LMFDB - Embedded newform 1620.2.e.b.971.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1620,2,Mod(971,1620)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1620, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("1620.971");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1620 = 2^{2} \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1620.e (of order $2$, degree $1$, 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:	$12.9357651274$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			971.21
Character	$\chi$	$=$	1620.971
Dual form			1620.2.e.b.971.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309220 - 1.37999i) q^{2} +(-1.80877 + 0.853443i) q^{4} +1.00000i q^{5} +0.937354i q^{7} +(1.73705 + 2.23218i) q^{8} +O(q^{10})$	\(q+(-0.309220 - 1.37999i) q^{2} +(-1.80877 + 0.853443i) q^{4} +1.00000i q^{5} +0.937354i q^{7} +(1.73705 + 2.23218i) q^{8} +(1.37999 - 0.309220i) q^{10} +0.583833 q^{11} +1.15930 q^{13} +(1.29354 - 0.289849i) q^{14} +(2.54327 - 3.08736i) q^{16} +0.238281i q^{17} -7.00703i q^{19} +(-0.853443 - 1.80877i) q^{20} +(-0.180533 - 0.805686i) q^{22} -5.06707 q^{23} -1.00000 q^{25} +(-0.358479 - 1.59983i) q^{26} +(-0.799978 - 1.69546i) q^{28} +9.14304i q^{29} +6.27506i q^{31} +(-5.04696 - 2.55503i) q^{32} +(0.328826 - 0.0736811i) q^{34} -0.937354 q^{35} +3.50937 q^{37} +(-9.66965 + 2.16671i) q^{38} +(-2.23218 + 1.73705i) q^{40} +3.30373i q^{41} +10.7990i q^{43} +(-1.05602 + 0.498268i) q^{44} +(1.56684 + 6.99252i) q^{46} +8.55084 q^{47} +6.12137 q^{49} +(0.309220 + 1.37999i) q^{50} +(-2.09691 + 0.989398i) q^{52} +11.9037i q^{53} +0.583833i q^{55} +(-2.09235 + 1.62823i) q^{56} +(12.6173 - 2.82721i) q^{58} -9.89209 q^{59} +6.66589 q^{61} +(8.65955 - 1.94037i) q^{62} +(-1.96530 + 7.75484i) q^{64} +1.15930i q^{65} -8.88817i q^{67} +(-0.203359 - 0.430994i) q^{68} +(0.289849 + 1.29354i) q^{70} -8.95946 q^{71} +11.7312 q^{73} +(-1.08517 - 4.84290i) q^{74} +(5.98010 + 12.6741i) q^{76} +0.547258i q^{77} +5.05089i q^{79} +(3.08736 + 2.54327i) q^{80} +(4.55912 - 1.02158i) q^{82} -4.72936 q^{83} -0.238281 q^{85} +(14.9026 - 3.33927i) q^{86} +(1.01415 + 1.30322i) q^{88} +2.36345i q^{89} +1.08668i q^{91} +(9.16514 - 4.32445i) q^{92} +(-2.64409 - 11.8001i) q^{94} +7.00703 q^{95} +4.53311 q^{97} +(-1.89285 - 8.44745i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 48 q^{25} + 12 q^{34} + 12 q^{40} - 12 q^{46} - 48 q^{49} + 36 q^{52} + 36 q^{58} - 48 q^{64} - 24 q^{73} - 12 q^{76} - 36 q^{82} - 36 q^{94} + 24 q^{97}+O(q^{100}) $ 48 * q - 48 * q^25 + 12 * q^34 + 12 * q^40 - 12 * q^46 - 48 * q^49 + 36 * q^52 + 36 * q^58 - 48 * q^64 - 24 * q^73 - 12 * q^76 - 36 * q^82 - 36 * q^94 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times$.

$n$	$811$	$1297$	$1541$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−0.309220	−	1.37999i	−0.218651	−	0.975803i
$2$	−0.309220	−	1.37999i	−0.218651	−	0.975803i
$3$		0			0
$3$		0			0
$4$	−1.80877	+	0.853443i	−0.904383	+	0.426721i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$			0.937354i			0.354287i	0.984185	+	0.177143i	$0.0566856\pi$
$7$			0.937354i			0.354287i	−0.984185	+	0.177143i	$0.943314\pi$
$8$	1.73705	+	2.23218i	0.614141	+	0.789197i
$9$		0			0
$10$	1.37999	−	0.309220i	0.436392	−	0.0977839i
$11$	0.583833			0.176032			0.0880161	−	0.996119i	$-0.471947\pi$
$11$	0.583833			0.176032			0.0880161	+	0.996119i	$0.471947\pi$
$12$		0			0
$13$	1.15930			0.321533			0.160766	−	0.986993i	$-0.448603\pi$
$13$	1.15930			0.321533			0.160766	+	0.986993i	$0.448603\pi$
$14$	1.29354	−	0.289849i	0.345714	−	0.0774653i
$15$		0			0
$16$	2.54327	−	3.08736i	0.635818	−	0.771839i
$17$			0.238281i			0.0577915i	0.999582	+	0.0288958i	$0.00919909\pi$
$17$			0.238281i			0.0577915i	−0.999582	+	0.0288958i	$0.990801\pi$
$18$		0			0
$19$		−	7.00703i		−	1.60752i	−0.594952	−	0.803761i	$-0.702829\pi$
$19$		−	7.00703i		−	1.60752i	0.594952	−	0.803761i	$-0.297171\pi$
$20$	−0.853443	−	1.80877i	−0.190836	−	0.404452i
$21$		0			0
$22$	−0.180533	−	0.805686i	−0.0384897	−	0.171773i
$23$	−5.06707			−1.05656			−0.528278	−	0.849071i	$-0.677162\pi$
$23$	−5.06707			−1.05656			−0.528278	+	0.849071i	$0.677162\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−0.358479	−	1.59983i	−0.0703036	−	0.313752i
$27$		0			0
$28$	−0.799978	−	1.69546i	−0.151182	−	0.320411i
$29$			9.14304i			1.69782i	0.528537	+	0.848910i	$0.322741\pi$
$29$			9.14304i			1.69782i	−0.528537	+	0.848910i	$0.677259\pi$
$30$		0			0
$31$			6.27506i			1.12703i	0.826104	+	0.563517i	$0.190552\pi$
$31$			6.27506i			1.12703i	−0.826104	+	0.563517i	$0.809448\pi$
$32$	−5.04696	−	2.55503i	−0.892186	−	0.451669i
$33$		0			0
$34$	0.328826	−	0.0736811i	0.0563931	−	0.0126362i
$35$	−0.937354			−0.158442
$36$		0			0
$37$	3.50937			0.576936			0.288468	−	0.957489i	$-0.406854\pi$
$37$	3.50937			0.576936			0.288468	+	0.957489i	$0.406854\pi$
$38$	−9.66965	+	2.16671i	−1.56862	+	0.351487i
$39$		0			0
$40$	−2.23218	+	1.73705i	−0.352939	+	0.274652i
$41$			3.30373i			0.515956i	0.966151	+	0.257978i	$0.0830562\pi$
$41$			3.30373i			0.515956i	−0.966151	+	0.257978i	$0.916944\pi$
$42$		0			0
$43$			10.7990i			1.64684i	0.567435	+	0.823419i	$0.307936\pi$
$43$			10.7990i			1.64684i	−0.567435	+	0.823419i	$0.692064\pi$
$44$	−1.05602	+	0.498268i	−0.159201	+	0.0751167i
$45$		0			0
$46$	1.56684	+	6.99252i	0.231018	+	1.03099i
$47$	8.55084			1.24727			0.623634	−	0.781716i	$-0.285655\pi$
$47$	8.55084			1.24727			0.623634	+	0.781716i	$0.285655\pi$
$48$		0			0
$49$	6.12137			0.874481
$50$	0.309220	+	1.37999i	0.0437303	+	0.195161i
$51$		0			0
$52$	−2.09691	+	0.989398i	−0.290789	+	0.137205i
$53$			11.9037i			1.63510i	0.575855	+	0.817552i	$0.304669\pi$
$53$			11.9037i			1.63510i	−0.575855	+	0.817552i	$0.695331\pi$
$54$		0			0
$55$			0.583833i			0.0787240i
$56$	−2.09235	+	1.62823i	−0.279602	+	0.217582i
$57$		0			0
$58$	12.6173	−	2.82721i	1.65674	−	0.371231i
$59$	−9.89209			−1.28784			−0.643920	−	0.765093i	$-0.722693\pi$
$59$	−9.89209			−1.28784			−0.643920	+	0.765093i	$0.722693\pi$
$60$		0			0
$61$	6.66589			0.853480			0.426740	−	0.904374i	$-0.359662\pi$
$61$	6.66589			0.853480			0.426740	+	0.904374i	$0.359662\pi$
$62$	8.65955	−	1.94037i	1.09976	−	0.246428i
$63$		0			0
$64$	−1.96530	+	7.75484i	−0.245662	+	0.969355i
$65$			1.15930i			0.143794i
$66$		0			0
$67$		−	8.88817i		−	1.08586i	−0.839777	−	0.542931i	$-0.817314\pi$
$67$		−	8.88817i		−	1.08586i	0.839777	−	0.542931i	$-0.182686\pi$
$68$	−0.203359	−	0.430994i	−0.0246609	−	0.0522657i
$69$		0			0
$70$	0.289849	+	1.29354i	0.0346435	+	0.154608i
$71$	−8.95946			−1.06329			−0.531646	−	0.846966i	$-0.678426\pi$
$71$	−8.95946			−1.06329			−0.531646	+	0.846966i	$0.678426\pi$
$72$		0			0
$73$	11.7312			1.37303			0.686517	−	0.727114i	$-0.259139\pi$
