LMFDB - Embedded newform 2646.2.h.p.667.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(361,2646)]

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, 4]))

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

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

chi := DirichletCharacter("2646.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.h (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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			667.2
Root			$0.500000 - 1.41036i$ of defining polynomial
Character	$\chi$	$=$	2646.667
Dual form			2646.2.h.p.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.76088 q^{5} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.76088 q^{5} -1.00000 q^{8} +(0.880438 + 1.52496i) q^{10} -6.12476 q^{11} +(0.380438 + 0.658939i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-3.42107 - 5.92546i) q^{17} +(-0.971410 + 1.68253i) q^{19} +(-0.880438 + 1.52496i) q^{20} +(-3.06238 - 5.30420i) q^{22} +0.421067 q^{23} -1.89931 q^{25} +(-0.380438 + 0.658939i) q^{26} +(-0.732287 + 1.26836i) q^{29} +(3.85185 - 6.67160i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.42107 - 5.92546i) q^{34} +(1.44282 - 2.49904i) q^{37} -1.94282 q^{38} -1.76088 q^{40} +(-3.47141 - 6.01266i) q^{41} +(4.33009 - 7.49994i) q^{43} +(3.06238 - 5.30420i) q^{44} +(0.210533 + 0.364654i) q^{46} +(-0.830095 - 1.43777i) q^{47} +(-0.949657 - 1.64485i) q^{50} -0.760877 q^{52} +(0.112725 + 0.195246i) q^{53} -10.7850 q^{55} -1.46457 q^{58} +(-0.993163 + 1.72021i) q^{59} +(-5.17511 - 8.96355i) q^{61} +7.70370 q^{62} +1.00000 q^{64} +(0.669905 + 1.16031i) q^{65} +(-3.39248 + 5.87594i) q^{67} +6.84213 q^{68} -10.7850 q^{71} +(-0.153353 - 0.265616i) q^{73} +2.88564 q^{74} +(-0.971410 - 1.68253i) q^{76} +(6.72257 + 11.6438i) q^{79} +(-0.880438 - 1.52496i) q^{80} +(3.47141 - 6.01266i) q^{82} +(-1.56238 + 2.70612i) q^{83} +(-6.02408 - 10.4340i) q^{85} +8.66019 q^{86} +6.12476 q^{88} +(1.30150 - 2.25427i) q^{89} +(-0.210533 + 0.364654i) q^{92} +(0.830095 - 1.43777i) q^{94} +(-1.71053 + 2.96273i) q^{95} +(1.81806 - 3.14897i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} + 10 q^{5} - 6 q^{8}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^4 + 10 * q^5 - 6 * q^8	$ 6 q + 3 q^{2} - 3 q^{4} + 10 q^{5} - 6 q^{8} + 5 q^{10} - 2 q^{11} + 2 q^{13} - 3 q^{16} - 4 q^{17} + 3 q^{19} - 5 q^{20} - q^{22} - 14 q^{23} + 4 q^{25} - 2 q^{26} + 5 q^{29} + 14 q^{31} + 3 q^{32} + 4 q^{34} - 9 q^{37} + 6 q^{38} - 10 q^{40} - 12 q^{41} + 18 q^{43} + q^{44} - 7 q^{46} + 3 q^{47} + 2 q^{50} - 4 q^{52} - 9 q^{53} - 14 q^{55} + 10 q^{58} + 4 q^{59} - 4 q^{61} + 28 q^{62} + 6 q^{64} + 12 q^{65} + 5 q^{67} + 8 q^{68} - 14 q^{71} + 25 q^{73} - 18 q^{74} + 3 q^{76} + 7 q^{79} - 5 q^{80} + 12 q^{82} + 8 q^{83} + 14 q^{85} + 36 q^{86} + 2 q^{88} - 9 q^{89} + 7 q^{92} - 3 q^{94} - 2 q^{95} + 28 q^{97}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 + 10 * q^5 - 6 * q^8 + 5 * q^10 - 2 * q^11 + 2 * q^13 - 3 * q^16 - 4 * q^17 + 3 * q^19 - 5 * q^20 - q^22 - 14 * q^23 + 4 * q^25 - 2 * q^26 + 5 * q^29 + 14 * q^31 + 3 * q^32 + 4 * q^34 - 9 * q^37 + 6 * q^38 - 10 * q^40 - 12 * q^41 + 18 * q^43 + q^44 - 7 * q^46 + 3 * q^47 + 2 * q^50 - 4 * q^52 - 9 * q^53 - 14 * q^55 + 10 * q^58 + 4 * q^59 - 4 * q^61 + 28 * q^62 + 6 * q^64 + 12 * q^65 + 5 * q^67 + 8 * q^68 - 14 * q^71 + 25 * q^73 - 18 * q^74 + 3 * q^76 + 7 * q^79 - 5 * q^80 + 12 * q^82 + 8 * q^83 + 14 * q^85 + 36 * q^86 + 2 * q^88 - 9 * q^89 + 7 * q^92 - 3 * q^94 - 2 * q^95 + 28 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.76088			0.787488			0.393744	−	0.919220i	$-0.371180\pi$
$5$	1.76088			0.787488			0.393744	+	0.919220i	$0.371180\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.880438	+	1.52496i	0.278419	+	0.482236i
$11$	−6.12476			−1.84669			−0.923343	−	0.383977i	$-0.874554\pi$
$11$	−6.12476			−1.84669			−0.923343	+	0.383977i	$0.874554\pi$
$12$		0			0
$13$	0.380438	+	0.658939i	0.105515	+	0.182757i	0.913948	−	0.405831i	$-0.133018\pi$
$13$	0.380438	+	0.658939i	0.105515	+	0.182757i	−0.808434	+	0.588587i	$0.799684\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.42107	−	5.92546i	−0.829731	−	1.43714i	−0.898250	−	0.439486i	$-0.855161\pi$
$17$	−3.42107	−	5.92546i	−0.829731	−	1.43714i	0.0685191	−	0.997650i	$-0.478173\pi$
$18$		0			0
$19$	−0.971410	+	1.68253i	−0.222857	+	0.385999i	−0.955674	−	0.294426i	$-0.904872\pi$
$19$	−0.971410	+	1.68253i	−0.222857	+	0.385999i	0.732818	+	0.680425i	$0.238205\pi$
$20$	−0.880438	+	1.52496i	−0.196872	+	0.340992i
$21$		0			0
$22$	−3.06238	−	5.30420i	−0.652902	−	1.13086i
$23$	0.421067			0.0877985			0.0438992	−	0.999036i	$-0.486022\pi$
$23$	0.421067			0.0877985			0.0438992	+	0.999036i	$0.486022\pi$
$24$		0			0
$25$	−1.89931			−0.379863
$26$	−0.380438	+	0.658939i	−0.0746101	+	0.129228i
$27$		0			0
$28$		0			0
$29$	−0.732287	+	1.26836i	−0.135982	+	0.235528i	−0.925972	−	0.377592i	$-0.876752\pi$
$29$	−0.732287	+	1.26836i	−0.135982	+	0.235528i	0.789990	+	0.613120i	$0.210086\pi$
$30$		0			0
$31$	3.85185	−	6.67160i	0.691812	−	1.19825i	−0.279431	−	0.960166i	$-0.590146\pi$
$31$	3.85185	−	6.67160i	0.691812	−	1.19825i	0.971243	−	0.238088i	$-0.0765208\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	3.42107	−	5.92546i	0.586708	−	1.01621i
$35$		0			0
$36$		0			0
$37$	1.44282	−	2.49904i	0.237198	−	0.410839i	−0.722711	−	0.691150i	$-0.757104\pi$
$37$	1.44282	−	2.49904i	0.237198	−	0.410839i	0.959909	+	0.280311i	$0.0904376\pi$
$38$	−1.94282			−0.315167
$39$		0			0
$40$	−1.76088			−0.278419
$41$	−3.47141	−	6.01266i	−0.542143	−	0.939020i	−0.998781	−	0.0493667i	$-0.984280\pi$
$41$	−3.47141	−	6.01266i	−0.542143	−	0.939020i	0.456638	−	0.889653i	$-0.349054\pi$
$42$		0			0
$43$	4.33009	−	7.49994i	0.660333	−	1.14373i	−0.320195	−	0.947352i	$-0.603748\pi$
$43$	4.33009	−	7.49994i	0.660333	−	1.14373i	0.980528	−	0.196379i	$-0.0629183\pi$
$44$	3.06238	−	5.30420i	0.461671	−	0.799638i
$45$		0			0
$46$	0.210533	+	0.364654i	0.0310414	+	0.0537654i
$47$	−0.830095	−	1.43777i	−0.121082	−	0.209720i	0.799113	−	0.601181i	$-0.205303\pi$
$47$	−0.830095	−	1.43777i	−0.121082	−	0.209720i	−0.920195	+	0.391461i	$0.871970\pi$
$48$		0			0
$49$		0			0
$50$	−0.949657	−	1.64485i	−0.134302	−	0.232617i
$51$		0			0
$52$	−0.760877			−0.105515
$53$	0.112725	+	0.195246i	0.0154840	+	0.0268190i	0.873664	−	0.486531i	$-0.161738\pi$
$53$	0.112725	+	0.195246i	0.0154840	+	0.0268190i	−0.858180	+	0.513350i	$0.828404\pi$
$54$		0			0
$55$	−10.7850			−1.45424
$56$		0			0
$57$		0			0
$58$	−1.46457			−0.192308
$59$	−0.993163	+	1.72021i	−0.129299	+	0.223952i	−0.923405	−	0.383827i	$-0.874606\pi$
$59$	−0.993163	+	1.72021i	−0.129299	+	0.223952i	0.794106	+	0.607779i	$0.207939\pi$
$60$		0			0
$61$	−5.17511	−	8.96355i	−0.662605	−	1.14766i	−0.979929	−	0.199348i	$-0.936118\pi$
$61$	−5.17511	−	8.96355i	−0.662605	−	1.14766i	0.317324	−	0.948317i	$-0.397216\pi$
$62$	7.70370			0.978370
$63$		0			0
$64$	1.00000			0.125000
$65$	0.669905	+	1.16031i	0.0830915	+	0.143919i
$66$		0			0
$67$	−3.39248	+	5.87594i	−0.414457	+	0.717861i	−0.995371	−	0.0961042i	$-0.969362\pi$
