LMFDB - Embedded newform 1148.2.i.d.165.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(165,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1148.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
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} + 14 x^{14} - 8 x^{13} + 136 x^{12} - 87 x^{11} + 706 x^{10} - 568 x^{9} + 2685 x^{8} + \cdots + 121 $ x^16 + 14x^14 - 8x^13 + 136x^12 - 87x^11 + 706x^10 - 568x^9 + 2685x^8 - 2100x^7 + 5529x^6 - 4919x^5 + 8145x^4 - 5182x^3 + 2775x^2 - 660x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.7
Root			$-1.05150 + 1.82125i$ of defining polynomial
Character	$\chi$	$=$	1148.165
Dual form			1148.2.i.d.821.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.05150 - 1.82125i) q^{3} +(1.46762 + 2.54199i) q^{5} +(2.64377 - 0.102404i) q^{7} +(-0.711302 - 1.23201i) q^{9} +O(q^{10})$	\(q+(1.05150 - 1.82125i) q^{3} +(1.46762 + 2.54199i) q^{5} +(2.64377 - 0.102404i) q^{7} +(-0.711302 - 1.23201i) q^{9} +(2.90295 - 5.02805i) q^{11} -1.53467 q^{13} +6.17281 q^{15} +(-2.84558 + 4.92869i) q^{17} +(-1.65281 - 2.86275i) q^{19} +(2.59342 - 4.92264i) q^{21} +(1.45388 + 2.51820i) q^{23} +(-1.80782 + 3.13123i) q^{25} +3.31726 q^{27} -1.53671 q^{29} +(3.33031 - 5.76827i) q^{31} +(-6.10489 - 10.5740i) q^{33} +(4.14036 + 6.57015i) q^{35} +(5.67164 + 9.82356i) q^{37} +(-1.61371 + 2.79503i) q^{39} +1.00000 q^{41} -2.99712 q^{43} +(2.08784 - 3.61625i) q^{45} +(-4.48611 - 7.77017i) q^{47} +(6.97903 - 0.541464i) q^{49} +(5.98425 + 10.3650i) q^{51} +(-1.43780 + 2.49035i) q^{53} +17.0417 q^{55} -6.95172 q^{57} +(-4.87988 + 8.45219i) q^{59} +(-3.28184 - 5.68432i) q^{61} +(-2.00668 - 3.18431i) q^{63} +(-2.25232 - 3.90113i) q^{65} +(-4.17670 + 7.23425i) q^{67} +6.11503 q^{69} +12.2707 q^{71} +(-1.01044 + 1.75012i) q^{73} +(3.80184 + 6.58498i) q^{75} +(7.15982 - 13.5903i) q^{77} +(-5.15823 - 8.93432i) q^{79} +(5.62200 - 9.73760i) q^{81} -8.68931 q^{83} -16.7049 q^{85} +(-1.61585 + 2.79873i) q^{87} +(2.40345 + 4.16289i) q^{89} +(-4.05733 + 0.157156i) q^{91} +(-7.00365 - 12.1307i) q^{93} +(4.85140 - 8.40287i) q^{95} -4.61153 q^{97} -8.25948 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{9}+O(q^{10}) $ 16 * q - 4 * q^9	$ 16 q - 4 q^{9} + 8 q^{11} - 14 q^{13} - 2 q^{15} + q^{17} - 4 q^{19} + 13 q^{21} + 3 q^{23} + 4 q^{25} - 24 q^{27} - 8 q^{29} - 4 q^{31} - 23 q^{33} + 12 q^{35} + 31 q^{37} - 5 q^{39} + 16 q^{41} - 16 q^{43} - q^{45} - 24 q^{47} + 16 q^{49} + 23 q^{51} + q^{53} + 4 q^{55} - 30 q^{57} - 4 q^{59} + 4 q^{61} + 23 q^{63} + 24 q^{65} - 42 q^{69} + 16 q^{71} - 11 q^{73} + 15 q^{75} + 25 q^{77} - 14 q^{79} + 28 q^{81} - 84 q^{83} - 40 q^{85} - 25 q^{87} + 11 q^{89} + 7 q^{91} + 27 q^{93} + 15 q^{95} - 32 q^{97} - 16 q^{99}+O(q^{100}) $ 16 * q - 4 * q^9 + 8 * q^11 - 14 * q^13 - 2 * q^15 + q^17 - 4 * q^19 + 13 * q^21 + 3 * q^23 + 4 * q^25 - 24 * q^27 - 8 * q^29 - 4 * q^31 - 23 * q^33 + 12 * q^35 + 31 * q^37 - 5 * q^39 + 16 * q^41 - 16 * q^43 - q^45 - 24 * q^47 + 16 * q^49 + 23 * q^51 + q^53 + 4 * q^55 - 30 * q^57 - 4 * q^59 + 4 * q^61 + 23 * q^63 + 24 * q^65 - 42 * q^69 + 16 * q^71 - 11 * q^73 + 15 * q^75 + 25 * q^77 - 14 * q^79 + 28 * q^81 - 84 * q^83 - 40 * q^85 - 25 * q^87 + 11 * q^89 + 7 * q^91 + 27 * q^93 + 15 * q^95 - 32 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	1.05150	−	1.82125i	0.607083	−	1.05150i	−0.384635	−	0.923069i	$-0.625673\pi$
$3$	1.05150	−	1.82125i	0.607083	−	1.05150i	0.991718	−	0.128431i	$-0.0409940\pi$
$4$		0			0
$5$	1.46762	+	2.54199i	0.656340	+	1.13681i	0.981556	+	0.191174i	$0.0612295\pi$
$5$	1.46762	+	2.54199i	0.656340	+	1.13681i	−0.325216	+	0.945640i	$0.605437\pi$
$6$		0			0
$7$	2.64377	−	0.102404i	0.999251	−	0.0387050i
$7$	2.64377	−	0.102404i	0.999251	−	0.0387050i
$8$		0			0
$9$	−0.711302	−	1.23201i	−0.237101	−	0.410670i
$10$		0			0
$11$	2.90295	−	5.02805i	0.875271	−	1.51601i	0.0187971	−	0.999823i	$-0.494016\pi$
$11$	2.90295	−	5.02805i	0.875271	−	1.51601i	0.856474	−	0.516190i	$-0.172650\pi$
$12$		0			0
$13$	−1.53467			−0.425642			−0.212821	−	0.977091i	$-0.568265\pi$
$13$	−1.53467			−0.425642			−0.212821	+	0.977091i	$0.568265\pi$
$14$		0			0
$15$	6.17281			1.59381
$16$		0			0
$17$	−2.84558	+	4.92869i	−0.690154	+	1.19538i	0.281633	+	0.959522i	$0.409124\pi$
$17$	−2.84558	+	4.92869i	−0.690154	+	1.19538i	−0.971787	+	0.235860i	$0.924209\pi$
$18$		0			0
$19$	−1.65281	−	2.86275i	−0.379181	−	0.656761i	0.611762	−	0.791042i	$-0.290461\pi$
$19$	−1.65281	−	2.86275i	−0.379181	−	0.656761i	−0.990943	+	0.134281i	$0.957128\pi$
$20$		0			0
$21$	2.59342	−	4.92264i	0.565930	−	1.07421i
$22$		0			0
$23$	1.45388	+	2.51820i	0.303156	+	0.525081i	0.976849	−	0.213930i	$-0.0686265\pi$
$23$	1.45388	+	2.51820i	0.303156	+	0.525081i	−0.673693	+	0.739011i	$0.735293\pi$
$24$		0			0
$25$	−1.80782	+	3.13123i	−0.361563	+	0.626246i
$26$		0			0
$27$	3.31726			0.638407
$28$		0			0
$29$	−1.53671			−0.285359			−0.142680	−	0.989769i	$-0.545572\pi$
$29$	−1.53671			−0.285359			−0.142680	+	0.989769i	$0.545572\pi$
$30$		0			0
$31$	3.33031	−	5.76827i	0.598142	−	1.03601i	−0.394953	−	0.918701i	$-0.629239\pi$
$31$	3.33031	−	5.76827i	0.598142	−	1.03601i	0.993095	−	0.117311i	$-0.0374275\pi$
$32$		0			0
$33$	−6.10489	−	10.5740i	−1.06273	−	1.84069i
$34$		0			0
$35$	4.14036	+	6.57015i	0.699848	+	1.11056i
$36$		0			0
$37$	5.67164	+	9.82356i	0.932411	+	1.61498i	0.779186	+	0.626792i	$0.215633\pi$
$37$	5.67164	+	9.82356i	0.932411	+	1.61498i	0.153225	+	0.988191i	$0.451034\pi$
$38$		0			0
$39$	−1.61371	+	2.79503i	−0.258400	+	0.447563i
$40$		0			0
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$		0			0
$43$	−2.99712			−0.457057			−0.228528	−	0.973537i	$-0.573391\pi$
$43$	−2.99712			−0.457057			−0.228528	+	0.973537i	$0.573391\pi$
$44$		0			0
$45$	2.08784	−	3.61625i	0.311237	−	0.539079i
$46$		0			0
$47$	−4.48611	−	7.77017i	−0.654366	−	1.13340i	−0.982052	−	0.188609i	$-0.939602\pi$
$47$	−4.48611	−	7.77017i	−0.654366	−	1.13340i	0.327686	−	0.944787i	$-0.393731\pi$
$48$		0			0
$49$	6.97903	−	0.541464i	0.997004	−	0.0773520i
$50$		0			0
$51$	5.98425	+	10.3650i	0.837963	+	1.45139i
$52$		0			0
$53$	−1.43780	+	2.49035i	−0.197498	+	0.342076i	−0.947716	−	0.319114i	$-0.896615\pi$
$53$	−1.43780	+	2.49035i	−0.197498	+	0.342076i	0.750219	+	0.661190i	$0.229948\pi$
$54$		0			0
$55$	17.0417			2.29790
$56$		0			0
$57$	−6.95172			−0.920778
$58$		0			0
$59$	−4.87988	+	8.45219i	−0.635306	+	1.10038i	0.351145	+	0.936321i	$0.385793\pi$
$59$	−4.87988	+	8.45219i	−0.635306	+	1.10038i	−0.986450	+	0.164060i	$0.947541\pi$
$60$		0			0
$61$	−3.28184	−	5.68432i	−0.420197	−	0.727802i	0.575762	−	0.817618i	$-0.304706\pi$