$73$	11.7312			1.37303			0.686517	+	0.727114i	$0.259139\pi$
$74$	−1.08517	−	4.84290i	−0.126148	−	0.562976i
$75$		0			0
$76$	5.98010	+	12.6741i	0.685964	+	1.45382i
$77$			0.547258i			0.0623659i
$78$		0			0
$79$			5.05089i			0.568270i	0.958784	+	0.284135i	$0.0917064\pi$
$79$			5.05089i			0.568270i	−0.958784	+	0.284135i	$0.908294\pi$
$80$	3.08736	+	2.54327i	0.345177	+	0.284346i
$81$		0			0
$82$	4.55912	−	1.02158i	0.503471	−	0.112814i
$83$	−4.72936			−0.519115			−0.259557	−	0.965728i	$-0.583577\pi$
$83$	−4.72936			−0.519115			−0.259557	+	0.965728i	$0.583577\pi$
$84$		0			0
$85$	−0.238281			−0.0258452
$86$	14.9026	−	3.33927i	1.60699	−	0.360083i
$87$		0			0
$88$	1.01415	+	1.30322i	0.108109	+	0.138924i
$89$			2.36345i			0.250525i	0.992124	+	0.125263i	$0.0399774\pi$
$89$			2.36345i			0.250525i	−0.992124	+	0.125263i	$0.960023\pi$
$90$		0			0
$91$			1.08668i			0.113915i
$92$	9.16514	−	4.32445i	0.955532	−	0.450855i
$93$		0			0
$94$	−2.64409	−	11.8001i	−0.272717	−	1.21709i
$95$	7.00703			0.718906
$96$		0			0
$97$	4.53311			0.460268			0.230134	−	0.973159i	$-0.426084\pi$
$97$	4.53311			0.460268			0.230134	+	0.973159i	$0.426084\pi$
$98$	−1.89285	−	8.44745i	−0.191206	−	0.853321i
$99$		0			0
$100$	1.80877	−	0.853443i	0.180877	−	0.0853443i
$101$		−	1.23146i		−	0.122535i	−0.998121	−	0.0612673i	$-0.980486\pi$
$101$		−	1.23146i		−	0.122535i	0.998121	−	0.0612673i	$-0.0195142\pi$
$102$		0			0
$103$			6.12978i			0.603985i	0.953310	+	0.301992i	$0.0976517\pi$
$103$			6.12978i			0.603985i	−0.953310	+	0.301992i	$0.902348\pi$
$104$	2.01377	+	2.58778i	0.197466	+	0.253752i
$105$		0			0
$106$	16.4271	−	3.68087i	1.59554	−	0.357518i
$107$	−7.54970			−0.729858			−0.364929	−	0.931035i	$-0.618907\pi$
$107$	−7.54970			−0.729858			−0.364929	+	0.931035i	$0.618907\pi$
$108$		0			0
$109$	−5.97087			−0.571905			−0.285953	−	0.958244i	$-0.592310\pi$
$109$	−5.97087			−0.571905			−0.285953	+	0.958244i	$0.592310\pi$
$110$	0.805686	−	0.180533i	0.0768191	−	0.0172131i
$111$		0			0
$112$	2.89395	+	2.38395i	0.273452	+	0.225262i
$113$			15.4237i			1.45094i	0.688254	+	0.725470i	$0.258378\pi$
$113$			15.4237i			1.45094i	−0.688254	+	0.725470i	$0.741622\pi$
$114$		0			0
$115$		−	5.06707i		−	0.472506i
$116$	−7.80306	−	16.5376i	−0.724496	−	1.53548i
$117$		0			0
$118$	3.05883	+	13.6510i	0.281588	+	1.25668i
$119$	−0.223353			−0.0204748
$120$		0			0
$121$	−10.6591			−0.969013
$122$	−2.06123	−	9.19889i	−0.186615	−	0.832828i
$123$		0			0
$124$	−5.35541	−	11.3501i	−0.480930	−	1.01927i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$			20.9805i			1.86172i	0.365375	+	0.930860i	$0.380941\pi$
$127$			20.9805i			1.86172i	−0.365375	+	0.930860i	$0.619059\pi$
$128$	11.3093	+	0.314150i	0.999614	+	0.0277672i
$129$		0			0
$130$	1.59983	−	0.358479i	0.140314	−	0.0314407i
$131$	12.0124			1.04953			0.524764	−	0.851248i	$-0.324154\pi$
$131$	12.0124			1.04953			0.524764	+	0.851248i	$0.324154\pi$
$132$		0			0
$133$	6.56807			0.569524
$134$	−12.2656	+	2.74840i	−1.05959	+	0.237425i
$135$		0			0
$136$	−0.531886	+	0.413906i	−0.0456089	+	0.0354921i
$137$			3.21169i			0.274394i	0.990544	+	0.137197i	$0.0438093\pi$
$137$			3.21169i			0.274394i	−0.990544	+	0.137197i	$0.956191\pi$
$138$		0			0
$139$			1.11194i			0.0943131i	0.998888	+	0.0471566i	$0.0150160\pi$
$139$			1.11194i			0.0943131i	−0.998888	+	0.0471566i	$0.984984\pi$
$140$	1.69546	−	0.799978i	0.143292	−	0.0676105i
$141$		0			0
$142$	2.77044	+	12.3640i	0.232490	+	1.03756i
$143$	0.676839			0.0566001
$144$		0			0
$145$	−9.14304			−0.759288
$146$	−3.62752	−	16.1890i	−0.300216	−	1.33981i
$147$		0			0
$148$	−6.34762	+	2.99504i	−0.521771	+	0.246191i
$149$		−	0.816859i		−	0.0669197i	−0.999440	−	0.0334599i	$-0.989347\pi$
$149$		−	0.816859i		−	0.0669197i	0.999440	−	0.0334599i	$-0.0106526\pi$
$150$		0			0
$151$		−	17.6348i		−	1.43510i	−0.696508	−	0.717549i	$-0.745264\pi$
$151$		−	17.6348i		−	1.43510i	0.696508	−	0.717549i	$-0.254736\pi$
$152$	15.6410	−	12.1716i	1.26865	−	0.987245i
$153$		0			0
$154$	0.755213	−	0.169223i	0.0608568	−	0.0136364i
$155$	−6.27506			−0.504025
$156$		0			0
$157$	20.7891			1.65915			0.829575	−	0.558396i	$-0.188583\pi$
$157$	20.7891			1.65915			0.829575	+	0.558396i	$0.188583\pi$
$158$	6.97020	−	1.56184i	0.554520	−	0.124253i
$159$		0			0
$160$	2.55503	−	5.04696i	0.201993	−	0.398998i
$161$		−	4.74964i		−	0.374324i
$162$		0			0
$163$		−	3.22298i		−	0.252443i	−0.992002	−	0.126222i	$-0.959715\pi$
$163$		−	3.22298i		−	0.252443i	0.992002	−	0.126222i	$-0.0402850\pi$
$164$	−2.81954	−	5.97567i	−0.220169	−	0.466622i
$165$		0			0
$166$	1.46241	+	6.52649i	0.113505	+	0.506554i
$167$	13.7030			1.06037			0.530184	−	0.847883i	$-0.322123\pi$
$167$	13.7030			1.06037			0.530184	+	0.847883i	$0.322123\pi$
$168$		0			0
$169$	−11.6560			−0.896617
$170$	0.0736811	+	0.328826i	0.00565108	+	0.0252198i
$171$		0			0
$172$	−9.21636	−	19.5329i	−0.702741	−	1.48937i
$173$			12.5387i			0.953300i	0.879093	+	0.476650i	$0.158149\pi$
$173$			12.5387i			0.953300i	−0.879093	+	0.476650i	$0.841851\pi$
$174$		0			0
$175$		−	0.937354i		−	0.0708573i
$176$	1.48485	−	1.80250i	0.111924	−	0.135869i
$177$		0			0
$178$	3.26155	−	0.730826i	0.244463	−	0.0547777i
$179$	23.1645			1.73140			0.865700	−	0.500564i	$-0.166874\pi$
$179$	23.1645			1.73140			0.865700	+	0.500564i	$0.166874\pi$
$180$		0			0
$181$	−3.42840			−0.254831			−0.127415	−	0.991849i	$-0.540668\pi$
$181$	−3.42840			−0.254831			−0.127415	+	0.991849i	$0.540668\pi$
$182$	1.49961	−	0.336022i	0.111158	−	0.0249076i
$183$		0			0
$184$	−8.80176	−	11.3106i	−0.648874	−	0.833831i
$185$			3.50937i			0.258014i
$186$		0			0
$187$			0.139116i			0.0101732i
$188$	−15.4665	+	7.29766i	−1.12801	+	0.532236i
$189$		0			0
$190$	−2.16671	−	9.66965i	−0.157190	−	0.701510i
$191$	−4.64106			−0.335815			−0.167908	−	0.985803i	$-0.553701\pi$
$191$	−4.64106			−0.335815			−0.167908	+	0.985803i	$0.553701\pi$
$192$		0			0
$193$	0.00850975			0.000612545			0.000306273	−	1.00000i	$-0.499903\pi$
$193$	0.00850975			0.000612545			0.000306273		1.00000i	$0.499903\pi$
$194$	−1.40173	−	6.25567i	−0.100638	−	0.449131i
$195$		0			0
$196$	−11.0721	+	5.22424i	−0.790866	+	0.373160i
$197$		−	5.83271i		−	0.415564i	−0.978175	−	0.207782i	$-0.933376\pi$
$197$		−	5.83271i		−	0.415564i	0.978175	−	0.207782i	$-0.0666244\pi$
$198$		0			0
$199$		−	8.61133i		−	0.610441i	−0.952282	−	0.305220i	$-0.901270\pi$
$199$		−	8.61133i		−	0.610441i	0.952282	−	0.305220i	$-0.0987302\pi$
$200$	−1.73705	−	2.23218i	−0.122828	−	0.157839i
$201$		0			0
$202$	−1.69940	+	0.380791i	−0.119570	+	0.0267924i
$203$	−8.57027			−0.601515
$204$		0			0
$205$	−3.30373			−0.230742
$206$	8.45905	−	1.89545i	0.589370	−	0.132062i
$207$		0			0
$208$	2.94842	−	3.57918i	0.204436	−	0.248171i
$209$		−	4.09093i		−	0.282976i
