LMFDB - Embedded newform 1620.2.e.a.971.1

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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			971.1
Character	$\chi$	$=$	1620.971
Dual form			1620.2.e.a.971.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41417 - 0.0114552i) q^{2} +(1.99974 + 0.0323992i) q^{4} +1.00000i q^{5} -2.33067i q^{7} +(-2.82759 - 0.0687254i) q^{8} +O(q^{10})$	\(q+(-1.41417 - 0.0114552i) q^{2} +(1.99974 + 0.0323992i) q^{4} +1.00000i q^{5} -2.33067i q^{7} +(-2.82759 - 0.0687254i) q^{8} +(0.0114552 - 1.41417i) q^{10} +4.21438 q^{11} -4.54122 q^{13} +(-0.0266984 + 3.29596i) q^{14} +(3.99790 + 0.129580i) q^{16} +7.60797i q^{17} -0.719258i q^{19} +(-0.0323992 + 1.99974i) q^{20} +(-5.95984 - 0.0482767i) q^{22} -7.46328 q^{23} -1.00000 q^{25} +(6.42204 + 0.0520207i) q^{26} +(0.0755120 - 4.66073i) q^{28} +4.77971i q^{29} -4.32264i q^{31} +(-5.65222 - 0.229044i) q^{32} +(0.0871510 - 10.7589i) q^{34} +2.33067 q^{35} +3.84857 q^{37} +(-0.00823926 + 1.01715i) q^{38} +(0.0687254 - 2.82759i) q^{40} +5.69942i q^{41} +12.1888i q^{43} +(8.42766 + 0.136543i) q^{44} +(10.5543 + 0.0854935i) q^{46} +9.42935 q^{47} +1.56796 q^{49} +(1.41417 + 0.0114552i) q^{50} +(-9.08124 - 0.147132i) q^{52} -5.00296i q^{53} +4.21438i q^{55} +(-0.160176 + 6.59019i) q^{56} +(0.0547527 - 6.75931i) q^{58} -0.00580811 q^{59} -5.10397 q^{61} +(-0.0495168 + 6.11293i) q^{62} +(7.99055 + 0.388655i) q^{64} -4.54122i q^{65} +9.45806i q^{67} +(-0.246492 + 15.2139i) q^{68} +(-3.29596 - 0.0266984i) q^{70} -11.3845 q^{71} +6.66077 q^{73} +(-5.44252 - 0.0440863i) q^{74} +(0.0233034 - 1.43833i) q^{76} -9.82235i q^{77} -3.40433i q^{79} +(-0.129580 + 3.99790i) q^{80} +(0.0652881 - 8.05993i) q^{82} +4.61733 q^{83} -7.60797 q^{85} +(0.139625 - 17.2370i) q^{86} +(-11.9166 - 0.289635i) q^{88} -3.08897i q^{89} +10.5841i q^{91} +(-14.9246 - 0.241804i) q^{92} +(-13.3347 - 0.108015i) q^{94} +0.719258 q^{95} -4.11195 q^{97} +(-2.21736 - 0.0179614i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 24 q^{16} - 24 q^{22} - 48 q^{25} + 24 q^{28} - 24 q^{34} - 24 q^{40} + 48 q^{46} - 48 q^{49} + 24 q^{58} + 24 q^{64} + 24 q^{76} + 24 q^{88}+O(q^{100}) $ 48 * q - 24 * q^16 - 24 * q^22 - 48 * q^25 + 24 * q^28 - 24 * q^34 - 24 * q^40 + 48 * q^46 - 48 * q^49 + 24 * q^58 + 24 * q^64 + 24 * q^76 + 24 * q^88

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 $

$2$	−1.41417	−	0.0114552i	−0.999967	−	0.00810007i
$2$	−1.41417	−	0.0114552i	−0.999967	−	0.00810007i
$3$		0			0
$3$		0			0
$4$	1.99974	+	0.0323992i	0.999869	+	0.0161996i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$		−	2.33067i		−	0.880912i	−0.897774	−	0.440456i	$-0.854817\pi$
$7$		−	2.33067i		−	0.880912i	0.897774	−	0.440456i	$-0.145183\pi$
$8$	−2.82759	−	0.0687254i	−0.999705	−	0.0242981i
$9$		0			0
$10$	0.0114552	−	1.41417i	0.00362246	−	0.447199i
$11$	4.21438			1.27068			0.635342	−	0.772231i	$-0.280859\pi$
$11$	4.21438			1.27068			0.635342	+	0.772231i	$0.280859\pi$
$12$		0			0
$13$	−4.54122			−1.25951			−0.629753	−	0.776795i	$-0.716844\pi$
$13$	−4.54122			−1.25951			−0.629753	+	0.776795i	$0.716844\pi$
$14$	−0.0266984	+	3.29596i	−0.00713545	+	0.880883i
$15$		0			0
$16$	3.99790	+	0.129580i	0.999475	+	0.0323950i
$17$			7.60797i			1.84520i	0.385753	+	0.922602i	$0.373942\pi$
$17$			7.60797i			1.84520i	−0.385753	+	0.922602i	$0.626058\pi$
$18$		0			0
$19$		−	0.719258i		−	0.165009i	−0.996591	−	0.0825045i	$-0.973708\pi$
$19$		−	0.719258i		−	0.165009i	0.996591	−	0.0825045i	$-0.0262919\pi$
$20$	−0.0323992	+	1.99974i	−0.00724469	+	0.447155i
$21$		0			0
$22$	−5.95984	−	0.0482767i	−1.27064	−	0.0102926i
$23$	−7.46328			−1.55620			−0.778100	−	0.628140i	$-0.783817\pi$
$23$	−7.46328			−1.55620			−0.778100	+	0.628140i	$0.783817\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	6.42204	+	0.0520207i	1.25947	+	0.0102021i
$27$		0			0
$28$	0.0755120	−	4.66073i	0.0142704	−	0.880796i
$29$			4.77971i			0.887570i	0.896133	+	0.443785i	$0.146365\pi$
$29$			4.77971i			0.887570i	−0.896133	+	0.443785i	$0.853635\pi$
$30$		0			0
$31$		−	4.32264i		−	0.776368i	−0.921582	−	0.388184i	$-0.873102\pi$
$31$		−	4.32264i		−	0.776368i	0.921582	−	0.388184i	$-0.126898\pi$
$32$	−5.65222	−	0.229044i	−0.999180	−	0.0404897i
$33$		0			0
$34$	0.0871510	−	10.7589i	0.0149463	−	1.84514i
$35$	2.33067			0.393956
$36$		0			0
$37$	3.84857			0.632701			0.316351	−	0.948642i	$-0.397542\pi$
$37$	3.84857			0.632701			0.316351	+	0.948642i	$0.397542\pi$
$38$	−0.00823926	+	1.01715i	−0.00133659	+	0.165004i
$39$		0			0
$40$	0.0687254	−	2.82759i	0.0108664	−	0.447082i
$41$			5.69942i			0.890099i	0.895506	+	0.445050i	$0.146814\pi$
$41$			5.69942i			0.890099i	−0.895506	+	0.445050i	$0.853186\pi$
$42$		0			0
$43$			12.1888i			1.85877i	0.369108	+	0.929386i	$0.379663\pi$
$43$			12.1888i			1.85877i	−0.369108	+	0.929386i	$0.620337\pi$
$44$	8.42766	+	0.136543i	1.27052	+	0.0205846i
$45$		0			0
$46$	10.5543	+	0.0854935i	1.55615	+	0.0126053i
$47$	9.42935			1.37541			0.687706	−	0.725989i	$-0.258618\pi$
$47$	9.42935			1.37541			0.687706	+	0.725989i	$0.258618\pi$
$48$		0			0
$49$	1.56796			0.223995
$50$	1.41417	+	0.0114552i	0.199993	+	0.00162001i
$51$		0			0
$52$	−9.08124	−	0.147132i	−1.25934	−	0.0204035i
$53$		−	5.00296i		−	0.687210i	−0.939114	−	0.343605i	$-0.888352\pi$
$53$		−	5.00296i		−	0.687210i	0.939114	−	0.343605i	$-0.111648\pi$
$54$		0			0
$55$			4.21438i			0.568267i
$56$	−0.160176	+	6.59019i	−0.0214045	+	0.880652i
$57$		0			0
$58$	0.0547527	−	6.75931i	0.00718938	−	0.887540i
$59$	−0.00580811			−0.000756151			−0.000378076	−	1.00000i	$-0.500120\pi$
$59$	−0.00580811			−0.000756151			−0.000378076		1.00000i	$0.500120\pi$
$60$		0			0
$61$	−5.10397			−0.653496			−0.326748	−	0.945111i	$-0.605953\pi$
$61$	−5.10397			−0.653496			−0.326748	+	0.945111i	$0.605953\pi$
$62$	−0.0495168	+	6.11293i	−0.00628864	+	0.776343i
$63$		0			0
$64$	7.99055	+	0.388655i	0.998819	+	0.0485818i
$65$		−	4.54122i		−	0.563269i
$66$		0			0
$67$			9.45806i			1.15549i	0.816219	+	0.577743i	$0.196066\pi$
$67$			9.45806i			1.15549i	−0.816219	+	0.577743i	$0.803934\pi$
$68$	−0.246492	+	15.2139i	−0.0298916	+	1.84496i
$69$		0			0
$70$	−3.29596	−	0.0266984i	−0.393943	−	0.00319107i
$71$	−11.3845			−1.35109			−0.675545	−	0.737319i	$-0.736091\pi$
$71$	−11.3845			−1.35109			−0.675545	+	0.737319i	$0.736091\pi$
$72$		0			0
$73$	6.66077			0.779584			0.389792	−	0.920903i	$-0.372547\pi$
$73$	6.66077			0.779584			0.389792	+	0.920903i	$0.372547\pi$
$74$	−5.44252	−	0.0440863i	−0.632681	−	0.00512493i
$75$		0			0
$76$	0.0233034	−	1.43833i	0.00267308	−	0.164987i
