LMFDB - Embedded newform 1152.2.i.f.385.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(385,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("1152.385");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1152 = 2^{7} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1152.i (of order $3$, degree $2$, 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:	$9.19876631285$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.8528759163648.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + x^{8} + 9x^{6} - 36x^{5} + 27x^{4} + 27x^{2} - 162x + 243 $ x^10 - 2x^9 + x^8 + 9x^6 - 36x^5 + 27x^4 + 27x^2 - 162x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			385.5
Root			$-1.41743 + 0.995434i$ of defining polynomial
Character	$\chi$	$=$	1152.385
Dual form			1152.2.i.f.769.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.57079 - 0.729814i) q^{3} +(-0.115851 - 0.200661i) q^{5} +(0.230793 - 0.399745i) q^{7} +(1.93474 - 2.29277i) q^{9} +O(q^{10})$	\(q+(1.57079 - 0.729814i) q^{3} +(-0.115851 - 0.200661i) q^{5} +(0.230793 - 0.399745i) q^{7} +(1.93474 - 2.29277i) q^{9} +(0.749014 - 1.29733i) q^{11} +(1.07079 + 1.85466i) q^{13} +(-0.328423 - 0.230645i) q^{15} +1.03644 q^{17} +2.94631 q^{19} +(0.0707868 - 0.796350i) q^{21} +(0.364866 + 0.631966i) q^{23} +(2.47316 - 4.28363i) q^{25} +(1.36578 - 5.01345i) q^{27} +(-2.33711 + 4.04800i) q^{29} +(-2.73632 - 4.73945i) q^{31} +(0.229731 - 2.58447i) q^{33} -0.106951 q^{35} +2.30039 q^{37} +(3.03553 + 2.13180i) q^{39} +(-1.84151 - 3.18959i) q^{41} +(2.41968 - 4.19101i) q^{43} +(-0.684210 - 0.122606i) q^{45} +(5.40881 - 9.36833i) q^{47} +(3.39347 + 5.87766i) q^{49} +(1.62803 - 0.756411i) q^{51} -10.0430 q^{53} -0.347097 q^{55} +(4.62803 - 2.15026i) q^{57} +(-2.71613 - 4.70447i) q^{59} +(-6.86526 + 11.8910i) q^{61} +(-0.469996 - 1.30256i) q^{63} +(0.248104 - 0.429729i) q^{65} +(5.58388 + 9.67156i) q^{67} +(1.03434 + 0.726400i) q^{69} +13.2942 q^{71} +4.24276 q^{73} +(0.758546 - 8.53362i) q^{75} +(-0.345734 - 0.598829i) q^{77} +(6.23617 - 10.8014i) q^{79} +(-1.51354 - 8.87182i) q^{81} +(-3.62651 + 6.28130i) q^{83} +(-0.120073 - 0.207973i) q^{85} +(-0.716820 + 8.06420i) q^{87} -11.8627 q^{89} +0.988520 q^{91} +(-7.75710 - 5.44766i) q^{93} +(-0.341335 - 0.591209i) q^{95} +(-2.21479 + 3.83613i) q^{97} +(-1.52532 - 4.22731i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{3} + 4 q^{7} - q^{9}+O(q^{10}) $ 10 * q - q^3 + 4 * q^7 - q^9	$ 10 q - q^{3} + 4 q^{7} - q^{9} + q^{11} - 6 q^{13} - 12 q^{15} - 6 q^{17} - 18 q^{19} - 16 q^{21} - 4 q^{23} + q^{25} + 2 q^{27} + 4 q^{29} + 8 q^{31} - 13 q^{33} + 24 q^{35} + 20 q^{37} + 18 q^{39} - 5 q^{41} + 13 q^{43} + 12 q^{45} + 6 q^{47} + 3 q^{49} - 3 q^{51} - 12 q^{55} + 27 q^{57} + 13 q^{59} - 10 q^{61} + 20 q^{63} + 17 q^{67} + 10 q^{69} - 8 q^{71} - 34 q^{73} + 29 q^{75} - 8 q^{77} + 6 q^{79} - q^{81} - 12 q^{83} - 18 q^{85} - 10 q^{87} + 44 q^{89} - 36 q^{91} - 26 q^{93} + 6 q^{95} + 27 q^{97} - 34 q^{99}+O(q^{100}) $ 10 * q - q^3 + 4 * q^7 - q^9 + q^11 - 6 * q^13 - 12 * q^15 - 6 * q^17 - 18 * q^19 - 16 * q^21 - 4 * q^23 + q^25 + 2 * q^27 + 4 * q^29 + 8 * q^31 - 13 * q^33 + 24 * q^35 + 20 * q^37 + 18 * q^39 - 5 * q^41 + 13 * q^43 + 12 * q^45 + 6 * q^47 + 3 * q^49 - 3 * q^51 - 12 * q^55 + 27 * q^57 + 13 * q^59 - 10 * q^61 + 20 * q^63 + 17 * q^67 + 10 * q^69 - 8 * q^71 - 34 * q^73 + 29 * q^75 - 8 * q^77 + 6 * q^79 - q^81 - 12 * q^83 - 18 * q^85 - 10 * q^87 + 44 * q^89 - 36 * q^91 - 26 * q^93 + 6 * q^95 + 27 * q^97 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.57079	−	0.729814i	0.906894	−	0.421358i
$3$	1.57079	−	0.729814i	0.906894	−	0.421358i
$4$		0			0
$5$	−0.115851	−	0.200661i	−0.0518103	−	0.0897381i	0.838957	−	0.544198i	$-0.183166\pi$
$5$	−0.115851	−	0.200661i	−0.0518103	−	0.0897381i	−0.890767	+	0.454459i	$0.849832\pi$
$6$		0			0
$7$	0.230793	−	0.399745i	0.0872315	−	0.151089i	−0.819108	−	0.573639i	$-0.805531\pi$
$7$	0.230793	−	0.399745i	0.0872315	−	0.151089i	0.906340	+	0.422549i	$0.138865\pi$
$8$		0			0
$9$	1.93474	−	2.29277i	0.644914	−	0.764255i
$10$		0			0
$11$	0.749014	−	1.29733i	0.225836	−	0.391160i	−0.730734	−	0.682663i	$-0.760822\pi$
$11$	0.749014	−	1.29733i	0.225836	−	0.391160i	0.956570	+	0.291503i	$0.0941552\pi$
$12$		0			0
$13$	1.07079	+	1.85466i	0.296983	+	0.514389i	0.975444	−	0.220247i	$-0.0706863\pi$
$13$	1.07079	+	1.85466i	0.296983	+	0.514389i	−0.678461	+	0.734636i	$0.737353\pi$
$14$		0			0
$15$	−0.328423	−	0.230645i	−0.0847984	−	0.0595523i
$16$		0			0
$17$	1.03644			0.251374			0.125687	−	0.992070i	$-0.459886\pi$
$17$	1.03644			0.251374			0.125687	+	0.992070i	$0.459886\pi$
$18$		0			0
$19$	2.94631			0.675931			0.337965	−	0.941159i	$-0.390261\pi$
$19$	2.94631			0.675931			0.337965	+	0.941159i	$0.390261\pi$
$20$		0			0
$21$	0.0707868	−	0.796350i	0.0154470	−	0.173778i
$22$		0			0
$23$	0.364866	+	0.631966i	0.0760798	+	0.131774i	0.901555	−	0.432664i	$-0.142426\pi$
$23$	0.364866	+	0.631966i	0.0760798	+	0.131774i	−0.825476	+	0.564438i	$0.809093\pi$
$24$		0			0
$25$	2.47316	−	4.28363i	0.494631	−	0.856727i
$26$		0			0
$27$	1.36578	−	5.01345i	0.262844	−	0.964838i
$28$		0			0
$29$	−2.33711	+	4.04800i	−0.433991	+	0.751694i	−0.997213	−	0.0746115i	$-0.976228\pi$
$29$	−2.33711	+	4.04800i	−0.433991	+	0.751694i	0.563222	+	0.826306i	$0.309562\pi$
$30$		0			0
$31$	−2.73632	−	4.73945i	−0.491458	−	0.851230i	0.508494	−	0.861066i	$-0.330203\pi$
$31$	−2.73632	−	4.73945i	−0.491458	−	0.851230i	−0.999952	+	0.00983556i	$0.996869\pi$
$32$		0			0
$33$	0.229731	−	2.58447i	0.0399911	−	0.449899i
$34$		0			0
$35$	−0.106951			−0.0180780
$36$		0			0
$37$	2.30039			0.378182			0.189091	−	0.981960i	$-0.439446\pi$
$37$	2.30039			0.378182			0.189091	+	0.981960i	$0.439446\pi$
$38$		0			0
$39$	3.03553	+	2.13180i	0.486074	+	0.341361i
$40$		0			0
$41$	−1.84151	−	3.18959i	−0.287596	−	0.498131i	0.685639	−	0.727941i	$-0.259523\pi$
$41$	−1.84151	−	3.18959i	−0.287596	−	0.498131i	−0.973235	+	0.229811i	$0.926189\pi$
$42$		0			0
$43$	2.41968	−	4.19101i	0.368998	−	0.639123i	−0.620411	−	0.784277i	$-0.713034\pi$
$43$	2.41968	−	4.19101i	0.368998	−	0.639123i	0.989409	+	0.145153i	$0.0463676\pi$
$44$		0			0
$45$	−0.684210	−	0.122606i	−0.101996	−	0.0182771i
$46$		0			0
$47$	5.40881	−	9.36833i	0.788956	−	1.36651i	−0.137651	−	0.990481i	$-0.543955\pi$
$47$	5.40881	−	9.36833i	0.788956	−	1.36651i	0.926607	−	0.376031i	$-0.122711\pi$
$48$		0			0
$49$	3.39347	+	5.87766i	0.484781	+	0.839666i
$50$		0			0
$51$	1.62803	−	0.756411i	0.227970	−	0.105919i
$52$		0			0
$53$	−10.0430			−1.37951			−0.689756	−	0.724042i	$-0.742282\pi$
$53$	−10.0430			−1.37951			−0.689756	+	0.724042i	$0.742282\pi$
$54$		0			0
$55$	−0.347097			−0.0468026
$56$		0			0
$57$	4.62803	−	2.15026i	0.612998	−	0.284809i
$58$		0			0
$59$	−2.71613	−	4.70447i	−0.353610	−	0.612470i	0.633269	−	0.773932i	$-0.281713\pi$
