7343i	−0.136570	−	0.949867i	0.800153	−	0.599796i	$-0.204752\pi$
$390$	−0.714111			−0.0361604
$391$	−1.25267	+	22.9148i	−0.0633504	+	1.15885i
$392$	52.8349			2.66856
$393$	0.0895679	+	0.622958i	0.00451810	+	0.0314241i
$394$	−22.5025	+	49.2737i	−1.13366	+	2.48237i
$395$	−13.0882	+	3.84304i	−0.658539	+	0.193364i
$396$	15.0835	−	17.4073i	0.757977	−	0.874752i
$397$	−11.6175	−	3.41120i	−0.583064	−	0.171203i	−0.0231190	−	0.999733i	$-0.507360\pi$
$397$	−11.6175	−	3.41120i	−0.583064	−	0.171203i	−0.559945	+	0.828530i	$0.689178\pi$
$398$	47.8229	−	30.7339i	2.39714	−	1.54055i
$399$	−0.146131	−	0.319981i	−0.00731568	−	0.0160191i
$400$	−11.3278	−	13.0730i	−0.566392	−	0.653651i
$401$	11.8052	+	7.58675i	0.589524	+	0.378864i	0.801129	−	0.598491i	$-0.204233\pi$
$401$	11.8052	+	7.58675i	0.589524	+	0.378864i	−0.211605	+	0.977355i	$0.567869\pi$
$402$	0.268092	−	1.86462i	0.0133712	−	0.0929988i
$403$	−1.38779	+	9.65226i	−0.0691305	+	0.480813i
$404$	45.5013	+	29.2419i	2.26377	+	1.45484i
$405$	−5.87443	−	6.77946i	−0.291903	−	0.336874i
$406$	1.56666	+	3.43050i	0.0777519	+	0.170253i
$407$	5.17097	−	3.32318i	0.256315	−	0.164724i
$408$	2.71910	+	0.798399i	0.134615	+	0.0395266i
$409$	−13.7072	+	15.8189i	−0.677777	+	0.782196i	−0.985572	−	0.169256i	$-0.945863\pi$
$409$	−13.7072	+	15.8189i	−0.677777	+	0.782196i	0.307795	+	0.951453i	$0.400409\pi$
$410$	−6.85199	+	2.01193i	−0.338396	+	0.0993620i
$411$	0.0340414	−	0.0745402i	0.00167914	−	0.00367680i
$412$	7.25249	+	50.4422i	0.357305	+	2.48511i
$413$	3.32825			0.163772
$414$	35.3684	+	18.5488i	1.73826	+	0.911622i
$415$	−4.34914			−0.213491
$416$	17.4902	+	121.647i	0.857528	+	5.96424i
$417$	−0.0405226	+	0.0887321i	−0.00198440	+	0.00434523i
$418$	−15.9975	+	4.69730i	−0.782465	+	0.229753i
$419$	−16.5994	+	19.1568i	−0.810935	+	0.935869i	−0.998928	−	0.0463013i	$-0.985257\pi$
$419$	−16.5994	+	19.1568i	−0.810935	+	0.935869i	0.187992	+	0.982171i	$0.439802\pi$
$420$	−0.432379	−	0.126958i	−0.0210979	−	0.00619491i
$421$	12.1501	−	7.80841i	0.592161	−	0.380559i	−0.209969	−	0.977708i	$-0.567336\pi$
$421$	12.1501	−	7.80841i	0.592161	−	0.380559i	0.802130	+	0.597149i	$0.203700\pi$
$422$	−20.2985	−	44.4474i	−0.988113	−	2.16367i
$423$	−7.18198	−	8.28845i	−0.349200	−	0.402998i
$424$	−7.77958	−	4.99963i	−0.377810	−	0.242804i
$425$	−0.681004	+	4.73649i	−0.0330335	+	0.229753i
$426$	0.171124	−	1.19019i	0.00829097	−	0.0576650i
$427$	−9.38963	−	6.03435i	−0.454396	−	0.292023i
$428$	23.6421	+	27.2844i	1.14278	+	1.31884i
$429$	0.143395	+	0.313991i	0.00692318	+	0.0151596i
$430$	−18.7754	+	12.0662i	−0.905430	+	0.581884i
$431$	−36.7603	−	10.7938i	−1.77068	−	0.519918i	−0.776737	−	0.629825i	$-0.783127\pi$
$431$	−36.7603	−	10.7938i	−1.77068	−	0.519918i	−0.993942	+	0.109906i	$0.964945\pi$
$432$	3.88947	−	4.48869i	0.187132	−	0.215962i
$433$	−0.151836	+	0.0445831i	−0.00729678	+	0.00214253i	−0.285379	−	0.958415i	$-0.592119\pi$
$433$	−0.151836	+	0.0445831i	−0.00729678	+	0.00214253i	0.278082	+	0.960557i	$0.410301\pi$
$434$	−3.44978	+	7.55397i	−0.165595	+	0.362602i
$435$	0.00804018	+	0.0559207i	0.000385497	+	0.00268119i
$436$	5.39191			0.258226
$437$	−10.5805	−	18.6264i	−0.506134	−	0.891022i
$438$	−1.32756			−0.0634331
$439$	2.03753	+	14.1713i	0.0972461	+	0.676361i	0.978881	+	0.204430i	$0.0655340\pi$
$439$	2.03753	+	14.1713i	0.0972461	+	0.676361i	−0.881635	+	0.471932i	$0.843557\pi$
$440$	−5.77151	+	12.6378i	−0.275146	+	0.602486i
$441$	−14.6877	+	4.31271i	−0.699417	+	0.205367i
$442$	39.0827	−	45.1038i	1.85897	−	2.14537i
$443$	12.8611	+	3.77635i	0.611047	+	0.179420i	0.572592	−	0.819841i	$-0.305938\pi$
$443$	12.8611	+	3.77635i	0.611047	+	0.179420i	0.0384556	+	0.999260i	$0.487756\pi$
$444$	1.26125	−	0.810558i	0.0598564	−	0.0384674i
$445$	−6.62960	−	14.5168i	−0.314273	−	0.688162i
$446$	15.0506	+	17.3693i	0.712666	+	0.822460i
$447$	−0.383001	−	0.246140i	−0.0181153	−	0.0116420i
$448$	−8.12273	+	56.4948i	−0.383763	+	2.66913i
$449$	0.438262	−	3.04818i	0.0206829	−	0.143852i	−0.976863	−	0.213865i	$-0.931395\pi$
$449$	0.438262	−	3.04818i	0.0206829	−	0.143852i	0.997546	+	0.0700124i	$0.0223039\pi$
$450$	7.00552	+	4.50218i	0.330244	+	0.212235i
$451$	2.26053	+	2.60879i	0.106444	+	0.122843i
$452$	−21.3311	−	46.7086i	−1.00333	−	2.19699i
$453$	0.483836	−	0.310942i	0.0227326	−	0.0146093i
$454$	12.1118	+	3.55635i	0.568436	+	0.166908i
$455$	−4.04256	+	4.66536i	−0.189518	+	0.218715i
$456$	−2.53814	+	0.745265i	−0.118859	+	0.0349002i
$457$	−11.6496	+	25.5090i	−0.544944	+	1.19326i	0.414159	+	0.910205i	$0.364076\pi$
$457$	−11.6496	+	25.5090i	−0.544944	+	1.19326i	−0.959103	+	0.283057i	$0.908651\pi$
$458$	−3.66186	−	25.4688i	−0.171108	−	1.19008i
$459$	−1.64302			−0.0766897
$460$	−26.9092	−	5.38229i	−1.25465	−	0.250951i
$461$	30.7064			1.43014			0.715069	−	0.699054i	$-0.246395\pi$
$461$	30.7064			1.43014			0.715069	+	0.699054i	$0.246395\pi$
$462$	0.0418350	+	0.290969i	0.00194634	+	0.0135371i
$463$	7.82196	−	17.1277i	0.363517	−	0.795992i	−0.636184	−	0.771538i	$-0.719488\pi$
$463$	7.82196	−	17.1277i	0.363517	−	0.795992i	0.999701	−	0.0244540i	$-0.00778472\pi$
$464$	16.3767	−	4.80862i	0.760268	−	0.223235i
$465$	−0.0814672	+	0.0940181i	−0.00377795	+	0.00435999i
$466$	−4.18434	−	1.22863i	−0.193836	−	0.0569153i
$467$	−31.4449	+	20.2084i	−1.45509	+	0.935133i	−0.456117	+	0.889920i	$0.650760\pi$
$467$	−31.4449	+	20.2084i	−1.45509	+	0.935133i	−0.998977	+	0.0452130i	$0.985603\pi$
$468$	−31.9706	−	70.0060i	−1.47784	−	3.23603i
$469$	−10.6641	−	12.3070i	−0.492422	−	0.568285i
$470$	8.55545	+	5.49826i	0.394634	+	0.253616i
$471$	0.0808568	−	0.562371i	0.00372568	−	0.0259127i
$472$	3.56189	−	24.7735i	0.163949	−	1.14029i
$473$	9.07560	+	5.83253i	0.417296	+	0.268180i
$474$	1.42129	+	1.64026i	0.0652822	+	0.0753397i
