LMFDB - Embedded newform 108.2.l.a.83.8

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			83.8
Character	$\chi$	$=$	108.83
Dual form			108.2.l.a.95.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.359456 - 1.36777i) q^{2} +(1.26343 + 1.18480i) q^{3} +(-1.74158 + 0.983306i) q^{4} +(2.20965 + 2.63335i) q^{5} +(1.16638 - 2.15396i) q^{6} +(-0.829620 - 2.27936i) q^{7} +(1.97096 + 2.02863i) q^{8} +(0.192513 + 2.99382i) q^{9} +O(q^{10})$	\(q+(-0.359456 - 1.36777i) q^{2} +(1.26343 + 1.18480i) q^{3} +(-1.74158 + 0.983306i) q^{4} +(2.20965 + 2.63335i) q^{5} +(1.16638 - 2.15396i) q^{6} +(-0.829620 - 2.27936i) q^{7} +(1.97096 + 2.02863i) q^{8} +(0.192513 + 2.99382i) q^{9} +(2.80755 - 3.96886i) q^{10} +(-2.28829 - 1.92011i) q^{11} +(-3.36539 - 0.821083i) q^{12} +(-0.901500 - 5.11266i) q^{13} +(-2.81943 + 1.95406i) q^{14} +(-0.328255 + 5.94504i) q^{15} +(2.06622 - 3.42502i) q^{16} +(-0.821854 + 0.474498i) q^{17} +(4.02565 - 1.33946i) q^{18} +(-2.43769 - 1.40740i) q^{19} +(-6.43767 - 2.41344i) q^{20} +(1.65241 - 3.86275i) q^{21} +(-1.80372 + 3.82005i) q^{22} +(4.13143 + 1.50372i) q^{23} +(0.0866582 + 4.89821i) q^{24} +(-1.18377 + 6.71352i) q^{25} +(-6.66889 + 3.07082i) q^{26} +(-3.30384 + 4.01057i) q^{27} +(3.68616 + 3.15393i) q^{28} +(0.819198 + 0.144447i) q^{29} +(8.24943 - 1.68800i) q^{30} +(-1.43188 + 3.93406i) q^{31} +(-5.42735 - 1.59496i) q^{32} +(-0.616163 - 5.13708i) q^{33} +(0.944424 + 0.953546i) q^{34} +(4.16920 - 7.22127i) q^{35} +(-3.27912 - 5.02468i) q^{36} +(-2.86337 - 4.95950i) q^{37} +(-1.04876 + 3.84010i) q^{38} +(4.91848 - 7.52758i) q^{39} +(-0.986971 + 9.67277i) q^{40} +(-6.41767 + 1.13161i) q^{41} +(-5.87732 - 0.871632i) q^{42} +(-1.90594 + 2.27141i) q^{43} +(5.87330 + 1.09393i) q^{44} +(-7.45839 + 7.12223i) q^{45} +(0.571669 - 6.19136i) q^{46} +(6.92611 - 2.52090i) q^{47} +(6.66847 - 1.87922i) q^{48} +(0.855086 - 0.717502i) q^{49} +(9.60805 - 0.794086i) q^{50} +(-1.60054 - 0.374236i) q^{51} +(6.59735 + 8.01767i) q^{52} +0.0316449i q^{53} +(6.67311 + 3.07726i) q^{54} -10.2686i q^{55} +(2.98883 - 6.17552i) q^{56} +(-1.41237 - 4.66632i) q^{57} +(-0.0968962 - 1.17240i) q^{58} +(-5.93006 + 4.97591i) q^{59} +(-5.27411 - 10.6766i) q^{60} +(11.4145 - 4.15453i) q^{61} +(5.89558 + 0.544359i) q^{62} +(6.66428 - 2.92254i) q^{63} +(-0.230649 + 7.99667i) q^{64} +(11.4714 - 13.6711i) q^{65} +(-6.80485 + 2.68933i) q^{66} +(0.702717 - 0.123908i) q^{67} +(0.964751 - 1.63451i) q^{68} +(3.43817 + 6.79475i) q^{69} +(-11.3757 - 3.10677i) q^{70} +(-0.820917 - 1.42187i) q^{71} +(-5.69390 + 6.29122i) q^{72} +(-3.76331 + 6.51824i) q^{73} +(-5.75419 + 5.69914i) q^{74} +(-9.44977 + 7.07953i) q^{75} +(5.62935 + 0.0541094i) q^{76} +(-2.47820 + 6.80881i) q^{77} +(-12.0640 - 4.02151i) q^{78} +(0.887038 + 0.156409i) q^{79} +(13.5849 - 2.12699i) q^{80} +(-8.92588 + 1.15270i) q^{81} +(3.85465 + 8.37112i) q^{82} +(-2.69743 + 15.2979i) q^{83} +(0.920447 + 8.35212i) q^{84} +(-3.06553 - 1.11576i) q^{85} +(3.79186 + 1.79041i) q^{86} +(0.863860 + 1.15308i) q^{87} +(-0.614952 - 8.42654i) q^{88} +(-4.19977 - 2.42474i) q^{89} +(12.4225 + 7.64122i) q^{90} +(-10.9057 + 6.29641i) q^{91} +(-8.67384 + 1.44361i) q^{92} +(-6.47014 + 3.27392i) q^{93} +(-5.93764 - 8.56716i) q^{94} +(-1.68025 - 9.52916i) q^{95} +(-4.96737 - 8.44543i) q^{96} +(8.55448 + 7.17806i) q^{97} +(-1.28874 - 0.911649i) q^{98} +(5.30792 - 7.22037i) 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 $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.359456	−	1.36777i	−0.254174	−	0.967159i
$2$	−0.359456	−	1.36777i	−0.254174	−	0.967159i
$3$	1.26343	+	1.18480i	0.729442	+	0.684043i
$3$	1.26343	+	1.18480i	0.729442	+	0.684043i
$4$	−1.74158	+	0.983306i	−0.870791	+	0.491653i
$5$	2.20965	+	2.63335i	0.988184	+	1.17767i	0.984088	+	0.177680i	$0.0568591\pi$
$5$	2.20965	+	2.63335i	0.988184	+	1.17767i	0.00409519	+	0.999992i	$0.498696\pi$
$6$	1.16638	−	2.15396i	0.476173	−	0.879352i
$7$	−0.829620	−	2.27936i	−0.313567	−	0.861518i	−0.991929	−	0.126791i	$-0.959532\pi$
$7$	−0.829620	−	2.27936i	−0.313567	−	0.861518i	0.678363	−	0.734727i	$-0.262690\pi$
$8$	1.97096	+	2.02863i	0.696839	+	0.717228i
$9$	0.192513	+	2.99382i	0.0641709	+	0.997939i
$10$	2.80755	−	3.96886i	0.887824	−	1.25506i
$11$	−2.28829	−	1.92011i	−0.689946	−	0.578934i	0.228948	−	0.973439i	$-0.426472\pi$
$11$	−2.28829	−	1.92011i	−0.689946	−	0.578934i	−0.918894	+	0.394505i	$0.870916\pi$
$12$	−3.36539	−	0.821083i	−0.971503	−	0.237026i
$13$	−0.901500	−	5.11266i	−0.250031	−	1.41800i	−0.808512	−	0.588479i	$-0.799727\pi$
$13$	−0.901500	−	5.11266i	−0.250031	−	1.41800i	0.558481	−	0.829517i	$-0.311384\pi$
$14$	−2.81943	+	1.95406i	−0.753524	+	0.522244i
$15$	−0.328255	+	5.94504i	−0.0847551	+	1.53500i
$16$	2.06622	−	3.42502i	0.516555	−	0.856254i
$17$	−0.821854	+	0.474498i	−0.199329	+	0.115083i	−0.596342	−	0.802730i	$-0.703380\pi$
$17$	−0.821854	+	0.474498i	−0.199329	+	0.115083i	0.397013	+	0.917813i	$0.370047\pi$
$18$	4.02565	−	1.33946i	0.948855	−	0.315714i
$19$	−2.43769	−	1.40740i	−0.559245	−	0.322880i	0.193597	−	0.981081i	$-0.437984\pi$
$19$	−2.43769	−	1.40740i	−0.559245	−	0.322880i	−0.752842	+	0.658201i	$0.771318\pi$
$20$	−6.43767	−	2.41344i	−1.43951	−	0.539662i
$21$	1.65241	−	3.86275i	0.360586	−	0.842921i
$22$	−1.80372	+	3.82005i	−0.384554	+	0.814437i
$23$	4.13143	+	1.50372i	0.861463	+	0.313547i	0.734705	−	0.678387i	$-0.237321\pi$
$23$	4.13143	+	1.50372i	0.861463	+	0.313547i	0.126758	+	0.991934i	$0.459543\pi$
$24$	0.0866582	+	4.89821i	0.0176890	+	0.999844i
$25$	−1.18377	+	6.71352i	−0.236755	+	1.34270i
$26$	−6.66889	+	3.07082i	−1.30788	+	0.602238i
$27$	−3.30384	+	4.01057i	−0.635824	+	0.771834i
$28$	3.68616	+	3.15393i	0.696619	+	0.596036i
$29$	0.819198	+	0.144447i	0.152121	+	0.0268231i	0.249190	−	0.968455i	$-0.419836\pi$
$29$	0.819198	+	0.144447i	0.152121	+	0.0268231i	−0.0970688	+	0.995278i	$0.530947\pi$
$30$	8.24943	−	1.68800i	1.50613	−	0.308186i
$31$	−1.43188	+	3.93406i	−0.257173	+	0.706578i	0.742165	+	0.670217i	$0.233799\pi$
$31$	−1.43188	+	3.93406i	−0.257173	+	0.706578i	−0.999339	+	0.0363611i	$0.988423\pi$
$32$	−5.42735	−	1.59496i	−0.959428	−	0.281953i
$33$	−0.616163	−	5.13708i	−0.107260	−	0.894251i
$34$	0.944424	+	0.953546i	0.161967	+	0.163532i
$35$	4.16920	−	7.22127i	0.704723	−	1.22062i
$36$	−3.27912	−	5.02468i	−0.546519	−	0.837447i
$37$	−2.86337	−	4.95950i	−0.470734	−	0.815336i	0.528705	−	0.848805i	$-0.322678\pi$
$37$	−2.86337	−	4.95950i	−0.470734	−	0.815336i	−0.999440	+	0.0334694i	$0.989344\pi$
$38$	−1.04876	+	3.84010i	−0.170131	+	0.622946i
$39$	4.91848	−	7.52758i	0.787587	−	1.20538i
$40$	−0.986971	+	9.67277i	−0.156054	+	1.52940i
$41$	−6.41767	+	1.13161i	−1.00227	+	0.176728i	−0.650620	−	0.759403i	$-0.725491\pi$
$41$	−6.41767	+	1.13161i	−1.00227	+	0.176728i	−0.351652	+	0.936131i	$0.614380\pi$
$42$	−5.87732	−	0.871632i	−0.906890	−	0.134496i
$43$	−1.90594	+	2.27141i	−0.290653	+	0.346387i	−0.891536	−	0.452951i	$-0.850371\pi$
$43$	−1.90594	+	2.27141i	−0.290653	+	0.346387i	0.600883	+	0.799337i	$0.294816\pi$
$44$	5.87330	+	1.09393i	0.885433	+	0.164916i
$45$	−7.45839	+	7.12223i	−1.11183	+	1.06172i
$46$	0.571669	−	6.19136i	0.0842880	−	0.912866i
$47$	6.92611	−	2.52090i	1.01028	−	0.367711i	0.216738	−	0.976230i	$-0.430458\pi$
$47$	6.92611	−	2.52090i	1.01028	−	0.367711i	0.793539	+	0.608519i	$0.208236\pi$
$48$	6.66847	−	1.87922i	0.962511	−	0.271242i
$49$	0.855086	−	0.717502i	0.122155	−	0.102500i
$50$	9.60805	−	0.794086i	1.35878	−	0.112301i
$51$	−1.60054	−	0.374236i	−0.224120	−	0.0524035i
$52$	6.59735	+	8.01767i	0.914887	+	1.11185i
$53$			0.0316449i			0.00434676i	0.999998	+	0.00217338i	$0.000691809\pi$
$53$			0.0316449i			0.00434676i	−0.999998	+	0.00217338i	$0.999308\pi$
$54$	6.67311	+	3.07726i	0.908096	+	0.418762i
$55$		−	10.2686i		−	1.38462i
$56$	2.98883	−	6.17552i	0.399399	−	0.825238i
$57$	−1.41237	−	4.66632i	−0.187073	−	0.618070i
$58$	−0.0968962	−	1.17240i	−0.0127231	−	0.153943i
$59$	−5.93006	+	4.97591i	−0.772028	+	0.647809i	−0.941228	−	0.337773i	$-0.890326\pi$
$59$	−5.93006	+	4.97591i	−0.772028	+	0.647809i	0.169199	+	0.985582i	$0.445882\pi$
$60$	−5.27411	−	10.6766i	−0.680885	−	1.37834i
$61$	11.4145	−	4.15453i	1.46148	−	0.531934i	0.515704	−	0.856767i	$-0.327530\pi$
$61$	11.4145	−	4.15453i	1.46148	−	0.531934i	0.945771	+	0.324833i	$0.105308\pi$
$62$	5.89558	+	0.544359i	0.748740	+	0.0691337i
$63$	6.66428	−	2.92254i	0.839621	−	0.368205i
$64$	−0.230649	+	7.99667i	−0.0288312	+	0.999584i
$65$	11.4714	−	13.6711i	1.42286	−	1.69570i
$66$	−6.80485	+	2.68933i	−0.837620	+	0.331033i
$67$	0.702717	−	0.123908i	0.0858506	−	0.0151378i	−0.130558	−	0.991441i	$-0.541677\pi$
$67$	0.702717	−	0.123908i	0.0858506	−	0.0151378i	0.216408	+	0.976303i	$0.430566\pi$
$68$	0.964751	−	1.63451i	0.116993	−	0.198214i
$69$	3.43817	+	6.79475i	0.413908	+	0.817991i
$70$	−11.3757	−	3.10677i	−1.35965	−	0.371330i
$71$	−0.820917	−	1.42187i	−0.0974249	−	0.168745i	0.813193	−	0.581994i	$-0.197727\pi$
$71$	−0.820917	−	1.42187i	−0.0974249	−	0.168745i	−0.910618	+	0.413249i	$0.864394\pi$
$72$	−5.69390	+	6.29122i	−0.671033	+	0.741428i
$73$	−3.76331	+	6.51824i	−0.440462	+	0.762903i	−0.997724	−	0.0674344i	$-0.978519\pi$
$73$	−3.76331	+	6.51824i	−0.440462	+	0.762903i	0.557262	+	0.830337i	$0.311852\pi$
$74$	−5.75419	+	5.69914i	−0.668911	+	0.662512i
$75$	−9.44977	+	7.07953i	−1.09117	+	0.817473i
$76$	5.62935	+	0.0541094i	0.645731	+	0.00620677i
$77$	−2.47820	+	6.80881i	−0.282417	+	0.775936i
$78$	−12.0640	−	4.02151i	−1.36598	−	0.455346i
