LMFDB - Embedded newform 486.2.g.b.73.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [486,2,Mod(19,486)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(486, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([52]))

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

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

chi := DirichletCharacter("486.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 486 = 2 \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	486.g (of order $27$, degree $18$, 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:	$3.88072953823$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$5$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 162)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			73.3
Character	$\chi$	$=$	486.73
Dual form			486.2.g.b.253.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.893633 + 0.448799i) q^{2} +(0.597159 - 0.802123i) q^{4} +(0.379535 - 1.26773i) q^{5} +(-0.768169 + 1.78082i) q^{7} +(-0.173648 + 0.984808i) q^{8} +(0.229793 + 1.30322i) q^{10} +(2.10911 + 0.499867i) q^{11} +(-1.69934 + 1.11767i) q^{13} +(-0.112768 - 1.93615i) q^{14} +(-0.286803 - 0.957990i) q^{16} +(7.02180 + 2.55572i) q^{17} +(2.13356 - 0.776551i) q^{19} +(-0.790236 - 1.06147i) q^{20} +(-2.10911 + 0.499867i) q^{22} +(-1.34938 - 3.12822i) q^{23} +(2.71434 + 1.78525i) q^{25} +(1.01697 - 1.76145i) q^{26} +(0.969715 + 1.67960i) q^{28} +(0.282496 - 4.85027i) q^{29} +(5.07563 + 0.593256i) q^{31} +(0.686242 + 0.727374i) q^{32} +(-7.42191 + 0.867497i) q^{34} +(1.96605 + 1.64972i) q^{35} +(4.70814 - 3.95060i) q^{37} +(-1.55810 + 1.65149i) q^{38} +(1.18257 + 0.593908i) q^{40} +(6.98634 + 3.50867i) q^{41} +(-4.77609 + 5.06236i) q^{43} +(1.66043 - 1.39326i) q^{44} +(2.60979 + 2.18988i) q^{46} +(-4.18562 + 0.489229i) q^{47} +(2.22247 + 2.35568i) q^{49} +(-3.22684 - 0.377163i) q^{50} +(-0.118264 + 2.03051i) q^{52} +(5.39818 + 9.34993i) q^{53} +(1.43418 - 2.48407i) q^{55} +(-1.62037 - 1.06573i) q^{56} +(1.92435 + 4.46115i) q^{58} +(-6.72062 + 1.59282i) q^{59} +(-5.37986 - 7.22641i) q^{61} +(-4.80200 + 1.74779i) q^{62} +(-0.939693 - 0.342020i) q^{64} +(0.771954 + 2.57851i) q^{65} +(0.661912 + 11.3646i) q^{67} +(6.24313 - 4.10617i) q^{68} +(-2.49732 - 0.591876i) q^{70} +(-0.518333 - 2.93961i) q^{71} +(1.80390 - 10.2304i) q^{73} +(-2.43432 + 5.64339i) q^{74} +(0.651182 - 2.17510i) q^{76} +(-2.51032 + 3.37195i) q^{77} +(9.16461 - 4.60264i) q^{79} -1.32333 q^{80} -7.81791 q^{82} +(-3.24547 + 1.62994i) q^{83} +(5.90499 - 7.93178i) q^{85} +(1.99609 - 6.66740i) q^{86} +(-0.858516 + 1.99026i) q^{88} +(-1.42927 + 8.10577i) q^{89} +(-0.684990 - 3.88477i) q^{91} +(-3.31501 - 0.785672i) q^{92} +(3.52084 - 2.31569i) q^{94} +(-0.174701 - 2.99951i) q^{95} +(-2.30761 - 7.70796i) q^{97} +(-3.04330 - 1.10767i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 18 q^{13} + 9 q^{20} - 27 q^{23} - 18 q^{25} + 27 q^{26} - 18 q^{28} + 27 q^{29} + 54 q^{31} + 27 q^{35} + 18 q^{38} + 9 q^{41} - 36 q^{43} + 18 q^{46} + 27 q^{47} + 36 q^{52} + 27 q^{53} - 54 q^{55}+ \cdots - 36 q^{98}+O(q^{100}) $ 90 * q - 18 * q^13 + 9 * q^20 - 27 * q^23 - 18 * q^25 + 27 * q^26 - 18 * q^28 + 27 * q^29 + 54 * q^31 + 27 * q^35 + 18 * q^38 + 9 * q^41 - 36 * q^43 + 18 * q^46 + 27 * q^47 + 36 * q^52 + 27 * q^53 - 54 * q^55 - 9 * q^58 + 45 * q^59 - 9 * q^65 + 81 * q^67 - 36 * q^68 - 72 * q^70 - 72 * q^71 - 36 * q^73 - 45 * q^74 - 18 * q^76 - 144 * q^77 - 99 * q^79 - 18 * q^80 + 72 * q^82 - 45 * q^83 - 117 * q^85 - 72 * q^86 - 18 * q^88 - 45 * q^89 - 63 * q^91 - 36 * q^92 - 72 * q^94 - 45 * q^95 + 117 * q^97 - 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/486\mathbb{Z}\right)^\times$.

$n$	$245$
$\chi(n)$	$e\left(\frac{23}{27}\right)$

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 $

$2$	−0.893633	+	0.448799i	−0.631894	+	0.317349i
$2$	−0.893633	+	0.448799i	−0.631894	+	0.317349i
$3$		0			0
$3$		0			0
$4$	0.597159	−	0.802123i	0.298579	−	0.401062i
$5$	0.379535	−	1.26773i	0.169733	−	0.566948i	−0.830222	−	0.557433i	$-0.811786\pi$
$5$	0.379535	−	1.26773i	0.169733	−	0.566948i	0.999955	−	0.00951452i	$-0.00302861\pi$
$6$		0			0
$7$	−0.768169	+	1.78082i	−0.290341	+	0.673085i	−0.999489	−	0.0319744i	$-0.989821\pi$
$7$	−0.768169	+	1.78082i	−0.290341	+	0.673085i	0.709148	+	0.705060i	$0.249080\pi$
$8$	−0.173648	+	0.984808i	−0.0613939	+	0.348182i
$9$		0			0
$10$	0.229793	+	1.30322i	0.0726671	+	0.412115i
$11$	2.10911	+	0.499867i	0.635919	+	0.150716i	0.535916	−	0.844271i	$-0.319966\pi$
$11$	2.10911	+	0.499867i	0.635919	+	0.150716i	0.100004	+	0.994987i	$0.468115\pi$
$12$		0			0
$13$	−1.69934	+	1.11767i	−0.471312	+	0.309987i	−0.762854	−	0.646571i	$-0.776202\pi$
$13$	−1.69934	+	1.11767i	−0.471312	+	0.309987i	0.291541	+	0.956558i	$0.405832\pi$
$14$	−0.112768	−	1.93615i	−0.0301385	−	0.517458i
$15$		0			0
$16$	−0.286803	−	0.957990i	−0.0717008	−	0.239497i
$17$	7.02180	+	2.55572i	1.70304	+	0.619854i	0.996165	−	0.0874893i	$-0.0278843\pi$
$17$	7.02180	+	2.55572i	1.70304	+	0.619854i	0.706870	+	0.707343i	$0.250107\pi$
$18$		0			0
$19$	2.13356	−	0.776551i	0.489471	−	0.178153i	−0.0854813	−	0.996340i	$-0.527243\pi$
$19$	2.13356	−	0.776551i	0.489471	−	0.178153i	0.574952	+	0.818187i	$0.305021\pi$
$20$	−0.790236	−	1.06147i	−0.176702	−	0.237352i
$21$		0			0
$22$	−2.10911	+	0.499867i	−0.449663	+	0.106572i
$23$	−1.34938	−	3.12822i	−0.281366	−	0.652279i	0.717661	−	0.696393i	$-0.245213\pi$
$23$	−1.34938	−	3.12822i	−0.281366	−	0.652279i	−0.999027	+	0.0441139i	$0.985954\pi$
$24$		0			0
$25$	2.71434	+	1.78525i	0.542867	+	0.357049i
$26$	1.01697	−	1.76145i	0.199445	−	0.345449i
$27$		0			0
$28$	0.969715	+	1.67960i	0.183259	+	0.317414i
$29$	0.282496	−	4.85027i	0.0524582	−	0.900673i	−0.864735	−	0.502229i	$-0.832513\pi$
$29$	0.282496	−	4.85027i	0.0524582	−	0.900673i	0.917193	−	0.398444i	$-0.130450\pi$
$30$		0			0
$31$	5.07563	+	0.593256i	0.911610	+	0.106552i	0.558952	−	0.829200i	$-0.311204\pi$
$31$	5.07563	+	0.593256i	0.911610	+	0.106552i	0.352658	+	0.935752i	$0.385278\pi$
$32$	0.686242	+	0.727374i	0.121312	+	0.128583i
$33$		0			0
$34$	−7.42191	+	0.867497i	−1.27285	+	0.148775i
$35$	1.96605	+	1.64972i	0.332324	+	0.278853i
$36$		0			0
$37$	4.70814	−	3.95060i	0.774013	−	0.649474i	−0.167720	−	0.985835i	$-0.553640\pi$
$37$	4.70814	−	3.95060i	0.774013	−	0.649474i	0.941733	+	0.336360i	$0.109196\pi$
$38$	−1.55810	+	1.65149i	−0.252757	+	0.267907i
$39$		0			0
$40$	1.18257	+	0.593908i	0.186981	+	0.0939052i
$41$	6.98634	+	3.50867i	1.09108	+	0.547962i	0.901006	−	0.433807i	$-0.142830\pi$
$41$	6.98634	+	3.50867i	1.09108	+	0.547962i	0.190077	+	0.981769i	$0.439126\pi$
$42$		0			0
$43$	−4.77609	+	5.06236i	−0.728347	+	0.772003i	−0.980676	−	0.195639i	$-0.937322\pi$
$43$	−4.77609	+	5.06236i	−0.728347	+	0.772003i	0.252329	+	0.967641i	$0.418803\pi$
$44$	1.66043	−	1.39326i	0.250319	−	0.210042i
$45$		0			0
$46$	2.60979	+	2.18988i	0.384793	+	0.322880i
$47$	−4.18562	+	0.489229i	−0.610535	+	0.0713614i	−0.415741	−	0.909483i	$-0.636478\pi$
$47$	−4.18562	+	0.489229i	−0.610535	+	0.0713614i	−0.194794	+	0.980844i	$0.562404\pi$
$48$		0			0
$49$	2.22247	+	2.35568i	0.317496	+	0.336526i
$50$	−3.22684	−	0.377163i	−0.456344	−	0.0533389i
$51$		0			0
$52$	−0.118264	+	2.03051i	−0.0164002	+	0.281581i
$53$	5.39818	+	9.34993i	0.741497	+	1.28431i	0.951813	+	0.306678i	$0.0992174\pi$
$53$	5.39818	+	9.34993i	0.741497	+	1.28431i	−0.210316	+	0.977633i	$0.567449\pi$
$54$		0			0
$55$	1.43418	−	2.48407i	0.193384	−	0.334952i
$56$	−1.62037	−	1.06573i	−0.216531	−	0.142415i
$57$		0			0
$58$	1.92435	+	4.46115i	0.252680	+	0.585777i
$59$	−6.72062	+	1.59282i	−0.874950	+	0.207367i	−0.643469	−	0.765472i	$-0.722505\pi$
$59$	−6.72062	+	1.59282i	−0.874950	+	0.207367i	−0.231481	+	0.972839i	$0.574357\pi$
$60$		0			0
$61$	−5.37986	−	7.22641i	−0.688820	−	0.925246i	0.310862	−	0.950455i	$-0.399382\pi$
