LMFDB - Embedded newform 1100.2.cb.c.449.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1100,2,Mod(49,1100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1100.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1100, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1100 = 2^{2} \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1100.cb (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,0,0,-6,0,10,0,0,0,0,0,0,0,14,0,56] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(21)] == traces)

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

Self dual:	no
Analytic conductor:	$8.78354422234$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	16.0.45212176000000000000.9
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 5x^{14} + 6x^{12} - 20x^{10} - 79x^{8} - 80x^{6} + 96x^{4} + 320x^{2} + 256 $ x^16 + 5x^14 + 6x^12 - 20x^10 - 79x^8 - 80x^6 + 96x^4 + 320*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 220)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			449.4
Root			$1.41395 + 0.0272949i$ of defining polynomial
Character	$\chi$	$=$	1100.449
Dual form			1100.2.cb.c.49.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.59076 + 2.18949i) q^{3} +(2.21063 - 3.04267i) q^{7} +(-1.33631 + 4.11275i) q^{9} +(2.98808 - 1.43922i) q^{11} +(-3.10977 - 1.01043i) q^{13} +(3.71739 - 1.20785i) q^{17} +(3.49851 - 2.54182i) q^{19} +10.1785 q^{21} +6.41755i q^{23} +(-3.40887 + 1.10761i) q^{27} +(5.25946 + 3.82122i) q^{29} +(1.69594 - 5.21956i) q^{31} +(7.90449 + 4.25294i) q^{33} +(-5.88836 + 8.10463i) q^{37} +(-2.73458 - 8.41617i) q^{39} +(-6.48659 + 4.71279i) q^{41} -0.906850i q^{43} +(-3.24853 - 4.47122i) q^{47} +(-2.20785 - 6.79507i) q^{49} +(8.55805 + 6.21779i) q^{51} +(-1.03790 - 0.337233i) q^{53} +(11.1306 + 3.61654i) q^{57} +(-5.36707 - 3.89940i) q^{59} +(-2.78882 - 8.58309i) q^{61} +(9.55965 + 13.1577i) q^{63} +13.9684i q^{67} +(-14.0512 + 10.2088i) q^{69} +(-3.20544 - 9.86533i) q^{71} +(2.16454 - 2.97923i) q^{73} +(2.22648 - 12.2734i) q^{77} +(-2.24798 + 6.91858i) q^{79} +(2.64774 + 1.92370i) q^{81} +(-5.81476 + 1.88933i) q^{83} +17.5942i q^{87} +12.1209 q^{89} +(-9.94895 + 7.22834i) q^{91} +(14.1260 - 4.58982i) q^{93} +(-11.7354 - 3.81305i) q^{97} +(1.92613 + 14.2125i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{9} + 10 q^{11} + 14 q^{19} + 56 q^{21} - 6 q^{29} - 4 q^{31} + 34 q^{39} - 24 q^{41} - 42 q^{49} + 42 q^{51} + 18 q^{59} - 68 q^{61} + 2 q^{69} - 52 q^{71} - 38 q^{79} + 24 q^{81} + 16 q^{89}+ \cdots + 40 q^{99}+O(q^{100}) $ 16 * q - 6 * q^9 + 10 * q^11 + 14 * q^19 + 56 * q^21 - 6 * q^29 - 4 * q^31 + 34 * q^39 - 24 * q^41 - 42 * q^49 + 42 * q^51 + 18 * q^59 - 68 * q^61 + 2 * q^69 - 52 * q^71 - 38 * q^79 + 24 * q^81 + 16 * q^89 - 36 * q^91 + 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$551$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.59076	+	2.18949i	0.918426	+	1.26410i	0.964206	+	0.265153i	$0.0854224\pi$
$3$	1.59076	+	2.18949i	0.918426	+	1.26410i	−0.0457808	+	0.998952i	$0.514578\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.21063	−	3.04267i	0.835540	−	1.15002i	−0.151326	−	0.988484i	$-0.548354\pi$
$7$	2.21063	−	3.04267i	0.835540	−	1.15002i	0.986866	−	0.161539i	$-0.0516457\pi$
$8$		0			0
$9$	−1.33631	+	4.11275i	−0.445437	+	1.37092i
$10$		0			0
$11$	2.98808	−	1.43922i	0.900941	−	0.433941i
$11$	2.98808	−	1.43922i	0.900941	−	0.433941i
$12$		0			0
$13$	−3.10977	−	1.01043i	−0.862495	−	0.280242i	−0.155825	−	0.987785i	$-0.549804\pi$
$13$	−3.10977	−	1.01043i	−0.862495	−	0.280242i	−0.706670	+	0.707543i	$0.749804\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.71739	−	1.20785i	0.901599	−	0.292947i	0.178702	−	0.983903i	$-0.442810\pi$
$17$	3.71739	−	1.20785i	0.901599	−	0.292947i	0.722897	+	0.690956i	$0.242810\pi$
$18$		0			0
$19$	3.49851	−	2.54182i	0.802613	−	0.583133i	−0.109066	−	0.994034i	$-0.534786\pi$
$19$	3.49851	−	2.54182i	0.802613	−	0.583133i	0.911680	+	0.410902i	$0.134786\pi$
$20$		0			0
$21$	10.1785			2.22113
$22$		0			0
$23$			6.41755i			1.33815i	0.743194	+	0.669075i	$0.233310\pi$
$23$			6.41755i			1.33815i	−0.743194	+	0.669075i	$0.766690\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−3.40887	+	1.10761i	−0.656037	+	0.213159i
$28$		0			0
$29$	5.25946	+	3.82122i	0.976658	+	0.709583i	0.956959	−	0.290223i	$-0.0937294\pi$
$29$	5.25946	+	3.82122i	0.976658	+	0.709583i	0.0196984	+	0.999806i	$0.493729\pi$
$30$		0			0
$31$	1.69594	−	5.21956i	0.304599	−	0.937460i	−0.675227	−	0.737610i	$-0.735954\pi$
$31$	1.69594	−	5.21956i	0.304599	−	0.937460i	0.979826	−	0.199850i	$-0.0640455\pi$
$32$		0			0
$33$	7.90449	+	4.25294i	1.37599	+	0.740341i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−5.88836	+	8.10463i	−0.968040	+	1.33239i	−0.0250091	+	0.999687i	$0.507961\pi$
$37$	−5.88836	+	8.10463i	−0.968040	+	1.33239i	−0.943031	+	0.332705i	$0.892039\pi$
$38$		0			0
$39$	−2.73458	−	8.41617i	−0.437883	−	1.34767i
$40$		0			0
$41$	−6.48659	+	4.71279i	−1.01304	+	0.736014i	−0.964844	−	0.262824i	$-0.915346\pi$
$41$	−6.48659	+	4.71279i	−1.01304	+	0.736014i	−0.0481922	+	0.998838i	$0.515346\pi$
$42$		0			0
$43$		−	0.906850i		−	0.138293i	−0.997607	−	0.0691467i	$-0.977972\pi$
$43$		−	0.906850i		−	0.138293i	0.997607	−	0.0691467i	$-0.0220276\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.24853	−	4.47122i	−0.473846	−	0.652194i	0.503461	−	0.864018i	$-0.332060\pi$
$47$	−3.24853	−	4.47122i	−0.473846	−	0.652194i	−0.977308	+	0.211824i	$0.932060\pi$
$48$		0			0
$49$	−2.20785	−	6.79507i	−0.315407	−	0.970724i
$50$		0			0
$51$	8.55805	+	6.21779i	1.19837	+	0.870665i
$52$		0			0
$53$	−1.03790	−	0.337233i	−0.142566	−	0.0463225i	0.236865	−	0.971543i	$-0.423880\pi$
$53$	−1.03790	−	0.337233i	−0.142566	−	0.0463225i	−0.379431	+	0.925220i	$0.623880\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	11.1306	+	3.61654i	1.47428	+	0.479023i
$58$		0			0
$59$	−5.36707	−	3.89940i	−0.698733	−	0.507659i	0.180786	−	0.983522i	$-0.442136\pi$
$59$	−5.36707	−	3.89940i	−0.698733	−	0.507659i	−0.879519	+	0.475863i	$0.842136\pi$
$60$		0			0
$61$	−2.78882	−	8.58309i	−0.357071	−	1.09895i	−0.954799	−	0.297253i	$-0.903929\pi$
$61$	−2.78882	−	8.58309i	−0.357071	−	1.09895i	0.597727	−	0.801699i	$-0.296071\pi$
$62$		0			0
$63$	9.55965	+	13.1577i	1.20440	+	1.65772i
$64$		0			0
$65$		0			0
$66$		0			0
$67$			13.9684i			1.70651i	0.521496	+	0.853254i	$0.325374\pi$
$67$			13.9684i			1.70651i	−0.521496	+	0.853254i	$0.674626\pi$
