LMFDB - Embedded newform 603.2.u.b.478.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [603,2,Mod(64,603)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(603, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("603.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 603 = 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	603.u (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:	$4.81497924188$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 67)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			478.1
Root			$0.959493 + 0.281733i$ of defining polynomial
Character	$\chi$	$=$	603.478
Dual form			603.2.u.b.82.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.01722 + 1.29639i) q^{2} +(1.55773 + 3.41095i) q^{4} +(-1.75667 + 2.02730i) q^{5} +(-0.938384 - 0.603063i) q^{7} +(-0.597131 + 4.15314i) q^{8} +O(q^{10})$	\(q+(2.01722 + 1.29639i) q^{2} +(1.55773 + 3.41095i) q^{4} +(-1.75667 + 2.02730i) q^{5} +(-0.938384 - 0.603063i) q^{7} +(-0.597131 + 4.15314i) q^{8} +(-6.17177 + 1.81219i) q^{10} +(-2.74302 + 3.16561i) q^{11} +(0.736164 + 5.12013i) q^{13} +(-1.11113 - 2.43303i) q^{14} +(-1.67742 + 1.93584i) q^{16} +(3.20004 - 7.00712i) q^{17} +(0.207501 - 0.133353i) q^{19} +(-9.65145 - 2.83392i) q^{20} +(-9.63714 + 2.82972i) q^{22} +(2.78922 + 0.818988i) q^{23} +(-0.312501 - 2.17349i) q^{25} +(-5.15269 + 11.2828i) q^{26} +(0.595270 - 4.14019i) q^{28} +0.379927 q^{29} +(-1.27013 + 8.83397i) q^{31} +(2.15843 - 0.633773i) q^{32} +(15.5392 - 9.98642i) q^{34} +(2.87102 - 0.843008i) q^{35} +5.05770 q^{37} +0.591454 q^{38} +(-7.37071 - 8.50625i) q^{40} +(0.891527 - 1.95217i) q^{41} +(2.84464 - 6.22889i) q^{43} +(-15.0706 - 4.42513i) q^{44} +(4.56474 + 5.26800i) q^{46} +(6.36350 + 1.86849i) q^{47} +(-2.39102 - 5.23561i) q^{49} +(2.18731 - 4.78954i) q^{50} +(-16.3178 + 10.4868i) q^{52} +(-2.32167 - 5.08374i) q^{53} +(-1.59908 - 11.1219i) q^{55} +(3.06494 - 3.53713i) q^{56} +(0.766398 + 0.492534i) q^{58} +(-1.02417 + 7.12328i) q^{59} +(0.986760 + 1.13878i) q^{61} +(-14.0144 + 16.1735i) q^{62} +(10.0911 + 2.96302i) q^{64} +(-11.6733 - 7.50195i) q^{65} +(7.52388 - 3.22355i) q^{67} +28.8858 q^{68} +(6.88436 + 2.02143i) q^{70} +(1.11816 + 2.44844i) q^{71} +(-5.12343 - 5.91275i) q^{73} +(10.2025 + 6.55675i) q^{74} +(0.778092 + 0.500049i) q^{76} +(4.48307 - 1.31635i) q^{77} +(-0.725553 - 5.04634i) q^{79} +(-0.977875 - 6.80127i) q^{80} +(4.32918 - 2.78220i) q^{82} +(2.54401 - 2.93594i) q^{83} +(8.58414 + 18.7967i) q^{85} +(13.8133 - 8.87729i) q^{86} +(-11.5093 - 13.2824i) q^{88} +(-12.5532 + 3.68596i) q^{89} +(2.39696 - 5.24861i) q^{91} +(1.55132 + 10.7896i) q^{92} +(10.4143 + 12.0187i) q^{94} +(-0.0941640 + 0.654925i) q^{95} -6.90141 q^{97} +(1.96417 - 13.6611i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 6 q^{2} + 10 q^{4} - 3 q^{5} - 6 q^{8}+O(q^{10}) $ 10 * q + 6 * q^2 + 10 * q^4 - 3 * q^5 - 6 * q^8	$ 10 q + 6 q^{2} + 10 q^{4} - 3 q^{5} - 6 q^{8} - 15 q^{10} - 15 q^{11} - 18 q^{13} - 6 q^{16} + 26 q^{17} - q^{19} - 25 q^{20} - 9 q^{22} + 6 q^{23} - 4 q^{25} - 24 q^{26} + 11 q^{28} - 28 q^{29} - 10 q^{31} + 4 q^{32} + 64 q^{34} - 22 q^{37} + 6 q^{38} - 18 q^{40} - 9 q^{41} + 21 q^{43} - 48 q^{44} - 25 q^{46} + 22 q^{47} + 7 q^{49} + 35 q^{50} - 62 q^{52} - 20 q^{53} - 23 q^{55} + 11 q^{56} - 8 q^{58} + 17 q^{59} + 13 q^{61} - 50 q^{62} + 10 q^{64} - 10 q^{65} + 23 q^{67} + 114 q^{68} + 11 q^{70} - q^{71} - 18 q^{73} - 22 q^{74} + 21 q^{76} + 22 q^{77} + 5 q^{79} - 18 q^{80} - 12 q^{82} + 12 q^{83} + 23 q^{85} + 61 q^{86} - 2 q^{88} - 51 q^{89} - 11 q^{91} - 38 q^{92} + 11 q^{94} - 3 q^{95} - 10 q^{97} + 2 q^{98}+O(q^{100}) $ 10 * q + 6 * q^2 + 10 * q^4 - 3 * q^5 - 6 * q^8 - 15 * q^10 - 15 * q^11 - 18 * q^13 - 6 * q^16 + 26 * q^17 - q^19 - 25 * q^20 - 9 * q^22 + 6 * q^23 - 4 * q^25 - 24 * q^26 + 11 * q^28 - 28 * q^29 - 10 * q^31 + 4 * q^32 + 64 * q^34 - 22 * q^37 + 6 * q^38 - 18 * q^40 - 9 * q^41 + 21 * q^43 - 48 * q^44 - 25 * q^46 + 22 * q^47 + 7 * q^49 + 35 * q^50 - 62 * q^52 - 20 * q^53 - 23 * q^55 + 11 * q^56 - 8 * q^58 + 17 * q^59 + 13 * q^61 - 50 * q^62 + 10 * q^64 - 10 * q^65 + 23 * q^67 + 114 * q^68 + 11 * q^70 - q^71 - 18 * q^73 - 22 * q^74 + 21 * q^76 + 22 * q^77 + 5 * q^79 - 18 * q^80 - 12 * q^82 + 12 * q^83 + 23 * q^85 + 61 * q^86 - 2 * q^88 - 51 * q^89 - 11 * q^91 - 38 * q^92 + 11 * q^94 - 3 * q^95 - 10 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/603\mathbb{Z}\right)^\times$.

$n$	$136$	$470$
$\chi(n)$	$e\left(\frac{2}{11}\right)$	$1$

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 $

$2$	2.01722	+	1.29639i	1.42639	+	0.916686i	0.999926	+	0.0121829i	$0.00387804\pi$
$2$	2.01722	+	1.29639i	1.42639	+	0.916686i	0.426466	+	0.904504i	$0.359758\pi$
$3$		0			0
$3$		0			0
$4$	1.55773	+	3.41095i	0.778865	+	1.70548i
$5$	−1.75667	+	2.02730i	−0.785606	+	0.906638i	−0.997501	−	0.0706548i	$-0.977491\pi$
$5$	−1.75667	+	2.02730i	−0.785606	+	0.906638i	0.211895	+	0.977292i	$0.432037\pi$
$6$		0			0
$7$	−0.938384	−	0.603063i	−0.354676	−	0.227936i	0.351154	−	0.936318i	$-0.385789\pi$
$7$	−0.938384	−	0.603063i	−0.354676	−	0.227936i	−0.705830	+	0.708381i	$0.749426\pi$
$8$	−0.597131	+	4.15314i	−0.211118	+	1.46836i
$9$		0			0
$10$	−6.17177	+	1.81219i	−1.95168	+	0.573066i
$11$	−2.74302	+	3.16561i	−0.827051	+	0.954467i	−0.999533	−	0.0305452i	$-0.990276\pi$
$11$	−2.74302	+	3.16561i	−0.827051	+	0.954467i	0.172483	+	0.985013i	$0.444821\pi$
$12$		0			0
$13$	0.736164	+	5.12013i	0.204175	+	1.42007i	0.791723	+	0.610880i	$0.209184\pi$
$13$	0.736164	+	5.12013i	0.204175	+	1.42007i	−0.587548	+	0.809189i	$0.699907\pi$
$14$	−1.11113	−	2.43303i	−0.296961	−	0.650253i
$15$		0			0
$16$	−1.67742	+	1.93584i	−0.419354	+	0.483961i
$17$	3.20004	−	7.00712i	0.776125	−	1.69948i	0.0634466	−	0.997985i	$-0.479791\pi$
$17$	3.20004	−	7.00712i	0.776125	−	1.69948i	0.712678	−	0.701491i	$-0.247482\pi$
$18$		0			0
$19$	0.207501	−	0.133353i	0.0476041	−	0.0305933i	−0.516622	−	0.856213i	$-0.672811\pi$
$19$	0.207501	−	0.133353i	0.0476041	−	0.0305933i	0.564226	+	0.825620i	$0.309175\pi$
$20$	−9.65145	−	2.83392i	−2.15813	−	0.633684i
$21$		0			0
$22$	−9.63714	+	2.82972i	−2.05465	+	0.603298i
$23$	2.78922	+	0.818988i	0.581592	+	0.170771i	0.559278	−	0.828980i	$-0.311078\pi$
$23$	2.78922	+	0.818988i	0.581592	+	0.170771i	0.0223140	+	0.999751i	$0.492897\pi$
$24$		0			0
$25$	−0.312501	−	2.17349i	−0.0625002	−	0.434699i
$26$	−5.15269	+	11.2828i	−1.01052	+	2.21274i
$27$		0			0
$28$	0.595270	−	4.14019i	0.112495	−	0.782423i
$29$	0.379927			0.0705508			0.0352754	−	0.999378i	$-0.488769\pi$
$29$	0.379927			0.0705508			0.0352754	+	0.999378i	$0.488769\pi$
$30$		0			0
$31$	−1.27013	+	8.83397i	−0.228123	+	1.58663i	0.477884	+	0.878423i	$0.341404\pi$
$31$	−1.27013	+	8.83397i	−0.228123	+	1.58663i	−0.706007	+	0.708205i	$0.749505\pi$
$32$	2.15843	−	0.633773i	0.381560	−	0.112036i
$33$		0			0
$34$	15.5392	−	9.98642i	2.66495	−	1.71266i
$35$	2.87102	−	0.843008i	0.485291	−	0.142494i
$36$		0			0
$37$	5.05770			0.831481			0.415740	−	0.909483i	$-0.363523\pi$
$37$	5.05770			0.831481			0.415740	+	0.909483i	$0.363523\pi$
$38$	0.591454			0.0959465
$39$		0			0
$40$	−7.37071	−	8.50625i	−1.16541	−	1.34496i
$41$	0.891527	−	1.95217i	0.139233	−	0.304878i	−0.827151	−	0.561979i	$-0.810040\pi$
$41$	0.891527	−	1.95217i	0.139233	−	0.304878i	0.966384	+	0.257101i	$0.0827674\pi$
$42$		0			0
$43$	2.84464	−	6.22889i	0.433803	−	0.949896i	−0.558891	−	0.829241i	$-0.688773\pi$
$43$	2.84464	−	6.22889i	0.433803	−	0.949896i	0.992694	−	0.120655i	$-0.0384996\pi$
$44$	−15.0706	−	4.42513i	−2.27198	−	0.667114i
$45$		0			0
$46$	4.56474	+	5.26800i	0.673035	+	0.776724i
$47$	6.36350	+	1.86849i	0.928211	+	0.272547i	0.710688	−	0.703508i	$-0.248384\pi$
$47$	6.36350	+	1.86849i	0.928211	+	0.272547i	0.217524	+	0.976055i	$0.430202\pi$
$48$		0			0
$49$	−2.39102	−	5.23561i	−0.341575	−	0.747945i
$50$	2.18731	−	4.78954i	0.309333	−	0.677344i
$51$		0			0
$52$	−16.3178	+	10.4868i	−2.26287	+	1.45426i
