LMFDB - Embedded newform 1480.2.q.b.1321.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1480,2,Mod(121,1480)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1480.121"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1480, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1480 = 2^{3} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1480.q (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [18,0,2,0,9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.8178594991$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 2 x^{17} + 18 x^{16} - 22 x^{15} + 194 x^{14} - 224 x^{13} + 1053 x^{12} - 770 x^{11} + \cdots + 441 $ x^18 - 2x^17 + 18x^16 - 22x^15 + 194x^14 - 224x^13 + 1053x^12 - 770x^11 + 3419x^10 - 2128x^9 + 7324x^8 - 2915x^7 + 9758x^6 - 3440x^5 + 7942x^4 - 786x^3 + 2419x^2 - 483*x + 441
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1321.6
Root			$0.579516 - 1.00375i$ of defining polynomial
Character	$\chi$	$=$	1480.1321
Dual form			1480.2.q.b.121.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.579516 - 1.00375i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.05730 + 1.83130i) q^{7} +(0.828323 + 1.43470i) q^{9} +1.33240 q^{11} +(-0.166509 + 0.288401i) q^{13} +(-0.579516 - 1.00375i) q^{15} +(-3.96884 - 6.87424i) q^{17} +(2.30116 - 3.98572i) q^{19} +(1.22545 + 2.12254i) q^{21} +1.88058 q^{23} +(-0.500000 - 0.866025i) q^{25} +5.39720 q^{27} +4.92639 q^{29} +8.17565 q^{31} +(0.772146 - 1.33740i) q^{33} +(1.05730 + 1.83130i) q^{35} +(1.07456 - 5.98710i) q^{37} +(0.192989 + 0.334266i) q^{39} +(-5.67758 + 9.83387i) q^{41} -0.0283197 q^{43} +1.65665 q^{45} +7.84019 q^{47} +(1.26422 + 2.18970i) q^{49} -9.20003 q^{51} +(2.86824 + 4.96793i) q^{53} +(0.666199 - 1.15389i) q^{55} +(-2.66712 - 4.61958i) q^{57} +(1.02570 + 1.77656i) q^{59} +(6.44385 - 11.1611i) q^{61} -3.50315 q^{63} +(0.166509 + 0.288401i) q^{65} +(5.07370 - 8.78790i) q^{67} +(1.08983 - 1.88764i) q^{69} +(2.32718 - 4.03079i) q^{71} -6.70986 q^{73} -1.15903 q^{75} +(-1.40875 + 2.44002i) q^{77} +(6.84041 - 11.8479i) q^{79} +(0.642795 - 1.11335i) q^{81} +(0.276189 + 0.478373i) q^{83} -7.93769 q^{85} +(2.85492 - 4.94487i) q^{87} +(-8.23445 - 14.2625i) q^{89} +(-0.352100 - 0.609855i) q^{91} +(4.73792 - 8.20631i) q^{93} +(-2.30116 - 3.98572i) q^{95} +0.0622295 q^{97} +(1.10366 + 1.91159i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{3} + 9 q^{5} - 5 q^{9} - 6 q^{11} + 2 q^{13} - 2 q^{15} + q^{17} - 5 q^{21} + 12 q^{23} - 9 q^{25} - 10 q^{27} - 20 q^{29} + 28 q^{31} + 11 q^{33} - 5 q^{39} - 5 q^{41} + 2 q^{43} - 10 q^{45}+ \cdots + 30 q^{99}+O(q^{100}) $ 18 * q + 2 * q^3 + 9 * q^5 - 5 * q^9 - 6 * q^11 + 2 * q^13 - 2 * q^15 + q^17 - 5 * q^21 + 12 * q^23 - 9 * q^25 - 10 * q^27 - 20 * q^29 + 28 * q^31 + 11 * q^33 - 5 * q^39 - 5 * q^41 + 2 * q^43 - 10 * q^45 - 36 * q^47 + 7 * q^49 - 2 * q^51 - 10 * q^53 - 3 * q^55 + 22 * q^57 - 10 * q^59 + 16 * q^61 + 42 * q^63 - 2 * q^65 - 4 * q^67 - 13 * q^69 + 17 * q^71 + 56 * q^73 - 4 * q^75 + 43 * q^77 - 23 * q^79 - 17 * q^81 + 29 * q^83 + 2 * q^85 - q^87 - 16 * q^89 - 4 * q^91 + 5 * q^93 + 26 * q^97 + 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1480\mathbb{Z}\right)^\times$.

$n$	$297$	$741$	$1001$	$1111$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.579516	−	1.00375i	0.334584	−	0.579516i	−0.648821	−	0.760941i	$-0.724738\pi$
$3$	0.579516	−	1.00375i	0.334584	−	0.579516i	0.983405	+	0.181425i	$0.0580710\pi$
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	−1.05730	+	1.83130i	−0.399623	+	0.692167i	−0.993679	−	0.112256i	$-0.964192\pi$
$7$	−1.05730	+	1.83130i	−0.399623	+	0.692167i	0.594056	+	0.804423i	$0.297526\pi$
$8$		0			0
$9$	0.828323	+	1.43470i	0.276108	+	0.478232i
$10$		0			0
$11$	1.33240			0.401733			0.200867	−	0.979619i	$-0.435624\pi$
$11$	1.33240			0.401733			0.200867	+	0.979619i	$0.435624\pi$
$12$		0			0
$13$	−0.166509	+	0.288401i	−0.0461812	+	0.0799881i	−0.888192	−	0.459472i	$-0.848038\pi$
$13$	−0.166509	+	0.288401i	−0.0461812	+	0.0799881i	0.842011	+	0.539461i	$0.181372\pi$
$14$		0			0
$15$	−0.579516	−	1.00375i	−0.149630	−	0.259167i
$16$		0			0
$17$	−3.96884	−	6.87424i	−0.962586	−	1.66725i	−0.715966	−	0.698135i	$-0.754014\pi$
$17$	−3.96884	−	6.87424i	−0.962586	−	1.66725i	−0.246620	−	0.969112i	$-0.579320\pi$
$18$		0			0
$19$	2.30116	−	3.98572i	0.527922	−	0.914388i	−0.471548	−	0.881840i	$-0.656305\pi$
$19$	2.30116	−	3.98572i	0.527922	−	0.914388i	0.999470	−	0.0325474i	$-0.0103620\pi$
$20$		0			0
$21$	1.22545	+	2.12254i	0.267415	+	0.463176i
$22$		0			0
$23$	1.88058			0.392128			0.196064	−	0.980591i	$-0.437184\pi$
$23$	1.88058			0.392128			0.196064	+	0.980591i	$0.437184\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	5.39720			1.03869
$28$		0			0
$29$	4.92639			0.914808			0.457404	−	0.889259i	$-0.348779\pi$
$29$	4.92639			0.914808			0.457404	+	0.889259i	$0.348779\pi$
$30$		0			0
$31$	8.17565			1.46839			0.734195	−	0.678939i	$-0.237560\pi$
$31$	8.17565			1.46839			0.734195	+	0.678939i	$0.237560\pi$
$32$		0			0
$33$	0.772146	−	1.33740i	0.134413	−	0.232811i
$34$		0			0
$35$	1.05730	+	1.83130i	0.178717	+	0.309547i
$36$		0			0
$37$	1.07456	−	5.98710i	0.176657	−	0.984272i
$37$	1.07456	−	5.98710i	0.176657	−	0.984272i
$38$		0			0
$39$	0.192989	+	0.334266i	0.0309029	+	0.0535254i
$40$		0			0
$41$	−5.67758	+	9.83387i	−0.886690	+	1.53579i	−0.0429252	+	0.999078i	$0.513668\pi$
$41$	−5.67758	+	9.83387i	−0.886690	+	1.53579i	−0.843765	+	0.536713i	$0.819666\pi$
$42$		0			0
$43$	−0.0283197			−0.00431871			−0.00215936	−	0.999998i	$-0.500687\pi$
$43$	−0.0283197			−0.00431871			−0.00215936	+	0.999998i	$0.500687\pi$
$44$		0			0
$45$	1.65665			0.246958
$46$		0			0
$47$	7.84019			1.14361			0.571805	−	0.820390i	$-0.306243\pi$
$47$	7.84019			1.14361			0.571805	+	0.820390i	$0.306243\pi$
$48$		0			0
$49$	1.26422	+	2.18970i	0.180603	+	0.312814i
$50$		0			0
$51$	−9.20003			−1.28826
$52$		0			0
$53$	2.86824	+	4.96793i	0.393983	+	0.682398i	0.992971	−	0.118360i	$-0.0377637\pi$
$53$	2.86824	+	4.96793i	0.393983	+	0.682398i	−0.598988	+	0.800758i	$0.704430\pi$
$54$		0			0
$55$	0.666199	−	1.15389i	0.0898303	−	0.155591i
$56$		0			0
$57$	−2.66712	−	4.61958i	−0.353268	−	0.611878i
$58$		0			0
$59$	1.02570	+	1.77656i	0.133534	+	0.231288i	0.925037	−	0.379878i	$-0.124034\pi$
$59$	1.02570	+	1.77656i	0.133534	+	0.231288i	−0.791502	+	0.611166i	$0.790701\pi$
$60$		0			0
$61$	6.44385	−	11.1611i	0.825051	−	1.42903i	−0.0768294	−	0.997044i	$-0.524480\pi$
