LMFDB - Embedded newform 1152.2.p.d.959.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(191,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("1152.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1152 = 2^{7} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1152.p (of order $6$, 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:	$9.19876631285$
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} - 16x^{14} + 178x^{12} - 1024x^{10} + 4267x^{8} - 7936x^{6} + 10594x^{4} - 2800x^{2} + 625 $ x^16 - 16x^14 + 178x^12 - 1024x^10 + 4267x^8 - 7936x^6 + 10594x^4 - 2800*x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			959.2
Root			$-2.12575 + 1.22730i$ of defining polynomial
Character	$\chi$	$=$	1152.959
Dual form			1152.2.p.d.191.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.65068 + 0.524648i) q^{3} +(1.01255 - 1.75379i) q^{5} +(4.09406 - 2.36371i) q^{7} +(2.44949 - 1.73205i) q^{9} +O(q^{10})$	\(q+(-1.65068 + 0.524648i) q^{3} +(1.01255 - 1.75379i) q^{5} +(4.09406 - 2.36371i) q^{7} +(2.44949 - 1.73205i) q^{9} +(-2.93038 + 1.69185i) q^{11} +(5.51787 + 3.18575i) q^{13} +(-0.751275 + 3.42617i) q^{15} -4.87832i q^{17} +1.48393 q^{19} +(-5.51787 + 6.04967i) q^{21} +(-0.751275 + 1.30125i) q^{23} +(0.449490 + 0.778539i) q^{25} +(-3.13461 + 4.14418i) q^{27} +(-3.49278 - 6.04967i) q^{29} +(-5.93430 - 3.42617i) q^{31} +(3.94949 - 4.33013i) q^{33} -9.57348i q^{35} -2.86392i q^{37} +(-10.7796 - 2.36371i) q^{39} +(4.62372 + 2.66951i) q^{41} +(2.76363 + 4.78674i) q^{43} +(-0.557419 - 6.04967i) q^{45} +(4.09406 + 7.09113i) q^{47} +(7.67423 - 13.2922i) q^{49} +(2.55940 + 8.05254i) q^{51} +4.96046 q^{53} +6.85234i q^{55} +(-2.44949 + 0.778539i) q^{57} +(-7.88242 - 4.55092i) q^{59} +(-5.51787 + 3.18575i) q^{61} +(5.93430 - 12.8810i) q^{63} +(11.1742 - 6.45145i) q^{65} +(5.48977 - 9.50857i) q^{67} +(0.557419 - 2.54209i) q^{69} +6.68558 q^{71} +0.449490 q^{73} +(-1.15042 - 1.04930i) q^{75} +(-7.99810 + 13.8531i) q^{77} +(5.93430 - 3.42617i) q^{79} +(3.00000 - 8.48528i) q^{81} +(6.06499 - 3.50162i) q^{83} +(-8.55552 - 4.93953i) q^{85} +(8.93940 + 8.15359i) q^{87} +0.142865i q^{89} +30.1207 q^{91} +(11.5932 + 2.54209i) q^{93} +(1.50255 - 2.60249i) q^{95} +(0.724745 + 1.25529i) q^{97} +(-4.24755 + 9.21975i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 32 q^{25} + 24 q^{33} - 24 q^{41} + 64 q^{49} + 120 q^{65} - 32 q^{73} + 48 q^{81} - 8 q^{97}+O(q^{100}) $ 16 * q - 32 * q^25 + 24 * q^33 - 24 * q^41 + 64 * q^49 + 120 * q^65 - 32 * q^73 + 48 * q^81 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

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
$3$	−1.65068	+	0.524648i	−0.953021	+	0.302905i
$3$	−1.65068	+	0.524648i	−0.953021	+	0.302905i
$4$		0			0
$5$	1.01255	−	1.75379i	0.452826	−	0.784317i	−0.545735	−	0.837958i	$-0.683749\pi$
$5$	1.01255	−	1.75379i	0.452826	−	0.784317i	0.998560	+	0.0536411i	$0.0170827\pi$
$6$		0			0
$7$	4.09406	−	2.36371i	1.54741	−	0.893398i	0.549072	−	0.835775i	$-0.314981\pi$
$7$	4.09406	−	2.36371i	1.54741	−	0.893398i	0.998338	−	0.0576227i	$-0.0183520\pi$
$8$		0			0
$9$	2.44949	−	1.73205i	0.816497	−	0.577350i
$10$		0			0
$11$	−2.93038	+	1.69185i	−0.883542	+	0.510113i	−0.871825	−	0.489818i	$-0.837063\pi$
$11$	−2.93038	+	1.69185i	−0.883542	+	0.510113i	−0.0117176	+	0.999931i	$0.503730\pi$
$12$		0			0
$13$	5.51787	+	3.18575i	1.53038	+	0.883567i	0.999344	+	0.0362198i	$0.0115316\pi$
$13$	5.51787	+	3.18575i	1.53038	+	0.883567i	0.531039	+	0.847347i	$0.321802\pi$
$14$		0			0
$15$	−0.751275	+	3.42617i	−0.193978	+	0.884634i
$16$		0			0
$17$		−	4.87832i		−	1.18317i	−0.806244	−	0.591583i	$-0.798503\pi$
$17$		−	4.87832i		−	1.18317i	0.806244	−	0.591583i	$-0.201497\pi$
$18$		0			0
$19$	1.48393			0.340436			0.170218	−	0.985406i	$-0.445553\pi$
$19$	1.48393			0.340436			0.170218	+	0.985406i	$0.445553\pi$
$20$		0			0
$21$	−5.51787	+	6.04967i	−1.20410	+	1.32015i
$22$		0			0
$23$	−0.751275	+	1.30125i	−0.156652	+	0.271328i	−0.933659	−	0.358163i	$-0.883403\pi$
$23$	−0.751275	+	1.30125i	−0.156652	+	0.271328i	0.777008	+	0.629491i	$0.216737\pi$
$24$		0			0
$25$	0.449490	+	0.778539i	0.0898979	+	0.155708i
$26$		0			0
$27$	−3.13461	+	4.14418i	−0.603256	+	0.797548i
$28$		0			0
$29$	−3.49278	−	6.04967i	−0.648592	−	1.12339i	−0.983459	−	0.181129i	$-0.942025\pi$
$29$	−3.49278	−	6.04967i	−0.648592	−	1.12339i	0.334867	−	0.942265i	$-0.391309\pi$
$30$		0			0
$31$	−5.93430	−	3.42617i	−1.06583	−	0.615358i	−0.138792	−	0.990321i	$-0.544322\pi$
$31$	−5.93430	−	3.42617i	−1.06583	−	0.615358i	−0.927040	+	0.374963i	$0.877655\pi$
$32$		0			0
$33$	3.94949	−	4.33013i	0.687518	−	0.753778i
$34$		0			0
$35$		−	9.57348i		−	1.61821i
$36$		0			0
$37$		−	2.86392i		−	0.470826i	−0.971895	−	0.235413i	$-0.924356\pi$
$37$		−	2.86392i		−	0.470826i	0.971895	−	0.235413i	$-0.0756442\pi$
$38$		0			0
$39$	−10.7796	−	2.36371i	−1.72612	−	0.378496i
$40$		0			0
$41$	4.62372	+	2.66951i	0.722104	+	0.416907i	0.815527	−	0.578719i	$-0.196447\pi$
$41$	4.62372	+	2.66951i	0.722104	+	0.416907i	−0.0934223	+	0.995627i	$0.529781\pi$
$42$		0			0
$43$	2.76363	+	4.78674i	0.421449	+	0.729971i	0.996081	−	0.0884405i	$-0.0281883\pi$
$43$	2.76363	+	4.78674i	0.421449	+	0.729971i	−0.574632	+	0.818412i	$0.694855\pi$
$44$		0			0
$45$	−0.557419	−	6.04967i	−0.0830950	−	0.901831i
$46$		0			0
$47$	4.09406	+	7.09113i	0.597180	+	1.03435i	0.993235	+	0.116120i	$0.0370457\pi$
$47$	4.09406	+	7.09113i	0.597180	+	1.03435i	−0.396055	+	0.918227i	$0.629621\pi$
$48$		0			0
$49$	7.67423	−	13.2922i	1.09632	−	1.89888i
$50$		0			0
$51$	2.55940	+	8.05254i	0.358387	+	1.12758i
$52$		0			0
$53$	4.96046			0.681371			0.340686	−	0.940177i	$-0.389341\pi$
$53$	4.96046			0.681371			0.340686	+	0.940177i	$0.389341\pi$
$54$		0			0
$55$			6.85234i			0.923970i
$56$		0			0
$57$	−2.44949	+	0.778539i	−0.324443	+	0.103120i
$58$		0			0
$59$	−7.88242	−	4.55092i	−1.02620	−	0.592479i	−0.110309	−	0.993897i	$-0.535184\pi$
$59$	−7.88242	−	4.55092i	−1.02620	−	0.592479i	−0.915895	+	0.401418i	$0.868517\pi$
$60$		0			0
$61$	−5.51787	+	3.18575i	−0.706491	+	0.407893i	−0.809761	−	0.586760i	$-0.800403\pi$
$61$	−5.51787	+	3.18575i	−0.706491	+	0.407893i	0.103269	+	0.994653i	$0.467070\pi$
$62$		0			0
$63$	5.93430	−	12.8810i	0.747652	−	1.62285i
$64$		0			0
$65$	11.1742	−	6.45145i	1.38599	−	0.800204i
$66$		0			0
$67$	5.48977	−	9.50857i	0.670683	−	1.16166i	−0.307028	−	0.951700i	$-0.599335\pi$
$67$	5.48977	−	9.50857i	0.670683	−	1.16166i	0.977711	−	0.209956i	$-0.0673321\pi$
$68$		0			0
$69$	0.557419	−	2.54209i	0.0671053	−	0.306032i
$70$		0			0
$71$	6.68558			0.793432			0.396716	−	0.917941i	$-0.370150\pi$
