LMFDB - Embedded newform 2646.2.e.t.2125.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(1549,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 2]))

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

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

chi := DirichletCharacter("2646.1549");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 882)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2125.1
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	2646.2125
Dual form			2646.2.e.t.1549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +(-0.965926 + 1.67303i) q^{5} +1.00000 q^{8} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{4} +(-0.965926 + 1.67303i) q^{5} +1.00000 q^{8} +(-0.965926 + 1.67303i) q^{10} +(2.73205 + 4.73205i) q^{11} +(-1.22474 - 2.12132i) q^{13} +1.00000 q^{16} +(3.15660 - 5.46739i) q^{17} +(0.965926 + 1.67303i) q^{19} +(-0.965926 + 1.67303i) q^{20} +(2.73205 + 4.73205i) q^{22} +(-2.96410 + 5.13397i) q^{23} +(0.633975 + 1.09808i) q^{25} +(-1.22474 - 2.12132i) q^{26} +(-0.366025 + 0.633975i) q^{29} -7.34847 q^{31} +1.00000 q^{32} +(3.15660 - 5.46739i) q^{34} +(4.00000 + 6.92820i) q^{37} +(0.965926 + 1.67303i) q^{38} +(-0.965926 + 1.67303i) q^{40} +(2.82843 + 4.89898i) q^{41} +(0.901924 - 1.56218i) q^{43} +(2.73205 + 4.73205i) q^{44} +(-2.96410 + 5.13397i) q^{46} +9.52056 q^{47} +(0.633975 + 1.09808i) q^{50} +(-1.22474 - 2.12132i) q^{52} +(1.63397 - 2.83013i) q^{53} -10.5558 q^{55} +(-0.366025 + 0.633975i) q^{58} -5.00052 q^{59} -2.96713 q^{61} -7.34847 q^{62} +1.00000 q^{64} +4.73205 q^{65} -14.1962 q^{67} +(3.15660 - 5.46739i) q^{68} +11.1962 q^{71} +(-4.76028 + 8.24504i) q^{73} +(4.00000 + 6.92820i) q^{74} +(0.965926 + 1.67303i) q^{76} -10.1244 q^{79} +(-0.965926 + 1.67303i) q^{80} +(2.82843 + 4.89898i) q^{82} +(-4.94975 + 8.57321i) q^{83} +(6.09808 + 10.5622i) q^{85} +(0.901924 - 1.56218i) q^{86} +(2.73205 + 4.73205i) q^{88} +(6.64136 + 11.5032i) q^{89} +(-2.96410 + 5.13397i) q^{92} +9.52056 q^{94} -3.73205 q^{95} +(-1.93185 + 3.34607i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^4 + 8 * q^8	$ 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8} + 8 q^{11} + 8 q^{16} + 8 q^{22} + 4 q^{23} + 12 q^{25} + 4 q^{29} + 8 q^{32} + 32 q^{37} + 28 q^{43} + 8 q^{44} + 4 q^{46} + 12 q^{50} + 20 q^{53} + 4 q^{58} + 8 q^{64} + 24 q^{65} - 72 q^{67} + 48 q^{71} + 32 q^{74} + 16 q^{79} + 28 q^{85} + 28 q^{86} + 8 q^{88} + 4 q^{92} - 16 q^{95}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^4 + 8 * q^8 + 8 * q^11 + 8 * q^16 + 8 * q^22 + 4 * q^23 + 12 * q^25 + 4 * q^29 + 8 * q^32 + 32 * q^37 + 28 * q^43 + 8 * q^44 + 4 * q^46 + 12 * q^50 + 20 * q^53 + 4 * q^58 + 8 * q^64 + 24 * q^65 - 72 * q^67 + 48 * q^71 + 32 * q^74 + 16 * q^79 + 28 * q^85 + 28 * q^86 + 8 * q^88 + 4 * q^92 - 16 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−0.965926	+	1.67303i	−0.431975	+	0.748203i	−0.997043	−	0.0768413i	$-0.975517\pi$
$5$	−0.965926	+	1.67303i	−0.431975	+	0.748203i	0.565068	+	0.825044i	$0.308850\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.965926	+	1.67303i	−0.305453	+	0.529059i
$11$	2.73205	+	4.73205i	0.823744	+	1.42677i	0.902875	+	0.429903i	$0.141452\pi$
$11$	2.73205	+	4.73205i	0.823744	+	1.42677i	−0.0791309	+	0.996864i	$0.525215\pi$
$12$		0			0
$13$	−1.22474	−	2.12132i	−0.339683	−	0.588348i	0.644690	−	0.764444i	$-0.276986\pi$
$13$	−1.22474	−	2.12132i	−0.339683	−	0.588348i	−0.984373	+	0.176096i	$0.943653\pi$
$14$		0			0
$15$		0			0
$16$	1.00000			0.250000
$17$	3.15660	−	5.46739i	0.765587	−	1.32604i	−0.174349	−	0.984684i	$-0.555782\pi$
$17$	3.15660	−	5.46739i	0.765587	−	1.32604i	0.939936	−	0.341352i	$-0.110885\pi$
$18$		0			0
$19$	0.965926	+	1.67303i	0.221599	+	0.383820i	0.955294	−	0.295659i	$-0.0955392\pi$
$19$	0.965926	+	1.67303i	0.221599	+	0.383820i	−0.733695	+	0.679479i	$0.762206\pi$
$20$	−0.965926	+	1.67303i	−0.215988	+	0.374101i
$21$		0			0
$22$	2.73205	+	4.73205i	0.582475	+	1.00888i
$23$	−2.96410	+	5.13397i	−0.618058	+	1.07051i	0.371782	+	0.928320i	$0.378747\pi$
$23$	−2.96410	+	5.13397i	−0.618058	+	1.07051i	−0.989840	+	0.142188i	$0.954586\pi$
$24$		0			0
$25$	0.633975	+	1.09808i	0.126795	+	0.219615i
$26$	−1.22474	−	2.12132i	−0.240192	−	0.416025i
$27$		0			0
$28$		0			0
$29$	−0.366025	+	0.633975i	−0.0679692	+	0.117726i	−0.898007	−	0.439981i	$-0.854985\pi$
$29$	−0.366025	+	0.633975i	−0.0679692	+	0.117726i	0.830038	+	0.557707i	$0.188319\pi$
$30$		0			0
$31$	−7.34847			−1.31982			−0.659912	−	0.751343i	$-0.729406\pi$
$31$	−7.34847			−1.31982			−0.659912	+	0.751343i	$0.729406\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	3.15660	−	5.46739i	0.541352	−	0.937649i
$35$		0			0
$36$		0			0
$37$	4.00000	+	6.92820i	0.657596	+	1.13899i	0.981236	+	0.192809i	$0.0617599\pi$
$37$	4.00000	+	6.92820i	0.657596	+	1.13899i	−0.323640	+	0.946180i	$0.604907\pi$
$38$	0.965926	+	1.67303i	0.156694	+	0.271402i
$39$		0			0
$40$	−0.965926	+	1.67303i	−0.152726	+	0.264530i
$41$	2.82843	+	4.89898i	0.441726	+	0.765092i	0.997818	−	0.0660290i	$-0.0210330\pi$
$41$	2.82843	+	4.89898i	0.441726	+	0.765092i	−0.556092	+	0.831121i	$0.687700\pi$
$42$		0			0
$43$	0.901924	−	1.56218i	0.137542	−	0.238230i	−0.789024	−	0.614363i	$-0.789413\pi$
$43$	0.901924	−	1.56218i	0.137542	−	0.238230i	0.926566	+	0.376133i	$0.122746\pi$
$44$	2.73205	+	4.73205i	0.411872	+	0.713384i
$45$		0			0
$46$	−2.96410	+	5.13397i	−0.437033	+	0.756963i
$47$	9.52056			1.38872			0.694358	−	0.719630i	$-0.255688\pi$
$47$	9.52056			1.38872			0.694358	+	0.719630i	$0.255688\pi$
$48$		0			0
$49$		0			0
$50$	0.633975	+	1.09808i	0.0896575	+	0.155291i
$51$		0			0
$52$	−1.22474	−	2.12132i	−0.169842	−	0.294174i
$53$	1.63397	−	2.83013i	0.224444	−	0.388748i	−0.731709	−	0.681617i	$-0.761277\pi$
$53$	1.63397	−	2.83013i	0.224444	−	0.388748i	0.956152	+	0.292870i	$0.0946102\pi$
$54$		0			0
$55$	−10.5558			−1.42335
$56$		0			0
$57$		0			0
$58$	−0.366025	+	0.633975i	−0.0480615	+	0.0832449i
$59$	−5.00052			−0.651012			−0.325506	−	0.945540i	$-0.605535\pi$
$59$	−5.00052			−0.651012			−0.325506	+	0.945540i	$0.605535\pi$
$60$		0			0
$61$	−2.96713			−0.379902			−0.189951	−	0.981794i	$-0.560833\pi$
$61$	−2.96713			−0.379902			−0.189951	+	0.981794i	$0.560833\pi$
$62$	−7.34847			−0.933257
$63$		0			0
$64$	1.00000			0.125000
$65$	4.73205			0.586939
$66$		0			0
$67$	−14.1962			−1.73434			−0.867168	−	0.498016i	$-0.834062\pi$
$67$	−14.1962			−1.73434			−0.867168	+	0.498016i	$0.834062\pi$
$68$	3.15660	−	5.46739i	0.382794	−	0.663018i
$69$		0			0
$70$		0			0
$71$	11.1962			1.32874			0.664369	−	0.747404i	$-0.268700\pi$
$71$	11.1962			1.32874			0.664369	+	0.747404i	$0.268700\pi$
$72$		0			0
$73$	−4.76028	+	8.24504i	−0.557148	+	0.965009i	0.440584	+	0.897711i	$0.354771\pi$
$73$	−4.76028	+	8.24504i	−0.557148	+	0.965009i	−0.997733	+	0.0672983i	$0.978562\pi$
$74$	4.00000	+	6.92820i	0.464991	+	0.805387i
