LMFDB - Embedded newform 1040.2.da.f.881.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1040,2,Mod(641,1040)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1040, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1040.641");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.da (of order $6$, 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 22x^{14} + 183x^{12} + 730x^{10} + 1485x^{8} + 1552x^{6} + 812x^{4} + 192x^{2} + 16 $ x^16 + 22x^14 + 183x^12 + 730x^10 + 1485x^8 + 1552x^6 + 812x^4 + 192*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 520)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.6
Root			$0.432338i$ of defining polynomial
Character	$\chi$	$=$	1040.881
Dual form			1040.2.da.f.641.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.19037 + 2.06179i) q^{3} -1.00000i q^{5} +(-3.14022 - 1.81301i) q^{7} +(-1.33398 + 2.31052i) q^{9} +O(q^{10})$	\(q+(1.19037 + 2.06179i) q^{3} -1.00000i q^{5} +(-3.14022 - 1.81301i) q^{7} +(-1.33398 + 2.31052i) q^{9} +(-5.16239 + 2.98051i) q^{11} +(-1.20102 - 3.39964i) q^{13} +(2.06179 - 1.19037i) q^{15} +(-0.935203 + 1.61982i) q^{17} +(0.301991 + 0.174354i) q^{19} -8.63262i q^{21} +(-3.66309 - 6.34466i) q^{23} -1.00000 q^{25} +0.790520 q^{27} +(-5.02765 - 8.70815i) q^{29} +7.65605i q^{31} +(-12.2903 - 7.09583i) q^{33} +(-1.81301 + 3.14022i) q^{35} +(-6.63047 + 3.82810i) q^{37} +(5.57968 - 6.52308i) q^{39} +(-0.472941 + 0.273052i) q^{41} +(2.58606 - 4.47919i) q^{43} +(2.31052 + 1.33398i) q^{45} +11.3065i q^{47} +(3.07398 + 5.32430i) q^{49} -4.45296 q^{51} +9.75169 q^{53} +(2.98051 + 5.16239i) q^{55} +0.830187i q^{57} +(-9.50578 - 5.48817i) q^{59} +(-2.24244 + 3.88402i) q^{61} +(8.37796 - 4.83702i) q^{63} +(-3.39964 + 1.20102i) q^{65} +(2.23276 - 1.28908i) q^{67} +(8.72089 - 15.1050i) q^{69} +(-5.31948 - 3.07120i) q^{71} +0.340151i q^{73} +(-1.19037 - 2.06179i) q^{75} +21.6147 q^{77} -6.43164 q^{79} +(4.94294 + 8.56143i) q^{81} -7.69307i q^{83} +(1.61982 + 0.935203i) q^{85} +(11.9696 - 20.7319i) q^{87} +(-1.21047 + 0.698863i) q^{89} +(-2.39212 + 12.8531i) q^{91} +(-15.7851 + 9.11355i) q^{93} +(0.174354 - 0.301991i) q^{95} +(3.22151 + 1.85994i) q^{97} -15.9037i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9}+O(q^{10}) $ 16 * q + 4 * q^3 - 6 * q^7 - 16 * q^9	$ 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9} + 6 q^{11} - 2 q^{13} + 4 q^{17} - 30 q^{19} - 6 q^{23} - 16 q^{25} - 44 q^{27} - 16 q^{29} + 24 q^{33} + 6 q^{35} - 24 q^{37} + 8 q^{39} - 24 q^{41} - 6 q^{43} + 12 q^{45} - 4 q^{49} + 40 q^{51} + 4 q^{53} + 6 q^{55} - 12 q^{59} - 2 q^{61} + 60 q^{63} - 10 q^{65} + 6 q^{67} + 52 q^{69} - 72 q^{71} - 4 q^{75} + 32 q^{77} - 36 q^{79} - 28 q^{81} + 22 q^{87} + 24 q^{89} + 22 q^{91} - 96 q^{93} - 10 q^{95} + 60 q^{97}+O(q^{100}) $ 16 * q + 4 * q^3 - 6 * q^7 - 16 * q^9 + 6 * q^11 - 2 * q^13 + 4 * q^17 - 30 * q^19 - 6 * q^23 - 16 * q^25 - 44 * q^27 - 16 * q^29 + 24 * q^33 + 6 * q^35 - 24 * q^37 + 8 * q^39 - 24 * q^41 - 6 * q^43 + 12 * q^45 - 4 * q^49 + 40 * q^51 + 4 * q^53 + 6 * q^55 - 12 * q^59 - 2 * q^61 + 60 * q^63 - 10 * q^65 + 6 * q^67 + 52 * q^69 - 72 * q^71 - 4 * q^75 + 32 * q^77 - 36 * q^79 - 28 * q^81 + 22 * q^87 + 24 * q^89 + 22 * q^91 - 96 * q^93 - 10 * q^95 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	1.19037	+	2.06179i	0.687262	+	1.19037i	0.972720	+	0.231982i	$0.0745210\pi$
$3$	1.19037	+	2.06179i	0.687262	+	1.19037i	−0.285458	+	0.958391i	$0.592146\pi$
$4$		0			0
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	−3.14022	−	1.81301i	−1.18689	−	0.685252i	−0.229293	−	0.973358i	$-0.573641\pi$
$7$	−3.14022	−	1.81301i	−1.18689	−	0.685252i	−0.957599	+	0.288106i	$0.906975\pi$
$8$		0			0
$9$	−1.33398	+	2.31052i	−0.444659	+	0.770172i
$10$		0			0
$11$	−5.16239	+	2.98051i	−1.55652	+	0.898657i	−0.558934	+	0.829212i	$0.688789\pi$
$11$	−5.16239	+	2.98051i	−1.55652	+	0.898657i	−0.997586	+	0.0694447i	$0.977877\pi$
$12$		0			0
$13$	−1.20102	−	3.39964i	−0.333102	−	0.942891i
$13$	−1.20102	−	3.39964i	−0.333102	−	0.942891i
$14$		0			0
$15$	2.06179	−	1.19037i	0.532351	−	0.307353i
$16$		0			0
$17$	−0.935203	+	1.61982i	−0.226820	+	0.392864i	−0.956864	−	0.290536i	$-0.906166\pi$
$17$	−0.935203	+	1.61982i	−0.226820	+	0.392864i	0.730044	+	0.683400i	$0.239500\pi$
$18$		0			0
$19$	0.301991	+	0.174354i	0.0692814	+	0.0399997i	0.534241	−	0.845332i	$-0.320598\pi$
$19$	0.301991	+	0.174354i	0.0692814	+	0.0399997i	−0.464959	+	0.885332i	$0.653931\pi$
$20$		0			0
$21$		−	8.63262i		−	1.88379i
$22$		0			0
$23$	−3.66309	−	6.34466i	−0.763807	−	1.32295i	−0.940875	−	0.338754i	$-0.889994\pi$
$23$	−3.66309	−	6.34466i	−0.763807	−	1.32295i	0.177068	−	0.984199i	$-0.443339\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$	0.790520			0.152136
$28$		0			0
$29$	−5.02765	−	8.70815i	−0.933611	−	1.61706i	−0.777091	−	0.629388i	$-0.783306\pi$
$29$	−5.02765	−	8.70815i	−0.933611	−	1.61706i	−0.156520	−	0.987675i	$-0.550028\pi$
$30$		0			0
$31$			7.65605i			1.37507i	0.726153	+	0.687533i	$0.241306\pi$
$31$			7.65605i			1.37507i	−0.726153	+	0.687533i	$0.758694\pi$
$32$		0			0
$33$	−12.2903	−	7.09583i	−2.13947	−	1.23523i
$34$		0			0
$35$	−1.81301	+	3.14022i	−0.306454	+	0.530794i
$36$		0			0
$37$	−6.63047	+	3.82810i	−1.09004	+	0.629336i	−0.933588	−	0.358349i	$-0.883340\pi$
$37$	−6.63047	+	3.82810i	−1.09004	+	0.629336i	−0.156454	+	0.987685i	$0.550006\pi$
$38$		0			0
$39$	5.57968	−	6.52308i	0.893464	−	1.04453i
$40$		0			0
$41$	−0.472941	+	0.273052i	−0.0738609	+	0.0426436i	−0.536476	−	0.843916i	$-0.680245\pi$
$41$	−0.472941	+	0.273052i	−0.0738609	+	0.0426436i	0.462615	+	0.886559i	$0.346911\pi$
$42$		0			0
$43$	2.58606	−	4.47919i	0.394370	−	0.683069i	−0.598650	−	0.801010i	$-0.704296\pi$
$43$	2.58606	−	4.47919i	0.394370	−	0.683069i	0.993021	+	0.117941i	$0.0376294\pi$
$44$		0			0
$45$	2.31052	+	1.33398i	0.344431	+	0.198857i
$46$		0			0
$47$			11.3065i			1.64922i	0.565705	+	0.824608i	$0.308604\pi$
$47$			11.3065i			1.64922i	−0.565705	+	0.824608i	$0.691396\pi$
$48$		0			0
$49$	3.07398	+	5.32430i	0.439141	+	0.760614i
$50$		0			0
$51$	−4.45296			−0.623539
$52$		0			0
$53$	9.75169			1.33950			0.669749	−	0.742588i	$-0.266402\pi$
$53$	9.75169			1.33950			0.669749	+	0.742588i	$0.266402\pi$
$54$		0			0
$55$	2.98051	+	5.16239i	0.401892	+	0.696097i
$56$		0			0
$57$			0.830187i			0.109961i
$58$		0			0
$59$	−9.50578	−	5.48817i	−1.23755	−	0.714498i	−0.268955	−	0.963153i	$-0.586678\pi$
$59$	−9.50578	−	5.48817i	−1.23755	−	0.714498i	−0.968592	+	0.248654i	$0.920012\pi$
$60$		0			0
$61$	−2.24244	+	3.88402i	−0.287115	+	0.497298i	−0.973120	−	0.230299i	$-0.926030\pi$
