LMFDB - Embedded newform 57.2.i.b.4.2

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			4.2
Root			$0.500000 - 0.168222i$ of defining polynomial
Character	$\chi$	$=$	57.4
Dual form			57.2.i.b.43.2

$q$-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 $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

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

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	0.606346	−	0.795201i	$-0.292635\pi$
$2$	0.791518	+	0.288089i	0.559688	+	0.203710i	−0.0466577	+	0.998911i	$0.514857\pi$
$3$	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	−0.301616	−	0.953429i	$-0.597526\pi$
$5$	1.30800	−	1.09754i	0.584953	−	0.490834i	0.886570	+	0.462595i	$0.153082\pi$
$6$	−0.146267	+	0.829520i	−0.0597131	+	0.338650i
$7$	−1.96517	+	3.40377i	−0.742763	+	1.28650i	0.208469	+	0.978029i	$0.433152\pi$
$7$	−1.96517	+	3.40377i	−0.742763	+	1.28650i	−0.951233	+	0.308475i	$0.900182\pi$
$8$	−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	−0.978698	−	0.205303i	$-0.934182\pi$
$11$	−2.21268	−	3.83247i	−0.667147	−	1.15553i	0.311551	−	0.950229i	$-0.399151\pi$
$12$	0.645252	−	1.11761i	0.186268	−	0.322626i
$13$	0.316842	−	1.79690i	0.0878763	−	0.498371i	−0.908823	−	0.417183i	$-0.863017\pi$
$13$	0.316842	−	1.79690i	0.0878763	−	0.498371i	0.996699	−	0.0811881i	$-0.0258714\pi$
$14$	−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	0.843922	−	0.536466i	$-0.180241\pi$
$17$	4.72331	+	1.71914i	1.14557	+	0.416954i	0.301648	+	0.953419i	$0.402463\pi$
$18$	−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	0.875753	−	0.482760i	$-0.160366\pi$
$23$	2.64922	+	2.22296i	0.552400	+	0.463519i	−0.323353	+	0.946278i	$0.604810\pi$
$24$	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	−0.212377	−	0.977188i	$-0.568120\pi$
$29$	1.36276	−	0.496003i	0.253058	−	0.0921055i	0.465434	+	0.885082i	$0.345898\pi$
$30$	0.719113	+	1.24554i	0.131292	+	0.227404i
$31$	1.43471	−	2.48499i	0.257682	−	0.446318i	−0.707939	−	0.706274i	$-0.750375\pi$
$31$	1.43471	−	2.48499i	0.257682	−	0.446318i	0.965621	+	0.259956i	$0.0837080\pi$
$32$	−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	−0.834313	−	0.551291i	$-0.814135\pi$
$41$	−1.52950	−	8.67423i	−0.238868	−	1.35469i	0.595445	−	0.803396i	$-0.296976\pi$
$42$	−2.53605	−	2.12800i	−0.391322	−	0.328358i
$43$	7.73836	−	6.49325i	1.18009	−	0.990212i	0.180110	−	0.983647i	$-0.442355\pi$
$43$	7.73836	−	6.49325i	1.18009	−	0.990212i	0.999978	−	0.00656507i	$-0.00208974\pi$
$44$	−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	−0.566548	−	0.824029i	$-0.691721\pi$
$47$	−3.22814	+	1.17495i	−0.470872	+	0.171384i	0.0956751	+	0.995413i	$0.469499\pi$
$48$	−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	0.524853	−	0.851193i	$-0.324120\pi$
$53$	−1.61814	−	1.35778i	−0.222269	−	0.186506i	−0.747122	+	0.664687i	$0.768565\pi$
$54$	−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	−0.0809810	−	0.996716i	$-0.525805\pi$
$59$	−6.01966	−	2.19098i	−0.783693	−	0.285241i	−0.702712	+	0.711475i	$0.748028\pi$
$60$	−0.382632	−	2.17002i	−0.0493976	−	0.280148i
$61$	0.0587523	+	0.0492990i	0.00752246	+	0.00631209i	0.646541	−	0.762879i	$-0.276215\pi$
$61$	0.0587523	+	0.0492990i	0.00752246	+	0.00631209i	−0.639019	+	0.769191i	$0.720659\pi$
$62$	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	−0.281212	−	0.959646i	$-0.590736\pi$
$67$	0.984002	−	0.358147i	0.120215	−	0.0437547i	0.401427	+	0.915891i	$0.368514\pi$
$68$	−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	−0.233632	+	0.972325i	$0.575061\pi$
$71$	−10.3790	+	8.70898i	−1.23176	+	1.03357i	−0.998123	+	0.0612406i	$0.980494\pi$
$72$	2.12320	+	1.78158i	0.250222	+	0.209961i