$77$		−	9.82235i		−	1.11936i
$78$		0			0
$79$		−	3.40433i		−	0.383018i	−0.981491	−	0.191509i	$-0.938662\pi$
$79$		−	3.40433i		−	0.383018i	0.981491	−	0.191509i	$-0.0613380\pi$
$80$	−0.129580	+	3.99790i	−0.0144875	+	0.446979i
$81$		0			0
$82$	0.0652881	−	8.05993i	0.00720987	−	0.890070i
$83$	4.61733			0.506818			0.253409	−	0.967359i	$-0.418448\pi$
$83$	4.61733			0.506818			0.253409	+	0.967359i	$0.418448\pi$
$84$		0			0
$85$	−7.60797			−0.825200
$86$	0.139625	−	17.2370i	0.0150562	−	1.85871i
$87$		0			0
$88$	−11.9166	−	0.289635i	−1.27031	−	0.0308752i
$89$		−	3.08897i		−	0.327430i	−0.986508	−	0.163715i	$-0.947652\pi$
$89$		−	3.08897i		−	0.327430i	0.986508	−	0.163715i	$-0.0523478\pi$
$90$		0			0
$91$			10.5841i			1.10951i
$92$	−14.9246	−	0.241804i	−1.55600	−	0.0252098i
$93$		0			0
$94$	−13.3347	−	0.108015i	−1.37537	−	0.0111409i
$95$	0.719258			0.0737943
$96$		0			0
$97$	−4.11195			−0.417505			−0.208753	−	0.977968i	$-0.566940\pi$
$97$	−4.11195			−0.417505			−0.208753	+	0.977968i	$0.566940\pi$
$98$	−2.21736	−	0.0179614i	−0.223987	−	0.00181437i
$99$		0			0
$100$	−1.99974	−	0.0323992i	−0.199974	−	0.00323992i
$101$			9.48737i			0.944028i	0.881591	+	0.472014i	$0.156473\pi$
$101$			9.48737i			0.944028i	−0.881591	+	0.472014i	$0.843527\pi$
$102$		0			0
$103$			5.10684i			0.503192i	0.967832	+	0.251596i	$0.0809554\pi$
$103$			5.10684i			0.503192i	−0.967832	+	0.251596i	$0.919045\pi$
$104$	12.8407	+	0.312097i	1.25914	+	0.0306036i
$105$		0			0
$106$	−0.0573101	+	7.07503i	−0.00556645	+	0.687187i
$107$	−2.38925			−0.230977			−0.115489	−	0.993309i	$-0.536843\pi$
$107$	−2.38925			−0.230977			−0.115489	+	0.993309i	$0.536843\pi$
$108$		0			0
$109$	16.2663			1.55803			0.779013	−	0.627008i	$-0.215721\pi$
$109$	16.2663			1.55803			0.779013	+	0.627008i	$0.215721\pi$
$110$	0.0482767	−	5.95984i	0.00460300	−	0.568248i
$111$		0			0
$112$	0.302008	−	9.31780i	0.0285371	−	0.880449i
$113$			16.1889i			1.52292i	0.648211	+	0.761461i	$0.275518\pi$
$113$			16.1889i			1.52292i	−0.648211	+	0.761461i	$0.724482\pi$
$114$		0			0
$115$		−	7.46328i		−	0.695954i
$116$	−0.154859	+	9.55816i	−0.0143783	+	0.887453i
$117$		0			0
$118$	0.00821363		6.65332e-5i	0.000756126		6.12488e-6i
$119$	17.7317			1.62546
$120$		0			0
$121$	6.76101			0.614637
$122$	7.21787	+	0.0584671i	0.653475	+	0.00529337i
$123$		0			0
$124$	0.140050	−	8.64414i	0.0125769	−	0.776267i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$		−	2.70385i		−	0.239928i	−0.992778	−	0.119964i	$-0.961722\pi$
$127$		−	2.70385i		−	0.239928i	0.992778	−	0.119964i	$-0.0382779\pi$
$128$	−11.2955	−	0.641156i	−0.998393	−	0.0566707i
$129$		0			0
$130$	−0.0520207	+	6.42204i	−0.00456252	+	0.563250i
$131$	−16.3775			−1.43091			−0.715457	−	0.698657i	$-0.753781\pi$
$131$	−16.3775			−1.43091			−0.715457	+	0.698657i	$0.753781\pi$
$132$		0			0
$133$	−1.67636			−0.145358
$134$	0.108344	−	13.3753i	0.00935952	−	1.15545i
$135$		0			0
$136$	0.522861	−	21.5122i	0.0448349	−	1.84466i
$137$			12.9838i			1.10928i	0.832091	+	0.554639i	$0.187144\pi$
$137$			12.9838i			1.10928i	−0.832091	+	0.554639i	$0.812856\pi$
$138$		0			0
$139$			16.9541i			1.43803i	0.694996	+	0.719013i	$0.255406\pi$
$139$			16.9541i			1.43803i	−0.694996	+	0.719013i	$0.744594\pi$
$140$	4.66073	+	0.0755120i	0.393904	+	0.00638193i
$141$		0			0
$142$	16.0996	+	0.130412i	1.35104	+	0.0109439i
$143$	−19.1384			−1.60043
$144$		0			0
$145$	−4.77971			−0.396933
$146$	−9.41944	−	0.0763006i	−0.779558	−	0.00631468i
$147$		0			0
$148$	7.69613	+	0.124691i	0.632618	+	0.0102495i
$149$			6.75342i			0.553261i	0.960976	+	0.276631i	$0.0892179\pi$
$149$			6.75342i			0.553261i	−0.960976	+	0.276631i	$0.910782\pi$
$150$		0			0
$151$			14.1253i			1.14950i	0.818329	+	0.574750i	$0.194901\pi$
$151$			14.1253i			1.14950i	−0.818329	+	0.574750i	$0.805099\pi$
$152$	−0.0494313	+	2.03377i	−0.00400940	+	0.164960i
$153$		0			0
$154$	−0.112517	+	13.8904i	−0.00906690	+	1.11932i
$155$	4.32264			0.347203
$156$		0			0
$157$	3.79475			0.302854			0.151427	−	0.988468i	$-0.451613\pi$
$157$	3.79475			0.302854			0.151427	+	0.988468i	$0.451613\pi$
$158$	−0.0389974	+	4.81430i	−0.00310247	+	0.383005i
$159$		0			0
$160$	0.229044	−	5.65222i	0.0181076	−	0.446847i
$161$			17.3945i			1.37088i
$162$		0			0
$163$		−	2.51879i		−	0.197287i	−0.995123	−	0.0986433i	$-0.968550\pi$
$163$		−	2.51879i		−	0.197287i	0.995123	−	0.0986433i	$-0.0314503\pi$
$164$	−0.184657	+	11.3973i	−0.0144193	+	0.889982i
$165$		0			0
$166$	−6.52968	−	0.0528926i	−0.506801	−	0.00410526i
$167$	1.98469			0.153580			0.0767901	−	0.997047i	$-0.475533\pi$
$167$	1.98469			0.153580			0.0767901	+	0.997047i	$0.475533\pi$
$168$		0			0
$169$	7.62265			0.586358
$170$	10.7589	+	0.0871510i	0.825173	+	0.00668418i
$171$		0			0
$172$	−0.394907	+	24.3744i	−0.0301114	+	1.85853i
$173$		−	19.9328i		−	1.51546i	−0.652565	−	0.757732i	$-0.726307\pi$
$173$		−	19.9328i		−	1.51546i	0.652565	−	0.757732i	$-0.273693\pi$
$174$		0			0
$175$			2.33067i			0.176182i
$176$	16.8487	+	0.546099i	1.27002	+	0.0411638i
$177$		0			0
$178$	−0.0353849	+	4.36832i	−0.00265221	+	0.327420i
$179$	5.05291			0.377672			0.188836	−	0.982009i	$-0.439529\pi$
$179$	5.05291			0.377672			0.188836	+	0.982009i	$0.439529\pi$
$180$		0			0
$181$	6.03251			0.448393			0.224196	−	0.974544i	$-0.428024\pi$
$181$	6.03251			0.448393			0.224196	+	0.974544i	$0.428024\pi$
$182$	0.121243	−	14.9677i	0.00898714	−	1.10948i
$183$		0			0
$184$	21.1031	+	0.512916i	1.55574	+	0.0378127i
$185$			3.84857i			0.282953i
$186$		0			0
$187$			32.0629i			2.34467i
$188$	18.8562	+	0.305504i	1.37523	+	0.0222811i
$189$		0			0
$190$	−1.01715	−	0.00823926i	−0.0737919	−	0.000597739i
$191$	−15.0989			−1.09251			−0.546257	−	0.837617i	$-0.683948\pi$
$191$	−15.0989			−1.09251			−0.546257	+	0.837617i	$0.683948\pi$
$192$		0			0
$193$	−22.4062			−1.61283			−0.806415	−	0.591350i	$-0.798595\pi$
$193$	−22.4062			−1.61283			−0.806415	+	0.591350i	$0.798595\pi$
$194$	5.81499	+	0.0471033i	0.417492	+	0.00338182i
$195$		0			0
$196$	3.13551	+	0.0508008i	0.223965	+	0.00362863i
$197$			4.26708i			0.304017i	0.988379	+	0.152008i	$0.0485741\pi$
$197$			4.26708i			0.304017i	−0.988379	+	0.152008i	$0.951426\pi$
$198$		0			0
$199$			21.6539i			1.53501i	0.641046	+	0.767503i	$0.278501\pi$
$199$			21.6539i			1.53501i	−0.641046	+	0.767503i	$0.721499\pi$
$200$	2.82759	+	0.0687254i	0.199941	+	0.00485962i
$201$		0			0
$202$	0.108680	−	13.4167i	0.00764669	−	0.943997i
$203$	11.1399			0.781870
$204$		0			0
$205$	−5.69942			−0.398064
$206$	0.0585000	−	7.22193i	0.00407589	−	0.503176i
$207$		0			0
$208$	−18.1553	−	0.588450i	−1.25885	−	0.0408017i