$61$	6.44385	−	11.1611i	0.825051	−	1.42903i	0.901880	−	0.431986i	$-0.142187\pi$
$62$		0			0
$63$	−3.50315			−0.441356
$64$		0			0
$65$	0.166509	+	0.288401i	0.0206528	+	0.0357718i
$66$		0			0
$67$	5.07370	−	8.78790i	0.619851	−	1.07361i	−0.369662	−	0.929166i	$-0.620527\pi$
$67$	5.07370	−	8.78790i	0.619851	−	1.07361i	0.989513	−	0.144446i	$-0.0461402\pi$
$68$		0			0
$69$	1.08983	−	1.88764i	0.131200	−	0.227245i
$70$		0			0
$71$	2.32718	−	4.03079i	0.276185	−	0.478367i	−0.694248	−	0.719735i	$-0.744263\pi$
$71$	2.32718	−	4.03079i	0.276185	−	0.478367i	0.970433	+	0.241369i	$0.0775964\pi$
$72$		0			0
$73$	−6.70986			−0.785329			−0.392665	−	0.919682i	$-0.628447\pi$
$73$	−6.70986			−0.785329			−0.392665	+	0.919682i	$0.628447\pi$
$74$		0			0
$75$	−1.15903			−0.133833
$76$		0			0
$77$	−1.40875	+	2.44002i	−0.160542	+	0.278067i
$78$		0			0
$79$	6.84041	−	11.8479i	0.769606	−	1.33300i	−0.168170	−	0.985758i	$-0.553786\pi$
$79$	6.84041	−	11.8479i	0.769606	−	1.33300i	0.937777	−	0.347239i	$-0.112881\pi$
$80$		0			0
$81$	0.642795	−	1.11335i	0.0714217	−	0.123706i
$82$		0			0
$83$	0.276189	+	0.478373i	0.0303156	+	0.0525082i	0.880785	−	0.473516i	$-0.157015\pi$
$83$	0.276189	+	0.478373i	0.0303156	+	0.0525082i	−0.850470	+	0.526024i	$0.823682\pi$
$84$		0			0
$85$	−7.93769			−0.860963
$86$		0			0
$87$	2.85492	−	4.94487i	0.306080	−	0.530146i
$88$		0			0
$89$	−8.23445	−	14.2625i	−0.872850	−	1.51182i	−0.859036	−	0.511915i	$-0.828936\pi$
$89$	−8.23445	−	14.2625i	−0.872850	−	1.51182i	−0.0138137	−	0.999905i	$-0.504397\pi$
$90$		0			0
$91$	−0.352100	−	0.609855i	−0.0369101	−	0.0639302i
$92$		0			0
$93$	4.73792	−	8.20631i	0.491299	−	0.850955i
$94$		0			0
$95$	−2.30116	−	3.98572i	−0.236094	−	0.408927i
$96$		0			0
$97$	0.0622295			0.00631844			0.00315922	−	0.999995i	$-0.498994\pi$
$97$	0.0622295			0.00631844			0.00315922	+	0.999995i	$0.498994\pi$
$98$		0			0
$99$	1.10366	+	1.91159i	0.110922	+	0.192122i
$100$		0			0
$101$	−11.3680			−1.13116			−0.565580	−	0.824693i	$-0.691348\pi$
$101$	−11.3680			−1.13116			−0.565580	+	0.824693i	$0.691348\pi$
$102$		0			0
$103$	−17.1621			−1.69104			−0.845518	−	0.533947i	$-0.820708\pi$
$103$	−17.1621			−1.69104			−0.845518	+	0.533947i	$0.820708\pi$
$104$		0			0
$105$	2.45090			0.239183
$106$		0			0
$107$	−2.66025	+	4.60769i	−0.257176	+	0.445443i	−0.965484	−	0.260461i	$-0.916125\pi$
$107$	−2.66025	+	4.60769i	−0.257176	+	0.445443i	0.708308	+	0.705904i	$0.249459\pi$
$108$		0			0
$109$	9.81219	+	16.9952i	0.939838	+	1.62785i	0.765772	+	0.643112i	$0.222357\pi$
$109$	9.81219	+	16.9952i	0.939838	+	1.62785i	0.174066	+	0.984734i	$0.444309\pi$
$110$		0			0
$111$	−5.38683	−	4.54821i	−0.511295	−	0.431697i
$112$		0			0
$113$	3.74604	+	6.48834i	0.352398	+	0.610372i	0.986669	−	0.162739i	$-0.0520329\pi$
$113$	3.74604	+	6.48834i	0.352398	+	0.610372i	−0.634271	+	0.773111i	$0.718700\pi$
$114$		0			0
$115$	0.940291	−	1.62863i	0.0876826	−	0.151871i
$116$		0			0
$117$	−0.551691			−0.0510039
$118$		0			0
$119$	16.7851			1.53869
$120$		0			0
$121$	−9.22471			−0.838610
$122$		0			0
$123$	6.58050	+	11.3978i	0.593344	+	1.02770i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−4.51826	−	7.82586i	−0.400931	−	0.694433i	0.592908	−	0.805270i	$-0.297980\pi$
$127$	−4.51826	−	7.82586i	−0.400931	−	0.694433i	−0.993839	+	0.110838i	$0.964647\pi$
$128$		0			0
$129$	−0.0164117	+	0.0284259i	−0.00144497	+	0.00250276i
$130$		0			0
$131$	5.66342	+	9.80934i	0.494816	+	0.857046i	0.999982	−	0.00597596i	$-0.00190222\pi$
$131$	5.66342	+	9.80934i	0.494816	+	0.857046i	−0.505166	+	0.863022i	$0.668569\pi$
$132$		0			0
$133$	4.86604	+	8.42823i	0.421939	+	0.730821i
$134$		0			0
$135$	2.69860	−	4.67411i	0.232259	−	0.402284i
$136$		0			0
$137$	−9.58054			−0.818521			−0.409260	−	0.912418i	$-0.634213\pi$
$137$	−9.58054			−0.818521			−0.409260	+	0.912418i	$0.634213\pi$
$138$		0			0
$139$	7.06695	+	12.2403i	0.599410	+	1.03821i	0.992908	+	0.118884i	$0.0379316\pi$
$139$	7.06695	+	12.2403i	0.599410	+	1.03821i	−0.393498	+	0.919326i	$0.628735\pi$
$140$		0			0
$141$	4.54352	−	7.86960i	0.382633	−	0.662740i
$142$		0			0
$143$	−0.221856	+	0.384265i	−0.0185525	+	0.0321339i
$144$		0			0
$145$	2.46320	−	4.26638i	0.204557	−	0.354304i
$146$		0			0
$147$	2.93055			0.241707
$148$		0			0
$149$	−18.3543			−1.50365			−0.751823	−	0.659365i	$-0.770825\pi$
$149$	−18.3543			−1.50365			−0.751823	+	0.659365i	$0.770825\pi$
$150$		0			0
$151$	−5.92511	+	10.2626i	−0.482179	+	0.835158i	−0.999791	−	0.0204572i	$-0.993488\pi$
$151$	−5.92511	+	10.2626i	−0.482179	+	0.835158i	0.517612	+	0.855616i	$0.326821\pi$
$152$		0			0
$153$	6.57496	−	11.3882i	0.531554	−	0.920679i
$154$		0			0
$155$	4.08782	−	7.08032i	0.328342	−	0.568705i
$156$		0			0
$157$	−7.49778	−	12.9865i	−0.598388	−	1.03644i	−0.993059	−	0.117616i	$-0.962475\pi$
$157$	−7.49778	−	12.9865i	−0.598388	−	1.03644i	0.394671	−	0.918822i	$-0.370858\pi$
$158$		0			0
$159$	6.64875			0.527280
$160$		0			0
$161$	−1.98834	+	3.44391i	−0.156703	+	0.271418i
$162$		0			0
$163$	6.74159	+	11.6768i	0.528042	+	0.914596i	0.999466	+	0.0326892i	$0.0104071\pi$
$163$	6.74159	+	11.6768i	0.528042	+	0.914596i	−0.471423	+	0.881907i	$0.656260\pi$
$164$		0			0
$165$	−0.772146	−	1.33740i	−0.0601115	−	0.104116i
$166$		0			0
$167$	3.62755	−	6.28310i	0.280708	−	0.486201i	−0.690851	−	0.722997i	$-0.742764\pi$
$167$	3.62755	−	6.28310i	0.280708	−	0.486201i	0.971559	+	0.236796i	$0.0760973\pi$
$168$		0			0
$169$	6.44455	+	11.1623i	0.495735	+	0.858638i
$170$		0			0
$171$	7.62441			0.583053
$172$		0			0
$173$	4.28159	+	7.41592i	0.325523	+	0.563822i	0.981618	−	0.190856i	$-0.0611263\pi$
$173$	4.28159	+	7.41592i	0.325523	+	0.563822i	−0.656095	+	0.754678i	$0.727793\pi$
$174$		0			0
$175$	2.11461			0.159849
$176$		0			0
$177$	2.37763			0.178714
$178$		0			0
$179$	−12.0613			−0.901502			−0.450751	−	0.892650i	$-0.648844\pi$
$179$	−12.0613			−0.901502			−0.450751	+	0.892650i	$0.648844\pi$
$180$		0			0
$181$	−3.22639	+	5.58828i	−0.239816	+	0.415373i	−0.960661	−	0.277722i	$-0.910420\pi$
$181$	−3.22639	+	5.58828i	−0.239816	+	0.415373i	0.720845	+	0.693096i	$0.243754\pi$
$182$		0			0
$183$	−7.46863	−	12.9360i	−0.552097	−	0.956260i
$184$		0			0
$185$	−4.64769	−	3.92415i	−0.341705	−	0.288509i
$186$		0			0
$187$	−5.28808	−	9.15922i	−0.386703	−	0.669789i
$188$		0			0
$189$	−5.70647	+	9.88390i	−0.415085	+	0.718948i
$190$		0			0
$191$	20.3453			1.47213			0.736067	−	0.676909i	$-0.236681\pi$
$191$	20.3453			1.47213			0.736067	+	0.676909i	$0.236681\pi$
$192$		0			0
$193$	−14.4284			−1.03858			−0.519288	−	0.854599i	$-0.673803\pi$