$68$		0			0
$69$	−14.0512	+	10.2088i	−1.69156	+	1.22899i
$70$		0			0
$71$	−3.20544	−	9.86533i	−0.380416	−	1.17080i	−0.939751	−	0.341858i	$-0.888944\pi$
$71$	−3.20544	−	9.86533i	−0.380416	−	1.17080i	0.559336	−	0.828941i	$-0.311056\pi$
$72$		0			0
$73$	2.16454	−	2.97923i	0.253340	−	0.348692i	−0.663338	−	0.748320i	$-0.730861\pi$
$73$	2.16454	−	2.97923i	0.253340	−	0.348692i	0.916677	+	0.399628i	$0.130861\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.22648	−	12.2734i	0.253731	−	1.39868i
$78$		0			0
$79$	−2.24798	+	6.91858i	−0.252918	+	0.778401i	0.741315	+	0.671157i	$0.234203\pi$
$79$	−2.24798	+	6.91858i	−0.252918	+	0.778401i	−0.994233	+	0.107244i	$0.965797\pi$
$80$		0			0
$81$	2.64774	+	1.92370i	0.294193	+	0.213744i
$82$		0			0
$83$	−5.81476	+	1.88933i	−0.638253	+	0.207381i	−0.610227	−	0.792226i	$-0.708922\pi$
$83$	−5.81476	+	1.88933i	−0.638253	+	0.207381i	−0.0280255	+	0.999607i	$0.508922\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$			17.5942i			1.88630i
$88$		0			0
$89$	12.1209			1.28482			0.642408	−	0.766363i	$-0.277936\pi$
$89$	12.1209			1.28482			0.642408	+	0.766363i	$0.277936\pi$
$90$		0			0
$91$	−9.94895	+	7.22834i	−1.04293	+	0.757736i
$92$		0			0
$93$	14.1260	−	4.58982i	1.46480	−	0.475942i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−11.7354	−	3.81305i	−1.19155	−	0.387157i	−0.354901	−	0.934904i	$-0.615486\pi$
$97$	−11.7354	−	3.81305i	−1.19155	−	0.387157i	−0.836644	+	0.547747i	$0.815486\pi$
$98$		0			0
$99$	1.92613	+	14.2125i	0.193583	+	1.42841i
$100$		0			0
$101$	0.0257235	−	0.0791689i	0.00255959	−	0.00787760i	−0.949769	−	0.312953i	$-0.898682\pi$
$101$	0.0257235	−	0.0791689i	0.00255959	−	0.00787760i	0.952328	+	0.305076i	$0.0986817\pi$
$102$		0			0
$103$	−6.52631	+	8.98269i	−0.643056	+	0.885091i	−0.998774	−	0.0495024i	$-0.984236\pi$
$103$	−6.52631	+	8.98269i	−0.643056	+	0.885091i	0.355718	+	0.934593i	$0.384236\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	7.56420	+	10.4112i	0.731259	+	1.00649i	0.999074	+	0.0430216i	$0.0136984\pi$
$107$	7.56420	+	10.4112i	0.731259	+	1.00649i	−0.267815	+	0.963470i	$0.586302\pi$
$108$		0			0
$109$	−7.51183			−0.719503			−0.359752	−	0.933048i	$-0.617139\pi$
$109$	−7.51183			−0.719503			−0.359752	+	0.933048i	$0.617139\pi$
$110$		0			0
$111$	−27.1120			−2.57336
$112$		0			0
$113$	0.274680	+	0.378065i	0.0258398	+	0.0355654i	0.821741	−	0.569861i	$-0.193003\pi$
$113$	0.274680	+	0.378065i	0.0258398	+	0.0355654i	−0.795902	+	0.605426i	$0.793003\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	8.31125	−	11.4395i	0.768375	−	1.05758i
$118$		0			0
$119$	4.54267	−	13.9809i	0.416426	−	1.28163i
$120$		0			0
$121$	6.85729	−	8.60102i	0.623390	−	0.781911i
$122$		0			0
$123$	−20.6372	−	6.70544i	−1.86080	−	0.604609i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−17.1681	+	5.57825i	−1.52342	+	0.494990i	−0.946746	−	0.321982i	$-0.895651\pi$
$127$	−17.1681	+	5.57825i	−1.52342	+	0.494990i	−0.576677	+	0.816972i	$0.695651\pi$
$128$		0			0
$129$	1.98554	−	1.44258i	0.174817	−	0.127012i
$130$		0			0
$131$	6.48010			0.566169			0.283085	−	0.959095i	$-0.408642\pi$
$131$	6.48010			0.566169			0.283085	+	0.959095i	$0.408642\pi$
$132$		0			0
$133$		−	16.2638i		−	1.41025i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.84278	+	0.598754i	−0.157439	+	0.0511550i	−0.386676	−	0.922216i	$-0.626377\pi$
$137$	−1.84278	+	0.598754i	−0.157439	+	0.0511550i	0.229237	+	0.973371i	$0.426377\pi$
$138$		0			0
$139$	11.1449	+	8.09724i	0.945297	+	0.686799i	0.949690	−	0.313192i	$-0.101398\pi$
$139$	11.1449	+	8.09724i	0.945297	+	0.686799i	−0.00439260	+	0.999990i	$0.501398\pi$
$140$		0			0
$141$	4.62207	−	14.2253i	0.389248	−	1.19798i
$142$		0			0
$143$	−10.7465	+	1.45641i	−0.898666	+	0.121791i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	11.3656	−	15.6434i	0.937419	−	1.29025i
$148$		0			0
$149$	−2.99396	−	9.21446i	−0.245275	−	0.754878i	−0.995591	−	0.0937990i	$-0.970099\pi$
$149$	−2.99396	−	9.21446i	−0.245275	−	0.754878i	0.750317	−	0.661079i	$-0.229901\pi$
$150$		0			0
$151$	13.4658	−	9.78349i	1.09583	−	0.796169i	0.115458	−	0.993312i	$-0.463166\pi$
$151$	13.4658	−	9.78349i	1.09583	−	0.796169i	0.980375	+	0.197143i	$0.0631663\pi$
$152$		0			0
$153$			16.9027i			1.36650i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−0.563214	−	0.775197i	−0.0449494	−	0.0618675i	0.785951	−	0.618289i	$-0.212174\pi$
$157$	−0.563214	−	0.775197i	−0.0449494	−	0.0618675i	−0.830900	+	0.556422i	$0.812174\pi$
$158$		0			0
$159$	−0.912674	−	2.80892i	−0.0723798	−	0.222762i
$160$		0			0
$161$	19.5265	+	14.1868i	1.53890	+	1.11808i
$162$		0			0
$163$	4.22775	+	1.37368i	0.331143	+	0.107595i	0.469870	−	0.882736i	$-0.344301\pi$
$163$	4.22775	+	1.37368i	0.331143	+	0.107595i	−0.138726	+	0.990331i	$0.544301\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	13.2666	+	4.31059i	1.02660	+	0.333563i	0.773446	−	0.633862i	$-0.218531\pi$
$167$	13.2666	+	4.31059i	1.02660	+	0.333563i	0.253156	+	0.967425i	$0.418531\pi$
$168$		0			0
$169$	−1.86751	−	1.35682i	−0.143654	−	0.104371i
$170$		0			0
$171$	5.77874	+	17.7851i	0.441911	+	1.36006i
$172$		0			0
$173$	−9.50098	−	13.0770i	−0.722346	−	0.994224i	−0.999443	−	0.0333821i	$-0.989372\pi$
$173$	−9.50098	−	13.0770i	−0.722346	−	0.994224i	0.277097	−	0.960842i	$-0.410628\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		−	17.9542i		−	1.34952i
$178$		0			0
$179$	14.8705	−	10.8041i	1.11148	−	0.807534i	0.128580	−	0.991699i	$-0.458958\pi$
$179$	14.8705	−	10.8041i	1.11148	−	0.807534i	0.982895	+	0.184165i	$0.0589579\pi$
$180$		0			0
$181$	3.42315	+	10.5354i	0.254441	+	0.783088i	0.993939	+	0.109930i	$0.0350627\pi$
$181$	3.42315	+	10.5354i	0.254441	+	0.783088i	−0.739499	+	0.673158i	$0.764937\pi$
$182$		0			0
$183$	14.3563	−	19.7597i	1.06125	−	1.46068i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	9.36950	−	8.95930i	0.685166	−	0.655169i
$188$		0			0
$189$	−4.16566	+	12.8206i	−0.303007	+	0.932561i
$190$		0			0
$191$	−7.78172	−	5.65375i	−0.563066	−	0.409091i	0.269514	−	0.962996i	$-0.413137\pi$
$191$	−7.78172	−	5.65375i	−0.563066	−	0.409091i	−0.832580	+	0.553905i	$0.813137\pi$
$192$		0			0
$193$	−18.6937	+	6.07395i	−1.34560	+	0.437213i	−0.891211	−	0.453590i	$-0.850143\pi$
$193$	−18.6937	+	6.07395i	−1.34560	+	0.437213i	−0.454391	+	0.890802i	$0.650143\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	12.1768i		−	0.867562i	−0.901018	−	0.433781i	$-0.857179\pi$