$59$	−2.71613	−	4.70447i	−0.353610	−	0.612470i	−0.986879	+	0.161461i	$0.948379\pi$
$60$		0			0
$61$	−6.86526	+	11.8910i	−0.879007	+	1.52248i	−0.0265746	+	0.999647i	$0.508460\pi$
$61$	−6.86526	+	11.8910i	−0.879007	+	1.52248i	−0.852432	+	0.522838i	$0.824873\pi$
$62$		0			0
$63$	−0.469996	−	1.30256i	−0.0592140	−	0.164107i
$64$		0			0
$65$	0.248104	−	0.429729i	0.0307736	−	0.0533014i
$66$		0			0
$67$	5.58388	+	9.67156i	0.682179	+	1.18157i	0.974314	+	0.225192i	$0.0723009\pi$
$67$	5.58388	+	9.67156i	0.682179	+	1.18157i	−0.292135	+	0.956377i	$0.594366\pi$
$68$		0			0
$69$	1.03434	+	0.726400i	0.124520	+	0.0874482i
$70$		0			0
$71$	13.2942			1.57773			0.788866	−	0.614565i	$-0.210669\pi$
$71$	13.2942			1.57773			0.788866	+	0.614565i	$0.210669\pi$
$72$		0			0
$73$	4.24276			0.496578			0.248289	−	0.968686i	$-0.420132\pi$
$73$	4.24276			0.496578			0.248289	+	0.968686i	$0.420132\pi$
$74$		0			0
$75$	0.758546	−	8.53362i	0.0875893	−	0.985378i
$76$		0			0
$77$	−0.345734	−	0.598829i	−0.0394001	−	0.0682429i
$78$		0			0
$79$	6.23617	−	10.8014i	0.701624	−	1.21525i	−0.266272	−	0.963898i	$-0.585792\pi$
$79$	6.23617	−	10.8014i	0.701624	−	1.21525i	0.967896	−	0.251351i	$-0.0808747\pi$
$80$		0			0
$81$	−1.51354	−	8.87182i	−0.168171	−	0.985758i
$82$		0			0
$83$	−3.62651	+	6.28130i	−0.398061	+	0.689463i	−0.993487	−	0.113948i	$-0.963650\pi$
$83$	−3.62651	+	6.28130i	−0.398061	+	0.689463i	0.595425	+	0.803411i	$0.296984\pi$
$84$		0			0
$85$	−0.120073	−	0.207973i	−0.0130238	−	0.0225579i
$86$		0			0
$87$	−0.716820	+	8.06420i	−0.0768511	+	0.864573i
$88$		0			0
$89$	−11.8627			−1.25745			−0.628724	−	0.777628i	$-0.716423\pi$
$89$	−11.8627			−1.25745			−0.628724	+	0.777628i	$0.716423\pi$
$90$		0			0
$91$	0.988520			0.103625
$92$		0			0
$93$	−7.75710	−	5.44766i	−0.804373	−	0.564896i
$94$		0			0
$95$	−0.341335	−	0.591209i	−0.0350202	−	0.0606567i
$96$		0			0
$97$	−2.21479	+	3.83613i	−0.224878	+	0.389500i	−0.956283	−	0.292444i	$-0.905532\pi$
$97$	−2.21479	+	3.83613i	−0.224878	+	0.389500i	0.731405	+	0.681943i	$0.238865\pi$
$98$		0			0
$99$	−1.52532	−	4.22731i	−0.153301	−	0.424861i
$100$		0			0
$101$	−7.47401	+	12.9454i	−0.743692	+	1.28811i	0.207112	+	0.978317i	$0.433594\pi$
$101$	−7.47401	+	12.9454i	−0.743692	+	1.28811i	−0.950804	+	0.309794i	$0.899740\pi$
$102$		0			0
$103$	−0.0310319	−	0.0537488i	−0.00305766	−	0.00529603i	0.864493	−	0.502646i	$-0.167640\pi$
$103$	−0.0310319	−	0.0537488i	−0.00305766	−	0.00529603i	−0.867550	+	0.497350i	$0.834307\pi$
$104$		0			0
$105$	−0.167997	+	0.0780541i	−0.0163948	+	0.00761730i
$106$		0			0
$107$	−11.9297			−1.15329			−0.576645	−	0.816995i	$-0.695638\pi$
$107$	−11.9297			−1.15329			−0.576645	+	0.816995i	$0.695638\pi$
$108$		0			0
$109$	10.1328			0.970544			0.485272	−	0.874363i	$-0.338721\pi$
$109$	10.1328			0.970544			0.485272	+	0.874363i	$0.338721\pi$
$110$		0			0
$111$	3.61342	−	1.67886i	0.342971	−	0.159350i
$112$		0			0
$113$	−0.743274	−	1.28739i	−0.0699213	−	0.121107i	0.828945	−	0.559330i	$-0.188941\pi$
$113$	−0.743274	−	1.28739i	−0.0699213	−	0.121107i	−0.898866	+	0.438223i	$0.855608\pi$
$114$		0			0
$115$	0.0845404	−	0.146428i	0.00788343	−	0.0136545i
$116$		0			0
$117$	6.32399	+	1.13322i	0.584653	+	0.104766i
$118$		0			0
$119$	0.239204	−	0.414313i	0.0219278	−	0.0379800i
$120$		0			0
$121$	4.37796	+	7.58284i	0.397996	+	0.689349i
$122$		0			0
$123$	−5.22043	−	3.66621i	−0.470711	−	0.330571i
$124$		0			0
$125$	−2.30459			−0.206129
$126$		0			0
$127$	−16.5663			−1.47002			−0.735010	−	0.678056i	$-0.762823\pi$
$127$	−16.5663			−1.47002			−0.735010	+	0.678056i	$0.762823\pi$
$128$		0			0
$129$	0.742144	−	8.34910i	0.0653422	−	0.735098i
$130$		0			0
$131$	1.43125	+	2.47900i	0.125049	+	0.216591i	0.921752	−	0.387780i	$-0.126758\pi$
$131$	1.43125	+	2.47900i	0.125049	+	0.216591i	−0.796703	+	0.604371i	$0.793424\pi$
$132$		0			0
$133$	0.679988	−	1.17777i	0.0589624	−	0.102126i
$134$		0			0
$135$	−1.16423	+	0.306758i	−0.100201	+	0.0264015i
$136$		0			0
$137$	−8.27650	+	14.3353i	−0.707109	+	1.22475i	0.258816	+	0.965927i	$0.416668\pi$
$137$	−8.27650	+	14.3353i	−0.707109	+	1.22475i	−0.965925	+	0.258822i	$0.916666\pi$
$138$		0			0
$139$	3.68545	+	6.38339i	0.312596	+	0.541432i	0.978923	−	0.204227i	$-0.0654682\pi$
$139$	3.68545	+	6.38339i	0.312596	+	0.541432i	−0.666328	+	0.745659i	$0.732135\pi$
$140$		0			0
$141$	1.65894	−	18.6631i	0.139708	−	1.57171i
$142$		0			0
$143$	3.20814			0.268278
$144$		0			0
$145$	1.08303			0.0899408
$146$		0			0
$147$	9.62002	+	6.75595i	0.793446	+	0.557221i
$148$		0			0
$149$	−1.06052	−	1.83688i	−0.0868814	−	0.150483i	0.819310	−	0.573351i	$-0.194357\pi$
$149$	−1.06052	−	1.83688i	−0.0868814	−	0.150483i	−0.906191	+	0.422868i	$0.861023\pi$
$150$		0			0
$151$	1.97197	−	3.41555i	0.160476	−	0.277953i	−0.774563	−	0.632497i	$-0.782030\pi$
$151$	1.97197	−	3.41555i	0.160476	−	0.277953i	0.935040	+	0.354543i	$0.115364\pi$
$152$		0			0
$153$	2.00525	−	2.37632i	0.162115	−	0.192114i
$154$		0			0
$155$	−0.634013	+	1.09814i	−0.0509252	+	0.0882050i
$156$		0			0
$157$	5.77046	+	9.99472i	0.460532	+	0.797666i	0.998987	−	0.0449886i	$-0.0143252\pi$
$157$	5.77046	+	9.99472i	0.460532	+	0.797666i	−0.538455	+	0.842654i	$0.680992\pi$
$158$		0			0
$159$	−15.7754	+	7.32952i	−1.25107	+	0.581269i
$160$		0			0
$161$	0.336834			0.0265462
$162$		0			0
$163$	−0.716550			−0.0561245			−0.0280623	−	0.999606i	$-0.508934\pi$
$163$	−0.716550			−0.0561245			−0.0280623	+	0.999606i	$0.508934\pi$
$164$		0			0
$165$	−0.545216	+	0.253317i	−0.0424450	+	0.0197207i
$166$		0			0
$167$	4.36210	+	7.55538i	0.337550	+	0.584653i	0.983971	−	0.178327i	$-0.0570686\pi$
$167$	4.36210	+	7.55538i	0.337550	+	0.584653i	−0.646422	+	0.762980i	$0.723735\pi$
$168$		0			0
$169$	4.20683	−	7.28645i	0.323602	−	0.560496i
$170$		0			0
$171$	5.70036	−	6.75521i	0.435917	−	0.516583i
$172$		0			0
$173$	8.96809	−	15.5332i	0.681832	−	1.18097i	−0.292590	−	0.956238i	$-0.594517\pi$
$173$	8.96809	−	15.5332i	0.681832	−	1.18097i	0.974421	−	0.224729i	$-0.0721496\pi$
$174$		0			0
$175$	−1.14157	−	1.97726i	−0.0862949	−	0.149467i
$176$		0			0
$177$	−7.69985	−	5.40746i	−0.578756	−	0.406449i
$178$		0			0
$179$	−6.66578			−0.498224			−0.249112	−	0.968475i	$-0.580139\pi$
$179$	−6.66578			−0.498224			−0.249112	+	0.968475i	$0.580139\pi$
$180$		0			0
$181$	19.1119			1.42058			0.710290	−	0.703909i	$-0.248564\pi$
$181$	19.1119			1.42058			0.710290	+	0.703909i	$0.248564\pi$
$182$		0			0
$183$	−2.10566	+	23.6886i	−0.155655	+	1.75111i
$184$		0			0
$185$	−0.266503	−	0.461598i	−0.0195937	−	0.0339373i
$186$		0			0
$187$	0.776311	−	1.34461i	0.0567695	−	0.0983276i
$188$		0			0
$189$	−1.68889	−	1.70303i	−0.122849	−	0.123877i
$190$		0			0
$191$	1.03948	−	1.80042i	0.0752138	−	0.130274i	−0.825965	−	0.563721i	$-0.809369\pi$
$191$	1.03948	−	1.80042i	0.0752138	−	0.130274i	0.901179	+	0.433447i	$0.142703\pi$
$192$		0			0
$193$	10.1978	+	17.6632i	0.734057	+	1.27142i	0.955136	+	0.296168i	$0.0957089\pi$
