LMFDB - Embedded newform 57.2.i.b.43.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [57,2,Mod(4,57)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(57, base_ring=CyclotomicField(18))

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("57.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 57 = 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	57.i (of order $9$, 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:	$0.455147291521$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 $ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			43.2
Root			$0.500000 + 0.168222i$ of defining polynomial
Character	$\chi$	$=$	57.43
Dual form			57.2.i.b.4.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.791518 - 0.288089i) q^{2} +(0.173648 - 0.984808i) q^{3} +(-0.988583 + 0.829520i) q^{4} +(1.30800 + 1.09754i) q^{5} +(-0.146267 - 0.829520i) q^{6} +(-1.96517 - 3.40377i) q^{7} +(-1.38582 + 2.40031i) q^{8} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})$	\(q+(0.791518 - 0.288089i) q^{2} +(0.173648 - 0.984808i) q^{3} +(-0.988583 + 0.829520i) q^{4} +(1.30800 + 1.09754i) q^{5} +(-0.146267 - 0.829520i) q^{6} +(-1.96517 - 3.40377i) q^{7} +(-1.38582 + 2.40031i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(1.35149 + 0.491903i) q^{10} +(-2.21268 + 3.83247i) q^{11} +(0.645252 + 1.11761i) q^{12} +(0.316842 + 1.79690i) q^{13} +(-2.53605 - 2.12800i) q^{14} +(1.30800 - 1.09754i) q^{15} +(0.0427879 - 0.242662i) q^{16} +(4.72331 - 1.71914i) q^{17} -0.842316 q^{18} +(-1.33604 - 4.14910i) q^{19} -2.20349 q^{20} +(-3.69330 + 1.34425i) q^{21} +(-0.647282 + 3.67092i) q^{22} +(2.64922 - 2.22296i) q^{23} +(2.12320 + 1.78158i) q^{24} +(-0.361980 - 2.05289i) q^{25} +(0.768454 + 1.33100i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(4.76622 + 1.73476i) q^{28} +(1.36276 + 0.496003i) q^{29} +(0.719113 - 1.24554i) q^{30} +(1.43471 + 2.48499i) q^{31} +(-0.998623 - 5.66347i) q^{32} +(3.39002 + 2.84456i) q^{33} +(3.24332 - 2.72147i) q^{34} +(1.16534 - 6.60896i) q^{35} +(1.21268 - 0.441378i) q^{36} -4.83123 q^{37} +(-2.25281 - 2.89919i) q^{38} +1.82462 q^{39} +(-4.44709 + 1.61861i) q^{40} +(-1.52950 + 8.67423i) q^{41} +(-2.53605 + 2.12800i) q^{42} +(7.73836 + 6.49325i) q^{43} +(-0.991693 - 5.62417i) q^{44} +(-0.853733 - 1.47871i) q^{45} +(1.45649 - 2.52272i) q^{46} +(-3.22814 - 1.17495i) q^{47} +(-0.231546 - 0.0842757i) q^{48} +(-4.22376 + 7.31577i) q^{49} +(-0.877928 - 1.52062i) q^{50} +(-0.872832 - 4.95008i) q^{51} +(-1.80379 - 1.51356i) q^{52} +(-1.61814 + 1.35778i) q^{53} +(-0.146267 + 0.829520i) q^{54} +(-7.10045 + 2.58435i) q^{55} +10.8935 q^{56} +(-4.31806 + 0.595259i) q^{57} +1.22154 q^{58} +(-6.01966 + 2.19098i) q^{59} +(-0.382632 + 2.17002i) q^{60} +(0.0587523 - 0.0492990i) q^{61} +(1.85150 + 1.55359i) q^{62} +(0.682495 + 3.87062i) q^{63} +(-2.17561 - 3.76826i) q^{64} +(-1.55774 + 2.69809i) q^{65} +(3.50275 + 1.27490i) q^{66} +(0.984002 + 0.358147i) q^{67} +(-3.24332 + 5.61759i) q^{68} +(-1.72915 - 2.99498i) q^{69} +(-0.981583 - 5.56683i) q^{70} +(-10.3790 - 8.70898i) q^{71} +(2.12320 - 1.78158i) q^{72} +(0.696538 - 3.95026i) q^{73} +(-3.82401 + 1.39182i) q^{74} -2.08456 q^{75} +(4.76254 + 2.99345i) q^{76} +17.3931 q^{77} +(1.44422 - 0.525654i) q^{78} +(2.94592 - 16.7071i) q^{79} +(0.322297 - 0.270440i) q^{80} +(0.766044 + 0.642788i) q^{81} +(1.28832 + 7.30645i) q^{82} +(6.51259 + 11.2801i) q^{83} +(2.53605 - 4.39257i) q^{84} +(8.06489 + 2.93538i) q^{85} +(7.99569 + 2.91019i) q^{86} +(0.725109 - 1.25592i) q^{87} +(-6.13275 - 10.6222i) q^{88} +(2.14695 + 12.1759i) q^{89} +(-1.10175 - 0.924474i) q^{90} +(5.49359 - 4.60967i) q^{91} +(-0.774984 + 4.39515i) q^{92} +(2.69638 - 0.981401i) q^{93} -2.89362 q^{94} +(2.80626 - 6.89335i) q^{95} -5.75084 q^{96} +(-0.164685 + 0.0599404i) q^{97} +(-1.23559 + 7.00738i) q^{98} +(3.39002 - 2.84456i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 3 q^{4} + 6 q^{5} - 3 q^{6} - 9 q^{7} + 3 q^{8}+O(q^{10}) $ 12 * q - 3 * q^2 - 3 * q^4 + 6 * q^5 - 3 * q^6 - 9 * q^7 + 3 * q^8	\( 12 q - 3 q^{2} - 3 q^{4} + 6 q^{5} - 3 q^{6} - 9 q^{7} + 3 q^{8} - 18 q^{10} - 9 q^{11} - 6 q^{12} - 3 q^{13} - 3 q^{14} + 6 q^{15} + 33 q^{16} + 12 q^{17} - 9 q^{19} - 18 q^{20} - 24 q^{22} + 9 q^{23} + 30 q^{24} - 12 q^{25} - 6 q^{27} + 30 q^{28} - 6 q^{30} - 3 q^{32} - 9 q^{33} + 21 q^{34} + 30 q^{35} - 3 q^{36} - 12 q^{37} + 18 q^{38} + 6 q^{39} - 3 q^{40} - 18 q^{41} - 3 q^{42} + 15 q^{43} + 15 q^{44} - 9 q^{45} + 27 q^{46} - 9 q^{47} - 12 q^{48} - 9 q^{49} + 9 q^{50} - 15 q^{51} - 27 q^{52} - 30 q^{53} - 3 q^{54} + 15 q^{55} - 78 q^{56} - 3 q^{57} - 24 q^{58} - 30 q^{59} - 15 q^{60} + 21 q^{61} + 3 q^{62} + 9 q^{63} - 21 q^{64} + 21 q^{65} + 30 q^{66} + 3 q^{67} - 21 q^{68} - 6 q^{69} + 18 q^{70} - 30 q^{71} + 30 q^{72} - 24 q^{73} + 39 q^{74} + 30 q^{75} - 60 q^{76} + 96 q^{77} + 9 q^{78} + 24 q^{79} + 42 q^{80} - 33 q^{82} + 3 q^{83} + 3 q^{84} + 3 q^{85} + 51 q^{86} + 15 q^{87} + 42 q^{88} + 3 q^{89} - 9 q^{90} + 24 q^{91} + 69 q^{92} - 6 q^{93} + 18 q^{94} - 54 q^{95} - 42 q^{96} - 27 q^{97} - 3 q^{98} - 9 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^4 + 6 * q^5 - 3 * q^6 - 9 * q^7 + 3 * q^8 - 18 * q^10 - 9 * q^11 - 6 * q^12 - 3 * q^13 - 3 * q^14 + 6 * q^15 + 33 * q^16 + 12 * q^17 - 9 * q^19 - 18 * q^20 - 24 * q^22 + 9 * q^23 + 30 * q^24 - 12 * q^25 - 6 * q^27 + 30 * q^28 - 6 * q^30 - 3 * q^32 - 9 * q^33 + 21 * q^34 + 30 * q^35 - 3 * q^36 - 12 * q^37 + 18 * q^38 + 6 * q^39 - 3 * q^40 - 18 * q^41 - 3 * q^42 + 15 * q^43 + 15 * q^44 - 9 * q^45 + 27 * q^46 - 9 * q^47 - 12 * q^48 - 9 * q^49 + 9 * q^50 - 15 * q^51 - 27 * q^52 - 30 * q^53 - 3 * q^54 + 15 * q^55 - 78 * q^56 - 3 * q^57 - 24 * q^58 - 30 * q^59 - 15 * q^60 + 21 * q^61 + 3 * q^62 + 9 * q^63 - 21 * q^64 + 21 * q^65 + 30 * q^66 + 3 * q^67 - 21 * q^68 - 6 * q^69 + 18 * q^70 - 30 * q^71 + 30 * q^72 - 24 * q^73 + 39 * q^74 + 30 * q^75 - 60 * q^76 + 96 * q^77 + 9 * q^78 + 24 * q^79 + 42 * q^80 - 33 * q^82 + 3 * q^83 + 3 * q^84 + 3 * q^85 + 51 * q^86 + 15 * q^87 + 42 * q^88 + 3 * q^89 - 9 * q^90 + 24 * q^91 + 69 * q^92 - 6 * q^93 + 18 * q^94 - 54 * q^95 - 42 * q^96 - 27 * q^97 - 3 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

$n$	$20$	$40$
$\chi(n)$	$1$	$e\left(\frac{8}{9}\right)$

Coefficient data

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

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

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

$2$	0.791518	−	0.288089i	0.559688	−	0.203710i	−0.0466577	−	0.998911i	$-0.514857\pi$
$2$	0.791518	−	0.288089i	0.559688	−	0.203710i	0.606346	+	0.795201i	$0.292635\pi$
$3$	0.173648	−	0.984808i	0.100256	−	0.568579i
$3$	0.173648	−	0.984808i	0.100256	−	0.568579i
$4$	−0.988583	+	0.829520i	−0.494291	+	0.414760i
$5$	1.30800	+	1.09754i	0.584953	+	0.490834i	0.886570	−	0.462595i	$-0.153082\pi$
$5$	1.30800	+	1.09754i	0.584953	+	0.490834i	−0.301616	+	0.953429i	$0.597526\pi$
$6$	−0.146267	−	0.829520i	−0.0597131	−	0.338650i
$7$	−1.96517	−	3.40377i	−0.742763	−	1.28650i	−0.951233	−	0.308475i	$-0.900182\pi$
$7$	−1.96517	−	3.40377i	−0.742763	−	1.28650i	0.208469	−	0.978029i	$-0.433152\pi$
$8$	−1.38582	+	2.40031i	−0.489962	+	0.848639i
$9$	−0.939693	−	0.342020i	−0.313231	−	0.114007i
$10$	1.35149	+	0.491903i	0.427379	+	0.155553i
$11$	−2.21268	+	3.83247i	−0.667147	+	1.15553i	0.311551	+	0.950229i	$0.399151\pi$
$11$	−2.21268	+	3.83247i	−0.667147	+	1.15553i	−0.978698	+	0.205303i	$0.934182\pi$
$12$	0.645252	+	1.11761i	0.186268	+	0.322626i
$13$	0.316842	+	1.79690i	0.0878763	+	0.498371i	0.996699	+	0.0811881i	$0.0258714\pi$
$13$	0.316842	+	1.79690i	0.0878763	+	0.498371i	−0.908823	+	0.417183i	$0.863017\pi$
$14$	−2.53605	−	2.12800i	−0.677789	−	0.568732i
$15$	1.30800	−	1.09754i	0.337723	−	0.283383i
$16$	0.0427879	−	0.242662i	0.0106970	−	0.0606655i
$17$	4.72331	−	1.71914i	1.14557	−	0.416954i	0.301648	−	0.953419i	$-0.402463\pi$
$17$	4.72331	−	1.71914i	1.14557	−	0.416954i	0.843922	+	0.536466i	$0.180241\pi$
$18$	−0.842316			−0.198536
$19$	−1.33604	−	4.14910i	−0.306508	−	0.951868i
$19$	−1.33604	−	4.14910i	−0.306508	−	0.951868i
$20$	−2.20349			−0.492716
$21$	−3.69330	+	1.34425i	−0.805945	+	0.293340i
$22$	−0.647282	+	3.67092i	−0.138001	+	0.782642i
$23$	2.64922	−	2.22296i	0.552400	−	0.463519i	−0.323353	−	0.946278i	$-0.604810\pi$
$23$	2.64922	−	2.22296i	0.552400	−	0.463519i	0.875753	+	0.482760i	$0.160366\pi$
$24$	2.12320	+	1.78158i	0.433397	+	0.363663i
$25$	−0.361980	−	2.05289i	−0.0723959	−	0.410578i
$26$	0.768454	+	1.33100i	0.150706	+	0.261031i
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$	4.76622	+	1.73476i	0.900731	+	0.327839i
$29$	1.36276	+	0.496003i	0.253058	+	0.0921055i	0.465434	−	0.885082i	$-0.345898\pi$
$29$	1.36276	+	0.496003i	0.253058	+	0.0921055i	−0.212377	+	0.977188i	$0.568120\pi$
$30$	0.719113	−	1.24554i	0.131292	−	0.227404i
$31$	1.43471	+	2.48499i	0.257682	+	0.446318i	0.965621	−	0.259956i	$-0.0837080\pi$
$31$	1.43471	+	2.48499i	0.257682	+	0.446318i	−0.707939	+	0.706274i	$0.750375\pi$
$32$	−0.998623	−	5.66347i	−0.176533	−	1.00117i
$33$	3.39002	+	2.84456i	0.590126	+	0.495175i
$34$	3.24332	−	2.72147i	0.556225	−	0.466728i
$35$	1.16534	−	6.60896i	0.196978	−	1.11712i
$36$	1.21268	−	0.441378i	0.202113	−	0.0735630i
$37$	−4.83123			−0.794249			−0.397124	−	0.917765i	$-0.629992\pi$
$37$	−4.83123			−0.794249			−0.397124	+	0.917765i	$0.629992\pi$
$38$	−2.25281	−	2.89919i	−0.365454	−	0.470310i
$39$	1.82462			0.292173
$40$	−4.44709	+	1.61861i	−0.703146	+	0.255924i
$41$	−1.52950	+	8.67423i	−0.238868	+	1.35469i	0.595445	+	0.803396i	$0.296976\pi$
$41$	−1.52950	+	8.67423i	−0.238868	+	1.35469i	−0.834313	+	0.551291i	$0.814135\pi$
$42$	−2.53605	+	2.12800i	−0.391322	+	0.328358i
$43$	7.73836	+	6.49325i	1.18009	+	0.990212i	0.999978	+	0.00656507i	$0.00208974\pi$
$43$	7.73836	+	6.49325i	1.18009	+	0.990212i	0.180110	+	0.983647i	$0.442355\pi$