$67$	−3.39248	+	5.87594i	−0.414457	+	0.717861i	0.580914	+	0.813965i	$0.302695\pi$
$68$	6.84213			0.829731
$69$		0			0
$70$		0			0
$71$	−10.7850			−1.27994			−0.639969	−	0.768401i	$-0.721053\pi$
$71$	−10.7850			−1.27994			−0.639969	+	0.768401i	$0.721053\pi$
$72$		0			0
$73$	−0.153353	−	0.265616i	−0.0179487	−	0.0310880i	0.856912	−	0.515463i	$-0.172380\pi$
$73$	−0.153353	−	0.265616i	−0.0179487	−	0.0310880i	−0.874860	+	0.484375i	$0.839047\pi$
$74$	2.88564			0.335449
$75$		0			0
$76$	−0.971410	−	1.68253i	−0.111428	−	0.193000i
$77$		0			0
$78$		0			0
$79$	6.72257	+	11.6438i	0.756348	+	1.31003i	0.944701	+	0.327932i	$0.106352\pi$
$79$	6.72257	+	11.6438i	0.756348	+	1.31003i	−0.188353	+	0.982101i	$0.560315\pi$
$80$	−0.880438	−	1.52496i	−0.0984360	−	0.170496i
$81$		0			0
$82$	3.47141	−	6.01266i	0.383353	−	0.663987i
$83$	−1.56238	+	2.70612i	−0.171494	+	0.297036i	−0.938942	−	0.344075i	$-0.888193\pi$
$83$	−1.56238	+	2.70612i	−0.171494	+	0.297036i	0.767449	+	0.641110i	$0.221526\pi$
$84$		0			0
$85$	−6.02408	−	10.4340i	−0.653403	−	1.13173i
$86$	8.66019			0.933852
$87$		0			0
$88$	6.12476			0.652902
$89$	1.30150	−	2.25427i	0.137959	−	0.238952i	−0.788765	−	0.614695i	$-0.789279\pi$
$89$	1.30150	−	2.25427i	0.137959	−	0.238952i	0.926724	+	0.375743i	$0.122612\pi$
$90$		0			0
$91$		0			0
$92$	−0.210533	+	0.364654i	−0.0219496	+	0.0380178i
$93$		0			0
$94$	0.830095	−	1.43777i	0.0856178	−	0.148294i
$95$	−1.71053	+	2.96273i	−0.175497	+	0.303970i
$96$		0			0
$97$	1.81806	−	3.14897i	0.184596	−	0.319729i	−0.758845	−	0.651272i	$-0.774236\pi$
$97$	1.81806	−	3.14897i	0.184596	−	0.319729i	0.943440	+	0.331543i	$0.107569\pi$
$98$		0			0
$99$		0			0
$100$	0.949657	−	1.64485i	0.0949657	−	0.164485i
$101$	−8.01040			−0.797065			−0.398532	−	0.917154i	$-0.630480\pi$
$101$	−8.01040			−0.797065			−0.398532	+	0.917154i	$0.630480\pi$
$102$		0			0
$103$	6.82846			0.672828			0.336414	−	0.941714i	$-0.390786\pi$
$103$	6.82846			0.672828			0.336414	+	0.941714i	$0.390786\pi$
$104$	−0.380438	−	0.658939i	−0.0373051	−	0.0646142i
$105$		0			0
$106$	−0.112725	+	0.195246i	−0.0109488	+	0.0189639i
$107$	−1.77292	+	3.07078i	−0.171394	+	0.296863i	−0.938908	−	0.344170i	$-0.888160\pi$
$107$	−1.77292	+	3.07078i	−0.171394	+	0.296863i	0.767513	+	0.641033i	$0.221494\pi$
$108$		0			0
$109$	0.351848	+	0.609419i	0.0337010	+	0.0583718i	0.882384	−	0.470530i	$-0.155937\pi$
$109$	0.351848	+	0.609419i	0.0337010	+	0.0583718i	−0.848683	+	0.528902i	$0.822604\pi$
$110$	−5.39248	−	9.34004i	−0.514152	−	0.890538i
$111$		0			0
$112$		0			0
$113$	−4.25116	−	7.36323i	−0.399916	−	0.692674i	0.593799	−	0.804613i	$-0.297627\pi$
$113$	−4.25116	−	7.36323i	−0.399916	−	0.692674i	−0.993715	+	0.111939i	$0.964294\pi$
$114$		0			0
$115$	0.741446			0.0691402
$116$	−0.732287	−	1.26836i	−0.0679911	−	0.117764i
$117$		0			0
$118$	−1.98633			−0.182856
$119$		0			0
$120$		0			0
$121$	26.5127			2.41025
$122$	5.17511	−	8.96355i	0.468532	−	0.811521i
$123$		0			0
$124$	3.85185	+	6.67160i	0.345906	+	0.599127i
$125$	−12.1488			−1.08663
$126$		0			0
$127$	−18.9532			−1.68183			−0.840913	−	0.541170i	$-0.817982\pi$
$127$	−18.9532			−1.68183			−0.840913	+	0.541170i	$0.817982\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−0.669905	+	1.16031i	−0.0587546	+	0.101766i
$131$	−7.29303			−0.637195			−0.318598	−	0.947890i	$-0.603212\pi$
$131$	−7.29303			−0.637195			−0.318598	+	0.947890i	$0.603212\pi$
$132$		0			0
$133$		0			0
$134$	−6.78495			−0.586131
$135$		0			0
$136$	3.42107	+	5.92546i	0.293354	+	0.508104i
$137$	8.18194			0.699031			0.349515	−	0.936931i	$-0.386346\pi$
$137$	8.18194			0.699031			0.349515	+	0.936931i	$0.386346\pi$
$138$		0			0
$139$	6.23229	+	10.7946i	0.528616	+	0.915589i	0.999443	+	0.0333640i	$0.0106220\pi$
$139$	6.23229	+	10.7946i	0.528616	+	0.915589i	−0.470828	+	0.882225i	$0.656045\pi$
$140$		0			0
$141$		0			0
$142$	−5.39248	−	9.34004i	−0.452527	−	0.783799i
$143$	−2.33009	−	4.03584i	−0.194852	−	0.337494i
$144$		0			0
$145$	−1.28947	+	2.23342i	−0.107084	+	0.185476i
$146$	0.153353	−	0.265616i	0.0126916	−	0.0219825i
$147$		0			0
$148$	1.44282	+	2.49904i	0.118599	+	0.205420i
$149$	−8.82846			−0.723256			−0.361628	−	0.932323i	$-0.617779\pi$
$149$	−8.82846			−0.723256			−0.361628	+	0.932323i	$0.617779\pi$
$150$		0			0
$151$	−14.9863			−1.21957			−0.609785	−	0.792567i	$-0.708744\pi$
$151$	−14.9863			−1.21957			−0.609785	+	0.792567i	$0.708744\pi$
$152$	0.971410	−	1.68253i	0.0787918	−	0.136471i
$153$		0			0
$154$		0			0
$155$	6.78263	−	11.7479i	0.544794	−	0.943611i
$156$		0			0
$157$	9.49028	−	16.4377i	0.757407	−	1.31187i	−0.186761	−	0.982405i	$-0.559799\pi$
$157$	9.49028	−	16.4377i	0.757407	−	1.31187i	0.944169	−	0.329462i	$-0.106868\pi$
$158$	−6.72257	+	11.6438i	−0.534819	+	0.926334i
$159$		0			0
$160$	0.880438	−	1.52496i	0.0696048	−	0.120559i
$161$		0			0
$162$		0			0
$163$	−7.51887	+	13.0231i	−0.588924	+	1.02005i	0.405450	+	0.914117i	$0.367115\pi$
$163$	−7.51887	+	13.0231i	−0.588924	+	1.02005i	−0.994374	+	0.105929i	$0.966219\pi$
$164$	6.94282			0.542143
$165$		0			0
$166$	−3.12476			−0.242529
$167$	0.572097	+	0.990901i	0.0442702	+	0.0766782i	0.887311	−	0.461171i	$-0.152570\pi$
$167$	0.572097	+	0.990901i	0.0442702	+	0.0766782i	−0.843041	+	0.537849i	$0.819237\pi$
$168$		0			0
$169$	6.21053	−	10.7570i	0.477733	−	0.827458i
$170$	6.02408	−	10.4340i	0.462026	−	0.800252i
$171$		0			0
$172$	4.33009	+	7.49994i	0.330167	+	0.571865i
$173$	−0.248838	−	0.431001i	−0.0189188	−	0.0327684i	0.856411	−	0.516295i	$-0.172689\pi$
$173$	−0.248838	−	0.431001i	−0.0189188	−	0.0327684i	−0.875330	+	0.483526i	$0.839356\pi$
$174$		0			0
$175$		0			0
$176$	3.06238	+	5.30420i	0.230836	+	0.399819i
$177$		0			0
$178$	2.60301			0.195104
$179$	−4.41423	−	7.64567i	−0.329935	−	0.571464i	0.652564	−	0.757734i	$-0.273694\pi$
$179$	−4.41423	−	7.64567i	−0.329935	−	0.571464i	−0.982499	+	0.186270i	$0.940360\pi$
$180$		0			0
$181$	−1.32941			−0.0988140			−0.0494070	−	0.998779i	$-0.515733\pi$
$181$	−1.32941			−0.0988140			−0.0494070	+	0.998779i	$0.515733\pi$
$182$		0			0
$183$		0			0
$184$	−0.421067			−0.0310414
$185$	2.54063	−	4.40050i	0.186791	−	0.323531i
$186$		0			0
$187$	20.9532	+	36.2920i	1.53225	+	2.65394i
$188$	1.66019			0.121082
$189$		0			0
$190$	−3.42107			−0.248190
$191$	−8.08414	−	14.0021i	−0.584947	−	1.01316i	−0.994882	−	0.101044i	$-0.967782\pi$
$191$	−8.08414	−	14.0021i	−0.584947	−	1.01316i	0.409934	−	0.912115i	$-0.365552\pi$
$192$		0			0
$193$	7.08414	−	12.2701i	0.509927	−	0.883220i	−0.490007	−	0.871719i	$-0.663006\pi$
$193$	7.08414	−	12.2701i	0.509927	−	0.883220i	0.999934	−	0.0115011i	$-0.00366101\pi$
$194$	3.63611			0.261058
$195$		0			0
$196$		0			0
$197$	−15.8421			−1.12871			−0.564353	−	0.825534i	$-0.690874\pi$
$197$	−15.8421			−1.12871			−0.564353	+	0.825534i	$0.690874\pi$
$198$		0			0
$199$	4.47141	+	7.74471i	0.316970	+	0.549008i	0.979854	−	0.199714i	$-0.0640013\pi$
$199$	4.47141	+	7.74471i	0.316970	+	0.549008i	−0.662884	+	0.748722i	$0.730668\pi$
$200$	1.89931			0.134302
$201$		0			0
$202$	−4.00520	−	6.93721i	−0.281805	−	0.488101i
$203$		0			0
$204$		0			0
$205$	−6.11273	−	10.5876i	−0.426931	−	0.739467i
$206$	3.41423	+	5.91362i	0.237881	+	0.412021i
$207$		0			0