$61$	−3.28184	−	5.68432i	−0.420197	−	0.727802i	−0.995958	+	0.0898155i	$0.971372\pi$
$62$		0			0
$63$	−2.00668	−	3.18431i	−0.252818	−	0.401186i
$64$		0			0
$65$	−2.25232	−	3.90113i	−0.279366	−	0.483876i
$66$		0			0
$67$	−4.17670	+	7.23425i	−0.510265	+	0.883804i	0.489665	+	0.871911i	$0.337119\pi$
$67$	−4.17670	+	7.23425i	−0.510265	+	0.883804i	−0.999929	+	0.0118934i	$0.996214\pi$
$68$		0			0
$69$	6.11503			0.736163
$70$		0			0
$71$	12.2707			1.45626			0.728131	−	0.685438i	$-0.240389\pi$
$71$	12.2707			1.45626			0.728131	+	0.685438i	$0.240389\pi$
$72$		0			0
$73$	−1.01044	+	1.75012i	−0.118262	+	0.204837i	−0.919079	−	0.394073i	$-0.871066\pi$
$73$	−1.01044	+	1.75012i	−0.118262	+	0.204837i	0.800817	+	0.598909i	$0.204399\pi$
$74$		0			0
$75$	3.80184	+	6.58498i	0.438998	+	0.760368i
$76$		0			0
$77$	7.15982	−	13.5903i	0.815938	−	1.54876i
$78$		0			0
$79$	−5.15823	−	8.93432i	−0.580346	−	1.00519i	−0.995438	−	0.0954099i	$-0.969584\pi$
$79$	−5.15823	−	8.93432i	−0.580346	−	1.00519i	0.415092	−	0.909780i	$-0.363750\pi$
$80$		0			0
$81$	5.62200	−	9.73760i	0.624667	−	1.08196i
$82$		0			0
$83$	−8.68931			−0.953775			−0.476888	−	0.878964i	$-0.658235\pi$
$83$	−8.68931			−0.953775			−0.476888	+	0.878964i	$0.658235\pi$
$84$		0			0
$85$	−16.7049			−1.81190
$86$		0			0
$87$	−1.61585	+	2.79873i	−0.173237	+	0.300055i
$88$		0			0
$89$	2.40345	+	4.16289i	0.254765	+	0.441266i	0.964832	−	0.262869i	$-0.0846686\pi$
$89$	2.40345	+	4.16289i	0.254765	+	0.441266i	−0.710067	+	0.704134i	$0.751335\pi$
$90$		0			0
$91$	−4.05733	+	0.157156i	−0.425323	+	0.0164745i
$92$		0			0
$93$	−7.00365	−	12.1307i	−0.726244	−	1.25789i
$94$		0			0
$95$	4.85140	−	8.40287i	0.497743	−	0.862116i
$96$		0			0
$97$	−4.61153			−0.468230			−0.234115	−	0.972209i	$-0.575219\pi$
$97$	−4.61153			−0.468230			−0.234115	+	0.972209i	$0.575219\pi$
$98$		0			0
$99$	−8.25948			−0.830109
$100$		0			0
$101$	−2.80328	+	4.85543i	−0.278937	+	0.483133i	−0.971121	−	0.238588i	$-0.923315\pi$
$101$	−2.80328	+	4.85543i	−0.278937	+	0.483133i	0.692184	+	0.721721i	$0.256649\pi$
$102$		0			0
$103$	−7.56872	−	13.1094i	−0.745768	−	1.29171i	−0.949835	−	0.312751i	$-0.898750\pi$
$103$	−7.56872	−	13.1094i	−0.745768	−	1.29171i	0.204067	−	0.978957i	$-0.434584\pi$
$104$		0			0
$105$	16.3195	−	0.632119i	1.59262	−	0.0616885i
$106$		0			0
$107$	−6.60934	−	11.4477i	−0.638949	−	1.10669i	−0.985664	−	0.168721i	$-0.946036\pi$
$107$	−6.60934	−	11.4477i	−0.638949	−	1.10669i	0.346715	−	0.937970i	$-0.387297\pi$
$108$		0			0
$109$	5.61331	−	9.72254i	0.537658	−	0.931250i	−0.461372	−	0.887207i	$-0.652643\pi$
$109$	5.61331	−	9.72254i	0.537658	−	0.931250i	0.999030	−	0.0440436i	$-0.0140241\pi$
$110$		0			0
$111$	23.8549			2.26421
$112$		0			0
$113$	2.08830			0.196451			0.0982255	−	0.995164i	$-0.468683\pi$
$113$	2.08830			0.196451			0.0982255	+	0.995164i	$0.468683\pi$
$114$		0			0
$115$	−4.26750	+	7.39152i	−0.397946	+	0.689263i
$116$		0			0
$117$	1.09162	+	1.89074i	0.100920	+	0.174799i
$118$		0			0
$119$	−7.01834	+	13.3217i	−0.643370	+	1.22120i
$120$		0			0
$121$	−11.3542	−	19.6660i	−1.03220	−	1.78782i
$122$		0			0
$123$	1.05150	−	1.82125i	0.0948105	−	0.164217i
$124$		0			0
$125$	4.06344			0.363445
$126$		0			0
$127$	−0.678117			−0.0601732			−0.0300866	−	0.999547i	$-0.509578\pi$
$127$	−0.678117			−0.0601732			−0.0300866	+	0.999547i	$0.509578\pi$
$128$		0			0
$129$	−3.15147	+	5.45851i	−0.277472	+	0.480595i
$130$		0			0
$131$	−0.913712	−	1.58260i	−0.0798314	−	0.138272i	0.823346	−	0.567540i	$-0.192105\pi$
$131$	−0.913712	−	1.58260i	−0.0798314	−	0.138272i	−0.903177	+	0.429268i	$0.858772\pi$
$132$		0			0
$133$	−4.66281	−	7.39920i	−0.404317	−	0.641592i
$134$		0			0
$135$	4.86848	+	8.43245i	0.419012	+	0.725750i
$136$		0			0
$137$	−0.918187	+	1.59035i	−0.0784460	+	0.135872i	−0.902580	−	0.430523i	$-0.858329\pi$
$137$	−0.918187	+	1.59035i	−0.0784460	+	0.135872i	0.824134	+	0.566395i	$0.191662\pi$
$138$		0			0
$139$	−1.74423			−0.147944			−0.0739719	−	0.997260i	$-0.523568\pi$
$139$	−1.74423			−0.147944			−0.0739719	+	0.997260i	$0.523568\pi$
$140$		0			0
$141$	−18.8686			−1.58902
$142$		0			0
$143$	−4.45508	+	7.71642i	−0.372552	+	0.645279i
$144$		0			0
$145$	−2.25530	−	3.90630i	−0.187293	−	0.324400i
$146$		0			0
$147$	6.35230	−	13.2799i	0.523929	−	1.09531i
$148$		0			0
$149$	3.61000	+	6.25271i	0.295743	+	0.512242i	0.975157	−	0.221513i	$-0.0710994\pi$
$149$	3.61000	+	6.25271i	0.295743	+	0.512242i	−0.679414	+	0.733755i	$0.737766\pi$
$150$		0			0
$151$	−2.46383	+	4.26747i	−0.200503	+	0.347282i	−0.948691	−	0.316205i	$-0.897591\pi$
$151$	−2.46383	+	4.26747i	−0.200503	+	0.347282i	0.748187	+	0.663488i	$0.230924\pi$
$152$		0			0
$153$	8.09627			0.654544
$154$		0			0
$155$	19.5505			1.57034
$156$		0			0
$157$	−8.18013	+	14.1684i	−0.652845	+	1.13076i	0.329584	+	0.944126i	$0.393091\pi$
$157$	−8.18013	+	14.1684i	−0.652845	+	1.13076i	−0.982429	+	0.186635i	$0.940242\pi$
$158$		0			0
$159$	3.02370	+	5.23720i	0.239795	+	0.415337i
$160$		0			0
$161$	4.10160	+	6.50865i	0.323252	+	0.512954i
$162$		0			0
$163$	10.5313	+	18.2408i	0.824877	+	1.42873i	0.902014	+	0.431708i	$0.142089\pi$
$163$	10.5313	+	18.2408i	0.824877	+	1.42873i	−0.0771370	+	0.997021i	$0.524578\pi$
$164$		0			0
$165$	17.9193	−	31.0372i	1.39502	−	2.41624i
$166$		0			0
$167$	−17.3127			−1.33970			−0.669849	−	0.742497i	$-0.733641\pi$
$167$	−17.3127			−1.33970			−0.669849	+	0.742497i	$0.733641\pi$
$168$		0			0
$169$	−10.6448			−0.818829
$170$		0			0
$171$	−2.35130	+	4.07257i	−0.179808	+	0.311437i
$172$		0			0
$173$	5.04790	+	8.74322i	0.383785	+	0.664735i	0.991600	−	0.129344i	$-0.0412871\pi$
$173$	5.04790	+	8.74322i	0.383785	+	0.664735i	−0.607815	+	0.794079i	$0.707954\pi$
$174$		0			0
$175$	−4.45880	+	8.46338i	−0.337054	+	0.639771i
$176$		0			0
$177$	10.2624	+	17.7750i	0.771367	+	1.33605i
$178$		0			0
$179$	−8.01347	+	13.8797i	−0.598955	+	1.03742i	0.394021	+	0.919101i	$0.371084\pi$
$179$	−8.01347	+	13.8797i	−0.598955	+	1.03742i	−0.992976	+	0.118318i	$0.962250\pi$
$180$		0			0
$181$	9.31417			0.692317			0.346158	−	0.938176i	$-0.387486\pi$
$181$	9.31417			0.692317			0.346158	+	0.938176i	$0.387486\pi$
$182$		0			0
$183$	−13.8034			−1.02038
$184$		0			0
$185$	−16.6476	+	28.8345i	−1.22396	+	2.11996i
$186$		0			0
$187$	16.5211	+	28.6154i	1.20814	+	2.09257i
$188$		0			0
$189$	8.77007	−	0.339700i	0.637929	−	0.0247095i
$190$		0			0
$191$	2.02020	+	3.49909i	0.146176	+	0.253185i	0.929811	−	0.368037i	$-0.119970\pi$
$191$	2.02020	+	3.49909i	0.146176	+	0.253185i	−0.783635	+	0.621222i	$0.786637\pi$
$192$		0			0
