LMFDB - Embedded newform 1040.2.cd.i.993.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1040,2,Mod(177,1040)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1040, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1040.177");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.cd (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:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 9 $ x^4 - 5*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			993.2
Root			$1.65831 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1040.993
Dual form			1040.2.cd.i.177.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15831 + 1.15831i) q^{3} +(1.65831 - 1.50000i) q^{5} -3.00000 q^{7} -0.316625i q^{9} +O(q^{10})$	\(q+(1.15831 + 1.15831i) q^{3} +(1.65831 - 1.50000i) q^{5} -3.00000 q^{7} -0.316625i q^{9} +(-3.31662 - 3.31662i) q^{11} +(-3.00000 - 2.00000i) q^{13} +(3.65831 + 0.183375i) q^{15} +(-3.15831 - 3.15831i) q^{17} +(-2.00000 - 2.00000i) q^{19} +(-3.47494 - 3.47494i) q^{21} +(3.31662 - 3.31662i) q^{23} +(0.500000 - 4.97494i) q^{25} +(3.84169 - 3.84169i) q^{27} +6.31662i q^{29} +(-1.00000 + 1.00000i) q^{31} -7.68338i q^{33} +(-4.97494 + 4.50000i) q^{35} +3.00000 q^{37} +(-1.15831 - 5.79156i) q^{39} +(-6.31662 + 6.31662i) q^{41} +(-2.47494 + 2.47494i) q^{43} +(-0.474937 - 0.525063i) q^{45} +9.31662 q^{47} +2.00000 q^{49} -7.31662i q^{51} +(9.63325 + 9.63325i) q^{53} +(-10.4749 - 0.525063i) q^{55} -4.63325i q^{57} +(-0.316625 + 0.316625i) q^{59} +2.00000 q^{61} +0.949874i q^{63} +(-7.97494 + 1.18338i) q^{65} -4.94987i q^{67} +7.68338 q^{69} +(2.84169 - 2.84169i) q^{71} -4.00000i q^{73} +(6.34169 - 5.18338i) q^{75} +(9.94987 + 9.94987i) q^{77} +12.9499i q^{79} +7.94987 q^{81} -6.31662 q^{83} +(-9.97494 - 0.500000i) q^{85} +(-7.31662 + 7.31662i) q^{87} +(0.316625 - 0.316625i) q^{89} +(9.00000 + 6.00000i) q^{91} -2.31662 q^{93} +(-6.31662 - 0.316625i) q^{95} -8.94987i q^{97} +(-1.05013 + 1.05013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 12 q^{7}+O(q^{10}) $ 4 * q - 2 * q^3 - 12 * q^7	$ 4 q - 2 q^{3} - 12 q^{7} - 12 q^{13} + 8 q^{15} - 6 q^{17} - 8 q^{19} + 6 q^{21} + 2 q^{25} + 22 q^{27} - 4 q^{31} + 12 q^{37} + 2 q^{39} - 12 q^{41} + 10 q^{43} + 18 q^{45} + 24 q^{47} + 8 q^{49} + 12 q^{53} - 22 q^{55} + 12 q^{59} + 8 q^{61} - 12 q^{65} + 44 q^{69} + 18 q^{71} + 32 q^{75} - 8 q^{81} - 12 q^{83} - 20 q^{85} - 16 q^{87} - 12 q^{89} + 36 q^{91} + 4 q^{93} - 12 q^{95} - 44 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - 12 * q^7 - 12 * q^13 + 8 * q^15 - 6 * q^17 - 8 * q^19 + 6 * q^21 + 2 * q^25 + 22 * q^27 - 4 * q^31 + 12 * q^37 + 2 * q^39 - 12 * q^41 + 10 * q^43 + 18 * q^45 + 24 * q^47 + 8 * q^49 + 12 * q^53 - 22 * q^55 + 12 * q^59 + 8 * q^61 - 12 * q^65 + 44 * q^69 + 18 * q^71 + 32 * q^75 - 8 * q^81 - 12 * q^83 - 20 * q^85 - 16 * q^87 - 12 * q^89 + 36 * q^91 + 4 * q^93 - 12 * q^95 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	1.15831	+	1.15831i	0.668752	+	0.668752i	0.957427	−	0.288675i	$-0.0932147\pi$
$3$	1.15831	+	1.15831i	0.668752	+	0.668752i	−0.288675	+	0.957427i	$0.593215\pi$
$4$		0			0
$5$	1.65831	−	1.50000i	0.741620	−	0.670820i
$5$	1.65831	−	1.50000i	0.741620	−	0.670820i
$6$		0			0
$7$	−3.00000			−1.13389			−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000			−1.13389			−0.566947	+	0.823754i	$0.691875\pi$
$8$		0			0
$9$		−	0.316625i		−	0.105542i
$10$		0			0
$11$	−3.31662	−	3.31662i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$11$	−3.31662	−	3.31662i	−1.00000	−	1.00000i	−1.00000			$\pi$
$12$		0			0
$13$	−3.00000	−	2.00000i	−0.832050	−	0.554700i
$13$	−3.00000	−	2.00000i	−0.832050	−	0.554700i
$14$		0			0
$15$	3.65831	+	0.183375i	0.944572	+	0.0473473i
$16$		0			0
$17$	−3.15831	−	3.15831i	−0.766003	−	0.766003i	0.211397	−	0.977400i	$-0.432199\pi$
$17$	−3.15831	−	3.15831i	−0.766003	−	0.766003i	−0.977400	+	0.211397i	$0.932199\pi$
$18$		0			0
$19$	−2.00000	−	2.00000i	−0.458831	−	0.458831i	0.439440	−	0.898272i	$-0.355177\pi$
$19$	−2.00000	−	2.00000i	−0.458831	−	0.458831i	−0.898272	+	0.439440i	$0.855177\pi$
$20$		0			0
$21$	−3.47494	−	3.47494i	−0.758293	−	0.758293i
$22$		0			0
$23$	3.31662	−	3.31662i	0.691564	−	0.691564i	−0.271012	−	0.962576i	$-0.587358\pi$
$23$	3.31662	−	3.31662i	0.691564	−	0.691564i	0.962576	+	0.271012i	$0.0873583\pi$
$24$		0			0
$25$	0.500000	−	4.97494i	0.100000	−	0.994987i
$26$		0			0
$27$	3.84169	−	3.84169i	0.739333	−	0.739333i
$28$		0			0
$29$			6.31662i			1.17297i	0.809961	+	0.586484i	$0.199488\pi$
$29$			6.31662i			1.17297i	−0.809961	+	0.586484i	$0.800512\pi$
$30$		0			0
$31$	−1.00000	+	1.00000i	−0.179605	+	0.179605i	−0.791184	−	0.611578i	$-0.790535\pi$
$31$	−1.00000	+	1.00000i	−0.179605	+	0.179605i	0.611578	+	0.791184i	$0.290535\pi$
$32$		0			0
$33$		−	7.68338i		−	1.33750i
$34$		0			0
$35$	−4.97494	+	4.50000i	−0.840918	+	0.760639i
$36$		0			0
$37$	3.00000			0.493197			0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000			0.493197			0.246598	+	0.969118i	$0.420687\pi$
$38$		0			0
$39$	−1.15831	−	5.79156i	−0.185478	−	0.927392i
$40$		0			0
$41$	−6.31662	+	6.31662i	−0.986491	+	0.986491i	−0.999910	−	0.0134189i	$-0.995729\pi$
$41$	−6.31662	+	6.31662i	−0.986491	+	0.986491i	0.0134189	+	0.999910i	$0.495729\pi$
$42$		0			0
$43$	−2.47494	+	2.47494i	−0.377424	+	0.377424i	−0.870172	−	0.492748i	$-0.835993\pi$
$43$	−2.47494	+	2.47494i	−0.377424	+	0.377424i	0.492748	+	0.870172i	$0.335993\pi$
$44$		0			0
$45$	−0.474937	−	0.525063i	−0.0707995	−	0.0782717i
$46$		0			0
$47$	9.31662			1.35897			0.679485	−	0.733690i	$-0.262203\pi$
$47$	9.31662			1.35897			0.679485	+	0.733690i	$0.262203\pi$
$48$		0			0
$49$	2.00000			0.285714
$50$		0			0
$51$		−	7.31662i		−	1.02453i
$52$		0			0
$53$	9.63325	+	9.63325i	1.32323	+	1.32323i	0.911147	+	0.412082i	$0.135198\pi$
$53$	9.63325	+	9.63325i	1.32323	+	1.32323i	0.412082	+	0.911147i	$0.364802\pi$
$54$		0			0
$55$	−10.4749	−	0.525063i	−1.41244	−	0.0707995i
$56$		0			0
$57$		−	4.63325i		−	0.613689i
$58$		0			0
$59$	−0.316625	+	0.316625i	−0.0412210	+	0.0412210i	−0.727417	−	0.686196i	$-0.759279\pi$
$59$	−0.316625	+	0.316625i	−0.0412210	+	0.0412210i	0.686196	+	0.727417i	$0.259279\pi$
$60$		0			0
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$		0			0
$63$			0.949874i			0.119673i
$64$		0			0
$65$	−7.97494	+	1.18338i	−0.989169	+	0.146780i
$66$		0			0
$67$		−	4.94987i		−	0.604723i	−0.953193	−	0.302362i	$-0.902225\pi$
$67$		−	4.94987i		−	0.604723i	0.953193	−	0.302362i	$-0.0977750\pi$
$68$		0			0
