LMFDB - Embedded newform 189.2.f.a.127.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(64,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("189.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.f (of order $3$, degree $2$, not 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			127.2
Root			$0.500000 - 1.41036i$ of defining polynomial
Character	$\chi$	$=$	189.127
Dual form			189.2.f.a.64.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.119562 + 0.207087i) q^{2} +(0.971410 + 1.68253i) q^{4} +(0.590972 + 1.02359i) q^{5} +(0.500000 - 0.866025i) q^{7} -0.942820 q^{8} -0.282630 q^{10} +(-1.85185 + 3.20750i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(0.119562 + 0.207087i) q^{14} +(-1.83009 + 3.16982i) q^{16} +6.94282 q^{17} +1.94282 q^{19} +(-1.14815 + 1.98866i) q^{20} +(-0.442820 - 0.766987i) q^{22} +(-2.80150 - 4.85235i) q^{23} +(1.80150 - 3.12030i) q^{25} +0.239123 q^{26} +1.94282 q^{28} +(0.119562 - 0.207087i) q^{29} +(-0.830095 - 1.43777i) q^{31} +(-1.38044 - 2.39099i) q^{32} +(-0.830095 + 1.43777i) q^{34} +1.18194 q^{35} -9.54583 q^{37} +(-0.232287 + 0.402332i) q^{38} +(-0.557180 - 0.965064i) q^{40} +(-5.09097 - 8.81782i) q^{41} +(-1.11273 + 1.92730i) q^{43} -7.19562 q^{44} +1.33981 q^{46} +(2.91423 - 5.04759i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(0.430782 + 0.746136i) q^{50} +(0.971410 - 1.68253i) q^{52} +11.6030 q^{53} -4.37756 q^{55} +(-0.471410 + 0.816506i) q^{56} +(0.0285900 + 0.0495193i) q^{58} +(1.30150 + 2.25427i) q^{59} +(3.80150 - 6.58440i) q^{61} +0.396990 q^{62} -6.66019 q^{64} +(0.590972 - 1.02359i) q^{65} +(-1.75404 - 3.03809i) q^{67} +(6.74433 + 11.6815i) q^{68} +(-0.141315 + 0.244765i) q^{70} -8.60301 q^{71} +15.1488 q^{73} +(1.14132 - 1.97682i) q^{74} +(1.88727 + 3.26886i) q^{76} +(1.85185 + 3.20750i) q^{77} +(-3.68878 + 6.38915i) q^{79} -4.32614 q^{80} +2.43474 q^{82} +(-3.47141 + 6.01266i) q^{83} +(4.10301 + 7.10662i) q^{85} +(-0.266078 - 0.460861i) q^{86} +(1.74596 - 3.02409i) q^{88} -2.74720 q^{89} -1.00000 q^{91} +(5.44282 - 9.42724i) q^{92} +(0.696860 + 1.20700i) q^{94} +(1.14815 + 1.98866i) q^{95} +(-3.58414 + 6.20790i) q^{97} +0.239123 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} - 3 q^{4} - 5 q^{5} + 3 q^{7} + 12 q^{8} - 2 q^{11} - 3 q^{13} + q^{14} - 3 q^{16} + 24 q^{17} - 6 q^{19} - 16 q^{20} + 15 q^{22} - 6 q^{25} + 2 q^{26} - 6 q^{28} + q^{29} + 3 q^{31} - 8 q^{32}+ \cdots + 2 q^{98}+O(q^{100}) $ 6 * q - q^2 - 3 * q^4 - 5 * q^5 + 3 * q^7 + 12 * q^8 - 2 * q^11 - 3 * q^13 + q^14 - 3 * q^16 + 24 * q^17 - 6 * q^19 - 16 * q^20 + 15 * q^22 - 6 * q^25 + 2 * q^26 - 6 * q^28 + q^29 + 3 * q^31 - 8 * q^32 + 3 * q^34 - 10 * q^35 - 6 * q^37 + 8 * q^38 - 21 * q^40 - 22 * q^41 + 3 * q^43 - 46 * q^44 + 24 * q^46 - 9 * q^47 - 3 * q^49 + 10 * q^50 - 3 * q^52 + 36 * q^53 - 12 * q^55 + 6 * q^56 + 9 * q^58 - 9 * q^59 + 6 * q^61 + 36 * q^62 - 24 * q^64 - 5 * q^65 + 6 * q^68 - 18 * q^71 + 6 * q^73 + 6 * q^74 + 21 * q^76 + 2 * q^77 - 15 * q^79 - 22 * q^80 + 18 * q^82 - 12 * q^83 - 9 * q^85 + 34 * q^86 + 21 * q^88 + 4 * q^89 - 6 * q^91 + 15 * q^92 - 24 * q^94 + 16 * q^95 - 3 * q^97 + 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.119562	+	0.207087i	−0.0845428	+	0.146433i	−0.905196	−	0.424994i	$-0.860276\pi$
$2$	−0.119562	+	0.207087i	−0.0845428	+	0.146433i	0.820653	+	0.571426i	$0.193610\pi$
$3$		0			0
$3$		0			0
$4$	0.971410	+	1.68253i	0.485705	+	0.841266i
$5$	0.590972	+	1.02359i	0.264291	+	0.457765i	0.967378	−	0.253339i	$-0.0815289\pi$
$5$	0.590972	+	1.02359i	0.264291	+	0.457765i	−0.703087	+	0.711104i	$0.748196\pi$
$6$		0			0
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	−0.942820			−0.333337
$9$		0			0
$10$	−0.282630			−0.0893755
$11$	−1.85185	+	3.20750i	−0.558353	+	0.967096i	0.439281	+	0.898350i	$0.355233\pi$
$11$	−1.85185	+	3.20750i	−0.558353	+	0.967096i	−0.997634	+	0.0687465i	$0.978100\pi$
$12$		0			0
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	0.788320	−	0.615265i	$-0.210951\pi$
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	−0.926995	+	0.375073i	$0.877618\pi$
$14$	0.119562	+	0.207087i	0.0319542	+	0.0553463i
$15$		0			0
$16$	−1.83009	+	3.16982i	−0.457524	+	0.792454i
$17$	6.94282			1.68388			0.841941	−	0.539570i	$-0.181413\pi$
$17$	6.94282			1.68388			0.841941	+	0.539570i	$0.181413\pi$
$18$		0			0
$19$	1.94282			0.445713			0.222857	−	0.974851i	$-0.428462\pi$
$19$	1.94282			0.445713			0.222857	+	0.974851i	$0.428462\pi$
$20$	−1.14815	+	1.98866i	−0.256735	+	0.444677i
$21$		0			0
$22$	−0.442820	−	0.766987i	−0.0944096	−	0.163522i
$23$	−2.80150	−	4.85235i	−0.584154	−	1.01178i	−0.994980	−	0.100071i	$-0.968093\pi$
$23$	−2.80150	−	4.85235i	−0.584154	−	1.01178i	0.410826	−	0.911714i	$-0.365240\pi$
$24$		0			0
$25$	1.80150	−	3.12030i	0.360301	−	0.624060i
$26$	0.239123			0.0468959
$27$		0			0
$28$	1.94282			0.367158
$29$	0.119562	−	0.207087i	0.0222020	−	0.0384551i	−0.854711	−	0.519104i	$-0.826266\pi$
$29$	0.119562	−	0.207087i	0.0222020	−	0.0384551i	0.876913	+	0.480649i	$0.159599\pi$
$30$		0			0
$31$	−0.830095	−	1.43777i	−0.149089	−	0.258231i	0.781802	−	0.623527i	$-0.214301\pi$
$31$	−0.830095	−	1.43777i	−0.149089	−	0.258231i	−0.930891	+	0.365297i	$0.880968\pi$
$32$	−1.38044	−	2.39099i	−0.244029	−	0.422671i
$33$		0			0
$34$	−0.830095	+	1.43777i	−0.142360	+	0.246575i
$35$	1.18194			0.199785
$36$		0			0
$37$	−9.54583			−1.56932			−0.784662	−	0.619923i	$-0.787164\pi$
$37$	−9.54583			−1.56932			−0.784662	+	0.619923i	$0.787164\pi$
$38$	−0.232287	+	0.402332i	−0.0376819	+	0.0652669i
$39$		0			0
$40$	−0.557180	−	0.965064i	−0.0880979	−	0.152590i
$41$	−5.09097	−	8.81782i	−0.795076	−	1.37711i	−0.922791	−	0.385301i	$-0.874097\pi$
$41$	−5.09097	−	8.81782i	−0.795076	−	1.37711i	0.127715	−	0.991811i	$-0.459236\pi$
$42$		0			0
$43$	−1.11273	+	1.92730i	−0.169689	+	0.293910i	−0.938311	−	0.345794i	$-0.887610\pi$
$43$	−1.11273	+	1.92730i	−0.169689	+	0.293910i	0.768622	+	0.639704i	$0.220943\pi$
$44$	−7.19562			−1.08478
$45$		0			0
$46$	1.33981			0.197544
$47$	2.91423	−	5.04759i	0.425084	−	0.736267i	−0.571344	−	0.820711i	$-0.693578\pi$
$47$	2.91423	−	5.04759i	0.425084	−	0.736267i	0.996428	+	0.0844432i	$0.0269112\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	0.430782	+	0.746136i	0.0609217	+	0.105520i
$51$		0			0
$52$	0.971410	−	1.68253i	0.134710	−	0.233325i
$53$	11.6030			1.59380			0.796898	−	0.604114i	$-0.206473\pi$
$53$	11.6030			1.59380			0.796898	+	0.604114i	$0.206473\pi$
$54$		0			0
$55$	−4.37756			−0.590270
$56$	−0.471410	+	0.816506i	−0.0629948	+	0.109110i
$57$		0			0
$58$	0.0285900	+	0.0495193i	0.00375405	+	0.00650220i
$59$	1.30150	+	2.25427i	0.169442	+	0.293481i	0.938224	−	0.346029i	$-0.112470\pi$
$59$	1.30150	+	2.25427i	0.169442	+	0.293481i	−0.768782	+	0.639511i	$0.779137\pi$
$60$		0			0
$61$	3.80150	−	6.58440i	0.486733	−	0.843046i	−0.513151	−	0.858298i	$-0.671522\pi$
$61$	3.80150	−	6.58440i	0.486733	−	0.843046i	0.999884	+	0.0152524i	$0.00485519\pi$
$62$	0.396990			0.0504178
$63$		0			0
$64$	−6.66019			−0.832524
$65$	0.590972	−	1.02359i	0.0733010	−	0.126961i
$66$		0			0
$67$	−1.75404	−	3.03809i	−0.214290	−	0.371161i	0.738763	−	0.673966i	$-0.235410\pi$
$67$	−1.75404	−	3.03809i	−0.214290	−	0.371161i	−0.953053	+	0.302804i	$0.902077\pi$
$68$	6.74433	+	11.6815i	0.817870	+	1.41659i
$69$		0			0
$70$	−0.141315	+	0.244765i	−0.0168904	+	0.0292550i
$71$	−8.60301			−1.02099			−0.510495	−	0.859881i	$-0.670538\pi$