$193$	10.1978	+	17.6632i	0.734057	+	1.27142i	−0.221079	+	0.975256i	$0.570958\pi$
$194$		0			0
$195$	0.0760965	−	0.856083i	0.00544938	−	0.0613054i
$196$		0			0
$197$	−16.5458			−1.17884			−0.589419	−	0.807828i	$-0.700643\pi$
$197$	−16.5458			−1.17884			−0.589419	+	0.807828i	$0.700643\pi$
$198$		0			0
$199$	−21.2942			−1.50951			−0.754753	−	0.656009i	$-0.772243\pi$
$199$	−21.2942			−1.50951			−0.754753	+	0.656009i	$0.772243\pi$
$200$		0			0
$201$	15.8295	+	11.1168i	1.11653	+	0.784116i
$202$		0			0
$203$	1.07878	+	1.86850i	0.0757153	+	0.131143i
$204$		0			0
$205$	−0.426684	+	0.739038i	−0.0298009	+	0.0516166i
$206$		0			0
$207$	2.15487	+	0.386140i	0.149774	+	0.0268386i
$208$		0			0
$209$	2.20683	−	3.82234i	0.152650	−	0.264397i
$210$		0			0
$211$	10.1986	+	17.6645i	0.702101	+	1.21607i	0.967728	+	0.251999i	$0.0810879\pi$
$211$	10.1986	+	17.6645i	0.702101	+	1.21607i	−0.265627	+	0.964076i	$0.585579\pi$
$212$		0			0
$213$	20.8824	−	9.70230i	1.43084	−	0.664791i
$214$		0			0
$215$	−1.12129			−0.0764716
$216$		0			0
$217$	−2.52609			−0.171482
$218$		0			0
$219$	6.66447	−	3.09643i	0.450343	−	0.209237i
$220$		0			0
$221$	1.10981	+	1.92225i	0.0746539	+	0.129304i
$222$		0			0
$223$	−2.52026	+	4.36522i	−0.168769	+	0.292317i	−0.937987	−	0.346669i	$-0.887313\pi$
$223$	−2.52026	+	4.36522i	−0.168769	+	0.292317i	0.769218	+	0.638986i	$0.220646\pi$
$224$		0			0
$225$	−5.03644	−	13.9581i	−0.335763	−	0.930540i
$226$		0			0
$227$	−8.12047	+	14.0651i	−0.538975	+	0.933531i	0.459985	+	0.887927i	$0.347855\pi$
$227$	−8.12047	+	14.0651i	−0.538975	+	0.933531i	−0.998960	+	0.0456047i	$0.985479\pi$
$228$		0			0
$229$	−2.92453	−	5.06544i	−0.193259	−	0.334734i	0.753070	−	0.657941i	$-0.228572\pi$
$229$	−2.92453	−	5.06544i	−0.193259	−	0.334734i	−0.946328	+	0.323207i	$0.895239\pi$
$230$		0			0
$231$	−0.980109	−	0.688311i	−0.0644864	−	0.0452876i
$232$		0			0
$233$	−20.7492			−1.35932			−0.679662	−	0.733526i	$-0.737873\pi$
$233$	−20.7492			−1.35932			−0.679662	+	0.733526i	$0.737873\pi$
$234$		0			0
$235$	−2.50647			−0.163504
$236$		0			0
$237$	1.91271	−	21.5179i	0.124244	−	1.39774i
$238$		0			0
$239$	2.09672	+	3.63163i	0.135626	+	0.234910i	0.925836	−	0.377925i	$-0.123362\pi$
$239$	2.09672	+	3.63163i	0.135626	+	0.234910i	−0.790211	+	0.612835i	$0.790029\pi$
$240$		0			0
$241$	−7.03921	+	12.1923i	−0.453435	+	0.785373i	−0.998597	−	0.0529581i	$-0.983135\pi$
$241$	−7.03921	+	12.1923i	−0.453435	+	0.785373i	0.545161	+	0.838331i	$0.316468\pi$
$242$		0			0
$243$	−8.85223	−	12.8311i	−0.567871	−	0.823118i
$244$		0			0
$245$	0.786276	−	1.36187i	0.0502334	−	0.0870067i
$246$		0			0
$247$	3.15487	+	5.46440i	0.200740	+	0.347692i
$248$		0			0
$249$	−1.11229	+	12.5133i	−0.0704887	+	0.792996i
$250$		0			0
$251$	−15.3752			−0.970476			−0.485238	−	0.874382i	$-0.661267\pi$
$251$	−15.3752			−0.970476			−0.485238	+	0.874382i	$0.661267\pi$
$252$		0			0
$253$	1.09316			0.0687263
$254$		0			0
$255$	−0.340391	−	0.239050i	−0.0213161	−	0.0149699i
$256$		0			0
$257$	3.51288	+	6.08448i	0.219127	+	0.379540i	0.954541	−	0.298078i	$-0.0963456\pi$
$257$	3.51288	+	6.08448i	0.219127	+	0.379540i	−0.735414	+	0.677618i	$0.763012\pi$
$258$		0			0
$259$	0.530914	−	0.919569i	0.0329894	−	0.0571393i
$260$		0			0
$261$	4.75940	+	13.1903i	0.294599	+	0.816458i
$262$		0			0
$263$	−5.62093	+	9.73573i	−0.346601	+	0.600331i	−0.985643	−	0.168841i	$-0.945998\pi$
$263$	−5.62093	+	9.73573i	−0.346601	+	0.600331i	0.639042	+	0.769172i	$0.279331\pi$
$264$		0			0
$265$	1.16350	+	2.01523i	0.0714730	+	0.123795i
$266$		0			0
$267$	−18.6338	+	8.65760i	−1.14037	+	0.529836i
$268$		0			0
$269$	20.5678			1.25404			0.627019	−	0.779004i	$-0.284275\pi$
$269$	20.5678			1.25404			0.627019	+	0.779004i	$0.284275\pi$
$270$		0			0
$271$	−8.25314			−0.501343			−0.250671	−	0.968072i	$-0.580651\pi$
$271$	−8.25314			−0.501343			−0.250671	+	0.968072i	$0.580651\pi$
$272$		0			0
$273$	1.55275	−	0.721436i	0.0939769	−	0.0436633i
$274$		0			0
$275$	−3.70486	−	6.41701i	−0.223411	−	0.386960i
$276$		0			0
$277$	6.49837	−	11.2555i	0.390449	−	0.676278i	−0.602060	−	0.798451i	$-0.705653\pi$
$277$	6.49837	−	11.2555i	0.390449	−	0.676278i	0.992509	+	0.122174i	$0.0389864\pi$
$278$		0			0
$279$	−16.1605	−	2.89587i	−0.967505	−	0.173371i
$280$		0			0
$281$	−9.29955	+	16.1073i	−0.554765	+	0.960880i	0.443157	+	0.896444i	$0.353858\pi$
$281$	−9.29955	+	16.1073i	−0.554765	+	0.960880i	−0.997922	+	0.0644365i	$0.979475\pi$
$282$		0			0
$283$	8.30074	+	14.3773i	0.493428	+	0.854642i	0.999971	−	0.00757254i	$-0.00241044\pi$
$283$	8.30074	+	14.3773i	0.493428	+	0.854642i	−0.506544	+	0.862214i	$0.669077\pi$
$284$		0			0
$285$	−0.967636	−	0.679552i	−0.0573178	−	0.0402532i
$286$		0			0
$287$	−1.70003			−0.100350
$288$		0			0
$289$	−15.9258			−0.936811
$290$		0			0
$291$	−0.679301	+	7.64212i	−0.0398214	+	0.447989i
$292$		0			0
$293$	−6.33729	−	10.9765i	−0.370228	−	0.641254i	0.619372	−	0.785098i	$-0.287387\pi$
$293$	−6.33729	−	10.9765i	−0.370228	−	0.641254i	−0.989601	+	0.143843i	$0.954054\pi$
$294$		0			0
$295$	−0.629335	+	1.09004i	−0.0366413	+	0.0634646i
$296$		0			0
$297$	−5.48111	−	5.52701i	−0.318047	−	0.320709i
$298$		0			0
$299$	−0.781387	+	1.35340i	−0.0451888	+	0.0782692i
$300$		0			0
$301$	−1.11689	−	1.93451i	−0.0643765	−	0.111503i
$302$		0			0
$303$	−2.29236	+	25.7890i	−0.131693	+	1.48154i
$304$		0			0
$305$	3.18140			0.182167
$306$		0			0
$307$	−15.4097			−0.879479			−0.439740	−	0.898125i	$-0.644929\pi$
$307$	−15.4097			−0.879479			−0.439740	+	0.898125i	$0.644929\pi$
$308$		0			0
$309$	−0.0879711	−	0.0617804i	−0.00500450	−	0.00351457i
$310$		0			0
$311$	−12.7683	−	22.1153i	−0.724022	−	1.25404i	−0.959375	−	0.282133i	$-0.908958\pi$
$311$	−12.7683	−	22.1153i	−0.724022	−	1.25404i	0.235354	−	0.971910i	$-0.424375\pi$
$312$		0			0
$313$	9.13328	−	15.8193i	0.516244	−	0.894160i	−0.483579	−	0.875301i	$-0.660663\pi$
$313$	9.13328	−	15.8193i	0.516244	−	0.894160i	0.999822	−	0.0188591i	$-0.00600341\pi$
$314$		0			0
$315$	−0.206922	+	0.245213i	−0.0116587	+	0.0138162i
$316$		0			0
$317$	−5.22172	+	9.04428i	−0.293281	+	0.507977i	−0.974584	−	0.224024i	$-0.928080\pi$
$317$	−5.22172	+	9.04428i	−0.293281	+	0.507977i	0.681303	+	0.732002i	$0.261414\pi$
$318$		0			0
$319$	3.50106	+	6.06402i	0.196022	+	0.339520i
$320$		0			0
$321$	−18.7391	+	8.70649i	−1.04591	+	0.485949i
$322$		0			0
$323$	3.05369			0.169912
$324$		0			0
$325$	10.5929			0.587588
$326$		0			0
$327$	15.9164	−	7.39504i	0.880181	−	0.408947i
$328$		0			0
$329$	−2.49663	−	4.32429i	−0.137644	−	0.238406i
$330$		0			0
$331$	−2.37887	+	4.12032i	−0.130754	+	0.226473i	−0.923968	−	0.382471i	$-0.875073\pi$
$331$	−2.37887	+	4.12032i	−0.130754	+	0.226473i	0.793213	+	0.608944i	$0.208407\pi$
$332$		0			0
$333$	4.45066	−	5.27425i	0.243895	−	0.289027i
$334$		0			0
$335$	1.29380	−	2.24093i	0.0706878	−	0.122435i
$336$		0			0
$337$	13.7810	+	23.8694i	0.750700	+	1.30025i	0.947484	+	0.319804i	$0.103617\pi$