$210$		0			0
$211$		−	2.27443i		−	0.156578i	−0.996931	−	0.0782891i	$-0.975054\pi$
$211$		−	2.27443i		−	0.156578i	0.996931	−	0.0782891i	$-0.0249457\pi$
$212$	−10.1592	−	21.5311i	−0.697734	−	1.47876i
$213$		0			0
$214$	2.33452	+	10.4185i	0.159584	+	0.712197i
$215$	−10.7990			−0.736488
$216$		0			0
$217$	−5.88196			−0.399293
$218$	1.84631	+	8.23976i	0.125048	+	0.558067i
$219$		0			0
$220$	−0.498268	−	1.05602i	−0.0335932	−	0.0711967i
$221$			0.276239i			0.0185819i
$222$		0			0
$223$		−	11.9828i		−	0.802430i	−0.915984	−	0.401215i	$-0.868588\pi$
$223$		−	11.9828i		−	0.802430i	0.915984	−	0.401215i	$-0.131412\pi$
$224$	2.39496	−	4.73079i	0.160020	−	0.316089i
$225$		0			0
$226$	21.2846	−	4.76932i	1.41583	−	0.317250i
$227$	−13.7868			−0.915059			−0.457530	−	0.889194i	$-0.651266\pi$
$227$	−13.7868			−0.915059			−0.457530	+	0.889194i	$0.651266\pi$
$228$		0			0
$229$	−12.8756			−0.850842			−0.425421	−	0.904995i	$-0.639874\pi$
$229$	−12.8756			−0.850842			−0.425421	+	0.904995i	$0.639874\pi$
$230$	−6.99252	+	1.56684i	−0.461073	+	0.103314i
$231$		0			0
$232$	−20.4090	+	15.8819i	−1.33991	+	1.04270i
$233$			10.2353i			0.670535i	0.942123	+	0.335268i	$0.108827\pi$
$233$			10.2353i			0.670535i	−0.942123	+	0.335268i	$0.891173\pi$
$234$		0			0
$235$			8.55084i			0.557796i
$236$	17.8925	−	8.44233i	1.16470	−	0.549549i
$237$		0			0
$238$	0.0690653	+	0.308226i	0.00447684	+	0.0199793i
$239$	−17.0727			−1.10434			−0.552171	−	0.833731i	$-0.686201\pi$
$239$	−17.0727			−1.10434			−0.552171	+	0.833731i	$0.686201\pi$
$240$		0			0
$241$	−21.5148			−1.38589			−0.692946	−	0.720990i	$-0.743688\pi$
$241$	−21.5148			−1.38589			−0.692946	+	0.720990i	$0.743688\pi$
$242$	3.29602	+	14.7095i	0.211876	+	0.945565i
$243$		0			0
$244$	−12.0570	+	5.68896i	−0.771873	+	0.364198i
$245$			6.12137i			0.391080i
$246$		0			0
$247$		−	8.12326i		−	0.516871i
$248$	−14.0071	+	10.9001i	−0.889452	+	0.692158i
$249$		0			0
$250$	−1.37999	+	0.309220i	−0.0872785	+	0.0195568i
$251$	29.3692			1.85377			0.926884	−	0.375348i	$-0.122477\pi$
$251$	29.3692			1.85377			0.926884	+	0.375348i	$0.122477\pi$
$252$		0			0
$253$	−2.95832			−0.185988
$254$	28.9530	−	6.48759i	1.81667	−	0.407068i
$255$		0			0
$256$	−3.06355	−	15.7040i	−0.191472	−	0.981498i
$257$		−	8.36711i		−	0.521926i	−0.965349	−	0.260963i	$-0.915960\pi$
$257$		−	8.36711i		−	0.521926i	0.965349	−	0.260963i	$-0.0840401\pi$
$258$		0			0
$259$			3.28952i			0.204401i
$260$	−0.989398	−	2.09691i	−0.0613599	−	0.130045i
$261$		0			0
$262$	−3.71447	−	16.5770i	−0.229481	−	1.02413i
$263$	0.404535			0.0249447			0.0124723	−	0.999922i	$-0.496030\pi$
$263$	0.404535			0.0249447			0.0124723	+	0.999922i	$0.496030\pi$
$264$		0			0
$265$	−11.9037			−0.731241
$266$	−2.03098	−	9.06389i	−0.124527	−	0.555743i
$267$		0			0
$268$	7.58554	+	16.0766i	0.463361	+	0.982036i
$269$			18.7650i			1.14412i	0.820211	+	0.572061i	$0.193856\pi$
$269$			18.7650i			1.14412i	−0.820211	+	0.572061i	$0.806144\pi$
$270$		0			0
$271$		−	12.2886i		−	0.746476i	−0.927736	−	0.373238i	$-0.878247\pi$
$271$		−	12.2886i		−	0.746476i	0.927736	−	0.373238i	$-0.121753\pi$
$272$	0.735657	+	0.606012i	0.0446058	+	0.0367449i
$273$		0			0
$274$	4.43212	−	0.993119i	0.267754	−	0.0599965i
$275$	−0.583833			−0.0352065
$276$		0			0
$277$	13.8971			0.834998			0.417499	−	0.908677i	$-0.362907\pi$
$277$	13.8971			0.834998			0.417499	+	0.908677i	$0.362907\pi$
$278$	1.53446	−	0.343832i	0.0920310	−	0.0206217i
$279$		0			0
$280$	−1.62823	−	2.09235i	−0.0973056	−	0.125042i
$281$		−	17.5117i		−	1.04466i	−0.852742	−	0.522332i	$-0.825062\pi$
$281$		−	17.5117i		−	1.04466i	0.852742	−	0.522332i	$-0.174938\pi$
$282$		0			0
$283$			3.59103i			0.213464i	0.994288	+	0.106732i	$0.0340388\pi$
$283$			3.59103i			0.213464i	−0.994288	+	0.106732i	$0.965961\pi$
$284$	16.2056	−	7.64639i	0.961624	−	0.453730i
$285$		0			0
$286$	−0.209292	−	0.934034i	−0.0123757	−	0.0552306i
$287$	−3.09676			−0.182796
$288$		0			0
$289$	16.9432			0.996660
$290$	2.82721	+	12.6173i	0.166019	+	0.740916i
$291$		0			0
$292$	−21.2190	+	10.0119i	−1.24175	+	0.585903i
$293$		−	0.795050i		−	0.0464473i	−0.999730	−	0.0232237i	$-0.992607\pi$
$293$		−	0.795050i		−	0.0464473i	0.999730	−	0.0232237i	$-0.00739299\pi$
$294$		0			0
$295$		−	9.89209i		−	0.575940i
$296$	6.09595	+	7.83356i	0.354320	+	0.455316i
$297$		0			0
$298$	−1.12726	+	0.252589i	−0.0653005	+	0.0146321i
$299$	−5.87426			−0.339717
$300$		0			0
$301$	−10.1225			−0.583452
$302$	−24.3359	+	5.45302i	−1.40037	+	0.313786i
$303$		0			0
$304$	−21.6332	−	17.8208i	−1.24075	−	1.02209i
$305$			6.66589i			0.381688i
$306$		0			0
$307$			10.0055i			0.571044i	0.958372	+	0.285522i	$0.0921669\pi$
$307$			10.0055i			0.571044i	−0.958372	+	0.285522i	$0.907833\pi$
$308$	−0.467054	−	0.989863i	−0.0266129	−	0.0564027i
$309$		0			0
$310$	1.94037	+	8.65955i	0.110206	+	0.491829i
$311$	1.73079			0.0981442			0.0490721	−	0.998795i	$-0.484374\pi$
$311$	1.73079			0.0981442			0.0490721	+	0.998795i	$0.484374\pi$
$312$		0			0
$313$	3.11120			0.175855			0.0879277	−	0.996127i	$-0.471976\pi$
$313$	3.11120			0.175855			0.0879277	+	0.996127i	$0.471976\pi$
$314$	−6.42840	−	28.6888i	−0.362775	−	1.61900i
$315$		0			0
$316$	−4.31065	−	9.13589i	−0.242493	−	0.513934i
$317$		−	3.74863i		−	0.210544i	−0.994443	−	0.105272i	$-0.966429\pi$
$317$		−	3.74863i		−	0.210544i	0.994443	−	0.105272i	$-0.0335713\pi$
$318$		0			0
$319$			5.33801i			0.298871i
$320$	−7.75484	−	1.96530i	−0.433509	−	0.109864i
$321$		0			0
$322$	−6.55447	+	1.46868i	−0.365266	+	0.0818464i
$323$	1.66964			0.0929011
$324$		0			0
$325$	−1.15930			−0.0643065
$326$	−4.44769	+	0.996609i	−0.246335	+	0.0551971i
$327$		0			0
$328$	−7.37453	+	5.73875i	−0.407190	+	0.316869i
$329$			8.01517i			0.441891i
$330$		0			0
$331$			21.3257i			1.17217i	0.810251	+	0.586083i	$0.199331\pi$
$331$			21.3257i			1.17217i	−0.810251	+	0.586083i	$0.800669\pi$
$332$	8.55431	−	4.03624i	0.469479	−	0.221517i
$333$		0			0
$334$	−4.23723	−	18.9100i	−0.231851	−	1.03471i
$335$	8.88817			0.485612
$336$		0			0
$337$	−0.987577			−0.0537967			−0.0268984	−	0.999638i	$-0.508563\pi$
$337$	−0.987577			−0.0537967			−0.0268984	+	0.999638i	$0.508563\pi$
$338$	3.60427	+	16.0852i	0.196047	+	0.874921i
$339$		0			0
$340$	0.430994	−	0.203359i	0.0233739	−	0.0110287i
$341$			3.66359i			0.198394i
$342$		0			0
$343$			12.2994i			0.664104i
$344$	−24.1054	+	18.7585i	−1.29968	+	1.01139i
$345$		0			0
$346$	17.3033	−	3.87722i	0.930233	−	0.208440i
$347$	17.9284			0.962446			0.481223	−	0.876598i	$-0.340193\pi$
$347$	17.9284			0.962446			0.481223	+	0.876598i	$0.340193\pi$
$348$		0			0
$349$	12.0029			0.642502			0.321251	−	0.946994i	$-0.395897\pi$
$349$	12.0029			0.642502			0.321251	+	0.946994i	$0.395897\pi$
$350$	−1.29354	+	0.289849i	−0.0691428	+	0.0154931i