$75$		0			0
$76$	0.965926	+	1.67303i	0.110799	+	0.191910i
$77$		0			0
$78$		0			0
$79$	−10.1244			−1.13908			−0.569540	−	0.821964i	$-0.692878\pi$
$79$	−10.1244			−1.13908			−0.569540	+	0.821964i	$0.692878\pi$
$80$	−0.965926	+	1.67303i	−0.107994	+	0.187051i
$81$		0			0
$82$	2.82843	+	4.89898i	0.312348	+	0.541002i
$83$	−4.94975	+	8.57321i	−0.543305	+	0.941033i	0.455406	+	0.890284i	$0.349494\pi$
$83$	−4.94975	+	8.57321i	−0.543305	+	0.941033i	−0.998711	+	0.0507487i	$0.983839\pi$
$84$		0			0
$85$	6.09808	+	10.5622i	0.661429	+	1.14563i
$86$	0.901924	−	1.56218i	0.0972569	−	0.168454i
$87$		0			0
$88$	2.73205	+	4.73205i	0.291238	+	0.504438i
$89$	6.64136	+	11.5032i	0.703983	+	1.21933i	0.967057	+	0.254559i	$0.0819302\pi$
$89$	6.64136	+	11.5032i	0.703983	+	1.21933i	−0.263074	+	0.964776i	$0.584736\pi$
$90$		0			0
$91$		0			0
$92$	−2.96410	+	5.13397i	−0.309029	+	0.535254i
$93$		0			0
$94$	9.52056			0.981971
$95$	−3.73205			−0.382900
$96$		0			0
$97$	−1.93185	+	3.34607i	−0.196150	+	0.339741i	−0.947277	−	0.320416i	$-0.896177\pi$
$97$	−1.93185	+	3.34607i	−0.196150	+	0.339741i	0.751127	+	0.660158i	$0.229511\pi$
$98$		0			0
$99$		0			0
$100$	0.633975	+	1.09808i	0.0633975	+	0.109808i
$101$	−0.776457	−	1.34486i	−0.0772604	−	0.133819i	0.824807	−	0.565415i	$-0.191284\pi$
$101$	−0.776457	−	1.34486i	−0.0772604	−	0.133819i	−0.902067	+	0.431596i	$0.857951\pi$
$102$		0			0
$103$	−4.19187	+	7.26054i	−0.413037	+	0.715402i	−0.995220	−	0.0976561i	$-0.968865\pi$
$103$	−4.19187	+	7.26054i	−0.413037	+	0.715402i	0.582183	+	0.813058i	$0.302199\pi$
$104$	−1.22474	−	2.12132i	−0.120096	−	0.208013i
$105$		0			0
$106$	1.63397	−	2.83013i	0.158706	−	0.274886i
$107$	8.46410	+	14.6603i	0.818256	+	1.41726i	0.906966	+	0.421203i	$0.138392\pi$
$107$	8.46410	+	14.6603i	0.818256	+	1.41726i	−0.0887109	+	0.996057i	$0.528275\pi$
$108$		0			0
$109$	10.2942	−	17.8301i	0.986008	−	1.70782i	0.348641	−	0.937256i	$-0.386643\pi$
$109$	10.2942	−	17.8301i	0.986008	−	1.70782i	0.637367	−	0.770560i	$-0.280023\pi$
$110$	−10.5558			−1.00646
$111$		0			0
$112$		0			0
$113$	1.33013	+	2.30385i	0.125128	+	0.216728i	0.921783	−	0.387706i	$-0.126733\pi$
$113$	1.33013	+	2.30385i	0.125128	+	0.216728i	−0.796655	+	0.604434i	$0.793399\pi$
$114$		0			0
$115$	−5.72620	−	9.91808i	−0.533971	−	0.924865i
$116$	−0.366025	+	0.633975i	−0.0339846	+	0.0588631i
$117$		0			0
$118$	−5.00052			−0.460335
$119$		0			0
$120$		0			0
$121$	−9.42820	+	16.3301i	−0.857109	+	1.48456i
$122$	−2.96713			−0.268631
$123$		0			0
$124$	−7.34847			−0.659912
$125$	−12.1087			−1.08304
$126$		0			0
$127$	7.92820			0.703514			0.351757	−	0.936091i	$-0.385584\pi$
$127$	7.92820			0.703514			0.351757	+	0.936091i	$0.385584\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	4.73205			0.415028
$131$	0.120118	−	0.208051i	0.0104948	−	0.0181775i	−0.860730	−	0.509061i	$-0.829993\pi$
$131$	0.120118	−	0.208051i	0.0104948	−	0.0181775i	0.871225	+	0.490884i	$0.163326\pi$
$132$		0			0
$133$		0			0
$134$	−14.1962			−1.22636
$135$		0			0
$136$	3.15660	−	5.46739i	0.270676	−	0.468824i
$137$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$137$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$138$		0			0
$139$	−0.915158	−	1.58510i	−0.0776227	−	0.134446i	0.824601	−	0.565715i	$-0.191400\pi$
$139$	−0.915158	−	1.58510i	−0.0776227	−	0.134446i	−0.902224	+	0.431268i	$0.858066\pi$
$140$		0			0
$141$		0			0
$142$	11.1962			0.939560
$143$	6.69213	−	11.5911i	0.559624	−	0.969297i
$144$		0			0
$145$	−0.707107	−	1.22474i	−0.0587220	−	0.101710i
$146$	−4.76028	+	8.24504i	−0.393963	+	0.682365i
$147$		0			0
$148$	4.00000	+	6.92820i	0.328798	+	0.569495i
$149$	9.19615	−	15.9282i	0.753378	−	1.30489i	−0.192798	−	0.981238i	$-0.561756\pi$
$149$	9.19615	−	15.9282i	0.753378	−	1.30489i	0.946177	−	0.323651i	$-0.104910\pi$
$150$		0			0
$151$	−1.69615	−	2.93782i	−0.138031	−	0.239077i	0.788720	−	0.614752i	$-0.210744\pi$
$151$	−1.69615	−	2.93782i	−0.138031	−	0.239077i	−0.926751	+	0.375676i	$0.877411\pi$
$152$	0.965926	+	1.67303i	0.0783469	+	0.135701i
$153$		0			0
$154$		0			0
$155$	7.09808	−	12.2942i	0.570131	−	0.987496i
$156$		0			0
$157$	24.3562			1.94384			0.971918	−	0.235320i	$-0.0756137\pi$
$157$	24.3562			1.94384			0.971918	+	0.235320i	$0.0756137\pi$
$158$	−10.1244			−0.805450
$159$		0			0
$160$	−0.965926	+	1.67303i	−0.0763631	+	0.132265i
$161$		0			0
$162$		0			0
$163$	10.4641	+	18.1244i	0.819612	+	1.41961i	0.905969	+	0.423345i	$0.139144\pi$
$163$	10.4641	+	18.1244i	0.819612	+	1.41961i	−0.0863569	+	0.996264i	$0.527523\pi$
$164$	2.82843	+	4.89898i	0.220863	+	0.382546i
$165$		0			0
$166$	−4.94975	+	8.57321i	−0.384175	+	0.665410i
$167$	−8.05558	−	13.9527i	−0.623359	−	1.07969i	−0.988856	−	0.148877i	$-0.952434\pi$
$167$	−8.05558	−	13.9527i	−0.623359	−	1.07969i	0.365497	−	0.930813i	$-0.380899\pi$
$168$		0			0
$169$	3.50000	−	6.06218i	0.269231	−	0.466321i
$170$	6.09808	+	10.5622i	0.467701	+	0.810082i
$171$		0			0
$172$	0.901924	−	1.56218i	0.0687710	−	0.119115i
$173$	14.5211			1.10402			0.552008	−	0.833839i	$-0.313862\pi$
$173$	14.5211			1.10402			0.552008	+	0.833839i	$0.313862\pi$
$174$		0			0
$175$		0			0
$176$	2.73205	+	4.73205i	0.205936	+	0.356692i
$177$		0			0
$178$	6.64136	+	11.5032i	0.497791	+	0.862200i
$179$	1.09808	−	1.90192i	0.0820741	−	0.142156i	−0.822067	−	0.569391i	$-0.807179\pi$
$179$	1.09808	−	1.90192i	0.0820741	−	0.142156i	0.904141	+	0.427235i	$0.140512\pi$
$180$		0			0
$181$	−8.72552			−0.648563			−0.324281	−	0.945961i	$-0.605122\pi$
$181$	−8.72552			−0.648563			−0.324281	+	0.945961i	$0.605122\pi$
$182$		0			0
$183$		0			0
$184$	−2.96410	+	5.13397i	−0.218516	+	0.378482i
$185$	−15.4548			−1.13626
$186$		0			0
$187$	34.4959			2.52259
$188$	9.52056			0.694358
$189$		0			0
$190$	−3.73205			−0.270751
$191$	−3.19615			−0.231265			−0.115633	−	0.993292i	$-0.536890\pi$
$191$	−3.19615			−0.231265			−0.115633	+	0.993292i	$0.536890\pi$
$192$		0			0
$193$	−20.2679			−1.45892			−0.729459	−	0.684024i	$-0.760228\pi$
$193$	−20.2679			−1.45892			−0.729459	+	0.684024i	$0.760228\pi$
$194$	−1.93185	+	3.34607i	−0.138699	+	0.240233i
$195$		0			0
$196$		0			0
$197$	7.66025			0.545771			0.272885	−	0.962047i	$-0.412022\pi$
$197$	7.66025			0.545771			0.272885	+	0.962047i	$0.412022\pi$
$198$		0			0
$199$	1.55291	−	2.68973i	0.110083	−	0.190670i	−0.805720	−	0.592296i	$-0.798222\pi$
$199$	1.55291	−	2.68973i	0.110083	−	0.190670i	0.915804	+	0.401626i	$0.131555\pi$
$200$	0.633975	+	1.09808i	0.0448288	+	0.0776457i
$201$		0			0
$202$	−0.776457	−	1.34486i	−0.0546313	−	0.0946242i
$203$		0			0
$204$		0			0
$205$	−10.9282			−0.763259
$206$	−4.19187	+	7.26054i	−0.292062	+	0.505866i
$207$		0			0
$208$	−1.22474	−	2.12132i	−0.0849208	−	0.147087i
$209$	−5.27792	+	9.14162i	−0.365081	+	0.632339i
$210$		0			0
$211$	−2.36603	−	4.09808i	−0.162884	−	0.282123i	0.773018	−	0.634384i	$-0.218746\pi$