$337$	13.7810	+	23.8694i	0.750700	+	1.30025i	−0.196783	+	0.980447i	$0.563050\pi$
$338$		0			0
$339$	−2.10708	−	1.47976i	−0.114441	−	0.0803696i
$340$		0			0
$341$	−8.19818			−0.443956
$342$		0			0
$343$	6.36385			0.343616
$344$		0			0
$345$	0.0259295	−	0.291706i	0.00139600	−	0.0157049i
$346$		0			0
$347$	10.5341	+	18.2457i	0.565502	+	0.979478i	0.997003	+	0.0773655i	$0.0246508\pi$
$347$	10.5341	+	18.2457i	0.565502	+	0.979478i	−0.431501	+	0.902113i	$0.642016\pi$
$348$		0			0
$349$	−17.7897	+	30.8126i	−0.952258	+	1.64936i	−0.211738	+	0.977327i	$0.567912\pi$
$349$	−17.7897	+	30.8126i	−0.952258	+	1.64936i	−0.740521	+	0.672033i	$0.765421\pi$
$350$		0			0
$351$	10.7607	−	2.83529i	0.574363	−	0.151336i
$352$		0			0
$353$	2.52544	−	4.37420i	0.134416	−	0.232815i	−0.790958	−	0.611870i	$-0.790418\pi$
$353$	2.52544	−	4.37420i	0.134416	−	0.232815i	0.925374	+	0.379055i	$0.123751\pi$
$354$		0			0
$355$	−1.54015	−	2.66762i	−0.0817428	−	0.141583i
$356$		0			0
$357$	0.0733665	−	0.825371i	0.00388297	−	0.0436833i
$358$		0			0
$359$	18.1271			0.956709			0.478355	−	0.878167i	$-0.341233\pi$
$359$	18.1271			0.956709			0.478355	+	0.878167i	$0.341233\pi$
$360$		0			0
$361$	−10.3192			−0.543118
$362$		0			0
$363$	12.4109	+	8.71593i	0.651403	+	0.457468i
$364$		0			0
$365$	−0.491530	−	0.851355i	−0.0257278	−	0.0445619i
$366$		0			0
$367$	4.83039	−	8.36649i	0.252145	−	0.436727i	−0.711972	−	0.702208i	$-0.752197\pi$
$367$	4.83039	−	8.36649i	0.252145	−	0.436727i	0.964116	+	0.265481i	$0.0855308\pi$
$368$		0			0
$369$	−10.8758	−	1.94889i	−0.566174	−	0.101455i
$370$		0			0
$371$	−2.31785	+	4.01464i	−0.120337	+	0.208430i
$372$		0			0
$373$	−16.0300	−	27.7647i	−0.830001	−	1.43760i	−0.898037	−	0.439921i	$-0.855007\pi$
$373$	−16.0300	−	27.7647i	−0.830001	−	1.43760i	0.0680357	−	0.997683i	$-0.478327\pi$
$374$		0			0
$375$	−3.62002	+	1.68192i	−0.186937	+	0.0868541i
$376$		0			0
$377$	−10.0102			−0.515551
$378$		0			0
$379$	−16.0684			−0.825377			−0.412689	−	0.910872i	$-0.635410\pi$
$379$	−16.0684			−0.825377			−0.412689	+	0.910872i	$0.635410\pi$
$380$		0			0
$381$	−26.0221	+	12.0903i	−1.33315	+	0.619406i
$382$		0			0
$383$	15.3129	+	26.5228i	0.782454	+	1.35525i	0.930509	+	0.366270i	$0.119365\pi$
$383$	15.3129	+	26.5228i	0.782454	+	1.35525i	−0.148055	+	0.988979i	$0.547301\pi$
$384$		0			0
$385$	−0.0801076	+	0.138750i	−0.00408266	+	0.00707138i
$386$		0			0
$387$	−4.92754	−	13.6563i	−0.250481	−	0.694188i
$388$		0			0
$389$	−7.37823	+	12.7795i	−0.374091	+	0.647945i	−0.990191	−	0.139723i	$-0.955379\pi$
$389$	−7.37823	+	12.7795i	−0.374091	+	0.647945i	0.616099	+	0.787669i	$0.288712\pi$
$390$		0			0
$391$	0.378162	+	0.654997i	0.0191245	+	0.0331246i
$392$		0			0
$393$	4.05740	+	2.84944i	0.204669	+	0.143735i
$394$		0			0
$395$	−2.88988			−0.145405
$396$		0			0
$397$	13.7032			0.687746			0.343873	−	0.939016i	$-0.388261\pi$
$397$	13.7032			0.687746			0.343873	+	0.939016i	$0.388261\pi$
$398$		0			0
$399$	0.208560	−	2.34630i	0.0104411	−	0.117462i
$400$		0			0
$401$	3.83939	+	6.65002i	0.191730	+	0.332086i	0.945824	−	0.324681i	$-0.105257\pi$
$401$	3.83939	+	6.65002i	0.191730	+	0.332086i	−0.754094	+	0.656767i	$0.771924\pi$
$402$		0			0
$403$	5.86004	−	10.1499i	0.291909	−	0.505601i
$404$		0			0
$405$	−1.60488	+	1.33152i	−0.0797470	+	0.0661638i
$406$		0			0
$407$	1.72303	−	2.98437i	0.0854072	−	0.147930i
$408$		0			0
$409$	−6.73882	−	11.6720i	−0.333213	−	0.577142i	0.649927	−	0.759997i	$-0.274800\pi$
$409$	−6.73882	−	11.6720i	−0.333213	−	0.577142i	−0.983140	+	0.182855i	$0.941466\pi$
$410$		0			0
$411$	−2.53850	+	28.5580i	−0.125215	+	1.40866i
$412$		0			0
$413$	−2.50745			−0.123384
$414$		0			0
$415$	1.68055			0.0824948
$416$		0			0
$417$	10.4477	+	7.33724i	0.511628	+	0.359306i
$418$		0			0
$419$	−18.0380	−	31.2427i	−0.881213	−	1.52630i	−0.849994	−	0.526792i	$-0.823395\pi$
$419$	−18.0380	−	31.2427i	−0.881213	−	1.52630i	−0.0312184	−	0.999513i	$-0.509939\pi$
$420$		0			0
$421$	−2.57726	+	4.46394i	−0.125608	+	0.217559i	−0.921970	−	0.387260i	$-0.873421\pi$
$421$	−2.57726	+	4.46394i	−0.125608	+	0.217559i	0.796362	+	0.604820i	$0.206755\pi$
$422$		0			0
$423$	−11.0147	−	30.5264i	−0.535555	−	1.48425i
$424$		0			0
$425$	2.56329	−	4.43974i	0.124338	−	0.215359i
$426$		0			0
$427$	3.16891	+	5.48871i	0.153354	+	0.265617i
$428$		0			0
$429$	5.03930	−	2.34134i	0.243300	−	0.113041i
$430$		0			0
$431$	−20.7200			−0.998045			−0.499022	−	0.866589i	$-0.666307\pi$
$431$	−20.7200			−0.998045			−0.499022	+	0.866589i	$0.666307\pi$
$432$		0			0
$433$	−23.3719			−1.12318			−0.561592	−	0.827414i	$-0.689811\pi$
$433$	−23.3719			−1.12318			−0.561592	+	0.827414i	$0.689811\pi$
$434$		0			0
$435$	1.70121	−	0.790411i	0.0815668	−	0.0378973i
$436$		0			0
$437$	1.07501	+	1.86197i	0.0514246	+	0.0890701i
$438$		0			0
$439$	19.0107	−	32.9274i	0.907330	−	1.57154i	0.0895708	−	0.995980i	$-0.471450\pi$
$439$	19.0107	−	32.9274i	0.907330	−	1.57154i	0.817759	−	0.575561i	$-0.195216\pi$
$440$		0			0
$441$	20.0416	+	3.59133i	0.954361	+	0.171016i
$442$		0			0
$443$	8.30811	−	14.3901i	0.394730	−	0.683693i	−0.598336	−	0.801245i	$-0.704171\pi$
$443$	8.30811	−	14.3901i	0.394730	−	0.683693i	0.993067	+	0.117552i	$0.0375047\pi$
$444$		0			0
$445$	1.37432	+	2.38038i	0.0651488	+	0.112841i
$446$		0			0
$447$	−3.00644	−	2.11136i	−0.142200	−	0.0998640i
$448$		0			0
$449$	12.9085			0.609192			0.304596	−	0.952482i	$-0.401479\pi$
$449$	12.9085			0.609192			0.304596	+	0.952482i	$0.401479\pi$
$450$		0			0
$451$	−5.51728			−0.259798
$452$		0			0
$453$	0.604825	−	6.80427i	0.0284172	−	0.319692i
$454$		0			0
$455$	−0.114521	−	0.198357i	−0.00536884	−	0.00929911i
$456$		0			0
$457$	13.4943	−	23.3728i	0.631237	−	1.09333i	−0.356063	−	0.934462i	$-0.615881\pi$
$457$	13.4943	−	23.3728i	0.631237	−	1.09333i	0.987299	−	0.158872i	$-0.0507856\pi$
$458$		0			0
$459$	1.41555	−	5.19615i	0.0660721	−	0.242536i
$460$		0			0
$461$	10.0800	−	17.4591i	0.469474	−	0.813152i	−0.529917	−	0.848049i	$-0.677777\pi$
$461$	10.0800	−	17.4591i	0.469474	−	0.813152i	0.999391	+	0.0348972i	$0.0111104\pi$
$462$		0			0
$463$	17.2220	+	29.8293i	0.800373	+	1.38629i	0.919371	+	0.393391i	$0.128698\pi$
$463$	17.2220	+	29.8293i	0.800373	+	1.38629i	−0.118999	+	0.992894i	$0.537968\pi$
$464$		0			0
$465$	−0.194459	+	2.18766i	−0.00901783	+	0.101450i
$466$		0			0
$467$	31.6194			1.46317			0.731585	−	0.681750i	$-0.238781\pi$
$467$	31.6194			1.46317			0.731585	+	0.681750i	$0.238781\pi$
$468$		0			0
$469$	5.15487			0.238030
$470$		0			0
$471$	16.3584	+	11.4882i	0.753757	+	0.529349i
$472$		0			0
$473$	−3.62475	−	6.27825i	−0.166666	−	0.288674i
$474$		0			0
$475$	7.28670	−	12.6209i	0.334337	−	0.579088i
$476$		0			0
$477$	−19.4306	+	23.0262i	−0.889667	+	1.05430i
$478$		0			0
$479$	3.72976	−	6.46014i	0.170417	−	0.295171i	−0.768149	−	0.640272i	$-0.778822\pi$
$479$	3.72976	−	6.46014i	0.170417	−	0.295171i	0.938566	+	0.345100i	$0.112155\pi$