$475$	−1.85555	−	4.06309i	−0.0851385	−	0.186427i
$476$	31.6825	−	20.3611i	1.45217	−	0.933250i
$477$	2.57077	+	0.754847i	0.117708	+	0.0345621i
$478$	34.3558	−	39.6487i	1.57140	−	1.81349i
$479$	21.6798	−	6.36575i	0.990573	−	0.290859i	0.253991	−	0.967207i	$-0.418257\pi$
$479$	21.6798	−	6.36575i	0.990573	−	0.290859i	0.736582	+	0.676348i	$0.236438\pi$
$480$	−0.651311	+	1.42617i	−0.0297281	+	0.0650956i
$481$	−2.92287	−	20.3290i	−0.133271	−	0.926923i
$482$	43.7004			1.99050
$483$	−0.351609	+	0.137910i	−0.0159987	+	0.00627512i
$484$	−52.6186			−2.39176
$485$	−2.45250	−	17.0575i	−0.111362	−	0.774542i
$486$	−1.78201	+	3.90206i	−0.0808336	+	0.177001i
$487$	−23.7002	+	6.95901i	−1.07396	+	0.315343i	−0.770459	−	0.637489i	$-0.779973\pi$
$487$	−23.7002	+	6.95901i	−1.07396	+	0.315343i	−0.303499	+	0.952832i	$0.598155\pi$
$488$	−54.9649	+	63.4329i	−2.48814	+	2.87147i
$489$	−0.130426	−	0.0382966i	−0.00589807	−	0.00173183i
$490$	11.9416	−	7.67438i	0.539465	−	0.346693i
$491$	−5.87923	−	12.8737i	−0.265326	−	0.580983i	0.729338	−	0.684154i	$-0.239828\pi$
$491$	−5.87923	−	12.8737i	−0.265326	−	0.580983i	−0.994664	+	0.103171i	$0.967101\pi$
$492$	0.551367	+	0.636312i	0.0248576	+	0.0286872i
$493$	−3.97202	−	2.55267i	−0.178891	−	0.114966i
$494$	−7.92823	+	55.1421i	−0.356708	+	2.48096i
$495$	0.572862	−	3.98435i	0.0257482	−	0.179083i
$496$	31.6176	+	20.3194i	1.41967	+	0.912368i
$497$	−6.80692	−	7.85560i	−0.305332	−	0.352372i
$498$	0.287463	+	0.629457i	0.0128815	+	0.0282067i
$499$	20.9399	−	13.4572i	0.937398	−	0.602429i	0.0197420	−	0.999805i	$-0.493716\pi$
$499$	20.9399	−	13.4572i	0.937398	−	0.602429i	0.917656	+	0.397376i	$0.130079\pi$
$500$	−5.49030	−	1.61210i	−0.245534	−	0.0720952i
$501$	−0.148179	+	0.171007i	−0.00662014	+	0.00764005i
$502$	16.7877	−	4.92932i	0.749273	−	0.220006i
$503$	−11.1275	+	24.3658i	−0.496151	+	1.08642i	0.481550	+	0.876419i	$0.340074\pi$
$503$	−11.1275	+	24.3658i	−0.496151	+	1.08642i	−0.977701	+	0.210001i	$0.932653\pi$
$504$	−6.06721	−	42.1984i	−0.270255	−	1.87966i
$505$	9.45240			0.420626
$506$	4.09830	+	17.4259i	0.182192	+	0.774674i
$507$	0.409022			0.0181653
$508$	−1.96593	−	13.6734i	−0.0872241	−	0.606657i
$509$	15.5721	−	34.0981i	0.690220	−	1.51137i	−0.161219	−	0.986919i	$-0.551543\pi$
$509$	15.5721	−	34.0981i	0.690220	−	1.51137i	0.851439	−	0.524453i	$-0.175730\pi$
$510$	0.730531	−	0.214503i	0.0323484	−	0.00949836i
$511$	−7.51526	+	8.67307i	−0.332455	+	0.383674i
$512$	111.142	+	32.6343i	4.91184	+	1.44225i
$513$	1.29021	−	0.829169i	0.0569642	−	0.0366087i
$514$	−2.58995	−	5.67121i	−0.114238	−	0.250146i
$515$	5.83219	+	6.73071i	0.256997	+	0.296590i
$516$	2.21363	+	1.42262i	0.0974498	+	0.0626272i
$517$	0.699605	−	4.86586i	0.0307686	−	0.214000i
$518$	2.48913	−	17.3123i	0.109366	−	0.760657i
$519$	0.00304968	+	0.00195991i	0.000133866	+	8.60305e-5i
$520$	30.3998	+	35.0833i	1.33312	+	1.53850i
$521$	−15.2664	−	33.4287i	−0.668831	−	1.46454i	−0.874058	−	0.485822i	$-0.838520\pi$
$521$	−15.2664	−	33.4287i	−0.668831	−	1.46454i	0.205227	−	0.978714i	$-0.434207\pi$
$522$	−6.91236	+	4.44230i	−0.302546	+	0.194434i
$523$	−11.7544	−	3.45139i	−0.513983	−	0.150919i	0.0144476	−	0.999896i	$-0.495401\pi$
$523$	−11.7544	−	3.45139i	−0.513983	−	0.150919i	−0.528430	+	0.848977i	$0.677219\pi$
$524$	41.1885	−	47.5340i	1.79933	−	2.07653i
$525$	−0.0755632	+	0.0221874i	−0.00329785	+	0.000968336i
$526$	−3.43757	+	7.52724i	−0.149885	+	0.328203i
$527$	−1.47963	−	10.2911i	−0.0644537	−	0.448286i
$528$	1.33040			0.0578982
$529$	−20.5890	+	10.2515i	−0.895174	+	0.445716i
$530$	−2.48452			−0.107921
$531$	1.03199	+	7.17762i	0.0447844	+	0.311482i
$532$	−14.6038	+	31.9778i	−0.633155	+	1.38642i
$533$	11.0667	−	3.24948i	0.479352	−	0.140750i
$534$	−1.66284	+	1.91902i	−0.0719582	+	0.0830442i
$535$	6.05375	+	1.77754i	0.261727	+	0.0768498i
$536$	−103.019	+	66.2062i	−4.44974	+	2.85967i
$537$	0.138620	+	0.303537i	0.00598192	+	0.0130986i
$538$	2.06214	+	2.37984i	0.0889053	+	0.102602i
$539$	−5.77228	−	3.70962i	−0.248630	−	0.159785i
$540$	0.279607	−	1.94471i	0.0120324	−	0.0836870i
$541$	0.827414	−	5.75479i	0.0355733	−	0.247418i	−0.964274	−	0.264908i	$-0.914658\pi$
$541$	0.827414	−	5.75479i	0.0355733	−	0.247418i	0.999847	+	0.0174901i	$0.00556757\pi$
$542$	−34.5954	−	22.2331i	−1.48600	−	0.954993i
$543$	−0.338566	−	0.390726i	−0.0145293	−	0.0167677i
$544$	−54.4325	−	119.190i	−2.33377	−	5.11025i
$545$	0.792711	−	0.509445i	0.0339560	−	0.0218222i
$546$	0.942424	+	0.276721i	0.0403320	+	0.0118425i
$547$	−3.18432	+	3.67490i	−0.136152	+	0.157127i	−0.819731	−	0.572749i	$-0.805877\pi$
$547$	−3.18432	+	3.67490i	−0.136152	+	0.157127i	0.683579	+	0.729876i	$0.260422\pi$
$548$	−7.85762	+	2.30721i	−0.335661	+	0.0985590i
$549$	10.1021	−	22.1205i	0.431147	−	0.944080i
$550$	0.531216	+	3.69469i	0.0226511	+	0.157542i
$551$	4.40733			0.187759
$552$	0.650229	+	2.76476i	0.0276756	+	0.117676i
$553$	18.7619			0.797837
$554$	1.90176	+	13.2271i	0.0807982	+	0.561964i
$555$	0.108844	−	0.238334i	0.00462016	−	0.0101167i
$556$	9.35366	−	2.74648i	0.396683	−	0.116477i
$557$	−12.6801	+	14.6337i	−0.537274	+	0.620048i	−0.957871	−	0.287200i	$-0.907275\pi$
$557$	−12.6801	+	14.6337i	−0.537274	+	0.620048i	0.420596	+	0.907248i	$0.361821\pi$
$558$	−17.3604	−	5.09747i	−0.734923	−	0.215793i
$559$	30.3243	−	19.4882i	1.28258	−	0.824264i
$560$	9.88369	+	21.6423i	0.417662	+	0.914552i
$561$	−0.241008	−	0.278138i	−0.0101754	−	0.0117430i
$562$	−6.42758	−	4.13076i	−0.271131	−	0.174245i
$563$	−5.44167	+	37.8476i	−0.229339	+	1.59509i	0.471564	+	0.881832i	$0.343689\pi$
$563$	−5.44167	+	37.8476i	−0.229339	+	1.59509i	−0.700903	+	0.713256i	$0.747220\pi$
$564$	0.170641	−	1.18683i	0.00718528	−	0.0499747i
$565$	−7.54925	−	4.85161i	−0.317599	−	0.204109i
$566$	−36.7223	−	42.3798i	−1.54355	−	1.78136i