$211$	−2.36603	−	4.09808i	−0.162884	−	0.282123i	−0.935902	+	0.352261i	$0.885413\pi$
$212$	1.63397	−	2.83013i	0.112222	−	0.194374i
$213$		0			0
$214$	8.46410	+	14.6603i	0.578594	+	1.00215i
$215$	1.74238	+	3.01790i	0.118830	+	0.205819i
$216$		0			0
$217$		0			0
$218$	10.2942	−	17.8301i	0.697213	−	1.20761i
$219$		0			0
$220$	−10.5558			−0.711674
$221$	−15.4641			−1.04023
$222$		0			0
$223$	10.3664	−	17.9551i	0.694183	−	1.20236i	−0.276272	−	0.961079i	$-0.589099\pi$
$223$	10.3664	−	17.9551i	0.694183	−	1.20236i	0.970455	−	0.241281i	$-0.0775676\pi$
$224$		0			0
$225$		0			0
$226$	1.33013	+	2.30385i	0.0884787	+	0.153250i
$227$	0.448288	+	0.776457i	0.0297539	+	0.0515353i	0.880519	−	0.474011i	$-0.157194\pi$
$227$	0.448288	+	0.776457i	0.0297539	+	0.0515353i	−0.850765	+	0.525546i	$0.823861\pi$
$228$		0			0
$229$	9.02150	−	15.6257i	0.596158	−	1.03258i	−0.397225	−	0.917721i	$-0.630027\pi$
$229$	9.02150	−	15.6257i	0.596158	−	1.03258i	0.993382	−	0.114854i	$-0.0366400\pi$
$230$	−5.72620	−	9.91808i	−0.377575	−	0.653979i
$231$		0			0
$232$	−0.366025	+	0.633975i	−0.0240307	+	0.0416225i
$233$	−9.69615	−	16.7942i	−0.635216	−	1.10023i	−0.986469	−	0.163946i	$-0.947578\pi$
$233$	−9.69615	−	16.7942i	−0.635216	−	1.10023i	0.351253	−	0.936280i	$-0.385756\pi$
$234$		0			0
$235$	−9.19615	+	15.9282i	−0.599891	+	1.03904i
$236$	−5.00052			−0.325506
$237$		0			0
$238$		0			0
$239$	−2.76795	−	4.79423i	−0.179044	−	0.310113i	0.762510	−	0.646977i	$-0.223967\pi$
$239$	−2.76795	−	4.79423i	−0.179044	−	0.310113i	−0.941553	+	0.336864i	$0.890634\pi$
$240$		0			0
$241$	−6.36396	−	11.0227i	−0.409939	−	0.710035i	0.584944	−	0.811074i	$-0.301117\pi$
$241$	−6.36396	−	11.0227i	−0.409939	−	0.710035i	−0.994882	+	0.101039i	$0.967783\pi$
$242$	−9.42820	+	16.3301i	−0.606068	+	1.04974i
$243$		0			0
$244$	−2.96713			−0.189951
$245$		0			0
$246$		0			0
$247$	2.36603	−	4.09808i	0.150547	−	0.260754i
$248$	−7.34847			−0.466628
$249$		0			0
$250$	−12.1087			−0.765824
$251$	−1.93185			−0.121937			−0.0609687	−	0.998140i	$-0.519419\pi$
$251$	−1.93185			−0.121937			−0.0609687	+	0.998140i	$0.519419\pi$
$252$		0			0
$253$	−32.3923			−2.03649
$254$	7.92820			0.497460
$255$		0			0
$256$	1.00000			0.0625000
$257$	−10.3664	+	17.9551i	−0.646636	+	1.12001i	0.337285	+	0.941403i	$0.390491\pi$
$257$	−10.3664	+	17.9551i	−0.646636	+	1.12001i	−0.983921	+	0.178604i	$0.942842\pi$
$258$		0			0
$259$		0			0
$260$	4.73205			0.293469
$261$		0			0
$262$	0.120118	−	0.208051i	0.00742094	−	0.0128534i
$263$	−7.33013	−	12.6962i	−0.451995	−	0.782878i	0.546515	−	0.837449i	$-0.315954\pi$
$263$	−7.33013	−	12.6962i	−0.451995	−	0.782878i	−0.998510	+	0.0545711i	$0.982621\pi$
$264$		0			0
$265$	3.15660	+	5.46739i	0.193908	+	0.335859i
$266$		0			0
$267$		0			0
$268$	−14.1962			−0.867168
$269$	−0.0185824	+	0.0321856i	−0.00113299	+	0.00196239i	−0.866591	−	0.499018i	$-0.833694\pi$
$269$	−0.0185824	+	0.0321856i	−0.00113299	+	0.00196239i	0.865458	+	0.500981i	$0.167027\pi$
$270$		0			0
$271$	−2.50026	−	4.33057i	−0.151880	−	0.263064i	0.780039	−	0.625731i	$-0.215199\pi$
$271$	−2.50026	−	4.33057i	−0.151880	−	0.263064i	−0.931919	+	0.362668i	$0.881866\pi$
$272$	3.15660	−	5.46739i	0.191397	−	0.331509i
$273$		0			0
$274$		0			0
$275$	−3.46410	+	6.00000i	−0.208893	+	0.361814i
$276$		0			0
$277$	2.90192	+	5.02628i	0.174360	+	0.302000i	0.939940	−	0.341341i	$-0.110881\pi$
$277$	2.90192	+	5.02628i	0.174360	+	0.302000i	−0.765580	+	0.643341i	$0.777548\pi$
$278$	−0.915158	−	1.58510i	−0.0548875	−	0.0950680i
$279$		0			0
$280$		0			0
$281$	1.69615	−	2.93782i	0.101184	−	0.175256i	−0.810989	−	0.585062i	$-0.801070\pi$
$281$	1.69615	−	2.93782i	0.101184	−	0.175256i	0.912173	+	0.409806i	$0.134404\pi$
$282$		0			0
$283$	17.1093			1.01704			0.508520	−	0.861050i	$-0.330193\pi$
$283$	17.1093			1.01704			0.508520	+	0.861050i	$0.330193\pi$
$284$	11.1962			0.664369
$285$		0			0
$286$	6.69213	−	11.5911i	0.395714	−	0.685397i
$287$		0			0
$288$		0			0
$289$	−11.4282	−	19.7942i	−0.672247	−	1.16437i
$290$	−0.707107	−	1.22474i	−0.0415227	−	0.0719195i
$291$		0			0
$292$	−4.76028	+	8.24504i	−0.278574	+	0.482505i
$293$	2.19067	+	3.79435i	0.127980	+	0.221668i	0.922894	−	0.385054i	$-0.125817\pi$
$293$	2.19067	+	3.79435i	0.127980	+	0.221668i	−0.794914	+	0.606723i	$0.792484\pi$
$294$		0			0
$295$	4.83013	−	8.36603i	0.281221	−	0.487089i
$296$	4.00000	+	6.92820i	0.232495	+	0.402694i
$297$		0			0
$298$	9.19615	−	15.9282i	0.532719	−	0.922696i
$299$	14.5211			0.839775
$300$		0			0
$301$		0			0
$302$	−1.69615	−	2.93782i	−0.0976026	−	0.169053i
$303$		0			0
$304$	0.965926	+	1.67303i	0.0553996	+	0.0959550i
$305$	2.86603	−	4.96410i	0.164108	−	0.284244i
$306$		0			0
$307$	−29.0793			−1.65964			−0.829822	−	0.558028i	$-0.811558\pi$
$307$	−29.0793			−1.65964			−0.829822	+	0.558028i	$0.811558\pi$
$308$		0			0
$309$		0			0
$310$	7.09808	−	12.2942i	0.403144	−	0.698265i
$311$	21.0101			1.19138			0.595688	−	0.803216i	$-0.296880\pi$
$311$	21.0101			1.19138			0.595688	+	0.803216i	$0.296880\pi$
$312$		0			0
$313$	−1.79315			−0.101355			−0.0506774	−	0.998715i	$-0.516138\pi$
$313$	−1.79315			−0.101355			−0.0506774	+	0.998715i	$0.516138\pi$
$314$	24.3562			1.37450
$315$		0			0
$316$	−10.1244			−0.569540
$317$	−1.41154			−0.0792801			−0.0396401	−	0.999214i	$-0.512621\pi$
$317$	−1.41154			−0.0792801			−0.0396401	+	0.999214i	$0.512621\pi$
$318$		0			0
$319$	−4.00000			−0.223957
$320$	−0.965926	+	1.67303i	−0.0539969	+	0.0935254i
$321$		0			0
$322$		0			0
$323$	12.1962			0.678612
$324$		0			0
$325$	1.55291	−	2.68973i	0.0861402	−	0.149199i
$326$	10.4641	+	18.1244i	0.579553	+	1.00382i
$327$		0			0
$328$	2.82843	+	4.89898i	0.156174	+	0.270501i
$329$		0			0
$330$		0			0
$331$	26.0526			1.43198			0.715989	−	0.698111i	$-0.245976\pi$
$331$	26.0526			1.43198			0.715989	+	0.698111i	$0.245976\pi$
$332$	−4.94975	+	8.57321i	−0.271653	+	0.470516i
$333$		0			0
$334$	−8.05558	−	13.9527i	−0.440782	−	0.763456i
$335$	13.7124	−	23.7506i	0.749190	−	1.29764i
$336$		0			0
$337$	−6.66025	−	11.5359i	−0.362807	−	0.628400i	0.625615	−	0.780132i	$-0.284848\pi$
$337$	−6.66025	−	11.5359i	−0.362807	−	0.628400i	−0.988422	+	0.151732i	$0.951515\pi$
$338$	3.50000	−	6.06218i	0.190375	−	0.329739i
$339$		0			0
$340$	6.09808	+	10.5622i	0.330715	+	0.572815i
$341$	−20.0764	−	34.7733i	−1.08720	−	1.88308i
$342$		0			0
$343$		0			0
$344$	0.901924	−	1.56218i	0.0486285	−	0.0842270i
$345$		0			0
$346$	14.5211			0.780658
$347$	33.7128			1.80980			0.904899	−	0.425626i	$-0.139946\pi$
$347$	33.7128			1.80980			0.904899	+	0.425626i	$0.139946\pi$
$348$		0			0
$349$	12.3998	−	21.4770i	0.663744	−	1.14964i	−0.315881	−	0.948799i	$-0.602300\pi$
$349$	12.3998	−	21.4770i	0.663744	−	1.14964i	0.979624	−	0.200839i	$-0.0643667\pi$
$350$		0			0
$351$		0			0
$352$	2.73205	+	4.73205i	0.145619	+	0.252219i
$353$	9.84873	+	17.0585i	0.524195	+	0.907932i	0.999603	+	0.0281669i	$0.00896698\pi$