$208$	0.380438	−	0.658939i	0.0263787	−	0.0456892i
$209$	5.94966	−	10.3051i	0.411546	−	0.712819i
$210$		0			0
$211$	11.3856	+	19.7205i	0.783820	+	1.35762i	0.929702	+	0.368314i	$0.120065\pi$
$211$	11.3856	+	19.7205i	0.783820	+	1.35762i	−0.145882	+	0.989302i	$0.546602\pi$
$212$	−0.225450			−0.0154840
$213$		0			0
$214$	−3.54583			−0.242388
$215$	7.62476	−	13.2065i	0.520005	−	0.900674i
$216$		0			0
$217$		0			0
$218$	−0.351848	+	0.609419i	−0.0238302	+	0.0412751i
$219$		0			0
$220$	5.39248	−	9.34004i	0.363561	−	0.629706i
$221$	2.60301	−	4.50855i	0.175097	−	0.303278i
$222$		0			0
$223$	6.44282	−	11.1593i	0.431443	−	0.747281i	−0.565555	−	0.824711i	$-0.691338\pi$
$223$	6.44282	−	11.1593i	0.431443	−	0.747281i	0.996998	+	0.0774293i	$0.0246712\pi$
$224$		0			0
$225$		0			0
$226$	4.25116	−	7.36323i	0.282783	−	0.489795i
$227$	21.9967			1.45997			0.729987	−	0.683461i	$-0.239526\pi$
$227$	21.9967			1.45997			0.729987	+	0.683461i	$0.239526\pi$
$228$		0			0
$229$	3.79863			0.251020			0.125510	−	0.992092i	$-0.459943\pi$
$229$	3.79863			0.251020			0.125510	+	0.992092i	$0.459943\pi$
$230$	0.370723	+	0.642111i	0.0244448	+	0.0423396i
$231$		0			0
$232$	0.732287	−	1.26836i	0.0480770	−	0.0832718i
$233$	3.33530	−	5.77690i	0.218503	−	0.378458i	−0.735848	−	0.677147i	$-0.763216\pi$
$233$	3.33530	−	5.77690i	0.218503	−	0.378458i	0.954350	+	0.298689i	$0.0965495\pi$
$234$		0			0
$235$	−1.46169	−	2.53173i	−0.0953505	−	0.165152i
$236$	−0.993163	−	1.72021i	−0.0646494	−	0.111976i
$237$		0			0
$238$		0			0
$239$	7.82038	+	13.5453i	0.505858	+	0.876172i	0.999977	+	0.00677786i	$0.00215748\pi$
$239$	7.82038	+	13.5453i	0.505858	+	0.876172i	−0.494119	+	0.869394i	$0.664509\pi$
$240$		0			0
$241$	−21.4120			−1.37927			−0.689635	−	0.724157i	$-0.742229\pi$
$241$	−21.4120			−1.37927			−0.689635	+	0.724157i	$0.742229\pi$
$242$	13.2564	+	22.9607i	0.852151	+	1.47597i
$243$		0			0
$244$	10.3502			0.662605
$245$		0			0
$246$		0			0
$247$	−1.47825			−0.0940586
$248$	−3.85185	+	6.67160i	−0.244593	+	0.423647i
$249$		0			0
$250$	−6.07442	−	10.5212i	−0.384180	−	0.665419i
$251$	−23.6030			−1.48981			−0.744904	−	0.667171i	$-0.767505\pi$
$251$	−23.6030			−1.48981			−0.744904	+	0.667171i	$0.767505\pi$
$252$		0			0
$253$	−2.57893			−0.162136
$254$	−9.47661	−	16.4140i	−0.594616	−	1.02990i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	20.2599			1.26378			0.631890	−	0.775058i	$-0.282279\pi$
$257$	20.2599			1.26378			0.631890	+	0.775058i	$0.282279\pi$
$258$		0			0
$259$		0			0
$260$	−1.33981			−0.0830915
$261$		0			0
$262$	−3.64652	−	6.31595i	−0.225283	−	0.390201i
$263$	22.4887			1.38671			0.693355	−	0.720596i	$-0.256132\pi$
$263$	22.4887			1.38671			0.693355	+	0.720596i	$0.256132\pi$
$264$		0			0
$265$	0.198495	+	0.343803i	0.0121935	+	0.0211197i
$266$		0			0
$267$		0			0
$268$	−3.39248	−	5.87594i	−0.207228	−	0.358930i
$269$	−12.6706	−	21.9461i	−0.772540	−	1.33808i	−0.936167	−	0.351556i	$-0.885653\pi$
$269$	−12.6706	−	21.9461i	−0.772540	−	1.33808i	0.163627	−	0.986522i	$-0.447681\pi$
$270$		0			0
$271$	6.87880	−	11.9144i	0.417858	−	0.723751i	−0.577866	−	0.816132i	$-0.696114\pi$
$271$	6.87880	−	11.9144i	0.417858	−	0.723751i	0.995724	+	0.0923810i	$0.0294478\pi$
$272$	−3.42107	+	5.92546i	−0.207433	+	0.359284i
$273$		0			0
$274$	4.09097	+	7.08577i	0.247145	+	0.428067i
$275$	11.6328			0.701487
$276$		0			0
$277$	−3.28263			−0.197234			−0.0986171	−	0.995125i	$-0.531442\pi$
$277$	−3.28263			−0.197234			−0.0986171	+	0.995125i	$0.531442\pi$
$278$	−6.23229	+	10.7946i	−0.373788	+	0.647419i
$279$		0			0
$280$		0			0
$281$	−0.634479	+	1.09895i	−0.0378498	+	0.0655578i	−0.884330	−	0.466863i	$-0.845384\pi$
$281$	−0.634479	+	1.09895i	−0.0378498	+	0.0655578i	0.846480	+	0.532421i	$0.178718\pi$
$282$		0			0
$283$	−4.09617	+	7.09478i	−0.243492	+	0.421741i	−0.961707	−	0.274081i	$-0.911626\pi$
$283$	−4.09617	+	7.09478i	−0.243492	+	0.421741i	0.718214	+	0.695822i	$0.244960\pi$
$284$	5.39248	−	9.34004i	0.319985	−	0.554230i
$285$		0			0
$286$	2.33009	−	4.03584i	0.137781	−	0.238644i
$287$		0			0
$288$		0			0
$289$	−14.9074	+	25.8204i	−0.876906	+	1.51884i
$290$	−2.57893			−0.151440
$291$		0			0
$292$	0.306707			0.0179487
$293$	7.72545	+	13.3809i	0.451326	+	0.781719i	0.998469	−	0.0553202i	$-0.0176180\pi$
$293$	7.72545	+	13.3809i	0.451326	+	0.781719i	−0.547143	+	0.837039i	$0.684285\pi$
$294$		0			0
$295$	−1.74884	+	3.02908i	−0.101821	+	0.176360i
$296$	−1.44282	+	2.49904i	−0.0838622	+	0.145254i
$297$		0			0
$298$	−4.41423	−	7.64567i	−0.255709	−	0.442902i
$299$	0.160190	+	0.277457i	0.00926402	+	0.0160458i
$300$		0			0
$301$		0			0
$302$	−7.49316	−	12.9785i	−0.431183	−	0.746831i
$303$		0			0
$304$	1.94282			0.111428
$305$	−9.11273	−	15.7837i	−0.521793	−	0.903772i
$306$		0			0
$307$	−4.89931			−0.279619			−0.139809	−	0.990178i	$-0.544649\pi$
$307$	−4.89931			−0.279619			−0.139809	+	0.990178i	$0.544649\pi$
$308$		0			0
$309$		0			0
$310$	13.5653			0.770455
$311$	3.84501	−	6.65976i	0.218031	−	0.377640i	−0.736175	−	0.676791i	$-0.763370\pi$
$311$	3.84501	−	6.65976i	0.218031	−	0.377640i	0.954206	+	0.299151i	$0.0967034\pi$
$312$		0			0
$313$	−0.861564	−	1.49227i	−0.0486985	−	0.0843482i	0.840649	−	0.541581i	$-0.182174\pi$
$313$	−0.861564	−	1.49227i	−0.0486985	−	0.0843482i	−0.889347	+	0.457233i	$0.848841\pi$
$314$	18.9806			1.07114
$315$		0			0
$316$	−13.4451			−0.756348
$317$	16.6014	+	28.7544i	0.932426	+	1.61501i	0.779161	+	0.626824i	$0.215646\pi$
$317$	16.6014	+	28.7544i	0.932426	+	1.61501i	0.153266	+	0.988185i	$0.451021\pi$
$318$		0			0
$319$	4.48508	−	7.76839i	0.251116	−	0.434946i
$320$	1.76088			0.0984360
$321$		0			0
$322$		0			0
$323$	13.2930			0.739644
$324$		0			0
$325$	−0.722572	−	1.25153i	−0.0400811	−	0.0694224i
$326$	−15.0377			−0.832864
$327$		0			0
$328$	3.47141	+	6.01266i	0.191677	+	0.331994i
$329$		0			0
$330$		0			0
$331$	−1.44445	−	2.50187i	−0.0793944	−	0.137515i	0.823594	−	0.567179i	$-0.191965\pi$
$331$	−1.44445	−	2.50187i	−0.0793944	−	0.137515i	−0.902989	+	0.429664i	$0.858632\pi$
$332$	−1.56238	−	2.70612i	−0.0857468	−	0.148518i
$333$		0			0
$334$	−0.572097	+	0.990901i	−0.0313037	+	0.0542197i
$335$	−5.97373	+	10.3468i	−0.326380	+	0.565307i
$336$		0			0
$337$	−4.36156	−	7.55445i	−0.237590	−	0.411517i	0.722433	−	0.691441i	$-0.243024\pi$
$337$	−4.36156	−	7.55445i	−0.237590	−	0.411517i	−0.960022	+	0.279924i	$0.909691\pi$
$338$	12.4211			0.675617
$339$		0			0
$340$	12.0482			0.653403
$341$	−23.5917	+	40.8620i	−1.27756	+	2.21280i
$342$		0			0
$343$		0			0
$344$	−4.33009	+	7.49994i	−0.233463	+	0.404370i
$345$		0			0
$346$	0.248838	−	0.431001i	0.0133776	−	0.0231707i
$347$	4.84733	−	8.39583i	0.260219	−	0.450712i	−0.706081	−	0.708131i	$-0.749539\pi$
$347$	4.84733	−	8.39583i	0.260219	−	0.450712i	0.966300	+	0.257419i	$0.0828720\pi$
$348$		0			0
$349$	−14.1992	+	24.5937i	−0.760065	+	1.31647i	0.182752	+	0.983159i	$0.441500\pi$
$349$	−14.1992	+	24.5937i	−0.760065	+	1.31647i	−0.942817	+	0.333312i	$0.891834\pi$
$350$		0			0
$351$		0			0
$352$	−3.06238	+	5.30420i	−0.163225	+	0.282715i
$353$	−4.39372			−0.233854			−0.116927	−	0.993141i	$-0.537304\pi$
$353$	−4.39372			−0.233854			−0.116927	+	0.993141i	$0.537304\pi$