$567$	5.12552	+	11.2233i	0.215252	+	0.471335i
$568$	−65.7572	+	42.2596i	−2.75911	+	1.77317i
$569$	43.3225	+	12.7206i	1.81618	+	0.533277i	0.999066	−	0.0432061i	$-0.0137572\pi$
$569$	43.3225	+	12.7206i	1.81618	+	0.533277i	0.817109	+	0.576483i	$0.195575\pi$
$570$	−0.465411	+	0.537113i	−0.0194939	+	0.0224972i
$571$	−1.95923	+	0.575282i	−0.0819912	+	0.0240748i	−0.322471	−	0.946579i	$-0.604513\pi$
$571$	−1.95923	+	0.575282i	−0.0819912	+	0.0240748i	0.240480	+	0.970654i	$0.422695\pi$
$572$	14.3304	−	31.3792i	0.599185	−	1.31203i
$573$	−0.111208	−	0.773470i	−0.00464579	−	0.0323122i
$574$	9.82232			0.409976
$575$	−4.46469	+	1.75117i	−0.186190	+	0.0730287i
$576$	−124.354			−5.18141
$577$	4.53084	+	31.5127i	0.188621	+	1.31189i	0.835582	+	0.549366i	$0.185131\pi$
$577$	4.53084	+	31.5127i	0.188621	+	1.31189i	−0.646961	+	0.762523i	$0.723960\pi$
$578$	−6.80864	+	14.9088i	−0.283202	+	0.620126i
$579$	−0.789497	+	0.231817i	−0.0328104	+	0.00963400i
$580$	3.69734	−	4.26695i	0.153523	−	0.177176i
$581$	5.73963	+	1.68531i	0.238120	+	0.0699183i
$582$	−2.30666	+	1.48240i	−0.0956140	+	0.0614474i
$583$	0.498898	+	1.09243i	0.0206622	+	0.0452440i
$584$	56.5143	+	65.2210i	2.33858	+	2.69887i
$585$	−11.3147	−	7.27150i	−0.467804	−	0.300639i
$586$	−8.12532	+	56.5129i	−0.335654	+	2.33453i
$587$	4.71425	−	32.7884i	0.194578	−	1.35332i	−0.625122	−	0.780527i	$-0.714951\pi$
$587$	4.71425	−	32.7884i	0.194578	−	1.35332i	0.819700	−	0.572793i	$-0.194140\pi$
$588$	−1.40792	−	0.904816i	−0.0580617	−	0.0373140i
$589$	6.35540	+	7.33453i	0.261870	+	0.302214i
$590$	−2.79336	−	6.11660i	−0.115001	−	0.251816i
$591$	0.938942	−	0.603421i	0.0386229	−	0.0248214i
$592$	−75.9506	−	22.3011i	−3.12155	−	0.916569i
$593$	−17.7135	+	20.4425i	−0.727407	+	0.839473i	−0.992177	−	0.124839i	$-0.960159\pi$
$593$	−17.7135	+	20.4425i	−0.727407	+	0.839473i	0.264770	+	0.964312i	$0.414704\pi$
$594$	−1.22972	+	0.361079i	−0.0504561	+	0.0148152i
$595$	2.73414	−	5.98693i	0.112089	−	0.245440i
$596$	6.47512	+	45.0355i	0.265231	+	1.84473i
$597$	−1.17131			−0.0479385
$598$	58.6518	+	11.7314i	2.39845	+	0.479731i
$599$	−13.6754			−0.558761			−0.279380	−	0.960181i	$-0.590129\pi$
$599$	−13.6754			−0.558761			−0.279380	+	0.960181i	$0.590129\pi$
$600$	0.0842818	+	0.586193i	0.00344079	+	0.0239312i
$601$	−15.9112	+	34.8406i	−0.649030	+	1.42118i	0.243371	+	0.969933i	$0.421747\pi$
$601$	−15.9112	+	34.8406i	−0.649030	+	1.42118i	−0.892401	+	0.451243i	$0.850981\pi$
$602$	29.4539	−	8.64844i	1.20045	−	0.352484i
$603$	23.2344	−	26.8139i	0.946178	−	1.09195i
$604$	−55.1490	−	16.1932i	−2.24398	−	0.658892i
$605$	−7.73592	+	4.97157i	−0.314510	+	0.202123i
$606$	−0.624772	−	1.36806i	−0.0253796	−	0.0555736i
$607$	−29.8121	−	34.4050i	−1.21004	−	1.39646i	−0.894215	−	0.447637i	$-0.852266\pi$
$607$	−29.8121	−	34.4050i	−1.21004	−	1.39646i	−0.315821	−	0.948819i	$-0.602280\pi$
$608$	102.895	+	66.1265i	4.17294	+	2.68178i
$609$	0.0110587	−	0.0769150i	0.000448121	−	0.00311675i
$610$	−3.20923	+	22.3207i	−0.129938	+	0.903737i
$611$	−13.8180	−	8.88027i	−0.559015	−	0.359257i
$612$	53.7340	+	62.0123i	2.17207	+	2.50670i
$613$	−2.60443	−	5.70291i	−0.105192	−	0.230339i	0.849716	−	0.527241i	$-0.176774\pi$
$613$	−2.60443	−	5.70291i	−0.105192	−	0.230339i	−0.954908	+	0.296903i	$0.904046\pi$
$614$	−55.3290	+	35.5578i	−2.23290	+	1.43500i
$615$	0.141182	+	0.0414548i	0.00569301	+	0.00167162i
$616$	12.5140	−	14.4419i	0.504202	−	0.581880i
$617$	23.5938	−	6.92777i	0.949851	−	0.278901i	0.230126	−	0.973161i	$-0.426086\pi$
$617$	23.5938	−	6.92777i	0.949851	−	0.278901i	0.719725	+	0.694260i	$0.244268\pi$
$618$	0.588657	−	1.28898i	0.0236792	−	0.0518503i
$619$	3.41152	+	23.7276i	0.137120	+	0.953694i	0.935949	+	0.352135i	$0.114544\pi$
$619$	3.41152	+	23.7276i	0.137120	+	0.953694i	−0.798829	+	0.601558i	$0.794547\pi$
$620$	12.4325			0.499301
$621$	−0.813317	−	1.43180i	−0.0326373	−	0.0574562i
$622$	−88.0264			−3.52954
$623$	3.12388	+	21.7270i	0.125155	+	0.870475i
$624$	1.84663	−	4.04354i	0.0739242	−	0.161871i
$625$	−0.959493	+	0.281733i	−0.0383797	+	0.0112693i
$626$	23.4284	−	27.0379i	0.936388	−	1.08065i
$627$	0.329622	+	0.0967857i	0.0131638	+	0.00386525i
$628$	−47.7659	+	30.6973i	−1.90607	+	1.22495i
$629$	9.09647	+	19.9185i	0.362700	+	0.794202i
$630$	−7.50069	−	8.65626i	−0.298835	−	0.344874i
$631$	36.2486	+	23.2956i	1.44303	+	0.927382i	0.999516	+	0.0311161i	$0.00990617\pi$
$631$	36.2486	+	23.2956i	1.44303	+	0.927382i	0.443518	+	0.896265i	$0.353730\pi$
$632$	20.0790	−	139.652i	0.798699	−	5.55508i
$633$	−0.143283	+	0.996553i	−0.00569497	+	0.0396094i
$634$	33.0289	+	21.2264i	1.31174	+	0.843007i
$635$	−1.58093	−	1.82449i	−0.0627373	−	0.0724027i
$636$	0.121686	+	0.266456i	0.00482518	+	0.0105657i
$637$	−19.2869	+	12.3949i	−0.764175	+	0.491105i
$638$	−3.53385	−	1.03763i	−0.139907	−	0.0410803i
$639$	14.8306	−	17.1154i	0.586689	−	0.677075i
$640$	58.0955	−	17.0584i	2.29642	−	0.674291i
$641$	16.5774	−	36.2995i	0.654769	−	1.43374i	−0.232549	−	0.972585i	$-0.574706\pi$
$641$	16.5774	−	36.2995i	0.654769	−	1.43374i	0.887317	−	0.461159i	$-0.152566\pi$
$642$	−0.142866	−	0.993658i	−0.00563849	−	0.0392165i
$643$	−1.64545			−0.0648904			−0.0324452	−	0.999474i	$-0.510329\pi$
$643$	−1.64545			−0.0648904			−0.0324452	+	0.999474i	$0.510329\pi$
$644$	33.4268	+	17.5305i	1.31720	+	0.690798i
$645$	0.459859			0.0181069
$646$	−8.45293	−	58.7914i	−0.332576	−	2.31312i
$647$	10.7513	−	23.5421i	0.422678	−	0.925535i	−0.571781	−	0.820406i	$-0.693747\pi$
$647$	10.7513	−	23.5421i	0.422678	−	0.925535i	0.994459	−	0.105128i	$-0.0335254\pi$
$648$	89.0251	−	26.1401i	3.49724	−	1.02688i
$649$	−2.12853	+	2.45645i	−0.0835521	+	0.0964243i
$650$	11.9668	+	3.51377i	0.469376	+	0.137821i
$651$	0.143946	−	0.0925084i	0.00564168	−	0.00362569i
$652$	5.64325	+	12.3570i	0.221007	+	0.483937i