$44$	−0.991693	−	5.62417i	−0.149503	−	0.847876i
$45$	−0.853733	−	1.47871i	−0.127267	−	0.220433i
$46$	1.45649	−	2.52272i	0.214748	−	0.371955i
$47$	−3.22814	−	1.17495i	−0.470872	−	0.171384i	0.0956751	−	0.995413i	$-0.469499\pi$
$47$	−3.22814	−	1.17495i	−0.470872	−	0.171384i	−0.566548	+	0.824029i	$0.691721\pi$
$48$	−0.231546	−	0.0842757i	−0.0334207	−	0.0121641i
$49$	−4.22376	+	7.31577i	−0.603394	+	1.04511i
$50$	−0.877928	−	1.52062i	−0.124158	−	0.215048i
$51$	−0.872832	−	4.95008i	−0.122221	−	0.693149i
$52$	−1.80379	−	1.51356i	−0.250141	−	0.209893i
$53$	−1.61814	+	1.35778i	−0.222269	+	0.186506i	−0.747122	−	0.664687i	$-0.768565\pi$
$53$	−1.61814	+	1.35778i	−0.222269	+	0.186506i	0.524853	+	0.851193i	$0.324120\pi$
$54$	−0.146267	+	0.829520i	−0.0199044	+	0.112883i
$55$	−7.10045	+	2.58435i	−0.957425	+	0.348474i
$56$	10.8935			1.45570
$57$	−4.31806	+	0.595259i	−0.571941	+	0.0788440i
$58$	1.22154			0.160396
$59$	−6.01966	+	2.19098i	−0.783693	+	0.285241i	−0.702712	−	0.711475i	$-0.748028\pi$
$59$	−6.01966	+	2.19098i	−0.783693	+	0.285241i	−0.0809810	+	0.996716i	$0.525805\pi$
$60$	−0.382632	+	2.17002i	−0.0493976	+	0.280148i
$61$	0.0587523	−	0.0492990i	0.00752246	−	0.00631209i	−0.639019	−	0.769191i	$-0.720659\pi$
$61$	0.0587523	−	0.0492990i	0.00752246	−	0.00631209i	0.646541	+	0.762879i	$0.276215\pi$
$62$	1.85150	+	1.55359i	0.235141	+	0.197307i
$63$	0.682495	+	3.87062i	0.0859863	+	0.487653i
$64$	−2.17561	−	3.76826i	−0.271951	−	0.471033i
$65$	−1.55774	+	2.69809i	−0.193214	+	0.334656i
$66$	3.50275	+	1.27490i	0.431158	+	0.156929i
$67$	0.984002	+	0.358147i	0.120215	+	0.0437547i	0.401427	−	0.915891i	$-0.368514\pi$
$67$	0.984002	+	0.358147i	0.120215	+	0.0437547i	−0.281212	+	0.959646i	$0.590736\pi$
$68$	−3.24332	+	5.61759i	−0.393310	+	0.681233i
$69$	−1.72915	−	2.99498i	−0.208166	−	0.360553i
$70$	−0.981583	−	5.56683i	−0.117322	−	0.665364i
$71$	−10.3790	−	8.70898i	−1.23176	−	1.03357i	−0.998123	−	0.0612406i	$-0.980494\pi$
$71$	−10.3790	−	8.70898i	−1.23176	−	1.03357i	−0.233632	−	0.972325i	$-0.575061\pi$
$72$	2.12320	−	1.78158i	0.250222	−	0.209961i
$73$	0.696538	−	3.95026i	0.0815236	−	0.462343i	−0.916529	−	0.399968i	$-0.869021\pi$
$73$	0.696538	−	3.95026i	0.0815236	−	0.462343i	0.998053	−	0.0623753i	$-0.0198676\pi$
$74$	−3.82401	+	1.39182i	−0.444532	+	0.161796i
$75$	−2.08456			−0.240704
$76$	4.76254	+	2.99345i	0.546301	+	0.343373i
$77$	17.3931			1.98213
$78$	1.44422	−	0.525654i	0.163526	−	0.0595186i
$79$	2.94592	−	16.7071i	0.331442	−	1.87970i	−0.128438	−	0.991718i	$-0.540996\pi$
$79$	2.94592	−	16.7071i	0.331442	−	1.87970i	0.459880	−	0.887981i	$-0.347893\pi$
$80$	0.322297	−	0.270440i	0.0360339	−	0.0302361i
$81$	0.766044	+	0.642788i	0.0851160	+	0.0714208i
$82$	1.28832	+	7.30645i	0.142272	+	0.806862i
$83$	6.51259	+	11.2801i	0.714850	+	1.23816i	0.963017	+	0.269440i	$0.0868384\pi$
$83$	6.51259	+	11.2801i	0.714850	+	1.23816i	−0.248167	+	0.968717i	$0.579828\pi$
$84$	2.53605	−	4.39257i	0.276706	−	0.479269i
$85$	8.06489	+	2.93538i	0.874760	+	0.318387i
$86$	7.99569	+	2.91019i	0.862197	+	0.313814i
$87$	0.725109	−	1.25592i	0.0777398	−	0.134649i
$88$	−6.13275	−	10.6222i	−0.653754	−	1.13233i
$89$	2.14695	+	12.1759i	0.227576	+	1.29065i	0.857699	+	0.514152i	$0.171893\pi$
$89$	2.14695	+	12.1759i	0.227576	+	1.29065i	−0.630123	+	0.776496i	$0.716995\pi$
$90$	−1.10175	−	0.924474i	−0.116134	−	0.0974482i
$91$	5.49359	−	4.60967i	0.575885	−	0.483225i
$92$	−0.774984	+	4.39515i	−0.0807977	+	0.458227i
$93$	2.69638	−	0.981401i	0.279601	−	0.101767i
$94$	−2.89362			−0.298454
$95$	2.80626	−	6.89335i	0.287916	−	0.707243i
$96$	−5.75084			−0.586943
$97$	−0.164685	+	0.0599404i	−0.0167212	+	0.00608603i	−0.350367	−	0.936612i	$-0.613943\pi$
$97$	−0.164685	+	0.0599404i	−0.0167212	+	0.00608603i	0.333646	+	0.942698i	$0.391721\pi$
$98$	−1.23559	+	7.00738i	−0.124813	+	0.707852i
$99$	3.39002	−	2.84456i	0.340710	−	0.285889i
$100$	2.06076	+	1.72918i	0.206076	+	0.172918i
$101$	−1.94720	−	11.0431i	−0.193754	−	1.09883i	−0.914183	−	0.405303i	$-0.867166\pi$
$101$	−1.94720	−	11.0431i	−0.193754	−	1.09883i	0.720429	−	0.693529i	$-0.243945\pi$
$102$	−2.11693	−	3.66662i	−0.209607	−	0.363050i
$103$	−4.76005	+	8.24465i	−0.469022	+	0.812369i	−0.999373	−	0.0354087i	$-0.988727\pi$
$103$	−4.76005	+	8.24465i	−0.469022	+	0.812369i	0.530351	+	0.847778i	$0.322060\pi$
$104$	−4.75222	−	1.72967i	−0.465993	−	0.169608i
$105$	−6.30620	−	2.29527i	−0.615422	−	0.223995i
$106$	−0.889627	+	1.54088i	−0.0864082	+	0.149663i
$107$	5.13450	+	8.89322i	0.496371	+	0.859740i	0.999991	−	0.00418546i	$-0.00133228\pi$
$107$	5.13450	+	8.89322i	0.496371	+	0.859740i	−0.503620	+	0.863925i	$0.667999\pi$
$108$	−0.224094	−	1.27090i	−0.0215634	−	0.122292i
$109$	−1.56399	−	1.31234i	−0.149803	−	0.125700i	0.564806	−	0.825224i	$-0.308951\pi$
$109$	−1.56399	−	1.31234i	−0.149803	−	0.125700i	−0.714609	+	0.699524i	$0.753395\pi$
$110$	−4.87561	+	4.09113i	−0.464872	+	0.390074i
$111$	−0.838934	+	4.75783i	−0.0796281	+	0.451593i
$112$	−0.910051	+	0.331231i	−0.0859917	+	0.0312984i
$113$	−13.9973			−1.31675			−0.658375	−	0.752690i	$-0.728756\pi$
$113$	−13.9973			−1.31675			−0.658375	+	0.752690i	$0.728756\pi$
$114$	−3.24634	+	1.71515i	−0.304047	+	0.160638i
$115$	5.90494			0.550639
$116$	−1.75864	+	0.640094i	−0.163286	+	0.0594312i
$117$	0.316842	−	1.79690i	0.0292921	−	0.166124i
$118$	−4.13347	+	3.46840i	−0.380517	+	0.319292i
$119$	−15.1337	−	12.6986i	−1.38730	−	1.16408i
$120$	0.821788	+	4.66059i	0.0750187	+	0.425452i
$121$	−4.29187	−	7.43374i	−0.390170	−	0.675795i
$122$	0.0323010	−	0.0559470i	0.00292440	−	0.00506520i
$123$	8.27685	+	3.01253i	0.746299	+	0.271631i
$124$	−3.47968	−	1.26650i	−0.312485	−	0.113735i
$125$	6.04832	−	10.4760i	0.540978	−	0.937002i
$126$	1.65529	+	2.86705i	0.147465	+	0.255417i
$127$	0.340225	+	1.92951i	0.0301901	+	0.171216i	0.996175	−	0.0873827i	$-0.0278503\pi$
$127$	0.340225	+	1.92951i	0.0301901	+	0.171216i	−0.965985	+	0.258599i	$0.916739\pi$
$128$	6.00317	+	5.03726i	0.530610	+	0.445235i
$129$	7.73836	−	6.49325i	0.681324	−	0.571699i
$130$	−0.455691	+	2.58435i	−0.0399668	+	0.226663i
$131$	1.46596	−	0.533566i	0.128082	−	0.0466179i	−0.277184	−	0.960817i	$-0.589401\pi$
$131$	1.46596	−	0.533566i	0.128082	−	0.0466179i	0.405266	+	0.914199i	$0.367179\pi$
$132$	−5.71093			−0.497073
$133$	−11.4970	+	12.7012i	−0.996918	+	1.10134i
$134$	0.882034			0.0761961
$135$	−1.60449	+	0.583988i	−0.138093	+	0.0502617i
$136$	−2.41918	+	13.7199i	−0.207443	+	1.17647i
$137$	11.7678	−	9.87434i	1.00539	−	0.843622i	0.0176677	−	0.999844i	$-0.494376\pi$
$137$	11.7678	−	9.87434i	1.00539	−	0.843622i	0.987722	+	0.156222i	$0.0499314\pi$
$138$	−2.23148	−	1.87243i	−0.189956	−	0.159392i
$139$	1.61632	+	9.16662i	0.137095	+	0.777502i	0.973378	+	0.229205i	$0.0736126\pi$
$139$	1.61632	+	9.16662i	0.137095	+	0.777502i	−0.836284	+	0.548297i	$0.815276\pi$
$140$	4.33023	+	7.50017i	0.365971	+	0.633880i
$141$	−1.71766	+	2.97507i	−0.144653	+	0.250546i
$142$	−10.7241	−	3.90325i	−0.899946	−	0.327554i
$143$	−7.58764	−	2.76167i	−0.634510	−	0.230943i
$144$	−0.123203	+	0.213394i	−0.0102669	+	0.0177828i
$145$	1.23810	+	2.14445i	0.102818	+	0.178087i
$146$	−0.586705	−	3.32737i	−0.0485560	−	0.275375i
$147$	6.47117	+	5.42996i	0.533733	+	0.447856i
$148$	4.77607	−	4.00760i	0.392590	−	0.329423i
$149$	0.900217	−	5.10538i	0.0737487	−	0.418249i	−0.925473	−	0.378813i	$-0.876332\pi$
$149$	0.900217	−	5.10538i	0.0737487	−	0.418249i	0.999222	−	0.0394368i	$-0.0125564\pi$
$150$	−1.64997	+	0.600538i	−0.134719	+	0.0490338i
$151$	13.0922			1.06543			0.532713	−	0.846296i	$-0.321173\pi$
$151$	13.0922			1.06543			0.532713	+	0.846296i	$0.321173\pi$
$152$	11.8106	+	2.54300i	0.957970	+	0.206264i
$153$	−5.02644			−0.406364
$154$	13.7670	−	5.01077i	1.10937	−	0.403779i
$155$	−0.850780	+	4.82501i	−0.0683363	+	0.387554i
$156$	−1.80379	+	1.51356i	−0.144419	+	0.121182i
$157$	−5.64550	−	4.73714i	−0.450560	−	0.378065i	0.389084	−	0.921202i	$-0.372792\pi$
$157$	−5.64550	−	4.73714i	−0.450560	−	0.378065i	−0.839644	+	0.543138i	$0.817236\pi$
$158$	−2.48139	−	14.0727i	−0.197409	−	1.11956i
$159$	1.05617	+	1.82934i	0.0837596	+	0.145076i
$160$	4.90968	−	8.50382i	0.388145	−	0.672286i
$161$	−12.7726	−	4.64884i	−1.00662	−	0.366380i
$162$	0.791518	+	0.288089i	0.0621876	+	0.0226344i
$163$	8.01404	−	13.8807i	0.627708	−	1.08722i	−0.360302	−	0.932836i	$-0.617326\pi$
$163$	8.01404	−	13.8807i	0.627708	−	1.08722i	0.988010	−	0.154387i	$-0.0493402\pi$
$164$	−5.68341	−	9.84395i	−0.443799	−	0.768683i
$165$	1.31211	+	7.44135i	0.102148	+	0.579308i
$166$	8.40453	+	7.05223i	0.652318	+	0.547360i
$167$	−10.0561	+	8.43808i	−0.778165	+	0.652958i	−0.942786	−	0.333399i	$-0.891804\pi$
$167$	−10.0561	+	8.43808i	−0.778165	+	0.652958i	0.164621	+	0.986357i	$0.447360\pi$
$168$	1.89163	−	10.7280i	0.145943	−	0.827682i
$169$	9.08754	−	3.30759i	0.699041	−	0.254430i
$170$	7.22916			0.554451
$171$	−0.163608	+	4.35583i	−0.0125114	+	0.333098i
$172$	−13.0363			−0.994007
$173$	17.3580	−	6.31781i	1.31971	−	0.480334i	0.416342	−	0.909208i	$-0.363312\pi$
$173$	17.3580	−	6.31781i	1.31971	−	0.480334i	0.903364	+	0.428874i	$0.141090\pi$
$174$	0.212118	−	1.20298i	0.0160807	−	0.0911979i
$175$	−6.27621	+	5.26636i	−0.474437	+	0.398100i
$176$	0.835319	+	0.700916i	0.0629646	+	0.0528335i
$177$	1.11239	+	6.30866i	0.0836122	+	0.474188i
$178$	5.20711	+	9.01897i	0.390289	+	0.676001i
$179$	−5.92941	+	10.2700i	−0.443185	+	0.767619i	−0.997924	−	0.0644059i	$-0.979485\pi$
$179$	−5.92941	+	10.2700i	−0.443185	+	0.767619i	0.554739	+	0.832024i	$0.312818\pi$
$180$	2.07060	+	0.753638i	0.154334	+	0.0561729i
$181$	−0.257216	−	0.0936191i	−0.0191187	−	0.00695866i	0.332443	−	0.943123i	$-0.392127\pi$
$181$	−0.257216	−	0.0936191i	−0.0191187	−	0.00695866i	−0.351562	+	0.936165i	$0.614349\pi$
$182$	3.02028	−	5.23128i	0.223878	−	0.387768i
$183$	−0.0383478	−	0.0664204i	−0.00283475	−	0.00490994i