$197$		−	12.1768i		−	0.867562i	0.901018	−	0.433781i	$-0.142821\pi$
$198$		0			0
$199$	−8.44164			−0.598412			−0.299206	−	0.954189i	$-0.596722\pi$
$199$	−8.44164			−0.598412			−0.299206	+	0.954189i	$0.596722\pi$
$200$		0			0
$201$	−30.5836	+	22.2203i	−2.15720	+	1.56730i
$202$		0			0
$203$	23.2535	−	7.55551i	1.63207	−	0.530293i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−26.3937	−	8.57584i	−1.83449	−	0.596062i
$208$		0			0
$209$	6.79561	−	12.6303i	0.470062	−	0.873655i
$210$		0			0
$211$	−6.75302	+	20.7837i	−0.464897	+	1.43081i	0.394215	+	0.919018i	$0.371016\pi$
$211$	−6.75302	+	20.7837i	−0.464897	+	1.43081i	−0.859112	+	0.511788i	$0.828984\pi$
$212$		0			0
$213$	16.5010	−	22.7117i	1.13063	−	1.55618i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−12.1323	−	16.6987i	−0.823595	−	1.13358i
$218$		0			0
$219$	9.96626			0.673458
$220$		0			0
$221$	−12.7807			−0.859721
$222$		0			0
$223$	−15.5319	−	21.3778i	−1.04009	−	1.43157i	−0.897092	−	0.441844i	$-0.854324\pi$
$223$	−15.5319	−	21.3778i	−1.04009	−	1.43157i	−0.143002	−	0.989722i	$-0.545676\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.83010	−	8.02445i	0.386957	−	0.532601i	−0.570454	−	0.821330i	$-0.693233\pi$
$227$	5.83010	−	8.02445i	0.386957	−	0.532601i	0.957411	+	0.288729i	$0.0932325\pi$
$228$		0			0
$229$	4.01140	−	12.3458i	0.265081	−	0.815834i	−0.726594	−	0.687067i	$-0.758898\pi$
$229$	4.01140	−	12.3458i	0.265081	−	0.815834i	0.991675	−	0.128767i	$-0.0411020\pi$
$230$		0			0
$231$	30.4142	−	14.6491i	2.00111	−	0.963839i
$232$		0			0
$233$	6.33388	+	2.05800i	0.414946	+	0.134824i	0.509048	−	0.860738i	$-0.329998\pi$
$233$	6.33388	+	2.05800i	0.414946	+	0.134824i	−0.0941012	+	0.995563i	$0.529998\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−18.7242	+	6.08386i	−1.21627	+	0.395189i
$238$		0			0
$239$	−17.7108	+	12.8677i	−1.14562	+	0.832340i	−0.987892	−	0.155143i	$-0.950416\pi$
$239$	−17.7108	+	12.8677i	−1.14562	+	0.832340i	−0.157726	+	0.987483i	$0.550416\pi$
$240$		0			0
$241$	10.6517			0.686134			0.343067	−	0.939311i	$-0.388534\pi$
$241$	10.6517			0.686134			0.343067	+	0.939311i	$0.388534\pi$
$242$		0			0
$243$			19.6102i			1.25800i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−13.4479	+	4.36948i	−0.855668	+	0.278023i
$248$		0			0
$249$	−13.3866	−	9.72591i	−0.848339	−	0.616354i
$250$		0			0
$251$	−3.75973	+	11.5713i	−0.237312	+	0.730372i	0.759494	+	0.650514i	$0.225447\pi$
$251$	−3.75973	+	11.5713i	−0.237312	+	0.730372i	−0.996806	+	0.0798576i	$0.974553\pi$
$252$		0			0
$253$	9.23626	+	19.1762i	0.580679	+	1.20560i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	3.59372	−	4.94633i	0.224170	−	0.308544i	−0.682087	−	0.731271i	$-0.738927\pi$
$257$	3.59372	−	4.94633i	0.224170	−	0.308544i	0.906257	+	0.422728i	$0.138927\pi$
$258$		0			0
$259$	11.6428	+	35.8327i	0.723445	+	2.22654i
$260$		0			0
$261$	−22.7440	+	16.5245i	−1.40782	+	1.02284i
$262$		0			0
$263$		−	0.446463i		−	0.0275301i	−0.999905	−	0.0137650i	$-0.995618\pi$
$263$		−	0.446463i		−	0.0275301i	0.999905	−	0.0137650i	$-0.00438168\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	19.2815	+	26.5387i	1.18001	+	1.62414i
$268$		0			0
$269$	−0.00246118	−	0.00757473i	−0.000150061	−	0.000461840i	0.950981	−	0.309248i	$-0.100077\pi$
$269$	−0.00246118	−	0.00757473i	−0.000150061	−	0.000461840i	−0.951132	+	0.308786i	$0.900077\pi$
$270$		0			0
$271$	−15.0380	−	10.9257i	−0.913493	−	0.663691i	0.0284029	−	0.999597i	$-0.490958\pi$
$271$	−15.0380	−	10.9257i	−0.913493	−	0.663691i	−0.941896	+	0.335905i	$0.890958\pi$
$272$		0			0
$273$	−31.6528	−	10.2846i	−1.91571	−	0.622453i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	6.61897	+	2.15063i	0.397695	+	0.129219i	0.501035	−	0.865427i	$-0.332953\pi$
$277$	6.61897	+	2.15063i	0.397695	+	0.129219i	−0.103339	+	0.994646i	$0.532953\pi$
$278$		0			0
$279$	19.2004	+	13.9499i	1.14950	+	0.835159i
$280$		0			0
$281$	−6.91031	−	21.2678i	−0.412235	−	1.26873i	−0.914701	−	0.404131i	$-0.867574\pi$
$281$	−6.91031	−	21.2678i	−0.412235	−	1.26873i	0.502466	−	0.864597i	$-0.332426\pi$
$282$		0			0
$283$	−13.7237	−	18.8891i	−0.815792	−	1.12284i	−0.990404	−	0.138204i	$-0.955867\pi$
$283$	−13.7237	−	18.8891i	−0.815792	−	1.12284i	0.174612	−	0.984637i	$-0.444133\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			30.1548i			1.77998i
$288$		0			0
$289$	−1.39323	+	1.01224i	−0.0819548	+	0.0595436i
$290$		0			0
$291$	−10.3195	−	31.7601i	−0.604939	−	1.86181i
$292$		0			0
$293$	−2.05796	+	2.83254i	−0.120227	+	0.165479i	−0.864889	−	0.501964i	$-0.832611\pi$
$293$	−2.05796	+	2.83254i	−0.120227	+	0.165479i	0.744661	+	0.667443i	$0.232611\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−8.59189	+	8.21574i	−0.498552	+	0.476725i
$298$		0			0
$299$	6.48445	−	19.9571i	0.375006	−	1.15415i
$300$		0			0
$301$	−2.75925	−	2.00471i	−0.159040	−	0.115550i
$302$		0			0
$303$	0.214260	−	0.0696172i	0.0123089	−	0.00399940i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	8.26358i		−	0.471628i	−0.971798	−	0.235814i	$-0.924224\pi$
$307$		−	8.26358i		−	0.471628i	0.971798	−	0.235814i	$-0.0757755\pi$
$308$		0			0
$309$	−30.0493			−1.70945
$310$		0			0
$311$	−9.35397	+	6.79606i	−0.530415	+	0.385369i	−0.820513	−	0.571628i	$-0.806312\pi$
$311$	−9.35397	+	6.79606i	−0.530415	+	0.385369i	0.290098	+	0.956997i	$0.406312\pi$
$312$		0			0
$313$	−18.3694	+	5.96859i	−1.03830	+	0.337364i	−0.778067	−	0.628181i	$-0.783800\pi$
$313$	−18.3694	+	5.96859i	−1.03830	+	0.337364i	−0.260234	+	0.965546i	$0.583800\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	21.2785	+	6.91381i	1.19512	+	0.388318i	0.837964	−	0.545726i	$-0.183746\pi$
$317$	21.2785	+	6.91381i	1.19512	+	0.388318i	0.357157	+	0.934044i	$0.383746\pi$
$318$		0			0
$319$	21.2153	+	3.84862i	1.18783	+	0.215481i
$320$		0			0
$321$	−10.7625	+	33.1235i	−0.600704	+	1.84878i
$322$		0			0
$323$	9.93518	−	13.6746i	0.552808	−	0.760875i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−11.9495	−	16.4471i	−0.660810	−	0.909527i
$328$		0			0
$329$	−20.7858			−1.14596
$330$		0			0
$331$	−5.17876			−0.284650			−0.142325	−	0.989820i	$-0.545458\pi$
$331$	−5.17876			−0.284650			−0.142325	+	0.989820i	$0.545458\pi$
$332$		0			0
$333$	−25.4636	−	35.0476i	−1.39540	−	1.92060i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	3.24843	−	4.47108i	0.176953	−	0.243555i	−0.711322	−	0.702866i	$-0.751903\pi$
$337$	3.24843	−	4.47108i	0.176953	−	0.243555i	0.888276	+	0.459310i	$0.151903\pi$