$71$	−8.60301			−1.02099			−0.510495	+	0.859881i	$0.670538\pi$
$72$		0			0
$73$	15.1488			1.77304			0.886519	−	0.462693i	$-0.153117\pi$
$73$	15.1488			1.77304			0.886519	+	0.462693i	$0.153117\pi$
$74$	1.14132	−	1.97682i	0.132675	−	0.229800i
$75$		0			0
$76$	1.88727	+	3.26886i	0.216485	+	0.374963i
$77$	1.85185	+	3.20750i	0.211038	+	0.365528i
$78$		0			0
$79$	−3.68878	+	6.38915i	−0.415020	+	0.718836i	−0.995431	−	0.0954881i	$-0.969559\pi$
$79$	−3.68878	+	6.38915i	−0.415020	+	0.718836i	0.580410	+	0.814324i	$0.302892\pi$
$80$	−4.32614			−0.483677
$81$		0			0
$82$	2.43474			0.268872
$83$	−3.47141	+	6.01266i	−0.381037	+	0.659975i	−0.991211	−	0.132292i	$-0.957766\pi$
$83$	−3.47141	+	6.01266i	−0.381037	+	0.659975i	0.610174	+	0.792267i	$0.291100\pi$
$84$		0			0
$85$	4.10301	+	7.10662i	0.445034	+	0.770821i
$86$	−0.266078	−	0.460861i	−0.0286920	−	0.0496960i
$87$		0			0
$88$	1.74596	−	3.02409i	0.186120	−	0.322369i
$89$	−2.74720			−0.291203			−0.145602	−	0.989343i	$-0.546512\pi$
$89$	−2.74720			−0.291203			−0.145602	+	0.989343i	$0.546512\pi$
$90$		0			0
$91$	−1.00000			−0.104828
$92$	5.44282	−	9.42724i	0.567453	−	0.982858i
$93$		0			0
$94$	0.696860	+	1.20700i	0.0718756	+	0.124492i
$95$	1.14815	+	1.98866i	0.117798	+	0.204032i
$96$		0			0
$97$	−3.58414	+	6.20790i	−0.363914	+	0.630317i	−0.988601	−	0.150558i	$-0.951893\pi$
$97$	−3.58414	+	6.20790i	−0.363914	+	0.630317i	0.624687	+	0.780875i	$0.285226\pi$
$98$	0.239123			0.0241551
$99$		0			0
$100$	7.00000			0.700000
$101$	−6.39248	+	11.0721i	−0.636075	+	1.10171i	0.350211	+	0.936671i	$0.386110\pi$
$101$	−6.39248	+	11.0721i	−0.636075	+	1.10171i	−0.986286	+	0.165044i	$0.947223\pi$
$102$		0			0
$103$	2.19850	+	3.80791i	0.216624	+	0.375204i	0.953774	−	0.300526i	$-0.0971621\pi$
$103$	2.19850	+	3.80791i	0.216624	+	0.375204i	−0.737150	+	0.675730i	$0.763829\pi$
$104$	0.471410	+	0.816506i	0.0462256	+	0.0800650i
$105$		0			0
$106$	−1.38727	+	2.40283i	−0.134744	+	0.233384i
$107$	−13.7278			−1.32711			−0.663557	−	0.748126i	$-0.730954\pi$
$107$	−13.7278			−1.32711			−0.663557	+	0.748126i	$0.730954\pi$
$108$		0			0
$109$	1.26320			0.120993			0.0604963	−	0.998168i	$-0.480732\pi$
$109$	1.26320			0.120993			0.0604963	+	0.998168i	$0.480732\pi$
$110$	0.523388	−	0.906535i	0.0499031	−	0.0864347i
$111$		0			0
$112$	1.83009	+	3.16982i	0.172928	+	0.299520i
$113$	6.08126	+	10.5330i	0.572076	+	0.990866i	0.996353	+	0.0853326i	$0.0271953\pi$
$113$	6.08126	+	10.5330i	0.572076	+	0.990866i	−0.424276	+	0.905533i	$0.639471\pi$
$114$		0			0
$115$	3.31122	−	5.73520i	0.308773	−	0.534810i
$116$	0.464574			0.0431346
$117$		0			0
$118$	−0.622440			−0.0573003
$119$	3.47141	−	6.01266i	0.318224	−	0.551180i
$120$		0			0
$121$	−1.35868	−	2.35331i	−0.123517	−	0.213937i
$122$	0.909028	+	1.57448i	0.0822996	+	0.142547i
$123$		0			0
$124$	1.61273	−	2.79332i	0.144827	−	0.250848i
$125$	10.1683			0.909478
$126$		0			0
$127$	1.33981			0.118889			0.0594445	−	0.998232i	$-0.481067\pi$
$127$	1.33981			0.118889			0.0594445	+	0.998232i	$0.481067\pi$
$128$	3.55718	−	6.16122i	0.314413	−	0.544580i
$129$		0			0
$130$	0.141315	+	0.244765i	0.0123942	+	0.0214673i
$131$	−2.48345	−	4.30146i	−0.216980	−	0.375820i	0.736903	−	0.675998i	$-0.236287\pi$
$131$	−2.48345	−	4.30146i	−0.216980	−	0.375820i	−0.953883	+	0.300178i	$0.902954\pi$
$132$		0			0
$133$	0.971410	−	1.68253i	0.0842319	−	0.145894i
$134$	0.838864			0.0724668
$135$		0			0
$136$	−6.54583			−0.561300
$137$	−2.16991	+	3.75839i	−0.185387	+	0.321101i	−0.943707	−	0.330782i	$-0.892687\pi$
$137$	−2.16991	+	3.75839i	−0.185387	+	0.321101i	0.758320	+	0.651883i	$0.226021\pi$
$138$		0			0
$139$	−1.97141	−	3.41458i	−0.167213	−	0.289621i	0.770226	−	0.637771i	$-0.220143\pi$
$139$	−1.97141	−	3.41458i	−0.167213	−	0.289621i	−0.937439	+	0.348150i	$0.886810\pi$
$140$	1.14815	+	1.98866i	0.0970365	+	0.168072i
$141$		0			0
$142$	1.02859	−	1.78157i	0.0863174	−	0.149506i
$143$	3.70370			0.309719
$144$		0			0
$145$	0.282630			0.0234712
$146$	−1.81122	+	3.13713i	−0.149898	+	0.259630i
$147$		0			0
$148$	−9.27292	−	16.0612i	−0.762229	−	1.32022i
$149$	5.55555	+	9.62249i	0.455128	+	0.788305i	0.998696	−	0.0510606i	$-0.0162602\pi$
$149$	5.55555	+	9.62249i	0.455128	+	0.788305i	−0.543568	+	0.839365i	$0.682927\pi$
$150$		0			0
$151$	−6.96169	+	12.0580i	−0.566535	+	0.981267i	0.430370	+	0.902652i	$0.358383\pi$
$151$	−6.96169	+	12.0580i	−0.566535	+	0.981267i	−0.996905	+	0.0786145i	$0.974950\pi$
$152$	−1.83173			−0.148573
$153$		0			0
$154$	−0.885640			−0.0713669
$155$	0.981125	−	1.69936i	0.0788059	−	0.136496i
$156$		0			0
$157$	−0.0285900	−	0.0495193i	−0.00228173	−	0.00395207i	0.864882	−	0.501975i	$-0.167393\pi$
$157$	−0.0285900	−	0.0495193i	−0.00228173	−	0.00395207i	−0.867164	+	0.498023i	$0.834060\pi$
$158$	−0.882073	−	1.52780i	−0.0701740	−	0.121545i
$159$		0			0
$160$	1.63160	−	2.82601i	0.128989	−	0.223416i
$161$	−5.60301			−0.441579
$162$		0			0
$163$	−1.50808			−0.118122			−0.0590610	−	0.998254i	$-0.518811\pi$
$163$	−1.50808			−0.118122			−0.0590610	+	0.998254i	$0.518811\pi$
$164$	9.89084	−	17.1314i	0.772345	−	1.33774i
$165$		0			0
$166$	−0.830095	−	1.43777i	−0.0644279	−	0.111592i
$167$	−7.34213	−	12.7169i	−0.568151	−	0.984067i	−0.996749	−	0.0805714i	$-0.974325\pi$
$167$	−7.34213	−	12.7169i	−0.568151	−	0.984067i	0.428598	−	0.903496i	$-0.359008\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$	−1.96225			−0.150498
$171$		0			0
$172$	−4.32365			−0.329675
$173$	0.126398	−	0.218928i	0.00960987	−	0.0166448i	−0.861180	−	0.508299i	$-0.830274\pi$
$173$	0.126398	−	0.218928i	0.00960987	−	0.0166448i	0.870790	+	0.491655i	$0.163608\pi$
$174$		0			0
$175$	−1.80150	−	3.12030i	−0.136181	−	0.235872i
$176$	−6.77812	−	11.7400i	−0.510920	−	0.884939i
$177$		0			0
$178$	0.328460	−	0.568910i	0.0246191	−	0.0426416i
$179$	−14.1923			−1.06079			−0.530393	−	0.847752i	$-0.677956\pi$
$179$	−14.1923			−1.06079			−0.530393	+	0.847752i	$0.677956\pi$
$180$		0			0
$181$	−1.43147			−0.106400			−0.0532002	−	0.998584i	$-0.516942\pi$
$181$	−1.43147			−0.106400			−0.0532002	+	0.998584i	$0.516942\pi$
$182$	0.119562	−	0.207087i	0.00886250	−	0.0153503i
$183$		0			0
$184$	2.64132	+	4.57489i	0.194720	+	0.337266i
$185$	−5.64132	−	9.77104i	−0.414758	−	0.718381i
$186$		0			0
$187$	−12.8571	+	22.2691i	−0.940201	+	1.62848i
$188$	11.3236			0.825862
$189$		0			0
$190$	−0.549100			−0.0398359
$191$	7.53379	−	13.0489i	0.545126	−	0.944186i	−0.453473	−	0.891270i	$-0.649815\pi$
$191$	7.53379	−	13.0489i	0.545126	−	0.944186i	0.998599	−	0.0529159i	$-0.0168515\pi$
$192$		0			0
$193$	3.92395	+	6.79647i	0.282452	+	0.489221i	0.971988	−	0.235030i	$-0.0755190\pi$
$193$	3.92395	+	6.79647i	0.282452	+	0.489221i	−0.689536	+	0.724251i	$0.742186\pi$
$194$	−0.857050	−	1.48445i	−0.0615326	−	0.106578i
$195$		0			0
$196$	0.971410	−	1.68253i	0.0693864	−	0.120181i
$197$	−6.69002			−0.476644			−0.238322	−	0.971186i	$-0.576597\pi$
$197$	−6.69002			−0.476644			−0.238322	+	0.971186i	$0.576597\pi$
$198$		0			0
$199$	−19.9396			−1.41348			−0.706739	−	0.707475i	$-0.749834\pi$
$199$	−19.9396			−1.41348			−0.706739	+	0.707475i	$0.749834\pi$
$200$	−1.69850	+	2.94188i	−0.120102	+	0.208022i
$201$		0			0
$202$	−1.52859	−	2.64760i	−0.107551	−	0.186284i
$203$	−0.119562	−	0.207087i	−0.00839158	−	0.0145346i
$204$		0			0
$205$	6.01724	−	10.4222i	0.420262	−	0.727916i
$206$	−1.05142			−0.0732561
$207$		0			0
$208$	3.66019			0.253789