$353$	9.84873	+	17.0585i	0.524195	+	0.907932i	−0.475408	+	0.879765i	$0.657700\pi$
$354$		0			0
$355$	−10.8147	+	18.7315i	−0.573982	+	0.994166i
$356$	6.64136	+	11.5032i	0.351992	+	0.609667i
$357$		0			0
$358$	1.09808	−	1.90192i	0.0580351	−	0.100520i
$359$	−0.0358984	−	0.0621778i	−0.00189464	−	0.00328162i	0.865077	−	0.501640i	$-0.167270\pi$
$359$	−0.0358984	−	0.0621778i	−0.00189464	−	0.00328162i	−0.866971	+	0.498358i	$0.833936\pi$
$360$		0			0
$361$	7.63397	−	13.2224i	0.401788	−	0.695917i
$362$	−8.72552			−0.458603
$363$		0			0
$364$		0			0
$365$	−9.19615	−	15.9282i	−0.481349	−	0.833720i
$366$		0			0
$367$	−7.20977	−	12.4877i	−0.376347	−	0.651852i	0.614181	−	0.789165i	$-0.289487\pi$
$367$	−7.20977	−	12.4877i	−0.376347	−	0.651852i	−0.990528	+	0.137313i	$0.956153\pi$
$368$	−2.96410	+	5.13397i	−0.154514	+	0.267627i
$369$		0			0
$370$	−15.4548			−0.803457
$371$		0			0
$372$		0			0
$373$	2.56218	−	4.43782i	0.132665	−	0.229782i	−0.792038	−	0.610471i	$-0.790980\pi$
$373$	2.56218	−	4.43782i	0.132665	−	0.229782i	0.924703	+	0.380690i	$0.124313\pi$
$374$	34.4959			1.78374
$375$		0			0
$376$	9.52056			0.490985
$377$	1.79315			0.0923520
$378$		0			0
$379$	17.5167			0.899770			0.449885	−	0.893086i	$-0.351465\pi$
$379$	17.5167			0.899770			0.449885	+	0.893086i	$0.351465\pi$
$380$	−3.73205			−0.191450
$381$		0			0
$382$	−3.19615			−0.163529
$383$	−9.76079	+	16.9062i	−0.498753	+	0.863866i	−0.999999	−	0.00143898i	$-0.999542\pi$
$383$	−9.76079	+	16.9062i	−0.498753	+	0.863866i	0.501246	+	0.865305i	$0.332875\pi$
$384$		0			0
$385$		0			0
$386$	−20.2679			−1.03161
$387$		0			0
$388$	−1.93185	+	3.34607i	−0.0980749	+	0.169871i
$389$	−14.5622	−	25.2224i	−0.738332	−	1.27883i	−0.953246	−	0.302195i	$-0.902281\pi$
$389$	−14.5622	−	25.2224i	−0.738332	−	1.27883i	0.214914	−	0.976633i	$-0.431053\pi$
$390$		0			0
$391$	18.7129	+	32.4118i	0.946354	+	1.63913i
$392$		0			0
$393$		0			0
$394$	7.66025			0.385918
$395$	9.77938	−	16.9384i	0.492054	−	0.852262i
$396$		0			0
$397$	−0.947343	−	1.64085i	−0.0475458	−	0.0823518i	0.841273	−	0.540610i	$-0.181807\pi$
$397$	−0.947343	−	1.64085i	−0.0475458	−	0.0823518i	−0.888819	+	0.458259i	$0.848473\pi$
$398$	1.55291	−	2.68973i	0.0778406	−	0.134824i
$399$		0			0
$400$	0.633975	+	1.09808i	0.0316987	+	0.0549038i
$401$	6.52628	−	11.3038i	0.325907	−	0.564487i	−0.655789	−	0.754945i	$-0.727664\pi$
$401$	6.52628	−	11.3038i	0.325907	−	0.564487i	0.981695	+	0.190457i	$0.0609971\pi$
$402$		0			0
$403$	9.00000	+	15.5885i	0.448322	+	0.776516i
$404$	−0.776457	−	1.34486i	−0.0386302	−	0.0669094i
$405$		0			0
$406$		0			0
$407$	−21.8564	+	37.8564i	−1.08338	+	1.87647i
$408$		0			0
$409$	−26.2880			−1.29986			−0.649930	−	0.759994i	$-0.725202\pi$
$409$	−26.2880			−1.29986			−0.649930	+	0.759994i	$0.725202\pi$
$410$	−10.9282			−0.539705
$411$		0			0
$412$	−4.19187	+	7.26054i	−0.206519	+	0.357701i
$413$		0			0
$414$		0			0
$415$	−9.56218	−	16.5622i	−0.469389	−	0.813005i
$416$	−1.22474	−	2.12132i	−0.0600481	−	0.104006i
$417$		0			0
$418$	−5.27792	+	9.14162i	−0.258151	+	0.447131i
$419$	2.13990	+	3.70642i	0.104541	+	0.181070i	0.913551	−	0.406725i	$-0.133329\pi$
$419$	2.13990	+	3.70642i	0.104541	+	0.181070i	−0.809010	+	0.587796i	$0.799996\pi$
$420$		0			0
$421$	5.02628	−	8.70577i	0.244966	−	0.424293i	−0.717156	−	0.696913i	$-0.754557\pi$
$421$	5.02628	−	8.70577i	0.244966	−	0.424293i	0.962122	+	0.272619i	$0.0878899\pi$
$422$	−2.36603	−	4.09808i	−0.115176	−	0.199491i
$423$		0			0
$424$	1.63397	−	2.83013i	0.0793528	−	0.137443i
$425$	8.00481			0.388290
$426$		0			0
$427$		0			0
$428$	8.46410	+	14.6603i	0.409128	+	0.708630i
$429$		0			0
$430$	1.74238	+	3.01790i	0.0840252	+	0.145536i
$431$	7.39230	−	12.8038i	0.356075	−	0.616740i	−0.631226	−	0.775599i	$-0.717448\pi$
$431$	7.39230	−	12.8038i	0.356075	−	0.616740i	0.987301	+	0.158859i	$0.0507815\pi$
$432$		0			0
$433$	28.7375			1.38104			0.690519	−	0.723314i	$-0.257382\pi$
$433$	28.7375			1.38104			0.690519	+	0.723314i	$0.257382\pi$
$434$		0			0
$435$		0			0
$436$	10.2942	−	17.8301i	0.493004	−	0.853908i
$437$	−11.4524			−0.547843
$438$		0			0
$439$	−1.31268			−0.0626507			−0.0313253	−	0.999509i	$-0.509973\pi$
$439$	−1.31268			−0.0626507			−0.0313253	+	0.999509i	$0.509973\pi$
$440$	−10.5558			−0.503230
$441$		0			0
$442$	−15.4641			−0.735552
$443$	−14.9808			−0.711757			−0.355879	−	0.934532i	$-0.615818\pi$
$443$	−14.9808			−0.711757			−0.355879	+	0.934532i	$0.615818\pi$
$444$		0			0
$445$	−25.6603			−1.21641
$446$	10.3664	−	17.9551i	0.490862	−	0.850197i
$447$		0			0
$448$		0			0
$449$	−17.7846			−0.839308			−0.419654	−	0.907684i	$-0.637849\pi$
$449$	−17.7846			−0.839308			−0.419654	+	0.907684i	$0.637849\pi$
$450$		0			0
$451$	−15.4548	+	26.7685i	−0.727739	+	1.26048i
$452$	1.33013	+	2.30385i	0.0625639	+	0.108364i
$453$		0			0
$454$	0.448288	+	0.776457i	0.0210392	+	0.0364409i
$455$		0			0
$456$		0			0
$457$	−25.7321			−1.20369			−0.601847	−	0.798611i	$-0.705568\pi$
$457$	−25.7321			−1.20369			−0.601847	+	0.798611i	$0.705568\pi$
$458$	9.02150	−	15.6257i	0.421547	−	0.730141i
$459$		0			0
$460$	−5.72620	−	9.91808i	−0.266986	−	0.462433i
$461$	10.9162	−	18.9074i	0.508418	−	0.880605i	−0.491535	−	0.870858i	$-0.663564\pi$
$461$	10.9162	−	18.9074i	0.508418	−	0.880605i	0.999952	−	0.00974723i	$-0.00310269\pi$
$462$		0			0
$463$	5.33013	+	9.23205i	0.247712	+	0.429050i	0.962891	−	0.269892i	$-0.0869880\pi$
$463$	5.33013	+	9.23205i	0.247712	+	0.429050i	−0.715179	+	0.698942i	$0.753655\pi$
$464$	−0.366025	+	0.633975i	−0.0169923	+	0.0294315i
$465$		0			0
$466$	−9.69615	−	16.7942i	−0.449166	−	0.777978i
$467$	−2.39872	−	4.15471i	−0.111000	−	0.192257i	0.805174	−	0.593039i	$-0.202072\pi$
$467$	−2.39872	−	4.15471i	−0.111000	−	0.192257i	−0.916174	+	0.400782i	$0.868739\pi$
$468$		0			0
$469$		0			0
$470$	−9.19615	+	15.9282i	−0.424187	+	0.734713i
$471$		0			0
$472$	−5.00052			−0.230167
$473$	9.85641			0.453198
$474$		0			0
$475$	−1.22474	+	2.12132i	−0.0561951	+	0.0973329i
$476$		0			0
$477$		0			0
$478$	−2.76795	−	4.79423i	−0.126603	−	0.219283i
$479$	8.05558	+	13.9527i	0.368069	+	0.637514i	0.989264	−	0.146142i	$-0.0466858\pi$
$479$	8.05558	+	13.9527i	0.368069	+	0.637514i	−0.621195	+	0.783656i	$0.713352\pi$
$480$		0			0
$481$	9.79796	−	16.9706i	0.446748	−	0.773791i
$482$	−6.36396	−	11.0227i	−0.289870	−	0.502070i
$483$		0			0
$484$	−9.42820	+	16.3301i	−0.428555	+	0.742279i
$485$	−3.73205	−	6.46410i	−0.169464	−	0.293520i
$486$		0			0
$487$	−1.16025	+	2.00962i	−0.0525761	+	0.0910645i	−0.891116	−	0.453776i	$-0.850077\pi$
$487$	−1.16025	+	2.00962i	−0.0525761	+	0.0910645i	0.838540	+	0.544841i	$0.183410\pi$
$488$	−2.96713			−0.134316
$489$		0			0
$490$		0			0
$491$	−9.46410	−	16.3923i	−0.427109	−	0.739774i	0.569506	−	0.821987i	$-0.307135\pi$
$491$	−9.46410	−	16.3923i	−0.427109	−	0.739774i	−0.996615	+	0.0822129i	$0.973801\pi$
$492$		0			0
$493$	2.31079	+	4.00240i	0.104073	+	0.180259i