$653$	22.6600	+	26.1510i	0.886754	+	1.02337i	0.999557	+	0.0297518i	$0.00947168\pi$
$653$	22.6600	+	26.1510i	0.886754	+	1.02337i	−0.112803	+	0.993617i	$0.535983\pi$
$654$	−0.126128	−	0.0810577i	−0.00493200	−	0.00316961i
$655$	1.56431	−	10.8800i	0.0611226	−	0.425117i
$656$	6.32639	−	44.0010i	0.247004	−	1.71795i
$657$	−21.0344	−	13.5180i	−0.820629	−	0.527386i
$658$	−9.16018	−	10.5714i	−0.357101	−	0.412116i
$659$	4.61030	+	10.0951i	0.179592	+	0.393251i	0.977922	−	0.208968i	$-0.0670105\pi$
$659$	4.61030	+	10.0951i	0.179592	+	0.393251i	−0.798331	+	0.602219i	$0.794283\pi$
$660$	0.370224	−	0.237929i	0.0144110	−	0.00926136i
$661$	29.5705	+	8.68267i	1.15016	+	0.337717i	0.800601	−	0.599198i	$-0.204514\pi$
$661$	29.5705	+	8.68267i	1.15016	+	0.337717i	0.349557	+	0.936915i	$0.386332\pi$
$662$	−56.8357	+	65.5919i	−2.20898	+	2.54930i
$663$	−1.17989	+	0.346446i	−0.0458229	+	0.0134548i
$664$	18.6870	−	40.9188i	0.725196	−	1.58796i
$665$	0.874338	+	6.08115i	0.0339054	+	0.235817i
$666$	38.1070			1.47662
$667$	0.258299	−	4.72500i	0.0100014	−	0.182953i
$668$	22.6132			0.874930
$669$	−0.0673934	−	0.468731i	−0.00260558	−	0.0181222i
$670$	−13.6674	+	29.9274i	−0.528017	+	1.15620i
$671$	10.4587	−	3.07095i	0.403754	−	0.118553i
$672$	1.41219	−	1.62976i	0.0544765	−	0.0628692i
$673$	−8.66804	−	2.54517i	−0.334128	−	0.0981090i	0.110365	−	0.993891i	$-0.464798\pi$
$673$	−8.66804	−	2.54517i	−0.334128	−	0.0981090i	−0.444493	+	0.895782i	$0.646616\pi$
$674$	−55.3595	+	35.5774i	−2.13237	+	1.37039i
$675$	−0.142635	−	0.312327i	−0.00549002	−	0.0120215i
$676$	−26.7683	−	30.8922i	−1.02955	−	1.18816i
$677$	8.41490	+	5.40793i	0.323411	+	0.207844i	0.692264	−	0.721644i	$-0.256613\pi$
$677$	8.41490	+	5.40793i	0.323411	+	0.207844i	−0.368853	+	0.929488i	$0.620250\pi$
$678$	−0.203200	+	1.41329i	−0.00780385	+	0.0542770i
$679$	−3.37324	+	23.4614i	−0.129453	+	0.900367i
$680$	−41.6371	−	26.7585i	−1.59671	−	1.02614i
$681$	−0.170325	−	0.196566i	−0.00652688	−	0.00753242i
$682$	−3.36905	−	7.37718i	−0.129007	−	0.282487i
$683$	35.6932	−	22.9386i	1.36576	−	0.877722i	0.367138	−	0.930167i	$-0.380338\pi$
$683$	35.6932	−	22.9386i	1.36576	−	0.877722i	0.998624	+	0.0524448i	$0.0167014\pi$
$684$	−73.4908	−	21.5788i	−2.80999	−	0.825088i
$685$	−0.937225	+	1.08162i	−0.0358095	+	0.0413264i
$686$	−44.4045	+	13.0383i	−1.69537	+	0.497806i
$687$	−0.220240	+	0.482259i	−0.00840269	+	0.0183993i
$688$	−19.7717	−	137.515i	−0.753787	−	5.24271i
$689$	4.01277			0.152874
$690$	0.548549	+	0.530434i	0.0208829	+	0.0201933i
$691$	15.2544			0.580306			0.290153	−	0.956980i	$-0.406294\pi$
$691$	15.2544			0.580306			0.290153	+	0.956980i	$0.406294\pi$
$692$	−0.0515587	−	0.358599i	−0.00195997	−	0.0136319i
$693$	−2.29996	+	5.03622i	−0.0873684	+	0.191310i
$694$	54.1881	−	15.9111i	2.05695	−	0.603976i
$695$	1.11567	−	1.28755i	0.0423196	−	0.0488395i
$696$	−0.560675	−	0.164629i	−0.0212523	−	0.00624024i
$697$	−10.3451	+	6.64839i	−0.391848	+	0.251826i
$698$	22.6916	+	49.6877i	0.858890	+	1.88071i
$699$	0.0588432	+	0.0679087i	0.00222565	+	0.00256854i
$700$	6.62094	+	4.25502i	0.250248	+	0.160825i
$701$	−3.79143	+	26.3699i	−0.143200	+	0.995979i	0.783826	+	0.620981i	$0.213266\pi$
$701$	−3.79143	+	26.3699i	−0.143200	+	0.995979i	−0.927026	+	0.374998i	$0.877643\pi$
$702$	−0.609438	+	4.23874i	−0.0230018	+	0.159981i
$703$	−17.1952	−	11.0507i	−0.648531	−	0.416785i
$704$	−36.5019	−	42.1254i	−1.37572	−	1.58766i
$705$	−0.0870484	−	0.190609i	−0.00327843	−	0.00717877i
$706$	−47.2721	+	30.3799i	−1.77911	+	1.14336i
$707$	−12.4745	−	3.66284i	−0.469151	−	0.137755i
$708$	−0.519171	+	0.599155i	−0.0195116	+	0.0225176i
$709$	−7.34445	+	2.15652i	−0.275827	+	0.0809900i	−0.416720	−	0.909035i	$-0.636821\pi$
$709$	−7.34445	+	2.15652i	−0.275827	+	0.0809900i	0.140894	+	0.990025i	$0.455002\pi$
$710$	−8.72393	+	19.1027i	−0.327403	+	0.716913i
$711$	5.81748	+	40.4614i	0.218172	+	1.51742i
$712$	165.066			6.18612
$713$	8.23564	−	6.38362i	0.308427	−	0.239069i
$714$	−1.04721			−0.0391910
$715$	−0.857971	−	5.96732i	−0.0320863	−	0.223165i
$716$	13.8533	−	30.3344i	0.517721	−	1.13365i
$717$	−1.03718	+	0.304544i	−0.0387343	+	0.0113734i
$718$	21.9373	−	25.3170i	0.818694	−	0.944824i
$719$	−1.59535	−	0.468438i	−0.0594967	−	0.0174698i	0.251849	−	0.967767i	$-0.418961\pi$
$719$	−1.59535	−	0.468438i	−0.0594967	−	0.0174698i	−0.311345	+	0.950297i	$0.600780\pi$
$720$	−43.6085	+	28.0255i	−1.62519	+	1.04445i
$721$	−5.08866	−	11.1426i	−0.189512	−	0.414973i
$722$	1.73194	+	1.99877i	0.0644563	+	0.0743865i
$723$	−0.757487	−	0.486807i	−0.0281712	−	0.0181046i
$724$	−7.35308	+	51.1418i	−0.273275	+	1.90067i
$725$	0.140422	−	0.976658i	0.00521515	−	0.0362722i
$726$	1.23086	+	0.791027i	0.0456815	+	0.0293577i
$727$	10.1840	+	11.7529i	0.377702	+	0.435892i	0.912493	−	0.409093i	$-0.134155\pi$
$727$	10.1840	+	11.7529i	0.377702	+	0.435892i	−0.534790	+	0.844985i	$0.679609\pi$
$728$	−26.5242	−	58.0800i	−0.983054	−	2.15259i
$729$	−22.5651	+	14.5017i	−0.835743	+	0.537099i
$730$	22.2467	+	6.53221i	0.823386	+	0.241768i
$731$	−25.1677	+	29.0451i	−0.930860	+	1.07427i
$732$	2.55099	−	0.749038i	0.0942873	−	0.0276852i
$733$	−10.6065	+	23.2251i	−0.391762	+	0.857839i	0.606278	+	0.795253i	$0.292662\pi$
$733$	−10.6065	+	23.2251i	−0.391762	+	0.857839i	−0.998040	+	0.0625857i	$0.980065\pi$
$734$	−11.6408	−	80.9632i	−0.429668	−	2.98841i
$735$	−0.292481			−0.0107883
$736$	76.9230	−	106.436i	2.83542	−	3.92327i
$737$	15.9034			0.585809
$738$	3.04559	+	21.1826i	0.112110	+	0.779741i
$739$	14.1984	−	31.0902i	0.522298	−	1.14367i	−0.446264	−	0.894901i	$-0.647246\pi$
$739$	14.1984	−	31.0902i	0.522298	−	1.14367i	0.968562	−	0.248772i	$-0.0800269\pi$
$740$	−25.1239	+	7.37704i	−0.923573	+	0.271186i
$741$	0.751688	−	0.867494i	0.0276140	−	0.0318682i