$73$	0.696538	+	3.95026i	0.0815236	+	0.462343i	0.998053	+	0.0623753i	$0.0198676\pi$
$73$	0.696538	+	3.95026i	0.0815236	+	0.462343i	−0.916529	+	0.399968i	$0.869021\pi$
$74$	−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	0.459880	+	0.887981i	$0.347893\pi$
$79$	2.94592	+	16.7071i	0.331442	+	1.87970i	−0.128438	+	0.991718i	$0.540996\pi$
$80$	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	−0.248167	−	0.968717i	$-0.579828\pi$
$83$	6.51259	−	11.2801i	0.714850	−	1.23816i	0.963017	−	0.269440i	$-0.0868384\pi$
$84$	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	−0.630123	−	0.776496i	$-0.716995\pi$
$89$	2.14695	−	12.1759i	0.227576	−	1.29065i	0.857699	−	0.514152i	$-0.171893\pi$
$90$	−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	0.333646	−	0.942698i	$-0.391721\pi$
$97$	−0.164685	−	0.0599404i	−0.0167212	−	0.00608603i	−0.350367	+	0.936612i	$0.613943\pi$
$98$	−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	0.720429	+	0.693529i	$0.243945\pi$
$101$	−1.94720	+	11.0431i	−0.193754	+	1.09883i	−0.914183	+	0.405303i	$0.867166\pi$
$102$	−2.11693	+	3.66662i	−0.209607	+	0.363050i
$103$	−4.76005	−	8.24465i	−0.469022	−	0.812369i	0.530351	−	0.847778i	$-0.322060\pi$
$103$	−4.76005	−	8.24465i	−0.469022	−	0.812369i	−0.999373	+	0.0354087i	$0.988727\pi$
$104$	−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	−0.503620	−	0.863925i	$-0.667999\pi$
$107$	5.13450	−	8.89322i	0.496371	−	0.859740i	0.999991	+	0.00418546i	$0.00133228\pi$
$108$	−0.224094	+	1.27090i	−0.0215634	+	0.122292i
$109$	−1.56399	+	1.31234i	−0.149803	+	0.125700i	−0.714609	−	0.699524i	$-0.753395\pi$
$109$	−1.56399	+	1.31234i	−0.149803	+	0.125700i	0.564806	+	0.825224i	$0.308951\pi$
$110$	−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	−0.965985	−	0.258599i	$-0.916739\pi$
$127$	0.340225	−	1.92951i	0.0301901	−	0.171216i	0.996175	+	0.0873827i	$0.0278503\pi$
$128$	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	0.405266	−	0.914199i	$-0.367179\pi$
$131$	1.46596	+	0.533566i	0.128082	+	0.0466179i	−0.277184	+	0.960817i	$0.589401\pi$
$132$	−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	0.987722	−	0.156222i	$-0.0499314\pi$
$137$	11.7678	+	9.87434i	1.00539	+	0.843622i	0.0176677	+	0.999844i	$0.494376\pi$
$138$	−2.23148	+	1.87243i	−0.189956	+	0.159392i
$139$	1.61632	−	9.16662i	0.137095	−	0.777502i	−0.836284	−	0.548297i	$-0.815276\pi$
$139$	1.61632	−	9.16662i	0.137095	−	0.777502i	0.973378	−	0.229205i	$-0.0736126\pi$
$140$	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	0.999222	+	0.0394368i	$0.0125564\pi$
$149$	0.900217	+	5.10538i	0.0737487	+	0.418249i	−0.925473	+	0.378813i	$0.876332\pi$
$150$	−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	−0.839644	−	0.543138i	$-0.817236\pi$
$157$	−5.64550	+	4.73714i	−0.450560	+	0.378065i	0.389084	+	0.921202i	$0.372792\pi$
$158$	−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	0.988010	+	0.154387i	$0.0493402\pi$
$163$	8.01404	+	13.8807i	0.627708	+	1.08722i	−0.360302	+	0.932836i	$0.617326\pi$
$164$	−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	0.164621	−	0.986357i	$-0.447360\pi$
$167$	−10.0561	−	8.43808i	−0.778165	−	0.652958i	−0.942786	+	0.333399i	$0.891804\pi$
$168$	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	0.903364	−	0.428874i	$-0.141090\pi$
$173$	17.3580	+	6.31781i	1.31971	+	0.480334i	0.416342	+	0.909208i	$0.363312\pi$
$174$	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	0.554739	−	0.832024i	$-0.312818\pi$
$179$	−5.92941	−	10.2700i	−0.443185	−	0.767619i	−0.997924	+	0.0644059i	$0.979485\pi$
$180$	2.07060	−	0.753638i	0.154334	−	0.0561729i
$181$	−0.257216	+	0.0936191i	−0.0191187	+	0.00695866i	−0.351562	−	0.936165i	$-0.614349\pi$