$494$	2.36603	−	4.09808i	0.106453	−	0.184381i
$495$		0			0
$496$	−7.34847			−0.329956
$497$		0			0
$498$		0			0
$499$	13.6603	−	23.6603i	0.611517	−	1.05918i	−0.379468	−	0.925205i	$-0.623893\pi$
$499$	13.6603	−	23.6603i	0.611517	−	1.05918i	0.990985	−	0.133974i	$-0.0427737\pi$
$500$	−12.1087			−0.541520
$501$		0			0
$502$	−1.93185			−0.0862228
$503$	−19.1427			−0.853529			−0.426764	−	0.904363i	$-0.640347\pi$
$503$	−19.1427			−0.853529			−0.426764	+	0.904363i	$0.640347\pi$
$504$		0			0
$505$	3.00000			0.133498
$506$	−32.3923			−1.44001
$507$		0			0
$508$	7.92820			0.351757
$509$	10.8840	−	18.8516i	0.482425	−	0.835585i	−0.517371	−	0.855761i	$-0.673089\pi$
$509$	10.8840	−	18.8516i	0.482425	−	0.835585i	0.999796	+	0.0201764i	$0.00642278\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	−10.3664	+	17.9551i	−0.457241	+	0.791964i
$515$	−8.09808	−	14.0263i	−0.356844	−	0.618072i
$516$		0			0
$517$	26.0106	+	45.0518i	1.14395	+	1.98137i
$518$		0			0
$519$		0			0
$520$	4.73205			0.207514
$521$	−16.2635	+	28.1691i	−0.712515	+	1.23411i	0.251395	+	0.967885i	$0.419111\pi$
$521$	−16.2635	+	28.1691i	−0.712515	+	1.23411i	−0.963910	+	0.266228i	$0.914223\pi$
$522$		0			0
$523$	−3.70642	−	6.41971i	−0.162070	−	0.280714i	0.773541	−	0.633747i	$-0.218484\pi$
$523$	−3.70642	−	6.41971i	−0.162070	−	0.280714i	−0.935611	+	0.353032i	$0.885151\pi$
$524$	0.120118	−	0.208051i	0.00524739	−	0.00908875i
$525$		0			0
$526$	−7.33013	−	12.6962i	−0.319609	−	0.553579i
$527$	−23.1962	+	40.1769i	−1.01044	+	1.75013i
$528$		0			0
$529$	−6.07180	−	10.5167i	−0.263991	−	0.457246i
$530$	3.15660	+	5.46739i	0.137114	+	0.237488i
$531$		0			0
$532$		0			0
$533$	6.92820	−	12.0000i	0.300094	−	0.519778i
$534$		0			0
$535$	−32.7028			−1.41386
$536$	−14.1962			−0.613180
$537$		0			0
$538$	−0.0185824	+	0.0321856i	−0.000801143	+	0.00138762i
$539$		0			0
$540$		0			0
$541$	−8.63397	−	14.9545i	−0.371204	−	0.642943i	0.618547	−	0.785747i	$-0.287721\pi$
$541$	−8.63397	−	14.9545i	−0.371204	−	0.642943i	−0.989751	+	0.142804i	$0.954388\pi$
$542$	−2.50026	−	4.33057i	−0.107395	−	0.186014i
$543$		0			0
$544$	3.15660	−	5.46739i	0.135338	−	0.234412i
$545$	19.8869	+	34.4452i	0.851862	+	1.47547i
$546$		0			0
$547$	2.26795	−	3.92820i	0.0969705	−	0.167958i	−0.813459	−	0.581623i	$-0.802418\pi$
$547$	2.26795	−	3.92820i	0.0969705	−	0.167958i	0.910429	+	0.413665i	$0.135751\pi$
$548$		0			0
$549$		0			0
$550$	−3.46410	+	6.00000i	−0.147710	+	0.255841i
$551$	−1.41421			−0.0602475
$552$		0			0
$553$		0			0
$554$	2.90192	+	5.02628i	0.123291	+	0.213546i
$555$		0			0
$556$	−0.915158	−	1.58510i	−0.0388113	−	0.0672232i
$557$	13.5622	−	23.4904i	0.574648	−	0.995319i	−0.421432	−	0.906860i	$-0.638472\pi$
$557$	13.5622	−	23.4904i	0.574648	−	0.995319i	0.996080	−	0.0884593i	$-0.0281943\pi$
$558$		0			0
$559$	−4.41851			−0.186883
$560$		0			0
$561$		0			0
$562$	1.69615	−	2.93782i	0.0715479	−	0.123925i
$563$	8.62398			0.363458			0.181729	−	0.983349i	$-0.441831\pi$
$563$	8.62398			0.363458			0.181729	+	0.983349i	$0.441831\pi$
$564$		0			0
$565$	−5.13922			−0.216208
$566$	17.1093			0.719156
$567$		0			0
$568$	11.1962			0.469780
$569$	−13.0718			−0.547998			−0.273999	−	0.961730i	$-0.588347\pi$
$569$	−13.0718			−0.547998			−0.273999	+	0.961730i	$0.588347\pi$
$570$		0			0
$571$	4.00000			0.167395			0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000			0.167395			0.0836974	+	0.996491i	$0.473327\pi$
$572$	6.69213	−	11.5911i	0.279812	−	0.484649i
$573$		0			0
$574$		0			0
$575$	−7.51666			−0.313466
$576$		0			0
$577$	8.90138	−	15.4176i	0.370569	−	0.641845i	−0.619084	−	0.785325i	$-0.712496\pi$
$577$	8.90138	−	15.4176i	0.370569	−	0.641845i	0.989653	+	0.143480i	$0.0458292\pi$
$578$	−11.4282	−	19.7942i	−0.475351	−	0.823331i
$579$		0			0
$580$	−0.707107	−	1.22474i	−0.0293610	−	0.0508548i
$581$		0			0
$582$		0			0
$583$	17.8564			0.739537
$584$	−4.76028	+	8.24504i	−0.196982	+	0.341182i
$585$		0			0
$586$	2.19067	+	3.79435i	0.0904958	+	0.156743i
$587$	−16.6102	+	28.7697i	−0.685577	+	1.18745i	0.287679	+	0.957727i	$0.407117\pi$
$587$	−16.6102	+	28.7697i	−0.685577	+	1.18745i	−0.973255	+	0.229727i	$0.926217\pi$
$588$		0			0
$589$	−7.09808	−	12.2942i	−0.292471	−	0.506575i
$590$	4.83013	−	8.36603i	0.198853	−	0.344424i
$591$		0			0
$592$	4.00000	+	6.92820i	0.164399	+	0.284747i
$593$	−10.7453	−	18.6114i	−0.441257	−	0.764279i	0.556526	−	0.830830i	$-0.312134\pi$
$593$	−10.7453	−	18.6114i	−0.441257	−	0.764279i	−0.997783	+	0.0665510i	$0.978801\pi$
$594$		0			0
$595$		0			0
$596$	9.19615	−	15.9282i	0.376689	−	0.652445i
$597$		0			0
$598$	14.5211			0.593811
$599$	−8.39230			−0.342900			−0.171450	−	0.985193i	$-0.554845\pi$
$599$	−8.39230			−0.342900			−0.171450	+	0.985193i	$0.554845\pi$
$600$		0			0
$601$	8.72552	−	15.1130i	0.355921	−	0.616474i	−0.631354	−	0.775495i	$-0.717500\pi$
$601$	8.72552	−	15.1130i	0.355921	−	0.616474i	0.987275	+	0.159021i	$0.0508338\pi$
$602$		0			0
$603$		0			0
$604$	−1.69615	−	2.93782i	−0.0690155	−	0.119538i
$605$	−18.2139	−	31.5474i	−0.740500	−	1.28258i
$606$		0			0
$607$	−6.45189	+	11.1750i	−0.261874	+	0.453580i	−0.966740	−	0.255761i	$-0.917674\pi$
$607$	−6.45189	+	11.1750i	−0.261874	+	0.453580i	0.704866	+	0.709341i	$0.251007\pi$
$608$	0.965926	+	1.67303i	0.0391735	+	0.0678504i
$609$		0			0
$610$	2.86603	−	4.96410i	0.116042	−	0.200991i
$611$	−11.6603	−	20.1962i	−0.471723	−	0.817049i
$612$		0			0
$613$	19.2224	−	33.2942i	0.776387	−	1.34474i	−0.157625	−	0.987499i	$-0.550384\pi$
$613$	19.2224	−	33.2942i	0.776387	−	1.34474i	0.934012	−	0.357242i	$-0.116283\pi$
$614$	−29.0793			−1.17355
$615$		0			0
$616$		0			0
$617$	10.8038	+	18.7128i	0.434947	+	0.753349i	0.997291	−	0.0735534i	$-0.0234339\pi$
$617$	10.8038	+	18.7128i	0.434947	+	0.753349i	−0.562345	+	0.826903i	$0.690101\pi$
$618$		0			0
$619$	−7.27912	−	12.6078i	−0.292572	−	0.506750i	0.681845	−	0.731497i	$-0.261178\pi$
$619$	−7.27912	−	12.6078i	−0.292572	−	0.506750i	−0.974417	+	0.224746i	$0.927845\pi$
$620$	7.09808	−	12.2942i	0.285066	−	0.493748i
$621$		0			0
$622$	21.0101			0.842430
$623$		0			0
$624$		0			0
$625$	8.52628	−	14.7679i	0.341051	−	0.590718i
$626$	−1.79315			−0.0716687
$627$		0			0
$628$	24.3562			0.971918
$629$	50.5055			2.01379
$630$		0			0
$631$	−28.1244			−1.11961			−0.559806	−	0.828623i	$-0.689125\pi$
$631$	−28.1244			−1.11961			−0.559806	+	0.828623i	$0.689125\pi$
$632$	−10.1244			−0.402725
$633$		0			0
$634$	−1.41154			−0.0560595
$635$	−7.65806	+	13.2641i	−0.303901	+	0.526371i
$636$		0			0
$637$		0			0
$638$	−4.00000			−0.158362
$639$		0			0
$640$	−0.965926	+	1.67303i	−0.0381816	+	0.0661324i
$641$	17.5263	+	30.3564i	0.692246	+	1.19901i	0.971100	+	0.238672i	$0.0767122\pi$
$641$	17.5263	+	30.3564i	0.692246	+	1.19901i	−0.278854	+	0.960334i	$0.589954\pi$
$642$		0			0
$643$	−6.50266	−	11.2629i	−0.256440	−	0.444167i	0.708846	−	0.705364i	$-0.249216\pi$