$69$	7.68338			0.924970
$70$		0			0
$71$	2.84169	−	2.84169i	0.337246	−	0.337246i	−0.518084	−	0.855330i	$-0.673354\pi$
$71$	2.84169	−	2.84169i	0.337246	−	0.337246i	0.855330	+	0.518084i	$0.173354\pi$
$72$		0			0
$73$		−	4.00000i		−	0.468165i	−0.972217	−	0.234082i	$-0.924791\pi$
$73$		−	4.00000i		−	0.468165i	0.972217	−	0.234082i	$-0.0752085\pi$
$74$		0			0
$75$	6.34169	−	5.18338i	0.732275	−	0.598525i
$76$		0			0
$77$	9.94987	+	9.94987i	1.13389	+	1.13389i
$78$		0			0
$79$			12.9499i			1.45697i	0.685059	+	0.728487i	$0.259776\pi$
$79$			12.9499i			1.45697i	−0.685059	+	0.728487i	$0.740224\pi$
$80$		0			0
$81$	7.94987			0.883319
$82$		0			0
$83$	−6.31662			−0.693340			−0.346670	−	0.937987i	$-0.612688\pi$
$83$	−6.31662			−0.693340			−0.346670	+	0.937987i	$0.612688\pi$
$84$		0			0
$85$	−9.97494	−	0.500000i	−1.08193	−	0.0542326i
$86$		0			0
$87$	−7.31662	+	7.31662i	−0.784425	+	0.784425i
$88$		0			0
$89$	0.316625	−	0.316625i	0.0335622	−	0.0335622i	−0.690127	−	0.723689i	$-0.742445\pi$
$89$	0.316625	−	0.316625i	0.0335622	−	0.0335622i	0.723689	+	0.690127i	$0.242445\pi$
$90$		0			0
$91$	9.00000	+	6.00000i	0.943456	+	0.628971i
$92$		0			0
$93$	−2.31662			−0.240223
$94$		0			0
$95$	−6.31662	−	0.316625i	−0.648072	−	0.0324850i
$96$		0			0
$97$		−	8.94987i		−	0.908722i	−0.890818	−	0.454361i	$-0.849868\pi$
$97$		−	8.94987i		−	0.908722i	0.890818	−	0.454361i	$-0.150132\pi$
$98$		0			0
$99$	−1.05013	+	1.05013i	−0.105542	+	0.105542i
$100$		0			0
$101$		−	19.2665i		−	1.91709i	−0.284944	−	0.958544i	$-0.591975\pi$
$101$		−	19.2665i		−	1.91709i	0.284944	−	0.958544i	$-0.408025\pi$
$102$		0			0
$103$	7.94987	−	7.94987i	0.783324	−	0.783324i	−0.197066	−	0.980390i	$-0.563141\pi$
$103$	7.94987	−	7.94987i	0.783324	−	0.783324i	0.980390	+	0.197066i	$0.0631413\pi$
$104$		0			0
$105$	−10.9749	−	0.550126i	−1.07104	−	0.0536868i
$106$		0			0
$107$	9.63325	−	9.63325i	0.931281	−	0.931281i	−0.0665047	−	0.997786i	$-0.521185\pi$
$107$	9.63325	−	9.63325i	0.931281	−	0.931281i	0.997786	+	0.0665047i	$0.0211847\pi$
$108$		0			0
$109$	−1.47494	−	1.47494i	−0.141273	−	0.141273i	0.632933	−	0.774206i	$-0.281851\pi$
$109$	−1.47494	−	1.47494i	−0.141273	−	0.141273i	−0.774206	+	0.632933i	$0.781851\pi$
$110$		0			0
$111$	3.47494	+	3.47494i	0.329826	+	0.329826i
$112$		0			0
$113$	2.68338	+	2.68338i	0.252431	+	0.252431i	0.821967	−	0.569536i	$-0.192877\pi$
$113$	2.68338	+	2.68338i	0.252431	+	0.252431i	−0.569536	+	0.821967i	$0.692877\pi$
$114$		0			0
$115$	0.525063	−	10.4749i	0.0489624	−	0.976793i
$116$		0			0
$117$	−0.633250	+	0.949874i	−0.0585439	+	0.0878159i
$118$		0			0
$119$	9.47494	+	9.47494i	0.868566	+	0.868566i
$120$		0			0
$121$			11.0000i			1.00000i
$122$		0			0
$123$	−14.6332			−1.31944
$124$		0			0
$125$	−6.63325	−	9.00000i	−0.593296	−	0.804984i
$126$		0			0
$127$	7.00000	+	7.00000i	0.621150	+	0.621150i	0.945825	−	0.324676i	$-0.105255\pi$
$127$	7.00000	+	7.00000i	0.621150	+	0.621150i	−0.324676	+	0.945825i	$0.605255\pi$
$128$		0			0
$129$	−5.73350			−0.504807
$130$		0			0
$131$	3.00000			0.262111			0.131056	−	0.991375i	$-0.458163\pi$
$131$	3.00000			0.262111			0.131056	+	0.991375i	$0.458163\pi$
$132$		0			0
$133$	6.00000	+	6.00000i	0.520266	+	0.520266i
$134$		0			0
$135$	0.608187	−	12.1332i	0.0523444	−	1.04426i
$136$		0			0
$137$	5.68338			0.485564			0.242782	−	0.970081i	$-0.421940\pi$
$137$	5.68338			0.485564			0.242782	+	0.970081i	$0.421940\pi$
$138$		0			0
$139$		−	15.9499i		−	1.35285i	−0.736511	−	0.676425i	$-0.763528\pi$
$139$		−	15.9499i		−	1.35285i	0.736511	−	0.676425i	$-0.236472\pi$
$140$		0			0
$141$	10.7916	+	10.7916i	0.908813	+	0.908813i
$142$		0			0
$143$	3.31662	+	16.5831i	0.277350	+	1.38675i
$144$		0			0
$145$	9.47494	+	10.4749i	0.786851	+	0.869896i
$146$		0			0
$147$	2.31662	+	2.31662i	0.191072	+	0.191072i
$148$		0			0
$149$	−15.3166	−	15.3166i	−1.25479	−	1.25479i	−0.953549	−	0.301238i	$-0.902600\pi$
$149$	−15.3166	−	15.3166i	−1.25479	−	1.25479i	−0.301238	−	0.953549i	$-0.597400\pi$
$150$		0			0
$151$	−4.47494	−	4.47494i	−0.364165	−	0.364165i	0.501179	−	0.865344i	$-0.332900\pi$
$151$	−4.47494	−	4.47494i	−0.364165	−	0.364165i	−0.865344	+	0.501179i	$0.832900\pi$
$152$		0			0
$153$	−1.00000	+	1.00000i	−0.0808452	+	0.0808452i
$154$		0			0
$155$	−0.158312	+	3.15831i	−0.0127160	+	0.253682i
$156$		0			0
$157$	10.0000	−	10.0000i	0.798087	−	0.798087i	−0.184707	−	0.982794i	$-0.559134\pi$
$157$	10.0000	−	10.0000i	0.798087	−	0.798087i	0.982794	+	0.184707i	$0.0591335\pi$
$158$		0			0
$159$			22.3166i			1.76982i
$160$		0			0
$161$	−9.94987	+	9.94987i	−0.784160	+	0.784160i
$162$		0			0
$163$		−	2.94987i		−	0.231052i	−0.993304	−	0.115526i	$-0.963145\pi$
$163$		−	2.94987i		−	0.231052i	0.993304	−	0.115526i	$-0.0368554\pi$
$164$		0			0
$165$	−11.5251	−	12.7414i	−0.897225	−	0.991919i
$166$		0			0
$167$	−12.6332			−0.977590			−0.488795	−	0.872399i	$-0.662563\pi$
$167$	−12.6332			−0.977590			−0.488795	+	0.872399i	$0.662563\pi$
$168$		0			0
$169$	5.00000	+	12.0000i	0.384615	+	0.923077i
$170$		0			0
$171$	−0.633250	+	0.633250i	−0.0484258	+	0.0484258i
$172$		0			0
$173$	−3.31662	+	3.31662i	−0.252158	+	0.252158i	−0.821855	−	0.569697i	$-0.807061\pi$
$173$	−3.31662	+	3.31662i	−0.252158	+	0.252158i	0.569697	+	0.821855i	$0.307061\pi$
$174$		0			0
$175$	−1.50000	+	14.9248i	−0.113389	+	1.12821i
$176$		0			0
$177$	−0.733501			−0.0551333
$178$		0			0
$179$	−15.0000			−1.12115			−0.560576	−	0.828103i	$-0.689420\pi$
$179$	−15.0000			−1.12115			−0.560576	+	0.828103i	$0.689420\pi$
$180$		0			0
$181$		−	6.94987i		−	0.516580i	−0.966067	−	0.258290i	$-0.916841\pi$
$181$		−	6.94987i		−	0.516580i	0.966067	−	0.258290i	$-0.0831590\pi$
$182$		0			0
$183$	2.31662	+	2.31662i	0.171250	+	0.171250i
$184$		0			0
$185$	4.97494	−	4.50000i	0.365765	−	0.330847i
$186$		0			0
$187$			20.9499i			1.53201i
$188$		0			0
$189$	−11.5251	+	11.5251i	−0.838325	+	0.838325i
$190$		0			0
$191$	−5.05013			−0.365414			−0.182707	−	0.983167i	$-0.558486\pi$
$191$	−5.05013			−0.365414			−0.182707	+	0.983167i	$0.558486\pi$
$192$		0			0
$193$		−	10.9499i		−	0.788189i	−0.919070	−	0.394095i	$-0.871058\pi$
$193$		−	10.9499i		−	0.788189i	0.919070	−	0.394095i	$-0.128942\pi$
$194$		0			0
$195$	−10.6082	−	7.86675i	−0.759668	−	0.563350i
$196$		0			0
$197$		−	3.94987i		−	0.281417i	−0.990051	−	0.140708i	$-0.955062\pi$
$197$		−	3.94987i		−	0.281417i	0.990051	−	0.140708i	$-0.0449380\pi$
$198$		0			0
$199$	−16.9499			−1.20154			−0.600772	−	0.799420i	$-0.705140\pi$
$199$	−16.9499			−1.20154			−0.600772	+	0.799420i	$0.705140\pi$