$71$	6.68558			0.793432			0.396716	+	0.917941i	$0.370150\pi$
$72$		0			0
$73$	0.449490			0.0526088			0.0263044	−	0.999654i	$-0.491626\pi$
$73$	0.449490			0.0526088			0.0263044	+	0.999654i	$0.491626\pi$
$74$		0			0
$75$	−1.15042	−	1.04930i	−0.132839	−	0.121162i
$76$		0			0
$77$	−7.99810	+	13.8531i	−0.911468	+	1.57871i
$78$		0			0
$79$	5.93430	−	3.42617i	0.667661	−	0.385474i	−0.127529	−	0.991835i	$-0.540704\pi$
$79$	5.93430	−	3.42617i	0.667661	−	0.385474i	0.795190	+	0.606361i	$0.207371\pi$
$80$		0			0
$81$	3.00000	−	8.48528i	0.333333	−	0.942809i
$82$		0			0
$83$	6.06499	−	3.50162i	0.665719	−	0.384353i	−0.128734	−	0.991679i	$-0.541091\pi$
$83$	6.06499	−	3.50162i	0.665719	−	0.384353i	0.794452	+	0.607326i	$0.207758\pi$
$84$		0			0
$85$	−8.55552	−	4.93953i	−0.927977	−	0.535768i
$86$		0			0
$87$	8.93940	+	8.15359i	0.958404	+	0.874156i
$88$		0			0
$89$			0.142865i			0.0151436i	0.999971	+	0.00757181i	$0.00241020\pi$
$89$			0.142865i			0.0151436i	−0.999971	+	0.00757181i	$0.997590\pi$
$90$		0			0
$91$	30.1207			3.15751
$92$		0			0
$93$	11.5932	+	2.54209i	1.20216	+	0.263603i
$94$		0			0
$95$	1.50255	−	2.60249i	0.154158	−	0.267010i
$96$		0			0
$97$	0.724745	+	1.25529i	0.0735867	+	0.127456i	0.900471	−	0.434916i	$-0.143222\pi$
$97$	0.724745	+	1.25529i	0.0735867	+	0.127456i	−0.826884	+	0.562372i	$0.809889\pi$
$98$		0			0
$99$	−4.24755	+	9.21975i	−0.426895	+	0.926619i
$100$		0			0
$101$	3.03765	+	5.26136i	0.302257	+	0.523525i	0.976647	−	0.214851i	$-0.0689265\pi$
$101$	3.03765	+	5.26136i	0.302257	+	0.523525i	−0.674390	+	0.738376i	$0.735593\pi$
$102$		0			0
$103$	−4.09406	−	2.36371i	−0.403400	−	0.232903i	0.284550	−	0.958661i	$-0.408156\pi$
$103$	−4.09406	−	2.36371i	−0.403400	−	0.232903i	−0.687950	+	0.725758i	$0.741489\pi$
$104$		0			0
$105$	5.02270	+	15.8028i	0.490166	+	1.54219i
$106$		0			0
$107$		−	11.9079i		−	1.15118i	−0.817739	−	0.575590i	$-0.804773\pi$
$107$		−	11.9079i		−	1.15118i	0.817739	−	0.575590i	$-0.195227\pi$
$108$		0			0
$109$		−	4.15122i		−	0.397615i	−0.980039	−	0.198808i	$-0.936293\pi$
$109$		−	4.15122i		−	0.397615i	0.980039	−	0.198808i	$-0.0637069\pi$
$110$		0			0
$111$	1.50255	+	4.72742i	0.142616	+	0.448707i
$112$		0			0
$113$	−6.39898	−	3.69445i	−0.601965	−	0.347545i	0.167849	−	0.985813i	$-0.446318\pi$
$113$	−6.39898	−	3.69445i	−0.601965	−	0.347545i	−0.769814	+	0.638268i	$0.779651\pi$
$114$		0			0
$115$	1.52140	+	2.63515i	0.141872	+	0.245729i
$116$		0			0
$117$	19.0339	−	1.75379i	1.75968	−	0.162138i
$118$		0			0
$119$	−11.5309	−	19.9721i	−1.05704	−	1.83084i
$120$		0			0
$121$	0.224745	−	0.389270i	0.0204314	−	0.0353881i
$122$		0			0
$123$	−9.03284	−	1.98068i	−0.814464	−	0.178592i
$124$		0			0
$125$	11.9460			1.06848
$126$		0			0
$127$			9.45483i			0.838981i	0.907760	+	0.419490i	$0.137791\pi$
$127$			9.45483i			0.838981i	−0.907760	+	0.419490i	$0.862209\pi$
$128$		0			0
$129$	−7.07321	−	6.45145i	−0.622762	−	0.568018i
$130$		0			0
$131$	−10.5168	−	6.07186i	−0.918854	−	0.530501i	−0.0355850	−	0.999367i	$-0.511329\pi$
$131$	−10.5168	−	6.07186i	−0.918854	−	0.530501i	−0.883269	+	0.468866i	$0.844663\pi$
$132$		0			0
$133$	6.07529	−	3.50757i	0.526795	−	0.304145i
$134$		0			0
$135$	4.09406	+	9.69362i	0.352361	+	0.834294i
$136$		0			0
$137$	−9.27526	+	5.35507i	−0.792439	+	0.457515i	−0.840820	−	0.541314i	$-0.817927\pi$
$137$	−9.27526	+	5.35507i	−0.792439	+	0.457515i	0.0483818	+	0.998829i	$0.484594\pi$
$138$		0			0
$139$	3.50559	−	6.07186i	0.297340	−	0.515008i	−0.678186	−	0.734890i	$-0.737234\pi$
$139$	3.50559	−	6.07186i	0.297340	−	0.515008i	0.975527	+	0.219882i	$0.0705671\pi$
$140$		0			0
$141$	−10.4783	−	9.55724i	−0.882435	−	0.804865i
$142$		0			0
$143$	−21.5593			−1.80288
$144$		0			0
$145$	−14.1464			−1.17480
$146$		0			0
$147$	−5.69400	+	25.9674i	−0.469634	+	2.14175i
$148$		0			0
$149$	−3.49278	+	6.04967i	−0.286139	+	0.495608i	−0.972885	−	0.231290i	$-0.925705\pi$
$149$	−3.49278	+	6.04967i	−0.286139	+	0.495608i	0.686745	+	0.726898i	$0.259039\pi$
$150$		0			0
$151$	−2.25382	+	1.30125i	−0.183414	+	0.105894i	−0.588896	−	0.808209i	$-0.700437\pi$
$151$	−2.25382	+	1.30125i	−0.183414	+	0.105894i	0.405482	+	0.914103i	$0.367104\pi$
$152$		0			0
$153$	−8.44949	−	11.9494i	−0.683101	−	0.966050i
$154$		0			0
$155$	−12.0175	+	6.93833i	−0.965272	+	0.557300i
$156$		0			0
$157$	−12.9586	−	7.48163i	−1.03421	−	0.597099i	−0.116019	−	0.993247i	$-0.537013\pi$
$157$	−12.9586	−	7.48163i	−1.03421	−	0.597099i	−0.918187	+	0.396148i	$0.870347\pi$
$158$		0			0
$159$	−8.18813	+	2.60249i	−0.649361	+	0.206391i
$160$		0			0
$161$			7.10318i			0.559809i
$162$		0			0
$163$	−3.63487			−0.284705			−0.142352	−	0.989816i	$-0.545467\pi$
$163$	−3.63487			−0.284705			−0.142352	+	0.989816i	$0.545467\pi$
$164$		0			0
$165$	−3.59506	−	11.3110i	−0.279875	−	0.880562i
$166$		0			0
$167$	−2.59151	+	4.48863i	−0.200537	+	0.347341i	−0.948702	−	0.316173i	$-0.897602\pi$
$167$	−2.59151	+	4.48863i	−0.200537	+	0.347341i	0.748164	+	0.663513i	$0.230935\pi$
$168$		0			0
$169$	13.7980	+	23.8988i	1.06138	+	1.83837i
$170$		0			0
$171$	3.63487	−	2.57024i	0.277965	−	0.196551i
$172$		0			0
$173$	1.01255	+	1.75379i	0.0769827	+	0.133338i	0.901947	−	0.431847i	$-0.142138\pi$
$173$	1.01255	+	1.75379i	0.0769827	+	0.133338i	−0.824964	+	0.565185i	$0.808805\pi$
$174$		0			0
$175$	3.68048	+	2.12493i	0.278218	+	0.160629i
$176$		0			0
$177$	15.3990	+	3.37662i	1.15746	+	0.253802i
$178$		0			0
$179$		−	16.5767i		−	1.23900i	−0.784996	−	0.619501i	$-0.787335\pi$
$179$		−	16.5767i		−	1.23900i	0.784996	−	0.619501i	$-0.212665\pi$
$180$		0			0
$181$			22.6220i			1.68148i	0.541436	+	0.840742i	$0.317881\pi$
$181$			22.6220i			1.68148i	−0.541436	+	0.840742i	$0.682119\pi$
$182$		0			0
$183$	7.43685	−	8.15359i	0.549748	−	0.602731i
$184$		0			0
$185$	−5.02270	−	2.89986i	−0.369277	−	0.213202i
$186$		0			0
$187$	8.25340	+	14.2953i	0.603548	+	1.04538i
$188$		0			0
$189$	−3.03765	+	24.3758i	−0.220956	+	1.77308i
$190$		0			0
$191$	2.59151	+	4.48863i	0.187515	+	0.324786i	0.944421	−	0.328738i	$-0.106623\pi$
$191$	2.59151	+	4.48863i	0.187515	+	0.324786i	−0.756906	+	0.653524i	$0.773290\pi$
$192$		0			0
$193$	−0.376276	+	0.651729i	−0.0270849	+	0.0469124i	−0.879250	−	0.476360i	$-0.841956\pi$
$193$	−0.376276	+	0.651729i	−0.0270849	+	0.0469124i	0.852165	+	0.523273i	$0.175289\pi$
$194$		0			0
$195$	−15.0604	+	16.5118i	−1.07849	+	1.18244i
$196$		0			0
$197$	−18.0213			−1.28396			−0.641982	−	0.766719i	$-0.721888\pi$
$197$	−18.0213			−1.28396			−0.641982	+	0.766719i	$0.721888\pi$
$198$		0			0
$199$		−	2.12493i		−	0.150632i	−0.997160	−	0.0753160i	$-0.976003\pi$
$199$		−	2.12493i		−	0.150632i	0.997160	−	0.0753160i	$-0.0239965\pi$
$200$		0			0