$193$	−5.92919	+	10.2696i	−0.426792	+	0.739226i	−0.996586	−	0.0825621i	$-0.973690\pi$
$193$	−5.92919	+	10.2696i	−0.426792	+	0.739226i	0.569794	+	0.821788i	$0.307023\pi$
$194$		0			0
$195$	−9.47325			−0.678394
$196$		0			0
$197$	−10.4773			−0.746473			−0.373237	−	0.927736i	$-0.621752\pi$
$197$	−10.4773			−0.746473			−0.373237	+	0.927736i	$0.621752\pi$
$198$		0			0
$199$	5.37853	−	9.31589i	0.381274	−	0.660386i	−0.609971	−	0.792424i	$-0.708819\pi$
$199$	5.37853	−	9.31589i	0.381274	−	0.660386i	0.991245	+	0.132038i	$0.0421521\pi$
$200$		0			0
$201$	8.78359	+	15.2136i	0.619546	+	1.07309i
$202$		0			0
$203$	−4.06270	+	0.157365i	−0.285145	+	0.0110448i
$204$		0			0
$205$	1.46762	+	2.54199i	0.102503	+	0.177540i
$206$		0			0
$207$	2.06830	−	3.58240i	0.143757	−	0.248994i
$208$		0			0
$209$	−19.1921			−1.32754
$210$		0			0
$211$	−23.7031			−1.63179			−0.815896	−	0.578199i	$-0.803756\pi$
$211$	−23.7031			−1.63179			−0.815896	+	0.578199i	$0.803756\pi$
$212$		0			0
$213$	12.9026	−	22.3480i	0.884072	−	1.53126i
$214$		0			0
$215$	−4.39864	−	7.61866i	−0.299985	−	0.519588i
$216$		0			0
$217$	8.21389	−	15.5910i	0.557595	−	1.05839i
$218$		0			0
$219$	2.12494	+	3.68051i	0.143590	+	0.248706i
$220$		0			0
$221$	4.36704	−	7.56393i	0.293759	−	0.508805i
$222$		0			0
$223$	−10.6405			−0.712538			−0.356269	−	0.934383i	$-0.615951\pi$
$223$	−10.6405			−0.712538			−0.356269	+	0.934383i	$0.615951\pi$
$224$		0			0
$225$	5.14362			0.342908
$226$		0			0
$227$	6.27505	−	10.8687i	0.416490	−	0.721381i	−0.579094	−	0.815261i	$-0.696594\pi$
$227$	6.27505	−	10.8687i	0.416490	−	0.721381i	0.995584	+	0.0938797i	$0.0299269\pi$
$228$		0			0
$229$	−7.63533	−	13.2248i	−0.504557	−	0.873919i	−0.999986	−	0.00527014i	$-0.998322\pi$
$229$	−7.63533	−	13.2248i	−0.504557	−	0.873919i	0.495429	−	0.868648i	$-0.335011\pi$
$230$		0			0
$231$	−17.2227	−	27.3300i	−1.13317	−	1.79818i
$232$		0			0
$233$	6.70109	+	11.6066i	0.439003	+	0.760376i	0.997613	−	0.0690549i	$-0.0219984\pi$
$233$	6.70109	+	11.6066i	0.439003	+	0.760376i	−0.558610	+	0.829431i	$0.688665\pi$
$234$		0			0
$235$	13.1678	−	22.8073i	0.858973	−	1.48778i
$236$		0			0
$237$	−21.6955			−1.40927
$238$		0			0
$239$	30.6159			1.98037			0.990187	−	0.139746i	$-0.0446287\pi$
$239$	30.6159			1.98037			0.990187	+	0.139746i	$0.0446287\pi$
$240$		0			0
$241$	−3.58210	+	6.20437i	−0.230743	+	0.399659i	−0.958027	−	0.286678i	$-0.907449\pi$
$241$	−3.58210	+	6.20437i	−0.230743	+	0.399659i	0.727284	+	0.686337i	$0.240782\pi$
$242$		0			0
$243$	−6.84718	−	11.8597i	−0.439247	−	0.760797i
$244$		0			0
$245$	11.6190	+	16.9460i	0.742308	+	1.08264i
$246$		0			0
$247$	2.53653	+	4.39340i	0.161395	+	0.279545i
$248$		0			0
$249$	−9.13680	+	15.8254i	−0.579021	+	1.00289i
$250$		0			0
$251$	−25.6079			−1.61636			−0.808179	−	0.588937i	$-0.799547\pi$
$251$	−25.6079			−1.61636			−0.808179	+	0.588937i	$0.799547\pi$
$252$		0			0
$253$	16.8822			1.06137
$254$		0			0
$255$	−17.5652	+	30.4238i	−1.09998	+	1.90521i
$256$		0			0
$257$	13.9083	+	24.0899i	0.867576	+	1.50269i	0.864466	+	0.502691i	$0.167657\pi$
$257$	13.9083	+	24.0899i	0.867576	+	1.50269i	0.00311042	+	0.999995i	$0.499010\pi$
$258$		0			0
$259$	16.0005	+	25.3904i	0.994221	+	1.57768i
$260$		0			0
$261$	1.09306	+	1.89324i	0.0676589	+	0.117189i
$262$		0			0
$263$	−12.0609	+	20.8900i	−0.743704	+	1.28813i	0.207093	+	0.978321i	$0.433600\pi$
$263$	−12.0609	+	20.8900i	−0.743704	+	1.28813i	−0.950798	+	0.309812i	$0.899734\pi$
$264$		0			0
$265$	−8.44060			−0.518502
$266$		0			0
$267$	10.1089			0.618654
$268$		0			0
$269$	−3.90028	+	6.75548i	−0.237804	+	0.411889i	−0.960084	−	0.279712i	$-0.909761\pi$
$269$	−3.90028	+	6.75548i	−0.237804	+	0.411889i	0.722280	+	0.691601i	$0.243094\pi$
$270$		0			0
$271$	−4.69005	−	8.12340i	−0.284900	−	0.493461i	0.687685	−	0.726009i	$-0.258627\pi$
$271$	−4.69005	−	8.12340i	−0.284900	−	0.493461i	−0.972585	+	0.232548i	$0.925294\pi$
$272$		0			0
$273$	−3.98005	+	7.55466i	−0.240884	+	0.457229i
$274$		0			0
$275$	10.4960	+	18.1796i	0.632932	+	1.09627i
$276$		0			0
$277$	14.7920	−	25.6205i	0.888764	−	1.53938i	0.0474254	−	0.998875i	$-0.484898\pi$
$277$	14.7920	−	25.6205i	0.888764	−	1.53938i	0.841338	−	0.540509i	$-0.181768\pi$
$278$		0			0
$279$	−9.47544			−0.567280
$280$		0			0
$281$	25.8917			1.54457			0.772285	−	0.635277i	$-0.219114\pi$
$281$	25.8917			1.54457			0.772285	+	0.635277i	$0.219114\pi$
$282$		0			0
$283$	−6.56137	+	11.3646i	−0.390033	+	0.675557i	−0.992453	−	0.122622i	$-0.960870\pi$
$283$	−6.56137	+	11.3646i	−0.390033	+	0.675557i	0.602421	+	0.798179i	$0.294203\pi$
$284$		0			0
$285$	−10.2025	−	17.6712i	−0.604343	−	1.04675i
$286$		0			0
$287$	2.64377	−	0.102404i	0.156057	−	0.00604470i
$288$		0			0
$289$	−7.69465	−	13.3275i	−0.452626	−	0.783972i
$290$		0			0
$291$	−4.84902	+	8.39875i	−0.284255	+	0.492344i
$292$		0			0
$293$	23.7546			1.38776			0.693880	−	0.720091i	$-0.255900\pi$
$293$	23.7546			1.38776			0.693880	+	0.720091i	$0.255900\pi$
$294$		0			0
$295$	−28.6472			−1.66791
$296$		0			0
$297$	9.62983	−	16.6794i	0.558779	−	0.967834i
$298$		0			0
$299$	−2.23124	−	3.86462i	−0.129036	−	0.223497i
$300$		0			0
$301$	−7.92370	+	0.306917i	−0.456714	+	0.0176904i
$302$		0			0
$303$	5.89530	+	10.2110i	0.338676	+	0.586604i
$304$		0			0
$305$	9.63299	−	16.6848i	0.551584	−	0.955371i
$306$		0			0
$307$	−26.9650			−1.53898			−0.769488	−	0.638662i	$-0.779488\pi$
$307$	−26.9650			−1.53898			−0.769488	+	0.638662i	$0.779488\pi$
$308$		0			0
$309$	−31.8340			−1.81097
$310$		0			0
$311$	−11.3999	+	19.7451i	−0.646426	+	1.11964i	0.337544	+	0.941310i	$0.390404\pi$
$311$	−11.3999	+	19.7451i	−0.646426	+	1.11964i	−0.983970	+	0.178333i	$0.942929\pi$
$312$		0			0
$313$	−11.3292	−	19.6228i	−0.640367	−	1.10915i	−0.985351	−	0.170539i	$-0.945449\pi$
$313$	−11.3292	−	19.6228i	−0.640367	−	1.10915i	0.344984	−	0.938609i	$-0.387884\pi$
$314$		0			0
$315$	5.14945	−	9.77433i	0.290139	−	0.550721i
$316$		0			0
$317$	0.576777	+	0.999007i	0.0323950	+	0.0561098i	0.881768	−	0.471683i	$-0.156353\pi$
$317$	0.576777	+	0.999007i	0.0323950	+	0.0561098i	−0.849373	+	0.527792i	$0.823020\pi$
$318$		0			0
$319$	−4.46098	+	7.72664i	−0.249767	+	0.432609i
$320$		0			0
$321$	−27.7989			−1.55158
$322$		0			0
$323$	18.8128			1.04677
$324$		0			0
$325$	2.77441	−	4.80542i	0.153897	−	0.266557i
$326$		0			0
$327$	−11.8048	−	20.4465i	−0.652806	−	1.13069i
$328$		0			0
$329$	−12.6559	−	20.0831i	−0.697744	−	1.10722i
$330$		0			0
$331$	10.9747	+	19.0088i	0.603225	+	1.04482i	0.992329	+	0.123622i	$0.0394512\pi$
$331$	10.9747	+	19.0088i	0.603225	+	1.04482i	−0.389105	+	0.921194i	$0.627216\pi$
$332$		0			0