$181$	−0.257216	+	0.0936191i	−0.0191187	+	0.00695866i	0.332443	+	0.943123i	$0.392127\pi$
$182$	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	0.692729	+	0.721198i	$0.256408\pi$
$193$	4.00715	+	22.7257i	0.288441	+	1.63583i	−0.404288	+	0.914632i	$0.632481\pi$
$194$	−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	−0.957937	−	0.286978i	$-0.907349\pi$
$197$	−3.23436	+	5.60208i	−0.230439	+	0.399132i	0.727498	+	0.686109i	$0.240683\pi$
$198$	1.86377	+	3.22815i	0.132453	+	0.229415i
$199$	−0.288569	+	0.105030i	−0.0204561	+	0.00744541i	−0.352228	−	0.935914i	$-0.614576\pi$
$199$	−0.288569	+	0.105030i	−0.0204561	+	0.00744541i	0.331772	+	0.943360i	$0.392354\pi$
$200$	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	−0.0238889	−	0.999715i	$-0.507605\pi$
$211$	−9.94719	−	3.62048i	−0.684793	−	0.249244i	−0.660904	+	0.750470i	$0.729827\pi$
$212$	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	−0.431849	−	0.901946i	$-0.642139\pi$
$223$	5.69559	−	4.77917i	0.381405	−	0.320037i	0.813254	+	0.581909i	$0.197694\pi$
$224$	−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	−0.779295	−	0.626657i	$-0.784423\pi$
$233$	−4.54086	+	3.81024i	−0.297482	+	0.249617i	0.481813	+	0.876274i	$0.339978\pi$
$234$	−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	0.509359	−	0.860554i	$-0.329883\pi$
$239$	−7.58422	−	13.1363i	−0.490583	−	0.849714i	−0.999941	+	0.0108402i	$0.996549\pi$
$240$	−0.210365	+	0.364362i	−0.0135790	+	0.0235195i
$241$	1.53896	−	8.72790i	0.0991334	−	0.562214i	−0.894269	−	0.447530i	$-0.852304\pi$
$241$	1.53896	−	8.72790i	0.0991334	−	0.562214i	0.993402	−	0.114683i	$-0.0365853\pi$
$242$	−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	0.880338	−	0.474347i	$-0.157316\pi$
$251$	8.96819	+	7.52520i	0.566067	+	0.474987i	−0.314271	+	0.949333i	$0.601760\pi$
$252$	−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	−0.0346328	−	0.999400i	$-0.511026\pi$
$257$	9.31797	−	3.39146i	0.581239	−	0.211554i	0.615872	+	0.787846i	$0.288804\pi$
$258$	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	−0.999396	−	0.0347546i	$-0.988935\pi$
$263$	−1.17020	−	6.63654i	−0.0721577	−	0.409227i	0.927238	−	0.374472i	$-0.122176\pi$
$264$	−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	0.988374	−	0.152042i	$-0.0485848\pi$
$269$	0.124730	+	0.707378i	0.00760491	+	0.0431296i	−0.980769	+	0.195171i	$0.937474\pi$
$270$	−1.10175	−	0.924474i	−0.0670501	−	0.0562617i
$271$	−22.0935	+	18.5387i	−1.34209	+	1.12614i	−0.361002	+	0.932565i	$0.617565\pi$
$271$	−22.0935	+	18.5387i	−1.34209	+	1.12614i	−0.981085	+	0.193579i	$0.937990\pi$
$272$	−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	0.917820	−	0.396996i	$-0.129947\pi$
$277$	1.91567	+	3.31804i	0.115101	+	0.199361i	−0.802719	+	0.596358i	$0.796614\pi$
$278$	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	−0.0212929	−	0.999773i	$-0.506778\pi$
$281$	−16.9236	−	14.2006i	−1.00957	−	0.847134i	−0.988282	+	0.152639i	$0.951223\pi$
$282$	−0.502472	−	2.84966i	−0.0299218	−	0.169695i
$283$	23.6300	+	8.60061i	1.40466	+	0.511253i	0.929557	−	0.368678i	$-0.120190\pi$
$283$	23.6300	+	8.60061i	1.40466	+	0.511253i	0.475100	+	0.879932i	$0.342412\pi$
$284$	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	0.939514	−	0.342512i	$-0.111278\pi$
$293$	2.96356	+	5.13304i	0.173133	+	0.299875i	−0.766381	+	0.642387i	$0.777944\pi$
$294$	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	−0.938982	−	0.343966i	$-0.888229\pi$
$307$	−3.05347	−	17.3171i	−0.174271	−	0.988339i	0.764711	−	0.644373i	$-0.222882\pi$
$308$	−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	−0.767817	−	0.640669i	$-0.778657\pi$
$311$	3.01433	−	5.22097i	0.170927	−	0.296054i	0.938744	+	0.344615i	$0.111990\pi$