$201$	−4.07321	+	18.5758i	−0.287302	+	1.31024i
$202$		0			0
$203$	−28.5993	−	16.5118i	−2.00728	−	1.15890i
$204$		0			0
$205$	9.36349	−	5.40602i	0.653975	−	0.377572i
$206$		0			0
$207$	0.413584	+	4.48863i	0.0287461	+	0.311982i
$208$		0			0
$209$	−4.34847	+	2.51059i	−0.300790	+	0.173661i
$210$		0			0
$211$	−3.33884	+	5.78304i	−0.229855	+	0.398121i	−0.957765	−	0.287552i	$-0.907159\pi$
$211$	−3.33884	+	5.78304i	−0.229855	+	0.398121i	0.727910	+	0.685673i	$0.240492\pi$
$212$		0			0
$213$	−11.0357	+	3.50757i	−0.756157	+	0.240335i
$214$		0			0
$215$	11.1932			0.763372
$216$		0			0
$217$	−32.3939			−2.19904
$218$		0			0
$219$	−0.741964	+	0.235824i	−0.0501373	+	0.0159355i
$220$		0			0
$221$	15.5411	−	26.9179i	1.04541	−	1.81070i
$222$		0			0
$223$	−15.9627	+	9.21605i	−1.06894	+	0.617152i	−0.927891	−	0.372850i	$-0.878380\pi$
$223$	−15.9627	+	9.21605i	−1.06894	+	0.617152i	−0.141048	+	0.990003i	$0.545047\pi$
$224$		0			0
$225$	2.44949	+	1.12848i	0.163299	+	0.0752323i
$226$		0			0
$227$	17.2862	−	9.98022i	1.14733	−	0.662410i	0.199093	−	0.979981i	$-0.436200\pi$
$227$	17.2862	−	9.98022i	1.14733	−	0.662410i	0.948235	+	0.317570i	$0.102867\pi$
$228$		0			0
$229$	12.9586	+	7.48163i	0.856326	+	0.494400i	0.862780	−	0.505579i	$-0.168721\pi$
$229$	12.9586	+	7.48163i	0.856326	+	0.494400i	−0.00645448	+	0.999979i	$0.502055\pi$
$230$		0			0
$231$	5.93430	−	27.0633i	0.390448	−	1.78063i
$232$		0			0
$233$			9.75663i			0.639178i	0.947556	+	0.319589i	$0.103545\pi$
$233$			9.75663i			0.639178i	−0.947556	+	0.319589i	$0.896455\pi$
$234$		0			0
$235$	16.5818			1.08167
$236$		0			0
$237$	−7.99810	+	8.76893i	−0.519533	+	0.569603i
$238$		0			0
$239$	12.6199	−	21.8583i	0.816312	−	1.41389i	−0.0920698	−	0.995753i	$-0.529348\pi$
$239$	12.6199	−	21.8583i	0.816312	−	1.41389i	0.908382	−	0.418142i	$-0.137318\pi$
$240$		0			0
$241$	4.94949	+	8.57277i	0.318825	+	0.552221i	0.980243	−	0.197797i	$-0.0633786\pi$
$241$	4.94949	+	8.57277i	0.318825	+	0.552221i	−0.661418	+	0.750017i	$0.730045\pi$
$242$		0			0
$243$	−0.500258	+	15.5804i	−0.0320915	+	0.999485i
$244$		0			0
$245$	−15.5411	−	26.9179i	−0.992883	−	1.71972i
$246$		0			0
$247$	8.18813	+	4.72742i	0.520998	+	0.300798i
$248$		0			0
$249$	−8.17423	+	8.96204i	−0.518021	+	0.567946i
$250$		0			0
$251$			18.2037i			1.14901i	0.818503	+	0.574503i	$0.194804\pi$
$251$			18.2037i			1.14901i	−0.818503	+	0.574503i	$0.805196\pi$
$252$		0			0
$253$		−	5.08419i		−	0.319640i
$254$		0			0
$255$	16.7139	+	3.66495i	1.04667	+	0.229508i
$256$		0			0
$257$	−5.05051	−	2.91591i	−0.315042	−	0.181890i	0.334138	−	0.942524i	$-0.391555\pi$
$257$	−5.05051	−	2.91591i	−0.315042	−	0.181890i	−0.649181	+	0.760634i	$0.724888\pi$
$258$		0			0
$259$	−6.76947	−	11.7251i	−0.420635	−	0.728560i
$260$		0			0
$261$	−19.0339	−	8.76893i	−1.17817	−	0.542783i
$262$		0			0
$263$	14.1224	+	24.4608i	0.870826	+	1.50832i	0.861143	+	0.508362i	$0.169749\pi$
$263$	14.1224	+	24.4608i	0.870826	+	1.50832i	0.00968287	+	0.999953i	$0.496918\pi$
$264$		0			0
$265$	5.02270	−	8.69958i	0.308542	−	0.534411i
$266$		0			0
$267$	−0.0749536	−	0.235824i	−0.00458708	−	0.0144322i
$268$		0			0
$269$	−0.910261			−0.0554996			−0.0277498	−	0.999615i	$-0.508834\pi$
$269$	−0.910261			−0.0554996			−0.0277498	+	0.999615i	$0.508834\pi$
$270$		0			0
$271$		−	18.9097i		−	1.14868i	−0.818617	−	0.574340i	$-0.805259\pi$
$271$		−	18.9097i		−	1.14868i	0.818617	−	0.574340i	$-0.194741\pi$
$272$		0			0
$273$	−49.7196	+	15.8028i	−3.00917	+	0.956426i
$274$		0			0
$275$	−2.63435	−	1.52094i	−0.158857	−	0.0917163i
$276$		0			0
$277$	9.11294	−	5.26136i	0.547543	−	0.316124i	−0.200587	−	0.979676i	$-0.564285\pi$
$277$	9.11294	−	5.26136i	0.547543	−	0.316124i	0.748131	+	0.663551i	$0.230952\pi$
$278$		0			0
$279$	−20.4703	+	1.88614i	−1.22553	+	0.112920i
$280$		0			0
$281$	−19.0732	+	11.0119i	−1.13781	+	0.656916i	−0.945888	−	0.324493i	$-0.894806\pi$
$281$	−19.0732	+	11.0119i	−1.13781	+	0.656916i	−0.191925	+	0.981410i	$0.561473\pi$
$282$		0			0
$283$	10.1083	−	17.5081i	0.600877	−	1.04075i	−0.391812	−	0.920045i	$-0.628152\pi$
$283$	10.1083	−	17.5081i	0.600877	−	1.04075i	0.992689	−	0.120704i	$-0.0385151\pi$
$284$		0			0
$285$	−1.11484	+	5.08419i	−0.0660372	+	0.301161i
$286$		0			0
$287$	25.2398			1.48986
$288$		0			0
$289$	−6.79796			−0.399880
$290$		0			0
$291$	−1.85491	−	1.69185i	−0.108737	−	0.0991783i
$292$		0			0
$293$	−1.01255	+	1.75379i	−0.0591537	+	0.102457i	−0.894086	−	0.447896i	$-0.852174\pi$
$293$	−1.01255	+	1.75379i	−0.0591537	+	0.102457i	0.834932	+	0.550353i	$0.185507\pi$
$294$		0			0
$295$	−15.9627	+	9.21605i	−0.929382	+	0.536579i
$296$		0			0
$297$	2.17423	−	17.4473i	0.126162	−	1.01240i
$298$		0			0
$299$	−8.29088	+	4.78674i	−0.479474	+	0.276824i
$300$		0			0
$301$	22.6289	+	13.0648i	1.30431	+	0.753043i
$302$		0			0
$303$	−7.77454	−	7.09113i	−0.446636	−	0.407374i
$304$		0			0
$305$			12.9029i			0.738818i
$306$		0			0
$307$	2.96786			0.169384			0.0846922	−	0.996407i	$-0.473009\pi$
$307$	2.96786			0.169384			0.0846922	+	0.996407i	$0.473009\pi$
$308$		0			0
$309$	7.99810	+	1.75379i	0.454996	+	0.0997694i
$310$		0			0
$311$	−15.6250	+	27.0633i	−0.886011	+	1.53462i	−0.0414609	+	0.999140i	$0.513201\pi$
$311$	−15.6250	+	27.0633i	−0.886011	+	1.53462i	−0.844550	+	0.535476i	$0.820132\pi$
$312$		0			0
$313$	−1.94949	−	3.37662i	−0.110192	−	0.190858i	0.805656	−	0.592384i	$-0.201813\pi$
$313$	−1.94949	−	3.37662i	−0.110192	−	0.190858i	−0.915847	+	0.401526i	$0.868480\pi$
$314$		0			0
$315$	−16.5818	−	23.4501i	−0.934276	−	1.32127i
$316$		0			0
$317$	8.45323	+	14.6414i	0.474781	+	0.822345i	0.999583	−	0.0288797i	$-0.00919399\pi$
$317$	8.45323	+	14.6414i	0.474781	+	0.822345i	−0.524802	+	0.851224i	$0.675861\pi$
$318$		0			0
$319$	20.4703	+	11.8185i	1.14612	+	0.661711i
$320$		0			0
$321$	6.24745	+	19.6561i	0.348699	+	1.09710i
$322$		0			0
$323$		−	7.23907i		−	0.402792i
$324$		0			0
$325$			5.72784i			0.317723i
$326$		0			0
$327$	2.17793	+	6.85234i	0.120440	+	0.378935i
$328$		0			0
$329$	33.5227	+	19.3543i	1.84817	+	1.06704i
$330$		0			0
$331$	16.8778	+	29.2332i	0.927687	+	1.60680i	0.787182	+	0.616721i	$0.211539\pi$
$331$	16.8778	+	29.2332i	0.927687	+	1.60680i	0.140505	+	0.990080i	$0.455127\pi$
$332$		0			0
$333$	−4.96046	−	7.01514i	−0.271831	−	0.384428i
$334$		0			0
$335$	−11.1173	−	19.2558i	−0.607405	−	1.05206i
$336$		0			0
$337$	−0.0505103	+	0.0874863i	−0.00275147	+	0.00476568i	−0.867398	−	0.497615i	$-0.834209\pi$
$337$	−0.0505103	+	0.0874863i	−0.00275147	+	0.00476568i	0.864646	+	0.502381i	$0.167542\pi$
$338$		0			0
$339$	12.5010	+	2.74115i	0.678959	+	0.148879i
$340$		0			0
$341$	23.1863			1.25561
$342$		0			0
$343$		−	39.4667i		−	2.13100i
$344$		0			0