$209$	−3.59781	+	6.23159i	−0.248866	+	0.431048i
$210$		0			0
$211$	9.04583	+	15.6678i	0.622741	+	1.07862i	0.988973	+	0.148095i	$0.0473141\pi$
$211$	9.04583	+	15.6678i	0.622741	+	1.07862i	−0.366233	+	0.930523i	$0.619353\pi$
$212$	11.2713	+	19.5224i	0.774115	+	1.34081i
$213$		0			0
$214$	1.64132	−	2.84284i	0.112198	−	0.194333i
$215$	−2.63036			−0.179389
$216$		0			0
$217$	−1.66019			−0.112701
$218$	−0.151030	+	0.261592i	−0.0102291	+	0.0177172i
$219$		0			0
$220$	−4.25241	−	7.36538i	−0.286697	−	0.496574i
$221$	−3.47141	−	6.01266i	−0.233512	−	0.404455i
$222$		0			0
$223$	11.3285	−	19.6215i	0.758610	−	1.31395i	−0.184950	−	0.982748i	$-0.559212\pi$
$223$	11.3285	−	19.6215i	0.758610	−	1.31395i	0.943560	−	0.331203i	$-0.107454\pi$
$224$	−2.76088			−0.184469
$225$		0			0
$226$	−2.90834			−0.193460
$227$	−2.64132	+	4.57489i	−0.175310	+	0.303646i	−0.940269	−	0.340433i	$-0.889426\pi$
$227$	−2.64132	+	4.57489i	−0.175310	+	0.303646i	0.764958	+	0.644080i	$0.222760\pi$
$228$		0			0
$229$	−9.66827	−	16.7459i	−0.638897	−	1.10660i	−0.985675	−	0.168655i	$-0.946058\pi$
$229$	−9.66827	−	16.7459i	−0.638897	−	1.10660i	0.346778	−	0.937947i	$-0.387276\pi$
$230$	0.791790	+	1.37142i	0.0522091	+	0.0904288i
$231$		0			0
$232$	−0.112725	+	0.195246i	−0.00740077	+	0.0128185i
$233$	16.9806			1.11243			0.556217	−	0.831037i	$-0.312252\pi$
$233$	16.9806			1.11243			0.556217	+	0.831037i	$0.312252\pi$
$234$		0			0
$235$	6.88891			0.449383
$236$	−2.52859	+	4.37965i	−0.164597	+	0.285091i
$237$		0			0
$238$	0.830095	+	1.43777i	0.0538071	+	0.0931966i
$239$	8.44282	+	14.6234i	0.546121	+	0.945909i	0.998535	+	0.0541011i	$0.0172293\pi$
$239$	8.44282	+	14.6234i	0.546121	+	0.945909i	−0.452415	+	0.891808i	$0.649437\pi$
$240$		0			0
$241$	−13.5728	+	23.5088i	−0.874300	+	1.51433i	−0.0167933	+	0.999859i	$0.505346\pi$
$241$	−13.5728	+	23.5088i	−0.874300	+	1.51433i	−0.857507	+	0.514473i	$0.827988\pi$
$242$	0.649786			0.0417699
$243$		0			0
$244$	14.7713			0.945634
$245$	0.590972	−	1.02359i	0.0377558	−	0.0653950i
$246$		0			0
$247$	−0.971410	−	1.68253i	−0.0618093	−	0.107057i
$248$	0.782630	+	1.35556i	0.0496971	+	0.0860778i
$249$		0			0
$250$	−1.21574	+	2.10571i	−0.0768898	+	0.133177i
$251$	19.0780			1.20419			0.602096	−	0.798424i	$-0.294332\pi$
$251$	19.0780			1.20419			0.602096	+	0.798424i	$0.294332\pi$
$252$		0			0
$253$	20.7518			1.30466
$254$	−0.160190	+	0.277457i	−0.0100512	+	0.0174092i
$255$		0			0
$256$	−5.80959	−	10.0625i	−0.363099	−	0.628906i
$257$	−7.42107	−	12.8537i	−0.462913	−	0.801790i	0.536191	−	0.844097i	$-0.319863\pi$
$257$	−7.42107	−	12.8537i	−0.462913	−	0.801790i	−0.999105	+	0.0423070i	$0.986529\pi$
$258$		0			0
$259$	−4.77292	+	8.26693i	−0.296575	+	0.513682i
$260$	2.29630			0.142411
$261$		0			0
$262$	1.18770			0.0733764
$263$	−3.87072	+	6.70429i	−0.238679	+	0.413404i	−0.960335	−	0.278847i	$-0.910048\pi$
$263$	−3.87072	+	6.70429i	−0.238679	+	0.413404i	0.721656	+	0.692251i	$0.243381\pi$
$264$		0			0
$265$	6.85705	+	11.8768i	0.421225	+	0.729584i
$266$	0.232287	+	0.402332i	0.0142424	+	0.0246686i
$267$		0			0
$268$	3.40778	−	5.90246i	0.208164	−	0.360550i
$269$	1.51135			0.0921486			0.0460743	−	0.998938i	$-0.485329\pi$
$269$	1.51135			0.0921486			0.0460743	+	0.998938i	$0.485329\pi$
$270$		0			0
$271$	−21.9806			−1.33522			−0.667612	−	0.744509i	$-0.732684\pi$
$271$	−21.9806			−1.33522			−0.667612	+	0.744509i	$0.732684\pi$
$272$	−12.7060	+	22.0075i	−0.770416	+	1.33440i
$273$		0			0
$274$	−0.518875	−	0.898718i	−0.0313464	−	0.0542935i
$275$	6.67223	+	11.5566i	0.402350	+	0.696892i
$276$		0			0
$277$	5.41423	−	9.37772i	0.325310	−	0.563453i	−0.656265	−	0.754530i	$-0.727865\pi$
$277$	5.41423	−	9.37772i	0.325310	−	0.563453i	0.981575	+	0.191077i	$0.0611982\pi$
$278$	0.942820			0.0565466
$279$		0			0
$280$	−1.11436			−0.0665957
$281$	−8.43831	+	14.6156i	−0.503387	+	0.871892i	0.496605	+	0.867977i	$0.334580\pi$
$281$	−8.43831	+	14.6156i	−0.503387	+	0.871892i	−0.999992	+	0.00391559i	$0.998754\pi$
$282$		0			0
$283$	7.65856	+	13.2650i	0.455254	+	0.788523i	0.998703	−	0.0509194i	$-0.0162152\pi$
$283$	7.65856	+	13.2650i	0.455254	+	0.788523i	−0.543449	+	0.839442i	$0.682882\pi$
$284$	−8.35705	−	14.4748i	−0.495900	−	0.858923i
$285$		0			0
$286$	−0.442820	+	0.766987i	−0.0261845	+	0.0453529i
$287$	−10.1819			−0.601021
$288$		0			0
$289$	31.2028			1.83546
$290$	−0.0337917	+	0.0585290i	−0.00198432	+	0.00343694i
$291$		0			0
$292$	14.7157	+	25.4884i	0.861173	+	1.49160i
$293$	−4.68482	−	8.11435i	−0.273690	−	0.474045i	0.696114	−	0.717932i	$-0.254911\pi$
$293$	−4.68482	−	8.11435i	−0.273690	−	0.474045i	−0.969804	+	0.243886i	$0.921578\pi$
$294$		0			0
$295$	−1.53831	+	2.66442i	−0.0895636	+	0.155129i
$296$	9.00000			0.523114
$297$		0			0
$298$	−2.65692			−0.153911
$299$	−2.80150	+	4.85235i	−0.162015	+	0.280619i
$300$		0			0
$301$	1.11273	+	1.92730i	0.0641364	+	0.111088i
$302$	−1.66470	−	2.88335i	−0.0957929	−	0.165918i
$303$		0			0
$304$	−3.55555	+	6.15838i	−0.203925	+	0.353208i
$305$	8.98633			0.514556
$306$		0			0
$307$	2.71410			0.154902			0.0774509	−	0.996996i	$-0.475322\pi$
$307$	2.71410			0.154902			0.0774509	+	0.996996i	$0.475322\pi$
$308$	−3.59781	+	6.23159i	−0.205004	+	0.355078i
$309$		0			0
$310$	0.234610	+	0.406356i	0.0133249	+	0.0230795i
$311$	−6.99028	−	12.1075i	−0.396383	−	0.686555i	0.596894	−	0.802320i	$-0.296401\pi$
$311$	−6.99028	−	12.1075i	−0.396383	−	0.686555i	−0.993277	+	0.115765i	$0.963068\pi$
$312$		0			0
$313$	9.52696	−	16.5012i	0.538495	−	0.932701i	−0.460490	−	0.887665i	$-0.652326\pi$
$313$	9.52696	−	16.5012i	0.538495	−	0.932701i	0.998985	−	0.0450364i	$-0.0143404\pi$
$314$	0.0136731			0.000771615
$315$		0			0
$316$	−14.3333			−0.806309
$317$	−2.00972	+	3.48093i	−0.112877	+	0.195508i	−0.916929	−	0.399050i	$-0.869340\pi$
$317$	−2.00972	+	3.48093i	−0.112877	+	0.195508i	0.804052	+	0.594559i	$0.202673\pi$
$318$		0			0
$319$	0.442820	+	0.766987i	0.0247932	+	0.0429430i
$320$	−3.93598	−	6.81732i	−0.220028	−	0.381100i
$321$		0			0
$322$	0.669905	−	1.16031i	0.0373323	−	0.0646615i
$323$	13.4887			0.750529
$324$		0			0
$325$	−3.60301			−0.199859
$326$	0.180309	−	0.312304i	0.00998637	−	0.0172969i
$327$		0			0
$328$	4.79987	+	8.31362i	0.265028	+	0.459043i
$329$	−2.91423	−	5.04759i	−0.160667	−	0.278283i
$330$		0			0
$331$	6.18878	−	10.7193i	0.340166	−	0.589185i	−0.644297	−	0.764775i	$-0.722850\pi$
$331$	6.18878	−	10.7193i	0.340166	−	0.589185i	0.984463	+	0.175590i	$0.0561834\pi$
$332$	−13.4887			−0.740286
$333$		0			0
$334$	3.51135			0.192133
$335$	2.07318	−	3.59085i	0.113270	−	0.196189i
$336$		0			0
$337$	−6.12997	−	10.6174i	−0.333920	−	0.578367i	0.649356	−	0.760484i	$-0.275038\pi$
$337$	−6.12997	−	10.6174i	−0.333920	−	0.578367i	−0.983277	+	0.182117i	$0.941705\pi$
$338$	1.43474	+	2.48504i	0.0780395	+	0.135168i
$339$		0			0
$340$	−7.97141	+	13.8069i	−0.432310	+	0.748784i
$341$	6.14884			0.332978
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	1.04910	−	1.81709i	0.0565637	−	0.0979711i
$345$		0			0
$346$	0.0302247	+	0.0523508i	0.00162489	+	0.00281440i
$347$	3.32489	+	5.75888i	0.178490	+	0.309153i	0.941363	−	0.337394i	$-0.109546\pi$
$347$	3.32489	+	5.75888i	0.178490	+	0.309153i	−0.762874	+	0.646547i	$0.776212\pi$
$348$		0			0
$349$	−5.71737	+	9.90278i	−0.306044	+	0.530083i	−0.977493	−	0.210967i	$-0.932339\pi$
$349$	−5.71737	+	9.90278i	−0.306044	+	0.530083i	0.671449	+	0.741050i	$0.265672\pi$
$350$	0.861564			0.0460525