$338$		0			0
$339$	−0.390820	+	1.20282i	−0.0212264	+	0.0653283i
$340$		0			0
$341$	−2.44448	−	18.0373i	−0.132376	−	0.976774i
$342$		0			0
$343$	−0.517788	−	0.168240i	−0.0279579	−	0.00908408i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−8.16765	+	2.65383i	−0.438463	+	0.142465i	−0.519926	−	0.854211i	$-0.674041\pi$
$347$	−8.16765	+	2.65383i	−0.438463	+	0.142465i	0.0814636	+	0.996676i	$0.474041\pi$
$348$		0			0
$349$	11.8706	−	8.62451i	0.635419	−	0.461659i	−0.222854	−	0.974852i	$-0.571537\pi$
$349$	11.8706	−	8.62451i	0.635419	−	0.461659i	0.858273	+	0.513193i	$0.171537\pi$
$350$		0			0
$351$	11.7200			0.625565
$352$		0			0
$353$		−	5.79041i		−	0.308192i	−0.988056	−	0.154096i	$-0.950753\pi$
$353$		−	5.79041i		−	0.308192i	0.988056	−	0.154096i	$-0.0492466\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	37.8374	−	12.2941i	2.00257	−	0.650674i
$358$		0			0
$359$	−9.19282	−	6.67898i	−0.485179	−	0.352503i	0.318148	−	0.948041i	$-0.396939\pi$
$359$	−9.19282	−	6.67898i	−0.485179	−	0.352503i	−0.803327	+	0.595538i	$0.796939\pi$
$360$		0			0
$361$	−0.0925809	+	0.284935i	−0.00487268	+	0.0149966i
$362$		0			0
$363$	29.7402	+	1.33185i	1.56095	+	0.0699038i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−2.69468	+	3.70890i	−0.140661	+	0.193603i	−0.873535	−	0.486761i	$-0.838178\pi$
$367$	−2.69468	+	3.70890i	−0.140661	+	0.193603i	0.732874	+	0.680364i	$0.238178\pi$
$368$		0			0
$369$	−10.7144	−	32.9755i	−0.557768	−	1.71663i
$370$		0			0
$371$	−3.32050	+	2.41248i	−0.172392	+	0.125250i
$372$		0			0
$373$			22.8487i			1.18306i	0.806283	+	0.591530i	$0.201476\pi$
$373$			22.8487i			1.18306i	−0.806283	+	0.591530i	$0.798524\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−12.4947	−	17.1974i	−0.643508	−	0.885712i
$378$		0			0
$379$	6.50498	+	20.0203i	0.334139	+	1.02837i	0.967145	+	0.254226i	$0.0818208\pi$
$379$	6.50498	+	20.0203i	0.334139	+	1.02837i	−0.633006	+	0.774147i	$0.718179\pi$
$380$		0			0
$381$	−39.5239	−	28.7158i	−2.02487	−	1.47115i
$382$		0			0
$383$	0.247179	+	0.0803134i	0.0126303	+	0.00410382i	0.315325	−	0.948984i	$-0.397886\pi$
$383$	0.247179	+	0.0803134i	0.0126303	+	0.00410382i	−0.302695	+	0.953087i	$0.597886\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	3.72964	+	1.21183i	0.189588	+	0.0616010i
$388$		0			0
$389$	−12.7514	−	9.26447i	−0.646524	−	0.469727i	0.215561	−	0.976490i	$-0.430842\pi$
$389$	−12.7514	−	9.26447i	−0.646524	−	0.469727i	−0.862085	+	0.506763i	$0.830842\pi$
$390$		0			0
$391$	7.75145	+	23.8565i	0.392008	+	1.20648i
$392$		0			0
$393$	10.3083	+	14.1881i	0.519984	+	0.715697i
$394$		0			0
$395$		0			0
$396$		0			0
$397$			7.62978i			0.382928i	0.981500	+	0.191464i	$0.0613235\pi$
$397$			7.62978i			0.382928i	−0.981500	+	0.191464i	$0.938677\pi$
$398$		0			0
$399$	35.6096	−	25.8719i	1.78271	−	1.29521i
$400$		0			0
$401$	−9.31703	−	28.6749i	−0.465270	−	1.43195i	−0.858642	−	0.512575i	$-0.828691\pi$
$401$	−9.31703	−	28.6749i	−0.465270	−	1.43195i	0.393372	−	0.919379i	$-0.371309\pi$
$402$		0			0
$403$	−10.5479	+	14.5180i	−0.525431	+	0.723193i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−5.93057	+	32.6919i	−0.293967	+	1.62048i
$408$		0			0
$409$	−9.62526	+	29.6235i	−0.475939	+	1.46479i	0.368749	+	0.929529i	$0.379786\pi$
$409$	−9.62526	+	29.6235i	−0.475939	+	1.46479i	−0.844688	+	0.535259i	$0.820214\pi$
$410$		0			0
$411$	−4.24238	−	3.08227i	−0.209261	−	0.152037i
$412$		0			0
$413$	−23.7292	+	7.71010i	−1.16764	+	0.379389i
$414$		0			0
$415$		0			0
$416$		0			0
$417$			37.2824i			1.82573i
$418$		0			0
$419$	−13.3733			−0.653328			−0.326664	−	0.945141i	$-0.605925\pi$
$419$	−13.3733			−0.653328			−0.326664	+	0.945141i	$0.605925\pi$
$420$		0			0
$421$	8.87736	−	6.44978i	0.432656	−	0.314343i	−0.350054	−	0.936730i	$-0.613837\pi$
$421$	8.87736	−	6.44978i	0.432656	−	0.314343i	0.782710	+	0.622386i	$0.213837\pi$
$422$		0			0
$423$	22.7300	−	7.38543i	1.10517	−	0.359092i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−32.2806	−	10.4886i	−1.56217	−	0.507579i
$428$		0			0
$429$	−20.2839	−	21.2126i	−0.979314	−	1.02415i
$430$		0			0
$431$	−5.01099	+	15.4223i	−0.241371	+	0.742864i	0.754841	+	0.655908i	$0.227714\pi$
$431$	−5.01099	+	15.4223i	−0.241371	+	0.742864i	−0.996212	+	0.0869561i	$0.972286\pi$
$432$		0			0
$433$	12.6163	−	17.3649i	0.606302	−	0.834503i	−0.389965	−	0.920830i	$-0.627513\pi$
$433$	12.6163	−	17.3649i	0.606302	−	0.834503i	0.996267	+	0.0863271i	$0.0275130\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	16.3122	+	22.4518i	0.780319	+	1.07402i
$438$		0			0
$439$	−5.94741			−0.283855			−0.141927	−	0.989877i	$-0.545330\pi$
$439$	−5.94741			−0.283855			−0.141927	+	0.989877i	$0.545330\pi$
$440$		0			0
$441$	30.8968			1.47127
$442$		0			0
$443$	−13.9546	−	19.2068i	−0.663003	−	0.912545i	0.336574	−	0.941657i	$-0.390732\pi$
$443$	−13.9546	−	19.2068i	−0.663003	−	0.912545i	−0.999576	+	0.0291124i	$0.990732\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	15.4123	−	21.2132i	0.728978	−	1.00335i
$448$		0			0
$449$	−10.6354	+	32.7325i	−0.501917	+	1.54474i	0.303975	+	0.952680i	$0.401686\pi$
$449$	−10.6354	+	32.7325i	−0.501917	+	1.54474i	−0.805892	+	0.592063i	$0.798314\pi$
$450$		0			0
$451$	−12.5998	+	23.4178i	−0.593299	+	1.10270i
$452$		0			0
$453$	42.8418	+	13.9201i	2.01288	+	0.654025i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−14.1043	+	4.58276i	−0.659770	+	0.214372i	−0.619717	−	0.784825i	$-0.712753\pi$
$457$	−14.1043	+	4.58276i	−0.659770	+	0.214372i	−0.0400529	+	0.999198i	$0.512753\pi$
$458$		0			0
$459$	−11.3343	+	8.23482i	−0.529038	+	0.384368i
$460$		0			0
$461$	29.8441			1.38998			0.694990	−	0.719020i	$-0.255409\pi$
$461$	29.8441			1.38998			0.694990	+	0.719020i	$0.255409\pi$
$462$		0			0
$463$			6.87337i			0.319433i	0.987163	+	0.159716i	$0.0510580\pi$
$463$			6.87337i			0.319433i	−0.987163	+	0.159716i	$0.948942\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.34034	−	0.435503i	0.0620236	−	0.0201527i	−0.277841	−	0.960627i	$-0.589619\pi$
$467$	1.34034	−	0.435503i	0.0620236	−	0.0201527i	0.339864	+	0.940474i	$0.389619\pi$
$468$		0			0
$469$	42.5012	+	30.8789i	1.96252	+	1.42586i
$470$		0			0
$471$	0.801351	−	2.46631i	0.0369243	−	0.113641i
$472$		0			0
$473$	−1.30516	−	2.70974i	−0.0600111	−	0.124594i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	2.77391	−	3.81795i	0.127008	−	0.174812i
$478$		0			0
$479$	7.19055	+	22.1302i	0.328544	+	1.01116i	0.969815	+	0.243841i	$0.0784075\pi$