$345$	−3.89388	−	3.55159i	−0.209639	−	0.191211i
$346$		0			0
$347$	9.60805	+	5.54721i	0.515787	+	0.297790i	0.735209	−	0.677840i	$-0.237084\pi$
$347$	9.60805	+	5.54721i	0.515787	+	0.297790i	−0.219422	+	0.975630i	$0.570417\pi$
$348$		0			0
$349$	−17.9190	+	10.3455i	−0.959183	+	0.553784i	−0.895921	−	0.444213i	$-0.853484\pi$
$349$	−17.9190	+	10.3455i	−0.959183	+	0.553784i	−0.0632614	+	0.997997i	$0.520150\pi$
$350$		0			0
$351$	−30.4987	+	12.8810i	−1.62790	+	0.687537i
$352$		0			0
$353$	−4.62372	+	2.66951i	−0.246096	+	0.142084i	−0.617975	−	0.786197i	$-0.712047\pi$
$353$	−4.62372	+	2.66951i	−0.246096	+	0.142084i	0.371879	+	0.928281i	$0.378714\pi$
$354$		0			0
$355$	6.76947	−	11.7251i	0.359286	−	0.622302i
$356$		0			0
$357$	29.5122	+	26.9179i	1.56195	+	1.42465i
$358$		0			0
$359$	−29.7474			−1.57001			−0.785004	−	0.619491i	$-0.787339\pi$
$359$	−29.7474			−1.57001			−0.785004	+	0.619491i	$0.787339\pi$
$360$		0			0
$361$	−16.7980			−0.884103
$362$		0			0
$363$	−0.166753	+	0.760471i	−0.00875224	+	0.0399144i
$364$		0			0
$365$	0.455130	−	0.788309i	0.0238226	−	0.0412620i
$366$		0			0
$367$	10.4419	−	6.02866i	0.545065	−	0.314694i	−0.202064	−	0.979372i	$-0.564765\pi$
$367$	10.4419	−	6.02866i	0.545065	−	0.314694i	0.747129	+	0.664679i	$0.231432\pi$
$368$		0			0
$369$	15.9495	−	1.46959i	0.830297	−	0.0765039i
$370$		0			0
$371$	20.3084	−	11.7251i	1.05436	−	0.608735i
$372$		0			0
$373$	−10.4783	−	6.04967i	−0.542547	−	0.313240i	0.203563	−	0.979062i	$-0.434748\pi$
$373$	−10.4783	−	6.04967i	−0.542547	−	0.313240i	−0.746111	+	0.665822i	$0.768081\pi$
$374$		0			0
$375$	−19.7190	+	6.26745i	−1.01829	+	0.323649i
$376$		0			0
$377$		−	44.5084i		−	2.29230i
$378$		0			0
$379$	7.60324			0.390552			0.195276	−	0.980748i	$-0.437440\pi$
$379$	7.60324			0.390552			0.195276	+	0.980748i	$0.437440\pi$
$380$		0			0
$381$	−4.96046	−	15.6069i	−0.254132	−	0.799566i
$382$		0			0
$383$	−12.2822	+	21.2734i	−0.627591	+	1.08702i	0.360443	+	0.932781i	$0.382625\pi$
$383$	−12.2822	+	21.2734i	−0.627591	+	1.08702i	−0.988034	+	0.154238i	$0.950708\pi$
$384$		0			0
$385$	16.1969	+	28.0539i	0.825472	+	1.42976i
$386$		0			0
$387$	15.0604	+	6.93833i	0.765561	+	0.352695i
$388$		0			0
$389$	12.9586	+	22.4449i	0.657025	+	1.13800i	0.981382	+	0.192066i	$0.0615187\pi$
$389$	12.9586	+	22.4449i	0.657025	+	1.13800i	−0.324357	+	0.945935i	$0.605148\pi$
$390$		0			0
$391$	6.34789	+	3.66495i	0.321026	+	0.185345i
$392$		0			0
$393$	20.5454	+	4.50510i	1.03638	+	0.227252i
$394$		0			0
$395$		−	13.8767i		−	0.698211i
$396$		0			0
$397$		−	23.9094i		−	1.19998i	−0.800009	−	0.599988i	$-0.795172\pi$
$397$		−	23.9094i		−	1.19998i	0.800009	−	0.599988i	$-0.204828\pi$
$398$		0			0
$399$	−8.18813	+	8.97727i	−0.409919	+	0.449426i
$400$		0			0
$401$	−16.6237	−	9.59771i	−0.830149	−	0.479287i	0.0237546	−	0.999718i	$-0.492438\pi$
$401$	−16.6237	−	9.59771i	−0.830149	−	0.479287i	−0.853904	+	0.520431i	$0.825771\pi$
$402$		0			0
$403$	−21.8298	−	37.8104i	−1.08742	−	1.88347i
$404$		0			0
$405$	−11.8437	−	13.8531i	−0.588519	−	0.688367i
$406$		0			0
$407$	4.84534	+	8.39237i	0.240174	+	0.415994i
$408$		0			0
$409$	17.3990	−	30.1359i	0.860324	−	1.49013i	−0.0112920	−	0.999936i	$-0.503594\pi$
$409$	17.3990	−	30.1359i	0.860324	−	1.49013i	0.871616	−	0.490189i	$-0.163072\pi$
$410$		0			0
$411$	12.5010	−	13.7057i	0.616627	−	0.676055i
$412$		0			0
$413$	−43.0282			−2.11728
$414$		0			0
$415$		−	14.1823i		−	0.696179i
$416$		0			0
$417$	−2.60102	+	11.8619i	−0.127373	+	0.580880i
$418$		0			0
$419$	30.8252	+	17.7969i	1.50591	+	0.869437i	0.999976	+	0.00686390i	$0.00218486\pi$
$419$	30.8252	+	17.7969i	1.50591	+	0.869437i	0.505933	+	0.862573i	$0.331148\pi$
$420$		0			0
$421$	−12.7080	+	7.33697i	−0.619350	+	0.357582i	−0.776616	−	0.629974i	$-0.783065\pi$
$421$	−12.7080	+	7.33697i	−0.619350	+	0.357582i	0.157266	+	0.987556i	$0.449732\pi$
$422$		0			0
$423$	22.3106	+	10.2785i	1.08478	+	0.499758i
$424$		0			0
$425$	3.79796	−	2.19275i	0.184228	−	0.106364i
$426$		0			0
$427$	−15.0604	+	26.0853i	−0.728821	+	1.26236i
$428$		0			0
$429$	35.5875	−	11.3110i	1.71818	−	0.546101i
$430$		0			0
$431$	−3.00510			−0.144750			−0.0723752	−	0.997377i	$-0.523058\pi$
$431$	−3.00510			−0.144750			−0.0723752	+	0.997377i	$0.523058\pi$
$432$		0			0
$433$	−26.2474			−1.26137			−0.630686	−	0.776038i	$-0.717226\pi$
$433$	−26.2474			−1.26137			−0.630686	+	0.776038i	$0.717226\pi$
$434$		0			0
$435$	23.3512	−	7.42189i	1.11961	−	0.355852i
$436$		0			0
$437$	−1.11484	+	1.93095i	−0.0533299	+	0.0923701i
$438$		0			0
$439$	10.4419	−	6.02866i	0.498367	−	0.287732i	−0.229672	−	0.973268i	$-0.573765\pi$
$439$	10.4419	−	6.02866i	0.498367	−	0.287732i	0.728039	+	0.685536i	$0.240432\pi$
$440$		0			0
$441$	−4.22474	−	45.8512i	−0.201178	−	2.18339i
$442$		0			0
$443$	−31.7339	+	18.3216i	−1.50772	+	0.870484i	−0.507764	+	0.861496i	$0.669528\pi$
$443$	−31.7339	+	18.3216i	−1.50772	+	0.870484i	−0.999960	+	0.00898805i	$0.997139\pi$
$444$		0			0
$445$	0.250554	+	0.144657i	0.0118774	+	0.00685742i
$446$		0			0
$447$	2.59151	−	11.8185i	0.122574	−	0.558998i
$448$		0			0
$449$			37.8980i			1.78852i	0.447549	+	0.894259i	$0.352297\pi$
$449$			37.8980i			1.78852i	−0.447549	+	0.894259i	$0.647703\pi$
$450$		0			0
$451$	−18.0657			−0.850680
$452$		0			0
$453$	3.03765	−	3.33040i	0.142721	−	0.156476i
$454$		0			0
$455$	30.4987	−	52.8253i	1.42980	−	2.47649i
$456$		0			0
$457$	12.0732	+	20.9114i	0.564761	+	0.978195i	0.997072	+	0.0764703i	$0.0243650\pi$
$457$	12.0732	+	20.9114i	0.564761	+	0.978195i	−0.432311	+	0.901725i	$0.642302\pi$
$458$		0			0
$459$	20.2166	+	15.2916i	0.943631	+	0.713751i
$460$		0			0
$461$	5.51787	+	9.55724i	0.256993	+	0.445125i	0.965435	−	0.260644i	$-0.0839349\pi$
$461$	5.51787	+	9.55724i	0.256993	+	0.445125i	−0.708442	+	0.705769i	$0.750602\pi$
$462$		0			0
$463$	5.93430	+	3.42617i	0.275790	+	0.159228i	0.631516	−	0.775363i	$-0.282433\pi$
$463$	5.93430	+	3.42617i	0.275790	+	0.159228i	−0.355726	+	0.934590i	$0.615766\pi$
$464$		0			0
$465$	16.1969	−	17.7579i	0.751115	−	0.823505i
$466$		0			0
$467$		−	20.7739i		−	0.961302i	−0.876912	−	0.480651i	$-0.840400\pi$
$467$		−	20.7739i		−	0.961302i	0.876912	−	0.480651i	$-0.159600\pi$
$468$		0			0
$469$		−	51.9049i		−	2.39675i
$470$		0			0
$471$	25.3157	+	5.55110i	1.16648	+	0.255781i
$472$		0			0
$473$	−16.1969	−	9.35131i	−0.744736	−	0.429974i
$474$		0			0
$475$	0.667010	+	1.15530i	0.0306045	+	0.0530086i
$476$		0			0
$477$	12.1506	−	8.59176i	0.556337	−	0.393390i
$478$		0			0
$479$	4.43175	+	7.67602i	0.202492	+	0.350726i	0.949331	−	0.314279i	$-0.101763\pi$
$479$	4.43175	+	7.67602i	0.202492	+	0.350726i	−0.746839	+	0.665005i	$0.768429\pi$
$480$		0			0