$200$		0			0
$201$	5.73350	−	5.73350i	0.404410	−	0.404410i
$202$		0			0
$203$		−	18.9499i		−	1.33002i
$204$		0			0
$205$	−1.00000	+	19.9499i	−0.0698430	+	1.39336i
$206$		0			0
$207$	−1.05013	−	1.05013i	−0.0729888	−	0.0729888i
$208$		0			0
$209$			13.2665i			0.917663i
$210$		0			0
$211$	19.9499			1.37341			0.686703	−	0.726938i	$-0.259057\pi$
$211$	19.9499			1.37341			0.686703	+	0.726938i	$0.259057\pi$
$212$		0			0
$213$	6.58312			0.451068
$214$		0			0
$215$	−0.391813	+	7.81662i	−0.0267214	+	0.533089i
$216$		0			0
$217$	3.00000	−	3.00000i	0.203653	−	0.203653i
$218$		0			0
$219$	4.63325	−	4.63325i	0.313086	−	0.313086i
$220$		0			0
$221$	3.15831	+	15.7916i	0.212451	+	1.06226i
$222$		0			0
$223$	−15.9499			−1.06808			−0.534041	−	0.845458i	$-0.679327\pi$
$223$	−15.9499			−1.06808			−0.534041	+	0.845458i	$0.679327\pi$
$224$		0			0
$225$	−1.57519	−	0.158312i	−0.105013	−	0.0105542i
$226$		0			0
$227$		−	18.0000i		−	1.19470i	−0.801980	−	0.597351i	$-0.796220\pi$
$227$		−	18.0000i		−	1.19470i	0.801980	−	0.597351i	$-0.203780\pi$
$228$		0			0
$229$	−3.52506	+	3.52506i	−0.232943	+	0.232943i	−0.813920	−	0.580977i	$-0.802671\pi$
$229$	−3.52506	+	3.52506i	−0.232943	+	0.232943i	0.580977	+	0.813920i	$0.302671\pi$
$230$		0			0
$231$			23.0501i			1.51659i
$232$		0			0
$233$	−6.79156	+	6.79156i	−0.444930	+	0.444930i	−0.893665	−	0.448735i	$-0.851875\pi$
$233$	−6.79156	+	6.79156i	−0.444930	+	0.444930i	0.448735	+	0.893665i	$0.351875\pi$
$234$		0			0
$235$	15.4499	−	13.9749i	1.00784	−	0.911624i
$236$		0			0
$237$	−15.0000	+	15.0000i	−0.974355	+	0.974355i
$238$		0			0
$239$	11.8417	+	11.8417i	0.765975	+	0.765975i	0.977395	−	0.211420i	$-0.0678088\pi$
$239$	11.8417	+	11.8417i	0.765975	+	0.765975i	−0.211420	+	0.977395i	$0.567809\pi$
$240$		0			0
$241$	16.0000	+	16.0000i	1.03065	+	1.03065i	0.999515	+	0.0311354i	$0.00991232\pi$
$241$	16.0000	+	16.0000i	1.03065	+	1.03065i	0.0311354	+	0.999515i	$0.490088\pi$
$242$		0			0
$243$	−2.31662	−	2.31662i	−0.148612	−	0.148612i
$244$		0			0
$245$	3.31662	−	3.00000i	0.211891	−	0.191663i
$246$		0			0
$247$	2.00000	+	10.0000i	0.127257	+	0.636285i
$248$		0			0
$249$	−7.31662	−	7.31662i	−0.463672	−	0.463672i
$250$		0			0
$251$			19.2665i			1.21609i	0.793902	+	0.608045i	$0.208046\pi$
$251$			19.2665i			1.21609i	−0.793902	+	0.608045i	$0.791954\pi$
$252$		0			0
$253$	−22.0000			−1.38313
$254$		0			0
$255$	−10.9749	−	12.1332i	−0.687277	−	0.759814i
$256$		0			0
$257$	11.8417	+	11.8417i	0.738664	+	0.738664i	0.972319	−	0.233655i	$-0.0750687\pi$
$257$	11.8417	+	11.8417i	0.738664	+	0.738664i	−0.233655	+	0.972319i	$0.575069\pi$
$258$		0			0
$259$	−9.00000			−0.559233
$260$		0			0
$261$	2.00000			0.123797
$262$		0			0
$263$	12.3166	+	12.3166i	0.759476	+	0.759476i	0.976227	−	0.216751i	$-0.0695461\pi$
$263$	12.3166	+	12.3166i	0.759476	+	0.759476i	−0.216751	+	0.976227i	$0.569546\pi$
$264$		0			0
$265$	30.4248	+	1.52506i	1.86898	+	0.0936839i
$266$		0			0
$267$	0.733501			0.0448895
$268$		0			0
$269$			13.2665i			0.808873i	0.914566	+	0.404436i	$0.132532\pi$
$269$			13.2665i			0.808873i	−0.914566	+	0.404436i	$0.867468\pi$
$270$		0			0
$271$	10.5251	+	10.5251i	0.639352	+	0.639352i	0.950396	−	0.311044i	$-0.100679\pi$
$271$	10.5251	+	10.5251i	0.639352	+	0.639352i	−0.311044	+	0.950396i	$0.600679\pi$
$272$		0			0
$273$	3.47494	+	17.3747i	0.210313	+	1.05156i
$274$		0			0
$275$	−18.1583	+	14.8417i	−1.09499	+	0.894987i
$276$		0			0
$277$	21.8997	+	21.8997i	1.31583	+	1.31583i	0.917045	+	0.398783i	$0.130567\pi$
$277$	21.8997	+	21.8997i	1.31583	+	1.31583i	0.398783	+	0.917045i	$0.369433\pi$
$278$		0			0
$279$	0.316625	+	0.316625i	0.0189558	+	0.0189558i
$280$		0			0
$281$	−11.6834	−	11.6834i	−0.696972	−	0.696972i	0.266784	−	0.963756i	$-0.414039\pi$
$281$	−11.6834	−	11.6834i	−0.696972	−	0.696972i	−0.963756	+	0.266784i	$0.914039\pi$
$282$		0			0
$283$	7.94987	−	7.94987i	0.472571	−	0.472571i	−0.430175	−	0.902746i	$-0.641548\pi$
$283$	7.94987	−	7.94987i	0.472571	−	0.472571i	0.902746	+	0.430175i	$0.141548\pi$
$284$		0			0
$285$	−6.94987	−	7.68338i	−0.411675	−	0.455124i
$286$		0			0
$287$	18.9499	−	18.9499i	1.11858	−	1.11858i
$288$		0			0
$289$			2.94987i			0.173522i
$290$		0			0
$291$	10.3668	−	10.3668i	0.607710	−	0.607710i
$292$		0			0
$293$		−	22.8997i		−	1.33782i	−0.743344	−	0.668909i	$-0.766762\pi$
$293$		−	22.8997i		−	1.33782i	0.743344	−	0.668909i	$-0.233238\pi$
$294$		0			0
$295$	−0.0501256	+	1.00000i	−0.00291843	+	0.0582223i
$296$		0			0
$297$	−25.4829			−1.47867
$298$		0			0
$299$	−16.5831	+	3.31662i	−0.959027	+	0.191805i
$300$		0			0
$301$	7.42481	−	7.42481i	0.427959	−	0.427959i
$302$		0			0
$303$	22.3166	−	22.3166i	1.28206	−	1.28206i
$304$		0			0
$305$	3.31662	−	3.00000i	0.189909	−	0.171780i
$306$		0			0
$307$	25.8997			1.47818			0.739088	−	0.673608i	$-0.235257\pi$
$307$	25.8997			1.47818			0.739088	+	0.673608i	$0.235257\pi$
$308$		0			0
$309$	18.4169			1.04770
$310$		0			0
$311$			19.2665i			1.09250i	0.837621	+	0.546251i	$0.183946\pi$
$311$			19.2665i			1.09250i	−0.837621	+	0.546251i	$0.816054\pi$
$312$		0			0
$313$	−15.4248	−	15.4248i	−0.871862	−	0.871862i	0.120813	−	0.992675i	$-0.461450\pi$
$313$	−15.4248	−	15.4248i	−0.871862	−	0.871862i	−0.992675	+	0.120813i	$0.961450\pi$
$314$		0			0
$315$	1.42481	+	1.57519i	0.0802790	+	0.0887518i
$316$		0			0
$317$		−	12.0000i		−	0.673987i	−0.941507	−	0.336994i	$-0.890590\pi$
$317$		−	12.0000i		−	0.673987i	0.941507	−	0.336994i	$-0.109410\pi$
$318$		0			0
$319$	20.9499	−	20.9499i	1.17297	−	1.17297i
$320$		0			0
$321$	22.3166			1.24559
$322$		0			0
$323$			12.6332i			0.702933i
$324$		0			0
$325$	−11.4499	+	13.9248i	−0.635125	+	0.772410i
$326$		0			0
$327$		−	3.41688i		−	0.188954i
$328$		0			0
$329$	−27.9499			−1.54093
$330$		0			0
$331$	−1.00000	+	1.00000i	−0.0549650	+	0.0549650i	−0.734055	−	0.679090i	$-0.762375\pi$
$331$	−1.00000	+	1.00000i	−0.0549650	+	0.0549650i	0.679090	+	0.734055i	$0.262375\pi$
$332$		0			0
$333$		−	0.949874i		−	0.0520528i
$334$		0			0
$335$	−7.42481	−	8.20844i	−0.405661	−	0.448475i
$336$		0			0
$337$	−3.52506	−	3.52506i	−0.192022	−	0.192022i	0.604547	−	0.796569i	$-0.293354\pi$
$337$	−3.52506	−	3.52506i	−0.192022	−	0.192022i	−0.796569	+	0.604547i	$0.793354\pi$
$338$		0			0
$339$			6.21637i			0.337627i
$340$		0			0
$341$	6.63325			0.359211
$342$		0			0
$343$	15.0000			0.809924
$344$		0			0
$345$	12.7414	−	11.5251i	0.685976	−	0.620489i
$346$		0			0
$347$	−0.791562	+	0.791562i	−0.0424933	+	0.0424933i	−0.728034	−	0.685541i	$-0.759566\pi$