$209$		−	3.03123i		−	0.209674i
$210$		0			0
$211$			9.55045i			0.657480i	0.944420	+	0.328740i	$0.106624\pi$
$211$			9.55045i			0.657480i	−0.944420	+	0.328740i	$0.893376\pi$
$212$	0.162092	−	10.0046i	0.0111325	−	0.687120i
$213$		0			0
$214$	3.37880	+	0.0273694i	0.230970	+	0.00187093i
$215$	−12.1888			−0.831268
$216$		0			0
$217$	−10.0747			−0.683912
$218$	−23.0032	−	0.186334i	−1.55797	−	0.0126201i
$219$		0			0
$220$	−0.136543	+	8.42766i	−0.00920570	+	0.568193i
$221$		−	34.5494i		−	2.32405i
$222$		0			0
$223$			0.618782i			0.0414367i	0.999785	+	0.0207184i	$0.00659533\pi$
$223$			0.618782i			0.0414367i	−0.999785	+	0.0207184i	$0.993405\pi$
$224$	−0.533828	+	13.1735i	−0.0356679	+	0.880189i
$225$		0			0
$226$	0.185447	−	22.8938i	0.0123358	−	1.52287i
$227$	8.05716			0.534773			0.267386	−	0.963589i	$-0.413840\pi$
$227$	8.05716			0.534773			0.267386	+	0.963589i	$0.413840\pi$
$228$		0			0
$229$	7.29429			0.482021			0.241010	−	0.970523i	$-0.422521\pi$
$229$	7.29429			0.482021			0.241010	+	0.970523i	$0.422521\pi$
$230$	−0.0854935	+	10.5543i	−0.00563728	+	0.695931i
$231$		0			0
$232$	0.328487	−	13.5151i	0.0215662	−	0.887308i
$233$		−	15.8741i		−	1.03995i	−0.854182	−	0.519973i	$-0.825942\pi$
$233$		−	15.8741i		−	1.03995i	0.854182	−	0.519973i	$-0.174058\pi$
$234$		0			0
$235$			9.42935i			0.615103i
$236$	−0.0116147		0.000188178i	−0.000756052		1.22494e-5i
$237$		0			0
$238$	−25.0756	−	0.203121i	−1.62541	−	0.0131664i
$239$	21.2711			1.37591			0.687956	−	0.725753i	$-0.258508\pi$
$239$	21.2711			1.37591			0.687956	+	0.725753i	$0.258508\pi$
$240$		0			0
$241$	23.6017			1.52032			0.760159	−	0.649737i	$-0.225121\pi$
$241$	23.6017			1.52032			0.760159	+	0.649737i	$0.225121\pi$
$242$	−9.56120	−	0.0774489i	−0.614617	−	0.00497861i
$243$		0			0
$244$	−10.2066	−	0.165365i	−0.653411	−	0.0105864i
$245$			1.56796i			0.100173i
$246$		0			0
$247$			3.26631i			0.207830i
$248$	−0.297075	+	12.2227i	−0.0188643	+	0.776139i
$249$		0			0
$250$	−0.0114552	+	1.41417i	−0.000724492	+	0.0894398i
$251$	−12.7663			−0.805800			−0.402900	−	0.915244i	$-0.631998\pi$
$251$	−12.7663			−0.805800			−0.402900	+	0.915244i	$0.631998\pi$
$252$		0			0
$253$	−31.4531			−1.97744
$254$	−0.0309732	+	3.82370i	−0.00194343	+	0.239920i
$255$		0			0
$256$	15.9664	+	1.03609i	0.997901	+	0.0647559i
$257$			2.33081i			0.145392i	0.997354	+	0.0726961i	$0.0231603\pi$
$257$			2.33081i			0.145392i	−0.997354	+	0.0726961i	$0.976840\pi$
$258$		0			0
$259$		−	8.96976i		−	0.557354i
$260$	0.147132	−	9.08124i	0.00912473	−	0.563195i
$261$		0			0
$262$	23.1606	+	0.187609i	1.43087	+	0.0115905i
$263$	4.37380			0.269700			0.134850	−	0.990866i	$-0.456945\pi$
$263$	4.37380			0.269700			0.134850	+	0.990866i	$0.456945\pi$
$264$		0			0
$265$	5.00296			0.307330
$266$	2.37065	+	0.0192030i	0.145354	+	0.00117741i
$267$		0			0
$268$	−0.306434	+	18.9136i	−0.0187184	+	1.15533i
$269$			7.41866i			0.452324i	0.974090	+	0.226162i	$0.0726178\pi$
$269$			7.41866i			0.452324i	−0.974090	+	0.226162i	$0.927382\pi$
$270$		0			0
$271$			28.9152i			1.75648i	0.478224	+	0.878238i	$0.341281\pi$
$271$			28.9152i			1.75648i	−0.478224	+	0.878238i	$0.658719\pi$
$272$	−0.985840	+	30.4159i	−0.0597753	+	1.84424i
$273$		0			0
$274$	0.148732	−	18.3612i	0.00898523	−	1.10924i
$275$	−4.21438			−0.254137
$276$		0			0
$277$	9.91355			0.595647			0.297824	−	0.954621i	$-0.403739\pi$
$277$	9.91355			0.595647			0.297824	+	0.954621i	$0.403739\pi$
$278$	0.194213	−	23.9759i	0.0116481	−	1.43798i
$279$		0			0
$280$	−6.59019	−	0.160176i	−0.393839	−	0.00957237i
$281$			7.95510i			0.474562i	0.971441	+	0.237281i	$0.0762562\pi$
$281$			7.95510i			0.474562i	−0.971441	+	0.237281i	$0.923744\pi$
$282$		0			0
$283$		−	18.6473i		−	1.10847i	−0.832361	−	0.554234i	$-0.813011\pi$
$283$		−	18.6473i		−	1.10847i	0.832361	−	0.554234i	$-0.186989\pi$
$284$	−22.7660	−	0.368848i	−1.35091	−	0.0218871i
$285$		0			0
$286$	27.0649	+	0.219235i	1.60038	+	0.0129636i
$287$	13.2835			0.784099
$288$		0			0
$289$	−40.8812			−2.40478
$290$	6.75931	+	0.0547527i	0.396920	+	0.00321519i
$291$		0			0
$292$	13.3198	+	0.215804i	0.779481	+	0.0126289i
$293$			9.41079i			0.549784i	0.961475	+	0.274892i	$0.0886421\pi$
$293$			9.41079i			0.549784i	−0.961475	+	0.274892i	$0.911358\pi$
$294$		0			0
$295$		−	0.00580811i		−	0.000338161i
$296$	−10.8822	−	0.264495i	−0.632515	−	0.0153734i
$297$		0			0
$298$	0.0773619	−	9.55046i	0.00448146	−	0.553243i
$299$	33.8924			1.96005
$300$		0			0
$301$	28.4081			1.63741
$302$	0.161808	−	19.9755i	0.00931103	−	1.14946i
$303$		0			0
$304$	0.0932013	−	2.87552i	0.00534546	−	0.164922i
$305$		−	5.10397i		−	0.292252i
$306$		0			0
$307$		−	34.1688i		−	1.95011i	−0.221955	−	0.975057i	$-0.571244\pi$
$307$		−	34.1688i		−	1.95011i	0.221955	−	0.975057i	$-0.428756\pi$
$308$	0.318236	−	19.6421i	0.0181332	−	1.11921i
$309$		0			0
$310$	−6.11293	−	0.0495168i	−0.347191	−	0.00281236i
$311$	−23.5280			−1.33415			−0.667074	−	0.744991i	$-0.732454\pi$
$311$	−23.5280			−1.33415			−0.667074	+	0.744991i	$0.732454\pi$
$312$		0			0
$313$	−15.6740			−0.885945			−0.442973	−	0.896535i	$-0.646076\pi$
$313$	−15.6740			−0.885945			−0.442973	+	0.896535i	$0.646076\pi$
$314$	−5.36641	−	0.0434697i	−0.302844	−	0.00245314i
$315$		0			0
$316$	0.110298	−	6.80778i	0.00620473	−	0.382967i
$317$		−	27.8991i		−	1.56697i	−0.621412	−	0.783484i	$-0.713441\pi$
$317$		−	27.8991i		−	1.56697i	0.621412	−	0.783484i	$-0.286559\pi$
$318$		0			0
$319$			20.1435i			1.12782i
$320$	−0.388655	+	7.99055i	−0.0217265	+	0.446686i
$321$		0			0
$322$	0.199257	−	24.5987i	0.0111042	−	1.37083i
$323$	5.47209			0.304475
$324$		0			0
$325$	4.54122			0.251901
$326$	−0.0288533	+	3.56199i	−0.00159804	+	0.197280i
$327$		0			0
$328$	0.391694	−	16.1156i	0.0216277	−	0.889836i
$329$		−	21.9767i		−	1.21162i
$330$		0			0
$331$		−	34.8895i		−	1.91770i	−0.283909	−	0.958851i	$-0.591631\pi$
$331$		−	34.8895i		−	1.91770i	0.283909	−	0.958851i	$-0.408369\pi$
$332$	9.23345	+	0.149598i	0.506752	+	0.00821026i
$333$		0			0
$334$	−2.80669	−	0.0227351i	−0.153575	−	0.00124401i
$335$	−9.45806			−0.516749
$336$		0			0
$337$	−1.67168			−0.0910623			−0.0455312	−	0.998963i	$-0.514498\pi$
$337$	−1.67168			−0.0910623			−0.0455312	+	0.998963i	$0.514498\pi$
$338$	−10.7797	−	0.0873192i	−0.586338	−	0.00474954i
$339$		0			0
$340$	−15.2139	−	0.246492i	−0.825092	−	0.0133679i
$341$		−	18.2172i		−	0.986519i
$342$		0			0
$343$		−	19.9691i		−	1.07823i
$344$	0.837679	−	34.4649i	0.0451646	−	1.85822i
$345$		0			0
$346$	−0.228335	+	28.1883i	−0.0122754	+	1.51542i
$347$	3.60719			0.193644			0.0968222	−	0.995302i	$-0.469132\pi$