$333$	8.06849	−	13.9750i	0.442151	−	0.765828i
$334$		0			0
$335$	−24.5192			−1.33963
$336$		0			0
$337$	−1.27042			−0.0692040			−0.0346020	−	0.999401i	$-0.511016\pi$
$337$	−1.27042			−0.0692040			−0.0346020	+	0.999401i	$0.511016\pi$
$338$		0			0
$339$	2.19585	−	3.80332i	0.119262	−	0.206568i
$340$		0			0
$341$	−19.3354	−	33.4900i	−1.04707	−	1.81358i
$342$		0			0
$343$	18.3955	−	2.14618i	0.993263	−	0.115883i
$344$		0			0
$345$	8.97454	+	15.5444i	0.483173	+	0.836880i
$346$		0			0
$347$	4.24048	−	7.34473i	0.227641	−	0.394286i	−0.729468	−	0.684015i	$-0.760232\pi$
$347$	4.24048	−	7.34473i	0.227641	−	0.394286i	0.957108	+	0.289730i	$0.0935654\pi$
$348$		0			0
$349$	−25.9408			−1.38858			−0.694290	−	0.719695i	$-0.744282\pi$
$349$	−25.9408			−1.38858			−0.694290	+	0.719695i	$0.744282\pi$
$350$		0			0
$351$	−5.09092			−0.271733
$352$		0			0
$353$	7.29234	−	12.6307i	0.388132	−	0.672264i	−0.604066	−	0.796934i	$-0.706454\pi$
$353$	7.29234	−	12.6307i	0.388132	−	0.672264i	0.992198	+	0.124670i	$0.0397871\pi$
$354$		0			0
$355$	18.0087	+	31.1920i	0.955802	+	1.65550i
$356$		0			0
$357$	16.8824	+	26.7899i	0.893511	+	1.41787i
$358$		0			0
$359$	−11.2509	−	19.4871i	−0.593799	−	1.02849i	−0.993715	−	0.111939i	$-0.964294\pi$
$359$	−11.2509	−	19.4871i	−0.593799	−	1.02849i	0.399916	−	0.916552i	$-0.369039\pi$
$360$		0			0
$361$	4.03643	−	6.99130i	0.212444	−	0.367963i
$362$		0			0
$363$	−47.7557			−2.50652
$364$		0			0
$365$	−5.93174			−0.310481
$366$		0			0
$367$	−1.66995	+	2.89245i	−0.0871709	+	0.150984i	−0.906314	−	0.422604i	$-0.861116\pi$
$367$	−1.66995	+	2.89245i	−0.0871709	+	0.150984i	0.819143	+	0.573589i	$0.194449\pi$
$368$		0			0
$369$	−0.711302	−	1.23201i	−0.0370289	−	0.0641359i
$370$		0			0
$371$	−3.54620	+	6.73115i	−0.184110	+	0.349464i
$372$		0			0
$373$	−13.8215	−	23.9395i	−0.715649	−	1.23954i	−0.962709	−	0.270540i	$-0.912798\pi$
$373$	−13.8215	−	23.9395i	−0.715649	−	1.23954i	0.247060	−	0.969000i	$-0.420536\pi$
$374$		0			0
$375$	4.27271	−	7.40055i	0.220642	−	0.382163i
$376$		0			0
$377$	2.35835			0.121461
$378$		0			0
$379$	−20.8269			−1.06981			−0.534903	−	0.844913i	$-0.679652\pi$
$379$	−20.8269			−1.06981			−0.534903	+	0.844913i	$0.679652\pi$
$380$		0			0
$381$	−0.713040	+	1.23502i	−0.0365301	+	0.0632720i
$382$		0			0
$383$	−5.65239	−	9.79023i	−0.288824	−	0.500258i	0.684705	−	0.728820i	$-0.259931\pi$
$383$	−5.65239	−	9.79023i	−0.288824	−	0.500258i	−0.973529	+	0.228562i	$0.926598\pi$
$384$		0			0
$385$	45.0543	−	1.74513i	2.29618	−	0.0889402i
$386$		0			0
$387$	2.13186	+	3.69249i	0.108368	+	0.187700i
$388$		0			0
$389$	−3.02303	+	5.23604i	−0.153274	+	0.265478i	−0.932429	−	0.361353i	$-0.882315\pi$
$389$	−3.02303	+	5.23604i	−0.153274	+	0.265478i	0.779155	+	0.626831i	$0.215648\pi$
$390$		0			0
$391$	−16.5486			−0.836897
$392$		0			0
$393$	−3.84307			−0.193857
$394$		0			0
$395$	15.1407	−	26.2244i	0.761809	−	1.31949i
$396$		0			0
$397$	7.08871	+	12.2780i	0.355772	+	0.616216i	0.987250	−	0.159178i	$-0.0508845\pi$
$397$	7.08871	+	12.2780i	0.355772	+	0.616216i	−0.631478	+	0.775394i	$0.717551\pi$
$398$		0			0
$399$	−18.3787	+	0.711882i	−0.920088	+	0.0356387i
$400$		0			0
$401$	6.06275	+	10.5010i	0.302759	+	0.524395i	0.976760	−	0.214336i	$-0.0687588\pi$
$401$	6.06275	+	10.5010i	0.302759	+	0.524395i	−0.674000	+	0.738731i	$0.735425\pi$
$402$		0			0
$403$	−5.11095	+	8.85242i	−0.254595	+	0.440971i
$404$		0			0
$405$	33.0039			1.63998
$406$		0			0
$407$	65.8578			3.26445
$408$		0			0
$409$	2.74328	−	4.75150i	0.135646	−	0.234946i	−0.790198	−	0.612852i	$-0.790022\pi$
$409$	2.74328	−	4.75150i	0.135646	−	0.234946i	0.925844	+	0.377905i	$0.123356\pi$
$410$		0			0
$411$	1.93095	+	3.34450i	0.0952465	+	0.164972i
$412$		0			0
$413$	−12.0357	+	22.8454i	−0.592239	+	1.12415i
$414$		0			0
$415$	−12.7526	−	22.0882i	−0.626001	−	1.08426i
$416$		0			0
$417$	−1.83406	+	3.17668i	−0.0898143	+	0.155563i
$418$		0			0
$419$	5.94192			0.290282			0.145141	−	0.989411i	$-0.453636\pi$
$419$	5.94192			0.290282			0.145141	+	0.989411i	$0.453636\pi$
$420$		0			0
$421$	−37.0802			−1.80718			−0.903588	−	0.428402i	$-0.859077\pi$
$421$	−37.0802			−1.80718			−0.903588	+	0.428402i	$0.859077\pi$
$422$		0			0
$423$	−6.38195	+	11.0539i	−0.310301	+	0.537458i
$424$		0			0
$425$	−10.2886	−	17.8203i	−0.499069	−	0.864413i
$426$		0			0
$427$	−9.25852	−	14.6919i	−0.448051	−	0.710993i
$428$		0			0
$429$	9.36902	+	16.2276i	0.452341	+	0.783477i
$430$		0			0
$431$	13.7982	−	23.8992i	0.664636	−	1.15118i	−0.314748	−	0.949175i	$-0.601920\pi$
$431$	13.7982	−	23.8992i	0.664636	−	1.15118i	0.979384	−	0.202008i	$-0.0647468\pi$
$432$		0			0
$433$	−19.3644			−0.930595			−0.465297	−	0.885154i	$-0.654053\pi$
$433$	−19.3644			−0.930595			−0.465297	+	0.885154i	$0.654053\pi$
$434$		0			0
$435$	−9.48579			−0.454809
$436$		0			0
$437$	4.80599	−	8.32422i	0.229902	−	0.398201i
$438$		0			0
$439$	12.6004	+	21.8246i	0.601387	+	1.04163i	0.992611	+	0.121337i	$0.0387181\pi$
$439$	12.6004	+	21.8246i	0.601387	+	1.04163i	−0.391225	+	0.920295i	$0.627949\pi$
$440$		0			0
$441$	−5.63129	−	8.21310i	−0.268156	−	0.391100i
$442$		0			0
$443$	−18.6182	−	32.2476i	−0.884576	−	1.53213i	−0.846199	−	0.532867i	$-0.821115\pi$
$443$	−18.6182	−	32.2476i	−0.884576	−	1.53213i	−0.0383770	−	0.999263i	$-0.512219\pi$
$444$		0			0
$445$	−7.05470	+	12.2191i	−0.334425	+	0.579241i
$446$		0			0
$447$	15.1837			0.718163
$448$		0			0
$449$	−17.6022			−0.830698			−0.415349	−	0.909662i	$-0.636341\pi$
$449$	−17.6022			−0.830698			−0.415349	+	0.909662i	$0.636341\pi$
$450$		0			0
$451$	2.90295	−	5.02805i	0.136694	−	0.236762i
$452$		0			0
$453$	5.18142	+	8.97449i	0.243445	+	0.421658i
$454$		0			0
$455$	−6.35410	−	10.0830i	−0.297885	−	0.472700i
$456$		0			0
$457$	13.8865	+	24.0521i	0.649581	+	1.12511i	0.983223	+	0.182408i	$0.0583891\pi$
$457$	13.8865	+	24.0521i	0.649581	+	1.12511i	−0.333642	+	0.942700i	$0.608278\pi$
$458$		0			0
$459$	−9.43953	+	16.3498i	−0.440600	+	0.763141i
$460$		0			0
$461$	−5.78612			−0.269486			−0.134743	−	0.990881i	$-0.543021\pi$
$461$	−5.78612			−0.269486			−0.134743	+	0.990881i	$0.543021\pi$
$462$		0			0
$463$	38.3113			1.78048			0.890238	−	0.455496i	$-0.150538\pi$
$463$	38.3113			1.78048			0.890238	+	0.455496i	$0.150538\pi$
$464$		0			0
$465$	20.5574	−	35.6064i	0.953326	−	1.65121i
$466$		0			0
$467$	9.80155	+	16.9768i	0.453562	+	0.785592i	0.998604	−	0.0528167i	$-0.0168199\pi$
$467$	9.80155	+	16.9768i	0.453562	+	0.785592i	−0.545043	+	0.838408i	$0.683487\pi$
$468$		0			0
$469$	−10.3014	+	19.5534i	−0.475675	+	0.902892i
$470$		0			0
$471$	17.2028	+	29.7961i	0.792663	+	1.37293i
$472$		0			0