$61$	−5.37986	−	7.22641i	−0.688820	−	0.925246i	−0.999682	+	0.0252087i	$0.991975\pi$
$62$	−4.80200	+	1.74779i	−0.609855	+	0.221969i
$63$		0			0
$64$	−0.939693	−	0.342020i	−0.117462	−	0.0427525i
$65$	0.771954	+	2.57851i	0.0957491	+	0.319824i
$66$		0			0
$67$	0.661912	+	11.3646i	0.0808654	+	1.38841i	0.757860	+	0.652417i	$0.226245\pi$
$67$	0.661912	+	11.3646i	0.0808654	+	1.38841i	−0.676994	+	0.735988i	$0.736718\pi$
$68$	6.24313	−	4.10617i	0.757091	−	0.497946i
$69$		0			0
$70$	−2.49732	−	0.591876i	−0.298487	−	0.0707427i
$71$	−0.518333	−	2.93961i	−0.0615148	−	0.348868i	−0.999994	−	0.00353124i	$-0.998876\pi$
$71$	−0.518333	−	2.93961i	−0.0615148	−	0.348868i	0.938479	−	0.345336i	$-0.112235\pi$
$72$		0			0
$73$	1.80390	−	10.2304i	0.211131	−	1.19738i	−0.676365	−	0.736567i	$-0.736446\pi$
$73$	1.80390	−	10.2304i	0.211131	−	1.19738i	0.887496	−	0.460816i	$-0.152443\pi$
$74$	−2.43432	+	5.64339i	−0.282984	+	0.656031i
$75$		0			0
$76$	0.651182	−	2.17510i	0.0746956	−	0.249501i
$77$	−2.51032	+	3.37195i	−0.286078	+	0.384269i
$78$		0			0
$79$	9.16461	−	4.60264i	1.03110	−	0.517837i	0.148968	−	0.988842i	$-0.452405\pi$
$79$	9.16461	−	4.60264i	1.03110	−	0.517837i	0.882131	+	0.471005i	$0.156108\pi$
$80$	−1.32333			−0.147953
$81$		0			0
$82$	−7.81791			−0.863344
$83$	−3.24547	+	1.62994i	−0.356237	+	0.178909i	−0.617912	−	0.786247i	$-0.712021\pi$
$83$	−3.24547	+	1.62994i	−0.356237	+	0.178909i	0.261675	+	0.965156i	$0.415725\pi$
$84$		0			0
$85$	5.90499	−	7.93178i	0.640486	−	0.860323i
$86$	1.99609	−	6.66740i	0.215244	−	0.718964i
$87$		0			0
$88$	−0.858516	+	1.99026i	−0.0915181	+	0.212163i
$89$	−1.42927	+	8.10577i	−0.151502	+	0.859210i	0.810413	+	0.585860i	$0.199243\pi$
$89$	−1.42927	+	8.10577i	−0.151502	+	0.859210i	−0.961915	+	0.273350i	$0.911868\pi$
$90$		0			0
$91$	−0.684990	−	3.88477i	−0.0718065	−	0.407235i
$92$	−3.31501	−	0.785672i	−0.345614	−	0.0819120i
$93$		0			0
$94$	3.52084	−	2.31569i	0.363147	−	0.238846i
$95$	−0.174701	−	2.99951i	−0.0179240	−	0.307743i
$96$		0			0
$97$	−2.30761	−	7.70796i	−0.234302	−	0.782624i	−0.991576	−	0.129527i	$-0.958654\pi$
$97$	−2.30761	−	7.70796i	−0.234302	−	0.782624i	0.757274	−	0.653098i	$-0.226531\pi$
$98$	−3.04330	−	1.10767i	−0.307420	−	0.111892i
$99$		0			0
$100$	3.05288	−	1.11116i	0.305288	−	0.111116i
$101$	−11.1155	−	14.9307i	−1.10603	−	1.48566i	−0.855678	−	0.517509i	$-0.826859\pi$
$101$	−11.1155	−	14.9307i	−1.10603	−	1.48566i	−0.250357	−	0.968153i	$-0.580548\pi$
$102$		0			0
$103$	−17.5969	+	4.17055i	−1.73388	+	0.410937i	−0.971660	−	0.236383i	$-0.924038\pi$
$103$	−17.5969	+	4.17055i	−1.73388	+	0.410937i	−0.762218	+	0.647320i	$0.775890\pi$
$104$	−0.805606	−	1.86761i	−0.0789962	−	0.183134i
$105$		0			0
$106$	−9.02023	−	5.93270i	−0.876122	−	0.576235i
$107$	−2.04335	+	3.53919i	−0.197538	+	0.342146i	−0.947730	−	0.319075i	$-0.896628\pi$
$107$	−2.04335	+	3.53919i	−0.197538	+	0.342146i	0.750192	+	0.661221i	$0.229961\pi$
$108$		0			0
$109$	−6.16219	−	10.6732i	−0.590231	−	1.02231i	−0.994201	−	0.107538i	$-0.965703\pi$
$109$	−6.16219	−	10.6732i	−0.590231	−	1.02231i	0.403970	−	0.914772i	$-0.367630\pi$
$110$	−0.166780	+	2.86350i	−0.0159019	+	0.273024i
$111$		0			0
$112$	1.92632	+	0.225154i	0.182020	+	0.0212751i
$113$	−10.6469	−	11.2851i	−1.00158	−	1.06161i	−0.998100	−	0.0616189i	$-0.980374\pi$
$113$	−10.6469	−	11.2851i	−1.00158	−	1.06161i	−0.00348030	−	0.999994i	$-0.501108\pi$
$114$		0			0
$115$	−4.47789	+	0.523390i	−0.417565	+	0.0488064i
$116$	−3.72182	−	3.12298i	−0.345562	−	0.289961i
$117$		0			0
$118$	5.29091	−	4.43960i	0.487068	−	0.408698i
$119$	−9.94520	+	10.5413i	−0.911675	+	0.966319i
$120$		0			0
$121$	−5.63150	−	2.82824i	−0.511954	−	0.257113i
$122$	8.05082	+	4.04328i	0.728887	+	0.366061i
$123$		0			0
$124$	3.50682	−	3.71701i	0.314922	−	0.333798i
$125$	8.36204	−	7.01659i	0.747924	−	0.627583i
$126$		0			0
$127$	13.4767	+	11.3083i	1.19586	+	1.00345i	0.999739	+	0.0228661i	$0.00727913\pi$
$127$	13.4767	+	11.3083i	1.19586	+	1.00345i	0.196121	+	0.980580i	$0.437165\pi$
$128$	0.993238	−	0.116093i	0.0877907	−	0.0102613i
$129$		0			0
$130$	−1.84708	−	1.95779i	−0.161999	−	0.171709i
$131$	4.78234	+	0.558975i	0.417835	+	0.0488379i	0.322413	−	0.946599i	$-0.395506\pi$
$131$	4.78234	+	0.558975i	0.417835	+	0.0488379i	0.0954217	+	0.995437i	$0.469580\pi$
$132$		0			0
$133$	−0.256037	+	4.39599i	−0.0222013	+	0.381181i
$134$	−5.69192	−	9.85870i	−0.491707	−	0.851662i
$135$		0			0
$136$	−3.73622	+	6.47132i	−0.320378	+	0.554911i
$137$	−0.519408	−	0.341620i	−0.0443760	−	0.0291866i	0.527127	−	0.849786i	$-0.323269\pi$
$137$	−0.519408	−	0.341620i	−0.0443760	−	0.0291866i	−0.571503	+	0.820600i	$0.693640\pi$
$138$		0			0
$139$	1.16974	+	2.71177i	0.0992164	+	0.230010i	0.960594	−	0.277956i	$-0.0896570\pi$
$139$	1.16974	+	2.71177i	0.0992164	+	0.230010i	−0.861377	+	0.507966i	$0.830398\pi$
$140$	2.49732	−	0.591876i	0.211062	−	0.0500227i
$141$		0			0
$142$	1.78249	+	2.39430i	0.149584	+	0.200926i
$143$	−4.14278	+	1.50785i	−0.346436	+	0.126093i
$144$		0			0
$145$	−6.04164	−	2.19898i	−0.501731	−	0.182615i
$146$	2.97939	+	9.95185i	0.246576	+	0.823621i
$147$		0			0
$148$	−0.357360	−	6.13564i	−0.0293748	−	0.504347i
$149$	1.10328	−	0.725642i	0.0903846	−	0.0594469i	−0.503512	−	0.863988i	$-0.667959\pi$
$149$	1.10328	−	0.725642i	0.0903846	−	0.0594469i	0.593897	+	0.804541i	$0.297589\pi$
$150$		0			0
$151$	−1.68015	−	0.398202i	−0.136728	−	0.0324052i	0.161682	−	0.986843i	$-0.448308\pi$
$151$	−1.68015	−	0.398202i	−0.136728	−	0.0324052i	−0.298410	+	0.954438i	$0.596456\pi$
$152$	0.394265	+	2.23599i	0.0319791	+	0.181363i
$153$		0			0
$154$	0.729978	−	4.13991i	0.0588233	−	0.333604i
$155$	2.67847	−	6.20939i	0.215140	−	0.498750i
$156$		0			0
$157$	−3.15286	+	10.5313i	−0.251625	+	0.840487i	0.735082	+	0.677979i	$0.237144\pi$
$157$	−3.15286	+	10.5313i	−0.251625	+	0.840487i	−0.986707	+	0.162509i	$0.948041\pi$
$158$	−6.12413	+	8.22614i	−0.487210	+	0.654436i
$159$		0			0
$160$	1.18257	−	0.593908i	0.0934903	−	0.0469526i
$161$	6.60734			0.520731
$162$		0			0
$163$	−18.8589			−1.47714			−0.738570	−	0.674177i	$-0.764498\pi$
$163$	−18.8589			−1.47714			−0.738570	+	0.674177i	$0.764498\pi$
$164$	6.98634	−	3.50867i	0.545541	−	0.273981i
$165$		0			0
$166$	2.16874	−	2.91313i	0.168327	−	0.226103i
$167$	2.91724	−	9.74426i	0.225743	−	0.754033i	−0.767812	−	0.640676i	$-0.778654\pi$
$167$	2.91724	−	9.74426i	0.225743	−	0.754033i	0.993554	−	0.113357i	$-0.0361605\pi$
$168$		0			0
$169$	−3.51047	+	8.13820i	−0.270037	+	0.626015i
$170$	−1.71712	+	9.73826i	−0.131697	+	0.746890i
$171$		0			0
$172$	1.20855	+	6.85404i	0.0921513	+	0.522616i
$173$	18.1978	+	4.31295i	1.38355	+	0.327908i	0.853957	−	0.520344i	$-0.174196\pi$
$173$	18.1978	+	4.31295i	1.38355	+	0.327908i	0.529594	+	0.848251i	$0.322344\pi$
$174$		0			0
$175$	−5.26427	+	3.46236i	−0.397941	+	0.261730i
$176$	−0.126031	−	2.16386i	−0.00949993	−	0.163107i
$177$		0			0
$178$	−2.36062	−	7.88504i	−0.176936	−	0.591008i
$179$	−16.1486	−	5.87760i	−1.20700	−	0.439312i	−0.341338	−	0.939941i	$-0.610880\pi$
$179$	−16.1486	−	5.87760i	−1.20700	−	0.439312i	−0.865662	+	0.500628i	$0.833102\pi$
$180$		0			0
$181$	−21.3524	+	7.77164i	−1.58711	+	0.577661i	−0.976735	−	0.214450i	$-0.931204\pi$
$181$	−21.3524	+	7.77164i	−1.58711	+	0.577661i	−0.610376	+	0.792112i	$0.708982\pi$
$182$	2.35561	+	3.16414i	0.174610	+	0.234541i
$183$		0			0
$184$	3.31501	−	0.785672i	0.244386	−	0.0579205i
$185$	−3.22141	−	7.46806i	−0.236842	−	0.549062i
$186$		0			0
$187$	13.5322	+	8.90026i	0.989571	+	0.650851i
$188$	−2.10706	+	3.64953i	−0.153673	+	0.266169i
$189$		0			0
$190$	1.50230	+	2.60205i	0.108988	+	0.188773i
$191$	0.341122	−	5.85684i	0.0246827	−	0.423786i	−0.963220	−	0.268713i	$-0.913402\pi$
$191$	0.341122	−	5.85684i	0.0246827	−	0.423786i	0.987903	−	0.155073i	$-0.0495613\pi$
$192$		0			0
$193$	11.7776	+	1.37661i	0.847771	+	0.0990903i	0.528875	−	0.848699i	$-0.322614\pi$
$193$	11.7776	+	1.37661i	0.847771	+	0.0990903i	0.318896	+	0.947790i	$0.396688\pi$