$479$	7.19055	+	22.1302i	0.328544	+	1.01116i	−0.641271	+	0.767315i	$0.721592\pi$
$480$		0			0
$481$	26.5006	−	19.2538i	1.20832	−	0.877897i
$482$		0			0
$483$			65.3210i			2.97221i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−10.9647	−	15.0917i	−0.496859	−	0.683868i	0.484775	−	0.874639i	$-0.338901\pi$
$487$	−10.9647	−	15.0917i	−0.496859	−	0.683868i	−0.981635	+	0.190770i	$0.938901\pi$
$488$		0			0
$489$	3.71768	+	11.4418i	0.168119	+	0.517418i
$490$		0			0
$491$	33.9898	+	24.6951i	1.53394	+	1.11447i	0.953997	+	0.299815i	$0.0969251\pi$
$491$	33.9898	+	24.6951i	1.53394	+	1.11447i	0.579943	+	0.814657i	$0.303075\pi$
$492$		0			0
$493$	24.1669	+	7.85231i	1.08842	+	0.353650i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−37.1030	−	12.0555i	−1.66430	−	0.540764i
$498$		0			0
$499$	−4.22493	−	3.06959i	−0.189134	−	0.137414i	0.489189	−	0.872178i	$-0.337293\pi$
$499$	−4.22493	−	3.06959i	−0.189134	−	0.137414i	−0.678323	+	0.734764i	$0.737293\pi$
$500$		0			0
$501$	11.6660	+	35.9043i	0.521199	+	1.60409i
$502$		0			0
$503$	16.9494	+	23.3289i	0.755737	+	1.04018i	0.997557	+	0.0698614i	$0.0222557\pi$
$503$	16.9494	+	23.3289i	0.755737	+	1.04018i	−0.241820	+	0.970321i	$0.577744\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		−	6.24728i		−	0.277451i
$508$		0			0
$509$	4.46973	−	3.24745i	0.198117	−	0.143940i	−0.484304	−	0.874900i	$-0.660927\pi$
$509$	4.46973	−	3.24745i	0.198117	−	0.143940i	0.682421	+	0.730959i	$0.260927\pi$
$510$		0			0
$511$	−4.27983	−	13.1720i	−0.189329	−	0.582693i
$512$		0			0
$513$	−9.11062	+	12.5397i	−0.402244	+	0.553641i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−16.1419	−	8.68502i	−0.709921	−	0.381967i
$518$		0			0
$519$	13.5182	−	41.6047i	0.593382	−	1.82624i
$520$		0			0
$521$	23.8297	+	17.3133i	1.04400	+	0.758509i	0.971062	−	0.238828i	$-0.0767631\pi$
$521$	23.8297	+	17.3133i	1.04400	+	0.758509i	0.0729362	+	0.997337i	$0.476763\pi$
$522$		0			0
$523$	−2.10696	+	0.684593i	−0.0921309	+	0.0299351i	−0.354720	−	0.934973i	$-0.615424\pi$
$523$	−2.10696	+	0.684593i	−0.0921309	+	0.0299351i	0.262589	+	0.964908i	$0.415424\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	21.4515i		−	0.934444i
$528$		0			0
$529$	−18.1849			−0.790648
$530$		0			0
$531$	23.2093	−	16.8626i	1.00720	−	0.731773i
$532$		0			0
$533$	24.9337	−	8.10146i	1.08000	−	0.350913i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	47.3109	+	15.3722i	2.04162	+	0.663361i
$538$		0			0
$539$	−16.3768	−	17.1267i	−0.705401	−	0.737697i
$540$		0			0
$541$	10.4175	−	32.0616i	0.447882	−	1.37844i	−0.431411	−	0.902156i	$-0.641984\pi$
$541$	10.4175	−	32.0616i	0.447882	−	1.37844i	0.879292	−	0.476282i	$-0.158016\pi$
$542$		0			0
$543$	−17.6217	+	24.2542i	−0.756220	+	1.04085i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	16.4992	+	22.7092i	0.705455	+	0.970976i	0.999883	+	0.0153018i	$0.00487092\pi$
$547$	16.4992	+	22.7092i	0.705455	+	0.970976i	−0.294428	+	0.955674i	$0.595129\pi$
$548$		0			0
$549$	39.0268			1.66562
$550$		0			0
$551$	28.1131			1.19766
$552$		0			0
$553$	16.0815	+	22.1343i	0.683856	+	0.941247i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	9.12189	−	12.5552i	0.386507	−	0.531981i	−0.570787	−	0.821098i	$-0.693362\pi$
$557$	9.12189	−	12.5552i	0.386507	−	0.531981i	0.957294	+	0.289117i	$0.0933617\pi$
$558$		0			0
$559$	−0.916305	+	2.82010i	−0.0387556	+	0.119277i
$560$		0			0
$561$	34.5209	+	6.26236i	1.45748	+	0.264397i
$562$		0			0
$563$	19.1581	+	6.22486i	0.807419	+	0.262346i	0.683504	−	0.729946i	$-0.260455\pi$
$563$	19.1581	+	6.22486i	0.807419	+	0.262346i	0.123915	+	0.992293i	$0.460455\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	11.7064	−	3.80363i	0.491621	−	0.159737i
$568$		0			0
$569$	25.4623	−	18.4994i	1.06743	−	0.775536i	0.0919848	−	0.995760i	$-0.470679\pi$
$569$	25.4623	−	18.4994i	1.06743	−	0.775536i	0.975449	+	0.220224i	$0.0706789\pi$
$570$		0			0
$571$	−14.3295			−0.599673			−0.299836	−	0.953991i	$-0.596932\pi$
$571$	−14.3295			−0.599673			−0.299836	+	0.953991i	$0.596932\pi$
$572$		0			0
$573$		−	26.0318i		−	1.08749i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	10.9004	−	3.54175i	0.453789	−	0.147445i	−0.0731994	−	0.997317i	$-0.523321\pi$
$577$	10.9004	−	3.54175i	0.453789	−	0.147445i	0.526989	+	0.849872i	$0.323321\pi$
$578$		0			0
$579$	−43.0361	−	31.2675i	−1.78852	−	1.29943i
$580$		0			0
$581$	−7.10568	+	21.8690i	−0.294793	+	0.907281i
$582$		0			0
$583$	−3.58667	+	0.486080i	−0.148545	+	0.0201314i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	5.53801	−	7.62242i	0.228578	−	0.314611i	−0.679287	−	0.733872i	$-0.737711\pi$
$587$	5.53801	−	7.62242i	0.228578	−	0.314611i	0.907865	+	0.419262i	$0.137711\pi$
$588$		0			0
$589$	−7.33390	−	22.5714i	−0.302188	−	0.930039i
$590$		0			0
$591$	26.6611	−	19.3704i	1.09669	−	0.796792i
$592$		0			0
$593$			28.2270i			1.15914i	0.814922	+	0.579571i	$0.196780\pi$
$593$			28.2270i			1.15914i	−0.814922	+	0.579571i	$0.803220\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−13.4286	−	18.4829i	−0.549597	−	0.756455i
$598$		0			0
$599$	−1.24633	−	3.83580i	−0.0509235	−	0.156726i	0.922361	−	0.386329i	$-0.126257\pi$
$599$	−1.24633	−	3.83580i	−0.0509235	−	0.156726i	−0.973284	+	0.229603i	$0.926257\pi$
$600$		0			0
$601$	−30.0829	−	21.8565i	−1.22711	−	0.891544i	−0.230435	−	0.973088i	$-0.574015\pi$
$601$	−30.0829	−	21.8565i	−1.22711	−	0.891544i	−0.996670	+	0.0815436i	$0.974015\pi$
$602$		0			0
$603$	−57.4483	−	18.6661i	−2.33948	−	0.760142i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−17.2426	−	5.60247i	−0.699856	−	0.227397i	−0.0625883	−	0.998039i	$-0.519936\pi$
$607$	−17.2426	−	5.60247i	−0.699856	−	0.227397i	−0.637268	+	0.770642i	$0.719936\pi$
$608$		0			0
$609$	53.5334	+	38.8943i	2.16928	+	1.57608i
$610$		0			0
$611$	5.58435	+	17.1868i	0.225918	+	0.695306i
$612$		0			0
$613$	−5.01682	−	6.90505i	−0.202627	−	0.278893i	0.695595	−	0.718434i	$-0.255141\pi$
$613$	−5.01682	−	6.90505i	−0.202627	−	0.278893i	−0.898222	+	0.439542i	$0.855141\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	24.5659i		−	0.988985i	−0.869182	−	0.494492i	$-0.835354\pi$
$617$		−	24.5659i		−	0.988985i	0.869182	−	0.494492i	$-0.164646\pi$
$618$		0			0
$619$	−30.9640	+	22.4967i	−1.24455	+	0.904218i	−0.997893	−	0.0648846i	$-0.979332\pi$
$619$	−30.9640	+	22.4967i	−1.24455	+	0.904218i	−0.246657	+	0.969103i	$0.579332\pi$
$620$		0			0
$621$	−7.10813	−	21.8766i	−0.285239	−	0.877876i