$347$	−0.791562	+	0.791562i	−0.0424933	+	0.0424933i	0.685541	+	0.728034i	$0.259566\pi$
$348$		0			0
$349$	18.4248	−	18.4248i	0.986258	−	0.986258i	−0.0136493	−	0.999907i	$-0.504345\pi$
$349$	18.4248	−	18.4248i	0.986258	−	0.986258i	0.999907	+	0.0136493i	$0.00434484\pi$
$350$		0			0
$351$	−19.2084	+	3.84169i	−1.02527	+	0.205054i
$352$		0			0
$353$	−7.58312			−0.403609			−0.201804	−	0.979426i	$-0.564681\pi$
$353$	−7.58312			−0.403609			−0.201804	+	0.979426i	$0.564681\pi$
$354$		0			0
$355$	0.449874	−	8.97494i	0.0238769	−	0.476340i
$356$		0			0
$357$			21.9499i			1.16171i
$358$		0			0
$359$	−22.2665	+	22.2665i	−1.17518	+	1.17518i	−0.194224	+	0.980957i	$0.562219\pi$
$359$	−22.2665	+	22.2665i	−1.17518	+	1.17518i	−0.980957	+	0.194224i	$0.937781\pi$
$360$		0			0
$361$		−	11.0000i		−	0.578947i
$362$		0			0
$363$	−12.7414	+	12.7414i	−0.668752	+	0.668752i
$364$		0			0
$365$	−6.00000	−	6.63325i	−0.314054	−	0.347200i
$366$		0			0
$367$	−1.94987	+	1.94987i	−0.101783	+	0.101783i	−0.756164	−	0.654382i	$-0.772929\pi$
$367$	−1.94987	+	1.94987i	−0.101783	+	0.101783i	0.654382	+	0.756164i	$0.272929\pi$
$368$		0			0
$369$	2.00000	+	2.00000i	0.104116	+	0.104116i
$370$		0			0
$371$	−28.8997	−	28.8997i	−1.50040	−	1.50040i
$372$		0			0
$373$	−20.0000	−	20.0000i	−1.03556	−	1.03556i	−0.999344	−	0.0362168i	$-0.988469\pi$
$373$	−20.0000	−	20.0000i	−1.03556	−	1.03556i	−0.0362168	−	0.999344i	$-0.511531\pi$
$374$		0			0
$375$	2.74144	−	18.1082i	0.141567	−	0.935103i
$376$		0			0
$377$	12.6332	−	18.9499i	0.650645	−	0.975968i
$378$		0			0
$379$	13.0000	+	13.0000i	0.667765	+	0.667765i	0.957198	−	0.289433i	$-0.0934668\pi$
$379$	13.0000	+	13.0000i	0.667765	+	0.667765i	−0.289433	+	0.957198i	$0.593467\pi$
$380$		0			0
$381$			16.2164i			0.830790i
$382$		0			0
$383$	−14.3668			−0.734107			−0.367053	−	0.930200i	$-0.619633\pi$
$383$	−14.3668			−0.734107			−0.367053	+	0.930200i	$0.619633\pi$
$384$		0			0
$385$	31.4248	+	1.57519i	1.60156	+	0.0802790i
$386$		0			0
$387$	0.783626	+	0.783626i	0.0398340	+	0.0398340i
$388$		0			0
$389$	−13.8997			−0.704745			−0.352373	−	0.935860i	$-0.614625\pi$
$389$	−13.8997			−0.704745			−0.352373	+	0.935860i	$0.614625\pi$
$390$		0			0
$391$	−20.9499			−1.05948
$392$		0			0
$393$	3.47494	+	3.47494i	0.175287	+	0.175287i
$394$		0			0
$395$	19.4248	+	21.4749i	0.977368	+	1.08052i
$396$		0			0
$397$	18.0000			0.903394			0.451697	−	0.892171i	$-0.350819\pi$
$397$	18.0000			0.903394			0.451697	+	0.892171i	$0.350819\pi$
$398$		0			0
$399$			13.8997i			0.695858i
$400$		0			0
$401$	−10.5831	−	10.5831i	−0.528496	−	0.528496i	0.391628	−	0.920124i	$-0.371912\pi$
$401$	−10.5831	−	10.5831i	−0.528496	−	0.528496i	−0.920124	+	0.391628i	$0.871912\pi$
$402$		0			0
$403$	5.00000	−	1.00000i	0.249068	−	0.0498135i
$404$		0			0
$405$	13.1834	−	11.9248i	0.655087	−	0.592549i
$406$		0			0
$407$	−9.94987	−	9.94987i	−0.493197	−	0.493197i
$408$		0			0
$409$	23.9499	+	23.9499i	1.18425	+	1.18425i	0.978634	+	0.205611i	$0.0659183\pi$
$409$	23.9499	+	23.9499i	1.18425	+	1.18425i	0.205611	+	0.978634i	$0.434082\pi$
$410$		0			0
$411$	6.58312	+	6.58312i	0.324722	+	0.324722i
$412$		0			0
$413$	0.949874	−	0.949874i	0.0467403	−	0.0467403i
$414$		0			0
$415$	−10.4749	+	9.47494i	−0.514194	+	0.465106i
$416$		0			0
$417$	18.4749	−	18.4749i	0.904722	−	0.904722i
$418$		0			0
$419$			8.68338i			0.424211i	0.977247	+	0.212105i	$0.0680320\pi$
$419$			8.68338i			0.424211i	−0.977247	+	0.212105i	$0.931968\pi$
$420$		0			0
$421$	−2.47494	+	2.47494i	−0.120621	+	0.120621i	−0.764841	−	0.644220i	$-0.777182\pi$
$421$	−2.47494	+	2.47494i	−0.120621	+	0.120621i	0.644220	+	0.764841i	$0.277182\pi$
$422$		0			0
$423$		−	2.94987i		−	0.143428i
$424$		0			0
$425$	−17.2916	+	14.1332i	−0.838764	+	0.685563i
$426$		0			0
$427$	−6.00000			−0.290360
$428$		0			0
$429$	−15.3668	+	23.0501i	−0.741914	+	1.11287i
$430$		0			0
$431$	−12.1583	+	12.1583i	−0.585645	+	0.585645i	−0.936449	−	0.350804i	$-0.885908\pi$
$431$	−12.1583	+	12.1583i	−0.585645	+	0.585645i	0.350804	+	0.936449i	$0.385908\pi$
$432$		0			0
$433$	−12.5251	+	12.5251i	−0.601916	+	0.601916i	−0.940821	−	0.338905i	$-0.889944\pi$
$433$	−12.5251	+	12.5251i	−0.601916	+	0.601916i	0.338905	+	0.940821i	$0.389944\pi$
$434$		0			0
$435$	−1.15831	+	23.1082i	−0.0555368	+	1.10795i
$436$		0			0
$437$	−13.2665			−0.634623
$438$		0			0
$439$	33.8997			1.61795			0.808973	−	0.587845i	$-0.200024\pi$
$439$	33.8997			1.61795			0.808973	+	0.587845i	$0.200024\pi$
$440$		0			0
$441$		−	0.633250i		−	0.0301547i
$442$		0			0
$443$	−20.0581	−	20.0581i	−0.952987	−	0.952987i	0.0459562	−	0.998943i	$-0.485367\pi$
$443$	−20.0581	−	20.0581i	−0.952987	−	0.952987i	−0.998943	+	0.0459562i	$0.985367\pi$
$444$		0			0
$445$	0.0501256	−	1.00000i	0.00237618	−	0.0474045i
$446$		0			0
$447$		−	35.4829i		−	1.67828i
$448$		0			0
$449$	−21.6332	+	21.6332i	−1.02094	+	1.02094i	−0.0211601	+	0.999776i	$0.506736\pi$
$449$	−21.6332	+	21.6332i	−1.02094	+	1.02094i	−0.999776	+	0.0211601i	$0.993264\pi$
$450$		0			0
$451$	41.8997			1.97298
$452$		0			0
$453$		−	10.3668i		−	0.487072i
$454$		0			0
$455$	23.9248	−	3.55013i	1.12161	−	0.166432i
$456$		0			0
$457$		−	2.00000i		−	0.0935561i	−0.998905	−	0.0467780i	$-0.985105\pi$
$457$		−	2.00000i		−	0.0935561i	0.998905	−	0.0467780i	$-0.0148953\pi$
$458$		0			0
$459$	−24.2665			−1.13266
$460$		0			0
$461$	4.10819	−	4.10819i	0.191337	−	0.191337i	−0.604936	−	0.796274i	$-0.706801\pi$
$461$	4.10819	−	4.10819i	0.191337	−	0.191337i	0.796274	+	0.604936i	$0.206801\pi$
$462$		0			0
$463$		−	9.89975i		−	0.460080i	−0.973181	−	0.230040i	$-0.926114\pi$
$463$		−	9.89975i		−	0.460080i	0.973181	−	0.230040i	$-0.0738858\pi$
$464$		0			0
$465$	−3.84169	+	3.47494i	−0.178154	+	0.161146i
$466$		0			0
$467$	−8.36675	−	8.36675i	−0.387167	−	0.387167i	0.486509	−	0.873676i	$-0.338270\pi$
$467$	−8.36675	−	8.36675i	−0.387167	−	0.387167i	−0.873676	+	0.486509i	$0.838270\pi$
$468$		0			0
$469$			14.8496i			0.685692i
$470$		0			0
$471$	23.1662			1.06744
$472$		0			0
$473$	16.4169			0.754849
$474$		0			0
$475$	−10.9499	+	8.94987i	−0.502415	+	0.410648i
$476$		0			0
$477$	3.05013	−	3.05013i	0.139656	−	0.139656i
$478$		0			0
$479$	3.15831	−	3.15831i	0.144307	−	0.144307i	−0.631262	−	0.775569i	$-0.717463\pi$
$479$	3.15831	−	3.15831i	0.144307	−	0.144307i	0.775569	+	0.631262i	$0.217463\pi$
$480$		0			0
$481$	−9.00000	−	6.00000i	−0.410365	−	0.273576i
$482$		0			0
$483$	−23.0501			−1.04882
$484$		0			0
$485$	−13.4248	−	14.8417i	−0.609589	−	0.673926i
$486$		0			0