$473$	−8.70048	+	15.0697i	−0.400049	+	0.692904i
$474$		0			0
$475$	11.9519			0.548392
$476$		0			0
$477$	4.09085			0.187307
$478$		0			0
$479$	−17.3790	+	30.1012i	−0.794065	+	1.37536i	0.129366	+	0.991597i	$0.458706\pi$
$479$	−17.3790	+	30.1012i	−0.794065	+	1.37536i	−0.923431	+	0.383764i	$0.874628\pi$
$480$		0			0
$481$	−8.70412	−	15.0760i	−0.396874	−	0.687405i
$482$		0			0
$483$	16.1667	−	0.626202i	0.735611	−	0.0284932i
$484$		0			0
$485$	−6.76798	−	11.7225i	−0.307318	−	0.532290i
$486$		0			0
$487$	−3.97304	+	6.88151i	−0.180036	+	0.311831i	−0.941892	−	0.335914i	$-0.890955\pi$
$487$	−3.97304	+	6.88151i	−0.180036	+	0.311831i	0.761857	+	0.647746i	$0.224288\pi$
$488$		0			0
$489$	44.2947			2.00308
$490$		0			0
$491$	14.6853			0.662736			0.331368	−	0.943502i	$-0.392490\pi$
$491$	14.6853			0.662736			0.331368	+	0.943502i	$0.392490\pi$
$492$		0			0
$493$	4.37282	−	7.57395i	0.196942	−	0.341114i
$494$		0			0
$495$	−12.1218	−	20.9955i	−0.544834	−	0.943680i
$496$		0			0
$497$	32.4408	−	1.25656i	1.45517	−	0.0563646i
$498$		0			0
$499$	0.149437	+	0.258832i	0.00668971	+	0.0115869i	0.869351	−	0.494195i	$-0.164537\pi$
$499$	0.149437	+	0.258832i	0.00668971	+	0.0115869i	−0.862661	+	0.505782i	$0.831204\pi$
$500$		0			0
$501$	−18.2043	+	31.5308i	−0.813309	+	1.40869i
$502$		0			0
$503$	17.9191			0.798971			0.399486	−	0.916739i	$-0.369189\pi$
$503$	17.9191			0.798971			0.399486	+	0.916739i	$0.369189\pi$
$504$		0			0
$505$	−16.4566			−0.732309
$506$		0			0
$507$	−11.1930	+	19.3868i	−0.497097	+	0.860998i
$508$		0			0
$509$	1.96363	+	3.40111i	0.0870363	+	0.150751i	0.906257	−	0.422727i	$-0.138927\pi$
$509$	1.96363	+	3.40111i	0.0870363	+	0.150751i	−0.819221	+	0.573478i	$0.805594\pi$
$510$		0			0
$511$	−2.49214	+	4.73040i	−0.110246	+	0.209260i
$512$		0			0
$513$	−5.48281	−	9.49650i	−0.242072	−	0.419281i
$514$		0			0
$515$	22.2160	−	38.4792i	0.978954	−	1.69560i
$516$		0			0
$517$	−52.0917			−2.29099
$518$		0			0
$519$	21.2315			0.931958
$520$		0			0
$521$	18.7766	−	32.5221i	0.822619	−	1.42482i	−0.0811069	−	0.996705i	$-0.525846\pi$
$521$	18.7766	−	32.5221i	0.822619	−	1.42482i	0.903726	−	0.428112i	$-0.140821\pi$
$522$		0			0
$523$	−0.673430	−	1.16641i	−0.0294470	−	0.0510038i	0.850926	−	0.525285i	$-0.176041\pi$
$523$	−0.673430	−	1.16641i	−0.0294470	−	0.0510038i	−0.880373	+	0.474281i	$0.842708\pi$
$524$		0			0
$525$	10.7255	+	17.0198i	0.468100	+	0.742806i
$526$		0			0
$527$	18.9534	+	32.8282i	0.825621	+	1.43002i
$528$		0			0
$529$	7.27245	−	12.5963i	0.316193	−	0.547663i
$530$		0			0
$531$	13.8843			0.602526
$532$		0			0
$533$	−1.53467			−0.0664741
$534$		0			0
$535$	19.4000	−	33.6018i	0.838735	−	1.45273i
$536$		0			0
$537$	16.8523	+	29.1891i	0.727231	+	1.25960i
$538$		0			0
$539$	17.5372	−	36.6627i	0.755382	−	1.57918i
$540$		0			0
$541$	6.23537	+	10.8000i	0.268080	+	0.464327i	0.968366	−	0.249535i	$-0.0802776\pi$
$541$	6.23537	+	10.8000i	0.268080	+	0.464327i	−0.700286	+	0.713862i	$0.746944\pi$
$542$		0			0
$543$	9.79385	−	16.9634i	0.420294	−	0.727971i
$544$		0			0
$545$	32.9528			1.41154
$546$		0			0
$547$	−8.05835			−0.344550			−0.172275	−	0.985049i	$-0.555112\pi$
$547$	−8.05835			−0.344550			−0.172275	+	0.985049i	$0.555112\pi$
$548$		0			0
$549$	−4.66876	+	8.08653i	−0.199258	+	0.345125i
$550$		0			0
$551$	2.53989	+	4.39921i	0.108203	+	0.187413i
$552$		0			0
$553$	−14.5521	−	23.0921i	−0.618817	−	0.981974i
$554$		0			0
$555$	35.0099	+	60.6390i	1.48609	+	2.57398i
$556$		0			0
$557$	9.45062	−	16.3690i	0.400436	−	0.693575i	−0.593343	−	0.804950i	$-0.702192\pi$
$557$	9.45062	−	16.3690i	0.400436	−	0.693575i	0.993778	+	0.111375i	$0.0355254\pi$
$558$		0			0
$559$	4.59961			0.194543
$560$		0			0
$561$	69.4878			2.93378
$562$		0			0
$563$	−14.9766	+	25.9403i	−0.631190	+	1.09325i	0.356119	+	0.934441i	$0.384100\pi$
$563$	−14.9766	+	25.9403i	−0.631190	+	1.09325i	−0.987309	+	0.158812i	$0.949234\pi$
$564$		0			0
$565$	3.06484	+	5.30845i	0.128939	+	0.223328i
$566$		0			0
$567$	13.8661	−	26.3197i	0.582322	−	1.10532i
$568$		0			0
$569$	3.62357	+	6.27620i	0.151908	+	0.263112i	0.931929	−	0.362641i	$-0.118125\pi$
$569$	3.62357	+	6.27620i	0.151908	+	0.263112i	−0.780021	+	0.625753i	$0.784792\pi$
$570$		0			0
$571$	17.4999	−	30.3107i	0.732348	−	1.26846i	−0.223529	−	0.974697i	$-0.571758\pi$
$571$	17.4999	−	30.3107i	0.732348	−	1.26846i	0.955877	−	0.293767i	$-0.0949089\pi$
$572$		0			0
$573$	8.49695			0.354965
$574$		0			0
$575$	−10.5134			−0.438440
$576$		0			0
$577$	21.0562	−	36.4705i	0.876583	−	1.51829i	0.0215164	−	0.999768i	$-0.493151\pi$
$577$	21.0562	−	36.4705i	0.876583	−	1.51829i	0.855067	−	0.518518i	$-0.173516\pi$
$578$		0			0
$579$	12.4691	+	21.5971i	0.518197	+	0.897543i
$580$		0			0
$581$	−22.9725	+	0.889818i	−0.953061	+	0.0369159i
$582$		0			0
$583$	8.34773	+	14.4587i	0.345728	+	0.598818i
$584$		0			0
$585$	−3.20416	+	5.54977i	−0.132476	+	0.229455i
$586$		0			0
$587$	30.8138			1.27182			0.635910	−	0.771763i	$-0.280625\pi$
$587$	30.8138			1.27182			0.635910	+	0.771763i	$0.280625\pi$
$588$		0			0
$589$	−22.0175			−0.907216
$590$		0			0
$591$	−11.0168	+	19.0817i	−0.453172	+	0.784916i
$592$		0			0
$593$	15.4133	+	26.6966i	0.632949	+	1.09630i	0.986946	+	0.161053i	$0.0514890\pi$
$593$	15.4133	+	26.6966i	0.632949	+	1.09630i	−0.353997	+	0.935247i	$0.615178\pi$
$594$		0			0
$595$	−44.1639	+	1.71065i	−1.81055	+	0.0701297i
$596$		0			0
$597$	−11.3110	−	19.5913i	−0.462930	−	0.801819i
$598$		0			0
$599$	5.35469	−	9.27460i	0.218787	−	0.378950i	−0.735651	−	0.677361i	$-0.763123\pi$
$599$	5.35469	−	9.27460i	0.218787	−	0.378950i	0.954437	+	0.298411i	$0.0964567\pi$
$600$		0			0
$601$	−9.62891			−0.392771			−0.196386	−	0.980527i	$-0.562920\pi$
$601$	−9.62891			−0.392771			−0.196386	+	0.980527i	$0.562920\pi$
$602$		0			0
$603$	11.8836			0.483936
$604$		0			0
$605$	33.3273	−	57.7245i	1.35495	−	2.34683i
$606$		0			0
$607$	−19.4694	−	33.7219i	−0.790238	−	1.36873i	−0.925820	−	0.377965i	$-0.876624\pi$
$607$	−19.4694	−	33.7219i	−0.790238	−	1.36873i	0.135582	−	0.990766i	$-0.456710\pi$
$608$		0			0
$609$	−3.98532	+	7.56466i	−0.161493	+	0.306535i
$610$		0			0
$611$	6.88472	+	11.9247i	0.278526	+	0.482421i
$612$		0			0
$613$	1.66003	−	2.87526i	0.0670481	−	0.116131i	−0.830553	−	0.556940i	$-0.811975\pi$
$613$	1.66003	−	2.87526i	0.0670481	−	0.116131i	0.897601	+	0.440810i	$0.145309\pi$
$614$		0			0
$615$	6.17281			0.248912
$616$		0			0
$617$	−0.562483			−0.0226447			−0.0113224	−	0.999936i	$-0.503604\pi$
$617$	−0.562483			−0.0226447			−0.0113224	+	0.999936i	$0.503604\pi$
$618$		0			0
$619$	1.10293	−	1.91033i	0.0443304	−	0.0767826i	−0.843009	−	0.537900i	$-0.819218\pi$