$351$		0			0
$352$	−2.94658	−	1.49171i	−0.157053	−	0.0795083i
$353$			27.4808i			1.46265i	0.682027	+	0.731327i	$0.261099\pi$
$353$			27.4808i			1.46265i	−0.682027	+	0.731327i	$0.738901\pi$
$354$		0			0
$355$		−	8.95946i		−	0.475519i
$356$	−2.01707	−	4.27493i	−0.106905	−	0.226571i
$357$		0			0
$358$	−7.16294	−	31.9669i	−0.378573	−	1.68950i
$359$	−7.30964			−0.385788			−0.192894	−	0.981220i	$-0.561787\pi$
$359$	−7.30964			−0.385788			−0.192894	+	0.981220i	$0.561787\pi$
$360$		0			0
$361$	−30.0984			−1.58413
$362$	1.06013	+	4.73117i	0.0557191	+	0.248665i
$363$		0			0
$364$	−0.927417	−	1.96554i	−0.0486098	−	0.103023i
$365$			11.7312i			0.614039i
$366$		0			0
$367$		−	17.1378i		−	0.894586i	−0.894387	−	0.447293i	$-0.852388\pi$
$367$		−	17.1378i		−	0.894586i	0.894387	−	0.447293i	$-0.147612\pi$
$368$	−12.8869	+	15.6438i	−0.671777	+	0.815492i
$369$		0			0
$370$	4.84290	−	1.08517i	0.251771	−	0.0564151i
$371$	−11.1580			−0.579295
$372$		0			0
$373$	15.9720			0.826997			0.413499	−	0.910505i	$-0.364307\pi$
$373$	15.9720			0.826997			0.413499	+	0.910505i	$0.364307\pi$
$374$	0.191979	−	0.0430174i	0.00992701	−	0.00222438i
$375$		0			0
$376$	14.8533	+	19.0871i	0.765998	+	0.984340i
$377$			10.5995i			0.545904i
$378$		0			0
$379$		−	27.3396i		−	1.40434i	−0.712010	−	0.702169i	$-0.752215\pi$
$379$		−	27.3396i		−	1.40434i	0.712010	−	0.702169i	$-0.247785\pi$
$380$	−12.6741	+	5.98010i	−0.650166	+	0.306772i
$381$		0			0
$382$	1.43511	+	6.40463i	0.0734264	+	0.327689i
$383$	−15.1449			−0.773869			−0.386934	−	0.922107i	$-0.626466\pi$
$383$	−15.1449			−0.773869			−0.386934	+	0.922107i	$0.626466\pi$
$384$		0			0
$385$	−0.547258			−0.0278909
$386$	−0.00263138	−	0.0117434i	−0.000133934	−	0.000597723i
$387$		0			0
$388$	−8.19934	+	3.86875i	−0.416259	+	0.196406i
$389$		−	20.7441i		−	1.05177i	−0.850557	−	0.525883i	$-0.823735\pi$
$389$		−	20.7441i		−	1.05177i	0.850557	−	0.525883i	$-0.176265\pi$
$390$		0			0
$391$		−	1.20738i		−	0.0610600i
$392$	10.6331	+	13.6640i	0.537054	+	0.690137i
$393$		0			0
$394$	−8.04911	+	1.80359i	−0.405508	+	0.0908636i
$395$	−5.05089			−0.254138
$396$		0			0
$397$	32.0445			1.60827			0.804133	−	0.594449i	$-0.202630\pi$
$397$	32.0445			1.60827			0.804133	+	0.594449i	$0.202630\pi$
$398$	−11.8836	+	2.66279i	−0.595670	+	0.133474i
$399$		0			0
$400$	−2.54327	+	3.08736i	−0.127164	+	0.154368i
$401$		−	29.6605i		−	1.48118i	−0.671960	−	0.740588i	$-0.734547\pi$
$401$		−	29.6605i		−	1.48118i	0.671960	−	0.740588i	$-0.265453\pi$
$402$		0			0
$403$			7.27469i			0.362378i
$404$	1.05098	+	2.22742i	0.0522881	+	0.110818i
$405$		0			0
$406$	2.65010	+	11.8269i	0.131522	+	0.586960i
$407$	2.04888			0.101559
$408$		0			0
$409$	−22.7174			−1.12330			−0.561652	−	0.827374i	$-0.689834\pi$
$409$	−22.7174			−1.12330			−0.561652	+	0.827374i	$0.689834\pi$
$410$	1.02158	+	4.55912i	0.0504521	+	0.225159i
$411$		0			0
$412$	−5.23141	−	11.0873i	−0.257733	−	0.546234i
$413$		−	9.27239i		−	0.456265i
$414$		0			0
$415$		−	4.72936i		−	0.232155i
$416$	−5.85096	−	2.96205i	−0.286867	−	0.145226i
$417$		0			0
$418$	−5.64546	+	1.26500i	−0.276129	+	0.0618730i
$419$	8.45974			0.413285			0.206643	−	0.978416i	$-0.433746\pi$
$419$	8.45974			0.413285			0.206643	+	0.978416i	$0.433746\pi$
$420$		0			0
$421$	−24.9034			−1.21372			−0.606860	−	0.794809i	$-0.707571\pi$
$421$	−24.9034			−1.21372			−0.606860	+	0.794809i	$0.707571\pi$
$422$	−3.13870	+	0.703299i	−0.152789	+	0.0342360i
$423$		0			0
$424$	−26.5713	+	20.6774i	−1.29042	+	1.00418i
$425$		−	0.238281i		−	0.0115583i
$426$		0			0
$427$			6.24830i			0.302377i
$428$	13.6557	−	6.44324i	0.660071	−	0.311446i
$429$		0			0
$430$	3.33927	+	14.9026i	0.161034	+	0.718667i
$431$	−9.37049			−0.451360			−0.225680	−	0.974201i	$-0.572460\pi$
$431$	−9.37049			−0.451360			−0.225680	+	0.974201i	$0.572460\pi$
$432$		0			0
$433$	−28.2137			−1.35586			−0.677932	−	0.735125i	$-0.737124\pi$
$433$	−28.2137			−1.35586			−0.677932	+	0.735125i	$0.737124\pi$
$434$	1.81882	+	8.11707i	0.0873060	+	0.389632i
$435$		0			0
$436$	10.7999	−	5.09579i	0.517222	−	0.244044i
$437$			35.5051i			1.69844i
$438$		0			0
$439$		−	9.57545i		−	0.457011i	−0.973543	−	0.228506i	$-0.926616\pi$
$439$		−	9.57545i		−	0.457011i	0.973543	−	0.228506i	$-0.0733839\pi$
$440$	−1.30322	+	1.01415i	−0.0621287	+	0.0483476i
$441$		0			0
$442$	0.381208	−	0.0854186i	0.0181322	−	0.00406295i
$443$	−7.35226			−0.349316			−0.174658	−	0.984629i	$-0.555882\pi$
$443$	−7.35226			−0.349316			−0.174658	+	0.984629i	$0.555882\pi$
$444$		0			0
$445$	−2.36345			−0.112038
$446$	−16.5362	+	3.70533i	−0.783014	+	0.175453i
$447$		0			0
$448$	−7.26904	−	1.84218i	−0.343430	−	0.0870349i
$449$		−	26.6328i		−	1.25688i	−0.777858	−	0.628440i	$-0.783694\pi$
$449$		−	26.6328i		−	1.25688i	0.777858	−	0.628440i	$-0.216306\pi$
$450$		0			0
$451$			1.92883i			0.0908248i
$452$	−13.1633	−	27.8979i	−0.619147	−	1.31221i
$453$		0			0
$454$	4.26314	+	19.0256i	0.200079	+	0.892917i
$455$	−1.08668			−0.0509442
$456$		0			0
$457$	5.28463			0.247205			0.123602	−	0.992332i	$-0.460555\pi$
$457$	5.28463			0.247205			0.123602	+	0.992332i	$0.460555\pi$
$458$	3.98138	+	17.7682i	0.186038	+	0.830254i
$459$		0			0
$460$	4.32445	+	9.16514i	0.201629	+	0.427327i
$461$			10.4495i			0.486683i	0.969941	+	0.243342i	$0.0782436\pi$
$461$			10.4495i			0.486683i	−0.969941	+	0.243342i	$0.921756\pi$
$462$		0			0
$463$			11.6136i			0.539728i	0.962898	+	0.269864i	$0.0869787\pi$
$463$			11.6136i			0.539728i	−0.962898	+	0.269864i	$0.913021\pi$
$464$	28.2278	+	23.2532i	1.31044	+	1.07950i
$465$		0			0
$466$	14.1246	−	3.16495i	0.654310	−	0.146613i
$467$	−32.6615			−1.51139			−0.755697	−	0.654921i	$-0.772702\pi$
$467$	−32.6615			−1.51139			−0.755697	+	0.654921i	$0.772702\pi$
$468$		0			0
$469$	8.33136			0.384707
$470$	11.8001	−	2.64409i	0.544299	−	0.121963i
$471$		0			0
$472$	−17.1831	−	22.0810i	−0.790915	−	1.01636i
$473$			6.30483i			0.289896i
$474$		0			0
$475$			7.00703i			0.321504i
$476$	0.403994	−	0.190619i	0.0185170	−	0.00873702i
$477$		0			0
$478$	5.27922	+	23.5602i	0.241466	+	1.07762i
$479$	14.9123			0.681362			0.340681	−	0.940179i	$-0.389342\pi$
$479$	14.9123			0.681362			0.340681	+	0.940179i	$0.389342\pi$
$480$		0			0
$481$	4.06842			0.185504
$482$	6.65281	+	29.6903i	0.303027	+	1.35236i
$483$		0			0
$484$	19.2799	−	9.09697i	0.876359	−	0.413498i
$485$			4.53311i			0.205838i
$486$		0			0
$487$			23.3946i			1.06011i	0.847964	+	0.530054i	$0.177829\pi$
$487$			23.3946i			1.06011i	−0.847964	+	0.530054i	$0.822171\pi$
$488$	11.5790	+	14.8795i	0.524157	+	0.673563i
$489$		0			0
$490$	8.44745	−	1.89285i	0.381617	−	0.0855101i
$491$	−28.4392			−1.28344			−0.641721	−	0.766938i	$-0.721779\pi$
$491$	−28.4392			−1.28344			−0.641721	+	0.766938i	$0.721779\pi$
$492$		0			0