$643$	−6.50266	−	11.2629i	−0.256440	−	0.444167i	−0.965286	+	0.261197i	$0.915883\pi$
$644$		0			0
$645$		0			0
$646$	12.1962			0.479851
$647$	−0.568406	+	0.984508i	−0.0223463	+	0.0387050i	−0.876982	−	0.480523i	$-0.840447\pi$
$647$	−0.568406	+	0.984508i	−0.0223463	+	0.0387050i	0.854636	+	0.519228i	$0.173780\pi$
$648$		0			0
$649$	−13.6617	−	23.6627i	−0.536267	−	0.928842i
$650$	1.55291	−	2.68973i	0.0609103	−	0.105500i
$651$		0			0
$652$	10.4641	+	18.1244i	0.409806	+	0.709805i
$653$	−3.33975	+	5.78461i	−0.130694	+	0.226369i	−0.923944	−	0.382527i	$-0.875054\pi$
$653$	−3.33975	+	5.78461i	−0.130694	+	0.226369i	0.793250	+	0.608896i	$0.208387\pi$
$654$		0			0
$655$	0.232051	+	0.401924i	0.00906698	+	0.0157045i
$656$	2.82843	+	4.89898i	0.110432	+	0.191273i
$657$		0			0
$658$		0			0
$659$	−7.43782	+	12.8827i	−0.289736	+	0.501838i	−0.973747	−	0.227634i	$-0.926901\pi$
$659$	−7.43782	+	12.8827i	−0.289736	+	0.501838i	0.684010	+	0.729472i	$0.260234\pi$
$660$		0			0
$661$	33.7009			1.31081			0.655406	−	0.755276i	$-0.272497\pi$
$661$	33.7009			1.31081			0.655406	+	0.755276i	$0.272497\pi$
$662$	26.0526			1.01256
$663$		0			0
$664$	−4.94975	+	8.57321i	−0.192087	+	0.332705i
$665$		0			0
$666$		0			0
$667$	−2.16987	−	3.75833i	−0.0840178	−	0.145523i
$668$	−8.05558	−	13.9527i	−0.311680	−	0.539845i
$669$		0			0
$670$	13.7124	−	23.7506i	0.529757	−	0.917567i
$671$	−8.10634	−	14.0406i	−0.312942	−	0.542031i
$672$		0			0
$673$	−11.0885	+	19.2058i	−0.427429	+	0.740328i	−0.996644	−	0.0818605i	$-0.973914\pi$
$673$	−11.0885	+	19.2058i	−0.427429	+	0.740328i	0.569215	+	0.822189i	$0.307247\pi$
$674$	−6.66025	−	11.5359i	−0.256543	−	0.444346i
$675$		0			0
$676$	3.50000	−	6.06218i	0.134615	−	0.233161i
$677$	−15.8338			−0.608540			−0.304270	−	0.952586i	$-0.598413\pi$
$677$	−15.8338			−0.608540			−0.304270	+	0.952586i	$0.598413\pi$
$678$		0			0
$679$		0			0
$680$	6.09808	+	10.5622i	0.233851	+	0.405041i
$681$		0			0
$682$	−20.0764	−	34.7733i	−0.768765	−	1.33154i
$683$	−17.1962	+	29.7846i	−0.657992	+	1.13968i	0.323142	+	0.946350i	$0.395261\pi$
$683$	−17.1962	+	29.7846i	−0.657992	+	1.13968i	−0.981135	+	0.193326i	$0.938073\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$	0.901924	−	1.56218i	0.0343855	−	0.0595575i
$689$	−8.00481			−0.304959
$690$		0			0
$691$	24.2547			0.922691			0.461345	−	0.887221i	$-0.347367\pi$
$691$	24.2547			0.922691			0.461345	+	0.887221i	$0.347367\pi$
$692$	14.5211			0.552008
$693$		0			0
$694$	33.7128			1.27972
$695$	3.53590			0.134124
$696$		0			0
$697$	35.7128			1.35272
$698$	12.3998	−	21.4770i	0.469338	−	0.812916i
$699$		0			0
$700$		0			0
$701$	−27.4641			−1.03730			−0.518652	−	0.854985i	$-0.673566\pi$
$701$	−27.4641			−1.03730			−0.518652	+	0.854985i	$0.673566\pi$
$702$		0			0
$703$	−7.72741	+	13.3843i	−0.291445	+	0.504797i
$704$	2.73205	+	4.73205i	0.102968	+	0.178346i
$705$		0			0
$706$	9.84873	+	17.0585i	0.370662	+	0.642005i
$707$		0			0
$708$		0			0
$709$	−29.4641			−1.10655			−0.553274	−	0.832999i	$-0.686622\pi$
$709$	−29.4641			−1.10655			−0.553274	+	0.832999i	$0.686622\pi$
$710$	−10.8147	+	18.7315i	−0.405867	+	0.702982i
$711$		0			0
$712$	6.64136	+	11.5032i	0.248896	+	0.431100i
$713$	21.7816	−	37.7269i	0.815728	−	1.41288i
$714$		0			0
$715$	12.9282	+	22.3923i	0.483487	+	0.837425i
$716$	1.09808	−	1.90192i	0.0410370	−	0.0710782i
$717$		0			0
$718$	−0.0358984	−	0.0621778i	−0.00133972	−	0.00232046i
$719$	9.93666	+	17.2108i	0.370575	+	0.641855i	0.989654	−	0.143474i	$-0.0458274\pi$
$719$	9.93666	+	17.2108i	0.370575	+	0.641855i	−0.619079	+	0.785329i	$0.712494\pi$
$720$		0			0
$721$		0			0
$722$	7.63397	−	13.2224i	0.284107	−	0.492088i
$723$		0			0
$724$	−8.72552			−0.324281
$725$	−0.928203			−0.0344726
$726$		0			0
$727$	−12.0580	+	20.8850i	−0.447206	+	0.774583i	−0.998203	−	0.0599240i	$-0.980914\pi$
$727$	−12.0580	+	20.8850i	−0.447206	+	0.774583i	0.550997	+	0.834507i	$0.314247\pi$
$728$		0			0
$729$		0			0
$730$	−9.19615	−	15.9282i	−0.340365	−	0.589529i
$731$	−5.69402	−	9.86233i	−0.210601	−	0.364771i
$732$		0			0
$733$	−4.03459	+	6.98811i	−0.149021	+	0.258112i	−0.930866	−	0.365361i	$-0.880946\pi$
$733$	−4.03459	+	6.98811i	−0.149021	+	0.258112i	0.781845	+	0.623473i	$0.214279\pi$
$734$	−7.20977	−	12.4877i	−0.266117	−	0.460929i
$735$		0			0
$736$	−2.96410	+	5.13397i	−0.109258	+	0.189241i
$737$	−38.7846	−	67.1769i	−1.42865	−	2.47449i
$738$		0			0
$739$	21.9282	−	37.9808i	0.806642	−	1.39714i	−0.108535	−	0.994093i	$-0.534616\pi$
$739$	21.9282	−	37.9808i	0.806642	−	1.39714i	0.915177	−	0.403052i	$-0.132051\pi$
$740$	−15.4548			−0.568130
$741$		0			0
$742$		0			0
$743$	10.1244	+	17.5359i	0.371427	+	0.643330i	0.989785	−	0.142566i	$-0.0455354\pi$
$743$	10.1244	+	17.5359i	0.371427	+	0.643330i	−0.618359	+	0.785896i	$0.712202\pi$
$744$		0			0
$745$	17.7656	+	30.7709i	0.650881	+	1.12736i
$746$	2.56218	−	4.43782i	0.0938080	−	0.162480i
$747$		0			0
$748$	34.4959			1.26130
$749$		0			0
$750$		0			0
$751$	−6.08846	+	10.5455i	−0.222171	+	0.384811i	−0.955467	−	0.295098i	$-0.904648\pi$
$751$	−6.08846	+	10.5455i	−0.222171	+	0.384811i	0.733296	+	0.679910i	$0.237981\pi$
$752$	9.52056			0.347179
$753$		0			0
$754$	1.79315			0.0653027
$755$	6.55343			0.238504
$756$		0			0
$757$	−28.2487			−1.02672			−0.513358	−	0.858174i	$-0.671599\pi$
$757$	−28.2487			−1.02672			−0.513358	+	0.858174i	$0.671599\pi$
$758$	17.5167			0.636234
$759$		0			0
$760$	−3.73205			−0.135376
$761$	−2.74049	+	4.74668i	−0.0993428	+	0.172067i	−0.911413	−	0.411493i	$-0.865007\pi$
$761$	−2.74049	+	4.74668i	−0.0993428	+	0.172067i	0.812070	+	0.583560i	$0.198341\pi$
$762$		0			0
$763$		0			0
$764$	−3.19615			−0.115633
$765$		0			0
$766$	−9.76079	+	16.9062i	−0.352672	+	0.610846i
$767$	6.12436	+	10.6077i	0.221138	+	0.383022i
$768$		0			0
$769$	2.20925	+	3.82654i	0.0796677	+	0.137989i	0.903107	−	0.429416i	$-0.141281\pi$
$769$	2.20925	+	3.82654i	0.0796677	+	0.137989i	−0.823439	+	0.567405i	$0.807947\pi$
$770$		0			0
$771$		0			0
$772$	−20.2679			−0.729459
$773$	−1.81173	+	3.13801i	−0.0651635	+	0.112867i	−0.896767	−	0.442504i	$-0.854090\pi$
$773$	−1.81173	+	3.13801i	−0.0651635	+	0.112867i	0.831603	+	0.555371i	$0.187424\pi$
$774$		0			0
$775$	−4.65874	−	8.06918i	−0.167347	−	0.289853i
$776$	−1.93185	+	3.34607i	−0.0693494	+	0.120117i
$777$		0			0
$778$	−14.5622	−	25.2224i	−0.522079	−	0.904268i
$779$	−5.46410	+	9.46410i	−0.195772	+	0.339087i
$780$		0			0
$781$	30.5885	+	52.9808i	1.09454	+	1.89580i
$782$	18.7129	+	32.4118i	0.669174	+	1.15904i
$783$		0			0
$784$		0			0
$785$	−23.5263	+	40.7487i	−0.839689	+	1.45438i
$786$		0			0
$787$	7.90327			0.281721			0.140861	−	0.990029i	$-0.455013\pi$
$787$	7.90327			0.281721			0.140861	+	0.990029i	$0.455013\pi$
$788$	7.66025			0.272885
$789$		0			0
$790$	9.77938	−	16.9384i	0.347935	−	0.602640i
$791$		0			0
$792$		0			0
$793$	3.63397	+	6.29423i	0.129046	+	0.223515i