$79$	0.887038	+	0.156409i	0.0997996	+	0.0175974i	0.223325	−	0.974744i	$-0.428309\pi$
$79$	0.887038	+	0.156409i	0.0997996	+	0.0175974i	−0.123525	+	0.992341i	$0.539420\pi$
$80$	13.5849	−	2.12699i	1.51884	−	0.237805i
$81$	−8.92588	+	1.15270i	−0.991764	+	0.128077i
$82$	3.85465	+	8.37112i	0.425675	+	0.924436i
$83$	−2.69743	+	15.2979i	−0.296082	+	1.67916i	0.366691	+	0.930343i	$0.380491\pi$
$83$	−2.69743	+	15.2979i	−0.296082	+	1.67916i	−0.662773	+	0.748820i	$0.730621\pi$
$84$	0.920447	+	8.35212i	0.100429	+	0.911291i
$85$	−3.06553	−	1.11576i	−0.332503	−	0.121021i
$86$	3.79186	+	1.79041i	0.408887	+	0.193065i
$87$	0.863860	+	1.15308i	0.0926155	+	0.123623i
$88$	−0.614952	−	8.42654i	−0.0655541	−	0.898272i
$89$	−4.19977	−	2.42474i	−0.445174	−	0.257021i	0.260616	−	0.965443i	$-0.416074\pi$
$89$	−4.19977	−	2.42474i	−0.445174	−	0.257021i	−0.705790	+	0.708421i	$0.749408\pi$
$90$	12.4225	+	7.64122i	1.30945	+	0.805456i
$91$	−10.9057	+	6.29641i	−1.14323	+	0.660043i
$92$	−8.67384	+	1.44361i	−0.904310	+	0.150507i
$93$	−6.47014	+	3.27392i	−0.670922	+	0.339490i
$94$	−5.93764	−	8.56716i	−0.612421	−	0.883635i
$95$	−1.68025	−	9.52916i	−0.172390	−	0.977672i
$96$	−4.96737	−	8.44543i	−0.506980	−	0.861958i
$97$	8.55448	+	7.17806i	0.868575	+	0.728821i	0.963798	−	0.266635i	$-0.0859117\pi$
$97$	8.55448	+	7.17806i	0.868575	+	0.728821i	−0.0952222	+	0.995456i	$0.530356\pi$
$98$	−1.28874	−	0.911649i	−0.130183	−	0.0920905i
$99$	5.30792	−	7.22037i	0.533466	−	0.725675i
$100$	−4.53980	−	12.8562i	−0.453980	−	1.28562i
$101$	−1.48621	−	4.08333i	−0.147883	−	0.406306i	0.843528	−	0.537085i	$-0.180475\pi$
$101$	−1.48621	−	4.08333i	−0.147883	−	0.406306i	−0.991412	+	0.130779i	$0.958252\pi$
$102$	0.0634564	+	2.32369i	0.00628312	+	0.230080i
$103$	4.19285	+	4.99685i	0.413134	+	0.492354i	0.931978	−	0.362515i	$-0.118082\pi$
$103$	4.19285	+	4.99685i	0.413134	+	0.492354i	−0.518844	+	0.854869i	$0.673637\pi$
$104$	8.59486	−	11.9056i	0.842795	−	1.16744i
$105$	13.8232	−	4.18391i	1.34901	−	0.408308i
$106$	0.0432829	−	0.0113750i	0.00420401	−	0.00110483i
$107$	5.70009			0.551049			0.275524	−	0.961294i	$-0.411149\pi$
$107$	5.70009			0.551049			0.275524	+	0.961294i	$0.411149\pi$
$108$	1.81029	−	10.2334i	0.174195	−	0.984711i
$109$	−9.79968			−0.938639			−0.469320	−	0.883028i	$-0.655501\pi$
$109$	−9.79968			−0.938639			−0.469320	+	0.883028i	$0.655501\pi$
$110$	−14.0451	+	3.69112i	−1.33915	+	0.351935i
$111$	2.25833	−	9.65848i	0.214351	−	0.916743i
$112$	−9.52103	−	1.86820i	−0.899653	−	0.176528i
$113$	8.08839	+	9.63937i	0.760892	+	0.906795i	0.997904	−	0.0647112i	$-0.0206126\pi$
$113$	8.08839	+	9.63937i	0.760892	+	0.906795i	−0.237012	+	0.971507i	$0.576168\pi$
$114$	−5.87477	+	3.60913i	−0.550222	+	0.338026i
$115$	5.16918	+	14.2022i	0.482028	+	1.32436i
$116$	−1.56874	+	0.553957i	−0.145654	+	0.0514336i
$117$	15.1328	−	3.68318i	1.39903	−	0.340510i
$118$	8.93750	+	6.32233i	0.822763	+	0.582018i
$119$	1.76338	+	1.47965i	0.161649	+	0.135639i
$120$	−12.7072	+	11.0515i	−1.16001	+	1.00886i
$121$	−0.360652	−	2.04536i	−0.0327866	−	0.185942i
$122$	−9.78545	−	14.1190i	−0.885933	−	1.27827i
$123$	−9.44900	−	6.17393i	−0.851988	−	0.556684i
$124$	−1.37465	−	8.25946i	−0.123447	−	0.741722i
$125$	−5.40954	+	3.12320i	−0.483844	+	0.279347i
$126$	−6.39287	−	8.06467i	−0.569522	−	0.718458i
$127$	17.6692	+	10.2013i	1.56789	+	0.905220i	0.996415	+	0.0845976i	$0.0269605\pi$
$127$	17.6692	+	10.2013i	1.56789	+	0.905220i	0.571471	+	0.820622i	$0.306373\pi$
$128$	11.0205	−	2.55898i	0.974085	−	0.226184i
$129$	−5.09918	+	0.611617i	−0.448958	+	0.0538499i
$130$	−22.8224	−	10.7761i	−2.00166	−	0.945127i
$131$	−5.86369	−	2.13421i	−0.512313	−	0.186467i	0.0729107	−	0.997338i	$-0.476771\pi$
$131$	−5.86369	−	2.13421i	−0.512313	−	0.186467i	−0.585224	+	0.810872i	$0.698993\pi$
$132$	6.12442	+	8.34077i	0.533063	+	0.725971i
$133$	−1.18562	+	6.72399i	−0.102806	+	0.583044i
$134$	−0.422074	−	0.916615i	−0.0364616	−	0.0791835i
$135$	−17.8616	+	0.161761i	−1.53728	+	0.0139222i
$136$	−2.58242	−	0.732020i	−0.221441	−	0.0627702i
$137$	5.03736	+	0.888222i	0.430371	+	0.0758859i	0.384637	−	0.923068i	$-0.374326\pi$
$137$	5.03736	+	0.888222i	0.430371	+	0.0758859i	0.0457332	+	0.998954i	$0.485438\pi$
$138$	8.05777	−	7.14504i	0.685923	−	0.608226i
$139$	5.09224	−	13.9908i	0.431918	−	1.18669i	−0.512715	−	0.858559i	$-0.671360\pi$
$139$	5.09224	−	13.9908i	0.431918	−	1.18669i	0.944634	−	0.328127i	$-0.106417\pi$
$140$	−0.160290	+	16.6760i	−0.0135470	+	1.40938i
$141$	11.7374	+	5.02105i	0.988468	+	0.422849i
$142$	−1.64970	+	1.63392i	−0.138440	+	0.137116i
$143$	−7.75395	+	13.4302i	−0.648418	+	1.12309i
$144$	10.6516	+	5.52652i	0.887637	+	0.460543i
$145$	1.42976	+	2.47641i	0.118735	+	0.205655i
$146$	10.2682	+	2.80431i	0.849802	+	0.232087i
$147$	1.93044	+	0.106589i	0.159220	+	0.00879131i
$148$	9.86349	+	5.82180i	0.810774	+	0.478549i
$149$	−5.44809	+	0.960645i	−0.446325	+	0.0786991i	−0.392293	−	0.919840i	$-0.628318\pi$
$149$	−5.44809	+	0.960645i	−0.446325	+	0.0786991i	−0.0540313	+	0.998539i	$0.517207\pi$
$150$	13.0799	+	10.3803i	1.06797	+	0.847549i
$151$	0.628856	−	0.749441i	0.0511755	−	0.0609886i	−0.739849	−	0.672772i	$-0.765103\pi$
$151$	0.628856	−	0.749441i	0.0511755	−	0.0609886i	0.791025	+	0.611784i	$0.209548\pi$
$152$	−1.94950	−	7.71910i	−0.158125	−	0.626101i
$153$	−1.57878	−	2.36913i	−0.127637	−	0.191533i
$154$	10.2037	+	0.942140i	0.822236	+	0.0759198i
$155$	−13.5237	+	4.92223i	−1.08625	+	0.395363i
$156$	−1.16402	+	17.9463i	−0.0931962	+	1.43685i
$157$	9.48180	−	7.95618i	0.756730	−	0.634972i	−0.180543	−	0.983567i	$-0.557786\pi$
$157$	9.48180	−	7.95618i	0.756730	−	0.634972i	0.937273	+	0.348595i	$0.113341\pi$
$158$	−0.104920	−	1.26948i	−0.00834702	−	0.100995i
$159$	−0.0374928	+	0.0399811i	−0.00297337	+	0.00317071i
$160$	−7.79241	−	17.8164i	−0.616044	−	1.40851i
$161$		−	10.6645i		−	0.840484i
$162$	4.78508	+	11.7942i	0.375952	+	0.926639i
$163$		−	19.1200i		−	1.49759i	−0.662800	−	0.748796i	$-0.730632\pi$
$163$		−	19.1200i		−	1.49759i	0.662800	−	0.748796i	$-0.269368\pi$
$164$	10.0642	−	8.28132i	0.785881	−	0.646663i
$165$	12.1662	−	12.9737i	0.947141	−	1.01000i
$166$	21.8936	−	1.80946i	1.69927	−	0.140442i
$167$	−13.1486	+	11.0330i	−1.01747	+	0.853760i	−0.989308	−	0.145843i	$-0.953410\pi$
$167$	−13.1486	+	11.0330i	−1.01747	+	0.853760i	−0.0281640	+	0.999603i	$0.508966\pi$
$168$	11.0929	−	4.26118i	0.855837	−	0.328757i
$169$	−13.1106	+	4.77186i	−1.00851	+	0.367066i
$170$	−0.424180	+	4.59400i	−0.0325331	+	0.352344i
$171$	3.74422	−	7.56895i	0.286327	−	0.578812i
$172$	1.08586	−	5.82997i	0.0827959	−	0.444531i
$173$	−13.7863	+	16.4299i	−1.04815	+	1.24914i	−0.0805286	+	0.996752i	$0.525661\pi$
$173$	−13.7863	+	16.4299i	−1.04815	+	1.24914i	−0.967626	+	0.252389i	$0.918784\pi$
$174$	1.26663	−	1.59604i	0.0960229	−	0.120996i
$175$	16.2846	−	2.87142i	1.23100	−	0.217059i
$176$	−11.3045	+	3.87008i	−0.852109	+	0.291719i
$177$	−13.3877	−	0.739199i	−1.00628	−	0.0555616i
$178$	−1.80685	+	6.61589i	−0.135429	+	0.495882i
$179$	−3.66434	−	6.34682i	−0.273886	−	0.474384i	0.695968	−	0.718073i	$-0.254976\pi$
$179$	−3.66434	−	6.34682i	−0.273886	−	0.474384i	−0.969853	+	0.243689i	$0.921642\pi$
$180$	5.98607	−	19.7378i	0.446176	−	1.47117i
$181$	−5.47518	+	9.48329i	−0.406967	+	0.704887i	−0.994548	−	0.104278i	$-0.966747\pi$
$181$	−5.47518	+	9.48329i	−0.406967	+	0.704887i	0.587581	+	0.809165i	$0.300080\pi$
$182$	12.5322	+	12.6532i	0.928945	+	0.937917i
$183$	19.3437	+	8.27489i	1.42993	+	0.611697i
$184$	5.09239	+	11.3449i	0.375416	+	0.836356i
$185$	6.73308	−	18.4990i	0.495026	−	1.36007i
$186$	6.80370	+	7.67283i	0.498872	+	0.562599i
$187$	2.79173	+	0.492257i	0.204151	+	0.0359974i
$188$	−9.58358	+	11.2008i	−0.698954	+	0.816905i
$189$	11.8825	+	4.20340i	0.864322	+	0.305752i
$190$	−12.4297	+	5.72351i	−0.901746	+	0.415227i
$191$	3.77854	−	21.4292i	0.273406	−	1.55056i	−0.470575	−	0.882360i	$-0.655953\pi$
$191$	3.77854	−	21.4292i	0.273406	−	1.55056i	0.743980	−	0.668201i	$-0.232936\pi$
$192$	−9.76584	+	9.82997i	−0.704789	+	0.709417i
$193$	2.43488	+	0.886224i	0.175267	+	0.0637918i	0.428163	−	0.903702i	$-0.359161\pi$
$193$	2.43488	+	0.886224i	0.175267	+	0.0637918i	−0.252896	+	0.967493i	$0.581383\pi$
$194$	6.74296	−	14.2807i	0.484117	−	1.02530i
$195$	30.6909	−	3.68120i	2.19782	−	0.263616i
$196$	−0.783678	+	2.09040i	−0.0559770	+	0.149314i
$197$	−20.7348	−	11.9712i	−1.47729	−	0.852914i	−0.477620	−	0.878567i	$-0.658500\pi$
$197$	−20.7348	−	11.9712i	−1.47729	−	0.852914i	−0.999671	+	0.0256523i	$0.991834\pi$
$198$	−11.7838	−	4.66460i	−0.837436	−	0.331498i
$199$	−10.8115	+	6.24199i	−0.766403	+	0.442483i	−0.831590	−	0.555390i	$-0.812569\pi$
$199$	−10.8115	+	6.24199i	−0.766403	+	0.442483i	0.0651867	+	0.997873i	$0.479236\pi$
$200$	−15.9524	+	10.8306i	−1.12800	+	0.765841i
$201$	1.03464	+	0.676028i	0.0729779	+	0.0476833i
$202$	−5.05082	+	3.50057i	−0.355374	+	0.246299i
$203$	−0.350377	−	1.98709i	−0.0245916	−	0.139466i
$204$	3.15546	−	0.922058i	0.220926	−	0.0645570i
$205$	−17.1607	−	14.3995i	−1.19856	−	1.00571i
$206$	5.32738	−	7.53100i	0.371176	−	0.524709i
$207$	−3.70650	+	12.6582i	−0.257620	+	0.879808i
$208$	−19.3736	−	7.47622i	−1.34332	−	0.518383i
$209$	2.87579	+	7.90117i	0.198923	+	0.546536i
$210$	−10.6915	−	17.4030i	−0.737782	−	1.20092i
$211$	−2.50624	−	2.98682i	−0.172537	−	0.205621i	0.672846	−	0.739783i	$-0.265072\pi$
$211$	−2.50624	−	2.98682i	−0.172537	−	0.205621i	−0.845382	+	0.534162i	$0.820627\pi$