$354$		0			0
$355$	−18.9910			−1.00794
$356$	1.30150	+	2.25427i	0.0689796	+	0.119476i
$357$		0			0
$358$	4.41423	−	7.64567i	0.233299	−	0.404086i
$359$	−16.0796	+	27.8507i	−0.848650	+	1.46990i	0.0337633	+	0.999430i	$0.489251\pi$
$359$	−16.0796	+	27.8507i	−0.848650	+	1.46990i	−0.882413	+	0.470475i	$0.844083\pi$
$360$		0			0
$361$	7.61273	+	13.1856i	0.400670	+	0.693980i
$362$	−0.664703	−	1.15130i	−0.0349360	−	0.0605110i
$363$		0			0
$364$		0			0
$365$	−0.270036	−	0.467717i	−0.0141343	−	0.0244814i
$366$		0			0
$367$	−34.6030			−1.80626			−0.903131	−	0.429365i	$-0.858738\pi$
$367$	−34.6030			−1.80626			−0.903131	+	0.429365i	$0.858738\pi$
$368$	−0.210533	−	0.364654i	−0.0109748	−	0.0190089i
$369$		0			0
$370$	5.08126			0.264162
$371$		0			0
$372$		0			0
$373$	10.9759			0.568312			0.284156	−	0.958778i	$-0.408287\pi$
$373$	10.9759			0.568312			0.284156	+	0.958778i	$0.408287\pi$
$374$	−20.9532	+	36.2920i	−1.08347	+	1.87662i
$375$		0			0
$376$	0.830095	+	1.43777i	0.0428089	+	0.0741472i
$377$	−1.11436			−0.0573925
$378$		0			0
$379$	33.9877			1.74583			0.872916	−	0.487871i	$-0.162226\pi$
$379$	33.9877			1.74583			0.872916	+	0.487871i	$0.162226\pi$
$380$	−1.71053	−	2.96273i	−0.0877485	−	0.151985i
$381$		0			0
$382$	8.08414	−	14.0021i	0.413620	−	0.716411i
$383$	−21.0241			−1.07428			−0.537140	−	0.843493i	$-0.680495\pi$
$383$	−21.0241			−1.07428			−0.537140	+	0.843493i	$0.680495\pi$
$384$		0			0
$385$		0			0
$386$	14.1683			0.721146
$387$		0			0
$388$	1.81806	+	3.14897i	0.0922978	+	0.159865i
$389$	−13.7382			−0.696553			−0.348277	−	0.937392i	$-0.613233\pi$
$389$	−13.7382			−0.696553			−0.348277	+	0.937392i	$0.613233\pi$
$390$		0			0
$391$	−1.44050	−	2.49501i	−0.0728491	−	0.126178i
$392$		0			0
$393$		0			0
$394$	−7.92107	−	13.7197i	−0.399058	−	0.691188i
$395$	11.8376	+	20.5034i	0.595615	+	1.03164i
$396$		0			0
$397$	3.57893	−	6.19889i	0.179622	−	0.311114i	−0.762129	−	0.647425i	$-0.775846\pi$
$397$	3.57893	−	6.19889i	0.179622	−	0.311114i	0.941751	+	0.336311i	$0.109179\pi$
$398$	−4.47141	+	7.74471i	−0.224132	+	0.388207i
$399$		0			0
$400$	0.949657	+	1.64485i	0.0474828	+	0.0822427i
$401$	9.27936			0.463389			0.231695	−	0.972789i	$-0.425573\pi$
$401$	9.27936			0.463389			0.231695	+	0.972789i	$0.425573\pi$
$402$		0			0
$403$	5.86156			0.291985
$404$	4.00520	−	6.93721i	0.199266	−	0.345139i
$405$		0			0
$406$		0			0
$407$	−8.83693	+	15.3060i	−0.438030	+	0.758691i
$408$		0			0
$409$	7.58414	−	13.1361i	0.375011	−	0.649539i	−0.615317	−	0.788279i	$-0.710972\pi$
$409$	7.58414	−	13.1361i	0.375011	−	0.649539i	0.990329	+	0.138741i	$0.0443055\pi$
$410$	6.11273	−	10.5876i	0.301886	−	0.522882i
$411$		0			0
$412$	−3.41423	+	5.91362i	−0.168207	+	0.291343i
$413$		0			0
$414$		0			0
$415$	−2.75116	+	4.76515i	−0.135049	+	0.233912i
$416$	0.760877			0.0373051
$417$		0			0
$418$	11.8993			0.582014
$419$	−4.16827	−	7.21966i	−0.203633	−	0.352703i	0.746063	−	0.665875i	$-0.231942\pi$
$419$	−4.16827	−	7.21966i	−0.203633	−	0.352703i	−0.949696	+	0.313172i	$0.898608\pi$
$420$		0			0
$421$	−3.50232	+	6.06620i	−0.170693	+	0.295649i	−0.938662	−	0.344838i	$-0.887934\pi$
$421$	−3.50232	+	6.06620i	−0.170693	+	0.295649i	0.767969	+	0.640486i	$0.221267\pi$
$422$	−11.3856	+	19.7205i	−0.554244	+	0.959979i
$423$		0			0
$424$	−0.112725	−	0.195246i	−0.00547442	−	0.00948197i
$425$	6.49768	+	11.2543i	0.315184	+	0.545914i
$426$		0			0
$427$		0			0
$428$	−1.77292	−	3.07078i	−0.0856971	−	0.148432i
$429$		0			0
$430$	15.2495			0.735397
$431$	1.72545	+	2.98857i	0.0831120	+	0.143954i	0.904585	−	0.426293i	$-0.140181\pi$
$431$	1.72545	+	2.98857i	0.0831120	+	0.143954i	−0.821473	+	0.570247i	$0.806847\pi$
$432$		0			0
$433$	−28.2599			−1.35809			−0.679043	−	0.734099i	$-0.737605\pi$
$433$	−28.2599			−1.35809			−0.679043	+	0.734099i	$0.737605\pi$
$434$		0			0
$435$		0			0
$436$	−0.703697			−0.0337010
$437$	−0.409028	+	0.708458i	−0.0195665	+	0.0338901i
$438$		0			0
$439$	−14.4480	−	25.0247i	−0.689566	−	1.19436i	−0.971978	−	0.235071i	$-0.924468\pi$
$439$	−14.4480	−	25.0247i	−0.689566	−	1.19436i	0.282412	−	0.959293i	$-0.408866\pi$
$440$	10.7850			0.514152
$441$		0			0
$442$	5.20602			0.247625
$443$	−6.88044	−	11.9173i	−0.326899	−	0.566207i	0.654995	−	0.755633i	$-0.272671\pi$
$443$	−6.88044	−	11.9173i	−0.326899	−	0.566207i	−0.981895	+	0.189426i	$0.939337\pi$
$444$		0			0
$445$	2.29179	−	3.96950i	0.108641	−	0.188172i
$446$	12.8856			0.610153
$447$		0			0
$448$		0			0
$449$	20.2003			0.953309			0.476655	−	0.879091i	$-0.341849\pi$
$449$	20.2003			0.953309			0.476655	+	0.879091i	$0.341849\pi$
$450$		0			0
$451$	21.2616	+	36.8261i	1.00117	+	1.73407i
$452$	8.50232			0.399916
$453$		0			0
$454$	10.9984	+	19.0497i	0.516179	+	0.894048i
$455$		0			0
$456$		0			0
$457$	−10.0149	−	17.3463i	−0.468478	−	0.811428i	0.530873	−	0.847451i	$-0.321864\pi$
$457$	−10.0149	−	17.3463i	−0.468478	−	0.811428i	−0.999351	+	0.0360237i	$0.988531\pi$
$458$	1.89931	+	3.28971i	0.0887491	+	0.153718i
$459$		0			0
$460$	−0.370723	+	0.642111i	−0.0172851	+	0.0299386i
$461$	5.97661	−	10.3518i	0.278359	−	0.482131i	−0.692618	−	0.721304i	$-0.743543\pi$
$461$	5.97661	−	10.3518i	0.278359	−	0.482131i	0.970977	+	0.239173i	$0.0768763\pi$
$462$		0			0
$463$	6.64527	+	11.5100i	0.308832	+	0.534913i	0.978107	−	0.208102i	$-0.0667286\pi$
$463$	6.64527	+	11.5100i	0.308832	+	0.534913i	−0.669275	+	0.743015i	$0.733395\pi$
$464$	1.46457			0.0679911
$465$		0			0
$466$	6.67059			0.309009
$467$	−5.61505	+	9.72555i	−0.259833	+	0.450045i	−0.966197	−	0.257804i	$-0.917001\pi$
$467$	−5.61505	+	9.72555i	−0.259833	+	0.450045i	0.706364	+	0.707849i	$0.250334\pi$
$468$		0			0
$469$		0			0
$470$	1.46169	−	2.53173i	0.0674230	−	0.116780i
$471$		0			0
$472$	0.993163	−	1.72021i	0.0457141	−	0.0791791i
$473$	−26.5208	+	45.9354i	−1.21943	+	2.11211i
$474$		0			0
$475$	1.84501	−	3.19565i	0.0846550	−	0.146627i
$476$		0			0
$477$		0			0
$478$	−7.82038	+	13.5453i	−0.357696	+	0.619547i
$479$	−32.6271			−1.49077			−0.745385	−	0.666634i	$-0.767734\pi$
$479$	−32.6271			−1.49077			−0.745385	+	0.666634i	$0.767734\pi$
$480$		0			0
$481$	2.19562			0.100111
$482$	−10.7060	−	18.5434i	−0.487646	−	0.844627i
$483$		0			0
$484$	−13.2564	+	22.9607i	−0.602562	+	1.04367i
$485$	3.20137	−	5.54494i	0.145367	−	0.251783i
$486$		0			0
$487$	1.84897	+	3.20251i	0.0837848	+	0.145120i	0.904873	−	0.425682i	$-0.139966\pi$
$487$	1.84897	+	3.20251i	0.0837848	+	0.145120i	−0.821088	+	0.570802i	$0.806632\pi$
$488$	5.17511	+	8.96355i	0.234266	+	0.405761i
$489$		0			0
$490$		0			0
$491$	18.7804	+	32.5287i	0.847549	+	1.46800i	0.883389	+	0.468641i	$0.155256\pi$
$491$	18.7804	+	32.5287i	0.847549	+	1.46800i	−0.0358393	+	0.999358i	$0.511410\pi$
$492$		0			0
$493$	10.0208			0.451314
$494$	−0.739123	−	1.28020i	−0.0332547	−	0.0575989i
$495$		0			0
$496$	−7.70370			−0.345906
$497$		0			0
$498$		0			0
$499$	−31.7954			−1.42336			−0.711678	−	0.702506i	$-0.752064\pi$
$499$	−31.7954			−1.42336			−0.711678	+	0.702506i	$0.752064\pi$
$500$	6.07442	−	10.5212i	0.271656	−	0.470523i
$501$		0			0
$502$	−11.8015	−	20.4408i	−0.526727	−	0.912318i
$503$	30.8252			1.37443			0.687214	−	0.726455i	$-0.258834\pi$