$184$	1.66445	+	9.43958i	0.122705	+	0.695895i
$185$	−6.31922	−	5.30246i	−0.464599	−	0.389844i
$186$	1.85150	−	1.55359i	0.135759	−	0.113915i
$187$	−3.86259	+	21.9058i	−0.282461	+	1.60191i
$188$	4.16592	−	1.51627i	0.303831	−	0.110586i
$189$	3.93033			0.285890
$190$	0.235306	−	6.26467i	0.0170709	−	0.454487i
$191$	−12.1649			−0.880218			−0.440109	−	0.897944i	$-0.645060\pi$
$191$	−12.1649			−0.880218			−0.440109	+	0.897944i	$0.645060\pi$
$192$	−4.08880	+	1.48820i	−0.295084	+	0.107402i
$193$	4.00715	−	22.7257i	0.288441	−	1.63583i	−0.404288	−	0.914632i	$-0.632481\pi$
$193$	4.00715	−	22.7257i	0.288441	−	1.63583i	0.692729	−	0.721198i	$-0.256408\pi$
$194$	−0.113083	+	0.0948879i	−0.00811889	+	0.00681255i
$195$	2.38660	+	2.00259i	0.170908	+	0.143409i
$196$	−1.89303	−	10.7359i	−0.135217	−	0.766852i
$197$	−3.23436	−	5.60208i	−0.230439	−	0.399132i	0.727498	−	0.686109i	$-0.240683\pi$
$197$	−3.23436	−	5.60208i	−0.230439	−	0.399132i	−0.957937	+	0.286978i	$0.907349\pi$
$198$	1.86377	−	3.22815i	0.132453	−	0.229415i
$199$	−0.288569	−	0.105030i	−0.0204561	−	0.00744541i	0.331772	−	0.943360i	$-0.392354\pi$
$199$	−0.288569	−	0.105030i	−0.0204561	−	0.00744541i	−0.352228	+	0.935914i	$0.614576\pi$
$200$	5.42922	+	1.97607i	0.383904	+	0.139730i
$201$	0.523576	−	0.906861i	0.0369302	−	0.0639650i
$202$	−4.72265	−	8.17986i	−0.332284	−	0.575533i
$203$	−0.989766	−	5.61324i	−0.0694680	−	0.393972i
$204$	4.96905	+	4.16953i	0.347903	+	0.291925i
$205$	−11.5209	+	9.66717i	−0.804653	+	0.675184i
$206$	−1.39247	+	7.89711i	−0.0970182	+	0.550218i
$207$	−3.24975	+	1.18281i	−0.225873	+	0.0822110i
$208$	0.449597			0.0311740
$209$	18.8575	+	4.06028i	1.30440	+	0.280855i
$210$	−5.65271			−0.390074
$211$	−9.94719	+	3.62048i	−0.684793	+	0.249244i	−0.660904	−	0.750470i	$-0.729827\pi$
$211$	−9.94719	+	3.62048i	−0.684793	+	0.249244i	−0.0238889	+	0.999715i	$0.507605\pi$
$212$	0.473361	−	2.68456i	0.0325106	−	0.184377i
$213$	−10.3790	+	8.70898i	−0.711154	+	0.596729i
$214$	6.62609	+	5.55995i	0.452950	+	0.380070i
$215$	2.99514	+	16.9863i	0.204267	+	1.15846i
$216$	−1.38582	−	2.40031i	−0.0942933	−	0.163321i
$217$	5.63890	−	9.76686i	0.382793	−	0.663018i
$218$	−1.61600	−	0.588175i	−0.109449	−	0.0398363i
$219$	−3.76929	−	1.37191i	−0.254705	−	0.0927052i
$220$	4.87561	−	8.44481i	0.328714	−	0.569349i
$221$	4.58568	+	7.94263i	0.308466	+	0.534279i
$222$	0.706648	+	4.00760i	0.0474271	+	0.268972i
$223$	5.69559	+	4.77917i	0.381405	+	0.320037i	0.813254	−	0.581909i	$-0.197694\pi$
$223$	5.69559	+	4.77917i	0.381405	+	0.320037i	−0.431849	+	0.901946i	$0.642139\pi$
$224$	−17.3147	+	14.5287i	−1.15689	+	0.970743i
$225$	−0.361980	+	2.05289i	−0.0241320	+	0.136859i
$226$	−11.0791	+	4.03246i	−0.736970	+	0.268235i
$227$	3.54389			0.235216			0.117608	−	0.993060i	$-0.462477\pi$
$227$	3.54389			0.235216			0.117608	+	0.993060i	$0.462477\pi$
$228$	3.77498	−	4.17038i	0.250004	−	0.276190i
$229$	−11.3492			−0.749973			−0.374987	−	0.927030i	$-0.622353\pi$
$229$	−11.3492			−0.749973			−0.374987	+	0.927030i	$0.622353\pi$
$230$	4.67387	−	1.70115i	0.308186	−	0.112171i
$231$	3.02028	−	17.1289i	0.198720	−	1.12700i
$232$	−3.07911	+	2.58368i	−0.202153	+	0.169627i
$233$	−4.54086	−	3.81024i	−0.297482	−	0.249617i	0.481813	−	0.876274i	$-0.339978\pi$
$233$	−4.54086	−	3.81024i	−0.297482	−	0.249617i	−0.779295	+	0.626657i	$0.784423\pi$
$234$	−0.266881	−	1.51356i	−0.0174466	−	0.0989445i
$235$	−2.93284	−	5.07983i	−0.191317	−	0.331372i
$236$	4.13347	−	7.15938i	0.269066	−	0.466036i
$237$	−15.9418	−	5.80232i	−1.03553	−	0.376901i
$238$	−15.6369	−	5.69137i	−1.01359	−	0.368917i
$239$	−7.58422	+	13.1363i	−0.490583	+	0.849714i	−0.999941	−	0.0108402i	$-0.996549\pi$
$239$	−7.58422	+	13.1363i	−0.490583	+	0.849714i	0.509359	+	0.860554i	$0.329883\pi$
$240$	−0.210365	−	0.364362i	−0.0135790	−	0.0235195i
$241$	1.53896	+	8.72790i	0.0991334	+	0.562214i	0.993402	+	0.114683i	$0.0365853\pi$
$241$	1.53896	+	8.72790i	0.0991334	+	0.562214i	−0.894269	+	0.447530i	$0.852304\pi$
$242$	−5.53868	−	4.64750i	−0.356040	−	0.298753i
$243$	0.766044	−	0.642788i	0.0491418	−	0.0412348i
$244$	−0.0171870	+	0.0974724i	−0.00110029	+	0.00624003i
$245$	−13.5540	+	4.93325i	−0.865933	+	0.315174i
$246$	7.41916			0.473028
$247$	7.03221	−	3.71534i	0.447449	−	0.236401i
$248$	−7.95303			−0.505018
$249$	12.2397	−	4.45488i	0.775658	−	0.282316i
$250$	1.76934	−	10.0344i	0.111903	−	0.634631i
$251$	8.96819	−	7.52520i	0.566067	−	0.474987i	−0.314271	−	0.949333i	$-0.601760\pi$
$251$	8.96819	−	7.52520i	0.566067	−	0.474987i	0.880338	+	0.474347i	$0.157316\pi$
$252$	−3.88546	−	3.26029i	−0.244761	−	0.205379i
$253$	2.65755	+	15.0717i	0.167079	+	0.947551i
$254$	0.825165	+	1.42923i	0.0517754	+	0.0896777i
$255$	4.29124	−	7.43264i	0.268728	−	0.465450i
$256$	14.3804	+	5.23404i	0.898775	+	0.327128i
$257$	9.31797	+	3.39146i	0.581239	+	0.211554i	0.615872	−	0.787846i	$-0.288804\pi$
$257$	9.31797	+	3.39146i	0.581239	+	0.211554i	−0.0346328	+	0.999400i	$0.511026\pi$
$258$	4.25442	−	7.36886i	0.264868	−	0.458765i
$259$	9.49417	+	16.4444i	0.589939	+	1.02180i
$260$	−0.698159	−	3.95946i	−0.0432980	−	0.245555i
$261$	−1.11093	−	0.932182i	−0.0687649	−	0.0577006i
$262$	1.00662	−	0.844655i	0.0621892	−	0.0521829i
$263$	−1.17020	+	6.63654i	−0.0721577	+	0.409227i	0.927238	+	0.374472i	$0.122176\pi$
$263$	−1.17020	+	6.63654i	−0.0721577	+	0.409227i	−0.999396	+	0.0347546i	$0.988935\pi$
$264$	−11.5258	+	4.19505i	−0.709364	+	0.258187i
$265$	−3.60674			−0.221560
$266$	−5.44102	+	13.3654i	−0.333610	+	0.819487i
$267$	12.3638			0.756651
$268$	−1.26986	+	0.462190i	−0.0775689	+	0.0282328i
$269$	0.124730	−	0.707378i	0.00760491	−	0.0431296i	−0.980769	−	0.195171i	$-0.937474\pi$
$269$	0.124730	−	0.707378i	0.00760491	−	0.0431296i	0.988374	+	0.152042i	$0.0485848\pi$
$270$	−1.10175	+	0.924474i	−0.0670501	+	0.0562617i
$271$	−22.0935	−	18.5387i	−1.34209	−	1.12614i	−0.981085	−	0.193579i	$-0.937990\pi$
$271$	−22.0935	−	18.5387i	−1.34209	−	1.12614i	−0.361002	−	0.932565i	$-0.617565\pi$
$272$	−0.215071	−	1.21973i	−0.0130406	−	0.0739568i
$273$	−3.58569	−	6.21059i	−0.217016	−	0.375882i
$274$	6.46973	−	11.2059i	0.390850	−	0.676973i
$275$	8.66857	+	3.15510i	0.522735	+	0.190260i
$276$	4.19381	+	1.52642i	0.252438	+	0.0918798i
$277$	1.91567	−	3.31804i	0.115101	−	0.199361i	−0.802719	−	0.596358i	$-0.796614\pi$
$277$	1.91567	−	3.31804i	0.115101	−	0.199361i	0.917820	+	0.396996i	$0.129947\pi$
$278$	3.92015	+	6.78990i	0.235115	+	0.407231i
$279$	−0.498270	−	2.82583i	−0.0298307	−	0.169178i
$280$	14.2486	+	11.9560i	0.851518	+	0.714509i
$281$	−16.9236	+	14.2006i	−1.00957	+	0.847134i	−0.988282	−	0.152639i	$-0.951223\pi$
$281$	−16.9236	+	14.2006i	−1.00957	+	0.847134i	−0.0212929	+	0.999773i	$0.506778\pi$
$282$	−0.502472	+	2.84966i	−0.0299218	+	0.169695i
$283$	23.6300	−	8.60061i	1.40466	−	0.511253i	0.475100	−	0.879932i	$-0.342412\pi$
$283$	23.6300	−	8.60061i	1.40466	−	0.511253i	0.929557	+	0.368678i	$0.120190\pi$
$284$	17.4847			1.03753
$285$	−6.30133	−	3.96064i	−0.373258	−	0.234608i
$286$	−6.80136			−0.402173
$287$	32.5308	−	11.8402i	1.92023	−	0.698907i
$288$	−0.998623	+	5.66347i	−0.0588444	+	0.333723i
$289$	6.33143	−	5.31270i	0.372437	−	0.312512i
$290$	1.59777	+	1.34069i	0.0938243	+	0.0787279i
$291$	0.0304326	+	0.172592i	0.00178399	+	0.0101175i
$292$	2.58823	+	4.48295i	0.151465	+	0.262345i
$293$	2.96356	−	5.13304i	0.173133	−	0.299875i	−0.766381	−	0.642387i	$-0.777944\pi$
$293$	2.96356	−	5.13304i	0.173133	−	0.299875i	0.939514	+	0.342512i	$0.111278\pi$
$294$	6.68637	+	2.43364i	0.389957	+	0.141933i
$295$	−10.2784	−	3.74102i	−0.598429	−	0.217811i
$296$	6.69522	−	11.5965i	0.389152	−	0.674031i
$297$	−2.21268	−	3.83247i	−0.128393	−	0.222382i
$298$	−0.758267	−	4.30035i	−0.0439253	−	0.249113i
$299$	4.83382	+	4.05606i	0.279547	+	0.234568i
$300$	2.06076	−	1.72918i	0.118978	−	0.0998343i
$301$	6.89437	−	39.0999i	0.397385	−	2.25368i
$302$	10.3627	−	3.77171i	0.596306	−	0.217038i
$303$	−11.2135			−0.644197
$304$	−1.06399	+	0.146675i	−0.0610243	+	0.00841240i
$305$	0.130955			0.00749848
$306$	−3.97852	+	1.44806i	−0.227437	+	0.0827802i
$307$	−3.05347	+	17.3171i	−0.174271	+	0.988339i	0.764711	+	0.644373i	$0.222882\pi$
$307$	−3.05347	+	17.3171i	−0.174271	+	0.988339i	−0.938982	+	0.343966i	$0.888229\pi$
$308$	−17.1945	+	14.4279i	−0.979749	+	0.822107i
$309$	7.29282	+	6.11940i	0.414874	+	0.348121i
$310$	0.716626	+	4.06419i	0.0407016	+	0.230830i
$311$	3.01433	+	5.22097i	0.170927	+	0.296054i	0.938744	−	0.344615i	$-0.111990\pi$
$311$	3.01433	+	5.22097i	0.170927	+	0.296054i	−0.767817	+	0.640669i	$0.778657\pi$
$312$	−2.52860	+	4.37967i	−0.143154	+	0.247950i
$313$	−15.6910	−	5.71107i	−0.886909	−	0.322809i	−0.141914	−	0.989879i	$-0.545326\pi$
$313$	−15.6910	−	5.71107i	−0.886909	−	0.322809i	−0.744995	+	0.667070i	$0.767548\pi$
$314$	−5.83323	−	2.12312i	−0.329188	−	0.119815i
$315$	−3.35546	+	5.81182i	−0.189059	+	0.327459i
$316$	10.9466	+	18.9601i	0.615795	+	1.06659i
$317$	−0.380819	−	2.15973i	−0.0213889	−	0.121303i	0.972244	−	0.233970i	$-0.0751717\pi$
$317$	−0.380819	−	2.15973i	−0.0213889	−	0.121303i	−0.993633	+	0.112667i	$0.964061\pi$
$318$	1.36299	+	1.14368i	0.0764326	+	0.0641345i
$319$	−4.91626	+	4.12523i	−0.275258	+	0.230969i
$320$	1.29013	−	7.31668i	0.0721204	−	0.409015i
$321$	9.64970	−	3.51221i	0.538594	−	0.196032i
$322$	−11.4490			−0.638029
$323$	−13.4434	−	17.3006i	−0.748012	−	0.962632i
$324$	−1.29050			−0.0716946
$325$	3.57415	−	1.30088i	0.198258	−	0.0721601i
$326$	2.34437	−	13.2956i	0.129843	−	0.736376i
$327$	−1.56399	+	1.31234i	−0.0864888	+	0.0725727i
$328$	−18.7013	−	15.6922i	−1.03260	−	0.866458i
$329$	2.34458	+	13.2968i	0.129261	+	0.733076i
$330$	3.18233	+	5.51196i	0.175182	+	0.303423i
$331$	−7.77039	+	13.4587i	−0.427099	+	0.739758i	−0.996614	−	0.0822234i	$-0.973798\pi$
$331$	−7.77039	+	13.4587i	−0.427099	+	0.739758i	0.569515	+	0.821981i	$0.307131\pi$
$332$	−15.7953	−	5.74903i	−0.866882	−	0.315519i