$481$	9.12372	−	15.8028i	0.416006	−	0.720544i
$482$		0			0
$483$	−3.72666	−	11.7251i	−0.169569	−	0.533509i
$484$		0			0
$485$	2.93536			0.133288
$486$		0			0
$487$			18.9097i			0.856879i	0.903571	+	0.428439i	$0.140936\pi$
$487$			18.9097i			0.856879i	−0.903571	+	0.428439i	$0.859064\pi$
$488$		0			0
$489$	6.00000	−	1.90702i	0.271329	−	0.0862386i
$490$		0			0
$491$	10.1083	+	5.83604i	0.456182	+	0.263377i	0.710437	−	0.703760i	$-0.248497\pi$
$491$	10.1083	+	5.83604i	0.456182	+	0.263377i	−0.254256	+	0.967137i	$0.581830\pi$
$492$		0			0
$493$	−29.5122	+	17.0389i	−1.32916	+	0.767392i
$494$		0			0
$495$	11.8686	+	16.7847i	0.533454	+	0.754418i
$496$		0			0
$497$	27.3712	−	15.8028i	1.22776	−	0.708850i
$498$		0			0
$499$	−14.0767	+	24.3815i	−0.630159	+	1.09147i	0.357360	+	0.933967i	$0.383677\pi$
$499$	−14.0767	+	24.3815i	−0.630159	+	1.09147i	−0.987519	+	0.157500i	$0.949656\pi$
$500$		0			0
$501$	1.92281	−	8.76893i	0.0859048	−	0.391767i
$502$		0			0
$503$	33.4279			1.49048			0.745238	−	0.666799i	$-0.232336\pi$
$503$	33.4279			1.49048			0.745238	+	0.666799i	$0.232336\pi$
$504$		0			0
$505$	12.3031			0.547479
$506$		0			0
$507$	−35.3144	−	32.2102i	−1.56837	−	1.43050i
$508$		0			0
$509$	−11.5932	+	20.0800i	−0.513858	+	0.890028i	0.486013	+	0.873952i	$0.338451\pi$
$509$	−11.5932	+	20.0800i	−0.513858	+	0.890028i	−0.999871	+	0.0160766i	$0.994882\pi$
$510$		0			0
$511$	1.84024	−	1.06246i	0.0814074	−	0.0470006i
$512$		0			0
$513$	−4.65153	+	6.14966i	−0.205370	+	0.271514i
$514$		0			0
$515$	−8.29088	+	4.78674i	−0.365340	+	0.210929i
$516$		0			0
$517$	−23.9943	−	13.8531i	−1.05527	−	0.609260i
$518$		0			0
$519$	−2.59151	−	2.36371i	−0.113755	−	0.103755i
$520$		0			0
$521$		−	27.0771i		−	1.18627i	−0.805103	−	0.593135i	$-0.797890\pi$
$521$		−	27.0771i		−	1.18627i	0.805103	−	0.593135i	$-0.202110\pi$
$522$		0			0
$523$	−36.9820			−1.61711			−0.808554	−	0.588421i	$-0.799750\pi$
$523$	−36.9820			−1.61711			−0.808554	+	0.588421i	$0.799750\pi$
$524$		0			0
$525$	−7.19013	−	1.57662i	−0.313803	−	0.0688092i
$526$		0			0
$527$	−16.7139	+	28.9494i	−0.728071	+	1.26106i
$528$		0			0
$529$	10.3712	+	17.9634i	0.450921	+	0.781017i
$530$		0			0
$531$	−27.1903	+	2.50533i	−1.17996	+	0.108722i
$532$		0			0
$533$	17.0088	+	29.4600i	0.736731	+	1.27606i
$534$		0			0
$535$	−20.8839	−	12.0573i	−0.902890	−	0.521284i
$536$		0			0
$537$	8.69694	+	27.3629i	0.375301	+	1.18079i
$538$		0			0
$539$			51.9348i			2.23699i
$540$		0			0
$541$			43.9568i			1.88985i	0.327287	+	0.944925i	$0.393866\pi$
$541$			43.9568i			1.88985i	−0.327287	+	0.944925i	$0.606134\pi$
$542$		0			0
$543$	−11.8686	−	37.3418i	−0.509331	−	1.60249i
$544$		0			0
$545$	−7.28036	−	4.20332i	−0.311856	−	0.180050i
$546$		0			0
$547$	6.23174	+	10.7937i	0.266450	+	0.461505i	0.967942	−	0.251172i	$-0.0808160\pi$
$547$	6.23174	+	10.7937i	0.266450	+	0.461505i	−0.701493	+	0.712677i	$0.747483\pi$
$548$		0			0
$549$	−7.99810	+	17.3607i	−0.341351	+	0.740936i
$550$		0			0
$551$	−5.18303	−	8.97727i	−0.220804	−	0.382444i
$552$		0			0
$553$	16.1969	−	28.0539i	0.688764	−	1.19297i
$554$		0			0
$555$	9.81228	+	2.15159i	0.416508	+	0.0913299i
$556$		0			0
$557$	−13.0608			−0.553406			−0.276703	−	0.960956i	$-0.589242\pi$
$557$	−13.0608			−0.553406			−0.276703	+	0.960956i	$0.589242\pi$
$558$		0			0
$559$			35.2168i			1.48951i
$560$		0			0
$561$	−21.1237	−	19.2669i	−0.891844	−	0.813447i
$562$		0			0
$563$	9.19959	+	5.31139i	0.387717	+	0.223848i	0.681170	−	0.732125i	$-0.261471\pi$
$563$	9.19959	+	5.31139i	0.387717	+	0.223848i	−0.293454	+	0.955973i	$0.594805\pi$
$564$		0			0
$565$	−12.9586	+	7.48163i	−0.545171	+	0.314754i
$566$		0			0
$567$	−7.77454	−	41.8304i	−0.326500	−	1.75671i
$568$		0			0
$569$	15.7020	−	9.06558i	0.658264	−	0.380049i	−0.133351	−	0.991069i	$-0.542574\pi$
$569$	15.7020	−	9.06558i	0.658264	−	0.380049i	0.791615	+	0.611020i	$0.209241\pi$
$570$		0			0
$571$	8.12412	−	14.0714i	0.339984	−	0.588870i	−0.644445	−	0.764650i	$-0.722912\pi$
$571$	8.12412	−	14.0714i	0.339984	−	0.588870i	0.984429	+	0.175781i	$0.0562450\pi$
$572$		0			0
$573$	−6.63271	−	6.04967i	−0.277085	−	0.252728i
$574$		0			0
$575$	−1.35076			−0.0563306
$576$		0			0
$577$	−6.44949			−0.268496			−0.134248	−	0.990948i	$-0.542862\pi$
$577$	−6.44949			−0.268496			−0.134248	+	0.990948i	$0.542862\pi$
$578$		0			0
$579$	0.279183	−	1.27321i	0.0116024	−	0.0529127i
$580$		0			0
$581$	16.5536	−	28.6717i	0.686760	−	1.18950i
$582$		0			0
$583$	−14.5360	+	8.39237i	−0.602020	+	0.347576i
$584$		0			0
$585$	16.1969	−	35.1571i	0.669661	−	1.45357i
$586$		0			0
$587$	1.20474	−	0.695560i	0.0497251	−	0.0287088i	−0.474931	−	0.880023i	$-0.657527\pi$
$587$	1.20474	−	0.695560i	0.0497251	−	0.0287088i	0.524656	+	0.851314i	$0.324194\pi$
$588$		0			0
$589$	−8.80607	−	5.08419i	−0.362848	−	0.209490i
$590$		0			0
$591$	29.7474	−	9.45483i	1.22364	−	0.388920i
$592$		0			0
$593$		−	2.04989i		−	0.0841788i	−0.999114	−	0.0420894i	$-0.986599\pi$
$593$		−	2.04989i		−	0.0841788i	0.999114	−	0.0420894i	$-0.0134014\pi$
$594$		0			0
$595$	−46.7025			−1.91461
$596$		0			0
$597$	1.11484	+	3.50757i	0.0456272	+	0.143555i
$598$		0			0
$599$	−2.59151	+	4.48863i	−0.105886	+	0.183401i	−0.914100	−	0.405489i	$-0.867101\pi$
$599$	−2.59151	+	4.48863i	−0.105886	+	0.183401i	0.808214	+	0.588889i	$0.200435\pi$
$600$		0			0
$601$	−16.7247	−	28.9681i	−0.682217	−	1.18163i	−0.974303	−	0.225242i	$-0.927683\pi$
$601$	−16.7247	−	28.9681i	−0.682217	−	1.18163i	0.292086	−	0.956392i	$-0.405651\pi$
$602$		0			0
$603$	−3.02218	−	32.7997i	−0.123073	−	1.33571i
$604$		0			0
$605$	−0.455130	−	0.788309i	−0.0185037	−	0.0320493i
$606$		0			0
$607$	−32.3389	−	18.6709i	−1.31260	−	0.757828i	−0.330071	−	0.943956i	$-0.607073\pi$
$607$	−32.3389	−	18.6709i	−1.31260	−	0.757828i	−0.982525	+	0.186128i	$0.940406\pi$
$608$		0			0
$609$	55.8712	+	12.2512i	2.26401	+	0.496442i
$610$		0			0
$611$			52.1706i			2.11060i
$612$		0			0
$613$			1.57662i			0.0636790i	0.999493	+	0.0318395i	$0.0101365\pi$
$613$			1.57662i			0.0636790i	−0.999493	+	0.0318395i	$0.989863\pi$
$614$		0			0
$615$	−12.6199	+	13.8361i	−0.508883	+	0.557927i
$616$		0			0
$617$	10.3763	+	5.99075i	0.417733	+	0.241178i	0.694107	−	0.719872i	$-0.255799\pi$
$617$	10.3763	+	5.99075i	0.417733	+	0.241178i	−0.276374	+	0.961050i	$0.589133\pi$
$618$		0			0
$619$	−16.5443	−	28.6555i	−0.664971	−	1.15176i	−0.979293	−	0.202447i	$-0.935111\pi$
$619$	−16.5443	−	28.6555i	−0.664971	−	1.15176i	0.314323	−	0.949316i	$-0.398223\pi$
$620$		0			0
$621$	−3.03765	−	7.19231i	−0.121897	−	0.288618i
$622$		0			0
$623$	0.337690	+	0.584897i	0.0135293	+	0.0234334i
$624$		0			0
$625$	9.84847	−	17.0580i	0.393939	−	0.682322i