$351$		0			0
$352$	10.2255			0.545018
$353$	−11.0978	+	19.2220i	−0.590677	+	1.02308i	0.403465	+	0.914995i	$0.367806\pi$
$353$	−11.0978	+	19.2220i	−0.590677	+	1.02308i	−0.994141	+	0.108087i	$0.965528\pi$
$354$		0			0
$355$	−5.08414	−	8.80598i	−0.269838	−	0.467373i
$356$	−2.66866	−	4.62226i	−0.141439	−	0.244979i
$357$		0			0
$358$	1.69686	−	2.93905i	0.0896819	−	0.155334i
$359$	7.55623			0.398803			0.199401	−	0.979918i	$-0.436100\pi$
$359$	7.55623			0.398803			0.199401	+	0.979918i	$0.436100\pi$
$360$		0			0
$361$	−15.2255			−0.801339
$362$	0.171149	−	0.296439i	0.00899539	−	0.0155805i
$363$		0			0
$364$	−0.971410	−	1.68253i	−0.0509157	−	0.0881886i
$365$	8.95254	+	15.5062i	0.468597	+	0.811634i
$366$		0			0
$367$	9.26157	−	16.0415i	0.483450	−	0.837360i	−0.516370	−	0.856366i	$-0.672717\pi$
$367$	9.26157	−	16.0415i	0.483450	−	0.837360i	0.999819	+	0.0190063i	$0.00605025\pi$
$368$	20.5081			1.06906
$369$		0			0
$370$	2.69794			0.140259
$371$	5.80150	−	10.0485i	0.301199	−	0.521692i
$372$		0			0
$373$	−7.83009	−	13.5621i	−0.405427	−	0.702220i	0.588944	−	0.808174i	$-0.299544\pi$
$373$	−7.83009	−	13.5621i	−0.405427	−	0.702220i	−0.994371	+	0.105954i	$0.966210\pi$
$374$	−3.07442	−	5.32505i	−0.158974	−	0.275352i
$375$		0			0
$376$	−2.74759	+	4.75897i	−0.141696	+	0.245425i
$377$	−0.239123			−0.0123155
$378$		0			0
$379$	4.03775			0.207405			0.103703	−	0.994608i	$-0.466931\pi$
$379$	4.03775			0.207405			0.103703	+	0.994608i	$0.466931\pi$
$380$	−2.23065	+	3.86360i	−0.114430	+	0.198199i
$381$		0			0
$382$	1.80150	+	3.12030i	0.0921730	+	0.159648i
$383$	0.112725	+	0.195246i	0.00575998	+	0.00997659i	0.868891	−	0.495003i	$-0.164833\pi$
$383$	0.112725	+	0.195246i	0.00575998	+	0.00997659i	−0.863131	+	0.504980i	$0.831500\pi$
$384$		0			0
$385$	−2.18878	+	3.79108i	−0.111551	+	0.193211i
$386$	−1.87661			−0.0955171
$387$		0			0
$388$	−13.9267			−0.707019
$389$	12.6316	−	21.8786i	0.640448	−	1.10929i	−0.344885	−	0.938645i	$-0.612082\pi$
$389$	12.6316	−	21.8786i	0.640448	−	1.10929i	0.985333	−	0.170643i	$-0.0545844\pi$
$390$		0			0
$391$	−19.4503	−	33.6890i	−0.983646	−	1.70373i
$392$	0.471410	+	0.816506i	0.0238098	+	0.0412398i
$393$		0			0
$394$	0.799870	−	1.38542i	0.0402969	−	0.0697962i
$395$	−8.71986			−0.438744
$396$		0			0
$397$	−20.3009			−1.01888			−0.509438	−	0.860508i	$-0.670147\pi$
$397$	−20.3009			−1.01888			−0.509438	+	0.860508i	$0.670147\pi$
$398$	2.38401	−	4.12922i	0.119499	−	0.206979i
$399$		0			0
$400$	6.59385	+	11.4209i	0.329693	+	0.571044i
$401$	−7.61273	−	13.1856i	−0.380161	−	0.658459i	0.610924	−	0.791689i	$-0.290798\pi$
$401$	−7.61273	−	13.1856i	−0.380161	−	0.658459i	−0.991085	+	0.133231i	$0.957465\pi$
$402$		0			0
$403$	−0.830095	+	1.43777i	−0.0413500	+	0.0716203i
$404$	−24.8389			−1.23578
$405$		0			0
$406$	0.0571799			0.00283779
$407$	17.6774	−	30.6182i	0.876238	−	1.51769i
$408$		0			0
$409$	−0.828460	−	1.43494i	−0.0409647	−	0.0709530i	0.844816	−	0.535057i	$-0.179710\pi$
$409$	−0.828460	−	1.43494i	−0.0409647	−	0.0709530i	−0.885781	+	0.464104i	$0.846376\pi$
$410$	1.43886	+	2.49218i	0.0710603	+	0.123080i
$411$		0			0
$412$	−4.27128	+	7.39807i	−0.210431	+	0.364477i
$413$	2.60301			0.128086
$414$		0			0
$415$	−8.20602			−0.402818
$416$	−1.38044	+	2.39099i	−0.0676816	+	0.117228i
$417$		0			0
$418$	−0.860320	−	1.49012i	−0.0420796	−	0.0728840i
$419$	16.6871	+	28.9030i	0.815220	+	1.41200i	0.909170	+	0.416426i	$0.136718\pi$
$419$	16.6871	+	28.9030i	0.815220	+	1.41200i	−0.0939492	+	0.995577i	$0.529949\pi$
$420$		0			0
$421$	−9.12025	+	15.7967i	−0.444494	+	0.769886i	−0.998017	−	0.0629481i	$-0.979950\pi$
$421$	−9.12025	+	15.7967i	−0.444494	+	0.769886i	0.553523	+	0.832834i	$0.313283\pi$
$422$	−4.32614			−0.210593
$423$		0			0
$424$	−10.9396			−0.531272
$425$	12.5075	−	21.6637i	0.606704	−	1.05084i
$426$		0			0
$427$	−3.80150	−	6.58440i	−0.183968	−	0.318641i
$428$	−13.3353	−	23.0974i	−0.644586	−	1.11646i
$429$		0			0
$430$	0.314490	−	0.544712i	0.0151660	−	0.0262684i
$431$	−29.2826			−1.41049			−0.705247	−	0.708961i	$-0.749164\pi$
$431$	−29.2826			−1.41049			−0.705247	+	0.708961i	$0.749164\pi$
$432$		0			0
$433$	−12.2449			−0.588451			−0.294226	−	0.955736i	$-0.595062\pi$
$433$	−12.2449			−0.588451			−0.294226	+	0.955736i	$0.595062\pi$
$434$	0.198495	−	0.343803i	0.00952807	−	0.0165031i
$435$		0			0
$436$	1.22708	+	2.12537i	0.0587667	+	0.101787i
$437$	−5.44282	−	9.42724i	−0.260365	−	0.450966i
$438$		0			0
$439$	2.41586	−	4.18440i	0.115303	−	0.199711i	−0.802598	−	0.596520i	$-0.796549\pi$
$439$	2.41586	−	4.18440i	0.115303	−	0.199711i	0.917901	+	0.396810i	$0.129883\pi$
$440$	4.12725			0.196759
$441$		0			0
$442$	1.66019			0.0789672
$443$	0.622440	−	1.07810i	0.0295730	−	0.0512220i	−0.850860	−	0.525392i	$-0.823919\pi$
$443$	0.622440	−	1.07810i	0.0295730	−	0.0512220i	0.880433	+	0.474170i	$0.157252\pi$
$444$		0			0
$445$	−1.62352	−	2.81202i	−0.0769622	−	0.133302i
$446$	2.70890	+	4.69195i	0.128270	+	0.222170i
$447$		0			0
$448$	−3.33009	+	5.76789i	−0.157332	+	0.272507i
$449$	−8.82846			−0.416641			−0.208320	−	0.978061i	$-0.566800\pi$
$449$	−8.82846			−0.416641			−0.208320	+	0.978061i	$0.566800\pi$
$450$		0			0
$451$	37.7108			1.77573
$452$	−11.8148	+	20.4638i	−0.555721	+	0.962537i
$453$		0			0
$454$	−0.631600	−	1.09396i	−0.0296425	−	0.0513422i
$455$	−0.590972	−	1.02359i	−0.0277052	−	0.0479868i
$456$		0			0
$457$	5.25404	−	9.10026i	0.245774	−	0.425692i	−0.716575	−	0.697510i	$-0.754291\pi$
$457$	5.25404	−	9.10026i	0.245774	−	0.425692i	0.962349	+	0.271817i	$0.0876247\pi$
$458$	4.62382			0.216057
$459$		0			0
$460$	12.8662			0.599890
$461$	11.2758	−	19.5302i	0.525166	−	0.909614i	−0.474404	−	0.880307i	$-0.657337\pi$
$461$	11.2758	−	19.5302i	0.525166	−	0.909614i	0.999570	−	0.0293073i	$-0.00933013\pi$
$462$		0			0
$463$	−5.19850	−	9.00406i	−0.241595	−	0.418454i	0.719574	−	0.694416i	$-0.244337\pi$
$463$	−5.19850	−	9.00406i	−0.241595	−	0.418454i	−0.961169	+	0.275962i	$0.911004\pi$
$464$	0.437618	+	0.757977i	0.0203159	+	0.0351882i
$465$		0			0
$466$	−2.03022	+	3.51645i	−0.0940483	+	0.162897i
$467$	−13.3171			−0.616242			−0.308121	−	0.951347i	$-0.599700\pi$
$467$	−13.3171			−0.616242			−0.308121	+	0.951347i	$0.599700\pi$
$468$		0			0
$469$	−3.50808			−0.161988
$470$	−0.823649	+	1.42660i	−0.0379921	+	0.0658043i
$471$		0			0
$472$	−1.22708	−	2.12537i	−0.0564812	−	0.0978282i
$473$	−4.12120	−	7.13812i	−0.189493	−	0.328211i
$474$		0			0
$475$	3.50000	−	6.06218i	0.160591	−	0.278152i
$476$	13.4887			0.618251
$477$		0			0
$478$	−4.03775			−0.184682
$479$	7.26771	−	12.5880i	0.332070	−	0.575163i	−0.650847	−	0.759209i	$-0.725586\pi$
$479$	7.26771	−	12.5880i	0.332070	−	0.575163i	0.982918	+	0.184046i	$0.0589195\pi$
$480$		0			0
$481$	4.77292	+	8.26693i	0.217626	+	0.376940i
$482$	−3.24557	−	5.62149i	−0.147832	−	0.256052i
$483$		0			0
$484$	2.63968	−	4.57206i	0.119985	−	0.207821i
$485$	−8.47249			−0.384716
$486$		0			0
$487$	13.0539			0.591529			0.295765	−	0.955261i	$-0.404426\pi$
$487$	13.0539			0.591529			0.295765	+	0.955261i	$0.404426\pi$
$488$	−3.58414	+	6.20790i	−0.162246	+	0.281019i
$489$		0			0
$490$	0.141315	+	0.244765i	0.00638396	+	0.0110574i
$491$	9.67223	+	16.7528i	0.436502	+	0.756043i	0.997417	−	0.0718303i	$-0.0228840\pi$
$491$	9.67223	+	16.7528i	0.436502	+	0.756043i	−0.560915	+	0.827873i	$0.689551\pi$
$492$		0			0
$493$	0.830095	−	1.43777i	0.0373856	−	0.0647538i
$494$	0.464574			0.0209022
$495$		0			0