$53$	−2.32167	−	5.08374i	−0.318906	−	0.698306i	0.680501	−	0.732747i	$-0.261762\pi$
$53$	−2.32167	−	5.08374i	−0.318906	−	0.698306i	−0.999407	+	0.0344411i	$0.989035\pi$
$54$		0			0
$55$	−1.59908	−	11.1219i	−0.215620	−	1.49967i
$56$	3.06494	−	3.53713i	0.409570	−	0.472669i
$57$		0			0
$58$	0.766398	+	0.492534i	0.100633	+	0.0646729i
$59$	−1.02417	+	7.12328i	−0.133336	+	0.927372i	0.807827	+	0.589419i	$0.200643\pi$
$59$	−1.02417	+	7.12328i	−0.133336	+	0.927372i	−0.941163	+	0.337953i	$0.890266\pi$
$60$		0			0
$61$	0.986760	+	1.13878i	0.126342	+	0.145806i	0.815396	−	0.578904i	$-0.196519\pi$
$61$	0.986760	+	1.13878i	0.126342	+	0.145806i	−0.689054	+	0.724710i	$0.741974\pi$
$62$	−14.0144	+	16.1735i	−1.77983	+	2.05404i
$63$		0			0
$64$	10.0911	+	2.96302i	1.26139	+	0.370377i
$65$	−11.6733	−	7.50195i	−1.44789	−	0.930502i
$66$		0			0
$67$	7.52388	−	3.22355i	0.919188	−	0.393819i
$67$	7.52388	−	3.22355i	0.919188	−	0.393819i
$68$	28.8858			3.50291
$69$		0			0
$70$	6.88436	+	2.02143i	0.822838	+	0.241607i
$71$	1.11816	+	2.44844i	0.132702	+	0.290576i	0.964305	−	0.264794i	$-0.0853039\pi$
$71$	1.11816	+	2.44844i	0.132702	+	0.290576i	−0.831603	+	0.555370i	$0.812577\pi$
$72$		0			0
$73$	−5.12343	−	5.91275i	−0.599652	−	0.692035i	0.372059	−	0.928209i	$-0.378652\pi$
$73$	−5.12343	−	5.91275i	−0.599652	−	0.692035i	−0.971711	+	0.236174i	$0.924106\pi$
$74$	10.2025	+	6.55675i	1.18602	+	0.762207i
$75$		0			0
$76$	0.778092	+	0.500049i	0.0892533	+	0.0573596i
$77$	4.48307	−	1.31635i	0.510893	−	0.150012i
$78$		0			0
$79$	−0.725553	−	5.04634i	−0.0816311	−	0.567757i	−0.989056	−	0.147542i	$-0.952864\pi$
$79$	−0.725553	−	5.04634i	−0.0816311	−	0.567757i	0.907425	−	0.420215i	$-0.138045\pi$
$80$	−0.977875	−	6.80127i	−0.109330	−	0.760405i
$81$		0			0
$82$	4.32918	−	2.78220i	0.478078	−	0.307242i
$83$	2.54401	−	2.93594i	0.279241	−	0.322261i	−0.598752	−	0.800934i	$-0.704337\pi$
$83$	2.54401	−	2.93594i	0.279241	−	0.322261i	0.877993	+	0.478673i	$0.158882\pi$
$84$		0			0
$85$	8.58414	+	18.7967i	0.931081	+	2.03878i
$86$	13.8133	−	8.87729i	1.48953	−	0.957263i
$87$		0			0
$88$	−11.5093	−	13.2824i	−1.22689	−	1.41591i
$89$	−12.5532	+	3.68596i	−1.33064	+	0.390711i	−0.868320	−	0.496004i	$-0.834800\pi$
$89$	−12.5532	+	3.68596i	−1.33064	+	0.390711i	−0.462318	+	0.886714i	$0.652982\pi$
$90$		0			0
$91$	2.39696	−	5.24861i	0.251270	−	0.550204i
$92$	1.55132	+	10.7896i	0.161736	+	1.12490i
$93$		0			0
$94$	10.4143	+	12.0187i	1.07415	+	1.23964i
$95$	−0.0941640	+	0.654925i	−0.00966103	+	0.0671939i
$96$		0			0
$97$	−6.90141			−0.700732			−0.350366	−	0.936613i	$-0.613943\pi$
$97$	−6.90141			−0.700732			−0.350366	+	0.936613i	$0.613943\pi$
$98$	1.96417	−	13.6611i	0.198411	−	1.37998i
$99$		0			0
$100$	6.92689	−	4.45164i	0.692689	−	0.445164i
$101$	3.87267	−	2.48881i	0.385345	−	0.247646i	−0.333598	−	0.942716i	$-0.608263\pi$
$101$	3.87267	−	2.48881i	0.385345	−	0.247646i	0.718943	+	0.695069i	$0.244626\pi$
$102$		0			0
$103$	−0.897824	+	6.24450i	−0.0884652	+	0.615289i	0.896566	+	0.442911i	$0.146054\pi$
$103$	−0.897824	+	6.24450i	−0.0884652	+	0.615289i	−0.985031	+	0.172378i	$0.944855\pi$
$104$	−21.7042			−2.12827
$105$		0			0
$106$	1.90719	−	13.2648i	0.185243	−	1.28839i
$107$	7.98332	+	9.21324i	0.771776	+	0.890678i	0.996487	−	0.0837481i	$-0.0266891\pi$
$107$	7.98332	+	9.21324i	0.771776	+	0.890678i	−0.224711	+	0.974426i	$0.572144\pi$
$108$		0			0
$109$	0.0818433	+	0.569233i	0.00783917	+	0.0545226i	0.993366	−	0.115000i	$-0.0366867\pi$
$109$	0.0818433	+	0.569233i	0.00783917	+	0.0545226i	−0.985526	+	0.169522i	$0.945778\pi$
$110$	11.1926	−	24.5083i	1.06717	−	2.33677i
$111$		0			0
$112$	2.74150	−	0.804977i	0.259047	−	0.0760631i
$113$	−0.251521	−	0.290271i	−0.0236611	−	0.0273064i	0.743796	−	0.668407i	$-0.233024\pi$
$113$	−0.251521	−	0.290271i	−0.0236611	−	0.0273064i	−0.767457	+	0.641101i	$0.778478\pi$
$114$		0			0
$115$	−6.56007	+	4.21590i	−0.611729	+	0.393135i
$116$	0.591824	+	1.29591i	0.0549495	+	0.120323i
$117$		0			0
$118$	−11.3005	+	13.0415i	−1.04030	+	1.20057i
$119$	−7.22861	+	4.64554i	−0.662645	+	0.425856i
$120$		0			0
$121$	−0.931483	−	6.47861i	−0.0846803	−	0.588964i
$122$	0.514209	+	3.57640i	0.0465543	+	0.323792i
$123$		0			0
$124$	−32.1108	+	9.42858i	−2.88363	+	0.846711i
$125$	−6.32805	−	4.06679i	−0.565998	−	0.363745i
$126$		0			0
$127$	4.73815	+	3.04502i	0.420443	+	0.270202i	0.733710	−	0.679463i	$-0.237787\pi$
$127$	4.73815	+	3.04502i	0.420443	+	0.270202i	−0.313267	+	0.949665i	$0.601423\pi$
$128$	13.5685	+	15.6589i	1.19930	+	1.38406i
$129$		0			0
$130$	−13.8221	−	30.2662i	−1.21228	−	2.65452i
$131$	−4.10713	−	1.20596i	−0.358842	−	0.105365i	0.0973421	−	0.995251i	$-0.468966\pi$
$131$	−4.10713	−	1.20596i	−0.358842	−	0.105365i	−0.456184	+	0.889886i	$0.650784\pi$
$132$		0			0
$133$	−0.275136			−0.0238573
$134$	19.3563	+	3.25127i	1.67213	+	0.280867i
$135$		0			0
$136$	27.1907	+	17.4744i	2.33158	+	1.49842i
$137$	−11.4728	−	3.36870i	−0.980183	−	0.287808i	−0.247883	−	0.968790i	$-0.579735\pi$
$137$	−11.4728	−	3.36870i	−0.980183	−	0.287808i	−0.732300	+	0.680982i	$0.761553\pi$
$138$		0			0
$139$	1.86103	−	2.14774i	0.157851	−	0.182169i	−0.671315	−	0.741172i	$-0.734270\pi$
$139$	1.86103	−	2.14774i	0.157851	−	0.182169i	0.829166	+	0.559003i	$0.188816\pi$
$140$	7.34774	+	8.47974i	0.620997	+	0.716669i
$141$		0			0
$142$	−0.918546	+	6.38863i	−0.0770827	+	0.536122i
$143$	−18.2277	−	11.7142i	−1.52427	−	0.979591i
$144$		0			0
$145$	−0.667407	+	0.770228i	−0.0554251	+	0.0639640i
$146$	−2.66986	−	18.5693i	−0.220959	−	1.53681i
$147$		0			0
$148$	7.87853	+	17.2516i	0.647611	+	1.41807i
$149$	17.3711	−	11.1637i	1.42310	−	0.914570i	0.423135	−	0.906067i	$-0.360930\pi$
$149$	17.3711	−	11.1637i	1.42310	−	0.914570i	0.999964	−	0.00850303i	$-0.00270663\pi$
$150$		0			0
$151$	5.23104	−	11.4544i	0.425696	−	0.932145i	−0.568309	−	0.822815i	$-0.692402\pi$
$151$	5.23104	−	11.4544i	0.425696	−	0.932145i	0.994006	−	0.109330i	$-0.0348705\pi$
$152$	0.429928	+	0.941411i	0.0348718	+	0.0763585i
$153$		0			0
$154$	10.7498	+	3.15644i	0.866247	+	0.254353i
$155$	−15.6779	−	18.0933i	−1.25928	−	1.45329i
$156$		0			0
$157$	−11.2196	−	3.29436i	−0.895418	−	0.262918i	−0.198527	−	0.980095i	$-0.563616\pi$
$157$	−11.2196	−	3.29436i	−0.895418	−	0.262918i	−0.696891	+	0.717177i	$0.745434\pi$
$158$	5.07842	−	11.1202i	0.404017	−	0.884674i
$159$		0			0
$160$	−2.50680	+	5.48912i	−0.198180	+	0.433953i
$161$	−2.12346	−	2.45060i	−0.167352	−	0.193134i
$162$		0			0
$163$	6.38670			0.500245			0.250122	−	0.968214i	$-0.419529\pi$
$163$	6.38670			0.500245			0.250122	+	0.968214i	$0.419529\pi$
$164$	8.04752			0.628406
$165$		0			0
$166$	8.93796	−	2.62442i	0.693720	−	0.203695i
$167$	5.40906	−	3.47619i	0.418566	−	0.268996i	−0.314361	−	0.949304i	$-0.601790\pi$
$167$	5.40906	−	3.47619i	0.418566	−	0.268996i	0.732927	+	0.680308i	$0.238154\pi$
$168$		0			0
$169$	−13.2004	+	3.87599i	−1.01542	+	0.298153i
$170$	−7.05167	+	49.0454i	−0.540838	+	3.76161i
$171$		0			0
$172$	25.6776			1.95790
$173$	0.238119	−	1.65616i	0.0181039	−	0.125915i	−0.978765	−	0.204984i	$-0.934286\pi$
$173$	0.238119	−	1.65616i	0.0181039	−	0.125915i	0.996869	+	0.0790691i	$0.0251948\pi$
$174$		0			0
$175$	−1.01751	+	2.22803i	−0.0769163	+	0.168423i
$176$	−1.52694	−	10.6201i	−0.115097	−	0.800520i
$177$		0			0
$178$	−30.1011	−	8.83847i	−2.25617	−	0.662471i
$179$	5.88491	−	1.72797i	0.439859	−	0.129154i	−0.0543021	−	0.998525i	$-0.517293\pi$
$179$	5.88491	−	1.72797i	0.439859	−	0.129154i	0.494161	+	0.869370i	$0.335475\pi$
$180$		0			0
$181$	−7.98839	−	2.34560i	−0.593772	−	0.174347i	−0.0289796	−	0.999580i	$-0.509226\pi$
$181$	−7.98839	−	2.34560i	−0.593772	−	0.174347i	−0.564793	+	0.825233i	$0.691044\pi$
$182$	11.6394	−	7.48022i	0.862773	−	0.554470i
$183$		0			0
$184$	−5.06690	+	11.0950i	−0.373537	+	0.817931i
$185$	−8.88470	+	10.2535i	−0.653216	+	0.753852i
$186$		0			0
$187$	13.4040	+	29.3507i	0.980200	+	2.14634i
$188$	3.53927	+	24.6162i	0.258128	+	1.79532i
$189$		0			0
$190$	−1.03899	+	1.19906i	−0.0753762	+	0.0869887i