$493$	−2.17861			−0.0981196
$494$	−11.2100	+	2.51187i	−0.504364	+	0.113015i
$495$		0			0
$496$	19.3734	+	15.9592i	0.869890	+	0.716589i
$497$		−	8.39819i		−	0.376710i
$498$		0			0
$499$			0.291283i			0.0130396i	0.999979	+	0.00651981i	$0.00207533\pi$
$499$			0.291283i			0.0130396i	−0.999979	+	0.00651981i	$0.997925\pi$
$500$	0.853443	+	1.80877i	0.0381671	+	0.0808905i
$501$		0			0
$502$	−9.08154	−	40.5293i	−0.405329	−	1.80891i
$503$	−15.1659			−0.676212			−0.338106	−	0.941108i	$-0.609786\pi$
$503$	−15.1659			−0.676212			−0.338106	+	0.941108i	$0.609786\pi$
$504$		0			0
$505$	1.23146			0.0547991
$506$	0.914771	+	4.08246i	0.0406665	+	0.181488i
$507$		0			0
$508$	−17.9057	−	37.9489i	−0.794436	−	1.68371i
$509$		−	32.5437i		−	1.44248i	−0.692688	−	0.721238i	$-0.743574\pi$
$509$		−	32.5437i		−	1.44248i	0.692688	−	0.721238i	$-0.256426\pi$
$510$		0			0
$511$			10.9963i			0.486447i
$512$	−20.7241	+	9.08366i	−0.915883	+	0.401445i
$513$		0			0
$514$	−11.5466	+	2.58728i	−0.509297	+	0.114120i
$515$	−6.12978			−0.270110
$516$		0			0
$517$	4.99226			0.219560
$518$	4.53952	−	1.01718i	0.199455	−	0.0446925i
$519$		0			0
$520$	−2.58778	+	2.01377i	−0.113482	+	0.0883096i
$521$		−	29.6176i		−	1.29757i	−0.760971	−	0.648786i	$-0.775277\pi$
$521$		−	29.6176i		−	1.29757i	0.760971	−	0.648786i	$-0.224723\pi$
$522$		0			0
$523$		−	33.5009i		−	1.46489i	−0.680824	−	0.732447i	$-0.738378\pi$
$523$		−	33.5009i		−	1.46489i	0.680824	−	0.732447i	$-0.261622\pi$
$524$	−21.7276	+	10.2519i	−0.949175	+	0.447856i
$525$		0			0
$526$	−0.125090	−	0.558255i	−0.00545419	−	0.0243411i
$527$	−1.49523			−0.0651330
$528$		0			0
$529$	2.67517			0.116312
$530$	3.68087	+	16.4271i	0.159887	+	0.713547i
$531$		0			0
$532$	−11.8801	+	5.60547i	−0.515068	+	0.243028i
$533$			3.83002i			0.165897i
$534$		0			0
$535$		−	7.54970i		−	0.326402i
$536$	19.8400	−	15.4392i	0.856959	−	0.666872i
$537$		0			0
$538$	25.8956	−	5.80251i	1.11644	−	0.250164i
$539$	3.57386			0.153937
$540$		0			0
$541$	−15.6319			−0.672069			−0.336035	−	0.941850i	$-0.609086\pi$
$541$	−15.6319			−0.672069			−0.336035	+	0.941850i	$0.609086\pi$
$542$	−16.9581	+	3.79986i	−0.728414	+	0.163218i
$543$		0			0
$544$	0.608813	−	1.20259i	0.0261026	−	0.0515608i
$545$		−	5.97087i		−	0.255764i
$546$		0			0
$547$			4.24155i			0.181355i	0.995880	+	0.0906777i	$0.0289033\pi$
$547$			4.24155i			0.181355i	−0.995880	+	0.0906777i	$0.971097\pi$
$548$	−2.74100	−	5.80920i	−0.117090	−	0.248157i
$549$		0			0
$550$	0.180533	+	0.805686i	0.00769794	+	0.0343546i
$551$	64.0655			2.72928
$552$		0			0
$553$	−4.73448			−0.201330
$554$	−4.29727	−	19.1780i	−0.182574	−	0.814794i
$555$		0			0
$556$	−0.948973	−	2.01123i	−0.0402454	−	0.0852952i
$557$		−	35.6028i		−	1.50854i	−0.656565	−	0.754270i	$-0.727991\pi$
$557$		−	35.6028i		−	1.50854i	0.656565	−	0.754270i	$-0.272009\pi$
$558$		0			0
$559$			12.5193i			0.529512i
$560$	−2.38395	+	2.89395i	−0.100740	+	0.122292i
$561$		0			0
$562$	−24.1661	+	5.41498i	−1.01939	+	0.228417i
$563$	20.4216			0.860669			0.430335	−	0.902669i	$-0.358396\pi$
$563$	20.4216			0.860669			0.430335	+	0.902669i	$0.358396\pi$
$564$		0			0
$565$	−15.4237			−0.648880
$566$	4.95560	−	1.11042i	0.208299	−	0.0466743i
$567$		0			0
$568$	−15.5631	−	19.9992i	−0.653011	−	0.839147i
$569$		−	3.22452i		−	0.135179i	−0.997713	−	0.0675895i	$-0.978469\pi$
$569$		−	3.22452i		−	0.135179i	0.997713	−	0.0675895i	$-0.0215308\pi$
$570$		0			0
$571$		−	39.5982i		−	1.65713i	−0.559892	−	0.828566i	$-0.689157\pi$
$571$		−	39.5982i		−	1.65713i	0.559892	−	0.828566i	$-0.310843\pi$
$572$	−1.22424	+	0.577643i	−0.0511882	+	0.0241525i
$573$		0			0
$574$	0.957581	+	4.27352i	0.0399686	+	0.178373i
$575$	5.06707			0.211311
$576$		0			0
$577$	−20.9763			−0.873254			−0.436627	−	0.899643i	$-0.643827\pi$
$577$	−20.9763			−0.873254			−0.436627	+	0.899643i	$0.643827\pi$
$578$	−5.23918	−	23.3815i	−0.217921	−	0.972544i
$579$		0			0
$580$	16.5376	−	7.80306i	0.686687	−	0.324005i
$581$		−	4.43309i		−	0.183915i
$582$		0			0
$583$			6.94979i			0.287831i
$584$	20.3777	+	26.1862i	0.843236	+	1.08359i
$585$		0			0
$586$	−1.09716	+	0.245845i	−0.0453234	+	0.0101558i
$587$	7.19898			0.297134			0.148567	−	0.988902i	$-0.452534\pi$
$587$	7.19898			0.297134			0.148567	+	0.988902i	$0.452534\pi$
$588$		0			0
$589$	43.9695			1.81173
$590$	−13.6510	+	3.05883i	−0.562004	+	0.125930i
$591$		0			0
$592$	8.92527	−	10.8347i	0.366826	−	0.445302i
$593$			5.52785i			0.227002i	0.993538	+	0.113501i	$0.0362065\pi$
$593$			5.52785i			0.227002i	−0.993538	+	0.113501i	$0.963794\pi$
$594$		0			0
$595$		−	0.223353i		−	0.00915659i
$596$	0.697143	+	1.47751i	0.0285561	+	0.0605211i
$597$		0			0
$598$	1.81644	+	8.10645i	0.0742797	+	0.331497i
$599$	16.5186			0.674931			0.337465	−	0.941338i	$-0.390430\pi$
$599$	16.5186			0.674931			0.337465	+	0.941338i	$0.390430\pi$
$600$		0			0
$601$	−19.1988			−0.783137			−0.391568	−	0.920149i	$-0.628067\pi$
$601$	−19.1988			−0.783137			−0.391568	+	0.920149i	$0.628067\pi$
$602$	3.13008	+	13.9690i	0.127573	+	0.569335i
$603$		0			0
$604$	15.0503	+	31.8972i	0.612387	+	1.29788i
$605$		−	10.6591i		−	0.433356i
$606$		0			0
$607$			10.1073i			0.410244i	0.978736	+	0.205122i	$0.0657591\pi$
$607$			10.1073i			0.410244i	−0.978736	+	0.205122i	$0.934241\pi$
$608$	−17.9031	+	35.3642i	−0.726068	+	1.43421i
$609$		0			0
$610$	9.19889	−	2.06123i	0.372452	−	0.0834566i
$611$	9.91301			0.401038
$612$		0			0
$613$	33.5309			1.35430			0.677151	−	0.735844i	$-0.263214\pi$
$613$	33.5309			1.35430			0.677151	+	0.735844i	$0.263214\pi$
$614$	13.8075	−	3.09390i	0.557226	−	0.124859i
$615$		0			0
$616$	−1.22158	+	0.950616i	−0.0492189	+	0.0383014i
$617$		−	36.9803i		−	1.48877i	−0.667751	−	0.744385i	$-0.732743\pi$
$617$		−	36.9803i		−	1.48877i	0.667751	−	0.744385i	$-0.267257\pi$
$618$		0			0
$619$			17.1466i			0.689182i	0.938753	+	0.344591i	$0.111982\pi$
$619$			17.1466i			0.689182i	−0.938753	+	0.344591i	$0.888018\pi$
$620$	11.3501	−	5.35541i	0.455832	−	0.215078i
$621$		0			0
$622$	−0.535195	−	2.38848i	−0.0214594	−	0.0957694i
$623$	−2.21539			−0.0887578
$624$		0			0
$625$	1.00000			0.0400000
$626$	−0.962045	−	4.29344i	−0.0384510	−	0.171600i
$627$		0			0
$628$	−37.6026	+	17.7423i	−1.50051	+	0.707995i
$629$			0.836214i			0.0333420i
$630$		0			0
$631$		−	3.80264i		−	0.151381i	−0.997131	−	0.0756904i	$-0.975884\pi$
$631$		−	3.80264i		−	0.151381i	0.997131	−	0.0756904i	$-0.0241161\pi$
$632$	−11.2745	+	8.77367i	−0.448477	+	0.348998i
$633$		0			0
$634$	−5.17309	+	1.15915i	−0.205449	+	0.0460357i
$635$	−20.9805			−0.832587
$636$		0			0
$637$	7.09651			0.281174
$638$	7.36642	−	1.65062i	0.291639	−	0.0653486i
$639$		0			0
$640$	−0.314150	+	11.3093i	−0.0124179	+	0.447041i
$641$		−	1.19800i		−	0.0473181i	−0.999720	−	0.0236590i	$-0.992468\pi$
