LMFDB - Embedded newform 960.2.s.c.241.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(241,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("960.241");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.s (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{18} - 4 x^{17} + 7 x^{16} + 16 x^{15} + 6 x^{14} - 36 x^{13} - 42 x^{12} + 40 x^{11} + \cdots + 1024 $ x^20 - 2x^18 - 4x^17 + 7x^16 + 16x^15 + 6x^14 - 36x^13 - 42x^12 + 40x^11 + 136x^10 + 80x^9 - 168x^8 - 288x^7 + 96x^6 + 512x^5 + 448x^4 - 512x^3 - 512*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{20} $
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			241.2
Root			$1.15787 - 0.811989i$ of defining polynomial
Character	$\chi$	$=$	960.241
Dual form			960.2.s.c.721.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{3} +(0.707107 + 0.707107i) q^{5} -2.18060i q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{3} +(0.707107 + 0.707107i) q^{5} -2.18060i q^{7} -1.00000i q^{9} +(0.00889637 + 0.00889637i) q^{11} +(1.72965 - 1.72965i) q^{13} -1.00000 q^{15} -5.54943 q^{17} +(4.94702 - 4.94702i) q^{19} +(1.54192 + 1.54192i) q^{21} -3.01309i q^{23} +1.00000i q^{25} +(0.707107 + 0.707107i) q^{27} +(3.20471 - 3.20471i) q^{29} -3.58009 q^{31} -0.0125814 q^{33} +(1.54192 - 1.54192i) q^{35} +(4.97761 + 4.97761i) q^{37} +2.44610i q^{39} -3.76487i q^{41} +(-6.81210 - 6.81210i) q^{43} +(0.707107 - 0.707107i) q^{45} +10.0800 q^{47} +2.24499 q^{49} +(3.92404 - 3.92404i) q^{51} +(-0.932644 - 0.932644i) q^{53} +0.0125814i q^{55} +6.99615i q^{57} +(4.60522 + 4.60522i) q^{59} +(4.17149 - 4.17149i) q^{61} -2.18060 q^{63} +2.44610 q^{65} +(11.0105 - 11.0105i) q^{67} +(2.13057 + 2.13057i) q^{69} +12.1092i q^{71} -7.12981i q^{73} +(-0.707107 - 0.707107i) q^{75} +(0.0193994 - 0.0193994i) q^{77} +3.41789 q^{79} -1.00000 q^{81} +(-5.31631 + 5.31631i) q^{83} +(-3.92404 - 3.92404i) q^{85} +4.53214i q^{87} -5.06405i q^{89} +(-3.77168 - 3.77168i) q^{91} +(2.53151 - 2.53151i) q^{93} +6.99615 q^{95} -10.3646 q^{97} +(0.00889637 - 0.00889637i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q+O(q^{10}) $ 20 * q	$ 20 q - 8 q^{11} - 20 q^{15} - 24 q^{17} + 4 q^{19} + 16 q^{29} + 16 q^{33} + 16 q^{37} + 8 q^{43} - 52 q^{49} - 4 q^{51} - 16 q^{53} + 16 q^{59} - 4 q^{61} + 8 q^{63} + 8 q^{67} - 4 q^{69} - 40 q^{77} - 56 q^{79} - 20 q^{81} + 48 q^{83} + 4 q^{85} + 8 q^{91} + 16 q^{93} + 56 q^{97} - 8 q^{99}+O(q^{100}) $ 20 * q - 8 * q^11 - 20 * q^15 - 24 * q^17 + 4 * q^19 + 16 * q^29 + 16 * q^33 + 16 * q^37 + 8 * q^43 - 52 * q^49 - 4 * q^51 - 16 * q^53 + 16 * q^59 - 4 * q^61 + 8 * q^63 + 8 * q^67 - 4 * q^69 - 40 * q^77 - 56 * q^79 - 20 * q^81 + 48 * q^83 + 4 * q^85 + 8 * q^91 + 16 * q^93 + 56 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		0			0
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$		0			0
$7$		−	2.18060i		−	0.824189i	−0.911141	−	0.412094i	$-0.864797\pi$
$7$		−	2.18060i		−	0.824189i	0.911141	−	0.412094i	$-0.135203\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	0.00889637	+	0.00889637i	0.00268236	+	0.00268236i	0.708447	−	0.705764i	$-0.249396\pi$
$11$	0.00889637	+	0.00889637i	0.00268236	+	0.00268236i	−0.705764	+	0.708447i	$0.749396\pi$
$12$		0			0
$13$	1.72965	−	1.72965i	0.479719	−	0.479719i	−0.425323	−	0.905042i	$-0.639839\pi$
$13$	1.72965	−	1.72965i	0.479719	−	0.479719i	0.905042	+	0.425323i	$0.139839\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	−5.54943			−1.34593			−0.672967	−	0.739673i	$-0.734980\pi$
$17$	−5.54943			−1.34593			−0.672967	+	0.739673i	$0.734980\pi$
$18$		0			0
$19$	4.94702	−	4.94702i	1.13493	−	1.13493i	0.145579	−	0.989347i	$-0.453496\pi$
$19$	4.94702	−	4.94702i	1.13493	−	1.13493i	0.989347	−	0.145579i	$-0.0465044\pi$
$20$		0			0
$21$	1.54192	+	1.54192i	0.336474	+	0.336474i
$22$		0			0
$23$		−	3.01309i		−	0.628272i	−0.949378	−	0.314136i	$-0.898285\pi$
$23$		−	3.01309i		−	0.628272i	0.949378	−	0.314136i	$-0.101715\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$	3.20471	−	3.20471i	0.595099	−	0.595099i	−0.343905	−	0.939004i	$-0.611750\pi$
$29$	3.20471	−	3.20471i	0.595099	−	0.595099i	0.939004	+	0.343905i	$0.111750\pi$
$30$		0			0
$31$	−3.58009			−0.643004			−0.321502	−	0.946909i	$-0.604188\pi$
$31$	−3.58009			−0.643004			−0.321502	+	0.946909i	$0.604188\pi$
$32$		0			0
$33$	−0.0125814			−0.00219013
$34$		0			0
$35$	1.54192	−	1.54192i	0.260631	−	0.260631i
$36$		0			0
$37$	4.97761	+	4.97761i	0.818314	+	0.818314i	0.985864	−	0.167550i	$-0.0535856\pi$
$37$	4.97761	+	4.97761i	0.818314	+	0.818314i	−0.167550	+	0.985864i	$0.553586\pi$
$38$		0			0
$39$			2.44610i			0.391689i
$40$		0			0
$41$		−	3.76487i		−	0.587975i	−0.955809	−	0.293987i	$-0.905018\pi$
$41$		−	3.76487i		−	0.587975i	0.955809	−	0.293987i	$-0.0949823\pi$
$42$		0			0
$43$	−6.81210	−	6.81210i	−1.03884	−	1.03884i	−0.999215	−	0.0396204i	$-0.987385\pi$
$43$	−6.81210	−	6.81210i	−1.03884	−	1.03884i	−0.0396204	−	0.999215i	$-0.512615\pi$
$44$		0			0
$45$	0.707107	−	0.707107i	0.105409	−	0.105409i
$46$		0			0
$47$	10.0800			1.47032			0.735158	−	0.677896i	$-0.237108\pi$
$47$	10.0800			1.47032			0.735158	+	0.677896i	$0.237108\pi$
$48$		0			0
$49$	2.24499			0.320713
$50$		0			0
$51$	3.92404	−	3.92404i	0.549475	−	0.549475i
$52$		0			0
$53$	−0.932644	−	0.932644i	−0.128108	−	0.128108i	0.640145	−	0.768254i	$-0.278874\pi$
$53$	−0.932644	−	0.932644i	−0.128108	−	0.128108i	−0.768254	+	0.640145i	$0.778874\pi$
$54$		0			0
$55$			0.0125814i			0.00169647i
$56$		0			0
$57$			6.99615i			0.926663i
$58$		0			0
$59$	4.60522	+	4.60522i	0.599548	+	0.599548i	0.940192	−	0.340644i	$-0.110645\pi$
$59$	4.60522	+	4.60522i	0.599548	+	0.599548i	−0.340644	+	0.940192i	$0.610645\pi$
$60$		0			0
$61$	4.17149	−	4.17149i	0.534105	−	0.534105i	−0.387686	−	0.921791i	$-0.626726\pi$
$61$	4.17149	−	4.17149i	0.534105	−	0.534105i	0.921791	+	0.387686i	$0.126726\pi$
$62$		0			0
$63$	−2.18060			−0.274730
$64$		0			0
$65$	2.44610			0.303401
$66$		0			0
$67$	11.0105	−	11.0105i	1.34515	−	1.34515i	0.454293	−	0.890852i	$-0.349892\pi$
$67$	11.0105	−	11.0105i	1.34515	−	1.34515i	0.890852	−	0.454293i	$-0.150108\pi$
$68$		0			0
$69$	2.13057	+	2.13057i	0.256491	+	0.256491i
$70$		0			0
$71$			12.1092i			1.43710i	0.695475	+	0.718550i	$0.255194\pi$