$347$	3.60719			0.193644			0.0968222	+	0.995302i	$0.469132\pi$
$348$		0			0
$349$	−21.9092			−1.17277			−0.586385	−	0.810032i	$-0.699450\pi$
$349$	−21.9092			−1.17277			−0.586385	+	0.810032i	$0.699450\pi$
$350$	0.0266984	−	3.29596i	0.00142709	−	0.176177i
$351$		0			0
$352$	−23.8206	−	0.965281i	−1.26964	−	0.0514496i
$353$		−	1.86627i		−	0.0993316i	−0.998766	−	0.0496658i	$-0.984184\pi$
$353$		−	1.86627i		−	0.0993316i	0.998766	−	0.0496658i	$-0.0158156\pi$
$354$		0			0
$355$		−	11.3845i		−	0.604225i
$356$	0.100080	−	6.17713i	0.00530424	−	0.327387i
$357$		0			0
$358$	−7.14566	−	0.0578822i	−0.377660	−	0.00305917i
$359$	15.6068			0.823698			0.411849	−	0.911252i	$-0.364883\pi$
$359$	15.6068			0.823698			0.411849	+	0.911252i	$0.364883\pi$
$360$		0			0
$361$	18.4827			0.972772
$362$	−8.53098	−	0.0691038i	−0.448378	−	0.00363201i
$363$		0			0
$364$	−0.342916	+	21.1654i	−0.0179737	+	1.10937i
$365$			6.66077i			0.348640i
$366$		0			0
$367$			5.10815i			0.266643i	0.991073	+	0.133322i	$0.0425644\pi$
$367$			5.10815i			0.266643i	−0.991073	+	0.133322i	$0.957436\pi$
$368$	−29.8374	−	0.967090i	−1.55538	−	0.0504131i
$369$		0			0
$370$	0.0440863	−	5.44252i	0.00229194	−	0.282943i
$371$	−11.6603			−0.605371
$372$		0			0
$373$	21.8897			1.13340			0.566702	−	0.823923i	$-0.308219\pi$
$373$	21.8897			1.13340			0.566702	+	0.823923i	$0.308219\pi$
$374$	0.367288	−	45.3423i	0.0189920	−	2.34459i
$375$		0			0
$376$	−26.6624	−	0.648035i	−1.37501	−	0.0334199i
$377$		−	21.7057i		−	1.11790i
$378$		0			0
$379$		−	19.7284i		−	1.01338i	−0.862128	−	0.506691i	$-0.830869\pi$
$379$		−	19.7284i		−	1.01338i	0.862128	−	0.506691i	$-0.169131\pi$
$380$	1.43833	+	0.0233034i	0.0737846	+	0.00119544i
$381$		0			0
$382$	21.3523	+	0.172961i	1.09248	+	0.00884944i
$383$	−26.6242			−1.36043			−0.680217	−	0.733011i	$-0.738114\pi$
$383$	−26.6242			−1.36043			−0.680217	+	0.733011i	$0.738114\pi$
$384$		0			0
$385$	9.82235			0.500593
$386$	31.6861	+	0.256668i	1.61278	+	0.0130640i
$387$		0			0
$388$	−8.22282	−	0.133224i	−0.417451	−	0.00676342i
$389$		−	10.6365i		−	0.539294i	−0.962959	−	0.269647i	$-0.913093\pi$
$389$		−	10.6365i		−	0.539294i	0.962959	−	0.269647i	$-0.0869070\pi$
$390$		0			0
$391$		−	56.7804i		−	2.87151i
$392$	−4.43356	−	0.107759i	−0.223929	−	0.00544264i
$393$		0			0
$394$	0.0488804	−	6.03437i	0.00246256	−	0.304007i
$395$	3.40433			0.171291
$396$		0			0
$397$	19.7903			0.993246			0.496623	−	0.867966i	$-0.334573\pi$
$397$	19.7903			0.993246			0.496623	+	0.867966i	$0.334573\pi$
$398$	0.248051	−	30.6223i	0.0124337	−	1.53496i
$399$		0			0
$400$	−3.99790	−	0.129580i	−0.199895	−	0.00647899i
$401$		−	34.9470i		−	1.74517i	−0.488464	−	0.872584i	$-0.662443\pi$
$401$		−	34.9470i		−	1.74517i	0.488464	−	0.872584i	$-0.337557\pi$
$402$		0			0
$403$			19.6300i			0.977841i
$404$	−0.307383	+	18.9722i	−0.0152929	+	0.943904i
$405$		0			0
$406$	−15.7537	−	0.127611i	−0.781845	−	0.00633320i
$407$	16.2194			0.803963
$408$		0			0
$409$	−16.0758			−0.794897			−0.397448	−	0.917625i	$-0.630104\pi$
$409$	−16.0758			−0.794897			−0.397448	+	0.917625i	$0.630104\pi$
$410$	8.05993	+	0.0652881i	0.398051	+	0.00322435i
$411$		0			0
$412$	−0.165458	+	10.2123i	−0.00815152	+	0.503126i
$413$			0.0135368i			0.000666102i
$414$		0			0
$415$			4.61733i			0.226656i
$416$	25.6679	+	1.04014i	1.25847	+	0.0509971i
$417$		0			0
$418$	−0.0347234	+	4.28666i	−0.00169838	+	0.209668i
$419$	−11.7231			−0.572711			−0.286356	−	0.958123i	$-0.592444\pi$
$419$	−11.7231			−0.572711			−0.286356	+	0.958123i	$0.592444\pi$
$420$		0			0
$421$	17.7318			0.864197			0.432098	−	0.901826i	$-0.357773\pi$
$421$	17.7318			0.864197			0.432098	+	0.901826i	$0.357773\pi$
$422$	0.109403	−	13.5059i	0.00532564	−	0.657459i
$423$		0			0
$424$	−0.343830	+	14.1463i	−0.0166979	+	0.687007i
$425$		−	7.60797i		−	0.369041i
$426$		0			0
$427$			11.8957i			0.575673i
$428$	−4.77787	−	0.0774098i	−0.230947	−	0.00374174i
$429$		0			0
$430$	17.2370	+	0.139625i	0.831241	+	0.00673333i
$431$	−4.15753			−0.200261			−0.100131	−	0.994974i	$-0.531926\pi$
$431$	−4.15753			−0.200261			−0.100131	+	0.994974i	$0.531926\pi$
$432$		0			0
$433$	−22.1688			−1.06537			−0.532683	−	0.846315i	$-0.678816\pi$
$433$	−22.1688			−1.06537			−0.532683	+	0.846315i	$0.678816\pi$
$434$	14.2472	+	0.115407i	0.683890	+	0.00553973i
$435$		0			0
$436$	32.5283	+	0.527014i	1.55782	+	0.0252394i
$437$			5.36802i			0.256787i
$438$		0			0
$439$		−	2.02588i		−	0.0966901i	−0.998831	−	0.0483451i	$-0.984605\pi$
$439$		−	2.02588i		−	0.0966901i	0.998831	−	0.0483451i	$-0.0153947\pi$
$440$	0.289635	−	11.9166i	0.0138078	−	0.568099i
$441$		0			0
$442$	−0.395772	+	48.8587i	−0.0188249	+	2.32397i
$443$	−18.3676			−0.872673			−0.436336	−	0.899784i	$-0.643724\pi$
$443$	−18.3676			−0.872673			−0.436336	+	0.899784i	$0.643724\pi$
$444$		0			0
$445$	3.08897			0.146431
$446$	0.00708829	−	0.875061i	0.000335640	−	0.0414353i
$447$		0			0
$448$	0.905827	−	18.6234i	0.0427963	−	0.879871i
$449$		−	12.6469i		−	0.596845i	−0.954434	−	0.298422i	$-0.903540\pi$
$449$		−	12.6469i		−	0.596845i	0.954434	−	0.298422i	$-0.0964604\pi$
$450$		0			0
$451$			24.0195i			1.13103i
$452$	−0.524507	+	32.3735i	−0.0246707	+	1.52272i
$453$		0			0
$454$	−11.3942	−	0.0922967i	−0.534755	−	0.00433170i
$455$	−10.5841			−0.496190
$456$		0			0
$457$	22.4435			1.04986			0.524932	−	0.851144i	$-0.324091\pi$
$457$	22.4435			1.04986			0.524932	+	0.851144i	$0.324091\pi$
$458$	−10.3154	−	0.0835578i	−0.482005	−	0.00390440i
$459$		0			0
$460$	0.241804	−	14.9246i	0.0112742	−	0.695863i
$461$			19.6051i			0.913099i	0.889698	+	0.456549i	$0.150915\pi$
$461$			19.6051i			0.913099i	−0.889698	+	0.456549i	$0.849085\pi$
$462$		0			0
$463$			24.9080i			1.15757i	0.815479	+	0.578787i	$0.196474\pi$
$463$			24.9080i			1.15757i	−0.815479	+	0.578787i	$0.803526\pi$
$464$	−0.619354	+	19.1088i	−0.0287528	+	0.887104i
$465$		0			0
$466$	−0.181841	+	22.4486i	−0.00842364	+	1.03991i
$467$	4.78965			0.221638			0.110819	−	0.993841i	$-0.464653\pi$
$467$	4.78965			0.221638			0.110819	+	0.993841i	$0.464653\pi$
$468$		0			0
$469$	22.0436			1.01788
$470$	0.108015	−	13.3347i	0.00498238	−	0.615083i
$471$		0			0
$472$	0.0164230		0.000399164i	0.000755928		1.83730e-5i
$473$			51.3682i			2.36191i
$474$		0			0
$475$			0.719258i			0.0330018i
$476$	35.4587	+	0.574493i	1.62525	+	0.0263318i
$477$		0			0
$478$	−30.0809	−	0.243665i	−1.37587	−	0.0111450i
$479$	−38.6856			−1.76759			−0.883794	−	0.467876i	$-0.845019\pi$
$479$	−38.6856			−1.76759			−0.883794	+	0.467876i	$0.845019\pi$
$480$		0			0
$481$	−17.4772			−0.796892
$482$	−33.3767	−	0.270363i	−1.52027	−	0.0123147i