$641$		−	1.19800i		−	0.0473181i	0.999720	−	0.0236590i	$-0.00753161\pi$
$642$		0			0
$643$		−	16.4025i		−	0.646850i	−0.946254	−	0.323425i	$-0.895166\pi$
$643$		−	16.4025i		−	0.646850i	0.946254	−	0.323425i	$-0.104834\pi$
$644$	4.05354	+	8.59098i	0.159732	+	0.338532i
$645$		0			0
$646$	−0.516285	−	2.30409i	−0.0203130	−	0.0906532i
$647$	−4.22993			−0.166296			−0.0831478	−	0.996537i	$-0.526497\pi$
$647$	−4.22993			−0.166296			−0.0831478	+	0.996537i	$0.526497\pi$
$648$		0			0
$649$	−5.77533			−0.226701
$650$	0.358479	+	1.59983i	0.0140607	+	0.0627505i
$651$		0			0
$652$	2.75063	+	5.82961i	0.107723	+	0.228305i
$653$		−	4.93688i		−	0.193195i	−0.995324	−	0.0965976i	$-0.969204\pi$
$653$		−	4.93688i		−	0.193195i	0.995324	−	0.0965976i	$-0.0307960\pi$
$654$		0			0
$655$			12.0124i			0.469363i
$656$	10.1998	+	8.40227i	0.398235	+	0.328054i
$657$		0			0
$658$	11.0609	−	2.47845i	0.431198	−	0.0966200i
$659$	18.9341			0.737570			0.368785	−	0.929515i	$-0.379774\pi$
$659$	18.9341			0.737570			0.368785	+	0.929515i	$0.379774\pi$
$660$		0			0
$661$	−26.1461			−1.01697			−0.508483	−	0.861072i	$-0.669794\pi$
$661$	−26.1461			−1.01697			−0.508483	+	0.861072i	$0.669794\pi$
$662$	29.4293	−	6.59433i	1.14380	−	0.256296i
$663$		0			0
$664$	−8.21515	−	10.5568i	−0.318810	−	0.409684i
$665$			6.56807i			0.254699i
$666$		0			0
$667$		−	46.3284i		−	1.79384i
$668$	−24.7855	+	11.6947i	−0.958978	+	0.452482i
$669$		0			0
$670$	−2.74840	−	12.2656i	−0.106180	−	0.473862i
$671$	3.89177			0.150240
$672$		0			0
$673$	−32.1139			−1.23790			−0.618949	−	0.785431i	$-0.712441\pi$
$673$	−32.1139			−1.23790			−0.618949	+	0.785431i	$0.712441\pi$
$674$	0.305378	+	1.36285i	0.0117627	+	0.0524950i
$675$		0			0
$676$	21.0830	−	9.94775i	0.810885	−	0.382606i
$677$		−	13.5593i		−	0.521125i	−0.965457	−	0.260563i	$-0.916092\pi$
$677$		−	13.5593i		−	0.521125i	0.965457	−	0.260563i	$-0.0839080\pi$
$678$		0			0
$679$			4.24913i			0.163067i
$680$	−0.413906	−	0.531886i	−0.0158726	−	0.0203969i
$681$		0			0
$682$	5.05573	−	1.13285i	0.193594	−	0.0433792i
$683$	20.9171			0.800369			0.400185	−	0.916435i	$-0.368946\pi$
$683$	20.9171			0.800369			0.400185	+	0.916435i	$0.368946\pi$
$684$		0			0
$685$	−3.21169			−0.122713
$686$	16.9731	−	3.80321i	0.648034	−	0.145207i
$687$		0			0
$688$	33.3405	+	27.4649i	1.27109	+	1.04709i
$689$			13.8000i			0.525739i
$690$		0			0
$691$			1.01908i			0.0387675i	0.999812	+	0.0193837i	$0.00617043\pi$
$691$			1.01908i			0.0387675i	−0.999812	+	0.0193837i	$0.993830\pi$
$692$	−10.7011	−	22.6796i	−0.406794	−	0.862149i
$693$		0			0
$694$	−5.54381	−	24.7411i	−0.210440	−	0.939158i
$695$	−1.11194			−0.0421781
$696$		0			0
$697$	−0.787214			−0.0298179
$698$	−3.71154	−	16.5640i	−0.140484	−	0.626956i
$699$		0			0
$700$	0.799978	+	1.69546i	0.0302363	+	0.0640822i
$701$		−	16.7130i		−	0.631241i	−0.948885	−	0.315621i	$-0.897787\pi$
$701$		−	16.7130i		−	0.631241i	0.948885	−	0.315621i	$-0.102213\pi$
$702$		0			0
$703$		−	24.5902i		−	0.927438i
$704$	−1.14741	+	4.52753i	−0.0432445	+	0.170638i
$705$		0			0
$706$	37.9233	−	8.49760i	1.42726	−	0.319811i
$707$	1.15431			0.0434124
$708$		0			0
$709$	46.6046			1.75027			0.875136	−	0.483877i	$-0.160772\pi$
$709$	46.6046			1.75027			0.875136	+	0.483877i	$0.160772\pi$
$710$	−12.3640	+	2.77044i	−0.464013	+	0.103973i
$711$		0			0
$712$	−5.27566	+	4.10544i	−0.197714	+	0.153858i
$713$		−	31.7962i		−	1.19078i
$714$		0			0
$715$			0.676839i			0.0253123i
$716$	−41.8992	+	19.7696i	−1.56585	+	0.738825i
$717$		0			0
$718$	2.26029	+	10.0873i	0.0843531	+	0.376453i
$719$	16.2028			0.604264			0.302132	−	0.953266i	$-0.402302\pi$
$719$	16.2028			0.604264			0.302132	+	0.953266i	$0.402302\pi$
$720$		0			0
$721$	−5.74577			−0.213984
$722$	9.30702	+	41.5356i	0.346372	+	1.54580i
$723$		0			0
$724$	6.20117	−	2.92594i	0.230465	−	0.108742i
$725$		−	9.14304i		−	0.339564i
$726$		0			0
$727$		−	10.2518i		−	0.380219i	−0.981763	−	0.190110i	$-0.939116\pi$
$727$		−	10.2518i		−	0.380219i	0.981763	−	0.190110i	$-0.0608844\pi$
$728$	−2.42566	+	1.88761i	−0.0899011	+	0.0699597i
$729$		0			0
$730$	16.1890	−	3.62752i	0.599181	−	0.134261i
$731$	−2.57320			−0.0951732
$732$		0			0
$733$	−14.5321			−0.536757			−0.268379	−	0.963314i	$-0.586488\pi$
$733$	−14.5321			−0.536757			−0.268379	+	0.963314i	$0.586488\pi$
$734$	−23.6501	+	5.29935i	−0.872940	+	0.195603i
$735$		0			0
$736$	25.5733	+	12.9465i	0.942644	+	0.477214i
$737$		−	5.18921i		−	0.191147i
$738$		0			0
$739$			34.5703i			1.27169i	0.771818	+	0.635844i	$0.219348\pi$
$739$			34.5703i			1.27169i	−0.771818	+	0.635844i	$0.780652\pi$
$740$	−2.99504	−	6.34762i	−0.110100	−	0.233343i
$741$		0			0
$742$	3.45028	+	15.3980i	0.126664	+	0.565278i
$743$	−0.463375			−0.0169996			−0.00849978	−	0.999964i	$-0.502706\pi$
$743$	−0.463375			−0.0169996			−0.00849978	+	0.999964i	$0.502706\pi$
$744$		0			0
$745$	0.816859			0.0299274
$746$	−4.93885	−	22.0412i	−0.180824	−	0.806987i
$747$		0			0
$748$	−0.118728	−	0.251628i	−0.00434111	−	0.00920045i
$749$		−	7.07675i		−	0.258579i
$750$		0			0
$751$			32.6565i			1.19165i	0.803114	+	0.595826i	$0.203175\pi$
$751$			32.6565i			1.19165i	−0.803114	+	0.595826i	$0.796825\pi$
$752$	21.7471	−	26.3995i	0.793035	−	0.962691i
$753$		0			0
$754$	14.6273	−	3.27759i	0.532695	−	0.119363i
$755$	17.6348			0.641795
$756$		0			0
$757$	46.0622			1.67416			0.837080	−	0.547081i	$-0.184261\pi$
$757$	46.0622			1.67416			0.837080	+	0.547081i	$0.184261\pi$
$758$	−37.7284	+	8.45393i	−1.37036	+	0.307061i
$759$		0			0
$760$	12.1716	+	15.6410i	0.441509	+	0.567358i
$761$		−	34.4792i		−	1.24987i	−0.780677	−	0.624935i	$-0.785125\pi$
$761$		−	34.4792i		−	1.24987i	0.780677	−	0.624935i	$-0.214875\pi$
$762$		0			0
$763$		−	5.59682i		−	0.202618i
$764$	8.39459	−	3.96088i	0.303705	−	0.143299i
$765$		0			0
$766$	4.68310	+	20.8999i	0.169207	+	0.755143i
$767$	−11.4679			−0.414083
$768$		0			0
$769$	25.6900			0.926406			0.463203	−	0.886252i	$-0.346700\pi$
$769$	25.6900			0.926406			0.463203	+	0.886252i	$0.346700\pi$
$770$	0.169223	+	0.755213i	0.00609838	+	0.0272160i
$771$		0			0
$772$	−0.0153921	+	0.00726258i	−0.000553976	+	0.000261386i
$773$			2.14085i			0.0770009i	0.999259	+	0.0385004i	$0.0122581\pi$
$773$			2.14085i			0.0770009i	−0.999259	+	0.0385004i	$0.987742\pi$
$774$		0			0
$775$		−	6.27506i		−	0.225407i
$776$	7.87425	+	10.1187i	0.282669	+	0.363242i
$777$		0			0
$778$	−28.6267	+	6.41448i	−1.02632	+	0.229970i
$779$	23.1493			0.829410
$780$		0			0
$781$	−5.23083			−0.187174
$782$	−1.66618	+	0.373347i	−0.0595825	+	0.0133509i
$783$		0			0
$784$	15.5683	−	18.8988i	0.556010	−	0.674959i
$785$			20.7891i			0.741994i
$786$		0			0
$787$			49.0731i			1.74927i	0.484784	+	0.874634i	$0.338898\pi$
$787$			49.0731i			1.74927i	−0.484784	+	0.874634i	$0.661102\pi$
$788$	4.97789	+	10.5500i	0.177330	+	0.375829i