$194$	5.52148	+	5.85243i	0.396419	+	0.420180i
$195$		0			0
$196$	3.21671	−	0.375980i	0.229765	−	0.0268557i
$197$	−2.29618	−	1.92672i	−0.163596	−	0.137273i	0.557315	−	0.830301i	$-0.311832\pi$
$197$	−2.29618	−	1.92672i	−0.163596	−	0.137273i	−0.720911	+	0.693028i	$0.756276\pi$
$198$		0			0
$199$	15.4208	−	12.9396i	1.09315	−	0.917261i	0.0962034	−	0.995362i	$-0.469330\pi$
$199$	15.4208	−	12.9396i	1.09315	−	0.917261i	0.996945	+	0.0781009i	$0.0248856\pi$
$200$	−2.22946	+	2.36309i	−0.157647	+	0.167096i
$201$		0			0
$202$	16.6341	+	8.35395i	1.17037	+	0.587782i
$203$	8.42044	+	4.22890i	0.590999	+	0.296811i
$204$		0			0
$205$	7.09962	−	7.52516i	0.495859	−	0.525580i
$206$	13.8535	−	11.6244i	0.965216	−	0.809913i
$207$		0			0
$208$	1.55810	+	1.30740i	0.108034	+	0.0906517i
$209$	4.88807	−	0.571333i	0.338115	−	0.0395199i
$210$		0			0
$211$	−9.85383	−	10.4445i	−0.678366	−	0.719026i	0.293133	−	0.956072i	$-0.405302\pi$
$211$	−9.85383	−	10.4445i	−0.678366	−	0.719026i	−0.971498	+	0.237046i	$0.923821\pi$
$212$	10.7234	+	1.25338i	0.736484	+	0.0860826i
$213$		0			0
$214$	0.237620	−	4.07979i	0.0162434	−	0.278888i
$215$	4.60503	+	7.97615i	0.314061	+	0.543969i
$216$		0			0
$217$	−4.95542	+	8.58304i	−0.336396	+	0.582655i
$218$	10.2969	+	6.77236i	0.697392	+	0.458682i
$219$		0			0
$220$	−1.13610	−	2.63377i	−0.0765957	−	0.177569i
$221$	−14.7889	+	3.50503i	−0.994808	+	0.235774i
$222$		0			0
$223$	6.68444	+	8.97876i	0.447623	+	0.601262i	0.967466	−	0.252999i	$-0.0814171\pi$
$223$	6.68444	+	8.97876i	0.447623	+	0.601262i	−0.519843	+	0.854262i	$0.674010\pi$
$224$	−1.82247	+	0.663324i	−0.121769	+	0.0443202i
$225$		0			0
$226$	14.5792	+	5.30639i	0.969794	+	0.352976i
$227$	4.56463	+	15.2469i	0.302965	+	1.01197i	0.964945	+	0.262453i	$0.0845314\pi$
$227$	4.56463	+	15.2469i	0.302965	+	1.01197i	−0.661980	+	0.749522i	$0.730283\pi$
$228$		0			0
$229$	0.625990	+	10.7478i	0.0413666	+	0.710236i	0.953695	+	0.300776i	$0.0972458\pi$
$229$	0.625990	+	10.7478i	0.0413666	+	0.710236i	−0.912328	+	0.409460i	$0.865717\pi$
$230$	3.76669	−	2.47739i	0.248368	−	0.163354i
$231$		0			0
$232$	4.72753	+	1.12045i	0.310378	+	0.0735608i
$233$	−2.99957	−	17.0114i	−0.196508	−	1.11445i	−0.910254	−	0.414050i	$-0.864114\pi$
$233$	−2.99957	−	17.0114i	−0.196508	−	1.11445i	0.713746	−	0.700405i	$-0.246997\pi$
$234$		0			0
$235$	−0.968376	+	5.49193i	−0.0631699	+	0.358254i
$236$	−2.73564	+	6.34193i	−0.178075	+	0.412824i
$237$		0			0
$238$	4.15643	−	13.8834i	0.269421	−	0.899930i
$239$	−14.5713	+	19.5727i	−0.942540	+	1.26605i	0.0213560	+	0.999772i	$0.493202\pi$
$239$	−14.5713	+	19.5727i	−0.942540	+	1.26605i	−0.963896	+	0.266279i	$0.914206\pi$
$240$		0			0
$241$	24.9082	−	12.5094i	1.60448	−	0.805800i	0.604522	−	0.796588i	$-0.293364\pi$
$241$	24.9082	−	12.5094i	1.60448	−	0.805800i	0.999958	−	0.00921168i	$-0.00293221\pi$
$242$	6.30180			0.405095
$243$		0			0
$244$	−9.00910			−0.576748
$245$	3.82988	−	1.92344i	0.244682	−	0.122884i
$246$		0			0
$247$	−2.75771	+	3.70424i	−0.175469	+	0.235695i
$248$	−1.46562	+	4.89550i	−0.0930668	+	0.310865i
$249$		0			0
$250$	−4.32356	+	10.0231i	−0.273446	+	0.633918i
$251$	2.51752	−	14.2776i	0.158904	−	0.901192i	−0.796224	−	0.605001i	$-0.793173\pi$
$251$	2.51752	−	14.2776i	0.158904	−	0.901192i	0.955129	−	0.296191i	$-0.0957164\pi$
$252$		0			0
$253$	−1.28230	−	7.27226i	−0.0806172	−	0.457203i
$254$	−17.1183	−	4.05712i	−1.07410	−	0.254566i
$255$		0			0
$256$	−0.835488	+	0.549509i	−0.0522180	+	0.0343443i
$257$	1.18052	+	20.2687i	0.0736386	+	1.26433i	0.809470	+	0.587161i	$0.199754\pi$
$257$	1.18052	+	20.2687i	0.0736386	+	1.26433i	−0.735832	+	0.677165i	$0.763208\pi$
$258$		0			0
$259$	3.41864	+	11.4191i	0.212424	+	0.709546i
$260$	2.52926	+	0.920575i	0.156858	+	0.0570916i
$261$		0			0
$262$	−4.52452	+	1.64679i	−0.279526	+	0.101739i
$263$	−5.30489	−	7.12570i	−0.327114	−	0.439390i	0.607894	−	0.794018i	$-0.292015\pi$
$263$	−5.30489	−	7.12570i	−0.327114	−	0.439390i	−0.935007	+	0.354629i	$0.884607\pi$
$264$		0			0
$265$	13.9020	−	3.29484i	0.853994	−	0.202400i
$266$	−1.74411	−	4.04331i	−0.106938	−	0.247911i
$267$		0			0
$268$	9.51107	+	6.25553i	0.580981	+	0.382117i
$269$	−0.798719	+	1.38342i	−0.0486987	+	0.0843487i	−0.889347	−	0.457232i	$-0.848841\pi$
$269$	−0.798719	+	1.38342i	−0.0486987	+	0.0843487i	0.840649	+	0.541581i	$0.182174\pi$
$270$		0			0
$271$	10.0971	+	17.4887i	0.613355	+	1.06236i	0.990671	+	0.136277i	$0.0435137\pi$
$271$	10.0971	+	17.4887i	0.613355	+	1.06236i	−0.377316	+	0.926084i	$0.623153\pi$
$272$	0.434484	−	7.45980i	0.0263444	−	0.452317i
$273$		0			0
$274$	0.617479	+	0.0721729i	0.0373033	+	0.00436013i
$275$	4.83244	+	5.12208i	0.291407	+	0.308873i
$276$		0			0
$277$	1.65097	−	0.192970i	0.0991970	−	0.0115945i	−0.0663496	−	0.997796i	$-0.521135\pi$
$277$	1.65097	−	0.192970i	0.0991970	−	0.0115945i	0.165547	+	0.986202i	$0.447061\pi$
$278$	−2.26236	−	1.89835i	−0.135688	−	0.113855i
$279$		0			0
$280$	−1.96605	+	1.64972i	−0.117494	+	0.0985894i
$281$	8.32617	−	8.82522i	0.496698	−	0.526469i	−0.429722	−	0.902961i	$-0.641388\pi$
$281$	8.32617	−	8.82522i	0.496698	−	0.526469i	0.926420	+	0.376492i	$0.122870\pi$
$282$		0			0
$283$	−12.6764	−	6.36632i	−0.753533	−	0.378439i	0.0301938	−	0.999544i	$-0.490388\pi$
$283$	−12.6764	−	6.36632i	−0.753533	−	0.378439i	−0.783727	+	0.621105i	$0.786684\pi$
$284$	−2.66746	−	1.33965i	−0.158284	−	0.0794934i
$285$		0			0
$286$	3.02540	−	3.20674i	0.178896	−	0.189618i
$287$	−11.6150	+	9.74613i	−0.685611	+	0.575296i
$288$		0			0
$289$	29.7511	+	24.9642i	1.75007	+	1.46848i
$290$	6.38590	−	0.746405i	0.374993	−	0.0438304i
$291$		0			0
$292$	−7.12886	−	7.55615i	−0.417185	−	0.442190i
$293$	19.9431	+	2.33102i	1.16509	+	0.136179i	0.676573	−	0.736375i	$-0.263464\pi$
$293$	19.9431	+	2.33102i	1.16509	+	0.136179i	0.488517	+	0.872555i	$0.337538\pi$
$294$		0			0
$295$	−0.531441	+	9.12449i	−0.0309417	+	0.531248i
$296$	3.07302	+	5.32263i	0.178616	+	0.309371i
$297$		0			0
$298$	−0.660264	+	1.14361i	−0.0382481	+	0.0662476i
$299$	5.78939	+	3.80774i	0.334809	+	0.220207i
$300$		0			0
$301$	−5.34629	−	12.3941i	−0.308155	−	0.714383i
$302$	1.68015	−	0.398202i	0.0966816	−	0.0229140i
$303$		0			0
$304$	−1.35584	−	1.82121i	−0.0777626	−	0.104453i
$305$	−11.2030	+	4.07756i	−0.641482	+	0.233480i
$306$		0			0
$307$	−24.0050	−	8.73709i	−1.37004	−	0.498652i	−0.450893	−	0.892578i	$-0.648894\pi$
$307$	−24.0050	−	8.73709i	−1.37004	−	0.498652i	−0.919142	+	0.393926i	$0.871117\pi$
$308$	1.20566	+	4.02717i	0.0686987	+	0.229470i
$309$		0			0
$310$	0.393201	+	6.75101i	0.0223323	+	0.383431i
$311$	−8.61224	+	5.66436i	−0.488355	+	0.321196i	−0.769695	−	0.638412i	$-0.779592\pi$
$311$	−8.61224	+	5.66436i	−0.488355	+	0.321196i	0.281340	+	0.959608i	$0.409221\pi$
$312$		0			0
$313$	−11.2681	−	2.67060i	−0.636913	−	0.150951i	−0.100541	−	0.994933i	$-0.532057\pi$
$313$	−11.2681	−	2.67060i	−0.636913	−	0.150951i	−0.536372	+	0.843982i	$0.680205\pi$
$314$	−1.90893	−	10.8261i	−0.107727	−	0.610952i
$315$		0			0
$316$	1.78084	−	10.0997i	0.100180	−	0.568150i
$317$	9.27900	−	21.5111i	0.521160	−	1.20819i	−0.430935	−	0.902383i	$-0.641816\pi$
$317$	9.27900	−	21.5111i	0.521160	−	1.20819i	0.952095	−	0.305802i	$-0.0989247\pi$
$318$		0			0
$319$	3.02031	−	10.0885i	0.169105	−	0.564849i
$320$	−0.790236	+	1.06147i	−0.0441756	+	0.0593381i
$321$		0			0
$322$	−5.90453	+	2.96537i	−0.329047	+	0.165253i
$323$	16.9660			0.944015
$324$		0			0
$325$	−6.60790			−0.366540
$326$	16.8529	−	8.46384i	0.933395	−	0.468769i
$327$		0			0
$328$	−4.66853	+	6.27093i	−0.257777	+	0.346254i
$329$	2.34404	−	7.82963i	0.129231	−	0.431661i
$330$		0			0
$331$	0.0953783	−	0.221112i	0.00524246	−	0.0121534i	−0.915575	−	0.402148i	$-0.868264\pi$
$331$	0.0953783	−	0.221112i	0.00524246	−	0.0121534i	0.920817	+	0.389994i	$0.127523\pi$
$332$	−0.630651	+	3.57660i	−0.0346115	+	0.196291i
$333$		0			0
$334$	1.76627	+	10.0170i	0.0966462	+	0.548108i
$335$	14.6585	+	3.47413i	0.800879	+	0.189812i