$333$	4.53987	+	1.65238i	0.248783	+	0.0905497i
$334$	−5.52868	+	9.57595i	−0.302516	+	0.523973i
$335$	0.893989	+	1.54843i	0.0488439	+	0.0846000i
$336$	0.168171	+	0.953743i	0.00917446	+	0.0520309i
$337$	9.48108	+	7.95557i	0.516467	+	0.433368i	0.863398	−	0.504523i	$-0.168332\pi$
$337$	9.48108	+	7.95557i	0.516467	+	0.433368i	−0.346931	+	0.937891i	$0.612776\pi$
$338$	6.24007	−	5.23604i	0.339415	−	0.284803i
$339$	−2.43060	+	13.7846i	−0.132012	+	0.748677i
$340$	−10.4078	+	3.78812i	−0.564441	+	0.205440i
$341$	−12.6982			−0.687647
$342$	1.12537	+	3.49485i	0.0608529	+	0.188980i
$343$	5.68923			0.307189
$344$	−26.3098	+	9.57600i	−1.41853	+	0.516303i
$345$	1.02538	−	5.81523i	0.0552047	−	0.313082i
$346$	11.9191	−	10.0013i	0.640775	−	0.537674i
$347$	−17.0105	−	14.2735i	−0.913171	−	0.766241i	0.0595486	−	0.998225i	$-0.481034\pi$
$347$	−17.0105	−	14.2735i	−0.913171	−	0.766241i	−0.972720	+	0.231984i	$0.925478\pi$
$348$	0.324984	+	1.84308i	0.0174210	+	0.0987993i
$349$	9.96461	+	17.2592i	0.533393	+	0.923864i	0.999239	+	0.0389982i	$0.0124167\pi$
$349$	9.96461	+	17.2592i	0.533393	+	0.923864i	−0.465846	+	0.884866i	$0.654250\pi$
$350$	−3.45055	+	5.97653i	−0.184440	+	0.319459i
$351$	−1.71458	−	0.624058i	−0.0915177	−	0.0333097i
$352$	23.9147	+	8.70424i	1.27466	+	0.463938i
$353$	2.60302	−	4.50856i	0.138545	−	0.239966i	−0.788401	−	0.615161i	$-0.789091\pi$
$353$	2.60302	−	4.50856i	0.138545	−	0.239966i	0.926946	+	0.375195i	$0.122424\pi$
$354$	2.69793	+	4.67296i	0.143393	+	0.248365i
$355$	−4.01719	−	22.7826i	−0.213210	−	1.20918i
$356$	−12.2226	−	10.2560i	−0.647798	−	0.543567i
$357$	−15.1337	+	12.6986i	−0.800958	+	0.672083i
$358$	−1.73455	+	9.83712i	−0.0916738	+	0.519908i
$359$	4.85658	−	1.76765i	0.256320	−	0.0932930i	−0.210664	−	0.977559i	$-0.567563\pi$
$359$	4.85658	−	1.76765i	0.256320	−	0.0932930i	0.466984	+	0.884266i	$0.345340\pi$
$360$	4.73249			0.249424
$361$	−15.4300	+	11.0867i	−0.812105	+	0.583511i
$362$	−0.230562			−0.0121181
$363$	−8.06609	+	2.93581i	−0.423360	+	0.154090i
$364$	−1.60706	+	9.11408i	−0.0842328	+	0.477708i
$365$	5.24663	−	4.40245i	0.274621	−	0.230435i
$366$	−0.0494880	−	0.0415254i	−0.00258678	−	0.00217057i
$367$	−1.05270	−	5.97015i	−0.0549504	−	0.311639i	0.944927	−	0.327280i	$-0.106132\pi$
$367$	−1.05270	−	5.97015i	−0.0549504	−	0.311639i	−0.999878	+	0.0156413i	$0.995021\pi$
$368$	−0.426073	−	0.737980i	−0.0222106	−	0.0384699i
$369$	4.40402	−	7.62799i	0.229264	−	0.397097i
$370$	−6.52936	−	2.37649i	−0.339445	−	0.123548i
$371$	7.80150	+	2.83951i	0.405034	+	0.147420i
$372$	−1.85150	+	3.20689i	−0.0959959	+	0.166270i
$373$	−4.99273	−	8.64766i	−0.258514	−	0.447759i	0.707330	−	0.706883i	$-0.249899\pi$
$373$	−4.99273	−	8.64766i	−0.258514	−	0.447759i	−0.965844	+	0.259124i	$0.916566\pi$
$374$	3.25352	+	18.4516i	0.168236	+	0.954112i
$375$	−9.26657	−	7.77557i	−0.478524	−	0.401529i
$376$	7.29387	−	6.12028i	0.376152	−	0.315629i
$377$	−0.459490	+	2.60590i	−0.0236649	+	0.134211i
$378$	3.11093	−	1.13229i	0.160009	−	0.0582385i
$379$	−13.7799			−0.707826			−0.353913	−	0.935278i	$-0.615149\pi$
$379$	−13.7799			−0.707826			−0.353913	+	0.935278i	$0.615149\pi$
$380$	2.94395	+	9.14250i	0.151022	+	0.469000i
$381$	1.95928			0.100377
$382$	−9.62871	+	3.50456i	−0.492648	+	0.179309i
$383$	2.83262	−	16.0646i	0.144740	−	0.820861i	−0.822836	−	0.568279i	$-0.807609\pi$
$383$	2.83262	−	16.0646i	0.144740	−	0.820861i	0.967576	−	0.252582i	$-0.0812796\pi$
$384$	6.00317	−	5.03726i	0.306348	−	0.257056i
$385$	22.7501	+	19.0896i	1.15945	+	0.972896i
$386$	−3.37529	−	19.1422i	−0.171798	−	0.974312i
$387$	−5.05085	−	8.74833i	−0.256749	−	0.444703i
$388$	0.113083	−	0.195866i	0.00574092	−	0.00994356i
$389$	10.7795	+	3.92341i	0.546541	+	0.198925i	0.600509	−	0.799618i	$-0.294965\pi$
$389$	10.7795	+	3.92341i	0.546541	+	0.198925i	−0.0539681	+	0.998543i	$0.517187\pi$
$390$	2.46596	+	0.897536i	0.124869	+	0.0454485i
$391$	8.69149	−	15.0541i	0.439547	−	0.761318i
$392$	−11.7068	−	20.2767i	−0.591281	−	1.02413i
$393$	−0.270899	−	1.53634i	−0.0136650	−	0.0774982i
$394$	−4.17396	−	3.50237i	−0.210281	−	0.176447i
$395$	22.1900	−	18.6196i	1.11650	−	0.936853i
$396$	−0.991693	+	5.62417i	−0.0498345	+	0.282625i
$397$	0.421085	−	0.153262i	0.0211336	−	0.00769201i	−0.331432	−	0.943479i	$-0.607532\pi$
$397$	0.421085	−	0.153262i	0.0211336	−	0.00769201i	0.352565	+	0.935787i	$0.385309\pi$
$398$	−0.258665			−0.0129657
$399$	10.5118	+	13.5279i	0.526250	+	0.677242i
$400$	−0.513647			−0.0256823
$401$	−13.6316	+	4.96149i	−0.680729	+	0.247765i	−0.659160	−	0.752002i	$-0.729088\pi$
$401$	−13.6316	+	4.96149i	−0.680729	+	0.247765i	−0.0215682	+	0.999767i	$0.506866\pi$
$402$	0.153164	−	0.868634i	0.00763910	−	0.0433235i
$403$	−4.01072	+	3.36539i	−0.199788	+	0.167642i
$404$	11.0855	+	9.30180i	0.551522	+	0.462782i
$405$	0.296498	+	1.68153i	0.0147331	+	0.0835557i
$406$	−2.40053	−	4.15784i	−0.119136	−	0.206350i
$407$	10.6899	−	18.5155i	0.529881	−	0.917781i
$408$	13.0913	+	4.76485i	0.648117	+	0.235895i
$409$	12.4030	+	4.51431i	0.613287	+	0.223218i	0.629941	−	0.776643i	$-0.283079\pi$
$409$	12.4030	+	4.51431i	0.613287	+	0.223218i	−0.0166536	+	0.999861i	$0.505301\pi$
$410$	−6.33398	+	10.9708i	−0.312813	+	0.541808i
$411$	−7.68088	−	13.3037i	−0.378870	−	0.656222i
$412$	−2.13339	−	12.0991i	−0.105105	−	0.596078i
$413$	19.2872	+	16.1839i	0.949061	+	0.796357i
$414$	−2.23148	+	1.87243i	−0.109671	+	0.0920250i
$415$	−3.86195	+	21.9022i	−0.189576	+	1.07514i
$416$	9.86030	−	3.58886i	0.483441	−	0.175958i
$417$	9.30803			0.455816
$418$	16.0958	−	2.21886i	0.787270	−	0.108528i
$419$	11.4229			0.558047			0.279024	−	0.960284i	$-0.409989\pi$
$419$	11.4229			0.558047			0.279024	+	0.960284i	$0.409989\pi$
$420$	8.13817	−	2.96205i	0.397102	−	0.144533i
$421$	−2.87973	+	16.3318i	−0.140349	+	0.795961i	0.830635	+	0.556818i	$0.187978\pi$
$421$	−2.87973	+	16.3318i	−0.140349	+	0.795961i	−0.970984	+	0.239144i	$0.923133\pi$
$422$	−6.83036	+	5.73136i	−0.332497	+	0.278998i
$423$	2.63160	+	2.20818i	0.127953	+	0.107365i
$424$	−1.01665	−	5.76570i	−0.0493728	−	0.280007i
$425$	−5.23895	−	9.07413i	−0.254126	−	0.440160i
$426$	−5.70617	+	9.88338i	−0.276465	+	0.478851i
$427$	−0.283261	−	0.103098i	−0.0137079	−	0.00498928i
$428$	−12.4530	−	4.53251i	−0.601937	−	0.219087i
$429$	−4.03730	+	6.99281i	−0.194923	+	0.337616i
$430$	7.26427	+	12.5821i	0.350314	+	0.606762i
$431$	4.94875	+	28.0658i	0.238373	+	1.35188i	0.835393	+	0.549654i	$0.185240\pi$
$431$	4.94875	+	28.0658i	0.238373	+	1.35188i	−0.597020	+	0.802227i	$0.703649\pi$
$432$	0.188758	+	0.158386i	0.00908161	+	0.00762037i
$433$	10.7227	−	8.99743i	0.515301	−	0.432389i	−0.347689	−	0.937610i	$-0.613034\pi$
$433$	10.7227	−	8.99743i	0.515301	−	0.432389i	0.862990	+	0.505221i	$0.168589\pi$
$434$	1.64957	−	9.35515i	0.0791817	−	0.449062i
$435$	2.32686	−	0.846909i	0.111565	−	0.0406062i
$436$	2.63475			0.126182
$437$	−12.7627	−	8.02190i	−0.610524	−	0.383739i
$438$	−3.37870			−0.161440
$439$	25.2111	−	9.17609i	1.20326	−	0.437951i	0.338900	−	0.940823i	$-0.389945\pi$
$439$	25.2111	−	9.17609i	1.20326	−	0.437951i	0.864361	+	0.502871i	$0.167723\pi$
$440$	3.63670	−	20.6248i	0.173373	−	0.983247i
$441$	6.47117	−	5.42996i	0.308151	−	0.258570i
$442$	5.91783	+	4.96565i	0.281483	+	0.236192i
$443$	−2.41688	−	13.7068i	−0.114829	−	0.651230i	−0.986834	−	0.161733i	$-0.948292\pi$
$443$	−2.41688	−	13.7068i	−0.114829	−	0.651230i	0.872005	−	0.489497i	$-0.162820\pi$
$444$	−3.11736	−	5.39942i	−0.147943	−	0.256245i
$445$	−10.5554	+	18.2824i	−0.500373	+	0.866671i
$446$	5.88499	+	2.14196i	0.278662	+	0.101425i
$447$	−4.87150	−	1.77308i	−0.230414	−	0.0838639i
$448$	−8.55086	+	14.8105i	−0.403990	+	0.699732i
$449$	−10.6420	−	18.4326i	−0.502229	−	0.869887i	−0.999997	−	0.00257601i	$-0.999180\pi$
$449$	−10.6420	−	18.4326i	−0.502229	−	0.869887i	0.497767	−	0.867311i	$-0.334153\pi$
$450$	0.304901	+	1.72918i	0.0143732	+	0.0815144i
$451$	−29.8594	−	25.0550i	−1.40603	−	1.17980i
$452$	13.8374	−	11.6110i	0.650859	−	0.546135i
$453$	2.27343	−	12.8933i	0.106815	−	0.605779i
$454$	2.80505	−	1.02096i	0.131648	−	0.0479158i
$455$	12.2449			0.574049
$456$	4.55526	−	11.1896i	0.213320	−	0.524003i
$457$	−0.745738			−0.0348842			−0.0174421	−	0.999848i	$-0.505552\pi$
$457$	−0.745738			−0.0348842			−0.0174421	+	0.999848i	$0.505552\pi$
$458$	−8.98306	+	3.26957i	−0.419751	+	0.152777i
$459$	−0.872832	+	4.95008i	−0.0407403	+	0.231050i
$460$	−5.83753	+	4.89827i	−0.272176	+	0.228383i
$461$	21.5980	+	18.1229i	1.00592	+	0.844068i	0.987794	−	0.155768i	$-0.0497852\pi$
$461$	21.5980	+	18.1229i	1.00592	+	0.844068i	0.0181272	+	0.999836i	$0.494230\pi$
$462$	−2.54403	−	14.4279i	−0.118359	−	0.671248i
$463$	−4.42852	−	7.67043i	−0.205811	−	0.356475i	0.744580	−	0.667533i	$-0.232650\pi$
$463$	−4.42852	−	7.67043i	−0.205811	−	0.356475i	−0.950391	+	0.311058i	$0.899317\pi$
$464$	0.178671	−	0.309467i	0.00829458	−	0.0143666i
$465$	4.60397	+	1.67571i	0.213504	+	0.0777092i
$466$	−4.69186	−	1.70770i	−0.217346	−	0.0791076i
$467$	−18.6388	+	32.2833i	−0.862500	+	1.49389i	0.00700866	+	0.999975i	$0.497769\pi$
$467$	−18.6388	+	32.2833i	−0.862500	+	1.49389i	−0.869508	+	0.493918i	$0.835564\pi$
$468$	1.17734	+	2.03921i	0.0544226	+	0.0942627i
$469$	−0.714677	−	4.05313i	−0.0330007	−	0.187156i
$470$	−3.78484	−	3.17586i	−0.174582	−	0.146491i
$471$	−5.64550	+	4.73714i	−0.260131	+	0.218276i
$472$	3.08314	−	17.4854i	0.141913	−	0.804830i
$473$	−42.0077	+	15.2895i	−1.93151	+	0.703014i
$474$	−14.2898			−0.656351
$475$	−8.03401	+	4.24463i	−0.368626	+	0.194757i
$476$	25.4946			1.16855
$477$	1.98495	−	0.722461i	0.0908844	−	0.0330792i
$478$	−2.21864	+	12.5825i	−0.101478	+	0.575511i
$479$	−22.8704	+	19.1905i	−1.04498	+	0.876838i	−0.992556	−	0.121787i	$-0.961138\pi$
$479$	−22.8704	+	19.1905i	−1.04498	+	0.876838i	−0.0524190	+	0.998625i	$0.516693\pi$
$480$	−7.52207	−	6.31177i	−0.343334	−	0.288091i
$481$	−1.53074	−	8.68124i	−0.0697956	−	0.395831i