$789$		0			0
$790$	1.56184	+	6.97020i	0.0555676	+	0.247989i
$791$	−14.4575			−0.514049
$792$		0			0
$793$	7.72778			0.274422
$794$	−9.90879	−	44.2212i	−0.351650	−	1.56935i
$795$		0			0
$796$	7.34928	+	15.5759i	0.260488	+	0.552072i
$797$		−	14.2059i		−	0.503197i	−0.967832	−	0.251599i	$-0.919044\pi$
$797$		−	14.2059i		−	0.503197i	0.967832	−	0.251599i	$-0.0809563\pi$
$798$		0			0
$799$			2.03750i			0.0720816i
$800$	5.04696	+	2.55503i	0.178437	+	0.0903338i
$801$		0			0
$802$	−40.9313	+	9.17162i	−1.44534	+	0.323861i
$803$	6.84906			0.241698
$804$		0			0
$805$	4.74964			0.167403
$806$	10.0390	−	2.24948i	0.353610	−	0.0792345i
$807$		0			0
$808$	2.74884	−	2.13911i	0.0967039	−	0.0752535i
$809$		−	1.60355i		−	0.0563779i	−0.999603	−	0.0281890i	$-0.991026\pi$
$809$		−	1.60355i		−	0.0563779i	0.999603	−	0.0281890i	$-0.00897401\pi$
$810$		0			0
$811$			12.3766i			0.434601i	0.976105	+	0.217301i	$0.0697252\pi$
$811$			12.3766i			0.434601i	−0.976105	+	0.217301i	$0.930275\pi$
$812$	15.5016	−	7.31423i	0.544000	−	0.256679i
$813$		0			0
$814$	−0.633555	−	2.82745i	−0.0222061	−	0.0991020i
$815$	3.22298			0.112896
$816$		0			0
$817$	75.6691			2.64733
$818$	7.02468	+	31.3499i	0.245612	+	1.09612i
$819$		0			0
$820$	5.97567	−	2.81954i	0.208680	−	0.0984627i
$821$		−	35.7613i		−	1.24808i	−0.781393	−	0.624040i	$-0.785490\pi$
$821$		−	35.7613i		−	1.24808i	0.781393	−	0.624040i	$-0.214510\pi$
$822$		0			0
$823$		−	29.2578i		−	1.01986i	−0.860215	−	0.509932i	$-0.829671\pi$
$823$		−	29.2578i		−	1.01986i	0.860215	−	0.509932i	$-0.170329\pi$
$824$	−13.6828	+	10.6477i	−0.476663	+	0.370932i
$825$		0			0
$826$	−12.7958	+	2.86721i	−0.445224	+	0.0997629i
$827$	45.0397			1.56619			0.783093	−	0.621905i	$-0.213641\pi$
$827$	45.0397			1.56619			0.783093	+	0.621905i	$0.213641\pi$
$828$		0			0
$829$	43.0934			1.49670			0.748349	−	0.663306i	$-0.230847\pi$
$829$	43.0934			1.49670			0.748349	+	0.663306i	$0.230847\pi$
$830$	−6.52649	+	1.46241i	−0.226538	+	0.0507611i
$831$		0			0
$832$	−2.27838	+	8.99021i	−0.0789885	+	0.311679i
$833$			1.45860i			0.0505376i
$834$		0			0
$835$			13.7030i			0.474211i
$836$	3.49138	+	7.39954i	0.120752	+	0.255918i
$837$		0			0
$838$	−2.61592	−	11.6744i	−0.0903654	−	0.403285i
$839$	−21.3937			−0.738592			−0.369296	−	0.929312i	$-0.620401\pi$
$839$	−21.3937			−0.738592			−0.369296	+	0.929312i	$0.620401\pi$
$840$		0			0
$841$	−54.5952			−1.88259
$842$	7.70064	+	34.3666i	0.265381	+	1.18435i
$843$		0			0
$844$	1.94110	+	4.11391i	0.0668153	+	0.141607i
$845$		−	11.6560i		−	0.400979i
$846$		0			0
$847$		−	9.99139i		−	0.343308i
$848$	36.7511	+	30.2744i	1.26204	+	1.03963i
$849$		0			0
$850$	−0.328826	+	0.0736811i	−0.0112786	+	0.00252724i
$851$	−17.7822			−0.609566
$852$		0			0
$853$	45.3181			1.55166			0.775831	−	0.630941i	$-0.217331\pi$
$853$	45.3181			1.55166			0.775831	+	0.630941i	$0.217331\pi$
$854$	8.62262	−	1.93210i	0.295060	−	0.0661150i
$855$		0			0
$856$	−13.1142	−	16.8523i	−0.448235	−	0.576001i
$857$		−	5.59359i		−	0.191074i	−0.995426	−	0.0955368i	$-0.969543\pi$
$857$		−	5.59359i		−	0.191074i	0.995426	−	0.0955368i	$-0.0304568\pi$
$858$		0			0
$859$			47.6418i			1.62552i	0.582601	+	0.812759i	$0.302035\pi$
$859$			47.6418i			1.62552i	−0.582601	+	0.812759i	$0.697965\pi$
$860$	19.5329	−	9.21636i	0.666067	−	0.314275i
$861$		0			0
$862$	2.89754	+	12.9312i	0.0986906	+	0.440439i
$863$	−13.3295			−0.453742			−0.226871	−	0.973925i	$-0.572850\pi$
$863$	−13.3295			−0.453742			−0.226871	+	0.973925i	$0.572850\pi$
$864$		0			0
$865$	−12.5387			−0.426329
$866$	8.72424	+	38.9347i	0.296462	+	1.32306i
$867$		0			0
$868$	10.6391	−	5.01991i	0.361114	−	0.170387i
$869$			2.94888i			0.100034i
$870$		0			0
$871$		−	10.3041i		−	0.349140i
$872$	−10.3717	−	13.3281i	−0.351230	−	0.451346i
$873$		0			0
$874$	48.9968	−	10.9789i	1.65734	−	0.371366i
$875$	0.937354			0.0316884
$876$		0			0
$877$	42.3108			1.42873			0.714367	−	0.699771i	$-0.246715\pi$
$877$	42.3108			1.42873			0.714367	+	0.699771i	$0.246715\pi$
$878$	−13.2141	+	2.96092i	−0.445953	+	0.0999262i
$879$		0			0
$880$	1.80250	+	1.48485i	0.0607623	+	0.0500541i
$881$			16.0135i			0.539507i	0.962929	+	0.269754i	$0.0869423\pi$
$881$			16.0135i			0.539507i	−0.962929	+	0.269754i	$0.913058\pi$
$882$		0			0
$883$			53.4024i			1.79713i	0.438836	+	0.898567i	$0.355391\pi$
$883$			53.4024i			1.79713i	−0.438836	+	0.898567i	$0.644609\pi$
$884$	−0.235754	−	0.499652i	−0.00792928	−	0.0168051i
$885$		0			0
$886$	2.27346	+	10.1461i	0.0763785	+	0.340864i
$887$	−6.26700			−0.210425			−0.105213	−	0.994450i	$-0.533552\pi$
$887$	−6.26700			−0.210425			−0.105213	+	0.994450i	$0.533552\pi$
$888$		0			0
$889$	−19.6662			−0.659583
$890$	0.730826	+	3.26155i	0.0244973	+	0.109327i
$891$		0			0
$892$	10.2267	+	21.6742i	0.342414	+	0.725704i
$893$		−	59.9160i		−	2.00501i
$894$		0			0
$895$			23.1645i			0.774305i
$896$	−0.294470	+	10.6009i	−0.00983755	+	0.354150i
$897$		0			0
$898$	−36.7531	+	8.23539i	−1.22647	+	0.274818i
$899$	−57.3732			−1.91350
$900$		0			0
$901$	−2.83643			−0.0944951
$902$	2.66177	−	0.596431i	0.0886272	−	0.0198590i
$903$		0			0
$904$	−34.4286	+	26.7918i	−1.14508	+	0.891082i
$905$		−	3.42840i		−	0.113964i
$906$		0			0
$907$			22.6376i			0.751669i	0.926687	+	0.375834i	$0.122644\pi$
$907$			22.6376i			0.751669i	−0.926687	+	0.375834i	$0.877356\pi$
$908$	24.9370	−	11.7662i	0.827564	−	0.390475i
$909$		0			0
$910$	0.336022	+	1.49961i	0.0111390	+	0.0497115i
$911$	−20.2045			−0.669404			−0.334702	−	0.942324i	$-0.608636\pi$
$911$	−20.2045			−0.669404			−0.334702	+	0.942324i	$0.608636\pi$
$912$		0			0
$913$	−2.76116			−0.0913810
$914$	−1.63411	−	7.29276i	−0.0540517	−	0.241223i
$915$		0			0
$916$	23.2889	−	10.9886i	0.769487	−	0.363073i
$917$			11.2599i			0.371834i
$918$		0			0
$919$			51.8610i			1.71074i	0.518021	+	0.855368i	$0.326669\pi$
$919$			51.8610i			1.71074i	−0.518021	+	0.855368i	$0.673331\pi$
$920$	11.3106	−	8.80176i	0.372900	−	0.290185i
$921$		0			0
$922$	14.4203	−	3.23120i	0.474907	−	0.106414i
$923$	−10.3867			−0.341883
$924$		0			0
$925$	−3.50937			−0.115387
$926$	16.0266	−	3.59114i	0.526668	−	0.118012i
$927$		0			0
$928$	23.3607	−	46.1446i	0.766853	−	1.51477i
$929$			12.9841i			0.425993i	0.977053	+	0.212997i	$0.0683223\pi$
$929$			12.9841i			0.425993i	−0.977053	+	0.212997i	$0.931678\pi$
$930$		0			0
$931$		−	42.8926i		−	1.40575i
$932$	−8.73522	−	18.5132i	−0.286132	−	0.606421i
$933$		0			0
$934$	10.0996	+	45.0727i	0.330469	+	1.47482i
$935$	−0.139116			−0.00454958
$936$		0			0
$937$	15.3666			0.502006			0.251003	−	0.967986i	$-0.419240\pi$
$937$	15.3666			0.502006			0.251003	+	0.967986i	$0.419240\pi$
$938$	−2.57622	−	11.4972i	−0.0841166	−	0.375398i
$939$		0			0
$940$	−7.29766	−	15.4665i	−0.238023	−	0.504461i