$336$		0			0
$337$	−6.75532	+	4.44304i	−0.367986	+	0.242028i	−0.720011	−	0.693962i	$-0.755863\pi$
$337$	−6.75532	+	4.44304i	−0.367986	+	0.242028i	0.352026	+	0.935990i	$0.385493\pi$
$338$	−0.515341	−	8.84805i	−0.0280308	−	0.481271i
$339$		0			0
$340$	−2.83605	−	9.47306i	−0.153806	−	0.513749i
$341$	10.4085	+	3.78838i	0.563651	+	0.205152i
$342$		0			0
$343$	−18.6595	+	6.79152i	−1.00752	+	0.366708i
$344$	−4.15609	−	5.58260i	−0.224081	−	0.300994i
$345$		0			0
$346$	−18.1978	+	4.31295i	−0.978318	+	0.231866i
$347$	3.71942	+	8.62258i	0.199669	+	0.462884i	0.988404	−	0.151849i	$-0.0485228\pi$
$347$	3.71942	+	8.62258i	0.199669	+	0.462884i	−0.788735	+	0.614733i	$0.789264\pi$
$348$		0			0
$349$	−2.98629	−	1.96411i	−0.159853	−	0.105137i	0.467062	−	0.884224i	$-0.345312\pi$
$349$	−2.98629	−	1.96411i	−0.159853	−	0.105137i	−0.626915	+	0.779088i	$0.715683\pi$
$350$	3.15041	−	5.45668i	0.168397	−	0.291672i
$351$		0			0
$352$	1.08377	+	1.87714i	0.0577649	+	0.100052i
$353$	0.231753	−	3.97905i	0.0123350	−	0.211783i	−0.986509	−	0.163709i	$-0.947654\pi$
$353$	0.231753	−	3.97905i	0.0123350	−	0.211783i	0.998844	−	0.0480749i	$-0.0153086\pi$
$354$		0			0
$355$	−3.92337	−	0.458576i	−0.208231	−	0.0243387i
$356$	5.64833	+	5.98688i	0.299361	+	0.317304i
$357$		0			0
$358$	17.0687	−	1.99505i	0.902111	−	0.105442i
$359$	−17.0190	−	14.2806i	−0.898227	−	0.753702i	0.0716159	−	0.997432i	$-0.477184\pi$
$359$	−17.0190	−	14.2806i	−0.898227	−	0.753702i	−0.969843	+	0.243730i	$0.921629\pi$
$360$		0			0
$361$	−10.6058	+	8.89934i	−0.558201	+	0.468386i
$362$	15.5933	−	16.5279i	0.819565	−	0.868688i
$363$		0			0
$364$	−3.52512	−	1.77038i	−0.184766	−	0.0927931i
$365$	−12.2848	−	6.16968i	−0.643018	−	0.322936i
$366$		0			0
$367$	−8.65683	+	9.17571i	−0.451883	+	0.478968i	−0.912760	−	0.408496i	$-0.866053\pi$
$367$	−8.65683	+	9.17571i	−0.451883	+	0.478968i	0.460877	+	0.887464i	$0.347535\pi$
$368$	−2.60979	+	2.18988i	−0.136045	+	0.114155i
$369$		0			0
$370$	6.23041	+	5.22794i	0.323904	+	0.271787i
$371$	−20.7972	+	2.43085i	−1.07974	+	0.126203i
$372$		0			0
$373$	−2.77388	−	2.94015i	−0.143626	−	0.152235i	0.651567	−	0.758591i	$-0.274112\pi$
$373$	−2.77388	−	2.94015i	−0.143626	−	0.152235i	−0.795193	+	0.606356i	$0.792631\pi$
$374$	−16.0872	−	1.88033i	−0.831851	−	0.0972294i
$375$		0			0
$376$	0.245029	−	4.20698i	0.0126364	−	0.216959i
$377$	4.94096	+	8.55800i	0.254473	+	0.440759i
$378$		0			0
$379$	18.2374	−	31.5882i	0.936795	−	1.62258i	0.165392	−	0.986228i	$-0.447111\pi$
$379$	18.2374	−	31.5882i	0.936795	−	1.62258i	0.771402	−	0.636348i	$-0.219556\pi$
$380$	−2.51030	−	1.65105i	−0.128776	−	0.0846971i
$381$		0			0
$382$	2.32371	+	5.38696i	0.118891	+	0.275621i
$383$	3.77992	−	0.895858i	0.193145	−	0.0457762i	−0.132905	−	0.991129i	$-0.542430\pi$
$383$	3.77992	−	0.895858i	0.193145	−	0.0457762i	0.326050	+	0.945353i	$0.394282\pi$
$384$		0			0
$385$	3.32198	+	4.46219i	0.169304	+	0.227414i
$386$	−11.1427	+	4.05560i	−0.567148	+	0.206425i
$387$		0			0
$388$	−7.56074	−	2.75188i	−0.383838	−	0.139706i
$389$	−7.91140	−	26.4259i	−0.401124	−	1.33985i	−0.885359	−	0.464909i	$-0.846087\pi$
$389$	−7.91140	−	26.4259i	−0.401124	−	1.33985i	0.484235	−	0.874938i	$-0.339098\pi$
$390$		0			0
$391$	−1.48022	−	25.4144i	−0.0748578	−	1.28526i
$392$	−2.70582	+	1.77965i	−0.136665	+	0.0898857i
$393$		0			0
$394$	2.91665	+	0.691259i	0.146939	+	0.0348251i
$395$	−2.35664	−	13.3651i	−0.118575	−	0.672474i
$396$		0			0
$397$	0.343883	−	1.95026i	0.0172590	−	0.0978806i	−0.974961	−	0.222374i	$-0.928619\pi$
$397$	0.343883	−	1.95026i	0.0172590	−	0.0978806i	0.992220	+	0.124493i	$0.0397305\pi$
$398$	−7.97323	+	18.4840i	−0.399662	+	0.926521i
$399$		0			0
$400$	0.931767	−	3.11232i	0.0465884	−	0.155616i
$401$	−15.0228	+	20.1791i	−0.750203	+	1.00770i	0.249028	+	0.968496i	$0.419889\pi$
$401$	−15.0228	+	20.1791i	−0.750203	+	1.00770i	−0.999231	+	0.0392012i	$0.987519\pi$
$402$		0			0
$403$	−9.28829	+	4.66475i	−0.462683	+	0.232368i
$404$	−18.6140			−0.926081
$405$		0			0
$406$	−9.42271			−0.467641
$407$	11.9047	−	5.97878i	0.590096	−	0.296357i
$408$		0			0
$409$	18.9183	−	25.4117i	0.935450	−	1.25653i	−0.0309600	−	0.999521i	$-0.509856\pi$
$409$	18.9183	−	25.4117i	0.935450	−	1.25653i	0.966410	−	0.257006i	$-0.0827361\pi$
$410$	−2.96717	+	9.91103i	−0.146538	+	0.489471i
$411$		0			0
$412$	−7.16287	+	16.6054i	−0.352889	+	0.818089i
$413$	2.32606	−	13.1917i	0.114458	−	0.649123i
$414$		0			0
$415$	0.834558	+	4.73301i	0.0409668	+	0.232334i
$416$	−1.97912	−	0.469061i	−0.0970345	−	0.0229976i
$417$		0			0
$418$	−4.11172	+	2.70432i	−0.201111	+	0.132273i
$419$	−0.100748	−	1.72977i	−0.00492185	−	0.0845049i	0.994953	−	0.100345i	$-0.0319947\pi$
$419$	−0.100748	−	1.72977i	−0.00492185	−	0.0845049i	−0.999875	+	0.0158403i	$0.994958\pi$
$420$		0			0
$421$	−8.06168	−	26.9279i	−0.392902	−	1.31238i	−0.894416	−	0.447235i	$-0.852409\pi$
$421$	−8.06168	−	26.9279i	−0.392902	−	1.31238i	0.501514	−	0.865149i	$-0.332777\pi$
$422$	13.4932	+	4.91111i	0.656837	+	0.239069i
$423$		0			0
$424$	−10.1453	+	3.69257i	−0.492698	+	0.179327i
$425$	14.4969	+	19.4727i	0.703204	+	0.944566i
$426$		0			0
$427$	17.0015	−	4.02944i	0.822762	−	0.194998i
$428$	1.61866	+	3.75247i	0.0782408	+	0.181383i
$429$		0			0
$430$	−7.69490	−	5.06102i	−0.371081	−	0.244064i
$431$	0.567396	−	0.982759i	0.0273305	−	0.0473378i	−0.852037	−	0.523482i	$-0.824633\pi$
$431$	0.567396	−	0.982759i	0.0273305	−	0.0473378i	0.879367	+	0.476144i	$0.157966\pi$
$432$		0			0
$433$	8.75124	+	15.1576i	0.420558	+	0.728427i	0.995994	−	0.0894194i	$-0.0285011\pi$
$433$	8.75124	+	15.1576i	0.420558	+	0.728427i	−0.575436	+	0.817846i	$0.695168\pi$
$434$	0.576264	−	9.89408i	0.0276616	−	0.474931i
$435$		0			0
$436$	−12.2410	−	1.43077i	−0.586240	−	0.0685216i
$437$	−5.30820	−	5.62636i	−0.253926	−	0.269146i
$438$		0			0
$439$	−16.5282	+	1.93187i	−0.788849	+	0.0922032i	−0.500971	−	0.865464i	$-0.667024\pi$
$439$	−16.5282	+	1.93187i	−0.788849	+	0.0922032i	−0.287878	+	0.957667i	$0.592950\pi$
$440$	2.19729	+	1.84374i	0.104752	+	0.0878970i
$441$		0			0
$442$	11.6428	−	9.76945i	0.553790	−	0.464685i
$443$	−18.5257	+	19.6360i	−0.880180	+	0.932937i	−0.998194	−	0.0600754i	$-0.980866\pi$
$443$	−18.5257	+	19.6360i	−0.880180	+	0.932937i	0.118014	+	0.993012i	$0.462347\pi$
$444$		0			0
$445$	9.73351	+	4.88835i	0.461412	+	0.231730i
$446$	−10.0031	−	5.02374i	−0.473660	−	0.237881i
$447$		0			0
$448$	1.33092	−	1.41069i	0.0628800	−	0.0666489i
$449$	−14.6102	+	12.2594i	−0.689499	+	0.578558i	−0.918765	−	0.394806i	$-0.870812\pi$
$449$	−14.6102	+	12.2594i	−0.689499	+	0.578558i	0.229266	+	0.973364i	$0.426367\pi$
$450$		0			0
$451$	12.9811	+	10.8924i	0.611254	+	0.512903i
$452$	−15.4100	+	1.80117i	−0.724823	+	0.0847197i
$453$		0			0
$454$	−10.9219	−	11.5766i	−0.512591	−	0.543315i
$455$	−5.18484	−	0.606021i	−0.243069	−	0.0284107i
$456$		0			0
$457$	−0.570163	+	9.78932i	−0.0266711	+	0.457925i	0.958362	+	0.285558i	$0.0921788\pi$
$457$	−0.570163	+	9.78932i	−0.0266711	+	0.457925i	−0.985033	+	0.172368i	$0.944858\pi$
$458$	−5.38302	−	9.32367i	−0.251532	−	0.435666i
$459$		0			0
$460$	−2.25419	+	3.90436i	−0.105102	+	0.182042i
$461$	12.2701	+	8.07018i	0.571476	+	0.375866i	0.802111	−	0.597175i	$-0.203710\pi$
$461$	12.2701	+	8.07018i	0.571476	+	0.375866i	−0.230635	+	0.973040i	$0.574080\pi$
$462$		0			0
$463$	−12.0622	−	27.9633i	−0.560577	−	1.29956i	−0.929060	−	0.369930i	$-0.879382\pi$
$463$	−12.0622	−	27.9633i	−0.560577	−	1.29956i	0.368482	−	0.929635i	$-0.379877\pi$
$464$	−4.72753	+	1.12045i	−0.219470	+	0.0520154i
$465$		0			0
$466$	10.3152	+	13.8558i	0.477844	+	0.641855i
$467$	4.51390	−	1.64293i	0.208879	−	0.0760256i	−0.235462	−	0.971884i	$-0.575660\pi$
$467$	4.51390	−	1.64293i	0.208879	−	0.0760256i	0.444340	+	0.895858i	$0.353438\pi$
$468$		0			0
$469$	−20.7467	−	7.55118i	−0.957994	−	0.348681i
$470$	−1.59940	−	5.34238i	−0.0737749	−	0.246425i
$471$		0			0
$472$	−0.401594	−	6.89511i	−0.0184849	−	0.317373i