$312$	−2.52860	−	4.37967i	−0.143154	−	0.247950i
$313$	−15.6910	+	5.71107i	−0.886909	+	0.322809i	−0.744995	−	0.667070i	$-0.767548\pi$
$313$	−15.6910	+	5.71107i	−0.886909	+	0.322809i	−0.141914	+	0.989879i	$0.545326\pi$
$314$	−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	−0.993633	−	0.112667i	$-0.964061\pi$
$317$	−0.380819	+	2.15973i	−0.0213889	+	0.121303i	0.972244	+	0.233970i	$0.0751717\pi$
$318$	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	0.569515	−	0.821981i	$-0.307131\pi$
$331$	−7.77039	−	13.4587i	−0.427099	−	0.739758i	−0.996614	+	0.0822234i	$0.973798\pi$
$332$	−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	−0.346931	−	0.937891i	$-0.612776\pi$
$337$	9.48108	−	7.95557i	0.516467	−	0.433368i	0.863398	+	0.504523i	$0.168332\pi$
$338$	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	−0.972720	−	0.231984i	$-0.925478\pi$
$347$	−17.0105	+	14.2735i	−0.913171	+	0.766241i	0.0595486	+	0.998225i	$0.481034\pi$
$348$	0.324984	−	1.84308i	0.0174210	−	0.0987993i
$349$	9.96461	−	17.2592i	0.533393	−	0.923864i	−0.465846	−	0.884866i	$-0.654250\pi$
$349$	9.96461	−	17.2592i	0.533393	−	0.923864i	0.999239	−	0.0389982i	$-0.0124167\pi$
$350$	−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	0.926946	−	0.375195i	$-0.122424\pi$
$353$	2.60302	+	4.50856i	0.138545	+	0.239966i	−0.788401	+	0.615161i	$0.789091\pi$
$354$	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	0.466984	−	0.884266i	$-0.345340\pi$
$359$	4.85658	+	1.76765i	0.256320	+	0.0932930i	−0.210664	+	0.977559i	$0.567563\pi$
$360$	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	−0.999878	−	0.0156413i	$-0.995021\pi$
$367$	−1.05270	+	5.97015i	−0.0549504	+	0.311639i	0.944927	+	0.327280i	$0.106132\pi$
$368$	−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	−0.965844	−	0.259124i	$-0.916566\pi$
$373$	−4.99273	+	8.64766i	−0.258514	+	0.447759i	0.707330	+	0.706883i	$0.249899\pi$
$374$	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	0.967576	+	0.252582i	$0.0812796\pi$
$383$	2.83262	+	16.0646i	0.144740	+	0.820861i	−0.822836	+	0.568279i	$0.807609\pi$
$384$	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	−0.0539681	−	0.998543i	$-0.517187\pi$
$389$	10.7795	−	3.92341i	0.546541	−	0.198925i	0.600509	+	0.799618i	$0.294965\pi$
$390$	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	0.352565	−	0.935787i	$-0.385309\pi$
$397$	0.421085	+	0.153262i	0.0211336	+	0.00769201i	−0.331432	+	0.943479i	$0.607532\pi$
$398$	−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	−0.0215682	−	0.999767i	$-0.506866\pi$
$401$	−13.6316	−	4.96149i	−0.680729	−	0.247765i	−0.659160	+	0.752002i	$0.729088\pi$
$402$	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	−0.0166536	−	0.999861i	$-0.505301\pi$
$409$	12.4030	−	4.51431i	0.613287	−	0.223218i	0.629941	+	0.776643i	$0.283079\pi$
$410$	−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	−0.970984	−	0.239144i	$-0.923133\pi$
$421$	−2.87973	−	16.3318i	−0.140349	−	0.795961i	0.830635	−	0.556818i	$-0.187978\pi$
$422$	−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	−0.597020	−	0.802227i	$-0.703649\pi$
$431$	4.94875	−	28.0658i	0.238373	−	1.35188i	0.835393	−	0.549654i	$-0.185240\pi$
$432$	0.188758	−	0.158386i	0.00908161	−	0.00762037i
$433$	10.7227	+	8.99743i	0.515301	+	0.432389i	0.862990	−	0.505221i	$-0.168589\pi$
$433$	10.7227	+	8.99743i	0.515301	+	0.432389i	−0.347689	+	0.937610i	$0.613034\pi$
$434$	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	0.864361	−	0.502871i	$-0.167723\pi$
$439$	25.2111	+	9.17609i	1.20326	+	0.437951i	0.338900	+	0.940823i	$0.389945\pi$
$440$	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	0.872005	+	0.489497i	$0.162820\pi$