$496$	6.07661			0.272848
$497$	−4.30150	+	7.45043i	−0.192949	+	0.334197i
$498$		0			0
$499$	18.1111	+	31.3693i	0.810764	+	1.40428i	0.912330	+	0.409455i	$0.134281\pi$
$499$	18.1111	+	31.3693i	0.810764	+	1.40428i	−0.101566	+	0.994829i	$0.532385\pi$
$500$	9.87756	+	17.1084i	0.441738	+	0.765112i
$501$		0			0
$502$	−2.28100	+	3.95080i	−0.101806	+	0.176333i
$503$	−15.6764			−0.698974			−0.349487	−	0.936941i	$-0.613644\pi$
$503$	−15.6764			−0.698974			−0.349487	+	0.936941i	$0.613644\pi$
$504$		0			0
$505$	−15.1111			−0.672435
$506$	−2.48113	+	4.29743i	−0.110299	+	0.191044i
$507$		0			0
$508$	1.30150	+	2.25427i	0.0577449	+	0.100017i
$509$	17.1517	+	29.7076i	0.760237	+	1.31677i	0.942729	+	0.333561i	$0.108250\pi$
$509$	17.1517	+	29.7076i	0.760237	+	1.31677i	−0.182492	+	0.983207i	$0.558416\pi$
$510$		0			0
$511$	7.57442	−	13.1193i	0.335073	−	0.580363i
$512$	17.0071			0.751616
$513$		0			0
$514$	3.54910			0.156544
$515$	−2.59850	+	4.50073i	−0.114503	+	0.198326i
$516$		0			0
$517$	10.7934	+	18.6948i	0.474694	+	0.822195i
$518$	−1.14132	−	1.97682i	−0.0501465	−	0.0868563i
$519$		0			0
$520$	−0.557180	+	0.965064i	−0.0244340	+	0.0423209i
$521$	10.2449			0.448836			0.224418	−	0.974493i	$-0.427952\pi$
$521$	10.2449			0.448836			0.224418	+	0.974493i	$0.427952\pi$
$522$		0			0
$523$	30.6030			1.33818			0.669088	−	0.743183i	$-0.266685\pi$
$523$	30.6030			1.33818			0.669088	+	0.743183i	$0.266685\pi$
$524$	4.82489	−	8.35696i	0.210776	−	0.365075i
$525$		0			0
$526$	−0.925580	−	1.60315i	−0.0403572	−	0.0699007i
$527$	−5.76320	−	9.98215i	−0.251049	−	0.434829i
$528$		0			0
$529$	−4.19686	+	7.26918i	−0.182472	+	0.316051i
$530$	−3.27936			−0.142446
$531$		0			0
$532$	3.77455			0.163647
$533$	−5.09097	+	8.81782i	−0.220514	+	0.381942i
$534$		0			0
$535$	−8.11273	−	14.0517i	−0.350744	−	0.607506i
$536$	1.65374	+	2.86437i	0.0714309	+	0.123722i
$537$		0			0
$538$	−0.180699	+	0.312981i	−0.00779051	+	0.0134936i
$539$	3.70370			0.159530
$540$		0			0
$541$	−26.0917			−1.12177			−0.560884	−	0.827894i	$-0.689539\pi$
$541$	−26.0917			−1.12177			−0.560884	+	0.827894i	$0.689539\pi$
$542$	2.62803	−	4.55189i	0.112884	−	0.195520i
$543$		0			0
$544$	−9.58414	−	16.6002i	−0.410916	−	0.711728i
$545$	0.746515	+	1.29300i	0.0319772	+	0.0553861i
$546$		0			0
$547$	5.46169	−	9.45993i	0.233525	−	0.404478i	−0.725318	−	0.688414i	$-0.758307\pi$
$547$	5.46169	−	9.45993i	0.233525	−	0.404478i	0.958843	+	0.283937i	$0.0916405\pi$
$548$	−8.43147			−0.360175
$549$		0			0
$550$	−3.19097			−0.136063
$551$	0.232287	−	0.402332i	0.00989575	−	0.0171399i
$552$		0			0
$553$	3.68878	+	6.38915i	0.156863	+	0.271694i
$554$	1.29467	+	2.24243i	0.0550052	+	0.0952718i
$555$		0			0
$556$	3.83009	−	6.63392i	0.162432	−	0.281341i
$557$	13.9442			0.590835			0.295417	−	0.955368i	$-0.404541\pi$
$557$	13.9442			0.590835			0.295417	+	0.955368i	$0.404541\pi$
$558$		0			0
$559$	2.22545			0.0941265
$560$	−2.16307	+	3.74654i	−0.0914063	+	0.158320i
$561$		0			0
$562$	−2.01780	−	3.49492i	−0.0851156	−	0.147424i
$563$	15.1287	+	26.2037i	0.637600	+	1.10435i	0.985958	+	0.166993i	$0.0534059\pi$
$563$	15.1287	+	26.2037i	0.637600	+	1.10435i	−0.348358	+	0.937361i	$0.613261\pi$
$564$		0			0
$565$	−7.18770	+	12.4495i	−0.302389	+	0.523753i
$566$	−3.66268			−0.153954
$567$		0			0
$568$	8.11109			0.340334
$569$	−10.5676	+	18.3036i	−0.443016	+	0.767326i	−0.997912	−	0.0645936i	$-0.979425\pi$
$569$	−10.5676	+	18.3036i	−0.443016	+	0.767326i	0.554896	+	0.831920i	$0.312758\pi$
$570$		0			0
$571$	16.3932	+	28.3938i	0.686033	+	1.18824i	0.973111	+	0.230336i	$0.0739826\pi$
$571$	16.3932	+	28.3938i	0.686033	+	1.18824i	−0.287078	+	0.957907i	$0.592684\pi$
$572$	3.59781	+	6.23159i	0.150432	+	0.260556i
$573$		0			0
$574$	1.21737	−	2.10855i	0.0508120	−	0.0880090i
$575$	−20.1877			−0.841885
$576$		0			0
$577$	−17.3743			−0.723301			−0.361651	−	0.932314i	$-0.617787\pi$
$577$	−17.3743			−0.723301			−0.361651	+	0.932314i	$0.617787\pi$
$578$	−3.73065	+	6.46168i	−0.155175	+	0.268770i
$579$		0			0
$580$	0.274550	+	0.475534i	0.0114001	+	0.0197455i
$581$	3.47141	+	6.01266i	0.144018	+	0.249447i
$582$		0			0
$583$	−21.4870	+	37.2166i	−0.889901	+	1.54135i
$584$	−14.2826			−0.591019
$585$		0			0
$586$	2.24050			0.0925542
$587$	8.48796	−	14.7016i	0.350336	−	0.606799i	−0.635973	−	0.771712i	$-0.719401\pi$
$587$	8.48796	−	14.7016i	0.350336	−	0.606799i	0.986308	+	0.164913i	$0.0527342\pi$
$588$		0			0
$589$	−1.61273	−	2.79332i	−0.0664512	−	0.115097i
$590$	−0.367845	−	0.637125i	−0.0151439	−	0.0262300i
$591$		0			0
$592$	17.4698	−	30.2585i	0.718003	−	1.24362i
$593$	13.0733			0.536858			0.268429	−	0.963300i	$-0.413496\pi$
$593$	13.0733			0.536858			0.268429	+	0.963300i	$0.413496\pi$
$594$		0			0
$595$	8.20602			0.336414
$596$	−10.7934	+	18.6948i	−0.442116	+	0.765767i
$597$		0			0
$598$	−0.669905	−	1.16031i	−0.0273945	−	0.0474486i
$599$	14.6030	+	25.2932i	0.596663	+	1.03345i	0.993310	+	0.115479i	$0.0368403\pi$
$599$	14.6030	+	25.2932i	0.596663	+	1.03345i	−0.396647	+	0.917971i	$0.629826\pi$
$600$		0			0
$601$	−3.89536	+	6.74695i	−0.158895	+	0.275214i	−0.934470	−	0.356041i	$-0.884126\pi$
$601$	−3.89536	+	6.74695i	−0.158895	+	0.275214i	0.775576	+	0.631255i	$0.217460\pi$
$602$	−0.532157			−0.0216891
$603$		0			0
$604$	−27.0506			−1.10067
$605$	1.60589	−	2.78148i	0.0652887	−	0.113083i
$606$		0			0
$607$	9.82038	+	17.0094i	0.398597	+	0.690390i	0.993553	−	0.113368i	$-0.0361639\pi$
$607$	9.82038	+	17.0094i	0.398597	+	0.690390i	−0.594956	+	0.803758i	$0.702831\pi$
$608$	−2.68194	−	4.64526i	−0.108767	−	0.188390i
$609$		0			0
$610$	−1.07442	+	1.86095i	−0.0435020	+	0.0753477i
$611$	−5.82846			−0.235794
$612$		0			0
$613$	23.5653			0.951792			0.475896	−	0.879502i	$-0.342124\pi$
$613$	23.5653			0.951792			0.475896	+	0.879502i	$0.342124\pi$
$614$	−0.324502	+	0.562054i	−0.0130958	+	0.0226827i
$615$		0			0
$616$	−1.74596	−	3.02409i	−0.0703467	−	0.121844i
$617$	−5.33009	−	9.23200i	−0.214582	−	0.371666i	0.738562	−	0.674186i	$-0.235505\pi$
$617$	−5.33009	−	9.23200i	−0.214582	−	0.371666i	−0.953143	+	0.302520i	$0.902172\pi$
$618$		0			0
$619$	9.00752	−	15.6015i	0.362043	−	0.627077i	−0.626254	−	0.779619i	$-0.715413\pi$
$619$	9.00752	−	15.6015i	0.362043	−	0.627077i	0.988297	+	0.152542i	$0.0487460\pi$
$620$	3.81230			0.153106
$621$		0			0
$622$	3.34308			0.134045
$623$	−1.37360	+	2.37915i	−0.0550322	+	0.0953186i
$624$		0			0
$625$	−2.99837	−	5.19332i	−0.119935	−	0.207733i
$626$	2.27812	+	3.94581i	0.0910519	+	0.157706i
$627$		0			0
$628$	0.0555452	−	0.0962071i	0.00221649	−	0.00383908i
$629$	−66.2750			−2.64256
$630$		0			0
$631$	12.4703			0.496436			0.248218	−	0.968704i	$-0.420155\pi$
$631$	12.4703			0.496436			0.248218	+	0.968704i	$0.420155\pi$
$632$	3.47786	−	6.02382i	0.138342	−	0.239615i
$633$		0			0
$634$	−0.480570	−	0.832371i	−0.0190859	−	0.0330577i
$635$	0.791790	+	1.37142i	0.0314212	+	0.0544232i
$636$		0			0
$637$	−0.500000	+	0.866025i	−0.0198107	+	0.0343132i
$638$	−0.211777			−0.00838434
$639$		0			0
$640$	8.40877			0.332386
$641$	9.57279	−	16.5806i	0.378102	−	0.654892i	−0.612684	−	0.790328i	$-0.709910\pi$
$641$	9.57279	−	16.5806i	0.378102	−	0.654892i	0.990786	+	0.135436i	$0.0432434\pi$
$642$		0			0
$643$	−3.24433	−	5.61934i	−0.127944	−	0.221605i	0.794936	−	0.606693i	$-0.207504\pi$
$643$	−3.24433	−	5.61934i	−0.127944	−	0.221605i	−0.922880	+	0.385088i	$0.874171\pi$
$644$	−5.44282	−	9.42724i	−0.214477	−	0.371485i
$645$		0			0