$71$			12.1092i			1.43710i	−0.695475	+	0.718550i	$0.744806\pi$
$72$		0			0
$73$		−	7.12981i		−	0.834481i	−0.908796	−	0.417240i	$-0.862997\pi$
$73$		−	7.12981i		−	0.834481i	0.908796	−	0.417240i	$-0.137003\pi$
$74$		0			0
$75$	−0.707107	−	0.707107i	−0.0816497	−	0.0816497i
$76$		0			0
$77$	0.0193994	−	0.0193994i	0.00221077	−	0.00221077i
$78$		0			0
$79$	3.41789			0.384543			0.192272	−	0.981342i	$-0.438415\pi$
$79$	3.41789			0.384543			0.192272	+	0.981342i	$0.438415\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−5.31631	+	5.31631i	−0.583541	+	0.583541i	−0.935875	−	0.352333i	$-0.885388\pi$
$83$	−5.31631	+	5.31631i	−0.583541	+	0.583541i	0.352333	+	0.935875i	$0.385388\pi$
$84$		0			0
$85$	−3.92404	−	3.92404i	−0.425622	−	0.425622i
$86$		0			0
$87$			4.53214i			0.485896i
$88$		0			0
$89$		−	5.06405i		−	0.536788i	−0.963309	−	0.268394i	$-0.913507\pi$
$89$		−	5.06405i		−	0.536788i	0.963309	−	0.268394i	$-0.0864929\pi$
$90$		0			0
$91$	−3.77168	−	3.77168i	−0.395379	−	0.395379i
$92$		0			0
$93$	2.53151	−	2.53151i	0.262505	−	0.262505i
$94$		0			0
$95$	6.99615			0.717790
$96$		0			0
$97$	−10.3646			−1.05237			−0.526184	−	0.850371i	$-0.676378\pi$
$97$	−10.3646			−1.05237			−0.526184	+	0.850371i	$0.676378\pi$
$98$		0			0
$99$	0.00889637	−	0.00889637i	0.000894119	−	0.000894119i
$100$		0			0
$101$	9.96414	+	9.96414i	0.991469	+	0.991469i	0.999964	−	0.00849458i	$-0.00270394\pi$
$101$	9.96414	+	9.96414i	0.991469	+	0.991469i	−0.00849458	+	0.999964i	$0.502704\pi$
$102$		0			0
$103$			2.25154i			0.221851i	0.993829	+	0.110926i	$0.0353815\pi$
$103$			2.25154i			0.221851i	−0.993829	+	0.110926i	$0.964618\pi$
$104$		0			0
$105$			2.18060i			0.212805i
$106$		0			0
$107$	−2.51098	−	2.51098i	−0.242746	−	0.242746i	0.575239	−	0.817985i	$-0.304909\pi$
$107$	−2.51098	−	2.51098i	−0.242746	−	0.242746i	−0.817985	+	0.575239i	$0.804909\pi$
$108$		0			0
$109$	12.0668	−	12.0668i	1.15579	−	1.15579i	0.170420	−	0.985372i	$-0.445488\pi$
$109$	12.0668	−	12.0668i	1.15579	−	1.15579i	0.985372	−	0.170420i	$-0.0545124\pi$
$110$		0			0
$111$	−7.03940			−0.668150
$112$		0			0
$113$	−19.7954			−1.86219			−0.931097	−	0.364772i	$-0.881147\pi$
$113$	−19.7954			−1.86219			−0.931097	+	0.364772i	$0.881147\pi$
$114$		0			0
$115$	2.13057	−	2.13057i	0.198677	−	0.198677i
$116$		0			0
$117$	−1.72965	−	1.72965i	−0.159906	−	0.159906i
$118$		0			0
$119$			12.1011i			1.10930i
$120$		0			0
$121$		−	10.9998i		−	0.999986i
$122$		0			0
$123$	2.66217	+	2.66217i	0.240040	+	0.240040i
$124$		0			0
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$		0			0
$127$	−14.3984			−1.27765			−0.638825	−	0.769352i	$-0.720579\pi$
$127$	−14.3984			−1.27765			−0.638825	+	0.769352i	$0.720579\pi$
$128$		0			0
$129$	9.63376			0.848205
$130$		0			0
$131$	0.574754	−	0.574754i	0.0502165	−	0.0502165i	−0.681553	−	0.731769i	$-0.738695\pi$
$131$	0.574754	−	0.574754i	0.0502165	−	0.0502165i	0.731769	+	0.681553i	$0.238695\pi$
$132$		0			0
$133$	−10.7875	−	10.7875i	−0.935393	−	0.935393i
$134$		0			0
$135$			1.00000i			0.0860663i
$136$		0			0
$137$		−	16.0077i		−	1.36763i	−0.729654	−	0.683817i	$-0.760319\pi$
$137$		−	16.0077i		−	1.36763i	0.729654	−	0.683817i	$-0.239681\pi$
$138$		0			0
$139$	1.52424	+	1.52424i	0.129284	+	0.129284i	0.768788	−	0.639504i	$-0.220860\pi$
$139$	1.52424	+	1.52424i	0.129284	+	0.129284i	−0.639504	+	0.768788i	$0.720860\pi$
$140$		0			0
$141$	−7.12762	+	7.12762i	−0.600254	+	0.600254i
$142$		0			0
$143$	0.0307753			0.00257356
$144$		0			0
$145$	4.53214			0.376374
$146$		0			0
$147$	−1.58745	+	1.58745i	−0.130931	+	0.130931i
$148$		0			0
$149$	12.1410	+	12.1410i	0.994629	+	0.994629i	0.999986	−	0.00535669i	$-0.00170510\pi$
$149$	12.1410	+	12.1410i	0.994629	+	0.994629i	−0.00535669	+	0.999986i	$0.501705\pi$
$150$		0			0
$151$			12.7940i			1.04116i	0.853813	+	0.520580i	$0.174284\pi$
$151$			12.7940i			1.04116i	−0.853813	+	0.520580i	$0.825716\pi$
$152$		0			0
$153$			5.54943i			0.448645i
$154$		0			0
$155$	−2.53151	−	2.53151i	−0.203336	−	0.203336i
$156$		0			0
$157$	−10.3333	+	10.3333i	−0.824686	+	0.824686i	−0.986776	−	0.162090i	$-0.948177\pi$
$157$	−10.3333	+	10.3333i	−0.824686	+	0.824686i	0.162090	+	0.986776i	$0.448177\pi$
$158$		0			0
$159$	1.31896			0.104600
$160$		0			0
$161$	−6.57033			−0.517814
$162$		0			0
$163$	−13.4362	+	13.4362i	−1.05241	+	1.05241i	−0.0538580	+	0.998549i	$0.517152\pi$
$163$	−13.4362	+	13.4362i	−1.05241	+	1.05241i	−0.998549	+	0.0538580i	$0.982848\pi$
$164$		0			0
$165$	−0.00889637	−	0.00889637i	−0.000692581	−	0.000692581i
$166$		0			0
$167$		−	5.08389i		−	0.393403i	−0.980463	−	0.196702i	$-0.936977\pi$
$167$		−	5.08389i		−	0.393403i	0.980463	−	0.196702i	$-0.0630230\pi$
$168$		0			0
$169$			7.01660i			0.539739i
$170$		0			0
$171$	−4.94702	−	4.94702i	−0.378308	−	0.378308i
$172$		0			0
$173$	−10.8821	+	10.8821i	−0.827350	+	0.827350i	−0.987150	−	0.159799i	$-0.948915\pi$
$173$	−10.8821	+	10.8821i	−0.827350	+	0.827350i	0.159799	+	0.987150i	$0.448915\pi$
$174$		0			0
$175$	2.18060			0.164838
$176$		0			0
$177$	−6.51276			−0.489529
$178$		0			0
$179$	−11.1719	+	11.1719i	−0.835028	+	0.835028i	−0.988200	−	0.153172i	$-0.951051\pi$
$179$	−11.1719	+	11.1719i	−0.835028	+	0.835028i	0.153172	+	0.988200i	$0.451051\pi$
$180$		0			0
$181$	−10.1479	−	10.1479i	−0.754290	−	0.754290i	0.220987	−	0.975277i	$-0.429072\pi$
$181$	−10.1479	−	10.1479i	−0.754290	−	0.754290i	−0.975277	+	0.220987i	$0.929072\pi$
$182$		0			0
$183$			5.89938i			0.436095i
$184$		0			0
$185$			7.03940i			0.517547i
$186$		0			0
$187$	−0.0493697	−	0.0493697i	−0.00361027	−	0.00361027i
$188$		0			0
$189$	1.54192	−	1.54192i	0.112158	−	0.112158i
$190$		0			0
$191$	−13.3716			−0.967532			−0.483766	−	0.875197i	$-0.660731\pi$
$191$	−13.3716			−0.967532			−0.483766	+	0.875197i	$0.660731\pi$
$192$		0			0
$193$	8.32925			0.599553			0.299776	−	0.954009i	$-0.403088\pi$
$193$	8.32925			0.599553			0.299776	+	0.954009i	$0.403088\pi$
$194$		0			0
$195$	−1.72965	+	1.72965i	−0.123863	+	0.123863i
$196$		0			0
$197$	13.1995	+	13.1995i	0.940427	+	0.940427i	0.998323	−	0.0578960i	$-0.0184392\pi$
$197$	13.1995	+	13.1995i	0.940427	+	0.940427i	−0.0578960	+	0.998323i	$0.518439\pi$
$198$		0			0
$199$		−	3.66713i		−	0.259956i	−0.991517	−	0.129978i	$-0.958509\pi$