$487$			2.00000i			0.0906287i	0.998973	+	0.0453143i	$0.0144289\pi$
$487$			2.00000i			0.0906287i	−0.998973	+	0.0453143i	$0.985571\pi$
$488$		0			0
$489$	3.41688	−	3.41688i	0.154516	−	0.154516i
$490$		0			0
$491$		−	32.6834i		−	1.47498i	−0.675358	−	0.737490i	$-0.736011\pi$
$491$		−	32.6834i		−	1.47498i	0.675358	−	0.737490i	$-0.263989\pi$
$492$		0			0
$493$	19.9499	−	19.9499i	0.898497	−	0.898497i
$494$		0			0
$495$	−0.166248	+	3.31662i	−0.00747229	+	0.149071i
$496$		0			0
$497$	−8.52506	+	8.52506i	−0.382401	+	0.382401i
$498$		0			0
$499$	−8.94987	−	8.94987i	−0.400651	−	0.400651i	0.477811	−	0.878463i	$-0.341430\pi$
$499$	−8.94987	−	8.94987i	−0.400651	−	0.400651i	−0.878463	+	0.477811i	$0.841430\pi$
$500$		0			0
$501$	−14.6332	−	14.6332i	−0.653765	−	0.653765i
$502$		0			0
$503$	−1.58312	−	1.58312i	−0.0705880	−	0.0705880i	0.670931	−	0.741519i	$-0.265894\pi$
$503$	−1.58312	−	1.58312i	−0.0705880	−	0.0705880i	−0.741519	+	0.670931i	$0.765894\pi$
$504$		0			0
$505$	−28.8997	−	31.9499i	−1.28602	−	1.42175i
$506$		0			0
$507$	−8.10819	+	19.6913i	−0.360097	+	0.874522i
$508$		0			0
$509$	−15.3166	−	15.3166i	−0.678897	−	0.678897i	0.280853	−	0.959751i	$-0.409383\pi$
$509$	−15.3166	−	15.3166i	−0.678897	−	0.678897i	−0.959751	+	0.280853i	$0.909383\pi$
$510$		0			0
$511$			12.0000i			0.530849i
$512$		0			0
$513$	−15.3668			−0.678459
$514$		0			0
$515$	1.25856	−	25.1082i	0.0554589	−	1.10640i
$516$		0			0
$517$	−30.8997	−	30.8997i	−1.35897	−	1.35897i
$518$		0			0
$519$	−7.68338			−0.337263
$520$		0			0
$521$	10.8997			0.477527			0.238763	−	0.971078i	$-0.423258\pi$
$521$	10.8997			0.477527			0.238763	+	0.971078i	$0.423258\pi$
$522$		0			0
$523$	5.00000	+	5.00000i	0.218635	+	0.218635i	0.807923	−	0.589288i	$-0.200592\pi$
$523$	5.00000	+	5.00000i	0.218635	+	0.218635i	−0.589288	+	0.807923i	$0.700592\pi$
$524$		0			0
$525$	−19.0251	+	15.5501i	−0.830322	+	0.678663i
$526$		0			0
$527$	6.31662			0.275156
$528$		0			0
$529$			1.00000i			0.0434783i
$530$		0			0
$531$	0.100251	+	0.100251i	0.00435053	+	0.00435053i
$532$		0			0
$533$	31.5831	−	6.31662i	1.36802	−	0.273603i
$534$		0			0
$535$	1.52506	−	30.4248i	0.0659342	−	1.31538i
$536$		0			0
$537$	−17.3747	−	17.3747i	−0.749773	−	0.749773i
$538$		0			0
$539$	−6.63325	−	6.63325i	−0.285714	−	0.285714i
$540$		0			0
$541$	4.47494	+	4.47494i	0.192393	+	0.192393i	0.796729	−	0.604337i	$-0.206562\pi$
$541$	4.47494	+	4.47494i	0.192393	+	0.192393i	−0.604337	+	0.796729i	$0.706562\pi$
$542$		0			0
$543$	8.05013	−	8.05013i	0.345464	−	0.345464i
$544$		0			0
$545$	−4.65831	−	0.233501i	−0.199540	−	0.0100021i
$546$		0			0
$547$	−21.5251	+	21.5251i	−0.920345	+	0.920345i	−0.997054	−	0.0767083i	$-0.975559\pi$
$547$	−21.5251	+	21.5251i	−0.920345	+	0.920345i	0.0767083	+	0.997054i	$0.475559\pi$
$548$		0			0
$549$		−	0.633250i		−	0.0270264i
$550$		0			0
$551$	12.6332	−	12.6332i	0.538195	−	0.538195i
$552$		0			0
$553$		−	38.8496i		−	1.65205i
$554$		0			0
$555$	10.9749	+	0.550126i	0.465860	+	0.0233515i
$556$		0			0
$557$	4.58312			0.194193			0.0970966	−	0.995275i	$-0.469044\pi$
$557$	4.58312			0.194193			0.0970966	+	0.995275i	$0.469044\pi$
$558$		0			0
$559$	12.3747	−	2.47494i	0.523393	−	0.104679i
$560$		0			0
$561$	−24.2665	+	24.2665i	−1.02453	+	1.02453i
$562$		0			0
$563$	6.79156	−	6.79156i	0.286230	−	0.286230i	−0.549357	−	0.835588i	$-0.685127\pi$
$563$	6.79156	−	6.79156i	0.286230	−	0.286230i	0.835588	+	0.549357i	$0.185127\pi$
$564$		0			0
$565$	8.47494	+	0.424812i	0.356543	+	0.0178720i
$566$		0			0
$567$	−23.8496			−1.00159
$568$		0			0
$569$	42.7995			1.79425			0.897124	−	0.441779i	$-0.145652\pi$
$569$	42.7995			1.79425			0.897124	+	0.441779i	$0.145652\pi$
$570$		0			0
$571$		−	28.8997i		−	1.20942i	−0.796447	−	0.604708i	$-0.793290\pi$
$571$		−	28.8997i		−	1.20942i	0.796447	−	0.604708i	$-0.206710\pi$
$572$		0			0
$573$	−5.84962	−	5.84962i	−0.244372	−	0.244372i
$574$		0			0
$575$	−14.8417	−	18.1583i	−0.618941	−	0.757254i
$576$		0			0
$577$			41.8997i			1.74431i	0.489230	+	0.872155i	$0.337278\pi$
$577$			41.8997i			1.74431i	−0.489230	+	0.872155i	$0.662722\pi$
$578$		0			0
$579$	12.6834	−	12.6834i	0.527103	−	0.527103i
$580$		0			0
$581$	18.9499			0.786173
$582$		0			0
$583$		−	63.8997i		−	2.64646i
$584$		0			0
$585$	0.374686	+	2.52506i	0.0154914	+	0.104398i
$586$		0			0
$587$		−	24.9499i		−	1.02979i	−0.857253	−	0.514896i	$-0.827831\pi$
$587$		−	24.9499i		−	1.02979i	0.857253	−	0.514896i	$-0.172169\pi$
$588$		0			0
$589$	4.00000			0.164817
$590$		0			0
$591$	4.57519	−	4.57519i	0.188198	−	0.188198i
$592$		0			0
$593$			12.9499i			0.531788i	0.964002	+	0.265894i	$0.0856671\pi$
$593$			12.9499i			0.531788i	−0.964002	+	0.265894i	$0.914333\pi$
$594$		0			0
$595$	29.9248	+	1.50000i	1.22680	+	0.0614940i
$596$		0			0
$597$	−19.6332	−	19.6332i	−0.803535	−	0.803535i
$598$		0			0
$599$		−	13.2665i		−	0.542054i	−0.962572	−	0.271027i	$-0.912637\pi$
$599$		−	13.2665i		−	0.542054i	0.962572	−	0.271027i	$-0.0873633\pi$
$600$		0			0
$601$	−6.05013			−0.246790			−0.123395	−	0.992358i	$-0.539378\pi$
$601$	−6.05013			−0.246790			−0.123395	+	0.992358i	$0.539378\pi$
$602$		0			0
$603$	−1.56725			−0.0638235
$604$		0			0
$605$	16.5000	+	18.2414i	0.670820	+	0.741620i
$606$		0			0
$607$	−3.05013	+	3.05013i	−0.123801	+	0.123801i	−0.766293	−	0.642492i	$-0.777901\pi$
$607$	−3.05013	+	3.05013i	−0.123801	+	0.123801i	0.642492	+	0.766293i	$0.277901\pi$
$608$		0			0
$609$	21.9499	−	21.9499i	0.889454	−	0.889454i
$610$		0			0
$611$	−27.9499	−	18.6332i	−1.13073	−	0.753821i
$612$		0			0
$613$	24.0000			0.969351			0.484675	−	0.874694i	$-0.338938\pi$
$613$	24.0000			0.969351			0.484675	+	0.874694i	$0.338938\pi$
$614$		0			0
$615$	−24.2665	+	21.9499i	−0.978520	+	0.885104i
$616$		0			0
$617$		−	12.0000i		−	0.483102i	−0.970388	−	0.241551i	$-0.922344\pi$
$617$		−	12.0000i		−	0.483102i	0.970388	−	0.241551i	$-0.0776561\pi$
$618$		0			0
$619$	−21.8997	+	21.8997i	−0.880225	+	0.880225i	−0.993557	−	0.113332i	$-0.963848\pi$
$619$	−21.8997	+	21.8997i	−0.880225	+	0.880225i	0.113332	+	0.993557i	$0.463848\pi$
$620$		0			0
$621$		−	25.4829i		−	1.02259i
$622$		0			0
$623$	−0.949874	+	0.949874i	−0.0380559	+	0.0380559i
$624$		0			0
$625$	−24.5000	−	4.97494i	−0.980000	−	0.198997i
$626$		0			0
$627$	−15.3668	+	15.3668i	−0.613689	+	0.613689i
$628$		0			0
$629$	−9.47494	−	9.47494i	−0.377790	−	0.377790i
$630$		0			0
$631$	−4.47494	−	4.47494i	−0.178144	−	0.178144i	0.612402	−	0.790546i	$-0.290203\pi$
$631$	−4.47494	−	4.47494i	−0.178144	−	0.178144i	−0.790546	+	0.612402i	$0.790203\pi$