$742$	3.27886	+	0.962762i	0.120371	+	0.0353441i
$743$	3.08210	−	1.98074i	0.113071	−	0.0726664i	−0.482883	−	0.875685i	$-0.660410\pi$
$743$	3.08210	−	1.98074i	0.113071	−	0.0726664i	0.595954	+	0.803018i	$0.296774\pi$
$744$	−0.534527	−	1.17045i	−0.0195967	−	0.0429108i
$745$	5.20706	+	6.00927i	0.190772	+	0.220163i
$746$	−69.6277	−	44.7470i	−2.54925	−	1.63831i
$747$	−1.85481	+	12.9005i	−0.0678640	+	0.472005i
$748$	−5.23429	+	36.4053i	−0.191385	+	1.33111i
$749$	−7.30043	−	4.69170i	−0.266752	−	0.171431i
$750$	0.104195	+	0.120247i	0.00380466	+	0.00439081i
$751$	−11.4969	−	25.1746i	−0.419527	−	0.918635i	−0.994912	−	0.100752i	$-0.967875\pi$
$751$	−11.4969	−	25.1746i	−0.419527	−	0.918635i	0.575385	−	0.817883i	$-0.304852\pi$
$752$	−53.2567	+	34.2260i	−1.94207	+	1.24809i
$753$	−0.345903	−	0.101566i	−0.0126054	−	0.00370128i
$754$	−8.05880	+	9.30035i	−0.293484	+	0.338699i
$755$	−9.63791	+	2.82995i	−0.350760	+	0.102992i
$756$	−1.12258	+	2.45812i	−0.0408280	+	0.0894009i
$757$	−1.90508	−	13.2502i	−0.0692415	−	0.481585i	−0.994707	−	0.102753i	$-0.967235\pi$
$757$	−1.90508	−	13.2502i	−0.0692415	−	0.481585i	0.925465	−	0.378832i	$-0.123674\pi$
$758$	7.62119			0.276814
$759$	0.123080	−	0.347707i	0.00446751	−	0.0126210i
$760$	46.2002			1.67586
$761$	−5.45664	−	37.9518i	−0.197803	−	1.37575i	−0.810641	−	0.585543i	$-0.800881\pi$
$761$	−5.45664	−	37.9518i	−0.197803	−	1.37575i	0.612838	−	0.790208i	$-0.290028\pi$
$762$	−0.159567	+	0.349403i	−0.00578051	+	0.0126575i
$763$	−1.24357	+	0.365144i	−0.0450201	+	0.0132191i
$764$	−51.1399	+	59.0186i	−1.85018	+	2.13522i
$765$	13.7590	+	4.04001i	0.497459	+	0.146067i
$766$	19.5145	−	12.5412i	0.705086	−	0.453131i
$767$	4.51157	+	9.87896i	0.162903	+	0.356709i
$768$	−3.19693	−	3.68945i	−0.115359	−	0.133132i
$769$	1.99895	+	1.28464i	0.0720838	+	0.0463255i	0.576186	−	0.817318i	$-0.304540\pi$
$769$	1.99895	+	1.28464i	0.0720838	+	0.0463255i	−0.504103	+	0.863644i	$0.668177\pi$
$770$	0.730651	−	5.08179i	0.0263308	−	0.183135i
$771$	−0.0182819	+	0.127154i	−0.000658408	+	0.00457933i
$772$	69.1768	+	44.4572i	2.48973	+	1.60005i
$773$	−1.74108	−	2.00931i	−0.0626221	−	0.0722698i	0.723574	−	0.690247i	$-0.242498\pi$
$773$	−1.74108	−	2.00931i	−0.0626221	−	0.0722698i	−0.786196	+	0.617977i	$0.787953\pi$
$774$	27.7837	+	60.8379i	0.998666	+	2.18677i
$775$	1.82781	−	1.17466i	0.0656568	−	0.0421951i
$776$	171.023	+	50.2169i	6.13937	+	1.80268i
$777$	−0.235998	+	0.272356i	−0.00846639	+	0.00977073i
$778$	50.4650	−	14.8179i	1.80926	−	0.531246i
$779$	4.76848	−	10.4415i	0.170849	−	0.374106i
$780$	−0.209268	−	1.45549i	−0.00749300	−	0.0521149i
$781$	10.1512			0.363238
$782$	−63.5243	+	5.61661i	−2.27162	+	0.200850i
$783$	0.338789			0.0121073
$784$	12.5752	+	87.4625i	0.449115	+	3.12366i
$785$	−4.12210	+	9.02614i	−0.147124	+	0.322157i
$786$	−1.67807	+	0.492727i	−0.0598549	+	0.0175750i
$787$	4.27068	−	4.92863i	0.152233	−	0.175687i	−0.674510	−	0.738265i	$-0.735645\pi$
$787$	4.27068	−	4.92863i	0.152233	−	0.175687i	0.826744	+	0.562579i	$0.190191\pi$
$788$	−107.023	−	31.4249i	−3.81255	−	1.11946i
$789$	0.143436	−	0.0921810i	0.00510647	−	0.00328173i
$790$	−15.7466	−	34.4803i	−0.560240	−	1.22675i
$791$	8.08285	+	9.32810i	0.287393	+	0.331669i
$792$	35.0252	+	22.5093i	1.24457	+	0.799834i
$793$	5.18324	−	36.0502i	0.184062	−	1.28018i
$794$	4.78837	−	33.3038i	0.169933	−	1.18191i
$795$	0.0430658	+	0.0276767i	0.00152739	+	0.000981592i
$796$	76.6557	+	88.4654i	2.71699	+	3.13557i
$797$	15.8399	+	34.6845i	0.561077	+	1.22859i	0.951414	+	0.307915i	$0.0996311\pi$
$797$	15.8399	+	34.6845i	0.561077	+	1.22859i	−0.390337	+	0.920672i	$0.627642\pi$
$798$	0.822343	−	0.528488i	0.0291106	−	0.0187083i
$799$	16.8031	+	4.93384i	0.594452	+	0.174547i
$800$	17.9319	−	20.6945i	0.633987	−	0.731660i
$801$	−45.8874	+	13.4737i	−1.62135	+	0.476071i
$802$	−16.1993	+	35.4715i	−0.572017	+	1.25254i
$803$	−1.59500	−	11.0935i	−0.0562862	−	0.391479i
$804$	3.87901			0.136802
$805$	6.57070	−	0.580960i	0.231587	−	0.0204762i
$806$	−27.0981			−0.954491
$807$	−0.00923384	−	0.0642228i	−0.000325047	−	0.00226075i
$808$	−40.6142	+	88.9327i	−1.42880	+	3.12864i
$809$	29.2033	−	8.57488i	1.02673	−	0.301477i	0.275352	−	0.961343i	$-0.411205\pi$
$809$	29.2033	−	8.57488i	1.02673	−	0.301477i	0.751383	+	0.659867i	$0.229387\pi$
$810$	16.3242	−	18.8392i	0.573576	−	0.661942i
$811$	39.0572	+	11.4682i	1.37148	+	0.402704i	0.882797	−	0.469755i	$-0.155658\pi$
$811$	39.0572	+	11.4682i	1.37148	+	0.402704i	0.488687	+	0.872459i	$0.337476\pi$
$812$	−6.53289	+	4.19844i	−0.229260	+	0.147336i
$813$	0.351994	+	0.770760i	0.0123450	+	0.0270317i
$814$	11.1856	+	12.9089i	0.392057	+	0.452457i
$815$	1.99719	+	1.28352i	0.0699586	+	0.0449596i
$816$	−0.674494	+	4.69121i	−0.0236120	+	0.164225i
$817$	5.10546	−	35.5093i	0.178618	−	1.24231i
$818$	−48.9321	−	31.4467i	−1.71087	−	1.09951i
$819$	12.1144	+	13.9808i	0.423312	+	0.488528i
$820$	−6.10864	−	13.3761i	−0.213323	−	0.467112i
$821$	8.18866	−	5.26253i	0.285786	−	0.183664i	−0.389892	−	0.920861i	$-0.627487\pi$
$821$	8.18866	−	5.26253i	0.285786	−	0.183664i	0.675678	+	0.737197i	$0.263851\pi$
$822$	0.218491	+	0.0641548i	0.00762076	+	0.00223766i
$823$	13.4911	−	15.5695i	0.470270	−	0.542720i	−0.470217	−	0.882551i	$-0.655824\pi$
$823$	13.4911	−	15.5695i	0.470270	−	0.542720i	0.940487	+	0.339831i	$0.110370\pi$
$824$	−88.3849	+	25.9521i	−3.07903	+	0.904086i
$825$	0.0319496	−	0.0699599i	0.00111234	−	0.00243569i
$826$	1.31623	+	9.15461i	0.0457977	+	0.318530i
$827$	−18.6033			−0.646900			−0.323450	−	0.946245i	$-0.604843\pi$
$827$	−18.6033			−0.646900			−0.323450	+	0.946245i	$0.604843\pi$
$828$	−27.4412	+	77.5230i	−0.953648	+	2.69411i
$829$	−37.9511			−1.31809			−0.659047	−	0.752102i	$-0.729040\pi$
$829$	−37.9511			−1.31809			−0.659047	+	0.752102i	$0.729040\pi$