$503$	30.8252			1.37443			0.687214	+	0.726455i	$0.258834\pi$
$504$		0			0
$505$	−14.1053			−0.627679
$506$	−1.28947	−	2.23342i	−0.0573238	−	0.0992877i
$507$		0			0
$508$	9.47661	−	16.4140i	0.420457	−	0.728252i
$509$	8.01616			0.355310			0.177655	−	0.984093i	$-0.443149\pi$
$509$	8.01616			0.355310			0.177655	+	0.984093i	$0.443149\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	10.1300	+	17.5456i	0.446814	+	0.773904i
$515$	12.0241			0.529844
$516$		0			0
$517$	5.08414	+	8.80598i	0.223600	+	0.387287i
$518$		0			0
$519$		0			0
$520$	−0.669905	−	1.16031i	−0.0293773	−	0.0508829i
$521$	14.8646	+	25.7462i	0.651229	+	1.12796i	0.982825	+	0.184540i	$0.0590795\pi$
$521$	14.8646	+	25.7462i	0.651229	+	1.12796i	−0.331596	+	0.943421i	$0.607587\pi$
$522$		0			0
$523$	−13.4698	+	23.3303i	−0.588992	+	1.02016i	0.405373	+	0.914152i	$0.367142\pi$
$523$	−13.4698	+	23.3303i	−0.588992	+	1.02016i	−0.994365	+	0.106013i	$0.966192\pi$
$524$	3.64652	−	6.31595i	0.159299	−	0.275914i
$525$		0			0
$526$	11.2443	+	19.4757i	0.490276	+	0.849183i
$527$	−52.7097			−2.29607
$528$		0			0
$529$	−22.8227			−0.992291
$530$	−0.198495	+	0.343803i	−0.00862207	+	0.0149339i
$531$		0			0
$532$		0			0
$533$	2.64132	−	4.57489i	0.114408	−	0.198161i
$534$		0			0
$535$	−3.12188	+	5.40726i	−0.134971	+	0.233776i
$536$	3.39248	−	5.87594i	0.146533	−	0.253802i
$537$		0			0
$538$	12.6706	−	21.9461i	0.546268	−	0.946164i
$539$		0			0
$540$		0			0
$541$	7.15568	−	12.3940i	0.307647	−	0.532859i	−0.670201	−	0.742180i	$-0.733792\pi$
$541$	7.15568	−	12.3940i	0.307647	−	0.532859i	0.977847	+	0.209321i	$0.0671252\pi$
$542$	13.7576			0.590940
$543$		0			0
$544$	−6.84213			−0.293354
$545$	0.619562	+	1.07311i	0.0265391	+	0.0459671i
$546$		0			0
$547$	1.02463	−	1.77471i	0.0438101	−	0.0758813i	−0.843289	−	0.537461i	$-0.819384\pi$
$547$	1.02463	−	1.77471i	0.0438101	−	0.0758813i	0.887099	+	0.461579i	$0.152717\pi$
$548$	−4.09097	+	7.08577i	−0.174758	+	0.302689i
$549$		0			0
$550$	5.81642	+	10.0743i	0.248013	+	0.429571i
$551$	−1.42270	−	2.46419i	−0.0606091	−	0.104978i
$552$		0			0
$553$		0			0
$554$	−1.64132	−	2.84284i	−0.0697328	−	0.120781i
$555$		0			0
$556$	−12.4646			−0.528616
$557$	−8.84338	−	15.3172i	−0.374706	−	0.649010i	0.615577	−	0.788077i	$-0.288923\pi$
$557$	−8.84338	−	15.3172i	−0.374706	−	0.649010i	−0.990283	+	0.139067i	$0.955590\pi$
$558$		0			0
$559$	6.58934			0.278699
$560$		0			0
$561$		0			0
$562$	−1.26896			−0.0535277
$563$	−0.468531	+	0.811520i	−0.0197462	+	0.0342015i	−0.875730	−	0.482802i	$-0.839619\pi$
$563$	−0.468531	+	0.811520i	−0.0197462	+	0.0342015i	0.855983	+	0.517003i	$0.172952\pi$
$564$		0			0
$565$	−7.48577	−	12.9657i	−0.314929	−	0.545473i
$566$	−8.19235			−0.344350
$567$		0			0
$568$	10.7850			0.452527
$569$	11.7632	+	20.3745i	0.493139	+	0.854142i	0.999969	−	0.00790437i	$-0.00251607\pi$
$569$	11.7632	+	20.3745i	0.493139	+	0.854142i	−0.506830	+	0.862046i	$0.669183\pi$
$570$		0			0
$571$	0.242002	−	0.419160i	0.0101275	−	0.0175413i	−0.860917	−	0.508745i	$-0.830110\pi$
$571$	0.242002	−	0.419160i	0.0101275	−	0.0175413i	0.871045	+	0.491204i	$0.163443\pi$
$572$	4.66019			0.194852
$573$		0			0
$574$		0			0
$575$	−0.799737			−0.0333514
$576$		0			0
$577$	2.23065	+	3.86360i	0.0928633	+	0.160844i	0.908715	−	0.417417i	$-0.137065\pi$
$577$	2.23065	+	3.86360i	0.0928633	+	0.160844i	−0.815852	+	0.578261i	$0.803731\pi$
$578$	−29.8148			−1.24013
$579$		0			0
$580$	−1.28947	−	2.23342i	−0.0535422	−	0.0927378i
$581$		0			0
$582$		0			0
$583$	−0.690415	−	1.19583i	−0.0285941	−	0.0495264i
$584$	0.153353	+	0.265616i	0.00634581	+	0.0109913i
$585$		0			0
$586$	−7.72545	+	13.3809i	−0.319135	+	0.552759i
$587$	8.31518	−	14.4023i	0.343204	−	0.594447i	−0.641822	−	0.766854i	$-0.721821\pi$
$587$	8.31518	−	14.4023i	0.343204	−	0.594447i	0.985026	+	0.172407i	$0.0551544\pi$
$588$		0			0
$589$	7.48345	+	12.9617i	0.308350	+	0.534078i
$590$	−3.49768			−0.143997
$591$		0			0
$592$	−2.88564			−0.118599
$593$	20.7632	−	35.9629i	0.852642	−	1.47682i	−0.0261726	−	0.999657i	$-0.508332\pi$
$593$	20.7632	−	35.9629i	0.852642	−	1.47682i	0.878815	−	0.477163i	$-0.158335\pi$
$594$		0			0
$595$		0			0
$596$	4.41423	−	7.64567i	0.180814	−	0.313179i
$597$		0			0
$598$	−0.160190	+	0.277457i	−0.00655065	+	0.0113461i
$599$	7.53831	−	13.0567i	0.308007	−	0.533483i	−0.669919	−	0.742434i	$-0.733671\pi$
$599$	7.53831	−	13.0567i	0.308007	−	0.533483i	0.977926	+	0.208950i	$0.0670047\pi$
$600$		0			0
$601$	8.05555	−	13.9526i	0.328593	−	0.569139i	−0.653640	−	0.756805i	$-0.726759\pi$
$601$	8.05555	−	13.9526i	0.328593	−	0.569139i	0.982233	+	0.187666i	$0.0600924\pi$
$602$		0			0
$603$		0			0
$604$	7.49316	−	12.9785i	0.304892	−	0.528089i
$605$	46.6856			1.89804
$606$		0			0
$607$	−19.5732			−0.794451			−0.397225	−	0.917721i	$-0.630027\pi$
$607$	−19.5732			−0.794451			−0.397225	+	0.917721i	$0.630027\pi$
$608$	0.971410	+	1.68253i	0.0393959	+	0.0682357i
$609$		0			0
$610$	9.11273	−	15.7837i	0.368963	−	0.639063i
$611$	0.631600	−	1.09396i	0.0255518	−	0.0442570i
$612$		0			0
$613$	−2.77579	−	4.80782i	−0.112113	−	0.194186i	0.804509	−	0.593941i	$-0.202429\pi$
$613$	−2.77579	−	4.80782i	−0.112113	−	0.194186i	−0.916622	+	0.399755i	$0.869095\pi$
$614$	−2.44966	−	4.24293i	−0.0988601	−	0.171231i
$615$		0			0
$616$		0			0
$617$	−0.634479	−	1.09895i	−0.0255431	−	0.0442420i	0.852971	−	0.521958i	$-0.174798\pi$
$617$	−0.634479	−	1.09895i	−0.0255431	−	0.0442420i	−0.878514	+	0.477716i	$0.841465\pi$
$618$		0			0
$619$	−4.50232			−0.180964			−0.0904818	−	0.995898i	$-0.528841\pi$
$619$	−4.50232			−0.180964			−0.0904818	+	0.995898i	$0.528841\pi$
$620$	6.78263	+	11.7479i	0.272397	+	0.471805i
$621$		0			0
$622$	7.69002			0.308342
$623$		0			0
$624$		0			0
$625$	−11.8960			−0.475842
$626$	0.861564	−	1.49227i	0.0344350	−	0.0596432i
$627$		0			0
$628$	9.49028	+	16.4377i	0.378704	+	0.655934i
$629$	−19.7439			−0.787242
$630$		0			0
$631$	−1.69905			−0.0676381			−0.0338191	−	0.999428i	$-0.510767\pi$
$631$	−1.69905			−0.0676381			−0.0338191	+	0.999428i	$0.510767\pi$
$632$	−6.72257	−	11.6438i	−0.267410	−	0.463167i
$633$		0			0
$634$	−16.6014	+	28.7544i	−0.659325	+	1.14198i
$635$	−33.3743			−1.32442
$636$		0			0
$637$		0			0
$638$	8.97017			0.355132
$639$		0			0
$640$	0.880438	+	1.52496i	0.0348024	+	0.0602795i
$641$	0.948577			0.0374666			0.0187333	−	0.999825i	$-0.494037\pi$
$641$	0.948577			0.0374666			0.0187333	+	0.999825i	$0.494037\pi$
$642$		0			0
$643$	9.84897	+	17.0589i	0.388405	+	0.672738i	0.992235	−	0.124375i	$-0.0396927\pi$
$643$	9.84897	+	17.0589i	0.388405	+	0.672738i	−0.603830	+	0.797113i	$0.706359\pi$
$644$		0			0
$645$		0			0
$646$	6.64652	+	11.5121i	0.261504	+	0.452938i
$647$	11.7271	+	20.3119i	0.461039	+	0.798543i	0.999013	−	0.0444181i	$-0.0141434\pi$
$647$	11.7271	+	20.3119i	0.461039	+	0.798543i	−0.537974	+	0.842962i	$0.680810\pi$
$648$		0			0
$649$	6.08289	−	10.5359i	0.238774	−	0.413569i
$650$	0.722572	−	1.25153i	0.0283416	−	0.0490891i
$651$		0			0
$652$	−7.51887	−	13.0231i	−0.294462	−	0.510023i
$653$	−22.7907			−0.891869			−0.445935	−	0.895065i	$-0.647129\pi$
$653$	−22.7907			−0.891869			−0.445935	+	0.895065i	$0.647129\pi$
$654$		0			0