$61$	−2.24244	+	3.88402i	−0.287115	+	0.497298i	0.686005	+	0.727597i	$0.259363\pi$
$62$		0			0
$63$	8.37796	−	4.83702i	1.05552	−	0.609407i
$64$		0			0
$65$	−3.39964	+	1.20102i	−0.421674	+	0.148968i
$66$		0			0
$67$	2.23276	−	1.28908i	0.272775	−	0.157486i	−0.357373	−	0.933962i	$-0.616328\pi$
$67$	2.23276	−	1.28908i	0.272775	−	0.157486i	0.630148	+	0.776475i	$0.282994\pi$
$68$		0			0
$69$	8.72089	−	15.1050i	1.04987	−	1.81843i
$70$		0			0
$71$	−5.31948	−	3.07120i	−0.631306	−	0.364485i	0.149952	−	0.988693i	$-0.452088\pi$
$71$	−5.31948	−	3.07120i	−0.631306	−	0.364485i	−0.781258	+	0.624209i	$0.785422\pi$
$72$		0			0
$73$			0.340151i			0.0398116i	0.999802	+	0.0199058i	$0.00633664\pi$
$73$			0.340151i			0.0398116i	−0.999802	+	0.0199058i	$0.993663\pi$
$74$		0			0
$75$	−1.19037	−	2.06179i	−0.137452	−	0.238075i
$76$		0			0
$77$	21.6147			2.46323
$78$		0			0
$79$	−6.43164			−0.723616			−0.361808	−	0.932253i	$-0.617840\pi$
$79$	−6.43164			−0.723616			−0.361808	+	0.932253i	$0.617840\pi$
$80$		0			0
$81$	4.94294	+	8.56143i	0.549216	+	0.951270i
$82$		0			0
$83$		−	7.69307i		−	0.844424i	−0.906497	−	0.422212i	$-0.861254\pi$
$83$		−	7.69307i		−	0.844424i	0.906497	−	0.422212i	$-0.138746\pi$
$84$		0			0
$85$	1.61982	+	0.935203i	0.175694	+	0.101437i
$86$		0			0
$87$	11.9696	−	20.7319i	1.28327	−	2.22269i
$88$		0			0
$89$	−1.21047	+	0.698863i	−0.128309	+	0.0740793i	−0.562781	−	0.826606i	$-0.690268\pi$
$89$	−1.21047	+	0.698863i	−0.128309	+	0.0740793i	0.434472	+	0.900686i	$0.356935\pi$
$90$		0			0
$91$	−2.39212	+	12.8531i	−0.250762	+	1.34737i
$92$		0			0
$93$	−15.7851	+	9.11355i	−1.63684	+	0.945031i
$94$		0			0
$95$	0.174354	−	0.301991i	0.0178884	−	0.0309836i
$96$		0			0
$97$	3.22151	+	1.85994i	0.327094	+	0.188848i	0.654550	−	0.756018i	$-0.272858\pi$
$97$	3.22151	+	1.85994i	0.327094	+	0.188848i	−0.327456	+	0.944866i	$0.606191\pi$
$98$		0			0
$99$		−	15.9037i		−	1.59838i
$100$		0			0
$101$	1.21814	+	2.10988i	0.121209	+	0.209941i	0.920245	−	0.391343i	$-0.127989\pi$
$101$	1.21814	+	2.10988i	0.121209	+	0.209941i	−0.799036	+	0.601284i	$0.794656\pi$
$102$		0			0
$103$	15.4831			1.52560			0.762798	−	0.646636i	$-0.223825\pi$
$103$	15.4831			1.52560			0.762798	+	0.646636i	$0.223825\pi$
$104$		0			0
$105$	−8.63262			−0.842457
$106$		0			0
$107$	0.410526	+	0.711051i	0.0396870	+	0.0687399i	0.885187	−	0.465236i	$-0.154031\pi$
$107$	0.410526	+	0.711051i	0.0396870	+	0.0687399i	−0.845500	+	0.533976i	$0.820697\pi$
$108$		0			0
$109$		−	3.71030i		−	0.355382i	−0.984086	−	0.177691i	$-0.943137\pi$
$109$		−	3.71030i		−	0.355382i	0.984086	−	0.177691i	$-0.0568628\pi$
$110$		0			0
$111$	−15.7855	−	9.11374i	−1.49829	−	0.865038i
$112$		0			0
$113$	−4.22275	+	7.31402i	−0.397243	+	0.688045i	−0.993385	−	0.114834i	$-0.963366\pi$
$113$	−4.22275	+	7.31402i	−0.397243	+	0.688045i	0.596142	+	0.802879i	$0.296700\pi$
$114$		0			0
$115$	−6.34466	+	3.66309i	−0.591643	+	0.341585i
$116$		0			0
$117$	9.45705	+	1.76008i	0.874304	+	0.162719i
$118$		0			0
$119$	5.87348	−	3.39106i	0.538421	−	0.310858i
$120$		0			0
$121$	12.2669	−	21.2468i	1.11517	−	1.93153i
$122$		0			0
$123$	−1.12595	−	0.650068i	−0.101524	−	0.0586147i
$124$		0			0
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	4.44271	+	7.69499i	0.394226	+	0.682820i	0.993002	−	0.118097i	$-0.0376792\pi$
$127$	4.44271	+	7.69499i	0.394226	+	0.682820i	−0.598776	+	0.800917i	$0.704346\pi$
$128$		0			0
$129$	12.3135			1.08414
$130$		0			0
$131$	−16.3590			−1.42929			−0.714645	−	0.699487i	$-0.753412\pi$
$131$	−16.3590			−1.42929			−0.714645	+	0.699487i	$0.753412\pi$
$132$		0			0
$133$	−0.632211	−	1.09502i	−0.0548197	−	0.0949505i
$134$		0			0
$135$		−	0.790520i		−	0.0680371i
$136$		0			0
$137$	10.3472	+	5.97399i	0.884025	+	0.510392i	0.871983	−	0.489535i	$-0.162834\pi$
$137$	10.3472	+	5.97399i	0.884025	+	0.510392i	0.0120415	+	0.999927i	$0.496167\pi$
$138$		0			0
$139$	0.388771	−	0.673372i	0.0329751	−	0.0571146i	−0.849067	−	0.528285i	$-0.822835\pi$
$139$	0.388771	−	0.673372i	0.0329751	−	0.0571146i	0.882042	+	0.471171i	$0.156168\pi$
$140$		0			0
$141$	−23.3115	+	13.4589i	−1.96318	+	1.13344i
$142$		0			0
$143$	16.3328	+	13.9706i	1.36581	+	1.16828i
$144$		0			0
$145$	−8.70815	+	5.02765i	−0.723172	+	0.417524i
$146$		0			0
$147$	−7.31838	+	12.6758i	−0.603610	+	1.04548i
$148$		0			0
$149$	−7.07245	−	4.08328i	−0.579398	−	0.334515i	0.181496	−	0.983392i	$-0.441906\pi$
$149$	−7.07245	−	4.08328i	−0.579398	−	0.334515i	−0.760894	+	0.648876i	$0.775239\pi$
$150$		0			0
$151$		−	19.3608i		−	1.57556i	−0.615957	−	0.787780i	$-0.711231\pi$
$151$		−	19.3608i		−	1.57556i	0.615957	−	0.787780i	$-0.288769\pi$
$152$		0			0
$153$	−2.49508	−	4.32160i	−0.201715	−	0.349381i
$154$		0			0
$155$	7.65605			0.614948
$156$		0			0
$157$	1.74943			0.139620			0.0698099	−	0.997560i	$-0.477761\pi$
$157$	1.74943			0.139620			0.0698099	+	0.997560i	$0.477761\pi$
$158$		0			0
$159$	11.6082	+	20.1059i	0.920586	+	1.59450i
$160$		0			0
$161$			26.5648i			2.09360i
$162$		0			0
$163$	−7.25986	−	4.19148i	−0.568636	−	0.328302i	0.187968	−	0.982175i	$-0.439810\pi$
$163$	−7.25986	−	4.19148i	−0.568636	−	0.328302i	−0.756604	+	0.653873i	$0.773143\pi$
$164$		0			0
$165$	−7.09583	+	12.2903i	−0.552410	+	0.956802i
$166$		0			0
$167$	−15.3405	+	8.85685i	−1.18708	+	0.685363i	−0.957643	−	0.287959i	$-0.907023\pi$
$167$	−15.3405	+	8.85685i	−1.18708	+	0.685363i	−0.229442	+	0.973322i	$0.573690\pi$
$168$		0			0
$169$	−10.1151	+	8.16604i	−0.778087	+	0.628157i
$170$		0			0
$171$	−0.805697	+	0.465169i	−0.0616132	+	0.0355724i
$172$		0			0
$173$	−7.79556	+	13.5023i	−0.592686	+	1.02656i	0.401183	+	0.915998i	$0.368599\pi$
$173$	−7.79556	+	13.5023i	−0.592686	+	1.02656i	−0.993869	+	0.110564i	$0.964734\pi$
$174$		0			0
$175$	3.14022	+	1.81301i	0.237378	+	0.137050i
$176$		0			0
$177$		−	26.1319i		−	1.96419i
$178$		0			0
$179$	−0.698498	−	1.20983i	−0.0522082	−	0.0904272i	0.838740	−	0.544532i	$-0.183293\pi$
$179$	−0.698498	−	1.20983i	−0.0522082	−	0.0904272i	−0.890948	+	0.454105i	$0.849959\pi$
$180$		0			0
$181$	−8.37081			−0.622198			−0.311099	−	0.950378i	$-0.600697\pi$
$181$	−8.37081			−0.622198			−0.311099	+	0.950378i	$0.600697\pi$
$182$		0			0
$183$	−10.6774			−0.789294
$184$		0			0
$185$	3.82810	+	6.63047i	0.281448	+	0.487482i
$186$		0			0
$187$		−	11.1495i		−	0.815334i
$188$		0			0
$189$	−2.48241	−	1.43322i	−0.180568	−	0.104251i
$190$		0			0
$191$	4.66477	−	8.07963i	0.337531	−	0.584621i	−0.646437	−	0.762968i	$-0.723741\pi$
$191$	4.66477	−	8.07963i	0.337531	−	0.584621i	0.983968	+	0.178347i	$0.0570748\pi$
$192$		0			0
$193$	8.99592	−	5.19380i	0.647541	−	0.373858i	−0.139973	−	0.990155i	$-0.544701\pi$