$646$	−1.61273	+	2.79332i	−0.0634518	+	0.109902i
$647$	48.0988			1.89096			0.945479	−	0.325682i	$-0.105594\pi$
$647$	48.0988			1.89096			0.945479	+	0.325682i	$0.105594\pi$
$648$		0			0
$649$	−9.64076			−0.378433
$650$	0.430782	−	0.746136i	0.0168967	−	0.0292659i
$651$		0			0
$652$	−1.46496	−	2.53739i	−0.0573724	−	0.0993720i
$653$	−21.6202	−	37.4474i	−0.846066	−	1.46543i	−0.884692	−	0.466175i	$-0.845632\pi$
$653$	−21.6202	−	37.4474i	−0.846066	−	1.46543i	0.0386267	−	0.999254i	$-0.487702\pi$
$654$		0			0
$655$	2.93530	−	5.08408i	0.114691	−	0.198651i
$656$	37.2678			1.45506
$657$		0			0
$658$	1.39372			0.0543329
$659$	−1.25404	+	2.17206i	−0.0488505	+	0.0846115i	−0.889417	−	0.457097i	$-0.848889\pi$
$659$	−1.25404	+	2.17206i	−0.0488505	+	0.0846115i	0.840566	+	0.541709i	$0.182222\pi$
$660$		0			0
$661$	21.1677	+	36.6636i	0.823329	+	1.42605i	0.903190	+	0.429241i	$0.141219\pi$
$661$	21.1677	+	36.6636i	0.823329	+	1.42605i	−0.0798613	+	0.996806i	$0.525448\pi$
$662$	1.47988	+	2.56323i	0.0575172	+	0.0996227i
$663$		0			0
$664$	3.27292	−	5.66886i	0.127014	−	0.219994i
$665$	2.29630			0.0890468
$666$		0			0
$667$	−1.33981			−0.0518777
$668$	14.2644	−	24.7067i	0.551908	−	0.955933i
$669$		0			0
$670$	0.495745	+	0.858655i	0.0191523	+	0.0331727i
$671$	14.0796	+	24.3866i	0.543538	+	0.941435i
$672$		0			0
$673$	−6.70765	+	11.6180i	−0.258561	+	0.447841i	−0.965857	−	0.259077i	$-0.916582\pi$
$673$	−6.70765	+	11.6180i	−0.258561	+	0.447841i	0.707296	+	0.706918i	$0.249915\pi$
$674$	2.93163			0.112922
$675$		0			0
$676$	23.3138			0.896686
$677$	0.981125	−	1.69936i	0.0377077	−	0.0653117i	−0.846556	−	0.532300i	$-0.821328\pi$
$677$	0.981125	−	1.69936i	0.0377077	−	0.0653117i	0.884263	+	0.466989i	$0.154661\pi$
$678$		0			0
$679$	3.58414	+	6.20790i	0.137546	+	0.238237i
$680$	−3.86840	−	6.70027i	−0.148346	−	0.256943i
$681$		0			0
$682$	−0.735165	+	1.27334i	−0.0281509	+	0.0487589i
$683$	−27.1672			−1.03952			−0.519761	−	0.854312i	$-0.673979\pi$
$683$	−27.1672			−1.03952			−0.519761	+	0.854312i	$0.673979\pi$
$684$		0			0
$685$	−5.12941			−0.195985
$686$	0.119562	−	0.207087i	0.00456488	−	0.00790661i
$687$		0			0
$688$	−4.07279	−	7.05427i	−0.155273	−	0.268942i
$689$	−5.80150	−	10.0485i	−0.221020	−	0.382817i
$690$		0			0
$691$	25.1586	−	43.5759i	0.957077	−	1.65771i	0.227534	−	0.973770i	$-0.426934\pi$
$691$	25.1586	−	43.5759i	0.957077	−	1.65771i	0.729543	−	0.683935i	$-0.239733\pi$
$692$	0.491138			0.0186703
$693$		0			0
$694$	−1.59012			−0.0603601
$695$	2.33009	−	4.03584i	0.0883855	−	0.153088i
$696$		0			0
$697$	−35.3457	−	61.2205i	−1.33881	−	2.31889i
$698$	−1.36716	−	2.36798i	−0.0517476	−	0.0896295i
$699$		0			0
$700$	3.50000	−	6.06218i	0.132288	−	0.229129i
$701$	−45.1672			−1.70594			−0.852970	−	0.521960i	$-0.825201\pi$
$701$	−45.1672			−1.70594			−0.852970	+	0.521960i	$0.825201\pi$
$702$		0			0
$703$	−18.5458			−0.699469
$704$	12.3337	−	21.3625i	0.464842	−	0.805131i
$705$		0			0
$706$	−2.65374	−	4.59642i	−0.0998750	−	0.172989i
$707$	6.39248	+	11.0721i	0.240414	+	0.416409i
$708$		0			0
$709$	−19.8090	+	34.3102i	−0.743944	+	1.28855i	0.206743	+	0.978395i	$0.433714\pi$
$709$	−19.8090	+	34.3102i	−0.743944	+	1.28855i	−0.950687	+	0.310153i	$0.899620\pi$
$710$	2.43147			0.0912514
$711$		0			0
$712$	2.59012			0.0970688
$713$	−4.65103	+	8.05582i	−0.174182	+	0.301693i
$714$		0			0
$715$	2.18878	+	3.79108i	0.0818557	+	0.141778i
$716$	−13.7866	−	23.8791i	−0.515229	−	0.892403i
$717$		0			0
$718$	−0.903436	+	1.56480i	−0.0337159	+	0.0583977i
$719$	22.0377			0.821869			0.410935	−	0.911665i	$-0.365202\pi$
$719$	22.0377			0.821869			0.410935	+	0.911665i	$0.365202\pi$
$720$		0			0
$721$	4.39699			0.163752
$722$	1.82038	−	3.15299i	0.0677475	−	0.117342i
$723$		0			0
$724$	−1.39054	−	2.40849i	−0.0516792	−	0.0895110i
$725$	−0.430782	−	0.746136i	−0.0159988	−	0.0277108i
$726$		0			0
$727$	−14.0555	+	24.3449i	−0.521291	+	0.902903i	0.478402	+	0.878141i	$0.341216\pi$
$727$	−14.0555	+	24.3449i	−0.521291	+	0.902903i	−0.999693	+	0.0247621i	$0.992117\pi$
$728$	0.942820			0.0349432
$729$		0			0
$730$	−4.28152			−0.158466
$731$	−7.72545	+	13.3809i	−0.285736	+	0.494909i
$732$		0			0
$733$	−5.93474	−	10.2793i	−0.219205	−	0.379674i	0.735360	−	0.677676i	$-0.237013\pi$
$733$	−5.93474	−	10.2793i	−0.219205	−	0.379674i	−0.954565	+	0.298003i	$0.903680\pi$
$734$	2.21466	+	3.83590i	0.0817444	+	0.141586i
$735$		0			0
$736$	−7.73461	+	13.3967i	−0.285102	+	0.493810i
$737$	12.9929			0.478598
$738$		0			0
$739$	−12.1844			−0.448212			−0.224106	−	0.974565i	$-0.571946\pi$
$739$	−12.1844			−0.448212			−0.224106	+	0.974565i	$0.571946\pi$
$740$	10.9601	−	18.9834i	0.402900	−	0.697843i
$741$		0			0
$742$	1.38727	+	2.40283i	0.0509285	+	0.0882107i
$743$	−22.2427	−	38.5255i	−0.816005	−	1.41336i	−0.908604	−	0.417659i	$-0.862851\pi$
$743$	−22.2427	−	38.5255i	−0.816005	−	1.41336i	0.0925987	−	0.995704i	$-0.470483\pi$
$744$		0			0
$745$	−6.56634	+	11.3732i	−0.240572	+	0.416683i
$746$	3.74472			0.137104
$747$		0			0
$748$	−49.9579			−1.82664
$749$	−6.86389	+	11.8886i	−0.250801	+	0.434400i
$750$		0			0
$751$	−21.4029	−	37.0709i	−0.781002	−	1.35274i	−0.931358	−	0.364104i	$-0.881375\pi$
$751$	−21.4029	−	37.0709i	−0.781002	−	1.35274i	0.150356	−	0.988632i	$-0.451958\pi$
$752$	10.6666	+	18.4752i	0.388972	+	0.673720i
$753$		0			0
$754$	0.0285900	−	0.0495193i	0.00104119	−	0.00180339i
$755$	−16.4567			−0.598919
$756$		0			0
$757$	−22.4919			−0.817483			−0.408741	−	0.912650i	$-0.634032\pi$
$757$	−22.4919			−0.817483			−0.408741	+	0.912650i	$0.634032\pi$
$758$	−0.482760	+	0.836165i	−0.0175346	+	0.0303709i
$759$		0			0
$760$	−1.08250	−	1.87495i	−0.0392664	−	0.0680114i
$761$	−7.16827	−	12.4158i	−0.259850	−	0.450073i	0.706352	−	0.707861i	$-0.250340\pi$
$761$	−7.16827	−	12.4158i	−0.259850	−	0.450073i	−0.966201	+	0.257788i	$0.917006\pi$
$762$		0			0
$763$	0.631600	−	1.09396i	0.0228655	−	0.0396041i
$764$	29.2736			1.05908
$765$		0			0
$766$	−0.0539104			−0.00194786
$767$	1.30150	−	2.25427i	0.0469946	−	0.0813971i
$768$		0			0
$769$	15.6105	+	27.0382i	0.562930	+	0.975024i	0.997239	+	0.0742597i	$0.0236594\pi$
$769$	15.6105	+	27.0382i	0.562930	+	0.975024i	−0.434309	+	0.900764i	$0.643007\pi$
$770$	−0.523388	−	0.906535i	−0.0188616	−	0.0326693i
$771$		0			0
$772$	−7.62352	+	13.2043i	−0.274376	+	0.475234i
$773$	−4.38005			−0.157539			−0.0787697	−	0.996893i	$-0.525099\pi$
$773$	−4.38005			−0.157539			−0.0787697	+	0.996893i	$0.525099\pi$
$774$		0			0
$775$	−5.98168			−0.214868
$776$	3.37919	−	5.85294i	0.121306	−	0.210108i
$777$		0			0
$778$	3.02051	+	5.23168i	0.108291	+	0.187565i
$779$	−9.89084	−	17.1314i	−0.354376	−	0.613798i
$780$		0			0
$781$	15.9315	−	27.5941i	0.570073	−	0.987395i
$782$	9.30206			0.332641
$783$		0			0
$784$	3.66019			0.130721
$785$	0.0337917	−	0.0585290i	0.00120608	−	0.00208899i
$786$		0			0
$787$	−13.8107	−	23.9208i	−0.492297	−	0.852683i	0.507664	−	0.861555i	$-0.330509\pi$
$787$	−13.8107	−	23.9208i	−0.492297	−	0.852683i	−0.999961	+	0.00887191i	$0.997176\pi$
$788$	−6.49876	−	11.2562i	−0.231509	−	0.400985i
$789$		0			0
$790$	1.04256	−	1.80577i	0.0370926	−	0.0642463i
$791$	12.1625			0.432449
$792$		0			0
$793$	−7.60301			−0.269991
$794$	2.42721	−	4.20406i	0.0861386	−	0.149196i
$795$		0			0
$796$	−19.3695	−	33.5489i	−0.686533	−	1.18911i
$797$	−1.48181	−	2.56658i	−0.0524885	−	0.0909128i	0.838587	−	0.544767i	$-0.183382\pi$