$794$	−0.947343	−	1.64085i	−0.0336200	−	0.0582315i
$795$		0			0
$796$	1.55291	−	2.68973i	0.0550416	−	0.0953348i
$797$	11.0549	+	19.1476i	0.391584	+	0.678244i	0.992659	−	0.120949i	$-0.0385938\pi$
$797$	11.0549	+	19.1476i	0.391584	+	0.678244i	−0.601074	+	0.799193i	$0.705260\pi$
$798$		0			0
$799$	30.0526	−	52.0526i	1.06318	−	1.84149i
$800$	0.633975	+	1.09808i	0.0224144	+	0.0388229i
$801$		0			0
$802$	6.52628	−	11.3038i	0.230451	−	0.399153i
$803$	−52.0213			−1.83579
$804$		0			0
$805$		0			0
$806$	9.00000	+	15.5885i	0.317011	+	0.549080i
$807$		0			0
$808$	−0.776457	−	1.34486i	−0.0273157	−	0.0473121i
$809$	−0.660254	+	1.14359i	−0.0232133	+	0.0402066i	−0.877399	−	0.479762i	$-0.840723\pi$
$809$	−0.660254	+	1.14359i	−0.0232133	+	0.0402066i	0.854185	+	0.519969i	$0.174056\pi$
$810$		0			0
$811$	17.6269			0.618964			0.309482	−	0.950905i	$-0.399844\pi$
$811$	17.6269			0.618964			0.309482	+	0.950905i	$0.399844\pi$
$812$		0			0
$813$		0			0
$814$	−21.8564	+	37.8564i	−0.766067	+	1.32687i
$815$	−40.4302			−1.41621
$816$		0			0
$817$	3.48477			0.121917
$818$	−26.2880			−0.919140
$819$		0			0
$820$	−10.9282			−0.381629
$821$	41.3205			1.44210			0.721048	−	0.692885i	$-0.243661\pi$
$821$	41.3205			1.44210			0.721048	+	0.692885i	$0.243661\pi$
$822$		0			0
$823$	27.3205			0.952333			0.476167	−	0.879355i	$-0.342026\pi$
$823$	27.3205			0.952333			0.476167	+	0.879355i	$0.342026\pi$
$824$	−4.19187	+	7.26054i	−0.146031	+	0.252933i
$825$		0			0
$826$		0			0
$827$	49.2679			1.71321			0.856607	−	0.515969i	$-0.172568\pi$
$827$	49.2679			1.71321			0.856607	+	0.515969i	$0.172568\pi$
$828$		0			0
$829$	13.1948	−	22.8541i	0.458274	−	0.793754i	−0.540596	−	0.841282i	$-0.681801\pi$
$829$	13.1948	−	22.8541i	0.458274	−	0.793754i	0.998870	+	0.0475285i	$0.0151345\pi$
$830$	−9.56218	−	16.5622i	−0.331908	−	0.574882i
$831$		0			0
$832$	−1.22474	−	2.12132i	−0.0424604	−	0.0735436i
$833$		0			0
$834$		0			0
$835$	31.1244			1.07710
$836$	−5.27792	+	9.14162i	−0.182541	+	0.316170i
$837$		0			0
$838$	2.13990	+	3.70642i	0.0739217	+	0.128036i
$839$	6.91876	−	11.9837i	0.238862	−	0.413722i	−0.721526	−	0.692388i	$-0.756559\pi$
$839$	6.91876	−	11.9837i	0.238862	−	0.413722i	0.960388	+	0.278666i	$0.0898922\pi$
$840$		0			0
$841$	14.2321	+	24.6506i	0.490760	+	0.850022i
$842$	5.02628	−	8.70577i	0.173217	−	0.300021i
$843$		0			0
$844$	−2.36603	−	4.09808i	−0.0814420	−	0.141062i
$845$	6.76148	+	11.7112i	0.232602	+	0.402878i
$846$		0			0
$847$		0			0
$848$	1.63397	−	2.83013i	0.0561109	−	0.0971870i
$849$		0			0
$850$	8.00481			0.274563
$851$	−47.4256			−1.62573
$852$		0			0
$853$	13.9205	−	24.1110i	0.476628	−	0.825544i	−0.523013	−	0.852325i	$-0.675192\pi$
$853$	13.9205	−	24.1110i	0.476628	−	0.825544i	0.999641	+	0.0267804i	$0.00852547\pi$
$854$		0			0
$855$		0			0
$856$	8.46410	+	14.6603i	0.289297	+	0.501077i
$857$	−16.8690	−	29.2180i	−0.576235	−	0.998068i	−0.995906	−	0.0903921i	$-0.971188\pi$
$857$	−16.8690	−	29.2180i	−0.576235	−	0.998068i	0.419671	−	0.907676i	$-0.362145\pi$
$858$		0			0
$859$	14.7477	−	25.5438i	0.503185	−	0.871542i	−0.496808	−	0.867860i	$-0.665495\pi$
$859$	14.7477	−	25.5438i	0.503185	−	0.871542i	0.999993	−	0.00368192i	$-0.00117200\pi$
$860$	1.74238	+	3.01790i	0.0594148	+	0.102909i
$861$		0			0
$862$	7.39230	−	12.8038i	0.251783	−	0.436101i
$863$	5.40192	+	9.35641i	0.183884	+	0.318496i	0.943200	−	0.332226i	$-0.107800\pi$
$863$	5.40192	+	9.35641i	0.183884	+	0.318496i	−0.759316	+	0.650722i	$0.774466\pi$
$864$		0			0
$865$	−14.0263	+	24.2942i	−0.476908	+	0.826029i
$866$	28.7375			0.976541
$867$		0			0
$868$		0			0
$869$	−27.6603	−	47.9090i	−0.938310	−	1.62520i
$870$		0			0
$871$	17.3867	+	30.1146i	0.589125	+	1.02039i
$872$	10.2942	−	17.8301i	0.348607	−	0.603804i
$873$		0			0
$874$	−11.4524			−0.387384
$875$		0			0
$876$		0			0
$877$	7.02628	−	12.1699i	0.237261	−	0.410947i	−0.722667	−	0.691197i	$-0.757084\pi$
$877$	7.02628	−	12.1699i	0.237261	−	0.410947i	0.959927	+	0.280249i	$0.0904171\pi$
$878$	−1.31268			−0.0443007
$879$		0			0
$880$	−10.5558			−0.355837
$881$	−24.9754			−0.841442			−0.420721	−	0.907190i	$-0.638223\pi$
$881$	−24.9754			−0.841442			−0.420721	+	0.907190i	$0.638223\pi$
$882$		0			0
$883$	−10.2487			−0.344897			−0.172448	−	0.985019i	$-0.555168\pi$
$883$	−10.2487			−0.344897			−0.172448	+	0.985019i	$0.555168\pi$
$884$	−15.4641			−0.520114
$885$		0			0
$886$	−14.9808			−0.503289
$887$	23.2838	−	40.3286i	0.781792	−	1.35410i	−0.149105	−	0.988821i	$-0.547639\pi$
$887$	23.2838	−	40.3286i	0.781792	−	1.35410i	0.930897	−	0.365282i	$-0.119027\pi$
$888$		0			0
$889$		0			0
$890$	−25.6603			−0.860134
$891$		0			0
$892$	10.3664	−	17.9551i	0.347092	−	0.601180i
$893$	9.19615	+	15.9282i	0.307738	+	0.533017i
$894$		0			0
$895$	2.12132	+	3.67423i	0.0709079	+	0.122816i
$896$		0			0
$897$		0			0
$898$	−17.7846			−0.593480
$899$	2.68973	−	4.65874i	0.0897074	−	0.155378i
$900$		0			0
$901$	−10.3156	−	17.8671i	−0.343662	−	0.595241i
$902$	−15.4548	+	26.7685i	−0.514589	+	0.891294i
$903$		0			0
$904$	1.33013	+	2.30385i	0.0442394	+	0.0766248i
$905$	8.42820	−	14.5981i	0.280163	−	0.485256i
$906$		0			0
$907$	−9.56218	−	16.5622i	−0.317507	−	0.549938i	0.662460	−	0.749097i	$-0.269512\pi$
$907$	−9.56218	−	16.5622i	−0.317507	−	0.549938i	−0.979967	+	0.199159i	$0.936179\pi$
$908$	0.448288	+	0.776457i	0.0148770	+	0.0257676i
$909$		0			0
$910$		0			0
$911$	−6.89230	+	11.9378i	−0.228352	+	0.395518i	−0.957320	−	0.289030i	$-0.906667\pi$
$911$	−6.89230	+	11.9378i	−0.228352	+	0.395518i	0.728968	+	0.684548i	$0.240000\pi$
$912$		0			0
$913$	−54.0918			−1.79018
$914$	−25.7321			−0.851141
$915$		0			0
$916$	9.02150	−	15.6257i	0.298079	−	0.516288i
$917$		0			0
$918$		0			0
$919$	28.1865	+	48.8205i	0.929788	+	1.61044i	0.783674	+	0.621172i	$0.213343\pi$
$919$	28.1865	+	48.8205i	0.929788	+	1.61044i	0.146114	+	0.989268i	$0.453323\pi$
$920$	−5.72620	−	9.91808i	−0.188787	−	0.326989i
$921$		0			0
$922$	10.9162	−	18.9074i	0.359506	−	0.622682i
$923$	−13.7124	−	23.7506i	−0.451350	−	0.781761i
$924$		0			0
$925$	−5.07180	+	8.78461i	−0.166760	+	0.288836i
$926$	5.33013	+	9.23205i	0.175159	+	0.303384i
$927$		0			0
$928$	−0.366025	+	0.633975i	−0.0120154	+	0.0208112i
$929$	35.1523			1.15331			0.576654	−	0.816988i	$-0.304358\pi$
$929$	35.1523			1.15331			0.576654	+	0.816988i	$0.304358\pi$
$930$		0			0
$931$		0			0
$932$	−9.69615	−	16.7942i	−0.317608	−	0.550113i
$933$		0			0
$934$	−2.39872	−	4.15471i	−0.0784886	−	0.135946i
$935$	−33.3205	+	57.7128i	−1.08970	+	1.88741i
$936$		0			0
$937$	21.9711			0.717764			0.358882	−	0.933383i	$-0.383158\pi$
$937$	21.9711			0.717764			0.358882	+	0.933383i	$0.383158\pi$
$938$		0			0
$939$		0			0
$940$	−9.19615	+	15.9282i	−0.299945	+	0.519521i
$941$	36.3535			1.18509			0.592544	−	0.805538i	$-0.298124\pi$
$941$	36.3535			1.18509			0.592544	+	0.805538i	$0.298124\pi$
$942$		0			0
$943$	−33.5350			−1.09205
$944$	−5.00052			−0.162753