$193$	8.99592	−	5.19380i	0.647541	−	0.373858i	0.787513	+	0.616298i	$0.211368\pi$
$194$		0			0
$195$	−6.52308	−	5.57968i	−0.467127	−	0.399569i
$196$		0			0
$197$	−11.1498	+	6.43733i	−0.794390	+	0.458641i	−0.841506	−	0.540248i	$-0.818330\pi$
$197$	−11.1498	+	6.43733i	−0.794390	+	0.458641i	0.0471160	+	0.998889i	$0.484997\pi$
$198$		0			0
$199$	−7.13830	+	12.3639i	−0.506020	+	0.876453i	0.493955	+	0.869487i	$0.335551\pi$
$199$	−7.13830	+	12.3639i	−0.506020	+	0.876453i	−0.999976	+	0.00696572i	$0.997783\pi$
$200$		0			0
$201$	5.31563	+	3.06898i	0.374935	+	0.216469i
$202$		0			0
$203$			36.4607i			2.55904i
$204$		0			0
$205$	0.273052	+	0.472941i	0.0190708	+	0.0330316i
$206$		0			0
$207$	19.5459			1.35853
$208$		0			0
$209$	−2.07866			−0.143784
$210$		0			0
$211$	0.563936	+	0.976766i	0.0388230	+	0.0672434i	0.884784	−	0.466001i	$-0.154306\pi$
$211$	0.563936	+	0.976766i	0.0388230	+	0.0672434i	−0.845961	+	0.533245i	$0.820972\pi$
$212$		0			0
$213$		−	14.6235i		−	1.00199i
$214$		0			0
$215$	−4.47919	−	2.58606i	−0.305478	−	0.176368i
$216$		0			0
$217$	13.8805	−	24.0417i	0.942267	−	1.63205i
$218$		0			0
$219$	−0.701318	+	0.404906i	−0.0473907	+	0.0273610i
$220$		0			0
$221$	6.63000	+	1.23393i	0.445982	+	0.0830029i
$222$		0			0
$223$	19.3879	−	11.1936i	1.29831	−	0.749578i	0.318195	−	0.948025i	$-0.396923\pi$
$223$	19.3879	−	11.1936i	1.29831	−	0.749578i	0.980111	+	0.198448i	$0.0635900\pi$
$224$		0			0
$225$	1.33398	−	2.31052i	0.0889318	−	0.154034i
$226$		0			0
$227$	−4.48017	−	2.58663i	−0.297359	−	0.171680i	0.343897	−	0.939007i	$-0.388253\pi$
$227$	−4.48017	−	2.58663i	−0.297359	−	0.171680i	−0.641256	+	0.767327i	$0.721586\pi$
$228$		0			0
$229$			10.0052i			0.661162i	0.943778	+	0.330581i	$0.107245\pi$
$229$			10.0052i			0.661162i	−0.943778	+	0.330581i	$0.892755\pi$
$230$		0			0
$231$	25.7296	+	44.5649i	1.69288	+	2.93216i
$232$		0			0
$233$	5.05208			0.330973			0.165486	−	0.986212i	$-0.447081\pi$
$233$	5.05208			0.330973			0.165486	+	0.986212i	$0.447081\pi$
$234$		0			0
$235$	11.3065			0.737552
$236$		0			0
$237$	−7.65605	−	13.2607i	−0.497314	−	0.861373i
$238$		0			0
$239$		−	10.3454i		−	0.669190i	−0.942362	−	0.334595i	$-0.891400\pi$
$239$		−	10.3454i		−	0.669190i	0.942362	−	0.334595i	$-0.108600\pi$
$240$		0			0
$241$	−1.44104	−	0.831986i	−0.0928256	−	0.0535929i	0.452869	−	0.891577i	$-0.350401\pi$
$241$	−1.44104	−	0.831986i	−0.0928256	−	0.0535929i	−0.545694	+	0.837984i	$0.683734\pi$
$242$		0			0
$243$	−10.5821	+	18.3288i	−0.678843	+	1.17579i
$244$		0			0
$245$	5.32430	−	3.07398i	0.340157	−	0.196390i
$246$		0			0
$247$	0.230047	−	1.23606i	0.0146375	−	0.0786488i
$248$		0			0
$249$	15.8615	−	9.15762i	1.00518	−	0.580341i
$250$		0			0
$251$	−6.69211	+	11.5911i	−0.422402	+	0.731622i	−0.996174	−	0.0873933i	$-0.972146\pi$
$251$	−6.69211	+	11.5911i	−0.422402	+	0.731622i	0.573772	+	0.819015i	$0.305480\pi$
$252$		0			0
$253$	37.8206	+	21.8357i	2.37776	+	1.37280i
$254$		0			0
$255$			4.45296i			0.278855i
$256$		0			0
$257$	−3.07447	−	5.32514i	−0.191780	−	0.332173i	0.754060	−	0.656805i	$-0.228093\pi$
$257$	−3.07447	−	5.32514i	−0.191780	−	0.332173i	−0.945840	+	0.324632i	$0.894759\pi$
$258$		0			0
$259$	27.7615			1.72501
$260$		0			0
$261$	26.8271			1.66055
$262$		0			0
$263$	−15.8955	−	27.5318i	−0.980160	−	1.69769i	−0.661734	−	0.749739i	$-0.730179\pi$
$263$	−15.8955	−	27.5318i	−0.980160	−	1.69769i	−0.318426	−	0.947948i	$-0.603154\pi$
$264$		0			0
$265$		−	9.75169i		−	0.599042i
$266$		0			0
$267$	−2.88181	−	1.66382i	−0.176364	−	0.101824i
$268$		0			0
$269$	4.42627	−	7.66652i	0.269874	−	0.467436i	−0.698955	−	0.715166i	$-0.746351\pi$
$269$	4.42627	−	7.66652i	0.269874	−	0.467436i	0.968829	+	0.247730i	$0.0796845\pi$
$270$		0			0
$271$	4.64386	−	2.68113i	0.282094	−	0.162867i	−0.352277	−	0.935896i	$-0.614592\pi$
$271$	4.64386	−	2.68113i	0.282094	−	0.162867i	0.634371	+	0.773029i	$0.281259\pi$
$272$		0			0
$273$	−29.3478	+	10.3679i	−1.77621	+	0.627494i
$274$		0			0
$275$	5.16239	−	2.98051i	0.311304	−	0.179731i
$276$		0			0
$277$	4.33473	−	7.50797i	0.260449	−	0.451110i	−0.705913	−	0.708299i	$-0.749463\pi$
$277$	4.33473	−	7.50797i	0.260449	−	0.451110i	0.966361	+	0.257189i	$0.0827962\pi$
$278$		0			0
$279$	−17.6894	−	10.2130i	−1.05904	−	0.611436i
$280$		0			0
$281$			23.4564i			1.39929i	0.714490	+	0.699645i	$0.246659\pi$
$281$			23.4564i			1.39929i	−0.714490	+	0.699645i	$0.753341\pi$
$282$		0			0
$283$	−1.18421	−	2.05111i	−0.0703938	−	0.121926i	0.828680	−	0.559722i	$-0.189092\pi$
$283$	−1.18421	−	2.05111i	−0.0703938	−	0.121926i	−0.899074	+	0.437797i	$0.855759\pi$
$284$		0			0
$285$	0.830187			0.0491761
$286$		0			0
$287$	1.98018			0.116886
$288$		0			0
$289$	6.75079	+	11.6927i	0.397105	+	0.687807i
$290$		0			0
$291$			8.85608i			0.519153i
$292$		0			0
$293$	0.613696	+	0.354318i	0.0358525	+	0.0206995i	0.517819	−	0.855490i	$-0.326744\pi$
$293$	0.613696	+	0.354318i	0.0358525	+	0.0206995i	−0.481967	+	0.876190i	$0.660077\pi$
$294$		0			0
$295$	−5.48817	+	9.50578i	−0.319533	+	0.553448i
$296$		0			0
$297$	−4.08097	+	2.35615i	−0.236802	+	0.136718i
$298$		0			0
$299$	−17.1701	+	20.0732i	−0.992975	+	1.16086i
$300$		0			0
$301$	−16.2416	+	9.37708i	−0.936149	+	0.540486i
$302$		0			0
$303$	−2.90008	+	5.02308i	−0.166605	+	0.288569i
$304$		0			0
$305$	3.88402	+	2.24244i	0.222399	+	0.128402i
$306$		0			0
$307$			2.85629i			0.163017i	0.996673	+	0.0815085i	$0.0259738\pi$
$307$			2.85629i			0.163017i	−0.996673	+	0.0815085i	$0.974026\pi$
$308$		0			0
$309$	18.4307	+	31.9229i	1.04849	+	1.81603i
$310$		0			0
$311$	−3.79716			−0.215317			−0.107658	−	0.994188i	$-0.534335\pi$
$311$	−3.79716			−0.215317			−0.107658	+	0.994188i	$0.534335\pi$
$312$		0			0
$313$	−22.9354			−1.29638			−0.648192	−	0.761477i	$-0.724474\pi$
$313$	−22.9354			−1.29638			−0.648192	+	0.761477i	$0.724474\pi$
$314$		0			0
$315$	−4.83702	−	8.37796i	−0.272535	−	0.472044i
$316$		0			0
$317$		−	10.8574i		−	0.609813i	−0.952382	−	0.304906i	$-0.901375\pi$
$317$		−	10.8574i		−	0.609813i	0.952382	−	0.304906i	$-0.0986252\pi$
$318$		0			0
$319$	51.9094	+	29.9699i	2.90637	+	1.67799i
$320$		0			0
$321$	−0.977358	+	1.69283i	−0.0545508	+	0.0944847i
$322$		0			0
$323$	−0.564845	+	0.326114i	−0.0314288	+	0.0181454i
$324$		0			0
$325$	1.20102	+	3.39964i	0.0666203	+	0.188578i
$326$		0			0
$327$	7.64985	−	4.41664i	0.423037	−	0.244241i
$328$		0			0
$329$	20.4987	−	35.5047i	1.13013	−	1.95744i
$330$		0			0
$331$	−5.52844	−	3.19185i	−0.303871	−	0.175440i	0.340310	−	0.940313i	$-0.389468\pi$
$331$	−5.52844	−	3.19185i	−0.303871	−	0.175440i	−0.644180	+	0.764874i	$0.722801\pi$
$332$		0			0
$333$		−	20.4264i		−	1.11936i
$334$		0			0
$335$	−1.28908	−	2.23276i	−0.0704301	−	0.121989i