$626$		0			0
$627$	5.86076	−	6.42559i	0.234056	−	0.256614i
$628$		0			0
$629$	−13.9711			−0.557065
$630$		0			0
$631$			46.3190i			1.84393i	0.387271	+	0.921966i	$0.373418\pi$
$631$			46.3190i			1.84393i	−0.387271	+	0.921966i	$0.626582\pi$
$632$		0			0
$633$	2.47730	−	11.2977i	0.0984637	−	0.449041i
$634$		0			0
$635$	16.5818	+	9.57348i	0.658027	+	0.379912i
$636$		0			0
$637$	84.6909	−	48.8963i	3.35558	−	1.93734i
$638$		0			0
$639$	16.3763	−	11.5798i	0.647835	−	0.458088i
$640$		0			0
$641$	29.2980	−	16.9152i	1.15720	−	0.668110i	0.206568	−	0.978432i	$-0.433770\pi$
$641$	29.2980	−	16.9152i	1.15720	−	0.668110i	0.950631	+	0.310323i	$0.100437\pi$
$642$		0			0
$643$	−7.71567	+	13.3639i	−0.304276	+	0.527022i	−0.977100	−	0.212781i	$-0.931748\pi$
$643$	−7.71567	+	13.3639i	−0.304276	+	0.527022i	0.672824	+	0.739803i	$0.265081\pi$
$644$		0			0
$645$	−18.4764	+	5.87250i	−0.727509	+	0.231229i
$646$		0			0
$647$	−49.1288			−1.93145			−0.965725	−	0.259566i	$-0.916420\pi$
$647$	−49.1288			−1.93145			−0.965725	+	0.259566i	$0.916420\pi$
$648$		0			0
$649$	30.7980			1.20893
$650$		0			0
$651$	53.4719	−	16.9954i	2.09573	−	0.666101i
$652$		0			0
$653$	14.0734	−	24.3758i	0.550735	−	0.953900i	−0.447487	−	0.894290i	$-0.647681\pi$
$653$	14.0734	−	24.3758i	0.550735	−	0.953900i	0.998222	−	0.0596098i	$-0.0189857\pi$
$654$		0			0
$655$	−21.2975	+	12.2961i	−0.832162	+	0.480449i
$656$		0			0
$657$	1.10102	−	0.778539i	0.0429549	−	0.0303737i
$658$		0			0
$659$	−2.33832	+	1.35003i	−0.0910881	+	0.0525897i	−0.544852	−	0.838532i	$-0.683414\pi$
$659$	−2.33832	+	1.35003i	−0.0910881	+	0.0525897i	0.453764	+	0.891122i	$0.350081\pi$
$660$		0			0
$661$	33.9152	+	19.5810i	1.31915	+	0.761611i	0.983592	−	0.180409i	$-0.0577420\pi$
$661$	33.9152	+	19.5810i	1.31915	+	0.761611i	0.335557	+	0.942020i	$0.391075\pi$
$662$		0			0
$663$	−11.5309	+	52.5865i	−0.447824	+	2.04229i
$664$		0			0
$665$		−	14.2064i		−	0.550899i
$666$		0			0
$667$	10.4961			0.406412
$668$		0			0
$669$	21.5141	−	23.5875i	0.831782	−	0.911946i
$670$		0			0
$671$	10.7796	−	18.6709i	0.416143	−	0.720781i
$672$		0			0
$673$	2.07321	+	3.59091i	0.0799165	+	0.138419i	0.903214	−	0.429191i	$-0.141201\pi$
$673$	2.07321	+	3.59091i	0.0799165	+	0.138419i	−0.823297	+	0.567611i	$0.807868\pi$
$674$		0			0
$675$	−4.63538	−	0.577648i	−0.178416	−	0.0222337i
$676$		0			0
$677$	−14.0734	−	24.3758i	−0.540885	−	0.936839i	−0.998854	−	0.0478713i	$-0.984756\pi$
$677$	−14.0734	−	24.3758i	−0.540885	−	0.936839i	0.457969	−	0.888968i	$-0.348577\pi$
$678$		0			0
$679$	5.93430	+	3.42617i	0.227738	+	0.131484i
$680$		0			0
$681$	−23.2980	+	25.5433i	−0.892780	+	0.978823i
$682$		0			0
$683$			3.51353i			0.134442i	0.997738	+	0.0672208i	$0.0214132\pi$
$683$			3.51353i			0.134442i	−0.997738	+	0.0672208i	$0.978587\pi$
$684$		0			0
$685$			21.6891i			0.828697i
$686$		0			0
$687$	−25.3157	−	5.55110i	−0.965852	−	0.211788i
$688$		0			0
$689$	27.3712	+	15.8028i	1.04276	+	0.602037i
$690$		0			0
$691$	−6.47344	−	11.2123i	−0.246261	−	0.426537i	0.716224	−	0.697870i	$-0.245869\pi$
$691$	−6.47344	−	11.2123i	−0.246261	−	0.426537i	−0.962486	+	0.271333i	$0.912536\pi$
$692$		0			0
$693$	4.40304	+	47.7862i	0.167258	+	1.81525i
$694$		0			0
$695$	−7.09916	−	12.2961i	−0.269287	−	0.466418i
$696$		0			0
$697$	13.0227	−	22.5560i	0.493270	−	0.854369i
$698$		0			0
$699$	−5.11879	−	16.1051i	−0.193611	−	0.609150i
$700$		0			0
$701$	33.3118			1.25817			0.629085	−	0.777336i	$-0.283430\pi$
$701$	33.3118			1.25817			0.629085	+	0.777336i	$0.283430\pi$
$702$		0			0
$703$		−	4.24985i		−	0.160286i
$704$		0			0
$705$	−27.3712	+	8.69958i	−1.03086	+	0.327645i
$706$		0			0
$707$	24.8726	+	14.3602i	0.935432	+	0.540072i
$708$		0			0
$709$	7.99810	−	4.61771i	0.300375	−	0.173422i	−0.342236	−	0.939614i	$-0.611184\pi$
$709$	7.99810	−	4.61771i	0.300375	−	0.173422i	0.642611	+	0.766192i	$0.277851\pi$
$710$		0			0
$711$	8.60171	−	18.6709i	0.322589	−	0.700213i
$712$		0			0
$713$	8.91658	−	5.14799i	0.333929	−	0.192794i
$714$		0			0
$715$	−21.8298	+	37.8104i	−0.816389	+	1.41403i
$716$		0			0
$717$	−9.36349	+	42.7020i	−0.349686	+	1.59474i
$718$		0			0
$719$	32.7525			1.22146			0.610731	−	0.791838i	$-0.290876\pi$
$719$	32.7525			1.22146			0.610731	+	0.791838i	$0.290876\pi$
$720$		0			0
$721$	−22.3485			−0.832300
$722$		0			0
$723$	−12.6677	−	11.5542i	−0.471117	−	0.429704i
$724$		0			0
$725$	3.13993	−	5.43853i	0.116614	−	0.201982i
$726$		0			0
$727$	25.9910	−	15.0059i	0.963954	−	0.556539i	0.0665663	−	0.997782i	$-0.478796\pi$
$727$	25.9910	−	15.0059i	0.963954	−	0.556539i	0.897388	+	0.441243i	$0.145462\pi$
$728$		0			0
$729$	−7.34847	−	25.9808i	−0.272166	−	0.962250i
$730$		0			0
$731$	23.3512	−	13.4818i	0.863676	−	0.498644i
$732$		0			0
$733$	4.40304	+	2.54209i	0.162630	+	0.0938944i	0.579106	−	0.815252i	$-0.303402\pi$
$733$	4.40304	+	2.54209i	0.162630	+	0.0938944i	−0.416476	+	0.909147i	$0.636735\pi$
$734$		0			0
$735$	39.7758	+	36.2793i	1.46715	+	1.33818i
$736$		0			0
$737$			37.1516i			1.36850i
$738$		0			0
$739$	−12.8719			−0.473502			−0.236751	−	0.971570i	$-0.576083\pi$
$739$	−12.8719			−0.473502			−0.236751	+	0.971570i	$0.576083\pi$
$740$		0			0
$741$	−15.9962	−	3.50757i	−0.587635	−	0.128854i
$742$		0			0
$743$	4.09406	−	7.09113i	0.150197	−	0.260148i	−0.781103	−	0.624402i	$-0.785343\pi$
$743$	4.09406	−	7.09113i	0.150197	−	0.260148i	0.931300	+	0.364254i	$0.118676\pi$
$744$		0			0
$745$	7.07321	+	12.2512i	0.259143	+	0.448848i
$746$		0			0
$747$	8.79114	−	19.0820i	0.321651	−	0.698176i
$748$		0			0
$749$	−28.1468	−	48.7517i	−1.02846	−	1.78135i
$750$		0			0
$751$	−11.4550	−	6.61356i	−0.418000	−	0.241332i	0.276221	−	0.961094i	$-0.410918\pi$
$751$	−11.4550	−	6.61356i	−0.418000	−	0.241332i	−0.694221	+	0.719762i	$0.744251\pi$
$752$		0			0
$753$	−9.55051	−	30.0484i	−0.348040	−	1.09503i
$754$		0			0
$755$			5.27030i			0.191806i
$756$		0			0
$757$			48.3973i			1.75903i	0.475870	+	0.879516i	$0.342133\pi$
$757$			48.3973i			1.75903i	−0.475870	+	0.879516i	$0.657867\pi$
$758$		0			0
$759$	2.66741	+	8.39237i	0.0968208	+	0.304624i
$760$		0			0
$761$	20.9722	+	12.1083i	0.760241	+	0.438926i	0.829382	−	0.558681i	$-0.188693\pi$
$761$	20.9722	+	12.1083i	0.760241	+	0.438926i	−0.0691410	+	0.997607i	$0.522026\pi$
$762$		0			0
$763$	−9.81228	−	16.9954i	−0.355228	−	0.615274i
$764$		0			0
$765$	−29.5122	+	2.71926i	−1.06702	+	0.0983152i
$766$		0			0
$767$	−28.9961	−	50.2228i	−1.04699	−	1.81344i
$768$		0			0
$769$	13.3990	−	23.2077i	0.483180	−	0.836892i	−0.516634	−	0.856206i	$-0.672815\pi$
$769$	13.3990	−	23.2077i	0.483180	−	0.836892i	0.999813	+	0.0193149i	$0.00614850\pi$
$770$		0			0
$771$	9.86660	+	2.16350i	0.355337	+	0.0779166i