$632$		0			0
$633$	23.1082	+	23.1082i	0.918468	+	0.918468i
$634$		0			0
$635$	22.1082	+	1.10819i	0.877337	+	0.0439771i
$636$		0			0
$637$	−6.00000	−	4.00000i	−0.237729	−	0.158486i
$638$		0			0
$639$	−0.899749	−	0.899749i	−0.0355935	−	0.0355935i
$640$		0			0
$641$		−	5.36675i		−	0.211974i	−0.994368	−	0.105987i	$-0.966200\pi$
$641$		−	5.36675i		−	0.211974i	0.994368	−	0.105987i	$-0.0338002\pi$
$642$		0			0
$643$	12.9499			0.510693			0.255347	−	0.966850i	$-0.417810\pi$
$643$	12.9499			0.510693			0.255347	+	0.966850i	$0.417810\pi$
$644$		0			0
$645$	−9.50794	+	8.60025i	−0.374375	+	0.338635i
$646$		0			0
$647$	6.63325	+	6.63325i	0.260780	+	0.260780i	0.825371	−	0.564591i	$-0.190966\pi$
$647$	6.63325	+	6.63325i	0.260780	+	0.260780i	−0.564591	+	0.825371i	$0.690966\pi$
$648$		0			0
$649$	2.10025			0.0824421
$650$		0			0
$651$	6.94987			0.272387
$652$		0			0
$653$	31.5831	+	31.5831i	1.23594	+	1.23594i	0.961645	+	0.274299i	$0.0884457\pi$
$653$	31.5831	+	31.5831i	1.23594	+	1.23594i	0.274299	+	0.961645i	$0.411554\pi$
$654$		0			0
$655$	4.97494	−	4.50000i	0.194387	−	0.175830i
$656$		0			0
$657$	−1.26650			−0.0494108
$658$		0			0
$659$			0.633250i			0.0246679i	0.999924	+	0.0123340i	$0.00392612\pi$
$659$			0.633250i			0.0246679i	−0.999924	+	0.0123340i	$0.996074\pi$
$660$		0			0
$661$	−12.8997	−	12.8997i	−0.501742	−	0.501742i	0.410237	−	0.911979i	$-0.365446\pi$
$661$	−12.8997	−	12.8997i	−0.501742	−	0.501742i	−0.911979	+	0.410237i	$0.865446\pi$
$662$		0			0
$663$	−14.6332	+	21.9499i	−0.568308	+	0.852462i
$664$		0			0
$665$	18.9499	+	0.949874i	0.734845	+	0.0368345i
$666$		0			0
$667$	20.9499	+	20.9499i	0.811182	+	0.811182i
$668$		0			0
$669$	−18.4749	−	18.4749i	−0.714282	−	0.714282i
$670$		0			0
$671$	−6.63325	−	6.63325i	−0.256074	−	0.256074i
$672$		0			0
$673$	−11.4248	+	11.4248i	−0.440394	+	0.440394i	−0.892144	−	0.451750i	$-0.850800\pi$
$673$	−11.4248	+	11.4248i	−0.440394	+	0.440394i	0.451750	+	0.892144i	$0.350800\pi$
$674$		0			0
$675$	−17.1913	−	21.0330i	−0.661694	−	0.809560i
$676$		0			0
$677$	−2.68338	+	2.68338i	−0.103130	+	0.103130i	−0.756789	−	0.653659i	$-0.773233\pi$
$677$	−2.68338	+	2.68338i	−0.103130	+	0.103130i	0.653659	+	0.756789i	$0.273233\pi$
$678$		0			0
$679$			26.8496i			1.03039i
$680$		0			0
$681$	20.8496	−	20.8496i	0.798959	−	0.798959i
$682$		0			0
$683$			30.9499i			1.18426i	0.805841	+	0.592132i	$0.201714\pi$
$683$			30.9499i			1.18426i	−0.805841	+	0.592132i	$0.798286\pi$
$684$		0			0
$685$	9.42481	−	8.52506i	0.360104	−	0.325726i
$686$		0			0
$687$	−8.16625			−0.311562
$688$		0			0
$689$	−9.63325	−	48.1662i	−0.366998	−	1.83499i
$690$		0			0
$691$	14.0000	−	14.0000i	0.532585	−	0.532585i	−0.388756	−	0.921341i	$-0.627095\pi$
$691$	14.0000	−	14.0000i	0.532585	−	0.532585i	0.921341	+	0.388756i	$0.127095\pi$
$692$		0			0
$693$	3.15038	−	3.15038i	0.119673	−	0.119673i
$694$		0			0
$695$	−23.9248	−	26.4499i	−0.907520	−	1.00330i
$696$		0			0
$697$	39.8997			1.51131
$698$		0			0
$699$	−15.7335			−0.595096
$700$		0			0
$701$			45.4829i			1.71786i	0.512089	+	0.858932i	$0.328872\pi$
$701$			45.4829i			1.71786i	−0.512089	+	0.858932i	$0.671128\pi$
$702$		0			0
$703$	−6.00000	−	6.00000i	−0.226294	−	0.226294i
$704$		0			0
$705$	34.0831	+	1.70844i	1.28364	+	0.0643435i
$706$		0			0
$707$			57.7995i			2.17377i
$708$		0			0
$709$	29.9499	−	29.9499i	1.12479	−	1.12479i	0.133780	−	0.991011i	$-0.457288\pi$
$709$	29.9499	−	29.9499i	1.12479	−	1.12479i	0.991011	−	0.133780i	$-0.0427116\pi$
$710$		0			0
$711$	4.10025			0.153771
$712$		0			0
$713$			6.63325i			0.248417i
$714$		0			0
$715$	30.3747	+	22.5251i	1.13595	+	0.842390i
$716$		0			0
$717$			27.4327i			1.02449i
$718$		0			0
$719$	6.94987			0.259187			0.129593	−	0.991567i	$-0.458633\pi$
$719$	6.94987			0.259187			0.129593	+	0.991567i	$0.458633\pi$
$720$		0			0
$721$	−23.8496	+	23.8496i	−0.888206	+	0.888206i
$722$		0			0
$723$			37.0660i			1.37850i
$724$		0			0
$725$	31.4248	+	3.15831i	1.16709	+	0.117297i
$726$		0			0
$727$	13.9499	+	13.9499i	0.517372	+	0.517372i	0.916775	−	0.399403i	$-0.130783\pi$
$727$	13.9499	+	13.9499i	0.517372	+	0.517372i	−0.399403	+	0.916775i	$0.630783\pi$
$728$		0			0
$729$		−	29.2164i		−	1.08209i
$730$		0			0
$731$	15.6332			0.578217
$732$		0			0
$733$	36.7995			1.35922			0.679610	−	0.733573i	$-0.262149\pi$
$733$	36.7995			1.35922			0.679610	+	0.733573i	$0.262149\pi$
$734$		0			0
$735$	7.31662	+	0.366750i	0.269878	+	0.0135278i
$736$		0			0
$737$	−16.4169	+	16.4169i	−0.604723	+	0.604723i
$738$		0			0
$739$	35.8997	−	35.8997i	1.32059	−	1.32059i	0.407299	−	0.913295i	$-0.366471\pi$
$739$	35.8997	−	35.8997i	1.32059	−	1.32059i	0.913295	−	0.407299i	$-0.133529\pi$
$740$		0			0
$741$	−9.26650	+	13.8997i	−0.340413	+	0.510620i
$742$		0			0
$743$	15.6332			0.573528			0.286764	−	0.958001i	$-0.407420\pi$
$743$	15.6332			0.573528			0.286764	+	0.958001i	$0.407420\pi$
$744$		0			0
$745$	−48.3747	−	2.42481i	−1.77231	−	0.0888382i
$746$		0			0
$747$			2.00000i			0.0731762i
$748$		0			0
$749$	−28.8997	+	28.8997i	−1.05597	+	1.05597i
$750$		0			0
$751$		−	13.8997i		−	0.507209i	−0.967308	−	0.253605i	$-0.918384\pi$
$751$		−	13.8997i		−	0.507209i	0.967308	−	0.253605i	$-0.0816162\pi$
$752$		0			0
$753$	−22.3166	+	22.3166i	−0.813263	+	0.813263i
$754$		0			0
$755$	−14.1332	−	0.708438i	−0.514362	−	0.0257827i
$756$		0			0
$757$	−5.00000	+	5.00000i	−0.181728	+	0.181728i	−0.792108	−	0.610380i	$-0.791017\pi$
$757$	−5.00000	+	5.00000i	−0.181728	+	0.181728i	0.610380	+	0.792108i	$0.291017\pi$
$758$		0			0
$759$	−25.4829	−	25.4829i	−0.924970	−	0.924970i
$760$		0			0
$761$	−25.5831	−	25.5831i	−0.927388	−	0.927388i	0.0701490	−	0.997537i	$-0.477653\pi$
$761$	−25.5831	−	25.5831i	−0.927388	−	0.927388i	−0.997537	+	0.0701490i	$0.977653\pi$
$762$		0			0
$763$	4.42481	+	4.42481i	0.160189	+	0.160189i
$764$		0			0
$765$	−0.158312	+	3.15831i	−0.00572380	+	0.114189i
$766$		0			0
$767$	1.58312	−	0.316625i	0.0571633	−	0.0114327i
$768$		0			0
$769$	−4.94987	−	4.94987i	−0.178497	−	0.178497i	0.612203	−	0.790700i	$-0.290283\pi$
$769$	−4.94987	−	4.94987i	−0.178497	−	0.178497i	−0.790700	+	0.612203i	$0.790283\pi$
$770$		0			0
$771$			27.4327i			0.987966i
$772$		0			0
$773$	−22.5831			−0.812259			−0.406129	−	0.913816i	$-0.633122\pi$
$773$	−22.5831			−0.812259			−0.406129	+	0.913816i	$0.633122\pi$
$774$		0			0
$775$	4.47494	+	5.47494i	0.160744	+	0.196666i
$776$		0			0
$777$	−10.4248	−	10.4248i	−0.373988	−	0.373988i
$778$		0			0
$779$	25.2665			0.905266
$780$		0			0
$781$	−18.8496			−0.674493