$212$	−0.0311166	−	0.0551122i	−0.00213710	−	0.00378512i
$213$	0.647455	−	2.76905i	0.0443629	−	0.189732i
$214$	−2.04893	−	7.79641i	−0.140062	−	0.532951i
$215$	−10.1929			−0.695148
$216$	−14.6477	+	1.20241i	−0.996648	+	0.0818135i
$217$	10.1551			0.689371
$218$	3.52256	+	13.4037i	0.238578	+	0.907813i
$219$	−12.4775	+	3.77659i	−0.843149	+	0.255198i
$220$	10.0972	+	17.8837i	0.680754	+	1.20572i
$221$	3.16685	+	3.77410i	0.213025	+	0.253874i
$222$	−14.0223	+	0.382929i	−0.941118	+	0.0257005i
$223$	−9.92318	−	27.2637i	−0.664505	−	1.82571i	−0.555223	−	0.831702i	$-0.687367\pi$
$223$	−9.92318	−	27.2637i	−0.664505	−	1.82571i	−0.109282	−	0.994011i	$-0.534855\pi$
$224$	0.867133	+	13.6941i	0.0579377	+	0.914976i
$225$	−20.3269	−	2.25156i	−1.35513	−	0.150104i
$226$	10.2770	−	14.5280i	0.683616	−	0.966387i
$227$	14.9666	+	12.5585i	0.993367	+	0.833534i	0.986052	−	0.166439i	$-0.0532269\pi$
$227$	14.9666	+	12.5585i	0.993367	+	0.833534i	0.00731551	+	0.999973i	$0.497671\pi$
$228$	7.04818	+	6.73800i	0.466777	+	0.446235i
$229$	0.858590	+	4.86930i	0.0567372	+	0.321773i	0.999946	−	0.0104289i	$-0.00331970\pi$
$229$	0.858590	+	4.86930i	0.0567372	+	0.321773i	−0.943208	+	0.332202i	$0.892209\pi$
$230$	17.5672	−	12.1753i	1.15835	−	0.802816i
$231$	−11.1981	+	5.66629i	−0.736780	+	0.372814i
$232$	1.32158	+	1.94655i	0.0867658	+	0.127797i
$233$	0.471437	−	0.272184i	0.0308849	−	0.0178314i	−0.484478	−	0.874803i	$-0.660990\pi$
$233$	0.471437	−	0.272184i	0.0308849	−	0.0178314i	0.515363	+	0.856972i	$0.327657\pi$
$234$	−10.4773	−	19.3743i	−0.684924	−	1.26653i
$235$	21.9427	+	12.6686i	1.43138	+	0.826408i
$236$	5.43485	−	14.4970i	0.353778	−	0.943676i
$237$	0.935398	+	1.24857i	0.0607606	+	0.0811034i
$238$	1.38996	−	2.94377i	0.0900979	−	0.190816i
$239$	15.6796	+	5.70692i	1.01423	+	0.369150i	0.795056	−	0.606536i	$-0.207441\pi$
$239$	15.6796	+	5.70692i	1.01423	+	0.369150i	0.219175	+	0.975686i	$0.429664\pi$
$240$	19.6836	+	13.4080i	1.27057	+	0.865485i
$241$	4.08197	−	23.1500i	0.262943	−	1.49122i	−0.511888	−	0.859052i	$-0.671054\pi$
$241$	4.08197	−	23.1500i	0.262943	−	1.49122i	0.774831	−	0.632169i	$-0.217835\pi$
$242$	−2.66794	+	1.22851i	−0.171502	+	0.0789714i
$243$	−12.6429	−	9.11900i	−0.811045	−	0.584984i
$244$	−15.7941	+	18.4594i	−1.01111	+	1.18174i
$245$	3.77887	+	0.666318i	0.241423	+	0.0425695i
$246$	−5.04800	+	15.1433i	−0.321849	+	0.965502i
$247$	−4.99799	+	13.7319i	−0.318014	+	0.873738i
$248$	−10.8029	+	4.84911i	−0.685986	+	0.307919i
$249$	−21.5329	+	16.1319i	−1.36459	+	1.02232i
$250$	6.21631	+	6.27635i	0.393154	+	0.396951i
$251$	1.40671	−	2.43650i	0.0887910	−	0.153790i	−0.818209	−	0.574920i	$-0.805033\pi$
$251$	1.40671	−	2.43650i	0.0887910	−	0.153790i	0.907000	+	0.421130i	$0.138366\pi$
$252$	−8.73265	+	11.6429i	−0.550105	+	0.733432i
$253$	−6.56662	−	11.3737i	−0.412840	−	0.715060i
$254$	7.60173	−	27.8343i	0.476975	−	1.74648i
$255$	−2.55113	−	5.04171i	−0.159758	−	0.315724i
$256$	−7.46148	−	14.1537i	−0.466343	−	0.884604i
$257$	19.0091	−	3.35182i	1.18576	−	0.209081i	0.454225	−	0.890887i	$-0.349916\pi$
$257$	19.0091	−	3.35182i	1.18576	−	0.209081i	0.731533	+	0.681806i	$0.238805\pi$
$258$	2.66948	+	6.75465i	0.166195	+	0.420526i
$259$	−8.92898	+	10.6411i	−0.554820	+	0.661209i
$260$	−6.53555	+	35.0893i	−0.405318	+	2.17615i
$261$	−0.274741	+	2.48034i	−0.0170060	+	0.153529i
$262$	−0.811364	+	8.78733i	−0.0501262	+	0.542883i
$263$	3.85139	−	1.40179i	0.237487	−	0.0864382i	−0.220535	−	0.975379i	$-0.570780\pi$
$263$	3.85139	−	1.40179i	0.237487	−	0.0864382i	0.458022	+	0.888941i	$0.348558\pi$
$264$	9.20679	−	11.3749i	0.566638	−	0.700079i
$265$	−0.0833322	+	0.0699240i	−0.00511906	+	0.00429540i
$266$	9.62305	−	0.795326i	0.590027	−	0.0487646i
$267$	−2.43329	−	8.03935i	−0.148915	−	0.492000i
$268$	−1.10200	+	0.906782i	−0.0673154	+	0.0553905i
$269$			12.2264i			0.745457i	0.927940	+	0.372728i	$0.121578\pi$
$269$			12.2264i			0.745457i	−0.927940	+	0.372728i	$0.878422\pi$
$270$	6.64170	+	24.3723i	0.404201	+	1.48325i
$271$			13.3154i			0.808854i	0.914570	+	0.404427i	$0.132529\pi$
$271$			13.3154i			0.808854i	−0.914570	+	0.404427i	$0.867471\pi$
$272$	−0.0729673	+	3.79528i	−0.00442429	+	0.230123i
$273$	−21.2386	−	4.96597i	−1.28542	−	0.300554i
$274$	−0.595828	−	7.20922i	−0.0359953	−	0.435525i
$275$	15.5995	−	13.0895i	0.940684	−	0.789327i
$276$	−12.6692	−	8.45283i	−0.762595	−	0.508801i
$277$	3.11375	−	1.13331i	0.187087	−	0.0680942i	−0.246778	−	0.969072i	$-0.579372\pi$
$277$	3.11375	−	1.13331i	0.187087	−	0.0680942i	0.433865	+	0.900978i	$0.357150\pi$
$278$	−20.9666	−	1.93592i	−1.25750	−	0.116109i
$279$	−12.0535	−	3.52943i	−0.721625	−	0.211301i
$280$	22.8666	−	5.77506i	1.36654	−	0.345126i
$281$	−7.07877	+	8.43614i	−0.422284	+	0.503258i	−0.934680	−	0.355491i	$-0.884314\pi$
$281$	−7.07877	+	8.43614i	−0.422284	+	0.503258i	0.512396	+	0.858749i	$0.328758\pi$
$282$	2.64856	−	17.8589i	0.157719	−	1.06348i
$283$	−31.3904	+	5.53497i	−1.86596	+	0.329020i	−0.988571	−	0.150753i	$-0.951830\pi$
$283$	−31.3904	+	5.53497i	−1.86596	+	0.329020i	−0.877393	+	0.479773i	$0.840719\pi$
$284$	2.82783	+	1.66909i	0.167801	+	0.0990423i
$285$	9.16725	−	14.0302i	0.543021	−	0.831077i
$286$	21.1567	+	5.77803i	1.25102	+	0.341662i
$287$	7.90357	+	13.6894i	0.466533	+	0.808059i
$288$	3.73020	−	16.5555i	0.219804	−	0.975544i
$289$	−8.04970	+	13.9425i	−0.473512	+	0.820147i
$290$	2.87323	−	2.84574i	0.168722	−	0.167108i
$291$	2.30345	+	19.2043i	0.135030	+	1.12578i
$292$	0.144685	−	15.0525i	0.00846706	−	0.880883i
$293$	3.28051	−	9.01312i	0.191649	−	0.526552i	−0.806233	−	0.591598i	$-0.798497\pi$
$293$	3.28051	−	9.01312i	0.191649	−	0.526552i	0.997882	+	0.0650459i	$0.0207194\pi$
$294$	−0.548118	−	2.67870i	−0.0319669	−	0.156225i
$295$	−26.2067	−	4.62094i	−1.52581	−	0.269042i
$296$	4.41739	−	15.5837i	0.256756	−	0.905782i
$297$	15.2609	−	2.83363i	0.885525	−	0.164424i
$298$	3.27229	+	7.10641i	0.189559	+	0.411663i
$299$	3.96351	−	22.4782i	0.229216	−	1.29995i
$300$	9.49621	−	21.6216i	0.548264	−	1.24832i
$301$	6.75857	+	2.45992i	0.389557	+	0.141787i
$302$	−1.25111	−	0.590738i	−0.0719932	−	0.0339931i
$303$	2.96019	−	6.91986i	0.170059	−	0.397535i
$304$	−9.85718	+	5.44114i	−0.565348	+	0.312071i
$305$	36.1623	+	20.8783i	2.07065	+	1.19549i
$306$	−2.67293	+	3.01100i	−0.152801	+	0.172128i
$307$	7.92646	−	4.57634i	0.452387	−	0.261186i	−0.256451	−	0.966557i	$-0.582553\pi$
$307$	7.92646	−	4.57634i	0.452387	−	0.261186i	0.708838	+	0.705372i	$0.249220\pi$
$308$	−2.37915	−	14.2949i	−0.135564	−	0.814529i
$309$	−0.622871	+	11.2808i	−0.0354339	+	0.641745i
$310$	11.5937	+	16.7280i	0.658475	+	0.950086i
$311$	−2.47151	−	14.0166i	−0.140146	−	0.794810i	−0.971137	−	0.238523i	$-0.923337\pi$
$311$	−2.47151	−	14.0166i	−0.140146	−	0.794810i	0.830990	−	0.556287i	$-0.187774\pi$
$312$	24.9648	−	4.85879i	1.41335	−	0.275075i
$313$	21.6878	+	18.1982i	1.22587	+	1.02862i	0.998497	+	0.0548152i	$0.0174570\pi$
$313$	21.6878	+	18.1982i	1.22587	+	1.02862i	0.227370	+	0.973809i	$0.426987\pi$
$314$	−14.2905	−	10.1090i	−0.806460	−	0.570485i
$315$	22.4218	+	11.0916i	1.26332	+	0.624943i
$316$	−1.69865	+	0.599831i	−0.0955564	+	0.0337431i
$317$	−2.29756	−	6.31250i	−0.129044	−	0.354545i	0.858298	−	0.513152i	$-0.171522\pi$
$317$	−2.29756	−	6.31250i	−0.129044	−	0.354545i	−0.987342	+	0.158606i	$0.949300\pi$
$318$	0.0681620	+	0.0369100i	0.00382233	+	0.00206981i
$319$	−1.59721	−	1.90348i	−0.0894267	−	0.106575i
$320$	−21.5677	+	17.0624i	−1.20567	+	0.953819i
$321$	7.20167	+	6.75345i	0.401958	+	0.376941i
$322$	−14.5866	+	3.83344i	−0.812881	+	0.213629i
$323$	2.67124			0.148632
$324$	14.4117	−	10.7844i	0.800650	−	0.599133i
$325$	35.3911			1.96314
$326$	−26.1517	+	6.87280i	−1.44841	+	0.380649i
$327$	−12.3812	−	11.6106i	−0.684683	−	0.642070i
$328$	−14.9446	−	10.7887i	−0.825176	−	0.595706i
$329$	−11.4921	−	13.6957i	−0.633579	−	0.755070i
$330$	−22.1183	−	11.9771i	−1.21757	−	0.659319i
$331$	5.00252	+	13.7443i	0.274964	+	0.755456i	0.997914	+	0.0645563i	$0.0205632\pi$
$331$	5.00252	+	13.7443i	0.274964	+	0.755456i	−0.722951	+	0.690900i	$0.757215\pi$
$332$	−10.3447	−	29.2950i	−0.567740	−	1.60777i
$333$	14.2966	−	9.52716i	0.783448	−	0.522085i
$334$	19.8170	+	14.0184i	1.08434	+	0.767053i
$335$	1.87905	+	1.57671i	0.102663	+	0.0861449i
$336$	−9.81573	−	13.6408i	−0.535492	−	0.744168i
$337$	3.97422	+	22.5389i	0.216490	+	1.22777i	0.878303	+	0.478105i	$0.158676\pi$
$337$	3.97422	+	22.5389i	0.216490	+	1.22777i	−0.661813	+	0.749669i	$0.730213\pi$
$338$	11.2395	+	16.2170i	0.611347	+	0.882087i
$339$	−1.20157	+	21.7618i	−0.0652606	+	1.18194i
$340$	6.43600	−	1.07116i	0.349041	−	0.0580920i
$341$	10.8304	−	6.25292i	0.586497	−	0.338614i
$342$	−11.6985	−	2.40052i	−0.632580	−	0.129805i
$343$	−17.0495	−	9.84356i	−0.920589	−	0.531502i
$344$	−8.36436	+	0.610415i	−0.450976	+	0.0329114i
$345$	−10.2958	+	24.0679i	−0.554308	+	1.29577i
$346$	27.4279	+	12.9507i	1.47453	+	0.696232i
$347$	11.3862	+	4.14424i	0.611243	+	0.222474i	0.629047	−	0.777367i	$-0.283445\pi$
$347$	11.3862	+	4.14424i	0.611243	+	0.222474i	−0.0178039	+	0.999841i	$0.505667\pi$
$348$	−2.63832	−	1.15875i	−0.141429	−	0.0621154i
$349$	1.78921	−	10.1471i	0.0957740	−	0.543161i	−0.898733	−	0.438495i	$-0.855512\pi$
$349$	1.78921	−	10.1471i	0.0957740	−	0.543161i	0.994507	−	0.104666i	$-0.0333773\pi$
$350$	−9.78104	−	21.2414i	−0.522819	−	1.13540i
$351$	23.4831	+	13.2759i	1.25343	+	0.708614i
$352$	9.35685	+	14.0708i	0.498722	+	0.749977i
$353$	−8.87778	−	1.56539i	−0.472516	−	0.0833174i	−0.0676810	−	0.997707i	$-0.521560\pi$