$199$		−	3.66713i		−	0.259956i	0.991517	−	0.129978i	$-0.0414906\pi$
$200$		0			0
$201$			15.5712i			1.09831i
$202$		0			0
$203$	−6.98817	−	6.98817i	−0.490474	−	0.490474i
$204$		0			0
$205$	2.66217	−	2.66217i	0.185934	−	0.185934i
$206$		0			0
$207$	−3.01309			−0.209424
$208$		0			0
$209$	0.0880211			0.00608855
$210$		0			0
$211$	12.6423	−	12.6423i	0.870332	−	0.870332i	−0.122176	−	0.992508i	$-0.538987\pi$
$211$	12.6423	−	12.6423i	0.870332	−	0.870332i	0.992508	+	0.122176i	$0.0389873\pi$
$212$		0			0
$213$	−8.56251	−	8.56251i	−0.586694	−	0.586694i
$214$		0			0
$215$		−	9.63376i		−	0.657017i
$216$		0			0
$217$			7.80675i			0.529956i
$218$		0			0
$219$	5.04154	+	5.04154i	0.340675	+	0.340675i
$220$		0			0
$221$	−9.59858	+	9.59858i	−0.645670	+	0.645670i
$222$		0			0
$223$	5.37431			0.359891			0.179945	−	0.983677i	$-0.442408\pi$
$223$	5.37431			0.359891			0.179945	+	0.983677i	$0.442408\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−1.92306	+	1.92306i	−0.127638	+	0.127638i	−0.768040	−	0.640402i	$-0.778768\pi$
$227$	−1.92306	+	1.92306i	−0.127638	+	0.127638i	0.640402	+	0.768040i	$0.278768\pi$
$228$		0			0
$229$	5.08104	+	5.08104i	0.335765	+	0.335765i	0.854771	−	0.519006i	$-0.173698\pi$
$229$	5.08104	+	5.08104i	0.335765	+	0.335765i	−0.519006	+	0.854771i	$0.673698\pi$
$230$		0			0
$231$			0.0274349i			0.00180508i
$232$		0			0
$233$			26.2417i			1.71915i	0.511011	+	0.859574i	$0.329271\pi$
$233$			26.2417i			1.71915i	−0.511011	+	0.859574i	$0.670729\pi$
$234$		0			0
$235$	7.12762	+	7.12762i	0.464955	+	0.464955i
$236$		0			0
$237$	−2.41682	+	2.41682i	−0.156989	+	0.156989i
$238$		0			0
$239$	7.40931			0.479268			0.239634	−	0.970863i	$-0.422973\pi$
$239$	7.40931			0.479268			0.239634	+	0.970863i	$0.422973\pi$
$240$		0			0
$241$	−19.6231			−1.26404			−0.632019	−	0.774953i	$-0.717773\pi$
$241$	−19.6231			−1.26404			−0.632019	+	0.774953i	$0.717773\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	1.58745	+	1.58745i	0.101418	+	0.101418i
$246$		0			0
$247$		−	17.1133i		−	1.08889i
$248$		0			0
$249$		−	7.51840i		−	0.476459i
$250$		0			0
$251$	−1.23610	−	1.23610i	−0.0780217	−	0.0780217i	0.667019	−	0.745041i	$-0.267570\pi$
$251$	−1.23610	−	1.23610i	−0.0780217	−	0.0780217i	−0.745041	+	0.667019i	$0.767570\pi$
$252$		0			0
$253$	0.0268055	−	0.0268055i	0.00168525	−	0.00168525i
$254$		0			0
$255$	5.54943			0.347519
$256$		0			0
$257$	3.01050			0.187790			0.0938948	−	0.995582i	$-0.470068\pi$
$257$	3.01050			0.187790			0.0938948	+	0.995582i	$0.470068\pi$
$258$		0			0
$259$	10.8542	−	10.8542i	0.674445	−	0.674445i
$260$		0			0
$261$	−3.20471	−	3.20471i	−0.198366	−	0.198366i
$262$		0			0
$263$		−	11.9000i		−	0.733788i	−0.930263	−	0.366894i	$-0.880421\pi$
$263$		−	11.9000i		−	0.733788i	0.930263	−	0.366894i	$-0.119579\pi$
$264$		0			0
$265$		−	1.31896i		−	0.0810229i
$266$		0			0
$267$	3.58082	+	3.58082i	0.219143	+	0.219143i
$268$		0			0
$269$	−15.4949	+	15.4949i	−0.944742	+	0.944742i	−0.998551	−	0.0538091i	$-0.982864\pi$
$269$	−15.4949	+	15.4949i	−0.944742	+	0.944742i	0.0538091	+	0.998551i	$0.482864\pi$
$270$		0			0
$271$	−7.30492			−0.443742			−0.221871	−	0.975076i	$-0.571216\pi$
$271$	−7.30492			−0.443742			−0.221871	+	0.975076i	$0.571216\pi$
$272$		0			0
$273$	5.33396			0.322826
$274$		0			0
$275$	−0.00889637	+	0.00889637i	−0.000536471	+	0.000536471i
$276$		0			0
$277$	2.23718	+	2.23718i	0.134419	+	0.134419i	0.771115	−	0.636696i	$-0.219699\pi$
$277$	2.23718	+	2.23718i	0.134419	+	0.134419i	−0.636696	+	0.771115i	$0.719699\pi$
$278$		0			0
$279$			3.58009i			0.214335i
$280$		0			0
$281$		−	4.85036i		−	0.289348i	−0.989479	−	0.144674i	$-0.953787\pi$
$281$		−	4.85036i		−	0.289348i	0.989479	−	0.144674i	$-0.0462134\pi$
$282$		0			0
$283$	−11.4295	−	11.4295i	−0.679414	−	0.679414i	0.280454	−	0.959867i	$-0.409515\pi$
$283$	−11.4295	−	11.4295i	−0.679414	−	0.679414i	−0.959867	+	0.280454i	$0.909515\pi$
$284$		0			0
$285$	−4.94702	+	4.94702i	−0.293036	+	0.293036i
$286$		0			0
$287$	−8.20968			−0.484602
$288$		0			0
$289$	13.7961			0.811537
$290$		0			0
$291$	7.32890	−	7.32890i	0.429627	−	0.429627i
$292$		0			0
$293$	−11.1686	−	11.1686i	−0.652475	−	0.652475i	0.301113	−	0.953588i	$-0.402642\pi$
$293$	−11.1686	−	11.1686i	−0.652475	−	0.652475i	−0.953588	+	0.301113i	$0.902642\pi$
$294$		0			0
$295$			6.51276i			0.379188i
$296$		0			0
$297$			0.0125814i			0.000730045i
$298$		0			0
$299$	−5.21159	−	5.21159i	−0.301394	−	0.301394i
$300$		0			0
$301$	−14.8544	+	14.8544i	−0.856196	+	0.856196i
$302$		0			0
$303$	−14.0914			−0.809531
$304$		0			0
$305$	5.89938			0.337798
$306$		0			0
$307$	−13.5366	+	13.5366i	−0.772575	+	0.772575i	−0.978556	−	0.205981i	$-0.933962\pi$
$307$	−13.5366	+	13.5366i	−0.772575	+	0.772575i	0.205981	+	0.978556i	$0.433962\pi$
$308$		0			0
$309$	−1.59208	−	1.59208i	−0.0905703	−	0.0905703i
$310$		0			0
$311$		−	16.4956i		−	0.935378i	−0.883893	−	0.467689i	$-0.845087\pi$
$311$		−	16.4956i		−	0.935378i	0.883893	−	0.467689i	$-0.154913\pi$
$312$		0			0
$313$			27.2549i			1.54054i	0.637719	+	0.770269i	$0.279878\pi$
$313$			27.2549i			1.54054i	−0.637719	+	0.770269i	$0.720122\pi$
$314$		0			0
$315$	−1.54192	−	1.54192i	−0.0868771	−	0.0868771i
$316$		0			0
$317$	23.2962	−	23.2962i	1.30845	−	1.30845i	0.385911	−	0.922536i	$-0.373887\pi$
$317$	23.2962	−	23.2962i	1.30845	−	1.30845i	0.922536	−	0.385911i	$-0.126113\pi$
$318$		0			0
$319$	0.0570205			0.00319253
$320$		0			0
$321$	3.55106			0.198201
$322$		0			0
$323$	−27.4531	+	27.4531i	−1.52753	+	1.52753i
$324$		0			0
$325$	1.72965	+	1.72965i	0.0959439	+	0.0959439i
$326$		0			0
$327$			17.0651i			0.943700i
$328$		0			0
$329$		−	21.9804i		−	1.21182i
$330$		0			0
$331$	15.9057	+	15.9057i	0.874257	+	0.874257i	0.992933	−	0.118676i	$-0.0378649\pi$
$331$	15.9057	+	15.9057i	0.874257	+	0.874257i	−0.118676	+	0.992933i	$0.537865\pi$
$332$		0			0
$333$	4.97761	−	4.97761i	0.272771	−	0.272771i
$334$		0			0
$335$	15.5712			0.850745
$336$		0			0
$337$	7.15503			0.389759			0.194880	−	0.980827i	$-0.437568\pi$
$337$	7.15503			0.389759			0.194880	+	0.980827i	$0.437568\pi$
$338$		0			0
$339$	13.9975	−	13.9975i	0.760237	−	0.760237i
$340$		0			0
$341$	−0.0318498	−	0.0318498i	−0.00172477	−	0.00172477i
$342$		0			0
$343$		−	20.1596i		−	1.08852i
$344$		0			0
$345$			3.01309i			0.162219i