$797$	−1.48181	−	2.56658i	−0.0524885	−	0.0909128i	−0.891076	+	0.453854i	$0.850049\pi$
$798$		0			0
$799$	20.2330	−	35.0445i	0.715791	−	1.23979i
$800$	−9.94747			−0.351696
$801$		0			0
$802$	3.64076			0.128560
$803$	−28.0534	+	48.5898i	−0.989981	+	1.71470i
$804$		0			0
$805$	−3.31122	−	5.73520i	−0.116705	−	0.202139i
$806$	−0.198495	−	0.343803i	−0.00699169	−	0.0121100i
$807$		0			0
$808$	6.02696	−	10.4390i	0.212028	−	0.367242i
$809$	24.7896			0.871556			0.435778	−	0.900054i	$-0.356473\pi$
$809$	24.7896			0.871556			0.435778	+	0.900054i	$0.356473\pi$
$810$		0			0
$811$	8.24377			0.289478			0.144739	−	0.989470i	$-0.453766\pi$
$811$	8.24377			0.289478			0.144739	+	0.989470i	$0.453766\pi$
$812$	0.232287	−	0.402332i	0.00815167	−	0.0141191i
$813$		0			0
$814$	4.22708	+	7.32153i	0.148159	+	0.256619i
$815$	−0.891233	−	1.54366i	−0.0312185	−	0.0540721i
$816$		0			0
$817$	−2.16182	+	3.74439i	−0.0756327	+	0.131000i
$818$	0.396208			0.0138531
$819$		0			0
$820$	23.3808			0.816494
$821$	−14.4497	+	25.0275i	−0.504296	+	0.873467i	0.495691	+	0.868499i	$0.334915\pi$
$821$	−14.4497	+	25.0275i	−0.504296	+	0.873467i	−0.999988	+	0.00496829i	$0.998419\pi$
$822$		0			0
$823$	18.0000	+	31.1769i	0.627441	+	1.08676i	0.988063	+	0.154047i	$0.0492308\pi$
$823$	18.0000	+	31.1769i	0.627441	+	1.08676i	−0.360623	+	0.932712i	$0.617436\pi$
$824$	−2.07279	−	3.59017i	−0.0722089	−	0.125069i
$825$		0			0
$826$	−0.311220	+	0.539049i	−0.0108287	+	0.0187559i
$827$	50.7108			1.76339			0.881694	−	0.471821i	$-0.156403\pi$
$827$	50.7108			1.76339			0.881694	+	0.471821i	$0.156403\pi$
$828$		0			0
$829$	14.8123			0.514452			0.257226	−	0.966351i	$-0.417191\pi$
$829$	14.8123			0.514452			0.257226	+	0.966351i	$0.417191\pi$
$830$	0.981125	−	1.69936i	0.0340554	−	0.0589856i
$831$		0			0
$832$	3.33009	+	5.76789i	0.115450	+	0.199966i
$833$	−3.47141	−	6.01266i	−0.120277	−	0.208326i
$834$		0			0
$835$	8.67799	−	15.0307i	0.300314	−	0.520159i
$836$	−13.9798			−0.483501
$837$		0			0
$838$	−7.98057			−0.275684
$839$	16.8606	−	29.2034i	0.582093	−	1.00821i	−0.413138	−	0.910669i	$-0.635567\pi$
$839$	16.8606	−	29.2034i	0.582093	−	1.00821i	0.995231	−	0.0975464i	$-0.0310994\pi$
$840$		0			0
$841$	14.4714	+	25.0652i	0.499014	+	0.864318i
$842$	−2.18086	−	3.77737i	−0.0751575	−	0.130177i
$843$		0			0
$844$	−17.5744	+	30.4398i	−0.604936	+	1.04778i
$845$	14.1833			0.487921
$846$		0			0
$847$	−2.71737			−0.0933699
$848$	−21.2346	+	36.7794i	−0.729199	+	1.26301i
$849$		0			0
$850$	2.99084	+	5.18029i	0.102585	+	0.177682i
$851$	26.7427	+	46.3197i	0.916728	+	1.58782i
$852$		0			0
$853$	−5.89480	+	10.2101i	−0.201834	+	0.349587i	−0.949119	−	0.314916i	$-0.898024\pi$
$853$	−5.89480	+	10.2101i	−0.201834	+	0.349587i	0.747285	+	0.664503i	$0.231357\pi$
$854$	1.81806			0.0622126
$855$		0			0
$856$	12.9428			0.442376
$857$	−15.6631	+	27.1292i	−0.535040	+	0.926717i	0.464121	+	0.885772i	$0.346370\pi$
$857$	−15.6631	+	27.1292i	−0.535040	+	0.926717i	−0.999161	+	0.0409451i	$0.986963\pi$
$858$		0			0
$859$	25.1947	+	43.6384i	0.859631	+	1.48892i	0.872281	+	0.489005i	$0.162640\pi$
$859$	25.1947	+	43.6384i	0.859631	+	1.48892i	−0.0126501	+	0.999920i	$0.504027\pi$
$860$	−2.55515	−	4.42566i	−0.0871300	−	0.150914i
$861$		0			0
$862$	3.50108	−	6.06405i	0.119247	−	0.206542i
$863$	−1.13268			−0.0385568			−0.0192784	−	0.999814i	$-0.506137\pi$
$863$	−1.13268			−0.0385568			−0.0192784	+	0.999814i	$0.506137\pi$
$864$		0			0
$865$	0.298791			0.0101592
$866$	1.46402	−	2.53575i	0.0497494	−	0.0861684i
$867$		0			0
$868$	−1.61273	−	2.79332i	−0.0547395	−	0.0948115i
$869$	−13.6621	−	23.6635i	−0.463456	−	0.802729i
$870$		0			0
$871$	−1.75404	+	3.03809i	−0.0594334	+	0.102942i
$872$	−1.19097			−0.0403313
$873$		0			0
$874$	2.60301			0.0880481
$875$	5.08414	−	8.80598i	0.171875	−	0.297696i
$876$		0			0
$877$	13.6969	+	23.7237i	0.462510	+	0.801091i	0.999085	−	0.0427615i	$-0.0136156\pi$
$877$	13.6969	+	23.7237i	0.462510	+	0.801091i	−0.536575	+	0.843853i	$0.680282\pi$
$878$	0.577690	+	1.00059i	0.0194961	+	0.0337682i
$879$		0			0
$880$	8.01135	−	13.8761i	0.270063	−	0.467762i
$881$	−1.20929			−0.0407420			−0.0203710	−	0.999792i	$-0.506485\pi$
$881$	−1.20929			−0.0407420			−0.0203710	+	0.999792i	$0.506485\pi$
$882$		0			0
$883$	−51.0884			−1.71926			−0.859631	−	0.510916i	$-0.829306\pi$
$883$	−51.0884			−1.71926			−0.859631	+	0.510916i	$0.829306\pi$
$884$	6.74433	−	11.6815i	0.226836	−	0.392892i
$885$		0			0
$886$	0.148840	+	0.257798i	0.00500038	+	0.00866091i
$887$	−20.7878	−	36.0056i	−0.697987	−	1.20895i	−0.969163	−	0.246419i	$-0.920746\pi$
$887$	−20.7878	−	36.0056i	−0.697987	−	1.20895i	0.271176	−	0.962530i	$-0.412587\pi$
$888$		0			0
$889$	0.669905	−	1.16031i	0.0224679	−	0.0389155i
$890$	0.776443			0.0260264
$891$		0			0
$892$	44.0183			1.47384
$893$	5.66182	−	9.80657i	0.189466	−	0.328164i
$894$		0			0
$895$	−8.38727	−	14.5272i	−0.280356	−	0.485590i
$896$	−3.55718	−	6.16122i	−0.118837	−	0.205832i
$897$		0			0
$898$	1.05555	−	1.82826i	0.0352240	−	0.0610098i
$899$	−0.396990			−0.0132404
$900$		0			0
$901$	80.5576			2.68376
$902$	−4.50877	+	7.80942i	−0.150126	+	0.260025i
$903$		0			0
$904$	−5.73353	−	9.93077i	−0.190694	−	0.330292i
$905$	−0.845958	−	1.46524i	−0.0281206	−	0.0487063i
$906$		0			0
$907$	−17.7255	+	30.7014i	−0.588564	+	1.01942i	0.405857	+	0.913937i	$0.366973\pi$
$907$	−17.7255	+	30.7014i	−0.588564	+	1.01942i	−0.994421	+	0.105486i	$0.966360\pi$
$908$	−10.2632			−0.340596
$909$		0			0
$910$	0.282630			0.00936910
$911$	−10.3554	+	17.9361i	−0.343090	+	0.594250i	−0.985005	−	0.172526i	$-0.944807\pi$
$911$	−10.3554	+	17.9361i	−0.343090	+	0.594250i	0.641915	+	0.766776i	$0.278140\pi$
$912$		0			0
$913$	−12.8571	−	22.2691i	−0.425506	−	0.736998i
$914$	1.25636	+	2.17609i	0.0415568	+	0.0719785i
$915$		0			0
$916$	18.7837	−	32.5343i	0.620631	−	1.07496i
$917$	−4.96690			−0.164021
$918$		0			0
$919$	14.3926			0.474768			0.237384	−	0.971416i	$-0.423710\pi$
$919$	14.3926			0.474768			0.237384	+	0.971416i	$0.423710\pi$
$920$	−3.12188	+	5.40726i	−0.102925	+	0.178272i
$921$		0			0
$922$	2.69630	+	4.67014i	0.0887981	+	0.153803i
$923$	4.30150	+	7.45043i	0.141586	+	0.245234i
$924$		0			0
$925$	−17.1969	+	29.7858i	−0.565429	+	0.979352i
$926$	2.48616			0.0817004
$927$		0			0
$928$	−0.660190			−0.0216718
$929$	−20.8714	+	36.1503i	−0.684769	+	1.18605i	0.288741	+	0.957407i	$0.406763\pi$
$929$	−20.8714	+	36.1503i	−0.684769	+	1.18605i	−0.973509	+	0.228647i	$0.926570\pi$
$930$		0			0
$931$	−0.971410	−	1.68253i	−0.0318367	−	0.0551427i
$932$	16.4951	+	28.5703i	0.540315	+	0.935853i
$933$		0			0
$934$	1.59222	−	2.75780i	0.0520989	−	0.0902379i
$935$	−30.3926			−0.993945
$936$		0			0
$937$	3.17154			0.103610			0.0518048	−	0.998657i	$-0.483503\pi$
$937$	3.17154			0.103610			0.0518048	+	0.998657i	$0.483503\pi$
$938$	0.419432	−	0.726477i	0.0136949	−	0.0237203i
$939$		0			0
$940$	6.69196	+	11.5908i	0.218268	+	0.378050i
$941$	−1.61040	−	2.78930i	−0.0524976	−	0.0909285i	0.838582	−	0.544775i	$-0.183385\pi$
$941$	−1.61040	−	2.78930i	−0.0524976	−	0.0909285i	−0.891080	+	0.453846i	$0.850052\pi$
$942$		0			0
$943$	−28.5248	+	49.4063i	−0.928894	+	1.60889i
$944$	−9.52751			−0.310094
$945$		0			0
$946$	1.97095			0.0640810
$947$	−22.6735	+	39.2716i	−0.736789	+	1.27616i	0.217145	+	0.976139i	$0.430325\pi$
$947$	−22.6735	+	39.2716i	−0.736789	+	1.27616i	−0.953934	+	0.300016i	$0.903008\pi$
$948$		0			0
$949$	−7.57442	−	13.1193i	−0.245876	−	0.425870i