$353$	−8.87778	−	1.56539i	−0.472516	−	0.0833174i	−0.404835	+	0.914390i	$0.632671\pi$
$354$	3.80123	+	18.5769i	0.202033	+	0.987353i
$355$	1.93035	−	5.30359i	0.102452	−	0.281485i
$356$	9.69849	+	0.0932221i	0.514019	+	0.00494076i
$357$	0.474821	+	3.95868i	0.0251302	+	0.209516i
$358$	−7.36382	+	7.29338i	−0.389190	+	0.385467i
$359$	−0.746879	+	1.29363i	−0.0394188	+	0.0682753i	−0.885062	−	0.465474i	$-0.845884\pi$
$359$	−0.746879	+	1.29363i	−0.0394188	+	0.0682753i	0.845643	+	0.533749i	$0.179217\pi$
$360$	−29.1485	−	1.09268i	−1.53626	−	0.0575891i
$361$	−5.53844	−	9.59286i	−0.291497	−	0.504887i
$362$	14.9390	+	4.07995i	0.785178	+	0.214438i
$363$	1.96768	−	3.01147i	0.103276	−	0.158061i
$364$	12.8019	−	21.6894i	0.671001	−	1.13683i
$365$	−25.4804	+	4.49288i	−1.33371	+	0.235168i
$366$	4.36492	−	29.4322i	0.228158	−	1.53844i
$367$	17.0674	−	20.3402i	0.890913	−	1.06175i	−0.106808	−	0.994280i	$-0.534063\pi$
$367$	17.0674	−	20.3402i	0.890913	−	1.06175i	0.997721	−	0.0674692i	$-0.0214924\pi$
$368$	13.6867	−	11.0432i	0.713468	−	0.575667i
$369$	−4.62331	−	18.9955i	−0.240680	−	0.988865i
$370$	−27.7226	−	2.55972i	−1.44123	−	0.133073i
$371$	0.0721302	−	0.0262533i	0.00374481	−	0.00136300i
$372$	8.04902	−	12.0639i	0.417322	−	0.625486i
$373$	−19.6194	+	16.4626i	−1.01585	+	0.852402i	−0.989101	−	0.147241i	$-0.952961\pi$
$373$	−19.6194	+	16.4626i	−1.01585	+	0.852402i	−0.0267519	+	0.999642i	$0.508516\pi$
$374$	−0.330211	−	3.99538i	−0.0170748	−	0.206596i
$375$	−10.5349	−	2.46326i	−0.544022	−	0.127202i
$376$	18.7650	+	9.08190i	0.967733	+	0.468363i
$377$		−	4.31850i		−	0.222414i
$378$	1.47805	−	17.7634i	0.0760226	−	0.913651i
$379$		−	23.4937i		−	1.20679i	−0.797442	−	0.603395i	$-0.793814\pi$
$379$		−	23.4937i		−	1.20679i	0.797442	−	0.603395i	$-0.206186\pi$
$380$	12.2964	+	14.9436i	0.630791	+	0.766592i
$381$	10.2373	+	33.8230i	0.524473	+	1.73281i
$382$	−30.6684	+	2.53468i	−1.56913	+	0.129686i
$383$	6.42764	−	5.39343i	0.328437	−	0.275591i	−0.463626	−	0.886031i	$-0.653452\pi$
$383$	6.42764	−	5.39343i	0.328437	−	0.275591i	0.792063	+	0.610440i	$0.209007\pi$
$384$	16.9555	+	9.82397i	0.865258	+	0.501327i
$385$	−23.4059	+	8.51907i	−1.19288	+	0.434172i
$386$	0.336916	−	3.64891i	0.0171486	−	0.185725i
$387$	−7.16710	−	5.26875i	−0.364324	−	0.267826i
$388$	−21.9566	−	4.08951i	−1.11468	−	0.207613i
$389$	2.87085	−	3.42135i	0.145558	−	0.173469i	−0.688339	−	0.725389i	$-0.741660\pi$
$389$	2.87085	−	3.42135i	0.145558	−	0.173469i	0.833897	+	0.551920i	$0.186104\pi$
$390$	−16.0671	−	40.6548i	−0.813587	−	2.05864i
$391$	−4.10894	+	0.724518i	−0.207798	+	0.0366404i
$392$	3.14088	+	0.320483i	0.158639	+	0.0161868i
$393$	−4.87976	−	9.64371i	−0.246152	−	0.486461i
$394$	−8.92062	+	32.6635i	−0.449414	+	1.64556i
$395$	1.54816	+	2.68149i	0.0778964	+	0.134920i
$396$	−2.14434	+	17.7942i	−0.107757	+	0.894191i
$397$	17.9923	−	31.1636i	0.903009	−	1.56406i	0.0794404	−	0.996840i	$-0.474687\pi$
$397$	17.9923	−	31.1636i	0.903009	−	1.56406i	0.823568	−	0.567217i	$-0.191980\pi$
$398$	12.4238	+	12.5438i	0.622751	+	0.628766i
$399$	−9.46452	+	7.09058i	−0.473819	+	0.354973i
$400$	20.5480	+	17.9260i	1.02740	+	0.896302i
$401$	−4.31346	+	11.8511i	−0.215404	+	0.591817i	−0.999588	−	0.0287111i	$-0.990860\pi$
$401$	−4.31346	+	11.8511i	−0.215404	+	0.591817i	0.784184	+	0.620529i	$0.213082\pi$
$402$	0.552742	−	1.65815i	0.0275683	−	0.0827011i
$403$	21.4043	+	3.77416i	1.06623	+	0.188004i
$404$	6.60352	+	5.65005i	0.328537	+	0.281101i
$405$	−22.7585	−	20.9579i	−1.13088	−	1.04141i
$406$	−2.59193	+	1.19351i	−0.128635	+	0.0592327i
$407$	−2.97053	+	16.8467i	−0.147244	+	0.835062i
$408$	−2.39541	−	3.98450i	−0.118591	−	0.197262i
$409$	3.56631	+	1.29803i	0.176343	+	0.0641835i	0.428683	−	0.903455i	$-0.358978\pi$
$409$	3.56631	+	1.29803i	0.176343	+	0.0641835i	−0.252340	+	0.967639i	$0.581200\pi$
$410$	−13.5267	+	28.6479i	−0.668037	+	1.41482i
$411$	5.31199	+	7.09045i	0.262021	+	0.349746i
$412$	−12.2156	−	4.57956i	−0.601821	−	0.225619i
$413$	16.2616	+	9.38864i	0.800181	+	0.461985i
$414$	18.6459	+	0.519557i	0.916394	+	0.0255348i
$415$	−46.2452	+	26.6997i	−2.27009	+	1.31063i
$416$	−3.26176	+	29.1860i	−0.159921	+	1.43096i
$417$	23.0100	−	11.6432i	1.12680	−	0.570168i
$418$	9.77326	−	6.77354i	0.478026	−	0.331305i
$419$	5.26779	+	29.8751i	0.257349	+	1.45950i	0.789972	+	0.613143i	$0.210095\pi$
$419$	5.26779	+	29.8751i	0.257349	+	1.45950i	−0.532623	+	0.846353i	$0.678794\pi$
$420$	−19.9602	+	20.8791i	−0.973959	+	1.01880i
$421$	−17.3035	−	14.5193i	−0.843319	−	0.707629i	0.114989	−	0.993367i	$-0.463317\pi$
$421$	−17.3035	−	14.5193i	−0.843319	−	0.707629i	−0.958308	+	0.285738i	$0.907761\pi$
$422$	−3.18440	+	4.50159i	−0.155014	+	0.219134i
$423$	8.88047	+	20.2502i	0.431783	+	0.984598i
$424$	−0.0641957	+	0.0623708i	−0.00311762	+	0.00302899i
$425$	−2.21266	−	6.07923i	−0.107330	−	0.294886i
$426$	−4.02016	+	0.109784i	−0.194777	+	0.00531906i
$427$	−18.9394	−	22.5711i	−0.916541	−	1.09229i
$428$	−9.92718	+	5.60494i	−0.479848	+	0.270925i
$429$	−25.7087	+	7.78131i	−1.24123	+	0.375685i
$430$	3.66389	+	13.9415i	0.176689	+	0.672318i
$431$	−2.22404			−0.107128			−0.0535641	−	0.998564i	$-0.517058\pi$
$431$	−2.22404			−0.107128			−0.0535641	+	0.998564i	$0.517058\pi$
$432$	6.90981	+	19.6024i	0.332448	+	0.943121i
$433$	−0.990478			−0.0475994			−0.0237997	−	0.999717i	$-0.507576\pi$
$433$	−0.990478			−0.0475994			−0.0237997	+	0.999717i	$0.507576\pi$
$434$	−3.65030	−	13.8898i	−0.175220	−	0.666731i
$435$	−1.12765	+	4.82275i	−0.0540666	+	0.231233i
$436$	17.0670	−	9.63609i	0.817359	−	0.461485i
$437$	−7.95482	−	9.48018i	−0.380531	−	0.453499i
$438$	9.65061	+	15.7088i	0.461124	+	0.750594i
$439$	9.24903	+	25.4115i	0.441432	+	1.21283i	0.938550	+	0.345142i	$0.112169\pi$
$439$	9.24903	+	25.4115i	0.441432	+	1.21283i	−0.497118	+	0.867683i	$0.665608\pi$
$440$	20.8312	−	20.2390i	0.993089	−	0.964859i
$441$	2.31269	+	2.42184i	0.110128	+	0.115326i
$442$	4.02376	−	5.68814i	0.191391	−	0.270557i
$443$	−30.0880	−	25.2468i	−1.42952	−	1.19951i	−0.945995	−	0.324182i	$-0.894911\pi$
$443$	−30.0880	−	25.2468i	−1.42952	−	1.19951i	−0.483527	−	0.875329i	$-0.660645\pi$
$444$	5.56418	+	19.0417i	0.264064	+	0.903678i
$445$	−2.89481	−	16.4173i	−0.137227	−	0.778253i
$446$	−33.7235	+	23.3727i	−1.59685	+	1.10673i
$447$	−8.02145	−	5.24117i	−0.379401	−	0.247899i
$448$	18.4187	−	6.10847i	0.870201	−	0.288598i
$449$	6.90674	−	3.98761i	0.325949	−	0.188187i	−0.328092	−	0.944646i	$-0.606406\pi$
$449$	6.90674	−	3.98761i	0.325949	−	0.188187i	0.654041	+	0.756459i	$0.273072\pi$
$450$	4.22702	+	28.6119i	0.199264	+	1.34878i
$451$	16.8583	+	9.73315i	0.793827	+	0.458316i
$452$	−23.5650	−	8.83439i	−1.10841	−	0.415535i
$453$	1.68245	−	0.201800i	0.0790484	−	0.00948141i
$454$	11.7972	−	24.9850i	0.553671	−	1.17261i
$455$	−40.6784	−	14.8057i	−1.90703	−	0.694103i
$456$	6.68251	−	12.0623i	0.312937	−	0.564869i
$457$	4.06394	−	23.0478i	0.190103	−	1.07813i	−0.729118	−	0.684388i	$-0.760069\pi$
$457$	4.06394	−	23.0478i	0.190103	−	1.07813i	0.919221	−	0.393741i	$-0.128819\pi$
$458$	6.35145	−	2.92465i	0.296784	−	0.136660i
$459$	0.812268	−	4.86377i	0.0379134	−	0.227021i
$460$	−22.9677	−	19.6514i	−1.07087	−	0.916252i
$461$	−11.6857	−	2.06050i	−0.544256	−	0.0959670i	−0.105241	−	0.994447i	$-0.533561\pi$
$461$	−11.6857	−	2.06050i	−0.544256	−	0.0959670i	−0.439015	+	0.898480i	$0.644672\pi$
$462$	11.7754	+	13.2796i	0.547841	+	0.617824i
$463$	3.08379	−	8.47264i	0.143316	−	0.393757i	−0.847179	−	0.531308i	$-0.821701\pi$
$463$	3.08379	−	8.47264i	0.143316	−	0.393757i	0.990495	+	0.137551i	$0.0439230\pi$
$464$	2.18738	−	2.50731i	0.101546	−	0.116399i
$465$	−22.9181	−	9.80396i	−1.06280	−	0.454648i
$466$	−0.541746	−	0.546978i	−0.0250959	−	0.0253383i
$467$	16.5509	−	28.6671i	0.765886	−	1.32655i	−0.173891	−	0.984765i	$-0.555634\pi$
$467$	16.5509	−	28.6671i	0.765886	−	1.32655i	0.939777	−	0.341788i	$-0.111033\pi$
$468$	−22.7334	+	21.2947i	−1.05085	+	0.984350i
$469$	−0.865420	−	1.49895i	−0.0399614	−	0.0692151i
$470$	9.44029	−	34.5663i	0.435448	−	1.59442i
$471$	21.4061	+	1.18193i	0.986339	+	0.0544606i
$472$	−21.7822	−	2.22256i	−1.00261	−	0.102302i
$473$	8.72269	−	1.53805i	0.401070	−	0.0707194i
$474$	1.37152	−	1.72822i	0.0629961	−	0.0793795i
$475$	12.3343	−	14.6994i	0.565936	−	0.674456i
$476$	−4.52602	−	0.842993i	−0.207450	−	0.0386385i
$477$	−0.0947390	+	0.00609205i	−0.00433780	+	0.000278936i
$478$	2.16960	−	23.4975i	0.0992353	−	1.07475i
$479$	1.78517	−	0.649748i	0.0815664	−	0.0296877i	−0.300915	−	0.953651i	$-0.597292\pi$
$479$	1.78517	−	0.649748i	0.0815664	−	0.0296877i	0.382481	+	0.923963i	$0.375070\pi$
$480$	11.2637	−	31.7422i	0.514114	−	1.44883i
$481$	−22.7749	+	19.1104i	−1.03845	+	0.871359i
$482$	−33.1311	+	2.73822i	−1.50908	+	0.124722i
$483$	12.6353	−	13.4739i	0.574927	−	0.613084i
$484$	2.63932	+	3.20753i	0.119969	+	0.145797i
$485$			38.3879i			1.74311i
$486$	−7.92810	+	20.5705i	−0.359626	+	0.933097i
$487$		−	11.9750i		−	0.542640i	−0.962489	−	0.271320i	$-0.912540\pi$
$487$		−	11.9750i		−	0.542640i	0.962489	−	0.271320i	$-0.0874602\pi$
$488$	30.9255	+	14.9673i	1.39993	+	0.677539i
$489$	22.6533	−	24.1568i	1.02442	−	1.09241i
$490$	−0.446972	−	5.40814i	−0.0201921	−	0.244315i
$491$	18.6697	−	15.6658i	0.842554	−	0.706987i	−0.115583	−	0.993298i	$-0.536874\pi$
$491$	18.6697	−	15.6658i	0.842554	−	0.706987i	0.958137	+	0.286311i	$0.0924291\pi$
$492$	22.5271	+	1.46114i	1.01560	+	0.0658732i
$493$	−0.741802	+	0.269994i	−0.0334091	+	0.0121599i
$494$	20.5786	+	1.90009i	0.925874	+	0.0854890i