$622$		0			0
$623$	26.7949	−	36.8800i	1.07352	−	1.47757i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	38.4641	−	5.21281i	1.53611	−	0.208179i
$628$		0			0
$629$	−12.1001	+	37.2403i	−0.482463	+	1.48487i
$630$		0			0
$631$	−16.7407	−	12.1628i	−0.666435	−	0.484194i	0.202395	−	0.979304i	$-0.435128\pi$
$631$	−16.7407	−	12.1628i	−0.666435	−	0.484194i	−0.868830	+	0.495110i	$0.835128\pi$
$632$		0			0
$633$	−56.2481	+	18.2761i	−2.23566	+	0.726410i
$634$		0			0
$635$		0			0
$636$		0			0
$637$			23.3620i			0.925635i
$638$		0			0
$639$	44.8571			1.77452
$640$		0			0
$641$	6.75967	−	4.91119i	0.266991	−	0.193980i	−0.446232	−	0.894917i	$-0.647234\pi$
$641$	6.75967	−	4.91119i	0.266991	−	0.193980i	0.713223	+	0.700937i	$0.247234\pi$
$642$		0			0
$643$	27.9623	−	9.08552i	1.10273	−	0.358298i	0.299576	−	0.954073i	$-0.403155\pi$
$643$	27.9623	−	9.08552i	1.10273	−	0.358298i	0.803152	+	0.595775i	$0.203155\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	22.3489	+	7.26160i	0.878626	+	0.285483i	0.713387	−	0.700770i	$-0.247160\pi$
$647$	22.3489	+	7.26160i	0.878626	+	0.285483i	0.165240	+	0.986253i	$0.447160\pi$
$648$		0			0
$649$	−21.6494	−	3.92736i	−0.849812	−	0.154162i
$650$		0			0
$651$	17.2621	−	53.1272i	0.676554	−	2.08222i
$652$		0			0
$653$	−9.06240	+	12.4733i	−0.354639	+	0.488119i	−0.948645	−	0.316342i	$-0.897545\pi$
$653$	−9.06240	+	12.4733i	−0.354639	+	0.488119i	0.594006	+	0.804460i	$0.297545\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	9.36032	+	12.8834i	0.365181	+	0.502628i
$658$		0			0
$659$	−12.2785			−0.478301			−0.239151	−	0.970982i	$-0.576869\pi$
$659$	−12.2785			−0.478301			−0.239151	+	0.970982i	$0.576869\pi$
$660$		0			0
$661$	25.8163			1.00414			0.502070	−	0.864827i	$-0.332572\pi$
$661$	25.8163			1.00414			0.502070	+	0.864827i	$0.332572\pi$
$662$		0			0
$663$	−20.3310	−	27.9832i	−0.789589	−	1.08678i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−24.5229	+	33.7528i	−0.949529	+	1.30692i
$668$		0			0
$669$	22.0991	−	68.0140i	0.854401	−	2.62957i
$670$		0			0
$671$	−20.6862	−	21.6333i	−0.798581	−	0.835144i
$672$		0			0
$673$	−30.7506	−	9.99147i	−1.18535	−	0.385143i	−0.350997	−	0.936377i	$-0.614157\pi$
$673$	−30.7506	−	9.99147i	−1.18535	−	0.385143i	−0.834351	+	0.551234i	$0.814157\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	29.9506	−	9.73155i	1.15110	−	0.374014i	0.329540	−	0.944142i	$-0.393106\pi$
$677$	29.9506	−	9.73155i	1.15110	−	0.374014i	0.821556	+	0.570128i	$0.193106\pi$
$678$		0			0
$679$	−37.5444	+	27.2776i	−1.44082	+	1.04682i
$680$		0			0
$681$	26.8438			1.02866
$682$		0			0
$683$			13.3758i			0.511812i	0.966702	+	0.255906i	$0.0823738\pi$
$683$			13.3758i			0.511812i	−0.966702	+	0.255906i	$0.917626\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	33.4122	−	10.8563i	1.27476	−	0.414193i
$688$		0			0
$689$	2.88687	+	2.09743i	0.109981	+	0.0799058i
$690$		0			0
$691$	−8.48261	+	26.1068i	−0.322694	+	0.993149i	0.649777	+	0.760125i	$0.274862\pi$
$691$	−8.48261	+	26.1068i	−0.322694	+	0.993149i	−0.972471	+	0.233024i	$0.925138\pi$
$692$		0			0
$693$	47.5019	+	25.5580i	1.80445	+	0.970867i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−18.4208	+	25.3541i	−0.697739	+	0.960355i
$698$		0			0
$699$	5.56970	+	17.1418i	0.210665	+	0.648362i
$700$		0			0
$701$	0.175085	−	0.127207i	0.00661287	−	0.00480453i	−0.584474	−	0.811413i	$-0.698699\pi$
$701$	0.175085	−	0.127207i	0.00661287	−	0.00480453i	0.591087	+	0.806608i	$0.298699\pi$
$702$		0			0
$703$			43.3212i			1.63389i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.184020	−	0.253282i	−0.00692078	−	0.00952564i
$708$		0			0
$709$	15.6953	+	48.3050i	0.589448	+	1.81413i	0.580624	+	0.814172i	$0.302809\pi$
$709$	15.6953	+	48.3050i	0.589448	+	1.81413i	0.00882347	+	0.999961i	$0.497191\pi$
$710$		0			0
$711$	−25.4504	−	18.4908i	−0.954463	−	0.693458i
$712$		0			0
$713$	33.4967	+	10.8838i	1.25446	+	0.407600i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−56.3473	−	18.3084i	−2.10433	−	0.683738i
$718$		0			0
$719$	−27.5398	−	20.0089i	−1.02706	−	0.746204i	−0.0593435	−	0.998238i	$-0.518901\pi$
$719$	−27.5398	−	20.0089i	−1.02706	−	0.746204i	−0.967719	+	0.252033i	$0.918901\pi$
$720$		0			0
$721$	12.9041	+	39.7149i	0.480575	+	1.47906i
$722$		0			0
$723$	16.9443	+	23.3218i	0.630163	+	0.867346i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			16.2361i			0.602162i	0.953599	+	0.301081i	$0.0973475\pi$
$727$			16.2361i			0.602162i	−0.953599	+	0.301081i	$0.902652\pi$
$728$		0			0
$729$	−34.9932	+	25.4241i	−1.29605	+	0.941633i
$730$		0			0
$731$	−1.09534	−	3.37111i	−0.0405126	−	0.124685i
$732$		0			0
$733$	17.5154	−	24.1078i	0.646944	−	0.890443i	−0.352018	−	0.935993i	$-0.614504\pi$
$733$	17.5154	−	24.1078i	0.646944	−	0.890443i	0.998962	+	0.0455508i	$0.0145043\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	20.1035	+	41.7387i	0.740524	+	1.53746i
$738$		0			0
$739$	13.0551	−	40.1794i	0.480239	−	1.47802i	−0.358522	−	0.933521i	$-0.616719\pi$
$739$	13.0551	−	40.1794i	0.480239	−	1.47802i	0.838760	−	0.544501i	$-0.183281\pi$
$740$		0			0
$741$	−30.9593	−	22.4932i	−1.13732	−	0.826310i
$742$		0			0
$743$	19.8890	−	6.46233i	0.729657	−	0.237080i	0.0794519	−	0.996839i	$-0.474683\pi$
$743$	19.8890	−	6.46233i	0.729657	−	0.237080i	0.650205	+	0.759759i	$0.274683\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		−	26.4394i		−	0.967366i
$748$		0			0
$749$	48.3997			1.76849
$750$		0			0
$751$	−23.0107	+	16.7182i	−0.839672	+	0.610058i	−0.922279	−	0.386525i	$-0.873675\pi$
$751$	−23.0107	+	16.7182i	−0.839672	+	0.610058i	0.0826069	+	0.996582i	$0.473675\pi$
$752$		0			0
$753$	−31.3160	+	10.1752i	−1.14122	+	0.370805i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−37.7291	−	12.2589i	−1.37129	−	0.445558i	−0.471492	−	0.881870i	$-0.656284\pi$
$757$	−37.7291	−	12.2589i	−1.37129	−	0.445558i	−0.899795	+	0.436312i	$0.856284\pi$
$758$		0			0
$759$	−27.2934	+	50.7274i	−0.990688	+	1.84129i
$760$		0			0
$761$	−15.0740	+	46.3929i	−0.546430	+	1.68174i	0.171134	+	0.985248i	$0.445257\pi$
$761$	−15.0740	+	46.3929i	−0.546430	+	1.68174i	−0.717565	+	0.696492i	$0.754743\pi$
$762$		0			0
$763$	−16.6059	+	22.8561i	−0.601174	+	0.827445i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	12.7503	+	17.5493i	0.460387	+	0.633668i
$768$		0			0
$769$	10.7632			0.388132			0.194066	−	0.980988i	$-0.437832\pi$
$769$	10.7632			0.388132			0.194066	+	0.980988i	$0.437832\pi$