$482$	3.73253	+	6.46494i	0.170012	+	0.294470i
$483$	−6.79615	+	11.7713i	−0.309235	+	0.535612i
$484$	10.4093	+	3.78868i	0.473150	+	0.172213i
$485$	−0.281194	−	0.102346i	−0.0127684	−	0.00464731i
$486$	0.421158	−	0.729467i	0.0191041	−	0.0330893i
$487$	−15.4404	−	26.7435i	−0.699671	−	1.21187i	−0.968581	−	0.248700i	$-0.919997\pi$
$487$	−15.4404	−	26.7435i	−0.699671	−	1.21187i	0.268910	−	0.963165i	$-0.413337\pi$
$488$	0.0369129	+	0.209344i	0.00167097	+	0.00947654i
$489$	−12.2782	−	10.3027i	−0.555240	−	0.465902i
$490$	−9.30702	+	7.80951i	−0.420448	+	0.352798i
$491$	1.75863	−	9.97370i	0.0793660	−	0.450107i	−0.919065	−	0.394107i	$-0.871054\pi$
$491$	1.75863	−	9.97370i	0.0793660	−	0.450107i	0.998431	−	0.0560004i	$-0.0178348\pi$
$492$	−10.6813	+	3.88768i	−0.481551	+	0.175270i
$493$	7.28943			0.328299
$494$	4.49577	−	4.96666i	0.202274	−	0.223461i
$495$	7.55614			0.339623
$496$	0.664403	−	0.241823i	0.0298326	−	0.0108582i
$497$	−9.24697	+	52.4422i	−0.414783	+	2.35235i
$498$	8.40453	−	7.05223i	0.376616	−	0.316018i
$499$	6.58385	+	5.52450i	0.294734	+	0.247311i	0.778148	−	0.628081i	$-0.216159\pi$
$499$	6.58385	+	5.52450i	0.294734	+	0.247311i	−0.483415	+	0.875391i	$0.660604\pi$
$500$	2.71078	+	15.3736i	0.121230	+	0.687528i
$501$	6.56366	+	11.3686i	0.293243	+	0.507911i
$502$	4.93056	−	8.53998i	0.220062	−	0.381158i
$503$	16.9775	+	6.17930i	0.756989	+	0.275521i	0.691543	−	0.722335i	$-0.256931\pi$
$503$	16.9775	+	6.17930i	0.756989	+	0.275521i	0.0654451	+	0.997856i	$0.479153\pi$
$504$	−10.2365	−	3.72579i	−0.455971	−	0.165960i
$505$	9.57332	−	16.5815i	0.426007	−	0.737866i
$506$	6.44550	+	11.1639i	0.286537	+	0.496297i
$507$	−1.67931	−	9.52383i	−0.0745807	−	0.422968i
$508$	−1.93691	−	1.62526i	−0.0859363	−	0.0721091i
$509$	24.0894	−	20.2134i	1.06774	−	0.895942i	0.0728963	−	0.997340i	$-0.476776\pi$
$509$	24.0894	−	20.2134i	1.06774	−	0.895942i	0.994846	+	0.101397i	$0.0323314\pi$
$510$	1.25533	−	7.11933i	0.0555870	−	0.315249i
$511$	−14.8146	+	5.39207i	−0.655359	+	0.238531i
$512$	−2.78294			−0.122990
$513$	4.26124	+	0.917504i	0.188138	+	0.0405088i
$514$	8.35239			0.368408
$515$	−15.2749	+	5.55962i	−0.673094	+	0.244986i
$516$	−2.26373	+	12.8382i	−0.0996550	+	0.565172i
$517$	11.6458	−	9.77196i	0.512180	−	0.429770i
$518$	12.2523	+	10.2809i	0.538333	+	0.451715i
$519$	−3.20763	−	18.1914i	−0.140800	−	0.798514i
$520$	−4.31750	−	7.47814i	−0.189335	−	0.327938i
$521$	−9.97505	+	17.2773i	−0.437015	+	0.756932i	−0.997458	−	0.0712610i	$-0.977298\pi$
$521$	−9.97505	+	17.2773i	−0.437015	+	0.756932i	0.560443	+	0.828193i	$0.310631\pi$
$522$	−1.14787	−	0.417792i	−0.0502411	−	0.0182862i
$523$	−2.97141	−	1.08150i	−0.129931	−	0.0472909i	0.276236	−	0.961090i	$-0.410913\pi$
$523$	−2.97141	−	1.08150i	−0.129931	−	0.0472909i	−0.406167	+	0.913799i	$0.633135\pi$
$524$	−1.00662	+	1.74352i	−0.0439744	+	0.0761659i
$525$	4.09650	+	7.09535i	0.178786	+	0.309667i
$526$	0.985680	+	5.59007i	0.0429777	+	0.243739i
$527$	11.0487	+	9.27092i	0.481287	+	0.403848i
$528$	0.835319	−	0.700916i	0.0363526	−	0.0305035i
$529$	−1.91710	+	10.8724i	−0.0833520	+	0.472713i
$530$	−2.85480	+	1.03906i	−0.124005	+	0.0451340i
$531$	6.40598			0.277996
$532$	0.829838	−	22.0932i	0.0359781	−	0.957863i
$533$	−16.0714			−0.696128
$534$	9.78616	−	3.56187i	0.423489	−	0.154137i
$535$	−3.04474	+	17.2676i	−0.131636	+	0.746543i
$536$	−2.22332	+	1.86559i	−0.0960327	+	0.0805810i
$537$	9.08438	+	7.62270i	0.392020	+	0.328944i
$538$	−0.105062	−	0.595836i	−0.00452954	−	0.0256883i
$539$	−18.6916	−	32.3748i	−0.805105	−	1.39448i
$540$	1.10175	−	1.90828i	0.0474116	−	0.0821193i
$541$	−0.558559	−	0.203299i	−0.0240143	−	0.00874050i	0.329985	−	0.943986i	$-0.392956\pi$
$541$	−0.558559	−	0.203299i	−0.0240143	−	0.00874050i	−0.353999	+	0.935246i	$0.615179\pi$
$542$	−22.8282	−	8.30880i	−0.980556	−	0.356893i
$543$	−0.136862	+	0.237052i	−0.00587331	+	0.0101729i
$544$	−14.4531	−	25.0335i	−0.619673	−	1.07330i
$545$	−0.605344	−	3.43308i	−0.0259301	−	0.147057i
$546$	−4.62734	−	3.88280i	−0.198032	−	0.166168i
$547$	20.3567	−	17.0813i	0.870392	−	0.730345i	−0.0937888	−	0.995592i	$-0.529898\pi$
$547$	20.3567	−	17.0813i	0.870392	−	0.730345i	0.964181	+	0.265247i	$0.0854534\pi$
$548$	−3.44247	+	19.5232i	−0.147055	+	0.833990i
$549$	−0.0720704	+	0.0262315i	−0.00307589	+	0.00111953i
$550$	7.77029			0.331326
$551$	0.237267	−	6.31690i	0.0101079	−	0.269109i
$552$	9.58520			0.407973
$553$	−62.6564	+	22.8051i	−2.66442	+	0.969770i
$554$	0.560397	−	3.17817i	0.0238090	−	0.135027i
$555$	−6.31922	+	5.30246i	−0.268236	+	0.225077i
$556$	−9.20176	−	7.72119i	−0.390241	−	0.327451i
$557$	5.93387	+	33.6527i	0.251426	+	1.42591i	0.805082	+	0.593163i	$0.202121\pi$
$557$	5.93387	+	33.6527i	0.251426	+	1.42591i	−0.553656	+	0.832745i	$0.686768\pi$
$558$	−1.20848	−	2.09315i	−0.0511591	−	0.0886102i
$559$	−9.21590	+	15.9624i	−0.389791	+	0.675138i
$560$	−1.55388	−	0.565567i	−0.0656635	−	0.0238996i
$561$	20.9023	+	7.60782i	0.882496	+	0.321202i
$562$	−9.30428	+	16.1155i	−0.392477	+	0.679791i
$563$	15.0358	+	26.0427i	0.633683	+	1.09757i	0.986793	+	0.161989i	$0.0517908\pi$
$563$	15.0358	+	26.0427i	0.633683	+	1.09757i	−0.353110	+	0.935582i	$0.614876\pi$
$564$	−0.769832	−	4.36593i	−0.0324158	−	0.183839i
$565$	−18.3083	−	15.3625i	−0.770238	−	0.646306i
$566$	16.2258	−	13.6151i	0.682023	−	0.572285i
$567$	0.682495	−	3.87062i	0.0286621	−	0.162551i
$568$	35.2877	−	12.8437i	1.48064	−	0.538908i
$569$	−24.7511			−1.03762			−0.518809	−	0.854890i	$-0.673624\pi$
$569$	−24.7511			−1.03762			−0.518809	+	0.854890i	$0.673624\pi$
$570$	−6.12863	−	1.31958i	−0.256700	−	0.0552711i
$571$	31.5869			1.32187			0.660934	−	0.750444i	$-0.270160\pi$
$571$	31.5869			1.32187			0.660934	+	0.750444i	$0.270160\pi$
$572$	9.79187	−	3.56395i	0.409419	−	0.149016i
$573$	−2.11241	+	11.9800i	−0.0882470	+	0.500474i
$574$	22.3377	−	18.7435i	0.932357	−	0.782340i
$575$	−5.52245	−	4.63388i	−0.230302	−	0.193246i
$576$	0.755581	+	4.28511i	0.0314825	+	0.178546i
$577$	15.4054	+	26.6830i	0.641337	+	1.11083i	0.985135	+	0.171784i	$0.0549531\pi$
$577$	15.4054	+	26.6830i	0.641337	+	1.11083i	−0.343798	+	0.939044i	$0.611714\pi$
$578$	3.48091	−	6.02912i	0.144787	−	0.250778i
$579$	−21.6846	−	7.89254i	−0.901180	−	0.328003i
$580$	−3.00283	−	1.09294i	−0.124686	−	0.0453818i
$581$	25.5967	−	44.3347i	1.06193	−	1.83931i
$582$	0.0738097	+	0.127842i	0.00305951	+	0.00529923i
$583$	−1.62323	−	9.20582i	−0.0672275	−	0.381266i
$584$	8.51659	+	7.14627i	0.352419	+	0.295715i
$585$	2.38660	−	2.00259i	0.0986737	−	0.0827970i
$586$	0.866940	−	4.91666i	0.0358130	−	0.203105i
$587$	13.2728	−	4.83091i	0.547828	−	0.199393i	−0.0532531	−	0.998581i	$-0.516959\pi$
$587$	13.2728	−	4.83091i	0.547828	−	0.199393i	0.601081	+	0.799188i	$0.294737\pi$
$588$	−10.9016			−0.449572
$589$	8.39365	−	9.27281i	0.345854	−	0.382080i
$590$	−9.21326			−0.379304
$591$	−6.07861	+	2.21243i	−0.250041	+	0.0910074i
$592$	−0.206718	+	1.17236i	−0.00849606	+	0.0481835i
$593$	28.8915	−	24.2428i	1.18643	−	0.995533i	0.186516	−	0.982452i	$-0.440280\pi$
$593$	28.8915	−	24.2428i	1.18643	−	0.995533i	0.999914	−	0.0130812i	$-0.00416400\pi$
$594$	−2.85547	−	2.39602i	−0.117161	−	0.0983099i
$595$	−5.85750	−	33.2195i	−0.240134	−	1.36187i
$596$	3.34508	+	5.79384i	0.137020	+	0.237325i
$597$	−0.153544	+	0.265946i	−0.00628414	+	0.0108845i
$598$	4.99456	+	1.81787i	0.204243	+	0.0743383i
$599$	−0.0872028	−	0.0317392i	−0.00356301	−	0.00129683i	0.340238	−	0.940339i	$-0.389492\pi$
$599$	−0.0872028	−	0.0317392i	−0.00356301	−	0.00129683i	−0.343801	+	0.939043i	$0.611715\pi$
$600$	2.88883	−	5.00359i	0.117936	−	0.204271i
$601$	11.5190	+	19.9515i	0.469870	+	0.813839i	0.999406	−	0.0344482i	$-0.0109674\pi$
$601$	11.5190	+	19.9515i	0.469870	+	0.813839i	−0.529536	+	0.848287i	$0.677634\pi$
$602$	−5.80724	−	32.9345i	−0.236685	−	1.34231i
$603$	−0.802166	−	0.673097i	−0.0326667	−	0.0274106i
$604$	−12.9427	+	10.8602i	−0.526631	+	0.441896i
$605$	2.54507	−	14.4338i	0.103472	−	0.586817i
$606$	−8.87567	+	3.23048i	−0.360550	+	0.131229i
$607$	31.9363			1.29625			0.648127	−	0.761532i	$-0.275553\pi$
$607$	31.9363			1.29625			0.648127	+	0.761532i	$0.275553\pi$
$608$	−22.1641	+	11.7100i	−0.898873	+	0.474903i
$609$	−5.69984			−0.230969
$610$	0.103654	−	0.0377268i	0.00419681	−	0.00152751i
$611$	1.08845	−	6.17292i	0.0440341	−	0.249730i
$612$	4.96905	−	4.16953i	0.200862	−	0.168543i
$613$	33.4848	+	28.0971i	1.35244	+	1.13483i	0.978239	+	0.207482i	$0.0665269\pi$
$613$	33.4848	+	28.0971i	1.35244	+	1.13483i	0.374199	+	0.927348i	$0.377918\pi$
$614$	2.57199	+	14.5865i	0.103797	+	0.588662i
$615$	7.51972	+	13.0245i	0.303224	+	0.525200i
$616$	−24.1038	+	41.7489i	−0.971168	+	1.68211i
$617$	12.6034	+	4.58726i	0.507394	+	0.184676i	0.583016	−	0.812460i	$-0.301872\pi$
$617$	12.6034	+	4.58726i	0.507394	+	0.184676i	−0.0756229	+	0.997136i	$0.524095\pi$
$618$	7.53533	+	2.74264i	0.303116	+	0.110325i
$619$	−11.4670	+	19.8615i	−0.460899	+	0.798300i	−0.999006	−	0.0445765i	$-0.985806\pi$
$619$	−11.4670	+	19.8615i	−0.460899	+	0.798300i	0.538107	+	0.842876i	$0.319139\pi$
$620$	−3.16138	−	5.47567i	−0.126964	−	0.219908i
$621$	0.600529	+	3.40577i	0.0240984	+	0.136669i
$622$	3.89000	+	3.26410i	0.155975	+	0.130879i
$623$	37.2250	−	31.2355i	1.49139	−	1.25142i
$624$	0.0780717	−	0.442767i	0.00312537	−	0.0177249i
$625$	9.61478	−	3.49949i	0.384591	−	0.139980i
$626$	−14.0650			−0.562152
$627$	7.27317	−	17.8660i	0.290462	−	0.713497i
$628$	9.51059			0.379514
$629$	−22.8194	+	8.30557i	−0.909868	+	0.331165i
$630$	−0.981583	+	5.56683i	−0.0391072	+	0.221788i
$631$	−16.3606	+	13.7282i	−0.651306	+	0.546510i	−0.907467	−	0.420124i	$-0.861987\pi$
$631$	−16.3606	+	13.7282i	−0.651306	+	0.546510i	0.256161	+	0.966634i	$0.417542\pi$
$632$	36.0198	+	30.2242i	1.43279	+	1.20226i
$633$	1.83817	+	10.4248i	0.0730606	+	0.414347i
$634$	−0.923621	−	1.59976i	−0.0366817	−	0.0635346i
$635$	−1.67270	+	2.89720i	−0.0663790	+	0.114972i