$336$		0			0
$337$	16.0882			0.876379			0.438190	−	0.898883i	$-0.355620\pi$
$337$	16.0882			0.876379			0.438190	+	0.898883i	$0.355620\pi$
$338$		0			0
$339$	−20.1066			−1.09204
$340$		0			0
$341$	−22.8189	−	39.5235i	−1.23571	−	2.14032i
$342$		0			0
$343$			3.08948i			0.166816i
$344$		0			0
$345$	−15.1050	−	8.72089i	−0.813227	−	0.469517i
$346$		0			0
$347$	14.7143	−	25.4860i	0.789908	−	1.36816i	−0.136115	−	0.990693i	$-0.543462\pi$
$347$	14.7143	−	25.4860i	0.789908	−	1.36816i	0.926023	−	0.377467i	$-0.123205\pi$
$348$		0			0
$349$	−4.03046	+	2.32699i	−0.215746	+	0.124561i	−0.603979	−	0.797000i	$-0.706419\pi$
$349$	−4.03046	+	2.32699i	−0.215746	+	0.124561i	0.388233	+	0.921561i	$0.373086\pi$
$350$		0			0
$351$	−0.949426	−	2.68748i	−0.0506766	−	0.143447i
$352$		0			0
$353$	20.9177	−	12.0768i	1.11334	−	0.642786i	0.173646	−	0.984808i	$-0.444445\pi$
$353$	20.9177	−	12.0768i	1.11334	−	0.642786i	0.939692	+	0.342023i	$0.111112\pi$
$354$		0			0
$355$	−3.07120	+	5.31948i	−0.163003	+	0.282329i
$356$		0			0
$357$	13.9833	+	8.07325i	0.740073	+	0.427282i
$358$		0			0
$359$			12.7251i			0.671605i	0.941932	+	0.335803i	$0.109007\pi$
$359$			12.7251i			0.671605i	−0.941932	+	0.335803i	$0.890993\pi$
$360$		0			0
$361$	−9.43920	−	16.3492i	−0.496800	−	0.860483i
$362$		0			0
$363$	58.4085			3.06565
$364$		0			0
$365$	0.340151			0.0178043
$366$		0			0
$367$	−1.66024	−	2.87561i	−0.0866637	−	0.150106i	0.819435	−	0.573172i	$-0.194287\pi$
$367$	−1.66024	−	2.87561i	−0.0866637	−	0.150106i	−0.906099	+	0.423066i	$0.860954\pi$
$368$		0			0
$369$		−	1.45698i		−	0.0758474i
$370$		0			0
$371$	−30.6224	−	17.6799i	−1.58984	−	0.917894i
$372$		0			0
$373$	7.74585	−	13.4162i	0.401065	−	0.694665i	−0.592790	−	0.805357i	$-0.701974\pi$
$373$	7.74585	−	13.4162i	0.401065	−	0.694665i	0.993855	+	0.110692i	$0.0353069\pi$
$374$		0			0
$375$	−2.06179	+	1.19037i	−0.106470	+	0.0614706i
$376$		0			0
$377$	−23.5663	+	27.5508i	−1.21373	+	1.41894i
$378$		0			0
$379$	13.8747	−	8.01057i	0.712696	−	0.411475i	−0.0993623	−	0.995051i	$-0.531680\pi$
$379$	13.8747	−	8.01057i	0.712696	−	0.411475i	0.812059	+	0.583576i	$0.198347\pi$
$380$		0			0
$381$	−10.5770	+	18.3198i	−0.541874	+	0.938553i
$382$		0			0
$383$	−5.35427	−	3.09129i	−0.273590	−	0.157957i	0.356928	−	0.934132i	$-0.383824\pi$
$383$	−5.35427	−	3.09129i	−0.273590	−	0.157957i	−0.630518	+	0.776175i	$0.717158\pi$
$384$		0			0
$385$		−	21.6147i		−	1.10159i
$386$		0			0
$387$	6.89948	+	11.9503i	0.350720	+	0.607466i
$388$		0			0
$389$	−18.6583			−0.946015			−0.473008	−	0.881058i	$-0.656832\pi$
$389$	−18.6583			−0.946015			−0.473008	+	0.881058i	$0.656832\pi$
$390$		0			0
$391$	13.7029			0.692987
$392$		0			0
$393$	−19.4733	−	33.7287i	−0.982297	−	1.70139i
$394$		0			0
$395$			6.43164i			0.323611i
$396$		0			0
$397$	−4.37713	−	2.52714i	−0.219682	−	0.126833i	0.386121	−	0.922448i	$-0.373815\pi$
$397$	−4.37713	−	2.52714i	−0.219682	−	0.126833i	−0.605803	+	0.795615i	$0.707148\pi$
$398$		0			0
$399$	1.50514	−	2.60697i	0.0753510	−	0.130512i
$400$		0			0
$401$	−2.82063	+	1.62849i	−0.140856	+	0.0813231i	−0.568772	−	0.822495i	$-0.692581\pi$
$401$	−2.82063	+	1.62849i	−0.140856	+	0.0813231i	0.427916	+	0.903818i	$0.359248\pi$
$402$		0			0
$403$	26.0278	−	9.19503i	1.29654	−	0.458037i
$404$		0			0
$405$	8.56143	−	4.94294i	0.425421	−	0.245617i
$406$		0			0
$407$	22.8194	−	39.5243i	1.13111	−	1.95915i
$408$		0			0
$409$	0.508890	+	0.293808i	0.0251630	+	0.0145279i	0.512529	−	0.858670i	$-0.328709\pi$
$409$	0.508890	+	0.293808i	0.0251630	+	0.0145279i	−0.487366	+	0.873198i	$0.662042\pi$
$410$		0			0
$411$			28.4451i			1.40309i
$412$		0			0
$413$	19.9002	+	34.4681i	0.979223	+	1.69606i
$414$		0			0
$415$	−7.69307			−0.377638
$416$		0			0
$417$	1.85113			0.0906503
$418$		0			0
$419$	−11.9744	−	20.7402i	−0.584986	−	1.01323i	−0.994877	−	0.101091i	$-0.967767\pi$
$419$	−11.9744	−	20.7402i	−0.584986	−	1.01323i	0.409891	−	0.912134i	$-0.365567\pi$
$420$		0			0
$421$			40.8630i			1.99154i	0.0918796	+	0.995770i	$0.470713\pi$
$421$			40.8630i			1.99154i	−0.0918796	+	0.995770i	$0.529287\pi$
$422$		0			0
$423$	−26.1237	−	15.0825i	−1.27018	−	0.733338i
$424$		0			0
$425$	0.935203	−	1.61982i	0.0453640	−	0.0785728i
$426$		0			0
$427$	14.0835	−	8.13112i	0.681549	−	0.393493i
$428$		0			0
$429$	−9.36240	+	50.3050i	−0.452021	+	2.42875i
$430$		0			0
$431$	−31.2923	+	18.0666i	−1.50730	+	0.870238i	−0.507332	+	0.861751i	$0.669368\pi$
$431$	−31.2923	+	18.0666i	−1.50730	+	0.870238i	−0.999964	+	0.00848686i	$0.997299\pi$
$432$		0			0
$433$	−9.89760	+	17.1432i	−0.475648	+	0.823847i	−0.999611	−	0.0278940i	$-0.991120\pi$
$433$	−9.89760	+	17.1432i	−0.475648	+	0.823847i	0.523962	+	0.851741i	$0.324453\pi$
$434$		0			0
$435$	−20.7319	−	11.9696i	−0.994018	−	0.573897i
$436$		0			0
$437$		−	2.55470i		−	0.122208i
$438$		0			0
$439$	10.0943	+	17.4839i	0.481777	+	0.834461i	0.999781	−	0.0209164i	$-0.00665837\pi$
$439$	10.0943	+	17.4839i	0.481777	+	0.834461i	−0.518005	+	0.855378i	$0.673325\pi$
$440$		0			0
$441$	−16.4025			−0.781071
$442$		0			0
$443$	−32.9021			−1.56323			−0.781613	−	0.623763i	$-0.785603\pi$
$443$	−32.9021			−1.56323			−0.781613	+	0.623763i	$0.785603\pi$
$444$		0			0
$445$	0.698863	+	1.21047i	0.0331293	+	0.0573816i
$446$		0			0
$447$		−	19.4425i		−	0.919599i
$448$		0			0
$449$	2.57065	+	1.48416i	0.121316	+	0.0700420i	0.559430	−	0.828877i	$-0.311020\pi$
$449$	2.57065	+	1.48416i	0.121316	+	0.0700420i	−0.438114	+	0.898919i	$0.644353\pi$
$450$		0			0
$451$	1.62767	−	2.81921i	0.0766440	−	0.132751i
$452$		0			0
$453$	39.9178	−	23.0466i	1.87550	−	1.08282i
$454$		0			0
$455$	12.8531	+	2.39212i	0.602561	+	0.112144i
$456$		0			0
$457$	22.9571	−	13.2543i	1.07389	−	0.620009i	0.144646	−	0.989483i	$-0.453796\pi$
$457$	22.9571	−	13.2543i	1.07389	−	0.620009i	0.929241	+	0.369475i	$0.120462\pi$
$458$		0			0
$459$	−0.739296	+	1.28050i	−0.0345074	+	0.0597686i
$460$		0			0
$461$	−32.6132	−	18.8292i	−1.51895	−	0.876965i	−0.999751	−	0.0223102i	$-0.992898\pi$
$461$	−32.6132	−	18.8292i	−1.51895	−	0.876965i	−0.519197	−	0.854655i	$-0.673769\pi$
$462$		0			0
$463$		−	38.5610i		−	1.79208i	−0.443972	−	0.896041i	$-0.646431\pi$
$463$		−	38.5610i		−	1.79208i	0.443972	−	0.896041i	$-0.353569\pi$
$464$		0			0
$465$	9.11355	+	15.7851i	0.422631	+	0.732018i
$466$		0			0
$467$	−13.2301			−0.612215			−0.306107	−	0.951997i	$-0.599027\pi$
$467$	−13.2301			−0.612215			−0.306107	+	0.951997i	$0.599027\pi$
$468$		0			0
$469$	−9.34846			−0.431672
$470$		0			0
$471$	2.08248	+	3.60695i	0.0959554	+	0.166200i
$472$		0			0
$473$			30.8311i			1.41761i
$474$		0			0
$475$	−0.301991	−	0.174354i	−0.0138563	−	0.00799993i