$619$	1.10293	−	1.91033i	0.0443304	−	0.0767826i	0.887339	+	0.461117i	$0.152551\pi$
$620$		0			0
$621$	4.82291	+	8.35353i	0.193537	+	0.335215i
$622$		0			0
$623$	6.78046	+	10.7596i	0.271653	+	0.431075i
$624$		0			0
$625$	15.0027	+	25.9854i	0.600107	+	1.03942i
$626$		0			0
$627$	−20.1805	+	34.9536i	−0.805930	+	1.39591i
$628$		0			0
$629$	−64.5564			−2.57403
$630$		0			0
$631$	25.9567			1.03332			0.516660	−	0.856191i	$-0.327175\pi$
$631$	25.9567			1.03332			0.516660	+	0.856191i	$0.327175\pi$
$632$		0			0
$633$	−24.9238	+	43.1693i	−0.990634	+	1.71583i
$634$		0			0
$635$	−0.995218	−	1.72377i	−0.0394940	−	0.0684057i
$636$		0			0
$637$	−10.7105	+	0.830971i	−0.424367	+	0.0329243i
$638$		0			0
$639$	−8.72816	−	15.1176i	−0.345281	−	0.598044i
$640$		0			0
$641$	11.3700	−	19.6934i	0.449088	−	0.777843i	−0.549239	−	0.835665i	$-0.685082\pi$
$641$	11.3700	−	19.6934i	0.449088	−	0.777843i	0.998327	+	0.0578224i	$0.0184157\pi$
$642$		0			0
$643$	−8.75563			−0.345288			−0.172644	−	0.984984i	$-0.555231\pi$
$643$	−8.75563			−0.345288			−0.172644	+	0.984984i	$0.555231\pi$
$644$		0			0
$645$	−18.5007			−0.728463
$646$		0			0
$647$	10.2566	−	17.7649i	0.403228	−	0.698411i	−0.590885	−	0.806755i	$-0.701221\pi$
$647$	10.2566	−	17.7649i	0.403228	−	0.698411i	0.994113	+	0.108344i	$0.0345548\pi$
$648$		0			0
$649$	28.3320	+	49.0725i	1.11213	+	1.92626i
$650$		0			0
$651$	−19.7583	−	31.3535i	−0.774387	−	1.22884i
$652$		0			0
$653$	6.24931	+	10.8241i	0.244554	+	0.423580i	0.962006	−	0.273028i	$-0.0880250\pi$
$653$	6.24931	+	10.8241i	0.244554	+	0.423580i	−0.717452	+	0.696608i	$0.754692\pi$
$654$		0			0
$655$	2.68196	−	4.64530i	0.104793	−	0.181507i
$656$		0			0
$657$	2.87490			0.112160
$658$		0			0
$659$	16.8784			0.657490			0.328745	−	0.944419i	$-0.393374\pi$
$659$	16.8784			0.657490			0.328745	+	0.944419i	$0.393374\pi$
$660$		0			0
$661$	−4.56461	+	7.90614i	−0.177543	+	0.307513i	−0.941038	−	0.338300i	$-0.890148\pi$
$661$	−4.56461	+	7.90614i	−0.177543	+	0.307513i	0.763495	+	0.645813i	$0.223482\pi$
$662$		0			0
$663$	−9.18388	−	15.9069i	−0.356672	−	0.617775i
$664$		0			0
$665$	11.9655	−	22.7120i	0.464002	−	0.880735i
$666$		0			0
$667$	−2.23419	−	3.86973i	−0.0865083	−	0.149837i
$668$		0			0
$669$	−11.1884	+	19.3789i	−0.432570	+	0.749233i
$670$		0			0
$671$	−38.1080			−1.47114
$672$		0			0
$673$	3.59435			0.138552			0.0692760	−	0.997598i	$-0.477931\pi$
$673$	3.59435			0.138552			0.0692760	+	0.997598i	$0.477931\pi$
$674$		0			0
$675$	−5.99700	+	10.3871i	−0.230825	+	0.399800i
$676$		0			0
$677$	−15.6913	−	27.1781i	−0.603066	−	1.04454i	−0.992354	−	0.123425i	$-0.960612\pi$
$677$	−15.6913	−	27.1781i	−0.603066	−	1.04454i	0.389288	−	0.921116i	$-0.372721\pi$
$678$		0			0
$679$	−12.1918	+	0.472238i	−0.467879	+	0.0181228i
$680$		0			0
$681$	−13.1964	−	22.8569i	−0.505688	−	0.875877i
$682$		0			0
$683$	17.5258	−	30.3556i	0.670607	−	1.16153i	−0.307125	−	0.951669i	$-0.599367\pi$
$683$	17.5258	−	30.3556i	0.670607	−	1.16153i	0.977732	−	0.209857i	$-0.0672997\pi$
$684$		0			0
$685$	−5.39020			−0.205949
$686$		0			0
$687$	−32.1142			−1.22523
$688$		0			0
$689$	2.20656	−	3.82188i	0.0840633	−	0.145602i
$690$		0			0
$691$	−19.9017	−	34.4707i	−0.757095	−	1.31133i	−0.944326	−	0.329011i	$-0.893285\pi$
$691$	−19.9017	−	34.4707i	−0.757095	−	1.31133i	0.187231	−	0.982316i	$-0.440049\pi$
$692$		0			0
$693$	−21.8362	+	0.845802i	−0.829487	+	0.0321294i
$694$		0			0
$695$	−2.55987	−	4.43383i	−0.0971014	−	0.168185i
$696$		0			0
$697$	−2.84558	+	4.92869i	−0.107784	+	0.186687i
$698$		0			0
$699$	28.1848			1.06605
$700$		0			0
$701$	23.7679			0.897703			0.448852	−	0.893606i	$-0.351833\pi$
$701$	23.7679			0.897703			0.448852	+	0.893606i	$0.351833\pi$
$702$		0			0
$703$	18.7483	−	32.4730i	0.707105	−	1.22474i
$704$		0			0
$705$	−27.6919	−	47.9637i	−1.04294	−	1.80642i
$706$		0			0
$707$	−6.91401	+	13.1237i	−0.260028	+	0.493567i
$708$		0			0
$709$	0.913629	+	1.58245i	0.0343120	+	0.0594302i	0.882671	−	0.469990i	$-0.155743\pi$
$709$	0.913629	+	1.58245i	0.0343120	+	0.0594302i	−0.848359	+	0.529421i	$0.822409\pi$
$710$		0			0
$711$	−7.33812	+	12.7100i	−0.275201	+	0.476662i
$712$		0			0
$713$	19.3675			0.725320
$714$		0			0
$715$	−26.1534			−0.978083
$716$		0			0
$717$	32.1925	−	55.7591i	1.20225	−	2.08236i
$718$		0			0
$719$	11.2496	+	19.4849i	0.419539	+	0.726663i	0.995893	−	0.0905374i	$-0.0288585\pi$
$719$	11.2496	+	19.4849i	0.419539	+	0.726663i	−0.576354	+	0.817200i	$0.695525\pi$
$720$		0			0
$721$	−21.3524	−	33.8832i	−0.795204	−	1.26187i
$722$		0			0
$723$	7.53315	+	13.0478i	0.280161	+	0.485253i
$724$		0			0
$725$	2.77809	−	4.81179i	0.103176	−	0.178705i
$726$		0			0
$727$	−16.1827			−0.600182			−0.300091	−	0.953911i	$-0.597017\pi$
$727$	−16.1827			−0.600182			−0.300091	+	0.953911i	$0.597017\pi$
$728$		0			0
$729$	4.93282			0.182697
$730$		0			0
$731$	8.52855	−	14.7719i	0.315440	−	0.546358i
$732$		0			0
$733$	23.7716	+	41.1736i	0.878023	+	1.52078i	0.853507	+	0.521081i	$0.174471\pi$
$733$	23.7716	+	41.1736i	0.878023	+	1.52078i	0.0245158	+	0.999699i	$0.492196\pi$
$734$		0			0
$735$	43.0802	−	3.34235i	1.58904	−	0.123284i
$736$		0			0
$737$	24.2494	+	42.0013i	0.893240	+	1.54714i
$738$		0			0
$739$	18.6130	−	32.2387i	0.684691	−	1.18592i	−0.288843	−	0.957377i	$-0.593271\pi$
$739$	18.6130	−	32.2387i	0.684691	−	1.18592i	0.973534	−	0.228543i	$-0.0733962\pi$
$740$		0			0
$741$	10.6686			0.391922
$742$		0			0
$743$	−10.8904			−0.399531			−0.199766	−	0.979844i	$-0.564018\pi$
$743$	−10.8904			−0.399531			−0.199766	+	0.979844i	$0.564018\pi$
$744$		0			0
$745$	−10.5962	+	18.3532i	−0.388216	+	0.672410i
$746$		0			0
$747$	6.18072	+	10.7053i	0.226141	+	0.391687i
$748$		0			0
$749$	−18.6458	−	29.5883i	−0.681304	−	1.08113i
$750$		0			0
$751$	−14.7735	−	25.5885i	−0.539094	−	0.933739i	−0.998953	−	0.0457467i	$-0.985433\pi$
$751$	−14.7735	−	25.5885i	−0.539094	−	0.933739i	0.459859	−	0.887992i	$-0.347900\pi$
$752$		0			0
$753$	−26.9267	+	46.6385i	−0.981265	+	1.69960i
$754$		0			0
$755$	−14.4638			−0.526393
$756$		0			0
$757$	−16.0007			−0.581557			−0.290778	−	0.956790i	$-0.593914\pi$
$757$	−16.0007			−0.581557			−0.290778	+	0.956790i	$0.593914\pi$
$758$		0			0
$759$	17.7516	−	30.7467i	0.644342	−	1.11603i
$760$		0			0
$761$	−18.2014	−	31.5257i	−0.659799	−	1.14281i	−0.980667	−	0.195682i	$-0.937308\pi$
$761$	−18.2014	−	31.5257i	−0.659799	−	1.14281i	0.320868	−	0.947124i	$-0.396025\pi$
$762$		0			0
$763$	13.8447	−	26.2790i	0.501211	−	0.951363i
$764$		0			0
$765$	11.8822	+	20.5807i	0.429603	+	0.744095i
$766$		0			0
$767$	7.48902	−	12.9714i	0.270413	−	0.468369i