$495$	30.7424	−	1.97684i	1.38177	−	0.0888525i
$496$	10.5156	+	13.0328i	0.472166	+	0.585192i
$497$	−2.55991	+	3.05078i	−0.114828	+	0.136846i
$498$	29.8049	+	23.6533i	1.33559	+	1.05993i
$499$	26.7787	−	4.72181i	1.19878	−	0.211377i	0.461608	−	0.887084i	$-0.347273\pi$
$499$	26.7787	−	4.72181i	1.19878	−	0.211377i	0.737171	+	0.675707i	$0.236161\pi$
$500$	6.35010	−	10.7585i	0.283985	−	0.481137i
$501$	−29.6843	−	1.63901i	−1.32619	−	0.0732258i
$502$	−3.83822	−	1.04824i	−0.171308	−	0.0467854i
$503$	4.33891	+	7.51521i	0.193462	+	0.335087i	0.946395	−	0.323010i	$-0.104695\pi$
$503$	4.33891	+	7.51521i	0.193462	+	0.335087i	−0.752933	+	0.658097i	$0.771362\pi$
$504$	19.0638	+	7.75914i	0.849167	+	0.345620i
$505$	7.46885	−	12.9364i	0.332359	−	0.575663i
$506$	−13.1962	+	13.0700i	−0.586643	+	0.581031i
$507$	−22.2180	−	9.50446i	−0.986736	−	0.422108i
$508$	−40.8033	−	0.392202i	−1.81036	−	0.0174012i
$509$	−1.70195	+	4.67607i	−0.0754376	+	0.207263i	−0.971680	−	0.236302i	$-0.924064\pi$
$509$	−1.70195	+	4.67607i	−0.0754376	+	0.207263i	0.896242	+	0.443565i	$0.146287\pi$
$510$	−5.97888	+	5.30163i	−0.264749	+	0.234760i
$511$	17.9796	+	3.17028i	0.795369	+	0.140245i
$512$	−16.6769	+	15.2932i	−0.737020	+	0.675871i
$513$	13.6982	−	5.12670i	0.604791	−	0.226349i
$514$	−11.4175	−	24.7953i	−0.503603	−	1.09367i
$515$	−3.89374	+	22.0825i	−0.171579	+	0.973072i
$516$	8.27923	−	6.07923i	0.364473	−	0.267623i
$517$	−20.6894	−	7.53031i	−0.909917	−	0.331183i
$518$	17.7642	+	8.38776i	0.780514	+	0.368537i
$519$	−36.8841	+	4.42404i	−1.61903	+	0.194194i
$520$	50.3434	−	3.67396i	2.20770	−	0.161114i
$521$	−8.95795	−	5.17188i	−0.392455	−	0.226584i	0.290768	−	0.956794i	$-0.406089\pi$
$521$	−8.95795	−	5.17188i	−0.392455	−	0.226584i	−0.683223	+	0.730209i	$0.739422\pi$
$522$	3.49129	−	0.515791i	0.152809	−	0.0225756i
$523$	10.7218	−	6.19021i	0.468829	−	0.270679i	−0.246920	−	0.969036i	$-0.579419\pi$
$523$	10.7218	−	6.19021i	0.468829	−	0.270679i	0.715750	+	0.698357i	$0.246085\pi$
$524$	12.3107	−	2.04890i	0.537795	−	0.0895068i
$525$	23.9765	+	15.6661i	1.04642	+	0.683726i
$526$	−3.30174	−	4.76393i	−0.143962	−	0.207717i
$527$	−0.689905	−	3.91265i	−0.0300528	−	0.170438i
$528$	−18.8677	−	8.50396i	−0.821112	−	0.370087i
$529$	−2.81148	−	2.35911i	−0.122238	−	0.102570i
$530$	0.125594	+	0.0888446i	0.00545546	+	0.00385916i
$531$	−16.0386	−	16.7956i	−0.696015	−	0.728867i
$532$	−4.54689	−	12.8762i	−0.197133	−	0.558255i
$533$	11.5711	+	31.7912i	0.501198	+	1.37703i
$534$	−10.1213	+	6.21798i	−0.437992	+	0.269078i
$535$	12.5952	+	15.0104i	0.544537	+	0.648954i
$536$	1.63639	+	1.18133i	0.0706813	+	0.0510258i
$537$	2.89006	−	12.3603i	0.124715	−	0.533385i
$538$	16.7229	−	4.39486i	0.720975	−	0.189476i
$539$	−3.33437			−0.143621
$540$	30.9483	−	17.8451i	1.33180	−	0.767931i
$541$	0.604524			0.0259905			0.0129953	−	0.999916i	$-0.495863\pi$
$541$	0.604524			0.0259905			0.0129953	+	0.999916i	$0.495863\pi$
$542$	18.2124	−	4.78631i	0.782290	−	0.205590i
$543$	−18.1533	+	5.49450i	−0.779032	+	0.235792i
$544$	5.21730	−	1.26444i	0.223690	−	0.0542122i
$545$	−21.6538	−	25.8060i	−0.927548	−	1.10541i
$546$	0.842042	+	30.8345i	0.0360361	+	1.31959i
$547$	−10.2873	−	28.2642i	−0.439854	−	1.20849i	−0.939587	−	0.342310i	$-0.888791\pi$
$547$	−10.2873	−	28.2642i	−0.439854	−	1.20849i	0.499733	−	0.866180i	$-0.333432\pi$
$548$	−9.64637	+	3.40635i	−0.412072	+	0.145512i
$549$	14.6353	+	33.3731i	0.624621	+	1.42433i
$550$	−23.5108	−	16.6314i	−1.00250	−	0.709164i
$551$	−1.79366	−	1.50506i	−0.0764124	−	0.0641176i
$552$	−7.00751	+	20.3669i	−0.298259	+	0.866874i
$553$	−0.379392	−	2.15164i	−0.0161334	−	0.0914971i
$554$	−2.66937	−	3.85152i	−0.113411	−	0.163635i
$555$	30.4243	−	15.3948i	1.29144	−	0.653475i
$556$	4.88870	+	29.3734i	0.207327	+	1.24571i
$557$	8.14110	−	4.70027i	0.344950	−	0.199157i	−0.317509	−	0.948255i	$-0.602846\pi$
$557$	8.14110	−	4.70027i	0.344950	−	0.199157i	0.662459	+	0.749099i	$0.269513\pi$
$558$	−0.494736	+	17.7551i	−0.0209438	+	0.751633i
$559$	13.3311	+	7.69674i	0.563847	+	0.325537i
$560$	−16.1185	−	29.2003i	−0.681130	−	1.23394i
$561$	2.94393	+	3.92956i	0.124293	+	0.165906i
$562$	14.0832	+	6.64969i	0.594064	+	0.280500i
$563$	25.3522	+	9.22746i	1.06847	+	0.388891i	0.815604	−	0.578610i	$-0.196405\pi$
$563$	25.3522	+	9.22746i	1.06847	+	0.388891i	0.252866	+	0.967501i	$0.418627\pi$
$564$	−25.3789	+	2.79689i	−1.06864	+	0.117770i
$565$	−7.51138	+	42.5992i	−0.316006	+	1.79216i
$566$	18.8540	+	40.9452i	0.792494	+	1.72105i
$567$	10.0325	+	19.3890i	0.421325	+	0.814262i
$568$	1.26645	−	4.46778i	0.0531390	−	0.187464i
$569$	−19.8771	−	3.50486i	−0.833290	−	0.146931i	−0.259303	−	0.965796i	$-0.583493\pi$
$569$	−19.8771	−	3.50486i	−0.833290	−	0.146931i	−0.573987	+	0.818865i	$0.694604\pi$
$570$	−22.4853	−	7.49543i	−0.941805	−	0.313949i
$571$	−15.5035	+	42.5955i	−0.648802	+	1.78257i	−0.0266839	+	0.999644i	$0.508495\pi$
$571$	−15.5035	+	42.5955i	−0.648802	+	1.78257i	−0.622118	+	0.782924i	$0.713727\pi$
$572$	0.298110	−	31.0144i	0.0124646	−	1.29678i
$573$	30.1632	−	22.5975i	1.26008	−	0.944023i
$574$	15.8829	−	15.7310i	0.662941	−	0.656599i
$575$	−14.9859	+	25.9564i	−0.624956	+	1.08245i
$576$	−23.9850	+	0.848941i	−0.999374	+	0.0353725i
$577$	17.4370	+	30.2018i	0.725913	+	1.25732i	0.958597	+	0.284765i	$0.0919157\pi$
$577$	17.4370	+	30.2018i	0.725913	+	1.25732i	−0.232685	+	0.972552i	$0.574751\pi$
$578$	21.9636	+	5.99841i	0.913566	+	0.249501i
$579$	2.02631	+	4.00452i	0.0842104	+	0.166422i
$580$	−4.92512	−	2.90699i	−0.204504	−	0.120706i
$581$	37.1073	−	6.54302i	1.53947	−	0.271450i
$582$	25.4390	−	10.0537i	1.05448	−	0.416739i
$583$	0.0607615	−	0.0724128i	0.00251649	−	0.00299903i
$584$	−20.6404	+	5.21283i	−0.854106	+	0.215709i
$585$	43.1373	+	31.7115i	1.78351	+	1.31111i
$586$	−13.5071	−	1.24715i	−0.557972	−	0.0515194i
$587$	−28.7879	+	10.4779i	−1.18820	+	0.432471i	−0.859092	−	0.511821i	$-0.828971\pi$
$587$	−28.7879	+	10.4779i	−1.18820	+	0.432471i	−0.329111	+	0.944291i	$0.606749\pi$
$588$	−3.46682	+	1.71258i	−0.142969	+	0.0706255i
$589$	9.02729	−	7.57479i	0.371963	−	0.312114i
$590$	3.09977	+	37.5057i	0.127616	+	1.54408i
$591$	−12.0135	−	39.6913i	−0.494168	−	1.63268i
$592$	−22.9027	−	0.440323i	−0.941295	−	0.0180972i
$593$		−	34.8291i		−	1.43026i	−0.698992	−	0.715129i	$-0.746368\pi$
$593$		−	34.8291i		−	1.43026i	0.698992	−	0.715129i	$-0.253632\pi$
$594$	−9.36137	−	19.8548i	−0.384102	−	0.814651i
$595$			7.91311i			0.324406i
$596$	8.54368	−	7.03018i	0.349963	−	0.287967i
$597$	−21.0550	−	4.92305i	−0.861724	−	0.201487i
$598$	−32.1697	+	2.65876i	−1.31552	+	0.108725i
$599$	−14.9648	+	12.5570i	−0.611447	+	0.513065i	−0.895102	−	0.445861i	$-0.852897\pi$
$599$	−14.9648	+	12.5570i	−0.611447	+	0.513065i	0.283655	+	0.958926i	$0.408453\pi$
$600$	−32.9868	−	5.21660i	−1.34668	−	0.212967i
$601$	5.62813	−	2.04847i	0.229576	−	0.0835588i	−0.224671	−	0.974435i	$-0.572131\pi$
$601$	5.62813	−	2.04847i	0.229576	−	0.0835588i	0.454247	+	0.890876i	$0.349908\pi$
$602$	0.935189	−	10.1284i	0.0381154	−	0.412802i
$603$	0.506240	+	2.07995i	0.0206157	+	0.0847022i
$604$	−0.358274	+	1.92357i	−0.0145780	+	0.0782690i
$605$	4.58924	−	5.46925i	0.186579	−	0.222357i
$606$	−10.5288	−	1.56147i	−0.427704	−	0.0634304i
$607$	5.25633	−	0.926833i	0.213348	−	0.0376190i	−0.0659525	−	0.997823i	$-0.521009\pi$
$607$	5.25633	−	0.926833i	0.213348	−	0.0376190i	0.279300	+	0.960204i	$0.409897\pi$
$608$	10.9854	+	11.5265i	0.445519	+	0.467461i
$609$	1.91162	−	2.92567i	0.0774626	−	0.118554i
$610$	15.5580	−	56.9665i	0.629923	−	2.30651i
$611$	−19.1324	−	33.1383i	−0.774013	−	1.34063i
$612$	5.07916	+	2.57362i	0.205313	+	0.104033i
$613$	−9.68872	+	16.7814i	−0.391324	+	0.677793i	−0.992624	−	0.121230i	$-0.961316\pi$
$613$	−9.68872	+	16.7814i	−0.391324	+	0.677793i	0.601301	+	0.799023i	$0.294649\pi$
$614$	−9.10859	−	9.19657i	−0.367593	−	0.371143i
$615$	−4.62082	−	38.5248i	−0.186330	−	1.55347i
$616$	−18.6970	+	8.39252i	−0.753322	+	0.338144i
$617$	−4.40204	+	12.0945i	−0.177220	+	0.486907i	−0.996218	−	0.0868890i	$-0.972307\pi$
$617$	−4.40204	+	12.0945i	−0.177220	+	0.486907i	0.818998	+	0.573796i	$0.194530\pi$
$618$	15.6535	−	3.20303i	0.629675	−	0.128845i
$619$	−3.39593	−	0.598794i	−0.136494	−	0.0240676i	0.104984	−	0.994474i	$-0.466521\pi$
$619$	−3.39593	−	0.598794i	−0.136494	−	0.0240676i	−0.241478	+	0.970406i	$0.577632\pi$
$620$	18.7126	−	21.8704i	0.751516	−	0.878337i
$621$	−19.6803	+	11.6013i	−0.789745	+	0.465546i
$622$	−18.2831	+	8.41882i	−0.733086	+	0.337564i
$623$	−2.04264	+	11.5844i	−0.0818367	+	0.464119i
$624$	−15.6194	−	32.3995i	−0.625278	−	1.29702i
$625$	11.8522	+	4.31383i	0.474086	+	0.172553i
$626$	17.0951	−	36.2053i	0.683259	−	1.44706i
$627$	−5.72792	+	13.3898i	−0.228751	+	0.534738i
$628$	−8.68998	+	23.1799i	−0.346768	+	0.924977i
$629$	4.70654	+	2.71732i	0.187662	+	0.108347i
$630$	7.11114	−	34.6548i	0.283315	−	1.38068i
$631$	5.86206	−	3.38446i	0.233365	−	0.134733i	−0.378758	−	0.925496i	$-0.623649\pi$
$631$	5.86206	−	3.38446i	0.233365	−	0.134733i	0.612123	+	0.790762i	$0.290316\pi$
$632$	1.43102	+	2.10774i	0.0569229	+	0.0838415i
$633$	0.372316	−	6.74303i	0.0147982	−	0.268011i
$634$	−7.80816	+	5.41160i	−0.310102	+	0.214922i
$635$	12.1790	+	69.0705i	0.483308	+	2.74098i
$636$	0.0259831	−	0.106497i	0.00103030	−	0.00422289i
$637$	−4.43921	−	3.72494i	−0.175888	−	0.147587i
$638$	−2.02940	+	2.86884i	−0.0803446	+	0.113578i
$639$	4.09878	−	2.73140i	0.162145	−	0.108053i
$640$	31.0901	+	23.3665i	1.22894	+	0.923640i