$476$		0			0
$477$	−13.0085	+	22.5314i	−0.595620	+	1.03164i
$478$		0			0
$479$	14.4407	−	8.33737i	0.659815	−	0.380944i	−0.132392	−	0.991197i	$-0.542266\pi$
$479$	14.4407	−	8.33737i	0.659815	−	0.380944i	0.792206	+	0.610253i	$0.208932\pi$
$480$		0			0
$481$	20.9775	+	17.9436i	0.956490	+	0.818158i
$482$		0			0
$483$	−54.7710	+	31.6221i	−2.49217	+	1.43885i
$484$		0			0
$485$	1.85994	−	3.22151i	0.0844554	−	0.146281i
$486$		0			0
$487$	−4.64632	−	2.68256i	−0.210545	−	0.121558i	0.391020	−	0.920382i	$-0.372122\pi$
$487$	−4.64632	−	2.68256i	−0.210545	−	0.121558i	−0.601565	+	0.798824i	$0.705456\pi$
$488$		0			0
$489$		−	19.9577i		−	0.902519i
$490$		0			0
$491$	15.7824	+	27.3359i	0.712248	+	1.23365i	0.964011	+	0.265861i	$0.0856562\pi$
$491$	15.7824	+	27.3359i	0.712248	+	1.23365i	−0.251763	+	0.967789i	$0.581010\pi$
$492$		0			0
$493$	18.8075			0.847047
$494$		0			0
$495$	−15.9037			−0.714819
$496$		0			0
$497$	11.1362	+	19.2885i	0.499528	+	0.865208i
$498$		0			0
$499$		−	42.3624i		−	1.89640i	−0.317673	−	0.948200i	$-0.602901\pi$
$499$		−	42.3624i		−	1.89640i	0.317673	−	0.948200i	$-0.397099\pi$
$500$		0			0
$501$	−36.5219	−	21.0859i	−1.63168	−	0.942049i
$502$		0			0
$503$	−11.1630	+	19.3348i	−0.497732	+	0.862096i	−0.999997	−	0.00261737i	$-0.999167\pi$
$503$	−11.1630	+	19.3348i	−0.497732	+	0.862096i	0.502265	+	0.864714i	$0.332500\pi$
$504$		0			0
$505$	2.10988	−	1.21814i	0.0938883	−	0.0542064i
$506$		0			0
$507$	−28.8774	−	11.1346i	−1.28249	−	0.494505i
$508$		0			0
$509$	2.73333	−	1.57809i	0.121153	−	0.0699477i	−0.438199	−	0.898878i	$-0.644383\pi$
$509$	2.73333	−	1.57809i	0.121153	−	0.0699477i	0.559352	+	0.828930i	$0.311050\pi$
$510$		0			0
$511$	0.616696	−	1.06815i	0.0272810	−	0.0472521i
$512$		0			0
$513$	0.238730	+	0.137831i	0.0105402	+	0.00608537i
$514$		0			0
$515$		−	15.4831i		−	0.682268i
$516$		0			0
$517$	−33.6990	−	58.3683i	−1.48208	−	2.56704i
$518$		0			0
$519$	−37.1185			−1.62932
$520$		0			0
$521$	2.66590			0.116795			0.0583975	−	0.998293i	$-0.481401\pi$
$521$	2.66590			0.116795			0.0583975	+	0.998293i	$0.481401\pi$
$522$		0			0
$523$	−5.26257	−	9.11504i	−0.230116	−	0.398573i	0.727726	−	0.685868i	$-0.240577\pi$
$523$	−5.26257	−	9.11504i	−0.230116	−	0.398573i	−0.957842	+	0.287295i	$0.907244\pi$
$524$		0			0
$525$			8.63262i			0.376758i
$526$		0			0
$527$	−12.4014	−	7.15996i	−0.540214	−	0.311893i
$528$		0			0
$529$	−15.3365	+	26.5635i	−0.666803	+	1.15494i
$530$		0			0
$531$	25.3610	−	14.6422i	1.10057	−	0.635416i
$532$		0			0
$533$	1.49629	+	1.27989i	0.0648115	+	0.0554381i
$534$		0			0
$535$	0.711051	−	0.410526i	0.0307414	−	0.0177486i
$536$		0			0
$537$	1.66295	−	2.88031i	0.0717614	−	0.124294i
$538$		0			0
$539$	−31.7382	−	18.3241i	−1.36706	−	0.789274i
$540$		0			0
$541$		−	26.5833i		−	1.14291i	−0.820635	−	0.571453i	$-0.806380\pi$
$541$		−	26.5833i		−	1.14291i	0.820635	−	0.571453i	$-0.193620\pi$
$542$		0			0
$543$	−9.96439	−	17.2588i	−0.427613	−	0.740647i
$544$		0			0
$545$	−3.71030			−0.158932
$546$		0			0
$547$	7.93394			0.339231			0.169615	−	0.985510i	$-0.445747\pi$
$547$	7.93394			0.339231			0.169615	+	0.985510i	$0.445747\pi$
$548$		0			0
$549$	−5.98273	−	10.3624i	−0.255337	−	0.442256i
$550$		0			0
$551$		−	3.50637i		−	0.149377i
$552$		0			0
$553$	20.1967	+	11.6606i	0.858853	+	0.495859i
$554$		0			0
$555$	−9.11374	+	15.7855i	−0.386857	+	0.670055i
$556$		0			0
$557$	−32.7439	+	18.9047i	−1.38740	+	0.801019i	−0.993022	−	0.117928i	$-0.962375\pi$
$557$	−32.7439	+	18.9047i	−1.38740	+	0.801019i	−0.394383	+	0.918946i	$0.629042\pi$
$558$		0			0
$559$	−18.3335	−	3.41210i	−0.775425	−	0.144317i
$560$		0			0
$561$	22.9879	−	13.2721i	0.970551	−	0.560348i
$562$		0			0
$563$	−0.190357	+	0.329709i	−0.00802261	+	0.0138956i	−0.870009	−	0.493036i	$-0.835887\pi$
$563$	−0.190357	+	0.329709i	−0.00802261	+	0.0138956i	0.861986	+	0.506932i	$0.169220\pi$
$564$		0			0
$565$	7.31402	+	4.22275i	0.307703	+	0.177652i
$566$		0			0
$567$		−	35.8463i		−	1.50541i
$568$		0			0
$569$	−19.7269	−	34.1680i	−0.826995	−	1.43240i	−0.900385	−	0.435094i	$-0.856715\pi$
$569$	−19.7269	−	34.1680i	−0.826995	−	1.43240i	0.0733899	−	0.997303i	$-0.476618\pi$
$570$		0			0
$571$	−14.9682			−0.626402			−0.313201	−	0.949687i	$-0.601401\pi$
$571$	−14.9682			−0.626402			−0.313201	+	0.949687i	$0.601401\pi$
$572$		0			0
$573$	22.2113			0.927890
$574$		0			0
$575$	3.66309	+	6.34466i	0.152761	+	0.264591i
$576$		0			0
$577$			23.7222i			0.987567i	0.869585	+	0.493784i	$0.164387\pi$
$577$			23.7222i			0.987567i	−0.869585	+	0.493784i	$0.835613\pi$
$578$		0			0
$579$	21.4170	+	12.3651i	0.890061	+	0.513877i
$580$		0			0
$581$	−13.9476	+	24.1579i	−0.578643	+	1.00224i
$582$		0			0
$583$	−50.3420	+	29.0650i	−2.08495	+	1.20375i
$584$		0			0
$585$	1.76008	−	9.45705i	0.0727703	−	0.391001i
$586$		0			0
$587$	26.7817	−	15.4624i	1.10540	−	0.638203i	0.167766	−	0.985827i	$-0.446345\pi$
$587$	26.7817	−	15.4624i	1.10540	−	0.638203i	0.937634	+	0.347624i	$0.113011\pi$
$588$		0			0
$589$	−1.33487	+	2.31206i	−0.0550022	+	0.0952666i
$590$		0			0
$591$	−26.5448	−	15.3257i	−1.09191	−	0.630413i
$592$		0			0
$593$		−	20.2931i		−	0.833339i	−0.909058	−	0.416669i	$-0.863197\pi$
$593$		−	20.2931i		−	0.833339i	0.909058	−	0.416669i	$-0.136803\pi$
$594$		0			0
$595$	−3.39106	−	5.87348i	−0.139020	−	0.240789i
$596$		0			0
$597$	−33.9889			−1.39107
$598$		0			0
$599$	33.0630			1.35092			0.675459	−	0.737397i	$-0.263945\pi$
$599$	33.0630			1.35092			0.675459	+	0.737397i	$0.263945\pi$
$600$		0			0
$601$	8.65945	+	14.9986i	0.353227	+	0.611806i	0.986813	−	0.161866i	$-0.0517512\pi$
$601$	8.65945	+	14.9986i	0.353227	+	0.611806i	−0.633586	+	0.773672i	$0.718418\pi$
$602$		0			0
$603$			6.87842i			0.280111i
$604$		0			0
$605$	−21.2468	−	12.2669i	−0.863806	−	0.498719i
$606$		0			0
$607$	−3.48716	+	6.03994i	−0.141540	+	0.245154i	−0.928077	−	0.372389i	$-0.878539\pi$
$607$	−3.48716	+	6.03994i	−0.141540	+	0.245154i	0.786537	+	0.617543i	$0.211872\pi$
$608$		0			0
$609$	−75.1741	+	43.4018i	−3.04621	+	1.75873i
$610$		0			0
$611$	38.4379	−	13.5792i	1.55503	−	0.549357i
$612$		0			0
$613$	−3.23629	+	1.86847i	−0.130713	+	0.0754670i	−0.563930	−	0.825822i	$-0.690711\pi$
$613$	−3.23629	+	1.86847i	−0.130713	+	0.0754670i	0.433218	+	0.901289i	$0.357378\pi$
$614$		0			0
$615$	−0.650068	+	1.12595i	−0.0262133	+	0.0454027i
$616$		0			0
$617$	−22.4571	−	12.9656i	−0.904088	−	0.521975i	−0.0255637	−	0.999673i	$-0.508138\pi$
$617$	−22.4571	−	12.9656i	−0.904088	−	0.521975i	−0.878524	+	0.477698i	$0.841471\pi$
$618$		0			0
$619$		−	27.7071i		−	1.11364i	−0.830633	−	0.556821i	$-0.812021\pi$
$619$		−	27.7071i		−	1.11364i	0.830633	−	0.556821i	$-0.187979\pi$