$772$		0			0
$773$	−0.910261			−0.0327398			−0.0163699	−	0.999866i	$-0.505211\pi$
$773$	−0.910261			−0.0327398			−0.0163699	+	0.999866i	$0.505211\pi$
$774$		0			0
$775$		−	6.16011i		−	0.221278i
$776$		0			0
$777$	17.3258	+	15.8028i	0.621558	+	0.566921i
$778$		0			0
$779$	6.86127	+	3.96136i	0.245831	+	0.141930i
$780$		0			0
$781$	−19.5913	+	11.3110i	−0.701031	+	0.404740i
$782$		0			0
$783$	36.0194	+	4.48863i	1.28723	+	0.160411i
$784$		0			0
$785$	−26.2423	+	15.1510i	−0.936629	+	0.540763i
$786$		0			0
$787$	−6.47344	+	11.2123i	−0.230753	+	0.399677i	−0.958030	−	0.286668i	$-0.907452\pi$
$787$	−6.47344	+	11.2123i	−0.230753	+	0.399677i	0.727277	+	0.686344i	$0.240786\pi$
$788$		0			0
$789$	−36.1449	−	32.9676i	−1.28679	−	1.17368i
$790$		0			0
$791$	−34.9304			−1.24198
$792$		0			0
$793$	−40.5959			−1.44160
$794$		0			0
$795$	−3.72666	+	16.9954i	−0.132171	+	0.602764i
$796$		0			0
$797$	−12.5034	+	21.6566i	−0.442894	+	0.767115i	−0.997903	−	0.0647294i	$-0.979382\pi$
$797$	−12.5034	+	21.6566i	−0.442894	+	0.767115i	0.555009	+	0.831845i	$0.312715\pi$
$798$		0			0
$799$	34.5927	−	19.9721i	1.22380	−	0.706563i
$800$		0			0
$801$	0.247449	+	0.349945i	0.00874317	+	0.0123647i
$802$		0			0
$803$	−1.31718	+	0.760471i	−0.0464821	+	0.0268365i
$804$		0			0
$805$	12.4575	+	7.19231i	0.439067	+	0.253496i
$806$		0			0
$807$	1.50255	−	0.477566i	0.0528922	−	0.0168111i
$808$		0			0
$809$		−	34.7839i		−	1.22294i	−0.791269	−	0.611468i	$-0.790579\pi$
$809$		−	34.7839i		−	1.22294i	0.791269	−	0.611468i	$-0.209421\pi$
$810$		0			0
$811$	−50.6708			−1.77929			−0.889647	−	0.456650i	$-0.849049\pi$
$811$	−50.6708			−1.77929			−0.889647	+	0.456650i	$0.849049\pi$
$812$		0			0
$813$	9.92091	+	31.2138i	0.347942	+	1.09472i
$814$		0			0
$815$	−3.68048	+	6.37478i	−0.128922	+	0.223299i
$816$		0			0
$817$	4.10102	+	7.10318i	0.143477	+	0.248509i
$818$		0			0
$819$	73.7803	−	52.1706i	2.57809	−	1.82299i
$820$		0			0
$821$	−8.45323	−	14.6414i	−0.295020	−	0.510989i	0.679970	−	0.733240i	$-0.261993\pi$
$821$	−8.45323	−	14.6414i	−0.295020	−	0.510989i	−0.974990	+	0.222251i	$0.928660\pi$
$822$		0			0
$823$	26.8182	+	15.4835i	0.934824	+	0.539721i	0.888334	−	0.459198i	$-0.151863\pi$
$823$	26.8182	+	15.4835i	0.934824	+	0.539721i	0.0464898	+	0.998919i	$0.485196\pi$
$824$		0			0
$825$	5.14643	+	1.12848i	0.179176	+	0.0392888i
$826$		0			0
$827$			11.4362i			0.397677i	0.980032	+	0.198839i	$0.0637170\pi$
$827$			11.4362i			0.397677i	−0.980032	+	0.198839i	$0.936283\pi$
$828$		0			0
$829$		−	1.57662i		−	0.0547582i	−0.999625	−	0.0273791i	$-0.991284\pi$
$829$		−	1.57662i		−	0.0547582i	0.999625	−	0.0273791i	$-0.00871613\pi$
$830$		0			0
$831$	−12.2822	+	13.4659i	−0.426064	+	0.467127i
$832$		0			0
$833$	−64.8434	−	37.4373i	−2.24669	−	1.29713i
$834$		0			0
$835$	5.24807	+	9.08992i	0.181617	+	0.314570i
$836$		0			0
$837$	32.8004	−	13.8531i	1.13375	−	0.478834i
$838$		0			0
$839$	20.4703	+	35.4556i	0.706714	+	1.22406i	0.966069	+	0.258282i	$0.0831565\pi$
$839$	20.4703	+	35.4556i	0.706714	+	1.22406i	−0.259356	+	0.965782i	$0.583510\pi$
$840$		0			0
$841$	−9.89898	+	17.1455i	−0.341344	+	0.591225i
$842$		0			0
$843$	25.7064	−	28.1839i	0.885375	−	0.970704i
$844$		0			0
$845$	55.8844			1.92248
$846$		0			0
$847$		−	2.12493i		−	0.0730133i
$848$		0			0
$849$	−7.50000	+	34.2036i	−0.257399	+	1.17386i
$850$		0			0
$851$	3.72666	+	2.15159i	0.127748	+	0.0737556i
$852$		0			0
$853$	19.2844	−	11.1339i	0.660285	−	0.381216i	−0.132100	−	0.991236i	$-0.542172\pi$
$853$	19.2844	−	11.1339i	0.660285	−	0.381216i	0.792386	+	0.610020i	$0.208839\pi$
$854$		0			0
$855$	−0.827169	−	8.97727i	−0.0282886	−	0.307016i
$856$		0			0
$857$	−46.3207	+	26.7432i	−1.58228	+	0.913532i	−0.587758	+	0.809037i	$0.699989\pi$
$857$	−46.3207	+	26.7432i	−1.58228	+	0.913532i	−0.994525	+	0.104495i	$0.966677\pi$
$858$		0			0
$859$	17.6197	−	30.5183i	0.601178	−	1.04127i	−0.391465	−	0.920193i	$-0.628032\pi$
$859$	17.6197	−	30.5183i	0.601178	−	1.04127i	0.992643	−	0.121078i	$-0.0386351\pi$
$860$		0			0
$861$	−41.6628	+	13.2420i	−1.41986	+	0.451285i
$862$		0			0
$863$	−3.00510			−0.102295			−0.0511474	−	0.998691i	$-0.516288\pi$
$863$	−3.00510			−0.102295			−0.0511474	+	0.998691i	$0.516288\pi$
$864$		0			0
$865$	4.10102			0.139439
$866$		0			0
$867$	11.2213	−	3.56653i	0.381094	−	0.121126i
$868$		0			0
$869$	−11.5932	+	20.0800i	−0.393271	+	0.681166i
$870$		0			0
$871$	60.5838	−	34.9781i	2.05280	−	1.18519i
$872$		0			0
$873$	3.94949	+	1.81954i	0.133670	+	0.0615820i
$874$		0			0
$875$	48.9077	−	28.2369i	1.65338	−	0.954581i
$876$		0			0
$877$	−39.7400	−	22.9439i	−1.34192	−	0.774760i	−0.354834	−	0.934929i	$-0.615462\pi$
$877$	−39.7400	−	22.9439i	−1.34192	−	0.774760i	−0.987089	+	0.160170i	$0.948796\pi$
$878$		0			0
$879$	0.751275	−	3.42617i	0.0253399	−	0.115562i
$880$		0			0
$881$		−	24.0416i		−	0.809983i	−0.914320	−	0.404992i	$-0.867274\pi$
$881$		−	24.0416i		−	0.809983i	0.914320	−	0.404992i	$-0.132726\pi$
$882$		0			0
$883$	−24.9270			−0.838859			−0.419429	−	0.907788i	$-0.637770\pi$
$883$	−24.9270			−0.838859			−0.419429	+	0.907788i	$0.637770\pi$
$884$		0			0
$885$	21.5141	−	23.5875i	0.723188	−	0.792886i
$886$		0			0
$887$	11.1173	−	19.2558i	0.373283	−	0.646546i	−0.616785	−	0.787132i	$-0.711565\pi$
$887$	11.1173	−	19.2558i	0.373283	−	0.646546i	0.990069	+	0.140586i	$0.0448986\pi$
$888$		0			0
$889$	22.3485	+	38.7087i	0.749544	+	1.29825i
$890$		0			0
$891$	5.56473	+	29.9406i	0.186425	+	1.00305i
$892$		0			0
$893$	6.07529	+	10.5227i	0.203302	+	0.352129i
$894$		0			0
$895$	−29.0720	−	16.7847i	−0.971771	−	0.561052i
$896$		0			0
$897$	11.1742	−	12.2512i	0.373097	−	0.409055i
$898$		0			0
$899$			47.8674i			1.59647i
$900$		0			0
$901$		−	24.1987i		−	0.806174i
$902$		0			0
$903$	−44.2075	−	9.69362i	−1.47113	−	0.322583i
$904$		0			0
$905$	39.6742	+	22.9059i	1.31882	+	0.761419i
$906$		0			0
$907$	2.09662	+	3.63144i	0.0696170	+	0.120580i	0.898733	−	0.438497i	$-0.144489\pi$
$907$	2.09662	+	3.63144i	0.0696170	+	0.120580i	−0.829116	+	0.559077i	$0.811156\pi$
$908$		0			0
$909$	16.5536	+	7.62628i	0.549049	+	0.252948i
$910$		0			0
$911$	22.3106	+	38.6430i	0.739182	+	1.28030i	0.952864	+	0.303397i	$0.0981208\pi$
$911$	22.3106	+	38.6430i	0.739182	+	1.28030i	−0.213683	+	0.976903i	$0.568546\pi$
$912$		0			0
$913$	−11.8485	+	20.5222i	−0.392127	+	0.679184i
$914$		0			0
$915$	−6.76947	−	21.2986i	−0.223792	−	0.704108i
$916$		0			0
$917$	−57.4084			−1.89579
$918$		0			0
$919$			14.6598i			0.483583i	0.970328	+	0.241791i	$0.0777350\pi$
$919$			14.6598i			0.483583i	−0.970328	+	0.241791i	$0.922265\pi$
$920$		0			0
$921$	−4.89898	+	1.55708i	−0.161427	+	0.0513075i
$922$		0			0