$641$	−8.57675	−	23.5644i	−0.338761	−	0.930738i	−0.985747	−	0.168236i	$-0.946193\pi$
$641$	−8.57675	−	23.5644i	−0.338761	−	0.930738i	0.646986	−	0.762502i	$-0.276029\pi$
$642$	6.64847	−	12.2778i	0.262394	−	0.484566i
$643$	16.8722	+	20.1075i	0.665374	+	0.792962i	0.988146	−	0.153515i	$-0.0490593\pi$
$643$	16.8722	+	20.1075i	0.665374	+	0.792962i	−0.322772	+	0.946477i	$0.604615\pi$
$644$	10.4865	+	18.5732i	0.413226	+	0.731886i
$645$	−12.8780	−	12.0765i	−0.507070	−	0.475511i
$646$	−0.960193	−	3.65364i	−0.0377783	−	0.143750i
$647$	16.9440			0.666138			0.333069	−	0.942902i	$-0.391916\pi$
$647$	16.9440			0.666138			0.333069	+	0.942902i	$0.391916\pi$
$648$	−19.9309	−	15.8354i	−0.782960	−	0.622071i
$649$	23.1240			0.907696
$650$	−12.7216	−	48.4068i	−0.498980	−	1.89867i
$651$	12.8302	+	12.0317i	0.502856	+	0.471559i
$652$	18.8008	+	33.2990i	0.736296	+	1.30409i
$653$	−14.2328	−	16.9619i	−0.556971	−	0.663772i	0.411932	−	0.911215i	$-0.364854\pi$
$653$	−14.2328	−	16.9619i	−0.556971	−	0.663772i	−0.968903	+	0.247443i	$0.920410\pi$
$654$	−11.4302	+	21.1082i	−0.446954	+	0.825394i
$655$	−7.33656	−	20.1570i	−0.286663	−	0.787600i
$656$	−9.38453	+	24.3188i	−0.366404	+	0.949489i
$657$	−20.2389	−	10.0118i	−0.789595	−	0.390598i
$658$	−14.6017	+	20.6415i	−0.569233	+	0.804690i
$659$	−31.2421	−	26.2153i	−1.21702	−	1.02120i	−0.998975	−	0.0452630i	$-0.985587\pi$
$659$	−31.2421	−	26.2153i	−1.21702	−	1.02120i	−0.218046	−	0.975939i	$-0.569968\pi$
$660$	−8.43140	+	34.5579i	−0.328192	+	1.34517i
$661$	0.796853	+	4.51918i	0.0309940	+	0.175776i	0.996375	−	0.0850674i	$-0.0271106\pi$
$661$	0.796853	+	4.51918i	0.0309940	+	0.175776i	−0.965381	+	0.260843i	$0.915999\pi$
$662$	17.0009	−	11.7828i	0.660757	−	0.457951i
$663$	−0.470453	+	8.52039i	−0.0182709	+	0.330904i
$664$	−36.3503	+	24.6794i	−1.41066	+	0.957748i
$665$	−20.3265	+	11.7355i	−0.788226	+	0.455083i
$666$	−18.1699	−	16.1298i	−0.704071	−	0.625018i
$667$	3.16725	+	1.82861i	0.122637	+	0.0708042i
$668$	12.0506	−	32.1440i	0.466252	−	1.24369i
$669$	19.7647	−	46.2027i	0.764148	−	1.78630i
$670$	1.48114	−	3.13686i	0.0572214	−	0.121188i
$671$	−34.0968	−	12.4102i	−1.31629	−	0.479092i
$672$	−15.1292	+	18.3289i	−0.583620	+	0.707054i
$673$	−5.89592	+	33.4374i	−0.227271	+	1.28892i	0.631025	+	0.775763i	$0.282635\pi$
$673$	−5.89592	+	33.4374i	−0.227271	+	1.28892i	−0.858296	+	0.513155i	$0.828477\pi$
$674$	29.3995	−	13.5376i	1.13243	−	0.521448i
$675$	−23.0140	−	26.9280i	−0.885810	−	1.03646i
$676$	18.1410	−	21.2023i	0.697729	−	0.815473i
$677$	−6.55631	−	1.15605i	−0.251979	−	0.0444308i	0.0462316	−	0.998931i	$-0.485279\pi$
$677$	−6.55631	−	1.15605i	−0.251979	−	0.0444308i	−0.298211	+	0.954500i	$0.596390\pi$
$678$	30.1970	−	6.17893i	1.15971	−	0.237300i
$679$	9.26443	−	25.4538i	0.355536	−	0.976828i
$680$	−3.77856	−	8.41793i	−0.144901	−	0.322813i
$681$	4.03002	+	33.5991i	0.154431	+	1.28752i
$682$	−12.4456	−	12.5658i	−0.476566	−	0.481169i
$683$	−20.1611	+	34.9201i	−0.771444	+	1.33618i	0.165328	+	0.986239i	$0.447132\pi$
$683$	−20.1611	+	34.9201i	−0.771444	+	1.33618i	−0.936772	+	0.349941i	$0.886202\pi$
$684$	0.921728	+	16.8637i	0.0352432	+	0.644798i
$685$	8.79177	+	15.2278i	0.335916	+	0.581824i
$686$	−7.33515	+	26.8582i	−0.280057	+	1.02545i
$687$	−4.68437	+	7.16928i	−0.178720	+	0.273525i
$688$	3.84153	+	11.2211i	0.146457	+	0.427800i
$689$	0.161790	−	0.0285279i	0.00616369	−	0.00108683i
$690$	36.6202	+	5.43094i	1.39411	+	0.206752i
$691$	−23.6759	+	28.2159i	−0.900674	+	1.07338i	0.0962771	+	0.995355i	$0.469306\pi$
$691$	−23.6759	+	28.2159i	−0.900674	+	1.07338i	−0.996951	+	0.0780271i	$0.975138\pi$
$692$	7.85439	−	42.1702i	0.298579	−	1.60307i
$693$	−20.8614	−	6.10850i	−0.792459	−	0.232043i
$694$	1.57552	−	17.0634i	0.0598058	−	0.647716i
$695$	48.0948	−	17.5051i	1.82434	−	0.664005i
$696$	−0.636541	+	4.02513i	−0.0241280	+	0.152572i
$697$	4.73744	−	3.97519i	0.179444	−	0.150571i
$698$	−14.5220	+	1.20022i	−0.549666	+	0.0454288i
$699$	0.918111	+	0.214671i	0.0347261	+	0.00811961i
$700$	−25.5375	+	21.0136i	−0.965228	+	0.794239i
$701$		−	12.7857i		−	0.482910i	−0.970412	−	0.241455i	$-0.922375\pi$
$701$		−	12.7857i		−	0.482910i	0.970412	−	0.241455i	$-0.0776247\pi$
$702$	9.71719	−	36.8915i	0.366752	−	1.39238i
$703$			16.1196i			0.607963i
$704$	15.8822	−	17.8559i	0.598585	−	0.672968i
$705$	12.7133	+	42.0035i	0.478811	+	1.58194i
$706$	1.05008	+	12.7054i	0.0395202	+	0.478175i
$707$	−8.07440	+	6.77522i	−0.303669	+	0.254808i
$708$	24.0426	−	11.8768i	0.903576	−	0.446357i
$709$	22.8910	−	8.33163i	0.859688	−	0.312901i	0.125704	−	0.992068i	$-0.459881\pi$
$709$	22.8910	−	8.33163i	0.859688	−	0.312901i	0.733984	+	0.679167i	$0.237659\pi$
$710$	−7.94796	−	0.733862i	−0.298282	−	0.0275414i
$711$	−0.297493	+	2.68574i	−0.0111569	+	0.100723i
$712$	−3.35868	−	13.2988i	−0.125872	−	0.498394i
$713$	−11.8314	+	14.1001i	−0.443090	+	0.528055i
$714$	5.24389	−	2.07242i	0.196248	−	0.0775584i
$715$	−52.5000	+	9.25717i	−1.96339	+	0.346199i
$716$	12.6226	+	7.45035i	0.471730	+	0.278433i
$717$	13.0486	+	25.7875i	0.487308	+	0.963051i
$718$	2.03786	+	0.556553i	0.0760522	+	0.0207704i
$719$	10.0151	+	17.3466i	0.373498	+	0.646918i	0.990101	−	0.140356i	$-0.0448248\pi$
$719$	10.0151	+	17.3466i	0.373498	+	0.646918i	−0.616603	+	0.787275i	$0.711491\pi$
$720$	8.98309	+	40.2612i	0.334780	+	1.50045i
$721$	7.91115	−	13.7025i	0.294627	−	0.510308i
$722$	−11.1300	+	11.0235i	−0.414215	+	0.410253i
$723$	32.5853	−	24.4121i	1.21186	−	0.907895i
$724$	0.210500	−	21.8997i	0.00782318	−	0.813896i
$725$	−1.93949	+	5.32871i	−0.0720309	+	0.197903i
$726$	−4.82629	−	1.60884i	−0.179120	−	0.0597095i
$727$	35.0136	+	6.17384i	1.29858	+	0.228975i	0.779852	−	0.625964i	$-0.215294\pi$
$727$	35.0136	+	6.17384i	1.29858	+	0.228975i	0.518729	+	0.854939i	$0.326405\pi$
$728$	−34.2677	−	9.71364i	−1.27005	−	0.360011i
$729$	−5.16931	−	26.5005i	−0.191456	−	0.981501i
$730$	15.3043	+	33.2363i	0.566438	+	1.23013i
$731$	0.488625	−	2.77113i	0.0180725	−	0.102494i
$732$	−41.8254	+	4.60937i	−1.54591	+	0.170367i
$733$	0.443127	+	0.161285i	0.0163673	+	0.00595721i	0.350191	−	0.936678i	$-0.386117\pi$
$733$	0.443127	+	0.161285i	0.0163673	+	0.00595721i	−0.333824	+	0.942636i	$0.608339\pi$
$734$	−33.9557	−	16.0329i	−1.25333	−	0.591785i
$735$	3.98489	+	5.31904i	0.146985	+	0.196196i
$736$	−20.0243	−	14.7507i	−0.738106	−	0.543717i
$737$	−1.84594	−	1.06575i	−0.0679960	−	0.0392575i
$738$	−24.3195	+	13.1517i	−0.895215	+	0.484119i
$739$	29.7805	−	17.1938i	1.09549	−	0.632483i	0.160459	−	0.987042i	$-0.448702\pi$
$739$	29.7805	−	17.1938i	1.09549	−	0.632483i	0.935033	+	0.354559i	$0.115369\pi$
$740$	6.46395	+	38.8382i	0.237620	+	1.42772i
$741$	−22.5841	+	11.4277i	−0.829647	+	0.419805i
$742$	−0.0618360	−	0.0892206i	−0.00227007	−	0.00327539i
$743$	−4.97552	−	28.2176i	−0.182534	−	1.03520i	−0.929083	−	0.369872i	$-0.879401\pi$
$743$	−4.97552	−	28.2176i	−0.182534	−	1.03520i	0.746548	−	0.665331i	$-0.231710\pi$
$744$	−19.3939	−	6.67274i	−0.711016	−	0.244634i
$745$	−14.5681	−	12.2241i	−0.533732	−	0.447855i
$746$	29.5693	+	20.9172i	1.08261	+	0.765832i
$747$	−46.3184	−	5.13058i	−1.69470	−	0.187718i
$748$	−5.34607	+	1.88782i	−0.195472	+	0.0690255i
$749$	−4.72891	−	12.9926i	−0.172791	−	0.474738i
$750$	0.417677	+	15.2948i	0.0152514	+	0.558487i
$751$	9.48329	+	11.3017i	0.346050	+	0.412407i	0.910795	−	0.412859i	$-0.135470\pi$
$751$	9.48329	+	11.3017i	0.346050	+	0.412407i	−0.564745	+	0.825266i	$0.691025\pi$
$752$	5.67674	−	28.9308i	0.207009	−	1.05500i
$753$	4.66404	−	1.41168i	0.169967	−	0.0514444i
$754$	−5.90671	+	1.55231i	−0.215110	+	0.0565319i
$755$	3.36309			0.122395
$756$	−24.8275	+	4.36354i	−0.902968	+	0.158700i
$757$	−16.0275			−0.582531			−0.291265	−	0.956642i	$-0.594076\pi$
$757$	−16.0275			−0.582531			−0.291265	+	0.956642i	$0.594076\pi$
$758$	−32.1339	+	8.44496i	−1.16716	+	0.306735i
$759$	5.17908	−	22.1500i	0.187989	−	0.803995i
$760$	16.0194	−	22.1902i	0.581085	−	0.804922i
$761$	30.3774	+	36.2023i	1.10118	+	1.31233i	0.945898	+	0.324463i	$0.105183\pi$
$761$	30.3774	+	36.2023i	1.10118	+	1.31233i	0.155280	+	0.987871i	$0.450372\pi$
$762$	42.5822	−	26.1602i	1.54259	−	0.947683i
$763$	8.13002	+	22.3370i	0.294326	+	0.808655i
$764$	14.4908	+	41.0362i	0.524259	+	1.48464i
$765$	2.75023	−	9.39243i	0.0994348	−	0.339584i
$766$	−9.68742	−	6.85282i	−0.350021	−	0.247602i
$767$	30.7861	+	25.8326i	1.11162	+	0.932761i
$768$	7.34215	−	26.7225i	0.264937	−	0.964266i
$769$	3.50396	+	19.8720i	0.126356	+	0.716602i	0.980493	+	0.196553i	$0.0629749\pi$
$769$	3.50396	+	19.8720i	0.126356	+	0.716602i	−0.854137	+	0.520048i	$0.825914\pi$
$770$	20.0655	+	28.9517i	0.723111	+	1.04335i
$771$	27.9880	+	18.2872i	1.00796	+	0.658596i
$772$	−5.11198	+	0.850801i	−0.183984	+	0.0306210i
$773$	31.6981	−	18.3009i	1.14010	−	0.658237i	0.193644	−	0.981072i	$-0.437969\pi$
$773$	31.6981	−	18.3009i	1.14010	−	0.658237i	0.946455	+	0.322835i	$0.104636\pi$
$774$	−4.63018	+	11.6968i	−0.166428	+	0.420434i
$775$	−24.7163	−	14.2700i	−0.887837	−	0.512593i
$776$	2.29892	+	31.5015i	0.0825263	+	1.13084i
$777$	−23.8887	+	2.86532i	−0.857004	+	0.102793i
$778$	−5.71156	−	2.69684i	−0.204769	−	0.0966863i
$779$	17.2369	+	6.27373i	0.617577	+	0.224780i
$780$	−49.8310	+	36.5896i	−1.78423	+	1.31012i
$781$	−0.851642	+	4.82990i	−0.0304741	+	0.172827i
$782$	2.46796	+	5.35965i	0.0882540	+	0.191661i
$783$	−3.28581	+	2.80822i	−0.117425	+	0.100358i
$784$	−0.690664	−	4.41120i	−0.0246666	−	0.157543i
$785$	41.9029	+	7.38860i	1.49558	+	0.263711i