$473$	−12.6038	+	8.28964i	−0.579523	+	0.381158i
$474$		0			0
$475$	7.17752	+	1.70110i	0.329327	+	0.0780520i
$476$	2.51656	+	14.2721i	0.115346	+	0.654161i
$477$		0			0
$478$	4.23720	−	24.0304i	0.193805	−	1.09912i
$479$	1.04518	−	2.42300i	0.0477555	−	0.110710i	−0.892668	−	0.450714i	$-0.851169\pi$
$479$	1.04518	−	2.42300i	0.0477555	−	0.110710i	0.940424	+	0.340005i	$0.110429\pi$
$480$		0			0
$481$	−3.58525	+	11.9756i	−0.163473	+	0.546039i
$482$	−16.6446	+	22.3576i	−0.758141	+	1.01836i
$483$		0			0
$484$	−5.63150	+	2.82824i	−0.255977	+	0.128557i
$485$	−10.6475			−0.483476
$486$		0			0
$487$	30.3949			1.37732			0.688662	−	0.725082i	$-0.258198\pi$
$487$	30.3949			1.37732			0.688662	+	0.725082i	$0.258198\pi$
$488$	8.05082	−	4.04328i	0.364444	−	0.183030i
$489$		0			0
$490$	−2.55927	+	3.43769i	−0.115616	+	0.155299i
$491$	5.83806	−	19.5005i	0.263468	−	0.880045i	−0.719221	−	0.694782i	$-0.755501\pi$
$491$	5.83806	−	19.5005i	0.263468	−	0.880045i	0.982689	−	0.185263i	$-0.0593138\pi$
$492$		0			0
$493$	14.3796	−	33.3356i	0.647624	−	1.50136i
$494$	0.801915	−	4.54789i	0.0360799	−	0.204619i
$495$		0			0
$496$	−0.887374	−	5.03255i	−0.0398443	−	0.225968i
$497$	5.63307	+	1.33506i	0.252678	+	0.0598857i
$498$		0			0
$499$	−0.982338	+	0.646094i	−0.0439755	+	0.0289231i	−0.571306	−	0.820737i	$-0.693563\pi$
$499$	−0.982338	+	0.646094i	−0.0439755	+	0.0289231i	0.527331	+	0.849660i	$0.323193\pi$
$500$	−0.634701	−	10.8974i	−0.0283847	−	0.487347i
$501$		0			0
$502$	4.15802	+	13.8888i	0.185582	+	0.619886i
$503$	−29.3121	−	10.6687i	−1.30696	−	0.475696i	−0.407705	−	0.913114i	$-0.633671\pi$
$503$	−29.3121	−	10.6687i	−1.30696	−	0.475696i	−0.899258	+	0.437418i	$0.855893\pi$
$504$		0			0
$505$	−23.1469	+	8.42479i	−1.03002	+	0.374898i
$506$	4.40968	+	5.92323i	0.196034	+	0.263320i
$507$		0			0
$508$	17.1183	−	4.05712i	0.759503	−	0.180005i
$509$	−0.914081	−	2.11908i	−0.0405159	−	0.0939265i	0.896756	−	0.442525i	$-0.145917\pi$
$509$	−0.914081	−	2.11908i	−0.0405159	−	0.0939265i	−0.937272	+	0.348598i	$0.886658\pi$
$510$		0			0
$511$	16.8328	+	11.0711i	0.744641	+	0.489758i
$512$	0.500000	−	0.866025i	0.0220971	−	0.0382733i
$513$		0			0
$514$	−10.1515	−	17.5829i	−0.447764	−	0.775550i
$515$	−1.39150	+	23.8911i	−0.0613168	+	1.05277i
$516$		0			0
$517$	−9.07246	−	1.06042i	−0.399007	−	0.0466372i
$518$	−8.17987	−	8.67016i	−0.359403	−	0.380945i
$519$		0			0
$520$	−2.67338	+	0.312474i	−0.117236	+	0.0137029i
$521$	20.8735	+	17.5150i	0.914485	+	0.767344i	0.972967	−	0.230944i	$-0.0741815\pi$
$521$	20.8735	+	17.5150i	0.914485	+	0.767344i	−0.0584819	+	0.998288i	$0.518626\pi$
$522$		0			0
$523$	20.3758	−	17.0974i	0.890973	−	0.747615i	−0.0774318	−	0.996998i	$-0.524672\pi$
$523$	20.3758	−	17.0974i	0.890973	−	0.747615i	0.968405	+	0.249382i	$0.0802276\pi$
$524$	3.30418	−	3.50223i	0.144344	−	0.152996i
$525$		0			0
$526$	7.93863	+	3.98693i	0.346141	+	0.173838i
$527$	34.1238	+	17.1376i	1.48646	+	0.746527i
$528$		0			0
$529$	7.81863	−	8.28727i	0.339941	−	0.360316i
$530$	−10.9446	+	9.18359i	−0.475402	+	0.398910i
$531$		0			0
$532$	3.37323	+	2.83048i	0.146248	+	0.122717i
$533$	−15.7937	+	1.84602i	−0.684102	+	0.0799600i
$534$		0			0
$535$	3.71122	+	3.93367i	0.160450	+	0.170067i
$536$	−11.3069	−	1.32158i	−0.488383	−	0.0570837i
$537$		0			0
$538$	0.0928827	−	1.59474i	0.00400446	−	0.0687539i
$539$	3.50990	+	6.07932i	0.151182	+	0.261855i
$540$		0			0
$541$	1.08463	−	1.87864i	0.0466321	−	0.0807692i	−0.841767	−	0.539841i	$-0.818484\pi$
$541$	1.08463	−	1.87864i	0.0466321	−	0.0807692i	0.888399	+	0.459071i	$0.151818\pi$
$542$	−16.8720	−	11.0969i	−0.724714	−	0.476652i
$543$		0			0
$544$	2.95968	+	6.86131i	0.126895	+	0.294176i
$545$	−15.8696	+	3.76116i	−0.679778	+	0.161110i
$546$		0			0
$547$	−14.1538	−	19.0118i	−0.605171	−	0.812886i	0.388939	−	0.921264i	$-0.372842\pi$
$547$	−14.1538	−	19.0118i	−0.605171	−	0.812886i	−0.994110	+	0.108378i	$0.965434\pi$
$548$	−0.584191	+	0.212628i	−0.0249554	+	0.00908302i
$549$		0			0
$550$	−6.61721	−	2.40847i	−0.282159	−	0.102697i
$551$	−3.16376	−	10.5677i	−0.134781	−	0.450199i
$552$		0			0
$553$	1.15649	+	19.8561i	0.0491788	+	0.844367i
$554$	−1.38875	+	0.913398i	−0.0590025	+	0.0388065i
$555$		0			0
$556$	2.87370	+	0.681079i	0.121872	+	0.0288842i
$557$	2.15153	+	12.2019i	0.0911633	+	0.517013i	0.995856	+	0.0909475i	$0.0289895\pi$
$557$	2.15153	+	12.2019i	0.0911633	+	0.517013i	−0.904692	+	0.426065i	$0.859899\pi$
$558$		0			0
$559$	2.45814	−	13.9408i	0.103968	−	0.589632i
$560$	1.01654	−	2.35660i	0.0429566	−	0.0995847i
$561$		0			0
$562$	−3.47978	+	11.6233i	−0.146786	+	0.490299i
$563$	27.7670	−	37.2976i	1.17024	−	1.57191i	0.424875	−	0.905252i	$-0.360318\pi$
$563$	27.7670	−	37.2976i	1.17024	−	1.57191i	0.745366	−	0.666655i	$-0.232275\pi$
$564$		0			0
$565$	−18.3474	+	9.21440i	−0.771880	+	0.387653i
$566$	14.1852			0.596250
$567$		0			0
$568$	2.98496			0.125246
$569$	−20.7775	+	10.4349i	−0.871038	+	0.437452i	−0.827411	−	0.561596i	$-0.810187\pi$
$569$	−20.7775	+	10.4349i	−0.871038	+	0.437452i	−0.0436265	+	0.999048i	$0.513891\pi$
$570$		0			0
$571$	−9.27277	+	12.4555i	−0.388053	+	0.521246i	−0.952629	−	0.304135i	$-0.901633\pi$
$571$	−9.27277	+	12.4555i	−0.388053	+	0.521246i	0.564575	+	0.825381i	$0.309040\pi$
$572$	−1.26442	+	4.22344i	−0.0528679	+	0.176591i
$573$		0			0
$574$	6.00548	−	13.9223i	0.250664	−	0.581104i
$575$	1.92197	−	10.9000i	0.0801516	−	0.454562i
$576$		0			0
$577$	5.56862	+	31.5812i	0.231825	+	1.31474i	0.849199	+	0.528074i	$0.177086\pi$
$577$	5.56862	+	31.5812i	0.231825	+	1.31474i	−0.617374	+	0.786670i	$0.711803\pi$
$578$	−37.7905	−	8.95651i	−1.57188	−	0.372542i
$579$		0			0
$580$	−5.37167	+	3.53300i	−0.223046	+	0.146700i
$581$	−0.409547	−	7.03166i	−0.0169909	−	0.291722i
$582$		0			0
$583$	6.71162	+	22.4184i	0.277967	+	0.928474i
$584$	9.76177	+	3.55299i	0.403945	+	0.147024i
$585$		0			0
$586$	−18.8680	+	6.86739i	−0.779429	+	0.283689i
$587$	20.4031	+	27.4061i	0.842127	+	1.13117i	0.989846	+	0.142143i	$0.0453993\pi$
$587$	20.4031	+	27.4061i	0.842127	+	1.13117i	−0.147719	+	0.989029i	$0.547193\pi$
$588$		0			0
$589$	11.2898	−	2.67574i	0.465189	−	0.110252i
$590$	−3.62015	−	8.39245i	−0.149039	−	0.345512i
$591$		0			0
$592$	−5.13494	−	3.37730i	−0.211045	−	0.138806i
$593$	−5.78538	+	10.0206i	−0.237577	+	0.411496i	−0.960019	−	0.279936i	$-0.909687\pi$
$593$	−5.78538	+	10.0206i	−0.237577	+	0.411496i	0.722441	+	0.691432i	$0.243020\pi$
$594$		0			0
$595$	9.58901	+	16.6087i	0.393111	+	0.680889i
$596$	0.0767819	−	1.31829i	0.00314511	−	0.0539994i
$597$		0			0
$598$	−6.88250	−	0.804448i	−0.281446	−	0.0328963i
$599$	15.6147	+	16.5506i	0.638000	+	0.676241i	0.963009	−	0.269470i	$-0.0868486\pi$
$599$	15.6147	+	16.5506i	0.638000	+	0.676241i	−0.325008	+	0.945711i	$0.605367\pi$
$600$		0			0
$601$	4.24750	−	0.496462i	0.173259	−	0.0202511i	−0.0290209	−	0.999579i	$-0.509239\pi$
$601$	4.24750	−	0.496462i	0.173259	−	0.0202511i	0.202280	+	0.979328i	$0.435165\pi$
$602$	10.3401	+	8.67635i	0.421430	+	0.353622i
$603$		0			0
$604$	−1.32272	+	1.10990i	−0.0538208	+	0.0451610i
$605$	−5.72281	+	6.06583i	−0.232665	+	0.246611i
$606$		0			0
$607$	9.54035	+	4.79135i	0.387231	+	0.194475i	0.631754	−	0.775169i	$-0.282335\pi$
$607$	9.54035	+	4.79135i	0.387231	+	0.194475i	−0.244523	+	0.969643i	$0.578631\pi$
$608$	2.02898	+	1.01899i	0.0822859	+	0.0413255i
$609$		0			0
$610$	8.18136	−	8.67174i	0.331254	−	0.351108i
$611$	6.56599	−	5.50952i	0.265632	−	0.222891i
$612$		0			0
$613$	7.81287	+	6.55577i	0.315559	+	0.264785i	0.786785	−	0.617227i	$-0.211744\pi$
$613$	7.81287	+	6.55577i	0.315559	+	0.264785i	−0.471226	+	0.882012i	$0.656188\pi$
$614$	25.3728	−	2.96566i	1.02396	−	0.119684i
$615$		0			0
$616$	−2.88481	−	3.05772i	−0.116232	−	0.123199i
$617$	33.5712	+	3.92391i	1.35153	+	0.157971i	0.760845	−	0.648934i	$-0.224785\pi$
$617$	33.5712	+	3.92391i	1.35153	+	0.157971i	0.590682	+	0.806905i	$0.298859\pi$
$618$		0			0