$191$	−2.13172	+	0.625929i	−0.154246	+	0.0452907i	−0.357944	−	0.933743i	$-0.616522\pi$
$191$	−2.13172	+	0.625929i	−0.154246	+	0.0452907i	0.203698	+	0.979034i	$0.434704\pi$
$192$		0			0
$193$	3.64766	−	25.3700i	0.262564	−	1.82617i	−0.250841	−	0.968028i	$-0.580707\pi$
$193$	3.64766	−	25.3700i	0.262564	−	1.82617i	0.513405	−	0.858146i	$-0.328384\pi$
$194$	−13.9217	−	8.94692i	−0.999519	−	0.642352i
$195$		0			0
$196$	14.1339	−	16.3113i	1.00956	−	1.16510i
$197$	7.42190	+	16.2517i	0.528788	+	1.15789i	0.966004	+	0.258528i	$0.0832375\pi$
$197$	7.42190	+	16.2517i	0.528788	+	1.15789i	−0.437215	+	0.899357i	$0.644035\pi$
$198$		0			0
$199$	−9.07773	−	5.83390i	−0.643503	−	0.413554i	0.177784	−	0.984070i	$-0.443107\pi$
$199$	−9.07773	−	5.83390i	−0.643503	−	0.413554i	−0.821287	+	0.570515i	$0.806744\pi$
$200$	9.21342			0.651487
$201$		0			0
$202$	11.0385			0.776667
$203$	−0.356518	−	0.229120i	−0.0250227	−	0.0160811i
$204$		0			0
$205$	2.39153	+	5.23671i	0.167031	+	0.365748i
$206$	−9.90643	+	11.4326i	−0.690213	+	0.796549i
$207$		0			0
$208$	−11.1466	−	7.16351i	−0.772880	−	0.496700i
$209$	−0.147036	+	1.02266i	−0.0101707	+	0.0707387i
$210$		0			0
$211$	−4.85594	+	1.42583i	−0.334296	+	0.0981583i	−0.444573	−	0.895743i	$-0.646645\pi$
$211$	−4.85594	+	1.42583i	−0.334296	+	0.0981583i	0.110276	+	0.993901i	$0.464826\pi$
$212$	13.7239	−	15.8382i	0.942560	−	1.08777i
$213$		0			0
$214$	4.16018	+	28.9347i	0.284384	+	1.97793i
$215$	7.63076	+	16.7090i	0.520414	+	1.13955i
$216$		0			0
$217$	6.51932	−	7.52369i	0.442560	−	0.510741i
$218$	−0.572852	+	1.25437i	−0.0387984	+	0.0849567i
$219$		0			0
$220$	35.4452	−	22.7792i	2.38971	−	1.53578i
$221$	38.2332	+	11.2263i	2.57184	+	0.755160i
$222$		0			0
$223$	−7.93570	+	2.33013i	−0.531414	+	0.156037i	−0.536421	−	0.843950i	$-0.680224\pi$
$223$	−7.93570	+	2.33013i	−0.531414	+	0.156037i	0.00500768	+	0.999987i	$0.498406\pi$
$224$	−2.40764	−	0.706948i	−0.160867	−	0.0472349i
$225$		0			0
$226$	−0.131070	−	0.911611i	−0.00871864	−	0.0606395i
$227$	−12.0123	+	26.3033i	−0.797286	+	1.74581i	−0.142784	+	0.989754i	$0.545605\pi$
$227$	−12.0123	+	26.3033i	−0.797286	+	1.74581i	−0.654503	+	0.756060i	$0.727122\pi$
$228$		0			0
$229$	−1.79454	+	12.4813i	−0.118586	+	0.824787i	0.840528	+	0.541768i	$0.182245\pi$
$229$	−1.79454	+	12.4813i	−0.118586	+	0.824787i	−0.959114	+	0.283019i	$0.908664\pi$
$230$	−18.6986			−1.23295
$231$		0			0
$232$	−0.226866	+	1.57789i	−0.0148945	+	0.103594i
$233$	−22.2083	+	6.52096i	−1.45492	+	0.427202i	−0.911164	−	0.412044i	$-0.864815\pi$
$233$	−22.2083	+	6.52096i	−1.45492	+	0.427202i	−0.543753	+	0.839246i	$0.682997\pi$
$234$		0			0
$235$	−14.9666	+	9.61842i	−0.976310	+	0.627436i
$236$	−25.8926	+	7.60274i	−1.68546	+	0.494896i
$237$		0			0
$238$	−20.6042			−1.33557
$239$	−23.3545			−1.51068			−0.755338	−	0.655335i	$-0.772527\pi$
$239$	−23.3545			−1.51068			−0.755338	+	0.655335i	$0.772527\pi$
$240$		0			0
$241$	8.80477	+	10.1612i	0.567165	+	0.654543i	0.964795	−	0.263003i	$-0.0847128\pi$
$241$	8.80477	+	10.1612i	0.567165	+	0.654543i	−0.397630	+	0.917546i	$0.630167\pi$
$242$	6.51979	−	14.2764i	0.419108	−	0.917719i
$243$		0			0
$244$	−2.34723	+	5.13971i	−0.150266	+	0.329036i
$245$	14.8144	+	4.34991i	0.946458	+	0.277905i
$246$		0			0
$247$	0.835540	+	0.964265i	0.0531642	+	0.0613547i
$248$	−35.9303	−	10.5501i	−2.28157	−	0.669930i
$249$		0			0
$250$	−7.49294	−	16.4072i	−0.473895	−	1.03769i
$251$	6.87564	−	15.0555i	0.433986	−	0.950298i	−0.558677	−	0.829385i	$-0.688691\pi$
$251$	6.87564	−	15.0555i	0.433986	−	0.950298i	0.992663	−	0.120912i	$-0.0385819\pi$
$252$		0			0
$253$	−10.2435	+	6.58308i	−0.644001	+	0.413874i
$254$	5.61037	+	12.2850i	0.352026	+	0.770829i
$255$		0			0
$256$	4.07718	+	28.3574i	0.254824	+	1.77234i
$257$	15.2960	−	17.6525i	0.954135	−	1.10113i	−0.0406534	−	0.999173i	$-0.512944\pi$
$257$	15.2960	−	17.6525i	0.954135	−	1.10113i	0.994789	−	0.101958i	$-0.0325106\pi$
$258$		0			0
$259$	−4.74607	−	3.05011i	−0.294906	−	0.189525i
$260$	7.40501	−	51.5030i	0.459239	−	3.19408i
$261$		0			0
$262$	−6.72160	−	7.75714i	−0.415262	−	0.479238i
$263$	12.1468	−	14.0181i	0.749002	−	0.864394i	−0.245469	−	0.969404i	$-0.578942\pi$
$263$	12.1468	−	14.0181i	0.749002	−	0.864394i	0.994471	+	0.105010i	$0.0334875\pi$
$264$		0			0
$265$	14.3847	+	4.22373i	0.883645	+	0.259461i
$266$	−0.555011	−	0.356684i	−0.0340299	−	0.0218697i
$267$		0			0
$268$	22.7155	+	20.6422i	1.38757	+	1.26092i
$269$	−17.6682			−1.07725			−0.538624	−	0.842546i	$-0.681056\pi$
$269$	−17.6682			−1.07725			−0.538624	+	0.842546i	$0.681056\pi$
$270$		0			0
$271$	−4.29154	−	1.26011i	−0.260692	−	0.0765461i	0.148775	−	0.988871i	$-0.452467\pi$
$271$	−4.29154	−	1.26011i	−0.260692	−	0.0765461i	−0.409467	+	0.912325i	$0.634285\pi$
$272$	8.19688	+	17.9487i	0.497009	+	1.08830i
$273$		0			0
$274$	−18.7759	−	21.6686i	−1.13430	−	1.30905i
$275$	7.73763	+	4.97267i	0.466597	+	0.299863i
$276$		0			0
$277$	−0.319672	−	0.205440i	−0.0192072	−	0.0123437i	0.531002	−	0.847371i	$-0.321816\pi$
$277$	−0.319672	−	0.205440i	−0.0192072	−	0.0123437i	−0.550209	+	0.835027i	$0.685452\pi$
$278$	6.53843	−	1.91986i	0.392149	−	0.115145i
$279$		0			0
$280$	1.78675	+	12.4271i	0.106779	+	0.742663i
$281$	−0.129569	−	0.901174i	−0.00772945	−	0.0537595i	0.985592	−	0.169142i	$-0.0540997\pi$
$281$	−0.129569	−	0.901174i	−0.00772945	−	0.0537595i	−0.993321	+	0.115383i	$0.963191\pi$
$282$		0			0
$283$	−11.3584	+	7.29957i	−0.675184	+	0.433914i	−0.832791	−	0.553588i	$-0.813258\pi$
$283$	−11.3584	+	7.29957i	−0.675184	+	0.433914i	0.157607	+	0.987502i	$0.449622\pi$
$284$	−6.60971	+	7.62802i	−0.392214	+	0.452639i
$285$		0			0
$286$	−21.5831	−	47.2603i	−1.27623	−	2.79456i
$287$	−2.01388	+	1.29424i	−0.118875	+	0.0763966i
$288$		0			0
$289$	−27.7268	−	31.9985i	−1.63099	−	1.88226i
$290$	−2.34482	+	0.688503i	−0.137693	+	0.0404303i
$291$		0			0
$292$	12.1872	−	26.6862i	0.713202	−	1.56169i
$293$	−2.23323	−	15.5325i	−0.130467	−	0.907417i	−0.944947	−	0.327225i	$-0.893887\pi$
$293$	−2.23323	−	15.5325i	−0.130467	−	0.907417i	0.814480	−	0.580192i	$-0.197022\pi$
$294$		0			0
$295$	−12.6419	−	14.5895i	−0.736041	−	0.849436i
$296$	−3.02011	+	21.0053i	−0.175540	+	1.22091i
$297$		0			0
$298$	49.5140			2.86827
$299$	−2.14001	+	14.8841i	−0.123760	+	0.860768i
$300$		0			0
$301$	−6.42577	+	4.12959i	−0.370376	+	0.238026i
$302$	25.4015	−	16.3246i	1.46169	−	0.939374i
$303$		0			0
$304$	−0.0899159	+	0.625379i	−0.00515703	+	0.0358679i
$305$	−4.04207			−0.231448
$306$		0			0
$307$	0.644746	−	4.48431i	0.0367976	−	0.255933i	−0.963116	−	0.269087i	$-0.913278\pi$
$307$	0.644746	−	4.48431i	0.0367976	−	0.255933i	0.999913	+	0.0131540i	$0.00418716\pi$
$308$	11.4734	+	13.2410i	0.653758	+	0.754477i
$309$		0			0
$310$	−8.16991	−	56.8230i	−0.464020	−	3.22733i
$311$	4.69662	−	10.2842i	0.266321	−	0.583162i	−0.728472	−	0.685075i	$-0.759769\pi$
$311$	4.69662	−	10.2842i	0.266321	−	0.583162i	0.994793	+	0.101914i	$0.0324965\pi$
$312$		0			0
$313$	6.17379	−	1.81279i	0.348963	−	0.102465i	−0.102554	−	0.994727i	$-0.532701\pi$
$313$	6.17379	−	1.81279i	0.348963	−	0.102465i	0.451517	+	0.892263i	$0.350883\pi$
$314$	−18.3616	−	21.1904i	−1.03620	−	1.19584i
$315$		0			0
$316$	16.0826	−	10.3357i	0.904717	−	0.581426i
$317$	−7.66063	−	16.7744i	−0.430264	−	0.942146i	−0.993284	−	0.115703i	$-0.963088\pi$
$317$	−7.66063	−	16.7744i	−0.430264	−	0.942146i	0.563020	−	0.826443i	$-0.309639\pi$
$318$		0			0
$319$	−1.04215	+	1.20270i	−0.0583491	+	0.0673384i
$320$	−23.7337	+	15.2527i	−1.32675	+	0.852652i
$321$		0			0
$322$	−1.10655	−	7.69623i	−0.0616657	−	0.428894i
$323$	−0.270407	−	1.88072i	−0.0150459	−	0.104646i
$324$		0			0
$325$	10.8985	−	3.20010i	0.604541	−	0.177509i
$326$	12.8834	+	8.27965i	0.713545	+	0.458567i
$327$		0			0
$328$	7.57528	+	4.86833i	0.418275	+	0.268809i
$329$	−4.84459	−	5.59095i	−0.267091	−	0.308239i
$330$		0			0
$331$	14.4376	+	31.6140i	0.793563	+	1.73766i	0.666159	+	0.745810i	$0.267937\pi$
$331$	14.4376	+	31.6140i	0.793563	+	1.73766i	0.127404	+	0.991851i	$0.459336\pi$