$483$		0			0
$484$	13.5202	+	0.219051i	0.614557	+	0.00995688i
$485$		−	4.11195i		−	0.186714i
$486$		0			0
$487$		−	27.5842i		−	1.24996i	−0.780641	−	0.624980i	$-0.785107\pi$
$487$		−	27.5842i		−	1.24996i	0.780641	−	0.624980i	$-0.214893\pi$
$488$	14.4319	+	0.350772i	0.653303	+	0.0158787i
$489$		0			0
$490$	0.0179614	−	2.21736i	0.000811412	−	0.100170i
$491$	19.0209			0.858402			0.429201	−	0.903209i	$-0.358795\pi$
$491$	19.0209			0.858402			0.429201	+	0.903209i	$0.358795\pi$
$492$		0			0
$493$	−36.3639			−1.63775
$494$	0.0374163	−	4.61910i	0.00168344	−	0.207823i
$495$		0			0
$496$	0.560127	−	17.2815i	0.0251504	−	0.775961i
$497$			26.5335i			1.19019i
$498$		0			0
$499$		−	34.5895i		−	1.54844i	−0.632916	−	0.774220i	$-0.718142\pi$
$499$		−	34.5895i		−	1.54844i	0.632916	−	0.774220i	$-0.281858\pi$
$500$	0.0323992	−	1.99974i	0.00144894	−	0.0894310i
$501$		0			0
$502$	18.0536	+	0.146241i	0.805774	+	0.00652704i
$503$	38.0061			1.69461			0.847305	−	0.531107i	$-0.178224\pi$
$503$	38.0061			1.69461			0.847305	+	0.531107i	$0.178224\pi$
$504$		0			0
$505$	−9.48737			−0.422182
$506$	44.4799	+	0.360302i	1.97737	+	0.0160174i
$507$		0			0
$508$	0.0876027	−	5.40699i	0.00388674	−	0.239897i
$509$		−	7.86095i		−	0.348431i	−0.984708	−	0.174215i	$-0.944261\pi$
$509$		−	7.86095i		−	0.348431i	0.984708	−	0.174215i	$-0.0557389\pi$
$510$		0			0
$511$		−	15.5241i		−	0.686744i
$512$	−22.5673	−	1.64811i	−0.997344	−	0.0728369i
$513$		0			0
$514$	0.0267000	−	3.29616i	0.00117769	−	0.145387i
$515$	−5.10684			−0.225034
$516$		0			0
$517$	39.7389			1.74771
$518$	−0.102751	+	12.6847i	−0.00451461	+	0.557336i
$519$		0			0
$520$	−0.312097	+	12.8407i	−0.0136863	+	0.563102i
$521$			36.6383i			1.60515i	0.596548	+	0.802577i	$0.296538\pi$
$521$			36.6383i			1.60515i	−0.596548	+	0.802577i	$0.703462\pi$
$522$		0			0
$523$			19.6392i			0.858764i	0.903123	+	0.429382i	$0.141269\pi$
$523$			19.6392i			0.858764i	−0.903123	+	0.429382i	$0.858731\pi$
$524$	−32.7508	−	0.530620i	−1.43073	−	0.0231802i
$525$		0			0
$526$	−6.18529	−	0.0501029i	−0.269691	−	0.00218459i
$527$	32.8865			1.43256
$528$		0			0
$529$	32.7005			1.42176
$530$	−7.07503	−	0.0573101i	−0.307319	−	0.00248939i
$531$		0			0
$532$	−3.35227	−	0.0543126i	−0.145339	−	0.00235475i
$533$		−	25.8823i		−	1.12109i
$534$		0			0
$535$		−	2.38925i		−	0.103296i
$536$	0.650009	−	26.7435i	0.0280761	−	1.15514i
$537$		0			0
$538$	0.0849824	−	10.4912i	0.00366385	−	0.452309i
$539$	6.60799			0.284626
$540$		0			0
$541$	−11.0009			−0.472966			−0.236483	−	0.971636i	$-0.575995\pi$
$541$	−11.0009			−0.472966			−0.236483	+	0.971636i	$0.575995\pi$
$542$	0.331231	−	40.8910i	0.0142276	−	1.75642i
$543$		0			0
$544$	1.74256	−	43.0019i	0.0747118	−	1.84369i
$545$			16.2663i			0.696770i
$546$		0			0
$547$		−	42.1738i		−	1.80322i	−0.432547	−	0.901611i	$-0.642385\pi$
$547$		−	42.1738i		−	1.80322i	0.432547	−	0.901611i	$-0.357615\pi$
$548$	−0.420664	+	25.9641i	−0.0179699	+	1.10913i
$549$		0			0
$550$	5.95984	+	0.0482767i	0.254128	+	0.00205853i
$551$	3.43784			0.146457
$552$		0			0
$553$	−7.93439			−0.337405
$554$	−14.0194	−	0.113562i	−0.595628	−	0.00482478i
$555$		0			0
$556$	−0.549299	+	33.9037i	−0.0232955	+	1.43784i
$557$		−	24.7879i		−	1.05030i	−0.851010	−	0.525149i	$-0.824010\pi$
$557$		−	24.7879i		−	1.05030i	0.851010	−	0.525149i	$-0.175990\pi$
$558$		0			0
$559$		−	55.3519i		−	2.34114i
$560$	9.31780	+	0.302008i	0.393749	+	0.0127622i
$561$		0			0
$562$	0.0911275	−	11.2498i	0.00384398	−	0.474546i
$563$	21.9247			0.924017			0.462008	−	0.886876i	$-0.347129\pi$
$563$	21.9247			0.924017			0.462008	+	0.886876i	$0.347129\pi$
$564$		0			0
$565$	−16.1889			−0.681071
$566$	−0.213609	+	26.3704i	−0.00897867	+	1.10843i
$567$		0			0
$568$	32.1907	+	0.782402i	1.35069	+	0.0328289i
$569$			1.64752i			0.0690676i	0.999404	+	0.0345338i	$0.0109946\pi$
$569$			1.64752i			0.0690676i	−0.999404	+	0.0345338i	$0.989005\pi$
$570$		0			0
$571$		−	11.6349i		−	0.486906i	−0.969913	−	0.243453i	$-0.921720\pi$
$571$		−	11.6349i		−	0.486906i	0.969913	−	0.243453i	$-0.0782801\pi$
$572$	−38.2718	−	0.620070i	−1.60022	−	0.0259264i
$573$		0			0
$574$	−18.7851	−	0.152165i	−0.784073	−	0.00635125i
$575$	7.46328			0.311240
$576$		0			0
$577$	−11.6000			−0.482912			−0.241456	−	0.970412i	$-0.577625\pi$
$577$	−11.6000			−0.482912			−0.241456	+	0.970412i	$0.577625\pi$
$578$	57.8129	+	0.468304i	2.40470	+	0.0194789i
$579$		0			0
$580$	−9.55816	−	0.154859i	−0.396881	−	0.00643016i
$581$		−	10.7615i		−	0.446462i
$582$		0			0
$583$		−	21.0844i		−	0.873226i
$584$	−18.8339	−	0.457764i	−0.779353	−	0.0189424i
$585$		0			0
$586$	0.107803	−	13.3084i	0.00445329	−	0.549766i
$587$	−9.46226			−0.390549			−0.195275	−	0.980749i	$-0.562560\pi$
$587$	−9.46226			−0.390549			−0.195275	+	0.980749i	$0.562560\pi$
$588$		0			0
$589$	−3.10909			−0.128108
$590$	−6.65332e−5		0.00821363i	−2.73913e−6		0.000338150i
$591$		0			0
$592$	15.3862	+	0.498697i	0.632369	+	0.0204963i
$593$			22.3051i			0.915960i	0.888962	+	0.457980i	$0.151427\pi$
$593$			22.3051i			0.915960i	−0.888962	+	0.457980i	$0.848573\pi$
$594$		0			0
$595$			17.7317i			0.726929i
$596$	−0.218805	+	13.5051i	−0.00896262	+	0.553189i
$597$		0			0
$598$	−47.9295	−	0.388245i	−1.95998	−	0.0158765i
$599$	10.0016			0.408656			0.204328	−	0.978902i	$-0.434499\pi$
$599$	10.0016			0.408656			0.204328	+	0.978902i	$0.434499\pi$
$600$		0			0
$601$	7.91679			0.322933			0.161466	−	0.986878i	$-0.448378\pi$
$601$	7.91679			0.322933			0.161466	+	0.986878i	$0.448378\pi$
$602$	−40.1738	−	0.325421i	−1.63736	−	0.0132632i
$603$		0			0
$604$	−0.457648	+	28.2469i	−0.0186214	+	1.14935i
$605$			6.76101i			0.274874i
$606$		0			0
$607$			24.7634i			1.00512i	0.864543	+	0.502559i	$0.167608\pi$
$607$			24.7634i			1.00512i	−0.864543	+	0.502559i	$0.832392\pi$
$608$	−0.164742	+	4.06540i	−0.00668117	+	0.164874i
$609$		0			0
$610$	−0.0584671	+	7.21787i	−0.00236727	+	0.292243i
$611$	−42.8207			−1.73234
$612$		0			0
$613$	−0.697779			−0.0281830			−0.0140915	−	0.999901i	$-0.504486\pi$
$613$	−0.697779			−0.0281830			−0.0140915	+	0.999901i	$0.504486\pi$
$614$	−0.391411	+	48.3203i	−0.0157961	+	1.95005i
$615$		0			0
$616$	−0.675044	+	27.7736i	−0.0271983	+	1.11903i
$617$		−	27.9820i		−	1.12651i	−0.826282	−	0.563257i	$-0.809548\pi$
$617$		−	27.9820i		−	1.12651i	0.826282	−	0.563257i	$-0.190452\pi$
$618$		0			0
$619$			17.3313i			0.696605i	0.937382	+	0.348302i	$0.113242\pi$
$619$			17.3313i			0.696605i	−0.937382	+	0.348302i	$0.886758\pi$
$620$	8.64414	+	0.140050i	0.347157	+	0.00562455i
$621$		0			0
$622$	33.2725	+	0.269518i	1.33410	+	0.0108067i
$623$	−7.19938			−0.288437