$346$		0			0
$347$	9.64716	+	9.64716i	0.517887	+	0.517887i	0.916931	−	0.399045i	$-0.130658\pi$
$347$	9.64716	+	9.64716i	0.517887	+	0.517887i	−0.399045	+	0.916931i	$0.630658\pi$
$348$		0			0
$349$	20.3332	−	20.3332i	1.08841	−	1.08841i	0.0927209	−	0.995692i	$-0.470444\pi$
$349$	20.3332	−	20.3332i	1.08841	−	1.08841i	0.995692	−	0.0927209i	$-0.0295564\pi$
$350$		0			0
$351$	2.44610			0.130563
$352$		0			0
$353$	32.1660			1.71202			0.856010	−	0.516958i	$-0.172936\pi$
$353$	32.1660			1.71202			0.856010	+	0.516958i	$0.172936\pi$
$354$		0			0
$355$	−8.56251	+	8.56251i	−0.454451	+	0.454451i
$356$		0			0
$357$	−8.55675	−	8.55675i	−0.452871	−	0.452871i
$358$		0			0
$359$		−	15.8239i		−	0.835155i	−0.908641	−	0.417578i	$-0.862879\pi$
$359$		−	15.8239i		−	0.835155i	0.908641	−	0.417578i	$-0.137121\pi$
$360$		0			0
$361$		−	29.9461i		−	1.57611i
$362$		0			0
$363$	7.77806	+	7.77806i	0.408242	+	0.408242i
$364$		0			0
$365$	5.04154	−	5.04154i	0.263886	−	0.263886i
$366$		0			0
$367$	−4.34838			−0.226984			−0.113492	−	0.993539i	$-0.536204\pi$
$367$	−4.34838			−0.226984			−0.113492	+	0.993539i	$0.536204\pi$
$368$		0			0
$369$	−3.76487			−0.195992
$370$		0			0
$371$	−2.03372	+	2.03372i	−0.105586	+	0.105586i
$372$		0			0
$373$	−17.3659	−	17.3659i	−0.899171	−	0.899171i	0.0961919	−	0.995363i	$-0.469334\pi$
$373$	−17.3659	−	17.3659i	−0.899171	−	0.899171i	−0.995363	+	0.0961919i	$0.969334\pi$
$374$		0			0
$375$		−	1.00000i		−	0.0516398i
$376$		0			0
$377$		−	11.0861i		−	0.570961i
$378$		0			0
$379$	15.3936	+	15.3936i	0.790717	+	0.790717i	0.981611	−	0.190893i	$-0.0611385\pi$
$379$	15.3936	+	15.3936i	0.790717	+	0.790717i	−0.190893	+	0.981611i	$0.561138\pi$
$380$		0			0
$381$	10.1812	−	10.1812i	0.521598	−	0.521598i
$382$		0			0
$383$	15.6393			0.799129			0.399564	−	0.916705i	$-0.369161\pi$
$383$	15.6393			0.799129			0.399564	+	0.916705i	$0.369161\pi$
$384$		0			0
$385$	0.0274349			0.00139821
$386$		0			0
$387$	−6.81210	+	6.81210i	−0.346278	+	0.346278i
$388$		0			0
$389$	17.0067	+	17.0067i	0.862276	+	0.862276i	0.991602	−	0.129326i	$-0.0412813\pi$
$389$	17.0067	+	17.0067i	0.862276	+	0.862276i	−0.129326	+	0.991602i	$0.541281\pi$
$390$		0			0
$391$			16.7209i			0.845612i
$392$		0			0
$393$			0.812825i			0.0410016i
$394$		0			0
$395$	2.41682	+	2.41682i	0.121603	+	0.121603i
$396$		0			0
$397$	−12.5043	+	12.5043i	−0.627572	+	0.627572i	−0.947457	−	0.319884i	$-0.896356\pi$
$397$	−12.5043	+	12.5043i	−0.627572	+	0.627572i	0.319884	+	0.947457i	$0.396356\pi$
$398$		0			0
$399$	15.2558			0.763745
$400$		0			0
$401$	−14.6398			−0.731079			−0.365539	−	0.930796i	$-0.619115\pi$
$401$	−14.6398			−0.731079			−0.365539	+	0.930796i	$0.619115\pi$
$402$		0			0
$403$	−6.19232	+	6.19232i	−0.308461	+	0.308461i
$404$		0			0
$405$	−0.707107	−	0.707107i	−0.0351364	−	0.0351364i
$406$		0			0
$407$			0.0885653i			0.00439002i
$408$		0			0
$409$			33.5504i			1.65896i	0.558537	+	0.829479i	$0.311363\pi$
$409$			33.5504i			1.65896i	−0.558537	+	0.829479i	$0.688637\pi$
$410$		0			0
$411$	11.3192	+	11.3192i	0.558334	+	0.558334i
$412$		0			0
$413$	10.0421	−	10.0421i	0.494141	−	0.494141i
$414$		0			0
$415$	−7.51840			−0.369064
$416$		0			0
$417$	−2.15559			−0.105560
$418$		0			0
$419$	−16.5641	+	16.5641i	−0.809211	+	0.809211i	−0.984514	−	0.175303i	$-0.943909\pi$
$419$	−16.5641	+	16.5641i	−0.809211	+	0.809211i	0.175303	+	0.984514i	$0.443909\pi$
$420$		0			0
$421$	14.1472	+	14.1472i	0.689492	+	0.689492i	0.962120	−	0.272628i	$-0.0878928\pi$
$421$	14.1472	+	14.1472i	0.689492	+	0.689492i	−0.272628	+	0.962120i	$0.587893\pi$
$422$		0			0
$423$		−	10.0800i		−	0.490105i
$424$		0			0
$425$		−	5.54943i		−	0.269187i
$426$		0			0
$427$	−9.09635	−	9.09635i	−0.440203	−	0.440203i
$428$		0			0
$429$	−0.0217614	+	0.0217614i	−0.00105065	+	0.00105065i
$430$		0			0
$431$	−13.1169			−0.631819			−0.315909	−	0.948789i	$-0.602310\pi$
$431$	−13.1169			−0.631819			−0.315909	+	0.948789i	$0.602310\pi$
$432$		0			0
$433$	0.300976			0.0144640			0.00723199	−	0.999974i	$-0.497698\pi$
$433$	0.300976			0.0144640			0.00723199	+	0.999974i	$0.497698\pi$
$434$		0			0
$435$	−3.20471	+	3.20471i	−0.153654	+	0.153654i
$436$		0			0
$437$	−14.9058	−	14.9058i	−0.713041	−	0.713041i
$438$		0			0
$439$		−	30.3358i		−	1.44785i	−0.689879	−	0.723925i	$-0.742336\pi$
$439$		−	30.3358i		−	1.44785i	0.689879	−	0.723925i	$-0.257664\pi$
$440$		0			0
$441$		−	2.24499i		−	0.106904i
$442$		0			0
$443$	3.99367	+	3.99367i	0.189745	+	0.189745i	0.795586	−	0.605841i	$-0.207163\pi$
$443$	3.99367	+	3.99367i	0.189745	+	0.189745i	−0.605841	+	0.795586i	$0.707163\pi$
$444$		0			0
$445$	3.58082	−	3.58082i	0.169747	−	0.169747i
$446$		0			0
$447$	−17.1700			−0.812111
$448$		0			0
$449$	−10.4806			−0.494610			−0.247305	−	0.968938i	$-0.579545\pi$
$449$	−10.4806			−0.494610			−0.247305	+	0.968938i	$0.579545\pi$
$450$		0			0
$451$	0.0334937	−	0.0334937i	0.00157716	−	0.00157716i
$452$		0			0
$453$	−9.04671	−	9.04671i	−0.425052	−	0.425052i
$454$		0			0
$455$		−	5.33396i		−	0.250060i
$456$		0			0
$457$		−	5.70188i		−	0.266723i	−0.991067	−	0.133361i	$-0.957423\pi$
$457$		−	5.70188i		−	0.266723i	0.991067	−	0.133361i	$-0.0425771\pi$
$458$		0			0
$459$	−3.92404	−	3.92404i	−0.183158	−	0.183158i
$460$		0			0
$461$	1.78282	−	1.78282i	0.0830341	−	0.0830341i	−0.664370	−	0.747404i	$-0.731300\pi$
$461$	1.78282	−	1.78282i	0.0830341	−	0.0830341i	0.747404	+	0.664370i	$0.231300\pi$
$462$		0			0
$463$	37.2015			1.72890			0.864451	−	0.502717i	$-0.167666\pi$
$463$	37.2015			1.72890			0.864451	+	0.502717i	$0.167666\pi$
$464$		0			0
$465$	3.58009			0.166023
$466$		0			0
$467$	14.3669	−	14.3669i	0.664822	−	0.664822i	−0.291691	−	0.956513i	$-0.594218\pi$
$467$	14.3669	−	14.3669i	0.664822	−	0.664822i	0.956513	+	0.291691i	$0.0942179\pi$
$468$		0			0
$469$	−24.0094	−	24.0094i	−1.10865	−	1.10865i
$470$		0			0
$471$		−	14.6135i		−	0.673353i
$472$		0			0
$473$		−	0.121206i		−	0.00557305i
$474$		0			0
$475$	4.94702	+	4.94702i	0.226985	+	0.226985i
$476$		0			0
$477$	−0.932644	+	0.932644i	−0.0427028	+	0.0427028i
$478$		0			0
$479$	36.6561			1.67486			0.837431	−	0.546544i	$-0.184057\pi$
$479$	36.6561			1.67486			0.837431	+	0.546544i	$0.184057\pi$
$480$		0			0
$481$	17.2191			0.785122
$482$		0			0
$483$	4.64592	−	4.64592i	0.211397	−	0.211397i