$655$	−12.8421			−0.501784
$656$	−3.47141	+	6.01266i	−0.135536	+	0.234755i
$657$		0			0
$658$		0			0
$659$	13.2398	−	22.9320i	0.515750	−	0.893305i	−0.484083	−	0.875022i	$-0.660847\pi$
$659$	13.2398	−	22.9320i	0.515750	−	0.893305i	0.999833	−	0.0182828i	$-0.00581993\pi$
$660$		0			0
$661$	−13.3691	+	23.1559i	−0.519997	+	0.900662i	0.479732	+	0.877415i	$0.340734\pi$
$661$	−13.3691	+	23.1559i	−0.519997	+	0.900662i	−0.999730	+	0.0232469i	$0.992600\pi$
$662$	1.44445	−	2.50187i	0.0561403	−	0.0972379i
$663$		0			0
$664$	1.56238	−	2.70612i	0.0606322	−	0.105018i
$665$		0			0
$666$		0			0
$667$	−0.308342	+	0.534063i	−0.0119390	+	0.0206790i
$668$	−1.14419			−0.0442702
$669$		0			0
$670$	−11.9475			−0.461571
$671$	31.6963	+	54.8996i	1.22362	+	2.11938i
$672$		0			0
$673$	−10.3856	+	17.9885i	−0.400337	+	0.693404i	−0.993766	−	0.111482i	$-0.964440\pi$
$673$	−10.3856	+	17.9885i	−0.400337	+	0.693404i	0.593429	+	0.804886i	$0.297774\pi$
$674$	4.36156	−	7.55445i	0.168001	−	0.290987i
$675$		0			0
$676$	6.21053	+	10.7570i	0.238867	+	0.413729i
$677$	10.3490	+	17.9249i	0.397743	+	0.688911i	0.993447	−	0.114293i	$-0.0364602\pi$
$677$	10.3490	+	17.9249i	0.397743	+	0.688911i	−0.595704	+	0.803204i	$0.703127\pi$
$678$		0			0
$679$		0			0
$680$	6.02408	+	10.4340i	0.231013	+	0.400126i
$681$		0			0
$682$	−47.1833			−1.80674
$683$	−14.2918	−	24.7541i	−0.546860	−	0.947190i	−0.998487	−	0.0549828i	$-0.982490\pi$
$683$	−14.2918	−	24.7541i	−0.546860	−	0.947190i	0.451627	−	0.892207i	$-0.350844\pi$
$684$		0			0
$685$	14.4074			0.550478
$686$		0			0
$687$		0			0
$688$	−8.66019			−0.330167
$689$	−0.0857699	+	0.148558i	−0.00326757	+	0.00565960i
$690$		0			0
$691$	−3.34897	−	5.80059i	−0.127401	−	0.220665i	0.795268	−	0.606258i	$-0.207330\pi$
$691$	−3.34897	−	5.80059i	−0.127401	−	0.220665i	−0.922669	+	0.385593i	$0.873997\pi$
$692$	0.497677			0.0189188
$693$		0			0
$694$	9.69467			0.368005
$695$	10.9743	+	19.0080i	0.416278	+	0.721016i
$696$		0			0
$697$	−23.7518	+	41.1394i	−0.899665	+	1.55827i
$698$	−28.3984			−1.07489
$699$		0			0
$700$		0			0
$701$	25.1442			0.949683			0.474842	−	0.880071i	$-0.342505\pi$
$701$	25.1442			0.949683			0.474842	+	0.880071i	$0.342505\pi$
$702$		0			0
$703$	2.80314	+	4.85518i	0.105722	+	0.183117i
$704$	−6.12476			−0.230836
$705$		0			0
$706$	−2.19686	−	3.80507i	−0.0826799	−	0.143206i
$707$		0			0
$708$		0			0
$709$	−4.43310	−	7.67836i	−0.166489	−	0.288367i	0.770694	−	0.637205i	$-0.219910\pi$
$709$	−4.43310	−	7.67836i	−0.166489	−	0.288367i	−0.937183	+	0.348838i	$0.886576\pi$
$710$	−9.49549	−	16.4467i	−0.356359	−	0.617232i
$711$		0			0
$712$	−1.30150	+	2.25427i	−0.0487760	+	0.0844824i
$713$	1.62188	−	2.80919i	0.0607401	−	0.105205i
$714$		0			0
$715$	−4.10301	−	7.10662i	−0.153444	−	0.265773i
$716$	8.82846			0.329935
$717$		0			0
$718$	−32.1592			−1.20017
$719$	11.8015	−	20.4408i	0.440122	−	0.762313i	−0.557576	−	0.830126i	$-0.688269\pi$
$719$	11.8015	−	20.4408i	0.440122	−	0.762313i	0.997698	+	0.0678123i	$0.0216019\pi$
$720$		0			0
$721$		0			0
$722$	−7.61273	+	13.1856i	−0.283316	+	0.490718i
$723$		0			0
$724$	0.664703	−	1.15130i	0.0247035	−	0.0427877i
$725$	1.39084	−	2.40901i	0.0516546	−	0.0894683i
$726$		0			0
$727$	−3.25692	+	5.64115i	−0.120792	+	0.209219i	−0.920080	−	0.391730i	$-0.871877\pi$
$727$	−3.25692	+	5.64115i	−0.120792	+	0.209219i	0.799288	+	0.600948i	$0.205210\pi$
$728$		0			0
$729$		0			0
$730$	0.270036	−	0.467717i	0.00999449	−	0.0173110i
$731$	−59.2542			−2.19159
$732$		0			0
$733$	23.1981			0.856842			0.428421	−	0.903579i	$-0.359070\pi$
$733$	23.1981			0.856842			0.428421	+	0.903579i	$0.359070\pi$
$734$	−17.3015	−	29.9671i	−0.638610	−	1.10611i
$735$		0			0
$736$	0.210533	−	0.364654i	0.00776036	−	0.0134413i
$737$	20.7781	−	35.9888i	0.765372	−	1.32566i
$738$		0			0
$739$	−7.57838	−	13.1261i	−0.278775	−	0.482853i	0.692305	−	0.721605i	$-0.256595\pi$
$739$	−7.57838	−	13.1261i	−0.278775	−	0.482853i	−0.971081	+	0.238752i	$0.923262\pi$
$740$	2.54063	+	4.40050i	0.0933954	+	0.161765i
$741$		0			0
$742$		0			0
$743$	5.21737	+	9.03675i	0.191407	+	0.331526i	0.945717	−	0.324992i	$-0.105362\pi$
$743$	5.21737	+	9.03675i	0.191407	+	0.331526i	−0.754310	+	0.656518i	$0.772028\pi$
$744$		0			0
$745$	−15.5458			−0.569555
$746$	5.48796	+	9.50543i	0.200929	+	0.348018i
$747$		0			0
$748$	−41.9064			−1.53225
$749$		0			0
$750$		0			0
$751$	40.2118			1.46735			0.733674	−	0.679501i	$-0.237804\pi$
$751$	40.2118			1.46735			0.733674	+	0.679501i	$0.237804\pi$
$752$	−0.830095	+	1.43777i	−0.0302704	+	0.0524300i
$753$		0			0
$754$	−0.557180	−	0.965064i	−0.0202913	−	0.0351456i
$755$	−26.3891			−0.960397
$756$		0			0
$757$	−21.5206			−0.782181			−0.391091	−	0.920352i	$-0.627902\pi$
$757$	−21.5206			−0.782181			−0.391091	+	0.920352i	$0.627902\pi$
$758$	16.9939	+	29.4342i	0.617244	+	1.06910i
$759$		0			0
$760$	1.71053	−	2.96273i	0.0620476	−	0.107470i
$761$	−23.6627			−0.857771			−0.428886	−	0.903359i	$-0.641094\pi$
$761$	−23.6627			−0.857771			−0.428886	+	0.903359i	$0.641094\pi$
$762$		0			0
$763$		0			0
$764$	16.1683			0.584947
$765$		0			0
$766$	−10.5120	−	18.2074i	−0.379815	−	0.657860i
$767$	−1.51135			−0.0545717
$768$		0			0
$769$	5.62764	+	9.74736i	0.202938	+	0.351499i	0.949474	−	0.313846i	$-0.101618\pi$
$769$	5.62764	+	9.74736i	0.202938	+	0.351499i	−0.746536	+	0.665345i	$0.768284\pi$
$770$		0			0
$771$		0			0
$772$	7.08414	+	12.2701i	0.254964	+	0.441610i
$773$	0.138992	+	0.240741i	0.00499919	+	0.00865886i	0.868514	−	0.495664i	$-0.165075\pi$
$773$	0.138992	+	0.240741i	0.00499919	+	0.00865886i	−0.863515	+	0.504323i	$0.831742\pi$
$774$		0			0
$775$	−7.31587	+	12.6715i	−0.262794	+	0.455172i
$776$	−1.81806	+	3.14897i	−0.0652644	+	0.113041i
$777$		0			0
$778$	−6.86909	−	11.8976i	−0.246269	−	0.426550i
$779$	13.4887			0.483281
$780$		0			0
$781$	66.0553			2.36364
$782$	1.44050	−	2.49501i	0.0515121	−	0.0892215i
$783$		0			0
$784$		0			0
$785$	16.7112	−	28.9447i	0.596449	−	1.03308i
$786$		0			0
$787$	−14.6940	+	25.4507i	−0.523784	+	0.907220i	0.475833	+	0.879536i	$0.342147\pi$
$787$	−14.6940	+	25.4507i	−0.523784	+	0.907220i	−0.999617	+	0.0276845i	$0.991187\pi$
$788$	7.92107	−	13.7197i	0.282176	−	0.488744i
$789$		0			0
$790$	−11.8376	+	20.5034i	−0.421164	+	0.729477i
$791$		0			0
$792$		0			0
$793$	3.93762	−	6.82015i	0.139829	−	0.242191i
$794$	7.15787			0.254023
$795$		0			0
$796$	−8.94282			−0.316970
$797$	0.433105	+	0.750160i	0.0153414	+	0.0265720i	0.873594	−	0.486655i	$-0.161783\pi$
$797$	0.433105	+	0.750160i	0.0153414	+	0.0265720i	−0.858253	+	0.513227i	$0.828450\pi$
$798$		0			0
$799$	−5.67962	+	9.83739i	−0.200931	+	0.348022i
$800$	−0.949657	+	1.64485i	−0.0335754	+	0.0581544i
$801$		0			0
$802$	4.63968	+	8.03616i	0.163833	+	0.283767i
$803$	0.939253	+	1.62683i	0.0331455	+	0.0574097i
$804$		0			0
$805$		0			0
$806$	2.93078	+	5.07626i	0.103232	+	0.178804i
$807$		0			0
$808$	8.01040			0.281805
$809$	−9.66703	−	16.7438i	−0.339875	−	0.588680i	0.644534	−	0.764575i	$-0.277051\pi$
$809$	−9.66703	−	16.7438i	−0.339875	−	0.588680i	−0.984409	+	0.175895i	$0.943718\pi$
$810$		0			0
$811$	47.0391			1.65177			0.825884	−	0.563841i	$-0.190677\pi$