$620$		0			0
$621$	−2.89575	−	5.01558i	−0.116202	−	0.201268i
$622$		0			0
$623$	5.06817			0.203052
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−2.47438	−	4.28575i	−0.0988172	−	0.171156i
$628$		0			0
$629$		−	14.3202i		−	0.570984i
$630$		0			0
$631$	−18.6661	−	10.7769i	−0.743087	−	0.429022i	0.0801035	−	0.996787i	$-0.474475\pi$
$631$	−18.6661	−	10.7769i	−0.743087	−	0.429022i	−0.823191	+	0.567765i	$0.807808\pi$
$632$		0			0
$633$	−1.34259	+	2.32543i	−0.0533631	+	0.0924276i
$634$		0			0
$635$	7.69499	−	4.44271i	0.305366	−	0.176303i
$636$		0			0
$637$	14.4088	−	16.8450i	0.570897	−	0.667423i
$638$		0			0
$639$	14.1921	−	8.19383i	0.561432	−	0.324143i
$640$		0			0
$641$	3.04011	−	5.26562i	0.120077	−	0.207979i	−0.799721	−	0.600372i	$-0.795019\pi$
$641$	3.04011	−	5.26562i	0.120077	−	0.207979i	0.919798	+	0.392393i	$0.128353\pi$
$642$		0			0
$643$	9.42734	+	5.44288i	0.371778	+	0.214646i	0.674235	−	0.738517i	$-0.264473\pi$
$643$	9.42734	+	5.44288i	0.371778	+	0.214646i	−0.302457	+	0.953163i	$0.597807\pi$
$644$		0			0
$645$		−	12.3135i		−	0.484844i
$646$		0			0
$647$	15.4298	+	26.7253i	0.606610	+	1.05068i	0.991795	+	0.127839i	$0.0408042\pi$
$647$	15.4298	+	26.7253i	0.606610	+	1.05068i	−0.385185	+	0.922839i	$0.625862\pi$
$648$		0			0
$649$	65.4301			2.56836
$650$		0			0
$651$	66.0917			2.59034
$652$		0			0
$653$	−21.5773	−	37.3729i	−0.844384	−	1.46252i	−0.886155	−	0.463388i	$-0.846634\pi$
$653$	−21.5773	−	37.3729i	−0.844384	−	1.46252i	0.0417717	−	0.999127i	$-0.486700\pi$
$654$		0			0
$655$			16.3590i			0.639198i
$656$		0			0
$657$	−0.785923	−	0.453753i	−0.0306618	−	0.0177026i
$658$		0			0
$659$	−7.39917	+	12.8157i	−0.288231	+	0.499230i	−0.973387	−	0.229165i	$-0.926400\pi$
$659$	−7.39917	+	12.8157i	−0.288231	+	0.499230i	0.685157	+	0.728396i	$0.259734\pi$
$660$		0			0
$661$	30.3280	−	17.5099i	1.17962	−	0.681056i	0.223696	−	0.974659i	$-0.428188\pi$
$661$	30.3280	−	17.5099i	1.17962	−	0.681056i	0.955927	+	0.293603i	$0.0948545\pi$
$662$		0			0
$663$	5.34807	+	15.1385i	0.207702	+	0.587930i
$664$		0			0
$665$	−1.09502	+	0.632211i	−0.0424631	+	0.0245161i
$666$		0			0
$667$	−36.8335	+	63.7975i	−1.42620	+	2.47025i
$668$		0			0
$669$	46.1576	+	26.6491i	1.78455	+	1.03031i
$670$		0			0
$671$		−	26.7345i		−	1.03207i
$672$		0			0
$673$	−8.20629	−	14.2137i	−0.316329	−	0.547898i	0.663390	−	0.748274i	$-0.269117\pi$
$673$	−8.20629	−	14.2137i	−0.316329	−	0.547898i	−0.979719	+	0.200376i	$0.935784\pi$
$674$		0			0
$675$	−0.790520			−0.0304271
$676$		0			0
$677$	20.1260			0.773505			0.386753	−	0.922183i	$-0.373597\pi$
$677$	20.1260			0.773505			0.386753	+	0.922183i	$0.373597\pi$
$678$		0			0
$679$	−6.74416	−	11.6812i	−0.258817	−	0.448284i
$680$		0			0
$681$		−	12.3162i		−	0.471958i
$682$		0			0
$683$	24.8842	+	14.3669i	0.952169	+	0.549735i	0.893754	−	0.448558i	$-0.148062\pi$
$683$	24.8842	+	14.3669i	0.952169	+	0.549735i	0.0584147	+	0.998292i	$0.481395\pi$
$684$		0			0
$685$	5.97399	−	10.3472i	0.228254	−	0.395348i
$686$		0			0
$687$	−20.6286	+	11.9099i	−0.787029	+	0.454392i
$688$		0			0
$689$	−11.7119	−	33.1523i	−0.446189	−	1.26300i
$690$		0			0
$691$	31.9724	−	18.4593i	1.21629	−	0.702225i	0.252167	−	0.967684i	$-0.418857\pi$
$691$	31.9724	−	18.4593i	1.21629	−	0.702225i	0.964122	+	0.265459i	$0.0855236\pi$
$692$		0			0
$693$	−28.8335	+	49.9411i	−1.09530	+	1.89711i
$694$		0			0
$695$	−0.673372	−	0.388771i	−0.0255424	−	0.0147469i
$696$		0			0
$697$		−	1.02144i		−	0.0386897i
$698$		0			0
$699$	6.01386	+	10.4163i	0.227465	+	0.393981i
$700$		0			0
$701$	17.5228			0.661825			0.330913	−	0.943661i	$-0.392643\pi$
$701$	17.5228			0.661825			0.330913	+	0.943661i	$0.392643\pi$
$702$		0			0
$703$	−2.66979			−0.100693
$704$		0			0
$705$	13.4589	+	23.3115i	0.506892	+	0.877962i
$706$		0			0
$707$		−	8.83397i		−	0.332236i
$708$		0			0
$709$	−9.04899	−	5.22443i	−0.339842	−	0.196208i	0.320360	−	0.947296i	$-0.396196\pi$
$709$	−9.04899	−	5.22443i	−0.339842	−	0.196208i	−0.660202	+	0.751088i	$0.729529\pi$
$710$		0			0
$711$	8.57965	−	14.8604i	0.321762	−	0.557308i
$712$		0			0
$713$	48.5750	−	28.0448i	1.81915	−	1.05029i
$714$		0			0
$715$	13.9706	−	16.3328i	0.522473	−	0.610811i
$716$		0			0
$717$	21.3301	−	12.3149i	0.796586	−	0.459909i
$718$		0			0
$719$	−19.2357	+	33.3172i	−0.717371	+	1.24252i	0.244667	+	0.969607i	$0.421321\pi$
$719$	−19.2357	+	33.3172i	−0.717371	+	1.24252i	−0.962038	+	0.272915i	$0.912012\pi$
$720$		0			0
$721$	−48.6204	−	28.0710i	−1.81072	−	1.04542i
$722$		0			0
$723$		−	3.96149i		−	0.147330i
$724$		0			0
$725$	5.02765	+	8.70815i	0.186722	+	0.323412i
$726$		0			0
$727$	19.9395			0.739515			0.369757	−	0.929128i	$-0.379441\pi$
$727$	19.9395			0.739515			0.369757	+	0.929128i	$0.379441\pi$
$728$		0			0
$729$	−20.7290			−0.767741
$730$		0			0
$731$	4.83698	+	8.37789i	0.178902	+	0.309868i
$732$		0			0
$733$			24.1856i			0.893316i	0.894705	+	0.446658i	$0.147386\pi$
$733$			24.1856i			0.893316i	−0.894705	+	0.446658i	$0.852614\pi$
$734$		0			0
$735$	12.6758	+	7.31838i	0.467554	+	0.269942i
$736$		0			0
$737$	−7.68424	+	13.3095i	−0.283053	+	0.490262i
$738$		0			0
$739$	10.9400	−	6.31621i	0.402434	−	0.232345i	−0.285100	−	0.958498i	$-0.592027\pi$
$739$	10.9400	−	6.31621i	0.402434	−	0.232345i	0.687534	+	0.726152i	$0.258693\pi$
$740$		0			0
$741$	2.82234	−	0.997068i	0.103681	−	0.0366282i
$742$		0			0
$743$	28.1993	−	16.2809i	1.03453	−	0.597287i	0.116252	−	0.993220i	$-0.462912\pi$
$743$	28.1993	−	16.2809i	1.03453	−	0.597287i	0.918280	+	0.395932i	$0.129579\pi$
$744$		0			0
$745$	−4.08328	+	7.07245i	−0.149600	+	0.259115i
$746$		0			0
$747$	17.7749	+	10.2624i	0.650351	+	0.375480i
$748$		0			0
$749$		−	2.97714i		−	0.108782i
$750$		0			0
$751$	−9.30961	−	16.1247i	−0.339712	−	0.588399i	0.644666	−	0.764464i	$-0.276996\pi$
$751$	−9.30961	−	16.1247i	−0.339712	−	0.588399i	−0.984379	+	0.176065i	$0.943663\pi$
$752$		0			0
$753$	−31.8644			−1.16120
$754$		0			0
$755$	−19.3608			−0.704612
$756$		0			0
$757$	−25.0580	−	43.4018i	−0.910749	−	1.57746i	−0.813008	−	0.582252i	$-0.802172\pi$
$757$	−25.0580	−	43.4018i	−0.910749	−	1.57746i	−0.0977414	−	0.995212i	$-0.531162\pi$
$758$		0			0
$759$			103.971i			3.77390i
$760$		0			0
$761$	−7.16753	−	4.13818i	−0.259823	−	0.150009i	0.364431	−	0.931230i	$-0.381264\pi$
$761$	−7.16753	−	4.13818i	−0.259823	−	0.150009i	−0.624254	+	0.781222i	$0.714597\pi$
$762$		0			0
$763$	−6.72680	+	11.6512i	−0.243526	+	0.421800i
$764$		0			0
$765$	−4.32160	+	2.49508i	−0.156248	+	0.0902097i
$766$		0			0
$767$	−7.24121	+	38.9076i	−0.261465	+	1.40487i
$768$		0			0
$769$	−6.31322	+	3.64494i	−0.227661	+	0.131440i	−0.609492	−	0.792792i	$-0.708627\pi$