$484$		0			0
$485$	−7.32890	−	7.32890i	−0.332788	−	0.332788i
$486$		0			0
$487$			34.3322i			1.55574i	0.628425	+	0.777870i	$0.283700\pi$
$487$			34.3322i			1.55574i	−0.628425	+	0.777870i	$0.716300\pi$
$488$		0			0
$489$		−	19.0017i		−	0.859286i
$490$		0			0
$491$	−17.6224	−	17.6224i	−0.795287	−	0.795287i	0.187061	−	0.982348i	$-0.440104\pi$
$491$	−17.6224	−	17.6224i	−0.795287	−	0.795287i	−0.982348	+	0.187061i	$0.940104\pi$
$492$		0			0
$493$	−17.7843	+	17.7843i	−0.800963	+	0.800963i
$494$		0			0
$495$	0.0125814			0.000565490
$496$		0			0
$497$	26.4053			1.18444
$498$		0			0
$499$	14.6801	−	14.6801i	0.657173	−	0.657173i	−0.297537	−	0.954710i	$-0.596165\pi$
$499$	14.6801	−	14.6801i	0.657173	−	0.657173i	0.954710	+	0.297537i	$0.0961652\pi$
$500$		0			0
$501$	3.59485	+	3.59485i	0.160606	+	0.160606i
$502$		0			0
$503$		−	13.0618i		−	0.582398i	−0.956663	−	0.291199i	$-0.905946\pi$
$503$		−	13.0618i		−	0.582398i	0.956663	−	0.291199i	$-0.0940541\pi$
$504$		0			0
$505$			14.0914i			0.627060i
$506$		0			0
$507$	−4.96149	−	4.96149i	−0.220347	−	0.220347i
$508$		0			0
$509$	−22.0202	+	22.0202i	−0.976027	+	0.976027i	−0.999719	−	0.0236921i	$-0.992458\pi$
$509$	−22.0202	+	22.0202i	−0.976027	+	0.976027i	0.0236921	+	0.999719i	$0.492458\pi$
$510$		0			0
$511$	−15.5472			−0.687770
$512$		0			0
$513$	6.99615			0.308888
$514$		0			0
$515$	−1.59208	+	1.59208i	−0.0701555	+	0.0701555i
$516$		0			0
$517$	0.0896752	+	0.0896752i	0.00394391	+	0.00394391i
$518$		0			0
$519$		−	15.3896i		−	0.675529i
$520$		0			0
$521$		−	22.0123i		−	0.964375i	−0.876068	−	0.482188i	$-0.839842\pi$
$521$		−	22.0123i		−	0.964375i	0.876068	−	0.482188i	$-0.160158\pi$
$522$		0			0
$523$	14.7575	+	14.7575i	0.645299	+	0.645299i	0.951853	−	0.306554i	$-0.0991760\pi$
$523$	14.7575	+	14.7575i	0.645299	+	0.645299i	−0.306554	+	0.951853i	$0.599176\pi$
$524$		0			0
$525$	−1.54192	+	1.54192i	−0.0672947	+	0.0672947i
$526$		0			0
$527$	19.8675			0.865441
$528$		0			0
$529$	13.9213			0.605275
$530$		0			0
$531$	4.60522	−	4.60522i	0.199849	−	0.199849i
$532$		0			0
$533$	−6.51192	−	6.51192i	−0.282063	−	0.282063i
$534$		0			0
$535$		−	3.55106i		−	0.153526i
$536$		0			0
$537$		−	15.7995i		−	0.681797i
$538$		0			0
$539$	0.0199723	+	0.0199723i	0.000860267	+	0.000860267i
$540$		0			0
$541$	8.39925	−	8.39925i	0.361112	−	0.361112i	−0.503110	−	0.864222i	$-0.667811\pi$
$541$	8.39925	−	8.39925i	0.361112	−	0.361112i	0.864222	+	0.503110i	$0.167811\pi$
$542$		0			0
$543$	14.3513			0.615875
$544$		0			0
$545$	17.0651			0.730987
$546$		0			0
$547$	8.81903	−	8.81903i	0.377074	−	0.377074i	−0.492971	−	0.870046i	$-0.664089\pi$
$547$	8.81903	−	8.81903i	0.377074	−	0.377074i	0.870046	+	0.492971i	$0.164089\pi$
$548$		0			0
$549$	−4.17149	−	4.17149i	−0.178035	−	0.178035i
$550$		0			0
$551$		−	31.7075i		−	1.35079i
$552$		0			0
$553$		−	7.45305i		−	0.316936i
$554$		0			0
$555$	−4.97761	−	4.97761i	−0.211288	−	0.211288i
$556$		0			0
$557$	6.98592	−	6.98592i	0.296003	−	0.296003i	−0.543443	−	0.839446i	$-0.682880\pi$
$557$	6.98592	−	6.98592i	0.296003	−	0.296003i	0.839446	+	0.543443i	$0.182880\pi$
$558$		0			0
$559$	−23.5651			−0.996699
$560$		0			0
$561$	0.0698194			0.00294778
$562$		0			0
$563$	−3.94396	+	3.94396i	−0.166218	+	0.166218i	−0.785315	−	0.619097i	$-0.787499\pi$
$563$	−3.94396	+	3.94396i	−0.166218	+	0.166218i	0.619097	+	0.785315i	$0.287499\pi$
$564$		0			0
$565$	−13.9975	−	13.9975i	−0.588877	−	0.588877i
$566$		0			0
$567$			2.18060i			0.0915765i
$568$		0			0
$569$			31.6307i			1.32603i	0.748607	+	0.663014i	$0.230723\pi$
$569$			31.6307i			1.32603i	−0.748607	+	0.663014i	$0.769277\pi$
$570$		0			0
$571$	−5.70590	−	5.70590i	−0.238785	−	0.238785i	0.577562	−	0.816347i	$-0.304004\pi$
$571$	−5.70590	−	5.70590i	−0.238785	−	0.238785i	−0.816347	+	0.577562i	$0.804004\pi$
$572$		0			0
$573$	9.45512	−	9.45512i	0.394993	−	0.394993i
$574$		0			0
$575$	3.01309			0.125654
$576$		0			0
$577$	21.9772			0.914921			0.457461	−	0.889230i	$-0.348759\pi$
$577$	21.9772			0.914921			0.457461	+	0.889230i	$0.348759\pi$
$578$		0			0
$579$	−5.88967	+	5.88967i	−0.244766	+	0.244766i
$580$		0			0
$581$	11.5927	+	11.5927i	0.480948	+	0.480948i
$582$		0			0
$583$		−	0.0165943i		−	0.000687265i
$584$		0			0
$585$		−	2.44610i		−	0.101134i
$586$		0			0
$587$	15.3747	+	15.3747i	0.634583	+	0.634583i	0.949214	−	0.314631i	$-0.101881\pi$
$587$	15.3747	+	15.3747i	0.634583	+	0.634583i	−0.314631	+	0.949214i	$0.601881\pi$
$588$		0			0
$589$	−17.7108	+	17.7108i	−0.729761	+	0.729761i
$590$		0			0
$591$	−18.6669			−0.767855
$592$		0			0
$593$	−16.9206			−0.694846			−0.347423	−	0.937708i	$-0.612943\pi$
$593$	−16.9206			−0.694846			−0.347423	+	0.937708i	$0.612943\pi$
$594$		0			0
$595$	−8.55675	+	8.55675i	−0.350792	+	0.350792i
$596$		0			0
$597$	2.59305	+	2.59305i	0.106127	+	0.106127i
$598$		0			0
$599$			19.1715i			0.783327i	0.920109	+	0.391663i	$0.128100\pi$
$599$			19.1715i			0.783327i	−0.920109	+	0.391663i	$0.871900\pi$
$600$		0			0
$601$		−	10.1428i		−	0.413735i	−0.978369	−	0.206867i	$-0.933673\pi$
$601$		−	10.1428i		−	0.413735i	0.978369	−	0.206867i	$-0.0663269\pi$
$602$		0			0
$603$	−11.0105	−	11.0105i	−0.448382	−	0.448382i
$604$		0			0
$605$	7.77806	−	7.77806i	0.316223	−	0.316223i
$606$		0			0
$607$	−6.80048			−0.276023			−0.138011	−	0.990431i	$-0.544071\pi$
$607$	−6.80048			−0.276023			−0.138011	+	0.990431i	$0.544071\pi$
$608$		0			0
$609$	9.88277			0.400470
$610$		0			0
$611$	17.4349	−	17.4349i	0.705339	−	0.705339i
$612$		0			0
$613$	18.1431	+	18.1431i	0.732793	+	0.732793i	0.971172	−	0.238379i	$-0.0766161\pi$
$613$	18.1431	+	18.1431i	0.732793	+	0.732793i	−0.238379	+	0.971172i	$0.576616\pi$
$614$		0			0
$615$			3.76487i			0.151814i
$616$		0			0
$617$		−	30.4488i		−	1.22582i	−0.790151	−	0.612912i	$-0.789998\pi$
$617$		−	30.4488i		−	1.22582i	0.790151	−	0.612912i	$-0.210002\pi$
$618$		0			0
$619$	12.1946	+	12.1946i	0.490143	+	0.490143i	0.908351	−	0.418208i	$-0.137342\pi$
$619$	12.1946	+	12.1946i	0.490143	+	0.490143i	−0.418208	+	0.908351i	$0.637342\pi$
$620$		0			0
$621$	2.13057	−	2.13057i	0.0854969	−	0.0854969i
$622$		0			0
$623$	−11.0427			−0.442415
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$	−0.0622403	+	0.0622403i	−0.00248564	+	0.00248564i
$628$		0			0