$624$		0			0
$625$	1.00000			0.0400000
$626$	22.1656	+	0.179549i	0.885916	+	0.00717622i
$627$		0			0
$628$	7.58850	+	0.122947i	0.302814	+	0.00490612i
$629$			29.2798i			1.16746i
$630$		0			0
$631$			18.5146i			0.737056i	0.929617	+	0.368528i	$0.120138\pi$
$631$			18.5146i			0.737056i	−0.929617	+	0.368528i	$0.879862\pi$
$632$	−0.233964	+	9.62607i	−0.00930659	+	0.382904i
$633$		0			0
$634$	−0.319590	+	39.4540i	−0.0126926	+	1.56692i
$635$	2.70385			0.107299
$636$		0			0
$637$	−7.12046			−0.282123
$638$	0.230749	−	28.4863i	0.00913542	−	1.12778i
$639$		0			0
$640$	0.641156	−	11.2955i	0.0253439	−	0.446495i
$641$		−	35.6783i		−	1.40921i	−0.709600	−	0.704605i	$-0.751124\pi$
$641$		−	35.6783i		−	1.40921i	0.709600	−	0.704605i	$-0.248876\pi$
$642$		0			0
$643$			4.93252i			0.194520i	0.995259	+	0.0972598i	$0.0310078\pi$
$643$			4.93252i			0.194520i	−0.995259	+	0.0972598i	$0.968992\pi$
$644$	−0.563567	+	34.7843i	−0.0222076	+	1.37070i
$645$		0			0
$646$	−7.73846	−	0.0626841i	−0.304465	−	0.00246627i
$647$	37.6103			1.47861			0.739306	−	0.673370i	$-0.235154\pi$
$647$	37.6103			1.47861			0.739306	+	0.673370i	$0.235154\pi$
$648$		0			0
$649$	−0.0244776			−0.000960829
$650$	−6.42204	−	0.0520207i	−0.251893	−	0.00204042i
$651$		0			0
$652$	0.0816067	−	5.03691i	0.00319597	−	0.197261i
$653$		−	20.2370i		−	0.791936i	−0.918264	−	0.395968i	$-0.870409\pi$
$653$		−	20.2370i		−	0.791936i	0.918264	−	0.395968i	$-0.129591\pi$
$654$		0			0
$655$		−	16.3775i		−	0.639924i
$656$	−0.738529	+	22.7857i	−0.0288347	+	0.889632i
$657$		0			0
$658$	−0.251748	+	31.0788i	−0.00981418	+	1.21158i
$659$	−41.0098			−1.59752			−0.798758	−	0.601652i	$-0.794509\pi$
$659$	−41.0098			−1.59752			−0.798758	+	0.601652i	$0.794509\pi$
$660$		0			0
$661$	−28.5883			−1.11195			−0.555977	−	0.831198i	$-0.687656\pi$
$661$	−28.5883			−1.11195			−0.555977	+	0.831198i	$0.687656\pi$
$662$	−0.399668	+	49.3396i	−0.0155335	+	1.91764i
$663$		0			0
$664$	−13.0559	−	0.317328i	−0.506668	−	0.0123147i
$665$		−	1.67636i		−	0.0650063i
$666$		0			0
$667$		−	35.6723i		−	1.38124i
$668$	3.96887	+	0.0643025i	0.153560	+	0.00248794i
$669$		0			0
$670$	13.3753	+	0.108344i	0.516732	+	0.00418570i
$671$	−21.5101			−0.830387
$672$		0			0
$673$	32.8253			1.26532			0.632661	−	0.774429i	$-0.281963\pi$
$673$	32.8253			1.26532			0.632661	+	0.774429i	$0.281963\pi$
$674$	2.36404	+	0.0191495i	0.0910593	+	0.000737611i
$675$		0			0
$676$	15.2433	+	0.246968i	0.586281	+	0.00949876i
$677$			28.4799i			1.09457i	0.836945	+	0.547287i	$0.184339\pi$
$677$			28.4799i			1.09457i	−0.836945	+	0.547287i	$0.815661\pi$
$678$		0			0
$679$			9.58361i			0.367785i
$680$	21.5122	+	0.522861i	0.824957	+	0.0200508i
$681$		0			0
$682$	−0.208683	+	25.7622i	−0.00799087	+	0.986486i
$683$	−5.71233			−0.218576			−0.109288	−	0.994010i	$-0.534857\pi$
$683$	−5.71233			−0.218576			−0.109288	+	0.994010i	$0.534857\pi$
$684$		0			0
$685$	−12.9838			−0.496084
$686$	−0.228751	+	28.2397i	−0.00873375	+	1.07820i
$687$		0			0
$688$	−1.57942	+	48.7296i	−0.0602149	+	1.85780i
$689$			22.7195i			0.865545i
$690$		0			0
$691$		−	6.88624i		−	0.261965i	−0.991385	−	0.130982i	$-0.958187\pi$
$691$		−	6.88624i		−	0.261965i	0.991385	−	0.130982i	$-0.0418131\pi$
$692$	0.645808	−	39.8604i	0.0245499	−	1.51527i
$693$		0			0
$694$	−5.10118	−	0.0413212i	−0.193638	−	0.00156853i
$695$	−16.9541			−0.643105
$696$		0			0
$697$	−43.3610			−1.64241
$698$	30.9832	+	0.250975i	1.17273	+	0.00949953i
$699$		0			0
$700$	−0.0755120	+	4.66073i	−0.00285408	+	0.176159i
$701$		−	29.0065i		−	1.09556i	−0.836622	−	0.547780i	$-0.815473\pi$
$701$		−	29.0065i		−	1.09556i	0.836622	−	0.547780i	$-0.184527\pi$
$702$		0			0
$703$		−	2.76812i		−	0.104401i
$704$	33.6752	+	1.63794i	1.26918	+	0.0617321i
$705$		0			0
$706$	−0.0213786	+	2.63922i	−0.000804593	+	0.0993283i
$707$	22.1119			0.831605
$708$		0			0
$709$	−23.4225			−0.879651			−0.439825	−	0.898083i	$-0.644960\pi$
$709$	−23.4225			−0.879651			−0.439825	+	0.898083i	$0.644960\pi$
$710$	−0.130412	+	16.0996i	−0.00489427	+	0.604206i
$711$		0			0
$712$	−0.212291	+	8.73435i	−0.00795593	+	0.327334i
$713$			32.2610i			1.20819i
$714$		0			0
$715$		−	19.1384i		−	0.715736i
$716$	10.1045	+	0.163710i	0.377623	+	0.00611814i
$717$		0			0
$718$	−22.0707	−	0.178780i	−0.823671	−	0.00667201i
$719$	−13.7011			−0.510965			−0.255483	−	0.966814i	$-0.582234\pi$
$719$	−13.7011			−0.510965			−0.255483	+	0.966814i	$0.582234\pi$
$720$		0			0
$721$	11.9024			0.443268
$722$	−26.1376	−	0.211723i	−0.972740	−	0.00787952i
$723$		0			0
$724$	12.0634	+	0.195449i	0.448334	+	0.00726379i
$725$		−	4.77971i		−	0.177514i
$726$		0			0
$727$			23.0967i			0.856610i	0.903634	+	0.428305i	$0.140889\pi$
$727$			23.0967i			0.856610i	−0.903634	+	0.428305i	$0.859111\pi$
$728$	0.727395	−	29.9275i	0.0269591	−	1.10919i
$729$		0			0
$730$	0.0763006	−	9.41944i	0.00282401	−	0.348629i
$731$	−92.7319			−3.42981
$732$		0			0
$733$	−18.2047			−0.672407			−0.336204	−	0.941789i	$-0.609143\pi$
$733$	−18.2047			−0.672407			−0.336204	+	0.941789i	$0.609143\pi$
$734$	0.0585151	−	7.22378i	0.00215983	−	0.266635i
$735$		0			0
$736$	42.1840	+	1.70942i	1.55492	+	0.0630101i
$737$			39.8599i			1.46826i
$738$		0			0
$739$		−	42.1961i		−	1.55221i	−0.630605	−	0.776104i	$-0.717193\pi$
$739$		−	42.1961i		−	1.55221i	0.630605	−	0.776104i	$-0.282807\pi$
$740$	−0.124691	+	7.69613i	−0.00458372	+	0.282916i
$741$		0			0
$742$	16.4896	+	0.133571i	0.605351	+	0.00490355i
$743$	25.2287			0.925549			0.462775	−	0.886476i	$-0.346854\pi$
$743$	25.2287			0.925549			0.462775	+	0.886476i	$0.346854\pi$
$744$		0			0
$745$	−6.75342			−0.247426
$746$	−30.9557	−	0.250751i	−1.13337	−	0.00918066i
$747$		0			0
$748$	−1.03881	+	64.1174i	−0.0379828	+	2.34436i
$749$			5.56856i			0.203471i
$750$		0			0
$751$		−	24.2760i		−	0.885843i	−0.896560	−	0.442921i	$-0.853942\pi$
$751$		−	24.2760i		−	0.885843i	0.896560	−	0.442921i	$-0.146058\pi$
$752$	37.6976	+	1.22185i	1.37469	+	0.0445564i
$753$		0			0
$754$	−0.248644	+	30.6955i	−0.00905507	+	1.11786i
$755$	−14.1253			−0.514072
$756$		0			0
$757$	33.4250			1.21485			0.607427	−	0.794376i	$-0.292202\pi$
$757$	33.4250			1.21485			0.607427	+	0.794376i	$0.292202\pi$
$758$	−0.225994	+	27.8993i	−0.00820846	+	1.01335i
$759$		0			0
$760$	−2.03377	−	0.0494313i	−0.0737725	−	0.00179306i
$761$			47.8297i			1.73383i	0.498459	+	0.866913i	$0.333900\pi$
$761$			47.8297i			1.73383i	−0.498459	+	0.866913i	$0.666100\pi$
$762$		0			0
$763$		−	37.9114i		−	1.37248i
$764$	−30.1937	−	0.489191i	−1.09237	−	0.0176983i
$765$		0			0
$766$	37.6511	+	0.304986i	1.36039	+	0.0110196i