$193$	−14.4284			−1.03858			−0.519288	+	0.854599i	$0.673803\pi$
$194$		0			0
$195$	0.385977			0.0276404
$196$		0			0
$197$	−0.257215	−	0.445509i	−0.0183258	−	0.0317412i	0.856717	−	0.515787i	$-0.172500\pi$
$197$	−0.257215	−	0.445509i	−0.0183258	−	0.0317412i	−0.875043	+	0.484045i	$0.839167\pi$
$198$		0			0
$199$	−6.14595			−0.435675			−0.217837	−	0.975985i	$-0.569900\pi$
$199$	−6.14595			−0.435675			−0.217837	+	0.975985i	$0.569900\pi$
$200$		0			0
$201$	−5.88057	−	10.1855i	−0.414784	−	0.718427i
$202$		0			0
$203$	−5.20869	+	9.02171i	−0.365578	+	0.633200i
$204$		0			0
$205$	5.67758	+	9.83387i	0.396540	+	0.686827i
$206$		0			0
$207$	1.55773	+	2.69806i	0.108270	+	0.187528i
$208$		0			0
$209$	3.06606	−	5.31057i	0.212084	−	0.367340i
$210$		0			0
$211$	14.1321			0.972895			0.486447	−	0.873710i	$-0.338293\pi$
$211$	14.1321			0.972895			0.486447	+	0.873710i	$0.338293\pi$
$212$		0			0
$213$	−2.69727	−	4.67181i	−0.184814	−	0.320107i
$214$		0			0
$215$	−0.0141598	+	0.0245256i	−0.000965693	+	0.00167263i
$216$		0			0
$217$	−8.64413	+	14.9721i	−0.586802	+	1.01637i
$218$		0			0
$219$	−3.88847	+	6.73503i	−0.262758	+	0.455111i
$220$		0			0
$221$	2.64338			0.177813
$222$		0			0
$223$	26.8757			1.79973			0.899866	−	0.436166i	$-0.143664\pi$
$223$	26.8757			1.79973			0.899866	+	0.436166i	$0.143664\pi$
$224$		0			0
$225$	0.828323	−	1.43470i	0.0552215	−	0.0956465i
$226$		0			0
$227$	−9.56489	+	16.5669i	−0.634844	+	1.09958i	0.351704	+	0.936111i	$0.385602\pi$
$227$	−9.56489	+	16.5669i	−0.634844	+	1.09958i	−0.986548	+	0.163471i	$0.947731\pi$
$228$		0			0
$229$	12.5663	−	21.7655i	0.830406	−	1.43831i	−0.0673100	−	0.997732i	$-0.521442\pi$
$229$	12.5663	−	21.7655i	0.830406	−	1.43831i	0.897716	−	0.440574i	$-0.145225\pi$
$230$		0			0
$231$	1.63278	+	2.82807i	0.107429	+	0.186073i
$232$		0			0
$233$	8.71343			0.570836			0.285418	−	0.958403i	$-0.407868\pi$
$233$	8.71343			0.570836			0.285418	+	0.958403i	$0.407868\pi$
$234$		0			0
$235$	3.92010	−	6.78981i	0.255719	−	0.442918i
$236$		0			0
$237$	−7.92825	−	13.7321i	−0.514995	−	0.891998i
$238$		0			0
$239$	2.04391	+	3.54015i	0.132209	+	0.228994i	0.924528	−	0.381114i	$-0.124460\pi$
$239$	2.04391	+	3.54015i	0.132209	+	0.228994i	−0.792319	+	0.610108i	$0.791126\pi$
$240$		0			0
$241$	0.637375	−	1.10397i	0.0410569	−	0.0711127i	−0.844767	−	0.535135i	$-0.820261\pi$
$241$	0.637375	−	1.10397i	0.0410569	−	0.0711127i	0.885824	+	0.464022i	$0.153594\pi$
$242$		0			0
$243$	7.35078	+	12.7319i	0.471553	+	0.816753i
$244$		0			0
$245$	2.52844			0.161536
$246$		0			0
$247$	0.766325	+	1.32731i	0.0487601	+	0.0844550i
$248$		0			0
$249$	0.640223			0.0405725
$250$		0			0
$251$	−17.7027			−1.11738			−0.558692	−	0.829375i	$-0.688697\pi$
$251$	−17.7027			−1.11738			−0.558692	+	0.829375i	$0.688697\pi$
$252$		0			0
$253$	2.50568			0.157531
$254$		0			0
$255$	−4.60001	+	7.96746i	−0.288064	+	0.498942i
$256$		0			0
$257$	−7.49772	−	12.9864i	−0.467695	−	0.810071i	0.531624	−	0.846981i	$-0.321582\pi$
$257$	−7.49772	−	12.9864i	−0.467695	−	0.810071i	−0.999319	+	0.0369094i	$0.988249\pi$
$258$		0			0
$259$	9.82804	+	8.29803i	0.610685	+	0.515614i
$260$		0			0
$261$	4.08064	+	7.06788i	0.252585	+	0.437491i
$262$		0			0
$263$	−15.5877	+	26.9987i	−0.961180	+	1.66481i	−0.241634	+	0.970368i	$0.577683\pi$
$263$	−15.5877	+	26.9987i	−0.961180	+	1.66481i	−0.719546	+	0.694445i	$0.755650\pi$
$264$		0			0
$265$	5.73647			0.352389
$266$		0			0
$267$	−19.0880			−1.16816
$268$		0			0
$269$	−7.35774			−0.448609			−0.224305	−	0.974519i	$-0.572011\pi$
$269$	−7.35774			−0.448609			−0.224305	+	0.974519i	$0.572011\pi$
$270$		0			0
$271$	9.03739	+	15.6532i	0.548982	+	0.950865i	0.998345	+	0.0575154i	$0.0183178\pi$
$271$	9.03739	+	15.6532i	0.548982	+	0.950865i	−0.449363	+	0.893350i	$0.648349\pi$
$272$		0			0
$273$	−0.816190			−0.0493981
$274$		0			0
$275$	−0.666199	−	1.15389i	−0.0401733	−	0.0695822i
$276$		0			0
$277$	−10.7376	+	18.5981i	−0.645160	+	1.11745i	0.339105	+	0.940749i	$0.389876\pi$
$277$	−10.7376	+	18.5981i	−0.645160	+	1.11745i	−0.984265	+	0.176701i	$0.943458\pi$
$278$		0			0
$279$	6.77207	+	11.7296i	0.405433	+	0.702231i
$280$		0			0
$281$	−7.67604	−	13.2953i	−0.457914	−	0.793131i	0.540936	−	0.841064i	$-0.318070\pi$
$281$	−7.67604	−	13.2953i	−0.457914	−	0.793131i	−0.998851	+	0.0479329i	$0.984737\pi$
$282$		0			0
$283$	5.10323	−	8.83905i	0.303355	−	0.525427i	−0.673538	−	0.739152i	$-0.735226\pi$
$283$	5.10323	−	8.83905i	0.303355	−	0.525427i	0.976894	+	0.213725i	$0.0685597\pi$
$284$		0			0
$285$	−5.33423			−0.315973
$286$		0			0
$287$	−12.0059	−	20.7947i	−0.708683	−	1.22748i
$288$		0			0
$289$	−23.0034	+	39.8431i	−1.35314	+	2.34371i
$290$		0			0
$291$	0.0360630	−	0.0624629i	0.00211405	−	0.00366164i
$292$		0			0
$293$	4.95047	−	8.57446i	0.289209	−	0.500925i	−0.684412	−	0.729096i	$-0.739941\pi$
$293$	4.95047	−	8.57446i	0.289209	−	0.500925i	0.973621	+	0.228170i	$0.0732743\pi$
$294$		0			0
$295$	2.05139			0.119437
$296$		0			0
$297$	7.19122			0.417277
$298$		0			0
$299$	−0.313133	+	0.542362i	−0.0181089	+	0.0313656i
$300$		0			0
$301$	0.0299425	−	0.0518619i	0.00172586	−	0.00298927i
$302$		0			0
$303$	−6.58795	+	11.4107i	−0.378468	+	0.655525i
$304$		0			0
$305$	−6.44385	−	11.1611i	−0.368974	−	0.639082i
$306$		0			0
$307$	−24.9863			−1.42604			−0.713022	−	0.701142i	$-0.752674\pi$
$307$	−24.9863			−1.42604			−0.713022	+	0.701142i	$0.752674\pi$
$308$		0			0
$309$	−9.94573	+	17.2265i	−0.565793	+	0.979982i
$310$		0			0
$311$	11.0652	+	19.1656i	0.627452	+	1.08678i	0.988061	+	0.154062i	$0.0492355\pi$
$311$	11.0652	+	19.1656i	0.627452	+	1.08678i	−0.360609	+	0.932717i	$0.617431\pi$
$312$		0			0
$313$	−1.96428	−	3.40223i	−0.111028	−	0.192305i	0.805157	−	0.593061i	$-0.202081\pi$
$313$	−1.96428	−	3.40223i	−0.111028	−	0.192305i	−0.916185	+	0.400756i	$0.868748\pi$
$314$		0			0
$315$	−1.75158	+	3.03382i	−0.0986901	+	0.170936i
$316$		0			0
$317$	−4.75818	−	8.24142i	−0.267246	−	0.462884i	0.700903	−	0.713256i	$-0.252780\pi$
$317$	−4.75818	−	8.24142i	−0.267246	−	0.462884i	−0.968150	+	0.250372i	$0.919447\pi$
$318$		0			0
$319$	6.56392			0.367509
$320$		0			0
$321$	3.08332	+	5.34046i	0.172094	+	0.298076i
$322$		0			0
$323$	−36.5317			−2.03268
$324$		0			0
$325$	0.333017			0.0184725
$326$		0			0
$327$	22.7453			1.25782
$328$		0			0
$329$	−8.28946	+	14.3578i	−0.457013	+	0.791569i
$330$		0			0
$331$	−11.0296	−	19.1039i	−0.606244	−	1.05005i	−0.991854	−	0.127383i	$-0.959342\pi$
$331$	−11.0296	−	19.1039i	−0.606244	−	1.05005i	0.385609	−	0.922662i	$-0.373991\pi$