$480$		0			0
$481$	2.46323	+	4.26644i	0.112314	+	0.194533i
$482$		0			0
$483$	0.529094	−	0.245826i	0.0240746	−	0.0111855i
$484$		0			0
$485$	1.02635			0.0466039
$486$		0			0
$487$	−29.4254			−1.33339			−0.666697	−	0.745329i	$-0.732293\pi$
$487$	−29.4254			−1.33339			−0.666697	+	0.745329i	$0.732293\pi$
$488$		0			0
$489$	−1.12555	+	0.522948i	−0.0508990	+	0.0236485i
$490$		0			0
$491$	14.4326	+	24.9979i	0.651332	+	1.12814i	0.982800	+	0.184674i	$0.0591229\pi$
$491$	14.4326	+	24.9979i	0.651332	+	1.12814i	−0.331467	+	0.943467i	$0.607544\pi$
$492$		0			0
$493$	−2.42228	+	4.19552i	−0.109094	+	0.188957i
$494$		0			0
$495$	−0.671544	+	0.795813i	−0.0301837	+	0.0357691i
$496$		0			0
$497$	3.06821	−	5.31429i	0.137628	−	0.238379i
$498$		0			0
$499$	−12.8470	−	22.2517i	−0.575111	−	0.996122i	−0.996030	−	0.0890236i	$-0.971625\pi$
$499$	−12.8470	−	22.2517i	−0.575111	−	0.996122i	0.420918	−	0.907099i	$-0.361708\pi$
$500$		0			0
$501$	12.3660	+	8.68437i	0.552470	+	0.387989i
$502$		0			0
$503$	−20.7071			−0.923286			−0.461643	−	0.887066i	$-0.652740\pi$
$503$	−20.7071			−0.923286			−0.461643	+	0.887066i	$0.652740\pi$
$504$		0			0
$505$	3.46350			0.154124
$506$		0			0
$507$	1.29028	−	14.5157i	0.0573035	−	0.644663i
$508$		0			0
$509$	10.7631	+	18.6421i	0.477064	+	0.826299i	0.999654	−	0.0262850i	$-0.00836772\pi$
$509$	10.7631	+	18.6421i	0.477064	+	0.826299i	−0.522591	+	0.852584i	$0.675034\pi$
$510$		0			0
$511$	0.979199	−	1.69602i	0.0433172	−	0.0750276i
$512$		0			0
$513$	4.02400	−	14.7712i	0.177664	−	0.652164i
$514$		0			0
$515$	−0.00719018	+	0.0124538i	−0.000316837	+	0.000548778i
$516$		0			0
$517$	−8.10255	−	14.0340i	−0.356350	−	0.617216i
$518$		0			0
$519$	2.75062	−	30.9444i	0.120739	−	1.35831i
$520$		0			0
$521$	22.2984			0.976911			0.488455	−	0.872589i	$-0.337560\pi$
$521$	22.2984			0.976911			0.488455	+	0.872589i	$0.337560\pi$
$522$		0			0
$523$	4.92665			0.215427			0.107714	−	0.994182i	$-0.465647\pi$
$523$	4.92665			0.215427			0.107714	+	0.994182i	$0.465647\pi$
$524$		0			0
$525$	−3.23620	−	2.27272i	−0.141240	−	0.0991898i
$526$		0			0
$527$	−2.83604	−	4.91217i	−0.123540	−	0.213977i
$528$		0			0
$529$	11.2337	−	19.4574i	0.488424	−	0.845975i
$530$		0			0
$531$	−16.0413	−	2.87450i	−0.696132	−	0.124743i
$532$		0			0
$533$	3.94373	−	6.83075i	0.170822	−	0.295873i
$534$		0			0
$535$	1.38208	+	2.39383i	0.0597523	+	0.103494i
$536$		0			0
$537$	−10.4705	+	4.86478i	−0.451836	+	0.209931i
$538$		0			0
$539$	10.1670			0.437925
$540$		0			0
$541$	−22.0179			−0.946622			−0.473311	−	0.880895i	$-0.656941\pi$
$541$	−22.0179			−0.946622			−0.473311	+	0.880895i	$0.656941\pi$
$542$		0			0
$543$	30.0208	−	13.9482i	1.28832	−	0.598573i
$544$		0			0
$545$	−1.17390	−	2.03325i	−0.0502842	−	0.0870948i
$546$		0			0
$547$	15.2563	−	26.4247i	0.652311	−	1.12984i	−0.330249	−	0.943894i	$-0.607133\pi$
$547$	15.2563	−	26.4247i	0.652311	−	1.12984i	0.982561	−	0.185943i	$-0.0595339\pi$
$548$		0			0
$549$	13.9807	+	38.7464i	0.596682	+	1.65366i
$550$		0			0
$551$	−6.88587	+	11.9267i	−0.293348	+	0.508093i
$552$		0			0
$553$	−2.87853	−	4.98575i	−0.122407	−	0.212016i
$554$		0			0
$555$	−0.755501	−	0.530573i	−0.0320692	−	0.0225216i
$556$		0			0
$557$	34.8358			1.47604			0.738021	−	0.674778i	$-0.235761\pi$
$557$	34.8358			1.47604			0.738021	+	0.674778i	$0.235761\pi$
$558$		0			0
$559$	10.3639			0.438344
$560$		0			0
$561$	0.238103	−	2.67866i	0.0100527	−	0.113093i
$562$		0			0
$563$	−6.86229	−	11.8858i	−0.289211	−	0.500928i	0.684411	−	0.729097i	$-0.260060\pi$
$563$	−6.86229	−	11.8858i	−0.289211	−	0.500928i	−0.973622	+	0.228169i	$0.926726\pi$
$564$		0			0
$565$	−0.172219	+	0.298292i	−0.00724529	+	0.0125492i
$566$		0			0
$567$	−3.89578	−	1.44252i	−0.163607	−	0.0605802i
$568$		0			0
$569$	14.6770	−	25.4213i	0.615291	−	1.06572i	−0.375042	−	0.927008i	$-0.622372\pi$
$569$	14.6770	−	25.4213i	0.615291	−	1.06572i	0.990333	−	0.138708i	$-0.0442950\pi$
$570$		0			0
$571$	1.60926	+	2.78732i	0.0673455	+	0.116646i	0.897732	−	0.440542i	$-0.145214\pi$
$571$	1.60926	+	2.78732i	0.0673455	+	0.116646i	−0.830387	+	0.557188i	$0.811880\pi$
$572$		0			0
$573$	0.318819	−	3.58671i	0.0133189	−	0.149837i
$574$		0			0
$575$	3.60948			0.150526
$576$		0			0
$577$	0.782693			0.0325839			0.0162920	−	0.999867i	$-0.494814\pi$
$577$	0.782693			0.0325839			0.0162920	+	0.999867i	$0.494814\pi$
$578$		0			0
$579$	28.9095	+	20.3026i	1.20144	+	0.843746i
$580$		0			0
$581$	1.67395	+	2.89936i	0.0694470	+	0.120286i
$582$		0			0
$583$	−7.52235	+	13.0291i	−0.311544	+	0.539610i
$584$		0			0
$585$	−0.505250	−	1.40026i	−0.0208895	−	0.0578936i
$586$		0			0
$587$	12.7201	−	22.0318i	0.525014	−	0.909350i	−0.474562	−	0.880222i	$-0.657394\pi$
$587$	12.7201	−	22.0318i	0.525014	−	0.909350i	0.999576	−	0.0291282i	$-0.00927309\pi$
$588$		0			0
$589$	−8.06206	−	13.9639i	−0.332192	−	0.575373i
$590$		0			0
$591$	−25.9899	+	12.0753i	−1.06908	+	0.496713i
$592$		0			0
$593$	44.4583			1.82569			0.912843	−	0.408311i	$-0.133882\pi$
$593$	44.4583			1.82569			0.912843	+	0.408311i	$0.133882\pi$
$594$		0			0
$595$	−0.110848			−0.00454434
$596$		0			0
$597$	−33.4487	+	15.5408i	−1.36896	+	0.636043i
$598$		0			0
$599$	−23.7554	−	41.1455i	−0.970618	−	1.68116i	−0.693696	−	0.720268i	$-0.744019\pi$
$599$	−23.7554	−	41.1455i	−0.970618	−	1.68116i	−0.276922	−	0.960892i	$-0.589314\pi$
$600$		0			0
$601$	3.61527	−	6.26183i	0.147470	−	0.255425i	−0.782822	−	0.622246i	$-0.786220\pi$
$601$	3.61527	−	6.26183i	0.147470	−	0.255425i	0.930292	+	0.366821i	$0.119554\pi$
$602$		0			0
$603$	32.9780	+	5.90946i	1.34297	+	0.240652i
$604$		0			0
$605$	1.01438	−	1.75697i	0.0412406	−	0.0714308i
$606$		0			0
$607$	7.00711	+	12.1367i	0.284410	+	0.492612i	0.972466	−	0.233045i	$-0.0748690\pi$
$607$	7.00711	+	12.1367i	0.284410	+	0.492612i	−0.688056	+	0.725658i	$0.741536\pi$
$608$		0			0
$609$	3.05819	+	2.14770i	0.123924	+	0.0870294i
$610$		0			0
$611$	23.1667			0.937225
$612$		0			0
$613$	−12.2357			−0.494194			−0.247097	−	0.968991i	$-0.579477\pi$
$613$	−12.2357			−0.494194			−0.247097	+	0.968991i	$0.579477\pi$
$614$		0			0
$615$	−0.130869	+	1.47227i	−0.00527714	+	0.0593677i
$616$		0			0
$617$	1.07716	+	1.86569i	0.0433647	+	0.0751099i	0.886893	−	0.461975i	$-0.152859\pi$
$617$	1.07716	+	1.86569i	0.0433647	+	0.0751099i	−0.843528	+	0.537085i	$0.819526\pi$
$618$		0			0
$619$	5.94519	−	10.2974i	0.238957	−	0.413886i	−0.721458	−	0.692458i	$-0.756528\pi$
$619$	5.94519	−	10.2974i	0.238957	−	0.413886i	0.960415	+	0.278572i	$0.0898611\pi$
$620$		0			0
$621$	3.66665	−	0.966111i	0.147138	−	0.0387687i
$622$		0			0
$623$	−2.73784	+	4.74207i	−0.109689	+	0.189987i
$624$		0			0
$625$	−12.0988	−	20.9557i	−0.483952	−	0.838229i
$626$		0			0
$627$	0.676861	−	7.61466i	0.0270312	−	0.304100i
$628$		0			0
$629$	2.38422			0.0950652
$630$		0			0
$631$	41.3492			1.64609			0.823043	−	0.567979i	$-0.192275\pi$