$782$		0			0
$783$	24.2665	+	24.2665i	0.867214	+	0.867214i
$784$		0			0
$785$	1.58312	−	31.5831i	0.0565041	−	1.12725i
$786$		0			0
$787$	25.8997			0.923226			0.461613	−	0.887081i	$-0.347271\pi$
$787$	25.8997			0.923226			0.461613	+	0.887081i	$0.347271\pi$
$788$		0			0
$789$			28.5330i			1.01580i
$790$		0			0
$791$	−8.05013	−	8.05013i	−0.286230	−	0.286230i
$792$		0			0
$793$	−6.00000	−	4.00000i	−0.213066	−	0.142044i
$794$		0			0
$795$	33.4749	+	37.0079i	1.18723	+	1.31254i
$796$		0			0
$797$	7.26650	+	7.26650i	0.257393	+	0.257393i	0.823993	−	0.566600i	$-0.191742\pi$
$797$	7.26650	+	7.26650i	0.257393	+	0.257393i	−0.566600	+	0.823993i	$0.691742\pi$
$798$		0			0
$799$	−29.4248	−	29.4248i	−1.04098	−	1.04098i
$800$		0			0
$801$	−0.100251	−	0.100251i	−0.00354220	−	0.00354220i
$802$		0			0
$803$	−13.2665	+	13.2665i	−0.468165	+	0.468165i
$804$		0			0
$805$	−1.57519	+	31.4248i	−0.0555181	+	1.10758i
$806$		0			0
$807$	−15.3668	+	15.3668i	−0.540935	+	0.540935i
$808$		0			0
$809$			14.3668i			0.505108i	0.967583	+	0.252554i	$0.0812705\pi$
$809$			14.3668i			0.505108i	−0.967583	+	0.252554i	$0.918729\pi$
$810$		0			0
$811$	−22.9499	+	22.9499i	−0.805879	+	0.805879i	−0.984007	−	0.178128i	$-0.942996\pi$
$811$	−22.9499	+	22.9499i	−0.805879	+	0.805879i	0.178128	+	0.984007i	$0.442996\pi$
$812$		0			0
$813$			24.3826i			0.855136i
$814$		0			0
$815$	−4.42481	−	4.89181i	−0.154994	−	0.171353i
$816$		0			0
$817$	9.89975			0.346348
$818$		0			0
$819$	1.89975	−	2.84962i	0.0663826	−	0.0995739i
$820$		0			0
$821$	−24.7916	+	24.7916i	−0.865231	+	0.865231i	−0.991940	−	0.126709i	$-0.959559\pi$
$821$	−24.7916	+	24.7916i	−0.865231	+	0.865231i	0.126709	+	0.991940i	$0.459559\pi$
$822$		0			0
$823$	−27.8997	+	27.8997i	−0.972524	+	0.972524i	−0.999632	−	0.0271084i	$-0.991370\pi$
$823$	−27.8997	+	27.8997i	−0.972524	+	0.972524i	0.0271084	+	0.999632i	$0.491370\pi$
$824$		0			0
$825$	−38.2243	−	3.84169i	−1.33080	−	0.133750i
$826$		0			0
$827$	31.2665			1.08724			0.543621	−	0.839331i	$-0.317053\pi$
$827$	31.2665			1.08724			0.543621	+	0.839331i	$0.317053\pi$
$828$		0			0
$829$	30.8496			1.07145			0.535726	−	0.844392i	$-0.320038\pi$
$829$	30.8496			1.07145			0.535726	+	0.844392i	$0.320038\pi$
$830$		0			0
$831$			50.7335i			1.75993i
$832$		0			0
$833$	−6.31662	−	6.31662i	−0.218858	−	0.218858i
$834$		0			0
$835$	−20.9499	+	18.9499i	−0.725000	+	0.655787i
$836$		0			0
$837$			7.68338i			0.265576i
$838$		0			0
$839$	21.6332	−	21.6332i	0.746863	−	0.746863i	−0.227026	−	0.973889i	$-0.572900\pi$
$839$	21.6332	−	21.6332i	0.746863	−	0.746863i	0.973889	+	0.227026i	$0.0729002\pi$
$840$		0			0
$841$	−10.8997			−0.375853
$842$		0			0
$843$		−	27.0660i		−	0.932202i
$844$		0			0
$845$	26.2916	+	12.3997i	0.904457	+	0.426564i
$846$		0			0
$847$		−	33.0000i		−	1.13389i
$848$		0			0
$849$	18.4169			0.632066
$850$		0			0
$851$	9.94987	−	9.94987i	0.341077	−	0.341077i
$852$		0			0
$853$			4.05013i			0.138674i	0.997593	+	0.0693368i	$0.0220883\pi$
$853$			4.05013i			0.138674i	−0.997593	+	0.0693368i	$0.977912\pi$
$854$		0			0
$855$	−0.100251	+	2.00000i	−0.00342852	+	0.0683986i
$856$		0			0
$857$	15.3166	+	15.3166i	0.523206	+	0.523206i	0.918538	−	0.395332i	$-0.129371\pi$
$857$	15.3166	+	15.3166i	0.523206	+	0.523206i	−0.395332	+	0.918538i	$0.629371\pi$
$858$		0			0
$859$			19.8997i			0.678971i	0.940611	+	0.339485i	$0.110253\pi$
$859$			19.8997i			0.678971i	−0.940611	+	0.339485i	$0.889747\pi$
$860$		0			0
$861$	43.8997			1.49610
$862$		0			0
$863$	22.5831			0.768738			0.384369	−	0.923179i	$-0.374419\pi$
$863$	22.5831			0.768738			0.384369	+	0.923179i	$0.374419\pi$
$864$		0			0
$865$	−0.525063	+	10.4749i	−0.0178527	+	0.356159i
$866$		0			0
$867$	−3.41688	+	3.41688i	−0.116043	+	0.116043i
$868$		0			0
$869$	42.9499	−	42.9499i	1.45697	−	1.45697i
$870$		0			0
$871$	−9.89975	+	14.8496i	−0.335440	+	0.503160i
$872$		0			0
$873$	−2.83375			−0.0959080
$874$		0			0
$875$	19.8997	+	27.0000i	0.672734	+	0.912767i
$876$		0			0
$877$			6.05013i			0.204298i	0.994769	+	0.102149i	$0.0325719\pi$
$877$			6.05013i			0.204298i	−0.994769	+	0.102149i	$0.967428\pi$
$878$		0			0
$879$	26.5251	−	26.5251i	0.894668	−	0.894668i
$880$		0			0
$881$			16.5831i			0.558700i	0.960189	+	0.279350i	$0.0901189\pi$
$881$			16.5831i			0.558700i	−0.960189	+	0.279350i	$0.909881\pi$
$882$		0			0
$883$	−24.4248	+	24.4248i	−0.821960	+	0.821960i	−0.986389	−	0.164429i	$-0.947422\pi$
$883$	−24.4248	+	24.4248i	−0.821960	+	0.821960i	0.164429	+	0.986389i	$0.447422\pi$
$884$		0			0
$885$	−1.21637	+	1.10025i	−0.0408879	+	0.0369845i
$886$		0			0
$887$	−5.36675	+	5.36675i	−0.180198	+	0.180198i	−0.791442	−	0.611244i	$-0.790669\pi$
$887$	−5.36675	+	5.36675i	−0.180198	+	0.180198i	0.611244	+	0.791442i	$0.290669\pi$
$888$		0			0
$889$	−21.0000	−	21.0000i	−0.704317	−	0.704317i
$890$		0			0
$891$	−26.3668	−	26.3668i	−0.883319	−	0.883319i
$892$		0			0
$893$	−18.6332	−	18.6332i	−0.623538	−	0.623538i
$894$		0			0
$895$	−24.8747	+	22.5000i	−0.831469	+	0.752092i
$896$		0			0
$897$	−23.0501	−	15.3668i	−0.769621	−	0.513081i
$898$		0			0
$899$	−6.31662	−	6.31662i	−0.210671	−	0.210671i
$900$		0			0
$901$		−	60.8496i		−	2.02719i
$902$		0			0
$903$	17.2005			0.572397
$904$		0			0
$905$	−10.4248	−	11.5251i	−0.346532	−	0.383106i
$906$		0			0
$907$	−32.3246	−	32.3246i	−1.07332	−	1.07332i	−0.997090	−	0.0762291i	$-0.975712\pi$
$907$	−32.3246	−	32.3246i	−1.07332	−	1.07332i	−0.0762291	−	0.997090i	$-0.524288\pi$
$908$		0			0
$909$	−6.10025			−0.202333
$910$		0			0
$911$	11.0501			0.366107			0.183053	−	0.983103i	$-0.441402\pi$
$911$	11.0501			0.366107			0.183053	+	0.983103i	$0.441402\pi$
$912$		0			0
$913$	20.9499	+	20.9499i	0.693340	+	0.693340i
$914$		0			0
$915$	7.31662	+	0.366750i	0.241880	+	0.0121244i
$916$		0			0
$917$	−9.00000			−0.297206
$918$		0			0
$919$		−	10.1003i		−	0.333177i	−0.986027	−	0.166588i	$-0.946725\pi$
$919$		−	10.1003i		−	0.333177i	0.986027	−	0.166588i	$-0.0532751\pi$
$920$		0			0
$921$	30.0000	+	30.0000i	0.988534	+	0.988534i
$922$		0			0
$923$	−14.2084	+	2.84169i	−0.467676	+	0.0935353i
$924$		0			0
$925$	1.50000	−	14.9248i	0.0493197	−	0.490725i
$926$		0			0
$927$	−2.51713	−	2.51713i	−0.0826733	−	0.0826733i
$928$		0			0
$929$	13.5831	+	13.5831i	0.445648	+	0.445648i	0.893905	−	0.448257i	$-0.147955\pi$
$929$	13.5831	+	13.5831i	0.445648	+	0.445648i	−0.448257	+	0.893905i	$0.647955\pi$
$930$		0			0
$931$	−4.00000	−	4.00000i	−0.131095	−	0.131095i
$932$		0			0
$933$	−22.3166	+	22.3166i	−0.730613	+	0.730613i
$934$		0			0