$443$	−2.41688	+	13.7068i	−0.114829	+	0.651230i	−0.986834	+	0.161733i	$0.948292\pi$
$444$	−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	0.497767	+	0.867311i	$0.334153\pi$
$449$	−10.6420	+	18.4326i	−0.502229	+	0.869887i	−0.999997	+	0.00257601i	$0.999180\pi$
$450$	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	0.0181272	−	0.999836i	$-0.494230\pi$
$461$	21.5980	−	18.1229i	1.00592	−	0.844068i	0.987794	+	0.155768i	$0.0497852\pi$
$462$	−2.54403	+	14.4279i	−0.118359	+	0.671248i
$463$	−4.42852	+	7.67043i	−0.205811	+	0.356475i	−0.950391	−	0.311058i	$-0.899317\pi$
$463$	−4.42852	+	7.67043i	−0.205811	+	0.356475i	0.744580	+	0.667533i	$0.232650\pi$
$464$	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	−0.869508	−	0.493918i	$-0.835564\pi$
$467$	−18.6388	−	32.2833i	−0.862500	−	1.49389i	0.00700866	−	0.999975i	$-0.497769\pi$
$468$	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	−0.0524190	−	0.998625i	$-0.516693\pi$
$479$	−22.8704	−	19.1905i	−1.04498	−	0.876838i	−0.992556	+	0.121787i	$0.961138\pi$
$480$	−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	0.268910	+	0.963165i	$0.413337\pi$
$487$	−15.4404	+	26.7435i	−0.699671	+	1.21187i	−0.968581	+	0.248700i	$0.919997\pi$
$488$	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	0.998431	+	0.0560004i	$0.0178348\pi$
$491$	1.75863	+	9.97370i	0.0793660	+	0.450107i	−0.919065	+	0.394107i	$0.871054\pi$
$492$	−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	−0.483415	−	0.875391i	$-0.660604\pi$
$499$	6.58385	−	5.52450i	0.294734	−	0.247311i	0.778148	+	0.628081i	$0.216159\pi$
$500$	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	0.0654451	−	0.997856i	$-0.479153\pi$
$503$	16.9775	−	6.17930i	0.756989	−	0.275521i	0.691543	+	0.722335i	$0.256931\pi$
$504$	−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	0.994846	−	0.101397i	$-0.0323314\pi$
$509$	24.0894	+	20.2134i	1.06774	+	0.895942i	0.0728963	+	0.997340i	$0.476776\pi$
$510$	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	0.560443	−	0.828193i	$-0.310631\pi$
$521$	−9.97505	−	17.2773i	−0.437015	−	0.756932i	−0.997458	+	0.0712610i	$0.977298\pi$
$522$	−1.14787	+	0.417792i	−0.0502411	+	0.0182862i
$523$	−2.97141	+	1.08150i	−0.129931	+	0.0472909i	−0.406167	−	0.913799i	$-0.633135\pi$
$523$	−2.97141	+	1.08150i	−0.129931	+	0.0472909i	0.276236	+	0.961090i	$0.410913\pi$
$524$	−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	−0.353999	−	0.935246i	$-0.615179\pi$
$541$	−0.558559	+	0.203299i	−0.0240143	+	0.00874050i	0.329985	+	0.943986i	$0.392956\pi$
$542$	−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	0.964181	−	0.265247i	$-0.0854534\pi$
$547$	20.3567	+	17.0813i	0.870392	+	0.730345i	−0.0937888	+	0.995592i	$0.529898\pi$
$548$	−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	−0.553656	−	0.832745i	$-0.686768\pi$
$557$	5.93387	−	33.6527i	0.251426	−	1.42591i	0.805082	−	0.593163i	$-0.202121\pi$
$558$	−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	−0.353110	−	0.935582i	$-0.614876\pi$
$563$	15.0358	−	26.0427i	0.633683	−	1.09757i	0.986793	−	0.161989i	$-0.0517908\pi$
$564$	−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	−0.343798	−	0.939044i	$-0.611714\pi$
$577$	15.4054	−	26.6830i	0.641337	−	1.11083i	0.985135	−	0.171784i	$-0.0549531\pi$
$578$	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	0.601081	−	0.799188i	$-0.294737\pi$
$587$	13.2728	+	4.83091i	0.547828	+	0.199393i	−0.0532531	+	0.998581i	$0.516959\pi$
$588$	−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	0.999914	+	0.0130812i	$0.00416400\pi$
$593$	28.8915	+	24.2428i	1.18643	+	0.995533i	0.186516	+	0.982452i	$0.440280\pi$