$619$	1.53303	−	26.3211i	0.0616177	−	1.05793i	−0.815839	−	0.578279i	$-0.803725\pi$
$619$	1.53303	−	26.3211i	0.0616177	−	1.05793i	0.877457	−	0.479656i	$-0.159238\pi$
$620$	−3.38122	−	5.85645i	−0.135793	−	0.235201i
$621$		0			0
$622$	5.15402	−	8.92702i	0.206657	−	0.357941i
$623$	−13.3370	−	8.77186i	−0.534334	−	0.351437i
$624$		0			0
$625$	0.712447	+	1.65164i	0.0284979	+	0.0660655i
$626$	11.2681	−	2.67060i	0.450365	−	0.106739i
$627$		0			0
$628$	6.56463	+	8.81782i	0.261957	+	0.351869i
$629$	43.1562	−	15.7076i	1.72075	−	0.626302i
$630$		0			0
$631$	−16.7461	−	6.09507i	−0.666650	−	0.242641i	−0.0135452	−	0.999908i	$-0.504312\pi$
$631$	−16.7461	−	6.09507i	−0.666650	−	0.242641i	−0.653105	+	0.757267i	$0.726534\pi$
$632$	2.94130	+	9.82462i	0.116999	+	0.390802i
$633$		0			0
$634$	1.36216	+	23.3875i	0.0540984	+	0.928834i
$635$	19.4507	−	12.7929i	0.771878	−	0.507672i
$636$		0			0
$637$	−6.40961	−	1.51911i	−0.253958	−	0.0601892i
$638$	1.82868	+	10.3709i	0.0723981	+	0.410590i
$639$		0			0
$640$	0.229793	−	1.30322i	0.00908338	−	0.0515144i
$641$	−8.32976	+	19.3106i	−0.329006	+	0.762721i	0.670772	+	0.741663i	$0.265963\pi$
$641$	−8.32976	+	19.3106i	−0.329006	+	0.762721i	−0.999778	+	0.0210581i	$0.993297\pi$
$642$		0			0
$643$	−0.298435	+	0.996842i	−0.0117691	+	0.0393116i	−0.963672	−	0.267087i	$-0.913939\pi$
$643$	−0.298435	+	0.996842i	−0.0117691	+	0.0393116i	0.951903	+	0.306399i	$0.0991241\pi$
$644$	3.94563	−	5.29990i	0.155480	−	0.208845i
$645$		0			0
$646$	−15.1614	+	7.61434i	−0.596517	+	0.299582i
$647$	3.98241			0.156565			0.0782823	−	0.996931i	$-0.475056\pi$
$647$	3.98241			0.156565			0.0782823	+	0.996931i	$0.475056\pi$
$648$		0			0
$649$	−14.9707			−0.587651
$650$	5.90504	−	2.96562i	0.231615	−	0.116321i
$651$		0			0
$652$	−11.2617	+	15.1271i	−0.441043	+	0.592424i
$653$	4.59762	−	15.3571i	0.179919	−	0.600970i	−0.819685	−	0.572815i	$-0.805851\pi$
$653$	4.59762	−	15.3571i	0.179919	−	0.600970i	0.999604	−	0.0281555i	$-0.00896335\pi$
$654$		0			0
$655$	2.52369	−	5.85058i	0.0986089	−	0.228601i
$656$	1.35757	−	7.69914i	0.0530040	−	0.300601i
$657$		0			0
$658$	1.41922	+	8.04881i	0.0553271	+	0.313775i
$659$	5.19134	+	1.23037i	0.202226	+	0.0479284i	0.330480	−	0.943813i	$-0.392789\pi$
$659$	5.19134	+	1.23037i	0.202226	+	0.0479284i	−0.128254	+	0.991741i	$0.540937\pi$
$660$		0			0
$661$	5.47643	−	3.60191i	0.213009	−	0.140098i	−0.438522	−	0.898721i	$-0.644498\pi$
$661$	5.47643	−	3.60191i	0.213009	−	0.140098i	0.651530	+	0.758623i	$0.274127\pi$
$662$	0.0140016	+	0.240398i	0.000544188	+	0.00934334i
$663$		0			0
$664$	−1.04160	−	3.47920i	−0.0404221	−	0.135019i
$665$	5.47577	+	1.99302i	0.212341	+	0.0772859i
$666$		0			0
$667$	−15.5539	+	5.66116i	−0.602250	+	0.219201i
$668$	−6.07404	−	8.15885i	−0.235012	−	0.315675i
$669$		0			0
$670$	−14.6585	+	3.47413i	−0.566307	+	0.134217i
$671$	−7.73445	−	17.9305i	−0.298585	−	0.692198i
$672$		0			0
$673$	−15.1546	−	9.96731i	−0.584165	−	0.384212i	0.222753	−	0.974875i	$-0.428496\pi$
$673$	−15.1546	−	9.96731i	−0.584165	−	0.384212i	−0.806918	+	0.590663i	$0.798866\pi$
$674$	4.04274	−	7.00223i	0.155720	−	0.269716i
$675$		0			0
$676$	4.43152	+	7.67563i	0.170443	+	0.295216i
$677$	−1.04089	+	17.8714i	−0.0400046	+	0.686853i	0.917376	+	0.398023i	$0.130303\pi$
$677$	−1.04089	+	17.8714i	−0.0400046	+	0.686853i	−0.957380	+	0.288830i	$0.906734\pi$
$678$		0			0
$679$	15.4991	+	1.81158i	0.594800	+	0.0695222i
$680$	6.78589	+	7.19262i	0.260227	+	0.275824i
$681$		0			0
$682$	−11.0016	+	1.28590i	−0.421273	+	0.0492397i
$683$	−19.3775	−	16.2596i	−0.741459	−	0.622158i	0.191770	−	0.981440i	$-0.438577\pi$
$683$	−19.3775	−	16.2596i	−0.741459	−	0.622158i	−0.933229	+	0.359282i	$0.883022\pi$
$684$		0			0
$685$	−0.630217	+	0.528815i	−0.0240793	+	0.0202050i
$686$	13.6267	−	14.4435i	0.520272	−	0.551456i
$687$		0			0
$688$	6.21949	+	3.12354i	0.237116	+	0.119084i
$689$	−19.6235	−	9.85530i	−0.747596	−	0.375457i
$690$		0			0
$691$	−3.92984	+	4.16539i	−0.149498	+	0.158459i	−0.797795	−	0.602929i	$-0.794000\pi$
$691$	−3.92984	+	4.16539i	−0.149498	+	0.158459i	0.648297	+	0.761388i	$0.275482\pi$
$692$	14.3265	−	12.0213i	0.544611	−	0.456983i
$693$		0			0
$694$	−7.19360	−	6.03614i	−0.273065	−	0.229129i
$695$	3.88176	−	0.453713i	0.147244	−	0.0172103i
$696$		0			0
$697$	40.0894	+	42.4923i	1.51850	+	1.60951i
$698$	3.55014	+	0.414952i	0.134375	+	0.0157062i
$699$		0			0
$700$	−0.366361	+	6.29017i	−0.0138471	+	0.237746i
$701$	−17.6846	−	30.6306i	−0.667937	−	1.15690i	−0.978480	−	0.206342i	$-0.933844\pi$
$701$	−17.6846	−	30.6306i	−0.667937	−	1.15690i	0.310543	−	0.950559i	$-0.399489\pi$
$702$		0			0
$703$	6.97724	−	12.0849i	0.263151	−	0.455792i
$704$	−1.81095	−	1.19108i	−0.0682526	−	0.0448905i
$705$		0			0
$706$	1.57869	+	3.65982i	0.0594148	+	0.137739i
$707$	35.1275	−	8.32536i	1.32110	−	0.313108i
$708$		0			0
$709$	−3.93861	−	5.29048i	−0.147918	−	0.198688i	0.721989	−	0.691905i	$-0.243228\pi$
$709$	−3.93861	−	5.29048i	−0.147918	−	0.198688i	−0.869906	+	0.493217i	$0.835821\pi$
$710$	3.71186	−	1.35101i	0.139304	−	0.0507024i
$711$		0			0
$712$	−7.73444	−	2.81510i	−0.289860	−	0.105501i
$713$	−4.99313	−	16.6782i	−0.186994	−	0.624604i
$714$		0			0
$715$	0.339222	+	5.82422i	0.0126862	+	0.217813i
$716$	−14.3578	+	9.44328i	−0.536577	+	0.352912i
$717$		0			0
$718$	21.6178	+	5.12352i	0.806771	+	0.191208i
$719$	8.53090	+	48.3811i	0.318149	+	1.80431i	0.553993	+	0.832521i	$0.313103\pi$
$719$	8.53090	+	48.3811i	0.318149	+	1.80431i	−0.235845	+	0.971791i	$0.575786\pi$
$720$		0			0
$721$	6.09044	−	34.5406i	0.226820	−	1.28636i
$722$	5.48369	−	12.7126i	0.204082	−	0.473115i
$723$		0			0
$724$	−6.51696	+	21.7682i	−0.242201	+	0.809007i
$725$	9.42572	−	12.6609i	0.350063	−	0.470216i
$726$		0			0
$727$	−32.4735	+	16.3088i	−1.20438	+	0.604860i	−0.933785	−	0.357835i	$-0.883515\pi$
$727$	−32.4735	+	16.3088i	−1.20438	+	0.604860i	−0.270590	+	0.962695i	$0.587219\pi$
$728$	3.94470			0.146200
$729$		0			0
$730$	13.7471			0.508802
$731$	−46.4747	+	23.3405i	−1.71893	+	0.863279i
$732$		0			0
$733$	−5.43505	+	7.30054i	−0.200748	+	0.269652i	−0.891085	−	0.453837i	$-0.850055\pi$
$733$	−5.43505	+	7.30054i	−0.200748	+	0.269652i	0.690337	+	0.723488i	$0.257462\pi$
$734$	3.61798	−	12.0849i	0.133542	−	0.446062i
$735$		0			0
$736$	1.34938	−	3.12822i	0.0497389	−	0.115308i
$737$	−4.28474	+	24.3000i	−0.157831	+	0.895102i
$738$		0			0
$739$	−1.83509	−	10.4073i	−0.0675048	−	0.382839i	−0.999778	−	0.0210830i	$-0.993289\pi$
$739$	−1.83509	−	10.4073i	−0.0675048	−	0.382839i	0.932273	−	0.361756i	$-0.117823\pi$
$740$	−7.91399	−	1.87565i	−0.290924	−	0.0689503i
$741$		0			0
$742$	17.4941	−	11.5061i	0.642229	−	0.422401i
$743$	−1.62018	−	27.8173i	−0.0594385	−	1.02052i	−0.887772	−	0.460284i	$-0.847748\pi$
$743$	−1.62018	−	27.8173i	−0.0594385	−	1.02052i	0.828333	−	0.560235i	$-0.189289\pi$
$744$		0			0
$745$	−0.501186	−	1.67408i	−0.0183620	−	0.0613335i
$746$	3.79837	+	1.38249i	0.139068	+	0.0506167i
$747$		0			0
$748$	15.2200	−	5.53961i	0.556497	−	0.202548i
$749$	−4.73300	−	6.35752i	−0.172940	−	0.232299i
$750$		0			0
$751$	2.57908	−	0.611252i	0.0941118	−	0.0223049i	−0.183290	−	0.983059i	$-0.558675\pi$
$751$	2.57908	−	0.611252i	0.0941118	−	0.0223049i	0.277402	+	0.960754i	$0.410527\pi$
$752$	1.66913	+	3.86947i	0.0608667	+	0.141105i
$753$		0			0
$754$	−8.25623	−	5.43021i	−0.300674	−	0.197757i
$755$	−1.14249	+	1.97885i	−0.0415794	+	0.0720177i
$756$		0			0
$757$	−7.00766	−	12.1376i	−0.254698	−	0.441149i	0.710116	−	0.704085i	$-0.248643\pi$
$757$	−7.00766	−	12.1376i	−0.254698	−	0.441149i	−0.964813	+	0.262936i	$0.915309\pi$
$758$	−2.12083	+	36.4132i	−0.0770319	+	1.32259i
$759$		0			0
$760$	2.98428	+	0.348812i	0.108251	+	0.0126527i
$761$	−12.0637	−	12.7867i	−0.437308	−	0.463519i	0.470810	−	0.882235i	$-0.343962\pi$
$761$	−12.0637	−	12.7867i	−0.437308	−	0.463519i	−0.908117	+	0.418716i	$0.862480\pi$
$762$		0			0
$763$	23.7407	−	2.77489i	0.859470	−	0.100458i