$768$		0			0
$769$	−22.5697			−0.813886			−0.406943	−	0.913454i	$-0.633405\pi$
$769$	−22.5697			−0.813886			−0.406943	+	0.913454i	$0.633405\pi$
$770$		0			0
$771$	58.4983			2.10677
$772$		0			0
$773$	−15.8152	+	27.3927i	−0.568832	+	0.985245i	0.427850	+	0.903850i	$0.359271\pi$
$773$	−15.8152	+	27.3927i	−0.568832	+	0.985245i	−0.996682	+	0.0813957i	$0.974062\pi$
$774$		0			0
$775$	12.0412	+	20.8560i	0.432533	+	0.749169i
$776$		0			0
$777$	63.0668	−	2.44283i	2.26251	−	0.0876361i
$778$		0			0
$779$	−1.65281	−	2.86275i	−0.0592181	−	0.102569i
$780$		0			0
$781$	35.6211	−	61.6976i	1.27462	−	2.20771i
$782$		0			0
$783$	−5.09766			−0.182175
$784$		0			0
$785$	−48.0213			−1.71395
$786$		0			0
$787$	−17.7172	+	30.6871i	−0.631551	+	1.09388i	0.355684	+	0.934606i	$0.384248\pi$
$787$	−17.7172	+	30.6871i	−0.631551	+	1.09388i	−0.987235	+	0.159272i	$0.949085\pi$
$788$		0			0
$789$	25.3640	+	43.9317i	0.902981	+	1.56401i
$790$		0			0
$791$	5.52099	−	0.213850i	0.196304	−	0.00760364i
$792$		0			0
$793$	5.03656	+	8.72358i	0.178853	+	0.309783i
$794$		0			0
$795$	−8.87529	+	15.3724i	−0.314774	+	0.545205i
$796$		0			0
$797$	19.9555			0.706861			0.353430	−	0.935461i	$-0.385015\pi$
$797$	19.9555			0.706861			0.353430	+	0.935461i	$0.385015\pi$
$798$		0			0
$799$	51.0623			1.80645
$800$		0			0
$801$	3.41915	−	5.92215i	0.120810	−	0.209249i
$802$		0			0
$803$	5.86648	+	10.1610i	0.207023	+	0.358575i
$804$		0			0
$805$	−10.5254	+	19.9785i	−0.370970	+	0.704149i
$806$		0			0
$807$	8.20227	+	14.2068i	0.288734	+	0.500102i
$808$		0			0
$809$	−14.8310	+	25.6881i	−0.521431	+	0.903145i	0.478258	+	0.878219i	$0.341268\pi$
$809$	−14.8310	+	25.6881i	−0.521431	+	0.903145i	−0.999689	+	0.0249258i	$0.992065\pi$
$810$		0			0
$811$	4.22988			0.148531			0.0742655	−	0.997239i	$-0.476339\pi$
$811$	4.22988			0.148531			0.0742655	+	0.997239i	$0.476339\pi$
$812$		0			0
$813$	−19.7263			−0.691832
$814$		0			0
$815$	−30.9120	+	53.5411i	−1.08280	+	1.87546i
$816$		0			0
$817$	4.95368	+	8.58002i	0.173307	+	0.300177i
$818$		0			0
$819$	3.07960	+	4.88689i	0.107610	+	0.170762i
$820$		0			0
$821$	5.93960	+	10.2877i	0.207293	+	0.359043i	0.950861	−	0.309618i	$-0.100201\pi$
$821$	5.93960	+	10.2877i	0.207293	+	0.359043i	−0.743568	+	0.668661i	$0.766868\pi$
$822$		0			0
$823$	4.96181	−	8.59411i	0.172958	−	0.299572i	−0.766495	−	0.642251i	$-0.778001\pi$
$823$	4.96181	−	8.59411i	0.172958	−	0.299572i	0.939453	+	0.342679i	$0.111334\pi$
$824$		0			0
$825$	44.1461			1.53697
$826$		0			0
$827$	34.7169			1.20723			0.603613	−	0.797278i	$-0.293727\pi$
$827$	34.7169			1.20723			0.603613	+	0.797278i	$0.293727\pi$
$828$		0			0
$829$	2.70484	−	4.68492i	0.0939431	−	0.162714i	−0.815224	−	0.579146i	$-0.803386\pi$
$829$	2.70484	−	4.68492i	0.0939431	−	0.162714i	0.909167	+	0.416432i	$0.136720\pi$
$830$		0			0
$831$	−31.1075	−	53.8798i	−1.07911	−	1.86907i
$832$		0			0
$833$	−17.1907	+	35.9382i	−0.595621	+	1.24519i
$834$		0			0
$835$	−25.4085	−	44.0088i	−0.879297	−	1.52299i
$836$		0			0
$837$	11.0475	−	19.1349i	0.381858	−	0.661398i
$838$		0			0
$839$	8.25395			0.284958			0.142479	−	0.989798i	$-0.454493\pi$
$839$	8.25395			0.284958			0.142479	+	0.989798i	$0.454493\pi$
$840$		0			0
$841$	−26.6385			−0.918570
$842$		0			0
$843$	27.2251	−	47.1553i	0.937682	−	1.62411i
$844$		0			0
$845$	−15.6225	−	27.0589i	−0.537430	−	0.930856i
$846$		0			0
$847$	−32.0317	−	50.8297i	−1.10062	−	1.74653i
$848$		0			0
$849$	13.7985	+	23.8998i	0.473565	+	0.820239i
$850$		0			0
$851$	−16.4918	+	28.5646i	−0.565331	+	0.979183i
$852$		0			0
$853$	0.615237			0.0210653			0.0105327	−	0.999945i	$-0.496647\pi$
$853$	0.615237			0.0210653			0.0105327	+	0.999945i	$0.496647\pi$
$854$		0			0
$855$	−13.8032			−0.472061
$856$		0			0
$857$	−25.5432	+	44.2421i	−0.872539	+	1.51128i	−0.0131780	+	0.999913i	$0.504195\pi$
$857$	−25.5432	+	44.2421i	−0.872539	+	1.51128i	−0.859361	+	0.511369i	$0.829139\pi$
$858$		0			0
$859$	−20.1302	−	34.8665i	−0.686834	−	1.18963i	−0.972857	−	0.231408i	$-0.925667\pi$
$859$	−20.1302	−	34.8665i	−0.686834	−	1.18963i	0.286023	−	0.958223i	$-0.407667\pi$
$860$		0			0
$861$	2.59342	−	4.92264i	0.0883835	−	0.167763i
$862$		0			0
$863$	26.5247	+	45.9421i	0.902911	+	1.56389i	0.823697	+	0.567030i	$0.191908\pi$
$863$	26.5247	+	45.9421i	0.902911	+	1.56389i	0.0792139	+	0.996858i	$0.474759\pi$
$864$		0			0
$865$	−14.8168	+	25.6635i	−0.503786	+	0.872584i
$866$		0			0
$867$	−32.3637			−1.09913
$868$		0			0
$869$	−59.8963			−2.03184
$870$		0			0
$871$	6.40987	−	11.1022i	0.217190	−	0.376184i
$872$		0			0
$873$	3.28019	+	5.68146i	0.111018	+	0.192288i
$874$		0			0
$875$	10.7428	−	0.416112i	0.363173	−	0.0140672i
$876$		0			0
$877$	−12.1018	−	20.9609i	−0.408648	−	0.707799i	0.586091	−	0.810246i	$-0.300666\pi$
$877$	−12.1018	−	20.9609i	−0.408648	−	0.707799i	−0.994739	+	0.102447i	$0.967333\pi$
$878$		0			0
$879$	24.9780	−	43.2631i	0.842486	−	1.45923i
$880$		0			0
$881$	38.2014			1.28704			0.643520	−	0.765430i	$-0.277473\pi$
$881$	38.2014			1.28704			0.643520	+	0.765430i	$0.277473\pi$
$882$		0			0
$883$	−7.92322			−0.266637			−0.133319	−	0.991073i	$-0.542563\pi$
$883$	−7.92322			−0.266637			−0.133319	+	0.991073i	$0.542563\pi$
$884$		0			0
$885$	−30.1225	+	52.1737i	−1.01256	+	1.75380i
$886$		0			0
$887$	−25.8441	−	44.7632i	−0.867758	−	1.50300i	−0.864282	−	0.503008i	$-0.832227\pi$
$887$	−25.8441	−	44.7632i	−0.867758	−	1.50300i	−0.00347661	−	0.999994i	$-0.501107\pi$
$888$		0			0
$889$	−1.79278	+	0.0694417i	−0.0601281	+	0.00232900i
$890$		0			0
$891$	−32.6407	−	56.5354i	−1.09351	−	1.89401i
$892$		0			0
$893$	−14.8294	+	25.6852i	−0.496246	+	0.859524i
$894$		0			0
$895$	−47.0429			−1.57247
$896$		0			0
$897$	−9.38458			−0.313342
$898$		0			0
$899$	−5.11772	+	8.86415i	−0.170685	+	0.295636i
$900$		0			0
$901$	−8.18277	−	14.1730i	−0.272608	−	0.472170i
$902$		0			0
$903$	−7.77279	+	14.7538i	−0.258662	+	0.490974i
$904$		0			0
$905$	13.6697	+	23.6766i	0.454395	+	0.787035i
$906$		0			0
$907$	16.7063	−	28.9361i	0.554722	−	0.960807i	−0.443203	−	0.896421i	$-0.646158\pi$
$907$	16.7063	−	28.9361i	0.554722	−	0.960807i	0.997925	−	0.0643858i	$-0.0205088\pi$
$908$		0			0
$909$	7.97592			0.264545
$910$		0			0
$911$	−46.1058			−1.52755			−0.763777	−	0.645480i	$-0.776657\pi$
$911$	−46.1058			−1.52755			−0.763777	+	0.645480i	$0.776657\pi$
$912$		0			0
$913$	−25.2246	+	43.6903i	−0.834812	+	1.44594i
$914$		0			0
$915$	−20.2582	−	35.0882i	−0.669714	−	1.15998i
$916$		0			0
$917$	−2.57771	−	4.09045i	−0.0851234	−	0.135079i
$918$		0			0
$919$	4.53535	+	7.85546i	0.149607	+	0.259128i	0.931082	−	0.364809i	$-0.118866\pi$