$594$	−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	−0.343801	−	0.939043i	$-0.611715\pi$
$599$	−0.0872028	+	0.0317392i	−0.00356301	+	0.00129683i	0.340238	+	0.940339i	$0.389492\pi$
$600$	2.88883	+	5.00359i	0.117936	+	0.204271i
$601$	11.5190	−	19.9515i	0.469870	−	0.813839i	−0.529536	−	0.848287i	$-0.677634\pi$
$601$	11.5190	−	19.9515i	0.469870	−	0.813839i	0.999406	+	0.0344482i	$0.0109674\pi$
$602$	−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	0.374199	−	0.927348i	$-0.377918\pi$
$613$	33.4848	−	28.0971i	1.35244	−	1.13483i	0.978239	−	0.207482i	$-0.0665269\pi$
$614$	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	−0.0756229	−	0.997136i	$-0.524095\pi$
$617$	12.6034	−	4.58726i	0.507394	−	0.184676i	0.583016	+	0.812460i	$0.301872\pi$
$618$	7.53533	−	2.74264i	0.303116	−	0.110325i
$619$	−11.4670	−	19.8615i	−0.460899	−	0.798300i	0.538107	−	0.842876i	$-0.319139\pi$
$619$	−11.4670	−	19.8615i	−0.460899	−	0.798300i	−0.999006	+	0.0445765i	$0.985806\pi$
$620$	−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	0.256161	−	0.966634i	$-0.417542\pi$
$631$	−16.3606	−	13.7282i	−0.651306	−	0.546510i	−0.907467	+	0.420124i	$0.861987\pi$
$632$	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	−0.968737	−	0.248091i	$-0.920197\pi$
$641$	−22.5997	+	18.9634i	−0.892634	+	0.749009i	0.0761030	+	0.997100i	$0.475752\pi$
$642$	6.62609	+	5.55995i	0.261511	+	0.219434i
$643$	1.18655	+	6.72928i	0.0467931	+	0.265377i	0.999224	−	0.0393763i	$-0.0125371\pi$
$643$	1.18655	+	6.72928i	0.0467931	+	0.265377i	−0.952431	+	0.304753i	$0.901426\pi$
$644$	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	0.468311	+	0.883564i	$0.344863\pi$
$653$	−13.5699	+	23.5038i	−0.531033	+	0.919776i	−0.999344	+	0.0362124i	$0.988471\pi$
$654$	−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	0.484613	+	0.874729i	$0.338960\pi$
$659$	−6.92986	+	39.3012i	−0.269949	+	1.53096i	−0.754562	+	0.656228i	$0.772151\pi$
$660$	−7.46987	+	6.26797i	−0.290764	+	0.243980i
$661$	−38.5678	−	32.3622i	−1.50011	−	1.25874i	−0.880697	−	0.473680i	$-0.842925\pi$
$661$	−38.5678	−	32.3622i	−1.50011	−	1.25874i	−0.619415	−	0.785064i	$-0.712630\pi$
$662$	−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	0.797131	+	0.603807i	$0.206350\pi$
$673$	23.9052	+	41.4050i	0.921477	+	1.59605i	0.124347	+	0.992239i	$0.460317\pi$
$674$	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	0.131274	+	0.991346i	$0.458093\pi$
$677$	−20.6305	+	35.7331i	−0.792894	+	1.37333i	−0.924168	+	0.381987i	$0.875240\pi$
$678$	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	−0.737882	−	0.674930i	$-0.764174\pi$
$691$	5.66655	−	9.81476i	0.215566	−	0.373371i	0.953447	+	0.301559i	$0.0975071\pi$
$692$	−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	0.216776	−	0.976221i	$-0.430446\pi$
$701$	−6.47788	−	2.35776i	−0.244666	−	0.0890512i	−0.461443	+	0.887170i	$0.652668\pi$
$702$	−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	0.139125	+	0.990275i	$0.455571\pi$
$709$	−8.79501	+	49.8790i	−0.330304	+	1.87325i	−0.469429	+	0.882970i	$0.655540\pi$
$710$	−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	0.979972	+	0.199133i	$0.0638126\pi$
$719$	3.41095	+	19.3445i	0.127207	+	0.721427i	−0.852765	+	0.522294i	$0.825076\pi$
$720$	−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	−0.860313	−	0.509766i	$-0.829732\pi$
$727$	−13.6886	+	11.4861i	−0.507684	+	0.425997i	0.352630	+	0.935763i	$0.385288\pi$
$728$	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	−0.959805	−	0.280668i	$-0.909444\pi$
$733$	−19.5736	−	33.9025i	−0.722968	−	1.25222i	0.236837	−	0.971549i	$-0.423889\pi$
$734$	−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	−0.254113	−	0.967175i	$-0.581784\pi$