$811$	47.0391			1.65177			0.825884	+	0.563841i	$0.190677\pi$
$812$		0			0
$813$		0			0
$814$	−17.6739			−0.619469
$815$	−13.2398	+	22.9320i	−0.463770	+	0.803274i
$816$		0			0
$817$	8.41260	+	14.5710i	0.294319	+	0.509776i
$818$	15.1683			0.530346
$819$		0			0
$820$	12.2255			0.426931
$821$	0.705332	+	1.22167i	0.0246162	+	0.0426366i	0.878071	−	0.478530i	$-0.158830\pi$
$821$	0.705332	+	1.22167i	0.0246162	+	0.0426366i	−0.853455	+	0.521167i	$0.825497\pi$
$822$		0			0
$823$	17.5196	−	30.3448i	0.610694	−	1.05775i	−0.380430	−	0.924810i	$-0.624224\pi$
$823$	17.5196	−	30.3448i	0.610694	−	1.05775i	0.991124	−	0.132943i	$-0.0424426\pi$
$824$	−6.82846			−0.237881
$825$		0			0
$826$		0			0
$827$	18.5997			0.646776			0.323388	−	0.946266i	$-0.395178\pi$
$827$	18.5997			0.646776			0.323388	+	0.946266i	$0.395178\pi$
$828$		0			0
$829$	−19.0848	−	33.0559i	−0.662843	−	1.14808i	−0.979865	−	0.199660i	$-0.936016\pi$
$829$	−19.0848	−	33.0559i	−0.662843	−	1.14808i	0.317022	−	0.948418i	$-0.397317\pi$
$830$	−5.50232			−0.190988
$831$		0			0
$832$	0.380438	+	0.658939i	0.0131893	+	0.0228446i
$833$		0			0
$834$		0			0
$835$	1.00739	+	1.74485i	0.0348622	+	0.0603832i
$836$	5.94966	+	10.3051i	0.205773	+	0.356410i
$837$		0			0
$838$	4.16827	−	7.21966i	0.143991	−	0.249399i
$839$	17.3691	−	30.0841i	0.599648	−	1.03862i	−0.393225	−	0.919442i	$-0.628641\pi$
$839$	17.3691	−	30.0841i	0.599648	−	1.03862i	0.992873	−	0.119178i	$-0.0380259\pi$
$840$		0			0
$841$	13.4275	+	23.2571i	0.463018	+	0.801970i
$842$	−7.00465			−0.241396
$843$		0			0
$844$	−22.7713			−0.783820
$845$	10.9360	−	18.9417i	0.376209	−	0.651614i
$846$		0			0
$847$		0			0
$848$	0.112725	−	0.195246i	0.00387100	−	0.00670476i
$849$		0			0
$850$	−6.49768	+	11.2543i	−0.222868	+	0.386020i
$851$	0.607523	−	1.05226i	0.0208256	−	0.0360711i
$852$		0			0
$853$	21.1586	−	36.6477i	0.724455	−	1.25479i	−0.234743	−	0.972058i	$-0.575425\pi$
$853$	21.1586	−	36.6477i	0.724455	−	1.25479i	0.959198	−	0.282736i	$-0.0912419\pi$
$854$		0			0
$855$		0			0
$856$	1.77292	−	3.07078i	0.0605970	−	0.104957i
$857$	14.9234			0.509773			0.254887	−	0.966971i	$-0.417962\pi$
$857$	14.9234			0.509773			0.254887	+	0.966971i	$0.417962\pi$
$858$		0			0
$859$	−19.4132			−0.662368			−0.331184	−	0.943566i	$-0.607448\pi$
$859$	−19.4132			−0.662368			−0.331184	+	0.943566i	$0.607448\pi$
$860$	7.62476	+	13.2065i	0.260002	+	0.450337i
$861$		0			0
$862$	−1.72545	+	2.98857i	−0.0587691	+	0.101791i
$863$	0.542263	−	0.939227i	0.0184588	−	0.0319717i	−0.856648	−	0.515901i	$-0.827457\pi$
$863$	0.542263	−	0.939227i	0.0184588	−	0.0319717i	0.875107	+	0.483929i	$0.160791\pi$
$864$		0			0
$865$	−0.438174	−	0.758939i	−0.0148984	−	0.0258047i
$866$	−14.1300	−	24.4738i	−0.480156	−	0.831654i
$867$		0			0
$868$		0			0
$869$	−41.1742	−	71.3157i	−1.39674	−	2.41922i
$870$		0			0
$871$	−5.16251			−0.174925
$872$	−0.351848	−	0.609419i	−0.0119151	−	0.0206375i
$873$		0			0
$874$	−0.818057			−0.0276712
$875$		0			0
$876$		0			0
$877$	−28.5699			−0.964737			−0.482369	−	0.875968i	$-0.660223\pi$
$877$	−28.5699			−0.964737			−0.482369	+	0.875968i	$0.660223\pi$
$878$	14.4480	−	25.0247i	0.487597	−	0.844543i
$879$		0			0
$880$	5.39248	+	9.34004i	0.181780	+	0.314853i
$881$	45.9967			1.54967			0.774835	−	0.632164i	$-0.217833\pi$
$881$	45.9967			1.54967			0.774835	+	0.632164i	$0.217833\pi$
$882$		0			0
$883$	32.9384			1.10847			0.554233	−	0.832361i	$-0.313012\pi$
$883$	32.9384			1.10847			0.554233	+	0.832361i	$0.313012\pi$
$884$	2.60301	+	4.50855i	0.0875487	+	0.151639i
$885$		0			0
$886$	6.88044	−	11.9173i	0.231153	−	0.400368i
$887$	−28.3398			−0.951558			−0.475779	−	0.879565i	$-0.657834\pi$
$887$	−28.3398			−0.951558			−0.475779	+	0.879565i	$0.657834\pi$
$888$		0			0
$889$		0			0
$890$	4.58358			0.153642
$891$		0			0
$892$	6.44282	+	11.1593i	0.215722	+	0.373641i
$893$	3.22545			0.107936
$894$		0			0
$895$	−7.77292	−	13.4631i	−0.259820	−	0.450021i
$896$		0			0
$897$		0			0
$898$	10.1001	+	17.4939i	0.337046	+	0.583780i
$899$	5.64132	+	9.77104i	0.188148	+	0.325883i
$900$		0			0
$901$	0.771280	−	1.33590i	0.0256951	−	0.0445052i
$902$	−21.2616	+	36.8261i	−0.707933	+	1.22618i
$903$		0			0
$904$	4.25116	+	7.36323i	0.141392	+	0.244897i
$905$	−2.34092			−0.0778149
$906$		0			0
$907$	7.94747			0.263891			0.131946	−	0.991257i	$-0.457878\pi$
$907$	7.94747			0.263891			0.131946	+	0.991257i	$0.457878\pi$
$908$	−10.9984	+	19.0497i	−0.364994	+	0.632187i
$909$		0			0
$910$		0			0
$911$	4.00808	−	6.94220i	0.132794	−	0.230005i	−0.791959	−	0.610575i	$-0.790939\pi$
$911$	4.00808	−	6.94220i	0.132794	−	0.230005i	0.924752	+	0.380569i	$0.124272\pi$
$912$		0			0
$913$	9.56922	−	16.5744i	0.316695	−	0.548532i
$914$	10.0149	−	17.3463i	0.331264	−	0.573766i
$915$		0			0
$916$	−1.89931	+	3.28971i	−0.0627551	+	0.108695i
$917$		0			0
$918$		0			0
$919$	−12.0224	+	20.8235i	−0.396584	+	0.686903i	−0.993302	−	0.115548i	$-0.963138\pi$
$919$	−12.0224	+	20.8235i	−0.396584	+	0.686903i	0.596718	+	0.802451i	$0.296471\pi$
$920$	−0.741446			−0.0244448
$921$		0			0
$922$	11.9532			0.393658
$923$	−4.10301	−	7.10662i	−0.135052	−	0.233917i
$924$		0			0
$925$	−2.74037	+	4.74646i	−0.0901027	+	0.156062i
$926$	−6.64527	+	11.5100i	−0.218377	+	0.378240i
$927$		0			0
$928$	0.732287	+	1.26836i	0.0240385	+	0.0416359i
$929$	−13.9331	−	24.1328i	−0.457130	−	0.791773i	0.541678	−	0.840586i	$-0.317789\pi$
$929$	−13.9331	−	24.1328i	−0.457130	−	0.791773i	−0.998808	+	0.0488134i	$0.984456\pi$
$930$		0			0
$931$		0			0
$932$	3.33530	+	5.77690i	0.109251	+	0.189229i
$933$		0			0
$934$	−11.2301			−0.367460
$935$	36.8960	+	63.9058i	1.20663	+	2.08994i
$936$		0			0
$937$	−53.2211			−1.73866			−0.869328	−	0.494235i	$-0.835448\pi$
$937$	−53.2211			−1.73866			−0.869328	+	0.494235i	$0.835448\pi$
$938$		0			0
$939$		0			0
$940$	2.92339			0.0953505
$941$	15.0241	−	26.0225i	0.489771	−	0.848308i	−0.510160	−	0.860080i	$-0.670414\pi$
$941$	15.0241	−	26.0225i	0.489771	−	0.848308i	0.999931	+	0.0117715i	$0.00374709\pi$
$942$		0			0
$943$	−1.46169	−	2.53173i	−0.0475993	−	0.0824445i
$944$	1.98633			0.0646494
$945$		0			0
$946$	−53.0416			−1.72453
$947$	−19.8445	−	34.3716i	−0.644858	−	1.11693i	−0.984334	−	0.176312i	$-0.943583\pi$
$947$	−19.8445	−	34.3716i	−0.644858	−	1.11693i	0.339476	−	0.940615i	$-0.389750\pi$
$948$		0			0
$949$	0.116683	−	0.202101i	0.00378769	−	0.00656047i
$950$	3.69002			0.119720
$951$		0			0
$952$		0			0
$953$	−23.0643			−0.747126			−0.373563	−	0.927605i	$-0.621864\pi$
$953$	−23.0643			−0.747126			−0.373563	+	0.927605i	$0.621864\pi$
$954$		0			0
$955$	−14.2352	−	24.6560i	−0.460639	−	0.797850i
$956$	−15.6408			−0.505858
$957$		0			0
$958$	−16.3135	−	28.2559i	−0.527067	−	0.912906i
$959$		0			0
$960$		0			0
$961$	−14.1735	−	24.5492i	−0.457209	−	0.791909i
$962$	1.09781	+	1.90146i	0.0353948	+	0.0613055i
$963$		0			0
$964$	10.7060	−	18.5434i	0.344818	−	0.597242i
$965$	12.4743	−	21.6061i	0.401562	−	0.695525i
$966$		0			0
$967$	15.2902	+	26.4833i	0.491698	+	0.851646i	0.999954	−	0.00955967i	$-0.00304298\pi$
$967$	15.2902	+	26.4833i	0.491698	+	0.851646i	−0.508256	+	0.861206i	$0.669710\pi$
$968$	−26.5127			−0.852151
$969$		0			0
$970$	6.40275			0.205580