$631$	41.3492			1.64609			0.823043	+	0.567979i	$0.192275\pi$
$632$		0			0
$633$	28.9116	+	20.3041i	1.14913	+	0.807015i
$634$		0			0
$635$	1.91923	+	3.32420i	0.0761623	+	0.131917i
$636$		0			0
$637$	−7.26736	+	12.5874i	−0.287943	+	0.498733i
$638$		0			0
$639$	25.7209	−	30.4805i	1.01750	−	1.20579i
$640$		0			0
$641$	12.6110	−	21.8429i	0.498106	−	0.862744i	−0.501892	−	0.864930i	$-0.667362\pi$
$641$	12.6110	−	21.8429i	0.498106	−	0.862744i	0.999998	+	0.00218592i	$0.000695802\pi$
$642$		0			0
$643$	−7.87820	−	13.6454i	−0.310686	−	0.538124i	0.667825	−	0.744318i	$-0.267225\pi$
$643$	−7.87820	−	13.6454i	−0.310686	−	0.538124i	−0.978511	+	0.206194i	$0.933892\pi$
$644$		0			0
$645$	−1.76131	+	0.818336i	−0.0693517	+	0.0322220i
$646$		0			0
$647$	21.8197			0.857823			0.428911	−	0.903347i	$-0.358897\pi$
$647$	21.8197			0.857823			0.428911	+	0.903347i	$0.358897\pi$
$648$		0			0
$649$	−8.13768			−0.319432
$650$		0			0
$651$	−3.96796	+	1.84358i	−0.155516	+	0.0722556i
$652$		0			0
$653$	−12.5168	−	21.6797i	−0.489819	−	0.848392i	0.510112	−	0.860108i	$-0.329604\pi$
$653$	−12.5168	−	21.6797i	−0.489819	−	0.848392i	−0.999931	+	0.0117162i	$0.996271\pi$
$654$		0			0
$655$	0.331625	−	0.574392i	0.0129577	−	0.0224433i
$656$		0			0
$657$	8.20865	−	9.72766i	0.320250	−	0.379512i
$658$		0			0
$659$	14.5079	−	25.1285i	0.565149	−	0.978867i	−0.431887	−	0.901928i	$-0.642152\pi$
$659$	14.5079	−	25.1285i	0.565149	−	0.978867i	0.997036	−	0.0769388i	$-0.0245146\pi$
$660$		0			0
$661$	−4.99232	−	8.64694i	−0.194179	−	0.336327i	0.752452	−	0.658647i	$-0.228871\pi$
$661$	−4.99232	−	8.64694i	−0.194179	−	0.336327i	−0.946631	+	0.322320i	$0.895537\pi$
$662$		0			0
$663$	3.14616	+	2.20948i	0.122187	+	0.0858093i
$664$		0			0
$665$	−0.315110			−0.0122195
$666$		0			0
$667$	−3.41093			−0.132072
$668$		0			0
$669$	−0.772993	+	8.69615i	−0.0298856	+	0.336213i
$670$		0			0
$671$	10.2844	+	17.8130i	0.397023	+	0.687665i
$672$		0			0
$673$	2.42824	−	4.20584i	0.0936019	−	0.162123i	−0.815422	−	0.578866i	$-0.803495\pi$
$673$	2.42824	−	4.20584i	0.0936019	−	0.162123i	0.909024	+	0.416743i	$0.136829\pi$
$674$		0			0
$675$	−18.0980	−	18.2495i	−0.696592	−	0.702425i
$676$		0			0
$677$	−7.10559	+	12.3072i	−0.273090	+	0.473006i	−0.969651	−	0.244491i	$-0.921379\pi$
$677$	−7.10559	+	12.3072i	−0.273090	+	0.473006i	0.696562	+	0.717497i	$0.254712\pi$
$678$		0			0
$679$	1.02231	+	1.77070i	0.0392328	+	0.0679533i
$680$		0			0
$681$	−2.49064	+	28.0197i	−0.0954416	+	1.07372i
$682$		0			0
$683$	20.7153			0.792648			0.396324	−	0.918111i	$-0.370286\pi$
$683$	20.7153			0.792648			0.396324	+	0.918111i	$0.370286\pi$
$684$		0			0
$685$	3.83538			0.146542
$686$		0			0
$687$	−8.29065	−	5.82236i	−0.316308	−	0.222137i
$688$		0			0
$689$	−10.7539	−	18.6263i	−0.409691	−	0.709606i
$690$		0			0
$691$	6.56378	−	11.3688i	0.249698	−	0.432489i	−0.713744	−	0.700407i	$-0.753002\pi$
$691$	6.56378	−	11.3688i	0.249698	−	0.432489i	0.963442	+	0.267917i	$0.0863353\pi$
$692$		0			0
$693$	−2.04188	−	0.365893i	−0.0775647	−	0.0138991i
$694$		0			0
$695$	0.853929	−	1.47905i	0.0323914	−	0.0561035i
$696$		0			0
$697$	−1.90862	−	3.30583i	−0.0722942	−	0.125217i
$698$		0			0
$699$	−32.5925	+	15.1430i	−1.23276	+	0.572762i
$700$		0			0
$701$	−13.3554			−0.504426			−0.252213	−	0.967672i	$-0.581158\pi$
$701$	−13.3554			−0.504426			−0.252213	+	0.967672i	$0.581158\pi$
$702$		0			0
$703$	6.77767			0.255625
$704$		0			0
$705$	−3.93713	+	1.82926i	−0.148281	+	0.0688939i
$706$		0			0
$707$	3.44989	+	5.97539i	0.129747	+	0.224728i
$708$		0			0
$709$	−13.5083	+	23.3971i	−0.507316	+	0.878697i	0.492648	+	0.870229i	$0.336029\pi$
$709$	−13.5083	+	23.3971i	−0.507316	+	0.878697i	−0.999964	+	0.00846836i	$0.997304\pi$
$710$		0			0
$711$	−12.6996	−	35.1959i	−0.476272	−	1.31995i
$712$		0			0
$713$	1.99678	−	3.45852i	0.0747800	−	0.129523i
$714$		0			0
$715$	−0.371667	−	0.643747i	−0.0138996	−	0.0240748i
$716$		0			0
$717$	5.94391	+	4.17429i	0.221979	+	0.155892i
$718$		0			0
$719$	−46.5794			−1.73712			−0.868559	−	0.495585i	$-0.834954\pi$
$719$	−46.5794			−1.73712			−0.868559	+	0.495585i	$0.834954\pi$
$720$		0			0
$721$	−0.0286478			−0.00106690
$722$		0			0
$723$	−2.15901	+	24.2888i	−0.0802943	+	0.903309i
$724$		0			0
$725$	11.5601	+	20.0227i	0.429331	+	0.743623i
$726$		0			0
$727$	12.5353	−	21.7119i	0.464910	−	0.805248i	−0.534287	−	0.845303i	$-0.679420\pi$
$727$	12.5353	−	21.7119i	0.464910	−	0.805248i	0.999197	+	0.0400549i	$0.0127533\pi$
$728$		0			0
$729$	−23.2693	−	13.6945i	−0.861826	−	0.507203i
$730$		0			0
$731$	2.50786	−	4.34374i	0.0927566	−	0.160659i
$732$		0			0
$733$	−11.8288	−	20.4881i	−0.436907	−	0.756746i	0.560542	−	0.828126i	$-0.310593\pi$
$733$	−11.8288	−	20.4881i	−0.436907	−	0.756746i	−0.997449	+	0.0713803i	$0.977260\pi$
$734$		0			0
$735$	0.241160	−	2.71304i	0.00889532	−	0.100072i
$736$		0			0
$737$	16.7296			0.616243
$738$		0			0
$739$	−32.9834			−1.21332			−0.606658	−	0.794963i	$-0.707490\pi$
$739$	−32.9834			−1.21332			−0.606658	+	0.794963i	$0.707490\pi$
$740$		0			0
$741$	8.94363	+	6.28094i	0.328553	+	0.230736i
$742$		0			0
$743$	5.16854	+	8.95218i	0.189615	+	0.328424i	0.945122	−	0.326717i	$-0.105943\pi$
$743$	5.16854	+	8.95218i	0.189615	+	0.328424i	−0.755507	+	0.655141i	$0.772609\pi$
$744$		0			0
$745$	−0.245726	+	0.425610i	−0.00900271	+	0.0155931i
$746$		0			0
$747$	7.38519	+	20.4674i	0.270210	+	0.748865i
$748$		0			0
$749$	−2.75330	+	4.76885i	−0.100603	+	0.174250i
$750$		0			0
$751$	11.5268	+	19.9650i	0.420620	+	0.728535i	0.996000	−	0.0893513i	$-0.0284794\pi$
$751$	11.5268	+	19.9650i	0.420620	+	0.728535i	−0.575381	+	0.817886i	$0.695146\pi$
$752$		0			0
$753$	−24.1512	+	11.2211i	−0.880119	+	0.408918i
$754$		0			0
$755$	−0.913821			−0.0332573
$756$		0			0
$757$	−4.86572			−0.176848			−0.0884239	−	0.996083i	$-0.528183\pi$
$757$	−4.86572			−0.176848			−0.0884239	+	0.996083i	$0.528183\pi$
$758$		0			0
$759$	1.71712	−	0.797803i	0.0623275	−	0.0289584i
$760$		0			0
$761$	19.3733	+	33.5556i	0.702283	+	1.21639i	0.967663	+	0.252246i	$0.0811694\pi$
$761$	19.3733	+	33.5556i	0.702283	+	1.21639i	−0.265380	+	0.964144i	$0.585497\pi$
$762$		0			0
$763$	2.33857	−	4.05052i	0.0846620	−	0.146639i
$764$		0			0
$765$	−0.709145	−	0.127075i	−0.0256392	−	0.00459439i
$766$		0			0
$767$	5.81679	−	10.0750i	0.210032	−	0.363786i
$768$		0			0
$769$	−14.0001	−	24.2489i	−0.504858	−	0.874439i	−0.999984	−	0.00561822i	$-0.998212\pi$
$769$	−14.0001	−	24.2489i	−0.504858	−	0.874439i	0.495127	−	0.868821i	$-0.335122\pi$
$770$		0			0
$771$	9.95853	+	6.99368i	0.358648	+	0.251871i
$772$		0			0
$773$	30.9662			1.11378			0.556888	−	0.830588i	$-0.311995\pi$
$773$	30.9662			1.11378			0.556888	+	0.830588i	$0.311995\pi$
$774$		0			0
$775$	−27.0694			−0.972362
$776$		0			0
$777$	0.162837	−	1.83192i	0.00584176	−	0.0657196i
$778$		0			0
$779$	−5.42567	−	9.39754i	−0.194395	−	0.336702i
$780$		0			0
$781$	9.95755	−	17.2470i	0.356309	−	0.617146i