$769$	−6.31322	+	3.64494i	−0.227661	+	0.131440i	0.381832	+	0.924232i	$0.375293\pi$
$770$		0			0
$771$	7.31953	−	12.6778i	0.263606	−	0.456580i
$772$		0			0
$773$	−11.8712	−	6.85386i	−0.426979	−	0.246516i	0.271080	−	0.962557i	$-0.412619\pi$
$773$	−11.8712	−	6.85386i	−0.426979	−	0.246516i	−0.698059	+	0.716041i	$0.745953\pi$
$774$		0			0
$775$		−	7.65605i		−	0.275013i
$776$		0			0
$777$	33.0465	+	57.2383i	1.18554	+	2.05341i
$778$		0			0
$779$	−0.190432			−0.00682292
$780$		0			0
$781$	36.6150			1.31019
$782$		0			0
$783$	−3.97446	−	6.88396i	−0.142036	−	0.246013i
$784$		0			0
$785$		−	1.74943i		−	0.0624399i
$786$		0			0
$787$	42.5408	+	24.5609i	1.51642	+	0.875503i	0.999814	+	0.0192772i	$0.00613651\pi$
$787$	42.5408	+	24.5609i	1.51642	+	0.875503i	0.516602	+	0.856226i	$0.327197\pi$
$788$		0			0
$789$	37.8432	−	65.5463i	1.34725	−	2.33351i
$790$		0			0
$791$	26.5207	−	15.3117i	0.942968	−	0.544423i
$792$		0			0
$793$	15.8975	+	2.95873i	0.564537	+	0.105068i
$794$		0			0
$795$	20.1059	−	11.6082i	0.713083	−	0.411699i
$796$		0			0
$797$	−2.43423	+	4.21621i	−0.0862248	+	0.149346i	−0.905912	−	0.423465i	$-0.860814\pi$
$797$	−2.43423	+	4.21621i	−0.0862248	+	0.149346i	0.819688	+	0.572811i	$0.194147\pi$
$798$		0			0
$799$	−18.3144	−	10.5738i	−0.647917	−	0.374075i
$800$		0			0
$801$		−	3.72907i		−	0.131760i
$802$		0			0
$803$	−1.01382	−	1.75599i	−0.0357770	−	0.0619676i
$804$		0			0
$805$	26.5648			0.936287
$806$		0			0
$807$	21.0756			0.741898
$808$		0			0
$809$	11.5535	+	20.0112i	0.406199	+	0.703558i	0.994460	−	0.105113i	$-0.0335205\pi$
$809$	11.5535	+	20.0112i	0.406199	+	0.703558i	−0.588261	+	0.808671i	$0.700187\pi$
$810$		0			0
$811$		−	38.4660i		−	1.35072i	−0.737487	−	0.675361i	$-0.763988\pi$
$811$		−	38.4660i		−	1.35072i	0.737487	−	0.675361i	$-0.236012\pi$
$812$		0			0
$813$	11.0559	+	6.38310i	0.387746	+	0.223865i
$814$		0			0
$815$	−4.19148	+	7.25986i	−0.146821	+	0.254302i
$816$		0			0
$817$	1.56193	−	0.901782i	0.0546451	−	0.0315493i
$818$		0			0
$819$	−26.5062	−	22.6727i	−0.926201	−	0.792249i
$820$		0			0
$821$	46.3003	−	26.7315i	1.61589	−	0.932935i	0.627922	−	0.778276i	$-0.283906\pi$
$821$	46.3003	−	26.7315i	1.61589	−	0.932935i	0.987968	−	0.154659i	$-0.0494278\pi$
$822$		0			0
$823$	0.826653	−	1.43180i	0.0288153	−	0.0499096i	−0.851258	−	0.524747i	$-0.824160\pi$
$823$	0.826653	−	1.43180i	0.0288153	−	0.0499096i	0.880073	+	0.474838i	$0.157493\pi$
$824$		0			0
$825$	12.2903	+	7.09583i	0.427895	+	0.247045i
$826$		0			0
$827$			8.97620i			0.312133i	0.987747	+	0.156067i	$0.0498814\pi$
$827$			8.97620i			0.312133i	−0.987747	+	0.156067i	$0.950119\pi$
$828$		0			0
$829$	−16.1109	−	27.9048i	−0.559553	−	0.969175i	−0.997534	−	0.0701902i	$-0.977639\pi$
$829$	−16.1109	−	27.9048i	−0.559553	−	0.969175i	0.437980	−	0.898985i	$-0.355694\pi$
$830$		0			0
$831$	20.6398			0.715986
$832$		0			0
$833$	−11.4992			−0.398424
$834$		0			0
$835$	8.85685	+	15.3405i	0.306504	+	0.530880i
$836$		0			0
$837$			6.05226i			0.209197i
$838$		0			0
$839$	−7.50412	−	4.33251i	−0.259071	−	0.149575i	0.364840	−	0.931070i	$-0.381124\pi$
$839$	−7.50412	−	4.33251i	−0.259071	−	0.149575i	−0.623911	+	0.781496i	$0.714457\pi$
$840$		0			0
$841$	−36.0546	+	62.4483i	−1.24326	+	2.15339i
$842$		0			0
$843$	−48.3621	+	27.9219i	−1.66568	+	0.961680i
$844$		0			0
$845$	8.16604	+	10.1151i	0.280920	+	0.347971i
$846$		0			0
$847$	−77.0412	+	44.4798i	−2.64717	+	1.52834i
$848$		0			0
$849$	2.81930	−	4.88316i	0.0967580	−	0.167590i
$850$		0			0
$851$	48.5760	+	28.0454i	1.66516	+	0.961383i
$852$		0			0
$853$		−	51.9072i		−	1.77727i	−0.458615	−	0.888635i	$-0.651654\pi$
$853$		−	51.9072i		−	1.77727i	0.458615	−	0.888635i	$-0.348346\pi$
$854$		0			0
$855$	0.465169	+	0.805697i	0.0159085	+	0.0275543i
$856$		0			0
$857$	20.2676			0.692329			0.346165	−	0.938174i	$-0.387484\pi$
$857$	20.2676			0.692329			0.346165	+	0.938174i	$0.387484\pi$
$858$		0			0
$859$	12.8525			0.438523			0.219262	−	0.975666i	$-0.429635\pi$
$859$	12.8525			0.438523			0.219262	+	0.975666i	$0.429635\pi$
$860$		0			0
$861$	2.35716	+	4.08271i	0.0803317	+	0.139139i
$862$		0			0
$863$		−	1.79735i		−	0.0611825i	−0.999532	−	0.0305913i	$-0.990261\pi$
$863$		−	1.79735i		−	0.0611825i	0.999532	−	0.0305913i	$-0.00973902\pi$
$864$		0			0
$865$	13.5023	+	7.79556i	0.459092	+	0.265057i
$866$		0			0
$867$	−16.0719	+	27.8374i	−0.545831	+	0.945407i
$868$		0			0
$869$	33.2026	−	19.1695i	1.12632	−	0.650282i
$870$		0			0
$871$	−7.06399	−	6.04236i	−0.239354	−	0.204738i
$872$		0			0
$873$	−8.59483	+	4.96223i	−0.290891	+	0.167946i
$874$		0			0
$875$	1.81301	−	3.14022i	0.0612908	−	0.106159i
$876$		0			0
$877$	−9.84509	−	5.68407i	−0.332445	−	0.191937i	0.324481	−	0.945892i	$-0.394810\pi$
$877$	−9.84509	−	5.68407i	−0.332445	−	0.191937i	−0.656926	+	0.753955i	$0.728144\pi$
$878$		0			0
$879$			1.68708i			0.0569038i
$880$		0			0
$881$	10.4483	+	18.0969i	0.352011	+	0.609701i	0.986602	−	0.163148i	$-0.0521647\pi$
$881$	10.4483	+	18.0969i	0.352011	+	0.609701i	−0.634591	+	0.772848i	$0.718831\pi$
$882$		0			0
$883$	22.9608			0.772692			0.386346	−	0.922354i	$-0.373737\pi$
$883$	22.9608			0.772692			0.386346	+	0.922354i	$0.373737\pi$
$884$		0			0
$885$	−26.1319			−0.878413
$886$		0			0
$887$	−2.87914	−	4.98682i	−0.0966721	−	0.167441i	0.813633	−	0.581379i	$-0.197486\pi$
$887$	−2.87914	−	4.98682i	−0.0966721	−	0.167441i	−0.910305	+	0.413938i	$0.864153\pi$
$888$		0			0
$889$		−	32.2186i		−	1.08058i
$890$		0			0
$891$	−51.0348	−	29.4650i	−1.70973	−	0.987113i
$892$		0			0
$893$	−1.97133	+	3.41444i	−0.0659681	+	0.114260i
$894$		0			0
$895$	−1.20983	+	0.698498i	−0.0404403	+	0.0233482i
$896$		0			0
$897$	−61.8256	−	11.5065i	−2.06430	−	0.384192i
$898$		0			0
$899$	66.6700	−	38.4919i	2.22357	−	1.28378i
$900$		0			0
$901$	−9.11981	+	15.7960i	−0.303825	+	0.526240i
$902$		0			0
$903$	−38.6671	−	22.3245i	−1.28676	−	0.742911i
$904$		0			0
$905$			8.37081i			0.278255i
$906$		0			0
$907$	−17.9332	−	31.0613i	−0.595464	−	1.03137i	−0.993481	−	0.113996i	$-0.963635\pi$
$907$	−17.9332	−	31.0613i	−0.595464	−	1.03137i	0.398017	−	0.917378i	$-0.369698\pi$
$908$		0			0
$909$	−6.49987			−0.215587
$910$		0			0
$911$	−1.17045			−0.0387789			−0.0193894	−	0.999812i	$-0.506172\pi$
$911$	−1.17045			−0.0387789			−0.0193894	+	0.999812i	$0.506172\pi$
$912$		0			0
$913$	22.9292	+	39.7146i	0.758847	+	1.31436i
$914$		0			0
$915$			10.6774i			0.352983i
$916$		0			0
$917$	51.3708	+	29.6589i	1.69641	+	0.979424i
$918$		0			0
$919$	−15.9797	+	27.6777i	−0.527122	+	0.913002i	0.472378	+	0.881396i	$0.343396\pi$
$919$	−15.9797	+	27.6777i	−0.527122	+	0.913002i	−0.999500	+	0.0316064i	$0.989938\pi$
$920$		0			0