$332$		0			0
$333$	9.47975	−	3.41757i	0.519487	−	0.187282i
$334$		0			0
$335$	−5.07370	−	8.78790i	−0.277206	−	0.480134i
$336$		0			0
$337$	12.2222	−	21.1694i	0.665783	−	1.15317i	−0.313289	−	0.949658i	$-0.601431\pi$
$337$	12.2222	−	21.1694i	0.665783	−	1.15317i	0.979072	−	0.203513i	$-0.0652358\pi$
$338$		0			0
$339$	8.68357			0.471627
$340$		0			0
$341$	10.8932			0.589901
$342$		0			0
$343$	−20.1489			−1.08794
$344$		0			0
$345$	−1.08983	−	1.88764i	−0.0586743	−	0.101627i
$346$		0			0
$347$	−8.32578			−0.446951			−0.223476	−	0.974710i	$-0.571740\pi$
$347$	−8.32578			−0.446951			−0.223476	+	0.974710i	$0.571740\pi$
$348$		0			0
$349$	2.18239	+	3.78001i	0.116821	+	0.202339i	0.918506	−	0.395407i	$-0.129396\pi$
$349$	2.18239	+	3.78001i	0.116821	+	0.202339i	−0.801685	+	0.597746i	$0.796063\pi$
$350$		0			0
$351$	−0.898680	+	1.55656i	−0.0479680	+	0.0830830i
$352$		0			0
$353$	3.28058	+	5.68213i	0.174607	+	0.302429i	0.940025	−	0.341105i	$-0.110801\pi$
$353$	3.28058	+	5.68213i	0.174607	+	0.302429i	−0.765418	+	0.643534i	$0.777468\pi$
$354$		0			0
$355$	−2.32718	−	4.03079i	−0.123514	−	0.213932i
$356$		0			0
$357$	9.72722	−	16.8480i	0.514819	−	0.891693i
$358$		0			0
$359$	2.53533			0.133810			0.0669048	−	0.997759i	$-0.478688\pi$
$359$	2.53533			0.133810			0.0669048	+	0.997759i	$0.478688\pi$
$360$		0			0
$361$	−1.09066	−	1.88908i	−0.0574033	−	0.0994254i
$362$		0			0
$363$	−5.34587	+	9.25932i	−0.280585	+	0.485988i
$364$		0			0
$365$	−3.35493	+	5.81091i	−0.175605	+	0.304157i
$366$		0			0
$367$	16.6186	−	28.7842i	0.867483	−	1.50252i	0.00292206	−	0.999996i	$-0.499070\pi$
$367$	16.6186	−	28.7842i	0.867483	−	1.50252i	0.864561	−	0.502528i	$-0.167597\pi$
$368$		0			0
$369$	−18.8115			−0.979287
$370$		0			0
$371$	−12.1304			−0.629778
$372$		0			0
$373$	−13.3785	+	23.1722i	−0.692711	+	1.19981i	0.278235	+	0.960513i	$0.410251\pi$
$373$	−13.3785	+	23.1722i	−0.692711	+	1.19981i	−0.970946	+	0.239298i	$0.923083\pi$
$374$		0			0
$375$	−0.579516	+	1.00375i	−0.0299261	+	0.0518335i
$376$		0			0
$377$	−0.820286	+	1.42078i	−0.0422469	+	0.0731738i
$378$		0			0
$379$	15.2192	+	26.3604i	0.781757	+	1.35404i	0.930918	+	0.365230i	$0.119009\pi$
$379$	15.2192	+	26.3604i	0.781757	+	1.35404i	−0.149161	+	0.988813i	$0.547657\pi$
$380$		0			0
$381$	−10.4736			−0.536580
$382$		0			0
$383$	1.08492	−	1.87913i	0.0554367	−	0.0960192i	−0.836975	−	0.547241i	$-0.815678\pi$
$383$	1.08492	−	1.87913i	0.0554367	−	0.0960192i	0.892412	+	0.451222i	$0.149012\pi$
$384$		0			0
$385$	1.40875	+	2.44002i	0.0717965	+	0.124355i
$386$		0			0
$387$	−0.0234578	−	0.0406302i	−0.00119243	−	0.00206535i
$388$		0			0
$389$	−13.1203	+	22.7250i	−0.665224	+	1.15220i	0.314000	+	0.949423i	$0.398331\pi$
$389$	−13.1203	+	22.7250i	−0.665224	+	1.15220i	−0.979224	+	0.202780i	$0.935003\pi$
$390$		0			0
$391$	−7.46373	−	12.9276i	−0.377457	−	0.653775i
$392$		0			0
$393$	13.1282			0.662229
$394$		0			0
$395$	−6.84041	−	11.8479i	−0.344178	−	0.596135i
$396$		0			0
$397$	−1.54228			−0.0774049			−0.0387024	−	0.999251i	$-0.512322\pi$
$397$	−1.54228			−0.0774049			−0.0387024	+	0.999251i	$0.512322\pi$
$398$		0			0
$399$	11.2798			0.564696
$400$		0			0
$401$	−3.24489			−0.162042			−0.0810211	−	0.996712i	$-0.525818\pi$
$401$	−3.24489			−0.162042			−0.0810211	+	0.996712i	$0.525818\pi$
$402$		0			0
$403$	−1.36131	+	2.35787i	−0.0678119	+	0.117454i
$404$		0			0
$405$	−0.642795	−	1.11335i	−0.0319407	−	0.0553230i
$406$		0			0
$407$	1.43175	−	7.97720i	0.0709691	−	0.395415i
$408$		0			0
$409$	18.3292	+	31.7471i	0.906319	+	1.56979i	0.819137	+	0.573598i	$0.194453\pi$
$409$	18.3292	+	31.7471i	0.906319	+	1.56979i	0.0871823	+	0.996192i	$0.472214\pi$
$410$		0			0
$411$	−5.55207	+	9.61647i	−0.273864	+	0.474346i
$412$		0			0
$413$	−4.33789			−0.213453
$414$		0			0
$415$	0.552377			0.0271151
$416$		0			0
$417$	16.3816			0.802212
$418$		0			0
$419$	−10.5878	−	18.3386i	−0.517248	−	0.895900i	−0.999799	−	0.0200324i	$-0.993623\pi$
$419$	−10.5878	−	18.3386i	−0.517248	−	0.895900i	0.482551	−	0.875868i	$-0.339710\pi$
$420$		0			0
$421$	17.9193			0.873333			0.436667	−	0.899623i	$-0.356159\pi$
$421$	17.9193			0.873333			0.436667	+	0.899623i	$0.356159\pi$
$422$		0			0
$423$	6.49421	+	11.2483i	0.315759	+	0.546911i
$424$		0			0
$425$	−3.96884	+	6.87424i	−0.192517	+	0.333449i
$426$		0			0
$427$	13.6262	+	23.6013i	0.659419	+	1.14215i
$428$		0			0
$429$	0.257138	+	0.445376i	0.0124147	+	0.0215029i
$430$		0			0
$431$	−8.61013	+	14.9132i	−0.414735	+	0.718342i	−0.995401	−	0.0957999i	$-0.969459\pi$
$431$	−8.61013	+	14.9132i	−0.414735	+	0.718342i	0.580665	+	0.814142i	$0.302792\pi$
$432$		0			0
$433$	40.4571			1.94424			0.972122	−	0.234475i	$-0.0753370\pi$
$433$	40.4571			1.94424			0.972122	+	0.234475i	$0.0753370\pi$
$434$		0			0
$435$	−2.85492	−	4.94487i	−0.136883	−	0.237088i
$436$		0			0
$437$	4.32752	−	7.49548i	0.207013	−	0.358557i
$438$		0			0
$439$	14.7398	−	25.5301i	0.703492	−	1.21848i	−0.263742	−	0.964593i	$-0.584957\pi$
$439$	14.7398	−	25.5301i	0.703492	−	1.21848i	0.967233	−	0.253890i	$-0.0817100\pi$
$440$		0			0
$441$	−2.09437	+	3.62755i	−0.0997317	+	0.172740i
$442$		0			0
$443$	−3.09221			−0.146915			−0.0734576	−	0.997298i	$-0.523403\pi$
$443$	−3.09221			−0.146915			−0.0734576	+	0.997298i	$0.523403\pi$
$444$		0			0
$445$	−16.4689			−0.780700
$446$		0			0
$447$	−10.6366	+	18.4232i	−0.503095	+	0.871386i
$448$		0			0
$449$	−17.0935	+	29.6068i	−0.806693	+	1.39723i	0.108449	+	0.994102i	$0.465412\pi$
$449$	−17.0935	+	29.6068i	−0.806693	+	1.39723i	−0.915142	+	0.403131i	$0.867922\pi$
$450$		0			0
$451$	−7.56480	+	13.1026i	−0.356213	+	0.616979i
$452$		0			0
$453$	6.86740	+	11.8947i	0.322658	+	0.558861i
$454$		0			0
$455$	−0.704200			−0.0330134
$456$		0			0
$457$	3.87073	−	6.70430i	0.181065	−	0.313614i	−0.761178	−	0.648542i	$-0.775379\pi$
$457$	3.87073	−	6.70430i	0.181065	−	0.313614i	0.942243	+	0.334929i	$0.108712\pi$
$458$		0			0
$459$	−21.4206	−	37.1016i	−0.999830	−	1.73176i
$460$		0			0
$461$	1.34540	+	2.33030i	0.0626616	+	0.108533i	0.895654	−	0.444751i	$-0.146708\pi$
$461$	1.34540	+	2.33030i	0.0626616	+	0.108533i	−0.832993	+	0.553284i	$0.813374\pi$
$462$		0			0
$463$	7.61567	−	13.1907i	0.353930	−	0.613025i	−0.633004	−	0.774149i	$-0.718178\pi$
$463$	7.61567	−	13.1907i	0.353930	−	0.613025i	0.986934	+	0.161123i	$0.0515116\pi$
$464$		0			0
$465$	−4.73792	−	8.20631i	−0.219716	−	0.380559i
$466$		0			0
$467$	13.3039			0.615631			0.307816	−	0.951446i	$-0.400402\pi$
$467$	13.3039			0.615631			0.307816	+	0.951446i	$0.400402\pi$