$636$	−2.56158	−	0.932339i	−0.101573	−	0.0369696i
$637$	−14.4840	−	5.27174i	−0.573876	−	0.208874i
$638$	−2.70288	+	4.68152i	−0.107008	+	0.185343i
$639$	6.77438	+	11.7336i	0.267990	+	0.464173i
$640$	2.32353	+	13.1774i	0.0918458	+	0.520883i
$641$	−22.5997	−	18.9634i	−0.892634	−	0.749009i	0.0761030	−	0.997100i	$-0.475752\pi$
$641$	−22.5997	−	18.9634i	−0.892634	−	0.749009i	−0.968737	+	0.248091i	$0.920197\pi$
$642$	6.62609	−	5.55995i	0.261511	−	0.219434i
$643$	1.18655	−	6.72928i	0.0467931	−	0.265377i	−0.952431	−	0.304753i	$-0.901426\pi$
$643$	1.18655	−	6.72928i	0.0467931	−	0.265377i	0.999224	+	0.0393763i	$0.0125371\pi$
$644$	16.4831	−	5.99934i	0.649524	−	0.236407i
$645$	17.2483			0.679152
$646$	−15.6248	−	9.82085i	−0.614751	−	0.386396i
$647$	−18.9452			−0.744812			−0.372406	−	0.928070i	$-0.621467\pi$
$647$	−18.9452			−0.744812			−0.372406	+	0.928070i	$0.621467\pi$
$648$	−2.60449	+	0.947958i	−0.102314	+	0.0372393i
$649$	4.92271	−	27.9181i	0.193233	−	1.09588i
$650$	2.45423	−	2.05935i	0.0962630	−	0.0807742i
$651$	−8.63929	−	7.24923i	−0.338601	−	0.284120i
$652$	3.59179	+	20.3701i	0.140665	+	0.797753i
$653$	−13.5699	−	23.5038i	−0.531033	−	0.919776i	−0.999344	−	0.0362124i	$-0.988471\pi$
$653$	−13.5699	−	23.5038i	−0.531033	−	0.919776i	0.468311	−	0.883564i	$-0.344863\pi$
$654$	−0.859855	+	1.48931i	−0.0336230	+	0.0582367i
$655$	2.50308	+	0.911046i	0.0978034	+	0.0355975i
$656$	2.03946	+	0.742304i	0.0796277	+	0.0289821i
$657$	−2.00560	+	3.47380i	−0.0782459	+	0.135526i
$658$	5.68645	+	9.84921i	0.221681	+	0.383962i
$659$	−6.92986	−	39.3012i	−0.269949	−	1.53096i	−0.754562	−	0.656228i	$-0.772151\pi$
$659$	−6.92986	−	39.3012i	−0.269949	−	1.53096i	0.484613	−	0.874729i	$-0.338960\pi$
$660$	−7.46987	−	6.26797i	−0.290764	−	0.243980i
$661$	−38.5678	+	32.3622i	−1.50011	+	1.25874i	−0.619415	+	0.785064i	$0.712630\pi$
$661$	−38.5678	+	32.3622i	−1.50011	+	1.25874i	−0.880697	+	0.473680i	$0.842925\pi$
$662$	−2.27310	+	12.8914i	−0.0883465	+	0.501038i
$663$	8.61825	−	3.13679i	0.334705	−	0.121823i
$664$	−36.1012			−1.40100
$665$	−28.9781	+	3.99473i	−1.12372	+	0.154909i
$666$	4.06942			0.157687
$667$	4.71284	−	1.71533i	0.182482	−	0.0664179i
$668$	2.94175	−	16.6835i	0.113820	−	0.645503i
$669$	5.69559	−	4.77917i	0.220204	−	0.184773i
$670$	1.15370	+	0.968066i	0.0445712	+	0.0373997i
$671$	0.0589371	+	0.334249i	0.00227524	+	0.0129035i
$672$	11.3014	+	19.5745i	0.435959	+	0.755104i
$673$	23.9052	−	41.4050i	0.921477	−	1.59605i	0.124347	−	0.992239i	$-0.460317\pi$
$673$	23.9052	−	41.4050i	0.921477	−	1.59605i	0.797131	−	0.603807i	$-0.206350\pi$
$674$	9.79636	+	3.56558i	0.377342	+	0.137341i
$675$	1.95884	+	0.712961i	0.0753959	+	0.0274419i
$676$	−6.24007	+	10.8081i	−0.240003	+	0.415697i
$677$	−20.6305	−	35.7331i	−0.792894	−	1.37333i	−0.924168	−	0.381987i	$-0.875240\pi$
$677$	−20.6305	−	35.7331i	−0.792894	−	1.37333i	0.131274	−	0.991346i	$-0.458093\pi$
$678$	2.04733	+	11.6110i	0.0786273	+	0.445918i
$679$	0.527657	+	0.442757i	0.0202496	+	0.0169914i
$680$	−18.2223	+	15.2904i	−0.698795	+	0.586359i
$681$	0.615390	−	3.49005i	0.0235818	−	0.133739i
$682$	−10.0509	+	3.65822i	−0.384868	+	0.140080i
$683$	−17.8805			−0.684178			−0.342089	−	0.939668i	$-0.611134\pi$
$683$	−17.8805			−0.684178			−0.342089	+	0.939668i	$0.611134\pi$
$684$	−3.45150	−	4.44181i	−0.131972	−	0.169837i
$685$	26.2297			1.00218
$686$	4.50313	−	1.63900i	0.171930	−	0.0625775i
$687$	−1.97076	+	11.1767i	−0.0751892	+	0.426419i
$688$	1.90677	−	1.59997i	0.0726951	−	0.0609984i
$689$	−2.95250	−	2.47744i	−0.112481	−	0.0943830i
$690$	−0.863697	−	4.89827i	−0.0328804	−	0.186474i
$691$	5.66655	+	9.81476i	0.215566	+	0.373371i	0.953447	−	0.301559i	$-0.0975071\pi$
$691$	5.66655	+	9.81476i	0.215566	+	0.373371i	−0.737882	+	0.674930i	$0.764174\pi$
$692$	−11.9191	+	20.6445i	−0.453097	+	0.784786i
$693$	−16.3442	−	5.94879i	−0.620864	−	0.225976i
$694$	−17.5762	−	6.39720i	−0.667182	−	0.242834i
$695$	−7.94657	+	13.7639i	−0.301431	+	0.522093i
$696$	2.00974	+	3.48098i	0.0761791	+	0.131946i
$697$	7.68794	+	43.6005i	0.291202	+	1.65149i
$698$	12.8594	+	10.7903i	0.486734	+	0.408418i
$699$	−4.54086	+	3.81024i	−0.171751	+	0.144116i
$700$	1.83600	−	10.4125i	0.0693943	−	0.393554i
$701$	−6.47788	+	2.35776i	−0.244666	+	0.0890512i	−0.461443	−	0.887170i	$-0.652668\pi$
$701$	−6.47788	+	2.35776i	−0.244666	+	0.0890512i	0.216776	+	0.976221i	$0.430446\pi$
$702$	−1.53691			−0.0580069
$703$	6.45471	+	20.0452i	0.243444	+	0.756020i
$704$	19.2557			0.725725
$705$	−5.51194	+	2.00618i	−0.207592	+	0.0755572i
$706$	0.761470	−	4.31851i	0.0286583	−	0.162529i
$707$	−33.7616	+	28.3294i	−1.26974	+	1.06544i
$708$	−6.33285	−	5.31389i	−0.238003	−	0.199708i
$709$	−8.79501	−	49.8790i	−0.330304	−	1.87325i	−0.469429	−	0.882970i	$-0.655540\pi$
$709$	−8.79501	−	49.8790i	−0.330304	−	1.87325i	0.139125	−	0.990275i	$-0.455571\pi$
$710$	−9.74310	−	16.8755i	−0.365652	−	0.633328i
$711$	−8.48243	+	14.6920i	−0.318116	+	0.550993i
$712$	−32.2014	−	11.7203i	−1.20680	−	0.439239i
$713$	9.32490	+	3.39399i	0.349220	+	0.127106i
$714$	−8.32022	+	14.4111i	−0.311377	+	0.539320i
$715$	−6.89355	−	11.9400i	−0.257804	−	0.446530i
$716$	−2.65748	−	15.0713i	−0.0993148	−	0.563242i
$717$	11.6197	+	9.75009i	0.433946	+	0.364124i
$718$	3.33483	−	2.79826i	0.124455	−	0.104430i
$719$	3.41095	−	19.3445i	0.127207	−	0.721427i	−0.852765	−	0.522294i	$-0.825076\pi$
$719$	3.41095	−	19.3445i	0.127207	−	0.721427i	0.979972	−	0.199133i	$-0.0638126\pi$
$720$	−0.395356	+	0.143898i	−0.0147341	+	0.00536276i
$721$	37.4172			1.39349
$722$	−9.01917	+	13.2205i	−0.335659	+	0.492018i
$723$	8.86254			0.329602
$724$	0.331939	−	0.120816i	0.0123364	−	0.00449008i
$725$	0.524949	−	2.97713i	0.0194961	−	0.110568i
$726$	−5.53868	+	4.64750i	−0.205560	+	0.172485i
$727$	−13.6886	−	11.4861i	−0.507684	−	0.425997i	0.352630	−	0.935763i	$-0.385288\pi$
$727$	−13.6886	−	11.4861i	−0.507684	−	0.425997i	−0.860313	+	0.509766i	$0.829732\pi$
$728$	3.45152	+	19.5745i	0.127922	+	0.725480i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	2.88451	−	4.99611i	0.106760	−	0.184914i
$731$	47.7135	+	17.3663i	1.76475	+	0.642315i
$732$	0.0930071	+	0.0338518i	0.00343764	+	0.00125120i
$733$	−19.5736	+	33.9025i	−0.722968	+	1.25222i	0.236837	+	0.971549i	$0.423889\pi$
$733$	−19.5736	+	33.9025i	−0.722968	+	1.25222i	−0.959805	+	0.280668i	$0.909444\pi$
$734$	−2.55316	−	4.42221i	−0.0942390	−	0.163227i
$735$	2.50468	+	14.2047i	0.0923864	+	0.523949i
$736$	−15.2352	−	12.7839i	−0.561578	−	0.471220i
$737$	−3.54987	+	2.97869i	−0.130761	+	0.109722i
$738$	1.28832	−	7.30645i	0.0474238	−	0.268954i
$739$	−29.1001	+	10.5916i	−1.07046	+	0.389617i	−0.816350	−	0.577558i	$-0.804006\pi$
$739$	−29.1001	+	10.5916i	−1.07046	+	0.389617i	−0.254113	+	0.967175i	$0.581784\pi$
$740$	10.6456			0.391339
$741$	−2.43777	−	7.57053i	−0.0895536	−	0.278110i
$742$	6.99306			0.256723
$743$	11.5042	−	4.18720i	0.422050	−	0.153614i	−0.122259	−	0.992498i	$-0.539014\pi$
$743$	11.5042	−	4.18720i	0.422050	−	0.153614i	0.544309	+	0.838885i	$0.316792\pi$
$744$	−1.38103	+	7.83220i	−0.0506310	+	0.287142i
$745$	6.78084	−	5.68980i	0.248431	−	0.208458i
$746$	−6.44313	−	5.40643i	−0.235900	−	0.197943i
$747$	−2.26180	−	12.8273i	−0.0827549	−	0.469327i
$748$	−14.3528	−	24.8598i	−0.524791	−	0.908965i
$749$	20.1803	−	34.9533i	0.737372	−	1.27717i
$750$	−9.57472	−	3.48491i	−0.349619	−	0.127251i
$751$	42.2047	+	15.3613i	1.54007	+	0.560541i	0.966063	−	0.258308i	$-0.0831649\pi$
$751$	42.2047	+	15.3613i	1.54007	+	0.560541i	0.574010	+	0.818848i	$0.305387\pi$
$752$	−0.423240	+	0.733074i	−0.0154340	+	0.0267324i
$753$	−5.85357	−	10.1387i	−0.213316	−	0.369474i
$754$	0.387036	+	2.19499i	0.0140950	+	0.0799368i
$755$	17.1245	+	14.3692i	0.623224	+	0.522947i
$756$	−3.88546	+	3.26029i	−0.141313	+	0.118576i
$757$	−2.64469	+	14.9988i	−0.0961228	+	0.545139i	0.898275	+	0.439434i	$0.144821\pi$
$757$	−2.64469	+	14.9988i	−0.0961228	+	0.545139i	−0.994398	+	0.105705i	$0.966290\pi$
$758$	−10.9071	+	3.96984i	−0.396162	+	0.144191i
$759$	15.3042			0.555508
$760$	12.6572	+	16.2889i	0.459126	+	0.590859i
$761$	−32.2300			−1.16834			−0.584169	−	0.811632i	$-0.698579\pi$
$761$	−32.2300			−1.16834			−0.584169	+	0.811632i	$0.698579\pi$
$762$	1.55080	−	0.564446i	0.0561796	−	0.0204477i
$763$	−1.39341	+	7.90243i	−0.0504449	+	0.286087i
$764$	12.0260	−	10.0910i	0.435084	−	0.365079i
$765$	−6.57456	−	5.51671i	−0.237704	−	0.199457i
$766$	−2.38596	−	13.5314i	−0.0862082	−	0.488911i
$767$	−5.84425	−	10.1225i	−0.211024	−	0.365504i
$768$	7.65165	−	13.2531i	0.276105	−	0.478228i
$769$	−10.0805	−	3.66902i	−0.363514	−	0.132308i	0.153804	−	0.988101i	$-0.450847\pi$
$769$	−10.0805	−	3.66902i	−0.363514	−	0.132308i	−0.517318	+	0.855793i	$0.673070\pi$
$770$	23.5066	+	8.55572i	0.847120	+	0.308327i
$771$	4.95799	−	8.58749i	0.178558	−	0.309271i
$772$	14.8900	+	25.7902i	0.535902	+	0.928210i
$773$	0.143553	+	0.814127i	0.00516323	+	0.0292821i	0.987281	−	0.158988i	$-0.0508231\pi$
$773$	0.143553	+	0.814127i	0.00516323	+	0.0292821i	−0.982117	+	0.188270i	$0.939712\pi$
$774$	−6.51814	−	5.46937i	−0.234290	−	0.196592i
$775$	4.58208	−	3.84482i	0.164593	−	0.138110i
$776$	0.0843482	−	0.478363i	0.00302792	−	0.0171722i
$777$	17.8432	−	6.49439i	0.640121	−	0.232985i
$778$	9.66244			0.346415
$779$	38.0337	−	5.24307i	1.36270	−	0.187852i
$780$	−4.02054			−0.143958
$781$	56.3422	−	20.5069i	2.01608	−	0.733793i
$782$	2.54255	−	14.4195i	0.0909214	−	0.515641i
$783$	−1.11093	+	0.932182i	−0.0397014	+	0.0333135i
$784$	1.59453	+	1.33797i	0.0569476	+	0.0477847i
$785$	−2.18510	−	12.3923i	−0.0779895	−	0.442300i
$786$	−0.657025	−	1.13800i	−0.0234353	−	0.0405911i
$787$	6.51330	−	11.2814i	0.232174	−	0.402137i	−0.726274	−	0.687406i	$-0.758749\pi$
$787$	6.51330	−	11.2814i	0.232174	−	0.402137i	0.958448	+	0.285269i	$0.0920828\pi$
$788$	7.84447	+	2.85515i	0.279448	+	0.101711i
$789$	6.33252	+	2.30485i	0.225444	+	0.0820547i
$790$	12.1997	−	21.1304i	0.434044	−	0.751787i