$332$	13.9772	+	4.10409i	0.767101	+	0.225241i
$333$		0			0
$334$	15.4178			0.843624
$335$	−6.68185	+	20.9159i	−0.365068	+	1.14276i
$336$		0			0
$337$	−13.2177	−	8.49449i	−0.720013	−	0.462725i	0.128628	−	0.991693i	$-0.458943\pi$
$337$	−13.2177	−	8.49449i	−0.720013	−	0.462725i	−0.848642	+	0.528968i	$0.822579\pi$
$338$	−31.6530	−	9.29416i	−1.72170	−	0.505536i
$339$		0			0
$340$	−50.7427	+	58.5602i	−2.75191	+	3.17587i
$341$	−24.4809	−	28.2525i	−1.32572	−	1.52996i
$342$		0			0
$343$	−2.02493	+	14.0837i	−0.109336	+	0.760448i
$344$	24.1708	+	15.5336i	1.30320	+	0.837517i
$345$		0			0
$346$	2.62736	−	3.03214i	0.141248	−	0.163009i
$347$	3.23017	+	22.4663i	0.173404	+	1.20605i	0.871626	+	0.490172i	$0.163066\pi$
$347$	3.23017	+	22.4663i	0.173404	+	1.20605i	−0.698221	+	0.715882i	$0.746025\pi$
$348$		0			0
$349$	−4.91043	−	10.7523i	−0.262849	−	0.575560i	0.731485	−	0.681857i	$-0.238828\pi$
$349$	−4.91043	−	10.7523i	−0.262849	−	0.575560i	−0.994334	+	0.106298i	$0.966100\pi$
$350$	−4.94094	+	3.17535i	−0.264104	+	0.169729i
$351$		0			0
$352$	−3.91434	+	8.57120i	−0.208635	+	0.456847i
$353$	3.85985	+	8.45189i	0.205439	+	0.449849i	0.984104	−	0.177591i	$-0.0568303\pi$
$353$	3.85985	+	8.45189i	0.205439	+	0.449849i	−0.778665	+	0.627439i	$0.784103\pi$
$354$		0			0
$355$	−6.92798	−	2.03424i	−0.367699	−	0.107966i
$356$	−32.1271	−	37.0767i	−1.70273	−	1.96506i
$357$		0			0
$358$	14.1113	+	4.14345i	0.745806	+	0.218988i
$359$	4.76035	−	10.4237i	0.251241	−	0.550142i	−0.741424	−	0.671037i	$-0.765849\pi$
$359$	4.76035	−	10.4237i	0.251241	−	0.550142i	0.992665	+	0.120895i	$0.0385764\pi$
$360$		0			0
$361$	−7.86761	+	17.2277i	−0.414085	+	0.906719i
$362$	−13.0735	−	15.0877i	−0.687130	−	0.792991i
$363$		0			0
$364$	21.6366			1.13406
$365$	20.9871			1.09851
$366$		0			0
$367$	17.7423	−	5.20961i	0.926140	−	0.271939i	0.216320	−	0.976322i	$-0.430594\pi$
$367$	17.7423	−	5.20961i	0.926140	−	0.271939i	0.709820	+	0.704383i	$0.248776\pi$
$368$	−6.26411	+	4.02570i	−0.326540	+	0.209854i
$369$		0			0
$370$	−31.2150	+	9.16554i	−1.62279	+	0.476494i
$371$	−0.887201	+	6.17062i	−0.0460612	+	0.320363i
$372$		0			0
$373$	36.7433			1.90250			0.951248	−	0.308427i	$-0.0998025\pi$
$373$	36.7433			1.90250			0.951248	+	0.308427i	$0.0998025\pi$
$374$	−11.0111	+	76.5838i	−0.569370	+	3.96006i
$375$		0			0
$376$	−11.5599	+	25.3127i	−0.596158	+	1.30540i
$377$	0.279689	+	1.94528i	0.0144047	+	0.100187i
$378$		0			0
$379$	7.48198	+	2.19691i	0.384324	+	0.112848i	0.468186	−	0.883630i	$-0.344908\pi$
$379$	7.48198	+	2.19691i	0.384324	+	0.112848i	−0.0838629	+	0.996477i	$0.526726\pi$
$380$	−2.38060	+	0.699008i	−0.122122	+	0.0358583i
$381$		0			0
$382$	−5.11160	−	1.50090i	−0.261532	−	0.0767928i
$383$	−29.5997	+	19.0226i	−1.51247	+	0.972007i	−0.519397	+	0.854533i	$0.673843\pi$
$383$	−29.5997	+	19.0226i	−1.51247	+	0.972007i	−0.993076	+	0.117474i	$0.962520\pi$
$384$		0			0
$385$	−5.20663	+	11.4009i	−0.265354	+	0.581045i
$386$	40.2476	−	46.4482i	2.04855	−	2.36415i
$387$		0			0
$388$	−10.7505	−	23.5404i	−0.545776	−	1.19508i
$389$	−0.815645	−	5.67293i	−0.0413548	−	0.287629i	−0.999995	−	0.00300989i	$-0.999042\pi$
$389$	−0.815645	−	5.67293i	−0.0413548	−	0.287629i	0.958641	−	0.284619i	$-0.0918672\pi$
$390$		0			0
$391$	14.6644	−	16.9236i	0.741609	−	0.855862i
$392$	23.1720	−	6.80391i	1.17036	−	0.343649i
$393$		0			0
$394$	−6.09691	+	42.4050i	−0.307158	+	2.13633i
$395$	11.5050	+	7.39382i	0.578880	+	0.372024i
$396$		0			0
$397$	6.32644	−	7.30110i	0.317515	−	0.366432i	−0.574447	−	0.818542i	$-0.694783\pi$
$397$	6.32644	−	7.30110i	0.317515	−	0.366432i	0.891962	+	0.452110i	$0.149328\pi$
$398$	−10.7488	−	23.5366i	−0.538788	−	1.17978i
$399$		0			0
$400$	4.73174	+	3.04090i	0.236587	+	0.152045i
$401$	−1.20154			−0.0600018			−0.0300009	−	0.999550i	$-0.509551\pi$
$401$	−1.20154			−0.0600018			−0.0300009	+	0.999550i	$0.509551\pi$
$402$		0			0
$403$	−46.1661			−2.29970
$404$	14.5218	+	9.33259i	0.722486	+	0.464314i
$405$		0			0
$406$	−0.422147	−	0.924373i	−0.0209508	−	0.0458759i
$407$	−13.8734	+	16.0107i	−0.687677	+	0.793621i
$408$		0			0
$409$	22.7473	+	14.6188i	1.12478	+	0.722853i	0.964464	−	0.264213i	$-0.0851122\pi$
$409$	22.7473	+	14.6188i	1.12478	+	0.722853i	0.160316	+	0.987066i	$0.448749\pi$
$410$	−1.96458	+	13.6640i	−0.0970238	+	0.674815i
$411$		0			0
$412$	−22.6983	+	6.66481i	−1.11826	+	0.328352i
$413$	5.25685	−	6.06673i	0.258673	−	0.298524i
$414$		0			0
$415$	1.48307	+	10.3150i	0.0728009	+	0.506341i
$416$	4.83396	+	10.5849i	0.237004	+	0.518967i
$417$		0			0
$418$	−1.62237	+	1.87231i	−0.0793526	+	0.0915778i
$419$	5.36631	−	11.7506i	0.262162	−	0.574054i	−0.732080	−	0.681219i	$-0.761450\pi$
$419$	5.36631	−	11.7506i	0.262162	−	0.574054i	0.994241	+	0.107165i	$0.0341774\pi$
$420$		0			0
$421$	28.2666	−	18.1658i	1.37763	−	0.885349i	0.378442	−	0.925625i	$-0.376460\pi$
$421$	28.2666	−	18.1658i	1.37763	−	0.885349i	0.999189	+	0.0402761i	$0.0128237\pi$
$422$	−11.6439	−	3.41897i	−0.566818	−	0.166433i
$423$		0			0
$424$	22.4998	−	6.60654i	1.09269	−	0.320842i
$425$	−16.2299	−	4.76554i	−0.787268	−	0.231163i
$426$		0			0
$427$	−0.239203	−	1.66369i	−0.0115759	−	0.0805118i
$428$	−18.9901	+	41.5825i	−0.917920	+	2.00996i
$429$		0			0
$430$	−6.26849	+	43.5983i	−0.302293	+	2.10250i
$431$	23.3405			1.12427			0.562137	−	0.827044i	$-0.309980\pi$
$431$	23.3405			1.12427			0.562137	+	0.827044i	$0.309980\pi$
$432$		0			0
$433$	3.40423	−	23.6769i	0.163597	−	1.13784i	−0.728187	−	0.685379i	$-0.759637\pi$
$433$	3.40423	−	23.6769i	0.163597	−	1.13784i	0.891784	−	0.452462i	$-0.149454\pi$
$434$	22.9046	−	6.72538i	1.09945	−	0.322829i
$435$		0			0
$436$	−1.81414	+	1.16587i	−0.0868814	+	0.0558353i
$437$	0.687981	−	0.202009i	0.0329106	−	0.00966342i
$438$		0			0
$439$	−4.61508			−0.220266			−0.110133	−	0.993917i	$-0.535128\pi$
$439$	−4.61508			−0.220266			−0.110133	+	0.993917i	$0.535128\pi$
$440$	47.1454			2.24757
$441$		0			0
$442$	62.5712	+	72.2110i	2.97621	+	3.43473i
$443$	3.08141	−	6.74734i	0.146402	−	0.320576i	−0.822197	−	0.569203i	$-0.807252\pi$
$443$	3.08141	−	6.74734i	0.146402	−	0.320576i	0.968599	+	0.248627i	$0.0799793\pi$
$444$		0			0
$445$	14.5793	−	31.9242i	0.691124	−	1.51335i
$446$	−19.0288	−	5.58737i	−0.901041	−	0.264570i
$447$		0			0
$448$	−7.68246	−	8.86603i	−0.362962	−	0.418880i
$449$	12.3308	+	3.62065i	0.581926	+	0.170869i	0.559429	−	0.828878i	$-0.311020\pi$
$449$	12.3308	+	3.62065i	0.581926	+	0.170869i	0.0224965	+	0.999747i	$0.492839\pi$
$450$		0			0
$451$	3.73434	+	8.17706i	0.175843	+	0.385043i
$452$	0.598299	−	1.31009i	0.0281416	−	0.0616215i
$453$		0			0
$454$	−58.3309	+	37.4870i	−2.73761	+	1.75935i
$455$	6.42986	+	14.0794i	0.301436	+	0.660054i
$456$		0			0
$457$	−3.81344	−	26.5231i	−0.178385	−	1.24070i	−0.860500	−	0.509451i	$-0.829848\pi$
$457$	−3.81344	−	26.5231i	−0.178385	−	1.24070i	0.682114	−	0.731246i	$-0.261061\pi$
$458$	−19.8006	+	22.8511i	−0.925222	+	1.06776i
$459$		0			0
$460$	−24.5990	−	15.8088i	−1.14694	−	0.737091i
$461$	2.82126	−	19.6223i	0.131399	−	0.913902i	−0.812333	−	0.583193i	$-0.801803\pi$
$461$	2.82126	−	19.6223i	0.131399	−	0.913902i	0.943733	−	0.330709i	$-0.107288\pi$
$462$		0			0
$463$	−8.08786	−	9.33389i	−0.375875	−	0.433783i	0.536021	−	0.844205i	$-0.319927\pi$
$463$	−8.08786	−	9.33389i	−0.375875	−	0.433783i	−0.911896	+	0.410422i	$0.865381\pi$
$464$	−0.637297	+	0.735480i	−0.0295858	+	0.0341438i
$465$		0			0
$466$	−53.2529	−	15.6365i	−2.46689	−	0.724345i
$467$	12.8760	+	8.27487i	0.595828	+	0.382915i	0.803519	−	0.595279i	$-0.202959\pi$
$467$	12.8760	+	8.27487i	0.595828	+	0.382915i	−0.207691	+	0.978194i	$0.566595\pi$
$468$		0			0
$469$	−9.00429	−	1.51245i	−0.415780	−	0.0698383i
$470$	−42.6601			−1.96776
$471$		0			0
$472$	−28.9724	−	8.50706i	−1.33356	−	0.391569i
$473$	11.9153	+	26.0910i	0.547868	+	1.19966i
$474$		0			0
$475$	−0.354686	−	0.409330i	−0.0162741	−	0.0187813i
$476$	−27.1059	−	17.4199i	−1.24240	−	0.798441i
$477$		0			0
$478$	−47.1112	−	30.2765i	−2.15482	−	1.38482i