$770$		0			0
$771$	16.5467			0.595915
$772$		0			0
$773$	14.3828	+	19.7962i	0.517313	+	0.712021i	0.985131	−	0.171804i	$-0.0549596\pi$
$773$	14.3828	+	19.7962i	0.517313	+	0.712021i	−0.467818	+	0.883825i	$0.654960\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−59.9346	+	82.4929i	−2.15014	+	2.95942i
$778$		0			0
$779$	−10.7144	+	32.9755i	−0.383882	+	1.18147i
$780$		0			0
$781$	−23.7765	−	24.8651i	−0.850790	−	0.889744i
$782$		0			0
$783$	−22.1612	−	7.20062i	−0.791978	−	0.257329i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	4.61653	−	1.50000i	0.164561	−	0.0534692i	−0.225578	−	0.974225i	$-0.572427\pi$
$787$	4.61653	−	1.50000i	0.164561	−	0.0534692i	0.390139	+	0.920756i	$0.372427\pi$
$788$		0			0
$789$	0.977527	−	0.710215i	0.0348009	−	0.0252843i
$790$		0			0
$791$	1.75755			0.0624911
$792$		0			0
$793$			29.5093i			1.04791i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	4.38135	−	1.42359i	0.155195	−	0.0504261i	−0.230389	−	0.973099i	$-0.574000\pi$
$797$	4.38135	−	1.42359i	0.155195	−	0.0504261i	0.385584	+	0.922673i	$0.374000\pi$
$798$		0			0
$799$	−17.4766	−	12.6975i	−0.618278	−	0.449205i
$800$		0			0
$801$	−16.1973	+	49.8503i	−0.572305	+	1.76137i
$802$		0			0
$803$	2.18005	−	12.0174i	0.0769324	−	0.424086i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	0.0126697	−	0.0174383i	0.000445994	−	0.000613858i
$808$		0			0
$809$	−9.79491	−	30.1456i	−0.344371	−	1.05986i	−0.961920	−	0.273331i	$-0.911874\pi$
$809$	−9.79491	−	30.1456i	−0.344371	−	1.05986i	0.617549	−	0.786532i	$-0.288126\pi$
$810$		0			0
$811$	−11.6743	+	8.48190i	−0.409941	+	0.297840i	−0.773578	−	0.633701i	$-0.781535\pi$
$811$	−11.6743	+	8.48190i	−0.409941	+	0.297840i	0.363637	+	0.931541i	$0.381535\pi$
$812$		0			0
$813$		−	50.3058i		−	1.76430i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−2.30505	−	3.17262i	−0.0806434	−	0.110996i
$818$		0			0
$819$	−16.4334	−	50.5768i	−0.574230	−	1.76730i
$820$		0			0
$821$	−44.0551	−	32.0079i	−1.53753	−	1.11708i	−0.951858	−	0.306539i	$-0.900829\pi$
$821$	−44.0551	−	32.0079i	−1.53753	−	1.11708i	−0.585677	−	0.810545i	$-0.699171\pi$
$822$		0			0
$823$	−0.0577411	−	0.0187612i	−0.00201273	−	0.000653975i	0.308010	−	0.951383i	$-0.400337\pi$
$823$	−0.0577411	−	0.0187612i	−0.00201273	−	0.000653975i	−0.310023	+	0.950729i	$0.600337\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−11.2485	−	3.65486i	−0.391149	−	0.127092i	0.106838	−	0.994276i	$-0.465927\pi$
$827$	−11.2485	−	3.65486i	−0.391149	−	0.127092i	−0.497987	+	0.867184i	$0.665927\pi$
$828$		0			0
$829$	13.5508	+	9.84525i	0.470640	+	0.341940i	0.797691	−	0.603067i	$-0.206055\pi$
$829$	13.5508	+	9.84525i	0.470640	+	0.341940i	−0.327051	+	0.945007i	$0.606055\pi$
$830$		0			0
$831$	5.82039	+	17.9133i	0.201907	+	0.621407i
$832$		0			0
$833$	−16.4149	−	22.5931i	−0.568742	−	0.782806i
$834$		0			0
$835$		0			0
$836$		0			0
$837$			19.6712i			0.679936i
$838$		0			0
$839$	−0.734439	+	0.533601i	−0.0253557	+	0.0184220i	−0.600391	−	0.799707i	$-0.704988\pi$
$839$	−0.734439	+	0.533601i	−0.0253557	+	0.0184220i	0.575035	+	0.818129i	$0.304988\pi$
$840$		0			0
$841$	4.09870	+	12.6145i	0.141335	+	0.434983i
$842$		0			0
$843$	35.5730	−	48.9620i	1.22520	−	1.68634i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−11.0111	−	39.8782i	−0.378347	−	1.37023i
$848$		0			0
$849$	19.5264	−	60.0961i	0.670144	−	2.06249i
$850$		0			0
$851$	−52.0118	−	37.7888i	−1.78294	−	1.29538i
$852$		0			0
$853$	50.6690	−	16.4634i	1.73487	−	0.563695i	0.740735	−	0.671798i	$-0.234478\pi$
$853$	50.6690	−	16.4634i	1.73487	−	0.563695i	0.994140	+	0.108103i	$0.0344776\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			37.1487i			1.26898i	0.772933	+	0.634488i	$0.218789\pi$
$857$			37.1487i			1.26898i	−0.772933	+	0.634488i	$0.781211\pi$
$858$		0			0
$859$	−26.8141			−0.914887			−0.457443	−	0.889239i	$-0.651235\pi$
$859$	−26.8141			−0.914887			−0.457443	+	0.889239i	$0.651235\pi$
$860$		0			0
$861$	−66.0238	+	47.9691i	−2.25008	+	1.63478i
$862$		0			0
$863$	−16.6726	+	5.41724i	−0.567541	+	0.184405i	−0.578711	−	0.815532i	$-0.696444\pi$
$863$	−16.6726	+	5.41724i	−0.567541	+	0.184405i	0.0111706	+	0.999938i	$0.496444\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−4.43259	−	1.44024i	−0.150539	−	0.0489130i
$868$		0			0
$869$	3.24019	+	23.9086i	0.109916	+	0.811045i
$870$		0			0
$871$	14.1140	−	43.4384i	0.478235	−	1.47185i
$872$		0			0
$873$	31.3642	−	43.1691i	1.06152	−	1.46105i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−12.2116	−	16.8079i	−0.412358	−	0.567562i	0.551434	−	0.834219i	$-0.314081\pi$
$877$	−12.2116	−	16.8079i	−0.412358	−	0.567562i	−0.963792	+	0.266657i	$0.914081\pi$
$878$		0			0
$879$	−9.47556			−0.319603
$880$		0			0
$881$	36.3078			1.22324			0.611621	−	0.791151i	$-0.290518\pi$
$881$	36.3078			1.22324			0.611621	+	0.791151i	$0.290518\pi$
$882$		0			0
$883$	−21.8070	−	30.0147i	−0.733863	−	1.01008i	−0.998948	−	0.0458509i	$-0.985400\pi$
$883$	−21.8070	−	30.0147i	−0.733863	−	1.01008i	0.265085	−	0.964225i	$-0.414600\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	12.9204	−	17.7834i	0.433825	−	0.597109i	−0.535001	−	0.844852i	$-0.679689\pi$
$887$	12.9204	−	17.7834i	0.433825	−	0.597109i	0.968826	+	0.247742i	$0.0796887\pi$
$888$		0			0
$889$	−20.9795	+	64.5684i	−0.703631	+	2.16555i
$890$		0			0
$891$	10.6803	+	1.93749i	0.357803	+	0.0649082i
$892$		0			0
$893$	−22.7300	−	7.38543i	−0.760631	−	0.247144i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	54.0111	−	17.5493i	1.80338	−	0.585953i
$898$		0			0
$899$	28.8648	−	20.9715i	0.962695	−	0.699439i
$900$		0			0
$901$	−4.26559			−0.142107
$902$		0			0
$903$		−	9.23037i		−	0.307168i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−19.6678	+	6.39045i	−0.653058	+	0.212191i	−0.616762	−	0.787150i	$-0.711556\pi$
$907$	−19.6678	+	6.39045i	−0.653058	+	0.212191i	−0.0362960	+	0.999341i	$0.511556\pi$
$908$		0			0
$909$	0.291227	+	0.211589i	0.00965939	+	0.00701796i
$910$		0			0
$911$	−10.5882	+	32.5873i	−0.350804	+	1.07966i	0.607598	+	0.794244i	$0.292133\pi$
$911$	−10.5882	+	32.5873i	−0.350804	+	1.07966i	−0.958403	+	0.285420i	$0.907867\pi$
$912$		0			0
$913$	−14.6558	+	14.0142i	−0.485037	+	0.463802i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	14.3251	−	19.7168i	0.473057	−	0.651107i
$918$		0			0
$919$	−5.15152	−	15.8548i	−0.169933	−	0.523000i	0.829433	−	0.558607i	$-0.188664\pi$
$919$	−5.15152	−	15.8548i	−0.169933	−	0.523000i	−0.999366	+	0.0356062i	$0.988664\pi$