$791$	27.5069	+	47.6434i	0.978034	+	1.69400i
$792$	2.12988	+	12.0792i	0.0756821	+	0.429214i
$793$	0.107201	+	0.0899521i	0.00380681	+	0.00319429i
$794$	0.289143	−	0.242620i	0.0102613	−	0.00861025i
$795$	−0.626304	+	3.55195i	−0.0222127	+	0.125975i
$796$	0.372399	−	0.135542i	0.0131993	−	0.00480416i
$797$	−47.0808			−1.66769			−0.833844	−	0.552000i	$-0.813865\pi$
$797$	−47.0808			−1.66769			−0.833844	+	0.552000i	$0.813865\pi$
$798$	12.2176	+	7.67924i	0.432497	+	0.271842i
$799$	−17.2674			−0.610877
$800$	−11.2650	+	4.10012i	−0.398278	+	0.144961i
$801$	2.14695	−	12.1759i	0.0758587	−	0.430216i
$802$	−9.36029	+	7.85422i	−0.330523	+	0.277342i
$803$	13.5980	+	11.4101i	0.479864	+	0.402654i
$804$	0.234660	+	1.33082i	0.00827583	+	0.0469346i
$805$	−11.6042	−	20.0991i	−0.408994	−	0.708399i
$806$	−2.20502	+	3.81921i	−0.0776686	+	0.134526i
$807$	−0.674972	−	0.245670i	−0.0237601	−	0.00864799i
$808$	29.2054	+	10.6299i	1.02744	+	0.373959i
$809$	5.00748	−	8.67320i	0.176053	−	0.304934i	−0.764472	−	0.644657i	$-0.777000\pi$
$809$	5.00748	−	8.67320i	0.176053	−	0.304934i	0.940525	+	0.339724i	$0.110333\pi$
$810$	0.719113	+	1.24554i	0.0252671	+	0.0437639i
$811$	−5.47946	−	31.0756i	−0.192410	−	1.09121i	−0.916059	−	0.401043i	$-0.868648\pi$
$811$	−5.47946	−	31.0756i	−0.192410	−	1.09121i	0.723649	−	0.690168i	$-0.242463\pi$
$812$	5.63476	+	4.72813i	0.197741	+	0.165925i
$813$	−22.0935	+	18.5387i	−0.774854	+	0.650180i
$814$	3.12717	−	17.7350i	0.109607	−	0.621613i
$815$	25.7170	−	9.36021i	0.900826	−	0.327874i
$816$	−1.23854			−0.0433577
$817$	16.6024	−	40.7824i	0.580844	−	1.42680i
$818$	11.1177			0.388721
$819$	−6.73889	+	2.45275i	−0.235476	+	0.0857062i
$820$	3.37024	−	19.1136i	0.117694	−	0.667476i
$821$	−29.3751	+	24.6487i	−1.02520	+	0.860244i	−0.990272	−	0.139146i	$-0.955564\pi$
$821$	−29.3751	+	24.6487i	−1.02520	+	0.860244i	−0.0349269	+	0.999390i	$0.511120\pi$
$822$	−9.91220	−	8.31732i	−0.345728	−	0.290100i
$823$	8.53261	+	48.3909i	0.297428	+	1.68680i	0.657166	+	0.753746i	$0.271755\pi$
$823$	8.53261	+	48.3909i	0.297428	+	1.68680i	−0.359738	+	0.933053i	$0.617134\pi$
$824$	−13.1932	−	22.8512i	−0.459606	−	0.796060i
$825$	4.61245	−	7.98900i	0.160585	−	0.278141i
$826$	19.9286	+	7.25341i	0.693404	+	0.252378i
$827$	−15.0574	−	5.48045i	−0.523597	−	0.190574i	0.0666799	−	0.997774i	$-0.478759\pi$
$827$	−15.0574	−	5.48045i	−0.523597	−	0.190574i	−0.590277	+	0.807201i	$0.700982\pi$
$828$	2.23148	−	3.86503i	0.0775492	−	0.134319i
$829$	−17.2476	−	29.8737i	−0.599033	−	1.03756i	−0.992964	−	0.118416i	$-0.962218\pi$
$829$	−17.2476	−	29.8737i	−0.599033	−	1.03756i	0.393931	−	0.919140i	$-0.371115\pi$
$830$	3.25298	+	18.4486i	0.112913	+	0.640359i
$831$	−2.93498	−	2.46274i	−0.101813	−	0.0854314i
$832$	6.08187	−	5.10330i	0.210851	−	0.176925i
$833$	−7.37326	+	41.8159i	−0.255468	+	1.44883i
$834$	7.36747	−	2.68154i	0.255115	−	0.0928542i
$835$	−22.4145			−0.775685
$836$	−22.0103	+	11.6287i	−0.761242	+	0.402189i
$837$	−2.86943			−0.0991818
$838$	9.04147	−	3.29083i	0.312332	−	0.113680i
$839$	−2.95759	+	16.7733i	−0.102107	+	0.579080i	0.890229	+	0.455514i	$0.150544\pi$
$839$	−2.95759	+	16.7733i	−0.102107	+	0.579080i	−0.992336	+	0.123567i	$0.960567\pi$
$840$	14.2486	−	11.9560i	0.491624	−	0.412522i
$841$	−20.6042	−	17.2890i	−0.710490	−	0.596172i
$842$	2.42564	+	13.7565i	0.0835932	+	0.474081i
$843$	11.0461	+	19.1324i	0.380447	+	0.658953i
$844$	6.83036	−	11.8305i	0.235111	−	0.407224i
$845$	15.5167	+	5.64760i	0.533789	+	0.194283i
$846$	2.71911	+	0.989676i	0.0934850	+	0.0340258i
$847$	−16.8685	+	29.2171i	−0.579608	+	1.00391i
$848$	0.260246	+	0.450759i	0.00893687	+	0.0154791i
$849$	−4.36665	−	24.7645i	−0.149863	−	0.849915i
$850$	−6.76088	−	5.67306i	−0.231896	−	0.194584i
$851$	−12.7990	+	10.7396i	−0.438743	+	0.368149i
$852$	3.03619	−	17.2191i	0.104018	−	0.589916i
$853$	−32.1506	+	11.7019i	−1.10082	+	0.400664i	−0.827617	−	0.561293i	$-0.810304\pi$
$853$	−32.1506	+	11.7019i	−1.10082	+	0.400664i	−0.273199	+	0.961957i	$0.588082\pi$
$854$	−0.253907			−0.00868853
$855$	−4.99469	+	5.51784i	−0.170815	+	0.188706i
$856$	−28.4620			−0.972812
$857$	−7.76834	+	2.82745i	−0.265362	+	0.0965837i	−0.471274	−	0.881987i	$-0.656206\pi$
$857$	−7.76834	+	2.82745i	−0.265362	+	0.0965837i	0.205913	+	0.978570i	$0.433984\pi$
$858$	−1.18104	+	6.69804i	−0.0403202	+	0.228667i
$859$	−38.6809	+	32.4571i	−1.31977	+	1.10742i	−0.333421	+	0.942778i	$0.608203\pi$
$859$	−38.6809	+	32.4571i	−1.31977	+	1.10742i	−0.986353	+	0.164643i	$0.947353\pi$
$860$	−17.0514	−	14.3078i	−0.581448	−	0.487893i
$861$	−6.01145	−	34.0926i	−0.204870	−	1.16187i
$862$	12.0025	+	20.7889i	0.408806	+	0.708072i
$863$	16.5035	−	28.5849i	0.561785	−	0.973040i	−0.435556	−	0.900162i	$-0.643448\pi$
$863$	16.5035	−	28.5849i	0.561785	−	0.973040i	0.997341	−	0.0728785i	$-0.0232185\pi$
$864$	5.40402	+	1.96690i	0.183849	+	0.0669154i
$865$	29.6383	+	10.7874i	1.00773	+	0.366784i
$866$	5.89516	−	10.2107i	0.200326	−	0.346975i
$867$	−4.13255	−	7.15778i	−0.140349	−	0.243091i
$868$	2.52728	+	14.3329i	0.0857815	+	0.486491i
$869$	57.5112	+	48.2576i	1.95093	+	1.63703i
$870$	1.59777	−	1.34069i	0.0541695	−	0.0454536i
$871$	−0.331782	+	1.88163i	−0.0112420	+	0.0637566i
$872$	5.31745	−	1.93539i	0.180072	−	0.0655407i
$873$	0.175254			0.00593145
$874$	−12.4129	−	2.67268i	−0.419874	−	0.0904047i
$875$	−47.5438			−1.60728
$876$	4.86429	−	1.77046i	0.164349	−	0.0598182i
$877$	0.367446	−	2.08389i	0.0124078	−	0.0703680i	−0.977975	−	0.208721i	$-0.933070\pi$
$877$	0.367446	−	2.08389i	0.0124078	−	0.0703680i	0.990383	+	0.138353i	$0.0441810\pi$
$878$	17.3115	−	14.5261i	0.584236	−	0.490232i
$879$	−4.54044	−	3.80988i	−0.153145	−	0.128504i
$880$	0.323311	+	1.83359i	0.0108988	+	0.0618103i
$881$	26.5203	+	45.9345i	0.893492	+	1.54757i	0.835660	+	0.549246i	$0.185085\pi$
$881$	26.5203	+	45.9345i	0.893492	+	1.54757i	0.0578312	+	0.998326i	$0.481581\pi$
$882$	3.55774	−	6.16219i	0.119795	−	0.207492i
$883$	−16.1473	−	5.87714i	−0.543401	−	0.197782i	0.0557114	−	0.998447i	$-0.482257\pi$
$883$	−16.1473	−	5.87714i	−0.543401	−	0.197782i	−0.599112	+	0.800665i	$0.704480\pi$
$884$	−11.1219	−	4.04804i	−0.374069	−	0.136150i
$885$	−5.46900	+	9.47259i	−0.183839	+	0.318418i
$886$	−5.86179	−	10.1529i	−0.196931	−	0.341094i
$887$	−0.676465	−	3.83642i	−0.0227135	−	0.128814i	0.971343	−	0.237684i	$-0.0763882\pi$
$887$	−0.676465	−	3.83642i	−0.0227135	−	0.128814i	−0.994056	+	0.108869i	$0.965277\pi$
$888$	−10.2577	−	8.60721i	−0.344225	−	0.288839i
$889$	5.89901	−	4.94985i	0.197846	−	0.166013i
$890$	−3.08780	+	17.5118i	−0.103503	+	0.586996i
$891$	−4.15847	+	1.51356i	−0.139314	+	0.0507062i
$892$	−9.59498			−0.321264
$893$	−0.562045	+	14.9636i	−0.0188081	+	0.500739i
$894$	−4.36669			−0.146044
$895$	−19.0274	+	6.92541i	−0.636016	+	0.231491i
$896$	5.34843	−	30.3324i	0.178678	−	1.01334i
$897$	4.83382	−	4.05606i	0.161397	−	0.135428i
$898$	−13.7336	−	11.5239i	−0.458296	−	0.384556i
$899$	0.722600	+	4.09807i	0.0241001	+	0.136678i
$900$	−1.34506	−	2.32972i	−0.0448355	−	0.0776573i
$901$	−5.30876	+	9.19505i	−0.176861	+	0.306331i
$902$	−30.8524	−	11.2293i	−1.02727	−	0.373896i
$903$	−37.3087	−	13.5792i	−1.24156	−	0.451889i
$904$	19.3977	−	33.5978i	0.645158	−	1.11745i
$905$	−0.233687	−	0.404758i	−0.00776803	−	0.0134546i
$906$	−1.91495	−	10.8602i	−0.0636199	−	0.360806i
$907$	−6.77309	−	5.68329i	−0.224897	−	0.188711i	0.523376	−	0.852102i	$-0.324672\pi$
$907$	−6.77309	−	5.68329i	−0.224897	−	0.188711i	−0.748273	+	0.663391i	$0.769117\pi$
$908$	−3.50343	+	2.93972i	−0.116265	+	0.0975582i
$909$	−1.94720	+	11.0431i	−0.0645845	+	0.366277i
$910$	9.69205	−	3.52762i	0.321288	−	0.116939i
$911$	18.4416			0.610997			0.305498	−	0.952193i	$-0.401177\pi$
$911$	18.4416			0.610997			0.305498	+	0.952193i	$0.401177\pi$
$912$	−0.0403140	+	1.07330i	−0.00133493	+	0.0355405i
$913$	−57.6411			−1.90764
$914$	−0.590265	+	0.214839i	−0.0195242	+	0.00710624i
$915$	0.0227402	−	0.128966i	0.000751766	−	0.00426348i
$916$	11.2196	−	9.41435i	0.370705	−	0.311059i
$917$	−4.69699	−	3.94124i	−0.155108	−	0.130151i
$918$	0.735201	+	4.16953i	0.0242652	+	0.137615i
$919$	22.7681	+	39.4355i	0.751051	+	1.30086i	0.947314	+	0.320307i	$0.103786\pi$
$919$	22.7681	+	39.4355i	0.751051	+	1.30086i	−0.196263	+	0.980551i	$0.562881\pi$
$920$	−8.18320	+	14.1737i	−0.269792	+	0.467294i
$921$	16.5238	+	6.01417i	0.544477	+	0.198174i
$922$	22.3163	+	8.12245i	0.734947	+	0.267499i
$923$	12.3607	−	21.4093i	0.406857	−	0.704697i
$924$	11.2229	+	19.4387i	0.369207	+	0.639486i
$925$	1.74881	+	9.91797i	0.0575004	+	0.326101i
$926$	−5.71503	−	4.79548i	−0.187807	−	0.157589i
$927$	7.29282	−	6.11940i	0.239528	−	0.200988i
$928$	1.44822	−	8.21326i	0.0475402	−	0.269614i
$929$	1.42489	−	0.518618i	0.0467492	−	0.0170153i	−0.318540	−	0.947910i	$-0.603192\pi$
$929$	1.42489	−	0.518618i	0.0467492	−	0.0170153i	0.365289	+	0.930894i	$0.380970\pi$
$930$	4.12688			0.135326
$931$	35.9969	+	7.75063i	1.17975	+	0.254017i
$932$	7.64968			0.250574
$933$	5.66509	−	2.06192i	0.185467	−	0.0675044i
$934$	−5.45246	+	30.9225i	−0.178410	+	1.01181i
$935$	−29.0947	+	24.4134i	−0.951500	+	0.798403i
$936$	3.87404	+	3.25071i	0.126627	+	0.106253i
$937$	1.23932	+	7.02855i	0.0404869	+	0.229613i	0.998336	−	0.0576578i	$-0.0183632\pi$
$937$	1.23932	+	7.02855i	0.0404869	+	0.229613i	−0.957849	+	0.287271i	$0.907252\pi$
$938$	−1.73334	−	3.00224i	−0.0565957	−	0.0980266i
$939$	−8.34902	+	14.4609i	−0.272460	+	0.471914i
$940$	7.11318	+	2.58898i	0.232006	+	0.0844434i
$941$	−46.7927	−	17.0311i	−1.52540	−	0.555200i	−0.562909	−	0.826519i	$-0.690318\pi$
$941$	−46.7927	−	17.0311i	−1.52540	−	0.555200i	−0.962489	+	0.271319i	$0.912540\pi$
$942$	−3.10380	+	5.37594i	−0.101127	+	0.175158i
$943$	15.2305	+	26.3799i	0.495972	+	0.859049i
$944$	0.274099	+	1.55449i	0.00892115	+	0.0505943i
$945$	5.14086	+	4.31369i	0.167232	+	0.140324i
$946$	−28.8451	+	24.2039i	−0.937835	+	0.786937i