$479$	−31.1206	+	9.13784i	−1.42194	+	0.417519i	−0.900159	−	0.435562i	$-0.856550\pi$
$479$	−31.1206	+	9.13784i	−1.42194	+	0.417519i	−0.521779	+	0.853081i	$0.674731\pi$
$480$		0			0
$481$	3.72330	+	25.8961i	0.169768	+	1.18076i
$482$	4.58824	+	31.9119i	0.208989	+	1.45355i
$483$		0			0
$484$	20.6472	−	13.2692i	0.938510	−	0.603144i
$485$	12.1235	−	13.9913i	0.550499	−	0.635310i
$486$		0			0
$487$	14.3338	+	31.3867i	0.649528	+	1.42227i	0.891967	+	0.452101i	$0.149325\pi$
$487$	14.3338	+	31.3867i	0.649528	+	1.42227i	−0.242439	+	0.970167i	$0.577947\pi$
$488$	−5.31874	+	3.41815i	−0.240768	+	0.154732i
$489$		0			0
$490$	24.2448	+	27.9800i	1.09527	+	1.26401i
$491$	−5.53642	+	1.62564i	−0.249855	+	0.0733640i	−0.404262	−	0.914643i	$-0.632472\pi$
$491$	−5.53642	+	1.62564i	−0.249855	+	0.0733640i	0.154407	+	0.988007i	$0.450653\pi$
$492$		0			0
$493$	1.21578	−	2.66220i	0.0547562	−	0.119899i
$494$	0.435407	+	3.02832i	0.0195899	+	0.136251i
$495$		0			0
$496$	−14.9706	−	17.2770i	−0.672202	−	0.775762i
$497$	0.427295	−	2.97190i	0.0191668	−	0.133308i
$498$		0			0
$499$	−1.30408			−0.0583785			−0.0291892	−	0.999574i	$-0.509293\pi$
$499$	−1.30408			−0.0583785			−0.0291892	+	0.999574i	$0.509293\pi$
$500$	4.01424	−	27.9196i	0.179522	−	1.24860i
$501$		0			0
$502$	33.3876	−	21.4569i	1.49016	−	0.957667i
$503$	12.3552	−	7.94018i	0.550890	−	0.354035i	−0.235395	−	0.971900i	$-0.575638\pi$
$503$	12.3552	−	7.94018i	0.550890	−	0.354035i	0.786285	+	0.617864i	$0.212002\pi$
$504$		0			0
$505$	−1.75742	+	12.2231i	−0.0782040	+	0.543921i
$506$	−29.1976			−1.29799
$507$		0			0
$508$	−3.00568	+	20.9049i	−0.133355	+	0.927506i
$509$	20.0652	+	23.1565i	0.889375	+	1.02639i	0.999473	+	0.0324723i	$0.0103381\pi$
$509$	20.0652	+	23.1565i	0.889375	+	1.02639i	−0.110098	+	0.993921i	$0.535116\pi$
$510$		0			0
$511$	1.24198	+	8.63818i	0.0549421	+	0.382131i
$512$	−11.3231	+	24.7942i	−0.500417	+	1.09576i
$513$		0			0
$514$	53.7398	−	15.7794i	2.37036	−	0.696001i
$515$	−11.0823	−	12.7897i	−0.488346	−	0.563581i
$516$		0			0
$517$	−23.3701	+	15.0190i	−1.02782	+	0.660537i
$518$	−5.61974	−	12.3055i	−0.246917	−	0.540673i
$519$		0			0
$520$	38.1271	−	44.0010i	1.67198	−	1.92957i
$521$	2.96369	−	1.90465i	0.129842	−	0.0834442i	−0.474108	−	0.880467i	$-0.657229\pi$
$521$	2.96369	−	1.90465i	0.129842	−	0.0834442i	0.603949	+	0.797023i	$0.293593\pi$
$522$		0			0
$523$	2.19378	+	15.2581i	0.0959272	+	0.667188i	0.979876	+	0.199605i	$0.0639660\pi$
$523$	2.19378	+	15.2581i	0.0959272	+	0.667188i	−0.883949	+	0.467583i	$0.845125\pi$
$524$	−2.28432	−	15.8878i	−0.0997910	−	0.694062i
$525$		0			0
$526$	42.6757	−	12.5307i	1.86075	−	0.546365i
$527$	57.8362	+	37.1691i	2.51939	+	1.61911i
$528$		0			0
$529$	−12.2398	−	7.86607i	−0.532167	−	0.342003i
$530$	23.5415	+	27.1684i	1.02258	+	1.18012i
$531$		0			0
$532$	−0.428588	−	0.938477i	−0.0185816	−	0.0406881i
$533$	10.6517	+	3.12762i	0.461376	+	0.135472i
$534$		0			0
$535$	−32.7021			−1.41383
$536$	8.89509	+	33.1726i	0.384210	+	1.43284i
$537$		0			0
$538$	−35.6406	−	22.9048i	−1.53658	−	0.987498i
$539$	23.1325	+	6.79232i	0.996389	+	0.292566i
$540$		0			0
$541$	13.4552	−	15.5281i	0.578484	−	0.667607i	−0.388794	−	0.921325i	$-0.627108\pi$
$541$	13.4552	−	15.5281i	0.578484	−	0.667607i	0.967278	+	0.253718i	$0.0816536\pi$
$542$	−7.02339	−	8.10543i	−0.301680	−	0.348158i
$543$		0			0
$544$	2.46616	−	17.1525i	0.105736	−	0.735407i
$545$	−1.29778	−	0.834032i	−0.0555908	−	0.0357260i
$546$		0			0
$547$	7.04610	−	8.13163i	0.301269	−	0.347683i	−0.584849	−	0.811142i	$-0.698846\pi$
$547$	7.04610	−	8.13163i	0.301269	−	0.347683i	0.886119	+	0.463459i	$0.153392\pi$
$548$	−6.38096	−	44.3805i	−0.272581	−	1.89584i
$549$		0			0
$550$	9.16200	+	20.0620i	0.390669	+	0.855446i
$551$	0.0788355	−	0.0506645i	0.00335850	−	0.00215838i
$552$		0			0
$553$	−2.36241	+	5.17296i	−0.100460	+	0.219977i
$554$	−0.378518	−	0.828838i	−0.0160817	−	0.0352140i
$555$		0			0
$556$	10.2248	+	3.00228i	0.433630	+	0.127325i
$557$	−11.5027	−	13.2748i	−0.487386	−	0.562473i	0.457779	−	0.889066i	$-0.348645\pi$
$557$	−11.5027	−	13.2748i	−0.487386	−	0.562473i	−0.945165	+	0.326592i	$0.894100\pi$
$558$		0			0
$559$	33.9869	+	9.97944i	1.43749	+	0.422085i
$560$	−3.18397	+	6.97193i	−0.134547	+	0.294618i
$561$		0			0
$562$	0.906903	−	1.98584i	0.0382554	−	0.0837676i
$563$	−13.4176	−	15.4848i	−0.565486	−	0.652605i	0.398935	−	0.916979i	$-0.369380\pi$
$563$	−13.4176	−	15.4848i	−0.565486	−	0.652605i	−0.964420	+	0.264374i	$0.914835\pi$
$564$		0			0
$565$	1.03031			0.0433454
$566$	−32.3754			−1.36084
$567$		0			0
$568$	−10.8364	+	3.18185i	−0.454685	+	0.133508i
$569$	28.7196	−	18.4569i	1.20399	−	0.773755i	0.224345	−	0.974510i	$-0.427976\pi$
$569$	28.7196	−	18.4569i	1.20399	−	0.773755i	0.979642	+	0.200755i	$0.0643394\pi$
$570$		0			0
$571$	−20.5334	+	6.02914i	−0.859294	+	0.252312i	−0.681556	−	0.731766i	$-0.738696\pi$
$571$	−20.5334	+	6.02914i	−0.859294	+	0.252312i	−0.177739	+	0.984078i	$0.556878\pi$
$572$	11.5628	−	80.4212i	0.483466	−	3.36258i
$573$		0			0
$574$	−5.74028			−0.239595
$575$	0.908432	−	6.31828i	0.0378842	−	0.263490i
$576$		0			0
$577$	−18.2944	+	40.0591i	−0.761604	+	1.66768i	−0.0172907	+	0.999851i	$0.505504\pi$
$577$	−18.2944	+	40.0591i	−0.761604	+	1.66768i	−0.744314	+	0.667830i	$0.767223\pi$
$578$	−14.4487	−	100.493i	−0.600986	−	4.17995i
$579$		0			0
$580$	−3.66685	−	1.07668i	−0.152258	−	0.0447069i
$581$	−4.15782	+	1.22084i	−0.172495	+	0.0506492i
$582$		0			0
$583$	22.4615	+	6.59530i	0.930261	+	0.273149i
$584$	27.6158	−	17.7476i	1.14275	−	0.734401i
$585$		0			0
$586$	15.6312	−	34.2276i	0.645720	−	1.41393i
$587$	−4.29711	+	4.95913i	−0.177361	+	0.204685i	−0.837468	−	0.546486i	$-0.815965\pi$
$587$	−4.29711	+	4.95913i	−0.177361	+	0.204685i	0.660108	+	0.751171i	$0.270511\pi$
$588$		0			0
$589$	0.914482	+	2.00244i	0.0376806	+	0.0825090i
$590$	−6.58781	−	45.8192i	−0.271216	−	1.88635i
$591$		0			0
$592$	−8.48388	+	9.79091i	−0.348685	+	0.402404i
$593$	2.92772	−	0.859656i	0.120227	−	0.0353018i	−0.221066	−	0.975259i	$-0.570953\pi$
$593$	2.92772	−	0.859656i	0.120227	−	0.0353018i	0.341293	+	0.939957i	$0.389135\pi$
$594$		0			0
$595$	3.28034	−	22.8153i	0.134481	−	0.935335i
$596$	65.1385	+	41.8620i	2.66818	+	1.71473i
$597$		0			0
$598$	−23.6124	+	27.2502i	−0.965584	+	1.11434i
$599$	−3.25348	−	7.12412i	−0.132933	−	0.291084i	0.831446	−	0.555605i	$-0.187513\pi$
$599$	−3.25348	−	7.12412i	−0.132933	−	0.291084i	−0.964380	+	0.264521i	$0.914786\pi$
$600$		0			0
$601$	22.4547	+	14.4307i	0.915945	+	0.588642i	0.911478	−	0.411348i	$-0.134942\pi$
$601$	22.4547	+	14.4307i	0.915945	+	0.588642i	0.00446638	+	0.999990i	$0.498578\pi$
$602$	−18.3158			−0.746496
$603$		0			0
$604$	47.2189			1.92131
$605$	14.7704	+	9.49236i	0.600502	+	0.385919i
$606$		0			0
$607$	10.8147	+	23.6810i	0.438957	+	0.961181i	0.991789	+	0.127888i	$0.0408199\pi$
$607$	10.8147	+	23.6810i	0.438957	+	0.961181i	−0.552832	+	0.833293i	$0.686453\pi$
$608$	0.363362	−	0.419342i	0.0147363	−	0.0170066i
$609$		0			0
$610$	−8.15375	−	5.24010i	−0.330136	−	0.212165i
$611$	−4.88235	+	33.9575i	−0.197519	+	1.37377i
$612$		0			0
$613$	−6.19922	+	1.82026i	−0.250384	+	0.0735194i	−0.404516	−	0.914531i	$-0.632560\pi$
$613$	−6.19922	+	1.82026i	−0.250384	+	0.0735194i	0.154132	+	0.988050i	$0.450742\pi$
$614$	7.11401	−	8.21001i	0.287098	−	0.331329i
$615$		0			0
$616$	2.78999	+	19.4048i	0.112412	+	0.781842i
$617$	−1.67071	−	3.65835i	−0.0672603	−	0.147279i	0.873016	−	0.487691i	$-0.162161\pi$
$617$	−1.67071	−	3.65835i	−0.0672603	−	0.147279i	−0.940276	+	0.340412i	$0.889434\pi$
$618$		0			0
$619$	14.9830	−	17.2913i	0.602217	−	0.694995i	−0.370012	−	0.929027i	$-0.620647\pi$
$619$	14.9830	−	17.2913i	0.602217	−	0.694995i	0.972229	+	0.234032i	$0.0751920\pi$
$620$	37.2934	−	81.6612i	1.49774	−	3.27959i
$621$		0			0
$622$	22.8064	−	14.6568i	0.914455	−	0.587684i
$623$	14.0026	+	4.11154i	0.561003	+	0.164725i
$624$		0			0
$625$	29.8954	−	8.77808i	1.19582	−	0.351123i
$626$	14.8040	+	4.34684i	0.591686	+	0.173735i
$627$		0			0
$628$	−6.24013	−	43.4011i	−0.249008	−	1.73189i