$830$	−1.71997	−	11.9627i	−0.0597010	−	0.415230i
$831$	0.114380	−	0.250458i	0.00396781	−	0.00868828i
$832$	−178.699	+	52.4709i	−6.19529	+	1.81910i
$833$	16.0072	−	18.4733i	0.554617	−	0.640062i
$834$	−0.260090	−	0.0763694i	−0.00900619	−	0.00264446i
$835$	3.32456	−	2.13656i	0.115051	−	0.0739389i
$836$	−14.2620	−	31.2294i	−0.493262	−	1.08009i
$837$	0.488536	+	0.563800i	0.0168863	+	0.0194878i
$838$	−59.2568	−	38.0821i	−2.04699	−	1.31552i
$839$	0.596429	−	4.14825i	0.0205910	−	0.143214i	−0.976932	−	0.213549i	$-0.931498\pi$
$839$	0.596429	−	4.14825i	0.0205910	−	0.143214i	0.997523	+	0.0703351i	$0.0224069\pi$
$840$	0.115924	−	0.806267i	0.00399975	−	0.0278189i
$841$	−23.5773	−	15.1522i	−0.813011	−	0.522491i
$842$	26.2827	+	30.3319i	0.905762	+	1.04530i
$843$	0.0653982	+	0.143202i	0.00225243	+	0.00493214i
$844$	84.6437	−	54.3972i	2.91356	−	1.87243i
$845$	−6.85423	−	2.01258i	−0.235793	−	0.0692350i
$846$	19.9577	−	23.0325i	0.686161	−	0.791873i
$847$	12.1357	−	3.56337i	0.416988	−	0.122439i
$848$	6.42475	−	14.0682i	0.220627	−	0.483105i
$849$	0.164435	+	1.14367i	0.00564339	+	0.0392506i
$850$	−13.2974			−0.456097
$851$	−12.8550	+	17.7870i	−0.440662	+	0.609729i
$852$	2.47598			0.0848257
$853$	3.79232	+	26.3762i	0.129847	+	0.903102i	0.945746	+	0.324908i	$0.105333\pi$
$853$	3.79232	+	26.3762i	0.129847	+	0.903102i	−0.815899	+	0.578194i	$0.803758\pi$
$854$	12.8846	−	28.2133i	0.440902	−	0.965441i
$855$	−12.8434	+	3.77115i	−0.439234	+	0.128971i
$856$	−42.7352	+	49.3190i	−1.46066	+	1.68569i
$857$	0.594650	+	0.174605i	0.0203129	+	0.00596440i	0.291873	−	0.956457i	$-0.405721\pi$
$857$	0.594650	+	0.174605i	0.0203129	+	0.00596440i	−0.271560	+	0.962421i	$0.587540\pi$
$858$	−0.806949	+	0.518595i	−0.0275488	+	0.0177045i
$859$	−19.6631	−	43.0562i	−0.670897	−	1.46906i	−0.872008	−	0.489491i	$-0.837183\pi$
$859$	−19.6631	−	43.0562i	−0.670897	−	1.46906i	0.201111	−	0.979568i	$-0.435545\pi$
$860$	−30.0953	−	34.7318i	−1.02624	−	1.18434i
$861$	−0.170256	−	0.109417i	−0.00580232	−	0.00372893i
$862$	15.1515	−	105.381i	0.516060	−	3.58928i
$863$	−2.27113	+	15.7960i	−0.0773101	+	0.537704i	0.913955	+	0.405816i	$0.133013\pi$
$863$	−2.27113	+	15.7960i	−0.0773101	+	0.537704i	−0.991265	+	0.131887i	$0.957896\pi$
$864$	7.90946	+	5.08310i	0.269085	+	0.172931i
$865$	−0.0414616	−	0.0478493i	−0.00140974	−	0.00162692i
$866$	−0.182676	−	0.400006i	−0.00620760	−	0.0135927i
$867$	0.284097	−	0.182578i	0.00964846	−	0.00620069i
$868$	−16.4074	−	4.81763i	−0.556902	−	0.163521i
$869$	−11.9989	+	13.8474i	−0.407034	+	0.469742i
$870$	−0.150635	+	0.0442303i	−0.00510699	+	0.00149955i
$871$	22.0743	−	48.3360i	0.747959	−	1.63780i
$872$	1.38705	+	9.64714i	0.0469714	+	0.326693i
$873$	−51.6423			−1.74783
$874$	47.0491	−	36.4688i	1.59146	−	1.23357i
$875$	1.37543			0.0464980
$876$	−0.389037	−	2.70581i	−0.0131443	−	0.0914208i
$877$	16.5849	−	36.3159i	0.560032	−	1.22630i	−0.391905	−	0.920006i	$-0.628184\pi$
$877$	16.5849	−	36.3159i	0.560032	−	1.22630i	0.951937	−	0.306294i	$-0.0990889\pi$
$878$	−38.1736	+	11.2088i	−1.28830	+	0.378278i
$879$	0.770375	−	0.889060i	0.0259841	−	0.0299872i
$880$	−22.2943	−	6.54619i	−0.751540	−	0.220672i
$881$	−35.1486	+	22.5887i	−1.18419	+	0.761031i	−0.976152	−	0.217090i	$-0.930344\pi$
$881$	−35.1486	+	22.5887i	−1.18419	+	0.761031i	−0.208036	+	0.978121i	$0.566707\pi$
$882$	−17.6711	−	38.6943i	−0.595016	−	1.30290i
$883$	15.4950	+	17.8822i	0.521448	+	0.601783i	0.953993	−	0.299829i	$-0.0969297\pi$
$883$	15.4950	+	17.8822i	0.521448	+	0.601783i	−0.432545	+	0.901612i	$0.642384\pi$
$884$	103.383	+	66.4402i	3.47715	+	2.23463i
$885$	−0.0197177	+	0.137140i	−0.000662805	+	0.00460991i
$886$	−5.30094	+	36.8688i	−0.178088	+	1.23863i
$887$	8.98726	+	5.77576i	0.301763	+	0.193931i	0.682756	−	0.730647i	$-0.260781\pi$
$887$	8.98726	+	5.77576i	0.301763	+	0.193931i	−0.380993	+	0.924578i	$0.624418\pi$
$888$	1.77469	+	2.04811i	0.0595548	+	0.0687299i
$889$	1.37938	+	3.02043i	0.0462630	+	0.101302i
$890$	37.3077	−	23.9762i	1.25056	−	0.803685i
$891$	−11.5615	−	3.39475i	−0.387323	−	0.113728i
$892$	−30.9913	+	35.7659i	−1.03767	+	1.19753i
$893$	−15.6849	+	4.60549i	−0.524874	+	0.154117i
$894$	0.525561	−	1.15082i	0.0175774	−	0.0384891i
$895$	−0.829403	−	5.76862i	−0.0277239	−	0.192824i
$896$	−83.2797			−2.78218
$897$	−0.885966	−	0.856708i	−0.0295815	−	0.0286046i
$898$	8.55758			0.285570
$899$	0.305098	+	2.12200i	0.0101756	+	0.0707728i
$900$	−7.12333	+	15.5979i	−0.237444	+	0.519930i
$901$	−4.10504	+	1.20535i	−0.136759	+	0.0401559i
$902$	−6.28171	+	7.24948i	−0.209158	+	0.241381i
$903$	−0.606883	−	0.178197i	−0.0201958	−	0.00593002i
$904$	78.0831	−	50.1810i	2.59701	−	1.66899i
$905$	3.75100	+	8.21354i	0.124687	+	0.273027i
$906$	1.04662	+	1.20786i	0.0347715	+	0.0401284i
$907$	−20.2974	−	13.0443i	−0.673964	−	0.433130i	0.158389	−	0.987377i	$-0.449370\pi$
$907$	−20.2974	−	13.0443i	−0.673964	−	0.433130i	−0.832352	+	0.554247i	$0.813006\pi$
$908$	−3.69918	+	25.7283i	−0.122761	+	0.853825i
$909$	4.03124	−	28.0379i	0.133708	−	0.929958i
$910$	−14.4312	−	9.27435i	−0.478388	−	0.307442i
$911$	−7.42553	−	8.56952i	−0.246019	−	0.283921i	0.619288	−	0.785164i	$-0.287422\pi$
$911$	−7.42553	−	8.56952i	−0.246019	−	0.283921i	−0.865306	+	0.501244i	$0.832876\pi$
$912$	−1.83781	−	4.02424i	−0.0608560	−	0.133256i
$913$	−4.91455	+	3.15839i	−0.162648	+	0.104527i
$914$	−74.7717	−	21.9549i	−2.47323	−	0.726205i
$915$	0.304272	−	0.351148i	0.0100589	−	0.0116086i
$916$	50.8371	−	14.9271i	1.67971	−	0.493206i
$917$	−6.28049	+	13.7523i	−0.207400	+	0.454142i
$918$	−0.649772	−	4.51926i	−0.0214457	−	0.149158i
$919$	−45.0516			−1.48612			−0.743058	−	0.669227i	$-0.766625\pi$
$919$	−45.0516			−1.48612			−0.743058	+	0.669227i	$0.766625\pi$
$920$	2.70764	−	49.5301i	0.0892684	−	1.63296i