$947$	−0.0606990	+	0.344241i	−0.00197245	+	0.0111863i	−0.985778	−	0.168052i	$-0.946252\pi$
$947$	−0.0606990	+	0.344241i	−0.00197245	+	0.0111863i	0.983806	+	0.179239i	$0.0573634\pi$
$948$	20.5729	−	7.48792i	0.668176	−	0.243196i
$949$	7.31892			0.237582
$950$	−5.13624	+	5.67421i	−0.166642	+	0.184096i
$951$	−2.19305			−0.0711146
$952$	51.4533	−	18.7275i	1.66761	−	0.606961i
$953$	3.64810	−	20.6894i	0.118174	−	0.670195i	−0.866956	−	0.498384i	$-0.833927\pi$
$953$	3.64810	−	20.6894i	0.118174	−	0.670195i	0.985130	−	0.171811i	$-0.0549619\pi$
$954$	1.36299	−	1.14368i	0.0441284	−	0.0370281i
$955$	−15.9116	−	13.3514i	−0.514887	−	0.432041i
$956$	−3.39915	−	19.2775i	−0.109936	−	0.623480i
$957$	3.20886	+	5.55791i	0.103728	+	0.179662i
$958$	−12.5738	+	21.7784i	−0.406240	+	0.703628i
$959$	−56.7356	−	20.6501i	−1.83209	−	0.666826i
$960$	−6.98150	−	2.54106i	−0.225327	−	0.0820123i
$961$	11.3832	−	19.7163i	0.367200	−	0.636009i
$962$	−3.71258	−	6.43037i	−0.119698	−	0.207324i
$963$	−1.78319	−	10.1130i	−0.0574626	−	0.325887i
$964$	−8.76136	−	7.35165i	−0.282184	−	0.236781i
$965$	30.1836	−	25.3271i	0.971645	−	0.815307i
$966$	−1.98810	+	11.2751i	−0.0639661	+	0.362770i
$967$	34.6193	−	12.6004i	1.11328	−	0.405201i	0.281085	−	0.959683i	$-0.409306\pi$
$967$	34.6193	−	12.6004i	1.11328	−	0.405201i	0.832196	+	0.554482i	$0.187084\pi$
$968$	23.7911			0.764675
$969$	−19.3722	+	10.2350i	−0.622325	+	0.328794i
$970$	−0.252055			−0.00809300
$971$	−5.06606	+	1.84390i	−0.162578	+	0.0591735i	−0.422027	−	0.906583i	$-0.638681\pi$
$971$	−5.06606	+	1.84390i	−0.162578	+	0.0591735i	0.259449	+	0.965757i	$0.416459\pi$
$972$	−0.224094	+	1.27090i	−0.00718780	+	0.0407641i
$973$	28.0247	−	23.5155i	0.898430	−	0.753873i
$974$	−19.9259	−	16.7198i	−0.638466	−	0.535737i
$975$	−0.660476	−	3.74575i	−0.0211522	−	0.119960i
$976$	−0.00944912	−	0.0163664i	−0.000302459	−	0.000523874i
$977$	20.3591	−	35.2630i	0.651345	−	1.12816i	−0.331451	−	0.943472i	$-0.607538\pi$
$977$	20.3591	−	35.2630i	0.651345	−	1.12816i	0.982797	−	0.184691i	$-0.0591283\pi$
$978$	−12.6865	−	4.61752i	−0.405670	−	0.147652i
$979$	−51.4144	−	18.7133i	−1.64321	−	0.598080i
$980$	9.30702	−	16.1202i	0.297302	−	0.514942i
$981$	1.02082	+	1.76812i	0.0325923	+	0.0564516i
$982$	−1.48133	−	8.40101i	−0.0472710	−	0.268087i
$983$	33.6989	+	28.2767i	1.07483	+	0.901887i	0.995481	−	0.0949603i	$-0.0302724\pi$
$983$	33.6989	+	28.2767i	1.07483	+	0.901887i	0.0793458	+	0.996847i	$0.474717\pi$
$984$	−18.7013	+	15.6922i	−0.596175	+	0.500250i
$985$	1.91797	−	10.8773i	0.0611115	−	0.346581i
$986$	5.76972	−	2.10001i	0.183745	−	0.0668778i
$987$	13.5019			0.429771
$988$	−3.86997	+	9.50628i	−0.123120	+	0.302435i
$989$	34.9348			1.11086
$990$	5.98083	−	2.17684i	0.190083	−	0.0691846i
$991$	5.77639	−	32.7595i	0.183493	−	1.04064i	−0.744383	−	0.667752i	$-0.767256\pi$
$991$	5.77639	−	32.7595i	0.183493	−	1.04064i	0.927876	−	0.372888i	$-0.121632\pi$
$992$	12.6410	−	10.6070i	0.401351	−	0.336773i
$993$	11.9049	+	9.98942i	0.377792	+	0.317005i
$994$	7.78887	+	44.1729i	0.247048	+	1.40108i
$995$	−0.262172	−	0.454094i	−0.00831140	−	0.0143958i
$996$	−8.40453	+	14.5571i	−0.266308	+	0.461258i
$997$	−25.4469	−	9.26192i	−0.805912	−	0.293328i	−0.0939778	−	0.995574i	$-0.529958\pi$
$997$	−25.4469	−	9.26192i	−0.805912	−	0.293328i	−0.711934	+	0.702246i	$0.752180\pi$
$998$	6.80279	+	2.47601i	0.215338	+	0.0783768i
$999$	2.41561	−	4.18397i	0.0764266	−	0.132375i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	57.2.i.b.43.2	yes	12
3.2	odd	2		171.2.u.e.100.1		12
4.3	odd	2		912.2.bo.j.385.1		12
19.2	odd	18		1083.2.a.p.1.4		6
19.4	even	9	inner	57.2.i.b.4.2	✓	12
19.17	even	9		1083.2.a.q.1.3		6
57.2	even	18		3249.2.a.bg.1.3		6
57.17	odd	18		3249.2.a.bh.1.4		6
57.23	odd	18		171.2.u.e.118.1		12
76.23	odd	18		912.2.bo.j.289.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.i.b.4.2	✓	12	19.4	even	9	inner
57.2.i.b.43.2	yes	12	1.1	even	1	trivial
171.2.u.e.100.1		12	3.2	odd	2
171.2.u.e.118.1		12	57.23	odd	18
912.2.bo.j.289.1		12	76.23	odd	18
912.2.bo.j.385.1		12	4.3	odd	2
1083.2.a.p.1.4		6	19.2	odd	18
1083.2.a.q.1.3		6	19.17	even	9
3249.2.a.bg.1.3		6	57.2	even	18
3249.2.a.bh.1.4		6	57.17	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:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	57.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.791518 - 0.288089i) q^{2} +(0.173648 - 0.984808i) q^{3} +(-0.988583 + 0.829520i) q^{4} +(1.30800 + 1.09754i) q^{5} +(-0.146267 - 0.829520i) q^{6} +(-1.96517 - 3.40377i) q^{7} +(-1.38582 + 2.40031i) q^{8} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})\)	\(q+(0.791518 - 0.288089i) q^{2} +(0.173648 - 0.984808i) q^{3} +(-0.988583 + 0.829520i) q^{4} +(1.30800 + 1.09754i) q^{5} +(-0.146267 - 0.829520i) q^{6} +(-1.96517 - 3.40377i) q^{7} +(-1.38582 + 2.40031i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(1.35149 + 0.491903i) q^{10} +(-2.21268 + 3.83247i) q^{11} +(0.645252 + 1.11761i) q^{12} +(0.316842 + 1.79690i) q^{13} +(-2.53605 - 2.12800i) q^{14} +(1.30800 - 1.09754i) q^{15} +(0.0427879 - 0.242662i) q^{16} +(4.72331 - 1.71914i) q^{17} -0.842316 q^{18} +(-1.33604 - 4.14910i) q^{19} -2.20349 q^{20} +(-3.69330 + 1.34425i) q^{21} +(-0.647282 + 3.67092i) q^{22} +(2.64922 - 2.22296i) q^{23} +(2.12320 + 1.78158i) q^{24} +(-0.361980 - 2.05289i) q^{25} +(0.768454 + 1.33100i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(4.76622 + 1.73476i) q^{28} +(1.36276 + 0.496003i) q^{29} +(0.719113 - 1.24554i) q^{30} +(1.43471 + 2.48499i) q^{31} +(-0.998623 - 5.66347i) q^{32} +(3.39002 + 2.84456i) q^{33} +(3.24332 - 2.72147i) q^{34} +(1.16534 - 6.60896i) q^{35} +(1.21268 - 0.441378i) q^{36} -4.83123 q^{37} +(-2.25281 - 2.89919i) q^{38} +1.82462 q^{39} +(-4.44709 + 1.61861i) q^{40} +(-1.52950 + 8.67423i) q^{41} +(-2.53605 + 2.12800i) q^{42} +(7.73836 + 6.49325i) q^{43} +(-0.991693 - 5.62417i) q^{44} +(-0.853733 - 1.47871i) q^{45} +(1.45649 - 2.52272i) q^{46} +(-3.22814 - 1.17495i) q^{47} +(-0.231546 - 0.0842757i) q^{48} +(-4.22376 + 7.31577i) q^{49} +(-0.877928 - 1.52062i) q^{50} +(-0.872832 - 4.95008i) q^{51} +(-1.80379 - 1.51356i) q^{52} +(-1.61814 + 1.35778i) q^{53} +(-0.146267 + 0.829520i) q^{54} +(-7.10045 + 2.58435i) q^{55} +10.8935 q^{56} +(-4.31806 + 0.595259i) q^{57} +1.22154 q^{58} +(-6.01966 + 2.19098i) q^{59} +(-0.382632 + 2.17002i) q^{60} +(0.0587523 - 0.0492990i) q^{61} +(1.85150 + 1.55359i) q^{62} +(0.682495 + 3.87062i) q^{63} +(-2.17561 - 3.76826i) q^{64} +(-1.55774 + 2.69809i) q^{65} +(3.50275 + 1.27490i) q^{66} +(0.984002 + 0.358147i) q^{67} +(-3.24332 + 5.61759i) q^{68} +(-1.72915 - 2.99498i) q^{69} +(-0.981583 - 5.56683i) q^{70} +(-10.3790 - 8.70898i) q^{71} +(2.12320 - 1.78158i) q^{72} +(0.696538 - 3.95026i) q^{73} +(-3.82401 + 1.39182i) q^{74} -2.08456 q^{75} +(4.76254 + 2.99345i) q^{76} +17.3931 q^{77} +(1.44422 - 0.525654i) q^{78} +(2.94592 - 16.7071i) q^{79} +(0.322297 - 0.270440i) q^{80} +(0.766044 + 0.642788i) q^{81} +(1.28832 + 7.30645i) q^{82} +(6.51259 + 11.2801i) q^{83} +(2.53605 - 4.39257i) q^{84} +(8.06489 + 2.93538i) q^{85} +(7.99569 + 2.91019i) q^{86} +(0.725109 - 1.25592i) q^{87} +(-6.13275 - 10.6222i) q^{88} +(2.14695 + 12.1759i) q^{89} +(-1.10175 - 0.924474i) q^{90} +(5.49359 - 4.60967i) q^{91} +(-0.774984 + 4.39515i) q^{92} +(2.69638 - 0.981401i) q^{93} -2.89362 q^{94} +(2.80626 - 6.89335i) q^{95} -5.75084 q^{96} +(-0.164685 + 0.0599404i) q^{97} +(-1.23559 + 7.00738i) q^{98} +(3.39002 - 2.84456i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{4} + 6 q^{5} - 3 q^{6} - 9 q^{7} + 3 q^{8}+O(q^{10}) \) 12 * q - 3 * q^2 - 3 * q^4 + 6 * q^5 - 3 * q^6 - 9 * q^7 + 3 * q^8	\( 12 q - 3 q^{2} - 3 q^{4} + 6 q^{5} - 3 q^{6} - 9 q^{7} + 3 q^{8} - 18 q^{10} - 9 q^{11} - 6 q^{12} - 3 q^{13} - 3 q^{14} + 6 q^{15} + 33 q^{16} + 12 q^{17} - 9 q^{19} - 18 q^{20} - 24 q^{22} + 9 q^{23} + 30 q^{24} - 12 q^{25} - 6 q^{27} + 30 q^{28} - 6 q^{30} - 3 q^{32} - 9 q^{33} + 21 q^{34} + 30 q^{35} - 3 q^{36} - 12 q^{37} + 18 q^{38} + 6 q^{39} - 3 q^{40} - 18 q^{41} - 3 q^{42} + 15 q^{43} + 15 q^{44} - 9 q^{45} + 27 q^{46} - 9 q^{47} - 12 q^{48} - 9 q^{49} + 9 q^{50} - 15 q^{51} - 27 q^{52} - 30 q^{53} - 3 q^{54} + 15 q^{55} - 78 q^{56} - 3 q^{57} - 24 q^{58} - 30 q^{59} - 15 q^{60} + 21 q^{61} + 3 q^{62} + 9 q^{63} - 21 q^{64} + 21 q^{65} + 30 q^{66} + 3 q^{67} - 21 q^{68} - 6 q^{69} + 18 q^{70} - 30 q^{71} + 30 q^{72} - 24 q^{73} + 39 q^{74} + 30 q^{75} - 60 q^{76} + 96 q^{77} + 9 q^{78} + 24 q^{79} + 42 q^{80} - 33 q^{82} + 3 q^{83} + 3 q^{84} + 3 q^{85} + 51 q^{86} + 15 q^{87} + 42 q^{88} + 3 q^{89} - 9 q^{90} + 24 q^{91} + 69 q^{92} - 6 q^{93} + 18 q^{94} - 54 q^{95} - 42 q^{96} - 27 q^{97} - 3 q^{98} - 9 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^4 + 6 * q^5 - 3 * q^6 - 9 * q^7 + 3 * q^8 - 18 * q^10 - 9 * q^11 - 6 * q^12 - 3 * q^13 - 3 * q^14 + 6 * q^15 + 33 * q^16 + 12 * q^17 - 9 * q^19 - 18 * q^20 - 24 * q^22 + 9 * q^23 + 30 * q^24 - 12 * q^25 - 6 * q^27 + 30 * q^28 - 6 * q^30 - 3 * q^32 - 9 * q^33 + 21 * q^34 + 30 * q^35 - 3 * q^36 - 12 * q^37 + 18 * q^38 + 6 * q^39 - 3 * q^40 - 18 * q^41 - 3 * q^42 + 15 * q^43 + 15 * q^44 - 9 * q^45 + 27 * q^46 - 9 * q^47 - 12 * q^48 - 9 * q^49 + 9 * q^50 - 15 * q^51 - 27 * q^52 - 30 * q^53 - 3 * q^54 + 15 * q^55 - 78 * q^56 - 3 * q^57 - 24 * q^58 - 30 * q^59 - 15 * q^60 + 21 * q^61 + 3 * q^62 + 9 * q^63 - 21 * q^64 + 21 * q^65 + 30 * q^66 + 3 * q^67 - 21 * q^68 - 6 * q^69 + 18 * q^70 - 30 * q^71 + 30 * q^72 - 24 * q^73 + 39 * q^74 + 30 * q^75 - 60 * q^76 + 96 * q^77 + 9 * q^78 + 24 * q^79 + 42 * q^80 - 33 * q^82 + 3 * q^83 + 3 * q^84 + 3 * q^85 + 51 * q^86 + 15 * q^87 + 42 * q^88 + 3 * q^89 - 9 * q^90 + 24 * q^91 + 69 * q^92 - 6 * q^93 + 18 * q^94 - 54 * q^95 - 42 * q^96 - 27 * q^97 - 3 * q^98 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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