$920$		0			0
$921$	18.0931	−	13.1454i	0.596186	−	0.433155i
$922$		0			0
$923$			33.9178i			1.11642i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−28.2223	−	38.8447i	−0.926943	−	1.27583i
$928$		0			0
$929$	−11.4967	−	35.3832i	−0.377194	−	1.16089i	−0.941986	−	0.335652i	$-0.891043\pi$
$929$	−11.4967	−	35.3832i	−0.377194	−	1.16089i	0.564792	−	0.825234i	$-0.308957\pi$
$930$		0			0
$931$	−24.9960	−	18.1607i	−0.819211	−	0.595192i
$932$		0			0
$933$	−29.7598	−	9.66956i	−0.974293	−	0.316567i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	14.8818	+	4.83539i	0.486167	+	0.157965i	0.541836	−	0.840484i	$-0.317729\pi$
$937$	14.8818	+	4.83539i	0.486167	+	0.157965i	−0.0556691	+	0.998449i	$0.517729\pi$
$938$		0			0
$939$	−42.2895	−	30.7251i	−1.38007	−	1.00268i
$940$		0			0
$941$	−4.47359	−	13.7683i	−0.145835	−	0.448834i	0.851282	−	0.524708i	$-0.175825\pi$
$941$	−4.47359	−	13.7683i	−0.145835	−	0.448834i	−0.997117	+	0.0758737i	$0.975825\pi$
$942$		0			0
$943$	−30.2445	−	41.6280i	−0.984897	−	1.35559i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	56.2394i		−	1.82754i	−0.406238	−	0.913768i	$-0.633159\pi$
$947$		−	56.2394i		−	1.82754i	0.406238	−	0.913768i	$-0.366841\pi$
$948$		0			0
$949$	−9.74150	+	7.07762i	−0.316223	+	0.229749i
$950$		0			0
$951$	18.7113	+	57.5874i	0.606755	+	1.86740i
$952$		0			0
$953$	13.0071	−	17.9028i	0.421342	−	0.579928i	−0.544597	−	0.838698i	$-0.683317\pi$
$953$	13.0071	−	17.9028i	0.421342	−	0.579928i	0.965939	+	0.258770i	$0.0833172\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	25.3219	+	52.5730i	0.818541	+	1.69944i
$958$		0			0
$959$	−2.25188	+	6.93059i	−0.0727171	+	0.223800i
$960$		0			0
$961$	0.711966	+	0.517274i	0.0229666	+	0.0166862i
$962$		0			0
$963$	−52.9269	+	17.1970i	−1.70555	+	0.554165i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			32.2808i			1.03808i	0.854750	+	0.519039i	$0.173710\pi$
$967$			32.2808i			1.03808i	−0.854750	+	0.519039i	$0.826290\pi$
$968$		0			0
$969$	45.7449			1.46954
$970$		0			0
$971$	22.5473	−	16.3816i	0.723576	−	0.525709i	−0.163948	−	0.986469i	$-0.552423\pi$
$971$	22.5473	−	16.3816i	0.723576	−	0.525709i	0.887525	+	0.460760i	$0.152423\pi$
$972$		0			0
$973$	49.2745	−	16.0103i	1.57967	−	0.513265i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	10.1409	+	3.29499i	0.324437	+	0.105416i	0.466707	−	0.884412i	$-0.345440\pi$
$977$	10.1409	+	3.29499i	0.324437	+	0.105416i	−0.142270	+	0.989828i	$0.545440\pi$
$978$		0			0
$979$	36.2184	−	17.4447i	1.15754	−	0.557534i
$980$		0			0
$981$	10.0382	−	30.8943i	0.320494	−	0.986378i
$982$		0			0
$983$	−17.9958	+	24.7691i	−0.573977	+	0.790011i	−0.993019	−	0.117955i	$-0.962366\pi$
$983$	−17.9958	+	24.7691i	−0.573977	+	0.790011i	0.419042	+	0.907967i	$0.362366\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−33.0651	−	45.5103i	−1.05247	−	1.44861i
$988$		0			0
$989$	5.81975			0.185057
$990$		0			0
$991$	12.2099			0.387859			0.193929	−	0.981015i	$-0.437877\pi$
$991$	12.2099			0.387859			0.193929	+	0.981015i	$0.437877\pi$
$992$		0			0
$993$	−8.23817	−	11.3389i	−0.261430	−	0.359828i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−7.95313	+	10.9465i	−0.251878	+	0.346681i	−0.916168	−	0.400795i	$-0.868734\pi$
$997$	−7.95313	+	10.9465i	−0.251878	+	0.346681i	0.664290	+	0.747475i	$0.268734\pi$
$998$		0			0
$999$	11.0959	−	34.1496i	0.351058	−	1.08045i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1100.2.cb.c.449.4		16
5.2	odd	4		1100.2.n.c.801.2		8
5.3	odd	4		220.2.m.a.141.1	✓	8
5.4	even	2	inner	1100.2.cb.c.449.1		16
11.5	even	5	inner	1100.2.cb.c.49.1		16
15.8	even	4		1980.2.z.c.361.1		8
20.3	even	4		880.2.bo.f.801.2		8
55.18	even	20		2420.2.a.m.1.4		4
55.27	odd	20		1100.2.n.c.401.2		8
55.38	odd	20		220.2.m.a.181.1	yes	8
55.48	odd	20		2420.2.a.n.1.4		4
55.49	even	10	inner	1100.2.cb.c.49.4		16
165.38	even	20		1980.2.z.c.181.1		8
220.103	even	20		9680.2.a.ck.1.1		4
220.183	odd	20		9680.2.a.cl.1.1		4
220.203	even	20		880.2.bo.f.401.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.m.a.141.1	✓	8	5.3	odd	4
220.2.m.a.181.1	yes	8	55.38	odd	20
880.2.bo.f.401.2		8	220.203	even	20
880.2.bo.f.801.2		8	20.3	even	4
1100.2.n.c.401.2		8	55.27	odd	20
1100.2.n.c.801.2		8	5.2	odd	4
1100.2.cb.c.49.1		16	11.5	even	5	inner
1100.2.cb.c.49.4		16	55.49	even	10	inner
1100.2.cb.c.449.1		16	5.4	even	2	inner
1100.2.cb.c.449.4		16	1.1	even	1	trivial
1980.2.z.c.181.1		8	165.38	even	20
1980.2.z.c.361.1		8	15.8	even	4
2420.2.a.m.1.4		4	55.18	even	20
2420.2.a.n.1.4		4	55.48	odd	20
9680.2.a.ck.1.1		4	220.103	even	20
9680.2.a.cl.1.1		4	220.183	odd	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1100.cb (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.59076 + 2.18949i) q^{3} +(2.21063 - 3.04267i) q^{7} +(-1.33631 + 4.11275i) q^{9} +(2.98808 - 1.43922i) q^{11} +(-3.10977 - 1.01043i) q^{13} +(3.71739 - 1.20785i) q^{17} +(3.49851 - 2.54182i) q^{19} +10.1785 q^{21} +6.41755i q^{23} +(-3.40887 + 1.10761i) q^{27} +(5.25946 + 3.82122i) q^{29} +(1.69594 - 5.21956i) q^{31} +(7.90449 + 4.25294i) q^{33} +(-5.88836 + 8.10463i) q^{37} +(-2.73458 - 8.41617i) q^{39} +(-6.48659 + 4.71279i) q^{41} -0.906850i q^{43} +(-3.24853 - 4.47122i) q^{47} +(-2.20785 - 6.79507i) q^{49} +(8.55805 + 6.21779i) q^{51} +(-1.03790 - 0.337233i) q^{53} +(11.1306 + 3.61654i) q^{57} +(-5.36707 - 3.89940i) q^{59} +(-2.78882 - 8.58309i) q^{61} +(9.55965 + 13.1577i) q^{63} +13.9684i q^{67} +(-14.0512 + 10.2088i) q^{69} +(-3.20544 - 9.86533i) q^{71} +(2.16454 - 2.97923i) q^{73} +(2.22648 - 12.2734i) q^{77} +(-2.24798 + 6.91858i) q^{79} +(2.64774 + 1.92370i) q^{81} +(-5.81476 + 1.88933i) q^{83} +17.5942i q^{87} +12.1209 q^{89} +(-9.94895 + 7.22834i) q^{91} +(14.1260 - 4.58982i) q^{93} +(-11.7354 - 3.81305i) q^{97} +(1.92613 + 14.2125i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{9} + 10 q^{11} + 14 q^{19} + 56 q^{21} - 6 q^{29} - 4 q^{31} + 34 q^{39} - 24 q^{41} - 42 q^{49} + 42 q^{51} + 18 q^{59} - 68 q^{61} + 2 q^{69} - 52 q^{71} - 38 q^{79} + 24 q^{81} + 16 q^{89}+ \cdots + 40 q^{99}+O(q^{100}) \) 16 * q - 6 * q^9 + 10 * q^11 + 14 * q^19 + 56 * q^21 - 6 * q^29 - 4 * q^31 + 34 * q^39 - 24 * q^41 - 42 * q^49 + 42 * q^51 + 18 * q^59 - 68 * q^61 + 2 * q^69 - 52 * q^71 - 38 * q^79 + 24 * q^81 + 16 * q^89 - 36 * q^91 + 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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