$629$	16.1849	−	35.4399i	0.645333	−	1.41308i
$630$		0			0
$631$	3.05652	−	21.2585i	0.121678	−	0.846289i	−0.833977	−	0.551800i	$-0.813941\pi$
$631$	3.05652	−	21.2585i	0.121678	−	0.846289i	0.955655	−	0.294489i	$-0.0951496\pi$
$632$	21.3914			0.850903
$633$		0			0
$634$	6.29302	−	43.7689i	0.249928	−	1.73829i
$635$	−14.4966	+	4.25657i	−0.575278	+	0.168917i
$636$		0			0
$637$	25.0469	−	16.0966i	0.992393	−	0.637772i
$638$	−3.66142	+	1.07509i	−0.144957	+	0.0425632i
$639$		0			0
$640$	−55.5807			−2.19702
$641$	−19.7512			−0.780126			−0.390063	−	0.920788i	$-0.627547\pi$
$641$	−19.7512			−0.780126			−0.390063	+	0.920788i	$0.627547\pi$
$642$		0			0
$643$	−20.8769	−	24.0932i	−0.823305	−	0.950145i	0.176109	−	0.984371i	$-0.443649\pi$
$643$	−20.8769	−	24.0932i	−0.823305	−	0.950145i	−0.999414	+	0.0342259i	$0.989103\pi$
$644$	5.05111	−	11.0604i	0.199041	−	0.435840i
$645$		0			0
$646$	1.89268	−	4.14439i	0.0744665	−	0.163059i
$647$	14.2762	+	4.19187i	0.561255	+	0.164799i	0.550041	−	0.835138i	$-0.314612\pi$
$647$	14.2762	+	4.19187i	0.561255	+	0.164799i	0.0112140	+	0.999937i	$0.496430\pi$
$648$		0			0
$649$	−19.7402	−	22.7814i	−0.774871	−	0.894248i
$650$	26.1333	+	7.67344i	1.02503	+	0.300977i
$651$		0			0
$652$	9.94875	+	21.7847i	0.389623	+	0.853155i
$653$	−4.57241	+	10.0122i	−0.178932	+	0.391807i	−0.977752	−	0.209763i	$-0.932731\pi$
$653$	−4.57241	+	10.0122i	−0.178932	+	0.391807i	0.798820	+	0.601570i	$0.205458\pi$
$654$		0			0
$655$	9.65972	−	6.20793i	0.377437	−	0.242564i
$656$	2.28363	+	5.00046i	0.0891610	+	0.195235i
$657$		0			0
$658$	−2.52456	−	17.5587i	−0.0984174	−	0.684508i
$659$	23.3879	−	26.9911i	0.911064	−	1.05142i	−0.0874088	−	0.996173i	$-0.527859\pi$
$659$	23.3879	−	26.9911i	0.911064	−	1.05142i	0.998472	−	0.0552510i	$-0.0175959\pi$
$660$		0			0
$661$	14.4429	+	9.28187i	0.561763	+	0.361023i	0.790497	−	0.612466i	$-0.209822\pi$
$661$	14.4429	+	9.28187i	0.561763	+	0.361023i	−0.228734	+	0.973489i	$0.573459\pi$
$662$	−11.8602	+	82.4892i	−0.460958	+	3.20603i
$663$		0			0
$664$	10.6743	+	12.3188i	0.414242	+	0.478060i
$665$	0.483323	−	0.557785i	0.0187425	−	0.0216300i
$666$		0			0
$667$	1.05970	+	0.311156i	0.0410318	+	0.0120480i
$668$	20.2830	+	13.0351i	0.784773	+	0.504343i
$669$		0			0
$670$	−40.5939	+	33.5297i	−1.56828	+	1.29537i
$671$	−6.31164			−0.243658
$672$		0			0
$673$	9.42152	+	2.76641i	0.363173	+	0.106637i	0.458228	−	0.888835i	$-0.348484\pi$
$673$	9.42152	+	2.76641i	0.363173	+	0.106637i	−0.0950548	+	0.995472i	$0.530303\pi$
$674$	−15.6508	−	34.2706i	−0.602848	−	1.32005i
$675$		0			0
$676$	−33.7835	−	38.9883i	−1.29937	−	1.49955i
$677$	−19.8005	−	12.7250i	−0.760993	−	0.489061i	0.101683	−	0.994817i	$-0.467577\pi$
$677$	−19.8005	−	12.7250i	−0.760993	−	0.489061i	−0.862677	+	0.505756i	$0.831214\pi$
$678$		0			0
$679$	6.47618	+	4.16199i	0.248533	+	0.159722i
$680$	−83.1909	+	24.4271i	−3.19023	+	0.936735i
$681$		0			0
$682$	−12.7572	−	88.7284i	−0.488499	−	3.39758i
$683$	1.09783	+	7.63560i	0.0420074	+	0.292168i	0.999986	+	0.00532769i	$0.00169586\pi$
$683$	1.09783	+	7.63560i	0.0420074	+	0.292168i	−0.957978	+	0.286840i	$0.907395\pi$
$684$		0			0
$685$	26.9832	−	17.3411i	1.03098	−	0.662568i
$686$	−22.3427	+	25.7849i	−0.853049	+	0.984470i
$687$		0			0
$688$	7.28650	+	15.9552i	0.277795	+	0.608287i
$689$	24.3203	−	15.6297i	0.926530	−	0.595445i
$690$		0			0
$691$	−3.56348	−	4.11247i	−0.135561	−	0.156446i	0.683910	−	0.729566i	$-0.260278\pi$
$691$	−3.56348	−	4.11247i	−0.135561	−	0.156446i	−0.819471	+	0.573121i	$0.805733\pi$
$692$	6.01999	−	1.76763i	0.228846	−	0.0671952i
$693$		0			0
$694$	−22.6091	+	49.5071i	−0.858231	+	1.87926i
$695$	1.08491	+	7.54575i	0.0411532	+	0.286227i
$696$		0			0
$697$	−10.8262	−	12.4941i	−0.410071	−	0.473247i
$698$	4.03380	−	28.0557i	0.152682	−	1.06192i
$699$		0			0
$700$	−9.18471			−0.347149
$701$	1.21326	−	8.43844i	0.0458244	−	0.318715i	−0.953997	−	0.299816i	$-0.903075\pi$
$701$	1.21326	−	8.43844i	0.0458244	−	0.318715i	0.999821	−	0.0188993i	$-0.00601620\pi$
$702$		0			0
$703$	1.04948	−	0.674460i	0.0395819	−	0.0254377i
$704$	−37.0599	+	23.8169i	−1.39675	+	0.897634i
$705$		0			0
$706$	−3.17077	+	22.0532i	−0.119334	+	0.829984i
$707$	−5.13496			−0.193120
$708$		0			0
$709$	−1.76579	+	12.2813i	−0.0663157	+	0.461236i	0.929423	+	0.369016i	$0.120305\pi$
$709$	−1.76579	+	12.2813i	−0.0663157	+	0.461236i	−0.995739	+	0.0922196i	$0.970604\pi$
$710$	−11.3381	−	13.0849i	−0.425512	−	0.491066i
$711$		0			0
$712$	−7.81237	−	54.3362i	−0.292781	−	2.03634i
$713$	−10.7776	+	23.5996i	−0.403624	+	0.883813i
$714$		0			0
$715$	55.7682	−	16.3750i	2.08561	−	0.612391i
$716$	15.0611	+	17.3815i	0.562860	+	0.649576i
$717$		0			0
$718$	23.1159	−	14.8557i	0.862676	−	0.554408i
$719$	−2.22917	−	4.88120i	−0.0831339	−	0.182038i	0.863500	−	0.504349i	$-0.168268\pi$
$719$	−2.22917	−	4.88120i	−0.0831339	−	0.182038i	−0.946634	+	0.322311i	$0.895540\pi$
$720$		0			0
$721$	4.60833	−	5.31830i	0.171623	−	0.198064i
$722$	−38.2045	+	24.5525i	−1.42182	+	0.913751i
$723$		0			0
$724$	−4.44301	−	30.9018i	−0.165123	−	1.14846i
$725$	−0.118728	−	0.825770i	−0.00440944	−	0.0306683i
$726$		0			0
$727$	−16.7669	+	4.92322i	−0.621851	+	0.182592i	−0.577456	−	0.816422i	$-0.695954\pi$
$727$	−16.7669	+	4.92322i	−0.621851	+	0.182592i	−0.0443957	+	0.999014i	$0.514136\pi$
$728$	20.3669	+	13.0890i	0.754847	+	0.485111i
$729$		0			0
$730$	42.3357	+	27.2075i	1.56691	+	1.00699i
$731$	−34.5436	−	39.8654i	−1.27764	−	1.47448i
$732$		0			0
$733$	4.06310	+	8.89694i	0.150074	+	0.328616i	0.969706	−	0.244274i	$-0.0785496\pi$
$733$	4.06310	+	8.89694i	0.150074	+	0.328616i	−0.819632	+	0.572890i	$0.805822\pi$
$734$	42.5438	+	12.4920i	1.57032	+	0.461088i
$735$		0			0
$736$	6.53939			0.241045
$737$	−10.4336	+	32.6599i	−0.384328	+	1.20304i
$738$		0			0
$739$	−34.3910	−	22.1018i	−1.26509	−	0.813026i	−0.276120	−	0.961123i	$-0.589049\pi$
$739$	−34.3910	−	22.1018i	−1.26509	−	0.813026i	−0.988973	+	0.148097i	$0.952685\pi$
$740$	−48.8141	−	14.3331i	−1.79444	−	0.526896i
$741$		0			0
$742$	−9.78921	+	11.2974i	−0.359373	+	0.414739i
$743$	17.5170	+	20.2157i	0.642635	+	0.741641i	0.979838	−	0.199791i	$-0.0640264\pi$
$743$	17.5170	+	20.2157i	0.642635	+	0.741641i	−0.337203	+	0.941432i	$0.609481\pi$
$744$		0			0
$745$	−7.88301	+	54.8276i	−0.288811	+	2.00873i
$746$	74.1194	+	47.6337i	2.71371	+	1.74399i
$747$		0			0
$748$	−79.2341	+	91.4411i	−2.89709	+	3.34342i
$749$	−1.93526	−	13.4600i	−0.0707127	−	0.491818i
$750$		0			0
$751$	20.9062	+	45.7781i	0.762877	+	1.67047i	0.741738	+	0.670690i	$0.234002\pi$
$751$	20.9062	+	45.7781i	0.762877	+	1.67047i	0.0211391	+	0.999777i	$0.493271\pi$
$752$	−14.2913	+	9.18449i	−0.521152	+	0.334924i
$753$		0			0
$754$	−1.95765	+	4.28665i	−0.0712933	+	0.156111i
$755$	14.0323	+	30.7265i	0.510688	+	1.11825i
$756$		0			0
$757$	8.60908	+	2.52785i	0.312902	+	0.0918764i	0.434413	−	0.900714i	$-0.356956\pi$
$757$	8.60908	+	2.52785i	0.312902	+	0.0918764i	−0.121511	+	0.992590i	$0.538774\pi$
$758$	12.2448	+	14.1312i	0.444750	+	0.513269i
$759$		0			0
$760$	−2.66377	−	0.782152i	−0.0966249	−	0.0283716i
$761$	7.62338	−	16.6929i	0.276347	−	0.605116i	−0.719666	−	0.694320i	$-0.755705\pi$
$761$	7.62338	−	16.6929i	0.276347	−	0.605116i	0.996013	+	0.0892041i	$0.0284323\pi$
$762$		0			0
$763$	0.266483	−	0.583516i	0.00964733	−	0.0211247i
$764$	−5.45566	−	6.29617i	−0.197379	−	0.227787i
$765$		0			0
$766$	−84.3698			−3.04840
$767$	−37.2261			−1.34416
$768$		0			0
$769$	17.7104	−	5.20026i	0.638655	−	0.187526i	0.0536553	−	0.998560i	$-0.482913\pi$
$769$	17.7104	−	5.20026i	0.638655	−	0.187526i	0.585000	+	0.811033i	$0.301095\pi$
$770$	−25.2830	+	16.2484i	−0.911135	+	0.585551i
$771$		0			0
$772$	92.2180	−	27.0777i	3.31900	−	0.974546i
$773$	−6.36543	+	44.2726i	−0.228949	+	1.59237i	0.473601	+	0.880739i	$0.342954\pi$
$773$	−6.36543	+	44.2726i	−0.228949	+	1.59237i	−0.702550	+	0.711634i	$0.747955\pi$
$774$		0			0
$775$	19.5975			0.703963
$776$	4.12105	−	28.6625i	0.147937	−	1.02892i
$777$		0			0