$629$	−27.6229	−	27.6229i	−1.10140	−	1.10140i
$630$		0			0
$631$			27.9943i			1.11444i	0.830366	+	0.557218i	$0.188131\pi$
$631$			27.9943i			1.11444i	−0.830366	+	0.557218i	$0.811869\pi$
$632$		0			0
$633$			17.8789i			0.710623i
$634$		0			0
$635$	−10.1812	−	10.1812i	−0.404028	−	0.404028i
$636$		0			0
$637$	3.88306	−	3.88306i	0.153852	−	0.153852i
$638$		0			0
$639$	12.1092			0.479033
$640$		0			0
$641$	5.01913			0.198244			0.0991219	−	0.995075i	$-0.468397\pi$
$641$	5.01913			0.198244			0.0991219	+	0.995075i	$0.468397\pi$
$642$		0			0
$643$	−1.55218	+	1.55218i	−0.0612118	+	0.0612118i	−0.737050	−	0.675838i	$-0.763782\pi$
$643$	−1.55218	+	1.55218i	−0.0612118	+	0.0612118i	0.675838	+	0.737050i	$0.263782\pi$
$644$		0			0
$645$	6.81210	+	6.81210i	0.268226	+	0.268226i
$646$		0			0
$647$		−	24.6915i		−	0.970722i	−0.874314	−	0.485361i	$-0.838688\pi$
$647$		−	24.6915i		−	0.970722i	0.874314	−	0.485361i	$-0.161312\pi$
$648$		0			0
$649$			0.0819394i			0.00321640i
$650$		0			0
$651$	−5.52020	−	5.52020i	−0.216354	−	0.216354i
$652$		0			0
$653$	−10.4301	+	10.4301i	−0.408161	+	0.408161i	−0.881097	−	0.472936i	$-0.843194\pi$
$653$	−10.4301	+	10.4301i	−0.408161	+	0.408161i	0.472936	+	0.881097i	$0.343194\pi$
$654$		0			0
$655$	0.812825			0.0317597
$656$		0			0
$657$	−7.12981			−0.278160
$658$		0			0
$659$	15.4151	−	15.4151i	0.600487	−	0.600487i	−0.339955	−	0.940442i	$-0.610412\pi$
$659$	15.4151	−	15.4151i	0.600487	−	0.600487i	0.940442	+	0.339955i	$0.110412\pi$
$660$		0			0
$661$	17.9150	+	17.9150i	0.696813	+	0.696813i	0.963722	−	0.266909i	$-0.0860022\pi$
$661$	17.9150	+	17.9150i	0.696813	+	0.696813i	−0.266909	+	0.963722i	$0.586002\pi$
$662$		0			0
$663$		−	13.5744i		−	0.527188i
$664$		0			0
$665$		−	15.2558i		−	0.591594i
$666$		0			0
$667$	−9.65605	−	9.65605i	−0.373884	−	0.373884i
$668$		0			0
$669$	−3.80021	+	3.80021i	−0.146925	+	0.146925i
$670$		0			0
$671$	0.0742223			0.00286532
$672$		0			0
$673$	28.8891			1.11359			0.556796	−	0.830649i	$-0.312030\pi$
$673$	28.8891			1.11359			0.556796	+	0.830649i	$0.312030\pi$
$674$		0			0
$675$	−0.707107	+	0.707107i	−0.0272166	+	0.0272166i
$676$		0			0
$677$	10.8421	+	10.8421i	0.416695	+	0.416695i	0.884063	−	0.467368i	$-0.154798\pi$
$677$	10.8421	+	10.8421i	0.416695	+	0.416695i	−0.467368	+	0.884063i	$0.654798\pi$
$678$		0			0
$679$			22.6011i			0.867350i
$680$		0			0
$681$		−	2.71961i		−	0.104216i
$682$		0			0
$683$	2.04256	+	2.04256i	0.0781564	+	0.0781564i	0.745104	−	0.666948i	$-0.232400\pi$
$683$	2.04256	+	2.04256i	0.0781564	+	0.0781564i	−0.666948	+	0.745104i	$0.732400\pi$
$684$		0			0
$685$	11.3192	−	11.3192i	0.432484	−	0.432484i
$686$		0			0
$687$	−7.18568			−0.274151
$688$		0			0
$689$	−3.22630			−0.122912
$690$		0			0
$691$	−33.4347	+	33.4347i	−1.27192	+	1.27192i	−0.326837	+	0.945081i	$0.605983\pi$
$691$	−33.4347	+	33.4347i	−1.27192	+	1.27192i	−0.945081	+	0.326837i	$0.894017\pi$
$692$		0			0
$693$	−0.0193994	−	0.0193994i	−0.000736922	−	0.000736922i
$694$		0			0
$695$			2.15559i			0.0817664i
$696$		0			0
$697$			20.8929i			0.791375i
$698$		0			0
$699$	−18.5557	−	18.5557i	−0.701839	−	0.701839i
$700$		0			0
$701$	4.02037	−	4.02037i	0.151847	−	0.151847i	−0.627095	−	0.778943i	$-0.715756\pi$
$701$	4.02037	−	4.02037i	0.151847	−	0.151847i	0.778943	+	0.627095i	$0.215756\pi$
$702$		0			0
$703$	49.2487			1.85745
$704$		0			0
$705$	−10.0800			−0.379634
$706$		0			0
$707$	21.7278	−	21.7278i	0.817158	−	0.817158i
$708$		0			0
$709$	18.0101	+	18.0101i	0.676385	+	0.676385i	0.959180	−	0.282795i	$-0.0912617\pi$
$709$	18.0101	+	18.0101i	0.676385	+	0.676385i	−0.282795	+	0.959180i	$0.591262\pi$
$710$		0			0
$711$		−	3.41789i		−	0.128181i
$712$		0			0
$713$			10.7871i			0.403981i
$714$		0			0
$715$	0.0217614	+	0.0217614i	0.000813830	+	0.000813830i
$716$		0			0
$717$	−5.23917	+	5.23917i	−0.195660	+	0.195660i
$718$		0			0
$719$	−50.2917			−1.87556			−0.937782	−	0.347224i	$-0.887124\pi$
$719$	−50.2917			−1.87556			−0.937782	+	0.347224i	$0.887124\pi$
$720$		0			0
$721$	4.90971			0.182847
$722$		0			0
$723$	13.8757	−	13.8757i	0.516041	−	0.516041i
$724$		0			0
$725$	3.20471	+	3.20471i	0.119020	+	0.119020i
$726$		0			0
$727$			15.1799i			0.562991i	0.959562	+	0.281496i	$0.0908305\pi$
$727$			15.1799i			0.562991i	−0.959562	+	0.281496i	$0.909169\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	37.8032	+	37.8032i	1.39820	+	1.39820i
$732$		0			0
$733$	−12.1524	+	12.1524i	−0.448859	+	0.448859i	−0.894975	−	0.446116i	$-0.852807\pi$
$733$	−12.1524	+	12.1524i	−0.448859	+	0.448859i	0.446116	+	0.894975i	$0.352807\pi$
$734$		0			0
$735$	−2.24499			−0.0828078
$736$		0			0
$737$	0.195907			0.00721632
$738$		0			0
$739$	17.9947	−	17.9947i	0.661947	−	0.661947i	−0.293892	−	0.955839i	$-0.594950\pi$
$739$	17.9947	−	17.9947i	0.661947	−	0.661947i	0.955839	+	0.293892i	$0.0949505\pi$
$740$		0			0
$741$	12.1009	+	12.1009i	0.444538	+	0.444538i
$742$		0			0
$743$			19.2456i			0.706051i	0.935614	+	0.353026i	$0.114847\pi$
$743$			19.2456i			0.706051i	−0.935614	+	0.353026i	$0.885153\pi$
$744$		0			0
$745$			17.1700i			0.629059i
$746$		0			0
$747$	5.31631	+	5.31631i	0.194514	+	0.194514i
$748$		0			0
$749$	−5.47544	+	5.47544i	−0.200068	+	0.200068i
$750$		0			0
$751$	53.5813			1.95521			0.977604	−	0.210451i	$-0.0674933\pi$
$751$	53.5813			1.95521			0.977604	+	0.210451i	$0.0674933\pi$
$752$		0			0
$753$	1.74810			0.0637044
$754$		0			0
$755$	−9.04671	+	9.04671i	−0.329244	+	0.329244i
$756$		0			0
$757$	10.4133	+	10.4133i	0.378477	+	0.378477i	0.870552	−	0.492076i	$-0.163762\pi$
$757$	10.4133	+	10.4133i	0.378477	+	0.378477i	−0.492076	+	0.870552i	$0.663762\pi$
$758$		0			0
$759$			0.0379087i			0.00137600i
$760$		0			0
$761$			38.1651i			1.38348i	0.722145	+	0.691742i	$0.243156\pi$
$761$			38.1651i			1.38348i	−0.722145	+	0.691742i	$0.756844\pi$
$762$		0			0
$763$	−26.3129	−	26.3129i	−0.952590	−	0.952590i
$764$		0			0
$765$	−3.92404	+	3.92404i	−0.141874	+	0.141874i
$766$		0			0
$767$	15.9309			0.575230
$768$		0			0
$769$	−38.1071			−1.37418			−0.687089	−	0.726573i	$-0.741112\pi$
$769$	−38.1071			−1.37418			−0.687089	+	0.726573i	$0.741112\pi$
$770$		0			0
$771$	−2.12874	+	2.12874i	−0.0766648	+	0.0766648i
$772$		0			0
$773$	−32.9401	−	32.9401i	−1.18477	−	1.18477i	−0.978493	−	0.206280i	$-0.933864\pi$