$921$	1.35515			0.0446539
$922$	12.1436	+	84.4603i	0.399927	+	2.78155i
$923$	14.0901	−	30.8530i	0.463781	−	1.01554i
$924$	−0.580789	+	0.170535i	−0.0191066	+	0.00561019i
$925$	−2.99668	+	3.45835i	−0.0985301	+	0.113710i
$926$	50.2045	+	14.7414i	1.64982	+	0.484431i
$927$	22.4520	−	14.4291i	0.737422	−	0.473912i
$928$	11.2239	+	24.5769i	0.368443	+	0.806777i
$929$	38.9310	+	44.9287i	1.27728	+	1.47406i	0.805797	+	0.592191i	$0.201737\pi$
$929$	38.9310	+	44.9287i	1.27728	+	1.47406i	0.471487	+	0.881873i	$0.343718\pi$
$930$	−0.290822	−	0.186900i	−0.00953644	−	0.00612870i
$931$	−3.24719	+	22.5847i	−0.106422	+	0.740184i
$932$	1.27797	−	8.88850i	0.0418614	−	0.291153i
$933$	1.52582	+	0.980583i	0.0499530	+	0.0321029i
$934$	−68.0204	−	78.4997i	−2.22569	−	2.56859i
$935$	2.67015	+	5.84681i	0.0873232	+	0.191211i
$936$	117.030	−	75.2103i	3.82523	−	2.45833i
$937$	−21.2130	−	6.22870i	−0.692998	−	0.203483i	−0.0837788	−	0.996484i	$-0.526699\pi$
$937$	−21.2130	−	6.22870i	−0.692998	−	0.203483i	−0.609219	+	0.793002i	$0.708517\pi$
$938$	29.6341	−	34.1995i	0.967586	−	1.11665i
$939$	−0.707292	+	0.207680i	−0.0230816	+	0.00677737i
$940$	−8.69932	+	19.0489i	−0.283741	+	0.621305i
$941$	0.995120	+	6.92121i	0.0324400	+	0.225625i	0.999592	−	0.0285750i	$-0.00909693\pi$
$941$	0.995120	+	6.92121i	0.0324400	+	0.225625i	−0.967152	+	0.254200i	$0.918188\pi$
$942$	1.57882			0.0514409
$943$	−10.9146	−	5.72412i	−0.355430	−	0.186403i
$944$	41.8577			1.36235
$945$	0.0672098	+	0.467455i	0.00218634	+	0.0152063i
$946$	−12.4537	+	27.2698i	−0.404904	+	0.886617i
$947$	40.8351	−	11.9903i	1.32696	−	0.389631i	0.459962	−	0.887939i	$-0.347863\pi$
$947$	40.8351	−	11.9903i	1.32696	−	0.389631i	0.867000	+	0.498308i	$0.166045\pi$
$948$	−2.92665	+	3.37754i	−0.0950533	+	0.109697i
$949$	−35.9308	−	10.5502i	−1.16636	−	0.342475i
$950$	10.4420	−	6.71068i	0.338784	−	0.217723i
$951$	−0.336056	−	0.735860i	−0.0108974	−	0.0238619i
$952$	44.5801	+	51.4482i	1.44485	+	1.66744i
$953$	−9.51037	−	6.11194i	−0.308071	−	0.197985i	0.377465	−	0.926024i	$-0.376796\pi$
$953$	−9.51037	−	6.11194i	−0.308071	−	0.197985i	−0.685536	+	0.728039i	$0.740432\pi$
$954$	−1.05959	+	7.36964i	−0.0343056	+	0.238601i
$955$	−1.94226	+	13.5087i	−0.0628500	+	0.437132i
$956$	90.8793	+	58.4046i	2.93925	+	1.88894i
$957$	0.0496956	+	0.0573518i	0.00160643	+	0.00185392i
$958$	26.0833	+	57.1144i	0.842712	+	1.84528i
$959$	1.65600	−	1.06425i	0.0534751	−	0.0343663i
$960$	−2.27974	−	0.669391i	−0.0735782	−	0.0216045i
$961$	17.2093	−	19.8606i	0.555138	−	0.640663i
$962$	54.7607	−	16.0792i	1.76555	−	0.518414i
$963$	7.85437	−	17.1987i	0.253104	−	0.554219i
$964$	12.8063	+	89.0696i	0.412463	+	2.86874i
$965$	14.3707			0.462610
$966$	−0.518384	−	0.912588i	−0.0166787	−	0.0293620i
$967$	−8.23635			−0.264863			−0.132432	−	0.991192i	$-0.542278\pi$
$967$	−8.23635			−0.264863			−0.132432	+	0.991192i	$0.542278\pi$
$968$	−13.5360	−	94.1446i	−0.435062	−	3.02592i
$969$	−0.508396	+	1.11323i	−0.0163320	+	0.0357621i
$970$	45.9482	−	13.4916i	1.47531	−	0.433189i
$971$	24.7568	−	28.5709i	0.794484	−	0.916883i	−0.203581	−	0.979058i	$-0.565258\pi$
$971$	24.7568	−	28.5709i	0.794484	−	0.916883i	0.998065	+	0.0621747i	$0.0198036\pi$
$972$	−8.47533	−	2.48858i	−0.271846	−	0.0798213i
$973$	−1.97129	+	1.26687i	−0.0631967	+	0.0406141i
$974$	−28.5141	−	62.4372i	−0.913651	−	2.00062i
$975$	−0.168286	−	0.194212i	−0.00538946	−	0.00621976i
$976$	−118.089	−	75.8909i	−3.77992	−	2.42921i
$977$	−0.100780	+	0.700939i	−0.00322423	+	0.0224250i	−0.991370	−	0.131093i	$-0.958151\pi$
$977$	−0.100780	+	0.700939i	−0.00322423	+	0.0224250i	0.988146	+	0.153518i	$0.0490604\pi$
$978$	0.0537576	−	0.373893i	0.00171898	−	0.0119558i
$979$	−18.0337	−	11.5896i	−0.576360	−	0.370404i
$980$	19.1413	+	22.0902i	0.611445	+	0.705645i
$981$	−1.17305	−	2.56862i	−0.0374526	−	0.0820098i
$982$	33.0851	−	21.2625i	1.05579	−	0.678514i
$983$	−26.3290	−	7.73089i	−0.839765	−	0.246577i	−0.166558	−	0.986032i	$-0.553265\pi$
$983$	−26.3290	−	7.73089i	−0.839765	−	0.246577i	−0.673207	+	0.739454i	$0.735084\pi$
$984$	−0.996645	+	1.15019i	−0.0317719	+	0.0366667i
$985$	−18.7035	+	5.49186i	−0.595944	+	0.174985i
$986$	5.45048	−	11.9349i	0.173579	−	0.380084i
$987$	0.0410174	+	0.285282i	0.00130560	+	0.00908062i
$988$	−114.713			−3.64951
$989$	−37.7694	−	7.55453i	−1.20100	−	0.240220i
$990$	11.1858			0.355508
$991$	−6.49869	−	45.1994i	−0.206438	−	1.43581i	−0.784660	−	0.619926i	$-0.787162\pi$
$991$	−6.49869	−	45.1994i	−0.206438	−	1.43581i	0.578222	−	0.815879i	$-0.303747\pi$
$992$	−24.7151	+	54.1185i	−0.784705	+	1.71826i
$993$	1.71584	−	0.503816i	0.0544505	−	0.0159881i
$994$	18.9155	−	21.8296i	0.599963	−	0.692394i
$995$	19.6283	+	5.76340i	0.622260	+	0.182712i
$996$	−1.19871	+	0.770365i	−0.0379826	+	0.0244099i
$997$	12.4926	+	27.3549i	0.395643	+	0.866338i	0.997694	+	0.0678796i	$0.0216234\pi$
$997$	12.4926	+	27.3549i	0.395643	+	0.866338i	−0.602050	+	0.798458i	$0.705649\pi$
$998$	45.2964	+	52.2748i	1.43383	+	1.65473i
$999$	−1.32179	−	0.849461i	−0.0418195	−	0.0268758i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.g.c.26.5	✓	50
5.2	odd	4		575.2.p.d.49.1		100
5.3	odd	4		575.2.p.d.49.10		100
5.4	even	2		575.2.k.d.26.1		50
23.8	even	11	inner	115.2.g.c.31.5	yes	50
23.10	odd	22		2645.2.a.x.1.1		25
23.13	even	11		2645.2.a.y.1.1		25
115.8	odd	44		575.2.p.d.399.1		100
115.54	even	22		575.2.k.d.376.1		50
115.77	odd	44		575.2.p.d.399.10		100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.c.26.5	✓	50	1.1	even	1	trivial
115.2.g.c.31.5	yes	50	23.8	even	11	inner
575.2.k.d.26.1		50	5.4	even	2
575.2.k.d.376.1		50	115.54	even	22
575.2.p.d.49.1		100	5.2	odd	4
575.2.p.d.49.10		100	5.3	odd	4
575.2.p.d.399.1		100	115.8	odd	44
575.2.p.d.399.10		100	115.77	odd	44
2645.2.a.x.1.1		25	23.10	odd	22