$786$	−11.4363	+	10.1409i	−0.407920	+	0.361713i
$787$	1.37262	−	3.77124i	0.0489285	−	0.134430i	−0.912821	−	0.408359i	$-0.866101\pi$
$787$	1.37262	−	3.77124i	0.0489285	−	0.134430i	0.961750	+	0.273929i	$0.0883233\pi$
$788$	47.8827	+	0.460249i	1.70575	+	0.0163957i
$789$	6.52681	+	2.79205i	0.232360	+	0.0993997i
$790$	3.11116	−	3.08140i	0.110690	−	0.109631i
$791$	15.2613	−	26.4334i	0.542630	−	0.939863i
$792$	25.1091	−	3.46327i	0.892214	−	0.123062i
$793$	−31.5309	−	54.6131i	−1.11969	−	1.93937i
$794$	−49.0921	−	13.4074i	−1.74221	−	0.475810i
$795$	−0.188130	−	0.0103876i	−0.00667229	−	0.000368410i
$796$	12.6912	−	21.5019i	0.449829	−	0.762115i
$797$	−5.80537	+	1.02364i	−0.205637	+	0.0362593i	−0.275518	−	0.961296i	$-0.588849\pi$
$797$	−5.80537	+	1.02364i	−0.205637	+	0.0362593i	0.0698808	+	0.997555i	$0.477738\pi$
$798$	13.1004	+	10.3965i	0.463747	+	0.368033i
$799$	−4.49609	+	5.35824i	−0.159060	+	0.189561i
$800$	17.1326	−	34.5485i	0.605728	−	1.22147i
$801$	6.45071	−	13.0401i	0.227924	−	0.460750i
$802$	17.7601	+	1.63985i	0.627131	+	0.0579052i
$803$	21.1273	−	7.68969i	0.745565	−	0.271363i
$804$	−2.46665	−	0.159991i	−0.0869922	−	0.00564243i
$805$	28.0835	−	23.5649i	0.989813	−	0.830552i
$806$	−2.53174	−	30.6328i	−0.0891769	−	1.07900i
$807$	−14.4858	+	15.4472i	−0.509924	+	0.543767i
$808$	5.35429	−	11.0630i	0.188363	−	0.389196i
$809$			20.8090i			0.731605i	0.930692	+	0.365803i	$0.119205\pi$
$809$			20.8090i			0.731605i	−0.930692	+	0.365803i	$0.880795\pi$
$810$	−20.4849	+	38.6618i	−0.719767	+	1.35844i
$811$			19.7332i			0.692927i	0.938063	+	0.346464i	$0.112618\pi$
$811$			19.7332i			0.692927i	−0.938063	+	0.346464i	$0.887382\pi$
$812$	2.56412	+	3.11615i	0.0899831	+	0.109355i
$813$	−15.7761	+	16.8231i	−0.553290	+	0.590012i
$814$	24.1102	−	1.99266i	0.845063	−	0.0698428i
$815$	50.3497	−	42.2484i	1.76367	−	1.47990i
$816$	−4.58883	+	4.70862i	−0.160641	+	0.164835i
$817$	7.84288	−	2.85457i	0.274388	−	0.0998689i
$818$	0.493473	−	5.34447i	0.0172539	−	0.186865i
$819$	−20.9498	−	31.4375i	−0.732045	−	1.09852i
$820$	44.0459	+	8.20376i	1.53815	+	0.286488i
$821$	35.2141	−	41.9666i	1.22898	−	1.46464i	0.389704	−	0.920940i	$-0.372577\pi$
$821$	35.2141	−	41.9666i	1.22898	−	1.46464i	0.839277	−	0.543703i	$-0.182978\pi$
$822$	7.78867	−	9.81428i	0.271661	−	0.342312i
$823$	42.0385	−	7.41253i	1.46537	−	0.258384i	0.616655	−	0.787234i	$-0.288487\pi$
$823$	42.0385	−	7.41253i	1.46537	−	0.258384i	0.848716	+	0.528849i	$0.177376\pi$
$824$	−1.87280	+	18.3543i	−0.0652420	+	0.639402i
$825$	35.2173	+	1.94452i	1.22611	+	0.0676995i
$826$	6.99616	−	25.6169i	0.243427	−	0.891327i
$827$	−4.60134	−	7.96975i	−0.160004	−	0.277135i	0.774866	−	0.632126i	$-0.217817\pi$
$827$	−4.60134	−	7.96975i	−0.160004	−	0.277135i	−0.934870	+	0.354991i	$0.884484\pi$
$828$	−5.99174	−	25.6900i	−0.208227	−	0.892788i
$829$	−14.3026	+	24.7728i	−0.496748	+	0.860393i	−0.999993	−	0.00375073i	$-0.998806\pi$
$829$	−14.3026	+	24.7728i	−0.496748	+	0.860393i	0.503245	+	0.864144i	$0.332139\pi$
$830$	53.1421	+	53.6553i	1.84459	+	1.86240i
$831$	5.27676	+	2.25730i	0.183049	+	0.0783050i
$832$	41.0922	−	6.02977i	1.42462	−	0.209045i
$833$	−0.362303	+	0.995419i	−0.0125531	+	0.0344892i
$834$	−24.1962	−	27.2871i	−0.837846	−	0.944875i
$835$	−58.1076	−	10.2459i	−2.01090	−	0.354575i
$836$	−12.7777	−	10.9328i	−0.441926	−	0.378117i
$837$	−11.0471	−	18.7401i	−0.381844	−	0.647754i
$838$	38.9687	−	17.9439i	1.34615	−	0.619863i
$839$	2.39387	−	13.5763i	0.0826457	−	0.468707i	−0.915194	−	0.403013i	$-0.867963\pi$
$839$	2.39387	−	13.5763i	0.0826457	−	0.468707i	0.997840	−	0.0656937i	$-0.0209260\pi$
$840$	35.7326	+	19.7958i	1.23289	+	0.683022i
$841$	−26.6009	−	9.68192i	−0.917271	−	0.333859i
$842$	−13.6392	+	28.8862i	−0.470040	+	0.995484i
$843$	−18.9386	+	2.27158i	−0.652282	+	0.0782374i
$844$	7.30178	+	2.73739i	0.251338	+	0.0942250i
$845$	−41.5357	−	23.9807i	−1.42887	−	0.824960i
$846$	24.5054	−	19.4255i	0.842515	−	0.667862i
$847$	−4.36292	+	2.51893i	−0.149912	+	0.0865515i
$848$	0.108384	+	0.0653853i	0.00372193	+	0.00224534i
$849$	−46.2174	−	30.1982i	−1.58618	−	1.03640i
$850$	−7.51963	+	5.21162i	−0.257921	+	0.178757i
$851$	−4.37212	−	24.7955i	−0.149874	−	0.849979i
$852$	1.59523	+	5.45918i	0.0546517	+	0.187028i
$853$	8.44449	+	7.08577i	0.289134	+	0.242612i	0.775804	−	0.630974i	$-0.217344\pi$
$853$	8.44449	+	7.08577i	0.289134	+	0.242612i	−0.486671	+	0.873586i	$0.661789\pi$
$854$	−24.0641	+	34.0180i	−0.823458	+	1.16407i
$855$	28.2051	−	6.86484i	0.964594	−	0.234773i
$856$	11.2346	+	11.5634i	0.383992	+	0.395227i
$857$	8.77810	+	24.1176i	0.299854	+	0.823843i	0.994523	+	0.104514i	$0.0333285\pi$
$857$	8.77810	+	24.1176i	0.299854	+	0.823843i	−0.694669	+	0.719329i	$0.744449\pi$
$858$	19.8842	+	32.3665i	0.678835	+	1.10497i
$859$	−30.2619	−	36.0648i	−1.03252	−	1.23051i	−0.972642	−	0.232309i	$-0.925372\pi$
$859$	−30.2619	−	36.0648i	−1.03252	−	1.23051i	−0.0598818	−	0.998205i	$-0.519072\pi$
$860$	17.7517	−	10.0227i	0.605329	−	0.341772i
$861$	−6.23353	+	26.6597i	−0.212438	+	0.908561i
$862$	0.799445	+	3.04197i	0.0272292	+	0.103610i
$863$	−32.3684			−1.10183			−0.550916	−	0.834561i	$-0.685722\pi$
$863$	−32.3684			−1.10183			−0.550916	+	0.834561i	$0.685722\pi$
$864$	24.3278	−	16.4972i	0.827648	−	0.561247i
$865$	−73.7286			−2.50685
$866$	0.356034	+	1.35475i	0.0120985	+	0.0460361i
$867$	−26.6893	+	8.07811i	−0.906415	+	0.274347i
$868$	−17.6859	+	9.98554i	−0.600298	+	0.338931i
$869$	−1.72948	−	2.06112i	−0.0586686	−	0.0699185i
$870$	7.00175	−	0.191207i	0.237381	−	0.00648252i
$871$	−1.26700	−	3.48105i	−0.0429306	−	0.117951i
$872$	−19.3148	−	19.8799i	−0.654080	−	0.673218i
$873$	−19.8429	+	26.9924i	−0.671582	+	0.913554i
$874$	−10.1073	+	14.2881i	−0.341884	+	0.483301i
$875$	11.6068	+	9.73924i	0.392380	+	0.329246i
$876$	18.0170	−	18.8464i	0.608738	−	0.636761i
$877$	4.78252	+	27.1230i	0.161494	+	0.915880i	0.952606	+	0.304208i	$0.0983918\pi$
$877$	4.78252	+	27.1230i	0.161494	+	0.915880i	−0.791111	+	0.611672i	$0.790497\pi$
$878$	31.4324	−	21.7849i	1.06079	−	0.735204i
$879$	14.8234	−	7.50072i	0.499981	−	0.252993i
$880$	−35.1702	−	21.2172i	−1.18559	−	0.715233i
$881$	−46.3687	+	26.7710i	−1.56220	+	0.901937i	−0.565166	+	0.824977i	$0.691188\pi$
$881$	−46.3687	+	26.7710i	−1.56220	+	0.901937i	−0.997034	+	0.0769590i	$0.975479\pi$
$882$	2.48121	−	4.03377i	0.0835467	−	0.135824i
$883$	−19.4984	−	11.2574i	−0.656175	−	0.378843i	0.134643	−	0.990894i	$-0.457011\pi$
$883$	−19.4984	−	11.2574i	−0.656175	−	0.378843i	−0.790818	+	0.612051i	$0.790345\pi$
$884$	−9.22642	−	3.45893i	−0.310318	−	0.116336i
$885$	−27.6354	−	36.8878i	−0.928955	−	1.23997i
$886$	−23.7165	+	50.2285i	−0.796770	+	1.68746i
$887$	−19.8056	−	7.20866i	−0.665008	−	0.242043i	−0.0126110	−	0.999920i	$-0.504014\pi$
$887$	−19.8056	−	7.20866i	−0.665008	−	0.242043i	−0.652397	+	0.757877i	$0.726237\pi$
$888$	24.0445	−	14.4552i	0.806882	−	0.485083i
$889$	8.59377	−	48.7377i	0.288226	−	1.63461i
$890$	−21.4145	+	9.86072i	−0.717815	+	0.330532i
$891$	22.6383	+	14.5009i	0.758412	+	0.485799i
$892$	44.0906	+	37.7245i	1.47626	+	1.26311i
$893$	−20.4316	−	3.60265i	−0.683719	−	0.120558i
$894$	−4.28535	+	12.8555i	−0.143323	+	0.429951i
$895$	8.61654	−	23.6737i	0.288019	−	0.791326i
$896$	−14.9757	−	22.9968i	−0.500302	−	0.768268i
$897$	31.6397	−	23.7037i	1.05642	−	0.791443i
$898$	−7.93679	−	8.01345i	−0.264854	−	0.267412i
$899$	−1.74126	+	3.01594i	−0.0580741	+	0.100587i
$900$	37.6150	−	16.0663i	1.25383	−	0.535544i
$901$	−0.0150154	−	0.0260075i	−0.000500237	−	0.000866436i
$902$	7.25287	−	26.5569i	0.241494	−	0.884248i
$903$	5.62448	+	11.1155i	0.187171	+	0.369900i
$904$	−3.61280	+	35.4071i	−0.120160	+	1.17762i
$905$	−37.0711	+	6.53663i	−1.23228	+	0.217285i
$906$	−0.880784	−	2.22866i	−0.0292621	−	0.0740424i
$907$	−0.995423	+	1.18630i	−0.0330525	+	0.0393904i	−0.782317	−	0.622880i	$-0.785963\pi$
$907$	−0.995423	+	1.18630i	−0.0330525	+	0.0393904i	0.749265	+	0.662270i	$0.230407\pi$
$908$	−38.4144	−	7.15485i	−1.27483	−	0.237442i
$909$	11.9386	−	5.23553i	0.395979	−	0.173652i
$910$	−5.62871	+	60.9607i	−0.186590	+	2.02083i
$911$	−17.5360	+	6.38258i	−0.580994	+	0.211464i	−0.615764	−	0.787931i	$-0.711152\pi$
$911$	−17.5360	+	6.38258i	−0.580994	+	0.211464i	0.0347700	+	0.999395i	$0.488930\pi$
$912$	−18.9005	−	4.80426i	−0.625858	−	0.159085i
$913$	35.5461	−	29.8267i	1.17640	−	0.987120i
$914$	−32.9848	+	2.72613i	−1.09104	+	0.0901724i
$915$	20.9520	+	69.2233i	0.692652	+	2.28845i
$916$	−6.28332	−	7.63604i	−0.207607	−	0.252302i
$917$			15.1361i			0.499837i
$918$	−6.94448	+	0.637317i	−0.229202	+	0.0210346i
$919$			13.4562i			0.443880i	0.975060	+	0.221940i	$0.0712389\pi$
$919$			13.4562i			0.443880i	−0.975060	+	0.221940i	$0.928761\pi$
$920$	−18.6227	+	38.4783i	−0.613973	+	1.26859i
$921$	15.4366	+	3.60935i	0.508652	+	0.118932i
$922$	1.38220	+	16.7239i	0.0455204	+	0.550774i
$923$	−6.52948	+	5.47888i	−0.214920	+	0.180340i
$924$	13.9307	−	20.8795i	0.458286	−	0.686884i
$925$	36.6852	−	13.3523i	1.20620	−	0.439022i
$926$	−12.6971	−	1.17237i	−0.417252	−	0.0385263i
$927$	−14.1525	+	13.5146i	−0.464828	+	0.443877i
$928$	−4.21569	−	2.09056i	−0.138387	−	0.0686258i
$929$	−0.782138	+	0.932116i	−0.0256611	+	0.0305817i	−0.778722	−	0.627369i	$-0.784132\pi$
$929$	−0.782138	+	0.932116i	−0.0256611	+	0.0305817i	0.753061	+	0.657950i	$0.228576\pi$
$930$	−5.17149	+	34.8708i	−0.169580	+	1.14346i
$931$	−3.09425	+	0.545600i	−0.101410	+	0.0178813i
$932$	−0.553406	+	0.937598i	−0.0181274	+	0.0307120i
$933$	13.4843	−	20.6373i	0.441455	−	0.675634i