$971$	13.1030	−	22.6951i	0.420496	−	0.728320i	−0.575492	−	0.817807i	$-0.695190\pi$
$971$	13.1030	−	22.6951i	0.420496	−	0.728320i	0.995988	+	0.0894874i	$0.0285229\pi$
$972$		0			0
$973$		0			0
$974$	−1.84897	+	3.20251i	−0.0592448	+	0.102615i
$975$		0			0
$976$	−5.17511	+	8.96355i	−0.165651	+	0.286916i
$977$	10.5270	−	18.2332i	0.336787	−	0.583332i	−0.647039	−	0.762457i	$-0.723993\pi$
$977$	10.5270	−	18.2332i	0.336787	−	0.583332i	0.983826	+	0.179124i	$0.0573264\pi$
$978$		0			0
$979$	−7.97141	+	13.8069i	−0.254767	+	0.441270i
$980$		0			0
$981$		0			0
$982$	−18.7804	+	32.5287i	−0.599308	+	1.03803i
$983$	−19.5297			−0.622900			−0.311450	−	0.950263i	$-0.600815\pi$
$983$	−19.5297			−0.622900			−0.311450	+	0.950263i	$0.600815\pi$
$984$		0			0
$985$	−27.8960			−0.888842
$986$	5.01040	+	8.67827i	0.159564	+	0.276373i
$987$		0			0
$988$	0.739123	−	1.28020i	0.0235146	−	0.0407286i
$989$	1.82326	−	3.15798i	0.0579762	−	0.100418i
$990$		0			0
$991$	−7.49837	−	12.9875i	−0.238193	−	0.412563i	0.722003	−	0.691890i	$-0.243222\pi$
$991$	−7.49837	−	12.9875i	−0.238193	−	0.412563i	−0.960196	+	0.279327i	$0.909889\pi$
$992$	−3.85185	−	6.67160i	−0.122296	−	0.211823i
$993$		0			0
$994$		0			0
$995$	7.87360	+	13.6375i	0.249610	+	0.432337i
$996$		0			0
$997$	58.5641			1.85475			0.927373	−	0.374139i	$-0.122062\pi$
$997$	58.5641			1.85475			0.927373	+	0.374139i	$0.122062\pi$
$998$	−15.8977	−	27.5356i	−0.503232	−	0.871624i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.h.p.667.2		6
3.2	odd	2		882.2.h.o.79.2		6
7.2	even	3		2646.2.f.n.883.2		6
7.3	odd	6		378.2.e.c.235.2		6
7.4	even	3		2646.2.e.o.2125.2		6
7.5	odd	6		2646.2.f.o.883.2		6
7.6	odd	2		378.2.h.d.289.2		6
9.4	even	3		2646.2.e.o.1549.2		6
9.5	odd	6		882.2.e.p.373.1		6
21.2	odd	6		882.2.f.m.295.3		6
21.5	even	6		882.2.f.l.295.1		6
21.11	odd	6		882.2.e.p.655.1		6
21.17	even	6		126.2.e.d.25.3	✓	6
21.20	even	2		126.2.h.c.79.2	yes	6
28.3	even	6		3024.2.q.h.2881.2		6
28.27	even	2		3024.2.t.g.289.2		6
63.2	odd	6		7938.2.a.by.1.2		3
63.4	even	3	inner	2646.2.h.p.361.2		6
63.5	even	6		882.2.f.l.589.1		6
63.13	odd	6		378.2.e.c.37.2		6
63.16	even	3		7938.2.a.bx.1.2		3
63.20	even	6		1134.2.g.k.163.2		6
63.23	odd	6		882.2.f.m.589.3		6
63.31	odd	6		378.2.h.d.361.2		6
63.32	odd	6		882.2.h.o.67.2		6
63.34	odd	6		1134.2.g.n.163.2		6
63.38	even	6		1134.2.g.k.487.2		6
63.40	odd	6		2646.2.f.o.1765.2		6
63.41	even	6		126.2.e.d.121.3	yes	6
63.47	even	6		7938.2.a.cb.1.2		3
63.52	odd	6		1134.2.g.n.487.2		6
63.58	even	3		2646.2.f.n.1765.2		6
63.59	even	6		126.2.h.c.67.2	yes	6
63.61	odd	6		7938.2.a.bu.1.2		3
84.59	odd	6		1008.2.q.h.529.1		6
84.83	odd	2		1008.2.t.g.961.2		6
252.31	even	6		3024.2.t.g.1873.2		6
252.59	odd	6		1008.2.t.g.193.2		6
252.139	even	6		3024.2.q.h.2305.2		6
252.167	odd	6		1008.2.q.h.625.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.d.25.3	✓	6	21.17	even	6
126.2.e.d.121.3	yes	6	63.41	even	6
126.2.h.c.67.2	yes	6	63.59	even	6
126.2.h.c.79.2	yes	6	21.20	even	2
378.2.e.c.37.2		6	63.13	odd	6
378.2.e.c.235.2		6	7.3	odd	6
378.2.h.d.289.2		6	7.6	odd	2
378.2.h.d.361.2		6	63.31	odd	6
882.2.e.p.373.1		6	9.5	odd	6
882.2.e.p.655.1		6	21.11	odd	6
882.2.f.l.295.1		6	21.5	even	6
882.2.f.l.589.1		6	63.5	even	6
882.2.f.m.295.3		6	21.2	odd	6
882.2.f.m.589.3		6	63.23	odd	6
882.2.h.o.67.2		6	63.32	odd	6
882.2.h.o.79.2		6	3.2	odd	2
1008.2.q.h.529.1		6	84.59	odd	6
1008.2.q.h.625.1		6	252.167	odd	6
1008.2.t.g.193.2		6	252.59	odd	6
1008.2.t.g.961.2		6	84.83	odd	2
1134.2.g.k.163.2		6	63.20	even	6
1134.2.g.k.487.2		6	63.38	even	6
1134.2.g.n.163.2		6	63.34	odd	6
1134.2.g.n.487.2		6	63.52	odd	6
2646.2.e.o.1549.2		6	9.4	even	3
2646.2.e.o.2125.2		6	7.4	even	3
2646.2.f.n.883.2		6	7.2	even	3
2646.2.f.n.1765.2		6	63.58	even	3
2646.2.f.o.883.2		6	7.5	odd	6
2646.2.f.o.1765.2		6	63.40	odd	6
2646.2.h.p.361.2		6	63.4	even	3	inner
2646.2.h.p.667.2		6	1.1	even	1	trivial
3024.2.q.h.2305.2		6	252.139	even	6
3024.2.q.h.2881.2		6	28.3	even	6
3024.2.t.g.289.2		6	28.27	even	2
3024.2.t.g.1873.2		6	252.31	even	6
7938.2.a.bu.1.2		3	63.61	odd	6
7938.2.a.bx.1.2		3	63.16	even	3
7938.2.a.by.1.2		3	63.2	odd	6
7938.2.a.cb.1.2		3	63.47	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.76088 q^{5} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.76088 q^{5} -1.00000 q^{8} +(0.880438 + 1.52496i) q^{10} -6.12476 q^{11} +(0.380438 + 0.658939i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-3.42107 - 5.92546i) q^{17} +(-0.971410 + 1.68253i) q^{19} +(-0.880438 + 1.52496i) q^{20} +(-3.06238 - 5.30420i) q^{22} +0.421067 q^{23} -1.89931 q^{25} +(-0.380438 + 0.658939i) q^{26} +(-0.732287 + 1.26836i) q^{29} +(3.85185 - 6.67160i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.42107 - 5.92546i) q^{34} +(1.44282 - 2.49904i) q^{37} -1.94282 q^{38} -1.76088 q^{40} +(-3.47141 - 6.01266i) q^{41} +(4.33009 - 7.49994i) q^{43} +(3.06238 - 5.30420i) q^{44} +(0.210533 + 0.364654i) q^{46} +(-0.830095 - 1.43777i) q^{47} +(-0.949657 - 1.64485i) q^{50} -0.760877 q^{52} +(0.112725 + 0.195246i) q^{53} -10.7850 q^{55} -1.46457 q^{58} +(-0.993163 + 1.72021i) q^{59} +(-5.17511 - 8.96355i) q^{61} +7.70370 q^{62} +1.00000 q^{64} +(0.669905 + 1.16031i) q^{65} +(-3.39248 + 5.87594i) q^{67} +6.84213 q^{68} -10.7850 q^{71} +(-0.153353 - 0.265616i) q^{73} +2.88564 q^{74} +(-0.971410 - 1.68253i) q^{76} +(6.72257 + 11.6438i) q^{79} +(-0.880438 - 1.52496i) q^{80} +(3.47141 - 6.01266i) q^{82} +(-1.56238 + 2.70612i) q^{83} +(-6.02408 - 10.4340i) q^{85} +8.66019 q^{86} +6.12476 q^{88} +(1.30150 - 2.25427i) q^{89} +(-0.210533 + 0.364654i) q^{92} +(0.830095 - 1.43777i) q^{94} +(-1.71053 + 2.96273i) q^{95} +(1.81806 - 3.14897i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} + 10 q^{5} - 6 q^{8}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^4 + 10 * q^5 - 6 * q^8	\( 6 q + 3 q^{2} - 3 q^{4} + 10 q^{5} - 6 q^{8} + 5 q^{10} - 2 q^{11} + 2 q^{13} - 3 q^{16} - 4 q^{17} + 3 q^{19} - 5 q^{20} - q^{22} - 14 q^{23} + 4 q^{25} - 2 q^{26} + 5 q^{29} + 14 q^{31} + 3 q^{32} + 4 q^{34} - 9 q^{37} + 6 q^{38} - 10 q^{40} - 12 q^{41} + 18 q^{43} + q^{44} - 7 q^{46} + 3 q^{47} + 2 q^{50} - 4 q^{52} - 9 q^{53} - 14 q^{55} + 10 q^{58} + 4 q^{59} - 4 q^{61} + 28 q^{62} + 6 q^{64} + 12 q^{65} + 5 q^{67} + 8 q^{68} - 14 q^{71} + 25 q^{73} - 18 q^{74} + 3 q^{76} + 7 q^{79} - 5 q^{80} + 12 q^{82} + 8 q^{83} + 14 q^{85} + 36 q^{86} + 2 q^{88} - 9 q^{89} + 7 q^{92} - 3 q^{94} - 2 q^{95} + 28 q^{97}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 + 10 * q^5 - 6 * q^8 + 5 * q^10 - 2 * q^11 + 2 * q^13 - 3 * q^16 - 4 * q^17 + 3 * q^19 - 5 * q^20 - q^22 - 14 * q^23 + 4 * q^25 - 2 * q^26 + 5 * q^29 + 14 * q^31 + 3 * q^32 + 4 * q^34 - 9 * q^37 + 6 * q^38 - 10 * q^40 - 12 * q^41 + 18 * q^43 + q^44 - 7 * q^46 + 3 * q^47 + 2 * q^50 - 4 * q^52 - 9 * q^53 - 14 * q^55 + 10 * q^58 + 4 * q^59 - 4 * q^61 + 28 * q^62 + 6 * q^64 + 12 * q^65 + 5 * q^67 + 8 * q^68 - 14 * q^71 + 25 * q^73 - 18 * q^74 + 3 * q^76 + 7 * q^79 - 5 * q^80 + 12 * q^82 + 8 * q^83 + 14 * q^85 + 36 * q^86 + 2 * q^88 - 9 * q^89 + 7 * q^92 - 3 * q^94 - 2 * q^95 + 28 * q^97

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