$921$	−5.88906	+	3.40005i	−0.194051	+	0.112035i
$922$		0			0
$923$	−4.05221	+	21.7729i	−0.133380	+	0.716663i
$924$		0			0
$925$	6.63047	−	3.82810i	0.218008	−	0.125867i
$926$		0			0
$927$	−20.6541	+	35.7740i	−0.678370	+	1.17497i
$928$		0			0
$929$	−21.4140	−	12.3634i	−0.702569	−	0.405629i	0.105734	−	0.994394i	$-0.466281\pi$
$929$	−21.4140	−	12.3634i	−0.702569	−	0.405629i	−0.808304	+	0.588766i	$0.799614\pi$
$930$		0			0
$931$			2.14385i			0.0702619i
$932$		0			0
$933$	−4.52003	−	7.82893i	−0.147979	−	0.256308i
$934$		0			0
$935$	−11.1495			−0.364628
$936$		0			0
$937$	37.5249			1.22589			0.612943	−	0.790127i	$-0.289986\pi$
$937$	37.5249			1.22589			0.612943	+	0.790127i	$0.289986\pi$
$938$		0			0
$939$	−27.3016	−	47.2878i	−0.890955	−	1.54318i
$940$		0			0
$941$			31.2572i			1.01896i	0.860484	+	0.509478i	$0.170161\pi$
$941$			31.2572i			1.01896i	−0.860484	+	0.509478i	$0.829839\pi$
$942$		0			0
$943$	3.46485	+	2.00043i	0.112831	+	0.0651430i
$944$		0			0
$945$	−1.43322	+	2.48241i	−0.0466226	+	0.0807526i
$946$		0			0
$947$	−23.8031	+	13.7427i	−0.773496	+	0.446578i	−0.834120	−	0.551582i	$-0.814024\pi$
$947$	−23.8031	+	13.7427i	−0.773496	+	0.446578i	0.0606240	+	0.998161i	$0.480691\pi$
$948$		0			0
$949$	1.15639	−	0.408526i	0.0375380	−	0.0132613i
$950$		0			0
$951$	22.3857	−	12.9244i	0.725905	−	0.419101i
$952$		0			0
$953$	−4.28347	+	7.41918i	−0.138755	+	0.240331i	−0.927026	−	0.374998i	$-0.877643\pi$
$953$	−4.28347	+	7.41918i	−0.138755	+	0.240331i	0.788271	+	0.615329i	$0.210977\pi$
$954$		0			0
$955$	−8.07963	−	4.66477i	−0.261451	−	0.150949i
$956$		0			0
$957$			142.702i			4.61288i
$958$		0			0
$959$	−21.6617	−	37.5192i	−0.699494	−	1.21156i
$960$		0			0
$961$	−27.6151			−0.890808
$962$		0			0
$963$	−2.19053			−0.0705887
$964$		0			0
$965$	−5.19380	−	8.99592i	−0.167194	−	0.289589i
$966$		0			0
$967$			46.2303i			1.48667i	0.668921	+	0.743333i	$0.266756\pi$
$967$			46.2303i			1.48667i	−0.668921	+	0.743333i	$0.733244\pi$
$968$		0			0
$969$	−1.34475	−	0.776394i	−0.0431997	−	0.0249414i
$970$		0			0
$971$	−17.9116	+	31.0238i	−0.574810	+	0.995600i	0.421252	+	0.906943i	$0.361591\pi$
$971$	−17.9116	+	31.0238i	−0.574810	+	0.995600i	−0.996062	+	0.0886564i	$0.971743\pi$
$972$		0			0
$973$	−2.44165	+	1.40969i	−0.0782758	+	0.0451926i
$974$		0			0
$975$	−5.57968	+	6.52308i	−0.178693	+	0.208906i
$976$		0			0
$977$	−42.4454	+	24.5059i	−1.35795	+	0.784013i	−0.989347	−	0.145575i	$-0.953497\pi$
$977$	−42.4454	+	24.5059i	−1.35795	+	0.784013i	−0.368602	+	0.929587i	$0.620164\pi$
$978$		0			0
$979$	4.16593	−	7.21561i	0.133144	−	0.230612i
$980$		0			0
$981$	8.57270	+	4.94945i	0.273705	+	0.158024i
$982$		0			0
$983$			4.84782i			0.154622i	0.997007	+	0.0773108i	$0.0246334\pi$
$983$			4.84782i			0.154622i	−0.997007	+	0.0773108i	$0.975367\pi$
$984$		0			0
$985$	6.43733	+	11.1498i	0.205111	+	0.355262i
$986$		0			0
$987$	97.6043			3.10678
$988$		0			0
$989$	−37.8919			−1.20489
$990$		0			0
$991$	9.82285	+	17.0137i	0.312033	+	0.540457i	0.978802	−	0.204807i	$-0.0656566\pi$
$991$	9.82285	+	17.0137i	0.312033	+	0.540457i	−0.666769	+	0.745264i	$0.732323\pi$
$992$		0			0
$993$		−	15.1980i		−	0.482293i
$994$		0			0
$995$	12.3639	+	7.13830i	0.391962	+	0.226299i
$996$		0			0
$997$	25.6415	−	44.4124i	0.812074	−	1.40655i	−0.0993356	−	0.995054i	$-0.531672\pi$
$997$	25.6415	−	44.4124i	0.812074	−	1.40655i	0.911410	−	0.411500i	$-0.134995\pi$
$998$		0			0
$999$	−5.24151	+	3.02619i	−0.165834	+	0.0957444i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.da.f.881.6		16
4.3	odd	2		520.2.bu.b.361.3	yes	16
13.4	even	6	inner	1040.2.da.f.641.6		16
52.11	even	12		6760.2.a.bl.1.6		8
52.15	even	12		6760.2.a.bk.1.6		8
52.43	odd	6		520.2.bu.b.121.3	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.bu.b.121.3	✓	16	52.43	odd	6
520.2.bu.b.361.3	yes	16	4.3	odd	2
1040.2.da.f.641.6		16	13.4	even	6	inner
1040.2.da.f.881.6		16	1.1	even	1	trivial
6760.2.a.bk.1.6		8	52.15	even	12
6760.2.a.bl.1.6		8	52.11	even	12

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.da (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.19037 + 2.06179i) q^{3} -1.00000i q^{5} +(-3.14022 - 1.81301i) q^{7} +(-1.33398 + 2.31052i) q^{9} +O(q^{10})\)	\(q+(1.19037 + 2.06179i) q^{3} -1.00000i q^{5} +(-3.14022 - 1.81301i) q^{7} +(-1.33398 + 2.31052i) q^{9} +(-5.16239 + 2.98051i) q^{11} +(-1.20102 - 3.39964i) q^{13} +(2.06179 - 1.19037i) q^{15} +(-0.935203 + 1.61982i) q^{17} +(0.301991 + 0.174354i) q^{19} -8.63262i q^{21} +(-3.66309 - 6.34466i) q^{23} -1.00000 q^{25} +0.790520 q^{27} +(-5.02765 - 8.70815i) q^{29} +7.65605i q^{31} +(-12.2903 - 7.09583i) q^{33} +(-1.81301 + 3.14022i) q^{35} +(-6.63047 + 3.82810i) q^{37} +(5.57968 - 6.52308i) q^{39} +(-0.472941 + 0.273052i) q^{41} +(2.58606 - 4.47919i) q^{43} +(2.31052 + 1.33398i) q^{45} +11.3065i q^{47} +(3.07398 + 5.32430i) q^{49} -4.45296 q^{51} +9.75169 q^{53} +(2.98051 + 5.16239i) q^{55} +0.830187i q^{57} +(-9.50578 - 5.48817i) q^{59} +(-2.24244 + 3.88402i) q^{61} +(8.37796 - 4.83702i) q^{63} +(-3.39964 + 1.20102i) q^{65} +(2.23276 - 1.28908i) q^{67} +(8.72089 - 15.1050i) q^{69} +(-5.31948 - 3.07120i) q^{71} +0.340151i q^{73} +(-1.19037 - 2.06179i) q^{75} +21.6147 q^{77} -6.43164 q^{79} +(4.94294 + 8.56143i) q^{81} -7.69307i q^{83} +(1.61982 + 0.935203i) q^{85} +(11.9696 - 20.7319i) q^{87} +(-1.21047 + 0.698863i) q^{89} +(-2.39212 + 12.8531i) q^{91} +(-15.7851 + 9.11355i) q^{93} +(0.174354 - 0.301991i) q^{95} +(3.22151 + 1.85994i) q^{97} -15.9037i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9}+O(q^{10}) \) 16 * q + 4 * q^3 - 6 * q^7 - 16 * q^9	\( 16 q + 4 q^{3} - 6 q^{7} - 16 q^{9} + 6 q^{11} - 2 q^{13} + 4 q^{17} - 30 q^{19} - 6 q^{23} - 16 q^{25} - 44 q^{27} - 16 q^{29} + 24 q^{33} + 6 q^{35} - 24 q^{37} + 8 q^{39} - 24 q^{41} - 6 q^{43} + 12 q^{45} - 4 q^{49} + 40 q^{51} + 4 q^{53} + 6 q^{55} - 12 q^{59} - 2 q^{61} + 60 q^{63} - 10 q^{65} + 6 q^{67} + 52 q^{69} - 72 q^{71} - 4 q^{75} + 32 q^{77} - 36 q^{79} - 28 q^{81} + 22 q^{87} + 24 q^{89} + 22 q^{91} - 96 q^{93} - 10 q^{95} + 60 q^{97}+O(q^{100}) \) 16 * q + 4 * q^3 - 6 * q^7 - 16 * q^9 + 6 * q^11 - 2 * q^13 + 4 * q^17 - 30 * q^19 - 6 * q^23 - 16 * q^25 - 44 * q^27 - 16 * q^29 + 24 * q^33 + 6 * q^35 - 24 * q^37 + 8 * q^39 - 24 * q^41 - 6 * q^43 + 12 * q^45 - 4 * q^49 + 40 * q^51 + 4 * q^53 + 6 * q^55 - 12 * q^59 - 2 * q^61 + 60 * q^63 - 10 * q^65 + 6 * q^67 + 52 * q^69 - 72 * q^71 - 4 * q^75 + 32 * q^77 - 36 * q^79 - 28 * q^81 + 22 * q^87 + 24 * q^89 + 22 * q^91 - 96 * q^93 - 10 * q^95 + 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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