$468$		0			0
$469$	10.7289	+	18.5829i	0.495413	+	0.858081i
$470$		0			0
$471$	−17.3803			−0.800843
$472$		0			0
$473$	−0.0377331			−0.00173497
$474$		0			0
$475$	−4.60232			−0.211169
$476$		0			0
$477$	−4.75165	+	8.23010i	−0.217563	+	0.376830i
$478$		0			0
$479$	−0.969846	−	1.67982i	−0.0443134	−	0.0767531i	0.843018	−	0.537885i	$-0.180777\pi$
$479$	−0.969846	−	1.67982i	−0.0443134	−	0.0767531i	−0.887331	+	0.461132i	$0.847443\pi$
$480$		0			0
$481$	1.54776	+	1.30681i	0.0705719	+	0.0595853i
$482$		0			0
$483$	2.30455	+	3.99160i	0.104861	+	0.181624i
$484$		0			0
$485$	0.0311147	−	0.0538923i	0.00141285	−	0.00244712i
$486$		0			0
$487$	−16.5404			−0.749519			−0.374760	−	0.927122i	$-0.622275\pi$
$487$	−16.5404			−0.749519			−0.374760	+	0.927122i	$0.622275\pi$
$488$		0			0
$489$	15.6274			0.706697
$490$		0			0
$491$	−25.3482			−1.14395			−0.571974	−	0.820271i	$-0.693822\pi$
$491$	−25.3482			−1.14395			−0.571974	+	0.820271i	$0.693822\pi$
$492$		0			0
$493$	−19.5521	−	33.8652i	−0.880581	−	1.52521i
$494$		0			0
$495$	2.20731			0.0992113
$496$		0			0
$497$	4.92106	+	8.52353i	0.220740	+	0.382332i
$498$		0			0
$499$	0.480873	−	0.832896i	0.0215268	−	0.0372855i	−0.855061	−	0.518527i	$-0.826481\pi$
$499$	0.480873	−	0.832896i	0.0215268	−	0.0372855i	0.876588	+	0.481241i	$0.159814\pi$
$500$		0			0
$501$	−4.20445	−	7.28232i	−0.187841	−	0.325350i
$502$		0			0
$503$	−21.7436	−	37.6611i	−0.969501	−	1.67922i	−0.697003	−	0.717068i	$-0.745483\pi$
$503$	−21.7436	−	37.6611i	−0.969501	−	1.67922i	−0.272498	−	0.962156i	$-0.587850\pi$
$504$		0			0
$505$	−5.68401	+	9.84499i	−0.252935	+	0.438096i
$506$		0			0
$507$	14.9389			0.663459
$508$		0			0
$509$	0.179617	+	0.311107i	0.00796140	+	0.0137896i	0.869979	−	0.493089i	$-0.164132\pi$
$509$	0.179617	+	0.311107i	0.00796140	+	0.0137896i	−0.862017	+	0.506879i	$0.830799\pi$
$510$		0			0
$511$	7.09435	−	12.2878i	0.313836	−	0.543579i
$512$		0			0
$513$	12.4198	−	21.5117i	0.548348	−	0.949767i
$514$		0			0
$515$	−8.58107	+	14.8629i	−0.378127	+	0.654935i
$516$		0			0
$517$	10.4463			0.459426
$518$		0			0
$519$	9.92499			0.435659
$520$		0			0
$521$	12.7623	−	22.1049i	0.559125	−	0.968433i	−0.438445	−	0.898758i	$-0.644471\pi$
$521$	12.7623	−	22.1049i	0.559125	−	0.968433i	0.997570	−	0.0696745i	$-0.0221961\pi$
$522$		0			0
$523$	−11.2172	+	19.4287i	−0.490492	+	0.849558i	−0.999940	−	0.0109439i	$-0.996516\pi$
$523$	−11.2172	+	19.4287i	−0.490492	+	0.849558i	0.509448	+	0.860502i	$0.329850\pi$
$524$		0			0
$525$	1.22545	−	2.12254i	0.0534829	−	0.0926351i
$526$		0			0
$527$	−32.4479	−	56.2013i	−1.41345	−	2.44817i
$528$		0			0
$529$	−19.4634			−0.846235
$530$		0			0
$531$	−1.69922	+	2.94313i	−0.0737397	+	0.127721i
$532$		0			0
$533$	−1.89073	−	3.27485i	−0.0818967	−	0.141849i
$534$		0			0
$535$	2.66025	+	4.60769i	0.115013	+	0.199208i
$536$		0			0
$537$	−6.98970	+	12.1065i	−0.301628	+	0.522435i
$538$		0			0
$539$	1.68445	+	2.91755i	0.0725542	+	0.125668i
$540$		0			0
$541$	13.0251			0.559994			0.279997	−	0.960001i	$-0.409667\pi$
$541$	13.0251			0.559994			0.279997	+	0.960001i	$0.409667\pi$
$542$		0			0
$543$	3.73949	+	6.47699i	0.160477	+	0.277954i
$544$		0			0
$545$	19.6244			0.840616
$546$		0			0
$547$	−14.8344			−0.634273			−0.317136	−	0.948380i	$-0.602721\pi$
$547$	−14.8344			−0.634273			−0.317136	+	0.948380i	$0.602721\pi$
$548$		0			0
$549$	21.3504			0.911211
$550$		0			0
$551$	11.3364	−	19.6352i	0.482947	−	0.836489i
$552$		0			0
$553$	14.4648	+	25.0537i	0.615105	+	1.06539i
$554$		0			0
$555$	−6.63228	+	2.39102i	−0.281525	+	0.101493i
$556$		0			0
$557$	−2.65892	−	4.60539i	−0.112662	−	0.195137i	0.804181	−	0.594385i	$-0.202604\pi$
$557$	−2.65892	−	4.60539i	−0.112662	−	0.195137i	−0.916843	+	0.399248i	$0.869271\pi$
$558$		0			0
$559$	0.00471547	−	0.00816743i	0.000199443	−	0.000345446i
$560$		0			0
$561$	−12.2581			−0.517538
$562$		0			0
$563$	0.490546			0.0206741			0.0103370	−	0.999947i	$-0.496710\pi$
$563$	0.490546			0.0206741			0.0103370	+	0.999947i	$0.496710\pi$
$564$		0			0
$565$	7.49209			0.315195
$566$		0			0
$567$	1.35926	+	2.35430i	0.0570835	+	0.0988715i
$568$		0			0
$569$	−0.803075			−0.0336666			−0.0168333	−	0.999858i	$-0.505358\pi$
$569$	−0.803075			−0.0336666			−0.0168333	+	0.999858i	$0.505358\pi$
$570$		0			0
$571$	12.9210	+	22.3799i	0.540729	+	0.936570i	0.998862	+	0.0476863i	$0.0151848\pi$
$571$	12.9210	+	22.3799i	0.540729	+	0.936570i	−0.458134	+	0.888883i	$0.651482\pi$
$572$		0			0
$573$	11.7904	−	20.4216i	0.492552	−	0.853125i
$574$		0			0
$575$	−0.940291	−	1.62863i	−0.0392128	−	0.0679186i
$576$		0			0
$577$	−14.6597	−	25.3913i	−0.610291	−	1.05706i	−0.991191	−	0.132439i	$-0.957719\pi$
$577$	−14.6597	−	25.3913i	−0.610291	−	1.05706i	0.380900	−	0.924616i	$-0.375614\pi$
$578$		0			0
$579$	−8.36147	+	14.4825i	−0.347491	+	0.601872i
$580$		0			0
$581$	−1.16806			−0.0484593
$582$		0			0
$583$	3.82163	+	6.61926i	0.158276	+	0.274142i
$584$		0			0
$585$	−0.275846	+	0.477779i	−0.0114048	+	0.0197537i
$586$		0			0
$587$	5.61625	−	9.72763i	0.231807	−	0.401502i	−0.726533	−	0.687132i	$-0.758869\pi$
$587$	5.61625	−	9.72763i	0.231807	−	0.401502i	0.958340	+	0.285630i	$0.0922028\pi$
$588$		0			0
$589$	18.8135	−	32.5859i	0.775195	−	1.34268i
$590$		0			0
$591$	−0.596240			−0.0245260
$592$		0			0
$593$	−15.3217			−0.629187			−0.314594	−	0.949226i	$-0.601868\pi$
$593$	−15.3217			−0.629187			−0.314594	+	0.949226i	$0.601868\pi$
$594$		0			0
$595$	8.39254	−	14.5363i	0.344060	−	0.595930i
$596$		0			0
$597$	−3.56168	+	6.16900i	−0.145770	+	0.252481i
$598$		0			0
$599$	3.71983	−	6.44293i	0.151988	−	0.263251i	−0.779970	−	0.625817i	$-0.784766\pi$
$599$	3.71983	−	6.44293i	0.151988	−	0.263251i	0.931958	+	0.362566i	$0.118099\pi$
$600$		0			0
$601$	23.2207	+	40.2195i	0.947194	+	1.64059i	0.751298	+	0.659963i	$0.229428\pi$
$601$	23.2207	+	40.2195i	0.947194	+	1.64059i	0.195896	+	0.980625i	$0.437239\pi$
$602$		0			0
$603$	16.8106			0.684582
$604$		0			0
$605$	−4.61236	+	7.98884i	−0.187519	+	0.324792i
$606$		0			0
$607$	−6.71616	−	11.6327i	−0.272601	−	0.472158i	0.696926	−	0.717143i	$-0.254550\pi$
$607$	−6.71616	−	11.6327i	−0.272601	−	0.472158i	−0.969527	+	0.244985i	$0.921217\pi$
$608$		0			0
$609$	6.03703	+	10.4565i	0.244633	+	0.423717i
$610$		0			0
$611$	−1.30546	+	2.26112i	−0.0528132	+	0.0914752i
$612$		0			0
$613$	9.75168	+	16.8904i	0.393867	+	0.682197i	0.992956	−	0.118485i	$-0.0378038\pi$
$613$	9.75168	+	16.8904i	0.393867	+	0.682197i	−0.599089	+	0.800682i	$0.704470\pi$
$614$		0			0
$615$	13.1610			0.530703