$773$	−32.9401	−	32.9401i	−1.18477	−	1.18477i	−0.206280	−	0.978493i	$-0.566136\pi$
$774$		0			0
$775$		−	3.58009i		−	0.128601i
$776$		0			0
$777$			15.3501i			0.550682i
$778$		0			0
$779$	−18.6249	−	18.6249i	−0.667307	−	0.667307i
$780$		0			0
$781$	−0.107728	+	0.107728i	−0.00385481	+	0.00385481i
$782$		0			0
$783$	4.53214			0.161965
$784$		0			0
$785$	−14.6135			−0.521577
$786$		0			0
$787$	−21.5631	+	21.5631i	−0.768642	+	0.768642i	−0.977867	−	0.209225i	$-0.932906\pi$
$787$	−21.5631	+	21.5631i	−0.768642	+	0.768642i	0.209225	+	0.977867i	$0.432906\pi$
$788$		0			0
$789$	8.41460	+	8.41460i	0.299568	+	0.299568i
$790$		0			0
$791$			43.1658i			1.53480i
$792$		0			0
$793$		−	14.4305i		−	0.512441i
$794$		0			0
$795$	0.932644	+	0.932644i	0.0330775	+	0.0330775i
$796$		0			0
$797$	7.81695	−	7.81695i	0.276891	−	0.276891i	−0.554976	−	0.831866i	$-0.687273\pi$
$797$	7.81695	−	7.81695i	0.276891	−	0.276891i	0.831866	+	0.554976i	$0.187273\pi$
$798$		0			0
$799$	−55.9381			−1.97895
$800$		0			0
$801$	−5.06405			−0.178929
$802$		0			0
$803$	0.0634294	−	0.0634294i	0.00223837	−	0.00223837i
$804$		0			0
$805$	−4.64592	−	4.64592i	−0.163747	−	0.163747i
$806$		0			0
$807$		−	21.9131i		−	0.771379i
$808$		0			0
$809$		−	8.21009i		−	0.288651i	−0.989530	−	0.144326i	$-0.953899\pi$
$809$		−	8.21009i		−	0.288651i	0.989530	−	0.144326i	$-0.0461013\pi$
$810$		0			0
$811$	0.466318	+	0.466318i	0.0163746	+	0.0163746i	0.715247	−	0.698872i	$-0.246314\pi$
$811$	0.466318	+	0.466318i	0.0163746	+	0.0163746i	−0.698872	+	0.715247i	$0.746314\pi$
$812$		0			0
$813$	5.16536	−	5.16536i	0.181157	−	0.181157i
$814$		0			0
$815$	−19.0017			−0.665600
$816$		0			0
$817$	−67.3992			−2.35800
$818$		0			0
$819$	−3.77168	+	3.77168i	−0.131793	+	0.131793i
$820$		0			0
$821$	22.1688	+	22.1688i	0.773696	+	0.773696i	0.978751	−	0.205054i	$-0.0657371\pi$
$821$	22.1688	+	22.1688i	0.773696	+	0.773696i	−0.205054	+	0.978751i	$0.565737\pi$
$822$		0			0
$823$		−	14.7926i		−	0.515636i	−0.966193	−	0.257818i	$-0.916996\pi$
$823$		−	14.7926i		−	0.515636i	0.966193	−	0.257818i	$-0.0830035\pi$
$824$		0			0
$825$		−	0.0125814i		−	0.000438027i
$826$		0			0
$827$	−27.9227	−	27.9227i	−0.970967	−	0.970967i	0.0286237	−	0.999590i	$-0.490888\pi$
$827$	−27.9227	−	27.9227i	−0.970967	−	0.970967i	−0.999590	+	0.0286237i	$0.990888\pi$
$828$		0			0
$829$	−0.798074	+	0.798074i	−0.0277182	+	0.0277182i	−0.720830	−	0.693112i	$-0.756239\pi$
$829$	−0.798074	+	0.798074i	−0.0277182	+	0.0277182i	0.693112	+	0.720830i	$0.256239\pi$
$830$		0			0
$831$	−3.16385			−0.109753
$832$		0			0
$833$	−12.4584			−0.431659
$834$		0			0
$835$	3.59485	−	3.59485i	0.124405	−	0.124405i
$836$		0			0
$837$	−2.53151	−	2.53151i	−0.0875018	−	0.0875018i
$838$		0			0
$839$			29.3983i			1.01494i	0.861669	+	0.507470i	$0.169419\pi$
$839$			29.3983i			1.01494i	−0.861669	+	0.507470i	$0.830581\pi$
$840$		0			0
$841$			8.45973i			0.291715i
$842$		0			0
$843$	3.42973	+	3.42973i	0.118126	+	0.118126i
$844$		0			0
$845$	−4.96149	+	4.96149i	−0.170680	+	0.170680i
$846$		0			0
$847$	−23.9862			−0.824177
$848$		0			0
$849$	16.1638			0.554739
$850$		0			0
$851$	14.9980	−	14.9980i	0.514123	−	0.514123i
$852$		0			0
$853$	24.2137	+	24.2137i	0.829060	+	0.829060i	0.987387	−	0.158326i	$-0.0506098\pi$
$853$	24.2137	+	24.2137i	0.829060	+	0.829060i	−0.158326	+	0.987387i	$0.550610\pi$
$854$		0			0
$855$		−	6.99615i		−	0.239263i
$856$		0			0
$857$		−	16.2011i		−	0.553419i	−0.960954	−	0.276709i	$-0.910756\pi$
$857$		−	16.2011i		−	0.553419i	0.960954	−	0.276709i	$-0.0892440\pi$
$858$		0			0
$859$	−0.266646	−	0.266646i	−0.00909783	−	0.00909783i	0.702543	−	0.711641i	$-0.252048\pi$
$859$	−0.266646	−	0.266646i	−0.00909783	−	0.00909783i	−0.711641	+	0.702543i	$0.752048\pi$
$860$		0			0
$861$	5.80512	−	5.80512i	0.197838	−	0.197838i
$862$		0			0
$863$	−10.2561			−0.349121			−0.174560	−	0.984646i	$-0.555850\pi$
$863$	−10.2561			−0.349121			−0.174560	+	0.984646i	$0.555850\pi$
$864$		0			0
$865$	−15.3896			−0.523262
$866$		0			0
$867$	−9.75534	+	9.75534i	−0.331309	+	0.331309i
$868$		0			0
$869$	0.0304068	+	0.0304068i	0.00103148	+	0.00103148i
$870$		0			0
$871$		−	38.0886i		−	1.29058i
$872$		0			0
$873$			10.3646i			0.350789i
$874$		0			0
$875$	1.54192	+	1.54192i	0.0521263	+	0.0521263i
$876$		0			0
$877$	−20.4974	+	20.4974i	−0.692149	+	0.692149i	−0.962704	−	0.270555i	$-0.912793\pi$
$877$	−20.4974	+	20.4974i	−0.692149	+	0.692149i	0.270555	+	0.962704i	$0.412793\pi$
$878$		0			0
$879$	15.7948			0.532744
$880$		0			0
$881$	−56.8144			−1.91413			−0.957063	−	0.289881i	$-0.906384\pi$
$881$	−56.8144			−1.91413			−0.957063	+	0.289881i	$0.906384\pi$
$882$		0			0
$883$	−26.2082	+	26.2082i	−0.881978	+	0.881978i	−0.993735	−	0.111758i	$-0.964352\pi$
$883$	−26.2082	+	26.2082i	−0.881978	+	0.881978i	0.111758	+	0.993735i	$0.464352\pi$
$884$		0			0
$885$	−4.60522	−	4.60522i	−0.154803	−	0.154803i
$886$		0			0
$887$			26.0161i			0.873537i	0.899574	+	0.436768i	$0.143877\pi$
$887$			26.0161i			0.873537i	−0.899574	+	0.436768i	$0.856123\pi$
$888$		0			0
$889$			31.3971i			1.05302i
$890$		0			0
$891$	−0.00889637	−	0.00889637i	−0.000298040	−	0.000298040i
$892$		0			0
$893$	49.8659	−	49.8659i	1.66870	−	1.66870i
$894$		0			0
$895$	−15.7995			−0.528118
$896$		0			0
$897$	7.37030			0.246087
$898$		0			0
$899$	−11.4731	+	11.4731i	−0.382651	+	0.382651i
$900$		0			0
$901$	5.17564	+	5.17564i	0.172425	+	0.172425i
$902$		0			0
$903$		−	21.0074i		−	0.699081i
$904$		0			0
$905$		−	14.3513i		−	0.477055i
$906$		0			0
$907$	27.6233	+	27.6233i	0.917218	+	0.917218i	0.996826	−	0.0796085i	$-0.0253670\pi$
$907$	27.6233	+	27.6233i	0.917218	+	0.917218i	−0.0796085	+	0.996826i	$0.525367\pi$
$908$		0			0
$909$	9.96414	−	9.96414i	0.330490	−	0.330490i
$910$		0			0
$911$	5.83194			0.193221			0.0966104	−	0.995322i	$-0.469200\pi$
$911$	5.83194			0.193221			0.0966104	+	0.995322i	$0.469200\pi$
$912$		0			0
$913$	−0.0945918			−0.00313053
$914$		0			0
$915$	−4.17149	+	4.17149i	−0.137905	+	0.137905i
$916$		0			0
$917$	−1.25331	−	1.25331i	−0.0413879	−	0.0413879i
$918$		0			0
$919$			11.8292i			0.390208i	0.980783	+	0.195104i	$0.0625045\pi$
$919$			11.8292i			0.390208i	−0.980783	+	0.195104i	$0.937496\pi$
$920$		0			0
$921$		−	19.1437i		−	0.630805i
$922$		0			0