$782$		0			0
$783$	17.1025	+	17.2456i	0.611192	+	0.616309i
$784$		0			0
$785$	1.33703	−	2.31580i	0.0477207	−	0.0826546i
$786$		0			0
$787$	8.48755	+	14.7009i	0.302549	+	0.524030i	0.976713	−	0.214552i	$-0.0688292\pi$
$787$	8.48755	+	14.7009i	0.302549	+	0.524030i	−0.674164	+	0.738582i	$0.735496\pi$
$788$		0			0
$789$	−1.72400	+	19.3950i	−0.0613762	+	0.690480i
$790$		0			0
$791$	−0.686169			−0.0243974
$792$		0			0
$793$	−29.4049			−1.04420
$794$		0			0
$795$	3.29835	+	2.31637i	0.116980	+	0.0821531i
$796$		0			0
$797$	12.5688	+	21.7698i	0.445210	+	0.771127i	0.998067	−	0.0621496i	$-0.0197956\pi$
$797$	12.5688	+	21.7698i	0.445210	+	0.771127i	−0.552857	+	0.833276i	$0.686462\pi$
$798$		0			0
$799$	5.60592	−	9.70974i	0.198323	−	0.343506i
$800$		0			0
$801$	−22.9514	+	27.1985i	−0.810946	+	0.961011i
$802$		0			0
$803$	3.17789	−	5.50427i	0.112145	−	0.194241i
$804$		0			0
$805$	−0.0390226	−	0.0675892i	−0.00137537	−	0.00238221i
$806$		0			0
$807$	32.3076	−	15.0106i	1.13728	−	0.528400i
$808$		0			0
$809$	−0.441024			−0.0155056			−0.00775279	−	0.999970i	$-0.502468\pi$
$809$	−0.441024			−0.0155056			−0.00775279	+	0.999970i	$0.502468\pi$
$810$		0			0
$811$	−44.8442			−1.57469			−0.787346	−	0.616511i	$-0.788545\pi$
$811$	−44.8442			−1.57469			−0.787346	+	0.616511i	$0.788545\pi$
$812$		0			0
$813$	−12.9639	+	6.02326i	−0.454665	+	0.211245i
$814$		0			0
$815$	0.0830133	+	0.143783i	0.00290783	+	0.00503651i
$816$		0			0
$817$	7.12914	−	12.3480i	0.249417	−	0.432003i
$818$		0			0
$819$	1.91253	−	2.26644i	0.0668292	−	0.0791959i
$820$		0			0
$821$	13.3775	−	23.1705i	0.466878	−	0.808656i	−0.532406	−	0.846489i	$-0.678712\pi$
$821$	13.3775	−	23.1705i	0.466878	−	0.808656i	0.999284	+	0.0378328i	$0.0120454\pi$
$822$		0			0
$823$	21.2608	+	36.8247i	0.741104	+	1.28363i	0.951993	+	0.306119i	$0.0990307\pi$
$823$	21.2608	+	36.8247i	0.741104	+	1.28363i	−0.210889	+	0.977510i	$0.567636\pi$
$824$		0			0
$825$	−10.5028	−	7.37589i	−0.365659	−	0.256795i
$826$		0			0
$827$	−17.4800			−0.607839			−0.303919	−	0.952698i	$-0.598295\pi$
$827$	−17.4800			−0.607839			−0.303919	+	0.952698i	$0.598295\pi$
$828$		0			0
$829$	−10.7798			−0.374399			−0.187200	−	0.982322i	$-0.559941\pi$
$829$	−10.7798			−0.374399			−0.187200	+	0.982322i	$0.559941\pi$
$830$		0			0
$831$	1.99312	−	22.4226i	0.0691407	−	0.777831i
$832$		0			0
$833$	3.51714	+	6.09186i	0.121862	+	0.211070i
$834$		0			0
$835$	1.01071	−	1.75060i	0.0349771	−	0.0605821i
$836$		0			0
$837$	−27.4982	+	7.24538i	−0.950476	+	0.250437i
$838$		0			0
$839$	−19.8649	+	34.4070i	−0.685811	+	1.18786i	0.287370	+	0.957820i	$0.407219\pi$
$839$	−19.8649	+	34.4070i	−0.685811	+	1.18786i	−0.973181	+	0.230040i	$0.926114\pi$
$840$		0			0
$841$	3.57581	+	6.19348i	0.123304	+	0.213568i
$842$		0			0
$843$	−2.85228	+	32.0881i	−0.0982377	+	1.10517i
$844$		0			0
$845$	−1.94947			−0.0670638
$846$		0			0
$847$	4.04160			0.138871
$848$		0			0
$849$	23.5314	+	16.5257i	0.807597	+	0.567160i
$850$		0			0
$851$	0.839334	+	1.45377i	0.0287720	+	0.0498345i
$852$		0			0
$853$	2.26964	−	3.93113i	0.0777110	−	0.134599i	−0.824551	−	0.565788i	$-0.808572\pi$
$853$	2.26964	−	3.93113i	0.0777110	−	0.134599i	0.902262	+	0.431188i	$0.141906\pi$
$854$		0			0
$855$	−2.01590	−	0.361237i	−0.0689422	−	0.0123540i
$856$		0			0
$857$	−1.41586	+	2.45234i	−0.0483648	+	0.0837702i	−0.889194	−	0.457530i	$-0.848734\pi$
$857$	−1.41586	+	2.45234i	−0.0483648	+	0.0837702i	0.840830	+	0.541300i	$0.182068\pi$
$858$		0			0
$859$	−11.6443	−	20.1684i	−0.397297	−	0.688138i	0.596095	−	0.802914i	$-0.296718\pi$
$859$	−11.6443	−	20.1684i	−0.397297	−	0.688138i	−0.993391	+	0.114776i	$0.963385\pi$
$860$		0			0
$861$	−2.67039	+	1.24071i	−0.0910065	+	0.0422832i
$862$		0			0
$863$	0.111891			0.00380882			0.00190441	−	0.999998i	$-0.499394\pi$
$863$	0.111891			0.00380882			0.00190441	+	0.999998i	$0.499394\pi$
$864$		0			0
$865$	−4.15586			−0.141304
$866$		0			0
$867$	−25.0160	+	11.6229i	−0.849588	+	0.394733i
$868$		0			0
$869$	−9.34196	−	16.1808i	−0.316904	−	0.548894i
$870$		0			0
$871$	−11.9583	+	20.7124i	−0.405191	+	0.701811i
$872$		0			0
$873$	4.51029	+	12.4999i	0.152650	+	0.423058i
$874$		0			0
$875$	−0.531882	+	0.921248i	−0.0179809	+	0.0311439i
$876$		0			0
$877$	−13.1933	−	22.8515i	−0.445506	−	0.771639i	0.552581	−	0.833459i	$-0.313643\pi$
$877$	−13.1933	−	22.8515i	−0.445506	−	0.771639i	−0.998087	+	0.0618200i	$0.980310\pi$
$878$		0			0
$879$	−17.9653	−	12.6167i	−0.605956	−	0.425551i
$880$		0			0
$881$	−46.5296			−1.56762			−0.783812	−	0.620999i	$-0.786727\pi$
$881$	−46.5296			−1.56762			−0.783812	+	0.620999i	$0.786727\pi$
$882$		0			0
$883$	−26.7129			−0.898959			−0.449480	−	0.893291i	$-0.648391\pi$
$883$	−26.7129			−0.898959			−0.449480	+	0.893291i	$0.648391\pi$
$884$		0			0
$885$	−0.193024	+	2.17152i	−0.00648844	+	0.0729948i
$886$		0			0
$887$	−20.6389	−	35.7476i	−0.692986	−	1.20029i	−0.970855	−	0.239668i	$-0.922961\pi$
$887$	−20.6389	−	35.7476i	−0.692986	−	1.20029i	0.277869	−	0.960619i	$-0.410372\pi$
$888$		0			0
$889$	−3.82338	+	6.62229i	−0.128232	+	0.222105i
$890$		0			0
$891$	−12.6434	−	4.68155i	−0.423568	−	0.156838i
$892$		0			0
$893$	15.9360	−	27.6020i	0.533280	−	0.923667i
$894$		0			0
$895$	0.772240	+	1.33756i	0.0258131	+	0.0447097i
$896$		0			0
$897$	−0.239660	+	2.69617i	−0.00800203	+	0.0900226i
$898$		0			0
$899$	25.5804			0.853153
$900$		0			0
$901$	−10.4090			−0.346774
$902$		0			0
$903$	−3.16623	−	2.22358i	−0.105366	−	0.0739962i
$904$		0			0
$905$	−2.21415	−	3.83501i	−0.0736007	−	0.127480i
$906$		0			0
$907$	9.75080	−	16.8889i	0.323770	−	0.560786i	−0.657493	−	0.753461i	$-0.728383\pi$
$907$	9.75080	−	16.8889i	0.323770	−	0.560786i	0.981263	+	0.192675i	$0.0617163\pi$
$908$		0			0
$909$	15.2204	+	42.1821i	0.504828	+	1.39909i
$910$		0			0
$911$	3.88772	−	6.73373i	0.128806	−	0.223098i	−0.794408	−	0.607384i	$-0.792219\pi$
$911$	3.88772	−	6.73373i	0.128806	−	0.223098i	0.923214	+	0.384286i	$0.125552\pi$
$912$		0			0
$913$	5.43262	+	9.40957i	0.179793	+	0.311411i
$914$		0			0
$915$	4.99730	−	2.32183i	0.165206	−	0.0767574i
$916$		0			0
$917$	1.32129			0.0436329
$918$		0			0
$919$	44.9999			1.48441			0.742205	−	0.670172i	$-0.233780\pi$
$919$	44.9999			1.48441			0.742205	+	0.670172i	$0.233780\pi$
$920$		0			0
$921$	−24.2054	+	11.2462i	−0.797595	+	0.370576i
$922$		0			0
$923$	14.2353	+	24.6562i	0.468559	+	0.811569i
$924$		0			0
$925$	5.68923	−	9.85403i	0.187061	−	0.323999i
$926$		0			0
$927$	−0.183272	−	0.0328413i	−0.00601945	−	0.00107865i
$928$		0			0
$929$	−1.77838	+	3.08024i	−0.0583467	+	0.101059i	−0.893723	−	0.448618i	$-0.851916\pi$
$929$	−1.77838	+	3.08024i	−0.0583467	+	0.101059i	0.835377	+	0.549678i	$0.185250\pi$
$930$		0			0
$931$	9.99823	+	17.3174i	0.327679	+	0.567556i
$932$		0			0
$933$	−36.1963	−	25.4199i	−1.18501	−	0.832211i
$934$		0			0
$935$	−0.359747			−0.0117650
$936$		0			0
$937$	−24.3496			−0.795467			−0.397734	−	0.917501i	$-0.630203\pi$