$616$		0			0
$617$	−14.1255	−	24.4660i	−0.568670	−	0.984965i	−0.996698	−	0.0811994i	$-0.974125\pi$
$617$	−14.1255	−	24.4660i	−0.568670	−	0.984965i	0.428028	−	0.903765i	$-0.359208\pi$
$618$		0			0
$619$	−45.3987			−1.82473			−0.912363	−	0.409382i	$-0.865744\pi$
$619$	−45.3987			−1.82473			−0.912363	+	0.409382i	$0.865744\pi$
$620$		0			0
$621$	10.1499			0.407300
$622$		0			0
$623$	34.8252			1.39524
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−3.55366	−	6.15512i	−0.141920	−	0.245812i
$628$		0			0
$629$	−45.4215	+	16.3750i	−1.81107	+	0.652915i
$630$		0			0
$631$	1.10770	+	1.91860i	0.0440970	+	0.0763783i	0.887231	−	0.461324i	$-0.152626\pi$
$631$	1.10770	+	1.91860i	0.0440970	+	0.0763783i	−0.843134	+	0.537703i	$0.819292\pi$
$632$		0			0
$633$	8.18978	−	14.1851i	0.325515	−	0.563808i
$634$		0			0
$635$	−9.03652			−0.358603
$636$		0			0
$637$	−0.842015			−0.0333618
$638$		0			0
$639$	7.71061			0.305027
$640$		0			0
$641$	−0.00620447	−	0.0107465i	−0.000245062	−	0.000424460i	0.865903	−	0.500212i	$-0.166745\pi$
$641$	−0.00620447	−	0.0107465i	−0.000245062	−	0.000424460i	−0.866148	+	0.499788i	$0.833411\pi$
$642$		0			0
$643$	−15.9563			−0.629256			−0.314628	−	0.949215i	$-0.601880\pi$
$643$	−15.9563			−0.629256			−0.314628	+	0.949215i	$0.601880\pi$
$644$		0			0
$645$	0.0164117	+	0.0284259i	0.000646210	+	0.00111927i
$646$		0			0
$647$	−20.3275	+	35.2082i	−0.799155	+	1.38418i	0.121013	+	0.992651i	$0.461386\pi$
$647$	−20.3275	+	35.2082i	−0.799155	+	1.38418i	−0.920167	+	0.391525i	$0.871948\pi$
$648$		0			0
$649$	1.36664	+	2.36708i	0.0536452	+	0.0929161i
$650$		0			0
$651$	10.0188	+	17.3531i	0.392669	+	0.680122i
$652$		0			0
$653$	3.73604	−	6.47102i	0.146203	−	0.253231i	−0.783618	−	0.621243i	$-0.786628\pi$
$653$	3.73604	−	6.47102i	0.146203	−	0.253231i	0.929821	+	0.368012i	$0.119961\pi$
$654$		0			0
$655$	11.3268			0.442577
$656$		0			0
$657$	−5.55793	−	9.62661i	−0.216835	−	0.375570i
$658$		0			0
$659$	−13.0456	+	22.5956i	−0.508183	+	0.880198i	0.491772	+	0.870724i	$0.336349\pi$
$659$	−13.0456	+	22.5956i	−0.508183	+	0.880198i	−0.999955	+	0.00947442i	$0.996984\pi$
$660$		0			0
$661$	−4.71341	+	8.16387i	−0.183330	+	0.317538i	−0.943013	−	0.332757i	$-0.892021\pi$
$661$	−4.71341	+	8.16387i	−0.183330	+	0.317538i	0.759682	+	0.650295i	$0.225355\pi$
$662$		0			0
$663$	1.53188	−	2.65330i	0.0594934	−	0.103046i
$664$		0			0
$665$	9.73209			0.377394
$666$		0			0
$667$	9.26448			0.358722
$668$		0			0
$669$	15.5749	−	26.9765i	0.602161	−	1.04297i
$670$		0			0
$671$	8.58578	−	14.8710i	0.331450	−	0.574089i
$672$		0			0
$673$	9.93393	−	17.2061i	0.382925	−	0.663245i	−0.608554	−	0.793512i	$-0.708250\pi$
$673$	9.93393	−	17.2061i	0.382925	−	0.663245i	0.991479	+	0.130267i	$0.0415835\pi$
$674$		0			0
$675$	−2.69860	−	4.67411i	−0.103869	−	0.179907i
$676$		0			0
$677$	−15.2768			−0.587134			−0.293567	−	0.955938i	$-0.594842\pi$
$677$	−15.2768			−0.587134			−0.293567	+	0.955938i	$0.594842\pi$
$678$		0			0
$679$	−0.0657954	+	0.113961i	−0.00252500	+	0.00437342i
$680$		0			0
$681$	11.0860	+	19.2015i	0.424817	+	0.735804i
$682$		0			0
$683$	4.22019	+	7.30959i	0.161481	+	0.279694i	0.935400	−	0.353591i	$-0.115040\pi$
$683$	4.22019	+	7.30959i	0.161481	+	0.279694i	−0.773919	+	0.633285i	$0.781706\pi$
$684$		0			0
$685$	−4.79027	+	8.29699i	−0.183027	+	0.317012i
$686$		0			0
$687$	−14.5648	−	25.2269i	−0.555681	−	0.962467i
$688$		0			0
$689$	−1.91034			−0.0727783
$690$		0			0
$691$	−13.5524	−	23.4735i	−0.515559	−	0.892974i	−0.999837	−	0.0180596i	$-0.994251\pi$
$691$	−13.5524	−	23.4735i	−0.515559	−	0.892974i	0.484278	−	0.874914i	$-0.339082\pi$
$692$		0			0
$693$	−4.66759			−0.177307
$694$		0			0
$695$	14.1339			0.536129
$696$		0			0
$697$	90.1338			3.41406
$698$		0			0
$699$	5.04957	−	8.74612i	0.190992	−	0.330809i
$700$		0			0
$701$	4.51376	+	7.81806i	0.170482	+	0.295284i	0.938589	−	0.345038i	$-0.112134\pi$
$701$	4.51376	+	7.81806i	0.170482	+	0.295284i	−0.768106	+	0.640322i	$0.778801\pi$
$702$		0			0
$703$	−21.3902	−	18.0602i	−0.806745	−	0.681152i
$704$		0			0
$705$	−4.54352	−	7.86960i	−0.171119	−	0.296386i
$706$		0			0
$707$	12.0194	−	20.8183i	0.452037	−	0.782952i
$708$		0			0
$709$	3.10642			0.116664			0.0583320	−	0.998297i	$-0.481422\pi$
$709$	3.10642			0.116664			0.0583320	+	0.998297i	$0.481422\pi$
$710$		0			0
$711$	22.6643			0.849977
$712$		0			0
$713$	15.3750			0.575797
$714$		0			0
$715$	0.221856	+	0.384265i	0.00829693	+	0.0143707i
$716$		0			0
$717$	4.73791			0.176941
$718$		0			0
$719$	1.54564	+	2.67713i	0.0576427	+	0.0998400i	0.893407	−	0.449249i	$-0.148308\pi$
$719$	1.54564	+	2.67713i	0.0576427	+	0.0998400i	−0.835764	+	0.549089i	$0.814975\pi$
$720$		0			0
$721$	18.1456	−	31.4291i	0.675777	−	1.17048i
$722$		0			0
$723$	−0.738738	−	1.27953i	−0.0274740	−	0.0475863i
$724$		0			0
$725$	−2.46320	−	4.26638i	−0.0914808	−	0.158449i
$726$		0			0
$727$	6.50596	−	11.2687i	0.241293	−	0.417931i	−0.719790	−	0.694192i	$-0.755762\pi$
$727$	6.50596	−	11.2687i	0.241293	−	0.417931i	0.961083	+	0.276261i	$0.0890953\pi$
$728$		0			0
$729$	20.8963			0.773939
$730$		0			0
$731$	0.112396	+	0.194676i	0.00415713	+	0.00720036i
$732$		0			0
$733$	−3.54090	+	6.13302i	−0.130786	+	0.226528i	−0.923980	−	0.382441i	$-0.875083\pi$
$733$	−3.54090	+	6.13302i	−0.130786	+	0.226528i	0.793194	+	0.608969i	$0.208417\pi$
$734$		0			0
$735$	1.46527	−	2.53793i	0.0540474	−	0.0936128i
$736$		0			0
$737$	6.76018	−	11.7090i	0.249015	−	0.431306i
$738$		0			0
$739$	41.8709			1.54025			0.770123	−	0.637895i	$-0.220195\pi$
$739$	41.8709			1.54025			0.770123	+	0.637895i	$0.220195\pi$
$740$		0			0
$741$	1.77639			0.0652573
$742$		0			0
$743$	25.6857	−	44.4890i	0.942318	−	1.63214i	0.181283	−	0.983431i	$-0.441975\pi$
$743$	25.6857	−	44.4890i	0.942318	−	1.63214i	0.761034	−	0.648711i	$-0.224692\pi$
$744$		0			0
$745$	−9.17717	+	15.8953i	−0.336225	+	0.582359i
$746$		0			0
$747$	−0.457547	+	0.792494i	−0.0167408	+	0.0289958i
$748$		0			0
$749$	−5.62539	−	9.74345i	−0.205547	−	0.356018i
$750$		0			0
$751$	−21.6234			−0.789050			−0.394525	−	0.918885i	$-0.629091\pi$
$751$	−21.6234			−0.789050			−0.394525	+	0.918885i	$0.629091\pi$
$752$		0			0
$753$	−10.2590	+	17.7691i	−0.373859	+	0.647542i
$754$		0			0
$755$	5.92511	+	10.2626i	0.215637	+	0.373494i
$756$		0			0
$757$	11.2105	+	19.4171i	0.407452	+	0.705727i	0.994603	−	0.103750i	$-0.0330842\pi$
$757$	11.2105	+	19.4171i	0.407452	+	0.705727i	−0.587152	+	0.809477i	$0.699751\pi$
$758$		0			0
$759$	1.45208	−	2.51508i	0.0527073	−	0.0912917i