$764$	−4.49421	−	3.77109i	−0.162595	−	0.136433i
$765$		0			0
$766$	−2.97580	+	2.49699i	−0.107520	+	0.0902200i
$767$	9.64037	−	10.2182i	0.348094	−	0.368958i
$768$		0			0
$769$	−7.88360	−	3.95929i	−0.284290	−	0.142776i	0.300940	−	0.953643i	$-0.402699\pi$
$769$	−7.88360	−	3.95929i	−0.284290	−	0.142776i	−0.585230	+	0.810867i	$0.698996\pi$
$770$	−4.97126	−	2.49666i	−0.179152	−	0.0899733i
$771$		0			0
$772$	8.13731	−	8.62505i	0.292868	−	0.310422i
$773$	−3.30370	+	2.77213i	−0.118826	+	0.0997066i	−0.700264	−	0.713884i	$-0.746935\pi$
$773$	−3.30370	+	2.77213i	−0.118826	+	0.0997066i	0.581439	+	0.813590i	$0.302490\pi$
$774$		0			0
$775$	12.7179	+	10.6715i	0.456839	+	0.383333i
$776$	7.99157	−	0.934080i	0.286881	−	0.0335315i
$777$		0			0
$778$	18.9298	+	20.0644i	0.678666	+	0.719344i
$779$	17.6304	+	2.06070i	0.631675	+	0.0738322i
$780$		0			0
$781$	0.376197	−	6.45905i	0.0134614	−	0.231123i
$782$	12.7287	+	22.0468i	0.455178	+	0.788391i
$783$		0			0
$784$	1.61931	−	2.80472i	0.0578323	−	0.100169i
$785$	12.1542	+	7.99397i	0.433803	+	0.285317i
$786$		0			0
$787$	19.1364	+	44.3631i	0.682138	+	1.58137i	0.807905	+	0.589313i	$0.200602\pi$
$787$	19.1364	+	44.3631i	0.682138	+	1.58137i	−0.125767	+	0.992060i	$0.540139\pi$
$788$	−2.91665	+	0.691259i	−0.103901	+	0.0246251i
$789$		0			0
$790$	8.10423	+	10.8859i	0.288336	+	0.387302i
$791$	28.2753	−	10.2914i	1.00536	−	0.365919i
$792$		0			0
$793$	17.2190	+	6.26719i	0.611464	+	0.222555i
$794$	0.567969	+	1.89715i	0.0201565	+	0.0673273i
$795$		0			0
$796$	−1.17048	−	20.0963i	−0.0414865	−	0.712295i
$797$	−21.2718	+	13.9907i	−0.753484	+	0.495574i	−0.867213	−	0.497938i	$-0.834091\pi$
$797$	−21.2718	+	13.9907i	−0.753484	+	0.495574i	0.113729	+	0.993512i	$0.463720\pi$
$798$		0			0
$799$	−30.6409	−	7.26203i	−1.08400	−	0.256912i
$800$	0.564149	+	3.19945i	0.0199457	+	0.113118i
$801$		0			0
$802$	4.36849	−	24.7749i	0.154257	−	0.874834i
$803$	8.91848	−	20.6754i	0.314726	−	0.729618i
$804$		0			0
$805$	2.50771	−	8.37635i	0.0883853	−	0.295227i
$806$	6.20678	−	8.33715i	0.218624	−	0.293664i
$807$		0			0
$808$	16.6341	−	8.35395i	0.585185	−	0.293891i
$809$	−17.8042			−0.625963			−0.312982	−	0.949759i	$-0.601328\pi$
$809$	−17.8042			−0.625963			−0.312982	+	0.949759i	$0.601328\pi$
$810$		0			0
$811$	17.6535			0.619898			0.309949	−	0.950753i	$-0.399688\pi$
$811$	17.6535			0.619898			0.309949	+	0.950753i	$0.399688\pi$
$812$	8.42044	−	4.22890i	0.295499	−	0.148405i
$813$		0			0
$814$	−7.95519	+	10.6857i	−0.278829	+	0.374533i
$815$	−7.15759	+	23.9080i	−0.250719	+	0.837461i
$816$		0			0
$817$	−6.25887	+	14.5097i	−0.218970	+	0.507630i
$818$	−5.50127	+	31.1992i	−0.192347	+	1.09086i
$819$		0			0
$820$	−1.79650	−	10.1885i	−0.0627367	−	0.355797i
$821$	11.3701	+	2.69476i	0.396819	+	0.0940478i	0.424180	−	0.905578i	$-0.360562\pi$
$821$	11.3701	+	2.69476i	0.396819	+	0.0940478i	−0.0273612	+	0.999626i	$0.508710\pi$
$822$		0			0
$823$	8.74128	−	5.74923i	0.304702	−	0.200406i	−0.387945	−	0.921683i	$-0.626815\pi$
$823$	8.74128	−	5.74923i	0.304702	−	0.200406i	0.692647	+	0.721277i	$0.256445\pi$
$824$	−1.05151	−	18.0538i	−0.0366313	−	0.628934i
$825$		0			0
$826$	3.84180	+	12.8325i	0.133673	+	0.446500i
$827$	−36.5997	−	13.3212i	−1.27270	−	0.463224i	−0.384687	−	0.923047i	$-0.625690\pi$
$827$	−36.5997	−	13.3212i	−1.27270	−	0.463224i	−0.888010	+	0.459823i	$0.847913\pi$
$828$		0			0
$829$	−9.00820	+	3.27872i	−0.312868	+	0.113875i	−0.493681	−	0.869643i	$-0.664349\pi$
$829$	−9.00820	+	3.27872i	−0.312868	+	0.113875i	0.180814	+	0.983517i	$0.442127\pi$
$830$	−2.86996	−	3.85503i	−0.0996178	−	0.133810i
$831$		0			0
$832$	1.97912	−	0.469061i	0.0686138	−	0.0162618i
$833$	9.58526	+	22.2211i	0.332109	+	0.769916i
$834$		0			0
$835$	−11.2459	−	7.39657i	−0.389182	−	0.255969i
$836$	2.46067	−	4.26201i	0.0851041	−	0.147405i
$837$		0			0
$838$	0.866352	+	1.50057i	0.0299276	+	0.0518362i
$839$	1.25711	−	21.5837i	0.0434001	−	0.745151i	−0.904479	−	0.426519i	$-0.859740\pi$
$839$	1.25711	−	21.5837i	0.0434001	−	0.745151i	0.947879	−	0.318632i	$-0.103223\pi$
$840$		0			0
$841$	5.35857	+	0.626327i	0.184778	+	0.0215975i
$842$	19.2894	+	20.4456i	0.664756	+	0.704601i
$843$		0			0
$844$	−14.2620	+	1.66699i	−0.490920	+	0.0573803i
$845$	8.98472	+	7.53908i	0.309084	+	0.259352i
$846$		0			0
$847$	9.36253	−	7.85609i	0.321700	−	0.269939i
$848$	7.40892	−	7.85299i	0.254423	−	0.269673i
$849$		0			0
$850$	−21.6943	−	10.8953i	−0.744107	−	0.373705i
$851$	−18.7114	−	9.39723i	−0.641419	−	0.322133i
$852$		0			0
$853$	−33.9735	+	36.0098i	−1.16323	+	1.23295i	−0.195570	+	0.980690i	$0.562656\pi$
$853$	−33.9735	+	36.0098i	−1.16323	+	1.23295i	−0.967659	+	0.252261i	$0.918826\pi$
$854$	−13.3847	+	11.2311i	−0.458016	+	0.384321i
$855$		0			0
$856$	−3.13059	−	2.62688i	−0.107001	−	0.0897849i
$857$	−32.9963	+	3.85671i	−1.12713	+	0.131743i	−0.659162	−	0.752001i	$-0.729089\pi$
$857$	−32.9963	+	3.85671i	−1.12713	+	0.131743i	−0.467970	+	0.883744i	$0.655015\pi$
$858$		0			0
$859$	−4.73995	−	5.02406i	−0.161725	−	0.171419i	0.641444	−	0.767170i	$-0.278336\pi$
$859$	−4.73995	−	5.02406i	−0.161725	−	0.171419i	−0.803169	+	0.595752i	$0.796854\pi$
$860$	9.14779	+	1.06922i	0.311937	+	0.0364602i
$861$		0			0
$862$	−0.0659823	+	1.13287i	−0.00224737	+	0.0385858i
$863$	−6.07200	−	10.5170i	−0.206693	−	0.358003i	0.743978	−	0.668205i	$-0.232937\pi$
$863$	−6.07200	−	10.5170i	−0.206693	−	0.358003i	−0.950671	+	0.310201i	$0.899604\pi$
$864$		0			0
$865$	12.3744	−	21.4330i	0.420741	−	0.728744i
$866$	−14.6231	−	9.61777i	−0.496913	−	0.326825i
$867$		0			0
$868$	3.92548	+	9.10030i	0.133240	+	0.308884i
$869$	21.6298	−	5.12637i	0.733742	−	0.173900i
$870$		0			0
$871$	−13.8267	−	18.5725i	−0.468500	−	0.629305i
$872$	11.5811	−	4.21519i	0.392187	−	0.142744i
$873$		0			0
$874$	7.26869	+	2.64559i	0.245867	+	0.0894883i
$875$	6.07179	+	20.2812i	0.205264	+	0.685629i
$876$		0			0
$877$	−0.965302	−	16.5736i	−0.0325959	−	0.559651i	−0.974587	−	0.224011i	$-0.928085\pi$
$877$	−0.965302	−	16.5736i	−0.0325959	−	0.559651i	0.941991	−	0.335639i	$-0.108952\pi$
$878$	13.9031	−	9.14424i	0.469208	−	0.308603i
$879$		0			0
$880$	−2.79104	−	0.661488i	−0.0940859	−	0.0222988i
$881$	1.14695	+	6.50466i	0.0386416	+	0.219147i	0.998014	−	0.0629963i	$-0.0200656\pi$
$881$	1.14695	+	6.50466i	0.0386416	+	0.219147i	−0.959372	+	0.282144i	$0.908955\pi$
$882$		0			0
$883$	8.02198	−	45.4949i	0.269961	−	1.53103i	−0.484565	−	0.874755i	$-0.661022\pi$
$883$	8.02198	−	45.4949i	0.269961	−	1.53103i	0.754526	−	0.656270i	$-0.227867\pi$
$884$	−6.01984	+	13.9556i	−0.202469	+	0.469376i
$885$		0			0
$886$	7.74249	−	25.8617i	0.260114	−	0.868841i
$887$	27.1247	−	36.4348i	0.910758	−	1.22336i	−0.0635135	−	0.997981i	$-0.520231\pi$
$887$	27.1247	−	36.4348i	0.910758	−	1.22336i	0.974271	−	0.225379i	$-0.0723620\pi$
$888$		0			0
$889$	−30.4903	+	15.3128i	−1.02261	+	0.513575i
$890$	−10.8921			−0.365103
$891$		0			0
$892$	11.1937			0.374794
$893$	−8.55034	+	4.29414i	−0.286126	+	0.143698i
$894$		0			0
$895$	−13.5802	+	18.2413i	−0.453935	+	0.609740i
$896$	−0.556235	+	1.85795i	−0.0185825	+	0.0620699i
$897$		0			0
$898$	7.55415	−	17.5125i	0.252085	−	0.584399i
$899$	4.31130	−	24.4506i	0.143790	−	0.815473i
$900$		0			0
$901$	14.0091	+	79.4495i	0.466711	+	2.64685i
$902$	−16.4888	−	3.90792i	−0.549017	−	0.130119i
$903$		0			0
$904$	12.9625	−	8.52555i	0.431126	−	0.283556i
$905$	1.74839	+	30.0188i	0.0581186	+	0.997857i
$906$		0			0
$907$	10.2417	+	34.2095i	0.340069	+	1.13591i	0.941508	+	0.336991i	$0.109409\pi$
$907$	10.2417	+	34.2095i	0.340069	+	1.13591i	−0.601439	+	0.798919i	$0.705406\pi$
$908$	14.9557	+	5.44344i	0.496323	+	0.180647i
$909$		0			0
$910$	4.90532	−	1.78539i	0.162610	−	0.0591851i
$911$	23.6477	+	31.7643i	0.783483	+	1.05240i	0.997146	+	0.0754926i	$0.0240529\pi$
$911$	23.6477	+	31.7643i	0.783483	+	1.05240i	−0.213664	+	0.976907i	$0.568540\pi$
$912$		0			0
$913$	−7.65980	+	1.81540i	−0.253502	+	0.0600811i
$914$	−3.88392	−	9.00395i	−0.128469	−	0.297824i