$778$	5.70900	−	12.5010i	0.204678	−	0.448181i
$779$	−0.0753349	−	0.523966i	−0.00269915	−	0.0187730i
$780$		0			0
$781$	−10.8180	−	3.17644i	−0.387097	−	0.113662i
$782$	51.5209	−	15.1279i	1.84238	−	0.540972i
$783$		0			0
$784$	14.1461	+	4.15366i	0.505217	+	0.148345i
$785$	26.3877	−	16.9583i	0.941817	−	0.605269i
$786$		0			0
$787$	−11.7909	+	25.8186i	−0.420302	+	0.920332i	0.574500	+	0.818504i	$0.305196\pi$
$787$	−11.7909	+	25.8186i	−0.420302	+	0.920332i	−0.994802	+	0.101828i	$0.967531\pi$
$788$	−43.8724	+	50.6315i	−1.56289	+	1.80367i
$789$		0			0
$790$	13.6229	+	29.8300i	0.484681	+	1.06130i
$791$	0.0609719	+	0.424069i	0.00216791	+	0.0150782i
$792$		0			0
$793$	−5.10430	+	5.89068i	−0.181259	+	0.209184i
$794$	22.2269	−	6.52641i	0.788804	−	0.231614i
$795$		0			0
$796$	5.75851	−	40.0514i	0.204105	−	1.41958i
$797$	−19.2668	−	12.3820i	−0.682466	−	0.438594i	0.152934	−	0.988236i	$-0.451128\pi$
$797$	−19.2668	−	12.3820i	−0.682466	−	0.438594i	−0.835400	+	0.549642i	$0.814764\pi$
$798$		0			0
$799$	33.4562	−	38.6105i	1.18360	−	1.36594i
$800$	−2.05201	−	4.49328i	−0.0725496	−	0.158862i
$801$		0			0
$802$	−2.42376	−	1.55766i	−0.0855861	−	0.0550028i
$803$	32.7711			1.15647
$804$		0			0
$805$	8.69832			0.306575
$806$	−93.1274	−	59.8493i	−3.28027	−	2.10810i
$807$		0			0
$808$	8.02389	+	17.5699i	0.282279	+	0.618106i
$809$	−6.17541	+	7.12680i	−0.217116	+	0.250565i	−0.853851	−	0.520518i	$-0.825739\pi$
$809$	−6.17541	+	7.12680i	−0.217116	+	0.250565i	0.636735	+	0.771083i	$0.280284\pi$
$810$		0			0
$811$	−28.0062	−	17.9985i	−0.983432	−	0.632013i	−0.0530450	−	0.998592i	$-0.516893\pi$
$811$	−28.0062	−	17.9985i	−0.983432	−	0.632013i	−0.930387	+	0.366579i	$0.880529\pi$
$812$	0.226159	−	1.57297i	0.00793664	−	0.0552005i
$813$		0			0
$814$	−48.7418	+	14.3119i	−1.70840	+	0.501631i
$815$	−11.2193	+	12.9478i	−0.392995	+	0.453541i
$816$		0			0
$817$	−0.240375	−	1.67184i	−0.00840965	−	0.0584904i
$818$	26.9347	+	58.9787i	0.941749	+	2.06214i
$819$		0			0
$820$	−14.1368	+	16.3148i	−0.493679	+	0.569736i
$821$	−17.6990	+	38.7554i	−0.617699	+	1.35257i	0.299482	+	0.954102i	$0.403186\pi$
$821$	−17.6990	+	38.7554i	−0.617699	+	1.35257i	−0.917181	+	0.398470i	$0.869541\pi$
$822$		0			0
$823$	−36.6503	+	23.5537i	−1.27755	+	0.821031i	−0.990584	−	0.136910i	$-0.956283\pi$
$823$	−36.6503	+	23.5537i	−1.27755	+	0.821031i	−0.286966	+	0.957941i	$0.592647\pi$
$824$	−25.3982	−	7.45757i	−0.884787	−	0.259797i
$825$		0			0
$826$	18.4691	−	5.42302i	0.642622	−	0.188691i
$827$	11.3855	+	3.34310i	0.395914	+	0.116251i	0.473628	−	0.880725i	$-0.342944\pi$
$827$	11.3855	+	3.34310i	0.395914	+	0.116251i	−0.0777141	+	0.996976i	$0.524762\pi$
$828$		0			0
$829$	−2.13847	−	14.8734i	−0.0742720	−	0.516573i	−0.992664	−	0.120902i	$-0.961421\pi$
$829$	−2.13847	−	14.8734i	−0.0742720	−	0.516573i	0.918392	−	0.395671i	$-0.129488\pi$
$830$	−10.3805	+	22.7302i	−0.360314	+	0.788977i
$831$		0			0
$832$	−7.74233	+	53.8491i	−0.268417	+	1.86688i
$833$	−44.3380			−1.53622
$834$		0			0
$835$	−2.45463	+	17.0723i	−0.0849460	+	0.590813i
$836$	−3.71728	+	1.09149i	−0.128565	+	0.0377500i
$837$		0			0
$838$	26.0584	−	16.7467i	0.900172	−	0.578506i
$839$	26.4120	−	7.75525i	0.911842	−	0.267741i	0.208026	−	0.978123i	$-0.433296\pi$
$839$	26.4120	−	7.75525i	0.911842	−	0.267741i	0.703816	+	0.710382i	$0.251478\pi$
$840$		0			0
$841$	−28.8557			−0.995023
$842$	80.5701			2.77663
$843$		0			0
$844$	−12.4277	−	14.3423i	−0.427778	−	0.493683i
$845$	15.3310	−	33.5701i	0.527401	−	1.15485i
$846$		0			0
$847$	−3.03292	+	6.64117i	−0.104212	+	0.228193i
$848$	13.7357	+	4.03318i	0.471687	+	0.138500i
$849$		0			0
$850$	−26.5614	−	30.6535i	−0.911049	−	1.05141i
$851$	14.1070	+	4.14220i	0.483582	+	0.141993i
$852$		0			0
$853$	−14.7891	−	32.3836i	−0.506370	−	1.10879i	−0.974346	−	0.225054i	$-0.927744\pi$
$853$	−14.7891	−	32.3836i	−0.506370	−	1.10879i	0.467977	−	0.883741i	$-0.344983\pi$
$854$	1.67427	−	3.66614i	0.0572924	−	0.125453i
$855$		0			0
$856$	−43.0309	+	27.6543i	−1.47077	+	0.945204i
$857$	−15.5796	−	34.1145i	−0.532188	−	1.16533i	−0.964616	−	0.263660i	$-0.915070\pi$
$857$	−15.5796	−	34.1145i	−0.532188	−	1.16533i	0.432428	−	0.901668i	$-0.357657\pi$
$858$		0			0
$859$	7.19982	+	50.0758i	0.245655	+	1.70857i	0.622775	+	0.782401i	$0.286005\pi$
$859$	7.19982	+	50.0758i	0.245655	+	1.70857i	−0.377120	+	0.926164i	$0.623086\pi$
$860$	−45.1071	+	52.0563i	−1.53814	+	1.77511i
$861$		0			0
$862$	47.0830	+	30.2584i	1.60365	+	1.03061i
$863$	6.22819	−	43.3180i	0.212010	−	1.47456i	−0.554422	−	0.832236i	$-0.687061\pi$
$863$	6.22819	−	43.3180i	0.212010	−	1.47456i	0.766432	−	0.642326i	$-0.222030\pi$
$864$		0			0
$865$	2.93923	+	3.39206i	0.0999369	+	0.115333i
$866$	37.5616	−	43.3484i	1.27640	−	1.47304i
$867$		0			0
$868$	35.8183	+	10.5172i	1.21575	+	0.356977i
$869$	17.9649	+	11.5454i	0.609419	+	0.391650i
$870$		0			0
$871$	22.0438	+	36.1502i	0.746926	+	1.22490i
$872$	−2.41297			−0.0817136
$873$		0			0
$874$	1.64969	+	0.484394i	0.0558017	+	0.0163849i
$875$	3.48561	+	7.63243i	0.117835	+	0.258023i
$876$		0			0
$877$	5.21476	+	6.01815i	0.176090	+	0.203219i	0.836933	−	0.547306i	$-0.184346\pi$
$877$	5.21476	+	6.01815i	0.176090	+	0.203219i	−0.660843	+	0.750524i	$0.729801\pi$
$878$	−9.30965	−	5.98295i	−0.314185	−	0.201915i
$879$		0			0
$880$	24.2125	+	15.5604i	0.816203	+	0.524542i
$881$	−39.4932	+	11.5963i	−1.33056	+	0.390688i	−0.868292	−	0.496053i	$-0.834782\pi$
$881$	−39.4932	+	11.5963i	−1.33056	+	0.390688i	−0.462268	+	0.886740i	$0.652964\pi$
$882$		0			0
$883$	−7.20740	−	50.1286i	−0.242548	−	1.68696i	−0.639239	−	0.769008i	$-0.720751\pi$
$883$	−7.20740	−	50.1286i	−0.242548	−	1.68696i	0.396691	−	0.917952i	$-0.370159\pi$
$884$	21.2647	+	147.899i	0.715208	+	4.97438i
$885$		0			0
$886$	14.9631	−	9.61618i	0.502694	−	0.323062i
$887$	−30.0269	+	34.6529i	−1.00821	+	1.16353i	−0.0217064	+	0.999764i	$0.506910\pi$
$887$	−30.0269	+	34.6529i	−1.00821	+	1.16353i	−0.986499	+	0.163767i	$0.947636\pi$
$888$		0			0
$889$	−2.60987	−	5.71481i	−0.0875321	−	0.191668i
$890$	70.7959	−	45.4977i	2.37308	−	1.52509i
$891$		0			0
$892$	−20.3096	−	23.4386i	−0.680017	−	0.784782i
$893$	1.56960	−	0.460877i	0.0525248	−	0.0154227i
$894$		0			0
$895$	−6.83473	+	14.9660i	−0.228460	+	0.500257i
$896$	−3.28918	−	22.8767i	−0.109884	−	0.764258i
$897$		0			0
$898$	20.1802	+	23.2892i	0.673421	+	0.777169i
$899$	−0.482559	+	3.35627i	−0.0160942	+	0.111938i
$900$		0			0
$901$	−43.0518			−1.43426
$902$	−3.06767	+	21.3361i	−0.102142	+	0.710415i
$903$		0			0
$904$	1.35573	−	0.871273i	0.0450908	−	0.0289781i
$905$	18.7882	−	12.0744i	0.624541	−	0.401368i
$906$		0			0
$907$	−8.29146	+	57.6684i	−0.275314	+	1.91485i	0.113512	+	0.993537i	$0.463790\pi$
$907$	−8.29146	+	57.6684i	−0.275314	+	1.91485i	−0.388826	+	0.921311i	$0.627119\pi$
$908$	−108.431			−3.59842
$909$		0			0
$910$	−5.28198	+	36.7369i	−0.175096	+	1.21782i
$911$	−19.9674	−	23.0436i	−0.661550	−	0.763469i	0.321480	−	0.946916i	$-0.395820\pi$
$911$	−19.9674	−	23.0436i	−0.661550	−	0.763469i	−0.983030	+	0.183447i	$0.941274\pi$
$912$		0			0
$913$	2.31579	+	16.1067i	0.0766415	+	0.533053i
$914$	26.6917	−	58.4466i	0.882883	−	1.93324i
$915$		0			0
$916$	−45.3685	+	13.3214i	−1.49902	+	0.440151i
$917$	3.12680	+	3.60852i	0.103256	+	0.119164i
$918$		0			0
$919$	24.3134	−	15.6252i	0.802024	−	0.515429i	−0.0742519	−	0.997240i	$-0.523657\pi$
$919$	24.3134	−	15.6252i	0.802024	−	0.515429i	0.876276	+	0.481810i	$0.160021\pi$
$920$	−13.5920	−	29.7623i	−0.448115	−	0.981234i
$921$		0			0
$922$	31.1293	−	35.9251i	1.02519	−	1.18313i
$923$	−11.7132	+	7.52761i	−0.385544	+	0.247774i
$924$		0			0
$925$	−1.58054	−	10.9929i	−0.0519677	−	0.361444i
$926$	−4.21465	−	29.3136i	−0.138502	−	0.963304i
$927$		0			0
$928$	0.820047	−	0.240788i	0.0269194	−	0.00790424i
$929$	−26.9490	−	17.3191i	−0.884169	−	0.568221i	0.0178868	−	0.999840i	$-0.494306\pi$
$929$	−26.9490	−	17.3191i	−0.884169	−	0.568221i	−0.902056	+	0.431619i	$0.857943\pi$
$930$		0			0
$931$	−1.19433	−	0.767547i	−0.0391424	−	0.0251553i