$760$		0			0
$761$	−6.67009	−	11.5529i	−0.241791	−	0.418793i	0.719434	−	0.694561i	$-0.244401\pi$
$761$	−6.67009	−	11.5529i	−0.241791	−	0.418793i	−0.961224	+	0.275768i	$0.911068\pi$
$762$		0			0
$763$	−41.4978			−1.50232
$764$		0			0
$765$	−6.57496	−	11.3882i	−0.237718	−	0.411740i
$766$		0			0
$767$	−0.683149			−0.0246671
$768$		0			0
$769$	−44.3490			−1.59926			−0.799632	−	0.600490i	$-0.794972\pi$
$769$	−44.3490			−1.59926			−0.799632	+	0.600490i	$0.794972\pi$
$770$		0			0
$771$	−17.3802			−0.625932
$772$		0			0
$773$	16.6627	−	28.8606i	0.599316	−	1.03805i	−0.393607	−	0.919279i	$-0.628773\pi$
$773$	16.6627	−	28.8606i	0.599316	−	1.03805i	0.992922	−	0.118766i	$-0.0378939\pi$
$774$		0			0
$775$	−4.08782	−	7.08032i	−0.146839	−	0.254333i
$776$		0			0
$777$	14.0247	−	5.05607i	0.503132	−	0.181385i
$778$		0			0
$779$	26.1300	+	45.2586i	0.936206	+	1.62156i
$780$		0			0
$781$	3.10073	−	5.37061i	0.110953	−	0.192176i
$782$		0			0
$783$	26.5887			0.950203
$784$		0			0
$785$	−14.9956			−0.535214
$786$		0			0
$787$	−23.9729			−0.854541			−0.427271	−	0.904124i	$-0.640525\pi$
$787$	−23.9729			−0.854541			−0.427271	+	0.904124i	$0.640525\pi$
$788$		0			0
$789$	18.0667	+	31.2924i	0.643190	+	1.11404i
$790$		0			0
$791$	−15.8428			−0.563306
$792$		0			0
$793$	2.14591	+	3.71683i	0.0762036	+	0.131989i
$794$		0			0
$795$	3.32438	−	5.75799i	0.117904	−	0.204215i
$796$		0			0
$797$	13.8252	+	23.9459i	0.489712	+	0.848206i	0.999930	−	0.0118392i	$-0.00376861\pi$
$797$	13.8252	+	23.9459i	0.489712	+	0.848206i	−0.510218	+	0.860045i	$0.670435\pi$
$798$		0			0
$799$	−31.1165	−	53.8953i	−1.10082	−	1.90668i
$800$		0			0
$801$	13.6416	−	23.6279i	0.482001	−	0.834850i
$802$		0			0
$803$	−8.94020			−0.315493
$804$		0			0
$805$	1.98834	+	3.44391i	0.0700799	+	0.121382i
$806$		0			0
$807$	−4.26393	+	7.38534i	−0.150097	+	0.259976i
$808$		0			0
$809$	11.8194	−	20.4718i	0.415549	−	0.719752i	−0.579937	−	0.814661i	$-0.696923\pi$
$809$	11.8194	−	20.4718i	0.415549	−	0.719752i	0.995486	+	0.0949096i	$0.0302562\pi$
$810$		0			0
$811$	23.5927	−	40.8638i	0.828453	−	1.43492i	−0.0707985	−	0.997491i	$-0.522555\pi$
$811$	23.5927	−	40.8638i	0.828453	−	1.43492i	0.899251	−	0.437432i	$-0.144112\pi$
$812$		0			0
$813$	20.9492			0.734722
$814$		0			0
$815$	13.4832			0.472296
$816$		0			0
$817$	−0.0651681	+	0.112874i	−0.00227994	+	0.00394898i
$818$		0			0
$819$	0.583305	−	1.01031i	0.0203823	−	0.0353032i
$820$		0			0
$821$	21.6382	−	37.4785i	0.755180	−	1.30801i	−0.190105	−	0.981764i	$-0.560883\pi$
$821$	21.6382	−	37.4785i	0.755180	−	1.30801i	0.945285	−	0.326246i	$-0.105784\pi$
$822$		0			0
$823$	13.8533	+	23.9946i	0.482895	+	0.836399i	0.999807	−	0.0196397i	$-0.00625190\pi$
$823$	13.8533	+	23.9946i	0.482895	+	0.836399i	−0.516912	+	0.856039i	$0.672919\pi$
$824$		0			0
$825$	−1.54429			−0.0537653
$826$		0			0
$827$	−19.7530	+	34.2133i	−0.686880	+	1.18971i	0.285962	+	0.958241i	$0.407687\pi$
$827$	−19.7530	+	34.2133i	−0.686880	+	1.18971i	−0.972842	+	0.231470i	$0.925646\pi$
$828$		0			0
$829$	−2.66910	−	4.62302i	−0.0927018	−	0.160564i	0.815945	−	0.578129i	$-0.196217\pi$
$829$	−2.66910	−	4.62302i	−0.0927018	−	0.160564i	−0.908647	+	0.417565i	$0.862884\pi$
$830$		0			0
$831$	12.4452	+	21.5557i	0.431720	+	0.747760i
$832$		0			0
$833$	10.0350	−	17.3811i	0.347692	−	0.602220i
$834$		0			0
$835$	−3.62755	−	6.28310i	−0.125537	−	0.217436i
$836$		0			0
$837$	44.1256			1.52520
$838$		0			0
$839$	8.40571	+	14.5591i	0.290197	+	0.502636i	0.973856	−	0.227165i	$-0.0729458\pi$
$839$	8.40571	+	14.5591i	0.290197	+	0.502636i	−0.683659	+	0.729802i	$0.739612\pi$
$840$		0			0
$841$	−4.73067			−0.163126
$842$		0			0
$843$	−17.7935			−0.612842
$844$		0			0
$845$	12.8891			0.443399
$846$		0			0
$847$	9.75332	−	16.8932i	0.335128	−	0.580459i
$848$		0			0
$849$	−5.91480	−	10.2447i	−0.202995	−	0.351598i
$850$		0			0
$851$	2.02081	−	11.2592i	0.0692724	−	0.385961i
$852$		0			0
$853$	5.45114	+	9.44165i	0.186643	+	0.323276i	0.944129	−	0.329576i	$-0.106906\pi$
$853$	5.45114	+	9.44165i	0.186643	+	0.323276i	−0.757486	+	0.652852i	$0.773572\pi$
$854$		0			0
$855$	3.81220	−	6.60293i	0.130375	−	0.225815i
$856$		0			0
$857$	−24.4064			−0.833707			−0.416854	−	0.908974i	$-0.636867\pi$
$857$	−24.4064			−0.833707			−0.416854	+	0.908974i	$0.636867\pi$
$858$		0			0
$859$	45.8914			1.56579			0.782897	−	0.622151i	$-0.213741\pi$
$859$	45.8914			1.56579			0.782897	+	0.622151i	$0.213741\pi$
$860$		0			0
$861$	−27.8303			−0.948455
$862$		0			0
$863$	24.1822	+	41.8848i	0.823172	+	1.42578i	0.903308	+	0.428992i	$0.141131\pi$
$863$	24.1822	+	41.8848i	0.823172	+	1.42578i	−0.0801363	+	0.996784i	$0.525536\pi$
$864$		0			0
$865$	8.56317			0.291157
$866$		0			0
$867$	26.6617	+	46.1794i	0.905479	+	1.56834i
$868$		0			0
$869$	9.11415	−	15.7862i	0.309176	−	0.535509i
$870$		0			0
$871$	1.68963	+	2.92652i	0.0572508	+	0.0991614i
$872$		0			0
$873$	0.0515461	+	0.0892804i	0.00174457	+	0.00302168i
$874$		0			0
$875$	1.05730	−	1.83130i	0.0357434	−	0.0619093i
$876$		0			0
$877$	17.4607			0.589607			0.294804	−	0.955558i	$-0.404746\pi$
$877$	17.4607			0.589607			0.294804	+	0.955558i	$0.404746\pi$
$878$		0			0
$879$	−5.73775	−	9.93807i	−0.193529	−	0.335203i
$880$		0			0
$881$	−0.914437	+	1.58385i	−0.0308082	+	0.0533613i	−0.881018	−	0.473082i	$-0.843141\pi$
$881$	−0.914437	+	1.58385i	−0.0308082	+	0.0533613i	0.850210	+	0.526443i	$0.176475\pi$
$882$		0			0
$883$	−21.5325	+	37.2954i	−0.724627	+	1.25509i	0.234500	+	0.972116i	$0.424655\pi$
$883$	−21.5325	+	37.2954i	−0.724627	+	1.25509i	−0.959127	+	0.282975i	$0.908679\pi$
$884$		0			0
$885$	1.18881	−	2.05909i	0.0399616	−	0.0692155i
$886$		0			0
$887$	7.78827			0.261505			0.130752	−	0.991415i	$-0.458261\pi$
$887$	7.78827			0.261505			0.130752	+	0.991415i	$0.458261\pi$
$888$		0			0
$889$	19.1087			0.640885
$890$		0			0
$891$	0.856459	−	1.48343i	0.0286925	−	0.0496968i
$892$		0			0
$893$	18.0415	−	31.2488i	0.603737	−	1.04570i
$894$		0			0
$895$	−6.03064	+	10.4454i	−0.201582	+	0.349150i
$896$		0			0
$897$	0.362931	+	0.628615i	0.0121179	+	0.0209888i
$898$		0			0
$899$	40.2764			1.34329
$900$		0			0
$901$	22.7672	−	39.4339i	0.758484	−	1.31373i
$902$		0			0
$903$	−0.0347043	−	0.0601096i	−0.00115489	−	0.00200032i
$904$		0			0
$905$	3.22639	+	5.58828i	0.107249	+	0.185761i
$906$		0			0
$907$	3.01183	−	5.21664i	0.100006	−	0.173216i	−0.811681	−	0.584101i	$-0.801447\pi$
$907$	3.01183	−	5.21664i	0.100006	−	0.173216i	0.911687	+	0.410886i	$0.134780\pi$
$908$		0			0
$909$	−9.41639	−	16.3097i	−0.312322	−	0.540957i