$919$	4.53535	+	7.85546i	0.149607	+	0.259128i	−0.781475	+	0.623937i	$0.785532\pi$
$920$		0			0
$921$	−28.3537	+	49.1101i	−0.934286	+	1.61823i
$922$		0			0
$923$	−18.8315			−0.619846
$924$		0			0
$925$	−41.0131			−1.34850
$926$		0			0
$927$	−10.7673	+	18.6495i	−0.353644	+	0.612530i
$928$		0			0
$929$	7.60326	+	13.1692i	0.249455	+	0.432069i	0.963375	−	0.268159i	$-0.0864152\pi$
$929$	7.60326	+	13.1692i	0.249455	+	0.432069i	−0.713920	+	0.700227i	$0.753082\pi$
$930$		0			0
$931$	−13.0851	−	19.0843i	−0.428847	−	0.625463i
$932$		0			0
$933$	23.9739	+	41.5240i	0.784869	+	1.35943i
$934$		0			0
$935$	−48.4935	+	83.9932i	−1.58591	+	2.74687i
$936$		0			0
$937$	40.5690			1.32533			0.662666	−	0.748915i	$-0.269425\pi$
$937$	40.5690			1.32533			0.662666	+	0.748915i	$0.269425\pi$
$938$		0			0
$939$	−47.6508			−1.55502
$940$		0			0
$941$	1.04745	−	1.81423i	0.0341457	−	0.0591422i	−0.848448	−	0.529280i	$-0.822462\pi$
$941$	1.04745	−	1.81423i	0.0341457	−	0.0591422i	0.882593	+	0.470137i	$0.155796\pi$
$942$		0			0
$943$	1.45388	+	2.51820i	0.0473449	+	0.0820038i
$944$		0			0
$945$	13.7347	+	21.7949i	0.446788	+	0.708988i
$946$		0			0
$947$	16.5993	+	28.7508i	0.539405	+	0.934277i	0.998936	+	0.0461151i	$0.0146841\pi$
$947$	16.5993	+	28.7508i	0.539405	+	0.934277i	−0.459531	+	0.888162i	$0.651983\pi$
$948$		0			0
$949$	1.55069	−	2.68587i	0.0503375	−	0.0871871i
$950$		0			0
$951$	2.42592			0.0786659
$952$		0			0
$953$	26.0205			0.842887			0.421443	−	0.906855i	$-0.361524\pi$
$953$	26.0205			0.842887			0.421443	+	0.906855i	$0.361524\pi$
$954$		0			0
$955$	−5.92977	+	10.2707i	−0.191883	+	0.332351i
$956$		0			0
$957$	9.38143	+	16.2491i	0.303258	+	0.525259i
$958$		0			0
$959$	−2.26462	+	4.29853i	−0.0731283	+	0.138807i
$960$		0			0
$961$	−6.68199	−	11.5735i	−0.215548	−	0.373340i
$962$		0			0
$963$	−9.40247	+	16.2856i	−0.302990	+	0.524795i
$964$		0			0
$965$	−34.8072			−1.12048
$966$		0			0
$967$	41.8805			1.34679			0.673394	−	0.739284i	$-0.264836\pi$
$967$	41.8805			1.34679			0.673394	+	0.739284i	$0.264836\pi$
$968$		0			0
$969$	19.7817	−	34.2629i	0.635479	−	1.10068i
$970$		0			0
$971$	23.3523	+	40.4474i	0.749411	+	1.29802i	0.948105	+	0.317956i	$0.102997\pi$
$971$	23.3523	+	40.4474i	0.749411	+	1.29802i	−0.198695	+	0.980061i	$0.563670\pi$
$972$		0			0
$973$	−4.61135	+	0.178616i	−0.147833	+	0.00572617i
$974$		0			0
$975$	−5.83459	−	10.1058i	−0.186856	−	0.323645i
$976$		0			0
$977$	−9.85845	+	17.0753i	−0.315400	+	0.546288i	−0.979522	−	0.201335i	$-0.935472\pi$
$977$	−9.85845	+	17.0753i	−0.315400	+	0.546288i	0.664123	+	0.747624i	$0.268805\pi$
$978$		0			0
$979$	27.9083			0.891954
$980$		0			0
$981$	−15.9710			−0.509916
$982$		0			0
$983$	16.1302	−	27.9382i	0.514472	−	0.891092i	−0.485387	−	0.874299i	$-0.661321\pi$
$983$	16.1302	−	27.9382i	0.514472	−	0.891092i	0.999859	−	0.0167923i	$-0.00534541\pi$
$984$		0			0
$985$	−15.3766	−	26.6331i	−0.489940	−	0.848601i
$986$		0			0
$987$	−49.8841	+	1.93221i	−1.58783	+	0.0615030i
$988$		0			0
$989$	−4.35746	−	7.54735i	−0.138559	−	0.239992i
$990$		0			0
$991$	−1.63647	+	2.83445i	−0.0519843	+	0.0900394i	−0.890847	−	0.454304i	$-0.849888\pi$
$991$	−1.63647	+	2.83445i	−0.0519843	+	0.0900394i	0.838862	+	0.544344i	$0.183221\pi$
$992$		0			0
$993$	46.1596			1.46483
$994$		0			0
$995$	31.5746			1.00098
$996$		0			0
$997$	−12.6932	+	21.9852i	−0.401997	+	0.696280i	−0.993967	−	0.109681i	$-0.965017\pi$
$997$	−12.6932	+	21.9852i	−0.401997	+	0.696280i	0.591970	+	0.805960i	$0.298351\pi$
$998$		0			0
$999$	18.8143	+	32.5873i	0.595258	+	1.03102i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.i.d.165.7	✓	16
7.2	even	3	inner	1148.2.i.d.821.7	yes	16
7.3	odd	6		8036.2.a.n.1.7		8
7.4	even	3		8036.2.a.m.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.i.d.165.7	✓	16	1.1	even	1	trivial
1148.2.i.d.821.7	yes	16	7.2	even	3	inner
8036.2.a.m.1.2		8	7.4	even	3
8036.2.a.n.1.7		8	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.05150 - 1.82125i) q^{3} +(1.46762 + 2.54199i) q^{5} +(2.64377 - 0.102404i) q^{7} +(-0.711302 - 1.23201i) q^{9} +O(q^{10})\)	\(q+(1.05150 - 1.82125i) q^{3} +(1.46762 + 2.54199i) q^{5} +(2.64377 - 0.102404i) q^{7} +(-0.711302 - 1.23201i) q^{9} +(2.90295 - 5.02805i) q^{11} -1.53467 q^{13} +6.17281 q^{15} +(-2.84558 + 4.92869i) q^{17} +(-1.65281 - 2.86275i) q^{19} +(2.59342 - 4.92264i) q^{21} +(1.45388 + 2.51820i) q^{23} +(-1.80782 + 3.13123i) q^{25} +3.31726 q^{27} -1.53671 q^{29} +(3.33031 - 5.76827i) q^{31} +(-6.10489 - 10.5740i) q^{33} +(4.14036 + 6.57015i) q^{35} +(5.67164 + 9.82356i) q^{37} +(-1.61371 + 2.79503i) q^{39} +1.00000 q^{41} -2.99712 q^{43} +(2.08784 - 3.61625i) q^{45} +(-4.48611 - 7.77017i) q^{47} +(6.97903 - 0.541464i) q^{49} +(5.98425 + 10.3650i) q^{51} +(-1.43780 + 2.49035i) q^{53} +17.0417 q^{55} -6.95172 q^{57} +(-4.87988 + 8.45219i) q^{59} +(-3.28184 - 5.68432i) q^{61} +(-2.00668 - 3.18431i) q^{63} +(-2.25232 - 3.90113i) q^{65} +(-4.17670 + 7.23425i) q^{67} +6.11503 q^{69} +12.2707 q^{71} +(-1.01044 + 1.75012i) q^{73} +(3.80184 + 6.58498i) q^{75} +(7.15982 - 13.5903i) q^{77} +(-5.15823 - 8.93432i) q^{79} +(5.62200 - 9.73760i) q^{81} -8.68931 q^{83} -16.7049 q^{85} +(-1.61585 + 2.79873i) q^{87} +(2.40345 + 4.16289i) q^{89} +(-4.05733 + 0.157156i) q^{91} +(-7.00365 - 12.1307i) q^{93} +(4.85140 - 8.40287i) q^{95} -4.61153 q^{97} -8.25948 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{9}+O(q^{10}) \) 16 * q - 4 * q^9	\( 16 q - 4 q^{9} + 8 q^{11} - 14 q^{13} - 2 q^{15} + q^{17} - 4 q^{19} + 13 q^{21} + 3 q^{23} + 4 q^{25} - 24 q^{27} - 8 q^{29} - 4 q^{31} - 23 q^{33} + 12 q^{35} + 31 q^{37} - 5 q^{39} + 16 q^{41} - 16 q^{43} - q^{45} - 24 q^{47} + 16 q^{49} + 23 q^{51} + q^{53} + 4 q^{55} - 30 q^{57} - 4 q^{59} + 4 q^{61} + 23 q^{63} + 24 q^{65} - 42 q^{69} + 16 q^{71} - 11 q^{73} + 15 q^{75} + 25 q^{77} - 14 q^{79} + 28 q^{81} - 84 q^{83} - 40 q^{85} - 25 q^{87} + 11 q^{89} + 7 q^{91} + 27 q^{93} + 15 q^{95} - 32 q^{97} - 16 q^{99}+O(q^{100}) \) 16 * q - 4 * q^9 + 8 * q^11 - 14 * q^13 - 2 * q^15 + q^17 - 4 * q^19 + 13 * q^21 + 3 * q^23 + 4 * q^25 - 24 * q^27 - 8 * q^29 - 4 * q^31 - 23 * q^33 + 12 * q^35 + 31 * q^37 - 5 * q^39 + 16 * q^41 - 16 * q^43 - q^45 - 24 * q^47 + 16 * q^49 + 23 * q^51 + q^53 + 4 * q^55 - 30 * q^57 - 4 * q^59 + 4 * q^61 + 23 * q^63 + 24 * q^65 - 42 * q^69 + 16 * q^71 - 11 * q^73 + 15 * q^75 + 25 * q^77 - 14 * q^79 + 28 * q^81 - 84 * q^83 - 40 * q^85 - 25 * q^87 + 11 * q^89 + 7 * q^91 + 27 * q^93 + 15 * q^95 - 32 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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