$767$	0.0263759			0.000952377
$768$		0			0
$769$	36.7975			1.32695			0.663476	−	0.748197i	$-0.269080\pi$
$769$	36.7975			1.32695			0.663476	+	0.748197i	$0.269080\pi$
$770$	−13.8904	−	0.112517i	−0.500577	−	0.00405484i
$771$		0			0
$772$	−44.8064	−	0.725942i	−1.61262	−	0.0261272i
$773$		−	19.9723i		−	0.718355i	−0.933269	−	0.359177i	$-0.883057\pi$
$773$		−	19.9723i		−	0.718355i	0.933269	−	0.359177i	$-0.116943\pi$
$774$		0			0
$775$			4.32264i			0.155274i
$776$	11.6269	+	0.282595i	0.417382	+	0.0101446i
$777$		0			0
$778$	−0.121844	+	15.0418i	−0.00436832	+	0.539276i
$779$	4.09935			0.146874
$780$		0			0
$781$	−47.9785			−1.71681
$782$	−0.650432	+	80.2970i	−0.0232594	+	2.87141i
$783$		0			0
$784$	6.26856	+	0.203176i	0.223877	+	0.00725630i
$785$			3.79475i			0.135440i
$786$		0			0
$787$			21.6916i			0.773222i	0.922243	+	0.386611i	$0.126354\pi$
$787$			21.6916i			0.773222i	−0.922243	+	0.386611i	$0.873646\pi$
$788$	−0.138250	+	8.53304i	−0.00492495	+	0.303977i
$789$		0			0
$790$	−4.81430	−	0.0389974i	−0.171285	−	0.00138747i
$791$	37.7310			1.34156
$792$		0			0
$793$	23.1782			0.823083
$794$	−27.9868	−	0.226702i	−0.993214	−	0.00804536i
$795$		0			0
$796$	−0.701570	+	43.3022i	−0.0248665	+	1.53480i
$797$		−	14.0080i		−	0.496187i	−0.968736	−	0.248094i	$-0.920196\pi$
$797$		−	14.0080i		−	0.496187i	0.968736	−	0.248094i	$-0.0798041\pi$
$798$		0			0
$799$			71.7382i			2.53792i
$800$	5.65222	+	0.229044i	0.199836	+	0.00809794i
$801$		0			0
$802$	−0.400325	+	49.4208i	−0.0141360	+	1.74511i
$803$	28.0710			0.990604
$804$		0			0
$805$	−17.3945			−0.613074
$806$	0.224866	−	27.7601i	0.00792058	−	0.977809i
$807$		0			0
$808$	0.652023	−	26.8264i	0.0229381	−	0.943749i
$809$			33.6942i			1.18462i	0.805709	+	0.592312i	$0.201785\pi$
$809$			33.6942i			1.18462i	−0.805709	+	0.592312i	$0.798215\pi$
$810$		0			0
$811$			54.6871i			1.92032i	0.279446	+	0.960161i	$0.409849\pi$
$811$			54.6871i			1.92032i	−0.279446	+	0.960161i	$0.590151\pi$
$812$	22.2770	+	0.360925i	0.781768	+	0.0126660i
$813$		0			0
$814$	−22.9369	−	0.185796i	−0.803937	−	0.00651216i
$815$	2.51879			0.0882293
$816$		0			0
$817$	8.76688			0.306714
$818$	22.7339	+	0.184152i	0.794871	+	0.00643872i
$819$		0			0
$820$	−11.3973	−	0.184657i	−0.398012	−	0.00644849i
$821$		−	1.36554i		−	0.0476575i	−0.999716	−	0.0238288i	$-0.992414\pi$
$821$		−	1.36554i		−	0.0476575i	0.999716	−	0.0238288i	$-0.00758565\pi$
$822$		0			0
$823$		−	16.8006i		−	0.585631i	−0.956169	−	0.292815i	$-0.905408\pi$
$823$		−	16.8006i		−	0.585631i	0.956169	−	0.292815i	$-0.0945921\pi$
$824$	0.350970	−	14.4401i	0.0122266	−	0.503044i
$825$		0			0
$826$	0.000155067	−	0.0191433i	5.39548e−6	−	0.000666080i
$827$	39.4465			1.37169			0.685844	−	0.727749i	$-0.259433\pi$
$827$	39.4465			1.37169			0.685844	+	0.727749i	$0.259433\pi$
$828$		0			0
$829$	20.5590			0.714044			0.357022	−	0.934096i	$-0.383792\pi$
$829$	20.5590			0.714044			0.357022	+	0.934096i	$0.383792\pi$
$830$	0.0528926	−	6.52968i	0.00183593	−	0.226649i
$831$		0			0
$832$	−36.2868	−	1.76496i	−1.25802	−	0.0611891i
$833$			11.9290i			0.413316i
$834$		0			0
$835$			1.98469i			0.0686832i
$836$	0.0982094	−	6.06166i	0.00339664	−	0.209647i
$837$		0			0
$838$	16.5784	+	0.134291i	0.572692	+	0.00463900i
$839$	−20.4312			−0.705364			−0.352682	−	0.935743i	$-0.614730\pi$
$839$	−20.4312			−0.705364			−0.352682	+	0.935743i	$0.614730\pi$
$840$		0			0
$841$	6.15439			0.212220
$842$	−25.0758	−	0.203122i	−0.864168	−	0.00700006i
$843$		0			0
$844$	−0.309427	+	19.0984i	−0.0106509	+	0.657394i
$845$			7.62265i			0.262227i
$846$		0			0
$847$		−	15.7577i		−	0.541441i
$848$	0.648283	−	20.0013i	0.0222621	−	0.686849i
$849$		0			0
$850$	−0.0871510	+	10.7589i	−0.00298926	+	0.369029i
$851$	−28.7230			−0.984610
$852$		0			0
$853$	−43.5478			−1.49105			−0.745525	−	0.666478i	$-0.767801\pi$
$853$	−43.5478			−1.49105			−0.745525	+	0.666478i	$0.767801\pi$
$854$	0.136268	−	16.8225i	0.00466299	−	0.575654i
$855$		0			0
$856$	6.75582	+	0.164202i	0.230909	+	0.00561231i
$857$		−	5.19598i		−	0.177491i	−0.996054	−	0.0887457i	$-0.971714\pi$
$857$		−	5.19598i		−	0.177491i	0.996054	−	0.0887457i	$-0.0282858\pi$
$858$		0			0
$859$		−	18.7903i		−	0.641115i	−0.947229	−	0.320558i	$-0.896130\pi$
$859$		−	18.7903i		−	0.641115i	0.947229	−	0.320558i	$-0.103870\pi$
$860$	−24.3744	−	0.394907i	−0.831159	−	0.0134662i
$861$		0			0
$862$	5.87945	+	0.0476255i	0.200255	+	0.00162213i
$863$	0.00612001			0.000208328			0.000104164	−	1.00000i	$-0.499967\pi$
$863$	0.00612001			0.000208328			0.000104164		1.00000i	$0.499967\pi$
$864$		0			0
$865$	19.9328			0.677736
$866$	31.3504	+	0.253949i	1.06533	+	0.00862954i
$867$		0			0
$868$	−20.1467	−	0.326411i	−0.683822	−	0.0110791i
$869$		−	14.3472i		−	0.486694i
$870$		0			0
$871$		−	42.9511i		−	1.45534i
$872$	−45.9944	−	1.11791i	−1.55757	−	0.0378570i
$873$		0			0
$874$	0.0614919	−	7.59128i	0.00207999	−	0.256779i
$875$	−2.33067			−0.0787911
$876$		0			0
$877$	−16.3640			−0.552574			−0.276287	−	0.961075i	$-0.589104\pi$
$877$	−16.3640			−0.552574			−0.276287	+	0.961075i	$0.589104\pi$
$878$	−0.0232070	+	2.86494i	−0.000783197	+	0.0966869i
$879$		0			0
$880$	−0.546099	+	16.8487i	−0.0184090	+	0.567969i
$881$			8.01603i			0.270067i	0.990841	+	0.135033i	$0.0431142\pi$
$881$			8.01603i			0.270067i	−0.990841	+	0.135033i	$0.956886\pi$
$882$		0			0
$883$		−	11.2285i		−	0.377870i	−0.981990	−	0.188935i	$-0.939496\pi$
$883$		−	11.2285i		−	0.377870i	0.981990	−	0.188935i	$-0.0605036\pi$
$884$	1.11937	−	69.0898i	0.0376487	−	2.32374i
$885$		0			0
$886$	25.9749	+	0.210405i	0.872644	+	0.00706871i
$887$	41.0844			1.37948			0.689740	−	0.724057i	$-0.257725\pi$
$887$	41.0844			1.37948			0.689740	+	0.724057i	$0.257725\pi$
$888$		0			0
$889$	−6.30179			−0.211355
$890$	−4.36832	−	0.0353849i	−0.146427	−	0.00118610i
$891$		0			0
$892$	−0.0200481	+	1.23740i	−0.000671258	+	0.0414313i
$893$		−	6.78213i		−	0.226955i
$894$		0			0
$895$			5.05291i			0.168900i
$896$	−1.49433	+	26.3262i	−0.0499219	+	0.879496i
$897$		0			0
$898$	−0.144873	+	17.8849i	−0.00483449	+	0.596825i
$899$	20.6609			0.689081
$900$		0			0
$901$	38.0624			1.26804
$902$	0.275149	−	33.9676i	0.00916146	−	1.13100i
$903$		0			0
$904$	1.11259	−	45.7756i	0.0370041	−	1.52247i
$905$			6.03251i			0.200527i
$906$		0			0
$907$			21.3655i			0.709431i	0.934974	+	0.354715i	$0.115422\pi$
$907$			21.3655i			0.709431i	−0.934974	+	0.354715i	$0.884578\pi$
$908$	16.1122	+	0.261046i	0.534703	+	0.00866311i
$909$		0			0
$910$	14.9677	+	0.121243i	0.496174	+	0.00401917i
$911$	3.34134			0.110703			0.0553517	−	0.998467i	$-0.482372\pi$