$739$	−29.1001	−	10.5916i	−1.07046	−	0.389617i	−0.816350	+	0.577558i	$0.804006\pi$
$740$	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	0.544309	−	0.838885i	$-0.316792\pi$
$743$	11.5042	+	4.18720i	0.422050	+	0.153614i	−0.122259	+	0.992498i	$0.539014\pi$
$744$	−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	0.574010	−	0.818848i	$-0.305387\pi$
$751$	42.2047	−	15.3613i	1.54007	−	0.560541i	0.966063	+	0.258308i	$0.0831649\pi$
$752$	−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	−0.994398	−	0.105705i	$-0.966290\pi$
$757$	−2.64469	−	14.9988i	−0.0961228	−	0.545139i	0.898275	−	0.439434i	$-0.144821\pi$
$758$	−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	−0.517318	−	0.855793i	$-0.673070\pi$
$769$	−10.0805	+	3.66902i	−0.363514	+	0.132308i	0.153804	+	0.988101i	$0.450847\pi$
$770$	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	−0.982117	−	0.188270i	$-0.939712\pi$
$773$	0.143553	−	0.814127i	0.00516323	−	0.0292821i	0.987281	+	0.158988i	$0.0508231\pi$
$774$	−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	0.958448	−	0.285269i	$-0.0920828\pi$
$787$	6.51330	+	11.2814i	0.232174	+	0.402137i	−0.726274	+	0.687406i	$0.758749\pi$
$788$	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	0.940525	−	0.339724i	$-0.110333\pi$
$809$	5.00748	+	8.67320i	0.176053	+	0.304934i	−0.764472	+	0.644657i	$0.777000\pi$
$810$	0.719113	−	1.24554i	0.0252671	−	0.0437639i
$811$	−5.47946	+	31.0756i	−0.192410	+	1.09121i	0.723649	+	0.690168i	$0.242463\pi$
$811$	−5.47946	+	31.0756i	−0.192410	+	1.09121i	−0.916059	+	0.401043i	$0.868648\pi$
$812$	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	−0.0349269	−	0.999390i	$-0.511120\pi$
$821$	−29.3751	−	24.6487i	−1.02520	−	0.860244i	−0.990272	+	0.139146i	$0.955564\pi$
$822$	−9.91220	+	8.31732i	−0.345728	+	0.290100i
$823$	8.53261	−	48.3909i	0.297428	−	1.68680i	−0.359738	−	0.933053i	$-0.617134\pi$
$823$	8.53261	−	48.3909i	0.297428	−	1.68680i	0.657166	−	0.753746i	$-0.271755\pi$
$824$	−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	−0.590277	−	0.807201i	$-0.700982\pi$
$827$	−15.0574	+	5.48045i	−0.523597	+	0.190574i	0.0666799	+	0.997774i	$0.478759\pi$
$828$	2.23148	+	3.86503i	0.0775492	+	0.134319i
$829$	−17.2476	+	29.8737i	−0.599033	+	1.03756i	0.393931	+	0.919140i	$0.371115\pi$
$829$	−17.2476	+	29.8737i	−0.599033	+	1.03756i	−0.992964	+	0.118416i	$0.962218\pi$
$830$	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	−0.992336	−	0.123567i	$-0.960567\pi$
$839$	−2.95759	−	16.7733i	−0.102107	−	0.579080i	0.890229	−	0.455514i	$-0.150544\pi$
$840$	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	−0.273199	−	0.961957i	$-0.588082\pi$
$853$	−32.1506	−	11.7019i	−1.10082	−	0.400664i	−0.827617	+	0.561293i	$0.810304\pi$
$854$	−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	0.205913	−	0.978570i	$-0.433984\pi$
$857$	−7.76834	−	2.82745i	−0.265362	−	0.0965837i	−0.471274	+	0.881987i	$0.656206\pi$
$858$	−1.18104	−	6.69804i	−0.0403202	−	0.228667i
$859$	−38.6809	−	32.4571i	−1.31977	−	1.10742i	−0.986353	−	0.164643i	$-0.947353\pi$
$859$	−38.6809	−	32.4571i	−1.31977	−	1.10742i	−0.333421	−	0.942778i	$-0.608203\pi$
$860$	−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	0.997341	+	0.0728785i	$0.0232185\pi$
$863$	16.5035	+	28.5849i	0.561785	+	0.973040i	−0.435556	+	0.900162i	$0.643448\pi$
$864$	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	0.990383	−	0.138353i	$-0.0441810\pi$
$877$	0.367446	+	2.08389i	0.0124078	+	0.0703680i	−0.977975	+	0.208721i	$0.933070\pi$
$878$	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	0.0578312	−	0.998326i	$-0.481581\pi$
$881$	26.5203	−	45.9345i	0.893492	−	1.54757i	0.835660	−	0.549246i	$-0.185085\pi$