$923$	20.9447	+	20.9447i	0.689405	+	0.689405i
$924$		0			0
$925$	−4.97761	+	4.97761i	−0.163663	+	0.163663i
$926$		0			0
$927$	2.25154			0.0739503
$928$		0			0
$929$	−45.8141			−1.50311			−0.751556	−	0.659669i	$-0.770696\pi$
$929$	−45.8141			−1.50311			−0.751556	+	0.659669i	$0.770696\pi$
$930$		0			0
$931$	11.1060	−	11.1060i	0.363986	−	0.363986i
$932$		0			0
$933$	11.6641	+	11.6641i	0.381867	+	0.381867i
$934$		0			0
$935$		−	0.0698194i		−	0.00228334i
$936$		0			0
$937$			6.21014i			0.202876i	0.994842	+	0.101438i	$0.0323444\pi$
$937$			6.21014i			0.202876i	−0.994842	+	0.101438i	$0.967656\pi$
$938$		0			0
$939$	−19.2721	−	19.2721i	−0.628922	−	0.628922i
$940$		0			0
$941$	−2.43886	+	2.43886i	−0.0795045	+	0.0795045i	−0.745741	−	0.666236i	$-0.767904\pi$
$941$	−2.43886	+	2.43886i	−0.0795045	+	0.0795045i	0.666236	+	0.745741i	$0.267904\pi$
$942$		0			0
$943$	−11.3439			−0.369408
$944$		0			0
$945$	2.18060			0.0709349
$946$		0			0
$947$	33.4856	−	33.4856i	1.08814	−	1.08814i	0.0924159	−	0.995720i	$-0.470541\pi$
$947$	33.4856	−	33.4856i	1.08814	−	1.08814i	0.995720	−	0.0924159i	$-0.0294589\pi$
$948$		0			0
$949$	−12.3321	−	12.3321i	−0.400317	−	0.400317i
$950$		0			0
$951$			32.9459i			1.06834i
$952$		0			0
$953$			14.3013i			0.463266i	0.972803	+	0.231633i	$0.0744068\pi$
$953$			14.3013i			0.463266i	−0.972803	+	0.231633i	$0.925593\pi$
$954$		0			0
$955$	−9.45512	−	9.45512i	−0.305961	−	0.305961i
$956$		0			0
$957$	−0.0403196	+	0.0403196i	−0.00130335	+	0.00130335i
$958$		0			0
$959$	−34.9064			−1.12719
$960$		0			0
$961$	−18.1829			−0.586546
$962$		0			0
$963$	−2.51098	+	2.51098i	−0.0809152	+	0.0809152i
$964$		0			0
$965$	5.88967	+	5.88967i	0.189595	+	0.189595i
$966$		0			0
$967$			53.0546i			1.70612i	0.521812	+	0.853060i	$0.325256\pi$
$967$			53.0546i			1.70612i	−0.521812	+	0.853060i	$0.674744\pi$
$968$		0			0
$969$		−	38.8246i		−	1.24723i
$970$		0			0
$971$	−4.58090	−	4.58090i	−0.147008	−	0.147008i	0.629772	−	0.776780i	$-0.283148\pi$
$971$	−4.58090	−	4.58090i	−0.147008	−	0.147008i	−0.776780	+	0.629772i	$0.783148\pi$
$972$		0			0
$973$	3.32375	−	3.32375i	0.106554	−	0.106554i
$974$		0			0
$975$	−2.44610			−0.0783378
$976$		0			0
$977$	11.2092			0.358614			0.179307	−	0.983793i	$-0.442615\pi$
$977$	11.2092			0.358614			0.179307	+	0.983793i	$0.442615\pi$
$978$		0			0
$979$	0.0450516	−	0.0450516i	0.00143986	−	0.00143986i
$980$		0			0
$981$	−12.0668	−	12.0668i	−0.385264	−	0.385264i
$982$		0			0
$983$			20.1018i			0.641147i	0.947224	+	0.320573i	$0.103876\pi$
$983$			20.1018i			0.641147i	−0.947224	+	0.320573i	$0.896124\pi$
$984$		0			0
$985$			18.6669i			0.594778i
$986$		0			0
$987$	15.5425	+	15.5425i	0.494723	+	0.494723i
$988$		0			0
$989$	−20.5254	+	20.5254i	−0.652671	+	0.652671i
$990$		0			0
$991$	−20.7088			−0.657835			−0.328918	−	0.944359i	$-0.606684\pi$
$991$	−20.7088			−0.657835			−0.328918	+	0.944359i	$0.606684\pi$
$992$		0			0
$993$	−22.4941			−0.713828
$994$		0			0
$995$	2.59305	−	2.59305i	0.0822052	−	0.0822052i
$996$		0			0
$997$	0.704128	+	0.704128i	0.0223000	+	0.0223000i	0.718169	−	0.695869i	$-0.244981\pi$
$997$	0.704128	+	0.704128i	0.0223000	+	0.0223000i	−0.695869	+	0.718169i	$0.744981\pi$
$998$		0			0
$999$			7.03940i			0.222717i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.s.c.241.2		20
3.2	odd	2		2880.2.t.d.2161.2		20
4.3	odd	2		240.2.s.c.181.7	yes	20
8.3	odd	2		1920.2.s.e.481.4		20
8.5	even	2		1920.2.s.f.481.7		20
12.11	even	2		720.2.t.d.181.4		20
16.3	odd	4		240.2.s.c.61.7	✓	20
16.5	even	4		1920.2.s.f.1441.9		20
16.11	odd	4		1920.2.s.e.1441.2		20
16.13	even	4	inner	960.2.s.c.721.4		20
48.29	odd	4		2880.2.t.d.721.4		20
48.35	even	4		720.2.t.d.541.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.s.c.61.7	✓	20	16.3	odd	4
240.2.s.c.181.7	yes	20	4.3	odd	2
720.2.t.d.181.4		20	12.11	even	2
720.2.t.d.541.4		20	48.35	even	4
960.2.s.c.241.2		20	1.1	even	1	trivial
960.2.s.c.721.4		20	16.13	even	4	inner
1920.2.s.e.481.4		20	8.3	odd	2
1920.2.s.e.1441.2		20	16.11	odd	4
1920.2.s.f.481.7		20	8.5	even	2
1920.2.s.f.1441.9		20	16.5	even	4
2880.2.t.d.721.4		20	48.29	odd	4
2880.2.t.d.2161.2		20	3.2	odd	2

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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(0.707107 + 0.707107i) q^{5} -2.18060i q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{3} +(0.707107 + 0.707107i) q^{5} -2.18060i q^{7} -1.00000i q^{9} +(0.00889637 + 0.00889637i) q^{11} +(1.72965 - 1.72965i) q^{13} -1.00000 q^{15} -5.54943 q^{17} +(4.94702 - 4.94702i) q^{19} +(1.54192 + 1.54192i) q^{21} -3.01309i q^{23} +1.00000i q^{25} +(0.707107 + 0.707107i) q^{27} +(3.20471 - 3.20471i) q^{29} -3.58009 q^{31} -0.0125814 q^{33} +(1.54192 - 1.54192i) q^{35} +(4.97761 + 4.97761i) q^{37} +2.44610i q^{39} -3.76487i q^{41} +(-6.81210 - 6.81210i) q^{43} +(0.707107 - 0.707107i) q^{45} +10.0800 q^{47} +2.24499 q^{49} +(3.92404 - 3.92404i) q^{51} +(-0.932644 - 0.932644i) q^{53} +0.0125814i q^{55} +6.99615i q^{57} +(4.60522 + 4.60522i) q^{59} +(4.17149 - 4.17149i) q^{61} -2.18060 q^{63} +2.44610 q^{65} +(11.0105 - 11.0105i) q^{67} +(2.13057 + 2.13057i) q^{69} +12.1092i q^{71} -7.12981i q^{73} +(-0.707107 - 0.707107i) q^{75} +(0.0193994 - 0.0193994i) q^{77} +3.41789 q^{79} -1.00000 q^{81} +(-5.31631 + 5.31631i) q^{83} +(-3.92404 - 3.92404i) q^{85} +4.53214i q^{87} -5.06405i q^{89} +(-3.77168 - 3.77168i) q^{91} +(2.53151 - 2.53151i) q^{93} +6.99615 q^{95} -10.3646 q^{97} +(0.00889637 - 0.00889637i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q+O(q^{10}) \) 20 * q	\( 20 q - 8 q^{11} - 20 q^{15} - 24 q^{17} + 4 q^{19} + 16 q^{29} + 16 q^{33} + 16 q^{37} + 8 q^{43} - 52 q^{49} - 4 q^{51} - 16 q^{53} + 16 q^{59} - 4 q^{61} + 8 q^{63} + 8 q^{67} - 4 q^{69} - 40 q^{77} - 56 q^{79} - 20 q^{81} + 48 q^{83} + 4 q^{85} + 8 q^{91} + 16 q^{93} + 56 q^{97} - 8 q^{99}+O(q^{100}) \) 20 * q - 8 * q^11 - 20 * q^15 - 24 * q^17 + 4 * q^19 + 16 * q^29 + 16 * q^33 + 16 * q^37 + 8 * q^43 - 52 * q^49 - 4 * q^51 - 16 * q^53 + 16 * q^59 - 4 * q^61 + 8 * q^63 + 8 * q^67 - 4 * q^69 - 40 * q^77 - 56 * q^79 - 20 * q^81 + 48 * q^83 + 4 * q^85 + 8 * q^91 + 16 * q^93 + 56 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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