2645.2.a.y.1.1		25	23.13	even	11

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.395474 + 2.75058i) q^{2} +(0.0237855 - 0.0520830i) q^{3} +(-5.49030 + 1.61210i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(0.152665 + 0.0448264i) q^{6} +(1.15709 - 0.743614i) q^{7} +(-4.29671 - 9.40848i) q^{8} +(1.96244 + 2.26477i) q^{9} +O(q^{10})\)	\(q+(0.395474 + 2.75058i) q^{2} +(0.0237855 - 0.0520830i) q^{3} +(-5.49030 + 1.61210i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(0.152665 + 0.0448264i) q^{6} +(1.15709 - 0.743614i) q^{7} +(-4.29671 - 9.40848i) q^{8} +(1.96244 + 2.26477i) q^{9} +(-2.33773 - 1.50237i) q^{10} +(-0.191163 + 1.32957i) q^{11} +(-0.0466267 + 0.324296i) q^{12} +(3.77568 + 2.42648i) q^{13} +(2.50297 + 2.88858i) q^{14} +(0.0237855 + 0.0520830i) q^{15} +(14.5521 - 9.35205i) q^{16} +(-4.59136 - 1.34814i) q^{17} +(-5.45334 + 6.29349i) q^{18} +(4.28580 - 1.25843i) q^{19} +(2.37704 - 5.20499i) q^{20} +(-0.0112078 - 0.0779517i) q^{21} -3.73268 q^{22} +(-1.09795 - 4.66846i) q^{23} -0.592221 q^{24} +(-0.142315 - 0.989821i) q^{25} +(-5.18105 + 11.3449i) q^{26} +(0.329447 - 0.0967344i) q^{27} +(-5.15397 + 5.94800i) q^{28} +(0.946733 + 0.277986i) q^{29} +(-0.133852 + 0.0860213i) q^{30} +(0.902580 + 1.97638i) q^{31} +(17.9319 + 20.6945i) q^{32} +(0.0647009 + 0.0415808i) q^{33} +(1.89242 - 13.1621i) q^{34} +(-0.195744 + 1.36143i) q^{35} +(-14.4254 - 9.27064i) q^{36} +(-2.99668 - 3.45835i) q^{37} +(5.15632 + 11.2908i) q^{38} +(0.216185 - 0.138934i) q^{39} +(9.92420 + 2.91401i) q^{40} +(1.68289 - 1.94216i) q^{41} +(0.209980 - 0.0616557i) q^{42} +(3.33639 - 7.30568i) q^{43} +(-1.09385 - 7.60790i) q^{44} -2.99672 q^{45} +(12.4068 - 4.86625i) q^{46} -3.65973 q^{47} +(-0.140954 - 0.980359i) q^{48} +(-2.12202 + 4.64657i) q^{49} +(2.66630 - 0.782896i) q^{50} +(-0.179423 + 0.207065i) q^{51} +(-24.6414 - 7.23536i) q^{52} +(0.752147 - 0.483375i) q^{53} +(0.396363 + 0.867914i) q^{54} +(-0.879635 - 1.01515i) q^{55} +(-11.9679 - 7.69133i) q^{56} +(0.0363974 - 0.253150i) q^{57} +(-0.390214 + 2.71400i) q^{58} +(2.03565 + 1.30824i) q^{59} +(-0.214552 - 0.247607i) q^{60} +(-3.37105 - 7.38156i) q^{61} +(-5.07923 + 3.26422i) q^{62} +(3.95482 + 1.16124i) q^{63} +(-27.1745 + 31.3611i) q^{64} +(-4.30636 + 1.26446i) q^{65} +(-0.0887837 + 0.194409i) q^{66} +(-1.68495 - 11.7191i) q^{67} +27.3813 q^{68} +(-0.269262 - 0.0538571i) q^{69} -3.82214 q^{70} +(-1.07551 - 7.48031i) q^{71} +(12.8760 - 28.1946i) q^{72} +(-8.00567 + 2.35068i) q^{73} +(8.32736 - 9.61028i) q^{74} +(-0.0549379 - 0.0161312i) q^{75} +(-21.5016 + 13.8183i) q^{76} +(0.767493 + 1.68058i) q^{77} +(0.467643 + 0.539689i) q^{78} +(11.4753 + 7.37474i) q^{79} +(-2.46178 + 17.1220i) q^{80} +(-1.27664 + 8.87920i) q^{81} +(6.00761 + 3.86086i) q^{82} +(2.84808 + 3.28686i) q^{83} +(0.187200 + 0.409910i) q^{84} +(4.02556 - 2.58707i) q^{85} +(21.4143 + 6.28780i) q^{86} +(0.0369968 - 0.0426966i) q^{87} +(13.3306 - 3.91421i) q^{88} +(-6.62960 + 14.5168i) q^{89} +(-1.18512 - 8.24272i) q^{90} +6.17316 q^{91} +(13.5541 + 23.8612i) q^{92} +0.124404 q^{93} +(-1.44733 - 10.0664i) q^{94} +(-1.85555 + 4.06309i) q^{95} +(1.50435 - 0.441716i) q^{96} +(-11.2852 + 13.0238i) q^{97} +(-13.6200 - 3.99918i) q^{98} +(-3.38631 + 2.17625i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9	\( 50 q - 5 q^{2} - 2 q^{3} - 11 q^{4} - 5 q^{5} - 11 q^{6} - 5 q^{7} - 2 q^{8} + 3 q^{9} - 5 q^{10} - 16 q^{11} - 9 q^{12} - 14 q^{13} - 12 q^{14} - 2 q^{15} + 27 q^{16} + 38 q^{17} - 42 q^{18} - 5 q^{19} - 11 q^{20} - 9 q^{21} + 6 q^{22} - 8 q^{23} + 102 q^{24} - 5 q^{25} - 19 q^{26} + 7 q^{27} - 34 q^{28} - 38 q^{29} - 11 q^{30} + 2 q^{31} + 49 q^{32} - 2 q^{33} - 31 q^{34} + 6 q^{35} - 59 q^{36} - 35 q^{37} + 30 q^{38} + 32 q^{39} + 42 q^{40} - 11 q^{41} - 102 q^{42} + 6 q^{43} - 55 q^{44} + 58 q^{45} + 153 q^{46} - 10 q^{47} + 84 q^{48} + 6 q^{50} - 20 q^{51} - 97 q^{52} - 29 q^{53} + 19 q^{54} + 17 q^{55} + 77 q^{56} - 49 q^{57} - 12 q^{58} - 50 q^{59} + 2 q^{60} + 4 q^{61} + 126 q^{62} + 74 q^{63} - 44 q^{64} - 14 q^{65} - 144 q^{66} - 43 q^{67} + 54 q^{68} - 50 q^{69} - 12 q^{70} - 25 q^{71} - 14 q^{72} - 20 q^{73} - 47 q^{74} - 2 q^{75} - 26 q^{76} + 150 q^{77} + 174 q^{78} + 72 q^{79} - 28 q^{80} - 71 q^{81} - 11 q^{82} + 36 q^{83} + 100 q^{84} - 6 q^{85} - 20 q^{86} + 85 q^{87} - 45 q^{88} - 24 q^{89} - 42 q^{90} + 38 q^{91} + 74 q^{92} + 100 q^{93} + 150 q^{94} - 5 q^{95} - 169 q^{96} - 14 q^{97} - 44 q^{98} + 36 q^{99}+O(q^{100}) \) 50 * q - 5 * q^2 - 2 * q^3 - 11 * q^4 - 5 * q^5 - 11 * q^6 - 5 * q^7 - 2 * q^8 + 3 * q^9 - 5 * q^10 - 16 * q^11 - 9 * q^12 - 14 * q^13 - 12 * q^14 - 2 * q^15 + 27 * q^16 + 38 * q^17 - 42 * q^18 - 5 * q^19 - 11 * q^20 - 9 * q^21 + 6 * q^22 - 8 * q^23 + 102 * q^24 - 5 * q^25 - 19 * q^26 + 7 * q^27 - 34 * q^28 - 38 * q^29 - 11 * q^30 + 2 * q^31 + 49 * q^32 - 2 * q^33 - 31 * q^34 + 6 * q^35 - 59 * q^36 - 35 * q^37 + 30 * q^38 + 32 * q^39 + 42 * q^40 - 11 * q^41 - 102 * q^42 + 6 * q^43 - 55 * q^44 + 58 * q^45 + 153 * q^46 - 10 * q^47 + 84 * q^48 + 6 * q^50 - 20 * q^51 - 97 * q^52 - 29 * q^53 + 19 * q^54 + 17 * q^55 + 77 * q^56 - 49 * q^57 - 12 * q^58 - 50 * q^59 + 2 * q^60 + 4 * q^61 + 126 * q^62 + 74 * q^63 - 44 * q^64 - 14 * q^65 - 144 * q^66 - 43 * q^67 + 54 * q^68 - 50 * q^69 - 12 * q^70 - 25 * q^71 - 14 * q^72 - 20 * q^73 - 47 * q^74 - 2 * q^75 - 26 * q^76 + 150 * q^77 + 174 * q^78 + 72 * q^79 - 28 * q^80 - 71 * q^81 - 11 * q^82 + 36 * q^83 + 100 * q^84 - 6 * q^85 - 20 * q^86 + 85 * q^87 - 45 * q^88 - 24 * q^89 - 42 * q^90 + 38 * q^91 + 74 * q^92 + 100 * q^93 + 150 * q^94 - 5 * q^95 - 169 * q^96 - 14 * q^97 - 44 * q^98 + 36 * q^99

Introduction

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