$937$	−24.3496			−0.795467			−0.397734	+	0.917501i	$0.630203\pi$
$938$		0			0
$939$	2.80128	−	31.5144i	0.0914164	−	1.02843i
$940$		0			0
$941$	−8.01758	−	13.8869i	−0.261366	−	0.452699i	0.705239	−	0.708969i	$-0.250840\pi$
$941$	−8.01758	−	13.8869i	−0.261366	−	0.452699i	−0.966605	+	0.256271i	$0.917506\pi$
$942$		0			0
$943$	1.34381	−	2.32755i	0.0437604	−	0.0757953i
$944$		0			0
$945$	−0.146071	+	0.536192i	−0.00475168	+	0.0174423i
$946$		0			0
$947$	−24.6766	+	42.7412i	−0.801882	+	1.38890i	0.116493	+	0.993191i	$0.462835\pi$
$947$	−24.6766	+	42.7412i	−0.801882	+	1.38890i	−0.918376	+	0.395710i	$0.870499\pi$
$948$		0			0
$949$	4.54309	+	7.86887i	0.147475	+	0.255434i
$950$		0			0
$951$	−1.60156	+	18.0175i	−0.0519342	+	0.584258i
$952$		0			0
$953$	43.4970			1.40900			0.704502	−	0.709702i	$-0.251170\pi$
$953$	43.4970			1.40900			0.704502	+	0.709702i	$0.251170\pi$
$954$		0			0
$955$	−0.481699			−0.0155874
$956$		0			0
$957$	9.92503	+	6.97015i	0.320831	+	0.225313i
$958$		0			0
$959$	3.82031	+	6.61697i	0.123364	+	0.213673i
$960$		0			0
$961$	0.525082	−	0.909469i	0.0169381	−	0.0293377i
$962$		0			0
$963$	−23.0810	+	27.3521i	−0.743773	+	0.881408i
$964$		0			0
$965$	2.36287	−	4.09261i	0.0760635	−	0.131746i
$966$		0			0
$967$	3.36451	+	5.82750i	0.108195	+	0.187400i	0.915039	−	0.403365i	$-0.132159\pi$
$967$	3.36451	+	5.82750i	0.108195	+	0.187400i	−0.806844	+	0.590765i	$0.798826\pi$
$968$		0			0
$969$	4.79669	−	2.22862i	0.154092	−	0.0715937i
$970$		0			0
$971$	−16.9519			−0.544013			−0.272007	−	0.962295i	$-0.587687\pi$
$971$	−16.9519			−0.544013			−0.272007	+	0.962295i	$0.587687\pi$
$972$		0			0
$973$	3.40230			0.109073
$974$		0			0
$975$	16.6392	−	7.73085i	0.532880	−	0.247585i
$976$		0			0
$977$	19.4250	+	33.6451i	0.621461	+	1.07640i	0.989214	+	0.146479i	$0.0467939\pi$
$977$	19.4250	+	33.6451i	0.621461	+	1.07640i	−0.367753	+	0.929924i	$0.619873\pi$
$978$		0			0
$979$	−8.88536	+	15.3899i	−0.283977	+	0.491863i
$980$		0			0
$981$	19.6043	−	23.2321i	0.625917	−	0.741743i
$982$		0			0
$983$	−22.4036	+	38.8041i	−0.714563	+	1.23766i	0.248565	+	0.968615i	$0.420041\pi$
$983$	−22.4036	+	38.8041i	−0.714563	+	1.23766i	−0.963128	+	0.269044i	$0.913292\pi$
$984$		0			0
$985$	1.91685	+	3.32008i	0.0610759	+	0.105787i
$986$		0			0
$987$	−7.07760	−	4.97046i	−0.225282	−	0.158211i
$988$		0			0
$989$	3.53144			0.112293
$990$		0			0
$991$	−21.1824			−0.672882			−0.336441	−	0.941705i	$-0.609223\pi$
$991$	−21.1824			−0.672882			−0.336441	+	0.941705i	$0.609223\pi$
$992$		0			0
$993$	−0.729626	+	8.20827i	−0.0231540	+	0.260481i
$994$		0			0
$995$	2.46696	+	4.27291i	0.0782080	+	0.135460i
$996$		0			0
$997$	6.90517	−	11.9601i	0.218689	−	0.378780i	−0.735719	−	0.677287i	$-0.763155\pi$
$997$	6.90517	−	11.9601i	0.218689	−	0.378780i	0.954407	+	0.298507i	$0.0964887\pi$
$998$		0			0
$999$	3.14182	−	11.5329i	0.0994027	−	0.364884i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.i.f.385.5	yes	10
3.2	odd	2		3456.2.i.g.1153.3		10
4.3	odd	2		1152.2.i.g.385.1	yes	10
8.3	odd	2		1152.2.i.e.385.5	✓	10
8.5	even	2		1152.2.i.h.385.1	yes	10
9.4	even	3	inner	1152.2.i.f.769.5	yes	10
9.5	odd	6		3456.2.i.g.2305.3		10
12.11	even	2		3456.2.i.f.1153.3		10
24.5	odd	2		3456.2.i.h.1153.3		10
24.11	even	2		3456.2.i.e.1153.3		10
36.23	even	6		3456.2.i.f.2305.3		10
36.31	odd	6		1152.2.i.g.769.1	yes	10
72.5	odd	6		3456.2.i.h.2305.3		10
72.13	even	6		1152.2.i.h.769.1	yes	10
72.59	even	6		3456.2.i.e.2305.3		10
72.67	odd	6		1152.2.i.e.769.5	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.i.e.385.5	✓	10	8.3	odd	2
1152.2.i.e.769.5	yes	10	72.67	odd	6
1152.2.i.f.385.5	yes	10	1.1	even	1	trivial
1152.2.i.f.769.5	yes	10	9.4	even	3	inner
1152.2.i.g.385.1	yes	10	4.3	odd	2
1152.2.i.g.769.1	yes	10	36.31	odd	6
1152.2.i.h.385.1	yes	10	8.5	even	2
1152.2.i.h.769.1	yes	10	72.13	even	6
3456.2.i.e.1153.3		10	24.11	even	2
3456.2.i.e.2305.3		10	72.59	even	6
3456.2.i.f.1153.3		10	12.11	even	2
3456.2.i.f.2305.3		10	36.23	even	6
3456.2.i.g.1153.3		10	3.2	odd	2
3456.2.i.g.2305.3		10	9.5	odd	6
3456.2.i.h.1153.3		10	24.5	odd	2
3456.2.i.h.2305.3		10	72.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.57079 - 0.729814i) q^{3} +(-0.115851 - 0.200661i) q^{5} +(0.230793 - 0.399745i) q^{7} +(1.93474 - 2.29277i) q^{9} +O(q^{10})\)	\(q+(1.57079 - 0.729814i) q^{3} +(-0.115851 - 0.200661i) q^{5} +(0.230793 - 0.399745i) q^{7} +(1.93474 - 2.29277i) q^{9} +(0.749014 - 1.29733i) q^{11} +(1.07079 + 1.85466i) q^{13} +(-0.328423 - 0.230645i) q^{15} +1.03644 q^{17} +2.94631 q^{19} +(0.0707868 - 0.796350i) q^{21} +(0.364866 + 0.631966i) q^{23} +(2.47316 - 4.28363i) q^{25} +(1.36578 - 5.01345i) q^{27} +(-2.33711 + 4.04800i) q^{29} +(-2.73632 - 4.73945i) q^{31} +(0.229731 - 2.58447i) q^{33} -0.106951 q^{35} +2.30039 q^{37} +(3.03553 + 2.13180i) q^{39} +(-1.84151 - 3.18959i) q^{41} +(2.41968 - 4.19101i) q^{43} +(-0.684210 - 0.122606i) q^{45} +(5.40881 - 9.36833i) q^{47} +(3.39347 + 5.87766i) q^{49} +(1.62803 - 0.756411i) q^{51} -10.0430 q^{53} -0.347097 q^{55} +(4.62803 - 2.15026i) q^{57} +(-2.71613 - 4.70447i) q^{59} +(-6.86526 + 11.8910i) q^{61} +(-0.469996 - 1.30256i) q^{63} +(0.248104 - 0.429729i) q^{65} +(5.58388 + 9.67156i) q^{67} +(1.03434 + 0.726400i) q^{69} +13.2942 q^{71} +4.24276 q^{73} +(0.758546 - 8.53362i) q^{75} +(-0.345734 - 0.598829i) q^{77} +(6.23617 - 10.8014i) q^{79} +(-1.51354 - 8.87182i) q^{81} +(-3.62651 + 6.28130i) q^{83} +(-0.120073 - 0.207973i) q^{85} +(-0.716820 + 8.06420i) q^{87} -11.8627 q^{89} +0.988520 q^{91} +(-7.75710 - 5.44766i) q^{93} +(-0.341335 - 0.591209i) q^{95} +(-2.21479 + 3.83613i) q^{97} +(-1.52532 - 4.22731i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{3} + 4 q^{7} - q^{9}+O(q^{10}) \) 10 * q - q^3 + 4 * q^7 - q^9	\( 10 q - q^{3} + 4 q^{7} - q^{9} + q^{11} - 6 q^{13} - 12 q^{15} - 6 q^{17} - 18 q^{19} - 16 q^{21} - 4 q^{23} + q^{25} + 2 q^{27} + 4 q^{29} + 8 q^{31} - 13 q^{33} + 24 q^{35} + 20 q^{37} + 18 q^{39} - 5 q^{41} + 13 q^{43} + 12 q^{45} + 6 q^{47} + 3 q^{49} - 3 q^{51} - 12 q^{55} + 27 q^{57} + 13 q^{59} - 10 q^{61} + 20 q^{63} + 17 q^{67} + 10 q^{69} - 8 q^{71} - 34 q^{73} + 29 q^{75} - 8 q^{77} + 6 q^{79} - q^{81} - 12 q^{83} - 18 q^{85} - 10 q^{87} + 44 q^{89} - 36 q^{91} - 26 q^{93} + 6 q^{95} + 27 q^{97} - 34 q^{99}+O(q^{100}) \) 10 * q - q^3 + 4 * q^7 - q^9 + q^11 - 6 * q^13 - 12 * q^15 - 6 * q^17 - 18 * q^19 - 16 * q^21 - 4 * q^23 + q^25 + 2 * q^27 + 4 * q^29 + 8 * q^31 - 13 * q^33 + 24 * q^35 + 20 * q^37 + 18 * q^39 - 5 * q^41 + 13 * q^43 + 12 * q^45 + 6 * q^47 + 3 * q^49 - 3 * q^51 - 12 * q^55 + 27 * q^57 + 13 * q^59 - 10 * q^61 + 20 * q^63 + 17 * q^67 + 10 * q^69 - 8 * q^71 - 34 * q^73 + 29 * q^75 - 8 * q^77 + 6 * q^79 - q^81 - 12 * q^83 - 18 * q^85 - 10 * q^87 + 44 * q^89 - 36 * q^91 - 26 * q^93 + 6 * q^95 + 27 * q^97 - 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more