$911$	3.34134			0.110703			0.0553517	+	0.998467i	$0.482372\pi$
$912$		0			0
$913$	19.4592			0.644006
$914$	−31.7389	−	0.257096i	−1.04983	−	0.00850398i
$915$		0			0
$916$	14.5867	+	0.236329i	0.481957	+	0.00780854i
$917$			38.1707i			1.26051i
$918$		0			0
$919$			18.2505i			0.602029i	0.953620	+	0.301015i	$0.0973253\pi$
$919$			18.2505i			0.602029i	−0.953620	+	0.301015i	$0.902675\pi$
$920$	−0.512916	+	21.1031i	−0.0169104	+	0.695749i
$921$		0			0
$922$	0.224580	−	27.7248i	0.00739616	−	0.913069i
$923$	51.6994			1.70171
$924$		0			0
$925$	−3.84857			−0.126540
$926$	0.285327	−	35.2241i	0.00937643	−	1.15754i
$927$		0			0
$928$	1.09477	−	27.0159i	0.0359374	−	0.886842i
$929$			37.4637i			1.22914i	0.788860	+	0.614572i	$0.210671\pi$
$929$			37.4637i			1.22914i	−0.788860	+	0.614572i	$0.789329\pi$
$930$		0			0
$931$		−	1.12777i		−	0.0369612i
$932$	0.514308	−	31.7440i	0.0168467	−	1.03981i
$933$		0			0
$934$	−6.77336	−	0.0548665i	−0.221631	−	0.00179529i
$935$	−32.0629			−1.04857
$936$		0			0
$937$	19.3024			0.630581			0.315291	−	0.948995i	$-0.397898\pi$
$937$	19.3024			0.630581			0.315291	+	0.948995i	$0.397898\pi$
$938$	−31.1734	−	0.252515i	−1.01785	−	0.00824491i
$939$		0			0
$940$	−0.305504	+	18.8562i	−0.00996443	+	0.615022i
$941$			32.3508i			1.05460i	0.849678	+	0.527302i	$0.176796\pi$
$941$			32.3508i			1.05460i	−0.849678	+	0.527302i	$0.823204\pi$
$942$		0			0
$943$		−	42.5363i		−	1.38517i
$944$	−0.0232202		0.000752614i	−0.000755754		2.44955e-5i
$945$		0			0
$946$	0.588435	−	72.6432i	0.0191317	−	2.36183i
$947$	21.1401			0.686962			0.343481	−	0.939160i	$-0.388394\pi$
$947$	21.1401			0.686962			0.343481	+	0.939160i	$0.388394\pi$
$948$		0			0
$949$	−30.2480			−0.981891
$950$	0.00823926	−	1.01715i	0.000267317	−	0.0330007i
$951$		0			0
$952$	−50.1380	−	1.21862i	−1.62498	−	0.0394956i
$953$		−	6.92287i		−	0.224254i	−0.993694	−	0.112127i	$-0.964234\pi$
$953$		−	6.92287i		−	0.224254i	0.993694	−	0.112127i	$-0.0357663\pi$
$954$		0			0
$955$		−	15.0989i		−	0.488587i
$956$	42.5366	+	0.689166i	1.37573	+	0.0222892i
$957$		0			0
$958$	54.7079	+	0.443152i	1.76753	+	0.0143176i
$959$	30.2609			0.977176
$960$		0			0
$961$	12.3148			0.397252
$962$	24.7157	+	0.200205i	0.796866	+	0.00645488i
$963$		0			0
$964$	47.1972	+	0.764676i	1.52012	+	0.0246286i
$965$		−	22.4062i		−	0.721280i
$966$		0			0
$967$		−	24.0407i		−	0.773096i	−0.922269	−	0.386548i	$-0.873667\pi$
$967$		−	24.0407i		−	0.773096i	0.922269	−	0.386548i	$-0.126333\pi$
$968$	−19.1174	−	0.464653i	−0.614456	−	0.0149345i
$969$		0			0
$970$	−0.0471033	+	5.81499i	−0.00151240	+	0.186708i
$971$	6.55338			0.210308			0.105154	−	0.994456i	$-0.466466\pi$
$971$	6.55338			0.210308			0.105154	+	0.994456i	$0.466466\pi$
$972$		0			0
$973$	39.5144			1.26677
$974$	−0.315983	+	39.0087i	−0.0101248	+	1.24992i
$975$		0			0
$976$	−20.4052	−	0.661372i	−0.653153	−	0.0211700i
$977$			12.1311i			0.388110i	0.980991	+	0.194055i	$0.0621640\pi$
$977$			12.1311i			0.388110i	−0.980991	+	0.194055i	$0.937836\pi$
$978$		0			0
$979$		−	13.0181i		−	0.416060i
$980$	−0.0508008	+	3.13551i	−0.00162277	+	0.100160i
$981$		0			0
$982$	−26.8987	−	0.217889i	−0.858373	−	0.00695311i
$983$	−18.1301			−0.578261			−0.289131	−	0.957290i	$-0.593366\pi$
$983$	−18.1301			−0.578261			−0.289131	+	0.957290i	$0.593366\pi$
$984$		0			0
$985$	−4.26708			−0.135960
$986$	51.4246	+	0.416557i	1.63769	+	0.0132659i
$987$		0			0
$988$	−0.105826	+	6.53175i	−0.00336677	+	0.207803i
$989$		−	90.9683i		−	2.89262i
$990$		0			0
$991$			25.0995i			0.797311i	0.917101	+	0.398656i	$0.130523\pi$
$991$			25.0995i			0.797311i	−0.917101	+	0.398656i	$0.869477\pi$
$992$	−0.990076	+	24.4325i	−0.0314349	+	0.775732i
$993$		0			0
$994$	0.303947	−	37.5228i	0.00964062	−	1.19015i
$995$	−21.6539			−0.686475
$996$		0			0
$997$	−44.8063			−1.41903			−0.709514	−	0.704691i	$-0.751086\pi$
$997$	−44.8063			−1.41903			−0.709514	+	0.704691i	$0.751086\pi$
$998$	−0.396231	+	48.9154i	−0.0125425	+	1.54839i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1620.2.e.a.971.1	✓	48
3.2	odd	2	inner	1620.2.e.a.971.48	yes	48
4.3	odd	2	inner	1620.2.e.a.971.47	yes	48
12.11	even	2	inner	1620.2.e.a.971.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1620.2.e.a.971.1	✓	48	1.1	even	1	trivial
1620.2.e.a.971.2	yes	48	12.11	even	2	inner
1620.2.e.a.971.47	yes	48	4.3	odd	2	inner
1620.2.e.a.971.48	yes	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)

\(f(q)\)	\(=\)	\(q+(-1.41417 - 0.0114552i) q^{2} +(1.99974 + 0.0323992i) q^{4} +1.00000i q^{5} -2.33067i q^{7} +(-2.82759 - 0.0687254i) q^{8} +O(q^{10})\)	\(q+(-1.41417 - 0.0114552i) q^{2} +(1.99974 + 0.0323992i) q^{4} +1.00000i q^{5} -2.33067i q^{7} +(-2.82759 - 0.0687254i) q^{8} +(0.0114552 - 1.41417i) q^{10} +4.21438 q^{11} -4.54122 q^{13} +(-0.0266984 + 3.29596i) q^{14} +(3.99790 + 0.129580i) q^{16} +7.60797i q^{17} -0.719258i q^{19} +(-0.0323992 + 1.99974i) q^{20} +(-5.95984 - 0.0482767i) q^{22} -7.46328 q^{23} -1.00000 q^{25} +(6.42204 + 0.0520207i) q^{26} +(0.0755120 - 4.66073i) q^{28} +4.77971i q^{29} -4.32264i q^{31} +(-5.65222 - 0.229044i) q^{32} +(0.0871510 - 10.7589i) q^{34} +2.33067 q^{35} +3.84857 q^{37} +(-0.00823926 + 1.01715i) q^{38} +(0.0687254 - 2.82759i) q^{40} +5.69942i q^{41} +12.1888i q^{43} +(8.42766 + 0.136543i) q^{44} +(10.5543 + 0.0854935i) q^{46} +9.42935 q^{47} +1.56796 q^{49} +(1.41417 + 0.0114552i) q^{50} +(-9.08124 - 0.147132i) q^{52} -5.00296i q^{53} +4.21438i q^{55} +(-0.160176 + 6.59019i) q^{56} +(0.0547527 - 6.75931i) q^{58} -0.00580811 q^{59} -5.10397 q^{61} +(-0.0495168 + 6.11293i) q^{62} +(7.99055 + 0.388655i) q^{64} -4.54122i q^{65} +9.45806i q^{67} +(-0.246492 + 15.2139i) q^{68} +(-3.29596 - 0.0266984i) q^{70} -11.3845 q^{71} +6.66077 q^{73} +(-5.44252 - 0.0440863i) q^{74} +(0.0233034 - 1.43833i) q^{76} -9.82235i q^{77} -3.40433i q^{79} +(-0.129580 + 3.99790i) q^{80} +(0.0652881 - 8.05993i) q^{82} +4.61733 q^{83} -7.60797 q^{85} +(0.139625 - 17.2370i) q^{86} +(-11.9166 - 0.289635i) q^{88} -3.08897i q^{89} +10.5841i q^{91} +(-14.9246 - 0.241804i) q^{92} +(-13.3347 - 0.108015i) q^{94} +0.719258 q^{95} -4.11195 q^{97} +(-2.21736 - 0.0179614i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 24 q^{16} - 24 q^{22} - 48 q^{25} + 24 q^{28} - 24 q^{34} - 24 q^{40} + 48 q^{46} - 48 q^{49} + 24 q^{58} + 24 q^{64} + 24 q^{76} + 24 q^{88}+O(q^{100}) \) 48 * q - 24 * q^16 - 24 * q^22 - 48 * q^25 + 24 * q^28 - 24 * q^34 - 24 * q^40 + 48 * q^46 - 48 * q^49 + 24 * q^58 + 24 * q^64 + 24 * q^76 + 24 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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