$910$		0			0
$911$	−48.4044			−1.60371			−0.801854	−	0.597520i	$-0.796153\pi$
$911$	−48.4044			−1.60371			−0.801854	+	0.597520i	$0.796153\pi$
$912$		0			0
$913$	0.367993	+	0.637383i	0.0121788	+	0.0210943i
$914$		0			0
$915$	−14.9373			−0.493811
$916$		0			0
$917$	−23.9518			−0.790959
$918$		0			0
$919$	−40.2174			−1.32665			−0.663324	−	0.748332i	$-0.730855\pi$
$919$	−40.2174			−1.32665			−0.663324	+	0.748332i	$0.730855\pi$
$920$		0			0
$921$	−14.4800	+	25.0800i	−0.477131	+	0.826415i
$922$		0			0
$923$	0.774990	+	1.34232i	0.0255091	+	0.0441830i
$924$		0			0
$925$	−5.72226	+	2.06295i	−0.188147	+	0.0678293i
$926$		0			0
$927$	−14.2158	−	24.6225i	−0.466908	−	0.808708i
$928$		0			0
$929$	−3.27362	+	5.67008i	−0.107404	+	0.186029i	−0.914718	−	0.404093i	$-0.867587\pi$
$929$	−3.27362	+	5.67008i	−0.107404	+	0.186029i	0.807314	+	0.590122i	$0.200921\pi$
$930$		0			0
$931$	11.6367			0.381377
$932$		0			0
$933$	25.6499			0.839741
$934$		0			0
$935$	−10.5762			−0.345877
$936$		0			0
$937$	6.50507	+	11.2671i	0.212511	+	0.368081i	0.952500	−	0.304539i	$-0.0985024\pi$
$937$	6.50507	+	11.2671i	0.212511	+	0.368081i	−0.739988	+	0.672620i	$0.765169\pi$
$938$		0			0
$939$	−4.55332			−0.148592
$940$		0			0
$941$	10.3312	+	17.8942i	0.336788	+	0.583334i	0.983827	−	0.179123i	$-0.0573261\pi$
$941$	10.3312	+	17.8942i	0.336788	+	0.583334i	−0.647039	+	0.762457i	$0.723993\pi$
$942$		0			0
$943$	−10.6772	+	18.4934i	−0.347696	+	0.602227i
$944$		0			0
$945$	5.70647	+	9.88390i	0.185632	+	0.321523i
$946$		0			0
$947$	8.71617	+	15.0969i	0.283238	+	0.490582i	0.972180	−	0.234234i	$-0.0752582\pi$
$947$	8.71617	+	15.0969i	0.283238	+	0.490582i	−0.688943	+	0.724816i	$0.741925\pi$
$948$		0			0
$949$	1.11725	−	1.93513i	0.0362674	−	0.0628170i
$950$		0			0
$951$	−11.0298			−0.357665
$952$		0			0
$953$	−25.5157	−	44.1945i	−0.826534	−	1.43160i	−0.900741	−	0.434356i	$-0.856976\pi$
$953$	−25.5157	−	44.1945i	−0.826534	−	1.43160i	0.0742069	−	0.997243i	$-0.476357\pi$
$954$		0			0
$955$	10.1726	−	17.6195i	0.329179	−	0.570155i
$956$		0			0
$957$	3.80389	−	6.58854i	0.122962	−	0.212977i
$958$		0			0
$959$	10.1295	−	17.5449i	0.327100	−	0.566553i
$960$		0			0
$961$	35.8412			1.15617
$962$		0			0
$963$	−8.81419			−0.284033
$964$		0			0
$965$	−7.21418	+	12.4953i	−0.232233	+	0.402239i
$966$		0			0
$967$	−2.78414	+	4.82226i	−0.0895318	+	0.155074i	−0.907313	−	0.420455i	$-0.861870\pi$
$967$	−2.78414	+	4.82226i	−0.0895318	+	0.155074i	0.817782	+	0.575529i	$0.195204\pi$
$968$		0			0
$969$	−21.1707	+	36.6688i	−0.680102	+	1.17797i
$970$		0			0
$971$	−17.4415	−	30.2096i	−0.559726	−	0.969473i	−0.997519	−	0.0703978i	$-0.977573\pi$
$971$	−17.4415	−	30.2096i	−0.559726	−	0.969473i	0.437793	−	0.899076i	$-0.355760\pi$
$972$		0			0
$973$	−29.8876			−0.958153
$974$		0			0
$975$	0.192989	−	0.334266i	0.00618058	−	0.0107051i
$976$		0			0
$977$	−12.8183	−	22.2019i	−0.410093	−	0.710302i	0.584806	−	0.811173i	$-0.301171\pi$
$977$	−12.8183	−	22.2019i	−0.410093	−	0.710302i	−0.994900	+	0.100871i	$0.967837\pi$
$978$		0			0
$979$	−10.9716	−	19.0033i	−0.350653	−	0.607348i
$980$		0			0
$981$	−16.2553	+	28.1550i	−0.518993	+	0.898921i
$982$		0			0
$983$	13.0998	+	22.6895i	0.417819	+	0.723684i	0.995720	−	0.0924231i	$-0.0294612\pi$
$983$	13.0998	+	22.6895i	0.417819	+	0.723684i	−0.577901	+	0.816107i	$0.696128\pi$
$984$		0			0
$985$	−0.514429			−0.0163911
$986$		0			0
$987$	9.60775	+	16.6411i	0.305818	+	0.529692i
$988$		0			0
$989$	−0.0532575			−0.00169349
$990$		0			0
$991$	29.7660			0.945547			0.472773	−	0.881184i	$-0.343253\pi$
$991$	29.7660			0.945547			0.472773	+	0.881184i	$0.343253\pi$
$992$		0			0
$993$	−25.5674			−0.811357
$994$		0			0
$995$	−3.07298	+	5.32255i	−0.0974199	+	0.168736i
$996$		0			0
$997$	18.6399	+	32.2853i	0.590332	+	1.02249i	0.994188	+	0.107662i	$0.0343365\pi$
$997$	18.6399	+	32.2853i	0.590332	+	1.02249i	−0.403855	+	0.914823i	$0.632330\pi$
$998$		0			0
$999$	5.79964	−	32.3136i	0.183493	−	1.02236i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1480.2.q.b.1321.6	yes	18
37.10	even	3	inner	1480.2.q.b.121.6	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1480.2.q.b.121.6	✓	18	37.10	even	3	inner
1480.2.q.b.1321.6	yes	18	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1480 = 2^{3} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1480.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.579516 - 1.00375i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.05730 + 1.83130i) q^{7} +(0.828323 + 1.43470i) q^{9} +1.33240 q^{11} +(-0.166509 + 0.288401i) q^{13} +(-0.579516 - 1.00375i) q^{15} +(-3.96884 - 6.87424i) q^{17} +(2.30116 - 3.98572i) q^{19} +(1.22545 + 2.12254i) q^{21} +1.88058 q^{23} +(-0.500000 - 0.866025i) q^{25} +5.39720 q^{27} +4.92639 q^{29} +8.17565 q^{31} +(0.772146 - 1.33740i) q^{33} +(1.05730 + 1.83130i) q^{35} +(1.07456 - 5.98710i) q^{37} +(0.192989 + 0.334266i) q^{39} +(-5.67758 + 9.83387i) q^{41} -0.0283197 q^{43} +1.65665 q^{45} +7.84019 q^{47} +(1.26422 + 2.18970i) q^{49} -9.20003 q^{51} +(2.86824 + 4.96793i) q^{53} +(0.666199 - 1.15389i) q^{55} +(-2.66712 - 4.61958i) q^{57} +(1.02570 + 1.77656i) q^{59} +(6.44385 - 11.1611i) q^{61} -3.50315 q^{63} +(0.166509 + 0.288401i) q^{65} +(5.07370 - 8.78790i) q^{67} +(1.08983 - 1.88764i) q^{69} +(2.32718 - 4.03079i) q^{71} -6.70986 q^{73} -1.15903 q^{75} +(-1.40875 + 2.44002i) q^{77} +(6.84041 - 11.8479i) q^{79} +(0.642795 - 1.11335i) q^{81} +(0.276189 + 0.478373i) q^{83} -7.93769 q^{85} +(2.85492 - 4.94487i) q^{87} +(-8.23445 - 14.2625i) q^{89} +(-0.352100 - 0.609855i) q^{91} +(4.73792 - 8.20631i) q^{93} +(-2.30116 - 3.98572i) q^{95} +0.0622295 q^{97} +(1.10366 + 1.91159i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{3} + 9 q^{5} - 5 q^{9} - 6 q^{11} + 2 q^{13} - 2 q^{15} + q^{17} - 5 q^{21} + 12 q^{23} - 9 q^{25} - 10 q^{27} - 20 q^{29} + 28 q^{31} + 11 q^{33} - 5 q^{39} - 5 q^{41} + 2 q^{43} - 10 q^{45}+ \cdots + 30 q^{99}+O(q^{100}) \) 18 * q + 2 * q^3 + 9 * q^5 - 5 * q^9 - 6 * q^11 + 2 * q^13 - 2 * q^15 + q^17 - 5 * q^21 + 12 * q^23 - 9 * q^25 - 10 * q^27 - 20 * q^29 + 28 * q^31 + 11 * q^33 - 5 * q^39 - 5 * q^41 + 2 * q^43 - 10 * q^45 - 36 * q^47 + 7 * q^49 - 2 * q^51 - 10 * q^53 - 3 * q^55 + 22 * q^57 - 10 * q^59 + 16 * q^61 + 42 * q^63 - 2 * q^65 - 4 * q^67 - 13 * q^69 + 17 * q^71 + 56 * q^73 - 4 * q^75 + 43 * q^77 - 23 * q^79 - 17 * q^81 + 29 * q^83 + 2 * q^85 - q^87 - 16 * q^89 - 4 * q^91 + 5 * q^93 + 26 * q^97 + 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more