$923$	36.8902	+	21.2986i	1.21425	+	0.701050i
$924$		0			0
$925$	2.22967	−	1.28730i	0.0733112	−	0.0423263i
$926$		0			0
$927$	−14.1224	+	1.30125i	−0.463841	+	0.0427385i
$928$		0			0
$929$	47.9722	−	27.6968i	1.57392	−	0.908701i	0.578235	−	0.815870i	$-0.303742\pi$
$929$	47.9722	−	27.6968i	1.57392	−	0.908701i	0.995682	−	0.0928307i	$-0.0295915\pi$
$930$		0			0
$931$	11.3880	−	19.7246i	0.373227	−	0.646448i
$932$		0			0
$933$	11.5932	−	52.8704i	0.379543	−	1.73090i
$934$		0			0
$935$	33.4279			1.09321
$936$		0			0
$937$	−37.1464			−1.21352			−0.606760	−	0.794885i	$-0.707531\pi$
$937$	−37.1464			−1.21352			−0.606760	+	0.794885i	$0.707531\pi$
$938$		0			0
$939$	4.98952	+	4.55092i	0.162827	+	0.148514i
$940$		0			0
$941$	5.97300	−	10.3455i	0.194714	−	0.337255i	−0.752092	−	0.659058i	$-0.770955\pi$
$941$	5.97300	−	10.3455i	0.194714	−	0.337255i	0.946807	+	0.321802i	$0.104289\pi$
$942$		0			0
$943$	−6.94737	+	4.01107i	−0.226238	+	0.130618i
$944$		0			0
$945$	39.6742	+	30.0091i	1.29060	+	0.976196i
$946$		0			0
$947$	−6.15679	+	3.55462i	−0.200069	+	0.115510i	−0.596687	−	0.802474i	$-0.703517\pi$
$947$	−6.15679	+	3.55462i	−0.200069	+	0.115510i	0.396619	+	0.917983i	$0.370183\pi$
$948$		0			0
$949$	2.48023	+	1.43196i	0.0805116	+	0.0464834i
$950$		0			0
$951$	−21.6352	−	19.7333i	−0.701569	−	0.639898i
$952$		0			0
$953$			27.5699i			0.893078i	0.894764	+	0.446539i	$0.147344\pi$
$953$			27.5699i			0.893078i	−0.894764	+	0.446539i	$0.852656\pi$
$954$		0			0
$955$	10.4961			0.339647
$956$		0			0
$957$	−39.9905	−	8.76893i	−1.29271	−	0.283459i
$958$		0			0
$959$	−25.3157	+	43.8480i	−0.817485	+	1.41593i
$960$		0			0
$961$	7.97730	+	13.8171i	0.257332	+	0.445712i
$962$		0			0
$963$	−20.6251	−	29.1683i	−0.664634	−	0.939934i
$964$		0			0
$965$	0.761995	+	1.31981i	0.0245295	+	0.0424863i
$966$		0			0
$967$	−34.1792	−	19.7333i	−1.09913	−	0.634582i	−0.163136	−	0.986604i	$-0.552161\pi$
$967$	−34.1792	−	19.7333i	−1.09913	−	0.634582i	−0.935992	+	0.352022i	$0.885494\pi$
$968$		0			0
$969$	3.79796	+	11.9494i	0.122008	+	0.383869i
$970$		0			0
$971$		−	15.7394i		−	0.505102i	−0.967584	−	0.252551i	$-0.918730\pi$
$971$		−	15.7394i		−	0.505102i	0.967584	−	0.252551i	$-0.0812696\pi$
$972$		0			0
$973$		−	33.1448i		−	1.06257i
$974$		0			0
$975$	−3.00510	−	9.45483i	−0.0962402	−	0.302797i
$976$		0			0
$977$	−9.94949	−	5.74434i	−0.318312	−	0.183778i	0.332328	−	0.943164i	$-0.392166\pi$
$977$	−9.94949	−	5.74434i	−0.318312	−	0.183778i	−0.650640	+	0.759386i	$0.725499\pi$
$978$		0			0
$979$	−0.241706	−	0.418647i	−0.00772496	−	0.0133800i
$980$		0			0
$981$	−7.19013	−	10.1684i	−0.229563	−	0.324651i
$982$		0			0
$983$	−4.43175	−	7.67602i	−0.141351	−	0.244827i	0.786655	−	0.617393i	$-0.211811\pi$
$983$	−4.43175	−	7.67602i	−0.141351	−	0.244827i	−0.928006	+	0.372566i	$0.878478\pi$
$984$		0			0
$985$	−18.2474	+	31.6055i	−0.581412	+	1.00704i
$986$		0			0
$987$	−65.4895	−	14.3602i	−2.08455	−	0.457091i
$988$		0			0
$989$	−8.30497			−0.264083
$990$		0			0
$991$			42.0692i			1.33637i	0.743994	+	0.668186i	$0.232929\pi$
$991$			42.0692i			1.33637i	−0.743994	+	0.668186i	$0.767071\pi$
$992$		0			0
$993$	−43.1969	−	39.3997i	−1.37081	−	1.25031i
$994$		0			0
$995$	−3.72666	−	2.15159i	−0.118143	−	0.0682100i
$996$		0			0
$997$	−35.0301	+	20.2246i	−1.10941	+	0.640520i	−0.938677	−	0.344797i	$-0.887948\pi$
$997$	−35.0301	+	20.2246i	−1.10941	+	0.640520i	−0.170736	+	0.985317i	$0.554614\pi$
$998$		0			0
$999$	11.8686	+	8.97727i	0.375506	+	0.284028i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.p.d.959.2	yes	16
3.2	odd	2		3456.2.p.d.2879.4		16
4.3	odd	2	inner	1152.2.p.d.959.8	yes	16
8.3	odd	2	inner	1152.2.p.d.959.1	yes	16
8.5	even	2	inner	1152.2.p.d.959.7	yes	16
9.2	odd	6	inner	1152.2.p.d.191.1	✓	16
9.7	even	3		3456.2.p.d.575.5		16
12.11	even	2		3456.2.p.d.2879.3		16
24.5	odd	2		3456.2.p.d.2879.6		16
24.11	even	2		3456.2.p.d.2879.5		16
36.7	odd	6		3456.2.p.d.575.6		16
36.11	even	6	inner	1152.2.p.d.191.7	yes	16
72.11	even	6	inner	1152.2.p.d.191.2	yes	16
72.29	odd	6	inner	1152.2.p.d.191.8	yes	16
72.43	odd	6		3456.2.p.d.575.4		16
72.61	even	6		3456.2.p.d.575.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.p.d.191.1	✓	16	9.2	odd	6	inner
1152.2.p.d.191.2	yes	16	72.11	even	6	inner
1152.2.p.d.191.7	yes	16	36.11	even	6	inner
1152.2.p.d.191.8	yes	16	72.29	odd	6	inner
1152.2.p.d.959.1	yes	16	8.3	odd	2	inner
1152.2.p.d.959.2	yes	16	1.1	even	1	trivial
1152.2.p.d.959.7	yes	16	8.5	even	2	inner
1152.2.p.d.959.8	yes	16	4.3	odd	2	inner
3456.2.p.d.575.3		16	72.61	even	6
3456.2.p.d.575.4		16	72.43	odd	6
3456.2.p.d.575.5		16	9.7	even	3
3456.2.p.d.575.6		16	36.7	odd	6
3456.2.p.d.2879.3		16	12.11	even	2
3456.2.p.d.2879.4		16	3.2	odd	2
3456.2.p.d.2879.5		16	24.11	even	2
3456.2.p.d.2879.6		16	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.65068 + 0.524648i) q^{3} +(1.01255 - 1.75379i) q^{5} +(4.09406 - 2.36371i) q^{7} +(2.44949 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(-1.65068 + 0.524648i) q^{3} +(1.01255 - 1.75379i) q^{5} +(4.09406 - 2.36371i) q^{7} +(2.44949 - 1.73205i) q^{9} +(-2.93038 + 1.69185i) q^{11} +(5.51787 + 3.18575i) q^{13} +(-0.751275 + 3.42617i) q^{15} -4.87832i q^{17} +1.48393 q^{19} +(-5.51787 + 6.04967i) q^{21} +(-0.751275 + 1.30125i) q^{23} +(0.449490 + 0.778539i) q^{25} +(-3.13461 + 4.14418i) q^{27} +(-3.49278 - 6.04967i) q^{29} +(-5.93430 - 3.42617i) q^{31} +(3.94949 - 4.33013i) q^{33} -9.57348i q^{35} -2.86392i q^{37} +(-10.7796 - 2.36371i) q^{39} +(4.62372 + 2.66951i) q^{41} +(2.76363 + 4.78674i) q^{43} +(-0.557419 - 6.04967i) q^{45} +(4.09406 + 7.09113i) q^{47} +(7.67423 - 13.2922i) q^{49} +(2.55940 + 8.05254i) q^{51} +4.96046 q^{53} +6.85234i q^{55} +(-2.44949 + 0.778539i) q^{57} +(-7.88242 - 4.55092i) q^{59} +(-5.51787 + 3.18575i) q^{61} +(5.93430 - 12.8810i) q^{63} +(11.1742 - 6.45145i) q^{65} +(5.48977 - 9.50857i) q^{67} +(0.557419 - 2.54209i) q^{69} +6.68558 q^{71} +0.449490 q^{73} +(-1.15042 - 1.04930i) q^{75} +(-7.99810 + 13.8531i) q^{77} +(5.93430 - 3.42617i) q^{79} +(3.00000 - 8.48528i) q^{81} +(6.06499 - 3.50162i) q^{83} +(-8.55552 - 4.93953i) q^{85} +(8.93940 + 8.15359i) q^{87} +0.142865i q^{89} +30.1207 q^{91} +(11.5932 + 2.54209i) q^{93} +(1.50255 - 2.60249i) q^{95} +(0.724745 + 1.25529i) q^{97} +(-4.24755 + 9.21975i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 32 q^{25} + 24 q^{33} - 24 q^{41} + 64 q^{49} + 120 q^{65} - 32 q^{73} + 48 q^{81} - 8 q^{97}+O(q^{100}) \) 16 * q - 32 * q^25 + 24 * q^33 - 24 * q^41 + 64 * q^49 + 120 * q^65 - 32 * q^73 + 48 * q^81 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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