$932$	−56.8373	−	65.5937i	−1.86177	−	2.14859i
$933$		0			0
$934$	15.2462	+	33.3845i	0.498871	+	1.09237i
$935$	−83.0493	−	24.3855i	−2.71600	−	0.797490i
$936$		0			0
$937$	27.1369			0.886523			0.443262	−	0.896392i	$-0.353821\pi$
$937$	27.1369			0.886523			0.443262	+	0.896392i	$0.353821\pi$
$938$	−16.2029	−	14.7240i	−0.529045	−	0.480756i
$939$		0			0
$940$	−56.1218	−	36.0673i	−1.83049	−	1.17639i
$941$	35.0494	+	10.2914i	1.14258	+	0.335491i	0.797640	−	0.603134i	$-0.206081\pi$
$941$	35.0494	+	10.2914i	1.14258	+	0.335491i	0.344939	+	0.938625i	$0.387900\pi$
$942$		0			0
$943$	4.08547	−	4.71488i	0.133041	−	0.153538i
$944$	−12.0716	−	13.9314i	−0.392897	−	0.453427i
$945$		0			0
$946$	−9.78817	+	68.0782i	−0.318241	+	2.21341i
$947$	−49.3919	−	31.7422i	−1.60502	−	1.03148i	−0.964691	−	0.263384i	$-0.915161\pi$
$947$	−49.3919	−	31.7422i	−1.60502	−	1.03148i	−0.640330	−	0.768100i	$-0.721202\pi$
$948$		0			0
$949$	26.5024	−	30.5854i	0.860304	−	0.992843i
$950$	−0.184830	−	1.28552i	−0.00599668	−	0.0417078i
$951$		0			0
$952$	−14.9772	−	32.7954i	−0.485412	−	1.06290i
$953$	3.11443	−	2.00152i	0.100886	−	0.0648356i	−0.489225	−	0.872158i	$-0.662720\pi$
$953$	3.11443	−	2.00152i	0.100886	−	0.0648356i	0.590111	+	0.807322i	$0.299084\pi$
$954$		0			0
$955$	2.47578	−	5.42119i	0.0801142	−	0.175426i
$956$	−36.3800	−	79.6611i	−1.17661	−	2.57642i
$957$		0			0
$958$	−74.6234	−	21.9114i	−2.41097	−	0.707926i
$959$	8.73431	+	10.0799i	0.282046	+	0.325498i
$960$		0			0
$961$	−46.6815	−	13.7069i	−1.50586	−	0.442159i
$962$	−26.0607	+	57.0650i	−0.840232	+	1.83985i
$963$		0			0
$964$	−20.9441	+	45.8611i	−0.674563	+	1.47709i
$965$	45.0250	+	51.9617i	1.44941	+	1.67270i
$966$		0			0
$967$	−25.4452			−0.818261			−0.409131	−	0.912476i	$-0.634168\pi$
$967$	−25.4452			−0.818261			−0.409131	+	0.912476i	$0.634168\pi$
$968$	27.4628			0.882686
$969$		0			0
$970$	42.5939	−	12.5067i	1.36761	−	0.401566i
$971$	−22.8752	+	14.7010i	−0.734100	+	0.471778i	−0.853516	−	0.521067i	$-0.825534\pi$
$971$	−22.8752	+	14.7010i	−0.734100	+	0.471778i	0.119416	+	0.992844i	$0.461898\pi$
$972$		0			0
$973$	−3.04159	+	0.893091i	−0.0975088	+	0.0286312i
$974$	−11.7749	+	81.8962i	−0.377292	+	2.62412i
$975$		0			0
$976$	−3.85971			−0.123546
$977$	−6.65048	+	46.2551i	−0.212768	+	1.47983i	0.551089	+	0.834447i	$0.314213\pi$
$977$	−6.65048	+	46.2551i	−0.212768	+	1.47983i	−0.763857	+	0.645386i	$0.776697\pi$
$978$		0			0
$979$	22.7654	−	49.8492i	0.727585	−	1.59319i
$980$	8.23954	+	57.3073i	0.263202	+	1.83061i
$981$		0			0
$982$	−13.2756	−	3.89808i	−0.423643	−	0.124393i
$983$	44.1761	−	12.9713i	1.40900	−	0.413720i	0.513235	−	0.858248i	$-0.328447\pi$
$983$	44.1761	−	12.9713i	1.40900	−	0.413720i	0.895765	+	0.444528i	$0.146629\pi$
$984$		0			0
$985$	−45.9849	−	13.5024i	−1.46520	−	0.430222i
$986$	5.90376	−	3.79411i	0.188014	−	0.120829i
$987$		0			0
$988$	−1.98752	+	4.35205i	−0.0632313	+	0.138457i
$989$	13.0357	−	15.0440i	0.414511	−	0.478371i
$990$		0			0
$991$	−16.6292	−	36.4128i	−0.528244	−	1.15669i	−0.966223	−	0.257707i	$-0.917033\pi$
$991$	−16.6292	−	36.4128i	−0.528244	−	1.15669i	0.437979	−	0.898985i	$-0.355694\pi$
$992$	2.85723	+	19.8725i	0.0907173	+	0.630952i
$993$		0			0
$994$	4.71469	−	5.44105i	0.149541	−	0.172580i
$995$	27.7737	−	8.15508i	0.880484	−	0.258533i
$996$		0			0
$997$	−0.836669	+	5.81916i	−0.0264976	+	0.184295i	−0.998772	−	0.0495494i	$-0.984221\pi$
$997$	−0.836669	+	5.81916i	−0.0264976	+	0.184295i	0.972274	+	0.233844i	$0.0751306\pi$
$998$	−2.63061	−	1.69059i	−0.0832706	−	0.0535147i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	603.2.u.b.478.1		10
3.2	odd	2		67.2.e.a.9.1	✓	10
67.15	even	11	inner	603.2.u.b.82.1		10
201.89	odd	22		4489.2.a.f.1.1		5
201.149	odd	22		67.2.e.a.15.1	yes	10
201.179	even	22		4489.2.a.k.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.2.e.a.9.1	✓	10	3.2	odd	2
67.2.e.a.15.1	yes	10	201.149	odd	22
603.2.u.b.82.1		10	67.15	even	11	inner
603.2.u.b.478.1		10	1.1	even	1	trivial
4489.2.a.f.1.1		5	201.89	odd	22
4489.2.a.k.1.5		5	201.179	even	22

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:	\( N \)	\(=\)	\( 603 = 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	603.u (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(2.01722 + 1.29639i) q^{2} +(1.55773 + 3.41095i) q^{4} +(-1.75667 + 2.02730i) q^{5} +(-0.938384 - 0.603063i) q^{7} +(-0.597131 + 4.15314i) q^{8} +O(q^{10})\)	\(q+(2.01722 + 1.29639i) q^{2} +(1.55773 + 3.41095i) q^{4} +(-1.75667 + 2.02730i) q^{5} +(-0.938384 - 0.603063i) q^{7} +(-0.597131 + 4.15314i) q^{8} +(-6.17177 + 1.81219i) q^{10} +(-2.74302 + 3.16561i) q^{11} +(0.736164 + 5.12013i) q^{13} +(-1.11113 - 2.43303i) q^{14} +(-1.67742 + 1.93584i) q^{16} +(3.20004 - 7.00712i) q^{17} +(0.207501 - 0.133353i) q^{19} +(-9.65145 - 2.83392i) q^{20} +(-9.63714 + 2.82972i) q^{22} +(2.78922 + 0.818988i) q^{23} +(-0.312501 - 2.17349i) q^{25} +(-5.15269 + 11.2828i) q^{26} +(0.595270 - 4.14019i) q^{28} +0.379927 q^{29} +(-1.27013 + 8.83397i) q^{31} +(2.15843 - 0.633773i) q^{32} +(15.5392 - 9.98642i) q^{34} +(2.87102 - 0.843008i) q^{35} +5.05770 q^{37} +0.591454 q^{38} +(-7.37071 - 8.50625i) q^{40} +(0.891527 - 1.95217i) q^{41} +(2.84464 - 6.22889i) q^{43} +(-15.0706 - 4.42513i) q^{44} +(4.56474 + 5.26800i) q^{46} +(6.36350 + 1.86849i) q^{47} +(-2.39102 - 5.23561i) q^{49} +(2.18731 - 4.78954i) q^{50} +(-16.3178 + 10.4868i) q^{52} +(-2.32167 - 5.08374i) q^{53} +(-1.59908 - 11.1219i) q^{55} +(3.06494 - 3.53713i) q^{56} +(0.766398 + 0.492534i) q^{58} +(-1.02417 + 7.12328i) q^{59} +(0.986760 + 1.13878i) q^{61} +(-14.0144 + 16.1735i) q^{62} +(10.0911 + 2.96302i) q^{64} +(-11.6733 - 7.50195i) q^{65} +(7.52388 - 3.22355i) q^{67} +28.8858 q^{68} +(6.88436 + 2.02143i) q^{70} +(1.11816 + 2.44844i) q^{71} +(-5.12343 - 5.91275i) q^{73} +(10.2025 + 6.55675i) q^{74} +(0.778092 + 0.500049i) q^{76} +(4.48307 - 1.31635i) q^{77} +(-0.725553 - 5.04634i) q^{79} +(-0.977875 - 6.80127i) q^{80} +(4.32918 - 2.78220i) q^{82} +(2.54401 - 2.93594i) q^{83} +(8.58414 + 18.7967i) q^{85} +(13.8133 - 8.87729i) q^{86} +(-11.5093 - 13.2824i) q^{88} +(-12.5532 + 3.68596i) q^{89} +(2.39696 - 5.24861i) q^{91} +(1.55132 + 10.7896i) q^{92} +(10.4143 + 12.0187i) q^{94} +(-0.0941640 + 0.654925i) q^{95} -6.90141 q^{97} +(1.96417 - 13.6611i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 6 q^{2} + 10 q^{4} - 3 q^{5} - 6 q^{8}+O(q^{10}) \) 10 * q + 6 * q^2 + 10 * q^4 - 3 * q^5 - 6 * q^8	\( 10 q + 6 q^{2} + 10 q^{4} - 3 q^{5} - 6 q^{8} - 15 q^{10} - 15 q^{11} - 18 q^{13} - 6 q^{16} + 26 q^{17} - q^{19} - 25 q^{20} - 9 q^{22} + 6 q^{23} - 4 q^{25} - 24 q^{26} + 11 q^{28} - 28 q^{29} - 10 q^{31} + 4 q^{32} + 64 q^{34} - 22 q^{37} + 6 q^{38} - 18 q^{40} - 9 q^{41} + 21 q^{43} - 48 q^{44} - 25 q^{46} + 22 q^{47} + 7 q^{49} + 35 q^{50} - 62 q^{52} - 20 q^{53} - 23 q^{55} + 11 q^{56} - 8 q^{58} + 17 q^{59} + 13 q^{61} - 50 q^{62} + 10 q^{64} - 10 q^{65} + 23 q^{67} + 114 q^{68} + 11 q^{70} - q^{71} - 18 q^{73} - 22 q^{74} + 21 q^{76} + 22 q^{77} + 5 q^{79} - 18 q^{80} - 12 q^{82} + 12 q^{83} + 23 q^{85} + 61 q^{86} - 2 q^{88} - 51 q^{89} - 11 q^{91} - 38 q^{92} + 11 q^{94} - 3 q^{95} - 10 q^{97} + 2 q^{98}+O(q^{100}) \) 10 * q + 6 * q^2 + 10 * q^4 - 3 * q^5 - 6 * q^8 - 15 * q^10 - 15 * q^11 - 18 * q^13 - 6 * q^16 + 26 * q^17 - q^19 - 25 * q^20 - 9 * q^22 + 6 * q^23 - 4 * q^25 - 24 * q^26 + 11 * q^28 - 28 * q^29 - 10 * q^31 + 4 * q^32 + 64 * q^34 - 22 * q^37 + 6 * q^38 - 18 * q^40 - 9 * q^41 + 21 * q^43 - 48 * q^44 - 25 * q^46 + 22 * q^47 + 7 * q^49 + 35 * q^50 - 62 * q^52 - 20 * q^53 - 23 * q^55 + 11 * q^56 - 8 * q^58 + 17 * q^59 + 13 * q^61 - 50 * q^62 + 10 * q^64 - 10 * q^65 + 23 * q^67 + 114 * q^68 + 11 * q^70 - q^71 - 18 * q^73 - 22 * q^74 + 21 * q^76 + 22 * q^77 + 5 * q^79 - 18 * q^80 - 12 * q^82 + 12 * q^83 + 23 * q^85 + 61 * q^86 - 2 * q^88 - 51 * q^89 - 11 * q^91 - 38 * q^92 + 11 * q^94 - 3 * q^95 - 10 * q^97 + 2 * q^98

Introduction

L-functions

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