$882$	3.55774	+	6.16219i	0.119795	+	0.207492i
$883$	−16.1473	+	5.87714i	−0.543401	+	0.197782i	−0.599112	−	0.800665i	$-0.704480\pi$
$883$	−16.1473	+	5.87714i	−0.543401	+	0.197782i	0.0557114	+	0.998447i	$0.482257\pi$
$884$	−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	−0.994056	−	0.108869i	$-0.965277\pi$
$887$	−0.676465	+	3.83642i	−0.0227135	+	0.128814i	0.971343	+	0.237684i	$0.0763882\pi$
$888$	−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	−0.748273	−	0.663391i	$-0.769117\pi$
$907$	−6.77309	+	5.68329i	−0.224897	+	0.188711i	0.523376	+	0.852102i	$0.324672\pi$
$908$	−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	−0.196263	−	0.980551i	$-0.562881\pi$
$919$	22.7681	−	39.4355i	0.751051	−	1.30086i	0.947314	−	0.320307i	$-0.103786\pi$
$920$	−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	0.365289	−	0.930894i	$-0.380970\pi$
$929$	1.42489	+	0.518618i	0.0467492	+	0.0170153i	−0.318540	+	0.947910i	$0.603192\pi$
$930$	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	−0.957849	−	0.287271i	$-0.907252\pi$
$937$	1.23932	−	7.02855i	0.0404869	−	0.229613i	0.998336	+	0.0576578i	$0.0183632\pi$
$938$	−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	−0.962489	−	0.271319i	$-0.912540\pi$
$941$	−46.7927	+	17.0311i	−1.52540	+	0.555200i	−0.562909	+	0.826519i	$0.690318\pi$
$942$	−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	0.983806	−	0.179239i	$-0.0573634\pi$
$947$	−0.0606990	−	0.344241i	−0.00197245	−	0.0111863i	−0.985778	+	0.168052i	$0.946252\pi$
$948$	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	0.985130	+	0.171811i	$0.0549619\pi$
$953$	3.64810	+	20.6894i	0.118174	+	0.670195i	−0.866956	+	0.498384i	$0.833927\pi$
$954$	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	0.832196	−	0.554482i	$-0.187084\pi$
$967$	34.6193	+	12.6004i	1.11328	+	0.405201i	0.281085	+	0.959683i	$0.409306\pi$
$968$	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	0.259449	−	0.965757i	$-0.416459\pi$
$971$	−5.06606	−	1.84390i	−0.162578	−	0.0591735i	−0.422027	+	0.906583i	$0.638681\pi$
$972$	−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	0.982797	+	0.184691i	$0.0591283\pi$
$977$	20.3591	+	35.2630i	0.651345	+	1.12816i	−0.331451	+	0.943472i	$0.607538\pi$
$978$	−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	0.0793458	−	0.996847i	$-0.474717\pi$
$983$	33.6989	−	28.2767i	1.07483	−	0.901887i	0.995481	+	0.0949603i	$0.0302724\pi$
$984$	−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	0.927876	+	0.372888i	$0.121632\pi$
$991$	5.77639	+	32.7595i	0.183493	+	1.04064i	−0.744383	+	0.667752i	$0.767256\pi$
$992$	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	−0.711934	−	0.702246i	$-0.752180\pi$
$997$	−25.4469	+	9.26192i	−0.805912	+	0.293328i	−0.0939778	+	0.995574i	$0.529958\pi$
$998$	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.4.2	✓	12
3.2	odd	2		171.2.u.e.118.1		12
4.3	odd	2		912.2.bo.j.289.1		12
19.5	even	9	inner	57.2.i.b.43.2	yes	12
19.9	even	9		1083.2.a.q.1.3		6
19.10	odd	18		1083.2.a.p.1.4		6
57.5	odd	18		171.2.u.e.100.1		12
57.29	even	18		3249.2.a.bg.1.3		6
57.47	odd	18		3249.2.a.bh.1.4		6
76.43	odd	18		912.2.bo.j.385.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.i.b.4.2	✓	12	1.1	even	1	trivial
57.2.i.b.43.2	yes	12	19.5	even	9	inner
171.2.u.e.100.1		12	57.5	odd	18
171.2.u.e.118.1		12	3.2	odd	2
912.2.bo.j.289.1		12	4.3	odd	2
912.2.bo.j.385.1		12	76.43	odd	18
1083.2.a.p.1.4		6	19.10	odd	18
1083.2.a.q.1.3		6	19.9	even	9
3249.2.a.bg.1.3		6	57.29	even	18
3249.2.a.bh.1.4		6	57.47	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

Groups

Database

Properties

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