$945$		0			0
$946$	9.85641			0.320459
$947$	18.3397			0.595962			0.297981	−	0.954572i	$-0.403687\pi$
$947$	18.3397			0.595962			0.297981	+	0.954572i	$0.403687\pi$
$948$		0			0
$949$	23.3205			0.757016
$950$	−1.22474	+	2.12132i	−0.0397360	+	0.0688247i
$951$		0			0
$952$		0			0
$953$	31.7128			1.02728			0.513639	−	0.858006i	$-0.328297\pi$
$953$	31.7128			1.02728			0.513639	+	0.858006i	$0.328297\pi$
$954$		0			0
$955$	3.08725	−	5.34727i	0.0999009	−	0.173034i
$956$	−2.76795	−	4.79423i	−0.0895219	−	0.155056i
$957$		0			0
$958$	8.05558	+	13.9527i	0.260264	+	0.450790i
$959$		0			0
$960$		0			0
$961$	23.0000			0.741935
$962$	9.79796	−	16.9706i	0.315899	−	0.547153i
$963$		0			0
$964$	−6.36396	−	11.0227i	−0.204969	−	0.355017i
$965$	19.5773	−	33.9089i	0.630217	−	1.09157i
$966$		0			0
$967$	−3.23205	−	5.59808i	−0.103936	−	0.180022i	0.809367	−	0.587303i	$-0.199810\pi$
$967$	−3.23205	−	5.59808i	−0.103936	−	0.180022i	−0.913303	+	0.407281i	$0.866477\pi$
$968$	−9.42820	+	16.3301i	−0.303034	+	0.524870i
$969$		0			0
$970$	−3.73205	−	6.46410i	−0.119829	−	0.207550i
$971$	−6.52124	−	11.2951i	−0.209277	−	0.362478i	0.742210	−	0.670167i	$-0.233778\pi$
$971$	−6.52124	−	11.2951i	−0.209277	−	0.362478i	−0.951487	+	0.307689i	$0.900444\pi$
$972$		0			0
$973$		0			0
$974$	−1.16025	+	2.00962i	−0.0371769	+	0.0643923i
$975$		0			0
$976$	−2.96713			−0.0949754
$977$	43.8564			1.40309			0.701545	−	0.712625i	$-0.252494\pi$
$977$	43.8564			1.40309			0.701545	+	0.712625i	$0.252494\pi$
$978$		0			0
$979$	−36.2891	+	62.8545i	−1.15980	+	2.00884i
$980$		0			0
$981$		0			0
$982$	−9.46410	−	16.3923i	−0.302012	−	0.523099i
$983$	27.3741	+	47.4133i	0.873098	+	1.51225i	0.858775	+	0.512353i	$0.171226\pi$
$983$	27.3741	+	47.4133i	0.873098	+	1.51225i	0.0143228	+	0.999897i	$0.495441\pi$
$984$		0			0
$985$	−7.39924	+	12.8159i	−0.235759	+	0.408347i
$986$	2.31079	+	4.00240i	0.0735905	+	0.127463i
$987$		0			0
$988$	2.36603	−	4.09808i	0.0752733	−	0.130377i
$989$	5.34679	+	9.26091i	0.170018	+	0.294480i
$990$		0			0
$991$	−24.6603	+	42.7128i	−0.783359	+	1.35682i	0.146616	+	0.989194i	$0.453162\pi$
$991$	−24.6603	+	42.7128i	−0.783359	+	1.35682i	−0.929975	+	0.367624i	$0.880171\pi$
$992$	−7.34847			−0.233314
$993$		0			0
$994$		0			0
$995$	3.00000	+	5.19615i	0.0951064	+	0.164729i
$996$		0			0
$997$	−8.46670	−	14.6648i	−0.268143	−	0.464437i	0.700239	−	0.713908i	$-0.253077\pi$
$997$	−8.46670	−	14.6648i	−0.268143	−	0.464437i	−0.968382	+	0.249471i	$0.919743\pi$
$998$	13.6603	−	23.6603i	0.432408	−	0.748952i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.e.t.2125.1		8
3.2	odd	2		882.2.e.q.655.1		8
7.2	even	3		2646.2.h.q.667.4		8
7.3	odd	6		2646.2.f.q.883.4		8
7.4	even	3		2646.2.f.q.883.1		8
7.5	odd	6		2646.2.h.q.667.1		8
7.6	odd	2	inner	2646.2.e.t.2125.4		8
9.4	even	3		2646.2.h.q.361.4		8
9.5	odd	6		882.2.h.t.67.3		8
21.2	odd	6		882.2.h.t.79.3		8
21.5	even	6		882.2.h.t.79.2		8
21.11	odd	6		882.2.f.s.295.4	yes	8
21.17	even	6		882.2.f.s.295.1	✓	8
21.20	even	2		882.2.e.q.655.4		8
63.4	even	3		2646.2.f.q.1765.1		8
63.5	even	6		882.2.e.q.373.4		8
63.11	odd	6		7938.2.a.cj.1.1		4
63.13	odd	6		2646.2.h.q.361.1		8
63.23	odd	6		882.2.e.q.373.1		8
63.25	even	3		7938.2.a.co.1.4		4
63.31	odd	6		2646.2.f.q.1765.4		8
63.32	odd	6		882.2.f.s.589.3	yes	8
63.38	even	6		7938.2.a.cj.1.4		4
63.40	odd	6	inner	2646.2.e.t.1549.4		8
63.41	even	6		882.2.h.t.67.2		8
63.52	odd	6		7938.2.a.co.1.1		4
63.58	even	3	inner	2646.2.e.t.1549.1		8
63.59	even	6		882.2.f.s.589.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.q.373.1		8	63.23	odd	6
882.2.e.q.373.4		8	63.5	even	6
882.2.e.q.655.1		8	3.2	odd	2
882.2.e.q.655.4		8	21.20	even	2
882.2.f.s.295.1	✓	8	21.17	even	6
882.2.f.s.295.4	yes	8	21.11	odd	6
882.2.f.s.589.2	yes	8	63.59	even	6
882.2.f.s.589.3	yes	8	63.32	odd	6
882.2.h.t.67.2		8	63.41	even	6
882.2.h.t.67.3		8	9.5	odd	6
882.2.h.t.79.2		8	21.5	even	6
882.2.h.t.79.3		8	21.2	odd	6
2646.2.e.t.1549.1		8	63.58	even	3	inner
2646.2.e.t.1549.4		8	63.40	odd	6	inner
2646.2.e.t.2125.1		8	1.1	even	1	trivial
2646.2.e.t.2125.4		8	7.6	odd	2	inner
2646.2.f.q.883.1		8	7.4	even	3
2646.2.f.q.883.4		8	7.3	odd	6
2646.2.f.q.1765.1		8	63.4	even	3
2646.2.f.q.1765.4		8	63.31	odd	6
2646.2.h.q.361.1		8	63.13	odd	6
2646.2.h.q.361.4		8	9.4	even	3
2646.2.h.q.667.1		8	7.5	odd	6
2646.2.h.q.667.4		8	7.2	even	3
7938.2.a.cj.1.1		4	63.11	odd	6
7938.2.a.cj.1.4		4	63.38	even	6
7938.2.a.co.1.1		4	63.52	odd	6
7938.2.a.co.1.4		4	63.25	even	3

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:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-0.965926 + 1.67303i) q^{5} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-0.965926 + 1.67303i) q^{5} +1.00000 q^{8} +(-0.965926 + 1.67303i) q^{10} +(2.73205 + 4.73205i) q^{11} +(-1.22474 - 2.12132i) q^{13} +1.00000 q^{16} +(3.15660 - 5.46739i) q^{17} +(0.965926 + 1.67303i) q^{19} +(-0.965926 + 1.67303i) q^{20} +(2.73205 + 4.73205i) q^{22} +(-2.96410 + 5.13397i) q^{23} +(0.633975 + 1.09808i) q^{25} +(-1.22474 - 2.12132i) q^{26} +(-0.366025 + 0.633975i) q^{29} -7.34847 q^{31} +1.00000 q^{32} +(3.15660 - 5.46739i) q^{34} +(4.00000 + 6.92820i) q^{37} +(0.965926 + 1.67303i) q^{38} +(-0.965926 + 1.67303i) q^{40} +(2.82843 + 4.89898i) q^{41} +(0.901924 - 1.56218i) q^{43} +(2.73205 + 4.73205i) q^{44} +(-2.96410 + 5.13397i) q^{46} +9.52056 q^{47} +(0.633975 + 1.09808i) q^{50} +(-1.22474 - 2.12132i) q^{52} +(1.63397 - 2.83013i) q^{53} -10.5558 q^{55} +(-0.366025 + 0.633975i) q^{58} -5.00052 q^{59} -2.96713 q^{61} -7.34847 q^{62} +1.00000 q^{64} +4.73205 q^{65} -14.1962 q^{67} +(3.15660 - 5.46739i) q^{68} +11.1962 q^{71} +(-4.76028 + 8.24504i) q^{73} +(4.00000 + 6.92820i) q^{74} +(0.965926 + 1.67303i) q^{76} -10.1244 q^{79} +(-0.965926 + 1.67303i) q^{80} +(2.82843 + 4.89898i) q^{82} +(-4.94975 + 8.57321i) q^{83} +(6.09808 + 10.5622i) q^{85} +(0.901924 - 1.56218i) q^{86} +(2.73205 + 4.73205i) q^{88} +(6.64136 + 11.5032i) q^{89} +(-2.96410 + 5.13397i) q^{92} +9.52056 q^{94} -3.73205 q^{95} +(-1.93185 + 3.34607i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^4 + 8 * q^8	\( 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8} + 8 q^{11} + 8 q^{16} + 8 q^{22} + 4 q^{23} + 12 q^{25} + 4 q^{29} + 8 q^{32} + 32 q^{37} + 28 q^{43} + 8 q^{44} + 4 q^{46} + 12 q^{50} + 20 q^{53} + 4 q^{58} + 8 q^{64} + 24 q^{65} - 72 q^{67} + 48 q^{71} + 32 q^{74} + 16 q^{79} + 28 q^{85} + 28 q^{86} + 8 q^{88} + 4 q^{92} - 16 q^{95}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^4 + 8 * q^8 + 8 * q^11 + 8 * q^16 + 8 * q^22 + 4 * q^23 + 12 * q^25 + 4 * q^29 + 8 * q^32 + 32 * q^37 + 28 * q^43 + 8 * q^44 + 4 * q^46 + 12 * q^50 + 20 * q^53 + 4 * q^58 + 8 * q^64 + 24 * q^65 - 72 * q^67 + 48 * q^71 + 32 * q^74 + 16 * q^79 + 28 * q^85 + 28 * q^86 + 8 * q^88 + 4 * q^92 - 16 * q^95

Introduction

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