$935$	31.4248	+	34.7414i	1.02770	+	1.13617i
$936$		0			0
$937$	1.94987	−	1.94987i	0.0636996	−	0.0636996i	−0.674539	−	0.738239i	$-0.735658\pi$
$937$	1.94987	−	1.94987i	0.0636996	−	0.0636996i	0.738239	+	0.674539i	$0.235658\pi$
$938$		0			0
$939$		−	35.7335i		−	1.16612i
$940$		0			0
$941$	−1.74144	+	1.74144i	−0.0567692	+	0.0567692i	−0.734921	−	0.678152i	$-0.762781\pi$
$941$	−1.74144	+	1.74144i	−0.0567692	+	0.0567692i	0.678152	+	0.734921i	$0.262781\pi$
$942$		0			0
$943$			41.8997i			1.36444i
$944$		0			0
$945$	−1.82456	+	36.3997i	−0.0593530	+	1.18408i
$946$		0			0
$947$	−5.68338			−0.184685			−0.0923424	−	0.995727i	$-0.529435\pi$
$947$	−5.68338			−0.184685			−0.0923424	+	0.995727i	$0.529435\pi$
$948$		0			0
$949$	−8.00000	+	12.0000i	−0.259691	+	0.389536i
$950$		0			0
$951$	13.8997	−	13.8997i	0.450730	−	0.450730i
$952$		0			0
$953$	21.0079	−	21.0079i	0.680514	−	0.680514i	−0.279602	−	0.960116i	$-0.590203\pi$
$953$	21.0079	−	21.0079i	0.680514	−	0.680514i	0.960116	+	0.279602i	$0.0902026\pi$
$954$		0			0
$955$	−8.37469	+	7.57519i	−0.270998	+	0.245127i
$956$		0			0
$957$	48.5330			1.56885
$958$		0			0
$959$	−17.0501			−0.550577
$960$		0			0
$961$			29.0000i			0.935484i
$962$		0			0
$963$	−3.05013	−	3.05013i	−0.0982889	−	0.0982889i
$964$		0			0
$965$	−16.4248	−	18.1583i	−0.528733	−	0.584537i
$966$		0			0
$967$		−	36.0501i		−	1.15929i	−0.814868	−	0.579647i	$-0.803190\pi$
$967$		−	36.0501i		−	1.15929i	0.814868	−	0.579647i	$-0.196810\pi$
$968$		0			0
$969$	−14.6332	+	14.6332i	−0.470088	+	0.470088i
$970$		0			0
$971$	−20.0501			−0.643439			−0.321720	−	0.946835i	$-0.604261\pi$
$971$	−20.0501			−0.643439			−0.321720	+	0.946835i	$0.604261\pi$
$972$		0			0
$973$			47.8496i			1.53399i
$974$		0			0
$975$	−29.3918	+	2.86675i	−0.941291	+	0.0918095i
$976$		0			0
$977$		−	35.0501i		−	1.12135i	−0.828035	−	0.560676i	$-0.810541\pi$
$977$		−	35.0501i		−	1.12135i	0.828035	−	0.560676i	$-0.189459\pi$
$978$		0			0
$979$	−2.10025			−0.0671243
$980$		0			0
$981$	−0.467002	+	0.467002i	−0.0149102	+	0.0149102i
$982$		0			0
$983$			2.05013i			0.0653889i	0.999465	+	0.0326944i	$0.0104088\pi$
$983$			2.05013i			0.0653889i	−0.999465	+	0.0326944i	$0.989591\pi$
$984$		0			0
$985$	−5.92481	−	6.55013i	−0.188780	−	0.208704i
$986$		0			0
$987$	−32.3747	−	32.3747i	−1.03050	−	1.03050i
$988$		0			0
$989$			16.4169i			0.522026i
$990$		0			0
$991$	−59.7995			−1.89959			−0.949797	−	0.312867i	$-0.898710\pi$
$991$	−59.7995			−1.89959			−0.949797	+	0.312867i	$0.898710\pi$
$992$		0			0
$993$	−2.31662			−0.0735159
$994$		0			0
$995$	−28.1082	+	25.4248i	−0.891089	+	0.806021i
$996$		0			0
$997$	8.89975	−	8.89975i	0.281858	−	0.281858i	−0.551992	−	0.833850i	$-0.686132\pi$
$997$	8.89975	−	8.89975i	0.281858	−	0.281858i	0.833850	+	0.551992i	$0.186132\pi$
$998$		0			0
$999$	11.5251	−	11.5251i	0.364637	−	0.364637i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.cd.i.993.2		4
4.3	odd	2		130.2.j.d.83.1	yes	4
5.2	odd	4		1040.2.bg.k.577.2		4
12.11	even	2		1170.2.w.e.343.1		4
13.8	odd	4		1040.2.bg.k.593.2		4
20.3	even	4		650.2.g.g.57.2		4
20.7	even	4		130.2.g.d.57.1	✓	4
20.19	odd	2		650.2.j.f.343.2		4
52.47	even	4		130.2.g.d.73.1	yes	4
60.47	odd	4		1170.2.m.e.577.2		4
65.47	even	4	inner	1040.2.cd.i.177.2		4
156.47	odd	4		1170.2.m.e.73.1		4
260.47	odd	4		130.2.j.d.47.1	yes	4
260.99	even	4		650.2.g.g.593.2		4
260.203	odd	4		650.2.j.f.307.2		4
780.47	even	4		1170.2.w.e.307.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.g.d.57.1	✓	4	20.7	even	4
130.2.g.d.73.1	yes	4	52.47	even	4
130.2.j.d.47.1	yes	4	260.47	odd	4
130.2.j.d.83.1	yes	4	4.3	odd	2
650.2.g.g.57.2		4	20.3	even	4
650.2.g.g.593.2		4	260.99	even	4
650.2.j.f.307.2		4	260.203	odd	4
650.2.j.f.343.2		4	20.19	odd	2
1040.2.bg.k.577.2		4	5.2	odd	4
1040.2.bg.k.593.2		4	13.8	odd	4
1040.2.cd.i.177.2		4	65.47	even	4	inner
1040.2.cd.i.993.2		4	1.1	even	1	trivial
1170.2.m.e.73.1		4	156.47	odd	4
1170.2.m.e.577.2		4	60.47	odd	4
1170.2.w.e.307.1		4	780.47	even	4
1170.2.w.e.343.1		4	12.11	even	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:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.cd (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.15831 + 1.15831i) q^{3} +(1.65831 - 1.50000i) q^{5} -3.00000 q^{7} -0.316625i q^{9} +O(q^{10})\)	\(q+(1.15831 + 1.15831i) q^{3} +(1.65831 - 1.50000i) q^{5} -3.00000 q^{7} -0.316625i q^{9} +(-3.31662 - 3.31662i) q^{11} +(-3.00000 - 2.00000i) q^{13} +(3.65831 + 0.183375i) q^{15} +(-3.15831 - 3.15831i) q^{17} +(-2.00000 - 2.00000i) q^{19} +(-3.47494 - 3.47494i) q^{21} +(3.31662 - 3.31662i) q^{23} +(0.500000 - 4.97494i) q^{25} +(3.84169 - 3.84169i) q^{27} +6.31662i q^{29} +(-1.00000 + 1.00000i) q^{31} -7.68338i q^{33} +(-4.97494 + 4.50000i) q^{35} +3.00000 q^{37} +(-1.15831 - 5.79156i) q^{39} +(-6.31662 + 6.31662i) q^{41} +(-2.47494 + 2.47494i) q^{43} +(-0.474937 - 0.525063i) q^{45} +9.31662 q^{47} +2.00000 q^{49} -7.31662i q^{51} +(9.63325 + 9.63325i) q^{53} +(-10.4749 - 0.525063i) q^{55} -4.63325i q^{57} +(-0.316625 + 0.316625i) q^{59} +2.00000 q^{61} +0.949874i q^{63} +(-7.97494 + 1.18338i) q^{65} -4.94987i q^{67} +7.68338 q^{69} +(2.84169 - 2.84169i) q^{71} -4.00000i q^{73} +(6.34169 - 5.18338i) q^{75} +(9.94987 + 9.94987i) q^{77} +12.9499i q^{79} +7.94987 q^{81} -6.31662 q^{83} +(-9.97494 - 0.500000i) q^{85} +(-7.31662 + 7.31662i) q^{87} +(0.316625 - 0.316625i) q^{89} +(9.00000 + 6.00000i) q^{91} -2.31662 q^{93} +(-6.31662 - 0.316625i) q^{95} -8.94987i q^{97} +(-1.05013 + 1.05013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 12 q^{7}+O(q^{10}) \) 4 * q - 2 * q^3 - 12 * q^7	\( 4 q - 2 q^{3} - 12 q^{7} - 12 q^{13} + 8 q^{15} - 6 q^{17} - 8 q^{19} + 6 q^{21} + 2 q^{25} + 22 q^{27} - 4 q^{31} + 12 q^{37} + 2 q^{39} - 12 q^{41} + 10 q^{43} + 18 q^{45} + 24 q^{47} + 8 q^{49} + 12 q^{53} - 22 q^{55} + 12 q^{59} + 8 q^{61} - 12 q^{65} + 44 q^{69} + 18 q^{71} + 32 q^{75} - 8 q^{81} - 12 q^{83} - 20 q^{85} - 16 q^{87} - 12 q^{89} + 36 q^{91} + 4 q^{93} - 12 q^{95} - 44 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - 12 * q^7 - 12 * q^13 + 8 * q^15 - 6 * q^17 - 8 * q^19 + 6 * q^21 + 2 * q^25 + 22 * q^27 - 4 * q^31 + 12 * q^37 + 2 * q^39 - 12 * q^41 + 10 * q^43 + 18 * q^45 + 24 * q^47 + 8 * q^49 + 12 * q^53 - 22 * q^55 + 12 * q^59 + 8 * q^61 - 12 * q^65 + 44 * q^69 + 18 * q^71 + 32 * q^75 - 8 * q^81 - 12 * q^83 - 20 * q^85 - 16 * q^87 - 12 * q^89 + 36 * q^91 + 4 * q^93 - 12 * q^95 - 44 * q^99

Introduction

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