$941$			4.61689i			0.150506i	0.997164	+	0.0752531i	$0.0239765\pi$
$941$			4.61689i			0.150506i	−0.997164	+	0.0752531i	$0.976024\pi$
$942$		0			0
$943$		−	16.7402i		−	0.545136i
$944$	−25.1583	+	30.5404i	−0.818832	+	0.994006i
$945$		0			0
$946$	8.70063	−	1.94958i	0.282882	−	0.0633863i
$947$	25.5595			0.830572			0.415286	−	0.909691i	$-0.363681\pi$
$947$	25.5595			0.830572			0.415286	+	0.909691i	$0.363681\pi$
$948$		0			0
$949$	13.6000			0.441475
$950$	9.66965	−	2.16671i	0.313725	−	0.0702974i
$951$		0			0
$952$	−0.387976	−	0.498566i	−0.0125744	−	0.0161586i
$953$		−	2.90773i		−	0.0941907i	−0.998890	−	0.0470954i	$-0.985004\pi$
$953$		−	2.90773i		−	0.0941907i	0.998890	−	0.0470954i	$-0.0149965\pi$
$954$		0			0
$955$		−	4.64106i		−	0.150181i
$956$	30.8806	−	14.5706i	0.998749	−	0.471247i
$957$		0			0
$958$	−4.61119	−	20.5789i	−0.148981	−	0.664875i
$959$	−3.01050			−0.0972140
$960$		0			0
$961$	−8.37642			−0.270207
$962$	−1.25803	−	5.61439i	−0.0405607	−	0.181015i
$963$		0			0
$964$	38.9153	−	18.3617i	1.25338	−	0.591390i
$965$			0.00850975i			0.000273939i
$966$		0			0
$967$		−	6.88149i		−	0.221294i	−0.993860	−	0.110647i	$-0.964708\pi$
$967$		−	6.88149i		−	0.221294i	0.993860	−	0.110647i	$-0.0352923\pi$
$968$	−18.5155	−	23.7932i	−0.595110	−	0.764741i
$969$		0			0
$970$	6.25567	−	1.40173i	0.200857	−	0.0450068i
$971$	37.7409			1.21116			0.605581	−	0.795784i	$-0.292941\pi$
$971$	37.7409			1.21116			0.605581	+	0.795784i	$0.292941\pi$
$972$		0			0
$973$	−1.04228			−0.0334139
$974$	32.2844	−	7.23406i	1.03446	−	0.231794i
$975$		0			0
$976$	16.9532	−	20.5800i	0.542658	−	0.658749i
$977$		−	7.57118i		−	0.242223i	−0.992639	−	0.121112i	$-0.961354\pi$
$977$		−	7.57118i		−	0.242223i	0.992639	−	0.121112i	$-0.0386459\pi$
$978$		0			0
$979$			1.37986i			0.0441006i
$980$	−5.22424	−	11.0721i	−0.166882	−	0.353686i
$981$		0			0
$982$	8.79395	+	39.2459i	0.280626	+	1.25239i
$983$	−12.5651			−0.400765			−0.200382	−	0.979718i	$-0.564218\pi$
$983$	−12.5651			−0.400765			−0.200382	+	0.979718i	$0.564218\pi$
$984$		0			0
$985$	5.83271			0.185846
$986$	0.673669	+	3.00647i	0.0214540	+	0.0957454i
$987$		0			0
$988$	6.93274	+	14.6931i	0.220560	+	0.467449i
$989$		−	54.7194i		−	1.73998i
$990$		0			0
$991$		−	39.4015i		−	1.25163i	−0.779972	−	0.625814i	$-0.784767\pi$
$991$		−	39.4015i		−	1.25163i	0.779972	−	0.625814i	$-0.215233\pi$
$992$	16.0329	−	31.6700i	0.509047	−	1.00552i
$993$		0			0
$994$	−11.5895	+	2.59689i	−0.367595	+	0.0823683i
$995$	8.61133			0.272997
$996$		0			0
$997$	−49.2680			−1.56033			−0.780166	−	0.625572i	$-0.784866\pi$
$997$	−49.2680			−1.56033			−0.780166	+	0.625572i	$0.784866\pi$
$998$	0.401969	−	0.0900705i	0.0127241	−	0.00285113i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.2.e.b.971.21		48
3.2	odd	2	inner	1620.2.e.b.971.28		48
4.3	odd	2	inner	1620.2.e.b.971.27		48
9.2	odd	6		180.2.q.a.131.18	yes	48
9.4	even	3		180.2.q.a.11.23	yes	48
9.5	odd	6		540.2.q.a.251.2		48
9.7	even	3		540.2.q.a.71.7		48
12.11	even	2	inner	1620.2.e.b.971.22		48
36.7	odd	6		540.2.q.a.71.2		48
36.11	even	6		180.2.q.a.131.23	yes	48
36.23	even	6		540.2.q.a.251.7		48
36.31	odd	6		180.2.q.a.11.18	✓	48
45.2	even	12		900.2.o.c.599.18		48
45.4	even	6		900.2.r.f.551.2		48
45.13	odd	12		900.2.o.c.299.15		48
45.22	odd	12		900.2.o.b.299.10		48
45.29	odd	6		900.2.r.f.851.7		48
45.38	even	12		900.2.o.b.599.7		48
180.47	odd	12		900.2.o.c.599.15		48
180.67	even	12		900.2.o.b.299.7		48
180.83	odd	12		900.2.o.b.599.10		48
180.103	even	12		900.2.o.c.299.18		48
180.119	even	6		900.2.r.f.851.2		48
180.139	odd	6		900.2.r.f.551.7		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.q.a.11.18	✓	48	36.31	odd	6
180.2.q.a.11.23	yes	48	9.4	even	3
180.2.q.a.131.18	yes	48	9.2	odd	6
180.2.q.a.131.23	yes	48	36.11	even	6
540.2.q.a.71.2		48	36.7	odd	6
540.2.q.a.71.7		48	9.7	even	3
540.2.q.a.251.2		48	9.5	odd	6
540.2.q.a.251.7		48	36.23	even	6
900.2.o.b.299.7		48	180.67	even	12
900.2.o.b.299.10		48	45.22	odd	12
900.2.o.b.599.7		48	45.38	even	12
900.2.o.b.599.10		48	180.83	odd	12
900.2.o.c.299.15		48	45.13	odd	12
900.2.o.c.299.18		48	180.103	even	12
900.2.o.c.599.15		48	180.47	odd	12
900.2.o.c.599.18		48	45.2	even	12
900.2.r.f.551.2		48	45.4	even	6
900.2.r.f.551.7		48	180.139	odd	6
900.2.r.f.851.2		48	180.119	even	6
900.2.r.f.851.7		48	45.29	odd	6
1620.2.e.b.971.21		48	1.1	even	1	trivial
1620.2.e.b.971.22		48	12.11	even	2	inner
1620.2.e.b.971.27		48	4.3	odd	2	inner
1620.2.e.b.971.28		48	3.2	odd	2	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:	\( N \)	\(=\)	\( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1620.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309220 - 1.37999i) q^{2} +(-1.80877 + 0.853443i) q^{4} +1.00000i q^{5} +0.937354i q^{7} +(1.73705 + 2.23218i) q^{8} +O(q^{10})\)	\(q+(-0.309220 - 1.37999i) q^{2} +(-1.80877 + 0.853443i) q^{4} +1.00000i q^{5} +0.937354i q^{7} +(1.73705 + 2.23218i) q^{8} +(1.37999 - 0.309220i) q^{10} +0.583833 q^{11} +1.15930 q^{13} +(1.29354 - 0.289849i) q^{14} +(2.54327 - 3.08736i) q^{16} +0.238281i q^{17} -7.00703i q^{19} +(-0.853443 - 1.80877i) q^{20} +(-0.180533 - 0.805686i) q^{22} -5.06707 q^{23} -1.00000 q^{25} +(-0.358479 - 1.59983i) q^{26} +(-0.799978 - 1.69546i) q^{28} +9.14304i q^{29} +6.27506i q^{31} +(-5.04696 - 2.55503i) q^{32} +(0.328826 - 0.0736811i) q^{34} -0.937354 q^{35} +3.50937 q^{37} +(-9.66965 + 2.16671i) q^{38} +(-2.23218 + 1.73705i) q^{40} +3.30373i q^{41} +10.7990i q^{43} +(-1.05602 + 0.498268i) q^{44} +(1.56684 + 6.99252i) q^{46} +8.55084 q^{47} +6.12137 q^{49} +(0.309220 + 1.37999i) q^{50} +(-2.09691 + 0.989398i) q^{52} +11.9037i q^{53} +0.583833i q^{55} +(-2.09235 + 1.62823i) q^{56} +(12.6173 - 2.82721i) q^{58} -9.89209 q^{59} +6.66589 q^{61} +(8.65955 - 1.94037i) q^{62} +(-1.96530 + 7.75484i) q^{64} +1.15930i q^{65} -8.88817i q^{67} +(-0.203359 - 0.430994i) q^{68} +(0.289849 + 1.29354i) q^{70} -8.95946 q^{71} +11.7312 q^{73} +(-1.08517 - 4.84290i) q^{74} +(5.98010 + 12.6741i) q^{76} +0.547258i q^{77} +5.05089i q^{79} +(3.08736 + 2.54327i) q^{80} +(4.55912 - 1.02158i) q^{82} -4.72936 q^{83} -0.238281 q^{85} +(14.9026 - 3.33927i) q^{86} +(1.01415 + 1.30322i) q^{88} +2.36345i q^{89} +1.08668i q^{91} +(9.16514 - 4.32445i) q^{92} +(-2.64409 - 11.8001i) q^{94} +7.00703 q^{95} +4.53311 q^{97} +(-1.89285 - 8.44745i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 48 q^{25} + 12 q^{34} + 12 q^{40} - 12 q^{46} - 48 q^{49} + 36 q^{52} + 36 q^{58} - 48 q^{64} - 24 q^{73} - 12 q^{76} - 36 q^{82} - 36 q^{94} + 24 q^{97}+O(q^{100}) \) 48 * q - 48 * q^25 + 12 * q^34 + 12 * q^40 - 12 * q^46 - 48 * q^49 + 36 * q^52 + 36 * q^58 - 48 * q^64 - 24 * q^73 - 12 * q^76 - 36 * q^82 - 36 * q^94 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more