$915$		0			0
$916$	8.99490	+	5.91604i	0.297200	+	0.195471i
$917$	−4.66908	+	8.08708i	−0.154186	+	0.267059i
$918$		0			0
$919$	10.6420	+	18.4325i	0.351047	+	0.608031i	0.986433	−	0.164163i	$-0.0524924\pi$
$919$	10.6420	+	18.4325i	0.351047	+	0.608031i	−0.635386	+	0.772194i	$0.719159\pi$
$920$	0.262138	−	4.50074i	0.00864245	−	0.148385i
$921$		0			0
$922$	−14.5869	−	1.70496i	−0.480392	−	0.0561498i
$923$	4.16635	+	4.41607i	0.137137	+	0.145357i
$924$		0			0
$925$	19.8323	−	2.31806i	0.652081	−	0.0762173i
$926$	23.3291	+	19.5754i	0.766641	+	0.643288i
$927$		0			0
$928$	3.72182	−	3.12298i	0.122175	−	0.102517i
$929$	−14.9295	+	15.8243i	−0.489820	+	0.519179i	−0.924385	−	0.381462i	$-0.875421\pi$
$929$	−14.9295	+	15.8243i	−0.489820	+	0.519179i	0.434565	+	0.900641i	$0.356902\pi$
$930$		0			0
$931$	6.57107	+	3.30011i	0.215358	+	0.108157i
$932$	−15.4365	−	7.75249i	−0.505638	−	0.253941i
$933$		0			0
$934$	−3.29643	+	3.49401i	−0.107862	+	0.114327i
$935$	16.4191	−	13.7773i	0.536962	−	0.450564i
$936$		0			0
$937$	−15.1205	−	12.6876i	−0.493965	−	0.414485i	0.361480	−	0.932380i	$-0.382272\pi$
$937$	−15.1205	−	12.6876i	−0.493965	−	0.414485i	−0.855445	+	0.517894i	$0.826716\pi$
$938$	21.9289	−	2.56312i	0.716004	−	0.0836888i
$939$		0			0
$940$	3.82693	+	4.05631i	0.124821	+	0.132302i
$941$	−30.4590	−	3.56014i	−0.992933	−	0.116057i	−0.395917	−	0.918286i	$-0.629573\pi$
$941$	−30.4590	−	3.56014i	−0.992933	−	0.116057i	−0.597016	+	0.802229i	$0.703647\pi$
$942$		0			0
$943$	1.54865	−	26.5893i	0.0504311	−	0.865868i
$944$	3.45340	+	5.98146i	0.112398	+	0.194680i
$945$		0			0
$946$	7.54277	−	13.0645i	0.245237	−	0.424762i
$947$	−33.4232	−	21.9828i	−1.08611	−	0.714345i	−0.125457	−	0.992099i	$-0.540040\pi$
$947$	−33.4232	−	21.9828i	−1.08611	−	0.714345i	−0.960652	+	0.277754i	$0.910410\pi$
$948$		0			0
$949$	8.36885	+	19.4012i	0.271664	+	0.629789i
$950$	−7.17752	+	1.70110i	−0.232869	+	0.0551911i
$951$		0			0
$952$	−8.65419	−	11.6246i	−0.280484	−	0.376755i
$953$	−36.9499	+	13.4487i	−1.19692	+	0.435645i	−0.862150	−	0.506654i	$-0.830882\pi$
$953$	−36.9499	+	13.4487i	−1.19692	+	0.435645i	−0.334774	+	0.942298i	$0.608660\pi$
$954$		0			0
$955$	−7.29545	−	2.65533i	−0.236075	−	0.0859244i
$956$	6.99831	+	23.3760i	0.226341	+	0.756033i
$957$		0			0
$958$	0.153433	+	2.63435i	0.00495720	+	0.0851119i
$959$	1.00736	−	0.662548i	0.0325292	−	0.0213948i
$960$		0			0
$961$	−4.75432	−	1.12680i	−0.153365	−	0.0363482i
$962$	−2.17073	−	12.3108i	−0.0699871	−	0.396917i
$963$		0			0
$964$	4.84010	−	27.4495i	0.155889	−	0.884090i
$965$	6.21518	−	14.4084i	0.200074	−	0.463823i
$966$		0			0
$967$	5.19840	−	17.3639i	0.167169	−	0.558384i	−0.832819	−	0.553545i	$-0.813275\pi$
$967$	5.19840	−	17.3639i	0.167169	−	0.558384i	0.999988	−	0.00483874i	$-0.00154022\pi$
$968$	3.76318	−	5.05482i	0.120953	−	0.162468i
$969$		0			0
$970$	9.51492	−	4.77857i	0.305506	−	0.153431i
$971$	−4.40089			−0.141231			−0.0706156	−	0.997504i	$-0.522496\pi$
$971$	−4.40089			−0.141231			−0.0706156	+	0.997504i	$0.522496\pi$
$972$		0			0
$973$	−5.72773			−0.183623
$974$	−27.1619	+	13.6412i	−0.870323	+	0.437092i
$975$		0			0
$976$	−5.37986	+	7.22641i	−0.172205	+	0.231312i
$977$	−8.04738	+	26.8801i	−0.257458	+	0.859971i	0.727341	+	0.686276i	$0.240756\pi$
$977$	−8.04738	+	26.8801i	−0.257458	+	0.859971i	−0.984800	+	0.173695i	$0.944429\pi$
$978$		0			0
$979$	−7.06628	+	16.3815i	−0.225839	+	0.523555i
$980$	0.744211	−	4.22063i	0.0237730	−	0.134823i
$981$		0			0
$982$	3.53472	+	20.0464i	0.112797	+	0.639706i
$983$	−0.938898	−	0.222523i	−0.0299462	−	0.00709738i	0.215615	−	0.976478i	$-0.430824\pi$
$983$	−0.938898	−	0.222523i	−0.0299462	−	0.00709738i	−0.245562	+	0.969381i	$0.578972\pi$
$984$		0			0
$985$	−3.31405	+	2.17968i	−0.105594	+	0.0694505i
$986$	2.11094	+	36.2434i	0.0672259	+	1.15422i
$987$		0			0
$988$	1.32447	+	4.42404i	0.0421370	+	0.140747i
$989$	22.2809	+	8.10960i	0.708493	+	0.257870i
$990$		0			0
$991$	−50.9827	+	18.5562i	−1.61952	+	0.589457i	−0.983291	−	0.182043i	$-0.941729\pi$
$991$	−50.9827	+	18.5562i	−1.61952	+	0.589457i	−0.636229	+	0.771500i	$0.719507\pi$
$992$	3.05159	+	4.09900i	0.0968881	+	0.130143i
$993$		0			0
$994$	−5.63307	+	1.33506i	−0.178670	+	0.0423456i
$995$	−10.5512	−	24.4604i	−0.334496	−	0.775448i
$996$		0			0
$997$	−12.5945	−	8.28354i	−0.398872	−	0.262342i	0.334188	−	0.942507i	$-0.391538\pi$
$997$	−12.5945	−	8.28354i	−0.398872	−	0.262342i	−0.733060	+	0.680164i	$0.761908\pi$
$998$	0.587883	−	1.01824i	0.0186091	−	0.0322319i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	486.2.g.b.73.3		90
3.2	odd	2		162.2.g.b.25.5	yes	90
81.13	even	27	inner	486.2.g.b.253.3		90
81.68	odd	54		162.2.g.b.13.5	✓	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.b.13.5	✓	90	81.68	odd	54
162.2.g.b.25.5	yes	90	3.2	odd	2
486.2.g.b.73.3		90	1.1	even	1	trivial
486.2.g.b.253.3		90	81.13	even	27	inner

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:	\( N \)	\(=\)	\( 486 = 2 \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	486.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.893633 + 0.448799i) q^{2} +(0.597159 - 0.802123i) q^{4} +(0.379535 - 1.26773i) q^{5} +(-0.768169 + 1.78082i) q^{7} +(-0.173648 + 0.984808i) q^{8} +(0.229793 + 1.30322i) q^{10} +(2.10911 + 0.499867i) q^{11} +(-1.69934 + 1.11767i) q^{13} +(-0.112768 - 1.93615i) q^{14} +(-0.286803 - 0.957990i) q^{16} +(7.02180 + 2.55572i) q^{17} +(2.13356 - 0.776551i) q^{19} +(-0.790236 - 1.06147i) q^{20} +(-2.10911 + 0.499867i) q^{22} +(-1.34938 - 3.12822i) q^{23} +(2.71434 + 1.78525i) q^{25} +(1.01697 - 1.76145i) q^{26} +(0.969715 + 1.67960i) q^{28} +(0.282496 - 4.85027i) q^{29} +(5.07563 + 0.593256i) q^{31} +(0.686242 + 0.727374i) q^{32} +(-7.42191 + 0.867497i) q^{34} +(1.96605 + 1.64972i) q^{35} +(4.70814 - 3.95060i) q^{37} +(-1.55810 + 1.65149i) q^{38} +(1.18257 + 0.593908i) q^{40} +(6.98634 + 3.50867i) q^{41} +(-4.77609 + 5.06236i) q^{43} +(1.66043 - 1.39326i) q^{44} +(2.60979 + 2.18988i) q^{46} +(-4.18562 + 0.489229i) q^{47} +(2.22247 + 2.35568i) q^{49} +(-3.22684 - 0.377163i) q^{50} +(-0.118264 + 2.03051i) q^{52} +(5.39818 + 9.34993i) q^{53} +(1.43418 - 2.48407i) q^{55} +(-1.62037 - 1.06573i) q^{56} +(1.92435 + 4.46115i) q^{58} +(-6.72062 + 1.59282i) q^{59} +(-5.37986 - 7.22641i) q^{61} +(-4.80200 + 1.74779i) q^{62} +(-0.939693 - 0.342020i) q^{64} +(0.771954 + 2.57851i) q^{65} +(0.661912 + 11.3646i) q^{67} +(6.24313 - 4.10617i) q^{68} +(-2.49732 - 0.591876i) q^{70} +(-0.518333 - 2.93961i) q^{71} +(1.80390 - 10.2304i) q^{73} +(-2.43432 + 5.64339i) q^{74} +(0.651182 - 2.17510i) q^{76} +(-2.51032 + 3.37195i) q^{77} +(9.16461 - 4.60264i) q^{79} -1.32333 q^{80} -7.81791 q^{82} +(-3.24547 + 1.62994i) q^{83} +(5.90499 - 7.93178i) q^{85} +(1.99609 - 6.66740i) q^{86} +(-0.858516 + 1.99026i) q^{88} +(-1.42927 + 8.10577i) q^{89} +(-0.684990 - 3.88477i) q^{91} +(-3.31501 - 0.785672i) q^{92} +(3.52084 - 2.31569i) q^{94} +(-0.174701 - 2.99951i) q^{95} +(-2.30761 - 7.70796i) q^{97} +(-3.04330 - 1.10767i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 18 q^{13} + 9 q^{20} - 27 q^{23} - 18 q^{25} + 27 q^{26} - 18 q^{28} + 27 q^{29} + 54 q^{31} + 27 q^{35} + 18 q^{38} + 9 q^{41} - 36 q^{43} + 18 q^{46} + 27 q^{47} + 36 q^{52} + 27 q^{53} - 54 q^{55}+ \cdots - 36 q^{98}+O(q^{100}) \) 90 * q - 18 * q^13 + 9 * q^20 - 27 * q^23 - 18 * q^25 + 27 * q^26 - 18 * q^28 + 27 * q^29 + 54 * q^31 + 27 * q^35 + 18 * q^38 + 9 * q^41 - 36 * q^43 + 18 * q^46 + 27 * q^47 + 36 * q^52 + 27 * q^53 - 54 * q^55 - 9 * q^58 + 45 * q^59 - 9 * q^65 + 81 * q^67 - 36 * q^68 - 72 * q^70 - 72 * q^71 - 36 * q^73 - 45 * q^74 - 18 * q^76 - 144 * q^77 - 99 * q^79 - 18 * q^80 + 72 * q^82 - 45 * q^83 - 117 * q^85 - 72 * q^86 - 18 * q^88 - 45 * q^89 - 63 * q^91 - 36 * q^92 - 72 * q^94 - 45 * q^95 + 117 * q^97 - 36 * q^98

Introduction

L-functions

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