$934$	−45.1592	−	12.3333i	−1.47766	−	0.403558i
$935$	4.87245	+	8.43932i	0.159346	+	0.275995i
$936$	37.2979	+	23.4394i	1.21912	+	0.766142i
$937$	−7.56910	+	13.1101i	−0.247272	+	0.428287i	−0.962768	−	0.270330i	$-0.912867\pi$
$937$	−7.56910	+	13.1101i	−0.247272	+	0.428287i	0.715496	+	0.698617i	$0.246201\pi$
$938$	−1.73914	+	1.72250i	−0.0567849	+	0.0562417i
$939$	5.83982	+	48.6878i	0.190575	+	1.58887i
$940$	−50.6721	−	0.487061i	−1.65274	−	0.0158862i
$941$	1.24988	−	3.43402i	0.0407449	−	0.111946i	−0.917652	−	0.397386i	$-0.869917\pi$
$941$	1.24988	−	3.43402i	0.0407449	−	0.111946i	0.958397	+	0.285440i	$0.0921397\pi$
$942$	−6.07793	−	29.7034i	−0.198030	−	0.967789i
$943$	−28.2158	−	4.97520i	−0.918832	−	0.162015i
$944$	4.78978	+	30.5919i	0.155894	+	0.995681i
$945$	15.1870	+	40.5788i	0.494034	+	1.32003i
$946$	−5.23912	−	11.3778i	−0.170338	−	0.369923i
$947$	−0.855100	+	4.84951i	−0.0277870	+	0.157588i	−0.995544	−	0.0942975i	$-0.969940\pi$
$947$	−0.855100	+	4.84951i	−0.0277870	+	0.157588i	0.967757	+	0.251885i	$0.0810506\pi$
$948$	−2.85680	−	1.25471i	−0.0927846	−	0.0407510i
$949$	36.7182	+	13.3643i	1.19192	+	0.433824i
$950$	−24.5391	−	11.5867i	−0.796153	−	0.375921i
$951$	4.57622	−	10.6975i	0.148394	−	0.346892i
$952$	0.473888	+	6.49357i	0.0153588	+	0.210458i
$953$	9.65515	+	5.57440i	0.312761	+	0.180573i	0.648161	−	0.761503i	$-0.275538\pi$
$953$	9.65515	+	5.57440i	0.312761	+	0.180573i	−0.335400	+	0.942076i	$0.608872\pi$
$954$	0.0423871	+	0.127391i	0.00137233	+	0.00412444i
$955$	64.7799	−	37.4007i	2.09623	−	1.21026i
$956$	−32.9190	+	5.47881i	−1.06468	+	0.177197i
$957$	0.237275	−	4.29729i	0.00767000	−	0.138912i
$958$	−1.53039	−	2.20814i	−0.0494448	−	0.0713418i
$959$	−2.15451	−	12.2189i	−0.0695729	−	0.394567i
$960$	−47.4648	−	3.99617i	−1.53192	−	0.128976i
$961$	10.3208	+	8.66021i	0.332930	+	0.279362i
$962$	34.3252	+	24.2814i	1.10669	+	0.782865i
$963$	1.09734	+	17.0650i	0.0353613	+	0.549913i
$964$	15.6544	+	44.3314i	0.504195	+	1.42782i
$965$	3.04648	+	8.37014i	0.0980698	+	0.269444i
$966$	−22.9710	−	12.4389i	−0.739081	−	0.400215i
$967$	6.48767	+	7.73171i	0.208630	+	0.248635i	0.860204	−	0.509949i	$-0.170336\pi$
$967$	6.48767	+	7.73171i	0.208630	+	0.248635i	−0.651575	+	0.758584i	$0.725891\pi$
$968$	3.43844	−	4.76295i	0.110516	−	0.153087i
$969$	3.37492	+	3.16487i	0.108418	+	0.101670i
$970$	52.5058	−	13.7988i	1.68586	−	0.443052i
$971$	−5.97185			−0.191646			−0.0958229	−	0.995398i	$-0.530548\pi$
$971$	−5.97185			−0.191646			−0.0958229	+	0.995398i	$0.530548\pi$
$972$	30.9855	+	3.44961i	0.993860	+	0.110646i
$973$	−36.1148			−1.15779
$974$	−16.3791	+	4.30450i	−0.524819	+	0.137925i
$975$	44.7142	+	41.9313i	1.43200	+	1.34287i
$976$	9.35547	−	47.6790i	0.299461	−	1.52617i
$977$	17.1521	+	20.4411i	0.548745	+	0.653968i	0.967124	−	0.254304i	$-0.0818463\pi$
$977$	17.1521	+	20.4411i	0.548745	+	0.653968i	−0.418380	+	0.908272i	$0.637402\pi$
$978$	−41.1837	−	22.3012i	−1.31691	−	0.713113i
$979$	4.95454	+	13.6125i	0.158348	+	0.435057i
$980$	−7.23642	+	2.55534i	−0.231159	+	0.0816274i
$981$	−1.88656	−	29.3385i	−0.0602334	−	0.936705i
$982$	−28.1381	−	19.9047i	−0.897923	−	0.635186i
$983$	18.8027	+	15.7773i	0.599713	+	0.503219i	0.891353	−	0.453309i	$-0.149757\pi$
$983$	18.8027	+	15.7773i	0.599713	+	0.503219i	−0.291641	+	0.956528i	$0.594201\pi$
$984$	−6.09900	−	31.3370i	−0.194429	−	0.998989i
$985$	−14.2920	−	81.0541i	−0.455382	−	2.58260i
$986$	0.635934	+	0.917562i	0.0202523	+	0.0292211i
$987$	1.70721	−	30.9194i	0.0543412	−	0.984175i
$988$	−4.79821	−	28.8297i	−0.152652	−	0.917196i
$989$	−11.2898	+	6.51817i	−0.358995	+	0.207266i
$990$	−13.7544	−	41.3379i	−0.437144	−	1.31381i
$991$	−47.4532	−	27.3971i	−1.50740	−	0.870299i	−0.999963	−	0.00861092i	$-0.997259\pi$
$991$	−47.4532	−	27.3971i	−1.50740	−	0.870299i	−0.507439	−	0.861688i	$-0.669408\pi$
$992$	14.0460	−	19.0677i	0.445961	−	0.605400i
$993$	−9.96389	+	23.2920i	−0.316194	+	0.739148i
$994$	5.09293	+	2.40474i	0.161538	+	0.0762737i
$995$	−40.3268	−	14.6778i	−1.27845	−	0.465317i
$996$	21.6387	−	49.2685i	0.685650	−	1.56113i
$997$	−1.38709	+	7.86659i	−0.0439297	+	0.249137i	−0.998862	−	0.0476847i	$-0.984816\pi$
$997$	−1.38709	+	7.86659i	−0.0439297	+	0.249137i	0.954933	+	0.296822i	$0.0959268\pi$
$998$	−16.0841	−	34.9298i	−0.509134	−	1.10568i
$999$	29.3505	+	4.90165i	0.928608	+	0.155081i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.2.l.a.83.8	yes	96
3.2	odd	2		324.2.l.a.251.9		96
4.3	odd	2	inner	108.2.l.a.83.6	✓	96
9.2	odd	6		972.2.l.a.431.13		96
9.4	even	3		972.2.l.c.107.14		96
9.5	odd	6		972.2.l.b.107.3		96
9.7	even	3		972.2.l.d.431.4		96
12.11	even	2		324.2.l.a.251.11		96
27.4	even	9		972.2.l.b.863.12		96
27.5	odd	18		972.2.l.d.539.16		96
27.13	even	9		324.2.l.a.71.11		96
27.14	odd	18	inner	108.2.l.a.95.6	yes	96
27.22	even	9		972.2.l.a.539.1		96
27.23	odd	18		972.2.l.c.863.5		96
36.7	odd	6		972.2.l.d.431.16		96
36.11	even	6		972.2.l.a.431.1		96
36.23	even	6		972.2.l.b.107.12		96
36.31	odd	6		972.2.l.c.107.5		96
108.23	even	18		972.2.l.c.863.14		96
108.31	odd	18		972.2.l.b.863.3		96
108.59	even	18		972.2.l.d.539.4		96
108.67	odd	18		324.2.l.a.71.9		96
108.95	even	18	inner	108.2.l.a.95.8	yes	96
108.103	odd	18		972.2.l.a.539.13		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.83.6	✓	96	4.3	odd	2	inner
108.2.l.a.83.8	yes	96	1.1	even	1	trivial
108.2.l.a.95.6	yes	96	27.14	odd	18	inner
108.2.l.a.95.8	yes	96	108.95	even	18	inner
324.2.l.a.71.9		96	108.67	odd	18
324.2.l.a.71.11		96	27.13	even	9
324.2.l.a.251.9		96	3.2	odd	2
324.2.l.a.251.11		96	12.11	even	2
972.2.l.a.431.1		96	36.11	even	6
972.2.l.a.431.13		96	9.2	odd	6
972.2.l.a.539.1		96	27.22	even	9
972.2.l.a.539.13		96	108.103	odd	18
972.2.l.b.107.3		96	9.5	odd	6
972.2.l.b.107.12		96	36.23	even	6
972.2.l.b.863.3		96	108.31	odd	18
972.2.l.b.863.12		96	27.4	even	9
972.2.l.c.107.5		96	36.31	odd	6
972.2.l.c.107.14		96	9.4	even	3
972.2.l.c.863.5		96	27.23	odd	18
972.2.l.c.863.14		96	108.23	even	18
972.2.l.d.431.4		96	9.7	even	3
972.2.l.d.431.16		96	36.7	odd	6
972.2.l.d.539.4		96	108.59	even	18
972.2.l.d.539.16		96	27.5	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.359456 - 1.36777i) q^{2} +(1.26343 + 1.18480i) q^{3} +(-1.74158 + 0.983306i) q^{4} +(2.20965 + 2.63335i) q^{5} +(1.16638 - 2.15396i) q^{6} +(-0.829620 - 2.27936i) q^{7} +(1.97096 + 2.02863i) q^{8} +(0.192513 + 2.99382i) q^{9} +O(q^{10})\)	\(q+(-0.359456 - 1.36777i) q^{2} +(1.26343 + 1.18480i) q^{3} +(-1.74158 + 0.983306i) q^{4} +(2.20965 + 2.63335i) q^{5} +(1.16638 - 2.15396i) q^{6} +(-0.829620 - 2.27936i) q^{7} +(1.97096 + 2.02863i) q^{8} +(0.192513 + 2.99382i) q^{9} +(2.80755 - 3.96886i) q^{10} +(-2.28829 - 1.92011i) q^{11} +(-3.36539 - 0.821083i) q^{12} +(-0.901500 - 5.11266i) q^{13} +(-2.81943 + 1.95406i) q^{14} +(-0.328255 + 5.94504i) q^{15} +(2.06622 - 3.42502i) q^{16} +(-0.821854 + 0.474498i) q^{17} +(4.02565 - 1.33946i) q^{18} +(-2.43769 - 1.40740i) q^{19} +(-6.43767 - 2.41344i) q^{20} +(1.65241 - 3.86275i) q^{21} +(-1.80372 + 3.82005i) q^{22} +(4.13143 + 1.50372i) q^{23} +(0.0866582 + 4.89821i) q^{24} +(-1.18377 + 6.71352i) q^{25} +(-6.66889 + 3.07082i) q^{26} +(-3.30384 + 4.01057i) q^{27} +(3.68616 + 3.15393i) q^{28} +(0.819198 + 0.144447i) q^{29} +(8.24943 - 1.68800i) q^{30} +(-1.43188 + 3.93406i) q^{31} +(-5.42735 - 1.59496i) q^{32} +(-0.616163 - 5.13708i) q^{33} +(0.944424 + 0.953546i) q^{34} +(4.16920 - 7.22127i) q^{35} +(-3.27912 - 5.02468i) q^{36} +(-2.86337 - 4.95950i) q^{37} +(-1.04876 + 3.84010i) q^{38} +(4.91848 - 7.52758i) q^{39} +(-0.986971 + 9.67277i) q^{40} +(-6.41767 + 1.13161i) q^{41} +(-5.87732 - 0.871632i) q^{42} +(-1.90594 + 2.27141i) q^{43} +(5.87330 + 1.09393i) q^{44} +(-7.45839 + 7.12223i) q^{45} +(0.571669 - 6.19136i) q^{46} +(6.92611 - 2.52090i) q^{47} +(6.66847 - 1.87922i) q^{48} +(0.855086 - 0.717502i) q^{49} +(9.60805 - 0.794086i) q^{50} +(-1.60054 - 0.374236i) q^{51} +(6.59735 + 8.01767i) q^{52} +0.0316449i q^{53} +(6.67311 + 3.07726i) q^{54} -10.2686i q^{55} +(2.98883 - 6.17552i) q^{56} +(-1.41237 - 4.66632i) q^{57} +(-0.0968962 - 1.17240i) q^{58} +(-5.93006 + 4.97591i) q^{59} +(-5.27411 - 10.6766i) q^{60} +(11.4145 - 4.15453i) q^{61} +(5.89558 + 0.544359i) q^{62} +(6.66428 - 2.92254i) q^{63} +(-0.230649 + 7.99667i) q^{64} +(11.4714 - 13.6711i) q^{65} +(-6.80485 + 2.68933i) q^{66} +(0.702717 - 0.123908i) q^{67} +(0.964751 - 1.63451i) q^{68} +(3.43817 + 6.79475i) q^{69} +(-11.3757 - 3.10677i) q^{70} +(-0.820917 - 1.42187i) q^{71} +(-5.69390 + 6.29122i) q^{72} +(-3.76331 + 6.51824i) q^{73} +(-5.75419 + 5.69914i) q^{74} +(-9.44977 + 7.07953i) q^{75} +(5.62935 + 0.0541094i) q^{76} +(-2.47820 + 6.80881i) q^{77} +(-12.0640 - 4.02151i) q^{78} +(0.887038 + 0.156409i) q^{79} +(13.5849 - 2.12699i) q^{80} +(-8.92588 + 1.15270i) q^{81} +(3.85465 + 8.37112i) q^{82} +(-2.69743 + 15.2979i) q^{83} +(0.920447 + 8.35212i) q^{84} +(-3.06553 - 1.11576i) q^{85} +(3.79186 + 1.79041i) q^{86} +(0.863860 + 1.15308i) q^{87} +(-0.614952 - 8.42654i) q^{88} +(-4.19977 - 2.42474i) q^{89} +(12.4225 + 7.64122i) q^{90} +(-10.9057 + 6.29641i) q^{91} +(-8.67384 + 1.44361i) q^{92} +(-6.47014 + 3.27392i) q^{93} +(-5.93764 - 8.56716i) q^{94} +(-1.68025 - 9.52916i) q^{95} +(-4.96737 - 8.44543i) q^{96} +(8.55448 + 7.17806i) q^{97} +(-1.28874 - 0.911649i) q^{98} +(5.30792 - 7.22037i) 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

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