$950$	0.836931	+	1.44961i	0.0271536	+	0.0470315i
$951$		0			0
$952$	−3.27292	+	5.66886i	−0.106076	+	0.183729i
$953$	54.2703			1.75799			0.878994	−	0.476832i	$-0.158215\pi$
$953$	54.2703			1.75799			0.878994	+	0.476832i	$0.158215\pi$
$954$		0			0
$955$	17.8090			0.576287
$956$	−16.4029	+	28.4106i	−0.530507	+	0.918865i
$957$		0			0
$958$	1.73788	+	3.01010i	0.0561483	+	0.0972518i
$959$	2.16991	+	3.75839i	0.0700699	+	0.121365i
$960$		0			0
$961$	14.1219	−	24.4598i	0.455545	−	0.789027i
$962$	−2.28263			−0.0735950
$963$		0			0
$964$	−52.7390			−1.69861
$965$	−4.63788	+	8.03305i	−0.149299	+	0.258593i
$966$		0			0
$967$	−12.8295	−	22.2214i	−0.412570	−	0.714593i	0.582600	−	0.812759i	$-0.302036\pi$
$967$	−12.8295	−	22.2214i	−0.412570	−	0.714593i	−0.995170	+	0.0981667i	$0.968702\pi$
$968$	1.28100	+	2.21875i	0.0411728	+	0.0713133i
$969$		0			0
$970$	1.01298	−	1.75454i	0.0325250	−	0.0563349i
$971$	21.0183			0.674510			0.337255	−	0.941413i	$-0.390502\pi$
$971$	21.0183			0.674510			0.337255	+	0.941413i	$0.390502\pi$
$972$		0			0
$973$	−3.94282			−0.126401
$974$	−1.56075	+	2.70329i	−0.0500096	+	0.0866191i
$975$		0			0
$976$	13.9142	+	24.1002i	0.445384	+	0.771427i
$977$	−1.04910	−	1.81709i	−0.0335637	−	0.0581340i	0.848756	−	0.528785i	$-0.177352\pi$
$977$	−1.04910	−	1.81709i	−0.0335637	−	0.0581340i	−0.882319	+	0.470651i	$0.844019\pi$
$978$		0			0
$979$	5.08740	−	8.81164i	0.162594	−	0.281621i
$980$	2.29630			0.0733527
$981$		0			0
$982$	−4.62571			−0.147612
$983$	21.4962	−	37.2325i	0.685622	−	1.18753i	−0.287620	−	0.957745i	$-0.592864\pi$
$983$	21.4962	−	37.2325i	0.685622	−	1.18753i	0.973241	−	0.229787i	$-0.0738028\pi$
$984$		0			0
$985$	−3.95361	−	6.84786i	−0.125973	−	0.218191i
$986$	0.198495	+	0.343803i	0.00632137	+	0.0109489i
$987$		0			0
$988$	1.88727	−	3.26886i	0.0600422	−	0.103996i
$989$	12.4692			0.396498
$990$		0			0
$991$	−17.2632			−0.548384			−0.274192	−	0.961675i	$-0.588410\pi$
$991$	−17.2632			−0.548384			−0.274192	+	0.961675i	$0.588410\pi$
$992$	−2.29179	+	3.96950i	−0.0727644	+	0.126032i
$993$		0			0
$994$	−1.02859	−	1.78157i	−0.0326249	−	0.0565080i
$995$	−11.7837	−	20.4100i	−0.373569	−	0.647040i
$996$		0			0
$997$	19.4509	−	33.6899i	0.616016	−	1.06697i	−0.374189	−	0.927352i	$-0.622079\pi$
$997$	19.4509	−	33.6899i	0.616016	−	1.06697i	0.990205	−	0.139619i	$-0.0445878\pi$
$998$	−8.66157			−0.274177
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.f.a.127.2		6
3.2	odd	2		63.2.f.b.43.2	yes	6
4.3	odd	2		3024.2.r.g.2017.3		6
7.2	even	3		1323.2.h.d.802.2		6
7.3	odd	6		1323.2.g.b.667.2		6
7.4	even	3		1323.2.g.c.667.2		6
7.5	odd	6		1323.2.h.e.802.2		6
7.6	odd	2		1323.2.f.c.883.2		6
9.2	odd	6		567.2.a.d.1.2		3
9.4	even	3	inner	189.2.f.a.64.2		6
9.5	odd	6		63.2.f.b.22.2	✓	6
9.7	even	3		567.2.a.g.1.2		3
12.11	even	2		1008.2.r.k.673.2		6
21.2	odd	6		441.2.h.c.214.2		6
21.5	even	6		441.2.h.b.214.2		6
21.11	odd	6		441.2.g.e.79.2		6
21.17	even	6		441.2.g.d.79.2		6
21.20	even	2		441.2.f.d.295.2		6
36.7	odd	6		9072.2.a.cd.1.1		3
36.11	even	6		9072.2.a.bq.1.3		3
36.23	even	6		1008.2.r.k.337.2		6
36.31	odd	6		3024.2.r.g.1009.3		6
63.4	even	3		1323.2.h.d.226.2		6
63.5	even	6		441.2.g.d.67.2		6
63.13	odd	6		1323.2.f.c.442.2		6
63.20	even	6		3969.2.a.m.1.2		3
63.23	odd	6		441.2.g.e.67.2		6
63.31	odd	6		1323.2.h.e.226.2		6
63.32	odd	6		441.2.h.c.373.2		6
63.34	odd	6		3969.2.a.p.1.2		3
63.40	odd	6		1323.2.g.b.361.2		6
63.41	even	6		441.2.f.d.148.2		6
63.58	even	3		1323.2.g.c.361.2		6
63.59	even	6		441.2.h.b.373.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.b.22.2	✓	6	9.5	odd	6
63.2.f.b.43.2	yes	6	3.2	odd	2
189.2.f.a.64.2		6	9.4	even	3	inner
189.2.f.a.127.2		6	1.1	even	1	trivial
441.2.f.d.148.2		6	63.41	even	6
441.2.f.d.295.2		6	21.20	even	2
441.2.g.d.67.2		6	63.5	even	6
441.2.g.d.79.2		6	21.17	even	6
441.2.g.e.67.2		6	63.23	odd	6
441.2.g.e.79.2		6	21.11	odd	6
441.2.h.b.214.2		6	21.5	even	6
441.2.h.b.373.2		6	63.59	even	6
441.2.h.c.214.2		6	21.2	odd	6
441.2.h.c.373.2		6	63.32	odd	6
567.2.a.d.1.2		3	9.2	odd	6
567.2.a.g.1.2		3	9.7	even	3
1008.2.r.k.337.2		6	36.23	even	6
1008.2.r.k.673.2		6	12.11	even	2
1323.2.f.c.442.2		6	63.13	odd	6
1323.2.f.c.883.2		6	7.6	odd	2
1323.2.g.b.361.2		6	63.40	odd	6
1323.2.g.b.667.2		6	7.3	odd	6
1323.2.g.c.361.2		6	63.58	even	3
1323.2.g.c.667.2		6	7.4	even	3
1323.2.h.d.226.2		6	63.4	even	3
1323.2.h.d.802.2		6	7.2	even	3
1323.2.h.e.226.2		6	63.31	odd	6
1323.2.h.e.802.2		6	7.5	odd	6
3024.2.r.g.1009.3		6	36.31	odd	6
3024.2.r.g.2017.3		6	4.3	odd	2
3969.2.a.m.1.2		3	63.20	even	6
3969.2.a.p.1.2		3	63.34	odd	6
9072.2.a.bq.1.3		3	36.11	even	6
9072.2.a.cd.1.1		3	36.7	odd	6

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.119562 + 0.207087i) q^{2} +(0.971410 + 1.68253i) q^{4} +(0.590972 + 1.02359i) q^{5} +(0.500000 - 0.866025i) q^{7} -0.942820 q^{8} -0.282630 q^{10} +(-1.85185 + 3.20750i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(0.119562 + 0.207087i) q^{14} +(-1.83009 + 3.16982i) q^{16} +6.94282 q^{17} +1.94282 q^{19} +(-1.14815 + 1.98866i) q^{20} +(-0.442820 - 0.766987i) q^{22} +(-2.80150 - 4.85235i) q^{23} +(1.80150 - 3.12030i) q^{25} +0.239123 q^{26} +1.94282 q^{28} +(0.119562 - 0.207087i) q^{29} +(-0.830095 - 1.43777i) q^{31} +(-1.38044 - 2.39099i) q^{32} +(-0.830095 + 1.43777i) q^{34} +1.18194 q^{35} -9.54583 q^{37} +(-0.232287 + 0.402332i) q^{38} +(-0.557180 - 0.965064i) q^{40} +(-5.09097 - 8.81782i) q^{41} +(-1.11273 + 1.92730i) q^{43} -7.19562 q^{44} +1.33981 q^{46} +(2.91423 - 5.04759i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(0.430782 + 0.746136i) q^{50} +(0.971410 - 1.68253i) q^{52} +11.6030 q^{53} -4.37756 q^{55} +(-0.471410 + 0.816506i) q^{56} +(0.0285900 + 0.0495193i) q^{58} +(1.30150 + 2.25427i) q^{59} +(3.80150 - 6.58440i) q^{61} +0.396990 q^{62} -6.66019 q^{64} +(0.590972 - 1.02359i) q^{65} +(-1.75404 - 3.03809i) q^{67} +(6.74433 + 11.6815i) q^{68} +(-0.141315 + 0.244765i) q^{70} -8.60301 q^{71} +15.1488 q^{73} +(1.14132 - 1.97682i) q^{74} +(1.88727 + 3.26886i) q^{76} +(1.85185 + 3.20750i) q^{77} +(-3.68878 + 6.38915i) q^{79} -4.32614 q^{80} +2.43474 q^{82} +(-3.47141 + 6.01266i) q^{83} +(4.10301 + 7.10662i) q^{85} +(-0.266078 - 0.460861i) q^{86} +(1.74596 - 3.02409i) q^{88} -2.74720 q^{89} -1.00000 q^{91} +(5.44282 - 9.42724i) q^{92} +(0.696860 + 1.20700i) q^{94} +(1.14815 + 1.98866i) q^{95} +(-3.58414 + 6.20790i) q^{97} +0.239123 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 3 q^{4} - 5 q^{5} + 3 q^{7} + 12 q^{8} - 2 q^{11} - 3 q^{13} + q^{14} - 3 q^{16} + 24 q^{17} - 6 q^{19} - 16 q^{20} + 15 q^{22} - 6 q^{25} + 2 q^{26} - 6 q^{28} + q^{29} + 3 q^{31} - 8 q^{32}+ \cdots + 2 q^{98}+O(q^{100}) \) 6 * q - q^2 - 3 * q^4 - 5 * q^5 + 3 * q^7 + 12 * q^8 - 2 * q^11 - 3 * q^13 + q^14 - 3 * q^16 + 24 * q^17 - 6 * q^19 - 16 * q^20 + 15 * q^22 - 6 * q^25 + 2 * q^26 - 6 * q^28 + q^29 + 3 * q^31 - 8 * q^32 + 3 * q^34 - 10 * q^35 - 6 * q^37 + 8 * q^38 - 21 * q^40 - 22 * q^41 + 3 * q^43 - 46 * q^44 + 24 * q^46 - 9 * q^47 - 3 * q^49 + 10 * q^50 - 3 * q^52 + 36 * q^53 - 12 * q^55 + 6 * q^56 + 9 * q^58 - 9 * q^59 + 6 * q^61 + 36 * q^62 - 24 * q^64 - 5 * q^65 + 6 * q^68 - 18 * q^71 + 6 * q^73 + 6 * q^74 + 21 * q^76 + 2 * q^77 - 15 * q^79 - 22 * q^80 + 18 * q^82 - 12 * q^83 - 9 * q^85 + 34 * q^86 + 21 * q^88 + 4 * q^89 - 6 * q^91 + 15 * q^92 - 24 * q^94 + 16 * q^95 - 3 * q^97 + 2 * q^98

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